LMFDB - Embedded newform 60.2.j.a.7.1

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			7.1
Root			$1.41127 + 0.0912546i$ of defining polynomial
Character	$\chi$	$=$	60.7
Dual form			60.2.j.a.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41127 + 0.0912546i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.98335 - 0.257569i) q^{4} +(1.32001 - 1.80487i) q^{5} +(1.06244 + 0.933389i) q^{6} +(1.86678 - 1.86678i) q^{7} +(-2.77552 + 0.544488i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-1.41127 + 0.0912546i) 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} +(-2.77552 + 0.544488i) q^{8} +1.00000i q^{9} +(-1.69819 + 2.66761i) q^{10} +0.728515i q^{11} +(-1.58457 - 1.22031i) 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} +(-0.0912546 - 1.41127i) q^{18} -3.73356 q^{19} +(2.15316 - 3.91968i) q^{20} -2.64002 q^{21} +(-0.0664803 - 1.02813i) 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} +(3.22164 - 4.18329i) q^{28} -2.64002i q^{29} +(3.08709 - 0.685490i) q^{30} +6.01008i q^{31} +(-5.36458 + 1.79480i) 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} +(5.26904 - 0.340704i) q^{38} +4.41926 q^{39} +(-2.68099 + 5.72820i) q^{40} -4.24977 q^{41} +(3.72578 - 0.240914i) 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} +(-3.45705 - 2.01216i) q^{48} +0.0302761i q^{49} +(2.57308 + 6.58629i) q^{50} -1.59083i q^{51} +(-5.39285 + 7.00260i) 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} +(0.240914 + 3.72578i) q^{58} -4.92834 q^{59} +(-4.29415 + 1.24912i) q^{60} +2.31032 q^{61} +(-0.548448 - 8.48183i) 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} +(2.52077 + 1.94130i) q^{68} -8.24977i q^{69} +(1.80971 + 8.14998i) q^{70} -13.1240i q^{71} +(-0.544488 - 2.77552i) 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} +(-6.23675 + 0.403277i) q^{78} +7.11388 q^{79} +(3.26087 - 8.32867i) q^{80} -1.00000 q^{81} +(5.99756 - 0.387811i) 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} +(-0.396668 - 2.02201i) q^{88} -1.03028i q^{89} +(-2.66761 - 1.69819i) q^{90} +11.6669i q^{91} +(13.0723 + 10.0673i) 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} +(-0.00276283 - 0.0427276i) 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 $

$2$	−1.41127	+	0.0912546i	−0.997916	+	0.0645267i
$2$	−1.41127	+	0.0912546i	−0.997916	+	0.0645267i
$3$	−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	$-0.583731\pi$
$7$	1.86678	−	1.86678i	0.705576	−	0.705576i	0.965602	+	0.260026i	$0.0837311\pi$
$8$	−2.77552	+	0.544488i	−0.981296	+	0.192506i
$9$			1.00000i			0.333333i
$10$	−1.69819	+	2.66761i	−0.537013	+	0.843574i
$11$			0.728515i			0.219656i	0.993951	+	0.109828i	$0.0350299\pi$
$11$			0.728515i			0.219656i	−0.993951	+	0.109828i	$0.964970\pi$
$12$	−1.58457	−	1.22031i	−0.457425	−	0.352273i
$13$	−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	$0.688205\pi$
$18$	−0.0912546	−	1.41127i	−0.0215089	−	0.332639i
$19$	−3.73356			−0.856537			−0.428268	−	0.903652i	$-0.640876\pi$
$19$	−3.73356			−0.856537			−0.428268	+	0.903652i	$0.640876\pi$
$20$	2.15316	−	3.91968i	0.481461	−	0.876467i
$21$	−2.64002			−0.576100
$22$	−0.0664803	−	1.02813i	−0.0141737	−	0.219198i
$23$	5.83347	+	5.83347i	1.21636	+	1.21636i	0.968897	+	0.247466i	$0.0795978\pi$
$23$	5.83347	+	5.83347i	1.21636	+	1.21636i	0.247466	+	0.968897i	$0.420402\pi$
$24$	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
$28$	3.22164	−	4.18329i	0.608833	−	0.790568i
$29$		−	2.64002i		−	0.490240i	−0.969493	−	0.245120i	$-0.921173\pi$
$29$		−	2.64002i		−	0.490240i	0.969493	−	0.245120i	$-0.0788274\pi$
$30$	3.08709	−	0.685490i	0.563622	−	0.125153i
$31$			6.01008i			1.07944i	0.841844	+	0.539721i	$0.181470\pi$
$31$			6.01008i			1.07944i	−0.841844	+	0.539721i	$0.818530\pi$
$32$	−5.36458	+	1.79480i	−0.948333	+	0.317278i
$33$	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	$0.631663\pi$
$38$	5.26904	−	0.340704i	0.854752	−	0.0552695i
$39$	4.41926			0.707647
$40$	−2.68099	+	5.72820i	−0.423902	+	0.905708i
$41$	−4.24977			−0.663703			−0.331851	−	0.943332i	$-0.607673\pi$
$41$	−4.24977			−0.663703			−0.331851	+	0.943332i	$0.607673\pi$
$42$	3.72578	−	0.240914i	0.574900	−	0.0371739i
$43$	−5.10495	−	5.10495i	−0.778498	−	0.778498i	0.201077	−	0.979575i	$-0.435556\pi$
$43$	−5.10495	−	5.10495i	−0.778498	−	0.778498i	−0.979575	+	0.201077i	$0.935556\pi$
$44$	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	$-0.819493\pi$
$47$	−2.09991	+	2.09991i	−0.306304	+	0.306304i	0.537170	+	0.843474i	$0.319493\pi$
$48$	−3.45705	−	2.01216i	−0.498983	−	0.290430i
$49$			0.0302761i			0.00432516i
$50$	2.57308	+	6.58629i	0.363889	+	0.931442i
$51$		−	1.59083i		−	0.222761i
$52$	−5.39285	+	7.00260i	−0.747854	+	0.971086i
$53$	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
$58$	0.240914	+	3.72578i	0.0316336	+	0.489218i
$59$	−4.92834			−0.641615			−0.320808	−	0.947144i	$-0.603954\pi$
$59$	−4.92834			−0.641615			−0.320808	+	0.947144i	$0.603954\pi$
$60$	−4.29415	+	1.24912i	−0.554372	+	0.161261i
$61$	2.31032			0.295807			0.147903	−	0.989002i	$-0.452748\pi$
$61$	2.31032			0.295807			0.147903	+	0.989002i	$0.452748\pi$
$62$	−0.548448	−	8.48183i	−0.0696529	−	1.07719i
$63$	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	$-0.604624\pi$
$67$	5.10495	−	5.10495i	0.623669	−	0.623669i	0.946468	+	0.322798i	$0.104624\pi$
$68$	2.52077	+	1.94130i	0.305688	+	0.235417i
$69$		−	8.24977i		−	0.993156i
$70$	1.80971	+	8.14998i	0.216302	+	0.974109i
$71$		−	13.1240i		−	1.55753i	−0.627317	−	0.778764i	$-0.715847\pi$
$71$		−	13.1240i		−	1.55753i	0.627317	−	0.778764i	$-0.284153\pi$
$72$	−0.544488	−	2.77552i	−0.0641685	−	0.327099i
$73$	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
$78$	−6.23675	+	0.403277i	−0.706172	+	0.0456622i
$79$	7.11388			0.800375			0.400187	−	0.916433i	$-0.368945\pi$
$79$	7.11388			0.800375			0.400187	+	0.916433i	$0.368945\pi$
$80$	3.26087	−	8.32867i	0.364576	−	0.931174i
$81$	−1.00000			−0.111111
$82$	5.99756	−	0.387811i	0.662320	−	0.0428266i
$83$	−3.55694	−	3.55694i	−0.390425	−	0.390425i	0.484414	−	0.874839i	$-0.339033\pi$
$83$	−3.55694	−	3.55694i	−0.390425	−	0.390425i	−0.874839	+	0.484414i	$0.839033\pi$
$84$	−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
$88$	−0.396668	−	2.02201i	−0.0422849	−	0.215547i
$89$		−	1.03028i		−	0.109209i	−0.998508	−	0.0546045i	$-0.982610\pi$
$89$		−	1.03028i		−	0.109209i	0.998508	−	0.0546045i	$-0.0173898\pi$
$90$	−2.66761	−	1.69819i	−0.281191	−	0.179004i
$91$			11.6669i			1.22303i
$92$	13.0723	+	10.0673i	1.36288	+	1.04958i
$93$	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	$-0.606133\pi$
$98$	−0.00276283	−	0.0427276i	−0.000279088	−	0.00431614i
$99$	−0.728515			−0.0732185
$100$	−4.23233	−	9.06021i	−0.423233	−	0.906021i
$101$	−5.67030			−0.564216			−0.282108	−	0.959383i	$-0.591034\pi$
$101$	−5.67030			−0.564216			−0.282108	+	0.959383i	$0.591034\pi$
$102$	0.145170	+	2.24508i	0.0143740	+	0.222296i
$103$	0.0565188	+	0.0565188i	0.00556896	+	0.00556896i	0.709886	−	0.704317i	$-0.248747\pi$
$103$	0.0565188	+	0.0565188i	0.00556896	+	0.00556896i	−0.704317	+	0.709886i	$0.748747\pi$
$104$	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	$-0.836129\pi$
$107$	−3.91017	+	3.91017i	−0.378011	+	0.378011i	0.492373	+	0.870384i	$0.336129\pi$
$108$	1.22031	−	1.58457i	0.117424	−	0.152475i
$109$			15.7796i			1.51141i	0.654912	+	0.755705i	$0.272706\pi$
$109$			15.7796i			1.51141i	−0.654912	+	0.755705i	$0.727294\pi$
$110$	−1.94340	−	1.23715i	−0.185296	−	0.117958i
$111$		−	4.41926i		−	0.419457i
$112$	5.31214	−	9.12670i	0.501950	−	0.862392i
$113$	−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
$118$	6.95520	−	0.449733i	0.640278	−	0.0414013i
$119$	4.19982			0.384997
$120$	5.94620	−	2.15470i	0.542811	−	0.196696i
$121$	10.4693			0.951751
$122$	−3.26048	+	0.210828i	−0.295190	+	0.0190874i
$123$	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	$-0.999655\pi$
$127$	−11.2572	+	11.2572i	−0.998914	+	0.998914i	0.00108535	+	0.999999i	$0.499655\pi$
$128$	−10.1775	+	4.94145i	−0.899575	+	0.436767i
$129$			7.21949i			0.635641i
$130$	−3.02936	−	13.6426i	−0.265692	−	1.19654i
$131$			4.57511i			0.399729i	0.979824	+	0.199865i	$0.0640502\pi$
$131$			4.57511i			0.399729i	−0.979824	+	0.199865i	$0.935950\pi$
$132$	0.889013	−	1.15438i	0.0773786	−	0.100476i
$133$	−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	$0.829564\pi$
$138$	0.752829	+	11.6426i	0.0640851	+	0.991086i
$139$	−13.5902			−1.15271			−0.576354	−	0.817200i	$-0.695525\pi$
$139$	−13.5902			−1.15271			−0.576354	+	0.817200i	$0.695525\pi$
$140$	−3.29771	−	11.3366i	−0.278707	−	0.958122i
$141$	2.96972			0.250096
$142$	1.19762	+	18.5214i	0.100502	+	1.55428i
$143$	−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
$148$	7.00260	+	5.39285i	0.575610	+	0.443290i
$149$			5.67030i			0.464529i	0.972653	+	0.232265i	$0.0746135\pi$
$149$			5.67030i			0.464529i	−0.972653	+	0.232265i	$0.925386\pi$
$150$	2.83777	−	6.47666i	0.231703	−	0.528817i
$151$		−	19.2471i		−	1.56631i	−0.621829	−	0.783153i	$-0.713610\pi$
$151$		−	19.2471i		−	1.56631i	0.621829	−	0.783153i	$-0.286390\pi$
$152$	10.3626	−	2.03288i	0.840516	−	0.164888i
$153$	−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	$0.787714\pi$
$158$	−10.0396	+	0.649175i	−0.798707	+	0.0516456i
$159$	−0.685698			−0.0543794
$160$	−3.84193	+	12.0515i	−0.303731	+	0.952758i
$161$	21.7796			1.71647
$162$	1.41127	−	0.0912546i	0.110880	−	0.00716964i
$163$	−4.28546	−	4.28546i	−0.335663	−	0.335663i	0.519069	−	0.854732i	$-0.326279\pi$
$163$	−4.28546	−	4.28546i	−0.335663	−	0.335663i	−0.854732	+	0.519069i	$0.826279\pi$
$164$	−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	$-0.673027\pi$
$167$	4.37644	−	4.37644i	0.338659	−	0.338659i	0.855862	+	0.517203i	$0.173027\pi$
$168$	7.32745	−	1.43746i	0.565325	−	0.110902i
$169$		−	6.52982i		−	0.502294i
$170$	−4.91102	+	1.09050i	−0.376658	+	0.0836373i
$171$		−	3.73356i		−	0.285512i
$172$	−11.4398	−	8.81001i	−0.872274	−	0.671757i
$173$	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
$178$	0.0940174	+	1.45399i	0.00704690	+	0.108981i
$179$	24.4156			1.82491			0.912455	−	0.409178i	$-0.134185\pi$
$179$	24.4156			1.82491			0.912455	+	0.409178i	$0.134185\pi$
$180$	3.91968	+	2.15316i	0.292156	+	0.160487i
$181$	11.2800			0.838439			0.419220	−	0.907885i	$-0.362304\pi$
$181$	11.2800			0.838439			0.419220	+	0.907885i	$0.362304\pi$
$182$	−1.06466	−	16.4652i	−0.0789180	−	1.22048i
$183$	−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
$188$	−3.62398	+	4.70572i	−0.264306	+	0.343200i
$189$		−	2.64002i		−	0.192033i
$190$	6.34027	−	9.95969i	0.459972	−	0.722552i
$191$			3.26729i			0.236413i	0.992989	+	0.118206i	$0.0377144\pi$
$191$			3.26729i			0.236413i	−0.992989	+	0.118206i	$0.962286\pi$
$192$	−7.37480	−	3.10037i	−0.532230	−	0.223750i
$193$	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	$0.773347\pi$
$198$	1.02813	−	0.0664803i	0.0730659	−	0.00472455i
$199$	−5.19059			−0.367951			−0.183975	−	0.982931i	$-0.558897\pi$
$199$	−5.19059			−0.367951			−0.183975	+	0.982931i	$0.558897\pi$
$200$	6.79974	+	12.4001i	0.480814	+	0.876823i
$201$	−7.21949			−0.509224
$202$	8.00230	−	0.517441i	0.563040	−	0.0364070i
$203$	−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
$208$	−8.89224	+	15.2776i	−0.616566	+	1.05931i
$209$		−	2.71995i		−	0.188143i
$210$	4.48325	−	7.04256i	0.309374	−	0.485983i
$211$			11.7800i			0.810967i	0.914102	+	0.405483i	$0.132897\pi$
$211$			11.7800i			0.810967i	−0.914102	+	0.405483i	$0.867103\pi$
$212$	0.836763	−	1.08653i	0.0574691	−	0.0746235i
$213$	−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
$218$	−1.43996	−	22.2692i	−0.0975264	−	1.50826i
$219$	−5.61404			−0.379361
$220$	2.85555	+	1.56861i	0.192521	+	0.105756i
$221$	−7.03028			−0.472908
$222$	0.403277	+	6.23675i	0.0270662	+	0.418583i
$223$	3.32381	+	3.32381i	0.222579	+	0.222579i	0.809583	−	0.587005i	$-0.199693\pi$
$223$	3.32381	+	3.32381i	0.222579	+	0.222579i	−0.587005	+	0.809583i	$0.699693\pi$
$224$	−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	$-0.613847\pi$
$227$	8.83851	−	8.83851i	0.586633	−	0.586633i	0.936718	+	0.350085i	$0.113847\pi$
$228$	5.91607	+	4.55609i	0.391801	+	0.301734i
$229$		−	7.09083i		−	0.468575i	−0.972167	−	0.234288i	$-0.924724\pi$
$229$		−	7.09083i		−	0.468575i	0.972167	−	0.234288i	$-0.0752757\pi$
$230$	−25.4678	+	5.65514i	−1.67929	+	0.372889i
$231$		−	1.92330i		−	0.126544i
$232$	1.43746	+	7.32745i	0.0943739	+	0.481071i
$233$	−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
$238$	−5.92707	+	0.383253i	−0.384195	+	0.0248426i
$239$	−0.706459			−0.0456970			−0.0228485	−	0.999739i	$-0.507274\pi$
$239$	−0.706459			−0.0456970			−0.0228485	+	0.999739i	$0.507274\pi$
$240$	−8.19504	+	3.58348i	−0.528988	+	0.231312i
$241$	−24.9991			−1.61033			−0.805166	−	0.593049i	$-0.797924\pi$
$241$	−24.9991			−1.61033			−0.805166	+	0.593049i	$0.797924\pi$
$242$	−14.7749	+	0.955368i	−0.949768	+	0.0614134i
$243$	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
$248$	−3.27242	−	16.6811i	−0.207799	−	1.05925i
$249$			5.03028i			0.318781i
$250$	15.2839	+	4.04989i	0.966640	+	0.256138i
$251$			28.6154i			1.80619i	0.429440	+	0.903095i	$0.358711\pi$
$251$			28.6154i			1.80619i	−0.429440	+	0.903095i	$0.641289\pi$
$252$	4.18329	+	3.22164i	0.263523	+	0.202944i
$253$	−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	$0.805107\pi$
$258$	−0.658812	−	10.1886i	−0.0410158	−	0.634316i
$259$	11.6669			0.724948
$260$	5.52018	+	18.9769i	0.342347	+	1.17690i
$261$	2.64002			0.163413
$262$	−0.417500	−	6.45670i	−0.0257932	−	0.398896i
$263$	−0.176615	−	0.176615i	−0.0108905	−	0.0108905i	0.701641	−	0.712531i	$-0.252451\pi$
$263$	−0.176615	−	0.176615i	−0.0108905	−	0.0108905i	−0.712531	+	0.701641i	$0.752451\pi$
$264$	−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
$268$	8.81001	−	11.4398i	0.538157	−	0.698795i
$269$		−	5.38934i		−	0.328594i	−0.986411	−	0.164297i	$-0.947465\pi$
$269$		−	5.38934i		−	0.328594i	0.986411	−	0.164297i	$-0.0525355\pi$
$270$	0.685490	+	3.08709i	0.0417176	+	0.187874i
$271$		−	15.4005i		−	0.935513i	−0.883857	−	0.467757i	$-0.845062\pi$
$271$		−	15.4005i		−	0.935513i	0.883857	−	0.467757i	$-0.154938\pi$
$272$	5.49958	+	3.20100i	0.333461	+	0.194089i
$273$	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	$0.631024\pi$
$278$	19.1794	−	1.24017i	1.15031	−	0.0743805i
$279$	−6.01008			−0.359814
$280$	5.68846	+	15.6981i	0.339951	+	0.938141i
$281$	−20.7493			−1.23780			−0.618900	−	0.785470i	$-0.712421\pi$
$281$	−20.7493			−1.23780			−0.618900	+	0.785470i	$0.712421\pi$
$282$	−4.19107	+	0.271001i	−0.249575	+	0.0161379i
$283$	18.5822	+	18.5822i	1.10459	+	1.10459i	0.993849	+	0.110745i	$0.0353238\pi$
$283$	18.5822	+	18.5822i	1.10459	+	1.10459i	0.110745	+	0.993849i	$0.464676\pi$
$284$	−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
$288$	−1.79480	−	5.36458i	−0.105759	−	0.316111i
$289$		−	14.4693i		−	0.851133i
$290$	7.04256	+	4.48325i	0.413554	+	0.263265i
$291$			17.7198i			1.03876i
$292$	6.85085	−	8.89581i	0.400916	−	0.520588i
$293$	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
$298$	−0.517441	−	8.00230i	−0.0299745	−	0.463561i
$299$	−36.4578			−2.10841
$300$	−3.41382	+	9.39925i	−0.197097	+	0.542666i
$301$	−19.0596			−1.09858
$302$	1.75639	+	27.1628i	0.101069	+	1.56304i
$303$	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	$-0.738370\pi$
$307$	0.905130	−	0.905130i	0.0516585	−	0.0516585i	0.732464	+	0.680806i	$0.238370\pi$
$308$	3.04759	+	2.34702i	0.173653	+	0.133734i
$309$		−	0.0799296i		−	0.00454704i
$310$	−16.0326	−	10.2062i	−0.910590	−	0.579675i
$311$		−	24.4377i		−	1.38573i	−0.721066	−	0.692867i	$-0.756347\pi$
$311$		−	24.4377i		−	1.38573i	0.721066	−	0.692867i	$-0.243653\pi$
$312$	−12.2657	+	2.40623i	−0.694411	+	0.136226i
$313$	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	$0.471718\pi$
$318$	0.967703	−	0.0625731i	0.0542661	−	0.00350893i
$319$	1.92330			0.107684
$320$	4.32222	−	17.3585i	0.241620	−	0.970371i
$321$	5.52982			0.308644
$322$	−30.7368	+	1.98749i	−1.71289	+	0.110758i
$323$	−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
$328$	11.7953	−	2.31395i	0.651289	−	0.127766i
$329$			7.84014i			0.432241i
$330$	0.499390	+	2.24899i	0.0274905	+	0.123803i
$331$		−	11.0294i		−	0.606231i	−0.952954	−	0.303115i	$-0.901973\pi$
$331$		−	11.0294i		−	0.606231i	0.952954	−	0.303115i	$-0.0980268\pi$
$332$	−7.97080	−	6.13849i	−0.437455	−	0.336893i
$333$	−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	$0.574197\pi$
$338$	0.595876	+	9.21531i	0.0324114	+	0.501247i
$339$	2.60900			0.141701
$340$	6.83125	−	1.98714i	0.370477	−	0.107768i
$341$	−4.37844			−0.237106
$342$	0.340704	+	5.26904i	0.0184232	+	0.284917i
$343$	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	$-0.514462\pi$
$347$	17.7627	−	17.7627i	0.953549	−	0.953549i	0.998968	+	0.0454187i	$0.0144622\pi$
$348$	−3.22164	+	4.18329i	−0.172698	+	0.224248i
$349$		−	14.6888i		−	0.786271i	−0.919480	−	0.393136i	$-0.871390\pi$
$349$		−	14.6888i		−	0.786271i	0.919480	−	0.393136i	$-0.128610\pi$
$350$	17.0985	+	7.49177i	0.913955	+	0.400452i
$351$			4.41926i			0.235882i
$352$	−1.30754	−	3.90818i	−0.0696919	−	0.208307i
$353$	−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
$358$	−34.4569	+	2.22804i	−1.82111	+	0.117755i
$359$	9.63060			0.508284			0.254142	−	0.967167i	$-0.418207\pi$
$359$	9.63060			0.508284			0.254142	+	0.967167i	$0.418207\pi$
$360$	−5.72820	−	2.68099i	−0.301903	−	0.141301i
$361$	−5.06055			−0.266345
$362$	−15.9192	+	1.02936i	−0.836692	+	0.0541017i
$363$	−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	$-0.943262\pi$
$367$	−15.4570	+	15.4570i	−0.806850	+	0.806850i	0.177306	+	0.984156i	$0.443262\pi$
$368$	28.5199	+	16.5998i	1.48670	+	0.865326i
$369$		−	4.24977i		−	0.221234i
$370$	−13.6426	+	3.02936i	−0.709246	+	0.157489i
$371$		−	1.81026i		−	0.0939840i
$372$	7.33415	−	9.52337i	0.380258	−	0.493764i
$373$	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
$378$	0.240914	+	3.72578i	0.0123913	+	0.191633i
$379$	5.89705			0.302911			0.151455	−	0.988464i	$-0.451604\pi$
$379$	5.89705			0.302911			0.151455	+	0.988464i	$0.451604\pi$
$380$	−8.03894	+	14.6344i	−0.412389	+	0.750727i
$381$	15.9201			0.815610
$382$	−0.298155	−	4.61102i	−0.0152549	−	0.235920i
$383$	0.642881	+	0.642881i	0.0328497	+	0.0328497i	0.723341	−	0.690491i	$-0.242606\pi$
$383$	0.642881	+	0.642881i	0.0328497	+	0.0328497i	−0.690491	+	0.723341i	$0.742606\pi$
$384$	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
$388$	−28.0782	−	21.6237i	−1.42546	−	1.09778i
$389$			18.8292i			0.954680i	0.878719	+	0.477340i	$0.158399\pi$
$389$			18.8292i			0.954680i	−0.878719	+	0.477340i	$0.841601\pi$
$390$	−7.50471	+	11.7889i	−0.380016	+	0.596953i
$391$			13.1240i			0.663708i
$392$	−0.0164850	−	0.0840320i	−0.000832616	−	0.00424426i
$393$	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	$-0.582017\pi$
$398$	7.32530	−	0.473665i	0.367184	−	0.0237427i
$399$	9.85668			0.493451
$400$	−10.7278	−	16.8794i	−0.536390	−	0.843970i
$401$	15.9394			0.795978			0.397989	−	0.917390i	$-0.369708\pi$
$401$	15.9394			0.795978			0.397989	+	0.917390i	$0.369708\pi$
$402$	10.1886	−	0.658812i	0.508163	−	0.0328586i
$403$	−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
$408$	0.866187	+	4.41538i	0.0428826	+	0.218594i
$409$			23.4087i			1.15749i	0.815510	+	0.578743i	$0.196457\pi$
$409$			23.4087i			1.15749i	−0.815510	+	0.578743i	$0.803543\pi$
$410$	7.21690	−	11.3368i	0.356417	−	0.559882i
$411$			5.79065i			0.285632i
$412$	0.126654	+	0.0975387i	0.00623978	+	0.00480539i
$413$	−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
$418$	0.248208	+	3.83858i	0.0121403	+	0.187751i
$419$	−28.0361			−1.36966			−0.684828	−	0.728705i	$-0.740122\pi$
$419$	−28.0361			−1.36966			−0.684828	+	0.728705i	$0.740122\pi$
$420$	−5.68439	+	10.3481i	−0.277370	+	0.504933i
$421$	17.4087			0.848449			0.424224	−	0.905557i	$-0.360547\pi$
$421$	17.4087			0.848449			0.424224	+	0.905557i	$0.360547\pi$
$422$	−1.07498	−	16.6247i	−0.0523290	−	0.809277i
$423$	−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
$428$	−6.74808	+	8.76236i	−0.326181	+	0.423545i
$429$			3.21949i			0.155439i
$430$	22.2872	−	4.94889i	1.07478	−	0.238657i
$431$			31.1542i			1.50065i	0.661071	+	0.750323i	$0.270102\pi$
$431$			31.1542i			1.50065i	−0.661071	+	0.750323i	$0.729898\pi$
$432$	2.01216	−	3.45705i	0.0968100	−	0.166328i
$433$	−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
$438$	7.92290	−	0.512307i	0.378571	−	0.0244790i
$439$	14.2967			0.682344			0.341172	−	0.940001i	$-0.389176\pi$
$439$	14.2967			0.682344			0.341172	+	0.940001i	$0.389176\pi$
$440$	−4.17308	−	1.95314i	−0.198944	−	0.0931125i
$441$	−0.0302761			−0.00144172
$442$	9.92159	−	0.641545i	0.471922	−	0.0305152i
$443$	7.02825	+	7.02825i	0.333922	+	0.333922i	0.854074	−	0.520152i	$-0.174125\pi$
$443$	7.02825	+	7.02825i	0.333922	+	0.333922i	−0.520152	+	0.854074i	$0.674125\pi$
$444$	−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
$448$	8.18505	−	19.4696i	0.386707	−	0.919854i
$449$		−	38.4608i		−	1.81508i	−0.419969	−	0.907538i	$-0.637959\pi$
$449$		−	38.4608i		−	1.81508i	0.419969	−	0.907538i	$-0.362041\pi$
$450$	−6.58629	+	2.57308i	−0.310481	+	0.121296i
$451$		−	3.09602i		−	0.145786i
$452$	−3.18378	+	4.13412i	−0.149752	+	0.194453i
$453$	−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	$0.697760\pi$
$458$	0.647071	+	10.0070i	0.0302356	+	0.467599i
$459$	1.59083			0.0742535
$460$	35.4257	−	10.3050i	1.65173	−	0.480471i
$461$	27.1689			1.26538			0.632691	−	0.774404i	$-0.281950\pi$
$461$	27.1689			1.26538			0.632691	+	0.774404i	$0.281950\pi$
$462$	0.175510	+	2.71428i	0.00816545	+	0.126280i
$463$	4.96280	+	4.96280i	0.230641	+	0.230641i	0.812960	−	0.582319i	$-0.197855\pi$
$463$	4.96280	+	4.96280i	0.230641	+	0.230641i	−0.582319	+	0.812960i	$0.697855\pi$
$464$	−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	$-0.994506\pi$
$467$	−21.2340	+	21.2340i	−0.982591	+	0.982591i	0.0172604	+	0.999851i	$0.494506\pi$
$468$	−7.00260	−	5.39285i	−0.323695	−	0.249285i
$469$		−	19.0596i		−	0.880092i
$470$	−2.03572	−	9.16779i	−0.0939006	−	0.422879i
$471$			2.96222i			0.136492i
$472$	13.6787	−	2.68342i	0.629614	−	0.123514i
$473$	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
$478$	0.997001	−	0.0644676i	0.0456018	−	0.00294868i
$479$	18.7808			0.858118			0.429059	−	0.903277i	$-0.358845\pi$
$479$	18.7808			0.858118			0.429059	+	0.903277i	$0.358845\pi$
$480$	11.2384	−	5.80507i	0.512959	−	0.264964i
$481$	−19.5298			−0.890483
$482$	35.2804	−	2.28128i	1.60698	−	0.103909i
$483$	−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	$-0.719656\pi$
$487$	2.97058	−	2.97058i	0.134610	−	0.134610i	0.771201	+	0.636591i	$0.219656\pi$
$488$	−6.41236	+	1.25794i	−0.290274	+	0.0569444i
$489$			6.06055i			0.274068i
$490$	−0.0807649	−	0.0514144i	−0.00364859	−	0.00232267i
$491$		−	29.5480i		−	1.33348i	−0.745290	−	0.666741i	$-0.767689\pi$
$491$		−	29.5480i		−	1.33348i	0.745290	−	0.666741i	$-0.232311\pi$
$492$	6.73404	+	5.18603i	0.303594	+	0.233804i
$493$	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
$498$	−0.459036	−	7.09906i	−0.0205699	−	0.318116i
$499$	15.0473			0.673608			0.336804	−	0.941575i	$-0.390654\pi$
$499$	15.0473			0.673608			0.336804	+	0.941575i	$0.390654\pi$
$500$	−21.9393	−	4.32075i	−0.981154	−	0.193230i
$501$	−6.18922			−0.276514
$502$	−2.61129	−	40.3840i	−0.116548	−	1.80243i
$503$	13.4136	+	13.4136i	0.598084	+	0.598084i	0.939802	−	0.341719i	$-0.111009\pi$
$503$	13.4136	+	13.4136i	0.598084	+	0.598084i	−0.341719	+	0.939802i	$0.611009\pi$
$504$	−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
$508$	−19.4274	+	25.2264i	−0.861951	+	1.11924i
$509$			41.4187i			1.83585i	0.396752	+	0.917926i	$0.370137\pi$
$509$			41.4187i			1.83585i	−0.396752	+	0.917926i	$0.629863\pi$
$510$	4.24372	+	2.70152i	0.187915	+	0.119625i
$511$		−	14.8212i		−	0.655651i
$512$	−18.9128	+	12.4220i	−0.835835	+	0.548981i
$513$	−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
$518$	−16.4652	+	1.06466i	−0.723437	+	0.0467785i
$519$	−23.2001			−1.01837
$520$	−9.52218	−	26.2778i	−0.417575	−	1.15236i
$521$	30.8392			1.35109			0.675545	−	0.737318i	$-0.263908\pi$
$521$	30.8392			1.35109			0.675545	+	0.737318i	$0.263908\pi$
$522$	−3.72578	+	0.240914i	−0.163073	+	0.0105445i
$523$	−17.1251	−	17.1251i	−0.748829	−	0.748829i	0.225430	−	0.974259i	$-0.427621\pi$
$523$	−17.1251	−	17.1251i	−0.748829	−	0.748829i	−0.974259	+	0.225430i	$0.927621\pi$
$524$	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
$528$	1.46589	−	2.51852i	0.0637945	−	0.109604i
$529$			45.0587i			1.95907i
$530$	0.470039	+	2.11681i	0.0204172	+	0.0919484i
$531$		−	4.92834i		−	0.213872i
$532$	−12.0282	+	15.6186i	−0.521488	+	0.677150i
$533$	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
$538$	0.491802	+	7.60579i	0.0212031	+	0.327909i
$539$	−0.0220566			−0.000950045
$540$	−1.24912	−	4.29415i	−0.0537536	−	0.184791i
$541$	−22.3397			−0.960458			−0.480229	−	0.877143i	$-0.659446\pi$
$541$	−22.3397			−0.960458			−0.480229	+	0.877143i	$0.659446\pi$
$542$	1.40537	+	21.7342i	0.0603656	+	0.933564i
$543$	−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	$0.527858\pi$
$547$	−25.3428	+	25.3428i	−1.08358	+	1.08358i	−0.996173	+	0.0874075i	$0.972142\pi$
$548$	−9.17567	−	7.06638i	−0.391965	−	0.301861i
$549$			2.31032i			0.0986022i
$550$	−4.79821	+	1.87453i	−0.204597	+	0.0799302i
$551$			9.85668i			0.419909i
$552$	4.49190	+	22.8974i	0.191188	+	0.974580i
$553$	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	$0.532093\pi$
$558$	8.48183	−	0.548448i	0.359064	−	0.0232176i
$559$	31.9048			1.34943
$560$	−9.46046	−	21.6351i	−0.399777	−	0.914250i
$561$	1.15894			0.0489306
$562$	29.2828	−	1.89347i	1.23522	−	0.0798712i
$563$	10.2955	+	10.2955i	0.433905	+	0.433905i	0.889955	−	0.456049i	$-0.150736\pi$
$563$	10.2955	+	10.2955i	0.433905	+	0.433905i	−0.456049	+	0.889955i	$0.650736\pi$
$564$	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
$568$	7.14584	+	36.4259i	0.299833	+	1.52840i
$569$		−	28.3179i		−	1.18715i	−0.804780	−	0.593574i	$-0.797717\pi$
$569$		−	28.3179i		−	1.18715i	0.804780	−	0.593574i	$-0.202283\pi$
$570$	−11.5258	+	2.55932i	−0.482763	+	0.107198i
$571$		−	27.2387i		−	1.13990i	−0.821678	−	0.569952i	$-0.806962\pi$
$571$		−	27.2387i		−	1.13990i	0.821678	−	0.569952i	$-0.193038\pi$
$572$	−5.10150	−	3.92878i	−0.213304	−	0.164270i
$573$	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	$0.704770\pi$
$578$	1.32039	+	20.4200i	0.0549208	+	0.849359i
$579$	−1.32858			−0.0552139
$580$	−10.3481	−	5.68439i	−0.429679	−	0.236032i
$581$	−13.2800			−0.550949
$582$	−1.61702	−	25.0074i	−0.0670275	−	1.03659i
$583$	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	$-0.704860\pi$
$587$	4.84271	−	4.84271i	0.199880	−	0.199880i	0.799948	+	0.600069i	$0.204860\pi$
$588$	0.0369462	−	0.0479745i	0.00152363	−	0.00197843i
$589$		−	22.4390i		−	0.924582i
$590$	8.36923	−	13.1469i	0.344556	−	0.541250i
$591$			2.05710i			0.0846176i
$592$	15.2776	+	8.89224i	0.627906	+	0.365469i
$593$	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
$598$	51.4517	−	3.32695i	2.10402	−	0.136049i
$599$	−30.2765			−1.23706			−0.618532	−	0.785760i	$-0.712272\pi$
$599$	−30.2765			−1.23706			−0.618532	+	0.785760i	$0.712272\pi$
$600$	3.96009	−	13.5764i	0.161670	−	0.554253i
$601$	30.1505			1.22986			0.614932	−	0.788581i	$-0.289184\pi$
$601$	30.1505			1.22986			0.614932	+	0.788581i	$0.289184\pi$
$602$	26.8982	−	1.73928i	1.09629	−	0.0708877i
$603$	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	$-0.560448\pi$
$607$	19.5438	−	19.5438i	0.793258	−	0.793258i	0.982022	+	0.188764i	$0.0604482\pi$
$608$	20.0290	−	6.70097i	0.812282	−	0.271760i
$609$			6.96972i			0.282427i
$610$	−3.92336	+	6.16305i	−0.158852	+	0.249535i
$611$		−	13.1240i		−	0.530939i
$612$	−1.94130	+	2.52077i	−0.0784724	+	0.101896i
$613$	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	$0.920558\pi$
$618$	0.00729394	+	0.112802i	0.000293405	+	0.00453756i
$619$	−38.9056			−1.56375			−0.781875	−	0.623435i	$-0.785736\pi$
$619$	−38.9056			−1.56375			−0.781875	+	0.623435i	$0.785736\pi$
$620$	23.5576	+	12.9407i	0.946097	+	0.519710i
$621$	8.24977			0.331052
$622$	2.23005	+	34.4881i	0.0894169	+	1.38285i
$623$	−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
$628$	−4.69384	−	3.61483i	−0.187305	−	0.144247i
$629$			7.03028i			0.280315i
$630$	−8.14998	+	1.80971i	−0.324703	+	0.0721006i
$631$		−	12.7707i		−	0.508395i	−0.967152	−	0.254198i	$-0.918189\pi$
$631$		−	12.7707i		−	0.508395i	0.967152	−	0.254198i	$-0.0818113\pi$
$632$	−19.7448	+	3.87342i	−0.785404	+	0.154077i
$633$	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
$638$	−2.71428	+	0.175510i	−0.107460	+	0.00694849i
$639$	13.1240			0.519176
$640$	−4.51576	+	24.8919i	−0.178501	+	0.983940i
$641$	−16.4683			−0.650461			−0.325230	−	0.945635i	$-0.605442\pi$
$641$	−16.4683			−0.650461			−0.325230	+	0.945635i	$0.605442\pi$
$642$	−7.80405	+	0.504621i	−0.308001	+	0.0199158i
$643$	5.74249	+	5.74249i	0.226462	+	0.226462i	0.811213	−	0.584751i	$-0.198808\pi$
$643$	5.74249	+	5.74249i	0.226462	+	0.226462i	−0.584751	+	0.811213i	$0.698808\pi$
$644$	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	$-0.790964\pi$
$647$	−4.61663	+	4.61663i	−0.181498	+	0.181498i	0.610510	+	0.792009i	$0.290964\pi$
$648$	2.77552	−	0.544488i	0.109033	−	0.0213895i
$649$		−	3.59037i		−	0.140934i
$650$	−28.6220	−	12.5408i	−1.12265	−	0.491891i
$651$		−	15.8668i		−	0.621867i
$652$	−9.60334	−	7.39574i	−0.376096	−	0.289640i
$653$	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
$658$	−0.715449	−	11.0645i	−0.0278911	−	0.431340i
$659$	35.5474			1.38473			0.692364	−	0.721548i	$-0.256569\pi$
$659$	35.5474			1.38473			0.692364	+	0.721548i	$0.256569\pi$
$660$	−0.910003	−	3.12835i	−0.0354218	−	0.121771i
$661$	15.1883			0.590756			0.295378	−	0.955380i	$-0.404554\pi$
$661$	15.1883			0.590756			0.295378	+	0.955380i	$0.404554\pi$
$662$	1.00648	+	15.5654i	0.0391181	+	0.604967i
$663$	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
$668$	7.55275	−	9.80722i	0.292225	−	0.379453i
$669$		−	4.70058i		−	0.181735i
$670$	4.94889	+	22.2872i	0.191192	+	0.861030i
$671$			1.68311i			0.0649756i
$672$	14.1626	−	4.73830i	0.546335	−	0.182784i
$673$	−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	$0.670774\pi$
$678$	−3.68199	+	0.238083i	−0.141406	+	0.00914351i
$679$	−46.7808			−1.79528
$680$	−9.45938	+	3.42776i	−0.362751	+	0.131449i
$681$	−12.4995			−0.478983
$682$	6.17914	−	0.399552i	0.236612	−	0.0152997i
$683$	−24.8545	−	24.8545i	−0.951030	−	0.951030i	0.0478253	−	0.998856i	$-0.484771\pi$
$683$	−24.8545	−	24.8545i	−0.951030	−	0.951030i	−0.998856	+	0.0478253i	$0.984771\pi$
$684$	−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
$688$	−24.9582	−	14.5268i	−0.951522	−	0.553827i
$689$			3.03028i			0.115444i
$690$	22.0072	+	14.0096i	0.837800	+	0.533338i
$691$			40.8979i			1.55583i	0.628371	+	0.777914i	$0.283722\pi$
$691$			40.8979i			1.55583i	−0.628371	+	0.777914i	$0.716278\pi$
$692$	28.3112	−	36.7620i	1.07623	−	1.39748i
$693$	−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
$698$	1.34042	+	20.7298i	0.0507355	+	0.784633i
$699$	21.7430			0.822398
$700$	−24.8142	−	9.01257i	−0.937890	−	0.340643i
$701$	−43.1396			−1.62936			−0.814679	−	0.579912i	$-0.803087\pi$
$701$	−43.1396			−1.62936			−0.814679	+	0.579912i	$0.803087\pi$
$702$	−0.403277	−	6.23675i	−0.0152207	−	0.235391i
$703$	−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
$708$	7.80928	+	6.01409i	0.293491	+	0.226023i
$709$		−	18.4702i		−	0.693662i	−0.937928	−	0.346831i	$-0.887258\pi$
$709$		−	18.4702i		−	0.693662i	0.937928	−	0.346831i	$-0.112742\pi$
$710$	35.0097	+	22.2869i	1.31389	+	0.836413i
$711$			7.11388i			0.266792i
$712$	0.560973	+	2.85956i	0.0210233	+	0.107166i
$713$	−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
$718$	−13.5913	+	0.878837i	−0.507225	+	0.0327979i
$719$	33.3725			1.24458			0.622292	−	0.782785i	$-0.286201\pi$
$719$	33.3725			1.24458			0.622292	+	0.782785i	$0.286201\pi$
$720$	8.32867	+	3.26087i	0.310391	+	0.121525i
$721$	0.211016			0.00785865
$722$	7.14179	−	0.461799i	0.265790	−	0.0171864i
$723$	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	$-0.959012\pi$
$727$	−23.2774	+	23.2774i	−0.863309	+	0.863309i	0.128412	+	0.991721i	$0.459012\pi$
$728$	−6.35251	−	32.3819i	−0.235440	−	1.20015i
$729$		−	1.00000i		−	0.0370370i
$730$	3.84837	+	17.3310i	0.142434	+	0.641450i
$731$		−	11.4850i		−	0.424787i
$732$	−3.66086	−	2.81931i	−0.135309	−	0.104205i
$733$	−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
$738$	0.387811	+	5.99756i	0.0142755	+	0.220773i
$739$	14.3408			0.527535			0.263768	−	0.964586i	$-0.415035\pi$
$739$	14.3408			0.527535			0.263768	+	0.964586i	$0.415035\pi$
$740$	18.9769	−	5.52018i	0.697606	−	0.202926i
$741$	−16.4995			−0.606126
$742$	0.165194	+	2.55476i	0.00606448	+	0.0937881i
$743$	−11.6034	−	11.6034i	−0.425686	−	0.425686i	0.461470	−	0.887156i	$-0.347322\pi$
$743$	−11.6034	−	11.6034i	−0.425686	−	0.425686i	−0.887156	+	0.461470i	$0.847322\pi$
$744$	−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
$748$	−1.41427	+	1.83642i	−0.0517107	+	0.0671462i
$749$			14.5988i			0.533430i
$750$	−7.94366	−	13.6711i	−0.290061	−	0.499197i
$751$			35.1721i			1.28345i	0.766936	+	0.641724i	$0.221780\pi$
$751$			35.1721i			1.28345i	−0.766936	+	0.641724i	$0.778220\pi$
$752$	−5.97555	+	10.2665i	−0.217906	+	0.374381i
$753$	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	$0.882611\pi$
$758$	−8.32230	+	0.538132i	−0.302280	+	0.0195459i
$759$	6.01008			0.218152
$760$	10.0096	−	21.3866i	0.363088	−	0.775772i
$761$	−24.4002			−0.884508			−0.442254	−	0.896890i	$-0.645821\pi$
$761$	−24.4002			−0.884508			−0.442254	+	0.896890i	$0.645821\pi$
$762$	−22.4675	+	1.45278i	−0.813910	+	0.0526286i
$763$	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
$768$	−15.4253	−	4.24959i	−0.556614	−	0.153344i
$769$		−	15.9688i		−	0.575850i	−0.957653	−	0.287925i	$-0.907035\pi$
$769$		−	15.9688i		−	0.575850i	0.957653	−	0.287925i	$-0.0929654\pi$
$770$	−5.93739	+	1.31840i	−0.213969	+	0.0475119i
$771$			5.52306i			0.198908i
$772$	1.62128	−	2.10522i	0.0583510	−	0.0757686i
$773$	−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
$778$	−1.71825	−	26.5731i	−0.0616024	−	0.952691i
$779$	15.8668			0.568486
$780$	9.51536	−	17.3221i	0.340705	−	0.620230i
$781$	9.56101			0.342120
$782$	−1.19762	−	18.5214i	−0.0428269	−	0.662324i
$783$	−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	$-0.810494\pi$
$787$	−7.49452	+	7.49452i	−0.267151	+	0.267151i	0.560800	+	0.827951i	$0.310494\pi$
$788$	−3.25960	−	2.51029i	−0.116119	−	0.0894254i
$789$			0.249771i			0.00889208i
$790$	−12.0807	+	18.9771i	−0.429812	+	0.675175i
$791$			6.88781i			0.244902i
$792$	2.02201	−	0.396668i	0.0718490	−	0.0140950i
$793$	−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	$0.522623\pi$
$798$	−13.9104	+	0.899467i	−0.492423	+	0.0318408i
$799$	−4.72432			−0.167134
$800$	16.6801	+	22.8424i	0.589731	+	0.807600i
$801$	1.03028			0.0364030
$802$	−22.4948	+	1.45455i	−0.794319	+	0.0513619i
$803$	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
$808$	15.7381	−	3.08741i	0.553663	−	0.108615i
$809$		−	23.7115i		−	0.833651i	−0.908987	−	0.416826i	$-0.863143\pi$
$809$		−	23.7115i		−	0.833651i	0.908987	−	0.416826i	$-0.136857\pi$
$810$	1.69819	−	2.66761i	0.0596681	−	0.0937304i
$811$		−	26.0077i		−	0.913255i	−0.889658	−	0.456628i	$-0.849057\pi$
$811$		−	26.0077i		−	0.913255i	0.889658	−	0.456628i	$-0.150943\pi$
$812$	−11.0440	−	8.50521i	−0.387568	−	0.298474i
$813$	−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
$818$	−2.13615	−	33.0359i	−0.0746888	−	1.15507i
$819$	−11.6669			−0.407676
$820$	−9.15043	+	16.6577i	−0.319547	+	0.581714i
$821$	33.0790			1.15447			0.577233	−	0.816580i	$-0.304133\pi$
$821$	33.0790			1.15447			0.577233	+	0.816580i	$0.304133\pi$
$822$	−0.528424	−	8.17215i	−0.0184309	−	0.285037i
$823$	−17.9737	−	17.9737i	−0.626525	−	0.626525i	0.320667	−	0.947192i	$-0.396093\pi$
$823$	−17.9737	−	17.9737i	−0.626525	−	0.626525i	−0.947192	+	0.320667i	$0.896093\pi$
$824$	−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	$-0.596450\pi$
$827$	18.8665	−	18.8665i	0.656051	−	0.656051i	0.954443	+	0.298392i	$0.0964504\pi$
$828$	−10.0673	+	13.0723i	−0.349862	+	0.454294i
$829$			3.28005i			0.113921i	0.998376	+	0.0569604i	$0.0181409\pi$
$829$			3.28005i			0.113921i	−0.998376	+	0.0569604i	$0.981859\pi$
$830$	15.5289	−	3.44820i	0.539016	−	0.119689i
$831$		−	12.1540i		−	0.421616i
$832$	−13.7013	+	32.5911i	−0.475008	+	1.12989i
$833$	−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
$838$	39.5665	−	2.55843i	1.36680	−	0.0883794i
$839$	−54.8854			−1.89486			−0.947428	−	0.319969i	$-0.896327\pi$
$839$	−54.8854			−1.89486			−0.947428	+	0.319969i	$0.896327\pi$
$840$	7.07788	−	15.1226i	0.244210	−	0.521779i
$841$	22.0303			0.759665
$842$	−24.5683	+	1.58862i	−0.846681	+	0.0547476i
$843$	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
$848$	1.37973	−	2.37050i	0.0473802	−	0.0814032i
$849$		−	26.2791i		−	0.901897i
$850$	−4.51440	+	10.3032i	−0.154843	+	0.353398i
$851$			36.4578i			1.24976i
$852$	−16.0153	+	20.7958i	−0.548675	+	0.712452i
$853$	−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	$0.819784\pi$
$858$	−0.293794	−	4.54356i	−0.0100299	−	0.155115i
$859$	24.6779			0.841998			0.420999	−	0.907061i	$-0.361680\pi$
$859$	24.6779			0.841998			0.420999	+	0.907061i	$0.361680\pi$
$860$	−31.0016	+	9.01801i	−1.05714	+	0.307512i
$861$	11.2195			0.382359
$862$	−2.84297	−	43.9669i	−0.0968318	−	1.49752i
$863$	−40.4811	−	40.4811i	−1.37799	−	1.37799i	−0.848009	−	0.529982i	$-0.822198\pi$
$863$	−40.4811	−	40.4811i	−1.37799	−	1.37799i	−0.529982	−	0.848009i	$-0.677802\pi$
$864$	−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
$868$	25.1419	+	19.3623i	0.853373	+	0.657201i
$869$			5.18257i			0.175807i
$870$	−1.80971	−	8.14998i	−0.0613549	−	0.276310i
$871$			31.9048i			1.08105i
$872$	−8.59179	−	43.7966i	−0.290955	−	1.48314i
$873$	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	$0.762126\pi$
$878$	−20.1764	+	1.30464i	−0.680922	+	0.0440294i
$879$	−8.81775			−0.297415
$880$	6.06756	+	2.37559i	0.204537	+	0.0800812i
$881$	33.2876			1.12149			0.560744	−	0.827989i	$-0.310515\pi$
$881$	33.2876			1.12149			0.560744	+	0.827989i	$0.310515\pi$
$882$	0.0427276	−	0.00276283i	0.00143871	−	9.30294e-5i
$883$	29.4296	+	29.4296i	0.990385	+	0.990385i	0.999954	−	0.00956956i	$-0.00304613\pi$
$883$	29.4296	+	29.4296i	0.990385	+	0.990385i	−0.00956956	+	0.999954i	$0.503046\pi$
$884$	−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	$-0.486957\pi$
$887$	30.9776	−	30.9776i	1.04013	−	1.04013i	0.999161	−	0.0409656i	$-0.0130434\pi$
$888$	2.40623	+	12.2657i	0.0807478	+	0.411612i
$889$			42.0294i			1.40962i
$890$	2.74838	+	1.74960i	0.0921259	+	0.0586467i
$891$		−	0.728515i		−	0.0244062i
$892$	7.44837	+	5.73615i	0.249390	+	0.192061i
$893$	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
$898$	3.50972	+	54.2784i	0.117121	+	1.81129i
$899$	15.8668			0.529186
$900$	9.06021	−	4.23233i	0.302007	−	0.141078i
$901$	1.09083			0.0363408
$902$	0.282526	+	4.36931i	0.00940709	+	0.145482i
$903$	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	$-0.514852\pi$
$907$	28.6790	−	28.6790i	0.952271	−	0.952271i	0.998912	+	0.0466405i	$0.0148515\pi$
$908$	15.2533	−	19.8063i	0.506198	−	0.657297i
$909$		−	5.67030i		−	0.188072i
$910$	−31.1229	−	19.8126i	−1.03171	−	0.656782i
$911$		−	31.8607i		−	1.05559i	−0.849371	−	0.527796i	$-0.823019\pi$
$911$		−	31.8607i		−	1.05559i	0.849371	−	0.527796i	$-0.176981\pi$
$912$	12.9071	+	7.51250i	0.427397	+	0.248764i
$913$	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
$918$	−2.24508	+	0.145170i	−0.0740988	+	0.00479134i
$919$	−55.4206			−1.82816			−0.914079	−	0.405536i	$-0.867085\pi$
$919$	−55.4206			−1.82816			−0.914079	+	0.405536i	$0.867085\pi$
$920$	−49.0548	+	17.7758i	−1.61729	+	0.586051i
$921$	−1.28005			−0.0421790
$922$	−38.3426	+	2.47929i	−1.26275	+	0.0816510i
$923$	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
$928$	4.73830	+	14.1626i	0.155542	+	0.464911i
$929$			46.9603i			1.54072i	0.637610	+	0.770359i	$0.279923\pi$
$929$			46.9603i			1.54072i	−0.637610	+	0.770359i	$0.720077\pi$
$930$	4.11985	+	18.5536i	0.135095	+	0.608398i
$931$		−	0.113038i		−	0.00370466i
$932$	−26.5332	+	34.4533i	−0.869124	+	1.12855i
$933$	−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	$0.672248\pi$
$938$	1.73928	+	26.8982i	0.0567895	+	0.878258i
$939$	−26.2908			−0.857966
$940$	3.70954	+	12.7524i	0.120992	+	0.415938i
$941$	−41.1084			−1.34009			−0.670047	−	0.742318i	$-0.733726\pi$
$941$	−41.1084			−1.34009			−0.670047	+	0.742318i	$0.733726\pi$
$942$	−0.270317	−	4.18049i	−0.00880739	−	0.136208i
$943$	−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	$-0.952072\pi$
$947$	−25.8091	+	25.8091i	−0.838682	+	0.838682i	0.150003	+	0.988685i	$0.452072\pi$
$948$	−11.2724	−	8.68113i	−0.366111	−	0.281950i
$949$			24.8099i			0.805362i
$950$	−9.60675	−	24.5903i	−0.311684	−	0.797815i
$951$		−	27.3143i		−	0.885726i
$952$	−11.6567	+	2.28675i	−0.377796	+	0.0741141i
$953$	−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
$958$	−26.5047	+	1.71384i	−0.856329	+	0.0553715i
$959$	−15.2875			−0.493658
$960$	−15.3306	+	9.21806i	−0.494793	+	0.297512i
$961$	−5.12110			−0.165197
$962$	27.5618	−	1.78219i	0.888627	−	0.0574600i
$963$	−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	$-0.664106\pi$
$967$	11.7235	−	11.7235i	0.377001	−	0.377001i	0.870019	+	0.493018i	$0.164106\pi$
$968$	−29.0577	+	5.70039i	−0.933950	+	0.183217i
$969$			5.93945i			0.190803i
$970$	54.7027	−	12.1468i	1.75640	−	0.390009i
$971$		−	12.9748i		−	0.416380i	−0.978088	−	0.208190i	$-0.933243\pi$
$971$		−	12.9748i		−	0.416380i	0.978088	−	0.208190i	$-0.0667572\pi$
$972$	1.58457	+	1.22031i	0.0508250	+	0.0391414i
$973$	−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	$0.851861\pi$
$978$	−0.553053	−	8.55305i	−0.0176847	−	0.273496i
$979$	0.750572			0.0239884
$980$	0.118673	+	0.0651893i	0.00379086	+	0.00208239i
$981$	−15.7796			−0.503803
$982$	2.69639	+	41.7001i	0.0860452	+	1.33070i
$983$	13.9381	+	13.9381i	0.444557	+	0.444557i	0.893540	−	0.448983i	$-0.148214\pi$
$983$	13.9381	+	13.9381i	0.444557	+	0.444557i	−0.448983	+	0.893540i	$0.648214\pi$
$984$	−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
$988$	20.1345	−	26.1446i	0.640565	−	0.831771i
$989$		−	59.5592i		−	1.89387i
$990$	1.23715	−	1.94340i	0.0393193	−	0.0617652i
$991$			52.9621i			1.68240i	0.540726	+	0.841199i	$0.318150\pi$
$991$			52.9621i			1.68240i	−0.540726	+	0.841199i	$0.681850\pi$
$992$	−10.7869	−	32.2416i	−0.342484	−	1.02367i
$993$	−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	$0.739059\pi$
$998$	−21.2357	+	1.37313i	−0.672204	+	0.0434657i
$999$	4.41926			0.139819

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.41127 + 0.0912546i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.98335 - 0.257569i) q^{4} +(1.32001 - 1.80487i) q^{5} +(1.06244 + 0.933389i) q^{6} +(1.86678 - 1.86678i) q^{7} +(-2.77552 + 0.544488i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-1.41127 + 0.0912546i) 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} +(-2.77552 + 0.544488i) q^{8} +1.00000i q^{9} +(-1.69819 + 2.66761i) q^{10} +0.728515i q^{11} +(-1.58457 - 1.22031i) 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} +(-0.0912546 - 1.41127i) q^{18} -3.73356 q^{19} +(2.15316 - 3.91968i) q^{20} -2.64002 q^{21} +(-0.0664803 - 1.02813i) 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} +(3.22164 - 4.18329i) q^{28} -2.64002i q^{29} +(3.08709 - 0.685490i) q^{30} +6.01008i q^{31} +(-5.36458 + 1.79480i) 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} +(5.26904 - 0.340704i) q^{38} +4.41926 q^{39} +(-2.68099 + 5.72820i) q^{40} -4.24977 q^{41} +(3.72578 - 0.240914i) 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} +(-3.45705 - 2.01216i) q^{48} +0.0302761i q^{49} +(2.57308 + 6.58629i) q^{50} -1.59083i q^{51} +(-5.39285 + 7.00260i) 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} +(0.240914 + 3.72578i) q^{58} -4.92834 q^{59} +(-4.29415 + 1.24912i) q^{60} +2.31032 q^{61} +(-0.548448 - 8.48183i) 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} +(2.52077 + 1.94130i) q^{68} -8.24977i q^{69} +(1.80971 + 8.14998i) q^{70} -13.1240i q^{71} +(-0.544488 - 2.77552i) 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} +(-6.23675 + 0.403277i) q^{78} +7.11388 q^{79} +(3.26087 - 8.32867i) q^{80} -1.00000 q^{81} +(5.99756 - 0.387811i) 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} +(-0.396668 - 2.02201i) q^{88} -1.03028i q^{89} +(-2.66761 - 1.69819i) q^{90} +11.6669i q^{91} +(13.0723 + 10.0673i) 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} +(-0.00276283 - 0.0427276i) 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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