LMFDB - Embedded newform 729.2.k.a.4.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(4,729)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(486))

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("729.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.k (of order $243$, degree $162$, 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:	$12960$
Relative dimension:	$80$ over $\Q(\zeta_{243})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{243}]$

Embedding invariants

Embedding label			4.14
Character	$\chi$	$=$	729.4
Dual form			729.2.k.a.547.14

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.03766 - 0.0263451i) q^{2} +(-1.63810 + 0.562705i) q^{3} +(2.15204 + 0.0556572i) q^{4} +(0.558373 + 0.171106i) q^{5} +(3.35271 - 1.10345i) q^{6} +(0.399839 - 0.997050i) q^{7} +(-0.311068 - 0.0120709i) q^{8} +(2.36673 - 1.84353i) q^{9} +O(q^{10})$	\(q+(-2.03766 - 0.0263451i) q^{2} +(-1.63810 + 0.562705i) q^{3} +(2.15204 + 0.0556572i) q^{4} +(0.558373 + 0.171106i) q^{5} +(3.35271 - 1.10345i) q^{6} +(0.399839 - 0.997050i) q^{7} +(-0.311068 - 0.0120709i) q^{8} +(2.36673 - 1.84353i) q^{9} +(-1.13327 - 0.363367i) q^{10} +(4.38987 + 2.49680i) q^{11} +(-3.55657 + 1.11979i) q^{12} +(-0.846483 - 1.89464i) q^{13} +(-0.841003 + 2.02112i) q^{14} +(-1.01095 + 0.0339100i) q^{15} +(-3.66623 - 0.189763i) q^{16} +(-0.958067 - 0.435495i) q^{17} +(-4.87116 + 3.69414i) q^{18} +(-0.947460 - 1.38143i) q^{19} +(1.19212 + 0.399306i) q^{20} +(-0.0939298 + 1.85826i) q^{21} +(-8.87930 - 5.20328i) q^{22} +(-0.543028 + 1.65668i) q^{23} +(0.516352 - 0.155266i) q^{24} +(-3.85907 - 2.61024i) q^{25} +(1.67493 + 3.88293i) q^{26} +(-2.83957 + 4.35165i) q^{27} +(0.915962 - 2.12344i) q^{28} +(5.87470 - 3.75596i) q^{29} +(2.06087 - 0.0424635i) q^{30} +(-0.116200 - 0.428125i) q^{31} +(8.08685 + 0.523478i) q^{32} +(-8.59600 - 1.61980i) q^{33} +(1.94074 + 0.912632i) q^{34} +(0.393861 - 0.488311i) q^{35} +(5.19590 - 3.83563i) q^{36} +(-4.10495 - 0.806186i) q^{37} +(1.89421 + 2.83985i) q^{38} +(2.45274 + 2.62728i) q^{39} +(-0.171627 - 0.0599658i) q^{40} +(-3.84549 + 1.45622i) q^{41} +(0.240353 - 3.78402i) q^{42} +(5.40724 - 2.37403i) q^{43} +(9.30822 + 5.61754i) q^{44} +(1.63696 - 0.624415i) q^{45} +(1.15015 - 3.36145i) q^{46} +(1.43666 - 5.29319i) q^{47} +(6.11243 - 1.75216i) q^{48} +(4.22622 + 4.03919i) q^{49} +(7.79471 + 5.42045i) q^{50} +(1.81446 + 0.174274i) q^{51} +(-1.71622 - 4.12445i) q^{52} +(-5.29848 + 5.61606i) q^{53} +(5.90072 - 8.79239i) q^{54} +(2.02397 + 2.14528i) q^{55} +(-0.136412 + 0.305324i) q^{56} +(2.32937 + 1.72978i) q^{57} +(-12.0696 + 7.49861i) q^{58} +(3.64869 - 0.619071i) q^{59} +(-2.17750 + 0.0167090i) q^{60} +(4.15586 - 7.64824i) q^{61} +(0.225497 + 0.875434i) q^{62} +(-0.891784 - 3.09686i) q^{63} +(-9.14427 - 0.710749i) q^{64} +(-0.148469 - 1.20275i) q^{65} +(17.4731 + 3.52706i) q^{66} +(11.8914 - 6.16587i) q^{67} +(-2.03756 - 0.990526i) q^{68} +(-0.0426893 - 3.01937i) q^{69} +(-0.815420 + 0.984636i) q^{70} +(11.2116 + 8.68968i) q^{71} +(-0.758467 + 0.544895i) q^{72} +(-3.21673 + 1.03140i) q^{73} +(8.34327 + 1.75088i) q^{74} +(7.79032 + 2.10431i) q^{75} +(-1.96209 - 3.02563i) q^{76} +(4.24467 - 3.37861i) q^{77} +(-4.92864 - 5.41812i) q^{78} +(2.66554 - 14.0522i) q^{79} +(-2.01465 - 0.733274i) q^{80} +(2.20279 - 8.72627i) q^{81} +(7.87417 - 2.86597i) q^{82} +(-2.50840 - 15.3865i) q^{83} +(-0.305566 + 3.99382i) q^{84} +(-0.460442 - 0.407100i) q^{85} +(-11.0807 + 4.69501i) q^{86} +(-7.50984 + 9.45835i) q^{87} +(-1.33541 - 0.829664i) q^{88} +(16.0137 + 6.54233i) q^{89} +(-3.35201 + 1.22922i) q^{90} +(-2.22750 + 0.0864373i) q^{91} +(-1.26082 + 3.53502i) q^{92} +(0.431255 + 0.635923i) q^{93} +(-3.06688 + 10.7479i) q^{94} +(-0.292664 - 0.933469i) q^{95} +(-13.5416 + 3.69300i) q^{96} +(0.177879 - 0.772757i) q^{97} +(-8.50520 - 8.34184i) q^{98} +(14.9926 - 2.18362i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) $ 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{243}\right)$

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 $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.03766	−	0.0263451i	−1.44084	−	0.0186288i	−0.711457	−	0.702729i	$-0.751964\pi$
$2$	−2.03766	−	0.0263451i	−1.44084	−	0.0186288i	−0.729388	+	0.684101i	$0.760195\pi$
$3$	−1.63810	+	0.562705i	−0.945756	+	0.324878i
$3$	−1.63810	+	0.562705i	−0.945756	+	0.324878i
$4$	2.15204	+	0.0556572i	1.07602	+	0.0278286i
$5$	0.558373	+	0.171106i	0.249712	+	0.0765211i	0.415337	−	0.909668i	$-0.363664\pi$
$5$	0.558373	+	0.171106i	0.249712	+	0.0765211i	−0.165625	+	0.986189i	$0.552964\pi$
$6$	3.35271	−	1.10345i	1.36874	−	0.450480i
$7$	0.399839	−	0.997050i	0.151125	−	0.376850i	−0.833260	−	0.552882i	$-0.813528\pi$
$7$	0.399839	−	0.997050i	0.151125	−	0.376850i	0.984384	+	0.176032i	$0.0563264\pi$
$8$	−0.311068	−	0.0120709i	−0.109979	−	0.00426770i
$9$	2.36673	−	1.84353i	0.788909	−	0.614510i
$10$	−1.13327	−	0.363367i	−0.358371	−	0.114907i
$11$	4.38987	+	2.49680i	1.32360	+	0.752813i	0.982331	−	0.187154i	$-0.0599263\pi$
$11$	4.38987	+	2.49680i	1.32360	+	0.752813i	0.341266	+	0.939967i	$0.389144\pi$
$12$	−3.55657	+	1.11979i	−1.02669	+	0.323256i
$13$	−0.846483	−	1.89464i	−0.234772	−	0.525477i	0.757012	−	0.653401i	$-0.226658\pi$
$13$	−0.846483	−	1.89464i	−0.234772	−	0.525477i	−0.991784	+	0.127924i	$0.959169\pi$
$14$	−0.841003	+	2.02112i	−0.224768	+	0.540166i
$15$	−1.01095	+	0.0339100i	−0.261027	+	0.00875552i
$16$	−3.66623	−	0.189763i	−0.916558	−	0.0474407i
$17$	−0.958067	−	0.435495i	−0.232365	−	0.105623i	0.294244	−	0.955730i	$-0.404932\pi$
$17$	−0.958067	−	0.435495i	−0.232365	−	0.105623i	−0.526610	+	0.850107i	$0.676537\pi$
$18$	−4.87116	+	3.69414i	−1.14814	+	0.870717i
$19$	−0.947460	−	1.38143i	−0.217362	−	0.316922i	0.700627	−	0.713528i	$-0.252904\pi$
$19$	−0.947460	−	1.38143i	−0.217362	−	0.316922i	−0.917989	+	0.396606i	$0.870188\pi$
$20$	1.19212	+	0.399306i	0.266566	+	0.0892875i
$21$	−0.0939298	+	1.85826i	−0.0204972	+	0.405505i
$22$	−8.87930	−	5.20328i	−1.89307	−	1.10934i
$23$	−0.543028	+	1.65668i	−0.113229	+	0.345442i	−0.991040	−	0.133566i	$-0.957357\pi$
$23$	−0.543028	+	1.65668i	−0.113229	+	0.345442i	0.877811	+	0.479007i	$0.159003\pi$
$24$	0.516352	−	0.155266i	0.105400	−	0.0316936i
$25$	−3.85907	−	2.61024i	−0.771813	−	0.522048i
$26$	1.67493	+	3.88293i	0.328481	+	0.761505i
$27$	−2.83957	+	4.35165i	−0.546475	+	0.837476i
$28$	0.915962	−	2.12344i	0.173101	−	0.401292i
$29$	5.87470	−	3.75596i	1.09091	−	0.697464i	0.134913	−	0.990857i	$-0.456924\pi$
$29$	5.87470	−	3.75596i	1.09091	−	0.697464i	0.955992	+	0.293393i	$0.0947845\pi$
$30$	2.06087	−	0.0424635i	0.376262	−	0.00775274i
$31$	−0.116200	−	0.428125i	−0.0208701	−	0.0768934i	0.953883	−	0.300178i	$-0.0970462\pi$
$31$	−0.116200	−	0.428125i	−0.0208701	−	0.0768934i	−0.974753	+	0.223285i	$0.928322\pi$
$32$	8.08685	+	0.523478i	1.42957	+	0.0925387i
$33$	−8.59600	−	1.61980i	−1.49637	−	0.281970i
$34$	1.94074	+	0.912632i	0.332835	+	0.156515i
$35$	0.393861	−	0.488311i	0.0665746	−	0.0825396i
$36$	5.19590	−	3.83563i	0.865983	−	0.639272i
$37$	−4.10495	−	0.806186i	−0.674850	−	0.132536i	−0.156465	−	0.987684i	$-0.550010\pi$
$37$	−4.10495	−	0.806186i	−0.674850	−	0.132536i	−0.518385	+	0.855147i	$0.673467\pi$
$38$	1.89421	+	2.83985i	0.307281	+	0.460684i
$39$	2.45274	+	2.62728i	0.392753	+	0.420701i
$40$	−0.171627	−	0.0599658i	−0.0271366	−	0.00948143i
$41$	−3.84549	+	1.45622i	−0.600565	+	0.227423i	−0.635670	−	0.771961i	$-0.719276\pi$
$41$	−3.84549	+	1.45622i	−0.600565	+	0.227423i	0.0351052	+	0.999384i	$0.488823\pi$
$42$	0.240353	−	3.78402i	0.0370873	−	0.583888i
$43$	5.40724	−	2.37403i	0.824596	−	0.362036i	0.0533523	−	0.998576i	$-0.483009\pi$
$43$	5.40724	−	2.37403i	0.824596	−	0.362036i	0.771244	+	0.636540i	$0.219635\pi$
$44$	9.30822	+	5.61754i	1.40327	+	0.846876i
$45$	1.63696	−	0.624415i	0.244023	−	0.0930823i
$46$	1.15015	−	3.36145i	0.169581	−	0.495618i
$47$	1.43666	−	5.29319i	0.209558	−	0.772092i	−0.779730	−	0.626116i	$-0.784644\pi$
$47$	1.43666	−	5.29319i	0.209558	−	0.772092i	0.989288	−	0.145976i	$-0.0466321\pi$
$48$	6.11243	−	1.75216i	0.882253	−	0.252902i
$49$	4.22622	+	4.03919i	0.603746	+	0.577027i
$50$	7.79471	+	5.42045i	1.10234	+	0.766568i
$51$	1.81446	+	0.174274i	0.254075	+	0.0244033i
$52$	−1.71622	−	4.12445i	−0.237996	−	0.571958i
$53$	−5.29848	+	5.61606i	−0.727802	+	0.771425i	−0.980584	−	0.196098i	$-0.937173\pi$
$53$	−5.29848	+	5.61606i	−0.727802	+	0.771425i	0.252782	+	0.967523i	$0.418654\pi$
$54$	5.90072	−	8.79239i	0.802986	−	1.19649i
$55$	2.02397	+	2.14528i	0.272912	+	0.289269i
$56$	−0.136412	+	0.305324i	−0.0182289	+	0.0408007i
$57$	2.32937	+	1.72978i	0.308532	+	0.229115i
$58$	−12.0696	+	7.49861i	−1.58482	+	0.984615i
$59$	3.64869	−	0.619071i	0.475019	−	0.0805962i	0.0751575	−	0.997172i	$-0.476054\pi$
$59$	3.64869	−	0.619071i	0.475019	−	0.0805962i	0.399862	+	0.916576i	$0.369058\pi$
$60$	−2.17750	+	0.0167090i	−0.281114	+	0.00215713i
$61$	4.15586	−	7.64824i	0.532103	−	0.979257i	−0.463546	−	0.886073i	$-0.653423\pi$
$61$	4.15586	−	7.64824i	0.532103	−	0.979257i	0.995649	−	0.0931838i	$-0.0297044\pi$
$62$	0.225497	+	0.875434i	0.0286382	+	0.111180i
$63$	−0.891784	−	3.09686i	−0.112354	−	0.390168i
$64$	−9.14427	−	0.710749i	−1.14303	−	0.0888437i
$65$	−0.148469	−	1.20275i	−0.0184153	−	0.149183i
$66$	17.4731	+	3.52706i	2.15079	+	0.434151i
$67$	11.8914	−	6.16587i	1.45277	−	0.753281i	0.461749	−	0.887011i	$-0.347222\pi$
$67$	11.8914	−	6.16587i	1.45277	−	0.753281i	0.991018	+	0.133730i	$0.0426954\pi$
$68$	−2.03756	−	0.990526i	−0.247091	−	0.120119i
$69$	−0.0426893	−	3.01937i	−0.00513918	−	0.363489i
$70$	−0.815420	+	0.984636i	−0.0974613	+	0.117686i
$71$	11.2116	+	8.68968i	1.33058	+	1.03128i	0.996041	+	0.0888920i	$0.0283326\pi$
$71$	11.2116	+	8.68968i	1.33058	+	1.03128i	0.334536	+	0.942383i	$0.391420\pi$
$72$	−0.758467	+	0.544895i	−0.0893861	+	0.0642165i
$73$	−3.21673	+	1.03140i	−0.376489	+	0.120716i	−0.487545	−	0.873098i	$-0.662108\pi$
$73$	−3.21673	+	1.03140i	−0.376489	+	0.120716i	0.111056	+	0.993814i	$0.464577\pi$
$74$	8.34327	+	1.75088i	0.969885	+	0.203536i
$75$	7.79032	+	2.10431i	0.899549	+	0.242985i
$76$	−1.96209	−	3.02563i	−0.225067	−	0.347063i
$77$	4.24467	−	3.37861i	0.483725	−	0.385028i
$78$	−4.92864	−	5.41812i	−0.558059	−	0.613481i
$79$	2.66554	−	14.0522i	0.299896	−	1.58099i	−0.433475	−	0.901166i	$-0.642713\pi$
$79$	2.66554	−	14.0522i	0.299896	−	1.58099i	0.733371	−	0.679828i	$-0.237946\pi$
$80$	−2.01465	−	0.733274i	−0.225245	−	0.0819826i
$81$	2.20279	−	8.72627i	0.244754	−	0.969585i
$82$	7.87417	−	2.86597i	0.869557	−	0.316493i
$83$	−2.50840	−	15.3865i	−0.275332	−	1.68888i	−0.648576	−	0.761150i	$-0.724635\pi$
$83$	−2.50840	−	15.3865i	−0.275332	−	1.68888i	0.373244	−	0.927733i	$-0.378246\pi$
$84$	−0.305566	+	3.99382i	−0.0333400	+	0.435761i
$85$	−0.460442	−	0.407100i	−0.0499420	−	0.0441562i
$86$	−11.0807	+	4.69501i	−1.19486	+	0.506276i
$87$	−7.50984	+	9.45835i	−0.805139	+	1.01404i
$88$	−1.33541	−	0.829664i	−0.142355	−	0.0884425i
$89$	16.0137	+	6.54233i	1.69745	+	0.693486i	0.999738	−	0.0228891i	$-0.00728647\pi$
$89$	16.0137	+	6.54233i	1.69745	+	0.693486i	0.697715	+	0.716375i	$0.254200\pi$
$90$	−3.35201	+	1.22922i	−0.353333	+	0.129571i
$91$	−2.22750	+	0.0864373i	−0.233506	+	0.00906109i
$92$	−1.26082	+	3.53502i	−0.131450	+	0.368551i
$93$	0.431255	+	0.635923i	0.0447190	+	0.0659422i
$94$	−3.06688	+	10.7479i	−0.316324	+	1.10856i
$95$	−0.292664	−	0.933469i	−0.0300267	−	0.0957719i
$96$	−13.5416	+	3.69300i	−1.38209	+	0.376915i
$97$	0.177879	−	0.772757i	0.0180609	−	0.0784616i	−0.964695	−	0.263370i	$-0.915166\pi$
$97$	0.177879	−	0.772757i	0.0180609	−	0.0784616i	0.982756	+	0.184908i	$0.0591989\pi$
$98$	−8.50520	−	8.34184i	−0.859154	−	0.842653i
$99$	14.9926	−	2.18362i	1.50681	−	0.219463i
$100$	−8.15960	−	5.83213i	−0.815960	−	0.583213i
$101$	0.724011	−	4.83378i	0.0720418	−	0.480979i	−0.923261	−	0.384172i	$-0.874487\pi$
$101$	0.724011	−	4.83378i	0.0720418	−	0.480979i	0.995303	−	0.0968070i	$-0.0308630\pi$
$102$	−3.69267	−	0.402914i	−0.365629	−	0.0398944i
$103$	0.700303	+	1.96346i	0.0690029	+	0.193466i	0.971405	−	0.237429i	$-0.0763048\pi$
$103$	0.700303	+	1.96346i	0.0690029	+	0.193466i	−0.902402	+	0.430895i	$0.858198\pi$
$104$	0.240444	+	0.599579i	0.0235775	+	0.0587935i
$105$	−0.370407	+	1.02153i	−0.0361481	+	0.0996909i
$106$	10.9445	−	11.3040i	1.06302	−	1.09795i
$107$	−0.103484	−	1.77675i	−0.0100042	−	0.171765i	−0.999609	−	0.0279532i	$-0.991101\pi$
$107$	−0.103484	−	1.77675i	−0.0100042	−	0.171765i	0.989605	−	0.143812i	$-0.0459360\pi$
$108$	−6.35306	+	9.20689i	−0.611324	+	0.885934i
$109$	−0.184216	+	3.16287i	−0.0176447	+	0.302948i	0.977927	+	0.208946i	$0.0670032\pi$
$109$	−0.184216	+	3.16287i	−0.0176447	+	0.302948i	−0.995572	+	0.0940025i	$0.970034\pi$
$110$	−4.06764	−	4.42468i	−0.387835	−	0.421876i
$111$	7.17796	−	0.989264i	0.681301	−	0.0938968i
$112$	−1.65510	+	3.57954i	−0.156393	+	0.338235i
$113$	−3.48352	+	2.55856i	−0.327702	+	0.240689i	−0.743450	−	0.668791i	$-0.766812\pi$
$113$	−3.48352	+	2.55856i	−0.327702	+	0.240689i	0.415748	+	0.909480i	$0.363520\pi$
$114$	−4.70089	−	3.58607i	−0.440279	−	0.335866i
$115$	−0.586680	+	0.832129i	−0.0547082	+	0.0775964i
$116$	12.8517	−	7.75601i	1.19325	−	0.720128i
$117$	−5.49621	−	2.92357i	−0.508125	−	0.270284i
$118$	−7.45111	+	1.16533i	−0.685930	+	0.107278i
$119$	−0.817282	+	0.781113i	−0.0749201	+	0.0716045i
$120$	0.314884	+	0.00165474i	0.0287449	+	0.000151056i
$121$	7.41428	+	12.4669i	0.674026	+	1.13335i
$122$	−8.66973	+	15.4750i	−0.784920	+	1.40104i
$123$	5.47987	−	4.54930i	0.494103	−	0.410196i
$124$	−0.226239	−	0.927809i	−0.0203169	−	0.0833197i
$125$	−3.54138	−	4.39063i	−0.316751	−	0.392710i
$126$	1.73557	+	6.33385i	0.154617	+	0.564264i
$127$	−0.0557401	−	2.87395i	−0.00494614	−	0.255022i	−0.994121	−	0.108278i	$-0.965466\pi$
$127$	−0.0557401	−	2.87395i	−0.00494614	−	0.255022i	0.989175	−	0.146744i	$-0.0468793\pi$
$128$	2.47299	+	0.224415i	0.218584	+	0.0198357i
$129$	−7.52171	+	6.93157i	−0.662249	+	0.610291i
$130$	0.270842	+	2.45471i	0.0237544	+	0.215293i
$131$	−9.83019	+	0.892055i	−0.858868	+	0.0779392i	−0.510976	−	0.859595i	$-0.670716\pi$
$131$	−9.83019	+	0.892055i	−0.858868	+	0.0779392i	−0.347893	+	0.937534i	$0.613103\pi$
$132$	−18.4088	−	3.96430i	−1.60228	−	0.345048i
$133$	−1.75619	+	0.392316i	−0.152281	+	0.0340181i
$134$	−24.3931	+	12.2507i	−2.10724	+	1.05830i
$135$	−2.33013	+	1.94398i	−0.200546	+	0.167311i
$136$	0.292767	+	0.147033i	0.0251046	+	0.0126080i
$137$	5.88233	+	1.47471i	0.502562	+	0.125993i	0.486155	−	0.873872i	$-0.338399\pi$
$137$	5.88233	+	1.47471i	0.502562	+	0.125993i	0.0164062	+	0.999865i	$0.494778\pi$
$138$	0.00744073	+	6.15358i	0.000633397	+	0.523827i
$139$	4.80724	+	0.688294i	0.407745	+	0.0583803i	0.342567	−	0.939493i	$-0.388704\pi$
$139$	4.80724	+	0.688294i	0.407745	+	0.0583803i	0.0651778	+	0.997874i	$0.479239\pi$
$140$	0.874783	−	1.02894i	0.0739326	−	0.0869616i
$141$	0.625117	+	9.47918i	0.0526444	+	0.798291i
$142$	−22.6166	−	18.0020i	−1.89794	−	1.51069i
$143$	1.01457	−	10.4307i	0.0848427	−	0.872259i
$144$	−9.02681	+	6.30970i	−0.752234	+	0.525808i
$145$	3.92294	−	1.09203i	0.325783	−	0.0906878i
$146$	6.58178	−	2.01690i	0.544712	−	0.166920i
$147$	−9.19583	−	4.23847i	−0.758459	−	0.349583i
$148$	−8.78916	−	1.96342i	−0.722464	−	0.161392i
$149$	−11.1734	+	2.80120i	−0.915364	+	0.229483i	−0.672086	−	0.740473i	$-0.734601\pi$
$149$	−11.1734	+	2.80120i	−0.915364	+	0.229483i	−0.243278	+	0.969957i	$0.578223\pi$
$150$	−15.8186	−	4.49311i	−1.29158	−	0.366861i
$151$	14.7305	+	17.3264i	1.19875	+	1.41001i	0.888204	+	0.459449i	$0.151953\pi$
$151$	14.7305	+	17.3264i	1.19875	+	1.41001i	0.310548	+	0.950558i	$0.399487\pi$
$152$	0.278050	+	0.441156i	0.0225528	+	0.0357824i
$153$	−3.07033	+	0.735528i	−0.248221	+	0.0594639i
$154$	−8.73822	+	6.77263i	−0.704146	+	0.545754i
$155$	0.00837195	−	0.258936i	0.000672451	−	0.0207982i
$156$	5.13218	+	5.79052i	0.410903	+	0.463613i
$157$	−0.145617	+	1.17965i	−0.0116215	+	0.0941467i	−0.997161	−	0.0752997i	$-0.976009\pi$
$157$	−0.145617	+	1.17965i	−0.0116215	+	0.0941467i	0.985539	+	0.169446i	$0.0541980\pi$
$158$	−5.80167	+	28.5634i	−0.461556	+	2.27238i
$159$	5.51924	−	12.1811i	0.437704	−	0.966026i
$160$	4.42591	+	1.67601i	0.349899	+	0.132500i
$161$	1.43467	+	1.20383i	0.113068	+	0.0948751i
$162$	−4.71844	+	17.7231i	−0.370715	+	1.39246i
$163$	−4.00364	+	3.35945i	−0.313589	+	0.263132i	−0.785974	−	0.618260i	$-0.787838\pi$
$163$	−4.00364	+	3.35945i	−0.313589	+	0.263132i	0.472385	+	0.881393i	$0.343393\pi$
$164$	−8.35670	+	2.91981i	−0.652549	+	0.227999i
$165$	−4.52261	−	2.37528i	−0.352085	−	0.184915i
$166$	4.70591	+	31.4185i	0.365249	+	2.43855i
$167$	1.21426	−	2.37932i	0.0939626	−	0.184118i	−0.838961	−	0.544191i	$-0.816837\pi$
$167$	1.21426	−	2.37932i	0.0939626	−	0.184118i	0.932924	+	0.360073i	$0.117248\pi$
$168$	0.0516493	−	0.576911i	0.00398483	−	0.0445096i
$169$	5.80058	−	6.47579i	0.446198	−	0.498138i
$170$	0.927501	+	0.841662i	0.0711361	+	0.0645525i
$171$	−4.78909	−	1.52280i	−0.366231	−	0.116451i
$172$	11.7687	−	4.80806i	0.897358	−	0.366611i
$173$	1.35270	+	0.229512i	0.102844	+	0.0174495i	0.218473	−	0.975843i	$-0.429892\pi$
$173$	1.35270	+	0.229512i	0.102844	+	0.0174495i	−0.115629	+	0.993292i	$0.536888\pi$
$174$	15.5517	−	19.0751i	1.17897	−	1.44608i
$175$	−4.14554	+	2.80401i	−0.313374	+	0.211963i
$176$	−15.6205	−	9.98688i	−1.17744	−	0.752789i
$177$	−5.62856	+	3.06723i	−0.423068	+	0.230547i
$178$	−32.4582	−	13.7530i	−2.43285	−	1.03083i
$179$	3.34687	+	6.99937i	0.250156	+	0.523158i	0.988492	−	0.151276i	$-0.0483383\pi$
$179$	3.34687	+	6.99937i	0.250156	+	0.523158i	−0.738335	+	0.674434i	$0.764388\pi$
$180$	3.55755	−	1.25266i	0.265164	−	0.0933677i
$181$	−20.3462	−	5.66375i	−1.51232	−	0.420983i	−0.589998	−	0.807405i	$-0.700872\pi$
$181$	−20.3462	−	5.66375i	−1.51232	−	0.420983i	−0.922322	+	0.386422i	$0.873711\pi$
$182$	4.54118	−	0.117446i	0.336614	−	0.00870569i
$183$	−2.50400	+	14.8671i	−0.185101	+	1.09901i
$184$	0.188916	−	0.508786i	0.0139271	−	0.0375082i
$185$	−2.15415	−	1.15254i	−0.158376	−	0.0847361i
$186$	−0.861998	−	1.30716i	−0.0632047	−	0.0958455i
$187$	−3.11845	−	4.30387i	−0.228044	−	0.314730i
$188$	3.38636	−	11.3112i	0.246975	−	0.824955i
$189$	3.20345	+	4.57115i	0.233016	+	0.332502i
$190$	0.571758	+	1.90980i	0.0414797	+	0.138552i
$191$	9.65258	−	12.6217i	0.698436	−	0.913272i	−0.300746	−	0.953704i	$-0.597236\pi$
$191$	9.65258	−	12.6217i	0.698436	−	0.913272i	0.999182	+	0.0404324i	$0.0128736\pi$
$192$	15.3792	−	3.98125i	1.10989	−	0.287322i
$193$	−3.96280	+	1.86350i	−0.285249	+	0.134138i	−0.562851	−	0.826558i	$-0.690296\pi$
$193$	−3.96280	+	1.86350i	−0.285249	+	0.134138i	0.277603	+	0.960696i	$0.410460\pi$
$194$	−0.382816	+	1.56993i	−0.0274846	+	0.112715i
$195$	0.920000	+	1.88668i	0.0658826	+	0.135108i
$196$	8.87019	+	8.92772i	0.633585	+	0.637694i
$197$	18.9601	−	3.72365i	1.35085	−	0.265299i	0.535634	−	0.844450i	$-0.320073\pi$
$197$	18.9601	−	3.72365i	1.35085	−	0.265299i	0.815220	+	0.579151i	$0.196616\pi$
$198$	−30.6073	+	4.05451i	−2.17516	+	0.288141i
$199$	20.5199	−	11.3224i	1.45462	−	0.802623i	0.458335	−	0.888780i	$-0.348446\pi$
$199$	20.5199	−	11.3224i	1.45462	−	0.802623i	0.996282	+	0.0861565i	$0.0274585\pi$
$200$	1.16893	+	0.858545i	0.0826555	+	0.0607083i
$201$	−16.0097	+	16.7916i	−1.12924	+	1.18439i
$202$	−1.60264	+	9.83054i	−0.112761	+	0.691675i
$203$	−1.39595	−	7.35915i	−0.0979762	−	0.516511i
$204$	3.89510	+	0.476033i	0.272711	+	0.0333290i
$205$	−2.39638	+	0.155123i	−0.167371	+	0.0108342i
$206$	−1.37525	−	4.01933i	−0.0958184	−	0.280040i
$207$	1.76894	+	4.92200i	0.122950	+	0.342102i
$208$	2.74387	+	7.10681i	0.190253	+	0.492768i
$209$	−0.710075	−	8.42992i	−0.0491169	−	0.583109i
$210$	0.781677	−	2.07177i	0.0539409	−	0.142966i
$211$	3.41806	−	5.12444i	0.235309	−	0.352781i	−0.695349	−	0.718672i	$-0.744750\pi$
$211$	3.41806	−	5.12444i	0.235309	−	0.352781i	0.930658	+	0.365891i	$0.119236\pi$
$212$	−11.7151	+	11.7911i	−0.804598	+	0.809816i
$213$	−23.2555	−	7.92570i	−1.59344	−	0.543060i
$214$	0.164057	+	3.62314i	0.0112147	+	0.247673i
$215$	3.42547	−	0.400380i	0.233615	−	0.0273057i
$216$	0.935827	−	1.31938i	0.0636750	−	0.0897727i
$217$	−0.473323	−	0.0553235i	−0.0321312	−	0.00375560i
$218$	0.458697	−	6.44001i	0.0310669	−	0.436173i
$219$	4.68894	−	3.49960i	0.316849	−	0.236481i
$220$	4.23626	+	4.72938i	0.285609	+	0.318855i
$221$	−0.0141168	+	2.18383i	−0.000949602	+	0.146900i
$222$	−14.6523	+	1.82668i	−0.983399	+	0.122599i
$223$	14.4750	−	12.7980i	0.969315	−	0.857019i	−0.0204410	−	0.999791i	$-0.506507\pi$
$223$	14.4750	−	12.7980i	0.969315	−	0.857019i	0.989756	+	0.142772i	$0.0456017\pi$
$224$	3.75537	−	7.85369i	0.250916	−	0.524747i
$225$	−13.9454	+	0.936586i	−0.929694	+	0.0624391i
$226$	7.16565	−	5.12170i	0.476652	−	0.340690i
$227$	7.13680	+	13.9844i	0.473686	+	0.928177i	0.997100	+	0.0760991i	$0.0242465\pi$
$227$	7.13680	+	13.9844i	0.473686	+	0.928177i	−0.523414	+	0.852078i	$0.675342\pi$
$228$	4.91662	+	3.85220i	0.325611	+	0.255118i
$229$	−6.24024	−	8.15971i	−0.412367	−	0.539209i	0.541000	−	0.841022i	$-0.318046\pi$
$229$	−6.24024	−	8.15971i	−0.412367	−	0.539209i	−0.953367	+	0.301814i	$0.902408\pi$
$230$	1.21738	−	1.68014i	0.0802716	−	0.110785i
$231$	−5.05203	+	7.92298i	−0.332399	+	0.521294i
$232$	−1.87277	+	1.09745i	−0.122953	+	0.0720509i
$233$	−2.75944	−	12.7390i	−0.180777	−	0.834560i	−0.974164	−	0.225842i	$-0.927487\pi$
$233$	−2.75944	−	12.7390i	−0.180777	−	0.834560i	0.793387	−	0.608718i	$-0.208316\pi$
$234$	11.1224	+	6.10204i	0.727094	+	0.398903i
$235$	1.70789	−	2.70975i	0.111411	−	0.176765i
$236$	7.88659	−	1.12919i	0.513373	−	0.0735041i
$237$	3.54082	+	24.5188i	0.230001	+	1.59266i
$238$	1.68592	−	1.57011i	0.109282	−	0.101775i
$239$	5.07860	+	9.34641i	0.328507	+	0.604569i	0.989282	−	0.146015i	$-0.0466448\pi$
$239$	5.07860	+	9.34641i	0.328507	+	0.604569i	−0.660775	+	0.750584i	$0.729772\pi$
$240$	3.71282	+	0.0675190i	0.239661	+	0.00435833i
$241$	−0.686873	+	1.15495i	−0.0442454	+	0.0743971i	−0.880806	−	0.473477i	$-0.842999\pi$
$241$	−0.686873	+	1.15495i	−0.0442454	+	0.0743971i	0.836561	+	0.547874i	$0.184563\pi$
$242$	−14.7794	−	25.5986i	−0.950053	−	1.64554i
$243$	1.30193	+	15.5340i	0.0835186	+	0.996506i
$244$	9.36926	−	16.2280i	0.599805	−	1.03889i
$245$	1.66867	+	2.97850i	0.106608	+	0.190290i
$246$	−11.2860	+	9.12557i	−0.719567	+	0.581825i
$247$	−1.81530	+	2.96445i	−0.115505	+	0.188623i
$248$	0.0309783	+	0.134579i	0.00196712	+	0.00854575i
$249$	12.7670	+	23.7930i	0.809078	+	1.50782i
$250$	7.10047	+	9.03991i	0.449073	+	0.571734i
$251$	5.85758	+	11.1203i	0.369727	+	0.701910i	0.997042	−	0.0768557i	$-0.0244881\pi$
$251$	5.85758	+	11.1203i	0.369727	+	0.701910i	−0.627315	+	0.778766i	$0.715846\pi$
$252$	−1.74679	−	6.71421i	−0.110038	−	0.422955i
$253$	−6.52022	+	5.91678i	−0.409923	+	0.371985i
$254$	0.0378651	+	5.85760i	0.00237587	+	0.367539i
$255$	0.983326	+	0.407776i	0.0615783	+	0.0255359i
$256$	13.2125	+	1.37142i	0.825780	+	0.0857137i
$257$	−8.65548	+	1.12529i	−0.539914	+	0.0701936i	−0.394012	−	0.919105i	$-0.628913\pi$
$257$	−8.65548	+	1.12529i	−0.539914	+	0.0701936i	−0.145902	+	0.989299i	$0.546609\pi$
$258$	15.5093	−	13.9260i	0.965567	−	0.866997i
$259$	−2.44513	+	3.77050i	−0.151933	+	0.234287i
$260$	−0.252569	−	2.59663i	−0.0156637	−	0.161036i
$261$	6.97959	−	19.7195i	0.432026	−	1.22061i
$262$	20.0541	−	1.55873i	1.23895	−	0.0962986i
$263$	−4.38999	−	21.6133i	−0.270698	−	1.33273i	−0.853915	−	0.520413i	$-0.825778\pi$
$263$	−4.38999	−	21.6133i	−0.270698	−	1.33273i	0.583216	−	0.812317i	$-0.301794\pi$
$264$	2.65439	+	0.607628i	0.163366	+	0.0373969i
$265$	−3.91947	+	2.22925i	−0.240771	+	0.136942i
$266$	3.58885	−	0.753140i	0.220046	−	0.0461780i
$267$	−29.9135	−	1.70597i	−1.83067	−	0.104404i
$268$	25.9340	−	12.6074i	1.58417	−	0.770118i
$269$	−5.79912	+	7.78956i	−0.353578	+	0.474938i	−0.942955	−	0.332920i	$-0.891966\pi$
$269$	−5.79912	+	7.78956i	−0.353578	+	0.474938i	0.589377	+	0.807858i	$0.299373\pi$
$270$	4.79923	−	3.89978i	0.292072	−	0.237333i
$271$	5.50945	+	7.40047i	0.334675	+	0.449547i	0.937324	−	0.348460i	$-0.113295\pi$
$271$	5.50945	+	7.40047i	0.334675	+	0.449547i	−0.602648	+	0.798007i	$0.705888\pi$
$272$	3.42986	+	1.77843i	0.207966	+	0.107833i
$273$	3.60023	−	1.39502i	0.217896	−	0.0844304i
$274$	−11.9474	−	3.15993i	−0.721766	−	0.190898i
$275$	−10.4236	−	21.0939i	−0.628565	−	1.27201i
$276$	0.0761804	−	6.50018i	0.00458552	−	0.391265i
$277$	2.42439	−	1.68593i	0.145668	−	0.101298i	−0.495841	−	0.868413i	$-0.665140\pi$
$277$	2.42439	−	1.68593i	0.145668	−	0.101298i	0.641509	+	0.767116i	$0.278309\pi$
$278$	−9.77740	−	1.52916i	−0.586410	−	0.0917128i
$279$	−1.06427	−	0.799035i	−0.0637164	−	0.0478370i
$280$	−0.128412	+	0.147144i	−0.00767408	+	0.00879352i
$281$	−2.83827	+	5.74373i	−0.169317	+	0.342642i	−0.964652	−	0.263528i	$-0.915114\pi$
$281$	−2.83827	+	5.74373i	−0.169317	+	0.342642i	0.795335	+	0.606170i	$0.207295\pi$
$282$	−1.02405	−	19.3318i	−0.0609812	−	1.15119i
$283$	10.0089	−	8.62137i	0.594965	−	0.512487i	−0.302746	−	0.953071i	$-0.597904\pi$
$283$	10.0089	−	8.62137i	0.594965	−	0.512487i	0.897711	+	0.440584i	$0.145229\pi$
$284$	23.6443	+	19.3246i	1.40303	+	1.14670i
$285$	1.00468	+	1.36443i	0.0595121	+	0.0808219i
$286$	−2.34215	+	21.2275i	−0.138494	+	1.25521i
$287$	−0.0856559	+	4.41640i	−0.00505611	+	0.260692i
$288$	20.1044	−	13.6694i	1.18466	−	0.805479i
$289$	−10.4496	−	11.9739i	−0.614684	−	0.704350i
$290$	−8.02240	+	2.12183i	−0.471092	+	0.124598i
$291$	0.143451	+	1.36595i	0.00840925	+	0.0800731i
$292$	−6.97994	+	2.04059i	−0.408470	+	0.119416i
$293$	−0.499539	+	5.93046i	−0.0291834	+	0.346461i	0.966706	+	0.255888i	$0.0823679\pi$
$293$	−0.499539	+	5.93046i	−0.0291834	+	0.346461i	−0.995890	+	0.0905732i	$0.971130\pi$
$294$	18.6263	+	8.87883i	1.08631	+	0.517824i
$295$	2.14326	+	0.278642i	0.124785	+	0.0162232i
$296$	1.26719	+	0.300329i	0.0736539	+	0.0174563i
$297$	−23.3305	+	12.0134i	−1.35377	+	0.697086i
$298$	22.8415	−	5.41354i	1.32317	−	0.313598i
$299$	3.59847	−	0.373511i	0.208105	−	0.0216007i
$300$	16.6480	+	4.96215i	0.961172	+	0.286490i
$301$	−0.205003	−	6.34052i	−0.0118162	−	0.365461i
$302$	−29.5594	−	35.6935i	−1.70095	−	2.05393i
$303$	1.53399	+	8.32561i	0.0881255	+	0.478294i
$304$	3.21146	+	5.24444i	0.184190	+	0.300789i
$305$	3.62918	−	3.55947i	0.207806	−	0.203815i
$306$	6.27567	−	1.41787i	0.358756	−	0.0810542i
$307$	−10.6283	+	15.4964i	−0.606588	+	0.884427i	−0.999380	−	0.0352001i	$-0.988793\pi$
$307$	−10.6283	+	15.4964i	−0.606588	+	0.884427i	0.392792	+	0.919627i	$0.371509\pi$
$308$	9.32276	−	7.03466i	0.531213	−	0.400837i
$309$	−2.25202	−	2.82228i	−0.128113	−	0.160554i
$310$	−0.0238809	+	0.527403i	−0.00135634	+	0.0299545i
$311$	−1.70321	−	23.9127i	−0.0965801	−	1.35597i	−0.779927	−	0.625871i	$-0.784744\pi$
$311$	−1.70321	−	23.9127i	−0.0965801	−	1.35597i	0.683346	−	0.730094i	$-0.260524\pi$
$312$	−0.731257	−	0.846869i	−0.0413992	−	0.0479445i
$313$	−0.418818	−	1.12795i	−0.0236730	−	0.0637556i	0.925083	−	0.379764i	$-0.123995\pi$
$313$	−0.418818	−	1.12795i	−0.0236730	−	0.0637556i	−0.948756	+	0.316008i	$0.897657\pi$
$314$	0.327797	−	2.39990i	0.0184987	−	0.135434i
$315$	0.0319450	−	1.88179i	0.00179990	−	0.106027i
$316$	6.51845	−	30.0925i	0.366692	−	1.69284i
$317$	3.23172	+	9.85940i	0.181512	+	0.553759i	0.999778	−	0.0210805i	$-0.00671062\pi$
$317$	3.23172	+	9.85940i	0.181512	+	0.553759i	−0.818266	+	0.574839i	$0.805065\pi$
$318$	−11.5673	+	24.6756i	−0.648660	+	1.38374i
$319$	35.1671	−	1.82023i	1.96898	−	0.101914i
$320$	−4.98430	−	1.96151i	−0.278631	−	0.109652i
$321$	1.16930	+	2.85226i	0.0652641	+	0.159198i
$322$	−2.89166	−	2.49080i	−0.161146	−	0.138807i
$323$	0.306124	+	1.73612i	0.0170332	+	0.0966001i
$324$	5.22618	−	18.6567i	0.290343	−	1.03648i
$325$	−1.67882	+	9.52105i	−0.0931240	+	0.528133i
$326$	8.24656	−	6.73995i	0.456735	−	0.373291i
$327$	−1.47800	−	5.28475i	−0.0817336	−	0.292248i
$328$	1.21379	−	0.406564i	0.0670202	−	0.0224487i
$329$	−4.70315	−	3.54884i	−0.259293	−	0.195654i
$330$	9.15298	+	4.95917i	0.503855	+	0.272993i
$331$	−23.4576	+	12.5505i	−1.28935	+	0.689841i	−0.966514	−	0.256615i	$-0.917393\pi$
$331$	−23.4576	+	12.5505i	−1.28935	+	0.689841i	−0.322834	+	0.946456i	$0.604636\pi$
$332$	−4.54181	−	33.2519i	−0.249264	−	1.82494i
$333$	−11.2015	+	5.65958i	−0.613840	+	0.310143i
$334$	−2.53694	+	4.81627i	−0.138815	+	0.263535i
$335$	7.69486	−	1.40816i	0.420415	−	0.0769359i
$336$	0.696996	−	6.79498i	0.0380243	−	0.370696i
$337$	22.0055	+	22.7285i	1.19872	+	1.23810i	0.963960	+	0.266046i	$0.0857174\pi$
$337$	22.0055	+	22.7285i	1.19872	+	1.23810i	0.234757	+	0.972054i	$0.424571\pi$
$338$	−11.9902	+	13.0427i	−0.652182	+	0.709427i
$339$	4.26664	−	6.15136i	0.231732	−	0.334096i
$340$	−0.968233	−	0.901723i	−0.0525098	−	0.0489028i
$341$	0.558837	−	2.16954i	0.0302627	−	0.117487i
$342$	9.71842	+	3.22911i	0.525512	+	0.174610i
$343$	12.5627	−	5.71044i	0.678321	−	0.308335i
$344$	−1.71068	+	0.673215i	−0.0922335	+	0.0362973i
$345$	0.492797	−	1.69324i	0.0265313	−	0.0911608i
$346$	−2.75031	−	0.503306i	−0.147857	−	0.0270579i
$347$	21.0839	−	26.8428i	1.13184	−	1.44100i	0.250749	−	0.968052i	$-0.419323\pi$
$347$	21.0839	−	26.8428i	1.13184	−	1.44100i	0.881093	−	0.472943i	$-0.156808\pi$
$348$	−16.6879	+	19.9368i	−0.894566	+	1.06872i
$349$	−6.46896	−	22.6705i	−0.346276	−	1.21353i	−0.919158	−	0.393888i	$-0.871130\pi$
$349$	−6.46896	−	22.6705i	−0.346276	−	1.21353i	0.572883	−	0.819637i	$-0.305825\pi$
$350$	8.52109	−	5.60441i	0.455471	−	0.299568i
$351$	10.6484	+	1.69634i	0.568371	+	0.0905441i
$352$	34.1932	+	22.4892i	1.82250	+	1.19868i
$353$	−3.55447	+	11.3372i	−0.189186	+	0.603418i	0.810654	+	0.585525i	$0.199112\pi$
$353$	−3.55447	+	11.3372i	−0.189186	+	0.603418i	−0.999840	+	0.0178934i	$0.994304\pi$
$354$	11.5499	−	6.10170i	0.613871	−	0.324302i
$355$	4.77341	+	6.77046i	0.253347	+	0.359339i
$356$	34.0981	+	14.9707i	1.80720	+	0.793443i
$357$	0.899252	−	1.73943i	0.0475935	−	0.0920603i
$358$	−6.63538	−	14.3505i	−0.350691	−	0.758449i
$359$	1.99055	+	1.09834i	0.105057	+	0.0579681i	0.534771	−	0.844997i	$-0.320398\pi$
$359$	1.99055	+	1.09834i	0.105057	+	0.0579681i	−0.429714	+	0.902965i	$0.641386\pi$
$360$	−0.516742	+	0.174476i	−0.0272347	+	0.00919570i
$361$	5.83271	−	15.1071i	0.306985	−	0.795110i
$362$	41.3094	+	12.0768i	2.17118	+	0.634744i
$363$	−19.1605	−	16.2499i	−1.00566	−	0.852898i
$364$	−4.79849	+	0.0620401i	−0.251509	+	0.00325178i
$365$	−1.97261	+	0.0255041i	−0.103251	+	0.00133494i
$366$	5.49397	−	30.2281i	0.287175	−	1.58005i
$367$	−3.49111	−	1.02063i	−0.182234	−	0.0532763i	0.188220	−	0.982127i	$-0.439728\pi$
$367$	−3.49111	−	1.02063i	−0.182234	−	0.0532763i	−0.370455	+	0.928851i	$0.620798\pi$
$368$	2.30524	−	5.97073i	0.120169	−	0.311246i
$369$	−6.41665	+	10.5357i	−0.334037	+	0.548469i
$370$	4.35907	+	2.40523i	0.226617	+	0.125042i
$371$	3.48096	+	7.52837i	0.180722	+	0.390853i
$372$	0.892684	+	1.39254i	0.0462835	+	0.0721996i
$373$	−2.03009	−	0.891303i	−0.105114	−	0.0461499i	0.348787	−	0.937202i	$-0.386594\pi$
$373$	−2.03009	−	0.891303i	−0.105114	−	0.0461499i	−0.453901	+	0.891052i	$0.649968\pi$
$374$	6.24096	+	8.85198i	0.322712	+	0.457725i
$375$	8.27176	+	5.19952i	0.427152	+	0.268502i
$376$	−0.510793	+	1.62920i	−0.0263421	+	0.0840197i
$377$	−12.0890	−	7.95107i	−0.622616	−	0.409501i
$378$	−6.40711	−	9.39885i	−0.329546	−	0.483425i
$379$	−0.909373	+	0.598104i	−0.0467114	+	0.0307226i	−0.572650	−	0.819800i	$-0.694085\pi$
$379$	−0.909373	+	0.598104i	−0.0467114	+	0.0307226i	0.525939	+	0.850523i	$0.323714\pi$
$380$	−0.577871	−	2.02515i	−0.0296442	−	0.103888i
$381$	1.70849	+	4.67644i	0.0875287	+	0.239581i
$382$	−20.0012	+	25.4644i	−1.02335	+	1.30287i
$383$	−17.7877	−	3.25515i	−0.908911	−	0.166331i	−0.294808	−	0.955557i	$-0.595256\pi$
$383$	−17.7877	−	3.25515i	−0.908911	−	0.166331i	−0.614103	+	0.789226i	$0.710482\pi$
$384$	−4.17728	+	1.02395i	−0.213171	+	0.0522533i
$385$	2.94821	−	1.16023i	0.150255	−	0.0591308i
$386$	8.12394	−	3.69278i	0.413498	−	0.187958i
$387$	8.42086	−	15.5871i	0.428056	−	0.792336i
$388$	0.425813	−	1.65311i	0.0216174	−	0.0839238i
$389$	14.4651	+	13.4714i	0.733409	+	0.683029i	0.956488	−	0.291771i	$-0.0942446\pi$
$389$	14.4651	+	13.4714i	0.733409	+	0.683029i	−0.223079	+	0.974800i	$0.571611\pi$
$390$	−1.82494	−	3.86865i	−0.0924096	−	0.195897i
$391$	1.24173	−	1.35072i	0.0627971	−	0.0683091i
$392$	−1.26589	−	1.30748i	−0.0639369	−	0.0660375i
$393$	15.6009	−	6.99277i	0.786959	−	0.352739i
$394$	−38.7325	+	7.08803i	−1.95131	+	0.357090i
$395$	3.89278	−	7.39026i	0.195867	−	0.371845i
$396$	32.3861	−	3.86481i	1.62746	−	0.194214i
$397$	−2.57332	−	18.8400i	−0.129151	−	0.945554i	−0.935304	−	0.353846i	$-0.884874\pi$
$397$	−2.57332	−	18.8400i	−0.129151	−	0.945554i	0.806152	−	0.591708i	$-0.201546\pi$
$398$	−42.1109	+	22.5306i	−2.11083	+	1.12936i
$399$	2.65605	−	1.63087i	0.132969	−	0.0816454i
$400$	13.6529	+	10.3021i	0.682646	+	0.515103i
$401$	−13.4420	+	4.50245i	−0.671259	+	0.224842i	−0.632679	−	0.774414i	$-0.718045\pi$
$401$	−13.4420	+	4.50245i	−0.671259	+	0.224842i	−0.0385802	+	0.999256i	$0.512284\pi$
$402$	33.0648	−	33.7939i	1.64912	−	1.68549i
$403$	−0.712779	+	0.582557i	−0.0355060	+	0.0290192i
$404$	1.82714	−	10.3622i	0.0909034	−	0.515539i
$405$	2.72310	−	4.49560i	0.135312	−	0.223388i
$406$	2.65059	+	15.0322i	0.131547	+	0.746038i
$407$	−16.0073	−	13.7883i	−0.793454	−	0.683460i
$408$	−0.562318	−	0.0761133i	−0.0278389	−	0.00376817i
$409$	6.00698	+	2.36397i	0.297026	+	0.116891i	0.510019	−	0.860163i	$-0.329638\pi$
$409$	6.00698	+	2.36397i	0.297026	+	0.116891i	−0.212993	+	0.977054i	$0.568321\pi$
$410$	4.88711	−	0.252955i	0.241357	−	0.0124925i
$411$	−10.4657	+	0.894297i	−0.516233	+	0.0441124i
$412$	1.39780	+	4.26444i	0.0688647	+	0.210094i
$413$	0.841643	−	3.88546i	0.0414145	−	0.191191i
$414$	−3.47483	−	10.0760i	−0.170779	−	0.495207i
$415$	1.23210	−	9.02058i	0.0604815	−	0.442803i
$416$	−5.85358	−	15.7647i	−0.286995	−	0.772930i
$417$	−8.26204	+	1.57757i	−0.404594	+	0.0772537i
$418$	1.22481	+	17.1960i	0.0599072	+	0.841085i
$419$	−1.35039	+	29.8230i	−0.0659710	+	1.45695i	0.650591	+	0.759428i	$0.274521\pi$
$419$	−1.35039	+	29.8230i	−0.0659710	+	1.45695i	−0.716562	+	0.697523i	$0.754285\pi$
$420$	−0.853988	+	2.17775i	−0.0416703	+	0.106264i
$421$	−18.7545	+	14.1515i	−0.914038	+	0.689703i	−0.950861	−	0.309618i	$-0.899799\pi$
$421$	−18.7545	+	14.1515i	−0.914038	+	0.689703i	0.0368234	+	0.999322i	$0.488276\pi$
$422$	−7.09985	+	10.3518i	−0.345615	+	0.503920i
$423$	−6.35798	−	15.1761i	−0.309136	−	0.737886i
$424$	1.71598	−	1.68302i	0.0833353	−	0.0817347i
$425$	2.56050	+	4.18139i	0.124202	+	0.202827i
$426$	47.1780	+	16.7626i	2.28578	+	0.812149i
$427$	−5.96401	−	7.20166i	−0.288618	−	0.348513i
$428$	−0.123813	−	3.82940i	−0.00598472	−	0.185101i
$429$	4.20744	+	17.6574i	0.203137	+	0.852508i
$430$	−6.99049	+	0.725594i	−0.337111	+	0.0349912i
$431$	−5.45574	+	1.29303i	−0.262794	+	0.0622833i	−0.359901	−	0.932991i	$-0.617189\pi$
$431$	−5.45574	+	1.29303i	−0.262794	+	0.0622833i	0.0971066	+	0.995274i	$0.469041\pi$
$432$	11.2363	−	15.4153i	0.540606	−	0.741670i
$433$	−21.2915	−	5.04617i	−1.02320	−	0.242503i	−0.315433	−	0.948948i	$-0.602150\pi$
$433$	−21.2915	−	5.04617i	−1.02320	−	0.242503i	−0.707769	+	0.706444i	$0.750298\pi$
$434$	0.963015	+	0.125200i	0.0462262	+	0.00600981i
$435$	−5.81167	+	3.99630i	−0.278648	+	0.191608i
$436$	−0.572478	+	6.79638i	−0.0274167	+	0.325488i
$437$	2.80308	−	0.819482i	0.134090	−	0.0392012i
$438$	−9.64667	+	7.00748i	−0.460936	+	0.334830i
$439$	10.0288	−	2.65250i	0.478649	−	0.126597i	−0.00841237	−	0.999965i	$-0.502678\pi$
$439$	10.0288	−	2.65250i	0.478649	−	0.126597i	0.487062	+	0.873368i	$0.338069\pi$
$440$	−0.603696	−	0.691759i	−0.0287801	−	0.0329783i
$441$	17.4487	+	1.76848i	0.830889	+	0.0842135i
$442$	0.0862985	−	4.44953i	0.00410480	−	0.211642i
$443$	−2.66444	+	24.1485i	−0.126591	+	1.14733i	0.748419	+	0.663226i	$0.230813\pi$
$443$	−2.66444	+	24.1485i	−0.126591	+	1.14733i	−0.875011	+	0.484104i	$0.839146\pi$
$444$	15.5023	−	1.72943i	0.735708	−	0.0820753i
$445$	7.82220	+	6.39311i	0.370808	+	0.303063i
$446$	−29.8322	+	25.6967i	−1.41260	+	1.21677i
$447$	16.7269	−	10.8760i	0.791157	−	0.514417i
$448$	−4.36489	+	8.83312i	−0.206222	+	0.417325i
$449$	14.4540	−	16.5624i	0.682126	−	0.781629i	−0.303087	−	0.952963i	$-0.598017\pi$
$449$	14.4540	−	16.5624i	0.682126	−	0.781629i	0.985213	+	0.171333i	$0.0548075\pi$
$450$	28.4407	−	1.54105i	1.34071	−	0.0726459i
$451$	−20.5171	−	3.20881i	−0.966112	−	0.151097i
$452$	−7.63909	+	5.31224i	−0.359313	+	0.249867i
$453$	−33.8797	−	20.0935i	−1.59181	−	0.944074i
$454$	−14.1740	−	28.6835i	−0.665217	−	1.34618i
$455$	−1.25857	−	0.332876i	−0.0590025	−	0.0156055i
$456$	−0.703713	−	0.566196i	−0.0329544	−	0.0265146i
$457$	4.18745	+	2.17126i	0.195881	+	0.101567i	0.555445	−	0.831553i	$-0.312548\pi$
$457$	4.18745	+	2.17126i	0.195881	+	0.101567i	−0.359564	+	0.933120i	$0.617075\pi$
$458$	12.5005	+	16.7911i	0.584112	+	0.784598i
$459$	4.61561	−	2.93256i	0.215438	−	0.136880i
$460$	−1.30887	+	1.75812i	−0.0610266	+	0.0819730i
$461$	−25.6151	+	12.4523i	−1.19301	+	0.579963i	−0.923710	−	0.383092i	$-0.874859\pi$
$461$	−25.6151	+	12.4523i	−1.19301	+	0.579963i	−0.269303	+	0.963055i	$0.586793\pi$
$462$	10.5031	−	16.0113i	0.488647	−	0.744912i
$463$	−13.3353	+	2.79848i	−0.619743	+	0.130057i	−0.504687	−	0.863302i	$-0.668392\pi$
$463$	−13.3353	+	2.79848i	−0.619743	+	0.130057i	−0.115056	+	0.993359i	$0.536705\pi$
$464$	−22.2508	+	12.6554i	−1.03297	+	0.587513i
$465$	0.131990	+	0.428873i	0.00612090	+	0.0198885i
$466$	5.28720	+	26.0305i	0.244925	+	1.20584i
$467$	−38.1990	+	2.96906i	−1.76764	+	0.137392i	−0.919679	−	0.392670i	$-0.871551\pi$
$467$	−38.1990	+	2.96906i	−1.76764	+	0.137392i	−0.847959	+	0.530062i	$0.822169\pi$
$468$	−11.6654	−	6.59754i	−0.539231	−	0.304972i
$469$	−1.39304	−	14.3217i	−0.0643245	−	0.661314i
$470$	−3.55149	+	5.47657i	−0.163818	+	0.252615i
$471$	−0.425262	−	2.01433i	−0.0195950	−	0.0928153i
$472$	−1.14246	+	0.148530i	−0.0525862	+	0.00683667i
$473$	29.6646	+	3.07910i	1.36398	+	0.141577i
$474$	−6.56905	−	50.0542i	−0.301726	−	2.29907i
$475$	0.0504480	+	7.80413i	0.00231471	+	0.358078i
$476$	−1.80230	+	1.63550i	−0.0826083	+	0.0749630i
$477$	−2.18667	+	23.0596i	−0.100121	+	1.05583i
$478$	−10.1022	−	19.1786i	−0.462065	−	0.877210i
$479$	20.3540	+	25.9136i	0.929999	+	1.18402i	0.982662	+	0.185409i	$0.0593609\pi$
$479$	20.3540	+	25.9136i	0.929999	+	1.18402i	−0.0526627	+	0.998612i	$0.516771\pi$
$480$	−8.19316	−	0.254986i	−0.373965	−	0.0116385i
$481$	1.94734	+	8.45981i	0.0887911	+	0.385734i
$482$	1.43004	−	2.33531i	0.0651366	−	0.106370i
$483$	−3.02753	−	1.16470i	−0.137757	−	0.0529955i
$484$	15.2620	+	27.2419i	0.693726	+	1.23827i
$485$	0.231547	−	0.401050i	0.0105140	−	0.0182108i
$486$	−2.24364	−	31.6873i	−0.101774	−	1.43737i
$487$	21.2492	+	36.8047i	0.962893	+	1.66778i	0.715173	+	0.698947i	$0.246348\pi$
$487$	21.2492	+	36.8047i	0.962893	+	1.66778i	0.247720	+	0.968832i	$0.420319\pi$
$488$	−1.38508	+	2.32896i	−0.0626994	+	0.105427i
$489$	4.66797	−	7.75597i	0.211093	−	0.350737i
$490$	−3.32173	−	6.11315i	−0.150060	−	0.276164i
$491$	16.2353	−	15.1200i	0.732688	−	0.682358i	−0.223634	−	0.974673i	$-0.571792\pi$
$491$	16.2353	−	15.1200i	0.732688	−	0.682358i	0.956322	+	0.292315i	$0.0944256\pi$
$492$	12.0461	−	9.48529i	0.543080	−	0.427630i
$493$	−7.26406	+	1.04006i	−0.327157	+	0.0468418i
$494$	3.77706	−	5.99272i	0.169938	−	0.269625i
$495$	8.74506	+	1.34605i	0.393061	+	0.0605002i
$496$	0.344774	+	1.59165i	0.0154808	+	0.0714674i
$497$	13.1469	−	7.70410i	0.589719	−	0.345576i
$498$	−25.3881	−	48.8185i	−1.13767	−	2.18761i
$499$	−11.5836	+	15.9868i	−0.518551	+	0.715668i	−0.985700	−	0.168510i	$-0.946104\pi$
$499$	−11.5836	+	15.9868i	−0.518551	+	0.715668i	0.467149	+	0.884179i	$0.345281\pi$
$500$	−7.37684	−	9.64592i	−0.329902	−	0.431379i
$501$	−0.650226	+	4.58084i	−0.0290500	+	0.204657i
$502$	−11.6428	−	22.8138i	−0.519644	−	1.01823i
$503$	−19.9433	+	14.2546i	−0.889226	+	0.635581i	−0.931586	−	0.363522i	$-0.881574\pi$
$503$	−19.9433	+	14.2546i	−0.889226	+	0.635581i	0.0423595	+	0.999102i	$0.486513\pi$
$504$	0.240024	+	0.974099i	0.0106915	+	0.0433898i
$505$	1.23136	−	2.57517i	0.0547948	−	0.114594i
$506$	13.4419	−	11.8846i	0.597564	−	0.528336i
$507$	−5.85796	+	13.8720i	−0.260161	+	0.616077i
$508$	0.0400006	−	6.18796i	0.00177474	−	0.274546i
$509$	−29.4233	−	32.8482i	−1.30416	−	1.45597i	−0.809787	−	0.586725i	$-0.800417\pi$
$509$	−29.4233	−	32.8482i	−1.30416	−	1.45597i	−0.494376	−	0.869248i	$-0.664603\pi$
$510$	−1.99294	−	0.856816i	−0.0882491	−	0.0379404i
$511$	−0.257812	+	3.61963i	−0.0114049	+	0.160123i
$512$	−31.8192	−	3.71913i	−1.40622	−	0.164364i
$513$	8.70187	−	0.200353i	0.384197	−	0.00884580i
$514$	17.6666	−	2.06493i	0.779240	−	0.0910801i
$515$	0.0550685	+	1.21617i	0.00242661	+	0.0535909i
$516$	−16.5728	+	14.4984i	−0.729578	+	0.638256i
$517$	19.5228	−	19.6494i	0.858611	−	0.864179i
$518$	5.08168	−	7.61859i	0.223276	−	0.334741i
$519$	−2.34501	+	0.385209i	−0.102934	+	0.0169088i
$520$	0.0316656	+	0.375930i	0.00138863	+	0.0164856i
$521$	−2.09127	−	5.41653i	−0.0916203	−	0.237303i	0.879497	−	0.475904i	$-0.157879\pi$
$521$	−2.09127	−	5.41653i	−0.0916203	−	0.237303i	−0.971118	+	0.238601i	$0.923311\pi$
$522$	−14.7416	+	39.9979i	−0.645221	+	1.75066i
$523$	1.64516	+	4.80815i	0.0719376	+	0.210246i	0.976259	−	0.216607i	$-0.0694989\pi$
$523$	1.64516	+	4.80815i	0.0719376	+	0.210246i	−0.904321	+	0.426852i	$0.859622\pi$
$524$	−21.2046	+	1.37262i	−0.926329	+	0.0599631i
$525$	5.21297	−	6.92596i	0.227513	−	0.302274i
$526$	8.37592	+	44.1562i	0.365207	+	1.92530i
$527$	−0.0751186	+	0.460776i	−0.00327222	+	0.0200717i
$528$	31.2076	+	7.56975i	1.35813	+	0.329431i
$529$	16.0875	+	11.8159i	0.699457	+	0.513733i
$530$	8.04528	−	4.43920i	0.349465	−	0.192827i
$531$	7.49418	−	8.19165i	0.325220	−	0.355487i
$532$	−3.80122	+	0.746535i	−0.164804	+	0.0323664i
$533$	6.01414	+	6.05314i	0.260501	+	0.262191i
$534$	60.9086	+	4.26427i	2.63577	+	0.184533i
$535$	0.246231	−	1.00980i	0.0106455	−	0.0436572i
$536$	−3.77347	+	1.77447i	−0.162989	+	0.0766453i
$537$	−9.42107	−	9.58236i	−0.406549	−	0.413509i
$538$	12.0219	−	15.7197i	0.518299	−	0.677725i
$539$	8.46753	+	28.2835i	0.364722	+	1.21826i
$540$	−5.12274	+	4.05383i	−0.220447	+	0.174449i
$541$	4.66641	−	15.5869i	0.200625	−	0.670133i	−0.797170	−	0.603755i	$-0.793670\pi$
$541$	4.66641	−	15.5869i	0.200625	−	0.670133i	0.997795	−	0.0663782i	$-0.0211444\pi$
$542$	−11.0314	−	15.2248i	−0.473840	−	0.653962i
$543$	36.5161	−	2.17113i	1.56705	−	0.0931719i
$544$	−7.51977	−	4.02331i	−0.322408	−	0.172498i
$545$	−0.644049	+	1.73454i	−0.0275880	+	0.0742996i
$546$	−7.37280	+	2.74773i	−0.315527	+	0.117592i
$547$	−38.1924	+	0.987749i	−1.63299	+	0.0422331i	−0.831410	−	0.555659i	$-0.812466\pi$
$547$	−38.1924	+	0.987749i	−1.63299	+	0.0422331i	−0.801577	+	0.597892i	$0.796005\pi$
$548$	12.5769	+	3.50103i	0.537261	+	0.149557i
$549$	−4.26399	−	25.7627i	−0.181983	−	1.09953i
$550$	20.6840	+	43.2569i	0.881969	+	1.84448i
$551$	−10.7546	−	4.55687i	−0.458163	−	0.194129i
$552$	−0.0231671	+	0.939745i	−0.000986057	+	0.0399982i
$553$	−12.9449	−	8.27628i	−0.550475	−	0.351943i
$554$	−4.98451	+	3.37148i	−0.211772	+	0.143240i
$555$	4.17724	+	0.675816i	0.177314	+	0.0286868i
$556$	10.3071	+	1.74880i	0.437118	+	0.0741654i
$557$	25.2700	−	10.3239i	1.07073	−	0.437439i	0.226823	−	0.973936i	$-0.427166\pi$
$557$	25.2700	−	10.3239i	1.07073	−	0.437439i	0.843902	+	0.536497i	$0.180253\pi$
$558$	2.14758	+	1.65620i	0.0909143	+	0.0701127i
$559$	−9.07505	−	8.23517i	−0.383834	−	0.348311i
$560$	−1.53665	+	1.71552i	−0.0649352	+	0.0724940i
$561$	7.53013	+	5.29539i	0.317922	+	0.223571i
$562$	5.93475	−	11.6290i	0.250342	−	0.490540i
$563$	6.16171	+	41.1380i	0.259685	+	1.73376i	0.605842	+	0.795585i	$0.292836\pi$
$563$	6.16171	+	41.1380i	0.259685	+	1.73376i	−0.346157	+	0.938177i	$0.612514\pi$
$564$	0.817694	+	20.4344i	0.0344311	+	0.860443i
$565$	−2.38289	+	0.832574i	−0.100249	+	0.0350267i
$566$	−20.6218	+	17.3038i	−0.866799	+	0.727331i
$567$	−7.81976	−	5.68539i	−0.328399	−	0.238764i
$568$	−3.38269	−	2.83842i	−0.141935	−	0.119097i
$569$	−22.1165	−	8.37510i	−0.927171	−	0.351102i	−0.156019	−	0.987754i	$-0.549866\pi$
$569$	−22.1165	−	8.37510i	−0.927171	−	0.351102i	−0.771152	+	0.636652i	$0.780319\pi$
$570$	−2.01125	−	2.80672i	−0.0842421	−	0.117560i
$571$	−1.38742	+	6.83069i	−0.0580618	+	0.285856i	−0.998541	−	0.0539950i	$-0.982804\pi$
$571$	−1.38742	+	6.83069i	−0.0580618	+	0.285856i	0.940479	+	0.339851i	$0.110377\pi$
$572$	2.76394	−	22.3908i	0.115566	−	0.936208i
$573$	−8.70959	+	26.1071i	−0.363848	+	1.09064i
$574$	0.290888	−	8.99687i	0.0121414	−	0.375522i
$575$	6.41991	−	4.97581i	0.267729	−	0.207505i
$576$	−22.9523	+	15.1756i	−0.956345	+	0.632317i
$577$	−1.13411	−	1.79939i	−0.0472137	−	0.0749096i	0.821550	−	0.570136i	$-0.193110\pi$
$577$	−1.13411	−	1.79939i	−0.0472137	−	0.0749096i	−0.868764	+	0.495227i	$0.835085\pi$
$578$	20.9774	+	24.6742i	0.872543	+	1.02631i
$579$	5.44285	−	5.28248i	0.226197	−	0.219532i
$580$	8.50312	−	2.13175i	0.353073	−	0.0885159i
$581$	−16.3440	−	3.65110i	−0.678064	−	0.151473i
$582$	−0.256319	−	2.78711i	−0.0106248	−	0.115530i
$583$	−37.2818	+	11.4245i	−1.54405	+	0.473156i
$584$	1.01307	−	0.282008i	0.0419212	−	0.0116696i
$585$	−2.56869	−	2.57288i	−0.106202	−	0.106375i
$586$	1.17413	−	12.0711i	0.0485029	−	0.498653i
$587$	27.5335	+	21.9156i	1.13643	+	0.904555i	0.996331	−	0.0855825i	$-0.0272751\pi$
$587$	27.5335	+	21.9156i	1.13643	+	0.904555i	0.140097	+	0.990138i	$0.455259\pi$
$588$	−19.5539	−	9.63317i	−0.806390	−	0.397265i
$589$	−0.481329	+	0.566153i	−0.0198328	+	0.0233279i
$590$	−4.35989	−	0.624243i	−0.179494	−	0.0256997i
$591$	−28.9632	+	16.7687i	−1.19139	+	0.689771i
$592$	14.8967	+	3.73463i	0.612252	+	0.153493i
$593$	−2.09131	−	1.05030i	−0.0858800	−	0.0431306i	0.405341	−	0.914166i	$-0.367153\pi$
$593$	−2.09131	−	1.05030i	−0.0858800	−	0.0431306i	−0.491221	+	0.871035i	$0.663449\pi$
$594$	47.8562	−	23.8645i	1.96356	−	0.979174i
$595$	−0.590002	+	0.296310i	−0.0241877	+	0.0121475i
$596$	−24.2016	+	5.40642i	−0.991337	+	0.221456i
$597$	−27.2424	+	30.0938i	−1.11496	+	1.23166i
$598$	−7.34230	+	0.666288i	−0.300249	+	0.0272465i
$599$	1.97644	+	17.9129i	0.0807550	+	0.731903i	0.964527	+	0.263985i	$0.0850369\pi$
$599$	1.97644	+	17.9129i	0.0807550	+	0.731903i	−0.883772	+	0.467918i	$0.845004\pi$
$600$	−2.39792	−	0.748620i	−0.0978947	−	0.0305623i
$601$	−38.0766	−	3.45531i	−1.55317	−	0.140945i	−0.720008	−	0.693966i	$-0.755862\pi$
$601$	−38.0766	−	3.45531i	−1.55317	−	0.140945i	−0.833167	+	0.553021i	$0.813475\pi$
$602$	0.250685	+	12.9252i	0.0102171	+	0.526793i
$603$	16.7767	−	36.5151i	0.683202	−	1.48701i
$604$	30.7364	+	38.1071i	1.25064	+	1.55056i
$605$	2.00677	+	8.22979i	0.0815868	+	0.334589i
$606$	−2.90642	−	17.0052i	−0.118065	−	0.690789i
$607$	−3.46967	+	6.19320i	−0.140830	+	0.251374i	−0.933731	−	0.357976i	$-0.883467\pi$
$607$	−3.46967	+	6.19320i	−0.140830	+	0.251374i	0.792901	+	0.609350i	$0.208570\pi$
$608$	−6.93881	−	11.6674i	−0.281406	−	0.473175i
$609$	6.42773	+	11.2695i	0.260465	+	0.456663i
$610$	−7.48882	+	7.15739i	−0.303213	+	0.289794i
$611$	−11.2448	+	1.75865i	−0.454915	+	0.0711474i
$612$	−6.64842	+	1.41200i	−0.268746	+	0.0570768i
$613$	−29.6965	+	17.9219i	−1.19943	+	0.723859i	−0.968476	−	0.249106i	$-0.919863\pi$
$613$	−29.6965	+	17.9219i	−1.19943	+	0.723859i	−0.230953	+	0.972965i	$0.574184\pi$
$614$	22.0651	−	31.2965i	0.890475	−	1.26302i
$615$	3.83822	−	1.60256i	0.154772	−	0.0646216i
$616$	−1.36117	+	0.999740i	−0.0548429	+	0.0402807i
$617$	−14.1560	+	30.6155i	−0.569897	+	1.23253i	0.381444	+	0.924392i	$0.375427\pi$
$617$	−14.1560	+	30.6155i	−0.569897	+	1.23253i	−0.951341	+	0.308141i	$0.900293\pi$
$618$	4.51449	+	5.81019i	0.181600	+	0.233720i
$619$	−23.3771	−	25.4290i	−0.939606	−	1.02208i	−0.999715	−	0.0238877i	$-0.992396\pi$
$619$	−23.3771	−	25.4290i	−0.939606	−	1.02208i	0.0601082	−	0.998192i	$-0.480855\pi$
$620$	0.0324284	−	0.556774i	0.00130236	−	0.0223606i
$621$	−5.66733	−	7.06732i	−0.227422	−	0.283602i
$622$	2.84058	+	48.7709i	0.113897	+	1.95553i
$623$	12.9259	−	13.3506i	0.517867	−	0.534882i
$624$	−8.49376	−	10.0977i	−0.340023	−	0.404230i
$625$	7.44433	+	18.5634i	0.297773	+	0.742537i
$626$	0.823693	+	2.30942i	0.0329214	+	0.0923030i
$627$	5.90673	+	13.4095i	0.235892	+	0.535522i
$628$	−0.379031	+	2.53056i	−0.0151250	+	0.100980i
$629$	3.58173	+	2.56007i	0.142813	+	0.102076i
$630$	−0.114669	+	3.83361i	−0.00456853	+	0.152735i
$631$	−12.9713	−	12.7222i	−0.516381	−	0.506463i	0.394633	−	0.918839i	$-0.370872\pi$
$631$	−12.9713	−	12.7222i	−0.516381	−	0.506463i	−0.911014	+	0.412376i	$0.864699\pi$
$632$	−0.998786	+	4.33901i	−0.0397296	+	0.172597i
$633$	−2.71556	+	10.3177i	−0.107934	+	0.410092i
$634$	−6.32541	−	20.1753i	−0.251214	−	0.801262i
$635$	0.460627	−	1.61427i	0.0182794	−	0.0640604i
$636$	12.5556	−	25.9071i	0.497862	−	1.02728i
$637$	4.07536	−	11.4262i	0.161472	−	0.452724i
$638$	−71.7066	+	2.78254i	−2.83889	+	0.110162i
$639$	42.5546	−	0.102912i	1.68343	−	0.00407112i
$640$	1.34245	+	0.548452i	0.0530651	+	0.0216795i
$641$	−21.5925	−	13.4150i	−0.852853	−	0.529860i	0.0299784	−	0.999551i	$-0.490456\pi$
$641$	−21.5925	−	13.4150i	−0.852853	−	0.529860i	−0.882831	+	0.469690i	$0.844366\pi$
$642$	−2.30750	−	5.84274i	−0.0910697	−	0.230595i
$643$	33.1072	−	14.0279i	1.30562	−	0.553208i	0.377681	−	0.925936i	$-0.376722\pi$
$643$	33.1072	−	14.0279i	1.30562	−	0.553208i	0.927941	+	0.372728i	$0.121578\pi$
$644$	3.02047	+	2.67054i	0.119023	+	0.105234i
$645$	−5.38595	+	2.58339i	−0.212072	+	0.101721i
$646$	−0.578039	−	3.54568i	−0.0227426	−	0.139503i
$647$	−24.2881	+	8.84015i	−0.954865	+	0.347542i	−0.772019	−	0.635599i	$-0.780753\pi$
$647$	−24.2881	+	8.84015i	−0.954865	+	0.347542i	−0.182845	+	0.983142i	$0.558531\pi$
$648$	−0.790552	+	2.68787i	−0.0310558	+	0.105590i
$649$	17.5630	+	6.39240i	0.689407	+	0.250924i
$650$	3.67170	−	19.3564i	0.144016	−	0.759222i
$651$	0.806480	−	0.175716i	0.0316084	−	0.00688684i
$652$	−8.80297	+	7.00684i	−0.344751	+	0.274409i
$653$	−10.1432	−	15.6413i	−0.396935	−	0.612092i	0.582746	−	0.812654i	$-0.301978\pi$
$653$	−10.1432	−	15.6413i	−0.396935	−	0.612092i	−0.979681	+	0.200562i	$0.935723\pi$
$654$	2.87244	+	10.8075i	0.112321	+	0.422606i
$655$	−5.64155	−	1.18391i	−0.220434	−	0.0462592i
$656$	14.3748	−	4.60909i	0.561242	−	0.179955i
$657$	−5.71169	+	8.37118i	−0.222834	+	0.326591i
$658$	9.48993	+	7.35525i	0.369956	+	0.286738i
$659$	−6.86461	+	8.28916i	−0.267407	+	0.322900i	−0.886775	−	0.462201i	$-0.847060\pi$
$659$	−6.86461	+	8.28916i	−0.267407	+	0.322900i	0.619368	+	0.785101i	$0.287389\pi$
$660$	−9.60065	−	5.36342i	−0.373705	−	0.208771i
$661$	−31.6487	−	15.3855i	−1.23099	−	0.598426i	−0.296712	−	0.954967i	$-0.595890\pi$
$661$	−31.6487	−	15.3855i	−1.23099	−	0.598426i	−0.934280	+	0.356541i	$0.883956\pi$
$662$	48.1294	−	24.9558i	1.87060	−	0.969934i
$663$	−1.20572	−	3.58526i	−0.0468265	−	0.139240i
$664$	0.594555	+	4.81652i	0.0230732	+	0.186917i
$665$	−1.04773	−	0.0814363i	−0.0406294	−	0.00315796i
$666$	22.9740	−	11.2372i	0.890226	−	0.435433i
$667$	3.03230	+	11.7721i	0.117411	+	0.455817i
$668$	2.74557	−	5.05282i	0.106229	−	0.195500i
$669$	−16.5099	+	29.1095i	−0.638309	+	1.12544i
$670$	−15.7166	+	2.66663i	−0.607186	+	0.103021i
$671$	37.3398	−	23.1985i	1.44149	−	0.895567i
$672$	−1.73235	+	14.9783i	−0.0668270	+	0.577799i
$673$	13.9374	−	31.1952i	0.537245	−	1.20249i	−0.418480	−	0.908226i	$-0.637437\pi$
$673$	13.9374	−	31.1952i	0.537245	−	1.20249i	0.955725	−	0.294261i	$-0.0950734\pi$
$674$	−44.2410	−	46.8928i	−1.70410	−	1.80624i
$675$	22.3169	−	9.38137i	0.858979	−	0.361089i
$676$	12.8435	−	13.6133i	0.493981	−	0.523590i
$677$	10.3914	+	24.9729i	0.399375	+	0.959786i	0.988428	+	0.151691i	$0.0484720\pi$
$677$	10.3914	+	24.9729i	0.399375	+	0.959786i	−0.589053	+	0.808094i	$0.700499\pi$
$678$	−8.85603	+	12.4220i	−0.340114	+	0.477064i
$679$	−0.699355	−	0.486333i	−0.0268388	−	0.0186637i
$680$	0.138315	+	0.132194i	0.00530414	+	0.00506940i
$681$	−19.5599	−	18.8919i	−0.749536	−	0.723939i
$682$	−1.19588	+	4.40607i	−0.0457926	+	0.168717i
$683$	−1.77452	+	5.18623i	−0.0679001	+	0.198446i	−0.974881	−	0.222726i	$-0.928504\pi$
$683$	−1.77452	+	5.18623i	−0.0679001	+	0.198446i	0.906981	+	0.421172i	$0.138381\pi$
$684$	−10.2216	−	3.54367i	−0.390831	−	0.135496i
$685$	3.03220	+	1.82994i	0.115854	+	0.0699185i
$686$	−25.7489	+	11.3050i	−0.983099	+	0.431626i
$687$	14.8136	+	9.85499i	0.565175	+	0.375991i
$688$	−20.2747	+	7.67765i	−0.772966	+	0.292708i
$689$	15.1255	+	5.28479i	0.576234	+	0.201334i
$690$	−1.04876	+	3.43726i	−0.0399257	+	0.130854i
$691$	−7.94245	−	11.9075i	−0.302145	−	0.452984i	0.649421	−	0.760429i	$-0.275011\pi$
$691$	−7.94245	−	11.9075i	−0.302145	−	0.452984i	−0.951566	+	0.307445i	$0.900526\pi$
$692$	2.89830	+	0.569208i	0.110177	+	0.0216380i
$693$	3.81742	−	15.8214i	0.145012	−	0.601006i
$694$	−43.6690	+	54.1410i	−1.65765	+	2.05517i
$695$	2.56646	+	1.20687i	0.0973514	+	0.0457794i
$696$	2.45024	−	2.85154i	0.0928762	−	0.108087i
$697$	4.31841	+	0.279539i	0.163571	+	0.0105883i
$698$	12.5843	+	46.3653i	0.476323	+	1.75495i
$699$	11.6885	+	19.3150i	0.442101	+	0.730559i
$700$	−9.07745	+	5.80362i	−0.343095	+	0.219356i
$701$	−12.7979	+	29.6690i	−0.483372	+	1.12058i	0.485772	+	0.874086i	$0.338539\pi$
$701$	−12.7979	+	29.6690i	−0.483372	+	1.12058i	−0.969144	+	0.246496i	$0.920721\pi$
$702$	−21.6532	−	3.73711i	−0.817248	−	0.141048i
$703$	2.77559	+	6.43453i	0.104683	+	0.242683i
$704$	−38.3676	−	25.9515i	−1.44603	−	0.978084i
$705$	−1.27290	+	5.39988i	−0.0479402	+	0.203371i
$706$	7.54150	−	23.0077i	0.283828	−	0.865908i
$707$	−4.53004	−	2.65461i	−0.170370	−	0.0998368i
$708$	−12.2836	+	6.28755i	−0.461646	+	0.236301i
$709$	0.817408	+	0.273795i	0.0306984	+	0.0102826i	0.332919	−	0.942956i	$-0.391967\pi$
$709$	0.817408	+	0.273795i	0.0306984	+	0.0102826i	−0.302220	+	0.953238i	$0.597728\pi$
$710$	−9.54824	−	13.9217i	−0.358339	−	0.522471i
$711$	−19.5970	−	38.1717i	−0.734946	−	1.43155i
$712$	−4.90240	−	2.22841i	−0.183725	−	0.0835133i
$713$	0.772365	+	0.0399773i	0.0289253	+	0.00149716i
$714$	−1.87820	+	3.52068i	−0.0702898	+	0.131758i
$715$	2.35127	−	5.65062i	0.0879325	−	0.211321i
$716$	6.81303	+	15.2492i	0.254615	+	0.569890i
$717$	−13.5785	−	12.4526i	−0.507099	−	0.465050i
$718$	−4.02713	−	2.29048i	−0.150291	−	0.0854801i
$719$	−21.2961	−	6.82832i	−0.794211	−	0.254653i	−0.119595	−	0.992823i	$-0.538160\pi$
$719$	−21.2961	−	6.82832i	−0.794211	−	0.254653i	−0.674616	+	0.738169i	$0.735691\pi$
$720$	−6.11995	+	1.97862i	−0.228077	+	0.0737387i
$721$	2.23768	+	0.0868322i	0.0833356	+	0.00323380i
$722$	−12.2831	+	30.6295i	−0.457129	+	1.13991i
$723$	0.475266	−	2.27843i	0.0176753	−	0.0847359i
$724$	−43.4706	−	13.3210i	−1.61557	−	0.495072i
$725$	−32.4748	−	0.839880i	−1.20608	−	0.0311924i
$726$	38.6145	+	33.6166i	1.43312	+	1.24763i
$727$	20.4583	+	0.264508i	0.758758	+	0.00981005i	0.391340	−	0.920246i	$-0.372011\pi$
$727$	20.4583	+	0.264508i	0.758758	+	0.00981005i	0.367418	+	0.930056i	$0.380242\pi$
$728$	0.693949			0.0257195
$729$	−10.8737	−	24.7136i	−0.402731	−	0.915318i
$730$	4.02019			0.148794
$731$	−6.21437	−	0.0803462i	−0.229847	−	0.00297171i
$732$	−6.21617	+	31.8552i	−0.229756	+	1.17740i
$733$	−27.8750	−	0.720918i	−1.02959	−	0.0266277i	−0.492632	−	0.870238i	$-0.663965\pi$
$733$	−27.8750	−	0.720918i	−1.02959	−	0.0266277i	−0.536956	+	0.843610i	$0.680426\pi$
$734$	7.08681	+	2.17167i	0.261579	+	0.0801576i
$735$	−4.40947	−	3.94011i	−0.162646	−	0.145333i
$736$	−5.25862	+	13.1131i	−0.193835	+	0.483354i
$737$	67.5967	+	2.62306i	2.48996	+	0.0966216i
$738$	13.3525	−	21.2992i	0.491513	−	0.784036i
$739$	−35.4759	−	11.3749i	−1.30500	−	0.418433i	−0.430123	−	0.902771i	$-0.641530\pi$
$739$	−35.4759	−	11.3749i	−1.30500	−	0.418433i	−0.874881	+	0.484338i	$0.839061\pi$
$740$	−4.57167	−	2.60020i	−0.168058	−	0.0955852i
$741$	1.30553	−	5.87753i	0.0479597	−	0.215916i
$742$	−6.89468	−	15.4320i	−0.253112	−	0.566525i
$743$	−7.82829	+	18.8131i	−0.287192	+	0.690186i	−0.999937	−	0.0112375i	$-0.996423\pi$
$743$	−7.82829	+	18.8131i	−0.287192	+	0.690186i	0.712745	+	0.701423i	$0.247452\pi$
$744$	−0.126473	−	0.203021i	−0.00463674	−	0.00744312i
$745$	−6.71825	−	0.347734i	−0.246138	−	0.0127400i
$746$	4.11315	+	1.86966i	0.150593	+	0.0684530i
$747$	−34.3021	−	31.7912i	−1.25505	−	1.16318i
$748$	−6.47149	−	9.43566i	−0.236621	−	0.345002i
$749$	−1.81289	−	0.607234i	−0.0662414	−	0.0221879i
$750$	−16.7181	−	10.8128i	−0.610458	−	0.394827i
$751$	−41.6107	−	24.3839i	−1.51840	−	0.889782i	−0.999387	−	0.0350131i	$-0.988853\pi$
$751$	−41.6107	−	24.3839i	−1.51840	−	0.889782i	−0.519009	−	0.854769i	$-0.673699\pi$
$752$	−6.27158	+	19.1335i	−0.228701	+	0.697725i
$753$	−15.8528	−	14.9201i	−0.577707	−	0.543719i
$754$	24.4238	+	16.5201i	0.889464	+	0.601626i
$755$	5.26045	+	12.1951i	0.191447	+	0.443825i
$756$	6.63953	+	10.0156i	0.241477	+	0.364264i
$757$	9.13423	−	21.1755i	0.331989	−	0.769638i	−0.667693	−	0.744437i	$-0.732718\pi$
$757$	9.13423	−	21.1755i	0.331989	−	0.769638i	0.999682	−	0.0252012i	$-0.00802263\pi$
$758$	1.86875	−	1.19478i	0.0678762	−	0.0433963i
$759$	7.35135	−	13.3612i	0.266837	−	0.484982i
$760$	0.0797707	+	0.293905i	0.00289359	+	0.0106611i
$761$	19.6178	+	1.26990i	0.711145	+	0.0460338i	0.415929	−	0.909397i	$-0.363456\pi$
$761$	19.6178	+	1.26990i	0.711145	+	0.0460338i	0.295215	+	0.955431i	$0.404609\pi$
$762$	−3.35813	−	9.57402i	−0.121652	−	0.346830i
$763$	3.07989	+	1.44831i	0.111499	+	0.0524324i
$764$	21.4752	−	26.6251i	0.776947	−	0.963263i
$765$	−1.84024	−	0.114654i	−0.0665341	−	0.00414533i
$766$	36.1596	+	7.10152i	1.30650	+	0.256588i
$767$	−4.26147	−	6.38891i	−0.153873	−

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.k (of order \(243\), degree \(162\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.03766 - 0.0263451i) q^{2} +(-1.63810 + 0.562705i) q^{3} +(2.15204 + 0.0556572i) q^{4} +(0.558373 + 0.171106i) q^{5} +(3.35271 - 1.10345i) q^{6} +(0.399839 - 0.997050i) q^{7} +(-0.311068 - 0.0120709i) q^{8} +(2.36673 - 1.84353i) q^{9} +O(q^{10})\)	\(q+(-2.03766 - 0.0263451i) q^{2} +(-1.63810 + 0.562705i) q^{3} +(2.15204 + 0.0556572i) q^{4} +(0.558373 + 0.171106i) q^{5} +(3.35271 - 1.10345i) q^{6} +(0.399839 - 0.997050i) q^{7} +(-0.311068 - 0.0120709i) q^{8} +(2.36673 - 1.84353i) q^{9} +(-1.13327 - 0.363367i) q^{10} +(4.38987 + 2.49680i) q^{11} +(-3.55657 + 1.11979i) q^{12} +(-0.846483 - 1.89464i) q^{13} +(-0.841003 + 2.02112i) q^{14} +(-1.01095 + 0.0339100i) q^{15} +(-3.66623 - 0.189763i) q^{16} +(-0.958067 - 0.435495i) q^{17} +(-4.87116 + 3.69414i) q^{18} +(-0.947460 - 1.38143i) q^{19} +(1.19212 + 0.399306i) q^{20} +(-0.0939298 + 1.85826i) q^{21} +(-8.87930 - 5.20328i) q^{22} +(-0.543028 + 1.65668i) q^{23} +(0.516352 - 0.155266i) q^{24} +(-3.85907 - 2.61024i) q^{25} +(1.67493 + 3.88293i) q^{26} +(-2.83957 + 4.35165i) q^{27} +(0.915962 - 2.12344i) q^{28} +(5.87470 - 3.75596i) q^{29} +(2.06087 - 0.0424635i) q^{30} +(-0.116200 - 0.428125i) q^{31} +(8.08685 + 0.523478i) q^{32} +(-8.59600 - 1.61980i) q^{33} +(1.94074 + 0.912632i) q^{34} +(0.393861 - 0.488311i) q^{35} +(5.19590 - 3.83563i) q^{36} +(-4.10495 - 0.806186i) q^{37} +(1.89421 + 2.83985i) q^{38} +(2.45274 + 2.62728i) q^{39} +(-0.171627 - 0.0599658i) q^{40} +(-3.84549 + 1.45622i) q^{41} +(0.240353 - 3.78402i) q^{42} +(5.40724 - 2.37403i) q^{43} +(9.30822 + 5.61754i) q^{44} +(1.63696 - 0.624415i) q^{45} +(1.15015 - 3.36145i) q^{46} +(1.43666 - 5.29319i) q^{47} +(6.11243 - 1.75216i) q^{48} +(4.22622 + 4.03919i) q^{49} +(7.79471 + 5.42045i) q^{50} +(1.81446 + 0.174274i) q^{51} +(-1.71622 - 4.12445i) q^{52} +(-5.29848 + 5.61606i) q^{53} +(5.90072 - 8.79239i) q^{54} +(2.02397 + 2.14528i) q^{55} +(-0.136412 + 0.305324i) q^{56} +(2.32937 + 1.72978i) q^{57} +(-12.0696 + 7.49861i) q^{58} +(3.64869 - 0.619071i) q^{59} +(-2.17750 + 0.0167090i) q^{60} +(4.15586 - 7.64824i) q^{61} +(0.225497 + 0.875434i) q^{62} +(-0.891784 - 3.09686i) q^{63} +(-9.14427 - 0.710749i) q^{64} +(-0.148469 - 1.20275i) q^{65} +(17.4731 + 3.52706i) q^{66} +(11.8914 - 6.16587i) q^{67} +(-2.03756 - 0.990526i) q^{68} +(-0.0426893 - 3.01937i) q^{69} +(-0.815420 + 0.984636i) q^{70} +(11.2116 + 8.68968i) q^{71} +(-0.758467 + 0.544895i) q^{72} +(-3.21673 + 1.03140i) q^{73} +(8.34327 + 1.75088i) q^{74} +(7.79032 + 2.10431i) q^{75} +(-1.96209 - 3.02563i) q^{76} +(4.24467 - 3.37861i) q^{77} +(-4.92864 - 5.41812i) q^{78} +(2.66554 - 14.0522i) q^{79} +(-2.01465 - 0.733274i) q^{80} +(2.20279 - 8.72627i) q^{81} +(7.87417 - 2.86597i) q^{82} +(-2.50840 - 15.3865i) q^{83} +(-0.305566 + 3.99382i) q^{84} +(-0.460442 - 0.407100i) q^{85} +(-11.0807 + 4.69501i) q^{86} +(-7.50984 + 9.45835i) q^{87} +(-1.33541 - 0.829664i) q^{88} +(16.0137 + 6.54233i) q^{89} +(-3.35201 + 1.22922i) q^{90} +(-2.22750 + 0.0864373i) q^{91} +(-1.26082 + 3.53502i) q^{92} +(0.431255 + 0.635923i) q^{93} +(-3.06688 + 10.7479i) q^{94} +(-0.292664 - 0.933469i) q^{95} +(-13.5416 + 3.69300i) q^{96} +(0.177879 - 0.772757i) q^{97} +(-8.50520 - 8.34184i) q^{98} +(14.9926 - 2.18362i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Introduction

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