LMFDB - Embedded newform 847.2.f.k.372.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (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:	$6.76332905120$
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 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			372.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	847.372
Dual form			847.2.f.k.148.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-1.61803 + 1.17557i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.618034 - 1.90211i) q^{5} +(-0.618034 - 1.90211i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-2.42705 + 1.76336i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-1.61803 + 1.17557i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.618034 - 1.90211i) q^{5} +(-0.618034 - 1.90211i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-2.42705 + 1.76336i) q^{8} +(0.309017 - 0.951057i) q^{9} +2.00000 q^{10} -2.00000 q^{12} +(-1.23607 + 3.80423i) q^{13} +(0.809017 - 0.587785i) q^{14} +(3.23607 + 2.35114i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-1.23607 - 3.80423i) q^{17} +(0.809017 + 0.587785i) q^{18} +(0.618034 - 1.90211i) q^{20} +2.00000 q^{21} -4.00000 q^{23} +(1.85410 - 5.70634i) q^{24} +(0.809017 - 0.587785i) q^{25} +(-3.23607 - 2.35114i) q^{26} +(-1.23607 - 3.80423i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(-4.85410 - 3.52671i) q^{29} +(-3.23607 + 2.35114i) q^{30} +(3.09017 - 9.51057i) q^{31} -5.00000 q^{32} +4.00000 q^{34} +(-0.618034 + 1.90211i) q^{35} +(0.809017 - 0.587785i) q^{36} +(4.85410 + 3.52671i) q^{37} +(-2.47214 - 7.60845i) q^{39} +(4.85410 + 3.52671i) q^{40} +(3.23607 - 2.35114i) q^{41} +(-0.618034 + 1.90211i) q^{42} -12.0000 q^{43} -2.00000 q^{45} +(1.23607 - 3.80423i) q^{46} +(8.09017 - 5.87785i) q^{47} +(1.61803 + 1.17557i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.309017 + 0.951057i) q^{50} +(6.47214 + 4.70228i) q^{51} +(-3.23607 + 2.35114i) q^{52} +(-1.85410 + 5.70634i) q^{53} +4.00000 q^{54} +3.00000 q^{56} +(4.85410 - 3.52671i) q^{58} +(-1.61803 - 1.17557i) q^{59} +(1.23607 + 3.80423i) q^{60} +(8.09017 + 5.87785i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(2.16312 - 6.65740i) q^{64} +8.00000 q^{65} +8.00000 q^{67} +(1.23607 - 3.80423i) q^{68} +(6.47214 - 4.70228i) q^{69} +(-1.61803 - 1.17557i) q^{70} +(-3.70820 - 11.4127i) q^{71} +(0.927051 + 2.85317i) q^{72} +(-6.47214 - 4.70228i) q^{73} +(-4.85410 + 3.52671i) q^{74} +(-0.618034 + 1.90211i) q^{75} +8.00000 q^{78} +(-2.47214 + 7.60845i) q^{79} +(-1.61803 + 1.17557i) q^{80} +(8.89919 + 6.46564i) q^{81} +(1.23607 + 3.80423i) q^{82} +(1.61803 + 1.17557i) q^{84} +(-6.47214 + 4.70228i) q^{85} +(3.70820 - 11.4127i) q^{86} +12.0000 q^{87} -6.00000 q^{89} +(0.618034 - 1.90211i) q^{90} +(3.23607 - 2.35114i) q^{91} +(-3.23607 - 2.35114i) q^{92} +(6.18034 + 19.0211i) q^{93} +(3.09017 + 9.51057i) q^{94} +(8.09017 - 5.87785i) q^{96} +(-3.09017 + 9.51057i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 2 q^{3} + q^{4} + 2 q^{5} + 2 q^{6} - q^{7} - 3 q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 - 2 * q^3 + q^4 + 2 * q^5 + 2 * q^6 - q^7 - 3 * q^8 - q^9	$ 4 q + q^{2} - 2 q^{3} + q^{4} + 2 q^{5} + 2 q^{6} - q^{7} - 3 q^{8} - q^{9} + 8 q^{10} - 8 q^{12} + 4 q^{13} + q^{14} + 4 q^{15} + q^{16} + 4 q^{17} + q^{18} - 2 q^{20} + 8 q^{21} - 16 q^{23} - 6 q^{24} + q^{25} - 4 q^{26} + 4 q^{27} + q^{28} - 6 q^{29} - 4 q^{30} - 10 q^{31} - 20 q^{32} + 16 q^{34} + 2 q^{35} + q^{36} + 6 q^{37} + 8 q^{39} + 6 q^{40} + 4 q^{41} + 2 q^{42} - 48 q^{43} - 8 q^{45} - 4 q^{46} + 10 q^{47} + 2 q^{48} - q^{49} - q^{50} + 8 q^{51} - 4 q^{52} + 6 q^{53} + 16 q^{54} + 12 q^{56} + 6 q^{58} - 2 q^{59} - 4 q^{60} + 10 q^{62} - q^{63} - 7 q^{64} + 32 q^{65} + 32 q^{67} - 4 q^{68} + 8 q^{69} - 2 q^{70} + 12 q^{71} - 3 q^{72} - 8 q^{73} - 6 q^{74} + 2 q^{75} + 32 q^{78} + 8 q^{79} - 2 q^{80} + 11 q^{81} - 4 q^{82} + 2 q^{84} - 8 q^{85} - 12 q^{86} + 48 q^{87} - 24 q^{89} - 2 q^{90} + 4 q^{91} - 4 q^{92} - 20 q^{93} - 10 q^{94} + 10 q^{96} + 10 q^{97} - 4 q^{98}+O(q^{100}) $ 4 * q + q^2 - 2 * q^3 + q^4 + 2 * q^5 + 2 * q^6 - q^7 - 3 * q^8 - q^9 + 8 * q^10 - 8 * q^12 + 4 * q^13 + q^14 + 4 * q^15 + q^16 + 4 * q^17 + q^18 - 2 * q^20 + 8 * q^21 - 16 * q^23 - 6 * q^24 + q^25 - 4 * q^26 + 4 * q^27 + q^28 - 6 * q^29 - 4 * q^30 - 10 * q^31 - 20 * q^32 + 16 * q^34 + 2 * q^35 + q^36 + 6 * q^37 + 8 * q^39 + 6 * q^40 + 4 * q^41 + 2 * q^42 - 48 * q^43 - 8 * q^45 - 4 * q^46 + 10 * q^47 + 2 * q^48 - q^49 - q^50 + 8 * q^51 - 4 * q^52 + 6 * q^53 + 16 * q^54 + 12 * q^56 + 6 * q^58 - 2 * q^59 - 4 * q^60 + 10 * q^62 - q^63 - 7 * q^64 + 32 * q^65 + 32 * q^67 - 4 * q^68 + 8 * q^69 - 2 * q^70 + 12 * q^71 - 3 * q^72 - 8 * q^73 - 6 * q^74 + 2 * q^75 + 32 * q^78 + 8 * q^79 - 2 * q^80 + 11 * q^81 - 4 * q^82 + 2 * q^84 - 8 * q^85 - 12 * q^86 + 48 * q^87 - 24 * q^89 - 2 * q^90 + 4 * q^91 - 4 * q^92 - 20 * q^93 - 10 * q^94 + 10 * q^96 + 10 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i	0.780378	+	0.625308i	$0.215027\pi$
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i	−0.998886	+	0.0471903i	$0.984973\pi$
$3$	−1.61803	+	1.17557i	−0.934172	+	0.678716i	−0.947011	−	0.321202i	$-0.895913\pi$
$3$	−1.61803	+	1.17557i	−0.934172	+	0.678716i	0.0128385	+	0.999918i	$0.495913\pi$
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−0.618034	−	1.90211i	−0.276393	−	0.850651i	−0.988847	−	0.148932i	$-0.952416\pi$
$5$	−0.618034	−	1.90211i	−0.276393	−	0.850651i	0.712454	−	0.701719i	$-0.247584\pi$
$6$	−0.618034	−	1.90211i	−0.252311	−	0.776534i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	−2.42705	+	1.76336i	−0.858092	+	0.623440i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	2.00000			0.632456
$11$		0			0
$11$		0			0
$12$	−2.00000			−0.577350
$13$	−1.23607	+	3.80423i	−0.342824	+	1.05510i	0.619915	+	0.784669i	$0.287167\pi$
$13$	−1.23607	+	3.80423i	−0.342824	+	1.05510i	−0.962739	+	0.270434i	$0.912833\pi$
$14$	0.809017	−	0.587785i	0.216219	−	0.157092i
$15$	3.23607	+	2.35114i	0.835549	+	0.607062i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	−1.23607	−	3.80423i	−0.299791	−	0.922660i	−0.981570	−	0.191103i	$-0.938794\pi$
$17$	−1.23607	−	3.80423i	−0.299791	−	0.922660i	0.681780	−	0.731558i	$-0.261206\pi$
$18$	0.809017	+	0.587785i	0.190687	+	0.138542i
$19$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$19$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$20$	0.618034	−	1.90211i	0.138197	−	0.425325i
$21$	2.00000			0.436436
$22$		0			0
$23$	−4.00000			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$	1.85410	−	5.70634i	0.378467	−	1.16480i
$25$	0.809017	−	0.587785i	0.161803	−	0.117557i
$26$	−3.23607	−	2.35114i	−0.634645	−	0.461097i
$27$	−1.23607	−	3.80423i	−0.237881	−	0.732124i
$28$	−0.309017	−	0.951057i	−0.0583987	−	0.179733i
$29$	−4.85410	−	3.52671i	−0.901384	−	0.654894i	0.0374370	−	0.999299i	$-0.488081\pi$
$29$	−4.85410	−	3.52671i	−0.901384	−	0.654894i	−0.938821	+	0.344405i	$0.888081\pi$
$30$	−3.23607	+	2.35114i	−0.590822	+	0.429258i
$31$	3.09017	−	9.51057i	0.555011	−	1.70815i	−0.140904	−	0.990023i	$-0.545001\pi$
$31$	3.09017	−	9.51057i	0.555011	−	1.70815i	0.695915	−	0.718125i	$-0.254999\pi$
$32$	−5.00000			−0.883883
$33$		0			0
$34$	4.00000			0.685994
$35$	−0.618034	+	1.90211i	−0.104467	+	0.321516i
$36$	0.809017	−	0.587785i	0.134836	−	0.0979642i
$37$	4.85410	+	3.52671i	0.798009	+	0.579788i	0.910330	−	0.413884i	$-0.135828\pi$
$37$	4.85410	+	3.52671i	0.798009	+	0.579788i	−0.112320	+	0.993672i	$0.535828\pi$
$38$		0			0
$39$	−2.47214	−	7.60845i	−0.395859	−	1.21833i
$40$	4.85410	+	3.52671i	0.767501	+	0.557622i
$41$	3.23607	−	2.35114i	0.505389	−	0.367187i	−0.305683	−	0.952133i	$-0.598885\pi$
$41$	3.23607	−	2.35114i	0.505389	−	0.367187i	0.811072	+	0.584947i	$0.198885\pi$
$42$	−0.618034	+	1.90211i	−0.0953647	+	0.293502i
$43$	−12.0000			−1.82998			−0.914991	−	0.403473i	$-0.867803\pi$
$43$	−12.0000			−1.82998			−0.914991	+	0.403473i	$0.867803\pi$
$44$		0			0
$45$	−2.00000			−0.298142
$46$	1.23607	−	3.80423i	0.182248	−	0.560903i
$47$	8.09017	−	5.87785i	1.18007	−	0.857373i	0.187893	−	0.982190i	$-0.439834\pi$
$47$	8.09017	−	5.87785i	1.18007	−	0.857373i	0.992180	+	0.124817i	$0.0398343\pi$
$48$	1.61803	+	1.17557i	0.233543	+	0.169679i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	0.309017	+	0.951057i	0.0437016	+	0.134500i
$51$	6.47214	+	4.70228i	0.906280	+	0.658451i
$52$	−3.23607	+	2.35114i	−0.448762	+	0.326045i
$53$	−1.85410	+	5.70634i	−0.254680	+	0.783826i	0.739212	+	0.673473i	$0.235198\pi$
$53$	−1.85410	+	5.70634i	−0.254680	+	0.783826i	−0.993892	+	0.110353i	$0.964802\pi$
$54$	4.00000			0.544331
$55$		0			0
$56$	3.00000			0.400892
$57$		0			0
$58$	4.85410	−	3.52671i	0.637375	−	0.463080i
$59$	−1.61803	−	1.17557i	−0.210650	−	0.153046i	0.477458	−	0.878655i	$-0.341558\pi$
$59$	−1.61803	−	1.17557i	−0.210650	−	0.153046i	−0.688108	+	0.725608i	$0.741558\pi$
$60$	1.23607	+	3.80423i	0.159576	+	0.491123i
$61$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$61$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$62$	8.09017	+	5.87785i	1.02745	+	0.746488i
$63$	−0.809017	+	0.587785i	−0.101927	+	0.0740540i
$64$	2.16312	−	6.65740i	0.270390	−	0.832174i
$65$	8.00000			0.992278
$66$		0			0
$67$	8.00000			0.977356			0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000			0.977356			0.488678	+	0.872464i	$0.337479\pi$
$68$	1.23607	−	3.80423i	0.149895	−	0.461330i
$69$	6.47214	−	4.70228i	0.779154	−	0.566088i
$70$	−1.61803	−	1.17557i	−0.193392	−	0.140508i
$71$	−3.70820	−	11.4127i	−0.440083	−	1.35444i	−0.887787	−	0.460254i	$-0.847758\pi$
$71$	−3.70820	−	11.4127i	−0.440083	−	1.35444i	0.447704	−	0.894182i	$-0.352242\pi$
$72$	0.927051	+	2.85317i	0.109254	+	0.336249i
$73$	−6.47214	−	4.70228i	−0.757506	−	0.550360i	0.140638	−	0.990061i	$-0.455085\pi$
$73$	−6.47214	−	4.70228i	−0.757506	−	0.550360i	−0.898144	+	0.439701i	$0.855085\pi$
$74$	−4.85410	+	3.52671i	−0.564278	+	0.409972i
$75$	−0.618034	+	1.90211i	−0.0713644	+	0.219637i
$76$		0			0
$77$		0			0
$78$	8.00000			0.905822
$79$	−2.47214	+	7.60845i	−0.278137	+	0.856018i	0.710235	+	0.703964i	$0.248589\pi$
$79$	−2.47214	+	7.60845i	−0.278137	+	0.856018i	−0.988372	+	0.152053i	$0.951411\pi$
$80$	−1.61803	+	1.17557i	−0.180902	+	0.131433i
$81$	8.89919	+	6.46564i	0.988799	+	0.718404i
$82$	1.23607	+	3.80423i	0.136501	+	0.420106i
$83$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$83$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$84$	1.61803	+	1.17557i	0.176542	+	0.128265i
$85$	−6.47214	+	4.70228i	−0.702002	+	0.510034i
$86$	3.70820	−	11.4127i	0.399866	−	1.23066i
$87$	12.0000			1.28654
$88$		0			0
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$	0.618034	−	1.90211i	0.0651465	−	0.200500i
$91$	3.23607	−	2.35114i	0.339232	−	0.246467i
$92$	−3.23607	−	2.35114i	−0.337383	−	0.245123i
$93$	6.18034	+	19.0211i	0.640871	+	1.97240i
$94$	3.09017	+	9.51057i	0.318727	+	0.980940i
$95$		0			0
$96$	8.09017	−	5.87785i	0.825700	−	0.599906i
$97$	−3.09017	+	9.51057i	−0.313759	+	0.965652i	0.662503	+	0.749059i	$0.269494\pi$
$97$	−3.09017	+	9.51057i	−0.313759	+	0.965652i	−0.976262	+	0.216592i	$0.930506\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	1.00000			0.100000
$101$	1.23607	−	3.80423i	0.122993	−	0.378535i	−0.870537	−	0.492103i	$-0.836228\pi$
$101$	1.23607	−	3.80423i	0.122993	−	0.378535i	0.993530	+	0.113569i	$0.0362282\pi$
$102$	−6.47214	+	4.70228i	−0.640837	+	0.465595i
$103$	−11.3262	−	8.22899i	−1.11601	−	0.810827i	−0.132408	−	0.991195i	$-0.542271\pi$
$103$	−11.3262	−	8.22899i	−1.11601	−	0.810827i	−0.983599	+	0.180368i	$0.942271\pi$
$104$	−3.70820	−	11.4127i	−0.363619	−	1.11911i
$105$	−1.23607	−	3.80423i	−0.120628	−	0.371254i
$106$	−4.85410	−	3.52671i	−0.471472	−	0.342545i
$107$	9.70820	−	7.05342i	0.938527	−	0.681880i	−0.00953827	−	0.999955i	$-0.503036\pi$
$107$	9.70820	−	7.05342i	0.938527	−	0.681880i	0.948066	+	0.318074i	$0.103036\pi$
$108$	1.23607	−	3.80423i	0.118941	−	0.366062i
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$		0			0
$111$	−12.0000			−1.13899
$112$	−0.309017	+	0.951057i	−0.0291994	+	0.0898664i
$113$	−14.5623	+	10.5801i	−1.36991	+	0.995295i	−0.372162	+	0.928168i	$0.621383\pi$
$113$	−14.5623	+	10.5801i	−1.36991	+	0.995295i	−0.997744	+	0.0671276i	$0.978617\pi$
$114$		0			0
$115$	2.47214	+	7.60845i	0.230528	+	0.709492i
$116$	−1.85410	−	5.70634i	−0.172149	−	0.529820i
$117$	3.23607	+	2.35114i	0.299175	+	0.217363i
$118$	1.61803	−	1.17557i	0.148952	−	0.108220i
$119$	−1.23607	+	3.80423i	−0.113310	+	0.348733i
$120$	−12.0000			−1.09545
$121$		0			0
$122$		0			0
$123$	−2.47214	+	7.60845i	−0.222905	+	0.686031i
$124$	8.09017	−	5.87785i	0.726519	−	0.527847i
$125$	−9.70820	−	7.05342i	−0.868328	−	0.630877i
$126$	−0.309017	−	0.951057i	−0.0275294	−	0.0847268i
$127$	−2.47214	−	7.60845i	−0.219367	−	0.675141i	−0.998815	−	0.0486742i	$-0.984500\pi$
$127$	−2.47214	−	7.60845i	−0.219367	−	0.675141i	0.779448	−	0.626467i	$-0.215500\pi$
$128$	−2.42705	−	1.76336i	−0.214523	−	0.155860i
$129$	19.4164	−	14.1068i	1.70952	−	1.24204i
$130$	−2.47214	+	7.60845i	−0.216821	+	0.667305i
$131$	−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
$134$	−2.47214	+	7.60845i	−0.213560	+	0.657270i
$135$	−6.47214	+	4.70228i	−0.557033	+	0.404708i
$136$	9.70820	+	7.05342i	0.832472	+	0.604826i
$137$	−3.09017	−	9.51057i	−0.264011	−	0.812542i	−0.991920	−	0.126868i	$-0.959507\pi$
$137$	−3.09017	−	9.51057i	−0.264011	−	0.812542i	0.727909	−	0.685674i	$-0.240493\pi$
$138$	2.47214	+	7.60845i	0.210442	+	0.647674i
$139$	−6.47214	−	4.70228i	−0.548959	−	0.398842i	0.278442	−	0.960453i	$-0.410182\pi$
$139$	−6.47214	−	4.70228i	−0.548959	−	0.398842i	−0.827402	+	0.561611i	$0.810182\pi$
$140$	−1.61803	+	1.17557i	−0.136749	+	0.0993538i
$141$	−6.18034	+	19.0211i	−0.520479	+	1.60187i
$142$	12.0000			1.00702
$143$		0			0
$144$	−1.00000			−0.0833333
$145$	−3.70820	+	11.4127i	−0.307950	+	0.947771i
$146$	6.47214	−	4.70228i	0.535638	−	0.389164i
$147$	−1.61803	−	1.17557i	−0.133453	−	0.0969594i
$148$	1.85410	+	5.70634i	0.152406	+	0.469058i
$149$	3.09017	+	9.51057i	0.253157	+	0.779136i	0.994187	+	0.107665i	$0.0343373\pi$
$149$	3.09017	+	9.51057i	0.253157	+	0.779136i	−0.741031	+	0.671471i	$0.765663\pi$
$150$	−1.61803	−	1.17557i	−0.132112	−	0.0959849i
$151$	−12.9443	+	9.40456i	−1.05339	+	0.765333i	−0.972854	−	0.231419i	$-0.925663\pi$
$151$	−12.9443	+	9.40456i	−1.05339	+	0.765333i	−0.0805358	+	0.996752i	$0.525663\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$		0			0
$155$	−20.0000			−1.60644
$156$	2.47214	−	7.60845i	0.197929	−	0.609164i
$157$	−11.3262	+	8.22899i	−0.903932	+	0.656745i	−0.939473	−	0.342623i	$-0.888685\pi$
$157$	−11.3262	+	8.22899i	−0.903932	+	0.656745i	0.0355408	+	0.999368i	$0.488685\pi$
$158$	−6.47214	−	4.70228i	−0.514895	−	0.374093i
$159$	−3.70820	−	11.4127i	−0.294080	−	0.905084i
$160$	3.09017	+	9.51057i	0.244299	+	0.751876i
$161$	3.23607	+	2.35114i	0.255038	+	0.185296i
$162$	−8.89919	+	6.46564i	−0.699186	+	0.507988i
$163$	−2.47214	+	7.60845i	−0.193633	+	0.595940i	0.806357	+	0.591429i	$0.201436\pi$
$163$	−2.47214	+	7.60845i	−0.193633	+	0.595940i	−0.999990	+	0.00451112i	$0.998564\pi$
$164$	4.00000			0.312348
$165$		0			0
$166$		0			0
$167$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$167$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$168$	−4.85410	+	3.52671i	−0.374502	+	0.272092i
$169$	−2.42705	−	1.76336i	−0.186696	−	0.135643i
$170$	−2.47214	−	7.60845i	−0.189604	−	0.583542i
$171$		0			0
$172$	−9.70820	−	7.05342i	−0.740244	−	0.537818i
$173$	9.70820	−	7.05342i	0.738101	−	0.536262i	−0.154015	−	0.988069i	$-0.549220\pi$
$173$	9.70820	−	7.05342i	0.738101	−	0.536262i	0.892116	+	0.451807i	$0.149220\pi$
$174$	−3.70820	+	11.4127i	−0.281118	+	0.865193i
$175$	−1.00000			−0.0755929
$176$		0			0
$177$	4.00000			0.300658
$178$	1.85410	−	5.70634i	0.138971	−	0.427708i
$179$	−9.70820	+	7.05342i	−0.725625	+	0.527198i	−0.888176	−	0.459503i	$-0.848028\pi$
$179$	−9.70820	+	7.05342i	−0.725625	+	0.527198i	0.162551	+	0.986700i	$0.448028\pi$
$180$	−1.61803	−	1.17557i	−0.120601	−	0.0876219i
$181$	3.09017	+	9.51057i	0.229691	+	0.706915i	0.997781	+	0.0665740i	$0.0212068\pi$
$181$	3.09017	+	9.51057i	0.229691	+	0.706915i	−0.768091	+	0.640341i	$0.778793\pi$
$182$	1.23607	+	3.80423i	0.0916235	+	0.281988i
$183$		0			0
$184$	9.70820	−	7.05342i	0.715698	−	0.519985i
$185$	3.70820	−	11.4127i	0.272633	−	0.839077i
$186$	−20.0000			−1.46647
$187$		0			0
$188$	10.0000			0.729325
$189$	−1.23607	+	3.80423i	−0.0899107	+	0.276717i
$190$		0			0
$191$	−6.47214	−	4.70228i	−0.468307	−	0.340245i	0.328474	−	0.944513i	$-0.393466\pi$
$191$	−6.47214	−	4.70228i	−0.468307	−	0.340245i	−0.796781	+	0.604268i	$0.793466\pi$
$192$	4.32624	+	13.3148i	0.312219	+	0.960912i
$193$	4.32624	+	13.3148i	0.311409	+	0.958420i	0.977207	+	0.212287i	$0.0680913\pi$
$193$	4.32624	+	13.3148i	0.311409	+	0.958420i	−0.665798	+	0.746132i	$0.731909\pi$
$194$	−8.09017	−	5.87785i	−0.580840	−	0.422005i
$195$	−12.9443	+	9.40456i	−0.926959	+	0.673475i
$196$	−0.309017	+	0.951057i	−0.0220726	+	0.0679326i
$197$	−22.0000			−1.56744			−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000			−1.56744			−0.783718	+	0.621117i	$0.786679\pi$
$198$		0			0
$199$	−18.0000			−1.27599			−0.637993	−	0.770042i	$-0.720235\pi$
$199$	−18.0000			−1.27599			−0.637993	+	0.770042i	$0.720235\pi$
$200$	−0.927051	+	2.85317i	−0.0655524	+	0.201750i
$201$	−12.9443	+	9.40456i	−0.913019	+	0.663347i
$202$	3.23607	+	2.35114i	0.227689	+	0.165426i
$203$	1.85410	+	5.70634i	0.130132	+	0.400506i
$204$	2.47214	+	7.60845i	0.173084	+	0.532698i
$205$	−6.47214	−	4.70228i	−0.452034	−	0.328422i
$206$	11.3262	−	8.22899i	0.789136	−	0.573341i
$207$	−1.23607	+	3.80423i	−0.0859127	+	0.264412i
$208$	4.00000			0.277350
$209$		0			0
$210$	4.00000			0.276026
$211$	3.70820	−	11.4127i	0.255283	−	0.785681i	−0.738490	−	0.674264i	$-0.764461\pi$
$211$	3.70820	−	11.4127i	0.255283	−	0.785681i	0.993774	−	0.111417i	$-0.0355390\pi$
$212$	−4.85410	+	3.52671i	−0.333381	+	0.242216i
$213$	19.4164	+	14.1068i	1.33039	+	0.966585i
$214$	3.70820	+	11.4127i	0.253488	+	0.780155i
$215$	7.41641	+	22.8254i	0.505795	+	1.55668i
$216$	9.70820	+	7.05342i	0.660560	+	0.479925i
$217$	−8.09017	+	5.87785i	−0.549197	+	0.399015i
$218$	−4.32624	+	13.3148i	−0.293010	+	0.901791i
$219$	16.0000			1.08118
$220$		0			0
$221$	16.0000			1.07628
$222$	3.70820	−	11.4127i	0.248878	−	0.765969i
$223$	−17.7984	+	12.9313i	−1.19187	+	0.865942i	−0.993460	−	0.114177i	$-0.963577\pi$
$223$	−17.7984	+	12.9313i	−1.19187	+	0.865942i	−0.198407	+	0.980120i	$0.563577\pi$
$224$	4.04508	+	2.93893i	0.270274	+	0.196365i
$225$	−0.309017	−	0.951057i	−0.0206011	−	0.0634038i
$226$	−5.56231	−	17.1190i	−0.369999	−	1.13874i
$227$	9.70820	+	7.05342i	0.644356	+	0.468152i	0.861344	−	0.508022i	$-0.169623\pi$
$227$	9.70820	+	7.05342i	0.644356	+	0.468152i	−0.216988	+	0.976174i	$0.569623\pi$
$228$		0			0
$229$	5.56231	−	17.1190i	0.367568	−	1.13126i	−0.580790	−	0.814053i	$-0.697256\pi$
$229$	5.56231	−	17.1190i	0.367568	−	1.13126i	0.948358	−	0.317203i	$-0.102744\pi$
$230$	−8.00000			−0.527504
$231$		0			0
$232$	18.0000			1.18176
$233$	5.56231	−	17.1190i	0.364399	−	1.12150i	−0.585958	−	0.810341i	$-0.699282\pi$
$233$	5.56231	−	17.1190i	0.364399	−	1.12150i	0.950357	−	0.311163i	$-0.100718\pi$
$234$	−3.23607	+	2.35114i	−0.211548	+	0.153699i
$235$	−16.1803	−	11.7557i	−1.05549	−	0.766858i
$236$	−0.618034	−	1.90211i	−0.0402306	−	0.123817i
$237$	−4.94427	−	15.2169i	−0.321165	−	0.988444i
$238$	−3.23607	−	2.35114i	−0.209763	−	0.152402i
$239$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$239$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$240$	1.23607	−	3.80423i	0.0797878	−	0.245562i
$241$	20.0000			1.28831			0.644157	−	0.764894i	$-0.277208\pi$
$241$	20.0000			1.28831			0.644157	+	0.764894i	$0.277208\pi$
$242$		0			0
$243$	−10.0000			−0.641500
$244$		0			0
$245$	1.61803	−	1.17557i	0.103372	−	0.0751044i
$246$	−6.47214	−	4.70228i	−0.412648	−	0.299807i
$247$		0			0
$248$	9.27051	+	28.5317i	0.588678	+	1.81176i
$249$		0			0
$250$	9.70820	−	7.05342i	0.614001	−	0.446098i
$251$	−0.618034	+	1.90211i	−0.0390100	+	0.120060i	−0.968665	−	0.248371i	$-0.920105\pi$
$251$	−0.618034	+	1.90211i	−0.0390100	+	0.120060i	0.929655	+	0.368431i	$0.120105\pi$
$252$	−1.00000			−0.0629941
$253$		0			0
$254$	8.00000			0.501965
$255$	4.94427	−	15.2169i	0.309622	−	0.952920i
$256$	13.7533	−	9.99235i	0.859581	−	0.624522i
$257$	11.3262	+	8.22899i	0.706511	+	0.513311i	0.882046	−	0.471163i	$-0.156166\pi$
$257$	11.3262	+	8.22899i	0.706511	+	0.513311i	−0.175535	+	0.984473i	$0.556166\pi$
$258$	7.41641	+	22.8254i	0.461725	+	1.42104i
$259$	−1.85410	−	5.70634i	−0.115208	−	0.354575i
$260$	6.47214	+	4.70228i	0.401385	+	0.291623i
$261$	−4.85410	+	3.52671i	−0.300461	+	0.218298i
$262$	3.70820	−	11.4127i	0.229094	−	0.705078i
$263$	−8.00000			−0.493301			−0.246651	−	0.969104i	$-0.579330\pi$
$263$	−8.00000			−0.493301			−0.246651	+	0.969104i	$0.579330\pi$
$264$		0			0
$265$	12.0000			0.737154
$266$		0			0
$267$	9.70820	−	7.05342i	0.594132	−	0.431662i
$268$	6.47214	+	4.70228i	0.395349	+	0.287238i
$269$	3.09017	+	9.51057i	0.188411	+	0.579869i	0.999990	−	0.00437267i	$-0.00139187\pi$
$269$	3.09017	+	9.51057i	0.188411	+	0.579869i	−0.811579	+	0.584242i	$0.801392\pi$
$270$	−2.47214	−	7.60845i	−0.150449	−	0.463036i
$271$	−3.23607	−	2.35114i	−0.196577	−	0.142822i	0.485143	−	0.874435i	$-0.338768\pi$
$271$	−3.23607	−	2.35114i	−0.196577	−	0.142822i	−0.681720	+	0.731613i	$0.738768\pi$
$272$	−3.23607	+	2.35114i	−0.196215	+	0.142559i
$273$	−2.47214	+	7.60845i	−0.149620	+	0.460484i
$274$	10.0000			0.604122
$275$		0			0
$276$	8.00000			0.481543
$277$	−6.79837	+	20.9232i	−0.408475	+	1.25716i	0.509484	+	0.860480i	$0.329836\pi$
$277$	−6.79837	+	20.9232i	−0.408475	+	1.25716i	−0.917959	+	0.396676i	$0.870164\pi$
$278$	6.47214	−	4.70228i	0.388173	−	0.282024i
$279$	−8.09017	−	5.87785i	−0.484346	−	0.351898i
$280$	−1.85410	−	5.70634i	−0.110804	−	0.341019i
$281$	−1.85410	−	5.70634i	−0.110606	−	0.340412i	0.880399	−	0.474234i	$-0.157275\pi$
$281$	−1.85410	−	5.70634i	−0.110606	−	0.340412i	−0.991005	+	0.133822i	$0.957275\pi$
$282$	−16.1803	−	11.7557i	−0.963525	−	0.700042i
$283$	3.23607	−	2.35114i	0.192364	−	0.139761i	−0.487434	−	0.873160i	$-0.662067\pi$
$283$	3.23607	−	2.35114i	0.192364	−	0.139761i	0.679799	+	0.733399i	$0.262067\pi$
$284$	3.70820	−	11.4127i	0.220041	−	0.677218i
$285$		0			0
$286$		0			0
$287$	−4.00000			−0.236113
$288$	−1.54508	+	4.75528i	−0.0910450	+	0.280208i
$289$	0.809017	−	0.587785i	0.0475892	−	0.0345756i
$290$	−9.70820	−	7.05342i	−0.570085	−	0.414191i
$291$	−6.18034	−	19.0211i	−0.362298	−	1.11504i
$292$	−2.47214	−	7.60845i	−0.144671	−	0.445251i
$293$	−19.4164	−	14.1068i	−1.13432	−	0.824131i	−0.148001	−	0.988987i	$-0.547284\pi$
$293$	−19.4164	−	14.1068i	−1.13432	−	0.824131i	−0.986318	+	0.164856i	$0.947284\pi$
$294$	1.61803	−	1.17557i	0.0943657	−	0.0685607i
$295$	−1.23607	+	3.80423i	−0.0719667	+	0.221491i
$296$	−18.0000			−1.04623
$297$		0			0
$298$	−10.0000			−0.579284
$299$	4.94427	−	15.2169i	0.285935	−	0.880016i
$300$	−1.61803	+	1.17557i	−0.0934172	+	0.0678716i
$301$	9.70820	+	7.05342i	0.559572	+	0.406553i
$302$	−4.94427	−	15.2169i	−0.284511	−	0.875634i
$303$	2.47214	+	7.60845i	0.142020	+	0.437094i
$304$		0			0
$305$		0			0
$306$	1.23607	−	3.80423i	0.0706613	−	0.217473i
$307$	−20.0000			−1.14146			−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000			−1.14146			−0.570730	+	0.821138i	$0.693340\pi$
$308$		0			0
$309$	28.0000			1.59286
$310$	6.18034	−	19.0211i	0.351020	−	1.08033i
$311$	14.5623	−	10.5801i	0.825753	−	0.599944i	−0.0926019	−	0.995703i	$-0.529518\pi$
$311$	14.5623	−	10.5801i	0.825753	−	0.599944i	0.918354	+	0.395759i	$0.129518\pi$
$312$	19.4164	+	14.1068i	1.09924	+	0.798643i
$313$	0.618034	+	1.90211i	0.0349333	+	0.107514i	0.967003	−	0.254766i	$-0.0819985\pi$
$313$	0.618034	+	1.90211i	0.0349333	+	0.107514i	−0.932069	+	0.362280i	$0.881998\pi$
$314$	−4.32624	−	13.3148i	−0.244144	−	0.751397i
$315$	1.61803	+	1.17557i	0.0911659	+	0.0662359i
$316$	−6.47214	+	4.70228i	−0.364086	+	0.264524i
$317$	−0.618034	+	1.90211i	−0.0347122	+	0.106833i	−0.966911	−	0.255113i	$-0.917887\pi$
$317$	−0.618034	+	1.90211i	−0.0347122	+	0.106833i	0.932199	+	0.361946i	$0.117887\pi$
$318$	12.0000			0.672927
$319$		0			0
$320$	−14.0000			−0.782624
$321$	−7.41641	+	22.8254i	−0.413944	+	1.27399i
$322$	−3.23607	+	2.35114i	−0.180339	+	0.131024i
$323$		0			0
$324$	3.39919	+	10.4616i	0.188844	+	0.581201i
$325$	1.23607	+	3.80423i	0.0685647	+	0.211020i
$326$	−6.47214	−	4.70228i	−0.358458	−	0.260435i
$327$	−22.6525	+	16.4580i	−1.25268	+	0.910129i
$328$	−3.70820	+	11.4127i	−0.204751	+	0.630160i
$329$	−10.0000			−0.551318
$330$		0			0
$331$	−20.0000			−1.09930			−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000			−1.09930			−0.549650	+	0.835395i	$0.685239\pi$
$332$		0			0
$333$	4.85410	−	3.52671i	0.266003	−	0.193263i
$334$		0			0
$335$	−4.94427	−	15.2169i	−0.270134	−	0.831388i
$336$	−0.618034	−	1.90211i	−0.0337165	−	0.103769i
$337$	11.3262	+	8.22899i	0.616979	+	0.448262i	0.851865	−	0.523761i	$-0.175472\pi$
$337$	11.3262	+	8.22899i	0.616979	+	0.448262i	−0.234886	+	0.972023i	$0.575472\pi$
$338$	2.42705	−	1.76336i	0.132014	−	0.0959139i
$339$	11.1246	−	34.2380i	0.604206	−	1.85955i
$340$	−8.00000			−0.433861
$341$		0			0
$342$		0			0
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	29.1246	−	21.1603i	1.57029	−	1.14089i
$345$	−12.9443	−	9.40456i	−0.696896	−	0.506325i
$346$	3.70820	+	11.4127i	0.199354	+	0.613549i
$347$	−1.23607	−	3.80423i	−0.0663556	−	0.204222i	0.912381	−	0.409342i	$-0.134242\pi$
$347$	−1.23607	−	3.80423i	−0.0663556	−	0.204222i	−0.978737	+	0.205120i	$0.934242\pi$
$348$	9.70820	+	7.05342i	0.520414	+	0.378103i
$349$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$349$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$350$	0.309017	−	0.951057i	0.0165177	−	0.0508361i
$351$	16.0000			0.854017
$352$		0			0
$353$	−30.0000			−1.59674			−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000			−1.59674			−0.798369	+	0.602168i	$0.794304\pi$
$354$	−1.23607	+	3.80423i	−0.0656963	+	0.202192i
$355$	−19.4164	+	14.1068i	−1.03052	+	0.748714i
$356$	−4.85410	−	3.52671i	−0.257267	−	0.186915i
$357$	−2.47214	−	7.60845i	−0.130839	−	0.402682i
$358$	−3.70820	−	11.4127i	−0.195985	−	0.603179i
$359$	12.9443	+	9.40456i	0.683173	+	0.496354i	0.874409	−	0.485190i	$-0.161250\pi$
$359$	12.9443	+	9.40456i	0.683173	+	0.496354i	−0.191236	+	0.981544i	$0.561250\pi$
$360$	4.85410	−	3.52671i	0.255834	−	0.185874i
$361$	−5.87132	+	18.0701i	−0.309017	+	0.951057i
$362$	−10.0000			−0.525588
$363$		0			0
$364$	4.00000			0.209657
$365$	−4.94427	+	15.2169i	−0.258795	+	0.796489i
$366$		0			0
$367$	−17.7984	−	12.9313i	−0.929068	−	0.675007i	0.0166968	−	0.999861i	$-0.494685\pi$
$367$	−17.7984	−	12.9313i	−0.929068	−	0.675007i	−0.945764	+	0.324854i	$0.894685\pi$
$368$	1.23607	+	3.80423i	0.0644345	+	0.198309i
$369$	−1.23607	−	3.80423i	−0.0643471	−	0.198040i
$370$	9.70820	+	7.05342i	0.504705	+	0.366690i
$371$	4.85410	−	3.52671i	0.252012	−	0.183098i
$372$	−6.18034	+	19.0211i	−0.320436	+	0.986200i
$373$	26.0000			1.34623			0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000			1.34623			0.673114	+	0.739538i	$0.264956\pi$
$374$		0			0
$375$	24.0000			1.23935
$376$	−9.27051	+	28.5317i	−0.478090	+	1.47141i
$377$	19.4164	−	14.1068i	0.999996	−	0.726540i
$378$	−3.23607	−	2.35114i	−0.166445	−	0.120930i
$379$	−2.47214	−	7.60845i	−0.126985	−	0.390820i	0.867272	−	0.497834i	$-0.165871\pi$
$379$	−2.47214	−	7.60845i	−0.126985	−	0.390820i	−0.994258	+	0.107014i	$0.965871\pi$
$380$		0			0
$381$	12.9443	+	9.40456i	0.663155	+	0.481810i
$382$	6.47214	−	4.70228i	0.331143	−	0.240590i
$383$	0.618034	−	1.90211i	0.0315801	−	0.0971934i	−0.934024	−	0.357210i	$-0.883728\pi$
$383$	0.618034	−	1.90211i	0.0315801	−	0.0971934i	0.965604	+	0.260017i	$0.0837280\pi$
$384$	6.00000			0.306186
$385$		0			0
$386$	−14.0000			−0.712581
$387$	−3.70820	+	11.4127i	−0.188499	+	0.580139i
$388$	−8.09017	+	5.87785i	−0.410716	+	0.298403i
$389$	−4.85410	−	3.52671i	−0.246113	−	0.178811i	0.457890	−	0.889009i	$-0.348606\pi$
$389$	−4.85410	−	3.52671i	−0.246113	−	0.178811i	−0.704002	+	0.710198i	$0.748606\pi$
$390$	−4.94427	−	15.2169i	−0.250363	−	0.770538i
$391$	4.94427	+	15.2169i	0.250043	+	0.769552i
$392$	−2.42705	−	1.76336i	−0.122585	−	0.0890629i
$393$	19.4164	−	14.1068i	0.979428	−	0.711596i
$394$	6.79837	−	20.9232i	0.342497	−	1.05410i
$395$	16.0000			0.805047
$396$		0			0
$397$	22.0000			1.10415			0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000			1.10415			0.552074	+	0.833795i	$0.313837\pi$
$398$	5.56231	−	17.1190i	0.278813	−	0.858099i
$399$		0			0
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	−6.79837	−	20.9232i	−0.339495	−	1.04486i	−0.964465	−	0.264209i	$-0.914889\pi$
$401$	−6.79837	−	20.9232i	−0.339495	−	1.04486i	0.624971	−	0.780648i	$-0.285111\pi$
$402$	−4.94427	−	15.2169i	−0.246598	−	0.758950i
$403$	32.3607	+	23.5114i	1.61200	+	1.17119i
$404$	3.23607	−	2.35114i	0.161000	−	0.116974i
$405$	6.79837	−	20.9232i	0.337814	−	1.03968i
$406$	−6.00000			−0.297775
$407$		0			0
$408$	−24.0000			−1.18818
$409$	−7.41641	+	22.8254i	−0.366718	+	1.12864i	0.582181	+	0.813059i	$0.302200\pi$
$409$	−7.41641	+	22.8254i	−0.366718	+	1.12864i	−0.948898	+	0.315582i	$0.897800\pi$
$410$	6.47214	−	4.70228i	0.319636	−	0.232229i
$411$	16.1803	+	11.7557i	0.798117	+	0.579866i
$412$	−4.32624	−	13.3148i	−0.213138	−	0.655973i
$413$	0.618034	+	1.90211i	0.0304115	+	0.0935969i
$414$	−3.23607	−	2.35114i	−0.159044	−	0.115552i
$415$		0			0
$416$	6.18034	−	19.0211i	0.303016	−	0.932588i
$417$	16.0000			0.783523
$418$		0			0
$419$	2.00000			0.0977064			0.0488532	−	0.998806i	$-0.484443\pi$
$419$	2.00000			0.0977064			0.0488532	+	0.998806i	$0.484443\pi$
$420$	1.23607	−	3.80423i	0.0603139	−	0.185627i
$421$	11.3262	−	8.22899i	0.552007	−	0.401057i	−0.276518	−	0.961009i	$-0.589181\pi$
$421$	11.3262	−	8.22899i	0.552007	−	0.401057i	0.828525	+	0.559952i	$0.189181\pi$
$422$	9.70820	+	7.05342i	0.472588	+	0.343355i
$423$	−3.09017	−	9.51057i	−0.150249	−	0.462420i
$424$	−5.56231	−	17.1190i	−0.270129	−	0.831373i
$425$	−3.23607	−	2.35114i	−0.156972	−	0.114047i
$426$	−19.4164	+	14.1068i	−0.940728	+	0.683479i
$427$		0			0
$428$	12.0000			0.580042
$429$		0			0
$430$	−24.0000			−1.15738
$431$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$431$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$432$	−3.23607	+	2.35114i	−0.155695	+	0.113119i
$433$	21.0344	+	15.2824i	1.01085	+	0.734426i	0.964387	−	0.264494i	$-0.0852049\pi$
$433$	21.0344	+	15.2824i	1.01085	+	0.734426i	0.0464634	+	0.998920i	$0.485205\pi$
$434$	−3.09017	−	9.51057i	−0.148333	−	0.456522i
$435$	−7.41641	−	22.8254i	−0.355590	−	1.09439i
$436$	11.3262	+	8.22899i	0.542428	+	0.394097i
$437$		0			0
$438$	−4.94427	+	15.2169i	−0.236246	+	0.727092i
$439$	20.0000			0.954548			0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000			0.954548			0.477274	+	0.878755i	$0.341625\pi$
$440$		0			0
$441$	1.00000			0.0476190
$442$	−4.94427	+	15.2169i	−0.235175	+	0.723794i
$443$	−3.23607	+	2.35114i	−0.153750	+	0.111706i	−0.662001	−	0.749503i	$-0.730292\pi$
$443$	−3.23607	+	2.35114i	−0.153750	+	0.111706i	0.508250	+	0.861209i	$0.330292\pi$
$444$	−9.70820	−	7.05342i	−0.460731	−	0.334741i
$445$	3.70820	+	11.4127i	0.175786	+	0.541013i
$446$	−6.79837	−	20.9232i	−0.321912	−	0.990744i
$447$	−16.1803	−	11.7557i	−0.765304	−	0.556026i
$448$	−5.66312	+	4.11450i	−0.267557	+	0.194392i
$449$	−3.09017	+	9.51057i	−0.145834	+	0.448831i	−0.997117	−	0.0758752i	$-0.975825\pi$
$449$	−3.09017	+	9.51057i	−0.145834	+	0.448831i	0.851283	+	0.524707i	$0.175825\pi$
$450$	1.00000			0.0471405
$451$		0			0
$452$	−18.0000			−0.846649
$453$	9.88854	−	30.4338i	0.464604	−	1.42991i
$454$	−9.70820	+	7.05342i	−0.455629	+	0.331034i
$455$	−6.47214	−	4.70228i	−0.303418	−	0.220446i
$456$		0			0
$457$	−5.56231	−	17.1190i	−0.260194	−	0.800794i	−0.992762	−	0.120100i	$-0.961678\pi$
$457$	−5.56231	−	17.1190i	−0.260194	−	0.800794i	0.732568	−	0.680694i	$-0.238322\pi$
$458$	14.5623	+	10.5801i	0.680452	+	0.494377i
$459$	−12.9443	+	9.40456i	−0.604187	+	0.438967i
$460$	−2.47214	+	7.60845i	−0.115264	+	0.354746i
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$	4.00000			0.185896			0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000			0.185896			0.0929479	+	0.995671i	$0.470371\pi$
$464$	−1.85410	+	5.70634i	−0.0860745	+	0.264910i
$465$	32.3607	−	23.5114i	1.50069	−	1.09032i
$466$	14.5623	+	10.5801i	0.674586	+	0.490115i
$467$	9.27051	+	28.5317i	0.428988	+	1.32029i	0.899123	+	0.437695i	$0.144205\pi$
$467$	9.27051	+	28.5317i	0.428988	+	1.32029i	−0.470135	+	0.882594i	$0.655795\pi$
$468$	1.23607	+	3.80423i	0.0571373	+	0.175850i
$469$	−6.47214	−	4.70228i	−0.298855	−	0.217131i
$470$	16.1803	−	11.7557i	0.746343	−	0.542250i
$471$	8.65248	−	26.6296i	0.398685	−	1.22703i
$472$	6.00000			0.276172
$473$		0			0
$474$	16.0000			0.734904
$475$		0			0
$476$	−3.23607	+	2.35114i	−0.148325	+	0.107764i
$477$	4.85410	+	3.52671i	0.222254	+	0.161477i
$478$		0			0
$479$	1.23607	+	3.80423i	0.0564774	+	0.173820i	0.975316	−	0.220814i	$-0.0708715\pi$
$479$	1.23607	+	3.80423i	0.0564774	+	0.173820i	−0.918838	+	0.394634i	$0.870871\pi$
$480$	−16.1803	−	11.7557i	−0.738528	−	0.536572i
$481$	−19.4164	+	14.1068i	−0.885312	+	0.643217i
$482$	−6.18034	+	19.0211i	−0.281507	+	0.866389i
$483$	−8.00000			−0.364013
$484$		0			0
$485$	20.0000			0.908153
$486$	3.09017	−	9.51057i	0.140173	−	0.431408i
$487$	22.6525	−	16.4580i	1.02648	−	0.745783i	0.0588802	−	0.998265i	$-0.481247\pi$
$487$	22.6525	−	16.4580i	1.02648	−	0.745783i	0.967601	+	0.252482i	$0.0812470\pi$
$488$		0			0
$489$	−4.94427	−	15.2169i	−0.223588	−	0.688132i
$490$	0.618034	+	1.90211i	0.0279199	+	0.0859287i
$491$	22.6525	+	16.4580i	1.02229	+	0.742739i	0.966751	−	0.255718i	$-0.0823118\pi$
$491$	22.6525	+	16.4580i	1.02229	+	0.742739i	0.0555405	+	0.998456i	$0.482312\pi$
$492$	−6.47214	+	4.70228i	−0.291786	+	0.211995i
$493$	−7.41641	+	22.8254i	−0.334018	+	1.02800i
$494$		0			0
$495$		0			0
$496$	−10.0000			−0.449013
$497$	−3.70820	+	11.4127i	−0.166336	+	0.511929i
$498$		0			0
$499$	12.9443	+	9.40456i	0.579465	+	0.421006i	0.838531	−	0.544853i	$-0.183415\pi$
$499$	12.9443	+	9.40456i	0.579465	+	0.421006i	−0.259066	+	0.965860i	$0.583415\pi$
$500$	−3.70820	−	11.4127i	−0.165836	−	0.510390i
$501$		0			0
$502$	−1.61803	−	1.17557i	−0.0722164	−	0.0524683i
$503$	3.23607	−	2.35114i	0.144289	−	0.104832i	−0.513299	−	0.858210i	$-0.671577\pi$
$503$	3.23607	−	2.35114i	0.144289	−	0.104832i	0.657588	+	0.753378i	$0.271577\pi$
$504$	0.927051	−	2.85317i	0.0412941	−	0.127090i
$505$	−8.00000			−0.355995
$506$		0			0
$507$	6.00000			0.266469
$508$	2.47214	−	7.60845i	0.109683	−	0.337570i
$509$	−14.5623	+	10.5801i	−0.645463	+	0.468956i	−0.861723	−	0.507380i	$-0.830614\pi$
$509$	−14.5623	+	10.5801i	−0.645463	+	0.468956i	0.216260	+	0.976336i	$0.430614\pi$
$510$	12.9443	+	9.40456i	0.573182	+	0.416441i
$511$	2.47214	+	7.60845i	0.109361	+	0.336578i
$512$	3.39919	+	10.4616i	0.150224	+	0.462343i
$513$		0			0
$514$	−11.3262	+	8.22899i	−0.499579	+	0.362965i
$515$	−8.65248	+	26.6296i	−0.381274	+	1.17344i
$516$	24.0000			1.05654
$517$		0			0
$518$	6.00000			0.263625
$519$	−7.41641	+	22.8254i	−0.325544	+	1.00192i
$520$	−19.4164	+	14.1068i	−0.851466	+	0.618626i
$521$	−4.85410	−	3.52671i	−0.212662	−	0.154508i	0.476355	−	0.879253i	$-0.341958\pi$
$521$	−4.85410	−	3.52671i	−0.212662	−	0.154508i	−0.689017	+	0.724745i	$0.741958\pi$
$522$	−1.85410	−	5.70634i	−0.0811518	−	0.249760i
$523$	−6.18034	−	19.0211i	−0.270247	−	0.831736i	−0.990438	−	0.137960i	$-0.955946\pi$
$523$	−6.18034	−	19.0211i	−0.270247	−	0.831736i	0.720190	−	0.693776i	$-0.244054\pi$
$524$	−9.70820	−	7.05342i	−0.424105	−	0.308130i
$525$	1.61803	−	1.17557i	0.0706168	−	0.0513061i
$526$	2.47214	−	7.60845i	0.107790	−	0.331744i
$527$	−40.0000			−1.74243
$528$		0			0
$529$	−7.00000			−0.304348
$530$	−3.70820	+	11.4127i	−0.161074	+	0.495735i
$531$	−1.61803	+	1.17557i	−0.0702167	+	0.0510154i
$532$		0			0
$533$	4.94427	+	15.2169i	0.214160	+	0.659117i
$534$	3.70820	+	11.4127i	0.160470	+	0.493875i
$535$	−19.4164	−	14.1068i	−0.839445	−	0.609892i
$536$	−19.4164	+	14.1068i	−0.838661	+	0.609323i
$537$	7.41641	−	22.8254i	0.320042	−	0.984987i
$538$	−10.0000			−0.431131
$539$		0			0
$540$	−8.00000			−0.344265
$541$	8.03444	−	24.7275i	0.345428	−	1.06312i	−0.615927	−	0.787803i	$-0.711218\pi$
$541$	8.03444	−	24.7275i	0.345428	−	1.06312i	0.961354	−	0.275314i	$-0.0887817\pi$
$542$	3.23607	−	2.35114i	0.139001	−	0.100990i
$543$	−16.1803	−	11.7557i	−0.694365	−	0.504486i
$544$	6.18034	+	19.0211i	0.264980	+	0.815524i
$545$	−8.65248	−	26.6296i	−0.370631	−	1.14069i
$546$	−6.47214	−	4.70228i	−0.276982	−	0.201239i
$547$	−22.6525	+	16.4580i	−0.968550	+	0.703693i	−0.955121	−	0.296217i	$-0.904275\pi$
$547$	−22.6525	+	16.4580i	−0.968550	+	0.703693i	−0.0134293	+	0.999910i	$0.504275\pi$
$548$	3.09017	−	9.51057i	0.132006	−	0.406271i
$549$		0			0
$550$		0			0
$551$		0			0
$552$	−7.41641	+	22.8254i	−0.315663	+	0.971512i
$553$	6.47214	−	4.70228i	0.275223	−	0.199961i
$554$	−17.7984	−	12.9313i	−0.756180	−	0.549397i
$555$	7.41641	+	22.8254i	0.314809	+	0.968882i
$556$	−2.47214	−	7.60845i	−0.104842	−	0.322670i
$557$	17.7984	+	12.9313i	0.754141	+	0.547916i	0.897108	−	0.441812i	$-0.145664\pi$
$557$	17.7984	+	12.9313i	0.754141	+	0.547916i	−0.142966	+	0.989728i	$0.545664\pi$
$558$	8.09017	−	5.87785i	0.342484	−	0.248829i
$559$	14.8328	−	45.6507i	0.627361	−	1.93082i
$560$	2.00000			0.0845154
$561$		0			0
$562$	6.00000			0.253095
$563$	9.88854	−	30.4338i	0.416752	−	1.28263i	−0.493922	−	0.869506i	$-0.664437\pi$
$563$	9.88854	−	30.4338i	0.416752	−	1.28263i	0.910674	−	0.413126i	$-0.135563\pi$
$564$	−16.1803	+	11.7557i	−0.681315	+	0.495004i
$565$	29.1246	+	21.1603i	1.22528	+	0.890219i
$566$	1.23607	+	3.80423i	0.0519558	+	0.159904i
$567$	−3.39919	−	10.4616i	−0.142752	−	0.439347i
$568$	29.1246	+	21.1603i	1.22204	+	0.887865i
$569$	24.2705	−	17.6336i	1.01747	−	0.739237i	0.0517094	−	0.998662i	$-0.483533\pi$
$569$	24.2705	−	17.6336i	1.01747	−	0.739237i	0.965763	+	0.259425i	$0.0835330\pi$
$570$		0			0
$571$	−20.0000			−0.836974			−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000			−0.836974			−0.418487	+	0.908223i	$0.637439\pi$
$572$		0			0
$573$	16.0000			0.668410
$574$	1.23607	−	3.80423i	0.0515925	−	0.158785i
$575$	−3.23607	+	2.35114i	−0.134953	+	0.0980494i
$576$	−5.66312	−	4.11450i	−0.235963	−	0.171437i
$577$	−5.56231	−	17.1190i	−0.231562	−	0.712674i	−0.997559	−	0.0698300i	$-0.977754\pi$
$577$	−5.56231	−	17.1190i	−0.231562	−	0.712674i	0.765997	−	0.642844i	$-0.222246\pi$
$578$	0.309017	+	0.951057i	0.0128534	+	0.0395587i
$579$	−22.6525	−	16.4580i	−0.941405	−	0.683971i
$580$	−9.70820	+	7.05342i	−0.403111	+	0.292877i
$581$		0			0
$582$	20.0000			0.829027
$583$		0			0
$584$	24.0000			0.993127
$585$	2.47214	−	7.60845i	0.102210	−	0.314571i
$586$	19.4164	−	14.1068i	0.802084	−	0.582748i
$587$	1.61803	+	1.17557i	0.0667834	+	0.0485210i	0.620676	−	0.784067i	$-0.286858\pi$
$587$	1.61803	+	1.17557i	0.0667834	+	0.0485210i	−0.553893	+	0.832588i	$0.686858\pi$
$588$	−0.618034	−	1.90211i	−0.0254873	−	0.0784418i
$589$		0			0
$590$	−3.23607	−	2.35114i	−0.133227	−	0.0967949i
$591$	35.5967	−	25.8626i	1.46425	−	1.06384i
$592$	1.85410	−	5.70634i	0.0762031	−	0.234529i
$593$	−32.0000			−1.31408			−0.657041	−	0.753855i	$-0.728192\pi$
$593$	−32.0000			−1.31408			−0.657041	+	0.753855i	$0.728192\pi$
$594$		0			0
$595$	8.00000			0.327968
$596$	−3.09017	+	9.51057i	−0.126578	+	0.389568i
$597$	29.1246	−	21.1603i	1.19199	−	0.866032i
$598$	12.9443	+	9.40456i	0.529331	+	0.384581i
$599$	−6.18034	−	19.0211i	−0.252522	−	0.777182i	−0.994308	−	0.106546i	$-0.966021\pi$
$599$	−6.18034	−	19.0211i	−0.252522	−	0.777182i	0.741786	−	0.670637i	$-0.233979\pi$
$600$	−1.85410	−	5.70634i	−0.0756934	−	0.232960i
$601$	−22.6525	−	16.4580i	−0.924014	−	0.671335i	0.0205061	−	0.999790i	$-0.493472\pi$
$601$	−22.6525	−	16.4580i	−0.924014	−	0.671335i	−0.944520	+	0.328454i	$0.893472\pi$
$602$	−9.70820	+	7.05342i	−0.395677	+	0.287476i
$603$	2.47214	−	7.60845i	0.100673	−	0.309840i
$604$	−16.0000			−0.651031
$605$		0			0
$606$	−8.00000			−0.324978
$607$	12.3607	−	38.0423i	0.501705	−	1.54409i	−0.304537	−	0.952501i	$-0.598502\pi$
$607$	12.3607	−	38.0423i	0.501705	−	1.54409i	0.806241	−	0.591587i	$-0.201498\pi$
$608$		0			0
$609$	−9.70820	−	7.05342i	−0.393396	−	0.285819i
$610$		0			0
$611$	12.3607	+	38.0423i	0.500060	+	1.53903i
$612$	−3.23607	−	2.35114i	−0.130810	−	0.0950392i
$613$	21.0344	−	15.2824i	0.849573	−	0.617251i	−0.0754552	−	0.997149i	$-0.524041\pi$
$613$	21.0344	−	15.2824i	0.849573	−	0.617251i	0.925028	+	0.379898i	$0.124041\pi$
$614$	6.18034	−	19.0211i	0.249418	−	0.767630i
$615$	16.0000			0.645182
$616$		0			0
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$	−8.65248	+	26.6296i	−0.348054	+	1.07120i
$619$	−11.3262	+	8.22899i	−0.455240	+	0.330751i	−0.791661	−	0.610960i	$-0.790783\pi$
$619$	−11.3262	+	8.22899i	−0.455240	+	0.330751i	0.336421	+	0.941712i	$0.390783\pi$
$620$	−16.1803	−	11.7557i	−0.649818	−	0.472120i
$621$	4.94427	+	15.2169i	0.198407	+	0.610633i
$622$	5.56231	+	17.1190i	0.223028	+	0.686410i
$623$	4.85410	+	3.52671i	0.194475	+	0.141295i
$624$	−6.47214	+	4.70228i	−0.259093	+	0.188242i
$625$	−5.87132	+	18.0701i	−0.234853	+	0.722803i
$626$	−2.00000			−0.0799361
$627$		0			0
$628$	−14.0000			−0.558661
$629$	7.41641	−	22.8254i	0.295712	−	0.910107i
$630$	−1.61803	+	1.17557i	−0.0644640	+	0.0468358i
$631$	6.47214	+	4.70228i	0.257652	+	0.187195i	0.709111	−	0.705097i	$-0.249096\pi$
$631$	6.47214	+	4.70228i	0.257652	+	0.187195i	−0.451459	+	0.892292i	$0.649096\pi$
$632$	−7.41641	−	22.8254i	−0.295009	−	0.907944i
$633$	7.41641	+	22.8254i	0.294776	+	0.907226i
$634$	−1.61803	−	1.17557i	−0.0642603	−	0.0466879i
$635$	−12.9443	+	9.40456i	−0.513678	+	0.373209i
$636$	3.70820	−	11.4127i	0.147040	−	0.452542i
$637$	−4.00000			−0.158486
$638$		0			0
$639$	−12.0000			−0.474713
$640$	−1.85410	+	5.70634i	−0.0732898	+	0.225563i
$641$	14.5623	−	10.5801i	0.575177	−	0.417890i	−0.261805	−	0.965121i	$-0.584318\pi$
$641$	14.5623	−	10.5801i	0.575177	−	0.417890i	0.836982	+	0.547230i	$0.184318\pi$
$642$	−19.4164	−	14.1068i	−0.766304	−	0.556753i
$643$	4.32624	+	13.3148i	0.170610	+	0.525084i	0.999406	−	0.0344673i	$-0.0109734\pi$
$643$	4.32624	+	13.3148i	0.170610	+	0.525084i	−0.828796	+	0.559551i	$0.810973\pi$
$644$	1.23607	+	3.80423i	0.0487079	+	0.149908i
$645$	−38.8328	−	28.2137i	−1.52904	−	1.11091i
$646$		0			0
$647$	−6.79837	+	20.9232i	−0.267272	+	0.822578i	0.723890	+	0.689916i	$0.242352\pi$
$647$	−6.79837	+	20.9232i	−0.267272	+	0.822578i	−0.991161	+	0.132662i	$0.957648\pi$
$648$	−33.0000			−1.29636
$649$		0			0
$650$	−4.00000			−0.156893
$651$	6.18034	−	19.0211i	0.242227	−	0.745497i
$652$	−6.47214	+	4.70228i	−0.253468	+	0.184156i
$653$	21.0344	+	15.2824i	0.823141	+	0.598047i	0.917611	−	0.397481i	$-0.130115\pi$
$653$	21.0344	+	15.2824i	0.823141	+	0.598047i	−0.0944693	+	0.995528i	$0.530115\pi$
$654$	−8.65248	−	26.6296i	−0.338339	−	1.04130i
$655$	7.41641	+	22.8254i	0.289783	+	0.891860i
$656$	−3.23607	−	2.35114i	−0.126347	−	0.0917966i
$657$	−6.47214	+	4.70228i	−0.252502	+	0.183453i
$658$	3.09017	−	9.51057i	0.120467	−	0.370760i
$659$	−4.00000			−0.155818			−0.0779089	−	0.996960i	$-0.524824\pi$
$659$	−4.00000			−0.155818			−0.0779089	+	0.996960i	$0.524824\pi$
$660$		0			0
$661$	22.0000			0.855701			0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000			0.855701			0.427850	+	0.903850i	$0.359271\pi$
$662$	6.18034	−	19.0211i	0.240206	−	0.739277i
$663$	−25.8885	+	18.8091i	−1.00543	+	0.730486i
$664$		0			0
$665$		0			0
$666$	1.85410	+	5.70634i	0.0718450	+	0.221116i
$667$	19.4164	+	14.1068i	0.751806	+	0.546219i
$668$		0			0
$669$	13.5967	−	41.8465i	0.525681	−	1.61788i
$670$	16.0000			0.618134
$671$		0			0
$672$	−10.0000			−0.385758
$673$	10.5066	−	32.3359i	0.404999	−	1.24646i	−0.515897	−	0.856650i	$-0.672541\pi$
$673$	10.5066	−	32.3359i	0.404999	−	1.24646i	0.920896	−	0.389808i	$-0.127459\pi$
$674$	−11.3262	+	8.22899i	−0.436270	+	0.316969i
$675$	−3.23607	−	2.35114i	−0.124556	−	0.0904955i
$676$	−0.927051	−	2.85317i	−0.0356558	−	0.109737i
$677$	3.70820	+	11.4127i	0.142518	+	0.438625i	0.996683	−	0.0813762i	$-0.0259315\pi$
$677$	3.70820	+	11.4127i	0.142518	+	0.438625i	−0.854166	+	0.520001i	$0.825932\pi$
$678$	29.1246	+	21.1603i	1.11852	+	0.812655i
$679$	8.09017	−	5.87785i	0.310472	−	0.225571i
$680$	7.41641	−	22.8254i	0.284406	−	0.875312i
$681$	−24.0000			−0.919682
$682$		0			0
$683$	−4.00000			−0.153056			−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000			−0.153056			−0.0765279	+	0.997067i	$0.524383\pi$
$684$		0			0
$685$	−16.1803	+	11.7557i	−0.618219	+	0.449162i
$686$	0.809017	+	0.587785i	0.0308884	+	0.0224417i
$687$	11.1246	+	34.2380i	0.424430	+	1.30626i
$688$	3.70820	+	11.4127i	0.141374	+	0.435104i
$689$	−19.4164	−	14.1068i	−0.739706	−	0.537428i
$690$	12.9443	−	9.40456i	0.492780	−	0.358026i
$691$	−14.2148	+	43.7486i	−0.540756	+	1.66428i	0.190117	+	0.981761i	$0.439113\pi$
$691$	−14.2148	+	43.7486i	−0.540756	+	1.66428i	−0.730873	+	0.682514i	$0.760887\pi$
$692$	12.0000			0.456172
$693$		0			0
$694$	4.00000			0.151838
$695$	−4.94427	+	15.2169i	−0.187547	+	0.577210i
$696$	−29.1246	+	21.1603i	−1.10397	+	0.802078i
$697$	−12.9443	−	9.40456i	−0.490299	−	0.356223i
$698$		0			0
$699$	11.1246	+	34.2380i	0.420771	+	1.29500i
$700$	−0.809017	−	0.587785i	−0.0305780	−	0.0222162i
$701$	−17.7984	+	12.9313i	−0.672235	+	0.488408i	−0.870773	−	0.491686i	$-0.836381\pi$
$701$	−17.7984	+	12.9313i	−0.672235	+	0.488408i	0.198537	+	0.980093i	$0.436381\pi$
$702$	−4.94427	+	15.2169i	−0.186610	+	0.574325i
$703$		0			0
$704$		0			0
$705$	40.0000			1.50649
$706$	9.27051	−	28.5317i	0.348900	−	1.07380i
$707$	−3.23607	+	2.35114i	−0.121705	+	0.0884238i
$708$	3.23607	+	2.35114i	0.121619	+	0.0883613i
$709$	−10.5066	−	32.3359i	−0.394583	−	1.21440i	−0.929286	−	0.369361i	$-0.879577\pi$
$709$	−10.5066	−	32.3359i	−0.394583	−	1.21440i	0.534703	−	0.845040i	$-0.320423\pi$
$710$	−7.41641	−	22.8254i	−0.278333	−	0.856620i
$711$	6.47214	+	4.70228i	0.242724	+	0.176349i
$712$	14.5623	−	10.5801i	0.545745	−	0.396507i
$713$	−12.3607	+	38.0423i	−0.462911	+	1.42469i
$714$	8.00000			0.299392
$715$		0			0
$716$	−12.0000			−0.448461
$717$		0			0
$718$	−12.9443	+	9.40456i	−0.483076	+	0.350975i
$719$	4.85410	+	3.52671i	0.181027	+	0.131524i	0.674609	−	0.738176i	$-0.264312\pi$
$719$	4.85410	+	3.52671i	0.181027	+	0.131524i	−0.493581	+	0.869700i	$0.664312\pi$
$720$	0.618034	+	1.90211i	0.0230328	+	0.0708876i
$721$	4.32624	+	13.3148i	0.161118	+	0.495869i
$722$	−15.3713	−	11.1679i	−0.572061	−	0.415627i
$723$	−32.3607	+	23.5114i	−1.20351	+	0.874399i
$724$	−3.09017	+	9.51057i	−0.114845	+	0.353457i
$725$	−6.00000			−0.222834
$726$		0			0
$727$	18.0000			0.667583			0.333792	−	0.942647i	$-0.391672\pi$
$727$	18.0000			0.667583			0.333792	+	0.942647i	$0.391672\pi$
$728$	−3.70820	+	11.4127i	−0.137435	+	0.422982i
$729$	−10.5172	+	7.64121i	−0.389527	+	0.283008i
$730$	−12.9443	−	9.40456i	−0.479089	−	0.348079i
$731$	14.8328	+	45.6507i	0.548612	+	1.68845i
$732$		0			0
$733$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$733$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$734$	17.7984	−	12.9313i	0.656950	−	0.477302i
$735$	−1.23607	+	3.80423i	−0.0455931	+	0.140321i
$736$	20.0000			0.737210
$737$		0			0
$738$	4.00000			0.147242
$739$	1.23607	−	3.80423i	0.0454695	−	0.139941i	−0.925744	−	0.378150i	$-0.876560\pi$
$739$	1.23607	−	3.80423i	0.0454695	−	0.139941i	0.971214	+	0.238209i	$0.0765604\pi$
$740$	9.70820	−	7.05342i	0.356881	−	0.259289i
$741$		0			0
$742$	1.85410	+	5.70634i	0.0680662	+	0.209486i
$743$	2.47214	+	7.60845i	0.0906939	+	0.279127i	0.986108	−	0.166108i	$-0.0531201\pi$
$743$	2.47214	+	7.60845i	0.0906939	+	0.279127i	−0.895414	+	0.445235i	$0.853120\pi$
$744$	−48.5410	−	35.2671i	−1.77960	−	1.29296i
$745$	16.1803	−	11.7557i	0.592802	−	0.430696i
$746$	−8.03444	+	24.7275i	−0.294162	+	0.905337i
$747$		0			0
$748$		0			0
$749$	−12.0000			−0.438470
$750$	−7.41641	+	22.8254i	−0.270809	+	0.833464i
$751$	16.1803	−	11.7557i	0.590429	−	0.428972i	−0.252040	−	0.967717i	$-0.581101\pi$
$751$	16.1803	−	11.7557i	0.590429	−	0.428972i	0.842469	+	0.538745i	$0.181101\pi$
$752$	−8.09017	−	5.87785i	−0.295018	−	0.214343i
$753$	−1.23607	−	3.80423i	−0.0450448	−	0.138634i
$754$	7.41641	+	22.8254i	0.270090	+	0.831250i
$755$	25.8885	+	18.8091i	0.942181	+	0.684534i
$756$	−3.23607	+	2.35114i	−0.117695	+	0.0855102i
$757$	−3.09017	+	9.51057i	−0.112314	+	0.345667i	−0.991377	−	0.131038i	$-0.958169\pi$
$757$	−3.09017	+	9.51057i	−0.112314	+	0.345667i	0.879063	+	0.476705i	$0.158169\pi$
$758$	8.00000			0.290573
$759$		0			0
$760$		0			0
$761$	−14.8328	+	45.6507i	−0.537689	+	1.65484i	0.200077	+	0.979780i	$0.435881\pi$
$761$	−14.8328	+	45.6507i	−0.537689	+	1.65484i	−0.737766	+	0.675057i	$0.764119\pi$
$762$	−12.9443	+	9.40456i	−0.468921	+	0.340691i
$763$	−11.3262	−	8.22899i	−0.410037	−	0.297910i
$764$	−2.47214	−	7.60845i	−0.0894387	−	0.275264i
$765$	2.47214	+	7.60845i	0.0893803	+	0.275084i
$766$	1.61803	+	1.17557i	0.0584619	+	0.0424751i
$767$	6.47214	−	4.70228i	0.233695	−	0.169790i
$768$	−10.5066	+	32.3359i	−0.379123	+	1.16682i
$769$	−32.0000			−1.15395			−0.576975	−	0.816762i	$-0.695767\pi$
$769$	−32.0000			−1.15395			−0.576975	+	0.816762i	$0.695767\pi$
$770$		0			0
$771$	−28.0000			−1.00840
$772$	−4.32624	+	13.3148i	−0.155705	+	0.479210i
$773$	24.2705	−	17.6336i	0.872950	−	0.634235i	−0.0584272	−	0.998292i	$-0.518609\pi$
$773$	24.2705	−	17.6336i	0.872950	−	0.634235i	0.931377	+	0.364057i	$0.118609\pi$
$774$	−9.70820	−	7.05342i	−0.348954	−	0.253530i
$775$	−3.09017	−	9.51057i	−0.111002	−	0.341630i
$776$	−9.27051	−	28.5317i	−0.332792	−	1.02423i
$777$	9.70820	+	7.05342i	0.348280	+	0.253040i
$778$	4.85410	−	3.52671i	0.174028	−	0.126439i
$779$		0			0
$780$	−16.0000			−0.572892
$781$		0			0
$782$	−16.0000			−0.572159
$783$	−7.41641	+	22.8254i	−0.265041	+	0.815712i
$784$	0.809017	−	0.587785i	0.0288935	−	0.0209923i
$785$	22.6525	+	16.4580i	0.808502	+	0.587411i
$786$	7.41641	+	22.8254i	0.264535	+	0.814154i
$787$	−4.94427	−	15.2169i	−0.176244	−	0.542424i	0.823444	−	0.567398i	$-0.192050\pi$
$787$	−4.94427	−	15.2169i	−0.176244	−	0.542424i	−0.999688	+	0.0249737i	$0.992050\pi$
$788$	−17.7984	−	12.9313i	−0.634041	−	0.460658i
$789$	12.9443	−	9.40456i	0.460828	−	0.334811i
$790$	−4.94427	+	15.2169i	−0.175909	+	0.541393i
$791$	18.0000			0.640006
$792$		0			0
$793$		0			0
$794$	−6.79837	+	20.9232i	−0.241265	+	0.742538i
$795$	−19.4164	+	14.1068i	−0.688629	+	0.500318i
$796$	−14.5623	−	10.5801i	−0.516147	−	0.375003i
$797$	4.32624	+	13.3148i	0.153243	+	0.471634i	0.997979	−	0.0635500i	$-0.0202422\pi$
$797$	4.32624	+	13.3148i	0.153243	+	0.471634i	−0.844735	+	0.535184i	$0.820242\pi$
$798$		0			0
$799$	−32.3607	−	23.5114i	−1.14484	−	0.831774i
$800$	−4.04508	+	2.93893i	−0.143015	+	0.103907i
$801$	−1.85410	+	5.70634i	−0.0655115	+	0.201624i
$802$	22.0000			0.776847
$803$		0			0
$804$	−16.0000			−0.564276
$805$	2.47214	−	7.60845i	0.0871313	−	0.268163i
$806$	−32.3607	+	23.5114i	−1.13986	+	0.828154i
$807$	−16.1803	−	11.7557i	−0.569575	−	0.413820i
$808$	3.70820	+	11.4127i	0.130454	+	0.401497i
$809$	9.27051	+	28.5317i	0.325934	+	1.00312i	0.971017	+	0.239009i	$0.0768225\pi$
$809$	9.27051	+	28.5317i	0.325934	+	1.00312i	−0.645084	+	0.764112i	$0.723177\pi$
$810$	17.7984	+	12.9313i	0.625371	+	0.454359i
$811$	22.6525	−	16.4580i	0.795436	−	0.577918i	−0.114136	−	0.993465i	$-0.536410\pi$
$811$	22.6525	−	16.4580i	0.795436	−	0.577918i	0.909572	+	0.415547i	$0.136410\pi$
$812$	−1.85410	+	5.70634i	−0.0650662	+	0.200253i
$813$	8.00000			0.280572
$814$		0			0
$815$	16.0000			0.560456
$816$	2.47214	−	7.60845i	0.0865421	−	0.266349i
$817$		0			0
$818$	−19.4164	−	14.1068i	−0.678879	−	0.493234i
$819$	−1.23607	−	3.80423i	−0.0431917	−	0.132930i
$820$	−2.47214	−	7.60845i	−0.0863307	−	0.265699i
$821$	37.2148	+	27.0381i	1.29880	+	0.943637i	0.999943	−	0.0106595i	$-0.00339309\pi$
$821$	37.2148	+	27.0381i	1.29880	+	0.943637i	0.298862	+	0.954296i	$0.403393\pi$
$822$	−16.1803	+	11.7557i	−0.564354	+	0.410027i
$823$	7.41641	−	22.8254i	0.258520	−	0.795642i	−0.734596	−	0.678505i	$-0.762628\pi$
$823$	7.41641	−	22.8254i	0.258520	−	0.795642i	0.993116	−	0.117137i	$-0.0373717\pi$
$824$	42.0000			1.46314
$825$		0			0
$826$	−2.00000			−0.0695889
$827$	8.65248	−	26.6296i	0.300876	−	0.926001i	−0.680308	−	0.732926i	$-0.738154\pi$
$827$	8.65248	−	26.6296i	0.300876	−	0.926001i	0.981184	−	0.193075i	$-0.0618460\pi$
$828$	−3.23607	+	2.35114i	−0.112461	+	0.0817078i
$829$	1.61803	+	1.17557i	0.0561966	+	0.0408293i	0.615529	−	0.788114i	$-0.288942\pi$
$829$	1.61803	+	1.17557i	0.0561966	+	0.0408293i	−0.559332	+	0.828944i	$0.688942\pi$
$830$		0			0
$831$	−13.5967	−	41.8465i	−0.471666	−	1.45164i
$832$	22.6525	+	16.4580i	0.785333	+	0.570578i
$833$	3.23607	−	2.35114i	0.112123	−	0.0814622i
$834$	−4.94427	+	15.2169i	−0.171206	+	0.526918i
$835$		0			0
$836$		0			0
$837$	−40.0000			−1.38260
$838$	−0.618034	+	1.90211i	−0.0213496	+	0.0657074i
$839$	−27.5066	+	19.9847i	−0.949633	+	0.689948i	−0.950720	−	0.310051i	$-0.899654\pi$
$839$	−27.5066	+	19.9847i	−0.949633	+	0.689948i	0.00108740	+	0.999999i	$0.499654\pi$
$840$	9.70820	+	7.05342i	0.334965	+	0.243366i
$841$	2.16312	+	6.65740i	0.0745903	+	0.229565i
$842$	4.32624	+	13.3148i	0.149092	+	0.458858i
$843$	9.70820	+	7.05342i	0.334368	+	0.242933i
$844$	9.70820	−	7.05342i	0.334170	−	0.242789i
$845$	−1.85410	+	5.70634i	−0.0637830	+	0.196304i
$846$	10.0000			0.343807
$847$		0			0
$848$	6.00000			0.206041
$849$	−2.47214	+	7.60845i	−0.0848435	+	0.261121i
$850$	3.23607	−	2.35114i	0.110996	−	0.0806435i
$851$	−19.4164	−	14.1068i	−0.665586	−	0.483576i
$852$	7.41641	+	22.8254i	0.254082	+	0.781984i
$853$	−13.5967	−	41.8465i	−0.465544	−	1.43280i	−0.858297	−	0.513153i	$-0.828477\pi$
$853$	−13.5967	−	41.8465i	−0.465544	−	1.43280i	0.392754	−	0.919644i	$-0.371523\pi$
$854$		0			0
$855$		0			0
$856$	−11.1246	+	34.2380i	−0.380231	+	1.17023i
$857$	−56.0000			−1.91292			−0.956462	−	0.291858i	$-0.905727\pi$
$857$	−56.0000			−1.91292			−0.956462	+	0.291858i	$0.905727\pi$
$858$		0			0
$859$	6.00000			0.204717			0.102359	−	0.994748i	$-0.467361\pi$
$859$	6.00000			0.204717			0.102359	+	0.994748i	$0.467361\pi$
$860$	−7.41641	+	22.8254i	−0.252897	+	0.778338i
$861$	6.47214	−	4.70228i	0.220570	−	0.160253i
$862$		0			0
$863$	7.41641	+	22.8254i	0.252457	+	0.776984i	0.994320	+	0.106432i	$0.0339427\pi$
$863$	7.41641	+	22.8254i	0.252457	+	0.776984i	−0.741863	+	0.670552i	$0.766057\pi$
$864$	6.18034	+	19.0211i	0.210259	+	0.647112i
$865$	−19.4164	−	14.1068i	−0.660178	−	0.479647i
$866$	−21.0344	+	15.2824i	−0.714779	+	0.519318i
$867$	−0.618034	+	1.90211i	−0.0209895	+	0.0645991i
$868$	−10.0000			−0.339422
$869$		0			0
$870$	24.0000			0.813676
$871$	−9.88854	+	30.4338i	−0.335061	+	1.03121i
$872$	−33.9787	+	24.6870i	−1.15066	+	0.836007i
$873$	8.09017	+	5.87785i	0.273811	+	0.198935i
$874$		0			0
$875$	3.70820	+	11.4127i	0.125360	+	0.385819i
$876$	12.9443	+	9.40456i	0.437346	+	0.317751i
$877$	33.9787	−	24.6870i	1.14738	−	0.833620i	0.159249	−	0.987238i	$-0.449093\pi$
$877$	33.9787	−	24.6870i	1.14738	−	0.833620i	0.988130	+	0.153618i	$0.0490926\pi$
$878$	−6.18034	+	19.0211i	−0.208576	+	0.641932i
$879$	48.0000			1.61900
$880$		0			0
$881$	−34.0000			−1.14549			−0.572745	−	0.819734i	$-0.694121\pi$
$881$	−34.0000			−1.14549			−0.572745	+	0.819734i	$0.694121\pi$
$882$	−0.309017	+	0.951057i	−0.0104051	+	0.0320237i
$883$	−22.6525	+	16.4580i	−0.762317	+	0.553855i	−0.899620	−	0.436674i	$-0.856156\pi$
$883$	−22.6525	+	16.4580i	−0.762317	+	0.553855i	0.137303	+	0.990529i	$0.456156\pi$
$884$	12.9443	+	9.40456i	0.435363	+	0.316310i
$885$	−2.47214	−	7.60845i	−0.0830999	−	0.255755i
$886$	−1.23607	−	3.80423i	−0.0415265	−	0.127805i
$887$	−22.6525	−	16.4580i	−0.760596	−	0.552605i	0.138497	−	0.990363i	$-0.455773\pi$
$887$	−22.6525	−	16.4580i	−0.760596	−	0.552605i	−0.899093	+	0.437758i	$0.855773\pi$
$888$	29.1246	−	21.1603i	0.977358	−	0.710092i
$889$	−2.47214	+	7.60845i	−0.0829128	+	0.255179i
$890$	−12.0000			−0.402241
$891$		0			0
$892$	−22.0000			−0.736614
$893$		0			0
$894$	16.1803	−	11.7557i	0.541152	−	0.393170i
$895$	19.4164	+	14.1068i	0.649019	+	0.471540i
$896$	0.927051	+	2.85317i	0.0309706	+	0.0953177i
$897$	9.88854	+	30.4338i	0.330169	+	1.01616i
$898$	−8.09017	−	5.87785i	−0.269972	−	0.196146i
$899$	−48.5410	+	35.2671i	−1.61893	+	1.17622i
$900$	0.309017	−	0.951057i	0.0103006	−	0.0317019i
$901$	24.0000			0.799556
$902$		0			0
$903$	−24.0000			−0.798670
$904$	16.6869	−	51.3571i	0.554999	−	1.70811i
$905$	16.1803	−	11.7557i	0.537853	−	0.390773i
$906$	25.8885	+	18.8091i	0.860089	+	0.624891i
$907$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$907$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$908$	3.70820	+	11.4127i	0.123061	+	0.378743i
$909$	−3.23607	−	2.35114i	−0.107334	−	0.0779824i
$910$	6.47214	−	4.70228i	0.214549	−	0.155879i
$911$	11.1246	−	34.2380i	0.368575	−	1.13436i	−0.579137	−	0.815230i	$-0.696610\pi$
$911$	11.1246	−	34.2380i	0.368575	−	1.13436i	0.947712	−	0.319127i	$-0.103390\pi$
$912$		0			0
$913$		0			0
$914$	18.0000			0.595387
$915$		0			0
$916$	14.5623	−	10.5801i	0.481152	−	0.349577i
$917$	9.70820	+	7.05342i	0.320593	+	0.232925i
$918$	−4.94427	−	15.2169i	−0.163185	−	0.502233i
$919$	−12.3607	−	38.0423i	−0.407741	−	1.25490i	−0.918585	−	0.395225i	$-0.870667\pi$
$919$	−12.3607	−	38.0423i	−0.407741	−	1.25490i	0.510843	−	0.859674i	$-0.329333\pi$
$920$	−19.4164	−	14.1068i	−0.640140	−	0.465089i
$921$	32.3607	−	23.5114i	1.06632	−	0.774727i
$922$		0			0
$923$	48.0000			1.57994
$924$		0			0
$925$	6.00000			0.197279
$926$	−1.23607	+	3.80423i	−0.0406197	+	0.125015i
$927$	−11.3262	+	8.22899i	−0.372002	+	0.270276i
$928$	24.2705	+	17.6336i	0.796719	+	0.578850i
$929$	1.85410	+	5.70634i	0.0608311	+	0.187219i	0.976854	−	0.213907i	$-0.0686190\pi$
$929$	1.85410	+	5.70634i	0.0608311	+	0.187219i	−0.916023	+	0.401126i	$0.868619\pi$
$930$	12.3607	+	38.0423i	0.405323	+	1.24745i
$931$		0			0
$932$	14.5623	−	10.5801i	0.477004	−	0.346564i
$933$	−11.1246	+	34.2380i	−0.364203	+	1.12090i
$934$	−30.0000			−0.981630
$935$		0			0
$936$	−12.0000			−0.392232
$937$	4.94427	−	15.2169i	0.161522	−	0.497115i	−0.837241	−	0.546834i	$-0.815833\pi$
$937$	4.94427	−	15.2169i	0.161522	−	0.497115i	0.998763	+	0.0497197i	$0.0158328\pi$
$938$	6.47214	−	4.70228i	0.211323	−	0.153535i
$939$	−3.23607	−	2.35114i	−0.105605	−	0.0767266i
$940$	−6.18034	−	19.0211i	−0.201580	−	0.620401i
$941$	7.41641	+	22.8254i	0.241768	+	0.744085i	0.996151	+	0.0876511i	$0.0279361\pi$
$941$	7.41641	+	22.8254i	0.241768	+	0.744085i	−0.754383	+	0.656434i	$0.772064\pi$
$942$	22.6525	+	16.4580i	0.738058	+	0.536230i
$943$	−12.9443	+	9.40456i	−0.421523	+	0.306255i
$944$	−0.618034	+	1.90211i	−0.0201153	+	0.0619085i
$945$	8.00000			0.260240
$946$		0			0
$947$	−36.0000			−1.16984			−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000			−1.16984			−0.584921	+	0.811090i	$0.698875\pi$
$948$	4.94427	−	15.2169i	0.160582	−	0.494222i
$949$	25.8885	−	18.8091i	0.840378	−	0.610570i
$950$		0			0
$951$	−1.23607	−	3.80423i	−0.0400823	−	0.123360i
$952$	−3.70820	−	11.4127i	−0.120184	−	0.369887i
$953$	27.5066	+	19.9847i	0.891025	+	0.647368i	0.936145	−	0.351614i	$-0.114367\pi$
$953$	27.5066	+	19.9847i	0.891025	+	0.647368i	−0.0451197	+	0.998982i	$0.514367\pi$
$954$	−4.85410	+	3.52671i	−0.157157	+	0.114182i
$955$	−4.94427	+	15.2169i	−0.159993	+	0.492407i
$956$		0			0
$957$		0			0
$958$	−4.00000			−0.129234
$959$	−3.09017	+	9.51057i	−0.0997868	+	0.307112i
$960$	22.6525	−	16.4580i	0.731106	−	0.531179i
$961$	−55.8222	−	40.5572i	−1.80072	−	1.30830i
$962$	−7.41641	−	22.8254i	−0.239115	−	0.735919i
$963$	−3.70820	−	11.4127i	−0.119495	−	0.367768i
$964$	16.1803	+	11.7557i	0.521134	+	0.378626i
$965$	22.6525	−	16.4580i	0.729209	−	0.529801i
$966$	2.47214	−	7.60845i	0.0795397	−	0.244798i
$967$	−40.0000			−1.28631			−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000			−1.28631			−0.643157	+	0.765735i	$0.722376\pi$
$968$		0			0
$969$		0			0
$970$	−6.18034	+	19.0211i	−0.198439	+	0.610732i
$971$	−11.3262	+	8.22899i	−0.363476	+	0.264081i	−0.754501	−	0.656299i	$-0.772121\pi$
$971$	−11.3262	+	8.22899i	−0.363476	+	0.264081i	0.391024	+	0.920380i	$0.372121\pi$
$972$	−8.09017	−	5.87785i	−0.259492	−	0.188532i
$973$	2.47214	+	7.60845i	0.0792530	+	0.243916i
$974$	8.65248	+	26.6296i	0.277243	+	0.853267i
$975$	−6.47214	−	4.70228i	−0.207274	−	0.150594i
$976$		0			0
$977$	12.9787	−	39.9444i	0.415226	−	1.27793i	−0.496823	−	0.867852i	$-0.665500\pi$
$977$	12.9787	−	39.9444i	0.415226	−	1.27793i	0.912049	−	0.410082i	$-0.134500\pi$
$978$	16.0000			0.511624
$979$		0			0
$980$	2.00000			0.0638877
$981$	4.32624	−	13.3148i	0.138126	−	0.425109i
$982$	−22.6525	+	16.4580i	−0.722870	+	0.525195i
$983$	−43.6869	−	31.7404i	−1.39340	−	1.01236i	−0.995483	−	0.0949386i	$-0.969735\pi$
$983$	−43.6869	−	31.7404i	−1.39340	−	1.01236i	−0.397913	−	0.917423i	$-0.630265\pi$
$984$	−7.41641	−	22.8254i	−0.236426	−	0.727646i
$985$	13.5967	+	41.8465i	0.433228	+	1.33334i
$986$	−19.4164	−	14.1068i	−0.618344	−	0.449254i
$987$	16.1803	−	11.7557i	0.515026	−	0.374188i
$988$		0			0
$989$	48.0000			1.52631
$990$		0			0
$991$	52.0000			1.65183			0.825917	−	0.563791i	$-0.190658\pi$
$991$	52.0000			1.65183			0.825917	+	0.563791i	$0.190658\pi$
$992$	−15.4508	+	47.5528i	−0.490565	+	1.50980i
$993$	32.3607	−	23.5114i	1.02694	−	0.746112i
$994$	−9.70820	−	7.05342i	−0.307926	−	0.223721i
$995$	11.1246	+	34.2380i	0.352674	+	1.08542i
$996$		0			0
$997$	16.1803	+	11.7557i	0.512437	+	0.372307i	0.813747	−	0.581219i	$-0.197424\pi$
$997$	16.1803	+	11.7557i	0.512437	+	0.372307i	−0.301311	+	0.953526i	$0.597424\pi$
$998$	−12.9443	+	9.40456i	−0.409744	+	0.297696i
$999$	7.41641	−	22.8254i	0.234645	−	0.722162i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.k.372.1		4
11.2	odd	10		847.2.f.e.729.1		4
11.3	even	5	inner	847.2.f.k.323.1		4
11.4	even	5		847.2.a.a.1.1		1
11.5	even	5	inner	847.2.f.k.148.1		4
11.6	odd	10		847.2.f.e.148.1		4
11.7	odd	10		77.2.a.c.1.1	✓	1
11.8	odd	10		847.2.f.e.323.1		4
11.9	even	5	inner	847.2.f.k.729.1		4
11.10	odd	2		847.2.f.e.372.1		4
33.26	odd	10		7623.2.a.n.1.1		1
33.29	even	10		693.2.a.a.1.1		1
44.7	even	10		1232.2.a.a.1.1		1
55.7	even	20		1925.2.b.d.1849.2		2
55.18	even	20		1925.2.b.d.1849.1		2
55.29	odd	10		1925.2.a.c.1.1		1
77.18	odd	30		539.2.e.a.177.1		2
77.40	even	30		539.2.e.b.67.1		2
77.48	odd	10		5929.2.a.b.1.1		1
77.51	odd	30		539.2.e.a.67.1		2
77.62	even	10		539.2.a.d.1.1		1
77.73	even	30		539.2.e.b.177.1		2
88.29	odd	10		4928.2.a.g.1.1		1
88.51	even	10		4928.2.a.bi.1.1		1
231.62	odd	10		4851.2.a.a.1.1		1
308.139	odd	10		8624.2.a.bc.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.a.c.1.1	✓	1	11.7	odd	10
539.2.a.d.1.1		1	77.62	even	10
539.2.e.a.67.1		2	77.51	odd	30
539.2.e.a.177.1		2	77.18	odd	30
539.2.e.b.67.1		2	77.40	even	30
539.2.e.b.177.1		2	77.73	even	30
693.2.a.a.1.1		1	33.29	even	10
847.2.a.a.1.1		1	11.4	even	5
847.2.f.e.148.1		4	11.6	odd	10
847.2.f.e.323.1		4	11.8	odd	10
847.2.f.e.372.1		4	11.10	odd	2
847.2.f.e.729.1		4	11.2	odd	10
847.2.f.k.148.1		4	11.5	even	5	inner
847.2.f.k.323.1		4	11.3	even	5	inner
847.2.f.k.372.1		4	1.1	even	1	trivial
847.2.f.k.729.1		4	11.9	even	5	inner
1232.2.a.a.1.1		1	44.7	even	10
1925.2.a.c.1.1		1	55.29	odd	10
1925.2.b.d.1849.1		2	55.18	even	20
1925.2.b.d.1849.2		2	55.7	even	20
4851.2.a.a.1.1		1	231.62	odd	10
4928.2.a.g.1.1		1	88.29	odd	10
4928.2.a.bi.1.1		1	88.51	even	10
5929.2.a.b.1.1		1	77.48	odd	10
7623.2.a.n.1.1		1	33.26	odd	10
8624.2.a.bc.1.1		1	308.139	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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-1.61803 + 1.17557i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.618034 - 1.90211i) q^{5} +(-0.618034 - 1.90211i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-2.42705 + 1.76336i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-1.61803 + 1.17557i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.618034 - 1.90211i) q^{5} +(-0.618034 - 1.90211i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-2.42705 + 1.76336i) q^{8} +(0.309017 - 0.951057i) q^{9} +2.00000 q^{10} -2.00000 q^{12} +(-1.23607 + 3.80423i) q^{13} +(0.809017 - 0.587785i) q^{14} +(3.23607 + 2.35114i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-1.23607 - 3.80423i) q^{17} +(0.809017 + 0.587785i) q^{18} +(0.618034 - 1.90211i) q^{20} +2.00000 q^{21} -4.00000 q^{23} +(1.85410 - 5.70634i) q^{24} +(0.809017 - 0.587785i) q^{25} +(-3.23607 - 2.35114i) q^{26} +(-1.23607 - 3.80423i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(-4.85410 - 3.52671i) q^{29} +(-3.23607 + 2.35114i) q^{30} +(3.09017 - 9.51057i) q^{31} -5.00000 q^{32} +4.00000 q^{34} +(-0.618034 + 1.90211i) q^{35} +(0.809017 - 0.587785i) q^{36} +(4.85410 + 3.52671i) q^{37} +(-2.47214 - 7.60845i) q^{39} +(4.85410 + 3.52671i) q^{40} +(3.23607 - 2.35114i) q^{41} +(-0.618034 + 1.90211i) q^{42} -12.0000 q^{43} -2.00000 q^{45} +(1.23607 - 3.80423i) q^{46} +(8.09017 - 5.87785i) q^{47} +(1.61803 + 1.17557i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.309017 + 0.951057i) q^{50} +(6.47214 + 4.70228i) q^{51} +(-3.23607 + 2.35114i) q^{52} +(-1.85410 + 5.70634i) q^{53} +4.00000 q^{54} +3.00000 q^{56} +(4.85410 - 3.52671i) q^{58} +(-1.61803 - 1.17557i) q^{59} +(1.23607 + 3.80423i) q^{60} +(8.09017 + 5.87785i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(2.16312 - 6.65740i) q^{64} +8.00000 q^{65} +8.00000 q^{67} +(1.23607 - 3.80423i) q^{68} +(6.47214 - 4.70228i) q^{69} +(-1.61803 - 1.17557i) q^{70} +(-3.70820 - 11.4127i) q^{71} +(0.927051 + 2.85317i) q^{72} +(-6.47214 - 4.70228i) q^{73} +(-4.85410 + 3.52671i) q^{74} +(-0.618034 + 1.90211i) q^{75} +8.00000 q^{78} +(-2.47214 + 7.60845i) q^{79} +(-1.61803 + 1.17557i) q^{80} +(8.89919 + 6.46564i) q^{81} +(1.23607 + 3.80423i) q^{82} +(1.61803 + 1.17557i) q^{84} +(-6.47214 + 4.70228i) q^{85} +(3.70820 - 11.4127i) q^{86} +12.0000 q^{87} -6.00000 q^{89} +(0.618034 - 1.90211i) q^{90} +(3.23607 - 2.35114i) q^{91} +(-3.23607 - 2.35114i) q^{92} +(6.18034 + 19.0211i) q^{93} +(3.09017 + 9.51057i) q^{94} +(8.09017 - 5.87785i) q^{96} +(-3.09017 + 9.51057i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 2 q^{3} + q^{4} + 2 q^{5} + 2 q^{6} - q^{7} - 3 q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 - 2 * q^3 + q^4 + 2 * q^5 + 2 * q^6 - q^7 - 3 * q^8 - q^9	\( 4 q + q^{2} - 2 q^{3} + q^{4} + 2 q^{5} + 2 q^{6} - q^{7} - 3 q^{8} - q^{9} + 8 q^{10} - 8 q^{12} + 4 q^{13} + q^{14} + 4 q^{15} + q^{16} + 4 q^{17} + q^{18} - 2 q^{20} + 8 q^{21} - 16 q^{23} - 6 q^{24} + q^{25} - 4 q^{26} + 4 q^{27} + q^{28} - 6 q^{29} - 4 q^{30} - 10 q^{31} - 20 q^{32} + 16 q^{34} + 2 q^{35} + q^{36} + 6 q^{37} + 8 q^{39} + 6 q^{40} + 4 q^{41} + 2 q^{42} - 48 q^{43} - 8 q^{45} - 4 q^{46} + 10 q^{47} + 2 q^{48} - q^{49} - q^{50} + 8 q^{51} - 4 q^{52} + 6 q^{53} + 16 q^{54} + 12 q^{56} + 6 q^{58} - 2 q^{59} - 4 q^{60} + 10 q^{62} - q^{63} - 7 q^{64} + 32 q^{65} + 32 q^{67} - 4 q^{68} + 8 q^{69} - 2 q^{70} + 12 q^{71} - 3 q^{72} - 8 q^{73} - 6 q^{74} + 2 q^{75} + 32 q^{78} + 8 q^{79} - 2 q^{80} + 11 q^{81} - 4 q^{82} + 2 q^{84} - 8 q^{85} - 12 q^{86} + 48 q^{87} - 24 q^{89} - 2 q^{90} + 4 q^{91} - 4 q^{92} - 20 q^{93} - 10 q^{94} + 10 q^{96} + 10 q^{97} - 4 q^{98}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 + q^4 + 2 * q^5 + 2 * q^6 - q^7 - 3 * q^8 - q^9 + 8 * q^10 - 8 * q^12 + 4 * q^13 + q^14 + 4 * q^15 + q^16 + 4 * q^17 + q^18 - 2 * q^20 + 8 * q^21 - 16 * q^23 - 6 * q^24 + q^25 - 4 * q^26 + 4 * q^27 + q^28 - 6 * q^29 - 4 * q^30 - 10 * q^31 - 20 * q^32 + 16 * q^34 + 2 * q^35 + q^36 + 6 * q^37 + 8 * q^39 + 6 * q^40 + 4 * q^41 + 2 * q^42 - 48 * q^43 - 8 * q^45 - 4 * q^46 + 10 * q^47 + 2 * q^48 - q^49 - q^50 + 8 * q^51 - 4 * q^52 + 6 * q^53 + 16 * q^54 + 12 * q^56 + 6 * q^58 - 2 * q^59 - 4 * q^60 + 10 * q^62 - q^63 - 7 * q^64 + 32 * q^65 + 32 * q^67 - 4 * q^68 + 8 * q^69 - 2 * q^70 + 12 * q^71 - 3 * q^72 - 8 * q^73 - 6 * q^74 + 2 * q^75 + 32 * q^78 + 8 * q^79 - 2 * q^80 + 11 * q^81 - 4 * q^82 + 2 * q^84 - 8 * q^85 - 12 * q^86 + 48 * q^87 - 24 * q^89 - 2 * q^90 + 4 * q^91 - 4 * q^92 - 20 * q^93 - 10 * q^94 + 10 * q^96 + 10 * q^97 - 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more