LMFDB - Embedded newform 60.2.j.a.7.3

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			7.3
Root			$-0.0912546 - 1.41127i$ of defining polynomial
Character	$\chi$	$=$	60.7
Dual form			60.2.j.a.43.3

$q$-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 $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

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

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	−0.965602	−	0.260026i	$-0.916269\pi$
$7$	−1.86678	+	1.86678i	−0.705576	+	0.705576i	0.260026	+	0.965602i	$0.416269\pi$
$8$	−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	$-0.964970\pi$
$11$		−	0.728515i		−	0.219656i	0.993951	−	0.109828i	$-0.0350299\pi$
$12$	−1.22031	−	1.58457i	−0.352273	−	0.457425i
$13$	−3.12489	+	3.12489i	−0.866687	+	0.866687i	−0.992104	−	0.125417i	$-0.959973\pi$
$13$	−3.12489	+	3.12489i	−0.866687	+	0.866687i	0.125417	+	0.992104i	$0.459973\pi$
$14$	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	0.830236	−	0.557412i	$-0.188205\pi$
$17$	1.12489	+	1.12489i	0.272825	+	0.272825i	−0.557412	+	0.830236i	$0.688205\pi$
$18$	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	−0.968897	−	0.247466i	$-0.920402\pi$
$23$	−5.83347	−	5.83347i	−1.21636	−	1.21636i	−0.247466	−	0.968897i	$-0.579598\pi$
$24$	−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	$-0.921173\pi$
$29$		−	2.64002i		−	0.490240i	0.969493	−	0.245120i	$-0.0788274\pi$
$30$	−0.282213	−	3.14966i	−0.0515248	−	0.575047i
$31$		−	6.01008i		−	1.07944i	−0.841844	−	0.539721i	$-0.818530\pi$
$31$		−	6.01008i		−	1.07944i	0.841844	−	0.539721i	$-0.181470\pi$
$32$	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	0.915667	−	0.401939i	$-0.131663\pi$
$37$	3.12489	+	3.12489i	0.513728	+	0.513728i	−0.401939	+	0.915667i	$0.631663\pi$
$38$	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	0.979575	−	0.201077i	$-0.0644442\pi$
$43$	5.10495	+	5.10495i	0.778498	+	0.778498i	−0.201077	+	0.979575i	$0.564444\pi$
$44$	−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	−0.537170	−	0.843474i	$-0.680507\pi$
$47$	2.09991	−	2.09991i	0.306304	−	0.306304i	0.843474	+	0.537170i	$0.180507\pi$
$48$	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	−0.673022	−	0.739623i	$-0.735004\pi$
$53$	0.484862	−	0.484862i	0.0666009	−	0.0666009i	0.739623	+	0.673022i	$0.235004\pi$
$54$	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	−0.946468	−	0.322798i	$-0.895376\pi$
$67$	−5.10495	+	5.10495i	−0.623669	+	0.623669i	0.322798	+	0.946468i	$0.395376\pi$
$68$	−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	$0.284153\pi$
$71$			13.1240i			1.55753i	−0.627317	+	0.778764i	$0.715847\pi$
$72$	−2.77552	−	0.544488i	−0.327099	−	0.0641685i
$73$	3.96972	−	3.96972i	0.464621	−	0.464621i	−0.435546	−	0.900167i	$-0.643445\pi$
$73$	3.96972	−	3.96972i	0.464621	−	0.464621i	0.900167	+	0.435546i	$0.143445\pi$
$74$	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	0.874839	−	0.484414i	$-0.160967\pi$
$83$	3.55694	+	3.55694i	0.390425	+	0.390425i	−0.484414	+	0.874839i	$0.660967\pi$
$84$	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	$-0.982610\pi$
$89$		−	1.03028i		−	0.109209i	0.998508	−	0.0546045i	$-0.0173898\pi$
$90$	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	−0.944926	−	0.327284i	$-0.893867\pi$
$97$	−12.5298	−	12.5298i	−1.27221	−	1.27221i	−0.327284	−	0.944926i	$-0.606133\pi$
$98$	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	0.704317	−	0.709886i	$-0.251253\pi$
$103$	−0.0565188	−	0.0565188i	−0.00556896	−	0.00556896i	−0.709886	+	0.704317i	$0.751253\pi$
$104$	−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	−0.492373	−	0.870384i	$-0.663871\pi$
$107$	3.91017	−	3.91017i	0.378011	−	0.378011i	0.870384	+	0.492373i	$0.163871\pi$
$108$	1.58457	−	1.22031i	0.152475	−	0.117424i
$109$			15.7796i			1.51141i	0.654912	+	0.755705i	$0.272706\pi$
$109$			15.7796i			1.51141i	−0.654912	+	0.755705i	$0.727294\pi$
$110$	−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	−0.788536	−	0.614988i	$-0.789161\pi$
$113$	−1.84484	+	1.84484i	−0.173548	+	0.173548i	0.614988	+	0.788536i	$0.289161\pi$
$114$	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	−0.00108535	−	0.999999i	$-0.500345\pi$
$127$	11.2572	−	11.2572i	0.998914	−	0.998914i	0.999999	+	0.00108535i	$0.000345478\pi$
$128$	−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	$-0.935950\pi$
$131$		−	4.57511i		−	0.399729i	0.979824	−	0.199865i	$-0.0640502\pi$
$132$	−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	0.510219	−	0.860045i	$-0.329564\pi$
$137$	−4.09461	−	4.09461i	−0.349826	−	0.349826i	−0.860045	+	0.510219i	$0.829564\pi$
$138$	−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	$0.0746135\pi$
$149$			5.67030i			0.464529i	−0.972653	+	0.232265i	$0.925386\pi$
$150$	−6.05726	−	3.64823i	−0.494573	−	0.297877i
$151$			19.2471i			1.56631i	0.621829	+	0.783153i	$0.286390\pi$
$151$			19.2471i			1.56631i	−0.621829	+	0.783153i	$0.713610\pi$
$152$	−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	0.618565	−	0.785733i	$-0.287714\pi$
$157$	−2.09461	−	2.09461i	−0.167168	−	0.167168i	−0.785733	+	0.618565i	$0.787714\pi$
$158$	−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	0.854732	−	0.519069i	$-0.173721\pi$
$163$	4.28546	+	4.28546i	0.335663	+	0.335663i	−0.519069	+	0.854732i	$0.673721\pi$
$164$	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	−0.855862	−	0.517203i	$-0.826973\pi$
$167$	−4.37644	+	4.37644i	−0.338659	+	0.338659i	0.517203	+	0.855862i	$0.326973\pi$
$168$	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	0.290312	−	0.956932i	$-0.406241\pi$
$173$	16.4049	−	16.4049i	1.24724	−	1.24724i	0.956932	−	0.290312i	$-0.0937590\pi$
$174$	−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	$-0.962286\pi$
$191$		−	3.26729i		−	0.236413i	0.992989	−	0.118206i	$-0.0377144\pi$
$192$	−3.10037	−	7.37480i	−0.223750	−	0.532230i
$193$	0.939448	−	0.939448i	0.0676229	−	0.0676229i	−0.672486	−	0.740109i	$-0.734774\pi$
$193$	0.939448	−	0.939448i	0.0676229	−	0.0676229i	0.740109	+	0.672486i	$0.234774\pi$
$194$	−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	0.653388	−	0.757023i	$-0.273347\pi$
$197$	−1.45459	−	1.45459i	−0.103635	−	0.103635i	−0.757023	+	0.653388i	$0.773347\pi$
$198$	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	$-0.867103\pi$
$211$		−	11.7800i		−	0.810967i	0.914102	−	0.405483i	$-0.132897\pi$
$212$	−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	0.587005	−	0.809583i	$-0.300307\pi$
$223$	−3.32381	−	3.32381i	−0.222579	−	0.222579i	−0.809583	+	0.587005i	$0.800307\pi$
$224$	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	−0.936718	−	0.350085i	$-0.886153\pi$
$227$	−8.83851	+	8.83851i	−0.586633	+	0.586633i	0.350085	+	0.936718i	$0.386153\pi$
$228$	−4.55609	−	5.91607i	−0.301734	−	0.391801i
$229$		−	7.09083i		−	0.468575i	−0.972167	−	0.234288i	$-0.924724\pi$
$229$		−	7.09083i		−	0.468575i	0.972167	−	0.234288i	$-0.0752757\pi$
$230$	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	−0.00725353	+	0.999974i	$0.502309\pi$
$233$	−15.3747	+	15.3747i	−1.00723	+	1.00723i	−0.999974	+	0.00725353i	$0.997691\pi$
$234$	−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	$-0.641289\pi$
$251$		−	28.6154i		−	1.80619i	0.429440	−	0.903095i	$-0.358711\pi$
$252$	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	0.574731	−	0.818342i	$-0.305107\pi$
$257$	−3.90539	−	3.90539i	−0.243612	−	0.243612i	−0.818342	+	0.574731i	$0.805107\pi$
$258$	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	0.712531	−	0.701641i	$-0.247549\pi$
$263$	0.176615	+	0.176615i	0.0108905	+	0.0108905i	−0.701641	+	0.712531i	$0.747549\pi$
$264$	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	$-0.947465\pi$
$269$		−	5.38934i		−	0.328594i	0.986411	−	0.164297i	$-0.0525355\pi$
$270$	3.14966	−	0.282213i	0.191682	−	0.0171749i
$271$			15.4005i			0.935513i	0.883857	+	0.467757i	$0.154938\pi$
$271$			15.4005i			0.935513i	−0.883857	+	0.467757i	$0.845062\pi$
$272$	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	0.916472	−	0.400099i	$-0.131024\pi$
$277$	8.59415	+	8.59415i	0.516372	+	0.516372i	−0.400099	+	0.916472i	$0.631024\pi$
$278$	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	−0.993849	−	0.110745i	$-0.964676\pi$
$283$	−18.5822	−	18.5822i	−1.10459	−	1.10459i	−0.110745	−	0.993849i	$-0.535324\pi$
$284$	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	−0.501120	−	0.865378i	$-0.667078\pi$
$293$	6.23509	−	6.23509i	0.364258	−	0.364258i	0.865378	+	0.501120i	$0.167078\pi$
$294$	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	−0.732464	−	0.680806i	$-0.761630\pi$
$307$	−0.905130	+	0.905130i	−0.0516585	+	0.0516585i	0.680806	+	0.732464i	$0.261630\pi$
$308$	−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	$0.243653\pi$
$311$			24.4377i			1.38573i	−0.721066	+	0.692867i	$0.756347\pi$
$312$	2.40623	−	12.2657i	0.136226	−	0.694411i
$313$	18.5904	−	18.5904i	1.05079	−	1.05079i	0.0521506	−	0.998639i	$-0.483392\pi$
$313$	18.5904	−	18.5904i	1.05079	−	1.05079i	0.998639	−	0.0521506i	$-0.0166076\pi$
$314$	−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	0.996055	+	0.0887327i	$0.0282817\pi$
$317$	19.3141	+	19.3141i	1.08479	+	1.08479i	0.0887327	+	0.996055i	$0.471718\pi$
$318$	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	$0.0980268\pi$
$331$			11.0294i			0.606231i	−0.952954	+	0.303115i	$0.901973\pi$
$332$	−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	0.972956	−	0.230992i	$-0.0741971\pi$
$337$	13.6206	+	13.6206i	0.741964	+	0.741964i	−0.230992	+	0.972956i	$0.574197\pi$
$338$	−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	−0.998968	−	0.0454187i	$-0.985538\pi$
$347$	−17.7627	+	17.7627i	−0.953549	+	0.953549i	0.0454187	+	0.998968i	$0.485538\pi$
$348$	−4.18329	+	3.22164i	−0.224248	+	0.172698i
$349$		−	14.6888i		−	0.786271i	−0.919480	−	0.393136i	$-0.871390\pi$
$349$		−	14.6888i		−	0.786271i	0.919480	−	0.393136i	$-0.128610\pi$
$350$	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	−0.999796	−	0.0202002i	$-0.993570\pi$
$353$	−18.4049	+	18.4049i	−0.979596	+	0.979596i	0.0202002	+	0.999796i	$0.493570\pi$
$354$	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	−0.177306	−	0.984156i	$-0.556738\pi$
$367$	15.4570	−	15.4570i	0.806850	−	0.806850i	0.984156	+	0.177306i	$0.0567383\pi$
$368$	−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	−0.614322	−	0.789055i	$-0.710570\pi$
$373$	3.37466	−	3.37466i	0.174733	−	0.174733i	0.789055	+	0.614322i	$0.210570\pi$
$374$	−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	0.690491	−	0.723341i	$-0.257394\pi$
$383$	−0.642881	−	0.642881i	−0.0328497	−	0.0328497i	−0.723341	+	0.690491i	$0.757394\pi$
$384$	−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	$0.158399\pi$
$389$			18.8292i			0.954680i	−0.878719	+	0.477340i	$0.841601\pi$
$390$	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	−0.966988	−	0.254821i	$-0.917983\pi$
$397$	−24.3444	−	24.3444i	−1.22181	−	1.22181i	−0.254821	−	0.966988i	$-0.582017\pi$
$398$	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	$0.196457\pi$
$409$			23.4087i			1.15749i	−0.815510	+	0.578743i	$0.803543\pi$
$410$	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	$-0.729898\pi$
$431$		−	31.1542i		−	1.50065i	0.661071	−	0.750323i	$-0.270102\pi$
$432$	−3.45705	+	2.01216i	−0.166328	+	0.0968100i
$433$	−12.1589	+	12.1589i	−0.584321	+	0.584321i	−0.936088	−	0.351766i	$-0.885581\pi$
$433$	−12.1589	+	12.1589i	−0.584321	+	0.584321i	0.351766	+	0.936088i	$0.385581\pi$
$434$	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	0.520152	−	0.854074i	$-0.325875\pi$
$443$	−7.02825	−	7.02825i	−0.333922	−	0.333922i	−0.854074	+	0.520152i	$0.825875\pi$
$444$	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	$-0.637959\pi$
$449$		−	38.4608i		−	1.81508i	0.419969	−	0.907538i	$-0.362041\pi$
$450$	−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	0.813134	−	0.582076i	$-0.197760\pi$
$457$	4.93945	+	4.93945i	0.231058	+	0.231058i	−0.582076	+	0.813134i	$0.697760\pi$
$458$	−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	0.582319	−	0.812960i	$-0.302145\pi$
$463$	−4.96280	−	4.96280i	−0.230641	−	0.230641i	−0.812960	+	0.582319i	$0.802145\pi$
$464$	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	−0.0172604	−	0.999851i	$-0.505494\pi$
$467$	21.2340	−	21.2340i	0.982591	−	0.982591i	0.999851	+	0.0172604i	$0.00549442\pi$
$468$	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	−0.771201	−	0.636591i	$-0.780344\pi$
$487$	−2.97058	+	2.97058i	−0.134610	+	0.134610i	0.636591	+	0.771201i	$0.280344\pi$
$488$	−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	$0.232311\pi$
$491$			29.5480i			1.33348i	−0.745290	+	0.666741i	$0.767689\pi$
$492$	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	0.341719	−	0.939802i	$-0.388991\pi$
$503$	−13.4136	−	13.4136i	−0.598084	−	0.598084i	−0.939802	+	0.341719i	$0.888991\pi$
$504$	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	$0.370137\pi$
$509$			41.4187i			1.83585i	−0.396752	+	0.917926i	$0.629863\pi$
$510$	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	0.974259	−	0.225430i	$-0.0723787\pi$
$523$	17.1251	+	17.1251i	0.748829	+	0.748829i	−0.225430	+	0.974259i	$0.572379\pi$
$524$	−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	0.0874075	−	0.996173i	$-0.472142\pi$
$547$	25.3428	−	25.3428i	1.08358	−	1.08358i	0.996173	−	0.0874075i	$-0.0278582\pi$
$548$	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	0.994922	−	0.100653i	$-0.0320931\pi$
$557$	21.1055	+	21.1055i	0.894269	+	0.894269i	−0.100653	+	0.994922i	$0.532093\pi$
$558$	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	0.456049	−	0.889955i	$-0.349264\pi$
$563$	−10.2955	−	10.2955i	−0.433905	−	0.433905i	−0.889955	+	0.456049i	$0.849264\pi$
$564$	−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	$-0.797717\pi$
$569$		−	28.3179i		−	1.18715i	0.804780	−	0.593574i	$-0.202283\pi$
$570$	−1.05366	−	11.7594i	−0.0441329	−	0.492548i
$571$			27.2387i			1.13990i	0.821678	+	0.569952i	$0.193038\pi$
$571$			27.2387i			1.13990i	−0.821678	+	0.569952i	$0.806962\pi$
$572$	−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	0.800118	−	0.599843i	$-0.204770\pi$
$577$	4.81078	+	4.81078i	0.200275	+	0.200275i	−0.599843	+	0.800118i	$0.704770\pi$
$578$	−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	−0.799948	−	0.600069i	$-0.795140\pi$
$587$	−4.84271	+	4.84271i	−0.199880	+	0.199880i	0.600069	+	0.799948i	$0.295140\pi$
$588$	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	−0.204946	−	0.978773i	$-0.565702\pi$
$593$	18.8439	−	18.8439i	0.773827	−	0.773827i	0.978773	+	0.204946i	$0.0657019\pi$
$594$	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	−0.982022	−	0.188764i	$-0.939552\pi$
$607$	−19.5438	+	19.5438i	−0.793258	+	0.793258i	0.188764	+	0.982022i	$0.439552\pi$
$608$	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	−0.0532993	−	0.998579i	$-0.516974\pi$
$613$	23.4040	−	23.4040i	0.945279	−	0.945279i	0.998579	+	0.0532993i	$0.0169737\pi$
$614$	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	0.246992	−	0.969018i	$-0.420558\pi$
$617$	−17.9348	−	17.9348i	−0.722026	−	0.722026i	−0.969018	+	0.246992i	$0.920558\pi$
$618$	−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	$0.0818113\pi$
$631$			12.7707i			0.508395i	−0.967152	+	0.254198i	$0.918189\pi$
$632$	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	0.584751	−	0.811213i	$-0.301192\pi$
$643$	−5.74249	−	5.74249i	−0.226462	−	0.226462i	−0.811213	+	0.584751i	$0.801192\pi$
$644$	−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	−0.610510	−	0.792009i	$-0.709036\pi$
$647$	4.61663	−	4.61663i	0.181498	−	0.181498i	0.792009	+	0.610510i	$0.209036\pi$
$648$	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	−0.364949	−	0.931027i	$-0.618914\pi$
$653$	14.4655	−	14.4655i	0.566078	−	0.566078i	0.931027	+	0.364949i	$0.118914\pi$
$654$	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	−0.980704	−	0.195500i	$-0.937367\pi$
$673$	−20.3700	+	20.3700i	−0.785204	+	0.785204i	0.195500	+	0.980704i	$0.437367\pi$
$674$	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	0.859502	−	0.511132i	$-0.170774\pi$
$677$	9.06433	+	9.06433i	0.348371	+	0.348371i	−0.511132	+	0.859502i	$0.670774\pi$
$678$	−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	0.998856	−	0.0478253i	$-0.0152291\pi$
$683$	24.8545	+	24.8545i	0.951030	+	0.951030i	−0.0478253	+	0.998856i	$0.515229\pi$
$684$	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	$-0.716278\pi$
$691$		−	40.8979i		−	1.55583i	0.628371	−	0.777914i	$-0.283722\pi$
$692$	−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	$-0.887258\pi$
$709$		−	18.4702i		−	0.693662i	0.937928	−	0.346831i	$-0.112742\pi$
$710$	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	−0.128412	−	0.991721i	$-0.540988\pi$
$727$	23.2774	−	23.2774i	0.863309	−	0.863309i	0.991721	+	0.128412i	$0.0409879\pi$
$728$	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	−0.940031	−	0.341090i	$-0.889204\pi$
$733$	−16.2157	+	16.2157i	−0.598941	+	0.598941i	0.341090	+	0.940031i	$0.389204\pi$
$734$	−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	0.887156	−	0.461470i	$-0.152678\pi$
$743$	11.6034	+	11.6034i	0.425686	+	0.425686i	−0.461470	+	0.887156i	$0.652678\pi$
$744$	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	$-0.778220\pi$
$751$		−	35.1721i		−	1.28345i	0.766936	−	0.641724i	$-0.221780\pi$
$752$	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	0.360484	−	0.932765i	$-0.382611\pi$
$757$	−15.7455	−	15.7455i	−0.572281	−	0.572281i	−0.932765	+	0.360484i	$0.882611\pi$
$758$	−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	$-0.907035\pi$
$769$		−	15.9688i		−	0.575850i	0.957653	−	0.287925i	$-0.0929654\pi$
$770$	−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	−0.756399	−	0.654110i	$-0.773043\pi$
$773$	−2.84392	+	2.84392i	−0.102289	+	0.102289i	0.654110	+	0.756399i	$0.273043\pi$
$774$	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	−0.560800	−	0.827951i	$-0.689506\pi$
$787$	7.49452	−	7.49452i	0.267151	−	0.267151i	0.827951	+	0.560800i	$0.189506\pi$
$788$	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	0.997475	−	0.0710121i	$-0.0226229\pi$
$797$	26.1552	+	26.1552i	0.926463	+	0.926463i	−0.0710121	+	0.997475i	$0.522623\pi$
$798$	−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	$-0.863143\pi$
$809$		−	23.7115i		−	0.833651i	0.908987	−	0.416826i	$-0.136857\pi$
$810$	2.42670	+	2.02759i	0.0852656	+	0.0712423i
$811$			26.0077i			0.913255i	0.889658	+	0.456628i	$0.150943\pi$
$811$			26.0077i			0.913255i	−0.889658	+	0.456628i	$0.849057\pi$
$812$	−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	0.947192	−	0.320667i	$-0.103907\pi$
$823$	17.9737	+	17.9737i	0.626525	+	0.626525i	−0.320667	+	0.947192i	$0.603907\pi$
$824$	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	−0.954443	−	0.298392i	$-0.903550\pi$
$827$	−18.8665	+	18.8665i	−0.656051	+	0.656051i	0.298392	+	0.954443i	$0.403550\pi$
$828$	−13.0723	+	10.0673i	−0.454294	+	0.349862i
$829$			3.28005i			0.113921i	0.998376	+	0.0569604i	$0.0181409\pi$
$829$			3.28005i			0.113921i	−0.998376	+	0.0569604i	$0.981859\pi$
$830$	−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	−0.944005	−	0.329931i	$-0.892975\pi$
$853$	−17.9348	+	17.9348i	−0.614074	+	0.614074i	0.329931	+	0.944005i	$0.392975\pi$
$854$	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	0.536400	−	0.843964i	$-0.319784\pi$
$857$	−9.00378	−	9.00378i	−0.307563	−	0.307563i	−0.843964	+	0.536400i	$0.819784\pi$
$858$	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	0.848009	+	0.529982i	$0.177802\pi$
$863$	40.4811	+	40.4811i	1.37799	+	1.37799i	0.529982	+	0.848009i	$0.322198\pi$
$864$	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	0.679663	−	0.733525i	$-0.262126\pi$
$877$	−1.59507	−	1.59507i	−0.0538616	−	0.0538616i	−0.733525	+	0.679663i	$0.762126\pi$
$878$	−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	0.00956956	−	0.999954i	$-0.496954\pi$
$883$	−29.4296	−	29.4296i	−0.990385	−	0.990385i	−0.999954	+	0.00956956i	$0.996954\pi$
$884$	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	−0.0409656	+	0.999161i	$0.513043\pi$
$887$	−30.9776	+	30.9776i	−1.04013	+	1.04013i	−0.999161	+	0.0409656i	$0.986957\pi$
$888$	−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	−0.998912	−	0.0466405i	$-0.985148\pi$
$907$	−28.6790	+	28.6790i	−0.952271	+	0.952271i	0.0466405	+	0.998912i	$0.485148\pi$
$908$	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	$0.176981\pi$
$911$			31.8607i			1.05559i	−0.849371	+	0.527796i	$0.823019\pi$
$912$	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	$0.279923\pi$
$929$			46.9603i			1.54072i	−0.637610	+	0.770359i	$0.720077\pi$
$930$	−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	0.857125	−	0.515109i	$-0.172248\pi$
$937$	10.4693	+	10.4693i	0.342016	+	0.342016i	−0.515109	+	0.857125i	$0.672248\pi$
$938$	−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	−0.150003	−	0.988685i	$-0.547928\pi$
$947$	25.8091	−	25.8091i	0.838682	−	0.838682i	0.988685	+	0.150003i	$0.0479284\pi$
$948$	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	−0.821855	−	0.569697i	$-0.807061\pi$
$953$	−7.78429	+	7.78429i	−0.252158	+	0.252158i	0.569697	+	0.821855i	$0.307061\pi$
$954$	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	−0.870019	−	0.493018i	$-0.835894\pi$
$967$	−11.7235	+	11.7235i	−0.377001	+	0.377001i	0.493018	+	0.870019i	$0.335894\pi$
$968$	−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	$0.0667572\pi$
$971$			12.9748i			0.416380i	−0.978088	+	0.208190i	$0.933243\pi$
$972$	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	0.448773	−	0.893646i	$-0.351861\pi$
$977$	−13.9054	−	13.9054i	−0.444873	−	0.444873i	−0.893646	+	0.448773i	$0.851861\pi$
$978$	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	0.448983	−	0.893540i	$-0.351786\pi$
$983$	−13.9381	−	13.9381i	−0.444557	−	0.444557i	−0.893540	+	0.448983i	$0.851786\pi$
$984$	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	$-0.681850\pi$
$991$		−	52.9621i		−	1.68240i	0.540726	−	0.841199i	$-0.318150\pi$
$992$	−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	0.730988	−	0.682390i	$-0.239059\pi$
$997$	1.53452	+	1.53452i	0.0485986	+	0.0485986i	−0.682390	+	0.730988i	$0.739059\pi$
$998$	−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.7.3	yes	12
3.2	odd	2		180.2.k.e.127.4		12
4.3	odd	2	inner	60.2.j.a.7.1	✓	12
5.2	odd	4		300.2.j.d.43.6		12
5.3	odd	4	inner	60.2.j.a.43.1	yes	12
5.4	even	2		300.2.j.d.7.4		12
8.3	odd	2		960.2.w.g.127.4		12
8.5	even	2		960.2.w.g.127.1		12
12.11	even	2		180.2.k.e.127.6		12
15.2	even	4		900.2.k.n.343.1		12
15.8	even	4		180.2.k.e.163.6		12
15.14	odd	2		900.2.k.n.307.3		12
20.3	even	4	inner	60.2.j.a.43.3	yes	12
20.7	even	4		300.2.j.d.43.4		12
20.19	odd	2		300.2.j.d.7.6		12
40.3	even	4		960.2.w.g.703.1		12
40.13	odd	4		960.2.w.g.703.4		12
60.23	odd	4		180.2.k.e.163.4		12
60.47	odd	4		900.2.k.n.343.3		12
60.59	even	2		900.2.k.n.307.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.j.a.7.1	✓	12	4.3	odd	2	inner
60.2.j.a.7.3	yes	12	1.1	even	1	trivial
60.2.j.a.43.1	yes	12	5.3	odd	4	inner
60.2.j.a.43.3	yes	12	20.3	even	4	inner
180.2.k.e.127.4		12	3.2	odd	2
180.2.k.e.127.6		12	12.11	even	2
180.2.k.e.163.4		12	60.23	odd	4
180.2.k.e.163.6		12	15.8	even	4
300.2.j.d.7.4		12	5.4	even	2
300.2.j.d.7.6		12	20.19	odd	2
300.2.j.d.43.4		12	20.7	even	4
300.2.j.d.43.6		12	5.2	odd	4
900.2.k.n.307.1		12	60.59	even	2
900.2.k.n.307.3		12	15.14	odd	2
900.2.k.n.343.1		12	15.2	even	4
900.2.k.n.343.3		12	60.47	odd	4
960.2.w.g.127.1		12	8.5	even	2
960.2.w.g.127.4		12	8.3	odd	2
960.2.w.g.703.1		12	40.3	even	4
960.2.w.g.703.4		12	40.13	odd	4

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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