LMFDB - Embedded newform 121.2.c.d.9.1

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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			9.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	121.9
Dual form			121.2.c.d.27.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-1.61803 + 1.17557i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.618034 - 1.90211i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(-2.42705 + 1.76336i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-1.61803 + 1.17557i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.618034 - 1.90211i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(-2.42705 + 1.76336i) q^{8} +(0.309017 - 0.951057i) q^{9} -1.00000 q^{10} -2.00000 q^{12} +(-0.309017 + 0.951057i) q^{13} +(1.61803 - 1.17557i) q^{14} +(-1.61803 - 1.17557i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(1.54508 + 4.75528i) q^{17} +(0.809017 + 0.587785i) q^{18} +(4.85410 - 3.52671i) q^{19} +(-0.309017 + 0.951057i) q^{20} +4.00000 q^{21} +2.00000 q^{23} +(1.85410 - 5.70634i) q^{24} +(3.23607 - 2.35114i) q^{25} +(-0.809017 - 0.587785i) q^{26} +(-1.23607 - 3.80423i) q^{27} +(-0.618034 - 1.90211i) q^{28} +(7.28115 + 5.29007i) q^{29} +(1.61803 - 1.17557i) q^{30} +(-0.618034 + 1.90211i) q^{31} -5.00000 q^{32} -5.00000 q^{34} +(0.618034 - 1.90211i) q^{35} +(0.809017 - 0.587785i) q^{36} +(2.42705 + 1.76336i) q^{37} +(1.85410 + 5.70634i) q^{38} +(-0.618034 - 1.90211i) q^{39} +(-2.42705 - 1.76336i) q^{40} +(-4.04508 + 2.93893i) q^{41} +(-1.23607 + 3.80423i) q^{42} +1.00000 q^{45} +(-0.618034 + 1.90211i) q^{46} +(-1.61803 + 1.17557i) q^{47} +(1.61803 + 1.17557i) q^{48} +(-0.927051 - 2.85317i) q^{49} +(1.23607 + 3.80423i) q^{50} +(-8.09017 - 5.87785i) q^{51} +(-0.809017 + 0.587785i) q^{52} +(2.78115 - 8.55951i) q^{53} +4.00000 q^{54} +6.00000 q^{56} +(-3.70820 + 11.4127i) q^{57} +(-7.28115 + 5.29007i) q^{58} +(-6.47214 - 4.70228i) q^{59} +(-0.618034 - 1.90211i) q^{60} +(-1.85410 - 5.70634i) q^{61} +(-1.61803 - 1.17557i) q^{62} +(-1.61803 + 1.17557i) q^{63} +(2.16312 - 6.65740i) q^{64} -1.00000 q^{65} +2.00000 q^{67} +(-1.54508 + 4.75528i) q^{68} +(-3.23607 + 2.35114i) q^{69} +(1.61803 + 1.17557i) q^{70} +(3.70820 + 11.4127i) q^{71} +(0.927051 + 2.85317i) q^{72} +(-1.61803 - 1.17557i) q^{73} +(-2.42705 + 1.76336i) q^{74} +(-2.47214 + 7.60845i) q^{75} +6.00000 q^{76} +2.00000 q^{78} +(3.09017 - 9.51057i) q^{79} +(0.809017 - 0.587785i) q^{80} +(8.89919 + 6.46564i) q^{81} +(-1.54508 - 4.75528i) q^{82} +(-1.85410 - 5.70634i) q^{83} +(3.23607 + 2.35114i) q^{84} +(-4.04508 + 2.93893i) q^{85} -18.0000 q^{87} -9.00000 q^{89} +(-0.309017 + 0.951057i) q^{90} +(1.61803 - 1.17557i) q^{91} +(1.61803 + 1.17557i) q^{92} +(-1.23607 - 3.80423i) q^{93} +(-0.618034 - 1.90211i) q^{94} +(4.85410 + 3.52671i) q^{95} +(8.09017 - 5.87785i) q^{96} +(-4.01722 + 12.3637i) q^{97} +3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 2 q^{3} + q^{4} - q^{5} + 2 q^{6} - 2 q^{7} - 3 q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 - 2 * q^3 + q^4 - q^5 + 2 * q^6 - 2 * q^7 - 3 * q^8 - q^9	$ 4 q + q^{2} - 2 q^{3} + q^{4} - q^{5} + 2 q^{6} - 2 q^{7} - 3 q^{8} - q^{9} - 4 q^{10} - 8 q^{12} + q^{13} + 2 q^{14} - 2 q^{15} + q^{16} - 5 q^{17} + q^{18} + 6 q^{19} + q^{20} + 16 q^{21} + 8 q^{23} - 6 q^{24} + 4 q^{25} - q^{26} + 4 q^{27} + 2 q^{28} + 9 q^{29} + 2 q^{30} + 2 q^{31} - 20 q^{32} - 20 q^{34} - 2 q^{35} + q^{36} + 3 q^{37} - 6 q^{38} + 2 q^{39} - 3 q^{40} - 5 q^{41} + 4 q^{42} + 4 q^{45} + 2 q^{46} - 2 q^{47} + 2 q^{48} + 3 q^{49} - 4 q^{50} - 10 q^{51} - q^{52} - 9 q^{53} + 16 q^{54} + 24 q^{56} + 12 q^{57} - 9 q^{58} - 8 q^{59} + 2 q^{60} + 6 q^{61} - 2 q^{62} - 2 q^{63} - 7 q^{64} - 4 q^{65} + 8 q^{67} + 5 q^{68} - 4 q^{69} + 2 q^{70} - 12 q^{71} - 3 q^{72} - 2 q^{73} - 3 q^{74} + 8 q^{75} + 24 q^{76} + 8 q^{78} - 10 q^{79} + q^{80} + 11 q^{81} + 5 q^{82} + 6 q^{83} + 4 q^{84} - 5 q^{85} - 72 q^{87} - 36 q^{89} + q^{90} + 2 q^{91} + 2 q^{92} + 4 q^{93} + 2 q^{94} + 6 q^{95} + 10 q^{96} + 13 q^{97} + 12 q^{98}+O(q^{100}) $ 4 * q + q^2 - 2 * q^3 + q^4 - q^5 + 2 * q^6 - 2 * q^7 - 3 * q^8 - q^9 - 4 * q^10 - 8 * q^12 + q^13 + 2 * q^14 - 2 * q^15 + q^16 - 5 * q^17 + q^18 + 6 * q^19 + q^20 + 16 * q^21 + 8 * q^23 - 6 * q^24 + 4 * q^25 - q^26 + 4 * q^27 + 2 * q^28 + 9 * q^29 + 2 * q^30 + 2 * q^31 - 20 * q^32 - 20 * q^34 - 2 * q^35 + q^36 + 3 * q^37 - 6 * q^38 + 2 * q^39 - 3 * q^40 - 5 * q^41 + 4 * q^42 + 4 * q^45 + 2 * q^46 - 2 * q^47 + 2 * q^48 + 3 * q^49 - 4 * q^50 - 10 * q^51 - q^52 - 9 * q^53 + 16 * q^54 + 24 * q^56 + 12 * q^57 - 9 * q^58 - 8 * q^59 + 2 * q^60 + 6 * q^61 - 2 * q^62 - 2 * q^63 - 7 * q^64 - 4 * q^65 + 8 * q^67 + 5 * q^68 - 4 * q^69 + 2 * q^70 - 12 * q^71 - 3 * q^72 - 2 * q^73 - 3 * q^74 + 8 * q^75 + 24 * q^76 + 8 * q^78 - 10 * q^79 + q^80 + 11 * q^81 + 5 * q^82 + 6 * q^83 + 4 * q^84 - 5 * q^85 - 72 * q^87 - 36 * q^89 + q^90 + 2 * q^91 + 2 * q^92 + 4 * q^93 + 2 * q^94 + 6 * q^95 + 10 * q^96 + 13 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i	0.780378	+	0.625308i	$0.215027\pi$
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i	−0.998886	+	0.0471903i	$0.984973\pi$
$3$	−1.61803	+	1.17557i	−0.934172	+	0.678716i	−0.947011	−	0.321202i	$-0.895913\pi$
$3$	−1.61803	+	1.17557i	−0.934172	+	0.678716i	0.0128385	+	0.999918i	$0.495913\pi$
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i	0.996074	−	0.0885298i	$-0.0282169\pi$
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i	−0.857877	+	0.513855i	$0.828217\pi$
$6$	−0.618034	−	1.90211i	−0.252311	−	0.776534i
$7$	−1.61803	−	1.17557i	−0.611559	−	0.444324i	0.238404	−	0.971166i	$-0.423376\pi$
$7$	−1.61803	−	1.17557i	−0.611559	−	0.444324i	−0.849963	+	0.526842i	$0.823376\pi$
$8$	−2.42705	+	1.76336i	−0.858092	+	0.623440i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−1.00000			−0.316228
$11$		0			0
$11$		0			0
$12$	−2.00000			−0.577350
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i	−0.984720	−	0.174143i	$-0.944284\pi$
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i	0.899014	+	0.437919i	$0.144284\pi$
$14$	1.61803	−	1.17557i	0.432438	−	0.314184i
$15$	−1.61803	−	1.17557i	−0.417775	−	0.303531i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	1.54508	+	4.75528i	0.374738	+	1.15333i	0.943655	+	0.330930i	$0.107363\pi$
$17$	1.54508	+	4.75528i	0.374738	+	1.15333i	−0.568917	+	0.822395i	$0.692637\pi$
$18$	0.809017	+	0.587785i	0.190687	+	0.138542i
$19$	4.85410	−	3.52671i	1.11361	−	0.809083i	0.130379	−	0.991464i	$-0.458380\pi$
$19$	4.85410	−	3.52671i	1.11361	−	0.809083i	0.983228	+	0.182381i	$0.0583804\pi$
$20$	−0.309017	+	0.951057i	−0.0690983	+	0.212663i
$21$	4.00000			0.872872
$22$		0			0
$23$	2.00000			0.417029			0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000			0.417029			0.208514	+	0.978019i	$0.433137\pi$
$24$	1.85410	−	5.70634i	0.378467	−	1.16480i
$25$	3.23607	−	2.35114i	0.647214	−	0.470228i
$26$	−0.809017	−	0.587785i	−0.158661	−	0.115274i
$27$	−1.23607	−	3.80423i	−0.237881	−	0.732124i
$28$	−0.618034	−	1.90211i	−0.116797	−	0.359466i
$29$	7.28115	+	5.29007i	1.35208	+	0.982341i	0.998905	+	0.0467821i	$0.0148966\pi$
$29$	7.28115	+	5.29007i	1.35208	+	0.982341i	0.353171	+	0.935559i	$0.385103\pi$
$30$	1.61803	−	1.17557i	0.295411	−	0.214629i
$31$	−0.618034	+	1.90211i	−0.111002	+	0.341630i	−0.991092	−	0.133177i	$-0.957482\pi$
$31$	−0.618034	+	1.90211i	−0.111002	+	0.341630i	0.880090	+	0.474807i	$0.157482\pi$
$32$	−5.00000			−0.883883
$33$		0			0
$34$	−5.00000			−0.857493
$35$	0.618034	−	1.90211i	0.104467	−	0.321516i
$36$	0.809017	−	0.587785i	0.134836	−	0.0979642i
$37$	2.42705	+	1.76336i	0.399005	+	0.289894i	0.769135	−	0.639086i	$-0.220687\pi$
$37$	2.42705	+	1.76336i	0.399005	+	0.289894i	−0.370131	+	0.928980i	$0.620687\pi$
$38$	1.85410	+	5.70634i	0.300775	+	0.925690i
$39$	−0.618034	−	1.90211i	−0.0989646	−	0.304582i
$40$	−2.42705	−	1.76336i	−0.383750	−	0.278811i
$41$	−4.04508	+	2.93893i	−0.631736	+	0.458983i	−0.857001	−	0.515314i	$-0.827675\pi$
$41$	−4.04508	+	2.93893i	−0.631736	+	0.458983i	0.225265	+	0.974298i	$0.427675\pi$
$42$	−1.23607	+	3.80423i	−0.190729	+	0.587005i
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$	−0.618034	+	1.90211i	−0.0911241	+	0.280451i
$47$	−1.61803	+	1.17557i	−0.236015	+	0.171475i	−0.699506	−	0.714627i	$-0.746597\pi$
$47$	−1.61803	+	1.17557i	−0.236015	+	0.171475i	0.463491	+	0.886101i	$0.346597\pi$
$48$	1.61803	+	1.17557i	0.233543	+	0.169679i
$49$	−0.927051	−	2.85317i	−0.132436	−	0.407596i
$50$	1.23607	+	3.80423i	0.174806	+	0.537999i
$51$	−8.09017	−	5.87785i	−1.13285	−	0.823064i
$52$	−0.809017	+	0.587785i	−0.112190	+	0.0815111i
$53$	2.78115	−	8.55951i	0.382021	−	1.17574i	−0.556598	−	0.830782i	$-0.687894\pi$
$53$	2.78115	−	8.55951i	0.382021	−	1.17574i	0.938619	−	0.344957i	$-0.112106\pi$
$54$	4.00000			0.544331
$55$		0			0
$56$	6.00000			0.801784
$57$	−3.70820	+	11.4127i	−0.491164	+	1.51165i
$58$	−7.28115	+	5.29007i	−0.956062	+	0.694620i
$59$	−6.47214	−	4.70228i	−0.842600	−	0.612185i	0.0804955	−	0.996755i	$-0.474350\pi$
$59$	−6.47214	−	4.70228i	−0.842600	−	0.612185i	−0.923096	+	0.384570i	$0.874350\pi$
$60$	−0.618034	−	1.90211i	−0.0797878	−	0.245562i
$61$	−1.85410	−	5.70634i	−0.237393	−	0.730622i	−0.996795	−	0.0799995i	$-0.974508\pi$
$61$	−1.85410	−	5.70634i	−0.237393	−	0.730622i	0.759401	−	0.650622i	$-0.225492\pi$
$62$	−1.61803	−	1.17557i	−0.205491	−	0.149298i
$63$	−1.61803	+	1.17557i	−0.203853	+	0.148108i
$64$	2.16312	−	6.65740i	0.270390	−	0.832174i
$65$	−1.00000			−0.124035
$66$		0			0
$67$	2.00000			0.244339			0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000			0.244339			0.122169	+	0.992509i	$0.461015\pi$
$68$	−1.54508	+	4.75528i	−0.187369	+	0.576663i
$69$	−3.23607	+	2.35114i	−0.389577	+	0.283044i
$70$	1.61803	+	1.17557i	0.193392	+	0.140508i
$71$	3.70820	+	11.4127i	0.440083	+	1.35444i	0.887787	+	0.460254i	$0.152242\pi$
$71$	3.70820	+	11.4127i	0.440083	+	1.35444i	−0.447704	+	0.894182i	$0.647758\pi$
$72$	0.927051	+	2.85317i	0.109254	+	0.336249i
$73$	−1.61803	−	1.17557i	−0.189377	−	0.137590i	0.489057	−	0.872252i	$-0.337341\pi$
$73$	−1.61803	−	1.17557i	−0.189377	−	0.137590i	−0.678434	+	0.734662i	$0.737341\pi$
$74$	−2.42705	+	1.76336i	−0.282139	+	0.204986i
$75$	−2.47214	+	7.60845i	−0.285458	+	0.878548i
$76$	6.00000			0.688247
$77$		0			0
$78$	2.00000			0.226455
$79$	3.09017	−	9.51057i	0.347671	−	1.07002i	−0.612467	−	0.790496i	$-0.709823\pi$
$79$	3.09017	−	9.51057i	0.347671	−	1.07002i	0.960138	−	0.279526i	$-0.0901773\pi$
$80$	0.809017	−	0.587785i	0.0904508	−	0.0657164i
$81$	8.89919	+	6.46564i	0.988799	+	0.718404i
$82$	−1.54508	−	4.75528i	−0.170626	−	0.525133i
$83$	−1.85410	−	5.70634i	−0.203514	−	0.626352i	−0.999771	−	0.0213936i	$-0.993190\pi$
$83$	−1.85410	−	5.70634i	−0.203514	−	0.626352i	0.796257	−	0.604959i	$-0.206810\pi$
$84$	3.23607	+	2.35114i	0.353084	+	0.256531i
$85$	−4.04508	+	2.93893i	−0.438751	+	0.318771i
$86$		0			0
$87$	−18.0000			−1.92980
$88$		0			0
$89$	−9.00000			−0.953998			−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000			−0.953998			−0.476999	+	0.878904i	$0.658275\pi$
$90$	−0.309017	+	0.951057i	−0.0325733	+	0.100250i
$91$	1.61803	−	1.17557i	0.169616	−	0.123233i
$92$	1.61803	+	1.17557i	0.168692	+	0.122562i
$93$	−1.23607	−	3.80423i	−0.128174	−	0.394480i
$94$	−0.618034	−	1.90211i	−0.0637453	−	0.196188i
$95$	4.85410	+	3.52671i	0.498020	+	0.361833i
$96$	8.09017	−	5.87785i	0.825700	−	0.599906i
$97$	−4.01722	+	12.3637i	−0.407887	+	1.25535i	0.510573	+	0.859834i	$0.329433\pi$
$97$	−4.01722	+	12.3637i	−0.407887	+	1.25535i	−0.918460	+	0.395513i	$0.870567\pi$
$98$	3.00000			0.303046
$99$		0			0
$100$	4.00000			0.400000
$101$	3.09017	−	9.51057i	0.307483	−	0.946337i	−0.671255	−	0.741226i	$-0.734245\pi$
$101$	3.09017	−	9.51057i	0.307483	−	0.946337i	0.978739	−	0.205110i	$-0.0657554\pi$
$102$	8.09017	−	5.87785i	0.801046	−	0.581994i
$103$	−6.47214	−	4.70228i	−0.637719	−	0.463330i	0.221347	−	0.975195i	$-0.428955\pi$
$103$	−6.47214	−	4.70228i	−0.637719	−	0.463330i	−0.859066	+	0.511865i	$0.828955\pi$
$104$	−0.927051	−	2.85317i	−0.0909048	−	0.279776i
$105$	1.23607	+	3.80423i	0.120628	+	0.371254i
$106$	7.28115	+	5.29007i	0.707208	+	0.513817i
$107$	4.85410	−	3.52671i	0.469264	−	0.340940i	−0.327891	−	0.944716i	$-0.606338\pi$
$107$	4.85410	−	3.52671i	0.469264	−	0.340940i	0.797154	+	0.603776i	$0.206338\pi$
$108$	1.23607	−	3.80423i	0.118941	−	0.366062i
$109$	11.0000			1.05361			0.526804	−	0.849987i	$-0.323390\pi$
$109$	11.0000			1.05361			0.526804	+	0.849987i	$0.323390\pi$
$110$		0			0
$111$	−6.00000			−0.569495
$112$	−0.618034	+	1.90211i	−0.0583987	+	0.179733i
$113$	7.28115	−	5.29007i	0.684953	−	0.497648i	−0.190044	−	0.981776i	$-0.560863\pi$
$113$	7.28115	−	5.29007i	0.684953	−	0.497648i	0.874997	+	0.484128i	$0.160863\pi$
$114$	−9.70820	−	7.05342i	−0.909257	−	0.660614i
$115$	0.618034	+	1.90211i	0.0576320	+	0.177373i
$116$	2.78115	+	8.55951i	0.258224	+	0.794730i
$117$	0.809017	+	0.587785i	0.0747936	+	0.0543408i
$118$	6.47214	−	4.70228i	0.595808	−	0.432880i
$119$	3.09017	−	9.51057i	0.283275	−	0.871832i
$120$	6.00000			0.547723
$121$		0			0
$122$	6.00000			0.543214
$123$	3.09017	−	9.51057i	0.278631	−	0.857539i
$124$	−1.61803	+	1.17557i	−0.145304	+	0.105569i
$125$	7.28115	+	5.29007i	0.651246	+	0.473158i
$126$	−0.618034	−	1.90211i	−0.0550588	−	0.169454i
$127$	4.94427	+	15.2169i	0.438733	+	1.35028i	0.889212	+	0.457495i	$0.151253\pi$
$127$	4.94427	+	15.2169i	0.438733	+	1.35028i	−0.450479	+	0.892787i	$0.648747\pi$
$128$	−2.42705	−	1.76336i	−0.214523	−	0.155860i
$129$		0			0
$130$	0.309017	−	0.951057i	0.0271026	−	0.0834132i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	−12.0000			−1.04053
$134$	−0.618034	+	1.90211i	−0.0533900	+	0.164318i
$135$	3.23607	−	2.35114i	0.278516	−	0.202354i
$136$	−12.1353	−	8.81678i	−1.04059	−	0.756033i
$137$	−3.09017	−	9.51057i	−0.264011	−	0.812542i	−0.991920	−	0.126868i	$-0.959507\pi$
$137$	−3.09017	−	9.51057i	−0.264011	−	0.812542i	0.727909	−	0.685674i	$-0.240493\pi$
$138$	−1.23607	−	3.80423i	−0.105221	−	0.323837i
$139$	−1.61803	−	1.17557i	−0.137240	−	0.0997106i	0.517047	−	0.855957i	$-0.327031\pi$
$139$	−1.61803	−	1.17557i	−0.137240	−	0.0997106i	−0.654287	+	0.756246i	$0.727031\pi$
$140$	1.61803	−	1.17557i	0.136749	−	0.0993538i
$141$	1.23607	−	3.80423i	0.104096	−	0.320374i
$142$	−12.0000			−1.00702
$143$		0			0
$144$	−1.00000			−0.0833333
$145$	−2.78115	+	8.55951i	−0.230962	+	0.710829i
$146$	1.61803	−	1.17557i	0.133909	−	0.0972909i
$147$	4.85410	+	3.52671i	0.400360	+	0.290878i
$148$	0.927051	+	2.85317i	0.0762031	+	0.234529i
$149$	−5.25329	−	16.1680i	−0.430366	−	1.32453i	−0.897761	−	0.440482i	$-0.854807\pi$
$149$	−5.25329	−	16.1680i	−0.430366	−	1.32453i	0.467395	−	0.884049i	$-0.345193\pi$
$150$	−6.47214	−	4.70228i	−0.528448	−	0.383940i
$151$	−12.9443	+	9.40456i	−1.05339	+	0.765333i	−0.972854	−	0.231419i	$-0.925663\pi$
$151$	−12.9443	+	9.40456i	−1.05339	+	0.765333i	−0.0805358	+	0.996752i	$0.525663\pi$
$152$	−5.56231	+	17.1190i	−0.451163	+	1.38854i
$153$	5.00000			0.404226
$154$		0			0
$155$	−2.00000			−0.160644
$156$	0.618034	−	1.90211i	0.0494823	−	0.152291i
$157$	−1.61803	+	1.17557i	−0.129133	+	0.0938207i	−0.650477	−	0.759526i	$-0.725431\pi$
$157$	−1.61803	+	1.17557i	−0.129133	+	0.0938207i	0.521344	+	0.853347i	$0.325431\pi$
$158$	8.09017	+	5.87785i	0.643619	+	0.467617i
$159$	5.56231	+	17.1190i	0.441120	+	1.35763i
$160$	−1.54508	−	4.75528i	−0.122150	−	0.375938i
$161$	−3.23607	−	2.35114i	−0.255038	−	0.185296i
$162$	−8.89919	+	6.46564i	−0.699186	+	0.507988i
$163$	−0.618034	+	1.90211i	−0.0484082	+	0.148985i	−0.972339	−	0.233575i	$-0.924958\pi$
$163$	−0.618034	+	1.90211i	−0.0484082	+	0.148985i	0.923931	+	0.382560i	$0.124958\pi$
$164$	−5.00000			−0.390434
$165$		0			0
$166$	6.00000			0.465690
$167$	−3.70820	+	11.4127i	−0.286949	+	0.883140i	0.698858	+	0.715260i	$0.253692\pi$
$167$	−3.70820	+	11.4127i	−0.286949	+	0.883140i	−0.985808	+	0.167879i	$0.946308\pi$
$168$	−9.70820	+	7.05342i	−0.749004	+	0.544183i
$169$	9.70820	+	7.05342i	0.746785	+	0.542571i
$170$	−1.54508	−	4.75528i	−0.118503	−	0.364714i
$171$	−1.85410	−	5.70634i	−0.141787	−	0.436375i
$172$		0			0
$173$	4.85410	−	3.52671i	0.369051	−	0.268131i	−0.387767	−	0.921758i	$-0.626753\pi$
$173$	4.85410	−	3.52671i	0.369051	−	0.268131i	0.756817	+	0.653627i	$0.226753\pi$
$174$	5.56231	−	17.1190i	0.421677	−	1.29779i
$175$	−8.00000			−0.604743
$176$		0			0
$177$	16.0000			1.20263
$178$	2.78115	−	8.55951i	0.208456	−	0.641562i
$179$	−19.4164	+	14.1068i	−1.45125	+	1.05440i	−0.465713	+	0.884936i	$0.654202\pi$
$179$	−19.4164	+	14.1068i	−1.45125	+	1.05440i	−0.985537	+	0.169460i	$0.945798\pi$
$180$	0.809017	+	0.587785i	0.0603006	+	0.0438109i
$181$	0.309017	+	0.951057i	0.0229691	+	0.0706915i	0.961884	−	0.273458i	$-0.0881674\pi$
$181$	0.309017	+	0.951057i	0.0229691	+	0.0706915i	−0.938915	+	0.344149i	$0.888167\pi$
$182$	0.618034	+	1.90211i	0.0458117	+	0.140994i
$183$	9.70820	+	7.05342i	0.717651	+	0.521404i
$184$	−4.85410	+	3.52671i	−0.357849	+	0.259993i
$185$	−0.927051	+	2.85317i	−0.0681581	+	0.209769i
$186$	4.00000			0.293294
$187$		0			0
$188$	−2.00000			−0.145865
$189$	−2.47214	+	7.60845i	−0.179821	+	0.553433i
$190$	−4.85410	+	3.52671i	−0.352154	+	0.255855i
$191$	−6.47214	−	4.70228i	−0.468307	−	0.340245i	0.328474	−	0.944513i	$-0.393466\pi$
$191$	−6.47214	−	4.70228i	−0.468307	−	0.340245i	−0.796781	+	0.604268i	$0.793466\pi$
$192$	4.32624	+	13.3148i	0.312219	+	0.960912i
$193$	1.54508	+	4.75528i	0.111218	+	0.342293i	0.991139	−	0.132826i	$-0.0424051\pi$
$193$	1.54508	+	4.75528i	0.111218	+	0.342293i	−0.879922	+	0.475119i	$0.842405\pi$
$194$	−10.5172	−	7.64121i	−0.755092	−	0.548607i
$195$	1.61803	−	1.17557i	0.115870	−	0.0841844i
$196$	0.927051	−	2.85317i	0.0662179	−	0.203798i
$197$	11.0000			0.783718			0.391859	−	0.920025i	$-0.371832\pi$
$197$	11.0000			0.783718			0.391859	+	0.920025i	$0.371832\pi$
$198$		0			0
$199$	24.0000			1.70131			0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000			1.70131			0.850657	+	0.525720i	$0.176204\pi$
$200$	−3.70820	+	11.4127i	−0.262210	+	0.806998i
$201$	−3.23607	+	2.35114i	−0.228255	+	0.165837i
$202$	8.09017	+	5.87785i	0.569222	+	0.413564i
$203$	−5.56231	−	17.1190i	−0.390397	−	1.20152i
$204$	−3.09017	−	9.51057i	−0.216355	−	0.665873i
$205$	−4.04508	−	2.93893i	−0.282521	−	0.205264i
$206$	6.47214	−	4.70228i	0.450935	−	0.327624i
$207$	0.618034	−	1.90211i	0.0429563	−	0.132206i
$208$	1.00000			0.0693375
$209$		0			0
$210$	−4.00000			−0.276026
$211$	−3.70820	+	11.4127i	−0.255283	+	0.785681i	0.738490	+	0.674264i	$0.235539\pi$
$211$	−3.70820	+	11.4127i	−0.255283	+	0.785681i	−0.993774	+	0.111417i	$0.964461\pi$
$212$	7.28115	−	5.29007i	0.500072	−	0.363323i
$213$	−19.4164	−	14.1068i	−1.33039	−	0.966585i
$214$	1.85410	+	5.70634i	0.126744	+	0.390077i
$215$		0			0
$216$	9.70820	+	7.05342i	0.660560	+	0.479925i
$217$	3.23607	−	2.35114i	0.219679	−	0.159606i
$218$	−3.39919	+	10.4616i	−0.230222	+	0.708550i
$219$	4.00000			0.270295
$220$		0			0
$221$	−5.00000			−0.336336
$222$	1.85410	−	5.70634i	0.124439	−	0.382984i
$223$	16.1803	−	11.7557i	1.08352	−	0.787220i	0.105223	−	0.994449i	$-0.466444\pi$
$223$	16.1803	−	11.7557i	1.08352	−	0.787220i	0.978293	+	0.207228i	$0.0664443\pi$
$224$	8.09017	+	5.87785i	0.540547	+	0.392731i
$225$	−1.23607	−	3.80423i	−0.0824045	−	0.253615i
$226$	2.78115	+	8.55951i	0.185000	+	0.569370i
$227$	−19.4164	−	14.1068i	−1.28871	−	0.936304i	−0.288934	−	0.957349i	$-0.593301\pi$
$227$	−19.4164	−	14.1068i	−1.28871	−	0.936304i	−0.999779	+	0.0210448i	$0.993301\pi$
$228$	−9.70820	+	7.05342i	−0.642942	+	0.467124i
$229$	2.78115	−	8.55951i	0.183784	−	0.565628i	−0.816142	−	0.577852i	$-0.803891\pi$
$229$	2.78115	−	8.55951i	0.183784	−	0.565628i	0.999925	+	0.0122238i	$0.00389106\pi$
$230$	−2.00000			−0.131876
$231$		0			0
$232$	−27.0000			−1.77264
$233$	6.48936	−	19.9722i	0.425132	−	1.30842i	−0.477736	−	0.878503i	$-0.658542\pi$
$233$	6.48936	−	19.9722i	0.425132	−	1.30842i	0.902868	−	0.429918i	$-0.141458\pi$
$234$	−0.809017	+	0.587785i	−0.0528871	+	0.0384247i
$235$	−1.61803	−	1.17557i	−0.105549	−	0.0766858i
$236$	−2.47214	−	7.60845i	−0.160922	−	0.495268i
$237$	6.18034	+	19.0211i	0.401456	+	1.23556i
$238$	8.09017	+	5.87785i	0.524408	+	0.381005i
$239$	4.85410	−	3.52671i	0.313986	−	0.228124i	−0.419619	−	0.907700i	$-0.637836\pi$
$239$	4.85410	−	3.52671i	0.313986	−	0.228124i	0.733605	+	0.679576i	$0.237836\pi$
$240$	−0.618034	+	1.90211i	−0.0398939	+	0.122781i
$241$	−22.0000			−1.41714			−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000			−1.41714			−0.708572	+	0.705638i	$0.750660\pi$
$242$		0			0
$243$	−10.0000			−0.641500
$244$	1.85410	−	5.70634i	0.118697	−	0.365311i
$245$	2.42705	−	1.76336i	0.155059	−	0.112657i
$246$	8.09017	+	5.87785i	0.515810	+	0.374758i
$247$	1.85410	+	5.70634i	0.117974	+	0.363086i
$248$	−1.85410	−	5.70634i	−0.117736	−	0.362353i
$249$	9.70820	+	7.05342i	0.615232	+	0.446993i
$250$	−7.28115	+	5.29007i	−0.460501	+	0.334573i
$251$	−0.618034	+	1.90211i	−0.0390100	+	0.120060i	−0.968665	−	0.248371i	$-0.920105\pi$
$251$	−0.618034	+	1.90211i	−0.0390100	+	0.120060i	0.929655	+	0.368431i	$0.120105\pi$
$252$	−2.00000			−0.125988
$253$		0			0
$254$	−16.0000			−1.00393
$255$	3.09017	−	9.51057i	0.193514	−	0.595575i
$256$	13.7533	−	9.99235i	0.859581	−	0.624522i
$257$	−15.3713	−	11.1679i	−0.958837	−	0.696636i	−0.00595648	−	0.999982i	$-0.501896\pi$
$257$	−15.3713	−	11.1679i	−0.958837	−	0.696636i	−0.952880	+	0.303347i	$0.901896\pi$
$258$		0			0
$259$	−1.85410	−	5.70634i	−0.115208	−	0.354575i
$260$	−0.809017	−	0.587785i	−0.0501731	−	0.0364529i
$261$	7.28115	−	5.29007i	0.450692	−	0.327447i
$262$		0			0
$263$	22.0000			1.35658			0.678289	−	0.734795i	$-0.262722\pi$
$263$	22.0000			1.35658			0.678289	+	0.734795i	$0.262722\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$	3.70820	−	11.4127i	0.227365	−	0.699756i
$267$	14.5623	−	10.5801i	0.891199	−	0.647494i
$268$	1.61803	+	1.17557i	0.0988372	+	0.0718094i
$269$	0.309017	+	0.951057i	0.0188411	+	0.0579869i	0.960035	−	0.279880i	$-0.0902946\pi$
$269$	0.309017	+	0.951057i	0.0188411	+	0.0579869i	−0.941194	+	0.337867i	$0.890295\pi$
$270$	1.23607	+	3.80423i	0.0752247	+	0.231518i
$271$	16.1803	+	11.7557i	0.982886	+	0.714108i	0.958352	−	0.285591i	$-0.0921898\pi$
$271$	16.1803	+	11.7557i	0.982886	+	0.714108i	0.0245340	+	0.999699i	$0.492190\pi$
$272$	4.04508	−	2.93893i	0.245269	−	0.178199i
$273$	−1.23607	+	3.80423i	−0.0748102	+	0.230242i
$274$	10.0000			0.604122
$275$		0			0
$276$	−4.00000			−0.240772
$277$	−0.309017	+	0.951057i	−0.0185670	+	0.0571434i	−0.959911	−	0.280306i	$-0.909564\pi$
$277$	−0.309017	+	0.951057i	−0.0185670	+	0.0571434i	0.941344	+	0.337449i	$0.109564\pi$
$278$	1.61803	−	1.17557i	0.0970432	−	0.0705060i
$279$	1.61803	+	1.17557i	0.0968692	+	0.0703796i
$280$	1.85410	+	5.70634i	0.110804	+	0.341019i
$281$	−1.85410	−	5.70634i	−0.110606	−	0.340412i	0.880399	−	0.474234i	$-0.157275\pi$
$281$	−1.85410	−	5.70634i	−0.110606	−	0.340412i	−0.991005	+	0.133822i	$0.957275\pi$
$282$	3.23607	+	2.35114i	0.192705	+	0.140008i
$283$	22.6525	−	16.4580i	1.34655	−	0.978326i	0.347374	−	0.937727i	$-0.387073\pi$
$283$	22.6525	−	16.4580i	1.34655	−	0.978326i	0.999176	−	0.0405993i	$-0.0129267\pi$
$284$	−3.70820	+	11.4127i	−0.220041	+	0.677218i
$285$	−12.0000			−0.710819
$286$		0			0
$287$	10.0000			0.590281
$288$	−1.54508	+	4.75528i	−0.0910450	+	0.280208i
$289$	−6.47214	+	4.70228i	−0.380714	+	0.276605i
$290$	−7.28115	−	5.29007i	−0.427564	−	0.310643i
$291$	−8.03444	−	24.7275i	−0.470987	−	1.44955i
$292$	−0.618034	−	1.90211i	−0.0361677	−	0.111313i
$293$	7.28115	+	5.29007i	0.425369	+	0.309049i	0.779795	−	0.626035i	$-0.215323\pi$
$293$	7.28115	+	5.29007i	0.425369	+	0.309049i	−0.354425	+	0.935084i	$0.615323\pi$
$294$	−4.85410	+	3.52671i	−0.283097	+	0.205682i
$295$	2.47214	−	7.60845i	0.143933	−	0.442981i
$296$	−9.00000			−0.523114
$297$		0			0
$298$	17.0000			0.984784
$299$	−0.618034	+	1.90211i	−0.0357418	+	0.110002i
$300$	−6.47214	+	4.70228i	−0.373669	+	0.271486i
$301$		0			0
$302$	−4.94427	−	15.2169i	−0.284511	−	0.875634i
$303$	6.18034	+	19.0211i	0.355051	+	1.09274i
$304$	−4.85410	−	3.52671i	−0.278402	−	0.202271i
$305$	4.85410	−	3.52671i	0.277945	−	0.201939i
$306$	−1.54508	+	4.75528i	−0.0883266	+	0.271841i
$307$	22.0000			1.25561			0.627803	−	0.778372i	$-0.283954\pi$
$307$	22.0000			1.25561			0.627803	+	0.778372i	$0.283954\pi$
$308$		0			0
$309$	16.0000			0.910208
$310$	0.618034	−	1.90211i	0.0351020	−	0.108033i
$311$	−19.4164	+	14.1068i	−1.10100	+	0.799926i	−0.981223	−	0.192875i	$-0.938219\pi$
$311$	−19.4164	+	14.1068i	−1.10100	+	0.799926i	−0.119780	+	0.992800i	$0.538219\pi$
$312$	4.85410	+	3.52671i	0.274809	+	0.199661i
$313$	7.10739	+	21.8743i	0.401733	+	1.23641i	0.923592	+	0.383377i	$0.125239\pi$
$313$	7.10739	+	21.8743i	0.401733	+	1.23641i	−0.521859	+	0.853032i	$0.674761\pi$
$314$	−0.618034	−	1.90211i	−0.0348777	−	0.107342i
$315$	−1.61803	−	1.17557i	−0.0911659	−	0.0662359i
$316$	8.09017	−	5.87785i	0.455108	−	0.330655i
$317$	−0.618034	+	1.90211i	−0.0347122	+	0.106833i	−0.966911	−	0.255113i	$-0.917887\pi$
$317$	−0.618034	+	1.90211i	−0.0347122	+	0.106833i	0.932199	+	0.361946i	$0.117887\pi$
$318$	−18.0000			−1.00939
$319$		0			0
$320$	7.00000			0.391312
$321$	−3.70820	+	11.4127i	−0.206972	+	0.636994i
$322$	3.23607	−	2.35114i	0.180339	−	0.131024i
$323$	24.2705	+	17.6336i	1.35045	+	0.981157i
$324$	3.39919	+	10.4616i	0.188844	+	0.581201i
$325$	1.23607	+	3.80423i	0.0685647	+	0.211020i
$326$	−1.61803	−	1.17557i	−0.0896146	−	0.0651088i
$327$	−17.7984	+	12.9313i	−0.984252	+	0.715101i
$328$	4.63525	−	14.2658i	0.255939	−	0.787700i
$329$	4.00000			0.220527
$330$		0			0
$331$	−20.0000			−1.09930			−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000			−1.09930			−0.549650	+	0.835395i	$0.685239\pi$
$332$	1.85410	−	5.70634i	0.101757	−	0.313176i
$333$	2.42705	−	1.76336i	0.133002	−	0.0966313i
$334$	−9.70820	−	7.05342i	−0.531209	−	0.385946i
$335$	0.618034	+	1.90211i	0.0337668	+	0.103924i
$336$	−1.23607	−	3.80423i	−0.0674330	−	0.207538i
$337$	−10.5172	−	7.64121i	−0.572910	−	0.416243i	0.263251	−	0.964727i	$-0.415205\pi$
$337$	−10.5172	−	7.64121i	−0.572910	−	0.416243i	−0.836161	+	0.548484i	$0.815205\pi$
$338$	−9.70820	+	7.05342i	−0.528057	+	0.383656i
$339$	−5.56231	+	17.1190i	−0.302103	+	0.929777i
$340$	−5.00000			−0.271163
$341$		0			0
$342$	6.00000			0.324443
$343$	−6.18034	+	19.0211i	−0.333707	+	1.02704i
$344$		0			0
$345$	−3.23607	−	2.35114i	−0.174224	−	0.126581i
$346$	1.85410	+	5.70634i	0.0996771	+	0.306775i
$347$	−8.65248	−	26.6296i	−0.464489	−	1.42955i	−0.859624	−	0.510928i	$-0.829302\pi$
$347$	−8.65248	−	26.6296i	−0.464489	−	1.42955i	0.395135	−	0.918623i	$-0.370698\pi$
$348$	−14.5623	−	10.5801i	−0.780622	−	0.567155i
$349$	−21.8435	+	15.8702i	−1.16925	+	0.849512i	−0.990919	−	0.134458i	$-0.957071\pi$
$349$	−21.8435	+	15.8702i	−1.16925	+	0.849512i	−0.178334	+	0.983970i	$0.557071\pi$
$350$	2.47214	−	7.60845i	0.132141	−	0.406689i
$351$	4.00000			0.213504
$352$		0			0
$353$	−9.00000			−0.479022			−0.239511	−	0.970894i	$-0.576987\pi$
$353$	−9.00000			−0.479022			−0.239511	+	0.970894i	$0.576987\pi$
$354$	−4.94427	+	15.2169i	−0.262785	+	0.808769i
$355$	−9.70820	+	7.05342i	−0.515258	+	0.374357i
$356$	−7.28115	−	5.29007i	−0.385900	−	0.280373i
$357$	6.18034	+	19.0211i	0.327098	+	1.00670i
$358$	−7.41641	−	22.8254i	−0.391969	−	1.20636i
$359$	−1.61803	−	1.17557i	−0.0853966	−	0.0620442i	0.544268	−	0.838912i	$-0.316808\pi$
$359$	−1.61803	−	1.17557i	−0.0853966	−	0.0620442i	−0.629664	+	0.776867i	$0.716808\pi$
$360$	−2.42705	+	1.76336i	−0.127917	+	0.0929370i
$361$	5.25329	−	16.1680i	0.276489	−	0.850945i
$362$	−1.00000			−0.0525588
$363$		0			0
$364$	2.00000			0.104828
$365$	0.618034	−	1.90211i	0.0323494	−	0.0995611i
$366$	−9.70820	+	7.05342i	−0.507456	+	0.368688i
$367$	11.3262	+	8.22899i	0.591225	+	0.429550i	0.842753	−	0.538300i	$-0.180933\pi$
$367$	11.3262	+	8.22899i	0.591225	+	0.429550i	−0.251529	+	0.967850i	$0.580933\pi$
$368$	−0.618034	−	1.90211i	−0.0322172	−	0.0991545i
$369$	1.54508	+	4.75528i	0.0804339	+	0.247550i
$370$	−2.42705	−	1.76336i	−0.126176	−	0.0916725i
$371$	−14.5623	+	10.5801i	−0.756037	+	0.549293i
$372$	1.23607	−	3.80423i	0.0640871	−	0.197240i
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$		0			0
$375$	−18.0000			−0.929516
$376$	1.85410	−	5.70634i	0.0956180	−	0.294282i
$377$	−7.28115	+	5.29007i	−0.374998	+	0.272452i
$378$	−6.47214	−	4.70228i	−0.332891	−	0.241859i
$379$	−9.88854	−	30.4338i	−0.507940	−	1.56328i	−0.795771	−	0.605598i	$-0.792934\pi$
$379$	−9.88854	−	30.4338i	−0.507940	−	1.56328i	0.287830	−	0.957681i	$-0.407066\pi$
$380$	1.85410	+	5.70634i	0.0951134	+	0.292729i
$381$	−25.8885	−	18.8091i	−1.32631	−	0.963621i
$382$	6.47214	−	4.70228i	0.331143	−	0.240590i
$383$	6.18034	−	19.0211i	0.315801	−	0.971934i	−0.659623	−	0.751597i	$-0.729284\pi$
$383$	6.18034	−	19.0211i	0.315801	−	0.971934i	0.975424	−	0.220338i	$-0.0707160\pi$
$384$	6.00000			0.306186
$385$		0			0
$386$	−5.00000			−0.254493
$387$		0			0
$388$	−10.5172	+	7.64121i	−0.533931	+	0.387924i
$389$	2.42705	+	1.76336i	0.123056	+	0.0894057i	0.647611	−	0.761971i	$-0.275768\pi$
$389$	2.42705	+	1.76336i	0.123056	+	0.0894057i	−0.524555	+	0.851377i	$0.675768\pi$
$390$	0.618034	+	1.90211i	0.0312954	+	0.0963172i
$391$	3.09017	+	9.51057i	0.156277	+	0.480970i
$392$	7.28115	+	5.29007i	0.367754	+	0.267189i
$393$		0			0
$394$	−3.39919	+	10.4616i	−0.171249	+	0.527049i
$395$	10.0000			0.503155
$396$		0			0
$397$	13.0000			0.652451			0.326226	−	0.945292i	$-0.394223\pi$
$397$	13.0000			0.652451			0.326226	+	0.945292i	$0.394223\pi$
$398$	−7.41641	+	22.8254i	−0.371751	+	1.14413i
$399$	19.4164	−	14.1068i	0.972036	−	0.706226i
$400$	−3.23607	−	2.35114i	−0.161803	−	0.117557i
$401$	7.10739	+	21.8743i	0.354926	+	1.09235i	0.956052	+	0.293196i	$0.0947189\pi$
$401$	7.10739	+	21.8743i	0.354926	+	1.09235i	−0.601126	+	0.799154i	$0.705281\pi$
$402$	−1.23607	−	3.80423i	−0.0616495	−	0.189738i
$403$	−1.61803	−	1.17557i	−0.0806000	−	0.0585593i
$404$	8.09017	−	5.87785i	0.402501	−	0.292434i
$405$	−3.39919	+	10.4616i	−0.168907	+	0.519842i
$406$	18.0000			0.893325
$407$		0			0
$408$	30.0000			1.48522
$409$	6.48936	−	19.9722i	0.320878	−	0.987561i	−0.652389	−	0.757884i	$-0.726233\pi$
$409$	6.48936	−	19.9722i	0.320878	−	0.987561i	0.973267	−	0.229677i	$-0.0737669\pi$
$410$	4.04508	−	2.93893i	0.199773	−	0.145143i
$411$	16.1803	+	11.7557i	0.798117	+	0.579866i
$412$	−2.47214	−	7.60845i	−0.121793	−	0.374842i
$413$	4.94427	+	15.2169i	0.243292	+	0.748775i
$414$	1.61803	+	1.17557i	0.0795220	+	0.0577761i
$415$	4.85410	−	3.52671i	0.238278	−	0.173119i
$416$	1.54508	−	4.75528i	0.0757540	−	0.233147i
$417$	4.00000			0.195881
$418$		0			0
$419$	2.00000			0.0977064			0.0488532	−	0.998806i	$-0.484443\pi$
$419$	2.00000			0.0977064			0.0488532	+	0.998806i	$0.484443\pi$
$420$	−1.23607	+	3.80423i	−0.0603139	+	0.185627i
$421$	−10.5172	+	7.64121i	−0.512578	+	0.372410i	−0.813801	−	0.581144i	$-0.802605\pi$
$421$	−10.5172	+	7.64121i	−0.512578	+	0.372410i	0.301223	+	0.953554i	$0.402605\pi$
$422$	−9.70820	−	7.05342i	−0.472588	−	0.343355i
$423$	0.618034	+	1.90211i	0.0300498	+	0.0924839i
$424$	8.34346	+	25.6785i	0.405194	+	1.24706i
$425$	16.1803	+	11.7557i	0.784862	+	0.570235i
$426$	19.4164	−	14.1068i	0.940728	−	0.683479i
$427$	−3.70820	+	11.4127i	−0.179453	+	0.552298i
$428$	6.00000			0.290021
$429$		0			0
$430$		0			0
$431$	−3.70820	+	11.4127i	−0.178618	+	0.549729i	−0.999780	−	0.0209654i	$-0.993326\pi$
$431$	−3.70820	+	11.4127i	−0.178618	+	0.549729i	0.821162	+	0.570695i	$0.193326\pi$
$432$	−3.23607	+	2.35114i	−0.155695	+	0.113119i
$433$	−15.3713	−	11.1679i	−0.738699	−	0.536696i	0.153605	−	0.988132i	$-0.450912\pi$
$433$	−15.3713	−	11.1679i	−0.738699	−	0.536696i	−0.892303	+	0.451436i	$0.850912\pi$
$434$	1.23607	+	3.80423i	0.0593332	+	0.182609i
$435$	−5.56231	−	17.1190i	−0.266692	−	0.820794i
$436$	8.89919	+	6.46564i	0.426194	+	0.309648i
$437$	9.70820	−	7.05342i	0.464406	−	0.337411i
$438$	−1.23607	+	3.80423i	−0.0590616	+	0.181773i
$439$	−22.0000			−1.05000			−0.525001	−	0.851101i	$-0.675935\pi$
$439$	−22.0000			−1.05000			−0.525001	+	0.851101i	$0.675935\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$	1.54508	−	4.75528i	0.0734922	−	0.226186i
$443$	16.1803	−	11.7557i	0.768751	−	0.558530i	−0.132831	−	0.991139i	$-0.542407\pi$
$443$	16.1803	−	11.7557i	0.768751	−	0.558530i	0.901582	+	0.432608i	$0.142407\pi$
$444$	−4.85410	−	3.52671i	−0.230365	−	0.167370i
$445$	−2.78115	−	8.55951i	−0.131839	−	0.405760i
$446$	6.18034	+	19.0211i	0.292648	+	0.900677i
$447$	27.5066	+	19.9847i	1.30102	+	0.945244i
$448$	−11.3262	+	8.22899i	−0.535114	+	0.388783i
$449$	−4.01722	+	12.3637i	−0.189584	+	0.583481i	−0.999997	−	0.00237857i	$-0.999243\pi$
$449$	−4.01722	+	12.3637i	−0.189584	+	0.583481i	0.810413	+	0.585859i	$0.199243\pi$
$450$	4.00000			0.188562
$451$		0			0
$452$	9.00000			0.423324
$453$	9.88854	−	30.4338i	0.464604	−	1.42991i
$454$	19.4164	−	14.1068i	0.911257	−	0.662067i
$455$	1.61803	+	1.17557i	0.0758546	+	0.0551116i
$456$	−11.1246	−	34.2380i	−0.520958	−	1.60334i
$457$	−12.0517	−	37.0912i	−0.563753	−	1.73505i	−0.671628	−	0.740889i	$-0.734405\pi$
$457$	−12.0517	−	37.0912i	−0.563753	−	1.73505i	0.107875	−	0.994165i	$-0.465595\pi$
$458$	7.28115	+	5.29007i	0.340226	+	0.247189i
$459$	16.1803	−	11.7557i	0.755234	−	0.548709i
$460$	−0.618034	+	1.90211i	−0.0288160	+	0.0886865i
$461$	−33.0000			−1.53696			−0.768482	−	0.639872i	$-0.778987\pi$
$461$	−33.0000			−1.53696			−0.768482	+	0.639872i	$0.778987\pi$
$462$		0			0
$463$	−20.0000			−0.929479			−0.464739	−	0.885448i	$-0.653852\pi$
$463$	−20.0000			−0.929479			−0.464739	+	0.885448i	$0.653852\pi$
$464$	2.78115	−	8.55951i	0.129112	−	0.397365i
$465$	3.23607	−	2.35114i	0.150069	−	0.109032i
$466$	16.9894	+	12.3435i	0.787017	+	0.571801i
$467$	3.70820	+	11.4127i	0.171595	+	0.528116i	0.999462	−	0.0328096i	$-0.0104455\pi$
$467$	3.70820	+	11.4127i	0.171595	+	0.528116i	−0.827866	+	0.560925i	$0.810445\pi$
$468$	0.309017	+	0.951057i	0.0142843	+	0.0439626i
$469$	−3.23607	−	2.35114i	−0.149428	−	0.108566i
$470$	1.61803	−	1.17557i	0.0746343	−	0.0542250i
$471$	1.23607	−	3.80423i	0.0569550	−	0.175289i
$472$	24.0000			1.10469
$473$		0			0
$474$	−20.0000			−0.918630
$475$	7.41641	−	22.8254i	0.340288	−	1.04730i
$476$	8.09017	−	5.87785i	0.370812	−	0.269411i
$477$	−7.28115	−	5.29007i	−0.333381	−	0.242216i
$478$	1.85410	+	5.70634i	0.0848047	+	0.261002i
$479$	4.94427	+	15.2169i	0.225910	+	0.695278i	0.998198	+	0.0600061i	$0.0191120\pi$
$479$	4.94427	+	15.2169i	0.225910	+	0.695278i	−0.772288	+	0.635272i	$0.780888\pi$
$480$	8.09017	+	5.87785i	0.369264	+	0.268286i
$481$	−2.42705	+	1.76336i	−0.110664	+	0.0804021i
$482$	6.79837	−	20.9232i	0.309657	−	0.953028i
$483$	8.00000			0.364013
$484$		0			0
$485$	−13.0000			−0.590300
$486$	3.09017	−	9.51057i	0.140173	−	0.431408i
$487$	−1.61803	+	1.17557i	−0.0733201	+	0.0532702i	−0.623842	−	0.781551i	$-0.714429\pi$
$487$	−1.61803	+	1.17557i	−0.0733201	+	0.0532702i	0.550521	+	0.834821i	$0.314429\pi$
$488$	14.5623	+	10.5801i	0.659205	+	0.478940i
$489$	−1.23607	−	3.80423i	−0.0558969	−	0.172033i
$490$	0.927051	+	2.85317i	0.0418799	+	0.128893i
$491$	−1.61803	−	1.17557i	−0.0730209	−	0.0530528i	0.550676	−	0.834719i	$-0.314370\pi$
$491$	−1.61803	−	1.17557i	−0.0730209	−	0.0530528i	−0.623697	+	0.781666i	$0.714370\pi$
$492$	8.09017	−	5.87785i	0.364733	−	0.264994i
$493$	−13.9058	+	42.7975i	−0.626284	+	1.92750i
$494$	−6.00000			−0.269953
$495$		0			0
$496$	2.00000			0.0898027
$497$	7.41641	−	22.8254i	0.332671	−	1.02386i
$498$	−9.70820	+	7.05342i	−0.435035	+	0.316071i
$499$	−6.47214	−	4.70228i	−0.289733	−	0.210503i	0.433419	−	0.901193i	$-0.357307\pi$
$499$	−6.47214	−	4.70228i	−0.289733	−	0.210503i	−0.723151	+	0.690690i	$0.757307\pi$
$500$	2.78115	+	8.55951i	0.124377	+	0.382793i
$501$	−7.41641	−	22.8254i	−0.331341	−	1.01976i
$502$	−1.61803	−	1.17557i	−0.0722164	−	0.0524683i
$503$	−30.7426	+	22.3358i	−1.37075	+	0.995906i	−0.373068	+	0.927804i	$0.621694\pi$
$503$	−30.7426	+	22.3358i	−1.37075	+	0.995906i	−0.997678	+	0.0681020i	$0.978306\pi$
$504$	1.85410	−	5.70634i	0.0825883	−	0.254181i
$505$	10.0000			0.444994
$506$		0			0
$507$	−24.0000			−1.06588
$508$	−4.94427	+	15.2169i	−0.219367	+	0.675141i
$509$	33.9787	−	24.6870i	1.50608	−	1.09423i	0.538200	−	0.842817i	$-0.319104\pi$
$509$	33.9787	−	24.6870i	1.50608	−	1.09423i	0.967880	−	0.251414i	$-0.0808957\pi$
$510$	8.09017	+	5.87785i	0.358239	+	0.260276i
$511$	1.23607	+	3.80423i	0.0546804	+	0.168289i
$512$	3.39919	+	10.4616i	0.150224	+	0.462343i
$513$	−19.4164	−	14.1068i	−0.857255	−	0.622832i
$514$	15.3713	−	11.1679i	0.678000	−	0.492596i
$515$	2.47214	−	7.60845i	0.108935	−	0.335268i
$516$		0			0
$517$		0			0
$518$	6.00000			0.263625
$519$	−3.70820	+	11.4127i	−0.162772	+	0.500961i
$520$	2.42705	−	1.76336i	0.106433	−	0.0773283i
$521$	−24.2705	−	17.6336i	−1.06331	−	0.772540i	−0.0886124	−	0.996066i	$-0.528243\pi$
$521$	−24.2705	−	17.6336i	−1.06331	−	0.772540i	−0.974698	+	0.223526i	$0.928243\pi$
$522$	2.78115	+	8.55951i	0.121728	+	0.374640i
$523$	4.94427	+	15.2169i	0.216198	+	0.665389i	0.999066	+	0.0432015i	$0.0137558\pi$
$523$	4.94427	+	15.2169i	0.216198	+	0.665389i	−0.782868	+	0.622187i	$0.786244\pi$
$524$		0			0
$525$	12.9443	−	9.40456i	0.564934	−	0.410449i
$526$	−6.79837	+	20.9232i	−0.296423	+	0.912297i
$527$	−10.0000			−0.435607
$528$		0			0
$529$	−19.0000			−0.826087
$530$	−2.78115	+	8.55951i	−0.120806	+	0.371801i
$531$	−6.47214	+	4.70228i	−0.280867	+	0.204062i
$532$	−9.70820	−	7.05342i	−0.420904	−	0.305805i
$533$	−1.54508	−	4.75528i	−0.0669251	−	0.205974i
$534$	5.56231	+	17.1190i	0.240705	+	0.740812i
$535$	4.85410	+	3.52671i	0.209861	+	0.152473i
$536$	−4.85410	+	3.52671i	−0.209665	+	0.152331i
$537$	14.8328	−	45.6507i	0.640083	−	1.96997i
$538$	−1.00000			−0.0431131
$539$		0			0
$540$	4.00000			0.172133
$541$	−10.5066	+	32.3359i	−0.451713	+	1.39023i	0.423238	+	0.906019i	$0.360893\pi$
$541$	−10.5066	+	32.3359i	−0.451713	+	1.39023i	−0.874951	+	0.484211i	$0.839107\pi$
$542$	−16.1803	+	11.7557i	−0.695005	+	0.504951i
$543$	−1.61803	−	1.17557i	−0.0694365	−	0.0504486i
$544$	−7.72542	−	23.7764i	−0.331225	−	1.01941i
$545$	3.39919	+	10.4616i	0.145605	+	0.448127i
$546$	−3.23607	−	2.35114i	−0.138491	−	0.100620i
$547$	−12.9443	+	9.40456i	−0.553457	+	0.402110i	−0.829058	−	0.559162i	$-0.811123\pi$
$547$	−12.9443	+	9.40456i	−0.553457	+	0.402110i	0.275601	+	0.961272i	$0.411123\pi$
$548$	3.09017	−	9.51057i	0.132006	−	0.406271i
$549$	−6.00000			−0.256074
$550$		0			0
$551$	54.0000			2.30048
$552$	3.70820	−	11.4127i	0.157832	−	0.485756i
$553$	−16.1803	+	11.7557i	−0.688058	+	0.499903i
$554$	−0.809017	−	0.587785i	−0.0343718	−	0.0249726i
$555$	−1.85410	−	5.70634i	−0.0787022	−	0.242221i
$556$	−0.618034	−	1.90211i	−0.0262105	−	0.0806676i
$557$	−1.61803	−	1.17557i	−0.0685583	−	0.0498105i	0.552978	−	0.833196i	$-0.313491\pi$
$557$	−1.61803	−	1.17557i	−0.0685583	−	0.0498105i	−0.621537	+	0.783385i	$0.713491\pi$
$558$	−1.61803	+	1.17557i	−0.0684968	+	0.0497659i
$559$		0			0
$560$	−2.00000			−0.0845154
$561$		0			0
$562$	6.00000			0.253095
$563$	−10.5066	+	32.3359i	−0.442799	+	1.36280i	0.442080	+	0.896976i	$0.354241\pi$
$563$	−10.5066	+	32.3359i	−0.442799	+	1.36280i	−0.884879	+	0.465821i	$0.845759\pi$
$564$	3.23607	−	2.35114i	0.136263	−	0.0990009i
$565$	7.28115	+	5.29007i	0.306320	+	0.222555i
$566$	8.65248	+	26.6296i	0.363691	+	1.11932i
$567$	−6.79837	−	20.9232i	−0.285505	−	0.878694i
$568$	−29.1246	−	21.1603i	−1.22204	−	0.887865i
$569$	4.85410	−	3.52671i	0.203495	−	0.147847i	−0.481371	−	0.876517i	$-0.659861\pi$
$569$	4.85410	−	3.52671i	0.203495	−	0.147847i	0.684865	+	0.728670i	$0.259861\pi$
$570$	3.70820	−	11.4127i	0.155320	−	0.478024i
$571$	22.0000			0.920671			0.460336	−	0.887745i	$-0.347729\pi$
$571$	22.0000			0.920671			0.460336	+	0.887745i	$0.347729\pi$
$572$		0			0
$573$	16.0000			0.668410
$574$	−3.09017	+	9.51057i	−0.128981	+	0.396963i
$575$	6.47214	−	4.70228i	0.269907	−	0.196099i
$576$	−5.66312	−	4.11450i	−0.235963	−	0.171437i
$577$	−6.48936	−	19.9722i	−0.270155	−	0.831453i	−0.990461	−	0.137796i	$-0.955998\pi$
$577$	−6.48936	−	19.9722i	−0.270155	−	0.831453i	0.720305	−	0.693657i	$-0.244002\pi$
$578$	−2.47214	−	7.60845i	−0.102827	−	0.316470i
$579$	−8.09017	−	5.87785i	−0.336216	−	0.244275i
$580$	−7.28115	+	5.29007i	−0.302333	+	0.219658i
$581$	−3.70820	+	11.4127i	−0.153842	+	0.473478i
$582$	26.0000			1.07773
$583$		0			0
$584$	6.00000			0.248282
$585$	−0.309017	+	0.951057i	−0.0127763	+	0.0393213i
$586$	−7.28115	+	5.29007i	−0.300782	+	0.218531i
$587$	11.3262	+	8.22899i	0.467484	+	0.339647i	0.796460	−	0.604691i	$-0.206704\pi$
$587$	11.3262	+	8.22899i	0.467484	+	0.339647i	−0.328976	+	0.944338i	$0.606704\pi$
$588$	1.85410	+	5.70634i	0.0764619	+	0.235325i
$589$	3.70820	+	11.4127i	0.152794	+	0.470251i
$590$	6.47214	+	4.70228i	0.266454	+	0.193590i
$591$	−17.7984	+	12.9313i	−0.732127	+	0.531922i
$592$	0.927051	−	2.85317i	0.0381016	−	0.117265i
$593$	−11.0000			−0.451716			−0.225858	−	0.974160i	$-0.572519\pi$
$593$	−11.0000			−0.451716			−0.225858	+	0.974160i	$0.572519\pi$
$594$		0			0
$595$	10.0000			0.409960
$596$	5.25329	−	16.1680i	0.215183	−	0.662265i
$597$	−38.8328	+	28.2137i	−1.58932	+	1.15471i
$598$	−1.61803	−	1.17557i	−0.0661663	−	0.0480727i
$599$	10.5066	+	32.3359i	0.429287	+	1.32121i	0.898829	+	0.438300i	$0.144419\pi$
$599$	10.5066	+	32.3359i	0.429287	+	1.32121i	−0.469542	+	0.882910i	$0.655581\pi$
$600$	−7.41641	−	22.8254i	−0.302774	−	0.931841i
$601$	−10.5172	−	7.64121i	−0.429006	−	0.311691i	0.352245	−	0.935908i	$-0.385418\pi$
$601$	−10.5172	−	7.64121i	−0.429006	−	0.311691i	−0.781251	+	0.624216i	$0.785418\pi$
$602$		0			0
$603$	0.618034	−	1.90211i	0.0251683	−	0.0774600i
$604$	−16.0000			−0.651031
$605$		0			0
$606$	−20.0000			−0.812444
$607$	3.09017	−	9.51057i	0.125426	−	0.386022i	−0.868552	−	0.495597i	$-0.834949\pi$
$607$	3.09017	−	9.51057i	0.125426	−	0.386022i	0.993978	+	0.109576i	$0.0349491\pi$
$608$	−24.2705	+	17.6336i	−0.984299	+	0.715135i
$609$	29.1246	+	21.1603i	1.18019	+	0.857457i
$610$	1.85410	+	5.70634i	0.0750704	+	0.231043i
$611$	−0.618034	−	1.90211i	−0.0250030	−	0.0769513i
$612$	4.04508	+	2.93893i	0.163513	+	0.118799i
$613$	13.7533	−	9.99235i	0.555490	−	0.403587i	−0.274315	−	0.961640i	$-0.588451\pi$
$613$	13.7533	−	9.99235i	0.555490	−	0.403587i	0.829806	+	0.558053i	$0.188451\pi$
$614$	−6.79837	+	20.9232i	−0.274360	+	0.844393i
$615$	10.0000			0.403239
$616$		0			0
$617$	−9.00000			−0.362326			−0.181163	−	0.983453i	$-0.557986\pi$
$617$	−9.00000			−0.362326			−0.181163	+	0.983453i	$0.557986\pi$
$618$	−4.94427	+	15.2169i	−0.198888	+	0.612114i
$619$	−1.61803	+	1.17557i	−0.0650343	+	0.0472502i	−0.619827	−	0.784738i	$-0.712797\pi$
$619$	−1.61803	+	1.17557i	−0.0650343	+	0.0472502i	0.554793	+	0.831988i	$0.312797\pi$
$620$	−1.61803	−	1.17557i	−0.0649818	−	0.0472120i
$621$	−2.47214	−	7.60845i	−0.0992034	−	0.305317i
$622$	−7.41641	−	22.8254i	−0.297371	−	0.915213i
$623$	14.5623	+	10.5801i	0.583426	+	0.423884i
$624$	−1.61803	+	1.17557i	−0.0647732	+	0.0470605i
$625$	3.39919	−	10.4616i	0.135967	−	0.418465i
$626$	−23.0000			−0.919265
$627$		0			0
$628$	−2.00000			−0.0798087
$629$	−4.63525	+	14.2658i	−0.184820	+	0.568817i
$630$	1.61803	−	1.17557i	0.0644640	−	0.0468358i
$631$	11.3262	+	8.22899i	0.450890	+	0.327591i	0.789947	−	0.613175i	$-0.210108\pi$
$631$	11.3262	+	8.22899i	0.450890	+	0.327591i	−0.339057	+	0.940766i	$0.610108\pi$
$632$	9.27051	+	28.5317i	0.368761	+	1.13493i
$633$	−7.41641	−	22.8254i	−0.294776	−	0.907226i
$634$	−1.61803	−	1.17557i	−0.0642603	−	0.0466879i
$635$	−12.9443	+	9.40456i	−0.513678	+	0.373209i
$636$	−5.56231	+	17.1190i	−0.220560	+	0.678813i
$637$	3.00000			0.118864
$638$		0			0
$639$	12.0000			0.474713
$640$	0.927051	−	2.85317i	0.0366449	−	0.112781i
$641$	7.28115	−	5.29007i	0.287588	−	0.208945i	−0.434632	−	0.900608i	$-0.643122\pi$
$641$	7.28115	−	5.29007i	0.287588	−	0.208945i	0.722220	+	0.691663i	$0.243122\pi$
$642$	−9.70820	−	7.05342i	−0.383152	−	0.278376i
$643$	−3.09017	−	9.51057i	−0.121864	−	0.375060i	0.871452	−	0.490480i	$-0.163179\pi$
$643$	−3.09017	−	9.51057i	−0.121864	−	0.375060i	−0.993317	+	0.115420i	$0.963179\pi$
$644$	−1.23607	−	3.80423i	−0.0487079	−	0.149908i
$645$		0			0
$646$	−24.2705	+	17.6336i	−0.954910	+	0.693783i
$647$	6.18034	−	19.0211i	0.242974	−	0.747798i	−0.752989	−	0.658033i	$-0.771389\pi$
$647$	6.18034	−	19.0211i	0.242974	−	0.747798i	0.995963	−	0.0897645i	$-0.0286114\pi$
$648$	−33.0000			−1.29636
$649$		0			0
$650$	−4.00000			−0.156893
$651$	−2.47214	+	7.60845i	−0.0968906	+	0.298199i
$652$	−1.61803	+	1.17557i	−0.0633671	+	0.0460389i
$653$	11.3262	+	8.22899i	0.443230	+	0.322025i	0.786917	−	0.617059i	$-0.211676\pi$
$653$	11.3262	+	8.22899i	0.443230	+	0.322025i	−0.343687	+	0.939084i	$0.611676\pi$
$654$	−6.79837	−	20.9232i	−0.265837	−	0.818164i
$655$		0			0
$656$	4.04508	+	2.93893i	0.157934	+	0.114746i
$657$	−1.61803	+	1.17557i	−0.0631255	+	0.0458634i
$658$	−1.23607	+	3.80423i	−0.0481869	+	0.148304i
$659$	−22.0000			−0.856998			−0.428499	−	0.903542i	$-0.640958\pi$
$659$	−22.0000			−0.856998			−0.428499	+	0.903542i	$0.640958\pi$
$660$		0			0
$661$	13.0000			0.505641			0.252821	−	0.967513i	$-0.418642\pi$
$661$	13.0000			0.505641			0.252821	+	0.967513i	$0.418642\pi$
$662$	6.18034	−	19.0211i	0.240206	−	0.739277i
$663$	8.09017	−	5.87785i	0.314196	−	0.228277i
$664$	14.5623	+	10.5801i	0.565127	+	0.410589i
$665$	−3.70820	−	11.4127i	−0.143798	−	0.442565i
$666$	0.927051	+	2.85317i	0.0359225	+	0.110558i
$667$	14.5623	+	10.5801i	0.563855	+	0.409664i
$668$	−9.70820	+	7.05342i	−0.375622	+	0.272905i
$669$	−12.3607	+	38.0423i	−0.477891	+	1.47080i
$670$	−2.00000			−0.0772667
$671$		0			0
$672$	−20.0000			−0.771517
$673$	3.09017	−	9.51057i	0.119117	−	0.366605i	−0.873666	−	0.486526i	$-0.838264\pi$
$673$	3.09017	−	9.51057i	0.119117	−	0.366605i	0.992784	+	0.119920i	$0.0382640\pi$
$674$	10.5172	−	7.64121i	0.405108	−	0.294328i
$675$	−12.9443	−	9.40456i	−0.498225	−	0.361982i
$676$	3.70820	+	11.4127i	0.142623	+	0.438949i
$677$	8.34346	+	25.6785i	0.320665	+	0.986906i	0.973359	+	0.229285i	$0.0736386\pi$
$677$	8.34346	+	25.6785i	0.320665	+	0.986906i	−0.652694	+	0.757621i	$0.726361\pi$
$678$	−14.5623	−	10.5801i	−0.559262	−	0.406328i
$679$	21.0344	−	15.2824i	0.807228	−	0.586485i
$680$	4.63525	−	14.2658i	0.177754	−	0.547070i
$681$	48.0000			1.83936
$682$		0			0
$683$	2.00000			0.0765279			0.0382639	−	0.999268i	$-0.487817\pi$
$683$	2.00000			0.0765279			0.0382639	+	0.999268i	$0.487817\pi$
$684$	1.85410	−	5.70634i	0.0708934	−	0.218187i
$685$	8.09017	−	5.87785i	0.309110	−	0.224581i
$686$	−16.1803	−	11.7557i	−0.617768	−	0.448835i
$687$	5.56231	+	17.1190i	0.212215	+	0.653131i
$688$		0			0
$689$	7.28115	+	5.29007i	0.277390	+	0.201536i
$690$	3.23607	−	2.35114i	0.123195	−	0.0895064i
$691$	6.18034	−	19.0211i	0.235111	−	0.723598i	−0.761995	−	0.647582i	$-0.775780\pi$
$691$	6.18034	−	19.0211i	0.235111	−	0.723598i	0.997107	−	0.0760155i	$-0.0242198\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	28.0000			1.06287
$695$	0.618034	−	1.90211i	0.0234434	−	0.0721513i
$696$	43.6869	−	31.7404i	1.65595	−	1.20312i
$697$	−20.2254	−	14.6946i	−0.766093	−	0.556599i
$698$	−8.34346	−	25.6785i	−0.315805	−	0.971947i
$699$	12.9787	+	39.9444i	0.490900	+	1.51083i
$700$	−6.47214	−	4.70228i	−0.244624	−	0.177730i
$701$	13.7533	−	9.99235i	0.519455	−	0.377406i	−0.296944	−	0.954895i	$-0.595967\pi$
$701$	13.7533	−	9.99235i	0.519455	−	0.377406i	0.816398	+	0.577489i	$0.195967\pi$
$702$	−1.23607	+	3.80423i	−0.0466524	+	0.143581i
$703$	18.0000			0.678883
$704$		0			0
$705$	4.00000			0.150649
$706$	2.78115	−	8.55951i	0.104670	−	0.322141i
$707$	−16.1803	+	11.7557i	−0.608524	+	0.442119i
$708$	12.9443	+	9.40456i	0.486476	+	0.353445i
$709$	−3.09017	−	9.51057i	−0.116054	−	0.357177i	0.876112	−	0.482108i	$-0.160129\pi$
$709$	−3.09017	−	9.51057i	−0.116054	−	0.357177i	−0.992165	+	0.124932i	$0.960129\pi$
$710$	−3.70820	−	11.4127i	−0.139166	−	0.428310i
$711$	−8.09017	−	5.87785i	−0.303405	−	0.220437i
$712$	21.8435	−	15.8702i	0.818618	−	0.594761i
$713$	−1.23607	+	3.80423i	−0.0462911	+	0.142469i
$714$	−20.0000			−0.748481
$715$		0			0
$716$	−24.0000			−0.896922
$717$	−3.70820	+	11.4127i	−0.138485	+	0.426214i
$718$	1.61803	−	1.17557i	0.0603845	−	0.0438719i
$719$	−24.2705	−	17.6336i	−0.905137	−	0.657621i	0.0346431	−	0.999400i	$-0.488971\pi$
$719$	−24.2705	−	17.6336i	−0.905137	−	0.657621i	−0.939780	+	0.341779i	$0.888971\pi$
$720$	−0.309017	−	0.951057i	−0.0115164	−	0.0354438i
$721$	4.94427	+	15.2169i	0.184134	+	0.566707i
$722$	13.7533	+	9.99235i	0.511844	+	0.371877i
$723$	35.5967	−	25.8626i	1.32386	−	0.961839i
$724$	−0.309017	+	0.951057i	−0.0114845	+	0.0353457i
$725$	36.0000			1.33701
$726$		0			0
$727$	−42.0000			−1.55769			−0.778847	−	0.627214i	$-0.784195\pi$
$727$	−42.0000			−1.55769			−0.778847	+	0.627214i	$0.784195\pi$
$728$	−1.85410	+	5.70634i	−0.0687176	+	0.211491i
$729$	−10.5172	+	7.64121i	−0.389527	+	0.283008i
$730$	1.61803	+	1.17557i	0.0598861	+	0.0435098i
$731$		0			0
$732$	3.70820	+	11.4127i	0.137059	+	0.421825i
$733$	7.28115	+	5.29007i	0.268936	+	0.195393i	0.714077	−	0.700067i	$-0.246847\pi$
$733$	7.28115	+	5.29007i	0.268936	+	0.195393i	−0.445141	+	0.895460i	$0.646847\pi$
$734$	−11.3262	+	8.22899i	−0.418059	+	0.303738i
$735$	−1.85410	+	5.70634i	−0.0683896	+	0.210481i
$736$	−10.0000			−0.368605
$737$		0			0
$738$	−5.00000			−0.184053
$739$	3.09017	−	9.51057i	0.113674	−	0.349852i	−0.877994	−	0.478671i	$-0.841119\pi$
$739$	3.09017	−	9.51057i	0.113674	−	0.349852i	0.991668	+	0.128819i	$0.0411187\pi$
$740$	−2.42705	+	1.76336i	−0.0892202	+	0.0648222i
$741$	−9.70820	−	7.05342i	−0.356640	−	0.259114i
$742$	−5.56231	−	17.1190i	−0.204199	−	0.628459i
$743$	11.7426	+	36.1401i	0.430796	+	1.32585i	0.897334	+	0.441352i	$0.145501\pi$
$743$	11.7426	+	36.1401i	0.430796	+	1.32585i	−0.466538	+	0.884501i	$0.654499\pi$
$744$	9.70820	+	7.05342i	0.355920	+	0.258591i
$745$	13.7533	−	9.99235i	0.503882	−	0.366091i
$746$	6.79837	−	20.9232i	0.248906	−	0.766054i
$747$	−6.00000			−0.219529
$748$		0			0
$749$	−12.0000			−0.438470
$750$	5.56231	−	17.1190i	0.203107	−	0.625098i
$751$	16.1803	−	11.7557i	0.590429	−	0.428972i	−0.252040	−	0.967717i	$-0.581101\pi$
$751$	16.1803	−	11.7557i	0.590429	−	0.428972i	0.842469	+	0.538745i	$0.181101\pi$
$752$	1.61803	+	1.17557i	0.0590036	+	0.0428686i
$753$	−1.23607	−	3.80423i	−0.0450448	−	0.138634i
$754$	−2.78115	−	8.55951i	−0.101284	−	0.311719i
$755$	−12.9443	−	9.40456i	−0.471090	−	0.342267i
$756$	−6.47214	+	4.70228i	−0.235389	+	0.171020i
$757$	16.3779	−	50.4060i	0.595265	−	1.83204i	0.0418620	−	0.999123i	$-0.486671\pi$
$757$	16.3779	−	50.4060i	0.595265	−	1.83204i	0.553403	−	0.832914i	$-0.313329\pi$
$758$	32.0000			1.16229
$759$		0			0
$760$	−18.0000			−0.652929
$761$	6.48936	−	19.9722i	0.235239	−	0.723991i	−0.761851	−	0.647753i	$-0.775709\pi$
$761$	6.48936	−	19.9722i	0.235239	−	0.723991i	0.997090	−	0.0762384i	$-0.0242910\pi$
$762$	25.8885	−	18.8091i	0.937843	−	0.681383i
$763$	−17.7984	−	12.9313i	−0.644344	−	0.468144i
$764$	−2.47214	−	7.60845i	−0.0894387	−	0.275264i
$765$	1.54508	+	4.75528i	0.0558627	+	0.171928i
$766$	16.1803	+	11.7557i	0.584619	+	0.424751i
$767$	6.47214	−	4.70228i	0.233695	−	0.169790i
$768$	−10.5066	+	32.3359i	−0.379123	+	1.16682i
$769$	−11.0000			−0.396670			−0.198335	−	0.980134i	$-0.563553\pi$
$769$	−11.0000			−0.396670			−0.198335	+	0.980134i	$0.563553\pi$
$770$		0			0
$771$	38.0000			1.36854
$772$	−1.54508	+	4.75528i	−0.0556088	+	0.171146i
$773$	33.9787	−	24.6870i	1.22213	−	0.887929i	0.225854	−	0.974161i	$-0.427483\pi$
$773$	33.9787	−	24.6870i	1.22213	−	0.887929i	0.996275	+	0.0862321i	$0.0274827\pi$
$774$		0			0
$775$	2.47214	+	7.60845i	0.0888017	+	0.273304i
$776$	−12.0517	−	37.0912i	−0.432629	−	1.33150i
$777$	9.70820	+	7.05342i	0.348280	+	0.253040i
$778$	−2.42705	+	1.76336i	−0.0870140	+	0.0632194i
$779$	−9.27051	+	28.5317i	−0.332150	+	1.02225i
$780$	2.00000			0.0716115
$781$		0			0
$782$	−10.0000			−0.357599
$783$	11.1246	−	34.2380i	0.397561	−	1.22357i
$784$	−2.42705	+	1.76336i	−0.0866804	+	0.0629770i
$785$	−1.61803	−	1.17557i	−0.0577501	−	0.0419579i
$786$		0			0
$787$	−8.65248	−	26.6296i	−0.308427	−	0.949242i	−0.978376	−	0.206835i	$-0.933684\pi$
$787$	−8.65248	−	26.6296i	−0.308427	−	0.949242i	0.669948	−	0.742408i	$-0.266316\pi$
$788$	8.89919	+	6.46564i	0.317020	+	0.230329i
$789$	−35.5967	+	25.8626i	−1.26728	+	0.920731i
$790$	−3.09017	+	9.51057i	−0.109943	+	0.338371i
$791$	−18.0000			−0.640006
$792$		0			0
$793$	6.00000			0.213066
$794$	−4.01722	+	12.3637i	−0.142566	+	0.438773i
$795$	−14.5623	+	10.5801i	−0.516472	+	0.375239i
$796$	19.4164	+	14.1068i	0.688196	+	0.500004i
$797$	−3.09017	−	9.51057i	−0.109459	−	0.336882i	0.881292	−	0.472573i	$-0.156675\pi$
$797$	−3.09017	−	9.51057i	−0.109459	−	0.336882i	−0.990751	+	0.135691i	$0.956675\pi$
$798$	7.41641	+	22.8254i	0.262538	+	0.808009i
$799$	−8.09017	−	5.87785i	−0.286210	−	0.207943i
$800$	−16.1803	+	11.7557i	−0.572061	+	0.415627i
$801$	−2.78115	+	8.55951i	−0.0982672	+	0.302435i
$802$	−23.0000			−0.812158
$803$		0			0
$804$	−4.00000			−0.141069
$805$	1.23607	−	3.80423i	0.0435657	−	0.134081i
$806$	1.61803	−	1.17557i	0.0569928	−	0.0414077i
$807$	−1.61803	−	1.17557i	−0.0569575	−	0.0413820i
$808$	9.27051	+	28.5317i	0.326135	+	1.00374i
$809$	−1.85410	−	5.70634i	−0.0651868	−	0.200624i	0.913158	−	0.407605i	$-0.133636\pi$
$809$	−1.85410	−	5.70634i	−0.0651868	−	0.200624i	−0.978345	+	0.206981i	$0.933636\pi$
$810$	−8.89919	−	6.46564i	−0.312686	−	0.227179i
$811$	22.6525	−	16.4580i	0.795436	−	0.577918i	−0.114136	−	0.993465i	$-0.536410\pi$
$811$	22.6525	−	16.4580i	0.795436	−	0.577918i	0.909572	+	0.415547i	$0.136410\pi$
$812$	5.56231	−	17.1190i	0.195199	−	0.600760i
$813$	−40.0000			−1.40286
$814$		0			0
$815$	−2.00000			−0.0700569
$816$	−3.09017	+	9.51057i	−0.108178	+	0.332936i
$817$		0			0
$818$	16.9894	+	12.3435i	0.594019	+	0.431580i
$819$	−0.618034	−	1.90211i	−0.0215959	−	0.0664652i
$820$	−1.54508	−	4.75528i	−0.0539567	−	0.166062i
$821$	−1.61803	−	1.17557i	−0.0564698	−	0.0410277i	0.559192	−	0.829038i	$-0.311111\pi$
$821$	−1.61803	−	1.17557i	−0.0564698	−	0.0410277i	−0.615662	+	0.788010i	$0.711111\pi$
$822$	−16.1803	+	11.7557i	−0.564354	+	0.410027i
$823$	−7.41641	+	22.8254i	−0.258520	+	0.795642i	0.734596	+	0.678505i	$0.237372\pi$
$823$	−7.41641	+	22.8254i	−0.258520	+	0.795642i	−0.993116	+	0.117137i	$0.962628\pi$
$824$	24.0000			0.836080
$825$		0			0
$826$	−16.0000			−0.556711
$827$	3.09017	−	9.51057i	0.107456	−	0.330715i	−0.882843	−	0.469668i	$-0.844374\pi$
$827$	3.09017	−	9.51057i	0.107456	−	0.330715i	0.990299	+	0.138953i	$0.0443737\pi$
$828$	1.61803	−	1.17557i	0.0562306	−	0.0408539i
$829$	38.0238	+	27.6259i	1.32062	+	0.959487i	0.999924	+	0.0123055i	$0.00391706\pi$
$829$	38.0238	+	27.6259i	1.32062	+	0.959487i	0.320697	+	0.947182i	$0.396083\pi$
$830$	1.85410	+	5.70634i	0.0643568	+	0.198070i
$831$	−0.618034	−	1.90211i	−0.0214394	−	0.0659836i
$832$	5.66312	+	4.11450i	0.196333	+	0.142645i
$833$	12.1353	−	8.81678i	0.420462	−	0.305483i
$834$	−1.23607	+	3.80423i	−0.0428015	+	0.131730i
$835$	−12.0000			−0.415277
$836$		0			0
$837$	8.00000			0.276520
$838$	−0.618034	+	1.90211i	−0.0213496	+	0.0657074i
$839$	−37.2148	+	27.0381i	−1.28480	+	0.933460i	−0.999687	−	0.0250351i	$-0.992030\pi$
$839$	−37.2148	+	27.0381i	−1.28480	+	0.933460i	−0.285110	+	0.958495i	$0.592030\pi$
$840$	−9.70820	−	7.05342i	−0.334965	−	0.243366i
$841$	16.0689	+	49.4549i	0.554099	+	1.70534i
$842$	−4.01722	−	12.3637i	−0.138443	−	0.426082i
$843$	9.70820	+	7.05342i	0.334368	+	0.242933i
$844$	−9.70820	+	7.05342i	−0.334170	+	0.242789i
$845$	−3.70820	+	11.4127i	−0.127566	+	0.392608i
$846$	−2.00000			−0.0687614
$847$		0			0
$848$	−9.00000			−0.309061
$849$	−17.3050	+	53.2592i	−0.593904	+	1.82785i
$850$	−16.1803	+	11.7557i	−0.554981	+	0.403217i
$851$	4.85410	+	3.52671i	0.166396	+	0.120894i
$852$	−7.41641	−	22.8254i	−0.254082	−	0.781984i
$853$	−5.25329	−	16.1680i	−0.179869	−	0.553580i	0.819953	−	0.572431i	$-0.193999\pi$
$853$	−5.25329	−	16.1680i	−0.179869	−	0.553580i	−0.999822	+	0.0188502i	$0.993999\pi$
$854$	−9.70820	−	7.05342i	−0.332208	−	0.241363i
$855$	4.85410	−	3.52671i	0.166007	−	0.120611i
$856$	−5.56231	+	17.1190i	−0.190116	+	0.585116i
$857$	22.0000			0.751506			0.375753	−	0.926720i	$-0.377384\pi$
$857$	22.0000			0.751506			0.375753	+	0.926720i	$0.377384\pi$
$858$		0			0
$859$	24.0000			0.818869			0.409435	−	0.912339i	$-0.365726\pi$
$859$	24.0000			0.818869			0.409435	+	0.912339i	$0.365726\pi$
$860$		0			0
$861$	−16.1803	+	11.7557i	−0.551425	+	0.400633i
$862$	−9.70820	−	7.05342i	−0.330663	−	0.240241i
$863$	−16.6869	−	51.3571i	−0.568029	−	1.74821i	−0.658775	−	0.752340i	$-0.728925\pi$
$863$	−16.6869	−	51.3571i	−0.568029	−	1.74821i	0.0907454	−	0.995874i	$-0.471075\pi$
$864$	6.18034	+	19.0211i	0.210259	+	0.647112i
$865$	4.85410	+	3.52671i	0.165044	+	0.119912i
$866$	15.3713	−	11.1679i	0.522339	−	0.379501i
$867$	4.94427	−	15.2169i	0.167916	−	0.516793i
$868$	4.00000			0.135769
$869$		0			0
$870$	18.0000			0.610257
$871$	−0.618034	+	1.90211i	−0.0209413	+	0.0644506i
$872$	−26.6976	+	19.3969i	−0.904093	+	0.656862i
$873$	10.5172	+	7.64121i	0.355954	+	0.258616i
$874$	3.70820	+	11.4127i	0.125432	+	0.386040i
$875$	−5.56231	−	17.1190i	−0.188040	−	0.578728i
$876$	3.23607	+	2.35114i	0.109337	+	0.0794377i
$877$	−21.8435	+	15.8702i	−0.737601	+	0.535899i	−0.891959	−	0.452116i	$-0.850669\pi$
$877$	−21.8435	+	15.8702i	−0.737601	+	0.535899i	0.154358	+	0.988015i	$0.450669\pi$
$878$	6.79837	−	20.9232i	0.229434	−	0.706125i
$879$	−18.0000			−0.607125
$880$		0			0
$881$	35.0000			1.17918			0.589590	−	0.807703i	$-0.299289\pi$
$881$	35.0000			1.17918			0.589590	+	0.807703i	$0.299289\pi$
$882$	0.927051	−	2.85317i	0.0312154	−	0.0960712i
$883$	16.1803	−	11.7557i	0.544512	−	0.395611i	−0.281246	−	0.959636i	$-0.590748\pi$
$883$	16.1803	−	11.7557i	0.544512	−	0.395611i	0.825758	+	0.564025i	$0.190748\pi$
$884$	−4.04508	−	2.93893i	−0.136051	−	0.0988468i
$885$	4.94427	+	15.2169i	0.166200	+	0.511511i
$886$	6.18034	+	19.0211i	0.207633	+	0.639027i
$887$	−37.2148	−	27.0381i	−1.24955	−	0.907851i	−0.251354	−	0.967895i	$-0.580876\pi$
$887$	−37.2148	−	27.0381i	−1.24955	−	0.907851i	−0.998196	+	0.0600439i	$0.980876\pi$
$888$	14.5623	−	10.5801i	0.488679	−	0.355046i
$889$	9.88854	−	30.4338i	0.331651	−	1.02072i
$890$	9.00000			0.301681
$891$		0			0
$892$	20.0000			0.669650
$893$	−3.70820	+	11.4127i	−0.124090	+	0.381911i
$894$	−27.5066	+	19.9847i	−0.919958	+	0.668388i
$895$	−19.4164	−	14.1068i	−0.649019	−	0.471540i
$896$	1.85410	+	5.70634i	0.0619412	+	0.190635i
$897$	−1.23607	−	3.80423i	−0.0412711	−	0.127019i
$898$	−10.5172	−	7.64121i	−0.350964	−	0.254990i
$899$	−14.5623	+	10.5801i	−0.485680	+	0.352867i
$900$	1.23607	−	3.80423i	0.0412023	−	0.126808i
$901$	45.0000			1.49917
$902$		0			0
$903$		0			0
$904$	−8.34346	+	25.6785i	−0.277499	+	0.854055i
$905$	−0.809017	+	0.587785i	−0.0268926	+	0.0195386i
$906$	25.8885	+	18.8091i	0.860089	+	0.624891i
$907$	3.70820	+	11.4127i	0.123129	+	0.378952i	0.993556	−	0.113346i	$-0.0361570\pi$
$907$	3.70820	+	11.4127i	0.123129	+	0.378952i	−0.870427	+	0.492298i	$0.836157\pi$
$908$	−7.41641	−	22.8254i	−0.246122	−	0.757486i
$909$	−8.09017	−	5.87785i	−0.268334	−	0.194956i
$910$	−1.61803	+	1.17557i	−0.0536373	+	0.0389698i
$911$	−7.41641	+	22.8254i	−0.245717	+	0.756238i	0.749801	+	0.661663i	$0.230149\pi$
$911$	−7.41641	+	22.8254i	−0.245717	+	0.756238i	−0.995518	+	0.0945746i	$0.969851\pi$
$912$	12.0000			0.397360
$913$		0			0
$914$	39.0000			1.29001
$915$	−3.70820	+	11.4127i	−0.122589	+	0.377292i
$916$	7.28115	−	5.29007i	0.240576	−	0.174789i
$917$		0			0
$918$	6.18034	+	19.0211i	0.203982	+	0.627791i
$919$	−8.65248	−	26.6296i	−0.285419	−	0.878429i	−0.986273	−	0.165124i	$-0.947198\pi$
$919$	−8.65248	−	26.6296i	−0.285419	−	0.878429i	0.700854	−	0.713305i	$-0.252802\pi$
$920$	−4.85410	−	3.52671i	−0.160035	−	0.116272i
$921$	−35.5967	+	25.8626i	−1.17295	+	0.852200i
$922$	10.1976	−	31.3849i	0.335839	−	1.03361i
$923$	−12.0000			−0.394985
$924$		0			0
$925$	12.0000			0.394558
$926$	6.18034	−	19.0211i	0.203099	−	0.625073i
$927$	−6.47214	+	4.70228i	−0.212573	+	0.154443i
$928$	−36.4058	−	26.4503i	−1.19508	−	0.868275i
$929$	−6.48936	−	19.9722i	−0.212909	−	0.655266i	−0.999295	−	0.0375315i	$-0.988051\pi$
$929$	−6.48936	−	19.9722i	−0.212909	−	0.655266i	0.786387	−	0.617735i	$-0.211949\pi$
$930$	1.23607	+	3.80423i	0.0405323	+	0.124745i
$931$	−14.5623	−	10.5801i	−0.477260	−	0.346750i
$932$	16.9894	−	12.3435i	0.556505	−	0.404324i
$933$	14.8328	−	45.6507i	0.485605	−	1.49454i
$934$	−12.0000			−0.392652
$935$		0			0
$936$	−3.00000			−0.0980581
$937$	−7.10739	+	21.8743i	−0.232188	+	0.714602i	0.765294	+	0.643681i	$0.222594\pi$
$937$	−7.10739	+	21.8743i	−0.232188	+	0.714602i	−0.997482	+	0.0709209i	$0.977406\pi$
$938$	3.23607	−	2.35114i	0.105661	−	0.0767675i
$939$	−37.2148	−	27.0381i	−1.21446	−	0.882356i
$940$	−0.618034	−	1.90211i	−0.0201580	−	0.0620401i
$941$	8.34346	+	25.6785i	0.271989	+	0.837096i	0.990000	+	0.141065i	$0.0450526\pi$
$941$	8.34346	+	25.6785i	0.271989	+	0.837096i	−0.718011	+	0.696031i	$0.754947\pi$
$942$	3.23607	+	2.35114i	0.105437	+	0.0766043i
$943$	−8.09017	+	5.87785i	−0.263452	+	0.191409i
$944$	−2.47214	+	7.60845i	−0.0804612	+	0.247634i
$945$	−8.00000			−0.260240
$946$		0			0
$947$	−42.0000			−1.36482			−0.682408	−	0.730971i	$-0.739067\pi$
$947$	−42.0000			−1.36482			−0.682408	+	0.730971i	$0.739067\pi$
$948$	−6.18034	+	19.0211i	−0.200728	+	0.617778i
$949$	1.61803	−	1.17557i	0.0525236	−	0.0381606i
$950$	19.4164	+	14.1068i	0.629951	+	0.457687i
$951$	−1.23607	−	3.80423i	−0.0400823	−	0.123360i
$952$	9.27051	+	28.5317i	0.300459	+	0.924718i
$953$	25.0795	+	18.2213i	0.812406	+	0.590247i	0.914527	−	0.404525i	$-0.132563\pi$
$953$	25.0795	+	18.2213i	0.812406	+	0.590247i	−0.102121	+	0.994772i	$0.532563\pi$
$954$	7.28115	−	5.29007i	0.235736	−	0.171272i
$955$	2.47214	−	7.60845i	0.0799964	−	0.246204i
$956$	6.00000			0.194054
$957$		0			0
$958$	−16.0000			−0.516937
$959$	−6.18034	+	19.0211i	−0.199574	+	0.614224i
$960$	−11.3262	+	8.22899i	−0.365553	+	0.265590i
$961$	21.8435	+	15.8702i	0.704628	+	0.511942i
$962$	−0.927051	−	2.85317i	−0.0298893	−	0.0919899i
$963$	−1.85410	−	5.70634i	−0.0597476	−	0.183884i
$964$	−17.7984	−	12.9313i	−0.573247	−	0.416488i
$965$	−4.04508	+	2.93893i	−0.130216	+	0.0946074i
$966$	−2.47214	+	7.60845i	−0.0795397	+	0.244798i
$967$	−22.0000			−0.707472			−0.353736	−	0.935345i	$-0.615089\pi$
$967$	−22.0000			−0.707472			−0.353736	+	0.935345i	$0.615089\pi$
$968$		0			0
$969$	−60.0000			−1.92748
$970$	4.01722	−	12.3637i	0.128985	−	0.396976i
$971$	−1.61803	+	1.17557i	−0.0519252	+	0.0377259i	−0.613445	−	0.789737i	$-0.710217\pi$
$971$	−1.61803	+	1.17557i	−0.0519252	+	0.0377259i	0.561520	+	0.827463i	$0.310217\pi$
$972$	−8.09017	−	5.87785i	−0.259492	−	0.188532i
$973$	1.23607	+	3.80423i	0.0396265	+	0.121958i
$974$	−0.618034	−	1.90211i	−0.0198031	−	0.0609476i
$975$	−6.47214	−	4.70228i	−0.207274	−	0.150594i
$976$	−4.85410	+	3.52671i	−0.155376	+	0.112887i
$977$	−17.6140	+	54.2102i	−0.563521	+	1.73434i	0.108785	+	0.994065i	$0.465304\pi$
$977$	−17.6140	+	54.2102i	−0.563521	+	1.73434i	−0.672306	+	0.740273i	$0.734696\pi$
$978$	4.00000			0.127906
$979$		0			0
$980$	3.00000			0.0958315
$981$	3.39919	−	10.4616i	0.108528	−	0.334014i
$982$	1.61803	−	1.17557i	0.0516335	−	0.0375140i
$983$	29.1246	+	21.1603i	0.928931	+	0.674908i	0.945731	−	0.324951i	$-0.105348\pi$
$983$	29.1246	+	21.1603i	0.928931	+	0.674908i	−0.0168000	+	0.999859i	$0.505348\pi$
$984$	9.27051	+	28.5317i	0.295533	+	0.909557i
$985$	3.39919	+	10.4616i	0.108307	+	0.333335i
$986$	−36.4058	−	26.4503i	−1.15940	−	0.842350i
$987$	−6.47214	+	4.70228i	−0.206010	+	0.149675i
$988$	−1.85410	+	5.70634i	−0.0589868	+	0.181543i
$989$		0			0
$990$		0			0
$991$	−20.0000			−0.635321			−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000			−0.635321			−0.317660	+	0.948205i	$0.602897\pi$
$992$	3.09017	−	9.51057i	0.0981130	−	0.301961i
$993$	32.3607	−	23.5114i	1.02694	−	0.746112i
$994$	19.4164	+	14.1068i	0.615851	+	0.447442i
$995$	7.41641	+	22.8254i	0.235116	+	0.723612i
$996$	3.70820	+	11.4127i	0.117499	+	0.361625i
$997$	42.8779	+	31.1526i	1.35796	+	0.986613i	0.998572	+	0.0534239i	$0.0170134\pi$
$997$	42.8779	+	31.1526i	1.35796	+	0.986613i	0.359385	+	0.933189i	$0.382987\pi$
$998$	6.47214	−	4.70228i	0.204872	−	0.148848i
$999$	3.70820	−	11.4127i	0.117322	−	0.361081i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.2.c.d.9.1		4
11.2	odd	10		121.2.c.b.3.1		4
11.3	even	5	inner	121.2.c.d.81.1		4
11.4	even	5		121.2.a.a.1.1	✓	1
11.5	even	5	inner	121.2.c.d.27.1		4
11.6	odd	10		121.2.c.b.27.1		4
11.7	odd	10		121.2.a.c.1.1	yes	1
11.8	odd	10		121.2.c.b.81.1		4
11.9	even	5	inner	121.2.c.d.3.1		4
11.10	odd	2		121.2.c.b.9.1		4
33.26	odd	10		1089.2.a.i.1.1		1
33.29	even	10		1089.2.a.c.1.1		1
44.7	even	10		1936.2.a.b.1.1		1
44.15	odd	10		1936.2.a.a.1.1		1
55.4	even	10		3025.2.a.e.1.1		1
55.29	odd	10		3025.2.a.b.1.1		1
77.48	odd	10		5929.2.a.a.1.1		1
77.62	even	10		5929.2.a.g.1.1		1
88.29	odd	10		7744.2.a.c.1.1		1
88.37	even	10		7744.2.a.f.1.1		1
88.51	even	10		7744.2.a.bf.1.1		1
88.59	odd	10		7744.2.a.be.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.2.a.a.1.1	✓	1	11.4	even	5
121.2.a.c.1.1	yes	1	11.7	odd	10
121.2.c.b.3.1		4	11.2	odd	10
121.2.c.b.9.1		4	11.10	odd	2
121.2.c.b.27.1		4	11.6	odd	10
121.2.c.b.81.1		4	11.8	odd	10
121.2.c.d.3.1		4	11.9	even	5	inner
121.2.c.d.9.1		4	1.1	even	1	trivial
121.2.c.d.27.1		4	11.5	even	5	inner
121.2.c.d.81.1		4	11.3	even	5	inner
1089.2.a.c.1.1		1	33.29	even	10
1089.2.a.i.1.1		1	33.26	odd	10
1936.2.a.a.1.1		1	44.15	odd	10
1936.2.a.b.1.1		1	44.7	even	10
3025.2.a.b.1.1		1	55.29	odd	10
3025.2.a.e.1.1		1	55.4	even	10
5929.2.a.a.1.1		1	77.48	odd	10
5929.2.a.g.1.1		1	77.62	even	10
7744.2.a.c.1.1		1	88.29	odd	10
7744.2.a.f.1.1		1	88.37	even	10
7744.2.a.be.1.1		1	88.59	odd	10
7744.2.a.bf.1.1		1	88.51	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)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-1.61803 + 1.17557i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.618034 - 1.90211i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(-2.42705 + 1.76336i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-1.61803 + 1.17557i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.618034 - 1.90211i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(-2.42705 + 1.76336i) q^{8} +(0.309017 - 0.951057i) q^{9} -1.00000 q^{10} -2.00000 q^{12} +(-0.309017 + 0.951057i) q^{13} +(1.61803 - 1.17557i) q^{14} +(-1.61803 - 1.17557i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(1.54508 + 4.75528i) q^{17} +(0.809017 + 0.587785i) q^{18} +(4.85410 - 3.52671i) q^{19} +(-0.309017 + 0.951057i) q^{20} +4.00000 q^{21} +2.00000 q^{23} +(1.85410 - 5.70634i) q^{24} +(3.23607 - 2.35114i) q^{25} +(-0.809017 - 0.587785i) q^{26} +(-1.23607 - 3.80423i) q^{27} +(-0.618034 - 1.90211i) q^{28} +(7.28115 + 5.29007i) q^{29} +(1.61803 - 1.17557i) q^{30} +(-0.618034 + 1.90211i) q^{31} -5.00000 q^{32} -5.00000 q^{34} +(0.618034 - 1.90211i) q^{35} +(0.809017 - 0.587785i) q^{36} +(2.42705 + 1.76336i) q^{37} +(1.85410 + 5.70634i) q^{38} +(-0.618034 - 1.90211i) q^{39} +(-2.42705 - 1.76336i) q^{40} +(-4.04508 + 2.93893i) q^{41} +(-1.23607 + 3.80423i) q^{42} +1.00000 q^{45} +(-0.618034 + 1.90211i) q^{46} +(-1.61803 + 1.17557i) q^{47} +(1.61803 + 1.17557i) q^{48} +(-0.927051 - 2.85317i) q^{49} +(1.23607 + 3.80423i) q^{50} +(-8.09017 - 5.87785i) q^{51} +(-0.809017 + 0.587785i) q^{52} +(2.78115 - 8.55951i) q^{53} +4.00000 q^{54} +6.00000 q^{56} +(-3.70820 + 11.4127i) q^{57} +(-7.28115 + 5.29007i) q^{58} +(-6.47214 - 4.70228i) q^{59} +(-0.618034 - 1.90211i) q^{60} +(-1.85410 - 5.70634i) q^{61} +(-1.61803 - 1.17557i) q^{62} +(-1.61803 + 1.17557i) q^{63} +(2.16312 - 6.65740i) q^{64} -1.00000 q^{65} +2.00000 q^{67} +(-1.54508 + 4.75528i) q^{68} +(-3.23607 + 2.35114i) q^{69} +(1.61803 + 1.17557i) q^{70} +(3.70820 + 11.4127i) q^{71} +(0.927051 + 2.85317i) q^{72} +(-1.61803 - 1.17557i) q^{73} +(-2.42705 + 1.76336i) q^{74} +(-2.47214 + 7.60845i) q^{75} +6.00000 q^{76} +2.00000 q^{78} +(3.09017 - 9.51057i) q^{79} +(0.809017 - 0.587785i) q^{80} +(8.89919 + 6.46564i) q^{81} +(-1.54508 - 4.75528i) q^{82} +(-1.85410 - 5.70634i) q^{83} +(3.23607 + 2.35114i) q^{84} +(-4.04508 + 2.93893i) q^{85} -18.0000 q^{87} -9.00000 q^{89} +(-0.309017 + 0.951057i) q^{90} +(1.61803 - 1.17557i) q^{91} +(1.61803 + 1.17557i) q^{92} +(-1.23607 - 3.80423i) q^{93} +(-0.618034 - 1.90211i) q^{94} +(4.85410 + 3.52671i) q^{95} +(8.09017 - 5.87785i) q^{96} +(-4.01722 + 12.3637i) q^{97} +3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 2 q^{3} + q^{4} - q^{5} + 2 q^{6} - 2 q^{7} - 3 q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 - 2 * q^3 + q^4 - q^5 + 2 * q^6 - 2 * q^7 - 3 * q^8 - q^9	\( 4 q + q^{2} - 2 q^{3} + q^{4} - q^{5} + 2 q^{6} - 2 q^{7} - 3 q^{8} - q^{9} - 4 q^{10} - 8 q^{12} + q^{13} + 2 q^{14} - 2 q^{15} + q^{16} - 5 q^{17} + q^{18} + 6 q^{19} + q^{20} + 16 q^{21} + 8 q^{23} - 6 q^{24} + 4 q^{25} - q^{26} + 4 q^{27} + 2 q^{28} + 9 q^{29} + 2 q^{30} + 2 q^{31} - 20 q^{32} - 20 q^{34} - 2 q^{35} + q^{36} + 3 q^{37} - 6 q^{38} + 2 q^{39} - 3 q^{40} - 5 q^{41} + 4 q^{42} + 4 q^{45} + 2 q^{46} - 2 q^{47} + 2 q^{48} + 3 q^{49} - 4 q^{50} - 10 q^{51} - q^{52} - 9 q^{53} + 16 q^{54} + 24 q^{56} + 12 q^{57} - 9 q^{58} - 8 q^{59} + 2 q^{60} + 6 q^{61} - 2 q^{62} - 2 q^{63} - 7 q^{64} - 4 q^{65} + 8 q^{67} + 5 q^{68} - 4 q^{69} + 2 q^{70} - 12 q^{71} - 3 q^{72} - 2 q^{73} - 3 q^{74} + 8 q^{75} + 24 q^{76} + 8 q^{78} - 10 q^{79} + q^{80} + 11 q^{81} + 5 q^{82} + 6 q^{83} + 4 q^{84} - 5 q^{85} - 72 q^{87} - 36 q^{89} + q^{90} + 2 q^{91} + 2 q^{92} + 4 q^{93} + 2 q^{94} + 6 q^{95} + 10 q^{96} + 13 q^{97} + 12 q^{98}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 + q^4 - q^5 + 2 * q^6 - 2 * q^7 - 3 * q^8 - q^9 - 4 * q^10 - 8 * q^12 + q^13 + 2 * q^14 - 2 * q^15 + q^16 - 5 * q^17 + q^18 + 6 * q^19 + q^20 + 16 * q^21 + 8 * q^23 - 6 * q^24 + 4 * q^25 - q^26 + 4 * q^27 + 2 * q^28 + 9 * q^29 + 2 * q^30 + 2 * q^31 - 20 * q^32 - 20 * q^34 - 2 * q^35 + q^36 + 3 * q^37 - 6 * q^38 + 2 * q^39 - 3 * q^40 - 5 * q^41 + 4 * q^42 + 4 * q^45 + 2 * q^46 - 2 * q^47 + 2 * q^48 + 3 * q^49 - 4 * q^50 - 10 * q^51 - q^52 - 9 * q^53 + 16 * q^54 + 24 * q^56 + 12 * q^57 - 9 * q^58 - 8 * q^59 + 2 * q^60 + 6 * q^61 - 2 * q^62 - 2 * q^63 - 7 * q^64 - 4 * q^65 + 8 * q^67 + 5 * q^68 - 4 * q^69 + 2 * q^70 - 12 * q^71 - 3 * q^72 - 2 * q^73 - 3 * q^74 + 8 * q^75 + 24 * q^76 + 8 * q^78 - 10 * q^79 + q^80 + 11 * q^81 + 5 * q^82 + 6 * q^83 + 4 * q^84 - 5 * q^85 - 72 * q^87 - 36 * q^89 + q^90 + 2 * q^91 + 2 * q^92 + 4 * q^93 + 2 * q^94 + 6 * q^95 + 10 * q^96 + 13 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more