LMFDB - Embedded newform 441.2.i.c.227.5

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			227.5
Root			$-1.29589 - 0.748185i$ of defining polynomial
Character	$\chi$	$=$	441.227
Dual form			441.2.i.c.68.1

$q$-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	−0.659920	−	0.751336i	$-0.729410\pi$
$5$	0.717144	−	1.24213i	0.320716	−	0.555497i	0.980636	+	0.195839i	$0.0627430\pi$
$6$	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	−0.966944	−	0.254990i	$-0.917928\pi$
$13$	−4.43334	+	2.55959i	−1.22959	+	0.709903i	−0.262644	+	0.964893i	$0.584594\pi$
$14$		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	−0.792237	−	0.610213i	$-0.791084\pi$
$17$	0.545658	−	0.945107i	0.132341	−	0.229222i	0.924579	+	0.380991i	$0.124417\pi$
$18$	−6.74433	−	1.07311i	−1.58965	−	0.252935i
$19$	−3.88768	+	2.24456i	−0.891896	+	0.514936i	−0.874562	−	0.484914i	$-0.838851\pi$
$19$	−3.88768	+	2.24456i	−0.891896	+	0.514936i	−0.0173336	+	0.999850i	$0.505518\pi$
$20$	−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	$0.109161\pi$
$31$			3.74440i			0.672514i	−0.941770	+	0.336257i	$0.890839\pi$
$32$		−	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	$-0.969574\pi$
$41$	−3.71620	−	6.43664i	−0.580373	−	1.00523i	0.415062	−	0.909793i	$-0.363760\pi$
$42$		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	$-0.599605\pi$
$47$	−4.22085			−0.615674			−0.307837	+	0.951439i	$0.599605\pi$
$48$	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	$-0.711444\pi$
$59$	−9.47061			−1.23297			−0.616484	+	0.787367i	$0.711444\pi$
$60$	7.77292	−	1.43777i	1.00348	−	0.185615i
$61$		−	3.26499i		−	0.418040i	−0.977911	−	0.209020i	$-0.932973\pi$
$61$		−	3.26499i		−	0.418040i	0.977911	−	0.209020i	$-0.0670273\pi$
$62$	−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	0.822440	−	0.568852i	$-0.192612\pi$
$73$	6.33127	+	3.65536i	0.741020	+	0.427828i	−0.0814203	+	0.996680i	$0.525946\pi$
$74$	−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	$-0.629103\pi$
$83$	5.45245	−	9.44392i	0.598484	−	1.03660i	0.993045	−	0.117735i	$-0.0375634\pi$
$84$		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	$0.0917923\pi$
$89$	6.84573	+	11.8572i	0.725646	+	1.25686i	−0.233061	+	0.972462i	$0.574874\pi$
$90$	−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	0.356787	−	0.934186i	$-0.383872\pi$
$97$	−2.69709	−	1.55716i	−0.273848	−	0.158106i	−0.630635	+	0.776080i	$0.717205\pi$
$98$		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	0.634012	−	0.773324i	$-0.281407\pi$
$101$	−3.54471	−	6.13962i	−0.352712	−	0.610915i	−0.986724	+	0.162408i	$0.948074\pi$
$102$	−0.782630	−	4.23109i	−0.0774919	−	0.418940i
$103$	1.47529	+	0.851761i	0.145365	+	0.0839265i	0.570918	−	0.821007i	$-0.306587\pi$
$103$	1.47529	+	0.851761i	0.145365	+	0.0839265i	−0.425553	+	0.904933i	$0.639921\pi$
$104$	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	−0.988119	−	0.153690i	$-0.950884\pi$
$131$	−4.13138	+	7.15575i	−0.360960	+	0.625201i	0.627159	+	0.778891i	$0.284218\pi$
$132$	−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	−0.982296	−	0.187334i	$-0.940015\pi$
$139$	−15.4589	+	8.92521i	−1.31121	+	0.757026i	−0.328912	+	0.944361i	$0.606682\pi$
$140$		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	$0.127326\pi$
$157$			9.75896i			0.778850i	−0.921058	+	0.389425i	$0.872674\pi$
$158$			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	$0.0669027\pi$
$167$	8.65419	+	14.9895i	0.669681	+	1.15992i	−0.308312	+	0.951285i	$0.599764\pi$
$168$		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	$-0.476307\pi$
$173$	1.95621			0.148728			0.0743638	+	0.997231i	$0.476307\pi$
$174$	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	$0.124711\pi$
$181$			10.2744i			0.763689i	−0.924226	+	0.381845i	$0.875289\pi$
$182$		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	0.311794	−	0.950150i	$-0.399070\pi$
$199$	−5.01020	−	2.89264i	−0.355164	−	0.205054i	−0.666957	+	0.745096i	$0.732404\pi$
$200$	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	−0.117871	−	0.993029i	$-0.537607\pi$
$223$	−15.4827	−	8.93892i	−1.03680	−	0.598594i	−0.918924	+	0.394435i	$0.870940\pi$
$224$		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	0.988609	−	0.150506i	$-0.0480902\pi$
$227$	5.48365	+	9.49796i	0.363963	+	0.630402i	−0.624646	+	0.780908i	$0.714757\pi$
$228$	−23.3187	−	8.26693i	−1.54432	−	0.547491i
$229$	−16.8349	−	9.71965i	−1.11248	−	0.642293i	−0.173012	−	0.984920i	$-0.555350\pi$
$229$	−16.8349	−	9.71965i	−1.11248	−	0.642293i	−0.939471	+	0.342627i	$0.888683\pi$
$230$	−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	−0.0735896	−	0.997289i	$-0.523445\pi$
$241$	11.6943	−	6.75168i	0.753293	−	0.434914i	0.826882	+	0.562375i	$0.190112\pi$
$242$	−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	$-0.576214\pi$
$251$	−7.51441			−0.474305			−0.237153	+	0.971472i	$0.576214\pi$
$252$		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	−0.961254	−	0.275664i	$-0.911102\pi$
$257$	−3.87788	+	6.71668i	−0.241895	+	0.418975i	0.719359	+	0.694639i	$0.244436\pi$
$258$	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	$0.455294\pi$
$269$	−12.9160	+	22.3712i	−0.787505	+	1.36400i	−0.927491	+	0.373846i	$0.878039\pi$
$270$	16.9601	−	0.426015i	1.03216	−	0.0259264i
$271$	−14.4225	+	8.32686i	−0.876107	+	0.505821i	−0.869373	−	0.494157i	$-0.835477\pi$
$271$	−14.4225	+	8.32686i	−0.876107	+	0.505821i	−0.00673411	+	0.999977i	$0.502144\pi$
$272$	−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	$0.155320\pi$
$283$			15.7735i			0.937638i	−0.883294	+	0.468819i	$0.844680\pi$
$284$			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	$-0.908002\pi$
$293$	−12.4287	−	21.5271i	−0.726090	−	1.25762i	0.232434	−	0.972612i	$-0.425331\pi$
$294$		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	$0.181195\pi$
$307$			18.8878i			1.07799i	−0.842310	+	0.538993i	$0.818805\pi$
$308$		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	$-0.427591\pi$
$311$	7.95431			0.451048			0.225524	+	0.974238i	$0.427591\pi$
$312$	7.97141	−	22.4852i	0.451292	−	1.27297i
$313$			11.1337i			0.629316i	0.949205	+	0.314658i	$0.101890\pi$
$313$			11.1337i			0.629316i	−0.949205	+	0.314658i	$0.898110\pi$
$314$	−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	0.971498	−	0.237048i	$-0.0761797\pi$
$349$	23.3885	+	13.5034i	1.25196	+	0.722818i	0.280460	+	0.959866i	$0.409513\pi$
$350$		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	$-0.877271\pi$
$353$	−14.8238	−	25.6755i	−0.788990	−	1.36657i	0.137596	−	0.990488i	$-0.456063\pi$
$354$	−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	−0.621357	−	0.783528i	$-0.713418\pi$
$367$	−4.85598	+	2.80360i	−0.253480	+	0.146347i	0.367877	+	0.929875i	$0.380085\pi$
$368$	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	−0.563262	−	0.826278i	$-0.690454\pi$
$383$	8.49251	−	14.7095i	0.433947	−	0.751618i	0.997209	+	0.0746601i	$0.0237872\pi$
$384$	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	−0.899057	−	0.437832i	$-0.855747\pi$
$397$	−19.3154	+	11.1518i	−0.969412	+	0.559690i	−0.0703551	+	0.997522i	$0.522413\pi$
$398$	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	$-0.774164\pi$
$409$		−	26.3492i		−	1.30289i	0.758698	−	0.651443i	$-0.225836\pi$
$410$		−	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	$0.123384\pi$
$419$	16.1761	+	28.0178i	0.790252	+	1.36876i	−0.135558	+	0.990769i	$0.543283\pi$
$420$		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	$-0.902606\pi$
$433$		−	12.5359i		−	0.602438i	0.953555	−	0.301219i	$-0.0973936\pi$
$434$		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	$-0.853416\pi$
$439$		−	18.6225i		−	0.888805i	0.895827	−	0.444403i	$-0.146584\pi$
$440$	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	$0.486836\pi$
$461$	−18.1346	+	31.4101i	−0.844613	+	1.46291i	−0.885957	+	0.463768i	$0.846497\pi$
$462$		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	0.894972	−	0.446123i	$-0.147196\pi$
$467$	1.32107	+	2.28817i	0.0611320	+	0.105884i	−0.833840	+	0.552007i	$0.813862\pi$
$468$	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	$0.0846760\pi$
$479$	15.5409	+	26.9177i	0.710083	+	1.22990i	−0.254742	+	0.967009i	$0.581991\pi$
$480$	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	$-0.180327\pi$
$503$	37.8479			1.68756			0.843778	+	0.536693i	$0.180327\pi$
$504$		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	$0.453593\pi$
$509$	−17.6924	+	30.6441i	−0.784200	+	1.35827i	−0.929476	+	0.368883i	$0.879740\pi$
$510$	−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	−0.890304	−	0.455366i	$-0.849509\pi$
$521$	−1.15939	+	2.00813i	−0.0507940	+	0.0879777i	0.839511	+	0.543343i	$0.182842\pi$
$522$	−6.29987	−	5.10896i	−0.275738	−	0.223613i
$523$	17.4799	−	10.0920i	0.764341	−	0.441293i	−0.0665110	−	0.997786i	$-0.521187\pi$
$523$	17.4799	−	10.0920i	0.764341	−	0.441293i	0.830852	+	0.556493i	$0.187853\pi$
$524$	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	$-0.304497\pi$
$563$	27.3484			1.15260			0.576299	+	0.817239i	$0.304497\pi$
$564$	−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	0.459185	−	0.888340i	$-0.348141\pi$
$577$	−1.93481	−	1.11706i	−0.0805472	−	0.0465039i	−0.539733	+	0.841836i	$0.681475\pi$
$578$	−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	$0.346763\pi$
$587$	−12.9883	+	22.4963i	−0.536083	+	0.928522i	−0.999110	+	0.0421784i	$0.986570\pi$
$588$		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	0.801339	−	0.598210i	$-0.204121\pi$
$593$	−2.85877	−	4.95153i	−0.117396	−	0.203335i	−0.918735	+	0.394875i	$0.870788\pi$
$594$	−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	$0.0635858\pi$
$601$	40.2546	+	23.2410i	1.64202	+	0.948021i	0.661907	+	0.749586i	$0.269748\pi$
$602$		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	0.618550	−	0.785745i	$-0.287720\pi$
$607$	6.09405	+	3.51840i	0.247350	+	0.142808i	−0.371200	+	0.928553i	$0.621054\pi$
$608$	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	−0.765546	−	0.643381i	$-0.777531\pi$
$619$	−14.7072	+	8.49123i	−0.591134	+	0.341291i	0.174412	+	0.984673i	$0.444198\pi$
$620$	−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	−0.165923	−	0.986139i	$-0.553060\pi$
$643$	15.3447	−	8.85928i	0.605136	−	0.349376i	0.771060	+	0.636763i	$0.219727\pi$
$644$		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	−0.568395	−	0.822756i	$-0.692435\pi$
$647$	10.8951	−	18.8709i	0.428330	−	0.741890i	0.996725	+	0.0808661i	$0.0257686\pi$
$648$	−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	$-0.676546\pi$
$661$		−	43.7116i		−	1.70019i	0.526633	−	0.850093i	$-0.323454\pi$
$662$		−	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	$-0.355375\pi$
$677$	22.8387			0.877763			0.438882	+	0.898545i	$0.355375\pi$
$678$	−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	$0.00156660\pi$
$691$			0.258747i			0.00984320i	−0.999988	+	0.00492160i	$0.998433\pi$
$692$	−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	0.945046	−	0.326937i	$-0.106016\pi$
$719$	5.07828	+	8.79584i	0.189388	+	0.328029i	−0.755658	+	0.654966i	$0.772683\pi$
$720$	−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	0.389593	−	0.920987i	$-0.372616\pi$
$727$	−5.74874	−	3.31904i	−0.213209	−	0.123096i	−0.602802	+	0.797891i	$0.705949\pi$
$728$		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	0.400858	−	0.916140i	$-0.368712\pi$
$733$	−5.20130	−	3.00297i	−0.192114	−	0.110917i	−0.592972	+	0.805223i	$0.702046\pi$
$734$	−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	−0.808000	−	0.589183i	$-0.799450\pi$
$761$	2.93098	−	5.07660i	0.106248	−	0.184027i	0.914247	+	0.405157i	$0.132783\pi$
$762$	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	0.0876307	−	0.996153i	$-0.472070\pi$
$769$	27.5683	−	15.9166i	0.994140	−	0.573967i	0.906509	+	0.422186i	$0.138737\pi$
$770$		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	−0.984874	−	0.173274i	$-0.944566\pi$
$773$	−9.51908	+	16.4875i	−0.342378	+	0.593015i	0.642496	+	0.766289i	$0.277899\pi$
$774$	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	$-0.890327\pi$
$787$		−	18.9513i		−	0.675540i	0.941229	−	0.337770i	$-0.109673\pi$
$788$			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	$-0.771262\pi$
$797$	−26.7207	−	46.2816i	−0.946497	−	1.63938i	−0.193770	−	0.981047i	$-0.562071\pi$
$798$		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	$0.0339844\pi$
$811$			6.06938i			0.213125i	−0.994306	+	0.106562i	$0.966016\pi$
$812$		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	0.579689	−	0.814837i	$-0.303174\pi$
$829$	4.71804	+	2.72396i	0.163864	+	0.0946071i	−0.415825	+	0.909445i	$0.636507\pi$
$830$	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	$0.482826\pi$
$839$	−24.2673	+	42.0322i	−0.837801	+	1.45111i	−0.891729	+	0.452569i	$0.850508\pi$
$840$		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	0.304152	−	0.952623i	$-0.401627\pi$
$853$	−10.7703	−	6.21823i	−0.368768	−	0.212908i	−0.672920	+	0.739715i	$0.734960\pi$
$854$		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	0.942129	−	0.335250i	$-0.108821\pi$
$857$	5.29077	+	9.16388i	0.180729	+	0.313032i	−0.761400	+	0.648283i	$0.775488\pi$
$858$	−11.8759	−	64.2041i	−0.405437	−	2.19189i
$859$	28.1452	+	16.2496i	0.960302	+	0.554431i	0.896266	−	0.443517i	$-0.146269\pi$
$859$	28.1452	+	16.2496i	0.960302	+	0.554431i	0.0640360	+	0.997948i	$0.479603\pi$
$860$	−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	$-0.710434\pi$
$881$	−36.4482			−1.22797			−0.613985	+	0.789318i	$0.710434\pi$
$882$		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	$-0.525448\pi$
$887$	24.5208	−	42.4713i	0.823329	−	1.42605i	0.903190	−	0.429241i	$-0.141219\pi$
$888$	−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	$-0.662253\pi$
$929$	−29.7445			−0.975885			−0.487943	+	0.872876i	$0.662253\pi$
$930$	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	$0.0210057\pi$
$937$			4.03712i			0.131887i	−0.997823	+	0.0659434i	$0.978994\pi$
$938$		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	$-0.575443\pi$
$941$	−14.4053			−0.469599			−0.234799	+	0.972044i	$0.575443\pi$
$942$	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	$-0.987616\pi$
$971$	−16.6183	−	28.7838i	−0.533307	−	0.923715i	0.465936	−	0.884818i	$-0.345718\pi$
$972$	−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	0.605438	−	0.795892i	$-0.292998\pi$
$983$	−12.1192	−	20.9911i	−0.386544	−	0.669513i	−0.991982	+	0.126379i	$0.959664\pi$
$984$	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	−0.633110	−	0.774062i	$-0.718222\pi$
$997$	−8.81920	+	5.09177i	−0.279307	+	0.161258i	0.353803	+	0.935320i	$0.384888\pi$
$998$	−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.227.5		12
3.2	odd	2		1323.2.i.c.521.1		12
7.2	even	3		441.2.s.c.362.6		12
7.3	odd	6		63.2.o.a.20.2	yes	12
7.4	even	3		63.2.o.a.20.1	✓	12
7.5	odd	6		441.2.s.c.362.5		12
7.6	odd	2	inner	441.2.i.c.227.6		12
9.4	even	3		1323.2.s.c.962.1		12
9.5	odd	6		441.2.s.c.374.5		12
21.2	odd	6		1323.2.s.c.656.2		12
21.5	even	6		1323.2.s.c.656.1		12
21.11	odd	6		189.2.o.a.62.5		12
21.17	even	6		189.2.o.a.62.6		12
21.20	even	2		1323.2.i.c.521.2		12
28.3	even	6		1008.2.cc.a.209.2		12
28.11	odd	6		1008.2.cc.a.209.5		12
63.4	even	3		189.2.o.a.125.6		12
63.5	even	6	inner	441.2.i.c.68.1		12
63.11	odd	6		567.2.c.c.566.2		12
63.13	odd	6		1323.2.s.c.962.2		12
63.23	odd	6	inner	441.2.i.c.68.2		12
63.25	even	3		567.2.c.c.566.11		12
63.31	odd	6		189.2.o.a.125.5		12
63.32	odd	6		63.2.o.a.41.2	yes	12
63.38	even	6		567.2.c.c.566.1		12
63.40	odd	6		1323.2.i.c.1097.5		12
63.41	even	6		441.2.s.c.374.6		12
63.52	odd	6		567.2.c.c.566.12		12
63.58	even	3		1323.2.i.c.1097.6		12
63.59	even	6		63.2.o.a.41.1	yes	12
84.11	even	6		3024.2.cc.a.2897.3		12
84.59	odd	6		3024.2.cc.a.2897.4		12
252.31	even	6		3024.2.cc.a.881.3		12
252.59	odd	6		1008.2.cc.a.545.5		12
252.67	odd	6		3024.2.cc.a.881.4		12
252.95	even	6		1008.2.cc.a.545.2		12

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