LMFDB - Embedded newform 847.2.f.a.323.1

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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			323.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	847.323
Dual form			847.2.f.a.729.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80902 - 1.31433i) q^{2} +(-0.381966 + 1.17557i) q^{3} +(0.927051 + 2.85317i) q^{4} +(1.61803 - 1.17557i) q^{5} +(2.23607 - 1.62460i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.690983 - 2.12663i) q^{8} +(1.19098 + 0.865300i) q^{9} +O(q^{10})$	\(q+(-1.80902 - 1.31433i) q^{2} +(-0.381966 + 1.17557i) q^{3} +(0.927051 + 2.85317i) q^{4} +(1.61803 - 1.17557i) q^{5} +(2.23607 - 1.62460i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.690983 - 2.12663i) q^{8} +(1.19098 + 0.865300i) q^{9} -4.47214 q^{10} -3.70820 q^{12} +(-2.61803 - 1.90211i) q^{13} +(0.690983 - 2.12663i) q^{14} +(0.763932 + 2.35114i) q^{15} +(0.809017 - 0.587785i) q^{16} +(2.61803 - 1.90211i) q^{17} +(-1.01722 - 3.13068i) q^{18} +(2.00000 - 6.15537i) q^{19} +(4.85410 + 3.52671i) q^{20} -1.23607 q^{21} +2.47214 q^{23} +(2.23607 + 1.62460i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(2.23607 + 6.88191i) q^{26} +(-4.47214 + 3.24920i) q^{27} +(-2.42705 + 1.76336i) q^{28} +(2.61803 + 8.05748i) q^{29} +(1.70820 - 5.25731i) q^{30} +(2.23607 + 1.62460i) q^{31} -6.70820 q^{32} -7.23607 q^{34} +(1.61803 + 1.17557i) q^{35} +(-1.36475 + 4.20025i) q^{36} +(-2.61803 - 8.05748i) q^{37} +(-11.7082 + 8.50651i) q^{38} +(3.23607 - 2.35114i) q^{39} +(-1.38197 - 4.25325i) q^{40} +(-3.47214 + 10.6861i) q^{41} +(2.23607 + 1.62460i) q^{42} +8.00000 q^{43} +2.94427 q^{45} +(-4.47214 - 3.24920i) q^{46} +(0.854102 - 2.62866i) q^{47} +(0.381966 + 1.17557i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(1.80902 - 1.31433i) q^{50} +(1.23607 + 3.80423i) q^{51} +(3.00000 - 9.23305i) q^{52} +(0.381966 + 0.277515i) q^{53} +12.3607 q^{54} +2.23607 q^{56} +(6.47214 + 4.70228i) q^{57} +(5.85410 - 18.0171i) q^{58} +(-0.381966 - 1.17557i) q^{59} +(-6.00000 + 4.35926i) q^{60} +(5.85410 - 4.25325i) q^{61} +(-1.90983 - 5.87785i) q^{62} +(-0.454915 + 1.40008i) q^{63} +(10.5172 + 7.64121i) q^{64} -6.47214 q^{65} +14.4721 q^{67} +(7.85410 + 5.70634i) q^{68} +(-0.944272 + 2.90617i) q^{69} +(-1.38197 - 4.25325i) q^{70} +(8.47214 - 6.15537i) q^{71} +(2.66312 - 1.93487i) q^{72} +(-0.236068 - 0.726543i) q^{73} +(-5.85410 + 18.0171i) q^{74} +(-1.00000 - 0.726543i) q^{75} +19.4164 q^{76} -8.94427 q^{78} +(7.23607 + 5.25731i) q^{79} +(0.618034 - 1.90211i) q^{80} +(-0.746711 - 2.29814i) q^{81} +(20.3262 - 14.7679i) q^{82} +(9.23607 - 6.71040i) q^{83} +(-1.14590 - 3.52671i) q^{84} +(2.00000 - 6.15537i) q^{85} +(-14.4721 - 10.5146i) q^{86} -10.4721 q^{87} +2.00000 q^{89} +(-5.32624 - 3.86974i) q^{90} +(1.00000 - 3.07768i) q^{91} +(2.29180 + 7.05342i) q^{92} +(-2.76393 + 2.00811i) q^{93} +(-5.00000 + 3.63271i) q^{94} +(-4.00000 - 12.3107i) q^{95} +(2.56231 - 7.88597i) q^{96} +(-14.0902 - 10.2371i) q^{97} +2.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{2} - 6 q^{3} - 3 q^{4} + 2 q^{5} - q^{7} + 5 q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q - 5 * q^2 - 6 * q^3 - 3 * q^4 + 2 * q^5 - q^7 + 5 * q^8 + 7 * q^9	$ 4 q - 5 q^{2} - 6 q^{3} - 3 q^{4} + 2 q^{5} - q^{7} + 5 q^{8} + 7 q^{9} + 12 q^{12} - 6 q^{13} + 5 q^{14} + 12 q^{15} + q^{16} + 6 q^{17} + 25 q^{18} + 8 q^{19} + 6 q^{20} + 4 q^{21} - 8 q^{23} + q^{25} - 3 q^{28} + 6 q^{29} - 20 q^{30} - 20 q^{34} + 2 q^{35} - 39 q^{36} - 6 q^{37} - 20 q^{38} + 4 q^{39} - 10 q^{40} + 4 q^{41} + 32 q^{43} - 24 q^{45} - 10 q^{47} + 6 q^{48} - q^{49} + 5 q^{50} - 4 q^{51} + 12 q^{52} + 6 q^{53} - 40 q^{54} + 8 q^{57} + 10 q^{58} - 6 q^{59} - 24 q^{60} + 10 q^{61} - 30 q^{62} - 13 q^{63} + 13 q^{64} - 8 q^{65} + 40 q^{67} + 18 q^{68} + 32 q^{69} - 10 q^{70} + 16 q^{71} - 5 q^{72} + 8 q^{73} - 10 q^{74} - 4 q^{75} + 24 q^{76} + 20 q^{79} - 2 q^{80} - 41 q^{81} + 50 q^{82} + 28 q^{83} - 18 q^{84} + 8 q^{85} - 40 q^{86} - 24 q^{87} + 8 q^{89} + 10 q^{90} + 4 q^{91} + 36 q^{92} - 20 q^{93} - 20 q^{94} - 16 q^{95} - 30 q^{96} - 34 q^{97}+O(q^{100}) $ 4 * q - 5 * q^2 - 6 * q^3 - 3 * q^4 + 2 * q^5 - q^7 + 5 * q^8 + 7 * q^9 + 12 * q^12 - 6 * q^13 + 5 * q^14 + 12 * q^15 + q^16 + 6 * q^17 + 25 * q^18 + 8 * q^19 + 6 * q^20 + 4 * q^21 - 8 * q^23 + q^25 - 3 * q^28 + 6 * q^29 - 20 * q^30 - 20 * q^34 + 2 * q^35 - 39 * q^36 - 6 * q^37 - 20 * q^38 + 4 * q^39 - 10 * q^40 + 4 * q^41 + 32 * q^43 - 24 * q^45 - 10 * q^47 + 6 * q^48 - q^49 + 5 * q^50 - 4 * q^51 + 12 * q^52 + 6 * q^53 - 40 * q^54 + 8 * q^57 + 10 * q^58 - 6 * q^59 - 24 * q^60 + 10 * q^61 - 30 * q^62 - 13 * q^63 + 13 * q^64 - 8 * q^65 + 40 * q^67 + 18 * q^68 + 32 * q^69 - 10 * q^70 + 16 * q^71 - 5 * q^72 + 8 * q^73 - 10 * q^74 - 4 * q^75 + 24 * q^76 + 20 * q^79 - 2 * q^80 - 41 * q^81 + 50 * q^82 + 28 * q^83 - 18 * q^84 + 8 * q^85 - 40 * q^86 - 24 * q^87 + 8 * q^89 + 10 * q^90 + 4 * q^91 + 36 * q^92 - 20 * q^93 - 20 * q^94 - 16 * q^95 - 30 * q^96 - 34 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.80902	−	1.31433i	−1.27917	−	0.929370i	−0.279641	−	0.960105i	$-0.590215\pi$
$2$	−1.80902	−	1.31433i	−1.27917	−	0.929370i	−0.999528	+	0.0307347i	$0.990215\pi$
$3$	−0.381966	+	1.17557i	−0.220528	+	0.678716i	0.778187	+	0.628033i	$0.216140\pi$
$3$	−0.381966	+	1.17557i	−0.220528	+	0.678716i	−0.998715	+	0.0506828i	$0.983860\pi$
$4$	0.927051	+	2.85317i	0.463525	+	1.42658i
$5$	1.61803	−	1.17557i	0.723607	−	0.525731i	−0.163928	−	0.986472i	$-0.552416\pi$
$5$	1.61803	−	1.17557i	0.723607	−	0.525731i	0.887535	+	0.460741i	$0.152416\pi$
$6$	2.23607	−	1.62460i	0.912871	−	0.663240i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	0.690983	−	2.12663i	0.244299	−	0.751876i
$9$	1.19098	+	0.865300i	0.396994	+	0.288433i
$10$	−4.47214			−1.41421
$11$		0			0
$11$		0			0
$12$	−3.70820			−1.07047
$13$	−2.61803	−	1.90211i	−0.726112	−	0.527551i	0.162219	−	0.986755i	$-0.448135\pi$
$13$	−2.61803	−	1.90211i	−0.726112	−	0.527551i	−0.888331	+	0.459204i	$0.848135\pi$
$14$	0.690983	−	2.12663i	0.184673	−	0.568365i
$15$	0.763932	+	2.35114i	0.197246	+	0.607062i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	2.61803	−	1.90211i	0.634967	−	0.461330i	−0.223151	−	0.974784i	$-0.571634\pi$
$17$	2.61803	−	1.90211i	0.634967	−	0.461330i	0.858117	+	0.513454i	$0.171634\pi$
$18$	−1.01722	−	3.13068i	−0.239761	−	0.737909i
$19$	2.00000	−	6.15537i	0.458831	−	1.41214i	−0.407746	−	0.913095i	$-0.633685\pi$
$19$	2.00000	−	6.15537i	0.458831	−	1.41214i	0.866577	−	0.499043i	$-0.166315\pi$
$20$	4.85410	+	3.52671i	1.08541	+	0.788597i
$21$	−1.23607			−0.269732
$22$		0			0
$23$	2.47214			0.515476			0.257738	−	0.966215i	$-0.417023\pi$
$23$	2.47214			0.515476			0.257738	+	0.966215i	$0.417023\pi$
$24$	2.23607	+	1.62460i	0.456435	+	0.331620i
$25$	−0.309017	+	0.951057i	−0.0618034	+	0.190211i
$26$	2.23607	+	6.88191i	0.438529	+	1.34965i
$27$	−4.47214	+	3.24920i	−0.860663	+	0.625308i
$28$	−2.42705	+	1.76336i	−0.458670	+	0.333243i
$29$	2.61803	+	8.05748i	0.486157	+	1.49624i	0.830299	+	0.557319i	$0.188170\pi$
$29$	2.61803	+	8.05748i	0.486157	+	1.49624i	−0.344142	+	0.938918i	$0.611830\pi$
$30$	1.70820	−	5.25731i	0.311874	−	0.959849i
$31$	2.23607	+	1.62460i	0.401610	+	0.291787i	0.770196	−	0.637807i	$-0.220158\pi$
$31$	2.23607	+	1.62460i	0.401610	+	0.291787i	−0.368587	+	0.929593i	$0.620158\pi$
$32$	−6.70820			−1.18585
$33$		0			0
$34$	−7.23607			−1.24098
$35$	1.61803	+	1.17557i	0.273498	+	0.198708i
$36$	−1.36475	+	4.20025i	−0.227458	+	0.700042i
$37$	−2.61803	−	8.05748i	−0.430402	−	1.32464i	−0.897726	−	0.440555i	$-0.854782\pi$
$37$	−2.61803	−	8.05748i	−0.430402	−	1.32464i	0.467323	−	0.884086i	$-0.345218\pi$
$38$	−11.7082	+	8.50651i	−1.89932	+	1.37994i
$39$	3.23607	−	2.35114i	0.518186	−	0.376484i
$40$	−1.38197	−	4.25325i	−0.218508	−	0.672499i
$41$	−3.47214	+	10.6861i	−0.542257	+	1.66889i	0.185168	+	0.982707i	$0.440717\pi$
$41$	−3.47214	+	10.6861i	−0.542257	+	1.66889i	−0.727425	+	0.686187i	$0.759283\pi$
$42$	2.23607	+	1.62460i	0.345033	+	0.250681i
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$	2.94427			0.438906
$46$	−4.47214	−	3.24920i	−0.659380	−	0.479068i
$47$	0.854102	−	2.62866i	0.124584	−	0.383429i	−0.869241	−	0.494388i	$-0.835392\pi$
$47$	0.854102	−	2.62866i	0.124584	−	0.383429i	0.993825	+	0.110959i	$0.0353922\pi$
$48$	0.381966	+	1.17557i	0.0551320	+	0.169679i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	1.80902	−	1.31433i	0.255834	−	0.185874i
$51$	1.23607	+	3.80423i	0.173084	+	0.532698i
$52$	3.00000	−	9.23305i	0.416025	−	1.28039i
$53$	0.381966	+	0.277515i	0.0524671	+	0.0381196i	0.613710	−	0.789532i	$-0.289677\pi$
$53$	0.381966	+	0.277515i	0.0524671	+	0.0381196i	−0.561243	+	0.827651i	$0.689677\pi$
$54$	12.3607			1.68208
$55$		0			0
$56$	2.23607			0.298807
$57$	6.47214	+	4.70228i	0.857255	+	0.622832i
$58$	5.85410	−	18.0171i	0.768681	−	2.36576i
$59$	−0.381966	−	1.17557i	−0.0497277	−	0.153046i	0.923109	−	0.384538i	$-0.125639\pi$
$59$	−0.381966	−	1.17557i	−0.0497277	−	0.153046i	−0.972837	+	0.231492i	$0.925639\pi$
$60$	−6.00000	+	4.35926i	−0.774597	+	0.562777i
$61$	5.85410	−	4.25325i	0.749541	−	0.544573i	−0.146144	−	0.989263i	$-0.546686\pi$
$61$	5.85410	−	4.25325i	0.749541	−	0.544573i	0.895685	+	0.444690i	$0.146686\pi$
$62$	−1.90983	−	5.87785i	−0.242549	−	0.746488i
$63$	−0.454915	+	1.40008i	−0.0573139	+	0.176394i
$64$	10.5172	+	7.64121i	1.31465	+	0.955151i
$65$	−6.47214			−0.802770
$66$		0			0
$67$	14.4721			1.76805			0.884026	−	0.467437i	$-0.154823\pi$
$67$	14.4721			1.76805			0.884026	+	0.467437i	$0.154823\pi$
$68$	7.85410	+	5.70634i	0.952450	+	0.691995i
$69$	−0.944272	+	2.90617i	−0.113677	+	0.349862i
$70$	−1.38197	−	4.25325i	−0.165177	−	0.508361i
$71$	8.47214	−	6.15537i	1.00546	−	0.730508i	0.0422061	−	0.999109i	$-0.486561\pi$
$71$	8.47214	−	6.15537i	1.00546	−	0.730508i	0.963251	+	0.268601i	$0.0865614\pi$
$72$	2.66312	−	1.93487i	0.313852	−	0.228027i
$73$	−0.236068	−	0.726543i	−0.0276297	−	0.0850354i	0.936291	−	0.351226i	$-0.114235\pi$
$73$	−0.236068	−	0.726543i	−0.0276297	−	0.0850354i	−0.963920	+	0.266190i	$0.914235\pi$
$74$	−5.85410	+	18.0171i	−0.680526	+	2.09444i
$75$	−1.00000	−	0.726543i	−0.115470	−	0.0838939i
$76$	19.4164			2.22721
$77$		0			0
$78$	−8.94427			−1.01274
$79$	7.23607	+	5.25731i	0.814121	+	0.591494i	0.915023	−	0.403403i	$-0.132173\pi$
$79$	7.23607	+	5.25731i	0.814121	+	0.591494i	−0.100901	+	0.994896i	$0.532173\pi$
$80$	0.618034	−	1.90211i	0.0690983	−	0.212663i
$81$	−0.746711	−	2.29814i	−0.0829679	−	0.255349i
$82$	20.3262	−	14.7679i	2.24466	−	1.63084i
$83$	9.23607	−	6.71040i	1.01379	−	0.736562i	0.0487895	−	0.998809i	$-0.484464\pi$
$83$	9.23607	−	6.71040i	1.01379	−	0.736562i	0.965001	+	0.262247i	$0.0844637\pi$
$84$	−1.14590	−	3.52671i	−0.125028	−	0.384796i
$85$	2.00000	−	6.15537i	0.216930	−	0.667643i
$86$	−14.4721	−	10.5146i	−1.56057	−	1.13382i
$87$	−10.4721			−1.12273
$88$		0			0
$89$	2.00000			0.212000			0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000			0.212000			0.106000	+	0.994366i	$0.466196\pi$
$90$	−5.32624	−	3.86974i	−0.561435	−	0.407906i
$91$	1.00000	−	3.07768i	0.104828	−	0.322629i
$92$	2.29180	+	7.05342i	0.238936	+	0.735370i
$93$	−2.76393	+	2.00811i	−0.286606	+	0.208232i
$94$	−5.00000	+	3.63271i	−0.515711	+	0.374686i
$95$	−4.00000	−	12.3107i	−0.410391	−	1.26305i
$96$	2.56231	−	7.88597i	0.261514	−	0.804858i
$97$	−14.0902	−	10.2371i	−1.43064	−	1.03942i	−0.989897	−	0.141787i	$-0.954715\pi$
$97$	−14.0902	−	10.2371i	−1.43064	−	1.03942i	−0.440743	−	0.897633i	$-0.645285\pi$
$98$	2.23607			0.225877
$99$		0			0
$100$	−3.00000			−0.300000
$101$	3.85410	+	2.80017i	0.383497	+	0.278627i	0.762786	−	0.646651i	$-0.223831\pi$
$101$	3.85410	+	2.80017i	0.383497	+	0.278627i	−0.379288	+	0.925279i	$0.623831\pi$
$102$	2.76393	−	8.50651i	0.273670	−	0.842270i
$103$	2.38197	+	7.33094i	0.234702	+	0.722339i	0.997161	+	0.0753019i	$0.0239920\pi$
$103$	2.38197	+	7.33094i	0.234702	+	0.722339i	−0.762459	+	0.647037i	$0.776008\pi$
$104$	−5.85410	+	4.25325i	−0.574042	+	0.417066i
$105$	−2.00000	+	1.45309i	−0.195180	+	0.141807i
$106$	−0.326238	−	1.00406i	−0.0316870	−	0.0975226i
$107$	−1.23607	+	3.80423i	−0.119495	+	0.367768i	−0.992858	−	0.119302i	$-0.961934\pi$
$107$	−1.23607	+	3.80423i	−0.119495	+	0.367768i	0.873363	+	0.487070i	$0.161934\pi$
$108$	−13.4164	−	9.74759i	−1.29099	−	0.937962i
$109$	−4.47214			−0.428353			−0.214176	−	0.976795i	$-0.568707\pi$
$109$	−4.47214			−0.428353			−0.214176	+	0.976795i	$0.568707\pi$
$110$		0			0
$111$	10.4721			0.993971
$112$	0.809017	+	0.587785i	0.0764449	+	0.0555405i
$113$	0.618034	−	1.90211i	0.0581397	−	0.178936i	−0.917769	−	0.397114i	$-0.870012\pi$
$113$	0.618034	−	1.90211i	0.0581397	−	0.178936i	0.975909	+	0.218179i	$0.0700116\pi$
$114$	−5.52786	−	17.0130i	−0.517732	−	1.59341i
$115$	4.00000	−	2.90617i	0.373002	−	0.271002i
$116$	−20.5623	+	14.9394i	−1.90916	+	1.38709i
$117$	−1.47214	−	4.53077i	−0.136099	−	0.418870i
$118$	−0.854102	+	2.62866i	−0.0786265	+	0.241987i
$119$	2.61803	+	1.90211i	0.239995	+	0.174366i
$120$	5.52786			0.504623
$121$		0			0
$122$	−16.1803			−1.46490
$123$	−11.2361	−	8.16348i	−1.01312	−	0.736076i
$124$	−2.56231	+	7.88597i	−0.230102	+	0.708181i
$125$	3.70820	+	11.4127i	0.331672	+	1.02078i
$126$	2.66312	−	1.93487i	0.237249	−	0.172372i
$127$	−2.47214	+	1.79611i	−0.219367	+	0.159379i	−0.692041	−	0.721858i	$-0.743288\pi$
$127$	−2.47214	+	1.79611i	−0.219367	+	0.159379i	0.472675	+	0.881237i	$0.343288\pi$
$128$	−4.83688	−	14.8864i	−0.427524	−	1.31578i
$129$	−3.05573	+	9.40456i	−0.269042	+	0.828026i
$130$	11.7082	+	8.50651i	1.02688	+	0.746070i
$131$	21.8885			1.91241			0.956205	−	0.292696i	$-0.0945525\pi$
$131$	21.8885			1.91241			0.956205	+	0.292696i	$0.0945525\pi$
$132$		0			0
$133$	6.47214			0.561205
$134$	−26.1803	−	19.0211i	−2.26164	−	1.64318i
$135$	−3.41641	+	10.5146i	−0.294038	+	0.904955i
$136$	−2.23607	−	6.88191i	−0.191741	−	0.590119i
$137$	−13.3262	+	9.68208i	−1.13854	+	0.827196i	−0.986915	−	0.161243i	$-0.948450\pi$
$137$	−13.3262	+	9.68208i	−1.13854	+	0.827196i	−0.151623	+	0.988438i	$0.548450\pi$
$138$	5.52786	−	4.01623i	0.470563	−	0.341884i
$139$	−0.472136	−	1.45309i	−0.0400460	−	0.123249i	0.929035	−	0.369992i	$-0.120640\pi$
$139$	−0.472136	−	1.45309i	−0.0400460	−	0.123249i	−0.969081	+	0.246743i	$0.920640\pi$
$140$	−1.85410	+	5.70634i	−0.156700	+	0.482274i
$141$	2.76393	+	2.00811i	0.232765	+	0.169114i
$142$	−23.4164			−1.96506
$143$		0			0
$144$	1.47214			0.122678
$145$	13.7082	+	9.95959i	1.13840	+	0.827099i
$146$	−0.527864	+	1.62460i	−0.0436863	+	0.134453i
$147$	−0.381966	−	1.17557i	−0.0315040	−	0.0969594i
$148$	20.5623	−	14.9394i	1.69021	−	1.22801i
$149$	−11.3262	+	8.22899i	−0.927882	+	0.674145i	−0.945473	−	0.325700i	$-0.894400\pi$
$149$	−11.3262	+	8.22899i	−0.927882	+	0.674145i	0.0175917	+	0.999845i	$0.494400\pi$
$150$	0.854102	+	2.62866i	0.0697371	+	0.214629i
$151$	2.76393	−	8.50651i	0.224926	−	0.692250i	−0.773374	−	0.633951i	$-0.781432\pi$
$151$	2.76393	−	8.50651i	0.224926	−	0.692250i	0.998299	−	0.0582992i	$-0.0185677\pi$
$152$	−11.7082	−	8.50651i	−0.949661	−	0.689969i
$153$	4.76393			0.385141
$154$		0			0
$155$	5.52786			0.444009
$156$	9.70820	+	7.05342i	0.777278	+	0.564726i
$157$	3.38197	−	10.4086i	0.269910	−	0.830698i	−0.720611	−	0.693340i	$-0.756139\pi$
$157$	3.38197	−	10.4086i	0.269910	−	0.830698i	0.990521	−	0.137359i	$-0.0438614\pi$
$158$	−6.18034	−	19.0211i	−0.491681	−	1.51324i
$159$	−0.472136	+	0.343027i	−0.0374428	+	0.0272038i
$160$	−10.8541	+	7.88597i	−0.858092	+	0.623440i
$161$	0.763932	+	2.35114i	0.0602063	+	0.185296i
$162$	−1.66970	+	5.13880i	−0.131184	+	0.403742i
$163$	2.76393	+	2.00811i	0.216488	+	0.157288i	0.690744	−	0.723099i	$-0.257283\pi$
$163$	2.76393	+	2.00811i	0.216488	+	0.157288i	−0.474256	+	0.880387i	$0.657283\pi$
$164$	−33.7082			−2.63217
$165$		0			0
$166$	−25.5279			−1.98135
$167$	−4.00000	−	2.90617i	−0.309529	−	0.224886i	0.422165	−	0.906519i	$-0.361270\pi$
$167$	−4.00000	−	2.90617i	−0.309529	−	0.224886i	−0.731694	+	0.681633i	$0.761270\pi$
$168$	−0.854102	+	2.62866i	−0.0658954	+	0.202805i
$169$	−0.781153	−	2.40414i	−0.0600887	−	0.184934i
$170$	−11.7082	+	8.50651i	−0.897978	+	0.652419i
$171$	7.70820	−	5.60034i	0.589461	−	0.428269i
$172$	7.41641	+	22.8254i	0.565496	+	1.74042i
$173$	−3.94427	+	12.1392i	−0.299877	+	0.922928i	0.681662	+	0.731667i	$0.261258\pi$
$173$	−3.94427	+	12.1392i	−0.299877	+	0.922928i	−0.981539	+	0.191261i	$0.938742\pi$
$174$	18.9443	+	13.7638i	1.43616	+	1.04343i
$175$	−1.00000			−0.0755929
$176$		0			0
$177$	1.52786			0.114841
$178$	−3.61803	−	2.62866i	−0.271183	−	0.197026i
$179$	−2.76393	+	8.50651i	−0.206586	+	0.635806i	0.793059	+	0.609145i	$0.208487\pi$
$179$	−2.76393	+	8.50651i	−0.206586	+	0.635806i	−0.999645	+	0.0266609i	$0.991513\pi$
$180$	2.72949	+	8.40051i	0.203444	+	0.626137i
$181$	20.5623	−	14.9394i	1.52838	−	1.11044i	0.571256	−	0.820772i	$-0.306456\pi$
$181$	20.5623	−	14.9394i	1.52838	−	1.11044i	0.957128	−	0.289664i	$-0.0935436\pi$
$182$	−5.85410	+	4.25325i	−0.433935	+	0.315272i
$183$	2.76393	+	8.50651i	0.204316	+	0.628819i
$184$	1.70820	−	5.25731i	0.125930	−	0.387574i
$185$	−13.7082	−	9.95959i	−1.00785	−	0.732244i
$186$	7.63932			0.560142
$187$		0			0
$188$	8.29180			0.604741
$189$	−4.47214	−	3.24920i	−0.325300	−	0.236344i
$190$	−8.94427	+	27.5276i	−0.648886	+	1.99706i
$191$	−0.944272	−	2.90617i	−0.0683251	−	0.210283i	0.911064	−	0.412264i	$-0.135262\pi$
$191$	−0.944272	−	2.90617i	−0.0683251	−	0.210283i	−0.979389	+	0.201981i	$0.935262\pi$
$192$	−13.0000	+	9.44505i	−0.938194	+	0.681638i
$193$	−9.61803	+	6.98791i	−0.692321	+	0.503001i	−0.877422	−	0.479719i	$-0.840739\pi$
$193$	−9.61803	+	6.98791i	−0.692321	+	0.503001i	0.185101	+	0.982719i	$0.440739\pi$
$194$	12.0344	+	37.0382i	0.864023	+	2.65919i
$195$	2.47214	−	7.60845i	0.177033	−	0.544853i
$196$	−2.42705	−	1.76336i	−0.173361	−	0.125954i
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	−2.18034			−0.154560			−0.0772801	−	0.997009i	$-0.524624\pi$
$199$	−2.18034			−0.154560			−0.0772801	+	0.997009i	$0.524624\pi$
$200$	1.80902	+	1.31433i	0.127917	+	0.0929370i
$201$	−5.52786	+	17.0130i	−0.389905	+	1.20001i
$202$	−3.29180	−	10.1311i	−0.231610	−	0.712822i
$203$	−6.85410	+	4.97980i	−0.481064	+	0.349513i
$204$	−9.70820	+	7.05342i	−0.679710	+	0.493838i
$205$	6.94427	+	21.3723i	0.485009	+	1.49270i
$206$	5.32624	−	16.3925i	0.371097	−	1.14212i
$207$	2.94427	+	2.13914i	0.204641	+	0.148680i
$208$	−3.23607			−0.224381
$209$		0			0
$210$	5.52786			0.381459
$211$	11.2361	+	8.16348i	0.773523	+	0.561997i	0.903028	−	0.429582i	$-0.141339\pi$
$211$	11.2361	+	8.16348i	0.773523	+	0.561997i	−0.129505	+	0.991579i	$0.541339\pi$
$212$	−0.437694	+	1.34708i	−0.0300610	+	0.0925181i
$213$	4.00000	+	12.3107i	0.274075	+	0.843518i
$214$	7.23607	−	5.25731i	0.494647	−	0.359382i
$215$	12.9443	−	9.40456i	0.882792	−	0.641386i
$216$	3.81966	+	11.7557i	0.259895	+	0.799874i
$217$	−0.854102	+	2.62866i	−0.0579802	+	0.178445i
$218$	8.09017	+	5.87785i	0.547935	+	0.398098i
$219$	0.944272			0.0638080
$220$		0			0
$221$	−10.4721			−0.704432
$222$	−18.9443	−	13.7638i	−1.27146	−	0.923767i
$223$	−3.14590	+	9.68208i	−0.210665	+	0.648360i	0.788768	+	0.614691i	$0.210719\pi$
$223$	−3.14590	+	9.68208i	−0.210665	+	0.648360i	−0.999433	+	0.0336691i	$0.989281\pi$
$224$	−2.07295	−	6.37988i	−0.138505	−	0.426274i
$225$	−1.19098	+	0.865300i	−0.0793989	+	0.0576867i
$226$	−3.61803	+	2.62866i	−0.240668	+	0.174856i
$227$	1.81966	+	5.60034i	0.120775	+	0.371707i	0.993108	−	0.117205i	$-0.0373936\pi$
$227$	1.81966	+	5.60034i	0.120775	+	0.371707i	−0.872333	+	0.488913i	$0.837394\pi$
$228$	−7.41641	+	22.8254i	−0.491164	+	1.51165i
$229$	3.61803	+	2.62866i	0.239086	+	0.173706i	0.700876	−	0.713283i	$-0.252793\pi$
$229$	3.61803	+	2.62866i	0.239086	+	0.173706i	−0.461790	+	0.886989i	$0.652793\pi$
$230$	−11.0557			−0.728993
$231$		0			0
$232$	18.9443			1.24375
$233$	−7.61803	−	5.53483i	−0.499074	−	0.362598i	0.309589	−	0.950870i	$-0.399808\pi$
$233$	−7.61803	−	5.53483i	−0.499074	−	0.362598i	−0.808663	+	0.588272i	$0.799808\pi$
$234$	−3.29180	+	10.1311i	−0.215191	+	0.662291i
$235$	−1.70820	−	5.25731i	−0.111431	−	0.342949i
$236$	3.00000	−	2.17963i	0.195283	−	0.141882i
$237$	−8.94427	+	6.49839i	−0.580993	+	0.422116i
$238$	−2.23607	−	6.88191i	−0.144943	−	0.446088i
$239$	−3.05573	+	9.40456i	−0.197659	+	0.608331i	0.802277	+	0.596952i	$0.203622\pi$
$239$	−3.05573	+	9.40456i	−0.197659	+	0.608331i	−0.999935	+	0.0113783i	$0.996378\pi$
$240$	2.00000	+	1.45309i	0.129099	+	0.0937962i
$241$	−13.1246			−0.845431			−0.422715	−	0.906263i	$-0.638923\pi$
$241$	−13.1246			−0.845431			−0.422715	+	0.906263i	$0.638923\pi$
$242$		0			0
$243$	−13.5967			−0.872232
$244$	17.5623	+	12.7598i	1.12431	+	0.816860i
$245$	−0.618034	+	1.90211i	−0.0394847	+	0.121522i
$246$	9.59675	+	29.5358i	0.611866	+	1.88313i
$247$	−16.9443	+	12.3107i	−1.07814	+	0.783313i
$248$	5.00000	−	3.63271i	0.317500	−	0.230677i
$249$	4.36068	+	13.4208i	0.276347	+	0.850508i
$250$	8.29180	−	25.5195i	0.524419	−	1.61400i
$251$	−3.47214	−	2.52265i	−0.219159	−	0.159229i	0.472789	−	0.881176i	$-0.343247\pi$
$251$	−3.47214	−	2.52265i	−0.219159	−	0.159229i	−0.691948	+	0.721947i	$0.743247\pi$
$252$	−4.41641			−0.278208
$253$		0			0
$254$	6.83282			0.428729
$255$	6.47214	+	4.70228i	0.405301	+	0.294468i
$256$	−2.78115	+	8.55951i	−0.173822	+	0.534969i
$257$	−1.85410	−	5.70634i	−0.115656	−	0.355952i	0.876428	−	0.481534i	$-0.159920\pi$
$257$	−1.85410	−	5.70634i	−0.115656	−	0.355952i	−0.992083	+	0.125582i	$0.959920\pi$
$258$	17.8885	−	12.9968i	1.11369	−	0.809145i
$259$	6.85410	−	4.97980i	0.425893	−	0.309430i
$260$	−6.00000	−	18.4661i	−0.372104	−	1.14522i
$261$	−3.85410	+	11.8617i	−0.238563	+	0.734221i
$262$	−39.5967	−	28.7687i	−2.44630	−	1.77734i
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$	0.944272			0.0580062
$266$	−11.7082	−	8.50651i	−0.717876	−	0.521567i
$267$	−0.763932	+	2.35114i	−0.0467519	+	0.143887i
$268$	13.4164	+	41.2915i	0.819538	+	2.52228i
$269$	−10.8541	+	7.88597i	−0.661786	+	0.480816i	−0.867266	−	0.497846i	$-0.834125\pi$
$269$	−10.8541	+	7.88597i	−0.661786	+	0.480816i	0.205479	+	0.978661i	$0.434125\pi$
$270$	20.0000	−	14.5309i	1.21716	−	0.884319i
$271$	−3.23607	−	9.95959i	−0.196577	−	0.605002i	−0.999955	−	0.00953205i	$-0.996966\pi$
$271$	−3.23607	−	9.95959i	−0.196577	−	0.605002i	0.803377	−	0.595470i	$-0.203034\pi$
$272$	1.00000	−	3.07768i	0.0606339	−	0.186612i
$273$	3.23607	+	2.35114i	0.195856	+	0.142298i
$274$	36.8328			2.22515
$275$		0			0
$276$	−9.16718			−0.551800
$277$	16.0902	+	11.6902i	0.966765	+	0.702396i	0.954712	−	0.297532i	$-0.0961634\pi$
$277$	16.0902	+	11.6902i	0.966765	+	0.702396i	0.0120527	+	0.999927i	$0.496163\pi$
$278$	−1.05573	+	3.24920i	−0.0633184	+	0.194874i
$279$	1.25735	+	3.86974i	0.0752758	+	0.231675i
$280$	3.61803	−	2.62866i	0.216219	−	0.157092i
$281$	2.85410	−	2.07363i	0.170261	−	0.123702i	−0.499391	−	0.866377i	$-0.666443\pi$
$281$	2.85410	−	2.07363i	0.170261	−	0.123702i	0.669653	+	0.742674i	$0.266443\pi$
$282$	−2.36068	−	7.26543i	−0.140576	−	0.432650i
$283$	9.23607	−	28.4257i	0.549027	−	1.68973i	−0.162190	−	0.986760i	$-0.551856\pi$
$283$	9.23607	−	28.4257i	0.549027	−	1.68973i	0.711217	−	0.702973i	$-0.248144\pi$
$284$	25.4164	+	18.4661i	1.50819	+	1.09576i
$285$	16.0000			0.947758
$286$		0			0
$287$	−11.2361			−0.663244
$288$	−7.98936	−	5.80461i	−0.470777	−	0.342040i
$289$	−2.01722	+	6.20837i	−0.118660	+	0.365198i
$290$	−11.7082	−	36.0341i	−0.687529	−	2.11600i
$291$	17.4164	−	12.6538i	1.02097	−	0.741777i
$292$	1.85410	−	1.34708i	0.108503	−	0.0788321i
$293$	−7.76393	−	23.8949i	−0.453574	−	1.39596i	−0.872801	−	0.488075i	$-0.837699\pi$
$293$	−7.76393	−	23.8949i	−0.453574	−	1.39596i	0.419228	−	0.907881i	$-0.362301\pi$
$294$	−0.854102	+	2.62866i	−0.0498122	+	0.153306i
$295$	−2.00000	−	1.45309i	−0.116445	−	0.0846019i
$296$	−18.9443			−1.10111
$297$		0			0
$298$	31.3050			1.81345
$299$	−6.47214	−	4.70228i	−0.374293	−	0.271940i
$300$	1.14590	−	3.52671i	0.0661585	−	0.203615i
$301$	2.47214	+	7.60845i	0.142492	+	0.438544i
$302$	−16.1803	+	11.7557i	−0.931074	+	0.676465i
$303$	−4.76393	+	3.46120i	−0.273681	+	0.198841i
$304$	−2.00000	−	6.15537i	−0.114708	−	0.353035i
$305$	4.47214	−	13.7638i	0.256074	−	0.788114i
$306$	−8.61803	−	6.26137i	−0.492660	−	0.357939i
$307$	−8.94427			−0.510477			−0.255238	−	0.966878i	$-0.582154\pi$
$307$	−8.94427			−0.510477			−0.255238	+	0.966878i	$0.582154\pi$
$308$		0			0
$309$	−9.52786			−0.542021
$310$	−10.0000	−	7.26543i	−0.567962	−	0.412648i
$311$	−2.56231	+	7.88597i	−0.145295	+	0.447172i	−0.997049	−	0.0767701i	$-0.975539\pi$
$311$	−2.56231	+	7.88597i	−0.145295	+	0.447172i	0.851754	+	0.523942i	$0.175539\pi$
$312$	−2.76393	−	8.50651i	−0.156477	−	0.481586i
$313$	−12.0902	+	8.78402i	−0.683377	+	0.496502i	−0.874476	−	0.485068i	$-0.838795\pi$
$313$	−12.0902	+	8.78402i	−0.683377	+	0.496502i	0.191099	+	0.981571i	$0.438795\pi$
$314$	−19.7984	+	14.3844i	−1.11729	+	0.811756i
$315$	0.909830	+	2.80017i	0.0512631	+	0.157772i
$316$	−8.29180	+	25.5195i	−0.466450	+	1.43559i
$317$	−11.3262	−	8.22899i	−0.636145	−	0.462186i	0.222379	−	0.974960i	$-0.428618\pi$
$317$	−11.3262	−	8.22899i	−0.636145	−	0.462186i	−0.858524	+	0.512774i	$0.828618\pi$
$318$	1.30495			0.0731781
$319$		0			0
$320$	26.0000			1.45344
$321$	−4.00000	−	2.90617i	−0.223258	−	0.162207i
$322$	1.70820	−	5.25731i	0.0951945	−	0.292978i
$323$	−6.47214	−	19.9192i	−0.360119	−	1.10833i
$324$	5.86475	−	4.26099i	0.325819	−	0.236721i
$325$	2.61803	−	1.90211i	0.145222	−	0.105510i
$326$	−2.36068	−	7.26543i	−0.130746	−	0.402395i
$327$	1.70820	−	5.25731i	0.0944639	−	0.290730i
$328$	20.3262	+	14.7679i	1.12233	+	0.815420i
$329$	2.76393			0.152381
$330$		0			0
$331$	−13.8885			−0.763383			−0.381692	−	0.924290i	$-0.624658\pi$
$331$	−13.8885			−0.763383			−0.381692	+	0.924290i	$0.624658\pi$
$332$	27.7082	+	20.1312i	1.52069	+	1.10484i
$333$	3.85410	−	11.8617i	0.211203	−	0.650017i
$334$	3.41641	+	10.5146i	0.186938	+	0.575335i
$335$	23.4164	−	17.0130i	1.27938	−	0.929520i
$336$	−1.00000	+	0.726543i	−0.0545545	+	0.0396361i
$337$	−3.56231	−	10.9637i	−0.194051	−	0.597228i	−0.999986	−	0.00522430i	$-0.998337\pi$
$337$	−3.56231	−	10.9637i	−0.194051	−	0.597228i	0.805935	−	0.592004i	$-0.201663\pi$
$338$	−1.74671	+	5.37582i	−0.0950086	+	0.292406i
$339$	2.00000	+	1.45309i	0.108625	+	0.0789207i
$340$	19.4164			1.05300
$341$		0			0
$342$	−21.3050			−1.15204
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	5.52786	−	17.0130i	0.298042	−	0.917280i
$345$	1.88854	+	5.81234i	0.101676	+	0.312926i
$346$	23.0902	−	16.7760i	1.24134	−	0.901883i
$347$	−16.9443	+	12.3107i	−0.909616	+	0.660875i	−0.940918	−	0.338635i	$-0.890035\pi$
$347$	−16.9443	+	12.3107i	−0.909616	+	0.660875i	0.0313016	+	0.999510i	$0.490035\pi$
$348$	−9.70820	−	29.8788i	−0.520414	−	1.60167i
$349$	−2.23607	+	6.88191i	−0.119694	+	0.368380i	−0.992897	−	0.118976i	$-0.962039\pi$
$349$	−2.23607	+	6.88191i	−0.119694	+	0.368380i	0.873203	+	0.487356i	$0.162039\pi$
$350$	1.80902	+	1.31433i	0.0966960	+	0.0702538i
$351$	17.8885			0.954820
$352$		0			0
$353$	19.8885			1.05856			0.529280	−	0.848447i	$-0.322462\pi$
$353$	19.8885			1.05856			0.529280	+	0.848447i	$0.322462\pi$
$354$	−2.76393	−	2.00811i	−0.146901	−	0.106730i
$355$	6.47214	−	19.9192i	0.343505	−	1.05720i
$356$	1.85410	+	5.70634i	0.0982672	+	0.302435i
$357$	−3.23607	+	2.35114i	−0.171271	+	0.124436i
$358$	16.1803	−	11.7557i	0.855158	−	0.621308i
$359$	−7.70820	−	23.7234i	−0.406823	−	1.25207i	−0.919363	−	0.393410i	$-0.871295\pi$
$359$	−7.70820	−	23.7234i	−0.406823	−	1.25207i	0.512540	−	0.858664i	$-0.328705\pi$
$360$	2.03444	−	6.26137i	0.107225	−	0.330003i
$361$	−18.5172	−	13.4535i	−0.974591	−	0.708082i
$362$	−56.8328			−2.98707
$363$		0			0
$364$	9.70820			0.508848
$365$	−1.23607	−	0.898056i	−0.0646988	−	0.0470064i
$366$	6.18034	−	19.0211i	0.323052	−	0.994250i
$367$	−7.14590	−	21.9928i	−0.373013	−	1.14802i	−0.944810	−	0.327620i	$-0.893753\pi$
$367$	−7.14590	−	21.9928i	−0.373013	−	1.14802i	0.571797	−	0.820395i	$-0.306247\pi$
$368$	2.00000	−	1.45309i	0.104257	−	0.0757473i
$369$	−13.3820	+	9.72257i	−0.696637	+	0.506137i
$370$	11.7082	+	36.0341i	0.608681	+	1.87333i
$371$	−0.145898	+	0.449028i	−0.00757465	+	0.0233124i
$372$	−8.29180	−	6.02434i	−0.429910	−	0.312348i
$373$	6.00000			0.310668			0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000			0.310668			0.155334	+	0.987862i	$0.450355\pi$
$374$		0			0
$375$	−14.8328			−0.765963
$376$	−5.00000	−	3.63271i	−0.257855	−	0.187343i
$377$	8.47214	−	26.0746i	0.436337	−	1.34291i
$378$	3.81966	+	11.7557i	0.196462	+	0.604648i
$379$	−30.1803	+	21.9273i	−1.55026	+	1.12633i	−0.606795	+	0.794859i	$0.707545\pi$
$379$	−30.1803	+	21.9273i	−1.55026	+	1.12633i	−0.943465	+	0.331471i	$0.892455\pi$
$380$	31.4164	−	22.8254i	1.61163	−	1.17092i
$381$	−1.16718	−	3.59222i	−0.0597967	−	0.184035i
$382$	−2.11146	+	6.49839i	−0.108031	+	0.332487i
$383$	3.76393	+	2.73466i	0.192328	+	0.139734i	0.679782	−	0.733414i	$-0.262074\pi$
$383$	3.76393	+	2.73466i	0.192328	+	0.139734i	−0.487454	+	0.873149i	$0.662074\pi$
$384$	19.3475			0.987324
$385$		0			0
$386$	26.5836			1.35307
$387$	9.52786	+	6.92240i	0.484329	+	0.351885i
$388$	16.1459	−	49.6920i	0.819684	−	2.52273i
$389$	4.90983	+	15.1109i	0.248938	+	0.766153i	0.994964	+	0.100236i	$0.0319597\pi$
$389$	4.90983	+	15.1109i	0.248938	+	0.766153i	−0.746025	+	0.665917i	$0.768040\pi$
$390$	−14.4721	+	10.5146i	−0.732825	+	0.532429i
$391$	6.47214	−	4.70228i	0.327310	−	0.237805i
$392$	0.690983	+	2.12663i	0.0348999	+	0.107411i
$393$	−8.36068	+	25.7315i	−0.421741	+	1.29798i
$394$	3.61803	+	2.62866i	0.182274	+	0.132430i
$395$	17.8885			0.900070
$396$		0			0
$397$	−35.8885			−1.80119			−0.900597	−	0.434655i	$-0.856870\pi$
$397$	−35.8885			−1.80119			−0.900597	+	0.434655i	$0.856870\pi$
$398$	3.94427	+	2.86568i	0.197708	+	0.143644i
$399$	−2.47214	+	7.60845i	−0.123762	+	0.380899i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	−18.5623	+	13.4863i	−0.926957	+	0.673474i	−0.945246	−	0.326359i	$-0.894178\pi$
$401$	−18.5623	+	13.4863i	−0.926957	+	0.673474i	0.0182886	+	0.999833i	$0.494178\pi$
$402$	32.3607	−	23.5114i	1.61400	−	1.17264i
$403$	−2.76393	−	8.50651i	−0.137681	−	0.423739i
$404$	−4.41641	+	13.5923i	−0.219725	+	0.676242i
$405$	−3.90983	−	2.84066i	−0.194281	−	0.141153i
$406$	18.9443			0.940188
$407$		0			0
$408$	8.94427			0.442807
$409$	−7.38197	−	5.36331i	−0.365015	−	0.265199i	0.390126	−	0.920762i	$-0.372431\pi$
$409$	−7.38197	−	5.36331i	−0.365015	−	0.265199i	−0.755141	+	0.655563i	$0.772431\pi$
$410$	15.5279	−	47.7899i	0.766867	−	2.36017i
$411$	−6.29180	−	19.3642i	−0.310351	−	0.955163i
$412$	−18.7082	+	13.5923i	−0.921687	+	0.669645i
$413$	1.00000	−	0.726543i	0.0492068	−	0.0357508i
$414$	−2.51471	−	7.73948i	−0.123591	−	0.380375i
$415$	7.05573	−	21.7153i	0.346352	−	1.06596i
$416$	17.5623	+	12.7598i	0.861063	+	0.625599i
$417$	1.88854			0.0924824
$418$		0			0
$419$	24.6525			1.20435			0.602176	−	0.798363i	$-0.294300\pi$
$419$	24.6525			1.20435			0.602176	+	0.798363i	$0.294300\pi$
$420$	−6.00000	−	4.35926i	−0.292770	−	0.212710i
$421$	6.90983	−	21.2663i	0.336765	−	1.03645i	−0.629082	−	0.777339i	$-0.716569\pi$
$421$	6.90983	−	21.2663i	0.336765	−	1.03645i	0.965846	−	0.259116i	$-0.0834310\pi$
$422$	−9.59675	−	29.5358i	−0.467162	−	1.43778i
$423$	3.29180	−	2.39163i	0.160053	−	0.116285i
$424$	0.854102	−	0.620541i	0.0414789	−	0.0301362i
$425$	1.00000	+	3.07768i	0.0485071	+	0.149290i
$426$	8.94427	−	27.5276i	0.433351	−	1.33372i
$427$	5.85410	+	4.25325i	0.283300	+	0.205829i
$428$	−12.0000			−0.580042
$429$		0			0
$430$	−35.7771			−1.72532
$431$	−9.70820	−	7.05342i	−0.467628	−	0.339751i	0.328888	−	0.944369i	$-0.393326\pi$
$431$	−9.70820	−	7.05342i	−0.467628	−	0.339751i	−0.796516	+	0.604617i	$0.793326\pi$
$432$	−1.70820	+	5.25731i	−0.0821860	+	0.252942i
$433$	−2.61803	−	8.05748i	−0.125815	−	0.387218i	0.868234	−	0.496155i	$-0.165255\pi$
$433$	−2.61803	−	8.05748i	−0.125815	−	0.387218i	−0.994049	+	0.108937i	$0.965255\pi$
$434$	5.00000	−	3.63271i	0.240008	−	0.174376i
$435$	−16.9443	+	12.3107i	−0.812416	+	0.590255i
$436$	−4.14590	−	12.7598i	−0.198553	−	0.611082i
$437$	4.94427	−	15.2169i	0.236517	−	0.727923i
$438$	−1.70820	−	1.24108i	−0.0816211	−	0.0593012i
$439$	10.4721			0.499808			0.249904	−	0.968271i	$-0.419601\pi$
$439$	10.4721			0.499808			0.249904	+	0.968271i	$0.419601\pi$
$440$		0			0
$441$	−1.47214			−0.0701017
$442$	18.9443	+	13.7638i	0.901087	+	0.654678i
$443$	−7.70820	+	23.7234i	−0.366228	+	1.12713i	0.582981	+	0.812486i	$0.301886\pi$
$443$	−7.70820	+	23.7234i	−0.366228	+	1.12713i	−0.949209	+	0.314647i	$0.898114\pi$
$444$	9.70820	+	29.8788i	0.460731	+	1.41798i
$445$	3.23607	−	2.35114i	0.153404	−	0.111455i
$446$	18.4164	−	13.3803i	0.872042	−	0.633576i
$447$	−5.34752	−	16.4580i	−0.252929	−	0.778436i
$448$	−4.01722	+	12.3637i	−0.189796	+	0.584132i
$449$	23.0344	+	16.7355i	1.08706	+	0.789797i	0.978901	−	0.204336i	$-0.0655036\pi$
$449$	23.0344	+	16.7355i	1.08706	+	0.789797i	0.108162	+	0.994133i	$0.465504\pi$
$450$	3.29180			0.155177
$451$		0			0
$452$	6.00000			0.282216
$453$	8.94427	+	6.49839i	0.420239	+	0.305321i
$454$	4.06888	−	12.5227i	0.190962	−	0.587721i
$455$	−2.00000	−	6.15537i	−0.0937614	−	0.288568i
$456$	14.4721	−	10.5146i	0.677720	−	0.492392i
$457$	23.3262	−	16.9475i	1.09116	−	0.792771i	0.111561	−	0.993758i	$-0.464415\pi$
$457$	23.3262	−	16.9475i	1.09116	−	0.792771i	0.979594	+	0.200987i	$0.0644148\pi$
$458$	−3.09017	−	9.51057i	−0.144394	−	0.444400i
$459$	−5.52786	+	17.0130i	−0.258019	+	0.794100i
$460$	12.0000	+	8.71851i	0.559503	+	0.406503i
$461$	−12.1803			−0.567295			−0.283647	−	0.958929i	$-0.591545\pi$
$461$	−12.1803			−0.567295			−0.283647	+	0.958929i	$0.591545\pi$
$462$		0			0
$463$	−5.52786			−0.256902			−0.128451	−	0.991716i	$-0.541000\pi$
$463$	−5.52786			−0.256902			−0.128451	+	0.991716i	$0.541000\pi$
$464$	6.85410	+	4.97980i	0.318194	+	0.231181i
$465$	−2.11146	+	6.49839i	−0.0979164	+	0.301356i
$466$	6.50658	+	20.0252i	0.301411	+	0.927649i
$467$	−19.4721	+	14.1473i	−0.901063	+	0.654661i	−0.938739	−	0.344629i	$-0.888005\pi$
$467$	−19.4721	+	14.1473i	−0.901063	+	0.654661i	0.0376758	+	0.999290i	$0.488005\pi$
$468$	11.5623	−	8.40051i	0.534468	−	0.388314i
$469$	4.47214	+	13.7638i	0.206504	+	0.635554i
$470$	−3.81966	+	11.7557i	−0.176188	+	0.542250i
$471$	10.9443	+	7.95148i	0.504285	+	0.366385i
$472$	−2.76393			−0.127220
$473$		0			0
$474$	24.7214			1.13549
$475$	5.23607	+	3.80423i	0.240247	+	0.174550i
$476$	−3.00000	+	9.23305i	−0.137505	+	0.423196i
$477$	0.214782	+	0.661030i	0.00983418	+	0.0302665i
$478$	17.8885	−	12.9968i	0.818203	−	0.594459i
$479$	−10.9443	+	7.95148i	−0.500057	+	0.363312i	−0.809039	−	0.587756i	$-0.800012\pi$
$479$	−10.9443	+	7.95148i	−0.500057	+	0.363312i	0.308982	+	0.951068i	$0.400012\pi$
$480$	−5.12461	−	15.7719i	−0.233905	−	0.719887i
$481$	−8.47214	+	26.0746i	−0.386296	+	1.18890i
$482$	23.7426	+	17.2500i	1.08145	+	0.785718i
$483$	−3.05573			−0.139040
$484$		0			0
$485$	−34.8328			−1.58168
$486$	24.5967	+	17.8706i	1.11573	+	0.810626i
$487$	−11.2361	+	34.5811i	−0.509155	+	1.56702i	0.284517	+	0.958671i	$0.408167\pi$
$487$	−11.2361	+	34.5811i	−0.509155	+	1.56702i	−0.793672	+	0.608346i	$0.791833\pi$
$488$	−5.00000	−	15.3884i	−0.226339	−	0.696601i
$489$	−3.41641	+	2.48217i	−0.154495	+	0.112247i
$490$	3.61803	−	2.62866i	0.163446	−	0.118751i
$491$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$491$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$492$	12.8754	−	39.6264i	0.580467	−	1.78649i
$493$	22.1803	+	16.1150i	0.998952	+	0.725781i
$494$	46.8328			2.10711
$495$		0			0
$496$	2.76393			0.124104
$497$	8.47214	+	6.15537i	0.380027	+	0.276106i
$498$	9.75078	−	30.0098i	0.436943	−	1.34477i
$499$	0.472136	+	1.45309i	0.0211357	+	0.0650490i	0.961068	−	0.276312i	$-0.0891122\pi$
$499$	0.472136	+	1.45309i	0.0211357	+	0.0650490i	−0.939932	+	0.341361i	$0.889112\pi$
$500$	−29.1246	+	21.1603i	−1.30249	+	0.946316i
$501$	4.94427	−	3.59222i	0.220894	−	0.160489i
$502$	2.96556	+	9.12705i	0.132359	+	0.407360i
$503$	7.23607	−	22.2703i	0.322640	−	0.992985i	−0.649854	−	0.760059i	$-0.725170\pi$
$503$	7.23607	−	22.2703i	0.322640	−	0.992985i	0.972494	−	0.232926i	$-0.0748300\pi$
$504$	2.66312	+	1.93487i	0.118625	+	0.0861859i
$505$	9.52786			0.423984
$506$		0			0
$507$	3.12461			0.138769
$508$	−7.41641	−	5.38834i	−0.329050	−	0.239069i
$509$	12.5066	−	38.4913i	0.554344	−	1.70610i	−0.143324	−	0.989676i	$-0.545779\pi$
$509$	12.5066	−	38.4913i	0.554344	−	1.70610i	0.697669	−	0.716421i	$-0.254221\pi$
$510$	−5.52786	−	17.0130i	−0.244778	−	0.753349i
$511$	0.618034	−	0.449028i	0.0273402	−	0.0198638i
$512$	−9.04508	+	6.57164i	−0.399740	+	0.290428i
$513$	11.0557	+	34.0260i	0.488122	+	1.50229i
$514$	−4.14590	+	12.7598i	−0.182868	+	0.562809i
$515$	12.4721	+	9.06154i	0.549588	+	0.399299i
$516$	−29.6656			−1.30596
$517$		0			0
$518$	−18.9443			−0.832364
$519$	−12.7639	−	9.27354i	−0.560274	−	0.407063i
$520$	−4.47214	+	13.7638i	−0.196116	+	0.603583i
$521$	9.38197	+	28.8747i	0.411031	+	1.26502i	0.915753	+	0.401742i	$0.131595\pi$
$521$	9.38197	+	28.8747i	0.411031	+	1.26502i	−0.504721	+	0.863282i	$0.668405\pi$
$522$	22.5623	−	16.3925i	0.987525	−	0.717479i
$523$	−35.5967	+	25.8626i	−1.55654	+	1.13089i	−0.617759	+	0.786367i	$0.711959\pi$
$523$	−35.5967	+	25.8626i	−1.55654	+	1.13089i	−0.938778	+	0.344523i	$0.888041\pi$
$524$	20.2918	+	62.4517i	0.886451	+	2.72822i
$525$	0.381966	−	1.17557i	0.0166704	−	0.0513061i
$526$		0			0
$527$	8.94427			0.389619
$528$		0			0
$529$	−16.8885			−0.734285
$530$	−1.70820	−	1.24108i	−0.0741996	−	0.0539092i
$531$	0.562306	−	1.73060i	0.0244020	−	0.0751016i
$532$	6.00000	+	18.4661i	0.260133	+	0.800607i
$533$	29.4164	−	21.3723i	1.27417	−	0.925736i
$534$	4.47214	−	3.24920i	0.193528	−	0.140607i
$535$	2.47214	+	7.60845i	0.106880	+	0.328942i
$536$	10.0000	−	30.7768i	0.431934	−	1.32936i
$537$	−8.94427	−	6.49839i	−0.385974	−	0.280426i
$538$	30.0000			1.29339
$539$		0			0
$540$	−33.1672			−1.42729
$541$	−16.8541	−	12.2452i	−0.724614	−	0.526463i	0.163241	−	0.986586i	$-0.447805\pi$
$541$	−16.8541	−	12.2452i	−0.724614	−	0.526463i	−0.887855	+	0.460123i	$0.847805\pi$
$542$	−7.23607	+	22.2703i	−0.310816	+	0.956592i
$543$	9.70820	+	29.8788i	0.416619	+	1.28222i
$544$	−17.5623	+	12.7598i	−0.752978	+	0.547070i
$545$	−7.23607	+	5.25731i	−0.309959	+	0.225198i
$546$	−2.76393	−	8.50651i	−0.118285	−	0.364045i
$547$	8.65248	−	26.6296i	0.369953	−	1.13860i	−0.576868	−	0.816838i	$-0.695725\pi$
$547$	8.65248	−	26.6296i	0.369953	−	1.13860i	0.946821	−	0.321761i	$-0.104275\pi$
$548$	−39.9787	−	29.0462i	−1.70781	−	1.24079i
$549$	10.6525			0.454637
$550$		0			0
$551$	54.8328			2.33596
$552$	5.52786	+	4.01623i	0.235282	+	0.170942i
$553$	−2.76393	+	8.50651i	−0.117534	+	0.361734i
$554$	−13.7426	−	42.2955i	−0.583869	−	1.79696i
$555$	16.9443	−	12.3107i	0.719244	−	0.522562i
$556$	3.70820	−	2.69417i	0.157263	−	0.114258i
$557$	−12.0344	−	37.0382i	−0.509916	−	1.56936i	−0.792346	−	0.610071i	$-0.791141\pi$
$557$	−12.0344	−	37.0382i	−0.509916	−	1.56936i	0.282431	−	0.959288i	$-0.408859\pi$
$558$	2.81153	−	8.65300i	0.119022	−	0.366311i
$559$	−20.9443	−	15.2169i	−0.885848	−	0.643606i
$560$	2.00000			0.0845154
$561$		0			0
$562$	−7.88854			−0.332758
$563$	−10.1803	−	7.39645i	−0.429050	−	0.311723i	0.352219	−	0.935918i	$-0.385427\pi$
$563$	−10.1803	−	7.39645i	−0.429050	−	0.311723i	−0.781269	+	0.624194i	$0.785427\pi$
$564$	−3.16718	+	9.74759i	−0.133363	+	0.410448i
$565$	−1.23607	−	3.80423i	−0.0520018	−	0.160045i
$566$	−54.0689	+	39.2833i	−2.27268	+	1.65120i
$567$	1.95492	−	1.42033i	0.0820987	−	0.0596482i
$568$	−7.23607	−	22.2703i	−0.303619	−	0.934442i
$569$	2.32624	−	7.15942i	0.0975210	−	0.300139i	−0.890382	−	0.455215i	$-0.849562\pi$
$569$	2.32624	−	7.15942i	0.0975210	−	0.300139i	0.987902	+	0.155076i	$0.0495624\pi$
$570$	−28.9443	−	21.0292i	−1.21234	−	0.880818i
$571$	−15.0557			−0.630063			−0.315031	−	0.949081i	$-0.602015\pi$
$571$	−15.0557			−0.630063			−0.315031	+	0.949081i	$0.602015\pi$
$572$		0			0
$573$	3.77709			0.157790
$574$	20.3262	+	14.7679i	0.848401	+	0.616399i
$575$	−0.763932	+	2.35114i	−0.0318582	+	0.0980494i
$576$	5.91390	+	18.2011i	0.246412	+	0.758379i
$577$	15.7984	−	11.4782i	0.657695	−	0.477843i	−0.208189	−	0.978089i	$-0.566757\pi$
$577$	15.7984	−	11.4782i	0.657695	−	0.477843i	0.865884	+	0.500245i	$0.166757\pi$
$578$	11.8090	−	8.57975i	0.491190	−	0.356871i
$579$	−4.54102	−	13.9758i	−0.188718	−	0.580815i
$580$	−15.7082	+	48.3449i	−0.652248	+	2.00741i
$581$	9.23607	+	6.71040i	0.383177	+	0.278394i
$582$	−48.1378			−1.99537
$583$		0			0
$584$	−1.70820			−0.0706860
$585$	−7.70820	−	5.60034i	−0.318695	−	0.231545i
$586$	−17.3607	+	53.4307i	−0.717163	+	2.20720i
$587$	8.38197	+	25.7970i	0.345961	+	1.06476i	0.961067	+	0.276314i	$0.0891129\pi$
$587$	8.38197	+	25.7970i	0.345961	+	1.06476i	−0.615107	+	0.788444i	$0.710887\pi$
$588$	3.00000	−	2.17963i	0.123718	−	0.0898863i
$589$	14.4721	−	10.5146i	0.596314	−	0.433247i
$590$	1.70820	+	5.25731i	0.0703256	+	0.216440i
$591$	0.763932	−	2.35114i	0.0314240	−	0.0967130i
$592$	−6.85410	−	4.97980i	−0.281702	−	0.204668i
$593$	−45.7082			−1.87701			−0.938505	−	0.345264i	$-0.887789\pi$
$593$	−45.7082			−1.87701			−0.938505	+	0.345264i	$0.887789\pi$
$594$		0			0
$595$	6.47214			0.265332
$596$	−33.9787	−	24.6870i	−1.39182	−	1.01122i
$597$	0.832816	−	2.56314i	0.0340849	−	0.104902i
$598$	5.52786	+	17.0130i	0.226051	+	0.695714i
$599$	18.9443	−	13.7638i	0.774042	−	0.562374i	−0.129143	−	0.991626i	$-0.541223\pi$
$599$	18.9443	−	13.7638i	0.774042	−	0.562374i	0.903185	+	0.429252i	$0.141223\pi$
$600$	−2.23607	+	1.62460i	−0.0912871	+	0.0663240i
$601$	−11.4721	−	35.3076i	−0.467958	−	1.44023i	−0.855224	−	0.518259i	$-0.826580\pi$
$601$	−11.4721	−	35.3076i	−0.467958	−	1.44023i	0.387266	−	0.921968i	$-0.373420\pi$
$602$	5.52786	−	17.0130i	0.225299	−	0.693399i
$603$	17.2361	+	12.5227i	0.701907	+	0.509965i
$604$	26.8328			1.09181
$605$		0			0
$606$	13.1672			0.534880
$607$	−10.4721	−	7.60845i	−0.425051	−	0.308818i	0.354616	−	0.935012i	$-0.384612\pi$
$607$	−10.4721	−	7.60845i	−0.425051	−	0.308818i	−0.779667	+	0.626194i	$0.784612\pi$
$608$	−13.4164	+	41.2915i	−0.544107	+	1.67459i
$609$	−3.23607	−	9.95959i	−0.131132	−	0.403583i
$610$	−26.1803	+	19.0211i	−1.06001	+	0.770143i
$611$	−7.23607	+	5.25731i	−0.292740	+	0.212688i
$612$	4.41641	+	13.5923i	0.178523	+	0.549436i
$613$	4.72949	−	14.5559i	0.191022	−	0.587906i	−0.808978	−	0.587839i	$-0.799979\pi$
$613$	4.72949	−	14.5559i	0.191022	−	0.587906i	1.00000		6.68672e-5i	$-2.12845e-5\pi$
$614$	16.1803	+	11.7557i	0.652985	+	0.474422i
$615$	−27.7771			−1.12008
$616$		0			0
$617$	6.58359			0.265045			0.132523	−	0.991180i	$-0.457692\pi$
$617$	6.58359			0.265045			0.132523	+	0.991180i	$0.457692\pi$
$618$	17.2361	+	12.5227i	0.693336	+	0.503738i
$619$	3.43769	−	10.5801i	0.138173	−	0.425252i	−0.857897	−	0.513821i	$-0.828230\pi$
$619$	3.43769	−	10.5801i	0.138173	−	0.425252i	0.996070	+	0.0885695i	$0.0282295\pi$
$620$	5.12461	+	15.7719i	0.205809	+	0.633416i
$621$	−11.0557	+	8.03246i	−0.443651	+	0.322331i
$622$	15.0000	−	10.8981i	0.601445	−	0.436976i
$623$	0.618034	+	1.90211i	0.0247610	+	0.0762065i
$624$	1.23607	−	3.80423i	0.0494823	−	0.152291i
$625$	15.3713	+	11.1679i	0.614853	+	0.446717i
$626$	33.4164			1.33559
$627$		0			0
$628$	32.8328			1.31017
$629$	−22.1803	−	16.1150i	−0.884388	−	0.642546i
$630$	2.03444	−	6.26137i	0.0810541	−	0.249459i
$631$	−7.41641	−	22.8254i	−0.295243	−	0.908663i	−0.983140	−	0.182855i	$-0.941466\pi$
$631$	−7.41641	−	22.8254i	−0.295243	−	0.908663i	0.687897	−	0.725808i	$-0.258534\pi$
$632$	16.1803	−	11.7557i	0.643619	−	0.467617i
$633$	−13.8885	+	10.0906i	−0.552020	+	0.401066i
$634$	9.67376	+	29.7728i	0.384194	+	1.18243i
$635$	−1.88854	+	5.81234i	−0.0749446	+	0.230656i
$636$	−1.41641	−	1.02908i	−0.0561642	−	0.0408057i
$637$	3.23607			0.128218
$638$		0			0
$639$	15.4164			0.609864
$640$	−25.3262	−	18.4006i	−1.00111	−	0.727347i
$641$	−4.79837	+	14.7679i	−0.189524	+	0.583296i	−0.999997	−	0.00248057i	$-0.999210\pi$
$641$	−4.79837	+	14.7679i	−0.189524	+	0.583296i	0.810473	+	0.585777i	$0.199210\pi$
$642$	3.41641	+	10.5146i	0.134835	+	0.414979i
$643$	−9.00000	+	6.53888i	−0.354925	+	0.257868i	−0.750932	−	0.660379i	$-0.770396\pi$
$643$	−9.00000	+	6.53888i	−0.354925	+	0.257868i	0.396007	+	0.918247i	$0.370396\pi$
$644$	−6.00000	+	4.35926i	−0.236433	+	0.171779i
$645$	6.11146	+	18.8091i	0.240638	+	0.740609i
$646$	−14.4721	+	44.5407i	−0.569399	+	1.75243i
$647$	−29.1803	−	21.2008i	−1.14720	−	0.833488i	−0.159092	−	0.987264i	$-0.550857\pi$
$647$	−29.1803	−	21.2008i	−1.14720	−	0.833488i	−0.988106	+	0.153776i	$0.950857\pi$
$648$	−5.40325			−0.212260
$649$		0			0
$650$	−7.23607			−0.283822
$651$	−2.76393	−	2.00811i	−0.108327	−	0.0787042i
$652$	−3.16718	+	9.74759i	−0.124037	+	0.381745i
$653$	7.74265	+	23.8294i	0.302993	+	0.932517i	0.980418	+	0.196925i	$0.0630957\pi$
$653$	7.74265	+	23.8294i	0.302993	+	0.932517i	−0.677425	+	0.735592i	$0.736904\pi$
$654$	−10.0000	+	7.26543i	−0.391031	+	0.284101i
$655$	35.4164	−	25.7315i	1.38383	−	1.00541i
$656$	3.47214	+	10.6861i	0.135564	+	0.417224i
$657$	0.347524	−	1.06957i	0.0135582	−	0.0417279i
$658$	−5.00000	−	3.63271i	−0.194920	−	0.141618i
$659$	−17.8885			−0.696839			−0.348419	−	0.937339i	$-0.613281\pi$
$659$	−17.8885			−0.696839			−0.348419	+	0.937339i	$0.613281\pi$
$660$		0			0
$661$	−40.8328			−1.58821			−0.794106	−	0.607779i	$-0.792061\pi$
$661$	−40.8328			−1.58821			−0.794106	+	0.607779i	$0.792061\pi$
$662$	25.1246	+	18.2541i	0.976496	+	0.709466i
$663$	4.00000	−	12.3107i	0.155347	−	0.478109i
$664$	−7.88854	−	24.2784i	−0.306135	−	0.942186i
$665$	10.4721	−	7.60845i	0.406092	−	0.295043i
$666$	−22.5623	+	16.3925i	−0.874272	+	0.635195i
$667$	6.47214	+	19.9192i	0.250602	+	0.771274i
$668$	4.58359	−	14.1068i	0.177345	−	0.545810i
$669$	−10.1803	−	7.39645i	−0.393595	−	0.285963i
$670$	−64.7214			−2.50040
$671$		0			0
$672$	8.29180			0.319863
$673$	17.3262	+	12.5882i	0.667877	+	0.485241i	0.869314	−	0.494260i	$-0.164561\pi$
$673$	17.3262	+	12.5882i	0.667877	+	0.485241i	−0.201437	+	0.979502i	$0.564561\pi$
$674$	−7.96556	+	24.5155i	−0.306822	+	0.944301i
$675$	−1.70820	−	5.25731i	−0.0657488	−	0.202354i
$676$	6.13525	−	4.45752i	0.235971	−	0.171443i
$677$	7.85410	−	5.70634i	0.301858	−	0.219312i	−0.426537	−	0.904470i	$-0.640267\pi$
$677$	7.85410	−	5.70634i	0.301858	−	0.219312i	0.728395	+	0.685158i	$0.240267\pi$
$678$	−1.70820	−	5.25731i	−0.0656032	−	0.201906i
$679$	5.38197	−	16.5640i	0.206541	−	0.635668i
$680$	−11.7082	−	8.50651i	−0.448989	−	0.326210i
$681$	−7.27864			−0.278918
$682$		0			0
$683$	−5.88854			−0.225319			−0.112659	−	0.993634i	$-0.535937\pi$
$683$	−5.88854			−0.225319			−0.112659	+	0.993634i	$0.535937\pi$
$684$	23.1246	+	16.8010i	0.884192	+	0.642403i
$685$	−10.1803	+	31.3319i	−0.388971	+	1.19713i
$686$	0.690983	+	2.12663i	0.0263819	+	0.0811950i
$687$	−4.47214	+	3.24920i	−0.170623	+	0.123965i
$688$	6.47214	−	4.70228i	0.246748	−	0.179273i
$689$	−0.472136	−	1.45309i	−0.0179869	−	0.0553581i
$690$	4.22291	−	12.9968i	0.160764	−	0.494779i
$691$	−15.0000	−	10.8981i	−0.570627	−	0.414585i	0.264706	−	0.964329i	$-0.414725\pi$
$691$	−15.0000	−	10.8981i	−0.570627	−	0.414585i	−0.835333	+	0.549744i	$0.814725\pi$
$692$	−38.2918			−1.45564
$693$		0			0
$694$	46.8328			1.77775
$695$	−2.47214	−	1.79611i	−0.0937735	−	0.0681304i
$696$	−7.23607	+	22.2703i	−0.274282	+	0.844155i
$697$	11.2361	+	34.5811i	0.425596	+	1.30985i
$698$	13.0902	−	9.51057i	0.495470	−	0.359980i
$699$	9.41641	−	6.84142i	0.356161	−	0.258766i
$700$	−0.927051	−	2.85317i	−0.0350392	−	0.107840i
$701$	−4.79837	+	14.7679i	−0.181232	+	0.557775i	−0.999863	−	0.0165448i	$-0.994733\pi$
$701$	−4.79837	+	14.7679i	−0.181232	+	0.557775i	0.818631	+	0.574320i	$0.194733\pi$
$702$	−32.3607	−	23.5114i	−1.22138	−	0.887381i
$703$	−54.8328			−2.06806
$704$		0			0
$705$	6.83282			0.257339
$706$	−35.9787	−	26.1401i	−1.35408	−	0.983794i
$707$	−1.47214	+	4.53077i	−0.0553654	+	0.170397i
$708$	1.41641	+	4.35926i	0.0532319	+	0.163831i
$709$	12.0902	−	8.78402i	0.454056	−	0.329891i	−0.337139	−	0.941455i	$-0.609459\pi$
$709$	12.0902	−	8.78402i	0.454056	−	0.329891i	0.791195	+	0.611564i	$0.209459\pi$
$710$	−37.8885	+	27.5276i	−1.42193	+	1.03309i
$711$	4.06888	+	12.5227i	0.152595	+	0.469639i
$712$	1.38197	−	4.25325i	0.0517914	−	0.159397i
$713$	5.52786	+	4.01623i	0.207020	+	0.150409i
$714$	8.94427			0.334731
$715$		0			0
$716$	−26.8328			−1.00279
$717$	−9.88854	−	7.18445i	−0.369294	−	0.268308i
$718$	−17.2361	+	53.0472i	−0.643244	+	1.97970i
$719$	−15.9098	−	48.9654i	−0.593337	−	1.82610i	−0.562838	−	0.826567i	$-0.690290\pi$
$719$	−15.9098	−	48.9654i	−0.593337	−	1.82610i	−0.0304986	−	0.999535i	$-0.509710\pi$
$720$	2.38197	−	1.73060i	0.0887706	−	0.0644956i
$721$	−6.23607	+	4.53077i	−0.232243	+	0.168735i
$722$	15.8156	+	48.6754i	0.588595	+	1.81151i
$723$	5.01316	−	15.4289i	0.186441	−	0.573807i
$724$	61.6869	+	44.8182i	2.29258	+	1.66565i
$725$	−8.47214			−0.314647
$726$		0			0
$727$	25.0132			0.927687			0.463843	−	0.885917i	$-0.346470\pi$
$727$	25.0132			0.927687			0.463843	+	0.885917i	$0.346470\pi$
$728$	−5.85410	−	4.25325i	−0.216967	−	0.157636i
$729$	7.43363	−	22.8784i	0.275320	−	0.847347i
$730$	1.05573	+	3.24920i	0.0390742	+	0.120258i
$731$	20.9443	−	15.2169i	0.774652	−	0.562818i
$732$	−21.7082	+	15.7719i	−0.802358	+	0.582947i
$733$	2.70820	+	8.33499i	0.100030	+	0.307860i	0.988532	−	0.151013i	$-0.0482534\pi$
$733$	2.70820	+	8.33499i	0.100030	+	0.307860i	−0.888502	+	0.458873i	$0.848253\pi$
$734$	−15.9787	+	49.1774i	−0.589785	+	1.81517i
$735$	−2.00000	−	1.45309i	−0.0737711	−	0.0535978i
$736$	−16.5836			−0.611279
$737$		0			0
$738$	36.9868			1.36150
$739$	−20.1803	−	14.6619i	−0.742346	−	0.539346i	0.151099	−	0.988519i	$-0.451719\pi$
$739$	−20.1803	−	14.6619i	−0.742346	−	0.539346i	−0.893445	+	0.449173i	$0.851719\pi$
$740$	15.7082	−	48.3449i	0.577445	−	1.77719i
$741$	−8.00000	−	24.6215i	−0.293887	−	0.904492i
$742$	0.854102	−	0.620541i	0.0313551	−	0.0227808i
$743$	−1.52786	+	1.11006i	−0.0560519	+	0.0407241i	−0.615458	−	0.788169i	$-0.711029\pi$
$743$	−1.52786	+	1.11006i	−0.0560519	+	0.0407241i	0.559407	+	0.828893i	$0.311029\pi$
$744$	2.36068	+	7.26543i	0.0865467	+	0.266363i
$745$	−8.65248	+	26.6296i	−0.317002	+	0.975632i
$746$	−10.8541	−	7.88597i	−0.397397	−	0.288726i
$747$	16.8065			0.614918
$748$		0			0
$749$	−4.00000			−0.146157
$750$	26.8328	+	19.4952i	0.979796	+	0.711863i
$751$	9.12461	−	28.0827i	0.332962	−	1.02475i	−0.634756	−	0.772713i	$-0.718899\pi$
$751$	9.12461	−	28.0827i	0.332962	−	1.02475i	0.967717	−	0.252038i	$-0.0811008\pi$
$752$	−0.854102	−	2.62866i	−0.0311459	−	0.0958572i
$753$	4.29180	−	3.11817i	0.156402	−	0.113633i
$754$	−49.5967	+	36.0341i	−1.80621	+	1.31229i
$755$	−5.52786	−	17.0130i	−0.201180	−	0.619167i
$756$	5.12461	−	15.7719i	0.186380	−	0.573620i
$757$	−12.8541	−	9.33905i	−0.467190	−	0.339434i	0.329155	−	0.944276i	$-0.393236\pi$
$757$	−12.8541	−	9.33905i	−0.467190	−	0.339434i	−0.796345	+	0.604842i	$0.793236\pi$
$758$	83.4164			3.02982
$759$		0			0
$760$	−28.9443			−1.04992
$761$	25.5623	+	18.5721i	0.926633	+	0.673238i	0.945166	−	0.326590i	$-0.105900\pi$
$761$	25.5623	+	18.5721i	0.926633	+	0.673238i	−0.0185332	+	0.999828i	$0.505900\pi$
$762$	−2.60990	+	8.03246i	−0.0945468	+	0.290985i
$763$	−1.38197	−	4.25325i	−0.0500305	−	0.153978i
$764$	7.41641	−	5.38834i	0.268316	−	0.194943i
$765$	7.70820	−	5.60034i	0.278691	−	0.202481i
$766$	−3.21478	−	9.89408i	−0.116155	−	0.357488i
$767$	−1.23607	+	3.80423i	−0.0446318	+	0.137363i
$768$	−9.00000	−	6.53888i	−0.324760	−	0.235952i
$769$	18.2918			0.659619			0.329810	−	0.944047i	$-0.393015\pi$
$769$	18.2918			0.659619			0.329810	+	0.944047i	$0.393015\pi$
$770$		0			0
$771$	7.41641			0.267095
$772$	−28.8541	−	20.9637i	−1.03848	−	0.754501i
$773$	−11.8541	+	36.4832i	−0.426362	+	1.31221i	0.475321	+	0.879812i	$0.342332\pi$
$773$	−11.8541	+	36.4832i	−0.426362	+	1.31221i	−0.901684	+	0.432396i	$0.857668\pi$
$774$	−8.13777	−	25.0455i	−0.292506	−	0.900241i
$775$	−2.23607	+	1.62460i	−0.0803219	+	0.0583573i
$776$	−31.5066	+	22.8909i	−1.13102	+	0.821734i
$777$	3.23607	+	9.95959i	0.116093	+	0.357298i
$778$	10.9787	−	33.7890i	0.393606	−	1.21139i
$779$	58.8328	+	42.7445i	2.10790	+	1.53148i
$780$	24.0000			0.859338
$781$		0			0
$782$	−17.8885			−0.639693
$783$	−37.8885	−	27.5276i	−1.35403	−	0.983758i
$784$	−0.309017	+	0.951057i	−0.0110363	+	0.0339663i
$785$	−6.76393	−	20.8172i	−0.241415	−	0.742999i
$786$	48.9443	−	35.5601i	1.74578	−	1.26839i
$787$	35.1246	−	25.5195i	1.25206	−	0.909673i	0.253718	−	0.967278i	$-0.418347\pi$
$787$	35.1246	−	25.5195i	1.25206	−	0.909673i	0.998339	+	0.0576055i	$0.0183466\pi$
$788$	−1.85410	−	5.70634i	−0.0660496	−	0.203280i
$789$		0			0
$790$	−32.3607	−	23.5114i	−1.15134	−	0.836498i
$791$	2.00000			0.0711118
$792$		0			0
$793$	−23.4164			−0.831541
$794$	64.9230	+	47.1693i	2.30403	+	1.67398i
$795$	−0.360680	+	1.11006i	−0.0127920	+	0.0393697i
$796$	−2.02129	−	6.22088i	−0.0716426	−	0.220493i
$797$	12.0902	−	8.78402i	0.428256	−	0.311146i	−0.352695	−	0.935738i	$-0.614735\pi$
$797$	12.0902	−	8.78402i	0.428256	−	0.311146i	0.780951	+	0.624592i	$0.214735\pi$
$798$	14.4721	−	10.5146i	0.512308	−	0.372214i
$799$	−2.76393	−	8.50651i	−0.0977809	−	0.300939i
$800$	2.07295	−	6.37988i	0.0732898	−	0.225563i
$801$	2.38197	+	1.73060i	0.0841626	+	0.0611477i
$802$	51.3050			1.81164
$803$		0			0
$804$	−53.6656			−1.89264
$805$	4.00000	+	2.90617i	0.140981	+	0.102429i
$806$	−6.18034	+	19.0211i	−0.217693	+	0.669991i
$807$	−5.12461	−	15.7719i	−0.180395	−	0.555198i
$808$	8.61803	−	6.26137i	0.303181	−	0.220274i
$809$	−17.0344	+	12.3762i	−0.598899	+	0.435126i	−0.845488	−	0.533995i	$-0.820690\pi$
$809$	−17.0344	+	12.3762i	−0.598899	+	0.435126i	0.246589	+	0.969120i	$0.420690\pi$
$810$	3.33939	+	10.2776i	0.117334	+	0.361118i
$811$	−10.7639	+	33.1280i	−0.377973	+	1.16328i	0.563478	+	0.826131i	$0.309463\pi$
$811$	−10.7639	+	33.1280i	−0.377973	+	1.16328i	−0.941451	+	0.337150i	$0.890537\pi$
$812$	−20.5623	−	14.9394i	−0.721595	−	0.524270i
$813$	12.9443			0.453975
$814$		0			0
$815$	6.83282			0.239343
$816$	3.23607	+	2.35114i	0.113285	+	0.0823064i
$817$	16.0000	−	49.2429i	0.559769	−	1.72279i
$818$	6.30495	+	19.4046i	0.220447	+	0.678468i
$819$	3.85410	−	2.80017i	0.134673	−	0.0978458i
$820$	−54.5410	+	39.6264i	−1.90466	+	1.38381i
$821$	13.8541	+	42.6385i	0.483511	+	1.48810i	0.834125	+	0.551575i	$0.185973\pi$
$821$	13.8541	+	42.6385i	0.483511	+	1.48810i	−0.350614	+	0.936520i	$0.614027\pi$
$822$	−14.0689	+	43.2996i	−0.490709	+	1.51025i
$823$	11.4164	+	8.29451i	0.397951	+	0.289128i	0.768706	−	0.639602i	$-0.220901\pi$
$823$	11.4164	+	8.29451i	0.397951	+	0.289128i	−0.370755	+	0.928731i	$0.620901\pi$
$824$	17.2361			0.600447
$825$		0			0
$826$	−2.76393			−0.0961695
$827$	10.4721	+	7.60845i	0.364152	+	0.264572i	0.754782	−	0.655976i	$-0.227743\pi$
$827$	10.4721	+	7.60845i	0.364152	+	0.264572i	−0.390630	+	0.920548i	$0.627743\pi$
$828$	−3.37384	+	10.3836i	−0.117249	+	0.360855i
$829$	11.3820	+	35.0301i	0.395312	+	1.21665i	0.928718	+	0.370786i	$0.120912\pi$
$829$	11.3820	+	35.0301i	0.395312	+	1.21665i	−0.533406	+	0.845859i	$0.679088\pi$
$830$	−41.3050	+	30.0098i	−1.43372	+	1.04166i
$831$	−19.8885	+	14.4499i	−0.689926	+	0.501261i
$832$	−13.0000	−	40.0099i	−0.450694	−	1.38709i
$833$	−1.00000	+	3.07768i	−0.0346479	+	0.106635i
$834$	−3.41641	−	2.48217i	−0.118301	−	0.0859504i
$835$	−9.88854			−0.342207
$836$		0			0
$837$	−15.2786			−0.528107
$838$	−44.5967	−	32.4014i	−1.54057	−	1.11929i
$839$	13.6180	−	41.9120i	0.470147	−	1.44696i	−0.382246	−	0.924061i	$-0.624849\pi$
$839$	13.6180	−	41.9120i	0.470147	−	1.44696i	0.852393	−	0.522902i	$-0.175151\pi$
$840$	1.70820	+	5.25731i	0.0589386	+	0.181394i
$841$	−34.6074	+	25.1437i	−1.19336	+	0.867026i
$842$	−40.4508	+	29.3893i	−1.39403	+	1.01282i
$843$	1.34752	+	4.14725i	0.0464112	+	0.142839i
$844$	−12.8754	+	39.6264i	−0.443189	+	1.36400i
$845$	−4.09017	−	2.97168i	−0.140706	−	0.102229i
$846$	−9.09830			−0.312806
$847$		0			0
$848$	0.472136			0.0162132
$849$	29.8885	+	21.7153i	1.02577	+	0.745267i
$850$	2.23607	−	6.88191i	0.0766965	−	0.236048i
$851$	−6.47214	−	19.9192i	−0.221862	−	0.682821i
$852$	−31.4164	+	22.8254i	−1.07631	+	0.781984i
$853$	24.7984	−	18.0171i	0.849080	−	0.616893i	−0.0758121	−	0.997122i	$-0.524155\pi$
$853$	24.7984	−	18.0171i	0.849080	−	0.616893i	0.924892	+	0.380229i	$0.124155\pi$
$854$	−5.00000	−	15.3884i	−0.171096	−	0.526581i
$855$	5.88854	−	18.1231i	0.201384	−	0.619796i
$856$	7.23607	+	5.25731i	0.247324	+	0.179691i
$857$	15.2361			0.520454			0.260227	−	0.965547i	$-0.416203\pi$
$857$	15.2361			0.520454			0.260227	+	0.965547i	$0.416203\pi$
$858$		0			0
$859$	−26.5410			−0.905568			−0.452784	−	0.891620i	$-0.649569\pi$
$859$	−26.5410			−0.905568			−0.452784	+	0.891620i	$0.649569\pi$
$860$	38.8328	+	28.2137i	1.32419	+	0.962079i
$861$	4.29180	−	13.2088i	0.146264	−	0.450154i
$862$	8.29180	+	25.5195i	0.282420	+	0.869198i
$863$	2.47214	−	1.79611i	0.0841525	−	0.0611404i	−0.544914	−	0.838492i	$-0.683438\pi$
$863$	2.47214	−	1.79611i	0.0841525	−	0.0611404i	0.629066	+	0.777352i	$0.283438\pi$
$864$	30.0000	−	21.7963i	1.02062	−	0.741524i
$865$	7.88854	+	24.2784i	0.268219	+	0.825492i
$866$	−5.85410	+	18.0171i	−0.198930	+	0.612245i
$867$	−6.52786	−	4.74277i	−0.221698	−	0.161073i
$868$	−8.29180			−0.281442
$869$		0			0
$870$	46.8328			1.58778
$871$	−37.8885	−	27.5276i	−1.28380	−	0.932738i
$872$	−3.09017	+	9.51057i	−0.104646	+	0.322068i
$873$	−7.92299	−	24.3844i	−0.268152	−	0.825288i
$874$	−28.9443	+	21.0292i	−0.979055	+	0.711325i
$875$	−9.70820	+	7.05342i	−0.328197	+	0.238449i
$876$	0.875388	+	2.69417i	0.0295766	+	0.0910275i
$877$	4.50658	−	13.8698i	0.152176	−	0.468351i	−0.845688	−	0.533678i	$-0.820809\pi$
$877$	4.50658	−	13.8698i	0.152176	−	0.468351i	0.997864	+	0.0653278i	$0.0208093\pi$
$878$	−18.9443	−	13.7638i	−0.639338	−	0.464506i
$879$	31.0557			1.04748
$880$		0			0
$881$	2.58359			0.0870434			0.0435217	−	0.999052i	$-0.486142\pi$
$881$	2.58359			0.0870434			0.0435217	+	0.999052i	$0.486142\pi$
$882$	2.66312	+	1.93487i	0.0896719	+	0.0651504i
$883$	−2.76393	+	8.50651i	−0.0930137	+	0.286267i	−0.986731	−	0.162364i	$-0.948088\pi$
$883$	−2.76393	+	8.50651i	−0.0930137	+	0.286267i	0.893717	+	0.448631i	$0.148088\pi$
$884$	−9.70820	−	29.8788i	−0.326522	−	1.00493i
$885$	2.47214	−	1.79611i	0.0830999	−	0.0603756i
$886$	45.1246	−	32.7849i	1.51599	−	1.10143i
$887$	−1.34752	−	4.14725i	−0.0452454	−	0.139251i	0.925882	−	0.377813i	$-0.123324\pi$
$887$	−1.34752	−	4.14725i	−0.0452454	−	0.139251i	−0.971127	+	0.238562i	$0.923324\pi$
$888$	7.23607	−	22.2703i	0.242827	−	0.747343i
$889$	−2.47214	−	1.79611i	−0.0829128	−	0.0602397i
$890$	−8.94427			−0.299813
$891$		0			0
$892$	−30.5410			−1.02259
$893$	−14.4721	−	10.5146i	−0.484292	−	0.351858i
$894$	−11.9574	+	36.8012i	−0.399916	+	1.23082i
$895$	5.52786	+	17.0130i	0.184776	+	0.568682i
$896$	12.6631	−	9.20029i	0.423045	−	0.307360i
$897$	8.00000	−	5.81234i	0.267112	−	0.194068i
$898$	−19.6738	−	60.5496i	−0.656522	−	2.02057i
$899$	−7.23607	+	22.2703i	−0.241336	+	0.742757i
$900$	−3.57295	−	2.59590i	−0.119098	−	0.0865300i
$901$	1.52786			0.0509005
$902$		0			0
$903$	−9.88854			−0.329070
$904$	−3.61803	−	2.62866i	−0.120334	−	0.0874278i
$905$	15.7082	−	48.3449i	0.522158	−	1.60704i
$906$	−7.63932	−	23.5114i	−0.253799	−	0.781114i
$907$	−18.1803	+	13.2088i	−0.603668	+	0.438591i	−0.847179	−	0.531308i	$-0.821701\pi$
$907$	−18.1803	+	13.2088i	−0.603668	+	0.438591i	0.243511	+	0.969898i	$0.421701\pi$
$908$	−14.2918	+	10.3836i	−0.474290	+	0.344592i
$909$	2.16718	+	6.66991i	0.0718810	+	0.221227i
$910$	−4.47214	+	13.7638i	−0.148250	+	0.456266i
$911$	−34.3607	−	24.9645i	−1.13842	−	0.827111i	−0.151522	−	0.988454i	$-0.548417\pi$
$911$	−34.3607	−	24.9645i	−1.13842	−	0.827111i	−0.986898	+	0.161343i	$0.948417\pi$
$912$	8.00000			0.264906
$913$		0			0
$914$	−64.4721			−2.13255
$915$	14.4721	+	10.5146i	0.478434	+	0.347603i
$916$	−4.14590	+	12.7598i	−0.136984	+	0.421594i
$917$	6.76393	+	20.8172i	0.223365	+	0.687446i
$918$	32.3607	−	23.5114i	1.06806	−	0.775992i
$919$	−33.8885	+	24.6215i	−1.11788	+	0.812187i	−0.983886	−	0.178795i	$-0.942780\pi$
$919$	−33.8885	+	24.6215i	−1.11788	+	0.812187i	−0.133994	+	0.990982i	$0.542780\pi$
$920$	−3.41641	−	10.5146i	−0.112636	−	0.346657i
$921$	3.41641	−	10.5146i	0.112574	−	0.346469i
$922$	22.0344	+	16.0090i	0.725666	+	0.527227i
$923$	−33.8885			−1.11546
$924$		0			0
$925$	8.47214			0.278562
$926$	10.0000	+	7.26543i	0.328620	+	0.238757i
$927$	−3.50658	+	10.7921i	−0.115171	+	0.354460i
$928$	−17.5623	−	54.0512i	−0.576511	−	1.77432i
$929$	42.2705	−	30.7113i	1.38685	−	1.00761i	0.390648	−	0.920540i	$-0.372251\pi$
$929$	42.2705	−	30.7113i	1.38685	−	1.00761i	0.996203	−	0.0870656i	$-0.0277490\pi$
$930$	12.3607	−	8.98056i	0.405323	−	0.294484i
$931$	2.00000	+	6.15537i	0.0655474	+	0.201734i
$932$	8.72949	−	26.8666i	0.285944	−	0.880045i
$933$	−8.29180	−	6.02434i	−0.271461	−	0.197228i
$934$	53.8197			1.76103
$935$		0			0
$936$	−10.6525			−0.348187
$937$	8.61803	+	6.26137i	0.281539	+	0.204550i	0.719588	−	0.694401i	$-0.244331\pi$
$937$	8.61803	+	6.26137i	0.281539	+	0.204550i	−0.438049	+	0.898951i	$0.644331\pi$
$938$	10.0000	−	30.7768i	0.326512	−	1.00490i
$939$	−5.70820	−	17.5680i	−0.186280	−	0.573311i
$940$	13.4164	−	9.74759i	0.437595	−	0.317931i
$941$	−6.14590	+	4.46526i	−0.200351	+	0.145563i	−0.683437	−	0.730009i	$-0.739516\pi$
$941$	−6.14590	+	4.46526i	−0.200351	+	0.145563i	0.483087	+	0.875573i	$0.339516\pi$
$942$	−9.34752	−	28.7687i	−0.304559	−	0.937336i
$943$	−8.58359	+	26.4176i	−0.279520	+	0.860275i
$944$	−1.00000	−	0.726543i	−0.0325472	−	0.0236469i
$945$	−11.0557			−0.359643
$946$		0			0
$947$	−5.16718			−0.167911			−0.0839555	−	0.996470i	$-0.526755\pi$
$947$	−5.16718			−0.167911			−0.0839555	+	0.996470i	$0.526755\pi$
$948$	−26.8328	−	19.4952i	−0.871489	−	0.633174i
$949$	−0.763932	+	2.35114i	−0.0247983	+	0.0763213i
$950$	−4.47214	−	13.7638i	−0.145095	−	0.446557i
$951$	14.0000	−	10.1716i	0.453981	−	0.329837i
$952$	5.85410	−	4.25325i	0.189733	−	0.137849i
$953$	7.09017	+	21.8213i	0.229673	+	0.706861i	0.997784	+	0.0665438i	$0.0211972\pi$
$953$	7.09017	+	21.8213i	0.229673	+	0.706861i	−0.768110	+	0.640317i	$0.778803\pi$
$954$	0.480267	−	1.47811i	0.0155492	−	0.0478555i
$955$	−4.94427	−	3.59222i	−0.159993	−	0.116242i
$956$	−29.6656			−0.959455
$957$		0			0
$958$	30.2492			0.977308
$959$	−13.3262	−	9.68208i	−0.430327	−	0.312651i
$960$	−9.93112	+	30.5648i	−0.320525	+	0.986476i
$961$	−7.21885	−	22.2173i	−0.232866	−	0.716688i
$962$	49.5967	−	36.0341i	1.59906	−	1.16179i
$963$	−4.76393	+	3.46120i	−0.153516	+	0.111536i
$964$	−12.1672	−	37.4467i	−0.391879	−	1.20608i
$965$	−7.34752	+	22.6134i	−0.236525	+	0.727950i
$966$	5.52786	+	4.01623i	0.177856	+	0.129220i
$967$	−13.8885			−0.446625			−0.223313	−	0.974747i	$-0.571687\pi$
$967$	−13.8885			−0.446625			−0.223313	+	0.974747i	$0.571687\pi$
$968$		0			0
$969$	25.8885			0.831660
$970$	63.0132	+	45.7817i	2.02323	+	1.46996i
$971$	3.43769	−	10.5801i	0.110321	−	0.339533i	−0.880622	−	0.473820i	$-0.842875\pi$
$971$	3.43769	−	10.5801i	0.110321	−	0.339533i	0.990942	+	0.134288i	$0.0428746\pi$
$972$	−12.6049	−	38.7938i	−0.404302	−	1.24431i
$973$	1.23607	−	0.898056i	0.0396265	−	0.0287904i
$974$	65.7771	−	47.7899i	2.10763	−	1.53129i
$975$	1.23607	+	3.80423i	0.0395859	+	0.121833i
$976$	2.23607	−	6.88191i	0.0715748	−	0.220285i
$977$	−18.5623	−	13.4863i	−0.593861	−	0.431465i	0.249834	−	0.968289i	$-0.419624\pi$
$977$	−18.5623	−	13.4863i	−0.593861	−	0.431465i	−0.843694	+	0.536824i	$0.819624\pi$
$978$	9.44272			0.301945
$979$		0			0
$980$	−6.00000			−0.191663
$981$	−5.32624	−	3.86974i	−0.170054	−	0.123551i
$982$		0			0
$983$	6.74265	+	20.7517i	0.215057	+	0.661877i	0.999150	+	0.0412335i	$0.0131287\pi$
$983$	6.74265	+	20.7517i	0.215057	+	0.661877i	−0.784093	+	0.620644i	$0.786871\pi$
$984$	−25.1246	+	18.2541i	−0.800943	+	0.581919i
$985$	−3.23607	+	2.35114i	−0.103110	+	0.0749136i
$986$	−18.9443	−	58.3045i	−0.603309	−	1.85679i
$987$	−1.05573	+	3.24920i	−0.0336042	+	0.103423i
$988$	−50.8328	−	36.9322i	−1.61721	−	1.17497i
$989$	19.7771			0.628875
$990$		0			0
$991$	54.2492			1.72328			0.861642	−	0.507517i	$-0.169437\pi$
$991$	54.2492			1.72328			0.861642	+	0.507517i	$0.169437\pi$
$992$	−15.0000	−	10.8981i	−0.476250	−	0.346016i
$993$	5.30495	−	16.3270i	0.168348	−	0.518120i
$994$	−7.23607	−	22.2703i	−0.229514	−	0.706372i
$995$	−3.52786	+	2.56314i	−0.111841	+	0.0812571i
$996$	−34.2492	+	24.8835i	−1.08523	+	0.788464i
$997$	0.416408	+	1.28157i	0.0131878	+	0.0405878i	0.957434	−	0.288653i	$-0.0932073\pi$
$997$	0.416408	+	1.28157i	0.0131878	+	0.0405878i	−0.944246	+	0.329241i	$0.893207\pi$
$998$	1.05573	−	3.24920i	0.0334185	−	0.102852i
$999$	37.8885	+	27.5276i	1.19874	+	0.870936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.a.323.1		4
11.2	odd	10		847.2.f.b.148.1		4
11.3	even	5	inner	847.2.f.a.729.1		4
11.4	even	5		847.2.f.n.372.1		4
11.5	even	5		77.2.a.d.1.2	✓	2
11.6	odd	10		847.2.a.f.1.1		2
11.7	odd	10		847.2.f.b.372.1		4
11.8	odd	10		847.2.f.m.729.1		4
11.9	even	5		847.2.f.n.148.1		4
11.10	odd	2		847.2.f.m.323.1		4
33.5	odd	10		693.2.a.h.1.1		2
33.17	even	10		7623.2.a.bl.1.2		2
44.27	odd	10		1232.2.a.m.1.2		2
55.27	odd	20		1925.2.b.h.1849.3		4
55.38	odd	20		1925.2.b.h.1849.2		4
55.49	even	10		1925.2.a.r.1.1		2
77.5	odd	30		539.2.e.j.67.1		4
77.6	even	10		5929.2.a.m.1.1		2
77.16	even	15		539.2.e.i.67.1		4
77.27	odd	10		539.2.a.f.1.2		2
77.38	odd	30		539.2.e.j.177.1		4
77.60	even	15		539.2.e.i.177.1		4
88.5	even	10		4928.2.a.bm.1.2		2
88.27	odd	10		4928.2.a.bv.1.1		2
231.104	even	10		4851.2.a.y.1.1		2
308.27	even	10		8624.2.a.ce.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.a.d.1.2	✓	2	11.5	even	5
539.2.a.f.1.2		2	77.27	odd	10
539.2.e.i.67.1		4	77.16	even	15
539.2.e.i.177.1		4	77.60	even	15
539.2.e.j.67.1		4	77.5	odd	30
539.2.e.j.177.1		4	77.38	odd	30
693.2.a.h.1.1		2	33.5	odd	10
847.2.a.f.1.1		2	11.6	odd	10
847.2.f.a.323.1		4	1.1	even	1	trivial
847.2.f.a.729.1		4	11.3	even	5	inner
847.2.f.b.148.1		4	11.2	odd	10
847.2.f.b.372.1		4	11.7	odd	10
847.2.f.m.323.1		4	11.10	odd	2
847.2.f.m.729.1		4	11.8	odd	10
847.2.f.n.148.1		4	11.9	even	5
847.2.f.n.372.1		4	11.4	even	5
1232.2.a.m.1.2		2	44.27	odd	10
1925.2.a.r.1.1		2	55.49	even	10
1925.2.b.h.1849.2		4	55.38	odd	20
1925.2.b.h.1849.3		4	55.27	odd	20
4851.2.a.y.1.1		2	231.104	even	10
4928.2.a.bm.1.2		2	88.5	even	10
4928.2.a.bv.1.1		2	88.27	odd	10
5929.2.a.m.1.1		2	77.6	even	10
7623.2.a.bl.1.2		2	33.17	even	10
8624.2.a.ce.1.1		2	308.27	even	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)

\(f(q)\)	\(=\)	\(q+(-1.80902 - 1.31433i) q^{2} +(-0.381966 + 1.17557i) q^{3} +(0.927051 + 2.85317i) q^{4} +(1.61803 - 1.17557i) q^{5} +(2.23607 - 1.62460i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.690983 - 2.12663i) q^{8} +(1.19098 + 0.865300i) q^{9} +O(q^{10})\)	\(q+(-1.80902 - 1.31433i) q^{2} +(-0.381966 + 1.17557i) q^{3} +(0.927051 + 2.85317i) q^{4} +(1.61803 - 1.17557i) q^{5} +(2.23607 - 1.62460i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.690983 - 2.12663i) q^{8} +(1.19098 + 0.865300i) q^{9} -4.47214 q^{10} -3.70820 q^{12} +(-2.61803 - 1.90211i) q^{13} +(0.690983 - 2.12663i) q^{14} +(0.763932 + 2.35114i) q^{15} +(0.809017 - 0.587785i) q^{16} +(2.61803 - 1.90211i) q^{17} +(-1.01722 - 3.13068i) q^{18} +(2.00000 - 6.15537i) q^{19} +(4.85410 + 3.52671i) q^{20} -1.23607 q^{21} +2.47214 q^{23} +(2.23607 + 1.62460i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(2.23607 + 6.88191i) q^{26} +(-4.47214 + 3.24920i) q^{27} +(-2.42705 + 1.76336i) q^{28} +(2.61803 + 8.05748i) q^{29} +(1.70820 - 5.25731i) q^{30} +(2.23607 + 1.62460i) q^{31} -6.70820 q^{32} -7.23607 q^{34} +(1.61803 + 1.17557i) q^{35} +(-1.36475 + 4.20025i) q^{36} +(-2.61803 - 8.05748i) q^{37} +(-11.7082 + 8.50651i) q^{38} +(3.23607 - 2.35114i) q^{39} +(-1.38197 - 4.25325i) q^{40} +(-3.47214 + 10.6861i) q^{41} +(2.23607 + 1.62460i) q^{42} +8.00000 q^{43} +2.94427 q^{45} +(-4.47214 - 3.24920i) q^{46} +(0.854102 - 2.62866i) q^{47} +(0.381966 + 1.17557i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(1.80902 - 1.31433i) q^{50} +(1.23607 + 3.80423i) q^{51} +(3.00000 - 9.23305i) q^{52} +(0.381966 + 0.277515i) q^{53} +12.3607 q^{54} +2.23607 q^{56} +(6.47214 + 4.70228i) q^{57} +(5.85410 - 18.0171i) q^{58} +(-0.381966 - 1.17557i) q^{59} +(-6.00000 + 4.35926i) q^{60} +(5.85410 - 4.25325i) q^{61} +(-1.90983 - 5.87785i) q^{62} +(-0.454915 + 1.40008i) q^{63} +(10.5172 + 7.64121i) q^{64} -6.47214 q^{65} +14.4721 q^{67} +(7.85410 + 5.70634i) q^{68} +(-0.944272 + 2.90617i) q^{69} +(-1.38197 - 4.25325i) q^{70} +(8.47214 - 6.15537i) q^{71} +(2.66312 - 1.93487i) q^{72} +(-0.236068 - 0.726543i) q^{73} +(-5.85410 + 18.0171i) q^{74} +(-1.00000 - 0.726543i) q^{75} +19.4164 q^{76} -8.94427 q^{78} +(7.23607 + 5.25731i) q^{79} +(0.618034 - 1.90211i) q^{80} +(-0.746711 - 2.29814i) q^{81} +(20.3262 - 14.7679i) q^{82} +(9.23607 - 6.71040i) q^{83} +(-1.14590 - 3.52671i) q^{84} +(2.00000 - 6.15537i) q^{85} +(-14.4721 - 10.5146i) q^{86} -10.4721 q^{87} +2.00000 q^{89} +(-5.32624 - 3.86974i) q^{90} +(1.00000 - 3.07768i) q^{91} +(2.29180 + 7.05342i) q^{92} +(-2.76393 + 2.00811i) q^{93} +(-5.00000 + 3.63271i) q^{94} +(-4.00000 - 12.3107i) q^{95} +(2.56231 - 7.88597i) q^{96} +(-14.0902 - 10.2371i) q^{97} +2.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{2} - 6 q^{3} - 3 q^{4} + 2 q^{5} - q^{7} + 5 q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q - 5 * q^2 - 6 * q^3 - 3 * q^4 + 2 * q^5 - q^7 + 5 * q^8 + 7 * q^9	\( 4 q - 5 q^{2} - 6 q^{3} - 3 q^{4} + 2 q^{5} - q^{7} + 5 q^{8} + 7 q^{9} + 12 q^{12} - 6 q^{13} + 5 q^{14} + 12 q^{15} + q^{16} + 6 q^{17} + 25 q^{18} + 8 q^{19} + 6 q^{20} + 4 q^{21} - 8 q^{23} + q^{25} - 3 q^{28} + 6 q^{29} - 20 q^{30} - 20 q^{34} + 2 q^{35} - 39 q^{36} - 6 q^{37} - 20 q^{38} + 4 q^{39} - 10 q^{40} + 4 q^{41} + 32 q^{43} - 24 q^{45} - 10 q^{47} + 6 q^{48} - q^{49} + 5 q^{50} - 4 q^{51} + 12 q^{52} + 6 q^{53} - 40 q^{54} + 8 q^{57} + 10 q^{58} - 6 q^{59} - 24 q^{60} + 10 q^{61} - 30 q^{62} - 13 q^{63} + 13 q^{64} - 8 q^{65} + 40 q^{67} + 18 q^{68} + 32 q^{69} - 10 q^{70} + 16 q^{71} - 5 q^{72} + 8 q^{73} - 10 q^{74} - 4 q^{75} + 24 q^{76} + 20 q^{79} - 2 q^{80} - 41 q^{81} + 50 q^{82} + 28 q^{83} - 18 q^{84} + 8 q^{85} - 40 q^{86} - 24 q^{87} + 8 q^{89} + 10 q^{90} + 4 q^{91} + 36 q^{92} - 20 q^{93} - 20 q^{94} - 16 q^{95} - 30 q^{96} - 34 q^{97}+O(q^{100}) \) 4 * q - 5 * q^2 - 6 * q^3 - 3 * q^4 + 2 * q^5 - q^7 + 5 * q^8 + 7 * q^9 + 12 * q^12 - 6 * q^13 + 5 * q^14 + 12 * q^15 + q^16 + 6 * q^17 + 25 * q^18 + 8 * q^19 + 6 * q^20 + 4 * q^21 - 8 * q^23 + q^25 - 3 * q^28 + 6 * q^29 - 20 * q^30 - 20 * q^34 + 2 * q^35 - 39 * q^36 - 6 * q^37 - 20 * q^38 + 4 * q^39 - 10 * q^40 + 4 * q^41 + 32 * q^43 - 24 * q^45 - 10 * q^47 + 6 * q^48 - q^49 + 5 * q^50 - 4 * q^51 + 12 * q^52 + 6 * q^53 - 40 * q^54 + 8 * q^57 + 10 * q^58 - 6 * q^59 - 24 * q^60 + 10 * q^61 - 30 * q^62 - 13 * q^63 + 13 * q^64 - 8 * q^65 + 40 * q^67 + 18 * q^68 + 32 * q^69 - 10 * q^70 + 16 * q^71 - 5 * q^72 + 8 * q^73 - 10 * q^74 - 4 * q^75 + 24 * q^76 + 20 * q^79 - 2 * q^80 - 41 * q^81 + 50 * q^82 + 28 * q^83 - 18 * q^84 + 8 * q^85 - 40 * q^86 - 24 * q^87 + 8 * q^89 + 10 * q^90 + 4 * q^91 + 36 * q^92 - 20 * q^93 - 20 * q^94 - 16 * q^95 - 30 * q^96 - 34 * q^97

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