LMFDB - Embedded newform 66.2.e.b.37.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [66,2,Mod(25,66)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(66, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("66.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 66 = 2 \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	66.e (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$0.527012653340$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			37.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	66.37
Dual form			66.2.e.b.25.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.11803 + 0.812299i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-0.500000 - 1.53884i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} -1.38197 q^{10} +(-3.23607 + 0.726543i) q^{11} +1.00000 q^{12} +(1.00000 + 0.726543i) q^{13} +(0.500000 - 1.53884i) q^{14} +(0.427051 + 1.31433i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-3.23607 + 2.35114i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(2.38197 - 7.33094i) q^{19} +(-1.11803 - 0.812299i) q^{20} -1.61803 q^{21} +(-3.04508 - 1.31433i) q^{22} +7.70820 q^{23} +(0.809017 + 0.587785i) q^{24} +(-0.954915 + 2.93893i) q^{25} +(0.381966 + 1.17557i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(1.30902 - 0.951057i) q^{28} +(0.0450850 + 0.138757i) q^{29} +(-0.427051 + 1.31433i) q^{30} +(4.54508 + 3.30220i) q^{31} -1.00000 q^{32} +(-0.309017 + 3.30220i) q^{33} -4.00000 q^{34} +(1.80902 + 1.31433i) q^{35} +(0.309017 - 0.951057i) q^{36} +(2.76393 + 8.50651i) q^{37} +(6.23607 - 4.53077i) q^{38} +(1.00000 - 0.726543i) q^{39} +(-0.427051 - 1.31433i) q^{40} +(2.38197 - 7.33094i) q^{41} +(-1.30902 - 0.951057i) q^{42} -9.23607 q^{43} +(-1.69098 - 2.85317i) q^{44} +1.38197 q^{45} +(6.23607 + 4.53077i) q^{46} +(1.23607 - 3.80423i) q^{47} +(0.309017 + 0.951057i) q^{48} +(3.54508 - 2.57565i) q^{49} +(-2.50000 + 1.81636i) q^{50} +(1.23607 + 3.80423i) q^{51} +(-0.381966 + 1.17557i) q^{52} +(-2.92705 - 2.12663i) q^{53} -1.00000 q^{54} +(3.02786 - 3.44095i) q^{55} +1.61803 q^{56} +(-6.23607 - 4.53077i) q^{57} +(-0.0450850 + 0.138757i) q^{58} +(-1.64590 - 5.06555i) q^{59} +(-1.11803 + 0.812299i) q^{60} +(-7.85410 + 5.70634i) q^{61} +(1.73607 + 5.34307i) q^{62} +(-0.500000 + 1.53884i) q^{63} +(-0.809017 - 0.587785i) q^{64} -1.70820 q^{65} +(-2.19098 + 2.48990i) q^{66} -12.9443 q^{67} +(-3.23607 - 2.35114i) q^{68} +(2.38197 - 7.33094i) q^{69} +(0.690983 + 2.12663i) q^{70} +(-4.85410 + 3.52671i) q^{71} +(0.809017 - 0.587785i) q^{72} +(-1.71885 - 5.29007i) q^{73} +(-2.76393 + 8.50651i) q^{74} +(2.50000 + 1.81636i) q^{75} +7.70820 q^{76} +(2.73607 + 4.61653i) q^{77} +1.23607 q^{78} +(0.118034 + 0.0857567i) q^{79} +(0.427051 - 1.31433i) q^{80} +(0.309017 + 0.951057i) q^{81} +(6.23607 - 4.53077i) q^{82} +(0.500000 - 0.363271i) q^{83} +(-0.500000 - 1.53884i) q^{84} +(1.70820 - 5.25731i) q^{85} +(-7.47214 - 5.42882i) q^{86} +0.145898 q^{87} +(0.309017 - 3.30220i) q^{88} +11.2361 q^{89} +(1.11803 + 0.812299i) q^{90} +(0.618034 - 1.90211i) q^{91} +(2.38197 + 7.33094i) q^{92} +(4.54508 - 3.30220i) q^{93} +(3.23607 - 2.35114i) q^{94} +(3.29180 + 10.1311i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(5.97214 + 4.33901i) q^{97} +4.38197 q^{98} +(3.04508 + 1.31433i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9} - 10 q^{10} - 4 q^{11} + 4 q^{12} + 4 q^{13} + 2 q^{14} - 5 q^{15} - q^{16} - 4 q^{17} + q^{18} + 14 q^{19} - 2 q^{21} - q^{22} + 4 q^{23}+ \cdots + q^{99}+O(q^{100}) $ 4 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9 - 10 * q^10 - 4 * q^11 + 4 * q^12 + 4 * q^13 + 2 * q^14 - 5 * q^15 - q^16 - 4 * q^17 + q^18 + 14 * q^19 - 2 * q^21 - q^22 + 4 * q^23 + q^24 - 15 * q^25 + 6 * q^26 - q^27 + 3 * q^28 - 11 * q^29 + 5 * q^30 + 7 * q^31 - 4 * q^32 + q^33 - 16 * q^34 + 5 * q^35 - q^36 + 20 * q^37 + 16 * q^38 + 4 * q^39 + 5 * q^40 + 14 * q^41 - 3 * q^42 - 28 * q^43 - 9 * q^44 + 10 * q^45 + 16 * q^46 - 4 * q^47 - q^48 + 3 * q^49 - 10 * q^50 - 4 * q^51 - 6 * q^52 - 5 * q^53 - 4 * q^54 + 30 * q^55 + 2 * q^56 - 16 * q^57 + 11 * q^58 - 20 * q^59 - 18 * q^61 - 2 * q^62 - 2 * q^63 - q^64 + 20 * q^65 - 11 * q^66 - 16 * q^67 - 4 * q^68 + 14 * q^69 + 5 * q^70 - 6 * q^71 + q^72 - 27 * q^73 - 20 * q^74 + 10 * q^75 + 4 * q^76 + 2 * q^77 - 4 * q^78 - 4 * q^79 - 5 * q^80 - q^81 + 16 * q^82 + 2 * q^83 - 2 * q^84 - 20 * q^85 - 12 * q^86 + 14 * q^87 - q^88 + 36 * q^89 - 2 * q^91 + 14 * q^92 + 7 * q^93 + 4 * q^94 + 40 * q^95 + q^96 + 6 * q^97 + 22 * q^98 + q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/66\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.11803	+	0.812299i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$5$	−1.11803	+	0.812299i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	−0.500000	−	1.53884i	−0.188982	−	0.581628i	0.811012	−	0.585030i	$-0.198917\pi$
$7$	−0.500000	−	1.53884i	−0.188982	−	0.581628i	−0.999994	+	0.00340203i	$0.998917\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−1.38197			−0.437016
$11$	−3.23607	+	0.726543i	−0.975711	+	0.219061i
$11$	−3.23607	+	0.726543i	−0.975711	+	0.219061i
$12$	1.00000			0.288675
$13$	1.00000	+	0.726543i	0.277350	+	0.201507i	0.717761	−	0.696290i	$-0.245167\pi$
$13$	1.00000	+	0.726543i	0.277350	+	0.201507i	−0.440411	+	0.897796i	$0.645167\pi$
$14$	0.500000	−	1.53884i	0.133631	−	0.411273i
$15$	0.427051	+	1.31433i	0.110264	+	0.339358i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−3.23607	+	2.35114i	−0.784862	+	0.570235i	−0.906434	−	0.422347i	$-0.861206\pi$
$17$	−3.23607	+	2.35114i	−0.784862	+	0.570235i	0.121572	+	0.992583i	$0.461206\pi$
$18$	−0.309017	−	0.951057i	−0.0728360	−	0.224166i
$19$	2.38197	−	7.33094i	0.546460	−	1.68183i	−0.171031	−	0.985266i	$-0.554710\pi$
$19$	2.38197	−	7.33094i	0.546460	−	1.68183i	0.717492	−	0.696567i	$-0.245290\pi$
$20$	−1.11803	−	0.812299i	−0.250000	−	0.181636i
$21$	−1.61803			−0.353084
$22$	−3.04508	−	1.31433i	−0.649214	−	0.280216i
$23$	7.70820			1.60727			0.803636	−	0.595121i	$-0.202896\pi$
$23$	7.70820			1.60727			0.803636	+	0.595121i	$0.202896\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	−0.954915	+	2.93893i	−0.190983	+	0.587785i
$26$	0.381966	+	1.17557i	0.0749097	+	0.230548i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	1.30902	−	0.951057i	0.247381	−	0.179733i
$29$	0.0450850	+	0.138757i	0.00837207	+	0.0257666i	0.955155	−	0.296105i	$-0.0956879\pi$
$29$	0.0450850	+	0.138757i	0.00837207	+	0.0257666i	−0.946783	+	0.321872i	$0.895688\pi$
$30$	−0.427051	+	1.31433i	−0.0779685	+	0.239962i
$31$	4.54508	+	3.30220i	0.816321	+	0.593092i	0.915656	−	0.401962i	$-0.131672\pi$
$31$	4.54508	+	3.30220i	0.816321	+	0.593092i	−0.0993351	+	0.995054i	$0.531672\pi$
$32$	−1.00000			−0.176777
$33$	−0.309017	+	3.30220i	−0.0537930	+	0.574839i
$34$	−4.00000			−0.685994
$35$	1.80902	+	1.31433i	0.305780	+	0.222162i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	2.76393	+	8.50651i	0.454388	+	1.39846i	0.871853	+	0.489768i	$0.162919\pi$
$37$	2.76393	+	8.50651i	0.454388	+	1.39846i	−0.417465	+	0.908693i	$0.637081\pi$
$38$	6.23607	−	4.53077i	1.01162	−	0.734988i
$39$	1.00000	−	0.726543i	0.160128	−	0.116340i
$40$	−0.427051	−	1.31433i	−0.0675227	−	0.207813i
$41$	2.38197	−	7.33094i	0.372001	−	1.14490i	−0.573479	−	0.819220i	$-0.694407\pi$
$41$	2.38197	−	7.33094i	0.372001	−	1.14490i	0.945480	−	0.325680i	$-0.105593\pi$
$42$	−1.30902	−	0.951057i	−0.201986	−	0.146751i
$43$	−9.23607			−1.40849			−0.704244	−	0.709958i	$-0.748714\pi$
$43$	−9.23607			−1.40849			−0.704244	+	0.709958i	$0.748714\pi$
$44$	−1.69098	−	2.85317i	−0.254925	−	0.430131i
$45$	1.38197			0.206011
$46$	6.23607	+	4.53077i	0.919458	+	0.668025i
$47$	1.23607	−	3.80423i	0.180299	−	0.554903i	−0.819537	−	0.573027i	$-0.805769\pi$
$47$	1.23607	−	3.80423i	0.180299	−	0.554903i	0.999836	+	0.0181233i	$0.00576913\pi$
$48$	0.309017	+	0.951057i	0.0446028	+	0.137273i
$49$	3.54508	−	2.57565i	0.506441	−	0.367951i
$50$	−2.50000	+	1.81636i	−0.353553	+	0.256872i
$51$	1.23607	+	3.80423i	0.173084	+	0.532698i
$52$	−0.381966	+	1.17557i	−0.0529692	+	0.163022i
$53$	−2.92705	−	2.12663i	−0.402061	−	0.292115i	0.368319	−	0.929700i	$-0.379934\pi$
$53$	−2.92705	−	2.12663i	−0.402061	−	0.292115i	−0.770380	+	0.637585i	$0.779934\pi$
$54$	−1.00000			−0.136083
$55$	3.02786	−	3.44095i	0.408277	−	0.463978i
$56$	1.61803			0.216219
$57$	−6.23607	−	4.53077i	−0.825987	−	0.600115i
$58$	−0.0450850	+	0.138757i	−0.00591995	+	0.0182197i
$59$	−1.64590	−	5.06555i	−0.214278	−	0.659479i	−0.999204	−	0.0398899i	$-0.987299\pi$
$59$	−1.64590	−	5.06555i	−0.214278	−	0.659479i	0.784926	−	0.619589i	$-0.212701\pi$
$60$	−1.11803	+	0.812299i	−0.144338	+	0.104867i
$61$	−7.85410	+	5.70634i	−1.00561	+	0.730622i	−0.963285	−	0.268482i	$-0.913478\pi$
$61$	−7.85410	+	5.70634i	−1.00561	+	0.730622i	−0.0423300	+	0.999104i	$0.513478\pi$
$62$	1.73607	+	5.34307i	0.220481	+	0.678570i
$63$	−0.500000	+	1.53884i	−0.0629941	+	0.193876i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−1.70820			−0.211877
$66$	−2.19098	+	2.48990i	−0.269691	+	0.306485i
$67$	−12.9443			−1.58139			−0.790697	−	0.612207i	$-0.790282\pi$
$67$	−12.9443			−1.58139			−0.790697	+	0.612207i	$0.790282\pi$
$68$	−3.23607	−	2.35114i	−0.392431	−	0.285118i
$69$	2.38197	−	7.33094i	0.286755	−	0.882541i
$70$	0.690983	+	2.12663i	0.0825883	+	0.254181i
$71$	−4.85410	+	3.52671i	−0.576076	+	0.418544i	−0.837307	−	0.546733i	$-0.815871\pi$
$71$	−4.85410	+	3.52671i	−0.576076	+	0.418544i	0.261231	+	0.965276i	$0.415871\pi$
$72$	0.809017	−	0.587785i	0.0953436	−	0.0692712i
$73$	−1.71885	−	5.29007i	−0.201176	−	0.619156i	−0.999849	−	0.0173902i	$-0.994464\pi$
$73$	−1.71885	−	5.29007i	−0.201176	−	0.619156i	0.798673	−	0.601765i	$-0.205536\pi$
$74$	−2.76393	+	8.50651i	−0.321301	+	0.988861i
$75$	2.50000	+	1.81636i	0.288675	+	0.209735i
$76$	7.70820			0.884192
$77$	2.73607	+	4.61653i	0.311804	+	0.526102i
$78$	1.23607			0.139957
$79$	0.118034	+	0.0857567i	0.0132799	+	0.00964838i	0.594405	−	0.804166i	$-0.297387\pi$
$79$	0.118034	+	0.0857567i	0.0132799	+	0.00964838i	−0.581126	+	0.813814i	$0.697387\pi$
$80$	0.427051	−	1.31433i	0.0477458	−	0.146946i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	6.23607	−	4.53077i	0.688659	−	0.500340i
$83$	0.500000	−	0.363271i	0.0548821	−	0.0398742i	−0.560006	−	0.828489i	$-0.689201\pi$
$83$	0.500000	−	0.363271i	0.0548821	−	0.0398742i	0.614888	+	0.788614i	$0.289201\pi$
$84$	−0.500000	−	1.53884i	−0.0545545	−	0.167901i
$85$	1.70820	−	5.25731i	0.185281	−	0.570235i
$86$	−7.47214	−	5.42882i	−0.805741	−	0.585405i
$87$	0.145898			0.0156419
$88$	0.309017	−	3.30220i	0.0329413	−	0.352015i
$89$	11.2361			1.19102			0.595510	−	0.803348i	$-0.296950\pi$
$89$	11.2361			1.19102			0.595510	+	0.803348i	$0.296950\pi$
$90$	1.11803	+	0.812299i	0.117851	+	0.0856239i
$91$	0.618034	−	1.90211i	0.0647876	−	0.199396i
$92$	2.38197	+	7.33094i	0.248337	+	0.764303i
$93$	4.54508	−	3.30220i	0.471303	−	0.342422i
$94$	3.23607	−	2.35114i	0.333775	−	0.242502i
$95$	3.29180	+	10.1311i	0.337731	+	1.03943i
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	5.97214	+	4.33901i	0.606379	+	0.440560i	0.848137	−	0.529777i	$-0.177724\pi$
$97$	5.97214	+	4.33901i	0.606379	+	0.440560i	−0.241759	+	0.970336i	$0.577724\pi$
$98$	4.38197			0.442645
$99$	3.04508	+	1.31433i	0.306043	+	0.132095i
$100$	−3.09017			−0.309017
$101$	−7.35410	−	5.34307i	−0.731760	−	0.531655i	0.158359	−	0.987382i	$-0.449380\pi$
$101$	−7.35410	−	5.34307i	−0.731760	−	0.531655i	−0.890120	+	0.455726i	$0.849380\pi$
$102$	−1.23607	+	3.80423i	−0.122389	+	0.376675i
$103$	−0.972136	−	2.99193i	−0.0957874	−	0.294803i	0.891671	−	0.452685i	$-0.149534\pi$
$103$	−0.972136	−	2.99193i	−0.0957874	−	0.294803i	−0.987458	+	0.157881i	$0.949534\pi$
$104$	−1.00000	+	0.726543i	−0.0980581	+	0.0712434i
$105$	1.80902	−	1.31433i	0.176542	−	0.128265i
$106$	−1.11803	−	3.44095i	−0.108593	−	0.334215i
$107$	−3.11803	+	9.59632i	−0.301432	+	0.927711i	0.679553	+	0.733626i	$0.262174\pi$
$107$	−3.11803	+	9.59632i	−0.301432	+	0.927711i	−0.980985	+	0.194085i	$0.937826\pi$
$108$	−0.809017	−	0.587785i	−0.0778477	−	0.0565597i
$109$	14.9443			1.43140			0.715701	−	0.698407i	$-0.246107\pi$
$109$	14.9443			1.43140			0.715701	+	0.698407i	$0.246107\pi$
$110$	4.47214	−	1.00406i	0.426401	−	0.0957331i
$111$	8.94427			0.848953
$112$	1.30902	+	0.951057i	0.123690	+	0.0898664i
$113$	−3.38197	+	10.4086i	−0.318149	+	0.979161i	0.656290	+	0.754508i	$0.272125\pi$
$113$	−3.38197	+	10.4086i	−0.318149	+	0.979161i	−0.974439	+	0.224652i	$0.927875\pi$
$114$	−2.38197	−	7.33094i	−0.223092	−	0.686605i
$115$	−8.61803	+	6.26137i	−0.803636	+	0.583876i
$116$	−0.118034	+	0.0857567i	−0.0109592	+	0.00796231i
$117$	−0.381966	−	1.17557i	−0.0353128	−	0.108682i
$118$	1.64590	−	5.06555i	0.151517	−	0.466322i
$119$	5.23607	+	3.80423i	0.479990	+	0.348733i
$120$	−1.38197			−0.126156
$121$	9.94427	−	4.70228i	0.904025	−	0.427480i
$122$	−9.70820			−0.878939
$123$	−6.23607	−	4.53077i	−0.562287	−	0.408526i
$124$	−1.73607	+	5.34307i	−0.155904	+	0.479822i
$125$	−3.45492	−	10.6331i	−0.309017	−	0.951057i
$126$	−1.30902	+	0.951057i	−0.116617	+	0.0847268i
$127$	−3.23607	+	2.35114i	−0.287155	+	0.208630i	−0.722032	−	0.691860i	$-0.756792\pi$
$127$	−3.23607	+	2.35114i	−0.287155	+	0.208630i	0.434877	+	0.900490i	$0.356792\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−2.85410	+	8.78402i	−0.251290	+	0.773390i
$130$	−1.38197	−	1.00406i	−0.121206	−	0.0880616i
$131$	−2.85410			−0.249364			−0.124682	−	0.992197i	$-0.539791\pi$
$131$	−2.85410			−0.249364			−0.124682	+	0.992197i	$0.539791\pi$
$132$	−3.23607	+	0.726543i	−0.281664	+	0.0632374i
$133$	−12.4721			−1.08147
$134$	−10.4721	−	7.60845i	−0.904655	−	0.657270i
$135$	0.427051	−	1.31433i	0.0367547	−	0.113119i
$136$	−1.23607	−	3.80423i	−0.105992	−	0.326210i
$137$	−6.61803	+	4.80828i	−0.565417	+	0.410799i	−0.833437	−	0.552614i	$-0.813630\pi$
$137$	−6.61803	+	4.80828i	−0.565417	+	0.410799i	0.268021	+	0.963413i	$0.413630\pi$
$138$	6.23607	−	4.53077i	0.530849	−	0.385685i
$139$	−0.708204	−	2.17963i	−0.0600691	−	0.184874i	0.916519	−	0.399991i	$-0.130987\pi$
$139$	−0.708204	−	2.17963i	−0.0600691	−	0.184874i	−0.976588	+	0.215117i	$0.930987\pi$
$140$	−0.690983	+	2.12663i	−0.0583987	+	0.179733i
$141$	−3.23607	−	2.35114i	−0.272526	−	0.198002i
$142$	−6.00000			−0.503509
$143$	−3.76393	−	1.62460i	−0.314756	−	0.135856i
$144$	1.00000			0.0833333
$145$	−0.163119	−	0.118513i	−0.0135463	−	0.00984196i
$146$	1.71885	−	5.29007i	0.142253	−	0.437809i
$147$	−1.35410	−	4.16750i	−0.111684	−	0.343729i
$148$	−7.23607	+	5.25731i	−0.594801	+	0.432148i
$149$	18.6353	−	13.5393i	1.52666	−	1.10918i	0.568600	−	0.822614i	$-0.307485\pi$
$149$	18.6353	−	13.5393i	1.52666	−	1.10918i	0.958060	−	0.286569i	$-0.0925147\pi$
$150$	0.954915	+	2.93893i	0.0779685	+	0.239962i
$151$	−1.48278	+	4.56352i	−0.120667	+	0.371374i	−0.993087	−	0.117383i	$-0.962550\pi$
$151$	−1.48278	+	4.56352i	−0.120667	+	0.371374i	0.872420	+	0.488757i	$0.162550\pi$
$152$	6.23607	+	4.53077i	0.505812	+	0.367494i
$153$	4.00000			0.323381
$154$	−0.500000	+	5.34307i	−0.0402911	+	0.430557i
$155$	−7.76393			−0.623614
$156$	1.00000	+	0.726543i	0.0800641	+	0.0581700i
$157$	−5.56231	+	17.1190i	−0.443920	+	1.36625i	0.439743	+	0.898124i	$0.355069\pi$
$157$	−5.56231	+	17.1190i	−0.443920	+	1.36625i	−0.883663	+	0.468123i	$0.844931\pi$
$158$	0.0450850	+	0.138757i	0.00358677	+	0.0110389i
$159$	−2.92705	+	2.12663i	−0.232130	+	0.168652i
$160$	1.11803	−	0.812299i	0.0883883	−	0.0642179i
$161$	−3.85410	−	11.8617i	−0.303746	−	0.934833i
$162$	−0.309017	+	0.951057i	−0.0242787	+	0.0747221i
$163$	6.85410	+	4.97980i	0.536855	+	0.390048i	0.822916	−	0.568164i	$-0.192346\pi$
$163$	6.85410	+	4.97980i	0.536855	+	0.390048i	−0.286061	+	0.958211i	$0.592346\pi$
$164$	7.70820			0.601910
$165$	−2.33688	−	3.94298i	−0.181926	−	0.306961i
$166$	0.618034			0.0479687
$167$	15.9443	+	11.5842i	1.23380	+	0.896412i	0.997169	−	0.0751869i	$-0.0239553\pi$
$167$	15.9443	+	11.5842i	1.23380	+	0.896412i	0.236635	+	0.971599i	$0.423955\pi$
$168$	0.500000	−	1.53884i	0.0385758	−	0.118724i
$169$	−3.54508	−	10.9106i	−0.272699	−	0.839281i
$170$	4.47214	−	3.24920i	0.342997	−	0.249202i
$171$	−6.23607	+	4.53077i	−0.476884	+	0.346477i
$172$	−2.85410	−	8.78402i	−0.217623	−	0.669775i
$173$	0.409830	−	1.26133i	0.0311588	−	0.0958969i	−0.934268	−	0.356572i	$-0.883945\pi$
$173$	0.409830	−	1.26133i	0.0311588	−	0.0958969i	0.965426	+	0.260676i	$0.0839453\pi$
$174$	0.118034	+	0.0857567i	0.00894813	+	0.00650120i
$175$	5.00000			0.377964
$176$	2.19098	−	2.48990i	0.165152	−	0.187683i
$177$	−5.32624			−0.400345
$178$	9.09017	+	6.60440i	0.681337	+	0.495020i
$179$	0.482779	−	1.48584i	0.0360846	−	0.111057i	−0.931392	−	0.364018i	$-0.881405\pi$
$179$	0.482779	−	1.48584i	0.0360846	−	0.111057i	0.967476	+	0.252961i	$0.0814045\pi$
$180$	0.427051	+	1.31433i	0.0318305	+	0.0979642i
$181$	4.38197	−	3.18368i	0.325709	−	0.236641i	−0.412899	−	0.910777i	$-0.635484\pi$
$181$	4.38197	−	3.18368i	0.325709	−	0.236641i	0.738608	+	0.674136i	$0.235484\pi$
$182$	1.61803	−	1.17557i	0.119937	−	0.0871391i
$183$	3.00000	+	9.23305i	0.221766	+	0.682527i
$184$	−2.38197	+	7.33094i	−0.175601	+	0.540444i
$185$	−10.0000	−	7.26543i	−0.735215	−	0.534165i
$186$	5.61803			0.411934
$187$	8.76393	−	9.95959i	0.640882	−	0.728318i
$188$	4.00000			0.291730
$189$	1.30902	+	0.951057i	0.0952170	+	0.0691792i
$190$	−3.29180	+	10.1311i	−0.238812	+	0.734988i
$191$	−6.47214	−	19.9192i	−0.468307	−	1.44130i	−0.854775	−	0.518999i	$-0.826305\pi$
$191$	−6.47214	−	19.9192i	−0.468307	−	1.44130i	0.386468	−	0.922303i	$-0.373695\pi$
$192$	−0.809017	+	0.587785i	−0.0583858	+	0.0424197i
$193$	1.92705	−	1.40008i	0.138712	−	0.100780i	−0.516265	−	0.856429i	$-0.672678\pi$
$193$	1.92705	−	1.40008i	0.138712	−	0.100780i	0.654977	+	0.755648i	$0.272678\pi$
$194$	2.28115	+	7.02067i	0.163777	+	0.504055i
$195$	−0.527864	+	1.62460i	−0.0378011	+	0.116340i
$196$	3.54508	+	2.57565i	0.253220	+	0.183975i
$197$	12.5066			0.891057			0.445528	−	0.895268i	$-0.353016\pi$
$197$	12.5066			0.891057			0.445528	+	0.895268i	$0.353016\pi$
$198$	1.69098	+	2.85317i	0.120173	+	0.202766i
$199$	−2.61803			−0.185588			−0.0927938	−	0.995685i	$-0.529580\pi$
$199$	−2.61803			−0.185588			−0.0927938	+	0.995685i	$0.529580\pi$
$200$	−2.50000	−	1.81636i	−0.176777	−	0.128436i
$201$	−4.00000	+	12.3107i	−0.282138	+	0.868332i
$202$	−2.80902	−	8.64527i	−0.197642	−	0.608279i
$203$	0.190983	−	0.138757i	0.0134044	−	0.00973885i
$204$	−3.23607	+	2.35114i	−0.226570	+	0.164613i
$205$	3.29180	+	10.1311i	0.229909	+	0.707587i
$206$	0.972136	−	2.99193i	0.0677319	−	0.208457i
$207$	−6.23607	−	4.53077i	−0.433437	−	0.314910i
$208$	−1.23607			−0.0857059
$209$	−2.38197	+	25.4540i	−0.164764	+	1.76069i
$210$	2.23607			0.154303
$211$	3.85410	+	2.80017i	0.265327	+	0.192772i	0.712492	−	0.701680i	$-0.247566\pi$
$211$	3.85410	+	2.80017i	0.265327	+	0.192772i	−0.447165	+	0.894451i	$0.647566\pi$
$212$	1.11803	−	3.44095i	0.0767869	−	0.236326i
$213$	1.85410	+	5.70634i	0.127041	+	0.390992i
$214$	−8.16312	+	5.93085i	−0.558019	+	0.405425i
$215$	10.3262	−	7.50245i	0.704244	−	0.511663i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	2.80902	−	8.64527i	0.190688	−	0.586879i
$218$	12.0902	+	8.78402i	0.818850	+	0.594929i
$219$	−5.56231			−0.375866
$220$	4.20820	+	1.81636i	0.283717	+	0.122459i
$221$	−4.94427			−0.332588
$222$	7.23607	+	5.25731i	0.485653	+	0.352848i
$223$	4.42705	−	13.6251i	0.296457	−	0.912402i	−0.686271	−	0.727346i	$-0.740754\pi$
$223$	4.42705	−	13.6251i	0.296457	−	0.912402i	0.982728	−	0.185056i	$-0.0592465\pi$
$224$	0.500000	+	1.53884i	0.0334077	+	0.102818i
$225$	2.50000	−	1.81636i	0.166667	−	0.121090i
$226$	−8.85410	+	6.43288i	−0.588966	+	0.427909i
$227$	−7.42705	−	22.8581i	−0.492951	−	1.51715i	−0.820126	−	0.572183i	$-0.806097\pi$
$227$	−7.42705	−	22.8581i	−0.492951	−	1.51715i	0.327176	−	0.944964i	$-0.393903\pi$
$228$	2.38197	−	7.33094i	0.157750	−	0.485503i
$229$	−17.3262	−	12.5882i	−1.14495	−	0.831855i	−0.157149	−	0.987575i	$-0.550230\pi$
$229$	−17.3262	−	12.5882i	−1.14495	−	0.831855i	−0.987801	+	0.155720i	$0.950230\pi$
$230$	−10.6525			−0.702403
$231$	5.23607	−	1.17557i	0.344508	−	0.0773469i
$232$	−0.145898			−0.00957868
$233$	−0.763932	−	0.555029i	−0.0500469	−	0.0363612i	0.562481	−	0.826810i	$-0.309847\pi$
$233$	−0.763932	−	0.555029i	−0.0500469	−	0.0363612i	−0.612527	+	0.790449i	$0.709847\pi$
$234$	0.381966	−	1.17557i	0.0249699	−	0.0768494i
$235$	1.70820	+	5.25731i	0.111431	+	0.342949i
$236$	4.30902	−	3.13068i	0.280493	−	0.203790i
$237$	0.118034	−	0.0857567i	0.00766713	−	0.00557050i
$238$	2.00000	+	6.15537i	0.129641	+	0.398993i
$239$	−5.09017	+	15.6659i	−0.329256	+	1.01334i	0.640227	+	0.768186i	$0.278840\pi$
$239$	−5.09017	+	15.6659i	−0.329256	+	1.01334i	−0.969483	+	0.245159i	$0.921160\pi$
$240$	−1.11803	−	0.812299i	−0.0721688	−	0.0524337i
$241$	6.38197			0.411099			0.205549	−	0.978647i	$-0.434102\pi$
$241$	6.38197			0.411099			0.205549	+	0.978647i	$0.434102\pi$
$242$	10.8090	+	2.04087i	0.694830	+	0.131192i
$243$	1.00000			0.0641500
$244$	−7.85410	−	5.70634i	−0.502807	−	0.365311i
$245$	−1.87132	+	5.75934i	−0.119554	+	0.367951i
$246$	−2.38197	−	7.33094i	−0.151869	−	0.467404i
$247$	7.70820	−	5.60034i	0.490461	−	0.356341i
$248$	−4.54508	+	3.30220i	−0.288613	+	0.209690i
$249$	−0.190983	−	0.587785i	−0.0121031	−	0.0372494i
$250$	3.45492	−	10.6331i	0.218508	−	0.672499i
$251$	0.263932	+	0.191758i	0.0166592	+	0.0121036i	0.596084	−	0.802922i	$-0.296723\pi$
$251$	0.263932	+	0.191758i	0.0166592	+	0.0121036i	−0.579424	+	0.815026i	$0.696723\pi$
$252$	−1.61803			−0.101927
$253$	−24.9443	+	5.60034i	−1.56823	+	0.352090i
$254$	−4.00000			−0.250982
$255$	−4.47214	−	3.24920i	−0.280056	−	0.203473i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	6.70820	+	20.6457i	0.418446	+	1.28785i	0.909132	+	0.416508i	$0.136746\pi$
$257$	6.70820	+	20.6457i	0.418446	+	1.28785i	−0.490686	+	0.871337i	$0.663254\pi$
$258$	−7.47214	+	5.42882i	−0.465195	+	0.337984i
$259$	11.7082	−	8.50651i	0.727512	−	0.528569i
$260$	−0.527864	−	1.62460i	−0.0327367	−	0.100753i
$261$	0.0450850	−	0.138757i	0.00279069	−	0.00858886i
$262$	−2.30902	−	1.67760i	−0.142652	−	0.103642i
$263$	−12.7639			−0.787058			−0.393529	−	0.919312i	$-0.628746\pi$
$263$	−12.7639			−0.787058			−0.393529	+	0.919312i	$0.628746\pi$
$264$	−3.04508	−	1.31433i	−0.187412	−	0.0808913i
$265$	5.00000			0.307148
$266$	−10.0902	−	7.33094i	−0.618668	−	0.449489i
$267$	3.47214	−	10.6861i	0.212491	−	0.653981i
$268$	−4.00000	−	12.3107i	−0.244339	−	0.751998i
$269$	−4.85410	+	3.52671i	−0.295960	+	0.215027i	−0.725849	−	0.687854i	$-0.758553\pi$
$269$	−4.85410	+	3.52671i	−0.295960	+	0.215027i	0.429889	+	0.902882i	$0.358553\pi$
$270$	1.11803	−	0.812299i	0.0680414	−	0.0494350i
$271$	5.41641	+	16.6700i	0.329023	+	1.01263i	0.969592	+	0.244729i	$0.0786988\pi$
$271$	5.41641	+	16.6700i	0.329023	+	1.01263i	−0.640568	+	0.767901i	$0.721301\pi$
$272$	1.23607	−	3.80423i	0.0749476	−	0.230665i
$273$	−1.61803	−	1.17557i	−0.0979279	−	0.0711488i
$274$	−8.18034			−0.494192
$275$	0.954915	−	10.2044i	0.0575835	−	0.615346i
$276$	7.70820			0.463979
$277$	−1.85410	−	1.34708i	−0.111402	−	0.0809384i	0.530689	−	0.847566i	$-0.321933\pi$
$277$	−1.85410	−	1.34708i	−0.111402	−	0.0809384i	−0.642092	+	0.766628i	$0.721933\pi$
$278$	0.708204	−	2.17963i	0.0424752	−	0.130725i
$279$	−1.73607	−	5.34307i	−0.103936	−	0.319881i
$280$	−1.80902	+	1.31433i	−0.108109	+	0.0785461i
$281$	−13.5623	+	9.85359i	−0.809059	+	0.587816i	−0.913558	−	0.406709i	$-0.866676\pi$
$281$	−13.5623	+	9.85359i	−0.809059	+	0.587816i	0.104498	+	0.994525i	$0.466676\pi$
$282$	−1.23607	−	3.80423i	−0.0736068	−	0.226538i
$283$	−5.09017	+	15.6659i	−0.302579	+	0.931243i	0.677990	+	0.735071i	$0.262851\pi$
$283$	−5.09017	+	15.6659i	−0.302579	+	0.931243i	−0.980569	+	0.196172i	$0.937149\pi$
$284$	−4.85410	−	3.52671i	−0.288038	−	0.209272i
$285$	10.6525			0.630998
$286$	−2.09017	−	3.52671i	−0.123594	−	0.208539i
$287$	−12.4721			−0.736207
$288$	0.809017	+	0.587785i	0.0476718	+	0.0346356i
$289$	−0.309017	+	0.951057i	−0.0181775	+	0.0559445i
$290$	−0.0623059	−	0.191758i	−0.00365873	−	0.0112604i
$291$	5.97214	−	4.33901i	0.350093	−	0.254357i
$292$	4.50000	−	3.26944i	0.263343	−	0.191330i
$293$	2.35410	+	7.24518i	0.137528	+	0.423268i	0.995975	−	0.0896350i	$-0.0285701\pi$
$293$	2.35410	+	7.24518i	0.137528	+	0.423268i	−0.858447	+	0.512903i	$0.828570\pi$
$294$	1.35410	−	4.16750i	0.0789728	−	0.243053i
$295$	5.95492	+	4.32650i	0.346709	+	0.251899i
$296$	−8.94427			−0.519875
$297$	2.19098	−	2.48990i	0.127134	−	0.144479i
$298$	23.0344			1.33435
$299$	7.70820	+	5.60034i	0.445777	+	0.323876i
$300$	−0.954915	+	2.93893i	−0.0551320	+	0.169679i
$301$	4.61803	+	14.2128i	0.266179	+	0.819215i
$302$	−3.88197	+	2.82041i	−0.223382	+	0.162297i
$303$	−7.35410	+	5.34307i	−0.422482	+	0.306951i
$304$	2.38197	+	7.33094i	0.136615	+	0.420458i
$305$	4.14590	−	12.7598i	0.237393	−	0.730622i
$306$	3.23607	+	2.35114i	0.184994	+	0.134406i
$307$	−12.7639			−0.728476			−0.364238	−	0.931306i	$-0.618671\pi$
$307$	−12.7639			−0.728476			−0.364238	+	0.931306i	$0.618671\pi$
$308$	−3.54508	+	4.02874i	−0.202000	+	0.229559i
$309$	−3.14590			−0.178964
$310$	−6.28115	−	4.56352i	−0.356746	−	0.259191i
$311$	2.32624	−	7.15942i	0.131909	−	0.405974i	−0.863188	−	0.504883i	$-0.831535\pi$
$311$	2.32624	−	7.15942i	0.131909	−	0.405974i	0.995096	+	0.0989097i	$0.0315355\pi$
$312$	0.381966	+	1.17557i	0.0216246	+	0.0665536i
$313$	20.2082	−	14.6821i	1.14224	−	0.829882i	0.154806	−	0.987945i	$-0.450525\pi$
$313$	20.2082	−	14.6821i	1.14224	−	0.829882i	0.987429	+	0.158062i	$0.0505247\pi$
$314$	−14.5623	+	10.5801i	−0.821798	+	0.597072i
$315$	−0.690983	−	2.12663i	−0.0389325	−	0.119822i
$316$	−0.0450850	+	0.138757i	−0.00253623	+	0.00780571i
$317$	21.7984	+	15.8374i	1.22432	+	0.889520i	0.996451	−	0.0841726i	$-0.0268247\pi$
$317$	21.7984	+	15.8374i	1.22432	+	0.889520i	0.227867	+	0.973692i	$0.426825\pi$
$318$	−3.61803			−0.202889
$319$	−0.246711	−	0.416272i	−0.0138132	−	0.0233067i
$320$	1.38197			0.0772542
$321$	8.16312	+	5.93085i	0.455621	+	0.331028i
$322$	3.85410	−	11.8617i	0.214781	−	0.661027i
$323$	9.52786	+	29.3238i	0.530145	+	1.63162i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	−3.09017	+	2.24514i	−0.171412	+	0.124538i
$326$	2.61803	+	8.05748i	0.144999	+	0.446263i
$327$	4.61803	−	14.2128i	0.255378	−	0.785972i
$328$	6.23607	+	4.53077i	0.344329	+	0.250170i
$329$	−6.47214			−0.356820
$330$	0.427051	−	4.56352i	0.0235084	−	0.251214i
$331$	28.3607			1.55884			0.779422	−	0.626499i	$-0.215513\pi$
$331$	28.3607			1.55884			0.779422	+	0.626499i	$0.215513\pi$
$332$	0.500000	+	0.363271i	0.0274411	+	0.0199371i
$333$	2.76393	−	8.50651i	0.151463	−	0.466154i
$334$	6.09017	+	18.7436i	0.333239	+	1.02561i
$335$	14.4721	−	10.5146i	0.790697	−	0.574475i
$336$	1.30902	−	0.951057i	0.0714127	−	0.0518844i
$337$	−4.90983	−	15.1109i	−0.267455	−	0.823143i	−0.991118	−	0.132989i	$-0.957543\pi$
$337$	−4.90983	−	15.1109i	−0.267455	−	0.823143i	0.723662	−	0.690155i	$-0.242457\pi$
$338$	3.54508	−	10.9106i	0.192827	−	0.593461i
$339$	8.85410	+	6.43288i	0.480889	+	0.349386i
$340$	5.52786			0.299791
$341$	−17.1074	−	7.38394i	−0.926417	−	0.399863i
$342$	−7.70820			−0.416812
$343$	−14.8992	−	10.8249i	−0.804480	−	0.584489i
$344$	2.85410	−	8.78402i	0.153883	−	0.473603i
$345$	3.29180	+	10.1311i	0.177224	+	0.545440i
$346$	1.07295	−	0.779543i	0.0576821	−	0.0419085i
$347$	15.1074	−	10.9762i	0.811007	−	0.589231i	−0.103115	−	0.994669i	$-0.532881\pi$
$347$	15.1074	−	10.9762i	0.811007	−	0.589231i	0.914122	+	0.405438i	$0.132881\pi$
$348$	0.0450850	+	0.138757i	0.00241681	+	0.00743817i
$349$	−7.94427	+	24.4500i	−0.425247	+	1.30878i	0.477510	+	0.878626i	$0.341539\pi$
$349$	−7.94427	+	24.4500i	−0.425247	+	1.30878i	−0.902757	+	0.430150i	$0.858461\pi$
$350$	4.04508	+	2.93893i	0.216219	+	0.157092i
$351$	−1.23607			−0.0659764
$352$	3.23607	−	0.726543i	0.172483	−	0.0387248i
$353$	11.2361			0.598036			0.299018	−	0.954248i	$-0.403341\pi$
$353$	11.2361			0.598036			0.299018	+	0.954248i	$0.403341\pi$
$354$	−4.30902	−	3.13068i	−0.229022	−	0.166394i
$355$	2.56231	−	7.88597i	0.135993	−	0.418544i
$356$	3.47214	+	10.6861i	0.184023	+	0.566364i
$357$	5.23607	−	3.80423i	0.277122	−	0.201341i
$358$	1.26393	−	0.918300i	0.0668009	−	0.0485337i
$359$	−1.79837	−	5.53483i	−0.0949145	−	0.292117i	0.892317	−	0.451410i	$-0.149079\pi$
$359$	−1.79837	−	5.53483i	−0.0949145	−	0.292117i	−0.987231	+	0.159293i	$0.949079\pi$
$360$	−0.427051	+	1.31433i	−0.0225076	+	0.0692712i
$361$	−32.6976	−	23.7562i	−1.72092	−	1.25032i
$362$	5.41641			0.284680
$363$	−1.39919	−	10.9106i	−0.0734383	−	0.572661i
$364$	2.00000			0.104828
$365$	6.21885	+	4.51826i	0.325509	+	0.236496i
$366$	−3.00000	+	9.23305i	−0.156813	+	0.482619i
$367$	3.10081	+	9.54332i	0.161861	+	0.498157i	0.998791	−	0.0491524i	$-0.0156520\pi$
$367$	3.10081	+	9.54332i	0.161861	+	0.498157i	−0.836930	+	0.547310i	$0.815652\pi$
$368$	−6.23607	+	4.53077i	−0.325078	+	0.236183i
$369$	−6.23607	+	4.53077i	−0.324637	+	0.235862i
$370$	−3.81966	−	11.7557i	−0.198575	−	0.611150i
$371$	−1.80902	+	5.56758i	−0.0939195	+	0.289054i
$372$	4.54508	+	3.30220i	0.235652	+	0.171211i
$373$		0			0			−	1.00000i	$-0.5\pi$
$373$		0			0				1.00000i	$0.5\pi$
$374$	12.9443	−	2.90617i	0.669332	−	0.150274i
$375$	−11.1803			−0.577350
$376$	3.23607	+	2.35114i	0.166887	+	0.121251i
$377$	−0.0557281	+	0.171513i	−0.00287014	+	0.00883339i
$378$	0.500000	+	1.53884i	0.0257172	+	0.0791495i
$379$	−3.09017	+	2.24514i	−0.158731	+	0.115325i	−0.664316	−	0.747452i	$-0.731277\pi$
$379$	−3.09017	+	2.24514i	−0.158731	+	0.115325i	0.505584	+	0.862777i	$0.331277\pi$
$380$	−8.61803	+	6.26137i	−0.442096	+	0.321201i
$381$	1.23607	+	3.80423i	0.0633257	+	0.194896i
$382$	6.47214	−	19.9192i	0.331143	−	1.01915i
$383$	−30.5066	−	22.1643i	−1.55881	−	1.13254i	−0.936974	−	0.349399i	$-0.886386\pi$
$383$	−30.5066	−	22.1643i	−1.55881	−	1.13254i	−0.621839	−	0.783145i	$-0.713614\pi$
$384$	−1.00000			−0.0510310
$385$	−6.80902	−	2.93893i	−0.347020	−	0.149782i
$386$	2.38197			0.121239
$387$	7.47214	+	5.42882i	0.379830	+	0.275963i
$388$	−2.28115	+	7.02067i	−0.115808	+	0.356420i
$389$	0.326238	+	1.00406i	0.0165409	+	0.0509077i	0.958986	−	0.283452i	$-0.0914798\pi$
$389$	0.326238	+	1.00406i	0.0165409	+	0.0509077i	−0.942445	+	0.334360i	$0.891480\pi$
$390$	−1.38197	+	1.00406i	−0.0699786	+	0.0508424i
$391$	−24.9443	+	18.1231i	−1.26149	+	0.916523i
$392$	1.35410	+	4.16750i	0.0683925	+	0.210490i
$393$	−0.881966	+	2.71441i	−0.0444893	+	0.136924i
$394$	10.1180	+	7.35118i	0.509739	+	0.370347i
$395$	−0.201626			−0.0101449
$396$	−0.309017	+	3.30220i	−0.0155287	+	0.165942i
$397$	−12.9443			−0.649654			−0.324827	−	0.945773i	$-0.605306\pi$
$397$	−12.9443			−0.649654			−0.324827	+	0.945773i	$0.605306\pi$
$398$	−2.11803	−	1.53884i	−0.106167	−	0.0771352i
$399$	−3.85410	+	11.8617i	−0.192946	+	0.593828i
$400$	−0.954915	−	2.93893i	−0.0477458	−	0.146946i
$401$	−9.47214	+	6.88191i	−0.473016	+	0.343666i	−0.798615	−	0.601842i	$-0.794434\pi$
$401$	−9.47214	+	6.88191i	−0.473016	+	0.343666i	0.325600	+	0.945508i	$0.394434\pi$
$402$	−10.4721	+	7.60845i	−0.522303	+	0.379475i
$403$	2.14590	+	6.60440i	0.106895	+	0.328988i
$404$	2.80902	−	8.64527i	0.139754	−	0.430118i
$405$	−1.11803	−	0.812299i	−0.0555556	−	0.0403635i
$406$	0.236068			0.0117159
$407$	−15.1246	−	25.5195i	−0.749699	−	1.26496i
$408$	−4.00000			−0.198030
$409$	−13.7361	−	9.97984i	−0.679205	−	0.493471i	0.193889	−	0.981023i	$-0.437890\pi$
$409$	−13.7361	−	9.97984i	−0.679205	−	0.493471i	−0.873094	+	0.487552i	$0.837890\pi$
$410$	−3.29180	+	10.1311i	−0.162570	+	0.500340i
$411$	2.52786	+	7.77997i	0.124690	+	0.383757i
$412$	2.54508	−	1.84911i	0.125387	−	0.0910992i
$413$	−6.97214	+	5.06555i	−0.343076	+	0.249260i
$414$	−2.38197	−	7.33094i	−0.117067	−	0.360296i
$415$	−0.263932	+	0.812299i	−0.0129559	+	0.0398742i
$416$	−1.00000	−	0.726543i	−0.0490290	−	0.0356217i
$417$	−2.29180			−0.112230
$418$	−16.8885	+	19.1926i	−0.826046	+	0.938743i
$419$	0.909830			0.0444481			0.0222241	−	0.999753i	$-0.492925\pi$
$419$	0.909830			0.0444481			0.0222241	+	0.999753i	$0.492925\pi$
$420$	1.80902	+	1.31433i	0.0882710	+	0.0641326i
$421$	12.2361	−	37.6587i	0.596349	−	1.83537i	0.0484585	−	0.998825i	$-0.484569\pi$
$421$	12.2361	−	37.6587i	0.596349	−	1.83537i	0.547891	−	0.836550i	$-0.315431\pi$
$422$	1.47214	+	4.53077i	0.0716625	+	0.220554i
$423$	−3.23607	+	2.35114i	−0.157343	+	0.114316i
$424$	2.92705	−	2.12663i	0.142150	−	0.103278i
$425$	−3.81966	−	11.7557i	−0.185281	−	0.570235i
$426$	−1.85410	+	5.70634i	−0.0898315	+	0.276473i
$427$	12.7082	+	9.23305i	0.614993	+	0.446819i
$428$	−10.0902			−0.487727
$429$	−2.70820	+	3.07768i	−0.130753	+	0.148592i
$430$	12.7639			0.615531
$431$	19.4721	+	14.1473i	0.937940	+	0.681453i	0.947924	−	0.318497i	$-0.103178\pi$
$431$	19.4721	+	14.1473i	0.937940	+	0.681453i	−0.00998408	+	0.999950i	$0.503178\pi$
$432$	0.309017	−	0.951057i	0.0148676	−	0.0457577i
$433$	2.97214	+	9.14729i	0.142832	+	0.439591i	0.996726	−	0.0808560i	$-0.0257654\pi$
$433$	2.97214	+	9.14729i	0.142832	+	0.439591i	−0.853894	+	0.520447i	$0.825765\pi$
$434$	7.35410	−	5.34307i	0.353008	−	0.256475i
$435$	−0.163119	+	0.118513i	−0.00782096	+	0.00568226i
$436$	4.61803	+	14.2128i	0.221164	+	0.680672i
$437$	18.3607	−	56.5084i	0.878310	−	2.70316i
$438$	−4.50000	−	3.26944i	−0.215018	−	0.156220i
$439$	−34.9230			−1.66678			−0.833392	−	0.552683i	$-0.813604\pi$
$439$	−34.9230			−1.66678			−0.833392	+	0.552683i	$0.813604\pi$
$440$	2.33688	+	3.94298i	0.111406	+	0.187974i
$441$	−4.38197			−0.208665
$442$	−4.00000	−	2.90617i	−0.190261	−	0.138232i
$443$	2.11803	−	6.51864i	0.100631	−	0.309710i	−0.888049	−	0.459748i	$-0.847940\pi$
$443$	2.11803	−	6.51864i	0.100631	−	0.309710i	0.988680	+	0.150038i	$0.0479397\pi$
$444$	2.76393	+	8.50651i	0.131170	+	0.403701i
$445$	−12.5623	+	9.12705i	−0.595510	+	0.432664i
$446$	11.5902	−	8.42075i	0.548810	−	0.398734i
$447$	−7.11803	−	21.9071i	−0.336671	−	1.03617i
$448$	−0.500000	+	1.53884i	−0.0236228	+	0.0727034i
$449$	6.85410	+	4.97980i	0.323465	+	0.235011i	0.737653	−	0.675180i	$-0.235934\pi$
$449$	6.85410	+	4.97980i	0.323465	+	0.235011i	−0.414188	+	0.910192i	$0.635934\pi$
$450$	3.09017			0.145672
$451$	−2.38197	+	25.4540i	−0.112162	+	1.19858i
$452$	−10.9443			−0.514775
$453$	3.88197	+	2.82041i	0.182391	+	0.132515i
$454$	7.42705	−	22.8581i	0.348569	−	1.07278i
$455$	0.854102	+	2.62866i	0.0400409	+	0.123233i
$456$	6.23607	−	4.53077i	0.292031	−	0.212173i
$457$	13.6803	−	9.93935i	0.639939	−	0.464943i	−0.219890	−	0.975525i	$-0.570570\pi$
$457$	13.6803	−	9.93935i	0.639939	−	0.464943i	0.859829	+	0.510582i	$0.170570\pi$
$458$	−6.61803	−	20.3682i	−0.309240	−	0.951744i
$459$	1.23607	−	3.80423i	0.0576947	−	0.177566i
$460$	−8.61803	−	6.26137i	−0.401818	−	0.291938i
$461$	22.0000			1.02464			0.512321	−	0.858794i	$-0.328786\pi$
$461$	22.0000			1.02464			0.512321	+	0.858794i	$0.328786\pi$
$462$	4.92705	+	2.12663i	0.229227	+	0.0989396i
$463$	34.7426			1.61463			0.807314	−	0.590122i	$-0.200920\pi$
$463$	34.7426			1.61463			0.807314	+	0.590122i	$0.200920\pi$
$464$	−0.118034	−	0.0857567i	−0.00547959	−	0.00398116i
$465$	−2.39919	+	7.38394i	−0.111260	+	0.342422i
$466$	−0.291796	−	0.898056i	−0.0135172	−	0.0416016i
$467$	9.54508	−	6.93491i	0.441694	−	0.320909i	−0.344614	−	0.938745i	$-0.611990\pi$
$467$	9.54508	−	6.93491i	0.441694	−	0.320909i	0.786308	+	0.617835i	$0.211990\pi$
$468$	1.00000	−	0.726543i	0.0462250	−	0.0335844i
$469$	6.47214	+	19.9192i	0.298855	+	0.919783i
$470$	−1.70820	+	5.25731i	−0.0787936	+	0.242502i
$471$	14.5623	+	10.5801i	0.670996	+	0.487507i
$472$	5.32624			0.245160
$473$	29.8885	−	6.71040i	1.37428	−	0.308544i
$474$	0.145898			0.00670132
$475$	19.2705	+	14.0008i	0.884192	+	0.642403i
$476$	−2.00000	+	6.15537i	−0.0916698	+	0.282131i
$477$	1.11803	+	3.44095i	0.0511913	+	0.157550i
$478$	−13.3262	+	9.68208i	−0.609528	+	0.442848i
$479$	−10.7082	+	7.77997i	−0.489270	+	0.355476i	−0.804904	−	0.593406i	$-0.797783\pi$
$479$	−10.7082	+	7.77997i	−0.489270	+	0.355476i	0.315633	+	0.948881i	$0.397783\pi$
$480$	−0.427051	−	1.31433i	−0.0194921	−	0.0599906i
$481$	−3.41641	+	10.5146i	−0.155775	+	0.479426i
$482$	5.16312	+	3.75123i	0.235174	+	0.170864i
$483$	−12.4721			−0.567502
$484$	7.54508	+	8.00448i	0.342958	+	0.363840i
$485$	−10.2016			−0.463232
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	−2.50000	+	7.69421i	−0.113286	+	0.348658i	−0.991586	−	0.129452i	$-0.958678\pi$
$487$	−2.50000	+	7.69421i	−0.113286	+	0.348658i	0.878300	+	0.478110i	$0.158678\pi$
$488$	−3.00000	−	9.23305i	−0.135804	−	0.417961i
$489$	6.85410	−	4.97980i	0.309953	−	0.225194i
$490$	−4.89919	+	3.55947i	−0.221323	+	0.160800i
$491$	10.2918	+	31.6749i	0.464462	+	1.42947i	0.859658	+	0.510871i	$0.170677\pi$
$491$	10.2918	+	31.6749i	0.464462	+	1.42947i	−0.395195	+	0.918597i	$0.629323\pi$
$492$	2.38197	−	7.33094i	0.107387	−	0.330504i
$493$	−0.472136	−	0.343027i	−0.0212639	−	0.0154492i
$494$	9.52786			0.428679
$495$	−4.47214	+	1.00406i	−0.201008	+	0.0451290i
$496$	−5.61803			−0.252257
$497$	7.85410	+	5.70634i	0.352305	+	0.255964i
$498$	0.190983	−	0.587785i	0.00855815	−	0.0263393i
$499$	−7.81966	−	24.0664i	−0.350056	−	1.07736i	−0.958821	−	0.284011i	$-0.908335\pi$
$499$	−7.81966	−	24.0664i	−0.350056	−	1.07736i	0.608765	−	0.793351i	$-0.291665\pi$
$500$	9.04508	−	6.57164i	0.404508	−	0.293893i
$501$	15.9443	−	11.5842i	0.712338	−	0.517544i
$502$	0.100813	+	0.310271i	0.00449951	+	0.0138481i
$503$	−9.70820	+	29.8788i	−0.432867	+	1.33223i	0.462389	+	0.886677i	$0.346992\pi$
$503$	−9.70820	+	29.8788i	−0.432867	+	1.33223i	−0.895256	+	0.445552i	$0.853008\pi$
$504$	−1.30902	−	0.951057i	−0.0583083	−	0.0423634i
$505$	12.5623			0.559015
$506$	−23.4721	−	10.1311i	−1.04346	−	0.450383i
$507$	−11.4721			−0.509495
$508$	−3.23607	−	2.35114i	−0.143577	−	0.104315i
$509$	−3.17376	+	9.76784i	−0.140675	+	0.432952i	−0.996429	−	0.0844297i	$-0.973093\pi$
$509$	−3.17376	+	9.76784i	−0.140675	+	0.432952i	0.855755	+	0.517381i	$0.173093\pi$
$510$	−1.70820	−	5.25731i	−0.0756405	−	0.232798i
$511$	−7.28115	+	5.29007i	−0.322099	+	0.234019i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	2.38197	+	7.33094i	0.105166	+	0.323669i
$514$	−6.70820	+	20.6457i	−0.295886	+	0.910644i
$515$	3.51722	+	2.55541i	0.154987	+	0.112605i
$516$	−9.23607			−0.406595
$517$	−1.23607	+	13.2088i	−0.0543622	+	0.580922i
$518$	14.4721			0.635869
$519$	−1.07295	−	0.779543i	−0.0470972	−	0.0342181i
$520$	0.527864	−	1.62460i	0.0231484	−	0.0712434i
$521$	−8.65248	−	26.6296i	−0.379072	−	1.16666i	−0.940690	−	0.339267i	$-0.889821\pi$
$521$	−8.65248	−	26.6296i	−0.379072	−	1.16666i	0.561618	−	0.827396i	$-0.310179\pi$
$522$	0.118034	−	0.0857567i	0.00516621	−	0.00375347i
$523$	13.4721	−	9.78808i	0.589095	−	0.428003i	−0.252896	−	0.967493i	$-0.581383\pi$
$523$	13.4721	−	9.78808i	0.589095	−	0.428003i	0.841992	+	0.539491i	$0.181383\pi$
$524$	−0.881966	−	2.71441i	−0.0385289	−	0.118580i
$525$	1.54508	−	4.75528i	0.0674330	−	0.207538i
$526$	−10.3262	−	7.50245i	−0.450245	−	0.327122i
$527$	−22.4721			−0.978902
$528$	−1.69098	−	2.85317i	−0.0735906	−	0.124168i
$529$	36.4164			1.58332
$530$	4.04508	+	2.93893i	0.175707	+	0.127659i
$531$	−1.64590	+	5.06555i	−0.0714259	+	0.219826i
$532$	−3.85410	−	11.8617i	−0.167097	−	0.514270i
$533$	7.70820	−	5.60034i	0.333879	−	0.242578i
$534$	9.09017	−	6.60440i	0.393370	−	0.285800i
$535$	−4.30902	−	13.2618i	−0.186295	−	0.573357i
$536$	4.00000	−	12.3107i	0.172774	−	0.531743i
$537$	−1.26393	−	0.918300i	−0.0545427	−	0.0396276i
$538$	−6.00000			−0.258678
$539$	−9.60081	+	10.9106i	−0.413536	+	0.469955i
$540$	1.38197			0.0594703
$541$	−3.61803	−	2.62866i	−0.155551	−	0.113015i	0.507287	−	0.861777i	$-0.330648\pi$
$541$	−3.61803	−	2.62866i	−0.155551	−	0.113015i	−0.662838	+	0.748762i	$0.730648\pi$
$542$	−5.41641	+	16.6700i	−0.232655	+	0.716037i
$543$	−1.67376	−	5.15131i	−0.0718280	−	0.221064i
$544$	3.23607	−	2.35114i	0.138745	−	0.100804i
$545$	−16.7082	+	12.1392i	−0.715701	+	0.519987i
$546$	−0.618034	−	1.90211i	−0.0264494	−	0.0814029i
$547$	−0.888544	+	2.73466i	−0.0379914	+	0.116925i	−0.968254	−	0.249970i	$-0.919579\pi$
$547$	−0.888544	+	2.73466i	−0.0379914	+	0.116925i	0.930262	+	0.366895i	$0.119579\pi$
$548$	−6.61803	−	4.80828i	−0.282708	−	0.205400i
$549$	9.70820			0.414336
$550$	6.77051	−	7.69421i	0.288696	−	0.328082i
$551$	1.12461			0.0479101
$552$	6.23607	+	4.53077i	0.265425	+	0.192842i
$553$	0.0729490	−	0.224514i	0.00310211	−	0.00954731i
$554$	−0.708204	−	2.17963i	−0.0300887	−	0.0926035i
$555$	−10.0000	+	7.26543i	−0.424476	+	0.308400i
$556$	1.85410	−	1.34708i	0.0786314	−	0.0571291i
$557$	4.11803	+	12.6740i	0.174487	+	0.537015i	0.999610	−	0.0279384i	$-0.00889421\pi$
$557$	4.11803	+	12.6740i	0.174487	+	0.537015i	−0.825123	+	0.564953i	$0.808894\pi$
$558$	1.73607	−	5.34307i	0.0734936	−	0.226190i
$559$	−9.23607	−	6.71040i	−0.390644	−	0.283820i
$560$	−2.23607			−0.0944911
$561$	−6.76393	−	11.4127i	−0.285573	−	0.481844i
$562$	−16.7639			−0.707144
$563$	−6.47214	−	4.70228i	−0.272768	−	0.198178i	0.442989	−	0.896527i	$-0.353918\pi$
$563$	−6.47214	−	4.70228i	−0.272768	−	0.198178i	−0.715757	+	0.698350i	$0.753918\pi$
$564$	1.23607	−	3.80423i	0.0520479	−	0.160187i
$565$	−4.67376	−	14.3844i	−0.196627	−	0.605155i
$566$	−13.3262	+	9.68208i	−0.560144	+	0.406968i
$567$	1.30902	−	0.951057i	0.0549735	−	0.0399406i
$568$	−1.85410	−	5.70634i	−0.0777964	−	0.239433i
$569$	−5.09017	+	15.6659i	−0.213391	+	0.656750i	0.785873	+	0.618388i	$0.212214\pi$
$569$	−5.09017	+	15.6659i	−0.213391	+	0.656750i	−0.999264	+	0.0383620i	$0.987786\pi$
$570$	8.61803	+	6.26137i	0.360970	+	0.262260i
$571$	1.34752			0.0563921			0.0281961	−	0.999602i	$-0.491024\pi$
$571$	1.34752			0.0563921			0.0281961	+	0.999602i	$0.491024\pi$
$572$	0.381966	−	4.08174i	0.0159708	−	0.170666i
$573$	−20.9443			−0.874960
$574$	−10.0902	−	7.33094i	−0.421156	−	0.305987i
$575$	−7.36068	+	22.6538i	−0.306962	+	0.944731i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	4.25329	−	3.09020i	0.177067	−	0.128647i	−0.495722	−	0.868481i	$-0.665096\pi$
$577$	4.25329	−	3.09020i	0.177067	−	0.128647i	0.672788	+	0.739835i	$0.265096\pi$
$578$	−0.809017	+	0.587785i	−0.0336507	+	0.0244486i
$579$	−0.736068	−	2.26538i	−0.0305899	−	0.0941462i
$580$	0.0623059	−	0.191758i	0.00258711	−	0.00796231i
$581$	−0.809017	−	0.587785i	−0.0335637	−	0.0243854i
$582$	7.38197			0.305992
$583$	11.0172	+	4.75528i	0.456287	+	0.196944i
$584$	5.56231			0.230170
$585$	1.38197	+	1.00406i	0.0571373	+	0.0415127i
$586$	−2.35410	+	7.24518i	−0.0972471	+	0.299296i
$587$	−6.55166	−	20.1639i	−0.270416	−	0.832255i	−0.990396	−	0.138260i	$-0.955849\pi$
$587$	−6.55166	−	20.1639i	−0.270416	−	0.832255i	0.719980	−	0.693995i	$-0.244151\pi$
$588$	3.54508	−	2.57565i	0.146197	−	0.106218i
$589$	35.0344	−	25.4540i	1.44357	−	1.04881i
$590$	2.27458	+	7.00042i	0.0936428	+	0.288203i
$591$	3.86475	−	11.8945i	0.158974	−	0.489273i
$592$	−7.23607	−	5.25731i	−0.297401	−	0.216074i
$593$	−7.88854			−0.323944			−0.161972	−	0.986795i	$-0.551785\pi$
$593$	−7.88854			−0.323944			−0.161972	+	0.986795i	$0.551785\pi$
$594$	3.23607	−	0.726543i	0.132777	−	0.0298104i
$595$	−8.94427			−0.366679
$596$	18.6353	+	13.5393i	0.763330	+	0.554592i
$597$	−0.809017	+	2.48990i	−0.0331109	+	0.101905i
$598$	2.94427	+	9.06154i	0.120400	+	0.370554i
$599$	−26.1803	+	19.0211i	−1.06970	+	0.777182i	−0.975858	−	0.218405i	$-0.929915\pi$
$599$	−26.1803	+	19.0211i	−1.06970	+	0.777182i	−0.0938414	+	0.995587i	$0.529915\pi$
$600$	−2.50000	+	1.81636i	−0.102062	+	0.0741524i
$601$	−6.20820	−	19.1069i	−0.253238	−	0.779386i	−0.994172	−	0.107808i	$-0.965617\pi$
$601$	−6.20820	−	19.1069i	−0.253238	−	0.779386i	0.740934	−	0.671578i	$-0.234383\pi$
$602$	−4.61803	+	14.2128i	−0.188217	+	0.579272i
$603$	10.4721	+	7.60845i	0.426458	+	0.309840i
$604$	−4.79837			−0.195243
$605$	−7.29837	+	13.3350i	−0.296721	+	0.542146i
$606$	−9.09017			−0.369263
$607$	−12.1803	−	8.84953i	−0.494385	−	0.359192i	0.312483	−	0.949923i	$-0.398839\pi$
$607$	−12.1803	−	8.84953i	−0.494385	−	0.359192i	−0.806868	+	0.590732i	$0.798839\pi$
$608$	−2.38197	+	7.33094i	−0.0966015	+	0.297309i
$609$	−0.0729490	−	0.224514i	−0.00295604	−	0.00909777i
$610$	10.8541	−	7.88597i	0.439470	−	0.319293i
$611$	4.00000	−	2.90617i	0.161823	−	0.117571i
$612$	1.23607	+	3.80423i	0.0499651	+	0.153777i
$613$	1.03444	−	3.18368i	0.0417807	−	0.128588i	−0.927990	−	0.372604i	$-0.878465\pi$
$613$	1.03444	−	3.18368i	0.0417807	−	0.128588i	0.969771	+	0.244016i	$0.0784650\pi$
$614$	−10.3262	−	7.50245i	−0.416733	−	0.302774i
$615$	10.6525			0.429549
$616$	−5.23607	+	1.17557i	−0.210967	+	0.0473651i
$617$	−15.1246			−0.608894			−0.304447	−	0.952529i	$-0.598472\pi$
$617$	−15.1246			−0.608894			−0.304447	+	0.952529i	$0.598472\pi$
$618$	−2.54508	−	1.84911i	−0.102378	−	0.0743822i
$619$	1.23607	−	3.80423i	0.0496818	−	0.152905i	−0.923138	−	0.384469i	$-0.874384\pi$
$619$	1.23607	−	3.80423i	0.0496818	−	0.152905i	0.972820	+	0.231565i	$0.0743845\pi$
$620$	−2.39919	−	7.38394i	−0.0963537	−	0.296546i
$621$	−6.23607	+	4.53077i	−0.250245	+	0.181813i
$622$	6.09017	−	4.42477i	0.244194	−	0.177417i
$623$	−5.61803	−	17.2905i	−0.225082	−	0.692730i
$624$	−0.381966	+	1.17557i	−0.0152909	+	0.0470605i
$625$		0			0
$626$	24.9787			0.998350
$627$	23.4721	+	10.1311i	0.937387	+	0.404597i
$628$	−18.0000			−0.718278
$629$	−28.9443	−	21.0292i	−1.15408	−	0.838491i
$630$	0.690983	−	2.12663i	0.0275294	−	0.0847268i
$631$	−7.48278	−	23.0296i	−0.297885	−	0.916795i	−0.982237	−	0.187644i	$-0.939915\pi$
$631$	−7.48278	−	23.0296i	−0.297885	−	0.916795i	0.684352	−	0.729151i	$-0.260085\pi$
$632$	−0.118034	+	0.0857567i	−0.00469514	+	0.00341122i
$633$	3.85410	−	2.80017i	0.153187	−	0.111297i
$634$	8.32624	+	25.6255i	0.330677	+	1.01772i
$635$	1.70820	−	5.25731i	0.0677880	−	0.208630i
$636$	−2.92705	−	2.12663i	−0.116065	−	0.0843262i
$637$	5.41641			0.214606
$638$	0.0450850	−	0.481784i	0.00178493	−	0.0190740i
$639$	6.00000			0.237356
$640$	1.11803	+	0.812299i	0.0441942	+	0.0321089i
$641$	−6.23607	+	19.1926i	−0.246310	+	0.758064i	0.749108	+	0.662447i	$0.230482\pi$
$641$	−6.23607	+	19.1926i	−0.246310	+	0.758064i	−0.995418	+	0.0956164i	$0.969518\pi$
$642$	3.11803	+	9.59632i	0.123059	+	0.378737i
$643$	−4.85410	+	3.52671i	−0.191427	+	0.139080i	−0.679371	−	0.733795i	$-0.737747\pi$
$643$	−4.85410	+	3.52671i	−0.191427	+	0.139080i	0.487944	+	0.872875i	$0.337747\pi$
$644$	10.0902	−	7.33094i	0.397608	−	0.288879i
$645$	−3.94427	−	12.1392i	−0.155306	−	0.477981i
$646$	−9.52786	+	29.3238i	−0.374869	+	1.15373i
$647$	17.1803	+	12.4822i	0.675429	+	0.490728i	0.871838	−	0.489794i	$-0.162928\pi$
$647$	17.1803	+	12.4822i	0.675429	+	0.490728i	−0.196409	+	0.980522i	$0.562928\pi$
$648$	−1.00000			−0.0392837
$649$	9.00658	+	15.1967i	0.353539	+	0.596521i
$650$	−3.81966			−0.149819
$651$	−7.35410	−	5.34307i	−0.288230	−	0.209411i
$652$	−2.61803	+	8.05748i	−0.102530	+	0.315555i
$653$	−1.10081	−	3.38795i	−0.0430781	−	0.132581i	0.927204	−	0.374556i	$-0.122205\pi$
$653$	−1.10081	−	3.38795i	−0.0430781	−	0.132581i	−0.970282	+	0.241975i	$0.922205\pi$
$654$	12.0902	−	8.78402i	0.472763	−	0.343482i
$655$	3.19098	−	2.31838i	0.124682	−	0.0905868i
$656$	2.38197	+	7.33094i	0.0930001	+	0.286225i
$657$	−1.71885	+	5.29007i	−0.0670586	+	0.206385i
$658$	−5.23607	−	3.80423i	−0.204123	−	0.148304i
$659$	45.9230			1.78891			0.894453	−	0.447162i	$-0.147565\pi$
$659$	45.9230			1.78891			0.894453	+	0.447162i	$0.147565\pi$
$660$	3.02786	−	3.44095i	0.117859	−	0.133939i
$661$	−11.5967			−0.451061			−0.225531	−	0.974236i	$-0.572412\pi$
$661$	−11.5967			−0.451061			−0.225531	+	0.974236i	$0.572412\pi$
$662$	22.9443	+	16.6700i	0.891754	+	0.647898i
$663$	−1.52786	+	4.70228i	−0.0593373	+	0.182622i
$664$	0.190983	+	0.587785i	0.00741158	+	0.0228105i
$665$	13.9443	−	10.1311i	0.540736	−	0.392867i
$666$	7.23607	−	5.25731i	0.280392	−	0.203717i
$667$	0.347524	+	1.06957i	0.0134562	+	0.0414139i
$668$	−6.09017	+	18.7436i	−0.235636	+	0.725212i
$669$	−11.5902	−	8.42075i	−0.448102	−	0.325565i
$670$	17.8885			0.691095
$671$	21.2705	−	24.1724i	0.821139	−	0.933167i
$672$	1.61803			0.0624170
$673$	−6.26393	−	4.55101i	−0.241457	−	0.175429i	0.460475	−	0.887673i	$-0.347679\pi$
$673$	−6.26393	−	4.55101i	−0.241457	−	0.175429i	−0.701932	+	0.712244i	$0.747679\pi$
$674$	4.90983	−	15.1109i	0.189120	−	0.582050i
$675$	−0.954915	−	2.93893i	−0.0367547	−	0.113119i
$676$	9.28115	−	6.74315i	0.356967	−	0.259352i
$677$	−41.1418	+	29.8913i	−1.58121	+	1.14882i	−0.665916	+	0.746026i	$0.731959\pi$
$677$	−41.1418	+	29.8913i	−1.58121	+	1.14882i	−0.915293	+	0.402789i	$0.868041\pi$
$678$	3.38197	+	10.4086i	0.129884	+	0.399741i
$679$	3.69098	−	11.3597i	0.141647	−	0.435944i
$680$	4.47214	+	3.24920i	0.171499	+	0.124601i
$681$	−24.0344			−0.921002
$682$	−9.50000	−	16.0292i	−0.363774	−	0.613790i
$683$	−14.4508			−0.552946			−0.276473	−	0.961022i	$-0.589166\pi$
$683$	−14.4508			−0.552946			−0.276473	+	0.961022i	$0.589166\pi$
$684$	−6.23607	−	4.53077i	−0.238442	−	0.173238i
$685$	3.49342	−	10.7516i	0.133477	−	0.410799i
$686$	−5.69098	−	17.5150i	−0.217283	−	0.668728i
$687$	−17.3262	+	12.5882i	−0.661037	+	0.480272i
$688$	7.47214	−	5.42882i	0.284873	−	0.206972i
$689$	−1.38197	−	4.25325i	−0.0526487	−	0.162036i
$690$	−3.29180	+	10.1311i	−0.125317	+	0.385685i
$691$	−4.14590	−	3.01217i	−0.157717	−	0.114588i	0.506128	−	0.862459i	$-0.331077\pi$
$691$	−4.14590	−	3.01217i	−0.157717	−	0.114588i	−0.663845	+	0.747870i	$0.731077\pi$
$692$	1.32624			0.0504160
$693$	0.500000	−	5.34307i	0.0189934	−	0.202966i
$694$	18.6738			0.708846
$695$	2.56231	+	1.86162i	0.0971938	+	0.0706154i
$696$	−0.0450850	+	0.138757i	−0.00170894	+	0.00525958i
$697$	9.52786	+	29.3238i	0.360894	+	1.11072i
$698$	−20.7984	+	15.1109i	−0.787230	+	0.571956i
$699$	−0.763932	+	0.555029i	−0.0288946	+	0.0209931i
$700$	1.54508	+	4.75528i	0.0583987	+	0.179733i
$701$	4.97871	−	15.3229i	0.188043	−	0.578738i	−0.811944	−	0.583735i	$-0.801591\pi$
$701$	4.97871	−	15.3229i	0.188043	−	0.578738i	0.999988	+	0.00499706i	$0.00159062\pi$
$702$	−1.00000	−	0.726543i	−0.0377426	−	0.0274216i
$703$	68.9443			2.60028
$704$	3.04508	+	1.31433i	0.114766	+	0.0495356i
$705$	5.52786			0.208191
$706$	9.09017	+	6.60440i	0.342113	+	0.248560i
$707$	−4.54508	+	13.9883i	−0.170936	+	0.526085i
$708$	−1.64590	−	5.06555i	−0.0618566	−	0.190375i
$709$	−27.9443	+	20.3027i	−1.04947	+	0.762484i	−0.972111	−	0.234519i	$-0.924648\pi$
$709$	−27.9443	+	20.3027i	−1.04947	+	0.762484i	−0.0773577	+	0.997003i	$0.524648\pi$
$710$	6.70820	−	4.87380i	0.251754	−	0.182910i
$711$	−0.0450850	−	0.138757i	−0.00169082	−	0.00520380i
$712$	−3.47214	+	10.6861i	−0.130124	+	0.400480i
$713$	35.0344	+	25.4540i	1.31205	+	0.953260i
$714$	6.47214			0.242214
$715$	5.52786	−	1.24108i	0.206730	−	0.0464139i
$716$	1.56231			0.0583861
$717$	13.3262	+	9.68208i	0.497677	+	0.361584i
$718$	1.79837	−	5.53483i	0.0671147	−	0.206558i
$719$	0.326238	+	1.00406i	0.0121666	+	0.0374450i	0.956956	−	0.290235i	$-0.0937333\pi$
$719$	0.326238	+	1.00406i	0.0121666	+	0.0374450i	−0.944789	+	0.327680i	$0.893733\pi$
$720$	−1.11803	+	0.812299i	−0.0416667	+	0.0302726i
$721$	−4.11803	+	2.99193i	−0.153364	+	0.111425i
$722$	−12.4894	−	38.4383i	−0.464806	−	1.43052i
$723$	1.97214	−	6.06961i	0.0733445	−	0.225731i
$724$	4.38197	+	3.18368i	0.162854	+	0.118321i
$725$	−0.450850			−0.0167441
$726$	5.28115	−	9.64932i	0.196002	−	0.358120i
$727$	−31.4164			−1.16517			−0.582585	−	0.812770i	$-0.697959\pi$
$727$	−31.4164			−1.16517			−0.582585	+	0.812770i	$0.697959\pi$
$728$	1.61803	+	1.17557i	0.0599683	+	0.0435695i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	2.37539	+	7.31069i	0.0879171	+	0.270581i
$731$	29.8885	−	21.7153i	1.10547	−	0.803169i
$732$	−7.85410	+	5.70634i	−0.290296	+	0.210912i
$733$	7.18034	+	22.0988i	0.265212	+	0.816238i	0.991645	+	0.129001i	$0.0411769\pi$
$733$	7.18034	+	22.0988i	0.265212	+	0.816238i	−0.726433	+	0.687238i	$0.758823\pi$
$734$	−3.10081	+	9.54332i	−0.114453	+	0.352250i
$735$	4.89919	+	3.55947i	0.180709	+	0.131293i
$736$	−7.70820			−0.284128
$737$	41.8885	−	9.40456i	1.54298	−	0.346422i
$738$	−7.70820			−0.283743
$739$	−27.1246	−	19.7072i	−0.997795	−	0.724940i	−0.0361807	−	0.999345i	$-0.511519\pi$
$739$	−27.1246	−	19.7072i	−0.997795	−	0.724940i	−0.961614	+	0.274405i	$0.911519\pi$
$740$	3.81966	−	11.7557i	0.140413	−	0.432148i
$741$	−2.94427	−	9.06154i	−0.108161	−	0.332884i
$742$	−4.73607	+	3.44095i	−0.173867	+	0.126321i
$743$	20.2705	−	14.7274i	0.743653	−	0.540295i	−0.150200	−	0.988656i	$-0.547992\pi$
$743$	20.2705	−	14.7274i	0.743653	−	0.540295i	0.893853	+	0.448360i	$0.147992\pi$
$744$	1.73607	+	5.34307i	0.0636473	+	0.195886i
$745$	−9.83688	+	30.2748i	−0.360395	+	1.10918i
$746$		0			0
$747$	−0.618034			−0.0226127
$748$	12.1803	+	5.25731i	0.445357	+	0.192226i
$749$	16.3262			0.596548
$750$	−9.04508	−	6.57164i	−0.330280	−	0.239962i
$751$	−5.81966	+	17.9111i	−0.212362	+	0.653584i	0.786968	+	0.616994i	$0.211650\pi$
$751$	−5.81966	+	17.9111i	−0.212362	+	0.653584i	−0.999330	+	0.0365904i	$0.988350\pi$
$752$	1.23607	+	3.80423i	0.0450748	+	0.138726i
$753$	0.263932	−	0.191758i	0.00961822	−	0.00698804i
$754$	−0.145898	+	0.106001i	−0.00531329	+	0.00386033i
$755$	−2.04915	−	6.30664i	−0.0745762	−	0.229522i
$756$	−0.500000	+	1.53884i	−0.0181848	+	0.0559671i
$757$	44.2148	+	32.1239i	1.60701	+	1.16756i	0.871992	+	0.489520i	$0.162828\pi$
$757$	44.2148	+	32.1239i	1.60701	+	1.16756i	0.735021	+	0.678044i	$0.237172\pi$
$758$	−3.81966			−0.138736
$759$	−2.38197	+	25.4540i	−0.0864599	+	0.923922i
$760$	−10.6525			−0.386406
$761$	−43.8328	−	31.8464i	−1.58894	−	1.15443i	−0.905436	−	0.424483i	$-0.860456\pi$
$761$	−43.8328	−	31.8464i	−1.58894	−	1.15443i	−0.683502	−	0.729948i	$-0.739544\pi$
$762$	−1.23607	+	3.80423i	−0.0447780	+	0.137813i
$763$	−7.47214	−	22.9969i	−0.270509	−	0.832543i
$764$	16.9443	−	12.3107i	0.613022	−	0.445387i
$765$	−4.47214	+	3.24920i	−0.161690	+	0.117475i
$766$	−11.6525	−	35.8626i	−0.421021	−	1.29577i
$767$	2.03444	−	6.26137i	0.0734594	−	0.226085i
$768$	−0.809017	−	0.587785i	−0.0291929	−	0.0212099i
$769$	−41.5623			−1.49878			−0.749388	−	0.662132i	$-0.769652\pi$
$769$	−41.5623			−1.49878			−0.749388	+	0.662132i	$0.769652\pi$
$770$	−3.78115	−	6.37988i	−0.136263	−	0.229915i
$771$	21.7082			0.781802
$772$	1.92705	+	1.40008i	0.0693561	+	0.0503901i
$773$	12.9894	−	39.9771i	0.467195	−	1.43788i	−0.389007	−	0.921235i	$-0.627182\pi$
$773$	12.9894	−	39.9771i	0.467195	−	1.43788i	0.856201	−	0.516642i	$-0.172818\pi$
$774$	2.85410	+	8.78402i	0.102589	+	0.315735i
$775$	−14.0451	+	10.2044i	−0.504514	+	0.366551i
$776$	−5.97214	+	4.33901i	−0.214387	+	0.155761i
$777$	−4.47214	−	13.7638i	−0.160437	−	0.493774i
$778$	−0.326238	+	1.00406i	−0.0116962	+	0.0359972i
$779$	−48.0689	−	34.9241i	−1.72225	−	1.25129i
$780$	−1.70820			−0.0611635
$781$	13.1459	−	14.9394i	0.470397	−	0.534573i
$782$	−30.8328			−1.10258
$783$	−0.118034	−	0.0857567i	−0.00421819	−	0.00306469i
$784$	−1.35410	+	4.16750i	−0.0483608	+	0.148839i
$785$	−7.68692	−	23.6579i	−0.274358	−	0.844387i
$786$	−2.30902	+	1.67760i	−0.0823599	+	0.0598380i
$787$	−16.4164	+	11.9272i	−0.585182	+	0.425159i	−0.840588	−	0.541674i	$-0.817791\pi$
$787$	−16.4164	+	11.9272i	−0.585182	+	0.425159i	0.255407	+	0.966834i	$0.417791\pi$
$788$	3.86475	+	11.8945i	0.137676	+	0.423723i
$789$	−3.94427	+	12.1392i	−0.140420	+	0.432168i
$790$	−0.163119	−	0.118513i	−0.00580351	−	0.00421650i
$791$	17.7082			0.629631
$792$	−2.19098	+	2.48990i	−0.0778532	+	0.0884747i
$793$	−12.0000			−0.426132
$794$	−10.4721	−	7.60845i	−0.371642	−	0.270014i
$795$	1.54508	−	4.75528i	0.0547985	−	0.168652i
$796$	−0.809017	−	2.48990i	−0.0286748	−	0.0882521i
$797$	−37.7254	+	27.4091i	−1.33630	+	0.970881i	−0.336732	+	0.941601i	$0.609322\pi$
$797$	−37.7254	+	27.4091i	−1.33630	+	0.970881i	−0.999571	+	0.0292805i	$0.990678\pi$
$798$	−10.0902	+	7.33094i	−0.357188	+	0.259512i
$799$	4.94427	+	15.2169i	0.174916	+	0.538335i
$800$	0.954915	−	2.93893i	0.0337613	−	0.103907i
$801$	−9.09017	−	6.60440i	−0.321185	−	0.233355i
$802$	−11.7082			−0.413431
$803$	9.40576	+	15.8702i	0.331922	+	0.560047i
$804$	−12.9443			−0.456509
$805$	13.9443	+	10.1311i	0.491471	+	0.357075i
$806$	−2.14590	+	6.60440i	−0.0755860	+	0.232630i
$807$	1.85410	+	5.70634i	0.0652675	+	0.200873i
$808$	7.35410	−	5.34307i	0.258716	−	0.187968i
$809$	2.47214	−	1.79611i	0.0869157	−	0.0631479i	−0.543479	−	0.839423i	$-0.682893\pi$
$809$	2.47214	−	1.79611i	0.0869157	−	0.0631479i	0.630394	+	0.776275i	$0.282893\pi$
$810$	−0.427051	−	1.31433i	−0.0150050	−	0.0461808i
$811$	6.74265	−	20.7517i	0.236766	−	0.728692i	−0.760116	−	0.649788i	$-0.774858\pi$
$811$	6.74265	−	20.7517i	0.236766	−	0.728692i	0.996882	−	0.0789043i	$-0.0251421\pi$
$812$	0.190983	+	0.138757i	0.00670219	+	0.00486943i
$813$	17.5279			0.614729
$814$	2.76393	−	29.5358i	0.0968758	−	1.03523i
$815$	−11.7082			−0.410120
$816$	−3.23607	−	2.35114i	−0.113285	−	0.0823064i
$817$	−22.0000	+	67.7090i	−0.769683	+	2.36884i
$818$	−5.24671	−	16.1477i	−0.183447	−	0.564592i
$819$	−1.61803	+	1.17557i	−0.0565387	+	0.0410778i
$820$	−8.61803	+	6.26137i	−0.300955	+	0.218656i
$821$	13.7705	+	42.3813i	0.480594	+	1.47912i	0.838262	+	0.545268i	$0.183572\pi$
$821$	13.7705	+	42.3813i	0.480594	+	1.47912i	−0.357668	+	0.933849i	$0.616428\pi$
$822$	−2.52786	+	7.77997i	−0.0881694	+	0.271357i
$823$	−19.2984	−	14.0211i	−0.672699	−	0.488744i	0.198229	−	0.980156i	$-0.436481\pi$
$823$	−19.2984	−	14.0211i	−0.672699	−	0.488744i	−0.870928	+	0.491411i	$0.836481\pi$
$824$	3.14590			0.109593
$825$	−9.40983	−	4.06150i	−0.327608	−	0.141403i
$826$	−8.61803			−0.299860
$827$	−5.25329	−	3.81674i	−0.182675	−	0.132721i	0.492690	−	0.870205i	$-0.336014\pi$
$827$	−5.25329	−	3.81674i	−0.182675	−	0.132721i	−0.675365	+	0.737484i	$0.736014\pi$
$828$	2.38197	−	7.33094i	0.0827790	−	0.254768i
$829$	−6.72949	−	20.7112i	−0.233725	−	0.719331i	−0.997288	−	0.0735980i	$-0.976552\pi$
$829$	−6.72949	−	20.7112i	−0.233725	−	0.719331i	0.763563	−	0.645733i	$-0.223448\pi$
$830$	−0.690983	+	0.502029i	−0.0239844	+	0.0174257i
$831$	−1.85410	+	1.34708i	−0.0643181	+	0.0467298i
$832$	−0.381966	−	1.17557i	−0.0132423	−	0.0407556i
$833$	−5.41641	+	16.6700i	−0.187667	+	0.577581i
$834$	−1.85410	−	1.34708i	−0.0642023	−	0.0466457i
$835$	−27.2361			−0.942543
$836$	−24.9443	+	5.60034i	−0.862716	+	0.193692i
$837$	−5.61803			−0.194188
$838$	0.736068	+	0.534785i	0.0254270	+	0.0184738i
$839$	15.7639	−	48.5164i	0.544231	−	1.67497i	−0.178579	−	0.983926i	$-0.557150\pi$
$839$	15.7639	−	48.5164i	0.544231	−	1.67497i	0.722810	−	0.691046i	$-0.242850\pi$
$840$	0.690983	+	2.12663i	0.0238412	+	0.0733756i
$841$	23.4443	−	17.0333i	0.808423	−	0.587354i
$842$	32.0344	−	23.2744i	1.10398	−	0.802088i
$843$	5.18034	+	15.9434i	0.178420	+	0.549121i
$844$	−1.47214	+	4.53077i	−0.0506730	+	0.155955i
$845$	12.8262	+	9.31881i	0.441236	+	0.320577i
$846$	−4.00000			−0.137523
$847$	−12.2082	−	12.9515i	−0.419479	−	0.445019i
$848$	3.61803			0.124244
$849$	13.3262	+	9.68208i	0.457355	+	0.332288i
$850$	3.81966	−	11.7557i	0.131013	−	0.403217i
$851$	21.3050	+	65.5699i	0.730324	+	2.24771i
$852$	−4.85410	+	3.52671i	−0.166299	+	0.120823i
$853$	−18.1803	+	13.2088i	−0.622483	+	0.452260i	−0.853788	−	0.520621i	$-0.825700\pi$
$853$	−18.1803	+	13.2088i	−0.622483	+	0.452260i	0.231305	+	0.972881i	$0.425700\pi$
$854$	4.85410	+	14.9394i	0.166104	+	0.511215i
$855$	3.29180	−	10.1311i	0.112577	−	0.346477i
$856$	−8.16312	−	5.93085i	−0.279010	−	0.202712i
$857$	−2.18034			−0.0744790			−0.0372395	−	0.999306i	$-0.511856\pi$
$857$	−2.18034			−0.0744790			−0.0372395	+	0.999306i	$0.511856\pi$
$858$	−4.00000	+	0.898056i	−0.136558	+	0.0306591i
$859$	41.9574			1.43157			0.715784	−	0.698321i	$-0.246069\pi$
$859$	41.9574			1.43157			0.715784	+	0.698321i	$0.246069\pi$
$860$	10.3262	+	7.50245i	0.352122	+	0.255831i
$861$	−3.85410	+	11.8617i	−0.131347	+	0.404246i
$862$	7.43769	+	22.8909i	0.253329	+	0.779666i
$863$	26.7984	−	19.4702i	0.912227	−	0.662772i	−0.0293499	−	0.999569i	$-0.509344\pi$
$863$	26.7984	−	19.4702i	0.912227	−	0.662772i	0.941577	+	0.336797i	$0.109344\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$	0.566371	+	1.74311i	0.0192572	+	0.0592676i
$866$	−2.97214	+	9.14729i	−0.100997	+	0.310838i
$867$	0.809017	+	0.587785i	0.0274757	+	0.0199622i
$868$	9.09017			0.308540
$869$	−0.444272	−	0.191758i	−0.0150709	−	0.00650494i
$870$	−0.201626			−0.00683577
$871$	−12.9443	−	9.40456i	−0.438600	−	0.318661i
$872$	−4.61803	+	14.2128i	−0.156386	+	0.481308i
$873$	−2.28115	−	7.02067i	−0.0772053	−	0.237614i
$874$	48.0689	−	34.9241i	1.62595	−	1.18132i
$875$	−14.6353	+	10.6331i	−0.494762	+	0.359466i
$876$	−1.71885	−	5.29007i	−0.0580745	−	0.178735i
$877$	7.67376	−	23.6174i	0.259125	−	0.797503i	−0.733864	−	0.679296i	$-0.762285\pi$
$877$	7.67376	−	23.6174i	0.259125	−	0.797503i	0.992989	−	0.118207i	$-0.0377147\pi$
$878$	−28.2533	−	20.5272i	−0.953502	−	0.692760i
$879$	7.61803			0.256950
$880$	−0.427051	+	4.56352i	−0.0143959	+	0.153836i
$881$	34.0689			1.14781			0.573905	−	0.818922i	$-0.305428\pi$
$881$	34.0689			1.14781			0.573905	+	0.818922i	$0.305428\pi$
$882$	−3.54508	−	2.57565i	−0.119369	−	0.0867268i
$883$	3.25735	−	10.0251i	0.109619	−	0.337372i	−0.881168	−	0.472803i	$-0.843242\pi$
$883$	3.25735	−	10.0251i	0.109619	−	0.337372i	0.990787	+	0.135432i	$0.0432421\pi$
$884$	−1.52786	−	4.70228i	−0.0513876	−	0.158155i
$885$	5.95492	−	4.32650i	0.200172	−	0.145434i
$886$	5.54508	−	4.02874i	0.186291	−	0.135348i
$887$	5.25735	+	16.1805i	0.176525	+	0.543287i	0.999700	−	0.0245004i	$-0.00779951\pi$
$887$	5.25735	+	16.1805i	0.176525	+	0.543287i	−0.823175	+	0.567788i	$0.807800\pi$
$888$	−2.76393	+	8.50651i	−0.0927515	+	0.285460i
$889$	5.23607	+	3.80423i	0.175612	+	0.127590i
$890$	−15.5279			−0.520495
$891$	−1.69098	−	2.85317i	−0.0566501	−	0.0955848i
$892$	14.3262			0.479678
$893$	−24.9443	−	18.1231i	−0.834728	−	0.606466i
$894$	7.11803	−	21.9071i	0.238063	−	0.732682i
$895$	0.667184	+	2.05338i	0.0223015	+	0.0686370i
$896$	−1.30902	+	0.951057i	−0.0437312	+	0.0317726i
$897$	7.70820	−	5.60034i	0.257369	−	0.186990i
$898$	2.61803	+	8.05748i	0.0873649	+	0.268882i
$899$	−0.253289	+	0.779543i	−0.00844766	+	0.0259992i
$900$	2.50000	+	1.81636i	0.0833333	+	0.0605452i
$901$	14.4721			0.482137
$902$	−16.8885	+	19.1926i	−0.562327	+	0.639045i
$903$	14.9443			0.497314
$904$	−8.85410	−	6.43288i	−0.294483	−	0.213954i
$905$	−2.31308	+	7.11894i	−0.0768895	+	0.236641i
$906$	1.48278	+	4.56352i	0.0492620	+	0.151613i
$907$	−9.47214	+	6.88191i	−0.314517	+	0.228510i	−0.733832	−	0.679331i	$-0.762270\pi$
$907$	−9.47214	+	6.88191i	−0.314517	+	0.228510i	0.419315	+	0.907841i	$0.362270\pi$
$908$	19.4443	−	14.1271i	0.645281	−	0.468824i
$909$	2.80902	+	8.64527i	0.0931692	+	0.286745i
$910$	−0.854102	+	2.62866i	−0.0283132	+	0.0871391i
$911$	32.7984	+	23.8294i	1.08666	+	0.789504i	0.978832	−	0.204666i	$-0.0656108\pi$
$911$	32.7984	+	23.8294i	1.08666	+	0.789504i	0.107827	+	0.994170i	$0.465611\pi$
$912$	7.70820			0.255244
$913$	−1.35410	+	1.53884i	−0.0448142	+	0.0509282i
$914$	16.9098			0.559327
$915$	−10.8541	−	7.88597i	−0.358826	−	0.260702i
$916$	6.61803	−	20.3682i	0.218666	−	0.672985i
$917$	1.42705	+	4.39201i	0.0471254	+	0.145037i
$918$	3.23607	−	2.35114i	0.106806	−	0.0775992i
$919$	8.64590	−	6.28161i	0.285202	−	0.207211i	−0.435981	−	0.899956i	$-0.643599\pi$
$919$	8.64590	−	6.28161i	0.285202	−	0.207211i	0.721183	+	0.692744i	$0.243599\pi$
$920$	−3.29180	−	10.1311i	−0.108527	−	0.334013i
$921$	−3.94427	+	12.1392i	−0.129968	+	0.400001i
$922$	17.7984	+	12.9313i	0.586158	+	0.425869i
$923$	−7.41641			−0.244114
$924$	2.73607	+	4.61653i	0.0900100	+	0.151873i
$925$	−27.6393			−0.908775
$926$	28.1074	+	20.4212i	0.923666	+	0.671083i
$927$	−0.972136	+	2.99193i	−0.0319291	+	0.0982678i
$928$	−0.0450850	−	0.138757i	−0.00147999	−	0.00455493i
$929$	−3.09017	+	2.24514i	−0.101385	+	0.0736607i	−0.637323	−	0.770597i	$-0.719958\pi$
$929$	−3.09017	+	2.24514i	−0.101385	+	0.0736607i	0.535938	+	0.844258i	$0.319958\pi$
$930$	−6.28115	+	4.56352i	−0.205967	+	0.149644i
$931$	−10.4377	−	32.1239i	−0.342082	−	1.05282i
$932$	0.291796	−	0.898056i	0.00955810	−	0.0294168i
$933$	−6.09017	−	4.42477i	−0.199383	−	0.144860i
$934$	11.7984			0.386055
$935$	−1.70820	+	18.2541i	−0.0558642	+	0.596973i
$936$	1.23607			0.0404021
$937$	42.4336	+	30.8298i	1.38625	+	1.00717i	0.996265	+	0.0863439i	$0.0275184\pi$
$937$	42.4336	+	30.8298i	1.38625	+	1.00717i	0.389981	+	0.920823i	$0.372482\pi$
$938$	−6.47214	+	19.9192i	−0.211323	+	0.650384i
$939$	−7.71885	−	23.7562i	−0.251895	−	0.775253i
$940$	−4.47214	+	3.24920i	−0.145865	+	0.105977i
$941$	27.3262	−	19.8537i	0.890810	−	0.647211i	−0.0452792	−	0.998974i	$-0.514418\pi$
$941$	27.3262	−	19.8537i	0.890810	−	0.647211i	0.936089	+	0.351763i	$0.114418\pi$
$942$	5.56231	+	17.1190i	0.181230	+	0.557768i
$943$	18.3607	−	56.5084i	0.597906	−	1.84017i
$944$	4.30902	+	3.13068i	0.140247	+	0.101895i
$945$	−2.23607			−0.0727393
$946$	28.1246	+	12.1392i	0.914410	+	0.394680i
$947$	−32.9230			−1.06985			−0.534927	−	0.844899i	$-0.679661\pi$
$947$	−32.9230			−1.06985			−0.534927	+	0.844899i	$0.679661\pi$
$948$	0.118034	+	0.0857567i	0.00383357	+	0.00278525i
$949$	2.12461	−	6.53888i	0.0689678	−	0.212261i
$950$	7.36068	+	22.6538i	0.238812	+	0.734988i
$951$	21.7984	−	15.8374i	0.706861	−	0.513564i
$952$	−5.23607	+	3.80423i	−0.169702	+	0.123296i
$953$	−8.18034	−	25.1765i	−0.264987	−	0.815547i	−0.991696	−	0.128601i	$-0.958951\pi$
$953$	−8.18034	−	25.1765i	−0.264987	−	0.815547i	0.726709	−	0.686945i	$-0.241049\pi$
$954$	−1.11803	+	3.44095i	−0.0361977	+	0.111405i
$955$	23.4164	+	17.0130i	0.757737	+	0.550528i
$956$	−16.4721			−0.532747
$957$	−0.472136	+	0.106001i	−0.0152620	+	0.00342653i
$958$	−13.2361			−0.427638
$959$	10.7082	+	7.77997i	0.345786	+	0.251228i
$960$	0.427051	−	1.31433i	0.0137830	−	0.0424197i
$961$	0.173762	+	0.534785i	0.00560523	+	0.0172511i
$962$	−8.94427	+	6.49839i	−0.288375	+	0.209517i
$963$	8.16312	−	5.93085i	0.263053	−	0.191119i
$964$	1.97214	+	6.06961i	0.0635182	+	0.195489i
$965$	−1.01722	+	3.13068i	−0.0327455	+	0.100780i
$966$	−10.0902	−	7.33094i	−0.324646	−	0.235869i
$967$	−17.3820			−0.558966			−0.279483	−	0.960151i	$-0.590163\pi$
$967$	−17.3820			−0.558966			−0.279483	+	0.960151i	$0.590163\pi$
$968$	1.39919	+	10.9106i	0.0449716	+	0.350682i
$969$	30.8328			0.990493
$970$	−8.25329	−	5.99637i	−0.264997	−	0.192532i
$971$	−4.47214	+	13.7638i	−0.143518	+	0.441702i	−0.996817	−	0.0797188i	$-0.974598\pi$
$971$	−4.47214	+	13.7638i	−0.143518	+	0.441702i	0.853300	+	0.521421i	$0.174598\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	−3.00000	+	2.17963i	−0.0961756	+	0.0698757i
$974$	−6.54508	+	4.75528i	−0.209718	+	0.152369i
$975$	1.18034	+	3.63271i	0.0378011	+	0.116340i
$976$	3.00000	−	9.23305i	0.0960277	−	0.295543i
$977$	−46.1246	−	33.5115i	−1.47566	−	1.07213i	−0.978924	−	0.204224i	$-0.934533\pi$
$977$	−46.1246	−	33.5115i	−1.47566	−	1.07213i	−0.496733	−	0.867903i	$-0.665467\pi$
$978$	8.47214			0.270909
$979$	−36.3607	+	8.16348i	−1.16209	+	0.260906i
$980$	−6.05573			−0.193443
$981$	−12.0902	−	8.78402i	−0.386009	−	0.280452i
$982$	−10.2918	+	31.6749i	−0.328424	+	1.01079i
$983$	9.14590	+	28.1482i	0.291709	+	0.897788i	0.984307	+	0.176464i	$0.0564659\pi$
$983$	9.14590	+	28.1482i	0.291709	+	0.897788i	−0.692598	+	0.721324i	$0.743534\pi$
$984$	6.23607	−	4.53077i	0.198799	−	0.144436i
$985$	−13.9828	+	10.1591i	−0.445528	+	0.323695i
$986$	−0.180340	−	0.555029i	−0.00574319	−	0.0176757i
$987$	−2.00000	+	6.15537i	−0.0636607	+	0.195927i
$988$	7.70820	+	5.60034i	0.245231	+	0.178170i
$989$	−71.1935			−2.26382
$990$	−4.20820	−	1.81636i	−0.133746	−	0.0577276i
$991$	−18.3951			−0.584340			−0.292170	−	0.956366i	$-0.594377\pi$
$991$	−18.3951			−0.584340			−0.292170	+	0.956366i	$0.594377\pi$
$992$	−4.54508	−	3.30220i	−0.144307	−	0.104845i
$993$	8.76393	−	26.9726i	0.278115	−	0.855950i
$994$	3.00000	+	9.23305i	0.0951542	+	0.292855i
$995$	2.92705	−	2.12663i	0.0927938	−	0.0674186i
$996$	0.500000	−	0.363271i	0.0158431	−	0.0115107i
$997$	−2.05573	−	6.32688i	−0.0651056	−	0.200374i	0.913212	−	0.407485i	$-0.133594\pi$
$997$	−2.05573	−	6.32688i	−0.0651056	−	0.200374i	−0.978318	+	0.207110i	$0.933594\pi$
$998$	7.81966	−	24.0664i	0.247527	−	0.761810i
$999$	−7.23607	−	5.25731i	−0.228939	−	0.166334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	66.2.e.b.37.1	yes	4
3.2	odd	2		198.2.f.a.37.1		4
4.3	odd	2		528.2.y.g.433.1		4
11.2	odd	10		726.2.e.a.511.1		4
11.3	even	5	inner	66.2.e.b.25.1	✓	4
11.4	even	5		726.2.e.j.493.1		4
11.5	even	5		726.2.a.k.1.1		2
11.6	odd	10		726.2.a.m.1.1		2
11.7	odd	10		726.2.e.a.493.1		4
11.8	odd	10		726.2.e.c.487.1		4
11.9	even	5		726.2.e.j.511.1		4
11.10	odd	2		726.2.e.c.565.1		4
33.5	odd	10		2178.2.a.v.1.2		2
33.14	odd	10		198.2.f.a.91.1		4
33.17	even	10		2178.2.a.o.1.2		2
44.3	odd	10		528.2.y.g.289.1		4
44.27	odd	10		5808.2.a.bz.1.1		2
44.39	even	10		5808.2.a.by.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.e.b.25.1	✓	4	11.3	even	5	inner
66.2.e.b.37.1	yes	4	1.1	even	1	trivial
198.2.f.a.37.1		4	3.2	odd	2
198.2.f.a.91.1		4	33.14	odd	10
528.2.y.g.289.1		4	44.3	odd	10
528.2.y.g.433.1		4	4.3	odd	2
726.2.a.k.1.1		2	11.5	even	5
726.2.a.m.1.1		2	11.6	odd	10
726.2.e.a.493.1		4	11.7	odd	10
726.2.e.a.511.1		4	11.2	odd	10
726.2.e.c.487.1		4	11.8	odd	10
726.2.e.c.565.1		4	11.10	odd	2
726.2.e.j.493.1		4	11.4	even	5
726.2.e.j.511.1		4	11.9	even	5
2178.2.a.o.1.2		2	33.17	even	10
2178.2.a.v.1.2		2	33.5	odd	10
5808.2.a.by.1.1		2	44.39	even	10
5808.2.a.bz.1.1		2	44.27	odd	10

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:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	66.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.11803 + 0.812299i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-0.500000 - 1.53884i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} -1.38197 q^{10} +(-3.23607 + 0.726543i) q^{11} +1.00000 q^{12} +(1.00000 + 0.726543i) q^{13} +(0.500000 - 1.53884i) q^{14} +(0.427051 + 1.31433i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-3.23607 + 2.35114i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(2.38197 - 7.33094i) q^{19} +(-1.11803 - 0.812299i) q^{20} -1.61803 q^{21} +(-3.04508 - 1.31433i) q^{22} +7.70820 q^{23} +(0.809017 + 0.587785i) q^{24} +(-0.954915 + 2.93893i) q^{25} +(0.381966 + 1.17557i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(1.30902 - 0.951057i) q^{28} +(0.0450850 + 0.138757i) q^{29} +(-0.427051 + 1.31433i) q^{30} +(4.54508 + 3.30220i) q^{31} -1.00000 q^{32} +(-0.309017 + 3.30220i) q^{33} -4.00000 q^{34} +(1.80902 + 1.31433i) q^{35} +(0.309017 - 0.951057i) q^{36} +(2.76393 + 8.50651i) q^{37} +(6.23607 - 4.53077i) q^{38} +(1.00000 - 0.726543i) q^{39} +(-0.427051 - 1.31433i) q^{40} +(2.38197 - 7.33094i) q^{41} +(-1.30902 - 0.951057i) q^{42} -9.23607 q^{43} +(-1.69098 - 2.85317i) q^{44} +1.38197 q^{45} +(6.23607 + 4.53077i) q^{46} +(1.23607 - 3.80423i) q^{47} +(0.309017 + 0.951057i) q^{48} +(3.54508 - 2.57565i) q^{49} +(-2.50000 + 1.81636i) q^{50} +(1.23607 + 3.80423i) q^{51} +(-0.381966 + 1.17557i) q^{52} +(-2.92705 - 2.12663i) q^{53} -1.00000 q^{54} +(3.02786 - 3.44095i) q^{55} +1.61803 q^{56} +(-6.23607 - 4.53077i) q^{57} +(-0.0450850 + 0.138757i) q^{58} +(-1.64590 - 5.06555i) q^{59} +(-1.11803 + 0.812299i) q^{60} +(-7.85410 + 5.70634i) q^{61} +(1.73607 + 5.34307i) q^{62} +(-0.500000 + 1.53884i) q^{63} +(-0.809017 - 0.587785i) q^{64} -1.70820 q^{65} +(-2.19098 + 2.48990i) q^{66} -12.9443 q^{67} +(-3.23607 - 2.35114i) q^{68} +(2.38197 - 7.33094i) q^{69} +(0.690983 + 2.12663i) q^{70} +(-4.85410 + 3.52671i) q^{71} +(0.809017 - 0.587785i) q^{72} +(-1.71885 - 5.29007i) q^{73} +(-2.76393 + 8.50651i) q^{74} +(2.50000 + 1.81636i) q^{75} +7.70820 q^{76} +(2.73607 + 4.61653i) q^{77} +1.23607 q^{78} +(0.118034 + 0.0857567i) q^{79} +(0.427051 - 1.31433i) q^{80} +(0.309017 + 0.951057i) q^{81} +(6.23607 - 4.53077i) q^{82} +(0.500000 - 0.363271i) q^{83} +(-0.500000 - 1.53884i) q^{84} +(1.70820 - 5.25731i) q^{85} +(-7.47214 - 5.42882i) q^{86} +0.145898 q^{87} +(0.309017 - 3.30220i) q^{88} +11.2361 q^{89} +(1.11803 + 0.812299i) q^{90} +(0.618034 - 1.90211i) q^{91} +(2.38197 + 7.33094i) q^{92} +(4.54508 - 3.30220i) q^{93} +(3.23607 - 2.35114i) q^{94} +(3.29180 + 10.1311i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(5.97214 + 4.33901i) q^{97} +4.38197 q^{98} +(3.04508 + 1.31433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9} - 10 q^{10} - 4 q^{11} + 4 q^{12} + 4 q^{13} + 2 q^{14} - 5 q^{15} - q^{16} - 4 q^{17} + q^{18} + 14 q^{19} - 2 q^{21} - q^{22} + 4 q^{23}+ \cdots + q^{99}+O(q^{100}) \) 4 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9 - 10 * q^10 - 4 * q^11 + 4 * q^12 + 4 * q^13 + 2 * q^14 - 5 * q^15 - q^16 - 4 * q^17 + q^18 + 14 * q^19 - 2 * q^21 - q^22 + 4 * q^23 + q^24 - 15 * q^25 + 6 * q^26 - q^27 + 3 * q^28 - 11 * q^29 + 5 * q^30 + 7 * q^31 - 4 * q^32 + q^33 - 16 * q^34 + 5 * q^35 - q^36 + 20 * q^37 + 16 * q^38 + 4 * q^39 + 5 * q^40 + 14 * q^41 - 3 * q^42 - 28 * q^43 - 9 * q^44 + 10 * q^45 + 16 * q^46 - 4 * q^47 - q^48 + 3 * q^49 - 10 * q^50 - 4 * q^51 - 6 * q^52 - 5 * q^53 - 4 * q^54 + 30 * q^55 + 2 * q^56 - 16 * q^57 + 11 * q^58 - 20 * q^59 - 18 * q^61 - 2 * q^62 - 2 * q^63 - q^64 + 20 * q^65 - 11 * q^66 - 16 * q^67 - 4 * q^68 + 14 * q^69 + 5 * q^70 - 6 * q^71 + q^72 - 27 * q^73 - 20 * q^74 + 10 * q^75 + 4 * q^76 + 2 * q^77 - 4 * q^78 - 4 * q^79 - 5 * q^80 - q^81 + 16 * q^82 + 2 * q^83 - 2 * q^84 - 20 * q^85 - 12 * q^86 + 14 * q^87 - q^88 + 36 * q^89 - 2 * q^91 + 14 * q^92 + 7 * q^93 + 4 * q^94 + 40 * q^95 + q^96 + 6 * q^97 + 22 * q^98 + q^99

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