LMFDB - Embedded newform 726.2.e.c.565.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,2,Mod(487,726)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(726, 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("726.487"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.e (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-1,-1,-1,0,-1,2,-1,-1,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$5.79713918674$
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:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			565.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	726.565
Dual form			726.2.e.c.487.1

$q$-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} +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} +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} -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} +1.38197 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} +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} -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} +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} +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} +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^{12} - 4 q^{13} + 2 q^{14} - 5 q^{15} - q^{16} + 4 q^{17} - q^{18} - 14 q^{19} + 2 q^{21} + 4 q^{23} - q^{24} - 15 q^{25}+ \cdots - 22 q^{98}+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^12 - 4 * q^13 + 2 * q^14 - 5 * q^15 - q^16 + 4 * q^17 - q^18 - 14 * q^19 + 2 * q^21 + 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 - 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 + 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 + 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 - 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 - 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 + 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

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−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	0.999994	−	0.00340203i	$-0.00108290\pi$
$7$	0.500000	+	1.53884i	0.188982	+	0.581628i	−0.811012	+	0.585030i	$0.801083\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	1.38197			0.437016
$11$		0			0
$11$		0			0
$12$	1.00000			0.288675
$13$	−1.00000	−	0.726543i	−0.277350	−	0.201507i	0.440411	−	0.897796i	$-0.354833\pi$
$13$	−1.00000	−	0.726543i	−0.277350	−	0.201507i	−0.717761	+	0.696290i	$0.754833\pi$
$14$	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	−0.121572	−	0.992583i	$-0.538794\pi$
$17$	3.23607	−	2.35114i	0.784862	−	0.570235i	0.906434	+	0.422347i	$0.138794\pi$
$18$	0.309017	+	0.951057i	0.0728360	+	0.224166i
$19$	−2.38197	+	7.33094i	−0.546460	+	1.68183i	0.171031	+	0.985266i	$0.445290\pi$
$19$	−2.38197	+	7.33094i	−0.546460	+	1.68183i	−0.717492	+	0.696567i	$0.754710\pi$
$20$	−1.11803	−	0.812299i	−0.250000	−	0.181636i
$21$	1.61803			0.353084
$22$		0			0
$23$	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	0.946783	−	0.321872i	$-0.104312\pi$
$29$	−0.0450850	−	0.138757i	−0.00837207	−	0.0257666i	−0.955155	+	0.296105i	$0.904312\pi$
$30$	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			0
$34$	−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	$0.305593\pi$
$41$	−2.38197	+	7.33094i	−0.372001	+	1.14490i	−0.945480	+	0.325680i	$0.894407\pi$
$42$	−1.30902	−	0.951057i	−0.201986	−	0.146751i
$43$	9.23607			1.40849			0.704244	−	0.709958i	$-0.251286\pi$
$43$	9.23607			1.40849			0.704244	+	0.709958i	$0.251286\pi$
$44$		0			0
$45$	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
$55$		0			0
$56$	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	0.0423300	−	0.999104i	$-0.486522\pi$
$61$	7.85410	−	5.70634i	1.00561	−	0.730622i	0.963285	+	0.268482i	$0.0865219\pi$
$62$	−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
$66$		0			0
$67$	−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	$0.00553575\pi$
$73$	1.71885	+	5.29007i	0.201176	+	0.619156i	−0.798673	+	0.601765i	$0.794464\pi$
$74$	2.76393	−	8.50651i	0.321301	−	0.988861i
$75$	2.50000	+	1.81636i	0.288675	+	0.209735i
$76$	−7.70820			−0.884192
$77$		0			0
$78$	1.23607			0.139957
$79$	−0.118034	−	0.0857567i	−0.0132799	−	0.00964838i	0.581126	−	0.813814i	$-0.302613\pi$
$79$	−0.118034	−	0.0857567i	−0.0132799	−	0.00964838i	−0.594405	+	0.804166i	$0.702613\pi$
$80$	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	−0.614888	−	0.788614i	$-0.710799\pi$
$83$	−0.500000	+	0.363271i	−0.0548821	+	0.0398742i	0.560006	+	0.828489i	$0.310799\pi$
$84$	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			0
$89$	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
$99$		0			0
$100$	−3.09017			−0.309017
$101$	7.35410	+	5.34307i	0.731760	+	0.531655i	0.890120	−	0.455726i	$-0.150620\pi$
$101$	7.35410	+	5.34307i	0.731760	+	0.531655i	−0.158359	+	0.987382i	$0.550620\pi$
$102$	−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	$-0.737826\pi$
$107$	3.11803	−	9.59632i	0.301432	−	0.927711i	0.980985	−	0.194085i	$-0.0621738\pi$
$108$	−0.809017	−	0.587785i	−0.0778477	−	0.0565597i
$109$	−14.9443			−1.43140			−0.715701	−	0.698407i	$-0.753893\pi$
$109$	−14.9443			−1.43140			−0.715701	+	0.698407i	$0.753893\pi$
$110$		0			0
$111$	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
$121$		0			0
$122$	−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	−0.434877	−	0.900490i	$-0.643208\pi$
$127$	3.23607	−	2.35114i	0.287155	−	0.208630i	0.722032	+	0.691860i	$0.243208\pi$
$128$	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	$-0.460209\pi$
$131$	2.85410			0.249364			0.124682	+	0.992197i	$0.460209\pi$
$132$		0			0
$133$	−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	0.976588	−	0.215117i	$-0.0690133\pi$
$139$	0.708204	+	2.17963i	0.0600691	+	0.184874i	−0.916519	+	0.399991i	$0.869013\pi$
$140$	0.690983	−	2.12663i	0.0583987	−	0.179733i
$141$	−3.23607	−	2.35114i	−0.272526	−	0.198002i
$142$	6.00000			0.503509
$143$		0			0
$144$	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	$0.692515\pi$
$149$	−18.6353	+	13.5393i	−1.52666	+	1.10918i	−0.958060	+	0.286569i	$0.907485\pi$
$150$	−0.954915	−	2.93893i	−0.0779685	−	0.239962i
$151$	1.48278	−	4.56352i	0.120667	−	0.371374i	−0.872420	−	0.488757i	$-0.837450\pi$
$151$	1.48278	−	4.56352i	0.120667	−	0.371374i	0.993087	+	0.117383i	$0.0374504\pi$
$152$	6.23607	+	4.53077i	0.505812	+	0.367494i
$153$	−4.00000			−0.323381
$154$		0			0
$155$	−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
$165$		0			0
$166$	0.618034			0.0479687
$167$	−15.9443	−	11.5842i	−1.23380	−	0.896412i	−0.236635	−	0.971599i	$-0.576045\pi$
$167$	−15.9443	−	11.5842i	−1.23380	−	0.896412i	−0.997169	+	0.0751869i	$0.976045\pi$
$168$	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	−0.965426	−	0.260676i	$-0.916055\pi$
$173$	−0.409830	+	1.26133i	−0.0311588	+	0.0958969i	0.934268	+	0.356572i	$0.116055\pi$
$174$	0.118034	+	0.0857567i	0.00894813	+	0.00650120i
$175$	−5.00000			−0.377964
$176$		0			0
$177$	−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
$187$		0			0
$188$	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	−0.654977	−	0.755648i	$-0.727322\pi$
$193$	−1.92705	+	1.40008i	−0.138712	+	0.100780i	0.516265	+	0.856429i	$0.327322\pi$
$194$	−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	$-0.646984\pi$
$197$	−12.5066			−0.891057			−0.445528	+	0.895268i	$0.646984\pi$
$198$		0			0
$199$	−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
$209$		0			0
$210$	2.23607			0.154303
$211$	−3.85410	−	2.80017i	−0.265327	−	0.192772i	0.447165	−	0.894451i	$-0.352434\pi$
$211$	−3.85410	−	2.80017i	−0.265327	−	0.192772i	−0.712492	+	0.701680i	$0.752434\pi$
$212$	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
$220$		0			0
$221$	−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	$0.193903\pi$
$227$	7.42705	+	22.8581i	0.492951	+	1.51715i	−0.327176	+	0.944964i	$0.606097\pi$
$228$	−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
$231$		0			0
$232$	−0.145898			−0.00957868
$233$	0.763932	+	0.555029i	0.0500469	+	0.0363612i	0.612527	−	0.790449i	$-0.290153\pi$
$233$	0.763932	+	0.555029i	0.0500469	+	0.0363612i	−0.562481	+	0.826810i	$0.690153\pi$
$234$	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	$-0.721160\pi$
$239$	5.09017	−	15.6659i	0.329256	−	1.01334i	0.969483	−	0.245159i	$-0.0788402\pi$
$240$	−1.11803	−	0.812299i	−0.0721688	−	0.0524337i
$241$	−6.38197			−0.411099			−0.205549	−	0.978647i	$-0.565898\pi$
$241$	−6.38197			−0.411099			−0.205549	+	0.978647i	$0.565898\pi$
$242$		0			0
$243$	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
$253$		0			0
$254$	−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	$-0.371254\pi$
$263$	12.7639			0.787058			0.393529	+	0.919312i	$0.371254\pi$
$264$		0			0
$265$	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	$-0.921301\pi$
$271$	−5.41641	−	16.6700i	−0.329023	−	1.01263i	0.640568	−	0.767901i	$-0.278699\pi$
$272$	−1.23607	+	3.80423i	−0.0749476	+	0.230665i
$273$	−1.61803	−	1.17557i	−0.0979279	−	0.0711488i
$274$	8.18034			0.494192
$275$		0			0
$276$	7.70820			0.463979
$277$	1.85410	+	1.34708i	0.111402	+	0.0809384i	0.642092	−	0.766628i	$-0.278067\pi$
$277$	1.85410	+	1.34708i	0.111402	+	0.0809384i	−0.530689	+	0.847566i	$0.678067\pi$
$278$	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	−0.104498	−	0.994525i	$-0.533324\pi$
$281$	13.5623	−	9.85359i	0.809059	−	0.587816i	0.913558	+	0.406709i	$0.133324\pi$
$282$	1.23607	+	3.80423i	0.0736068	+	0.226538i
$283$	5.09017	−	15.6659i	0.302579	−	0.931243i	−0.677990	−	0.735071i	$-0.737149\pi$
$283$	5.09017	−	15.6659i	0.302579	−	0.931243i	0.980569	−	0.196172i	$-0.0628511\pi$
$284$	−4.85410	−	3.52671i	−0.288038	−	0.209272i
$285$	−10.6525			−0.630998
$286$		0			0
$287$	−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	0.858447	−	0.512903i	$-0.171430\pi$
$293$	−2.35410	−	7.24518i	−0.137528	−	0.423268i	−0.995975	+	0.0896350i	$0.971430\pi$
$294$	−1.35410	+	4.16750i	−0.0789728	+	0.243053i
$295$	5.95492	+	4.32650i	0.346709	+	0.251899i
$296$	8.94427			0.519875
$297$		0			0
$298$	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	$-0.381329\pi$
$307$	12.7639			0.728476			0.364238	+	0.931306i	$0.381329\pi$
$308$		0			0
$309$	−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			0
$320$	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			0
$331$	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	$0.0424574\pi$
$337$	4.90983	+	15.1109i	0.267455	+	0.823143i	−0.723662	+	0.690155i	$0.757543\pi$
$338$	−3.54508	+	10.9106i	−0.192827	+	0.593461i
$339$	8.85410	+	6.43288i	0.480889	+	0.349386i
$340$	−5.52786			−0.299791
$341$		0			0
$342$	−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	−0.914122	−	0.405438i	$-0.867119\pi$
$347$	−15.1074	+	10.9762i	−0.811007	+	0.589231i	0.103115	+	0.994669i	$0.467119\pi$
$348$	−0.0450850	−	0.138757i	−0.00241681	−	0.00743817i
$349$	7.94427	−	24.4500i	0.425247	−	1.30878i	−0.477510	−	0.878626i	$-0.658461\pi$
$349$	7.94427	−	24.4500i	0.425247	−	1.30878i	0.902757	−	0.430150i	$-0.141539\pi$
$350$	4.04508	+	2.93893i	0.216219	+	0.157092i
$351$	1.23607			0.0659764
$352$		0			0
$353$	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	0.987231	−	0.159293i	$-0.0509213\pi$
$359$	1.79837	+	5.53483i	0.0949145	+	0.292117i	−0.892317	+	0.451410i	$0.850921\pi$
$360$	0.427051	−	1.31433i	0.0225076	−	0.0692712i
$361$	−32.6976	−	23.7562i	−1.72092	−	1.25032i
$362$	−5.41641			−0.284680
$363$		0			0
$364$	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	$0.5\pi$
$374$		0			0
$375$	−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
$385$		0			0
$386$	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			0
$397$	−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
$407$		0			0
$408$	−4.00000			−0.198030
$409$	13.7361	+	9.97984i	0.679205	+	0.493471i	0.873094	−	0.487552i	$-0.162110\pi$
$409$	13.7361	+	9.97984i	0.679205	+	0.493471i	−0.193889	+	0.981023i	$0.562110\pi$
$410$	−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
$418$		0			0
$419$	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
$429$		0			0
$430$	12.7639			0.615531
$431$	−19.4721	−	14.1473i	−0.937940	−	0.681453i	0.00998408	−	0.999950i	$-0.496822\pi$
$431$	−19.4721	−	14.1473i	−0.937940	−	0.681453i	−0.947924	+	0.318497i	$0.896822\pi$
$432$	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	$-0.186396\pi$
$439$	34.9230			1.66678			0.833392	+	0.552683i	$0.186396\pi$
$440$		0			0
$441$	−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
$451$		0			0
$452$	−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	−0.859829	−	0.510582i	$-0.829430\pi$
$457$	−13.6803	+	9.93935i	−0.639939	+	0.464943i	0.219890	+	0.975525i	$0.429430\pi$
$458$	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	$-0.671214\pi$
$461$	−22.0000			−1.02464			−0.512321	+	0.858794i	$0.671214\pi$
$462$		0			0
$463$	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
$473$		0			0
$474$	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	−0.315633	−	0.948881i	$-0.602217\pi$
$479$	10.7082	−	7.77997i	0.489270	−	0.355476i	0.804904	+	0.593406i	$0.202217\pi$
$480$	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
$484$		0			0
$485$	−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	$-0.829323\pi$
$491$	−10.2918	−	31.6749i	−0.464462	−	1.42947i	0.395195	−	0.918597i	$-0.370677\pi$
$492$	−2.38197	+	7.33094i	−0.107387	+	0.330504i
$493$	−0.472136	−	0.343027i	−0.0212639	−	0.0154492i
$494$	−9.52786			−0.428679
$495$		0			0
$496$	−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	$-0.653008\pi$
$503$	9.70820	−	29.8788i	0.432867	−	1.33223i	0.895256	−	0.445552i	$-0.146992\pi$
$504$	−1.30902	−	0.951057i	−0.0583083	−	0.0423634i
$505$	−12.5623			−0.559015
$506$		0			0
$507$	−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
$517$		0			0
$518$	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	−0.841992	−	0.539491i	$-0.818617\pi$
$523$	−13.4721	+	9.78808i	−0.589095	+	0.428003i	0.252896	+	0.967493i	$0.418617\pi$
$524$	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
$528$		0			0
$529$	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
$539$		0			0
$540$	1.38197			0.0594703
$541$	3.61803	+	2.62866i	0.155551	+	0.113015i	0.662838	−	0.748762i	$-0.269352\pi$
$541$	3.61803	+	2.62866i	0.155551	+	0.113015i	−0.507287	+	0.861777i	$0.669352\pi$
$542$	−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	−0.930262	−	0.366895i	$-0.880421\pi$
$547$	0.888544	−	2.73466i	0.0379914	−	0.116925i	0.968254	+	0.249970i	$0.0804207\pi$
$548$	−6.61803	−	4.80828i	−0.282708	−	0.205400i
$549$	−9.70820			−0.414336
$550$		0			0
$551$	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	0.825123	−	0.564953i	$-0.191106\pi$
$557$	−4.11803	−	12.6740i	−0.174487	−	0.537015i	−0.999610	+	0.0279384i	$0.991106\pi$
$558$	−1.73607	+	5.34307i	−0.0734936	+	0.226190i
$559$	−9.23607	−	6.71040i	−0.390644	−	0.283820i
$560$	2.23607			0.0944911
$561$		0			0
$562$	−16.7639			−0.707144
$563$	6.47214	+	4.70228i	0.272768	+	0.198178i	0.715757	−	0.698350i	$-0.246082\pi$
$563$	6.47214	+	4.70228i	0.272768	+	0.198178i	−0.442989	+	0.896527i	$0.646082\pi$
$564$	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	$-0.787786\pi$
$569$	5.09017	−	15.6659i	0.213391	−	0.656750i	0.999264	−	0.0383620i	$-0.0122140\pi$
$570$	8.61803	+	6.26137i	0.360970	+	0.262260i
$571$	−1.34752			−0.0563921			−0.0281961	−	0.999602i	$-0.508976\pi$
$571$	−1.34752			−0.0563921			−0.0281961	+	0.999602i	$0.508976\pi$
$572$		0			0
$573$	−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
$583$		0			0
$584$	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	$-0.448215\pi$
$593$	7.88854			0.323944			0.161972	+	0.986795i	$0.448215\pi$
$594$		0			0
$595$	−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	$0.0343832\pi$
$601$	6.20820	+	19.1069i	0.253238	+	0.779386i	−0.740934	+	0.671578i	$0.765617\pi$
$602$	4.61803	−	14.2128i	0.188217	−	0.579272i
$603$	10.4721	+	7.60845i	0.426458	+	0.309840i
$604$	4.79837			0.195243
$605$		0			0
$606$	−9.09017			−0.369263
$607$	12.1803	+	8.84953i	0.494385	+	0.359192i	0.806868	−	0.590732i	$-0.201161\pi$
$607$	12.1803	+	8.84953i	0.494385	+	0.359192i	−0.312483	+	0.949923i	$0.601161\pi$
$608$	−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	−0.969771	−	0.244016i	$-0.921535\pi$
$613$	−1.03444	+	3.18368i	−0.0417807	+	0.128588i	0.927990	+	0.372604i	$0.121535\pi$
$614$	−10.3262	−	7.50245i	−0.416733	−	0.302774i
$615$	−10.6525			−0.429549
$616$		0			0
$617$	−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
$627$		0			0
$628$	−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			0
$639$	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
$649$		0			0
$650$	−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	$-0.852435\pi$
$659$	−45.9230			−1.78891			−0.894453	+	0.447162i	$0.852435\pi$
$660$		0			0
$661$	−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
$671$		0			0
$672$	1.61803			0.0624170
$673$	6.26393	+	4.55101i	0.241457	+	0.175429i	0.701932	−	0.712244i	$-0.252321\pi$
$673$	6.26393	+	4.55101i	0.241457	+	0.175429i	−0.460475	+	0.887673i	$0.652321\pi$
$674$	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	$-0.268041\pi$
$677$	41.1418	−	29.8913i	1.58121	−	1.14882i	0.915293	−	0.402789i	$-0.131959\pi$
$678$	−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
$682$		0			0
$683$	−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			0
$694$	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	−0.999988	−	0.00499706i	$-0.998409\pi$
$701$	−4.97871	+	15.3229i	−0.188043	+	0.578738i	0.811944	+	0.583735i	$0.198409\pi$
$702$	−1.00000	−	0.726543i	−0.0377426	−	0.0274216i
$703$	−68.9443			−2.60028
$704$		0			0
$705$	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
$715$		0			0
$716$	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
$726$		0			0
$727$	−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	$-0.958823\pi$
$733$	−7.18034	−	22.0988i	−0.265212	−	0.816238i	0.726433	−	0.687238i	$-0.241177\pi$
$734$	3.10081	−	9.54332i	0.114453	−	0.352250i
$735$	4.89919	+	3.55947i	0.180709	+	0.131293i
$736$	7.70820			0.284128
$737$		0			0
$738$	−7.70820			−0.283743
$739$	27.1246	+	19.7072i	0.997795	+	0.724940i	0.961614	−	0.274405i	$-0.0884808\pi$
$739$	27.1246	+	19.7072i	0.997795	+	0.724940i	0.0361807	+	0.999345i	$0.488481\pi$
$740$	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	−0.893853	−	0.448360i	$-0.852008\pi$
$743$	−20.2705	+	14.7274i	−0.743653	+	0.540295i	0.150200	+	0.988656i	$0.452008\pi$
$744$	−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
$748$		0			0
$749$	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
$759$		0			0
$760$	−10.6525			−0.386406
$761$	43.8328	+	31.8464i	1.58894	+	1.15443i	0.905436	+	0.424483i	$0.139544\pi$
$761$	43.8328	+	31.8464i	1.58894	+	1.15443i	0.683502	+	0.729948i	$0.260456\pi$
$762$	−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	$-0.230348\pi$
$769$	41.5623			1.49878			0.749388	+	0.662132i	$0.230348\pi$
$770$		0			0
$771$	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
$781$		0			0
$782$	−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	−0.255407	−	0.966834i	$-0.582209\pi$
$787$	16.4164	−	11.9272i	0.585182	−	0.425159i	0.840588	+	0.541674i	$0.182209\pi$
$788$	−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
$792$		0			0
$793$	−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
$803$		0			0
$804$	−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	−0.630394	−	0.776275i	$-0.717107\pi$
$809$	−2.47214	+	1.79611i	−0.0869157	+	0.0631479i	0.543479	+	0.839423i	$0.317107\pi$
$810$	0.427051	+	1.31433i	0.0150050	+	0.0461808i
$811$	−6.74265	+	20.7517i	−0.236766	+	0.728692i	0.760116	+	0.649788i	$0.225142\pi$
$811$	−6.74265	+	20.7517i	−0.236766	+	0.728692i	−0.996882	+	0.0789043i	$0.974858\pi$
$812$	0.190983	+	0.138757i	0.00670219	+	0.00486943i
$813$	−17.5279			−0.614729
$814$		0			0
$815$	−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	$-0.816428\pi$
$821$	−13.7705	−	42.3813i	−0.480594	−	1.47912i	0.357668	−	0.933849i	$-0.383572\pi$
$822$	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
$825$		0			0
$826$	−8.61803			−0.299860
$827$	5.25329	+	3.81674i	0.182675	+	0.132721i	0.675365	−	0.737484i	$-0.263986\pi$
$827$	5.25329	+	3.81674i	0.182675	+	0.132721i	−0.492690	+	0.870205i	$0.663986\pi$
$828$	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
$836$		0			0
$837$	−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
$847$		0			0
$848$	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	−0.231305	−	0.972881i	$-0.574300\pi$
$853$	18.1803	−	13.2088i	0.622483	−	0.452260i	0.853788	+	0.520621i	$0.174300\pi$
$854$	−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	$-0.488144\pi$
$857$	2.18034			0.0744790			0.0372395	+	0.999306i	$0.488144\pi$
$858$		0			0
$859$	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			0
$870$	−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	$0.237715\pi$
$877$	−7.67376	+	23.6174i	−0.259125	+	0.797503i	−0.992989	+	0.118207i	$0.962285\pi$
$878$	−28.2533	−	20.5272i	−0.953502	−	0.692760i
$879$	−7.61803			−0.256950
$880$		0			0
$881$	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	0.823175	−	0.567788i	$-0.192200\pi$
$887$	−5.25735	−	16.1805i	−0.176525	−	0.543287i	−0.999700	+	0.0245004i	$0.992200\pi$
$888$	2.76393	−	8.50651i	0.0927515	−	0.285460i
$889$	5.23607	+	3.80423i	0.175612	+	0.127590i
$890$	15.5279			0.520495
$891$		0			0
$892$	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
$902$		0			0
$903$	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
$913$		0			0
$914$	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	−0.721183	−	0.692744i	$-0.756401\pi$
$919$	−8.64590	+	6.28161i	−0.285202	+	0.207211i	0.435981	+	0.899956i	$0.356401\pi$
$920$	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
$924$		0			0
$925$	−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
$935$		0			0
$936$	1.23607			0.0404021
$937$	−42.4336	−	30.8298i	−1.38625	−	1.00717i	−0.996265	−	0.0863439i	$-0.972482\pi$
$937$	−42.4336	−	30.8298i	−1.38625	−	1.00717i	−0.389981	−	0.920823i	$-0.627518\pi$
$938$	−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	−0.936089	−	0.351763i	$-0.885582\pi$
$941$	−27.3262	+	19.8537i	−0.890810	+	0.647211i	0.0452792	+	0.998974i	$0.485582\pi$
$942$	−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
$946$		0			0
$947$	−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	$0.0410488\pi$
$953$	8.18034	+	25.1765i	0.264987	+	0.815547i	−0.726709	+	0.686945i	$0.758951\pi$
$954$	1.11803	−	3.44095i	0.0361977	−	0.111405i
$955$	23.4164	+	17.0130i	0.757737	+	0.550528i
$956$	16.4721			0.532747
$957$		0			0
$958$	−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	$-0.409837\pi$
$967$	17.3820			0.558966			0.279483	+	0.960151i	$0.409837\pi$
$968$		0			0
$969$	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
$979$		0			0
$980$	−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
$990$		0			0
$991$	−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	0.978318	−	0.207110i	$-0.0664059\pi$
$997$	2.05573	+	6.32688i	0.0651056	+	0.200374i	−0.913212	+	0.407485i	$0.866406\pi$
$998$	−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	726.2.e.c.565.1		4
11.2	odd	10		726.2.e.j.511.1		4
11.3	even	5	inner	726.2.e.c.487.1		4
11.4	even	5		726.2.e.a.493.1		4
11.5	even	5		726.2.a.m.1.1		2
11.6	odd	10		726.2.a.k.1.1		2
11.7	odd	10		726.2.e.j.493.1		4
11.8	odd	10		66.2.e.b.25.1	✓	4
11.9	even	5		726.2.e.a.511.1		4
11.10	odd	2		66.2.e.b.37.1	yes	4
33.5	odd	10		2178.2.a.o.1.2		2
33.8	even	10		198.2.f.a.91.1		4
33.17	even	10		2178.2.a.v.1.2		2
33.32	even	2		198.2.f.a.37.1		4
44.19	even	10		528.2.y.g.289.1		4
44.27	odd	10		5808.2.a.by.1.1		2
44.39	even	10		5808.2.a.bz.1.1		2
44.43	even	2		528.2.y.g.433.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.e.b.25.1	✓	4	11.8	odd	10
66.2.e.b.37.1	yes	4	11.10	odd	2
198.2.f.a.37.1		4	33.32	even	2
198.2.f.a.91.1		4	33.8	even	10
528.2.y.g.289.1		4	44.19	even	10
528.2.y.g.433.1		4	44.43	even	2
726.2.a.k.1.1		2	11.6	odd	10
726.2.a.m.1.1		2	11.5	even	5
726.2.e.a.493.1		4	11.4	even	5
726.2.e.a.511.1		4	11.9	even	5
726.2.e.c.487.1		4	11.3	even	5	inner
726.2.e.c.565.1		4	1.1	even	1	trivial
726.2.e.j.493.1		4	11.7	odd	10
726.2.e.j.511.1		4	11.2	odd	10
2178.2.a.o.1.2		2	33.5	odd	10
2178.2.a.v.1.2		2	33.17	even	10
5808.2.a.by.1.1		2	44.27	odd	10
5808.2.a.bz.1.1		2	44.39	even	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:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.e (of order \(5\), degree \(4\), not 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} +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} +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} -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} +1.38197 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} +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} -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} +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} +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} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{3} - q^{4} - q^{6} + 2 q^{7} - q^{8} - q^{9} + 10 q^{10} + 4 q^{12} - 4 q^{13} + 2 q^{14} - 5 q^{15} - q^{16} + 4 q^{17} - q^{18} - 14 q^{19} + 2 q^{21} + 4 q^{23} - q^{24} - 15 q^{25}+ \cdots - 22 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^3 - q^4 - q^6 + 2 * q^7 - q^8 - q^9 + 10 * q^10 + 4 * q^12 - 4 * q^13 + 2 * q^14 - 5 * q^15 - q^16 + 4 * q^17 - q^18 - 14 * q^19 + 2 * q^21 + 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 - 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 + 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 + 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 - 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 - 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 + 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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