LMFDB - Embedded newform 63.2.o.a.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,2,Mod(20,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("63.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.503057532734$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.1
Root			$-1.29589 + 0.748185i$ of defining polynomial
Character	$\chi$	$=$	63.41
Dual form			63.2.o.a.20.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.97141 + 1.13819i) q^{2} +(-0.578751 - 1.63250i) q^{3} +(1.59097 - 2.75564i) q^{4} +(0.717144 - 1.24213i) q^{5} +(2.99905 + 2.55959i) q^{6} +(2.16235 - 1.52455i) q^{7} +2.69056i q^{8} +(-2.33009 + 1.88962i) q^{9} +O(q^{10})$	\(q+(-1.97141 + 1.13819i) q^{2} +(-0.578751 - 1.63250i) q^{3} +(1.59097 - 2.75564i) q^{4} +(0.717144 - 1.24213i) q^{5} +(2.99905 + 2.55959i) q^{6} +(2.16235 - 1.52455i) q^{7} +2.69056i q^{8} +(-2.33009 + 1.88962i) q^{9} +3.26499i q^{10} +(2.80150 - 1.61745i) q^{11} +(-5.41936 - 1.00243i) q^{12} +(-4.43334 - 2.55959i) q^{13} +(-2.52764 + 5.46668i) q^{14} +(-2.44282 - 0.451852i) q^{15} +(0.119562 + 0.207087i) q^{16} -1.09132 q^{17} +(2.44282 - 6.37731i) q^{18} +4.48911i q^{19} +(-2.28191 - 3.95238i) q^{20} +(-3.74028 - 2.64769i) q^{21} +(-3.68194 + 6.37731i) q^{22} +(3.47141 + 2.00422i) q^{23} +(4.39234 - 1.55716i) q^{24} +(1.47141 + 2.54856i) q^{25} +11.6532 q^{26} +(4.43334 + 2.71026i) q^{27} +(-0.760877 - 8.38418i) q^{28} +(1.02859 - 0.593857i) q^{29} +(5.33009 - 1.88962i) q^{30} +(3.24275 + 1.87220i) q^{31} +(-5.13160 - 2.96273i) q^{32} +(-4.26186 - 3.63735i) q^{33} +(2.15143 - 1.24213i) q^{34} +(-0.342971 - 3.77924i) q^{35} +(1.50000 + 9.42724i) q^{36} -0.239123 q^{37} +(-5.10948 - 8.84988i) q^{38} +(-1.61273 + 8.71878i) q^{39} +(3.34203 + 1.92952i) q^{40} +(-3.71620 + 6.43664i) q^{41} +(10.3872 + 0.962525i) q^{42} +(-3.82326 - 6.62208i) q^{43} -10.2933i q^{44} +(0.676137 + 4.24941i) q^{45} -9.12476 q^{46} +(2.11042 + 3.65536i) q^{47} +(0.268872 - 0.315036i) q^{48} +(2.35150 - 6.59321i) q^{49} +(-5.80150 - 3.34950i) q^{50} +(0.631600 + 1.78157i) q^{51} +(-14.1066 + 8.14447i) q^{52} +7.01414i q^{53} +(-11.8247 - 0.297022i) q^{54} -4.63977i q^{55} +(4.10189 + 5.81793i) q^{56} +(7.32846 - 2.59808i) q^{57} +(-1.35185 + 2.34147i) q^{58} +(4.73531 - 8.20179i) q^{59} +(-5.13160 + 6.01266i) q^{60} +(2.82757 - 1.63250i) q^{61} -8.52371 q^{62} +(-2.15766 + 7.63836i) q^{63} +13.0104 q^{64} +(-6.35868 + 3.67119i) q^{65} +(12.5419 + 2.31989i) q^{66} +(-0.330095 + 0.571741i) q^{67} +(-1.73625 + 3.00728i) q^{68} +(1.26280 - 6.82701i) q^{69} +(4.97764 + 7.06006i) q^{70} +3.82347i q^{71} +(-5.08414 - 6.26926i) q^{72} +7.31073i q^{73} +(0.471410 - 0.272169i) q^{74} +(3.30893 - 3.87705i) q^{75} +(12.3704 + 7.14205i) q^{76} +(3.59195 - 7.76852i) q^{77} +(-6.74433 - 19.0239i) q^{78} +(-1.83009 - 3.16982i) q^{79} +0.342971 q^{80} +(1.85868 - 8.80598i) q^{81} -16.9190i q^{82} +(5.45245 + 9.44392i) q^{83} +(-13.2468 + 6.09448i) q^{84} +(-0.782630 + 1.35556i) q^{85} +(15.0744 + 8.70322i) q^{86} +(-1.56477 - 1.33548i) q^{87} +(4.35185 + 7.53762i) q^{88} -13.6915 q^{89} +(-6.16959 - 7.60775i) q^{90} +(-13.4887 + 1.22412i) q^{91} +(11.0458 - 6.37731i) q^{92} +(1.17962 - 6.37731i) q^{93} +(-8.32102 - 4.80415i) q^{94} +(5.57605 + 3.21934i) q^{95} +(-1.86673 + 10.0920i) q^{96} +(-2.69709 + 1.55716i) q^{97} +(2.86857 + 15.6744i) q^{98} +(-3.47141 + 9.06259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 2 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 + 2 * q^4 - 2 * q^7 - 12 * q^9	$ 12 q - 6 q^{2} + 2 q^{4} - 2 q^{7} - 12 q^{9} - 12 q^{14} + 6 q^{15} + 2 q^{16} - 6 q^{18} - 24 q^{21} - 10 q^{22} + 24 q^{23} - 8 q^{28} + 30 q^{29} + 48 q^{30} - 12 q^{32} + 18 q^{36} - 4 q^{37} + 36 q^{42} - 10 q^{43} - 40 q^{46} + 6 q^{49} - 36 q^{50} - 42 q^{51} + 42 q^{56} - 18 q^{57} + 2 q^{58} - 12 q^{60} + 24 q^{63} + 16 q^{64} - 78 q^{65} + 12 q^{67} + 18 q^{70} - 24 q^{72} - 12 q^{74} - 24 q^{77} - 12 q^{78} - 6 q^{79} + 24 q^{81} - 60 q^{84} - 6 q^{85} + 96 q^{86} + 34 q^{88} - 24 q^{91} + 30 q^{92} + 78 q^{93} + 72 q^{95} - 24 q^{99}+O(q^{100}) $ 12 * q - 6 * q^2 + 2 * q^4 - 2 * q^7 - 12 * q^9 - 12 * q^14 + 6 * q^15 + 2 * q^16 - 6 * q^18 - 24 * q^21 - 10 * q^22 + 24 * q^23 - 8 * q^28 + 30 * q^29 + 48 * q^30 - 12 * q^32 + 18 * q^36 - 4 * q^37 + 36 * q^42 - 10 * q^43 - 40 * q^46 + 6 * q^49 - 36 * q^50 - 42 * q^51 + 42 * q^56 - 18 * q^57 + 2 * q^58 - 12 * q^60 + 24 * q^63 + 16 * q^64 - 78 * q^65 + 12 * q^67 + 18 * q^70 - 24 * q^72 - 12 * q^74 - 24 * q^77 - 12 * q^78 - 6 * q^79 + 24 * q^81 - 60 * q^84 - 6 * q^85 + 96 * q^86 + 34 * q^88 - 24 * q^91 + 30 * q^92 + 78 * q^93 + 72 * q^95 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.97141	+	1.13819i	−1.39400	+	0.804825i	−0.993755	−	0.111585i	$-0.964407\pi$
$2$	−1.97141	+	1.13819i	−1.39400	+	0.804825i	−0.400242	+	0.916409i	$0.631074\pi$
$3$	−0.578751	−	1.63250i	−0.334142	−	0.942523i
$3$	−0.578751	−	1.63250i	−0.334142	−	0.942523i
$4$	1.59097	−	2.75564i	0.795486	−	1.37782i
$5$	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
$7$	2.16235	−	1.52455i	0.817291	−	0.576225i
$7$	2.16235	−	1.52455i	0.817291	−	0.576225i
$8$			2.69056i			0.951257i
$9$	−2.33009	+	1.88962i	−0.776698	+	0.629873i
$10$			3.26499i			1.03248i
$11$	2.80150	−	1.61745i	0.844686	−	0.487679i	−0.0141686	−	0.999900i	$-0.504510\pi$
$11$	2.80150	−	1.61745i	0.844686	−	0.487679i	0.858854	+	0.512220i	$0.171177\pi$
$12$	−5.41936	−	1.00243i	−1.56443	−	0.289375i
$13$	−4.43334	−	2.55959i	−1.22959	−	0.709903i	−0.262644	−	0.964893i	$-0.584594\pi$
$13$	−4.43334	−	2.55959i	−1.22959	−	0.709903i	−0.966944	+	0.254990i	$0.917928\pi$
$14$	−2.52764	+	5.46668i	−0.675541	+	1.46103i
$15$	−2.44282	−	0.451852i	−0.630733	−	0.116668i
$16$	0.119562	+	0.207087i	0.0298904	+	0.0517717i
$17$	−1.09132			−0.264683			−0.132341	−	0.991204i	$-0.542250\pi$
$17$	−1.09132			−0.264683			−0.132341	+	0.991204i	$0.542250\pi$
$18$	2.44282	−	6.37731i	0.575778	−	1.50315i
$19$			4.48911i			1.02987i	0.857228	+	0.514936i	$0.172184\pi$
$19$			4.48911i			1.02987i	−0.857228	+	0.514936i	$0.827816\pi$
$20$	−2.28191	−	3.95238i	−0.510251	−	0.883780i
$21$	−3.74028	−	2.64769i	−0.816197	−	0.577774i
$22$	−3.68194	+	6.37731i	−0.784993	+	1.35965i
$23$	3.47141	+	2.00422i	0.723839	+	0.417909i	0.816164	−	0.577820i	$-0.196097\pi$
$23$	3.47141	+	2.00422i	0.723839	+	0.417909i	−0.0923250	+	0.995729i	$0.529430\pi$
$24$	4.39234	−	1.55716i	0.896582	−	0.317855i
$25$	1.47141	+	2.54856i	0.294282	+	0.509711i
$26$	11.6532			2.28539
$27$	4.43334	+	2.71026i	0.853197	+	0.521589i
$28$	−0.760877	−	8.38418i	−0.143792	−	1.58446i
$29$	1.02859	−	0.593857i	0.191004	−	0.110276i	−0.401448	−	0.915882i	$-0.631493\pi$
$29$	1.02859	−	0.593857i	0.191004	−	0.110276i	0.592453	+	0.805605i	$0.298160\pi$
$30$	5.33009	−	1.88962i	0.973138	−	0.344996i
$31$	3.24275	+	1.87220i	0.582414	+	0.336257i	0.762092	−	0.647468i	$-0.224172\pi$
$31$	3.24275	+	1.87220i	0.582414	+	0.336257i	−0.179678	+	0.983726i	$0.557506\pi$
$32$	−5.13160	−	2.96273i	−0.907147	−	0.523742i
$33$	−4.26186	−	3.63735i	−0.741894	−	0.633181i
$34$	2.15143	−	1.24213i	0.368967	−	0.213023i
$35$	−0.342971	−	3.77924i	−0.0579728	−	0.638808i
$36$	1.50000	+	9.42724i	0.250000	+	1.57121i
$37$	−0.239123			−0.0393116			−0.0196558	−	0.999807i	$-0.506257\pi$
$37$	−0.239123			−0.0393116			−0.0196558	+	0.999807i	$0.506257\pi$
$38$	−5.10948	−	8.84988i	−0.828867	−	1.43564i
$39$	−1.61273	+	8.71878i	−0.258243	+	1.39612i
$40$	3.34203	+	1.92952i	0.528421	+	0.305084i
$41$	−3.71620	+	6.43664i	−0.580373	+	1.00523i	0.415062	+	0.909793i	$0.363760\pi$
$41$	−3.71620	+	6.43664i	−0.580373	+	1.00523i	−0.995435	+	0.0954418i	$0.969574\pi$
$42$	10.3872	+	0.962525i	1.60278	+	0.148521i
$43$	−3.82326	−	6.62208i	−0.583041	−	1.00986i	−0.995116	−	0.0987075i	$-0.968529\pi$
$43$	−3.82326	−	6.62208i	−0.583041	−	1.00986i	0.412075	−	0.911150i	$-0.364804\pi$
$44$		−	10.2933i		−	1.55177i
$45$	0.676137	+	4.24941i	0.100793	+	0.633464i
$46$	−9.12476			−1.34537
$47$	2.11042	+	3.65536i	0.307837	+	0.533189i	0.977889	−	0.209125i	$-0.0670615\pi$
$47$	2.11042	+	3.65536i	0.307837	+	0.533189i	−0.670052	+	0.742314i	$0.733728\pi$
$48$	0.268872	−	0.315036i	0.0388084	−	0.0454715i
$49$	2.35150	−	6.59321i	0.335929	−	0.941887i
$50$	−5.80150	−	3.34950i	−0.820457	−	0.473691i
$51$	0.631600	+	1.78157i	0.0884417	+	0.249470i
$52$	−14.1066	+	8.14447i	−1.95624	+	1.12944i
$53$			7.01414i			0.963466i	0.876318	+	0.481733i	$0.159992\pi$
$53$			7.01414i			0.963466i	−0.876318	+	0.481733i	$0.840008\pi$
$54$	−11.8247	−	0.297022i	−1.60914	−	0.0404196i
$55$		−	4.63977i		−	0.625627i
$56$	4.10189	+	5.81793i	0.548138	+	0.777454i
$57$	7.32846	−	2.59808i	0.970678	−	0.344124i
$58$	−1.35185	+	2.34147i	−0.177506	+	0.307450i
$59$	4.73531	−	8.20179i	0.616484	−	1.06778i	−0.373638	−	0.927575i	$-0.621890\pi$
$59$	4.73531	−	8.20179i	0.616484	−	1.06778i	0.990122	−	0.140208i	$-0.0447770\pi$
$60$	−5.13160	+	6.01266i	−0.662487	+	0.776231i
$61$	2.82757	−	1.63250i	0.362033	−	0.209020i	−0.307939	−	0.951406i	$-0.599639\pi$
$61$	2.82757	−	1.63250i	0.362033	−	0.209020i	0.669972	+	0.742386i	$0.266306\pi$
$62$	−8.52371			−1.08251
$63$	−2.15766	+	7.63836i	−0.271840	+	0.962342i
$64$	13.0104			1.62630
$65$	−6.35868	+	3.67119i	−0.788698	+	0.455355i
$66$	12.5419	+	2.31989i	1.54380	+	0.285558i
$67$	−0.330095	+	0.571741i	−0.0403275	+	0.0698493i	−0.885485	−	0.464669i	$-0.846173\pi$
$67$	−0.330095	+	0.571741i	−0.0403275	+	0.0698493i	0.845157	+	0.534518i	$0.179507\pi$
$68$	−1.73625	+	3.00728i	−0.210552	+	0.364686i
$69$	1.26280	−	6.82701i	0.152023	−	0.821876i
$70$	4.97764	+	7.06006i	0.594942	+	0.843838i
$71$			3.82347i			0.453762i	0.973922	+	0.226881i	$0.0728529\pi$
$71$			3.82347i			0.453762i	−0.973922	+	0.226881i	$0.927147\pi$
$72$	−5.08414	−	6.26926i	−0.599171	−	0.738840i
$73$			7.31073i			0.855656i	0.903860	+	0.427828i	$0.140721\pi$
$73$			7.31073i			0.855656i	−0.903860	+	0.427828i	$0.859279\pi$
$74$	0.471410	−	0.272169i	0.0548003	−	0.0316390i
$75$	3.30893	−	3.87705i	0.382083	−	0.447683i
$76$	12.3704	+	7.14205i	1.41898	+	0.819249i
$77$	3.59195	−	7.76852i	0.409341	−	0.885305i
$78$	−6.74433	−	19.0239i	−0.763644	−	2.15403i
$79$	−1.83009	−	3.16982i	−0.205902	−	0.356632i	0.744518	−	0.667602i	$-0.232679\pi$
$79$	−1.83009	−	3.16982i	−0.205902	−	0.356632i	−0.950420	+	0.310970i	$0.899346\pi$
$80$	0.342971			0.0383454
$81$	1.85868	−	8.80598i	0.206521	−	0.978442i
$82$		−	16.9190i		−	1.86839i
$83$	5.45245	+	9.44392i	0.598484	+	1.03660i	0.993045	+	0.117735i	$0.0375634\pi$
$83$	5.45245	+	9.44392i	0.598484	+	1.03660i	−0.394561	+	0.918870i	$0.629103\pi$
$84$	−13.2468	+	6.09448i	−1.44534	+	0.664962i
$85$	−0.782630	+	1.35556i	−0.0848882	+	0.147031i
$86$	15.0744	+	8.70322i	1.62552	+	0.938492i
$87$	−1.56477	−	1.33548i	−0.167761	−	0.143178i
$88$	4.35185	+	7.53762i	0.463909	+	0.803513i
$89$	−13.6915			−1.45129			−0.725646	−	0.688068i	$-0.758459\pi$
$89$	−13.6915			−1.45129			−0.725646	+	0.688068i	$0.758459\pi$
$90$	−6.16959	−	7.60775i	−0.650332	−	0.801927i
$91$	−13.4887	+	1.22412i	−1.41399	+	0.128322i
$92$	11.0458	−	6.37731i	1.15161	−	0.664881i
$93$	1.17962	−	6.37731i	0.122321	−	0.661297i
$94$	−8.32102	−	4.80415i	−0.858248	−	0.495510i
$95$	5.57605	+	3.21934i	0.572091	+	0.330297i
$96$	−1.86673	+	10.0920i	−0.190523	+	1.03001i
$97$	−2.69709	+	1.55716i	−0.273848	+	0.158106i	−0.630635	−	0.776080i	$-0.717205\pi$
$97$	−2.69709	+	1.55716i	−0.273848	+	0.158106i	0.356787	+	0.934186i	$0.383872\pi$
$98$	2.86857	+	15.6744i	0.289770	+	1.58335i
$99$	−3.47141	+	9.06259i	−0.348890	+	0.910824i
$100$	9.36389			0.936389
$101$	−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	$0.948074\pi$
$102$	−3.27292	−	2.79332i	−0.324067	−	0.276580i
$103$	−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
$105$	−5.97110	+	2.74714i	−0.582720	+	0.268093i
$106$	−7.98345	−	13.8277i	−0.775421	−	1.34307i
$107$		−	4.93582i		−	0.477164i	−0.971122	−	0.238582i	$-0.923317\pi$
$107$		−	4.93582i		−	0.477164i	0.971122	−	0.238582i	$-0.0766826\pi$
$108$	14.5218	−	7.90477i	1.39736	−	0.760637i
$109$	8.13844			0.779521			0.389760	−	0.920916i	$-0.372558\pi$
$109$	8.13844			0.779521			0.389760	+	0.920916i	$0.372558\pi$
$110$	5.28096	+	9.14690i	0.503520	+	0.872123i
$111$	0.138393	+	0.390368i	0.0131357	+	0.0370521i
$112$	0.574248	+	0.265516i	0.0542613	+	0.0250889i
$113$	−3.39699	−	1.96125i	−0.319562	−	0.184499i	0.331635	−	0.943408i	$-0.392400\pi$
$113$	−3.39699	−	1.96125i	−0.319562	−	0.184499i	−0.651197	+	0.758908i	$0.725733\pi$
$114$	−11.4903	+	13.4631i	−1.07616	+	1.26093i
$115$	4.97900	−	2.87463i	0.464294	−	0.268060i
$116$		−	3.77924i		−	0.350893i
$117$	15.1668	−	2.41323i	1.40217	−	0.223104i
$118$			21.5588i			1.98465i
$119$	−2.35981	+	1.66376i	−0.216323	+	0.152517i
$120$	1.21574	−	6.57256i	0.110981	−	0.599990i
$121$	−0.267713	+	0.463693i	−0.0243376	+	0.0421539i
$122$	−3.71620	+	6.43664i	−0.336449	+	0.582746i
$123$	12.6586	+	2.34147i	1.14138	+	0.211123i
$124$	10.3182	−	5.95724i	0.926605	−	0.534976i
$125$	11.3923			1.01896
$126$	−4.44029	−	17.5142i	−0.395573	−	1.56029i
$127$	6.16827			0.547345			0.273673	−	0.961823i	$-0.411761\pi$
$127$	6.16827			0.547345			0.273673	+	0.961823i	$0.411761\pi$
$128$	−15.3856	+	8.88290i	−1.35991	+	0.785145i
$129$	−8.59781	+	10.0740i	−0.756995	+	0.886966i
$130$	8.35705	−	14.4748i	0.732962	−	1.26953i
$131$	−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
$133$	6.84387	+	9.70702i	0.593438	+	0.841706i
$134$		−	1.50285i		−	0.129826i
$135$	6.54583	−	3.56314i	0.563375	−	0.306666i
$136$		−	2.93625i		−	0.251782i
$137$	−8.96169	+	5.17404i	−0.765649	+	0.442048i	−0.831320	−	0.555794i	$-0.812415\pi$
$137$	−8.96169	+	5.17404i	−0.765649	+	0.442048i	0.0656711	+	0.997841i	$0.479081\pi$
$138$	5.28096	+	14.8962i	0.449546	+	1.26804i
$139$	−15.4589	−	8.92521i	−1.31121	−	0.757026i	−0.328912	−	0.944361i	$-0.606682\pi$
$139$	−15.4589	−	8.92521i	−1.31121	−	0.757026i	−0.982296	+	0.187334i	$0.940015\pi$
$140$	−10.9599	−	5.06755i	−0.926280	−	0.428286i
$141$	4.74596	−	5.56081i	0.399682	−	0.468304i
$142$	−4.35185	−	7.53762i	−0.365199	−	0.632543i
$143$	−16.5600			−1.38482
$144$	−0.669905	−	0.256606i	−0.0558254	−	0.0213838i
$145$		−	1.70352i		−	0.141470i
$146$	−8.32102	−	14.4124i	−0.688653	−	1.19278i
$147$	−12.1243	−	0.0229982i	−0.999998	−	0.00189686i
$148$	−0.380438	+	0.658939i	−0.0312718	+	0.0541644i
$149$	−15.1758	−	8.76175i	−1.24325	−	0.717790i	−0.273495	−	0.961873i	$-0.588180\pi$
$149$	−15.1758	−	8.76175i	−1.24325	−	0.717790i	−0.969754	+	0.244083i	$0.921513\pi$
$150$	−2.11042	+	11.4095i	−0.172315	+	0.931579i
$151$	−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	$0.847594\pi$
$152$	−12.0782			−0.979674
$153$	2.54287	−	2.06217i	0.205579	−	0.166717i
$154$	1.76088	+	19.4033i	0.141895	+	1.56356i
$155$	4.65103	−	2.68527i	0.373580	−	0.215686i
$156$	21.4601	+	18.3154i	1.71818	+	1.46641i
$157$	8.45150	+	4.87948i	0.674503	+	0.389425i	0.797781	−	0.602947i	$-0.206007\pi$
$157$	8.45150	+	4.87948i	0.674503	+	0.389425i	−0.123277	+	0.992372i	$0.539340\pi$
$158$	7.21574	+	4.16601i	0.574053	+	0.331430i
$159$	11.4506	−	4.05944i	0.908088	−	0.321934i
$160$	−7.36019	+	4.24941i	−0.581874	+	0.335945i
$161$	10.5619	−	0.958511i	0.832397	−	0.0755413i
$162$	6.35868	+	19.4757i	0.499585	+	1.53016i
$163$	−7.22545			−0.565941			−0.282970	−	0.959129i	$-0.591320\pi$
$163$	−7.22545			−0.565941			−0.282970	+	0.959129i	$0.591320\pi$
$164$	11.8247	+	20.4810i	0.923356	+	1.59930i
$165$	−7.57442	+	2.68527i	−0.589668	+	0.209048i
$166$	−21.4980	−	12.4119i	−1.66857	−	0.963350i
$167$	8.65419	−	14.9895i	0.669681	−	1.15992i	−0.308312	−	0.951285i	$-0.599764\pi$
$167$	8.65419	−	14.9895i	0.669681	−	1.15992i	0.977993	−	0.208637i	$-0.0669027\pi$
$168$	7.12379	−	10.0635i	0.549612	−	0.776413i
$169$	6.60301	+	11.4367i	0.507924	+	0.879750i
$170$		−	3.56314i		−	0.273280i
$171$	−8.48270	−	10.4601i	−0.648689	−	0.799900i
$172$	−24.3308			−1.85520
$173$	−0.978103	−	1.69412i	−0.0743638	−	0.128802i	0.826446	−	0.563017i	$-0.190359\pi$
$173$	−0.978103	−	1.69412i	−0.0743638	−	0.128802i	−0.900809	+	0.434215i	$0.857026\pi$
$174$	4.60483	+	0.851761i	0.349091	+	0.0645718i
$175$	7.06710	+	3.26763i	0.534223	+	0.247010i
$176$	0.669905	+	0.386770i	0.0504960	+	0.0291539i
$177$	−16.1300	−	2.98358i	−1.21240	−	0.224260i
$178$	26.9915	−	15.5835i	2.02310	−	1.16804i
$179$		−	23.2017i		−	1.73418i	−0.498152	−	0.867090i	$-0.665988\pi$
$179$		−	23.2017i		−	1.73418i	0.498152	−	0.867090i	$-0.334012\pi$
$180$	12.7856	+	4.89749i	0.952980	+	0.365037i
$181$		−	10.2744i		−	0.763689i	−0.924226	−	0.381845i	$-0.875289\pi$
$181$		−	10.2744i		−	0.763689i	0.924226	−	0.381845i	$-0.124711\pi$
$182$	25.1984	−	17.7659i	1.86783	−	1.31690i
$183$	−4.30150	−	3.67119i	−0.317976	−	0.271382i
$184$	−5.39248	+	9.34004i	−0.397539	+	0.688557i
$185$	−0.171486	+	0.297022i	−0.0126079	+	0.0218375i
$186$	4.93310	+	13.9149i	0.361713	+	1.02029i
$187$	−3.05733	+	1.76515i	−0.223574	+	0.129080i
$188$	13.4305			0.979520
$189$	13.7183	−	0.898326i	0.997863	−	0.0653436i
$190$	−14.6569			−1.06332
$191$	19.6758	−	11.3598i	1.42369	−	0.821968i	0.427079	−	0.904215i	$-0.359543\pi$
$191$	19.6758	−	11.3598i	1.42369	−	0.821968i	0.996612	+	0.0822464i	$0.0262094\pi$
$192$	−7.52978	−	21.2394i	−0.543415	−	1.53283i
$193$	−8.43598	+	14.6116i	−0.607235	+	1.05176i	0.384459	+	0.923142i	$0.374388\pi$
$193$	−8.43598	+	14.6116i	−0.607235	+	1.05176i	−0.991694	+	0.128620i	$0.958945\pi$
$194$	3.54471	−	6.13962i	0.254495	−	0.440799i
$195$	9.67330	+	8.25583i	0.692719	+	0.591212i
$196$	−14.4274	−	16.9695i	−1.03053	−	1.21211i
$197$			8.94426i			0.637252i	0.947880	+	0.318626i	$0.103221\pi$
$197$			8.94426i			0.637252i	−0.947880	+	0.318626i	$0.896779\pi$
$198$	−3.47141	−	21.8172i	−0.246702	−	1.55048i
$199$		−	5.78528i		−	0.410108i	−0.978751	−	0.205054i	$-0.934263\pi$
$199$		−	5.78528i		−	0.410108i	0.978751	−	0.205054i	$-0.0657369\pi$
$200$	−6.85705	+	3.95892i	−0.484867	+	0.279938i
$201$	1.12441	+	0.207983i	0.0793097	+	0.0146700i
$202$	13.9762	+	8.06914i	0.983359	+	0.567743i
$203$	1.31881	−	2.85226i	0.0925621	−	0.200189i
$204$	5.91423	+	1.09396i	0.414079	+	0.0765927i
$205$	5.33009	+	9.23200i	0.372270	+	0.644791i
$206$	3.87788			0.270185
$207$	−11.8759	+	1.88962i	−0.825434	+	0.131338i
$208$		−	1.22412i		−	0.0848771i
$209$	7.26091	+	12.5763i	0.502248	+	0.869918i
$210$	8.64471	−	12.2120i	0.596542	−	0.842708i
$211$	−12.9451	+	22.4216i	−0.891180	+	1.54357i	−0.0527186	+	0.998609i	$0.516789\pi$
$211$	−12.9451	+	22.4216i	−0.891180	+	1.54357i	−0.838462	+	0.544960i	$0.816545\pi$
$212$	19.3285	+	11.1593i	1.32748	+	0.766423i
$213$	6.24180	−	2.21284i	0.427681	−	0.151621i
$214$	5.61793	+	9.73053i	0.384034	+	0.665166i
$215$	−10.9673			−0.747964
$216$	−7.29211	+	11.9282i	−0.496165	+	0.811610i
$217$	9.86621	−	0.895374i	0.669762	−	0.0607819i
$218$	−16.0442	+	9.26312i	−1.08665	+	0.627378i
$219$	11.9347	−	4.23109i	0.806475	−	0.285910i
$220$	−12.7856	−	7.38175i	−0.862003	−	0.497678i
$221$	4.83818	+	2.79332i	0.325451	+	0.187899i
$222$	−0.717144	−	0.612058i	−0.0481315	−	0.0410786i
$223$	−15.4827	+	8.93892i	−1.03680	+	0.598594i	−0.918924	−	0.394435i	$-0.870940\pi$
$223$	−15.4827	+	8.93892i	−1.03680	+	0.598594i	−0.117871	+	0.993029i	$0.537607\pi$
$224$	−15.6131	+	1.41692i	−1.04320	+	0.0946717i
$225$	−8.24433	−	3.15798i	−0.549622	−	0.210532i
$226$	8.92915			0.593958
$227$	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	$0.714757\pi$
$228$	4.50000	−	24.3281i	0.298020	−	1.61117i
$229$	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
$231$	−14.7609	−	1.36781i	−0.971198	−	0.0899954i
$232$	1.59781	+	2.76748i	0.104901	+	0.181694i
$233$		−	2.94031i		−	0.192626i	−0.995351	−	0.0963131i	$-0.969295\pi$
$233$		−	2.94031i		−	0.192626i	0.995351	−	0.0963131i	$-0.0307050\pi$
$234$	−27.1532	+	22.0202i	−1.77506	+	1.43950i
$235$	6.05391			0.394914
$236$	−15.0675	−	26.0976i	−0.980809	−	1.69881i
$237$	−4.11555	+	4.82216i	−0.267334	+	0.313233i
$238$	2.75846	−	5.96588i	0.178804	−	0.386710i
$239$	−10.7255	−	6.19234i	−0.693772	−	0.400549i	0.111252	−	0.993792i	$-0.464514\pi$
$239$	−10.7255	−	6.19234i	−0.693772	−	0.400549i	−0.805023	+	0.593243i	$0.797847\pi$
$240$	−0.198495	−	0.559900i	−0.0128128	−	0.0361414i
$241$	−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	$0.476555\pi$
$242$		−	1.21884i		−	0.0783499i
$243$	−15.4515	+	2.06217i	−0.991211	+	0.132288i
$244$		−	10.3890i		−	0.665089i
$245$	−6.50325	−	7.64915i	−0.415478	−	0.488686i
$246$	−27.6202	+	9.79190i	−1.76100	+	0.624308i
$247$	11.4903	−	19.9018i	0.731109	−	1.26632i
$248$	−5.03727	+	8.72481i	−0.319867	+	0.554026i
$249$	12.2616	−	14.3668i	0.777045	−	0.910458i
$250$	−22.4589	+	12.9666i	−1.42042	+	0.820082i
$251$	−7.51441			−0.474305			−0.237153	−	0.971472i	$-0.576214\pi$
$251$	−7.51441			−0.474305			−0.237153	+	0.971472i	$0.576214\pi$
$252$	17.6158	+	18.0982i	1.10969	+	1.14008i
$253$	12.9669			0.815222
$254$	−12.1602	+	7.02069i	−0.762998	+	0.440517i
$255$	2.66589	+	0.493113i	0.166944	+	0.0308799i
$256$	7.21053	−	12.4890i	0.450658	−	0.780563i
$257$	−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
$259$	−0.517068	+	0.364555i	−0.0321290	+	0.0226523i
$260$			23.3630i			1.44891i
$261$	−1.27455	+	3.32738i	−0.0788927	+	0.205960i
$262$		−	18.8092i		−	1.16204i
$263$	−12.1127	+	6.99329i	−0.746903	+	0.431224i	−0.824574	−	0.565755i	$-0.808585\pi$
$263$	−12.1127	+	6.99329i	−0.746903	+	0.431224i	0.0776710	+	0.996979i	$0.475252\pi$
$264$	9.78651	−	11.4668i	0.602318	−	0.705732i
$265$	8.71246	+	5.03014i	0.535202	+	0.308999i
$266$	−24.5405	−	11.3469i	−1.50468	−	0.695721i
$267$	7.92395	+	22.3513i	0.484938	+	1.36788i
$268$	1.05034	+	1.81925i	0.0641599	+	0.111128i
$269$	25.8321			1.57501			0.787505	−	0.616308i	$-0.211372\pi$
$269$	25.8321			1.57501			0.787505	+	0.616308i	$0.211372\pi$
$270$	−8.84897	+	14.4748i	−0.538531	+	0.880910i
$271$			16.6537i			1.01164i	0.862639	+	0.505821i	$0.168810\pi$
$271$			16.6537i			1.01164i	−0.862639	+	0.505821i	$0.831190\pi$
$272$	−0.130480	−	0.225997i	−0.00791148	−	0.0137031i
$273$	9.80493	+	21.3117i	0.593422	+	1.28984i
$274$	11.7781	−	20.4003i	0.711542	−	1.23243i
$275$	8.24433	+	4.75986i	0.497152	+	0.287031i
$276$	−16.8037	−	14.3414i	−1.01147	−	0.863252i
$277$	−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	$-0.559237\pi$
$278$	40.6345			2.43709
$279$	−11.0937	+	1.76515i	−0.664160	+	0.105677i
$280$	10.1683	−	0.922786i	0.607670	−	0.0551470i
$281$	8.10464	−	4.67922i	0.483483	−	0.279139i	−0.238384	−	0.971171i	$-0.576618\pi$
$281$	8.10464	−	4.67922i	0.483483	−	0.279139i	0.721867	+	0.692032i	$0.243284\pi$
$282$	−3.02696	+	16.3645i	−0.180253	+	0.974489i
$283$	13.6603	+	7.88676i	0.812018	+	0.468819i	0.847656	−	0.530546i	$-0.178013\pi$
$283$	13.6603	+	7.88676i	0.812018	+	0.468819i	−0.0356380	+	0.999365i	$0.511346\pi$
$284$	10.5361	+	6.08303i	0.625203	+	0.360961i
$285$	2.02841	−	10.9661i	0.120153	−	0.649575i
$286$	32.6466	−	18.8485i	1.93044	−	1.11454i
$287$	1.77726	+	19.5838i	0.104908	+	1.15599i
$288$	17.5555	−	2.79332i	1.03447	−	0.164598i
$289$	−15.8090			−0.929943
$290$	1.93894	+	3.35834i	0.113858	+	0.197209i
$291$	4.10301	+	3.50178i	0.240523	+	0.205278i
$292$	20.1458	+	11.6312i	1.17894	+	0.680662i
$293$	−12.4287	+	21.5271i	−0.726090	+	1.25762i	0.232434	+	0.972612i	$0.425331\pi$
$293$	−12.4287	+	21.5271i	−0.726090	+	1.25762i	−0.958524	+	0.285013i	$0.908002\pi$
$294$	23.9282	−	13.7545i	1.39552	−	0.802179i
$295$	−6.79179	−	11.7637i	−0.395433	−	0.684911i
$296$		−	0.643376i		−	0.0373955i
$297$	16.8037	+	0.422088i	0.975051	+	0.0244920i
$298$	39.8903			2.31078
$299$	−10.2600	−	17.7708i	−0.593349	−	1.02771i
$300$	−5.41936	−	15.2865i	−0.312887	−	0.882568i
$301$	−18.3629	−	8.49050i	−1.05842	−	0.489384i
$302$	2.16991	+	1.25280i	0.124864	+	0.0720903i
$303$	−7.97141	+	9.34004i	−0.457946	+	0.536571i
$304$	−0.929636	+	0.536725i	−0.0533183	+	0.0307833i
$305$		−	4.68294i		−	0.268144i
$306$	−2.66589	+	6.95966i	−0.152399	+	0.397857i
$307$		−	18.8878i		−	1.07799i	−0.842310	−	0.538993i	$-0.818805\pi$
$307$		−	18.8878i		−	1.07799i	0.842310	−	0.538993i	$-0.181195\pi$
$308$	−15.6926	−	22.2576i	−0.894168	−	1.26825i
$309$	−0.536670	+	2.90137i	−0.0305301	+	0.165053i
$310$	−6.11273	+	10.5876i	−0.347179	+	0.601332i
$311$	−3.97716	+	6.88864i	−0.225524	+	0.390619i	−0.956476	−	0.291809i	$-0.905743\pi$
$311$	−3.97716	+	6.88864i	−0.225524	+	0.390619i	0.730953	+	0.682428i	$0.239076\pi$
$312$	−23.4584	−	4.33914i	−1.32807	−	0.245655i
$313$	−9.64210	+	5.56687i	−0.545004	+	0.314658i	−0.747104	−	0.664707i	$-0.768556\pi$
$313$	−9.64210	+	5.56687i	−0.545004	+	0.314658i	0.202101	+	0.979365i	$0.435223\pi$
$314$	−22.2152			−1.25367
$315$	7.94047	+	8.15790i	0.447395	+	0.459645i
$316$	−11.6465			−0.655168
$317$	−20.1380	+	11.6267i	−1.13107	+	0.653021i	−0.944203	−	0.329365i	$-0.893165\pi$
$317$	−20.1380	+	11.6267i	−1.13107	+	0.653021i	−0.186863	+	0.982386i	$0.559832\pi$
$318$	−17.9533	+	21.0358i	−1.00677	+	1.17963i
$319$	1.92107	−	3.32738i	0.107559	−	0.186298i
$320$	9.33033	−	16.1606i	0.521581	−	0.903405i
$321$	−8.05772	+	2.85661i	−0.449738	+	0.159441i
$322$	−19.7309	+	13.9111i	−1.09956	+	0.775238i
$323$		−	4.89904i		−	0.272590i
$324$	−21.3090	−	19.1319i	−1.18383	−	1.06289i
$325$		−	15.0648i		−	0.835646i
$326$	14.2443	−	8.22396i	0.788920	−	0.455483i
$327$	−4.71013	−	13.2860i	−0.260471	−	0.734716i
$328$	−17.3182	−	9.99866i	−0.956237	−	0.552084i
$329$	10.1363	+	4.68672i	0.558830	+	0.258387i
$330$	11.8759	−	13.9149i	0.653748	−	0.765992i
$331$	9.57962	+	16.5924i	0.526544	+	0.912000i	0.999522	+	0.0309261i	$0.00984566\pi$
$331$	9.57962	+	16.5924i	0.526544	+	0.912000i	−0.472978	+	0.881074i	$0.656821\pi$
$332$	34.6988			1.90434
$333$	0.557180	−	0.451852i	0.0305333	−	0.0247613i
$334$			39.4006i			2.15590i
$335$	0.473451	+	0.820041i	0.0258674	+	0.0448036i
$336$	0.101108	−	1.09113i	0.00551592	−	0.0595258i
$337$	14.2781	−	24.7304i	0.777779	−	1.34715i	−0.155441	−	0.987845i	$-0.549680\pi$
$337$	14.2781	−	24.7304i	0.777779	−	1.34715i	0.933219	−	0.359307i	$-0.116987\pi$
$338$	−26.0345	−	15.0310i	−1.41609	−	0.817579i
$339$	−1.23573	+	6.68065i	−0.0671156	+	0.362843i
$340$	2.49028	+	4.31330i	0.135055	+	0.233922i
$341$	12.1128			0.655943
$342$	28.6285	+	10.9661i	1.54805	+	0.592978i
$343$	−4.96690	−	17.8418i	−0.268187	−	0.963367i
$344$	17.8171	−	10.2867i	0.960634	−	0.554622i
$345$	−7.57442	−	6.46451i	−0.407793	−	0.348038i
$346$	3.85648	+	2.22654i	0.207326	+	0.119700i
$347$	2.56690	+	1.48200i	0.137798	+	0.0795578i	0.567314	−	0.823501i	$-0.307983\pi$
$347$	2.56690	+	1.48200i	0.137798	+	0.0795578i	−0.429516	+	0.903059i	$0.641316\pi$
$348$	−6.16959	+	2.18724i	−0.330725	+	0.117248i
$349$	23.3885	−	13.5034i	1.25196	−	0.722818i	0.280460	−	0.959866i	$-0.409513\pi$
$349$	23.3885	−	13.5034i	1.25196	−	0.722818i	0.971498	+	0.237048i	$0.0761797\pi$
$350$	−17.6514	+	1.60189i	−0.943504	+	0.0856245i
$351$	−12.7174	−	23.3630i	−0.678803	−	1.24703i
$352$	−19.1683			−1.02167
$353$	−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	$-0.456063\pi$
$354$	35.1947	−	12.4772i	1.87058	−	0.663154i
$355$	4.74924	+	2.74198i	0.252064	+	0.145529i
$356$	−21.7827	+	37.7288i	−1.15448	+	1.99962i
$357$	4.08183	+	2.88947i	0.216033	+	0.152927i
$358$	26.4081	+	45.7401i	1.39571	+	2.41744i
$359$			24.6261i			1.29972i	0.760056	+	0.649858i	$0.225172\pi$
$359$			24.6261i			1.29972i	−0.760056	+	0.649858i	$0.774828\pi$
$360$	−11.4333	+	1.81919i	−0.602587	+	0.0958797i
$361$	−1.15211			−0.0606373
$362$	11.6943	+	20.2550i	0.614636	+	1.06458i
$363$	0.911917	+	0.168678i	0.0478632	+	0.00885332i
$364$	−18.0868	+	39.1174i	−0.948008	+	2.05031i
$365$	9.08087	+	5.24284i	0.475314	+	0.274423i
$366$	12.6586	+	2.34147i	0.661673	+	0.122391i
$367$	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	$0.286582\pi$
$368$			0.958511i			0.0499658i
$369$	−3.50371	−	22.0202i	−0.182396	−	1.14633i
$370$		−	0.780736i		−	0.0405885i
$371$	10.6934	+	15.1670i	0.555173	+	0.787432i
$372$	−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	$0.135852\pi$
$374$	4.01816	−	6.95966i	0.207774	−	0.359876i
$375$	−6.59329	−	18.5979i	−0.340476	−	0.960390i
$376$	−9.83498	+	5.67823i	−0.507200	+	0.292832i
$377$	−6.08012			−0.313142
$378$	−26.0220	+	17.3851i	−1.33843	+	0.894194i
$379$	−30.4419			−1.56369			−0.781847	−	0.623470i	$-0.785722\pi$
$379$	−30.4419			−1.56369			−0.781847	+	0.623470i	$0.785722\pi$
$380$	17.7427	−	10.2437i	0.910181	−	0.525493i
$381$	−3.56989	−	10.0697i	−0.182891	−	0.515886i
$382$	−25.8594	+	44.7897i	−1.32308	+	2.29164i
$383$	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
$385$	−7.07356	−	10.0328i	−0.360502	−	0.511319i
$386$		−	38.4071i		−	1.95487i
$387$	21.4218	+	8.20557i	1.08893	+	0.417113i
$388$			9.90962i			0.503085i
$389$	9.43310	−	5.44621i	0.478277	−	0.276134i	−0.241421	−	0.970420i	$-0.577613\pi$
$389$	9.43310	−	5.44621i	0.478277	−	0.276134i	0.719698	+	0.694287i	$0.244280\pi$
$390$	−28.4668	−	5.26554i	−1.44147	−	0.266631i
$391$	−3.78840	−	2.18724i	−0.191588	−	0.110613i
$392$	17.7394	+	6.32687i	0.895977	+	0.319555i
$393$	14.0728	+	2.60306i	0.709878	+	0.131307i
$394$	−10.1803	−	17.6328i	−0.512877	−	0.888328i
$395$	−5.24976			−0.264144
$396$	19.4503	+	23.9843i	0.977417	+	1.20526i
$397$			22.3035i			1.11938i	0.828702	+	0.559690i	$0.189080\pi$
$397$			22.3035i			1.11938i	−0.828702	+	0.559690i	$0.810920\pi$
$398$	6.58477	+	11.4052i	0.330065	+	0.571689i
$399$	11.8858	−	16.7905i	0.595034	−	0.840578i
$400$	−0.351848	+	0.609419i	−0.0175924	+	0.0304710i
$401$	20.8554	+	12.0409i	1.04147	+	0.601293i	0.920249	−	0.391333i	$-0.127986\pi$
$401$	20.8554	+	12.0409i	1.04147	+	0.601293i	0.121221	+	0.992626i	$0.461319\pi$
$402$	−2.45340	+	0.869775i	−0.122364	+	0.0433804i
$403$	−9.58414	−	16.6002i	−0.477420	−	0.826915i
$404$	−22.5581			−1.12231
$405$	−9.60522	−	8.62388i	−0.477287	−	0.428524i
$406$	0.646517	+	7.12403i	0.0320861	+	0.353560i
$407$	−0.669905	+	0.386770i	−0.0332060	+	0.0191715i
$408$	−4.79342	+	1.69936i	−0.237310	+	0.0841308i
$409$	−22.8191	−	13.1746i	−1.12833	−	0.651443i	−0.184817	−	0.982773i	$-0.559169\pi$
$409$	−22.8191	−	13.1746i	−1.12833	−	0.651443i	−0.943515	+	0.331330i	$0.892503\pi$
$410$	−21.0156	−	12.1334i	−1.03789	−	0.599224i
$411$	13.6332	+	11.6355i	0.672476	+	0.573935i
$412$	−4.69430	+	2.71026i	−0.231272	+	0.133525i
$413$	−2.26464	−	24.9543i	−0.111436	−	1.22792i
$414$	21.2616	−	17.2423i	1.04495	−	0.847414i
$415$	15.6408			0.767775
$416$	15.1668	+	26.2696i	0.743611	+	1.28797i
$417$	−5.62352	+	30.4021i	−0.275385	+	1.48880i
$418$	−28.6285	−	16.5286i	−1.40026	−	0.808443i
$419$	16.1761	−	28.0178i	0.790252	−	1.36876i	−0.135558	−	0.990769i	$-0.543283\pi$
$419$	16.1761	−	28.0178i	0.790252	−	1.36876i	0.925811	−	0.377988i	$-0.123384\pi$
$420$	−1.92972	+	20.8248i	−0.0941607	+	1.01615i
$421$	−5.54746	−	9.60849i	−0.270367	−	0.468289i	0.698589	−	0.715523i	$-0.253812\pi$
$421$	−5.54746	−	9.60849i	−0.270367	−	0.468289i	−0.968956	+	0.247234i	$0.920478\pi$
$422$		−	58.9363i		−	2.86898i
$423$	−11.8247	−	4.52945i	−0.574938	−	0.220229i
$424$	−18.8720			−0.916504
$425$	−1.60577	−	2.78128i	−0.0778914	−	0.134912i
$426$	−9.78651	+	11.4668i	−0.474158	+	0.555568i
$427$	3.62537	−	7.84079i	0.175444	−	0.379443i
$428$	−13.6014	−	7.85276i	−0.657447	−	0.379577i
$429$	9.58414	+	27.0342i	0.462726	+	1.30522i
$430$	21.6210	−	12.4829i	1.04266	−	0.601980i
$431$			16.3047i			0.785368i	0.919673	+	0.392684i	$0.128453\pi$
$431$			16.3047i			0.785368i	−0.919673	+	0.392684i	$0.871547\pi$
$432$	−0.0312007	+	1.24213i	−0.00150114	+	0.0597620i
$433$			12.5359i			0.602438i	0.953555	+	0.301219i	$0.0973936\pi$
$433$			12.5359i			0.602438i	−0.953555	+	0.301219i	$0.902606\pi$
$434$	−18.4312	+	12.9948i	−0.884728	+	0.623771i
$435$	−2.78100	+	0.985915i	−0.133339	+	0.0472710i
$436$	12.9480	−	22.4266i	0.620098	−	1.07404i
$437$	−8.99716	+	15.5835i	−0.430393	+	0.745462i
$438$	−18.7125	+	21.9253i	−0.894116	+	1.04763i
$439$	16.1276	−	9.31127i	0.769728	−	0.444403i	−0.0630496	−	0.998010i	$-0.520083\pi$
$439$	16.1276	−	9.31127i	0.769728	−	0.444403i	0.832778	+	0.553608i	$0.186749\pi$
$440$	12.4836			0.595132
$441$	6.97942	+	19.8063i	0.332354	+	0.943155i
$442$	−12.7174			−0.604904
$443$	4.11436	−	2.37543i	0.195479	−	0.112860i	−0.399066	−	0.916922i	$-0.630666\pi$
$443$	4.11436	−	2.37543i	0.195479	−	0.112860i	0.594545	+	0.804062i	$0.297332\pi$
$444$	1.29589	+	0.239703i	0.0615004	+	0.0113758i
$445$	−9.81875	+	17.0066i	−0.465453	+	0.806189i
$446$	20.3484	−	35.2445i	0.963527	−	1.66888i
$447$	−5.52053	+	29.8453i	−0.261112	+	1.41163i
$448$	28.1330	−	19.8350i	1.32916	−	0.937115i
$449$			16.2393i			0.766379i	0.923670	+	0.383189i	$0.125174\pi$
$449$			16.2393i			0.766379i	−0.923670	+	0.383189i	$0.874826\pi$
$450$	19.8473	−	3.15798i	0.935612	−	0.148868i
$451$			24.0431i			1.13214i
$452$	−10.8090	+	6.24060i	−0.508414	+	0.293533i
$453$	−1.23762	+	1.45011i	−0.0581485	+	0.0681322i
$454$	−21.6210	−	12.4829i	−1.01473	−	0.585852i
$455$	−8.15279	+	17.6325i	−0.382209	+	0.826625i
$456$	6.99028	+	19.7177i	0.327350	+	0.923365i
$457$	2.87360	+	4.97722i	0.134421	+	0.232825i	0.925376	−	0.379050i	$-0.123749\pi$
$457$	2.87360	+	4.97722i	0.134421	+	0.232825i	−0.790955	+	0.611874i	$0.790416\pi$
$458$	−44.2514			−2.06773
$459$	−4.83818	−	2.95774i	−0.225827	−	0.138056i
$460$		−	18.2938i		−	0.852953i
$461$	−18.1346	−	31.4101i	−0.844613	−	1.46291i	−0.885957	−	0.463768i	$-0.846497\pi$
$461$	−18.1346	−	31.4101i	−0.844613	−	1.46291i	0.0413440	−	0.999145i	$-0.486836\pi$
$462$	30.6567	−	14.1043i	1.42628	−	0.656191i
$463$	14.6202	−	25.3230i	0.679461	−	1.17686i	−0.295683	−	0.955286i	$-0.595547\pi$
$463$	14.6202	−	25.3230i	0.679461	−	1.17686i	0.975144	−	0.221574i	$-0.0711195\pi$
$464$	0.245960	+	0.142005i	0.0114184	+	0.00659241i
$465$	−7.07549	−	6.03869i	−0.328118	−	0.280038i
$466$	3.34665	+	5.79656i	0.155030	+	0.268521i
$467$	−2.64215			−0.122264			−0.0611320	−	0.998130i	$-0.519471\pi$
$467$	−2.64215			−0.122264			−0.0611320	+	0.998130i	$0.519471\pi$
$468$	17.4799	−	45.6336i	0.808007	−	2.10941i
$469$	0.157867	+	1.73955i	0.00728961	+	0.0803249i
$470$	−11.9347	+	6.89053i	−0.550508	+	0.317836i
$471$	3.07442	−	16.6211i	0.141662	−	0.765858i
$472$	22.0674	+	12.7406i	1.01574	+	0.586435i
$473$	−21.4218	−	12.3679i	−0.984973	−	0.568675i
$474$	2.62488	−	14.1907i	0.120565	−	0.651803i
$475$	−11.4408	+	6.60532i	−0.524938	+	0.303073i
$476$	0.830357	+	9.14978i	0.0380593	+	0.419380i
$477$	−13.2540	−	16.3436i	−0.606861	−	0.748322i
$478$	28.1923			1.28949
$479$	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	$0.581991\pi$
$480$	11.1969	+	9.55614i	0.511064	+	0.436176i
$481$	1.06012	+	0.612058i	0.0483371	+	0.0279074i
$482$	15.3694	−	26.6207i	0.700059	−	1.21254i
$483$	−7.67749	−	16.6876i	−0.349338	−	0.759311i
$484$	0.851848	+	1.47544i	0.0387204	+	0.0670657i
$485$			4.46684i			0.202829i
$486$	28.1140	−	21.6521i	1.27528	−	0.982161i
$487$	34.8720			1.58020			0.790100	−	0.612978i	$-0.210029\pi$
$487$	34.8720			1.58020			0.790100	+	0.612978i	$0.210029\pi$
$488$	4.39234	+	7.60775i	0.198832	+	0.344387i
$489$	4.18174	+	11.7955i	0.189105	+	0.533412i
$490$	21.5268	+	7.67765i	0.972482	+	0.346841i
$491$	−22.6758	−	13.0919i	−1.02334	−	0.590828i	−0.108273	−	0.994121i	$-0.534532\pi$
$491$	−22.6758	−	13.0919i	−1.02334	−	0.590828i	−0.915071	+	0.403293i	$0.867866\pi$
$492$	26.5917	−	31.1573i	1.19884	−	1.40468i
$493$	−1.12252	+	0.648085i	−0.0505556	+	0.0291883i
$494$			52.3127i			2.35366i
$495$	8.76740	+	10.8111i	0.394065	+	0.485924i
$496$			0.895374i			0.0402035i
$497$	5.82906	+	8.26767i	0.261469	+	0.370856i
$498$	−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	$0.256770\pi$
$500$	18.1248	−	31.3931i	0.810566	−	1.40394i
$501$	−29.4789	−	5.45276i	−1.31702	−	0.243611i
$502$	14.8140	−	8.55285i	0.661180	−	0.381733i
$503$	37.8479			1.68756			0.843778	−	0.536693i	$-0.180327\pi$
$503$	37.8479			1.68756			0.843778	+	0.536693i	$0.180327\pi$
$504$	−20.5515	−	5.80533i	−0.915435	−	0.258590i
$505$	−10.1683			−0.452482
$506$	−25.5631	+	14.7588i	−1.13642	+	0.656111i
$507$	14.8490	−	17.3984i	0.659466	−	0.772691i
$508$	9.81354	−	16.9976i	0.435406	−	0.754145i
$509$	−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
$511$	11.1456	+	15.8083i	0.493050	+	0.699320i
$512$		−	2.70367i		−	0.119486i
$513$	−12.1666	+	19.9018i	−0.537170	+	0.878684i
$514$		−	17.6551i		−	0.778734i
$515$	−2.11599	+	1.22167i	−0.0932419	+	0.0538332i
$516$	14.0815	+	39.7199i	0.619902	+	1.74857i
$517$	11.8247	+	6.82701i	0.520051	+	0.300252i
$518$	0.604419	−	1.30721i	0.0265566	−	0.0574356i
$519$	−2.19957	+	2.57723i	−0.0965506	+	0.113128i
$520$	−9.87756	−	17.1084i	−0.433160	−	0.750255i
$521$	2.31879			0.101588			0.0507940	−	0.998709i	$-0.483825\pi$
$521$	2.31879			0.101588			0.0507940	+	0.998709i	$0.483825\pi$
$522$	−1.27455	−	8.01033i	−0.0557855	−	0.350602i
$523$		−	20.1840i		−	0.882585i	−0.897363	−	0.441293i	$-0.854520\pi$
$523$		−	20.1840i		−	0.882585i	0.897363	−	0.441293i	$-0.145480\pi$
$524$	13.1458	+	22.7692i	0.574277	+	0.994677i
$525$	1.24431	−	13.4282i	0.0543062	−	0.586053i
$526$	15.9194	−	27.5733i	0.694120	−	1.20225i
$527$	−3.53886	−	2.04316i	−0.154155	−	0.0890015i
$528$	0.243693	−	1.31746i	0.0106054	−	0.0573352i
$529$	−3.46621	−	6.00365i	−0.150705	−	0.261028i
$530$	−22.9011			−0.994761
$531$	4.46454	+	28.0589i	0.193745	+	1.21765i
$532$	37.6375	−	3.41566i	1.63179	−	0.148088i
$533$	32.9503	−	19.0239i	1.42724	−	0.824016i
$534$	−41.0614	−	35.0445i	−1.77690	−	1.51653i
$535$	−6.13093	−	3.53970i	−0.265063	−	0.153034i
$536$	−1.53831	−	0.888141i	−0.0664447	−	0.0383618i
$537$	−37.8768	+	13.4280i	−1.63450	+	0.579462i
$538$	−50.9256	+	29.4019i	−2.19556	+	1.26761i
$539$	−4.07644	−	22.2744i	−0.175585	−	0.959424i
$540$	0.595485	−	23.7068i	0.0256256	−	1.02018i
$541$	−22.7713			−0.979014			−0.489507	−	0.871999i	$-0.662823\pi$
$541$	−22.7713			−0.979014			−0.489507	+	0.871999i	$0.662823\pi$
$542$	−18.9552	−	32.8313i	−0.814194	−	1.41023i
$543$	−16.7729	+	5.94631i	−0.719795	+	0.255181i
$544$	5.60020	+	3.23327i	0.240106	+	0.138626i
$545$	5.83643	−	10.1090i	0.250005	−	0.433022i
$546$	−43.5864	−	30.8542i	−1.86533	−	1.32044i
$547$	14.7918	+	25.6201i	0.632451	+	1.09544i	0.987049	+	0.160419i	$0.0512845\pi$
$547$	14.7918	+	25.6201i	0.632451	+	1.09544i	−0.354598	+	0.935019i	$0.615382\pi$
$548$			32.9270i			1.40657i
$549$	−3.50371	+	9.14690i	−0.149535	+	0.390380i
$550$	−21.6706			−0.924037
$551$	2.66589	+	4.61745i	0.113571	+	0.196710i
$552$	18.3685	+	3.39765i	0.781815	+	0.144613i
$553$	−8.78984	−	4.06418i	−0.373782	−	0.172827i
$554$	61.9196	+	35.7493i	2.63071	+	1.51884i
$555$	0.584135	+	0.108048i	0.0247952	+	0.00458639i
$556$	−49.1894	+	28.3995i	−2.08609	+	1.20441i
$557$		−	4.71407i		−	0.199741i	−0.995000	−	0.0998707i	$-0.968157\pi$
$557$		−	4.71407i		−	0.199741i	0.995000	−	0.0998707i	$-0.0318429\pi$
$558$	19.8611	−	16.1066i	0.840786	−	0.681845i
$559$			39.1439i			1.65561i
$560$	0.741624	−	0.522877i	0.0313393	−	0.0220956i
$561$	4.65103	+	3.96950i	0.196367	+	0.167592i
$562$	−10.6517	+	18.4493i	−0.449316	+	0.778238i
$563$	−13.6742	+	23.6844i	−0.576299	+	0.998179i	0.419601	+	0.907709i	$0.362170\pi$
$563$	−13.6742	+	23.6844i	−0.576299	+	0.998179i	−0.995899	+	0.0904697i	$0.971163\pi$
$564$	−7.77292	−	21.9253i	−0.327299	−	0.923220i
$565$	−4.87226	+	2.81300i	−0.204977	+	0.118344i
$566$	−35.9066			−1.50927
$567$	−9.40602	−	21.8753i	−0.395016	−	0.918674i
$568$	−10.2873			−0.431645
$569$	20.4018	−	11.7790i	0.855288	−	0.493801i	−0.00714355	−	0.999974i	$-0.502274\pi$
$569$	20.4018	−	11.7790i	0.855288	−	0.493801i	0.862432	+	0.506174i	$0.168941\pi$
$570$	8.48270	+	23.9274i	0.355301	+	1.00221i
$571$	−9.59385	+	16.6170i	−0.401490	+	0.695401i	−0.993906	−	0.110231i	$-0.964841\pi$
$571$	−9.59385	+	16.6170i	−0.401490	+	0.695401i	0.592416	+	0.805632i	$0.298174\pi$
$572$	−26.3465	+	45.6336i	−1.10160	+	1.90804i
$573$	−29.9323	−	25.5462i	−1.25044	−	1.06721i
$574$	−25.7939	−	36.5848i	−1.07661	−	1.52702i
$575$			11.7961i			0.491932i
$576$	−30.3155	+	24.5847i	−1.26314	+	1.02436i
$577$		−	2.23413i		−	0.0930079i	−0.998918	−	0.0465039i	$-0.985192\pi$
$577$		−	2.23413i		−	0.0930079i	0.998918	−	0.0465039i	$-0.0148080\pi$
$578$	31.1661	−	17.9937i	1.29634	−	0.748441i
$579$	28.7357	+	5.31527i	1.19421	+	0.220895i
$580$	−4.69430	−	2.71026i	−0.194920	−	0.112537i
$581$	26.1878	+	12.1085i	1.08645	+	0.502346i
$582$	−12.0744	−	2.23342i	−0.500501	−	0.0925783i
$583$	11.3450	+	19.6501i	0.469862	+	0.813826i
$584$	−19.6700			−0.813949
$585$	7.87919	−	20.5697i	0.325765	−	0.850453i
$586$		−	56.5849i		−	2.33750i
$587$	−12.9883	−	22.4963i	−0.536083	−	0.928522i	−0.999110	−	0.0421784i	$-0.986570\pi$
$587$	−12.9883	−	22.4963i	−0.536083	−	0.928522i	0.463028	−	0.886344i	$-0.346763\pi$
$588$	−19.3528	+	33.3738i	−0.798098	+	1.37631i
$589$	−8.40451	+	14.5570i	−0.346302	+	0.599813i
$590$	26.7788	+	15.4608i	1.10247	+	0.636509i
$591$	14.6015	−	5.17650i	0.600625	−	0.212933i
$592$	−0.0285900	−	0.0495193i	−0.00117504	−	0.00203523i
$593$	5.71754			0.234791			0.117396	−	0.993085i	$-0.462545\pi$
$593$	5.71754			0.234791			0.117396	+	0.993085i	$0.462545\pi$
$594$	−33.6075	+	18.2938i	−1.37893	+	0.750604i
$595$	0.374290	+	4.12434i	0.0153444	+	0.169081i
$596$	−48.2885	+	27.8794i	−1.97797	+	1.14198i
$597$	−9.44445	+	3.34824i	−0.386536	+	0.137034i
$598$	40.4532	+	23.3557i	1.65425	+	0.955084i
$599$	21.8662	+	12.6245i	0.893429	+	0.515822i	0.875063	−	0.484010i	$-0.160820\pi$
$599$	21.8662	+	12.6245i	0.893429	+	0.515822i	0.0183665	+	0.999831i	$0.494153\pi$
$600$	10.4314	+	8.90289i	0.425862	+	0.363459i
$601$	40.2546	−	23.2410i	1.64202	−	0.948021i	0.661907	−	0.749586i	$-0.269748\pi$
$601$	40.2546	−	23.2410i	1.64202	−	0.948021i	0.980114	−	0.198435i	$-0.0635858\pi$
$602$	45.8646	−	4.16229i	1.86930	−	0.169642i
$603$	−0.311220	−	1.95596i	−0.0126739	−	0.0796530i
$604$	−3.50232			−0.142508
$605$	0.383978	+	0.665069i	0.0156109	+	0.0270389i
$606$	5.08414	−	27.4861i	0.206529	−	1.11655i
$607$	−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
$609$	−5.41957	−	0.502201i	−0.219612	−	0.0203502i
$610$	5.33009	+	9.23200i	0.215809	+	0.373793i
$611$		−	21.6073i		−	0.874138i
$612$	−1.63697	−	10.2881i	−0.0661707	−	0.415872i
$613$	6.54256			0.264252			0.132126	−	0.991233i	$-0.457820\pi$
$613$	6.54256			0.264252			0.132126	+	0.991233i	$0.457820\pi$
$614$	21.4980	+	37.2357i	0.867590	+	1.50271i
$615$	11.9864	−	14.0444i	0.483339	−	0.566324i
$616$	20.9017	+	9.66437i	0.842153	+	0.389388i
$617$	−30.0043	−	17.3230i	−1.20793	−	0.697396i	−0.245620	−	0.969366i	$-0.578992\pi$
$617$	−30.0043	−	17.3230i	−1.20793	−	0.697396i	−0.962306	+	0.271970i	$0.912325\pi$
$618$	−2.24433	−	6.33063i	−0.0902800	−	0.254655i
$619$	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	$0.222469\pi$
$620$		−	17.0888i		−	0.686302i
$621$	9.95800	+	18.2938i	0.399601	+	0.734105i
$622$		−	18.1071i		−	0.726029i
$623$	−29.6057	+	20.8733i	−1.18613	+	0.836271i
$624$	−1.99837	+	0.708458i	−0.0799986	+	0.0283610i
$625$	0.812855	−	1.40791i	0.0325142	−	0.0563162i
$626$	12.6724	−	21.9492i	0.506489	−	0.877265i
$627$	16.3285	−	19.1319i	0.652096	−	0.764056i
$628$	26.8922	−	15.5262i	1.07312	−	0.619564i
$629$	0.260959			0.0104051
$630$	−24.9392	−	7.04476i	−0.993601	−	0.280670i
$631$	26.2438			1.04475			0.522374	−	0.852716i	$-0.325047\pi$
$631$	26.2438			1.04475			0.522374	+	0.852716i	$0.325047\pi$
$632$	8.52859	−	4.92398i	0.339249	−	0.195866i
$633$	44.0953	+	8.15637i	1.75263	+	0.324186i
$634$	26.4669	−	45.8420i	1.05113	−	1.82062i
$635$	4.42354	−	7.66179i	0.175543	−	0.304049i
$636$	7.03115	−	38.0121i	0.278803	−	1.50728i
$637$	−27.3009	+	23.2111i	−1.08170	+	0.919656i
$638$			8.74619i			0.346265i
$639$	−7.22489	−	8.90904i	−0.285812	−	0.352436i
$640$			25.4813i			1.00724i
$641$	16.5092	−	9.53157i	0.652073	−	0.376474i	−0.137177	−	0.990547i	$-0.543803\pi$
$641$	16.5092	−	9.53157i	0.652073	−	0.376474i	0.789250	+	0.614072i	$0.210470\pi$
$642$	12.6337	−	14.8028i	0.498612	−	0.584220i
$643$	15.3447	+	8.85928i	0.605136	+	0.349376i	0.771060	−	0.636763i	$-0.219727\pi$
$643$	15.3447	+	8.85928i	0.605136	+	0.349376i	−0.165923	+	0.986139i	$0.553060\pi$
$644$	14.1624	−	30.6299i	0.558077	−	1.20699i
$645$	6.34733	+	17.9041i	0.249926	+	0.704973i
$646$	5.57605	+	9.65801i	0.219387	+	0.379989i
$647$	−21.7902			−0.856661			−0.428330	−	0.903622i	$-0.640898\pi$
$647$	−21.7902			−0.856661			−0.428330	+	0.903622i	$0.640898\pi$
$648$	23.6930	+	5.00091i	0.930750	+	0.196454i
$649$		−	30.6365i		−	1.20259i
$650$	17.1467	+	29.6990i	0.672549	+	1.16489i
$651$	−7.17177	−	15.5884i	−0.281084	−	0.610956i
$652$	−11.4955	+	19.9108i	−0.450198	+	0.779766i
$653$	−13.0852	−	7.55475i	−0.512064	−	0.295640i	0.221618	−	0.975134i	$-0.428866\pi$
$653$	−13.0852	−	7.55475i	−0.512064	−	0.295640i	−0.733682	+	0.679493i	$0.762200\pi$
$654$	24.4076	+	20.8311i	0.954413	+	0.814559i
$655$	5.92558	+	10.2634i	0.231532	+	0.401024i
$656$	−1.77726			−0.0693903
$657$	−13.8145	−	17.0347i	−0.538954	−	0.664586i
$658$	−25.3171	+	2.29757i	−0.986964	+	0.0895685i
$659$	−27.1850	+	15.6952i	−1.05898	+	0.611400i	−0.925149	−	0.379605i	$-0.876060\pi$
$659$	−27.1850	+	15.6952i	−1.05898	+	0.611400i	−0.133827	+	0.991005i	$0.542727\pi$
$660$	−4.65103	+	25.1446i	−0.181041	+	0.978752i
$661$	−37.8554	−	21.8558i	−1.47240	−	0.850093i	−0.472885	−	0.881124i	$-0.656787\pi$
$661$	−37.8554	−	21.8558i	−1.47240	−	0.850093i	−0.999518	+	0.0310314i	$0.990121\pi$
$662$	−37.7707	−	21.8069i	−1.46800	−	0.847551i
$663$	1.75999	−	9.51495i	0.0683524	−	0.369530i
$664$	−25.4095	+	14.6702i	−0.986078	+	0.569312i
$665$	16.9654	−	1.53964i	0.657890	−	0.0597046i
$666$	−0.584135	+	1.52496i	−0.0226348	+	0.0590912i
$667$	4.76088			0.184342
$668$	−27.5371	−	47.6957i	−1.06544	−	1.84540i
$669$	23.5534	+	20.1020i	0.910625	+	0.777188i
$670$	−1.86673	−	1.07776i	−0.0721181	−	0.0416374i
$671$	5.28096	−	9.14690i	0.203869	−	0.353112i
$672$	11.3492	+	24.6684i	0.437806	+	0.951603i
$673$	−4.60589	−	7.97763i	−0.177544	−	0.307515i	0.763495	−	0.645814i	$-0.223482\pi$
$673$	−4.60589	−	7.97763i	−0.177544	−	0.307515i	−0.941039	+	0.338299i	$0.890149\pi$
$674$			65.0051i			2.50390i
$675$	−0.383978	+	15.2865i	−0.0147793	+	0.588378i
$676$	42.0208			1.61618
$677$	−11.4194	−	19.7789i	−0.438882	−	0.760165i	0.558722	−	0.829355i	$-0.311292\pi$
$677$	−11.4194	−	19.7789i	−0.438882	−	0.760165i	−0.997604	+	0.0691899i	$0.977959\pi$
$678$	−5.16775	−	14.5768i	−0.198466	−	0.559819i
$679$	−3.45807	+	7.47898i	−0.132709	+	0.287017i
$680$	−3.64721	−	2.10571i	−0.139864	−	0.0807505i
$681$	12.3317	−	14.4490i	0.472553	−	0.553687i
$682$	−23.8792	+	13.7867i	−0.914383	+	0.527919i
$683$		−	34.1826i		−	1.30796i	−0.756511	−	0.653981i	$-0.773098\pi$
$683$		−	34.1826i		−	1.30796i	0.756511	−	0.653981i	$-0.226902\pi$
$684$	−42.3199	+	6.73367i	−1.61814	+	0.257468i
$685$			14.8421i			0.567088i
$686$	30.0992	+	29.5202i	1.14919	+	1.12709i
$687$	6.12408	−	33.1082i	0.233648	−	1.26316i
$688$	0.914230	−	1.58349i	0.0348547	−	0.0603701i
$689$	17.9533	−	31.0961i	0.683967	−	1.18467i
$690$	22.2902	+	4.12304i	0.848572	+	0.156961i
$691$	−0.224082	+	0.129374i	−0.00852446	+	0.00492160i	−0.504256	−	0.863554i	$-0.668233\pi$
$691$	−0.224082	+	0.129374i	−0.00852446	+	0.00492160i	0.495732	+	0.868476i	$0.334900\pi$
$692$	−6.22453			−0.236621
$693$	6.30995	+	24.8888i	0.239695	+	0.945448i
$694$	−6.74720			−0.256120
$695$	−22.1725	+	12.8013i	−0.841052	+	0.485582i
$696$	3.59318	−	4.21010i	0.136199	−	0.159583i
$697$	4.05555	−	7.02441i	0.153615	−	0.266069i
$698$	−30.7389	+	53.2413i	−1.16348	+	2.01521i
$699$	−4.80005	+	1.70171i	−0.181555	+	0.0643645i
$700$	20.2480	−	14.2757i	0.765302	−	0.539571i
$701$		−	5.16189i		−	0.194962i	−0.995237	−	0.0974810i	$-0.968921\pi$
$701$		−	5.16189i		−	0.194962i	0.995237	−	0.0974810i	$-0.0310785\pi$
$702$	51.6628	+	31.5833i	1.94989	+	1.19203i
$703$		−	1.07345i		−	0.0404860i
$704$	36.4487	−	21.0437i	1.37371	−	0.793113i
$705$	−3.50371	−	9.88299i	−0.131957	−	0.372215i
$706$	58.4475	+	33.7447i	2.19970	+	1.27000i
$707$	−17.0251	−	7.87192i	−0.640293	−	0.296054i
$708$	−33.8840	+	39.7016i	−1.27344	+	1.49208i
$709$	−11.7472	−	20.3468i	−0.441175	−	0.764138i	0.556602	−	0.830780i	$-0.312105\pi$
$709$	−11.7472	−	20.3468i	−0.441175	−	0.764138i	−0.997777	+	0.0666412i	$0.978772\pi$
$710$	−12.4836			−0.468501
$711$	10.2540	+	3.92779i	0.384557	+	0.147304i
$712$		−	36.8377i		−	1.38055i
$713$	7.50460	+	12.9984i	0.281050	+	0.486792i
$714$	−11.3357	−	1.05042i	−0.424229	−	0.0393109i
$715$	−11.8759	+	20.5697i	−0.444134	+	0.769263i
$716$	−63.9357	−	36.9133i	−2.38939	−	1.37952i
$717$	−3.90162	+	21.0931i	−0.145709	+	0.787736i
$718$	−28.0293	−	48.5481i	−1.04604	−	1.81180i
$719$	−10.1566			−0.378776			−0.189388	−	0.981902i	$-0.560650\pi$
$719$	−10.1566			−0.378776			−0.189388	+	0.981902i	$0.560650\pi$
$720$	−0.799156	+	0.648085i	−0.0297828	+	0.0241527i
$721$	−4.48865	+	0.407352i	−0.167166	+	0.0151706i
$722$	2.27128	−	1.31132i	0.0845283	−	0.0488024i
$723$	17.7902	+	15.1833i	0.661623	+	0.564673i
$724$	−28.3126	−	16.3463i	−1.05223	−	0.607504i
$725$	3.02696	+	1.74761i	0.112418	+	0.0649047i
$726$	−1.98975	+	0.705404i	−0.0738466	+	0.0261800i
$727$	−5.74874	+	3.31904i	−0.213209	+	0.123096i	−0.602802	−	0.797891i	$-0.705949\pi$
$727$	−5.74874	+	3.31904i	−0.213209	+	0.123096i	0.389593	+	0.920987i	$0.372616\pi$
$728$	−3.29356	−	36.2920i	−0.122067	−	1.34507i
$729$	12.3090	+	24.0310i	0.455890	+	0.890036i
$730$	−23.8695			−0.883449
$731$	4.17238	+	7.22678i	0.154321	+	0.267292i
$732$	−16.9601	+	6.01266i	−0.626862	+	0.222234i
$733$	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
$735$	−8.72346	+	15.0435i	−0.321770	+	0.554888i
$736$	−11.8759	−	20.5697i	−0.437752	−	0.758209i
$737$			2.13565i			0.0786676i
$738$	31.9705	+	39.4229i	1.17685	+	1.45118i
$739$	−15.6386			−0.575275			−0.287638	−	0.957739i	$-0.592870\pi$
$739$	−15.6386			−0.575275			−0.287638	+	0.957739i	$0.592870\pi$
$740$	0.545658	+	0.945107i	0.0200588	+	0.0347428i
$741$	−39.1396	−	7.23970i	−1.43783	−	0.265957i
$742$	−38.3441	−	17.7292i	−1.40765	−	0.650861i
$743$	27.3807	+	15.8083i	1.00450	+	0.579949i	0.909577	−	0.415535i	$-0.136406\pi$
$743$	27.3807	+	15.8083i	1.00450	+	0.579949i	0.0949246	+	0.995484i	$0.469739\pi$
$744$	17.1586	+	3.17384i	0.629063	+	0.116359i
$745$	−21.7664	+	12.5669i	−0.797461	+	0.460414i
$746$			8.49897i			0.311169i
$747$	−30.5501	−	11.7022i	−1.11777	−	0.428160i
$748$			11.2332i			0.410727i
$749$	−7.52490	−	10.6730i	−0.274954	−	0.389982i
$750$	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	$0.0828038\pi$
$752$	−0.504652	+	0.874082i	−0.0184028	+	0.0318745i
$753$	4.34897	+	12.2673i	0.158485	+	0.447043i
$754$	11.9864	−	6.92036i	0.436519	−	0.252025i
$755$	−1.57870			−0.0574548
$756$	19.3500	−	39.2321i	0.703754	−	1.42686i
$757$	−10.8227			−0.393358			−0.196679	−	0.980468i	$-0.563016\pi$
$757$	−10.8227			−0.393358			−0.196679	+	0.980468i	$0.563016\pi$
$758$	60.0134	−	34.6488i	2.17979	−	1.25850i
$759$	−7.50460	−	21.1684i	−0.272400	−	0.768365i
$760$	−8.66182	+	15.0027i	−0.314197	+	0.544206i
$761$	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
$763$	17.5981	−	12.4074i	0.637095	−	0.449180i
$764$		−	72.2926i		−	2.61546i
$765$	−0.737879	−	4.63744i	−0.0266781	−	0.167667i
$766$			38.6645i			1.39701i
$767$	−41.9865	+	24.2409i	−1.51604	+	0.875288i
$768$	−24.5614	−	4.54315i	−0.886282	−	0.163937i
$769$	27.5683	+	15.9166i	0.994140	+	0.573967i	0.906509	−	0.422186i	$-0.138737\pi$
$769$	27.5683	+	15.9166i	0.994140	+	0.573967i	0.0876307	+	0.996153i	$0.472070\pi$
$770$	25.3642	+	11.7277i	0.914061	+	0.422637i
$771$	13.2093	+	2.44334i	0.475721	+	0.0879947i
$772$	26.8428	+	46.4931i	0.966094	+	1.67332i
$773$	19.0382			0.684755			0.342378	−	0.939562i	$-0.388768\pi$
$773$	19.0382			0.684755			0.342378	+	0.939562i	$0.388768\pi$
$774$	−51.5706	+	8.20557i	−1.85367	+	0.294943i
$775$			11.0191i			0.395818i
$776$	−4.18965	−	7.25668i	−0.150400	−	0.260500i
$777$	0.894389	+	0.633125i	0.0320860	+	0.0227132i
$778$	−12.3977	+	21.4734i	−0.444478	+	0.769859i
$779$	−28.8948	−	16.6824i	−1.03526	−	0.597710i
$780$	38.1401	−	13.5214i	1.36563	−	0.484143i
$781$	6.18427	+	10.7115i	0.221290	+	0.383286i
$782$	9.95800			0.356097
$783$	6.16959	+	0.154972i	0.220483	+	0.00553826i
$784$	1.64652	−	0.301330i	0.0588042	−	0.0107618i
$785$	12.1219	−	6.99857i	0.432649	−	0.249790i
$786$	−30.7060	+	10.8859i	−1.09525	+	0.388286i
$787$	−16.4123	−	9.47564i	−0.585035	−	0.337770i	0.178097	−	0.984013i	$-0.443006\pi$
$787$	−16.4123	−	9.47564i	−0.585035	−	0.337770i	−0.763132	+	0.646243i	$0.776339\pi$
$788$	24.6472	+	14.2301i	0.878020	+	0.506925i
$789$	18.4268	+	15.7266i	0.656010	+	0.559883i
$790$	10.3494	−	5.97525i	0.368216	−	0.212590i
$791$	−10.3355	+	0.937963i	−0.367488	+	0.0333501i
$792$	−24.3834	−	9.34004i	−0.866428	−	0.331884i
$793$	−16.7141			−0.593535
$794$	−25.3857	−	43.9693i	−0.900905	−	1.56041i
$795$	3.16935	−	17.1343i	0.112405	−	0.607690i
$796$	−15.9422	−	9.20422i	−0.565055	−	0.326235i
$797$	−26.7207	+	46.2816i	−0.946497	+	1.63938i	−0.193770	+	0.981047i	$0.562071\pi$
$797$	−26.7207	+	46.2816i	−0.946497	+	1.63938i	−0.752727	+	0.658333i	$0.771262\pi$
$798$	−4.32088	+	46.6294i	−0.152958	+	1.65066i
$799$	−2.30314	−	3.98916i	−0.0814792	−	0.141126i
$800$		−	17.4376i		−	0.616511i
$801$	31.9024	−	25.8716i	1.12722	−	0.914129i
$802$	−54.8194			−1.93574
$803$	11.8247	+	20.4810i	0.417286	+	0.722760i
$804$	2.36203	−	2.76757i	0.0833024	−	0.0976048i
$805$	6.38383	−	13.8067i	0.225000	−	0.486621i
$806$	37.7885	+	21.8172i	1.33104	+	0.768479i
$807$	−14.9503	−	42.1708i	−0.526277	−	1.48448i
$808$	16.5190	−	9.53727i	0.581137	−	0.335520i
$809$			2.58095i			0.0907413i	0.998970	+	0.0453706i	$0.0144469\pi$
$809$			2.58095i			0.0907413i	−0.998970	+	0.0453706i	$0.985553\pi$
$810$	28.7515	+	6.06860i	1.01022	+	0.213229i
$811$		−	6.06938i		−	0.213125i	−0.994306	−	0.106562i	$-0.966016\pi$
$811$		−	6.06938i		−	0.213125i	0.994306	−	0.106562i	$-0.0339844\pi$
$812$	−5.76163	−	8.17203i	−0.202194	−	0.286782i
$813$	27.1871	−	9.63835i	0.953495	−	0.338032i
$814$	0.880438	−	1.52496i	0.0308593	−	0.0534500i
$815$	−5.18169	+	8.97494i	−0.181507	+	0.314379i
$816$	−0.293425	+	0.343803i	−0.0102719	+	0.0120355i
$817$	29.7272	−	17.1630i	1.04002	−	0.600458i
$818$	59.9811			2.09719
$819$	29.1167	−	28.3407i	1.01742	−	0.990304i
$820$	33.9201			1.18454
$821$	8.03938	−	4.64154i	0.280576	−	0.161991i	−0.353108	−	0.935583i	$-0.614875\pi$
$821$	8.03938	−	4.64154i	0.280576	−	0.161991i	0.633684	+	0.773592i	$0.281542\pi$
$822$	−40.1200	−	7.42106i	−1.39935	−	0.258839i
$823$	−9.03448	+	15.6482i	−0.314922	+	0.545461i	−0.979421	−	0.201828i	$-0.935312\pi$
$823$	−9.03448	+	15.6482i	−0.314922	+	0.545461i	0.664499	+	0.747289i	$0.268645\pi$
$824$	2.29172	−	3.96937i	0.0798357	−	0.138280i
$825$	2.99905	−	16.2136i	0.104414	−	0.564486i
$826$	32.8674	+	46.6176i	1.14360	+	1.62203i
$827$			48.5440i			1.68804i	0.536310	+	0.844021i	$0.319818\pi$
$827$			48.5440i			1.68804i	−0.536310	+	0.844021i	$0.680182\pi$
$828$	−13.6871	+	35.7321i	−0.475661	+	1.24178i
$829$			5.44792i			0.189214i	0.995515	+	0.0946071i	$0.0301595\pi$
$829$			5.44792i			0.189214i	−0.995515	+	0.0946071i	$0.969841\pi$
$830$	−30.8344	+	17.8022i	−1.07028	+	0.617924i
$831$	−35.3163	+	41.3798i	−1.22511	+	1.43545i
$832$	−57.6796	−	33.3013i	−1.99968	−	1.15452i
$833$	−2.56623	+	7.19527i	−0.0889147	+	0.249302i
$834$	−23.5172	−	66.3357i	−0.814335	−	2.29702i
$835$	−12.4126	−	21.4992i	−0.429556	−	0.744012i
$836$	46.2076			1.59812
$837$	9.30206	+	17.0888i	0.321526	+	0.590675i
$838$			73.6460i			2.54406i
$839$	−24.2673	−	42.0322i	−0.837801	−	1.45111i	−0.891729	−	0.452569i	$-0.850508\pi$
$839$	−24.2673	−	42.0322i	−0.837801	−	1.45111i	0.0539281	−	0.998545i	$-0.482826\pi$
$840$	−7.39134	−	16.0656i	−0.255025	−	0.554316i
$841$	−13.7947	+	23.8931i	−0.475678	+	0.823899i
$842$	21.8727	+	12.6282i	0.753781	+	0.435196i
$843$	−12.3294	−	10.5227i	−0.424646	−	0.362421i
$844$	41.1907	+	71.3444i	1.41784	+	2.45578i
$845$	18.9412			0.651598
$846$	28.4668	−	4.52945i	0.978708	−	0.155726i
$847$	0.128033	+	1.41081i	0.00439926	+	0.0484759i
$848$	−1.45254	+	0.838622i	−0.0498803	+	0.0287984i
$849$	4.96922	−	26.8648i	0.170543	−	0.921998i
$850$	6.33127	+	3.65536i	0.217161	+	0.125378i
$851$	−0.830095	−	0.479256i	−0.0284553	−	0.0164287i
$852$	3.83274	−	20.7207i	0.131308	−	0.709881i
$853$	−10.7703	+	6.21823i	−0.368768	+	0.212908i	−0.672920	−	0.739715i	$-0.734960\pi$
$853$	−10.7703	+	6.21823i	−0.368768	+	0.212908i	0.304152	+	0.952623i	$0.401627\pi$
$854$	1.77726	+	19.5838i	0.0608165	+	0.670144i
$855$	−19.0761	+	3.03526i	−0.652387	+	0.103804i
$856$	13.2801			0.453906
$857$	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	$0.775488\pi$
$858$	−49.6644	−	42.3869i	−1.69552	−	1.44707i
$859$	−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
$861$	30.9419	−	14.2355i	1.05450	−	0.485145i
$862$	−18.5579	−	32.1432i	−0.632084	−	1.09480i
$863$			25.2203i			0.858510i	0.903183	+	0.429255i	$0.141224\pi$
$863$			25.2203i			0.858510i	−0.903183	+	0.429255i	$0.858776\pi$
$864$	−14.7204	−	27.0427i	−0.500797	−	0.920013i
$865$	−2.80576			−0.0953987
$866$	−14.2683	−	24.7135i	−0.484857	−	0.839797i
$867$	9.14949	+	25.8082i	0.310733	+	0.876492i
$868$	13.2295	−	28.6123i	0.449040	−	0.971164i
$869$	−10.2540	−	5.92017i	−0.347844	−	0.200828i
$870$	4.36032	−	5.10896i	0.147829	−	0.173210i
$871$	2.92685	−	1.68982i	0.0991724	−	0.0572572i
$872$			21.8970i			0.741525i
$873$	3.34203	−	8.72481i	0.113110	−	0.295290i
$874$		−	40.9621i		−	1.38556i
$875$	24.6341	−	17.3681i	0.832784	−	0.587149i
$876$	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	$0.0853989\pi$
$878$	−21.1961	+	36.7127i	−0.715333	+	1.23899i
$879$	42.3360	+	7.83094i	1.42796	+	0.264131i
$880$	0.960836	−	0.554739i	0.0323898	−	0.0187003i
$881$	−36.4482			−1.22797			−0.613985	−	0.789318i	$-0.710434\pi$
$881$	−36.4482			−1.22797			−0.613985	+	0.789318i	$0.710434\pi$
$882$	−36.3027	−	31.1023i	−1.22237	−	1.04727i
$883$	15.9831			0.537873			0.268936	−	0.963158i	$-0.413328\pi$
$883$	15.9831			0.537873			0.268936	+	0.963158i	$0.413328\pi$
$884$	15.3948	−	8.88819i	0.517783	−	0.298942i
$885$	−15.2735	+	17.8958i	−0.513413	+	0.601562i
$886$	−5.40739	+	9.36588i	−0.181665	+	0.314653i
$887$	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
$889$	13.3380	−	9.40383i	0.447341	−	0.315394i
$890$		−	44.7026i		−	1.49843i
$891$	−9.03611	−	27.6763i	−0.302721	−	0.927192i
$892$			56.8862i			1.90469i
$893$	−16.4093	+	9.47393i	−0.549117	+	0.317033i
$894$	−23.0865	−	65.1208i	−0.772129	−	2.17796i
$895$	−28.8196	−	16.6390i	−0.963332	−	0.556180i
$896$	−19.7267	+	42.6641i	−0.659023	+	1.42531i
$897$	−23.0728	+	27.0342i	−0.770378	+	0.902646i
$898$	−18.4834	−	32.0143i	−0.616801	−	1.06833i
$899$	4.44728			0.148325
$900$	−21.8187	+	17.6942i	−0.727292	+	0.589806i
$901$		−	7.65464i		−	0.255013i
$902$	−27.3657	−	47.3987i	−0.911177	−	1.57820i
$903$	−3.23318	+	34.8913i	−0.107593	+	1.16111i
$904$	5.27687	−	9.13981i	0.175506	−	0.303986i
$905$	−12.7621	−	7.36821i	−0.424227	−	0.244928i
$906$	0.789351	−	4.26742i	0.0262244	−	0.141776i
$907$	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	$0.807631\pi$
$908$	34.8973			1.15811
$909$	19.8611	+	7.60775i	0.658750	+	0.252333i
$910$	−3.99673	−	44.0404i	−0.132490	−	1.45992i
$911$	14.4945	−	8.36843i	0.480226	−	0.277258i	−0.240285	−	0.970702i	$-0.577241\pi$
$911$	14.4945	−	8.36843i	0.480226	−	0.277258i	0.720510	+	0.693444i	$0.243908\pi$
$912$	1.41423	+	1.20700i	0.0468298	+	0.0399677i
$913$	30.5501	+	17.6381i	1.01106	+	0.583737i
$914$	−11.3301	−	6.54143i	−0.374766	−	0.216371i
$915$	−7.64489	+	2.71026i	−0.252732	+	0.0895983i
$916$	53.5678	−	30.9274i	1.76993	−	1.02187i
$917$	1.97582	+	21.7717i	0.0652472	+	0.718965i
$918$	12.9045	+	0.324145i	0.425912	+	0.0106984i
$919$	30.6400			1.01072			0.505360	−	0.862909i	$-0.331360\pi$
$919$	30.6400			1.01072			0.505360	+	0.862909i	$0.331360\pi$
$920$	7.73436	+	13.3963i	0.254994	+	0.441663i
$921$	−30.8344	+	10.9314i	−1.01603	+	0.360200i
$922$	71.5015	+	41.2814i	2.35478	+	1.35953i
$923$	9.78651	−	16.9507i	0.322127	−	0.557940i
$924$	−27.2534	+	38.4997i	−0.896572	+	1.26655i
$925$	−0.351848	−	0.609419i	−0.0115687	−	0.0200376i
$926$			66.5627i			2.18739i
$927$	5.04708	−	0.803057i	0.165768	−	0.0263759i
$928$	−7.03775			−0.231025
$929$	14.8723	+	25.7595i	0.487943	+	0.845142i	0.999904	−	0.0138670i	$-0.00441415\pi$
$929$	14.8723	+	25.7595i	0.487943	+	0.845142i	−0.511961	+	0.859009i	$0.671081\pi$
$930$	20.8219	+	3.85145i	0.682777	+	0.126294i
$931$	29.5976	+	10.5562i	0.970024	+	0.345964i
$932$	−8.10245	−	4.67795i	−0.265405	−	0.153231i
$933$	13.5475	+	2.50589i	0.443524	+	0.0820393i
$934$	5.20876	−	3.00728i	0.170436	−	0.0984011i
$935$			5.06346i			0.165593i
$936$	6.49295	+	40.8071i	0.212229	+	1.33382i
$937$		−	4.03712i		−	0.131887i	−0.997823	−	0.0659434i	$-0.978994\pi$
$937$		−	4.03712i		−	0.131887i	0.997823	−	0.0659434i	$-0.0210057\pi$
$938$	−2.29117	−	3.24968i	−0.0748092	−	0.106106i
$939$	14.6683	+	12.5189i	0.478681	+	0.408538i
$940$	9.63160	−	16.6824i	0.314148	−	0.544121i
$941$	7.20264	−	12.4753i	0.234799	−	0.406684i	−0.724415	−	0.689364i	$-0.757890\pi$
$941$	7.20264	−	12.4753i	0.234799	−	0.406684i	0.959214	+	0.282680i	$0.0912234\pi$
$942$	12.8571	+	36.2662i	0.418905	+	1.18162i
$943$	−25.8009	+	14.8962i	−0.840193	+	0.485085i
$944$	2.26464			0.0737079
$945$	8.72219	−	17.6842i	0.283733	−	0.575267i
$946$	56.3081			1.83073
$947$	27.0334	−	15.6077i	0.878467	−	0.507183i	0.00831468	−	0.999965i	$-0.497353\pi$
$947$	27.0334	−	15.6077i	0.878467	−	0.507183i	0.870153	+	0.492782i	$0.164020\pi$
$948$	6.74043	+	19.0129i	0.218919	+	0.617511i
$949$	18.7125	−	32.4109i	0.607432	−	1.05210i
$950$	15.0363	−	26.0436i	0.487841	−	0.844966i
$951$	30.6355	+	26.1463i	0.993423	+	0.847853i
$952$	−4.47646	−	6.34920i	−0.145083	−	0.205779i
$953$		−	8.55869i		−	0.277243i	−0.990345	−	0.138622i	$-0.955733\pi$
$953$		−	8.55869i		−	0.277243i	0.990345	−	0.138622i	$-0.0442672\pi$
$954$	44.7313	+	17.1343i	1.44823	+	0.554743i
$955$		−	32.5865i		−	1.05447i
$956$	−34.1278	+	19.7037i	−1.10377	+	0.637263i
$957$	−6.54377	−	1.21041i	−0.211530	−	0.0391270i
$958$	−61.2751	−	35.3772i	−1.97971	−	1.14298i
$959$	−11.4902	+	24.8506i	−0.371039	+	0.802468i
$960$	−31.7821	−	5.87877i	−1.02576	−	0.189737i
$961$	−8.48973	−	14.7046i	−0.273862	−	0.474343i
$962$	−2.78656			−0.0898424
$963$	9.32683	+	11.5009i	0.300553	+	0.370613i
$964$			42.9669i			1.38387i
$965$	12.0996	+	20.9572i	0.389501	+	0.674635i
$966$	34.1292	+	24.1596i	1.09809	+	0.777322i
$967$	16.0280	−	27.7614i	0.515427	−	0.892745i	−0.484413	−	0.874840i	$-0.660967\pi$
$967$	16.0280	−	27.7614i	0.515427	−	0.892745i	0.999840	−	0.0179059i	$-0.00569994\pi$
$968$	−1.24759	−	0.720299i	−0.0400992	−	0.0231513i
$969$	−7.99766	+	2.83532i	−0.256922	+	0.0910837i
$970$	−5.08414	−	8.80598i	−0.163242	−	0.282743i
$971$	33.2366			1.06661			0.533307	−	0.845922i	$-0.320949\pi$
$971$	33.2366			1.06661			0.533307	+	0.845922i	$0.320949\pi$
$972$	−18.9002	+	45.8596i	−0.606225	+	1.47095i
$973$	−47.0345	+	4.26845i	−1.50786	+	0.136840i
$974$	−68.7469	+	39.6911i	−2.20279	+	1.27178i
$975$	−24.5933	+	8.71878i	−0.787616	+	0.279225i
$976$	0.676137	+	0.390368i	0.0216426	+	0.0124954i
$977$	45.1558	+	26.0707i	1.44466	+	0.834076i	0.998156	−	0.0607042i	$-0.0193346\pi$
$977$	45.1558	+	26.0707i	1.44466	+	0.834076i	0.446507	+	0.894780i	$0.352668\pi$
$978$	−21.6695	−	18.4942i	−0.692915	−	0.591379i
$979$	−38.3567	+	22.1453i	−1.22589	+	0.707765i
$980$	−31.4248	+	5.75107i	−1.00383	+	0.183711i
$981$	−18.9633	+	15.3785i	−0.605453	+	0.490999i
$982$	59.6044			1.90205
$983$	−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	$0.959664\pi$
$984$	−6.29987	+	34.0586i	−0.200833	+	1.08575i
$985$	11.1099	+	6.41432i	0.353992	+	0.204377i
$986$	1.47529	−	2.55528i	0.0469829	−	0.0813768i
$987$	1.78470	−	19.2598i	0.0568077	−	0.613048i
$988$	−36.5614	−	63.3263i	−1.16317	−	2.01468i
$989$		−	30.6506i		−	0.974632i
$990$	−29.5893	−	11.3341i	−0.940410	−	0.360222i
$991$	−24.1981			−0.768678			−0.384339	−	0.923192i	$-0.625571\pi$
$991$	−24.1981			−0.768678			−0.384339	+	0.923192i	$0.625571\pi$
$992$	−11.0937	−	19.2148i	−0.352224	−	0.610070i
$993$	21.5428	−	25.2416i	0.683641	−	0.801017i
$994$	−20.9017	−	9.66437i	−0.662961	−	0.306535i
$995$	−7.18607	−	4.14888i	−0.227814	−	0.131528i
$996$	−20.0819	−	56.6457i	−0.636321	−	1.79489i
$997$	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	$0.281778\pi$
$998$		−	28.4053i		−	0.899155i
$999$	−1.06012	−	0.648085i	−0.0335406	−	0.0205045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.o.a.41.1	yes	12
3.2	odd	2		189.2.o.a.125.5		12
4.3	odd	2		1008.2.cc.a.545.5		12
7.2	even	3		441.2.s.c.374.6		12
7.3	odd	6		441.2.i.c.68.2		12
7.4	even	3		441.2.i.c.68.1		12
7.5	odd	6		441.2.s.c.374.5		12
7.6	odd	2	inner	63.2.o.a.41.2	yes	12
9.2	odd	6	inner	63.2.o.a.20.2	yes	12
9.4	even	3		567.2.c.c.566.1		12
9.5	odd	6		567.2.c.c.566.12		12
9.7	even	3		189.2.o.a.62.6		12
12.11	even	2		3024.2.cc.a.881.3		12
21.2	odd	6		1323.2.s.c.962.2		12
21.5	even	6		1323.2.s.c.962.1		12
21.11	odd	6		1323.2.i.c.1097.5		12
21.17	even	6		1323.2.i.c.1097.6		12
21.20	even	2		189.2.o.a.125.6		12
28.27	even	2		1008.2.cc.a.545.2		12
36.7	odd	6		3024.2.cc.a.2897.4		12
36.11	even	6		1008.2.cc.a.209.2		12
63.2	odd	6		441.2.i.c.227.6		12
63.11	odd	6		441.2.s.c.362.5		12
63.13	odd	6		567.2.c.c.566.2		12
63.16	even	3		1323.2.i.c.521.2		12
63.20	even	6	inner	63.2.o.a.20.1	✓	12
63.25	even	3		1323.2.s.c.656.1		12
63.34	odd	6		189.2.o.a.62.5		12
63.38	even	6		441.2.s.c.362.6		12
63.41	even	6		567.2.c.c.566.11		12
63.47	even	6		441.2.i.c.227.5		12
63.52	odd	6		1323.2.s.c.656.2		12
63.61	odd	6		1323.2.i.c.521.1		12
84.83	odd	2		3024.2.cc.a.881.4		12
252.83	odd	6		1008.2.cc.a.209.5		12
252.223	even	6		3024.2.cc.a.2897.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.1	✓	12	63.20	even	6	inner
63.2.o.a.20.2	yes	12	9.2	odd	6	inner
63.2.o.a.41.1	yes	12	1.1	even	1	trivial
63.2.o.a.41.2	yes	12	7.6	odd	2	inner
189.2.o.a.62.5		12	63.34	odd	6
189.2.o.a.62.6		12	9.7	even	3
189.2.o.a.125.5		12	3.2	odd	2
189.2.o.a.125.6		12	21.20	even	2
441.2.i.c.68.1		12	7.4	even	3
441.2.i.c.68.2		12	7.3	odd	6
441.2.i.c.227.5		12	63.47	even	6
441.2.i.c.227.6		12	63.2	odd	6
441.2.s.c.362.5		12	63.11	odd	6
441.2.s.c.362.6		12	63.38	even	6
441.2.s.c.374.5		12	7.5	odd	6
441.2.s.c.374.6		12	7.2	even	3
567.2.c.c.566.1		12	9.4	even	3
567.2.c.c.566.2		12	63.13	odd	6
567.2.c.c.566.11		12	63.41	even	6
567.2.c.c.566.12		12	9.5	odd	6
1008.2.cc.a.209.2		12	36.11	even	6
1008.2.cc.a.209.5		12	252.83	odd	6
1008.2.cc.a.545.2		12	28.27	even	2
1008.2.cc.a.545.5		12	4.3	odd	2
1323.2.i.c.521.1		12	63.61	odd	6
1323.2.i.c.521.2		12	63.16	even	3
1323.2.i.c.1097.5		12	21.11	odd	6
1323.2.i.c.1097.6		12	21.17	even	6
1323.2.s.c.656.1		12	63.25	even	3
1323.2.s.c.656.2		12	63.52	odd	6
1323.2.s.c.962.1		12	21.5	even	6
1323.2.s.c.962.2		12	21.2	odd	6
3024.2.cc.a.881.3		12	12.11	even	2
3024.2.cc.a.881.4		12	84.83	odd	2
3024.2.cc.a.2897.3		12	252.223	even	6
3024.2.cc.a.2897.4		12	36.7	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.97141 + 1.13819i) q^{2} +(-0.578751 - 1.63250i) q^{3} +(1.59097 - 2.75564i) q^{4} +(0.717144 - 1.24213i) q^{5} +(2.99905 + 2.55959i) q^{6} +(2.16235 - 1.52455i) q^{7} +2.69056i q^{8} +(-2.33009 + 1.88962i) q^{9} +O(q^{10})\)	\(q+(-1.97141 + 1.13819i) q^{2} +(-0.578751 - 1.63250i) q^{3} +(1.59097 - 2.75564i) q^{4} +(0.717144 - 1.24213i) q^{5} +(2.99905 + 2.55959i) q^{6} +(2.16235 - 1.52455i) q^{7} +2.69056i q^{8} +(-2.33009 + 1.88962i) q^{9} +3.26499i q^{10} +(2.80150 - 1.61745i) q^{11} +(-5.41936 - 1.00243i) q^{12} +(-4.43334 - 2.55959i) q^{13} +(-2.52764 + 5.46668i) q^{14} +(-2.44282 - 0.451852i) q^{15} +(0.119562 + 0.207087i) q^{16} -1.09132 q^{17} +(2.44282 - 6.37731i) q^{18} +4.48911i q^{19} +(-2.28191 - 3.95238i) q^{20} +(-3.74028 - 2.64769i) q^{21} +(-3.68194 + 6.37731i) q^{22} +(3.47141 + 2.00422i) q^{23} +(4.39234 - 1.55716i) q^{24} +(1.47141 + 2.54856i) q^{25} +11.6532 q^{26} +(4.43334 + 2.71026i) q^{27} +(-0.760877 - 8.38418i) q^{28} +(1.02859 - 0.593857i) q^{29} +(5.33009 - 1.88962i) q^{30} +(3.24275 + 1.87220i) q^{31} +(-5.13160 - 2.96273i) q^{32} +(-4.26186 - 3.63735i) q^{33} +(2.15143 - 1.24213i) q^{34} +(-0.342971 - 3.77924i) q^{35} +(1.50000 + 9.42724i) q^{36} -0.239123 q^{37} +(-5.10948 - 8.84988i) q^{38} +(-1.61273 + 8.71878i) q^{39} +(3.34203 + 1.92952i) q^{40} +(-3.71620 + 6.43664i) q^{41} +(10.3872 + 0.962525i) q^{42} +(-3.82326 - 6.62208i) q^{43} -10.2933i q^{44} +(0.676137 + 4.24941i) q^{45} -9.12476 q^{46} +(2.11042 + 3.65536i) q^{47} +(0.268872 - 0.315036i) q^{48} +(2.35150 - 6.59321i) q^{49} +(-5.80150 - 3.34950i) q^{50} +(0.631600 + 1.78157i) q^{51} +(-14.1066 + 8.14447i) q^{52} +7.01414i q^{53} +(-11.8247 - 0.297022i) q^{54} -4.63977i q^{55} +(4.10189 + 5.81793i) q^{56} +(7.32846 - 2.59808i) q^{57} +(-1.35185 + 2.34147i) q^{58} +(4.73531 - 8.20179i) q^{59} +(-5.13160 + 6.01266i) q^{60} +(2.82757 - 1.63250i) q^{61} -8.52371 q^{62} +(-2.15766 + 7.63836i) q^{63} +13.0104 q^{64} +(-6.35868 + 3.67119i) q^{65} +(12.5419 + 2.31989i) q^{66} +(-0.330095 + 0.571741i) q^{67} +(-1.73625 + 3.00728i) q^{68} +(1.26280 - 6.82701i) q^{69} +(4.97764 + 7.06006i) q^{70} +3.82347i q^{71} +(-5.08414 - 6.26926i) q^{72} +7.31073i q^{73} +(0.471410 - 0.272169i) q^{74} +(3.30893 - 3.87705i) q^{75} +(12.3704 + 7.14205i) q^{76} +(3.59195 - 7.76852i) q^{77} +(-6.74433 - 19.0239i) q^{78} +(-1.83009 - 3.16982i) q^{79} +0.342971 q^{80} +(1.85868 - 8.80598i) q^{81} -16.9190i q^{82} +(5.45245 + 9.44392i) q^{83} +(-13.2468 + 6.09448i) q^{84} +(-0.782630 + 1.35556i) q^{85} +(15.0744 + 8.70322i) q^{86} +(-1.56477 - 1.33548i) q^{87} +(4.35185 + 7.53762i) q^{88} -13.6915 q^{89} +(-6.16959 - 7.60775i) q^{90} +(-13.4887 + 1.22412i) q^{91} +(11.0458 - 6.37731i) q^{92} +(1.17962 - 6.37731i) q^{93} +(-8.32102 - 4.80415i) q^{94} +(5.57605 + 3.21934i) q^{95} +(-1.86673 + 10.0920i) q^{96} +(-2.69709 + 1.55716i) q^{97} +(2.86857 + 15.6744i) q^{98} +(-3.47141 + 9.06259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 2 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 + 2 * q^4 - 2 * q^7 - 12 * q^9	\( 12 q - 6 q^{2} + 2 q^{4} - 2 q^{7} - 12 q^{9} - 12 q^{14} + 6 q^{15} + 2 q^{16} - 6 q^{18} - 24 q^{21} - 10 q^{22} + 24 q^{23} - 8 q^{28} + 30 q^{29} + 48 q^{30} - 12 q^{32} + 18 q^{36} - 4 q^{37} + 36 q^{42} - 10 q^{43} - 40 q^{46} + 6 q^{49} - 36 q^{50} - 42 q^{51} + 42 q^{56} - 18 q^{57} + 2 q^{58} - 12 q^{60} + 24 q^{63} + 16 q^{64} - 78 q^{65} + 12 q^{67} + 18 q^{70} - 24 q^{72} - 12 q^{74} - 24 q^{77} - 12 q^{78} - 6 q^{79} + 24 q^{81} - 60 q^{84} - 6 q^{85} + 96 q^{86} + 34 q^{88} - 24 q^{91} + 30 q^{92} + 78 q^{93} + 72 q^{95} - 24 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 + 2 * q^4 - 2 * q^7 - 12 * q^9 - 12 * q^14 + 6 * q^15 + 2 * q^16 - 6 * q^18 - 24 * q^21 - 10 * q^22 + 24 * q^23 - 8 * q^28 + 30 * q^29 + 48 * q^30 - 12 * q^32 + 18 * q^36 - 4 * q^37 + 36 * q^42 - 10 * q^43 - 40 * q^46 + 6 * q^49 - 36 * q^50 - 42 * q^51 + 42 * q^56 - 18 * q^57 + 2 * q^58 - 12 * q^60 + 24 * q^63 + 16 * q^64 - 78 * q^65 + 12 * q^67 + 18 * q^70 - 24 * q^72 - 12 * q^74 - 24 * q^77 - 12 * q^78 - 6 * q^79 + 24 * q^81 - 60 * q^84 - 6 * q^85 + 96 * q^86 + 34 * q^88 - 24 * q^91 + 30 * q^92 + 78 * q^93 + 72 * q^95 - 24 * q^99

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