Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4730,2,Mod(1,4730)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4730, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4730.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4730.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: | \(37.7692401561\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 32 x^{11} - 5 x^{10} + 376 x^{9} + 100 x^{8} - 1985 x^{7} - 576 x^{6} + 4708 x^{5} + 889 x^{4} + \cdots - 128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.16663\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4730.1 |
$q$-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 | ||||||||
\(3\) | −1.16663 | −0.673552 | −0.336776 | − | 0.941585i | \(-0.609337\pi\) | ||||
−0.336776 | + | 0.941585i | \(0.609337\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.16663 | −0.476273 | ||||||||
\(7\) | −3.85859 | −1.45841 | −0.729204 | − | 0.684296i | \(-0.760110\pi\) | ||||
−0.729204 | + | 0.684296i | \(0.760110\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.63898 | −0.546327 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.16663 | −0.336776 | ||||||||
\(13\) | −3.76512 | −1.04426 | −0.522129 | − | 0.852867i | \(-0.674862\pi\) | ||||
−0.522129 | + | 0.852867i | \(0.674862\pi\) | |||||||
\(14\) | −3.85859 | −1.03125 | ||||||||
\(15\) | 1.16663 | 0.301222 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.05803 | −1.22675 | −0.613376 | − | 0.789791i | \(-0.710189\pi\) | ||||
−0.613376 | + | 0.789791i | \(0.710189\pi\) | |||||||
\(18\) | −1.63898 | −0.386312 | ||||||||
\(19\) | −2.28887 | −0.525103 | −0.262551 | − | 0.964918i | \(-0.584564\pi\) | ||||
−0.262551 | + | 0.964918i | \(0.584564\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 4.50153 | 0.982314 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −3.15631 | −0.658136 | −0.329068 | − | 0.944306i | \(-0.606734\pi\) | ||||
−0.329068 | + | 0.944306i | \(0.606734\pi\) | |||||||
\(24\) | −1.16663 | −0.238137 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.76512 | −0.738401 | ||||||||
\(27\) | 5.41196 | 1.04153 | ||||||||
\(28\) | −3.85859 | −0.729204 | ||||||||
\(29\) | 8.35160 | 1.55085 | 0.775427 | − | 0.631437i | \(-0.217535\pi\) | ||||
0.775427 | + | 0.631437i | \(0.217535\pi\) | |||||||
\(30\) | 1.16663 | 0.212996 | ||||||||
\(31\) | −3.01484 | −0.541482 | −0.270741 | − | 0.962652i | \(-0.587269\pi\) | ||||
−0.270741 | + | 0.962652i | \(0.587269\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.16663 | −0.203084 | ||||||||
\(34\) | −5.05803 | −0.867444 | ||||||||
\(35\) | 3.85859 | 0.652220 | ||||||||
\(36\) | −1.63898 | −0.273164 | ||||||||
\(37\) | −4.67122 | −0.767943 | −0.383972 | − | 0.923345i | \(-0.625444\pi\) | ||||
−0.383972 | + | 0.923345i | \(0.625444\pi\) | |||||||
\(38\) | −2.28887 | −0.371304 | ||||||||
\(39\) | 4.39249 | 0.703362 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −9.20945 | −1.43827 | −0.719137 | − | 0.694868i | \(-0.755463\pi\) | ||||
−0.719137 | + | 0.694868i | \(0.755463\pi\) | |||||||
\(42\) | 4.50153 | 0.694601 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 1.63898 | 0.244325 | ||||||||
\(46\) | −3.15631 | −0.465372 | ||||||||
\(47\) | 6.69155 | 0.976064 | 0.488032 | − | 0.872826i | \(-0.337715\pi\) | ||||
0.488032 | + | 0.872826i | \(0.337715\pi\) | |||||||
\(48\) | −1.16663 | −0.168388 | ||||||||
\(49\) | 7.88868 | 1.12695 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 5.90083 | 0.826281 | ||||||||
\(52\) | −3.76512 | −0.522129 | ||||||||
\(53\) | 4.13953 | 0.568608 | 0.284304 | − | 0.958734i | \(-0.408238\pi\) | ||||
0.284304 | + | 0.958734i | \(0.408238\pi\) | |||||||
\(54\) | 5.41196 | 0.736475 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −3.85859 | −0.515625 | ||||||||
\(57\) | 2.67026 | 0.353684 | ||||||||
\(58\) | 8.35160 | 1.09662 | ||||||||
\(59\) | 10.9802 | 1.42950 | 0.714752 | − | 0.699378i | \(-0.246540\pi\) | ||||
0.714752 | + | 0.699378i | \(0.246540\pi\) | |||||||
\(60\) | 1.16663 | 0.150611 | ||||||||
\(61\) | 7.94861 | 1.01772 | 0.508858 | − | 0.860851i | \(-0.330068\pi\) | ||||
0.508858 | + | 0.860851i | \(0.330068\pi\) | |||||||
\(62\) | −3.01484 | −0.382885 | ||||||||
\(63\) | 6.32415 | 0.796768 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.76512 | 0.467006 | ||||||||
\(66\) | −1.16663 | −0.143602 | ||||||||
\(67\) | 7.87269 | 0.961802 | 0.480901 | − | 0.876775i | \(-0.340310\pi\) | ||||
0.480901 | + | 0.876775i | \(0.340310\pi\) | |||||||
\(68\) | −5.05803 | −0.613376 | ||||||||
\(69\) | 3.68223 | 0.443289 | ||||||||
\(70\) | 3.85859 | 0.461189 | ||||||||
\(71\) | −0.268322 | −0.0318439 | −0.0159220 | − | 0.999873i | \(-0.505068\pi\) | ||||
−0.0159220 | + | 0.999873i | \(0.505068\pi\) | |||||||
\(72\) | −1.63898 | −0.193156 | ||||||||
\(73\) | −3.06434 | −0.358654 | −0.179327 | − | 0.983790i | \(-0.557392\pi\) | ||||
−0.179327 | + | 0.983790i | \(0.557392\pi\) | |||||||
\(74\) | −4.67122 | −0.543018 | ||||||||
\(75\) | −1.16663 | −0.134710 | ||||||||
\(76\) | −2.28887 | −0.262551 | ||||||||
\(77\) | −3.85859 | −0.439727 | ||||||||
\(78\) | 4.39249 | 0.497352 | ||||||||
\(79\) | −12.8076 | −1.44096 | −0.720482 | − | 0.693474i | \(-0.756079\pi\) | ||||
−0.720482 | + | 0.693474i | \(0.756079\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −1.39679 | −0.155199 | ||||||||
\(82\) | −9.20945 | −1.01701 | ||||||||
\(83\) | −9.21995 | −1.01202 | −0.506010 | − | 0.862527i | \(-0.668880\pi\) | ||||
−0.506010 | + | 0.862527i | \(0.668880\pi\) | |||||||
\(84\) | 4.50153 | 0.491157 | ||||||||
\(85\) | 5.05803 | 0.548620 | ||||||||
\(86\) | 1.00000 | 0.107833 | ||||||||
\(87\) | −9.74320 | −1.04458 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −4.61307 | −0.488985 | −0.244492 | − | 0.969651i | \(-0.578621\pi\) | ||||
−0.244492 | + | 0.969651i | \(0.578621\pi\) | |||||||
\(90\) | 1.63898 | 0.172764 | ||||||||
\(91\) | 14.5280 | 1.52295 | ||||||||
\(92\) | −3.15631 | −0.329068 | ||||||||
\(93\) | 3.51719 | 0.364716 | ||||||||
\(94\) | 6.69155 | 0.690181 | ||||||||
\(95\) | 2.28887 | 0.234833 | ||||||||
\(96\) | −1.16663 | −0.119068 | ||||||||
\(97\) | −11.3046 | −1.14781 | −0.573904 | − | 0.818923i | \(-0.694572\pi\) | ||||
−0.573904 | + | 0.818923i | \(0.694572\pi\) | |||||||
\(98\) | 7.88868 | 0.796877 | ||||||||
\(99\) | −1.63898 | −0.164724 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 15.7257 | 1.56476 | 0.782382 | − | 0.622799i | \(-0.214004\pi\) | ||||
0.782382 | + | 0.622799i | \(0.214004\pi\) | |||||||
\(102\) | 5.90083 | 0.584269 | ||||||||
\(103\) | 0.0209618 | 0.00206543 | 0.00103271 | − | 0.999999i | \(-0.499671\pi\) | ||||
0.00103271 | + | 0.999999i | \(0.499671\pi\) | |||||||
\(104\) | −3.76512 | −0.369201 | ||||||||
\(105\) | −4.50153 | −0.439304 | ||||||||
\(106\) | 4.13953 | 0.402067 | ||||||||
\(107\) | −2.59376 | −0.250748 | −0.125374 | − | 0.992110i | \(-0.540013\pi\) | ||||
−0.125374 | + | 0.992110i | \(0.540013\pi\) | |||||||
\(108\) | 5.41196 | 0.520766 | ||||||||
\(109\) | 10.4693 | 1.00278 | 0.501391 | − | 0.865221i | \(-0.332822\pi\) | ||||
0.501391 | + | 0.865221i | \(0.332822\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | 5.44957 | 0.517250 | ||||||||
\(112\) | −3.85859 | −0.364602 | ||||||||
\(113\) | 11.2356 | 1.05696 | 0.528478 | − | 0.848947i | \(-0.322763\pi\) | ||||
0.528478 | + | 0.848947i | \(0.322763\pi\) | |||||||
\(114\) | 2.67026 | 0.250093 | ||||||||
\(115\) | 3.15631 | 0.294327 | ||||||||
\(116\) | 8.35160 | 0.775427 | ||||||||
\(117\) | 6.17097 | 0.570506 | ||||||||
\(118\) | 10.9802 | 1.01081 | ||||||||
\(119\) | 19.5168 | 1.78910 | ||||||||
\(120\) | 1.16663 | 0.106498 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 7.94861 | 0.719634 | ||||||||
\(123\) | 10.7440 | 0.968753 | ||||||||
\(124\) | −3.01484 | −0.270741 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 6.32415 | 0.563400 | ||||||||
\(127\) | −6.04085 | −0.536038 | −0.268019 | − | 0.963414i | \(-0.586369\pi\) | ||||
−0.268019 | + | 0.963414i | \(0.586369\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −1.16663 | −0.102716 | ||||||||
\(130\) | 3.76512 | 0.330223 | ||||||||
\(131\) | 1.66995 | 0.145904 | 0.0729519 | − | 0.997335i | \(-0.476758\pi\) | ||||
0.0729519 | + | 0.997335i | \(0.476758\pi\) | |||||||
\(132\) | −1.16663 | −0.101542 | ||||||||
\(133\) | 8.83180 | 0.765814 | ||||||||
\(134\) | 7.87269 | 0.680097 | ||||||||
\(135\) | −5.41196 | −0.465787 | ||||||||
\(136\) | −5.05803 | −0.433722 | ||||||||
\(137\) | 5.55653 | 0.474727 | 0.237363 | − | 0.971421i | \(-0.423717\pi\) | ||||
0.237363 | + | 0.971421i | \(0.423717\pi\) | |||||||
\(138\) | 3.68223 | 0.313452 | ||||||||
\(139\) | 16.6438 | 1.41171 | 0.705853 | − | 0.708358i | \(-0.250564\pi\) | ||||
0.705853 | + | 0.708358i | \(0.250564\pi\) | |||||||
\(140\) | 3.85859 | 0.326110 | ||||||||
\(141\) | −7.80655 | −0.657430 | ||||||||
\(142\) | −0.268322 | −0.0225171 | ||||||||
\(143\) | −3.76512 | −0.314855 | ||||||||
\(144\) | −1.63898 | −0.136582 | ||||||||
\(145\) | −8.35160 | −0.693563 | ||||||||
\(146\) | −3.06434 | −0.253606 | ||||||||
\(147\) | −9.20315 | −0.759063 | ||||||||
\(148\) | −4.67122 | −0.383972 | ||||||||
\(149\) | 13.2473 | 1.08526 | 0.542629 | − | 0.839972i | \(-0.317429\pi\) | ||||
0.542629 | + | 0.839972i | \(0.317429\pi\) | |||||||
\(150\) | −1.16663 | −0.0952547 | ||||||||
\(151\) | −9.37827 | −0.763193 | −0.381597 | − | 0.924329i | \(-0.624626\pi\) | ||||
−0.381597 | + | 0.924329i | \(0.624626\pi\) | |||||||
\(152\) | −2.28887 | −0.185652 | ||||||||
\(153\) | 8.29001 | 0.670208 | ||||||||
\(154\) | −3.85859 | −0.310934 | ||||||||
\(155\) | 3.01484 | 0.242158 | ||||||||
\(156\) | 4.39249 | 0.351681 | ||||||||
\(157\) | −12.4335 | −0.992301 | −0.496150 | − | 0.868237i | \(-0.665254\pi\) | ||||
−0.496150 | + | 0.868237i | \(0.665254\pi\) | |||||||
\(158\) | −12.8076 | −1.01892 | ||||||||
\(159\) | −4.82928 | −0.382987 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 12.1789 | 0.959830 | ||||||||
\(162\) | −1.39679 | −0.109742 | ||||||||
\(163\) | −3.64178 | −0.285246 | −0.142623 | − | 0.989777i | \(-0.545554\pi\) | ||||
−0.142623 | + | 0.989777i | \(0.545554\pi\) | |||||||
\(164\) | −9.20945 | −0.719137 | ||||||||
\(165\) | 1.16663 | 0.0908218 | ||||||||
\(166\) | −9.21995 | −0.715607 | ||||||||
\(167\) | −18.5093 | −1.43229 | −0.716147 | − | 0.697949i | \(-0.754096\pi\) | ||||
−0.716147 | + | 0.697949i | \(0.754096\pi\) | |||||||
\(168\) | 4.50153 | 0.347300 | ||||||||
\(169\) | 1.17615 | 0.0904728 | ||||||||
\(170\) | 5.05803 | 0.387933 | ||||||||
\(171\) | 3.75142 | 0.286878 | ||||||||
\(172\) | 1.00000 | 0.0762493 | ||||||||
\(173\) | 10.1268 | 0.769927 | 0.384963 | − | 0.922932i | \(-0.374214\pi\) | ||||
0.384963 | + | 0.922932i | \(0.374214\pi\) | |||||||
\(174\) | −9.74320 | −0.738630 | ||||||||
\(175\) | −3.85859 | −0.291682 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −12.8098 | −0.962845 | ||||||||
\(178\) | −4.61307 | −0.345765 | ||||||||
\(179\) | 21.3948 | 1.59912 | 0.799561 | − | 0.600585i | \(-0.205065\pi\) | ||||
0.799561 | + | 0.600585i | \(0.205065\pi\) | |||||||
\(180\) | 1.63898 | 0.122163 | ||||||||
\(181\) | −3.69809 | −0.274877 | −0.137438 | − | 0.990510i | \(-0.543887\pi\) | ||||
−0.137438 | + | 0.990510i | \(0.543887\pi\) | |||||||
\(182\) | 14.5280 | 1.07689 | ||||||||
\(183\) | −9.27306 | −0.685485 | ||||||||
\(184\) | −3.15631 | −0.232686 | ||||||||
\(185\) | 4.67122 | 0.343435 | ||||||||
\(186\) | 3.51719 | 0.257893 | ||||||||
\(187\) | −5.05803 | −0.369879 | ||||||||
\(188\) | 6.69155 | 0.488032 | ||||||||
\(189\) | −20.8825 | −1.51898 | ||||||||
\(190\) | 2.28887 | 0.166052 | ||||||||
\(191\) | 4.35977 | 0.315462 | 0.157731 | − | 0.987482i | \(-0.449582\pi\) | ||||
0.157731 | + | 0.987482i | \(0.449582\pi\) | |||||||
\(192\) | −1.16663 | −0.0841940 | ||||||||
\(193\) | 19.7345 | 1.42052 | 0.710259 | − | 0.703940i | \(-0.248578\pi\) | ||||
0.710259 | + | 0.703940i | \(0.248578\pi\) | |||||||
\(194\) | −11.3046 | −0.811623 | ||||||||
\(195\) | −4.39249 | −0.314553 | ||||||||
\(196\) | 7.88868 | 0.563477 | ||||||||
\(197\) | −1.78207 | −0.126967 | −0.0634837 | − | 0.997983i | \(-0.520221\pi\) | ||||
−0.0634837 | + | 0.997983i | \(0.520221\pi\) | |||||||
\(198\) | −1.63898 | −0.116477 | ||||||||
\(199\) | −2.27826 | −0.161502 | −0.0807509 | − | 0.996734i | \(-0.525732\pi\) | ||||
−0.0807509 | + | 0.996734i | \(0.525732\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −9.18449 | −0.647824 | ||||||||
\(202\) | 15.7257 | 1.10646 | ||||||||
\(203\) | −32.2254 | −2.26178 | ||||||||
\(204\) | 5.90083 | 0.413141 | ||||||||
\(205\) | 9.20945 | 0.643216 | ||||||||
\(206\) | 0.0209618 | 0.00146048 | ||||||||
\(207\) | 5.17313 | 0.359558 | ||||||||
\(208\) | −3.76512 | −0.261064 | ||||||||
\(209\) | −2.28887 | −0.158325 | ||||||||
\(210\) | −4.50153 | −0.310635 | ||||||||
\(211\) | 9.06403 | 0.623994 | 0.311997 | − | 0.950083i | \(-0.399002\pi\) | ||||
0.311997 | + | 0.950083i | \(0.399002\pi\) | |||||||
\(212\) | 4.13953 | 0.284304 | ||||||||
\(213\) | 0.313031 | 0.0214485 | ||||||||
\(214\) | −2.59376 | −0.177306 | ||||||||
\(215\) | −1.00000 | −0.0681994 | ||||||||
\(216\) | 5.41196 | 0.368237 | ||||||||
\(217\) | 11.6330 | 0.789701 | ||||||||
\(218\) | 10.4693 | 0.709074 | ||||||||
\(219\) | 3.57494 | 0.241572 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | 19.0441 | 1.28104 | ||||||||
\(222\) | 5.44957 | 0.365751 | ||||||||
\(223\) | 16.9366 | 1.13416 | 0.567078 | − | 0.823664i | \(-0.308074\pi\) | ||||
0.567078 | + | 0.823664i | \(0.308074\pi\) | |||||||
\(224\) | −3.85859 | −0.257813 | ||||||||
\(225\) | −1.63898 | −0.109265 | ||||||||
\(226\) | 11.2356 | 0.747381 | ||||||||
\(227\) | −1.38386 | −0.0918498 | −0.0459249 | − | 0.998945i | \(-0.514623\pi\) | ||||
−0.0459249 | + | 0.998945i | \(0.514623\pi\) | |||||||
\(228\) | 2.67026 | 0.176842 | ||||||||
\(229\) | 2.27661 | 0.150443 | 0.0752213 | − | 0.997167i | \(-0.476034\pi\) | ||||
0.0752213 | + | 0.997167i | \(0.476034\pi\) | |||||||
\(230\) | 3.15631 | 0.208121 | ||||||||
\(231\) | 4.50153 | 0.296179 | ||||||||
\(232\) | 8.35160 | 0.548310 | ||||||||
\(233\) | −13.2311 | −0.866800 | −0.433400 | − | 0.901202i | \(-0.642686\pi\) | ||||
−0.433400 | + | 0.901202i | \(0.642686\pi\) | |||||||
\(234\) | 6.17097 | 0.403409 | ||||||||
\(235\) | −6.69155 | −0.436509 | ||||||||
\(236\) | 10.9802 | 0.714752 | ||||||||
\(237\) | 14.9416 | 0.970564 | ||||||||
\(238\) | 19.5168 | 1.26509 | ||||||||
\(239\) | −4.10701 | −0.265661 | −0.132830 | − | 0.991139i | \(-0.542407\pi\) | ||||
−0.132830 | + | 0.991139i | \(0.542407\pi\) | |||||||
\(240\) | 1.16663 | 0.0753054 | ||||||||
\(241\) | −29.9152 | −1.92700 | −0.963502 | − | 0.267700i | \(-0.913736\pi\) | ||||
−0.963502 | + | 0.267700i | \(0.913736\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −14.6063 | −0.936998 | ||||||||
\(244\) | 7.94861 | 0.508858 | ||||||||
\(245\) | −7.88868 | −0.503989 | ||||||||
\(246\) | 10.7440 | 0.685012 | ||||||||
\(247\) | 8.61788 | 0.548342 | ||||||||
\(248\) | −3.01484 | −0.191443 | ||||||||
\(249\) | 10.7562 | 0.681649 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −13.7265 | −0.866406 | −0.433203 | − | 0.901296i | \(-0.642617\pi\) | ||||
−0.433203 | + | 0.901296i | \(0.642617\pi\) | |||||||
\(252\) | 6.32415 | 0.398384 | ||||||||
\(253\) | −3.15631 | −0.198435 | ||||||||
\(254\) | −6.04085 | −0.379036 | ||||||||
\(255\) | −5.90083 | −0.369524 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 27.0551 | 1.68765 | 0.843824 | − | 0.536620i | \(-0.180299\pi\) | ||||
0.843824 | + | 0.536620i | \(0.180299\pi\) | |||||||
\(258\) | −1.16663 | −0.0726310 | ||||||||
\(259\) | 18.0243 | 1.11997 | ||||||||
\(260\) | 3.76512 | 0.233503 | ||||||||
\(261\) | −13.6881 | −0.847274 | ||||||||
\(262\) | 1.66995 | 0.103170 | ||||||||
\(263\) | −25.1289 | −1.54951 | −0.774756 | − | 0.632260i | \(-0.782127\pi\) | ||||
−0.774756 | + | 0.632260i | \(0.782127\pi\) | |||||||
\(264\) | −1.16663 | −0.0718009 | ||||||||
\(265\) | −4.13953 | −0.254289 | ||||||||
\(266\) | 8.83180 | 0.541513 | ||||||||
\(267\) | 5.38174 | 0.329357 | ||||||||
\(268\) | 7.87269 | 0.480901 | ||||||||
\(269\) | −6.21186 | −0.378744 | −0.189372 | − | 0.981905i | \(-0.560645\pi\) | ||||
−0.189372 | + | 0.981905i | \(0.560645\pi\) | |||||||
\(270\) | −5.41196 | −0.329361 | ||||||||
\(271\) | 17.5757 | 1.06765 | 0.533824 | − | 0.845595i | \(-0.320754\pi\) | ||||
0.533824 | + | 0.845595i | \(0.320754\pi\) | |||||||
\(272\) | −5.05803 | −0.306688 | ||||||||
\(273\) | −16.9488 | −1.02579 | ||||||||
\(274\) | 5.55653 | 0.335682 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 3.68223 | 0.221644 | ||||||||
\(277\) | 16.0544 | 0.964615 | 0.482308 | − | 0.876002i | \(-0.339799\pi\) | ||||
0.482308 | + | 0.876002i | \(0.339799\pi\) | |||||||
\(278\) | 16.6438 | 0.998227 | ||||||||
\(279\) | 4.94127 | 0.295826 | ||||||||
\(280\) | 3.85859 | 0.230595 | ||||||||
\(281\) | 24.8877 | 1.48468 | 0.742339 | − | 0.670024i | \(-0.233716\pi\) | ||||
0.742339 | + | 0.670024i | \(0.233716\pi\) | |||||||
\(282\) | −7.80655 | −0.464873 | ||||||||
\(283\) | −16.8565 | −1.00201 | −0.501006 | − | 0.865444i | \(-0.667037\pi\) | ||||
−0.501006 | + | 0.865444i | \(0.667037\pi\) | |||||||
\(284\) | −0.268322 | −0.0159220 | ||||||||
\(285\) | −2.67026 | −0.158172 | ||||||||
\(286\) | −3.76512 | −0.222636 | ||||||||
\(287\) | 35.5355 | 2.09759 | ||||||||
\(288\) | −1.63898 | −0.0965780 | ||||||||
\(289\) | 8.58362 | 0.504919 | ||||||||
\(290\) | −8.35160 | −0.490423 | ||||||||
\(291\) | 13.1882 | 0.773109 | ||||||||
\(292\) | −3.06434 | −0.179327 | ||||||||
\(293\) | −21.4833 | −1.25507 | −0.627535 | − | 0.778589i | \(-0.715936\pi\) | ||||
−0.627535 | + | 0.778589i | \(0.715936\pi\) | |||||||
\(294\) | −9.20315 | −0.536738 | ||||||||
\(295\) | −10.9802 | −0.639293 | ||||||||
\(296\) | −4.67122 | −0.271509 | ||||||||
\(297\) | 5.41196 | 0.314034 | ||||||||
\(298\) | 13.2473 | 0.767393 | ||||||||
\(299\) | 11.8839 | 0.687263 | ||||||||
\(300\) | −1.16663 | −0.0673552 | ||||||||
\(301\) | −3.85859 | −0.222405 | ||||||||
\(302\) | −9.37827 | −0.539659 | ||||||||
\(303\) | −18.3460 | −1.05395 | ||||||||
\(304\) | −2.28887 | −0.131276 | ||||||||
\(305\) | −7.94861 | −0.455136 | ||||||||
\(306\) | 8.29001 | 0.473909 | ||||||||
\(307\) | −10.0990 | −0.576380 | −0.288190 | − | 0.957573i | \(-0.593054\pi\) | ||||
−0.288190 | + | 0.957573i | \(0.593054\pi\) | |||||||
\(308\) | −3.85859 | −0.219863 | ||||||||
\(309\) | −0.0244546 | −0.00139117 | ||||||||
\(310\) | 3.01484 | 0.171231 | ||||||||
\(311\) | −22.4101 | −1.27076 | −0.635381 | − | 0.772199i | \(-0.719157\pi\) | ||||
−0.635381 | + | 0.772199i | \(0.719157\pi\) | |||||||
\(312\) | 4.39249 | 0.248676 | ||||||||
\(313\) | 18.7363 | 1.05904 | 0.529518 | − | 0.848299i | \(-0.322373\pi\) | ||||
0.529518 | + | 0.848299i | \(0.322373\pi\) | |||||||
\(314\) | −12.4335 | −0.701663 | ||||||||
\(315\) | −6.32415 | −0.356326 | ||||||||
\(316\) | −12.8076 | −0.720482 | ||||||||
\(317\) | 30.9181 | 1.73653 | 0.868266 | − | 0.496100i | \(-0.165235\pi\) | ||||
0.868266 | + | 0.496100i | \(0.165235\pi\) | |||||||
\(318\) | −4.82928 | −0.270813 | ||||||||
\(319\) | 8.35160 | 0.467600 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 3.02595 | 0.168892 | ||||||||
\(322\) | 12.1789 | 0.678703 | ||||||||
\(323\) | 11.5772 | 0.644171 | ||||||||
\(324\) | −1.39679 | −0.0775994 | ||||||||
\(325\) | −3.76512 | −0.208851 | ||||||||
\(326\) | −3.64178 | −0.201700 | ||||||||
\(327\) | −12.2138 | −0.675426 | ||||||||
\(328\) | −9.20945 | −0.508507 | ||||||||
\(329\) | −25.8199 | −1.42350 | ||||||||
\(330\) | 1.16663 | 0.0642207 | ||||||||
\(331\) | −4.28823 | −0.235702 | −0.117851 | − | 0.993031i | \(-0.537601\pi\) | ||||
−0.117851 | + | 0.993031i | \(0.537601\pi\) | |||||||
\(332\) | −9.21995 | −0.506010 | ||||||||
\(333\) | 7.65604 | 0.419549 | ||||||||
\(334\) | −18.5093 | −1.01279 | ||||||||
\(335\) | −7.87269 | −0.430131 | ||||||||
\(336\) | 4.50153 | 0.245579 | ||||||||
\(337\) | 2.20531 | 0.120131 | 0.0600655 | − | 0.998194i | \(-0.480869\pi\) | ||||
0.0600655 | + | 0.998194i | \(0.480869\pi\) | |||||||
\(338\) | 1.17615 | 0.0639739 | ||||||||
\(339\) | −13.1077 | −0.711915 | ||||||||
\(340\) | 5.05803 | 0.274310 | ||||||||
\(341\) | −3.01484 | −0.163263 | ||||||||
\(342\) | 3.75142 | 0.202853 | ||||||||
\(343\) | −3.42905 | −0.185152 | ||||||||
\(344\) | 1.00000 | 0.0539164 | ||||||||
\(345\) | −3.68223 | −0.198245 | ||||||||
\(346\) | 10.1268 | 0.544421 | ||||||||
\(347\) | −13.2410 | −0.710816 | −0.355408 | − | 0.934711i | \(-0.615658\pi\) | ||||
−0.355408 | + | 0.934711i | \(0.615658\pi\) | |||||||
\(348\) | −9.74320 | −0.522291 | ||||||||
\(349\) | 28.1887 | 1.50891 | 0.754454 | − | 0.656353i | \(-0.227902\pi\) | ||||
0.754454 | + | 0.656353i | \(0.227902\pi\) | |||||||
\(350\) | −3.85859 | −0.206250 | ||||||||
\(351\) | −20.3767 | −1.08763 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 34.0257 | 1.81100 | 0.905502 | − | 0.424342i | \(-0.139494\pi\) | ||||
0.905502 | + | 0.424342i | \(0.139494\pi\) | |||||||
\(354\) | −12.8098 | −0.680834 | ||||||||
\(355\) | 0.268322 | 0.0142410 | ||||||||
\(356\) | −4.61307 | −0.244492 | ||||||||
\(357\) | −22.7688 | −1.20506 | ||||||||
\(358\) | 21.3948 | 1.13075 | ||||||||
\(359\) | 31.7592 | 1.67619 | 0.838094 | − | 0.545527i | \(-0.183670\pi\) | ||||
0.838094 | + | 0.545527i | \(0.183670\pi\) | |||||||
\(360\) | 1.63898 | 0.0863820 | ||||||||
\(361\) | −13.7611 | −0.724267 | ||||||||
\(362\) | −3.69809 | −0.194367 | ||||||||
\(363\) | −1.16663 | −0.0612320 | ||||||||
\(364\) | 14.5280 | 0.761477 | ||||||||
\(365\) | 3.06434 | 0.160395 | ||||||||
\(366\) | −9.27306 | −0.484711 | ||||||||
\(367\) | 7.76648 | 0.405407 | 0.202703 | − | 0.979240i | \(-0.435027\pi\) | ||||
0.202703 | + | 0.979240i | \(0.435027\pi\) | |||||||
\(368\) | −3.15631 | −0.164534 | ||||||||
\(369\) | 15.0941 | 0.785769 | ||||||||
\(370\) | 4.67122 | 0.242845 | ||||||||
\(371\) | −15.9727 | −0.829262 | ||||||||
\(372\) | 3.51719 | 0.182358 | ||||||||
\(373\) | −26.4763 | −1.37089 | −0.685445 | − | 0.728124i | \(-0.740392\pi\) | ||||
−0.685445 | + | 0.728124i | \(0.740392\pi\) | |||||||
\(374\) | −5.05803 | −0.261544 | ||||||||
\(375\) | 1.16663 | 0.0602443 | ||||||||
\(376\) | 6.69155 | 0.345091 | ||||||||
\(377\) | −31.4448 | −1.61949 | ||||||||
\(378\) | −20.8825 | −1.07408 | ||||||||
\(379\) | −3.14282 | −0.161436 | −0.0807180 | − | 0.996737i | \(-0.525721\pi\) | ||||
−0.0807180 | + | 0.996737i | \(0.525721\pi\) | |||||||
\(380\) | 2.28887 | 0.117417 | ||||||||
\(381\) | 7.04741 | 0.361050 | ||||||||
\(382\) | 4.35977 | 0.223065 | ||||||||
\(383\) | 23.6271 | 1.20729 | 0.603645 | − | 0.797253i | \(-0.293714\pi\) | ||||
0.603645 | + | 0.797253i | \(0.293714\pi\) | |||||||
\(384\) | −1.16663 | −0.0595342 | ||||||||
\(385\) | 3.85859 | 0.196652 | ||||||||
\(386\) | 19.7345 | 1.00446 | ||||||||
\(387\) | −1.63898 | −0.0833142 | ||||||||
\(388\) | −11.3046 | −0.573904 | ||||||||
\(389\) | 28.0363 | 1.42150 | 0.710748 | − | 0.703447i | \(-0.248357\pi\) | ||||
0.710748 | + | 0.703447i | \(0.248357\pi\) | |||||||
\(390\) | −4.39249 | −0.222422 | ||||||||
\(391\) | 15.9647 | 0.807369 | ||||||||
\(392\) | 7.88868 | 0.398439 | ||||||||
\(393\) | −1.94820 | −0.0982738 | ||||||||
\(394\) | −1.78207 | −0.0897795 | ||||||||
\(395\) | 12.8076 | 0.644419 | ||||||||
\(396\) | −1.63898 | −0.0823620 | ||||||||
\(397\) | 11.7912 | 0.591786 | 0.295893 | − | 0.955221i | \(-0.404383\pi\) | ||||
0.295893 | + | 0.955221i | \(0.404383\pi\) | |||||||
\(398\) | −2.27826 | −0.114199 | ||||||||
\(399\) | −10.3034 | −0.515816 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −4.46116 | −0.222780 | −0.111390 | − | 0.993777i | \(-0.535530\pi\) | ||||
−0.111390 | + | 0.993777i | \(0.535530\pi\) | |||||||
\(402\) | −9.18449 | −0.458081 | ||||||||
\(403\) | 11.3512 | 0.565446 | ||||||||
\(404\) | 15.7257 | 0.782382 | ||||||||
\(405\) | 1.39679 | 0.0694071 | ||||||||
\(406\) | −32.2254 | −1.59932 | ||||||||
\(407\) | −4.67122 | −0.231544 | ||||||||
\(408\) | 5.90083 | 0.292134 | ||||||||
\(409\) | −8.24320 | −0.407600 | −0.203800 | − | 0.979013i | \(-0.565329\pi\) | ||||
−0.203800 | + | 0.979013i | \(0.565329\pi\) | |||||||
\(410\) | 9.20945 | 0.454822 | ||||||||
\(411\) | −6.48240 | −0.319753 | ||||||||
\(412\) | 0.0209618 | 0.00103271 | ||||||||
\(413\) | −42.3681 | −2.08480 | ||||||||
\(414\) | 5.17313 | 0.254246 | ||||||||
\(415\) | 9.21995 | 0.452589 | ||||||||
\(416\) | −3.76512 | −0.184600 | ||||||||
\(417\) | −19.4171 | −0.950858 | ||||||||
\(418\) | −2.28887 | −0.111952 | ||||||||
\(419\) | 2.25172 | 0.110003 | 0.0550017 | − | 0.998486i | \(-0.482484\pi\) | ||||
0.0550017 | + | 0.998486i | \(0.482484\pi\) | |||||||
\(420\) | −4.50153 | −0.219652 | ||||||||
\(421\) | −36.6258 | −1.78503 | −0.892517 | − | 0.451013i | \(-0.851063\pi\) | ||||
−0.892517 | + | 0.451013i | \(0.851063\pi\) | |||||||
\(422\) | 9.06403 | 0.441230 | ||||||||
\(423\) | −10.9673 | −0.533250 | ||||||||
\(424\) | 4.13953 | 0.201033 | ||||||||
\(425\) | −5.05803 | −0.245350 | ||||||||
\(426\) | 0.313031 | 0.0151664 | ||||||||
\(427\) | −30.6704 | −1.48424 | ||||||||
\(428\) | −2.59376 | −0.125374 | ||||||||
\(429\) | 4.39249 | 0.212072 | ||||||||
\(430\) | −1.00000 | −0.0482243 | ||||||||
\(431\) | −20.8183 | −1.00278 | −0.501391 | − | 0.865221i | \(-0.667178\pi\) | ||||
−0.501391 | + | 0.865221i | \(0.667178\pi\) | |||||||
\(432\) | 5.41196 | 0.260383 | ||||||||
\(433\) | −14.0428 | −0.674852 | −0.337426 | − | 0.941352i | \(-0.609556\pi\) | ||||
−0.337426 | + | 0.941352i | \(0.609556\pi\) | |||||||
\(434\) | 11.6330 | 0.558403 | ||||||||
\(435\) | 9.74320 | 0.467151 | ||||||||
\(436\) | 10.4693 | 0.501391 | ||||||||
\(437\) | 7.22438 | 0.345589 | ||||||||
\(438\) | 3.57494 | 0.170817 | ||||||||
\(439\) | −18.1912 | −0.868219 | −0.434110 | − | 0.900860i | \(-0.642937\pi\) | ||||
−0.434110 | + | 0.900860i | \(0.642937\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | −12.9294 | −0.615686 | ||||||||
\(442\) | 19.0441 | 0.905835 | ||||||||
\(443\) | −15.2466 | −0.724387 | −0.362194 | − | 0.932103i | \(-0.617972\pi\) | ||||
−0.362194 | + | 0.932103i | \(0.617972\pi\) | |||||||
\(444\) | 5.44957 | 0.258625 | ||||||||
\(445\) | 4.61307 | 0.218681 | ||||||||
\(446\) | 16.9366 | 0.801969 | ||||||||
\(447\) | −15.4546 | −0.730978 | ||||||||
\(448\) | −3.85859 | −0.182301 | ||||||||
\(449\) | 33.2136 | 1.56745 | 0.783724 | − | 0.621109i | \(-0.213318\pi\) | ||||
0.783724 | + | 0.621109i | \(0.213318\pi\) | |||||||
\(450\) | −1.63898 | −0.0772624 | ||||||||
\(451\) | −9.20945 | −0.433656 | ||||||||
\(452\) | 11.2356 | 0.528478 | ||||||||
\(453\) | 10.9409 | 0.514050 | ||||||||
\(454\) | −1.38386 | −0.0649476 | ||||||||
\(455\) | −14.5280 | −0.681085 | ||||||||
\(456\) | 2.67026 | 0.125046 | ||||||||
\(457\) | −9.26528 | −0.433412 | −0.216706 | − | 0.976237i | \(-0.569531\pi\) | ||||
−0.216706 | + | 0.976237i | \(0.569531\pi\) | |||||||
\(458\) | 2.27661 | 0.106379 | ||||||||
\(459\) | −27.3738 | −1.27770 | ||||||||
\(460\) | 3.15631 | 0.147164 | ||||||||
\(461\) | −2.70163 | −0.125828 | −0.0629138 | − | 0.998019i | \(-0.520039\pi\) | ||||
−0.0629138 | + | 0.998019i | \(0.520039\pi\) | |||||||
\(462\) | 4.50153 | 0.209430 | ||||||||
\(463\) | 4.80337 | 0.223231 | 0.111616 | − | 0.993751i | \(-0.464397\pi\) | ||||
0.111616 | + | 0.993751i | \(0.464397\pi\) | |||||||
\(464\) | 8.35160 | 0.387713 | ||||||||
\(465\) | −3.51719 | −0.163106 | ||||||||
\(466\) | −13.2311 | −0.612920 | ||||||||
\(467\) | 18.0499 | 0.835250 | 0.417625 | − | 0.908619i | \(-0.362863\pi\) | ||||
0.417625 | + | 0.908619i | \(0.362863\pi\) | |||||||
\(468\) | 6.17097 | 0.285253 | ||||||||
\(469\) | −30.3774 | −1.40270 | ||||||||
\(470\) | −6.69155 | −0.308658 | ||||||||
\(471\) | 14.5052 | 0.668366 | ||||||||
\(472\) | 10.9802 | 0.505406 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | 14.9416 | 0.686293 | ||||||||
\(475\) | −2.28887 | −0.105021 | ||||||||
\(476\) | 19.5168 | 0.894552 | ||||||||
\(477\) | −6.78461 | −0.310646 | ||||||||
\(478\) | −4.10701 | −0.187850 | ||||||||
\(479\) | −6.10912 | −0.279133 | −0.139566 | − | 0.990213i | \(-0.544571\pi\) | ||||
−0.139566 | + | 0.990213i | \(0.544571\pi\) | |||||||
\(480\) | 1.16663 | 0.0532490 | ||||||||
\(481\) | 17.5877 | 0.801930 | ||||||||
\(482\) | −29.9152 | −1.36260 | ||||||||
\(483\) | −14.2082 | −0.646496 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 11.3046 | 0.513315 | ||||||||
\(486\) | −14.6063 | −0.662557 | ||||||||
\(487\) | 23.7496 | 1.07620 | 0.538099 | − | 0.842881i | \(-0.319143\pi\) | ||||
0.538099 | + | 0.842881i | \(0.319143\pi\) | |||||||
\(488\) | 7.94861 | 0.359817 | ||||||||
\(489\) | 4.24860 | 0.192128 | ||||||||
\(490\) | −7.88868 | −0.356374 | ||||||||
\(491\) | −14.1754 | −0.639727 | −0.319864 | − | 0.947464i | \(-0.603637\pi\) | ||||
−0.319864 | + | 0.947464i | \(0.603637\pi\) | |||||||
\(492\) | 10.7440 | 0.484377 | ||||||||
\(493\) | −42.2426 | −1.90251 | ||||||||
\(494\) | 8.61788 | 0.387737 | ||||||||
\(495\) | 1.63898 | 0.0736668 | ||||||||
\(496\) | −3.01484 | −0.135370 | ||||||||
\(497\) | 1.03534 | 0.0464414 | ||||||||
\(498\) | 10.7562 | 0.481998 | ||||||||
\(499\) | 27.1431 | 1.21509 | 0.607547 | − | 0.794284i | \(-0.292154\pi\) | ||||
0.607547 | + | 0.794284i | \(0.292154\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 21.5935 | 0.964725 | ||||||||
\(502\) | −13.7265 | −0.612642 | ||||||||
\(503\) | −30.7431 | −1.37077 | −0.685383 | − | 0.728183i | \(-0.740365\pi\) | ||||
−0.685383 | + | 0.728183i | \(0.740365\pi\) | |||||||
\(504\) | 6.32415 | 0.281700 | ||||||||
\(505\) | −15.7257 | −0.699784 | ||||||||
\(506\) | −3.15631 | −0.140315 | ||||||||
\(507\) | −1.37212 | −0.0609382 | ||||||||
\(508\) | −6.04085 | −0.268019 | ||||||||
\(509\) | 25.8806 | 1.14714 | 0.573568 | − | 0.819158i | \(-0.305559\pi\) | ||||
0.573568 | + | 0.819158i | \(0.305559\pi\) | |||||||
\(510\) | −5.90083 | −0.261293 | ||||||||
\(511\) | 11.8240 | 0.523064 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −12.3873 | −0.546912 | ||||||||
\(514\) | 27.0551 | 1.19335 | ||||||||
\(515\) | −0.0209618 | −0.000923688 0 | ||||||||
\(516\) | −1.16663 | −0.0513579 | ||||||||
\(517\) | 6.69155 | 0.294294 | ||||||||
\(518\) | 18.0243 | 0.791942 | ||||||||
\(519\) | −11.8142 | −0.518586 | ||||||||
\(520\) | 3.76512 | 0.165112 | ||||||||
\(521\) | −33.3838 | −1.46257 | −0.731286 | − | 0.682071i | \(-0.761079\pi\) | ||||
−0.731286 | + | 0.682071i | \(0.761079\pi\) | |||||||
\(522\) | −13.6881 | −0.599113 | ||||||||
\(523\) | 4.19598 | 0.183478 | 0.0917388 | − | 0.995783i | \(-0.470758\pi\) | ||||
0.0917388 | + | 0.995783i | \(0.470758\pi\) | |||||||
\(524\) | 1.66995 | 0.0729519 | ||||||||
\(525\) | 4.50153 | 0.196463 | ||||||||
\(526\) | −25.1289 | −1.09567 | ||||||||
\(527\) | 15.2491 | 0.664263 | ||||||||
\(528\) | −1.16663 | −0.0507709 | ||||||||
\(529\) | −13.0377 | −0.566857 | ||||||||
\(530\) | −4.13953 | −0.179810 | ||||||||
\(531\) | −17.9964 | −0.780977 | ||||||||
\(532\) | 8.83180 | 0.382907 | ||||||||
\(533\) | 34.6747 | 1.50193 | ||||||||
\(534\) | 5.38174 | 0.232890 | ||||||||
\(535\) | 2.59376 | 0.112138 | ||||||||
\(536\) | 7.87269 | 0.340048 | ||||||||
\(537\) | −24.9597 | −1.07709 | ||||||||
\(538\) | −6.21186 | −0.267812 | ||||||||
\(539\) | 7.88868 | 0.339790 | ||||||||
\(540\) | −5.41196 | −0.232894 | ||||||||
\(541\) | −5.64222 | −0.242578 | −0.121289 | − | 0.992617i | \(-0.538703\pi\) | ||||
−0.121289 | + | 0.992617i | \(0.538703\pi\) | |||||||
\(542\) | 17.5757 | 0.754942 | ||||||||
\(543\) | 4.31429 | 0.185144 | ||||||||
\(544\) | −5.05803 | −0.216861 | ||||||||
\(545\) | −10.4693 | −0.448458 | ||||||||
\(546\) | −16.9488 | −0.725342 | ||||||||
\(547\) | −6.02043 | −0.257415 | −0.128707 | − | 0.991683i | \(-0.541083\pi\) | ||||
−0.128707 | + | 0.991683i | \(0.541083\pi\) | |||||||
\(548\) | 5.55653 | 0.237363 | ||||||||
\(549\) | −13.0276 | −0.556006 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | −19.1157 | −0.814358 | ||||||||
\(552\) | 3.68223 | 0.156726 | ||||||||
\(553\) | 49.4191 | 2.10151 | ||||||||
\(554\) | 16.0544 | 0.682086 | ||||||||
\(555\) | −5.44957 | −0.231321 | ||||||||
\(556\) | 16.6438 | 0.705853 | ||||||||
\(557\) | 11.2765 | 0.477801 | 0.238900 | − | 0.971044i | \(-0.423213\pi\) | ||||
0.238900 | + | 0.971044i | \(0.423213\pi\) | |||||||
\(558\) | 4.94127 | 0.209181 | ||||||||
\(559\) | −3.76512 | −0.159248 | ||||||||
\(560\) | 3.85859 | 0.163055 | ||||||||
\(561\) | 5.90083 | 0.249133 | ||||||||
\(562\) | 24.8877 | 1.04983 | ||||||||
\(563\) | 11.7883 | 0.496818 | 0.248409 | − | 0.968655i | \(-0.420092\pi\) | ||||
0.248409 | + | 0.968655i | \(0.420092\pi\) | |||||||
\(564\) | −7.80655 | −0.328715 | ||||||||
\(565\) | −11.2356 | −0.472685 | ||||||||
\(566\) | −16.8565 | −0.708530 | ||||||||
\(567\) | 5.38963 | 0.226343 | ||||||||
\(568\) | −0.268322 | −0.0112585 | ||||||||
\(569\) | 22.6922 | 0.951305 | 0.475653 | − | 0.879633i | \(-0.342212\pi\) | ||||
0.475653 | + | 0.879633i | \(0.342212\pi\) | |||||||
\(570\) | −2.67026 | −0.111845 | ||||||||
\(571\) | 12.6479 | 0.529300 | 0.264650 | − | 0.964345i | \(-0.414744\pi\) | ||||
0.264650 | + | 0.964345i | \(0.414744\pi\) | |||||||
\(572\) | −3.76512 | −0.157428 | ||||||||
\(573\) | −5.08623 | −0.212480 | ||||||||
\(574\) | 35.5355 | 1.48322 | ||||||||
\(575\) | −3.15631 | −0.131627 | ||||||||
\(576\) | −1.63898 | −0.0682909 | ||||||||
\(577\) | 17.2584 | 0.718478 | 0.359239 | − | 0.933246i | \(-0.383036\pi\) | ||||
0.359239 | + | 0.933246i | \(0.383036\pi\) | |||||||
\(578\) | 8.58362 | 0.357031 | ||||||||
\(579\) | −23.0228 | −0.956793 | ||||||||
\(580\) | −8.35160 | −0.346781 | ||||||||
\(581\) | 35.5760 | 1.47594 | ||||||||
\(582\) | 13.1882 | 0.546670 | ||||||||
\(583\) | 4.13953 | 0.171442 | ||||||||
\(584\) | −3.06434 | −0.126803 | ||||||||
\(585\) | −6.17097 | −0.255138 | ||||||||
\(586\) | −21.4833 | −0.887468 | ||||||||
\(587\) | −29.1683 | −1.20391 | −0.601953 | − | 0.798532i | \(-0.705610\pi\) | ||||
−0.601953 | + | 0.798532i | \(0.705610\pi\) | |||||||
\(588\) | −9.20315 | −0.379531 | ||||||||
\(589\) | 6.90058 | 0.284334 | ||||||||
\(590\) | −10.9802 | −0.452049 | ||||||||
\(591\) | 2.07901 | 0.0855192 | ||||||||
\(592\) | −4.67122 | −0.191986 | ||||||||
\(593\) | −32.4227 | −1.33144 | −0.665720 | − | 0.746202i | \(-0.731875\pi\) | ||||
−0.665720 | + | 0.746202i | \(0.731875\pi\) | |||||||
\(594\) | 5.41196 | 0.222055 | ||||||||
\(595\) | −19.5168 | −0.800112 | ||||||||
\(596\) | 13.2473 | 0.542629 | ||||||||
\(597\) | 2.65788 | 0.108780 | ||||||||
\(598\) | 11.8839 | 0.485968 | ||||||||
\(599\) | −38.8717 | −1.58826 | −0.794128 | − | 0.607751i | \(-0.792072\pi\) | ||||
−0.794128 | + | 0.607751i | \(0.792072\pi\) | |||||||
\(600\) | −1.16663 | −0.0476273 | ||||||||
\(601\) | −6.81472 | −0.277978 | −0.138989 | − | 0.990294i | \(-0.544385\pi\) | ||||
−0.138989 | + | 0.990294i | \(0.544385\pi\) | |||||||
\(602\) | −3.85859 | −0.157264 | ||||||||
\(603\) | −12.9032 | −0.525459 | ||||||||
\(604\) | −9.37827 | −0.381597 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | −18.3460 | −0.745255 | ||||||||
\(607\) | −38.9902 | −1.58256 | −0.791282 | − | 0.611451i | \(-0.790586\pi\) | ||||
−0.791282 | + | 0.611451i | \(0.790586\pi\) | |||||||
\(608\) | −2.28887 | −0.0928260 | ||||||||
\(609\) | 37.5950 | 1.52343 | ||||||||
\(610\) | −7.94861 | −0.321830 | ||||||||
\(611\) | −25.1945 | −1.01926 | ||||||||
\(612\) | 8.29001 | 0.335104 | ||||||||
\(613\) | 36.6149 | 1.47886 | 0.739430 | − | 0.673233i | \(-0.235095\pi\) | ||||
0.739430 | + | 0.673233i | \(0.235095\pi\) | |||||||
\(614\) | −10.0990 | −0.407563 | ||||||||
\(615\) | −10.7440 | −0.433240 | ||||||||
\(616\) | −3.85859 | −0.155467 | ||||||||
\(617\) | −25.6334 | −1.03196 | −0.515980 | − | 0.856600i | \(-0.672572\pi\) | ||||
−0.515980 | + | 0.856600i | \(0.672572\pi\) | |||||||
\(618\) | −0.0244546 | −0.000983708 0 | ||||||||
\(619\) | 39.4243 | 1.58460 | 0.792298 | − | 0.610134i | \(-0.208885\pi\) | ||||
0.792298 | + | 0.610134i | \(0.208885\pi\) | |||||||
\(620\) | 3.01484 | 0.121079 | ||||||||
\(621\) | −17.0818 | −0.685469 | ||||||||
\(622\) | −22.4101 | −0.898565 | ||||||||
\(623\) | 17.7999 | 0.713140 | ||||||||
\(624\) | 4.39249 | 0.175840 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 18.7363 | 0.748852 | ||||||||
\(627\) | 2.67026 | 0.106640 | ||||||||
\(628\) | −12.4335 | −0.496150 | ||||||||
\(629\) | 23.6271 | 0.942076 | ||||||||
\(630\) | −6.32415 | −0.251960 | ||||||||
\(631\) | −8.96733 | −0.356984 | −0.178492 | − | 0.983941i | \(-0.557122\pi\) | ||||
−0.178492 | + | 0.983941i | \(0.557122\pi\) | |||||||
\(632\) | −12.8076 | −0.509458 | ||||||||
\(633\) | −10.5743 | −0.420292 | ||||||||
\(634\) | 30.9181 | 1.22791 | ||||||||
\(635\) | 6.04085 | 0.239724 | ||||||||
\(636\) | −4.82928 | −0.191494 | ||||||||
\(637\) | −29.7019 | −1.17683 | ||||||||
\(638\) | 8.35160 | 0.330643 | ||||||||
\(639\) | 0.439775 | 0.0173972 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 20.2791 | 0.800975 | 0.400487 | − | 0.916302i | \(-0.368841\pi\) | ||||
0.400487 | + | 0.916302i | \(0.368841\pi\) | |||||||
\(642\) | 3.02595 | 0.119425 | ||||||||
\(643\) | −32.8809 | −1.29670 | −0.648349 | − | 0.761343i | \(-0.724540\pi\) | ||||
−0.648349 | + | 0.761343i | \(0.724540\pi\) | |||||||
\(644\) | 12.1789 | 0.479915 | ||||||||
\(645\) | 1.16663 | 0.0459359 | ||||||||
\(646\) | 11.5772 | 0.455498 | ||||||||
\(647\) | −7.90777 | −0.310886 | −0.155443 | − | 0.987845i | \(-0.549681\pi\) | ||||
−0.155443 | + | 0.987845i | \(0.549681\pi\) | |||||||
\(648\) | −1.39679 | −0.0548711 | ||||||||
\(649\) | 10.9802 | 0.431011 | ||||||||
\(650\) | −3.76512 | −0.147680 | ||||||||
\(651\) | −13.5714 | −0.531905 | ||||||||
\(652\) | −3.64178 | −0.142623 | ||||||||
\(653\) | 17.0189 | 0.666001 | 0.333001 | − | 0.942927i | \(-0.391939\pi\) | ||||
0.333001 | + | 0.942927i | \(0.391939\pi\) | |||||||
\(654\) | −12.2138 | −0.477598 | ||||||||
\(655\) | −1.66995 | −0.0652502 | ||||||||
\(656\) | −9.20945 | −0.359569 | ||||||||
\(657\) | 5.02240 | 0.195942 | ||||||||
\(658\) | −25.8199 | −1.00657 | ||||||||
\(659\) | −5.57919 | −0.217334 | −0.108667 | − | 0.994078i | \(-0.534658\pi\) | ||||
−0.108667 | + | 0.994078i | \(0.534658\pi\) | |||||||
\(660\) | 1.16663 | 0.0454109 | ||||||||
\(661\) | −30.8866 | −1.20135 | −0.600674 | − | 0.799494i | \(-0.705101\pi\) | ||||
−0.600674 | + | 0.799494i | \(0.705101\pi\) | |||||||
\(662\) | −4.28823 | −0.166667 | ||||||||
\(663\) | −22.2173 | −0.862850 | ||||||||
\(664\) | −9.21995 | −0.357803 | ||||||||
\(665\) | −8.83180 | −0.342483 | ||||||||
\(666\) | 7.65604 | 0.296666 | ||||||||
\(667\) | −26.3602 | −1.02067 | ||||||||
\(668\) | −18.5093 | −0.716147 | ||||||||
\(669\) | −19.7586 | −0.763913 | ||||||||
\(670\) | −7.87269 | −0.304148 | ||||||||
\(671\) | 7.94861 | 0.306853 | ||||||||
\(672\) | 4.50153 | 0.173650 | ||||||||
\(673\) | 18.5532 | 0.715172 | 0.357586 | − | 0.933880i | \(-0.383600\pi\) | ||||
0.357586 | + | 0.933880i | \(0.383600\pi\) | |||||||
\(674\) | 2.20531 | 0.0849455 | ||||||||
\(675\) | 5.41196 | 0.208306 | ||||||||
\(676\) | 1.17615 | 0.0452364 | ||||||||
\(677\) | 34.7398 | 1.33516 | 0.667580 | − | 0.744538i | \(-0.267330\pi\) | ||||
0.667580 | + | 0.744538i | \(0.267330\pi\) | |||||||
\(678\) | −13.1077 | −0.503400 | ||||||||
\(679\) | 43.6198 | 1.67397 | ||||||||
\(680\) | 5.05803 | 0.193966 | ||||||||
\(681\) | 1.61444 | 0.0618656 | ||||||||
\(682\) | −3.01484 | −0.115444 | ||||||||
\(683\) | 2.46507 | 0.0943232 | 0.0471616 | − | 0.998887i | \(-0.484982\pi\) | ||||
0.0471616 | + | 0.998887i | \(0.484982\pi\) | |||||||
\(684\) | 3.75142 | 0.143439 | ||||||||
\(685\) | −5.55653 | −0.212304 | ||||||||
\(686\) | −3.42905 | −0.130922 | ||||||||
\(687\) | −2.65595 | −0.101331 | ||||||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | −15.5858 | −0.593773 | ||||||||
\(690\) | −3.68223 | −0.140180 | ||||||||
\(691\) | 37.1239 | 1.41226 | 0.706130 | − | 0.708082i | \(-0.250439\pi\) | ||||
0.706130 | + | 0.708082i | \(0.250439\pi\) | |||||||
\(692\) | 10.1268 | 0.384963 | ||||||||
\(693\) | 6.32415 | 0.240235 | ||||||||
\(694\) | −13.2410 | −0.502623 | ||||||||
\(695\) | −16.6438 | −0.631334 | ||||||||
\(696\) | −9.74320 | −0.369315 | ||||||||
\(697\) | 46.5816 | 1.76441 | ||||||||
\(698\) | 28.1887 | 1.06696 | ||||||||
\(699\) | 15.4358 | 0.583835 | ||||||||
\(700\) | −3.85859 | −0.145841 | ||||||||
\(701\) | 11.6976 | 0.441811 | 0.220905 | − | 0.975295i | \(-0.429099\pi\) | ||||
0.220905 | + | 0.975295i | \(0.429099\pi\) | |||||||
\(702\) | −20.3767 | −0.769069 | ||||||||
\(703\) | 10.6918 | 0.403249 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 7.80655 | 0.294012 | ||||||||
\(706\) | 34.0257 | 1.28057 | ||||||||
\(707\) | −60.6789 | −2.28206 | ||||||||
\(708\) | −12.8098 | −0.481423 | ||||||||
\(709\) | 28.8600 | 1.08386 | 0.541930 | − | 0.840424i | \(-0.317694\pi\) | ||||
0.541930 | + | 0.840424i | \(0.317694\pi\) | |||||||
\(710\) | 0.268322 | 0.0100699 | ||||||||
\(711\) | 20.9914 | 0.787238 | ||||||||
\(712\) | −4.61307 | −0.172882 | ||||||||
\(713\) | 9.51577 | 0.356368 | ||||||||
\(714\) | −22.7688 | −0.852103 | ||||||||
\(715\) | 3.76512 | 0.140808 | ||||||||
\(716\) | 21.3948 | 0.799561 | ||||||||
\(717\) | 4.79135 | 0.178936 | ||||||||
\(718\) | 31.7592 | 1.18524 | ||||||||
\(719\) | 7.37005 | 0.274857 | 0.137428 | − | 0.990512i | \(-0.456116\pi\) | ||||
0.137428 | + | 0.990512i | \(0.456116\pi\) | |||||||
\(720\) | 1.63898 | 0.0610813 | ||||||||
\(721\) | −0.0808829 | −0.00301224 | ||||||||
\(722\) | −13.7611 | −0.512134 | ||||||||
\(723\) | 34.8998 | 1.29794 | ||||||||
\(724\) | −3.69809 | −0.137438 | ||||||||
\(725\) | 8.35160 | 0.310171 | ||||||||
\(726\) | −1.16663 | −0.0432976 | ||||||||
\(727\) | −51.1623 | −1.89750 | −0.948752 | − | 0.316021i | \(-0.897653\pi\) | ||||
−0.948752 | + | 0.316021i | \(0.897653\pi\) | |||||||
\(728\) | 14.5280 | 0.538445 | ||||||||
\(729\) | 21.2305 | 0.786316 | ||||||||
\(730\) | 3.06434 | 0.113416 | ||||||||
\(731\) | −5.05803 | −0.187078 | ||||||||
\(732\) | −9.27306 | −0.342742 | ||||||||
\(733\) | −7.81541 | −0.288669 | −0.144334 | − | 0.989529i | \(-0.546104\pi\) | ||||
−0.144334 | + | 0.989529i | \(0.546104\pi\) | |||||||
\(734\) | 7.76648 | 0.286666 | ||||||||
\(735\) | 9.20315 | 0.339463 | ||||||||
\(736\) | −3.15631 | −0.116343 | ||||||||
\(737\) | 7.87269 | 0.289994 | ||||||||
\(738\) | 15.0941 | 0.555623 | ||||||||
\(739\) | −24.5364 | −0.902587 | −0.451293 | − | 0.892376i | \(-0.649037\pi\) | ||||
−0.451293 | + | 0.892376i | \(0.649037\pi\) | |||||||
\(740\) | 4.67122 | 0.171717 | ||||||||
\(741\) | −10.0538 | −0.369337 | ||||||||
\(742\) | −15.9727 | −0.586377 | ||||||||
\(743\) | 39.5998 | 1.45278 | 0.726388 | − | 0.687285i | \(-0.241198\pi\) | ||||
0.726388 | + | 0.687285i | \(0.241198\pi\) | |||||||
\(744\) | 3.51719 | 0.128947 | ||||||||
\(745\) | −13.2473 | −0.485342 | ||||||||
\(746\) | −26.4763 | −0.969366 | ||||||||
\(747\) | 15.1113 | 0.552895 | ||||||||
\(748\) | −5.05803 | −0.184940 | ||||||||
\(749\) | 10.0083 | 0.365694 | ||||||||
\(750\) | 1.16663 | 0.0425992 | ||||||||
\(751\) | −2.91107 | −0.106227 | −0.0531133 | − | 0.998588i | \(-0.516914\pi\) | ||||
−0.0531133 | + | 0.998588i | \(0.516914\pi\) | |||||||
\(752\) | 6.69155 | 0.244016 | ||||||||
\(753\) | 16.0137 | 0.583570 | ||||||||
\(754\) | −31.4448 | −1.14515 | ||||||||
\(755\) | 9.37827 | 0.341310 | ||||||||
\(756\) | −20.8825 | −0.759490 | ||||||||
\(757\) | −9.30032 | −0.338026 | −0.169013 | − | 0.985614i | \(-0.554058\pi\) | ||||
−0.169013 | + | 0.985614i | \(0.554058\pi\) | |||||||
\(758\) | −3.14282 | −0.114152 | ||||||||
\(759\) | 3.68223 | 0.133657 | ||||||||
\(760\) | 2.28887 | 0.0830261 | ||||||||
\(761\) | −6.37837 | −0.231216 | −0.115608 | − | 0.993295i | \(-0.536882\pi\) | ||||
−0.115608 | + | 0.993295i | \(0.536882\pi\) | |||||||
\(762\) | 7.04741 | 0.255301 | ||||||||
\(763\) | −40.3969 | −1.46246 | ||||||||
\(764\) | 4.35977 | 0.157731 | ||||||||
\(765\) | −8.29001 | −0.299726 | ||||||||
\(766\) | 23.6271 | 0.853683 | ||||||||
\(767\) | −41.3419 | −1.49277 | ||||||||
\(768\) | −1.16663 | −0.0420970 | ||||||||
\(769\) | 2.53071 | 0.0912598 | 0.0456299 | − | 0.998958i | \(-0.485471\pi\) | ||||
0.0456299 | + | 0.998958i | \(0.485471\pi\) | |||||||
\(770\) | 3.85859 | 0.139054 | ||||||||
\(771\) | −31.5631 | −1.13672 | ||||||||
\(772\) | 19.7345 | 0.710259 | ||||||||
\(773\) | −26.4419 | −0.951048 | −0.475524 | − | 0.879703i | \(-0.657741\pi\) | ||||
−0.475524 | + | 0.879703i | \(0.657741\pi\) | |||||||
\(774\) | −1.63898 | −0.0589120 | ||||||||
\(775\) | −3.01484 | −0.108296 | ||||||||
\(776\) | −11.3046 | −0.405811 | ||||||||
\(777\) | −21.0276 | −0.754362 | ||||||||
\(778\) | 28.0363 | 1.00515 | ||||||||
\(779\) | 21.0792 | 0.755242 | ||||||||
\(780\) | −4.39249 | −0.157276 | ||||||||
\(781\) | −0.268322 | −0.00960131 | ||||||||
\(782\) | 15.9647 | 0.570896 | ||||||||
\(783\) | 45.1985 | 1.61526 | ||||||||
\(784\) | 7.88868 | 0.281739 | ||||||||
\(785\) | 12.4335 | 0.443770 | ||||||||
\(786\) | −1.94820 | −0.0694901 | ||||||||
\(787\) | 42.1429 | 1.50223 | 0.751116 | − | 0.660170i | \(-0.229516\pi\) | ||||
0.751116 | + | 0.660170i | \(0.229516\pi\) | |||||||
\(788\) | −1.78207 | −0.0634837 | ||||||||
\(789\) | 29.3160 | 1.04368 | ||||||||
\(790\) | 12.8076 | 0.455673 | ||||||||
\(791\) | −43.3535 | −1.54147 | ||||||||
\(792\) | −1.63898 | −0.0582387 | ||||||||
\(793\) | −29.9275 | −1.06276 | ||||||||
\(794\) | 11.7912 | 0.418456 | ||||||||
\(795\) | 4.82928 | 0.171277 | ||||||||
\(796\) | −2.27826 | −0.0807509 | ||||||||
\(797\) | 25.2137 | 0.893117 | 0.446558 | − | 0.894754i | \(-0.352650\pi\) | ||||
0.446558 | + | 0.894754i | \(0.352650\pi\) | |||||||
\(798\) | −10.3034 | −0.364737 | ||||||||
\(799\) | −33.8461 | −1.19739 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 7.56075 | 0.267146 | ||||||||
\(802\) | −4.46116 | −0.157529 | ||||||||
\(803\) | −3.06434 | −0.108138 | ||||||||
\(804\) | −9.18449 | −0.323912 | ||||||||
\(805\) | −12.1789 | −0.429249 | ||||||||
\(806\) | 11.3512 | 0.399831 | ||||||||
\(807\) | 7.24692 | 0.255104 | ||||||||
\(808\) | 15.7257 | 0.553228 | ||||||||
\(809\) | 26.8631 | 0.944456 | 0.472228 | − | 0.881476i | \(-0.343450\pi\) | ||||
0.472228 | + | 0.881476i | \(0.343450\pi\) | |||||||
\(810\) | 1.39679 | 0.0490782 | ||||||||
\(811\) | −25.5513 | −0.897229 | −0.448614 | − | 0.893725i | \(-0.648082\pi\) | ||||
−0.448614 | + | 0.893725i | \(0.648082\pi\) | |||||||
\(812\) | −32.2254 | −1.13089 | ||||||||
\(813\) | −20.5043 | −0.719117 | ||||||||
\(814\) | −4.67122 | −0.163726 | ||||||||
\(815\) | 3.64178 | 0.127566 | ||||||||
\(816\) | 5.90083 | 0.206570 | ||||||||
\(817\) | −2.28887 | −0.0800775 | ||||||||
\(818\) | −8.24320 | −0.288217 | ||||||||
\(819\) | −23.8112 | −0.832031 | ||||||||
\(820\) | 9.20945 | 0.321608 | ||||||||
\(821\) | 52.8976 | 1.84614 | 0.923069 | − | 0.384633i | \(-0.125672\pi\) | ||||
0.923069 | + | 0.384633i | \(0.125672\pi\) | |||||||
\(822\) | −6.48240 | −0.226100 | ||||||||
\(823\) | −28.6027 | −0.997027 | −0.498513 | − | 0.866882i | \(-0.666121\pi\) | ||||
−0.498513 | + | 0.866882i | \(0.666121\pi\) | |||||||
\(824\) | 0.0209618 | 0.000730239 0 | ||||||||
\(825\) | −1.16663 | −0.0406167 | ||||||||
\(826\) | −42.3681 | −1.47418 | ||||||||
\(827\) | −21.9377 | −0.762848 | −0.381424 | − | 0.924400i | \(-0.624566\pi\) | ||||
−0.381424 | + | 0.924400i | \(0.624566\pi\) | |||||||
\(828\) | 5.17313 | 0.179779 | ||||||||
\(829\) | 52.8622 | 1.83598 | 0.917990 | − | 0.396603i | \(-0.129811\pi\) | ||||
0.917990 | + | 0.396603i | \(0.129811\pi\) | |||||||
\(830\) | 9.21995 | 0.320029 | ||||||||
\(831\) | −18.7295 | −0.649719 | ||||||||
\(832\) | −3.76512 | −0.130532 | ||||||||
\(833\) | −39.9012 | −1.38249 | ||||||||
\(834\) | −19.4171 | −0.672358 | ||||||||
\(835\) | 18.5093 | 0.640542 | ||||||||
\(836\) | −2.28887 | −0.0791623 | ||||||||
\(837\) | −16.3162 | −0.563970 | ||||||||
\(838\) | 2.25172 | 0.0777842 | ||||||||
\(839\) | −4.98574 | −0.172127 | −0.0860634 | − | 0.996290i | \(-0.527429\pi\) | ||||
−0.0860634 | + | 0.996290i | \(0.527429\pi\) | |||||||
\(840\) | −4.50153 | −0.155317 | ||||||||
\(841\) | 40.7493 | 1.40515 | ||||||||
\(842\) | −36.6258 | −1.26221 | ||||||||
\(843\) | −29.0347 | −1.00001 | ||||||||
\(844\) | 9.06403 | 0.311997 | ||||||||
\(845\) | −1.17615 | −0.0404607 | ||||||||
\(846\) | −10.9673 | −0.377065 | ||||||||
\(847\) | −3.85859 | −0.132583 | ||||||||
\(848\) | 4.13953 | 0.142152 | ||||||||
\(849\) | 19.6652 | 0.674908 | ||||||||
\(850\) | −5.05803 | −0.173489 | ||||||||
\(851\) | 14.7438 | 0.505411 | ||||||||
\(852\) | 0.313031 | 0.0107243 | ||||||||
\(853\) | 39.6940 | 1.35910 | 0.679548 | − | 0.733631i | \(-0.262176\pi\) | ||||
0.679548 | + | 0.733631i | \(0.262176\pi\) | |||||||
\(854\) | −30.6704 | −1.04952 | ||||||||
\(855\) | −3.75142 | −0.128296 | ||||||||
\(856\) | −2.59376 | −0.0886530 | ||||||||
\(857\) | −24.1322 | −0.824340 | −0.412170 | − | 0.911107i | \(-0.635229\pi\) | ||||
−0.412170 | + | 0.911107i | \(0.635229\pi\) | |||||||
\(858\) | 4.39249 | 0.149957 | ||||||||
\(859\) | 17.2624 | 0.588987 | 0.294493 | − | 0.955653i | \(-0.404849\pi\) | ||||
0.294493 | + | 0.955653i | \(0.404849\pi\) | |||||||
\(860\) | −1.00000 | −0.0340997 | ||||||||
\(861\) | −41.4566 | −1.41284 | ||||||||
\(862\) | −20.8183 | −0.709074 | ||||||||
\(863\) | −32.7803 | −1.11586 | −0.557928 | − | 0.829889i | \(-0.688403\pi\) | ||||
−0.557928 | + | 0.829889i | \(0.688403\pi\) | |||||||
\(864\) | 5.41196 | 0.184119 | ||||||||
\(865\) | −10.1268 | −0.344322 | ||||||||
\(866\) | −14.0428 | −0.477193 | ||||||||
\(867\) | −10.0139 | −0.340089 | ||||||||
\(868\) | 11.6330 | 0.394851 | ||||||||
\(869\) | −12.8076 | −0.434467 | ||||||||
\(870\) | 9.74320 | 0.330326 | ||||||||
\(871\) | −29.6416 | −1.00437 | ||||||||
\(872\) | 10.4693 | 0.354537 | ||||||||
\(873\) | 18.5280 | 0.627079 | ||||||||
\(874\) | 7.22438 | 0.244368 | ||||||||
\(875\) | 3.85859 | 0.130444 | ||||||||
\(876\) | 3.57494 | 0.120786 | ||||||||
\(877\) | 37.3756 | 1.26208 | 0.631042 | − | 0.775749i | \(-0.282628\pi\) | ||||
0.631042 | + | 0.775749i | \(0.282628\pi\) | |||||||
\(878\) | −18.1912 | −0.613924 | ||||||||
\(879\) | 25.0630 | 0.845354 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | 4.33370 | 0.146006 | 0.0730029 | − | 0.997332i | \(-0.476742\pi\) | ||||
0.0730029 | + | 0.997332i | \(0.476742\pi\) | |||||||
\(882\) | −12.9294 | −0.435356 | ||||||||
\(883\) | 44.1723 | 1.48651 | 0.743257 | − | 0.669006i | \(-0.233280\pi\) | ||||
0.743257 | + | 0.669006i | \(0.233280\pi\) | |||||||
\(884\) | 19.0441 | 0.640522 | ||||||||
\(885\) | 12.8098 | 0.430597 | ||||||||
\(886\) | −15.2466 | −0.512219 | ||||||||
\(887\) | 6.30202 | 0.211601 | 0.105801 | − | 0.994387i | \(-0.466259\pi\) | ||||
0.105801 | + | 0.994387i | \(0.466259\pi\) | |||||||
\(888\) | 5.44957 | 0.182875 | ||||||||
\(889\) | 23.3091 | 0.781763 | ||||||||
\(890\) | 4.61307 | 0.154631 | ||||||||
\(891\) | −1.39679 | −0.0467942 | ||||||||
\(892\) | 16.9366 | 0.567078 | ||||||||
\(893\) | −15.3161 | −0.512534 | ||||||||
\(894\) | −15.4546 | −0.516879 | ||||||||
\(895\) | −21.3948 | −0.715149 | ||||||||
\(896\) | −3.85859 | −0.128906 | ||||||||
\(897\) | −13.8641 | −0.462907 | ||||||||
\(898\) | 33.2136 | 1.10835 | ||||||||
\(899\) | −25.1788 | −0.839759 | ||||||||
\(900\) | −1.63898 | −0.0546327 | ||||||||
\(901\) | −20.9378 | −0.697540 | ||||||||
\(902\) | −9.20945 | −0.306641 | ||||||||
\(903\) | 4.50153 | 0.149801 | ||||||||
\(904\) | 11.2356 | 0.373690 | ||||||||
\(905\) | 3.69809 | 0.122929 | ||||||||
\(906\) | 10.9409 | 0.363488 | ||||||||
\(907\) | −49.5306 | −1.64464 | −0.822318 | − | 0.569028i | \(-0.807320\pi\) | ||||
−0.822318 | + | 0.569028i | \(0.807320\pi\) | |||||||
\(908\) | −1.38386 | −0.0459249 | ||||||||
\(909\) | −25.7741 | −0.854874 | ||||||||
\(910\) | −14.5280 | −0.481600 | ||||||||
\(911\) | −10.3520 | −0.342978 | −0.171489 | − | 0.985186i | \(-0.554858\pi\) | ||||
−0.171489 | + | 0.985186i | \(0.554858\pi\) | |||||||
\(912\) | 2.67026 | 0.0884211 | ||||||||
\(913\) | −9.21995 | −0.305136 | ||||||||
\(914\) | −9.26528 | −0.306468 | ||||||||
\(915\) | 9.27306 | 0.306558 | ||||||||
\(916\) | 2.27661 | 0.0752213 | ||||||||
\(917\) | −6.44363 | −0.212787 | ||||||||
\(918\) | −27.3738 | −0.903471 | ||||||||
\(919\) | −7.21290 | −0.237932 | −0.118966 | − | 0.992898i | \(-0.537958\pi\) | ||||
−0.118966 | + | 0.992898i | \(0.537958\pi\) | |||||||
\(920\) | 3.15631 | 0.104060 | ||||||||
\(921\) | 11.7818 | 0.388222 | ||||||||
\(922\) | −2.70163 | −0.0889735 | ||||||||
\(923\) | 1.01026 | 0.0332532 | ||||||||
\(924\) | 4.50153 | 0.148089 | ||||||||
\(925\) | −4.67122 | −0.153589 | ||||||||
\(926\) | 4.80337 | 0.157848 | ||||||||
\(927\) | −0.0343560 | −0.00112840 | ||||||||
\(928\) | 8.35160 | 0.274155 | ||||||||
\(929\) | −11.4708 | −0.376344 | −0.188172 | − | 0.982136i | \(-0.560256\pi\) | ||||
−0.188172 | + | 0.982136i | \(0.560256\pi\) | |||||||
\(930\) | −3.51719 | −0.115333 | ||||||||
\(931\) | −18.0562 | −0.591767 | ||||||||
\(932\) | −13.2311 | −0.433400 | ||||||||
\(933\) | 26.1443 | 0.855925 | ||||||||
\(934\) | 18.0499 | 0.590611 | ||||||||
\(935\) | 5.05803 | 0.165415 | ||||||||
\(936\) | 6.17097 | 0.201704 | ||||||||
\(937\) | 45.2862 | 1.47944 | 0.739718 | − | 0.672917i | \(-0.234959\pi\) | ||||
0.739718 | + | 0.672917i | \(0.234959\pi\) | |||||||
\(938\) | −30.3774 | −0.991859 | ||||||||
\(939\) | −21.8582 | −0.713316 | ||||||||
\(940\) | −6.69155 | −0.218254 | ||||||||
\(941\) | −38.4723 | −1.25416 | −0.627081 | − | 0.778954i | \(-0.715750\pi\) | ||||
−0.627081 | + | 0.778954i | \(0.715750\pi\) | |||||||
\(942\) | 14.5052 | 0.472606 | ||||||||
\(943\) | 29.0679 | 0.946580 | ||||||||
\(944\) | 10.9802 | 0.357376 | ||||||||
\(945\) | 20.8825 | 0.679308 | ||||||||
\(946\) | 1.00000 | 0.0325128 | ||||||||
\(947\) | −57.4837 | −1.86797 | −0.933985 | − | 0.357312i | \(-0.883693\pi\) | ||||
−0.933985 | + | 0.357312i | \(0.883693\pi\) | |||||||
\(948\) | 14.9416 | 0.485282 | ||||||||
\(949\) | 11.5376 | 0.374527 | ||||||||
\(950\) | −2.28887 | −0.0742608 | ||||||||
\(951\) | −36.0698 | −1.16964 | ||||||||
\(952\) | 19.5168 | 0.632544 | ||||||||
\(953\) | −3.41714 | −0.110692 | −0.0553460 | − | 0.998467i | \(-0.517626\pi\) | ||||
−0.0553460 | + | 0.998467i | \(0.517626\pi\) | |||||||
\(954\) | −6.78461 | −0.219660 | ||||||||
\(955\) | −4.35977 | −0.141079 | ||||||||
\(956\) | −4.10701 | −0.132830 | ||||||||
\(957\) | −9.74320 | −0.314953 | ||||||||
\(958\) | −6.10912 | −0.197377 | ||||||||
\(959\) | −21.4404 | −0.692345 | ||||||||
\(960\) | 1.16663 | 0.0376527 | ||||||||
\(961\) | −21.9107 | −0.706798 | ||||||||
\(962\) | 17.5877 | 0.567050 | ||||||||
\(963\) | 4.25113 | 0.136991 | ||||||||
\(964\) | −29.9152 | −0.963502 | ||||||||
\(965\) | −19.7345 | −0.635275 | ||||||||
\(966\) | −14.2082 | −0.457142 | ||||||||
\(967\) | 37.5678 | 1.20810 | 0.604050 | − | 0.796947i | \(-0.293553\pi\) | ||||
0.604050 | + | 0.796947i | \(0.293553\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −13.5062 | −0.433883 | ||||||||
\(970\) | 11.3046 | 0.362969 | ||||||||
\(971\) | 4.51313 | 0.144833 | 0.0724166 | − | 0.997374i | \(-0.476929\pi\) | ||||
0.0724166 | + | 0.997374i | \(0.476929\pi\) | |||||||
\(972\) | −14.6063 | −0.468499 | ||||||||
\(973\) | −64.2214 | −2.05884 | ||||||||
\(974\) | 23.7496 | 0.760987 | ||||||||
\(975\) | 4.39249 | 0.140672 | ||||||||
\(976\) | 7.94861 | 0.254429 | ||||||||
\(977\) | −53.3121 | −1.70561 | −0.852803 | − | 0.522232i | \(-0.825099\pi\) | ||||
−0.852803 | + | 0.522232i | \(0.825099\pi\) | |||||||
\(978\) | 4.24860 | 0.135855 | ||||||||
\(979\) | −4.61307 | −0.147435 | ||||||||
\(980\) | −7.88868 | −0.251995 | ||||||||
\(981\) | −17.1591 | −0.547847 | ||||||||
\(982\) | −14.1754 | −0.452356 | ||||||||
\(983\) | 57.7544 | 1.84208 | 0.921039 | − | 0.389470i | \(-0.127342\pi\) | ||||
0.921039 | + | 0.389470i | \(0.127342\pi\) | |||||||
\(984\) | 10.7440 | 0.342506 | ||||||||
\(985\) | 1.78207 | 0.0567816 | ||||||||
\(986\) | −42.2426 | −1.34528 | ||||||||
\(987\) | 30.1222 | 0.958801 | ||||||||
\(988\) | 8.61788 | 0.274171 | ||||||||
\(989\) | −3.15631 | −0.100365 | ||||||||
\(990\) | 1.63898 | 0.0520903 | ||||||||
\(991\) | −11.9262 | −0.378848 | −0.189424 | − | 0.981895i | \(-0.560662\pi\) | ||||
−0.189424 | + | 0.981895i | \(0.560662\pi\) | |||||||
\(992\) | −3.01484 | −0.0957213 | ||||||||
\(993\) | 5.00276 | 0.158758 | ||||||||
\(994\) | 1.03534 | 0.0328391 | ||||||||
\(995\) | 2.27826 | 0.0722258 | ||||||||
\(996\) | 10.7562 | 0.340824 | ||||||||
\(997\) | 46.9692 | 1.48753 | 0.743765 | − | 0.668442i | \(-0.233038\pi\) | ||||
0.743765 | + | 0.668442i | \(0.233038\pi\) | |||||||
\(998\) | 27.1431 | 0.859201 | ||||||||
\(999\) | −25.2804 | −0.799838 |
(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 | 4730.2.a.bf.1.5 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4730.2.a.bf.1.5 | ✓ | 13 | 1.1 | even | 1 | trivial |