LMFDB - Embedded newform 121.2.c.e.27.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,2,Mod(3,121)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("121.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	121.c (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:	$0.966189864457$
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 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			27.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	121.27
Dual form			121.2.c.e.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.618034 - 1.90211i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-1.61803 + 1.17557i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.618034 - 1.90211i) q^{6} +(1.61803 - 1.17557i) q^{7} +(-0.618034 - 1.90211i) q^{9} +O(q^{10})$	\(q+(-0.618034 - 1.90211i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-1.61803 + 1.17557i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.618034 - 1.90211i) q^{6} +(1.61803 - 1.17557i) q^{7} +(-0.618034 - 1.90211i) q^{9} -2.00000 q^{10} -2.00000 q^{12} +(1.23607 + 3.80423i) q^{13} +(-3.23607 - 2.35114i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-0.618034 + 1.90211i) q^{17} +(-3.23607 + 2.35114i) q^{18} +(0.618034 + 1.90211i) q^{20} +2.00000 q^{21} -1.00000 q^{23} +(3.23607 + 2.35114i) q^{25} +(6.47214 - 4.70228i) q^{26} +(1.54508 - 4.75528i) q^{27} +(-1.23607 + 3.80423i) q^{28} +(-1.61803 - 1.17557i) q^{30} +(2.16312 + 6.65740i) q^{31} +8.00000 q^{32} +4.00000 q^{34} +(-0.618034 - 1.90211i) q^{35} +(3.23607 + 2.35114i) q^{36} +(-2.42705 + 1.76336i) q^{37} +(-1.23607 + 3.80423i) q^{39} +(6.47214 + 4.70228i) q^{41} +(-1.23607 - 3.80423i) q^{42} -6.00000 q^{43} -2.00000 q^{45} +(0.618034 + 1.90211i) q^{46} +(-6.47214 - 4.70228i) q^{47} +(-3.23607 + 2.35114i) q^{48} +(-0.927051 + 2.85317i) q^{49} +(2.47214 - 7.60845i) q^{50} +(-1.61803 + 1.17557i) q^{51} +(-6.47214 - 4.70228i) q^{52} +(-1.85410 - 5.70634i) q^{53} -10.0000 q^{54} +(-4.04508 + 2.93893i) q^{59} +(-0.618034 + 1.90211i) q^{60} +(3.70820 - 11.4127i) q^{61} +(11.3262 - 8.22899i) q^{62} +(-3.23607 - 2.35114i) q^{63} +(-2.47214 - 7.60845i) q^{64} +4.00000 q^{65} -7.00000 q^{67} +(-1.23607 - 3.80423i) q^{68} +(-0.809017 - 0.587785i) q^{69} +(-3.23607 + 2.35114i) q^{70} +(-0.927051 + 2.85317i) q^{71} +(-3.23607 + 2.35114i) q^{73} +(4.85410 + 3.52671i) q^{74} +(1.23607 + 3.80423i) q^{75} +8.00000 q^{78} +(-3.09017 - 9.51057i) q^{79} +(3.23607 + 2.35114i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(4.94427 - 15.2169i) q^{82} +(-1.85410 + 5.70634i) q^{83} +(-3.23607 + 2.35114i) q^{84} +(1.61803 + 1.17557i) q^{85} +(3.70820 + 11.4127i) q^{86} +15.0000 q^{89} +(1.23607 + 3.80423i) q^{90} +(6.47214 + 4.70228i) q^{91} +(1.61803 - 1.17557i) q^{92} +(-2.16312 + 6.65740i) q^{93} +(-4.94427 + 15.2169i) q^{94} +(6.47214 + 4.70228i) q^{96} +(-2.16312 - 6.65740i) q^{97} +6.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + q^{3} - 2 q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + q^3 - 2 * q^4 - q^5 - 2 * q^6 + 2 * q^7 + 2 * q^9	$ 4 q + 2 q^{2} + q^{3} - 2 q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{9} - 8 q^{10} - 8 q^{12} - 4 q^{13} - 4 q^{14} + q^{15} + 4 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{20} + 8 q^{21} - 4 q^{23} + 4 q^{25} + 8 q^{26} - 5 q^{27} + 4 q^{28} - 2 q^{30} - 7 q^{31} + 32 q^{32} + 16 q^{34} + 2 q^{35} + 4 q^{36} - 3 q^{37} + 4 q^{39} + 8 q^{41} + 4 q^{42} - 24 q^{43} - 8 q^{45} - 2 q^{46} - 8 q^{47} - 4 q^{48} + 3 q^{49} - 8 q^{50} - 2 q^{51} - 8 q^{52} + 6 q^{53} - 40 q^{54} - 5 q^{59} + 2 q^{60} - 12 q^{61} + 14 q^{62} - 4 q^{63} + 8 q^{64} + 16 q^{65} - 28 q^{67} + 4 q^{68} - q^{69} - 4 q^{70} + 3 q^{71} - 4 q^{73} + 6 q^{74} - 4 q^{75} + 32 q^{78} + 10 q^{79} + 4 q^{80} - q^{81} - 16 q^{82} + 6 q^{83} - 4 q^{84} + 2 q^{85} - 12 q^{86} + 60 q^{89} - 4 q^{90} + 8 q^{91} + 2 q^{92} + 7 q^{93} + 16 q^{94} + 8 q^{96} + 7 q^{97} + 24 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + q^3 - 2 * q^4 - q^5 - 2 * q^6 + 2 * q^7 + 2 * q^9 - 8 * q^10 - 8 * q^12 - 4 * q^13 - 4 * q^14 + q^15 + 4 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^20 + 8 * q^21 - 4 * q^23 + 4 * q^25 + 8 * q^26 - 5 * q^27 + 4 * q^28 - 2 * q^30 - 7 * q^31 + 32 * q^32 + 16 * q^34 + 2 * q^35 + 4 * q^36 - 3 * q^37 + 4 * q^39 + 8 * q^41 + 4 * q^42 - 24 * q^43 - 8 * q^45 - 2 * q^46 - 8 * q^47 - 4 * q^48 + 3 * q^49 - 8 * q^50 - 2 * q^51 - 8 * q^52 + 6 * q^53 - 40 * q^54 - 5 * q^59 + 2 * q^60 - 12 * q^61 + 14 * q^62 - 4 * q^63 + 8 * q^64 + 16 * q^65 - 28 * q^67 + 4 * q^68 - q^69 - 4 * q^70 + 3 * q^71 - 4 * q^73 + 6 * q^74 - 4 * q^75 + 32 * q^78 + 10 * q^79 + 4 * q^80 - q^81 - 16 * q^82 + 6 * q^83 - 4 * q^84 + 2 * q^85 - 12 * q^86 + 60 * q^89 - 4 * q^90 + 8 * q^91 + 2 * q^92 + 7 * q^93 + 16 * q^94 + 8 * q^96 + 7 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.618034	−	1.90211i	−0.437016	−	1.34500i	−0.891007	−	0.453990i	$-0.850000\pi$
$2$	−0.618034	−	1.90211i	−0.437016	−	1.34500i	0.453990	−	0.891007i	$-0.350000\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i	0.796305	−	0.604896i	$-0.206785\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i	−0.329218	+	0.944254i	$0.606785\pi$
$4$	−1.61803	+	1.17557i	−0.809017	+	0.587785i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i	−0.857877	−	0.513855i	$-0.828217\pi$
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i	0.996074	+	0.0885298i	$0.0282169\pi$
$6$	0.618034	−	1.90211i	0.252311	−	0.776534i
$7$	1.61803	−	1.17557i	0.611559	−	0.444324i	−0.238404	−	0.971166i	$-0.576624\pi$
$7$	1.61803	−	1.17557i	0.611559	−	0.444324i	0.849963	+	0.526842i	$0.176624\pi$
$8$		0			0
$9$	−0.618034	−	1.90211i	−0.206011	−	0.634038i
$10$	−2.00000			−0.632456
$11$		0			0
$11$		0			0
$12$	−2.00000			−0.577350
$13$	1.23607	+	3.80423i	0.342824	+	1.05510i	0.962739	+	0.270434i	$0.0871670\pi$
$13$	1.23607	+	3.80423i	0.342824	+	1.05510i	−0.619915	+	0.784669i	$0.712833\pi$
$14$	−3.23607	−	2.35114i	−0.864876	−	0.628369i
$15$	0.809017	−	0.587785i	0.208887	−	0.151765i
$16$	−1.23607	+	3.80423i	−0.309017	+	0.951057i
$17$	−0.618034	+	1.90211i	−0.149895	+	0.461330i	−0.997608	−	0.0691254i	$-0.977979\pi$
$17$	−0.618034	+	1.90211i	−0.149895	+	0.461330i	0.847713	+	0.530456i	$0.177979\pi$
$18$	−3.23607	+	2.35114i	−0.762749	+	0.554169i
$19$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$19$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$20$	0.618034	+	1.90211i	0.138197	+	0.425325i
$21$	2.00000			0.436436
$22$		0			0
$23$	−1.00000			−0.208514			−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000			−0.208514			−0.104257	+	0.994550i	$0.533247\pi$
$24$		0			0
$25$	3.23607	+	2.35114i	0.647214	+	0.470228i
$26$	6.47214	−	4.70228i	1.26929	−	0.922193i
$27$	1.54508	−	4.75528i	0.297352	−	0.915155i
$28$	−1.23607	+	3.80423i	−0.233595	+	0.718931i
$29$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$29$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$30$	−1.61803	−	1.17557i	−0.295411	−	0.214629i
$31$	2.16312	+	6.65740i	0.388508	+	1.19570i	0.933904	+	0.357525i	$0.116379\pi$
$31$	2.16312	+	6.65740i	0.388508	+	1.19570i	−0.545396	+	0.838179i	$0.683621\pi$
$32$	8.00000			1.41421
$33$		0			0
$34$	4.00000			0.685994
$35$	−0.618034	−	1.90211i	−0.104467	−	0.321516i
$36$	3.23607	+	2.35114i	0.539345	+	0.391857i
$37$	−2.42705	+	1.76336i	−0.399005	+	0.289894i	−0.769135	−	0.639086i	$-0.779313\pi$
$37$	−2.42705	+	1.76336i	−0.399005	+	0.289894i	0.370131	+	0.928980i	$0.379313\pi$
$38$		0			0
$39$	−1.23607	+	3.80423i	−0.197929	+	0.609164i
$40$		0			0
$41$	6.47214	+	4.70228i	1.01078	+	0.734373i	0.964372	−	0.264550i	$-0.0852233\pi$
$41$	6.47214	+	4.70228i	1.01078	+	0.734373i	0.0464057	+	0.998923i	$0.485223\pi$
$42$	−1.23607	−	3.80423i	−0.190729	−	0.587005i
$43$	−6.00000			−0.914991			−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000			−0.914991			−0.457496	+	0.889212i	$0.651253\pi$
$44$		0			0
$45$	−2.00000			−0.298142
$46$	0.618034	+	1.90211i	0.0911241	+	0.280451i
$47$	−6.47214	−	4.70228i	−0.944058	−	0.685898i	0.00533600	−	0.999986i	$-0.498301\pi$
$47$	−6.47214	−	4.70228i	−0.944058	−	0.685898i	−0.949394	+	0.314087i	$0.898301\pi$
$48$	−3.23607	+	2.35114i	−0.467086	+	0.339358i
$49$	−0.927051	+	2.85317i	−0.132436	+	0.407596i
$50$	2.47214	−	7.60845i	0.349613	−	1.07600i
$51$	−1.61803	+	1.17557i	−0.226570	+	0.164613i
$52$	−6.47214	−	4.70228i	−0.897524	−	0.652089i
$53$	−1.85410	−	5.70634i	−0.254680	−	0.783826i	−0.993892	−	0.110353i	$-0.964802\pi$
$53$	−1.85410	−	5.70634i	−0.254680	−	0.783826i	0.739212	−	0.673473i	$-0.235198\pi$
$54$	−10.0000			−1.36083
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.04508	+	2.93893i	−0.526625	+	0.382616i	−0.819094	−	0.573659i	$-0.805523\pi$
$59$	−4.04508	+	2.93893i	−0.526625	+	0.382616i	0.292469	+	0.956275i	$0.405523\pi$
$60$	−0.618034	+	1.90211i	−0.0797878	+	0.245562i
$61$	3.70820	−	11.4127i	0.474787	−	1.46124i	−0.371458	−	0.928450i	$-0.621142\pi$
$61$	3.70820	−	11.4127i	0.474787	−	1.46124i	0.846245	−	0.532794i	$-0.178858\pi$
$62$	11.3262	−	8.22899i	1.43843	−	1.04508i
$63$	−3.23607	−	2.35114i	−0.407706	−	0.296216i
$64$	−2.47214	−	7.60845i	−0.309017	−	0.951057i
$65$	4.00000			0.496139
$66$		0			0
$67$	−7.00000			−0.855186			−0.427593	−	0.903971i	$-0.640638\pi$
$67$	−7.00000			−0.855186			−0.427593	+	0.903971i	$0.640638\pi$
$68$	−1.23607	−	3.80423i	−0.149895	−	0.461330i
$69$	−0.809017	−	0.587785i	−0.0973942	−	0.0707610i
$70$	−3.23607	+	2.35114i	−0.386784	+	0.281015i
$71$	−0.927051	+	2.85317i	−0.110021	+	0.338609i	−0.990876	−	0.134777i	$-0.956968\pi$
$71$	−0.927051	+	2.85317i	−0.110021	+	0.338609i	0.880855	+	0.473386i	$0.156968\pi$
$72$		0			0
$73$	−3.23607	+	2.35114i	−0.378753	+	0.275180i	−0.760831	−	0.648950i	$-0.775209\pi$
$73$	−3.23607	+	2.35114i	−0.378753	+	0.275180i	0.382078	+	0.924130i	$0.375209\pi$
$74$	4.85410	+	3.52671i	0.564278	+	0.409972i
$75$	1.23607	+	3.80423i	0.142729	+	0.439274i
$76$		0			0
$77$		0			0
$78$	8.00000			0.905822
$79$	−3.09017	−	9.51057i	−0.347671	−	1.07002i	−0.960138	−	0.279526i	$-0.909823\pi$
$79$	−3.09017	−	9.51057i	−0.347671	−	1.07002i	0.612467	−	0.790496i	$-0.290177\pi$
$80$	3.23607	+	2.35114i	0.361803	+	0.262866i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	4.94427	−	15.2169i	0.546003	−	1.68043i
$83$	−1.85410	+	5.70634i	−0.203514	+	0.626352i	0.796257	+	0.604959i	$0.206810\pi$
$83$	−1.85410	+	5.70634i	−0.203514	+	0.626352i	−0.999771	+	0.0213936i	$0.993190\pi$
$84$	−3.23607	+	2.35114i	−0.353084	+	0.256531i
$85$	1.61803	+	1.17557i	0.175500	+	0.127509i
$86$	3.70820	+	11.4127i	0.399866	+	1.23066i
$87$		0			0
$88$		0			0
$89$	15.0000			1.59000			0.794998	−	0.606612i	$-0.207472\pi$
$89$	15.0000			1.59000			0.794998	+	0.606612i	$0.207472\pi$
$90$	1.23607	+	3.80423i	0.130293	+	0.401001i
$91$	6.47214	+	4.70228i	0.678464	+	0.492933i
$92$	1.61803	−	1.17557i	0.168692	−	0.122562i
$93$	−2.16312	+	6.65740i	−0.224305	+	0.690340i
$94$	−4.94427	+	15.2169i	−0.509963	+	1.56950i
$95$		0			0
$96$	6.47214	+	4.70228i	0.660560	+	0.479925i
$97$	−2.16312	−	6.65740i	−0.219631	−	0.675956i	−0.998792	−	0.0491321i	$-0.984354\pi$
$97$	−2.16312	−	6.65740i	−0.219631	−	0.675956i	0.779161	−	0.626824i	$-0.215646\pi$
$98$	6.00000			0.606092
$99$		0			0
$100$	−8.00000			−0.800000
$101$	0.618034	+	1.90211i	0.0614967	+	0.189267i	0.977085	−	0.212850i	$-0.0682745\pi$
$101$	0.618034	+	1.90211i	0.0614967	+	0.189267i	−0.915588	+	0.402117i	$0.868274\pi$
$102$	3.23607	+	2.35114i	0.320418	+	0.232798i
$103$	12.9443	−	9.40456i	1.27544	−	0.926659i	0.276032	−	0.961148i	$-0.410980\pi$
$103$	12.9443	−	9.40456i	1.27544	−	0.926659i	0.999405	+	0.0344892i	$0.0109804\pi$
$104$		0			0
$105$	0.618034	−	1.90211i	0.0603139	−	0.185627i
$106$	−9.70820	+	7.05342i	−0.942944	+	0.685089i
$107$	−14.5623	−	10.5801i	−1.40779	−	1.02282i	−0.993639	−	0.112613i	$-0.964078\pi$
$107$	−14.5623	−	10.5801i	−1.40779	−	1.02282i	−0.414152	−	0.910208i	$-0.635922\pi$
$108$	3.09017	+	9.51057i	0.297352	+	0.915155i
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$		0			0
$111$	−3.00000			−0.284747
$112$	2.47214	+	7.60845i	0.233595	+	0.718931i
$113$	−7.28115	−	5.29007i	−0.684953	−	0.497648i	0.190044	−	0.981776i	$-0.439137\pi$
$113$	−7.28115	−	5.29007i	−0.684953	−	0.497648i	−0.874997	+	0.484128i	$0.839137\pi$
$114$		0			0
$115$	−0.309017	+	0.951057i	−0.0288160	+	0.0886865i
$116$		0			0
$117$	6.47214	−	4.70228i	0.598349	−	0.434726i
$118$	8.09017	+	5.87785i	0.744761	+	0.541100i
$119$	1.23607	+	3.80423i	0.113310	+	0.348733i
$120$		0			0
$121$		0			0
$122$	−24.0000			−2.17286
$123$	2.47214	+	7.60845i	0.222905	+	0.686031i
$124$	−11.3262	−	8.22899i	−1.01713	−	0.738985i
$125$	7.28115	−	5.29007i	0.651246	−	0.473158i
$126$	−2.47214	+	7.60845i	−0.220235	+	0.677815i
$127$	2.47214	−	7.60845i	0.219367	−	0.675141i	−0.779448	−	0.626467i	$-0.784500\pi$
$127$	2.47214	−	7.60845i	0.219367	−	0.675141i	0.998815	−	0.0486742i	$-0.0154996\pi$
$128$		0			0
$129$	−4.85410	−	3.52671i	−0.427380	−	0.310510i
$130$	−2.47214	−	7.60845i	−0.216821	−	0.667305i
$131$	−18.0000			−1.57267			−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000			−1.57267			−0.786334	+	0.617802i	$0.788023\pi$
$132$		0			0
$133$		0			0
$134$	4.32624	+	13.3148i	0.373730	+	1.15022i
$135$	−4.04508	−	2.93893i	−0.348145	−	0.252942i
$136$		0			0
$137$	−2.16312	+	6.65740i	−0.184808	+	0.568780i	−0.999945	−	0.0104881i	$-0.996661\pi$
$137$	−2.16312	+	6.65740i	−0.184808	+	0.568780i	0.815137	+	0.579268i	$0.196661\pi$
$138$	−0.618034	+	1.90211i	−0.0526105	+	0.161919i
$139$	−8.09017	+	5.87785i	−0.686199	+	0.498553i	−0.875409	−	0.483384i	$-0.839408\pi$
$139$	−8.09017	+	5.87785i	−0.686199	+	0.498553i	0.189209	+	0.981937i	$0.439408\pi$
$140$	3.23607	+	2.35114i	0.273498	+	0.198708i
$141$	−2.47214	−	7.60845i	−0.208191	−	0.640747i
$142$	6.00000			0.503509
$143$		0			0
$144$	8.00000			0.666667
$145$		0			0
$146$	6.47214	+	4.70228i	0.535638	+	0.389164i
$147$	−2.42705	+	1.76336i	−0.200180	+	0.145439i
$148$	1.85410	−	5.70634i	0.152406	−	0.469058i
$149$	−3.09017	+	9.51057i	−0.253157	+	0.779136i	0.741031	+	0.671471i	$0.234337\pi$
$149$	−3.09017	+	9.51057i	−0.253157	+	0.779136i	−0.994187	+	0.107665i	$0.965663\pi$
$150$	6.47214	−	4.70228i	0.528448	−	0.383940i
$151$	−1.61803	−	1.17557i	−0.131674	−	0.0956666i	0.519999	−	0.854167i	$-0.325932\pi$
$151$	−1.61803	−	1.17557i	−0.131674	−	0.0956666i	−0.651673	+	0.758500i	$0.725932\pi$
$152$		0			0
$153$	4.00000			0.323381
$154$		0			0
$155$	7.00000			0.562254
$156$	−2.47214	−	7.60845i	−0.197929	−	0.609164i
$157$	5.66312	+	4.11450i	0.451966	+	0.328373i	0.790372	−	0.612628i	$-0.209888\pi$
$157$	5.66312	+	4.11450i	0.451966	+	0.328373i	−0.338405	+	0.941000i	$0.609888\pi$
$158$	−16.1803	+	11.7557i	−1.28724	+	0.935234i
$159$	1.85410	−	5.70634i	0.147040	−	0.452542i
$160$	2.47214	−	7.60845i	0.195440	−	0.601501i
$161$	−1.61803	+	1.17557i	−0.127519	+	0.0926479i
$162$	1.61803	+	1.17557i	0.127125	+	0.0923615i
$163$	1.23607	+	3.80423i	0.0968163	+	0.297970i	0.987723	−	0.156217i	$-0.0499299\pi$
$163$	1.23607	+	3.80423i	0.0968163	+	0.297970i	−0.890906	+	0.454187i	$0.849930\pi$
$164$	−16.0000			−1.24939
$165$		0			0
$166$	12.0000			0.931381
$167$	−3.70820	−	11.4127i	−0.286949	−	0.883140i	−0.985808	−	0.167879i	$-0.946308\pi$
$167$	−3.70820	−	11.4127i	−0.286949	−	0.883140i	0.698858	−	0.715260i	$-0.253692\pi$
$168$		0			0
$169$	−2.42705	+	1.76336i	−0.186696	+	0.135643i
$170$	1.23607	−	3.80423i	0.0948021	−	0.291771i
$171$		0			0
$172$	9.70820	−	7.05342i	0.740244	−	0.537818i
$173$	4.85410	+	3.52671i	0.369051	+	0.268131i	0.756817	−	0.653627i	$-0.226753\pi$
$173$	4.85410	+	3.52671i	0.369051	+	0.268131i	−0.387767	+	0.921758i	$0.626753\pi$
$174$		0			0
$175$	8.00000			0.604743
$176$		0			0
$177$	−5.00000			−0.375823
$178$	−9.27051	−	28.5317i	−0.694854	−	2.13854i
$179$	12.1353	+	8.81678i	0.907032	+	0.658997i	0.940262	−	0.340451i	$-0.110580\pi$
$179$	12.1353	+	8.81678i	0.907032	+	0.658997i	−0.0332308	+	0.999448i	$0.510580\pi$
$180$	3.23607	−	2.35114i	0.241202	−	0.175244i
$181$	2.16312	−	6.65740i	0.160783	−	0.494840i	−0.837918	−	0.545797i	$-0.816227\pi$
$181$	2.16312	−	6.65740i	0.160783	−	0.494840i	0.998701	+	0.0509566i	$0.0162270\pi$
$182$	4.94427	−	15.2169i	0.366494	−	1.12795i
$183$	9.70820	−	7.05342i	0.717651	−	0.521404i
$184$		0			0
$185$	0.927051	+	2.85317i	0.0681581	+	0.209769i
$186$	14.0000			1.02653
$187$		0			0
$188$	16.0000			1.16692
$189$	−3.09017	−	9.51057i	−0.224777	−	0.691792i
$190$		0			0
$191$	−13.7533	+	9.99235i	−0.995153	+	0.723021i	−0.961044	−	0.276397i	$-0.910860\pi$
$191$	−13.7533	+	9.99235i	−0.995153	+	0.723021i	−0.0341095	+	0.999418i	$0.510860\pi$
$192$	2.47214	−	7.60845i	0.178411	−	0.549093i
$193$	1.23607	−	3.80423i	0.0889741	−	0.273834i	−0.896662	−	0.442715i	$-0.854015\pi$
$193$	1.23607	−	3.80423i	0.0889741	−	0.273834i	0.985636	+	0.168881i	$0.0540153\pi$
$194$	−11.3262	+	8.22899i	−0.813176	+	0.590807i
$195$	3.23607	+	2.35114i	0.231740	+	0.168369i
$196$	−1.85410	−	5.70634i	−0.132436	−	0.407596i
$197$	−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
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$		0			0
$201$	−5.66312	−	4.11450i	−0.399446	−	0.290214i
$202$	3.23607	−	2.35114i	0.227689	−	0.165426i
$203$		0			0
$204$	1.23607	−	3.80423i	0.0865421	−	0.266349i
$205$	6.47214	−	4.70228i	0.452034	−	0.328422i
$206$	−25.8885	−	18.8091i	−1.80374	−	1.31049i
$207$	0.618034	+	1.90211i	0.0429563	+	0.132206i
$208$	−16.0000			−1.10940
$209$		0			0
$210$	−4.00000			−0.276026
$211$	3.70820	+	11.4127i	0.255283	+	0.785681i	0.993774	+	0.111417i	$0.0355390\pi$
$211$	3.70820	+	11.4127i	0.255283	+	0.785681i	−0.738490	+	0.674264i	$0.764461\pi$
$212$	9.70820	+	7.05342i	0.666762	+	0.484431i
$213$	−2.42705	+	1.76336i	−0.166299	+	0.120823i
$214$	−11.1246	+	34.2380i	−0.760463	+	2.34046i
$215$	−1.85410	+	5.70634i	−0.126449	+	0.389169i
$216$		0			0
$217$	11.3262	+	8.22899i	0.768875	+	0.558620i
$218$	−6.18034	−	19.0211i	−0.418585	−	1.28827i
$219$	−4.00000			−0.270295
$220$		0			0
$221$	−8.00000			−0.538138
$222$	1.85410	+	5.70634i	0.124439	+	0.382984i
$223$	−15.3713	−	11.1679i	−1.02934	−	0.747859i	−0.0611635	−	0.998128i	$-0.519481\pi$
$223$	−15.3713	−	11.1679i	−1.02934	−	0.747859i	−0.968176	+	0.250269i	$0.919481\pi$
$224$	12.9443	−	9.40456i	0.864876	−	0.628369i
$225$	2.47214	−	7.60845i	0.164809	−	0.507230i
$226$	−5.56231	+	17.1190i	−0.369999	+	1.13874i
$227$	−14.5623	+	10.5801i	−0.966534	+	0.702228i	−0.954659	−	0.297701i	$-0.903780\pi$
$227$	−14.5623	+	10.5801i	−0.966534	+	0.702228i	−0.0118751	+	0.999929i	$0.503780\pi$
$228$		0			0
$229$	4.63525	+	14.2658i	0.306306	+	0.942714i	0.979187	+	0.202962i	$0.0650569\pi$
$229$	4.63525	+	14.2658i	0.306306	+	0.942714i	−0.672880	+	0.739751i	$0.734943\pi$
$230$	2.00000			0.131876
$231$		0			0
$232$		0			0
$233$	7.41641	+	22.8254i	0.485865	+	1.49534i	0.830724	+	0.556684i	$0.187927\pi$
$233$	7.41641	+	22.8254i	0.485865	+	1.49534i	−0.344859	+	0.938654i	$0.612073\pi$
$234$	−12.9443	−	9.40456i	−0.846194	−	0.614796i
$235$	−6.47214	+	4.70228i	−0.422196	+	0.306743i
$236$	3.09017	−	9.51057i	0.201153	−	0.619085i
$237$	3.09017	−	9.51057i	0.200728	−	0.617778i
$238$	6.47214	−	4.70228i	0.419526	−	0.304804i
$239$	24.2705	+	17.6336i	1.56993	+	1.14062i	0.927225	+	0.374505i	$0.122188\pi$
$239$	24.2705	+	17.6336i	1.56993	+	1.14062i	0.642704	+	0.766115i	$0.277812\pi$
$240$	1.23607	+	3.80423i	0.0797878	+	0.245562i
$241$	−8.00000			−0.515325			−0.257663	−	0.966235i	$-0.582952\pi$
$241$	−8.00000			−0.515325			−0.257663	+	0.966235i	$0.582952\pi$
$242$		0			0
$243$	−16.0000			−1.02640
$244$	7.41641	+	22.8254i	0.474787	+	1.46124i
$245$	2.42705	+	1.76336i	0.155059	+	0.112657i
$246$	12.9443	−	9.40456i	0.825297	−	0.599613i
$247$		0			0
$248$		0			0
$249$	−4.85410	+	3.52671i	−0.307616	+	0.223496i
$250$	−14.5623	−	10.5801i	−0.921001	−	0.669146i
$251$	−7.10739	−	21.8743i	−0.448615	−	1.38069i	−0.878471	−	0.477796i	$-0.841436\pi$
$251$	−7.10739	−	21.8743i	−0.448615	−	1.38069i	0.429856	−	0.902897i	$-0.358564\pi$
$252$	8.00000			0.503953
$253$		0			0
$254$	−16.0000			−1.00393
$255$	0.618034	+	1.90211i	0.0387028	+	0.119115i
$256$	−12.9443	−	9.40456i	−0.809017	−	0.587785i
$257$	1.61803	−	1.17557i	0.100930	−	0.0733301i	−0.536175	−	0.844107i	$-0.680131\pi$
$257$	1.61803	−	1.17557i	0.100930	−	0.0733301i	0.637106	+	0.770776i	$0.280131\pi$
$258$	−3.70820	+	11.4127i	−0.230863	+	0.710522i
$259$	−1.85410	+	5.70634i	−0.115208	+	0.354575i
$260$	−6.47214	+	4.70228i	−0.401385	+	0.291623i
$261$		0			0
$262$	11.1246	+	34.2380i	0.687281	+	2.11523i
$263$	14.0000			0.863277			0.431638	−	0.902047i	$-0.357936\pi$
$263$	14.0000			0.863277			0.431638	+	0.902047i	$0.357936\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$		0			0
$267$	12.1353	+	8.81678i	0.742666	+	0.539578i
$268$	11.3262	−	8.22899i	0.691860	−	0.502666i
$269$	3.09017	−	9.51057i	0.188411	−	0.579869i	−0.811579	−	0.584242i	$-0.801392\pi$
$269$	3.09017	−	9.51057i	0.188411	−	0.579869i	0.999990	+	0.00437267i	$0.00139187\pi$
$270$	−3.09017	+	9.51057i	−0.188062	+	0.578795i
$271$	22.6525	−	16.4580i	1.37604	−	0.999752i	0.378802	−	0.925478i	$-0.376336\pi$
$271$	22.6525	−	16.4580i	1.37604	−	0.999752i	0.997238	−	0.0742738i	$-0.0236639\pi$
$272$	−6.47214	−	4.70228i	−0.392431	−	0.285118i
$273$	2.47214	+	7.60845i	0.149620	+	0.460484i
$274$	14.0000			0.845771
$275$		0			0
$276$	2.00000			0.120386
$277$	−0.618034	−	1.90211i	−0.0371341	−	0.114287i	0.930771	−	0.365602i	$-0.119137\pi$
$277$	−0.618034	−	1.90211i	−0.0371341	−	0.114287i	−0.967905	+	0.251315i	$0.919137\pi$
$278$	16.1803	+	11.7557i	0.970432	+	0.705060i
$279$	11.3262	−	8.22899i	0.678084	−	0.492657i
$280$		0			0
$281$	−5.56231	+	17.1190i	−0.331819	+	1.02123i	0.636448	+	0.771319i	$0.280403\pi$
$281$	−5.56231	+	17.1190i	−0.331819	+	1.02123i	−0.968268	+	0.249916i	$0.919597\pi$
$282$	−12.9443	+	9.40456i	−0.770820	+	0.560034i
$283$	−3.23607	−	2.35114i	−0.192364	−	0.139761i	0.487434	−	0.873160i	$-0.337933\pi$
$283$	−3.23607	−	2.35114i	−0.192364	−	0.139761i	−0.679799	+	0.733399i	$0.737933\pi$
$284$	−1.85410	−	5.70634i	−0.110021	−	0.338609i
$285$		0			0
$286$		0			0
$287$	16.0000			0.944450
$288$	−4.94427	−	15.2169i	−0.291344	−	0.896665i
$289$	10.5172	+	7.64121i	0.618660	+	0.449483i
$290$		0			0
$291$	2.16312	−	6.65740i	0.126804	−	0.390263i
$292$	2.47214	−	7.60845i	0.144671	−	0.445251i
$293$	−19.4164	+	14.1068i	−1.13432	+	0.824131i	−0.986318	−	0.164856i	$-0.947284\pi$
$293$	−19.4164	+	14.1068i	−1.13432	+	0.824131i	−0.148001	+	0.988987i	$0.547284\pi$
$294$	4.85410	+	3.52671i	0.283097	+	0.205682i
$295$	1.54508	+	4.75528i	0.0899583	+	0.276863i
$296$		0			0
$297$		0			0
$298$	20.0000			1.15857
$299$	−1.23607	−	3.80423i	−0.0714837	−	0.220004i
$300$	−6.47214	−	4.70228i	−0.373669	−	0.271486i
$301$	−9.70820	+	7.05342i	−0.559572	+	0.406553i
$302$	−1.23607	+	3.80423i	−0.0711277	+	0.218909i
$303$	−0.618034	+	1.90211i	−0.0355051	+	0.109274i
$304$		0			0
$305$	−9.70820	−	7.05342i	−0.555890	−	0.403878i
$306$	−2.47214	−	7.60845i	−0.141323	−	0.434946i
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$		0			0
$309$	16.0000			0.910208
$310$	−4.32624	−	13.3148i	−0.245714	−	0.756229i
$311$	−9.70820	−	7.05342i	−0.550502	−	0.399963i	0.277469	−	0.960735i	$-0.410505\pi$
$311$	−9.70820	−	7.05342i	−0.550502	−	0.399963i	−0.827970	+	0.560772i	$0.810505\pi$
$312$		0			0
$313$	−0.309017	+	0.951057i	−0.0174667	+	0.0537569i	−0.959410	−	0.282015i	$-0.908997\pi$
$313$	−0.309017	+	0.951057i	−0.0174667	+	0.0537569i	0.941943	+	0.335772i	$0.108997\pi$
$314$	4.32624	−	13.3148i	0.244144	−	0.751397i
$315$	−3.23607	+	2.35114i	−0.182332	+	0.132472i
$316$	16.1803	+	11.7557i	0.910215	+	0.661310i
$317$	4.01722	+	12.3637i	0.225630	+	0.694417i	0.998227	+	0.0595204i	$0.0189571\pi$
$317$	4.01722	+	12.3637i	0.225630	+	0.694417i	−0.772597	+	0.634896i	$0.781043\pi$
$318$	−12.0000			−0.672927
$319$		0			0
$320$	−8.00000			−0.447214
$321$	−5.56231	−	17.1190i	−0.310458	−	0.955490i
$322$	3.23607	+	2.35114i	0.180339	+	0.131024i
$323$		0			0
$324$	0.618034	−	1.90211i	0.0343352	−	0.105673i
$325$	−4.94427	+	15.2169i	−0.274259	+	0.844082i
$326$	6.47214	−	4.70228i	0.358458	−	0.260435i
$327$	8.09017	+	5.87785i	0.447387	+	0.325046i
$328$		0			0
$329$	−16.0000			−0.882109
$330$		0			0
$331$	7.00000			0.384755			0.192377	−	0.981321i	$-0.438380\pi$
$331$	7.00000			0.384755			0.192377	+	0.981321i	$0.438380\pi$
$332$	−3.70820	−	11.4127i	−0.203514	−	0.626352i
$333$	4.85410	+	3.52671i	0.266003	+	0.193263i
$334$	−19.4164	+	14.1068i	−1.06242	+	0.771892i
$335$	−2.16312	+	6.65740i	−0.118184	+	0.363732i
$336$	−2.47214	+	7.60845i	−0.134866	+	0.415075i
$337$	17.7984	−	12.9313i	0.969539	−	0.704411i	0.0141927	−	0.999899i	$-0.495482\pi$
$337$	17.7984	−	12.9313i	0.969539	−	0.704411i	0.955347	+	0.295488i	$0.0954822\pi$
$338$	4.85410	+	3.52671i	0.264028	+	0.191828i
$339$	−2.78115	−	8.55951i	−0.151051	−	0.464889i
$340$	−4.00000			−0.216930
$341$		0			0
$342$		0			0
$343$	6.18034	+	19.0211i	0.333707	+	1.02704i
$344$		0			0
$345$	−0.809017	+	0.587785i	−0.0435560	+	0.0316453i
$346$	3.70820	−	11.4127i	0.199354	−	0.613549i
$347$	8.65248	−	26.6296i	0.464489	−	1.42955i	−0.395135	−	0.918623i	$-0.629302\pi$
$347$	8.65248	−	26.6296i	0.464489	−	1.42955i	0.859624	−	0.510928i	$-0.170698\pi$
$348$		0			0
$349$	−24.2705	−	17.6336i	−1.29917	−	0.943903i	−0.299223	−	0.954183i	$-0.596728\pi$
$349$	−24.2705	−	17.6336i	−1.29917	−	0.943903i	−0.999947	+	0.0102804i	$0.996728\pi$
$350$	−4.94427	−	15.2169i	−0.264282	−	0.813378i
$351$	20.0000			1.06752
$352$		0			0
$353$	−21.0000			−1.11772			−0.558859	−	0.829263i	$-0.688761\pi$
$353$	−21.0000			−1.11772			−0.558859	+	0.829263i	$0.688761\pi$
$354$	3.09017	+	9.51057i	0.164241	+	0.505481i
$355$	2.42705	+	1.76336i	0.128814	+	0.0935892i
$356$	−24.2705	+	17.6336i	−1.28633	+	0.934577i
$357$	−1.23607	+	3.80423i	−0.0654197	+	0.201341i
$358$	9.27051	−	28.5317i	0.489962	−	1.50795i
$359$	16.1803	−	11.7557i	0.853966	−	0.620442i	−0.0722709	−	0.997385i	$-0.523025\pi$
$359$	16.1803	−	11.7557i	0.853966	−	0.620442i	0.926237	+	0.376943i	$0.123025\pi$
$360$		0			0
$361$	−5.87132	−	18.0701i	−0.309017	−	0.951057i
$362$	−14.0000			−0.735824
$363$		0			0
$364$	−16.0000			−0.838628
$365$	1.23607	+	3.80423i	0.0646988	+	0.199122i
$366$	−19.4164	−	14.1068i	−1.01491	−	0.737377i
$367$	13.7533	−	9.99235i	0.717916	−	0.521596i	−0.167802	−	0.985821i	$-0.553667\pi$
$367$	13.7533	−	9.99235i	0.717916	−	0.521596i	0.885718	+	0.464224i	$0.153667\pi$
$368$	1.23607	−	3.80423i	0.0644345	−	0.198309i
$369$	4.94427	−	15.2169i	0.257389	−	0.792160i
$370$	4.85410	−	3.52671i	0.252353	−	0.183345i
$371$	−9.70820	−	7.05342i	−0.504025	−	0.366195i
$372$	−4.32624	−	13.3148i	−0.224305	−	0.690340i
$373$	−26.0000			−1.34623			−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000			−1.34623			−0.673114	+	0.739538i	$0.735044\pi$
$374$		0			0
$375$	9.00000			0.464758
$376$		0			0
$377$		0			0
$378$	−16.1803	+	11.7557i	−0.832227	+	0.604648i
$379$	−1.54508	+	4.75528i	−0.0793657	+	0.244262i	−0.982865	−	0.184327i	$-0.940989\pi$
$379$	−1.54508	+	4.75528i	−0.0793657	+	0.244262i	0.903499	+	0.428590i	$0.140989\pi$
$380$		0			0
$381$	6.47214	−	4.70228i	0.331578	−	0.240905i
$382$	27.5066	+	19.9847i	1.40736	+	1.02251i
$383$	−0.309017	−	0.951057i	−0.0157900	−	0.0485967i	0.942851	−	0.333214i	$-0.108133\pi$
$383$	−0.309017	−	0.951057i	−0.0157900	−	0.0485967i	−0.958641	+	0.284618i	$0.908133\pi$
$384$		0			0
$385$		0			0
$386$	−8.00000			−0.407189
$387$	3.70820	+	11.4127i	0.188499	+	0.580139i
$388$	11.3262	+	8.22899i	0.575003	+	0.417764i
$389$	12.1353	−	8.81678i	0.615282	−	0.447028i	−0.235988	−	0.971756i	$-0.575833\pi$
$389$	12.1353	−	8.81678i	0.615282	−	0.447028i	0.851270	+	0.524727i	$0.175833\pi$
$390$	2.47214	−	7.60845i	0.125181	−	0.385269i
$391$	0.618034	−	1.90211i	0.0312553	−	0.0961940i
$392$		0			0
$393$	−14.5623	−	10.5801i	−0.734571	−	0.533697i
$394$	1.23607	+	3.80423i	0.0622722	+	0.191654i
$395$	−10.0000			−0.503155
$396$		0			0
$397$	−2.00000			−0.100377			−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000			−0.100377			−0.0501886	+	0.998740i	$0.515982\pi$
$398$		0			0
$399$		0			0
$400$	−12.9443	+	9.40456i	−0.647214	+	0.470228i
$401$	0.618034	−	1.90211i	0.0308631	−	0.0949870i	−0.934438	−	0.356125i	$-0.884098\pi$
$401$	0.618034	−	1.90211i	0.0308631	−	0.0949870i	0.965301	+	0.261138i	$0.0840977\pi$
$402$	−4.32624	+	13.3148i	−0.215773	+	0.664081i
$403$	−22.6525	+	16.4580i	−1.12840	+	0.819831i
$404$	−3.23607	−	2.35114i	−0.161000	−	0.116974i
$405$	0.309017	+	0.951057i	0.0153552	+	0.0472584i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−9.27051	−	28.5317i	−0.458397	−	1.41080i	−0.867100	−	0.498134i	$-0.834019\pi$
$409$	−9.27051	−	28.5317i	−0.458397	−	1.41080i	0.408703	−	0.912668i	$-0.365981\pi$
$410$	−12.9443	−	9.40456i	−0.639272	−	0.464458i
$411$	−5.66312	+	4.11450i	−0.279341	+	0.202953i
$412$	−9.88854	+	30.4338i	−0.487174	+	1.49937i
$413$	−3.09017	+	9.51057i	−0.152057	+	0.467984i
$414$	3.23607	−	2.35114i	0.159044	−	0.115552i
$415$	4.85410	+	3.52671i	0.238278	+	0.173119i
$416$	9.88854	+	30.4338i	0.484826	+	1.49214i
$417$	−10.0000			−0.489702
$418$		0			0
$419$	20.0000			0.977064			0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000			0.977064			0.488532	+	0.872546i	$0.337533\pi$
$420$	1.23607	+	3.80423i	0.0603139	+	0.185627i
$421$	−17.7984	−	12.9313i	−0.867440	−	0.630232i	0.0624590	−	0.998048i	$-0.480106\pi$
$421$	−17.7984	−	12.9313i	−0.867440	−	0.630232i	−0.929899	+	0.367816i	$0.880106\pi$
$422$	19.4164	−	14.1068i	0.945176	−	0.686711i
$423$	−4.94427	+	15.2169i	−0.240399	+	0.739871i
$424$		0			0
$425$	−6.47214	+	4.70228i	−0.313945	+	0.228094i
$426$	4.85410	+	3.52671i	0.235182	+	0.170870i
$427$	−7.41641	−	22.8254i	−0.358905	−	1.10460i
$428$	36.0000			1.74013
$429$		0			0
$430$	12.0000			0.578691
$431$	−5.56231	−	17.1190i	−0.267927	−	0.824594i	−0.991005	−	0.133827i	$-0.957273\pi$
$431$	−5.56231	−	17.1190i	−0.267927	−	0.824594i	0.723078	−	0.690767i	$-0.242727\pi$
$432$	16.1803	+	11.7557i	0.778477	+	0.565597i
$433$	8.89919	−	6.46564i	0.427668	−	0.310719i	−0.353048	−	0.935605i	$-0.614855\pi$
$433$	8.89919	−	6.46564i	0.427668	−	0.310719i	0.780716	+	0.624886i	$0.214855\pi$
$434$	8.65248	−	26.6296i	0.415332	−	1.27826i
$435$		0			0
$436$	−16.1803	+	11.7557i	−0.774898	+	0.562996i
$437$		0			0
$438$	2.47214	+	7.60845i	0.118123	+	0.363546i
$439$	40.0000			1.90910			0.954548	−	0.298057i	$-0.0963387\pi$
$439$	40.0000			1.90910			0.954548	+	0.298057i	$0.0963387\pi$
$440$		0			0
$441$	6.00000			0.285714
$442$	4.94427	+	15.2169i	0.235175	+	0.723794i
$443$	8.89919	+	6.46564i	0.422813	+	0.307192i	0.778769	−	0.627311i	$-0.215845\pi$
$443$	8.89919	+	6.46564i	0.422813	+	0.307192i	−0.355956	+	0.934503i	$0.615845\pi$
$444$	4.85410	−	3.52671i	0.230365	−	0.167370i
$445$	4.63525	−	14.2658i	0.219732	−	0.676266i
$446$	−11.7426	+	36.1401i	−0.556030	+	1.71129i
$447$	−8.09017	+	5.87785i	−0.382652	+	0.278013i
$448$	−12.9443	−	9.40456i	−0.611559	−	0.444324i
$449$	10.8156	+	33.2870i	0.510419	+	1.57091i	0.791465	+	0.611215i	$0.209319\pi$
$449$	10.8156	+	33.2870i	0.510419	+	1.57091i	−0.281045	+	0.959695i	$0.590681\pi$
$450$	−16.0000			−0.754247
$451$		0			0
$452$	18.0000			0.846649
$453$	−0.618034	−	1.90211i	−0.0290378	−	0.0893691i
$454$	29.1246	+	21.1603i	1.36689	+	0.993101i
$455$	6.47214	−	4.70228i	0.303418	−	0.220446i
$456$		0			0
$457$	−3.70820	+	11.4127i	−0.173462	+	0.533863i	−0.999560	−	0.0296647i	$-0.990556\pi$
$457$	−3.70820	+	11.4127i	−0.173462	+	0.533863i	0.826097	+	0.563527i	$0.190556\pi$
$458$	24.2705	−	17.6336i	1.13409	−	0.823962i
$459$	8.09017	+	5.87785i	0.377617	+	0.274355i
$460$	−0.618034	−	1.90211i	−0.0288160	−	0.0886865i
$461$	12.0000			0.558896			0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000			0.558896			0.279448	+	0.960161i	$0.409849\pi$
$462$		0			0
$463$	−11.0000			−0.511213			−0.255607	−	0.966781i	$-0.582275\pi$
$463$	−11.0000			−0.511213			−0.255607	+	0.966781i	$0.582275\pi$
$464$		0			0
$465$	5.66312	+	4.11450i	0.262621	+	0.190805i
$466$	38.8328	−	28.2137i	1.79890	−	1.30697i
$467$	−8.34346	+	25.6785i	−0.386089	+	1.18826i	0.549598	+	0.835429i	$0.314781\pi$
$467$	−8.34346	+	25.6785i	−0.386089	+	1.18826i	−0.935687	+	0.352831i	$0.885219\pi$
$468$	−4.94427	+	15.2169i	−0.228549	+	0.703402i
$469$	−11.3262	+	8.22899i	−0.522997	+	0.379980i
$470$	12.9443	+	9.40456i	0.597075	+	0.433800i
$471$	2.16312	+	6.65740i	0.0996713	+	0.306757i
$472$		0			0
$473$		0			0
$474$	−20.0000			−0.918630
$475$		0			0
$476$	−6.47214	−	4.70228i	−0.296650	−	0.215529i
$477$	−9.70820	+	7.05342i	−0.444508	+	0.322954i
$478$	18.5410	−	57.0634i	0.848047	−	2.61002i
$479$	6.18034	−	19.0211i	0.282387	−	0.869098i	−0.704783	−	0.709423i	$-0.748956\pi$
$479$	6.18034	−	19.0211i	0.282387	−	0.869098i	0.987170	−	0.159674i	$-0.0510445\pi$
$480$	6.47214	−	4.70228i	0.295411	−	0.214629i
$481$	−9.70820	−	7.05342i	−0.442656	−	0.321608i
$482$	4.94427	+	15.2169i	0.225205	+	0.693111i
$483$	−2.00000			−0.0910032
$484$		0			0
$485$	−7.00000			−0.317854
$486$	9.88854	+	30.4338i	0.448553	+	1.38051i
$487$	−18.6074	−	13.5191i	−0.843181	−	0.612607i	0.0800762	−	0.996789i	$-0.474484\pi$
$487$	−18.6074	−	13.5191i	−0.843181	−	0.612607i	−0.923258	+	0.384182i	$0.874484\pi$
$488$		0			0
$489$	−1.23607	+	3.80423i	−0.0558969	+	0.172033i
$490$	1.85410	−	5.70634i	0.0837598	−	0.257786i
$491$	6.47214	−	4.70228i	0.292083	−	0.212211i	−0.432087	−	0.901832i	$-0.642223\pi$
$491$	6.47214	−	4.70228i	0.292083	−	0.212211i	0.724171	+	0.689621i	$0.242223\pi$
$492$	−12.9443	−	9.40456i	−0.583573	−	0.423990i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−28.0000			−1.25724
$497$	1.85410	+	5.70634i	0.0831678	+	0.255964i
$498$	9.70820	+	7.05342i	0.435035	+	0.316071i
$499$	−16.1803	+	11.7557i	−0.724331	+	0.526258i	−0.887765	−	0.460297i	$-0.847743\pi$
$499$	−16.1803	+	11.7557i	−0.724331	+	0.526258i	0.163434	+	0.986554i	$0.447743\pi$
$500$	−5.56231	+	17.1190i	−0.248754	+	0.765586i
$501$	3.70820	−	11.4127i	0.165670	−	0.509881i
$502$	−37.2148	+	27.0381i	−1.66098	+	1.20677i
$503$	21.0344	+	15.2824i	0.937879	+	0.681409i	0.947909	−	0.318540i	$-0.103193\pi$
$503$	21.0344	+	15.2824i	0.937879	+	0.681409i	−0.0100299	+	0.999950i	$0.503193\pi$
$504$		0			0
$505$	2.00000			0.0889988
$506$		0			0
$507$	−3.00000			−0.133235
$508$	4.94427	+	15.2169i	0.219367	+	0.675141i
$509$	−12.1353	−	8.81678i	−0.537886	−	0.390797i	0.285413	−	0.958404i	$-0.407869\pi$
$509$	−12.1353	−	8.81678i	−0.537886	−	0.390797i	−0.823299	+	0.567608i	$0.807869\pi$
$510$	3.23607	−	2.35114i	0.143295	−	0.104110i
$511$	−2.47214	+	7.60845i	−0.109361	+	0.336578i
$512$	−9.88854	+	30.4338i	−0.437016	+	1.34500i
$513$		0			0
$514$	−3.23607	−	2.35114i	−0.142737	−	0.103704i
$515$	−4.94427	−	15.2169i	−0.217871	−	0.670537i
$516$	12.0000			0.528271
$517$		0			0
$518$	12.0000			0.527250
$519$	1.85410	+	5.70634i	0.0813860	+	0.250480i
$520$		0			0
$521$	2.42705	−	1.76336i	0.106331	−	0.0772540i	−0.533349	−	0.845895i	$-0.679067\pi$
$521$	2.42705	−	1.76336i	0.106331	−	0.0772540i	0.639680	+	0.768641i	$0.279067\pi$
$522$		0			0
$523$	−4.94427	+	15.2169i	−0.216198	+	0.665389i	0.782868	+	0.622187i	$0.213756\pi$
$523$	−4.94427	+	15.2169i	−0.216198	+	0.665389i	−0.999066	+	0.0432015i	$0.986244\pi$
$524$	29.1246	−	21.1603i	1.27231	−	0.924391i
$525$	6.47214	+	4.70228i	0.282467	+	0.205224i
$526$	−8.65248	−	26.6296i	−0.377266	−	1.16110i
$527$	−14.0000			−0.609850
$528$		0			0
$529$	−22.0000			−0.956522
$530$	3.70820	+	11.4127i	0.161074	+	0.495735i
$531$	8.09017	+	5.87785i	0.351083	+	0.255077i
$532$		0			0
$533$	−9.88854	+	30.4338i	−0.428320	+	1.31823i
$534$	9.27051	−	28.5317i	0.401174	−	1.23469i
$535$	−14.5623	+	10.5801i	−0.629583	+	0.457419i
$536$		0			0
$537$	4.63525	+	14.2658i	0.200026	+	0.615617i
$538$	−20.0000			−0.862261
$539$		0			0
$540$	10.0000			0.430331
$541$	−2.47214	−	7.60845i	−0.106285	−	0.327113i	0.883745	−	0.467970i	$-0.155014\pi$
$541$	−2.47214	−	7.60845i	−0.106285	−	0.327113i	−0.990030	+	0.140857i	$0.955014\pi$
$542$	−45.3050	−	32.9160i	−1.94601	−	1.41386i
$543$	5.66312	−	4.11450i	0.243028	−	0.176570i
$544$	−4.94427	+	15.2169i	−0.211984	+	0.652419i
$545$	3.09017	−	9.51057i	0.132368	−	0.407388i
$546$	12.9443	−	9.40456i	0.553964	−	0.402478i
$547$	−6.47214	−	4.70228i	−0.276729	−	0.201055i	0.440761	−	0.897625i	$-0.354709\pi$
$547$	−6.47214	−	4.70228i	−0.276729	−	0.201055i	−0.717489	+	0.696570i	$0.754709\pi$
$548$	−4.32624	−	13.3148i	−0.184808	−	0.568780i
$549$	−24.0000			−1.02430
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−16.1803	−	11.7557i	−0.688058	−	0.499903i
$554$	−3.23607	+	2.35114i	−0.137487	+	0.0998904i
$555$	−0.927051	+	2.85317i	−0.0393511	+	0.121110i
$556$	6.18034	−	19.0211i	0.262105	−	0.806676i
$557$	1.61803	−	1.17557i	0.0685583	−	0.0498105i	−0.552978	−	0.833196i	$-0.686509\pi$
$557$	1.61803	−	1.17557i	0.0685583	−	0.0498105i	0.621537	+	0.783385i	$0.286509\pi$
$558$	−22.6525	−	16.4580i	−0.958956	−	0.696722i
$559$	−7.41641	−	22.8254i	−0.313681	−	0.965410i
$560$	8.00000			0.338062
$561$		0			0
$562$	36.0000			1.51857
$563$	1.23607	+	3.80423i	0.0520941	+	0.160329i	0.973719	−	0.227753i	$-0.0731378\pi$
$563$	1.23607	+	3.80423i	0.0520941	+	0.160329i	−0.921625	+	0.388082i	$0.873138\pi$
$564$	12.9443	+	9.40456i	0.545052	+	0.396004i
$565$	−7.28115	+	5.29007i	−0.306320	+	0.222555i
$566$	−2.47214	+	7.60845i	−0.103912	+	0.319807i
$567$	−0.618034	+	1.90211i	−0.0259550	+	0.0798812i
$568$		0			0
$569$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$569$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$570$		0			0
$571$	−28.0000			−1.17176			−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000			−1.17176			−0.585882	+	0.810397i	$0.699252\pi$
$572$		0			0
$573$	−17.0000			−0.710185
$574$	−9.88854	−	30.4338i	−0.412740	−	1.27028i
$575$	−3.23607	−	2.35114i	−0.134953	−	0.0980494i
$576$	−12.9443	+	9.40456i	−0.539345	+	0.391857i
$577$	10.1976	−	31.3849i	0.424530	−	1.30657i	−0.478914	−	0.877862i	$-0.658969\pi$
$577$	10.1976	−	31.3849i	0.424530	−	1.30657i	0.903444	−	0.428707i	$-0.141031\pi$
$578$	8.03444	−	24.7275i	0.334189	−	1.02853i
$579$	3.23607	−	2.35114i	0.134486	−	0.0977101i
$580$		0			0
$581$	3.70820	+	11.4127i	0.153842	+	0.473478i
$582$	−14.0000			−0.580319
$583$		0			0
$584$		0			0
$585$	−2.47214	−	7.60845i	−0.102210	−	0.314571i
$586$	38.8328	+	28.2137i	1.60417	+	1.16550i
$587$	−22.6525	+	16.4580i	−0.934968	+	0.679294i	−0.947204	−	0.320631i	$-0.896105\pi$
$587$	−22.6525	+	16.4580i	−0.934968	+	0.679294i	0.0122363	+	0.999925i	$0.496105\pi$
$588$	1.85410	−	5.70634i	0.0764619	−	0.235325i
$589$		0			0
$590$	8.09017	−	5.87785i	0.333067	−	0.241987i
$591$	−1.61803	−	1.17557i	−0.0665570	−	0.0483565i
$592$	−3.70820	−	11.4127i	−0.152406	−	0.469058i
$593$	44.0000			1.80686			0.903432	−	0.428732i	$-0.141040\pi$
$593$	44.0000			1.80686			0.903432	+	0.428732i	$0.141040\pi$
$594$		0			0
$595$	4.00000			0.163984
$596$	−6.18034	−	19.0211i	−0.253157	−	0.779136i
$597$		0			0
$598$	−6.47214	+	4.70228i	−0.264665	+	0.192291i
$599$	12.3607	−	38.0423i	0.505044	−	1.55436i	−0.295653	−	0.955295i	$-0.595537\pi$
$599$	12.3607	−	38.0423i	0.505044	−	1.55436i	0.800697	−	0.599069i	$-0.204463\pi$
$600$		0			0
$601$	−1.61803	+	1.17557i	−0.0660010	+	0.0479525i	−0.620297	−	0.784367i	$-0.712988\pi$
$601$	−1.61803	+	1.17557i	−0.0660010	+	0.0479525i	0.554296	+	0.832320i	$0.312988\pi$
$602$	19.4164	+	14.1068i	0.791354	+	0.574952i
$603$	4.32624	+	13.3148i	0.176178	+	0.542220i
$604$	4.00000			0.162758
$605$		0			0
$606$	4.00000			0.162489
$607$	−6.79837	−	20.9232i	−0.275937	−	0.849248i	−0.988970	−	0.148117i	$-0.952679\pi$
$607$	−6.79837	−	20.9232i	−0.275937	−	0.849248i	0.713032	−	0.701131i	$-0.247321\pi$
$608$		0			0
$609$		0			0
$610$	−7.41641	+	22.8254i	−0.300282	+	0.924172i
$611$	9.88854	−	30.4338i	0.400048	−	1.23122i
$612$	−6.47214	+	4.70228i	−0.261621	+	0.190078i
$613$	12.9443	+	9.40456i	0.522814	+	0.379847i	0.817663	−	0.575697i	$-0.195269\pi$
$613$	12.9443	+	9.40456i	0.522814	+	0.379847i	−0.294849	+	0.955544i	$0.595269\pi$
$614$	−4.94427	−	15.2169i	−0.199535	−	0.614104i
$615$	8.00000			0.322591
$616$		0			0
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$	−9.88854	−	30.4338i	−0.397776	−	1.22423i
$619$	20.2254	+	14.6946i	0.812928	+	0.590627i	0.914678	−	0.404183i	$-0.132444\pi$
$619$	20.2254	+	14.6946i	0.812928	+	0.590627i	−0.101750	+	0.994810i	$0.532444\pi$
$620$	−11.3262	+	8.22899i	−0.454873	+	0.330484i
$621$	−1.54508	+	4.75528i	−0.0620021	+	0.190823i
$622$	−7.41641	+	22.8254i	−0.297371	+	0.915213i
$623$	24.2705	−	17.6336i	0.972377	−	0.706474i
$624$	−12.9443	−	9.40456i	−0.518186	−	0.376484i
$625$	3.39919	+	10.4616i	0.135967	+	0.418465i
$626$	2.00000			0.0799361
$627$		0			0
$628$	−14.0000			−0.558661
$629$	−1.85410	−	5.70634i	−0.0739279	−	0.227527i
$630$	6.47214	+	4.70228i	0.257856	+	0.187343i
$631$	−5.66312	+	4.11450i	−0.225445	+	0.163796i	−0.694774	−	0.719228i	$-0.744496\pi$
$631$	−5.66312	+	4.11450i	−0.225445	+	0.163796i	0.469329	+	0.883023i	$0.344496\pi$
$632$		0			0
$633$	−3.70820	+	11.4127i	−0.147388	+	0.453613i
$634$	21.0344	−	15.2824i	0.835384	−	0.606942i
$635$	−6.47214	−	4.70228i	−0.256839	−	0.186604i
$636$	3.70820	+	11.4127i	0.147040	+	0.452542i
$637$	−12.0000			−0.475457
$638$		0			0
$639$	6.00000			0.237356
$640$		0			0
$641$	26.6976	+	19.3969i	1.05449	+	0.766132i	0.973061	−	0.230547i	$-0.0740516\pi$
$641$	26.6976	+	19.3969i	1.05449	+	0.766132i	0.0814291	+	0.996679i	$0.474052\pi$
$642$	−29.1246	+	21.1603i	−1.14946	+	0.835129i
$643$	8.96149	−	27.5806i	0.353407	−	1.08767i	−0.603521	−	0.797347i	$-0.706236\pi$
$643$	8.96149	−	27.5806i	0.353407	−	1.08767i	0.956928	−	0.290327i	$-0.0937641\pi$
$644$	1.23607	−	3.80423i	0.0487079	−	0.149908i
$645$	−4.85410	+	3.52671i	−0.191130	+	0.138864i
$646$		0			0
$647$	−2.16312	−	6.65740i	−0.0850410	−	0.261729i	0.899490	−	0.436942i	$-0.143939\pi$
$647$	−2.16312	−	6.65740i	−0.0850410	−	0.261729i	−0.984531	+	0.175213i	$0.943939\pi$
$648$		0			0
$649$		0			0
$650$	32.0000			1.25514
$651$	4.32624	+	13.3148i	0.169559	+	0.521848i
$652$	−6.47214	−	4.70228i	−0.253468	−	0.184156i
$653$	33.1697	−	24.0992i	1.29803	−	0.943074i	0.298096	−	0.954536i	$-0.403648\pi$
$653$	33.1697	−	24.0992i	1.29803	−	0.943074i	0.999934	+	0.0114614i	$0.00364837\pi$
$654$	6.18034	−	19.0211i	0.241670	−	0.743785i
$655$	−5.56231	+	17.1190i	−0.217337	+	0.668895i
$656$	−25.8885	+	18.8091i	−1.01078	+	0.734373i
$657$	6.47214	+	4.70228i	0.252502	+	0.183453i
$658$	9.88854	+	30.4338i	0.385496	+	1.18643i
$659$	10.0000			0.389545			0.194772	−	0.980848i	$-0.437603\pi$
$659$	10.0000			0.389545			0.194772	+	0.980848i	$0.437603\pi$
$660$		0			0
$661$	37.0000			1.43913			0.719567	−	0.694423i	$-0.244340\pi$
$661$	37.0000			1.43913			0.719567	+	0.694423i	$0.244340\pi$
$662$	−4.32624	−	13.3148i	−0.168144	−	0.517494i
$663$	−6.47214	−	4.70228i	−0.251357	−	0.182622i
$664$		0			0
$665$		0			0
$666$	3.70820	−	11.4127i	0.143690	−	0.442232i
$667$		0			0
$668$	19.4164	+	14.1068i	0.751243	+	0.545810i
$669$	−5.87132	−	18.0701i	−0.226998	−	0.698629i
$670$	14.0000			0.540867
$671$		0			0
$672$	16.0000			0.617213
$673$	4.32624	+	13.3148i	0.166764	+	0.513247i	0.999162	−	0.0409312i	$-0.0130324\pi$
$673$	4.32624	+	13.3148i	0.166764	+	0.513247i	−0.832398	+	0.554179i	$0.813032\pi$
$674$	−35.5967	−	25.8626i	−1.37114	−	0.996188i
$675$	16.1803	−	11.7557i	0.622782	−	0.452477i
$676$	1.85410	−	5.70634i	0.0713116	−	0.219475i
$677$	−12.9787	+	39.9444i	−0.498812	+	1.53519i	0.312117	+	0.950044i	$0.398962\pi$
$677$	−12.9787	+	39.9444i	−0.498812	+	1.53519i	−0.810930	+	0.585143i	$0.801038\pi$
$678$	−14.5623	+	10.5801i	−0.559262	+	0.406328i
$679$	−11.3262	−	8.22899i	−0.434661	−	0.315800i
$680$		0			0
$681$	−18.0000			−0.689761
$682$		0			0
$683$	−16.0000			−0.612223			−0.306111	−	0.951996i	$-0.599028\pi$
$683$	−16.0000			−0.612223			−0.306111	+	0.951996i	$0.599028\pi$
$684$		0			0
$685$	5.66312	+	4.11450i	0.216377	+	0.157207i
$686$	32.3607	−	23.5114i	1.23554	−	0.897670i
$687$	−4.63525	+	14.2658i	−0.176846	+	0.544276i
$688$	7.41641	−	22.8254i	0.282748	−	0.870209i
$689$	19.4164	−	14.1068i	0.739706	−	0.537428i
$690$	1.61803	+	1.17557i	0.0615975	+	0.0447532i
$691$	5.25329	+	16.1680i	0.199845	+	0.615058i	0.999886	+	0.0151132i	$0.00481087\pi$
$691$	5.25329	+	16.1680i	0.199845	+	0.615058i	−0.800041	+	0.599945i	$0.795189\pi$
$692$	−12.0000			−0.456172
$693$		0			0
$694$	−56.0000			−2.12573
$695$	3.09017	+	9.51057i	0.117217	+	0.360756i
$696$		0			0
$697$	−12.9443	+	9.40456i	−0.490299	+	0.356223i
$698$	−18.5410	+	57.0634i	−0.701788	+	2.15988i
$699$	−7.41641	+	22.8254i	−0.280514	+	0.863334i
$700$	−12.9443	+	9.40456i	−0.489247	+	0.355459i
$701$	−1.61803	−	1.17557i	−0.0611123	−	0.0444007i	0.556810	−	0.830640i	$-0.312025\pi$
$701$	−1.61803	−	1.17557i	−0.0611123	−	0.0444007i	−0.617922	+	0.786239i	$0.712025\pi$
$702$	−12.3607	−	38.0423i	−0.466524	−	1.43581i
$703$		0			0
$704$		0			0
$705$	−8.00000			−0.301297
$706$	12.9787	+	39.9444i	0.488460	+	1.50333i
$707$	3.23607	+	2.35114i	0.121705	+	0.0884238i
$708$	8.09017	−	5.87785i	0.304047	−	0.220903i
$709$	−7.72542	+	23.7764i	−0.290134	+	0.892942i	0.694678	+	0.719321i	$0.255547\pi$
$709$	−7.72542	+	23.7764i	−0.290134	+	0.892942i	−0.984813	+	0.173621i	$0.944453\pi$
$710$	1.85410	−	5.70634i	0.0695832	−	0.214155i
$711$	−16.1803	+	11.7557i	−0.606810	+	0.440873i
$712$		0			0
$713$	−2.16312	−	6.65740i	−0.0810094	−	0.249321i
$714$	8.00000			0.299392
$715$		0			0
$716$	−30.0000			−1.12115
$717$	9.27051	+	28.5317i	0.346214	+	1.06554i
$718$	−32.3607	−	23.5114i	−1.20769	−	0.877438i
$719$	−12.1353	+	8.81678i	−0.452569	+	0.328810i	−0.790609	−	0.612321i	$-0.790236\pi$
$719$	−12.1353	+	8.81678i	−0.452569	+	0.328810i	0.338040	+	0.941132i	$0.390236\pi$
$720$	2.47214	−	7.60845i	0.0921311	−	0.283550i
$721$	9.88854	−	30.4338i	0.368269	−	1.13341i
$722$	−30.7426	+	22.3358i	−1.14412	+	0.831254i
$723$	−6.47214	−	4.70228i	−0.240701	−	0.174880i
$724$	4.32624	+	13.3148i	0.160783	+	0.494840i
$725$		0			0
$726$		0			0
$727$	3.00000			0.111264			0.0556319	−	0.998451i	$-0.482283\pi$
$727$	3.00000			0.111264			0.0556319	+	0.998451i	$0.482283\pi$
$728$		0			0
$729$	−10.5172	−	7.64121i	−0.389527	−	0.283008i
$730$	6.47214	−	4.70228i	0.239544	−	0.174039i
$731$	3.70820	−	11.4127i	0.137153	−	0.422113i
$732$	−7.41641	+	22.8254i	−0.274118	+	0.843649i
$733$	29.1246	−	21.1603i	1.07574	−	0.781572i	0.0988065	−	0.995107i	$-0.468498\pi$
$733$	29.1246	−	21.1603i	1.07574	−	0.781572i	0.976936	+	0.213534i	$0.0684975\pi$
$734$	−27.5066	−	19.9847i	−1.01529	−	0.737649i
$735$	0.927051	+	2.85317i	0.0341948	+	0.105241i
$736$	−8.00000			−0.294884
$737$		0			0
$738$	−32.0000			−1.17794
$739$	15.4508	+	47.5528i	0.568369	+	1.74926i	0.657724	+	0.753259i	$0.271519\pi$
$739$	15.4508	+	47.5528i	0.568369	+	1.74926i	−0.0893552	+	0.996000i	$0.528481\pi$
$740$	−4.85410	−	3.52671i	−0.178440	−	0.129644i
$741$		0			0
$742$	−7.41641	+	22.8254i	−0.272265	+	0.837945i
$743$	1.23607	−	3.80423i	0.0453469	−	0.139564i	−0.925820	−	0.377966i	$-0.876624\pi$
$743$	1.23607	−	3.80423i	0.0453469	−	0.139564i	0.971166	+	0.238402i	$0.0766237\pi$
$744$		0			0
$745$	8.09017	+	5.87785i	0.296401	+	0.215348i
$746$	16.0689	+	49.4549i	0.588324	+	1.81067i
$747$	12.0000			0.439057
$748$		0			0
$749$	−36.0000			−1.31541
$750$	−5.56231	−	17.1190i	−0.203107	−	0.625098i
$751$	18.6074	+	13.5191i	0.678993	+	0.493318i	0.873024	−	0.487678i	$-0.162156\pi$
$751$	18.6074	+	13.5191i	0.678993	+	0.493318i	−0.194030	+	0.980996i	$0.562156\pi$
$752$	25.8885	−	18.8091i	0.944058	−	0.685898i
$753$	7.10739	−	21.8743i	0.259008	−	0.797144i
$754$		0			0
$755$	−1.61803	+	1.17557i	−0.0588863	+	0.0427834i
$756$	16.1803	+	11.7557i	0.588473	+	0.427551i
$757$	−6.79837	−	20.9232i	−0.247091	−	0.760468i	−0.995285	−	0.0969886i	$-0.969079\pi$
$757$	−6.79837	−	20.9232i	−0.247091	−	0.760468i	0.748194	−	0.663480i	$-0.230921\pi$
$758$	10.0000			0.363216
$759$		0			0
$760$		0			0
$761$	3.70820	+	11.4127i	0.134422	+	0.413709i	0.995500	−	0.0947646i	$-0.0302098\pi$
$761$	3.70820	+	11.4127i	0.134422	+	0.413709i	−0.861077	+	0.508474i	$0.830210\pi$
$762$	−12.9443	−	9.40456i	−0.468921	−	0.340691i
$763$	16.1803	−	11.7557i	0.585768	−	0.425585i
$764$	10.5066	−	32.3359i	0.380115	−	1.16987i
$765$	1.23607	−	3.80423i	0.0446901	−	0.137542i
$766$	−1.61803	+	1.17557i	−0.0584619	+	0.0424751i
$767$	−16.1803	−	11.7557i	−0.584238	−	0.424474i
$768$	−4.94427	−	15.2169i	−0.178411	−	0.549093i
$769$	20.0000			0.721218			0.360609	−	0.932717i	$-0.382569\pi$
$769$	20.0000			0.721218			0.360609	+	0.932717i	$0.382569\pi$
$770$		0			0
$771$	2.00000			0.0720282
$772$	2.47214	+	7.60845i	0.0889741	+	0.273834i
$773$	4.85410	+	3.52671i	0.174590	+	0.126847i	0.671648	−	0.740870i	$-0.265587\pi$
$773$	4.85410	+	3.52671i	0.174590	+	0.126847i	−0.497059	+	0.867717i	$0.665587\pi$
$774$	19.4164	−	14.1068i	0.697908	−	0.507060i
$775$	−8.65248	+	26.6296i	−0.310806	+	0.956563i
$776$		0			0
$777$	−4.85410	+	3.52671i	−0.174140	+	0.126520i
$778$	−24.2705	−	17.6336i	−0.870140	−	0.632194i
$779$		0			0
$780$	−8.00000			−0.286446
$781$		0			0
$782$	−4.00000			−0.143040
$783$		0			0
$784$	−9.70820	−	7.05342i	−0.346722	−	0.251908i
$785$	5.66312	−	4.11450i	0.202125	−	0.146853i
$786$	−11.1246	+	34.2380i	−0.396802	+	1.22123i
$787$	−9.88854	+	30.4338i	−0.352489	+	1.08485i	0.604963	+	0.796254i	$0.293188\pi$
$787$	−9.88854	+	30.4338i	−0.352489	+	1.08485i	−0.957451	+	0.288594i	$0.906812\pi$
$788$	3.23607	−	2.35114i	0.115280	−	0.0837559i
$789$	11.3262	+	8.22899i	0.403225	+	0.292960i
$790$	6.18034	+	19.0211i	0.219887	+	0.676741i
$791$	−18.0000			−0.640006
$792$		0			0
$793$	48.0000			1.70453
$794$	1.23607	+	3.80423i	0.0438664	+	0.135007i
$795$	−4.85410	−	3.52671i	−0.172157	−	0.125080i
$796$		0			0
$797$	16.3779	−	50.4060i	0.580135	−	1.78547i	−0.0378516	−	0.999283i	$-0.512051\pi$
$797$	16.3779	−	50.4060i	0.580135	−	1.78547i	0.617987	−	0.786189i	$-0.287949\pi$
$798$		0			0
$799$	12.9443	−	9.40456i	0.457935	−	0.332710i
$800$	25.8885	+	18.8091i	0.915298	+	0.665003i
$801$	−9.27051	−	28.5317i	−0.327557	−	1.00812i
$802$	−4.00000			−0.141245
$803$		0			0
$804$	14.0000			0.493742
$805$	0.618034	+	1.90211i	0.0217828	+	0.0670407i
$806$	45.3050	+	32.9160i	1.59580	+	1.15942i
$807$	8.09017	−	5.87785i	0.284787	−	0.206910i
$808$		0			0
$809$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$809$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$810$	1.61803	−	1.17557i	0.0568519	−	0.0413053i
$811$	30.7426	+	22.3358i	1.07952	+	0.784317i	0.977599	−	0.210475i	$-0.0675011\pi$
$811$	30.7426	+	22.3358i	1.07952	+	0.784317i	0.101921	+	0.994792i	$0.467501\pi$
$812$		0			0
$813$	28.0000			0.982003
$814$		0			0
$815$	4.00000			0.140114
$816$	−2.47214	−	7.60845i	−0.0865421	−	0.266349i
$817$		0			0
$818$	−48.5410	+	35.2671i	−1.69720	+	1.23309i
$819$	4.94427	−	15.2169i	0.172767	−	0.531722i
$820$	−4.94427	+	15.2169i	−0.172661	+	0.531397i
$821$	−17.7984	+	12.9313i	−0.621168	+	0.451305i	−0.853329	−	0.521373i	$-0.825420\pi$
$821$	−17.7984	+	12.9313i	−0.621168	+	0.451305i	0.232162	+	0.972677i	$0.425420\pi$
$822$	11.3262	+	8.22899i	0.395048	+	0.287019i
$823$	12.0517	+	37.0912i	0.420095	+	1.29292i	0.907614	+	0.419806i	$0.137902\pi$
$823$	12.0517	+	37.0912i	0.420095	+	1.29292i	−0.487519	+	0.873112i	$0.662098\pi$
$824$		0			0
$825$		0			0
$826$	20.0000			0.695889
$827$	−16.0689	−	49.4549i	−0.558770	−	1.71972i	−0.685774	−	0.727815i	$-0.740536\pi$
$827$	−16.0689	−	49.4549i	−0.558770	−	1.71972i	0.127004	−	0.991902i	$-0.459464\pi$
$828$	−3.23607	−	2.35114i	−0.112461	−	0.0817078i
$829$	−20.2254	+	14.6946i	−0.702458	+	0.510366i	−0.880732	−	0.473615i	$-0.842949\pi$
$829$	−20.2254	+	14.6946i	−0.702458	+	0.510366i	0.178274	+	0.983981i	$0.442949\pi$
$830$	3.70820	−	11.4127i	0.128714	−	0.396140i
$831$	0.618034	−	1.90211i	0.0214394	−	0.0659836i
$832$	25.8885	−	18.8091i	0.897524	−	0.652089i
$833$	−4.85410	−	3.52671i	−0.168185	−	0.122193i
$834$	6.18034	+	19.0211i	0.214008	+	0.658648i
$835$	−12.0000			−0.415277
$836$		0			0
$837$	35.0000			1.20978
$838$	−12.3607	−	38.0423i	−0.426993	−	1.31415i
$839$	4.04508	+	2.93893i	0.139652	+	0.101463i	0.655418	−	0.755267i	$-0.272493\pi$
$839$	4.04508	+	2.93893i	0.139652	+	0.101463i	−0.515766	+	0.856730i	$0.672493\pi$
$840$		0			0
$841$	−8.96149	+	27.5806i	−0.309017	+	0.951057i
$842$	−13.5967	+	41.8465i	−0.468575	+	1.44213i
$843$	−14.5623	+	10.5801i	−0.501552	+	0.364399i
$844$	−19.4164	−	14.1068i	−0.668340	−	0.485578i
$845$	0.927051	+	2.85317i	0.0318915	+	0.0981520i
$846$	32.0000			1.10018
$847$		0			0
$848$	24.0000			0.824163
$849$	−1.23607	−	3.80423i	−0.0424217	−	0.130561i
$850$	12.9443	+	9.40456i	0.443985	+	0.322574i
$851$	2.42705	−	1.76336i	0.0831982	−	0.0604471i
$852$	1.85410	−	5.70634i	0.0635205	−	0.195496i
$853$	4.32624	−	13.3148i	0.148128	−	0.455890i	−0.849272	−	0.527955i	$-0.822959\pi$
$853$	4.32624	−	13.3148i	0.148128	−	0.455890i	0.997400	+	0.0720652i	$0.0229590\pi$
$854$	−38.8328	+	28.2137i	−1.32883	+	0.965453i
$855$		0			0
$856$		0			0
$857$	8.00000			0.273275			0.136637	−	0.990621i	$-0.456370\pi$
$857$	8.00000			0.273275			0.136637	+	0.990621i	$0.456370\pi$
$858$		0			0
$859$	−15.0000			−0.511793			−0.255897	−	0.966704i	$-0.582371\pi$
$859$	−15.0000			−0.511793			−0.255897	+	0.966704i	$0.582371\pi$
$860$	−3.70820	−	11.4127i	−0.126449	−	0.389169i
$861$	12.9443	+	9.40456i	0.441140	+	0.320507i
$862$	−29.1246	+	21.1603i	−0.991988	+	0.720722i
$863$	7.41641	−	22.8254i	0.252457	−	0.776984i	−0.741863	−	0.670552i	$-0.766057\pi$
$863$	7.41641	−	22.8254i	0.252457	−	0.776984i	0.994320	−	0.106432i	$-0.0339427\pi$
$864$	12.3607	−	38.0423i	0.420519	−	1.29422i
$865$	4.85410	−	3.52671i	0.165044	−	0.119912i
$866$	−17.7984	−	12.9313i	−0.604813	−	0.439423i
$867$	4.01722	+	12.3637i	0.136432	+	0.419894i
$868$	−28.0000			−0.950382
$869$		0			0
$870$		0			0
$871$	−8.65248	−	26.6296i	−0.293178	−	0.902309i
$872$		0			0
$873$	−11.3262	+	8.22899i	−0.383335	+	0.278509i
$874$		0			0
$875$	5.56231	−	17.1190i	0.188040	−	0.578728i
$876$	6.47214	−	4.70228i	0.218673	−	0.158875i
$877$	9.70820	+	7.05342i	0.327823	+	0.238177i	0.739506	−	0.673150i	$-0.235059\pi$
$877$	9.70820	+	7.05342i	0.327823	+	0.238177i	−0.411683	+	0.911327i	$0.635059\pi$
$878$	−24.7214	−	76.0845i	−0.834305	−	2.56773i
$879$	−24.0000			−0.809500
$880$		0			0
$881$	−43.0000			−1.44871			−0.724353	−	0.689429i	$-0.757862\pi$
$881$	−43.0000			−1.44871			−0.724353	+	0.689429i	$0.757862\pi$
$882$	−3.70820	−	11.4127i	−0.124862	−	0.384285i
$883$	−3.23607	−	2.35114i	−0.108902	−	0.0791222i	0.532001	−	0.846744i	$-0.321440\pi$
$883$	−3.23607	−	2.35114i	−0.108902	−	0.0791222i	−0.640904	+	0.767621i	$0.721440\pi$
$884$	12.9443	−	9.40456i	0.435363	−	0.316310i
$885$	−1.54508	+	4.75528i	−0.0519375	+	0.159847i
$886$	6.79837	−	20.9232i	0.228396	−	0.702930i
$887$	17.7984	−	12.9313i	0.597611	−	0.434190i	−0.247419	−	0.968909i	$-0.579582\pi$
$887$	17.7984	−	12.9313i	0.597611	−	0.434190i	0.845030	+	0.534719i	$0.179582\pi$
$888$		0			0
$889$	−4.94427	−	15.2169i	−0.165826	−	0.510359i
$890$	−30.0000			−1.00560
$891$		0			0
$892$	38.0000			1.27233
$893$		0			0
$894$	16.1803	+	11.7557i	0.541152	+	0.393170i
$895$	12.1353	−	8.81678i	0.405637	−	0.294712i
$896$		0			0
$897$	1.23607	−	3.80423i	0.0412711	−	0.127019i
$898$	56.6312	−	41.1450i	1.88981	−	1.37303i
$899$		0			0
$900$	4.94427	+	15.2169i	0.164809	+	0.507230i
$901$	12.0000			0.399778
$902$		0			0
$903$	−12.0000			−0.399335
$904$		0			0
$905$	−5.66312	−	4.11450i	−0.188248	−	0.136771i
$906$	−3.23607	+	2.35114i	−0.107511	+	0.0781114i
$907$	−3.70820	+	11.4127i	−0.123129	+	0.378952i	−0.993556	−	0.113346i	$-0.963843\pi$
$907$	−3.70820	+	11.4127i	−0.123129	+	0.378952i	0.870427	+	0.492298i	$0.163843\pi$
$908$	11.1246	−	34.2380i	0.369183	−	1.13623i
$909$	3.23607	−	2.35114i	0.107334	−	0.0779824i
$910$	−12.9443	−	9.40456i	−0.429098	−	0.311758i
$911$	3.70820	+	11.4127i	0.122858	+	0.378119i	0.993505	−	0.113790i	$-0.0362992\pi$
$911$	3.70820	+	11.4127i	0.122858	+	0.378119i	−0.870647	+	0.491909i	$0.836299\pi$
$912$		0			0
$913$		0			0
$914$	24.0000			0.793849
$915$	−3.70820	−	11.4127i	−0.122589	−	0.377292i
$916$	−24.2705	−	17.6336i	−0.801920	−	0.582629i
$917$	−29.1246	+	21.1603i	−0.961779	+	0.698774i
$918$	6.18034	−	19.0211i	0.203982	−	0.627791i
$919$	3.09017	−	9.51057i	0.101935	−	0.313725i	−0.887064	−	0.461647i	$-0.847259\pi$
$919$	3.09017	−	9.51057i	0.101935	−	0.313725i	0.988999	+	0.147923i	$0.0472586\pi$
$920$		0			0
$921$	6.47214	+	4.70228i	0.213264	+	0.154945i
$922$	−7.41641	−	22.8254i	−0.244246	−	0.751713i
$923$	−12.0000			−0.394985
$924$		0			0
$925$	−12.0000			−0.394558
$926$	6.79837	+	20.9232i	0.223408	+	0.687580i
$927$	−25.8885	−	18.8091i	−0.850291	−	0.617773i
$928$		0			0
$929$	−9.27051	+	28.5317i	−0.304156	+	0.936095i	0.675835	+	0.737053i	$0.263783\pi$
$929$	−9.27051	+	28.5317i	−0.304156	+	0.936095i	−0.979991	+	0.199042i	$0.936217\pi$
$930$	4.32624	−	13.3148i	0.141863	−	0.436609i
$931$		0			0
$932$	−38.8328	−	28.2137i	−1.27201	−	0.924170i
$933$	−3.70820	−	11.4127i	−0.121401	−	0.373634i
$934$	54.0000			1.76693
$935$		0			0
$936$		0			0
$937$	2.47214	+	7.60845i	0.0807612	+	0.248557i	0.983282	−	0.182089i	$-0.0582858\pi$
$937$	2.47214	+	7.60845i	0.0807612	+	0.248557i	−0.902521	+	0.430646i	$0.858286\pi$
$938$	22.6525	+	16.4580i	0.739630	+	0.537372i
$939$	−0.809017	+	0.587785i	−0.0264013	+	0.0191816i
$940$	4.94427	−	15.2169i	0.161264	−	0.496321i
$941$	12.9787	−	39.9444i	0.423094	−	1.30215i	−0.481714	−	0.876329i	$-0.659985\pi$
$941$	12.9787	−	39.9444i	0.423094	−	1.30215i	0.904808	−	0.425821i	$-0.140015\pi$
$942$	11.3262	−	8.22899i	0.369029	−	0.268115i
$943$	−6.47214	−	4.70228i	−0.210762	−	0.153127i
$944$	−6.18034	−	19.0211i	−0.201153	−	0.619085i
$945$	−10.0000			−0.325300
$946$		0			0
$947$	−27.0000			−0.877382			−0.438691	−	0.898638i	$-0.644558\pi$
$947$	−27.0000			−0.877382			−0.438691	+	0.898638i	$0.644558\pi$
$948$	6.18034	+	19.0211i	0.200728	+	0.617778i
$949$	−12.9443	−	9.40456i	−0.420189	−	0.305285i
$950$		0			0
$951$	−4.01722	+	12.3637i	−0.130267	+	0.400922i
$952$		0			0
$953$	−27.5066	+	19.9847i	−0.891025	+	0.647368i	−0.936145	−	0.351614i	$-0.885633\pi$
$953$	−27.5066	+	19.9847i	−0.891025	+	0.647368i	0.0451197	+	0.998982i	$0.485633\pi$
$954$	19.4164	+	14.1068i	0.628629	+	0.456726i
$955$	5.25329	+	16.1680i	0.169992	+	0.523183i
$956$	−60.0000			−1.94054
$957$		0			0
$958$	−40.0000			−1.29234
$959$	4.32624	+	13.3148i	0.139702	+	0.429957i
$960$	−6.47214	−	4.70228i	−0.208887	−	0.151765i
$961$	−14.5623	+	10.5801i	−0.469752	+	0.341295i
$962$	−7.41641	+	22.8254i	−0.239115	+	0.735919i
$963$	−11.1246	+	34.2380i	−0.358486	+	1.10331i
$964$	12.9443	−	9.40456i	0.416907	−	0.302901i
$965$	−3.23607	−	2.35114i	−0.104173	−	0.0756859i
$966$	1.23607	+	3.80423i	0.0397698	+	0.122399i
$967$	−32.0000			−1.02905			−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000			−1.02905			−0.514525	+	0.857475i	$0.672032\pi$
$968$		0			0
$969$		0			0
$970$	4.32624	+	13.3148i	0.138907	+	0.427512i
$971$	−38.0238	−	27.6259i	−1.22024	−	0.886558i	−0.224122	−	0.974561i	$-0.571951\pi$
$971$	−38.0238	−	27.6259i	−1.22024	−	0.886558i	−0.996120	+	0.0880036i	$0.971951\pi$
$972$	25.8885	−	18.8091i	0.830375	−	0.603303i
$973$	−6.18034	+	19.0211i	−0.198133	+	0.609789i
$974$	−14.2148	+	43.7486i	−0.455471	+	1.40180i
$975$	−12.9443	+	9.40456i	−0.414548	+	0.301187i
$976$	38.8328	+	28.2137i	1.24301	+	0.903098i
$977$	−8.34346	−	25.6785i	−0.266931	−	0.821529i	−0.991242	−	0.132056i	$-0.957842\pi$
$977$	−8.34346	−	25.6785i	−0.266931	−	0.821529i	0.724311	−	0.689473i	$-0.242158\pi$
$978$	8.00000			0.255812
$979$		0			0
$980$	−6.00000			−0.191663
$981$	−6.18034	−	19.0211i	−0.197323	−	0.607298i
$982$	−12.9443	−	9.40456i	−0.413068	−	0.300112i
$983$	−31.5517	+	22.9236i	−1.00634	+	0.731150i	−0.963439	−	0.267929i	$-0.913661\pi$
$983$	−31.5517	+	22.9236i	−1.00634	+	0.731150i	−0.0429031	+	0.999079i	$0.513661\pi$
$984$		0			0
$985$	−0.618034	+	1.90211i	−0.0196922	+	0.0606064i
$986$		0			0
$987$	−12.9443	−	9.40456i	−0.412021	−	0.299351i
$988$		0			0
$989$	6.00000			0.190789
$990$		0			0
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$	17.3050	+	53.2592i	0.549433	+	1.69098i
$993$	5.66312	+	4.11450i	0.179714	+	0.130570i
$994$	9.70820	−	7.05342i	0.307926	−	0.223721i
$995$		0			0
$996$	3.70820	−	11.4127i	0.117499	−	0.361625i
$997$	−30.7426	+	22.3358i	−0.973629	+	0.707383i	−0.956276	−	0.292466i	$-0.905524\pi$
$997$	−30.7426	+	22.3358i	−0.973629	+	0.707383i	−0.0173535	+	0.999849i	$0.505524\pi$
$998$	32.3607	+	23.5114i	1.02436	+	0.744241i
$999$	4.63525	+	14.2658i	0.146653	+	0.451351i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.2.c.e.27.1		4
11.2	odd	10		121.2.c.a.9.1		4
11.3	even	5		11.2.a.a.1.1	✓	1
11.4	even	5	inner	121.2.c.e.3.1		4
11.5	even	5	inner	121.2.c.e.81.1		4
11.6	odd	10		121.2.c.a.81.1		4
11.7	odd	10		121.2.c.a.3.1		4
11.8	odd	10		121.2.a.d.1.1		1
11.9	even	5	inner	121.2.c.e.9.1		4
11.10	odd	2		121.2.c.a.27.1		4
33.8	even	10		1089.2.a.b.1.1		1
33.14	odd	10		99.2.a.d.1.1		1
44.3	odd	10		176.2.a.b.1.1		1
44.19	even	10		1936.2.a.i.1.1		1
55.3	odd	20		275.2.b.a.199.2		2
55.14	even	10		275.2.a.b.1.1		1
55.19	odd	10		3025.2.a.a.1.1		1
55.47	odd	20		275.2.b.a.199.1		2
77.3	odd	30		539.2.e.g.177.1		2
77.25	even	15		539.2.e.h.177.1		2
77.41	even	10		5929.2.a.h.1.1		1
77.47	odd	30		539.2.e.g.67.1		2
77.58	even	15		539.2.e.h.67.1		2
77.69	odd	10		539.2.a.a.1.1		1
88.3	odd	10		704.2.a.c.1.1		1
88.19	even	10		7744.2.a.k.1.1		1
88.69	even	10		704.2.a.h.1.1		1
88.85	odd	10		7744.2.a.x.1.1		1
99.14	odd	30		891.2.e.b.298.1		2
99.25	even	15		891.2.e.k.595.1		2
99.47	odd	30		891.2.e.b.595.1		2
99.58	even	15		891.2.e.k.298.1		2
132.47	even	10		1584.2.a.g.1.1		1
143.25	even	10		1859.2.a.b.1.1		1
165.14	odd	10		2475.2.a.a.1.1		1
165.47	even	20		2475.2.c.a.199.2		2
165.113	even	20		2475.2.c.a.199.1		2
176.3	odd	20		2816.2.c.f.1409.2		2
176.69	even	20		2816.2.c.j.1409.2		2
176.91	odd	20		2816.2.c.f.1409.1		2
176.157	even	20		2816.2.c.j.1409.1		2
187.135	even	10		3179.2.a.a.1.1		1
209.113	odd	10		3971.2.a.b.1.1		1
220.3	even	20		4400.2.b.h.4049.2		2
220.47	even	20		4400.2.b.h.4049.1		2
220.179	odd	10		4400.2.a.i.1.1		1
231.146	even	10		4851.2.a.t.1.1		1
253.91	odd	10		5819.2.a.a.1.1		1
264.179	even	10		6336.2.a.bu.1.1		1
264.245	odd	10		6336.2.a.br.1.1		1
308.223	even	10		8624.2.a.j.1.1		1
319.289	even	10		9251.2.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.2.a.a.1.1	✓	1	11.3	even	5
99.2.a.d.1.1		1	33.14	odd	10
121.2.a.d.1.1		1	11.8	odd	10
121.2.c.a.3.1		4	11.7	odd	10
121.2.c.a.9.1		4	11.2	odd	10
121.2.c.a.27.1		4	11.10	odd	2
121.2.c.a.81.1		4	11.6	odd	10
121.2.c.e.3.1		4	11.4	even	5	inner
121.2.c.e.9.1		4	11.9	even	5	inner
121.2.c.e.27.1		4	1.1	even	1	trivial
121.2.c.e.81.1		4	11.5	even	5	inner
176.2.a.b.1.1		1	44.3	odd	10
275.2.a.b.1.1		1	55.14	even	10
275.2.b.a.199.1		2	55.47	odd	20
275.2.b.a.199.2		2	55.3	odd	20
539.2.a.a.1.1		1	77.69	odd	10
539.2.e.g.67.1		2	77.47	odd	30
539.2.e.g.177.1		2	77.3	odd	30
539.2.e.h.67.1		2	77.58	even	15
539.2.e.h.177.1		2	77.25	even	15
704.2.a.c.1.1		1	88.3	odd	10
704.2.a.h.1.1		1	88.69	even	10
891.2.e.b.298.1		2	99.14	odd	30
891.2.e.b.595.1		2	99.47	odd	30
891.2.e.k.298.1		2	99.58	even	15
891.2.e.k.595.1		2	99.25	even	15
1089.2.a.b.1.1		1	33.8	even	10
1584.2.a.g.1.1		1	132.47	even	10
1859.2.a.b.1.1		1	143.25	even	10
1936.2.a.i.1.1		1	44.19	even	10
2475.2.a.a.1.1		1	165.14	odd	10
2475.2.c.a.199.1		2	165.113	even	20
2475.2.c.a.199.2		2	165.47	even	20
2816.2.c.f.1409.1		2	176.91	odd	20
2816.2.c.f.1409.2		2	176.3	odd	20
2816.2.c.j.1409.1		2	176.157	even	20
2816.2.c.j.1409.2		2	176.69	even	20
3025.2.a.a.1.1		1	55.19	odd	10
3179.2.a.a.1.1		1	187.135	even	10
3971.2.a.b.1.1		1	209.113	odd	10
4400.2.a.i.1.1		1	220.179	odd	10
4400.2.b.h.4049.1		2	220.47	even	20
4400.2.b.h.4049.2		2	220.3	even	20
4851.2.a.t.1.1		1	231.146	even	10
5819.2.a.a.1.1		1	253.91	odd	10
5929.2.a.h.1.1		1	77.41	even	10
6336.2.a.br.1.1		1	264.245	odd	10
6336.2.a.bu.1.1		1	264.179	even	10
7744.2.a.k.1.1		1	88.19	even	10
7744.2.a.x.1.1		1	88.85	odd	10
8624.2.a.j.1.1		1	308.223	even	10
9251.2.a.d.1.1		1	319.289	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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	121.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.618034 - 1.90211i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-1.61803 + 1.17557i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.618034 - 1.90211i) q^{6} +(1.61803 - 1.17557i) q^{7} +(-0.618034 - 1.90211i) q^{9} +O(q^{10})\)	\(q+(-0.618034 - 1.90211i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-1.61803 + 1.17557i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.618034 - 1.90211i) q^{6} +(1.61803 - 1.17557i) q^{7} +(-0.618034 - 1.90211i) q^{9} -2.00000 q^{10} -2.00000 q^{12} +(1.23607 + 3.80423i) q^{13} +(-3.23607 - 2.35114i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-0.618034 + 1.90211i) q^{17} +(-3.23607 + 2.35114i) q^{18} +(0.618034 + 1.90211i) q^{20} +2.00000 q^{21} -1.00000 q^{23} +(3.23607 + 2.35114i) q^{25} +(6.47214 - 4.70228i) q^{26} +(1.54508 - 4.75528i) q^{27} +(-1.23607 + 3.80423i) q^{28} +(-1.61803 - 1.17557i) q^{30} +(2.16312 + 6.65740i) q^{31} +8.00000 q^{32} +4.00000 q^{34} +(-0.618034 - 1.90211i) q^{35} +(3.23607 + 2.35114i) q^{36} +(-2.42705 + 1.76336i) q^{37} +(-1.23607 + 3.80423i) q^{39} +(6.47214 + 4.70228i) q^{41} +(-1.23607 - 3.80423i) q^{42} -6.00000 q^{43} -2.00000 q^{45} +(0.618034 + 1.90211i) q^{46} +(-6.47214 - 4.70228i) q^{47} +(-3.23607 + 2.35114i) q^{48} +(-0.927051 + 2.85317i) q^{49} +(2.47214 - 7.60845i) q^{50} +(-1.61803 + 1.17557i) q^{51} +(-6.47214 - 4.70228i) q^{52} +(-1.85410 - 5.70634i) q^{53} -10.0000 q^{54} +(-4.04508 + 2.93893i) q^{59} +(-0.618034 + 1.90211i) q^{60} +(3.70820 - 11.4127i) q^{61} +(11.3262 - 8.22899i) q^{62} +(-3.23607 - 2.35114i) q^{63} +(-2.47214 - 7.60845i) q^{64} +4.00000 q^{65} -7.00000 q^{67} +(-1.23607 - 3.80423i) q^{68} +(-0.809017 - 0.587785i) q^{69} +(-3.23607 + 2.35114i) q^{70} +(-0.927051 + 2.85317i) q^{71} +(-3.23607 + 2.35114i) q^{73} +(4.85410 + 3.52671i) q^{74} +(1.23607 + 3.80423i) q^{75} +8.00000 q^{78} +(-3.09017 - 9.51057i) q^{79} +(3.23607 + 2.35114i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(4.94427 - 15.2169i) q^{82} +(-1.85410 + 5.70634i) q^{83} +(-3.23607 + 2.35114i) q^{84} +(1.61803 + 1.17557i) q^{85} +(3.70820 + 11.4127i) q^{86} +15.0000 q^{89} +(1.23607 + 3.80423i) q^{90} +(6.47214 + 4.70228i) q^{91} +(1.61803 - 1.17557i) q^{92} +(-2.16312 + 6.65740i) q^{93} +(-4.94427 + 15.2169i) q^{94} +(6.47214 + 4.70228i) q^{96} +(-2.16312 - 6.65740i) q^{97} +6.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + q^{3} - 2 q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + q^3 - 2 * q^4 - q^5 - 2 * q^6 + 2 * q^7 + 2 * q^9	\( 4 q + 2 q^{2} + q^{3} - 2 q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{9} - 8 q^{10} - 8 q^{12} - 4 q^{13} - 4 q^{14} + q^{15} + 4 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{20} + 8 q^{21} - 4 q^{23} + 4 q^{25} + 8 q^{26} - 5 q^{27} + 4 q^{28} - 2 q^{30} - 7 q^{31} + 32 q^{32} + 16 q^{34} + 2 q^{35} + 4 q^{36} - 3 q^{37} + 4 q^{39} + 8 q^{41} + 4 q^{42} - 24 q^{43} - 8 q^{45} - 2 q^{46} - 8 q^{47} - 4 q^{48} + 3 q^{49} - 8 q^{50} - 2 q^{51} - 8 q^{52} + 6 q^{53} - 40 q^{54} - 5 q^{59} + 2 q^{60} - 12 q^{61} + 14 q^{62} - 4 q^{63} + 8 q^{64} + 16 q^{65} - 28 q^{67} + 4 q^{68} - q^{69} - 4 q^{70} + 3 q^{71} - 4 q^{73} + 6 q^{74} - 4 q^{75} + 32 q^{78} + 10 q^{79} + 4 q^{80} - q^{81} - 16 q^{82} + 6 q^{83} - 4 q^{84} + 2 q^{85} - 12 q^{86} + 60 q^{89} - 4 q^{90} + 8 q^{91} + 2 q^{92} + 7 q^{93} + 16 q^{94} + 8 q^{96} + 7 q^{97} + 24 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + q^3 - 2 * q^4 - q^5 - 2 * q^6 + 2 * q^7 + 2 * q^9 - 8 * q^10 - 8 * q^12 - 4 * q^13 - 4 * q^14 + q^15 + 4 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^20 + 8 * q^21 - 4 * q^23 + 4 * q^25 + 8 * q^26 - 5 * q^27 + 4 * q^28 - 2 * q^30 - 7 * q^31 + 32 * q^32 + 16 * q^34 + 2 * q^35 + 4 * q^36 - 3 * q^37 + 4 * q^39 + 8 * q^41 + 4 * q^42 - 24 * q^43 - 8 * q^45 - 2 * q^46 - 8 * q^47 - 4 * q^48 + 3 * q^49 - 8 * q^50 - 2 * q^51 - 8 * q^52 + 6 * q^53 - 40 * q^54 - 5 * q^59 + 2 * q^60 - 12 * q^61 + 14 * q^62 - 4 * q^63 + 8 * q^64 + 16 * q^65 - 28 * q^67 + 4 * q^68 - q^69 - 4 * q^70 + 3 * q^71 - 4 * q^73 + 6 * q^74 - 4 * q^75 + 32 * q^78 + 10 * q^79 + 4 * q^80 - q^81 - 16 * q^82 + 6 * q^83 - 4 * q^84 + 2 * q^85 - 12 * q^86 + 60 * q^89 - 4 * q^90 + 8 * q^91 + 2 * q^92 + 7 * q^93 + 16 * q^94 + 8 * q^96 + 7 * q^97 + 24 * q^98

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