Properties

Label 729.2.c.e.244.2
Level $729$
Weight $2$
Character 729.244
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [729,2,Mod(244,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.244");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.c (of order \(3\), degree \(2\), 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: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: 12.0.1952986685049.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} - 258 x^{3} + 108 x^{2} - 27 x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 244.2
Root \(0.500000 - 1.68614i\) of defining polynomial
Character \(\chi\) \(=\) 729.244
Dual form 729.2.c.e.487.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.527162 - 0.913072i) q^{2} +(0.444200 - 0.769376i) q^{4} +(0.872894 - 1.51190i) q^{5} +(-1.22962 - 2.12977i) q^{7} -3.04531 q^{8} +O(q^{10})\) \(q+(-0.527162 - 0.913072i) q^{2} +(0.444200 - 0.769376i) q^{4} +(0.872894 - 1.51190i) q^{5} +(-1.22962 - 2.12977i) q^{7} -3.04531 q^{8} -1.84063 q^{10} +(0.627106 + 1.08618i) q^{11} +(2.27451 - 3.93958i) q^{13} +(-1.29642 + 2.24547i) q^{14} +(0.716974 + 1.24184i) q^{16} -6.64717 q^{17} +0.249156 q^{19} +(-0.775478 - 1.34317i) q^{20} +(0.661174 - 1.14519i) q^{22} +(-0.421000 + 0.729194i) q^{23} +(0.976114 + 1.69068i) q^{25} -4.79615 q^{26} -2.18479 q^{28} +(0.256192 + 0.443737i) q^{29} +(0.410002 - 0.710144i) q^{31} +(-2.28939 + 3.96533i) q^{32} +(3.50414 + 6.06935i) q^{34} -4.29332 q^{35} +2.60806 q^{37} +(-0.131346 - 0.227498i) q^{38} +(-2.65823 + 4.60419i) q^{40} +(4.07641 - 7.06054i) q^{41} +(-2.16357 - 3.74742i) q^{43} +1.11424 q^{44} +0.887743 q^{46} +(2.65117 + 4.59196i) q^{47} +(0.476053 - 0.824548i) q^{49} +(1.02914 - 1.78252i) q^{50} +(-2.02068 - 3.49992i) q^{52} -10.4841 q^{53} +2.18959 q^{55} +(3.74459 + 6.48581i) q^{56} +(0.270109 - 0.467843i) q^{58} +(1.50310 - 2.60345i) q^{59} +(-1.44159 - 2.49690i) q^{61} -0.864550 q^{62} +7.69541 q^{64} +(-3.97082 - 6.87766i) q^{65} +(-5.04313 + 8.73496i) q^{67} +(-2.95267 + 5.11417i) q^{68} +(2.26328 + 3.92011i) q^{70} +0.0894756 q^{71} -5.32114 q^{73} +(-1.37487 - 2.38135i) q^{74} +(0.110675 - 0.191695i) q^{76} +(1.54221 - 2.67119i) q^{77} +(-2.38846 - 4.13693i) q^{79} +2.50337 q^{80} -8.59571 q^{82} +(-4.02033 - 6.96342i) q^{83} +(-5.80227 + 10.0498i) q^{85} +(-2.28111 + 3.95099i) q^{86} +(-1.90973 - 3.30776i) q^{88} +6.70377 q^{89} -11.1872 q^{91} +(0.374016 + 0.647816i) q^{92} +(2.79519 - 4.84141i) q^{94} +(0.217487 - 0.376698i) q^{95} +(-2.74529 - 4.75498i) q^{97} -1.00383 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8} + 6 q^{10} + 12 q^{11} + 6 q^{14} + 3 q^{16} - 18 q^{17} + 6 q^{19} + 6 q^{20} - 6 q^{22} + 15 q^{23} + 6 q^{25} - 30 q^{26} - 12 q^{28} + 12 q^{29} - 24 q^{35} + 6 q^{37} - 3 q^{38} - 6 q^{40} + 15 q^{41} - 6 q^{44} + 6 q^{46} + 21 q^{47} + 12 q^{49} + 3 q^{50} - 12 q^{52} - 18 q^{53} - 12 q^{55} - 6 q^{56} + 12 q^{58} + 24 q^{59} + 9 q^{61} + 24 q^{62} - 24 q^{64} - 6 q^{65} + 9 q^{67} - 9 q^{68} - 15 q^{70} - 54 q^{71} - 12 q^{73} - 12 q^{74} - 6 q^{76} - 12 q^{77} + 42 q^{80} - 12 q^{82} + 12 q^{83} - 21 q^{86} - 12 q^{88} - 18 q^{89} - 12 q^{91} + 6 q^{92} - 6 q^{94} + 12 q^{95} + 90 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.527162 0.913072i −0.372760 0.645639i 0.617229 0.786784i \(-0.288255\pi\)
−0.989989 + 0.141144i \(0.954922\pi\)
\(3\) 0 0
\(4\) 0.444200 0.769376i 0.222100 0.384688i
\(5\) 0.872894 1.51190i 0.390370 0.676140i −0.602128 0.798399i \(-0.705680\pi\)
0.992498 + 0.122259i \(0.0390138\pi\)
\(6\) 0 0
\(7\) −1.22962 2.12977i −0.464754 0.804977i 0.534436 0.845209i \(-0.320524\pi\)
−0.999190 + 0.0402312i \(0.987191\pi\)
\(8\) −3.04531 −1.07668
\(9\) 0 0
\(10\) −1.84063 −0.582057
\(11\) 0.627106 + 1.08618i 0.189080 + 0.327496i 0.944944 0.327233i \(-0.106116\pi\)
−0.755864 + 0.654729i \(0.772783\pi\)
\(12\) 0 0
\(13\) 2.27451 3.93958i 0.630837 1.09264i −0.356544 0.934279i \(-0.616045\pi\)
0.987381 0.158363i \(-0.0506216\pi\)
\(14\) −1.29642 + 2.24547i −0.346483 + 0.600127i
\(15\) 0 0
\(16\) 0.716974 + 1.24184i 0.179244 + 0.310459i
\(17\) −6.64717 −1.61218 −0.806088 0.591796i \(-0.798419\pi\)
−0.806088 + 0.591796i \(0.798419\pi\)
\(18\) 0 0
\(19\) 0.249156 0.0571604 0.0285802 0.999592i \(-0.490901\pi\)
0.0285802 + 0.999592i \(0.490901\pi\)
\(20\) −0.775478 1.34317i −0.173402 0.300341i
\(21\) 0 0
\(22\) 0.661174 1.14519i 0.140963 0.244155i
\(23\) −0.421000 + 0.729194i −0.0877847 + 0.152048i −0.906574 0.422046i \(-0.861312\pi\)
0.818790 + 0.574093i \(0.194645\pi\)
\(24\) 0 0
\(25\) 0.976114 + 1.69068i 0.195223 + 0.338136i
\(26\) −4.79615 −0.940603
\(27\) 0 0
\(28\) −2.18479 −0.412887
\(29\) 0.256192 + 0.443737i 0.0475736 + 0.0823998i 0.888832 0.458234i \(-0.151518\pi\)
−0.841258 + 0.540634i \(0.818184\pi\)
\(30\) 0 0
\(31\) 0.410002 0.710144i 0.0736385 0.127546i −0.826855 0.562415i \(-0.809872\pi\)
0.900493 + 0.434870i \(0.143206\pi\)
\(32\) −2.28939 + 3.96533i −0.404710 + 0.700979i
\(33\) 0 0
\(34\) 3.50414 + 6.06935i 0.600955 + 1.04088i
\(35\) −4.29332 −0.725704
\(36\) 0 0
\(37\) 2.60806 0.428763 0.214381 0.976750i \(-0.431226\pi\)
0.214381 + 0.976750i \(0.431226\pi\)
\(38\) −0.131346 0.227498i −0.0213071 0.0369050i
\(39\) 0 0
\(40\) −2.65823 + 4.60419i −0.420303 + 0.727987i
\(41\) 4.07641 7.06054i 0.636628 1.10267i −0.349540 0.936921i \(-0.613662\pi\)
0.986168 0.165750i \(-0.0530046\pi\)
\(42\) 0 0
\(43\) −2.16357 3.74742i −0.329942 0.571476i 0.652558 0.757739i \(-0.273696\pi\)
−0.982500 + 0.186263i \(0.940362\pi\)
\(44\) 1.11424 0.167978
\(45\) 0 0
\(46\) 0.887743 0.130890
\(47\) 2.65117 + 4.59196i 0.386713 + 0.669806i 0.992005 0.126197i \(-0.0402772\pi\)
−0.605293 + 0.796003i \(0.706944\pi\)
\(48\) 0 0
\(49\) 0.476053 0.824548i 0.0680076 0.117793i
\(50\) 1.02914 1.78252i 0.145543 0.252087i
\(51\) 0 0
\(52\) −2.02068 3.49992i −0.280217 0.485351i
\(53\) −10.4841 −1.44010 −0.720052 0.693920i \(-0.755882\pi\)
−0.720052 + 0.693920i \(0.755882\pi\)
\(54\) 0 0
\(55\) 2.18959 0.295244
\(56\) 3.74459 + 6.48581i 0.500391 + 0.866703i
\(57\) 0 0
\(58\) 0.270109 0.467843i 0.0354671 0.0614307i
\(59\) 1.50310 2.60345i 0.195687 0.338940i −0.751438 0.659803i \(-0.770640\pi\)
0.947126 + 0.320863i \(0.103973\pi\)
\(60\) 0 0
\(61\) −1.44159 2.49690i −0.184576 0.319695i 0.758857 0.651257i \(-0.225758\pi\)
−0.943434 + 0.331561i \(0.892425\pi\)
\(62\) −0.864550 −0.109798
\(63\) 0 0
\(64\) 7.69541 0.961927
\(65\) −3.97082 6.87766i −0.492519 0.853069i
\(66\) 0 0
\(67\) −5.04313 + 8.73496i −0.616117 + 1.06715i 0.374071 + 0.927400i \(0.377962\pi\)
−0.990187 + 0.139745i \(0.955372\pi\)
\(68\) −2.95267 + 5.11417i −0.358064 + 0.620185i
\(69\) 0 0
\(70\) 2.26328 + 3.92011i 0.270513 + 0.468543i
\(71\) 0.0894756 0.0106188 0.00530940 0.999986i \(-0.498310\pi\)
0.00530940 + 0.999986i \(0.498310\pi\)
\(72\) 0 0
\(73\) −5.32114 −0.622792 −0.311396 0.950280i \(-0.600797\pi\)
−0.311396 + 0.950280i \(0.600797\pi\)
\(74\) −1.37487 2.38135i −0.159826 0.276826i
\(75\) 0 0
\(76\) 0.110675 0.191695i 0.0126953 0.0219889i
\(77\) 1.54221 2.67119i 0.175751 0.304410i
\(78\) 0 0
\(79\) −2.38846 4.13693i −0.268723 0.465441i 0.699810 0.714329i \(-0.253268\pi\)
−0.968532 + 0.248888i \(0.919935\pi\)
\(80\) 2.50337 0.279885
\(81\) 0 0
\(82\) −8.59571 −0.949238
\(83\) −4.02033 6.96342i −0.441289 0.764334i 0.556497 0.830850i \(-0.312145\pi\)
−0.997785 + 0.0665154i \(0.978812\pi\)
\(84\) 0 0
\(85\) −5.80227 + 10.0498i −0.629345 + 1.09006i
\(86\) −2.28111 + 3.95099i −0.245978 + 0.426047i
\(87\) 0 0
\(88\) −1.90973 3.30776i −0.203578 0.352608i
\(89\) 6.70377 0.710598 0.355299 0.934753i \(-0.384379\pi\)
0.355299 + 0.934753i \(0.384379\pi\)
\(90\) 0 0
\(91\) −11.1872 −1.17274
\(92\) 0.374016 + 0.647816i 0.0389939 + 0.0675394i
\(93\) 0 0
\(94\) 2.79519 4.84141i 0.288302 0.499354i
\(95\) 0.217487 0.376698i 0.0223137 0.0386484i
\(96\) 0 0
\(97\) −2.74529 4.75498i −0.278742 0.482795i 0.692330 0.721581i \(-0.256584\pi\)
−0.971072 + 0.238786i \(0.923251\pi\)
\(98\) −1.00383 −0.101402
\(99\) 0 0
\(100\) 1.73436 0.173436
\(101\) −2.50273 4.33486i −0.249031 0.431335i 0.714226 0.699915i \(-0.246779\pi\)
−0.963257 + 0.268580i \(0.913445\pi\)
\(102\) 0 0
\(103\) −5.80958 + 10.0625i −0.572435 + 0.991486i 0.423880 + 0.905718i \(0.360668\pi\)
−0.996315 + 0.0857682i \(0.972666\pi\)
\(104\) −6.92660 + 11.9972i −0.679209 + 1.17643i
\(105\) 0 0
\(106\) 5.52683 + 9.57275i 0.536813 + 0.929788i
\(107\) 19.4581 1.88109 0.940544 0.339673i \(-0.110316\pi\)
0.940544 + 0.339673i \(0.110316\pi\)
\(108\) 0 0
\(109\) 6.31515 0.604881 0.302441 0.953168i \(-0.402199\pi\)
0.302441 + 0.953168i \(0.402199\pi\)
\(110\) −1.15427 1.99925i −0.110055 0.190621i
\(111\) 0 0
\(112\) 1.76322 3.05398i 0.166608 0.288574i
\(113\) 3.45786 5.98919i 0.325288 0.563416i −0.656282 0.754515i \(-0.727872\pi\)
0.981571 + 0.191099i \(0.0612053\pi\)
\(114\) 0 0
\(115\) 0.734977 + 1.27302i 0.0685370 + 0.118710i
\(116\) 0.455201 0.0422643
\(117\) 0 0
\(118\) −3.16951 −0.291777
\(119\) 8.17351 + 14.1569i 0.749265 + 1.29776i
\(120\) 0 0
\(121\) 4.71347 8.16398i 0.428498 0.742180i
\(122\) −1.51990 + 2.63254i −0.137605 + 0.238339i
\(123\) 0 0
\(124\) −0.364245 0.630891i −0.0327102 0.0566557i
\(125\) 12.1371 1.08558
\(126\) 0 0
\(127\) 12.0232 1.06689 0.533445 0.845835i \(-0.320897\pi\)
0.533445 + 0.845835i \(0.320897\pi\)
\(128\) 0.522042 + 0.904203i 0.0461424 + 0.0799210i
\(129\) 0 0
\(130\) −4.18653 + 7.25129i −0.367183 + 0.635980i
\(131\) 7.04240 12.1978i 0.615297 1.06573i −0.375035 0.927011i \(-0.622369\pi\)
0.990332 0.138715i \(-0.0442973\pi\)
\(132\) 0 0
\(133\) −0.306368 0.530645i −0.0265655 0.0460128i
\(134\) 10.6342 0.918655
\(135\) 0 0
\(136\) 20.2427 1.73580
\(137\) −1.12907 1.95561i −0.0964630 0.167079i 0.813755 0.581208i \(-0.197420\pi\)
−0.910218 + 0.414129i \(0.864086\pi\)
\(138\) 0 0
\(139\) 3.98755 6.90663i 0.338219 0.585813i −0.645879 0.763440i \(-0.723509\pi\)
0.984098 + 0.177627i \(0.0568421\pi\)
\(140\) −1.90709 + 3.30318i −0.161179 + 0.279170i
\(141\) 0 0
\(142\) −0.0471682 0.0816977i −0.00395827 0.00685592i
\(143\) 5.70545 0.477114
\(144\) 0 0
\(145\) 0.894512 0.0742851
\(146\) 2.80510 + 4.85858i 0.232152 + 0.402099i
\(147\) 0 0
\(148\) 1.15850 2.00658i 0.0952281 0.164940i
\(149\) 0.0534692 0.0926114i 0.00438037 0.00758702i −0.863827 0.503789i \(-0.831939\pi\)
0.868207 + 0.496202i \(0.165272\pi\)
\(150\) 0 0
\(151\) 10.1297 + 17.5452i 0.824344 + 1.42781i 0.902420 + 0.430858i \(0.141789\pi\)
−0.0780761 + 0.996947i \(0.524878\pi\)
\(152\) −0.758758 −0.0615434
\(153\) 0 0
\(154\) −3.25198 −0.262052
\(155\) −0.715776 1.23976i −0.0574925 0.0995799i
\(156\) 0 0
\(157\) 10.3749 17.9699i 0.828009 1.43415i −0.0715893 0.997434i \(-0.522807\pi\)
0.899598 0.436719i \(-0.143860\pi\)
\(158\) −2.51821 + 4.36167i −0.200338 + 0.346996i
\(159\) 0 0
\(160\) 3.99678 + 6.92263i 0.315973 + 0.547282i
\(161\) 2.07069 0.163193
\(162\) 0 0
\(163\) −20.1346 −1.57706 −0.788531 0.614995i \(-0.789158\pi\)
−0.788531 + 0.614995i \(0.789158\pi\)
\(164\) −3.62148 6.27258i −0.282790 0.489806i
\(165\) 0 0
\(166\) −4.23873 + 7.34170i −0.328990 + 0.569827i
\(167\) 9.93130 17.2015i 0.768507 1.33109i −0.169865 0.985467i \(-0.554333\pi\)
0.938372 0.345626i \(-0.112333\pi\)
\(168\) 0 0
\(169\) −3.84683 6.66291i −0.295910 0.512532i
\(170\) 12.2350 0.938378
\(171\) 0 0
\(172\) −3.84423 −0.293120
\(173\) −9.46256 16.3896i −0.719425 1.24608i −0.961228 0.275755i \(-0.911072\pi\)
0.241803 0.970325i \(-0.422261\pi\)
\(174\) 0 0
\(175\) 2.40050 4.15780i 0.181461 0.314300i
\(176\) −0.899239 + 1.55753i −0.0677827 + 0.117403i
\(177\) 0 0
\(178\) −3.53398 6.12103i −0.264883 0.458790i
\(179\) 10.9137 0.815725 0.407863 0.913043i \(-0.366274\pi\)
0.407863 + 0.913043i \(0.366274\pi\)
\(180\) 0 0
\(181\) −17.9479 −1.33405 −0.667027 0.745033i \(-0.732433\pi\)
−0.667027 + 0.745033i \(0.732433\pi\)
\(182\) 5.89746 + 10.2147i 0.437149 + 0.757164i
\(183\) 0 0
\(184\) 1.28208 2.22062i 0.0945160 0.163707i
\(185\) 2.27656 3.94312i 0.167376 0.289904i
\(186\) 0 0
\(187\) −4.16848 7.22002i −0.304830 0.527980i
\(188\) 4.71059 0.343555
\(189\) 0 0
\(190\) −0.458604 −0.0332706
\(191\) 13.4830 + 23.3533i 0.975598 + 1.68978i 0.677948 + 0.735110i \(0.262869\pi\)
0.297649 + 0.954675i \(0.403797\pi\)
\(192\) 0 0
\(193\) 8.57740 14.8565i 0.617415 1.06939i −0.372541 0.928016i \(-0.621513\pi\)
0.989956 0.141378i \(-0.0451534\pi\)
\(194\) −2.89443 + 5.01329i −0.207808 + 0.359933i
\(195\) 0 0
\(196\) −0.422925 0.732528i −0.0302089 0.0523234i
\(197\) 2.51225 0.178990 0.0894951 0.995987i \(-0.471475\pi\)
0.0894951 + 0.995987i \(0.471475\pi\)
\(198\) 0 0
\(199\) 18.5388 1.31418 0.657092 0.753810i \(-0.271786\pi\)
0.657092 + 0.753810i \(0.271786\pi\)
\(200\) −2.97257 5.14864i −0.210192 0.364064i
\(201\) 0 0
\(202\) −2.63869 + 4.57035i −0.185658 + 0.321569i
\(203\) 0.630038 1.09126i 0.0442200 0.0765913i
\(204\) 0 0
\(205\) −7.11654 12.3262i −0.497041 0.860900i
\(206\) 12.2504 0.853524
\(207\) 0 0
\(208\) 6.52307 0.452294
\(209\) 0.156247 + 0.270629i 0.0108079 + 0.0187198i
\(210\) 0 0
\(211\) 1.84559 3.19666i 0.127056 0.220067i −0.795479 0.605981i \(-0.792781\pi\)
0.922535 + 0.385914i \(0.126114\pi\)
\(212\) −4.65704 + 8.06623i −0.319847 + 0.553991i
\(213\) 0 0
\(214\) −10.2576 17.7667i −0.701194 1.21450i
\(215\) −7.55427 −0.515197
\(216\) 0 0
\(217\) −2.01659 −0.136895
\(218\) −3.32911 5.76619i −0.225476 0.390535i
\(219\) 0 0
\(220\) 0.972614 1.68462i 0.0655736 0.113577i
\(221\) −15.1191 + 26.1870i −1.01702 + 1.76153i
\(222\) 0 0
\(223\) 10.6205 + 18.3953i 0.711203 + 1.23184i 0.964406 + 0.264426i \(0.0851826\pi\)
−0.253203 + 0.967413i \(0.581484\pi\)
\(224\) 11.2603 0.752363
\(225\) 0 0
\(226\) −7.29142 −0.485018
\(227\) 7.17002 + 12.4188i 0.475891 + 0.824268i 0.999619 0.0276182i \(-0.00879225\pi\)
−0.523727 + 0.851886i \(0.675459\pi\)
\(228\) 0 0
\(229\) −8.44291 + 14.6235i −0.557923 + 0.966351i 0.439747 + 0.898122i \(0.355068\pi\)
−0.997670 + 0.0682290i \(0.978265\pi\)
\(230\) 0.774905 1.34217i 0.0510957 0.0885004i
\(231\) 0 0
\(232\) −0.780183 1.35132i −0.0512215 0.0887183i
\(233\) 5.59945 0.366832 0.183416 0.983035i \(-0.441284\pi\)
0.183416 + 0.983035i \(0.441284\pi\)
\(234\) 0 0
\(235\) 9.25675 0.603844
\(236\) −1.33535 2.31290i −0.0869241 0.150557i
\(237\) 0 0
\(238\) 8.61754 14.9260i 0.558592 0.967510i
\(239\) 2.63714 4.56766i 0.170582 0.295457i −0.768041 0.640400i \(-0.778768\pi\)
0.938624 + 0.344943i \(0.112102\pi\)
\(240\) 0 0
\(241\) 4.45124 + 7.70977i 0.286730 + 0.496630i 0.973027 0.230691i \(-0.0740986\pi\)
−0.686298 + 0.727321i \(0.740765\pi\)
\(242\) −9.93907 −0.638907
\(243\) 0 0
\(244\) −2.56141 −0.163977
\(245\) −0.831087 1.43949i −0.0530962 0.0919654i
\(246\) 0 0
\(247\) 0.566709 0.981570i 0.0360589 0.0624558i
\(248\) −1.24858 + 2.16261i −0.0792851 + 0.137326i
\(249\) 0 0
\(250\) −6.39823 11.0821i −0.404659 0.700891i
\(251\) −7.78021 −0.491082 −0.245541 0.969386i \(-0.578966\pi\)
−0.245541 + 0.969386i \(0.578966\pi\)
\(252\) 0 0
\(253\) −1.05605 −0.0663932
\(254\) −6.33820 10.9781i −0.397694 0.688827i
\(255\) 0 0
\(256\) 8.24581 14.2822i 0.515363 0.892636i
\(257\) 10.2183 17.6986i 0.637399 1.10401i −0.348603 0.937270i \(-0.613344\pi\)
0.986002 0.166736i \(-0.0533228\pi\)
\(258\) 0 0
\(259\) −3.20693 5.55457i −0.199269 0.345144i
\(260\) −7.05534 −0.437554
\(261\) 0 0
\(262\) −14.8500 −0.917433
\(263\) −5.63990 9.76860i −0.347771 0.602358i 0.638082 0.769969i \(-0.279728\pi\)
−0.985853 + 0.167611i \(0.946395\pi\)
\(264\) 0 0
\(265\) −9.15152 + 15.8509i −0.562173 + 0.973712i
\(266\) −0.323012 + 0.559473i −0.0198051 + 0.0343035i
\(267\) 0 0
\(268\) 4.48031 + 7.76013i 0.273679 + 0.474025i
\(269\) −0.307761 −0.0187645 −0.00938226 0.999956i \(-0.502987\pi\)
−0.00938226 + 0.999956i \(0.502987\pi\)
\(270\) 0 0
\(271\) −2.22251 −0.135008 −0.0675040 0.997719i \(-0.521504\pi\)
−0.0675040 + 0.997719i \(0.521504\pi\)
\(272\) −4.76585 8.25469i −0.288972 0.500514i
\(273\) 0 0
\(274\) −1.19041 + 2.06184i −0.0719151 + 0.124561i
\(275\) −1.22425 + 2.12047i −0.0738253 + 0.127869i
\(276\) 0 0
\(277\) 11.6649 + 20.2041i 0.700874 + 1.21395i 0.968160 + 0.250332i \(0.0805397\pi\)
−0.267286 + 0.963617i \(0.586127\pi\)
\(278\) −8.40834 −0.504299
\(279\) 0 0
\(280\) 13.0745 0.781351
\(281\) −3.61273 6.25743i −0.215517 0.373287i 0.737915 0.674893i \(-0.235810\pi\)
−0.953432 + 0.301607i \(0.902477\pi\)
\(282\) 0 0
\(283\) −3.56015 + 6.16635i −0.211629 + 0.366552i −0.952224 0.305399i \(-0.901210\pi\)
0.740596 + 0.671951i \(0.234543\pi\)
\(284\) 0.0397450 0.0688404i 0.00235843 0.00408493i
\(285\) 0 0
\(286\) −3.00770 5.20949i −0.177849 0.308044i
\(287\) −20.0498 −1.18350
\(288\) 0 0
\(289\) 27.1849 1.59911
\(290\) −0.471553 0.816754i −0.0276905 0.0479614i
\(291\) 0 0
\(292\) −2.36365 + 4.09396i −0.138322 + 0.239581i
\(293\) −0.276243 + 0.478466i −0.0161383 + 0.0279523i −0.873982 0.485959i \(-0.838471\pi\)
0.857843 + 0.513911i \(0.171804\pi\)
\(294\) 0 0
\(295\) −2.62410 4.54507i −0.152781 0.264624i
\(296\) −7.94236 −0.461640
\(297\) 0 0
\(298\) −0.112748 −0.00653131
\(299\) 1.91514 + 3.31713i 0.110756 + 0.191834i
\(300\) 0 0
\(301\) −5.32076 + 9.21582i −0.306683 + 0.531191i
\(302\) 10.6800 18.4983i 0.614565 1.06446i
\(303\) 0 0
\(304\) 0.178639 + 0.309411i 0.0102456 + 0.0177459i
\(305\) −5.03340 −0.288212
\(306\) 0 0
\(307\) 6.72876 0.384031 0.192015 0.981392i \(-0.438498\pi\)
0.192015 + 0.981392i \(0.438498\pi\)
\(308\) −1.37010 2.37308i −0.0780686 0.135219i
\(309\) 0 0
\(310\) −0.754660 + 1.30711i −0.0428618 + 0.0742389i
\(311\) −7.71173 + 13.3571i −0.437292 + 0.757412i −0.997480 0.0709539i \(-0.977396\pi\)
0.560188 + 0.828366i \(0.310729\pi\)
\(312\) 0 0
\(313\) 11.7804 + 20.4043i 0.665870 + 1.15332i 0.979049 + 0.203626i \(0.0652726\pi\)
−0.313179 + 0.949694i \(0.601394\pi\)
\(314\) −21.8771 −1.23459
\(315\) 0 0
\(316\) −4.24381 −0.238733
\(317\) −3.62602 6.28045i −0.203658 0.352745i 0.746047 0.665894i \(-0.231950\pi\)
−0.949704 + 0.313148i \(0.898616\pi\)
\(318\) 0 0
\(319\) −0.321319 + 0.556540i −0.0179904 + 0.0311603i
\(320\) 6.71728 11.6347i 0.375507 0.650397i
\(321\) 0 0
\(322\) −1.09159 1.89069i −0.0608319 0.105364i
\(323\) −1.65618 −0.0921525
\(324\) 0 0
\(325\) 8.88074 0.492615
\(326\) 10.6142 + 18.3843i 0.587866 + 1.01821i
\(327\) 0 0
\(328\) −12.4139 + 21.5016i −0.685444 + 1.18722i
\(329\) 6.51987 11.2928i 0.359452 0.622590i
\(330\) 0 0
\(331\) −14.5172 25.1446i −0.797939 1.38207i −0.920956 0.389667i \(-0.872590\pi\)
0.123017 0.992405i \(-0.460743\pi\)
\(332\) −7.14332 −0.392040
\(333\) 0 0
\(334\) −20.9416 −1.14588
\(335\) 8.80423 + 15.2494i 0.481027 + 0.833163i
\(336\) 0 0
\(337\) 0.579548 1.00381i 0.0315700 0.0546808i −0.849809 0.527091i \(-0.823283\pi\)
0.881379 + 0.472410i \(0.156616\pi\)
\(338\) −4.05581 + 7.02487i −0.220607 + 0.382103i
\(339\) 0 0
\(340\) 5.15473 + 8.92826i 0.279555 + 0.484203i
\(341\) 1.02846 0.0556942
\(342\) 0 0
\(343\) −19.5562 −1.05594
\(344\) 6.58875 + 11.4120i 0.355242 + 0.615296i
\(345\) 0 0
\(346\) −9.97661 + 17.2800i −0.536346 + 0.928978i
\(347\) −2.94485 + 5.10064i −0.158088 + 0.273817i −0.934179 0.356804i \(-0.883866\pi\)
0.776091 + 0.630621i \(0.217200\pi\)
\(348\) 0 0
\(349\) 15.2963 + 26.4940i 0.818795 + 1.41819i 0.906571 + 0.422054i \(0.138691\pi\)
−0.0877762 + 0.996140i \(0.527976\pi\)
\(350\) −5.06182 −0.270566
\(351\) 0 0
\(352\) −5.74276 −0.306090
\(353\) −18.4806 32.0094i −0.983625 1.70369i −0.647894 0.761731i \(-0.724350\pi\)
−0.335731 0.941958i \(-0.608983\pi\)
\(354\) 0 0
\(355\) 0.0781027 0.135278i 0.00414526 0.00717980i
\(356\) 2.97781 5.15772i 0.157824 0.273359i
\(357\) 0 0
\(358\) −5.75327 9.96496i −0.304070 0.526664i
\(359\) −26.3761 −1.39207 −0.696037 0.718006i \(-0.745055\pi\)
−0.696037 + 0.718006i \(0.745055\pi\)
\(360\) 0 0
\(361\) −18.9379 −0.996733
\(362\) 9.46144 + 16.3877i 0.497282 + 0.861318i
\(363\) 0 0
\(364\) −4.96934 + 8.60715i −0.260464 + 0.451137i
\(365\) −4.64479 + 8.04501i −0.243119 + 0.421095i
\(366\) 0 0
\(367\) 5.65657 + 9.79746i 0.295270 + 0.511423i 0.975048 0.221995i \(-0.0712570\pi\)
−0.679777 + 0.733418i \(0.737924\pi\)
\(368\) −1.20739 −0.0629394
\(369\) 0 0
\(370\) −4.80047 −0.249564
\(371\) 12.8915 + 22.3288i 0.669294 + 1.15925i
\(372\) 0 0
\(373\) −2.92204 + 5.06112i −0.151297 + 0.262055i −0.931705 0.363217i \(-0.881678\pi\)
0.780407 + 0.625272i \(0.215012\pi\)
\(374\) −4.39494 + 7.61225i −0.227257 + 0.393620i
\(375\) 0 0
\(376\) −8.07363 13.9839i −0.416366 0.721166i
\(377\) 2.33085 0.120045
\(378\) 0 0
\(379\) 24.3265 1.24957 0.624783 0.780798i \(-0.285187\pi\)
0.624783 + 0.780798i \(0.285187\pi\)
\(380\) −0.193215 0.334658i −0.00991173 0.0171676i
\(381\) 0 0
\(382\) 14.2155 24.6220i 0.727328 1.25977i
\(383\) 1.90803 3.30480i 0.0974955 0.168867i −0.813152 0.582052i \(-0.802250\pi\)
0.910647 + 0.413184i \(0.135583\pi\)
\(384\) 0 0
\(385\) −2.69237 4.66332i −0.137216 0.237665i
\(386\) −18.0867 −0.920591
\(387\) 0 0
\(388\) −4.87782 −0.247634
\(389\) −5.42092 9.38932i −0.274852 0.476057i 0.695246 0.718772i \(-0.255295\pi\)
−0.970098 + 0.242715i \(0.921962\pi\)
\(390\) 0 0
\(391\) 2.79846 4.84708i 0.141524 0.245127i
\(392\) −1.44973 + 2.51101i −0.0732224 + 0.126825i
\(393\) 0 0
\(394\) −1.32436 2.29386i −0.0667204 0.115563i
\(395\) −8.33948 −0.419605
\(396\) 0 0
\(397\) −10.5092 −0.527442 −0.263721 0.964599i \(-0.584950\pi\)
−0.263721 + 0.964599i \(0.584950\pi\)
\(398\) −9.77298 16.9273i −0.489875 0.848489i
\(399\) 0 0
\(400\) −1.39970 + 2.42435i −0.0699849 + 0.121217i
\(401\) −7.18279 + 12.4410i −0.358691 + 0.621272i −0.987742 0.156092i \(-0.950110\pi\)
0.629051 + 0.777364i \(0.283444\pi\)
\(402\) 0 0
\(403\) −1.86511 3.23047i −0.0929078 0.160921i
\(404\) −4.44685 −0.221239
\(405\) 0 0
\(406\) −1.32853 −0.0659338
\(407\) 1.63553 + 2.83283i 0.0810703 + 0.140418i
\(408\) 0 0
\(409\) −8.84113 + 15.3133i −0.437166 + 0.757193i −0.997470 0.0710938i \(-0.977351\pi\)
0.560304 + 0.828287i \(0.310684\pi\)
\(410\) −7.50314 + 12.9958i −0.370554 + 0.641818i
\(411\) 0 0
\(412\) 5.16123 + 8.93951i 0.254275 + 0.440418i
\(413\) −7.39299 −0.363785
\(414\) 0 0
\(415\) −14.0373 −0.689063
\(416\) 10.4145 + 18.0384i 0.510612 + 0.884407i
\(417\) 0 0
\(418\) 0.164736 0.285330i 0.00805748 0.0139560i
\(419\) −4.56688 + 7.91007i −0.223107 + 0.386432i −0.955750 0.294181i \(-0.904953\pi\)
0.732643 + 0.680613i \(0.238287\pi\)
\(420\) 0 0
\(421\) −12.0975 20.9534i −0.589594 1.02121i −0.994286 0.106753i \(-0.965954\pi\)
0.404692 0.914453i \(-0.367379\pi\)
\(422\) −3.89170 −0.189445
\(423\) 0 0
\(424\) 31.9274 1.55053
\(425\) −6.48839 11.2382i −0.314733 0.545134i
\(426\) 0 0
\(427\) −3.54522 + 6.14049i −0.171565 + 0.297159i
\(428\) 8.64329 14.9706i 0.417789 0.723632i
\(429\) 0 0
\(430\) 3.98233 + 6.89760i 0.192045 + 0.332632i
\(431\) −29.5332 −1.42256 −0.711282 0.702907i \(-0.751885\pi\)
−0.711282 + 0.702907i \(0.751885\pi\)
\(432\) 0 0
\(433\) 0.669754 0.0321863 0.0160932 0.999870i \(-0.494877\pi\)
0.0160932 + 0.999870i \(0.494877\pi\)
\(434\) 1.06307 + 1.84129i 0.0510290 + 0.0883849i
\(435\) 0 0
\(436\) 2.80519 4.85872i 0.134344 0.232691i
\(437\) −0.104895 + 0.181683i −0.00501780 + 0.00869109i
\(438\) 0 0
\(439\) 3.17443 + 5.49828i 0.151507 + 0.262419i 0.931782 0.363019i \(-0.118254\pi\)
−0.780274 + 0.625437i \(0.784921\pi\)
\(440\) −6.66798 −0.317883
\(441\) 0 0
\(442\) 31.8809 1.51642
\(443\) −7.67696 13.2969i −0.364743 0.631754i 0.623991 0.781431i \(-0.285510\pi\)
−0.988735 + 0.149677i \(0.952177\pi\)
\(444\) 0 0
\(445\) 5.85168 10.1354i 0.277396 0.480464i
\(446\) 11.1975 19.3946i 0.530216 0.918361i
\(447\) 0 0
\(448\) −9.46246 16.3895i −0.447059 0.774329i
\(449\) −32.0398 −1.51205 −0.756027 0.654541i \(-0.772862\pi\)
−0.756027 + 0.654541i \(0.772862\pi\)
\(450\) 0 0
\(451\) 10.2254 0.481494
\(452\) −3.07196 5.32079i −0.144493 0.250269i
\(453\) 0 0
\(454\) 7.55954 13.0935i 0.354787 0.614508i
\(455\) −9.76522 + 16.9139i −0.457801 + 0.792934i
\(456\) 0 0
\(457\) −9.58402 16.6000i −0.448321 0.776516i 0.549955 0.835194i \(-0.314645\pi\)
−0.998277 + 0.0586784i \(0.981311\pi\)
\(458\) 17.8031 0.831886
\(459\) 0 0
\(460\) 1.30591 0.0608882
\(461\) 2.61015 + 4.52091i 0.121567 + 0.210560i 0.920386 0.391012i \(-0.127875\pi\)
−0.798819 + 0.601571i \(0.794542\pi\)
\(462\) 0 0
\(463\) −0.848695 + 1.46998i −0.0394422 + 0.0683159i −0.885073 0.465453i \(-0.845891\pi\)
0.845630 + 0.533769i \(0.179225\pi\)
\(464\) −0.367365 + 0.636296i −0.0170545 + 0.0295393i
\(465\) 0 0
\(466\) −2.95182 5.11270i −0.136740 0.236841i
\(467\) 19.6827 0.910808 0.455404 0.890285i \(-0.349495\pi\)
0.455404 + 0.890285i \(0.349495\pi\)
\(468\) 0 0
\(469\) 24.8046 1.14537
\(470\) −4.87981 8.45208i −0.225089 0.389865i
\(471\) 0 0
\(472\) −4.57741 + 7.92831i −0.210692 + 0.364930i
\(473\) 2.71358 4.70006i 0.124771 0.216109i
\(474\) 0 0
\(475\) 0.243205 + 0.421243i 0.0111590 + 0.0193280i
\(476\) 14.5227 0.665646
\(477\) 0 0
\(478\) −5.56080 −0.254345
\(479\) 14.6267 + 25.3342i 0.668311 + 1.15755i 0.978376 + 0.206834i \(0.0663160\pi\)
−0.310065 + 0.950716i \(0.600351\pi\)
\(480\) 0 0
\(481\) 5.93207 10.2747i 0.270479 0.468484i
\(482\) 4.69305 8.12861i 0.213763 0.370248i
\(483\) 0 0
\(484\) −4.18745 7.25287i −0.190339 0.329676i
\(485\) −9.58538 −0.435250
\(486\) 0 0
\(487\) −20.5056 −0.929199 −0.464600 0.885521i \(-0.653802\pi\)
−0.464600 + 0.885521i \(0.653802\pi\)
\(488\) 4.39008 + 7.60384i 0.198729 + 0.344210i
\(489\) 0 0
\(490\) −0.876236 + 1.51769i −0.0395843 + 0.0685620i
\(491\) −8.76350 + 15.1788i −0.395491 + 0.685011i −0.993164 0.116730i \(-0.962759\pi\)
0.597673 + 0.801740i \(0.296092\pi\)
\(492\) 0 0
\(493\) −1.70295 2.94959i −0.0766969 0.132843i
\(494\) −1.19499 −0.0537652
\(495\) 0 0
\(496\) 1.17584 0.0527969
\(497\) −0.110021 0.190563i −0.00493513 0.00854790i
\(498\) 0 0
\(499\) 9.55299 16.5463i 0.427651 0.740713i −0.569013 0.822328i \(-0.692675\pi\)
0.996664 + 0.0816157i \(0.0260080\pi\)
\(500\) 5.39130 9.33800i 0.241106 0.417608i
\(501\) 0 0
\(502\) 4.10143 + 7.10389i 0.183056 + 0.317062i
\(503\) −10.9676 −0.489022 −0.244511 0.969646i \(-0.578627\pi\)
−0.244511 + 0.969646i \(0.578627\pi\)
\(504\) 0 0
\(505\) −8.73847 −0.388857
\(506\) 0.556709 + 0.964248i 0.0247487 + 0.0428661i
\(507\) 0 0
\(508\) 5.34072 9.25040i 0.236956 0.410420i
\(509\) 9.94968 17.2333i 0.441012 0.763855i −0.556753 0.830678i \(-0.687953\pi\)
0.997765 + 0.0668233i \(0.0212864\pi\)
\(510\) 0 0
\(511\) 6.54300 + 11.3328i 0.289445 + 0.501334i
\(512\) −15.2994 −0.676143
\(513\) 0 0
\(514\) −21.5468 −0.950387
\(515\) 10.1423 + 17.5670i 0.446923 + 0.774093i
\(516\) 0 0
\(517\) −3.32513 + 5.75929i −0.146239 + 0.253293i
\(518\) −3.38115 + 5.85632i −0.148559 + 0.257312i
\(519\) 0 0
\(520\) 12.0924 + 20.9446i 0.530286 + 0.918482i
\(521\) 35.1167 1.53849 0.769244 0.638955i \(-0.220633\pi\)
0.769244 + 0.638955i \(0.220633\pi\)
\(522\) 0 0
\(523\) −14.2454 −0.622907 −0.311453 0.950261i \(-0.600816\pi\)
−0.311453 + 0.950261i \(0.600816\pi\)
\(524\) −6.25646 10.8365i −0.273315 0.473395i
\(525\) 0 0
\(526\) −5.94629 + 10.2993i −0.259271 + 0.449070i
\(527\) −2.72535 + 4.72045i −0.118718 + 0.205626i
\(528\) 0 0
\(529\) 11.1455 + 19.3046i 0.484588 + 0.839331i
\(530\) 19.2973 0.838223
\(531\) 0 0
\(532\) −0.544355 −0.0236008
\(533\) −18.5437 32.1186i −0.803217 1.39121i
\(534\) 0 0
\(535\) 16.9849 29.4187i 0.734320 1.27188i
\(536\) 15.3579 26.6007i 0.663360 1.14897i
\(537\) 0 0
\(538\) 0.162240 + 0.281008i 0.00699466 + 0.0121151i
\(539\) 1.19414 0.0514354
\(540\) 0 0
\(541\) −13.2368 −0.569094 −0.284547 0.958662i \(-0.591843\pi\)
−0.284547 + 0.958662i \(0.591843\pi\)
\(542\) 1.17163 + 2.02932i 0.0503256 + 0.0871666i
\(543\) 0 0
\(544\) 15.2179 26.3583i 0.652464 1.13010i
\(545\) 5.51245 9.54785i 0.236127 0.408985i
\(546\) 0 0
\(547\) 8.15246 + 14.1205i 0.348574 + 0.603748i 0.985996 0.166767i \(-0.0533327\pi\)
−0.637422 + 0.770515i \(0.719999\pi\)
\(548\) −2.00613 −0.0856976
\(549\) 0 0
\(550\) 2.58152 0.110077
\(551\) 0.0638317 + 0.110560i 0.00271932 + 0.00471000i
\(552\) 0 0
\(553\) −5.87381 + 10.1737i −0.249780 + 0.432631i
\(554\) 12.2986 21.3017i 0.522516 0.905023i
\(555\) 0 0
\(556\) −3.54253 6.13585i −0.150237 0.260218i
\(557\) 30.8972 1.30915 0.654577 0.755995i \(-0.272847\pi\)
0.654577 + 0.755995i \(0.272847\pi\)
\(558\) 0 0
\(559\) −19.6843 −0.832557
\(560\) −3.07820 5.33160i −0.130078 0.225301i
\(561\) 0 0
\(562\) −3.80899 + 6.59736i −0.160672 + 0.278293i
\(563\) −13.3880 + 23.1887i −0.564236 + 0.977285i 0.432884 + 0.901449i \(0.357496\pi\)
−0.997120 + 0.0758357i \(0.975838\pi\)
\(564\) 0 0
\(565\) −6.03669 10.4559i −0.253966 0.439881i
\(566\) 7.50710 0.315547
\(567\) 0 0
\(568\) −0.272481 −0.0114331
\(569\) −9.53032 16.5070i −0.399532 0.692009i 0.594136 0.804364i \(-0.297494\pi\)
−0.993668 + 0.112355i \(0.964161\pi\)
\(570\) 0 0
\(571\) 9.38710 16.2589i 0.392838 0.680415i −0.599985 0.800012i \(-0.704827\pi\)
0.992823 + 0.119596i \(0.0381600\pi\)
\(572\) 2.53436 4.38964i 0.105967 0.183540i
\(573\) 0 0
\(574\) 10.5695 + 18.3069i 0.441162 + 0.764115i
\(575\) −1.64378 −0.0685503
\(576\) 0 0
\(577\) −4.85962 −0.202309 −0.101154 0.994871i \(-0.532254\pi\)
−0.101154 + 0.994871i \(0.532254\pi\)
\(578\) −14.3308 24.8217i −0.596084 1.03245i
\(579\) 0 0
\(580\) 0.397342 0.688216i 0.0164987 0.0285766i
\(581\) −9.88698 + 17.1248i −0.410181 + 0.710455i
\(582\) 0 0
\(583\) −6.57466 11.3876i −0.272294 0.471628i
\(584\) 16.2045 0.670548
\(585\) 0 0
\(586\) 0.582499 0.0240628
\(587\) 16.3987 + 28.4033i 0.676846 + 1.17233i 0.975926 + 0.218103i \(0.0699869\pi\)
−0.299080 + 0.954228i \(0.596680\pi\)
\(588\) 0 0
\(589\) 0.102154 0.176937i 0.00420920 0.00729055i
\(590\) −2.76665 + 4.79198i −0.113901 + 0.197283i
\(591\) 0 0
\(592\) 1.86991 + 3.23878i 0.0768530 + 0.133113i
\(593\) 17.3446 0.712258 0.356129 0.934437i \(-0.384096\pi\)
0.356129 + 0.934437i \(0.384096\pi\)
\(594\) 0 0
\(595\) 28.5384 1.16996
\(596\) −0.0475020 0.0822759i −0.00194576 0.00337015i
\(597\) 0 0
\(598\) 2.01918 3.49733i 0.0825706 0.143016i
\(599\) −12.2040 + 21.1379i −0.498640 + 0.863670i −0.999999 0.00156953i \(-0.999500\pi\)
0.501359 + 0.865240i \(0.332834\pi\)
\(600\) 0 0
\(601\) −3.93513 6.81585i −0.160517 0.278024i 0.774537 0.632529i \(-0.217983\pi\)
−0.935054 + 0.354504i \(0.884650\pi\)
\(602\) 11.2196 0.457277
\(603\) 0 0
\(604\) 17.9984 0.732346
\(605\) −8.22872 14.2526i −0.334545 0.579449i
\(606\) 0 0
\(607\) 5.11873 8.86591i 0.207763 0.359856i −0.743247 0.669018i \(-0.766715\pi\)
0.951010 + 0.309162i \(0.100048\pi\)
\(608\) −0.570415 + 0.987988i −0.0231334 + 0.0400682i
\(609\) 0 0
\(610\) 2.65342 + 4.59586i 0.107434 + 0.186081i
\(611\) 24.1205 0.975810
\(612\) 0 0
\(613\) 2.23507 0.0902736 0.0451368 0.998981i \(-0.485628\pi\)
0.0451368 + 0.998981i \(0.485628\pi\)
\(614\) −3.54715 6.14384i −0.143151 0.247945i
\(615\) 0 0
\(616\) −4.69651 + 8.13459i −0.189228 + 0.327752i
\(617\) −16.9878 + 29.4238i −0.683905 + 1.18456i 0.289875 + 0.957065i \(0.406386\pi\)
−0.973780 + 0.227493i \(0.926947\pi\)
\(618\) 0 0
\(619\) 14.4280 + 24.9900i 0.579910 + 1.00443i 0.995489 + 0.0948761i \(0.0302455\pi\)
−0.415579 + 0.909557i \(0.636421\pi\)
\(620\) −1.27179 −0.0510763
\(621\) 0 0
\(622\) 16.2613 0.652020
\(623\) −8.24311 14.2775i −0.330253 0.572015i
\(624\) 0 0
\(625\) 5.71383 9.89665i 0.228553 0.395866i
\(626\) 12.4204 21.5128i 0.496419 0.859823i
\(627\) 0 0
\(628\) −9.21707 15.9644i −0.367801 0.637050i
\(629\) −17.3362 −0.691241
\(630\) 0 0
\(631\) −3.14078 −0.125032 −0.0625162 0.998044i \(-0.519913\pi\)
−0.0625162 + 0.998044i \(0.519913\pi\)
\(632\) 7.27360 + 12.5982i 0.289328 + 0.501131i
\(633\) 0 0
\(634\) −3.82300 + 6.62164i −0.151831 + 0.262979i
\(635\) 10.4950 18.1779i 0.416482 0.721368i
\(636\) 0 0
\(637\) −2.16558 3.75089i −0.0858034 0.148616i
\(638\) 0.677549 0.0268244
\(639\) 0 0
\(640\) 1.82275 0.0720504
\(641\) 15.9113 + 27.5591i 0.628457 + 1.08852i 0.987861 + 0.155338i \(0.0496467\pi\)
−0.359404 + 0.933182i \(0.617020\pi\)
\(642\) 0 0
\(643\) 6.42353 11.1259i 0.253319 0.438762i −0.711118 0.703072i \(-0.751811\pi\)
0.964438 + 0.264310i \(0.0851443\pi\)
\(644\) 0.919799 1.59314i 0.0362451 0.0627784i
\(645\) 0 0
\(646\) 0.873078 + 1.51221i 0.0343508 + 0.0594973i
\(647\) 28.2444 1.11040 0.555200 0.831717i \(-0.312642\pi\)
0.555200 + 0.831717i \(0.312642\pi\)
\(648\) 0 0
\(649\) 3.77042 0.148002
\(650\) −4.68159 8.10876i −0.183627 0.318052i
\(651\) 0 0
\(652\) −8.94377 + 15.4911i −0.350265 + 0.606677i
\(653\) −12.9952 + 22.5084i −0.508543 + 0.880823i 0.491408 + 0.870930i \(0.336482\pi\)
−0.999951 + 0.00989323i \(0.996851\pi\)
\(654\) 0 0
\(655\) −12.2945 21.2947i −0.480387 0.832055i
\(656\) 11.6907 0.456446
\(657\) 0 0
\(658\) −13.7481 −0.535958
\(659\) 23.8089 + 41.2382i 0.927463 + 1.60641i 0.787551 + 0.616250i \(0.211349\pi\)
0.139912 + 0.990164i \(0.455318\pi\)
\(660\) 0 0
\(661\) 0.438254 0.759078i 0.0170461 0.0295247i −0.857377 0.514690i \(-0.827907\pi\)
0.874423 + 0.485165i \(0.161240\pi\)
\(662\) −15.3059 + 26.5106i −0.594880 + 1.03036i
\(663\) 0 0
\(664\) 12.2432 + 21.2058i 0.475127 + 0.822943i
\(665\) −1.06971 −0.0414815
\(666\) 0 0
\(667\) −0.431427 −0.0167049
\(668\) −8.82296 15.2818i −0.341371 0.591271i
\(669\) 0 0
\(670\) 9.28252 16.0778i 0.358615 0.621140i
\(671\) 1.80806 3.13164i 0.0697992 0.120896i
\(672\) 0 0
\(673\) −18.6697 32.3369i −0.719665 1.24650i −0.961133 0.276087i \(-0.910962\pi\)
0.241468 0.970409i \(-0.422371\pi\)
\(674\) −1.22206 −0.0470721
\(675\) 0 0
\(676\) −6.83505 −0.262886
\(677\) 6.85958 + 11.8811i 0.263635 + 0.456630i 0.967205 0.253996i \(-0.0817451\pi\)
−0.703570 + 0.710626i \(0.748412\pi\)
\(678\) 0 0
\(679\) −6.75134 + 11.6937i −0.259093 + 0.448762i
\(680\) 17.6697 30.6049i 0.677603 1.17364i
\(681\) 0 0
\(682\) −0.542165 0.939057i −0.0207606 0.0359584i
\(683\) 49.9887 1.91276 0.956381 0.292121i \(-0.0943611\pi\)
0.956381 + 0.292121i \(0.0943611\pi\)
\(684\) 0 0
\(685\) −3.94223 −0.150625
\(686\) 10.3093 + 17.8562i 0.393610 + 0.681753i
\(687\) 0 0
\(688\) 3.10245 5.37360i 0.118280 0.204867i
\(689\) −23.8463 + 41.3030i −0.908471 + 1.57352i
\(690\) 0 0
\(691\) −11.9075 20.6244i −0.452984 0.784591i 0.545586 0.838055i \(-0.316307\pi\)
−0.998570 + 0.0534640i \(0.982974\pi\)
\(692\) −16.8131 −0.639137
\(693\) 0 0
\(694\) 6.20967 0.235716
\(695\) −6.96141 12.0575i −0.264061 0.457367i
\(696\) 0 0
\(697\) −27.0966 + 46.9326i −1.02636 + 1.77770i
\(698\) 16.1273 27.9333i 0.610428 1.05729i
\(699\) 0 0
\(700\) −2.13261 3.69378i −0.0806049 0.139612i
\(701\) 34.4493 1.30113 0.650565 0.759450i \(-0.274532\pi\)
0.650565 + 0.759450i \(0.274532\pi\)
\(702\) 0 0
\(703\) 0.649815 0.0245082
\(704\) 4.82584 + 8.35861i 0.181881 + 0.315027i
\(705\) 0 0
\(706\) −19.4846 + 33.7483i −0.733312 + 1.27013i
\(707\) −6.15484 + 10.6605i −0.231476 + 0.400929i
\(708\) 0 0
\(709\) −7.76164 13.4435i −0.291494 0.504883i 0.682669 0.730728i \(-0.260819\pi\)
−0.974163 + 0.225845i \(0.927486\pi\)
\(710\) −0.164691 −0.00618075
\(711\) 0 0
\(712\) −20.4151 −0.765087
\(713\) 0.345222 + 0.597942i 0.0129287 + 0.0223931i
\(714\) 0 0
\(715\) 4.98025 8.62605i 0.186251 0.322596i
\(716\) 4.84784 8.39671i 0.181172 0.313800i
\(717\) 0 0
\(718\) 13.9045 + 24.0832i 0.518910 + 0.898778i
\(719\) 12.0537 0.449528 0.224764 0.974413i \(-0.427839\pi\)
0.224764 + 0.974413i \(0.427839\pi\)
\(720\) 0 0
\(721\) 28.5744 1.06417
\(722\) 9.98336 + 17.2917i 0.371542 + 0.643530i
\(723\) 0 0
\(724\) −7.97243 + 13.8087i −0.296293 + 0.513195i
\(725\) −0.500144 + 0.866275i −0.0185749 + 0.0321726i
\(726\) 0 0
\(727\) 15.8151 + 27.3926i 0.586550 + 1.01594i 0.994680 + 0.103011i \(0.0328478\pi\)
−0.408130 + 0.912924i \(0.633819\pi\)
\(728\) 34.0685 1.26266
\(729\) 0 0
\(730\) 9.79423 0.362501
\(731\) 14.3816 + 24.9097i 0.531924 + 0.921319i
\(732\) 0 0
\(733\) 9.51539 16.4811i 0.351459 0.608745i −0.635046 0.772474i \(-0.719019\pi\)
0.986505 + 0.163729i \(0.0523523\pi\)
\(734\) 5.96386 10.3297i 0.220130 0.381276i
\(735\) 0 0
\(736\) −1.92767 3.33882i −0.0710547 0.123070i
\(737\) −12.6503 −0.465981
\(738\) 0 0
\(739\) 16.6007 0.610668 0.305334 0.952245i \(-0.401232\pi\)
0.305334 + 0.952245i \(0.401232\pi\)
\(740\) −2.02249 3.50306i −0.0743484 0.128775i
\(741\) 0 0
\(742\) 13.5918 23.5418i 0.498972 0.864245i
\(743\) 16.6518 28.8417i 0.610894 1.05810i −0.380196 0.924906i \(-0.624143\pi\)
0.991090 0.133194i \(-0.0425232\pi\)
\(744\) 0 0
\(745\) −0.0933458 0.161680i −0.00341993 0.00592349i
\(746\) 6.16156 0.225591
\(747\) 0 0
\(748\) −7.40655 −0.270810
\(749\) −23.9262 41.4413i −0.874243 1.51423i
\(750\) 0 0
\(751\) −13.8908 + 24.0596i −0.506882 + 0.877946i 0.493086 + 0.869981i \(0.335869\pi\)
−0.999968 + 0.00796554i \(0.997464\pi\)
\(752\) −3.80164 + 6.58463i −0.138631 + 0.240117i
\(753\) 0 0
\(754\) −1.22873 2.12823i −0.0447479 0.0775056i
\(755\) 35.3686 1.28720
\(756\) 0 0
\(757\) −3.12036 −0.113411 −0.0567057 0.998391i \(-0.518060\pi\)
−0.0567057 + 0.998391i \(0.518060\pi\)
\(758\) −12.8240 22.2118i −0.465789 0.806769i
\(759\) 0 0
\(760\) −0.662315 + 1.14716i −0.0240247 + 0.0416120i
\(761\) 21.9796 38.0698i 0.796760 1.38003i −0.124956 0.992162i \(-0.539879\pi\)
0.921716 0.387866i \(-0.126788\pi\)
\(762\) 0 0
\(763\) −7.76525 13.4498i −0.281121 0.486916i
\(764\) 23.9566 0.866720
\(765\) 0 0
\(766\) −4.02336 −0.145370
\(767\) −6.83765 11.8432i −0.246893 0.427632i
\(768\) 0 0
\(769\) −1.85643 + 3.21543i −0.0669445 + 0.115951i −0.897555 0.440903i \(-0.854658\pi\)
0.830610 + 0.556854i \(0.187992\pi\)
\(770\) −2.83863 + 4.91665i −0.102297 + 0.177184i
\(771\) 0 0
\(772\) −7.62016 13.1985i −0.274256 0.475024i
\(773\) −8.96903 −0.322594 −0.161297 0.986906i \(-0.551568\pi\)
−0.161297 + 0.986906i \(0.551568\pi\)
\(774\) 0 0
\(775\) 1.60083 0.0575036
\(776\) 8.36026 + 14.4804i 0.300116 + 0.519816i
\(777\) 0 0
\(778\) −5.71541 + 9.89939i −0.204908 + 0.354910i
\(779\) 1.01566 1.75918i 0.0363899 0.0630291i
\(780\) 0 0
\(781\) 0.0561108 + 0.0971867i 0.00200780 + 0.00347761i
\(782\) −5.90098 −0.211018
\(783\) 0 0
\(784\) 1.36527 0.0487597
\(785\) −18.1124 31.3716i −0.646459 1.11970i
\(786\) 0 0
\(787\) −21.9257 + 37.9765i −0.781567 + 1.35371i 0.149461 + 0.988768i \(0.452246\pi\)
−0.931028 + 0.364947i \(0.881087\pi\)
\(788\) 1.11594 1.93286i 0.0397537 0.0688554i
\(789\) 0 0
\(790\) 4.39626 + 7.61455i 0.156412 + 0.270914i
\(791\) −17.0075 −0.604716
\(792\) 0 0
\(793\) −13.1156 −0.465750
\(794\) 5.54006 + 9.59567i 0.196609 + 0.340537i
\(795\) 0 0
\(796\) 8.23495 14.2633i 0.291880 0.505551i
\(797\) −6.00801 + 10.4062i −0.212815 + 0.368606i −0.952594 0.304243i \(-0.901596\pi\)
0.739780 + 0.672849i \(0.234930\pi\)
\(798\) 0 0
\(799\) −17.6228 30.5235i −0.623448 1.07984i
\(800\) −8.93881 −0.316035
\(801\) 0 0
\(802\) 15.1460 0.534823
\(803\) −3.33692 5.77972i −0.117757 0.203962i
\(804\) 0 0
\(805\) 1.80749 3.13066i 0.0637057 0.110341i
\(806\) −1.96643 + 3.40596i −0.0692646 + 0.119970i
\(807\) 0 0
\(808\) 7.62160 + 13.2010i 0.268127 + 0.464409i
\(809\) −8.02937 −0.282298 −0.141149 0.989988i \(-0.545080\pi\)
−0.141149 + 0.989988i \(0.545080\pi\)
\(810\) 0 0
\(811\) −12.8345 −0.450681 −0.225341 0.974280i \(-0.572349\pi\)
−0.225341 + 0.974280i \(0.572349\pi\)
\(812\) −0.559725 0.969473i −0.0196425 0.0340218i
\(813\) 0 0
\(814\) 1.72438 2.98672i 0.0604396 0.104684i
\(815\) −17.5753 + 30.4414i −0.615637 + 1.06632i
\(816\) 0 0
\(817\) −0.539067 0.933692i −0.0188596 0.0326658i
\(818\) 18.6428 0.651832
\(819\) 0 0
\(820\) −12.6447 −0.441570
\(821\) 14.8327 + 25.6910i 0.517665 + 0.896621i 0.999789 + 0.0205189i \(0.00653183\pi\)
−0.482125 + 0.876103i \(0.660135\pi\)
\(822\) 0 0
\(823\) −24.7704 + 42.9035i −0.863441 + 1.49552i 0.00514683 + 0.999987i \(0.498362\pi\)
−0.868587 + 0.495536i \(0.834972\pi\)
\(824\) 17.6920 30.6434i 0.616329 1.06751i
\(825\) 0 0
\(826\) 3.89731 + 6.75034i 0.135605 + 0.234874i
\(827\) 40.8431 1.42025 0.710126 0.704074i \(-0.248638\pi\)
0.710126 + 0.704074i \(0.248638\pi\)
\(828\) 0 0
\(829\) −9.45276 −0.328308 −0.164154 0.986435i \(-0.552489\pi\)
−0.164154 + 0.986435i \(0.552489\pi\)
\(830\) 7.39993 + 12.8171i 0.256855 + 0.444886i
\(831\) 0 0
\(832\) 17.5033 30.3167i 0.606819 1.05104i
\(833\) −3.16441 + 5.48091i −0.109640 + 0.189902i
\(834\) 0 0
\(835\) −17.3379 30.0302i −0.600004 1.03924i
\(836\) 0.277620 0.00960170
\(837\) 0 0
\(838\) 9.62995 0.332661
\(839\) 6.14344 + 10.6408i 0.212095 + 0.367360i 0.952370 0.304945i \(-0.0986380\pi\)
−0.740275 + 0.672304i \(0.765305\pi\)
\(840\) 0 0
\(841\) 14.3687 24.8874i 0.495474 0.858185i
\(842\) −12.7546 + 22.0917i −0.439554 + 0.761330i
\(843\) 0 0
\(844\) −1.63962 2.83991i −0.0564381 0.0977536i
\(845\) −13.4315 −0.462058
\(846\) 0 0
\(847\) −23.1832 −0.796584
\(848\) −7.51684 13.0196i −0.258129 0.447093i
\(849\) 0 0
\(850\) −6.84087 + 11.8487i −0.234640 + 0.406409i
\(851\) −1.09800 + 1.90178i −0.0376388 + 0.0651923i
\(852\) 0 0
\(853\) 15.4329 + 26.7306i 0.528413 + 0.915239i 0.999451 + 0.0331257i \(0.0105462\pi\)
−0.471038 + 0.882113i \(0.656120\pi\)
\(854\) 7.47562 0.255810
\(855\) 0 0
\(856\) −59.2560 −2.02533
\(857\) −5.57302 9.65275i −0.190371 0.329731i 0.755003 0.655722i \(-0.227636\pi\)
−0.945373 + 0.325990i \(0.894302\pi\)
\(858\) 0 0
\(859\) −2.07434 + 3.59286i −0.0707755 + 0.122587i −0.899241 0.437453i \(-0.855881\pi\)
0.828466 + 0.560040i \(0.189214\pi\)
\(860\) −3.35560 + 5.81208i −0.114425 + 0.198190i
\(861\) 0 0
\(862\) 15.5688 + 26.9659i 0.530275 + 0.918463i
\(863\) −47.2534 −1.60852 −0.804262 0.594275i \(-0.797439\pi\)
−0.804262 + 0.594275i \(0.797439\pi\)
\(864\) 0 0
\(865\) −33.0392 −1.12337
\(866\) −0.353069 0.611534i −0.0119978 0.0207808i
\(867\) 0 0
\(868\) −0.895769 + 1.55152i −0.0304044 + 0.0526619i
\(869\) 2.99564 5.18860i 0.101620 0.176011i
\(870\) 0 0
\(871\) 22.9414 + 39.7356i 0.777338 + 1.34639i
\(872\) −19.2316 −0.651264
\(873\) 0 0
\(874\) 0.221187 0.00748175
\(875\) −14.9241 25.8493i −0.504526 0.873864i
\(876\) 0 0
\(877\) −17.5752 + 30.4412i −0.593473 + 1.02793i 0.400288 + 0.916390i \(0.368910\pi\)
−0.993760 + 0.111536i \(0.964423\pi\)
\(878\) 3.34689 5.79698i 0.112952 0.195638i
\(879\) 0 0
\(880\) 1.56988 + 2.71911i 0.0529206 + 0.0916612i
\(881\) −19.3596 −0.652242 −0.326121 0.945328i \(-0.605742\pi\)
−0.326121 + 0.945328i \(0.605742\pi\)
\(882\) 0 0
\(883\) −13.7860 −0.463937 −0.231969 0.972723i \(-0.574517\pi\)
−0.231969 + 0.972723i \(0.574517\pi\)
\(884\) 13.4318 + 23.2645i 0.451760 + 0.782471i
\(885\) 0 0
\(886\) −8.09401 + 14.0192i −0.271924 + 0.470986i
\(887\) 14.9087 25.8227i 0.500586 0.867041i −0.499414 0.866364i \(-0.666451\pi\)
1.00000 0.000676951i \(-0.000215480\pi\)
\(888\) 0 0
\(889\) −14.7841 25.6067i −0.495842 0.858823i
\(890\) −12.3391 −0.413609
\(891\) 0 0
\(892\) 18.8705 0.631832
\(893\) 0.660555 + 1.14411i 0.0221046 + 0.0382863i
\(894\) 0 0
\(895\) 9.52646 16.5003i 0.318435 0.551545i
\(896\) 1.28383 2.22366i 0.0428897 0.0742872i
\(897\) 0 0
\(898\) 16.8902 + 29.2547i 0.563633 + 0.976241i
\(899\) 0.420156 0.0140130
\(900\) 0 0
\(901\) 69.6897 2.32170
\(902\) −5.39043 9.33650i −0.179482 0.310871i
\(903\) 0 0
\(904\) −10.5303 + 18.2390i −0.350231 + 0.606619i
\(905\) −15.6666 + 27.1353i −0.520775 + 0.902008i
\(906\) 0 0
\(907\) 3.11579 + 5.39670i 0.103458 + 0.179194i 0.913107 0.407720i \(-0.133676\pi\)
−0.809649 + 0.586914i \(0.800343\pi\)
\(908\) 12.7397 0.422781
\(909\) 0 0
\(910\) 20.5914 0.682599
\(911\) 15.8197 + 27.4006i 0.524131 + 0.907822i 0.999605 + 0.0280921i \(0.00894318\pi\)
−0.475474 + 0.879730i \(0.657723\pi\)
\(912\) 0 0
\(913\) 5.04235 8.73361i 0.166877 0.289040i
\(914\) −10.1047 + 17.5018i −0.334233 + 0.578908i
\(915\) 0 0
\(916\) 7.50067 + 12.9915i 0.247829 + 0.429253i
\(917\) −34.6380 −1.14385
\(918\) 0 0
\(919\) 36.0031 1.18763 0.593816 0.804601i \(-0.297621\pi\)
0.593816 + 0.804601i \(0.297621\pi\)
\(920\) −2.23823 3.87674i −0.0737924 0.127812i
\(921\) 0 0
\(922\) 2.75194 4.76650i 0.0906304 0.156976i
\(923\) 0.203514 0.352496i 0.00669873 0.0116025i
\(924\) 0 0
\(925\) 2.54576 + 4.40939i 0.0837042 + 0.144980i
\(926\) 1.78960 0.0588099
\(927\) 0 0
\(928\) −2.34609 −0.0770141
\(929\) −12.7239 22.0384i −0.417456 0.723056i 0.578227 0.815876i \(-0.303745\pi\)
−0.995683 + 0.0928207i \(0.970412\pi\)
\(930\) 0 0
\(931\) 0.118612 0.205441i 0.00388734 0.00673307i
\(932\) 2.48727 4.30808i 0.0814733 0.141116i
\(933\) 0 0
\(934\) −10.3760 17.9717i −0.339513 0.588053i
\(935\) −14.5546 −0.475985
\(936\) 0 0
\(937\) 28.3048 0.924677 0.462338 0.886704i \(-0.347011\pi\)
0.462338 + 0.886704i \(0.347011\pi\)
\(938\) −13.0761 22.6484i −0.426948 0.739496i
\(939\) 0 0
\(940\) 4.11184 7.12192i 0.134114 0.232291i
\(941\) −4.14722 + 7.18320i −0.135196 + 0.234165i −0.925672 0.378327i \(-0.876500\pi\)
0.790477 + 0.612492i \(0.209833\pi\)
\(942\) 0 0
\(943\) 3.43234 + 5.94499i 0.111772 + 0.193595i
\(944\) 4.31074 0.140303
\(945\) 0 0
\(946\) −5.72199 −0.186038
\(947\) 22.2253 + 38.4954i 0.722225 + 1.25093i 0.960106 + 0.279637i \(0.0902140\pi\)
−0.237881 + 0.971294i \(0.576453\pi\)
\(948\) 0 0
\(949\) −12.1030 + 20.9630i −0.392880 + 0.680489i
\(950\) 0.256417 0.444127i 0.00831926 0.0144094i
\(951\) 0 0
\(952\) −24.8909 43.1123i −0.806718 1.39728i
\(953\) −9.67149 −0.313290 −0.156645 0.987655i \(-0.550068\pi\)
−0.156645 + 0.987655i \(0.550068\pi\)
\(954\) 0 0
\(955\) 47.0770 1.52338
\(956\) −2.34283 4.05790i −0.0757726 0.131242i
\(957\) 0 0
\(958\) 15.4213 26.7105i 0.498240 0.862977i
\(959\) −2.77666 + 4.80932i −0.0896631 + 0.155301i
\(960\) 0 0
\(961\) 15.1638 + 26.2645i 0.489155 + 0.847241i
\(962\) −12.5087 −0.403296
\(963\) 0 0
\(964\) 7.90895 0.254730
\(965\) −14.9743 25.9363i −0.482040 0.834919i
\(966\) 0 0
\(967\) 16.5575 28.6785i 0.532455 0.922238i −0.466827 0.884349i \(-0.654603\pi\)
0.999282 0.0378900i \(-0.0120636\pi\)
\(968\) −14.3540 + 24.8619i −0.461355 + 0.799090i
\(969\) 0 0
\(970\) 5.05305 + 8.75214i 0.162244 + 0.281014i
\(971\) −27.4309 −0.880298 −0.440149 0.897925i \(-0.645074\pi\)
−0.440149 + 0.897925i \(0.645074\pi\)
\(972\) 0 0
\(973\) −19.6127 −0.628755
\(974\) 10.8098 + 18.7231i 0.346368 + 0.599928i
\(975\) 0 0
\(976\) 2.06716 3.58043i 0.0661682 0.114607i
\(977\) −18.1888 + 31.5039i −0.581911 + 1.00790i 0.413342 + 0.910576i \(0.364361\pi\)
−0.995253 + 0.0973232i \(0.968972\pi\)
\(978\) 0 0
\(979\) 4.20398 + 7.28150i 0.134360 + 0.232718i
\(980\) −1.47667 −0.0471706
\(981\) 0 0
\(982\) 18.4791 0.589693
\(983\) −21.0686 36.4919i −0.671984 1.16391i −0.977341 0.211673i \(-0.932109\pi\)
0.305356 0.952238i \(-0.401224\pi\)
\(984\) 0 0
\(985\) 2.19292 3.79826i 0.0698724 0.121022i
\(986\) −1.79546 + 3.10983i −0.0571791 + 0.0990371i
\(987\) 0 0
\(988\) −0.503464 0.872026i −0.0160173 0.0277428i
\(989\) 3.64346 0.115855
\(990\) 0 0
\(991\) 25.5409 0.811333 0.405667 0.914021i \(-0.367039\pi\)
0.405667 + 0.914021i \(0.367039\pi\)
\(992\) 1.87731 + 3.25159i 0.0596045 + 0.103238i
\(993\) 0 0
\(994\) −0.115998 + 0.200915i −0.00367924 + 0.00637263i
\(995\) 16.1824 28.0288i 0.513018 0.888573i
\(996\) 0 0
\(997\) −11.7664 20.3801i −0.372647 0.645443i 0.617325 0.786708i \(-0.288216\pi\)
−0.989972 + 0.141265i \(0.954883\pi\)
\(998\) −20.1439 −0.637644
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 729.2.c.e.244.2 12
3.2 odd 2 729.2.c.b.244.5 12
9.2 odd 6 729.2.c.b.487.5 12
9.4 even 3 729.2.a.a.1.5 6
9.5 odd 6 729.2.a.d.1.2 6
9.7 even 3 inner 729.2.c.e.487.2 12
27.2 odd 18 81.2.e.a.10.1 12
27.4 even 9 27.2.e.a.25.2 yes 12
27.5 odd 18 243.2.e.a.55.2 12
27.7 even 9 243.2.e.d.190.1 12
27.11 odd 18 243.2.e.b.109.1 12
27.13 even 9 243.2.e.c.136.2 12
27.14 odd 18 243.2.e.b.136.1 12
27.16 even 9 243.2.e.c.109.2 12
27.20 odd 18 243.2.e.a.190.2 12
27.22 even 9 243.2.e.d.55.1 12
27.23 odd 18 81.2.e.a.73.1 12
27.25 even 9 27.2.e.a.13.2 12
108.31 odd 18 432.2.u.c.241.2 12
108.79 odd 18 432.2.u.c.337.2 12
135.4 even 18 675.2.l.c.376.1 12
135.52 odd 36 675.2.u.b.499.2 24
135.58 odd 36 675.2.u.b.349.2 24
135.79 even 18 675.2.l.c.526.1 12
135.112 odd 36 675.2.u.b.349.3 24
135.133 odd 36 675.2.u.b.499.3 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.2.e.a.13.2 12 27.25 even 9
27.2.e.a.25.2 yes 12 27.4 even 9
81.2.e.a.10.1 12 27.2 odd 18
81.2.e.a.73.1 12 27.23 odd 18
243.2.e.a.55.2 12 27.5 odd 18
243.2.e.a.190.2 12 27.20 odd 18
243.2.e.b.109.1 12 27.11 odd 18
243.2.e.b.136.1 12 27.14 odd 18
243.2.e.c.109.2 12 27.16 even 9
243.2.e.c.136.2 12 27.13 even 9
243.2.e.d.55.1 12 27.22 even 9
243.2.e.d.190.1 12 27.7 even 9
432.2.u.c.241.2 12 108.31 odd 18
432.2.u.c.337.2 12 108.79 odd 18
675.2.l.c.376.1 12 135.4 even 18
675.2.l.c.526.1 12 135.79 even 18
675.2.u.b.349.2 24 135.58 odd 36
675.2.u.b.349.3 24 135.112 odd 36
675.2.u.b.499.2 24 135.52 odd 36
675.2.u.b.499.3 24 135.133 odd 36
729.2.a.a.1.5 6 9.4 even 3
729.2.a.d.1.2 6 9.5 odd 6
729.2.c.b.244.5 12 3.2 odd 2
729.2.c.b.487.5 12 9.2 odd 6
729.2.c.e.244.2 12 1.1 even 1 trivial
729.2.c.e.487.2 12 9.7 even 3 inner