Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(881,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.f (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + x^{14} - 4 x^{13} + 10 x^{12} - 32 x^{11} + 71 x^{10} - 70 x^{9} + 74 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.3 | ||
Root | \(1.14188 + 1.30235i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.881 |
Dual form | 1680.2.f.l.881.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.30235 | − | 1.14188i | −0.751913 | − | 0.659263i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.35345 | − | 2.27336i | 0.511557 | − | 0.859249i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.392236 | + | 2.97425i | 0.130745 | + | 0.991416i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.73062i | − | 1.72785i | −0.503624 | − | 0.863923i | \(-0.668000\pi\) | ||
0.503624 | − | 0.863923i | \(-0.332000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.24338i | − | 0.622202i | −0.950377 | − | 0.311101i | \(-0.899302\pi\) | ||
0.950377 | − | 0.311101i | \(-0.100698\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.30235 | − | 1.14188i | −0.336266 | − | 0.294831i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.50062 | −1.57663 | −0.788316 | − | 0.615270i | \(-0.789047\pi\) | ||||
−0.788316 | + | 0.615270i | \(0.789047\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.217877i | 0.0499845i | 0.999688 | + | 0.0249923i | \(0.00795611\pi\) | ||||
−0.999688 | + | 0.0249923i | \(0.992044\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.35857 | + | 1.41524i | −0.951117 | + | 0.308830i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.57998i | 1.16351i | 0.813365 | + | 0.581753i | \(0.197633\pi\) | ||||
−0.813365 | + | 0.581753i | \(0.802367\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.88539 | − | 4.32140i | 0.555294 | − | 0.831654i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.11432i | − | 0.206925i | −0.994633 | − | 0.103462i | \(-0.967008\pi\) | ||
0.994633 | − | 0.103462i | \(-0.0329921\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.49827i | − | 0.987519i | −0.869599 | − | 0.493759i | \(-0.835622\pi\) | ||
0.869599 | − | 0.493759i | \(-0.164378\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.54366 | + | 7.46328i | −1.13910 | + | 1.29919i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.35345 | − | 2.27336i | 0.228775 | − | 0.384268i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.0863 | 1.65818 | 0.829091 | − | 0.559113i | \(-0.188858\pi\) | ||||
0.829091 | + | 0.559113i | \(0.188858\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.56167 | + | 2.92167i | −0.410195 | + | 0.467842i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.11802 | 0.174606 | 0.0873030 | − | 0.996182i | \(-0.472175\pi\) | ||||
0.0873030 | + | 0.996182i | \(0.472175\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.89592 | −0.899119 | −0.449560 | − | 0.893250i | \(-0.648419\pi\) | ||||
−0.449560 | + | 0.893250i | \(0.648419\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.392236 | + | 2.97425i | 0.0584712 | + | 0.443375i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.70789 | −1.12431 | −0.562156 | − | 0.827031i | \(-0.690028\pi\) | ||||
−0.562156 | + | 0.827031i | \(0.690028\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.33633 | − | 6.15377i | −0.476618 | − | 0.879110i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.46609 | + | 7.42291i | 1.18549 | + | 1.03941i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.37883i | 1.15092i | 0.817829 | + | 0.575461i | \(0.195177\pi\) | ||||
−0.817829 | + | 0.575461i | \(0.804823\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.73062i | − | 0.772716i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.248789 | − | 0.283753i | 0.0329529 | − | 0.0375840i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.4209 | 1.74725 | 0.873624 | − | 0.486602i | \(-0.161764\pi\) | ||||
0.873624 | + | 0.486602i | \(0.161764\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.33454i | 0.170870i | 0.996344 | + | 0.0854349i | \(0.0272280\pi\) | ||||
−0.996344 | + | 0.0854349i | \(0.972772\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.29241 | + | 3.13381i | 0.918757 | + | 0.394823i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.24338i | − | 0.278257i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.5144 | −1.77322 | −0.886610 | − | 0.462517i | \(-0.846946\pi\) | ||||
−0.886610 | + | 0.462517i | \(0.846946\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.37165 | − | 7.26709i | 0.767056 | − | 0.874855i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.41245i | − | 0.879696i | −0.898072 | − | 0.439848i | \(-0.855032\pi\) | ||
0.898072 | − | 0.439848i | \(-0.144968\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.1828i | − | 1.42589i | −0.701220 | − | 0.712945i | \(-0.747361\pi\) | ||
0.701220 | − | 0.712945i | \(-0.252639\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.30235 | − | 1.14188i | −0.150383 | − | 0.131853i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.0278 | − | 7.75612i | −1.48465 | − | 0.883892i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.54501 | −0.511354 | −0.255677 | − | 0.966762i | \(-0.582298\pi\) | ||||
−0.255677 | + | 0.966762i | \(0.582298\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.69230 | + | 2.33322i | −0.965811 | + | 0.259246i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.9184 | −1.19845 | −0.599223 | − | 0.800582i | \(-0.704524\pi\) | ||||
−0.599223 | + | 0.800582i | \(0.704524\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.50062 | −0.705091 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.27242 | + | 1.45124i | −0.136418 | + | 0.155589i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.45092 | −0.471797 | −0.235898 | − | 0.971778i | \(-0.575803\pi\) | ||||
−0.235898 | + | 0.971778i | \(0.575803\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.10002 | − | 3.03631i | −0.534627 | − | 0.318292i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.27835 | + | 7.16068i | −0.651034 | + | 0.742528i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.217877i | 0.0223537i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.33620i | 0.947948i | 0.880539 | + | 0.473974i | \(0.157181\pi\) | ||||
−0.880539 | + | 0.473974i | \(0.842819\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 17.0443 | − | 2.24776i | 1.71301 | − | 0.225908i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.12564 | −0.808531 | −0.404266 | − | 0.914642i | \(-0.632473\pi\) | ||||
−0.404266 | + | 0.914642i | \(0.632473\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.21987i | 0.317263i | 0.987338 | + | 0.158632i | \(0.0507082\pi\) | ||||
−0.987338 | + | 0.158632i | \(0.949292\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.35857 | + | 1.41524i | −0.425353 | + | 0.138113i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.352062i | 0.0340351i | 0.999855 | + | 0.0170175i | \(0.00541711\pi\) | ||||
−0.999855 | + | 0.0170175i | \(0.994583\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.8035 | 1.32214 | 0.661069 | − | 0.750325i | \(-0.270103\pi\) | ||||
0.661069 | + | 0.750325i | \(0.270103\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.1359 | − | 11.5173i | −1.24681 | − | 1.09318i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.52753i | − | 0.237770i | −0.992908 | − | 0.118885i | \(-0.962068\pi\) | ||
0.992908 | − | 0.118885i | \(-0.0379320\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.57998i | 0.520336i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.67238 | − | 0.879936i | 0.616861 | − | 0.0813502i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.79829 | + | 14.7783i | −0.806538 | + | 1.35472i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −21.8400 | −1.98545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.45606 | − | 1.27664i | −0.131288 | − | 0.115111i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.2059 | −1.17183 | −0.585916 | − | 0.810372i | \(-0.699265\pi\) | ||||
−0.585916 | + | 0.810372i | \(0.699265\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.67856 | + | 6.73241i | 0.676059 | + | 0.592756i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.2780 | −0.897992 | −0.448996 | − | 0.893534i | \(-0.648218\pi\) | ||||
−0.448996 | + | 0.893534i | \(0.648218\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.495314 | + | 0.294887i | 0.0429491 | + | 0.0255699i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.88539 | − | 4.32140i | 0.248335 | − | 0.371927i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.43330i | 0.464198i | 0.972692 | + | 0.232099i | \(0.0745594\pi\) | ||||
−0.972692 | + | 0.232099i | \(0.925441\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.2976i | 1.38235i | 0.722689 | + | 0.691173i | \(0.242906\pi\) | ||||
−0.722689 | + | 0.691173i | \(0.757094\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.0384 | + | 8.80146i | 0.845384 | + | 0.741217i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.8560 | −1.07507 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.11432i | − | 0.0925395i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.68178 | + | 11.8240i | −0.221189 | + | 0.975231i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 9.85697i | − | 0.807514i | −0.914866 | − | 0.403757i | \(-0.867704\pi\) | ||
0.914866 | − | 0.403757i | \(-0.132296\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.96893 | −0.485744 | −0.242872 | − | 0.970058i | \(-0.578090\pi\) | ||||
−0.242872 | + | 0.970058i | \(0.578090\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.54978 | − | 19.3345i | −0.206138 | − | 1.56310i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 5.49827i | − | 0.441632i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 7.94202i | − | 0.633842i | −0.948452 | − | 0.316921i | \(-0.897351\pi\) | ||
0.948452 | − | 0.316921i | \(-0.102649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.56759 | − | 10.9122i | 0.758759 | − | 0.865392i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.6853 | + | 7.55224i | 0.999742 | + | 0.595200i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.4764 | 1.44718 | 0.723591 | − | 0.690229i | \(-0.242490\pi\) | ||||
0.723591 | + | 0.690229i | \(0.242490\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.54366 | + | 7.46328i | −0.509423 | + | 0.581015i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.29590 | −0.177662 | −0.0888310 | − | 0.996047i | \(-0.528313\pi\) | ||||
−0.0888310 | + | 0.996047i | \(0.528313\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.96723 | 0.612864 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.648021 | + | 0.0854595i | −0.0495554 | + | 0.00653525i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.10485 | −0.0839999 | −0.0420000 | − | 0.999118i | \(-0.513373\pi\) | ||||
−0.0420000 | + | 0.999118i | \(0.513373\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.35345 | − | 2.27336i | 0.102311 | − | 0.171850i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.4787 | − | 15.3250i | −1.31378 | − | 1.15190i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 14.4797i | − | 1.08227i | −0.840937 | − | 0.541133i | \(-0.817996\pi\) | ||
0.840937 | − | 0.541133i | \(-0.182004\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.5405i | − | 0.857800i | −0.903352 | − | 0.428900i | \(-0.858901\pi\) | ||
0.903352 | − | 0.428900i | \(-0.141099\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.52388 | − | 1.73803i | 0.112648 | − | 0.128479i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.0863 | 0.741562 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 37.2526i | 2.72418i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.91885 | − | 12.4084i | −0.430533 | − | 0.902575i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 10.8880i | − | 0.787828i | −0.919147 | − | 0.393914i | \(-0.871121\pi\) | ||
0.919147 | − | 0.393914i | \(-0.128879\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.56607 | 0.400654 | 0.200327 | − | 0.979729i | \(-0.435800\pi\) | ||||
0.200327 | + | 0.979729i | \(0.435800\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.56167 | + | 2.92167i | −0.183445 | + | 0.209225i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 22.6465i | − | 1.61349i | −0.590898 | − | 0.806746i | \(-0.701226\pi\) | ||
0.590898 | − | 0.806746i | \(-0.298774\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.111663i | 0.00791557i | 0.999992 | + | 0.00395778i | \(0.00125980\pi\) | ||||
−0.999992 | + | 0.00395778i | \(0.998740\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.9029 | + | 16.5737i | 1.33331 | + | 1.16902i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.53326 | − | 1.50818i | −0.177800 | − | 0.105854i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.11802 | 0.0780861 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.5962 | + | 2.18867i | −1.15352 | + | 0.152123i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.24857 | 0.0863655 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.8842 | 1.50657 | 0.753284 | − | 0.657696i | \(-0.228469\pi\) | ||||
0.753284 | + | 0.657696i | \(0.228469\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.46410 | + | 9.65361i | −0.579951 | + | 0.661454i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.89592 | −0.402098 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.4995 | − | 7.44165i | −0.848525 | − | 0.505172i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.9113 | + | 15.8663i | −0.940036 | + | 1.07214i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.5834i | 0.980984i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 21.6804i | − | 1.45183i | −0.687787 | − | 0.725913i | \(-0.741418\pi\) | ||
0.687787 | − | 0.725913i | \(-0.258582\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.392236 | + | 2.97425i | 0.0261491 | + | 0.198283i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.04028 | 0.334535 | 0.167268 | − | 0.985912i | \(-0.446506\pi\) | ||||
0.167268 | + | 0.985912i | \(0.446506\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 12.7545i | − | 0.842838i | −0.906866 | − | 0.421419i | \(-0.861532\pi\) | ||
0.906866 | − | 0.421419i | \(-0.138468\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.11018 | + | 24.9773i | 0.533611 | + | 1.64338i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 26.1291i | − | 1.71178i | −0.517161 | − | 0.855888i | \(-0.673011\pi\) | ||
0.517161 | − | 0.855888i | \(-0.326989\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.70789 | −0.502807 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.91920 | + | 5.18984i | 0.384494 | + | 0.337117i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.92107i | 0.124264i | 0.998068 | + | 0.0621319i | \(0.0197899\pi\) | ||||
−0.998068 | + | 0.0621319i | \(0.980210\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.6464i | 0.685795i | 0.939373 | + | 0.342898i | \(0.111408\pi\) | ||||
−0.939373 | + | 0.342898i | \(0.888592\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.9847 | + | 6.88687i | 0.897117 | + | 0.441793i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.33633 | − | 6.15377i | −0.213150 | − | 0.393150i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.488782 | 0.0311005 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.2195 | + | 12.4674i | 0.901127 | + | 0.790091i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.6445 | 0.798113 | 0.399056 | − | 0.916926i | \(-0.369338\pi\) | ||||
0.399056 | + | 0.916926i | \(0.369338\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 31.9767 | 2.01036 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.46609 | + | 7.42291i | 0.530167 | + | 0.464840i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.25380 | −0.452479 | −0.226240 | − | 0.974072i | \(-0.572643\pi\) | ||||
−0.226240 | + | 0.974072i | \(0.572643\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.6514 | − | 22.9299i | 0.848255 | − | 1.42479i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.31427 | − | 0.437078i | 0.205148 | − | 0.0270545i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.7889i | 1.22024i | 0.792311 | + | 0.610118i | \(0.208878\pi\) | ||||
−0.792311 | + | 0.610118i | \(0.791122\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.37883i | 0.514708i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.79666 | + | 5.08240i | 0.354750 | + | 0.311038i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.0527 | 1.40555 | 0.702773 | − | 0.711415i | \(-0.251945\pi\) | ||||
0.702773 | + | 0.711415i | \(0.251945\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.2292i | 1.10734i | 0.832735 | + | 0.553672i | \(0.186774\pi\) | ||||
−0.832735 | + | 0.553672i | \(0.813226\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.17492 | + | 9.77793i | 0.192155 | + | 0.591787i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 5.73062i | − | 0.345569i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.8032 | −1.18986 | −0.594928 | − | 0.803779i | \(-0.702819\pi\) | ||||
−0.594928 | + | 0.803779i | \(0.702819\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16.3532 | − | 2.15662i | 0.979042 | − | 0.129114i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.0541878i | 0.00323257i | 0.999999 | + | 0.00161629i | \(0.000514480\pi\) | ||||
−0.999999 | + | 0.00161629i | \(0.999486\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.74845i | − | 0.163378i | −0.996658 | − | 0.0816891i | \(-0.973969\pi\) | ||
0.996658 | − | 0.0816891i | \(-0.0260315\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.248789 | − | 0.283753i | 0.0147370 | − | 0.0168081i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.51319 | − | 2.54167i | 0.0893209 | − | 0.150030i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.2581 | 1.48577 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.6608 | − | 12.1590i | 0.624947 | − | 0.712774i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.46410 | 0.260795 | 0.130398 | − | 0.991462i | \(-0.458375\pi\) | ||||
0.130398 | + | 0.991462i | \(0.458375\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.4209 | 0.781393 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −24.7643 | − | 16.5351i | −1.43697 | − | 0.959463i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.5180 | 0.723937 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.97985 | + | 13.4035i | −0.459951 | + | 0.772568i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.5824 | + | 9.27848i | 0.607945 | + | 0.533034i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.33454i | 0.0764153i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.39682i | 0.193867i | 0.995291 | + | 0.0969334i | \(0.0309034\pi\) | ||||
−0.995291 | + | 0.0969334i | \(0.969097\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.67670 | − | 4.19340i | 0.209160 | − | 0.238554i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.473808 | 0.0268672 | 0.0134336 | − | 0.999910i | \(-0.495724\pi\) | ||||
0.0134336 | + | 0.999910i | \(0.495724\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.5169i | 0.707497i | 0.935341 | + | 0.353749i | \(0.115093\pi\) | ||||
−0.935341 | + | 0.353749i | \(0.884907\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.29241 | + | 3.13381i | 0.410881 | + | 0.176570i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 30.3962i | − | 1.70722i | −0.520913 | − | 0.853610i | \(-0.674408\pi\) | ||
0.520913 | − | 0.853610i | \(-0.325592\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.38576 | −0.357534 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.402011 | − | 0.458508i | 0.0224381 | − | 0.0255914i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.41634i | − | 0.0788072i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.24338i | − | 0.124440i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.9770 | − | 15.7619i | −0.994132 | − | 0.871636i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.4323 | + | 17.5228i | −0.575150 | + | 0.966064i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.8653 | 1.09190 | 0.545948 | − | 0.837819i | \(-0.316169\pi\) | ||||
0.545948 | + | 0.837819i | \(0.316169\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.95623 | + | 29.9992i | 0.216800 | + | 1.64395i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.5144 | −0.793008 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.7104 | 1.78185 | 0.890924 | − | 0.454153i | \(-0.150058\pi\) | ||||
0.890924 | + | 0.454153i | \(0.150058\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.88613 | + | 3.29173i | −0.156753 | + | 0.178782i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −31.5085 | −1.70628 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5053 | − | 0.744166i | −0.999192 | − | 0.0401812i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.37165 | − | 7.26709i | 0.343038 | − | 0.391247i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 22.7318i | − | 1.22031i | −0.792283 | − | 0.610154i | \(-0.791107\pi\) | ||
0.792283 | − | 0.610154i | \(-0.208893\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.77997i | 0.469981i | 0.971998 | + | 0.234990i | \(0.0755059\pi\) | ||||
−0.971998 | + | 0.234990i | \(0.924494\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.69455 | − | 6.47304i | −0.517457 | − | 0.345505i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.5148 | 0.666098 | 0.333049 | − | 0.942910i | \(-0.391923\pi\) | ||||
0.333049 | + | 0.942910i | \(0.391923\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 7.41245i | − | 0.393412i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 28.3334 | − | 9.19991i | 1.49956 | − | 0.486911i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.22814i | 0.275931i | 0.990437 | + | 0.137965i | \(0.0440563\pi\) | ||||
−0.990437 | + | 0.137965i | \(0.955944\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9525 | 0.997502 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.4433 | + | 24.9386i | 1.49289 | + | 1.30894i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 12.1828i | − | 0.637677i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.7583i | 1.55337i | 0.629888 | + | 0.776686i | \(0.283101\pi\) | ||||
−0.629888 | + | 0.776686i | \(0.716899\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.438530 | + | 3.32528i | 0.0228289 | + | 0.173107i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.0481 | + | 11.3404i | 0.988928 | + | 0.588762i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.0263 | −0.726256 | −0.363128 | − | 0.931739i | \(-0.618291\pi\) | ||||
−0.363128 | + | 0.931739i | \(0.618291\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.30235 | − | 1.14188i | −0.0672531 | − | 0.0589662i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.49985 | −0.128749 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.5017 | 0.744902 | 0.372451 | − | 0.928052i | \(-0.378517\pi\) | ||||
0.372451 | + | 0.928052i | \(0.378517\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.1987 | + | 15.0795i | 0.881115 | + | 0.772545i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.35624 | −0.478081 | −0.239041 | − | 0.971010i | \(-0.576833\pi\) | ||||
−0.239041 | + | 0.971010i | \(0.576833\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.0278 | − | 7.75612i | −0.663956 | − | 0.395289i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.31259 | − | 17.5359i | −0.117556 | − | 0.891401i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.16415i | 0.363237i | 0.983369 | + | 0.181618i | \(0.0581336\pi\) | ||||
−0.983369 | + | 0.181618i | \(0.941866\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 36.2733i | − | 1.83442i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.3855 | + | 11.7362i | 0.675211 | + | 0.592012i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.54501 | −0.228684 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.2936i | 1.16907i | 0.811367 | + | 0.584537i | \(0.198724\pi\) | ||||
−0.811367 | + | 0.584537i | \(0.801276\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.308348 | − | 0.949633i | −0.0154367 | − | 0.0475411i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.2990i | 0.714060i | 0.934093 | + | 0.357030i | \(0.116211\pi\) | ||||
−0.934093 | + | 0.357030i | \(0.883789\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.3347 | −0.614436 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.69230 | + | 2.33322i | −0.431924 | + | 0.115938i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 57.8009i | − | 2.86508i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.0357i | 1.04015i | 0.854120 | + | 0.520075i | \(0.174096\pi\) | ||||
−0.854120 | + | 0.520075i | \(0.825904\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.20416 | − | 7.07607i | 0.306029 | − | 0.349037i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.1645 | − | 30.5105i | 0.893817 | − | 1.50132i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.9184 | −0.535962 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.6099 | − | 21.2252i | 0.911330 | − | 1.03940i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.7044 | 1.59771 | 0.798857 | − | 0.601521i | \(-0.205439\pi\) | ||||
0.798857 | + | 0.601521i | \(0.205439\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.1758 | −0.934569 | −0.467285 | − | 0.884107i | \(-0.654768\pi\) | ||||
−0.467285 | + | 0.884107i | \(0.654768\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.02332 | − | 22.9252i | −0.146999 | − | 1.11466i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.50062 | −0.315326 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.03388 | + | 1.80623i | 0.146820 | + | 0.0874097i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.7430 | + | 14.6799i | 0.808359 | + | 0.708754i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 19.3591i | − | 0.932495i | −0.884654 | − | 0.466248i | \(-0.845606\pi\) | ||
0.884654 | − | 0.466248i | \(-0.154394\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.02981i | 0.193660i | 0.995301 | + | 0.0968302i | \(0.0308704\pi\) | ||||
−0.995301 | + | 0.0968302i | \(0.969130\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.27242 | + | 1.45124i | −0.0610079 | + | 0.0695817i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.21575 | −0.0581573 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 3.28426i | − | 0.156749i | −0.996924 | − | 0.0783746i | \(-0.975027\pi\) | ||
0.996924 | − | 0.0783746i | \(-0.0249730\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.9942 | − | 12.3368i | 0.809248 | − | 0.587467i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 20.2006i | − | 0.959760i | −0.877334 | − | 0.479880i | \(-0.840680\pi\) | ||
0.877334 | − | 0.479880i | \(-0.159320\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.45092 | −0.210994 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.2554 | + | 12.8372i | −0.532364 | + | 0.607180i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.84898i | 0.134452i | 0.997738 | + | 0.0672259i | \(0.0214148\pi\) | ||||
−0.997738 | + | 0.0672259i | \(0.978585\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 6.40697i | − | 0.301692i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.77364 | + | 6.81578i | 0.365237 | + | 0.320233i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.10002 | − | 3.03631i | −0.239092 | − | 0.142345i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.6864 | −1.06123 | −0.530613 | − | 0.847614i | \(-0.678038\pi\) | ||||
−0.530613 | + | 0.847614i | \(0.678038\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18.7569 | + | 28.0918i | −0.875495 | + | 1.31121i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.6309 | −0.774579 | −0.387290 | − | 0.921958i | \(-0.626589\pi\) | ||||
−0.387290 | + | 0.921958i | \(0.626589\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.8319 | 0.782247 | 0.391123 | − | 0.920338i | \(-0.372087\pi\) | ||||
0.391123 | + | 0.920338i | \(0.372087\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.27835 | + | 7.16068i | −0.291151 | + | 0.332069i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 40.2591 | 1.86297 | 0.931484 | − | 0.363782i | \(-0.118515\pi\) | ||||
0.931484 | + | 0.363782i | \(0.118515\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.6446 | + | 32.9965i | −0.907104 | + | 1.52364i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.06880 | + | 10.3433i | −0.417868 | + | 0.476594i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.7873i | 1.55354i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.217877i | 0.00999690i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.9207 | + | 3.28648i | −1.14104 | + | 0.150478i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.90837 | −0.315651 | −0.157826 | − | 0.987467i | \(-0.550448\pi\) | ||||
−0.157826 | + | 0.987467i | \(0.550448\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 22.6275i | − | 1.03173i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.89699 | − | 24.3207i | −0.359326 | − | 1.10663i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.33620i | 0.423935i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.57854 | −0.207473 | −0.103737 | − | 0.994605i | \(-0.533080\pi\) | ||||
−0.103737 | + | 0.994605i | \(0.533080\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.0627 | − | 21.0977i | −1.08815 | − | 0.954073i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 20.0323i | − | 0.904046i | −0.892006 | − | 0.452023i | \(-0.850703\pi\) | ||
0.892006 | − | 0.452023i | \(-0.149297\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.24380i | 0.326244i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.0443 | − | 2.24776i | 0.766083 | − | 0.101029i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.8512 | − | 10.0324i | −0.755878 | − | 0.450015i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.4917 | 0.648739 | 0.324369 | − | 0.945930i | \(-0.394848\pi\) | ||||
0.324369 | + | 0.945930i | \(0.394848\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.99007 | + | 2.62163i | 0.133586 | + | 0.117126i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 44.1442 | 1.96829 | 0.984145 | − | 0.177363i | \(-0.0567568\pi\) | ||||
0.984145 | + | 0.177363i | \(0.0567568\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.12564 | −0.361586 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.3761 | − | 9.09760i | −0.460820 | − | 0.404038i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.8389 | 1.23394 | 0.616968 | − | 0.786988i | \(-0.288361\pi\) | ||||
0.616968 | + | 0.786988i | \(0.288361\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.6959 | − | 16.4889i | −1.22519 | − | 0.729424i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.941535 | + | 0.628662i | 0.0415698 | + | 0.0277561i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.21987i | 0.141884i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.1710i | 1.94264i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.43890 | + | 1.26160i | 0.0631606 | + | 0.0553780i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.5640 | 0.681873 | 0.340936 | − | 0.940086i | \(-0.389256\pi\) | ||||
0.340936 | + | 0.940086i | \(0.389256\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.3413i | 1.76400i | 0.471246 | + | 0.882002i | \(0.343804\pi\) | ||||
−0.471246 | + | 0.882002i | \(0.656196\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.35857 | + | 1.41524i | −0.190223 | + | 0.0617660i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 35.7422i | 1.55695i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.13619 | −0.353748 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.26415 | + | 39.9170i | 0.228445 | + | 1.73225i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.50815i | − | 0.108640i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.352062i | 0.0152209i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.5341 | + | 18.8577i | −0.713498 | + | 0.813770i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −35.2649 | + | 19.1192i | −1.51897 | + | 0.823523i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.24259 | 0.354377 | 0.177188 | − | 0.984177i | \(-0.443300\pi\) | ||||
0.177188 | + | 0.984177i | \(0.443300\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.1778 | + | 15.0298i | −0.565515 | + | 0.644990i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.8035 | 0.591278 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.2243 | 0.565430 | 0.282715 | − | 0.959204i | \(-0.408765\pi\) | ||||
0.282715 | + | 0.959204i | \(0.408765\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.96924 | + | 0.523454i | −0.169403 | + | 0.0223405i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.242786 | 0.0103430 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.15146 | + | 10.3324i | −0.261587 | + | 0.439380i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.1359 | − | 11.5173i | −0.557590 | − | 0.488884i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.39173i | 0.186083i | 0.995662 | + | 0.0930417i | \(0.0296590\pi\) | ||||
−0.995662 | + | 0.0930417i | \(0.970341\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.2268i | 0.559434i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 42.5378 | − | 48.5159i | 1.79595 | − | 2.04834i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.30197 | −0.223451 | −0.111726 | − | 0.993739i | \(-0.535638\pi\) | ||||
−0.111726 | + | 0.993739i | \(0.535638\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 2.52753i | − | 0.106334i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.46038 | + | 22.9186i | −0.271310 | + | 0.962492i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.1380i | 0.676541i | 0.941049 | + | 0.338271i | \(0.109842\pi\) | ||||
−0.941049 | + | 0.338271i | \(0.890158\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.4724 | −0.773044 | −0.386522 | − | 0.922280i | \(-0.626324\pi\) | ||||
−0.386522 | + | 0.922280i | \(0.626324\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.4327 | + | 14.1800i | −0.519385 | + | 0.592378i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.57998i | 0.232701i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.2609i | 0.676950i | 0.940975 | + | 0.338475i | \(0.109911\pi\) | ||||
−0.940975 | + | 0.338475i | \(0.890089\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.24897 | − | 6.35576i | −0.301257 | − | 0.264136i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.7775 | + | 24.8214i | −0.613074 | + | 1.02976i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 48.0159 | 1.98862 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.67238 | − | 0.879936i | 0.275869 | − | 0.0363809i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −43.2616 | −1.78560 | −0.892798 | − | 0.450456i | \(-0.851261\pi\) | ||||
−0.892798 | + | 0.450456i | \(0.851261\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.19795 | 0.0493606 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.8594 | + | 29.4936i | −1.06372 | + | 1.21321i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.6653 | 0.766490 | 0.383245 | − | 0.923647i | \(-0.374806\pi\) | ||||
0.383245 | + | 0.923647i | \(0.374806\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.79829 | + | 14.7783i | −0.360695 | + | 0.605849i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.127505 | − | 0.145424i | 0.00521844 | − | 0.00595181i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.16911i | 0.0886273i | 0.999018 | + | 0.0443136i | \(0.0141101\pi\) | ||||
−0.999018 | + | 0.0443136i | \(0.985890\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 22.6531i | − | 0.924040i | −0.886870 | − | 0.462020i | \(-0.847125\pi\) | ||
0.886870 | − | 0.462020i | \(-0.152875\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.69309 | − | 43.1695i | −0.231841 | − | 1.75800i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −21.8400 | −0.887922 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 38.7693i | − | 1.57360i | −0.617210 | − | 0.786798i | \(-0.711737\pi\) | ||
0.617210 | − | 0.786798i | \(-0.288263\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.57703 | + | 4.85685i | 0.0639045 | + | 0.196810i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.2918i | 0.699549i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.8640 | −1.28697 | −0.643486 | − | 0.765458i | \(-0.722513\pi\) | ||||
−0.643486 | + | 0.765458i | \(0.722513\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.45606 | − | 1.27664i | −0.0587140 | − | 0.0514793i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 11.0328i | − | 0.444164i | −0.975028 | − | 0.222082i | \(-0.928715\pi\) | ||
0.975028 | − | 0.222082i | \(-0.0712853\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 22.0902i | − | 0.887881i | −0.896056 | − | 0.443941i | \(-0.853580\pi\) | ||
0.896056 | − | 0.443941i | \(-0.146420\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 24.1133 | + | 16.1004i | 0.967635 | + | 0.646089i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.02412 | + | 10.1185i | −0.241351 | + | 0.405391i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.62608 | − | 1.42572i | −0.0649394 | − | 0.0569376i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −65.5674 | −2.61434 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.3052 | −0.410244 | −0.205122 | − | 0.978736i | \(-0.565759\pi\) | ||||
−0.205122 | + | 0.978736i | \(0.565759\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −28.5008 | − | 24.9890i | −1.13281 | − | 0.993223i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.2059 | −0.524059 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.8053 | + | 7.48466i | −0.546985 | + | 0.296553i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22.0465 | − | 2.90743i | 0.872144 | − | 0.115016i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 49.4982i | − | 1.95506i | −0.210790 | − | 0.977531i | \(-0.567604\pi\) | ||
0.210790 | − | 0.977531i | \(-0.432396\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.6429i | 0.459150i | 0.973291 | + | 0.229575i | \(0.0737336\pi\) | ||||
−0.973291 | + | 0.229575i | \(0.926266\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.67856 | + | 6.73241i | 0.302343 | + | 0.265088i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.0790 | 0.710757 | 0.355379 | − | 0.934722i | \(-0.384352\pi\) | ||||
0.355379 | + | 0.934722i | \(0.384352\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 76.9099i | − | 3.01898i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.78135 | + | 23.9646i | 0.304975 | + | 0.939246i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 30.6974i | − | 1.20128i | −0.799518 | − | 0.600642i | \(-0.794912\pi\) | ||
0.799518 | − | 0.600642i | \(-0.205088\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.2780 | −0.401594 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 36.2347 | − | 4.77854i | 1.41365 | − | 0.186429i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 0.244430i | − | 0.00952164i | −0.999989 | − | 0.00476082i | \(-0.998485\pi\) | ||
0.999989 | − | 0.00476082i | \(-0.00151542\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 24.0272i | − | 0.934550i | −0.884112 | − | 0.467275i | \(-0.845236\pi\) | ||
0.884112 | − | 0.467275i | \(-0.154764\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.6524 | − | 18.9927i | 0.646726 | − | 0.737615i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.495314 | + | 0.294887i | 0.0192074 | + | 0.0114352i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.21790 | 0.240758 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.7563 | + | 28.2355i | −0.957134 | + | 1.09165i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.64772 | 0.295237 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.2656 | −0.395712 | −0.197856 | − | 0.980231i | \(-0.563398\pi\) | ||||
−0.197856 | + | 0.980231i | \(0.563398\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.88539 | − | 4.32140i | 0.111059 | − | 0.166331i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.72154 | −0.181463 | −0.0907317 | − | 0.995875i | \(-0.528921\pi\) | ||||
−0.0907317 | + | 0.995875i | \(0.528921\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.2245 | + | 12.6361i | 0.814523 | + | 0.484930i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.56422 | − | 5.75538i | −0.251541 | − | 0.220547i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.9227i | 1.33628i | 0.744036 | + | 0.668139i | \(0.232909\pi\) | ||||
−0.744036 | + | 0.668139i | \(0.767091\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.43330i | 0.207596i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.5640 | + | 16.6108i | −0.555652 | + | 0.633741i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.7969 | 0.716106 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 42.9041i | − | 1.63215i | −0.577948 | − | 0.816074i | \(-0.696146\pi\) | ||
0.577948 | − | 0.816074i | \(-0.303854\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.9587 | − | 41.7900i | 0.682194 | − | 1.58747i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.2976i | 0.618204i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.26785 | −0.275289 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −29.8362 | + | 34.0293i | −1.12851 | + | 1.28711i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 14.1880i | − | 0.535874i | −0.963436 | − | 0.267937i | \(-0.913658\pi\) | ||
0.963436 | − | 0.267937i | \(-0.0863419\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.19758i | 0.0828834i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.0384 | + | 8.80146i | 0.378067 | + | 0.331482i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.9977 | + | 18.4725i | −0.413610 | + | 0.694730i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 43.7048 | 1.64137 | 0.820684 | − | 0.571382i | \(-0.193593\pi\) | ||||
0.820684 | + | 0.571382i | \(0.193593\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.78272 | − | 13.5180i | −0.0668572 | − | 0.506964i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.6803 | 1.14898 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.8560 | −0.480786 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.19363 | − | 2.50191i | 0.0819225 | − | 0.0934355i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.64243 | −0.359602 | −0.179801 | − | 0.983703i | \(-0.557545\pi\) | ||||
−0.179801 | + | 0.983703i | \(0.557545\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.31993 | + | 4.35794i | 0.272608 | + | 0.162298i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.1569 | − | 13.8654i | 0.452119 | − | 0.515658i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1.11432i | − | 0.0413849i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 47.0202i | − | 1.74388i | −0.489611 | − | 0.871941i | \(-0.662861\pi\) | ||
0.489611 | − | 0.871941i | \(-0.337139\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.3490 | − | 24.9379i | −0.383296 | − | 0.923625i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.3271 | 1.41758 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 40.3873i | − | 1.49174i | −0.666093 | − | 0.745869i | \(-0.732035\pi\) | ||
0.666093 | − | 0.745869i | \(-0.267965\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.68178 | + | 11.8240i | −0.0989188 | + | 0.436137i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 83.1767i | 3.06385i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.5093 | 0.460160 | 0.230080 | − | 0.973172i | \(-0.426101\pi\) | ||||
0.230080 | + | 0.973172i | \(0.426101\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.636566 | − | 0.558129i | −0.0233848 | − | 0.0205034i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.6376i | 1.38079i | 0.723433 | + | 0.690395i | \(0.242563\pi\) | ||||
−0.723433 | + | 0.690395i | \(0.757437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 9.85697i | − | 0.361131i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.28258 | − | 32.4739i | −0.156691 | − | 1.18816i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.800363 | + | 0.476499i | 0.0292446 | + | 0.0174109i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.45321 | −0.0530282 | −0.0265141 | − | 0.999648i | \(-0.508441\pi\) | ||||
−0.0265141 | + | 0.999648i | \(0.508441\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.4676 | − | 14.4384i | −0.600111 | − | 0.526166i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.96893 | −0.217231 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.1113 | 0.403848 | 0.201924 | − | 0.979401i | \(-0.435281\pi\) | ||||
0.201924 | + | 0.979401i | \(0.435281\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −41.6449 | − | 36.5135i | −1.51162 | − | 1.32536i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.4744 | −0.850946 | −0.425473 | − | 0.904971i | \(-0.639892\pi\) | ||||
−0.425473 | + | 0.904971i | \(0.639892\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.6824 | − | 31.3804i | 0.676349 | − | 1.13605i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.54978 | − | 19.3345i | −0.0921875 | − | 0.699039i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 30.1081i | − | 1.08714i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.1458i | 0.474051i | 0.971503 | + | 0.237026i | \(0.0761725\pi\) | ||||
−0.971503 | + | 0.237026i | \(0.923827\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.44699 | + | 8.28294i | 0.340225 | + | 0.298303i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.2816 | 1.23302 | 0.616512 | − | 0.787346i | \(-0.288545\pi\) | ||||
0.616512 | + | 0.787346i | \(0.288545\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 5.49827i | − | 0.197504i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −43.9619 | + | 14.2745i | −1.57713 | + | 0.512096i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.243592i | 0.00872759i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42.4779 | −1.51998 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.81544 | − | 3.21526i | −0.172090 | − | 0.114904i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 7.94202i | − | 0.283463i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.1687i | 0.611996i | 0.952032 | + | 0.305998i | \(0.0989901\pi\) | ||||
−0.952032 | + | 0.305998i | \(0.901010\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.5965 | − | 25.7721i | 0.804456 | − | 0.917511i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.74599 | − | 3.42089i | −0.204304 | − | 0.121633i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.99387 | 0.106316 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.56759 | − | 10.9122i | 0.339328 | − | 0.387015i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43.9928 | 1.55830 | 0.779152 | − | 0.626834i | \(-0.215650\pi\) | ||||
0.779152 | + | 0.626834i | \(0.215650\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 50.1061 | 1.77263 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.74581 | − | 13.2381i | −0.0616853 | − | 0.467747i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −69.8150 | −2.46372 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.6853 | + | 7.55224i | 0.447098 | + | 0.266182i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.0226 | − | 26.3233i | −1.05685 | − | 0.926623i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.6874i | 0.973436i | 0.873559 | + | 0.486718i | \(0.161806\pi\) | ||||
−0.873559 | + | 0.486718i | \(0.838194\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 6.48782i | − | 0.227818i | −0.993491 | − | 0.113909i | \(-0.963663\pi\) | ||
0.993491 | − | 0.113909i | \(-0.0363372\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.8155 | − | 23.7408i | 0.730031 | − | 0.832627i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.4764 | 0.647199 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.28459i | − | 0.0449420i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.03034 | − | 16.3597i | 0.245660 | − | 0.571653i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.97361i | 0.103780i | 0.998653 | + | 0.0518899i | \(0.0165245\pi\) | ||||
−0.998653 | + | 0.0518899i | \(0.983476\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.0592 | 0.734078 | 0.367039 | − | 0.930206i | \(-0.380372\pi\) | ||||
0.367039 | + | 0.930206i | \(0.380372\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.54366 | + | 7.46328i | −0.227821 | + | 0.259838i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 8.53762i | − | 0.296882i | −0.988921 | − | 0.148441i | \(-0.952574\pi\) | ||
0.988921 | − | 0.148441i | \(-0.0474255\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 38.7564i | − | 1.34607i | −0.739612 | − | 0.673033i | \(-0.764991\pi\) | ||
0.739612 | − | 0.673033i | \(-0.235009\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.7907 | + | 22.6128i | 0.894668 | + | 0.784428i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.6882 | + | 40.0033i | 0.751452 | + | 1.38603i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.29590 | −0.0794529 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.7602 | − | 15.8647i | −0.821274 | − | 0.548364i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.5028 | −0.880455 | −0.440228 | − | 0.897886i | \(-0.645102\pi\) | ||||
−0.440228 | + | 0.897886i | \(0.645102\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.7583 | 0.957182 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.0618758 | − | 0.0705715i | 0.00213111 | − | 0.00243061i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.96723 | 0.274081 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29.5594 | + | 49.6501i | −1.01567 | + | 1.70600i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.13839 | + | 3.57944i | −0.107709 | + | 0.122846i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 56.2815i | 1.92931i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 33.9572i | − | 1.16267i | −0.813664 | − | 0.581336i | \(-0.802530\pi\) | ||
0.813664 | − | 0.581336i | \(-0.197470\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.648021 | + | 0.0854595i | −0.0221619 | + | 0.00292265i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.7208 | −0.537012 | −0.268506 | − | 0.963278i | \(-0.586530\pi\) | ||||
−0.268506 | + | 0.963278i | \(0.586530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.3593i | 0.421693i | 0.977519 | + | 0.210846i | \(0.0676220\pi\) | ||||
−0.977519 | + | 0.210846i | \(0.932378\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.87298 | + | 1.58227i | −0.166071 | + | 0.0539235i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 31.4856i | − | 1.07178i | −0.844287 | − | 0.535892i | \(-0.819976\pi\) | ||
0.844287 | − | 0.535892i | \(-0.180024\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.10485 | −0.0375659 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −32.8949 | − | 28.8416i | −1.11717 | − | 0.979512i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.0457i | 0.883541i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.5614i | 1.10330i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −27.7682 | + | 3.66200i | −0.939811 | + | 0.123940i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.35345 | − | 2.27336i | 0.0457551 | − | 0.0768536i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.74226 | −0.193902 | −0.0969511 | − | 0.995289i | \(-0.530909\pi\) | ||||
−0.0969511 | + | 0.995289i | \(0.530909\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.81382 | − | 5.09745i | −0.196095 | − | 0.171933i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.8840 | 0.568835 | 0.284417 | − | 0.958701i | \(-0.408200\pi\) | ||||
0.284417 | + | 0.958701i | \(0.408200\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.1875 | −0.982236 | −0.491118 | − | 0.871093i | \(-0.663412\pi\) | ||||
−0.491118 | + | 0.871093i | \(0.663412\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −17.4787 | − | 15.3250i | −0.587539 | − | 0.515143i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −50.3734 | −1.69137 | −0.845687 | − | 0.533680i | \(-0.820809\pi\) | ||||
−0.845687 | + | 0.533680i | \(0.820809\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.8735 | + | 30.0217i | −0.599459 | + | 1.00690i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.3708 | + | 49.8123i | 0.447938 | + | 1.66877i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1.67938i | − | 0.0561982i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 14.4797i | − | 0.484004i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.3029 | − | 14.2940i | −0.544337 | − | 0.477264i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.12685 | −0.204342 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 54.4676i | − | 1.81458i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.6978 | − | 8.34412i | 0.855168 | − | 0.277675i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 11.5405i | − | 0.383620i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.7202 | 1.61773 | 0.808864 | − | 0.587996i | \(-0.200083\pi\) | ||||
0.808864 | + | 0.587996i | \(0.200083\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.18717 | − | 24.1677i | −0.105712 | − | 0.801591i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.0878283i | 0.00290988i | 0.999999 | + | 0.00145494i | \(0.000463122\pi\) | ||||
−0.999999 | + | 0.00145494i | \(0.999537\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 62.5690i | 2.07073i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.52388 | − | 1.73803i | 0.0503778 | − | 0.0574576i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.9108 | + | 23.3656i | −0.459374 | + | 0.771599i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −53.5379 | −1.76605 | −0.883026 | − | 0.469325i | \(-0.844497\pi\) | ||||
−0.883026 | + | 0.469325i | \(0.844497\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.87875 | − | 4.42385i | 0.127809 | − | 0.145771i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.6290 | −0.547349 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.0863 | 0.331637 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.57670 | + | 1.26295i | −0.314540 | + | 0.0414808i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.34086 | 0.175228 | 0.0876140 | − | 0.996155i | \(-0.472076\pi\) | ||||
0.0876140 | + | 0.996155i | \(0.472076\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.34077 | − | 0.726911i | 0.0439419 | − | 0.0238235i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.617065 | − | 0.541031i | −0.0202018 | − | 0.0177126i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 37.2526i | 1.21829i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.5412i | 1.12841i | 0.825634 | + | 0.564206i | \(0.190818\pi\) | ||||
−0.825634 | + | 0.564206i | \(0.809182\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.2928 | − | 16.3014i | 0.466427 | − | 0.531976i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.7648 | −0.383522 | −0.191761 | − | 0.981442i | \(-0.561420\pi\) | ||||
−0.191761 | + | 0.981442i | \(0.561420\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.23855i | 0.203155i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.91885 | − | 12.4084i | −0.192540 | − | 0.403644i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 9.67044i | − | 0.314247i | −0.987579 | − | 0.157124i | \(-0.949778\pi\) | ||
0.987579 | − | 0.157124i | \(-0.0502221\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.3307 | −0.887192 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −34.7087 | + | 39.5865i | −1.12551 | + | 1.28368i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.9312i | 0.483667i | 0.970318 | + | 0.241834i | \(0.0777489\pi\) | ||||
−0.970318 | + | 0.241834i | \(0.922251\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 10.8880i | − | 0.352327i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.31651 | + | 7.29175i | 0.268834 | + | 0.235709i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.3518 | + | 7.35372i | 0.398862 | + | 0.237464i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.769012 | 0.0248068 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.04712 | + | 0.138091i | −0.0337429 | + | 0.00444993i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.56607 | 0.179178 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 60.0002 | 1.92948 | 0.964738 | − | 0.263211i | \(-0.0847815\pi\) | ||||
0.964738 | + | 0.263211i | \(0.0847815\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.61728 | + | 1.84457i | −0.0519546 | + | 0.0592561i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.8832 | −0.477623 | −0.238812 | − | 0.971066i | \(-0.576758\pi\) | ||||
−0.238812 | + | 0.971066i | \(0.576758\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 37.0504 | + | 22.0581i | 1.18778 | + | 0.707150i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.56167 | + | 2.92167i | −0.0820390 | + | 0.0935684i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 4.39064i | − | 0.140469i | −0.997531 | − | 0.0702345i | \(-0.977625\pi\) | ||
0.997531 | − | 0.0702345i | \(-0.0223748\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.5065i | 0.815192i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.41424 | + | 41.0551i | 0.172863 | + | 1.31079i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.2167 | 1.12324 | 0.561620 | − | 0.827396i | \(-0.310178\pi\) | ||||
0.561620 | + | 0.827396i | \(0.310178\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 22.6465i | − | 0.721576i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 33.5954 | − | 10.9085i | 1.06935 | − | 0.347221i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 32.8991i | − | 1.04613i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.1235 | −1.14750 | −0.573750 | − | 0.819030i | \(-0.694512\pi\) | ||||
−0.573750 | + | 0.819030i | \(0.694512\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.8716 | − | 22.6837i | −0.821011 | − | 0.719847i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.111663i | 0.00353995i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 36.1961i | − | 1.14634i | −0.819436 | − | 0.573170i | \(-0.805713\pi\) | ||
0.819436 | − | 0.573170i | \(-0.194287\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 29.1030 | − | 43.5871i | 0.920779 | − | 1.37903i |
(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 | 1680.2.f.l.881.3 | 16 | ||
3.2 | odd | 2 | 1680.2.f.k.881.13 | 16 | |||
4.3 | odd | 2 | 840.2.f.b.41.14 | yes | 16 | ||
7.6 | odd | 2 | 1680.2.f.k.881.14 | 16 | |||
12.11 | even | 2 | 840.2.f.a.41.4 | yes | 16 | ||
21.20 | even | 2 | inner | 1680.2.f.l.881.4 | 16 | ||
28.27 | even | 2 | 840.2.f.a.41.3 | ✓ | 16 | ||
84.83 | odd | 2 | 840.2.f.b.41.13 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.f.a.41.3 | ✓ | 16 | 28.27 | even | 2 | ||
840.2.f.a.41.4 | yes | 16 | 12.11 | even | 2 | ||
840.2.f.b.41.13 | yes | 16 | 84.83 | odd | 2 | ||
840.2.f.b.41.14 | yes | 16 | 4.3 | odd | 2 | ||
1680.2.f.k.881.13 | 16 | 3.2 | odd | 2 | |||
1680.2.f.k.881.14 | 16 | 7.6 | odd | 2 | |||
1680.2.f.l.881.3 | 16 | 1.1 | even | 1 | trivial | ||
1680.2.f.l.881.4 | 16 | 21.20 | even | 2 | inner |