LMFDB - Embedded newform 441.2.bb.f.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			37.4
Character	$\chi$	$=$	441.37
Dual form			441.2.bb.f.298.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.715278 - 0.487668i) q^{2} +(-0.456880 + 1.16411i) q^{4} +(-2.34510 - 0.723367i) q^{5} +(2.39271 - 1.12913i) q^{7} +(0.626178 + 2.74347i) q^{8} +O(q^{10})$	\(q+(0.715278 - 0.487668i) q^{2} +(-0.456880 + 1.16411i) q^{4} +(-2.34510 - 0.723367i) q^{5} +(2.39271 - 1.12913i) q^{7} +(0.626178 + 2.74347i) q^{8} +(-2.03016 + 0.626222i) q^{10} +(0.411946 + 5.49704i) q^{11} +(5.78955 + 2.78810i) q^{13} +(1.16081 - 1.97449i) q^{14} +(-0.0476513 - 0.0442140i) q^{16} +(-2.62691 - 0.395943i) q^{17} +(-0.101537 + 0.175867i) q^{19} +(1.91351 - 2.39946i) q^{20} +(2.97539 + 3.73102i) q^{22} +(7.70460 - 1.16128i) q^{23} +(0.845035 + 0.576135i) q^{25} +(5.50081 - 0.829113i) q^{26} +(0.221255 + 3.30126i) q^{28} +(-1.61308 + 2.02274i) q^{29} +(0.571660 + 0.990144i) q^{31} +(-5.62083 - 0.847203i) q^{32} +(-2.07206 + 0.997851i) q^{34} +(-6.42792 + 0.917121i) q^{35} +(1.92467 + 4.90398i) q^{37} +(0.0131377 + 0.175310i) q^{38} +(0.516084 - 6.88666i) q^{40} +(-2.09373 - 9.17325i) q^{41} +(-1.85254 + 8.11651i) q^{43} +(-6.58737 - 2.03194i) q^{44} +(4.94461 - 4.58793i) q^{46} +(-5.74194 + 3.91479i) q^{47} +(4.45012 - 5.40337i) q^{49} +0.885398 q^{50} +(-5.89078 + 5.46584i) q^{52} +(-0.00277004 + 0.00705794i) q^{53} +(3.01033 - 13.1891i) q^{55} +(4.59600 + 5.85728i) q^{56} +(-0.167375 + 2.23347i) q^{58} +(12.4808 - 3.84981i) q^{59} +(-2.85330 - 7.27009i) q^{61} +(0.891758 + 0.429448i) q^{62} +(-4.31648 + 2.07870i) q^{64} +(-11.5602 - 10.7263i) q^{65} +(-7.57144 - 13.1141i) q^{67} +(1.66110 - 2.87711i) q^{68} +(-4.15050 + 3.79069i) q^{70} +(-5.51833 - 6.91977i) q^{71} +(-7.21908 - 4.92189i) q^{73} +(3.76819 + 2.56911i) q^{74} +(-0.158338 - 0.198550i) q^{76} +(7.19256 + 12.6877i) q^{77} +(-2.71788 + 4.70751i) q^{79} +(0.0797642 + 0.138156i) q^{80} +(-5.97111 - 5.54038i) q^{82} +(8.39791 - 4.04422i) q^{83} +(5.87395 + 2.82874i) q^{85} +(2.63308 + 6.70899i) q^{86} +(-14.8230 + 4.57229i) q^{88} +(-0.485734 + 6.48168i) q^{89} +(17.0008 + 0.133942i) q^{91} +(-2.16822 + 9.49957i) q^{92} +(-2.19796 + 5.60032i) q^{94} +(0.365330 - 0.338977i) q^{95} +2.63246 q^{97} +(0.548017 - 6.03510i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 14 q^{4} - 28 q^{7}+O(q^{10}) $ 72 * q + 14 * q^4 - 28 * q^7	$ 72 q + 14 q^{4} - 28 q^{7} + 42 q^{13} - 26 q^{16} + 28 q^{19} + 8 q^{22} - 24 q^{25} - 28 q^{28} + 28 q^{31} + 28 q^{34} - 106 q^{37} + 70 q^{40} - 2 q^{43} + 60 q^{46} + 28 q^{49} + 70 q^{52} - 42 q^{55} + 56 q^{58} + 112 q^{61} + 38 q^{64} - 36 q^{67} - 14 q^{70} - 28 q^{73} + 56 q^{76} + 62 q^{79} - 70 q^{82} - 100 q^{85} - 262 q^{88} - 154 q^{91} - 294 q^{94} + 56 q^{97}+O(q^{100}) $ 72 * q + 14 * q^4 - 28 * q^7 + 42 * q^13 - 26 * q^16 + 28 * q^19 + 8 * q^22 - 24 * q^25 - 28 * q^28 + 28 * q^31 + 28 * q^34 - 106 * q^37 + 70 * q^40 - 2 * q^43 + 60 * q^46 + 28 * q^49 + 70 * q^52 - 42 * q^55 + 56 * q^58 + 112 * q^61 + 38 * q^64 - 36 * q^67 - 14 * q^70 - 28 * q^73 + 56 * q^76 + 62 * q^79 - 70 * q^82 - 100 * q^85 - 262 * q^88 - 154 * q^91 - 294 * q^94 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{16}{21}\right)$	$1$

Coefficient data

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

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 $

$2$	0.715278	−	0.487668i	0.505778	−	0.344834i	−0.283396	−	0.959003i	$-0.591461\pi$
$2$	0.715278	−	0.487668i	0.505778	−	0.344834i	0.789174	+	0.614169i	$0.210509\pi$
$3$		0			0
$3$		0			0
$4$	−0.456880	+	1.16411i	−0.228440	+	0.582055i
$5$	−2.34510	−	0.723367i	−1.04876	−	0.323500i	−0.277971	−	0.960590i	$-0.589662\pi$
$5$	−2.34510	−	0.723367i	−1.04876	−	0.323500i	−0.770790	+	0.637090i	$0.780138\pi$
$6$		0			0
$7$	2.39271	−	1.12913i	0.904359	−	0.426772i
$7$	2.39271	−	1.12913i	0.904359	−	0.426772i
$8$	0.626178	+	2.74347i	0.221387	+	0.969962i
$9$		0			0
$10$	−2.03016	+	0.626222i	−0.641994	+	0.198029i
$11$	0.411946	+	5.49704i	0.124207	+	1.65742i	0.616769	+	0.787144i	$0.288441\pi$
$11$	0.411946	+	5.49704i	0.124207	+	1.65742i	−0.492563	+	0.870277i	$0.663940\pi$
$12$		0			0
$13$	5.78955	+	2.78810i	1.60573	+	0.773280i	0.999754	−	0.0222019i	$-0.00706768\pi$
$13$	5.78955	+	2.78810i	1.60573	+	0.773280i	0.605978	+	0.795481i	$0.292782\pi$
$14$	1.16081	−	1.97449i	0.310240	−	0.527706i
$15$		0			0
$16$	−0.0476513	−	0.0442140i	−0.0119128	−	0.0110535i
$17$	−2.62691	−	0.395943i	−0.637119	−	0.0960302i	−0.177463	−	0.984127i	$-0.556789\pi$
$17$	−2.62691	−	0.395943i	−0.637119	−	0.0960302i	−0.459656	+	0.888097i	$0.652027\pi$
$18$		0			0
$19$	−0.101537	+	0.175867i	−0.0232941	+	0.0403466i	−0.877437	−	0.479691i	$-0.840749\pi$
$19$	−0.101537	+	0.175867i	−0.0232941	+	0.0403466i	0.854143	+	0.520038i	$0.174082\pi$
$20$	1.91351	−	2.39946i	0.427873	−	0.536536i
$21$		0			0
$22$	2.97539	+	3.73102i	0.634355	+	0.795457i
$23$	7.70460	−	1.16128i	1.60652	−	0.242144i	0.716340	−	0.697751i	$-0.245816\pi$
$23$	7.70460	−	1.16128i	1.60652	−	0.242144i	0.890181	+	0.455607i	$0.150578\pi$
$24$		0			0
$25$	0.845035	+	0.576135i	0.169007	+	0.115227i
$26$	5.50081	−	0.829113i	1.07880	−	0.162602i
$27$		0			0
$28$	0.221255	+	3.30126i	0.0418133	+	0.623879i
$29$	−1.61308	+	2.02274i	−0.299541	+	0.375613i	−0.908710	−	0.417428i	$-0.862932\pi$
$29$	−1.61308	+	2.02274i	−0.299541	+	0.375613i	0.609169	+	0.793040i	$0.291503\pi$
$30$		0			0
$31$	0.571660	+	0.990144i	0.102673	+	0.177835i	0.912785	−	0.408440i	$-0.133927\pi$
$31$	0.571660	+	0.990144i	0.102673	+	0.177835i	−0.810112	+	0.586275i	$0.800594\pi$
$32$	−5.62083	−	0.847203i	−0.993631	−	0.149766i
$33$		0			0
$34$	−2.07206	+	0.997851i	−0.355355	+	0.171130i
$35$	−6.42792	+	0.917121i	−1.08652	+	0.155022i
$36$		0			0
$37$	1.92467	+	4.90398i	0.316414	+	0.806209i	0.997273	+	0.0737951i	$0.0235111\pi$
$37$	1.92467	+	4.90398i	0.316414	+	0.806209i	−0.680860	+	0.732414i	$0.738394\pi$
$38$	0.0131377	+	0.175310i	0.00213121	+	0.0284391i
$39$		0			0
$40$	0.516084	−	6.88666i	0.0816000	−	1.08888i
$41$	−2.09373	−	9.17325i	−0.326986	−	1.43262i	−0.824843	−	0.565361i	$-0.808737\pi$
$41$	−2.09373	−	9.17325i	−0.326986	−	1.43262i	0.497857	−	0.867259i	$-0.334120\pi$
$42$		0			0
$43$	−1.85254	+	8.11651i	−0.282510	+	1.23776i	0.612054	+	0.790816i	$0.290344\pi$
$43$	−1.85254	+	8.11651i	−0.282510	+	1.23776i	−0.894564	+	0.446940i	$0.852514\pi$
$44$	−6.58737	−	2.03194i	−0.993084	−	0.306326i
$45$		0			0
$46$	4.94461	−	4.58793i	0.729044	−	0.676454i
$47$	−5.74194	+	3.91479i	−0.837548	+	0.571030i	−0.904377	−	0.426734i	$-0.859664\pi$
$47$	−5.74194	+	3.91479i	−0.837548	+	0.571030i	0.0668295	+	0.997764i	$0.478712\pi$
$48$		0			0
$49$	4.45012	−	5.40337i	0.635731	−	0.771911i
$50$	0.885398			0.125214
$51$		0			0
$52$	−5.89078	+	5.46584i	−0.816904	+	0.757976i
$53$	−0.00277004	+	0.00705794i	−0.000380494	+	0.000969482i	−0.931064	−	0.364856i	$-0.881118\pi$
$53$	−0.00277004	+	0.00705794i	−0.000380494	+	0.000969482i	0.930683	+	0.365826i	$0.119213\pi$
$54$		0			0
$55$	3.01033	−	13.1891i	0.405912	−	1.77842i
$56$	4.59600	+	5.85728i	0.614167	+	0.782712i
$57$		0			0
$58$	−0.167375	+	2.23347i	−0.0219774	+	0.293269i
$59$	12.4808	−	3.84981i	1.62486	−	0.501202i	0.657252	−	0.753671i	$-0.271719\pi$
$59$	12.4808	−	3.84981i	1.62486	−	0.501202i	0.967605	+	0.252469i	$0.0812426\pi$
$60$		0			0
$61$	−2.85330	−	7.27009i	−0.365328	−	0.930839i	−0.988834	−	0.149021i	$-0.952388\pi$
$61$	−2.85330	−	7.27009i	−0.365328	−	0.930839i	0.623506	−	0.781818i	$-0.285707\pi$
$62$	0.891758	+	0.429448i	0.113253	+	0.0545400i
$63$		0			0
$64$	−4.31648	+	2.07870i	−0.539559	+	0.259838i
$65$	−11.5602	−	10.7263i	−1.43387	−	1.33044i
$66$		0			0
$67$	−7.57144	−	13.1141i	−0.924998	−	1.60214i	−0.791564	−	0.611087i	$-0.790733\pi$
$67$	−7.57144	−	13.1141i	−0.924998	−	1.60214i	−0.133435	−	0.991058i	$-0.542601\pi$
$68$	1.66110	−	2.87711i	0.201438	−	0.348901i
$69$		0			0
$70$	−4.15050	+	3.79069i	−0.496080	+	0.453074i
$71$	−5.51833	−	6.91977i	−0.654906	−	0.821226i	0.337872	−	0.941192i	$-0.390293\pi$
$71$	−5.51833	−	6.91977i	−0.654906	−	0.821226i	−0.992778	+	0.119966i	$0.961721\pi$
$72$		0			0
$73$	−7.21908	−	4.92189i	−0.844929	−	0.576063i	0.0616503	−	0.998098i	$-0.480364\pi$
$73$	−7.21908	−	4.92189i	−0.844929	−	0.576063i	−0.906580	+	0.422035i	$0.861316\pi$
$74$	3.76819	+	2.56911i	0.438043	+	0.298653i
$75$		0			0
$76$	−0.158338	−	0.198550i	−0.0181627	−	0.0227753i
$77$	7.19256	+	12.6877i	0.819668	+	1.44590i
$78$		0			0
$79$	−2.71788	+	4.70751i	−0.305785	+	0.529636i	−0.977436	−	0.211232i	$-0.932252\pi$
$79$	−2.71788	+	4.70751i	−0.305785	+	0.529636i	0.671650	+	0.740868i	$0.265586\pi$
$80$	0.0797642	+	0.138156i	0.00891791	+	0.0154463i
$81$		0			0
$82$	−5.97111	−	5.54038i	−0.659398	−	0.611832i
$83$	8.39791	−	4.04422i	0.921790	−	0.443911i	0.0880802	−	0.996113i	$-0.471927\pi$
$83$	8.39791	−	4.04422i	0.921790	−	0.443911i	0.833710	+	0.552203i	$0.186213\pi$
$84$		0			0
$85$	5.87395	+	2.82874i	0.637119	+	0.306820i
$86$	2.63308	+	6.70899i	0.283933	+	0.723449i
$87$		0			0
$88$	−14.8230	+	4.57229i	−1.58014	+	0.487408i
$89$	−0.485734	+	6.48168i	−0.0514878	+	0.687056i	0.910421	+	0.413684i	$0.135758\pi$
$89$	−0.485734	+	6.48168i	−0.0514878	+	0.687056i	−0.961908	+	0.273372i	$0.911861\pi$
$90$		0			0
$91$	17.0008	+	0.133942i	1.78217	+	0.0140410i
$92$	−2.16822	+	9.49957i	−0.226052	+	0.990399i
$93$		0			0
$94$	−2.19796	+	5.60032i	−0.226703	+	0.577629i
$95$	0.365330	−	0.338977i	0.0374821	−	0.0347783i
$96$		0			0
$97$	2.63246			0.267285			0.133643	−	0.991030i	$-0.457333\pi$
$97$	2.63246			0.267285			0.133643	+	0.991030i	$0.457333\pi$
$98$	0.548017	−	6.03510i	0.0553581	−	0.609637i
$99$		0			0
$100$	−1.05676	+	0.720490i	−0.105676	+	0.0720490i
$101$	6.62187	−	6.14420i	0.658901	−	0.611371i	−0.278161	−	0.960535i	$-0.589725\pi$
$101$	6.62187	−	6.14420i	0.658901	−	0.611371i	0.937062	+	0.349164i	$0.113534\pi$
$102$		0			0
$103$	4.73061	+	1.45920i	0.466121	+	0.143779i	0.518914	−	0.854826i	$-0.326336\pi$
$103$	4.73061	+	1.45920i	0.466121	+	0.143779i	−0.0527937	+	0.998605i	$0.516813\pi$
$104$	−4.02377	+	17.6293i	−0.394563	+	1.72869i
$105$		0			0
$106$	0.00146059	+	0.00639925i	0.000141865	+	0.000621550i
$107$	−0.425703	+	5.68062i	−0.0411543	+	0.549166i	0.938078	+	0.346424i	$0.112604\pi$
$107$	−0.425703	+	5.68062i	−0.0411543	+	0.549166i	−0.979232	+	0.202742i	$0.935015\pi$
$108$		0			0
$109$	−0.00476987	−	0.0636494i	−0.000456870	−	0.00609651i	0.996971	−	0.0777780i	$-0.0247825\pi$
$109$	−0.00476987	−	0.0636494i	−0.000456870	−	0.00609651i	−0.997428	+	0.0716815i	$0.977163\pi$
$110$	−4.27869	−	10.9019i	−0.407957	−	1.03946i
$111$		0			0
$112$	−0.163939	−	0.0519865i	−0.0154908	−	0.00491226i
$113$	1.92097	−	0.925090i	0.180710	−	0.0870252i	−0.341342	−	0.939939i	$-0.610881\pi$
$113$	1.92097	−	0.925090i	0.180710	−	0.0870252i	0.522051	+	0.852914i	$0.325167\pi$
$114$		0			0
$115$	−18.9081	−	2.84994i	−1.76319	−	0.265758i
$116$	−1.61771	−	2.80195i	−0.150200	−	0.260154i
$117$		0			0
$118$	7.04979	−	8.84016i	0.648986	−	0.813802i
$119$	−6.73250	+	2.01875i	−0.617167	+	0.185059i
$120$		0			0
$121$	−19.1706	+	2.88951i	−1.74279	+	0.262683i
$122$	−5.58630	−	3.80867i	−0.505759	−	0.344821i
$123$		0			0
$124$	−1.41382	+	0.213099i	−0.126964	+	0.0191368i
$125$	6.08569	+	7.63121i	0.544321	+	0.682556i
$126$		0			0
$127$	7.59846	−	9.52817i	0.674254	−	0.845488i	−0.320557	−	0.947229i	$-0.603870\pi$
$127$	7.59846	−	9.52817i	0.674254	−	0.845488i	0.994811	+	0.101741i	$0.0324414\pi$
$128$	3.61055	−	6.25366i	0.319131	−	0.552751i
$129$		0			0
$130$	−13.4997	−	2.03475i	−1.18400	−	0.178459i
$131$	−4.27882	−	3.97016i	−0.373842	−	0.346875i	0.470768	−	0.882257i	$-0.343977\pi$
$131$	−4.27882	−	3.97016i	−0.373842	−	0.346875i	−0.844610	+	0.535383i	$0.820167\pi$
$132$		0			0
$133$	−0.0443710	+	0.535447i	−0.00384745	+	0.0464292i
$134$	−11.8110	−	5.68789i	−1.02032	−	0.491359i
$135$		0			0
$136$	−0.558658	−	7.45477i	−0.0479045	−	0.639241i
$137$	14.9003	−	4.59612i	1.27301	−	0.392673i	0.416661	−	0.909062i	$-0.363200\pi$
$137$	14.9003	−	4.59612i	1.27301	−	0.392673i	0.856354	+	0.516389i	$0.172724\pi$
$138$		0			0
$139$	−0.587619	−	2.57452i	−0.0498412	−	0.218368i	0.943874	−	0.330305i	$-0.107152\pi$
$139$	−0.587619	−	2.57452i	−0.0498412	−	0.218368i	−0.993715	+	0.111937i	$0.964295\pi$
$140$	1.86915	−	7.90182i	0.157972	−	0.667826i
$141$		0			0
$142$	−7.32170	−	2.25845i	−0.614423	−	0.189525i
$143$	−12.9413	+	32.9739i	−1.08221	+	2.75742i
$144$		0			0
$145$	5.24601	−	3.57667i	0.435657	−	0.297026i
$146$	−7.56390			−0.625993
$147$		0			0
$148$	−6.58811			−0.541539
$149$	−5.55009	+	3.78399i	−0.454681	+	0.309997i	−0.768917	−	0.639348i	$-0.779204\pi$
$149$	−5.55009	+	3.78399i	−0.454681	+	0.309997i	0.314236	+	0.949345i	$0.398252\pi$
$150$		0			0
$151$	1.89593	−	4.83075i	0.154289	−	0.393121i	−0.832740	−	0.553664i	$-0.813229\pi$
$151$	1.89593	−	4.83075i	0.154289	−	0.393121i	0.987029	+	0.160543i	$0.0513244\pi$
$152$	−0.546065	−	0.168439i	−0.0442917	−	0.0136622i
$153$		0			0
$154$	11.3321	+	5.56764i	0.913164	+	0.448653i
$155$	−0.624361	−	2.73551i	−0.0501499	−	0.219721i
$156$		0			0
$157$	6.50593	−	2.00681i	0.519230	−	0.160161i	−0.0240534	−	0.999711i	$-0.507657\pi$
$157$	6.50593	−	2.00681i	0.519230	−	0.160161i	0.543283	+	0.839549i	$0.317181\pi$
$158$	0.351662	+	4.69260i	0.0279767	+	0.373323i
$159$		0			0
$160$	12.5686	+	6.05270i	0.993631	+	0.478508i
$161$	17.1236	−	11.4781i	1.34953	−	0.904603i
$162$		0			0
$163$	3.58040	+	3.32212i	0.280438	+	0.260209i	0.807833	−	0.589412i	$-0.200640\pi$
$163$	3.58040	+	3.32212i	0.280438	+	0.260209i	−0.527394	+	0.849621i	$0.676831\pi$
$164$	11.6353	+	1.75373i	0.908561	+	0.136943i
$165$		0			0
$166$	4.03460	−	6.98814i	0.313146	−	0.542385i
$167$	0.634458	−	0.795585i	0.0490958	−	0.0615642i	−0.756677	−	0.653788i	$-0.773179\pi$
$167$	0.634458	−	0.795585i	0.0490958	−	0.0615642i	0.805773	+	0.592224i	$0.201750\pi$
$168$		0			0
$169$	17.6400	+	22.1199i	1.35692	+	1.70153i
$170$	5.58100	−	0.841200i	0.428043	−	0.0645171i
$171$		0			0
$172$	−8.60213	−	5.86483i	−0.655906	−	0.447189i
$173$	−18.9891	+	2.86215i	−1.44371	+	0.217605i	−0.823718	−	0.567000i	$-0.808104\pi$
$173$	−18.9891	+	2.86215i	−1.44371	+	0.217605i	−0.619996	+	0.784605i	$0.712866\pi$
$174$		0			0
$175$	2.67246	+	0.424367i	0.202019	+	0.0320791i
$176$	0.223416	−	0.280155i	0.0168406	−	0.0211175i
$177$		0			0
$178$	2.81347	+	4.87308i	0.210879	+	0.365253i
$179$	1.86154	+	0.280582i	0.139138	+	0.0209717i	0.218242	−	0.975895i	$-0.429968\pi$
$179$	1.86154	+	0.280582i	0.139138	+	0.0209717i	−0.0791039	+	0.996866i	$0.525206\pi$
$180$		0			0
$181$	2.90371	−	1.39835i	0.215831	−	0.103939i	−0.322845	−	0.946452i	$-0.604639\pi$
$181$	2.90371	−	1.39835i	0.215831	−	0.103939i	0.538676	+	0.842513i	$0.318925\pi$
$182$	12.2257	−	8.19497i	0.906226	−	0.607451i
$183$		0			0
$184$	8.01039	+	20.4102i	0.590534	+	1.50466i
$185$	−0.966164	−	12.8926i	−0.0710338	−	0.947880i
$186$		0			0
$187$	1.09437	−	14.6033i	0.0800282	−	1.06790i
$188$	−1.93387	−	8.47283i	−0.141042	−	0.617945i
$189$		0			0
$190$	0.0960045	−	0.420623i	0.00696490	−	0.0305152i
$191$	0.891840	+	0.275096i	0.0645312	+	0.0199053i	0.326853	−	0.945075i	$-0.394012\pi$
$191$	0.891840	+	0.275096i	0.0645312	+	0.0199053i	−0.262321	+	0.964981i	$0.584488\pi$
$192$		0			0
$193$	−7.44331	+	6.90638i	−0.535781	+	0.497132i	−0.901018	−	0.433783i	$-0.857179\pi$
$193$	−7.44331	+	6.90638i	−0.535781	+	0.497132i	0.365237	+	0.930915i	$0.380988\pi$
$194$	1.88294	−	1.28377i	0.135187	−	0.0921690i
$195$		0			0
$196$	4.25695	+	7.64912i	0.304068	+	0.546366i
$197$	13.0052			0.926584			0.463292	−	0.886206i	$-0.346668\pi$
$197$	13.0052			0.926584			0.463292	+	0.886206i	$0.346668\pi$
$198$		0			0
$199$	−1.05273	+	0.976787i	−0.0746258	+	0.0692426i	−0.716604	−	0.697480i	$-0.754304\pi$
$199$	−1.05273	+	0.976787i	−0.0746258	+	0.0692426i	0.641978	+	0.766723i	$0.278114\pi$
$200$	−1.05147	+	2.67909i	−0.0743498	+	0.189440i
$201$		0			0
$202$	1.74015	−	7.62409i	0.122436	−	0.536429i
$203$	−1.57569	+	6.66120i	−0.110592	+	0.467525i
$204$		0			0
$205$	−1.72561	+	23.0267i	−0.120522	+	1.60826i
$206$	4.09531	−	1.26323i	0.285333	−	0.0880137i
$207$		0			0
$208$	−0.152607	−	0.388836i	−0.0105814	−	0.0269609i
$209$	−1.00858	−	0.485705i	−0.0697647	−	0.0335969i
$210$		0			0
$211$	6.54703	−	3.15288i	0.450716	−	0.217053i	−0.194734	−	0.980856i	$-0.562384\pi$
$211$	6.54703	−	3.15288i	0.450716	−	0.217053i	0.645450	+	0.763803i	$0.276670\pi$
$212$	−0.00695064	−	0.00644925i	−0.000477372	−	0.000442937i
$213$		0			0
$214$	2.46576	+	4.27082i	0.168556	+	0.291948i
$215$	10.2156	−	17.6940i	0.696699	−	1.20672i
$216$		0			0
$217$	2.48582	+	1.72365i	0.168749	+	0.117009i
$218$	−0.0344516	−	0.0432010i	−0.00233336	−	0.00292594i
$219$		0			0
$220$	13.9782	+	9.53018i	0.942410	+	0.642525i
$221$	−14.1047	−	9.61641i	−0.948784	−	0.646870i
$222$		0			0
$223$	−16.3606	−	20.5156i	−1.09559	−	1.37382i	−0.921174	−	0.389151i	$-0.872768\pi$
$223$	−16.3606	−	20.5156i	−1.09559	−	1.37382i	−0.174414	−	0.984672i	$-0.555803\pi$
$224$	−14.4056	+	4.31955i	−0.962515	+	0.288612i
$225$		0			0
$226$	0.922891	−	1.59849i	0.0613898	−	0.106330i
$227$	−0.636915	−	1.10317i	−0.0422735	−	0.0732199i	0.844114	−	0.536163i	$-0.180127\pi$
$227$	−0.636915	−	1.10317i	−0.0422735	−	0.0732199i	−0.886388	+	0.462943i	$0.846793\pi$
$228$		0			0
$229$	0.650070	+	0.603177i	0.0429578	+	0.0398590i	0.701360	−	0.712808i	$-0.252577\pi$
$229$	0.650070	+	0.603177i	0.0429578	+	0.0398590i	−0.658402	+	0.752667i	$0.728767\pi$
$230$	−14.9144	+	7.18238i	−0.983424	+	0.473592i
$231$		0			0
$232$	−6.55939	−	3.15883i	−0.430645	−	0.207388i
$233$	6.17562	+	15.7352i	0.404578	+	1.03085i	0.977443	+	0.211198i	$0.0677366\pi$
$233$	6.17562	+	15.7352i	0.404578	+	1.03085i	−0.572865	+	0.819650i	$0.694168\pi$
$234$		0			0
$235$	16.2972	−	5.02703i	1.06311	−	0.327927i
$236$	−1.22061	+	16.2879i	−0.0794548	+	1.06025i
$237$		0			0
$238$	−3.83113	+	4.72720i	−0.248335	+	0.306419i
$239$	0.700468	−	3.06895i	0.0453095	−	0.198514i	−0.947207	−	0.320622i	$-0.896108\pi$
$239$	0.700468	−	3.06895i	0.0453095	−	0.198514i	0.992517	+	0.122108i	$0.0389653\pi$
$240$		0			0
$241$	−6.43272	+	16.3903i	−0.414368	+	1.05579i	0.559531	+	0.828809i	$0.310981\pi$
$241$	−6.43272	+	16.3903i	−0.414368	+	1.05579i	−0.973899	+	0.226983i	$0.927114\pi$
$242$	−12.3032	+	11.4157i	−0.790881	+	0.733830i
$243$		0			0
$244$	9.76680			0.625255
$245$	−14.3446	+	9.45238i	−0.916442	+	0.603890i
$246$		0			0
$247$	−1.07819	+	0.735095i	−0.0686034	+	0.0467730i
$248$	−2.35847	+	2.18834i	−0.149763	+	0.138960i
$249$		0			0
$250$	8.07446	+	2.49064i	0.510674	+	0.157522i
$251$	5.88302	−	25.7752i	0.371333	−	1.62692i	−0.351707	−	0.936110i	$-0.614399\pi$
$251$	5.88302	−	25.7752i	0.371333	−	1.62692i	0.723040	−	0.690806i	$-0.242744\pi$
$252$		0			0
$253$	9.55750	+	41.8741i	0.600875	+	2.63260i
$254$	0.788426	−	10.5208i	0.0494703	−	0.660135i
$255$		0			0
$256$	−1.18322	−	15.7889i	−0.0739510	−	0.986807i
$257$	6.58388	+	16.7755i	0.410691	+	1.04642i	0.975265	+	0.221041i	$0.0709455\pi$
$257$	6.58388	+	16.7755i	0.410691	+	1.04642i	−0.564573	+	0.825383i	$0.690959\pi$
$258$		0			0
$259$	10.1424	+	9.56059i	0.630219	+	0.594066i
$260$	17.7683	−	8.55675i	1.10194	−	0.530667i
$261$		0			0
$262$	−4.99667	−	0.753126i	−0.308695	−	0.0465283i
$263$	−13.1964	−	22.8569i	−0.813725	−	1.40941i	−0.910239	−	0.414082i	$-0.864103\pi$
$263$	−13.1964	−	22.8569i	−0.813725	−	1.40941i	0.0965140	−	0.995332i	$-0.469231\pi$
$264$		0			0
$265$	0.0116015	−	0.0145478i	0.000712674	−	0.000893665i
$266$	0.229383	+	0.404632i	0.0140644	+	0.0248096i
$267$		0			0
$268$	18.7255	−	2.82242i	1.14384	−	0.172407i
$269$	−14.8243	−	10.1070i	−0.903854	−	0.616237i	0.0196582	−	0.999807i	$-0.493742\pi$
$269$	−14.8243	−	10.1070i	−0.903854	−	0.616237i	−0.923512	+	0.383570i	$0.874695\pi$
$270$		0			0
$271$	−4.63621	+	0.698797i	−0.281630	+	0.0424489i	−0.288338	−	0.957529i	$-0.593103\pi$
$271$	−4.63621	+	0.698797i	−0.281630	+	0.0424489i	0.00670837	+	0.999977i	$0.497865\pi$
$272$	0.107670	+	0.135013i	0.00652842	+	0.00818638i
$273$		0			0
$274$	8.41645	−	10.5539i	0.508456	−	0.637584i
$275$	−2.81893	+	4.88253i	−0.169988	+	0.294428i
$276$		0			0
$277$	9.26556	+	1.39656i	0.556714	+	0.0839111i	0.421372	−	0.906888i	$-0.361549\pi$
$277$	9.26556	+	1.39656i	0.556714	+	0.0839111i	0.135342	+	0.990799i	$0.456787\pi$
$278$	−1.67583	−	1.55494i	−0.100509	−	0.0932590i
$279$		0			0
$280$	−6.54111	−	17.0605i	−0.390906	−	1.01956i
$281$	18.2899	+	8.80797i	1.09109	+	0.525440i	0.890845	−	0.454307i	$-0.150113\pi$
$281$	18.2899	+	8.80797i	1.09109	+	0.525440i	0.200242	+	0.979747i	$0.435827\pi$
$282$		0			0
$283$	−1.51730	−	20.2470i	−0.0901943	−	1.20356i	−0.840256	−	0.542191i	$-0.817595\pi$
$283$	−1.51730	−	20.2470i	−0.0901943	−	1.20356i	0.750061	−	0.661368i	$-0.230024\pi$
$284$	10.5766	−	3.26245i	0.627605	−	0.193591i
$285$		0			0
$286$	6.82371	+	29.8966i	0.403494	+	1.76782i
$287$	−15.3675	−	19.5848i	−0.907116	−	1.15605i
$288$		0			0
$289$	−9.50086	−	2.93063i	−0.558874	−	0.172390i
$290$	2.00813	−	5.11663i	0.117921	−	0.300459i
$291$		0			0
$292$	9.02787	−	6.15510i	0.528316	−	0.360200i
$293$	4.75284			0.277664			0.138832	−	0.990316i	$-0.455665\pi$
$293$	4.75284			0.277664			0.138832	+	0.990316i	$0.455665\pi$
$294$		0			0
$295$	−32.0534			−1.86622
$296$	−12.2487	+	8.35103i	−0.711942	+	0.485394i
$297$		0			0
$298$	−2.12453	+	5.41321i	−0.123071	+	0.313579i
$299$	47.8439	+	14.7579i	2.76689	+	0.853471i
$300$		0			0
$301$	4.73203	+	21.5122i	0.272750	+	1.23994i
$302$	−0.999688	−	4.37992i	−0.0575256	−	0.252036i
$303$		0			0
$304$	0.0126141	−	0.00389095i	0.000723471	−	0.000223161i
$305$	1.43233	+	19.1131i	0.0820147	+	1.09441i
$306$		0			0
$307$	−7.51535	−	3.61920i	−0.428924	−	0.206559i	0.206951	−	0.978351i	$-0.433646\pi$
$307$	−7.51535	−	3.61920i	−0.428924	−	0.206559i	−0.635874	+	0.771793i	$0.719360\pi$
$308$	−18.0560	+	2.57619i	−1.02884	+	0.146792i
$309$		0			0
$310$	−1.78061	−	1.65217i	−0.101132	−	0.0938368i
$311$	−6.04738	−	0.911495i	−0.342915	−	0.0516862i	−0.0246730	−	0.999696i	$-0.507854\pi$
$311$	−6.04738	−	0.911495i	−0.342915	−	0.0516862i	−0.318242	+	0.948009i	$0.603093\pi$
$312$		0			0
$313$	−10.4395	+	18.0818i	−0.590076	+	1.02204i	0.404145	+	0.914695i	$0.367569\pi$
$313$	−10.4395	+	18.0818i	−0.590076	+	1.02204i	−0.994222	+	0.107348i	$0.965764\pi$
$314$	3.67489	−	4.60817i	0.207386	−	0.260054i
$315$		0			0
$316$	−4.23831	−	5.31468i	−0.238424	−	0.298974i
$317$	2.97363	−	0.448203i	0.167016	−	0.0251736i	−0.0650020	−	0.997885i	$-0.520705\pi$
$317$	2.97363	−	0.448203i	0.167016	−	0.0251736i	0.232018	+	0.972712i	$0.425467\pi$
$318$		0			0
$319$	−11.7836	−	8.03390i	−0.659753	−	0.449812i
$320$	11.6262	−	1.75237i	0.649926	−	0.0979606i
$321$		0			0
$322$	6.65064	−	16.5607i	0.370626	−	0.922893i
$323$	0.336361	−	0.421784i	0.0187156	−	0.0234687i
$324$		0			0
$325$	3.28605	+	5.69160i	0.182277	+	0.315713i
$326$	4.18108	+	0.630196i	0.231568	+	0.0349033i
$327$		0			0
$328$	23.8554	−	11.4882i	1.31720	−	0.634329i
$329$	−9.31847	+	15.8504i	−0.513744	+	0.873858i
$330$		0			0
$331$	−3.58735	−	9.14042i	−0.197179	−	0.502403i	0.797750	−	0.602989i	$-0.206024\pi$
$331$	−3.58735	−	9.14042i	−0.197179	−	0.502403i	−0.994928	+	0.100586i	$0.967928\pi$
$332$	0.871084	+	11.6238i	0.0478070	+	0.637939i
$333$		0			0
$334$	0.0658322	−	0.878470i	0.00360218	−	0.0480678i
$335$	8.26945	+	36.2308i	0.451808	+	1.97950i
$336$		0			0
$337$	8.03215	−	35.1912i	0.437539	−	1.91699i	0.0405103	−	0.999179i	$-0.487102\pi$
$337$	8.03215	−	35.1912i	0.437539	−	1.91699i	0.397029	−	0.917806i	$-0.370041\pi$
$338$	23.4047	+	7.21938i	1.27305	+	0.392683i
$339$		0			0
$340$	−5.97666	+	5.54553i	−0.324130	+	0.300748i
$341$	−5.20737	+	3.55033i	−0.281995	+	0.192261i
$342$		0			0
$343$	4.54671	−	17.9535i	0.245499	−	0.969397i
$344$	−23.4274			−1.26312
$345$		0			0
$346$	−12.1867	+	11.3076i	−0.655162	+	0.607901i
$347$	2.50107	−	6.37262i	0.134264	−	0.342100i	−0.847891	−	0.530170i	$-0.822128\pi$
$347$	2.50107	−	6.37262i	0.134264	−	0.342100i	0.982156	+	0.188070i	$0.0602232\pi$
$348$		0			0
$349$	−3.54943	+	15.5511i	−0.189997	+	0.832430i	0.786619	+	0.617439i	$0.211830\pi$
$349$	−3.54943	+	15.5511i	−0.189997	+	0.832430i	−0.976616	+	0.214992i	$0.931028\pi$
$350$	2.11850	−	0.999733i	0.113239	−	0.0534380i
$351$		0			0
$352$	2.34163	−	31.2469i	0.124809	−	1.66547i
$353$	−12.2145	+	3.76766i	−0.650110	+	0.200532i	−0.602232	−	0.798321i	$-0.705722\pi$
$353$	−12.2145	+	3.76766i	−0.650110	+	0.200532i	−0.0478776	+	0.998853i	$0.515246\pi$
$354$		0			0
$355$	7.93550	+	20.2193i	0.421173	+	1.07313i
$356$	−7.32346	−	3.52679i	−0.388143	−	0.186920i
$357$		0			0
$358$	1.46835	−	0.707120i	0.0776047	−	0.0373725i
$359$	2.03186	+	1.88529i	0.107238	+	0.0995020i	0.731970	−	0.681337i	$-0.238601\pi$
$359$	2.03186	+	1.88529i	0.107238	+	0.0995020i	−0.624732	+	0.780839i	$0.714792\pi$
$360$		0			0
$361$	9.47938	+	16.4188i	0.498915	+	0.864146i
$362$	1.39503	−	2.41626i	0.0733210	−	0.126996i
$363$		0			0
$364$	−7.92326	+	19.7297i	−0.415292	+	1.03411i
$365$	13.3691	+	16.7644i	0.699772	+	0.877486i
$366$		0			0
$367$	−19.2710	−	13.1387i	−1.00594	−	0.685836i	−0.0560487	−	0.998428i	$-0.517850\pi$
$367$	−19.2710	−	13.1387i	−1.00594	−	0.685836i	−0.949887	+	0.312592i	$0.898803\pi$
$368$	−0.418480	−	0.285315i	−0.0218148	−	0.0148730i
$369$		0			0
$370$	−6.97837	−	8.75060i	−0.362788	−	0.454922i
$371$	0.00134146	+	0.0200153i	6.96450e−5	+	0.00103914i
$372$		0			0
$373$	4.44833	−	7.70473i	0.230326	−	0.398936i	−0.727578	−	0.686025i	$-0.759354\pi$
$373$	4.44833	−	7.70473i	0.230326	−	0.398936i	0.957904	+	0.287089i	$0.0926875\pi$
$374$	−6.33881	−	10.9791i	−0.327772	−	0.567718i
$375$		0			0
$376$	−14.3356	−	13.3015i	−0.739300	−	0.685970i
$377$	−14.9786	+	7.21331i	−0.771436	+	0.371504i
$378$		0			0
$379$	7.16470	+	3.45034i	0.368026	+	0.177232i	0.608751	−	0.793361i	$-0.291671\pi$
$379$	7.16470	+	3.45034i	0.368026	+	0.177232i	−0.240725	+	0.970593i	$0.577385\pi$
$380$	0.227695	+	0.580156i	0.0116805	+	0.0297614i
$381$		0			0
$382$	0.772069	−	0.238152i	0.0395025	−	0.0121849i
$383$	1.37534	−	18.3527i	0.0702766	−	0.937777i	−0.844952	−	0.534842i	$-0.820371\pi$
$383$	1.37534	−	18.3527i	0.0702766	−	0.937777i	0.915229	−	0.402935i	$-0.132010\pi$
$384$		0			0
$385$	−7.68941	−	34.9567i	−0.391889	−	1.78156i
$386$	−1.95601	+	8.56985i	−0.0995584	+	0.436194i
$387$		0			0
$388$	−1.20271	+	3.06447i	−0.0610586	+	0.155575i
$389$	16.7903	−	15.5791i	0.851302	−	0.789893i	−0.128111	−	0.991760i	$-0.540891\pi$
$389$	16.7903	−	15.5791i	0.851302	−	0.789893i	0.979413	+	0.201867i	$0.0647008\pi$
$390$		0			0
$391$	−20.6991			−1.04680
$392$	17.6105	+	8.82527i	0.889467	+	0.445744i
$393$		0			0
$394$	9.30236	−	6.34224i	0.468646	−	0.319517i
$395$	9.77896	−	9.07355i	0.492033	−	0.456540i
$396$		0			0
$397$	−27.6341	−	8.52399i	−1.38692	−	0.427807i	−0.490662	−	0.871350i	$-0.663245\pi$
$397$	−27.6341	−	8.52399i	−1.38692	−	0.427807i	−0.896253	+	0.443543i	$0.853721\pi$
$398$	−0.276644	+	1.21206i	−0.0138669	+	0.0607549i
$399$		0			0
$400$	−0.0147938	−	0.0648160i	−0.000739691	−	0.00324080i
$401$	2.52977	−	33.7575i	0.126331	−	1.68577i	−0.469715	−	0.882818i	$-0.655643\pi$
$401$	2.52977	−	33.7575i	0.126331	−	1.68577i	0.596046	−	0.802950i	$-0.296738\pi$
$402$		0			0
$403$	0.549033	+	7.32633i	0.0273493	+	0.364951i
$404$	4.12713	+	10.5157i	0.205332	+	0.523178i
$405$		0			0
$406$	2.12140	+	5.53303i	0.105283	+	0.274600i
$407$	−26.1645	+	12.6002i	−1.29693	+	0.624567i
$408$		0			0
$409$	−24.2674	−	3.65773i	−1.19995	−	0.180863i	−0.481501	−	0.876446i	$-0.659908\pi$
$409$	−24.2674	−	3.65773i	−1.19995	−	0.180863i	−0.718446	+	0.695583i	$0.755146\pi$
$410$	9.99511	+	17.3120i	0.493623	+	0.854980i
$411$		0			0
$412$	−3.85999	+	4.84027i	−0.190168	+	0.238463i
$413$	25.5159	−	23.3039i	1.25556	−	1.14671i
$414$		0			0
$415$	−22.6194	+	3.40932i	−1.11034	+	0.167357i
$416$	−30.1799	−	20.5763i	−1.47969	−	1.00884i
$417$		0			0
$418$	−0.958275	+	0.144437i	−0.0468708	+	0.00706463i
$419$	−13.1604	−	16.5027i	−0.642930	−	0.806208i	0.348436	−	0.937332i	$-0.386713\pi$
$419$	−13.1604	−	16.5027i	−0.642930	−	0.806208i	−0.991366	+	0.131124i	$0.958141\pi$
$420$		0			0
$421$	−8.41825	+	10.5562i	−0.410281	+	0.514476i	−0.943442	−	0.331538i	$-0.892432\pi$
$421$	−8.41825	+	10.5562i	−0.410281	+	0.514476i	0.533161	+	0.846014i	$0.321004\pi$
$422$	3.14539	−	5.44797i	0.153115	−	0.265203i
$423$		0			0
$424$	−0.0210977	−	0.00317997i	−0.00102460	−	0.000154433i
$425$	−1.99171	−	1.84804i	−0.0966123	−	0.0896431i
$426$		0			0
$427$	−15.0360	−	14.1735i	−0.727644	−	0.685901i
$428$	−6.41837	−	3.09092i	−0.310244	−	0.149405i
$429$		0			0
$430$	−1.32178	−	17.6379i	−0.0637419	−	0.850577i
$431$	17.7910	−	5.48778i	0.856960	−	0.264337i	0.165018	−	0.986291i	$-0.447232\pi$
$431$	17.7910	−	5.48778i	0.856960	−	0.264337i	0.691942	+	0.721953i	$0.256755\pi$
$432$		0			0
$433$	6.34892	+	27.8164i	0.305110	+	1.33677i	0.862304	+	0.506391i	$0.169021\pi$
$433$	6.34892	+	27.8164i	0.305110	+	1.33677i	−0.557195	+	0.830382i	$0.688122\pi$
$434$	2.61862	+	0.0206310i	0.125698	+	0.000990321i
$435$		0			0
$436$	0.0762742	+	0.0235275i	0.00365287	+	0.00112676i
$437$	−0.578070	+	1.47290i	−0.0276528	+	0.0704583i
$438$		0			0
$439$	−6.66846	+	4.54648i	−0.318268	+	0.216992i	−0.711907	−	0.702274i	$-0.752168\pi$
$439$	−6.66846	+	4.54648i	−0.318268	+	0.216992i	0.393639	+	0.919265i	$0.371216\pi$
$440$	38.0688			1.81486
$441$		0			0
$442$	−14.7784			−0.702936
$443$	−11.4450	+	7.80305i	−0.543767	+	0.370734i	−0.803831	−	0.594857i	$-0.797209\pi$
$443$	−11.4450	+	7.80305i	−0.543767	+	0.370734i	0.260065	+	0.965591i	$0.416256\pi$
$444$		0			0
$445$	5.82773	−	14.8488i	0.276261	−	0.703901i
$446$	−21.7072	−	6.69578i	−1.02786	−	0.317054i
$447$		0			0
$448$	−7.98094	+	9.84761i	−0.377064	+	0.465256i
$449$	0.768322	+	3.36624i	0.0362593	+	0.158863i	0.989816	−	0.142350i	$-0.0454658\pi$
$449$	0.768322	+	3.36624i	0.0362593	+	0.158863i	−0.953557	+	0.301212i	$0.902609\pi$
$450$		0			0
$451$	49.5632	−	15.2882i	2.33384	−	0.719895i
$452$	0.199255	+	2.65888i	0.00937217	+	0.125063i
$453$		0			0
$454$	−0.993552	−	0.478470i	−0.0466297	−	0.0224557i
$455$	−39.7718	−	12.6120i	−1.86453	−	0.591258i
$456$		0			0
$457$	4.79892	+	4.45275i	0.224484	+	0.208291i	0.784394	−	0.620263i	$-0.212974\pi$
$457$	4.79892	+	4.45275i	0.224484	+	0.208291i	−0.559910	+	0.828553i	$0.689164\pi$
$458$	0.759131	+	0.114421i	0.0354719	+	0.00534652i
$459$		0			0
$460$	11.9564	−	20.7090i	0.557468	−	0.965563i
$461$	−17.5052	+	21.9509i	−0.815300	+	1.02235i	0.183923	+	0.982941i	$0.441120\pi$
$461$	−17.5052	+	21.9509i	−0.815300	+	1.02235i	−0.999223	+	0.0394132i	$0.987451\pi$
$462$		0			0
$463$	3.18730	+	3.99674i	0.148126	+	0.185744i	0.850359	−	0.526203i	$-0.176385\pi$
$463$	3.18730	+	3.99674i	0.148126	+	0.185744i	−0.702233	+	0.711948i	$0.747813\pi$
$464$	0.166299	−	0.0250655i	0.00772022	−	0.00116364i
$465$		0			0
$466$	12.0909	+	8.24340i	0.560098	+	0.381868i
$467$	−14.1700	+	2.13579i	−0.655711	+	0.0988326i	−0.468467	−	0.883481i	$-0.655194\pi$
$467$	−14.1700	+	2.13579i	−0.655711	+	0.0988326i	−0.187244	+	0.982313i	$0.559956\pi$
$468$		0			0
$469$	−32.9238	−	22.8291i	−1.52028	−	1.05415i
$470$	9.20554	−	11.5434i	0.424620	−	0.532456i
$471$		0			0
$472$	18.3770	+	31.8299i	0.845870	+	1.46509i
$473$	−45.3800	−	6.83993i	−2.08657	−	0.314500i
$474$		0			0
$475$	−0.187125	+	0.0901148i	−0.00858590	+	0.00413475i
$476$	0.725891	−	8.75970i	0.0332712	−	0.401500i
$477$		0			0
$478$	−0.995602	−	2.53675i	−0.0455378	−	0.116028i
$479$	0.640927	+	8.55257i	0.0292847	+	0.390777i	0.992517	+	0.122107i	$0.0389651\pi$
$479$	0.640927	+	8.55257i	0.0292847	+	0.390777i	−0.963232	+	0.268670i	$0.913416\pi$
$480$		0			0
$481$	−2.52981	+	33.7580i	−0.115349	+	1.53923i
$482$	3.39185	+	14.8607i	0.154494	+	0.676884i
$483$		0			0
$484$	5.39497	−	23.6369i	0.245226	−	1.07440i
$485$	−6.17337	−	1.90423i	−0.280318	−	0.0864667i
$486$		0			0
$487$	−5.78221	+	5.36511i	−0.262017	+	0.243116i	−0.800231	−	0.599692i	$-0.795290\pi$
$487$	−5.78221	+	5.36511i	−0.262017	+	0.243116i	0.538214	+	0.842808i	$0.319099\pi$
$488$	18.1586	−	12.3803i	0.822000	−	0.560430i
$489$		0			0
$490$	−5.65075	+	13.7565i	−0.255275	+	0.621455i
$491$	15.1722			0.684712			0.342356	−	0.939570i	$-0.388775\pi$
$491$	15.1722			0.684712			0.342356	+	0.939570i	$0.388775\pi$
$492$		0			0
$493$	5.03830	−	4.67486i	0.226914	−	0.210545i
$494$	−0.412721	+	1.05160i	−0.0185692	+	0.0473135i
$495$		0			0
$496$	0.0165379	−	0.0724571i	0.000742572	−	0.00325342i
$497$	−21.0171	−	10.3261i	−0.942746	−	0.463188i
$498$		0			0
$499$	−1.16753	+	15.5797i	−0.0522660	+	0.697441i	0.908110	+	0.418732i	$0.137525\pi$
$499$	−1.16753	+	15.5797i	−0.0522660	+	0.697441i	−0.960376	+	0.278709i	$0.910094\pi$
$500$	−11.6640	+	3.59787i	−0.521630	+	0.160901i
$501$		0			0
$502$	−8.36176	−	21.3054i	−0.373204	−	0.950907i
$503$	−3.43357	−	1.65352i	−0.153095	−	0.0737268i	0.355767	−	0.934575i	$-0.384220\pi$
$503$	−3.43357	−	1.65352i	−0.153095	−	0.0737268i	−0.508863	+	0.860848i	$0.669934\pi$
$504$		0			0
$505$	−19.9735	+	9.61871i	−0.888807	+	0.428027i
$506$	27.2570	+	25.2908i	1.21172	+	1.12431i
$507$		0			0
$508$	7.62025	+	13.1987i	0.338094	+	0.585596i
$509$	−7.84013	+	13.5795i	−0.347508	+	0.601901i	−0.985806	−	0.167888i	$-0.946305\pi$
$509$	−7.84013	+	13.5795i	−0.347508	+	0.601901i	0.638298	+	0.769789i	$0.279639\pi$
$510$		0			0
$511$	−22.8306	−	3.62534i	−1.00997	−	0.160376i
$512$	0.458483	+	0.574919i	0.0202623	+	0.0254081i
$513$		0			0
$514$	12.8902	+	8.78837i	0.568561	+	0.387638i
$515$	−10.0382	−	6.84393i	−0.442336	−	0.301580i
$516$		0			0
$517$	−23.8851	−	29.9510i	−1.05047	−	1.31724i
$518$	11.9170	+	1.89234i	0.523605	+	0.0831448i
$519$		0			0
$520$	22.1886	−	38.4317i	0.973033	−	1.68534i
$521$	15.4285	+	26.7229i	0.675934	+	1.17075i	0.976195	+	0.216895i	$0.0695930\pi$
$521$	15.4285	+	26.7229i	0.675934	+	1.17075i	−0.300261	+	0.953857i	$0.597074\pi$
$522$		0			0
$523$	13.6692	+	12.6832i	0.597714	+	0.554597i	0.919937	−	0.392066i	$-0.128240\pi$
$523$	13.6692	+	12.6832i	0.597714	+	0.554597i	−0.322223	+	0.946664i	$0.604430\pi$
$524$	6.57661	−	3.16713i	0.287300	−	0.138357i
$525$		0			0
$526$	−20.5857	−	9.91354i	−0.897578	−	0.432251i
$527$	−1.10966	−	2.82736i	−0.0483375	−	0.123162i
$528$		0			0
$529$	36.0342	−	11.1151i	1.56670	−	0.483264i
$530$	0.00120379	−	0.0160634i	5.22891e−5	−	0.000697750i
$531$		0			0
$532$	−0.603047	−	0.296288i	−0.0261454	−	0.0128457i
$533$	13.4542	−	58.9465i	0.582764	−	2.55326i
$534$		0			0
$535$	5.10749	−	13.0137i	0.220816	−	0.562630i
$536$	31.2371	−	28.9838i	1.34924	−	1.25191i
$537$		0			0
$538$	−15.5324			−0.669649
$539$	31.5358	+	22.2366i	1.35834	+	0.957797i
$540$		0			0
$541$	6.20827	−	4.23273i	0.266914	−	0.181979i	−0.422466	−	0.906379i	$-0.638835\pi$
$541$	6.20827	−	4.23273i	0.266914	−	0.181979i	0.689380	+	0.724400i	$0.257883\pi$
$542$	−2.97540	+	2.76077i	−0.127804	+	0.118585i
$543$		0			0
$544$	14.4299	+	4.45105i	0.618679	+	0.190837i
$545$	−0.0348561	+	0.152715i	−0.00149307	+	0.00654157i
$546$		0			0
$547$	−0.639806	−	2.80317i	−0.0273561	−	0.119855i	0.959406	−	0.282028i	$-0.0910070\pi$
$547$	−0.639806	−	2.80317i	−0.0273561	−	0.119855i	−0.986762	+	0.162173i	$0.948150\pi$
$548$	−1.45723	+	19.4454i	−0.0622499	+	0.830667i
$549$		0			0
$550$	0.364737	+	4.86707i	0.0155524	+	0.207533i
$551$	−0.191946	−	0.489070i	−0.00817716	−	0.0208351i
$552$		0			0
$553$	−1.18770	+	14.3325i	−0.0505060	+	0.609482i
$554$	7.30851	−	3.51959i	0.310509	−	0.149533i
$555$		0			0
$556$	3.26550	+	0.492195i	0.138488	+	0.0208737i
$557$	2.00332	+	3.46986i	0.0848835	+	0.147023i	0.905342	−	0.424684i	$-0.139615\pi$
$557$	2.00332	+	3.46986i	0.0848835	+	0.147023i	−0.820458	+	0.571707i	$0.806282\pi$
$558$		0			0
$559$	−33.3550	+	41.8259i	−1.41077	+	1.76905i
$560$	0.346849	+	0.240502i	0.0146570	+	0.0101631i
$561$		0			0
$562$	17.3778	−	2.61928i	0.733037	−	0.110488i
$563$	36.4893	+	24.8780i	1.53784	+	1.04848i	0.975077	+	0.221865i	$0.0712146\pi$
$563$	36.4893	+	24.8780i	1.53784	+	1.04848i	0.562764	+	0.826617i	$0.309738\pi$
$564$		0			0
$565$	−5.17404	+	0.779862i	−0.217674	+	0.0328090i
$566$	−10.9591	−	13.7423i	−0.460646	−	0.577632i
$567$		0			0
$568$	15.5287	−	19.4724i	0.651570	−	0.817043i
$569$	−0.825275	+	1.42942i	−0.0345973	+	0.0599243i	−0.882806	−	0.469739i	$-0.844348\pi$
$569$	−0.825275	+	1.42942i	−0.0345973	+	0.0599243i	0.848208	+	0.529663i	$0.177682\pi$
$570$		0			0
$571$	13.0987	+	1.97431i	0.548163	+	0.0826222i	0.417284	−	0.908776i	$-0.362982\pi$
$571$	13.0987	+	1.97431i	0.548163	+	0.0826222i	0.130879	+	0.991398i	$0.458220\pi$
$572$	−32.4727	−	30.1302i	−1.35775	−	1.25981i
$573$		0			0
$574$	−20.5429	−	6.51434i	−0.857446	−	0.271903i
$575$	7.17972	+	3.45757i	0.299415	+	0.144191i
$576$		0			0
$577$	−2.17299	−	28.9966i	−0.0904629	−	1.20714i	−0.839030	−	0.544084i	$-0.816877\pi$
$577$	−2.17299	−	28.9966i	−0.0904629	−	1.20714i	0.748568	−	0.663058i	$-0.230742\pi$
$578$	−8.22493	+	2.53706i	−0.342112	+	0.105528i
$579$		0			0
$580$	1.76684	+	7.74104i	0.0733641	+	0.321429i
$581$	15.5273	−	19.1590i	0.644181	−	0.794849i
$582$		0			0
$583$	−0.0399389	−	0.0123195i	−0.00165410	−	0.000510222i
$584$	8.98260	−	22.8873i	0.371703	−	0.947083i
$585$		0			0
$586$	3.39960	−	2.31781i	0.140436	−	0.0957479i
$587$	−23.7479			−0.980179			−0.490089	−	0.871672i	$-0.663036\pi$
$587$	−23.7479			−0.980179			−0.490089	+	0.871672i	$0.663036\pi$
$588$		0			0
$589$	−0.232178			−0.00956674
$590$	−22.9271	+	15.6315i	−0.943895	+	0.643537i
$591$		0			0
$592$	0.125111	−	0.318778i	0.00514204	−	0.0131017i
$593$	12.2292	+	3.77221i	0.502194	+	0.154906i	0.535494	−	0.844539i	$-0.320126\pi$
$593$	12.2292	+	3.77221i	0.502194	+	0.154906i	−0.0333001	+	0.999445i	$0.510602\pi$
$594$		0			0
$595$	17.2487	+	0.135895i	0.707127	+	0.00557116i
$596$	−1.86926	−	8.18975i	−0.0765677	−	0.335465i
$597$		0			0
$598$	41.4187	−	12.7760i	1.69374	−	0.522448i
$599$	0.940067	+	12.5443i	0.0384101	+	0.512547i	0.982916	+	0.184053i	$0.0589219\pi$
$599$	0.940067	+	12.5443i	0.0384101	+	0.512547i	−0.944506	+	0.328494i	$0.893459\pi$
$600$		0			0
$601$	26.3817	+	12.7047i	1.07613	+	0.518237i	0.886078	−	0.463537i	$-0.153420\pi$
$601$	26.3817	+	12.7047i	1.07613	+	0.518237i	0.190052	+	0.981774i	$0.439134\pi$
$602$	13.8756	+	13.0796i	0.565525	+	0.533083i
$603$		0			0
$604$	4.75732	+	4.41415i	0.193573	+	0.179609i
$605$	47.0472	+	7.09123i	1.91274	+	0.288299i
$606$		0			0
$607$	−12.5476	+	21.7330i	−0.509290	+	0.882116i	0.490652	+	0.871355i	$0.336759\pi$
$607$	−12.5476	+	21.7330i	−0.509290	+	0.882116i	−0.999942	+	0.0107603i	$0.996575\pi$
$608$	0.719716	−	0.902495i	0.0291883	−	0.0366010i
$609$		0			0
$610$	10.3453	+	12.9727i	0.418871	+	0.525247i
$611$	−44.1580	+	6.65575i	−1.78644	+	0.269263i
$612$		0			0
$613$	21.8967	+	14.9289i	0.884398	+	0.602972i	0.918051	−	0.396462i	$-0.129762\pi$
$613$	21.8967	+	14.9289i	0.884398	+	0.602972i	−0.0336538	+	0.999434i	$0.510714\pi$
$614$	−7.14054	+	1.07626i	−0.288169	+	0.0434344i
$615$		0			0
$616$	−30.3044	+	27.6773i	−1.22100	+	1.11515i
$617$	−3.77859	+	4.73820i	−0.152120	+	0.190753i	−0.852052	−	0.523457i	$-0.824642\pi$
$617$	−3.77859	+	4.73820i	−0.152120	+	0.190753i	0.699932	+	0.714210i	$0.253214\pi$
$618$		0			0
$619$	14.9017	+	25.8105i	0.598949	+	1.03741i	0.992977	+	0.118312i	$0.0377481\pi$
$619$	14.9017	+	25.8105i	0.598949	+	1.03741i	−0.394027	+	0.919099i	$0.628919\pi$
$620$	3.46969	+	0.522971i	0.139346	+	0.0210030i
$621$		0			0
$622$	−4.77006	+	2.29714i	−0.191262	+	0.0921070i
$623$	6.15645	+	16.0572i	0.246653	+	0.643319i
$624$		0			0
$625$	−10.6196	−	27.0584i	−0.424785	−	1.08234i
$626$	1.35075	+	18.0245i	0.0539869	+	0.720405i
$627$		0			0
$628$	−0.636274	+	8.49049i	−0.0253901	+	0.338808i
$629$	−3.11424	−	13.6444i	−0.124173	−	0.544036i
$630$		0			0
$631$	4.54119	−	19.8963i	0.180782	−	0.792057i	−0.800477	−	0.599363i	$-0.795420\pi$
$631$	4.54119	−	19.8963i	0.180782	−	0.792057i	0.981259	−	0.192694i	$-0.0617224\pi$
$632$	−14.6168	−	4.50868i	−0.581424	−	0.179346i
$633$		0			0
$634$	1.90840	−	1.77074i	0.0757922	−	0.0703249i
$635$	−24.7115	+	16.8480i	−0.980646	+	0.668593i
$636$		0			0
$637$	40.8293	−	18.8757i	1.61772	−	0.747883i
$638$	−12.3464			−0.488799
$639$		0			0
$640$	−12.9908	+	12.0537i	−0.513506	+	0.476464i
$641$	−12.6603	+	32.2580i	−0.500053	+	1.27411i	0.428711	+	0.903442i	$0.358968\pi$
$641$	−12.6603	+	32.2580i	−0.500053	+	1.27411i	−0.928764	+	0.370672i	$0.879127\pi$
$642$		0			0
$643$	6.02008	−	26.3757i	0.237409	−	1.04016i	−0.705919	−	0.708293i	$-0.749466\pi$
$643$	6.02008	−	26.3757i	0.237409	−	1.04016i	0.943328	−	0.331863i	$-0.107677\pi$
$644$	5.53837	+	25.1779i	0.218242	+	0.992149i
$645$		0			0
$646$	0.0349013	−	0.465725i	0.00137317	−	0.0183237i
$647$	−21.3737	+	6.59292i	−0.840288	+	0.259194i	−0.684880	−	0.728656i	$-0.740145\pi$
$647$	−21.3737	+	6.59292i	−0.840288	+	0.259194i	−0.155408	+	0.987850i	$0.549669\pi$
$648$		0			0
$649$	26.3039	+	67.0214i	1.03252	+	2.63082i
$650$	5.12606	+	2.46858i	0.201060	+	0.0968256i
$651$		0			0
$652$	−5.50313	+	2.65017i	−0.215519	+	0.103789i
$653$	1.94601	+	1.80563i	0.0761532	+	0.0706599i	0.717331	−	0.696732i	$-0.245363\pi$
$653$	1.94601	+	1.80563i	0.0761532	+	0.0706599i	−0.641178	+	0.767392i	$0.721554\pi$
$654$		0			0
$655$	7.16236	+	12.4056i	0.279857	+	0.484726i
$656$	−0.305817	+	0.529690i	−0.0119401	+	0.0206809i
$657$		0			0
$658$	1.06442	+	15.8817i	0.0414953	+	0.619135i
$659$	−9.47382	−	11.8798i	−0.369048	−	0.462771i	0.562284	−	0.826944i	$-0.309923\pi$
$659$	−9.47382	−	11.8798i	−0.369048	−	0.462771i	−0.931331	+	0.364174i	$0.881352\pi$
$660$		0			0
$661$	11.4731	+	7.82220i	0.446251	+	0.304248i	0.765516	−	0.643417i	$-0.222484\pi$
$661$	11.4731	+	7.82220i	0.446251	+	0.304248i	−0.319265	+	0.947665i	$0.603436\pi$
$662$	−7.02345	−	4.78850i	−0.272974	−	0.186111i
$663$		0			0
$664$	16.3538	+	20.5070i	0.634649	+	0.795825i
$665$	0.491379	−	1.22358i	0.0190549	−	0.0474484i
$666$		0			0
$667$	−10.0792	+	17.4576i	−0.390267	+	0.675962i
$668$	0.636278	+	1.10207i	0.0246183	+	0.0426402i
$669$		0			0
$670$	23.5836	+	21.8824i	0.911114	+	0.845390i
$671$	38.7886	−	18.6796i	1.49742	−	0.721118i
$672$		0			0
$673$	−32.3269	−	15.5678i	−1.24611	−	0.600095i	−0.309644	−	0.950853i	$-0.600210\pi$
$673$	−32.3269	−	15.5678i	−1.24611	−	0.600095i	−0.936466	+	0.350757i	$0.885924\pi$
$674$	−11.4164	−	29.0885i	−0.439743	−	1.12045i
$675$		0			0
$676$	−33.8093	+	10.4288i	−1.30036	+	0.401107i
$677$	−1.18375	+	15.7960i	−0.0454951	+	0.607090i	0.927135	+	0.374729i	$0.122264\pi$
$677$	−1.18375	+	15.7960i	−0.0454951	+	0.607090i	−0.972630	+	0.232361i	$0.925355\pi$
$678$		0			0
$679$	6.29870	−	2.97239i	0.241722	−	0.114070i
$680$	−4.08243	+	17.8863i	−0.156554	+	0.685908i
$681$		0			0
$682$	−1.99334	+	5.07894i	−0.0763288	+	0.194483i
$683$	−10.4181	+	9.66663i	−0.398639	+	0.369883i	−0.853866	−	0.520492i	$-0.825749\pi$
$683$	−10.4181	+	9.66663i	−0.398639	+	0.369883i	0.455227	+	0.890375i	$0.349558\pi$
$684$		0			0
$685$	−38.2673			−1.46212
$686$	−5.50318	−	15.0590i	−0.210112	−	0.574956i
$687$		0			0
$688$	0.447139	−	0.304855i	0.0170470	−	0.0116225i
$689$	−0.0357155	+	0.0331391i	−0.00136065	+	0.00126250i
$690$		0			0
$691$	25.1449	+	7.75616i	0.956555	+	0.295058i	0.733456	−	0.679737i	$-0.237906\pi$
$691$	25.1449	+	7.75616i	0.956555	+	0.295058i	0.223100	+	0.974796i	$0.428382\pi$
$692$	5.34388	−	23.4131i	0.203144	−	0.890031i
$693$		0			0
$694$	−1.31877	−	5.77789i	−0.0500597	−	0.219326i
$695$	−0.484303	+	6.46258i	−0.0183707	+	0.245140i
$696$		0			0
$697$	1.86797	+	24.9263i	0.0707543	+	0.944150i
$698$	5.04494	+	12.8543i	0.190954	+	0.486542i
$699$		0			0
$700$	−1.71500	+	2.91715i	−0.0648210	+	0.110258i
$701$	−31.4591	+	15.1499i	−1.18819	+	0.572204i	−0.920288	−	0.391241i	$-0.872046\pi$
$701$	−31.4591	+	15.1499i	−1.18819	+	0.572204i	−0.267906	+	0.963445i	$0.586332\pi$
$702$		0			0
$703$	−1.05787	−	0.159449i	−0.0398984	−	0.00601372i
$704$	−13.2049	−	22.8715i	−0.497678	−	0.862003i
$705$		0			0
$706$	−6.89937	+	8.65153i	−0.259661	+	0.325605i
$707$	8.90660	−	22.1783i	0.334967	−	0.834099i
$708$		0			0
$709$	45.6854	−	6.88596i	1.71575	−	0.258608i	0.783753	−	0.621072i	$-0.213303\pi$
$709$	45.6854	−	6.88596i	1.71575	−	0.258608i	0.931998	+	0.362465i	$0.118065\pi$
$710$	15.5364	+	10.5926i	0.583072	+	0.397531i
$711$		0			0
$712$	−18.0864	+	2.72609i	−0.677817	+	0.102165i
$713$	5.55425	+	6.96481i	0.208008	+	0.260834i
$714$		0			0
$715$	54.2009	−	67.9658i	2.02700	−	2.54178i
$716$	−1.17713	+	2.03885i	−0.0439913	+	0.0761952i
$717$		0			0
$718$	2.37275	+	0.357634i	0.0885501	+	0.0133468i
$719$	−15.3217	−	14.2165i	−0.571404	−	0.530186i	0.340685	−	0.940178i	$-0.389341\pi$
$719$	−15.3217	−	14.2165i	−0.571404	−	0.530186i	−0.912089	+	0.409992i	$0.865532\pi$
$720$		0			0
$721$	12.9666	−	1.85004i	0.482901	−	0.0688993i
$722$	14.7873	+	7.12119i	0.550327	+	0.265023i
$723$		0			0
$724$	0.301191	+	4.01911i	0.0111937	+	0.149369i
$725$	−2.52848	+	0.779932i	−0.0939053	+	0.0289660i
$726$		0			0
$727$	−0.323281	−	1.41639i	−0.0119898	−	0.0525309i	0.968579	−	0.248706i	$-0.0800052\pi$
$727$	−0.323281	−	1.41639i	−0.0119898	−	0.0525309i	−0.980569	+	0.196175i	$0.937148\pi$
$728$	10.2781	+	46.7251i	0.380931	+	1.73175i
$729$		0			0
$730$	17.7381	+	5.47148i	0.656516	+	0.202508i
$731$	8.08013	−	20.5878i	0.298854	−	0.761469i
$732$		0			0
$733$	−12.5200	+	8.53599i	−0.462436	+	0.315284i	−0.772031	−	0.635585i	$-0.780759\pi$
$733$	−12.5200	+	8.53599i	−0.462436	+	0.315284i	0.309595	+	0.950869i	$0.399807\pi$
$734$	−20.1914			−0.745280
$735$		0			0
$736$	−44.2901			−1.63255
$737$	68.9698	−	47.0228i	2.54054	−	1.73211i
$738$		0			0
$739$	−13.0251	+	33.1873i	−0.479134	+	1.22081i	0.463233	+	0.886236i	$0.346689\pi$
$739$	−13.0251	+	33.1873i	−0.479134	+	1.22081i	−0.942368	+	0.334578i	$0.891406\pi$
$740$	15.4498	+	4.76562i	0.567945	+	0.175188i
$741$		0			0
$742$	0.0107204	+	0.0136623i	0.000393557	+	0.000501560i
$743$	5.34076	+	23.3994i	0.195933	+	0.858441i	0.973326	+	0.229425i	$0.0736846\pi$
$743$	5.34076	+	23.3994i	0.195933	+	0.858441i	−0.777393	+	0.629015i	$0.783458\pi$
$744$		0			0
$745$	15.7527	−	4.85907i	0.577136	−	0.178023i
$746$	−0.575562	−	7.68034i	−0.0210728	−	0.281197i
$747$		0			0
$748$	16.4999	+	7.94593i	0.603296	+	0.290532i
$749$	5.39559	+	14.0727i	0.197150	+	0.514207i
$750$		0			0
$751$	−23.6128	−	21.9095i	−0.861643	−	0.799488i	0.119487	−	0.992836i	$-0.461875\pi$
$751$	−23.6128	−	21.9095i	−0.861643	−	0.799488i	−0.981130	+	0.193348i	$0.938065\pi$
$752$	0.446699	+	0.0673291i	0.0162894	+	0.00245524i
$753$		0			0
$754$	−7.19616	+	12.4641i	−0.262069	+	0.453916i
$755$	−7.94056	+	9.95714i	−0.288986	+	0.362378i
$756$		0			0
$757$	18.9828	+	23.8036i	0.689940	+	0.865158i	0.996227	−	0.0867813i	$-0.0276581\pi$
$757$	18.9828	+	23.8036i	0.689940	+	0.865158i	−0.306287	+	0.951939i	$0.599087\pi$
$758$	6.80737	−	1.02605i	0.247255	−	0.0372677i
$759$		0			0
$760$	1.15873	+	0.790012i	0.0420317	+	0.0286567i
$761$	5.22181	−	0.787061i	0.189290	−	0.0285310i	−0.0537127	−	0.998556i	$-0.517106\pi$
$761$	5.22181	−	0.787061i	0.189290	−	0.0285310i	0.243003	+	0.970025i	$0.421867\pi$
$762$		0			0
$763$	−0.0832816	−	0.146909i	−0.00301500	−	0.00531846i
$764$	−0.727705	+	0.912514i	−0.0263275	+	0.0330136i
$765$		0			0
$766$	−7.96626	−	13.7980i	−0.287833	−	0.498541i
$767$	82.9916	+	12.5090i	2.99665	+	0.451673i
$768$		0			0
$769$	−10.4914	+	5.05239i	−0.378330	+	0.182194i	−0.613378	−	0.789790i	$-0.710190\pi$
$769$	−10.4914	+	5.05239i	−0.378330	+	0.182194i	0.235048	+	0.971984i	$0.424475\pi$
$770$	−22.5474	−	21.2539i	−0.812551	−	0.765938i
$771$		0			0
$772$	−4.63909	−	11.8202i	−0.166965	−	0.425419i
$773$	−3.12689	−	41.7254i	−0.112466	−	1.50076i	−0.713002	−	0.701162i	$-0.752665\pi$
$773$	−3.12689	−	41.7254i	−0.112466	−	1.50076i	0.600536	−	0.799598i	$-0.294954\pi$
$774$		0			0
$775$	−0.0873841	+	1.16606i	−0.00313893	+	0.0418861i
$776$	1.64839	+	7.22205i	0.0591736	+	0.259257i
$777$		0			0
$778$	4.41229	−	19.3315i	0.158188	−	0.693068i
$779$	1.82586	+	0.563204i	0.0654183	+	0.0201789i
$780$		0			0
$781$	35.7650	−	33.1851i	1.27977	−	1.18746i
$782$	−14.8056	+	10.0943i	−0.529447	+	0.360971i
$783$		0			0
$784$	−0.450959	+	0.0607206i	−0.0161057	+	0.00216859i
$785$	−16.7087			−0.596360
$786$		0			0
$787$	32.3468	−	30.0134i	1.15304	−	1.06986i	0.156421	−	0.987691i	$-0.450004\pi$
$787$	32.3468	−	30.0134i	1.15304	−	1.06986i	0.996618	−	0.0821730i	$-0.0261860\pi$
$788$	−5.94182	+	15.1395i	−0.211669	+	0.539323i
$789$		0			0
$790$	2.56979	−	11.2590i	0.0914291	−	0.400577i
$791$	3.55177	−	4.38250i	0.126287	−	0.155824i
$792$		0			0
$793$	3.75041	−	50.0458i	0.133181	−	1.77718i
$794$	−23.9230	+	7.37925i	−0.848994	+	0.261880i
$795$		0			0
$796$	−0.656119	−	1.67176i	−0.0232555	−	0.0592541i
$797$	34.4929	+	16.6109i	1.22180	+	0.588388i	0.929812	−	0.368034i	$-0.119969\pi$
$797$	34.4929	+	16.6109i	1.22180	+	0.588388i	0.291988	+	0.956422i	$0.405683\pi$
$798$		0			0
$799$	16.6336	−	8.01031i	0.588454	−	0.283384i
$800$	−4.26169	−	3.95427i	−0.150674	−	0.139805i
$801$		0			0
$802$	−14.6530	−	25.3797i	−0.517414	−	0.896188i
$803$	24.0819	−	41.7111i	0.849833	−	1.47195i
$804$		0			0
$805$	−48.4595	+	14.5307i	−1.70797	+	0.512139i
$806$	3.96553	+	4.97262i	0.139680	+	0.175153i
$807$		0			0
$808$	21.0029	+	14.3195i	0.738879	+	0.503759i
$809$	−29.7833	−	20.3059i	−1.04713	−	0.713918i	−0.0877765	−	0.996140i	$-0.527976\pi$
$809$	−29.7833	−	20.3059i	−1.04713	−	0.713918i	−0.959349	+	0.282222i	$0.908928\pi$
$810$		0			0
$811$	−1.32006	−	1.65530i	−0.0463535	−	0.0581254i	0.758114	−	0.652122i	$-0.226121\pi$
$811$	−1.32006	−	1.65530i	−0.0463535	−	0.0581254i	−0.804468	+	0.593996i	$0.797549\pi$
$812$	−7.03447	−	4.87764i	−0.246862	−	0.171172i
$813$		0			0
$814$	−12.5702	+	21.7722i	−0.440585	+	0.763116i
$815$	−5.99327	−	10.3807i	−0.209935	−	0.363618i
$816$		0			0
$817$	−1.23933	−	1.14993i	−0.0433585	−	0.0402308i
$818$	−19.1417	+	9.21817i	−0.669274	+	0.322306i
$819$		0			0
$820$	−26.0172	−	12.5292i	−0.908561	−	0.437540i
$821$	−9.08601	−	23.1508i	−0.317104	−	0.807967i	−0.997196	−	0.0748404i	$-0.976155\pi$
$821$	−9.08601	−	23.1508i	−0.317104	−	0.807967i	0.680092	−	0.733127i	$-0.261940\pi$
$822$		0			0
$823$	−21.2669	+	6.55996i	−0.741316	+	0.228666i	−0.642336	−	0.766424i	$-0.722034\pi$
$823$	−21.2669	+	6.55996i	−0.741316	+	0.228666i	−0.0989808	+	0.995089i	$0.531558\pi$
$824$	−1.04106	+	13.8920i	−0.0362670	+	0.483950i
$825$		0			0
$826$	6.88639	−	29.1121i	0.239608	−	1.01294i
$827$	−4.25043	+	18.6223i	−0.147802	+	0.647562i	0.845691	+	0.533672i	$0.179188\pi$
$827$	−4.25043	+	18.6223i	−0.147802	+	0.647562i	−0.993493	+	0.113890i	$0.963669\pi$
$828$		0			0
$829$	−12.6338	+	32.1903i	−0.438789	+	1.11802i	0.524941	+	0.851138i	$0.324087\pi$
$829$	−12.6338	+	32.1903i	−0.438789	+	1.11802i	−0.963730	+	0.266878i	$0.914008\pi$
$830$	−14.5165	+	13.4694i	−0.503876	+	0.467529i
$831$		0			0
$832$	−30.7861			−1.06732
$833$	−13.8295	+	12.4322i	−0.479163	+	0.430749i
$834$		0			0
$835$	−2.06337	+	1.40678i	−0.0714058	+	0.0486836i
$836$	1.02621	−	0.952185i	0.0354923	−	0.0329320i
$837$		0			0
$838$	−17.4612	−	5.38607i	−0.603187	−	0.186059i
$839$	−3.87480	+	16.9766i	−0.133773	+	0.586098i	0.862956	+	0.505279i	$0.168611\pi$
$839$	−3.87480	+	16.9766i	−0.133773	+	0.586098i	−0.996729	+	0.0808183i	$0.974247\pi$
$840$		0			0
$841$	4.96367	+	21.7472i	0.171161	+	0.749905i
$842$	−0.873489	+	11.6559i	−0.0301024	+	0.401689i
$843$		0			0
$844$	0.679099	+	9.06195i	0.0233756	+	0.311925i
$845$	−25.3668	−	64.6334i	−0.872643	−	2.22346i
$846$		0			0
$847$	−42.6071	+	28.5600i	−1.46400	+	0.981331i
$848$	0.000444055	0	0.000213846i	1.52489e−5	0	7.34350e-6i
$849$		0			0
$850$	−2.32586	−	0.350567i	−0.0797764	−	0.0120244i
$851$	20.5237	+	35.5481i	0.703544	+	1.21857i
$852$		0			0
$853$	−19.6225	+	24.6058i	−0.671860	+	0.842486i	−0.994576	−	0.104010i	$-0.966833\pi$
$853$	−19.6225	+	24.6058i	−0.671860	+	0.842486i	0.322716	+	0.946496i	$0.395404\pi$
$854$	−17.6669	−	2.80537i	−0.604548	−	0.0959980i
$855$		0			0
$856$	−15.8512	+	2.38918i	−0.541781	+	0.0816604i
$857$	−24.4720	−	16.6847i	−0.835946	−	0.569938i	0.0679510	−	0.997689i	$-0.478354\pi$
$857$	−24.4720	−	16.6847i	−0.835946	−	0.569938i	−0.903897	+	0.427750i	$0.859306\pi$
$858$		0			0
$859$	53.7050	−	8.09473i	1.83239	−	0.276189i	0.860128	−	0.510078i	$-0.170384\pi$
$859$	53.7050	−	8.09473i	1.83239	−	0.276189i	0.972263	+	0.233890i	$0.0751455\pi$
$860$	15.9304	+	19.9761i	0.543223	+	0.681179i
$861$		0			0
$862$	10.0493	−	12.6014i	0.342279	−	0.429205i
$863$	5.19387	−	8.99605i	0.176801	−	0.306229i	−0.763982	−	0.645238i	$-0.776758\pi$
$863$	5.19387	−	8.99605i	0.176801	−	0.306229i	0.940783	+	0.339009i	$0.110092\pi$
$864$		0			0
$865$	46.6017	+	7.02407i	1.58450	+	0.238826i
$866$	18.1064	+	16.8003i	0.615282	+	0.570898i
$867$		0			0
$868$	−3.14224	+	2.10627i	−0.106654	+	0.0714915i
$869$	−26.9970	−	13.0011i	−0.915810	−	0.441031i
$870$		0			0
$871$	−7.27175	−	97.0347i	−0.246394	−	3.28790i
$872$	0.171633	−	0.0529419i	0.00581224	−	0.00179284i
$873$		0			0
$874$	0.304805	+	1.33544i	0.0103102	+	0.0451719i
$875$	23.1779	+	11.3877i	0.783557	+	0.384975i
$876$		0			0
$877$	−17.8046	−	5.49199i	−0.601218	−	0.185451i	−0.0208188	−	0.999783i	$-0.506627\pi$
$877$	−17.8046	−	5.49199i	−0.601218	−	0.185451i	−0.580399	+	0.814332i	$0.697104\pi$
$878$	−2.55263	+	6.50399i	−0.0861471	+	0.219499i
$879$		0			0
$880$	−0.726589	+	0.495380i	−0.0244933	+	0.0166992i
$881$	−3.31166			−0.111573			−0.0557863	−	0.998443i	$-0.517767\pi$
$881$	−3.31166			−0.111573			−0.0557863	+	0.998443i	$0.517767\pi$
$882$		0			0
$883$	−53.6374			−1.80504			−0.902521	−	0.430646i	$-0.858286\pi$
$883$	−53.6374			−1.80504			−0.902521	+	0.430646i	$0.858286\pi$
$884$	17.6387	−	12.0259i	0.593254	−	0.404474i
$885$		0			0
$886$	−4.38104	+	11.1627i	−0.147184	+	0.375018i
$887$	10.6460	+	3.28385i	0.357457	+	0.110261i	0.468282	−	0.883579i	$-0.344873\pi$
$887$	10.6460	+	3.28385i	0.357457	+	0.110261i	−0.110825	+	0.993840i	$0.535349\pi$
$888$		0			0
$889$	7.42234	−	31.3778i	0.248937	−	1.05238i
$890$	−3.07285	−	13.4630i	−0.103002	−	0.451282i
$891$		0			0
$892$	31.3572	−	9.67241i	1.04992	−	0.323856i
$893$	−0.105463	−	1.40731i	−0.00352920	−	0.0470939i
$894$		0			0
$895$	−4.16253	−	2.00457i	−0.139138	−	0.0670054i
$896$	1.57779	−	19.0400i	0.0527102	−	0.636081i
$897$		0			0
$898$	2.19117	+	2.03311i	0.0731203	+	0.0678458i
$899$	−2.92493	−	0.440863i	−0.0975520	−	0.0147036i
$900$		0			0
$901$	0.0100712	−	0.0174438i	0.000335519	−	0.000581136i
$902$	27.9959	−	35.1058i	0.932162	−	1.16889i
$903$		0			0
$904$	3.74082	+	4.69085i	0.124418	+	0.156015i
$905$	−7.82100	+	1.17883i	−0.259979	+	0.0391855i
$906$		0			0
$907$	34.1886	+	23.3094i	1.13521	+	0.773976i	0.976960	−	0.213422i	$-0.0684609\pi$
$907$	34.1886	+	23.3094i	1.13521	+	0.773976i	0.158255	+	0.987398i	$0.449413\pi$
$908$	1.57520	−	0.237424i	0.0522750	−	0.00787919i
$909$		0			0
$910$	−34.5983	+	10.3744i	−1.14692	+	0.343907i
$911$	−23.9220	+	29.9972i	−0.792570	+	0.993852i	0.207308	+	0.978276i	$0.433530\pi$
$911$	−23.9220	+	29.9972i	−0.792570	+	0.993852i	−0.999879	+	0.0155762i	$0.995042\pi$
$912$		0			0
$913$	25.6907	+	44.4977i	0.850239	+	1.47266i
$914$	5.60403	+	0.844671i	0.185365	+	0.0279392i
$915$		0			0
$916$	−0.999168	+	0.481174i	−0.0330134	+	0.0158984i
$917$	−14.7208	−	4.66809i	−0.486124	−	0.154154i
$918$		0			0
$919$	14.9721	+	38.1483i	0.493884	+	1.25839i	0.932971	+	0.359951i	$0.117206\pi$
$919$	14.9721	+	38.1483i	0.493884	+	1.25839i	−0.439088	+	0.898444i	$0.644698\pi$
$920$	−4.02113	−	53.6583i	−0.132573	−	1.76906i
$921$		0			0
$922$	−1.81637	+	24.2377i	−0.0598189	+	0.798227i
$923$	−12.6556	−	55.4480i	−0.416566	−	1.82509i
$924$		0			0
$925$	−1.19894	+	5.25290i	−0.0394209	+	0.172714i
$926$	4.22889	+	1.30444i	0.138970	+	0.0428666i
$927$		0			0
$928$	10.7805	−	10.0028i	0.353887	−	0.328359i
$929$	5.73208	−	3.90807i	0.188064	−	0.128220i	−0.465628	−	0.884980i	$-0.654172\pi$
$929$	5.73208	−	3.90807i	0.188064	−	0.128220i	0.653692	+	0.756761i	$0.273219\pi$
$930$		0			0
$931$	0.498424	+	1.33127i	0.0163352	+	0.0436306i
$932$	−21.1390			−0.692432
$933$		0			0
$934$	−9.09397	+	8.43797i	−0.297564	+	0.276099i
$935$	−13.1300	+	33.4546i	−0.429396	+	1.09408i
$936$		0			0
$937$	8.40609	−	36.8295i	0.274615	−	1.20317i	−0.629884	−	0.776690i	$-0.716897\pi$
$937$	8.40609	−	36.8295i	0.274615	−	1.20317i	0.904499	−	0.426477i	$-0.140245\pi$
$938$	−34.6827	−	0.273251i	−1.13243	−	0.00892195i
$939$		0			0
$940$	−1.59386	+	21.2685i	−0.0519858	+	0.693703i
$941$	−28.4778	+	8.78425i	−0.928351	+	0.286358i	−0.721819	−	0.692082i	$-0.756694\pi$
$941$	−28.4778	+	8.78425i	−0.928351	+	0.286358i	−0.206532	+	0.978440i	$0.566218\pi$
$942$		0			0
$943$	−26.7841	−	68.2448i	−0.872211	−	2.22236i
$944$	−0.764940	−	0.368376i	−0.0248967	−	0.0119896i
$945$		0			0
$946$	−35.7949	+	17.2379i	−1.16379	+	0.560453i
$947$	−28.0339	−	26.0117i	−0.910981	−	0.845266i	0.0774414	−	0.996997i	$-0.475325\pi$
$947$	−28.0339	−	26.0117i	−0.910981	−	0.845266i	−0.988422	+	0.151730i	$0.951515\pi$
$948$		0			0
$949$	−28.0725	−	48.6230i	−0.911272	−	1.57837i
$950$	−0.0899006	+	0.155712i	−0.00291676	+	0.00505198i
$951$		0			0
$952$	−9.75413	−	17.2063i	−0.316133	−	0.557659i
$953$	15.4604	+	19.3867i	0.500811	+	0.627997i	0.966412	−	0.256998i	$-0.0827334\pi$
$953$	15.4604	+	19.3867i	0.500811	+	0.627997i	−0.465601	+	0.884995i	$0.654162\pi$
$954$		0			0
$955$	−1.89246	−	1.29025i	−0.0612385	−	0.0417517i
$956$	3.25257	+	2.21756i	0.105196	+	0.0717211i
$957$		0			0
$958$	4.62926	+	5.80491i	0.149565	+	0.187548i
$959$	30.4624	−	27.8216i	0.983681	−	0.898405i
$960$		0			0
$961$	14.8464	−	25.7147i	0.478916	−	0.829508i
$962$	14.6532	+	25.3801i	0.472438	+	0.818286i
$963$		0			0
$964$	−16.1411	−	14.9768i	−0.519871	−	0.482370i
$965$	22.4511	−	10.8119i	0.722728	−	0.348047i
$966$		0			0
$967$	5.57325	+	2.68393i	0.179223	+	0.0863095i	0.521344	−	0.853347i	$-0.325431\pi$
$967$	5.57325	+	2.68393i	0.179223	+	0.0863095i	−0.342121	+	0.939656i	$0.611145\pi$
$968$	−19.9315	−	50.7847i	−0.640623	−	1.63228i
$969$		0			0
$970$	−5.34431	+	1.64850i	−0.171595	+	0.0529302i
$971$	−2.82747	+	37.7300i	−0.0907378	+	1.21081i	0.747032	+	0.664788i	$0.231478\pi$
$971$	−2.82747	+	37.7300i	−0.0907378	+	1.21081i	−0.837770	+	0.546024i	$0.816141\pi$
$972$		0			0
$973$	−4.31298	−	5.49659i	−0.138268	−	0.176213i
$974$	−1.51950	+	6.65735i	−0.0486878	+	0.213315i
$975$		0			0
$976$	−0.185476	+	0.472585i	−0.00593694	+	0.0151271i
$977$	16.6747	−	15.4718i	0.533470	−	0.494987i	−0.366812	−	0.930295i	$-0.619551\pi$
$977$	16.6747	−	15.4718i	0.533470	−	0.494987i	0.900282	+	0.435308i	$0.143360\pi$
$978$		0			0
$979$	−35.8301			−1.14514
$980$	−4.44986	−	21.0173i	−0.142146	−	0.671372i
$981$		0			0
$982$	10.8523	−	7.39900i	0.346312	−	0.236112i
$983$	20.2260	−	18.7670i	0.645110	−	0.598575i	−0.288233	−	0.957560i	$-0.593068\pi$
$983$	20.2260	−	18.7670i	0.645110	−	0.598575i	0.933343	+	0.358986i	$0.116877\pi$
$984$		0			0
$985$	−30.4985	−	9.40755i	−0.971764	−	0.299750i
$986$	1.32400	−	5.80084i	0.0421649	−	0.184736i
$987$		0			0
$988$	−0.363130	−	1.59098i	−0.0115527	−	0.0506158i
$989$	−4.84753	+	64.6858i	−0.154143	+	2.05689i
$990$		0			0
$991$	0.375149	+	5.00601i	0.0119170	+	0.159021i	0.999987	+	0.00501847i	$0.00159744\pi$
$991$	0.375149	+	5.00601i	0.0119170	+	0.159021i	−0.988070	+	0.154003i	$0.950784\pi$
$992$	−2.37435	−	6.04974i	−0.0753856	−	0.192079i
$993$		0			0
$994$	−20.0688	+	2.86337i	−0.636543	+	0.0908205i
$995$	3.17532	−	1.52915i	0.100665	−	0.0484775i
$996$		0			0
$997$	−42.4613	−	6.40002i	−1.34476	−	0.202691i	−0.563099	−	0.826389i	$-0.690391\pi$
$997$	−42.4613	−	6.40002i	−1.34476	−	0.202691i	−0.781665	+	0.623699i	$0.785629\pi$
$998$	6.76259	+	11.7132i	0.214066	+	0.370773i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.f.37.4	yes	72
3.2	odd	2	inner	441.2.bb.f.37.3	✓	72
49.4	even	21	inner	441.2.bb.f.298.4	yes	72
147.53	odd	42	inner	441.2.bb.f.298.3	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bb.f.37.3	✓	72	3.2	odd	2	inner
441.2.bb.f.37.4	yes	72	1.1	even	1	trivial
441.2.bb.f.298.3	yes	72	147.53	odd	42	inner
441.2.bb.f.298.4	yes	72	49.4	even	21	inner

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.715278 - 0.487668i) q^{2} +(-0.456880 + 1.16411i) q^{4} +(-2.34510 - 0.723367i) q^{5} +(2.39271 - 1.12913i) q^{7} +(0.626178 + 2.74347i) q^{8} +O(q^{10})\)	\(q+(0.715278 - 0.487668i) q^{2} +(-0.456880 + 1.16411i) q^{4} +(-2.34510 - 0.723367i) q^{5} +(2.39271 - 1.12913i) q^{7} +(0.626178 + 2.74347i) q^{8} +(-2.03016 + 0.626222i) q^{10} +(0.411946 + 5.49704i) q^{11} +(5.78955 + 2.78810i) q^{13} +(1.16081 - 1.97449i) q^{14} +(-0.0476513 - 0.0442140i) q^{16} +(-2.62691 - 0.395943i) q^{17} +(-0.101537 + 0.175867i) q^{19} +(1.91351 - 2.39946i) q^{20} +(2.97539 + 3.73102i) q^{22} +(7.70460 - 1.16128i) q^{23} +(0.845035 + 0.576135i) q^{25} +(5.50081 - 0.829113i) q^{26} +(0.221255 + 3.30126i) q^{28} +(-1.61308 + 2.02274i) q^{29} +(0.571660 + 0.990144i) q^{31} +(-5.62083 - 0.847203i) q^{32} +(-2.07206 + 0.997851i) q^{34} +(-6.42792 + 0.917121i) q^{35} +(1.92467 + 4.90398i) q^{37} +(0.0131377 + 0.175310i) q^{38} +(0.516084 - 6.88666i) q^{40} +(-2.09373 - 9.17325i) q^{41} +(-1.85254 + 8.11651i) q^{43} +(-6.58737 - 2.03194i) q^{44} +(4.94461 - 4.58793i) q^{46} +(-5.74194 + 3.91479i) q^{47} +(4.45012 - 5.40337i) q^{49} +0.885398 q^{50} +(-5.89078 + 5.46584i) q^{52} +(-0.00277004 + 0.00705794i) q^{53} +(3.01033 - 13.1891i) q^{55} +(4.59600 + 5.85728i) q^{56} +(-0.167375 + 2.23347i) q^{58} +(12.4808 - 3.84981i) q^{59} +(-2.85330 - 7.27009i) q^{61} +(0.891758 + 0.429448i) q^{62} +(-4.31648 + 2.07870i) q^{64} +(-11.5602 - 10.7263i) q^{65} +(-7.57144 - 13.1141i) q^{67} +(1.66110 - 2.87711i) q^{68} +(-4.15050 + 3.79069i) q^{70} +(-5.51833 - 6.91977i) q^{71} +(-7.21908 - 4.92189i) q^{73} +(3.76819 + 2.56911i) q^{74} +(-0.158338 - 0.198550i) q^{76} +(7.19256 + 12.6877i) q^{77} +(-2.71788 + 4.70751i) q^{79} +(0.0797642 + 0.138156i) q^{80} +(-5.97111 - 5.54038i) q^{82} +(8.39791 - 4.04422i) q^{83} +(5.87395 + 2.82874i) q^{85} +(2.63308 + 6.70899i) q^{86} +(-14.8230 + 4.57229i) q^{88} +(-0.485734 + 6.48168i) q^{89} +(17.0008 + 0.133942i) q^{91} +(-2.16822 + 9.49957i) q^{92} +(-2.19796 + 5.60032i) q^{94} +(0.365330 - 0.338977i) q^{95} +2.63246 q^{97} +(0.548017 - 6.03510i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 14 q^{4} - 28 q^{7}+O(q^{10}) \) 72 * q + 14 * q^4 - 28 * q^7	\( 72 q + 14 q^{4} - 28 q^{7} + 42 q^{13} - 26 q^{16} + 28 q^{19} + 8 q^{22} - 24 q^{25} - 28 q^{28} + 28 q^{31} + 28 q^{34} - 106 q^{37} + 70 q^{40} - 2 q^{43} + 60 q^{46} + 28 q^{49} + 70 q^{52} - 42 q^{55} + 56 q^{58} + 112 q^{61} + 38 q^{64} - 36 q^{67} - 14 q^{70} - 28 q^{73} + 56 q^{76} + 62 q^{79} - 70 q^{82} - 100 q^{85} - 262 q^{88} - 154 q^{91} - 294 q^{94} + 56 q^{97}+O(q^{100}) \) 72 * q + 14 * q^4 - 28 * q^7 + 42 * q^13 - 26 * q^16 + 28 * q^19 + 8 * q^22 - 24 * q^25 - 28 * q^28 + 28 * q^31 + 28 * q^34 - 106 * q^37 + 70 * q^40 - 2 * q^43 + 60 * q^46 + 28 * q^49 + 70 * q^52 - 42 * q^55 + 56 * q^58 + 112 * q^61 + 38 * q^64 - 36 * q^67 - 14 * q^70 - 28 * q^73 + 56 * q^76 + 62 * q^79 - 70 * q^82 - 100 * q^85 - 262 * q^88 - 154 * q^91 - 294 * q^94 + 56 * q^97

Introduction

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