LMFDB - Embedded newform 726.2.e.m.487.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [726,2,Mod(487,726)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(726, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("726.487");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			487.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	726.487
Dual form			726.2.e.m.565.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(3.23607 + 2.35114i) q^{5} +(0.809017 + 0.587785i) q^{6} +(0.618034 - 1.90211i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(3.23607 + 2.35114i) q^{5} +(0.809017 + 0.587785i) q^{6} +(0.618034 - 1.90211i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +4.00000 q^{10} +1.00000 q^{12} +(3.23607 - 2.35114i) q^{13} +(-0.618034 - 1.90211i) q^{14} +(-1.23607 + 3.80423i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.61803 - 1.17557i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(3.23607 - 2.35114i) q^{20} +2.00000 q^{21} -6.00000 q^{23} +(0.809017 - 0.587785i) q^{24} +(3.39919 + 10.4616i) q^{25} +(1.23607 - 3.80423i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.61803 - 1.17557i) q^{28} +(-3.09017 + 9.51057i) q^{29} +(1.23607 + 3.80423i) q^{30} +(6.47214 - 4.70228i) q^{31} -1.00000 q^{32} -2.00000 q^{34} +(6.47214 - 4.70228i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-0.618034 + 1.90211i) q^{37} +(3.23607 + 2.35114i) q^{39} +(1.23607 - 3.80423i) q^{40} +(-0.618034 - 1.90211i) q^{41} +(1.61803 - 1.17557i) q^{42} -4.00000 q^{43} -4.00000 q^{45} +(-4.85410 + 3.52671i) q^{46} +(-0.618034 - 1.90211i) q^{47} +(0.309017 - 0.951057i) q^{48} +(2.42705 + 1.76336i) q^{49} +(8.89919 + 6.46564i) q^{50} +(0.618034 - 1.90211i) q^{51} +(-1.23607 - 3.80423i) q^{52} +(-3.23607 + 2.35114i) q^{53} -1.00000 q^{54} -2.00000 q^{56} +(3.09017 + 9.51057i) q^{58} +(3.23607 + 2.35114i) q^{60} +(-6.47214 - 4.70228i) q^{61} +(2.47214 - 7.60845i) q^{62} +(0.618034 + 1.90211i) q^{63} +(-0.809017 + 0.587785i) q^{64} +16.0000 q^{65} -12.0000 q^{67} +(-1.61803 + 1.17557i) q^{68} +(-1.85410 - 5.70634i) q^{69} +(2.47214 - 7.60845i) q^{70} +(-1.61803 - 1.17557i) q^{71} +(0.809017 + 0.587785i) q^{72} +(1.85410 - 5.70634i) q^{73} +(0.618034 + 1.90211i) q^{74} +(-8.89919 + 6.46564i) q^{75} +4.00000 q^{78} +(8.09017 - 5.87785i) q^{79} +(-1.23607 - 3.80423i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-1.61803 - 1.17557i) q^{82} +(3.23607 + 2.35114i) q^{83} +(0.618034 - 1.90211i) q^{84} +(-2.47214 - 7.60845i) q^{85} +(-3.23607 + 2.35114i) q^{86} -10.0000 q^{87} +10.0000 q^{89} +(-3.23607 + 2.35114i) q^{90} +(-2.47214 - 7.60845i) q^{91} +(-1.85410 + 5.70634i) q^{92} +(6.47214 + 4.70228i) q^{93} +(-1.61803 - 1.17557i) q^{94} +(-0.309017 - 0.951057i) q^{96} +(1.61803 - 1.17557i) q^{97} +3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{3} - q^{4} + 4 q^{5} + q^{6} - 2 q^{7} + q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 - q^3 - q^4 + 4 * q^5 + q^6 - 2 * q^7 + q^8 - q^9	$ 4 q + q^{2} - q^{3} - q^{4} + 4 q^{5} + q^{6} - 2 q^{7} + q^{8} - q^{9} + 16 q^{10} + 4 q^{12} + 4 q^{13} + 2 q^{14} + 4 q^{15} - q^{16} - 2 q^{17} + q^{18} + 4 q^{20} + 8 q^{21} - 24 q^{23} + q^{24} - 11 q^{25} - 4 q^{26} - q^{27} - 2 q^{28} + 10 q^{29} - 4 q^{30} + 8 q^{31} - 4 q^{32} - 8 q^{34} + 8 q^{35} - q^{36} + 2 q^{37} + 4 q^{39} - 4 q^{40} + 2 q^{41} + 2 q^{42} - 16 q^{43} - 16 q^{45} - 6 q^{46} + 2 q^{47} - q^{48} + 3 q^{49} + 11 q^{50} - 2 q^{51} + 4 q^{52} - 4 q^{53} - 4 q^{54} - 8 q^{56} - 10 q^{58} + 4 q^{60} - 8 q^{61} - 8 q^{62} - 2 q^{63} - q^{64} + 64 q^{65} - 48 q^{67} - 2 q^{68} + 6 q^{69} - 8 q^{70} - 2 q^{71} + q^{72} - 6 q^{73} - 2 q^{74} - 11 q^{75} + 16 q^{78} + 10 q^{79} + 4 q^{80} - q^{81} - 2 q^{82} + 4 q^{83} - 2 q^{84} + 8 q^{85} - 4 q^{86} - 40 q^{87} + 40 q^{89} - 4 q^{90} + 8 q^{91} + 6 q^{92} + 8 q^{93} - 2 q^{94} + q^{96} + 2 q^{97} + 12 q^{98}+O(q^{100}) $ 4 * q + q^2 - q^3 - q^4 + 4 * q^5 + q^6 - 2 * q^7 + q^8 - q^9 + 16 * q^10 + 4 * q^12 + 4 * q^13 + 2 * q^14 + 4 * q^15 - q^16 - 2 * q^17 + q^18 + 4 * q^20 + 8 * q^21 - 24 * q^23 + q^24 - 11 * q^25 - 4 * q^26 - q^27 - 2 * q^28 + 10 * q^29 - 4 * q^30 + 8 * q^31 - 4 * q^32 - 8 * q^34 + 8 * q^35 - q^36 + 2 * q^37 + 4 * q^39 - 4 * q^40 + 2 * q^41 + 2 * q^42 - 16 * q^43 - 16 * q^45 - 6 * q^46 + 2 * q^47 - q^48 + 3 * q^49 + 11 * q^50 - 2 * q^51 + 4 * q^52 - 4 * q^53 - 4 * q^54 - 8 * q^56 - 10 * q^58 + 4 * q^60 - 8 * q^61 - 8 * q^62 - 2 * q^63 - q^64 + 64 * q^65 - 48 * q^67 - 2 * q^68 + 6 * q^69 - 8 * q^70 - 2 * q^71 + q^72 - 6 * q^73 - 2 * q^74 - 11 * q^75 + 16 * q^78 + 10 * q^79 + 4 * q^80 - q^81 - 2 * q^82 + 4 * q^83 - 2 * q^84 + 8 * q^85 - 4 * q^86 - 40 * q^87 + 40 * q^89 - 4 * q^90 + 8 * q^91 + 6 * q^92 + 8 * q^93 - 2 * q^94 + q^96 + 2 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$485$	$607$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	3.23607	+	2.35114i	1.44721	+	1.05146i	0.986472	+	0.163928i	$0.0524164\pi$
$5$	3.23607	+	2.35114i	1.44721	+	1.05146i	0.460741	+	0.887535i	$0.347584\pi$
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	0.618034	−	1.90211i	0.233595	−	0.718931i	−0.763710	−	0.645560i	$-0.776624\pi$
$7$	0.618034	−	1.90211i	0.233595	−	0.718931i	0.997305	−	0.0733714i	$-0.0233759\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	4.00000			1.26491
$11$		0			0
$11$		0			0
$12$	1.00000			0.288675
$13$	3.23607	−	2.35114i	0.897524	−	0.652089i	−0.0403050	−	0.999187i	$-0.512833\pi$
$13$	3.23607	−	2.35114i	0.897524	−	0.652089i	0.937829	+	0.347098i	$0.112833\pi$
$14$	−0.618034	−	1.90211i	−0.165177	−	0.508361i
$15$	−1.23607	+	3.80423i	−0.319151	+	0.982247i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−1.61803	−	1.17557i	−0.392431	−	0.285118i	0.374020	−	0.927421i	$-0.377979\pi$
$17$	−1.61803	−	1.17557i	−0.392431	−	0.285118i	−0.766451	+	0.642303i	$0.777979\pi$
$18$	−0.309017	+	0.951057i	−0.0728360	+	0.224166i
$19$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$19$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$20$	3.23607	−	2.35114i	0.723607	−	0.525731i
$21$	2.00000			0.436436
$22$		0			0
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$	0.809017	−	0.587785i	0.165140	−	0.119981i
$25$	3.39919	+	10.4616i	0.679837	+	2.09232i
$26$	1.23607	−	3.80423i	0.242413	−	0.746070i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−1.61803	−	1.17557i	−0.305780	−	0.222162i
$29$	−3.09017	+	9.51057i	−0.573830	+	1.76607i	0.0662984	+	0.997800i	$0.478881\pi$
$29$	−3.09017	+	9.51057i	−0.573830	+	1.76607i	−0.640129	+	0.768268i	$0.721119\pi$
$30$	1.23607	+	3.80423i	0.225674	+	0.694553i
$31$	6.47214	−	4.70228i	1.16243	−	0.844555i	0.172347	−	0.985036i	$-0.444865\pi$
$31$	6.47214	−	4.70228i	1.16243	−	0.844555i	0.990083	+	0.140482i	$0.0448651\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−2.00000			−0.342997
$35$	6.47214	−	4.70228i	1.09399	−	0.794831i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−0.618034	+	1.90211i	−0.101604	+	0.312705i	−0.988918	−	0.148460i	$-0.952568\pi$
$37$	−0.618034	+	1.90211i	−0.101604	+	0.312705i	0.887314	+	0.461165i	$0.152568\pi$
$38$		0			0
$39$	3.23607	+	2.35114i	0.518186	+	0.376484i
$40$	1.23607	−	3.80423i	0.195440	−	0.601501i
$41$	−0.618034	−	1.90211i	−0.0965207	−	0.297060i	0.891126	−	0.453755i	$-0.149916\pi$
$41$	−0.618034	−	1.90211i	−0.0965207	−	0.297060i	−0.987647	+	0.156695i	$0.949916\pi$
$42$	1.61803	−	1.17557i	0.249668	−	0.181394i
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	−4.00000			−0.596285
$46$	−4.85410	+	3.52671i	−0.715698	+	0.519985i
$47$	−0.618034	−	1.90211i	−0.0901495	−	0.277452i	0.895810	−	0.444438i	$-0.146597\pi$
$47$	−0.618034	−	1.90211i	−0.0901495	−	0.277452i	−0.985959	+	0.166986i	$0.946597\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	2.42705	+	1.76336i	0.346722	+	0.251908i
$50$	8.89919	+	6.46564i	1.25854	+	0.914379i
$51$	0.618034	−	1.90211i	0.0865421	−	0.266349i
$52$	−1.23607	−	3.80423i	−0.171412	−	0.527551i
$53$	−3.23607	+	2.35114i	−0.444508	+	0.322954i	−0.787424	−	0.616412i	$-0.788586\pi$
$53$	−3.23607	+	2.35114i	−0.444508	+	0.322954i	0.342916	+	0.939366i	$0.388586\pi$
$54$	−1.00000			−0.136083
$55$		0			0
$56$	−2.00000			−0.267261
$57$		0			0
$58$	3.09017	+	9.51057i	0.405759	+	1.24880i
$59$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$59$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$60$	3.23607	+	2.35114i	0.417775	+	0.303531i
$61$	−6.47214	−	4.70228i	−0.828672	−	0.602066i	0.0905112	−	0.995895i	$-0.471150\pi$
$61$	−6.47214	−	4.70228i	−0.828672	−	0.602066i	−0.919183	+	0.393830i	$0.871150\pi$
$62$	2.47214	−	7.60845i	0.313962	−	0.966274i
$63$	0.618034	+	1.90211i	0.0778650	+	0.239644i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	16.0000			1.98456
$66$		0			0
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$	−1.61803	+	1.17557i	−0.196215	+	0.142559i
$69$	−1.85410	−	5.70634i	−0.223208	−	0.686963i
$70$	2.47214	−	7.60845i	0.295477	−	0.909384i
$71$	−1.61803	−	1.17557i	−0.192025	−	0.139515i	0.487619	−	0.873057i	$-0.337866\pi$
$71$	−1.61803	−	1.17557i	−0.192025	−	0.139515i	−0.679644	+	0.733542i	$0.737866\pi$
$72$	0.809017	+	0.587785i	0.0953436	+	0.0692712i
$73$	1.85410	−	5.70634i	0.217006	−	0.667876i	−0.781999	−	0.623280i	$-0.785800\pi$
$73$	1.85410	−	5.70634i	0.217006	−	0.667876i	0.999005	−	0.0445966i	$-0.0142003\pi$
$74$	0.618034	+	1.90211i	0.0718450	+	0.221116i
$75$	−8.89919	+	6.46564i	−1.02759	+	0.746588i
$76$		0			0
$77$		0			0
$78$	4.00000			0.452911
$79$	8.09017	−	5.87785i	0.910215	−	0.661310i	−0.0308541	−	0.999524i	$-0.509823\pi$
$79$	8.09017	−	5.87785i	0.910215	−	0.661310i	0.941069	+	0.338214i	$0.109823\pi$
$80$	−1.23607	−	3.80423i	−0.138197	−	0.425325i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−1.61803	−	1.17557i	−0.178682	−	0.129820i
$83$	3.23607	+	2.35114i	0.355205	+	0.258071i	0.751049	−	0.660246i	$-0.229548\pi$
$83$	3.23607	+	2.35114i	0.355205	+	0.258071i	−0.395845	+	0.918318i	$0.629548\pi$
$84$	0.618034	−	1.90211i	0.0674330	−	0.207538i
$85$	−2.47214	−	7.60845i	−0.268141	−	0.825253i
$86$	−3.23607	+	2.35114i	−0.348954	+	0.253530i
$87$	−10.0000			−1.07211
$88$		0			0
$89$	10.0000			1.06000			0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000			1.06000			0.529999	+	0.847998i	$0.322192\pi$
$90$	−3.23607	+	2.35114i	−0.341112	+	0.247832i
$91$	−2.47214	−	7.60845i	−0.259150	−	0.797582i
$92$	−1.85410	+	5.70634i	−0.193303	+	0.594927i
$93$	6.47214	+	4.70228i	0.671129	+	0.487604i
$94$	−1.61803	−	1.17557i	−0.166887	−	0.121251i
$95$		0			0
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	1.61803	−	1.17557i	0.164286	−	0.119361i	−0.502604	−	0.864517i	$-0.667625\pi$
$97$	1.61803	−	1.17557i	0.164286	−	0.119361i	0.666891	+	0.745155i	$0.267625\pi$
$98$	3.00000			0.303046
$99$		0			0
$100$	11.0000			1.10000
$101$	1.61803	−	1.17557i	0.161000	−	0.116974i	−0.504368	−	0.863489i	$-0.668274\pi$
$101$	1.61803	−	1.17557i	0.161000	−	0.116974i	0.665368	+	0.746515i	$0.268274\pi$
$102$	−0.618034	−	1.90211i	−0.0611945	−	0.188337i
$103$	1.23607	−	3.80423i	0.121793	−	0.374842i	−0.871510	−	0.490378i	$-0.836859\pi$
$103$	1.23607	−	3.80423i	0.121793	−	0.374842i	0.993303	+	0.115536i	$0.0368587\pi$
$104$	−3.23607	−	2.35114i	−0.317323	−	0.230548i
$105$	6.47214	+	4.70228i	0.631616	+	0.458896i
$106$	−1.23607	+	3.80423i	−0.120058	+	0.369499i
$107$	3.70820	+	11.4127i	0.358486	+	1.10331i	0.953961	+	0.299932i	$0.0969638\pi$
$107$	3.70820	+	11.4127i	0.358486	+	1.10331i	−0.595475	+	0.803374i	$0.703036\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	−20.0000			−1.91565			−0.957826	−	0.287348i	$-0.907226\pi$
$109$	−20.0000			−1.91565			−0.957826	+	0.287348i	$0.907226\pi$
$110$		0			0
$111$	−2.00000			−0.189832
$112$	−1.61803	+	1.17557i	−0.152890	+	0.111081i
$113$	−1.85410	−	5.70634i	−0.174419	−	0.536807i	0.825187	−	0.564859i	$-0.191070\pi$
$113$	−1.85410	−	5.70634i	−0.174419	−	0.536807i	−0.999606	+	0.0280521i	$0.991070\pi$
$114$		0			0
$115$	−19.4164	−	14.1068i	−1.81059	−	1.31547i
$116$	8.09017	+	5.87785i	0.751153	+	0.545745i
$117$	−1.23607	+	3.80423i	−0.114275	+	0.351701i
$118$		0			0
$119$	−3.23607	+	2.35114i	−0.296650	+	0.215529i
$120$	4.00000			0.365148
$121$		0			0
$122$	−8.00000			−0.724286
$123$	1.61803	−	1.17557i	0.145893	−	0.105998i
$124$	−2.47214	−	7.60845i	−0.222004	−	0.683259i
$125$	−7.41641	+	22.8254i	−0.663344	+	2.04156i
$126$	1.61803	+	1.17557i	0.144146	+	0.104728i
$127$	−17.7984	−	12.9313i	−1.57935	−	1.14747i	−0.917434	−	0.397887i	$-0.869744\pi$
$127$	−17.7984	−	12.9313i	−1.57935	−	1.14747i	−0.661916	−	0.749578i	$-0.730256\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−1.23607	−	3.80423i	−0.108830	−	0.334943i
$130$	12.9443	−	9.40456i	1.13529	−	0.824835i
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$		0			0
$133$		0			0
$134$	−9.70820	+	7.05342i	−0.838661	+	0.609323i
$135$	−1.23607	−	3.80423i	−0.106384	−	0.327416i
$136$	−0.618034	+	1.90211i	−0.0529960	+	0.163105i
$137$	1.61803	+	1.17557i	0.138238	+	0.100436i	0.654755	−	0.755841i	$-0.272772\pi$
$137$	1.61803	+	1.17557i	0.138238	+	0.100436i	−0.516517	+	0.856277i	$0.672772\pi$
$138$	−4.85410	−	3.52671i	−0.413209	−	0.300214i
$139$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$139$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$140$	−2.47214	−	7.60845i	−0.208934	−	0.643032i
$141$	1.61803	−	1.17557i	0.136263	−	0.0990009i
$142$	−2.00000			−0.167836
$143$		0			0
$144$	1.00000			0.0833333
$145$	−32.3607	+	23.5114i	−2.68741	+	1.95252i
$146$	−1.85410	−	5.70634i	−0.153447	−	0.472260i
$147$	−0.927051	+	2.85317i	−0.0764619	+	0.235325i
$148$	1.61803	+	1.17557i	0.133002	+	0.0966313i
$149$	−8.09017	−	5.87785i	−0.662773	−	0.481532i	0.204826	−	0.978798i	$-0.434337\pi$
$149$	−8.09017	−	5.87785i	−0.662773	−	0.481532i	−0.867598	+	0.497266i	$0.834337\pi$
$150$	−3.39919	+	10.4616i	−0.277542	+	0.854188i
$151$	−0.618034	−	1.90211i	−0.0502949	−	0.154792i	0.922755	−	0.385388i	$-0.125932\pi$
$151$	−0.618034	−	1.90211i	−0.0502949	−	0.154792i	−0.973050	+	0.230596i	$0.925932\pi$
$152$		0			0
$153$	2.00000			0.161690
$154$		0			0
$155$	32.0000			2.57030
$156$	3.23607	−	2.35114i	0.259093	−	0.188242i
$157$	5.56231	+	17.1190i	0.443920	+	1.36625i	0.883663	+	0.468123i	$0.155069\pi$
$157$	5.56231	+	17.1190i	0.443920	+	1.36625i	−0.439743	+	0.898124i	$0.644931\pi$
$158$	3.09017	−	9.51057i	0.245841	−	0.756620i
$159$	−3.23607	−	2.35114i	−0.256637	−	0.186458i
$160$	−3.23607	−	2.35114i	−0.255834	−	0.185874i
$161$	−3.70820	+	11.4127i	−0.292247	+	0.899445i
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	−3.23607	+	2.35114i	−0.253468	+	0.184156i	−0.707263	−	0.706951i	$-0.750070\pi$
$163$	−3.23607	+	2.35114i	−0.253468	+	0.184156i	0.453794	+	0.891107i	$0.350070\pi$
$164$	−2.00000			−0.156174
$165$		0			0
$166$	4.00000			0.310460
$167$	−9.70820	+	7.05342i	−0.751243	+	0.545810i	−0.896212	−	0.443626i	$-0.853692\pi$
$167$	−9.70820	+	7.05342i	−0.751243	+	0.545810i	0.144969	+	0.989436i	$0.453692\pi$
$168$	−0.618034	−	1.90211i	−0.0476824	−	0.146751i
$169$	0.927051	−	2.85317i	0.0713116	−	0.219475i
$170$	−6.47214	−	4.70228i	−0.496390	−	0.360649i
$171$		0			0
$172$	−1.23607	+	3.80423i	−0.0942493	+	0.290070i
$173$	1.85410	+	5.70634i	0.140965	+	0.433845i	0.996470	−	0.0839492i	$-0.0267533\pi$
$173$	1.85410	+	5.70634i	0.140965	+	0.433845i	−0.855505	+	0.517794i	$0.826753\pi$
$174$	−8.09017	+	5.87785i	−0.613314	+	0.445599i
$175$	22.0000			1.66304
$176$		0			0
$177$		0			0
$178$	8.09017	−	5.87785i	0.606384	−	0.440564i
$179$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$179$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$180$	−1.23607	+	3.80423i	−0.0921311	+	0.283550i
$181$	−1.61803	−	1.17557i	−0.120268	−	0.0873795i	0.526026	−	0.850469i	$-0.323682\pi$
$181$	−1.61803	−	1.17557i	−0.120268	−	0.0873795i	−0.646293	+	0.763089i	$0.723682\pi$
$182$	−6.47214	−	4.70228i	−0.479747	−	0.348556i
$183$	2.47214	−	7.60845i	0.182746	−	0.562433i
$184$	1.85410	+	5.70634i	0.136686	+	0.420677i
$185$	−6.47214	+	4.70228i	−0.475841	+	0.345719i
$186$	8.00000			0.586588
$187$		0			0
$188$	−2.00000			−0.145865
$189$	−1.61803	+	1.17557i	−0.117695	+	0.0855102i
$190$		0			0
$191$	6.79837	−	20.9232i	0.491913	−	1.51395i	−0.329800	−	0.944051i	$-0.606981\pi$
$191$	6.79837	−	20.9232i	0.491913	−	1.51395i	0.821713	−	0.569902i	$-0.193019\pi$
$192$	−0.809017	−	0.587785i	−0.0583858	−	0.0424197i
$193$	11.3262	+	8.22899i	0.815280	+	0.592336i	0.915357	−	0.402644i	$-0.131909\pi$
$193$	11.3262	+	8.22899i	0.815280	+	0.592336i	−0.100076	+	0.994980i	$0.531909\pi$
$194$	0.618034	−	1.90211i	0.0443723	−	0.136564i
$195$	4.94427	+	15.2169i	0.354067	+	1.08971i
$196$	2.42705	−	1.76336i	0.173361	−	0.125954i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	20.0000			1.41776			0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000			1.41776			0.708881	+	0.705328i	$0.249200\pi$
$200$	8.89919	−	6.46564i	0.629268	−	0.457190i
$201$	−3.70820	−	11.4127i	−0.261557	−	0.804988i
$202$	0.618034	−	1.90211i	0.0434847	−	0.133832i
$203$	16.1803	+	11.7557i	1.13564	+	0.825089i
$204$	−1.61803	−	1.17557i	−0.113285	−	0.0823064i
$205$	2.47214	−	7.60845i	0.172661	−	0.531397i
$206$	−1.23607	−	3.80423i	−0.0861209	−	0.265053i
$207$	4.85410	−	3.52671i	0.337383	−	0.245123i
$208$	−4.00000			−0.277350
$209$		0			0
$210$	8.00000			0.552052
$211$	9.70820	−	7.05342i	0.668340	−	0.485578i	−0.201129	−	0.979565i	$-0.564461\pi$
$211$	9.70820	−	7.05342i	0.668340	−	0.485578i	0.869469	+	0.493987i	$0.164461\pi$
$212$	1.23607	+	3.80423i	0.0848935	+	0.261275i
$213$	0.618034	−	1.90211i	0.0423470	−	0.130331i
$214$	9.70820	+	7.05342i	0.663639	+	0.482162i
$215$	−12.9443	−	9.40456i	−0.882792	−	0.641386i
$216$	−0.309017	+	0.951057i	−0.0210259	+	0.0647112i
$217$	−4.94427	−	15.2169i	−0.335639	−	1.03299i
$218$	−16.1803	+	11.7557i	−1.09587	+	0.796197i
$219$	6.00000			0.405442
$220$		0			0
$221$	−8.00000			−0.538138
$222$	−1.61803	+	1.17557i	−0.108595	+	0.0788991i
$223$	−4.94427	−	15.2169i	−0.331093	−	1.01900i	−0.968615	−	0.248567i	$-0.920040\pi$
$223$	−4.94427	−	15.2169i	−0.331093	−	1.01900i	0.637522	−	0.770432i	$-0.279960\pi$
$224$	−0.618034	+	1.90211i	−0.0412941	+	0.127090i
$225$	−8.89919	−	6.46564i	−0.593279	−	0.431043i
$226$	−4.85410	−	3.52671i	−0.322890	−	0.234593i
$227$	3.70820	−	11.4127i	0.246122	−	0.757486i	−0.749328	−	0.662199i	$-0.769623\pi$
$227$	3.70820	−	11.4127i	0.246122	−	0.757486i	0.995450	−	0.0952867i	$-0.0303768\pi$
$228$		0			0
$229$	−8.09017	+	5.87785i	−0.534613	+	0.388419i	−0.822081	−	0.569371i	$-0.807187\pi$
$229$	−8.09017	+	5.87785i	−0.534613	+	0.388419i	0.287467	+	0.957790i	$0.407187\pi$
$230$	−24.0000			−1.58251
$231$		0			0
$232$	10.0000			0.656532
$233$	−4.85410	+	3.52671i	−0.318003	+	0.231043i	−0.735323	−	0.677717i	$-0.762969\pi$
$233$	−4.85410	+	3.52671i	−0.318003	+	0.231043i	0.417320	+	0.908760i	$0.362969\pi$
$234$	1.23607	+	3.80423i	0.0808043	+	0.248690i
$235$	2.47214	−	7.60845i	0.161264	−	0.496321i
$236$		0			0
$237$	8.09017	+	5.87785i	0.525513	+	0.381808i
$238$	−1.23607	+	3.80423i	−0.0801224	+	0.246591i
$239$	6.18034	+	19.0211i	0.399773	+	1.23037i	0.925182	+	0.379525i	$0.123912\pi$
$239$	6.18034	+	19.0211i	0.399773	+	1.23037i	−0.525409	+	0.850850i	$0.676088\pi$
$240$	3.23607	−	2.35114i	0.208887	−	0.151765i
$241$	18.0000			1.15948			0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000			1.15948			0.579741	+	0.814801i	$0.303154\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$	−6.47214	+	4.70228i	−0.414336	+	0.301033i
$245$	3.70820	+	11.4127i	0.236908	+	0.729129i
$246$	0.618034	−	1.90211i	0.0394044	−	0.121274i
$247$		0			0
$248$	−6.47214	−	4.70228i	−0.410981	−	0.298595i
$249$	−1.23607	+	3.80423i	−0.0783326	+	0.241083i
$250$	7.41641	+	22.8254i	0.469055	+	1.44360i
$251$	6.47214	−	4.70228i	0.408518	−	0.296805i	−0.364484	−	0.931210i	$-0.618755\pi$
$251$	6.47214	−	4.70228i	0.408518	−	0.296805i	0.773001	+	0.634404i	$0.218755\pi$
$252$	2.00000			0.125988
$253$		0			0
$254$	−22.0000			−1.38040
$255$	6.47214	−	4.70228i	0.405301	−	0.294468i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	5.56231	−	17.1190i	0.346967	−	1.06785i	−0.613555	−	0.789652i	$-0.710261\pi$
$257$	5.56231	−	17.1190i	0.346967	−	1.06785i	0.960522	−	0.278203i	$-0.0897388\pi$
$258$	−3.23607	−	2.35114i	−0.201469	−	0.146376i
$259$	3.23607	+	2.35114i	0.201079	+	0.146093i
$260$	4.94427	−	15.2169i	0.306631	−	0.943712i
$261$	−3.09017	−	9.51057i	−0.191277	−	0.588689i
$262$	−9.70820	+	7.05342i	−0.599775	+	0.435762i
$263$	16.0000			0.986602			0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000			0.986602			0.493301	+	0.869859i	$0.335790\pi$
$264$		0			0
$265$	−16.0000			−0.982872
$266$		0			0
$267$	3.09017	+	9.51057i	0.189115	+	0.582037i
$268$	−3.70820	+	11.4127i	−0.226515	+	0.697140i
$269$	16.1803	+	11.7557i	0.986533	+	0.716758i	0.959159	−	0.282867i	$-0.0912856\pi$
$269$	16.1803	+	11.7557i	0.986533	+	0.716758i	0.0273737	+	0.999625i	$0.491286\pi$
$270$	−3.23607	−	2.35114i	−0.196941	−	0.143086i
$271$	−6.79837	+	20.9232i	−0.412972	+	1.27100i	0.501081	+	0.865401i	$0.332936\pi$
$271$	−6.79837	+	20.9232i	−0.412972	+	1.27100i	−0.914052	+	0.405596i	$0.867064\pi$
$272$	0.618034	+	1.90211i	0.0374738	+	0.115333i
$273$	6.47214	−	4.70228i	0.391711	−	0.284595i
$274$	2.00000			0.120824
$275$		0			0
$276$	−6.00000			−0.361158
$277$	6.47214	−	4.70228i	0.388873	−	0.282533i	−0.376121	−	0.926571i	$-0.622742\pi$
$277$	6.47214	−	4.70228i	0.388873	−	0.282533i	0.764994	+	0.644038i	$0.222742\pi$
$278$		0			0
$279$	−2.47214	+	7.60845i	−0.148003	+	0.455506i
$280$	−6.47214	−	4.70228i	−0.386784	−	0.281015i
$281$	17.7984	+	12.9313i	1.06176	+	0.771415i	0.974414	−	0.224763i	$-0.0721607\pi$
$281$	17.7984	+	12.9313i	1.06176	+	0.771415i	0.0873484	+	0.996178i	$0.472161\pi$
$282$	0.618034	−	1.90211i	0.0368034	−	0.113269i
$283$	−1.23607	−	3.80423i	−0.0734766	−	0.226138i	0.907573	−	0.419894i	$-0.137933\pi$
$283$	−1.23607	−	3.80423i	−0.0734766	−	0.226138i	−0.981050	+	0.193756i	$0.937933\pi$
$284$	−1.61803	+	1.17557i	−0.0960127	+	0.0697573i
$285$		0			0
$286$		0			0
$287$	−4.00000			−0.236113
$288$	0.809017	−	0.587785i	0.0476718	−	0.0346356i
$289$	−4.01722	−	12.3637i	−0.236307	−	0.727279i
$290$	−12.3607	+	38.0423i	−0.725844	+	2.23392i
$291$	1.61803	+	1.17557i	0.0948508	+	0.0689132i
$292$	−4.85410	−	3.52671i	−0.284065	−	0.206385i
$293$	−4.32624	+	13.3148i	−0.252742	+	0.777858i	0.741525	+	0.670926i	$0.234103\pi$
$293$	−4.32624	+	13.3148i	−0.252742	+	0.777858i	−0.994266	+	0.106933i	$0.965897\pi$
$294$	0.927051	+	2.85317i	0.0540667	+	0.166400i
$295$		0			0
$296$	2.00000			0.116248
$297$		0			0
$298$	−10.0000			−0.579284
$299$	−19.4164	+	14.1068i	−1.12288	+	0.815820i
$300$	3.39919	+	10.4616i	0.196252	+	0.604002i
$301$	−2.47214	+	7.60845i	−0.142492	+	0.438544i
$302$	−1.61803	−	1.17557i	−0.0931074	−	0.0676465i
$303$	1.61803	+	1.17557i	0.0929536	+	0.0675348i
$304$		0			0
$305$	−9.88854	−	30.4338i	−0.566216	−	1.74263i
$306$	1.61803	−	1.17557i	0.0924968	−	0.0672029i
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$		0			0
$309$	4.00000			0.227552
$310$	25.8885	−	18.8091i	1.47037	−	1.06829i
$311$	0.618034	+	1.90211i	0.0350455	+	0.107859i	0.967049	−	0.254590i	$-0.0819406\pi$
$311$	0.618034	+	1.90211i	0.0350455	+	0.107859i	−0.932004	+	0.362449i	$0.881941\pi$
$312$	1.23607	−	3.80423i	0.0699786	−	0.215372i
$313$	4.85410	+	3.52671i	0.274370	+	0.199342i	0.716458	−	0.697630i	$-0.245762\pi$
$313$	4.85410	+	3.52671i	0.274370	+	0.199342i	−0.442088	+	0.896972i	$0.645762\pi$
$314$	14.5623	+	10.5801i	0.821798	+	0.597072i
$315$	−2.47214	+	7.60845i	−0.139289	+	0.428688i
$316$	−3.09017	−	9.51057i	−0.173836	−	0.535011i
$317$	25.8885	−	18.8091i	1.45405	−	1.05643i	0.469181	−	0.883102i	$-0.344549\pi$
$317$	25.8885	−	18.8091i	1.45405	−	1.05643i	0.984865	−	0.173324i	$-0.0554507\pi$
$318$	−4.00000			−0.224309
$319$		0			0
$320$	−4.00000			−0.223607
$321$	−9.70820	+	7.05342i	−0.541859	+	0.393684i
$322$	3.70820	+	11.4127i	0.206650	+	0.636004i
$323$		0			0
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	35.5967	+	25.8626i	1.97455	+	1.43460i
$326$	−1.23607	+	3.80423i	−0.0684595	+	0.210697i
$327$	−6.18034	−	19.0211i	−0.341774	−	1.05187i
$328$	−1.61803	+	1.17557i	−0.0893410	+	0.0649100i
$329$	−4.00000			−0.220527
$330$		0			0
$331$	−28.0000			−1.53902			−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000			−1.53902			−0.769510	+	0.638635i	$0.779499\pi$
$332$	3.23607	−	2.35114i	0.177602	−	0.129036i
$333$	−0.618034	−	1.90211i	−0.0338681	−	0.104235i
$334$	−3.70820	+	11.4127i	−0.202904	+	0.624474i
$335$	−38.8328	−	28.2137i	−2.12166	−	1.54148i
$336$	−1.61803	−	1.17557i	−0.0882710	−	0.0641326i
$337$	6.79837	−	20.9232i	0.370331	−	1.13976i	−0.576244	−	0.817278i	$-0.695482\pi$
$337$	6.79837	−	20.9232i	0.370331	−	1.13976i	0.946575	−	0.322484i	$-0.104518\pi$
$338$	−0.927051	−	2.85317i	−0.0504249	−	0.155192i
$339$	4.85410	−	3.52671i	0.263639	−	0.191545i
$340$	−8.00000			−0.433861
$341$		0			0
$342$		0			0
$343$	16.1803	−	11.7557i	0.873656	−	0.634748i
$344$	1.23607	+	3.80423i	0.0666443	+	0.205110i
$345$	7.41641	−	22.8254i	0.399286	−	1.22888i
$346$	4.85410	+	3.52671i	0.260958	+	0.189597i
$347$	−9.70820	−	7.05342i	−0.521164	−	0.378648i	0.295878	−	0.955226i	$-0.404388\pi$
$347$	−9.70820	−	7.05342i	−0.521164	−	0.378648i	−0.817042	+	0.576578i	$0.804388\pi$
$348$	−3.09017	+	9.51057i	−0.165650	+	0.509820i
$349$	6.18034	+	19.0211i	0.330826	+	1.01818i	0.968742	+	0.248072i	$0.0797968\pi$
$349$	6.18034	+	19.0211i	0.330826	+	1.01818i	−0.637916	+	0.770106i	$0.720203\pi$
$350$	17.7984	−	12.9313i	0.951363	−	0.691206i
$351$	−4.00000			−0.213504
$352$		0			0
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$		0			0
$355$	−2.47214	−	7.60845i	−0.131207	−	0.403815i
$356$	3.09017	−	9.51057i	0.163779	−	0.504059i
$357$	−3.23607	−	2.35114i	−0.171271	−	0.124436i
$358$		0			0
$359$	6.18034	−	19.0211i	0.326186	−	1.00390i	−0.644717	−	0.764422i	$-0.723025\pi$
$359$	6.18034	−	19.0211i	0.326186	−	1.00390i	0.970902	−	0.239475i	$-0.0769754\pi$
$360$	1.23607	+	3.80423i	0.0651465	+	0.200500i
$361$	15.3713	−	11.1679i	0.809017	−	0.587785i
$362$	−2.00000			−0.105118
$363$		0			0
$364$	−8.00000			−0.419314
$365$	19.4164	−	14.1068i	1.01630	−	0.738386i
$366$	−2.47214	−	7.60845i	−0.129221	−	0.397700i
$367$	2.47214	−	7.60845i	0.129044	−	0.397158i	−0.865572	−	0.500785i	$-0.833045\pi$
$367$	2.47214	−	7.60845i	0.129044	−	0.397158i	0.994616	+	0.103627i	$0.0330448\pi$
$368$	4.85410	+	3.52671i	0.253038	+	0.183843i
$369$	1.61803	+	1.17557i	0.0842315	+	0.0611978i
$370$	−2.47214	+	7.60845i	−0.128520	+	0.395545i
$371$	2.47214	+	7.60845i	0.128347	+	0.395011i
$372$	6.47214	−	4.70228i	0.335565	−	0.243802i
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$		0			0
$375$	−24.0000			−1.23935
$376$	−1.61803	+	1.17557i	−0.0834437	+	0.0606254i
$377$	12.3607	+	38.0423i	0.636607	+	1.95928i
$378$	−0.618034	+	1.90211i	−0.0317882	+	0.0978341i
$379$	16.1803	+	11.7557i	0.831128	+	0.603850i	0.919878	−	0.392204i	$-0.128287\pi$
$379$	16.1803	+	11.7557i	0.831128	+	0.603850i	−0.0887501	+	0.996054i	$0.528287\pi$
$380$		0			0
$381$	6.79837	−	20.9232i	0.348291	−	1.07193i
$382$	−6.79837	−	20.9232i	−0.347835	−	1.07053i
$383$	4.85410	−	3.52671i	0.248033	−	0.180207i	−0.456822	−	0.889558i	$-0.651012\pi$
$383$	4.85410	−	3.52671i	0.248033	−	0.180207i	0.704855	+	0.709352i	$0.251012\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	14.0000			0.712581
$387$	3.23607	−	2.35114i	0.164499	−	0.119515i
$388$	−0.618034	−	1.90211i	−0.0313759	−	0.0965652i
$389$	−6.18034	+	19.0211i	−0.313356	+	0.964410i	0.663070	+	0.748557i	$0.269253\pi$
$389$	−6.18034	+	19.0211i	−0.313356	+	0.964410i	−0.976426	+	0.215852i	$0.930747\pi$
$390$	12.9443	+	9.40456i	0.655459	+	0.476219i
$391$	9.70820	+	7.05342i	0.490965	+	0.356707i
$392$	0.927051	−	2.85317i	0.0468231	−	0.144107i
$393$	−3.70820	−	11.4127i	−0.187054	−	0.575693i
$394$	−14.5623	+	10.5801i	−0.733638	+	0.533019i
$395$	40.0000			2.01262
$396$		0			0
$397$	18.0000			0.903394			0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000			0.903394			0.451697	+	0.892171i	$0.350819\pi$
$398$	16.1803	−	11.7557i	0.811047	−	0.589260i
$399$		0			0
$400$	3.39919	−	10.4616i	0.169959	−	0.523081i
$401$	14.5623	+	10.5801i	0.727207	+	0.528347i	0.888679	−	0.458531i	$-0.151624\pi$
$401$	14.5623	+	10.5801i	0.727207	+	0.528347i	−0.161472	+	0.986877i	$0.551624\pi$
$402$	−9.70820	−	7.05342i	−0.484201	−	0.351793i
$403$	9.88854	−	30.4338i	0.492583	−	1.51602i
$404$	−0.618034	−	1.90211i	−0.0307483	−	0.0946337i
$405$	3.23607	−	2.35114i	0.160802	−	0.116829i
$406$	20.0000			0.992583
$407$		0			0
$408$	−2.00000			−0.0990148
$409$	−8.09017	+	5.87785i	−0.400033	+	0.290641i	−0.769554	−	0.638581i	$-0.779522\pi$
$409$	−8.09017	+	5.87785i	−0.400033	+	0.290641i	0.369521	+	0.929222i	$0.379522\pi$
$410$	−2.47214	−	7.60845i	−0.122090	−	0.375755i
$411$	−0.618034	+	1.90211i	−0.0304854	+	0.0938243i
$412$	−3.23607	−	2.35114i	−0.159430	−	0.115832i
$413$		0			0
$414$	1.85410	−	5.70634i	0.0911241	−	0.280451i
$415$	4.94427	+	15.2169i	0.242705	+	0.746968i
$416$	−3.23607	+	2.35114i	−0.158661	+	0.115274i
$417$		0			0
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$	6.47214	−	4.70228i	0.315808	−	0.229448i
$421$	−5.56231	−	17.1190i	−0.271090	−	0.834330i	−0.990227	−	0.139462i	$-0.955463\pi$
$421$	−5.56231	−	17.1190i	−0.271090	−	0.834330i	0.719137	−	0.694868i	$-0.244537\pi$
$422$	3.70820	−	11.4127i	0.180513	−	0.555560i
$423$	1.61803	+	1.17557i	0.0786715	+	0.0571582i
$424$	3.23607	+	2.35114i	0.157157	+	0.114182i
$425$	6.79837	−	20.9232i	0.329770	−	1.01493i
$426$	−0.618034	−	1.90211i	−0.0299438	−	0.0921577i
$427$	−12.9443	+	9.40456i	−0.626417	+	0.455119i
$428$	12.0000			0.580042
$429$		0			0
$430$	−16.0000			−0.771589
$431$	25.8885	−	18.8091i	1.24701	−	0.906004i	0.248963	−	0.968513i	$-0.419910\pi$
$431$	25.8885	−	18.8091i	1.24701	−	0.906004i	0.998044	+	0.0625092i	$0.0199103\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	−1.85410	+	5.70634i	−0.0891025	+	0.274229i	−0.985672	−	0.168674i	$-0.946051\pi$
$433$	−1.85410	+	5.70634i	−0.0891025	+	0.274229i	0.896569	+	0.442903i	$0.146051\pi$
$434$	−12.9443	−	9.40456i	−0.621345	−	0.451434i
$435$	−32.3607	−	23.5114i	−1.55158	−	1.12729i
$436$	−6.18034	+	19.0211i	−0.295985	+	0.910947i
$437$		0			0
$438$	4.85410	−	3.52671i	0.231938	−	0.168513i
$439$	−10.0000			−0.477274			−0.238637	−	0.971109i	$-0.576701\pi$
$439$	−10.0000			−0.477274			−0.238637	+	0.971109i	$0.576701\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$	−6.47214	+	4.70228i	−0.307848	+	0.223665i
$443$	7.41641	+	22.8254i	0.352364	+	1.08447i	0.957522	+	0.288360i	$0.0931100\pi$
$443$	7.41641	+	22.8254i	0.352364	+	1.08447i	−0.605158	+	0.796105i	$0.706890\pi$
$444$	−0.618034	+	1.90211i	−0.0293306	+	0.0902703i
$445$	32.3607	+	23.5114i	1.53404	+	1.11455i
$446$	−12.9443	−	9.40456i	−0.612929	−	0.445319i
$447$	3.09017	−	9.51057i	0.146160	−	0.449834i
$448$	0.618034	+	1.90211i	0.0291994	+	0.0898664i
$449$	−24.2705	+	17.6336i	−1.14540	+	0.832179i	−0.987862	−	0.155334i	$-0.950354\pi$
$449$	−24.2705	+	17.6336i	−1.14540	+	0.832179i	−0.157534	+	0.987514i	$0.550354\pi$
$450$	−11.0000			−0.518545
$451$		0			0
$452$	−6.00000			−0.282216
$453$	1.61803	−	1.17557i	0.0760219	−	0.0552331i
$454$	−3.70820	−	11.4127i	−0.174035	−	0.535624i
$455$	9.88854	−	30.4338i	0.463582	−	1.42676i
$456$		0			0
$457$	−1.61803	−	1.17557i	−0.0756884	−	0.0549909i	0.549298	−	0.835627i	$-0.314895\pi$
$457$	−1.61803	−	1.17557i	−0.0756884	−	0.0549909i	−0.624986	+	0.780636i	$0.714895\pi$
$458$	−3.09017	+	9.51057i	−0.144394	+	0.444400i
$459$	0.618034	+	1.90211i	0.0288474	+	0.0887830i
$460$	−19.4164	+	14.1068i	−0.905295	+	0.657735i
$461$	18.0000			0.838344			0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$		0			0
$463$	4.00000			0.185896			0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000			0.185896			0.0929479	+	0.995671i	$0.470371\pi$
$464$	8.09017	−	5.87785i	0.375577	−	0.272872i
$465$	9.88854	+	30.4338i	0.458570	+	1.41133i
$466$	−1.85410	+	5.70634i	−0.0858896	+	0.264341i
$467$	−22.6525	−	16.4580i	−1.04823	−	0.761585i	−0.0763562	−	0.997081i	$-0.524329\pi$
$467$	−22.6525	−	16.4580i	−1.04823	−	0.761585i	−0.971875	+	0.235496i	$0.924329\pi$
$468$	3.23607	+	2.35114i	0.149587	+	0.108682i
$469$	−7.41641	+	22.8254i	−0.342458	+	1.05398i
$470$	−2.47214	−	7.60845i	−0.114031	−	0.350952i
$471$	−14.5623	+	10.5801i	−0.670996	+	0.487507i
$472$		0			0
$473$		0			0
$474$	10.0000			0.459315
$475$		0			0
$476$	1.23607	+	3.80423i	0.0566551	+	0.174366i
$477$	1.23607	−	3.80423i	0.0565957	−	0.174184i
$478$	16.1803	+	11.7557i	0.740072	+	0.537693i
$479$	32.3607	+	23.5114i	1.47860	+	1.07426i	0.978005	+	0.208580i	$0.0668843\pi$
$479$	32.3607	+	23.5114i	1.47860	+	1.07426i	0.500592	+	0.865683i	$0.333116\pi$
$480$	1.23607	−	3.80423i	0.0564185	−	0.173638i
$481$	2.47214	+	7.60845i	0.112720	+	0.346916i
$482$	14.5623	−	10.5801i	0.663295	−	0.481912i
$483$	−12.0000			−0.546019
$484$		0			0
$485$	8.00000			0.363261
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	8.65248	+	26.6296i	0.392081	+	1.20670i	0.931212	+	0.364479i	$0.118753\pi$
$487$	8.65248	+	26.6296i	0.392081	+	1.20670i	−0.539130	+	0.842222i	$0.681247\pi$
$488$	−2.47214	+	7.60845i	−0.111908	+	0.344418i
$489$	−3.23607	−	2.35114i	−0.146340	−	0.106322i
$490$	9.70820	+	7.05342i	0.438572	+	0.318641i
$491$	−3.70820	+	11.4127i	−0.167349	+	0.515047i	−0.999202	−	0.0399494i	$-0.987280\pi$
$491$	−3.70820	+	11.4127i	−0.167349	+	0.515047i	0.831853	+	0.554996i	$0.187280\pi$
$492$	−0.618034	−	1.90211i	−0.0278631	−	0.0857539i
$493$	16.1803	−	11.7557i	0.728726	−	0.529450i
$494$		0			0
$495$		0			0
$496$	−8.00000			−0.359211
$497$	−3.23607	+	2.35114i	−0.145157	+	0.105463i
$498$	1.23607	+	3.80423i	0.0553895	+	0.170471i
$499$	−6.18034	+	19.0211i	−0.276670	+	0.851503i	0.712103	+	0.702075i	$0.247743\pi$
$499$	−6.18034	+	19.0211i	−0.276670	+	0.851503i	−0.988773	+	0.149427i	$0.952257\pi$
$500$	19.4164	+	14.1068i	0.868328	+	0.630877i
$501$	−9.70820	−	7.05342i	−0.433731	−	0.315124i
$502$	2.47214	−	7.60845i	0.110337	−	0.339582i
$503$	−1.23607	−	3.80423i	−0.0551135	−	0.169622i	0.919711	−	0.392597i	$-0.128423\pi$
$503$	−1.23607	−	3.80423i	−0.0551135	−	0.169622i	−0.974824	+	0.222975i	$0.928423\pi$
$504$	1.61803	−	1.17557i	0.0720730	−	0.0523641i
$505$	8.00000			0.355995
$506$		0			0
$507$	3.00000			0.133235
$508$	−17.7984	+	12.9313i	−0.789675	+	0.573733i
$509$	−6.18034	−	19.0211i	−0.273939	−	0.843097i	−0.989498	−	0.144545i	$-0.953828\pi$
$509$	−6.18034	−	19.0211i	−0.273939	−	0.843097i	0.715559	−	0.698552i	$-0.246172\pi$
$510$	2.47214	−	7.60845i	0.109468	−	0.336908i
$511$	−9.70820	−	7.05342i	−0.429466	−	0.312025i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$		0			0
$514$	−5.56231	−	17.1190i	−0.245343	−	0.755087i
$515$	12.9443	−	9.40456i	0.570393	−	0.414415i
$516$	−4.00000			−0.176090
$517$		0			0
$518$	4.00000			0.175750
$519$	−4.85410	+	3.52671i	−0.213071	+	0.154805i
$520$	−4.94427	−	15.2169i	−0.216821	−	0.667305i
$521$	−5.56231	+	17.1190i	−0.243689	+	0.749998i	0.752160	+	0.658980i	$0.229012\pi$
$521$	−5.56231	+	17.1190i	−0.243689	+	0.749998i	−0.995849	+	0.0910175i	$0.970988\pi$
$522$	−8.09017	−	5.87785i	−0.354097	−	0.257267i
$523$	35.5967	+	25.8626i	1.55654	+	1.13089i	0.938778	+	0.344523i	$0.111959\pi$
$523$	35.5967	+	25.8626i	1.55654	+	1.13089i	0.617759	+	0.786367i	$0.288041\pi$
$524$	−3.70820	+	11.4127i	−0.161994	+	0.498565i
$525$	6.79837	+	20.9232i	0.296705	+	0.913165i
$526$	12.9443	−	9.40456i	0.564397	−	0.410058i
$527$	−16.0000			−0.696971
$528$		0			0
$529$	13.0000			0.565217
$530$	−12.9443	+	9.40456i	−0.562263	+	0.408508i
$531$		0			0
$532$		0			0
$533$	−6.47214	−	4.70228i	−0.280339	−	0.203678i
$534$	8.09017	+	5.87785i	0.350096	+	0.254360i
$535$	−14.8328	+	45.6507i	−0.641279	+	1.97365i
$536$	3.70820	+	11.4127i	0.160170	+	0.492953i
$537$		0			0
$538$	20.0000			0.862261
$539$		0			0
$540$	−4.00000			−0.172133
$541$	9.70820	−	7.05342i	0.417388	−	0.303250i	−0.359198	−	0.933261i	$-0.616950\pi$
$541$	9.70820	−	7.05342i	0.417388	−	0.303250i	0.776586	+	0.630011i	$0.216950\pi$
$542$	6.79837	+	20.9232i	0.292015	+	0.898730i
$543$	0.618034	−	1.90211i	0.0265224	−	0.0816275i
$544$	1.61803	+	1.17557i	0.0693726	+	0.0504022i
$545$	−64.7214	−	47.0228i	−2.77236	−	2.01424i
$546$	2.47214	−	7.60845i	0.105798	−	0.325612i
$547$	9.88854	+	30.4338i	0.422804	+	1.30126i	0.905082	+	0.425238i	$0.139809\pi$
$547$	9.88854	+	30.4338i	0.422804	+	1.30126i	−0.482278	+	0.876018i	$0.660191\pi$
$548$	1.61803	−	1.17557i	0.0691190	−	0.0502179i
$549$	8.00000			0.341432
$550$		0			0
$551$		0			0
$552$	−4.85410	+	3.52671i	−0.206604	+	0.150107i
$553$	−6.18034	−	19.0211i	−0.262815	−	0.808861i
$554$	2.47214	−	7.60845i	0.105031	−	0.323252i
$555$	−6.47214	−	4.70228i	−0.274727	−	0.199601i
$556$		0			0
$557$	−11.7426	+	36.1401i	−0.497552	+	1.53131i	0.315390	+	0.948962i	$0.397865\pi$
$557$	−11.7426	+	36.1401i	−0.497552	+	1.53131i	−0.812942	+	0.582345i	$0.802135\pi$
$558$	2.47214	+	7.60845i	0.104654	+	0.322091i
$559$	−12.9443	+	9.40456i	−0.547484	+	0.397771i
$560$	−8.00000			−0.338062
$561$		0			0
$562$	22.0000			0.928014
$563$	−29.1246	+	21.1603i	−1.22746	+	0.891799i	−0.996697	−	0.0812119i	$-0.974121\pi$
$563$	−29.1246	+	21.1603i	−1.22746	+	0.891799i	−0.230759	+	0.973011i	$0.574121\pi$
$564$	−0.618034	−	1.90211i	−0.0260239	−	0.0800934i
$565$	7.41641	−	22.8254i	0.312011	−	0.960270i
$566$	−3.23607	−	2.35114i	−0.136022	−	0.0988258i
$567$	−1.61803	−	1.17557i	−0.0679510	−	0.0493693i
$568$	−0.618034	+	1.90211i	−0.0259321	+	0.0798109i
$569$	3.09017	+	9.51057i	0.129547	+	0.398704i	0.994702	−	0.102800i	$-0.0327803\pi$
$569$	3.09017	+	9.51057i	0.129547	+	0.398704i	−0.865155	+	0.501504i	$0.832780\pi$
$570$		0			0
$571$	−32.0000			−1.33916			−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000			−1.33916			−0.669579	+	0.742741i	$0.733526\pi$
$572$		0			0
$573$	22.0000			0.919063
$574$	−3.23607	+	2.35114i	−0.135071	+	0.0981347i
$575$	−20.3951	−	62.7697i	−0.850535	−	2.61768i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	1.61803	+	1.17557i	0.0673596	+	0.0489396i	0.620956	−	0.783846i	$-0.286745\pi$
$577$	1.61803	+	1.17557i	0.0673596	+	0.0489396i	−0.553596	+	0.832785i	$0.686745\pi$
$578$	−10.5172	−	7.64121i	−0.437459	−	0.317832i
$579$	−4.32624	+	13.3148i	−0.179792	+	0.553344i
$580$	12.3607	+	38.0423i	0.513249	+	1.57962i
$581$	6.47214	−	4.70228i	0.268509	−	0.195084i
$582$	2.00000			0.0829027
$583$		0			0
$584$	−6.00000			−0.248282
$585$	−12.9443	+	9.40456i	−0.535180	+	0.388831i
$586$	4.32624	+	13.3148i	0.178715	+	0.550029i
$587$	2.47214	−	7.60845i	0.102036	−	0.314034i	−0.886987	−	0.461794i	$-0.847206\pi$
$587$	2.47214	−	7.60845i	0.102036	−	0.314034i	0.989023	+	0.147759i	$0.0472061\pi$
$588$	2.42705	+	1.76336i	0.100090	+	0.0727196i
$589$		0			0
$590$		0			0
$591$	−5.56231	−	17.1190i	−0.228803	−	0.704182i
$592$	1.61803	−	1.17557i	0.0665008	−	0.0483157i
$593$	−14.0000			−0.574911			−0.287456	−	0.957794i	$-0.592809\pi$
$593$	−14.0000			−0.574911			−0.287456	+	0.957794i	$0.592809\pi$
$594$		0			0
$595$	−16.0000			−0.655936
$596$	−8.09017	+	5.87785i	−0.331386	+	0.240766i
$597$	6.18034	+	19.0211i	0.252944	+	0.778483i
$598$	−7.41641	+	22.8254i	−0.303279	+	0.933398i
$599$	24.2705	+	17.6336i	0.991666	+	0.720488i	0.960285	−	0.279020i	$-0.0900095\pi$
$599$	24.2705	+	17.6336i	0.991666	+	0.720488i	0.0313808	+	0.999508i	$0.490010\pi$
$600$	8.89919	+	6.46564i	0.363308	+	0.263959i
$601$	−12.9787	+	39.9444i	−0.529413	+	1.62936i	0.226008	+	0.974125i	$0.427432\pi$
$601$	−12.9787	+	39.9444i	−0.529413	+	1.62936i	−0.755421	+	0.655240i	$0.772568\pi$
$602$	2.47214	+	7.60845i	0.100757	+	0.310097i
$603$	9.70820	−	7.05342i	0.395349	−	0.287238i
$604$	−2.00000			−0.0813788
$605$		0			0
$606$	2.00000			0.0812444
$607$	−17.7984	+	12.9313i	−0.722414	+	0.524864i	−0.887154	−	0.461473i	$-0.847321\pi$
$607$	−17.7984	+	12.9313i	−0.722414	+	0.524864i	0.164741	+	0.986337i	$0.447321\pi$
$608$		0			0
$609$	−6.18034	+	19.0211i	−0.250440	+	0.770775i
$610$	−25.8885	−	18.8091i	−1.04820	−	0.761559i
$611$	−6.47214	−	4.70228i	−0.261835	−	0.190234i
$612$	0.618034	−	1.90211i	0.0249825	−	0.0768884i
$613$	4.94427	+	15.2169i	0.199697	+	0.614605i	0.999890	+	0.0148615i	$0.00473072\pi$
$613$	4.94427	+	15.2169i	0.199697	+	0.614605i	−0.800192	+	0.599744i	$0.795269\pi$
$614$	−6.47214	+	4.70228i	−0.261194	+	0.189769i
$615$	8.00000			0.322591
$616$		0			0
$617$	−22.0000			−0.885687			−0.442843	−	0.896599i	$-0.646030\pi$
$617$	−22.0000			−0.885687			−0.442843	+	0.896599i	$0.646030\pi$
$618$	3.23607	−	2.35114i	0.130174	−	0.0945768i
$619$	−6.18034	−	19.0211i	−0.248409	−	0.764524i	−0.995057	−	0.0993047i	$-0.968338\pi$
$619$	−6.18034	−	19.0211i	−0.248409	−	0.764524i	0.746648	−	0.665219i	$-0.231662\pi$
$620$	9.88854	−	30.4338i	0.397133	−	1.22225i
$621$	4.85410	+	3.52671i	0.194788	+	0.141522i
$622$	1.61803	+	1.17557i	0.0648773	+	0.0471361i
$623$	6.18034	−	19.0211i	0.247610	−	0.762065i
$624$	−1.23607	−	3.80423i	−0.0494823	−	0.152291i
$625$	−33.1697	+	24.0992i	−1.32679	+	0.963968i
$626$	6.00000			0.239808
$627$		0			0
$628$	18.0000			0.718278
$629$	3.23607	−	2.35114i	0.129030	−	0.0937461i
$630$	2.47214	+	7.60845i	0.0984923	+	0.303128i
$631$	−14.8328	+	45.6507i	−0.590485	+	1.81733i	−0.0144581	+	0.999895i	$0.504602\pi$
$631$	−14.8328	+	45.6507i	−0.590485	+	1.81733i	−0.576027	+	0.817431i	$0.695398\pi$
$632$	−8.09017	−	5.87785i	−0.321810	−	0.233808i
$633$	9.70820	+	7.05342i	0.385866	+	0.280348i
$634$	9.88854	−	30.4338i	0.392724	−	1.20868i
$635$	−27.1935	−	83.6930i	−1.07914	−	3.32125i
$636$	−3.23607	+	2.35114i	−0.128318	+	0.0932288i
$637$	12.0000			0.475457
$638$		0			0
$639$	2.00000			0.0791188
$640$	−3.23607	+	2.35114i	−0.127917	+	0.0929370i
$641$	−5.56231	−	17.1190i	−0.219698	−	0.676161i	−0.998787	−	0.0492469i	$-0.984318\pi$
$641$	−5.56231	−	17.1190i	−0.219698	−	0.676161i	0.779089	−	0.626914i	$-0.215682\pi$
$642$	−3.70820	+	11.4127i	−0.146351	+	0.450422i
$643$	−35.5967	−	25.8626i	−1.40380	−	1.01992i	−0.994188	−	0.107659i	$-0.965665\pi$
$643$	−35.5967	−	25.8626i	−1.40380	−	1.01992i	−0.409611	−	0.912260i	$-0.634335\pi$
$644$	9.70820	+	7.05342i	0.382557	+	0.277944i
$645$	4.94427	−	15.2169i	0.194681	−	0.599165i
$646$		0			0
$647$	17.7984	−	12.9313i	0.699726	−	0.508381i	−0.180117	−	0.983645i	$-0.557648\pi$
$647$	17.7984	−	12.9313i	0.699726	−	0.508381i	0.879843	+	0.475264i	$0.157648\pi$
$648$	−1.00000			−0.0392837
$649$		0			0
$650$	44.0000			1.72582
$651$	12.9443	−	9.40456i	0.507326	−	0.368594i
$652$	1.23607	+	3.80423i	0.0484082	+	0.148985i
$653$	7.41641	−	22.8254i	0.290226	−	0.893225i	−0.694557	−	0.719438i	$-0.744399\pi$
$653$	7.41641	−	22.8254i	0.290226	−	0.893225i	0.984783	−	0.173787i	$-0.0556005\pi$
$654$	−16.1803	−	11.7557i	−0.632701	−	0.459684i
$655$	−38.8328	−	28.2137i	−1.51732	−	1.10240i
$656$	−0.618034	+	1.90211i	−0.0241302	+	0.0742650i
$657$	1.85410	+	5.70634i	0.0723354	+	0.222625i
$658$	−3.23607	+	2.35114i	−0.126155	+	0.0916570i
$659$	20.0000			0.779089			0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000			0.779089			0.389545	+	0.921008i	$0.372632\pi$
$660$		0			0
$661$	42.0000			1.63361			0.816805	−	0.576913i	$-0.195743\pi$
$661$	42.0000			1.63361			0.816805	+	0.576913i	$0.195743\pi$
$662$	−22.6525	+	16.4580i	−0.880413	+	0.639658i
$663$	−2.47214	−	7.60845i	−0.0960098	−	0.295488i
$664$	1.23607	−	3.80423i	0.0479687	−	0.147633i
$665$		0			0
$666$	−1.61803	−	1.17557i	−0.0626975	−	0.0455524i
$667$	18.5410	−	57.0634i	0.717911	−	2.20950i
$668$	3.70820	+	11.4127i	0.143475	+	0.441570i
$669$	12.9443	−	9.40456i	0.500454	−	0.363601i
$670$	−48.0000			−1.85440
$671$		0			0
$672$	−2.00000			−0.0771517
$673$	11.3262	−	8.22899i	0.436594	−	0.317204i	−0.347686	−	0.937611i	$-0.613032\pi$
$673$	11.3262	−	8.22899i	0.436594	−	0.317204i	0.784280	+	0.620407i	$0.213032\pi$
$674$	−6.79837	−	20.9232i	−0.261864	−	0.805933i
$675$	3.39919	−	10.4616i	0.130835	−	0.402668i
$676$	−2.42705	−	1.76336i	−0.0933481	−	0.0678214i
$677$	−17.7984	−	12.9313i	−0.684047	−	0.496989i	0.190651	−	0.981658i	$-0.438940\pi$
$677$	−17.7984	−	12.9313i	−0.684047	−	0.496989i	−0.874698	+	0.484669i	$0.838940\pi$
$678$	1.85410	−	5.70634i	0.0712064	−	0.219151i
$679$	−1.23607	−	3.80423i	−0.0474359	−	0.145993i
$680$	−6.47214	+	4.70228i	−0.248195	+	0.180324i
$681$	12.0000			0.459841
$682$		0			0
$683$	−16.0000			−0.612223			−0.306111	−	0.951996i	$-0.599028\pi$
$683$	−16.0000			−0.612223			−0.306111	+	0.951996i	$0.599028\pi$
$684$		0			0
$685$	2.47214	+	7.60845i	0.0944555	+	0.290704i
$686$	6.18034	−	19.0211i	0.235966	−	0.726230i
$687$	−8.09017	−	5.87785i	−0.308659	−	0.224254i
$688$	3.23607	+	2.35114i	0.123374	+	0.0896364i
$689$	−4.94427	+	15.2169i	−0.188362	+	0.579718i
$690$	−7.41641	−	22.8254i	−0.282338	−	0.868946i
$691$	−42.0689	+	30.5648i	−1.60038	+	1.16274i	−0.713586	+	0.700567i	$0.752930\pi$
$691$	−42.0689	+	30.5648i	−1.60038	+	1.16274i	−0.886789	+	0.462174i	$0.847070\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−12.0000			−0.455514
$695$		0			0
$696$	3.09017	+	9.51057i	0.117133	+	0.360497i
$697$	−1.23607	+	3.80423i	−0.0468194	+	0.144095i
$698$	16.1803	+	11.7557i	0.612435	+	0.444960i
$699$	−4.85410	−	3.52671i	−0.183599	−	0.133392i
$700$	6.79837	−	20.9232i	0.256954	−	0.790824i
$701$	5.56231	+	17.1190i	0.210085	+	0.646576i	0.999466	+	0.0326724i	$0.0104018\pi$
$701$	5.56231	+	17.1190i	0.210085	+	0.646576i	−0.789381	+	0.613904i	$0.789598\pi$
$702$	−3.23607	+	2.35114i	−0.122138	+	0.0887381i
$703$		0			0
$704$		0			0
$705$	8.00000			0.301297
$706$	−4.85410	+	3.52671i	−0.182687	+	0.132730i
$707$	−1.23607	−	3.80423i	−0.0464871	−	0.143073i
$708$		0			0
$709$	−8.09017	−	5.87785i	−0.303833	−	0.220747i	0.425413	−	0.904999i	$-0.360129\pi$
$709$	−8.09017	−	5.87785i	−0.303833	−	0.220747i	−0.729246	+	0.684252i	$0.760129\pi$
$710$	−6.47214	−	4.70228i	−0.242895	−	0.176473i
$711$	−3.09017	+	9.51057i	−0.115890	+	0.356674i
$712$	−3.09017	−	9.51057i	−0.115809	−	0.356423i
$713$	−38.8328	+	28.2137i	−1.45430	+	1.05661i
$714$	−4.00000			−0.149696
$715$		0			0
$716$		0			0
$717$	−16.1803	+	11.7557i	−0.604266	+	0.439025i
$718$	−6.18034	−	19.0211i	−0.230648	−	0.709862i
$719$	3.09017	−	9.51057i	0.115244	−	0.354684i	−0.876754	−	0.480939i	$-0.840296\pi$
$719$	3.09017	−	9.51057i	0.115244	−	0.354684i	0.991998	+	0.126255i	$0.0402958\pi$
$720$	3.23607	+	2.35114i	0.120601	+	0.0876219i
$721$	−6.47214	−	4.70228i	−0.241035	−	0.175122i
$722$	5.87132	−	18.0701i	0.218508	−	0.672499i
$723$	5.56231	+	17.1190i	0.206864	+	0.636663i
$724$	−1.61803	+	1.17557i	−0.0601338	+	0.0436897i
$725$	−110.000			−4.08530
$726$		0			0
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$	−6.47214	+	4.70228i	−0.239873	+	0.174278i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	7.41641	−	22.8254i	0.274494	−	0.844804i
$731$	6.47214	+	4.70228i	0.239381	+	0.173920i
$732$	−6.47214	−	4.70228i	−0.239217	−	0.173801i
$733$	−1.23607	+	3.80423i	−0.0456552	+	0.140512i	−0.971286	−	0.237917i	$-0.923536\pi$
$733$	−1.23607	+	3.80423i	−0.0456552	+	0.140512i	0.925630	+	0.378429i	$0.123536\pi$
$734$	−2.47214	−	7.60845i	−0.0912482	−	0.280833i
$735$	−9.70820	+	7.05342i	−0.358092	+	0.260169i
$736$	6.00000			0.221163
$737$		0			0
$738$	2.00000			0.0736210
$739$	16.1803	−	11.7557i	0.595203	−	0.432441i	−0.248970	−	0.968511i	$-0.580092\pi$
$739$	16.1803	−	11.7557i	0.595203	−	0.432441i	0.844173	+	0.536071i	$0.180092\pi$
$740$	2.47214	+	7.60845i	0.0908775	+	0.279692i
$741$		0			0
$742$	6.47214	+	4.70228i	0.237600	+	0.172626i
$743$	35.5967	+	25.8626i	1.30592	+	0.948805i	0.999995	−	0.00325118i	$-0.00103489\pi$
$743$	35.5967	+	25.8626i	1.30592	+	0.948805i	0.305923	+	0.952056i	$0.401035\pi$
$744$	2.47214	−	7.60845i	0.0906329	−	0.278939i
$745$	−12.3607	−	38.0423i	−0.452860	−	1.39376i
$746$	−3.23607	+	2.35114i	−0.118481	+	0.0860814i
$747$	−4.00000			−0.146352
$748$		0			0
$749$	24.0000			0.876941
$750$	−19.4164	+	14.1068i	−0.708987	+	0.515109i
$751$	−2.47214	−	7.60845i	−0.0902095	−	0.277636i	0.895766	−	0.444526i	$-0.146628\pi$
$751$	−2.47214	−	7.60845i	−0.0902095	−	0.277636i	−0.985976	+	0.166889i	$0.946628\pi$
$752$	−0.618034	+	1.90211i	−0.0225374	+	0.0693629i
$753$	6.47214	+	4.70228i	0.235858	+	0.171361i
$754$	32.3607	+	23.5114i	1.17851	+	0.856235i
$755$	2.47214	−	7.60845i	0.0899702	−	0.276900i
$756$	0.618034	+	1.90211i	0.0224777	+	0.0691792i
$757$	33.9787	−	24.6870i	1.23498	−	0.897264i	0.237724	−	0.971333i	$-0.423599\pi$
$757$	33.9787	−	24.6870i	1.23498	−	0.897264i	0.997253	+	0.0740691i	$0.0235985\pi$
$758$	20.0000			0.726433
$759$		0			0
$760$		0			0
$761$	17.7984	−	12.9313i	0.645191	−	0.468758i	−0.216439	−	0.976296i	$-0.569444\pi$
$761$	17.7984	−	12.9313i	0.645191	−	0.468758i	0.861630	+	0.507538i	$0.169444\pi$
$762$	−6.79837	−	20.9232i	−0.246279	−	0.757969i
$763$	−12.3607	+	38.0423i	−0.447487	+	1.37722i
$764$	−17.7984	−	12.9313i	−0.643923	−	0.467837i
$765$	6.47214	+	4.70228i	0.234001	+	0.170011i
$766$	1.85410	−	5.70634i	0.0669914	−	0.206178i
$767$		0			0
$768$	−0.809017	+	0.587785i	−0.0291929	+	0.0212099i
$769$	50.0000			1.80305			0.901523	−	0.432731i	$-0.142450\pi$
$769$	50.0000			1.80305			0.901523	+	0.432731i	$0.142450\pi$
$770$		0			0
$771$	18.0000			0.648254
$772$	11.3262	−	8.22899i	0.407640	−	0.296168i
$773$	1.23607	+	3.80423i	0.0444583	+	0.136829i	0.970822	−	0.239802i	$-0.0770826\pi$
$773$	1.23607	+	3.80423i	0.0444583	+	0.136829i	−0.926363	+	0.376631i	$0.877083\pi$
$774$	1.23607	−	3.80423i	0.0444295	−	0.136740i
$775$	71.1935	+	51.7251i	2.55735	+	1.85802i
$776$	−1.61803	−	1.17557i	−0.0580840	−	0.0422005i
$777$	−1.23607	+	3.80423i	−0.0443437	+	0.136476i
$778$	6.18034	+	19.0211i	0.221576	+	0.681941i
$779$		0			0
$780$	16.0000			0.572892
$781$		0			0
$782$	12.0000			0.429119
$783$	8.09017	−	5.87785i	0.289119	−	0.210057i
$784$	−0.927051	−	2.85317i	−0.0331090	−	0.101899i
$785$	−22.2492	+	68.4761i	−0.794109	+	2.44402i
$786$	−9.70820	−	7.05342i	−0.346280	−	0.251587i
$787$	−42.0689	−	30.5648i	−1.49959	−	1.08952i	−0.970543	−	0.240929i	$-0.922548\pi$
$787$	−42.0689	−	30.5648i	−1.49959	−	1.08952i	−0.529051	−	0.848590i	$-0.677452\pi$
$788$	−5.56231	+	17.1190i	−0.198149	+	0.609840i
$789$	4.94427	+	15.2169i	0.176021	+	0.541736i
$790$	32.3607	−	23.5114i	1.15134	−	0.836498i
$791$	−12.0000			−0.426671
$792$		0			0
$793$	−32.0000			−1.13635
$794$	14.5623	−	10.5801i	0.516797	−	0.375475i
$795$	−4.94427	−	15.2169i	−0.175355	−	0.539688i
$796$	6.18034	−	19.0211i	0.219056	−	0.674186i
$797$	−22.6525	−	16.4580i	−0.802392	−	0.582972i	0.109223	−	0.994017i	$-0.465164\pi$
$797$	−22.6525	−	16.4580i	−0.802392	−	0.582972i	−0.911615	+	0.411045i	$0.865164\pi$
$798$		0			0
$799$	−1.23607	+	3.80423i	−0.0437289	+	0.134584i
$800$	−3.39919	−	10.4616i	−0.120179	−	0.369874i
$801$	−8.09017	+	5.87785i	−0.285852	+	0.207684i
$802$	18.0000			0.635602
$803$		0			0
$804$	−12.0000			−0.423207
$805$	−38.8328	+	28.2137i	−1.36868	+	0.994402i
$806$	−9.88854	−	30.4338i	−0.348309	−	1.07199i
$807$	−6.18034	+	19.0211i	−0.217558	+	0.669575i
$808$	−1.61803	−	1.17557i	−0.0569222	−	0.0413564i
$809$	8.09017	+	5.87785i	0.284435	+	0.206654i	0.720850	−	0.693091i	$-0.243752\pi$
$809$	8.09017	+	5.87785i	0.284435	+	0.206654i	−0.436414	+	0.899746i	$0.643752\pi$
$810$	1.23607	−	3.80423i	0.0434310	−	0.133667i
$811$	−3.70820	−	11.4127i	−0.130213	−	0.400753i	0.864602	−	0.502457i	$-0.167571\pi$
$811$	−3.70820	−	11.4127i	−0.130213	−	0.400753i	−0.994815	+	0.101704i	$0.967571\pi$
$812$	16.1803	−	11.7557i	0.567819	−	0.412544i
$813$	−22.0000			−0.771574
$814$		0			0
$815$	−16.0000			−0.560456
$816$	−1.61803	+	1.17557i	−0.0566425	+	0.0411532i
$817$		0			0
$818$	−3.09017	+	9.51057i	−0.108045	+	0.332529i
$819$	6.47214	+	4.70228i	0.226155	+	0.164311i
$820$	−6.47214	−	4.70228i	−0.226017	−	0.164211i
$821$	11.7426	−	36.1401i	0.409821	−	1.26130i	−0.506981	−	0.861957i	$-0.669238\pi$
$821$	11.7426	−	36.1401i	0.409821	−	1.26130i	0.916802	−	0.399342i	$-0.130762\pi$
$822$	0.618034	+	1.90211i	0.0215564	+	0.0663438i
$823$	−19.4164	+	14.1068i	−0.676813	+	0.491734i	−0.872299	−	0.488973i	$-0.837372\pi$
$823$	−19.4164	+	14.1068i	−0.676813	+	0.491734i	0.195486	+	0.980707i	$0.437372\pi$
$824$	−4.00000			−0.139347
$825$		0			0
$826$		0			0
$827$	−9.70820	+	7.05342i	−0.337587	+	0.245272i	−0.743643	−	0.668577i	$-0.766904\pi$
$827$	−9.70820	+	7.05342i	−0.337587	+	0.245272i	0.406056	+	0.913848i	$0.366904\pi$
$828$	−1.85410	−	5.70634i	−0.0644345	−	0.198309i
$829$	9.27051	−	28.5317i	0.321978	−	0.990947i	−0.650808	−	0.759242i	$-0.725570\pi$
$829$	9.27051	−	28.5317i	0.321978	−	0.990947i	0.972786	−	0.231704i	$-0.0744302\pi$
$830$	12.9443	+	9.40456i	0.449302	+	0.326437i
$831$	6.47214	+	4.70228i	0.224516	+	0.163120i
$832$	−1.23607	+	3.80423i	−0.0428529	+	0.131888i
$833$	−1.85410	−	5.70634i	−0.0642408	−	0.197713i
$834$		0			0
$835$	−48.0000			−1.66111
$836$		0			0
$837$	−8.00000			−0.276520
$838$		0			0
$839$	9.27051	+	28.5317i	0.320054	+	0.985024i	0.973624	+	0.228158i	$0.0732703\pi$
$839$	9.27051	+	28.5317i	0.320054	+	0.985024i	−0.653571	+	0.756866i	$0.726730\pi$
$840$	2.47214	−	7.60845i	0.0852968	−	0.262517i
$841$	−57.4402	−	41.7328i	−1.98070	−	1.43906i
$842$	−14.5623	−	10.5801i	−0.501850	−	0.364616i
$843$	−6.79837	+	20.9232i	−0.234148	+	0.720635i
$844$	−3.70820	−	11.4127i	−0.127642	−	0.392841i
$845$	9.70820	−	7.05342i	0.333972	−	0.242645i
$846$	2.00000			0.0687614
$847$		0			0
$848$	4.00000			0.137361
$849$	3.23607	−	2.35114i	0.111062	−	0.0806910i
$850$	−6.79837	−	20.9232i	−0.233182	−	0.717661i
$851$	3.70820	−	11.4127i	0.127116	−	0.391222i
$852$	−1.61803	−	1.17557i	−0.0554329	−	0.0402744i
$853$	19.4164	+	14.1068i	0.664805	+	0.483009i	0.868282	−	0.496070i	$-0.165224\pi$
$853$	19.4164	+	14.1068i	0.664805	+	0.483009i	−0.203477	+	0.979080i	$0.565224\pi$
$854$	−4.94427	+	15.2169i	−0.169190	+	0.520712i
$855$		0			0
$856$	9.70820	−	7.05342i	0.331820	−	0.241081i
$857$	22.0000			0.751506			0.375753	−	0.926720i	$-0.377384\pi$
$857$	22.0000			0.751506			0.375753	+	0.926720i	$0.377384\pi$
$858$		0			0
$859$	−20.0000			−0.682391			−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000			−0.682391			−0.341196	+	0.939992i	$0.610832\pi$
$860$	−12.9443	+	9.40456i	−0.441396	+	0.320693i
$861$	−1.23607	−	3.80423i	−0.0421251	−	0.129648i
$862$	9.88854	−	30.4338i	0.336805	−	1.03658i
$863$	−43.6869	−	31.7404i	−1.48712	−	1.08046i	−0.975174	−	0.221438i	$-0.928925\pi$
$863$	−43.6869	−	31.7404i	−1.48712	−	1.08046i	−0.511946	−	0.859018i	$-0.671075\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	−7.41641	+	22.8254i	−0.252165	+	0.776085i
$866$	1.85410	+	5.70634i	0.0630049	+	0.193909i
$867$	10.5172	−	7.64121i	0.357184	−	0.259509i
$868$	−16.0000			−0.543075
$869$		0			0
$870$	−40.0000			−1.35613
$871$	−38.8328	+	28.2137i	−1.31580	+	0.955984i
$872$	6.18034	+	19.0211i	0.209293	+	0.644137i
$873$	−0.618034	+	1.90211i	−0.0209173	+	0.0643768i
$874$		0			0
$875$	38.8328	+	28.2137i	1.31279	+	0.953797i
$876$	1.85410	−	5.70634i	0.0626443	−	0.192799i
$877$	−8.65248	−	26.6296i	−0.292173	−	0.899217i	−0.984156	−	0.177303i	$-0.943263\pi$
$877$	−8.65248	−	26.6296i	−0.292173	−	0.899217i	0.691983	−	0.721914i	$-0.256737\pi$
$878$	−8.09017	+	5.87785i	−0.273030	+	0.198368i
$879$	−14.0000			−0.472208
$880$		0			0
$881$	−38.0000			−1.28025			−0.640126	−	0.768270i	$-0.721118\pi$
$881$	−38.0000			−1.28025			−0.640126	+	0.768270i	$0.721118\pi$
$882$	−2.42705	+	1.76336i	−0.0817231	+	0.0593753i
$883$	13.5967	+	41.8465i	0.457567	+	1.40825i	0.868095	+	0.496398i	$0.165344\pi$
$883$	13.5967	+	41.8465i	0.457567	+	1.40825i	−0.410528	+	0.911848i	$0.634656\pi$
$884$	−2.47214	+	7.60845i	−0.0831469	+	0.255900i
$885$		0			0
$886$	19.4164	+	14.1068i	0.652307	+	0.473929i
$887$	3.70820	−	11.4127i	0.124509	−	0.383200i	−0.869302	−	0.494281i	$-0.835431\pi$
$887$	3.70820	−	11.4127i	0.124509	−	0.383200i	0.993811	+	0.111081i	$0.0354313\pi$
$888$	0.618034	+	1.90211i	0.0207399	+	0.0638307i
$889$	−35.5967	+	25.8626i	−1.19388	+	0.867402i
$890$	40.0000			1.34080
$891$		0			0
$892$	−16.0000			−0.535720
$893$		0			0
$894$	−3.09017	−	9.51057i	−0.103351	−	0.318081i
$895$		0			0
$896$	1.61803	+	1.17557i	0.0540547	+	0.0392731i
$897$	−19.4164	−	14.1068i	−0.648295	−	0.471014i
$898$	−9.27051	+	28.5317i	−0.309361	+	0.952115i
$899$	24.7214	+	76.0845i	0.824504	+	2.53756i
$900$	−8.89919	+	6.46564i	−0.296640	+	0.215521i
$901$	8.00000			0.266519
$902$		0			0
$903$	−8.00000			−0.266223
$904$	−4.85410	+	3.52671i	−0.161445	+	0.117297i
$905$	−2.47214	−	7.60845i	−0.0821766	−	0.252914i
$906$	0.618034	−	1.90211i	0.0205328	−	0.0631935i
$907$	9.70820	+	7.05342i	0.322356	+	0.234205i	0.737180	−	0.675696i	$-0.236157\pi$
$907$	9.70820	+	7.05342i	0.322356	+	0.234205i	−0.414824	+	0.909902i	$0.636157\pi$
$908$	−9.70820	−	7.05342i	−0.322178	−	0.234076i
$909$	−0.618034	+	1.90211i	−0.0204989	+	0.0630891i
$910$	−9.88854	−	30.4338i	−0.327802	−	1.00887i
$911$	−1.61803	+	1.17557i	−0.0536079	+	0.0389484i	−0.614266	−	0.789099i	$-0.710548\pi$
$911$	−1.61803	+	1.17557i	−0.0536079	+	0.0389484i	0.560659	+	0.828047i	$0.310548\pi$
$912$		0			0
$913$		0			0
$914$	−2.00000			−0.0661541
$915$	25.8885	−	18.8091i	0.855849	−	0.621811i
$916$	3.09017	+	9.51057i	0.102102	+	0.314238i
$917$	−7.41641	+	22.8254i	−0.244911	+	0.753760i
$918$	1.61803	+	1.17557i	0.0534031	+	0.0387996i
$919$	−8.09017	−	5.87785i	−0.266870	−	0.193892i	0.446300	−	0.894883i	$-0.352741\pi$
$919$	−8.09017	−	5.87785i	−0.266870	−	0.193892i	−0.713170	+	0.700991i	$0.752741\pi$
$920$	−7.41641	+	22.8254i	−0.244512	+	0.752530i
$921$	−2.47214	−	7.60845i	−0.0814596	−	0.250707i
$922$	14.5623	−	10.5801i	0.479584	−	0.348438i
$923$	−8.00000			−0.263323
$924$		0			0
$925$	−22.0000			−0.723356
$926$	3.23607	−	2.35114i	0.106344	−	0.0772633i
$927$	1.23607	+	3.80423i	0.0405978	+	0.124947i
$928$	3.09017	−	9.51057i	0.101440	−	0.312200i
$929$	−24.2705	−	17.6336i	−0.796290	−	0.578538i	0.113534	−	0.993534i	$-0.463783\pi$
$929$	−24.2705	−	17.6336i	−0.796290	−	0.578538i	−0.909823	+	0.414996i	$0.863783\pi$
$930$	25.8885	+	18.8091i	0.848919	+	0.616776i
$931$		0			0
$932$	1.85410	+	5.70634i	0.0607331	+	0.186917i
$933$	−1.61803	+	1.17557i	−0.0529721	+	0.0384865i
$934$	−28.0000			−0.916188
$935$		0			0
$936$	4.00000			0.130744
$937$	46.9230	−	34.0915i	1.53291	−	1.11372i	0.578312	−	0.815816i	$-0.303712\pi$
$937$	46.9230	−	34.0915i	1.53291	−	1.11372i	0.954595	−	0.297907i	$-0.0962884\pi$
$938$	7.41641	+	22.8254i	0.242154	+	0.745274i
$939$	−1.85410	+	5.70634i	−0.0605063	+	0.186219i
$940$	−6.47214	−	4.70228i	−0.211098	−	0.153372i
$941$	33.9787	+	24.6870i	1.10767	+	0.804773i	0.982296	−	0.187336i	$-0.0599854\pi$
$941$	33.9787	+	24.6870i	1.10767	+	0.804773i	0.125379	+	0.992109i	$0.459985\pi$
$942$	−5.56231	+	17.1190i	−0.181230	+	0.557768i
$943$	3.70820	+	11.4127i	0.120756	+	0.371648i
$944$		0			0
$945$	−8.00000			−0.260240
$946$		0			0
$947$	28.0000			0.909878			0.454939	−	0.890523i	$-0.349661\pi$
$947$	28.0000			0.909878			0.454939	+	0.890523i	$0.349661\pi$
$948$	8.09017	−	5.87785i	0.262757	−	0.190904i
$949$	−7.41641	−	22.8254i	−0.240747	−	0.740942i
$950$		0			0
$951$	25.8885	+	18.8091i	0.839494	+	0.609928i
$952$	3.23607	+	2.35114i	0.104882	+	0.0762009i
$953$	1.85410	−	5.70634i	0.0600603	−	0.184846i	−0.916525	−	0.399978i	$-0.869018\pi$
$953$	1.85410	−	5.70634i	0.0600603	−	0.184846i	0.976585	+	0.215131i	$0.0690179\pi$
$954$	−1.23607	−	3.80423i	−0.0400192	−	0.123166i
$955$	71.1935	−	51.7251i	2.30377	−	1.67379i
$956$	20.0000			0.646846
$957$		0			0
$958$	40.0000			1.29234
$959$	3.23607	−	2.35114i	0.104498	−	0.0759223i
$960$	−1.23607	−	3.80423i	−0.0398939	−	0.122781i
$961$	10.1976	−	31.3849i	0.328954	−	1.01242i
$962$	6.47214	+	4.70228i	0.208670	+	0.151608i
$963$	−9.70820	−	7.05342i	−0.312842	−	0.227293i
$964$	5.56231	−	17.1190i	0.179150	−	0.551366i
$965$	17.3050	+	53.2592i	0.557066	+	1.71447i
$966$	−9.70820	+	7.05342i	−0.312356	+	0.226940i
$967$	22.0000			0.707472			0.353736	−	0.935345i	$-0.384911\pi$
$967$	22.0000			0.707472			0.353736	+	0.935345i	$0.384911\pi$
$968$		0			0
$969$		0			0
$970$	6.47214	−	4.70228i	0.207808	−	0.150981i
$971$	9.88854	+	30.4338i	0.317338	+	0.976667i	0.974781	+	0.223163i	$0.0716382\pi$
$971$	9.88854	+	30.4338i	0.317338	+	0.976667i	−0.657443	+	0.753505i	$0.728362\pi$
$972$	0.309017	−	0.951057i	0.00991172	−	0.0305052i
$973$		0			0
$974$	22.6525	+	16.4580i	0.725832	+	0.527348i
$975$	−13.5967	+	41.8465i	−0.435444	+	1.34016i
$976$	2.47214	+	7.60845i	0.0791311	+	0.243541i
$977$	−30.7426	+	22.3358i	−0.983544	+	0.714587i	−0.958498	−	0.285099i	$-0.907973\pi$
$977$	−30.7426	+	22.3358i	−0.983544	+	0.714587i	−0.0250464	+	0.999686i	$0.507973\pi$
$978$	−4.00000			−0.127906
$979$		0			0
$980$	12.0000			0.383326
$981$	16.1803	−	11.7557i	0.516598	−	0.375331i
$982$	3.70820	+	11.4127i	0.118334	+	0.364193i
$983$	−14.2148	+	43.7486i	−0.453381	+	1.39536i	0.419644	+	0.907689i	$0.362155\pi$
$983$	−14.2148	+	43.7486i	−0.453381	+	1.39536i	−0.873025	+	0.487675i	$0.837845\pi$
$984$	−1.61803	−	1.17557i	−0.0515810	−	0.0374758i
$985$	−58.2492	−	42.3205i	−1.85597	−	1.34844i
$986$	6.18034	−	19.0211i	0.196822	−	0.605756i
$987$	−1.23607	−	3.80423i	−0.0393445	−	0.121090i
$988$		0			0
$989$	24.0000			0.763156
$990$		0			0
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$	−6.47214	+	4.70228i	−0.205491	+	0.149298i
$993$	−8.65248	−	26.6296i	−0.274578	−	0.845064i
$994$	−1.23607	+	3.80423i	−0.0392057	+	0.120663i
$995$	64.7214	+	47.0228i	2.05181	+	1.49072i
$996$	3.23607	+	2.35114i	0.102539	+	0.0744988i
$997$	16.0689	−	49.4549i	0.508907	−	1.56625i	−0.285196	−	0.958469i	$-0.592059\pi$
$997$	16.0689	−	49.4549i	0.508907	−	1.56625i	0.794102	−	0.607784i	$-0.207941\pi$
$998$	6.18034	+	19.0211i	0.195635	+	0.602103i
$999$	1.61803	−	1.17557i	0.0511923	−	0.0371934i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.e.m.487.1		4
11.2	odd	10		66.2.a.c.1.1	✓	1
11.3	even	5	inner	726.2.e.m.511.1		4
11.4	even	5	inner	726.2.e.m.565.1		4
11.5	even	5	inner	726.2.e.m.493.1		4
11.6	odd	10		726.2.e.e.493.1		4
11.7	odd	10		726.2.e.e.565.1		4
11.8	odd	10		726.2.e.e.511.1		4
11.9	even	5		726.2.a.d.1.1		1
11.10	odd	2		726.2.e.e.487.1		4
33.2	even	10		198.2.a.c.1.1		1
33.20	odd	10		2178.2.a.m.1.1		1
44.31	odd	10		5808.2.a.b.1.1		1
44.35	even	10		528.2.a.a.1.1		1
55.2	even	20		1650.2.c.m.199.2		2
55.13	even	20		1650.2.c.m.199.1		2
55.24	odd	10		1650.2.a.c.1.1		1
77.13	even	10		3234.2.a.s.1.1		1
88.13	odd	10		2112.2.a.n.1.1		1
88.35	even	10		2112.2.a.bd.1.1		1
99.2	even	30		1782.2.e.n.595.1		2
99.13	odd	30		1782.2.e.l.1189.1		2
99.68	even	30		1782.2.e.n.1189.1		2
99.79	odd	30		1782.2.e.l.595.1		2
132.35	odd	10		1584.2.a.s.1.1		1
165.2	odd	20		4950.2.c.d.199.1		2
165.68	odd	20		4950.2.c.d.199.2		2
165.134	even	10		4950.2.a.bo.1.1		1
231.167	odd	10		9702.2.a.a.1.1		1
264.35	odd	10		6336.2.a.d.1.1		1
264.101	even	10		6336.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.a.c.1.1	✓	1	11.2	odd	10
198.2.a.c.1.1		1	33.2	even	10
528.2.a.a.1.1		1	44.35	even	10
726.2.a.d.1.1		1	11.9	even	5
726.2.e.e.487.1		4	11.10	odd	2
726.2.e.e.493.1		4	11.6	odd	10
726.2.e.e.511.1		4	11.8	odd	10
726.2.e.e.565.1		4	11.7	odd	10
726.2.e.m.487.1		4	1.1	even	1	trivial
726.2.e.m.493.1		4	11.5	even	5	inner
726.2.e.m.511.1		4	11.3	even	5	inner
726.2.e.m.565.1		4	11.4	even	5	inner
1584.2.a.s.1.1		1	132.35	odd	10
1650.2.a.c.1.1		1	55.24	odd	10
1650.2.c.m.199.1		2	55.13	even	20
1650.2.c.m.199.2		2	55.2	even	20
1782.2.e.l.595.1		2	99.79	odd	30
1782.2.e.l.1189.1		2	99.13	odd	30
1782.2.e.n.595.1		2	99.2	even	30
1782.2.e.n.1189.1		2	99.68	even	30
2112.2.a.n.1.1		1	88.13	odd	10
2112.2.a.bd.1.1		1	88.35	even	10
2178.2.a.m.1.1		1	33.20	odd	10
3234.2.a.s.1.1		1	77.13	even	10
4950.2.a.bo.1.1		1	165.134	even	10
4950.2.c.d.199.1		2	165.2	odd	20
4950.2.c.d.199.2		2	165.68	odd	20
5808.2.a.b.1.1		1	44.31	odd	10
6336.2.a.c.1.1		1	264.101	even	10
6336.2.a.d.1.1		1	264.35	odd	10
9702.2.a.a.1.1		1	231.167	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(3.23607 + 2.35114i) q^{5} +(0.809017 + 0.587785i) q^{6} +(0.618034 - 1.90211i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(3.23607 + 2.35114i) q^{5} +(0.809017 + 0.587785i) q^{6} +(0.618034 - 1.90211i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +4.00000 q^{10} +1.00000 q^{12} +(3.23607 - 2.35114i) q^{13} +(-0.618034 - 1.90211i) q^{14} +(-1.23607 + 3.80423i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.61803 - 1.17557i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(3.23607 - 2.35114i) q^{20} +2.00000 q^{21} -6.00000 q^{23} +(0.809017 - 0.587785i) q^{24} +(3.39919 + 10.4616i) q^{25} +(1.23607 - 3.80423i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.61803 - 1.17557i) q^{28} +(-3.09017 + 9.51057i) q^{29} +(1.23607 + 3.80423i) q^{30} +(6.47214 - 4.70228i) q^{31} -1.00000 q^{32} -2.00000 q^{34} +(6.47214 - 4.70228i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-0.618034 + 1.90211i) q^{37} +(3.23607 + 2.35114i) q^{39} +(1.23607 - 3.80423i) q^{40} +(-0.618034 - 1.90211i) q^{41} +(1.61803 - 1.17557i) q^{42} -4.00000 q^{43} -4.00000 q^{45} +(-4.85410 + 3.52671i) q^{46} +(-0.618034 - 1.90211i) q^{47} +(0.309017 - 0.951057i) q^{48} +(2.42705 + 1.76336i) q^{49} +(8.89919 + 6.46564i) q^{50} +(0.618034 - 1.90211i) q^{51} +(-1.23607 - 3.80423i) q^{52} +(-3.23607 + 2.35114i) q^{53} -1.00000 q^{54} -2.00000 q^{56} +(3.09017 + 9.51057i) q^{58} +(3.23607 + 2.35114i) q^{60} +(-6.47214 - 4.70228i) q^{61} +(2.47214 - 7.60845i) q^{62} +(0.618034 + 1.90211i) q^{63} +(-0.809017 + 0.587785i) q^{64} +16.0000 q^{65} -12.0000 q^{67} +(-1.61803 + 1.17557i) q^{68} +(-1.85410 - 5.70634i) q^{69} +(2.47214 - 7.60845i) q^{70} +(-1.61803 - 1.17557i) q^{71} +(0.809017 + 0.587785i) q^{72} +(1.85410 - 5.70634i) q^{73} +(0.618034 + 1.90211i) q^{74} +(-8.89919 + 6.46564i) q^{75} +4.00000 q^{78} +(8.09017 - 5.87785i) q^{79} +(-1.23607 - 3.80423i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-1.61803 - 1.17557i) q^{82} +(3.23607 + 2.35114i) q^{83} +(0.618034 - 1.90211i) q^{84} +(-2.47214 - 7.60845i) q^{85} +(-3.23607 + 2.35114i) q^{86} -10.0000 q^{87} +10.0000 q^{89} +(-3.23607 + 2.35114i) q^{90} +(-2.47214 - 7.60845i) q^{91} +(-1.85410 + 5.70634i) q^{92} +(6.47214 + 4.70228i) q^{93} +(-1.61803 - 1.17557i) q^{94} +(-0.309017 - 0.951057i) q^{96} +(1.61803 - 1.17557i) q^{97} +3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{3} - q^{4} + 4 q^{5} + q^{6} - 2 q^{7} + q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 - q^3 - q^4 + 4 * q^5 + q^6 - 2 * q^7 + q^8 - q^9	\( 4 q + q^{2} - q^{3} - q^{4} + 4 q^{5} + q^{6} - 2 q^{7} + q^{8} - q^{9} + 16 q^{10} + 4 q^{12} + 4 q^{13} + 2 q^{14} + 4 q^{15} - q^{16} - 2 q^{17} + q^{18} + 4 q^{20} + 8 q^{21} - 24 q^{23} + q^{24} - 11 q^{25} - 4 q^{26} - q^{27} - 2 q^{28} + 10 q^{29} - 4 q^{30} + 8 q^{31} - 4 q^{32} - 8 q^{34} + 8 q^{35} - q^{36} + 2 q^{37} + 4 q^{39} - 4 q^{40} + 2 q^{41} + 2 q^{42} - 16 q^{43} - 16 q^{45} - 6 q^{46} + 2 q^{47} - q^{48} + 3 q^{49} + 11 q^{50} - 2 q^{51} + 4 q^{52} - 4 q^{53} - 4 q^{54} - 8 q^{56} - 10 q^{58} + 4 q^{60} - 8 q^{61} - 8 q^{62} - 2 q^{63} - q^{64} + 64 q^{65} - 48 q^{67} - 2 q^{68} + 6 q^{69} - 8 q^{70} - 2 q^{71} + q^{72} - 6 q^{73} - 2 q^{74} - 11 q^{75} + 16 q^{78} + 10 q^{79} + 4 q^{80} - q^{81} - 2 q^{82} + 4 q^{83} - 2 q^{84} + 8 q^{85} - 4 q^{86} - 40 q^{87} + 40 q^{89} - 4 q^{90} + 8 q^{91} + 6 q^{92} + 8 q^{93} - 2 q^{94} + q^{96} + 2 q^{97} + 12 q^{98}+O(q^{100}) \) 4 * q + q^2 - q^3 - q^4 + 4 * q^5 + q^6 - 2 * q^7 + q^8 - q^9 + 16 * q^10 + 4 * q^12 + 4 * q^13 + 2 * q^14 + 4 * q^15 - q^16 - 2 * q^17 + q^18 + 4 * q^20 + 8 * q^21 - 24 * q^23 + q^24 - 11 * q^25 - 4 * q^26 - q^27 - 2 * q^28 + 10 * q^29 - 4 * q^30 + 8 * q^31 - 4 * q^32 - 8 * q^34 + 8 * q^35 - q^36 + 2 * q^37 + 4 * q^39 - 4 * q^40 + 2 * q^41 + 2 * q^42 - 16 * q^43 - 16 * q^45 - 6 * q^46 + 2 * q^47 - q^48 + 3 * q^49 + 11 * q^50 - 2 * q^51 + 4 * q^52 - 4 * q^53 - 4 * q^54 - 8 * q^56 - 10 * q^58 + 4 * q^60 - 8 * q^61 - 8 * q^62 - 2 * q^63 - q^64 + 64 * q^65 - 48 * q^67 - 2 * q^68 + 6 * q^69 - 8 * q^70 - 2 * q^71 + q^72 - 6 * q^73 - 2 * q^74 - 11 * q^75 + 16 * q^78 + 10 * q^79 + 4 * q^80 - q^81 - 2 * q^82 + 4 * q^83 - 2 * q^84 + 8 * q^85 - 4 * q^86 - 40 * q^87 + 40 * q^89 - 4 * q^90 + 8 * q^91 + 6 * q^92 + 8 * q^93 - 2 * q^94 + q^96 + 2 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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