LMFDB - Embedded newform 363.2.e.g.148.1

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			148.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	363.148
Dual form			363.2.e.g.130.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.618034 + 1.90211i) q^{5} +(0.309017 - 0.951057i) q^{6} +(3.23607 - 2.35114i) q^{7} +(-2.42705 - 1.76336i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.618034 + 1.90211i) q^{5} +(0.309017 - 0.951057i) q^{6} +(3.23607 - 2.35114i) q^{7} +(-2.42705 - 1.76336i) q^{8} +(0.309017 + 0.951057i) q^{9} +2.00000 q^{10} +1.00000 q^{12} +(0.618034 + 1.90211i) q^{13} +(-3.23607 - 2.35114i) q^{14} +(-1.61803 + 1.17557i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(0.618034 - 1.90211i) q^{17} +(0.809017 - 0.587785i) q^{18} +(0.618034 + 1.90211i) q^{20} +4.00000 q^{21} +8.00000 q^{23} +(-0.927051 - 2.85317i) q^{24} +(0.809017 + 0.587785i) q^{25} +(1.61803 - 1.17557i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.23607 - 3.80423i) q^{28} +(-4.85410 + 3.52671i) q^{29} +(1.61803 + 1.17557i) q^{30} +(-2.47214 - 7.60845i) q^{31} -5.00000 q^{32} -2.00000 q^{34} +(2.47214 + 7.60845i) q^{35} +(0.809017 + 0.587785i) q^{36} +(-4.85410 + 3.52671i) q^{37} +(-0.618034 + 1.90211i) q^{39} +(4.85410 - 3.52671i) q^{40} +(-1.61803 - 1.17557i) q^{41} +(-1.23607 - 3.80423i) q^{42} -2.00000 q^{45} +(-2.47214 - 7.60845i) q^{46} +(-6.47214 - 4.70228i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(2.78115 - 8.55951i) q^{49} +(0.309017 - 0.951057i) q^{50} +(1.61803 - 1.17557i) q^{51} +(1.61803 + 1.17557i) q^{52} +(1.85410 + 5.70634i) q^{53} +1.00000 q^{54} -12.0000 q^{56} +(4.85410 + 3.52671i) q^{58} +(3.23607 - 2.35114i) q^{59} +(-0.618034 + 1.90211i) q^{60} +(-1.85410 + 5.70634i) q^{61} +(-6.47214 + 4.70228i) q^{62} +(3.23607 + 2.35114i) q^{63} +(2.16312 + 6.65740i) q^{64} -4.00000 q^{65} -4.00000 q^{67} +(-0.618034 - 1.90211i) q^{68} +(6.47214 + 4.70228i) q^{69} +(6.47214 - 4.70228i) q^{70} +(0.927051 - 2.85317i) q^{72} +(-11.3262 + 8.22899i) q^{73} +(4.85410 + 3.52671i) q^{74} +(0.309017 + 0.951057i) q^{75} +2.00000 q^{78} +(1.23607 + 3.80423i) q^{79} +(-1.61803 - 1.17557i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-0.618034 + 1.90211i) q^{82} +(-3.70820 + 11.4127i) q^{83} +(3.23607 - 2.35114i) q^{84} +(3.23607 + 2.35114i) q^{85} -6.00000 q^{87} -6.00000 q^{89} +(0.618034 + 1.90211i) q^{90} +(6.47214 + 4.70228i) q^{91} +(6.47214 - 4.70228i) q^{92} +(2.47214 - 7.60845i) q^{93} +(-2.47214 + 7.60845i) q^{94} +(-4.04508 - 2.93893i) q^{96} +(0.618034 + 1.90211i) 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 $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i	−0.998886	−	0.0471903i	$-0.984973\pi$
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i	0.780378	−	0.625308i	$-0.215027\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−0.618034	+	1.90211i	−0.276393	+	0.850651i	0.712454	+	0.701719i	$0.247584\pi$
$5$	−0.618034	+	1.90211i	−0.276393	+	0.850651i	−0.988847	+	0.148932i	$0.952416\pi$
$6$	0.309017	−	0.951057i	0.126156	−	0.388267i
$7$	3.23607	−	2.35114i	1.22312	−	0.888648i	0.226764	−	0.973950i	$-0.427186\pi$
$7$	3.23607	−	2.35114i	1.22312	−	0.888648i	0.996355	+	0.0853021i	$0.0271855\pi$
$8$	−2.42705	−	1.76336i	−0.858092	−	0.623440i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	2.00000			0.632456
$11$		0			0
$11$		0			0
$12$	1.00000			0.288675
$13$	0.618034	+	1.90211i	0.171412	+	0.527551i	0.999451	−	0.0331183i	$-0.0105438\pi$
$13$	0.618034	+	1.90211i	0.171412	+	0.527551i	−0.828040	+	0.560670i	$0.810544\pi$
$14$	−3.23607	−	2.35114i	−0.864876	−	0.628369i
$15$	−1.61803	+	1.17557i	−0.417775	+	0.303531i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	0.618034	−	1.90211i	0.149895	−	0.461330i	−0.847713	−	0.530456i	$-0.822021\pi$
$17$	0.618034	−	1.90211i	0.149895	−	0.461330i	0.997608	+	0.0691254i	$0.0220209\pi$
$18$	0.809017	−	0.587785i	0.190687	−	0.138542i
$19$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$19$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$20$	0.618034	+	1.90211i	0.138197	+	0.425325i
$21$	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	$0.186012\pi$
$24$	−0.927051	−	2.85317i	−0.189233	−	0.582401i
$25$	0.809017	+	0.587785i	0.161803	+	0.117557i
$26$	1.61803	−	1.17557i	0.317323	−	0.230548i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	1.23607	−	3.80423i	0.233595	−	0.718931i
$29$	−4.85410	+	3.52671i	−0.901384	+	0.654894i	−0.938821	−	0.344405i	$-0.888081\pi$
$29$	−4.85410	+	3.52671i	−0.901384	+	0.654894i	0.0374370	+	0.999299i	$0.488081\pi$
$30$	1.61803	+	1.17557i	0.295411	+	0.214629i
$31$	−2.47214	−	7.60845i	−0.444009	−	1.36652i	−0.883567	−	0.468304i	$-0.844865\pi$
$31$	−2.47214	−	7.60845i	−0.444009	−	1.36652i	0.439558	−	0.898214i	$-0.355135\pi$
$32$	−5.00000			−0.883883
$33$		0			0
$34$	−2.00000			−0.342997
$35$	2.47214	+	7.60845i	0.417867	+	1.28606i
$36$	0.809017	+	0.587785i	0.134836	+	0.0979642i
$37$	−4.85410	+	3.52671i	−0.798009	+	0.579788i	−0.910330	−	0.413884i	$-0.864172\pi$
$37$	−4.85410	+	3.52671i	−0.798009	+	0.579788i	0.112320	+	0.993672i	$0.464172\pi$
$38$		0			0
$39$	−0.618034	+	1.90211i	−0.0989646	+	0.304582i
$40$	4.85410	−	3.52671i	0.767501	−	0.557622i
$41$	−1.61803	−	1.17557i	−0.252694	−	0.183593i	0.454226	−	0.890887i	$-0.349916\pi$
$41$	−1.61803	−	1.17557i	−0.252694	−	0.183593i	−0.706920	+	0.707293i	$0.749916\pi$
$42$	−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
$45$	−2.00000			−0.298142
$46$	−2.47214	−	7.60845i	−0.364497	−	1.12181i
$47$	−6.47214	−	4.70228i	−0.944058	−	0.685898i	0.00533600	−	0.999986i	$-0.498301\pi$
$47$	−6.47214	−	4.70228i	−0.944058	−	0.685898i	−0.949394	+	0.314087i	$0.898301\pi$
$48$	−0.809017	+	0.587785i	−0.116772	+	0.0848395i
$49$	2.78115	−	8.55951i	0.397308	−	1.22279i
$50$	0.309017	−	0.951057i	0.0437016	−	0.134500i
$51$	1.61803	−	1.17557i	0.226570	−	0.164613i
$52$	1.61803	+	1.17557i	0.224381	+	0.163022i
$53$	1.85410	+	5.70634i	0.254680	+	0.783826i	0.993892	+	0.110353i	$0.0351982\pi$
$53$	1.85410	+	5.70634i	0.254680	+	0.783826i	−0.739212	+	0.673473i	$0.764802\pi$
$54$	1.00000			0.136083
$55$		0			0
$56$	−12.0000			−1.60357
$57$		0			0
$58$	4.85410	+	3.52671i	0.637375	+	0.463080i
$59$	3.23607	−	2.35114i	0.421300	−	0.306092i	−0.356861	−	0.934158i	$-0.616153\pi$
$59$	3.23607	−	2.35114i	0.421300	−	0.306092i	0.778161	+	0.628065i	$0.216153\pi$
$60$	−0.618034	+	1.90211i	−0.0797878	+	0.245562i
$61$	−1.85410	+	5.70634i	−0.237393	+	0.730622i	0.759401	+	0.650622i	$0.225492\pi$
$61$	−1.85410	+	5.70634i	−0.237393	+	0.730622i	−0.996795	+	0.0799995i	$0.974508\pi$
$62$	−6.47214	+	4.70228i	−0.821962	+	0.597190i
$63$	3.23607	+	2.35114i	0.407706	+	0.296216i
$64$	2.16312	+	6.65740i	0.270390	+	0.832174i
$65$	−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	$0.578571\pi$
$68$	−0.618034	−	1.90211i	−0.0749476	−	0.230665i
$69$	6.47214	+	4.70228i	0.779154	+	0.566088i
$70$	6.47214	−	4.70228i	0.773568	−	0.562030i
$71$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$71$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$72$	0.927051	−	2.85317i	0.109254	−	0.336249i
$73$	−11.3262	+	8.22899i	−1.32564	+	0.963131i	−0.325792	+	0.945441i	$0.605631\pi$
$73$	−11.3262	+	8.22899i	−1.32564	+	0.963131i	−0.999844	+	0.0176895i	$0.994369\pi$
$74$	4.85410	+	3.52671i	0.564278	+	0.409972i
$75$	0.309017	+	0.951057i	0.0356822	+	0.109819i
$76$		0			0
$77$		0			0
$78$	2.00000			0.226455
$79$	1.23607	+	3.80423i	0.139069	+	0.428009i	0.996201	−	0.0870877i	$-0.0277560\pi$
$79$	1.23607	+	3.80423i	0.139069	+	0.428009i	−0.857132	+	0.515097i	$0.827756\pi$
$80$	−1.61803	−	1.17557i	−0.180902	−	0.131433i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−0.618034	+	1.90211i	−0.0682504	+	0.210053i
$83$	−3.70820	+	11.4127i	−0.407028	+	1.25270i	0.512161	+	0.858889i	$0.328845\pi$
$83$	−3.70820	+	11.4127i	−0.407028	+	1.25270i	−0.919190	+	0.393815i	$0.871155\pi$
$84$	3.23607	−	2.35114i	0.353084	−	0.256531i
$85$	3.23607	+	2.35114i	0.351001	+	0.255017i
$86$		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	$0.603011\pi$
$90$	0.618034	+	1.90211i	0.0651465	+	0.200500i
$91$	6.47214	+	4.70228i	0.678464	+	0.492933i
$92$	6.47214	−	4.70228i	0.674767	−	0.490247i
$93$	2.47214	−	7.60845i	0.256349	−	0.788960i
$94$	−2.47214	+	7.60845i	−0.254981	+	0.784752i
$95$		0			0
$96$	−4.04508	−	2.93893i	−0.412850	−	0.299953i
$97$	0.618034	+	1.90211i	0.0627518	+	0.193130i	0.977517	−	0.210855i	$-0.0676247\pi$
$97$	0.618034	+	1.90211i	0.0627518	+	0.193130i	−0.914766	+	0.403985i	$0.867625\pi$
$98$	−9.00000			−0.909137
$99$		0			0
$100$	1.00000			0.100000
$101$	−0.618034	−	1.90211i	−0.0614967	−	0.189267i	0.915588	−	0.402117i	$-0.131726\pi$
$101$	−0.618034	−	1.90211i	−0.0614967	−	0.189267i	−0.977085	+	0.212850i	$0.931726\pi$
$102$	−1.61803	−	1.17557i	−0.160209	−	0.116399i
$103$	−6.47214	+	4.70228i	−0.637719	+	0.463330i	−0.859066	−	0.511865i	$-0.828955\pi$
$103$	−6.47214	+	4.70228i	−0.637719	+	0.463330i	0.221347	+	0.975195i	$0.428955\pi$
$104$	1.85410	−	5.70634i	0.181810	−	0.559553i
$105$	−2.47214	+	7.60845i	−0.241256	+	0.742509i
$106$	4.85410	−	3.52671i	0.471472	−	0.342545i
$107$	−9.70820	−	7.05342i	−0.938527	−	0.681880i	0.00953827	−	0.999955i	$-0.496964\pi$
$107$	−9.70820	−	7.05342i	−0.938527	−	0.681880i	−0.948066	+	0.318074i	$0.896964\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	−6.00000			−0.569495
$112$	1.23607	+	3.80423i	0.116797	+	0.359466i
$113$	4.85410	+	3.52671i	0.456636	+	0.331765i	0.792210	−	0.610249i	$-0.208930\pi$
$113$	4.85410	+	3.52671i	0.456636	+	0.331765i	−0.335575	+	0.942014i	$0.608930\pi$
$114$		0			0
$115$	−4.94427	+	15.2169i	−0.461056	+	1.41898i
$116$	−1.85410	+	5.70634i	−0.172149	+	0.529820i
$117$	−1.61803	+	1.17557i	−0.149587	+	0.108682i
$118$	−3.23607	−	2.35114i	−0.297904	−	0.216440i
$119$	−2.47214	−	7.60845i	−0.226620	−	0.697466i
$120$	6.00000			0.547723
$121$		0			0
$122$	6.00000			0.543214
$123$	−0.618034	−	1.90211i	−0.0557262	−	0.171508i
$124$	−6.47214	−	4.70228i	−0.581215	−	0.422277i
$125$	−9.70820	+	7.05342i	−0.868328	+	0.630877i
$126$	1.23607	−	3.80423i	0.110118	−	0.338907i
$127$	1.23607	−	3.80423i	0.109683	−	0.337570i	−0.881118	−	0.472897i	$-0.843208\pi$
$127$	1.23607	−	3.80423i	0.109683	−	0.337570i	0.990801	+	0.135326i	$0.0432083\pi$
$128$	−2.42705	+	1.76336i	−0.214523	+	0.155860i
$129$		0			0
$130$	1.23607	+	3.80423i	0.108410	+	0.333653i
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$		0			0
$134$	1.23607	+	3.80423i	0.106780	+	0.328635i
$135$	−1.61803	−	1.17557i	−0.139258	−	0.101177i
$136$	−4.85410	+	3.52671i	−0.416236	+	0.302413i
$137$	0.618034	−	1.90211i	0.0528022	−	0.162508i	−0.921178	−	0.389141i	$-0.872772\pi$
$137$	0.618034	−	1.90211i	0.0528022	−	0.162508i	0.973980	+	0.226633i	$0.0727718\pi$
$138$	2.47214	−	7.60845i	0.210442	−	0.647674i
$139$	−6.47214	+	4.70228i	−0.548959	+	0.398842i	−0.827402	−	0.561611i	$-0.810182\pi$
$139$	−6.47214	+	4.70228i	−0.548959	+	0.398842i	0.278442	+	0.960453i	$0.410182\pi$
$140$	6.47214	+	4.70228i	0.546995	+	0.397415i
$141$	−2.47214	−	7.60845i	−0.208191	−	0.640747i
$142$		0			0
$143$		0			0
$144$	−1.00000			−0.0833333
$145$	−3.70820	−	11.4127i	−0.307950	−	0.947771i
$146$	11.3262	+	8.22899i	0.937366	+	0.681036i
$147$	7.28115	−	5.29007i	0.600539	−	0.436317i
$148$	−1.85410	+	5.70634i	−0.152406	+	0.469058i
$149$	6.79837	−	20.9232i	0.556944	−	1.71410i	−0.133808	−	0.991007i	$-0.542720\pi$
$149$	6.79837	−	20.9232i	0.556944	−	1.71410i	0.690752	−	0.723092i	$-0.257280\pi$
$150$	0.809017	−	0.587785i	0.0660560	−	0.0479925i
$151$	16.1803	+	11.7557i	1.31674	+	0.956666i	0.999967	+	0.00816356i	$0.00259857\pi$
$151$	16.1803	+	11.7557i	1.31674	+	0.956666i	0.316771	+	0.948502i	$0.397401\pi$
$152$		0			0
$153$	2.00000			0.161690
$154$		0			0
$155$	16.0000			1.28515
$156$	0.618034	+	1.90211i	0.0494823	+	0.152291i
$157$	−11.3262	−	8.22899i	−0.903932	−	0.656745i	0.0355408	−	0.999368i	$-0.488685\pi$
$157$	−11.3262	−	8.22899i	−0.903932	−	0.656745i	−0.939473	+	0.342623i	$0.888685\pi$
$158$	3.23607	−	2.35114i	0.257448	−	0.187047i
$159$	−1.85410	+	5.70634i	−0.147040	+	0.452542i
$160$	3.09017	−	9.51057i	0.244299	−	0.751876i
$161$	25.8885	−	18.8091i	2.04030	−	1.48237i
$162$	0.809017	+	0.587785i	0.0635624	+	0.0461808i
$163$	1.23607	+	3.80423i	0.0968163	+	0.297970i	0.987723	−	0.156217i	$-0.0499299\pi$
$163$	1.23607	+	3.80423i	0.0968163	+	0.297970i	−0.890906	+	0.454187i	$0.849930\pi$
$164$	−2.00000			−0.156174
$165$		0			0
$166$	12.0000			0.931381
$167$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$167$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$168$	−9.70820	−	7.05342i	−0.749004	−	0.544183i
$169$	7.28115	−	5.29007i	0.560089	−	0.406928i
$170$	1.23607	−	3.80423i	0.0948021	−	0.291771i
$171$		0			0
$172$		0			0
$173$	−4.85410	−	3.52671i	−0.369051	−	0.268131i	0.387767	−	0.921758i	$-0.373247\pi$
$173$	−4.85410	−	3.52671i	−0.369051	−	0.268131i	−0.756817	+	0.653627i	$0.773247\pi$
$174$	1.85410	+	5.70634i	0.140559	+	0.432596i
$175$	4.00000			0.302372
$176$		0			0
$177$	4.00000			0.300658
$178$	1.85410	+	5.70634i	0.138971	+	0.427708i
$179$	−9.70820	−	7.05342i	−0.725625	−	0.527198i	0.162551	−	0.986700i	$-0.448028\pi$
$179$	−9.70820	−	7.05342i	−0.725625	−	0.527198i	−0.888176	+	0.459503i	$0.848028\pi$
$180$	−1.61803	+	1.17557i	−0.120601	+	0.0876219i
$181$	6.79837	−	20.9232i	0.505319	−	1.55521i	−0.294914	−	0.955524i	$-0.595291\pi$
$181$	6.79837	−	20.9232i	0.505319	−	1.55521i	0.800233	−	0.599689i	$-0.204709\pi$
$182$	2.47214	−	7.60845i	0.183247	−	0.563976i
$183$	−4.85410	+	3.52671i	−0.358826	+	0.260702i
$184$	−19.4164	−	14.1068i	−1.43140	−	1.03997i
$185$	−3.70820	−	11.4127i	−0.272633	−	0.839077i
$186$	−8.00000			−0.586588
$187$		0			0
$188$	−8.00000			−0.583460
$189$	1.23607	+	3.80423i	0.0899107	+	0.276717i
$190$		0			0
$191$	−6.47214	+	4.70228i	−0.468307	+	0.340245i	−0.796781	−	0.604268i	$-0.793466\pi$
$191$	−6.47214	+	4.70228i	−0.468307	+	0.340245i	0.328474	+	0.944513i	$0.393466\pi$
$192$	−2.16312	+	6.65740i	−0.156110	+	0.480456i
$193$	4.32624	−	13.3148i	0.311409	−	0.958420i	−0.665798	−	0.746132i	$-0.731909\pi$
$193$	4.32624	−	13.3148i	0.311409	−	0.958420i	0.977207	−	0.212287i	$-0.0680913\pi$
$194$	1.61803	−	1.17557i	0.116168	−	0.0844010i
$195$	−3.23607	−	2.35114i	−0.231740	−	0.168369i
$196$	−2.78115	−	8.55951i	−0.198654	−	0.611393i
$197$	14.0000			0.997459			0.498729	−	0.866758i	$-0.333800\pi$
$197$	14.0000			0.997459			0.498729	+	0.866758i	$0.333800\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−0.927051	−	2.85317i	−0.0655524	−	0.201750i
$201$	−3.23607	−	2.35114i	−0.228255	−	0.165837i
$202$	−1.61803	+	1.17557i	−0.113844	+	0.0827129i
$203$	−7.41641	+	22.8254i	−0.520530	+	1.60203i
$204$	0.618034	−	1.90211i	0.0432710	−	0.133175i
$205$	3.23607	−	2.35114i	0.226017	−	0.164211i
$206$	6.47214	+	4.70228i	0.450935	+	0.327624i
$207$	2.47214	+	7.60845i	0.171825	+	0.528824i
$208$	−2.00000			−0.138675
$209$		0			0
$210$	8.00000			0.552052
$211$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$211$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$212$	4.85410	+	3.52671i	0.333381	+	0.242216i
$213$		0			0
$214$	−3.70820	+	11.4127i	−0.253488	+	0.780155i
$215$		0			0
$216$	2.42705	−	1.76336i	0.165140	−	0.119981i
$217$	−25.8885	−	18.8091i	−1.75743	−	1.27685i
$218$	−0.618034	−	1.90211i	−0.0418585	−	0.128827i
$219$	−14.0000			−0.946032
$220$		0			0
$221$	4.00000			0.269069
$222$	1.85410	+	5.70634i	0.124439	+	0.382984i
$223$	−12.9443	−	9.40456i	−0.866813	−	0.629776i	0.0629172	−	0.998019i	$-0.479960\pi$
$223$	−12.9443	−	9.40456i	−0.866813	−	0.629776i	−0.929730	+	0.368243i	$0.879960\pi$
$224$	−16.1803	+	11.7557i	−1.08109	+	0.785461i
$225$	−0.309017	+	0.951057i	−0.0206011	+	0.0634038i
$226$	1.85410	−	5.70634i	0.123333	−	0.379580i
$227$	9.70820	−	7.05342i	0.644356	−	0.468152i	−0.216988	−	0.976174i	$-0.569623\pi$
$227$	9.70820	−	7.05342i	0.644356	−	0.468152i	0.861344	+	0.508022i	$0.169623\pi$
$228$		0			0
$229$	1.85410	+	5.70634i	0.122523	+	0.377086i	0.993442	−	0.114341i	$-0.0364756\pi$
$229$	1.85410	+	5.70634i	0.122523	+	0.377086i	−0.870919	+	0.491426i	$0.836476\pi$
$230$	16.0000			1.05501
$231$		0			0
$232$	18.0000			1.18176
$233$	−9.27051	−	28.5317i	−0.607331	−	1.86917i	−0.479893	−	0.877327i	$-0.659325\pi$
$233$	−9.27051	−	28.5317i	−0.607331	−	1.86917i	−0.127438	−	0.991847i	$-0.540675\pi$
$234$	1.61803	+	1.17557i	0.105774	+	0.0768494i
$235$	12.9443	−	9.40456i	0.844391	−	0.613486i
$236$	1.23607	−	3.80423i	0.0804612	−	0.247634i
$237$	−1.23607	+	3.80423i	−0.0802912	+	0.247111i
$238$	−6.47214	+	4.70228i	−0.419526	+	0.304804i
$239$	19.4164	+	14.1068i	1.25594	+	0.912496i	0.998551	−	0.0538111i	$-0.0171369\pi$
$239$	19.4164	+	14.1068i	1.25594	+	0.912496i	0.257392	+	0.966307i	$0.417137\pi$
$240$	−0.618034	−	1.90211i	−0.0398939	−	0.122781i
$241$	−10.0000			−0.644157			−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000			−0.644157			−0.322078	+	0.946713i	$0.604381\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$	1.85410	+	5.70634i	0.118697	+	0.365311i
$245$	14.5623	+	10.5801i	0.930352	+	0.675940i
$246$	−1.61803	+	1.17557i	−0.103162	+	0.0749516i
$247$		0			0
$248$	−7.41641	+	22.8254i	−0.470942	+	1.44941i
$249$	−9.70820	+	7.05342i	−0.615232	+	0.446993i
$250$	9.70820	+	7.05342i	0.614001	+	0.446098i
$251$	1.23607	+	3.80423i	0.0780199	+	0.240121i	0.982458	−	0.186485i	$-0.0597094\pi$
$251$	1.23607	+	3.80423i	0.0780199	+	0.240121i	−0.904438	+	0.426605i	$0.859709\pi$
$252$	4.00000			0.251976
$253$		0			0
$254$	−4.00000			−0.250982
$255$	1.23607	+	3.80423i	0.0774056	+	0.238230i
$256$	13.7533	+	9.99235i	0.859581	+	0.624522i
$257$	11.3262	−	8.22899i	0.706511	−	0.513311i	−0.175535	−	0.984473i	$-0.556166\pi$
$257$	11.3262	−	8.22899i	0.706511	−	0.513311i	0.882046	+	0.471163i	$0.156166\pi$
$258$		0			0
$259$	−7.41641	+	22.8254i	−0.460833	+	1.41830i
$260$	−3.23607	+	2.35114i	−0.200692	+	0.145812i
$261$	−4.85410	−	3.52671i	−0.300461	−	0.218298i
$262$	−3.70820	−	11.4127i	−0.229094	−	0.705078i
$263$	16.0000			0.986602			0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000			0.986602			0.493301	+	0.869859i	$0.335790\pi$
$264$		0			0
$265$	−12.0000			−0.737154
$266$		0			0
$267$	−4.85410	−	3.52671i	−0.297066	−	0.215831i
$268$	−3.23607	+	2.35114i	−0.197674	+	0.143619i
$269$	−0.618034	+	1.90211i	−0.0376822	+	0.115974i	−0.968128	−	0.250455i	$-0.919420\pi$
$269$	−0.618034	+	1.90211i	−0.0376822	+	0.115974i	0.930446	+	0.366429i	$0.119420\pi$
$270$	−0.618034	+	1.90211i	−0.0376124	+	0.115759i
$271$	16.1803	−	11.7557i	0.982886	−	0.714108i	0.0245340	−	0.999699i	$-0.492190\pi$
$271$	16.1803	−	11.7557i	0.982886	−	0.714108i	0.958352	+	0.285591i	$0.0921898\pi$
$272$	1.61803	+	1.17557i	0.0981077	+	0.0712794i
$273$	2.47214	+	7.60845i	0.149620	+	0.460484i
$274$	−2.00000			−0.120824
$275$		0			0
$276$	8.00000			0.481543
$277$	8.03444	+	24.7275i	0.482743	+	1.48573i	0.835224	+	0.549911i	$0.185338\pi$
$277$	8.03444	+	24.7275i	0.482743	+	1.48573i	−0.352481	+	0.935819i	$0.614662\pi$
$278$	6.47214	+	4.70228i	0.388173	+	0.282024i
$279$	6.47214	−	4.70228i	0.387477	−	0.281518i
$280$	7.41641	−	22.8254i	0.443215	−	1.36408i
$281$	5.56231	−	17.1190i	0.331819	−	1.02123i	−0.636448	−	0.771319i	$-0.719597\pi$
$281$	5.56231	−	17.1190i	0.331819	−	1.02123i	0.968268	−	0.249916i	$-0.0804029\pi$
$282$	−6.47214	+	4.70228i	−0.385410	+	0.280017i
$283$	12.9443	+	9.40456i	0.769457	+	0.559043i	0.901796	−	0.432161i	$-0.142249\pi$
$283$	12.9443	+	9.40456i	0.769457	+	0.559043i	−0.132339	+	0.991204i	$0.542249\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−8.00000			−0.472225
$288$	−1.54508	−	4.75528i	−0.0910450	−	0.280208i
$289$	10.5172	+	7.64121i	0.618660	+	0.449483i
$290$	−9.70820	+	7.05342i	−0.570085	+	0.414191i
$291$	−0.618034	+	1.90211i	−0.0362298	+	0.111504i
$292$	−4.32624	+	13.3148i	−0.253174	+	0.779189i
$293$	−4.85410	+	3.52671i	−0.283580	+	0.206033i	−0.720477	−	0.693479i	$-0.756077\pi$
$293$	−4.85410	+	3.52671i	−0.283580	+	0.206033i	0.436898	+	0.899511i	$0.356077\pi$
$294$	−7.28115	−	5.29007i	−0.424645	−	0.308523i
$295$	2.47214	+	7.60845i	0.143933	+	0.442981i
$296$	18.0000			1.04623
$297$		0			0
$298$	−22.0000			−1.27443
$299$	4.94427	+	15.2169i	0.285935	+	0.880016i
$300$	0.809017	+	0.587785i	0.0467086	+	0.0339358i
$301$		0			0
$302$	6.18034	−	19.0211i	0.355639	−	1.09454i
$303$	0.618034	−	1.90211i	0.0355051	−	0.109274i
$304$		0			0
$305$	−9.70820	−	7.05342i	−0.555890	−	0.403878i
$306$	−0.618034	−	1.90211i	−0.0353307	−	0.108737i
$307$	−32.0000			−1.82634			−0.913168	−	0.407583i	$-0.866372\pi$
$307$	−32.0000			−1.82634			−0.913168	+	0.407583i	$0.866372\pi$
$308$		0			0
$309$	−8.00000			−0.455104
$310$	−4.94427	−	15.2169i	−0.280816	−	0.864262i
$311$	19.4164	+	14.1068i	1.10100	+	0.799926i	0.981223	−	0.192875i	$-0.0617811\pi$
$311$	19.4164	+	14.1068i	1.10100	+	0.799926i	0.119780	+	0.992800i	$0.461781\pi$
$312$	4.85410	−	3.52671i	0.274809	−	0.199661i
$313$	−6.79837	+	20.9232i	−0.384267	+	1.18265i	0.552744	+	0.833351i	$0.313581\pi$
$313$	−6.79837	+	20.9232i	−0.384267	+	1.18265i	−0.937011	+	0.349300i	$0.886419\pi$
$314$	−4.32624	+	13.3148i	−0.244144	+	0.751397i
$315$	−6.47214	+	4.70228i	−0.364664	+	0.264944i
$316$	3.23607	+	2.35114i	0.182043	+	0.132262i
$317$	6.79837	+	20.9232i	0.381835	+	1.17517i	0.938751	+	0.344597i	$0.111985\pi$
$317$	6.79837	+	20.9232i	0.381835	+	1.17517i	−0.556916	+	0.830569i	$0.688015\pi$
$318$	6.00000			0.336463
$319$		0			0
$320$	−14.0000			−0.782624
$321$	−3.70820	−	11.4127i	−0.206972	−	0.636994i
$322$	−25.8885	−	18.8091i	−1.44271	−	1.04819i
$323$		0			0
$324$	−0.309017	+	0.951057i	−0.0171676	+	0.0528365i
$325$	−0.618034	+	1.90211i	−0.0342824	+	0.105510i
$326$	3.23607	−	2.35114i	0.179229	−	0.130218i
$327$	1.61803	+	1.17557i	0.0894775	+	0.0650092i
$328$	1.85410	+	5.70634i	0.102376	+	0.315080i
$329$	−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	$0.685239\pi$
$332$	3.70820	+	11.4127i	0.203514	+	0.626352i
$333$	−4.85410	−	3.52671i	−0.266003	−	0.193263i
$334$		0			0
$335$	2.47214	−	7.60845i	0.135067	−	0.415694i
$336$	−1.23607	+	3.80423i	−0.0674330	+	0.207538i
$337$	−17.7984	+	12.9313i	−0.969539	+	0.704411i	−0.955347	−	0.295488i	$-0.904518\pi$
$337$	−17.7984	+	12.9313i	−0.969539	+	0.704411i	−0.0141927	+	0.999899i	$0.504518\pi$
$338$	−7.28115	−	5.29007i	−0.396043	−	0.287742i
$339$	1.85410	+	5.70634i	0.100701	+	0.309926i
$340$	4.00000			0.216930
$341$		0			0
$342$		0			0
$343$	−2.47214	−	7.60845i	−0.133483	−	0.410818i
$344$		0			0
$345$	−12.9443	+	9.40456i	−0.696896	+	0.506325i
$346$	−1.85410	+	5.70634i	−0.0996771	+	0.306775i
$347$	−1.23607	+	3.80423i	−0.0663556	+	0.204222i	−0.978737	−	0.205120i	$-0.934242\pi$
$347$	−1.23607	+	3.80423i	−0.0663556	+	0.204222i	0.912381	+	0.409342i	$0.134242\pi$
$348$	−4.85410	+	3.52671i	−0.260207	+	0.189052i
$349$	4.85410	+	3.52671i	0.259834	+	0.188781i	0.710074	−	0.704127i	$-0.248662\pi$
$349$	4.85410	+	3.52671i	0.259834	+	0.188781i	−0.450240	+	0.892908i	$0.648662\pi$
$350$	−1.23607	−	3.80423i	−0.0660706	−	0.203344i
$351$	−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	$0.340992\pi$
$354$	−1.23607	−	3.80423i	−0.0656963	−	0.202192i
$355$		0			0
$356$	−4.85410	+	3.52671i	−0.257267	+	0.186915i
$357$	2.47214	−	7.60845i	0.130839	−	0.402682i
$358$	−3.70820	+	11.4127i	−0.195985	+	0.603179i
$359$	−6.47214	+	4.70228i	−0.341586	+	0.248177i	−0.745331	−	0.666695i	$-0.767708\pi$
$359$	−6.47214	+	4.70228i	−0.341586	+	0.248177i	0.403745	+	0.914872i	$0.367708\pi$
$360$	4.85410	+	3.52671i	0.255834	+	0.185874i
$361$	−5.87132	−	18.0701i	−0.309017	−	0.951057i
$362$	−22.0000			−1.15629
$363$		0			0
$364$	8.00000			0.419314
$365$	−8.65248	−	26.6296i	−0.452891	−	1.39386i
$366$	4.85410	+	3.52671i	0.253728	+	0.184344i
$367$	25.8885	−	18.8091i	1.35137	−	0.981828i	0.352429	−	0.935839i	$-0.385356\pi$
$367$	25.8885	−	18.8091i	1.35137	−	0.981828i	0.998942	−	0.0459900i	$-0.0146442\pi$
$368$	−2.47214	+	7.60845i	−0.128869	+	0.396618i
$369$	0.618034	−	1.90211i	0.0321736	−	0.0990200i
$370$	−9.70820	+	7.05342i	−0.504705	+	0.366690i
$371$	19.4164	+	14.1068i	1.00805	+	0.732391i
$372$	−2.47214	−	7.60845i	−0.128174	−	0.394480i
$373$	2.00000			0.103556			0.0517780	−	0.998659i	$-0.483511\pi$
$373$	2.00000			0.103556			0.0517780	+	0.998659i	$0.483511\pi$
$374$		0			0
$375$	−12.0000			−0.619677
$376$	7.41641	+	22.8254i	0.382472	+	1.17713i
$377$	−9.70820	−	7.05342i	−0.499998	−	0.363270i
$378$	3.23607	−	2.35114i	0.166445	−	0.120930i
$379$	8.65248	−	26.6296i	0.444448	−	1.36787i	−0.438640	−	0.898663i	$-0.644540\pi$
$379$	8.65248	−	26.6296i	0.444448	−	1.36787i	0.883088	−	0.469207i	$-0.155460\pi$
$380$		0			0
$381$	3.23607	−	2.35114i	0.165789	−	0.120453i
$382$	6.47214	+	4.70228i	0.331143	+	0.240590i
$383$	−4.94427	−	15.2169i	−0.252640	−	0.777547i	−0.994285	−	0.106755i	$-0.965954\pi$
$383$	−4.94427	−	15.2169i	−0.252640	−	0.777547i	0.741645	−	0.670793i	$-0.234046\pi$
$384$	−3.00000			−0.153093
$385$		0			0
$386$	−14.0000			−0.712581
$387$		0			0
$388$	1.61803	+	1.17557i	0.0821432	+	0.0596806i
$389$	14.5623	−	10.5801i	0.738338	−	0.536434i	−0.153852	−	0.988094i	$-0.549168\pi$
$389$	14.5623	−	10.5801i	0.738338	−	0.536434i	0.892190	+	0.451660i	$0.149168\pi$
$390$	−1.23607	+	3.80423i	−0.0625907	+	0.192634i
$391$	4.94427	−	15.2169i	0.250043	−	0.769552i
$392$	−21.8435	+	15.8702i	−1.10326	+	0.801566i
$393$	9.70820	+	7.05342i	0.489714	+	0.355798i
$394$	−4.32624	−	13.3148i	−0.217953	−	0.670789i
$395$	−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
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	8.03444	−	24.7275i	0.401221	−	1.23483i	−0.522789	−	0.852462i	$-0.675108\pi$
$401$	8.03444	−	24.7275i	0.401221	−	1.23483i	0.924010	−	0.382369i	$-0.124892\pi$
$402$	−1.23607	+	3.80423i	−0.0616495	+	0.189738i
$403$	12.9443	−	9.40456i	0.644800	−	0.468475i
$404$	−1.61803	−	1.17557i	−0.0805002	−	0.0584868i
$405$	−0.618034	−	1.90211i	−0.0307104	−	0.0945168i
$406$	24.0000			1.19110
$407$		0			0
$408$	−6.00000			−0.297044
$409$	−5.56231	−	17.1190i	−0.275038	−	0.846481i	−0.989209	−	0.146510i	$-0.953196\pi$
$409$	−5.56231	−	17.1190i	−0.275038	−	0.846481i	0.714171	−	0.699971i	$-0.246804\pi$
$410$	−3.23607	−	2.35114i	−0.159818	−	0.116115i
$411$	1.61803	−	1.17557i	0.0798117	−	0.0579866i
$412$	−2.47214	+	7.60845i	−0.121793	+	0.374842i
$413$	4.94427	−	15.2169i	0.243292	−	0.748775i
$414$	6.47214	−	4.70228i	0.318088	−	0.231105i
$415$	−19.4164	−	14.1068i	−0.953114	−	0.692478i
$416$	−3.09017	−	9.51057i	−0.151508	−	0.466294i
$417$	−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	$0.531151\pi$
$420$	2.47214	+	7.60845i	0.120628	+	0.371254i
$421$	21.0344	+	15.2824i	1.02516	+	0.744819i	0.967333	−	0.253507i	$-0.0815842\pi$
$421$	21.0344	+	15.2824i	1.02516	+	0.744819i	0.0578225	+	0.998327i	$0.481584\pi$
$422$		0			0
$423$	2.47214	−	7.60845i	0.120199	−	0.369936i
$424$	5.56231	−	17.1190i	0.270129	−	0.831373i
$425$	1.61803	−	1.17557i	0.0784862	−	0.0570235i
$426$		0			0
$427$	7.41641	+	22.8254i	0.358905	+	1.10460i
$428$	−12.0000			−0.580042
$429$		0			0
$430$		0			0
$431$	7.41641	+	22.8254i	0.357236	+	1.09946i	0.954702	+	0.297564i	$0.0961743\pi$
$431$	7.41641	+	22.8254i	0.357236	+	1.09946i	−0.597466	+	0.801894i	$0.703826\pi$
$432$	−0.809017	−	0.587785i	−0.0389238	−	0.0282798i
$433$	−27.5066	+	19.9847i	−1.32188	+	0.960403i	−0.321975	+	0.946748i	$0.604347\pi$
$433$	−27.5066	+	19.9847i	−1.32188	+	0.960403i	−0.999907	+	0.0136552i	$0.995653\pi$
$434$	−9.88854	+	30.4338i	−0.474665	+	1.46087i
$435$	3.70820	−	11.4127i	0.177795	−	0.547196i
$436$	1.61803	−	1.17557i	0.0774898	−	0.0562996i
$437$		0			0
$438$	4.32624	+	13.3148i	0.206716	+	0.636205i
$439$	20.0000			0.954548			0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000			0.954548			0.477274	+	0.878755i	$0.341625\pi$
$440$		0			0
$441$	9.00000			0.428571
$442$	−1.23607	−	3.80423i	−0.0587938	−	0.180949i
$443$	−22.6525	−	16.4580i	−1.07625	−	0.781943i	−0.0992261	−	0.995065i	$-0.531637\pi$
$443$	−22.6525	−	16.4580i	−1.07625	−	0.781943i	−0.977026	+	0.213122i	$0.931637\pi$
$444$	−4.85410	+	3.52671i	−0.230365	+	0.167370i
$445$	3.70820	−	11.4127i	0.175786	−	0.541013i
$446$	−4.94427	+	15.2169i	−0.234118	+	0.720541i
$447$	17.7984	−	12.9313i	0.841834	−	0.611628i
$448$	22.6525	+	16.4580i	1.07023	+	0.777567i
$449$	0.618034	+	1.90211i	0.0291668	+	0.0897663i	0.964580	−	0.263790i	$-0.0849724\pi$
$449$	0.618034	+	1.90211i	0.0291668	+	0.0897663i	−0.935413	+	0.353556i	$0.884972\pi$
$450$	1.00000			0.0471405
$451$		0			0
$452$	6.00000			0.282216
$453$	6.18034	+	19.0211i	0.290378	+	0.893691i
$454$	−9.70820	−	7.05342i	−0.455629	−	0.331034i
$455$	−12.9443	+	9.40456i	−0.606837	+	0.440893i
$456$		0			0
$457$	−5.56231	+	17.1190i	−0.260194	+	0.800794i	0.732568	+	0.680694i	$0.238322\pi$
$457$	−5.56231	+	17.1190i	−0.260194	+	0.800794i	−0.992762	+	0.120100i	$0.961678\pi$
$458$	4.85410	−	3.52671i	0.226817	−	0.164792i
$459$	1.61803	+	1.17557i	0.0755234	+	0.0548709i
$460$	4.94427	+	15.2169i	0.230528	+	0.709492i
$461$	30.0000			1.39724			0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	−1.85410	−	5.70634i	−0.0860745	−	0.264910i
$465$	12.9443	+	9.40456i	0.600276	+	0.436126i
$466$	−24.2705	+	17.6336i	−1.12431	+	0.816859i
$467$	−3.70820	+	11.4127i	−0.171595	+	0.528116i	−0.999462	−	0.0328096i	$-0.989555\pi$
$467$	−3.70820	+	11.4127i	−0.171595	+	0.528116i	0.827866	+	0.560925i	$0.189555\pi$
$468$	−0.618034	+	1.90211i	−0.0285686	+	0.0879252i
$469$	−12.9443	+	9.40456i	−0.597711	+	0.434262i
$470$	−12.9443	−	9.40456i	−0.597075	−	0.433800i
$471$	−4.32624	−	13.3148i	−0.199343	−	0.613513i
$472$	−12.0000			−0.552345
$473$		0			0
$474$	4.00000			0.183726
$475$		0			0
$476$	−6.47214	−	4.70228i	−0.296650	−	0.215529i
$477$	−4.85410	+	3.52671i	−0.222254	+	0.161477i
$478$	7.41641	−	22.8254i	0.339219	−	1.04401i
$479$	−2.47214	+	7.60845i	−0.112955	+	0.347639i	−0.991515	−	0.129993i	$-0.958505\pi$
$479$	−2.47214	+	7.60845i	−0.112955	+	0.347639i	0.878560	+	0.477632i	$0.158505\pi$
$480$	8.09017	−	5.87785i	0.369264	−	0.268286i
$481$	−9.70820	−	7.05342i	−0.442656	−	0.321608i
$482$	3.09017	+	9.51057i	0.140753	+	0.433194i
$483$	32.0000			1.45605
$484$		0			0
$485$	−4.00000			−0.181631
$486$	0.309017	+	0.951057i	0.0140173	+	0.0431408i
$487$	12.9443	+	9.40456i	0.586561	+	0.426161i	0.841083	−	0.540905i	$-0.181918\pi$
$487$	12.9443	+	9.40456i	0.586561	+	0.426161i	−0.254523	+	0.967067i	$0.581918\pi$
$488$	14.5623	−	10.5801i	0.659205	−	0.478940i
$489$	−1.23607	+	3.80423i	−0.0558969	+	0.172033i
$490$	5.56231	−	17.1190i	0.251279	−	0.773358i
$491$	3.23607	−	2.35114i	0.146042	−	0.106106i	−0.512365	−	0.858768i	$-0.671231\pi$
$491$	3.23607	−	2.35114i	0.146042	−	0.106106i	0.658407	+	0.752662i	$0.271231\pi$
$492$	−1.61803	−	1.17557i	−0.0729466	−	0.0529988i
$493$	3.70820	+	11.4127i	0.167009	+	0.514001i
$494$		0			0
$495$		0			0
$496$	8.00000			0.359211
$497$		0			0
$498$	9.70820	+	7.05342i	0.435035	+	0.316071i
$499$	3.23607	−	2.35114i	0.144866	−	0.105252i	−0.512992	−	0.858394i	$-0.671463\pi$
$499$	3.23607	−	2.35114i	0.144866	−	0.105252i	0.657858	+	0.753142i	$0.271463\pi$
$500$	−3.70820	+	11.4127i	−0.165836	+	0.510390i
$501$		0			0
$502$	3.23607	−	2.35114i	0.144433	−	0.104937i
$503$	−25.8885	−	18.8091i	−1.15431	−	0.838658i	−0.165265	−	0.986249i	$-0.552848\pi$
$503$	−25.8885	−	18.8091i	−1.15431	−	0.838658i	−0.989048	+	0.147592i	$0.952848\pi$
$504$	−3.70820	−	11.4127i	−0.165177	−	0.508361i
$505$	4.00000			0.177998
$506$		0			0
$507$	9.00000			0.399704
$508$	−1.23607	−	3.80423i	−0.0548416	−	0.168785i
$509$	−24.2705	−	17.6336i	−1.07577	−	0.781594i	−0.0988307	−	0.995104i	$-0.531510\pi$
$509$	−24.2705	−	17.6336i	−1.07577	−	0.781594i	−0.976941	+	0.213511i	$0.931510\pi$
$510$	3.23607	−	2.35114i	0.143295	−	0.104110i
$511$	−17.3050	+	53.2592i	−0.765526	+	2.35605i
$512$	3.39919	−	10.4616i	0.150224	−	0.462343i
$513$		0			0
$514$	−11.3262	−	8.22899i	−0.499579	−	0.362965i
$515$	−4.94427	−	15.2169i	−0.217871	−	0.670537i
$516$		0			0
$517$		0			0
$518$	24.0000			1.05450
$519$	−1.85410	−	5.70634i	−0.0813860	−	0.250480i
$520$	9.70820	+	7.05342i	0.425733	+	0.309313i
$521$	24.2705	−	17.6336i	1.06331	−	0.772540i	0.0886124	−	0.996066i	$-0.471757\pi$
$521$	24.2705	−	17.6336i	1.06331	−	0.772540i	0.974698	+	0.223526i	$0.0717568\pi$
$522$	−1.85410	+	5.70634i	−0.0811518	+	0.249760i
$523$	4.94427	−	15.2169i	0.216198	−	0.665389i	−0.782868	−	0.622187i	$-0.786244\pi$
$523$	4.94427	−	15.2169i	0.216198	−	0.665389i	0.999066	−	0.0432015i	$-0.0137558\pi$
$524$	9.70820	−	7.05342i	0.424105	−	0.308130i
$525$	3.23607	+	2.35114i	0.141234	+	0.102612i
$526$	−4.94427	−	15.2169i	−0.215580	−	0.663489i
$527$	−16.0000			−0.696971
$528$		0			0
$529$	41.0000			1.78261
$530$	3.70820	+	11.4127i	0.161074	+	0.495735i
$531$	3.23607	+	2.35114i	0.140433	+	0.102031i
$532$		0			0
$533$	1.23607	−	3.80423i	0.0535400	−	0.164779i
$534$	−1.85410	+	5.70634i	−0.0802348	+	0.246937i
$535$	19.4164	−	14.1068i	0.839445	−	0.609892i
$536$	9.70820	+	7.05342i	0.419331	+	0.304661i
$537$	−3.70820	−	11.4127i	−0.160021	−	0.492493i
$538$	2.00000			0.0862261
$539$		0			0
$540$	−2.00000			−0.0860663
$541$	−14.2148	−	43.7486i	−0.611141	−	1.88090i	−0.447215	−	0.894427i	$-0.647584\pi$
$541$	−14.2148	−	43.7486i	−0.611141	−	1.88090i	−0.163927	−	0.986473i	$-0.552416\pi$
$542$	−16.1803	−	11.7557i	−0.695005	−	0.504951i
$543$	17.7984	−	12.9313i	0.763801	−	0.554934i
$544$	−3.09017	+	9.51057i	−0.132490	+	0.407762i
$545$	−1.23607	+	3.80423i	−0.0529473	+	0.162955i
$546$	6.47214	−	4.70228i	0.276982	−	0.201239i
$547$	6.47214	+	4.70228i	0.276729	+	0.201055i	0.717489	−	0.696570i	$-0.245291\pi$
$547$	6.47214	+	4.70228i	0.276729	+	0.201055i	−0.440761	+	0.897625i	$0.645291\pi$
$548$	−0.618034	−	1.90211i	−0.0264011	−	0.0812542i
$549$	−6.00000			−0.256074
$550$		0			0
$551$		0			0
$552$	−7.41641	−	22.8254i	−0.315663	−	0.971512i
$553$	12.9443	+	9.40456i	0.550446	+	0.399923i
$554$	21.0344	−	15.2824i	0.893668	−	0.649288i
$555$	3.70820	−	11.4127i	0.157404	−	0.484441i
$556$	−2.47214	+	7.60845i	−0.104842	+	0.322670i
$557$	−11.3262	+	8.22899i	−0.479908	+	0.348674i	−0.801290	−	0.598276i	$-0.795853\pi$
$557$	−11.3262	+	8.22899i	−0.479908	+	0.348674i	0.321382	+	0.946950i	$0.395853\pi$
$558$	−6.47214	−	4.70228i	−0.273987	−	0.199063i
$559$		0			0
$560$	−8.00000			−0.338062
$561$		0			0
$562$	−18.0000			−0.759284
$563$	13.5967	+	41.8465i	0.573035	+	1.76362i	0.642776	+	0.766054i	$0.277783\pi$
$563$	13.5967	+	41.8465i	0.573035	+	1.76362i	−0.0697416	+	0.997565i	$0.522217\pi$
$564$	−6.47214	−	4.70228i	−0.272526	−	0.198002i
$565$	−9.70820	+	7.05342i	−0.408427	+	0.296740i
$566$	4.94427	−	15.2169i	0.207823	−	0.639614i
$567$	−1.23607	+	3.80423i	−0.0519100	+	0.159762i
$568$		0			0
$569$	−33.9787	−	24.6870i	−1.42446	−	1.03493i	−0.991015	−	0.133753i	$-0.957297\pi$
$569$	−33.9787	−	24.6870i	−1.42446	−	1.03493i	−0.433447	−	0.901179i	$-0.642703\pi$
$570$		0			0
$571$	16.0000			0.669579			0.334790	−	0.942293i	$-0.391335\pi$
$571$	16.0000			0.669579			0.334790	+	0.942293i	$0.391335\pi$
$572$		0			0
$573$	−8.00000			−0.334205
$574$	2.47214	+	7.60845i	0.103185	+	0.317571i
$575$	6.47214	+	4.70228i	0.269907	+	0.196099i
$576$	−5.66312	+	4.11450i	−0.235963	+	0.171437i
$577$	−9.27051	+	28.5317i	−0.385936	+	1.18779i	0.549862	+	0.835255i	$0.314680\pi$
$577$	−9.27051	+	28.5317i	−0.385936	+	1.18779i	−0.935799	+	0.352535i	$0.885320\pi$
$578$	4.01722	−	12.3637i	0.167094	−	0.514264i
$579$	11.3262	−	8.22899i	0.470702	−	0.341985i
$580$	−9.70820	−	7.05342i	−0.403111	−	0.292877i
$581$	14.8328	+	45.6507i	0.615369	+	1.89391i
$582$	2.00000			0.0829027
$583$		0			0
$584$	42.0000			1.73797
$585$	−1.23607	−	3.80423i	−0.0511051	−	0.157285i
$586$	4.85410	+	3.52671i	0.200521	+	0.145687i
$587$	−22.6525	+	16.4580i	−0.934968	+	0.679294i	−0.947204	−	0.320631i	$-0.896105\pi$
$587$	−22.6525	+	16.4580i	−0.934968	+	0.679294i	0.0122363	+	0.999925i	$0.496105\pi$
$588$	2.78115	−	8.55951i	0.114693	−	0.352988i
$589$		0			0
$590$	6.47214	−	4.70228i	0.266454	−	0.193590i
$591$	11.3262	+	8.22899i	0.465899	+	0.338496i
$592$	−1.85410	−	5.70634i	−0.0762031	−	0.234529i
$593$	−38.0000			−1.56047			−0.780236	−	0.625485i	$-0.784901\pi$
$593$	−38.0000			−1.56047			−0.780236	+	0.625485i	$0.784901\pi$
$594$		0			0
$595$	16.0000			0.655936
$596$	−6.79837	−	20.9232i	−0.278472	−	0.857049i
$597$		0			0
$598$	12.9443	−	9.40456i	0.529331	−	0.384581i
$599$	−2.47214	+	7.60845i	−0.101009	+	0.310873i	−0.988773	−	0.149425i	$-0.952258\pi$
$599$	−2.47214	+	7.60845i	−0.101009	+	0.310873i	0.887764	+	0.460298i	$0.152258\pi$
$600$	0.927051	−	2.85317i	0.0378467	−	0.116480i
$601$	21.0344	−	15.2824i	0.858013	−	0.623383i	−0.0693308	−	0.997594i	$-0.522086\pi$
$601$	21.0344	−	15.2824i	0.858013	−	0.623383i	0.927344	+	0.374211i	$0.122086\pi$
$602$		0			0
$603$	−1.23607	−	3.80423i	−0.0503366	−	0.154920i
$604$	20.0000			0.813788
$605$		0			0
$606$	−2.00000			−0.0812444
$607$	1.23607	+	3.80423i	0.0501705	+	0.154409i	0.973003	−	0.230793i	$-0.0741319\pi$
$607$	1.23607	+	3.80423i	0.0501705	+	0.154409i	−0.922832	+	0.385202i	$0.874132\pi$
$608$		0			0
$609$	−19.4164	+	14.1068i	−0.786793	+	0.571638i
$610$	−3.70820	+	11.4127i	−0.150141	+	0.462086i
$611$	4.94427	−	15.2169i	0.200024	−	0.615610i
$612$	1.61803	−	1.17557i	0.0654051	−	0.0475196i
$613$	11.3262	+	8.22899i	0.457462	+	0.332366i	0.792535	−	0.609826i	$-0.208761\pi$
$613$	11.3262	+	8.22899i	0.457462	+	0.332366i	−0.335073	+	0.942192i	$0.608761\pi$
$614$	9.88854	+	30.4338i	0.399069	+	1.22821i
$615$	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	$0.706378\pi$
$618$	2.47214	+	7.60845i	0.0994439	+	0.306057i
$619$	−35.5967	−	25.8626i	−1.43075	−	1.03950i	−0.989876	−	0.141937i	$-0.954667\pi$
$619$	−35.5967	−	25.8626i	−1.43075	−	1.03950i	−0.440878	−	0.897567i	$-0.645333\pi$
$620$	12.9443	−	9.40456i	0.519854	−	0.377696i
$621$	−2.47214	+	7.60845i	−0.0992034	+	0.305317i
$622$	7.41641	−	22.8254i	0.297371	−	0.915213i
$623$	−19.4164	+	14.1068i	−0.777902	+	0.565179i
$624$	−1.61803	−	1.17557i	−0.0647732	−	0.0470605i
$625$	−5.87132	−	18.0701i	−0.234853	−	0.722803i
$626$	22.0000			0.879297
$627$		0			0
$628$	−14.0000			−0.558661
$629$	3.70820	+	11.4127i	0.147856	+	0.455053i
$630$	6.47214	+	4.70228i	0.257856	+	0.187343i
$631$	−12.9443	+	9.40456i	−0.515303	+	0.374390i	−0.814832	−	0.579698i	$-0.803171\pi$
$631$	−12.9443	+	9.40456i	−0.515303	+	0.374390i	0.299528	+	0.954087i	$0.403171\pi$
$632$	3.70820	−	11.4127i	0.147504	−	0.453972i
$633$		0			0
$634$	17.7984	−	12.9313i	0.706864	−	0.513567i
$635$	6.47214	+	4.70228i	0.256839	+	0.186604i
$636$	1.85410	+	5.70634i	0.0735199	+	0.226271i
$637$	18.0000			0.713186
$638$		0			0
$639$		0			0
$640$	−1.85410	−	5.70634i	−0.0732898	−	0.225563i
$641$	−14.5623	−	10.5801i	−0.575177	−	0.417890i	0.261805	−	0.965121i	$-0.415682\pi$
$641$	−14.5623	−	10.5801i	−0.575177	−	0.417890i	−0.836982	+	0.547230i	$0.815682\pi$
$642$	−9.70820	+	7.05342i	−0.383152	+	0.278376i
$643$	6.18034	−	19.0211i	0.243729	−	0.750120i	−0.752114	−	0.659033i	$-0.770966\pi$
$643$	6.18034	−	19.0211i	0.243729	−	0.750120i	0.995843	−	0.0910872i	$-0.0290342\pi$
$644$	9.88854	−	30.4338i	0.389663	−	1.19926i
$645$		0			0
$646$		0			0
$647$	2.47214	+	7.60845i	0.0971897	+	0.299119i	0.987818	−	0.155613i	$-0.0497351\pi$
$647$	2.47214	+	7.60845i	0.0971897	+	0.299119i	−0.890628	+	0.454732i	$0.849735\pi$
$648$	3.00000			0.117851
$649$		0			0
$650$	2.00000			0.0784465
$651$	−9.88854	−	30.4338i	−0.387563	−	1.19279i
$652$	3.23607	+	2.35114i	0.126734	+	0.0920778i
$653$	1.61803	−	1.17557i	0.0633186	−	0.0460036i	−0.555676	−	0.831399i	$-0.687540\pi$
$653$	1.61803	−	1.17557i	0.0633186	−	0.0460036i	0.618994	+	0.785395i	$0.287540\pi$
$654$	0.618034	−	1.90211i	0.0241670	−	0.0743785i
$655$	−7.41641	+	22.8254i	−0.289783	+	0.891860i
$656$	1.61803	−	1.17557i	0.0631736	−	0.0458983i
$657$	−11.3262	−	8.22899i	−0.441879	−	0.321044i
$658$	9.88854	+	30.4338i	0.385496	+	1.18643i
$659$	−4.00000			−0.155818			−0.0779089	−	0.996960i	$-0.524824\pi$
$659$	−4.00000			−0.155818			−0.0779089	+	0.996960i	$0.524824\pi$
$660$		0			0
$661$	−26.0000			−1.01128			−0.505641	−	0.862744i	$-0.668744\pi$
$661$	−26.0000			−1.01128			−0.505641	+	0.862744i	$0.668744\pi$
$662$	6.18034	+	19.0211i	0.240206	+	0.739277i
$663$	3.23607	+	2.35114i	0.125678	+	0.0913108i
$664$	29.1246	−	21.1603i	1.13025	−	0.821178i
$665$		0			0
$666$	−1.85410	+	5.70634i	−0.0718450	+	0.221116i
$667$	−38.8328	+	28.2137i	−1.50361	+	1.09244i
$668$		0			0
$669$	−4.94427	−	15.2169i	−0.191157	−	0.588320i
$670$	−8.00000			−0.309067
$671$		0			0
$672$	−20.0000			−0.771517
$673$	14.2148	+	43.7486i	0.547940	+	1.68638i	0.713896	+	0.700252i	$0.246929\pi$
$673$	14.2148	+	43.7486i	0.547940	+	1.68638i	−0.165957	+	0.986133i	$0.553071\pi$
$674$	17.7984	+	12.9313i	0.685568	+	0.498094i
$675$	−0.809017	+	0.587785i	−0.0311391	+	0.0226239i
$676$	2.78115	−	8.55951i	0.106967	−	0.329212i
$677$	−5.56231	+	17.1190i	−0.213777	+	0.657937i	0.785461	+	0.618911i	$0.212426\pi$
$677$	−5.56231	+	17.1190i	−0.213777	+	0.657937i	−0.999238	+	0.0390266i	$0.987574\pi$
$678$	4.85410	−	3.52671i	0.186421	−	0.135443i
$679$	6.47214	+	4.70228i	0.248378	+	0.180457i
$680$	−3.70820	−	11.4127i	−0.142203	−	0.437656i
$681$	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
$685$	3.23607	+	2.35114i	0.123644	+	0.0898325i
$686$	−6.47214	+	4.70228i	−0.247107	+	0.179534i
$687$	−1.85410	+	5.70634i	−0.0707384	+	0.217710i
$688$		0			0
$689$	−9.70820	+	7.05342i	−0.369853	+	0.268714i
$690$	12.9443	+	9.40456i	0.492780	+	0.358026i
$691$	−8.65248	−	26.6296i	−0.329156	−	1.01304i	−0.969530	−	0.244974i	$-0.921221\pi$
$691$	−8.65248	−	26.6296i	−0.329156	−	1.01304i	0.640374	−	0.768063i	$-0.278779\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	4.00000			0.151838
$695$	−4.94427	−	15.2169i	−0.187547	−	0.577210i
$696$	14.5623	+	10.5801i	0.551983	+	0.401039i
$697$	−3.23607	+	2.35114i	−0.122575	+	0.0890558i
$698$	1.85410	−	5.70634i	0.0701788	−	0.215988i
$699$	9.27051	−	28.5317i	0.350643	−	1.07917i
$700$	3.23607	−	2.35114i	0.122312	−	0.0888648i
$701$	40.4508	+	29.3893i	1.52781	+	1.11002i	0.957442	+	0.288626i	$0.0931985\pi$
$701$	40.4508	+	29.3893i	1.52781	+	1.11002i	0.570366	+	0.821391i	$0.306802\pi$
$702$	0.618034	+	1.90211i	0.0233262	+	0.0717906i
$703$		0			0
$704$		0			0
$705$	16.0000			0.602595
$706$	−5.56231	−	17.1190i	−0.209340	−	0.644283i
$707$	−6.47214	−	4.70228i	−0.243410	−	0.176848i
$708$	3.23607	−	2.35114i	0.121619	−	0.0883613i
$709$	11.7426	−	36.1401i	0.441004	−	1.35727i	−0.445802	−	0.895131i	$-0.647082\pi$
$709$	11.7426	−	36.1401i	0.441004	−	1.35727i	0.886807	−	0.462140i	$-0.152918\pi$
$710$		0			0
$711$	−3.23607	+	2.35114i	−0.121362	+	0.0881747i
$712$	14.5623	+	10.5801i	0.545745	+	0.396507i
$713$	−19.7771	−	60.8676i	−0.740658	−	2.27951i
$714$	−8.00000			−0.299392
$715$		0			0
$716$	−12.0000			−0.448461
$717$	7.41641	+	22.8254i	0.276971	+	0.852429i
$718$	6.47214	+	4.70228i	0.241538	+	0.175488i
$719$	−19.4164	+	14.1068i	−0.724110	+	0.526097i	−0.887695	−	0.460433i	$-0.847694\pi$
$719$	−19.4164	+	14.1068i	−0.724110	+	0.526097i	0.163585	+	0.986529i	$0.447694\pi$
$720$	0.618034	−	1.90211i	0.0230328	−	0.0708876i
$721$	−9.88854	+	30.4338i	−0.368269	+	1.13341i
$722$	−15.3713	+	11.1679i	−0.572061	+	0.415627i
$723$	−8.09017	−	5.87785i	−0.300877	−	0.218600i
$724$	−6.79837	−	20.9232i	−0.252660	−	0.777606i
$725$	−6.00000			−0.222834
$726$		0			0
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	−7.41641	−	22.8254i	−0.274870	−	0.845964i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−22.6525	+	16.4580i	−0.838406	+	0.609137i
$731$		0			0
$732$	−1.85410	+	5.70634i	−0.0685296	+	0.210912i
$733$	24.2705	−	17.6336i	0.896452	−	0.651310i	−0.0411004	−	0.999155i	$-0.513086\pi$
$733$	24.2705	−	17.6336i	0.896452	−	0.651310i	0.937552	+	0.347845i	$0.113086\pi$
$734$	−25.8885	−	18.8091i	−0.955564	−	0.694258i
$735$	5.56231	+	17.1190i	0.205169	+	0.631444i
$736$	−40.0000			−1.47442
$737$		0			0
$738$	−2.00000			−0.0736210
$739$	−2.47214	−	7.60845i	−0.0909390	−	0.279881i	0.895235	−	0.445594i	$-0.147008\pi$
$739$	−2.47214	−	7.60845i	−0.0909390	−	0.279881i	−0.986174	+	0.165713i	$0.947008\pi$
$740$	−9.70820	−	7.05342i	−0.356881	−	0.259289i
$741$		0			0
$742$	7.41641	−	22.8254i	0.272265	−	0.837945i
$743$	−12.3607	+	38.0423i	−0.453469	+	1.39564i	0.419453	+	0.907777i	$0.362222\pi$
$743$	−12.3607	+	38.0423i	−0.453469	+	1.39564i	−0.872923	+	0.487858i	$0.837778\pi$
$744$	−19.4164	+	14.1068i	−0.711840	+	0.517182i
$745$	35.5967	+	25.8626i	1.30416	+	0.947531i
$746$	−0.618034	−	1.90211i	−0.0226278	−	0.0696413i
$747$	−12.0000			−0.439057
$748$		0			0
$749$	−48.0000			−1.75388
$750$	3.70820	+	11.4127i	0.135404	+	0.416732i
$751$	6.47214	+	4.70228i	0.236172	+	0.171589i	0.699576	−	0.714558i	$-0.253372\pi$
$751$	6.47214	+	4.70228i	0.236172	+	0.171589i	−0.463404	+	0.886147i	$0.653372\pi$
$752$	6.47214	−	4.70228i	0.236015	−	0.171475i
$753$	−1.23607	+	3.80423i	−0.0450448	+	0.138634i
$754$	−3.70820	+	11.4127i	−0.135045	+	0.415625i
$755$	−32.3607	+	23.5114i	−1.17773	+	0.855668i
$756$	3.23607	+	2.35114i	0.117695	+	0.0855102i
$757$	−3.09017	−	9.51057i	−0.112314	−	0.345667i	0.879063	−	0.476705i	$-0.158169\pi$
$757$	−3.09017	−	9.51057i	−0.112314	−	0.345667i	−0.991377	+	0.131038i	$0.958169\pi$
$758$	−28.0000			−1.01701
$759$		0			0
$760$		0			0
$761$	−1.85410	−	5.70634i	−0.0672111	−	0.206855i	0.911810	−	0.410612i	$-0.134685\pi$
$761$	−1.85410	−	5.70634i	−0.0672111	−	0.206855i	−0.979022	+	0.203757i	$0.934685\pi$
$762$	−3.23607	−	2.35114i	−0.117230	−	0.0851729i
$763$	6.47214	−	4.70228i	0.234307	−	0.170234i
$764$	−2.47214	+	7.60845i	−0.0894387	+	0.275264i
$765$	−1.23607	+	3.80423i	−0.0446901	+	0.137542i
$766$	−12.9443	+	9.40456i	−0.467696	+	0.339801i
$767$	6.47214	+	4.70228i	0.233695	+	0.169790i
$768$	5.25329	+	16.1680i	0.189562	+	0.583411i
$769$	−2.00000			−0.0721218			−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000			−0.0721218			−0.0360609	+	0.999350i	$0.511481\pi$
$770$		0			0
$771$	14.0000			0.504198
$772$	−4.32624	−	13.3148i	−0.155705	−	0.479210i
$773$	−4.85410	−	3.52671i	−0.174590	−	0.126847i	0.497059	−	0.867717i	$-0.334413\pi$
$773$	−4.85410	−	3.52671i	−0.174590	−	0.126847i	−0.671648	+	0.740870i	$0.734413\pi$
$774$		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)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.618034 + 1.90211i) q^{5} +(0.309017 - 0.951057i) q^{6} +(3.23607 - 2.35114i) q^{7} +(-2.42705 - 1.76336i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.618034 + 1.90211i) q^{5} +(0.309017 - 0.951057i) q^{6} +(3.23607 - 2.35114i) q^{7} +(-2.42705 - 1.76336i) q^{8} +(0.309017 + 0.951057i) q^{9} +2.00000 q^{10} +1.00000 q^{12} +(0.618034 + 1.90211i) q^{13} +(-3.23607 - 2.35114i) q^{14} +(-1.61803 + 1.17557i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(0.618034 - 1.90211i) q^{17} +(0.809017 - 0.587785i) q^{18} +(0.618034 + 1.90211i) q^{20} +4.00000 q^{21} +8.00000 q^{23} +(-0.927051 - 2.85317i) q^{24} +(0.809017 + 0.587785i) q^{25} +(1.61803 - 1.17557i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.23607 - 3.80423i) q^{28} +(-4.85410 + 3.52671i) q^{29} +(1.61803 + 1.17557i) q^{30} +(-2.47214 - 7.60845i) q^{31} -5.00000 q^{32} -2.00000 q^{34} +(2.47214 + 7.60845i) q^{35} +(0.809017 + 0.587785i) q^{36} +(-4.85410 + 3.52671i) q^{37} +(-0.618034 + 1.90211i) q^{39} +(4.85410 - 3.52671i) q^{40} +(-1.61803 - 1.17557i) q^{41} +(-1.23607 - 3.80423i) q^{42} -2.00000 q^{45} +(-2.47214 - 7.60845i) q^{46} +(-6.47214 - 4.70228i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(2.78115 - 8.55951i) q^{49} +(0.309017 - 0.951057i) q^{50} +(1.61803 - 1.17557i) q^{51} +(1.61803 + 1.17557i) q^{52} +(1.85410 + 5.70634i) q^{53} +1.00000 q^{54} -12.0000 q^{56} +(4.85410 + 3.52671i) q^{58} +(3.23607 - 2.35114i) q^{59} +(-0.618034 + 1.90211i) q^{60} +(-1.85410 + 5.70634i) q^{61} +(-6.47214 + 4.70228i) q^{62} +(3.23607 + 2.35114i) q^{63} +(2.16312 + 6.65740i) q^{64} -4.00000 q^{65} -4.00000 q^{67} +(-0.618034 - 1.90211i) q^{68} +(6.47214 + 4.70228i) q^{69} +(6.47214 - 4.70228i) q^{70} +(0.927051 - 2.85317i) q^{72} +(-11.3262 + 8.22899i) q^{73} +(4.85410 + 3.52671i) q^{74} +(0.309017 + 0.951057i) q^{75} +2.00000 q^{78} +(1.23607 + 3.80423i) q^{79} +(-1.61803 - 1.17557i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-0.618034 + 1.90211i) q^{82} +(-3.70820 + 11.4127i) q^{83} +(3.23607 - 2.35114i) q^{84} +(3.23607 + 2.35114i) q^{85} -6.00000 q^{87} -6.00000 q^{89} +(0.618034 + 1.90211i) q^{90} +(6.47214 + 4.70228i) q^{91} +(6.47214 - 4.70228i) q^{92} +(2.47214 - 7.60845i) q^{93} +(-2.47214 + 7.60845i) q^{94} +(-4.04508 - 2.93893i) q^{96} +(0.618034 + 1.90211i) 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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