LMFDB - Embedded newform 60.2.j.a.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,2,Mod(7,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("60.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	60.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.479102412128$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.3
Root			$-0.0912546 + 1.41127i$ of defining polynomial
Character	$\chi$	$=$	60.43
Dual form			60.2.j.a.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0912546 + 1.41127i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.98335 + 0.257569i) q^{4} +(1.32001 + 1.80487i) q^{5} +(1.06244 + 0.933389i) q^{6} +(-1.86678 - 1.86678i) q^{7} +(-0.544488 - 2.77552i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(0.0912546 + 1.41127i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.98335 + 0.257569i) q^{4} +(1.32001 + 1.80487i) q^{5} +(1.06244 + 0.933389i) q^{6} +(-1.86678 - 1.86678i) q^{7} +(-0.544488 - 2.77552i) q^{8} -1.00000i q^{9} +(-2.42670 + 2.02759i) q^{10} +0.728515i q^{11} +(-1.22031 + 1.58457i) q^{12} +(-3.12489 - 3.12489i) q^{13} +(2.46417 - 2.80487i) q^{14} +(2.20963 + 0.342849i) q^{15} +(3.86732 - 1.02170i) q^{16} +(1.12489 - 1.12489i) q^{17} +(1.41127 - 0.0912546i) q^{18} +3.73356 q^{19} +(-3.08292 - 3.23969i) q^{20} -2.64002 q^{21} +(-1.02813 + 0.0664803i) q^{22} +(-5.83347 + 5.83347i) q^{23} +(-2.34760 - 1.57758i) q^{24} +(-1.51514 + 4.76491i) q^{25} +(4.12489 - 4.69521i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(4.18329 + 3.22164i) q^{28} +2.64002i q^{29} +(-0.282213 + 3.14966i) q^{30} +6.01008i q^{31} +(1.79480 + 5.36458i) q^{32} +(0.515138 + 0.515138i) q^{33} +(1.69016 + 1.48486i) q^{34} +(0.905130 - 5.83347i) q^{35} +(0.257569 + 1.98335i) q^{36} +(3.12489 - 3.12489i) q^{37} +(0.340704 + 5.26904i) q^{38} -4.41926 q^{39} +(4.29074 - 4.64646i) q^{40} -4.24977 q^{41} +(-0.240914 - 3.72578i) q^{42} +(5.10495 - 5.10495i) q^{43} +(-0.187643 - 1.44490i) q^{44} +(1.80487 - 1.32001i) q^{45} +(-8.76491 - 7.70025i) q^{46} +(2.09991 + 2.09991i) q^{47} +(2.01216 - 3.45705i) q^{48} -0.0302761i q^{49} +(-6.86282 - 1.70344i) q^{50} -1.59083i q^{51} +(7.00260 + 5.39285i) q^{52} +(0.484862 + 0.484862i) q^{53} +(0.933389 - 1.06244i) q^{54} +(-1.31488 + 0.961649i) q^{55} +(-4.16485 + 6.19773i) q^{56} +(2.64002 - 2.64002i) q^{57} +(-3.72578 + 0.240914i) q^{58} +4.92834 q^{59} +(-4.47076 - 0.110857i) q^{60} +2.31032 q^{61} +(-8.48183 + 0.548448i) q^{62} +(-1.86678 + 1.86678i) q^{63} +(-7.40707 + 3.02248i) q^{64} +(1.51514 - 9.76491i) q^{65} +(-0.679988 + 0.774006i) q^{66} +(-5.10495 - 5.10495i) q^{67} +(-1.94130 + 2.52077i) q^{68} +8.24977i q^{69} +(8.31518 + 0.745049i) q^{70} -13.1240i q^{71} +(-2.77552 + 0.544488i) q^{72} +(3.96972 + 3.96972i) q^{73} +(4.69521 + 4.12489i) q^{74} +(2.29793 + 4.44066i) q^{75} +(-7.40493 + 0.961649i) q^{76} +(1.35998 - 1.35998i) q^{77} +(-0.403277 - 6.23675i) q^{78} -7.11388 q^{79} +(6.94894 + 5.63137i) q^{80} -1.00000 q^{81} +(-0.387811 - 5.99756i) q^{82} +(3.55694 - 3.55694i) q^{83} +(5.23608 - 0.679988i) q^{84} +(3.51514 + 0.545414i) q^{85} +(7.67030 + 6.73860i) q^{86} +(1.86678 + 1.86678i) q^{87} +(2.02201 - 0.396668i) q^{88} +1.03028i q^{89} +(2.02759 + 2.42670i) q^{90} +11.6669i q^{91} +(10.0673 - 13.0723i) q^{92} +(4.24977 + 4.24977i) q^{93} +(-2.77191 + 3.15516i) q^{94} +(4.92834 + 6.73860i) q^{95} +(5.06244 + 2.52422i) q^{96} +(-12.5298 + 12.5298i) q^{97} +(0.0427276 - 0.00276283i) q^{98} +0.728515 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{6} - 12 q^{8}+O(q^{10}) $ 12 * q - 4 * q^6 - 12 * q^8	$ 12 q - 4 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 4 q^{13} + 12 q^{16} - 20 q^{17} + 20 q^{20} + 12 q^{22} - 20 q^{25} + 16 q^{26} - 4 q^{28} + 8 q^{30} + 20 q^{32} + 8 q^{33} + 4 q^{36} + 4 q^{37} + 16 q^{38} - 8 q^{40} + 16 q^{41} + 20 q^{42} + 4 q^{45} - 40 q^{46} + 16 q^{48} - 16 q^{50} - 8 q^{52} + 4 q^{53} - 64 q^{56} - 20 q^{58} - 20 q^{60} - 32 q^{61} - 56 q^{62} + 20 q^{65} - 24 q^{66} - 16 q^{68} + 44 q^{70} - 12 q^{72} + 44 q^{73} + 8 q^{76} + 48 q^{77} - 24 q^{78} + 4 q^{80} - 12 q^{81} + 16 q^{82} + 44 q^{85} + 64 q^{86} + 60 q^{88} + 12 q^{90} + 56 q^{92} - 16 q^{93} + 44 q^{96} - 20 q^{97} + 24 q^{98}+O(q^{100}) $ 12 * q - 4 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 4 * q^13 + 12 * q^16 - 20 * q^17 + 20 * q^20 + 12 * q^22 - 20 * q^25 + 16 * q^26 - 4 * q^28 + 8 * q^30 + 20 * q^32 + 8 * q^33 + 4 * q^36 + 4 * q^37 + 16 * q^38 - 8 * q^40 + 16 * q^41 + 20 * q^42 + 4 * q^45 - 40 * q^46 + 16 * q^48 - 16 * q^50 - 8 * q^52 + 4 * q^53 - 64 * q^56 - 20 * q^58 - 20 * q^60 - 32 * q^61 - 56 * q^62 + 20 * q^65 - 24 * q^66 - 16 * q^68 + 44 * q^70 - 12 * q^72 + 44 * q^73 + 8 * q^76 + 48 * q^77 - 24 * q^78 + 4 * q^80 - 12 * q^81 + 16 * q^82 + 44 * q^85 + 64 * q^86 + 60 * q^88 + 12 * q^90 + 56 * q^92 - 16 * q^93 + 44 * q^96 - 20 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	0.0912546	+	1.41127i	0.0645267	+	0.997916i
$2$	0.0912546	+	1.41127i	0.0645267	+	0.997916i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−1.98335	+	0.257569i	−0.991673	+	0.128785i
$5$	1.32001	+	1.80487i	0.590327	+	0.807164i
$5$	1.32001	+	1.80487i	0.590327	+	0.807164i
$6$	1.06244	+	0.933389i	0.433740	+	0.381055i
$7$	−1.86678	−	1.86678i	−0.705576	−	0.705576i	0.260026	−	0.965602i	$-0.416269\pi$
$7$	−1.86678	−	1.86678i	−0.705576	−	0.705576i	−0.965602	+	0.260026i	$0.916269\pi$
$8$	−0.544488	−	2.77552i	−0.192506	−	0.981296i
$9$		−	1.00000i		−	0.333333i
$10$	−2.42670	+	2.02759i	−0.767390	+	0.641181i
$11$			0.728515i			0.219656i	0.993951	+	0.109828i	$0.0350299\pi$
$11$			0.728515i			0.219656i	−0.993951	+	0.109828i	$0.964970\pi$
$12$	−1.22031	+	1.58457i	−0.352273	+	0.457425i
$13$	−3.12489	−	3.12489i	−0.866687	−	0.866687i	0.125417	−	0.992104i	$-0.459973\pi$
$13$	−3.12489	−	3.12489i	−0.866687	−	0.866687i	−0.992104	+	0.125417i	$0.959973\pi$
$14$	2.46417	−	2.80487i	0.658577	−	0.749634i
$15$	2.20963	+	0.342849i	0.570523	+	0.0885233i
$16$	3.86732	−	1.02170i	0.966829	−	0.255424i
$17$	1.12489	−	1.12489i	0.272825	−	0.272825i	−0.557412	−	0.830236i	$-0.688205\pi$
$17$	1.12489	−	1.12489i	0.272825	−	0.272825i	0.830236	+	0.557412i	$0.188205\pi$
$18$	1.41127	−	0.0912546i	0.332639	−	0.0215089i
$19$	3.73356			0.856537			0.428268	−	0.903652i	$-0.359124\pi$
$19$	3.73356			0.856537			0.428268	+	0.903652i	$0.359124\pi$
$20$	−3.08292	−	3.23969i	−0.689362	−	0.724417i
$21$	−2.64002			−0.576100
$22$	−1.02813	+	0.0664803i	−0.219198	+	0.0141737i
$23$	−5.83347	+	5.83347i	−1.21636	+	1.21636i	−0.247466	+	0.968897i	$0.579598\pi$
$23$	−5.83347	+	5.83347i	−1.21636	+	1.21636i	−0.968897	+	0.247466i	$0.920402\pi$
$24$	−2.34760	−	1.57758i	−0.479202	−	0.322022i
$25$	−1.51514	+	4.76491i	−0.303028	+	0.952982i
$26$	4.12489	−	4.69521i	0.808957	−	0.920806i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	4.18329	+	3.22164i	0.790568	+	0.608833i
$29$			2.64002i			0.490240i	0.969493	+	0.245120i	$0.0788274\pi$
$29$			2.64002i			0.490240i	−0.969493	+	0.245120i	$0.921173\pi$
$30$	−0.282213	+	3.14966i	−0.0515248	+	0.575047i
$31$			6.01008i			1.07944i	0.841844	+	0.539721i	$0.181470\pi$
$31$			6.01008i			1.07944i	−0.841844	+	0.539721i	$0.818530\pi$
$32$	1.79480	+	5.36458i	0.317278	+	0.948333i
$33$	0.515138	+	0.515138i	0.0896740	+	0.0896740i
$34$	1.69016	+	1.48486i	0.289861	+	0.254652i
$35$	0.905130	−	5.83347i	0.152995	−	0.986036i
$36$	0.257569	+	1.98335i	0.0429282	+	0.330558i
$37$	3.12489	−	3.12489i	0.513728	−	0.513728i	−0.401939	−	0.915667i	$-0.631663\pi$
$37$	3.12489	−	3.12489i	0.513728	−	0.513728i	0.915667	+	0.401939i	$0.131663\pi$
$38$	0.340704	+	5.26904i	0.0552695	+	0.854752i
$39$	−4.41926			−0.707647
$40$	4.29074	−	4.64646i	0.678426	−	0.734669i
$41$	−4.24977			−0.663703			−0.331851	−	0.943332i	$-0.607673\pi$
$41$	−4.24977			−0.663703			−0.331851	+	0.943332i	$0.607673\pi$
$42$	−0.240914	−	3.72578i	−0.0371739	−	0.574900i
$43$	5.10495	−	5.10495i	0.778498	−	0.778498i	−0.201077	−	0.979575i	$-0.564444\pi$
$43$	5.10495	−	5.10495i	0.778498	−	0.778498i	0.979575	+	0.201077i	$0.0644442\pi$
$44$	−0.187643	−	1.44490i	−0.0282882	−	0.217826i
$45$	1.80487	−	1.32001i	0.269055	−	0.196776i
$46$	−8.76491	−	7.70025i	−1.29232	−	1.13534i
$47$	2.09991	+	2.09991i	0.306304	+	0.306304i	0.843474	−	0.537170i	$-0.180507\pi$
$47$	2.09991	+	2.09991i	0.306304	+	0.306304i	−0.537170	+	0.843474i	$0.680507\pi$
$48$	2.01216	−	3.45705i	0.290430	−	0.498983i
$49$		−	0.0302761i		−	0.00432516i
$50$	−6.86282	−	1.70344i	−0.970549	−	0.240903i
$51$		−	1.59083i		−	0.222761i
$52$	7.00260	+	5.39285i	0.971086	+	0.747854i
$53$	0.484862	+	0.484862i	0.0666009	+	0.0666009i	0.739623	−	0.673022i	$-0.235004\pi$
$53$	0.484862	+	0.484862i	0.0666009	+	0.0666009i	−0.673022	+	0.739623i	$0.735004\pi$
$54$	0.933389	−	1.06244i	0.127018	−	0.144580i
$55$	−1.31488	+	0.961649i	−0.177298	+	0.129669i
$56$	−4.16485	+	6.19773i	−0.556552	+	0.828206i
$57$	2.64002	−	2.64002i	0.349680	−	0.349680i
$58$	−3.72578	+	0.240914i	−0.489218	+	0.0316336i
$59$	4.92834			0.641615			0.320808	−	0.947144i	$-0.396046\pi$
$59$	4.92834			0.641615			0.320808	+	0.947144i	$0.396046\pi$
$60$	−4.47076	−	0.110857i	−0.577173	−	0.0143115i
$61$	2.31032			0.295807			0.147903	−	0.989002i	$-0.452748\pi$
$61$	2.31032			0.295807			0.147903	+	0.989002i	$0.452748\pi$
$62$	−8.48183	+	0.548448i	−1.07719	+	0.0696529i
$63$	−1.86678	+	1.86678i	−0.235192	+	0.235192i
$64$	−7.40707	+	3.02248i	−0.925883	+	0.377810i
$65$	1.51514	−	9.76491i	0.187930	−	1.21119i
$66$	−0.679988	+	0.774006i	−0.0837008	+	0.0952735i
$67$	−5.10495	−	5.10495i	−0.623669	−	0.623669i	0.322798	−	0.946468i	$-0.395376\pi$
$67$	−5.10495	−	5.10495i	−0.623669	−	0.623669i	−0.946468	+	0.322798i	$0.895376\pi$
$68$	−1.94130	+	2.52077i	−0.235417	+	0.305688i
$69$			8.24977i			0.993156i
$70$	8.31518	+	0.745049i	0.993854	+	0.0890503i
$71$		−	13.1240i		−	1.55753i	−0.627317	−	0.778764i	$-0.715847\pi$
$71$		−	13.1240i		−	1.55753i	0.627317	−	0.778764i	$-0.284153\pi$
$72$	−2.77552	+	0.544488i	−0.327099	+	0.0641685i
$73$	3.96972	+	3.96972i	0.464621	+	0.464621i	0.900167	−	0.435546i	$-0.143445\pi$
$73$	3.96972	+	3.96972i	0.464621	+	0.464621i	−0.435546	+	0.900167i	$0.643445\pi$
$74$	4.69521	+	4.12489i	0.545807	+	0.479508i
$75$	2.29793	+	4.44066i	0.265343	+	0.512764i
$76$	−7.40493	+	0.961649i	−0.849404	+	0.110309i
$77$	1.35998	−	1.35998i	0.154984	−	0.154984i
$78$	−0.403277	−	6.23675i	−0.0456622	−	0.706172i
$79$	−7.11388			−0.800375			−0.400187	−	0.916433i	$-0.631055\pi$
$79$	−7.11388			−0.800375			−0.400187	+	0.916433i	$0.631055\pi$
$80$	6.94894	+	5.63137i	0.776915	+	0.629606i
$81$	−1.00000			−0.111111
$82$	−0.387811	−	5.99756i	−0.0428266	−	0.662320i
$83$	3.55694	−	3.55694i	0.390425	−	0.390425i	−0.484414	−	0.874839i	$-0.660967\pi$
$83$	3.55694	−	3.55694i	0.390425	−	0.390425i	0.874839	+	0.484414i	$0.160967\pi$
$84$	5.23608	−	0.679988i	0.571303	−	0.0741928i
$85$	3.51514	+	0.545414i	0.381270	+	0.0591585i
$86$	7.67030	+	6.73860i	0.827110	+	0.726642i
$87$	1.86678	+	1.86678i	0.200140	+	0.200140i
$88$	2.02201	−	0.396668i	0.215547	−	0.0422849i
$89$			1.03028i			0.109209i	0.998508	+	0.0546045i	$0.0173898\pi$
$89$			1.03028i			0.109209i	−0.998508	+	0.0546045i	$0.982610\pi$
$90$	2.02759	+	2.42670i	0.213727	+	0.255797i
$91$			11.6669i			1.22303i
$92$	10.0673	−	13.0723i	1.04958	−	1.36288i
$93$	4.24977	+	4.24977i	0.440681	+	0.440681i
$94$	−2.77191	+	3.15516i	−0.285901	+	0.325430i
$95$	4.92834	+	6.73860i	0.505637	+	0.691366i
$96$	5.06244	+	2.52422i	0.516683	+	0.257627i
$97$	−12.5298	+	12.5298i	−1.27221	+	1.27221i	−0.327284	+	0.944926i	$0.606133\pi$
$97$	−12.5298	+	12.5298i	−1.27221	+	1.27221i	−0.944926	+	0.327284i	$0.893867\pi$
$98$	0.0427276	−	0.00276283i	0.00431614	−	0.000279088i
$99$	0.728515			0.0732185
$100$	1.77775	−	9.84071i	0.177775	−	0.984071i
$101$	−5.67030			−0.564216			−0.282108	−	0.959383i	$-0.591034\pi$
$101$	−5.67030			−0.564216			−0.282108	+	0.959383i	$0.591034\pi$
$102$	2.24508	−	0.145170i	0.222296	−	0.0143740i
$103$	−0.0565188	+	0.0565188i	−0.00556896	+	0.00556896i	−0.709886	−	0.704317i	$-0.751253\pi$
$103$	−0.0565188	+	0.0565188i	−0.00556896	+	0.00556896i	0.704317	+	0.709886i	$0.251253\pi$
$104$	−6.97173	+	10.3747i	−0.683635	+	1.01732i
$105$	−3.48486	−	4.76491i	−0.340088	−	0.465007i
$106$	−0.640023	+	0.728515i	−0.0621646	+	0.0707597i
$107$	3.91017	+	3.91017i	0.378011	+	0.378011i	0.870384	−	0.492373i	$-0.163871\pi$
$107$	3.91017	+	3.91017i	0.378011	+	0.378011i	−0.492373	+	0.870384i	$0.663871\pi$
$108$	1.58457	+	1.22031i	0.152475	+	0.117424i
$109$		−	15.7796i		−	1.51141i	−0.654912	−	0.755705i	$-0.727294\pi$
$109$		−	15.7796i		−	1.51141i	0.654912	−	0.755705i	$-0.272706\pi$
$110$	−1.47713	−	1.76789i	−0.140839	−	0.168562i
$111$		−	4.41926i		−	0.419457i
$112$	−9.12670	−	5.31214i	−0.862392	−	0.501950i
$113$	−1.84484	−	1.84484i	−0.173548	−	0.173548i	0.614988	−	0.788536i	$-0.289161\pi$
$113$	−1.84484	−	1.84484i	−0.173548	−	0.173548i	−0.788536	+	0.614988i	$0.789161\pi$
$114$	3.96669	+	3.48486i	0.371515	+	0.326387i
$115$	−18.2289	−	2.82843i	−1.69986	−	0.263752i
$116$	−0.679988	−	5.23608i	−0.0631353	−	0.486158i
$117$	−3.12489	+	3.12489i	−0.288896	+	0.288896i
$118$	0.449733	+	6.95520i	0.0414013	+	0.640278i
$119$	−4.19982			−0.384997
$120$	−0.251529	−	6.31955i	−0.0229614	−	0.576893i
$121$	10.4693			0.951751
$122$	0.210828	+	3.26048i	0.0190874	+	0.295190i
$123$	−3.00504	+	3.00504i	−0.270955	+	0.270955i
$124$	−1.54801	−	11.9201i	−0.139016	−	1.07045i
$125$	−10.6001	+	3.55510i	−0.948098	+	0.317978i
$126$	−2.80487	−	2.46417i	−0.249878	−	0.219526i
$127$	11.2572	+	11.2572i	0.998914	+	0.998914i	0.999999	−	0.00108535i	$-0.000345478\pi$
$127$	11.2572	+	11.2572i	0.998914	+	0.998914i	−0.00108535	+	0.999999i	$0.500345\pi$
$128$	−4.94145	−	10.1775i	−0.436767	−	0.899575i
$129$		−	7.21949i		−	0.635641i
$130$	13.9192	+	1.24717i	1.22079	+	0.109384i
$131$			4.57511i			0.399729i	0.979824	+	0.199865i	$0.0640502\pi$
$131$			4.57511i			0.399729i	−0.979824	+	0.199865i	$0.935950\pi$
$132$	−1.15438	−	0.889013i	−0.100476	−	0.0773786i
$133$	−6.96972	−	6.96972i	−0.604352	−	0.604352i
$134$	6.73860	−	7.67030i	0.582126	−	0.662613i
$135$	0.342849	−	2.20963i	0.0295078	−	0.190174i
$136$	−3.73463	−	2.50966i	−0.320242	−	0.215202i
$137$	−4.09461	+	4.09461i	−0.349826	+	0.349826i	−0.860045	−	0.510219i	$-0.829564\pi$
$137$	−4.09461	+	4.09461i	−0.349826	+	0.349826i	0.510219	+	0.860045i	$0.329564\pi$
$138$	−11.6426	+	0.752829i	−0.991086	+	0.0640851i
$139$	13.5902			1.15271			0.576354	−	0.817200i	$-0.304475\pi$
$139$	13.5902			1.15271			0.576354	+	0.817200i	$0.304475\pi$
$140$	−0.292664	+	11.8029i	−0.0247346	+	0.997528i
$141$	2.96972			0.250096
$142$	18.5214	−	1.19762i	1.55428	−	0.100502i
$143$	2.27653	−	2.27653i	0.190373	−	0.190373i
$144$	−1.02170	−	3.86732i	−0.0851414	−	0.322276i
$145$	−4.76491	+	3.48486i	−0.395704	+	0.289402i
$146$	−5.24008	+	5.96459i	−0.433672	+	0.493633i
$147$	−0.0214084	−	0.0214084i	−0.00176574	−	0.00176574i
$148$	−5.39285	+	7.00260i	−0.443290	+	0.575610i
$149$		−	5.67030i		−	0.464529i	−0.972653	−	0.232265i	$-0.925386\pi$
$149$		−	5.67030i		−	0.464529i	0.972653	−	0.232265i	$-0.0746135\pi$
$150$	−6.05726	+	3.64823i	−0.494573	+	0.297877i
$151$		−	19.2471i		−	1.56631i	−0.621829	−	0.783153i	$-0.713610\pi$
$151$		−	19.2471i		−	1.56631i	0.621829	−	0.783153i	$-0.286390\pi$
$152$	−2.03288	−	10.3626i	−0.164888	−	0.840516i
$153$	−1.12489	−	1.12489i	−0.0909416	−	0.0909416i
$154$	2.04339	+	1.79518i	0.164661	+	0.144660i
$155$	−10.8474	+	7.93338i	−0.871287	+	0.637224i
$156$	8.76491	−	1.13826i	0.701754	−	0.0911340i
$157$	−2.09461	+	2.09461i	−0.167168	+	0.167168i	−0.785733	−	0.618565i	$-0.787714\pi$
$157$	−2.09461	+	2.09461i	−0.167168	+	0.167168i	0.618565	+	0.785733i	$0.287714\pi$
$158$	−0.649175	−	10.0396i	−0.0516456	−	0.798707i
$159$	0.685698			0.0543794
$160$	−7.31324	+	10.3207i	−0.578162	+	0.815922i
$161$	21.7796			1.71647
$162$	−0.0912546	−	1.41127i	−0.00716964	−	0.110880i
$163$	4.28546	−	4.28546i	0.335663	−	0.335663i	−0.519069	−	0.854732i	$-0.673721\pi$
$163$	4.28546	−	4.28546i	0.335663	−	0.335663i	0.854732	+	0.519069i	$0.173721\pi$
$164$	8.42876	−	1.09461i	0.658176	−	0.0854746i
$165$	−0.249771	+	1.60975i	−0.0194446	+	0.125319i
$166$	5.34438	+	4.69521i	0.414804	+	0.364419i
$167$	−4.37644	−	4.37644i	−0.338659	−	0.338659i	0.517203	−	0.855862i	$-0.326973\pi$
$167$	−4.37644	−	4.37644i	−0.338659	−	0.338659i	−0.855862	+	0.517203i	$0.826973\pi$
$168$	1.43746	+	7.32745i	0.110902	+	0.565325i
$169$			6.52982i			0.502294i
$170$	−0.448952	+	5.01057i	−0.0344331	+	0.384293i
$171$		−	3.73356i		−	0.285512i
$172$	−8.81001	+	11.4398i	−0.671757	+	0.872274i
$173$	16.4049	+	16.4049i	1.24724	+	1.24724i	0.956932	+	0.290312i	$0.0937590\pi$
$173$	16.4049	+	16.4049i	1.24724	+	1.24724i	0.290312	+	0.956932i	$0.406241\pi$
$174$	−2.46417	+	2.80487i	−0.186808	+	0.212637i
$175$	11.7235	−	6.06660i	0.886210	−	0.458592i
$176$	0.744321	+	2.81740i	0.0561053	+	0.212369i
$177$	3.48486	−	3.48486i	0.261938	−	0.261938i
$178$	−1.45399	+	0.0940174i	−0.108981	+	0.00704690i
$179$	−24.4156			−1.82491			−0.912455	−	0.409178i	$-0.865815\pi$
$179$	−24.4156			−1.82491			−0.912455	+	0.409178i	$0.865815\pi$
$180$	−3.23969	+	3.08292i	−0.241472	+	0.229787i
$181$	11.2800			0.838439			0.419220	−	0.907885i	$-0.362304\pi$
$181$	11.2800			0.838439			0.419220	+	0.907885i	$0.362304\pi$
$182$	−16.4652	+	1.06466i	−1.22048	+	0.0789180i
$183$	1.63365	−	1.63365i	0.120763	−	0.120763i
$184$	19.3672	+	13.0147i	1.42777	+	0.959455i
$185$	9.76491	+	1.51514i	0.717930	+	0.111395i
$186$	−5.60975	+	6.38537i	−0.411327	+	0.468198i
$187$	0.819496	+	0.819496i	0.0599275	+	0.0599275i
$188$	−4.70572	−	3.62398i	−0.343200	−	0.264306i
$189$			2.64002i			0.192033i
$190$	−9.06022	+	7.57013i	−0.657298	+	0.549195i
$191$			3.26729i			0.236413i	0.992989	+	0.118206i	$0.0377144\pi$
$191$			3.26729i			0.236413i	−0.992989	+	0.118206i	$0.962286\pi$
$192$	−3.10037	+	7.37480i	−0.223750	+	0.532230i
$193$	0.939448	+	0.939448i	0.0676229	+	0.0676229i	0.740109	−	0.672486i	$-0.234774\pi$
$193$	0.939448	+	0.939448i	0.0676229	+	0.0676229i	−0.672486	+	0.740109i	$0.734774\pi$
$194$	−18.8263	−	16.5395i	−1.35165	−	1.18747i
$195$	−5.83347	−	7.97620i	−0.417743	−	0.571187i
$196$	0.00779818	+	0.0600479i	0.000557013	+	0.00428914i
$197$	−1.45459	+	1.45459i	−0.103635	+	0.103635i	−0.757023	−	0.653388i	$-0.773347\pi$
$197$	−1.45459	+	1.45459i	−0.103635	+	0.103635i	0.653388	+	0.757023i	$0.273347\pi$
$198$	0.0664803	+	1.02813i	0.00472455	+	0.0730659i
$199$	5.19059			0.367951			0.183975	−	0.982931i	$-0.441103\pi$
$199$	5.19059			0.367951			0.183975	+	0.982931i	$0.441103\pi$
$200$	14.0501	+	1.61087i	0.993492	+	0.113906i
$201$	−7.21949			−0.509224
$202$	−0.517441	−	8.00230i	−0.0364070	−	0.563040i
$203$	4.92834	−	4.92834i	0.345902	−	0.345902i
$204$	0.409748	+	3.15516i	0.0286881	+	0.220905i
$205$	−5.60975	−	7.67030i	−0.391802	−	0.535717i
$206$	−0.0849206	−	0.0746054i	−0.00591670	−	0.00519801i
$207$	5.83347	+	5.83347i	0.405454	+	0.405454i
$208$	−15.2776	−	8.89224i	−1.05931	−	0.616566i
$209$			2.71995i			0.188143i
$210$	6.40655	−	5.35289i	0.442094	−	0.369384i
$211$			11.7800i			0.810967i	0.914102	+	0.405483i	$0.132897\pi$
$211$			11.7800i			0.810967i	−0.914102	+	0.405483i	$0.867103\pi$
$212$	−1.08653	−	0.836763i	−0.0746235	−	0.0574691i
$213$	−9.28005	−	9.28005i	−0.635858	−	0.635858i
$214$	−5.16147	+	5.87511i	−0.352831	+	0.401615i
$215$	15.9524	+	2.47520i	1.08794	+	0.168807i
$216$	−1.57758	+	2.34760i	−0.107341	+	0.159734i
$217$	11.2195	−	11.2195i	0.761629	−	0.761629i
$218$	22.2692	−	1.43996i	1.50826	−	0.0975264i
$219$	5.61404			0.379361
$220$	2.36017	−	2.24595i	0.159122	−	0.151422i
$221$	−7.03028			−0.472908
$222$	6.23675	−	0.403277i	0.418583	−	0.0270662i
$223$	−3.32381	+	3.32381i	−0.222579	+	0.222579i	−0.809583	−	0.587005i	$-0.800307\pi$
$223$	−3.32381	+	3.32381i	−0.222579	+	0.222579i	0.587005	+	0.809583i	$0.300307\pi$
$224$	6.66399	−	13.3650i	0.445257	−	0.892984i
$225$	4.76491	+	1.51514i	0.317661	+	0.101009i
$226$	2.43521	−	2.77191i	0.161988	−	0.184385i
$227$	−8.83851	−	8.83851i	−0.586633	−	0.586633i	0.350085	−	0.936718i	$-0.386153\pi$
$227$	−8.83851	−	8.83851i	−0.586633	−	0.586633i	−0.936718	+	0.350085i	$0.886153\pi$
$228$	−4.55609	+	5.91607i	−0.301734	+	0.391801i
$229$			7.09083i			0.468575i	0.972167	+	0.234288i	$0.0752757\pi$
$229$			7.09083i			0.468575i	−0.972167	+	0.234288i	$0.924724\pi$
$230$	2.32819	−	25.9840i	0.153516	−	1.71333i
$231$		−	1.92330i		−	0.126544i
$232$	7.32745	−	1.43746i	0.481071	−	0.0943739i
$233$	−15.3747	−	15.3747i	−1.00723	−	1.00723i	−0.999974	−	0.00725353i	$-0.997691\pi$
$233$	−15.3747	−	15.3747i	−1.00723	−	1.00723i	−0.00725353	−	0.999974i	$-0.502309\pi$
$234$	−4.69521	−	4.12489i	−0.306935	−	0.269652i
$235$	−1.01817	+	6.56198i	−0.0664179	+	0.428057i
$236$	−9.77460	+	1.26939i	−0.636272	+	0.0826301i
$237$	−5.03028	+	5.03028i	−0.326752	+	0.326752i
$238$	−0.383253	−	5.92707i	−0.0248426	−	0.384195i
$239$	0.706459			0.0456970			0.0228485	−	0.999739i	$-0.492726\pi$
$239$	0.706459			0.0456970			0.0228485	+	0.999739i	$0.492726\pi$
$240$	8.89562	−	0.931663i	0.574210	−	0.0601386i
$241$	−24.9991			−1.61033			−0.805166	−	0.593049i	$-0.797924\pi$
$241$	−24.9991			−1.61033			−0.805166	+	0.593049i	$0.797924\pi$
$242$	0.955368	+	14.7749i	0.0614134	+	0.949768i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−4.58217	+	0.595068i	−0.293343	+	0.0380953i
$245$	0.0546445	−	0.0399648i	0.00349111	−	0.00255326i
$246$	−4.51514	−	3.96669i	−0.287875	−	0.252907i
$247$	−11.6669	−	11.6669i	−0.742349	−	0.742349i
$248$	16.6811	−	3.27242i	1.05925	−	0.207799i
$249$		−	5.03028i		−	0.318781i
$250$	−5.98450	−	14.6351i	−0.378493	−	0.925604i
$251$			28.6154i			1.80619i	0.429440	+	0.903095i	$0.358711\pi$
$251$			28.6154i			1.80619i	−0.429440	+	0.903095i	$0.641289\pi$
$252$	3.22164	−	4.18329i	0.202944	−	0.263523i
$253$	−4.24977	−	4.24977i	−0.267181	−	0.267181i
$254$	−14.8596	+	16.9142i	−0.932376	+	1.06129i
$255$	2.87124	−	2.09991i	0.179804	−	0.131502i
$256$	13.9123	−	7.90245i	0.869517	−	0.493903i
$257$	−3.90539	+	3.90539i	−0.243612	+	0.243612i	−0.818342	−	0.574731i	$-0.805107\pi$
$257$	−3.90539	+	3.90539i	−0.243612	+	0.243612i	0.574731	+	0.818342i	$0.305107\pi$
$258$	10.1886	−	0.658812i	0.634316	−	0.0410158i
$259$	−11.6669			−0.724948
$260$	−0.489904	+	19.7574i	−0.0303825	+	1.22530i
$261$	2.64002			0.163413
$262$	−6.45670	+	0.417500i	−0.398896	+	0.0257932i
$263$	0.176615	−	0.176615i	0.0108905	−	0.0108905i	−0.701641	−	0.712531i	$-0.747549\pi$
$263$	0.176615	−	0.176615i	0.0108905	−	0.0108905i	0.712531	+	0.701641i	$0.247549\pi$
$264$	1.14929	−	1.71026i	0.0707340	−	0.105259i
$265$	−0.235091	+	1.51514i	−0.0144415	+	0.0930742i
$266$	9.20012	−	10.4722i	0.564095	−	0.642089i
$267$	0.728515	+	0.728515i	0.0445844	+	0.0445844i
$268$	11.4398	+	8.81001i	0.698795	+	0.538157i
$269$			5.38934i			0.328594i	0.986411	+	0.164297i	$0.0525355\pi$
$269$			5.38934i			0.328594i	−0.986411	+	0.164297i	$0.947465\pi$
$270$	3.14966	+	0.282213i	0.191682	+	0.0171749i
$271$		−	15.4005i		−	0.935513i	−0.883857	−	0.467757i	$-0.845062\pi$
$271$		−	15.4005i		−	0.935513i	0.883857	−	0.467757i	$-0.154938\pi$
$272$	3.20100	−	5.49958i	0.194089	−	0.333461i
$273$	8.24977	+	8.24977i	0.499299	+	0.499299i
$274$	−6.15224	−	5.40493i	−0.371670	−	0.326524i
$275$	−3.47131	−	1.10380i	−0.209328	−	0.0665617i
$276$	−2.12489	−	16.3621i	−0.127903	−	0.984885i
$277$	8.59415	−	8.59415i	0.516372	−	0.516372i	−0.400099	−	0.916472i	$-0.631024\pi$
$277$	8.59415	−	8.59415i	0.516372	−	0.516372i	0.916472	+	0.400099i	$0.131024\pi$
$278$	1.24017	+	19.1794i	0.0743805	+	1.15031i
$279$	6.01008			0.359814
$280$	−16.6838	+	0.664043i	−0.997046	+	0.0396842i
$281$	−20.7493			−1.23780			−0.618900	−	0.785470i	$-0.712421\pi$
$281$	−20.7493			−1.23780			−0.618900	+	0.785470i	$0.712421\pi$
$282$	0.271001	+	4.19107i	0.0161379	+	0.249575i
$283$	−18.5822	+	18.5822i	−1.10459	+	1.10459i	−0.110745	+	0.993849i	$0.535324\pi$
$283$	−18.5822	+	18.5822i	−1.10459	+	1.10459i	−0.993849	+	0.110745i	$0.964676\pi$
$284$	3.38033	+	26.0294i	0.200586	+	1.54456i
$285$	8.24977	+	1.28005i	0.488674	+	0.0758234i
$286$	3.42053	+	3.00504i	0.202260	+	0.177692i
$287$	7.93338	+	7.93338i	0.468293	+	0.468293i
$288$	5.36458	−	1.79480i	0.316111	−	0.105759i
$289$			14.4693i			0.851133i
$290$	−5.35289	−	6.40655i	−0.314332	−	0.376205i
$291$			17.7198i			1.03876i
$292$	−8.89581	−	6.85085i	−0.520588	−	0.400916i
$293$	6.23509	+	6.23509i	0.364258	+	0.364258i	0.865378	−	0.501120i	$-0.167078\pi$
$293$	6.23509	+	6.23509i	0.364258	+	0.364258i	−0.501120	+	0.865378i	$0.667078\pi$
$294$	0.0282594	−	0.0321666i	0.00164812	−	0.00187600i
$295$	6.50547	+	8.89503i	0.378763	+	0.517889i
$296$	−10.3747	−	6.97173i	−0.603015	−	0.405224i
$297$	0.515138	−	0.515138i	0.0298913	−	0.0298913i
$298$	8.00230	−	0.517441i	0.463561	−	0.0299745i
$299$	36.4578			2.10841
$300$	−5.70138	−	8.21549i	−0.329169	−	0.474322i
$301$	−19.0596			−1.09858
$302$	27.1628	−	1.75639i	1.56304	−	0.101069i
$303$	−4.00951	+	4.00951i	−0.230340	+	0.230340i
$304$	14.4388	−	3.81456i	0.828125	−	0.218780i
$305$	3.04965	+	4.16984i	0.174623	+	0.238764i
$306$	1.48486	−	1.69016i	0.0848839	−	0.0966202i
$307$	−0.905130	−	0.905130i	−0.0516585	−	0.0516585i	0.680806	−	0.732464i	$-0.261630\pi$
$307$	−0.905130	−	0.905130i	−0.0516585	−	0.0516585i	−0.732464	+	0.680806i	$0.761630\pi$
$308$	−2.34702	+	3.04759i	−0.133734	+	0.173653i
$309$			0.0799296i			0.00454704i
$310$	−12.1860	−	14.5847i	−0.692118	−	0.828354i
$311$		−	24.4377i		−	1.38573i	−0.721066	−	0.692867i	$-0.756347\pi$
$311$		−	24.4377i		−	1.38573i	0.721066	−	0.692867i	$-0.243653\pi$
$312$	2.40623	+	12.2657i	0.136226	+	0.694411i
$313$	18.5904	+	18.5904i	1.05079	+	1.05079i	0.998639	+	0.0521506i	$0.0166076\pi$
$313$	18.5904	+	18.5904i	1.05079	+	1.05079i	0.0521506	+	0.998639i	$0.483392\pi$
$314$	−3.14719	−	2.76491i	−0.177606	−	0.156033i
$315$	−5.83347	−	0.905130i	−0.328679	−	0.0509983i
$316$	14.1093	−	1.83232i	0.793710	−	0.103076i
$317$	19.3141	−	19.3141i	1.08479	−	1.08479i	0.0887327	−	0.996055i	$-0.471718\pi$
$317$	19.3141	−	19.3141i	1.08479	−	1.08479i	0.996055	−	0.0887327i	$-0.0282817\pi$
$318$	0.0625731	+	0.967703i	0.00350893	+	0.0542661i
$319$	−1.92330			−0.107684
$320$	−15.2326	−	9.37911i	−0.851529	−	0.524308i
$321$	5.52982			0.308644
$322$	1.98749	+	30.7368i	0.110758	+	1.71289i
$323$	4.19982	−	4.19982i	0.233684	−	0.233684i
$324$	1.98335	−	0.257569i	0.110186	−	0.0143094i
$325$	19.6244	−	10.1552i	1.08857	−	0.563307i
$326$	6.43899	+	5.65685i	0.356623	+	0.313304i
$327$	−11.1579	−	11.1579i	−0.617031	−	0.617031i
$328$	2.31395	+	11.7953i	0.127766	+	0.651289i
$329$		−	7.84014i		−	0.432241i
$330$	−2.29457	−	0.205596i	−0.126312	−	0.0113177i
$331$		−	11.0294i		−	0.606231i	−0.952954	−	0.303115i	$-0.901973\pi$
$331$		−	11.0294i		−	0.606231i	0.952954	−	0.303115i	$-0.0980268\pi$
$332$	−6.13849	+	7.97080i	−0.336893	+	0.437455i
$333$	−3.12489	−	3.12489i	−0.171243	−	0.171243i
$334$	5.77695	−	6.57569i	0.316101	−	0.359806i
$335$	2.47520	−	15.9524i	0.135235	−	0.871572i
$336$	−10.2098	+	2.69730i	−0.556991	+	0.147150i
$337$	13.6206	−	13.6206i	0.741964	−	0.741964i	−0.230992	−	0.972956i	$-0.574197\pi$
$337$	13.6206	−	13.6206i	0.741964	−	0.741964i	0.972956	+	0.230992i	$0.0741971\pi$
$338$	−9.21531	+	0.595876i	−0.501247	+	0.0324114i
$339$	−2.60900			−0.141701
$340$	−7.11221	−	0.176354i	−0.385714	−	0.00956413i
$341$	−4.37844			−0.237106
$342$	5.26904	−	0.340704i	0.284917	−	0.0184232i
$343$	−13.1240	+	13.1240i	−0.708628	+	0.708628i
$344$	−16.9485	−	11.3893i	−0.913802	−	0.614072i
$345$	−14.8898	+	10.8898i	−0.801640	+	0.586287i
$346$	−21.6547	+	24.6488i	−1.16416	+	1.32513i
$347$	−17.7627	−	17.7627i	−0.953549	−	0.953549i	0.0454187	−	0.998968i	$-0.485538\pi$
$347$	−17.7627	−	17.7627i	−0.953549	−	0.953549i	−0.998968	+	0.0454187i	$0.985538\pi$
$348$	−4.18329	−	3.22164i	−0.224248	−	0.172698i
$349$			14.6888i			0.786271i	0.919480	+	0.393136i	$0.128610\pi$
$349$			14.6888i			0.786271i	−0.919480	+	0.393136i	$0.871390\pi$
$350$	9.63141	+	15.9913i	0.514821	+	0.854772i
$351$			4.41926i			0.235882i
$352$	−3.90818	+	1.30754i	−0.208307	+	0.0696919i
$353$	−18.4049	−	18.4049i	−0.979596	−	0.979596i	0.0202002	−	0.999796i	$-0.493570\pi$
$353$	−18.4049	−	18.4049i	−0.979596	−	0.979596i	−0.999796	+	0.0202002i	$0.993570\pi$
$354$	5.23608	+	4.60006i	0.278294	+	0.244490i
$355$	23.6871	−	17.3238i	1.25718	−	0.919451i
$356$	−0.265367	−	2.04339i	−0.0140644	−	0.108300i
$357$	−2.96972	+	2.96972i	−0.157174	+	0.157174i
$358$	−2.22804	−	34.4569i	−0.117755	−	1.82111i
$359$	−9.63060			−0.508284			−0.254142	−	0.967167i	$-0.581793\pi$
$359$	−9.63060			−0.508284			−0.254142	+	0.967167i	$0.581793\pi$
$360$	−4.64646	−	4.29074i	−0.244890	−	0.226142i
$361$	−5.06055			−0.266345
$362$	1.02936	+	15.9192i	0.0541017	+	0.836692i
$363$	7.40289	−	7.40289i	0.388551	−	0.388551i
$364$	−3.00504	−	23.1396i	−0.157507	−	1.21284i
$365$	−1.92477	+	12.4049i	−0.100747	+	0.649304i
$366$	2.45459	+	2.15643i	0.128303	+	0.112718i
$367$	15.4570	+	15.4570i	0.806850	+	0.806850i	0.984156	−	0.177306i	$-0.0567383\pi$
$367$	15.4570	+	15.4570i	0.806850	+	0.806850i	−0.177306	+	0.984156i	$0.556738\pi$
$368$	−16.5998	+	28.5199i	−0.865326	+	1.48670i
$369$			4.24977i			0.221234i
$370$	−1.24717	+	13.9192i	−0.0648373	+	0.723622i
$371$		−	1.81026i		−	0.0939840i
$372$	−9.52337	−	7.33415i	−0.493764	−	0.380258i
$373$	3.37466	+	3.37466i	0.174733	+	0.174733i	0.789055	−	0.614322i	$-0.210570\pi$
$373$	3.37466	+	3.37466i	0.174733	+	0.174733i	−0.614322	+	0.789055i	$0.710570\pi$
$374$	−1.08174	+	1.23131i	−0.0559357	+	0.0636695i
$375$	−4.98154	+	10.0092i	−0.257245	+	0.516873i
$376$	4.68498	−	6.97173i	0.241609	−	0.359540i
$377$	8.24977	−	8.24977i	0.424885	−	0.424885i
$378$	−3.72578	+	0.240914i	−0.191633	+	0.0123913i
$379$	−5.89705			−0.302911			−0.151455	−	0.988464i	$-0.548396\pi$
$379$	−5.89705			−0.302911			−0.151455	+	0.988464i	$0.548396\pi$
$380$	−11.5103	−	12.0956i	−0.590463	−	0.620490i
$381$	15.9201			0.815610
$382$	−4.61102	+	0.298155i	−0.235920	+	0.0152549i
$383$	−0.642881	+	0.642881i	−0.0328497	+	0.0328497i	−0.723341	−	0.690491i	$-0.757394\pi$
$383$	−0.642881	+	0.642881i	−0.0328497	+	0.0328497i	0.690491	+	0.723341i	$0.257394\pi$
$384$	−10.6907	−	3.70247i	−0.545559	−	0.188941i
$385$	4.24977	+	0.659401i	0.216588	+	0.0336062i
$386$	−1.24008	+	1.41154i	−0.0631185	+	0.0718455i
$387$	−5.10495	−	5.10495i	−0.259499	−	0.259499i
$388$	21.6237	−	28.0782i	1.09778	−	1.42546i
$389$		−	18.8292i		−	0.954680i	−0.878719	−	0.477340i	$-0.841601\pi$
$389$		−	18.8292i		−	0.954680i	0.878719	−	0.477340i	$-0.158399\pi$
$390$	10.7242	−	8.96044i	0.543041	−	0.453730i
$391$			13.1240i			0.663708i
$392$	−0.0840320	+	0.0164850i	−0.00424426	+	0.000832616i
$393$	3.23509	+	3.23509i	0.163189	+	0.163189i
$394$	−2.18555	−	1.92007i	−0.110106	−	0.0967317i
$395$	−9.39041	−	12.8397i	−0.472483	−	0.646034i
$396$	−1.44490	+	0.187643i	−0.0726088	+	0.00942941i
$397$	−24.3444	+	24.3444i	−1.22181	+	1.22181i	−0.254821	+	0.966988i	$0.582017\pi$
$397$	−24.3444	+	24.3444i	−1.22181	+	1.22181i	−0.966988	+	0.254821i	$0.917983\pi$
$398$	0.473665	+	7.32530i	0.0237427	+	0.367184i
$399$	−9.85668			−0.493451
$400$	−0.991227	+	19.9754i	−0.0495614	+	0.998771i
$401$	15.9394			0.795978			0.397989	−	0.917390i	$-0.369708\pi$
$401$	15.9394			0.795978			0.397989	+	0.917390i	$0.369708\pi$
$402$	−0.658812	−	10.1886i	−0.0328586	−	0.508163i
$403$	18.7808	−	18.7808i	0.935539	−	0.935539i
$404$	11.2462	−	1.46049i	0.559517	−	0.0726623i
$405$	−1.32001	−	1.80487i	−0.0655919	−	0.0896849i
$406$	7.40493	+	6.50547i	0.367501	+	0.322861i
$407$	2.27653	+	2.27653i	0.112843	+	0.112843i
$408$	−4.41538	+	0.866187i	−0.218594	+	0.0428826i
$409$		−	23.4087i		−	1.15749i	−0.815510	−	0.578743i	$-0.803543\pi$
$409$		−	23.4087i		−	1.15749i	0.815510	−	0.578743i	$-0.196457\pi$
$410$	10.3129	−	8.61680i	0.509319	−	0.425553i
$411$			5.79065i			0.285632i
$412$	0.0975387	−	0.126654i	0.00480539	−	0.00623978i
$413$	−9.20012	−	9.20012i	−0.452708	−	0.452708i
$414$	−7.70025	+	8.76491i	−0.378447	+	0.430772i
$415$	11.1150	+	1.72463i	0.545616	+	0.0846586i
$416$	11.1552	−	22.3722i	0.546927	−	1.09689i
$417$	9.60975	−	9.60975i	0.470591	−	0.470591i
$418$	−3.83858	+	0.248208i	−0.187751	+	0.0121403i
$419$	28.0361			1.36966			0.684828	−	0.728705i	$-0.259878\pi$
$419$	28.0361			1.36966			0.684828	+	0.728705i	$0.259878\pi$
$420$	8.13898	+	8.55287i	0.397141	+	0.417337i
$421$	17.4087			0.848449			0.424224	−	0.905557i	$-0.360547\pi$
$421$	17.4087			0.848449			0.424224	+	0.905557i	$0.360547\pi$
$422$	−16.6247	+	1.07498i	−0.809277	+	0.0523290i
$423$	2.09991	−	2.09991i	0.102101	−	0.102101i
$424$	1.08174	−	1.60975i	0.0525342	−	0.0781762i
$425$	3.65562	+	7.06433i	0.177324	+	0.342670i
$426$	12.2498	−	13.9435i	0.593503	−	0.675563i
$427$	−4.31286	−	4.31286i	−0.208714	−	0.208714i
$428$	−8.76236	−	6.74808i	−0.423545	−	0.326181i
$429$		−	3.21949i		−	0.155439i
$430$	−2.03743	+	22.7390i	−0.0982538	+	1.09657i
$431$			31.1542i			1.50065i	0.661071	+	0.750323i	$0.270102\pi$
$431$			31.1542i			1.50065i	−0.661071	+	0.750323i	$0.729898\pi$
$432$	−3.45705	−	2.01216i	−0.166328	−	0.0968100i
$433$	−12.1589	−	12.1589i	−0.584321	−	0.584321i	0.351766	−	0.936088i	$-0.385581\pi$
$433$	−12.1589	−	12.1589i	−0.584321	−	0.584321i	−0.936088	+	0.351766i	$0.885581\pi$
$434$	16.8575	+	14.8099i	0.809187	+	0.710896i
$435$	−0.905130	+	5.83347i	−0.0433977	+	0.279693i
$436$	4.06433	+	31.2964i	0.194646	+	1.49882i
$437$	−21.7796	+	21.7796i	−1.04186	+	1.04186i
$438$	0.512307	+	7.92290i	0.0244790	+	0.378571i
$439$	−14.2967			−0.682344			−0.341172	−	0.940001i	$-0.610824\pi$
$439$	−14.2967			−0.682344			−0.341172	+	0.940001i	$0.610824\pi$
$440$	3.38501	+	3.12587i	0.161374	+	0.149020i
$441$	−0.0302761			−0.00144172
$442$	−0.641545	−	9.92159i	−0.0305152	−	0.471922i
$443$	−7.02825	+	7.02825i	−0.333922	+	0.333922i	−0.854074	−	0.520152i	$-0.825875\pi$
$443$	−7.02825	+	7.02825i	−0.333922	+	0.333922i	0.520152	+	0.854074i	$0.325875\pi$
$444$	1.13826	+	8.76491i	0.0540196	+	0.415964i
$445$	−1.85952	+	1.35998i	−0.0881496	+	0.0644691i
$446$	−4.99409	−	4.38747i	−0.236477	−	0.207753i
$447$	−4.00951	−	4.00951i	−0.189643	−	0.189643i
$448$	19.4696	+	8.18505i	0.919854	+	0.386707i
$449$			38.4608i			1.81508i	0.419969	+	0.907538i	$0.362041\pi$
$449$			38.4608i			1.81508i	−0.419969	+	0.907538i	$0.637959\pi$
$450$	−1.70344	+	6.86282i	−0.0803011	+	0.323516i
$451$		−	3.09602i		−	0.145786i
$452$	4.13412	+	3.18378i	0.194453	+	0.149752i
$453$	−13.6097	−	13.6097i	−0.639442	−	0.639442i
$454$	11.6669	−	13.2800i	0.547557	−	0.623263i
$455$	−21.0573	+	15.4005i	−0.987184	+	0.721986i
$456$	−8.76491	−	5.88999i	−0.410454	−	0.275824i
$457$	4.93945	−	4.93945i	0.231058	−	0.231058i	−0.582076	−	0.813134i	$-0.697760\pi$
$457$	4.93945	−	4.93945i	0.231058	−	0.231058i	0.813134	+	0.582076i	$0.197760\pi$
$458$	−10.0070	+	0.647071i	−0.467599	+	0.0302356i
$459$	−1.59083			−0.0742535
$460$	36.8828	+	0.914542i	1.71967	+	0.0426407i
$461$	27.1689			1.26538			0.632691	−	0.774404i	$-0.281950\pi$
$461$	27.1689			1.26538			0.632691	+	0.774404i	$0.281950\pi$
$462$	2.71428	−	0.175510i	0.126280	−	0.00816545i
$463$	−4.96280	+	4.96280i	−0.230641	+	0.230641i	−0.812960	−	0.582319i	$-0.802145\pi$
$463$	−4.96280	+	4.96280i	−0.230641	+	0.230641i	0.582319	+	0.812960i	$0.302145\pi$
$464$	2.69730	+	10.2098i	0.125219	+	0.473978i
$465$	−2.06055	+	13.2800i	−0.0955558	+	0.615847i
$466$	20.2947	−	23.1007i	0.940135	−	1.07012i
$467$	21.2340	+	21.2340i	0.982591	+	0.982591i	0.999851	−	0.0172604i	$-0.00549442\pi$
$467$	21.2340	+	21.2340i	0.982591	+	0.982591i	−0.0172604	+	0.999851i	$0.505494\pi$
$468$	5.39285	−	7.00260i	0.249285	−	0.323695i
$469$			19.0596i			0.880092i
$470$	−9.35362	−	0.838094i	−0.431450	−	0.0386584i
$471$			2.96222i			0.136492i
$472$	−2.68342	−	13.6787i	−0.123514	−	0.629614i
$473$	3.71904	+	3.71904i	0.171001	+	0.171001i
$474$	−7.55809	−	6.64002i	−0.347155	−	0.304986i
$475$	−5.65685	+	17.7901i	−0.259554	+	0.816264i
$476$	8.32970	−	1.08174i	0.381791	−	0.0495817i
$477$	0.484862	−	0.484862i	0.0222003	−	0.0222003i
$478$	0.0644676	+	0.997001i	0.00294868	+	0.0456018i
$479$	−18.7808			−0.858118			−0.429059	−	0.903277i	$-0.641155\pi$
$479$	−18.7808			−0.858118			−0.429059	+	0.903277i	$0.641155\pi$
$480$	2.12659	+	12.4691i	0.0970651	+	0.569132i
$481$	−19.5298			−0.890483
$482$	−2.28128	−	35.2804i	−0.103909	−	1.60698i
$483$	15.4005	−	15.4005i	0.700747	−	0.700747i
$484$	−20.7642	+	2.69656i	−0.943826	+	0.122571i
$485$	−39.1542	−	6.07523i	−1.77790	−	0.275862i
$486$	−1.06244	−	0.933389i	−0.0481934	−	0.0423394i
$487$	−2.97058	−	2.97058i	−0.134610	−	0.134610i	0.636591	−	0.771201i	$-0.280344\pi$
$487$	−2.97058	−	2.97058i	−0.134610	−	0.134610i	−0.771201	+	0.636591i	$0.780344\pi$
$488$	−1.25794	−	6.41236i	−0.0569444	−	0.290274i
$489$		−	6.06055i		−	0.274068i
$490$	0.0613875	+	0.0734710i	0.00277321	+	0.00331908i
$491$		−	29.5480i		−	1.33348i	−0.745290	−	0.666741i	$-0.767689\pi$
$491$		−	29.5480i		−	1.33348i	0.745290	−	0.666741i	$-0.232311\pi$
$492$	5.18603	−	6.73404i	0.233804	−	0.303594i
$493$	2.96972	+	2.96972i	0.133750	+	0.133750i
$494$	15.4005	−	17.5298i	0.692901	−	0.788704i
$495$	0.961649	+	1.31488i	0.0432229	+	0.0590994i
$496$	6.14048	+	23.2429i	0.275716	+	1.04364i
$497$	−24.4995	+	24.4995i	−1.09895	+	1.09895i
$498$	7.09906	−	0.459036i	0.318116	−	0.0205699i
$499$	−15.0473			−0.673608			−0.336804	−	0.941575i	$-0.609346\pi$
$499$	−15.0473			−0.673608			−0.336804	+	0.941575i	$0.609346\pi$
$500$	20.1079	−	9.78124i	0.899252	−	0.437430i
$501$	−6.18922			−0.276514
$502$	−40.3840	+	2.61129i	−1.80243	+	0.116548i
$503$	−13.4136	+	13.4136i	−0.598084	+	0.598084i	−0.939802	−	0.341719i	$-0.888991\pi$
$503$	−13.4136	+	13.4136i	−0.598084	+	0.598084i	0.341719	+	0.939802i	$0.388991\pi$
$504$	6.19773	+	4.16485i	0.276069	+	0.185517i
$505$	−7.48486	−	10.2342i	−0.333072	−	0.455415i
$506$	5.60975	−	6.38537i	0.249384	−	0.283864i
$507$	4.61728	+	4.61728i	0.205061	+	0.205061i
$508$	−25.2264	−	19.4274i	−1.11924	−	0.861951i
$509$		−	41.4187i		−	1.83585i	−0.396752	−	0.917926i	$-0.629863\pi$
$509$		−	41.4187i		−	1.83585i	0.396752	−	0.917926i	$-0.370137\pi$
$510$	3.22555	+	3.86046i	0.142830	+	0.170944i
$511$		−	14.8212i		−	0.655651i
$512$	12.4220	+	18.9128i	0.548981	+	0.835835i
$513$	−2.64002	−	2.64002i	−0.116560	−	0.116560i
$514$	−5.86793	−	5.15516i	−0.258823	−	0.227384i
$515$	−0.176615	−	0.0274038i	−0.00778257	−	0.00120756i
$516$	1.85952	+	14.3188i	0.0818607	+	0.630348i
$517$	−1.52982	+	1.52982i	−0.0672813	+	0.0672813i
$518$	−1.06466	−	16.4652i	−0.0467785	−	0.723437i
$519$	23.2001			1.01837
$520$	−27.9277	+	1.11157i	−1.22471	+	0.0487457i
$521$	30.8392			1.35109			0.675545	−	0.737318i	$-0.263908\pi$
$521$	30.8392			1.35109			0.675545	+	0.737318i	$0.263908\pi$
$522$	0.240914	+	3.72578i	0.0105445	+	0.163073i
$523$	17.1251	−	17.1251i	0.748829	−	0.748829i	−0.225430	−	0.974259i	$-0.572379\pi$
$523$	17.1251	−	17.1251i	0.748829	−	0.748829i	0.974259	+	0.225430i	$0.0723787\pi$
$524$	−1.17841	−	9.07402i	−0.0514789	−	0.396400i
$525$	4.00000	−	12.5795i	0.174574	−	0.549013i
$526$	0.265367	+	0.233133i	0.0115706	+	0.0101651i
$527$	6.76066	+	6.76066i	0.294499	+	0.294499i
$528$	2.51852	+	1.46589i	0.109604	+	0.0637945i
$529$		−	45.0587i		−	1.95907i
$530$	−2.15972	−	0.193513i	−0.0938121	−	0.00840566i
$531$		−	4.92834i		−	0.213872i
$532$	15.6186	+	12.0282i	0.677150	+	0.521488i
$533$	13.2800	+	13.2800i	0.575223	+	0.575223i
$534$	−0.961649	+	1.09461i	−0.0416146	+	0.0473684i
$535$	−1.89589	+	12.2188i	−0.0819666	+	0.528266i
$536$	−11.3893	+	16.9485i	−0.491944	+	0.732064i
$537$	−17.2645	+	17.2645i	−0.745016	+	0.745016i
$538$	−7.60579	+	0.491802i	−0.327909	+	0.0212031i
$539$	0.0220566			0.000950045
$540$	−0.110857	+	4.47076i	−0.00477051	+	0.192391i
$541$	−22.3397			−0.960458			−0.480229	−	0.877143i	$-0.659446\pi$
$541$	−22.3397			−0.960458			−0.480229	+	0.877143i	$0.659446\pi$
$542$	21.7342	−	1.40537i	0.933564	−	0.0603656i
$543$	7.97620	−	7.97620i	0.342291	−	0.342291i
$544$	8.05348	+	4.01560i	0.345290	+	0.172167i
$545$	28.4802	−	20.8292i	1.21996	−	0.892227i
$546$	−10.8898	+	12.3955i	−0.466040	+	0.530476i
$547$	25.3428	+	25.3428i	1.08358	+	1.08358i	0.996173	+	0.0874075i	$0.0278582\pi$
$547$	25.3428	+	25.3428i	1.08358	+	1.08358i	0.0874075	+	0.996173i	$0.472142\pi$
$548$	7.06638	−	9.17567i	0.301861	−	0.391965i
$549$		−	2.31032i		−	0.0986022i
$550$	1.24098	−	4.99967i	0.0529158	−	0.213187i
$551$			9.85668i			0.419909i
$552$	22.8974	−	4.49190i	0.974580	−	0.191188i
$553$	13.2800	+	13.2800i	0.564725	+	0.564725i
$554$	12.9129	+	11.3444i	0.548616	+	0.481977i
$555$	7.97620	−	5.83347i	0.338571	−	0.247617i
$556$	−26.9541	+	3.50042i	−1.14311	+	0.148451i
$557$	21.1055	−	21.1055i	0.894269	−	0.894269i	−0.100653	−	0.994922i	$-0.532093\pi$
$557$	21.1055	−	21.1055i	0.894269	−	0.894269i	0.994922	+	0.100653i	$0.0320931\pi$
$558$	0.548448	+	8.48183i	0.0232176	+	0.359064i
$559$	−31.9048			−1.34943
$560$	−2.45961	−	23.4846i	−0.103938	−	0.992407i
$561$	1.15894			0.0489306
$562$	−1.89347	−	29.2828i	−0.0798712	−	1.23522i
$563$	−10.2955	+	10.2955i	−0.433905	+	0.433905i	−0.889955	−	0.456049i	$-0.849264\pi$
$563$	−10.2955	+	10.2955i	−0.433905	+	0.433905i	0.456049	+	0.889955i	$0.349264\pi$
$564$	−5.88999	+	0.764909i	−0.248013	+	0.0322085i
$565$	0.894492	−	5.76491i	0.0376316	−	0.242532i
$566$	−27.9201	−	24.5287i	−1.17357	−	1.03102i
$567$	1.86678	+	1.86678i	0.0783973	+	0.0783973i
$568$	−36.4259	+	7.14584i	−1.52840	+	0.299833i
$569$			28.3179i			1.18715i	0.804780	+	0.593574i	$0.202283\pi$
$569$			28.3179i			1.18715i	−0.804780	+	0.593574i	$0.797717\pi$
$570$	−1.05366	+	11.7594i	−0.0441329	+	0.492548i
$571$		−	27.2387i		−	1.13990i	−0.821678	−	0.569952i	$-0.806962\pi$
$571$		−	27.2387i		−	1.13990i	0.821678	−	0.569952i	$-0.193038\pi$
$572$	−3.92878	+	5.10150i	−0.164270	+	0.213304i
$573$	2.31032	+	2.31032i	0.0965151	+	0.0965151i
$574$	−10.4722	+	11.9201i	−0.437099	+	0.497534i
$575$	−18.9574	−	36.6345i	−0.790580	−	1.52776i
$576$	3.02248	+	7.40707i	0.125937	+	0.308628i
$577$	4.81078	−	4.81078i	0.200275	−	0.200275i	−0.599843	−	0.800118i	$-0.704770\pi$
$577$	4.81078	−	4.81078i	0.200275	−	0.200275i	0.800118	+	0.599843i	$0.204770\pi$
$578$	−20.4200	+	1.32039i	−0.849359	+	0.0549208i
$579$	1.32858			0.0552139
$580$	8.55287	−	8.13898i	0.355138	−	0.337953i
$581$	−13.2800			−0.550949
$582$	−25.0074	+	1.61702i	−1.03659	+	0.0670275i
$583$	−0.353229	+	0.353229i	−0.0146293	+	0.0146293i
$584$	8.85660	−	13.1795i	0.366489	−	0.545373i
$585$	−9.76491	−	1.51514i	−0.403729	−	0.0626432i
$586$	−8.23039	+	9.36835i	−0.339994	+	0.387003i
$587$	−4.84271	−	4.84271i	−0.199880	−	0.199880i	0.600069	−	0.799948i	$-0.295140\pi$
$587$	−4.84271	−	4.84271i	−0.199880	−	0.199880i	−0.799948	+	0.600069i	$0.795140\pi$
$588$	0.0479745	+	0.0369462i	0.00197843	+	0.00152363i
$589$			22.4390i			0.924582i
$590$	−11.9596	+	9.99266i	−0.492369	+	0.411391i
$591$			2.05710i			0.0846176i
$592$	8.89224	−	15.2776i	0.365469	−	0.627906i
$593$	18.8439	+	18.8439i	0.773827	+	0.773827i	0.978773	−	0.204946i	$-0.0657019\pi$
$593$	18.8439	+	18.8439i	0.773827	+	0.773827i	−0.204946	+	0.978773i	$0.565702\pi$
$594$	0.774006	+	0.679988i	0.0317578	+	0.0279003i
$595$	−5.54382	−	7.58015i	−0.227274	−	0.310756i
$596$	1.46049	+	11.2462i	0.0598241	+	0.460661i
$597$	3.67030	−	3.67030i	0.150215	−	0.150215i
$598$	3.32695	+	51.4517i	0.136049	+	2.10402i
$599$	30.2765			1.23706			0.618532	−	0.785760i	$-0.287728\pi$
$599$	30.2765			1.23706			0.618532	+	0.785760i	$0.287728\pi$
$600$	11.0740	−	8.79586i	0.452093	−	0.359090i
$601$	30.1505			1.22986			0.614932	−	0.788581i	$-0.289184\pi$
$601$	30.1505			1.22986			0.614932	+	0.788581i	$0.289184\pi$
$602$	−1.73928	−	26.8982i	−0.0708877	−	1.09629i
$603$	−5.10495	+	5.10495i	−0.207890	+	0.207890i
$604$	4.95745	+	38.1736i	0.201716	+	1.55326i
$605$	13.8196	+	18.8957i	0.561845	+	0.768220i
$606$	−6.02437	−	5.29260i	−0.244723	−	0.214997i
$607$	−19.5438	−	19.5438i	−0.793258	−	0.793258i	0.188764	−	0.982022i	$-0.439552\pi$
$607$	−19.5438	−	19.5438i	−0.793258	−	0.793258i	−0.982022	+	0.188764i	$0.939552\pi$
$608$	6.70097	+	20.0290i	0.271760	+	0.812282i
$609$		−	6.96972i		−	0.282427i
$610$	−5.60646	+	4.68439i	−0.226999	+	0.189665i
$611$		−	13.1240i		−	0.530939i
$612$	2.52077	+	1.94130i	0.101896	+	0.0784724i
$613$	23.4040	+	23.4040i	0.945279	+	0.945279i	0.998579	−	0.0532993i	$-0.0169737\pi$
$613$	23.4040	+	23.4040i	0.945279	+	0.945279i	−0.0532993	+	0.998579i	$0.516974\pi$
$614$	1.19478	−	1.35998i	0.0482175	−	0.0548842i
$615$	−9.39041	−	1.45703i	−0.378658	−	0.0587531i
$616$	−4.51514	−	3.03416i	−0.181920	−	0.122250i
$617$	−17.9348	+	17.9348i	−0.722026	+	0.722026i	−0.969018	−	0.246992i	$-0.920558\pi$
$617$	−17.9348	+	17.9348i	−0.722026	+	0.722026i	0.246992	+	0.969018i	$0.420558\pi$
$618$	−0.112802	+	0.00729394i	−0.00453756	+	0.000293405i
$619$	38.9056			1.56375			0.781875	−	0.623435i	$-0.214264\pi$
$619$	38.9056			1.56375			0.781875	+	0.623435i	$0.214264\pi$
$620$	19.4708	−	18.5286i	0.781967	−	0.744126i
$621$	8.24977			0.331052
$622$	34.4881	−	2.23005i	1.38285	−	0.0894169i
$623$	1.92330	−	1.92330i	0.0770553	−	0.0770553i
$624$	−17.0907	+	4.51514i	−0.684174	+	0.180750i
$625$	−20.4087	−	14.4390i	−0.816349	−	0.577560i
$626$	−24.5395	+	27.9324i	−0.980796	+	1.11640i
$627$	1.92330	+	1.92330i	0.0768091	+	0.0768091i
$628$	3.61483	−	4.69384i	0.144247	−	0.187305i
$629$		−	7.03028i		−	0.280315i
$630$	0.745049	−	8.31518i	0.0296834	−	0.331285i
$631$		−	12.7707i		−	0.508395i	−0.967152	−	0.254198i	$-0.918189\pi$
$631$		−	12.7707i		−	0.508395i	0.967152	−	0.254198i	$-0.0818113\pi$
$632$	3.87342	+	19.7448i	0.154077	+	0.785404i
$633$	8.32970	+	8.32970i	0.331076	+	0.331076i
$634$	29.0198	+	25.4948i	1.15253	+	1.01253i
$635$	−5.45818	+	35.1774i	−0.216601	+	1.39597i
$636$	−1.35998	+	0.176615i	−0.0539266	+	0.00700323i
$637$	−0.0946093	+	0.0946093i	−0.00374856	+	0.00374856i
$638$	−0.175510	−	2.71428i	−0.00694849	−	0.107460i
$639$	−13.1240			−0.519176
$640$	11.8464	−	22.3531i	0.468269	−	0.883586i
$641$	−16.4683			−0.650461			−0.325230	−	0.945635i	$-0.605442\pi$
$641$	−16.4683			−0.650461			−0.325230	+	0.945635i	$0.605442\pi$
$642$	0.504621	+	7.80405i	0.0199158	+	0.308001i
$643$	−5.74249	+	5.74249i	−0.226462	+	0.226462i	−0.811213	−	0.584751i	$-0.801192\pi$
$643$	−5.74249	+	5.74249i	−0.226462	+	0.226462i	0.584751	+	0.811213i	$0.301192\pi$
$644$	−43.1964	+	5.60975i	−1.70218	+	0.221055i
$645$	13.0303	−	9.52982i	0.513067	−	0.375236i
$646$	6.31032	+	5.54382i	0.248276	+	0.218119i
$647$	4.61663	+	4.61663i	0.181498	+	0.181498i	0.792009	−	0.610510i	$-0.209036\pi$
$647$	4.61663	+	4.61663i	0.181498	+	0.181498i	−0.610510	+	0.792009i	$0.709036\pi$
$648$	0.544488	+	2.77552i	0.0213895	+	0.109033i
$649$			3.59037i			0.140934i
$650$	16.1225	+	26.7686i	0.632375	+	1.04995i
$651$		−	15.8668i		−	0.621867i
$652$	−7.39574	+	9.60334i	−0.289640	+	0.376096i
$653$	14.4655	+	14.4655i	0.566078	+	0.566078i	0.931027	−	0.364949i	$-0.118914\pi$
$653$	14.4655	+	14.4655i	0.566078	+	0.566078i	−0.364949	+	0.931027i	$0.618914\pi$
$654$	14.7285	−	16.7649i	0.575930	−	0.655560i
$655$	−8.25750	+	6.03920i	−0.322647	+	0.235971i
$656$	−16.4352	+	4.34198i	−0.641687	+	0.169526i
$657$	3.96972	−	3.96972i	0.154874	−	0.154874i
$658$	11.0645	−	0.715449i	0.431340	−	0.0278911i
$659$	−35.5474			−1.38473			−0.692364	−	0.721548i	$-0.743431\pi$
$659$	−35.5474			−1.38473			−0.692364	+	0.721548i	$0.743431\pi$
$660$	0.0807607	−	3.25702i	0.00314361	−	0.126779i
$661$	15.1883			0.590756			0.295378	−	0.955380i	$-0.404554\pi$
$661$	15.1883			0.590756			0.295378	+	0.955380i	$0.404554\pi$
$662$	15.5654	−	1.00648i	0.604967	−	0.0391181i
$663$	−4.97116	+	4.97116i	−0.193064	+	0.193064i
$664$	−11.8091	−	7.93567i	−0.458282	−	0.307964i
$665$	3.37935	−	21.7796i	0.131046	−	0.844576i
$666$	4.12489	−	4.69521i	0.159836	−	0.181936i
$667$	−15.4005	−	15.4005i	−0.596310	−	0.596310i
$668$	9.80722	+	7.55275i	0.379453	+	0.292225i
$669$			4.70058i			0.181735i
$670$	22.7390	+	2.03743i	0.878482	+	0.0787129i
$671$			1.68311i			0.0649756i
$672$	−4.73830	−	14.1626i	−0.182784	−	0.546335i
$673$	−20.3700	−	20.3700i	−0.785204	−	0.785204i	0.195500	−	0.980704i	$-0.437367\pi$
$673$	−20.3700	−	20.3700i	−0.785204	−	0.785204i	−0.980704	+	0.195500i	$0.937367\pi$
$674$	20.4653	+	17.9794i	0.788294	+	0.692541i
$675$	4.44066	−	2.29793i	0.170921	−	0.0884476i
$676$	−1.68188	−	12.9509i	−0.0646876	−	0.498111i
$677$	9.06433	−	9.06433i	0.348371	−	0.348371i	−0.511132	−	0.859502i	$-0.670774\pi$
$677$	9.06433	−	9.06433i	0.348371	−	0.348371i	0.859502	+	0.511132i	$0.170774\pi$
$678$	−0.238083	−	3.68199i	−0.00914351	−	0.141406i
$679$	46.7808			1.79528
$680$	−0.400140	−	10.0533i	−0.0153447	−	0.385527i
$681$	−12.4995			−0.478983
$682$	−0.399552	−	6.17914i	−0.0152997	−	0.236612i
$683$	24.8545	−	24.8545i	0.951030	−	0.951030i	−0.0478253	−	0.998856i	$-0.515229\pi$
$683$	24.8545	−	24.8545i	0.951030	−	0.951030i	0.998856	+	0.0478253i	$0.0152291\pi$
$684$	0.961649	+	7.40493i	0.0367696	+	0.283135i
$685$	−12.7952	−	1.98532i	−0.488879	−	0.0758552i
$686$	−19.7190	−	17.3238i	−0.752876	−	0.661425i
$687$	5.01397	+	5.01397i	0.191295	+	0.191295i
$688$	14.5268	−	24.9582i	0.553827	−	0.951522i
$689$		−	3.03028i		−	0.115444i
$690$	−16.7272	−	20.0197i	−0.636792	−	0.762138i
$691$			40.8979i			1.55583i	0.628371	+	0.777914i	$0.283722\pi$
$691$			40.8979i			1.55583i	−0.628371	+	0.777914i	$0.716278\pi$
$692$	−36.7620	−	28.3112i	−1.39748	−	1.07623i
$693$	−1.35998	−	1.35998i	−0.0516612	−	0.0516612i
$694$	23.4469	−	26.6888i	0.890033	−	1.01309i
$695$	17.9393	+	24.5287i	0.680475	+	0.930425i
$696$	4.16485	−	6.19773i	0.157868	−	0.234924i
$697$	−4.78051	+	4.78051i	−0.181075	+	0.181075i
$698$	−20.7298	+	1.34042i	−0.784633	+	0.0507355i
$699$	−21.7430			−0.822398
$700$	−21.6891	+	15.0518i	−0.819771	+	0.568903i
$701$	−43.1396			−1.62936			−0.814679	−	0.579912i	$-0.803087\pi$
$701$	−43.1396			−1.62936			−0.814679	+	0.579912i	$0.803087\pi$
$702$	−6.23675	+	0.403277i	−0.235391	+	0.0152207i
$703$	11.6669	−	11.6669i	0.440027	−	0.440027i
$704$	−2.20192	−	5.39616i	−0.0829880	−	0.203375i
$705$	3.92007	+	5.35998i	0.147638	+	0.201868i
$706$	24.2947	−	27.6538i	0.914344	−	1.04076i
$707$	10.5852	+	10.5852i	0.398097	+	0.398097i
$708$	−6.01409	+	7.80928i	−0.226023	+	0.293491i
$709$			18.4702i			0.693662i	0.937928	+	0.346831i	$0.112742\pi$
$709$			18.4702i			0.693662i	−0.937928	+	0.346831i	$0.887258\pi$
$710$	26.6100	+	31.8479i	0.998657	+	1.19523i
$711$			7.11388i			0.266792i
$712$	2.85956	−	0.560973i	0.107166	−	0.0210233i
$713$	−35.0596	−	35.0596i	−1.31299	−	1.31299i
$714$	−4.46207	−	3.92007i	−0.166989	−	0.146705i
$715$	7.11388	+	1.10380i	0.266044	+	0.0412798i
$716$	48.4246	−	6.28871i	1.80971	−	0.235020i
$717$	0.499542	−	0.499542i	0.0186557	−	0.0186557i
$718$	−0.878837	−	13.5913i	−0.0327979	−	0.507225i
$719$	−33.3725			−1.24458			−0.622292	−	0.782785i	$-0.713799\pi$
$719$	−33.3725			−1.24458			−0.622292	+	0.782785i	$0.713799\pi$
$720$	5.63137	−	6.94894i	0.209869	−	0.258972i
$721$	0.211016			0.00785865
$722$	−0.461799	−	7.14179i	−0.0171864	−	0.265790i
$723$	−17.6770	+	17.6770i	−0.657415	+	0.657415i
$724$	−22.3722	+	2.90539i	−0.831457	+	0.107978i
$725$	−12.5795	−	4.00000i	−0.467190	−	0.148556i
$726$	11.1230	+	9.77190i	0.412813	+	0.362669i
$727$	23.2774	+	23.2774i	0.863309	+	0.863309i	0.991721	−	0.128412i	$-0.0409879\pi$
$727$	23.2774	+	23.2774i	0.863309	+	0.863309i	−0.128412	+	0.991721i	$0.540988\pi$
$728$	32.3819	−	6.35251i	1.20015	−	0.235440i
$729$			1.00000i			0.0370370i
$730$	−17.6823	−	1.58435i	−0.654452	−	0.0586396i
$731$		−	11.4850i		−	0.424787i
$732$	−2.81931	+	3.66086i	−0.104205	+	0.135309i
$733$	−16.2157	−	16.2157i	−0.598941	−	0.598941i	0.341090	−	0.940031i	$-0.389204\pi$
$733$	−16.2157	−	16.2157i	−0.598941	−	0.598941i	−0.940031	+	0.341090i	$0.889204\pi$
$734$	−20.4034	+	23.2245i	−0.753105	+	0.857231i
$735$	0.0103801	−	0.0668989i	0.000382877	−	0.00246760i
$736$	−41.7640	−	20.8242i	−1.53944	−	0.767591i
$737$	3.71904	−	3.71904i	0.136992	−	0.136992i
$738$	−5.99756	+	0.387811i	−0.220773	+	0.0142755i
$739$	−14.3408			−0.527535			−0.263768	−	0.964586i	$-0.584965\pi$
$739$	−14.3408			−0.527535			−0.263768	+	0.964586i	$0.584965\pi$
$740$	−19.7574	−	0.489904i	−0.726298	−	0.0180092i
$741$	−16.4995			−0.606126
$742$	2.55476	−	0.165194i	0.0937881	−	0.00606448i
$743$	11.6034	−	11.6034i	0.425686	−	0.425686i	−0.461470	−	0.887156i	$-0.652678\pi$
$743$	11.6034	−	11.6034i	0.425686	−	0.425686i	0.887156	+	0.461470i	$0.152678\pi$
$744$	9.48139	−	14.1093i	0.347605	−	0.517272i
$745$	10.2342	−	7.48486i	0.374951	−	0.274224i
$746$	−4.45459	+	5.07049i	−0.163094	+	0.185644i
$747$	−3.55694	−	3.55694i	−0.130142	−	0.130142i
$748$	−1.83642	−	1.41427i	−0.0671462	−	0.0517107i
$749$		−	14.5988i		−	0.533430i
$750$	−14.5802	−	6.11689i	−0.532395	−	0.223357i
$751$			35.1721i			1.28345i	0.766936	+	0.641724i	$0.221780\pi$
$751$			35.1721i			1.28345i	−0.766936	+	0.641724i	$0.778220\pi$
$752$	10.2665	+	5.97555i	0.374381	+	0.217906i
$753$	20.2342	+	20.2342i	0.737374	+	0.737374i
$754$	12.3955	+	10.8898i	0.451416	+	0.396583i
$755$	34.7386	−	25.4064i	1.26427	−	0.924633i
$756$	−0.679988	−	5.23608i	−0.0247309	−	0.190434i
$757$	−15.7455	+	15.7455i	−0.572281	+	0.572281i	−0.932765	−	0.360484i	$-0.882611\pi$
$757$	−15.7455	+	15.7455i	−0.572281	+	0.572281i	0.360484	+	0.932765i	$0.382611\pi$
$758$	−0.538132	−	8.32230i	−0.0195459	−	0.302280i
$759$	−6.01008			−0.218152
$760$	16.0197	−	17.3478i	0.581096	−	0.629271i
$761$	−24.4002			−0.884508			−0.442254	−	0.896890i	$-0.645821\pi$
$761$	−24.4002			−0.884508			−0.442254	+	0.896890i	$0.645821\pi$
$762$	1.45278	+	22.4675i	0.0526286	+	0.813910i
$763$	−29.4570	+	29.4570i	−1.06641	+	1.06641i
$764$	−0.841553	−	6.48016i	−0.0304463	−	0.234444i
$765$	0.545414	−	3.51514i	0.0197195	−	0.127090i
$766$	−0.965943	−	0.848611i	−0.0349009	−	0.0306616i
$767$	−15.4005	−	15.4005i	−0.556080	−	0.556080i
$768$	4.24959	−	15.4253i	0.153344	−	0.556614i
$769$			15.9688i			0.575850i	0.957653	+	0.287925i	$0.0929654\pi$
$769$			15.9688i			0.575850i	−0.957653	+	0.287925i	$0.907035\pi$
$770$	−0.542779	+	6.05773i	−0.0195604	+	0.218305i
$771$			5.52306i			0.198908i
$772$	−2.10522	−	1.62128i	−0.0757686	−	0.0583510i
$773$	−2.84392	−	2.84392i	−0.102289	−	0.102289i	0.654110	−	0.756399i	$-0.273043\pi$
$773$	−2.84392	−	2.84392i	−0.102289	−	0.102289i	−0.756399	+	0.654110i	$0.773043\pi$
$774$	6.73860	−	7.67030i	0.242214	−	0.275703i
$775$	−28.6375	−	9.10611i	−1.02869	−	0.327101i
$776$	41.5991	+	27.9545i	1.49332	+	1.00351i
$777$	−8.24977	+	8.24977i	−0.295959	+	0.295959i
$778$	26.5731	−	1.71825i	0.952691	−	0.0616024i
$779$	−15.8668			−0.568486
$780$	13.6242	+	14.3170i	0.487825	+	0.512632i
$781$	9.56101			0.342120
$782$	−18.5214	+	1.19762i	−0.662324	+	0.0428269i
$783$	1.86678	−	1.86678i	0.0667132	−	0.0667132i
$784$	−0.0309330	−	0.117087i	−0.00110475	−	0.00418169i
$785$	−6.54541	−	1.01560i	−0.233616	−	0.0362482i
$786$	−4.27036	+	4.86079i	−0.152319	+	0.173379i
$787$	7.49452	+	7.49452i	0.267151	+	0.267151i	0.827951	−	0.560800i	$-0.189506\pi$
$787$	7.49452	+	7.49452i	0.267151	+	0.267151i	−0.560800	+	0.827951i	$0.689506\pi$
$788$	2.51029	−	3.25960i	0.0894254	−	0.116119i
$789$		−	0.249771i		−	0.00889208i
$790$	17.2633	−	14.4240i	0.614199	−	0.513185i
$791$			6.88781i			0.244902i
$792$	−0.396668	−	2.02201i	−0.0140950	−	0.0718490i
$793$	−7.21949	−	7.21949i	−0.256372	−	0.256372i
$794$	−36.5779	−	32.1349i	−1.29810	−	1.14042i
$795$	0.905130	+	1.23760i	0.0321016	+	0.0438931i
$796$	−10.2947	+	1.33693i	−0.364887	+	0.0473864i
$797$	26.1552	−	26.1552i	0.926463	−	0.926463i	−0.0710121	−	0.997475i	$-0.522623\pi$
$797$	26.1552	−	26.1552i	0.926463	−	0.926463i	0.997475	+	0.0710121i	$0.0226229\pi$
$798$	−0.899467	−	13.9104i	−0.0318408	−	0.492423i
$799$	4.72432			0.167134
$800$	−28.2811	+	0.423963i	−0.999888	+	0.0149894i
$801$	1.03028			0.0364030
$802$	1.45455	+	22.4948i	0.0513619	+	0.794319i
$803$	−2.89200	+	2.89200i	−0.102057	+	0.102057i
$804$	14.3188	−	1.85952i	0.504983	−	0.0655802i
$805$	28.7493	+	39.3094i	1.01328	+	1.38547i
$806$	28.2186	+	24.7909i	0.993957	+	0.873222i
$807$	3.81084	+	3.81084i	0.134148	+	0.134148i
$808$	3.08741	+	15.7381i	0.108615	+	0.553663i
$809$			23.7115i			0.833651i	0.908987	+	0.416826i	$0.136857\pi$
$809$			23.7115i			0.833651i	−0.908987	+	0.416826i	$0.863143\pi$
$810$	2.42670	−	2.02759i	0.0852656	−	0.0712423i
$811$		−	26.0077i		−	0.913255i	−0.889658	−	0.456628i	$-0.849057\pi$
$811$		−	26.0077i		−	0.913255i	0.889658	−	0.456628i	$-0.150943\pi$
$812$	−8.50521	+	11.0440i	−0.298474	+	0.387568i
$813$	−10.8898	−	10.8898i	−0.381922	−	0.381922i
$814$	−3.00504	+	3.42053i	−0.105327	+	0.119889i
$815$	13.3916	+	2.07786i	0.469086	+	0.0727841i
$816$	−1.62534	−	6.15224i	−0.0568984	−	0.215371i
$817$	19.0596	−	19.0596i	0.666812	−	0.666812i
$818$	33.0359	−	2.13615i	1.15507	−	0.0746888i
$819$	11.6669			0.407676
$820$	13.1017	+	13.7680i	0.457531	+	0.480798i
$821$	33.0790			1.15447			0.577233	−	0.816580i	$-0.304133\pi$
$821$	33.0790			1.15447			0.577233	+	0.816580i	$0.304133\pi$
$822$	−8.17215	+	0.528424i	−0.285037	+	0.0184309i
$823$	17.9737	−	17.9737i	0.626525	−	0.626525i	−0.320667	−	0.947192i	$-0.603907\pi$
$823$	17.9737	−	17.9737i	0.626525	−	0.626525i	0.947192	+	0.320667i	$0.103907\pi$
$824$	0.187643	+	0.126095i	0.00653685	+	0.00439274i
$825$	−3.23509	+	1.67408i	−0.112631	+	0.0582840i
$826$	12.1443	−	13.8234i	0.422553	−	0.480977i
$827$	−18.8665	−	18.8665i	−0.656051	−	0.656051i	0.298392	−	0.954443i	$-0.403550\pi$
$827$	−18.8665	−	18.8665i	−0.656051	−	0.656051i	−0.954443	+	0.298392i	$0.903550\pi$
$828$	−13.0723	−	10.0673i	−0.454294	−	0.349862i
$829$		−	3.28005i		−	0.113921i	−0.998376	−	0.0569604i	$-0.981859\pi$
$829$		−	3.28005i		−	0.113921i	0.998376	−	0.0569604i	$-0.0181409\pi$
$830$	−1.41961	+	15.8437i	−0.0492753	+	0.549941i
$831$		−	12.1540i		−	0.421616i
$832$	32.5911	+	13.7013i	1.12989	+	0.475008i
$833$	−0.0340571	−	0.0340571i	−0.00118001	−	0.00118001i
$834$	14.4388	+	12.6850i	0.499976	+	0.439245i
$835$	2.12197	−	13.6759i	0.0734337	−	0.473273i
$836$	−0.700576	−	5.39461i	−0.0242299	−	0.186576i
$837$	4.24977	−	4.24977i	0.146894	−	0.146894i
$838$	2.55843	+	39.5665i	0.0883794	+	1.36680i
$839$	54.8854			1.89486			0.947428	−	0.319969i	$-0.103673\pi$
$839$	54.8854			1.89486			0.947428	+	0.319969i	$0.103673\pi$
$840$	−11.3277	+	12.2668i	−0.390841	+	0.423243i
$841$	22.0303			0.759665
$842$	1.58862	+	24.5683i	0.0547476	+	0.846681i
$843$	−14.6720	+	14.6720i	−0.505330	+	0.505330i
$844$	−3.03416	−	23.3638i	−0.104440	−	0.804214i
$845$	−11.7855	+	8.61944i	−0.405433	+	0.296518i
$846$	3.15516	+	2.77191i	0.108477	+	0.0953002i
$847$	−19.5438	−	19.5438i	−0.671533	−	0.671533i
$848$	2.37050	+	1.37973i	0.0814032	+	0.0473802i
$849$			26.2791i			0.901897i
$850$	−9.63606	+	5.80371i	−0.330514	+	0.199065i
$851$			36.4578i			1.24976i
$852$	20.7958	+	16.0153i	0.712452	+	0.548675i
$853$	−17.9348	−	17.9348i	−0.614074	−	0.614074i	0.329931	−	0.944005i	$-0.392975\pi$
$853$	−17.9348	−	17.9348i	−0.614074	−	0.614074i	−0.944005	+	0.329931i	$0.892975\pi$
$854$	5.69303	−	6.48016i	0.194811	−	0.221747i
$855$	6.73860	−	4.92834i	0.230455	−	0.168546i
$856$	8.72373	−	12.9818i	0.298171	−	0.443709i
$857$	−9.00378	+	9.00378i	−0.307563	+	0.307563i	−0.843964	−	0.536400i	$-0.819784\pi$
$857$	−9.00378	+	9.00378i	−0.307563	+	0.307563i	0.536400	+	0.843964i	$0.319784\pi$
$858$	4.54356	−	0.293794i	0.155115	−	0.0100299i
$859$	−24.6779			−0.841998			−0.420999	−	0.907061i	$-0.638320\pi$
$859$	−24.6779			−0.841998			−0.420999	+	0.907061i	$0.638320\pi$
$860$	−32.2766	−	0.800329i	−1.10062	−	0.0272910i
$861$	11.2195			0.382359
$862$	−43.9669	+	2.84297i	−1.49752	+	0.0968318i
$863$	40.4811	−	40.4811i	1.37799	−	1.37799i	0.529982	−	0.848009i	$-0.322198\pi$
$863$	40.4811	−	40.4811i	1.37799	−	1.37799i	0.848009	−	0.529982i	$-0.177802\pi$
$864$	2.52422	−	5.06244i	0.0858756	−	0.172228i
$865$	−7.95413	+	51.2635i	−0.270448	+	1.74301i
$866$	16.0499	−	18.2691i	0.545399	−	0.620808i
$867$	10.2313	+	10.2313i	0.347474	+	0.347474i
$868$	−19.3623	+	25.1419i	−0.657201	+	0.853373i
$869$		−	5.18257i		−	0.175807i
$870$	−8.31518	−	0.745049i	−0.281911	−	0.0252595i
$871$			31.9048i			1.08105i
$872$	−43.7966	+	8.59179i	−1.48314	+	0.290955i
$873$	12.5298	+	12.5298i	0.424070	+	0.424070i
$874$	−32.7243	−	28.7493i	−1.10692	−	0.972460i
$875$	26.4246	+	13.1514i	0.893313	+	0.444598i
$876$	−11.1346	+	1.44600i	−0.376202	+	0.0488559i
$877$	−1.59507	+	1.59507i	−0.0538616	+	0.0538616i	−0.733525	−	0.679663i	$-0.762126\pi$
$877$	−1.59507	+	1.59507i	−0.0538616	+	0.0538616i	0.679663	+	0.733525i	$0.262126\pi$
$878$	−1.30464	−	20.1764i	−0.0440294	−	0.680922i
$879$	8.81775			0.297415
$880$	−4.10254	+	5.06241i	−0.138296	+	0.170654i
$881$	33.2876			1.12149			0.560744	−	0.827989i	$-0.310515\pi$
$881$	33.2876			1.12149			0.560744	+	0.827989i	$0.310515\pi$
$882$	−0.00276283	−	0.0427276i	−9.30294e−5	−	0.00143871i
$883$	−29.4296	+	29.4296i	−0.990385	+	0.990385i	−0.999954	−	0.00956956i	$-0.996954\pi$
$883$	−29.4296	+	29.4296i	−0.990385	+	0.990385i	0.00956956	+	0.999954i	$0.496954\pi$
$884$	13.9435	−	1.81078i	0.468969	−	0.0609032i
$885$	10.8898	+	1.68968i	0.366056	+	0.0567979i
$886$	−10.5601	−	9.27737i	−0.354773	−	0.311679i
$887$	−30.9776	−	30.9776i	−1.04013	−	1.04013i	−0.999161	−	0.0409656i	$-0.986957\pi$
$887$	−30.9776	−	30.9776i	−1.04013	−	1.04013i	−0.0409656	−	0.999161i	$-0.513043\pi$
$888$	−12.2657	+	2.40623i	−0.411612	+	0.0807478i
$889$		−	42.0294i		−	1.40962i
$890$	−2.08898	−	2.50017i	−0.0700227	−	0.0838059i
$891$		−	0.728515i		−	0.0244062i
$892$	5.73615	−	7.44837i	0.192061	−	0.249390i
$893$	7.84014	+	7.84014i	0.262360	+	0.262360i
$894$	5.29260	−	6.02437i	0.177011	−	0.201485i
$895$	−32.2289	−	44.0671i	−1.07729	−	1.47300i
$896$	−9.77460	+	28.2238i	−0.326546	+	0.942890i
$897$	25.7796	−	25.7796i	0.860755	−	0.860755i
$898$	−54.2784	+	3.50972i	−1.81129	+	0.117121i
$899$	−15.8668			−0.529186
$900$	−9.84071	−	1.77775i	−0.328024	−	0.0592583i
$901$	1.09083			0.0363408
$902$	4.36931	−	0.282526i	0.145482	−	0.00940709i
$903$	−13.4772	+	13.4772i	−0.448493	+	0.448493i
$904$	−4.11590	+	6.12489i	−0.136893	+	0.203711i
$905$	14.8898	+	20.3591i	0.494954	+	0.676758i
$906$	17.9650	−	20.4489i	0.596848	−	0.679370i
$907$	−28.6790	−	28.6790i	−0.952271	−	0.952271i	0.0466405	−	0.998912i	$-0.485148\pi$
$907$	−28.6790	−	28.6790i	−0.952271	−	0.952271i	−0.998912	+	0.0466405i	$0.985148\pi$
$908$	19.8063	+	15.2533i	0.657297	+	0.506198i
$909$			5.67030i			0.188072i
$910$	−23.6558	−	28.3122i	−0.784181	−	0.938539i
$911$		−	31.8607i		−	1.05559i	−0.849371	−	0.527796i	$-0.823019\pi$
$911$		−	31.8607i		−	1.05559i	0.849371	−	0.527796i	$-0.176981\pi$
$912$	7.51250	−	12.9071i	0.248764	−	0.427397i
$913$	2.59129	+	2.59129i	0.0857591	+	0.0857591i
$914$	7.42162	+	6.52013i	0.245485	+	0.215667i
$915$	5.10495	+	0.792092i	0.168765	+	0.0261858i
$916$	−1.82638	−	14.0636i	−0.0603452	−	0.464673i
$917$	8.54072	−	8.54072i	0.282039	−	0.282039i
$918$	−0.145170	−	2.24508i	−0.00479134	−	0.0740988i
$919$	55.4206			1.82816			0.914079	−	0.405536i	$-0.132915\pi$
$919$	55.4206			1.82816			0.914079	+	0.405536i	$0.132915\pi$
$920$	2.07506	+	52.1349i	0.0684127	+	1.71884i
$921$	−1.28005			−0.0421790
$922$	2.47929	+	38.3426i	0.0816510	+	1.26275i
$923$	−41.0109	+	41.0109i	−1.34989	+	1.34989i
$924$	0.495382	+	3.81456i	0.0162969	+	0.125490i
$925$	10.1552	+	19.6244i	0.333900	+	0.645247i
$926$	−7.45671	−	6.55096i	−0.245043	−	0.215278i
$927$	0.0565188	+	0.0565188i	0.00185632	+	0.00185632i
$928$	−14.1626	+	4.73830i	−0.464911	+	0.155542i
$929$		−	46.9603i		−	1.54072i	−0.637610	−	0.770359i	$-0.720077\pi$
$929$		−	46.9603i		−	1.54072i	0.637610	−	0.770359i	$-0.279923\pi$
$930$	−18.9297	−	1.69612i	−0.620730	−	0.0556181i
$931$		−	0.113038i		−	0.00370466i
$932$	34.4533	+	26.5332i	1.12855	+	0.869124i
$933$	−17.2800	−	17.2800i	−0.565723	−	0.565723i
$934$	−28.0291	+	31.9045i	−0.917140	+	1.04395i
$935$	−0.397342	+	2.56083i	−0.0129945	+	0.0837481i
$936$	10.3747	+	6.97173i	0.339106	+	0.227878i
$937$	10.4693	−	10.4693i	0.342016	−	0.342016i	−0.515109	−	0.857125i	$-0.672248\pi$
$937$	10.4693	−	10.4693i	0.342016	−	0.342016i	0.857125	+	0.515109i	$0.172248\pi$
$938$	−26.8982	+	1.73928i	−0.878258	+	0.0567895i
$939$	26.2908			0.857966
$940$	0.329214	−	13.2769i	0.0107378	−	0.433046i
$941$	−41.1084			−1.34009			−0.670047	−	0.742318i	$-0.733726\pi$
$941$	−41.1084			−1.34009			−0.670047	+	0.742318i	$0.733726\pi$
$942$	−4.18049	+	0.270317i	−0.136208	+	0.00880739i
$943$	24.7909	−	24.7909i	0.807303	−	0.807303i
$944$	19.0594	−	5.03527i	0.620332	−	0.163884i
$945$	−4.76491	+	3.48486i	−0.155002	+	0.113363i
$946$	−4.90917	+	5.58793i	−0.159611	+	0.181679i
$947$	25.8091	+	25.8091i	0.838682	+	0.838682i	0.988685	−	0.150003i	$-0.0479284\pi$
$947$	25.8091	+	25.8091i	0.838682	+	0.838682i	−0.150003	+	0.988685i	$0.547928\pi$
$948$	8.68113	−	11.2724i	0.281950	−	0.366111i
$949$		−	24.8099i		−	0.805362i
$950$	−25.6227	−	6.35990i	−0.831311	−	0.206343i
$951$		−	27.3143i		−	0.885726i
$952$	2.28675	+	11.6567i	0.0741141	+	0.377796i
$953$	−7.78429	−	7.78429i	−0.252158	−	0.252158i	0.569697	−	0.821855i	$-0.307061\pi$
$953$	−7.78429	−	7.78429i	−0.252158	−	0.252158i	−0.821855	+	0.569697i	$0.807061\pi$
$954$	0.728515	+	0.640023i	0.0235866	+	0.0207215i
$955$	−5.89705	+	4.31286i	−0.190824	+	0.139561i
$956$	−1.40115	+	0.181962i	−0.0453165	+	0.00588507i
$957$	−1.35998	+	1.35998i	−0.0439618	+	0.0439618i
$958$	−1.71384	−	26.5047i	−0.0553715	−	0.856329i
$959$	15.2875			0.493658
$960$	−17.4031	+	4.13904i	−0.561683	+	0.133587i
$961$	−5.12110			−0.165197
$962$	−1.78219	−	27.5618i	−0.0574600	−	0.888627i
$963$	3.91017	−	3.91017i	0.126004	−	0.126004i
$964$	49.5818	−	6.43899i	1.59692	−	0.207386i
$965$	−0.455503	+	2.93567i	−0.0146631	+	0.0945025i
$966$	23.1396	+	20.3288i	0.744503	+	0.654070i
$967$	−11.7235	−	11.7235i	−0.377001	−	0.377001i	0.493018	−	0.870019i	$-0.335894\pi$
$967$	−11.7235	−	11.7235i	−0.377001	−	0.377001i	−0.870019	+	0.493018i	$0.835894\pi$
$968$	−5.70039	−	29.0577i	−0.183217	−	0.933950i
$969$		−	5.93945i		−	0.190803i
$970$	5.00077	−	55.8115i	0.160565	−	1.79200i
$971$		−	12.9748i		−	0.416380i	−0.978088	−	0.208190i	$-0.933243\pi$
$971$		−	12.9748i		−	0.416380i	0.978088	−	0.208190i	$-0.0667572\pi$
$972$	1.22031	−	1.58457i	0.0391414	−	0.0508250i
$973$	−25.3700	−	25.3700i	−0.813324	−	0.813324i
$974$	3.92120	−	4.46336i	0.125643	−	0.143015i
$975$	6.69578	−	21.0573i	0.214437	−	0.674375i
$976$	8.93475	−	2.36045i	0.285994	−	0.0755561i
$977$	−13.9054	+	13.9054i	−0.444873	+	0.444873i	−0.893646	−	0.448773i	$-0.851861\pi$
$977$	−13.9054	+	13.9054i	−0.444873	+	0.444873i	0.448773	+	0.893646i	$0.351861\pi$
$978$	8.55305	−	0.553053i	0.273496	−	0.0176847i
$979$	−0.750572			−0.0239884
$980$	−0.0980853	+	0.0933387i	−0.00313322	+	0.00298160i
$981$	−15.7796			−0.503803
$982$	41.7001	−	2.69639i	1.33070	−	0.0860452i
$983$	−13.9381	+	13.9381i	−0.444557	+	0.444557i	−0.893540	−	0.448983i	$-0.851786\pi$
$983$	−13.9381	+	13.9381i	−0.444557	+	0.444557i	0.448983	+	0.893540i	$0.351786\pi$
$984$	9.97677	+	6.70436i	0.318048	+	0.213727i
$985$	−4.54541	−	0.705273i	−0.144829	−	0.0224719i
$986$	−3.92007	+	4.46207i	−0.124840	+	0.142101i
$987$	−5.54382	−	5.54382i	−0.176462	−	0.176462i
$988$	26.1446	+	20.1345i	0.831771	+	0.640565i
$989$			59.5592i			1.89387i
$990$	−1.76789	+	1.47713i	−0.0561872	+	0.0469463i
$991$			52.9621i			1.68240i	0.540726	+	0.841199i	$0.318150\pi$
$991$			52.9621i			1.68240i	−0.540726	+	0.841199i	$0.681850\pi$
$992$	−32.2416	+	10.7869i	−1.02367	+	0.342484i
$993$	−7.79897	−	7.79897i	−0.247493	−	0.247493i
$994$	−36.8111	−	32.3397i	−1.16758	−	1.02575i
$995$	6.85164	+	9.36835i	0.217211	+	0.296997i
$996$	1.29564	+	9.97677i	0.0410540	+	0.316126i
$997$	1.53452	−	1.53452i	0.0485986	−	0.0485986i	−0.682390	−	0.730988i	$-0.739059\pi$
$997$	1.53452	−	1.53452i	0.0485986	−	0.0485986i	0.730988	+	0.682390i	$0.239059\pi$
$998$	−1.37313	−	21.2357i	−0.0434657	−	0.672204i
$999$	−4.41926			−0.139819

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.2.j.a.43.3	yes	12
3.2	odd	2		180.2.k.e.163.4		12
4.3	odd	2	inner	60.2.j.a.43.1	yes	12
5.2	odd	4	inner	60.2.j.a.7.1	✓	12
5.3	odd	4		300.2.j.d.7.6		12
5.4	even	2		300.2.j.d.43.4		12
8.3	odd	2		960.2.w.g.703.4		12
8.5	even	2		960.2.w.g.703.1		12
12.11	even	2		180.2.k.e.163.6		12
15.2	even	4		180.2.k.e.127.6		12
15.8	even	4		900.2.k.n.307.1		12
15.14	odd	2		900.2.k.n.343.3		12
20.3	even	4		300.2.j.d.7.4		12
20.7	even	4	inner	60.2.j.a.7.3	yes	12
20.19	odd	2		300.2.j.d.43.6		12
40.27	even	4		960.2.w.g.127.1		12
40.37	odd	4		960.2.w.g.127.4		12
60.23	odd	4		900.2.k.n.307.3		12
60.47	odd	4		180.2.k.e.127.4		12
60.59	even	2		900.2.k.n.343.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.j.a.7.1	✓	12	5.2	odd	4	inner
60.2.j.a.7.3	yes	12	20.7	even	4	inner
60.2.j.a.43.1	yes	12	4.3	odd	2	inner
60.2.j.a.43.3	yes	12	1.1	even	1	trivial
180.2.k.e.127.4		12	60.47	odd	4
180.2.k.e.127.6		12	15.2	even	4
180.2.k.e.163.4		12	3.2	odd	2
180.2.k.e.163.6		12	12.11	even	2
300.2.j.d.7.4		12	20.3	even	4
300.2.j.d.7.6		12	5.3	odd	4
300.2.j.d.43.4		12	5.4	even	2
300.2.j.d.43.6		12	20.19	odd	2
900.2.k.n.307.1		12	15.8	even	4
900.2.k.n.307.3		12	60.23	odd	4
900.2.k.n.343.1		12	60.59	even	2
900.2.k.n.343.3		12	15.14	odd	2
960.2.w.g.127.1		12	40.27	even	4
960.2.w.g.127.4		12	40.37	odd	4
960.2.w.g.703.1		12	8.5	even	2
960.2.w.g.703.4		12	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	60.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0912546 + 1.41127i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.98335 + 0.257569i) q^{4} +(1.32001 + 1.80487i) q^{5} +(1.06244 + 0.933389i) q^{6} +(-1.86678 - 1.86678i) q^{7} +(-0.544488 - 2.77552i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.0912546 + 1.41127i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.98335 + 0.257569i) q^{4} +(1.32001 + 1.80487i) q^{5} +(1.06244 + 0.933389i) q^{6} +(-1.86678 - 1.86678i) q^{7} +(-0.544488 - 2.77552i) q^{8} -1.00000i q^{9} +(-2.42670 + 2.02759i) q^{10} +0.728515i q^{11} +(-1.22031 + 1.58457i) q^{12} +(-3.12489 - 3.12489i) q^{13} +(2.46417 - 2.80487i) q^{14} +(2.20963 + 0.342849i) q^{15} +(3.86732 - 1.02170i) q^{16} +(1.12489 - 1.12489i) q^{17} +(1.41127 - 0.0912546i) q^{18} +3.73356 q^{19} +(-3.08292 - 3.23969i) q^{20} -2.64002 q^{21} +(-1.02813 + 0.0664803i) q^{22} +(-5.83347 + 5.83347i) q^{23} +(-2.34760 - 1.57758i) q^{24} +(-1.51514 + 4.76491i) q^{25} +(4.12489 - 4.69521i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(4.18329 + 3.22164i) q^{28} +2.64002i q^{29} +(-0.282213 + 3.14966i) q^{30} +6.01008i q^{31} +(1.79480 + 5.36458i) q^{32} +(0.515138 + 0.515138i) q^{33} +(1.69016 + 1.48486i) q^{34} +(0.905130 - 5.83347i) q^{35} +(0.257569 + 1.98335i) q^{36} +(3.12489 - 3.12489i) q^{37} +(0.340704 + 5.26904i) q^{38} -4.41926 q^{39} +(4.29074 - 4.64646i) q^{40} -4.24977 q^{41} +(-0.240914 - 3.72578i) q^{42} +(5.10495 - 5.10495i) q^{43} +(-0.187643 - 1.44490i) q^{44} +(1.80487 - 1.32001i) q^{45} +(-8.76491 - 7.70025i) q^{46} +(2.09991 + 2.09991i) q^{47} +(2.01216 - 3.45705i) q^{48} -0.0302761i q^{49} +(-6.86282 - 1.70344i) q^{50} -1.59083i q^{51} +(7.00260 + 5.39285i) q^{52} +(0.484862 + 0.484862i) q^{53} +(0.933389 - 1.06244i) q^{54} +(-1.31488 + 0.961649i) q^{55} +(-4.16485 + 6.19773i) q^{56} +(2.64002 - 2.64002i) q^{57} +(-3.72578 + 0.240914i) q^{58} +4.92834 q^{59} +(-4.47076 - 0.110857i) q^{60} +2.31032 q^{61} +(-8.48183 + 0.548448i) q^{62} +(-1.86678 + 1.86678i) q^{63} +(-7.40707 + 3.02248i) q^{64} +(1.51514 - 9.76491i) q^{65} +(-0.679988 + 0.774006i) q^{66} +(-5.10495 - 5.10495i) q^{67} +(-1.94130 + 2.52077i) q^{68} +8.24977i q^{69} +(8.31518 + 0.745049i) q^{70} -13.1240i q^{71} +(-2.77552 + 0.544488i) q^{72} +(3.96972 + 3.96972i) q^{73} +(4.69521 + 4.12489i) q^{74} +(2.29793 + 4.44066i) q^{75} +(-7.40493 + 0.961649i) q^{76} +(1.35998 - 1.35998i) q^{77} +(-0.403277 - 6.23675i) q^{78} -7.11388 q^{79} +(6.94894 + 5.63137i) q^{80} -1.00000 q^{81} +(-0.387811 - 5.99756i) q^{82} +(3.55694 - 3.55694i) q^{83} +(5.23608 - 0.679988i) q^{84} +(3.51514 + 0.545414i) q^{85} +(7.67030 + 6.73860i) q^{86} +(1.86678 + 1.86678i) q^{87} +(2.02201 - 0.396668i) q^{88} +1.03028i q^{89} +(2.02759 + 2.42670i) q^{90} +11.6669i q^{91} +(10.0673 - 13.0723i) q^{92} +(4.24977 + 4.24977i) q^{93} +(-2.77191 + 3.15516i) q^{94} +(4.92834 + 6.73860i) q^{95} +(5.06244 + 2.52422i) q^{96} +(-12.5298 + 12.5298i) q^{97} +(0.0427276 - 0.00276283i) q^{98} +0.728515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{6} - 12 q^{8}+O(q^{10}) \) 12 * q - 4 * q^6 - 12 * q^8	\( 12 q - 4 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 4 q^{13} + 12 q^{16} - 20 q^{17} + 20 q^{20} + 12 q^{22} - 20 q^{25} + 16 q^{26} - 4 q^{28} + 8 q^{30} + 20 q^{32} + 8 q^{33} + 4 q^{36} + 4 q^{37} + 16 q^{38} - 8 q^{40} + 16 q^{41} + 20 q^{42} + 4 q^{45} - 40 q^{46} + 16 q^{48} - 16 q^{50} - 8 q^{52} + 4 q^{53} - 64 q^{56} - 20 q^{58} - 20 q^{60} - 32 q^{61} - 56 q^{62} + 20 q^{65} - 24 q^{66} - 16 q^{68} + 44 q^{70} - 12 q^{72} + 44 q^{73} + 8 q^{76} + 48 q^{77} - 24 q^{78} + 4 q^{80} - 12 q^{81} + 16 q^{82} + 44 q^{85} + 64 q^{86} + 60 q^{88} + 12 q^{90} + 56 q^{92} - 16 q^{93} + 44 q^{96} - 20 q^{97} + 24 q^{98}+O(q^{100}) \) 12 * q - 4 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 4 * q^13 + 12 * q^16 - 20 * q^17 + 20 * q^20 + 12 * q^22 - 20 * q^25 + 16 * q^26 - 4 * q^28 + 8 * q^30 + 20 * q^32 + 8 * q^33 + 4 * q^36 + 4 * q^37 + 16 * q^38 - 8 * q^40 + 16 * q^41 + 20 * q^42 + 4 * q^45 - 40 * q^46 + 16 * q^48 - 16 * q^50 - 8 * q^52 + 4 * q^53 - 64 * q^56 - 20 * q^58 - 20 * q^60 - 32 * q^61 - 56 * q^62 + 20 * q^65 - 24 * q^66 - 16 * q^68 + 44 * q^70 - 12 * q^72 + 44 * q^73 + 8 * q^76 + 48 * q^77 - 24 * q^78 + 4 * q^80 - 12 * q^81 + 16 * q^82 + 44 * q^85 + 64 * q^86 + 60 * q^88 + 12 * q^90 + 56 * q^92 - 16 * q^93 + 44 * q^96 - 20 * q^97 + 24 * q^98

Introduction

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