Properties

Label 729.2.e.n.325.2
Level $729$
Weight $2$
Character 729.325
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $12$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [729,2,Mod(82,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.e (of order \(9\), degree \(6\), 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: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\Q(\zeta_{36})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{6} + 1 \) 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 243)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 325.2
Root \(0.642788 - 0.766044i\) of defining polynomial
Character \(\chi\) \(=\) 729.325
Dual form 729.2.e.n.406.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.32683 - 1.11334i) q^{2} +(0.173648 - 0.984808i) q^{4} +(-3.25519 + 1.18479i) q^{5} +(-0.173648 - 0.984808i) q^{7} +(0.866025 + 1.50000i) q^{8} +O(q^{10})\) \(q+(1.32683 - 1.11334i) q^{2} +(0.173648 - 0.984808i) q^{4} +(-3.25519 + 1.18479i) q^{5} +(-0.173648 - 0.984808i) q^{7} +(0.866025 + 1.50000i) q^{8} +(-3.00000 + 5.19615i) q^{10} +(3.25519 + 1.18479i) q^{11} +(3.83022 + 3.21394i) q^{13} +(-1.32683 - 1.11334i) q^{14} +(4.69846 + 1.71010i) q^{16} +(0.500000 + 0.866025i) q^{19} +(0.601535 + 3.41147i) q^{20} +(5.63816 - 2.05212i) q^{22} +(-1.20307 + 6.82295i) q^{23} +(5.36231 - 4.49951i) q^{25} +8.66025 q^{26} -1.00000 q^{28} +(-2.65366 + 2.22668i) q^{29} +(0.868241 - 4.92404i) q^{31} +(4.88279 - 1.77719i) q^{32} +(1.73205 + 3.00000i) q^{35} +(0.500000 - 0.866025i) q^{37} +(1.62760 + 0.592396i) q^{38} +(-4.59627 - 3.85673i) q^{40} +(2.65366 + 2.22668i) q^{41} +(0.939693 + 0.342020i) q^{43} +(1.73205 - 3.00000i) q^{44} +(6.00000 + 10.3923i) q^{46} +(-0.601535 - 3.41147i) q^{47} +(5.63816 - 2.05212i) q^{49} +(2.10537 - 11.9402i) q^{50} +(3.83022 - 3.21394i) q^{52} -10.3923 q^{53} -12.0000 q^{55} +(1.32683 - 1.11334i) q^{56} +(-1.04189 + 5.90885i) q^{58} +(-3.25519 + 1.18479i) q^{59} +(0.347296 + 1.96962i) q^{61} +(-4.33013 - 7.50000i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-16.2760 - 5.92396i) q^{65} +(6.12836 + 5.14230i) q^{67} +(5.63816 + 2.05212i) q^{70} +(-5.19615 + 9.00000i) q^{71} +(-1.00000 - 1.73205i) q^{73} +(-0.300767 - 1.70574i) q^{74} +(0.939693 - 0.342020i) q^{76} +(0.601535 - 3.41147i) q^{77} +(-0.766044 + 0.642788i) q^{79} -17.3205 q^{80} +6.00000 q^{82} +(5.30731 - 4.45336i) q^{83} +(1.62760 - 0.592396i) q^{86} +(1.04189 + 5.90885i) q^{88} +(-5.19615 - 9.00000i) q^{89} +(2.50000 - 4.33013i) q^{91} +(6.51038 + 2.36959i) q^{92} +(-4.59627 - 3.85673i) q^{94} +(-2.65366 - 2.22668i) q^{95} +(-15.9748 - 5.81434i) q^{97} +(5.19615 - 9.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 36 q^{10} + 6 q^{19} - 12 q^{28} + 6 q^{37} + 72 q^{46} - 144 q^{55} - 6 q^{64} - 12 q^{73} + 72 q^{82} + 30 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.32683 1.11334i 0.938209 0.787251i −0.0390637 0.999237i \(-0.512438\pi\)
0.977273 + 0.211986i \(0.0679931\pi\)
\(3\) 0 0
\(4\) 0.173648 0.984808i 0.0868241 0.492404i
\(5\) −3.25519 + 1.18479i −1.45577 + 0.529855i −0.944195 0.329386i \(-0.893158\pi\)
−0.511570 + 0.859241i \(0.670936\pi\)
\(6\) 0 0
\(7\) −0.173648 0.984808i −0.0656328 0.372222i −0.999878 0.0155920i \(-0.995037\pi\)
0.934246 0.356630i \(-0.116074\pi\)
\(8\) 0.866025 + 1.50000i 0.306186 + 0.530330i
\(9\) 0 0
\(10\) −3.00000 + 5.19615i −0.948683 + 1.64317i
\(11\) 3.25519 + 1.18479i 0.981477 + 0.357228i 0.782414 0.622758i \(-0.213988\pi\)
0.199063 + 0.979987i \(0.436210\pi\)
\(12\) 0 0
\(13\) 3.83022 + 3.21394i 1.06231 + 0.891386i 0.994334 0.106301i \(-0.0339006\pi\)
0.0679785 + 0.997687i \(0.478345\pi\)
\(14\) −1.32683 1.11334i −0.354610 0.297553i
\(15\) 0 0
\(16\) 4.69846 + 1.71010i 1.17462 + 0.427525i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0 0
\(19\) 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i \(-0.130073\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 0.601535 + 3.41147i 0.134507 + 0.762829i
\(21\) 0 0
\(22\) 5.63816 2.05212i 1.20206 0.437514i
\(23\) −1.20307 + 6.82295i −0.250857 + 1.42268i 0.555629 + 0.831430i \(0.312478\pi\)
−0.806486 + 0.591253i \(0.798634\pi\)
\(24\) 0 0
\(25\) 5.36231 4.49951i 1.07246 0.899903i
\(26\) 8.66025 1.69842
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) −2.65366 + 2.22668i −0.492772 + 0.413484i −0.855018 0.518598i \(-0.826454\pi\)
0.362247 + 0.932082i \(0.382010\pi\)
\(30\) 0 0
\(31\) 0.868241 4.92404i 0.155941 0.884383i −0.801980 0.597351i \(-0.796220\pi\)
0.957921 0.287033i \(-0.0926689\pi\)
\(32\) 4.88279 1.77719i 0.863163 0.314166i
\(33\) 0 0
\(34\) 0 0
\(35\) 1.73205 + 3.00000i 0.292770 + 0.507093i
\(36\) 0 0
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 1.62760 + 0.592396i 0.264031 + 0.0960994i
\(39\) 0 0
\(40\) −4.59627 3.85673i −0.726734 0.609802i
\(41\) 2.65366 + 2.22668i 0.414431 + 0.347749i 0.826040 0.563611i \(-0.190588\pi\)
−0.411609 + 0.911361i \(0.635033\pi\)
\(42\) 0 0
\(43\) 0.939693 + 0.342020i 0.143302 + 0.0521576i 0.412675 0.910878i \(-0.364594\pi\)
−0.269374 + 0.963036i \(0.586817\pi\)
\(44\) 1.73205 3.00000i 0.261116 0.452267i
\(45\) 0 0
\(46\) 6.00000 + 10.3923i 0.884652 + 1.53226i
\(47\) −0.601535 3.41147i −0.0877429 0.497615i −0.996731 0.0807925i \(-0.974255\pi\)
0.908988 0.416822i \(-0.136856\pi\)
\(48\) 0 0
\(49\) 5.63816 2.05212i 0.805451 0.293160i
\(50\) 2.10537 11.9402i 0.297745 1.68859i
\(51\) 0 0
\(52\) 3.83022 3.21394i 0.531156 0.445693i
\(53\) −10.3923 −1.42749 −0.713746 0.700404i \(-0.753003\pi\)
−0.713746 + 0.700404i \(0.753003\pi\)
\(54\) 0 0
\(55\) −12.0000 −1.61808
\(56\) 1.32683 1.11334i 0.177305 0.148776i
\(57\) 0 0
\(58\) −1.04189 + 5.90885i −0.136807 + 0.775870i
\(59\) −3.25519 + 1.18479i −0.423790 + 0.154247i −0.545106 0.838367i \(-0.683511\pi\)
0.121316 + 0.992614i \(0.461288\pi\)
\(60\) 0 0
\(61\) 0.347296 + 1.96962i 0.0444667 + 0.252183i 0.998936 0.0461272i \(-0.0146880\pi\)
−0.954469 + 0.298311i \(0.903577\pi\)
\(62\) −4.33013 7.50000i −0.549927 0.952501i
\(63\) 0 0
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) −16.2760 5.92396i −2.01878 0.734777i
\(66\) 0 0
\(67\) 6.12836 + 5.14230i 0.748698 + 0.628232i 0.935158 0.354230i \(-0.115257\pi\)
−0.186460 + 0.982462i \(0.559702\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 5.63816 + 2.05212i 0.673889 + 0.245275i
\(71\) −5.19615 + 9.00000i −0.616670 + 1.06810i 0.373419 + 0.927663i \(0.378185\pi\)
−0.990089 + 0.140441i \(0.955148\pi\)
\(72\) 0 0
\(73\) −1.00000 1.73205i −0.117041 0.202721i 0.801553 0.597924i \(-0.204008\pi\)
−0.918594 + 0.395203i \(0.870674\pi\)
\(74\) −0.300767 1.70574i −0.0349635 0.198288i
\(75\) 0 0
\(76\) 0.939693 0.342020i 0.107790 0.0392324i
\(77\) 0.601535 3.41147i 0.0685513 0.388774i
\(78\) 0 0
\(79\) −0.766044 + 0.642788i −0.0861867 + 0.0723193i −0.684863 0.728672i \(-0.740138\pi\)
0.598676 + 0.800991i \(0.295694\pi\)
\(80\) −17.3205 −1.93649
\(81\) 0 0
\(82\) 6.00000 0.662589
\(83\) 5.30731 4.45336i 0.582553 0.488820i −0.303231 0.952917i \(-0.598065\pi\)
0.885784 + 0.464097i \(0.153621\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.62760 0.592396i 0.175508 0.0638797i
\(87\) 0 0
\(88\) 1.04189 + 5.90885i 0.111066 + 0.629885i
\(89\) −5.19615 9.00000i −0.550791 0.953998i −0.998218 0.0596775i \(-0.980993\pi\)
0.447427 0.894321i \(-0.352341\pi\)
\(90\) 0 0
\(91\) 2.50000 4.33013i 0.262071 0.453921i
\(92\) 6.51038 + 2.36959i 0.678754 + 0.247046i
\(93\) 0 0
\(94\) −4.59627 3.85673i −0.474069 0.397791i
\(95\) −2.65366 2.22668i −0.272259 0.228453i
\(96\) 0 0
\(97\) −15.9748 5.81434i −1.62199 0.590357i −0.638232 0.769844i \(-0.720334\pi\)
−0.983760 + 0.179487i \(0.942556\pi\)
\(98\) 5.19615 9.00000i 0.524891 0.909137i
\(99\) 0 0
\(100\) −3.50000 6.06218i −0.350000 0.606218i
\(101\) −2.40614 13.6459i −0.239420 1.35782i −0.833103 0.553118i \(-0.813438\pi\)
0.593683 0.804699i \(-0.297673\pi\)
\(102\) 0 0
\(103\) −7.51754 + 2.73616i −0.740725 + 0.269602i −0.684698 0.728827i \(-0.740066\pi\)
−0.0560277 + 0.998429i \(0.517844\pi\)
\(104\) −1.50384 + 8.52869i −0.147463 + 0.836306i
\(105\) 0 0
\(106\) −13.7888 + 11.5702i −1.33929 + 1.12379i
\(107\) 10.3923 1.00466 0.502331 0.864675i \(-0.332476\pi\)
0.502331 + 0.864675i \(0.332476\pi\)
\(108\) 0 0
\(109\) 17.0000 1.62830 0.814152 0.580651i \(-0.197202\pi\)
0.814152 + 0.580651i \(0.197202\pi\)
\(110\) −15.9219 + 13.3601i −1.51810 + 1.27383i
\(111\) 0 0
\(112\) 0.868241 4.92404i 0.0820411 0.465278i
\(113\) 16.2760 5.92396i 1.53111 0.557280i 0.567219 0.823567i \(-0.308019\pi\)
0.963894 + 0.266287i \(0.0857970\pi\)
\(114\) 0 0
\(115\) −4.16756 23.6354i −0.388627 2.20401i
\(116\) 1.73205 + 3.00000i 0.160817 + 0.278543i
\(117\) 0 0
\(118\) −3.00000 + 5.19615i −0.276172 + 0.478345i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.766044 + 0.642788i 0.0696404 + 0.0584352i
\(122\) 2.65366 + 2.22668i 0.240251 + 0.201594i
\(123\) 0 0
\(124\) −4.69846 1.71010i −0.421934 0.153572i
\(125\) −3.46410 + 6.00000i −0.309839 + 0.536656i
\(126\) 0 0
\(127\) −8.50000 14.7224i −0.754253 1.30640i −0.945745 0.324910i \(-0.894666\pi\)
0.191492 0.981494i \(-0.438667\pi\)
\(128\) 2.10537 + 11.9402i 0.186090 + 1.05537i
\(129\) 0 0
\(130\) −28.1908 + 10.2606i −2.47249 + 0.899915i
\(131\) 0.601535 3.41147i 0.0525564 0.298062i −0.947188 0.320679i \(-0.896089\pi\)
0.999744 + 0.0226174i \(0.00719995\pi\)
\(132\) 0 0
\(133\) 0.766044 0.642788i 0.0664245 0.0557368i
\(134\) 13.8564 1.19701
\(135\) 0 0
\(136\) 0 0
\(137\) 5.30731 4.45336i 0.453434 0.380476i −0.387274 0.921965i \(-0.626583\pi\)
0.840708 + 0.541488i \(0.182139\pi\)
\(138\) 0 0
\(139\) −2.25743 + 12.8025i −0.191472 + 1.08589i 0.725881 + 0.687820i \(0.241432\pi\)
−0.917353 + 0.398074i \(0.869679\pi\)
\(140\) 3.25519 1.18479i 0.275114 0.100133i
\(141\) 0 0
\(142\) 3.12567 + 17.7265i 0.262300 + 1.48758i
\(143\) 8.66025 + 15.0000i 0.724207 + 1.25436i
\(144\) 0 0
\(145\) 6.00000 10.3923i 0.498273 0.863034i
\(146\) −3.25519 1.18479i −0.269402 0.0980541i
\(147\) 0 0
\(148\) −0.766044 0.642788i −0.0629685 0.0528368i
\(149\) −5.30731 4.45336i −0.434792 0.364834i 0.398964 0.916966i \(-0.369370\pi\)
−0.833756 + 0.552133i \(0.813814\pi\)
\(150\) 0 0
\(151\) 15.0351 + 5.47232i 1.22354 + 0.445331i 0.871380 0.490609i \(-0.163226\pi\)
0.352158 + 0.935941i \(0.385448\pi\)
\(152\) −0.866025 + 1.50000i −0.0702439 + 0.121666i
\(153\) 0 0
\(154\) −3.00000 5.19615i −0.241747 0.418718i
\(155\) 3.00767 + 17.0574i 0.241582 + 1.37008i
\(156\) 0 0
\(157\) 12.2160 4.44626i 0.974943 0.354850i 0.195071 0.980789i \(-0.437506\pi\)
0.779872 + 0.625939i \(0.215284\pi\)
\(158\) −0.300767 + 1.70574i −0.0239278 + 0.135701i
\(159\) 0 0
\(160\) −13.7888 + 11.5702i −1.09010 + 0.914703i
\(161\) 6.92820 0.546019
\(162\) 0 0
\(163\) −1.00000 −0.0783260 −0.0391630 0.999233i \(-0.512469\pi\)
−0.0391630 + 0.999233i \(0.512469\pi\)
\(164\) 2.65366 2.22668i 0.207216 0.173875i
\(165\) 0 0
\(166\) 2.08378 11.8177i 0.161733 0.917231i
\(167\) −22.7863 + 8.29355i −1.76326 + 0.641774i −0.999991 0.00430705i \(-0.998629\pi\)
−0.763269 + 0.646081i \(0.776407\pi\)
\(168\) 0 0
\(169\) 2.08378 + 11.8177i 0.160291 + 0.909053i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.500000 0.866025i 0.0381246 0.0660338i
\(173\) 13.0208 + 4.73917i 0.989950 + 0.360312i 0.785701 0.618606i \(-0.212302\pi\)
0.204249 + 0.978919i \(0.434525\pi\)
\(174\) 0 0
\(175\) −5.36231 4.49951i −0.405353 0.340131i
\(176\) 13.2683 + 11.1334i 1.00013 + 0.839212i
\(177\) 0 0
\(178\) −16.9145 6.15636i −1.26779 0.461439i
\(179\) 10.3923 18.0000i 0.776757 1.34538i −0.157044 0.987592i \(-0.550196\pi\)
0.933801 0.357792i \(-0.116470\pi\)
\(180\) 0 0
\(181\) −8.50000 14.7224i −0.631800 1.09431i −0.987184 0.159589i \(-0.948983\pi\)
0.355383 0.934721i \(-0.384350\pi\)
\(182\) −1.50384 8.52869i −0.111472 0.632188i
\(183\) 0 0
\(184\) −11.2763 + 4.10424i −0.831301 + 0.302569i
\(185\) −0.601535 + 3.41147i −0.0442257 + 0.250817i
\(186\) 0 0
\(187\) 0 0
\(188\) −3.46410 −0.252646
\(189\) 0 0
\(190\) −6.00000 −0.435286
\(191\) 5.30731 4.45336i 0.384024 0.322234i −0.430256 0.902707i \(-0.641577\pi\)
0.814280 + 0.580473i \(0.197132\pi\)
\(192\) 0 0
\(193\) −1.73648 + 9.84808i −0.124995 + 0.708880i 0.856316 + 0.516452i \(0.172747\pi\)
−0.981311 + 0.192428i \(0.938364\pi\)
\(194\) −27.6691 + 10.0707i −1.98653 + 0.723037i
\(195\) 0 0
\(196\) −1.04189 5.90885i −0.0744206 0.422060i
\(197\) 5.19615 + 9.00000i 0.370211 + 0.641223i 0.989598 0.143862i \(-0.0459522\pi\)
−0.619387 + 0.785086i \(0.712619\pi\)
\(198\) 0 0
\(199\) 9.50000 16.4545i 0.673437 1.16643i −0.303486 0.952836i \(-0.598151\pi\)
0.976923 0.213591i \(-0.0685161\pi\)
\(200\) 11.3932 + 4.14677i 0.805619 + 0.293221i
\(201\) 0 0
\(202\) −18.3851 15.4269i −1.29357 1.08543i
\(203\) 2.65366 + 2.22668i 0.186250 + 0.156282i
\(204\) 0 0
\(205\) −11.2763 4.10424i −0.787572 0.286653i
\(206\) −6.92820 + 12.0000i −0.482711 + 0.836080i
\(207\) 0 0
\(208\) 12.5000 + 21.6506i 0.866719 + 1.50120i
\(209\) 0.601535 + 3.41147i 0.0416090 + 0.235977i
\(210\) 0 0
\(211\) −4.69846 + 1.71010i −0.323456 + 0.117728i −0.498644 0.866807i \(-0.666169\pi\)
0.175189 + 0.984535i \(0.443946\pi\)
\(212\) −1.80460 + 10.2344i −0.123941 + 0.702903i
\(213\) 0 0
\(214\) 13.7888 11.5702i 0.942583 0.790921i
\(215\) −3.46410 −0.236250
\(216\) 0 0
\(217\) −5.00000 −0.339422
\(218\) 22.5561 18.9268i 1.52769 1.28188i
\(219\) 0 0
\(220\) −2.08378 + 11.8177i −0.140488 + 0.796749i
\(221\) 0 0
\(222\) 0 0
\(223\) −3.29932 18.7113i −0.220938 1.25300i −0.870299 0.492524i \(-0.836074\pi\)
0.649360 0.760481i \(-0.275037\pi\)
\(224\) −2.59808 4.50000i −0.173591 0.300669i
\(225\) 0 0
\(226\) 15.0000 25.9808i 0.997785 1.72821i
\(227\) 13.0208 + 4.73917i 0.864218 + 0.314550i 0.735824 0.677173i \(-0.236795\pi\)
0.128395 + 0.991723i \(0.459018\pi\)
\(228\) 0 0
\(229\) 3.83022 + 3.21394i 0.253108 + 0.212383i 0.760509 0.649327i \(-0.224949\pi\)
−0.507401 + 0.861710i \(0.669394\pi\)
\(230\) −31.8439 26.7202i −2.09972 1.76188i
\(231\) 0 0
\(232\) −5.63816 2.05212i −0.370163 0.134728i
\(233\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(234\) 0 0
\(235\) 6.00000 + 10.3923i 0.391397 + 0.677919i
\(236\) 0.601535 + 3.41147i 0.0391566 + 0.222068i
\(237\) 0 0
\(238\) 0 0
\(239\) −1.20307 + 6.82295i −0.0778201 + 0.441340i 0.920856 + 0.389903i \(0.127491\pi\)
−0.998676 + 0.0514372i \(0.983620\pi\)
\(240\) 0 0
\(241\) −14.5548 + 12.2130i −0.937560 + 0.786706i −0.977159 0.212509i \(-0.931836\pi\)
0.0395991 + 0.999216i \(0.487392\pi\)
\(242\) 1.73205 0.111340
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) −15.9219 + 13.3601i −1.01722 + 0.853545i
\(246\) 0 0
\(247\) −0.868241 + 4.92404i −0.0552448 + 0.313309i
\(248\) 8.13798 2.96198i 0.516762 0.188086i
\(249\) 0 0
\(250\) 2.08378 + 11.8177i 0.131790 + 0.747417i
\(251\) −10.3923 18.0000i −0.655956 1.13615i −0.981653 0.190676i \(-0.938932\pi\)
0.325697 0.945474i \(-0.394401\pi\)
\(252\) 0 0
\(253\) −12.0000 + 20.7846i −0.754434 + 1.30672i
\(254\) −27.6691 10.0707i −1.73612 0.631894i
\(255\) 0 0
\(256\) 14.5548 + 12.2130i 0.909678 + 0.763310i
\(257\) 2.65366 + 2.22668i 0.165531 + 0.138897i 0.721790 0.692112i \(-0.243320\pi\)
−0.556260 + 0.831009i \(0.687764\pi\)
\(258\) 0 0
\(259\) −0.939693 0.342020i −0.0583897 0.0212521i
\(260\) −8.66025 + 15.0000i −0.537086 + 0.930261i
\(261\) 0 0
\(262\) −3.00000 5.19615i −0.185341 0.321019i
\(263\) −2.40614 13.6459i −0.148369 0.841442i −0.964600 0.263717i \(-0.915052\pi\)
0.816231 0.577725i \(-0.196060\pi\)
\(264\) 0 0
\(265\) 33.8289 12.3127i 2.07809 0.756365i
\(266\) 0.300767 1.70574i 0.0184412 0.104585i
\(267\) 0 0
\(268\) 6.12836 5.14230i 0.374349 0.314116i
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 2.08378 11.8177i 0.125886 0.713933i
\(275\) 22.7863 8.29355i 1.37407 0.500120i
\(276\) 0 0
\(277\) 2.95202 + 16.7417i 0.177370 + 1.00591i 0.935373 + 0.353663i \(0.115064\pi\)
−0.758003 + 0.652251i \(0.773825\pi\)
\(278\) 11.2583 + 19.5000i 0.675230 + 1.16953i
\(279\) 0 0
\(280\) −3.00000 + 5.19615i −0.179284 + 0.310530i
\(281\) 13.0208 + 4.73917i 0.776754 + 0.282715i 0.699818 0.714321i \(-0.253264\pi\)
0.0769353 + 0.997036i \(0.475487\pi\)
\(282\) 0 0
\(283\) −9.95858 8.35624i −0.591976 0.496727i 0.296879 0.954915i \(-0.404054\pi\)
−0.888855 + 0.458188i \(0.848499\pi\)
\(284\) 7.96097 + 6.68004i 0.472397 + 0.396388i
\(285\) 0 0
\(286\) 28.1908 + 10.2606i 1.66696 + 0.606722i
\(287\) 1.73205 3.00000i 0.102240 0.177084i
\(288\) 0 0
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) −3.60921 20.4688i −0.211940 1.20197i
\(291\) 0 0
\(292\) −1.87939 + 0.684040i −0.109983 + 0.0400304i
\(293\) 2.40614 13.6459i 0.140568 0.797202i −0.830251 0.557390i \(-0.811803\pi\)
0.970819 0.239812i \(-0.0770859\pi\)
\(294\) 0 0
\(295\) 9.19253 7.71345i 0.535210 0.449094i
\(296\) 1.73205 0.100673
\(297\) 0 0
\(298\) −12.0000 −0.695141
\(299\) −26.5366 + 22.2668i −1.53465 + 1.28772i
\(300\) 0 0
\(301\) 0.173648 0.984808i 0.0100089 0.0567634i
\(302\) 26.0415 9.47834i 1.49852 0.545417i
\(303\) 0 0
\(304\) 0.868241 + 4.92404i 0.0497970 + 0.282413i
\(305\) −3.46410 6.00000i −0.198354 0.343559i
\(306\) 0 0
\(307\) −10.0000 + 17.3205i −0.570730 + 0.988534i 0.425761 + 0.904836i \(0.360006\pi\)
−0.996491 + 0.0836980i \(0.973327\pi\)
\(308\) −3.25519 1.18479i −0.185482 0.0675098i
\(309\) 0 0
\(310\) 22.9813 + 19.2836i 1.30525 + 1.09524i
\(311\) 10.6146 + 8.90673i 0.601900 + 0.505054i 0.892056 0.451925i \(-0.149263\pi\)
−0.290156 + 0.956979i \(0.593707\pi\)
\(312\) 0 0
\(313\) 0.939693 + 0.342020i 0.0531146 + 0.0193321i 0.368441 0.929651i \(-0.379892\pi\)
−0.315326 + 0.948983i \(0.602114\pi\)
\(314\) 11.2583 19.5000i 0.635344 1.10045i
\(315\) 0 0
\(316\) 0.500000 + 0.866025i 0.0281272 + 0.0487177i
\(317\) 4.81228 + 27.2918i 0.270285 + 1.53286i 0.753553 + 0.657387i \(0.228338\pi\)
−0.483268 + 0.875472i \(0.660550\pi\)
\(318\) 0 0
\(319\) −11.2763 + 4.10424i −0.631352 + 0.229793i
\(320\) 0.601535 3.41147i 0.0336268 0.190707i
\(321\) 0 0
\(322\) 9.19253 7.71345i 0.512280 0.429854i
\(323\) 0 0
\(324\) 0 0
\(325\) 35.0000 1.94145
\(326\) −1.32683 + 1.11334i −0.0734862 + 0.0616622i
\(327\) 0 0
\(328\) −1.04189 + 5.90885i −0.0575287 + 0.326261i
\(329\) −3.25519 + 1.18479i −0.179464 + 0.0653197i
\(330\) 0 0
\(331\) −3.29932 18.7113i −0.181347 1.02847i −0.930560 0.366140i \(-0.880679\pi\)
0.749213 0.662329i \(-0.230432\pi\)
\(332\) −3.46410 6.00000i −0.190117 0.329293i
\(333\) 0 0
\(334\) −21.0000 + 36.3731i −1.14907 + 1.99025i
\(335\) −26.0415 9.47834i −1.42280 0.517857i
\(336\) 0 0
\(337\) 3.83022 + 3.21394i 0.208645 + 0.175074i 0.741122 0.671370i \(-0.234294\pi\)
−0.532476 + 0.846445i \(0.678738\pi\)
\(338\) 15.9219 + 13.3601i 0.866039 + 0.726693i
\(339\) 0 0
\(340\) 0 0
\(341\) 8.66025 15.0000i 0.468979 0.812296i
\(342\) 0 0
\(343\) −6.50000 11.2583i −0.350967 0.607893i
\(344\) 0.300767 + 1.70574i 0.0162163 + 0.0919672i
\(345\) 0 0
\(346\) 22.5526 8.20848i 1.21244 0.441291i
\(347\) 4.21074 23.8803i 0.226045 1.28196i −0.634634 0.772813i \(-0.718849\pi\)
0.860678 0.509149i \(-0.170040\pi\)
\(348\) 0 0
\(349\) −0.766044 + 0.642788i −0.0410054 + 0.0344076i −0.663060 0.748566i \(-0.730743\pi\)
0.622055 + 0.782974i \(0.286298\pi\)
\(350\) −12.1244 −0.648074
\(351\) 0 0
\(352\) 18.0000 0.959403
\(353\) 13.2683 11.1334i 0.706199 0.592572i −0.217331 0.976098i \(-0.569735\pi\)
0.923530 + 0.383527i \(0.125291\pi\)
\(354\) 0 0
\(355\) 6.25133 35.4531i 0.331786 1.88165i
\(356\) −9.76557 + 3.55438i −0.517574 + 0.188382i
\(357\) 0 0
\(358\) −6.25133 35.4531i −0.330393 1.87375i
\(359\) −15.5885 27.0000i −0.822727 1.42501i −0.903644 0.428285i \(-0.859118\pi\)
0.0809166 0.996721i \(-0.474215\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) −27.6691 10.0707i −1.45426 0.529306i
\(363\) 0 0
\(364\) −3.83022 3.21394i −0.200758 0.168456i
\(365\) 5.30731 + 4.45336i 0.277797 + 0.233100i
\(366\) 0 0
\(367\) 15.0351 + 5.47232i 0.784825 + 0.285653i 0.703183 0.711009i \(-0.251761\pi\)
0.0816418 + 0.996662i \(0.473984\pi\)
\(368\) −17.3205 + 30.0000i −0.902894 + 1.56386i
\(369\) 0 0
\(370\) 3.00000 + 5.19615i 0.155963 + 0.270135i
\(371\) 1.80460 + 10.2344i 0.0936904 + 0.531345i
\(372\) 0 0
\(373\) −21.6129 + 7.86646i −1.11908 + 0.407310i −0.834315 0.551289i \(-0.814136\pi\)
−0.284761 + 0.958599i \(0.591914\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 4.59627 3.85673i 0.237034 0.198895i
\(377\) −17.3205 −0.892052
\(378\) 0 0
\(379\) −19.0000 −0.975964 −0.487982 0.872854i \(-0.662267\pi\)
−0.487982 + 0.872854i \(0.662267\pi\)
\(380\) −2.65366 + 2.22668i −0.136130 + 0.114226i
\(381\) 0 0
\(382\) 2.08378 11.8177i 0.106615 0.604646i
\(383\) 16.2760 5.92396i 0.831662 0.302700i 0.109121 0.994028i \(-0.465196\pi\)
0.722541 + 0.691328i \(0.242974\pi\)
\(384\) 0 0
\(385\) 2.08378 + 11.8177i 0.106199 + 0.602285i
\(386\) 8.66025 + 15.0000i 0.440795 + 0.763480i
\(387\) 0 0
\(388\) −8.50000 + 14.7224i −0.431522 + 0.747418i
\(389\) −6.51038 2.36959i −0.330089 0.120143i 0.171659 0.985156i \(-0.445087\pi\)
−0.501748 + 0.865014i \(0.667310\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 7.96097 + 6.68004i 0.402090 + 0.337393i
\(393\) 0 0
\(394\) 16.9145 + 6.15636i 0.852139 + 0.310153i
\(395\) 1.73205 3.00000i 0.0871489 0.150946i
\(396\) 0 0
\(397\) 0.500000 + 0.866025i 0.0250943 + 0.0434646i 0.878300 0.478110i \(-0.158678\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) −5.71458 32.4090i −0.286446 1.62452i
\(399\) 0 0
\(400\) 32.8892 11.9707i 1.64446 0.598535i
\(401\) 0.601535 3.41147i 0.0300392 0.170361i −0.966097 0.258178i \(-0.916878\pi\)
0.996137 + 0.0878170i \(0.0279891\pi\)
\(402\) 0 0
\(403\) 19.1511 16.0697i 0.953985 0.800488i
\(404\) −13.8564 −0.689382
\(405\) 0 0
\(406\) 6.00000 0.297775
\(407\) 2.65366 2.22668i 0.131537 0.110373i
\(408\) 0 0
\(409\) 0.868241 4.92404i 0.0429317 0.243478i −0.955788 0.294055i \(-0.904995\pi\)
0.998720 + 0.0505773i \(0.0161061\pi\)
\(410\) −19.5311 + 7.10876i −0.964574 + 0.351076i
\(411\) 0 0
\(412\) 1.38919 + 7.87846i 0.0684403 + 0.388144i
\(413\) 1.73205 + 3.00000i 0.0852286 + 0.147620i
\(414\) 0 0
\(415\) −12.0000 + 20.7846i −0.589057 + 1.02028i
\(416\) 24.4139 + 8.88594i 1.19699 + 0.435669i
\(417\) 0 0
\(418\) 4.59627 + 3.85673i 0.224811 + 0.188639i
\(419\) −29.1902 24.4935i −1.42604 1.19659i −0.948010 0.318239i \(-0.896908\pi\)
−0.478025 0.878346i \(-0.658647\pi\)
\(420\) 0 0
\(421\) 17.8542 + 6.49838i 0.870159 + 0.316712i 0.738231 0.674548i \(-0.235661\pi\)
0.131927 + 0.991259i \(0.457883\pi\)
\(422\) −4.33013 + 7.50000i −0.210787 + 0.365094i
\(423\) 0 0
\(424\) −9.00000 15.5885i −0.437079 0.757042i
\(425\) 0 0
\(426\) 0 0
\(427\) 1.87939 0.684040i 0.0909498 0.0331030i
\(428\) 1.80460 10.2344i 0.0872289 0.494699i
\(429\) 0 0
\(430\) −4.59627 + 3.85673i −0.221652 + 0.185988i
\(431\) −20.7846 −1.00116 −0.500580 0.865690i \(-0.666880\pi\)
−0.500580 + 0.865690i \(0.666880\pi\)
\(432\) 0 0
\(433\) −1.00000 −0.0480569 −0.0240285 0.999711i \(-0.507649\pi\)
−0.0240285 + 0.999711i \(0.507649\pi\)
\(434\) −6.63414 + 5.56670i −0.318449 + 0.267210i
\(435\) 0 0
\(436\) 2.95202 16.7417i 0.141376 0.801784i
\(437\) −6.51038 + 2.36959i −0.311434 + 0.113353i
\(438\) 0 0
\(439\) 3.47296 + 19.6962i 0.165756 + 0.940046i 0.948282 + 0.317429i \(0.102820\pi\)
−0.782527 + 0.622617i \(0.786069\pi\)
\(440\) −10.3923 18.0000i −0.495434 0.858116i
\(441\) 0 0
\(442\) 0 0
\(443\) 13.0208 + 4.73917i 0.618635 + 0.225165i 0.632277 0.774742i \(-0.282120\pi\)
−0.0136422 + 0.999907i \(0.504343\pi\)
\(444\) 0 0
\(445\) 27.5776 + 23.1404i 1.30730 + 1.09696i
\(446\) −25.2097 21.1535i −1.19372 1.00165i
\(447\) 0 0
\(448\) 0.939693 + 0.342020i 0.0443963 + 0.0161589i
\(449\) 5.19615 9.00000i 0.245222 0.424736i −0.716972 0.697102i \(-0.754473\pi\)
0.962194 + 0.272365i \(0.0878059\pi\)
\(450\) 0 0
\(451\) 6.00000 + 10.3923i 0.282529 + 0.489355i
\(452\) −3.00767 17.0574i −0.141469 0.802311i
\(453\) 0 0
\(454\) 22.5526 8.20848i 1.05845 0.385243i
\(455\) −3.00767 + 17.0574i −0.141002 + 0.799662i
\(456\) 0 0
\(457\) 13.0228 10.9274i 0.609179 0.511162i −0.285202 0.958467i \(-0.592061\pi\)
0.894381 + 0.447306i \(0.147616\pi\)
\(458\) 8.66025 0.404667
\(459\) 0 0
\(460\) −24.0000 −1.11901
\(461\) 21.2292 17.8135i 0.988745 0.829655i 0.00335908 0.999994i \(-0.498931\pi\)
0.985385 + 0.170339i \(0.0544863\pi\)
\(462\) 0 0
\(463\) −5.38309 + 30.5290i −0.250174 + 1.41880i 0.557990 + 0.829847i \(0.311573\pi\)
−0.808164 + 0.588957i \(0.799539\pi\)
\(464\) −16.2760 + 5.92396i −0.755592 + 0.275013i
\(465\) 0 0
\(466\) 0 0
\(467\) 5.19615 + 9.00000i 0.240449 + 0.416470i 0.960842 0.277096i \(-0.0893719\pi\)
−0.720393 + 0.693566i \(0.756039\pi\)
\(468\) 0 0
\(469\) 4.00000 6.92820i 0.184703 0.319915i
\(470\) 19.5311 + 7.10876i 0.900905 + 0.327902i
\(471\) 0 0
\(472\) −4.59627 3.85673i −0.211560 0.177520i
\(473\) 2.65366 + 2.22668i 0.122015 + 0.102383i
\(474\) 0 0
\(475\) 6.57785 + 2.39414i 0.301812 + 0.109851i
\(476\) 0 0
\(477\) 0 0
\(478\) 6.00000 + 10.3923i 0.274434 + 0.475333i
\(479\) −2.40614 13.6459i −0.109939 0.623497i −0.989132 0.147030i \(-0.953028\pi\)
0.879193 0.476466i \(-0.158083\pi\)
\(480\) 0 0
\(481\) 4.69846 1.71010i 0.214231 0.0779739i
\(482\) −5.71458 + 32.4090i −0.260292 + 1.47619i
\(483\) 0 0
\(484\) 0.766044 0.642788i 0.0348202 0.0292176i
\(485\) 58.8897 2.67404
\(486\) 0 0
\(487\) −19.0000 −0.860972 −0.430486 0.902597i \(-0.641658\pi\)
−0.430486 + 0.902597i \(0.641658\pi\)
\(488\) −2.65366 + 2.22668i −0.120125 + 0.100797i
\(489\) 0 0
\(490\) −6.25133 + 35.4531i −0.282407 + 1.60161i
\(491\) 35.8071 13.0327i 1.61595 0.588158i 0.633347 0.773868i \(-0.281681\pi\)
0.982605 + 0.185710i \(0.0594584\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 4.33013 + 7.50000i 0.194822 + 0.337441i
\(495\) 0 0
\(496\) 12.5000 21.6506i 0.561267 0.972142i
\(497\) 9.76557 + 3.55438i 0.438046 + 0.159436i
\(498\) 0 0
\(499\) −21.4492 17.9981i −0.960200 0.805704i 0.0207856 0.999784i \(-0.493383\pi\)
−0.980986 + 0.194080i \(0.937828\pi\)
\(500\) 5.30731 + 4.45336i 0.237350 + 0.199160i
\(501\) 0 0
\(502\) −33.8289 12.3127i −1.50986 0.549544i
\(503\) −20.7846 + 36.0000i −0.926740 + 1.60516i −0.138001 + 0.990432i \(0.544068\pi\)
−0.788739 + 0.614729i \(0.789266\pi\)
\(504\) 0 0
\(505\) 24.0000 + 41.5692i 1.06799 + 1.84981i
\(506\) 7.21842 + 40.9377i 0.320898 + 1.81990i
\(507\) 0 0
\(508\) −15.9748 + 5.81434i −0.708766 + 0.257970i
\(509\) −4.81228 + 27.2918i −0.213301 + 1.20969i 0.670531 + 0.741882i \(0.266066\pi\)
−0.883831 + 0.467806i \(0.845045\pi\)
\(510\) 0 0
\(511\) −1.53209 + 1.28558i −0.0677756 + 0.0568705i
\(512\) 8.66025 0.382733
\(513\) 0 0
\(514\) 6.00000 0.264649
\(515\) 21.2292 17.8135i 0.935472 0.784955i
\(516\) 0 0
\(517\) 2.08378 11.8177i 0.0916445 0.519742i
\(518\) −1.62760 + 0.592396i −0.0715124 + 0.0260284i
\(519\) 0 0
\(520\) −5.20945 29.5442i −0.228449 1.29560i
\(521\) 10.3923 + 18.0000i 0.455295 + 0.788594i 0.998705 0.0508731i \(-0.0162004\pi\)
−0.543410 + 0.839467i \(0.682867\pi\)
\(522\) 0 0
\(523\) −10.0000 + 17.3205i −0.437269 + 0.757373i −0.997478 0.0709788i \(-0.977388\pi\)
0.560208 + 0.828352i \(0.310721\pi\)
\(524\) −3.25519 1.18479i −0.142204 0.0517579i
\(525\) 0 0
\(526\) −18.3851 15.4269i −0.801627 0.672645i
\(527\) 0 0
\(528\) 0 0
\(529\) −23.4923 8.55050i −1.02141 0.371761i
\(530\) 31.1769 54.0000i 1.35424 2.34561i
\(531\) 0 0
\(532\) −0.500000 0.866025i −0.0216777 0.0375470i
\(533\) 3.00767 + 17.0574i 0.130277 + 0.738837i
\(534\) 0 0
\(535\) −33.8289 + 12.3127i −1.46255 + 0.532326i
\(536\) −2.40614 + 13.6459i −0.103929 + 0.589413i
\(537\) 0 0
\(538\) 0 0
\(539\) 20.7846 0.895257
\(540\) 0 0
\(541\) 17.0000 0.730887 0.365444 0.930834i \(-0.380917\pi\)
0.365444 + 0.930834i \(0.380917\pi\)
\(542\) −21.2292 + 17.8135i −0.911874 + 0.765153i
\(543\) 0 0
\(544\) 0 0
\(545\) −55.3382 + 20.1415i −2.37043 + 0.862766i
\(546\) 0 0
\(547\) 3.47296 + 19.6962i 0.148493 + 0.842147i 0.964496 + 0.264098i \(0.0850744\pi\)
−0.816003 + 0.578048i \(0.803815\pi\)
\(548\) −3.46410 6.00000i −0.147979 0.256307i
\(549\) 0 0
\(550\) 21.0000 36.3731i 0.895443 1.55095i
\(551\) −3.25519 1.18479i −0.138676 0.0504739i
\(552\) 0 0
\(553\) 0.766044 + 0.642788i 0.0325755 + 0.0273341i
\(554\) 22.5561 + 18.9268i 0.958316 + 0.804122i
\(555\) 0 0
\(556\) 12.2160 + 4.44626i 0.518074 + 0.188564i
\(557\) −5.19615 + 9.00000i −0.220168 + 0.381342i −0.954859 0.297060i \(-0.903994\pi\)
0.734691 + 0.678402i \(0.237327\pi\)
\(558\) 0 0
\(559\) 2.50000 + 4.33013i 0.105739 + 0.183145i
\(560\) 3.00767 + 17.0574i 0.127097 + 0.720805i
\(561\) 0 0
\(562\) 22.5526 8.20848i 0.951325 0.346254i
\(563\) 6.01535 34.1147i 0.253517 1.43776i −0.546335 0.837567i \(-0.683977\pi\)
0.799851 0.600198i \(-0.204912\pi\)
\(564\) 0 0
\(565\) −45.9627 + 38.5673i −1.93366 + 1.62254i
\(566\) −22.5167 −0.946446
\(567\) 0 0
\(568\) −18.0000 −0.755263
\(569\) −18.5756 + 15.5868i −0.778729 + 0.653431i −0.942928 0.332996i \(-0.891941\pi\)
0.164199 + 0.986427i \(0.447496\pi\)
\(570\) 0 0
\(571\) 7.11958 40.3771i 0.297945 1.68973i −0.357041 0.934089i \(-0.616214\pi\)
0.654986 0.755641i \(-0.272675\pi\)
\(572\) 16.2760 5.92396i 0.680532 0.247693i
\(573\) 0 0
\(574\) −1.04189 5.90885i −0.0434876 0.246630i
\(575\) 24.2487 + 42.0000i 1.01124 + 1.75152i
\(576\) 0 0
\(577\) 17.0000 29.4449i 0.707719 1.22581i −0.257982 0.966150i \(-0.583058\pi\)
0.965701 0.259656i \(-0.0836092\pi\)
\(578\) 27.6691 + 10.0707i 1.15088 + 0.418887i
\(579\) 0 0
\(580\) −9.19253 7.71345i −0.381699 0.320284i
\(581\) −5.30731 4.45336i −0.220184 0.184757i
\(582\) 0 0
\(583\) −33.8289 12.3127i −1.40105 0.509941i
\(584\) 1.73205 3.00000i 0.0716728 0.124141i
\(585\) 0 0
\(586\) −12.0000 20.7846i −0.495715 0.858604i
\(587\) 1.20307 + 6.82295i 0.0496560 + 0.281613i 0.999518 0.0310575i \(-0.00988749\pi\)
−0.949862 + 0.312671i \(0.898776\pi\)
\(588\) 0 0
\(589\) 4.69846 1.71010i 0.193597 0.0704635i
\(590\) 3.60921 20.4688i 0.148589 0.842689i
\(591\) 0 0
\(592\) 3.83022 3.21394i 0.157421 0.132092i
\(593\) 20.7846 0.853522 0.426761 0.904365i \(-0.359655\pi\)
0.426761 + 0.904365i \(0.359655\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −5.30731 + 4.45336i −0.217396 + 0.182417i
\(597\) 0 0
\(598\) −10.4189 + 59.0885i −0.426060 + 2.41631i
\(599\) −22.7863 + 8.29355i −0.931024 + 0.338865i −0.762616 0.646852i \(-0.776085\pi\)
−0.168409 + 0.985717i \(0.553863\pi\)
\(600\) 0 0
\(601\) 6.07769 + 34.4683i 0.247914 + 1.40599i 0.813627 + 0.581388i \(0.197490\pi\)
−0.565713 + 0.824602i \(0.691399\pi\)
\(602\) −0.866025 1.50000i −0.0352966 0.0611354i
\(603\) 0 0
\(604\) 8.00000 13.8564i 0.325515 0.563809i
\(605\) −3.25519 1.18479i −0.132342 0.0481687i
\(606\) 0 0
\(607\) −9.95858 8.35624i −0.404206 0.339169i 0.417911 0.908488i \(-0.362763\pi\)
−0.822117 + 0.569319i \(0.807207\pi\)
\(608\) 3.98048 + 3.34002i 0.161430 + 0.135456i
\(609\) 0 0
\(610\) −11.2763 4.10424i −0.456565 0.166176i
\(611\) 8.66025 15.0000i 0.350356 0.606835i
\(612\) 0 0
\(613\) −1.00000 1.73205i −0.0403896 0.0699569i 0.845124 0.534570i \(-0.179527\pi\)
−0.885514 + 0.464614i \(0.846193\pi\)
\(614\) 6.01535 + 34.1147i 0.242760 + 1.37676i
\(615\) 0 0
\(616\) 5.63816 2.05212i 0.227168 0.0826823i
\(617\) −1.20307 + 6.82295i −0.0484338 + 0.274682i −0.999401 0.0346105i \(-0.988981\pi\)
0.950967 + 0.309292i \(0.100092\pi\)
\(618\) 0 0
\(619\) 15.3209 12.8558i 0.615799 0.516716i −0.280681 0.959801i \(-0.590560\pi\)
0.896480 + 0.443085i \(0.146116\pi\)
\(620\) 17.3205 0.695608
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) −7.96097 + 6.68004i −0.318949 + 0.267630i
\(624\) 0 0
\(625\) −1.91013 + 10.8329i −0.0764052 + 0.433315i
\(626\) 1.62760 0.592396i 0.0650518 0.0236769i
\(627\) 0 0
\(628\) −2.25743 12.8025i −0.0900811 0.510875i
\(629\) 0 0
\(630\) 0 0
\(631\) −8.50000 + 14.7224i −0.338380 + 0.586091i −0.984128 0.177459i \(-0.943212\pi\)
0.645748 + 0.763550i \(0.276545\pi\)
\(632\) −1.62760 0.592396i −0.0647423 0.0235643i
\(633\) 0 0
\(634\) 36.7701 + 30.8538i 1.46033 + 1.22536i
\(635\) 45.1121 + 37.8536i 1.79022 + 1.50217i
\(636\) 0 0
\(637\) 28.1908 + 10.2606i 1.11696 + 0.406540i
\(638\) −10.3923 + 18.0000i −0.411435 + 0.712627i
\(639\) 0 0
\(640\) −21.0000 36.3731i −0.830098 1.43777i
\(641\) −7.81995 44.3492i −0.308870 1.75169i −0.604707 0.796448i \(-0.706710\pi\)
0.295837 0.955238i \(-0.404401\pi\)
\(642\) 0 0
\(643\) −41.3465 + 15.0489i −1.63055 + 0.593470i −0.985350 0.170547i \(-0.945447\pi\)
−0.645196 + 0.764017i \(0.723224\pi\)
\(644\) 1.20307 6.82295i 0.0474076 0.268862i
\(645\) 0 0
\(646\) 0 0
\(647\) −20.7846 −0.817127 −0.408564 0.912730i \(-0.633970\pi\)
−0.408564 + 0.912730i \(0.633970\pi\)
\(648\) 0 0
\(649\) −12.0000 −0.471041
\(650\) 46.4390 38.9669i 1.82149 1.52841i
\(651\) 0 0
\(652\) −0.173648 + 0.984808i −0.00680059 + 0.0385680i
\(653\) 16.2760 5.92396i 0.636927 0.231823i −0.00331633 0.999995i \(-0.501056\pi\)
0.640244 + 0.768172i \(0.278833\pi\)
\(654\) 0 0
\(655\) 2.08378 + 11.8177i 0.0814199 + 0.461755i
\(656\) 8.66025 + 15.0000i 0.338126 + 0.585652i
\(657\) 0 0
\(658\) −3.00000 + 5.19615i −0.116952 + 0.202567i
\(659\) −26.0415 9.47834i −1.01443 0.369224i −0.219300 0.975658i \(-0.570377\pi\)
−0.795134 + 0.606434i \(0.792600\pi\)
\(660\) 0 0
\(661\) −7.66044 6.42788i −0.297957 0.250015i 0.481536 0.876426i \(-0.340079\pi\)
−0.779493 + 0.626411i \(0.784523\pi\)
\(662\) −25.2097 21.1535i −0.979804 0.822153i
\(663\) 0 0
\(664\) 11.2763 + 4.10424i 0.437606 + 0.159275i
\(665\) −1.73205 + 3.00000i −0.0671660 + 0.116335i
\(666\) 0 0
\(667\) −12.0000 20.7846i −0.464642 0.804783i
\(668\) 4.21074 + 23.8803i 0.162919 + 0.923957i
\(669\) 0 0
\(670\) −45.1052 + 16.4170i −1.74257 + 0.634243i
\(671\) −1.20307 + 6.82295i −0.0464440 + 0.263397i
\(672\) 0 0
\(673\) −28.3436 + 23.7831i −1.09257 + 0.916773i −0.996903 0.0786409i \(-0.974942\pi\)
−0.0956642 + 0.995414i \(0.530497\pi\)
\(674\) 8.66025 0.333581
\(675\) 0 0
\(676\) 12.0000 0.461538
\(677\) 13.2683 11.1334i 0.509941 0.427892i −0.351167 0.936313i \(-0.614215\pi\)
0.861109 + 0.508421i \(0.169771\pi\)
\(678\) 0 0
\(679\) −2.95202 + 16.7417i −0.113288 + 0.642489i
\(680\) 0 0
\(681\) 0 0
\(682\) −5.20945 29.5442i −0.199480 1.13131i
\(683\) −20.7846 36.0000i −0.795301 1.37750i −0.922648 0.385643i \(-0.873979\pi\)
0.127347 0.991858i \(-0.459354\pi\)
\(684\) 0 0
\(685\) −12.0000 + 20.7846i −0.458496 + 0.794139i
\(686\) −21.1587 7.70115i −0.807844 0.294031i
\(687\) 0 0
\(688\) 3.83022 + 3.21394i 0.146026 + 0.122530i
\(689\) −39.8048 33.4002i −1.51644 1.27245i
\(690\) 0 0
\(691\) −15.9748 5.81434i −0.607709 0.221188i 0.0197915 0.999804i \(-0.493700\pi\)
−0.627501 + 0.778616i \(0.715922\pi\)
\(692\) 6.92820 12.0000i 0.263371 0.456172i
\(693\) 0 0
\(694\) −21.0000 36.3731i −0.797149 1.38070i
\(695\) −7.81995 44.3492i −0.296628 1.68226i
\(696\) 0 0
\(697\) 0 0
\(698\) −0.300767 + 1.70574i −0.0113842 + 0.0645631i
\(699\) 0 0
\(700\) −5.36231 + 4.49951i −0.202676 + 0.170066i
\(701\) −41.5692 −1.57005 −0.785024 0.619466i \(-0.787349\pi\)
−0.785024 + 0.619466i \(0.787349\pi\)
\(702\) 0 0
\(703\) 1.00000 0.0377157
\(704\) −2.65366 + 2.22668i −0.100013 + 0.0839212i
\(705\) 0 0
\(706\) 5.20945 29.5442i 0.196060 1.11191i
\(707\) −13.0208 + 4.73917i −0.489696 + 0.178235i
\(708\) 0 0
\(709\) −3.29932 18.7113i −0.123908 0.702719i −0.981950 0.189140i \(-0.939430\pi\)
0.858042 0.513580i \(-0.171681\pi\)
\(710\) −31.1769 54.0000i −1.17005 2.02658i
\(711\) 0 0
\(712\) 9.00000 15.5885i 0.337289 0.584202i
\(713\) 32.5519 + 11.8479i 1.21908 + 0.443708i
\(714\) 0 0
\(715\) −45.9627 38.5673i −1.71891 1.44233i
\(716\) −15.9219 13.3601i −0.595031 0.499290i
\(717\) 0 0
\(718\) −50.7434 18.4691i −1.89373 0.689260i
\(719\) −5.19615 + 9.00000i −0.193784 + 0.335643i −0.946501 0.322700i \(-0.895409\pi\)
0.752717 + 0.658344i \(0.228743\pi\)
\(720\) 0 0
\(721\) 4.00000 + 6.92820i 0.148968 + 0.258020i
\(722\) −5.41381 30.7033i −0.201481 1.14266i
\(723\) 0 0
\(724\) −15.9748 + 5.81434i −0.593698 + 0.216088i
\(725\) −4.21074 + 23.8803i −0.156383 + 0.886893i
\(726\) 0 0
\(727\) −12.2567 + 10.2846i −0.454576 + 0.381435i −0.841131 0.540832i \(-0.818110\pi\)
0.386555 + 0.922267i \(0.373665\pi\)
\(728\) 8.66025 0.320970
\(729\) 0 0
\(730\) 12.0000 0.444140
\(731\) 0 0
\(732\) 0 0
\(733\) 7.11958 40.3771i 0.262968 1.49136i −0.511793 0.859109i \(-0.671019\pi\)
0.774761 0.632254i \(-0.217870\pi\)
\(734\) 26.0415 9.47834i 0.961210 0.349852i
\(735\) 0 0
\(736\) 6.25133 + 35.4531i 0.230427 + 1.30682i
\(737\) 13.8564 + 24.0000i 0.510407 + 0.884051i
\(738\) 0 0
\(739\) 9.50000 16.4545i 0.349463 0.605288i −0.636691 0.771119i \(-0.719697\pi\)
0.986154 + 0.165831i \(0.0530307\pi\)
\(740\) 3.25519 + 1.18479i 0.119663 + 0.0435538i
\(741\) 0 0
\(742\) 13.7888 + 11.5702i 0.506203 + 0.424755i
\(743\) −5.30731 4.45336i −0.194706 0.163378i 0.540223 0.841522i \(-0.318340\pi\)
−0.734929 + 0.678144i \(0.762785\pi\)
\(744\) 0 0
\(745\) 22.5526 + 8.20848i 0.826264 + 0.300736i
\(746\) −19.9186 + 34.5000i −0.729271 + 1.26313i
\(747\) 0 0
\(748\) 0 0
\(749\) −1.80460 10.2344i −0.0659388 0.373958i
\(750\) 0 0
\(751\) −4.69846 + 1.71010i −0.171449 + 0.0624025i −0.426319 0.904573i \(-0.640190\pi\)
0.254869 + 0.966976i \(0.417968\pi\)
\(752\) 3.00767 17.0574i 0.109679 0.622018i
\(753\) 0 0
\(754\) −22.9813 + 19.2836i −0.836931 + 0.702268i
\(755\) −55.4256 −2.01715
\(756\) 0 0
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) −25.2097 + 21.1535i −0.915659 + 0.768329i
\(759\) 0 0
\(760\) 1.04189 5.90885i 0.0377933 0.214336i
\(761\) 26.0415 9.47834i 0.944005 0.343590i 0.176259 0.984344i \(-0.443601\pi\)
0.767746 + 0.640754i \(0.221378\pi\)
\(762\) 0 0
\(763\) −2.95202 16.7417i −0.106870 0.606091i
\(764\) −3.46410 6.00000i −0.125327 0.217072i
\(765\) 0 0
\(766\) 15.0000 25.9808i 0.541972 0.938723i
\(767\) −16.2760 5.92396i −0.587691 0.213902i
\(768\) 0 0
\(769\) −9.95858 8.35624i −0.359115 0.301334i 0.445323 0.895370i \(-0.353089\pi\)
−0.804438 + 0.594037i \(0.797533\pi\)
\(770\) 15.9219 + 13.3601i 0.573787 + 0.481464i
\(771\) 0 0
\(772\) 9.39693 + 3.42020i 0.338203 + 0.123096i
\(773\) −10.3923 + 18.0000i −0.373785 + 0.647415i −0.990144 0.140050i \(-0.955274\pi\)
0.616359 + 0.787465i \(0.288607\pi\)
\(774\) 0 0
\(775\) −17.5000 30.3109i −0.628619 1.08880i
\(776\) −5.11305 28.9975i −0.183548 1.04095i
\(777\) 0 0
\(778\) −11.2763 + 4.10424i −0.404275 + 0.147144i
\(779\) −0.601535 + 3.41147i −0.0215522 + 0.122229i
\(780\) 0 0
\(781\) −27.5776 + 23.1404i −0.986804 + 0.828027i
\(782\) 0 0
\(783\) 0 0
\(784\) 30.0000 1.07143
\(785\) −34.4975 + 28.9469i −1.23127 + 1.03316i
\(786\) 0 0
\(787\) −4.86215 + 27.5746i −0.173317 + 0.982929i 0.766752 + 0.641944i \(0.221872\pi\)
−0.940069 + 0.340985i \(0.889239\pi\)
\(788\) 9.76557 3.55438i 0.347884 0.126619i
\(789\) 0 0
\(790\) −1.04189 5.90885i −0.0370687 0.210227i
\(791\) −8.66025 15.0000i −0.307923 0.533339i
\(792\) 0 0
\(793\) −5.00000 + 8.66025i −0.177555 + 0.307535i
\(794\) 1.62760 + 0.592396i 0.0577612 + 0.0210234i
\(795\) 0 0
\(796\) −14.5548 12.2130i −0.515883 0.432877i
\(797\) 10.6146 + 8.90673i 0.375989 + 0.315492i 0.811125 0.584872i \(-0.198855\pi\)
−0.435136 + 0.900365i \(0.643300\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 18.1865 31.5000i 0.642991 1.11369i
\(801\) 0 0
\(802\) −3.00000 5.19615i −0.105934 0.183483i
\(803\) −1.20307 6.82295i −0.0424554 0.240777i
\(804\) 0 0
\(805\) −22.5526 + 8.20848i −0.794876 + 0.289311i
\(806\) 7.51919 42.6434i 0.264852 1.50205i
\(807\) 0 0
\(808\) 18.3851 15.4269i 0.646784 0.542717i
\(809\) −31.1769 −1.09612 −0.548061 0.836438i \(-0.684634\pi\)
−0.548061 + 0.836438i \(0.684634\pi\)
\(810\) 0 0
\(811\) 35.0000 1.22902 0.614508 0.788911i \(-0.289355\pi\)
0.614508 + 0.788911i \(0.289355\pi\)
\(812\) 2.65366 2.22668i 0.0931251 0.0781412i
\(813\) 0 0
\(814\) 1.04189 5.90885i 0.0365182 0.207105i
\(815\) 3.25519 1.18479i 0.114024 0.0415015i
\(816\) 0 0
\(817\) 0.173648 + 0.984808i 0.00607518 + 0.0344541i
\(818\) −4.33013 7.50000i −0.151399 0.262231i
\(819\) 0 0
\(820\) −6.00000 + 10.3923i −0.209529 + 0.362915i
\(821\) −35.8071 13.0327i −1.24968 0.454845i −0.369384 0.929277i \(-0.620431\pi\)
−0.880292 + 0.474432i \(0.842654\pi\)
\(822\) 0 0
\(823\) 17.6190 + 14.7841i 0.614161 + 0.515342i 0.895962 0.444131i \(-0.146487\pi\)
−0.281801 + 0.959473i \(0.590932\pi\)
\(824\) −10.6146 8.90673i −0.369778 0.310281i
\(825\) 0 0
\(826\) 5.63816 + 2.05212i 0.196177 + 0.0714024i
\(827\) 5.19615 9.00000i 0.180688 0.312961i −0.761427 0.648251i \(-0.775501\pi\)
0.942115 + 0.335290i \(0.108834\pi\)
\(828\) 0 0
\(829\) 9.50000 + 16.4545i 0.329949 + 0.571488i 0.982501 0.186256i \(-0.0596352\pi\)
−0.652553 + 0.757743i \(0.726302\pi\)
\(830\) 7.21842 + 40.9377i 0.250555 + 1.42097i
\(831\) 0 0
\(832\) −4.69846 + 1.71010i −0.162890 + 0.0592871i
\(833\) 0 0
\(834\) 0 0
\(835\) 64.3477 53.9942i 2.22685 1.86854i
\(836\) 3.46410 0.119808
\(837\) 0 0
\(838\) −66.0000 −2.27993
\(839\) −2.65366 + 2.22668i −0.0916144 + 0.0768736i −0.687445 0.726237i \(-0.741268\pi\)
0.595830 + 0.803110i \(0.296823\pi\)
\(840\) 0 0
\(841\) −2.95202 + 16.7417i −0.101794 + 0.577301i
\(842\) 30.9243 11.2555i 1.06572 0.387891i
\(843\) 0 0
\(844\) 0.868241 + 4.92404i 0.0298861 + 0.169492i
\(845\) −20.7846 36.0000i −0.715012 1.23844i
\(846\) 0 0
\(847\) 0.500000 0.866025i 0.0171802 0.0297570i
\(848\) −48.8279 17.7719i −1.67676 0.610289i
\(849\) 0 0
\(850\) 0 0
\(851\) 5.30731 + 4.45336i 0.181932 + 0.152659i
\(852\) 0 0
\(853\) −1.87939 0.684040i −0.0643489 0.0234211i 0.309645 0.950852i \(-0.399790\pi\)
−0.373994 + 0.927431i \(0.622012\pi\)
\(854\) 1.73205 3.00000i 0.0592696 0.102658i
\(855\) 0 0
\(856\) 9.00000 + 15.5885i 0.307614 + 0.532803i
\(857\) 6.61688 + 37.5262i 0.226028 + 1.28187i 0.860709 + 0.509097i \(0.170020\pi\)
−0.634681 + 0.772774i \(0.718868\pi\)
\(858\) 0 0
\(859\) 46.0449 16.7590i 1.57103 0.571809i 0.597803 0.801643i \(-0.296040\pi\)
0.973230 + 0.229834i \(0.0738182\pi\)
\(860\) −0.601535 + 3.41147i −0.0205122 + 0.116330i
\(861\) 0 0
\(862\) −27.5776 + 23.1404i −0.939297 + 0.788164i
\(863\) 10.3923 0.353758 0.176879 0.984233i \(-0.443400\pi\)
0.176879 + 0.984233i \(0.443400\pi\)
\(864\) 0 0
\(865\) −48.0000 −1.63205
\(866\) −1.32683 + 1.11334i −0.0450874 + 0.0378329i
\(867\) 0 0
\(868\) −0.868241 + 4.92404i −0.0294700 + 0.167133i
\(869\) −3.25519 + 1.18479i −0.110425 + 0.0401913i
\(870\) 0 0
\(871\) 6.94593 + 39.3923i 0.235354 + 1.33476i
\(872\) 14.7224 + 25.5000i 0.498564 + 0.863539i
\(873\) 0 0
\(874\) −6.00000 + 10.3923i −0.202953 + 0.351525i
\(875\) 6.51038 + 2.36959i 0.220091 + 0.0801066i
\(876\) 0 0
\(877\) 17.6190 + 14.7841i 0.594952 + 0.499224i 0.889819 0.456314i \(-0.150831\pi\)
−0.294867 + 0.955538i \(0.595275\pi\)
\(878\) 26.5366 + 22.2668i 0.895565 + 0.751469i
\(879\) 0 0
\(880\) −56.3816 20.5212i −1.90062 0.691770i
\(881\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(882\) 0 0
\(883\) 9.50000 + 16.4545i 0.319700 + 0.553737i 0.980425 0.196891i \(-0.0630844\pi\)
−0.660725 + 0.750628i \(0.729751\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 22.5526 8.20848i 0.757670 0.275769i
\(887\) 2.40614 13.6459i 0.0807903 0.458184i −0.917396 0.397977i \(-0.869713\pi\)
0.998186 0.0602078i \(-0.0191763\pi\)
\(888\) 0 0
\(889\) −13.0228 + 10.9274i −0.436769 + 0.366493i
\(890\) 62.3538 2.09011
\(891\) 0 0
\(892\) −19.0000 −0.636167
\(893\) 2.65366 2.22668i 0.0888012 0.0745131i
\(894\) 0 0
\(895\) −12.5027 + 70.9062i −0.417918 + 2.37013i
\(896\) 11.3932 4.14677i 0.380619 0.138534i
\(897\) 0 0
\(898\) −3.12567 17.7265i −0.104305 0.591542i
\(899\) 8.66025 + 15.0000i 0.288836 + 0.500278i
\(900\) 0 0
\(901\) 0 0
\(902\) 19.5311 + 7.10876i 0.650316 + 0.236696i
\(903\) 0 0
\(904\) 22.9813 + 19.2836i 0.764348 + 0.641364i
\(905\) 45.1121 + 37.8536i 1.49958 + 1.25830i
\(906\) 0 0
\(907\) 34.7686 + 12.6547i 1.15447 + 0.420194i 0.847120 0.531402i \(-0.178334\pi\)
0.307353 + 0.951595i \(0.400557\pi\)
\(908\) 6.92820 12.0000i 0.229920 0.398234i
\(909\) 0 0
\(910\) 15.0000 + 25.9808i 0.497245 + 0.861254i
\(911\) 4.81228 + 27.2918i 0.159438 + 0.904217i 0.954616 + 0.297841i \(0.0962665\pi\)
−0.795178 + 0.606377i \(0.792622\pi\)
\(912\) 0 0
\(913\) 22.5526 8.20848i 0.746383 0.271661i
\(914\) 5.11305 28.9975i 0.169125 0.959153i
\(915\) 0 0
\(916\) 3.83022 3.21394i 0.126554 0.106192i
\(917\) −3.46410 −0.114395
\(918\) 0 0
\(919\) −16.0000 −0.527791 −0.263896 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 31.8439 26.7202i 1.04986 0.880938i
\(921\) 0 0
\(922\) 8.33511 47.2708i 0.274502 1.55678i
\(923\) −48.8279 + 17.7719i −1.60719 + 0.584969i
\(924\) 0 0
\(925\) −1.21554 6.89365i −0.0399666 0.226662i
\(926\) 26.8468 + 46.5000i 0.882240 + 1.52808i
\(927\) 0 0
\(928\) −9.00000 + 15.5885i −0.295439 + 0.511716i
\(929\) −6.51038 2.36959i −0.213599 0.0777436i 0.233005 0.972476i \(-0.425144\pi\)
−0.446603 + 0.894732i \(0.647366\pi\)
\(930\) 0 0
\(931\) 4.59627 + 3.85673i 0.150637 + 0.126399i
\(932\) 0 0
\(933\) 0 0
\(934\) 16.9145 + 6.15636i 0.553458 + 0.201442i
\(935\) 0 0
\(936\) 0 0
\(937\) 18.5000 + 32.0429i 0.604369 + 1.04680i 0.992151 + 0.125046i \(0.0399079\pi\)
−0.387782 + 0.921751i \(0.626759\pi\)
\(938\) −2.40614 13.6459i −0.0785632 0.445554i
\(939\) 0 0
\(940\) 11.2763 4.10424i 0.367793 0.133866i
\(941\) 0.601535 3.41147i 0.0196095 0.111211i −0.973432 0.228977i \(-0.926462\pi\)
0.993041 + 0.117766i \(0.0375732\pi\)
\(942\) 0 0
\(943\) −18.3851 + 15.4269i −0.598700 + 0.502369i
\(944\) −17.3205 −0.563735
\(945\) 0 0
\(946\) 6.00000 0.195077
\(947\) −10.6146 + 8.90673i −0.344929 + 0.289430i −0.798750 0.601663i \(-0.794505\pi\)
0.453821 + 0.891093i \(0.350061\pi\)
\(948\) 0 0
\(949\) 1.73648 9.84808i 0.0563686 0.319682i
\(950\) 11.3932 4.14677i 0.369643 0.134539i
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(954\) 0 0
\(955\) −12.0000 + 20.7846i −0.388311 + 0.672574i
\(956\) 6.51038 + 2.36959i 0.210561 + 0.0766379i
\(957\) 0 0
\(958\) −18.3851 15.4269i −0.593995 0.498421i
\(959\) −5.30731 4.45336i −0.171382 0.143807i
\(960\) 0 0
\(961\) 5.63816 + 2.05212i 0.181876 + 0.0661974i
\(962\) 4.33013 7.50000i 0.139609 0.241810i
\(963\) 0 0
\(964\) 9.50000 + 16.4545i 0.305974 + 0.529963i
\(965\) −6.01535 34.1147i −0.193641 1.09819i
\(966\) 0 0
\(967\) −7.51754 + 2.73616i −0.241748 + 0.0879890i −0.460053 0.887892i \(-0.652169\pi\)
0.218305 + 0.975881i \(0.429947\pi\)
\(968\) −0.300767 + 1.70574i −0.00966703 + 0.0548245i
\(969\) 0 0
\(970\) 78.1365 65.5643i 2.50881 2.10514i
\(971\) 51.9615 1.66752 0.833762 0.552124i \(-0.186182\pi\)
0.833762 + 0.552124i \(0.186182\pi\)
\(972\) 0 0
\(973\) 13.0000 0.416761
\(974\) −25.2097 + 21.1535i −0.807772 + 0.677801i
\(975\) 0 0
\(976\) −1.73648 + 9.84808i −0.0555834 + 0.315229i
\(977\) −3.25519 + 1.18479i −0.104143 + 0.0379049i −0.393566 0.919296i \(-0.628759\pi\)
0.289423 + 0.957201i \(0.406537\pi\)
\(978\) 0 0
\(979\) −6.25133 35.4531i −0.199794 1.13309i
\(980\) 10.3923 + 18.0000i 0.331970 + 0.574989i
\(981\) 0 0
\(982\) 33.0000 57.1577i 1.05307 1.82397i
\(983\) −6.51038 2.36959i −0.207649 0.0755780i 0.236102 0.971728i \(-0.424130\pi\)
−0.443751 + 0.896150i \(0.646352\pi\)
\(984\) 0 0
\(985\) −27.5776 23.1404i −0.878695 0.737313i
\(986\) 0 0
\(987\) 0 0
\(988\) 4.69846 + 1.71010i 0.149478 + 0.0544056i
\(989\) −3.46410 + 6.00000i −0.110152 + 0.190789i
\(990\) 0 0
\(991\) −10.0000 17.3205i −0.317660 0.550204i 0.662339 0.749204i \(-0.269564\pi\)
−0.979999 + 0.199000i \(0.936231\pi\)
\(992\) −4.51151 25.5861i −0.143241 0.812358i
\(993\) 0 0
\(994\) 16.9145 6.15636i 0.536494 0.195268i
\(995\) −11.4292 + 64.8180i −0.362329 + 2.05487i
\(996\) 0 0
\(997\) 1.53209 1.28558i 0.0485217 0.0407146i −0.618204 0.786017i \(-0.712140\pi\)
0.666726 + 0.745303i \(0.267695\pi\)
\(998\) −48.4974 −1.53516
\(999\) 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.e.n.325.2 12
3.2 odd 2 inner 729.2.e.n.325.1 12
9.2 odd 6 inner 729.2.e.n.568.2 12
9.4 even 3 inner 729.2.e.n.82.2 12
9.5 odd 6 inner 729.2.e.n.82.1 12
9.7 even 3 inner 729.2.e.n.568.1 12
27.2 odd 18 inner 729.2.e.n.163.2 12
27.4 even 9 243.2.a.c.1.2 yes 2
27.5 odd 18 243.2.c.d.82.2 4
27.7 even 9 inner 729.2.e.n.649.2 12
27.11 odd 18 inner 729.2.e.n.406.1 12
27.13 even 9 243.2.c.d.163.1 4
27.14 odd 18 243.2.c.d.163.2 4
27.16 even 9 inner 729.2.e.n.406.2 12
27.20 odd 18 inner 729.2.e.n.649.1 12
27.22 even 9 243.2.c.d.82.1 4
27.23 odd 18 243.2.a.c.1.1 2
27.25 even 9 inner 729.2.e.n.163.1 12
108.23 even 18 3888.2.a.ba.1.1 2
108.31 odd 18 3888.2.a.ba.1.2 2
135.4 even 18 6075.2.a.bm.1.1 2
135.104 odd 18 6075.2.a.bm.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
243.2.a.c.1.1 2 27.23 odd 18
243.2.a.c.1.2 yes 2 27.4 even 9
243.2.c.d.82.1 4 27.22 even 9
243.2.c.d.82.2 4 27.5 odd 18
243.2.c.d.163.1 4 27.13 even 9
243.2.c.d.163.2 4 27.14 odd 18
729.2.e.n.82.1 12 9.5 odd 6 inner
729.2.e.n.82.2 12 9.4 even 3 inner
729.2.e.n.163.1 12 27.25 even 9 inner
729.2.e.n.163.2 12 27.2 odd 18 inner
729.2.e.n.325.1 12 3.2 odd 2 inner
729.2.e.n.325.2 12 1.1 even 1 trivial
729.2.e.n.406.1 12 27.11 odd 18 inner
729.2.e.n.406.2 12 27.16 even 9 inner
729.2.e.n.568.1 12 9.7 even 3 inner
729.2.e.n.568.2 12 9.2 odd 6 inner
729.2.e.n.649.1 12 27.20 odd 18 inner
729.2.e.n.649.2 12 27.7 even 9 inner
3888.2.a.ba.1.1 2 108.23 even 18
3888.2.a.ba.1.2 2 108.31 odd 18
6075.2.a.bm.1.1 2 135.4 even 18
6075.2.a.bm.1.2 2 135.104 odd 18