LMFDB - Embedded newform 363.2.e.e.124.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(124,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("363.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.e (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			124.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	363.124
Dual form			363.2.e.e.202.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.61803 + 1.17557i) q^{5} +(0.809017 + 0.587785i) q^{6} +(1.23607 - 3.80423i) q^{7} +(-0.927051 - 2.85317i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.61803 + 1.17557i) q^{5} +(0.809017 + 0.587785i) q^{6} +(1.23607 - 3.80423i) q^{7} +(-0.927051 - 2.85317i) q^{8} +(-0.809017 + 0.587785i) q^{9} -2.00000 q^{10} +1.00000 q^{12} +(1.61803 - 1.17557i) q^{13} +(1.23607 + 3.80423i) q^{14} +(0.618034 - 1.90211i) q^{15} +(0.809017 + 0.587785i) q^{16} +(1.61803 + 1.17557i) q^{17} +(0.309017 - 0.951057i) q^{18} +(-1.61803 + 1.17557i) q^{20} -4.00000 q^{21} +8.00000 q^{23} +(-2.42705 + 1.76336i) q^{24} +(-0.309017 - 0.951057i) q^{25} +(-0.618034 + 1.90211i) q^{26} +(0.809017 + 0.587785i) q^{27} +(3.23607 + 2.35114i) q^{28} +(-1.85410 + 5.70634i) q^{29} +(0.618034 + 1.90211i) q^{30} +(6.47214 - 4.70228i) q^{31} +5.00000 q^{32} -2.00000 q^{34} +(6.47214 - 4.70228i) q^{35} +(-0.309017 - 0.951057i) q^{36} +(1.85410 - 5.70634i) q^{37} +(-1.61803 - 1.17557i) q^{39} +(1.85410 - 5.70634i) q^{40} +(-0.618034 - 1.90211i) q^{41} +(3.23607 - 2.35114i) q^{42} -2.00000 q^{45} +(-6.47214 + 4.70228i) q^{46} +(2.47214 + 7.60845i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-7.28115 - 5.29007i) q^{49} +(0.809017 + 0.587785i) q^{50} +(0.618034 - 1.90211i) q^{51} +(0.618034 + 1.90211i) q^{52} +(-4.85410 + 3.52671i) q^{53} -1.00000 q^{54} -12.0000 q^{56} +(-1.85410 - 5.70634i) q^{58} +(-1.23607 + 3.80423i) q^{59} +(1.61803 + 1.17557i) q^{60} +(-4.85410 - 3.52671i) q^{61} +(-2.47214 + 7.60845i) q^{62} +(1.23607 + 3.80423i) q^{63} +(-5.66312 + 4.11450i) q^{64} +4.00000 q^{65} -4.00000 q^{67} +(-1.61803 + 1.17557i) q^{68} +(-2.47214 - 7.60845i) q^{69} +(-2.47214 + 7.60845i) q^{70} +(2.42705 + 1.76336i) q^{72} +(-4.32624 + 13.3148i) q^{73} +(1.85410 + 5.70634i) q^{74} +(-0.809017 + 0.587785i) q^{75} +2.00000 q^{78} +(3.23607 - 2.35114i) q^{79} +(0.618034 + 1.90211i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.61803 + 1.17557i) q^{82} +(-9.70820 - 7.05342i) q^{83} +(1.23607 - 3.80423i) q^{84} +(1.23607 + 3.80423i) q^{85} +6.00000 q^{87} -6.00000 q^{89} +(1.61803 - 1.17557i) q^{90} +(-2.47214 - 7.60845i) q^{91} +(-2.47214 + 7.60845i) q^{92} +(-6.47214 - 4.70228i) q^{93} +(-6.47214 - 4.70228i) q^{94} +(-1.54508 - 4.75528i) q^{96} +(-1.61803 + 1.17557i) q^{97} +9.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{3} + q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 3 q^{8} - q^{9}+O(q^{10}) $ 4 * q - q^2 + q^3 + q^4 + 2 * q^5 + q^6 - 4 * q^7 + 3 * q^8 - q^9	$ 4 q - q^{2} + q^{3} + q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 3 q^{8} - q^{9} - 8 q^{10} + 4 q^{12} + 2 q^{13} - 4 q^{14} - 2 q^{15} + q^{16} + 2 q^{17} - q^{18} - 2 q^{20} - 16 q^{21} + 32 q^{23} - 3 q^{24} + q^{25} + 2 q^{26} + q^{27} + 4 q^{28} + 6 q^{29} - 2 q^{30} + 8 q^{31} + 20 q^{32} - 8 q^{34} + 8 q^{35} + q^{36} - 6 q^{37} - 2 q^{39} - 6 q^{40} + 2 q^{41} + 4 q^{42} - 8 q^{45} - 8 q^{46} - 8 q^{47} - q^{48} - 9 q^{49} + q^{50} - 2 q^{51} - 2 q^{52} - 6 q^{53} - 4 q^{54} - 48 q^{56} + 6 q^{58} + 4 q^{59} + 2 q^{60} - 6 q^{61} + 8 q^{62} - 4 q^{63} - 7 q^{64} + 16 q^{65} - 16 q^{67} - 2 q^{68} + 8 q^{69} + 8 q^{70} + 3 q^{72} + 14 q^{73} - 6 q^{74} - q^{75} + 8 q^{78} + 4 q^{79} - 2 q^{80} - q^{81} + 2 q^{82} - 12 q^{83} - 4 q^{84} - 4 q^{85} + 24 q^{87} - 24 q^{89} + 2 q^{90} + 8 q^{91} + 8 q^{92} - 8 q^{93} - 8 q^{94} + 5 q^{96} - 2 q^{97} + 36 q^{98}+O(q^{100}) $ 4 * q - q^2 + q^3 + q^4 + 2 * q^5 + q^6 - 4 * q^7 + 3 * q^8 - q^9 - 8 * q^10 + 4 * q^12 + 2 * q^13 - 4 * q^14 - 2 * q^15 + q^16 + 2 * q^17 - q^18 - 2 * q^20 - 16 * q^21 + 32 * q^23 - 3 * q^24 + q^25 + 2 * q^26 + q^27 + 4 * q^28 + 6 * q^29 - 2 * q^30 + 8 * q^31 + 20 * q^32 - 8 * q^34 + 8 * q^35 + q^36 - 6 * q^37 - 2 * q^39 - 6 * q^40 + 2 * q^41 + 4 * q^42 - 8 * q^45 - 8 * q^46 - 8 * q^47 - q^48 - 9 * q^49 + q^50 - 2 * q^51 - 2 * q^52 - 6 * q^53 - 4 * q^54 - 48 * q^56 + 6 * q^58 + 4 * q^59 + 2 * q^60 - 6 * q^61 + 8 * q^62 - 4 * q^63 - 7 * q^64 + 16 * q^65 - 16 * q^67 - 2 * q^68 + 8 * q^69 + 8 * q^70 + 3 * q^72 + 14 * q^73 - 6 * q^74 - q^75 + 8 * q^78 + 4 * q^79 - 2 * q^80 - q^81 + 2 * q^82 - 12 * q^83 - 4 * q^84 - 4 * q^85 + 24 * q^87 - 24 * q^89 + 2 * q^90 + 8 * q^91 + 8 * q^92 - 8 * q^93 - 8 * q^94 + 5 * q^96 - 2 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i	−0.835853	−	0.548953i	$-0.815027\pi$
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i	0.263792	+	0.964580i	$0.415027\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	1.61803	+	1.17557i	0.723607	+	0.525731i	0.887535	−	0.460741i	$-0.152416\pi$
$5$	1.61803	+	1.17557i	0.723607	+	0.525731i	−0.163928	+	0.986472i	$0.552416\pi$
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	1.23607	−	3.80423i	0.467190	−	1.43786i	−0.389018	−	0.921230i	$-0.627186\pi$
$7$	1.23607	−	3.80423i	0.467190	−	1.43786i	0.856208	−	0.516632i	$-0.172814\pi$
$8$	−0.927051	−	2.85317i	−0.327762	−	1.00875i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−2.00000			−0.632456
$11$		0			0
$11$		0			0
$12$	1.00000			0.288675
$13$	1.61803	−	1.17557i	0.448762	−	0.326045i	−0.340345	−	0.940301i	$-0.610544\pi$
$13$	1.61803	−	1.17557i	0.448762	−	0.326045i	0.789107	+	0.614256i	$0.210544\pi$
$14$	1.23607	+	3.80423i	0.330353	+	1.01672i
$15$	0.618034	−	1.90211i	0.159576	−	0.491123i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	1.61803	+	1.17557i	0.392431	+	0.285118i	0.766451	−	0.642303i	$-0.222021\pi$
$17$	1.61803	+	1.17557i	0.392431	+	0.285118i	−0.374020	+	0.927421i	$0.622021\pi$
$18$	0.309017	−	0.951057i	0.0728360	−	0.224166i
$19$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$19$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$20$	−1.61803	+	1.17557i	−0.361803	+	0.262866i
$21$	−4.00000			−0.872872
$22$		0			0
$23$	8.00000			1.66812			0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000			1.66812			0.834058	+	0.551677i	$0.186012\pi$
$24$	−2.42705	+	1.76336i	−0.495420	+	0.359943i
$25$	−0.309017	−	0.951057i	−0.0618034	−	0.190211i
$26$	−0.618034	+	1.90211i	−0.121206	+	0.373035i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	3.23607	+	2.35114i	0.611559	+	0.444324i
$29$	−1.85410	+	5.70634i	−0.344298	+	1.05964i	0.617660	+	0.786445i	$0.288081\pi$
$29$	−1.85410	+	5.70634i	−0.344298	+	1.05964i	−0.961958	+	0.273196i	$0.911919\pi$
$30$	0.618034	+	1.90211i	0.112837	+	0.347277i
$31$	6.47214	−	4.70228i	1.16243	−	0.844555i	0.172347	−	0.985036i	$-0.444865\pi$
$31$	6.47214	−	4.70228i	1.16243	−	0.844555i	0.990083	+	0.140482i	$0.0448651\pi$
$32$	5.00000			0.883883
$33$		0			0
$34$	−2.00000			−0.342997
$35$	6.47214	−	4.70228i	1.09399	−	0.794831i
$36$	−0.309017	−	0.951057i	−0.0515028	−	0.158509i
$37$	1.85410	−	5.70634i	0.304812	−	0.938116i	−0.674935	−	0.737878i	$-0.735828\pi$
$37$	1.85410	−	5.70634i	0.304812	−	0.938116i	0.979747	−	0.200239i	$-0.0641718\pi$
$38$		0			0
$39$	−1.61803	−	1.17557i	−0.259093	−	0.188242i
$40$	1.85410	−	5.70634i	0.293159	−	0.902251i
$41$	−0.618034	−	1.90211i	−0.0965207	−	0.297060i	0.891126	−	0.453755i	$-0.149916\pi$
$41$	−0.618034	−	1.90211i	−0.0965207	−	0.297060i	−0.987647	+	0.156695i	$0.949916\pi$
$42$	3.23607	−	2.35114i	0.499336	−	0.362789i
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$	−2.00000			−0.298142
$46$	−6.47214	+	4.70228i	−0.954264	+	0.693314i
$47$	2.47214	+	7.60845i	0.360598	+	1.10981i	0.952692	+	0.303938i	$0.0983015\pi$
$47$	2.47214	+	7.60845i	0.360598	+	1.10981i	−0.592094	+	0.805869i	$0.701699\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−7.28115	−	5.29007i	−1.04016	−	0.755724i
$50$	0.809017	+	0.587785i	0.114412	+	0.0831254i
$51$	0.618034	−	1.90211i	0.0865421	−	0.266349i
$52$	0.618034	+	1.90211i	0.0857059	+	0.263776i
$53$	−4.85410	+	3.52671i	−0.666762	+	0.484431i	−0.868940	−	0.494918i	$-0.835198\pi$
$53$	−4.85410	+	3.52671i	−0.666762	+	0.484431i	0.202178	+	0.979349i	$0.435198\pi$
$54$	−1.00000			−0.136083
$55$		0			0
$56$	−12.0000			−1.60357
$57$		0			0
$58$	−1.85410	−	5.70634i	−0.243456	−	0.749279i
$59$	−1.23607	+	3.80423i	−0.160922	+	0.495268i	−0.998713	−	0.0507240i	$-0.983847\pi$
$59$	−1.23607	+	3.80423i	−0.160922	+	0.495268i	0.837790	+	0.545992i	$0.183847\pi$
$60$	1.61803	+	1.17557i	0.208887	+	0.151765i
$61$	−4.85410	−	3.52671i	−0.621504	−	0.451549i	0.231942	−	0.972730i	$-0.425492\pi$
$61$	−4.85410	−	3.52671i	−0.621504	−	0.451549i	−0.853447	+	0.521180i	$0.825492\pi$
$62$	−2.47214	+	7.60845i	−0.313962	+	0.966274i
$63$	1.23607	+	3.80423i	0.155730	+	0.479287i
$64$	−5.66312	+	4.11450i	−0.707890	+	0.514312i
$65$	4.00000			0.496139
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$	−1.61803	+	1.17557i	−0.196215	+	0.142559i
$69$	−2.47214	−	7.60845i	−0.297610	−	0.915950i
$70$	−2.47214	+	7.60845i	−0.295477	+	0.909384i
$71$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$71$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$72$	2.42705	+	1.76336i	0.286031	+	0.207813i
$73$	−4.32624	+	13.3148i	−0.506348	+	1.55838i	0.292145	+	0.956374i	$0.405631\pi$
$73$	−4.32624	+	13.3148i	−0.506348	+	1.55838i	−0.798493	+	0.602004i	$0.794369\pi$
$74$	1.85410	+	5.70634i	0.215535	+	0.663348i
$75$	−0.809017	+	0.587785i	−0.0934172	+	0.0678716i
$76$		0			0
$77$		0			0
$78$	2.00000			0.226455
$79$	3.23607	−	2.35114i	0.364086	−	0.264524i	−0.390668	−	0.920532i	$-0.627756\pi$
$79$	3.23607	−	2.35114i	0.364086	−	0.264524i	0.754754	+	0.656007i	$0.227756\pi$
$80$	0.618034	+	1.90211i	0.0690983	+	0.212663i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	1.61803	+	1.17557i	0.178682	+	0.129820i
$83$	−9.70820	−	7.05342i	−1.06561	−	0.774214i	−0.0904951	−	0.995897i	$-0.528845\pi$
$83$	−9.70820	−	7.05342i	−1.06561	−	0.774214i	−0.975119	+	0.221683i	$0.928845\pi$
$84$	1.23607	−	3.80423i	0.134866	−	0.415075i
$85$	1.23607	+	3.80423i	0.134070	+	0.412626i
$86$		0			0
$87$	6.00000			0.643268
$88$		0			0
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$	1.61803	−	1.17557i	0.170556	−	0.123916i
$91$	−2.47214	−	7.60845i	−0.259150	−	0.797582i
$92$	−2.47214	+	7.60845i	−0.257738	+	0.793236i
$93$	−6.47214	−	4.70228i	−0.671129	−	0.487604i
$94$	−6.47214	−	4.70228i	−0.667550	−	0.485003i
$95$		0			0
$96$	−1.54508	−	4.75528i	−0.157695	−	0.485334i
$97$	−1.61803	+	1.17557i	−0.164286	+	0.119361i	−0.666891	−	0.745155i	$-0.732375\pi$
$97$	−1.61803	+	1.17557i	−0.164286	+	0.119361i	0.502604	+	0.864517i	$0.332375\pi$
$98$	9.00000			0.909137
$99$		0			0
$100$	1.00000			0.100000
$101$	−1.61803	+	1.17557i	−0.161000	+	0.116974i	−0.665368	−	0.746515i	$-0.731726\pi$
$101$	−1.61803	+	1.17557i	−0.161000	+	0.116974i	0.504368	+	0.863489i	$0.331726\pi$
$102$	0.618034	+	1.90211i	0.0611945	+	0.188337i
$103$	2.47214	−	7.60845i	0.243587	−	0.749683i	−0.752279	−	0.658845i	$-0.771045\pi$
$103$	2.47214	−	7.60845i	0.243587	−	0.749683i	0.995866	−	0.0908382i	$-0.0289546\pi$
$104$	−4.85410	−	3.52671i	−0.475984	−	0.345823i
$105$	−6.47214	−	4.70228i	−0.631616	−	0.458896i
$106$	1.85410	−	5.70634i	0.180086	−	0.554249i
$107$	−3.70820	−	11.4127i	−0.358486	−	1.10331i	−0.953961	−	0.299932i	$-0.903036\pi$
$107$	−3.70820	−	11.4127i	−0.358486	−	1.10331i	0.595475	−	0.803374i	$-0.296964\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$	−6.00000			−0.569495
$112$	3.23607	−	2.35114i	0.305780	−	0.222162i
$113$	−1.85410	−	5.70634i	−0.174419	−	0.536807i	0.825187	−	0.564859i	$-0.191070\pi$
$113$	−1.85410	−	5.70634i	−0.174419	−	0.536807i	−0.999606	+	0.0280521i	$0.991070\pi$
$114$		0			0
$115$	12.9443	+	9.40456i	1.20706	+	0.876980i
$116$	−4.85410	−	3.52671i	−0.450692	−	0.327447i
$117$	−0.618034	+	1.90211i	−0.0571373	+	0.175850i
$118$	−1.23607	−	3.80423i	−0.113789	−	0.350207i
$119$	6.47214	−	4.70228i	0.593300	−	0.431057i
$120$	−6.00000			−0.547723
$121$		0			0
$122$	6.00000			0.543214
$123$	−1.61803	+	1.17557i	−0.145893	+	0.105998i
$124$	2.47214	+	7.60845i	0.222004	+	0.683259i
$125$	3.70820	−	11.4127i	0.331672	−	1.02078i
$126$	−3.23607	−	2.35114i	−0.288292	−	0.209456i
$127$	3.23607	+	2.35114i	0.287155	+	0.208630i	0.722032	−	0.691860i	$-0.243208\pi$
$127$	3.23607	+	2.35114i	0.287155	+	0.208630i	−0.434877	+	0.900490i	$0.643208\pi$
$128$	−0.927051	+	2.85317i	−0.0819405	+	0.252187i
$129$		0			0
$130$	−3.23607	+	2.35114i	−0.283822	+	0.206209i
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$		0			0
$133$		0			0
$134$	3.23607	−	2.35114i	0.279554	−	0.203108i
$135$	0.618034	+	1.90211i	0.0531919	+	0.163708i
$136$	1.85410	−	5.70634i	0.158988	−	0.489315i
$137$	−1.61803	−	1.17557i	−0.138238	−	0.100436i	0.516517	−	0.856277i	$-0.327228\pi$
$137$	−1.61803	−	1.17557i	−0.138238	−	0.100436i	−0.654755	+	0.755841i	$0.727228\pi$
$138$	6.47214	+	4.70228i	0.550945	+	0.400285i
$139$	−2.47214	+	7.60845i	−0.209684	+	0.645340i	0.789805	+	0.613359i	$0.210182\pi$
$139$	−2.47214	+	7.60845i	−0.209684	+	0.645340i	−0.999488	+	0.0319820i	$0.989818\pi$
$140$	2.47214	+	7.60845i	0.208934	+	0.643032i
$141$	6.47214	−	4.70228i	0.545052	−	0.396004i
$142$		0			0
$143$		0			0
$144$	−1.00000			−0.0833333
$145$	−9.70820	+	7.05342i	−0.806222	+	0.585755i
$146$	−4.32624	−	13.3148i	−0.358042	−	1.10194i
$147$	−2.78115	+	8.55951i	−0.229386	+	0.705976i
$148$	4.85410	+	3.52671i	0.399005	+	0.289894i
$149$	17.7984	+	12.9313i	1.45810	+	1.05937i	0.983853	+	0.178979i	$0.0572796\pi$
$149$	17.7984	+	12.9313i	1.45810	+	1.05937i	0.474247	+	0.880392i	$0.342720\pi$
$150$	0.309017	−	0.951057i	0.0252311	−	0.0776534i
$151$	6.18034	+	19.0211i	0.502949	+	1.54792i	0.804192	+	0.594370i	$0.202599\pi$
$151$	6.18034	+	19.0211i	0.502949	+	1.54792i	−0.301243	+	0.953548i	$0.597401\pi$
$152$		0			0
$153$	−2.00000			−0.161690
$154$		0			0
$155$	16.0000			1.28515
$156$	1.61803	−	1.17557i	0.129546	−	0.0941210i
$157$	4.32624	+	13.3148i	0.345271	+	1.06264i	0.961438	+	0.275020i	$0.0886846\pi$
$157$	4.32624	+	13.3148i	0.345271	+	1.06264i	−0.616167	+	0.787616i	$0.711315\pi$
$158$	−1.23607	+	3.80423i	−0.0983363	+	0.302648i
$159$	4.85410	+	3.52671i	0.384955	+	0.279686i
$160$	8.09017	+	5.87785i	0.639584	+	0.464685i
$161$	9.88854	−	30.4338i	0.779326	−	2.39852i
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	−3.23607	+	2.35114i	−0.253468	+	0.184156i	−0.707263	−	0.706951i	$-0.750070\pi$
$163$	−3.23607	+	2.35114i	−0.253468	+	0.184156i	0.453794	+	0.891107i	$0.350070\pi$
$164$	2.00000			0.156174
$165$		0			0
$166$	12.0000			0.931381
$167$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$167$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$168$	3.70820	+	11.4127i	0.286094	+	0.880507i
$169$	−2.78115	+	8.55951i	−0.213935	+	0.658424i
$170$	−3.23607	−	2.35114i	−0.248195	−	0.180324i
$171$		0			0
$172$		0			0
$173$	−1.85410	−	5.70634i	−0.140965	−	0.433845i	0.855505	−	0.517794i	$-0.173247\pi$
$173$	−1.85410	−	5.70634i	−0.140965	−	0.433845i	−0.996470	+	0.0839492i	$0.973247\pi$
$174$	−4.85410	+	3.52671i	−0.367989	+	0.267359i
$175$	−4.00000			−0.302372
$176$		0			0
$177$	4.00000			0.300658
$178$	4.85410	−	3.52671i	0.363830	−	0.264338i
$179$	3.70820	+	11.4127i	0.277164	+	0.853024i	0.988639	+	0.150312i	$0.0480277\pi$
$179$	3.70820	+	11.4127i	0.277164	+	0.853024i	−0.711474	+	0.702712i	$0.751972\pi$
$180$	0.618034	−	1.90211i	0.0460655	−	0.141775i
$181$	−17.7984	−	12.9313i	−1.32294	−	0.961174i	−0.999891	−	0.0147930i	$-0.995291\pi$
$181$	−17.7984	−	12.9313i	−1.32294	−	0.961174i	−0.323052	−	0.946381i	$-0.604709\pi$
$182$	6.47214	+	4.70228i	0.479747	+	0.348556i
$183$	−1.85410	+	5.70634i	−0.137059	+	0.421825i
$184$	−7.41641	−	22.8254i	−0.546745	−	1.68271i
$185$	9.70820	−	7.05342i	0.713761	−	0.518578i
$186$	8.00000			0.586588
$187$		0			0
$188$	−8.00000			−0.583460
$189$	3.23607	−	2.35114i	0.235389	−	0.171020i
$190$		0			0
$191$	2.47214	−	7.60845i	0.178877	−	0.550528i	−0.820912	−	0.571055i	$-0.806534\pi$
$191$	2.47214	−	7.60845i	0.178877	−	0.550528i	0.999789	+	0.0205267i	$0.00653431\pi$
$192$	5.66312	+	4.11450i	0.408700	+	0.296938i
$193$	11.3262	+	8.22899i	0.815280	+	0.592336i	0.915357	−	0.402644i	$-0.131909\pi$
$193$	11.3262	+	8.22899i	0.815280	+	0.592336i	−0.100076	+	0.994980i	$0.531909\pi$
$194$	0.618034	−	1.90211i	0.0443723	−	0.136564i
$195$	−1.23607	−	3.80423i	−0.0885167	−	0.272426i
$196$	7.28115	−	5.29007i	0.520082	−	0.377862i
$197$	−14.0000			−0.997459			−0.498729	−	0.866758i	$-0.666200\pi$
$197$	−14.0000			−0.997459			−0.498729	+	0.866758i	$0.666200\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−2.42705	+	1.76336i	−0.171618	+	0.124688i
$201$	1.23607	+	3.80423i	0.0871855	+	0.268329i
$202$	0.618034	−	1.90211i	0.0434847	−	0.133832i
$203$	19.4164	+	14.1068i	1.36276	+	0.990106i
$204$	1.61803	+	1.17557i	0.113285	+	0.0823064i
$205$	1.23607	−	3.80423i	0.0863307	−	0.265699i
$206$	2.47214	+	7.60845i	0.172242	+	0.530106i
$207$	−6.47214	+	4.70228i	−0.449845	+	0.326831i
$208$	2.00000			0.138675
$209$		0			0
$210$	8.00000			0.552052
$211$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$211$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$212$	−1.85410	−	5.70634i	−0.127340	−	0.391913i
$213$		0			0
$214$	9.70820	+	7.05342i	0.663639	+	0.482162i
$215$		0			0
$216$	0.927051	−	2.85317i	0.0630778	−	0.194134i
$217$	−9.88854	−	30.4338i	−0.671278	−	2.06598i
$218$	1.61803	−	1.17557i	0.109587	−	0.0796197i
$219$	14.0000			0.946032
$220$		0			0
$221$	4.00000			0.269069
$222$	4.85410	−	3.52671i	0.325786	−	0.236697i
$223$	4.94427	+	15.2169i	0.331093	+	1.01900i	0.968615	+	0.248567i	$0.0799596\pi$
$223$	4.94427	+	15.2169i	0.331093	+	1.01900i	−0.637522	+	0.770432i	$0.720040\pi$
$224$	6.18034	−	19.0211i	0.412941	−	1.27090i
$225$	0.809017	+	0.587785i	0.0539345	+	0.0391857i
$226$	4.85410	+	3.52671i	0.322890	+	0.234593i
$227$	3.70820	−	11.4127i	0.246122	−	0.757486i	−0.749328	−	0.662199i	$-0.769623\pi$
$227$	3.70820	−	11.4127i	0.246122	−	0.757486i	0.995450	−	0.0952867i	$-0.0303768\pi$
$228$		0			0
$229$	−4.85410	+	3.52671i	−0.320768	+	0.233052i	−0.736503	−	0.676434i	$-0.763524\pi$
$229$	−4.85410	+	3.52671i	−0.320768	+	0.233052i	0.415735	+	0.909486i	$0.363524\pi$
$230$	−16.0000			−1.05501
$231$		0			0
$232$	18.0000			1.18176
$233$	−24.2705	+	17.6336i	−1.59001	+	1.15521i	−0.686092	+	0.727514i	$0.740675\pi$
$233$	−24.2705	+	17.6336i	−1.59001	+	1.15521i	−0.903921	+	0.427698i	$0.859325\pi$
$234$	−0.618034	−	1.90211i	−0.0404021	−	0.124345i
$235$	−4.94427	+	15.2169i	−0.322529	+	0.992641i
$236$	−3.23607	−	2.35114i	−0.210650	−	0.153046i
$237$	−3.23607	−	2.35114i	−0.210205	−	0.152723i
$238$	−2.47214	+	7.60845i	−0.160245	+	0.493183i
$239$	7.41641	+	22.8254i	0.479728	+	1.47645i	0.839474	+	0.543400i	$0.182863\pi$
$239$	7.41641	+	22.8254i	0.479728	+	1.47645i	−0.359747	+	0.933050i	$0.617137\pi$
$240$	1.61803	−	1.17557i	0.104444	−	0.0758827i
$241$	10.0000			0.644157			0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000			0.644157			0.322078	+	0.946713i	$0.395619\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$	4.85410	−	3.52671i	0.310752	−	0.225775i
$245$	−5.56231	−	17.1190i	−0.355363	−	1.09369i
$246$	0.618034	−	1.90211i	0.0394044	−	0.121274i
$247$		0			0
$248$	−19.4164	−	14.1068i	−1.23294	−	0.895786i
$249$	−3.70820	+	11.4127i	−0.234998	+	0.723249i
$250$	3.70820	+	11.4127i	0.234527	+	0.721801i
$251$	−3.23607	+	2.35114i	−0.204259	+	0.148403i	−0.685212	−	0.728343i	$-0.740291\pi$
$251$	−3.23607	+	2.35114i	−0.204259	+	0.148403i	0.480953	+	0.876746i	$0.340291\pi$
$252$	−4.00000			−0.251976
$253$		0			0
$254$	−4.00000			−0.250982
$255$	3.23607	−	2.35114i	0.202650	−	0.147234i
$256$	−5.25329	−	16.1680i	−0.328331	−	1.01050i
$257$	−4.32624	+	13.3148i	−0.269863	+	0.830554i	0.720670	+	0.693279i	$0.243834\pi$
$257$	−4.32624	+	13.3148i	−0.269863	+	0.830554i	−0.990533	+	0.137275i	$0.956166\pi$
$258$		0			0
$259$	−19.4164	−	14.1068i	−1.20648	−	0.876557i
$260$	−1.23607	+	3.80423i	−0.0766577	+	0.235928i
$261$	−1.85410	−	5.70634i	−0.114766	−	0.353214i
$262$	9.70820	−	7.05342i	0.599775	−	0.435762i
$263$	−16.0000			−0.986602			−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000			−0.986602			−0.493301	+	0.869859i	$0.664210\pi$
$264$		0			0
$265$	−12.0000			−0.737154
$266$		0			0
$267$	1.85410	+	5.70634i	0.113469	+	0.349222i
$268$	1.23607	−	3.80423i	0.0755049	−	0.232380i
$269$	1.61803	+	1.17557i	0.0986533	+	0.0716758i	0.636018	−	0.771674i	$-0.280580\pi$
$269$	1.61803	+	1.17557i	0.0986533	+	0.0716758i	−0.537365	+	0.843350i	$0.680580\pi$
$270$	−1.61803	−	1.17557i	−0.0984704	−	0.0715429i
$271$	6.18034	−	19.0211i	0.375429	−	1.15545i	−0.567760	−	0.823194i	$-0.692190\pi$
$271$	6.18034	−	19.0211i	0.375429	−	1.15545i	0.943189	−	0.332257i	$-0.107810\pi$
$272$	0.618034	+	1.90211i	0.0374738	+	0.115333i
$273$	−6.47214	+	4.70228i	−0.391711	+	0.284595i
$274$	2.00000			0.120824
$275$		0			0
$276$	8.00000			0.481543
$277$	21.0344	−	15.2824i	1.26384	−	0.918231i	0.264898	−	0.964277i	$-0.414662\pi$
$277$	21.0344	−	15.2824i	1.26384	−	0.918231i	0.998939	+	0.0460451i	$0.0146618\pi$
$278$	−2.47214	−	7.60845i	−0.148269	−	0.456325i
$279$	−2.47214	+	7.60845i	−0.148003	+	0.455506i
$280$	−19.4164	−	14.1068i	−1.16035	−	0.843045i
$281$	14.5623	+	10.5801i	0.868714	+	0.631158i	0.930242	−	0.366947i	$-0.119597\pi$
$281$	14.5623	+	10.5801i	0.868714	+	0.631158i	−0.0615273	+	0.998105i	$0.519597\pi$
$282$	−2.47214	+	7.60845i	−0.147214	+	0.453077i
$283$	4.94427	+	15.2169i	0.293906	+	0.904551i	0.983587	+	0.180437i	$0.0577512\pi$
$283$	4.94427	+	15.2169i	0.293906	+	0.904551i	−0.689680	+	0.724114i	$0.742249\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−8.00000			−0.472225
$288$	−4.04508	+	2.93893i	−0.238359	+	0.173178i
$289$	−4.01722	−	12.3637i	−0.236307	−	0.727279i
$290$	3.70820	−	11.4127i	0.217753	−	0.670176i
$291$	1.61803	+	1.17557i	0.0948508	+	0.0689132i
$292$	−11.3262	−	8.22899i	−0.662818	−	0.481565i
$293$	−1.85410	+	5.70634i	−0.108318	+	0.333368i	−0.990495	−	0.137550i	$-0.956077\pi$
$293$	−1.85410	+	5.70634i	−0.108318	+	0.333368i	0.882177	+	0.470918i	$0.156077\pi$
$294$	−2.78115	−	8.55951i	−0.162200	−	0.499201i
$295$	−6.47214	+	4.70228i	−0.376822	+	0.273777i
$296$	−18.0000			−1.04623
$297$		0			0
$298$	−22.0000			−1.27443
$299$	12.9443	−	9.40456i	0.748587	−	0.543880i
$300$	−0.309017	−	0.951057i	−0.0178411	−	0.0549093i
$301$		0			0
$302$	−16.1803	−	11.7557i	−0.931074	−	0.676465i
$303$	1.61803	+	1.17557i	0.0929536	+	0.0675348i
$304$		0			0
$305$	−3.70820	−	11.4127i	−0.212331	−	0.653488i
$306$	1.61803	−	1.17557i	0.0924968	−	0.0672029i
$307$	32.0000			1.82634			0.913168	−	0.407583i	$-0.133628\pi$
$307$	32.0000			1.82634			0.913168	+	0.407583i	$0.133628\pi$
$308$		0			0
$309$	−8.00000			−0.455104
$310$	−12.9443	+	9.40456i	−0.735185	+	0.534143i
$311$	−7.41641	−	22.8254i	−0.420546	−	1.29431i	−0.907195	−	0.420710i	$-0.861781\pi$
$311$	−7.41641	−	22.8254i	−0.420546	−	1.29431i	0.486649	−	0.873597i	$-0.338219\pi$
$312$	−1.85410	+	5.70634i	−0.104968	+	0.323058i
$313$	17.7984	+	12.9313i	1.00602	+	0.730919i	0.963371	−	0.268171i	$-0.0864192\pi$
$313$	17.7984	+	12.9313i	1.00602	+	0.730919i	0.0426523	+	0.999090i	$0.486419\pi$
$314$	−11.3262	−	8.22899i	−0.639177	−	0.464389i
$315$	−2.47214	+	7.60845i	−0.139289	+	0.428688i
$316$	1.23607	+	3.80423i	0.0695343	+	0.214004i
$317$	−17.7984	+	12.9313i	−0.999656	+	0.726293i	−0.962014	−	0.272999i	$-0.911985\pi$
$317$	−17.7984	+	12.9313i	−0.999656	+	0.726293i	−0.0376418	+	0.999291i	$0.511985\pi$
$318$	−6.00000			−0.336463
$319$		0			0
$320$	−14.0000			−0.782624
$321$	−9.70820	+	7.05342i	−0.541859	+	0.393684i
$322$	9.88854	+	30.4338i	0.551067	+	1.69601i
$323$		0			0
$324$	0.809017	+	0.587785i	0.0449454	+	0.0326547i
$325$	−1.61803	−	1.17557i	−0.0897524	−	0.0652089i
$326$	1.23607	−	3.80423i	0.0684595	−	0.210697i
$327$	0.618034	+	1.90211i	0.0341774	+	0.105187i
$328$	−4.85410	+	3.52671i	−0.268023	+	0.194730i
$329$	32.0000			1.76422
$330$		0			0
$331$	−20.0000			−1.09930			−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000			−1.09930			−0.549650	+	0.835395i	$0.685239\pi$
$332$	9.70820	−	7.05342i	0.532807	−	0.387107i
$333$	1.85410	+	5.70634i	0.101604	+	0.312705i
$334$		0			0
$335$	−6.47214	−	4.70228i	−0.353611	−	0.256913i
$336$	−3.23607	−	2.35114i	−0.176542	−	0.128265i
$337$	−6.79837	+	20.9232i	−0.370331	+	1.13976i	0.576244	+	0.817278i	$0.304518\pi$
$337$	−6.79837	+	20.9232i	−0.370331	+	1.13976i	−0.946575	+	0.322484i	$0.895482\pi$
$338$	−2.78115	−	8.55951i	−0.151275	−	0.465576i
$339$	−4.85410	+	3.52671i	−0.263639	+	0.191545i
$340$	−4.00000			−0.216930
$341$		0			0
$342$		0			0
$343$	−6.47214	+	4.70228i	−0.349462	+	0.253899i
$344$		0			0
$345$	4.94427	−	15.2169i	0.266191	−	0.819251i
$346$	4.85410	+	3.52671i	0.260958	+	0.189597i
$347$	−3.23607	−	2.35114i	−0.173721	−	0.126216i	0.497527	−	0.867448i	$-0.334242\pi$
$347$	−3.23607	−	2.35114i	−0.173721	−	0.126216i	−0.671248	+	0.741233i	$0.734242\pi$
$348$	−1.85410	+	5.70634i	−0.0993903	+	0.305892i
$349$	1.85410	+	5.70634i	0.0992478	+	0.305453i	0.988337	−	0.152280i	$-0.0486615\pi$
$349$	1.85410	+	5.70634i	0.0992478	+	0.305453i	−0.889090	+	0.457733i	$0.848662\pi$
$350$	3.23607	−	2.35114i	0.172975	−	0.125674i
$351$	2.00000			0.106752
$352$		0			0
$353$	18.0000			0.958043			0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000			0.958043			0.479022	+	0.877803i	$0.340992\pi$
$354$	−3.23607	+	2.35114i	−0.171995	+	0.124962i
$355$		0			0
$356$	1.85410	−	5.70634i	0.0982672	−	0.302435i
$357$	−6.47214	−	4.70228i	−0.342542	−	0.248871i
$358$	−9.70820	−	7.05342i	−0.513095	−	0.372785i
$359$	−2.47214	+	7.60845i	−0.130474	+	0.401559i	−0.994859	−	0.101273i	$-0.967708\pi$
$359$	−2.47214	+	7.60845i	−0.130474	+	0.401559i	0.864384	+	0.502832i	$0.167708\pi$
$360$	1.85410	+	5.70634i	0.0977198	+	0.300750i
$361$	15.3713	−	11.1679i	0.809017	−	0.587785i
$362$	22.0000			1.15629
$363$		0			0
$364$	8.00000			0.419314
$365$	−22.6525	+	16.4580i	−1.18568	+	0.861450i
$366$	−1.85410	−	5.70634i	−0.0969155	−	0.298275i
$367$	−9.88854	+	30.4338i	−0.516178	+	1.58863i	0.264951	+	0.964262i	$0.414644\pi$
$367$	−9.88854	+	30.4338i	−0.516178	+	1.58863i	−0.781129	+	0.624370i	$0.785356\pi$
$368$	6.47214	+	4.70228i	0.337383	+	0.245123i
$369$	1.61803	+	1.17557i	0.0842315	+	0.0611978i
$370$	−3.70820	+	11.4127i	−0.192780	+	0.593317i
$371$	7.41641	+	22.8254i	0.385041	+	1.18503i
$372$	6.47214	−	4.70228i	0.335565	−	0.243802i
$373$	−2.00000			−0.103556			−0.0517780	−	0.998659i	$-0.516489\pi$
$373$	−2.00000			−0.103556			−0.0517780	+	0.998659i	$0.516489\pi$
$374$		0			0
$375$	−12.0000			−0.619677
$376$	19.4164	−	14.1068i	1.00132	−	0.727505i
$377$	3.70820	+	11.4127i	0.190982	+	0.587783i
$378$	−1.23607	+	3.80423i	−0.0635765	+	0.195668i
$379$	−22.6525	−	16.4580i	−1.16358	−	0.845390i	−0.173353	−	0.984860i	$-0.555460\pi$
$379$	−22.6525	−	16.4580i	−1.16358	−	0.845390i	−0.990226	+	0.139470i	$0.955460\pi$
$380$		0			0
$381$	1.23607	−	3.80423i	0.0633257	−	0.194896i
$382$	2.47214	+	7.60845i	0.126485	+	0.389282i
$383$	12.9443	−	9.40456i	0.661421	−	0.480551i	−0.205721	−	0.978611i	$-0.565954\pi$
$383$	12.9443	−	9.40456i	0.661421	−	0.480551i	0.867143	+	0.498060i	$0.165954\pi$
$384$	3.00000			0.153093
$385$		0			0
$386$	−14.0000			−0.712581
$387$		0			0
$388$	−0.618034	−	1.90211i	−0.0313759	−	0.0965652i
$389$	−5.56231	+	17.1190i	−0.282020	+	0.867969i	0.705256	+	0.708953i	$0.250832\pi$
$389$	−5.56231	+	17.1190i	−0.282020	+	0.867969i	−0.987276	+	0.159016i	$0.949168\pi$
$390$	3.23607	+	2.35114i	0.163865	+	0.119055i
$391$	12.9443	+	9.40456i	0.654620	+	0.475609i
$392$	−8.34346	+	25.6785i	−0.421408	+	1.29696i
$393$	3.70820	+	11.4127i	0.187054	+	0.575693i
$394$	11.3262	−	8.22899i	0.570608	−	0.414571i
$395$	8.00000			0.402524
$396$		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
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	−21.0344	−	15.2824i	−1.05041	−	0.763167i	−0.0781195	−	0.996944i	$-0.524892\pi$
$401$	−21.0344	−	15.2824i	−1.05041	−	0.763167i	−0.972290	+	0.233777i	$0.924892\pi$
$402$	−3.23607	−	2.35114i	−0.161400	−	0.117264i
$403$	4.94427	−	15.2169i	0.246292	−	0.758008i
$404$	−0.618034	−	1.90211i	−0.0307483	−	0.0946337i
$405$	1.61803	−	1.17557i	0.0804008	−	0.0584146i
$406$	−24.0000			−1.19110
$407$		0			0
$408$	−6.00000			−0.297044
$409$	−14.5623	+	10.5801i	−0.720060	+	0.523154i	−0.886403	−	0.462914i	$-0.846804\pi$
$409$	−14.5623	+	10.5801i	−0.720060	+	0.523154i	0.166344	+	0.986068i	$0.446804\pi$
$410$	1.23607	+	3.80423i	0.0610450	+	0.187877i
$411$	−0.618034	+	1.90211i	−0.0304854	+	0.0938243i
$412$	6.47214	+	4.70228i	0.318859	+	0.231665i
$413$	12.9443	+	9.40456i	0.636946	+	0.462768i
$414$	2.47214	−	7.60845i	0.121499	−	0.373935i
$415$	−7.41641	−	22.8254i	−0.364057	−	1.12045i
$416$	8.09017	−	5.87785i	0.396653	−	0.288185i
$417$	8.00000			0.391762
$418$		0			0
$419$	−4.00000			−0.195413			−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000			−0.195413			−0.0977064	+	0.995215i	$0.531151\pi$
$420$	6.47214	−	4.70228i	0.315808	−	0.229448i
$421$	−8.03444	−	24.7275i	−0.391575	−	1.20514i	−0.931597	−	0.363492i	$-0.881584\pi$
$421$	−8.03444	−	24.7275i	−0.391575	−	1.20514i	0.540022	−	0.841651i	$-0.318416\pi$
$422$		0			0
$423$	−6.47214	−	4.70228i	−0.314686	−	0.228633i
$424$	14.5623	+	10.5801i	0.707208	+	0.513817i
$425$	0.618034	−	1.90211i	0.0299791	−	0.0922660i
$426$		0			0
$427$	−19.4164	+	14.1068i	−0.939626	+	0.682678i
$428$	12.0000			0.580042
$429$		0			0
$430$		0			0
$431$	19.4164	−	14.1068i	0.935255	−	0.679503i	−0.0120185	−	0.999928i	$-0.503826\pi$
$431$	19.4164	−	14.1068i	0.935255	−	0.679503i	0.947274	+	0.320425i	$0.103826\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	10.5066	−	32.3359i	0.504914	−	1.55397i	−0.296001	−	0.955188i	$-0.595653\pi$
$433$	10.5066	−	32.3359i	0.504914	−	1.55397i	0.800915	−	0.598778i	$-0.204347\pi$
$434$	25.8885	+	18.8091i	1.24269	+	0.902867i
$435$	9.70820	+	7.05342i	0.465473	+	0.338186i
$436$	0.618034	−	1.90211i	0.0295985	−	0.0910947i
$437$		0			0
$438$	−11.3262	+	8.22899i	−0.541189	+	0.393197i
$439$	−20.0000			−0.954548			−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000			−0.954548			−0.477274	+	0.878755i	$0.658375\pi$
$440$		0			0
$441$	9.00000			0.428571
$442$	−3.23607	+	2.35114i	−0.153924	+	0.111832i
$443$	8.65248	+	26.6296i	0.411092	+	1.26521i	0.915700	+	0.401862i	$0.131637\pi$
$443$	8.65248	+	26.6296i	0.411092	+	1.26521i	−0.504609	+	0.863348i	$0.668363\pi$
$444$	1.85410	−	5.70634i	0.0879918	−	0.270811i
$445$	−9.70820	−	7.05342i	−0.460213	−	0.334364i
$446$	−12.9443	−	9.40456i	−0.612929	−	0.445319i
$447$	6.79837	−	20.9232i	0.321552	−	0.989635i
$448$	8.65248	+	26.6296i	0.408791	+	1.25813i
$449$	−1.61803	+	1.17557i	−0.0763597	+	0.0554786i	−0.625310	−	0.780376i	$-0.715028\pi$
$449$	−1.61803	+	1.17557i	−0.0763597	+	0.0554786i	0.548950	+	0.835855i	$0.315028\pi$
$450$	−1.00000			−0.0471405
$451$		0			0
$452$	6.00000			0.282216
$453$	16.1803	−	11.7557i	0.760219	−	0.552331i
$454$	3.70820	+	11.4127i	0.174035	+	0.535624i
$455$	4.94427	−	15.2169i	0.231791	−	0.713379i
$456$		0			0
$457$	−14.5623	−	10.5801i	−0.681196	−	0.494918i	0.192558	−	0.981286i	$-0.438322\pi$
$457$	−14.5623	−	10.5801i	−0.681196	−	0.494918i	−0.873754	+	0.486368i	$0.838322\pi$
$458$	1.85410	−	5.70634i	0.0866365	−	0.266640i
$459$	0.618034	+	1.90211i	0.0288474	+	0.0887830i
$460$	−12.9443	+	9.40456i	−0.603530	+	0.438490i
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	−4.85410	+	3.52671i	−0.225346	+	0.163723i
$465$	−4.94427	−	15.2169i	−0.229285	−	0.705667i
$466$	9.27051	−	28.5317i	0.429448	−	1.32171i
$467$	9.70820	+	7.05342i	0.449242	+	0.326393i	0.789296	−	0.614012i	$-0.210445\pi$
$467$	9.70820	+	7.05342i	0.449242	+	0.326393i	−0.340054	+	0.940406i	$0.610445\pi$
$468$	−1.61803	−	1.17557i	−0.0747936	−	0.0543408i
$469$	−4.94427	+	15.2169i	−0.228305	+	0.702651i
$470$	−4.94427	−	15.2169i	−0.228062	−	0.701903i
$471$	11.3262	−	8.22899i	0.521885	−	0.379172i
$472$	12.0000			0.552345
$473$		0			0
$474$	4.00000			0.183726
$475$		0			0
$476$	2.47214	+	7.60845i	0.113310	+	0.348733i
$477$	1.85410	−	5.70634i	0.0848935	−	0.261275i
$478$	−19.4164	−	14.1068i	−0.888086	−	0.645232i
$479$	−6.47214	−	4.70228i	−0.295719	−	0.214853i	0.430025	−	0.902817i	$-0.358505\pi$
$479$	−6.47214	−	4.70228i	−0.295719	−	0.214853i	−0.725745	+	0.687964i	$0.758505\pi$
$480$	3.09017	−	9.51057i	0.141046	−	0.434096i
$481$	−3.70820	−	11.4127i	−0.169080	−	0.520373i
$482$	−8.09017	+	5.87785i	−0.368497	+	0.267729i
$483$	−32.0000			−1.45605
$484$		0			0
$485$	−4.00000			−0.181631
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	−4.94427	−	15.2169i	−0.224046	−	0.689544i	−0.998387	−	0.0567748i	$-0.981918\pi$
$487$	−4.94427	−	15.2169i	−0.224046	−	0.689544i	0.774341	−	0.632769i	$-0.218082\pi$
$488$	−5.56231	+	17.1190i	−0.251794	+	0.774942i
$489$	3.23607	+	2.35114i	0.146340	+	0.106322i
$490$	14.5623	+	10.5801i	0.657858	+	0.477962i
$491$	1.23607	−	3.80423i	0.0557830	−	0.171682i	−0.919283	−	0.393597i	$-0.871231\pi$
$491$	1.23607	−	3.80423i	0.0557830	−	0.171682i	0.975066	+	0.221915i	$0.0712306\pi$
$492$	−0.618034	−	1.90211i	−0.0278631	−	0.0857539i
$493$	−9.70820	+	7.05342i	−0.437236	+	0.317670i
$494$		0			0
$495$		0			0
$496$	8.00000			0.359211
$497$		0			0
$498$	−3.70820	−	11.4127i	−0.166169	−	0.511414i
$499$	−1.23607	+	3.80423i	−0.0553340	+	0.170301i	−0.974904	−	0.222626i	$-0.928537\pi$
$499$	−1.23607	+	3.80423i	−0.0553340	+	0.170301i	0.919570	+	0.392926i	$0.128537\pi$
$500$	9.70820	+	7.05342i	0.434164	+	0.315439i
$501$		0			0
$502$	1.23607	−	3.80423i	0.0551684	−	0.169791i
$503$	−9.88854	−	30.4338i	−0.440908	−	1.35698i	−0.886909	−	0.461944i	$-0.847152\pi$
$503$	−9.88854	−	30.4338i	−0.440908	−	1.35698i	0.446001	−	0.895033i	$-0.352848\pi$
$504$	9.70820	−	7.05342i	0.432438	−	0.314184i
$505$	−4.00000			−0.177998
$506$		0			0
$507$	9.00000			0.399704
$508$	−3.23607	+	2.35114i	−0.143577	+	0.104315i
$509$	9.27051	+	28.5317i	0.410908	+	1.26465i	0.915860	+	0.401498i	$0.131510\pi$
$509$	9.27051	+	28.5317i	0.410908	+	1.26465i	−0.504952	+	0.863147i	$0.668490\pi$
$510$	−1.23607	+	3.80423i	−0.0547340	+	0.168454i
$511$	45.3050	+	32.9160i	2.00417	+	1.45612i
$512$	8.89919	+	6.46564i	0.393292	+	0.285744i
$513$		0			0
$514$	−4.32624	−	13.3148i	−0.190822	−	0.587290i
$515$	12.9443	−	9.40456i	0.570393	−	0.414415i
$516$		0			0
$517$		0			0
$518$	24.0000			1.05450
$519$	−4.85410	+	3.52671i	−0.213071	+	0.154805i
$520$	−3.70820	−	11.4127i	−0.162615	−	0.500479i
$521$	−9.27051	+	28.5317i	−0.406148	+	1.25000i	0.513784	+	0.857920i	$0.328243\pi$
$521$	−9.27051	+	28.5317i	−0.406148	+	1.25000i	−0.919933	+	0.392077i	$0.871757\pi$
$522$	4.85410	+	3.52671i	0.212458	+	0.154360i
$523$	12.9443	+	9.40456i	0.566013	+	0.411233i	0.833655	−	0.552286i	$-0.186244\pi$
$523$	12.9443	+	9.40456i	0.566013	+	0.411233i	−0.267641	+	0.963519i	$0.586244\pi$
$524$	3.70820	−	11.4127i	0.161994	−	0.498565i
$525$	1.23607	+	3.80423i	0.0539464	+	0.166030i
$526$	12.9443	−	9.40456i	0.564397	−	0.410058i
$527$	16.0000			0.696971
$528$		0			0
$529$	41.0000			1.78261
$530$	9.70820	−	7.05342i	0.421697	−	0.306381i
$531$	−1.23607	−	3.80423i	−0.0536408	−	0.165089i
$532$		0			0
$533$	−3.23607	−	2.35114i	−0.140170	−	0.101839i
$534$	−4.85410	−	3.52671i	−0.210058	−	0.152616i
$535$	7.41641	−	22.8254i	0.320639	−	0.986826i
$536$	3.70820	+	11.4127i	0.160170	+	0.492953i
$537$	9.70820	−	7.05342i	0.418940	−	0.304378i
$538$	−2.00000			−0.0862261
$539$		0			0
$540$	−2.00000			−0.0860663
$541$	−37.2148	+	27.0381i	−1.59999	+	1.16246i	−0.712453	+	0.701719i	$0.752416\pi$
$541$	−37.2148	+	27.0381i	−1.59999	+	1.16246i	−0.887535	+	0.460740i	$0.847584\pi$
$542$	6.18034	+	19.0211i	0.265468	+	0.817028i
$543$	−6.79837	+	20.9232i	−0.291746	+	0.897902i
$544$	8.09017	+	5.87785i	0.346863	+	0.252011i
$545$	−3.23607	−	2.35114i	−0.138618	−	0.100712i
$546$	2.47214	−	7.60845i	0.105798	−	0.325612i
$547$	2.47214	+	7.60845i	0.105701	+	0.325314i	0.989894	−	0.141807i	$-0.0452913\pi$
$547$	2.47214	+	7.60845i	0.105701	+	0.325314i	−0.884193	+	0.467121i	$0.845291\pi$
$548$	1.61803	−	1.17557i	0.0691190	−	0.0502179i
$549$	6.00000			0.256074
$550$		0			0
$551$		0			0
$552$	−19.4164	+	14.1068i	−0.826417	+	0.600427i
$553$	−4.94427	−	15.2169i	−0.210252	−	0.647089i
$554$	−8.03444	+	24.7275i	−0.341351	+	1.05057i
$555$	−9.70820	−	7.05342i	−0.412090	−	0.299401i
$556$	−6.47214	−	4.70228i	−0.274480	−	0.199421i
$557$	−4.32624	+	13.3148i	−0.183309	+	0.564166i	−0.999915	−	0.0130289i	$-0.995853\pi$
$557$	−4.32624	+	13.3148i	−0.183309	+	0.564166i	0.816607	+	0.577195i	$0.195853\pi$
$558$	−2.47214	−	7.60845i	−0.104654	−	0.322091i
$559$		0			0
$560$	8.00000			0.338062
$561$		0			0
$562$	−18.0000			−0.759284
$563$	35.5967	−	25.8626i	1.50022	−	1.08998i	0.529932	−	0.848040i	$-0.322217\pi$
$563$	35.5967	−	25.8626i	1.50022	−	1.08998i	0.970292	−	0.241936i	$-0.0777825\pi$
$564$	2.47214	+	7.60845i	0.104096	+	0.320374i
$565$	3.70820	−	11.4127i	0.156005	−	0.480135i
$566$	−12.9443	−	9.40456i	−0.544088	−	0.395303i
$567$	−3.23607	−	2.35114i	−0.135902	−	0.0987386i
$568$		0			0
$569$	−12.9787	−	39.9444i	−0.544096	−	1.67456i	−0.723130	−	0.690712i	$-0.757297\pi$
$569$	−12.9787	−	39.9444i	−0.544096	−	1.67456i	0.179034	−	0.983843i	$-0.442703\pi$
$570$		0			0
$571$	−16.0000			−0.669579			−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000			−0.669579			−0.334790	+	0.942293i	$0.608665\pi$
$572$		0			0
$573$	−8.00000			−0.334205
$574$	6.47214	−	4.70228i	0.270142	−	0.196269i
$575$	−2.47214	−	7.60845i	−0.103095	−	0.317294i
$576$	2.16312	−	6.65740i	0.0901300	−	0.277391i
$577$	24.2705	+	17.6336i	1.01039	+	0.734095i	0.964292	−	0.264842i	$-0.0853198\pi$
$577$	24.2705	+	17.6336i	1.01039	+	0.734095i	0.0461028	+	0.998937i	$0.485320\pi$
$578$	10.5172	+	7.64121i	0.437459	+	0.317832i
$579$	4.32624	−	13.3148i	0.179792	−	0.553344i
$580$	−3.70820	−	11.4127i	−0.153975	−	0.473886i
$581$	−38.8328	+	28.2137i	−1.61106	+	1.17050i
$582$	−2.00000			−0.0829027
$583$		0			0
$584$	42.0000			1.73797
$585$	−3.23607	+	2.35114i	−0.133795	+	0.0972077i
$586$	−1.85410	−	5.70634i	−0.0765922	−	0.235727i
$587$	8.65248	−	26.6296i	0.357126	−	1.09912i	−0.597641	−	0.801764i	$-0.703895\pi$
$587$	8.65248	−	26.6296i	0.357126	−	1.09912i	0.954767	−	0.297356i	$-0.0961050\pi$
$588$	−7.28115	−	5.29007i	−0.300270	−	0.218159i
$589$		0			0
$590$	2.47214	−	7.60845i	0.101776	−	0.313235i
$591$	4.32624	+	13.3148i	0.177958	+	0.547697i
$592$	4.85410	−	3.52671i	0.199502	−	0.144947i
$593$	38.0000			1.56047			0.780236	−	0.625485i	$-0.215099\pi$
$593$	38.0000			1.56047			0.780236	+	0.625485i	$0.215099\pi$
$594$		0			0
$595$	16.0000			0.655936
$596$	−17.7984	+	12.9313i	−0.729050	+	0.529686i
$597$		0			0
$598$	−4.94427	+	15.2169i	−0.202186	+	0.622265i
$599$	6.47214	+	4.70228i	0.264444	+	0.192130i	0.712104	−	0.702074i	$-0.247742\pi$
$599$	6.47214	+	4.70228i	0.264444	+	0.192130i	−0.447660	+	0.894204i	$0.647742\pi$
$600$	2.42705	+	1.76336i	0.0990839	+	0.0719887i
$601$	8.03444	−	24.7275i	0.327732	−	1.00865i	−0.642461	−	0.766319i	$-0.722086\pi$
$601$	8.03444	−	24.7275i	0.327732	−	1.00865i	0.970192	−	0.242336i	$-0.0779136\pi$
$602$		0			0
$603$	3.23607	−	2.35114i	0.131783	−	0.0957459i
$604$	−20.0000			−0.813788
$605$		0			0
$606$	−2.00000			−0.0812444
$607$	3.23607	−	2.35114i	0.131348	−	0.0954299i	−0.520171	−	0.854062i	$-0.674132\pi$
$607$	3.23607	−	2.35114i	0.131348	−	0.0954299i	0.651519	+	0.758632i	$0.274132\pi$
$608$		0			0
$609$	7.41641	−	22.8254i	0.300528	−	0.924930i
$610$	9.70820	+	7.05342i	0.393074	+	0.285585i
$611$	12.9443	+	9.40456i	0.523669	+	0.380468i
$612$	0.618034	−	1.90211i	0.0249825	−	0.0768884i
$613$	4.32624	+	13.3148i	0.174735	+	0.537779i	0.999621	−	0.0275195i	$-0.00876084\pi$
$613$	4.32624	+	13.3148i	0.174735	+	0.537779i	−0.824886	+	0.565299i	$0.808761\pi$
$614$	−25.8885	+	18.8091i	−1.04478	+	0.759075i
$615$	−4.00000			−0.161296
$616$		0			0
$617$	−30.0000			−1.20775			−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000			−1.20775			−0.603877	+	0.797077i	$0.706378\pi$
$618$	6.47214	−	4.70228i	0.260347	−	0.189154i
$619$	13.5967	+	41.8465i	0.546499	+	1.68195i	0.717398	+	0.696664i	$0.245333\pi$
$619$	13.5967	+	41.8465i	0.546499	+	1.68195i	−0.170898	+	0.985289i	$0.554667\pi$
$620$	−4.94427	+	15.2169i	−0.198567	+	0.611126i
$621$	6.47214	+	4.70228i	0.259718	+	0.188696i
$622$	19.4164	+	14.1068i	0.778527	+	0.565633i
$623$	−7.41641	+	22.8254i	−0.297132	+	0.914479i
$624$	−0.618034	−	1.90211i	−0.0247412	−	0.0761455i
$625$	15.3713	−	11.1679i	0.614853	−	0.446717i
$626$	−22.0000			−0.879297
$627$		0			0
$628$	−14.0000			−0.558661
$629$	9.70820	−	7.05342i	0.387091	−	0.281238i
$630$	−2.47214	−	7.60845i	−0.0984923	−	0.303128i
$631$	4.94427	−	15.2169i	0.196828	−	0.605775i	−0.803122	−	0.595815i	$-0.796829\pi$
$631$	4.94427	−	15.2169i	0.196828	−	0.605775i	0.999950	−	0.00996082i	$-0.00317068\pi$
$632$	−9.70820	−	7.05342i	−0.386172	−	0.280570i
$633$		0			0
$634$	6.79837	−	20.9232i	0.269998	−	0.830968i
$635$	2.47214	+	7.60845i	0.0981037	+	0.301932i
$636$	−4.85410	+	3.52671i	−0.192478	+	0.139843i
$637$	−18.0000			−0.713186
$638$		0			0
$639$		0			0
$640$	−4.85410	+	3.52671i	−0.191875	+	0.139406i
$641$	5.56231	+	17.1190i	0.219698	+	0.676161i	0.998787	+	0.0492469i	$0.0156821\pi$
$641$	5.56231	+	17.1190i	0.219698	+	0.676161i	−0.779089	+	0.626914i	$0.784318\pi$
$642$	3.70820	−	11.4127i	0.146351	−	0.450422i
$643$	−16.1803	−	11.7557i	−0.638090	−	0.463600i	0.221103	−	0.975250i	$-0.429034\pi$
$643$	−16.1803	−	11.7557i	−0.638090	−	0.463600i	−0.859194	+	0.511651i	$0.829034\pi$
$644$	25.8885	+	18.8091i	1.02015	+	0.741183i
$645$		0			0
$646$		0			0
$647$	−6.47214	+	4.70228i	−0.254446	+	0.184866i	−0.707695	−	0.706518i	$-0.750265\pi$
$647$	−6.47214	+	4.70228i	−0.254446	+	0.184866i	0.453249	+	0.891384i	$0.350265\pi$
$648$	−3.00000			−0.117851
$649$		0			0
$650$	2.00000			0.0784465
$651$	−25.8885	+	18.8091i	−1.01465	+	0.737188i
$652$	−1.23607	−	3.80423i	−0.0484082	−	0.148985i
$653$	−0.618034	+	1.90211i	−0.0241855	+	0.0744354i	−0.962421	−	0.271563i	$-0.912460\pi$
$653$	−0.618034	+	1.90211i	−0.0241855	+	0.0744354i	0.938235	+	0.345998i	$0.112460\pi$
$654$	−1.61803	−	1.17557i	−0.0632701	−	0.0459684i
$655$	−19.4164	−	14.1068i	−0.758662	−	0.551200i
$656$	0.618034	−	1.90211i	0.0241302	−	0.0742650i
$657$	−4.32624	−	13.3148i	−0.168783	−	0.519459i
$658$	−25.8885	+	18.8091i	−1.00924	+	0.733256i
$659$	4.00000			0.155818			0.0779089	−	0.996960i	$-0.475176\pi$
$659$	4.00000			0.155818			0.0779089	+	0.996960i	$0.475176\pi$
$660$		0			0
$661$	−26.0000			−1.01128			−0.505641	−	0.862744i	$-0.668744\pi$
$661$	−26.0000			−1.01128			−0.505641	+	0.862744i	$0.668744\pi$
$662$	16.1803	−	11.7557i	0.628867	−	0.456898i
$663$	−1.23607	−	3.80423i	−0.0480049	−	0.147744i
$664$	−11.1246	+	34.2380i	−0.431719	+	1.32869i
$665$		0			0
$666$	−4.85410	−	3.52671i	−0.188093	−	0.136657i
$667$	−14.8328	+	45.6507i	−0.574329	+	1.76760i
$668$		0			0
$669$	12.9443	−	9.40456i	0.500454	−	0.363601i
$670$	8.00000			0.309067
$671$		0			0
$672$	−20.0000			−0.771517
$673$	37.2148	−	27.0381i	1.43452	−	1.04224i	0.445373	−	0.895345i	$-0.353071\pi$
$673$	37.2148	−	27.0381i	1.43452	−	1.04224i	0.989152	−	0.146898i	$-0.0469288\pi$
$674$	−6.79837	−	20.9232i	−0.261864	−	0.805933i
$675$	0.309017	−	0.951057i	0.0118941	−	0.0366062i
$676$	−7.28115	−	5.29007i	−0.280044	−	0.203464i
$677$	−14.5623	−	10.5801i	−0.559675	−	0.406628i	0.271665	−	0.962392i	$-0.412426\pi$
$677$	−14.5623	−	10.5801i	−0.559675	−	0.406628i	−0.831340	+	0.555764i	$0.812426\pi$
$678$	1.85410	−	5.70634i	0.0712064	−	0.219151i
$679$	2.47214	+	7.60845i	0.0948719	+	0.291986i
$680$	9.70820	−	7.05342i	0.372293	−	0.270486i
$681$	−12.0000			−0.459841
$682$		0			0
$683$	20.0000			0.765279			0.382639	−	0.923898i	$-0.375015\pi$
$683$	20.0000			0.765279			0.382639	+	0.923898i	$0.375015\pi$
$684$		0			0
$685$	−1.23607	−	3.80423i	−0.0472277	−	0.145352i
$686$	2.47214	−	7.60845i	0.0943866	−	0.290492i
$687$	4.85410	+	3.52671i	0.185196	+	0.134552i
$688$		0			0
$689$	−3.70820	+	11.4127i	−0.141271	+	0.434788i
$690$	4.94427	+	15.2169i	0.188225	+	0.579298i
$691$	22.6525	−	16.4580i	0.861741	−	0.626091i	−0.0666172	−	0.997779i	$-0.521221\pi$
$691$	22.6525	−	16.4580i	0.861741	−	0.626091i	0.928358	+	0.371687i	$0.121221\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	4.00000			0.151838
$695$	−12.9443	+	9.40456i	−0.491004	+	0.356735i
$696$	−5.56231	−	17.1190i	−0.210839	−	0.648895i
$697$	1.23607	−	3.80423i	0.0468194	−	0.144095i
$698$	−4.85410	−	3.52671i	−0.183730	−	0.133488i
$699$	24.2705	+	17.6336i	0.917995	+	0.666962i
$700$	1.23607	−	3.80423i	0.0467190	−	0.143786i
$701$	15.4508	+	47.5528i	0.583571	+	1.79605i	0.604936	+	0.796274i	$0.293198\pi$
$701$	15.4508	+	47.5528i	0.583571	+	1.79605i	−0.0213660	+	0.999772i	$0.506802\pi$
$702$	−1.61803	+	1.17557i	−0.0610688	+	0.0443690i
$703$		0			0
$704$		0			0
$705$	16.0000			0.602595
$706$	−14.5623	+	10.5801i	−0.548060	+	0.398189i
$707$	2.47214	+	7.60845i	0.0929742	+	0.286145i
$708$	−1.23607	+	3.80423i	−0.0464543	+	0.142972i
$709$	−30.7426	−	22.3358i	−1.15456	−	0.838840i	−0.165483	−	0.986213i	$-0.552918\pi$
$709$	−30.7426	−	22.3358i	−1.15456	−	0.838840i	−0.989081	+	0.147373i	$0.952918\pi$
$710$		0			0
$711$	−1.23607	+	3.80423i	−0.0463562	+	0.142670i
$712$	5.56231	+	17.1190i	0.208456	+	0.641562i
$713$	51.7771	−	37.6183i	1.93907	−	1.40881i
$714$	8.00000			0.299392
$715$		0			0
$716$	−12.0000			−0.448461
$717$	19.4164	−	14.1068i	0.725119	−	0.526830i
$718$	−2.47214	−	7.60845i	−0.0922593	−	0.283945i
$719$	7.41641	−	22.8254i	0.276585	−	0.851242i	−0.712210	−	0.701966i	$-0.752306\pi$
$719$	7.41641	−	22.8254i	0.276585	−	0.851242i	0.988796	−	0.149276i	$-0.0476943\pi$
$720$	−1.61803	−	1.17557i	−0.0603006	−	0.0438109i
$721$	−25.8885	−	18.8091i	−0.964140	−	0.700489i
$722$	−5.87132	+	18.0701i	−0.218508	+	0.672499i
$723$	−3.09017	−	9.51057i	−0.114925	−	0.353702i
$724$	17.7984	−	12.9313i	0.661471	−	0.480587i
$725$	6.00000			0.222834
$726$		0			0
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	−19.4164	+	14.1068i	−0.719620	+	0.522834i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	8.65248	−	26.6296i	0.320242	−	0.985605i
$731$		0			0
$732$	−4.85410	−	3.52671i	−0.179413	−	0.130351i
$733$	9.27051	−	28.5317i	0.342414	−	1.05384i	−0.620540	−	0.784175i	$-0.713086\pi$
$733$	9.27051	−	28.5317i	0.342414	−	1.05384i	0.962954	−	0.269667i	$-0.0869136\pi$
$734$	−9.88854	−	30.4338i	−0.364993	−	1.12333i
$735$	−14.5623	+	10.5801i	−0.537139	+	0.390254i
$736$	40.0000			1.47442
$737$		0			0
$738$	−2.00000			−0.0736210
$739$	−6.47214	+	4.70228i	−0.238081	+	0.172976i	−0.700428	−	0.713723i	$-0.747008\pi$
$739$	−6.47214	+	4.70228i	−0.238081	+	0.172976i	0.462347	+	0.886699i	$0.347008\pi$
$740$	3.70820	+	11.4127i	0.136316	+	0.419538i
$741$		0			0
$742$	−19.4164	−	14.1068i	−0.712799	−	0.517879i
$743$	−32.3607	−	23.5114i	−1.18720	−	0.862550i	−0.194233	−	0.980955i	$-0.562222\pi$
$743$	−32.3607	−	23.5114i	−1.18720	−	0.862550i	−0.992965	+	0.118405i	$0.962222\pi$
$744$	−7.41641	+	22.8254i	−0.271899	+	0.836818i
$745$	13.5967	+	41.8465i	0.498146	+	1.53314i
$746$	1.61803	−	1.17557i	0.0592404	−	0.0430407i
$747$	12.0000			0.439057
$748$		0			0
$749$	−48.0000			−1.75388
$750$	9.70820	−	7.05342i	0.354493	−	0.257555i
$751$	−2.47214	−	7.60845i	−0.0902095	−	0.277636i	0.895766	−	0.444526i	$-0.146628\pi$
$751$	−2.47214	−	7.60845i	−0.0902095	−	0.277636i	−0.985976	+	0.166889i	$0.946628\pi$
$752$	−2.47214	+	7.60845i	−0.0901495	+	0.277452i
$753$	3.23607	+	2.35114i	0.117929	+	0.0856803i
$754$	−9.70820	−	7.05342i	−0.353552	−	0.256871i
$755$	−12.3607	+	38.0423i	−0.449851	+	1.38450i
$756$	1.23607	+	3.80423i	0.0449554	+	0.138358i
$757$	8.09017	−	5.87785i	0.294042	−	0.213634i	−0.430977	−	0.902363i	$-0.641831\pi$
$757$	8.09017	−	5.87785i	0.294042	−	0.213634i	0.725019	+	0.688729i	$0.241831\pi$
$758$	28.0000			1.01701
$759$		0			0
$760$		0			0
$761$	−4.85410	+	3.52671i	−0.175961	+	0.127843i	−0.672280	−	0.740297i	$-0.734685\pi$
$761$	−4.85410	+	3.52671i	−0.175961	+	0.127843i	0.496319	+	0.868140i	$0.334685\pi$
$762$	1.23607	+	3.80423i	0.0447780	+	0.137813i
$763$	−2.47214	+	7.60845i	−0.0894973	+	0.275444i
$764$	6.47214	+	4.70228i	0.234154	+	0.170123i
$765$	−3.23607	−	2.35114i	−0.117000	−	0.0850057i
$766$	−4.94427	+	15.2169i	−0.178644	+	0.549809i
$767$	2.47214	+	7.60845i	0.0892637	+	0.274725i
$768$	−13.7533	+	9.99235i	−0.496279	+	0.360568i
$769$	2.00000			0.0721218			0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000			0.0721218			0.0360609	+	0.999350i	$0.488519\pi$
$770$		0			0
$771$	14.0000			0.504198
$772$	−11.3262	+	8.22899i	−0.407640	+	0.296168i
$773$	1.85410	+	5.70634i	0.0666874	+	0.205243i	0.978847	−	0.204591i	$-0.0655866\pi$
$773$	1.85410	+	5.70634i	0.0666874	+	0.205243i	−0.912160	+	0.409834i	$0.865587\pi$
$774$		0			0

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.61803 + 1.17557i) q^{5} +(0.809017 + 0.587785i) q^{6} +(1.23607 - 3.80423i) q^{7} +(-0.927051 - 2.85317i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.61803 + 1.17557i) q^{5} +(0.809017 + 0.587785i) q^{6} +(1.23607 - 3.80423i) q^{7} +(-0.927051 - 2.85317i) q^{8} +(-0.809017 + 0.587785i) q^{9} -2.00000 q^{10} +1.00000 q^{12} +(1.61803 - 1.17557i) q^{13} +(1.23607 + 3.80423i) q^{14} +(0.618034 - 1.90211i) q^{15} +(0.809017 + 0.587785i) q^{16} +(1.61803 + 1.17557i) q^{17} +(0.309017 - 0.951057i) q^{18} +(-1.61803 + 1.17557i) q^{20} -4.00000 q^{21} +8.00000 q^{23} +(-2.42705 + 1.76336i) q^{24} +(-0.309017 - 0.951057i) q^{25} +(-0.618034 + 1.90211i) q^{26} +(0.809017 + 0.587785i) q^{27} +(3.23607 + 2.35114i) q^{28} +(-1.85410 + 5.70634i) q^{29} +(0.618034 + 1.90211i) q^{30} +(6.47214 - 4.70228i) q^{31} +5.00000 q^{32} -2.00000 q^{34} +(6.47214 - 4.70228i) q^{35} +(-0.309017 - 0.951057i) q^{36} +(1.85410 - 5.70634i) q^{37} +(-1.61803 - 1.17557i) q^{39} +(1.85410 - 5.70634i) q^{40} +(-0.618034 - 1.90211i) q^{41} +(3.23607 - 2.35114i) q^{42} -2.00000 q^{45} +(-6.47214 + 4.70228i) q^{46} +(2.47214 + 7.60845i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-7.28115 - 5.29007i) q^{49} +(0.809017 + 0.587785i) q^{50} +(0.618034 - 1.90211i) q^{51} +(0.618034 + 1.90211i) q^{52} +(-4.85410 + 3.52671i) q^{53} -1.00000 q^{54} -12.0000 q^{56} +(-1.85410 - 5.70634i) q^{58} +(-1.23607 + 3.80423i) q^{59} +(1.61803 + 1.17557i) q^{60} +(-4.85410 - 3.52671i) q^{61} +(-2.47214 + 7.60845i) q^{62} +(1.23607 + 3.80423i) q^{63} +(-5.66312 + 4.11450i) q^{64} +4.00000 q^{65} -4.00000 q^{67} +(-1.61803 + 1.17557i) q^{68} +(-2.47214 - 7.60845i) q^{69} +(-2.47214 + 7.60845i) q^{70} +(2.42705 + 1.76336i) q^{72} +(-4.32624 + 13.3148i) q^{73} +(1.85410 + 5.70634i) q^{74} +(-0.809017 + 0.587785i) q^{75} +2.00000 q^{78} +(3.23607 - 2.35114i) q^{79} +(0.618034 + 1.90211i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.61803 + 1.17557i) q^{82} +(-9.70820 - 7.05342i) q^{83} +(1.23607 - 3.80423i) q^{84} +(1.23607 + 3.80423i) q^{85} +6.00000 q^{87} -6.00000 q^{89} +(1.61803 - 1.17557i) q^{90} +(-2.47214 - 7.60845i) q^{91} +(-2.47214 + 7.60845i) q^{92} +(-6.47214 - 4.70228i) q^{93} +(-6.47214 - 4.70228i) q^{94} +(-1.54508 - 4.75528i) q^{96} +(-1.61803 + 1.17557i) q^{97} +9.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{3} + q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 3 q^{8} - q^{9}+O(q^{10}) \) 4 * q - q^2 + q^3 + q^4 + 2 * q^5 + q^6 - 4 * q^7 + 3 * q^8 - q^9	\( 4 q - q^{2} + q^{3} + q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 3 q^{8} - q^{9} - 8 q^{10} + 4 q^{12} + 2 q^{13} - 4 q^{14} - 2 q^{15} + q^{16} + 2 q^{17} - q^{18} - 2 q^{20} - 16 q^{21} + 32 q^{23} - 3 q^{24} + q^{25} + 2 q^{26} + q^{27} + 4 q^{28} + 6 q^{29} - 2 q^{30} + 8 q^{31} + 20 q^{32} - 8 q^{34} + 8 q^{35} + q^{36} - 6 q^{37} - 2 q^{39} - 6 q^{40} + 2 q^{41} + 4 q^{42} - 8 q^{45} - 8 q^{46} - 8 q^{47} - q^{48} - 9 q^{49} + q^{50} - 2 q^{51} - 2 q^{52} - 6 q^{53} - 4 q^{54} - 48 q^{56} + 6 q^{58} + 4 q^{59} + 2 q^{60} - 6 q^{61} + 8 q^{62} - 4 q^{63} - 7 q^{64} + 16 q^{65} - 16 q^{67} - 2 q^{68} + 8 q^{69} + 8 q^{70} + 3 q^{72} + 14 q^{73} - 6 q^{74} - q^{75} + 8 q^{78} + 4 q^{79} - 2 q^{80} - q^{81} + 2 q^{82} - 12 q^{83} - 4 q^{84} - 4 q^{85} + 24 q^{87} - 24 q^{89} + 2 q^{90} + 8 q^{91} + 8 q^{92} - 8 q^{93} - 8 q^{94} + 5 q^{96} - 2 q^{97} + 36 q^{98}+O(q^{100}) \) 4 * q - q^2 + q^3 + q^4 + 2 * q^5 + q^6 - 4 * q^7 + 3 * q^8 - q^9 - 8 * q^10 + 4 * q^12 + 2 * q^13 - 4 * q^14 - 2 * q^15 + q^16 + 2 * q^17 - q^18 - 2 * q^20 - 16 * q^21 + 32 * q^23 - 3 * q^24 + q^25 + 2 * q^26 + q^27 + 4 * q^28 + 6 * q^29 - 2 * q^30 + 8 * q^31 + 20 * q^32 - 8 * q^34 + 8 * q^35 + q^36 - 6 * q^37 - 2 * q^39 - 6 * q^40 + 2 * q^41 + 4 * q^42 - 8 * q^45 - 8 * q^46 - 8 * q^47 - q^48 - 9 * q^49 + q^50 - 2 * q^51 - 2 * q^52 - 6 * q^53 - 4 * q^54 - 48 * q^56 + 6 * q^58 + 4 * q^59 + 2 * q^60 - 6 * q^61 + 8 * q^62 - 4 * q^63 - 7 * q^64 + 16 * q^65 - 16 * q^67 - 2 * q^68 + 8 * q^69 + 8 * q^70 + 3 * q^72 + 14 * q^73 - 6 * q^74 - q^75 + 8 * q^78 + 4 * q^79 - 2 * q^80 - q^81 + 2 * q^82 - 12 * q^83 - 4 * q^84 - 4 * q^85 + 24 * q^87 - 24 * q^89 + 2 * q^90 + 8 * q^91 + 8 * q^92 - 8 * q^93 - 8 * q^94 + 5 * q^96 - 2 * q^97 + 36 * q^98

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