LMFDB - Embedded newform 1110.2.o.a.487.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			487.3
Character	$\chi$	$=$	1110.487
Dual form			1110.2.o.a.253.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(0.0687789 + 2.23501i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.13605 + 2.13605i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(0.0687789 + 2.23501i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.13605 + 2.13605i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +(-0.0687789 - 2.23501i) q^{10} +2.07347i q^{11} +(-0.707107 - 0.707107i) q^{12} +4.31443 q^{13} +(-2.13605 - 2.13605i) q^{14} +(1.53176 - 1.62902i) q^{15} +1.00000 q^{16} +2.62056i q^{17} -1.00000i q^{18} +(1.48007 - 1.48007i) q^{19} +(0.0687789 + 2.23501i) q^{20} -3.02083i q^{21} -2.07347i q^{22} -3.49438 q^{23} +(0.707107 + 0.707107i) q^{24} +(-4.99054 + 0.307443i) q^{25} -4.31443 q^{26} +(0.707107 - 0.707107i) q^{27} +(2.13605 + 2.13605i) q^{28} +(0.364989 + 0.364989i) q^{29} +(-1.53176 + 1.62902i) q^{30} +(0.391381 - 0.391381i) q^{31} -1.00000 q^{32} +(1.46616 - 1.46616i) q^{33} -2.62056i q^{34} +(-4.62718 + 4.92101i) q^{35} +1.00000i q^{36} +(-2.65855 + 5.47103i) q^{37} +(-1.48007 + 1.48007i) q^{38} +(-3.05076 - 3.05076i) q^{39} +(-0.0687789 - 2.23501i) q^{40} -3.80013i q^{41} +3.02083i q^{42} -6.28607 q^{43} +2.07347i q^{44} +(-2.23501 + 0.0687789i) q^{45} +3.49438 q^{46} +(3.37898 + 3.37898i) q^{47} +(-0.707107 - 0.707107i) q^{48} +2.12544i q^{49} +(4.99054 - 0.307443i) q^{50} +(1.85302 - 1.85302i) q^{51} +4.31443 q^{52} +(-1.87850 + 1.87850i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(-4.63422 + 0.142611i) q^{55} +(-2.13605 - 2.13605i) q^{56} -2.09313 q^{57} +(-0.364989 - 0.364989i) q^{58} +(-0.917356 + 0.917356i) q^{59} +(1.53176 - 1.62902i) q^{60} +(5.87589 - 5.87589i) q^{61} +(-0.391381 + 0.391381i) q^{62} +(-2.13605 + 2.13605i) q^{63} +1.00000 q^{64} +(0.296742 + 9.64280i) q^{65} +(-1.46616 + 1.46616i) q^{66} +(-3.05783 + 3.05783i) q^{67} +2.62056i q^{68} +(2.47090 + 2.47090i) q^{69} +(4.62718 - 4.92101i) q^{70} -9.16581 q^{71} -1.00000i q^{72} +(8.50139 + 8.50139i) q^{73} +(2.65855 - 5.47103i) q^{74} +(3.74624 + 3.31145i) q^{75} +(1.48007 - 1.48007i) q^{76} +(-4.42903 + 4.42903i) q^{77} +(3.05076 + 3.05076i) q^{78} +(9.01137 - 9.01137i) q^{79} +(0.0687789 + 2.23501i) q^{80} -1.00000 q^{81} +3.80013i q^{82} +(-0.381394 + 0.381394i) q^{83} -3.02083i q^{84} +(-5.85698 + 0.180239i) q^{85} +6.28607 q^{86} -0.516172i q^{87} -2.07347i q^{88} +(3.68659 + 3.68659i) q^{89} +(2.23501 - 0.0687789i) q^{90} +(9.21585 + 9.21585i) q^{91} -3.49438 q^{92} -0.553497 q^{93} +(-3.37898 - 3.37898i) q^{94} +(3.40977 + 3.20617i) q^{95} +(0.707107 + 0.707107i) q^{96} +14.1415i q^{97} -2.12544i q^{98} -2.07347 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	1.00000			0.500000
$5$	0.0687789	+	2.23501i	0.0307589	+	0.999527i
$5$	0.0687789	+	2.23501i	0.0307589	+	0.999527i
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	2.13605	+	2.13605i	0.807352	+	0.807352i	0.984232	−	0.176880i	$-0.0566006\pi$
$7$	2.13605	+	2.13605i	0.807352	+	0.807352i	−0.176880	+	0.984232i	$0.556601\pi$
$8$	−1.00000			−0.353553
$9$			1.00000i			0.333333i
$10$	−0.0687789	−	2.23501i	−0.0217498	−	0.706772i
$11$			2.07347i			0.625174i	0.949889	+	0.312587i	$0.101196\pi$
$11$			2.07347i			0.625174i	−0.949889	+	0.312587i	$0.898804\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	4.31443			1.19661			0.598304	−	0.801269i	$-0.295842\pi$
$13$	4.31443			1.19661			0.598304	+	0.801269i	$0.295842\pi$
$14$	−2.13605	−	2.13605i	−0.570884	−	0.570884i
$15$	1.53176	−	1.62902i	0.395498	−	0.420612i
$16$	1.00000			0.250000
$17$			2.62056i			0.635579i	0.948161	+	0.317790i	$0.102941\pi$
$17$			2.62056i			0.635579i	−0.948161	+	0.317790i	$0.897059\pi$
$18$		−	1.00000i		−	0.235702i
$19$	1.48007	−	1.48007i	0.339551	−	0.339551i	−0.516647	−	0.856198i	$-0.672820\pi$
$19$	1.48007	−	1.48007i	0.339551	−	0.339551i	0.856198	+	0.516647i	$0.172820\pi$
$20$	0.0687789	+	2.23501i	0.0153794	+	0.499763i
$21$		−	3.02083i		−	0.659200i
$22$		−	2.07347i		−	0.442065i
$23$	−3.49438			−0.728628			−0.364314	−	0.931276i	$-0.618697\pi$
$23$	−3.49438			−0.728628			−0.364314	+	0.931276i	$0.618697\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$	−4.99054	+	0.307443i	−0.998108	+	0.0614886i
$26$	−4.31443			−0.846129
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	2.13605	+	2.13605i	0.403676	+	0.403676i
$29$	0.364989	+	0.364989i	0.0677767	+	0.0677767i	0.740183	−	0.672406i	$-0.234739\pi$
$29$	0.364989	+	0.364989i	0.0677767	+	0.0677767i	−0.672406	+	0.740183i	$0.734739\pi$
$30$	−1.53176	+	1.62902i	−0.279659	+	0.297418i
$31$	0.391381	−	0.391381i	0.0702942	−	0.0702942i	−0.671086	−	0.741380i	$-0.734172\pi$
$31$	0.391381	−	0.391381i	0.0702942	−	0.0702942i	0.741380	+	0.671086i	$0.234172\pi$
$32$	−1.00000			−0.176777
$33$	1.46616	−	1.46616i	0.255226	−	0.255226i
$34$		−	2.62056i		−	0.449422i
$35$	−4.62718	+	4.92101i	−0.782137	+	0.831803i
$36$			1.00000i			0.166667i
$37$	−2.65855	+	5.47103i	−0.437062	+	0.899431i
$37$	−2.65855	+	5.47103i	−0.437062	+	0.899431i
$38$	−1.48007	+	1.48007i	−0.240099	+	0.240099i
$39$	−3.05076	−	3.05076i	−0.488513	−	0.488513i
$40$	−0.0687789	−	2.23501i	−0.0108749	−	0.353386i
$41$		−	3.80013i		−	0.593481i	−0.954958	−	0.296740i	$-0.904100\pi$
$41$		−	3.80013i		−	0.593481i	0.954958	−	0.296740i	$-0.0958996\pi$
$42$			3.02083i			0.466125i
$43$	−6.28607			−0.958617			−0.479308	−	0.877647i	$-0.659112\pi$
$43$	−6.28607			−0.958617			−0.479308	+	0.877647i	$0.659112\pi$
$44$			2.07347i			0.312587i
$45$	−2.23501	+	0.0687789i	−0.333176	+	0.0102530i
$46$	3.49438			0.515218
$47$	3.37898	+	3.37898i	0.492876	+	0.492876i	0.909211	−	0.416336i	$-0.136686\pi$
$47$	3.37898	+	3.37898i	0.492876	+	0.492876i	−0.416336	+	0.909211i	$0.636686\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$			2.12544i			0.303634i
$50$	4.99054	−	0.307443i	0.705769	−	0.0434790i
$51$	1.85302	−	1.85302i	0.259474	−	0.259474i
$52$	4.31443			0.598304
$53$	−1.87850	+	1.87850i	−0.258031	+	0.258031i	−0.824253	−	0.566222i	$-0.808405\pi$
$53$	−1.87850	+	1.87850i	−0.258031	+	0.258031i	0.566222	+	0.824253i	$0.308405\pi$
$54$	−0.707107	+	0.707107i	−0.0962250	+	0.0962250i
$55$	−4.63422	+	0.142611i	−0.624878	+	0.0192296i
$56$	−2.13605	−	2.13605i	−0.285442	−	0.285442i
$57$	−2.09313			−0.277242
$58$	−0.364989	−	0.364989i	−0.0479254	−	0.0479254i
$59$	−0.917356	+	0.917356i	−0.119430	+	0.119430i	−0.764296	−	0.644866i	$-0.776913\pi$
$59$	−0.917356	+	0.917356i	−0.119430	+	0.119430i	0.644866	+	0.764296i	$0.276913\pi$
$60$	1.53176	−	1.62902i	0.197749	−	0.210306i
$61$	5.87589	−	5.87589i	0.752331	−	0.752331i	−0.222583	−	0.974914i	$-0.571449\pi$
$61$	5.87589	−	5.87589i	0.752331	−	0.752331i	0.974914	+	0.222583i	$0.0714489\pi$
$62$	−0.391381	+	0.391381i	−0.0497055	+	0.0497055i
$63$	−2.13605	+	2.13605i	−0.269117	+	0.269117i
$64$	1.00000			0.125000
$65$	0.296742	+	9.64280i	0.0368063	+	1.19604i
$66$	−1.46616	+	1.46616i	−0.180472	+	0.180472i
$67$	−3.05783	+	3.05783i	−0.373573	+	0.373573i	−0.868777	−	0.495204i	$-0.835093\pi$
$67$	−3.05783	+	3.05783i	−0.373573	+	0.373573i	0.495204	+	0.868777i	$0.335093\pi$
$68$			2.62056i			0.317790i
$69$	2.47090	+	2.47090i	0.297461	+	0.297461i
$70$	4.62718	−	4.92101i	0.553054	−	0.588174i
$71$	−9.16581			−1.08778			−0.543891	−	0.839156i	$-0.683049\pi$
$71$	−9.16581			−1.08778			−0.543891	+	0.839156i	$0.683049\pi$
$72$		−	1.00000i		−	0.117851i
$73$	8.50139	+	8.50139i	0.995012	+	0.995012i	0.999988	−	0.00497545i	$-0.00158374\pi$
$73$	8.50139	+	8.50139i	0.995012	+	0.995012i	−0.00497545	+	0.999988i	$0.501584\pi$
$74$	2.65855	−	5.47103i	0.309050	−	0.635994i
$75$	3.74624	+	3.31145i	0.432578	+	0.382373i
$76$	1.48007	−	1.48007i	0.169776	−	0.169776i
$77$	−4.42903	+	4.42903i	−0.504735	+	0.504735i
$78$	3.05076	+	3.05076i	0.345431	+	0.345431i
$79$	9.01137	−	9.01137i	1.01386	−	1.01386i	0.0139555	−	0.999903i	$-0.495558\pi$
$79$	9.01137	−	9.01137i	1.01386	−	1.01386i	0.999903	−	0.0139555i	$-0.00444231\pi$
$80$	0.0687789	+	2.23501i	0.00768972	+	0.249882i
$81$	−1.00000			−0.111111
$82$			3.80013i			0.419654i
$83$	−0.381394	+	0.381394i	−0.0418634	+	0.0418634i	−0.727729	−	0.685865i	$-0.759424\pi$
$83$	−0.381394	+	0.381394i	−0.0418634	+	0.0418634i	0.685865	+	0.727729i	$0.259424\pi$
$84$		−	3.02083i		−	0.329600i
$85$	−5.85698	+	0.180239i	−0.635278	+	0.0195497i
$86$	6.28607			0.677844
$87$		−	0.516172i		−	0.0553395i
$88$		−	2.07347i		−	0.221032i
$89$	3.68659	+	3.68659i	0.390778	+	0.390778i	0.874965	−	0.484187i	$-0.160884\pi$
$89$	3.68659	+	3.68659i	0.390778	+	0.390778i	−0.484187	+	0.874965i	$0.660884\pi$
$90$	2.23501	−	0.0687789i	0.235591	−	0.00724994i
$91$	9.21585	+	9.21585i	0.966084	+	0.966084i
$92$	−3.49438			−0.364314
$93$	−0.553497			−0.0573950
$94$	−3.37898	−	3.37898i	−0.348516	−	0.348516i
$95$	3.40977	+	3.20617i	0.349835	+	0.328946i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$			14.1415i			1.43586i	0.696117	+	0.717928i	$0.254909\pi$
$97$			14.1415i			1.43586i	−0.696117	+	0.717928i	$0.745091\pi$
$98$		−	2.12544i		−	0.214702i
$99$	−2.07347			−0.208391
$100$	−4.99054	+	0.307443i	−0.499054	+	0.0307443i
$101$			7.64384i			0.760591i	0.924865	+	0.380295i	$0.124178\pi$
$101$			7.64384i			0.760591i	−0.924865	+	0.380295i	$0.875822\pi$
$102$	−1.85302	+	1.85302i	−0.183476	+	0.183476i
$103$			9.85885i			0.971422i	0.874120	+	0.485711i	$0.161439\pi$
$103$			9.85885i			0.971422i	−0.874120	+	0.485711i	$0.838561\pi$
$104$	−4.31443			−0.423065
$105$	6.75159	−	0.207770i	0.658888	−	0.0202763i
$106$	1.87850	−	1.87850i	0.182456	−	0.182456i
$107$	4.17096	+	4.17096i	0.403222	+	0.403222i	0.879367	−	0.476145i	$-0.157966\pi$
$107$	4.17096	+	4.17096i	0.403222	+	0.403222i	−0.476145	+	0.879367i	$0.657966\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	−0.461041	+	0.461041i	−0.0441597	+	0.0441597i	−0.728842	−	0.684682i	$-0.759941\pi$
$109$	−0.461041	+	0.461041i	−0.0441597	+	0.0441597i	0.684682	+	0.728842i	$0.259941\pi$
$110$	4.63422	−	0.142611i	0.441856	−	0.0135974i
$111$	5.74848	−	1.98872i	0.545621	−	0.188761i
$112$	2.13605	+	2.13605i	0.201838	+	0.201838i
$113$			17.3203i			1.62936i	0.579913	+	0.814678i	$0.303086\pi$
$113$			17.3203i			1.62936i	−0.579913	+	0.814678i	$0.696914\pi$
$114$	2.09313			0.196040
$115$	−0.240340	−	7.80997i	−0.0224118	−	0.728284i
$116$	0.364989	+	0.364989i	0.0338884	+	0.0338884i
$117$			4.31443i			0.398869i
$118$	0.917356	−	0.917356i	0.0844495	−	0.0844495i
$119$	−5.59765	+	5.59765i	−0.513136	+	0.513136i
$120$	−1.53176	+	1.62902i	−0.139830	+	0.148709i
$121$	6.70073			0.609158
$122$	−5.87589	+	5.87589i	−0.531978	+	0.531978i
$123$	−2.68710	+	2.68710i	−0.242287	+	0.242287i
$124$	0.391381	−	0.391381i	0.0351471	−	0.0351471i
$125$	−1.03038	−	11.1328i	−0.0921602	−	0.995744i
$126$	2.13605	−	2.13605i	0.190295	−	0.190295i
$127$	−6.18161	−	6.18161i	−0.548529	−	0.548529i	0.377486	−	0.926015i	$-0.376789\pi$
$127$	−6.18161	−	6.18161i	−0.548529	−	0.548529i	−0.926015	+	0.377486i	$0.876789\pi$
$128$	−1.00000			−0.0883883
$129$	4.44492	+	4.44492i	0.391354	+	0.391354i
$130$	−0.296742	−	9.64280i	−0.0260260	−	0.845729i
$131$	1.03836	−	1.03836i	0.0907217	−	0.0907217i	−0.660289	−	0.751011i	$-0.729566\pi$
$131$	1.03836	−	1.03836i	0.0907217	−	0.0907217i	0.751011	+	0.660289i	$0.229566\pi$
$132$	1.46616	−	1.46616i	0.127613	−	0.127613i
$133$	6.32301			0.548275
$134$	3.05783	−	3.05783i	0.264156	−	0.264156i
$135$	1.62902	+	1.53176i	0.140204	+	0.131833i
$136$		−	2.62056i		−	0.224711i
$137$	−13.3475	−	13.3475i	−1.14035	−	1.14035i	−0.988386	−	0.151966i	$-0.951440\pi$
$137$	−13.3475	−	13.3475i	−1.14035	−	1.14035i	−0.151966	−	0.988386i	$-0.548560\pi$
$138$	−2.47090	−	2.47090i	−0.210337	−	0.210337i
$139$	−12.1026			−1.02653			−0.513267	−	0.858229i	$-0.671565\pi$
$139$	−12.1026			−1.02653			−0.513267	+	0.858229i	$0.671565\pi$
$140$	−4.62718	+	4.92101i	−0.391068	+	0.415902i
$141$		−	4.77861i		−	0.402431i
$142$	9.16581			0.769177
$143$			8.94583i			0.748088i
$144$			1.00000i			0.0833333i
$145$	−0.790650	+	0.840857i	−0.0656599	+	0.0698294i
$146$	−8.50139	−	8.50139i	−0.703580	−	0.703580i
$147$	1.50291	−	1.50291i	0.123958	−	0.123958i
$148$	−2.65855	+	5.47103i	−0.218531	+	0.449716i
$149$			1.78006i			0.145828i	0.997338	+	0.0729141i	$0.0232299\pi$
$149$			1.78006i			0.145828i	−0.997338	+	0.0729141i	$0.976770\pi$
$150$	−3.74624	−	3.31145i	−0.305879	−	0.270379i
$151$		−	14.7620i		−	1.20132i	−0.799506	−	0.600658i	$-0.794905\pi$
$151$		−	14.7620i		−	1.20132i	0.799506	−	0.600658i	$-0.205095\pi$
$152$	−1.48007	+	1.48007i	−0.120049	+	0.120049i
$153$	−2.62056			−0.211860
$154$	4.42903	−	4.42903i	0.356902	−	0.356902i
$155$	0.901660	+	0.847823i	0.0724231	+	0.0680988i
$156$	−3.05076	−	3.05076i	−0.244257	−	0.244257i
$157$	3.02964	+	3.02964i	0.241792	+	0.241792i	0.817591	−	0.575799i	$-0.195309\pi$
$157$	3.02964	+	3.02964i	0.241792	+	0.241792i	−0.575799	+	0.817591i	$0.695309\pi$
$158$	−9.01137	+	9.01137i	−0.716906	+	0.716906i
$159$	2.65660			0.210682
$160$	−0.0687789	−	2.23501i	−0.00543745	−	0.176693i
$161$	−7.46418	−	7.46418i	−0.588260	−	0.588260i
$162$	1.00000			0.0785674
$163$		−	6.39530i		−	0.500918i	−0.968127	−	0.250459i	$-0.919418\pi$
$163$		−	6.39530i		−	0.500918i	0.968127	−	0.250459i	$-0.0805816\pi$
$164$		−	3.80013i		−	0.296740i
$165$	3.37773	+	3.17605i	0.262956	+	0.247255i
$166$	0.381394	−	0.381394i	0.0296019	−	0.0296019i
$167$		−	7.40255i		−	0.572826i	−0.958106	−	0.286413i	$-0.907537\pi$
$167$		−	7.40255i		−	0.572826i	0.958106	−	0.286413i	$-0.0924630\pi$
$168$			3.02083i			0.233062i
$169$	5.61431			0.431870
$170$	5.85698	−	0.180239i	0.449210	−	0.0138237i
$171$	1.48007	+	1.48007i	0.113184	+	0.113184i
$172$	−6.28607			−0.479308
$173$	16.3983	+	16.3983i	1.24674	+	1.24674i	0.957152	+	0.289586i	$0.0935175\pi$
$173$	16.3983	+	16.3983i	1.24674	+	1.24674i	0.289586	+	0.957152i	$0.406483\pi$
$174$			0.516172i			0.0391309i
$175$	−11.3168	−	10.0033i	−0.855467	−	0.756181i
$176$			2.07347i			0.156293i
$177$	1.29734			0.0975139
$178$	−3.68659	−	3.68659i	−0.276322	−	0.276322i
$179$	16.2448	+	16.2448i	1.21419	+	1.21419i	0.969634	+	0.244559i	$0.0786432\pi$
$179$	16.2448	+	16.2448i	1.21419	+	1.21419i	0.244559	+	0.969634i	$0.421357\pi$
$180$	−2.23501	+	0.0687789i	−0.166588	+	0.00512648i
$181$	−5.45708			−0.405621			−0.202811	−	0.979218i	$-0.565008\pi$
$181$	−5.45708			−0.405621			−0.202811	+	0.979218i	$0.565008\pi$
$182$	−9.21585	−	9.21585i	−0.683124	−	0.683124i
$183$	−8.30976			−0.614275
$184$	3.49438			0.257609
$185$	−12.4107	−	5.56559i	−0.912449	−	0.409190i
$186$	0.553497			0.0405844
$187$	−5.43364			−0.397347
$188$	3.37898	+	3.37898i	0.246438	+	0.246438i
$189$	3.02083			0.219733
$190$	−3.40977	−	3.20617i	−0.247370	−	0.232600i
$191$	−8.47691	−	8.47691i	−0.613367	−	0.613367i	0.330455	−	0.943822i	$-0.392798\pi$
$191$	−8.47691	−	8.47691i	−0.613367	−	0.613367i	−0.943822	+	0.330455i	$0.892798\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	−0.815237			−0.0586820			−0.0293410	−	0.999569i	$-0.509341\pi$
$193$	−0.815237			−0.0586820			−0.0293410	+	0.999569i	$0.509341\pi$
$194$		−	14.1415i		−	1.01530i
$195$	6.60866	−	7.02831i	0.473256	−	0.503308i
$196$			2.12544i			0.151817i
$197$	−12.1517	−	12.1517i	−0.865772	−	0.865772i	0.126229	−	0.992001i	$-0.459713\pi$
$197$	−12.1517	−	12.1517i	−0.865772	−	0.865772i	−0.992001	+	0.126229i	$0.959713\pi$
$198$	2.07347			0.147355
$199$	−6.43148	−	6.43148i	−0.455915	−	0.455915i	0.441397	−	0.897312i	$-0.354483\pi$
$199$	−6.43148	−	6.43148i	−0.455915	−	0.455915i	−0.897312	+	0.441397i	$0.854483\pi$
$200$	4.99054	−	0.307443i	0.352884	−	0.0217395i
$201$	4.32442			0.305021
$202$		−	7.64384i		−	0.537819i
$203$			1.55927i			0.109439i
$204$	1.85302	−	1.85302i	0.129737	−	0.129737i
$205$	8.49333	−	0.261369i	0.593200	−	0.0182548i
$206$		−	9.85885i		−	0.686899i
$207$		−	3.49438i		−	0.242876i
$208$	4.31443			0.299152
$209$	3.06887	+	3.06887i	0.212279	+	0.212279i
$210$	−6.75159	+	0.207770i	−0.465904	+	0.0143375i
$211$	−1.84896			−0.127287			−0.0636437	−	0.997973i	$-0.520272\pi$
$211$	−1.84896			−0.127287			−0.0636437	+	0.997973i	$0.520272\pi$
$212$	−1.87850	+	1.87850i	−0.129016	+	0.129016i
$213$	6.48120	+	6.48120i	0.444085	+	0.444085i
$214$	−4.17096	−	4.17096i	−0.285121	−	0.285121i
$215$	−0.432349	−	14.0494i	−0.0294860	−	0.958163i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	1.67202			0.113504
$218$	0.461041	−	0.461041i	0.0312256	−	0.0312256i
$219$		−	12.0228i		−	0.812424i
$220$	−4.63422	+	0.142611i	−0.312439	+	0.00961482i
$221$			11.3062i			0.760539i
$222$	−5.74848	+	1.98872i	−0.385812	+	0.133474i
$223$	4.85478	−	4.85478i	0.325100	−	0.325100i	−0.525620	−	0.850720i	$-0.676166\pi$
$223$	4.85478	−	4.85478i	0.325100	−	0.325100i	0.850720	+	0.525620i	$0.176166\pi$
$224$	−2.13605	−	2.13605i	−0.142721	−	0.142721i
$225$	−0.307443	−	4.99054i	−0.0204962	−	0.332703i
$226$		−	17.3203i		−	1.15213i
$227$		−	19.5601i		−	1.29825i	−0.760683	−	0.649123i	$-0.775136\pi$
$227$		−	19.5601i		−	1.29825i	0.760683	−	0.649123i	$-0.224864\pi$
$228$	−2.09313			−0.138621
$229$			5.52626i			0.365186i	0.983189	+	0.182593i	$0.0584490\pi$
$229$			5.52626i			0.365186i	−0.983189	+	0.182593i	$0.941551\pi$
$230$	0.240340	+	7.80997i	0.0158475	+	0.514974i
$231$	6.26360			0.412115
$232$	−0.364989	−	0.364989i	−0.0239627	−	0.0239627i
$233$	8.07622	+	8.07622i	0.529091	+	0.529091i	0.920301	−	0.391210i	$-0.127944\pi$
$233$	8.07622	+	8.07622i	0.529091	+	0.529091i	−0.391210	+	0.920301i	$0.627944\pi$
$234$		−	4.31443i		−	0.282043i
$235$	−7.31966	+	7.78447i	−0.477482	+	0.507803i
$236$	−0.917356	+	0.917356i	−0.0597148	+	0.0597148i
$237$	−12.7440			−0.827812
$238$	5.59765	−	5.59765i	0.362842	−	0.362842i
$239$	−1.04218	+	1.04218i	−0.0674129	+	0.0674129i	−0.740009	−	0.672597i	$-0.765179\pi$
$239$	−1.04218	+	1.04218i	−0.0674129	+	0.0674129i	0.672597	+	0.740009i	$0.265179\pi$
$240$	1.53176	−	1.62902i	0.0988745	−	0.105153i
$241$	2.39676	+	2.39676i	0.154389	+	0.154389i	0.780075	−	0.625686i	$-0.215181\pi$
$241$	2.39676	+	2.39676i	0.154389	+	0.154389i	−0.625686	+	0.780075i	$0.715181\pi$
$242$	−6.70073			−0.430739
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	5.87589	−	5.87589i	0.376165	−	0.376165i
$245$	−4.75038	+	0.146186i	−0.303491	+	0.00933945i
$246$	2.68710	−	2.68710i	0.171323	−	0.171323i
$247$	6.38566	−	6.38566i	0.406310	−	0.406310i
$248$	−0.391381	+	0.391381i	−0.0248527	+	0.0248527i
$249$	0.539372			0.0341813
$250$	1.03038	+	11.1328i	0.0651671	+	0.704097i
$251$	14.2994	−	14.2994i	0.902571	−	0.902571i	−0.0930871	−	0.995658i	$-0.529674\pi$
$251$	14.2994	−	14.2994i	0.902571	−	0.902571i	0.995658	+	0.0930871i	$0.0296735\pi$
$252$	−2.13605	+	2.13605i	−0.134559	+	0.134559i
$253$		−	7.24548i		−	0.455519i
$254$	6.18161	+	6.18161i	0.387869	+	0.387869i
$255$	4.26896	+	4.01406i	0.267332	+	0.251370i
$256$	1.00000			0.0625000
$257$		−	22.9481i		−	1.43146i	−0.698376	−	0.715731i	$-0.746094\pi$
$257$		−	22.9481i		−	1.43146i	0.698376	−	0.715731i	$-0.253906\pi$
$258$	−4.44492	−	4.44492i	−0.276729	−	0.276729i
$259$	−17.3652	+	6.00760i	−1.07902	+	0.373294i
$260$	0.296742	+	9.64280i	0.0184032	+	0.598021i
$261$	−0.364989	+	0.364989i	−0.0225922	+	0.0225922i
$262$	−1.03836	+	1.03836i	−0.0641499	+	0.0641499i
$263$	0.797307	+	0.797307i	0.0491641	+	0.0491641i	0.731261	−	0.682097i	$-0.238932\pi$
$263$	0.797307	+	0.797307i	0.0491641	+	0.0491641i	−0.682097	+	0.731261i	$0.738932\pi$
$264$	−1.46616	+	1.46616i	−0.0902361	+	0.0902361i
$265$	−4.32766	−	4.06926i	−0.265846	−	0.249973i
$266$	−6.32301			−0.387689
$267$		−	5.21363i		−	0.319069i
$268$	−3.05783	+	3.05783i	−0.186787	+	0.186787i
$269$			17.8697i			1.08954i	0.838587	+	0.544768i	$0.183382\pi$
$269$			17.8697i			1.08954i	−0.838587	+	0.544768i	$0.816618\pi$
$270$	−1.62902	−	1.53176i	−0.0991393	−	0.0932197i
$271$	−20.7623			−1.26122			−0.630610	−	0.776100i	$-0.717195\pi$
$271$	−20.7623			−1.26122			−0.630610	+	0.776100i	$0.717195\pi$
$272$			2.62056i			0.158895i
$273$		−	13.0332i		−	0.788804i
$274$	13.3475	+	13.3475i	0.806350	+	0.806350i
$275$	−0.637473	−	10.3477i	−0.0384411	−	0.623991i
$276$	2.47090	+	2.47090i	0.148731	+	0.148731i
$277$	17.8467			1.07230			0.536152	−	0.844122i	$-0.319878\pi$
$277$	17.8467			1.07230			0.536152	+	0.844122i	$0.319878\pi$
$278$	12.1026			0.725869
$279$	0.391381	+	0.391381i	0.0234314	+	0.0234314i
$280$	4.62718	−	4.92101i	0.276527	−	0.294087i
$281$	−10.2645	−	10.2645i	−0.612330	−	0.612330i	0.331223	−	0.943553i	$-0.392539\pi$
$281$	−10.2645	−	10.2645i	−0.612330	−	0.612330i	−0.943553	+	0.331223i	$0.892539\pi$
$282$			4.77861i			0.284562i
$283$			9.49377i			0.564346i	0.959364	+	0.282173i	$0.0910552\pi$
$283$			9.49377i			0.564346i	−0.959364	+	0.282173i	$0.908945\pi$
$284$	−9.16581			−0.543891
$285$	−0.143963	−	4.67818i	−0.00852766	−	0.277111i
$286$		−	8.94583i		−	0.528978i
$287$	8.11728	−	8.11728i	0.479148	−	0.479148i
$288$		−	1.00000i		−	0.0589256i
$289$	10.1327			0.596039
$290$	0.790650	−	0.840857i	0.0464286	−	0.0493768i
$291$	9.99958	−	9.99958i	0.586186	−	0.586186i
$292$	8.50139	+	8.50139i	0.497506	+	0.497506i
$293$	−1.37161	+	1.37161i	−0.0801303	+	0.0801303i	−0.746036	−	0.665906i	$-0.768045\pi$
$293$	−1.37161	+	1.37161i	−0.0801303	+	0.0801303i	0.665906	+	0.746036i	$0.268045\pi$
$294$	−1.50291	+	1.50291i	−0.0876517	+	0.0876517i
$295$	−2.11340	−	1.98721i	−0.123047	−	0.115700i
$296$	2.65855	−	5.47103i	0.154525	−	0.317997i
$297$	1.46616	+	1.46616i	0.0850754	+	0.0850754i
$298$		−	1.78006i		−	0.103116i
$299$	−15.0763			−0.871882
$300$	3.74624	+	3.31145i	0.216289	+	0.191187i
$301$	−13.4274	−	13.4274i	−0.773941	−	0.773941i
$302$			14.7620i			0.849459i
$303$	5.40501	−	5.40501i	0.310510	−	0.310510i
$304$	1.48007	−	1.48007i	0.0848878	−	0.0848878i
$305$	13.5368	+	12.7285i	0.775115	+	0.728834i
$306$	2.62056			0.149807
$307$	12.9742	−	12.9742i	0.740476	−	0.740476i	−0.232194	−	0.972670i	$-0.574590\pi$
$307$	12.9742	−	12.9742i	0.740476	−	0.740476i	0.972670	+	0.232194i	$0.0745903\pi$
$308$	−4.42903	+	4.42903i	−0.252368	+	0.252368i
$309$	6.97126	−	6.97126i	0.396581	−	0.396581i
$310$	−0.901660	−	0.847823i	−0.0512109	−	0.0481531i
$311$	21.1073	−	21.1073i	1.19689	−	1.19689i	0.221794	−	0.975094i	$-0.428809\pi$
$311$	21.1073	−	21.1073i	1.19689	−	1.19689i	0.975094	−	0.221794i	$-0.0711911\pi$
$312$	3.05076	+	3.05076i	0.172715	+	0.172715i
$313$	27.9746			1.58122			0.790608	−	0.612323i	$-0.209765\pi$
$313$	27.9746			1.58122			0.790608	+	0.612323i	$0.209765\pi$
$314$	−3.02964	−	3.02964i	−0.170973	−	0.170973i
$315$	−4.92101	−	4.62718i	−0.277268	−	0.260712i
$316$	9.01137	−	9.01137i	0.506929	−	0.506929i
$317$	4.72175	−	4.72175i	0.265200	−	0.265200i	−0.561963	−	0.827163i	$-0.689954\pi$
$317$	4.72175	−	4.72175i	0.265200	−	0.265200i	0.827163	+	0.561963i	$0.189954\pi$
$318$	−2.65660			−0.148975
$319$	−0.756793	+	0.756793i	−0.0423722	+	0.0423722i
$320$	0.0687789	+	2.23501i	0.00384486	+	0.124941i
$321$		−	5.89863i		−	0.329229i
$322$	7.46418	+	7.46418i	0.415962	+	0.415962i
$323$	3.87861	+	3.87861i	0.215812	+	0.215812i
$324$	−1.00000			−0.0555556
$325$	−21.5313	+	1.32644i	−1.19434	+	0.0735778i
$326$			6.39530i			0.354203i
$327$	0.652011			0.0360563
$328$			3.80013i			0.209827i
$329$			14.4354i			0.795848i
$330$	−3.37773	−	3.17605i	−0.185938	−	0.174836i
$331$	5.59691	+	5.59691i	0.307634	+	0.307634i	0.843991	−	0.536357i	$-0.180200\pi$
$331$	5.59691	+	5.59691i	0.307634	+	0.307634i	−0.536357	+	0.843991i	$0.680200\pi$
$332$	−0.381394	+	0.381394i	−0.0209317	+	0.0209317i
$333$	−5.47103	−	2.65855i	−0.299810	−	0.145687i
$334$			7.40255i			0.405049i
$335$	−7.04459	−	6.62397i	−0.384887	−	0.361906i
$336$		−	3.02083i		−	0.164800i
$337$	−15.5752	+	15.5752i	−0.848433	+	0.848433i	−0.989938	−	0.141505i	$-0.954806\pi$
$337$	−15.5752	+	15.5752i	−0.848433	+	0.848433i	0.141505	+	0.989938i	$0.454806\pi$
$338$	−5.61431			−0.305378
$339$	12.2473	−	12.2473i	0.665182	−	0.665182i
$340$	−5.85698	+	0.180239i	−0.317639	+	0.00977485i
$341$	0.811517	+	0.811517i	0.0439461	+	0.0439461i
$342$	−1.48007	−	1.48007i	−0.0800330	−	0.0800330i
$343$	10.4123	−	10.4123i	0.562212	−	0.562212i
$344$	6.28607			0.338922
$345$	−5.35254	+	5.69243i	−0.288171	+	0.306470i
$346$	−16.3983	−	16.3983i	−0.881577	−	0.881577i
$347$	7.34661			0.394386			0.197193	−	0.980365i	$-0.436817\pi$
$347$	7.34661			0.394386			0.197193	+	0.980365i	$0.436817\pi$
$348$		−	0.516172i		−	0.0276697i
$349$		−	5.62756i		−	0.301236i	−0.988592	−	0.150618i	$-0.951874\pi$
$349$		−	5.62756i		−	0.301236i	0.988592	−	0.150618i	$-0.0481264\pi$
$350$	11.3168	+	10.0033i	0.604907	+	0.534701i
$351$	3.05076	−	3.05076i	0.162838	−	0.162838i
$352$		−	2.07347i		−	0.110516i
$353$		−	25.6724i		−	1.36640i	−0.730231	−	0.683201i	$-0.760587\pi$
$353$		−	25.6724i		−	1.36640i	0.730231	−	0.683201i	$-0.239413\pi$
$354$	−1.29734			−0.0689527
$355$	−0.630414	−	20.4857i	−0.0334589	−	1.08727i
$356$	3.68659	+	3.68659i	0.195389	+	0.195389i
$357$	7.91628			0.418974
$358$	−16.2448	−	16.2448i	−0.858564	−	0.858564i
$359$		−	29.6458i		−	1.56465i	−0.622872	−	0.782324i	$-0.714034\pi$
$359$		−	29.6458i		−	1.56465i	0.622872	−	0.782324i	$-0.285966\pi$
$360$	2.23501	−	0.0687789i	0.117795	−	0.00362497i
$361$			14.6188i			0.769410i
$362$	5.45708			0.286818
$363$	−4.73813	−	4.73813i	−0.248688	−	0.248688i
$364$	9.21585	+	9.21585i	0.483042	+	0.483042i
$365$	−18.4160	+	19.5854i	−0.963936	+	1.02515i
$366$	8.30976			0.434358
$367$	−22.3758	−	22.3758i	−1.16801	−	1.16801i	−0.982677	−	0.185329i	$-0.940665\pi$
$367$	−22.3758	−	22.3758i	−1.16801	−	1.16801i	−0.185329	−	0.982677i	$-0.559335\pi$
$368$	−3.49438			−0.182157
$369$	3.80013			0.197827
$370$	12.4107	+	5.56559i	0.645199	+	0.289341i
$371$	−8.02514			−0.416644
$372$	−0.553497			−0.0286975
$373$	2.58745	+	2.58745i	0.133973	+	0.133973i	0.770913	−	0.636940i	$-0.219800\pi$
$373$	2.58745	+	2.58745i	0.133973	+	0.133973i	−0.636940	+	0.770913i	$0.719800\pi$
$374$	5.43364			0.280967
$375$	−7.14346	+	8.60064i	−0.368887	+	0.444135i
$376$	−3.37898	−	3.37898i	−0.174258	−	0.174258i
$377$	1.57472	+	1.57472i	0.0811022	+	0.0811022i
$378$	−3.02083			−0.155375
$379$			30.1390i			1.54814i	0.633102	+	0.774069i	$0.281781\pi$
$379$			30.1390i			1.54814i	−0.633102	+	0.774069i	$0.718219\pi$
$380$	3.40977	+	3.20617i	0.174917	+	0.164473i
$381$			8.74212i			0.447872i
$382$	8.47691	+	8.47691i	0.433716	+	0.433716i
$383$	−27.3379			−1.39690			−0.698451	−	0.715658i	$-0.746127\pi$
$383$	−27.3379			−1.39690			−0.698451	+	0.715658i	$0.746127\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	−10.2036	−	9.59431i	−0.520022	−	0.488971i
$386$	0.815237			0.0414945
$387$		−	6.28607i		−	0.319539i
$388$			14.1415i			0.717928i
$389$	−7.29908	+	7.29908i	−0.370078	+	0.370078i	−0.867506	−	0.497428i	$-0.834278\pi$
$389$	−7.29908	+	7.29908i	−0.370078	+	0.370078i	0.497428	+	0.867506i	$0.334278\pi$
$390$	−6.60866	+	7.02831i	−0.334642	+	0.355893i
$391$		−	9.15723i		−	0.463101i
$392$		−	2.12544i		−	0.107351i
$393$	−1.46846			−0.0740739
$394$	12.1517	+	12.1517i	0.612194	+	0.612194i
$395$	20.7603	+	19.5207i	1.04456	+	0.982193i
$396$	−2.07347			−0.104196
$397$	−23.8828	+	23.8828i	−1.19864	+	1.19864i	−0.224069	+	0.974573i	$0.571934\pi$
$397$	−23.8828	+	23.8828i	−1.19864	+	1.19864i	−0.974573	+	0.224069i	$0.928066\pi$
$398$	6.43148	+	6.43148i	0.322381	+	0.322381i
$399$	−4.47104	−	4.47104i	−0.223832	−	0.223832i
$400$	−4.99054	+	0.307443i	−0.249527	+	0.0153722i
$401$	9.30160	−	9.30160i	0.464500	−	0.464500i	−0.435627	−	0.900127i	$-0.643473\pi$
$401$	9.30160	−	9.30160i	0.464500	−	0.464500i	0.900127	+	0.435627i	$0.143473\pi$
$402$	−4.32442			−0.215683
$403$	1.68859	−	1.68859i	0.0841146	−	0.0841146i
$404$			7.64384i			0.380295i
$405$	−0.0687789	−	2.23501i	−0.00341765	−	0.111059i
$406$		−	1.55927i		−	0.0773853i
$407$	−11.3440	−	5.51241i	−0.562301	−	0.273240i
$408$	−1.85302	+	1.85302i	−0.0917379	+	0.0917379i
$409$	24.5847	+	24.5847i	1.21563	+	1.21563i	0.969146	+	0.246487i	$0.0792763\pi$
$409$	24.5847	+	24.5847i	1.21563	+	1.21563i	0.246487	+	0.969146i	$0.420724\pi$
$410$	−8.49333	+	0.261369i	−0.419456	+	0.0129081i
$411$			18.8762i			0.931093i
$412$			9.85885i			0.485711i
$413$	−3.91904			−0.192844
$414$			3.49438i			0.171739i
$415$	−0.878651	−	0.826187i	−0.0431313	−	0.0405559i
$416$	−4.31443			−0.211532
$417$	8.55786	+	8.55786i	0.419080	+	0.419080i
$418$	−3.06887	−	3.06887i	−0.150104	−	0.150104i
$419$		−	23.6748i		−	1.15659i	−0.815829	−	0.578294i	$-0.803719\pi$
$419$		−	23.6748i		−	1.15659i	0.815829	−	0.578294i	$-0.196281\pi$
$420$	6.75159	−	0.207770i	0.329444	−	0.0101381i
$421$	−26.6921	+	26.6921i	−1.30089	+	1.30089i	−0.373102	+	0.927790i	$0.621706\pi$
$421$	−26.6921	+	26.6921i	−1.30089	+	1.30089i	−0.927790	+	0.373102i	$0.878294\pi$
$422$	1.84896			0.0900058
$423$	−3.37898	+	3.37898i	−0.164292	+	0.164292i
$424$	1.87850	−	1.87850i	0.0912279	−	0.0912279i
$425$	−0.805673	−	13.0780i	−0.0390809	−	0.634376i
$426$	−6.48120	−	6.48120i	−0.314015	−	0.314015i
$427$	25.1024			1.21479
$428$	4.17096	+	4.17096i	0.201611	+	0.201611i
$429$	6.32566	−	6.32566i	0.305406	−	0.305406i
$430$	0.432349	+	14.0494i	0.0208497	+	0.677524i
$431$	25.8053	−	25.8053i	1.24300	−	1.24300i	0.284245	−	0.958752i	$-0.408257\pi$
$431$	25.8053	−	25.8053i	1.24300	−	1.24300i	0.958752	−	0.284245i	$-0.0917428\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−2.62555	+	2.62555i	−0.126176	+	0.126176i	−0.767375	−	0.641199i	$-0.778437\pi$
$433$	−2.62555	+	2.62555i	−0.126176	+	0.126176i	0.641199	+	0.767375i	$0.278437\pi$
$434$	−1.67202			−0.0802597
$435$	1.15365	−	0.0355018i	0.0553133	−	0.00170218i
$436$	−0.461041	+	0.461041i	−0.0220799	+	0.0220799i
$437$	−5.17192	+	5.17192i	−0.247407	+	0.247407i
$438$			12.0228i			0.574471i
$439$	−4.04448	−	4.04448i	−0.193033	−	0.193033i	0.603973	−	0.797005i	$-0.293584\pi$
$439$	−4.04448	−	4.04448i	−0.193033	−	0.193033i	−0.797005	+	0.603973i	$0.793584\pi$
$440$	4.63422	−	0.142611i	0.220928	−	0.00679871i
$441$	−2.12544			−0.101211
$442$		−	11.3062i		−	0.537782i
$443$	−0.534873	−	0.534873i	−0.0254126	−	0.0254126i	0.694286	−	0.719699i	$-0.255720\pi$
$443$	−0.534873	−	0.534873i	−0.0254126	−	0.0254126i	−0.719699	+	0.694286i	$0.755720\pi$
$444$	5.74848	−	1.98872i	0.272811	−	0.0943806i
$445$	−7.98601	+	8.49313i	−0.378573	+	0.402613i
$446$	−4.85478	+	4.85478i	−0.229881	+	0.229881i
$447$	1.25869	−	1.25869i	0.0595341	−	0.0595341i
$448$	2.13605	+	2.13605i	0.100919	+	0.100919i
$449$	15.2168	−	15.2168i	0.718124	−	0.718124i	−0.250097	−	0.968221i	$-0.580462\pi$
$449$	15.2168	−	15.2168i	0.718124	−	0.718124i	0.968221	+	0.250097i	$0.0804625\pi$
$450$	0.307443	+	4.99054i	0.0144930	+	0.235256i
$451$	7.87944			0.371029
$452$			17.3203i			0.814678i
$453$	−10.4383	+	10.4383i	−0.490435	+	0.490435i
$454$			19.5601i			0.917999i
$455$	−19.9637	+	21.2314i	−0.935911	+	0.995342i
$456$	2.09313			0.0980200
$457$		−	26.8366i		−	1.25536i	−0.778470	−	0.627682i	$-0.784004\pi$
$457$		−	26.8366i		−	1.25536i	0.778470	−	0.627682i	$-0.215996\pi$
$458$		−	5.52626i		−	0.258225i
$459$	1.85302	+	1.85302i	0.0864914	+	0.0864914i
$460$	−0.240340	−	7.80997i	−0.0112059	−	0.364142i
$461$	9.31792	+	9.31792i	0.433979	+	0.433979i	0.889980	−	0.456001i	$-0.150718\pi$
$461$	9.31792	+	9.31792i	0.433979	+	0.433979i	−0.456001	+	0.889980i	$0.650718\pi$
$462$	−6.26360			−0.291409
$463$	31.8446			1.47995			0.739973	−	0.672637i	$-0.234838\pi$
$463$	31.8446			1.47995			0.739973	+	0.672637i	$0.234838\pi$
$464$	0.364989	+	0.364989i	0.0169442	+	0.0169442i
$465$	−0.0380689	−	1.23707i	−0.00176540	−	0.0573678i
$466$	−8.07622	−	8.07622i	−0.374124	−	0.374124i
$467$			24.6295i			1.13972i	0.821743	+	0.569859i	$0.193002\pi$
$467$			24.6295i			1.13972i	−0.821743	+	0.569859i	$0.806998\pi$
$468$			4.31443i			0.199435i
$469$	−13.0634			−0.603210
$470$	7.31966	−	7.78447i	0.337631	−	0.359071i
$471$		−	4.28456i		−	0.197422i
$472$	0.917356	−	0.917356i	0.0422248	−	0.0422248i
$473$		−	13.0340i		−	0.599302i
$474$	12.7440			0.585351
$475$	−6.93131	+	7.84138i	−0.318030	+	0.359787i
$476$	−5.59765	+	5.59765i	−0.256568	+	0.256568i
$477$	−1.87850	−	1.87850i	−0.0860105	−	0.0860105i
$478$	1.04218	−	1.04218i	0.0476681	−	0.0476681i
$479$	3.98964	−	3.98964i	0.182291	−	0.182291i	−0.610062	−	0.792353i	$-0.708856\pi$
$479$	3.98964	−	3.98964i	0.182291	−	0.182291i	0.792353	+	0.610062i	$0.208856\pi$
$480$	−1.53176	+	1.62902i	−0.0699148	+	0.0743545i
$481$	−11.4701	+	23.6044i	−0.522992	+	1.07627i
$482$	−2.39676	−	2.39676i	−0.109169	−	0.109169i
$483$			10.5559i			0.480312i
$484$	6.70073			0.304579
$485$	−31.6065	+	0.972640i	−1.43518	+	0.0441653i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$			33.5571i			1.52062i	0.649561	+	0.760309i	$0.274953\pi$
$487$			33.5571i			1.52062i	−0.649561	+	0.760309i	$0.725047\pi$
$488$	−5.87589	+	5.87589i	−0.265989	+	0.265989i
$489$	−4.52216	+	4.52216i	−0.204499	+	0.204499i
$490$	4.75038	−	0.146186i	0.214600	−	0.00660399i
$491$	31.9342			1.44117			0.720585	−	0.693366i	$-0.243873\pi$
$491$	31.9342			1.44117			0.720585	+	0.693366i	$0.243873\pi$
$492$	−2.68710	+	2.68710i	−0.121144	+	0.121144i
$493$	−0.956475	+	0.956475i	−0.0430775	+	0.0430775i
$494$	−6.38566	+	6.38566i	−0.287304	+	0.287304i
$495$	−0.142611	−	4.63422i	−0.00640988	−	0.208293i
$496$	0.391381	−	0.391381i	0.0175735	−	0.0175735i
$497$	−19.5786	−	19.5786i	−0.878222	−	0.878222i
$498$	−0.539372			−0.0241698
$499$	25.1910	+	25.1910i	1.12770	+	1.12770i	0.990550	+	0.137154i	$0.0437956\pi$
$499$	25.1910	+	25.1910i	1.12770	+	1.12770i	0.137154	+	0.990550i	$0.456204\pi$
$500$	−1.03038	−	11.1328i	−0.0460801	−	0.497872i
$501$	−5.23439	+	5.23439i	−0.233855	+	0.233855i
$502$	−14.2994	+	14.2994i	−0.638214	+	0.638214i
$503$	6.19986			0.276438			0.138219	−	0.990402i	$-0.455862\pi$
$503$	6.19986			0.276438			0.138219	+	0.990402i	$0.455862\pi$
$504$	2.13605	−	2.13605i	0.0951473	−	0.0951473i
$505$	−17.0841	+	0.525735i	−0.760231	+	0.0233949i
$506$			7.24548i			0.322101i
$507$	−3.96992	−	3.96992i	−0.176310	−	0.176310i
$508$	−6.18161	−	6.18161i	−0.274265	−	0.274265i
$509$	2.76652			0.122624			0.0613120	−	0.998119i	$-0.480472\pi$
$509$	2.76652			0.122624			0.0613120	+	0.998119i	$0.480472\pi$
$510$	−4.26896	−	4.01406i	−0.189033	−	0.177746i
$511$			36.3188i			1.60665i
$512$	−1.00000			−0.0441942
$513$		−	2.09313i		−	0.0924141i
$514$			22.9481i			1.01220i
$515$	−22.0346	+	0.678081i	−0.970962	+	0.0298798i
$516$	4.44492	+	4.44492i	0.195677	+	0.195677i
$517$	−7.00621	+	7.00621i	−0.308133	+	0.308133i
$518$	17.3652	−	6.00760i	0.762983	−	0.263959i
$519$		−	23.1907i		−	1.01796i
$520$	−0.296742	−	9.64280i	−0.0130130	−	0.422865i
$521$			9.79854i			0.429282i	0.976693	+	0.214641i	$0.0688581\pi$
$521$			9.79854i			0.429282i	−0.976693	+	0.214641i	$0.931142\pi$
$522$	0.364989	−	0.364989i	0.0159751	−	0.0159751i
$523$	−10.5951			−0.463289			−0.231645	−	0.972800i	$-0.574411\pi$
$523$	−10.5951			−0.463289			−0.231645	+	0.972800i	$0.574411\pi$
$524$	1.03836	−	1.03836i	0.0453608	−	0.0453608i
$525$	0.928735	+	15.0756i	0.0405333	+	0.657953i
$526$	−0.797307	−	0.797307i	−0.0347642	−	0.0347642i
$527$	1.02564	+	1.02564i	0.0446775	+	0.0446775i
$528$	1.46616	−	1.46616i	0.0638065	−	0.0638065i
$529$	−10.7893			−0.469101
$530$	4.32766	+	4.06926i	0.187982	+	0.176757i
$531$	−0.917356	−	0.917356i	−0.0398099	−	0.0398099i
$532$	6.32301			0.274137
$533$		−	16.3954i		−	0.710163i
$534$			5.21363i			0.225616i
$535$	−9.03526	+	9.60901i	−0.390629	+	0.415434i
$536$	3.05783	−	3.05783i	0.132078	−	0.132078i
$537$		−	22.9736i		−	0.991385i
$538$		−	17.8697i		−	0.770418i
$539$	−4.40703			−0.189824
$540$	1.62902	+	1.53176i	0.0701021	+	0.0659163i
$541$	23.3766	+	23.3766i	1.00504	+	1.00504i	0.999987	+	0.00505037i	$0.00160759\pi$
$541$	23.3766	+	23.3766i	1.00504	+	1.00504i	0.00505037	+	0.999987i	$0.498392\pi$
$542$	20.7623			0.891818
$543$	3.85874	+	3.85874i	0.165594	+	0.165594i
$544$		−	2.62056i		−	0.112356i
$545$	−1.06214	−	0.998722i	−0.0454971	−	0.0427805i
$546$			13.0332i			0.557769i
$547$	−17.2554			−0.737787			−0.368894	−	0.929472i	$-0.620263\pi$
$547$	−17.2554			−0.737787			−0.368894	+	0.929472i	$0.620263\pi$
$548$	−13.3475	−	13.3475i	−0.570176	−	0.570176i
$549$	5.87589	+	5.87589i	0.250777	+	0.250777i
$550$	0.637473	+	10.3477i	0.0271820	+	0.441228i
$551$	1.08042			0.0460273
$552$	−2.47090	−	2.47090i	−0.105168	−	0.105168i
$553$	38.4975			1.63708
$554$	−17.8467			−0.758233
$555$	4.84019	+	12.7111i	0.205455	+	0.539557i
$556$	−12.1026			−0.513267
$557$	17.6010			0.745779			0.372889	−	0.927876i	$-0.378367\pi$
$557$	17.6010			0.745779			0.372889	+	0.927876i	$0.378367\pi$
$558$	−0.391381	−	0.391381i	−0.0165685	−	0.0165685i
$559$	−27.1208			−1.14709
$560$	−4.62718	+	4.92101i	−0.195534	+	0.207951i
$561$	3.84217	+	3.84217i	0.162216	+	0.162216i
$562$	10.2645	+	10.2645i	0.432983	+	0.432983i
$563$	24.3413			1.02586			0.512932	−	0.858429i	$-0.328559\pi$
$563$	24.3413			1.02586			0.512932	+	0.858429i	$0.328559\pi$
$564$		−	4.77861i		−	0.201216i
$565$	−38.7110	+	1.19127i	−1.62859	+	0.0501172i
$566$		−	9.49377i		−	0.399053i
$567$	−2.13605	−	2.13605i	−0.0897058	−	0.0897058i
$568$	9.16581			0.384589
$569$	3.96188	+	3.96188i	0.166090	+	0.166090i	0.785259	−	0.619168i	$-0.212530\pi$
$569$	3.96188	+	3.96188i	0.166090	+	0.166090i	−0.619168	+	0.785259i	$0.712530\pi$
$570$	0.143963	+	4.67818i	0.00602997	+	0.195947i
$571$	−12.7277			−0.532638			−0.266319	−	0.963885i	$-0.585807\pi$
$571$	−12.7277			−0.532638			−0.266319	+	0.963885i	$0.585807\pi$
$572$			8.94583i			0.374044i
$573$			11.9882i			0.500812i
$574$	−8.11728	+	8.11728i	−0.338809	+	0.338809i
$575$	17.4388	−	1.07432i	0.727250	−	0.0448024i
$576$			1.00000i			0.0416667i
$577$		−	30.3340i		−	1.26282i	−0.775449	−	0.631410i	$-0.782476\pi$
$577$		−	30.3340i		−	1.26282i	0.775449	−	0.631410i	$-0.217524\pi$
$578$	−10.1327			−0.421463
$579$	0.576459	+	0.576459i	0.0239568	+	0.0239568i
$580$	−0.790650	+	0.840857i	−0.0328300	+	0.0349147i
$581$	−1.62935			−0.0675970
$582$	−9.99958	+	9.99958i	−0.414496	+	0.414496i
$583$	−3.89500	−	3.89500i	−0.161315	−	0.161315i
$584$	−8.50139	−	8.50139i	−0.351790	−	0.351790i
$585$	−9.64280	+	0.296742i	−0.398681	+	0.0122688i
$586$	1.37161	−	1.37161i	0.0566606	−	0.0566606i
$587$	−25.0340			−1.03327			−0.516633	−	0.856207i	$-0.672815\pi$
$587$	−25.0340			−1.03327			−0.516633	+	0.856207i	$0.672815\pi$
$588$	1.50291	−	1.50291i	0.0619791	−	0.0619791i
$589$		−	1.15854i		−	0.0477369i
$590$	2.11340	+	1.98721i	0.0870071	+	0.0818120i
$591$			17.1851i			0.706900i
$592$	−2.65855	+	5.47103i	−0.109266	+	0.224858i
$593$	16.2930	−	16.2930i	0.669073	−	0.669073i	−0.288428	−	0.957502i	$-0.593133\pi$
$593$	16.2930	−	16.2930i	0.669073	−	0.669073i	0.957502	+	0.288428i	$0.0931327\pi$
$594$	−1.46616	−	1.46616i	−0.0601574	−	0.0601574i
$595$	−12.8958	−	12.1258i	−0.528677	−	0.497110i
$596$			1.78006i			0.0729141i
$597$			9.09548i			0.372253i
$598$	15.0763			0.616514
$599$			18.7185i			0.764818i	0.923993	+	0.382409i	$0.124905\pi$
$599$			18.7185i			0.764818i	−0.923993	+	0.382409i	$0.875095\pi$
$600$	−3.74624	−	3.31145i	−0.152940	−	0.135189i
$601$	−34.1418			−1.39267			−0.696337	−	0.717715i	$-0.745188\pi$
$601$	−34.1418			−1.39267			−0.696337	+	0.717715i	$0.745188\pi$
$602$	13.4274	+	13.4274i	0.547259	+	0.547259i
$603$	−3.05783	−	3.05783i	−0.124524	−	0.124524i
$604$		−	14.7620i		−	0.600658i
$605$	0.460869	+	14.9762i	0.0187370	+	0.608869i
$606$	−5.40501	+	5.40501i	−0.219564	+	0.219564i
$607$	15.4550			0.627298			0.313649	−	0.949539i	$-0.398449\pi$
$607$	15.4550			0.627298			0.313649	+	0.949539i	$0.398449\pi$
$608$	−1.48007	+	1.48007i	−0.0600247	+	0.0600247i
$609$	1.10257	−	1.10257i	0.0446784	−	0.0446784i
$610$	−13.5368	−	12.7285i	−0.548089	−	0.515363i
$611$	14.5784	+	14.5784i	0.589779	+	0.589779i
$612$	−2.62056			−0.105930
$613$	−25.2055	−	25.2055i	−1.01804	−	1.01804i	−0.999834	−	0.0182063i	$-0.994204\pi$
$613$	−25.2055	−	25.2055i	−1.01804	−	1.01804i	−0.0182063	−	0.999834i	$-0.505796\pi$
$614$	−12.9742	+	12.9742i	−0.523596	+	0.523596i
$615$	−6.19050	−	5.82087i	−0.249625	−	0.234720i
$616$	4.42903	−	4.42903i	0.178451	−	0.178451i
$617$	14.0812	−	14.0812i	0.566887	−	0.566887i	−0.364368	−	0.931255i	$-0.618715\pi$
$617$	14.0812	−	14.0812i	0.566887	−	0.566887i	0.931255	+	0.364368i	$0.118715\pi$
$618$	−6.97126	+	6.97126i	−0.280425	+	0.280425i
$619$	−11.5159			−0.462861			−0.231431	−	0.972851i	$-0.574341\pi$
$619$	−11.5159			−0.462861			−0.231431	+	0.972851i	$0.574341\pi$
$620$	0.901660	+	0.847823i	0.0362115	+	0.0340494i
$621$	−2.47090	+	2.47090i	−0.0991538	+	0.0991538i
$622$	−21.1073	+	21.1073i	−0.846327	+	0.846327i
$623$			15.7495i			0.630991i
$624$	−3.05076	−	3.05076i	−0.122128	−	0.122128i
$625$	24.8110	−	3.06861i	0.992438	−	0.122745i
$626$	−27.9746			−1.11809
$627$		−	4.34004i		−	0.173325i
$628$	3.02964	+	3.02964i	0.120896	+	0.120896i
$629$	−14.3372	−	6.96688i	−0.571660	−	0.277788i
$630$	4.92101	+	4.62718i	0.196058	+	0.184351i
$631$	24.9435	−	24.9435i	0.992985	−	0.992985i	−0.00699059	−	0.999976i	$-0.502225\pi$
$631$	24.9435	−	24.9435i	0.992985	−	0.992985i	0.999976	+	0.00699059i	$0.00222519\pi$
$632$	−9.01137	+	9.01137i	−0.358453	+	0.358453i
$633$	1.30741	+	1.30741i	0.0519649	+	0.0519649i
$634$	−4.72175	+	4.72175i	−0.187525	+	0.187525i
$635$	13.3908	−	14.2411i	0.531398	−	0.565142i
$636$	2.65660			0.105341
$637$			9.17007i			0.363331i
$638$	0.756793	−	0.756793i	0.0299617	−	0.0299617i
$639$		−	9.16581i		−	0.362594i
$640$	−0.0687789	−	2.23501i	−0.00271873	−	0.0883465i
$641$	41.0494			1.62136			0.810678	−	0.585492i	$-0.199099\pi$
$641$	41.0494			1.62136			0.810678	+	0.585492i	$0.199099\pi$
$642$			5.89863i			0.232800i
$643$		−	16.4624i		−	0.649212i	−0.945849	−	0.324606i	$-0.894768\pi$
$643$		−	16.4624i		−	0.649212i	0.945849	−	0.324606i	$-0.105232\pi$
$644$	−7.46418	−	7.46418i	−0.294130	−	0.294130i
$645$	−9.62873	+	10.2402i	−0.379131	+	0.403206i
$646$	−3.87861	−	3.87861i	−0.152602	−	0.152602i
$647$	40.3405			1.58595			0.792974	−	0.609256i	$-0.208532\pi$
$647$	40.3405			1.58595			0.792974	+	0.609256i	$0.208532\pi$
$648$	1.00000			0.0392837
$649$	−1.90211	−	1.90211i	−0.0746643	−	0.0746643i
$650$	21.5313	−	1.32644i	0.844528	−	0.0520273i
$651$	−1.18230	−	1.18230i	−0.0463379	−	0.0463379i
$652$		−	6.39530i		−	0.250459i
$653$			34.2938i			1.34202i	0.741449	+	0.671009i	$0.234139\pi$
$653$			34.2938i			1.34202i	−0.741449	+	0.671009i	$0.765861\pi$
$654$	−0.652011			−0.0254956
$655$	2.39216	+	2.24932i	0.0934692	+	0.0878883i
$656$		−	3.80013i		−	0.148370i
$657$	−8.50139	+	8.50139i	−0.331671	+	0.331671i
$658$		−	14.4354i		−	0.562750i
$659$	35.9415			1.40008			0.700040	−	0.714104i	$-0.253165\pi$
$659$	35.9415			1.40008			0.700040	+	0.714104i	$0.253165\pi$
$660$	3.37773	+	3.17605i	0.131478	+	0.123627i
$661$	15.5165	−	15.5165i	0.603520	−	0.603520i	−0.337725	−	0.941245i	$-0.609657\pi$
$661$	15.5165	−	15.5165i	0.603520	−	0.603520i	0.941245	+	0.337725i	$0.109657\pi$
$662$	−5.59691	−	5.59691i	−0.217530	−	0.217530i
$663$	7.99471	−	7.99471i	0.310489	−	0.310489i
$664$	0.381394	−	0.381394i	0.0148009	−	0.0148009i
$665$	0.434890	+	14.1320i	0.0168643	+	0.548015i
$666$	5.47103	+	2.65855i	0.211998	+	0.103017i
$667$	−1.27541	−	1.27541i	−0.0493841	−	0.0493841i
$668$		−	7.40255i		−	0.286413i
$669$	−6.86570			−0.265443
$670$	7.04459	+	6.62397i	0.272156	+	0.255906i
$671$	12.1835	+	12.1835i	0.470337	+	0.470337i
$672$			3.02083i			0.116531i
$673$	32.7754	−	32.7754i	1.26340	−	1.26340i	0.313966	−	0.949434i	$-0.398342\pi$
$673$	32.7754	−	32.7754i	1.26340	−	1.26340i	0.949434	−	0.313966i	$-0.101658\pi$
$674$	15.5752	−	15.5752i	0.599933	−	0.599933i
$675$	−3.31145	+	3.74624i	−0.127458	+	0.144193i
$676$	5.61431			0.215935
$677$	−5.04971	+	5.04971i	−0.194076	+	0.194076i	−0.797455	−	0.603379i	$-0.793821\pi$
$677$	−5.04971	+	5.04971i	−0.194076	+	0.194076i	0.603379	+	0.797455i	$0.293821\pi$
$678$	−12.2473	+	12.2473i	−0.470355	+	0.470355i
$679$	−30.2071	+	30.2071i	−1.15924	+	1.15924i
$680$	5.85698	−	0.180239i	0.224605	−	0.00691186i
$681$	−13.8310	+	13.8310i	−0.530007	+	0.530007i
$682$	−0.811517	−	0.811517i	−0.0310746	−	0.0310746i
$683$	35.9730			1.37647			0.688235	−	0.725488i	$-0.258386\pi$
$683$	35.9730			1.37647			0.688235	+	0.725488i	$0.258386\pi$
$684$	1.48007	+	1.48007i	0.0565919	+	0.0565919i
$685$	28.9137	−	30.7498i	1.10474	−	1.17489i
$686$	−10.4123	+	10.4123i	−0.397544	+	0.397544i
$687$	3.90766	−	3.90766i	0.149086	−	0.149086i
$688$	−6.28607			−0.239654
$689$	−8.10465	+	8.10465i	−0.308762	+	0.308762i
$690$	5.35254	−	5.69243i	0.203768	−	0.216707i
$691$		−	18.4832i		−	0.703135i	−0.936163	−	0.351567i	$-0.885649\pi$
$691$		−	18.4832i		−	0.703135i	0.936163	−	0.351567i	$-0.114351\pi$
$692$	16.3983	+	16.3983i	0.623369	+	0.623369i
$693$	−4.42903	−	4.42903i	−0.168245	−	0.168245i
$694$	−7.34661			−0.278873
$695$	−0.832407	−	27.0495i	−0.0315750	−	1.02605i
$696$			0.516172i			0.0195655i
$697$	9.95847			0.377204
$698$			5.62756i			0.213006i
$699$		−	11.4215i		−	0.432001i
$700$	−11.3168	−	10.0033i	−0.427734	−	0.378091i
$701$	−14.1983	−	14.1983i	−0.536264	−	0.536264i	0.386166	−	0.922429i	$-0.373799\pi$
$701$	−14.1983	−	14.1983i	−0.536264	−	0.536264i	−0.922429	+	0.386166i	$0.873799\pi$
$702$	−3.05076	+	3.05076i	−0.115144	+	0.115144i
$703$	4.16266	+	12.0323i	0.156998	+	0.453808i
$704$			2.07347i			0.0781467i
$705$	10.6802	−	0.328667i	0.402241	−	0.0123783i
$706$			25.6724i			0.966192i
$707$	−16.3276	+	16.3276i	−0.614064	+	0.614064i
$708$	1.29734			0.0487569
$709$	19.8820	−	19.8820i	0.746684	−	0.746684i	−0.227171	−	0.973855i	$-0.572947\pi$
$709$	19.8820	−	19.8820i	0.746684	−	0.746684i	0.973855	+	0.227171i	$0.0729475\pi$
$710$	0.630414	+	20.4857i	0.0236590	+	0.768814i
$711$	9.01137	+	9.01137i	0.337953	+	0.337953i
$712$	−3.68659	−	3.68659i	−0.138161	−	0.138161i
$713$	−1.36764	+	1.36764i	−0.0512183	+	0.0512183i
$714$	−7.91628			−0.296259
$715$	−19.9940	+	0.615285i	−0.747734	+	0.0230103i
$716$	16.2448	+	16.2448i	0.607097	+	0.607097i
$717$	1.47386			0.0550424
$718$			29.6458i			1.10637i
$719$		−	5.03356i		−	0.187720i	−0.995585	−	0.0938601i	$-0.970079\pi$
$719$		−	5.03356i		−	0.187720i	0.995585	−	0.0938601i	$-0.0299206\pi$
$720$	−2.23501	+	0.0687789i	−0.0832939	+	0.00256324i
$721$	−21.0590	+	21.0590i	−0.784279	+	0.784279i
$722$		−	14.6188i		−	0.544055i
$723$		−	3.38953i		−	0.126058i
$724$	−5.45708			−0.202811
$725$	−1.93370	−	1.70928i	−0.0718160	−	0.0634810i
$726$	4.73813	+	4.73813i	0.175849	+	0.175849i
$727$	−6.59381			−0.244551			−0.122275	−	0.992496i	$-0.539019\pi$
$727$	−6.59381			−0.244551			−0.122275	+	0.992496i	$0.539019\pi$
$728$	−9.21585	−	9.21585i	−0.341562	−	0.341562i
$729$		−	1.00000i		−	0.0370370i
$730$	18.4160	−	19.5854i	0.681606	−	0.724888i
$731$		−	16.4730i		−	0.609277i
$732$	−8.30976			−0.307138
$733$	32.6674	+	32.6674i	1.20660	+	1.20660i	0.972122	+	0.234474i	$0.0753369\pi$
$733$	32.6674	+	32.6674i	1.20660	+	1.20660i	0.234474	+	0.972122i	$0.424663\pi$
$734$	22.3758	+	22.3758i	0.825904	+	0.825904i
$735$	3.46240	+	3.25566i	0.127712	+	0.120087i
$736$	3.49438			0.128805
$737$	−6.34031	−	6.34031i	−0.233548	−	0.233548i
$738$	−3.80013			−0.139885
$739$	−2.57619			−0.0947665			−0.0473833	−	0.998877i	$-0.515088\pi$
$739$	−2.57619			−0.0947665			−0.0473833	+	0.998877i	$0.515088\pi$
$740$	−12.4107	−	5.56559i	−0.456225	−	0.204595i
$741$	−9.03068			−0.331750
$742$	8.02514			0.294612
$743$	−16.2323	−	16.2323i	−0.595504	−	0.595504i	0.343609	−	0.939113i	$-0.388351\pi$
$743$	−16.2323	−	16.2323i	−0.595504	−	0.595504i	−0.939113	+	0.343609i	$0.888351\pi$
$744$	0.553497			0.0202922
$745$	−3.97845	+	0.122431i	−0.145759	+	0.00448551i
$746$	−2.58745	−	2.58745i	−0.0947334	−	0.0947334i
$747$	−0.381394	−	0.381394i	−0.0139545	−	0.0139545i
$748$	−5.43364			−0.198674
$749$			17.8188i			0.651084i
$750$	7.14346	−	8.60064i	0.260842	−	0.314051i
$751$		−	9.18070i		−	0.335009i	−0.985871	−	0.167504i	$-0.946429\pi$
$751$		−	9.18070i		−	0.335009i	0.985871	−	0.167504i	$-0.0535708\pi$
$752$	3.37898	+	3.37898i	0.123219	+	0.123219i
$753$	−20.2224			−0.736946
$754$	−1.57472	−	1.57472i	−0.0573479	−	0.0573479i
$755$	32.9933	−	1.01532i	1.20075	−	0.0369511i
$756$	3.02083			0.109867
$757$			7.11882i			0.258738i	0.991597	+	0.129369i	$0.0412951\pi$
$757$			7.11882i			0.258738i	−0.991597	+	0.129369i	$0.958705\pi$
$758$		−	30.1390i		−	1.09470i
$759$	−5.12333	+	5.12333i	−0.185965	+	0.185965i
$760$	−3.40977	−	3.20617i	−0.123685	−	0.116300i
$761$			7.70500i			0.279306i	0.990200	+	0.139653i	$0.0445987\pi$
$761$			7.70500i			0.279306i	−0.990200	+	0.139653i	$0.955401\pi$
$762$		−	8.74212i		−	0.316694i
$763$	−1.96962			−0.0713049
$764$	−8.47691	−	8.47691i	−0.306684	−	0.306684i
$765$	−0.180239	−	5.85698i	−0.00651656	−	0.211759i
$766$	27.3379			0.987759
$767$	−3.95787	+	3.95787i	−0.142910	+	0.142910i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−30.6954	−	30.6954i	−1.10690	−	1.10690i	−0.993555	−	0.113349i	$-0.963842\pi$
$769$	−30.6954	−	30.6954i	−1.10690	−	1.10690i	−0.113349	−	0.993555i	$-0.536158\pi$
$770$	10.2036	+	9.59431i	0.367711	+	0.345755i
$771$	−16.2267	+	16.2267i	−0.584392	+	0.584392i
$772$	−0.815237			−0.0293410
$773$	−26.9674	+	26.9674i	−0.969949	+	0.969949i	−0.999561	−	0.0296121i	$-0.990573\pi$
$773$	−26.9674	+	26.9674i	−0.969949	+	0.969949i	0.0296121	+	0.999561i	$0.490573\pi$
$774$			6.28607i			0.225948i
$775$	−1.83288	+	2.07353i	−0.0658389	+	0.0744835i
$776$		−	14.1415i		−	0.507652i
$777$	16.5271	+	8.03103i	0.592905	+	0.288112i
$778$	7.29908	−	7.29908i	0.261685	−	0.261685i
$779$	−5.62445	−	5.62445i	−0.201517	−	0.201517i
$780$	6.60866	−	7.02831i	0.236628	−	0.251654i
$781$		−	19.0050i		−	0.680052i
$782$			9.15723i			0.327462i
$783$	0.516172			0.0184465
$784$			2.12544i			0.0759086i
$785$	−6.56290	+	6.97966i	−0.234240	+	0.249115i
$786$	1.46846			0.0523782
$787$	5.73093	+	5.73093i	0.204286	+	0.204286i	0.801833	−	0.597548i	$-0.203858\pi$
$787$	5.73093	+	5.73093i	0.204286	+	0.204286i	−0.597548	+	0.801833i	$0.703858\pi$
$788$	−12.1517	−	12.1517i	−0.432886	−	0.432886i
$789$		−	1.12756i		−	0.0401423i
$790$	−20.7603	−	19.5207i	−0.738618	−	0.694515i
$791$	−36.9971	+	36.9971i	−1.31546	+	1.31546i
$792$	2.07347			0.0736774
$793$	25.3511	−	25.3511i	0.900245	−	0.900245i
$794$	23.8828	−	23.8828i	0.847568	−	0.847568i
$795$	0.182718	+	5.93752i	0.00648033	+	0.210582i
$796$	−6.43148	−	6.43148i	−0.227958	−	0.227958i
$797$	53.4909			1.89474			0.947372	−	0.320135i	$-0.103728\pi$
$797$	53.4909			1.89474			0.947372	+	0.320135i	$0.103728\pi$
$798$	4.47104	+	4.47104i	0.158273	+	0.158273i
$799$	−8.85483	+	8.85483i	−0.313261	+	0.313261i
$800$	4.99054	−	0.307443i	0.176442	−	0.0108698i
$801$	−3.68659	+	3.68659i	−0.130259	+	0.130259i
$802$	−9.30160	+	9.30160i	−0.328451	+	0.328451i
$803$	−17.6273	+	17.6273i	−0.622056	+	0.622056i
$804$	4.32442			0.152511
$805$	16.1691	−	17.1959i	0.569887	−	0.606075i
$806$	−1.68859	+	1.68859i	−0.0594780	+	0.0594780i
$807$	12.6358	−	12.6358i	0.444801	−	0.444801i
$808$		−	7.64384i		−	0.268909i
$809$	−18.8689	−	18.8689i	−0.663396	−	0.663396i	0.292783	−	0.956179i	$-0.405419\pi$
$809$	−18.8689	−	18.8689i	−0.663396	−	0.663396i	−0.956179	+	0.292783i	$0.905419\pi$
$810$	0.0687789	+	2.23501i	0.00241665	+	0.0785302i
$811$	−7.19705			−0.252723			−0.126361	−	0.991984i	$-0.540330\pi$
$811$	−7.19705			−0.252723			−0.126361	+	0.991984i	$0.540330\pi$
$812$			1.55927i			0.0547197i
$813$	14.6812	+	14.6812i	0.514891	+	0.514891i
$814$	11.3440	+	5.51241i	0.397607	+	0.193210i
$815$	14.2936	−	0.439862i	0.500681	−	0.0154077i
$816$	1.85302	−	1.85302i	0.0648685	−	0.0648685i
$817$	−9.30382	+	9.30382i	−0.325499	+	0.325499i
$818$	−24.5847	−	24.5847i	−0.859583	−	0.859583i
$819$	−9.21585	+	9.21585i	−0.322028	+	0.322028i
$820$	8.49333	−	0.261369i	0.296600	−	0.00912739i
$821$	18.4340			0.643352			0.321676	−	0.946850i	$-0.395754\pi$
$821$	18.4340			0.643352			0.321676	+	0.946850i	$0.395754\pi$
$822$		−	18.8762i		−	0.658382i
$823$	−34.1801	+	34.1801i	−1.19144	+	1.19144i	−0.214782	+	0.976662i	$0.568904\pi$
$823$	−34.1801	+	34.1801i	−1.19144	+	1.19144i	−0.976662	+	0.214782i	$0.931096\pi$
$824$		−	9.85885i		−	0.343449i
$825$	−6.86618	+	7.76770i	−0.239050	+	0.270437i
$826$	3.91904			0.136361
$827$			22.3642i			0.777681i	0.921305	+	0.388840i	$0.127124\pi$
$827$			22.3642i			0.777681i	−0.921305	+	0.388840i	$0.872876\pi$
$828$		−	3.49438i		−	0.121438i
$829$	13.4981	+	13.4981i	0.468809	+	0.468809i	0.901529	−	0.432719i	$-0.142446\pi$
$829$	13.4981	+	13.4981i	0.468809	+	0.468809i	−0.432719	+	0.901529i	$0.642446\pi$
$830$	0.878651	+	0.826187i	0.0304984	+	0.0286774i
$831$	−12.6195	−	12.6195i	−0.437766	−	0.437766i
$832$	4.31443			0.149576
$833$	−5.56984			−0.192984
$834$	−8.55786	−	8.55786i	−0.296335	−	0.296335i
$835$	16.5448	−	0.509139i	0.572555	−	0.0176195i
$836$	3.06887	+	3.06887i	0.106139	+	0.106139i
$837$		−	0.553497i		−	0.0191317i
$838$			23.6748i			0.817831i
$839$	−17.9355			−0.619202			−0.309601	−	0.950867i	$-0.600195\pi$
$839$	−17.9355			−0.619202			−0.309601	+	0.950867i	$0.600195\pi$
$840$	−6.75159	+	0.207770i	−0.232952	+	0.00716874i
$841$		−	28.7336i		−	0.990813i
$842$	26.6921	−	26.6921i	0.919870	−	0.919870i
$843$			14.5162i			0.499965i
$844$	−1.84896			−0.0636437
$845$	0.386146	+	12.5480i	0.0132838	+	0.431666i
$846$	3.37898	−	3.37898i	0.116172	−	0.116172i
$847$	14.3131	+	14.3131i	0.491805	+	0.491805i
$848$	−1.87850	+	1.87850i	−0.0645079	+	0.0645079i
$849$	6.71311	−	6.71311i	0.230393	−	0.230393i
$850$	0.805673	+	13.0780i	0.0276344	+	0.448572i
$851$	9.28997	−	19.1178i	0.318456	−	0.655351i
$852$	6.48120	+	6.48120i	0.222042	+	0.222042i
$853$		−	48.5949i		−	1.66386i	−0.554883	−	0.831929i	$-0.687237\pi$
$853$		−	48.5949i		−	1.66386i	0.554883	−	0.831929i	$-0.312763\pi$
$854$	−25.1024			−0.858987
$855$	−3.20617	+	3.40977i	−0.109649	+	0.116612i
$856$	−4.17096	−	4.17096i	−0.142560	−	0.142560i
$857$		−	27.6764i		−	0.945409i	−0.881221	−	0.472704i	$-0.843278\pi$
$857$		−	27.6764i		−	0.945409i	0.881221	−	0.472704i	$-0.156722\pi$
$858$	−6.32566	+	6.32566i	−0.215954	+	0.215954i
$859$	−1.92645	+	1.92645i	−0.0657295	+	0.0657295i	−0.739207	−	0.673478i	$-0.764800\pi$
$859$	−1.92645	+	1.92645i	−0.0657295	+	0.0657295i	0.673478	+	0.739207i	$0.264800\pi$
$860$	−0.432349	−	14.0494i	−0.0147430	−	0.479081i
$861$	−11.4796			−0.391222
$862$	−25.8053	+	25.8053i	−0.878931	+	0.878931i
$863$	4.85716	−	4.85716i	0.165340	−	0.165340i	−0.619588	−	0.784927i	$-0.712700\pi$
$863$	4.85716	−	4.85716i	0.165340	−	0.165340i	0.784927	+	0.619588i	$0.212700\pi$
$864$	−0.707107	+	0.707107i	−0.0240563	+	0.0240563i
$865$	−35.5224	+	37.7782i	−1.20780	+	1.28450i
$866$	2.62555	−	2.62555i	0.0892197	−	0.0892197i
$867$	−7.16488	−	7.16488i	−0.243332	−	0.243332i
$868$	1.67202			0.0567522
$869$	18.6848	+	18.6848i	0.633838	+	0.633838i
$870$	−1.15365	+	0.0355018i	−0.0391124	+	0.00120362i
$871$	−13.1928	+	13.1928i	−0.447021	+	0.447021i
$872$	0.461041	−	0.461041i	0.0156128	−	0.0156128i
$873$	−14.1415			−0.478619
$874$	5.17192	−	5.17192i	0.174943	−	0.174943i
$875$	21.5792	−	25.9811i	0.729510	−	0.878322i
$876$		−	12.0228i		−	0.406212i
$877$	41.2031	+	41.2031i	1.39133	+	1.39133i	0.822353	+	0.568978i	$0.192661\pi$
$877$	41.2031	+	41.2031i	1.39133	+	1.39133i	0.568978	+	0.822353i	$0.307339\pi$
$878$	4.04448	+	4.04448i	0.136495	+	0.136495i
$879$	1.93975			0.0654261
$880$	−4.63422	+	0.142611i	−0.156220	+	0.00480741i
$881$			4.54000i			0.152957i	0.997071	+	0.0764783i	$0.0243676\pi$
$881$			4.54000i			0.152957i	−0.997071	+	0.0764783i	$0.975632\pi$
$882$	2.12544			0.0715673
$883$			0.358056i			0.0120495i	0.999982	+	0.00602477i	$0.00191776\pi$
$883$			0.358056i			0.0120495i	−0.999982	+	0.00602477i	$0.998082\pi$
$884$			11.3062i			0.380269i
$885$	0.0892295	+	2.89956i	0.00299942	+	0.0974678i
$886$	0.534873	+	0.534873i	0.0179694	+	0.0179694i
$887$	15.5018	−	15.5018i	0.520498	−	0.520498i	−0.397223	−	0.917722i	$-0.630026\pi$
$887$	15.5018	−	15.5018i	0.520498	−	0.520498i	0.917722	+	0.397223i	$0.130026\pi$
$888$	−5.74848	+	1.98872i	−0.192906	+	0.0667372i
$889$		−	26.4085i		−	0.885712i
$890$	7.98601	−	8.49313i	0.267692	−	0.284690i
$891$		−	2.07347i		−	0.0694638i
$892$	4.85478	−	4.85478i	0.162550	−	0.162550i
$893$	10.0023			0.334713
$894$	−1.25869	+	1.25869i	−0.0420970	+	0.0420970i
$895$	−35.1900	+	37.4246i	−1.17627	+	1.25097i
$896$	−2.13605	−	2.13605i	−0.0713605	−	0.0713605i
$897$	10.6605	+	10.6605i	0.355945	+	0.355945i
$898$	−15.2168	+	15.2168i	−0.507790	+	0.507790i
$899$	0.285700			0.00952862
$900$	−0.307443	−	4.99054i	−0.0102481	−	0.166351i
$901$	−4.92271	−	4.92271i	−0.163999	−	0.163999i
$902$	−7.87944			−0.262357
$903$			18.9892i			0.631920i
$904$		−	17.3203i		−	0.576064i
$905$	−0.375332	−	12.1966i	−0.0124765	−	0.405429i
$906$	10.4383	−	10.4383i	0.346790	−	0.346790i
$907$		−	28.0078i		−	0.929984i	−0.885315	−	0.464992i	$-0.846057\pi$
$907$		−	28.0078i		−	0.929984i	0.885315	−	0.464992i	$-0.153943\pi$
$908$		−	19.5601i		−	0.649123i
$909$	−7.64384			−0.253530
$910$	19.9637	−	21.2314i	0.661789	−	0.703813i
$911$	−28.1566	−	28.1566i	−0.932870	−	0.932870i	0.0650140	−	0.997884i	$-0.479291\pi$
$911$	−28.1566	−	28.1566i	−0.932870	−	0.932870i	−0.997884	+	0.0650140i	$0.979291\pi$
$912$	−2.09313			−0.0693106
$913$	−0.790807	−	0.790807i	−0.0261719	−	0.0261719i
$914$			26.8366i			0.887676i
$915$	−0.571537	−	18.5724i	−0.0188944	−	0.613985i
$916$			5.52626i			0.182593i
$917$	4.43597			0.146489
$918$	−1.85302	−	1.85302i	−0.0611586	−	0.0611586i
$919$	23.6708	+	23.6708i	0.780828	+	0.780828i	0.979970	−	0.199143i	$-0.0638158\pi$
$919$	23.6708	+	23.6708i	0.780828	+	0.780828i	−0.199143	+	0.979970i	$0.563816\pi$
$920$	0.240340	+	7.80997i	0.00792376	+	0.257487i
$921$	−18.3483			−0.604596
$922$	−9.31792	−	9.31792i	−0.306869	−	0.306869i
$923$	−39.5452			−1.30165
$924$	6.26360			0.206057
$925$	11.5856	−	28.1207i	0.380931	−	0.924604i
$926$	−31.8446			−1.04648
$927$	−9.85885			−0.323807
$928$	−0.364989	−	0.364989i	−0.0119813	−	0.0119813i
$929$	−23.2278			−0.762081			−0.381040	−	0.924558i	$-0.624434\pi$
$929$	−23.2278			−0.762081			−0.381040	+	0.924558i	$0.624434\pi$
$930$	0.0380689	+	1.23707i	0.00124833	+	0.0405652i
$931$	3.14580	+	3.14580i	0.103099	+	0.103099i
$932$	8.07622	+	8.07622i	0.264545	+	0.264545i
$933$	−29.8503			−0.977254
$934$		−	24.6295i		−	0.805902i
$935$	−0.373720	−	12.1442i	−0.0122220	−	0.397159i
$936$		−	4.31443i		−	0.141022i
$937$	12.8916	+	12.8916i	0.421152	+	0.421152i	0.885600	−	0.464449i	$-0.153747\pi$
$937$	12.8916	+	12.8916i	0.421152	+	0.421152i	−0.464449	+	0.885600i	$0.653747\pi$
$938$	13.0634			0.426534
$939$	−19.7810	−	19.7810i	−0.645529	−	0.645529i
$940$	−7.31966	+	7.78447i	−0.238741	+	0.253901i
$941$	13.8545			0.451643			0.225821	−	0.974169i	$-0.427493\pi$
$941$	13.8545			0.451643			0.225821	+	0.974169i	$0.427493\pi$
$942$			4.28456i			0.139599i
$943$			13.2791i			0.432427i
$944$	−0.917356	+	0.917356i	−0.0298574	+	0.0298574i
$945$	0.207770	+	6.75159i	0.00675875	+	0.219629i
$946$			13.0340i			0.423771i
$947$		−	45.6796i		−	1.48439i	−0.670185	−	0.742194i	$-0.733785\pi$
$947$		−	45.6796i		−	1.48439i	0.670185	−	0.742194i	$-0.266215\pi$
$948$	−12.7440			−0.413906
$949$	36.6786	+	36.6786i	1.19064	+	1.19064i
$950$	6.93131	−	7.84138i	0.224881	−	0.254408i
$951$	−6.67756			−0.216535
$952$	5.59765	−	5.59765i	0.181421	−	0.181421i
$953$	9.42694	+	9.42694i	0.305368	+	0.305368i	0.843110	−	0.537741i	$-0.180722\pi$
$953$	9.42694	+	9.42694i	0.305368	+	0.305368i	−0.537741	+	0.843110i	$0.680722\pi$
$954$	1.87850	+	1.87850i	0.0608186	+	0.0608186i
$955$	18.3629	−	19.5290i	0.594211	−	0.631944i
$956$	−1.04218	+	1.04218i	−0.0337065	+	0.0337065i
$957$	1.07027			0.0345968
$958$	−3.98964	+	3.98964i	−0.128899	+	0.128899i
$959$		−	57.0218i		−	1.84133i
$960$	1.53176	−	1.62902i	0.0494372	−	0.0525765i
$961$			30.6936i			0.990117i
$962$	11.4701	−	23.6044i	0.369811	−	0.761035i
$963$	−4.17096	+	4.17096i	−0.134407	+	0.134407i
$964$	2.39676	+	2.39676i	0.0771944	+	0.0771944i
$965$	−0.0560711	−	1.82206i	−0.00180499	−	0.0586543i
$966$		−	10.5559i		−	0.339632i
$967$			44.8271i			1.44154i	0.693173	+	0.720772i	$0.256212\pi$
$967$			44.8271i			1.44154i	−0.693173	+	0.720772i	$0.743788\pi$
$968$	−6.70073			−0.215370
$969$		−	5.48518i		−	0.176209i
$970$	31.6065	−	0.972640i	1.01482	−	0.0312296i
$971$	14.5531			0.467030			0.233515	−	0.972353i	$-0.424977\pi$
$971$	14.5531			0.467030			0.233515	+	0.972353i	$0.424977\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	−25.8519	−	25.8519i	−0.828774	−	0.828774i
$974$		−	33.5571i		−	1.07524i
$975$	16.1629	+	14.2870i	0.517627	+	0.457551i
$976$	5.87589	−	5.87589i	0.188083	−	0.188083i
$977$	3.38584			0.108323			0.0541613	−	0.998532i	$-0.482751\pi$
$977$	3.38584			0.108323			0.0541613	+	0.998532i	$0.482751\pi$
$978$	4.52216	−	4.52216i	0.144603	−	0.144603i
$979$	−7.64403	+	7.64403i	−0.244304	+	0.244304i
$980$	−4.75038	+	0.146186i	−0.151745	+	0.00466973i
$981$	−0.461041	−	0.461041i	−0.0147199	−	0.0147199i
$982$	−31.9342			−1.01906
$983$	−22.1865	−	22.1865i	−0.707640	−	0.707640i	0.258398	−	0.966038i	$-0.416805\pi$
$983$	−22.1865	−	22.1865i	−0.707640	−	0.707640i	−0.966038	+	0.258398i	$0.916805\pi$
$984$	2.68710	−	2.68710i	0.0856615	−	0.0856615i
$985$	26.3234	−	27.9949i	0.838733	−	0.891993i
$986$	0.956475	−	0.956475i	0.0304604	−	0.0304604i
$987$	10.2074	−	10.2074i	0.324904	−	0.324904i
$988$	6.38566	−	6.38566i	0.203155	−	0.203155i
$989$	21.9659			0.698475
$990$	0.142611	+	4.63422i	0.00453247	+	0.147285i
$991$	−0.255920	+	0.255920i	−0.00812958	+	0.00812958i	−0.711160	−	0.703030i	$-0.751830\pi$
$991$	−0.255920	+	0.255920i	−0.00812958	+	0.00812958i	0.703030	+	0.711160i	$0.251830\pi$
$992$	−0.391381	+	0.391381i	−0.0124264	+	0.0124264i
$993$		−	7.91522i		−	0.251182i
$994$	19.5786	+	19.5786i	0.620997	+	0.620997i
$995$	13.9321	−	14.8168i	0.441676	−	0.469723i
$996$	0.539372			0.0170907
$997$		−	35.1093i		−	1.11192i	−0.831208	−	0.555962i	$-0.812350\pi$
$997$		−	35.1093i		−	1.11192i	0.831208	−	0.555962i	$-0.187650\pi$
$998$	−25.1910	−	25.1910i	−0.797407	−	0.797407i
$999$	1.98872	+	5.74848i	0.0629204	+	0.181874i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.o.a.487.3	yes	36
5.3	odd	4		1110.2.l.a.43.16	✓	36
37.31	odd	4		1110.2.l.a.697.16	yes	36
185.68	even	4	inner	1110.2.o.a.253.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.16	✓	36	5.3	odd	4
1110.2.l.a.697.16	yes	36	37.31	odd	4
1110.2.o.a.253.3	yes	36	185.68	even	4	inner
1110.2.o.a.487.3	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(0.0687789 + 2.23501i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.13605 + 2.13605i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(0.0687789 + 2.23501i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.13605 + 2.13605i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +(-0.0687789 - 2.23501i) q^{10} +2.07347i q^{11} +(-0.707107 - 0.707107i) q^{12} +4.31443 q^{13} +(-2.13605 - 2.13605i) q^{14} +(1.53176 - 1.62902i) q^{15} +1.00000 q^{16} +2.62056i q^{17} -1.00000i q^{18} +(1.48007 - 1.48007i) q^{19} +(0.0687789 + 2.23501i) q^{20} -3.02083i q^{21} -2.07347i q^{22} -3.49438 q^{23} +(0.707107 + 0.707107i) q^{24} +(-4.99054 + 0.307443i) q^{25} -4.31443 q^{26} +(0.707107 - 0.707107i) q^{27} +(2.13605 + 2.13605i) q^{28} +(0.364989 + 0.364989i) q^{29} +(-1.53176 + 1.62902i) q^{30} +(0.391381 - 0.391381i) q^{31} -1.00000 q^{32} +(1.46616 - 1.46616i) q^{33} -2.62056i q^{34} +(-4.62718 + 4.92101i) q^{35} +1.00000i q^{36} +(-2.65855 + 5.47103i) q^{37} +(-1.48007 + 1.48007i) q^{38} +(-3.05076 - 3.05076i) q^{39} +(-0.0687789 - 2.23501i) q^{40} -3.80013i q^{41} +3.02083i q^{42} -6.28607 q^{43} +2.07347i q^{44} +(-2.23501 + 0.0687789i) q^{45} +3.49438 q^{46} +(3.37898 + 3.37898i) q^{47} +(-0.707107 - 0.707107i) q^{48} +2.12544i q^{49} +(4.99054 - 0.307443i) q^{50} +(1.85302 - 1.85302i) q^{51} +4.31443 q^{52} +(-1.87850 + 1.87850i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(-4.63422 + 0.142611i) q^{55} +(-2.13605 - 2.13605i) q^{56} -2.09313 q^{57} +(-0.364989 - 0.364989i) q^{58} +(-0.917356 + 0.917356i) q^{59} +(1.53176 - 1.62902i) q^{60} +(5.87589 - 5.87589i) q^{61} +(-0.391381 + 0.391381i) q^{62} +(-2.13605 + 2.13605i) q^{63} +1.00000 q^{64} +(0.296742 + 9.64280i) q^{65} +(-1.46616 + 1.46616i) q^{66} +(-3.05783 + 3.05783i) q^{67} +2.62056i q^{68} +(2.47090 + 2.47090i) q^{69} +(4.62718 - 4.92101i) q^{70} -9.16581 q^{71} -1.00000i q^{72} +(8.50139 + 8.50139i) q^{73} +(2.65855 - 5.47103i) q^{74} +(3.74624 + 3.31145i) q^{75} +(1.48007 - 1.48007i) q^{76} +(-4.42903 + 4.42903i) q^{77} +(3.05076 + 3.05076i) q^{78} +(9.01137 - 9.01137i) q^{79} +(0.0687789 + 2.23501i) q^{80} -1.00000 q^{81} +3.80013i q^{82} +(-0.381394 + 0.381394i) q^{83} -3.02083i q^{84} +(-5.85698 + 0.180239i) q^{85} +6.28607 q^{86} -0.516172i q^{87} -2.07347i q^{88} +(3.68659 + 3.68659i) q^{89} +(2.23501 - 0.0687789i) q^{90} +(9.21585 + 9.21585i) q^{91} -3.49438 q^{92} -0.553497 q^{93} +(-3.37898 - 3.37898i) q^{94} +(3.40977 + 3.20617i) q^{95} +(0.707107 + 0.707107i) q^{96} +14.1415i q^{97} -2.12544i q^{98} -2.07347 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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