LMFDB - Embedded newform 441.2.i.c.227.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(68,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.68"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			227.6
Root			$1.29589 + 0.748185i$ of defining polynomial
Character	$\chi$	$=$	441.227
Dual form			441.2.i.c.68.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.27639i q^{2} +(1.12441 + 1.31746i) q^{3} -3.18194 q^{4} +(-0.717144 + 1.24213i) q^{5} +(-2.99905 + 2.55959i) q^{6} -2.69056i q^{8} +(-0.471410 + 2.96273i) q^{9} +(-2.82757 - 1.63250i) q^{10} +(-2.80150 + 1.61745i) q^{11} +(-3.57780 - 4.19209i) q^{12} +(4.43334 - 2.55959i) q^{13} +(-2.44282 + 0.451852i) q^{15} -0.239123 q^{16} +(-0.545658 + 0.945107i) q^{17} +(-6.74433 - 1.07311i) q^{18} +(3.88768 - 2.24456i) q^{19} +(2.28191 - 3.95238i) q^{20} +(-3.68194 - 6.37731i) q^{22} +(-3.47141 - 2.00422i) q^{23} +(3.54471 - 3.02529i) q^{24} +(1.47141 + 2.54856i) q^{25} +(5.82662 + 10.0920i) q^{26} +(-4.43334 + 2.71026i) q^{27} +(1.02859 + 0.593857i) q^{29} +(-1.02859 - 5.56081i) q^{30} -3.74440i q^{31} -5.92546i q^{32} +(-5.28096 - 1.87220i) q^{33} +(-2.15143 - 1.24213i) q^{34} +(1.50000 - 9.42724i) q^{36} +(0.119562 + 0.207087i) q^{37} +(5.10948 + 8.84988i) q^{38} +(8.35705 + 2.96273i) q^{39} +(3.34203 + 1.92952i) q^{40} +(3.71620 + 6.43664i) q^{41} +(-3.82326 + 6.62208i) q^{43} +(8.91423 - 5.14663i) q^{44} +(-3.34203 - 2.71026i) q^{45} +(4.56238 - 7.90228i) q^{46} +4.22085 q^{47} +(-0.268872 - 0.315036i) q^{48} +(-5.80150 + 3.34950i) q^{50} +(-1.85868 + 0.343803i) q^{51} +(-14.1066 + 8.14447i) q^{52} +(6.07442 + 3.50707i) q^{53} +(-6.16959 - 10.0920i) q^{54} -4.63977i q^{55} +(7.32846 + 2.59808i) q^{57} +(-1.35185 + 2.34147i) q^{58} +9.47061 q^{59} +(7.77292 - 1.43777i) q^{60} +3.26499i q^{61} +8.52371 q^{62} +13.0104 q^{64} +7.34238i q^{65} +(4.26186 - 12.0215i) q^{66} +0.660190 q^{67} +(1.73625 - 3.00728i) q^{68} +(-1.26280 - 6.82701i) q^{69} -3.82347i q^{71} +(7.97141 + 1.26836i) q^{72} +(-6.33127 - 3.65536i) q^{73} +(-0.471410 + 0.272169i) q^{74} +(-1.70316 + 4.80415i) q^{75} +(-12.3704 + 7.14205i) q^{76} +(-6.74433 + 19.0239i) q^{78} +3.66019 q^{79} +(0.171486 - 0.297022i) q^{80} +(-8.55555 - 2.79332i) q^{81} +(-14.6523 + 8.45951i) q^{82} +(-5.45245 + 9.44392i) q^{83} +(-0.782630 - 1.35556i) q^{85} +(-15.0744 - 8.70322i) q^{86} +(0.374172 + 2.02287i) q^{87} +(4.35185 + 7.53762i) q^{88} +(-6.84573 - 11.8572i) q^{89} +(6.16959 - 7.60775i) q^{90} +(11.0458 + 6.37731i) q^{92} +(4.93310 - 4.21024i) q^{93} +9.60829i q^{94} +6.43867i q^{95} +(7.80657 - 6.66264i) q^{96} +(2.69709 + 1.55716i) q^{97} +(-3.47141 - 9.06259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4} + 12 q^{9} + 6 q^{15} - 4 q^{16} - 12 q^{18} - 10 q^{22} - 24 q^{23} + 30 q^{29} - 30 q^{30} + 18 q^{36} + 2 q^{37} + 12 q^{39} - 10 q^{43} + 54 q^{44} + 20 q^{46} - 36 q^{50} - 24 q^{51}+ \cdots - 24 q^{99}+O(q^{100}) $ 12 * q - 4 * q^4 + 12 * q^9 + 6 * q^15 - 4 * q^16 - 12 * q^18 - 10 * q^22 - 24 * q^23 + 30 * q^29 - 30 * q^30 + 18 * q^36 + 2 * q^37 + 12 * q^39 - 10 * q^43 + 54 * q^44 + 20 * q^46 - 36 * q^50 - 24 * q^51 - 12 * q^53 - 18 * q^57 + 2 * q^58 + 42 * q^60 + 16 * q^64 - 24 * q^67 + 78 * q^72 + 12 * q^74 - 12 * q^78 + 12 * q^79 - 48 * q^81 - 6 * q^85 - 96 * q^86 + 34 * q^88 + 30 * q^92 - 24 * q^93 - 24 * q^99

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			2.27639i			1.60965i	0.593512	+	0.804825i	$0.297741\pi$
$2$			2.27639i			1.60965i	−0.593512	+	0.804825i	$0.702259\pi$
$3$	1.12441	+	1.31746i	0.649178	+	0.760637i
$3$	1.12441	+	1.31746i	0.649178	+	0.760637i
$4$	−3.18194			−1.59097
$5$	−0.717144	+	1.24213i	−0.320716	+	0.555497i	−0.980636	−	0.195839i	$-0.937257\pi$
$5$	−0.717144	+	1.24213i	−0.320716	+	0.555497i	0.659920	+	0.751336i	$0.270590\pi$
$6$	−2.99905	+	2.55959i	−1.22436	+	1.04495i
$7$		0			0
$7$		0			0
$8$		−	2.69056i		−	0.951257i
$9$	−0.471410	+	2.96273i	−0.157137	+	0.987577i
$10$	−2.82757	−	1.63250i	−0.894156	−	0.516241i
$11$	−2.80150	+	1.61745i	−0.844686	+	0.487679i	−0.858854	−	0.512220i	$-0.828823\pi$
$11$	−2.80150	+	1.61745i	−0.844686	+	0.487679i	0.0141686	+	0.999900i	$0.495490\pi$
$12$	−3.57780	−	4.19209i	−1.03282	−	1.21015i
$13$	4.43334	−	2.55959i	1.22959	−	0.709903i	0.262644	−	0.964893i	$-0.415406\pi$
$13$	4.43334	−	2.55959i	1.22959	−	0.709903i	0.966944	+	0.254990i	$0.0820722\pi$
$14$		0			0
$15$	−2.44282	+	0.451852i	−0.630733	+	0.116668i
$16$	−0.239123			−0.0597808
$17$	−0.545658	+	0.945107i	−0.132341	+	0.229222i	−0.924579	−	0.380991i	$-0.875583\pi$
$17$	−0.545658	+	0.945107i	−0.132341	+	0.229222i	0.792237	+	0.610213i	$0.208916\pi$
$18$	−6.74433	−	1.07311i	−1.58965	−	0.252935i
$19$	3.88768	−	2.24456i	0.891896	−	0.514936i	0.0173336	−	0.999850i	$-0.494482\pi$
$19$	3.88768	−	2.24456i	0.891896	−	0.514936i	0.874562	+	0.484914i	$0.161149\pi$
$20$	2.28191	−	3.95238i	0.510251	−	0.883780i
$21$		0			0
$22$	−3.68194	−	6.37731i	−0.784993	−	1.35965i
$23$	−3.47141	−	2.00422i	−0.723839	−	0.417909i	0.0923250	−	0.995729i	$-0.470570\pi$
$23$	−3.47141	−	2.00422i	−0.723839	−	0.417909i	−0.816164	+	0.577820i	$0.803903\pi$
$24$	3.54471	−	3.02529i	0.723561	−	0.617535i
$25$	1.47141	+	2.54856i	0.294282	+	0.509711i
$26$	5.82662	+	10.0920i	1.14269	+	1.97921i
$27$	−4.43334	+	2.71026i	−0.853197	+	0.521589i
$28$		0			0
$29$	1.02859	+	0.593857i	0.191004	+	0.110276i	0.592453	−	0.805605i	$-0.298160\pi$
$29$	1.02859	+	0.593857i	0.191004	+	0.110276i	−0.401448	+	0.915882i	$0.631493\pi$
$30$	−1.02859	−	5.56081i	−0.187794	−	1.01526i
$31$		−	3.74440i		−	0.672514i	−0.941770	−	0.336257i	$-0.890839\pi$
$31$		−	3.74440i		−	0.672514i	0.941770	−	0.336257i	$-0.109161\pi$
$32$		−	5.92546i		−	1.04748i
$33$	−5.28096	−	1.87220i	−0.919298	−	0.325908i
$34$	−2.15143	−	1.24213i	−0.368967	−	0.213023i
$35$		0			0
$36$	1.50000	−	9.42724i	0.250000	−	1.57121i
$37$	0.119562	+	0.207087i	0.0196558	+	0.0340449i	0.875686	−	0.482881i	$-0.160410\pi$
$37$	0.119562	+	0.207087i	0.0196558	+	0.0340449i	−0.856030	+	0.516926i	$0.827076\pi$
$38$	5.10948	+	8.84988i	0.828867	+	1.43564i
$39$	8.35705	+	2.96273i	1.33820	+	0.474417i
$40$	3.34203	+	1.92952i	0.528421	+	0.305084i
$41$	3.71620	+	6.43664i	0.580373	+	1.00523i	0.995435	+	0.0954418i	$0.0304264\pi$
$41$	3.71620	+	6.43664i	0.580373	+	1.00523i	−0.415062	+	0.909793i	$0.636240\pi$
$42$		0			0
$43$	−3.82326	+	6.62208i	−0.583041	+	1.00986i	0.412075	+	0.911150i	$0.364804\pi$
$43$	−3.82326	+	6.62208i	−0.583041	+	1.00986i	−0.995116	+	0.0987075i	$0.968529\pi$
$44$	8.91423	−	5.14663i	1.34387	−	0.775884i
$45$	−3.34203	−	2.71026i	−0.498200	−	0.404021i
$46$	4.56238	−	7.90228i	0.672686	−	1.16513i
$47$	4.22085			0.615674			0.307837	−	0.951439i	$-0.400395\pi$
$47$	4.22085			0.615674			0.307837	+	0.951439i	$0.400395\pi$
$48$	−0.268872	−	0.315036i	−0.0388084	−	0.0454715i
$49$		0			0
$50$	−5.80150	+	3.34950i	−0.820457	+	0.473691i
$51$	−1.85868	+	0.343803i	−0.260268	+	0.0481421i
$52$	−14.1066	+	8.14447i	−1.95624	+	1.12944i
$53$	6.07442	+	3.50707i	0.834386	+	0.481733i	0.855352	−	0.518047i	$-0.173341\pi$
$53$	6.07442	+	3.50707i	0.834386	+	0.481733i	−0.0209662	+	0.999780i	$0.506674\pi$
$54$	−6.16959	−	10.0920i	−0.839575	−	1.37335i
$55$		−	4.63977i		−	0.625627i
$56$		0			0
$57$	7.32846	+	2.59808i	0.970678	+	0.344124i
$58$	−1.35185	+	2.34147i	−0.177506	+	0.307450i
$59$	9.47061			1.23297			0.616484	−	0.787367i	$-0.288556\pi$
$59$	9.47061			1.23297			0.616484	+	0.787367i	$0.288556\pi$
$60$	7.77292	−	1.43777i	1.00348	−	0.185615i
$61$			3.26499i			0.418040i	0.977911	+	0.209020i	$0.0670273\pi$
$61$			3.26499i			0.418040i	−0.977911	+	0.209020i	$0.932973\pi$
$62$	8.52371			1.08251
$63$		0			0
$64$	13.0104			1.62630
$65$			7.34238i			0.910710i
$66$	4.26186	−	12.0215i	0.524598	−	1.47975i
$67$	0.660190			0.0806550			0.0403275	−	0.999187i	$-0.487160\pi$
$67$	0.660190			0.0806550			0.0403275	+	0.999187i	$0.487160\pi$
$68$	1.73625	−	3.00728i	0.210552	−	0.364686i
$69$	−1.26280	−	6.82701i	−0.152023	−	0.821876i
$70$		0			0
$71$		−	3.82347i		−	0.453762i	−0.973922	−	0.226881i	$-0.927147\pi$
$71$		−	3.82347i		−	0.453762i	0.973922	−	0.226881i	$-0.0728529\pi$
$72$	7.97141	+	1.26836i	0.939440	+	0.149477i
$73$	−6.33127	−	3.65536i	−0.741020	−	0.427828i	0.0814203	−	0.996680i	$-0.474054\pi$
$73$	−6.33127	−	3.65536i	−0.741020	−	0.427828i	−0.822440	+	0.568852i	$0.807388\pi$
$74$	−0.471410	+	0.272169i	−0.0548003	+	0.0316390i
$75$	−1.70316	+	4.80415i	−0.196664	+	0.554735i
$76$	−12.3704	+	7.14205i	−1.41898	+	0.819249i
$77$		0			0
$78$	−6.74433	+	19.0239i	−0.763644	+	2.15403i
$79$	3.66019			0.411804			0.205902	−	0.978573i	$-0.433987\pi$
$79$	3.66019			0.411804			0.205902	+	0.978573i	$0.433987\pi$
$80$	0.171486	−	0.297022i	0.0191727	−	0.0332081i
$81$	−8.55555	−	2.79332i	−0.950616	−	0.310369i
$82$	−14.6523	+	8.45951i	−1.61808	+	0.934196i
$83$	−5.45245	+	9.44392i	−0.598484	+	1.03660i	0.394561	+	0.918870i	$0.370897\pi$
$83$	−5.45245	+	9.44392i	−0.598484	+	1.03660i	−0.993045	+	0.117735i	$0.962437\pi$
$84$		0			0
$85$	−0.782630	−	1.35556i	−0.0848882	−	0.147031i
$86$	−15.0744	−	8.70322i	−1.62552	−	0.938492i
$87$	0.374172	+	2.02287i	0.0401155	+	0.216874i
$88$	4.35185	+	7.53762i	0.463909	+	0.803513i
$89$	−6.84573	−	11.8572i	−0.725646	−	1.25686i	−0.958708	−	0.284394i	$-0.908208\pi$
$89$	−6.84573	−	11.8572i	−0.725646	−	1.25686i	0.233061	−	0.972462i	$-0.425126\pi$
$90$	6.16959	−	7.60775i	0.650332	−	0.801927i
$91$		0			0
$92$	11.0458	+	6.37731i	1.15161	+	0.664881i
$93$	4.93310	−	4.21024i	0.511539	−	0.436581i
$94$			9.60829i			0.991020i
$95$			6.43867i			0.660594i
$96$	7.80657	−	6.66264i	0.796754	−	0.680003i
$97$	2.69709	+	1.55716i	0.273848	+	0.158106i	0.630635	−	0.776080i	$-0.282795\pi$
$97$	2.69709	+	1.55716i	0.273848	+	0.158106i	−0.356787	+	0.934186i	$0.616128\pi$
$98$		0			0
$99$	−3.47141	−	9.06259i	−0.348890	−	0.910824i
$100$	−4.68194	−	8.10936i	−0.468194	−	0.810936i
$101$	3.54471	+	6.13962i	0.352712	+	0.610915i	0.986724	−	0.162408i	$-0.0519262\pi$
$101$	3.54471	+	6.13962i	0.352712	+	0.610915i	−0.634012	+	0.773324i	$0.718593\pi$
$102$	−0.782630	−	4.23109i	−0.0774919	−	0.418940i
$103$	−1.47529	−	0.851761i	−0.145365	−	0.0839265i	0.425553	−	0.904933i	$-0.360079\pi$
$103$	−1.47529	−	0.851761i	−0.145365	−	0.0839265i	−0.570918	+	0.821007i	$0.693413\pi$
$104$	−6.88674	−	11.9282i	−0.675300	−	1.16965i
$105$		0			0
$106$	−7.98345	+	13.8277i	−0.775421	+	1.34307i
$107$	4.27455	−	2.46791i	0.413236	−	0.238582i	−0.278943	−	0.960308i	$-0.589984\pi$
$107$	4.27455	−	2.46791i	0.413236	−	0.238582i	0.692179	+	0.721726i	$0.256651\pi$
$108$	14.1066	−	8.62388i	1.35741	−	0.829833i
$109$	−4.06922	+	7.04809i	−0.389760	+	0.675085i	−0.992417	−	0.122916i	$-0.960776\pi$
$109$	−4.06922	+	7.04809i	−0.389760	+	0.675085i	0.602657	+	0.798001i	$0.294109\pi$
$110$	10.5619			1.00704
$111$	−0.138393	+	0.390368i	−0.0131357	+	0.0370521i
$112$		0			0
$113$	−3.39699	+	1.96125i	−0.319562	+	0.184499i	−0.651197	−	0.758908i	$-0.725733\pi$
$113$	−3.39699	+	1.96125i	−0.319562	+	0.184499i	0.331635	+	0.943408i	$0.392400\pi$
$114$	−5.91423	+	16.6824i	−0.553918	+	1.56245i
$115$	4.97900	−	2.87463i	0.464294	−	0.268060i
$116$	−3.27292	−	1.88962i	−0.303883	−	0.175447i
$117$	5.49346	+	14.3414i	0.507870	+	1.32586i
$118$			21.5588i			1.98465i
$119$		0			0
$120$	1.21574	+	6.57256i	0.110981	+	0.599990i
$121$	−0.267713	+	0.463693i	−0.0243376	+	0.0421539i
$122$	−7.43240			−0.672897
$123$	−4.30150	+	12.1334i	−0.387854	+	1.09403i
$124$			11.9145i			1.06995i
$125$	−11.3923			−1.01896
$126$		0			0
$127$	6.16827			0.547345			0.273673	−	0.961823i	$-0.411761\pi$
$127$	6.16827			0.547345			0.273673	+	0.961823i	$0.411761\pi$
$128$			17.7658i			1.57029i
$129$	−13.0232	+	2.40893i	−1.14663	+	0.212094i
$130$	−16.7141			−1.46592
$131$	4.13138	−	7.15575i	0.360960	−	0.625201i	−0.627159	−	0.778891i	$-0.715782\pi$
$131$	4.13138	−	7.15575i	0.360960	−	0.625201i	0.988119	+	0.153690i	$0.0491158\pi$
$132$	16.8037	+	5.95724i	1.46258	+	0.518511i
$133$		0			0
$134$			1.50285i			0.129826i
$135$	−0.187145	−	7.45043i	−0.0161069	−	0.641231i
$136$	2.54287	+	1.46813i	0.218049	+	0.125891i
$137$	8.96169	−	5.17404i	0.765649	−	0.442048i	−0.0656711	−	0.997841i	$-0.520919\pi$
$137$	8.96169	−	5.17404i	0.765649	−	0.442048i	0.831320	+	0.555794i	$0.187585\pi$
$138$	15.5409	−	2.87463i	1.32293	−	0.244704i
$139$	15.4589	−	8.92521i	1.31121	−	0.757026i	0.328912	−	0.944361i	$-0.393318\pi$
$139$	15.4589	−	8.92521i	1.31121	−	0.757026i	0.982296	+	0.187334i	$0.0599848\pi$
$140$		0			0
$141$	4.74596	+	5.56081i	0.399682	+	0.468304i
$142$	8.70370			0.730398
$143$	−8.28002	+	14.3414i	−0.692410	+	1.19929i
$144$	0.112725	−	0.708458i	0.00939376	−	0.0590382i
$145$	−1.47529	+	0.851761i	−0.122516	+	0.0707349i
$146$	8.32102	−	14.4124i	0.688653	−	1.19278i
$147$		0			0
$148$	−0.380438	−	0.658939i	−0.0312718	−	0.0541644i
$149$	15.1758	+	8.76175i	1.24325	+	0.717790i	0.969754	−	0.244083i	$-0.0784869\pi$
$149$	15.1758	+	8.76175i	1.24325	+	0.717790i	0.273495	+	0.961873i	$0.411820\pi$
$150$	−10.9361	−	3.87705i	−0.892929	−	0.316560i
$151$	−0.550343	−	0.953223i	−0.0447863	−	0.0775722i	0.842763	−	0.538284i	$-0.180927\pi$
$151$	−0.550343	−	0.953223i	−0.0447863	−	0.0775722i	−0.887550	+	0.460712i	$0.847594\pi$
$152$	−6.03911	−	10.4601i	−0.489837	−	0.848422i
$153$	−2.54287	−	2.06217i	−0.205579	−	0.166717i
$154$		0			0
$155$	4.65103	+	2.68527i	0.373580	+	0.215686i
$156$	−26.5917	−	9.42724i	−2.12904	−	0.754783i
$157$		−	9.75896i		−	0.778850i	−0.921058	−	0.389425i	$-0.872674\pi$
$157$		−	9.75896i		−	0.778850i	0.921058	−	0.389425i	$-0.127326\pi$
$158$			8.33201i			0.662859i
$159$	2.20970	+	11.9462i	0.175241	+	0.947395i
$160$	7.36019	+	4.24941i	0.581874	+	0.335945i
$161$		0			0
$162$	6.35868	−	19.4757i	0.499585	−	1.53016i
$163$	3.61273	+	6.25742i	0.282970	+	0.490119i	0.972115	−	0.234505i	$-0.0753468\pi$
$163$	3.61273	+	6.25742i	0.282970	+	0.490119i	−0.689145	+	0.724624i	$0.742013\pi$
$164$	−11.8247	−	20.4810i	−0.923356	−	1.59930i
$165$	6.11273	−	5.21700i	0.475875	−	0.406143i
$166$	−21.4980	−	12.4119i	−1.66857	−	0.963350i
$167$	−8.65419	−	14.9895i	−0.669681	−	1.15992i	−0.977993	−	0.208637i	$-0.933097\pi$
$167$	−8.65419	−	14.9895i	−0.669681	−	1.15992i	0.308312	−	0.951285i	$-0.400236\pi$
$168$		0			0
$169$	6.60301	−	11.4367i	0.507924	−	0.879750i
$170$	3.08577	−	1.78157i	0.236668	−	0.136640i
$171$	4.81732	+	12.5763i	0.368390	+	0.961731i
$172$	12.1654	−	21.0711i	0.927602	−	1.60665i
$173$	−1.95621			−0.148728			−0.0743638	−	0.997231i	$-0.523693\pi$
$173$	−1.95621			−0.148728			−0.0743638	+	0.997231i	$0.523693\pi$
$174$	−4.60483	+	0.851761i	−0.349091	+	0.0645718i
$175$		0			0
$176$	0.669905	−	0.386770i	0.0504960	−	0.0291539i
$177$	10.6488	+	12.4772i	0.800416	+	0.937841i
$178$	26.9915	−	15.5835i	2.02310	−	1.16804i
$179$	−20.0933	−	11.6009i	−1.50184	−	0.867090i	−0.999998	−	0.00213247i	$-0.999321\pi$
$179$	−20.0933	−	11.6009i	−1.50184	−	0.867090i	−0.501846	−	0.864957i	$-0.667345\pi$
$180$	10.6341	+	8.62388i	0.792622	+	0.642786i
$181$		−	10.2744i		−	0.763689i	−0.924226	−	0.381845i	$-0.875289\pi$
$181$		−	10.2744i		−	0.763689i	0.924226	−	0.381845i	$-0.124711\pi$
$182$		0			0
$183$	−4.30150	+	3.67119i	−0.317976	+	0.271382i
$184$	−5.39248	+	9.34004i	−0.397539	+	0.688557i
$185$	−0.342971			−0.0252158
$186$	9.58414	+	11.2297i	0.702743	+	0.823399i
$187$		−	3.53030i		−	0.258161i
$188$	−13.4305			−0.979520
$189$		0			0
$190$	−14.6569			−1.06332
$191$		−	22.7197i		−	1.64394i	−0.569533	−	0.821968i	$-0.692876\pi$
$191$		−	22.7197i		−	1.64394i	0.569533	−	0.821968i	$-0.307124\pi$
$192$	14.6290	+	17.1407i	1.05576	+	1.23702i
$193$	16.8720			1.21447			0.607235	−	0.794522i	$-0.292278\pi$
$193$	16.8720			1.21447			0.607235	+	0.794522i	$0.292278\pi$
$194$	−3.54471	+	6.13962i	−0.254495	+	0.440799i
$195$	−9.67330	+	8.25583i	−0.692719	+	0.591212i
$196$		0			0
$197$		−	8.94426i		−	0.637252i	−0.947880	−	0.318626i	$-0.896779\pi$
$197$		−	8.94426i		−	0.637252i	0.947880	−	0.318626i	$-0.103221\pi$
$198$	20.6300	−	7.90228i	1.46611	−	0.561590i
$199$	5.01020	+	2.89264i	0.355164	+	0.205054i	0.666957	−	0.745096i	$-0.267596\pi$
$199$	5.01020	+	2.89264i	0.355164	+	0.205054i	−0.311794	+	0.950150i	$0.600930\pi$
$200$	6.85705	−	3.95892i	0.484867	−	0.279938i
$201$	0.742323	+	0.869775i	0.0523594	+	0.0613492i
$202$	−13.9762	+	8.06914i	−0.983359	+	0.567743i
$203$		0			0
$204$	5.91423	−	1.09396i	0.414079	−	0.0765927i
$205$	−10.6602			−0.744540
$206$	1.93894	−	3.35834i	0.135092	−	0.233987i
$207$	7.57442	−	9.34004i	0.526459	−	0.649178i
$208$	−1.06012	+	0.612058i	−0.0735058	+	0.0424386i
$209$	−7.26091	+	12.5763i	−0.502248	+	0.869918i
$210$		0			0
$211$	−12.9451	−	22.4216i	−0.891180	−	1.54357i	−0.838462	−	0.544960i	$-0.816545\pi$
$211$	−12.9451	−	22.4216i	−0.891180	−	1.54357i	−0.0527186	−	0.998609i	$-0.516789\pi$
$212$	−19.3285	−	11.1593i	−1.32748	−	0.766423i
$213$	5.03727	−	4.29914i	0.345148	−	0.294572i
$214$	5.61793	+	9.73053i	0.384034	+	0.665166i
$215$	−5.48365	−	9.49796i	−0.373982	−	0.647756i
$216$	7.29211	+	11.9282i	0.496165	+	0.811610i
$217$		0			0
$218$	−16.0442	−	9.26312i	−1.08665	−	0.627378i
$219$	−2.30314	−	12.4513i	−0.155632	−	0.841383i
$220$			14.7635i			0.995355i
$221$			5.58664i			0.375798i
$222$	−0.888629	−	0.315036i	−0.0596409	−	0.0211438i
$223$	15.4827	+	8.93892i	1.03680	+	0.598594i	0.918924	−	0.394435i	$-0.129060\pi$
$223$	15.4827	+	8.93892i	1.03680	+	0.598594i	0.117871	+	0.993029i	$0.462393\pi$
$224$		0			0
$225$	−8.24433	+	3.15798i	−0.549622	+	0.210532i
$226$	−4.46457	−	7.73287i	−0.296979	−	0.514383i
$227$	−5.48365	−	9.49796i	−0.363963	−	0.630402i	0.624646	−	0.780908i	$-0.285243\pi$
$227$	−5.48365	−	9.49796i	−0.363963	−	0.630402i	−0.988609	+	0.150506i	$0.951910\pi$
$228$	−23.3187	−	8.26693i	−1.54432	−	0.547491i
$229$	16.8349	+	9.71965i	1.11248	+	0.642293i	0.939471	−	0.342627i	$-0.111317\pi$
$229$	16.8349	+	9.71965i	1.11248	+	0.642293i	0.173012	+	0.984920i	$0.444650\pi$
$230$	6.54377	+	11.3341i	0.431483	+	0.747351i
$231$		0			0
$232$	1.59781	−	2.76748i	0.104901	−	0.181694i
$233$	2.54639	−	1.47016i	0.166819	−	0.0963131i	−0.414266	−	0.910156i	$-0.635962\pi$
$233$	2.54639	−	1.47016i	0.166819	−	0.0963131i	0.581085	+	0.813843i	$0.302628\pi$
$234$	−32.6466	+	12.5052i	−2.13418	+	0.817493i
$235$	−3.02696	+	5.24284i	−0.197457	+	0.342005i
$236$	−30.1350			−1.96162
$237$	4.11555	+	4.82216i	0.267334	+	0.313233i
$238$		0			0
$239$	−10.7255	+	6.19234i	−0.693772	+	0.400549i	−0.805023	−	0.593243i	$-0.797847\pi$
$239$	−10.7255	+	6.19234i	−0.693772	+	0.400549i	0.111252	+	0.993792i	$0.464514\pi$
$240$	0.584135	−	0.108048i	0.0377058	−	0.00697449i
$241$	−11.6943	+	6.75168i	−0.753293	+	0.434914i	−0.826882	−	0.562375i	$-0.809888\pi$
$241$	−11.6943	+	6.75168i	−0.753293	+	0.434914i	0.0735896	+	0.997289i	$0.476555\pi$
$242$	−1.05555	−	0.609419i	−0.0678530	−	0.0391750i
$243$	−5.93984	−	14.4124i	−0.381041	−	0.924558i
$244$		−	10.3890i		−	0.665089i
$245$		0			0
$246$	−27.6202	−	9.79190i	−1.76100	−	0.624308i
$247$	11.4903	−	19.9018i	0.731109	−	1.26632i
$248$	−10.0745			−0.639734
$249$	−18.5728	+	3.43543i	−1.17700	+	0.217712i
$250$		−	25.9333i		−	1.64016i
$251$	7.51441			0.474305			0.237153	−	0.971472i	$-0.423786\pi$
$251$	7.51441			0.474305			0.237153	+	0.971472i	$0.423786\pi$
$252$		0			0
$253$	12.9669			0.815222
$254$			14.0414i			0.881034i
$255$	0.905896	−	2.55528i	0.0567294	−	0.160018i
$256$	−14.4211			−0.901317
$257$	3.87788	−	6.71668i	0.241895	−	0.418975i	−0.719359	−	0.694639i	$-0.755564\pi$
$257$	3.87788	−	6.71668i	0.241895	−	0.418975i	0.961254	+	0.275664i	$0.0888976\pi$
$258$	−5.48365	−	29.6459i	−0.341397	−	1.84568i
$259$		0			0
$260$		−	23.3630i		−	1.44891i
$261$	−2.24433	+	2.76748i	−0.138920	+	0.171303i
$262$	16.2893	+	9.40462i	1.00635	+	0.581019i
$263$	12.1127	−	6.99329i	0.746903	−	0.431224i	−0.0776710	−	0.996979i	$-0.524748\pi$
$263$	12.1127	−	6.99329i	0.746903	−	0.431224i	0.824574	+	0.565755i	$0.191415\pi$
$264$	−5.03727	+	14.2088i	−0.310023	+	0.874489i
$265$	−8.71246	+	5.03014i	−0.535202	+	0.308999i
$266$		0			0
$267$	7.92395	−	22.3513i	0.484938	−	1.36788i
$268$	−2.10069			−0.128320
$269$	12.9160	−	22.3712i	0.787505	−	1.36400i	−0.139986	−	0.990154i	$-0.544706\pi$
$269$	12.9160	−	22.3712i	0.787505	−	1.36400i	0.927491	−	0.373846i	$-0.121961\pi$
$270$	16.9601	−	0.426015i	1.03216	−	0.0259264i
$271$	14.4225	−	8.32686i	0.876107	−	0.505821i	0.00673411	−	0.999977i	$-0.497856\pi$
$271$	14.4225	−	8.32686i	0.876107	−	0.505821i	0.869373	+	0.494157i	$0.164523\pi$
$272$	0.130480	−	0.225997i	0.00791148	−	0.0137031i
$273$		0			0
$274$	11.7781	+	20.4003i	0.711542	+	1.23243i
$275$	−8.24433	−	4.75986i	−0.497152	−	0.287031i
$276$	4.01816	+	21.7232i	0.241865	+	1.30758i
$277$	−15.7044	−	27.2008i	−0.943585	−	1.63434i	−0.758560	−	0.651603i	$-0.774097\pi$
$277$	−15.7044	−	27.2008i	−0.943585	−	1.63434i	−0.185025	−	0.982734i	$-0.559237\pi$
$278$	20.3172	+	35.1905i	1.21855	+	2.11059i
$279$	11.0937	+	1.76515i	0.664160	+	0.105677i
$280$		0			0
$281$	8.10464	+	4.67922i	0.483483	+	0.279139i	0.721867	−	0.692032i	$-0.243284\pi$
$281$	8.10464	+	4.67922i	0.483483	+	0.279139i	−0.238384	+	0.971171i	$0.576618\pi$
$282$	−12.6586	+	10.8036i	−0.753806	+	0.643348i
$283$		−	15.7735i		−	0.937638i	−0.883294	−	0.468819i	$-0.844680\pi$
$283$		−	15.7735i		−	0.937638i	0.883294	−	0.468819i	$-0.155320\pi$
$284$			12.1661i			0.721923i
$285$	−8.48270	+	7.23970i	−0.502472	+	0.428843i
$286$	−32.6466	−	18.8485i	−1.93044	−	1.11454i
$287$		0			0
$288$	17.5555	+	2.79332i	1.03447	+	0.164598i
$289$	7.90451	+	13.6910i	0.464971	+	0.805354i
$290$	−1.93894	−	3.35834i	−0.113858	−	0.197209i
$291$	0.981125	+	5.30420i	0.0575146	+	0.310938i
$292$	20.1458	+	11.6312i	1.17894	+	0.680662i
$293$	12.4287	+	21.5271i	0.726090	+	1.25762i	0.958524	+	0.285013i	$0.0919978\pi$
$293$	12.4287	+	21.5271i	0.726090	+	1.25762i	−0.232434	+	0.972612i	$0.574669\pi$
$294$		0			0
$295$	−6.79179	+	11.7637i	−0.395433	+	0.684911i
$296$	0.557180	−	0.321688i	0.0323854	−	0.0186977i
$297$	8.03633	−	14.7635i	0.466315	−	0.856665i
$298$	−19.9451	+	34.5460i	−1.15539	+	2.00120i
$299$	−20.5199			−1.18670
$300$	5.41936	−	15.2865i	0.312887	−	0.882568i
$301$		0			0
$302$	2.16991	−	1.25280i	0.124864	−	0.0720903i
$303$	−4.10301	+	11.5735i	−0.235712	+	0.664878i
$304$	−0.929636	+	0.536725i	−0.0533183	+	0.0307833i
$305$	−4.05555	−	2.34147i	−0.232220	−	0.134072i
$306$	4.69430	−	5.78856i	0.268355	−	0.330910i
$307$		−	18.8878i		−	1.07799i	−0.842310	−	0.538993i	$-0.818805\pi$
$307$		−	18.8878i		−	1.07799i	0.842310	−	0.538993i	$-0.181195\pi$
$308$		0			0
$309$	−0.536670	−	2.90137i	−0.0305301	−	0.165053i
$310$	−6.11273	+	10.5876i	−0.347179	+	0.601332i
$311$	−7.95431			−0.451048			−0.225524	−	0.974238i	$-0.572409\pi$
$311$	−7.95431			−0.451048			−0.225524	+	0.974238i	$0.572409\pi$
$312$	7.97141	−	22.4852i	0.451292	−	1.27297i
$313$		−	11.1337i		−	0.629316i	−0.949205	−	0.314658i	$-0.898110\pi$
$313$		−	11.1337i		−	0.629316i	0.949205	−	0.314658i	$-0.101890\pi$
$314$	22.2152			1.25367
$315$		0			0
$316$	−11.6465			−0.655168
$317$			23.2534i			1.30604i	0.757340	+	0.653021i	$0.226499\pi$
$317$			23.2534i			1.30604i	−0.757340	+	0.653021i	$0.773501\pi$
$318$	−27.1942	+	5.03014i	−1.52497	+	0.282076i
$319$	−3.84213			−0.215118
$320$	−9.33033	+	16.1606i	−0.521581	+	0.903405i
$321$	8.05772	+	2.85661i	0.449738	+	0.159441i
$322$		0			0
$323$			4.89904i			0.272590i
$324$	27.2233	+	8.88819i	1.51240	+	0.493788i
$325$	13.0465	+	7.53242i	0.723691	+	0.417823i
$326$	−14.2443	+	8.22396i	−0.788920	+	0.455483i
$327$	−13.8611	+	2.56390i	−0.766518	+	0.141784i
$328$	17.3182	−	9.99866i	0.956237	−	0.552084i
$329$		0			0
$330$	11.8759	+	13.9149i	0.653748	+	0.765992i
$331$	−19.1592			−1.05309			−0.526544	−	0.850148i	$-0.676512\pi$
$331$	−19.1592			−1.05309			−0.526544	+	0.850148i	$0.676512\pi$
$332$	17.3494	−	30.0500i	0.952171	−	1.64921i
$333$	−0.669905	+	0.256606i	−0.0367106	+	0.0140619i
$334$	34.1219	−	19.7003i	1.86707	−	1.07795i
$335$	−0.473451	+	0.820041i	−0.0258674	+	0.0448036i
$336$		0			0
$337$	14.2781	+	24.7304i	0.777779	+	1.34715i	0.933219	+	0.359307i	$0.116987\pi$
$337$	14.2781	+	24.7304i	0.777779	+	1.34715i	−0.155441	+	0.987845i	$0.549680\pi$
$338$	26.0345	+	15.0310i	1.41609	+	0.817579i
$339$	−6.40348	−	2.27015i	−0.347789	−	0.123298i
$340$	2.49028	+	4.31330i	0.135055	+	0.233922i
$341$	6.05638	+	10.4900i	0.327971	+	0.568063i
$342$	−28.6285	+	10.9661i	−1.54805	+	0.592978i
$343$		0			0
$344$	17.8171	+	10.2867i	0.960634	+	0.554622i
$345$	9.38564	+	3.32738i	0.505306	+	0.179140i
$346$		−	4.45308i		−	0.239399i
$347$			2.96400i			0.159116i	0.996830	+	0.0795578i	$0.0253508\pi$
$347$			2.96400i			0.159116i	−0.996830	+	0.0795578i	$0.974649\pi$
$348$	−1.19059	−	6.43664i	−0.0638226	−	0.345040i
$349$	−23.3885	−	13.5034i	−1.25196	−	0.722818i	−0.280460	−	0.959866i	$-0.590487\pi$
$349$	−23.3885	−	13.5034i	−1.25196	−	0.722818i	−0.971498	+	0.237048i	$0.923820\pi$
$350$		0			0
$351$	−12.7174	+	23.3630i	−0.678803	+	1.24703i
$352$	9.58414	+	16.6002i	0.510836	+	0.884794i
$353$	14.8238	+	25.6755i	0.788990	+	1.36657i	0.926586	+	0.376083i	$0.122729\pi$
$353$	14.8238	+	25.6755i	0.788990	+	1.36657i	−0.137596	+	0.990488i	$0.543937\pi$
$354$	−28.4029	+	24.2409i	−1.50960	+	1.28839i
$355$	4.74924	+	2.74198i	0.252064	+	0.145529i
$356$	21.7827	+	37.7288i	1.15448	+	1.99962i
$357$		0			0
$358$	26.4081	−	45.7401i	1.39571	−	2.41744i
$359$	−21.3268	+	12.3130i	−1.12559	+	0.649858i	−0.942821	−	0.333299i	$-0.891838\pi$
$359$	−21.3268	+	12.3130i	−1.12559	+	0.649858i	−0.182766	+	0.983157i	$0.558505\pi$
$360$	−7.29211	+	8.99193i	−0.384328	+	0.473916i
$361$	0.576055	−	0.997756i	0.0303187	−	0.0525135i
$362$	23.3885			1.22927
$363$	−0.911917	+	0.168678i	−0.0478632	+	0.00885332i
$364$		0			0
$365$	9.08087	−	5.24284i	0.475314	−	0.274423i
$366$	−8.35705	−	9.79190i	−0.436830	−	0.511831i
$367$	4.85598	−	2.80360i	0.253480	−	0.146347i	−0.367877	−	0.929875i	$-0.619915\pi$
$367$	4.85598	−	2.80360i	0.253480	−	0.146347i	0.621357	+	0.783528i	$0.286582\pi$
$368$	0.830095	+	0.479256i	0.0432717	+	0.0249829i
$369$	−20.8219	+	7.97579i	−1.08394	+	0.415203i
$370$		−	0.780736i		−	0.0405885i
$371$		0			0
$372$	−15.6969	+	13.3967i	−0.813844	+	0.694588i
$373$	1.86677	−	3.23333i	0.0966574	−	0.167416i	−0.813642	−	0.581367i	$-0.802518\pi$
$373$	1.86677	−	3.23333i	0.0966574	−	0.167416i	0.910299	+	0.413951i	$0.135852\pi$
$374$	8.03633			0.415549
$375$	−12.8096	−	15.0089i	−0.661484	−	0.775056i
$376$		−	11.3565i		−	0.585665i
$377$	6.08012			0.313142
$378$		0			0
$379$	−30.4419			−1.56369			−0.781847	−	0.623470i	$-0.785722\pi$
$379$	−30.4419			−1.56369			−0.781847	+	0.623470i	$0.785722\pi$
$380$		−	20.4875i		−	1.05099i
$381$	6.93566	+	8.12646i	0.355324	+	0.416331i
$382$	51.7187			2.64616
$383$	−8.49251	+	14.7095i	−0.433947	+	0.751618i	−0.997209	−	0.0746601i	$-0.976213\pi$
$383$	−8.49251	+	14.7095i	−0.433947	+	0.751618i	0.563262	+	0.826278i	$0.309546\pi$
$384$	−23.4058	+	19.9760i	−1.19442	+	1.01940i
$385$		0			0
$386$			38.4071i			1.95487i
$387$	−17.8171	−	14.4490i	−0.905695	−	0.734484i
$388$	−8.58198	−	4.95481i	−0.435684	−	0.251542i
$389$	−9.43310	+	5.44621i	−0.478277	+	0.276134i	−0.719698	−	0.694287i	$-0.755720\pi$
$389$	−9.43310	+	5.44621i	−0.478277	+	0.276134i	0.241421	+	0.970420i	$0.422387\pi$
$390$	−18.7935	−	22.0202i	−0.951645	−	1.11504i
$391$	3.78840	−	2.18724i	0.191588	−	0.110613i
$392$		0			0
$393$	14.0728	−	2.60306i	0.709878	−	0.131307i
$394$	20.3606			1.02575
$395$	−2.62488	+	4.54643i	−0.132072	+	0.228756i
$396$	11.0458	+	28.8366i	0.555074	+	1.44910i
$397$	19.3154	−	11.1518i	0.969412	−	0.559690i	0.0703551	−	0.997522i	$-0.477587\pi$
$397$	19.3154	−	11.1518i	0.969412	−	0.559690i	0.899057	+	0.437832i	$0.144253\pi$
$398$	−6.58477	+	11.4052i	−0.330065	+	0.571689i
$399$		0			0
$400$	−0.351848	−	0.609419i	−0.0175924	−	0.0304710i
$401$	−20.8554	−	12.0409i	−1.04147	−	0.601293i	−0.121221	−	0.992626i	$-0.538681\pi$
$401$	−20.8554	−	12.0409i	−1.04147	−	0.601293i	−0.920249	+	0.391333i	$0.872014\pi$
$402$	−1.97995	+	1.68982i	−0.0987507	+	0.0842804i
$403$	−9.58414	−	16.6002i	−0.477420	−	0.826915i
$404$	−11.2791	−	19.5359i	−0.561155	−	0.971949i
$405$	9.60522	−	8.62388i	0.477287	−	0.428524i
$406$		0			0
$407$	−0.669905	−	0.386770i	−0.0332060	−	0.0191715i
$408$	0.925025	+	5.00091i	0.0457955	+	0.247582i
$409$			26.3492i			1.30289i	0.758698	+	0.651443i	$0.225836\pi$
$409$			26.3492i			1.30289i	−0.758698	+	0.651443i	$0.774164\pi$
$410$		−	24.2667i		−	1.19845i
$411$	16.8932	+	5.98896i	0.833280	+	0.295413i
$412$	4.69430	+	2.71026i	0.231272	+	0.133525i
$413$		0			0
$414$	21.2616	+	17.2423i	1.04495	+	0.847414i
$415$	−7.82038	−	13.5453i	−0.383887	−	0.664912i
$416$	−15.1668	−	26.2696i	−0.743611	−	1.28797i
$417$	29.1408	+	10.3309i	1.42703	+	0.505909i
$418$	−28.6285	−	16.5286i	−1.40026	−	0.808443i
$419$	−16.1761	−	28.0178i	−0.790252	−	1.36876i	−0.925811	−	0.377988i	$-0.876616\pi$
$419$	−16.1761	−	28.0178i	−0.790252	−	1.36876i	0.135558	−	0.990769i	$-0.456717\pi$
$420$		0			0
$421$	−5.54746	+	9.60849i	−0.270367	+	0.468289i	−0.968956	−	0.247234i	$-0.920478\pi$
$421$	−5.54746	+	9.60849i	−0.270367	+	0.468289i	0.698589	+	0.715523i	$0.253812\pi$
$422$	51.0404	−	29.4682i	2.48461	−	1.43449i
$423$	−1.98975	+	12.5052i	−0.0967450	+	0.608026i
$424$	9.43598	−	16.3436i	0.458252	−	0.793716i
$425$	−3.21155			−0.155783
$426$	9.78651	+	11.4668i	0.474158	+	0.555568i
$427$		0			0
$428$	−13.6014	+	7.85276i	−0.657447	+	0.379577i
$429$	−28.2044	+	5.21700i	−1.36172	+	0.251879i
$430$	21.6210	−	12.4829i	1.04266	−	0.601980i
$431$	14.1202	+	8.15233i	0.680149	+	0.392684i	0.799911	−	0.600119i	$-0.204880\pi$
$431$	14.1202	+	8.15233i	0.680149	+	0.392684i	−0.119762	+	0.992803i	$0.538213\pi$
$432$	1.06012	−	0.648085i	0.0510048	−	0.0311810i
$433$			12.5359i			0.602438i	0.953555	+	0.301219i	$0.0973936\pi$
$433$			12.5359i			0.602438i	−0.953555	+	0.301219i	$0.902606\pi$
$434$		0			0
$435$	−2.78100	−	0.985915i	−0.133339	−	0.0472710i
$436$	12.9480	−	22.4266i	0.620098	−	1.07404i
$437$	−17.9943			−0.860785
$438$	28.3441	−	5.24284i	1.35433	−	0.250513i
$439$			18.6225i			0.888805i	0.895827	+	0.444403i	$0.146584\pi$
$439$			18.6225i			0.888805i	−0.895827	+	0.444403i	$0.853416\pi$
$440$	−12.4836			−0.595132
$441$		0			0
$442$	−12.7174			−0.604904
$443$		−	4.75085i		−	0.225720i	−0.993611	−	0.112860i	$-0.963999\pi$
$443$		−	4.75085i		−	0.225720i	0.993611	−	0.112860i	$-0.0360011\pi$
$444$	0.440358	−	1.24213i	0.0208985	−	0.0589488i
$445$	19.6375			0.930906
$446$	−20.3484	+	35.2445i	−0.963527	+	1.66888i
$447$	5.52053	+	29.8453i	0.261112	+	1.41163i
$448$		0			0
$449$		−	16.2393i		−	0.766379i	−0.923670	−	0.383189i	$-0.874826\pi$
$449$		−	16.2393i		−	0.766379i	0.923670	−	0.383189i	$-0.125174\pi$
$450$	−7.18878	−	18.7673i	−0.338882	−	0.884698i
$451$	−20.8219	−	12.0215i	−0.980465	−	0.566072i
$452$	10.8090	−	6.24060i	0.508414	−	0.293533i
$453$	0.637023	−	1.79687i	0.0299300	−	0.0844242i
$454$	21.6210	−	12.4829i	1.01473	−	0.585852i
$455$		0			0
$456$	6.99028	−	19.7177i	0.327350	−	0.923365i
$457$	−5.74720			−0.268843			−0.134421	−	0.990924i	$-0.542918\pi$
$457$	−5.74720			−0.268843			−0.134421	+	0.990924i	$0.542918\pi$
$458$	−22.1257	+	38.3228i	−1.03387	+	1.79071i
$459$	−0.142394	−	5.66886i	−0.00664640	−	0.264599i
$460$	−15.8429	+	9.14690i	−0.738679	+	0.426476i
$461$	18.1346	−	31.4101i	0.844613	−	1.46291i	−0.0413440	−	0.999145i	$-0.513164\pi$
$461$	18.1346	−	31.4101i	0.844613	−	1.46291i	0.885957	−	0.463768i	$-0.153503\pi$
$462$		0			0
$463$	14.6202	+	25.3230i	0.679461	+	1.17686i	0.975144	+	0.221574i	$0.0711195\pi$
$463$	14.6202	+	25.3230i	0.679461	+	1.17686i	−0.295683	+	0.955286i	$0.595547\pi$
$464$	−0.245960	−	0.142005i	−0.0114184	−	0.00659241i
$465$	1.69191	+	9.14690i	0.0784606	+	0.424177i
$466$	3.34665	+	5.79656i	0.155030	+	0.268521i
$467$	−1.32107	−	2.28817i	−0.0611320	−	0.105884i	0.833840	−	0.552007i	$-0.186138\pi$
$467$	−1.32107	−	2.28817i	−0.0611320	−	0.105884i	−0.894972	+	0.446123i	$0.852804\pi$
$468$	−17.4799	−	45.6336i	−0.808007	−	2.10941i
$469$		0			0
$470$	−11.9347	−	6.89053i	−0.550508	−	0.317836i
$471$	12.8571	−	10.9731i	0.592422	−	0.505612i
$472$		−	25.4813i		−	1.17287i
$473$		−	24.7357i		−	1.13735i
$474$	−10.9771	+	9.36859i	−0.504195	+	0.430314i
$475$	11.4408	+	6.60532i	0.524938	+	0.303073i
$476$		0			0
$477$	−13.2540	+	16.3436i	−0.606861	+	0.748322i
$478$	−14.0962	−	24.4153i	−0.644744	−	1.11673i
$479$	−15.5409	−	26.9177i	−0.710083	−	1.22990i	−0.964826	−	0.262891i	$-0.915324\pi$
$479$	−15.5409	−	26.9177i	−0.710083	−	1.22990i	0.254742	−	0.967009i	$-0.418009\pi$
$480$	2.67743	+	14.4748i	0.122207	+	0.660683i
$481$	1.06012	+	0.612058i	0.0483371	+	0.0279074i
$482$	−15.3694	−	26.6207i	−0.700059	−	1.21254i
$483$		0			0
$484$	0.851848	−	1.47544i	0.0387204	−	0.0670657i
$485$	−3.86840	+	2.23342i	−0.175655	+	0.101414i
$486$	32.8083	−	13.5214i	1.48821	−	0.613342i
$487$	−17.4360	+	30.2000i	−0.790100	+	1.36849i	0.135805	+	0.990736i	$0.456638\pi$
$487$	−17.4360	+	30.2000i	−0.790100	+	1.36849i	−0.925905	+	0.377757i	$0.876695\pi$
$488$	8.78467			0.397663
$489$	−4.18174	+	11.7955i	−0.189105	+	0.533412i
$490$		0			0
$491$	−22.6758	+	13.0919i	−1.02334	+	0.590828i	−0.915071	−	0.403293i	$-0.867866\pi$
$491$	−22.6758	+	13.0919i	−1.02334	+	0.590828i	−0.108273	+	0.994121i	$0.534532\pi$
$492$	13.6871	−	38.6077i	0.617064	−	1.74057i
$493$	−1.12252	+	0.648085i	−0.0505556	+	0.0291883i
$494$	45.3041	+	26.1563i	2.03833	+	1.17683i
$495$	13.7464	+	2.18724i	0.617855	+	0.0983090i
$496$			0.895374i			0.0402035i
$497$		0			0
$498$	−7.82038	−	42.2789i	−0.350440	−	1.89456i
$499$	−6.23912	+	10.8065i	−0.279302	+	0.483764i	−0.971211	−	0.238220i	$-0.923436\pi$
$499$	−6.23912	+	10.8065i	−0.279302	+	0.483764i	0.691910	+	0.721984i	$0.256770\pi$
$500$	36.2496			1.62113
$501$	10.0172	−	28.2559i	0.447537	−	1.26238i
$502$			17.1057i			0.763465i
$503$	−37.8479			−1.68756			−0.843778	−	0.536693i	$-0.819673\pi$
$503$	−37.8479			−1.68756			−0.843778	+	0.536693i	$0.819673\pi$
$504$		0			0
$505$	−10.1683			−0.452482
$506$			29.5177i			1.31222i
$507$	22.4920	−	4.16037i	0.998903	−	0.184768i
$508$	−19.6271			−0.870811
$509$	17.6924	−	30.6441i	0.784200	−	1.35827i	−0.145276	−	0.989391i	$-0.546407\pi$
$509$	17.6924	−	30.6441i	0.784200	−	1.35827i	0.929476	−	0.368883i	$-0.120260\pi$
$510$	5.81682	+	2.06217i	0.257573	+	0.0913144i
$511$		0			0
$512$			2.70367i			0.119486i
$513$	−11.1521	+	20.4875i	−0.492378	+	0.904545i
$514$	15.2898	+	8.82756i	0.674403	+	0.389367i
$515$	2.11599	−	1.22167i	0.0932419	−	0.0538332i
$516$	41.4392	−	7.66507i	1.82426	−	0.337436i
$517$	−11.8247	+	6.82701i	−0.520051	+	0.300252i
$518$		0			0
$519$	−2.19957	−	2.57723i	−0.0965506	−	0.113128i
$520$	19.7551			0.866319
$521$	1.15939	−	2.00813i	0.0507940	−	0.0879777i	−0.839511	−	0.543343i	$-0.817158\pi$
$521$	1.15939	−	2.00813i	0.0507940	−	0.0879777i	0.890304	+	0.455366i	$0.150491\pi$
$522$	−6.29987	−	5.10896i	−0.275738	−	0.223613i
$523$	−17.4799	+	10.0920i	−0.764341	+	0.441293i	−0.830852	−	0.556493i	$-0.812147\pi$
$523$	−17.4799	+	10.0920i	−0.764341	+	0.441293i	0.0665110	+	0.997786i	$0.478813\pi$
$524$	−13.1458	+	22.7692i	−0.574277	+	0.994677i
$525$		0			0
$526$	15.9194	+	27.5733i	0.694120	+	1.20225i
$527$	3.53886	+	2.04316i	0.154155	+	0.0890015i
$528$	1.26280	+	0.447687i	0.0549564	+	0.0194831i
$529$	−3.46621	−	6.00365i	−0.150705	−	0.261028i
$530$	−11.4506	−	19.8329i	−0.497380	−	0.861488i
$531$	−4.46454	+	28.0589i	−0.193745	+	1.21765i
$532$		0			0
$533$	32.9503	+	19.0239i	1.42724	+	0.824016i
$534$	50.8802	+	18.0380i	2.20180	+	0.780580i
$535$			7.07939i			0.306069i
$536$		−	1.77628i		−	0.0767237i
$537$	−7.30938	−	39.5163i	−0.315423	−	1.70525i
$538$	50.9256	+	29.4019i	2.19556	+	1.26761i
$539$		0			0
$540$	0.595485	+	23.7068i	0.0256256	+	1.02018i
$541$	11.3856	+	19.7205i	0.489507	+	0.847851i	0.999927	−	0.0120743i	$-0.00384346\pi$
$541$	11.3856	+	19.7205i	0.489507	+	0.847851i	−0.510420	+	0.859925i	$0.670510\pi$
$542$	18.9552	+	32.8313i	0.814194	+	1.41023i
$543$	13.5361	−	11.5526i	0.580890	−	0.495770i
$544$	5.60020	+	3.23327i	0.240106	+	0.138626i
$545$	−5.83643	−	10.1090i	−0.250005	−	0.433022i
$546$		0			0
$547$	14.7918	−	25.6201i	0.632451	−	1.09544i	−0.354598	−	0.935019i	$-0.615382\pi$
$547$	14.7918	−	25.6201i	0.632451	−	1.09544i	0.987049	−	0.160419i	$-0.0512845\pi$
$548$	−28.5156	+	16.4635i	−1.21813	+	0.703286i
$549$	−9.67330	−	1.53915i	−0.412846	−	0.0656894i
$550$	10.8353	−	18.7673i	0.462019	−	0.800240i
$551$	5.33178			0.227141
$552$	−18.3685	+	3.39765i	−0.781815	+	0.144613i
$553$		0			0
$554$	61.9196	−	35.7493i	2.63071	−	1.51884i
$555$	−0.385640	−	0.451852i	−0.0163695	−	0.0191800i
$556$	−49.1894	+	28.3995i	−2.08609	+	1.20441i
$557$	−4.08250	−	2.35703i	−0.172981	−	0.0998707i	0.411010	−	0.911631i	$-0.365176\pi$
$557$	−4.08250	−	2.35703i	−0.172981	−	0.0998707i	−0.583991	+	0.811760i	$0.698510\pi$
$558$	−4.01816	+	25.2535i	−0.170102	+	1.06906i
$559$			39.1439i			1.65561i
$560$		0			0
$561$	4.65103	−	3.96950i	0.196367	−	0.167592i
$562$	−10.6517	+	18.4493i	−0.449316	+	0.778238i
$563$	−27.3484			−1.15260			−0.576299	−	0.817239i	$-0.695503\pi$
$563$	−27.3484			−1.15260			−0.576299	+	0.817239i	$0.695503\pi$
$564$	−15.1014	−	17.6942i	−0.635883	−	0.745059i
$565$		−	5.62600i		−	0.236688i
$566$	35.9066			1.50927
$567$		0			0
$568$	−10.2873			−0.431645
$569$		−	23.5580i		−	0.987601i	−0.869575	−	0.493801i	$-0.835607\pi$
$569$		−	23.5580i		−	0.987601i	0.869575	−	0.493801i	$-0.164393\pi$
$570$	−16.4804	−	19.3099i	−0.690287	−	0.808804i
$571$	19.1877			0.802980			0.401490	−	0.915863i	$-0.368492\pi$
$571$	19.1877			0.802980			0.401490	+	0.915863i	$0.368492\pi$
$572$	26.3465	−	45.6336i	1.10160	−	1.90804i
$573$	29.9323	−	25.5462i	1.25044	−	1.06721i
$574$		0			0
$575$		−	11.7961i		−	0.491932i
$576$	−6.13323	+	38.5463i	−0.255551	+	1.60610i
$577$	1.93481	+	1.11706i	0.0805472	+	0.0465039i	0.539733	−	0.841836i	$-0.318525\pi$
$577$	1.93481	+	1.11706i	0.0805472	+	0.0465039i	−0.459185	+	0.888340i	$0.651859\pi$
$578$	−31.1661	+	17.9937i	−1.29634	+	0.748441i
$579$	18.9710	+	22.2282i	0.788407	+	0.923771i
$580$	4.69430	−	2.71026i	0.194920	−	0.112537i
$581$		0			0
$582$	−12.0744	+	2.23342i	−0.500501	+	0.0925783i
$583$	−22.6900			−0.939725
$584$	−9.83498	+	17.0347i	−0.406974	+	0.704900i
$585$	−21.7535	−	3.46127i	−0.899396	−	0.143106i
$586$	−49.0040	+	28.2925i	−2.02434	+	1.16875i
$587$	12.9883	−	22.4963i	0.536083	−	0.928522i	−0.463028	−	0.886344i	$-0.653237\pi$
$587$	12.9883	−	22.4963i	0.536083	−	0.928522i	0.999110	−	0.0421784i	$-0.0134298\pi$
$588$		0			0
$589$	−8.40451	−	14.5570i	−0.346302	−	0.599813i
$590$	−26.7788	−	15.4608i	−1.10247	−	0.636509i
$591$	11.7837	−	10.0570i	0.484718	−	0.413690i
$592$	−0.0285900	−	0.0495193i	−0.00117504	−	0.00203523i
$593$	2.85877	+	4.95153i	0.117396	+	0.203335i	0.918735	−	0.394875i	$-0.129212\pi$
$593$	2.85877	+	4.95153i	0.117396	+	0.203335i	−0.801339	+	0.598210i	$0.795879\pi$
$594$	33.6075	+	18.2938i	1.37893	+	0.750604i
$595$		0			0
$596$	−48.2885	−	27.8794i	−1.97797	−	1.14198i
$597$	1.82257	+	9.85326i	0.0745928	+	0.403267i
$598$		−	46.7113i		−	1.91017i
$599$			25.2489i			1.03164i	0.856696	+	0.515822i	$0.172513\pi$
$599$			25.2489i			1.03164i	−0.856696	+	0.515822i	$0.827487\pi$
$600$	12.9259	+	4.58246i	0.527696	+	0.187078i
$601$	−40.2546	−	23.2410i	−1.64202	−	0.948021i	−0.980114	−	0.198435i	$-0.936414\pi$
$601$	−40.2546	−	23.2410i	−1.64202	−	0.948021i	−0.661907	−	0.749586i	$-0.730252\pi$
$602$		0			0
$603$	−0.311220	+	1.95596i	−0.0126739	+	0.0796530i
$604$	1.75116	+	3.03310i	0.0712538	+	0.123415i
$605$	−0.383978	−	0.665069i	−0.0156109	−	0.0270389i
$606$	−26.3457	−	9.34004i	−1.07022	−	0.379413i
$607$	−6.09405	−	3.51840i	−0.247350	−	0.142808i	0.371200	−	0.928553i	$-0.378946\pi$
$607$	−6.09405	−	3.51840i	−0.247350	−	0.142808i	−0.618550	+	0.785745i	$0.712280\pi$
$608$	−13.3000	−	23.0363i	−0.539387	−	0.934246i
$609$		0			0
$610$	5.33009	−	9.23200i	0.215809	−	0.373793i
$611$	18.7125	−	10.8036i	0.757025	−	0.437069i
$612$	8.09127	+	6.56171i	0.327070	+	0.265241i
$613$	−3.27128	+	5.66602i	−0.132126	+	0.228849i	−0.924496	−	0.381192i	$-0.875514\pi$
$613$	−3.27128	+	5.66602i	−0.132126	+	0.228849i	0.792370	+	0.610041i	$0.208847\pi$
$614$	42.9961			1.73518
$615$	−11.9864	−	14.0444i	−0.483339	−	0.566324i
$616$		0			0
$617$	−30.0043	+	17.3230i	−1.20793	+	0.697396i	−0.962306	−	0.271970i	$-0.912325\pi$
$617$	−30.0043	+	17.3230i	−1.20793	+	0.697396i	−0.245620	+	0.969366i	$0.578992\pi$
$618$	6.60464	−	1.22167i	0.265678	−	0.0491428i
$619$	14.7072	−	8.49123i	0.591134	−	0.341291i	−0.174412	−	0.984673i	$-0.555802\pi$
$619$	14.7072	−	8.49123i	0.591134	−	0.341291i	0.765546	+	0.643381i	$0.222469\pi$
$620$	−14.7993	−	8.54439i	−0.594355	−	0.343151i
$621$	20.8219	−	0.523019i	0.835554	−	0.0209880i
$622$		−	18.1071i		−	0.726029i
$623$		0			0
$624$	−1.99837	−	0.708458i	−0.0799986	−	0.0283610i
$625$	0.812855	−	1.40791i	0.0325142	−	0.0563162i
$626$	25.3447			1.01298
$627$	−24.7330	+	4.57489i	−0.987740	+	0.182704i
$628$			31.0524i			1.23913i
$629$	−0.260959			−0.0104051
$630$		0			0
$631$	26.2438			1.04475			0.522374	−	0.852716i	$-0.325047\pi$
$631$	26.2438			1.04475			0.522374	+	0.852716i	$0.325047\pi$
$632$		−	9.84797i		−	0.391731i
$633$	14.9840	−	42.2658i	0.595562	−	1.67992i
$634$	−52.9338			−2.10227
$635$	−4.42354	+	7.66179i	−0.175543	+	0.304049i
$636$	−7.03115	−	38.0121i	−0.278803	−	1.50728i
$637$		0			0
$638$		−	8.74619i		−	0.346265i
$639$	11.3279	+	1.80242i	0.448125	+	0.0713027i
$640$	−22.0674	−	12.7406i	−0.872292	−	0.503618i
$641$	−16.5092	+	9.53157i	−0.652073	+	0.376474i	−0.789250	−	0.614072i	$-0.789530\pi$
$641$	−16.5092	+	9.53157i	−0.652073	+	0.376474i	0.137177	+	0.990547i	$0.456197\pi$
$642$	−6.50276	+	18.3425i	−0.256643	+	0.723921i
$643$	−15.3447	+	8.85928i	−0.605136	+	0.349376i	−0.771060	−	0.636763i	$-0.780273\pi$
$643$	−15.3447	+	8.85928i	−0.605136	+	0.349376i	0.165923	+	0.986139i	$0.446940\pi$
$644$		0			0
$645$	6.34733	−	17.9041i	0.249926	−	0.704973i
$646$	−11.1521			−0.438774
$647$	−10.8951	+	18.8709i	−0.428330	+	0.741890i	−0.996725	−	0.0808661i	$-0.974231\pi$
$647$	−10.8951	+	18.8709i	−0.428330	+	0.741890i	0.568395	+	0.822756i	$0.307565\pi$
$648$	−7.51561	+	23.0192i	−0.295241	+	0.904281i
$649$	−26.5320	+	15.3182i	−1.04147	+	0.601294i
$650$	−17.1467	+	29.6990i	−0.672549	+	1.16489i
$651$		0			0
$652$	−11.4955	−	19.9108i	−0.450198	−	0.779766i
$653$	13.0852	+	7.55475i	0.512064	+	0.295640i	0.733682	−	0.679493i	$-0.237800\pi$
$653$	13.0852	+	7.55475i	0.512064	+	0.295640i	−0.221618	+	0.975134i	$0.571134\pi$
$654$	−5.83643	−	31.5531i	−0.228222	−	1.23383i
$655$	5.92558	+	10.2634i	0.231532	+	0.401024i
$656$	−0.888629	−	1.53915i	−0.0346951	−	0.0600938i
$657$	13.8145	−	17.0347i	0.538954	−	0.664586i
$658$		0			0
$659$	−27.1850	−	15.6952i	−1.05898	−	0.611400i	−0.133827	−	0.991005i	$-0.542727\pi$
$659$	−27.1850	−	15.6952i	−1.05898	−	0.611400i	−0.925149	+	0.379605i	$0.876060\pi$
$660$	−19.4503	+	16.6002i	−0.757104	+	0.646162i
$661$			43.7116i			1.70019i	0.526633	+	0.850093i	$0.323454\pi$
$661$			43.7116i			1.70019i	−0.526633	+	0.850093i	$0.676546\pi$
$662$		−	43.6139i		−	1.69510i
$663$	−7.36019	+	6.28167i	−0.285846	+	0.243960i
$664$	25.4095	+	14.6702i	0.986078	+	0.569312i
$665$		0			0
$666$	−0.584135	−	1.52496i	−0.0226348	−	0.0590912i
$667$	−2.38044	−	4.12304i	−0.0921709	−	0.159645i
$668$	27.5371	+	47.6957i	1.06544	+	1.84540i
$669$	5.63216	+	30.4488i	0.217752	+	1.17722i
$670$	−1.86673	−	1.07776i	−0.0721181	−	0.0416374i
$671$	−5.28096	−	9.14690i	−0.203869	−	0.353112i
$672$		0			0
$673$	−4.60589	+	7.97763i	−0.177544	+	0.307515i	−0.941039	−	0.338299i	$-0.890149\pi$
$673$	−4.60589	+	7.97763i	−0.177544	+	0.307515i	0.763495	+	0.645814i	$0.223482\pi$
$674$	−56.2960	+	32.5025i	−2.16844	+	1.25195i
$675$	−13.4305	−	7.31073i	−0.516940	−	0.281390i
$676$	−21.0104	+	36.3911i	−0.808092	+	1.39966i
$677$	−22.8387			−0.877763			−0.438882	−	0.898545i	$-0.644625\pi$
$677$	−22.8387			−0.877763			−0.438882	+	0.898545i	$0.644625\pi$
$678$	5.16775	−	14.5768i	0.198466	−	0.559819i
$679$		0			0
$680$	−3.64721	+	2.10571i	−0.139864	+	0.0807505i
$681$	6.34733	−	17.9041i	0.243230	−	0.686086i
$682$	−23.8792	+	13.7867i	−0.914383	+	0.527919i
$683$	−29.6030	−	17.0913i	−1.13273	−	0.653981i	−0.188108	−	0.982148i	$-0.560236\pi$
$683$	−29.6030	−	17.0913i	−1.13273	−	0.653981i	−0.944619	+	0.328168i	$0.893569\pi$
$684$	−15.3284	−	40.0170i	−0.586097	−	1.53009i
$685$			14.8421i			0.567088i
$686$		0			0
$687$	6.12408	+	33.1082i	0.233648	+	1.26316i
$688$	0.914230	−	1.58349i	0.0348547	−	0.0603701i
$689$	35.9066			1.36793
$690$	−7.57442	+	21.3654i	−0.288353	+	0.813365i
$691$		−	0.258747i		−	0.00984320i	−0.999988	−	0.00492160i	$-0.998433\pi$
$691$		−	0.258747i		−	0.00984320i	0.999988	−	0.00492160i	$-0.00156660\pi$
$692$	6.22453			0.236621
$693$		0			0
$694$	−6.74720			−0.256120
$695$			25.6026i			0.971163i
$696$	5.44264	−	1.00673i	0.206303	−	0.0381601i
$697$	−8.11109			−0.307229
$698$	30.7389	−	53.2413i	1.16348	−	2.01521i
$699$	4.80005	+	1.70171i	0.181555	+	0.0643645i
$700$		0			0
$701$			5.16189i			0.194962i	0.995237	+	0.0974810i	$0.0310785\pi$
$701$			5.16189i			0.194962i	−0.995237	+	0.0974810i	$0.968921\pi$
$702$	−53.1833	−	28.9497i	−2.00728	−	1.09263i
$703$	0.929636	+	0.536725i	0.0350619	+	0.0202430i
$704$	−36.4487	+	21.0437i	−1.37371	+	0.793113i
$705$	−10.3108	+	1.90720i	−0.388326	+	0.0718292i
$706$	−58.4475	+	33.7447i	−2.19970	+	1.27000i
$707$		0			0
$708$	−33.8840	−	39.7016i	−1.27344	−	1.49208i
$709$	23.4944			0.882351			0.441175	−	0.897421i	$-0.354562\pi$
$709$	23.4944			0.882351			0.441175	+	0.897421i	$0.354562\pi$
$710$	−6.24180	+	10.8111i	−0.234251	+	0.405734i
$711$	−1.72545	+	10.8442i	−0.0647094	+	0.406688i
$712$	−31.9024	+	18.4189i	−1.19559	+	0.690276i
$713$	−7.50460	+	12.9984i	−0.281050	+	0.486792i
$714$		0			0
$715$	−11.8759	−	20.5697i	−0.444134	−	0.769263i
$716$	63.9357	+	36.9133i	2.38939	+	1.37952i
$717$	−20.2180	−	7.16765i	−0.755054	−	0.267681i
$718$	−28.0293	−	48.5481i	−1.04604	−	1.81180i
$719$	−5.07828	−	8.79584i	−0.189388	−	0.328029i	0.755658	−	0.654966i	$-0.227317\pi$
$719$	−5.07828	−	8.79584i	−0.189388	−	0.328029i	−0.945046	+	0.326937i	$0.893984\pi$
$720$	0.799156	+	0.648085i	0.0297828	+	0.0241527i
$721$		0			0
$722$	2.27128	+	1.31132i	0.0845283	+	0.0488024i
$723$	−22.0442	−	7.81508i	−0.819832	−	0.290646i
$724$			32.6925i			1.21501i
$725$			3.49523i			0.129809i
$726$	−0.383978	−	2.07588i	−0.0142507	−	0.0770430i
$727$	5.74874	+	3.31904i	0.213209	+	0.123096i	0.602802	−	0.797891i	$-0.294051\pi$
$727$	5.74874	+	3.31904i	0.213209	+	0.123096i	−0.389593	+	0.920987i	$0.627384\pi$
$728$		0			0
$729$	12.3090	−	24.0310i	0.455890	−	0.890036i
$730$	11.9347	+	20.6716i	0.441725	+	0.765089i
$731$	−4.17238	−	7.22678i	−0.154321	−	0.267292i
$732$	13.6871	−	11.6815i	0.505891	−	0.431761i
$733$	5.20130	+	3.00297i	0.192114	+	0.110917i	0.592972	−	0.805223i	$-0.297954\pi$
$733$	5.20130	+	3.00297i	0.192114	+	0.110917i	−0.400858	+	0.916140i	$0.631288\pi$
$734$	6.38209	+	11.0541i	0.235567	+	0.408014i
$735$		0			0
$736$	−11.8759	+	20.5697i	−0.437752	+	0.758209i
$737$	−1.84953	+	1.06782i	−0.0681281	+	0.0393338i
$738$	−18.1560	−	47.3987i	−0.668332	−	1.74477i
$739$	7.81930	−	13.5434i	0.287638	−	0.498203i	−0.685608	−	0.727971i	$-0.740463\pi$
$739$	7.81930	−	13.5434i	0.287638	−	0.498203i	0.973245	+	0.229768i	$0.0737968\pi$
$740$	1.09132			0.0401176
$741$	39.1396	−	7.23970i	1.43783	−	0.265957i
$742$		0			0
$743$	27.3807	−	15.8083i	1.00450	−	0.579949i	0.0949246	−	0.995484i	$-0.469739\pi$
$743$	27.3807	−	15.8083i	1.00450	−	0.579949i	0.909577	+	0.415535i	$0.136406\pi$
$744$	−11.3279	−	13.2728i	−0.415301	−	0.486605i
$745$	−21.7664	+	12.5669i	−0.797461	+	0.460414i
$746$	7.36032	+	4.24948i	0.269480	+	0.155585i
$747$	−25.4095	−	20.6061i	−0.929683	−	0.753938i
$748$			11.2332i			0.410727i
$749$		0			0
$750$	34.1661	−	29.1596i	1.24757	−	1.06476i
$751$	7.13680	−	12.3613i	0.260426	−	0.451070i	−0.705929	−	0.708282i	$-0.749470\pi$
$751$	7.13680	−	12.3613i	0.260426	−	0.451070i	0.966355	+	0.257212i	$0.0828038\pi$
$752$	−1.00930			−0.0368055
$753$	8.44927	+	9.89994i	0.307908	+	0.360774i
$754$			13.8407i			0.504049i
$755$	1.57870			0.0574548
$756$		0			0
$757$	−10.8227			−0.393358			−0.196679	−	0.980468i	$-0.563016\pi$
$757$	−10.8227			−0.393358			−0.196679	+	0.980468i	$0.563016\pi$
$758$		−	69.2975i		−	2.51700i
$759$	14.5801	+	17.0834i	0.529224	+	0.620088i
$760$	17.3236			0.628395
$761$	−2.93098	+	5.07660i	−0.106248	+	0.184027i	−0.914247	−	0.405157i	$-0.867217\pi$
$761$	−2.93098	+	5.07660i	−0.106248	+	0.184027i	0.808000	+	0.589183i	$0.200550\pi$
$762$	−18.4990	+	15.7882i	−0.670147	+	0.571948i
$763$		0			0
$764$			72.2926i			2.61546i
$765$	4.38508	−	1.67970i	0.158543	−	0.0607297i
$766$	−33.4844	−	19.3323i	−1.20984	−	0.698503i
$767$	41.9865	−	24.2409i	1.51604	−	0.875288i
$768$	−16.2152	−	18.9992i	−0.585115	−	0.685575i
$769$	−27.5683	+	15.9166i	−0.994140	+	0.573967i	−0.906509	−	0.422186i	$-0.861263\pi$
$769$	−27.5683	+	15.9166i	−0.994140	+	0.573967i	−0.0876307	+	0.996153i	$0.527930\pi$
$770$		0			0
$771$	13.2093	−	2.44334i	0.475721	−	0.0879947i
$772$	−53.6856			−1.93219
$773$	9.51908	−	16.4875i	0.342378	−	0.593015i	−0.642496	−	0.766289i	$-0.722101\pi$
$773$	9.51908	−	16.4875i	0.342378	−	0.593015i	0.984874	+	0.173274i	$0.0554345\pi$
$774$	32.8915	−	40.5587i	1.18226	−	1.45785i
$775$	9.54282	−	5.50955i	0.342788	−	0.197909i
$776$	4.18965	−	7.25668i	0.150400	−	0.260500i
$777$		0			0
$778$	−12.3977	−	21.4734i	−0.444478	−	0.769859i
$779$	28.8948	+	16.6824i	1.03526	+	0.597710i
$780$	30.7799	−	26.2696i	1.10210	−	0.940602i
$781$	6.18427	+	10.7115i	0.221290	+	0.383286i
$782$	4.97900	+	8.62388i	0.178049	+	0.308389i
$783$	−6.16959	+	0.154972i	−0.220483	+	0.00553826i
$784$		0			0
$785$	12.1219	+	6.99857i	0.432649	+	0.249790i
$786$	5.92558	+	32.0351i	0.211358	+	1.14265i
$787$			18.9513i			0.675540i	0.941229	+	0.337770i	$0.109673\pi$
$787$			18.9513i			0.675540i	−0.941229	+	0.337770i	$0.890327\pi$
$788$			28.4601i			1.01385i
$789$	22.8330	+	8.09474i	0.812878	+	0.288180i
$790$	−10.3494	−	5.97525i	−0.368216	−	0.212590i
$791$		0			0
$792$	−24.3834	+	9.34004i	−0.866428	+	0.331884i
$793$	8.35705	+	14.4748i	0.296768	+	0.514016i
$794$	25.3857	+	43.9693i	0.900905	+	1.56041i
$795$	−16.4234	−	5.82240i	−0.582478	−	0.206499i
$796$	−15.9422	−	9.20422i	−0.565055	−	0.326235i
$797$	26.7207	+	46.2816i	0.946497	+	1.63938i	0.752727	+	0.658333i	$0.228738\pi$
$797$	26.7207	+	46.2816i	0.946497	+	1.63938i	0.193770	+	0.981047i	$0.437929\pi$
$798$		0			0
$799$	−2.30314	+	3.98916i	−0.0814792	+	0.141126i
$800$	15.1014	−	8.71878i	0.533914	−	0.308256i
$801$	38.3567	−	14.6925i	1.35527	−	0.519133i
$802$	27.4097	−	47.4750i	0.967871	−	1.67640i
$803$	23.6495			0.834571
$804$	−2.36203	−	2.76757i	−0.0833024	−	0.0976048i
$805$		0			0
$806$	37.7885	−	21.8172i	1.33104	−	0.768479i
$807$	43.9962	−	8.13803i	1.54874	−	0.286472i
$808$	16.5190	−	9.53727i	0.581137	−	0.335520i
$809$	2.23517	+	1.29047i	0.0785842	+	0.0453706i	0.538777	−	0.842448i	$-0.318886\pi$
$809$	2.23517	+	1.29047i	0.0785842	+	0.0453706i	−0.460193	+	0.887819i	$0.652220\pi$
$810$	19.6313	+	21.8652i	0.689773	+	0.768265i
$811$		−	6.06938i		−	0.213125i	−0.994306	−	0.106562i	$-0.966016\pi$
$811$		−	6.06938i		−	0.213125i	0.994306	−	0.106562i	$-0.0339844\pi$
$812$		0			0
$813$	27.1871	+	9.63835i	0.953495	+	0.338032i
$814$	0.880438	−	1.52496i	0.0308593	−	0.0534500i
$815$	−10.3634			−0.363013
$816$	0.444455	−	0.0822114i	0.0155590	−	0.00287798i
$817$			34.3261i			1.20092i
$818$	−59.9811			−2.09719
$819$		0			0
$820$	33.9201			1.18454
$821$		−	9.28308i		−	0.323982i	−0.986792	−	0.161991i	$-0.948208\pi$
$821$		−	9.28308i		−	0.323982i	0.986792	−	0.161991i	$-0.0517915\pi$
$822$	−13.6332	+	38.4555i	−0.475512	+	1.34129i
$823$	18.0690			0.629844			0.314922	−	0.949117i	$-0.398022\pi$
$823$	18.0690			0.629844			0.314922	+	0.949117i	$0.398022\pi$
$824$	−2.29172	+	3.96937i	−0.0798357	+	0.138280i
$825$	−2.99905	−	16.2136i	−0.104414	−	0.564486i
$826$		0			0
$827$		−	48.5440i		−	1.68804i	−0.536310	−	0.844021i	$-0.680182\pi$
$827$		−	48.5440i		−	1.68804i	0.536310	−	0.844021i	$-0.319818\pi$
$828$	−24.1014	+	29.7195i	−0.837581	+	1.03282i
$829$	−4.71804	−	2.72396i	−0.163864	−	0.0946071i	0.415825	−	0.909445i	$-0.363493\pi$
$829$	−4.71804	−	2.72396i	−0.163864	−	0.0946071i	−0.579689	+	0.814837i	$0.696826\pi$
$830$	30.8344	−	17.8022i	1.07028	−	0.617924i
$831$	18.1779	−	51.2747i	0.630583	−	1.77870i
$832$	57.6796	−	33.3013i	1.99968	−	1.15452i
$833$		0			0
$834$	−23.5172	+	66.3357i	−0.814335	+	2.29702i
$835$	24.8252			0.859111
$836$	23.1038	−	40.0170i	0.799062	−	1.38402i
$837$	10.1483	+	16.6002i	0.350776	+	0.573787i
$838$	63.7793	−	36.8230i	2.20322	−	1.27203i
$839$	24.2673	−	42.0322i	0.837801	−	1.45111i	−0.0539281	−	0.998545i	$-0.517174\pi$
$839$	24.2673	−	42.0322i	0.837801	−	1.45111i	0.891729	−	0.452569i	$-0.149492\pi$
$840$		0			0
$841$	−13.7947	−	23.8931i	−0.475678	−	0.823899i
$842$	−21.8727	−	12.6282i	−0.753781	−	0.435196i
$843$	2.94824	+	15.9389i	0.101543	+	0.548965i
$844$	41.1907	+	71.3444i	1.41784	+	2.45578i
$845$	9.47061	+	16.4036i	0.325799	+	0.564300i
$846$	−28.4668	−	4.52945i	−0.978708	−	0.155726i
$847$		0			0
$848$	−1.45254	−	0.838622i	−0.0498803	−	0.0287984i
$849$	20.7810	−	17.7359i	0.713202	−	0.608694i
$850$		−	7.31073i		−	0.250756i
$851$		−	0.958511i		−	0.0328573i
$852$	−16.0283	+	13.6796i	−0.549121	+	0.468656i
$853$	10.7703	+	6.21823i	0.368768	+	0.212908i	0.672920	−	0.739715i	$-0.265040\pi$
$853$	10.7703	+	6.21823i	0.368768	+	0.212908i	−0.304152	+	0.952623i	$0.598373\pi$
$854$		0			0
$855$	−19.0761	−	3.03526i	−0.652387	−	0.103804i
$856$	−6.64007	−	11.5009i	−0.226953	−	0.393094i
$857$	−5.29077	−	9.16388i	−0.180729	−	0.313032i	0.761400	−	0.648283i	$-0.224512\pi$
$857$	−5.29077	−	9.16388i	−0.180729	−	0.313032i	−0.942129	+	0.335250i	$0.891179\pi$
$858$	−11.8759	−	64.2041i	−0.405437	−	2.19189i
$859$	−28.1452	−	16.2496i	−0.960302	−	0.554431i	−0.0640360	−	0.997948i	$-0.520397\pi$
$859$	−28.1452	−	16.2496i	−0.960302	−	0.554431i	−0.896266	+	0.443517i	$0.853731\pi$
$860$	17.4487	+	30.2220i	0.594995	+	1.03056i
$861$		0			0
$862$	−18.5579	+	32.1432i	−0.632084	+	1.09480i
$863$	−21.8414	+	12.6102i	−0.743491	+	0.429255i	−0.823337	−	0.567552i	$-0.807890\pi$
$863$	−21.8414	+	12.6102i	−0.743491	+	0.429255i	0.0798460	+	0.996807i	$0.474557\pi$
$864$	16.0595	+	26.2696i	0.546356	+	0.893710i
$865$	1.40288	−	2.42986i	0.0476994	−	0.0826177i
$866$	−28.5366			−0.969715
$867$	−9.14949	+	25.8082i	−0.310733	+	0.876492i
$868$		0			0
$869$	−10.2540	+	5.92017i	−0.347844	+	0.200828i
$870$	2.24433	−	6.33063i	0.0760897	−	0.214628i
$871$	2.92685	−	1.68982i	0.0991724	−	0.0572572i
$872$	18.9633	+	10.9485i	0.642179	+	0.370762i
$873$	−5.88489	+	7.25668i	−0.199174	+	0.245602i
$874$		−	40.9621i		−	1.38556i
$875$		0			0
$876$	7.32846	+	39.6194i	0.247606	+	1.33862i
$877$	7.47893	−	12.9539i	0.252546	−	0.437422i	−0.711680	−	0.702503i	$-0.752066\pi$
$877$	7.47893	−	12.9539i	0.252546	−	0.437422i	0.964226	+	0.265082i	$0.0853989\pi$
$878$	−42.3921			−1.43067
$879$	−14.3862	+	40.5795i	−0.485234	+	1.36871i
$880$			1.10948i			0.0374005i
$881$	36.4482			1.22797			0.613985	−	0.789318i	$-0.289566\pi$
$881$	36.4482			1.22797			0.613985	+	0.789318i	$0.289566\pi$
$882$		0			0
$883$	15.9831			0.537873			0.268936	−	0.963158i	$-0.413328\pi$
$883$	15.9831			0.537873			0.268936	+	0.963158i	$0.413328\pi$
$884$		−	17.7764i		−	0.597884i
$885$	−23.1350	+	4.27931i	−0.777675	+	0.143848i
$886$	10.8148			0.363330
$887$	−24.5208	+	42.4713i	−0.823329	+	1.42605i	0.0798613	+	0.996806i	$0.474552\pi$
$887$	−24.5208	+	42.4713i	−0.823329	+	1.42605i	−0.903190	+	0.429241i	$0.858781\pi$
$888$	1.05031	+	0.372354i	0.0352461	+	0.0124954i
$889$		0			0
$890$			44.7026i			1.49843i
$891$	28.4865	−	6.01266i	0.954332	−	0.201432i
$892$	−49.2649	−	28.4431i	−1.64951	−	0.952346i
$893$	16.4093	−	9.47393i	0.549117	−	0.317033i
$894$	−67.9395	+	12.5669i	−2.27224	+	0.420299i
$895$	28.8196	−	16.6390i	0.963332	−	0.556180i
$896$		0			0
$897$	−23.0728	−	27.0342i	−0.770378	−	0.902646i
$898$	36.9669			1.23360
$899$	2.22364	−	3.85145i	0.0741625	−	0.128453i
$900$	26.2330	−	10.0485i	0.874433	−	0.334950i
$901$	−6.62911	+	3.82732i	−0.220848	+	0.127506i
$902$	27.3657	−	47.3987i	0.911177	−	1.57820i
$903$		0			0
$904$	5.27687	+	9.13981i	0.175506	+	0.303986i
$905$	12.7621	+	7.36821i	0.424227	+	0.244928i
$906$	4.09037	+	1.45011i	0.135893	+	0.0481768i
$907$	2.42915	+	4.20741i	0.0806585	+	0.139705i	0.903533	−	0.428519i	$-0.140964\pi$
$907$	2.42915	+	4.20741i	0.0806585	+	0.139705i	−0.822874	+	0.568223i	$0.807631\pi$
$908$	17.4487	+	30.2220i	0.579054	+	1.00295i
$909$	−19.8611	+	7.60775i	−0.658750	+	0.252333i
$910$		0			0
$911$	14.4945	+	8.36843i	0.480226	+	0.277258i	0.720510	−	0.693444i	$-0.243908\pi$
$911$	14.4945	+	8.36843i	0.480226	+	0.277258i	−0.240285	+	0.970702i	$0.577241\pi$
$912$	−1.75241	−	0.621261i	−0.0580279	−	0.0205720i
$913$		−	35.2763i		−	1.16747i
$914$		−	13.0829i		−	0.432743i
$915$	−1.47529	−	7.97579i	−0.0487717	−	0.263672i
$916$	−53.5678	−	30.9274i	−1.76993	−	1.02187i
$917$		0			0
$918$	12.9045	−	0.324145i	0.425912	−	0.0106984i
$919$	−15.3200	−	26.5350i	−0.505360	−	0.875309i	−0.999981	−	0.00620006i	$-0.998026\pi$
$919$	−15.3200	−	26.5350i	−0.505360	−	0.875309i	0.494621	−	0.869109i	$-0.335307\pi$
$920$	−7.73436	−	13.3963i	−0.254994	−	0.441663i
$921$	24.8840	−	21.2377i	0.819956	−	0.699804i
$922$	71.5015	+	41.2814i	2.35478	+	1.35953i
$923$	−9.78651	−	16.9507i	−0.322127	−	0.557940i
$924$		0			0
$925$	−0.351848	+	0.609419i	−0.0115687	+	0.0200376i
$926$	−57.6450	+	33.2814i	−1.89433	+	1.09369i
$927$	3.21901	−	3.96937i	0.105726	−	0.130371i
$928$	3.51887	−	6.09487i	0.115513	−	0.200074i
$929$	29.7445			0.975885			0.487943	−	0.872876i	$-0.337747\pi$
$929$	29.7445			0.975885			0.487943	+	0.872876i	$0.337747\pi$
$930$	−20.8219	+	3.85145i	−0.682777	+	0.126294i
$931$		0			0
$932$	−8.10245	+	4.67795i	−0.265405	+	0.153231i
$933$	−8.94390	−	10.4795i	−0.292810	−	0.343083i
$934$	5.20876	−	3.00728i	0.170436	−	0.0984011i
$935$	4.38508	+	2.53173i	0.143408	+	0.0827964i
$936$	38.5865	−	14.7805i	1.26124	−	0.483115i
$937$		−	4.03712i		−	0.131887i	−0.997823	−	0.0659434i	$-0.978994\pi$
$937$		−	4.03712i		−	0.131887i	0.997823	−	0.0659434i	$-0.0210057\pi$
$938$		0			0
$939$	14.6683	−	12.5189i	0.478681	−	0.408538i
$940$	9.63160	−	16.6824i	0.314148	−	0.544121i
$941$	14.4053			0.469599			0.234799	−	0.972044i	$-0.424557\pi$
$941$	14.4053			0.469599			0.234799	+	0.972044i	$0.424557\pi$
$942$	24.9789	+	29.2676i	0.813858	+	0.953591i
$943$		−	29.7923i		−	0.970171i
$944$	−2.26464			−0.0737079
$945$		0			0
$946$	56.3081			1.83073
$947$		−	31.2155i		−	1.01437i	−0.861838	−	0.507183i	$-0.830687\pi$
$947$		−	31.2155i		−	1.01437i	0.861838	−	0.507183i	$-0.169313\pi$
$948$	−13.0954	−	15.3438i	−0.425320	−	0.498345i
$949$	−37.4249			−1.21486
$950$	−15.0363	+	26.0436i	−0.487841	+	0.844966i
$951$	−30.6355	+	26.1463i	−0.993423	+	0.847853i
$952$		0			0
$953$			8.55869i			0.277243i	0.990345	+	0.138622i	$0.0442672\pi$
$953$			8.55869i			0.277243i	−0.990345	+	0.138622i	$0.955733\pi$
$954$	−37.2044	−	30.1713i	−1.20454	−	0.976833i
$955$	28.2207	+	16.2933i	0.913202	+	0.527237i
$956$	34.1278	−	19.7037i	1.10377	−	0.637263i
$957$	−4.32013	−	5.06186i	−0.139650	−	0.163627i
$958$	61.2751	−	35.3772i	1.97971	−	1.14298i
$959$		0			0
$960$	−31.7821	+	5.87877i	−1.02576	+	0.189737i
$961$	16.9795			0.547724
$962$	−1.39328	+	2.41323i	−0.0449212	+	0.0778058i
$963$	5.29669	+	13.8277i	0.170684	+	0.445593i
$964$	37.2104	−	21.4835i	1.19847	−	0.691936i
$965$	−12.0996	+	20.9572i	−0.389501	+	0.674635i
$966$		0			0
$967$	16.0280	+	27.7614i	0.515427	+	0.892745i	0.999840	+	0.0179059i	$0.00569994\pi$
$967$	16.0280	+	27.7614i	0.515427	+	0.892745i	−0.484413	+	0.874840i	$0.660967\pi$
$968$	1.24759	+	0.720299i	0.0400992	+	0.0231513i
$969$	−6.45429	+	5.50852i	−0.207342	+	0.176959i
$970$	−5.08414	−	8.80598i	−0.163242	−	0.282743i
$971$	16.6183	+	28.7838i	0.533307	+	0.923715i	0.999243	+	0.0388964i	$0.0123842\pi$
$971$	16.6183	+	28.7838i	0.533307	+	0.923715i	−0.465936	+	0.884818i	$0.654282\pi$
$972$	18.9002	+	45.8596i	0.606225	+	1.47095i
$973$		0			0
$974$	−68.7469	−	39.6911i	−2.20279	−	1.27178i
$975$	4.74596	+	25.6578i	0.151992	+	0.821708i
$976$		−	0.780736i		−	0.0249908i
$977$			52.1414i			1.66815i	0.551649	+	0.834076i	$0.313999\pi$
$977$			52.1414i			1.66815i	−0.551649	+	0.834076i	$0.686001\pi$
$978$	−26.8512	−	9.51925i	−0.858607	−	0.304392i
$979$	38.3567	+	22.1453i	1.22589	+	0.707765i
$980$		0			0
$981$	−18.9633	−	15.3785i	−0.605453	−	0.490999i
$982$	−29.8022	−	51.6189i	−0.951026	−	1.64723i
$983$	12.1192	+	20.9911i	0.386544	+	0.669513i	0.991982	−	0.126379i	$-0.0403356\pi$
$983$	12.1192	+	20.9911i	0.386544	+	0.669513i	−0.605438	+	0.795892i	$0.707002\pi$
$984$	32.6456	+	11.5735i	1.04070	+	0.368949i
$985$	11.1099	+	6.41432i	0.353992	+	0.204377i
$986$	−1.47529	−	2.55528i	−0.0469829	−	0.0813768i
$987$		0			0
$988$	−36.5614	+	63.3263i	−1.16317	+	2.01468i
$989$	26.5442	−	15.3253i	0.844056	−	0.487316i
$990$	−4.97900	+	31.2921i	−0.158243	+	0.994530i
$991$	12.0991	−	20.9562i	0.384339	−	0.665695i	−0.607338	−	0.794443i	$-0.707763\pi$
$991$	12.0991	−	20.9562i	0.384339	−	0.665695i	0.991677	+	0.128749i	$0.0410960\pi$
$992$	−22.1873			−0.704448
$993$	−21.5428	−	25.2416i	−0.683641	−	0.801017i
$994$		0			0
$995$	−7.18607	+	4.14888i	−0.227814	+	0.131528i
$996$	59.0976	−	10.9314i	1.87258	−	0.346373i
$997$	8.81920	−	5.09177i	0.279307	−	0.161258i	−0.353803	−	0.935320i	$-0.615112\pi$
$997$	8.81920	−	5.09177i	0.279307	−	0.161258i	0.633110	+	0.774062i	$0.281778\pi$
$998$	−24.5997	−	14.2027i	−0.778691	−	0.449578i
$999$	−1.09132	−	0.594044i	−0.0345277	−	0.0187947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.i.c.227.6		12
3.2	odd	2		1323.2.i.c.521.2		12
7.2	even	3		441.2.s.c.362.5		12
7.3	odd	6		63.2.o.a.20.1	✓	12
7.4	even	3		63.2.o.a.20.2	yes	12
7.5	odd	6		441.2.s.c.362.6		12
7.6	odd	2	inner	441.2.i.c.227.5		12
9.4	even	3		1323.2.s.c.962.2		12
9.5	odd	6		441.2.s.c.374.6		12
21.2	odd	6		1323.2.s.c.656.1		12
21.5	even	6		1323.2.s.c.656.2		12
21.11	odd	6		189.2.o.a.62.6		12
21.17	even	6		189.2.o.a.62.5		12
21.20	even	2		1323.2.i.c.521.1		12
28.3	even	6		1008.2.cc.a.209.5		12
28.11	odd	6		1008.2.cc.a.209.2		12
63.4	even	3		189.2.o.a.125.5		12
63.5	even	6	inner	441.2.i.c.68.2		12
63.11	odd	6		567.2.c.c.566.1		12
63.13	odd	6		1323.2.s.c.962.1		12
63.23	odd	6	inner	441.2.i.c.68.1		12
63.25	even	3		567.2.c.c.566.12		12
63.31	odd	6		189.2.o.a.125.6		12
63.32	odd	6		63.2.o.a.41.1	yes	12
63.38	even	6		567.2.c.c.566.2		12
63.40	odd	6		1323.2.i.c.1097.6		12
63.41	even	6		441.2.s.c.374.5		12
63.52	odd	6		567.2.c.c.566.11		12
63.58	even	3		1323.2.i.c.1097.5		12
63.59	even	6		63.2.o.a.41.2	yes	12
84.11	even	6		3024.2.cc.a.2897.4		12
84.59	odd	6		3024.2.cc.a.2897.3		12
252.31	even	6		3024.2.cc.a.881.4		12
252.59	odd	6		1008.2.cc.a.545.2		12
252.67	odd	6		3024.2.cc.a.881.3		12
252.95	even	6		1008.2.cc.a.545.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.1	✓	12	7.3	odd	6
63.2.o.a.20.2	yes	12	7.4	even	3
63.2.o.a.41.1	yes	12	63.32	odd	6
63.2.o.a.41.2	yes	12	63.59	even	6
189.2.o.a.62.5		12	21.17	even	6
189.2.o.a.62.6		12	21.11	odd	6
189.2.o.a.125.5		12	63.4	even	3
189.2.o.a.125.6		12	63.31	odd	6
441.2.i.c.68.1		12	63.23	odd	6	inner
441.2.i.c.68.2		12	63.5	even	6	inner
441.2.i.c.227.5		12	7.6	odd	2	inner
441.2.i.c.227.6		12	1.1	even	1	trivial
441.2.s.c.362.5		12	7.2	even	3
441.2.s.c.362.6		12	7.5	odd	6
441.2.s.c.374.5		12	63.41	even	6
441.2.s.c.374.6		12	9.5	odd	6
567.2.c.c.566.1		12	63.11	odd	6
567.2.c.c.566.2		12	63.38	even	6
567.2.c.c.566.11		12	63.52	odd	6
567.2.c.c.566.12		12	63.25	even	3
1008.2.cc.a.209.2		12	28.11	odd	6
1008.2.cc.a.209.5		12	28.3	even	6
1008.2.cc.a.545.2		12	252.59	odd	6
1008.2.cc.a.545.5		12	252.95	even	6
1323.2.i.c.521.1		12	21.20	even	2
1323.2.i.c.521.2		12	3.2	odd	2
1323.2.i.c.1097.5		12	63.58	even	3
1323.2.i.c.1097.6		12	63.40	odd	6
1323.2.s.c.656.1		12	21.2	odd	6
1323.2.s.c.656.2		12	21.5	even	6
1323.2.s.c.962.1		12	63.13	odd	6
1323.2.s.c.962.2		12	9.4	even	3
3024.2.cc.a.881.3		12	252.67	odd	6
3024.2.cc.a.881.4		12	252.31	even	6
3024.2.cc.a.2897.3		12	84.59	odd	6
3024.2.cc.a.2897.4		12	84.11	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.27639i q^{2} +(1.12441 + 1.31746i) q^{3} -3.18194 q^{4} +(-0.717144 + 1.24213i) q^{5} +(-2.99905 + 2.55959i) q^{6} -2.69056i q^{8} +(-0.471410 + 2.96273i) q^{9} +(-2.82757 - 1.63250i) q^{10} +(-2.80150 + 1.61745i) q^{11} +(-3.57780 - 4.19209i) q^{12} +(4.43334 - 2.55959i) q^{13} +(-2.44282 + 0.451852i) q^{15} -0.239123 q^{16} +(-0.545658 + 0.945107i) q^{17} +(-6.74433 - 1.07311i) q^{18} +(3.88768 - 2.24456i) q^{19} +(2.28191 - 3.95238i) q^{20} +(-3.68194 - 6.37731i) q^{22} +(-3.47141 - 2.00422i) q^{23} +(3.54471 - 3.02529i) q^{24} +(1.47141 + 2.54856i) q^{25} +(5.82662 + 10.0920i) q^{26} +(-4.43334 + 2.71026i) q^{27} +(1.02859 + 0.593857i) q^{29} +(-1.02859 - 5.56081i) q^{30} -3.74440i q^{31} -5.92546i q^{32} +(-5.28096 - 1.87220i) q^{33} +(-2.15143 - 1.24213i) q^{34} +(1.50000 - 9.42724i) q^{36} +(0.119562 + 0.207087i) q^{37} +(5.10948 + 8.84988i) q^{38} +(8.35705 + 2.96273i) q^{39} +(3.34203 + 1.92952i) q^{40} +(3.71620 + 6.43664i) q^{41} +(-3.82326 + 6.62208i) q^{43} +(8.91423 - 5.14663i) q^{44} +(-3.34203 - 2.71026i) q^{45} +(4.56238 - 7.90228i) q^{46} +4.22085 q^{47} +(-0.268872 - 0.315036i) q^{48} +(-5.80150 + 3.34950i) q^{50} +(-1.85868 + 0.343803i) q^{51} +(-14.1066 + 8.14447i) q^{52} +(6.07442 + 3.50707i) q^{53} +(-6.16959 - 10.0920i) q^{54} -4.63977i q^{55} +(7.32846 + 2.59808i) q^{57} +(-1.35185 + 2.34147i) q^{58} +9.47061 q^{59} +(7.77292 - 1.43777i) q^{60} +3.26499i q^{61} +8.52371 q^{62} +13.0104 q^{64} +7.34238i q^{65} +(4.26186 - 12.0215i) q^{66} +0.660190 q^{67} +(1.73625 - 3.00728i) q^{68} +(-1.26280 - 6.82701i) q^{69} -3.82347i q^{71} +(7.97141 + 1.26836i) q^{72} +(-6.33127 - 3.65536i) q^{73} +(-0.471410 + 0.272169i) q^{74} +(-1.70316 + 4.80415i) q^{75} +(-12.3704 + 7.14205i) q^{76} +(-6.74433 + 19.0239i) q^{78} +3.66019 q^{79} +(0.171486 - 0.297022i) q^{80} +(-8.55555 - 2.79332i) q^{81} +(-14.6523 + 8.45951i) q^{82} +(-5.45245 + 9.44392i) q^{83} +(-0.782630 - 1.35556i) q^{85} +(-15.0744 - 8.70322i) q^{86} +(0.374172 + 2.02287i) q^{87} +(4.35185 + 7.53762i) q^{88} +(-6.84573 - 11.8572i) q^{89} +(6.16959 - 7.60775i) q^{90} +(11.0458 + 6.37731i) q^{92} +(4.93310 - 4.21024i) q^{93} +9.60829i q^{94} +6.43867i q^{95} +(7.80657 - 6.66264i) q^{96} +(2.69709 + 1.55716i) q^{97} +(-3.47141 - 9.06259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4} + 12 q^{9} + 6 q^{15} - 4 q^{16} - 12 q^{18} - 10 q^{22} - 24 q^{23} + 30 q^{29} - 30 q^{30} + 18 q^{36} + 2 q^{37} + 12 q^{39} - 10 q^{43} + 54 q^{44} + 20 q^{46} - 36 q^{50} - 24 q^{51}+ \cdots - 24 q^{99}+O(q^{100}) \) 12 * q - 4 * q^4 + 12 * q^9 + 6 * q^15 - 4 * q^16 - 12 * q^18 - 10 * q^22 - 24 * q^23 + 30 * q^29 - 30 * q^30 + 18 * q^36 + 2 * q^37 + 12 * q^39 - 10 * q^43 + 54 * q^44 + 20 * q^46 - 36 * q^50 - 24 * q^51 - 12 * q^53 - 18 * q^57 + 2 * q^58 + 42 * q^60 + 16 * q^64 - 24 * q^67 + 78 * q^72 + 12 * q^74 - 12 * q^78 + 12 * q^79 - 48 * q^81 - 6 * q^85 - 96 * q^86 + 34 * q^88 + 30 * q^92 - 24 * q^93 - 24 * q^99

Introduction

L-functions

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