Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1791,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("2240.1791");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.k (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: | \(17.8864900528\) |
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: | \( x^{16} - 4 x^{15} - 6 x^{14} + 68 x^{13} - 126 x^{12} - 148 x^{11} + 1006 x^{10} - 1516 x^{9} + \cdots + 5956 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | no (minimal twist has level 1120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1791.4 | ||
Root | \(1.40610 + 1.29043i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1791 |
Dual form | 2240.2.k.g.1791.3 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −2.58086 | −1.49006 | −0.745030 | − | 0.667032i | \(-0.767565\pi\) | ||||
−0.745030 | + | 0.667032i | \(0.767565\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.319247 | − | 2.62642i | 0.120664 | − | 0.992693i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.66083 | 1.22028 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.0961900i | − | 0.0290024i | −0.999895 | − | 0.0145012i | \(-0.995384\pi\) | ||
0.999895 | − | 0.0145012i | \(-0.00461604\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44063i | 0.676910i | 0.940983 | + | 0.338455i | \(0.109904\pi\) | ||||
−0.940983 | + | 0.338455i | \(0.890096\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.58086i | − | 0.666375i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.17371i | 0.527203i | 0.964632 | + | 0.263601i | \(0.0849103\pi\) | ||||
−0.964632 | + | 0.263601i | \(0.915090\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.11309 | −0.484777 | −0.242389 | − | 0.970179i | \(-0.577931\pi\) | ||||
−0.242389 | + | 0.970179i | \(0.577931\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.823932 | + | 6.77842i | −0.179797 | + | 1.47917i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.75159i | − | 0.573746i | −0.957969 | − | 0.286873i | \(-0.907384\pi\) | ||
0.957969 | − | 0.286873i | \(-0.0926158\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.70550 | −0.328224 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.89769 | −1.28087 | −0.640434 | − | 0.768013i | \(-0.721246\pi\) | ||||
−0.640434 | + | 0.768013i | \(0.721246\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00611 | −0.360308 | −0.180154 | − | 0.983638i | \(-0.557660\pi\) | ||||
−0.180154 | + | 0.983638i | \(0.557660\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.248253i | 0.0432153i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.62642 | + | 0.319247i | 0.443946 | + | 0.0539627i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.95159 | 0.649637 | 0.324819 | − | 0.945776i | \(-0.394697\pi\) | ||||
0.324819 | + | 0.945776i | \(0.394697\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 6.29893i | − | 1.00864i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.44638i | − | 1.00676i | −0.864066 | − | 0.503378i | \(-0.832090\pi\) | ||
0.864066 | − | 0.503378i | \(-0.167910\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.88147i | − | 1.04941i | −0.851283 | − | 0.524707i | \(-0.824175\pi\) | ||
0.851283 | − | 0.524707i | \(-0.175825\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.66083i | 0.545724i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.4808 | 1.82052 | 0.910259 | − | 0.414040i | \(-0.135883\pi\) | ||||
0.910259 | + | 0.414040i | \(0.135883\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.79616 | − | 1.67696i | −0.970880 | − | 0.239565i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 5.61004i | − | 0.785563i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.6314 | 1.87241 | 0.936207 | − | 0.351450i | \(-0.114311\pi\) | ||||
0.936207 | + | 0.351450i | \(0.114311\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0961900 | 0.0129703 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.45360 | 0.722346 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.2454 | −1.46403 | −0.732015 | − | 0.681288i | \(-0.761420\pi\) | ||||
−0.732015 | + | 0.681288i | \(0.761420\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.32907i | 1.06643i | 0.845980 | + | 0.533214i | \(0.179016\pi\) | ||||
−0.845980 | + | 0.533214i | \(0.820984\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.16871 | − | 9.61487i | 0.147244 | − | 1.21136i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.44063 | −0.302723 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 0.286360i | − | 0.0349844i | −0.999847 | − | 0.0174922i | \(-0.994432\pi\) | ||
0.999847 | − | 0.0174922i | \(-0.00556823\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.10146i | 0.854915i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.7829i | 1.51705i | 0.651641 | + | 0.758527i | \(0.274081\pi\) | ||||
−0.651641 | + | 0.758527i | \(0.725919\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.38647i | 0.513398i | 0.966491 | + | 0.256699i | \(0.0826349\pi\) | ||||
−0.966491 | + | 0.256699i | \(0.917365\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.58086 | 0.298012 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.252635 | − | 0.0307084i | −0.0287905 | − | 0.00349955i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.94679i | 1.11910i | 0.828796 | + | 0.559551i | \(0.189026\pi\) | ||||
−0.828796 | + | 0.559551i | \(0.810974\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.58082 | −0.731203 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.06774 | −0.995313 | −0.497657 | − | 0.867374i | \(-0.665806\pi\) | ||||
−0.497657 | + | 0.867374i | \(0.665806\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.17371 | −0.235772 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 17.8020 | 1.90857 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.14416i | 0.439281i | 0.975581 | + | 0.219640i | \(0.0704884\pi\) | ||||
−0.975581 | + | 0.219640i | \(0.929512\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.41013 | + | 0.779166i | 0.671964 | + | 0.0816788i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.17749 | 0.536881 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 2.11309i | − | 0.216799i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.3766i | 1.66280i | 0.555678 | + | 0.831398i | \(0.312459\pi\) | ||||
−0.555678 | + | 0.831398i | \(0.687541\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 0.352135i | − | 0.0353909i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.25054i | 0.522449i | 0.965278 | + | 0.261224i | \(0.0841262\pi\) | ||||
−0.965278 | + | 0.261224i | \(0.915874\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.93477 | −0.781836 | −0.390918 | − | 0.920425i | \(-0.627842\pi\) | ||||
−0.390918 | + | 0.920425i | \(0.627842\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.77842 | − | 0.823932i | −0.661506 | − | 0.0804076i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 7.00937i | − | 0.677621i | −0.940855 | − | 0.338811i | \(-0.889975\pi\) | ||
0.940855 | − | 0.338811i | \(-0.110025\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.242259 | 0.0232042 | 0.0116021 | − | 0.999933i | \(-0.496307\pi\) | ||||
0.0116021 | + | 0.999933i | \(0.496307\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.1985 | −0.967998 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.40368 | −0.696479 | −0.348240 | − | 0.937406i | \(-0.613220\pi\) | ||||
−0.348240 | + | 0.937406i | \(0.613220\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.75159 | 0.256587 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.93474i | 0.826017i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.70908 | + | 0.693952i | 0.523350 | + | 0.0636145i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9907 | 0.999159 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.6372i | 1.50013i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.4423i | 1.90269i | 0.308124 | + | 0.951346i | \(0.400299\pi\) | ||||
−0.308124 | + | 0.951346i | \(0.599701\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.7601i | 1.56369i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.2773 | 1.07267 | 0.536337 | − | 0.844004i | \(-0.319808\pi\) | ||||
0.536337 | + | 0.844004i | \(0.319808\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.674600 | + | 5.54987i | −0.0584952 | + | 0.481235i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 1.70550i | − | 0.146786i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.71383 | 0.744473 | 0.372237 | − | 0.928138i | \(-0.378591\pi\) | ||||
0.372237 | + | 0.928138i | \(0.378591\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.4497 | −1.31042 | −0.655212 | − | 0.755445i | \(-0.727421\pi\) | ||||
−0.655212 | + | 0.755445i | \(0.727421\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −32.2113 | −2.71268 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.234765 | 0.0196320 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 6.89769i | − | 0.572822i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.5399 | + | 4.32798i | 1.44667 | + | 0.356966i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.8803 | 1.79250 | 0.896251 | − | 0.443548i | \(-0.146280\pi\) | ||||
0.896251 | + | 0.443548i | \(0.146280\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.0963i | 0.903003i | 0.892270 | + | 0.451501i | \(0.149111\pi\) | ||||
−0.892270 | + | 0.451501i | \(0.850889\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.95758i | 0.643333i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.00611i | − | 0.161135i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.08502i | − | 0.326020i | −0.986624 | − | 0.163010i | \(-0.947880\pi\) | ||
0.986624 | − | 0.163010i | \(-0.0521203\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −35.1806 | −2.79001 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.22683 | − | 0.878438i | −0.569554 | − | 0.0692306i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.4556i | 1.13225i | 0.824318 | + | 0.566127i | \(0.191559\pi\) | ||||
−0.824318 | + | 0.566127i | \(0.808441\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.248253 | −0.0193265 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.04383 | 0.467686 | 0.233843 | − | 0.972274i | \(-0.424870\pi\) | ||||
0.233843 | + | 0.972274i | \(0.424870\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.04331 | 0.541793 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.73567 | −0.591562 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.6150i | 1.26321i | 0.775289 | + | 0.631607i | \(0.217604\pi\) | ||||
−0.775289 | + | 0.631607i | \(0.782396\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.319247 | + | 2.62642i | −0.0241328 | + | 0.198539i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 29.0229 | 2.18149 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.9687i | 1.41779i | 0.705314 | + | 0.708895i | \(0.250806\pi\) | ||||
−0.705314 | + | 0.708895i | \(0.749194\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.25354i | 0.241834i | 0.992663 | + | 0.120917i | \(0.0385834\pi\) | ||||
−0.992663 | + | 0.120917i | \(0.961417\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 21.4962i | − | 1.58904i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.95159i | 0.290527i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.209089 | 0.0152901 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.544477 | + | 4.47936i | −0.0396049 | + | 0.325826i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.18747i | 0.158280i | 0.996864 | + | 0.0791400i | \(0.0252174\pi\) | ||||
−0.996864 | + | 0.0791400i | \(0.974783\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.7569 | −1.13421 | −0.567103 | − | 0.823647i | \(-0.691936\pi\) | ||||
−0.567103 | + | 0.823647i | \(0.691936\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.29893 | 0.451076 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.08761 | −0.504971 | −0.252486 | − | 0.967601i | \(-0.581248\pi\) | ||||
−0.252486 | + | 0.967601i | \(0.581248\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.86744 | 0.274155 | 0.137078 | − | 0.990560i | \(-0.456229\pi\) | ||||
0.137078 | + | 0.990560i | \(0.456229\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.739054i | 0.0521288i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.20207 | + | 18.1162i | −0.154555 | + | 1.27151i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.44638 | 0.450235 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 10.0731i | − | 0.700128i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.203259i | 0.0140597i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.85197i | 0.402866i | 0.979502 | + | 0.201433i | \(0.0645599\pi\) | ||||
−0.979502 | + | 0.201433i | \(0.935440\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 32.9909i | − | 2.26050i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.88147 | 0.469312 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.640446 | + | 5.26889i | −0.0434763 | + | 0.357676i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 11.3209i | − | 0.764993i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.30523 | −0.356869 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.2236 | −1.15338 | −0.576688 | − | 0.816964i | \(-0.695655\pi\) | ||||
−0.576688 | + | 0.816964i | \(0.695655\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.66083 | −0.244055 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.8499 | 0.919252 | 0.459626 | − | 0.888112i | \(-0.347983\pi\) | ||||
0.459626 | + | 0.888112i | \(0.347983\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 19.1389i | − | 1.26473i | −0.774669 | − | 0.632367i | \(-0.782084\pi\) | ||
0.774669 | − | 0.632367i | \(-0.217916\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.652016 | + | 0.0792541i | 0.0428995 | + | 0.00521454i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.67086 | 0.568047 | 0.284023 | − | 0.958817i | \(-0.408331\pi\) | ||||
0.284023 | + | 0.958817i | \(0.408331\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.4808i | 0.814160i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 25.6713i | − | 1.66753i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.0440i | 1.03780i | 0.854834 | + | 0.518901i | \(0.173659\pi\) | ||||
−0.854834 | + | 0.518901i | \(0.826341\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.7228i | 1.20604i | 0.797725 | + | 0.603022i | \(0.206037\pi\) | ||||
−0.797725 | + | 0.603022i | \(0.793963\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.1007 | 1.41776 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.67696 | − | 6.79616i | 0.107137 | − | 0.434191i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 5.15729i | − | 0.328150i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 23.4025 | 1.48308 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.9154 | −1.19393 | −0.596965 | − | 0.802267i | \(-0.703627\pi\) | ||||
−0.596965 | + | 0.802267i | \(0.703627\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.264675 | −0.0166400 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.61004 | 0.351314 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 29.2323i | − | 1.82346i | −0.410787 | − | 0.911732i | \(-0.634746\pi\) | ||
0.410787 | − | 0.911732i | \(-0.365254\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.26154 | − | 10.3785i | 0.0783880 | − | 0.644891i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −25.2512 | −1.56301 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.1498i | 0.810851i | 0.914128 | + | 0.405425i | \(0.132877\pi\) | ||||
−0.914128 | + | 0.405425i | \(0.867123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.6314i | 0.837369i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 10.6955i | − | 0.654554i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.98850i | − | 0.121241i | −0.998161 | − | 0.0606205i | \(-0.980692\pi\) | ||
0.998161 | − | 0.0606205i | \(-0.0193079\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.2835 | −0.746170 | −0.373085 | − | 0.927797i | \(-0.621700\pi\) | ||||
−0.373085 | + | 0.927797i | \(0.621700\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.5436 | − | 2.01092i | −1.00127 | − | 0.121706i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.0961900i | 0.00580048i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.6834 | 1.12258 | 0.561289 | − | 0.827620i | \(-0.310305\pi\) | ||||
0.561289 | + | 0.827620i | \(0.310305\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.34403 | −0.439676 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.47899 | −0.386504 | −0.193252 | − | 0.981149i | \(-0.561903\pi\) | ||||
−0.193252 | + | 0.981149i | \(0.561903\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.57795 | 0.272131 | 0.136065 | − | 0.990700i | \(-0.456554\pi\) | ||||
0.136065 | + | 0.990700i | \(0.456554\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.45360i | 0.323043i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.9309 | − | 2.05799i | −0.999400 | − | 0.121479i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.2750 | 0.722057 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 42.2658i | − | 2.47766i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 2.98667i | − | 0.174483i | −0.996187 | − | 0.0872415i | \(-0.972195\pi\) | ||
0.996187 | − | 0.0872415i | \(-0.0278052\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 11.2454i | − | 0.654734i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.164052i | 0.00951928i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.71562 | 0.388374 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.0736 | − | 2.19689i | −1.04175 | − | 0.126627i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 13.5509i | − | 0.778479i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.32907 | −0.476921 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.3527 | 1.38988 | 0.694940 | − | 0.719068i | \(-0.255431\pi\) | ||||
0.694940 | + | 0.719068i | \(0.255431\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.4785 | 1.16498 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.1000 | 1.59340 | 0.796702 | − | 0.604372i | \(-0.206576\pi\) | ||||
0.796702 | + | 0.604372i | \(0.206576\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.9497i | 1.57981i | 0.613230 | + | 0.789905i | \(0.289870\pi\) | ||||
−0.613230 | + | 0.789905i | \(0.710130\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.61487 | + | 1.16871i | 0.541737 | + | 0.0658493i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.7666 | 1.50336 | 0.751681 | − | 0.659527i | \(-0.229243\pi\) | ||||
0.751681 | + | 0.659527i | \(0.229243\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.663489i | 0.0371483i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.0902i | 1.00970i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.59326i | − | 0.255576i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.44063i | − | 0.135382i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.625237 | −0.0345757 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.98448 | − | 32.7799i | 0.219671 | − | 1.80722i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.54702i | 0.304892i | 0.988312 | + | 0.152446i | \(0.0487149\pi\) | ||||
−0.988312 | + | 0.152446i | \(0.951285\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.4661 | 0.792737 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.286360 | 0.0156455 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.8804 | −0.974007 | −0.487004 | − | 0.873400i | \(-0.661910\pi\) | ||||
−0.487004 | + | 0.873400i | \(0.661910\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.1078 | 1.03780 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.192968i | 0.0104498i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.57405 | + | 17.3142i | −0.354965 | + | 0.934880i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.10146 | −0.382330 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 7.98633i | − | 0.428729i | −0.976754 | − | 0.214364i | \(-0.931232\pi\) | ||
0.976754 | − | 0.214364i | \(-0.0687680\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.19042i | 0.491952i | 0.969276 | + | 0.245976i | \(0.0791084\pi\) | ||||
−0.969276 | + | 0.245976i | \(0.920892\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 4.16250i | − | 0.222178i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 19.6743i | − | 1.04716i | −0.851977 | − | 0.523579i | \(-0.824597\pi\) | ||
0.851977 | − | 0.523579i | \(-0.175403\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.7829 | −0.678447 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.7343 | − | 1.79099i | −0.779823 | − | 0.0947893i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 5.29652i | − | 0.279540i | −0.990184 | − | 0.139770i | \(-0.955364\pi\) | ||
0.990184 | − | 0.139770i | \(-0.0446363\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.5348 | −0.764991 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −28.3656 | −1.48881 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.38647 | −0.229598 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.0652 | 1.15179 | 0.575896 | − | 0.817523i | \(-0.304653\pi\) | ||||
0.575896 | + | 0.817523i | \(0.304653\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 23.5991i | − | 1.22852i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.35178 | − | 35.8017i | 0.225933 | − | 1.85873i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.6025 | 1.22209 | 0.611045 | − | 0.791596i | \(-0.290750\pi\) | ||||
0.611045 | + | 0.791596i | \(0.290750\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.58086i | 0.133275i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 16.8347i | − | 0.867032i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 24.1233i | − | 1.23913i | −0.784945 | − | 0.619565i | \(-0.787309\pi\) | ||
0.784945 | − | 0.619565i | \(-0.212691\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 55.3394i | − | 2.83512i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.3930 | −1.14423 | −0.572114 | − | 0.820174i | \(-0.693877\pi\) | ||||
−0.572114 | + | 0.820174i | \(0.693877\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0307084 | − | 0.252635i | 0.00156505 | − | 0.0128755i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 25.1919i | − | 1.28057i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.8594 | −1.15902 | −0.579509 | − | 0.814966i | \(-0.696756\pi\) | ||||
−0.579509 | + | 0.814966i | \(0.696756\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.98116 | 0.302480 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −31.6860 | −1.59835 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.94679 | −0.500477 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.9051i | 1.90240i | 0.308572 | + | 0.951201i | \(0.400149\pi\) | ||||
−0.308572 | + | 0.951201i | \(0.599851\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.74105 | − | 14.3234i | 0.0871614 | − | 0.717068i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.968706 | −0.0483749 | −0.0241874 | − | 0.999707i | \(-0.507700\pi\) | ||||
−0.0241874 | + | 0.999707i | \(0.507700\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 4.89618i | − | 0.243896i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 6.58082i | − | 0.327004i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.380104i | − | 0.0188410i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.4020i | 1.70107i | 0.525917 | + | 0.850536i | \(0.323722\pi\) | ||||
−0.525917 | + | 0.850536i | \(0.676278\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.4892 | −1.10931 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.59008 | + | 29.5352i | −0.176656 | + | 1.45333i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 9.06774i | − | 0.445118i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 39.8734 | 1.95261 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.4628 | −1.14623 | −0.573115 | − | 0.819475i | \(-0.694265\pi\) | ||||
−0.573115 | + | 0.819475i | \(0.694265\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.6064 | −1.44293 | −0.721465 | − | 0.692451i | \(-0.756531\pi\) | ||||
−0.721465 | + | 0.692451i | \(0.756531\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 45.6902 | 2.22153 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 2.17371i | − | 0.105441i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.8756 | + | 2.65904i | 1.05864 | + | 0.128680i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.605894 | −0.0292528 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 10.2335i | − | 0.492931i | −0.969152 | − | 0.246465i | \(-0.920731\pi\) | ||
0.969152 | − | 0.246465i | \(-0.0792691\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 36.3963i | − | 1.74909i | −0.484942 | − | 0.874547i | \(-0.661159\pi\) | ||
0.484942 | − | 0.874547i | \(-0.338841\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.8020i | 0.853538i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.81437i | 0.278139i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.0302 | −1.14690 | −0.573450 | − | 0.819241i | \(-0.694395\pi\) | ||||
−0.573450 | + | 0.819241i | \(0.694395\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −24.8796 | − | 6.13905i | −1.18474 | − | 0.292336i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.7426i | 0.795466i | 0.917501 | + | 0.397733i | \(0.130203\pi\) | ||||
−0.917501 | + | 0.397733i | \(0.869797\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.14416 | −0.196452 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −56.4699 | −2.67093 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.7762 | −0.555753 | −0.277876 | − | 0.960617i | \(-0.589631\pi\) | ||||
−0.277876 | + | 0.960617i | \(0.589631\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.620078 | −0.0291983 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 28.6379i | − | 1.34553i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.779166 | + | 6.41013i | −0.0365279 | + | 0.300511i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.52642 | −0.258515 | −0.129258 | − | 0.991611i | \(-0.541259\pi\) | ||||
−0.129258 | + | 0.991611i | \(0.541259\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 3.70727i | − | 0.173041i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 19.2213i | − | 0.895227i | −0.894227 | − | 0.447613i | \(-0.852274\pi\) | ||
0.894227 | − | 0.447613i | \(-0.147726\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.2231i | − | 0.753949i | −0.926224 | − | 0.376975i | \(-0.876964\pi\) | ||
0.926224 | − | 0.376975i | \(-0.123036\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.17749i | 0.240100i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.1653 | −1.67353 | −0.836766 | − | 0.547561i | \(-0.815557\pi\) | ||||
−0.836766 | + | 0.547561i | \(0.815557\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.752101 | − | 0.0914197i | −0.0347288 | − | 0.00422137i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.5429i | 0.485789i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.661929 | −0.0304355 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.11309 | 0.0969554 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 49.9021 | 2.28486 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.2579 | 0.971299 | 0.485649 | − | 0.874154i | \(-0.338583\pi\) | ||||
0.485649 | + | 0.874154i | \(0.338583\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.64438i | 0.439746i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18.6514 | + | 2.26712i | 0.848669 | + | 0.103158i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.3766 | −0.743625 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 0.766893i | − | 0.0347513i | −0.999849 | − | 0.0173756i | \(-0.994469\pi\) | ||
0.999849 | − | 0.0173756i | \(-0.00553111\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 37.3080i | − | 1.68712i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.4594i | 1.10384i | 0.833898 | + | 0.551919i | \(0.186104\pi\) | ||||
−0.833898 | + | 0.551919i | \(0.813896\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 14.9936i | − | 0.675277i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.352135 | 0.0158273 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 33.5733 | + | 4.08092i | 1.50597 | + | 0.183054i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.2272i | 1.44269i | 0.692578 | + | 0.721343i | \(0.256475\pi\) | ||||
−0.692578 | + | 0.721343i | \(0.743525\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.5983 | −0.696879 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.28701 | 0.146561 | 0.0732804 | − | 0.997311i | \(-0.476653\pi\) | ||||
0.0732804 | + | 0.997311i | \(0.476653\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.25054 | −0.233646 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.1778 | −0.807304 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 36.0143i | − | 1.59631i | −0.602455 | − | 0.798153i | \(-0.705811\pi\) | ||
0.602455 | − | 0.798153i | \(-0.294189\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.5207 | + | 1.40037i | 0.509647 | + | 0.0619487i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.60389 | 0.159115 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 7.93477i | − | 0.349648i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.20053i | − | 0.0527993i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 42.8809i | − | 1.88226i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 37.6167i | − | 1.64802i | −0.566578 | − | 0.824008i | \(-0.691733\pi\) | ||
0.566578 | − | 0.824008i | \(-0.308267\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.03753 | −0.0453682 | −0.0226841 | − | 0.999743i | \(-0.507221\pi\) | ||||
−0.0226841 | + | 0.999743i | \(0.507221\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.823932 | − | 6.77842i | 0.0359594 | − | 0.295834i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 4.36071i | − | 0.189955i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.4288 | 0.670816 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −41.1676 | −1.78652 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.7333 | 0.681483 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.00937 | 0.303041 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 48.9556i | − | 2.11259i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.161306 | + | 0.653723i | −0.00694796 | + | 0.0281578i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.93689 | −0.298240 | −0.149120 | − | 0.988819i | \(-0.547644\pi\) | ||||
−0.149120 | + | 0.988819i | \(0.547644\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 8.39692i | − | 0.360346i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.242259i | 0.0103772i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.8129i | 1.01817i | 0.860717 | + | 0.509084i | \(0.170016\pi\) | ||||
−0.860717 | + | 0.509084i | \(0.829984\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.4913i | 1.30134i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.5755 | 0.620936 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.1245 | + | 3.17549i | 1.11092 | + | 0.135035i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 10.1985i | − | 0.432902i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.3648 | −1.15949 | −0.579743 | − | 0.814799i | \(-0.696847\pi\) | ||||
−0.579743 | + | 0.814799i | \(0.696847\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.7951 | 0.710359 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.539630 | −0.0227832 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.58823 | 0.319806 | 0.159903 | − | 0.987133i | \(-0.448882\pi\) | ||||
0.159903 | + | 0.987133i | \(0.448882\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 7.40368i | − | 0.311475i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.10091 | + | 17.2840i | −0.0882300 | + | 0.725860i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.93366 | −0.290674 | −0.145337 | − | 0.989382i | \(-0.546427\pi\) | ||||
−0.145337 | + | 0.989382i | \(0.546427\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 4.07049i | − | 0.170345i | −0.996366 | − | 0.0851724i | \(-0.972856\pi\) | ||
0.996366 | − | 0.0851724i | \(-0.0271441\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 5.64556i | − | 0.235846i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.75159i | 0.114749i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 9.41228i | − | 0.391838i | −0.980620 | − | 0.195919i | \(-0.937231\pi\) | ||
0.980620 | − | 0.195919i | \(-0.0627690\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 40.6663 | 1.69003 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.89485 | + | 23.8157i | −0.120099 | + | 0.988041i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.31120i | − | 0.0543045i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.93474 | −0.369406 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.5572 | −1.01358 | −0.506792 | − | 0.862069i | \(-0.669169\pi\) | ||||
−0.506792 | + | 0.862069i | \(0.669169\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.23910 | 0.174669 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.2921 | 0.752437 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 19.0241i | − | 0.781225i | −0.920555 | − | 0.390612i | \(-0.872263\pi\) | ||
0.920555 | − | 0.390612i | \(-0.127737\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.693952 | + | 5.70908i | −0.0284493 | + | 0.234049i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.98131 | −0.408508 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.44908i | 0.181785i | 0.995861 | + | 0.0908923i | \(0.0289719\pi\) | ||||
−0.995861 | + | 0.0908923i | \(0.971028\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 13.5897i | − | 0.554335i | −0.960822 | − | 0.277167i | \(-0.910604\pi\) | ||
0.960822 | − | 0.277167i | \(-0.0893956\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.04831i | − | 0.0426906i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.9907i | 0.446837i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.10701 | 0.0449320 | 0.0224660 | − | 0.999748i | \(-0.492848\pi\) | ||||
0.0224660 | + | 0.999748i | \(0.492848\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.68323 | − | 46.7554i | 0.230296 | − | 1.89462i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.4611i | 1.23233i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.5780 | −1.31581 | −0.657906 | − | 0.753100i | \(-0.728558\pi\) | ||||
−0.657906 | + | 0.753100i | \(0.728558\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −16.6372 | −0.670877 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.6569 | 0.469289 | 0.234644 | − | 0.972081i | \(-0.424607\pi\) | ||||
0.234644 | + | 0.972081i | \(0.424607\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.5426 | 0.463936 | 0.231968 | − | 0.972723i | \(-0.425484\pi\) | ||||
0.231968 | + | 0.972723i | \(0.425484\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.69284i | 0.188317i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.8843 | + | 1.32301i | 0.436071 | + | 0.0530054i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 0.524582i | − | 0.0209498i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.58962i | 0.342490i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 33.7609i | − | 1.34400i | −0.740552 | − | 0.672000i | \(-0.765436\pi\) | ||
0.740552 | − | 0.672000i | \(-0.234564\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 15.1031i | − | 0.600295i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21.4423 | −0.850910 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.09283 | − | 16.5869i | 0.162164 | − | 0.657198i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 46.7961i | 1.85122i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.15841 | −0.243242 | −0.121621 | − | 0.992577i | \(-0.538809\pi\) | ||||
−0.121621 | + | 0.992577i | \(0.538809\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.578014 | 0.0227946 | 0.0113973 | − | 0.999935i | \(-0.496372\pi\) | ||||
0.0113973 | + | 0.999935i | \(0.496372\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.7601 | −0.699303 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.5224 | 0.610249 | 0.305124 | − | 0.952313i | \(-0.401302\pi\) | ||||
0.305124 | + | 0.952313i | \(0.401302\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.08170i | 0.0424604i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.65290 | − | 13.5983i | 0.0647823 | − | 0.532958i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.6566 | 0.769224 | 0.384612 | − | 0.923078i | \(-0.374335\pi\) | ||||
0.384612 | + | 0.923078i | \(0.374335\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.2773i | 0.479714i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.0581i | 0.626487i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.1914i | 1.25400i | 0.779019 | + | 0.627000i | \(0.215717\pi\) | ||||
−0.779019 | + | 0.627000i | \(0.784283\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.9375i | 0.853271i | 0.904424 | + | 0.426636i | \(0.140301\pi\) | ||||
−0.904424 | + | 0.426636i | \(0.859699\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.6921 | 0.531755 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.54987 | − | 0.674600i | −0.215215 | − | 0.0261599i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.9796i | 0.734893i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 44.4516 | 1.71860 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.801174 | 0.0309290 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.9652 | 0.731056 | 0.365528 | − | 0.930800i | \(-0.380889\pi\) | ||||
0.365528 | + | 0.930800i | \(0.380889\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.70550 | 0.0656448 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.5065i | 1.17246i | 0.810144 | + | 0.586231i | \(0.199389\pi\) | ||||
−0.810144 | + | 0.586231i | \(0.800611\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 43.0119 | + | 5.22820i | 1.65065 | + | 0.200640i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −35.7447 | −1.36974 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.6121i | 1.13307i | 0.824036 | + | 0.566537i | \(0.191717\pi\) | ||||
−0.824036 | + | 0.566537i | \(0.808283\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.71383i | 0.332938i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 49.3947i | 1.88453i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 33.2692i | 1.26745i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.2229 | 1.60623 | 0.803117 | − | 0.595821i | \(-0.203173\pi\) | ||||
0.803117 | + | 0.595821i | \(0.203173\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.924855 | − | 0.112418i | −0.0351323 | − | 0.00427042i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 15.4497i | − | 0.586039i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.0126 | 0.530764 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.3782 | −0.846423 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.60356 | −0.287183 | −0.143591 | − | 0.989637i | \(-0.545865\pi\) | ||||
−0.143591 | + | 0.989637i | \(0.545865\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.35008 | −0.314929 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 32.2113i | − | 1.21315i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.7901 | + | 1.67622i | 0.518631 | + | 0.0630408i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.76601 | −0.141435 | −0.0707177 | − | 0.997496i | \(-0.522529\pi\) | ||||
−0.0707177 | + | 0.997496i | \(0.522529\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 36.4135i | 1.36561i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.52000i | 0.206725i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.234765i | 0.00877970i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 41.4074i | − | 1.54639i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.6389 | 0.620526 | 0.310263 | − | 0.950651i | \(-0.399583\pi\) | ||||
0.310263 | + | 0.950651i | \(0.399583\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.53316 | + | 20.8400i | −0.0943396 | + | 0.776124i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 48.3209i | − | 1.79708i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.89769 | 0.256174 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.9344 | −1.48109 | −0.740543 | − | 0.672009i | \(-0.765431\pi\) | ||||
−0.740543 | + | 0.672009i | \(0.765431\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −37.2962 | −1.38134 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.9583 | 0.553254 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 50.4219i | 1.86238i | 0.364539 | + | 0.931188i | \(0.381226\pi\) | ||||
−0.364539 | + | 0.931188i | \(0.618774\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.32798 | + | 17.5399i | −0.159640 | + | 0.646970i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.0275450 | −0.00101463 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 41.8406i | − | 1.53913i | −0.638568 | − | 0.769566i | \(-0.720473\pi\) | ||
0.638568 | − | 0.769566i | \(-0.279527\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.3102i | 0.488963i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.00362i | − | 0.0368192i | −0.999831 | − | 0.0184096i | \(-0.994140\pi\) | ||
0.999831 | − | 0.0184096i | \(-0.00586029\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.8803i | 0.801631i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −33.1954 | −1.21456 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.4095 | − | 2.23772i | −0.672670 | − | 0.0817646i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.62558i | 0.351242i | 0.984458 | + | 0.175621i | \(0.0561934\pi\) | ||||
−0.984458 | + | 0.175621i | \(0.943807\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 48.8180 | 1.77903 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.0963 | −0.403835 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 50.2015 | 1.82460 | 0.912302 | − | 0.409519i | \(-0.134303\pi\) | ||||
0.912302 | + | 0.409519i | \(0.134303\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.683090 | 0.0247946 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 7.43989i | − | 0.269696i | −0.990866 | − | 0.134848i | \(-0.956945\pi\) | ||
0.990866 | − | 0.134848i | \(-0.0430546\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.0773406 | − | 0.636274i | 0.00279992 | − | 0.0230347i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.95758 | −0.287707 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 27.4460i | − | 0.991016i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.4969i | 1.49642i | 0.663463 | + | 0.748209i | \(0.269086\pi\) | ||||
−0.663463 | + | 0.748209i | \(0.730914\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 75.4445i | 2.71707i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 32.2305i | − | 1.15925i | −0.814884 | − | 0.579624i | \(-0.803199\pi\) | ||
0.814884 | − | 0.579624i | \(-0.196801\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.00611 | 0.0720617 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.25584 | + | 26.7855i | −0.116803 | + | 0.960925i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.6218i | 0.488052i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.22959 | 0.0439982 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.7640 | 0.420412 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.08502 | 0.145801 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.5361 | −1.33802 | −0.669008 | − | 0.743255i | \(-0.733281\pi\) | ||||
−0.669008 | + | 0.743255i | \(0.733281\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 33.9377i | − | 1.20822i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.36361 | + | 19.4452i | −0.0840401 | + | 0.691391i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.3282 | −0.721876 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 35.1806i | − | 1.24773i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 33.5055i | − | 1.18682i | −0.804899 | − | 0.593412i | \(-0.797780\pi\) | ||
0.804899 | − | 0.593412i | \(-0.202220\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.1297i | 0.959781i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.1711i | 0.536043i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.421935 | 0.0148898 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.878438 | − | 7.22683i | 0.0309609 | − | 0.254712i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.13204i | 0.180656i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −44.4512 | −1.56282 | −0.781411 | − | 0.624017i | \(-0.785500\pi\) | ||||
−0.781411 | + | 0.624017i | \(0.785500\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.5900 | 0.933701 | 0.466850 | − | 0.884336i | \(-0.345389\pi\) | ||||
0.466850 | + | 0.884336i | \(0.345389\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 31.7020 | 1.11184 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.4556 | −0.506359 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.5412i | 0.508732i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 23.4664 | + | 2.85239i | 0.819981 | + | 0.0996706i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.00415 | −0.104845 | −0.0524227 | − | 0.998625i | \(-0.516694\pi\) | ||||
−0.0524227 | + | 0.998625i | \(0.516694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.4150i | 0.711624i | 0.934558 | + | 0.355812i | \(0.115796\pi\) | ||||
−0.934558 | + | 0.355812i | \(0.884204\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 0.248253i | − | 0.00864305i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 15.8666i | − | 0.551735i | −0.961196 | − | 0.275868i | \(-0.911035\pi\) | ||
0.961196 | − | 0.275868i | \(-0.0889652\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.7081i | 0.615028i | 0.951543 | + | 0.307514i | \(0.0994972\pi\) | ||||
−0.951543 | + | 0.307514i | \(0.900503\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −48.2193 | −1.67271 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.64522 | − | 14.7729i | 0.126299 | − | 0.511851i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.04383i | 0.209155i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.42143 | 0.118262 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.0811 | 1.59090 | 0.795449 | − | 0.606021i | \(-0.207235\pi\) | ||||
0.795449 | + | 0.606021i | \(0.207235\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.5781 | 0.640624 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.7213 | 0.575914 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.04331i | 0.242297i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.50877 | − | 28.8663i | 0.120563 | − | 0.991858i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.8150 | −0.405491 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 10.8732i | − | 0.372727i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 5.53228i | − | 0.189422i | −0.995505 | − | 0.0947109i | \(-0.969807\pi\) | ||
0.995505 | − | 0.0947109i | \(-0.0301927\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 7.73567i | − | 0.264554i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 42.8657i | − | 1.46426i | −0.681163 | − | 0.732132i | \(-0.738525\pi\) | ||
0.681163 | − | 0.732132i | \(-0.261475\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.4601 | 0.732209 | 0.366105 | − | 0.930574i | \(-0.380691\pi\) | ||||
0.366105 | + | 0.930574i | \(0.380691\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 43.6963 | + | 5.31138i | 1.48916 | + | 0.181011i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.8881i | 0.472755i | 0.971661 | + | 0.236377i | \(0.0759602\pi\) | ||||
−0.971661 | + | 0.236377i | \(0.924040\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.6150 | −0.564926 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −31.6800 | −1.07591 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.956782 | 0.0324566 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.698899 | 0.0236813 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 59.9520i | 2.02907i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.62642 | − | 0.319247i | −0.0887892 | − | 0.0107925i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.3202 | 1.26021 | 0.630106 | − | 0.776509i | \(-0.283011\pi\) | ||||
0.630106 | + | 0.776509i | \(0.283011\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.70816i | 0.259990i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 18.1185i | − | 0.610427i | −0.952284 | − | 0.305214i | \(-0.901272\pi\) | ||
0.952284 | − | 0.305214i | \(-0.0987279\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 23.0468i | − | 0.775586i | −0.921746 | − | 0.387793i | \(-0.873237\pi\) | ||
0.921746 | − | 0.387793i | \(-0.126763\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 29.0229i | 0.975593i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.9214 | 0.366703 | 0.183352 | − | 0.983047i | \(-0.441305\pi\) | ||||
0.183352 | + | 0.983047i | \(0.441305\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 56.3164 | + | 6.84539i | 1.88879 | + | 0.229587i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.633010i | 0.0212066i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.3732 | −0.882545 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.9687 | −0.634055 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.3321 | −0.578701 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.8375 | 0.461508 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.6307i | 0.987141i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 46.6455 | + | 5.66986i | 1.55226 | + | 0.188681i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.25354 | −0.108151 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.8749i | 1.45684i | 0.685129 | + | 0.728421i | \(0.259746\pi\) | ||||
−0.685129 | + | 0.728421i | \(0.740254\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.2213i | 0.637531i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 10.5105i | − | 0.348228i | −0.984725 | − | 0.174114i | \(-0.944294\pi\) | ||
0.984725 | − | 0.174114i | \(-0.0557062\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.872226i | 0.0288665i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 21.4962 | 0.710641 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.91950 | − | 32.2454i | 0.129433 | − | 1.06484i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 16.6088i | − | 0.547873i | −0.961748 | − | 0.273936i | \(-0.911674\pi\) | ||
0.961748 | − | 0.273936i | \(-0.0883258\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −62.8507 | −2.07100 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −31.1984 | −1.02691 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.95159 | −0.129927 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −29.0478 | −0.954056 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.56827i | 0.149880i | 0.997188 | + | 0.0749401i | \(0.0238766\pi\) | ||||
−0.997188 | + | 0.0749401i | \(0.976123\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.3609 | + | 3.54357i | 0.470660 | + | 0.116136i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −72.5221 | −2.37427 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.209089i | 0.00683796i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.8979i | 1.49942i | 0.661767 | + | 0.749710i | \(0.269807\pi\) | ||||
−0.661767 | + | 0.749710i | \(0.730193\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 72.1341i | − | 2.35401i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 3.53734i | − | 0.115314i | −0.998336 | − | 0.0576569i | \(-0.981637\pi\) | ||
0.998336 | − | 0.0576569i | \(-0.0183629\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.7378 | −0.577622 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.47936 | − | 0.544477i | −0.145714 | − | 0.0177118i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 25.1805i | − | 0.818255i | −0.912477 | − | 0.409127i | \(-0.865833\pi\) | ||
0.912477 | − | 0.409127i | \(-0.134167\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.7058 | −0.347524 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −69.0808 | −2.24010 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 55.0349 | 1.78276 | 0.891378 | − | 0.453260i | \(-0.149739\pi\) | ||||
0.891378 | + | 0.453260i | \(0.149739\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.18747 | −0.0707849 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 1.71237i | − | 0.0553531i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.78187 | − | 22.8862i | 0.0898313 | − | 0.739033i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.9755 | −0.870178 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 25.6601i | − | 0.826885i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 15.7569i | − | 0.507232i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.8454i | 0.413081i | 0.978438 | + | 0.206540i | \(0.0662205\pi\) | ||||
−0.978438 | + | 0.206540i | \(0.933780\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.8545i | 0.380823i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.14824 | −0.0689404 | −0.0344702 | − | 0.999406i | \(-0.510974\pi\) | ||||
−0.0344702 | + | 0.999406i | \(0.510974\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.93227 | + | 40.5773i | −0.158121 | + | 1.30085i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.29893i | 0.201727i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.0936 | −0.642850 | −0.321425 | − | 0.946935i | \(-0.604162\pi\) | ||||
−0.321425 | + | 0.946935i | \(0.604162\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.398627 | 0.0127402 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.886869 | 0.0283156 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −47.7437 | −1.52279 | −0.761393 | − | 0.648291i | \(-0.775484\pi\) | ||||
−0.761393 | + | 0.648291i | \(0.775484\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 7.08761i | − | 0.225830i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.2834 | + | 84.6003i | −0.327323 | + | 2.69286i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.9350 | −0.602097 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 15.4637i | − | 0.491219i | −0.969369 | − | 0.245610i | \(-0.921012\pi\) | ||
0.969369 | − | 0.245610i | \(-0.0789881\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 14.3161i | − | 0.454306i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.86744i | 0.122606i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.20881i | 0.101624i | 0.998708 | + | 0.0508121i | \(0.0161809\pi\) | ||||
−0.998708 | + | 0.0508121i | \(0.983819\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.73944 | −0.213227 |
(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 | 2240.2.k.g.1791.4 | 16 | ||
4.3 | odd | 2 | 2240.2.k.f.1791.14 | 16 | |||
7.6 | odd | 2 | 2240.2.k.f.1791.13 | 16 | |||
8.3 | odd | 2 | 1120.2.k.a.671.3 | ✓ | 16 | ||
8.5 | even | 2 | 1120.2.k.b.671.13 | yes | 16 | ||
28.27 | even | 2 | inner | 2240.2.k.g.1791.3 | 16 | ||
56.13 | odd | 2 | 1120.2.k.a.671.4 | yes | 16 | ||
56.27 | even | 2 | 1120.2.k.b.671.14 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1120.2.k.a.671.3 | ✓ | 16 | 8.3 | odd | 2 | ||
1120.2.k.a.671.4 | yes | 16 | 56.13 | odd | 2 | ||
1120.2.k.b.671.13 | yes | 16 | 8.5 | even | 2 | ||
1120.2.k.b.671.14 | yes | 16 | 56.27 | even | 2 | ||
2240.2.k.f.1791.13 | 16 | 7.6 | odd | 2 | |||
2240.2.k.f.1791.14 | 16 | 4.3 | odd | 2 | |||
2240.2.k.g.1791.3 | 16 | 28.27 | even | 2 | inner | ||
2240.2.k.g.1791.4 | 16 | 1.1 | even | 1 | trivial |