LMFDB - Embedded newform 546.2.bu.b.323.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(71,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			323.9
Character	$\chi$	$=$	546.323
Dual form			546.2.bu.b.71.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-0.884905 - 1.48894i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.36895 + 1.36895i) q^{5} +(-0.469386 - 1.66724i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.43389 + 2.63514i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(-0.884905 - 1.48894i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.36895 + 1.36895i) q^{5} +(-0.469386 - 1.66724i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.43389 + 2.63514i) q^{9} +(-1.67662 + 0.967996i) q^{10} +(-1.29660 + 4.83896i) q^{11} +(-0.0218795 - 1.73191i) q^{12} +(3.60411 - 0.102093i) q^{13} +1.00000i q^{14} +(3.24968 + 0.826897i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.540322 + 0.935866i) q^{17} +(-2.06705 + 2.17423i) q^{18} +(2.27592 - 0.609830i) q^{19} +(-1.87002 + 0.501072i) q^{20} +(1.20918 - 1.24012i) q^{21} +(-2.50483 + 4.33849i) q^{22} +(1.57110 + 2.72123i) q^{23} +(0.427118 - 1.67856i) q^{24} +1.25194i q^{25} +(3.50772 + 0.834197i) q^{26} +(5.19242 - 0.196874i) q^{27} +(-0.258819 + 0.965926i) q^{28} +(0.710895 - 0.410435i) q^{29} +(2.92494 + 1.63980i) q^{30} +(-4.20449 - 4.20449i) q^{31} +(0.258819 + 0.965926i) q^{32} +(8.35229 - 2.35146i) q^{33} +(-0.764131 + 0.764131i) q^{34} +(-1.67662 - 0.967996i) q^{35} +(-2.55935 + 1.56515i) q^{36} +(0.524550 + 0.140553i) q^{37} +2.35620 q^{38} +(-3.34130 - 5.27596i) q^{39} -1.93599 q^{40} +(5.18191 + 1.38849i) q^{41} +(1.48894 - 0.884905i) q^{42} +(-4.92064 - 2.84093i) q^{43} +(-3.54236 + 3.54236i) q^{44} +(-1.64446 - 5.57031i) q^{45} +(0.813262 + 3.03513i) q^{46} +(-0.118229 - 0.118229i) q^{47} +(0.847008 - 1.51082i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-0.324025 + 1.20928i) q^{50} +(1.87158 - 0.0236440i) q^{51} +(3.17229 + 1.71364i) q^{52} +14.4313i q^{53} +(5.06645 + 1.15373i) q^{54} +(-4.84933 - 8.39929i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-2.92197 - 2.84906i) q^{57} +(0.792900 - 0.212457i) q^{58} +(-1.65760 + 0.444152i) q^{59} +(2.40086 + 2.34095i) q^{60} +(-4.49739 + 7.78972i) q^{61} +(-2.97302 - 5.14943i) q^{62} +(-2.91647 - 0.703005i) q^{63} +1.00000i q^{64} +(-4.79409 + 5.07361i) q^{65} +(8.67629 - 0.109609i) q^{66} +(3.08685 - 11.5203i) q^{67} +(-0.935866 + 0.540322i) q^{68} +(2.66147 - 4.74730i) q^{69} +(-1.36895 - 1.36895i) q^{70} +(-2.61215 - 9.74866i) q^{71} +(-2.87724 + 0.849414i) q^{72} +(1.51217 - 1.51217i) q^{73} +(0.470299 + 0.271527i) q^{74} +(1.86406 - 1.10784i) q^{75} +(2.27592 + 0.609830i) q^{76} -5.00966 q^{77} +(-1.86193 - 5.96097i) q^{78} -1.54869 q^{79} +(-1.87002 - 0.501072i) q^{80} +(-4.88793 - 7.55699i) q^{81} +(4.64597 + 2.68235i) q^{82} +(-0.338916 + 0.338916i) q^{83} +(1.66724 - 0.469386i) q^{84} +(-0.541480 - 2.02083i) q^{85} +(-4.01769 - 4.01769i) q^{86} +(-1.24019 - 0.695284i) q^{87} +(-4.33849 + 2.50483i) q^{88} +(4.35686 - 16.2600i) q^{89} +(-0.146723 - 5.80612i) q^{90} +(1.03143 + 3.45488i) q^{91} +3.14220i q^{92} +(-2.53966 + 9.98081i) q^{93} +(-0.0836003 - 0.144800i) q^{94} +(-2.28079 + 3.95045i) q^{95} +(1.20918 - 1.24012i) q^{96} +(4.07964 - 1.09314i) q^{97} +(-0.965926 + 0.258819i) q^{98} +(-10.8922 - 10.3552i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{6} - 24 q^{9}+O(q^{10}) $ 56 * q + 8 * q^6 - 24 * q^9	$ 56 q + 8 q^{6} - 24 q^{9} + 24 q^{10} + 8 q^{11} + 24 q^{13} + 4 q^{15} + 28 q^{16} - 4 q^{17} - 8 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{79} + 12 q^{81} - 4 q^{83} - 4 q^{84} + 32 q^{85} - 16 q^{86} - 144 q^{87} + 88 q^{89} - 8 q^{90} - 8 q^{91} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 q^{99}+O(q^{100}) $ 56 * q + 8 * q^6 - 24 * q^9 + 24 * q^10 + 8 * q^11 + 24 * q^13 + 4 * q^15 + 28 * q^16 - 4 * q^17 - 8 * q^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 16 * q^79 + 12 * q^81 - 4 * q^83 - 4 * q^84 + 32 * q^85 - 16 * q^86 - 144 * q^87 + 88 * q^89 - 8 * q^90 - 8 * q^91 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	−0.884905	−	1.48894i	−0.510900	−	0.859640i
$3$	−0.884905	−	1.48894i	−0.510900	−	0.859640i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−1.36895	+	1.36895i	−0.612214	+	0.612214i	−0.943523	−	0.331308i	$-0.892510\pi$
$5$	−1.36895	+	1.36895i	−0.612214	+	0.612214i	0.331308	+	0.943523i	$0.392510\pi$
$6$	−0.469386	−	1.66724i	−0.191626	−	0.680646i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.43389	+	2.63514i	−0.477963	+	0.878380i
$10$	−1.67662	+	0.967996i	−0.530193	+	0.306107i
$11$	−1.29660	+	4.83896i	−0.390938	+	1.45900i	0.437651	+	0.899145i	$0.355810\pi$
$11$	−1.29660	+	4.83896i	−0.390938	+	1.45900i	−0.828590	+	0.559856i	$0.810856\pi$
$12$	−0.0218795	−	1.73191i	−0.00631608	−	0.499960i
$13$	3.60411	−	0.102093i	0.999599	−	0.0283155i
$13$	3.60411	−	0.102093i	0.999599	−	0.0283155i
$14$			1.00000i			0.267261i
$15$	3.24968	+	0.826897i	0.839064	+	0.213504i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.540322	+	0.935866i	−0.131047	+	0.226981i	−0.924081	−	0.382198i	$-0.875167\pi$
$17$	−0.540322	+	0.935866i	−0.131047	+	0.226981i	0.793033	+	0.609178i	$0.208501\pi$
$18$	−2.06705	+	2.17423i	−0.487209	+	0.512472i
$19$	2.27592	−	0.609830i	0.522131	−	0.139905i	0.0118790	−	0.999929i	$-0.496219\pi$
$19$	2.27592	−	0.609830i	0.522131	−	0.139905i	0.510252	+	0.860025i	$0.329552\pi$
$20$	−1.87002	+	0.501072i	−0.418150	+	0.112043i
$21$	1.20918	−	1.24012i	0.263864	−	0.270616i
$22$	−2.50483	+	4.33849i	−0.534032	+	0.924970i
$23$	1.57110	+	2.72123i	0.327597	+	0.567415i	0.982035	−	0.188701i	$-0.0604278\pi$
$23$	1.57110	+	2.72123i	0.327597	+	0.567415i	−0.654437	+	0.756116i	$0.727094\pi$
$24$	0.427118	−	1.67856i	0.0871851	−	0.342635i
$25$			1.25194i			0.250387i
$26$	3.50772	+	0.834197i	0.687921	+	0.163599i
$27$	5.19242	−	0.196874i	0.999282	−	0.0378884i
$28$	−0.258819	+	0.965926i	−0.0489122	+	0.182543i
$29$	0.710895	−	0.410435i	0.132010	−	0.0762159i	−0.432541	−	0.901614i	$-0.642383\pi$
$29$	0.710895	−	0.410435i	0.132010	−	0.0762159i	0.564551	+	0.825398i	$0.309049\pi$
$30$	2.92494	+	1.63980i	0.534018	+	0.299385i
$31$	−4.20449	−	4.20449i	−0.755149	−	0.755149i	0.220286	−	0.975435i	$-0.429301\pi$
$31$	−4.20449	−	4.20449i	−0.755149	−	0.755149i	−0.975435	+	0.220286i	$0.929301\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	8.35229	−	2.35146i	1.45395	−	0.409337i
$34$	−0.764131	+	0.764131i	−0.131047	+	0.131047i
$35$	−1.67662	−	0.967996i	−0.283400	−	0.163621i
$36$	−2.55935	+	1.56515i	−0.426559	+	0.260859i
$37$	0.524550	+	0.140553i	0.0862355	+	0.0231067i	0.301679	−	0.953410i	$-0.402453\pi$
$37$	0.524550	+	0.140553i	0.0862355	+	0.0231067i	−0.215443	+	0.976516i	$0.569120\pi$
$38$	2.35620			0.382227
$39$	−3.34130	−	5.27596i	−0.535036	−	0.844829i
$40$	−1.93599			−0.306107
$41$	5.18191	+	1.38849i	0.809278	+	0.216845i	0.639654	−	0.768663i	$-0.279078\pi$
$41$	5.18191	+	1.38849i	0.809278	+	0.216845i	0.169625	+	0.985509i	$0.445744\pi$
$42$	1.48894	−	0.884905i	0.229749	−	0.136544i
$43$	−4.92064	−	2.84093i	−0.750391	−	0.433239i	0.0754441	−	0.997150i	$-0.475963\pi$
$43$	−4.92064	−	2.84093i	−0.750391	−	0.433239i	−0.825835	+	0.563912i	$0.809296\pi$
$44$	−3.54236	+	3.54236i	−0.534032	+	0.534032i
$45$	−1.64446	−	5.57031i	−0.245141	−	0.830373i
$46$	0.813262	+	3.03513i	0.119909	+	0.447506i
$47$	−0.118229	−	0.118229i	−0.0172454	−	0.0172454i	0.698431	−	0.715677i	$-0.253882\pi$
$47$	−0.118229	−	0.118229i	−0.0172454	−	0.0172454i	−0.715677	+	0.698431i	$0.753882\pi$
$48$	0.847008	−	1.51082i	0.122255	−	0.218068i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	−0.324025	+	1.20928i	−0.0458240	+	0.171018i
$51$	1.87158	−	0.0236440i	0.262074	−	0.00331082i
$52$	3.17229	+	1.71364i	0.439918	+	0.237639i
$53$			14.4313i			1.98229i	0.132795	+	0.991144i	$0.457605\pi$
$53$			14.4313i			1.98229i	−0.132795	+	0.991144i	$0.542395\pi$
$54$	5.06645	+	1.15373i	0.689456	+	0.157003i
$55$	−4.84933	−	8.39929i	−0.653884	−	1.13256i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	−2.92197	−	2.84906i	−0.387024	−	0.377368i
$58$	0.792900	−	0.212457i	0.104113	−	0.0278970i
$59$	−1.65760	+	0.444152i	−0.215801	+	0.0578237i	−0.365100	−	0.930968i	$-0.618965\pi$
$59$	−1.65760	+	0.444152i	−0.215801	+	0.0578237i	0.149299	+	0.988792i	$0.452298\pi$
$60$	2.40086	+	2.34095i	0.309950	+	0.302216i
$61$	−4.49739	+	7.78972i	−0.575832	+	0.997371i	0.420118	+	0.907469i	$0.361989\pi$
$61$	−4.49739	+	7.78972i	−0.575832	+	0.997371i	−0.995951	+	0.0899015i	$0.971345\pi$
$62$	−2.97302	−	5.14943i	−0.377574	−	0.653978i
$63$	−2.91647	−	0.703005i	−0.367440	−	0.0885703i
$64$			1.00000i			0.125000i
$65$	−4.79409	+	5.07361i	−0.594634	+	0.629304i
$66$	8.67629	−	0.109609i	1.06798	−	0.0134919i
$67$	3.08685	−	11.5203i	0.377118	−	1.40742i	−0.473107	−	0.881005i	$-0.656867\pi$
$67$	3.08685	−	11.5203i	0.377118	−	1.40742i	0.850225	−	0.526420i	$-0.176466\pi$
$68$	−0.935866	+	0.540322i	−0.113490	+	0.0655237i
$69$	2.66147	−	4.74730i	0.320403	−	0.571508i
$70$	−1.36895	−	1.36895i	−0.163621	−	0.163621i
$71$	−2.61215	−	9.74866i	−0.310005	−	1.15695i	−0.928551	−	0.371205i	$-0.878945\pi$
$71$	−2.61215	−	9.74866i	−0.310005	−	1.15695i	0.618546	−	0.785748i	$-0.287722\pi$
$72$	−2.87724	+	0.849414i	−0.339086	+	0.100104i
$73$	1.51217	−	1.51217i	0.176986	−	0.176986i	−0.613055	−	0.790040i	$-0.710059\pi$
$73$	1.51217	−	1.51217i	0.176986	−	0.176986i	0.790040	+	0.613055i	$0.210059\pi$
$74$	0.470299	+	0.271527i	0.0546711	+	0.0315644i
$75$	1.86406	−	1.10784i	0.215243	−	0.127923i
$76$	2.27592	+	0.609830i	0.261066	+	0.0699523i
$77$	−5.00966			−0.570904
$78$	−1.86193	−	5.96097i	−0.210822	−	0.674947i
$79$	−1.54869			−0.174241			−0.0871205	−	0.996198i	$-0.527767\pi$
$79$	−1.54869			−0.174241			−0.0871205	+	0.996198i	$0.527767\pi$
$80$	−1.87002	−	0.501072i	−0.209075	−	0.0560215i
$81$	−4.88793	−	7.55699i	−0.543103	−	0.839666i
$82$	4.64597	+	2.68235i	0.513062	+	0.296216i
$83$	−0.338916	+	0.338916i	−0.0372008	+	0.0372008i	−0.725463	−	0.688262i	$-0.758374\pi$
$83$	−0.338916	+	0.338916i	−0.0372008	+	0.0372008i	0.688262	+	0.725463i	$0.258374\pi$
$84$	1.66724	−	0.469386i	0.181910	−	0.0512142i
$85$	−0.541480	−	2.02083i	−0.0587318	−	0.219190i
$86$	−4.01769	−	4.01769i	−0.433239	−	0.433239i
$87$	−1.24019	−	0.695284i	−0.132962	−	0.0745423i
$88$	−4.33849	+	2.50483i	−0.462485	+	0.267016i
$89$	4.35686	−	16.2600i	0.461826	−	1.72356i	−0.205376	−	0.978683i	$-0.565842\pi$
$89$	4.35686	−	16.2600i	0.461826	−	1.72356i	0.667202	−	0.744877i	$-0.267492\pi$
$90$	−0.146723	−	5.80612i	−0.0154659	−	0.612019i
$91$	1.03143	+	3.45488i	0.108123	+	0.362169i
$92$			3.14220i			0.327597i
$93$	−2.53966	+	9.98081i	−0.263351	+	1.03496i
$94$	−0.0836003	−	0.144800i	−0.00862272	−	0.0149350i
$95$	−2.28079	+	3.95045i	−0.234005	+	0.405308i
$96$	1.20918	−	1.24012i	0.123411	−	0.126569i
$97$	4.07964	−	1.09314i	0.414225	−	0.110991i	−0.0456868	−	0.998956i	$-0.514548\pi$
$97$	4.07964	−	1.09314i	0.414225	−	0.110991i	0.459912	+	0.887965i	$0.347881\pi$
$98$	−0.965926	+	0.258819i	−0.0975732	+	0.0261447i
$99$	−10.8922	−	10.3552i	−1.09470	−	1.04074i
$100$	−0.625968	+	1.08421i	−0.0625968	+	0.108421i
$101$	−6.25605	−	10.8358i	−0.622501	−	1.07820i	−0.989018	−	0.147792i	$-0.952783\pi$
$101$	−6.25605	−	10.8358i	−0.622501	−	1.07820i	0.366518	−	0.930411i	$-0.380550\pi$
$102$	1.81393	+	0.461563i	0.179606	+	0.0457015i
$103$			1.28719i			0.126830i	0.997987	+	0.0634152i	$0.0201992\pi$
$103$			1.28719i			0.126830i	−0.997987	+	0.0634152i	$0.979801\pi$
$104$	2.62068	+	2.47630i	0.256979	+	0.242821i
$105$	0.0423586	+	3.35297i	0.00413378	+	0.327216i
$106$	−3.73509	+	13.9395i	−0.362784	+	1.35393i
$107$	−4.87154	+	2.81258i	−0.470949	+	0.271903i	−0.716637	−	0.697446i	$-0.754320\pi$
$107$	−4.87154	+	2.81258i	−0.470949	+	0.271903i	0.245688	+	0.969349i	$0.420986\pi$
$108$	4.59521	+	2.42571i	0.442174	+	0.233414i
$109$	13.5487	+	13.5487i	1.29773	+	1.29773i	0.929891	+	0.367834i	$0.119901\pi$
$109$	13.5487	+	13.5487i	1.29773	+	1.29773i	0.367834	+	0.929891i	$0.380099\pi$
$110$	−2.51020	−	9.36819i	−0.239338	−	0.893221i
$111$	−0.254902	−	0.905400i	−0.0241942	−	0.0859367i
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$	11.4378	+	6.60364i	1.07598	+	0.621218i	0.929809	−	0.368041i	$-0.119971\pi$
$113$	11.4378	+	6.60364i	1.07598	+	0.621218i	0.146172	+	0.989259i	$0.453305\pi$
$114$	−2.08501	−	3.50825i	−0.195279	−	0.328577i
$115$	−5.87600	−	1.57447i	−0.547939	−	0.146820i
$116$	0.820871			0.0762159
$117$	−4.89885	+	9.64371i	−0.452899	+	0.891562i
$118$	−1.71607			−0.157977
$119$	−1.04382	−	0.279691i	−0.0956870	−	0.0256393i
$120$	1.71317	+	2.88258i	0.156390	+	0.263142i
$121$	−12.2081	−	7.04835i	−1.10983	−	0.640759i
$122$	−6.36028	+	6.36028i	−0.575832	+	0.575832i
$123$	−2.51812	−	8.94423i	−0.227051	−	0.806474i
$124$	−1.53895	−	5.74344i	−0.138202	−	0.515776i
$125$	−8.55861	−	8.55861i	−0.765505	−	0.765505i
$126$	−2.63514	−	1.43389i	−0.234757	−	0.127741i
$127$	12.1302	−	7.00340i	1.07638	−	0.621451i	0.146466	−	0.989216i	$-0.453210\pi$
$127$	12.1302	−	7.00340i	1.07638	−	0.621451i	0.929919	+	0.367765i	$0.119877\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	0.124317	+	9.84050i	0.0109455	+	0.866408i
$130$	−5.94388	+	3.65993i	−0.521313	+	0.320997i
$131$			1.86345i			0.162810i	0.996681	+	0.0814051i	$0.0259407\pi$
$131$			1.86345i			0.162810i	−0.996681	+	0.0814051i	$0.974059\pi$
$132$	8.40902	+	2.13972i	0.731912	+	0.186238i
$133$	1.17810	+	2.04053i	0.102154	+	0.176937i
$134$	5.96333	−	10.3288i	0.515153	−	0.892272i
$135$	−6.83867	+	7.37769i	−0.588579	+	0.634971i
$136$	−1.04382	+	0.279691i	−0.0895070	+	0.0239833i
$137$	−15.0687	+	4.03765i	−1.28741	+	0.344959i	−0.836675	−	0.547700i	$-0.815503\pi$
$137$	−15.0687	+	4.03765i	−1.28741	+	0.344959i	−0.450731	+	0.892660i	$0.648837\pi$
$138$	3.79948	−	3.89670i	0.323433	−	0.331709i
$139$	4.68734	−	8.11872i	0.397575	−	0.688620i	−0.595851	−	0.803095i	$-0.703185\pi$
$139$	4.68734	−	8.11872i	0.397575	−	0.688620i	0.993426	+	0.114475i	$0.0365184\pi$
$140$	−0.967996	−	1.67662i	−0.0818106	−	0.141700i
$141$	−0.0714144	+	0.280657i	−0.00601418	+	0.0236356i
$142$		−	10.0926i		−	0.846949i
$143$	−4.17904	+	17.5725i	−0.349469	+	1.46949i
$144$	−2.99904	+	0.0757869i	−0.249920	+	0.00631558i
$145$	−0.411315	+	1.53505i	−0.0341578	+	0.127479i
$146$	1.85202	−	1.06926i	0.153274	−	0.0884929i
$147$	1.51082	+	0.847008i	0.124610	+	0.0698600i
$148$	0.383997	+	0.383997i	0.0315644	+	0.0315644i
$149$	−2.84144	−	10.6044i	−0.232780	−	0.868746i	−0.979137	−	0.203201i	$-0.934866\pi$
$149$	−2.84144	−	10.6044i	−0.232780	−	0.868746i	0.746357	−	0.665546i	$-0.231801\pi$
$150$	2.08727	−	0.587641i	0.170425	−	0.0479807i
$151$	14.2677	−	14.2677i	1.16109	−	1.16109i	0.176854	−	0.984237i	$-0.443408\pi$
$151$	14.2677	−	14.2677i	1.16109	−	1.16109i	0.984237	−	0.176854i	$-0.0565919\pi$
$152$	2.04053	+	1.17810i	0.165509	+	0.0955566i
$153$	−1.69138	−	2.76575i	−0.136740	−	0.223598i
$154$	−4.83896	−	1.29660i	−0.389934	−	0.104483i
$155$	11.5115			0.924626
$156$	−0.255672	−	6.23976i	−0.0204702	−	0.499581i
$157$	1.60781			0.128317			0.0641585	−	0.997940i	$-0.479564\pi$
$157$	1.60781			0.128317			0.0641585	+	0.997940i	$0.479564\pi$
$158$	−1.49592	−	0.400830i	−0.119009	−	0.0318883i
$159$	21.4873	−	12.7703i	1.70405	−	1.01275i
$160$	−1.67662	−	0.967996i	−0.132548	−	0.0765268i
$161$	−2.22187	+	2.22187i	−0.175108	+	0.175108i
$162$	−2.76549	−	8.56458i	−0.217277	−	0.672897i
$163$	1.98526	+	7.40908i	0.155497	+	0.580324i	0.999062	+	0.0432967i	$0.0137861\pi$
$163$	1.98526	+	7.40908i	0.155497	+	0.580324i	−0.843565	+	0.537027i	$0.819547\pi$
$164$	3.79342	+	3.79342i	0.296216	+	0.296216i
$165$	−8.21484	+	14.6529i	−0.639525	+	1.14073i
$166$	−0.415085	+	0.239650i	−0.0322169	+	0.0186004i
$167$	5.14088	−	19.1860i	0.397813	−	1.48466i	−0.419123	−	0.907929i	$-0.637662\pi$
$167$	5.14088	−	19.1860i	0.397813	−	1.48466i	0.816936	−	0.576729i	$-0.195671\pi$
$168$	1.73191	−	0.0218795i	0.133620	−	0.00168804i
$169$	12.9792	−	0.735908i	0.998396	−	0.0566083i
$170$		−	2.09212i		−	0.160458i
$171$	−1.65642	+	6.87179i	−0.126670	+	0.525499i
$172$	−2.84093	−	4.92064i	−0.216619	−	0.375196i
$173$	0.377787	−	0.654347i	0.0287226	−	0.0497490i	−0.851307	−	0.524668i	$-0.824189\pi$
$173$	0.377787	−	0.654347i	0.0287226	−	0.0497490i	0.880029	+	0.474919i	$0.157523\pi$
$174$	−1.01798	−	0.992577i	−0.0771726	−	0.0752471i
$175$	−1.20928	+	0.324025i	−0.0914128	+	0.0244940i
$176$	−4.83896	+	1.29660i	−0.364750	+	0.0977346i
$177$	2.12813	+	2.07503i	0.159960	+	0.155969i
$178$	8.41681	−	14.5783i	0.630867	−	1.09269i
$179$	−5.46883	−	9.47230i	−0.408760	−	0.707993i	0.585991	−	0.810317i	$-0.300705\pi$
$179$	−5.46883	−	9.47230i	−0.408760	−	0.707993i	−0.994751	+	0.102325i	$0.967372\pi$
$180$	1.36101	−	5.64626i	0.101444	−	0.420847i
$181$			21.7176i			1.61425i	0.590378	+	0.807127i	$0.298979\pi$
$181$			21.7176i			1.61425i	−0.590378	+	0.807127i	$0.701021\pi$
$182$	0.102093	+	3.60411i	0.00756764	+	0.267154i
$183$	15.5782	−	0.196802i	1.15157	−	0.0145480i
$184$	−0.813262	+	3.03513i	−0.0599545	+	0.223753i
$185$	−0.910494	+	0.525674i	−0.0669409	+	0.0386483i
$186$	−5.03635	+	8.98341i	−0.369283	+	0.658696i
$187$	−3.82804	−	3.82804i	−0.279934	−	0.279934i
$188$	−0.0432747	−	0.161503i	−0.00315613	−	0.0117788i
$189$	1.53406	+	4.96454i	0.111587	+	0.361117i
$190$	−3.22553	+	3.22553i	−0.234005	+	0.234005i
$191$	17.2727	+	9.97242i	1.24981	+	0.721579i	0.971072	−	0.238788i	$-0.0767501\pi$
$191$	17.2727	+	9.97242i	1.24981	+	0.721579i	0.278739	+	0.960367i	$0.410083\pi$
$192$	1.48894	−	0.884905i	0.107455	−	0.0638625i
$193$	23.9757	+	6.42428i	1.72581	+	0.462429i	0.979211	−	0.202845i	$-0.0650186\pi$
$193$	23.9757	+	6.42428i	1.72581	+	0.462429i	0.746599	+	0.665274i	$0.231685\pi$
$194$	4.22356			0.303234
$195$	11.7966	+	2.64845i	0.844773	+	0.189660i
$196$	−1.00000			−0.0714286
$197$	20.2111	+	5.41554i	1.43998	+	0.385841i	0.892527	−	0.450995i	$-0.148931\pi$
$197$	20.2111	+	5.41554i	1.43998	+	0.385841i	0.547453	+	0.836836i	$0.315597\pi$
$198$	−7.84089	−	12.8215i	−0.557228	−	0.911184i
$199$	−9.02261	−	5.20920i	−0.639596	−	0.369271i	0.144863	−	0.989452i	$-0.453726\pi$
$199$	−9.02261	−	5.20920i	−0.639596	−	0.369271i	−0.784459	+	0.620181i	$0.787059\pi$
$200$	−0.885252	+	0.885252i	−0.0625968	+	0.0625968i
$201$	−19.8846	+	5.59821i	−1.40255	+	0.394867i
$202$	−3.23837	−	12.0858i	−0.227851	−	0.850352i
$203$	0.580443	+	0.580443i	0.0407391	+	0.0407391i
$204$	1.63266	+	0.915315i	0.114309	+	0.0640848i
$205$	−8.99456	+	5.19301i	−0.628208	+	0.362696i
$206$	−0.333149	+	1.24333i	−0.0232116	+	0.0866268i
$207$	−9.42360	+	0.238138i	−0.654985	+	0.0165517i
$208$	1.89047	+	3.07020i	0.131080	+	0.212880i
$209$			11.8038i			0.816484i
$210$	−0.826897	+	3.24968i	−0.0570613	+	0.224249i
$211$	1.54901	+	2.68296i	0.106638	+	0.184702i	0.914406	−	0.404798i	$-0.132658\pi$
$211$	1.54901	+	2.68296i	0.106638	+	0.184702i	−0.807768	+	0.589500i	$0.799325\pi$
$212$	−7.21563	+	12.4978i	−0.495572	+	0.858355i
$213$	−12.2037	+	12.5160i	−0.836182	+	0.857580i
$214$	−5.43349	+	1.45590i	−0.371426	+	0.0995233i
$215$	10.6252	−	2.84702i	0.724635	−	0.194165i
$216$	3.81081	+	3.53239i	0.259293	+	0.240348i
$217$	2.97302	−	5.14943i	0.201822	−	0.349566i
$218$	9.58034	+	16.5936i	0.648863	+	1.12386i
$219$	−3.58965	−	0.913403i	−0.242566	−	0.0617221i
$220$		−	9.69866i		−	0.653884i
$221$	−1.85183	+	3.42812i	−0.124568	+	0.230600i
$222$	−0.0118818	−	0.940522i	−0.000797453	−	0.0631237i
$223$	−0.441102	+	1.64622i	−0.0295384	+	0.110239i	−0.979121	−	0.203278i	$-0.934841\pi$
$223$	−0.441102	+	1.64622i	−0.0295384	+	0.110239i	0.949583	+	0.313517i	$0.101507\pi$
$224$	−0.866025	+	0.500000i	−0.0578638	+	0.0334077i
$225$	−3.29903	−	1.79514i	−0.219935	−	0.119676i
$226$	9.33895	+	9.33895i	0.621218	+	0.621218i
$227$	2.39763	+	8.94809i	0.159136	+	0.593905i	0.998716	+	0.0506680i	$0.0161350\pi$
$227$	2.39763	+	8.94809i	0.159136	+	0.593905i	−0.839579	+	0.543238i	$0.817198\pi$
$228$	−1.10597	−	3.92835i	−0.0732446	−	0.260161i
$229$	13.2081	−	13.2081i	0.872816	−	0.872816i	−0.119962	−	0.992778i	$-0.538277\pi$
$229$	13.2081	−	13.2081i	0.872816	−	0.872816i	0.992778	+	0.119962i	$0.0382774\pi$
$230$	−5.26827	−	3.04164i	−0.347380	−	0.200560i
$231$	4.43307	+	7.45909i	0.291675	+	0.490772i
$232$	0.792900	+	0.212457i	0.0520565	+	0.0139485i
$233$	−19.6826			−1.28945			−0.644724	−	0.764415i	$-0.723028\pi$
$233$	−19.6826			−1.28945			−0.644724	+	0.764415i	$0.723028\pi$
$234$	−7.22791	+	8.04720i	−0.472503	+	0.526062i
$235$	0.323699			0.0211158
$236$	−1.65760	−	0.444152i	−0.107900	−	0.0289119i
$237$	1.37044	+	2.30591i	0.0890198	+	0.149785i
$238$	−0.935866	−	0.540322i	−0.0606632	−	0.0350239i
$239$	16.5276	−	16.5276i	1.06908	−	1.06908i	0.0716537	−	0.997430i	$-0.477172\pi$
$239$	16.5276	−	16.5276i	1.06908	−	1.06908i	0.997430	−	0.0716537i	$-0.0228276\pi$
$240$	0.908727	+	3.22776i	0.0586581	+	0.208351i
$241$	0.895014	+	3.34024i	0.0576529	+	0.215164i	0.988743	−	0.149627i	$-0.0478072\pi$
$241$	0.895014	+	3.34024i	0.0576529	+	0.215164i	−0.931090	+	0.364791i	$0.881141\pi$
$242$	−9.96787	−	9.96787i	−0.640759	−	0.640759i
$243$	−6.92656	+	13.9651i	−0.444339	+	0.895859i
$244$	−7.78972	+	4.49739i	−0.498685	+	0.287916i
$245$	0.501072	−	1.87002i	0.0320123	−	0.119471i
$246$	−0.117377	−	9.29120i	−0.00748371	−	0.592385i
$247$	8.14039	−	2.43025i	0.517960	−	0.154633i
$248$		−	5.94605i		−	0.377574i
$249$	0.804533	+	0.204717i	0.0509852	+	0.0129734i
$250$	−6.05185	−	10.4821i	−0.382752	−	0.662947i
$251$	−9.03954	+	15.6569i	−0.570571	+	0.988258i	0.425936	+	0.904753i	$0.359945\pi$
$251$	−9.03954	+	15.6569i	−0.570571	+	0.988258i	−0.996507	+	0.0835047i	$0.973389\pi$
$252$	−2.17423	−	2.06705i	−0.136964	−	0.130212i
$253$	−15.2050	+	4.07417i	−0.955930	+	0.256141i
$254$	13.5295	−	3.62522i	0.848918	−	0.227467i
$255$	−2.52974	+	2.59447i	−0.158418	+	0.162472i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.6193	−	18.3931i	−0.662411	−	1.14733i	−0.979980	−	0.199095i	$-0.936200\pi$
$257$	−10.6193	−	18.3931i	−0.662411	−	1.14733i	0.317569	−	0.948235i	$-0.397134\pi$
$258$	−2.42683	+	9.53737i	−0.151088	+	0.593771i
$259$			0.543054i			0.0337437i
$260$	−6.68861	+	1.99683i	−0.414810	+	0.123838i
$261$	0.0622113	+	2.46183i	0.00385078	+	0.152383i
$262$	−0.482296	+	1.79995i	−0.0297963	+	0.111201i
$263$	8.58055	−	4.95399i	0.529100	−	0.305476i	−0.211550	−	0.977367i	$-0.567851\pi$
$263$	8.58055	−	4.95399i	0.529100	−	0.305476i	0.740650	+	0.671891i	$0.234518\pi$
$264$	7.56869	+	4.24322i	0.465821	+	0.261152i
$265$	−19.7557	−	19.7557i	−1.21358	−	1.21358i
$266$	0.609830	+	2.27592i	0.0373911	+	0.139545i
$267$	−28.0656	+	7.90147i	−1.71759	+	0.483562i
$268$	8.43342	−	8.43342i	0.515153	−	0.515153i
$269$	21.2435	+	12.2650i	1.29524	+	0.747808i	0.979578	−	0.201063i	$-0.0644396\pi$
$269$	21.2435	+	12.2650i	1.29524	+	0.747808i	0.315663	+	0.948871i	$0.397773\pi$
$270$	−8.51513	+	5.35633i	−0.518215	+	0.325976i
$271$	15.4032	+	4.12726i	0.935675	+	0.250713i	0.694273	−	0.719712i	$-0.255726\pi$
$271$	15.4032	+	4.12726i	0.935675	+	0.250713i	0.241402	+	0.970425i	$0.422393\pi$
$272$	−1.08064			−0.0655237
$273$	4.23139	−	4.59297i	0.256095	−	0.277979i
$274$	−15.6003			−0.942446
$275$	−6.05807	−	1.62325i	−0.365315	−	0.0978859i
$276$	4.67855	−	2.78055i	0.281616	−	0.167369i
$277$	−12.4005	−	7.15946i	−0.745077	−	0.430170i	0.0788355	−	0.996888i	$-0.474880\pi$
$277$	−12.4005	−	7.15946i	−0.745077	−	0.430170i	−0.823912	+	0.566717i	$0.808213\pi$
$278$	6.62890	−	6.62890i	0.397575	−	0.397575i
$279$	17.1082	−	5.05066i	1.02424	−	0.302375i
$280$	−0.501072	−	1.87002i	−0.0299448	−	0.111755i
$281$	2.01093	+	2.01093i	0.119962	+	0.119962i	0.764539	−	0.644577i	$-0.222967\pi$
$281$	2.01093	+	2.01093i	0.119962	+	0.119962i	−0.644577	+	0.764539i	$0.722967\pi$
$282$	−0.141620	+	0.252610i	−0.00843337	+	0.0150427i
$283$	−18.6556	+	10.7708i	−1.10896	+	0.640260i	−0.938560	−	0.345115i	$-0.887840\pi$
$283$	−18.6556	+	10.7708i	−1.10896	+	0.640260i	−0.170402	+	0.985375i	$0.554507\pi$
$284$	2.61215	−	9.74866i	0.155002	−	0.578477i
$285$	7.90027	−	0.0998055i	0.467972	−	0.00591197i
$286$	−8.58474	+	15.8921i	−0.507626	+	0.939720i
$287$			5.36471i			0.316669i
$288$	−2.91647	−	0.703005i	−0.171855	−	0.0414250i
$289$	7.91610	+	13.7111i	0.465653	+	0.806535i
$290$	−0.794600	+	1.37629i	−0.0466605	+	0.0808183i
$291$	−5.23771	−	5.10703i	−0.307040	−	0.299379i
$292$	2.06566	−	0.553492i	0.120884	−	0.0323906i
$293$	−12.9513	+	3.47030i	−0.756626	+	0.202737i	−0.616455	−	0.787390i	$-0.711432\pi$
$293$	−12.9513	+	3.47030i	−0.756626	+	0.202737i	−0.140171	+	0.990127i	$0.544765\pi$
$294$	1.24012	+	1.20918i	0.0723252	+	0.0705206i
$295$	1.66115	−	2.87720i	0.0967160	−	0.167517i
$296$	0.271527	+	0.470299i	0.0157822	+	0.0273356i
$297$	−5.77980	+	25.3812i	−0.335378	+	1.47277i
$298$		−	10.9785i		−	0.635966i
$299$	5.94023	+	9.64719i	0.343533	+	0.557912i
$300$	2.16824	−	0.0273918i	0.125184	−	0.00158147i
$301$	1.47058	−	5.48826i	0.0847626	−	0.316338i
$302$	17.4743	−	10.0888i	1.00553	−	0.580545i
$303$	−10.5979	+	18.9035i	−0.608831	+	1.08598i
$304$	1.66609	+	1.66609i	0.0955566	+	0.0955566i
$305$	−4.50703	−	16.8205i	−0.258072	−	0.963138i
$306$	−0.917914	−	3.10927i	−0.0524737	−	0.177745i
$307$	−12.2012	+	12.2012i	−0.696358	+	0.696358i	−0.963623	−	0.267265i	$-0.913880\pi$
$307$	−12.2012	+	12.2012i	−0.696358	+	0.696358i	0.267265	+	0.963623i	$0.413880\pi$
$308$	−4.33849	−	2.50483i	−0.247209	−	0.142726i
$309$	1.91655	−	1.13904i	0.109029	−	0.0647976i
$310$	11.1193	+	2.97940i	0.631531	+	0.169218i
$311$	−10.8848			−0.617221			−0.308610	−	0.951189i	$-0.599864\pi$
$311$	−10.8848			−0.617221			−0.308610	+	0.951189i	$0.599864\pi$
$312$	1.36801	−	6.09332i	0.0774482	−	0.344966i
$313$	−26.3524			−1.48953			−0.744763	−	0.667329i	$-0.767438\pi$
$313$	−26.3524			−1.48953			−0.744763	+	0.667329i	$0.767438\pi$
$314$	1.55302	+	0.416131i	0.0876421	+	0.0234836i
$315$	4.95489	−	3.03013i	0.279176	−	0.170728i
$316$	−1.34120	−	0.774344i	−0.0754486	−	0.0435603i
$317$	−16.1698	+	16.1698i	−0.908185	+	0.908185i	−0.996126	−	0.0879406i	$-0.971971\pi$
$317$	−16.1698	+	16.1698i	−0.908185	+	0.908185i	0.0879406	+	0.996126i	$0.471971\pi$
$318$	24.0603	−	6.77383i	1.34924	−	0.379858i
$319$	1.06434	+	3.97216i	0.0595914	+	0.222398i
$320$	−1.36895	−	1.36895i	−0.0765268	−	0.0765268i
$321$	8.49861	+	4.76456i	0.474346	+	0.265932i
$322$	−2.72123	+	1.57110i	−0.151648	+	0.0875541i
$323$	−0.659010	+	2.45946i	−0.0366683	+	0.136848i
$324$	−0.454576	−	8.98851i	−0.0252542	−	0.499362i
$325$	0.127814	+	4.51211i	0.00708984	+	0.250287i
$326$			7.67044i			0.424827i
$327$	8.18387	−	32.1624i	0.452569	−	1.77858i
$328$	2.68235	+	4.64597i	0.148108	+	0.256531i
$329$	0.0836003	−	0.144800i	0.00460904	−	0.00798308i
$330$	−11.7274	+	12.0275i	−0.645571	+	0.662091i
$331$	−14.3227	+	3.83777i	−0.787249	+	0.210943i	−0.629978	−	0.776613i	$-0.716936\pi$
$331$	−14.3227	+	3.83777i	−0.787249	+	0.210943i	−0.157271	+	0.987556i	$0.550270\pi$
$332$	−0.462967	+	0.124052i	−0.0254086	+	0.00680822i
$333$	−1.12252	+	1.18073i	−0.0615138	+	0.0647034i
$334$	9.93141	−	17.2017i	0.543423	−	0.941235i
$335$	11.5450	+	19.9965i	0.630768	+	1.09252i
$336$	1.67856	+	0.427118i	0.0915731	+	0.0233012i
$337$		−	18.7747i		−	1.02272i	−0.859366	−	0.511361i	$-0.829141\pi$
$337$		−	18.7747i		−	1.02272i	0.859366	−	0.511361i	$-0.170859\pi$
$338$	12.7274	+	2.64842i	0.692278	+	0.144055i
$339$	−0.288969	−	22.8738i	−0.0156947	−	1.24234i
$340$	0.541480	−	2.02083i	0.0293659	−	0.109595i
$341$	25.7969	−	14.8938i	1.39698	−	0.806547i
$342$	−3.37853	+	6.20893i	−0.182690	+	0.335740i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−1.47058	−	5.48826i	−0.0792881	−	0.295907i
$345$	2.85541	+	10.1423i	0.153730	+	0.546041i
$346$	0.534272	−	0.534272i	0.0287226	−	0.0287226i
$347$	8.16785	+	4.71571i	0.438473	+	0.253152i	0.702950	−	0.711240i	$-0.251866\pi$
$347$	8.16785	+	4.71571i	0.438473	+	0.253152i	−0.264477	+	0.964392i	$0.585199\pi$
$348$	−0.726392	−	1.22223i	−0.0389387	−	0.0655183i
$349$	29.6009	+	7.93153i	1.58450	+	0.424565i	0.940315	−	0.340305i	$-0.110530\pi$
$349$	29.6009	+	7.93153i	1.58450	+	0.424565i	0.644184	+	0.764871i	$0.277197\pi$
$350$	−1.25194			−0.0669188
$351$	18.6939	−	1.23966i	0.997808	−	0.0661684i
$352$	−5.00966			−0.267016
$353$	20.9033	+	5.60102i	1.11257	+	0.298112i	0.767873	−	0.640602i	$-0.221315\pi$
$353$	20.9033	+	5.60102i	1.11257	+	0.298112i	0.344696	+	0.938714i	$0.387982\pi$
$354$	1.51856	+	2.55513i	0.0807106	+	0.135804i
$355$	16.9214	+	9.76956i	0.898093	+	0.518514i
$356$	11.9032	−	11.9032i	0.630867	−	0.630867i
$357$	0.507239	+	1.80169i	0.0268460	+	0.0953555i
$358$	−2.83088	−	10.5650i	−0.149616	−	0.558376i
$359$	−17.6778	−	17.6778i	−0.932998	−	0.932998i	0.0648939	−	0.997892i	$-0.479329\pi$
$359$	−17.6778	−	17.6778i	−0.932998	−	0.932998i	−0.997892	+	0.0648939i	$0.979329\pi$
$360$	2.77600	−	5.10161i	0.146308	−	0.268878i
$361$	−11.6466	+	6.72415i	−0.612978	+	0.353903i
$362$	−5.62092	+	20.9776i	−0.295429	+	1.10256i
$363$	0.308429	+	24.4142i	0.0161883	+	1.28142i
$364$	−0.834197	+	3.50772i	−0.0437238	+	0.183855i
$365$			4.14017i			0.216706i
$366$	15.0983	+	3.84184i	0.789201	+	0.200816i
$367$	9.29298	+	16.0959i	0.485090	+	0.840200i	0.999853	−	0.0171324i	$-0.00545369\pi$
$367$	9.29298	+	16.0959i	0.485090	+	0.840200i	−0.514764	+	0.857332i	$0.672120\pi$
$368$	−1.57110	+	2.72123i	−0.0818993	+	0.141854i
$369$	−11.0891	+	11.6641i	−0.577277	+	0.607210i
$370$	−1.01552	+	0.272109i	−0.0527946	+	0.0141463i
$371$	−13.9395	+	3.73509i	−0.723705	+	0.193916i
$372$	−7.18982	+	7.37380i	−0.372775	+	0.382314i
$373$	6.06668	−	10.5078i	0.314121	−	0.544073i	−0.665130	−	0.746728i	$-0.731624\pi$
$373$	6.06668	−	10.5078i	0.314121	−	0.544073i	0.979250	+	0.202655i	$0.0649571\pi$
$374$	−2.70683	−	4.68837i	−0.139967	−	0.242430i
$375$	−5.16971	+	20.3168i	−0.266962	+	1.04916i
$376$		−	0.167201i		−	0.00862272i
$377$	2.52024	−	1.55183i	0.129799	−	0.0799233i
$378$	0.196874	+	5.19242i	0.0101261	+	0.267069i
$379$	−0.775456	+	2.89404i	−0.0398325	+	0.148657i	−0.982978	−	0.183723i	$-0.941185\pi$
$379$	−0.775456	+	2.89404i	−0.0398325	+	0.148657i	0.943146	+	0.332380i	$0.107852\pi$
$380$	−3.95045	+	2.28079i	−0.202654	+	0.117002i
$381$	−21.1617	−	11.8639i	−1.08415	−	0.607804i
$382$	14.1031	+	14.1031i	0.721579	+	0.721579i
$383$	−5.60300	−	20.9107i	−0.286300	−	1.06848i	−0.947884	−	0.318615i	$-0.896782\pi$
$383$	−5.60300	−	20.9107i	−0.286300	−	1.06848i	0.661585	−	0.749870i	$-0.269884\pi$
$384$	1.66724	−	0.469386i	0.0850808	−	0.0239533i
$385$	6.85799	−	6.85799i	0.349515	−	0.349515i
$386$	21.4960	+	12.4107i	1.09412	+	0.631690i
$387$	14.5419	−	8.89301i	0.739207	−	0.452057i
$388$	4.07964	+	1.09314i	0.207113	+	0.0554956i
$389$	35.3336			1.79148			0.895742	−	0.444575i	$-0.146645\pi$
$389$	35.3336			1.79148			0.895742	+	0.444575i	$0.146645\pi$
$390$	10.7092	+	5.61140i	0.542281	+	0.284144i
$391$	−3.39560			−0.171723
$392$	−0.965926	−	0.258819i	−0.0487866	−	0.0130723i
$393$	2.77456	−	1.64897i	0.139958	−	0.0831797i
$394$	18.1208	+	10.4620i	0.912911	+	0.527069i
$395$	2.12008	−	2.12008i	0.106673	−	0.106673i
$396$	−4.25527	−	14.4140i	−0.213836	−	0.724330i
$397$	5.30676	+	19.8051i	0.266338	+	0.993988i	0.961426	+	0.275063i	$0.0886989\pi$
$397$	5.30676	+	19.8051i	0.266338	+	0.993988i	−0.695088	+	0.718925i	$0.744634\pi$
$398$	−7.36693	−	7.36693i	−0.369271	−	0.369271i
$399$	1.99572	−	3.55980i	0.0999111	−	0.178213i
$400$	−1.08421	+	0.625968i	−0.0542104	+	0.0312984i
$401$	8.51826	−	31.7906i	0.425381	−	1.58755i	−0.337707	−	0.941251i	$-0.609651\pi$
$401$	8.51826	−	31.7906i	0.425381	−	1.58755i	0.763088	−	0.646294i	$-0.223682\pi$
$402$	−20.6559	+	0.260950i	−1.03022	+	0.0130150i
$403$	−15.5827	−	14.7242i	−0.776229	−	0.733464i
$404$		−	12.5121i		−	0.622501i
$405$	17.0365	+	3.65382i	0.846551	+	0.181560i
$406$	0.410435	+	0.710895i	0.0203696	+	0.0352811i
$407$	−1.36026	+	2.35604i	−0.0674255	+	0.116784i
$408$	1.34013	+	1.30669i	0.0663462	+	0.0646908i
$409$	−23.0665	+	6.18065i	−1.14057	+	0.305614i	−0.779178	−	0.626802i	$-0.784363\pi$
$409$	−23.0665	+	6.18065i	−1.14057	+	0.305614i	−0.361387	+	0.932416i	$0.617697\pi$
$410$	−10.0321	+	2.68810i	−0.495452	+	0.132756i
$411$	19.3462	+	18.8635i	0.954276	+	0.930466i
$412$	−0.643594	+	1.11474i	−0.0317076	+	0.0549192i
$413$	−0.858036	−	1.48616i	−0.0422212	−	0.0731293i
$414$	−9.16413	−	2.20898i	−0.450393	−	0.108566i
$415$		−	0.927919i		−	0.0455498i
$416$	1.03143	+	3.45488i	0.0505698	+	0.169389i
$417$	−16.2361	+	0.205114i	−0.795087	+	0.0100445i
$418$	−3.05504	+	11.4016i	−0.149427	+	0.557669i
$419$	22.2097	−	12.8228i	1.08501	−	0.626433i	0.152769	−	0.988262i	$-0.451181\pi$
$419$	22.2097	−	12.8228i	1.08501	−	0.626433i	0.932244	+	0.361829i	$0.117848\pi$
$420$	−1.63980	+	2.92494i	−0.0800141	+	0.142722i
$421$	−5.05403	−	5.05403i	−0.246318	−	0.246318i	0.573140	−	0.819458i	$-0.305725\pi$
$421$	−5.05403	−	5.05403i	−0.246318	−	0.246318i	−0.819458	+	0.573140i	$0.805725\pi$
$422$	0.801825	+	2.99245i	0.0390322	+	0.145670i
$423$	0.481076	−	0.142023i	0.0233907	−	0.00690537i
$424$	−10.2044	+	10.2044i	−0.495572	+	0.495572i
$425$	−1.17164	−	0.676449i	−0.0568331	−	0.0328126i
$426$	−15.0272	+	8.93095i	−0.728071	+	0.432706i
$427$	−8.68830	−	2.32802i	−0.420456	−	0.112661i
$428$	−5.62516			−0.271903
$429$	29.8625	−	9.32763i	1.44177	−	0.450342i
$430$	11.0001			0.530470
$431$	−12.6301	−	3.38424i	−0.608372	−	0.163013i	−0.0585360	−	0.998285i	$-0.518643\pi$
$431$	−12.6301	−	3.38424i	−0.608372	−	0.163013i	−0.549836	+	0.835272i	$0.685310\pi$
$432$	2.76671	+	4.39833i	0.133113	+	0.211615i
$433$	−4.68915	−	2.70728i	−0.225346	−	0.130104i	0.383077	−	0.923716i	$-0.374864\pi$
$433$	−4.68915	−	2.70728i	−0.225346	−	0.130104i	−0.608423	+	0.793613i	$0.708198\pi$
$434$	4.20449	−	4.20449i	0.201822	−	0.201822i
$435$	2.64957	−	0.745948i	0.127037	−	0.0357655i
$436$	4.95915	+	18.5078i	0.237500	+	0.886363i
$437$	5.23518	+	5.23518i	0.250433	+	0.250433i
$438$	−3.23093	−	1.81135i	−0.154380	−	0.0865496i
$439$	32.3470	−	18.6755i	1.54384	−	0.891335i	0.545245	−	0.838277i	$-0.316437\pi$
$439$	32.3470	−	18.6755i	1.54384	−	0.891335i	0.998591	−	0.0530580i	$-0.0168968\pi$
$440$	2.51020	−	9.36819i	0.119669	−	0.446611i
$441$	−0.0757869	−	2.99904i	−0.00360890	−	0.142812i
$442$	−2.67600	+	2.83202i	−0.127284	+	0.134706i
$443$		−	31.1461i		−	1.47980i	−0.672720	−	0.739898i	$-0.734874\pi$
$443$		−	31.1461i		−	1.47980i	0.672720	−	0.739898i	$-0.265126\pi$
$444$	0.231948	−	0.911550i	0.0110078	−	0.0432602i
$445$	16.2949	+	28.2236i	0.772451	+	1.33792i
$446$	−0.852144	+	1.47596i	−0.0403502	+	0.0698886i
$447$	−13.2749	+	13.6146i	−0.627882	+	0.643949i
$448$	−0.965926	+	0.258819i	−0.0456357	+	0.0122281i
$449$	−14.2072	+	3.80679i	−0.670477	+	0.179654i	−0.577970	−	0.816058i	$-0.696155\pi$
$449$	−14.2072	+	3.80679i	−0.670477	+	0.179654i	−0.0925073	+	0.995712i	$0.529488\pi$
$450$	−2.72200	−	2.58782i	−0.128316	−	0.121991i
$451$	−13.4377	+	23.2747i	−0.632756	+	1.09596i
$452$	6.60364	+	11.4378i	0.310609	+	0.537991i
$453$	−33.8694	−	8.61822i	−1.59132	−	0.404919i
$454$			9.26374i			0.434769i
$455$	−6.14153	−	3.31759i	−0.287920	−	0.155531i
$456$	−0.0515526	−	4.08074i	−0.00241417	−	0.191098i
$457$	2.20870	−	8.24299i	0.103319	−	0.385591i	−0.894830	−	0.446406i	$-0.852704\pi$
$457$	2.20870	−	8.24299i	0.103319	−	0.385591i	0.998149	+	0.0608158i	$0.0193702\pi$
$458$	16.1766	−	9.33954i	0.755881	−	0.436408i
$459$	−2.62133	+	4.96578i	−0.122353	+	0.231783i
$460$	−4.30153	−	4.30153i	−0.200560	−	0.200560i
$461$	−1.14954	−	4.29016i	−0.0535396	−	0.199812i	0.933975	−	0.357337i	$-0.116315\pi$
$461$	−1.14954	−	4.29016i	−0.0535396	−	0.199812i	−0.987515	+	0.157525i	$0.949649\pi$
$462$	2.35146	+	8.35229i	0.109400	+	0.388584i
$463$	−16.3629	+	16.3629i	−0.760446	+	0.760446i	−0.976403	−	0.215957i	$-0.930713\pi$
$463$	−16.3629	+	16.3629i	−0.760446	+	0.760446i	0.215957	+	0.976403i	$0.430713\pi$
$464$	0.710895	+	0.410435i	0.0330025	+	0.0190540i
$465$	−10.1866	−	17.1399i	−0.472391	−	0.794846i
$466$	−19.0119	−	5.09423i	−0.880710	−	0.235985i
$467$	−35.6614			−1.65021			−0.825106	−	0.564978i	$-0.808884\pi$
$467$	−35.6614			−1.65021			−0.825106	+	0.564978i	$0.808884\pi$
$468$	−9.06439	+	5.90227i	−0.419002	+	0.272833i
$469$	11.9267			0.550722
$470$	0.312669	+	0.0837795i	0.0144224	+	0.00386446i
$471$	−1.42276	−	2.39393i	−0.0655571	−	0.110306i
$472$	−1.48616	−	0.858036i	−0.0684062	−	0.0394943i
$473$	20.1273	−	20.1273i	0.925452	−	0.925452i
$474$	0.726933	+	2.58203i	0.0333891	+	0.118597i
$475$	0.763468	+	2.84930i	0.0350303	+	0.130735i
$476$	−0.764131	−	0.764131i	−0.0350239	−	0.0350239i
$477$	−38.0284	−	20.6928i	−1.74120	−	0.947459i
$478$	20.2421	−	11.6868i	0.925853	−	0.534542i
$479$	−1.80118	+	6.72208i	−0.0822978	+	0.307140i	−0.994789	−	0.101957i	$-0.967490\pi$
$479$	−1.80118	+	6.72208i	−0.0822978	+	0.307140i	0.912491	+	0.409097i	$0.134156\pi$
$480$	0.0423586	+	3.35297i	0.00193340	+	0.153041i
$481$	1.90488	+	0.453014i	0.0868552	+	0.0206557i
$482$			3.45807i			0.157511i
$483$	5.27438	+	1.34209i	0.239993	+	0.0610673i
$484$	−7.04835	−	12.2081i	−0.320379	−	0.554913i
$485$	−4.08839	+	7.08130i	−0.185644	+	0.321545i
$486$	−10.3050	+	11.6965i	−0.467443	+	0.530563i
$487$	20.4001	−	5.46620i	0.924419	−	0.247697i	0.234946	−	0.972009i	$-0.424509\pi$
$487$	20.4001	−	5.46620i	0.924419	−	0.247697i	0.689473	+	0.724311i	$0.257842\pi$
$488$	−8.68830	+	2.32802i	−0.393301	+	0.105385i
$489$	9.27491	−	9.51226i	0.419426	−	0.430159i
$490$	0.967996	−	1.67662i	0.0437296	−	0.0757419i
$491$	4.70139	+	8.14304i	0.212171	+	0.367490i	0.952394	−	0.304871i	$-0.0986134\pi$
$491$	4.70139	+	8.14304i	0.212171	+	0.367490i	−0.740223	+	0.672361i	$0.765280\pi$
$492$	2.29136	−	9.00499i	0.103303	−	0.405976i
$493$			0.887069i			0.0399516i
$494$	8.49200	−	0.240552i	0.382073	−	0.0108229i
$495$	29.0867	−	0.735032i	1.30735	−	0.0330372i
$496$	1.53895	−	5.74344i	0.0691009	−	0.257888i
$497$	8.74041	−	5.04628i	0.392061	−	0.226357i
$498$	0.724135	+	0.405970i	0.0324493	+	0.0181920i
$499$	−29.6535	−	29.6535i	−1.32747	−	1.32747i	−0.907568	−	0.419905i	$-0.862063\pi$
$499$	−29.6535	−	29.6535i	−1.32747	−	1.32747i	−0.419905	−	0.907568i	$-0.637937\pi$
$500$	−3.13267	−	11.6913i	−0.140097	−	0.522850i
$501$	−33.1160	+	9.32333i	−1.47951	+	0.416536i
$502$	−12.7838	+	12.7838i	−0.570571	+	0.570571i
$503$	−17.6305	−	10.1790i	−0.786105	−	0.453858i	0.0524842	−	0.998622i	$-0.483286\pi$
$503$	−17.6305	−	10.1790i	−0.786105	−	0.453858i	−0.838590	+	0.544764i	$0.816619\pi$
$504$	−1.56515	−	2.55935i	−0.0697175	−	0.114003i
$505$	23.3979	+	6.26946i	1.04120	+	0.278987i
$506$	−15.7414			−0.699789
$507$	−12.5810	−	18.6740i	−0.558743	−	0.829341i
$508$	14.0068			0.621451
$509$	−40.7355	−	10.9151i	−1.80557	−	0.483801i	−0.810745	−	0.585399i	$-0.800938\pi$
$509$	−40.7355	−	10.9151i	−1.80557	−	0.483801i	−0.994826	+	0.101598i	$0.967604\pi$
$510$	−3.11504	+	1.85133i	−0.137936	+	0.0819781i
$511$	1.85202	+	1.06926i	0.0819285	+	0.0473014i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	11.6975	−	3.61456i	0.516456	−	0.159587i
$514$	−5.49693	−	20.5148i	−0.242459	−	0.904871i
$515$	−1.76210	−	1.76210i	−0.0776474	−	0.0776474i
$516$	−4.81259	+	8.58428i	−0.211862	+	0.377902i
$517$	0.725399	−	0.418809i	0.0319030	−	0.0184192i
$518$	−0.140553	+	0.524550i	−0.00617553	+	0.0230474i
$519$	−1.30859	+	0.0165316i	−0.0574407	+	0.000725658i
$520$	−6.97752	+	0.197651i	−0.305984	+	0.00866758i
$521$		−	44.6047i		−	1.95417i	−0.212854	−	0.977084i	$-0.568276\pi$
$521$		−	44.6047i		−	1.95417i	0.212854	−	0.977084i	$-0.431724\pi$
$522$	−0.577076	+	2.39404i	−0.0252579	+	0.104784i
$523$	8.20723	+	14.2153i	0.358877	+	0.621593i	0.987774	−	0.155896i	$-0.0498264\pi$
$523$	8.20723	+	14.2153i	0.358877	+	0.621593i	−0.628896	+	0.777489i	$0.716493\pi$
$524$	−0.931723	+	1.61379i	−0.0407025	+	0.0704988i
$525$	1.55255	+	1.51381i	0.0677588	+	0.0660681i
$526$	9.57036	−	2.56437i	0.417288	−	0.111812i
$527$	6.20662	−	1.66306i	0.270365	−	0.0724440i
$528$	6.21257	+	6.05756i	0.270367	+	0.263621i
$529$	6.56328	−	11.3679i	0.285360	−	0.494258i
$530$	−13.9694	−	24.1957i	−0.606792	−	1.05100i
$531$	1.20641	−	5.00487i	0.0523536	−	0.217193i
$532$			2.35620i			0.102154i
$533$	18.8179	+	4.47522i	0.815094	+	0.193843i
$534$	−29.1544	+	0.368312i	−1.26163	+	0.0159384i
$535$	2.81861	−	10.5192i	0.121859	−	0.454784i
$536$	10.3288	−	5.96333i	0.446136	−	0.257577i
$537$	−9.26429	+	16.5248i	−0.399784	+	0.713100i
$538$	17.3453	+	17.3453i	0.747808	+	0.747808i
$539$	−1.29660	−	4.83896i	−0.0558483	−	0.208429i
$540$	−9.61131	+	2.96993i	−0.413605	+	0.127806i
$541$	26.3985	−	26.3985i	1.13496	−	1.13496i	0.145619	−	0.989341i	$-0.453483\pi$
$541$	26.3985	−	26.3985i	1.13496	−	1.13496i	0.989341	−	0.145619i	$-0.0465173\pi$
$542$	13.8101	+	7.97326i	0.593194	+	0.342481i
$543$	32.3362	−	19.2180i	1.38768	−	0.824722i
$544$	−1.04382	−	0.279691i	−0.0447535	−	0.0119917i
$545$	−37.0949			−1.58897
$546$	5.27596	−	3.34130i	0.225790	−	0.142994i
$547$	13.5658			0.580032			0.290016	−	0.957022i	$-0.406339\pi$
$547$	13.5658			0.580032			0.290016	+	0.957022i	$0.406339\pi$
$548$	−15.0687	−	4.03765i	−0.643703	−	0.172480i
$549$	−14.0782	−	23.0208i	−0.600844	−	0.982506i
$550$	−5.43151	−	3.13589i	−0.231601	−	0.133715i
$551$	1.36764	−	1.36764i	0.0582635	−	0.0582635i
$552$	5.23879	−	1.47491i	0.222978	−	0.0627762i
$553$	−0.400830	−	1.49592i	−0.0170450	−	0.0636129i
$554$	−10.1250	−	10.1250i	−0.430170	−	0.430170i
$555$	1.58840	+	0.890500i	0.0674237	+	0.0377996i
$556$	8.11872	−	4.68734i	0.344310	−	0.198788i
$557$	−4.55992	+	17.0179i	−0.193210	+	0.721070i	0.799513	+	0.600649i	$0.205091\pi$
$557$	−4.55992	+	17.0179i	−0.193210	+	0.721070i	−0.992723	+	0.120421i	$0.961576\pi$
$558$	17.8325	−	0.450633i	0.754908	−	0.0190768i
$559$	−18.0246	−	9.73667i	−0.762358	−	0.411817i
$560$		−	1.93599i		−	0.0818106i
$561$	−2.31227	+	9.08717i	−0.0976242	+	0.383660i
$562$	1.42194	+	2.46287i	0.0599809	+	0.103890i
$563$	13.1207	−	22.7258i	0.552972	−	0.957776i	−0.445086	−	0.895488i	$-0.646827\pi$
$563$	13.1207	−	22.7258i	0.552972	−	0.957776i	0.998058	−	0.0622884i	$-0.0198398\pi$
$564$	−0.202175	+	0.207349i	−0.00851310	+	0.00873095i
$565$	−24.6979	+	6.61779i	−1.03905	+	0.278413i
$566$	−20.8077	+	5.57539i	−0.874611	+	0.234351i
$567$	6.03440	−	6.67727i	0.253421	−	0.280419i
$568$	5.04628	−	8.74041i	0.211737	−	0.366740i
$569$	7.41148	+	12.8371i	0.310705	+	0.538157i	0.978515	−	0.206174i	$-0.0661014\pi$
$569$	7.41148	+	12.8371i	0.310705	+	0.538157i	−0.667810	+	0.744332i	$0.732768\pi$
$570$	7.65691	+	1.94834i	0.320713	+	0.0816068i
$571$			7.26369i			0.303976i	0.988382	+	0.151988i	$0.0485675\pi$
$571$			7.26369i			0.303976i	−0.988382	+	0.151988i	$0.951432\pi$
$572$	−12.4054	+	13.1287i	−0.518696	+	0.548939i
$573$	−0.436384	−	34.5427i	−0.0182302	−	1.44304i
$574$	−1.38849	+	5.18191i	−0.0579544	+	0.216289i
$575$	−3.40680	+	1.96692i	−0.142073	+	0.0820262i
$576$	−2.63514	−	1.43389i	−0.109798	−	0.0597453i
$577$	15.1240	+	15.1240i	0.629619	+	0.629619i	0.947972	−	0.318353i	$-0.103130\pi$
$577$	15.1240	+	15.1240i	0.629619	+	0.629619i	−0.318353	+	0.947972i	$0.603130\pi$
$578$	4.09768	+	15.2927i	0.170441	+	0.636094i
$579$	−11.6509	−	41.3833i	−0.484193	−	1.71983i
$580$	−1.12373	+	1.12373i	−0.0466605	+	0.0466605i
$581$	−0.415085	−	0.239650i	−0.0172206	−	0.00994234i
$582$	−3.73745	−	6.28863i	−0.154922	−	0.260672i
$583$	−69.8323	−	18.7115i	−2.89216	−	0.774952i
$584$	2.13853			0.0884929
$585$	−6.49549	−	19.9081i	−0.268555	−	0.823098i
$586$	−13.4082			−0.553888
$587$	−14.4371	−	3.86840i	−0.595881	−	0.159666i	−0.0517414	−	0.998661i	$-0.516477\pi$
$587$	−14.4371	−	3.86840i	−0.595881	−	0.159666i	−0.544140	+	0.838995i	$0.683144\pi$
$588$	0.884905	+	1.48894i	0.0364928	+	0.0614029i
$589$	−12.1331	−	7.00505i	−0.499936	−	0.288638i
$590$	2.34922	−	2.34922i	0.0967160	−	0.0967160i
$591$	−9.82146	−	34.8853i	−0.404001	−	1.43499i
$592$	0.140553	+	0.524550i	0.00577668	+	0.0215589i
$593$	11.2075	+	11.2075i	0.460239	+	0.460239i	0.898734	−	0.438495i	$-0.144488\pi$
$593$	11.2075	+	11.2075i	0.460239	+	0.460239i	−0.438495	+	0.898734i	$0.644488\pi$
$594$	−12.1520	+	23.0204i	−0.498602	+	0.944539i
$595$	1.81183	−	1.04606i	0.0742777	−	0.0428843i
$596$	2.84144	−	10.6044i	0.116390	−	0.434373i
$597$	0.227950	+	18.0438i	0.00932937	+	0.738483i
$598$	3.24095	+	10.8559i	0.132532	+	0.443931i
$599$			19.7299i			0.806143i	0.915168	+	0.403072i	$0.132057\pi$
$599$			19.7299i			0.806143i	−0.915168	+	0.403072i	$0.867943\pi$
$600$	2.10145	+	0.534724i	0.0857914	+	0.0218300i
$601$	−21.8523	−	37.8493i	−0.891374	−	1.54390i	−0.838229	−	0.545318i	$-0.816409\pi$
$601$	−21.8523	−	37.8493i	−0.891374	−	1.54390i	−0.0531444	−	0.998587i	$-0.516924\pi$
$602$	2.84093	−	4.92064i	0.115788	−	0.200550i
$603$	25.9313	+	24.6530i	1.05601	+	1.00395i
$604$	19.4901	−	5.22235i	0.793040	−	0.212494i
$605$	26.3612	−	7.06345i	1.07173	−	0.287170i
$606$	−15.1293	+	15.5165i	−0.614587	+	0.630315i
$607$	−0.403192	+	0.698348i	−0.0163650	+	0.0283451i	−0.874092	−	0.485760i	$-0.838543\pi$
$607$	−0.403192	+	0.698348i	−0.0163650	+	0.0283451i	0.857727	+	0.514106i	$0.171876\pi$
$608$	1.17810	+	2.04053i	0.0477783	+	0.0827545i
$609$	0.350609	−	1.37788i	0.0142074	−	0.0558346i
$610$		−	17.4138i		−	0.705066i
$611$	−0.438179	−	0.414038i	−0.0177268	−	0.0167502i
$612$	−0.0818987	−	3.24090i	−0.00331056	−	0.131006i
$613$	−1.19793	+	4.47072i	−0.0483838	+	0.180571i	−0.985889	−	0.167401i	$-0.946463\pi$
$613$	−1.19793	+	4.47072i	−0.0483838	+	0.180571i	0.937505	+	0.347971i	$0.113129\pi$
$614$	−14.9433	+	8.62754i	−0.603064	+	0.348179i
$615$	15.6914	+	8.79705i	0.632739	+	0.354731i
$616$	−3.54236	−	3.54236i	−0.142726	−	0.142726i
$617$	5.55124	+	20.7175i	0.223484	+	0.834055i	0.983006	+	0.183573i	$0.0587664\pi$
$617$	5.55124	+	20.7175i	0.223484	+	0.834055i	−0.759522	+	0.650482i	$0.774567\pi$
$618$	2.14605	−	0.604188i	0.0863267	−	0.0243040i
$619$	−33.9860	+	33.9860i	−1.36601	+	1.36601i	−0.499969	+	0.866043i	$0.666655\pi$
$619$	−33.9860	+	33.9860i	−1.36601	+	1.36601i	−0.866043	+	0.499969i	$0.833345\pi$
$620$	9.96925	+	5.75575i	0.400375	+	0.231157i
$621$	8.69356	+	13.8204i	0.348861	+	0.554596i
$622$	−10.5139	−	2.81720i	−0.421570	−	0.112959i
$623$	16.8336			0.674425
$624$	2.89846	−	5.53163i	0.116031	−	0.221442i
$625$	17.1730			0.686919
$626$	−25.4545	−	6.82051i	−1.01737	−	0.272602i
$627$	17.5751	−	10.4452i	0.701883	−	0.417142i
$628$	1.39240	+	0.803903i	0.0555629	+	0.0320792i
$629$	−0.414964	+	0.414964i	−0.0165457	+	0.0165457i
$630$	5.57031	−	1.64446i	0.221926	−	0.0655168i
$631$	−2.19913	−	8.20725i	−0.0875458	−	0.326725i	0.908238	−	0.418453i	$-0.137428\pi$
$631$	−2.19913	−	8.20725i	−0.0875458	−	0.326725i	−0.995784	+	0.0917279i	$0.970761\pi$
$632$	−1.09509	−	1.09509i	−0.0435603	−	0.0435603i
$633$	2.62404	−	4.68054i	0.104296	−	0.186035i
$634$	−19.8039	+	11.4338i	−0.786511	+	0.454093i
$635$	−7.01841	+	26.1930i	−0.278517	+	1.03944i
$636$	24.9937	−	0.315750i	0.991064	−	0.0125203i
$637$	−3.07020	+	1.89047i	−0.121646	+	0.0749031i
$638$			4.11228i			0.162807i
$639$	29.4346	+	7.09512i	1.16442	+	0.280679i
$640$	−0.967996	−	1.67662i	−0.0382634	−	0.0662741i
$641$	−9.14555	+	15.8406i	−0.361228	+	0.625664i	−0.988163	−	0.153407i	$-0.950976\pi$
$641$	−9.14555	+	15.8406i	−0.361228	+	0.625664i	0.626936	+	0.779071i	$0.284309\pi$
$642$	6.97587	+	6.80181i	0.275316	+	0.268446i
$643$	−23.2648	+	6.23377i	−0.917472	+	0.245836i	−0.686505	−	0.727125i	$-0.740856\pi$
$643$	−23.2648	+	6.23377i	−0.917472	+	0.245836i	−0.230968	+	0.972961i	$0.574189\pi$
$644$	−3.03513	+	0.813262i	−0.119601	+	0.0320470i
$645$	−13.6414	−	13.3010i	−0.537128	−	0.523726i
$646$	−1.27311	+	2.20509i	−0.0500898	+	0.0867581i
$647$	−4.83585	−	8.37595i	−0.190117	−	0.329292i	0.755172	−	0.655527i	$-0.227553\pi$
$647$	−4.83585	−	8.37595i	−0.190117	−	0.329292i	−0.945289	+	0.326235i	$0.894220\pi$
$648$	1.88731	−	8.79989i	0.0741406	−	0.345692i
$649$		−	8.59694i		−	0.337459i
$650$	−1.04436	+	4.39144i	−0.0409632	+	0.172247i
$651$	−10.2980	+	0.130097i	−0.403612	+	0.00509890i
$652$	−1.98526	+	7.40908i	−0.0777486	+	0.290162i
$653$	−22.6224	+	13.0610i	−0.885282	+	0.511118i	−0.872396	−	0.488799i	$-0.837435\pi$
$653$	−22.6224	+	13.0610i	−0.885282	+	0.511118i	−0.0128859	+	0.999917i	$0.504102\pi$
$654$	16.2293	−	28.9484i	0.634614	−	1.13197i
$655$	−2.55097	−	2.55097i	−0.0996747	−	0.0996747i
$656$	1.38849	+	5.18191i	0.0542114	+	0.202320i
$657$	1.81649	+	6.15305i	0.0708682	+	0.240053i
$658$	0.118229	−	0.118229i	0.00460904	−	0.00460904i
$659$	19.6160	+	11.3253i	0.764132	+	0.441172i	0.830777	−	0.556605i	$-0.187896\pi$
$659$	19.6160	+	11.3253i	0.764132	+	0.441172i	−0.0666453	+	0.997777i	$0.521230\pi$
$660$	−14.4407	+	8.58239i	−0.562105	+	0.334069i
$661$	29.3854	+	7.87378i	1.14296	+	0.306255i	0.780140	−	0.625605i	$-0.215148\pi$
$661$	29.3854	+	7.87378i	1.14296	+	0.306255i	0.362818	+	0.931860i	$0.381815\pi$
$662$	−14.8280			−0.576306
$663$	6.74296	−	0.276291i	0.261875	−	0.0107303i
$664$	−0.479299			−0.0186004
$665$	−4.40616	−	1.18063i	−0.170863	−	0.0457827i
$666$	−1.38987	+	0.849964i	−0.0538563	+	0.0329354i
$667$	2.23378	+	1.28967i	0.0864921	+	0.0499363i
$668$	14.0451	−	14.0451i	0.543423	−	0.543423i
$669$	2.84145	−	0.799969i	0.109857	−	0.0309286i
$670$	5.97611	+	22.3031i	0.230877	+	0.861646i
$671$	−31.8628	−	31.8628i	−1.23005	−	1.23005i
$672$	1.51082	+	0.847008i	0.0582812	+	0.0326740i
$673$	16.9366	−	9.77835i	0.652858	−	0.376928i	−0.136692	−	0.990614i	$-0.543647\pi$
$673$	16.9366	−	9.77835i	0.652858	−	0.376928i	0.789550	+	0.613686i	$0.210314\pi$
$674$	4.85925	−	18.1350i	0.187171	−	0.698533i
$675$	0.246474	+	6.50058i	0.00948677	+	0.250207i
$676$	11.6082	+	5.85226i	0.446470	+	0.225087i
$677$			47.5793i			1.82862i	0.405015	+	0.914310i	$0.367266\pi$
$677$			47.5793i			1.82862i	−0.405015	+	0.914310i	$0.632734\pi$
$678$	5.64106	−	22.1692i	0.216644	−	0.851404i
$679$	2.11178	+	3.65771i	0.0810427	+	0.140370i
$680$	1.04606	−	1.81183i	0.0401145	−	0.0694804i
$681$	11.2015	−	11.4881i	0.429242	−	0.440226i
$682$	28.7727	−	7.70962i	1.10176	−	0.295217i
$683$	29.7216	−	7.96389i	1.13727	−	0.304730i	0.359415	−	0.933178i	$-0.382976\pi$
$683$	29.7216	−	7.96389i	1.13727	−	0.304730i	0.777852	+	0.628448i	$0.216309\pi$
$684$	−4.87040	+	5.12293i	−0.186224	+	0.195880i
$685$	15.1010	−	26.1557i	0.576979	−	0.999357i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$	−31.3540	−	7.97817i	−1.19623	−	0.304386i
$688$		−	5.68187i		−	0.216619i
$689$	1.47333	+	52.0118i	0.0561295	+	1.98149i
$690$	0.133099	+	10.5357i	0.00506701	+	0.401087i
$691$	−3.74279	+	13.9683i	−0.142383	+	0.531379i	0.857475	+	0.514525i	$0.172032\pi$
$691$	−3.74279	+	13.9683i	−0.142383	+	0.531379i	−0.999858	+	0.0168540i	$0.994635\pi$
$692$	0.654347	−	0.377787i	0.0248745	−	0.0143613i
$693$	7.18329	−	13.2012i	0.272871	−	0.501470i
$694$	6.66902	+	6.66902i	0.253152	+	0.253152i
$695$	4.69739	+	17.5309i	0.178182	+	0.664985i
$696$	−0.385305	−	1.36859i	−0.0146050	−	0.0518761i
$697$	−4.09934	+	4.09934i	−0.155274	+	0.155274i
$698$	26.5394	+	15.3225i	1.00453	+	0.579967i
$699$	17.4172	+	29.3062i	0.658779	+	1.10846i
$700$	−1.20928	−	0.324025i	−0.0457064	−	0.0122470i
$701$	−0.0793469			−0.00299689			−0.00149845	−	0.999999i	$-0.500477\pi$
$701$	−0.0793469			−0.00299689			−0.00149845	+	0.999999i	$0.500477\pi$
$702$	18.3778	+	3.64092i	0.693626	+	0.137418i
$703$	1.27955			0.0482590
$704$	−4.83896	−	1.29660i	−0.182375	−	0.0488673i
$705$	−0.286443	−	0.481969i	−0.0107881	−	0.0181520i
$706$	18.7414	+	10.8203i	0.705341	+	0.407229i
$707$	8.84740	−	8.84740i	0.332741	−	0.332741i
$708$	0.805500	+	2.86110i	0.0302726	+	0.107527i
$709$	0.737752	+	2.75333i	0.0277068	+	0.103403i	0.978395	−	0.206746i	$-0.0662875\pi$
$709$	0.737752	+	2.75333i	0.0277068	+	0.103403i	−0.950688	+	0.310150i	$0.899621\pi$
$710$	13.8162	+	13.8162i	0.518514	+	0.518514i
$711$	2.22065	−	4.08101i	0.0832807	−	0.153050i
$712$	14.5783	−	8.41681i	0.546347	−	0.315433i
$713$	4.83570	−	18.0471i	0.181098	−	0.675868i
$714$	0.0236440	+	1.87158i	0.000884855	+	0.0700422i
$715$	−18.3350	−	29.7768i	−0.685690	−	1.11359i
$716$		−	10.9377i		−	0.408760i
$717$	−39.2340	−	9.98328i	−1.46522	−	0.372832i
$718$	−12.5001	−	21.6508i	−0.466499	−	0.808000i
$719$	−0.842006	+	1.45840i	−0.0314015	+	0.0543890i	−0.881299	−	0.472559i	$-0.843330\pi$
$719$	−0.842006	+	1.45840i	−0.0314015	+	0.0543890i	0.849898	+	0.526948i	$0.176664\pi$
$720$	4.00180	−	4.20930i	0.149138	−	0.156871i
$721$	−1.24333	+	0.333149i	−0.0463040	+	0.0124071i
$722$	−12.9901	+	3.48068i	−0.483440	+	0.129537i
$723$	4.18141	−	4.28842i	0.155508	−	0.159488i
$724$	−10.8588	+	18.8080i	−0.403564	+	0.698993i
$725$	0.513839	+	0.889995i	0.0190835	+	0.0330536i
$726$	−6.02095	+	23.6622i	−0.223458	+	0.878185i
$727$			34.6532i			1.28521i	0.766196	+	0.642607i	$0.222147\pi$
$727$			34.6532i			1.28521i	−0.766196	+	0.642607i	$0.777853\pi$
$728$	−1.71364	+	3.17229i	−0.0635116	+	0.117573i
$729$	26.9225	−	2.04451i	0.997129	−	0.0757224i
$730$	−1.07156	+	3.99910i	−0.0396600	+	0.148013i
$731$	5.31747	−	3.07004i	0.196674	−	0.113550i
$732$	13.5895	+	7.61866i	0.502283	+	0.281594i
$733$	−27.6020	−	27.6020i	−1.01950	−	1.01950i	−0.999806	−	0.0196968i	$-0.993730\pi$
$733$	−27.6020	−	27.6020i	−1.01950	−	1.01950i	−0.0196968	−	0.999806i	$-0.506270\pi$
$734$	4.81040	+	17.9527i	0.177555	+	0.662645i
$735$	−3.22776	+	0.908727i	−0.119058	+	0.0335189i
$736$	−2.22187	+	2.22187i	−0.0818993	+	0.0818993i
$737$	51.7437	+	29.8743i	1.90600	+	1.10043i
$738$	−13.7302	+	8.39660i	−0.505415	+	0.309083i
$739$	−27.2046	−	7.28945i	−1.00074	−	0.268147i	−0.278983	−	0.960296i	$-0.589997\pi$
$739$	−27.2046	−	7.28945i	−1.00074	−	0.268147i	−0.721754	+	0.692149i	$0.756664\pi$
$740$	−1.05135			−0.0386483
$741$	−10.8220	−	9.97001i	−0.397555	−	0.366258i
$742$	−14.4313			−0.529789
$743$	11.2794	+	3.02232i	0.413803	+	0.110878i	0.459713	−	0.888067i	$-0.347952\pi$
$743$	11.2794	+	3.02232i	0.413803	+	0.110878i	−0.0459104	+	0.998946i	$0.514619\pi$
$744$	−8.85331	+	5.26169i	−0.324578	+	0.192903i
$745$	18.4067	+	10.6271i	0.674370	+	0.389348i
$746$	8.57957	−	8.57957i	0.314121	−	0.314121i
$747$	−0.407123	−	1.37906i	−0.0148959	−	0.0504571i
$748$	−1.40116	−	5.22919i	−0.0512314	−	0.191198i
$749$	−3.97759	−	3.97759i	−0.145338	−	0.145338i
$750$	−10.2519	+	18.2865i	−0.374347	+	0.667729i
$751$	−12.5124	+	7.22401i	−0.456582	+	0.263608i	−0.710606	−	0.703590i	$-0.751579\pi$
$751$	−12.5124	+	7.22401i	−0.456582	+	0.263608i	0.254024	+	0.967198i	$0.418246\pi$
$752$	0.0432747	−	0.161503i	0.00157807	−	0.00588942i
$753$	31.3114	−	0.395562i	1.14105	−	0.0144151i
$754$	2.83601	−	0.846667i	0.103281	−	0.0308338i
$755$			39.0637i			1.42167i
$756$	−1.15373	+	5.06645i	−0.0419608	+	0.184265i
$757$	13.1472	+	22.7715i	0.477842	+	0.827646i	0.999677	−	0.0254000i	$-0.00808594\pi$
$757$	13.1472	+	22.7715i	0.477842	+	0.827646i	−0.521836	+	0.853046i	$0.674753\pi$
$758$	−1.49807	+	2.59473i	−0.0544122	+	0.0942448i
$759$	19.5212	+	19.0341i	0.708573	+	0.690893i
$760$	−4.40616	+	1.18063i	−0.159828	+	0.0428258i
$761$	−34.8239	+	9.33104i	−1.26237	+	0.338250i	−0.827101	−	0.562053i	$-0.810012\pi$
$761$	−34.8239	+	9.33104i	−1.26237	+	0.338250i	−0.435264	+	0.900303i	$0.643345\pi$
$762$	−17.3701	−	16.9367i	−0.629252	−	0.613551i
$763$	−9.58034	+	16.5936i	−0.346832	+	0.600730i
$764$	9.97242	+	17.2727i	0.360789	+	0.624905i
$765$	6.10160	+	1.47077i	0.220604	+	0.0531758i
$766$		−	21.6483i		−	0.782185i
$767$	−5.92882	+	1.77000i	−0.214077	+	0.0639110i
$768$	1.73191	−	0.0218795i	0.0624950	−	0.000789510i
$769$	8.80289	−	32.8528i	0.317440	−	1.18470i	−0.604256	−	0.796791i	$-0.706529\pi$
$769$	8.80289	−	32.8528i	0.317440	−	1.18470i	0.921696	−	0.387913i	$-0.126804\pi$
$770$	8.39929	−	4.84933i	0.302689	−	0.174758i
$771$	−17.9892	+	32.0876i	−0.647865	+	1.15561i
$772$	17.5514	+	17.5514i	0.631690	+	0.631690i
$773$	−3.54196	−	13.2188i	−0.127396	−	0.475447i	0.872518	−	0.488582i	$-0.162486\pi$
$773$	−3.54196	−	13.2188i	−0.127396	−	0.475447i	−0.999914	+	0.0131349i	$0.995819\pi$
$774$	16.3481	−	4.82626i	0.587620	−	0.173476i
$775$	5.26375	−	5.26375i	0.189080	−	0.189080i
$776$	3.65771	+	2.11178i	0.131304	+	0.0758085i
$777$	0.808575	−	0.480551i	0.0290075	−	0.0172397i
$778$	34.1296	+	9.14500i	1.22361	+	0.327864i
$779$	12.6403			0.452887
$780$	8.89194	+	8.19194i	0.318383	+	0.293318i
$781$	50.5603			1.80919
$782$	−3.27990	−	0.878847i	−0.117289	−	0.0314275i
$783$	3.61046	−	2.27111i	0.129027	−	0.0811629i
$784$	−0.866025	−	0.500000i	−0.0309295	−	0.0178571i
$785$	−2.20101	+	2.20101i	−0.0785575	+	0.0785575i
$786$	3.10681	−	0.874676i	0.110816	−	0.0311987i
$787$	3.23906	+	12.0883i	0.115460	+	0.430903i	0.999321	−	0.0368470i	$-0.0117314\pi$
$787$	3.23906	+	12.0883i	0.115460	+	0.430903i	−0.883861	+	0.467750i	$0.845065\pi$
$788$	14.7955	+	14.7955i	0.527069	+	0.527069i
$789$	−14.9692	−	8.39213i	−0.532916	−	0.298768i
$790$	2.59656	−	1.49912i	0.0923814	−	0.0533365i
$791$	−3.41829	+	12.7572i	−0.121541	+	0.453596i
$792$	−0.379667	−	15.0242i	−0.0134909	−	0.533861i
$793$	−15.4138	+	28.5341i	−0.547360	+	1.01328i
$794$			20.5037i			0.727650i
$795$	−11.9332	+	46.8970i	−0.423226	+	1.66327i
$796$	−5.20920	−	9.02261i	−0.184635	−	0.319798i
$797$	3.71160	−	6.42868i	0.131472	−	0.227716i	−0.792772	−	0.609518i	$-0.791363\pi$
$797$	3.71160	−	6.42868i	0.131472	−	0.227716i	0.924244	+	0.381802i	$0.124696\pi$
$798$	2.84906	−	2.92197i	0.100856	−	0.103437i
$799$	0.174528	−	0.0467646i	0.00617435	−	0.00165441i
$800$	−1.20928	+	0.324025i	−0.0427544	+	0.0114560i
$801$	36.6002	+	34.7960i	1.29320	+	1.22946i
$802$	16.4560	−	28.5026i	0.581082	−	1.00646i
$803$	5.35665	+	9.27798i	0.189032	+	0.327413i
$804$	−20.0196	−	5.09409i	−0.706038	−	0.179655i
$805$		−	6.08328i		−	0.214407i
$806$	−11.2408	−	18.2556i	−0.395941	−	0.643025i
$807$	−0.536704	−	42.4837i	−0.0188929	−	1.49550i
$808$	3.23837	−	12.0858i	0.113926	−	0.425176i
$809$	37.3624	−	21.5712i	1.31359	−	0.758403i	0.330903	−	0.943665i	$-0.392647\pi$
$809$	37.3624	−	21.5712i	1.31359	−	0.758403i	0.982689	+	0.185262i	$0.0593132\pi$
$810$	15.5103	+	7.93869i	0.544977	+	0.278937i
$811$	−12.4189	−	12.4189i	−0.436088	−	0.436088i	0.454605	−	0.890693i	$-0.349780\pi$
$811$	−12.4189	−	12.4189i	−0.436088	−	0.436088i	−0.890693	+	0.454605i	$0.849780\pi$
$812$	0.212457	+	0.792900i	0.00745578	+	0.0278253i
$813$	−7.48507	−	26.5866i	−0.262513	−	0.932433i
$814$	−1.92370	+	1.92370i	−0.0674255	+	0.0674255i
$815$	−12.8604	−	7.42496i	−0.450480	−	0.260085i
$816$	0.956267	+	1.60902i	0.0334760	+	0.0563268i
$817$	−12.9315	−	3.46498i	−0.452415	−	0.121224i
$818$	−23.8802			−0.834952
$819$	−10.5830	−	2.23595i	−0.369801	−	0.0781305i
$820$	−10.3860			−0.362696
$821$	17.7860	+	4.76575i	0.620736	+	0.166326i	0.555462	−	0.831542i	$-0.312541\pi$
$821$	17.7860	+	4.76575i	0.620736	+	0.166326i	0.0652737	+	0.997867i	$0.479208\pi$
$822$	13.8047	+	23.2279i	0.481496	+	0.810165i
$823$	−21.7279	−	12.5446i	−0.757387	−	0.437277i	0.0709700	−	0.997478i	$-0.477391\pi$
$823$	−21.7279	−	12.5446i	−0.757387	−	0.437277i	−0.828357	+	0.560201i	$0.810724\pi$
$824$	−0.910179	+	0.910179i	−0.0317076	+	0.0317076i
$825$	2.94388	+	10.4565i	0.102493	+	0.364050i
$826$	−0.444152	−	1.65760i	−0.0154540	−	0.0576752i
$827$	−26.1867	−	26.1867i	−0.910600	−	0.910600i	0.0857194	−	0.996319i	$-0.472681\pi$
$827$	−26.1867	−	26.1867i	−0.910600	−	0.910600i	−0.996319	+	0.0857194i	$0.972681\pi$
$828$	−8.28015	−	4.50557i	−0.287755	−	0.156579i
$829$	44.5004	−	25.6923i	1.54556	−	0.892331i	0.547090	−	0.837074i	$-0.315736\pi$
$829$	44.5004	−	25.6923i	1.54556	−	0.892331i	0.998472	−	0.0552565i	$-0.0175977\pi$
$830$	0.240163	−	0.896301i	0.00833619	−	0.0311111i
$831$	0.313291	+	24.7991i	0.0108680	+	0.860272i
$832$	0.102093	+	3.60411i	0.00353944	+	0.124950i
$833$		−	1.08064i		−	0.0374421i
$834$	−15.7360	−	4.00410i	−0.544893	−	0.138651i
$835$	19.2271	+	33.3024i	0.665382	+	1.15248i
$836$	−5.90189	+	10.2224i	−0.204121	+	0.353548i
$837$	−22.6592	−	21.0037i	−0.783218	−	0.725995i
$838$	24.7717	−	6.63755i	0.855723	−	0.229290i
$839$	5.72503	−	1.53402i	0.197650	−	0.0529601i	−0.158636	−	0.987337i	$-0.550710\pi$
$839$	5.72503	−	1.53402i	0.197650	−	0.0529601i	0.356286	+	0.934377i	$0.384043\pi$
$840$	−2.34095	+	2.40086i	−0.0807706	+	0.0828375i
$841$	−14.1631	+	24.5312i	−0.488382	+	0.845903i
$842$	−3.57374	−	6.18989i	−0.123159	−	0.213318i
$843$	1.21467	−	4.77363i	0.0418355	−	0.164412i
$844$			3.09801i			0.106638i
$845$	−16.7604	+	18.7753i	−0.576576	+	0.645889i
$846$	0.501442	−	0.0126716i	0.0172399	−	0.000435659i
$847$	3.64849	−	13.6164i	0.125364	−	0.467864i
$848$	−12.4978	+	7.21563i	−0.429178	+	0.247786i
$849$	32.5456	+	18.2460i	1.11696	+	0.626200i
$850$	−0.956643	−	0.956643i	−0.0328126	−	0.0328126i
$851$	0.441645	+	1.64824i	0.0151394	+	0.0565010i
$852$	−16.8267	+	4.73731i	−0.576473	+	0.162297i
$853$	4.35862	−	4.35862i	0.149236	−	0.149236i	−0.628540	−	0.777777i	$-0.716347\pi$
$853$	4.35862	−	4.35862i	0.149236	−	0.149236i	0.777777	+	0.628540i	$0.216347\pi$
$854$	−7.78972	−	4.49739i	−0.266559	−	0.153898i
$855$	−7.13959	−	11.6747i	−0.244169	−	0.399267i
$856$	−5.43349	−	1.45590i	−0.185713	−	0.0497616i
$857$	−21.7425			−0.742711			−0.371356	−	0.928491i	$-0.621107\pi$
$857$	−21.7425			−0.742711			−0.371356	+	0.928491i	$0.621107\pi$
$858$	31.2591	−	1.28083i	1.06717	−	0.0437269i
$859$	−3.52824			−0.120382			−0.0601910	−	0.998187i	$-0.519171\pi$
$859$	−3.52824			−0.120382			−0.0601910	+	0.998187i	$0.519171\pi$
$860$	10.6252	+	2.84702i	0.362318	+	0.0970827i
$861$	7.98773	−	4.74725i	0.272221	−	0.161786i
$862$	−11.3239	−	6.53784i	−0.385693	−	0.222680i
$863$	−13.3323	+	13.3323i	−0.453836	+	0.453836i	−0.896625	−	0.442790i	$-0.853989\pi$
$863$	−13.3323	+	13.3323i	−0.453836	+	0.453836i	0.442790	+	0.896625i	$0.353989\pi$
$864$	1.53406	+	4.96454i	0.0521899	+	0.168897i
$865$	0.378597	+	1.41294i	0.0128727	+	0.0480415i
$866$	−3.82867	−	3.82867i	−0.130104	−	0.130104i
$867$	13.4100	−	23.9196i	0.455428	−	0.812353i
$868$	5.14943	−	2.97302i	0.174783	−	0.100911i
$869$	2.00802	−	7.49404i	0.0681175	−	0.254218i
$870$	2.75235	−	0.0347709i	0.0933135	−	0.00117885i
$871$	9.94918	−	41.8354i	0.337115	−	1.41754i
$872$			19.1607i			0.648863i
$873$	−2.96918	+	12.3179i	−0.100492	+	0.416897i
$874$	3.70183	+	6.41176i	0.125216	+	0.216881i
$875$	6.05185	−	10.4821i	0.204590	−	0.354360i
$876$	−2.65203	−	2.58586i	−0.0896037	−	0.0873680i
$877$	−8.74624	+	2.34355i	−0.295340	+	0.0791360i	−0.403446	−	0.915003i	$-0.632188\pi$
$877$	−8.74624	+	2.34355i	−0.295340	+	0.0791360i	0.108107	+	0.994139i	$0.465521\pi$
$878$	36.0784	−	9.66717i	1.21759	−	0.326251i
$879$	16.6278	+	16.2129i	0.560841	+	0.546847i
$880$	4.84933	−	8.39929i	0.163471	−	0.283140i
$881$	4.54322	+	7.86909i	0.153065	+	0.265116i	0.932353	−	0.361550i	$-0.117752\pi$
$881$	4.54322	+	7.86909i	0.153065	+	0.265116i	−0.779288	+	0.626666i	$0.784419\pi$
$882$	0.703005	−	2.91647i	0.0236714	−	0.0982026i
$883$			11.8352i			0.398285i	0.979971	+	0.199142i	$0.0638157\pi$
$883$			11.8352i			0.398285i	−0.979971	+	0.199142i	$0.936184\pi$
$884$	−3.31780	+	2.04292i	−0.111590	+	0.0687110i
$885$	−5.75394	+	0.0726905i	−0.193416	+	0.00244346i
$886$	8.06120	−	30.0848i	0.270821	−	1.01072i
$887$	−49.8352	+	28.7724i	−1.67330	+	0.966082i	−0.707535	+	0.706678i	$0.750193\pi$
$887$	−49.8352	+	28.7724i	−1.67330	+	0.966082i	−0.965769	+	0.259404i	$0.916474\pi$
$888$	0.459971	−	0.820457i	0.0154356	−	0.0275327i
$889$	9.90430	+	9.90430i	0.332180	+	0.332180i
$890$	8.43485	+	31.4793i	0.282737	+	1.05519i
$891$	42.9056	−	13.8541i	1.43739	−	0.464131i
$892$	−1.20511	+	1.20511i	−0.0403502	+	0.0403502i
$893$	−0.341178	−	0.196979i	−0.0114171	−	0.00659166i
$894$	−16.3463	+	9.71491i	−0.546702	+	0.324915i
$895$	20.4537	+	5.48055i	0.683692	+	0.183195i
$896$	−1.00000			−0.0334077
$897$	9.10756	−	17.3815i	0.304092	−	0.580351i
$898$	−14.7083			−0.490823
$899$	−4.71462	−	1.26328i	−0.157242	−	0.0421327i
$900$	−1.95947	−	3.20415i	−0.0653158	−	0.106805i
$901$	−13.5057	−	7.79753i	−0.449941	−	0.259774i
$902$	−19.0037	+	19.0037i	−0.632756	+	0.632756i
$903$	−9.47302	+	2.66699i	−0.315242	+	0.0887519i
$904$	3.41829	+	12.7572i	0.113691	+	0.424300i
$905$	−29.7303	−	29.7303i	−0.988270	−	0.988270i
$906$	−30.4847	−	17.0906i	−1.01279	−	0.567797i
$907$	−31.4200	+	18.1404i	−1.04328	+	0.602341i	−0.920762	−	0.390125i	$-0.872432\pi$
$907$	−31.4200	+	18.1404i	−1.04328	+	0.602341i	−0.122523	+	0.992466i	$0.539098\pi$
$908$	−2.39763	+	8.94809i	−0.0795682	+	0.296953i
$909$	37.5243	−	0.948254i	1.24460	−	0.0314516i
$910$	−5.07361	−	4.79409i	−0.168189	−	0.158923i
$911$			52.0683i			1.72510i	0.505973	+	0.862549i	$0.331133\pi$
$911$			52.0683i			1.72510i	−0.505973	+	0.862549i	$0.668867\pi$
$912$	1.00638	−	3.95503i	0.0333245	−	0.130964i
$913$	−1.20056	−	2.07944i	−0.0397328	−	0.0688193i
$914$	4.26688	−	7.39046i	0.141136	−	0.244455i
$915$	−21.0564	+	21.5952i	−0.696103	+	0.713916i
$916$	18.0426	−	4.83450i	0.596144	−	0.159736i
$917$	−1.79995	+	0.482296i	−0.0594396	+	0.0159268i
$918$	−3.81725	+	4.11813i	−0.125988	+	0.135918i
$919$	−7.22692	+	12.5174i	−0.238394	+	0.412911i	−0.960254	−	0.279129i	$-0.909954\pi$
$919$	−7.22692	+	12.5174i	−0.238394	+	0.412911i	0.721860	+	0.692040i	$0.243288\pi$
$920$	−3.04164	−	5.26827i	−0.100280	−	0.173690i
$921$	28.9637	+	7.36995i	0.954387	+	0.242848i
$922$		−	4.44150i		−	0.146273i
$923$	−10.4097	−	34.8685i	−0.342640	−	1.14771i
$924$	0.109609	+	8.67629i	0.00360587	+	0.285429i
$925$	−0.175963	+	0.656703i	−0.00578563	+	0.0215923i
$926$	−20.0403	+	11.5703i	−0.658566	+	0.380223i
$927$	−3.39192	−	1.84568i	−0.111405	−	0.0606202i
$928$	0.580443	+	0.580443i	0.0190540	+	0.0190540i
$929$	4.12844	+	15.4075i	0.135450	+	0.505505i	0.999996	+	0.00295146i	$0.000939479\pi$
$929$	4.12844	+	15.4075i	0.135450	+	0.505505i	−0.864546	+	0.502554i	$0.832394\pi$
$930$	−5.40334	−	19.1924i	−0.177182	−	0.629343i
$931$	−1.66609	+	1.66609i	−0.0546038	+	0.0546038i
$932$	−17.0456	−	9.84129i	−0.558348	−	0.322362i
$933$	9.63202	+	16.2068i	0.315338	+	0.530588i
$934$	−34.4462	−	9.22984i	−1.12712	−	0.302010i
$935$	10.4808			0.342759
$936$	−10.2831	+	3.35512i	−0.336115	+	0.109666i
$937$	−46.0175			−1.50333			−0.751663	−	0.659548i	$-0.770748\pi$
$937$	−46.0175			−1.50333			−0.751663	+	0.659548i	$0.770748\pi$
$938$	11.5203	+	3.08685i	0.376150	+	0.100789i
$939$	23.3194	+	39.2372i	0.760999	+	1.28046i
$940$	0.280332	+	0.161850i	0.00914341	+	0.00527895i
$941$	−1.86084	+	1.86084i	−0.0606616	+	0.0606616i	−0.736787	−	0.676125i	$-0.763658\pi$
$941$	−1.86084	+	1.86084i	−0.0606616	+	0.0606616i	0.676125	+	0.736787i	$0.263658\pi$
$942$	−0.754682	−	2.68059i	−0.0245889	−	0.0873385i
$943$	4.36291	+	16.2826i	0.142076	+	0.530235i
$944$	−1.21345	−	1.21345i	−0.0394943	−	0.0394943i
$945$	−8.89628	−	4.69616i	−0.289396	−	0.152766i
$946$	24.6507	−	14.2321i	0.801465	−	0.462726i
$947$	−3.16917	+	11.8275i	−0.102984	+	0.384342i	−0.998109	−	0.0614741i	$-0.980420\pi$
$947$	−3.16917	+	11.8275i	−0.102984	+	0.384342i	0.895125	+	0.445816i	$0.147087\pi$
$948$	0.0338846	+	2.68219i	0.00110052	+	0.0871136i
$949$	5.29563	−	5.60439i	0.171903	−	0.181926i
$950$			2.94981i			0.0957046i
$951$	38.3845	+	9.76713i	1.24470	+	0.316721i
$952$	−0.540322	−	0.935866i	−0.0175119	−	0.0303316i
$953$	−10.7134	+	18.5561i	−0.347040	+	0.601091i	−0.985722	−	0.168379i	$-0.946147\pi$
$953$	−10.7134	+	18.5561i	−0.347040	+	0.601091i	0.638682	+	0.769471i	$0.279480\pi$
$954$	−31.3769	−	29.8302i	−1.01587	−	0.965789i
$955$	−37.2973	+	9.99379i	−1.20691	+	0.323391i
$956$	22.5772	−	6.04953i	0.730197	−	0.195656i
$957$	4.97247	−	5.09972i	0.160737	−	0.164850i
$958$	−3.47960	+	6.02685i	−0.112421	+	0.194719i
$959$	−7.80013	−	13.5102i	−0.251879	−	0.436268i
$960$	−0.826897	+	3.24968i	−0.0266880	+	0.104883i
$961$			4.35550i			0.140500i
$962$	1.72273	+	0.930598i	0.0555429	+	0.0300037i
$963$	−0.426314	−	16.8701i	−0.0137378	−	0.543632i
$964$	−0.895014	+	3.34024i	−0.0288265	+	0.107582i
$965$	−41.6162	+	24.0271i	−1.33967	+	0.773460i
$966$	4.74730	+	2.66147i	0.152742	+	0.0856314i
$967$	14.4200	+	14.4200i	0.463717	+	0.463717i	0.899872	−	0.436155i	$-0.143660\pi$
$967$	14.4200	+	14.4200i	0.463717	+	0.463717i	−0.436155	+	0.899872i	$0.643660\pi$
$968$	−3.64849	−	13.6164i	−0.117267	−	0.437646i
$969$	4.24515	−	1.19516i	0.136374	−	0.0383940i
$970$	−5.78185	+	5.78185i	−0.185644	+	0.185644i
$971$	−34.4575	−	19.8940i	−1.10579	−	0.638430i	−0.168057	−	0.985777i	$-0.553749\pi$
$971$	−34.4575	−	19.8940i	−1.10579	−	0.638430i	−0.937737	+	0.347347i	$0.887083\pi$
$972$	−12.9811	+	8.63081i	−0.416369	+	0.276833i
$973$	9.05525	+	2.42635i	0.290298	+	0.0777851i
$974$	21.1198			0.676721
$975$	6.60516	−	4.18309i	0.211534	−	0.133966i
$976$	−8.99479			−0.287916
$977$	−23.8452	−	6.38931i	−0.762877	−	0.204412i	−0.143654	−	0.989628i	$-0.545885\pi$
$977$	−23.8452	−	6.38931i	−0.762877	−	0.204412i	−0.619222	+	0.785216i	$0.712552\pi$
$978$	11.4208	−	6.78761i	0.365198	−	0.217044i
$979$	73.0325	+	42.1654i	2.33413	+	1.34761i
$980$	1.36895	−	1.36895i	0.0437296	−	0.0437296i
$981$	−55.1299	+	16.2754i	−1.76016	+	0.519632i
$982$	2.43362	+	9.08238i	0.0776598	+	0.289830i
$983$	40.2203	+	40.2203i	1.28283	+	1.28283i	0.939051	+	0.343778i	$0.111707\pi$
$983$	40.2203	+	40.2203i	1.28283	+	1.28283i	0.343778	+	0.939051i	$0.388293\pi$
$984$	4.54395	−	8.10511i	0.144856	−	0.258381i
$985$	−35.0816	+	20.2544i	−1.11779	+	0.645359i
$986$	−0.229590	+	0.856843i	−0.00731165	+	0.0272874i
$987$	−0.289577	+	0.00365827i	−0.00921734	+	0.000116444i
$988$	8.26490	+	1.96554i	0.262942	+	0.0625321i
$989$		−	17.8536i		−	0.567711i
$990$	28.2858	+	6.81820i	0.898983	+	0.216697i
$991$	8.91385	+	15.4392i	0.283158	+	0.490443i	0.972161	−	0.234315i	$-0.0752847\pi$
$991$	8.91385	+	15.4392i	0.283158	+	0.490443i	−0.689003	+	0.724758i	$0.741951\pi$
$992$	2.97302	−	5.14943i	0.0943936	−	0.163495i
$993$	18.3885	+	17.9297i	0.583540	+	0.568980i
$994$	9.74866	−	2.61215i	0.309209	−	0.0828523i
$995$	19.4827	−	5.22037i	0.617642	−	0.165497i
$996$	0.594388	+	0.579557i	0.0188339	+	0.0183640i
$997$	12.3556	−	21.4006i	0.391306	−	0.677762i	−0.601316	−	0.799011i	$-0.705357\pi$
$997$	12.3556	−	21.4006i	0.391306	−	0.677762i	0.992622	+	0.121249i	$0.0386900\pi$
$998$	−20.9682	−	36.3180i	−0.663737	−	1.14963i
$999$	2.75136	+	0.626539i	0.0870490	+	0.0198228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.b.323.9	yes	56
3.2	odd	2		546.2.bu.a.323.3	yes	56
13.6	odd	12		546.2.bu.a.71.3	✓	56
39.32	even	12	inner	546.2.bu.b.71.9	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.71.3	✓	56	13.6	odd	12
546.2.bu.a.323.3	yes	56	3.2	odd	2
546.2.bu.b.71.9	yes	56	39.32	even	12	inner
546.2.bu.b.323.9	yes	56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.884905 - 1.48894i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.36895 + 1.36895i) q^{5} +(-0.469386 - 1.66724i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.43389 + 2.63514i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.884905 - 1.48894i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.36895 + 1.36895i) q^{5} +(-0.469386 - 1.66724i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.43389 + 2.63514i) q^{9} +(-1.67662 + 0.967996i) q^{10} +(-1.29660 + 4.83896i) q^{11} +(-0.0218795 - 1.73191i) q^{12} +(3.60411 - 0.102093i) q^{13} +1.00000i q^{14} +(3.24968 + 0.826897i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.540322 + 0.935866i) q^{17} +(-2.06705 + 2.17423i) q^{18} +(2.27592 - 0.609830i) q^{19} +(-1.87002 + 0.501072i) q^{20} +(1.20918 - 1.24012i) q^{21} +(-2.50483 + 4.33849i) q^{22} +(1.57110 + 2.72123i) q^{23} +(0.427118 - 1.67856i) q^{24} +1.25194i q^{25} +(3.50772 + 0.834197i) q^{26} +(5.19242 - 0.196874i) q^{27} +(-0.258819 + 0.965926i) q^{28} +(0.710895 - 0.410435i) q^{29} +(2.92494 + 1.63980i) q^{30} +(-4.20449 - 4.20449i) q^{31} +(0.258819 + 0.965926i) q^{32} +(8.35229 - 2.35146i) q^{33} +(-0.764131 + 0.764131i) q^{34} +(-1.67662 - 0.967996i) q^{35} +(-2.55935 + 1.56515i) q^{36} +(0.524550 + 0.140553i) q^{37} +2.35620 q^{38} +(-3.34130 - 5.27596i) q^{39} -1.93599 q^{40} +(5.18191 + 1.38849i) q^{41} +(1.48894 - 0.884905i) q^{42} +(-4.92064 - 2.84093i) q^{43} +(-3.54236 + 3.54236i) q^{44} +(-1.64446 - 5.57031i) q^{45} +(0.813262 + 3.03513i) q^{46} +(-0.118229 - 0.118229i) q^{47} +(0.847008 - 1.51082i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-0.324025 + 1.20928i) q^{50} +(1.87158 - 0.0236440i) q^{51} +(3.17229 + 1.71364i) q^{52} +14.4313i q^{53} +(5.06645 + 1.15373i) q^{54} +(-4.84933 - 8.39929i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-2.92197 - 2.84906i) q^{57} +(0.792900 - 0.212457i) q^{58} +(-1.65760 + 0.444152i) q^{59} +(2.40086 + 2.34095i) q^{60} +(-4.49739 + 7.78972i) q^{61} +(-2.97302 - 5.14943i) q^{62} +(-2.91647 - 0.703005i) q^{63} +1.00000i q^{64} +(-4.79409 + 5.07361i) q^{65} +(8.67629 - 0.109609i) q^{66} +(3.08685 - 11.5203i) q^{67} +(-0.935866 + 0.540322i) q^{68} +(2.66147 - 4.74730i) q^{69} +(-1.36895 - 1.36895i) q^{70} +(-2.61215 - 9.74866i) q^{71} +(-2.87724 + 0.849414i) q^{72} +(1.51217 - 1.51217i) q^{73} +(0.470299 + 0.271527i) q^{74} +(1.86406 - 1.10784i) q^{75} +(2.27592 + 0.609830i) q^{76} -5.00966 q^{77} +(-1.86193 - 5.96097i) q^{78} -1.54869 q^{79} +(-1.87002 - 0.501072i) q^{80} +(-4.88793 - 7.55699i) q^{81} +(4.64597 + 2.68235i) q^{82} +(-0.338916 + 0.338916i) q^{83} +(1.66724 - 0.469386i) q^{84} +(-0.541480 - 2.02083i) q^{85} +(-4.01769 - 4.01769i) q^{86} +(-1.24019 - 0.695284i) q^{87} +(-4.33849 + 2.50483i) q^{88} +(4.35686 - 16.2600i) q^{89} +(-0.146723 - 5.80612i) q^{90} +(1.03143 + 3.45488i) q^{91} +3.14220i q^{92} +(-2.53966 + 9.98081i) q^{93} +(-0.0836003 - 0.144800i) q^{94} +(-2.28079 + 3.95045i) q^{95} +(1.20918 - 1.24012i) q^{96} +(4.07964 - 1.09314i) q^{97} +(-0.965926 + 0.258819i) q^{98} +(-10.8922 - 10.3552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{6} - 24 q^{9}+O(q^{10}) \) 56 * q + 8 * q^6 - 24 * q^9	\( 56 q + 8 q^{6} - 24 q^{9} + 24 q^{10} + 8 q^{11} + 24 q^{13} + 4 q^{15} + 28 q^{16} - 4 q^{17} - 8 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{79} + 12 q^{81} - 4 q^{83} - 4 q^{84} + 32 q^{85} - 16 q^{86} - 144 q^{87} + 88 q^{89} - 8 q^{90} - 8 q^{91} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 q^{99}+O(q^{100}) \) 56 * q + 8 * q^6 - 24 * q^9 + 24 * q^10 + 8 * q^11 + 24 * q^13 + 4 * q^15 + 28 * q^16 - 4 * q^17 - 8 * q^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 16 * q^79 + 12 * q^81 - 4 * q^83 - 4 * q^84 + 32 * q^85 - 16 * q^86 - 144 * q^87 + 88 * q^89 - 8 * q^90 - 8 * q^91 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

Introduction

L-functions

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