LMFDB - Embedded newform 66.2.e.a.37.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [66,2,Mod(25,66)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(66, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("66.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 66 = 2 \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	66.e (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$0.527012653340$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			37.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	66.37
Dual form			66.2.e.a.25.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(3.11803 - 2.26538i) q^{5} +(0.809017 - 0.587785i) q^{6} +(0.736068 + 2.26538i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} -3.85410 q^{10} +(-3.23607 - 0.726543i) q^{11} -1.00000 q^{12} +(-1.00000 - 0.726543i) q^{13} +(0.736068 - 2.26538i) q^{14} +(1.19098 + 3.66547i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-5.23607 + 3.80423i) q^{17} +(0.309017 + 0.951057i) q^{18} +(0.381966 - 1.17557i) q^{19} +(3.11803 + 2.26538i) q^{20} -2.38197 q^{21} +(2.19098 + 2.48990i) q^{22} +1.23607 q^{23} +(0.809017 + 0.587785i) q^{24} +(3.04508 - 9.37181i) q^{25} +(0.381966 + 1.17557i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-1.92705 + 1.40008i) q^{28} +(-0.809017 - 2.48990i) q^{29} +(1.19098 - 3.66547i) q^{30} +(-5.16312 - 3.75123i) q^{31} +1.00000 q^{32} +(1.69098 - 2.85317i) q^{33} +6.47214 q^{34} +(7.42705 + 5.39607i) q^{35} +(0.309017 - 0.951057i) q^{36} +(3.23607 + 9.95959i) q^{37} +(-1.00000 + 0.726543i) q^{38} +(1.00000 - 0.726543i) q^{39} +(-1.19098 - 3.66547i) q^{40} +(0.381966 - 1.17557i) q^{41} +(1.92705 + 1.40008i) q^{42} +1.23607 q^{43} +(-0.309017 - 3.30220i) q^{44} -3.85410 q^{45} +(-1.00000 - 0.726543i) q^{46} +(-2.00000 + 6.15537i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(1.07295 - 0.779543i) q^{49} +(-7.97214 + 5.79210i) q^{50} +(-2.00000 - 6.15537i) q^{51} +(0.381966 - 1.17557i) q^{52} +(-2.30902 - 1.67760i) q^{53} -1.00000 q^{54} +(-11.7361 + 5.06555i) q^{55} +2.38197 q^{56} +(1.00000 + 0.726543i) q^{57} +(-0.809017 + 2.48990i) q^{58} +(0.881966 + 2.71441i) q^{59} +(-3.11803 + 2.26538i) q^{60} +(9.09017 - 6.60440i) q^{61} +(1.97214 + 6.06961i) q^{62} +(0.736068 - 2.26538i) q^{63} +(-0.809017 - 0.587785i) q^{64} -4.76393 q^{65} +(-3.04508 + 1.31433i) q^{66} +4.00000 q^{67} +(-5.23607 - 3.80423i) q^{68} +(-0.381966 + 1.17557i) q^{69} +(-2.83688 - 8.73102i) q^{70} +(-2.85410 + 2.07363i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(1.33688 + 4.11450i) q^{73} +(3.23607 - 9.95959i) q^{74} +(7.97214 + 5.79210i) q^{75} +1.23607 q^{76} +(-0.736068 - 7.86572i) q^{77} -1.23607 q^{78} +(-5.11803 - 3.71847i) q^{79} +(-1.19098 + 3.66547i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-1.00000 + 0.726543i) q^{82} +(13.2082 - 9.59632i) q^{83} +(-0.736068 - 2.26538i) q^{84} +(-7.70820 + 23.7234i) q^{85} +(-1.00000 - 0.726543i) q^{86} +2.61803 q^{87} +(-1.69098 + 2.85317i) q^{88} +1.70820 q^{89} +(3.11803 + 2.26538i) q^{90} +(0.909830 - 2.80017i) q^{91} +(0.381966 + 1.17557i) q^{92} +(5.16312 - 3.75123i) q^{93} +(5.23607 - 3.80423i) q^{94} +(-1.47214 - 4.53077i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(3.50000 + 2.54290i) q^{97} -1.32624 q^{98} +(2.19098 + 2.48990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{3} - q^{4} + 8 q^{5} + q^{6} - 6 q^{7} - q^{8} - q^{9} - 2 q^{10} - 4 q^{11} - 4 q^{12} - 4 q^{13} - 6 q^{14} + 7 q^{15} - q^{16} - 12 q^{17} - q^{18} + 6 q^{19} + 8 q^{20} - 14 q^{21}+ \cdots + 11 q^{99}+O(q^{100}) $ 4 * q - q^2 + q^3 - q^4 + 8 * q^5 + q^6 - 6 * q^7 - q^8 - q^9 - 2 * q^10 - 4 * q^11 - 4 * q^12 - 4 * q^13 - 6 * q^14 + 7 * q^15 - q^16 - 12 * q^17 - q^18 + 6 * q^19 + 8 * q^20 - 14 * q^21 + 11 * q^22 - 4 * q^23 + q^24 + q^25 + 6 * q^26 + q^27 - q^28 - q^29 + 7 * q^30 - 5 * q^31 + 4 * q^32 + 9 * q^33 + 8 * q^34 + 23 * q^35 - q^36 + 4 * q^37 - 4 * q^38 + 4 * q^39 - 7 * q^40 + 6 * q^41 + q^42 - 4 * q^43 + q^44 - 2 * q^45 - 4 * q^46 - 8 * q^47 + q^48 + 11 * q^49 - 14 * q^50 - 8 * q^51 + 6 * q^52 - 7 * q^53 - 4 * q^54 - 38 * q^55 + 14 * q^56 + 4 * q^57 - q^58 + 8 * q^59 - 8 * q^60 + 14 * q^61 - 10 * q^62 - 6 * q^63 - q^64 - 28 * q^65 - q^66 + 16 * q^67 - 12 * q^68 - 6 * q^69 - 27 * q^70 + 2 * q^71 - q^72 + 21 * q^73 + 4 * q^74 + 14 * q^75 - 4 * q^76 + 6 * q^77 + 4 * q^78 - 16 * q^79 - 7 * q^80 - q^81 - 4 * q^82 + 26 * q^83 + 6 * q^84 - 4 * q^85 - 4 * q^86 + 6 * q^87 - 9 * q^88 - 20 * q^89 + 8 * q^90 + 26 * q^91 + 6 * q^92 + 5 * q^93 + 12 * q^94 + 12 * q^95 + q^96 + 14 * q^97 + 26 * q^98 + 11 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/66\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	3.11803	−	2.26538i	1.39443	−	1.01311i	0.399064	−	0.916923i	$-0.369335\pi$
$5$	3.11803	−	2.26538i	1.39443	−	1.01311i	0.995363	−	0.0961876i	$-0.0306649\pi$
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	0.736068	+	2.26538i	0.278208	+	0.856235i	0.988353	+	0.152180i	$0.0486292\pi$
$7$	0.736068	+	2.26538i	0.278208	+	0.856235i	−0.710145	+	0.704055i	$0.751371\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−3.85410			−1.21877
$11$	−3.23607	−	0.726543i	−0.975711	−	0.219061i
$11$	−3.23607	−	0.726543i	−0.975711	−	0.219061i
$12$	−1.00000			−0.288675
$13$	−1.00000	−	0.726543i	−0.277350	−	0.201507i	0.440411	−	0.897796i	$-0.354833\pi$
$13$	−1.00000	−	0.726543i	−0.277350	−	0.201507i	−0.717761	+	0.696290i	$0.754833\pi$
$14$	0.736068	−	2.26538i	0.196722	−	0.605449i
$15$	1.19098	+	3.66547i	0.307510	+	0.946420i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−5.23607	+	3.80423i	−1.26993	+	0.922660i	−0.999200	−	0.0399941i	$-0.987266\pi$
$17$	−5.23607	+	3.80423i	−1.26993	+	0.922660i	−0.270733	+	0.962654i	$0.587266\pi$
$18$	0.309017	+	0.951057i	0.0728360	+	0.224166i
$19$	0.381966	−	1.17557i	0.0876290	−	0.269694i	−0.897634	−	0.440742i	$-0.854715\pi$
$19$	0.381966	−	1.17557i	0.0876290	−	0.269694i	0.985263	+	0.171048i	$0.0547153\pi$
$20$	3.11803	+	2.26538i	0.697214	+	0.506555i
$21$	−2.38197			−0.519788
$22$	2.19098	+	2.48990i	0.467119	+	0.530848i
$23$	1.23607			0.257738			0.128869	−	0.991662i	$-0.458865\pi$
$23$	1.23607			0.257738			0.128869	+	0.991662i	$0.458865\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	3.04508	−	9.37181i	0.609017	−	1.87436i
$26$	0.381966	+	1.17557i	0.0749097	+	0.230548i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−1.92705	+	1.40008i	−0.364178	+	0.264591i
$29$	−0.809017	−	2.48990i	−0.150231	−	0.462363i	0.847416	−	0.530930i	$-0.178157\pi$
$29$	−0.809017	−	2.48990i	−0.150231	−	0.462363i	−0.997646	+	0.0685673i	$0.978157\pi$
$30$	1.19098	−	3.66547i	0.217443	−	0.669220i
$31$	−5.16312	−	3.75123i	−0.927324	−	0.673740i	0.0180125	−	0.999838i	$-0.494266\pi$
$31$	−5.16312	−	3.75123i	−0.927324	−	0.673740i	−0.945336	+	0.326098i	$0.894266\pi$
$32$	1.00000			0.176777
$33$	1.69098	−	2.85317i	0.294362	−	0.496673i
$34$	6.47214			1.10996
$35$	7.42705	+	5.39607i	1.25540	+	0.912102i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	3.23607	+	9.95959i	0.532006	+	1.63735i	0.750030	+	0.661404i	$0.230039\pi$
$37$	3.23607	+	9.95959i	0.532006	+	1.63735i	−0.218024	+	0.975943i	$0.569961\pi$
$38$	−1.00000	+	0.726543i	−0.162221	+	0.117861i
$39$	1.00000	−	0.726543i	0.160128	−	0.116340i
$40$	−1.19098	−	3.66547i	−0.188311	−	0.579562i
$41$	0.381966	−	1.17557i	0.0596531	−	0.183593i	−0.916789	−	0.399371i	$-0.869229\pi$
$41$	0.381966	−	1.17557i	0.0596531	−	0.183593i	0.976443	+	0.215778i	$0.0692286\pi$
$42$	1.92705	+	1.40008i	0.297350	+	0.216038i
$43$	1.23607			0.188499			0.0942493	−	0.995549i	$-0.469955\pi$
$43$	1.23607			0.188499			0.0942493	+	0.995549i	$0.469955\pi$
$44$	−0.309017	−	3.30220i	−0.0465861	−	0.497825i
$45$	−3.85410			−0.574536
$46$	−1.00000	−	0.726543i	−0.147442	−	0.107123i
$47$	−2.00000	+	6.15537i	−0.291730	+	0.897853i	0.692570	+	0.721350i	$0.256478\pi$
$47$	−2.00000	+	6.15537i	−0.291730	+	0.897853i	−0.984300	+	0.176502i	$0.943522\pi$
$48$	−0.309017	−	0.951057i	−0.0446028	−	0.137273i
$49$	1.07295	−	0.779543i	0.153278	−	0.111363i
$50$	−7.97214	+	5.79210i	−1.12743	+	0.819126i
$51$	−2.00000	−	6.15537i	−0.280056	−	0.861924i
$52$	0.381966	−	1.17557i	0.0529692	−	0.163022i
$53$	−2.30902	−	1.67760i	−0.317168	−	0.230436i	0.417798	−	0.908540i	$-0.362802\pi$
$53$	−2.30902	−	1.67760i	−0.317168	−	0.230436i	−0.734966	+	0.678104i	$0.762802\pi$
$54$	−1.00000			−0.136083
$55$	−11.7361	+	5.06555i	−1.58249	+	0.683039i
$56$	2.38197			0.318304
$57$	1.00000	+	0.726543i	0.132453	+	0.0962329i
$58$	−0.809017	+	2.48990i	−0.106229	+	0.326940i
$59$	0.881966	+	2.71441i	0.114822	+	0.353386i	0.991910	−	0.126944i	$-0.0405168\pi$
$59$	0.881966	+	2.71441i	0.114822	+	0.353386i	−0.877088	+	0.480330i	$0.840517\pi$
$60$	−3.11803	+	2.26538i	−0.402536	+	0.292460i
$61$	9.09017	−	6.60440i	1.16388	−	0.845606i	0.173614	−	0.984814i	$-0.444456\pi$
$61$	9.09017	−	6.60440i	1.16388	−	0.845606i	0.990263	+	0.139208i	$0.0444556\pi$
$62$	1.97214	+	6.06961i	0.250462	+	0.770841i
$63$	0.736068	−	2.26538i	0.0927358	−	0.285412i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−4.76393			−0.590893
$66$	−3.04508	+	1.31433i	−0.374824	+	0.161783i
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$	−5.23607	−	3.80423i	−0.634967	−	0.461330i
$69$	−0.381966	+	1.17557i	−0.0459833	+	0.141522i
$70$	−2.83688	−	8.73102i	−0.339072	−	1.04356i
$71$	−2.85410	+	2.07363i	−0.338720	+	0.246094i	−0.744121	−	0.668044i	$-0.767132\pi$
$71$	−2.85410	+	2.07363i	−0.338720	+	0.246094i	0.405402	+	0.914139i	$0.367132\pi$
$72$	−0.809017	+	0.587785i	−0.0953436	+	0.0692712i
$73$	1.33688	+	4.11450i	0.156470	+	0.481565i	0.998307	−	0.0581668i	$-0.0185255\pi$
$73$	1.33688	+	4.11450i	0.156470	+	0.481565i	−0.841837	+	0.539732i	$0.818526\pi$
$74$	3.23607	−	9.95959i	0.376185	−	1.15778i
$75$	7.97214	+	5.79210i	0.920543	+	0.668814i
$76$	1.23607			0.141787
$77$	−0.736068	−	7.86572i	−0.0838827	−	0.896382i
$78$	−1.23607			−0.139957
$79$	−5.11803	−	3.71847i	−0.575824	−	0.418360i	0.261392	−	0.965233i	$-0.415818\pi$
$79$	−5.11803	−	3.71847i	−0.575824	−	0.418360i	−0.837216	+	0.546872i	$0.815818\pi$
$80$	−1.19098	+	3.66547i	−0.133156	+	0.409812i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−1.00000	+	0.726543i	−0.110432	+	0.0802332i
$83$	13.2082	−	9.59632i	1.44979	−	1.05333i	0.463908	−	0.885883i	$-0.346447\pi$
$83$	13.2082	−	9.59632i	1.44979	−	1.05333i	0.985881	−	0.167450i	$-0.0535532\pi$
$84$	−0.736068	−	2.26538i	−0.0803116	−	0.247174i
$85$	−7.70820	+	23.7234i	−0.836072	+	2.57317i
$86$	−1.00000	−	0.726543i	−0.107833	−	0.0783451i
$87$	2.61803			0.280683
$88$	−1.69098	+	2.85317i	−0.180259	+	0.304149i
$89$	1.70820			0.181069			0.0905346	−	0.995893i	$-0.471142\pi$
$89$	1.70820			0.181069			0.0905346	+	0.995893i	$0.471142\pi$
$90$	3.11803	+	2.26538i	0.328670	+	0.238792i
$91$	0.909830	−	2.80017i	0.0953761	−	0.293537i
$92$	0.381966	+	1.17557i	0.0398227	+	0.122562i
$93$	5.16312	−	3.75123i	0.535390	−	0.388984i
$94$	5.23607	−	3.80423i	0.540059	−	0.392376i
$95$	−1.47214	−	4.53077i	−0.151038	−	0.464847i
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	3.50000	+	2.54290i	0.355371	+	0.258192i	0.751119	−	0.660167i	$-0.229515\pi$
$97$	3.50000	+	2.54290i	0.355371	+	0.258192i	−0.395748	+	0.918359i	$0.629515\pi$
$98$	−1.32624			−0.133970
$99$	2.19098	+	2.48990i	0.220202	+	0.250244i
$100$	9.85410			0.985410
$101$	11.8262	+	8.59226i	1.17675	+	0.854962i	0.991802	−	0.127785i	$-0.0407868\pi$
$101$	11.8262	+	8.59226i	1.17675	+	0.854962i	0.184953	+	0.982747i	$0.440787\pi$
$102$	−2.00000	+	6.15537i	−0.198030	+	0.609472i
$103$	−5.26393	−	16.2007i	−0.518671	−	1.59630i	−0.776502	−	0.630114i	$-0.783008\pi$
$103$	−5.26393	−	16.2007i	−0.518671	−	1.59630i	0.257832	−	0.966190i	$-0.416992\pi$
$104$	−1.00000	+	0.726543i	−0.0980581	+	0.0712434i
$105$	−7.42705	+	5.39607i	−0.724806	+	0.526602i
$106$	0.881966	+	2.71441i	0.0856641	+	0.263647i
$107$	2.35410	−	7.24518i	0.227580	−	0.700418i	−0.770440	−	0.637513i	$-0.779963\pi$
$107$	2.35410	−	7.24518i	0.227580	−	0.700418i	0.998019	−	0.0629054i	$-0.0200366\pi$
$108$	0.809017	+	0.587785i	0.0778477	+	0.0565597i
$109$	−9.41641			−0.901928			−0.450964	−	0.892542i	$-0.648920\pi$
$109$	−9.41641			−0.901928			−0.450964	+	0.892542i	$0.648920\pi$
$110$	12.4721	+	2.80017i	1.18917	+	0.266986i
$111$	−10.4721			−0.993971
$112$	−1.92705	−	1.40008i	−0.182089	−	0.132296i
$113$	−1.09017	+	3.35520i	−0.102555	+	0.315630i	−0.989149	−	0.146918i	$-0.953065\pi$
$113$	−1.09017	+	3.35520i	−0.102555	+	0.315630i	0.886594	+	0.462548i	$0.153065\pi$
$114$	−0.381966	−	1.17557i	−0.0357744	−	0.110102i
$115$	3.85410	−	2.80017i	0.359397	−	0.261117i
$116$	2.11803	−	1.53884i	0.196655	−	0.142878i
$117$	0.381966	+	1.17557i	0.0353128	+	0.108682i
$118$	0.881966	−	2.71441i	0.0811916	−	0.249882i
$119$	−12.4721	−	9.06154i	−1.14332	−	0.830670i
$120$	3.85410			0.351830
$121$	9.94427	+	4.70228i	0.904025	+	0.427480i
$122$	−11.2361			−1.01727
$123$	1.00000	+	0.726543i	0.0901670	+	0.0655101i
$124$	1.97214	−	6.06961i	0.177103	−	0.545067i
$125$	−5.78115	−	17.7926i	−0.517082	−	1.59141i
$126$	−1.92705	+	1.40008i	−0.171675	+	0.124729i
$127$	−9.70820	+	7.05342i	−0.861464	+	0.625890i	−0.928283	−	0.371875i	$-0.878715\pi$
$127$	−9.70820	+	7.05342i	−0.861464	+	0.625890i	0.0668190	+	0.997765i	$0.478715\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−0.381966	+	1.17557i	−0.0336302	+	0.103503i
$130$	3.85410	+	2.80017i	0.338027	+	0.245591i
$131$	18.2705			1.59630			0.798151	−	0.602458i	$-0.205812\pi$
$131$	18.2705			1.59630			0.798151	+	0.602458i	$0.205812\pi$
$132$	3.23607	+	0.726543i	0.281664	+	0.0632374i
$133$	2.94427			0.255301
$134$	−3.23607	−	2.35114i	−0.279554	−	0.203108i
$135$	1.19098	−	3.66547i	0.102503	−	0.315473i
$136$	2.00000	+	6.15537i	0.171499	+	0.527818i
$137$	−13.8541	+	10.0656i	−1.18364	+	0.859962i	−0.992577	−	0.121617i	$-0.961192\pi$
$137$	−13.8541	+	10.0656i	−1.18364	+	0.859962i	−0.191059	+	0.981579i	$0.561192\pi$
$138$	1.00000	−	0.726543i	0.0851257	−	0.0618474i
$139$	2.70820	+	8.33499i	0.229707	+	0.706965i	0.997780	+	0.0666024i	$0.0212159\pi$
$139$	2.70820	+	8.33499i	0.229707	+	0.706965i	−0.768073	+	0.640363i	$0.778784\pi$
$140$	−2.83688	+	8.73102i	−0.239760	+	0.737906i
$141$	−5.23607	−	3.80423i	−0.440956	−	0.320374i
$142$	3.52786			0.296052
$143$	2.70820	+	3.07768i	0.226471	+	0.257369i
$144$	1.00000			0.0833333
$145$	−8.16312	−	5.93085i	−0.677910	−	0.492531i
$146$	1.33688	−	4.11450i	0.110641	−	0.340518i
$147$	0.409830	+	1.26133i	0.0338022	+	0.104033i
$148$	−8.47214	+	6.15537i	−0.696405	+	0.505968i
$149$	−2.92705	+	2.12663i	−0.239793	+	0.174220i	−0.701191	−	0.712973i	$-0.747348\pi$
$149$	−2.92705	+	2.12663i	−0.239793	+	0.174220i	0.461398	+	0.887193i	$0.347348\pi$
$150$	−3.04508	−	9.37181i	−0.248630	−	0.765205i
$151$	−1.95492	+	6.01661i	−0.159089	+	0.489625i	−0.998552	−	0.0537914i	$-0.982869\pi$
$151$	−1.95492	+	6.01661i	−0.159089	+	0.489625i	0.839463	+	0.543416i	$0.182869\pi$
$152$	−1.00000	−	0.726543i	−0.0811107	−	0.0589304i
$153$	6.47214			0.523241
$154$	−4.02786	+	6.79615i	−0.324575	+	0.547650i
$155$	−24.5967			−1.97566
$156$	1.00000	+	0.726543i	0.0800641	+	0.0581700i
$157$	−1.38197	+	4.25325i	−0.110293	+	0.339447i	−0.990936	−	0.134333i	$-0.957111\pi$
$157$	−1.38197	+	4.25325i	−0.110293	+	0.339447i	0.880643	+	0.473780i	$0.157111\pi$
$158$	1.95492	+	6.01661i	0.155525	+	0.478656i
$159$	2.30902	−	1.67760i	0.183117	−	0.133042i
$160$	3.11803	−	2.26538i	0.246502	−	0.179094i
$161$	0.909830	+	2.80017i	0.0717047	+	0.220684i
$162$	0.309017	−	0.951057i	0.0242787	−	0.0747221i
$163$	−10.8541	−	7.88597i	−0.850159	−	0.617677i	0.0750310	−	0.997181i	$-0.476094\pi$
$163$	−10.8541	−	7.88597i	−0.850159	−	0.617677i	−0.925190	+	0.379505i	$0.876094\pi$
$164$	1.23607			0.0965207
$165$	−1.19098	−	12.7270i	−0.0927179	−	0.990796i
$166$	−16.3262			−1.26716
$167$	−2.23607	−	1.62460i	−0.173032	−	0.125715i	0.497899	−	0.867235i	$-0.334105\pi$
$167$	−2.23607	−	1.62460i	−0.173032	−	0.125715i	−0.670931	+	0.741520i	$0.734105\pi$
$168$	−0.736068	+	2.26538i	−0.0567889	+	0.174778i
$169$	−3.54508	−	10.9106i	−0.272699	−	0.839281i
$170$	20.1803	−	14.6619i	1.54776	−	1.12451i
$171$	−1.00000	+	0.726543i	−0.0764719	+	0.0555601i
$172$	0.381966	+	1.17557i	0.0291246	+	0.0896364i
$173$	−3.35410	+	10.3229i	−0.255008	+	0.784833i	0.738821	+	0.673902i	$0.235383\pi$
$173$	−3.35410	+	10.3229i	−0.255008	+	0.784833i	−0.993828	+	0.110931i	$0.964617\pi$
$174$	−2.11803	−	1.53884i	−0.160568	−	0.116659i
$175$	23.4721			1.77433
$176$	3.04508	−	1.31433i	0.229532	−	0.0990712i
$177$	−2.85410			−0.214527
$178$	−1.38197	−	1.00406i	−0.103583	−	0.0752573i
$179$	−2.66312	+	8.19624i	−0.199051	+	0.612616i	0.800855	+	0.598859i	$0.204379\pi$
$179$	−2.66312	+	8.19624i	−0.199051	+	0.612616i	−0.999905	+	0.0137566i	$0.995621\pi$
$180$	−1.19098	−	3.66547i	−0.0887706	−	0.273208i
$181$	6.09017	−	4.42477i	0.452679	−	0.328890i	−0.337974	−	0.941156i	$-0.609742\pi$
$181$	6.09017	−	4.42477i	0.452679	−	0.328890i	0.790652	+	0.612265i	$0.209742\pi$
$182$	−2.38197	+	1.73060i	−0.176563	+	0.128281i
$183$	3.47214	+	10.6861i	0.256668	+	0.789942i
$184$	0.381966	−	1.17557i	0.0281589	−	0.0866642i
$185$	32.6525	+	23.7234i	2.40066	+	1.74418i
$186$	−6.38197			−0.467948
$187$	19.7082	−	8.50651i	1.44121	−	0.622057i
$188$	−6.47214			−0.472029
$189$	1.92705	+	1.40008i	0.140172	+	0.101841i
$190$	−1.47214	+	4.53077i	−0.106800	+	0.328697i
$191$	4.18034	+	12.8658i	0.302479	+	0.930934i	0.980606	+	0.195989i	$0.0627918\pi$
$191$	4.18034	+	12.8658i	0.302479	+	0.930934i	−0.678127	+	0.734945i	$0.737208\pi$
$192$	0.809017	−	0.587785i	0.0583858	−	0.0424197i
$193$	12.3992	−	9.00854i	0.892513	−	0.648449i	−0.0440190	−	0.999031i	$-0.514016\pi$
$193$	12.3992	−	9.00854i	0.892513	−	0.648449i	0.936532	+	0.350582i	$0.114016\pi$
$194$	−1.33688	−	4.11450i	−0.0959825	−	0.295404i
$195$	1.47214	−	4.53077i	0.105422	−	0.324455i
$196$	1.07295	+	0.779543i	0.0766392	+	0.0556816i
$197$	−5.09017			−0.362660			−0.181330	−	0.983422i	$-0.558040\pi$
$197$	−5.09017			−0.362660			−0.181330	+	0.983422i	$0.558040\pi$
$198$	−0.309017	−	3.30220i	−0.0219609	−	0.234677i
$199$	19.8541			1.40742			0.703710	−	0.710487i	$-0.251525\pi$
$199$	19.8541			1.40742			0.703710	+	0.710487i	$0.251525\pi$
$200$	−7.97214	−	5.79210i	−0.563715	−	0.409563i
$201$	−1.23607	+	3.80423i	−0.0871855	+	0.268329i
$202$	−4.51722	−	13.9026i	−0.317831	−	0.978182i
$203$	5.04508	−	3.66547i	0.354096	−	0.257265i
$204$	5.23607	−	3.80423i	0.366598	−	0.266349i
$205$	−1.47214	−	4.53077i	−0.102818	−	0.316443i
$206$	−5.26393	+	16.2007i	−0.366756	+	1.12876i
$207$	−1.00000	−	0.726543i	−0.0695048	−	0.0504982i
$208$	1.23607			0.0857059
$209$	−2.09017	+	3.52671i	−0.144580	+	0.243948i
$210$	9.18034			0.633504
$211$	−21.5623	−	15.6659i	−1.48441	−	1.07849i	−0.976102	−	0.217312i	$-0.930271\pi$
$211$	−21.5623	−	15.6659i	−1.48441	−	1.07849i	−0.508308	−	0.861175i	$-0.669729\pi$
$212$	0.881966	−	2.71441i	0.0605737	−	0.186427i
$213$	−1.09017	−	3.35520i	−0.0746972	−	0.229894i
$214$	−6.16312	+	4.47777i	−0.421302	+	0.306094i
$215$	3.85410	−	2.80017i	0.262848	−	0.190970i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	4.69756	−	14.4576i	0.318891	−	0.981446i
$218$	7.61803	+	5.53483i	0.515958	+	0.374866i
$219$	−4.32624			−0.292340
$220$	−8.44427	−	9.59632i	−0.569313	−	0.646984i
$221$	8.00000			0.538138
$222$	8.47214	+	6.15537i	0.568613	+	0.413121i
$223$	−4.04508	+	12.4495i	−0.270879	+	0.833680i	0.719402	+	0.694594i	$0.244416\pi$
$223$	−4.04508	+	12.4495i	−0.270879	+	0.833680i	−0.990280	+	0.139085i	$0.955584\pi$
$224$	0.736068	+	2.26538i	0.0491806	+	0.151362i
$225$	−7.97214	+	5.79210i	−0.531476	+	0.386140i
$226$	2.85410	−	2.07363i	0.189852	−	0.137936i
$227$	−4.28115	−	13.1760i	−0.284150	−	0.874524i	−0.986652	−	0.162842i	$-0.947934\pi$
$227$	−4.28115	−	13.1760i	−0.284150	−	0.874524i	0.702502	−	0.711682i	$-0.252066\pi$
$228$	−0.381966	+	1.17557i	−0.0252963	+	0.0778541i
$229$	−4.09017	−	2.97168i	−0.270286	−	0.196374i	0.444383	−	0.895837i	$-0.353423\pi$
$229$	−4.09017	−	2.97168i	−0.270286	−	0.196374i	−0.714669	+	0.699462i	$0.753423\pi$
$230$	−4.76393			−0.314124
$231$	7.70820	+	1.73060i	0.507163	+	0.113865i
$232$	−2.61803			−0.171882
$233$	−7.23607	−	5.25731i	−0.474051	−	0.344418i	0.324967	−	0.945725i	$-0.394647\pi$
$233$	−7.23607	−	5.25731i	−0.474051	−	0.344418i	−0.799018	+	0.601307i	$0.794647\pi$
$234$	0.381966	−	1.17557i	0.0249699	−	0.0768494i
$235$	7.70820	+	23.7234i	0.502828	+	1.54754i
$236$	−2.30902	+	1.67760i	−0.150304	+	0.109202i
$237$	5.11803	−	3.71847i	0.332452	−	0.241541i
$238$	4.76393	+	14.6619i	0.308800	+	0.950388i
$239$	−2.32624	+	7.15942i	−0.150472	+	0.463105i	−0.997674	−	0.0681660i	$-0.978285\pi$
$239$	−2.32624	+	7.15942i	−0.150472	+	0.463105i	0.847202	+	0.531271i	$0.178285\pi$
$240$	−3.11803	−	2.26538i	−0.201268	−	0.146230i
$241$	−22.5623			−1.45337			−0.726683	−	0.686973i	$-0.758939\pi$
$241$	−22.5623			−1.45337			−0.726683	+	0.686973i	$0.758939\pi$
$242$	−5.28115	−	9.64932i	−0.339485	−	0.620282i
$243$	−1.00000			−0.0641500
$244$	9.09017	+	6.60440i	0.581938	+	0.422803i
$245$	1.57953	−	4.86128i	0.100912	−	0.310576i
$246$	−0.381966	−	1.17557i	−0.0243533	−	0.0749516i
$247$	−1.23607	+	0.898056i	−0.0786491	+	0.0571419i
$248$	−5.16312	+	3.75123i	−0.327858	+	0.238203i
$249$	5.04508	+	15.5272i	0.319719	+	0.983995i
$250$	−5.78115	+	17.7926i	−0.365632	+	1.12530i
$251$	2.97214	+	2.15938i	0.187600	+	0.136299i	0.677621	−	0.735411i	$-0.263011\pi$
$251$	2.97214	+	2.15938i	0.187600	+	0.136299i	−0.490021	+	0.871710i	$0.663011\pi$
$252$	2.38197			0.150050
$253$	−4.00000	−	0.898056i	−0.251478	−	0.0564603i
$254$	12.0000			0.752947
$255$	−20.1803	−	14.6619i	−1.26374	−	0.918162i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−7.47214	−	22.9969i	−0.466099	−	1.43451i	−0.857595	−	0.514326i	$-0.828042\pi$
$257$	−7.47214	−	22.9969i	−0.466099	−	1.43451i	0.391496	−	0.920180i	$-0.371958\pi$
$258$	1.00000	−	0.726543i	0.0622573	−	0.0452326i
$259$	−20.1803	+	14.6619i	−1.25395	+	0.911045i
$260$	−1.47214	−	4.53077i	−0.0912980	−	0.280986i
$261$	−0.809017	+	2.48990i	−0.0500769	+	0.154121i
$262$	−14.7812	−	10.7391i	−0.913183	−	0.663466i
$263$	−5.70820			−0.351983			−0.175991	−	0.984392i	$-0.556313\pi$
$263$	−5.70820			−0.351983			−0.175991	+	0.984392i	$0.556313\pi$
$264$	−2.19098	−	2.48990i	−0.134846	−	0.153243i
$265$	−11.0000			−0.675725
$266$	−2.38197	−	1.73060i	−0.146048	−	0.106110i
$267$	−0.527864	+	1.62460i	−0.0323048	+	0.0994238i
$268$	1.23607	+	3.80423i	0.0755049	+	0.232380i
$269$	−12.0902	+	8.78402i	−0.737151	+	0.535571i	−0.891817	−	0.452395i	$-0.850570\pi$
$269$	−12.0902	+	8.78402i	−0.737151	+	0.535571i	0.154667	+	0.987967i	$0.450570\pi$
$270$	−3.11803	+	2.26538i	−0.189758	+	0.137867i
$271$	−1.05573	−	3.24920i	−0.0641309	−	0.197375i	0.913857	−	0.406036i	$-0.133089\pi$
$271$	−1.05573	−	3.24920i	−0.0641309	−	0.197375i	−0.977988	+	0.208662i	$0.933089\pi$
$272$	2.00000	−	6.15537i	0.121268	−	0.373224i
$273$	2.38197	+	1.73060i	0.144163	+	0.104741i
$274$	17.1246			1.03454
$275$	−16.6631	+	28.1154i	−1.00482	+	1.69542i
$276$	−1.23607			−0.0744025
$277$	23.5623	+	17.1190i	1.41572	+	1.02858i	0.992459	+	0.122575i	$0.0391152\pi$
$277$	23.5623	+	17.1190i	1.41572	+	1.02858i	0.423262	+	0.906007i	$0.360885\pi$
$278$	2.70820	−	8.33499i	0.162427	−	0.499900i
$279$	1.97214	+	6.06961i	0.118069	+	0.363378i
$280$	7.42705	−	5.39607i	0.443851	−	0.322477i
$281$	13.8541	−	10.0656i	0.826466	−	0.600463i	−0.0920910	−	0.995751i	$-0.529355\pi$
$281$	13.8541	−	10.0656i	0.826466	−	0.600463i	0.918557	+	0.395288i	$0.129355\pi$
$282$	2.00000	+	6.15537i	0.119098	+	0.366547i
$283$	3.67376	−	11.3067i	0.218382	−	0.672112i	−0.780514	−	0.625139i	$-0.785042\pi$
$283$	3.67376	−	11.3067i	0.218382	−	0.672112i	0.998896	−	0.0469734i	$-0.0149576\pi$
$284$	−2.85410	−	2.07363i	−0.169360	−	0.123047i
$285$	4.76393			0.282191
$286$	−0.381966	−	4.08174i	−0.0225861	−	0.241358i
$287$	2.94427			0.173795
$288$	−0.809017	−	0.587785i	−0.0476718	−	0.0346356i
$289$	7.69098	−	23.6704i	0.452411	−	1.39238i
$290$	3.11803	+	9.59632i	0.183097	+	0.563515i
$291$	−3.50000	+	2.54290i	−0.205174	+	0.149067i
$292$	−3.50000	+	2.54290i	−0.204822	+	0.148812i
$293$	−7.40983	−	22.8051i	−0.432887	−	1.33229i	−0.895237	−	0.445591i	$-0.852994\pi$
$293$	−7.40983	−	22.8051i	−0.432887	−	1.33229i	0.462350	−	0.886698i	$-0.347006\pi$
$294$	0.409830	−	1.26133i	0.0239018	−	0.0735621i
$295$	8.89919	+	6.46564i	0.518131	+	0.376444i
$296$	10.4721			0.608681
$297$	−3.04508	+	1.31433i	−0.176694	+	0.0762650i
$298$	3.61803			0.209587
$299$	−1.23607	−	0.898056i	−0.0714837	−	0.0519359i
$300$	−3.04508	+	9.37181i	−0.175808	+	0.541082i
$301$	0.909830	+	2.80017i	0.0524417	+	0.161399i
$302$	5.11803	−	3.71847i	0.294510	−	0.213974i
$303$	−11.8262	+	8.59226i	−0.679400	+	0.493613i
$304$	0.381966	+	1.17557i	0.0219073	+	0.0674236i
$305$	13.3820	−	41.1855i	0.766249	−	2.35827i
$306$	−5.23607	−	3.80423i	−0.299326	−	0.217473i
$307$	14.6525			0.836261			0.418130	−	0.908387i	$-0.362685\pi$
$307$	14.6525			0.836261			0.418130	+	0.908387i	$0.362685\pi$
$308$	7.25329	−	3.13068i	0.413294	−	0.178387i
$309$	17.0344			0.969056
$310$	19.8992	+	14.4576i	1.13020	+	0.821137i
$311$	3.67376	−	11.3067i	0.208320	−	0.641143i	−0.791241	−	0.611505i	$-0.790565\pi$
$311$	3.67376	−	11.3067i	0.208320	−	0.641143i	0.999561	−	0.0296381i	$-0.00943548\pi$
$312$	−0.381966	−	1.17557i	−0.0216246	−	0.0665536i
$313$	−17.6803	+	12.8455i	−0.999352	+	0.726072i	−0.961949	−	0.273229i	$-0.911908\pi$
$313$	−17.6803	+	12.8455i	−0.999352	+	0.726072i	−0.0374028	+	0.999300i	$0.511908\pi$
$314$	3.61803	−	2.62866i	0.204177	−	0.148344i
$315$	−2.83688	−	8.73102i	−0.159840	−	0.491937i
$316$	1.95492	−	6.01661i	0.109973	−	0.338461i
$317$	−12.8541	−	9.33905i	−0.721958	−	0.524533i	0.165051	−	0.986285i	$-0.447221\pi$
$317$	−12.8541	−	9.33905i	−0.721958	−	0.524533i	−0.887009	+	0.461752i	$0.847221\pi$
$318$	−2.85410			−0.160050
$319$	0.809017	+	8.64527i	0.0452963	+	0.484042i
$320$	−3.85410			−0.215451
$321$	6.16312	+	4.47777i	0.343992	+	0.249925i
$322$	0.909830	−	2.80017i	0.0507028	−	0.156047i
$323$	2.47214	+	7.60845i	0.137553	+	0.423346i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	−9.85410	+	7.15942i	−0.546607	+	0.397133i
$326$	4.14590	+	12.7598i	0.229620	+	0.706698i
$327$	2.90983	−	8.95554i	0.160914	−	0.495242i
$328$	−1.00000	−	0.726543i	−0.0552158	−	0.0401166i
$329$	−15.4164			−0.849934
$330$	−6.51722	+	10.9964i	−0.358761	+	0.605332i
$331$	−8.94427			−0.491622			−0.245811	−	0.969318i	$-0.579054\pi$
$331$	−8.94427			−0.491622			−0.245811	+	0.969318i	$0.579054\pi$
$332$	13.2082	+	9.59632i	0.724894	+	0.526667i
$333$	3.23607	−	9.95959i	0.177335	−	0.545782i
$334$	0.854102	+	2.62866i	0.0467344	+	0.143834i
$335$	12.4721	−	9.06154i	0.681426	−	0.495085i
$336$	1.92705	−	1.40008i	0.105129	−	0.0763809i
$337$	−3.38197	−	10.4086i	−0.184227	−	0.566994i	0.815707	−	0.578466i	$-0.196348\pi$
$337$	−3.38197	−	10.4086i	−0.184227	−	0.566994i	−0.999934	+	0.0114719i	$0.996348\pi$
$338$	−3.54508	+	10.9106i	−0.192827	+	0.593461i
$339$	−2.85410	−	2.07363i	−0.155014	−	0.112624i
$340$	−24.9443			−1.35279
$341$	13.9828	+	15.8904i	0.757210	+	0.860516i
$342$	1.23607			0.0668389
$343$	16.0451	+	11.6574i	0.866353	+	0.629442i
$344$	0.381966	−	1.17557i	0.0205942	−	0.0633825i
$345$	1.47214	+	4.53077i	0.0792571	+	0.243928i
$346$	8.78115	−	6.37988i	0.472078	−	0.342985i
$347$	−4.16312	+	3.02468i	−0.223488	+	0.162373i	−0.693895	−	0.720076i	$-0.744107\pi$
$347$	−4.16312	+	3.02468i	−0.223488	+	0.162373i	0.470407	+	0.882449i	$0.344107\pi$
$348$	0.809017	+	2.48990i	0.0433679	+	0.133473i
$349$	−2.70820	+	8.33499i	−0.144967	+	0.446162i	−0.997007	−	0.0773148i	$-0.975365\pi$
$349$	−2.70820	+	8.33499i	−0.144967	+	0.446162i	0.852040	+	0.523477i	$0.175365\pi$
$350$	−18.9894	−	13.7966i	−1.01502	−	0.737458i
$351$	−1.23607			−0.0659764
$352$	−3.23607	−	0.726543i	−0.172483	−	0.0387248i
$353$	27.5967			1.46883			0.734413	−	0.678702i	$-0.237457\pi$
$353$	27.5967			1.46883			0.734413	+	0.678702i	$0.237457\pi$
$354$	2.30902	+	1.67760i	0.122723	+	0.0891634i
$355$	−4.20163	+	12.9313i	−0.222999	+	0.686321i
$356$	0.527864	+	1.62460i	0.0279767	+	0.0861035i
$357$	12.4721	−	9.06154i	0.660095	−	0.479587i
$358$	6.97214	−	5.06555i	0.368489	−	0.267723i
$359$	5.32624	+	16.3925i	0.281108	+	0.865162i	0.987538	+	0.157379i	$0.0503044\pi$
$359$	5.32624	+	16.3925i	0.281108	+	0.865162i	−0.706430	+	0.707783i	$0.749696\pi$
$360$	−1.19098	+	3.66547i	−0.0627703	+	0.193187i
$361$	14.1353	+	10.2699i	0.743961	+	0.540519i
$362$	−7.52786			−0.395656
$363$	−7.54508	+	8.00448i	−0.396014	+	0.420126i
$364$	2.94427			0.154322
$365$	13.4894	+	9.80059i	0.706065	+	0.512986i
$366$	3.47214	−	10.6861i	0.181491	−	0.558573i
$367$	0.156541	+	0.481784i	0.00817138	+	0.0251489i	0.955059	−	0.296416i	$-0.0957913\pi$
$367$	0.156541	+	0.481784i	0.00817138	+	0.0251489i	−0.946888	+	0.321564i	$0.895791\pi$
$368$	−1.00000	+	0.726543i	−0.0521286	+	0.0378736i
$369$	−1.00000	+	0.726543i	−0.0520579	+	0.0378223i
$370$	−12.4721	−	38.3853i	−0.648395	−	1.99556i
$371$	2.10081	−	6.46564i	0.109069	−	0.335679i
$372$	5.16312	+	3.75123i	0.267695	+	0.194492i
$373$	−18.4721			−0.956451			−0.478225	−	0.878237i	$-0.658720\pi$
$373$	−18.4721			−0.956451			−0.478225	+	0.878237i	$0.658720\pi$
$374$	−20.9443	−	4.70228i	−1.08300	−	0.243149i
$375$	18.7082			0.966087
$376$	5.23607	+	3.80423i	0.270030	+	0.196188i
$377$	−1.00000	+	3.07768i	−0.0515026	+	0.158509i
$378$	−0.736068	−	2.26538i	−0.0378593	−	0.116519i
$379$	7.85410	−	5.70634i	0.403438	−	0.293115i	−0.367502	−	0.930023i	$-0.619787\pi$
$379$	7.85410	−	5.70634i	0.403438	−	0.293115i	0.770940	+	0.636908i	$0.219787\pi$
$380$	3.85410	−	2.80017i	0.197711	−	0.143646i
$381$	−3.70820	−	11.4127i	−0.189977	−	0.584689i
$382$	4.18034	−	12.8658i	0.213885	−	0.658270i
$383$	−7.09017	−	5.15131i	−0.362291	−	0.263220i	0.391716	−	0.920086i	$-0.371882\pi$
$383$	−7.09017	−	5.15131i	−0.362291	−	0.263220i	−0.754007	+	0.656866i	$0.771882\pi$
$384$	−1.00000			−0.0510310
$385$	−20.1140	−	22.8581i	−1.02510	−	1.16496i
$386$	−15.3262			−0.780085
$387$	−1.00000	−	0.726543i	−0.0508329	−	0.0369322i
$388$	−1.33688	+	4.11450i	−0.0678699	+	0.208882i
$389$	6.50658	+	20.0252i	0.329897	+	1.01532i	0.969182	+	0.246347i	$0.0792304\pi$
$389$	6.50658	+	20.0252i	0.329897	+	1.01532i	−0.639285	+	0.768970i	$0.720770\pi$
$390$	−3.85410	+	2.80017i	−0.195160	+	0.141792i
$391$	−6.47214	+	4.70228i	−0.327310	+	0.237805i
$392$	−0.409830	−	1.26133i	−0.0206995	−	0.0637066i
$393$	−5.64590	+	17.3763i	−0.284798	+	0.876518i
$394$	4.11803	+	2.99193i	0.207464	+	0.150731i
$395$	−24.3820			−1.22679
$396$	−1.69098	+	2.85317i	−0.0849751	+	0.143377i
$397$	−25.8885			−1.29931			−0.649654	−	0.760230i	$-0.725086\pi$
$397$	−25.8885			−1.29931			−0.649654	+	0.760230i	$0.725086\pi$
$398$	−16.0623	−	11.6699i	−0.805131	−	0.584962i
$399$	−0.909830	+	2.80017i	−0.0455485	+	0.140184i
$400$	3.04508	+	9.37181i	0.152254	+	0.468590i
$401$	−19.1803	+	13.9353i	−0.957820	+	0.695897i	−0.952644	−	0.304089i	$-0.901648\pi$
$401$	−19.1803	+	13.9353i	−0.957820	+	0.695897i	−0.00517693	+	0.999987i	$0.501648\pi$
$402$	3.23607	−	2.35114i	0.161400	−	0.117264i
$403$	2.43769	+	7.50245i	0.121430	+	0.373724i
$404$	−4.51722	+	13.9026i	−0.224740	+	0.691679i
$405$	3.11803	+	2.26538i	0.154936	+	0.112568i
$406$	−6.23607			−0.309491
$407$	−3.23607	−	34.5811i	−0.160406	−	1.71412i
$408$	−6.47214			−0.320418
$409$	0.736068	+	0.534785i	0.0363962	+	0.0264434i	0.605835	−	0.795591i	$-0.292839\pi$
$409$	0.736068	+	0.534785i	0.0363962	+	0.0264434i	−0.569438	+	0.822034i	$0.692839\pi$
$410$	−1.47214	+	4.53077i	−0.0727036	+	0.223759i
$411$	−5.29180	−	16.2865i	−0.261025	−	0.803353i
$412$	13.7812	−	10.0126i	0.678949	−	0.493285i
$413$	−5.50000	+	3.99598i	−0.270637	+	0.196630i
$414$	0.381966	+	1.17557i	0.0187726	+	0.0577761i
$415$	19.4443	−	59.8433i	0.954482	−	2.93759i
$416$	−1.00000	−	0.726543i	−0.0490290	−	0.0356217i
$417$	−8.76393			−0.429172
$418$	3.76393	−	1.62460i	0.184100	−	0.0794617i
$419$	28.9787			1.41570			0.707851	−	0.706361i	$-0.249665\pi$
$419$	28.9787			1.41570			0.707851	+	0.706361i	$0.249665\pi$
$420$	−7.42705	−	5.39607i	−0.362403	−	0.263301i
$421$	−1.58359	+	4.87380i	−0.0771796	+	0.237534i	−0.982201	−	0.187831i	$-0.939854\pi$
$421$	−1.58359	+	4.87380i	−0.0771796	+	0.237534i	0.905022	+	0.425365i	$0.139854\pi$
$422$	8.23607	+	25.3480i	0.400926	+	1.23392i
$423$	5.23607	−	3.80423i	0.254586	−	0.184968i
$424$	−2.30902	+	1.67760i	−0.112136	+	0.0814714i
$425$	19.7082	+	60.6556i	0.955988	+	2.94223i
$426$	−1.09017	+	3.35520i	−0.0528189	+	0.162560i
$427$	21.6525	+	15.7314i	1.04784	+	0.761298i
$428$	7.61803			0.368232
$429$	−3.76393	+	1.62460i	−0.181724	+	0.0784364i
$430$	−4.76393			−0.229737
$431$	2.23607	+	1.62460i	0.107708	+	0.0782542i	0.640335	−	0.768095i	$-0.278795\pi$
$431$	2.23607	+	1.62460i	0.107708	+	0.0782542i	−0.532628	+	0.846350i	$0.678795\pi$
$432$	−0.309017	+	0.951057i	−0.0148676	+	0.0457577i
$433$	−1.02786	−	3.16344i	−0.0493960	−	0.152025i	0.923316	−	0.384041i	$-0.125468\pi$
$433$	−1.02786	−	3.16344i	−0.0493960	−	0.152025i	−0.972712	+	0.232016i	$0.925468\pi$
$434$	−12.2984	+	8.93529i	−0.590341	+	0.428908i
$435$	8.16312	−	5.93085i	0.391392	−	0.284363i
$436$	−2.90983	−	8.95554i	−0.139356	−	0.428892i
$437$	0.472136	−	1.45309i	0.0225853	−	0.0695105i
$438$	3.50000	+	2.54290i	0.167236	+	0.121504i
$439$	−13.0344			−0.622100			−0.311050	−	0.950394i	$-0.600681\pi$
$439$	−13.0344			−0.622100			−0.311050	+	0.950394i	$0.600681\pi$
$440$	1.19098	+	12.7270i	0.0567779	+	0.606736i
$441$	−1.32624			−0.0631542
$442$	−6.47214	−	4.70228i	−0.307848	−	0.223665i
$443$	−5.35410	+	16.4782i	−0.254381	+	0.782904i	0.739570	+	0.673080i	$0.235029\pi$
$443$	−5.35410	+	16.4782i	−0.254381	+	0.782904i	−0.993951	+	0.109825i	$0.964971\pi$
$444$	−3.23607	−	9.95959i	−0.153577	−	0.472661i
$445$	5.32624	−	3.86974i	0.252488	−	0.183443i
$446$	10.5902	−	7.69421i	0.501459	−	0.364331i
$447$	−1.11803	−	3.44095i	−0.0528812	−	0.162752i
$448$	0.736068	−	2.26538i	0.0347759	−	0.107029i
$449$	−0.0901699	−	0.0655123i	−0.00425538	−	0.00309172i	0.585656	−	0.810560i	$-0.300837\pi$
$449$	−0.0901699	−	0.0655123i	−0.00425538	−	0.00309172i	−0.589911	+	0.807468i	$0.700837\pi$
$450$	9.85410			0.464527
$451$	−2.09017	+	3.52671i	−0.0984223	+	0.166066i
$452$	−3.52786			−0.165937
$453$	−5.11803	−	3.71847i	−0.240466	−	0.174709i
$454$	−4.28115	+	13.1760i	−0.200924	+	0.618382i
$455$	−3.50658	−	10.7921i	−0.164391	−	0.505943i
$456$	1.00000	−	0.726543i	0.0468293	−	0.0340235i
$457$	−20.2082	+	14.6821i	−0.945300	+	0.686801i	−0.949691	−	0.313190i	$-0.898602\pi$
$457$	−20.2082	+	14.6821i	−0.945300	+	0.686801i	0.00439065	+	0.999990i	$0.498602\pi$
$458$	1.56231	+	4.80828i	0.0730018	+	0.224676i
$459$	−2.00000	+	6.15537i	−0.0933520	+	0.287308i
$460$	3.85410	+	2.80017i	0.179698	+	0.130559i
$461$	−12.8328			−0.597684			−0.298842	−	0.954303i	$-0.596600\pi$
$461$	−12.8328			−0.597684			−0.298842	+	0.954303i	$0.596600\pi$
$462$	−5.21885	−	5.93085i	−0.242803	−	0.275928i
$463$	7.90983			0.367601			0.183800	−	0.982964i	$-0.441160\pi$
$463$	7.90983			0.367601			0.183800	+	0.982964i	$0.441160\pi$
$464$	2.11803	+	1.53884i	0.0983273	+	0.0714389i
$465$	7.60081	−	23.3929i	0.352479	−	1.08482i
$466$	2.76393	+	8.50651i	0.128037	+	0.394056i
$467$	0.454915	−	0.330515i	0.0210510	−	0.0152944i	−0.577210	−	0.816596i	$-0.695859\pi$
$467$	0.454915	−	0.330515i	0.0210510	−	0.0152944i	0.598261	+	0.801301i	$0.295859\pi$
$468$	−1.00000	+	0.726543i	−0.0462250	+	0.0335844i
$469$	2.94427	+	9.06154i	0.135954	+	0.418423i
$470$	7.70820	−	23.7234i	0.355553	−	1.09428i
$471$	−3.61803	−	2.62866i	−0.166710	−	0.121122i
$472$	2.85410			0.131371
$473$	−4.00000	−	0.898056i	−0.183920	−	0.0412927i
$474$	−6.32624			−0.290574
$475$	−9.85410	−	7.15942i	−0.452137	−	0.328497i
$476$	4.76393	−	14.6619i	0.218354	−	0.672026i
$477$	0.881966	+	2.71441i	0.0403824	+	0.124284i
$478$	6.09017	−	4.42477i	0.278558	−	0.202384i
$479$	2.23607	−	1.62460i	0.102169	−	0.0742298i	−0.535528	−	0.844517i	$-0.679887\pi$
$479$	2.23607	−	1.62460i	0.102169	−	0.0742298i	0.637697	+	0.770288i	$0.279887\pi$
$480$	1.19098	+	3.66547i	0.0543607	+	0.167305i
$481$	4.00000	−	12.3107i	0.182384	−	0.561321i
$482$	18.2533	+	13.2618i	0.831415	+	0.604058i
$483$	−2.94427			−0.133969
$484$	−1.39919	+	10.9106i	−0.0635994	+	0.495939i
$485$	16.6738			0.757117
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	−6.79180	+	20.9030i	−0.307766	+	0.947205i	0.670865	+	0.741579i	$0.265923\pi$
$487$	−6.79180	+	20.9030i	−0.307766	+	0.947205i	−0.978631	+	0.205626i	$0.934077\pi$
$488$	−3.47214	−	10.6861i	−0.157176	−	0.483739i
$489$	10.8541	−	7.88597i	0.490839	−	0.356616i
$490$	−4.13525	+	3.00444i	−0.186812	+	0.135727i
$491$	−11.8197	−	36.3772i	−0.533414	−	1.64168i	−0.747052	−	0.664766i	$-0.768531\pi$
$491$	−11.8197	−	36.3772i	−0.533414	−	1.64168i	0.213638	−	0.976913i	$-0.431469\pi$
$492$	−0.381966	+	1.17557i	−0.0172204	+	0.0529988i
$493$	13.7082	+	9.95959i	0.617386	+	0.448558i
$494$	1.52786			0.0687419
$495$	12.4721	+	2.80017i	0.560581	+	0.125858i
$496$	6.38197			0.286559
$497$	−6.79837	−	4.93931i	−0.304949	−	0.221558i
$498$	5.04508	−	15.5272i	0.226076	−	0.695789i
$499$	6.00000	+	18.4661i	0.268597	+	0.826656i	0.990843	+	0.135020i	$0.0431099\pi$
$499$	6.00000	+	18.4661i	0.268597	+	0.826656i	−0.722246	+	0.691636i	$0.756890\pi$
$500$	15.1353	−	10.9964i	0.676869	−	0.491774i
$501$	2.23607	−	1.62460i	0.0999001	−	0.0725817i
$502$	−1.13525	−	3.49396i	−0.0506689	−	0.155943i
$503$	−12.4721	+	38.3853i	−0.556105	+	1.71152i	0.136902	+	0.990585i	$0.456285\pi$
$503$	−12.4721	+	38.3853i	−0.556105	+	1.71152i	−0.693007	+	0.720931i	$0.743715\pi$
$504$	−1.92705	−	1.40008i	−0.0858377	−	0.0623647i
$505$	56.3394			2.50707
$506$	2.70820	+	3.07768i	0.120394	+	0.136820i
$507$	11.4721			0.509495
$508$	−9.70820	−	7.05342i	−0.430732	−	0.312945i
$509$	8.59017	−	26.4378i	0.380753	−	1.17184i	−0.558762	−	0.829328i	$-0.688724\pi$
$509$	8.59017	−	26.4378i	0.380753	−	1.17184i	0.939515	−	0.342508i	$-0.111276\pi$
$510$	7.70820	+	23.7234i	0.341325	+	1.05049i
$511$	−8.33688	+	6.05710i	−0.368802	+	0.267950i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−0.381966	−	1.17557i	−0.0168642	−	0.0519027i
$514$	−7.47214	+	22.9969i	−0.329582	+	1.01435i
$515$	−53.1140	−	38.5896i	−2.34048	−	1.70046i
$516$	−1.23607			−0.0544149
$517$	10.9443	−	18.4661i	0.481329	−	0.812138i
$518$	24.9443			1.09599
$519$	−8.78115	−	6.37988i	−0.385450	−	0.280046i
$520$	−1.47214	+	4.53077i	−0.0645574	+	0.198687i
$521$	1.41641	+	4.35926i	0.0620540	+	0.190982i	0.977277	−	0.211964i	$-0.0679860\pi$
$521$	1.41641	+	4.35926i	0.0620540	+	0.190982i	−0.915223	+	0.402947i	$0.867986\pi$
$522$	2.11803	−	1.53884i	0.0927038	−	0.0673533i
$523$	23.9443	−	17.3965i	1.04701	−	0.760697i	0.0753683	−	0.997156i	$-0.475987\pi$
$523$	23.9443	−	17.3965i	1.04701	−	0.760697i	0.971642	+	0.236459i	$0.0759867\pi$
$524$	5.64590	+	17.3763i	0.246642	+	0.759087i
$525$	−7.25329	+	22.3233i	−0.316559	+	0.974270i
$526$	4.61803	+	3.35520i	0.201356	+	0.146294i
$527$	41.3050			1.79927
$528$	0.309017	+	3.30220i	0.0134482	+	0.143710i
$529$	−21.4721			−0.933571
$530$	8.89919	+	6.46564i	0.386556	+	0.280849i
$531$	0.881966	−	2.71441i	0.0382741	−	0.117795i
$532$	0.909830	+	2.80017i	0.0394461	+	0.121403i
$533$	−1.23607	+	0.898056i	−0.0535400	+	0.0388991i
$534$	1.38197	−	1.00406i	0.0598035	−	0.0434498i
$535$	−9.07295	−	27.9237i	−0.392258	−	1.20725i
$536$	1.23607	−	3.80423i	0.0533900	−	0.164318i
$537$	−6.97214	−	5.06555i	−0.300870	−	0.218595i
$538$	14.9443			0.644293
$539$	−4.03851	+	1.74311i	−0.173951	+	0.0750811i
$540$	3.85410			0.165854
$541$	−13.3262	−	9.68208i	−0.572940	−	0.416265i	0.263232	−	0.964733i	$-0.415211\pi$
$541$	−13.3262	−	9.68208i	−0.572940	−	0.416265i	−0.836172	+	0.548467i	$0.815211\pi$
$542$	−1.05573	+	3.24920i	−0.0453474	+	0.139565i
$543$	2.32624	+	7.15942i	0.0998284	+	0.307240i
$544$	−5.23607	+	3.80423i	−0.224495	+	0.163105i
$545$	−29.3607	+	21.3318i	−1.25767	+	0.913753i
$546$	−0.909830	−	2.80017i	−0.0389371	−	0.119836i
$547$	−1.29180	+	3.97574i	−0.0552332	+	0.169990i	−0.974868	−	0.222785i	$-0.928485\pi$
$547$	−1.29180	+	3.97574i	−0.0552332	+	0.169990i	0.919634	+	0.392776i	$0.128485\pi$
$548$	−13.8541	−	10.0656i	−0.591818	−	0.429981i
$549$	−11.2361			−0.479544
$550$	30.0066	−	12.9515i	1.27948	−	0.552255i
$551$	−3.23607			−0.137861
$552$	1.00000	+	0.726543i	0.0425628	+	0.0309237i
$553$	4.65654	−	14.3314i	0.198016	−	0.609431i
$554$	−9.00000	−	27.6992i	−0.382373	−	1.17682i
$555$	−32.6525	+	23.7234i	−1.38602	+	1.00700i
$556$	−7.09017	+	5.15131i	−0.300690	+	0.218464i
$557$	−4.00658	−	12.3310i	−0.169764	−	0.522480i	0.829592	−	0.558371i	$-0.188573\pi$
$557$	−4.00658	−	12.3310i	−0.169764	−	0.522480i	−0.999356	+	0.0358903i	$0.988573\pi$
$558$	1.97214	−	6.06961i	0.0834872	−	0.256947i
$559$	−1.23607	−	0.898056i	−0.0522801	−	0.0379837i
$560$	−9.18034			−0.387940
$561$	2.00000	+	21.3723i	0.0844401	+	0.902338i
$562$	−17.1246			−0.722358
$563$	−5.52786	−	4.01623i	−0.232972	−	0.169264i	0.465175	−	0.885219i	$-0.345992\pi$
$563$	−5.52786	−	4.01623i	−0.232972	−	0.169264i	−0.698146	+	0.715955i	$0.745992\pi$
$564$	2.00000	−	6.15537i	0.0842152	−	0.259188i
$565$	4.20163	+	12.9313i	0.176764	+	0.544023i
$566$	−9.61803	+	6.98791i	−0.404276	+	0.293724i
$567$	−1.92705	+	1.40008i	−0.0809285	+	0.0587980i
$568$	1.09017	+	3.35520i	0.0457425	+	0.140781i
$569$	−5.20163	+	16.0090i	−0.218064	+	0.671130i	0.780858	+	0.624708i	$0.214782\pi$
$569$	−5.20163	+	16.0090i	−0.218064	+	0.671130i	−0.998922	+	0.0464224i	$0.985218\pi$
$570$	−3.85410	−	2.80017i	−0.161431	−	0.117286i
$571$	−39.5967			−1.65707			−0.828536	−	0.559936i	$-0.810826\pi$
$571$	−39.5967			−1.65707			−0.828536	+	0.559936i	$0.810826\pi$
$572$	−2.09017	+	3.52671i	−0.0873944	+	0.147459i
$573$	−13.5279			−0.565135
$574$	−2.38197	−	1.73060i	−0.0994213	−	0.0722338i
$575$	3.76393	−	11.5842i	0.156967	−	0.483094i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	3.30902	−	2.40414i	0.137756	−	0.100086i	−0.516773	−	0.856122i	$-0.672867\pi$
$577$	3.30902	−	2.40414i	0.137756	−	0.100086i	0.654529	+	0.756037i	$0.272867\pi$
$578$	−20.1353	+	14.6291i	−0.837516	+	0.608491i
$579$	4.73607	+	14.5761i	0.196824	+	0.605763i
$580$	3.11803	−	9.59632i	0.129469	−	0.398466i
$581$	31.4615	+	22.8581i	1.30524	+	0.948314i
$582$	4.32624			0.179328
$583$	6.25329	+	7.10642i	0.258985	+	0.294318i
$584$	4.32624			0.179021
$585$	3.85410	+	2.80017i	0.159348	+	0.115773i
$586$	−7.40983	+	22.8051i	−0.306097	+	0.942070i
$587$	−3.98936	−	12.2780i	−0.164658	−	0.506766i	0.834353	−	0.551231i	$-0.185842\pi$
$587$	−3.98936	−	12.2780i	−0.164658	−	0.506766i	−0.999011	+	0.0444648i	$0.985842\pi$
$588$	−1.07295	+	0.779543i	−0.0442477	+	0.0321478i
$589$	−6.38197	+	4.63677i	−0.262964	+	0.191055i
$590$	−3.39919	−	10.4616i	−0.139942	−	0.430698i
$591$	1.57295	−	4.84104i	0.0647025	−	0.199134i
$592$	−8.47214	−	6.15537i	−0.348203	−	0.252984i
$593$	15.5279			0.637653			0.318826	−	0.947813i	$-0.396711\pi$
$593$	15.5279			0.637653			0.318826	+	0.947813i	$0.396711\pi$
$594$	3.23607	+	0.726543i	0.132777	+	0.0298104i
$595$	−59.4164			−2.43584
$596$	−2.92705	−	2.12663i	−0.119897	−	0.0871100i
$597$	−6.13525	+	18.8824i	−0.251099	+	0.772804i
$598$	0.472136	+	1.45309i	0.0193071	+	0.0594211i
$599$	29.4164	−	21.3723i	1.20192	−	0.873247i	0.207449	−	0.978246i	$-0.433484\pi$
$599$	29.4164	−	21.3723i	1.20192	−	0.873247i	0.994472	+	0.104998i	$0.0334837\pi$
$600$	7.97214	−	5.79210i	0.325461	−	0.236461i
$601$	5.79180	+	17.8253i	0.236252	+	0.727110i	0.996953	+	0.0780068i	$0.0248556\pi$
$601$	5.79180	+	17.8253i	0.236252	+	0.727110i	−0.760701	+	0.649103i	$0.775144\pi$
$602$	0.909830	−	2.80017i	0.0370819	−	0.114126i
$603$	−3.23607	−	2.35114i	−0.131783	−	0.0957459i
$604$	−6.32624			−0.257411
$605$	41.6591	−	7.86572i	1.69368	−	0.319787i
$606$	14.6180			0.593817
$607$	38.6525	+	28.0827i	1.56886	+	1.13984i	0.928242	+	0.371977i	$0.121320\pi$
$607$	38.6525	+	28.0827i	1.56886	+	1.13984i	0.640614	+	0.767863i	$0.278680\pi$
$608$	0.381966	−	1.17557i	0.0154908	−	0.0476757i
$609$	1.92705	+	5.93085i	0.0780880	+	0.240330i
$610$	−35.0344	+	25.4540i	−1.41850	+	1.03060i
$611$	6.47214	−	4.70228i	0.261835	−	0.190234i
$612$	2.00000	+	6.15537i	0.0808452	+	0.248816i
$613$	−8.56231	+	26.3521i	−0.345828	+	1.06435i	0.615311	+	0.788285i	$0.289031\pi$
$613$	−8.56231	+	26.3521i	−0.345828	+	1.06435i	−0.961139	+	0.276065i	$0.910969\pi$
$614$	−11.8541	−	8.61251i	−0.478393	−	0.347573i
$615$	4.76393			0.192100
$616$	−7.70820	−	1.73060i	−0.310572	−	0.0697278i
$617$	−43.7082			−1.75963			−0.879813	−	0.475320i	$-0.842332\pi$
$617$	−43.7082			−1.75963			−0.879813	+	0.475320i	$0.842332\pi$
$618$	−13.7812	−	10.0126i	−0.554359	−	0.402766i
$619$	11.5279	−	35.4791i	0.463344	−	1.42603i	−0.397709	−	0.917511i	$-0.630195\pi$
$619$	11.5279	−	35.4791i	0.463344	−	1.42603i	0.861053	−	0.508515i	$-0.169805\pi$
$620$	−7.60081	−	23.3929i	−0.305256	−	0.939481i
$621$	1.00000	−	0.726543i	0.0401286	−	0.0291551i
$622$	−9.61803	+	6.98791i	−0.385648	+	0.280190i
$623$	1.25735	+	3.86974i	0.0503748	+	0.155038i
$624$	−0.381966	+	1.17557i	−0.0152909	+	0.0470605i
$625$	−18.4721	−	13.4208i	−0.738885	−	0.536832i
$626$	21.8541			0.873466
$627$	−2.70820	−	3.07768i	−0.108155	−	0.122911i
$628$	−4.47214			−0.178458
$629$	−54.8328	−	39.8384i	−2.18633	−	1.58846i
$630$	−2.83688	+	8.73102i	−0.113024	+	0.347852i
$631$	−7.37132	−	22.6866i	−0.293448	−	0.903139i	−0.983738	−	0.179607i	$-0.942517\pi$
$631$	−7.37132	−	22.6866i	−0.293448	−	0.903139i	0.690291	−	0.723532i	$-0.257483\pi$
$632$	−5.11803	+	3.71847i	−0.203584	+	0.147913i
$633$	21.5623	−	15.6659i	0.857025	−	0.622665i
$634$	4.90983	+	15.1109i	0.194994	+	0.600131i
$635$	−14.2918	+	43.9856i	−0.567153	+	1.74552i
$636$	2.30902	+	1.67760i	0.0915585	+	0.0665211i
$637$	−1.63932			−0.0649522
$638$	4.42705	−	7.46969i	0.175269	−	0.295728i
$639$	3.52786			0.139560
$640$	3.11803	+	2.26538i	0.123251	+	0.0895472i
$641$	2.12461	−	6.53888i	0.0839171	−	0.258270i	−0.900290	−	0.435290i	$-0.856646\pi$
$641$	2.12461	−	6.53888i	0.0839171	−	0.258270i	0.984207	+	0.177020i	$0.0566457\pi$
$642$	−2.35410	−	7.24518i	−0.0929090	−	0.285944i
$643$	5.61803	−	4.08174i	0.221554	−	0.160968i	−0.471472	−	0.881881i	$-0.656277\pi$
$643$	5.61803	−	4.08174i	0.221554	−	0.160968i	0.693026	+	0.720913i	$0.256277\pi$
$644$	−2.38197	+	1.73060i	−0.0938626	+	0.0681952i
$645$	1.47214	+	4.53077i	0.0579653	+	0.178399i
$646$	2.47214	−	7.60845i	0.0972649	−	0.299351i
$647$	34.8885	+	25.3480i	1.37161	+	0.996533i	0.997609	+	0.0691047i	$0.0220143\pi$
$647$	34.8885	+	25.3480i	1.37161	+	0.996533i	0.374001	+	0.927428i	$0.377986\pi$
$648$	1.00000			0.0392837
$649$	−0.881966	−	9.42481i	−0.0346202	−	0.369956i
$650$	12.1803			0.477752
$651$	12.2984	+	8.93529i	0.482011	+	0.350202i
$652$	4.14590	−	12.7598i	0.162366	−	0.499711i
$653$	−8.60739	−	26.4908i	−0.336833	−	1.03667i	−0.965812	−	0.259244i	$-0.916527\pi$
$653$	−8.60739	−	26.4908i	−0.336833	−	1.03667i	0.628979	−	0.777423i	$-0.283473\pi$
$654$	−7.61803	+	5.53483i	−0.297889	+	0.216429i
$655$	56.9681	−	41.3897i	2.22593	−	1.61723i
$656$	0.381966	+	1.17557i	0.0149133	+	0.0458983i
$657$	1.33688	−	4.11450i	0.0521567	−	0.160522i
$658$	12.4721	+	9.06154i	0.486214	+	0.353255i
$659$	49.8541			1.94204			0.971020	−	0.238998i	$-0.0768190\pi$
$659$	49.8541			1.94204			0.971020	+	0.238998i	$0.0768190\pi$
$660$	11.7361	−	5.06555i	0.456826	−	0.197176i
$661$	28.1803			1.09609			0.548044	−	0.836449i	$-0.315373\pi$
$661$	28.1803			1.09609			0.548044	+	0.836449i	$0.315373\pi$
$662$	7.23607	+	5.25731i	0.281238	+	0.204331i
$663$	−2.47214	+	7.60845i	−0.0960098	+	0.295488i
$664$	−5.04508	−	15.5272i	−0.195787	−	0.602571i
$665$	9.18034	−	6.66991i	0.355998	−	0.258648i
$666$	−8.47214	+	6.15537i	−0.328289	+	0.238516i
$667$	−1.00000	−	3.07768i	−0.0387202	−	0.119168i
$668$	0.854102	−	2.62866i	0.0330462	−	0.101706i
$669$	−10.5902	−	7.69421i	−0.409440	−	0.297475i
$670$	−15.4164			−0.595588
$671$	−34.2148	+	14.7679i	−1.32085	+	0.570108i
$672$	−2.38197			−0.0918863
$673$	29.1525	+	21.1805i	1.12375	+	0.816449i	0.984773	−	0.173847i	$-0.0556200\pi$
$673$	29.1525	+	21.1805i	1.12375	+	0.816449i	0.138973	+	0.990296i	$0.455620\pi$
$674$	−3.38197	+	10.4086i	−0.130268	+	0.400925i
$675$	−3.04508	−	9.37181i	−0.117205	−	0.360721i
$676$	9.28115	−	6.74315i	0.356967	−	0.259352i
$677$	2.01722	−	1.46560i	0.0775281	−	0.0563275i	−0.548346	−	0.836252i	$-0.684742\pi$
$677$	2.01722	−	1.46560i	0.0775281	−	0.0563275i	0.625874	+	0.779924i	$0.284742\pi$
$678$	1.09017	+	3.35520i	0.0418677	+	0.128856i
$679$	−3.18441	+	9.80059i	−0.122206	+	0.376112i
$680$	20.1803	+	14.6619i	0.773881	+	0.562257i
$681$	13.8541			0.530890
$682$	−1.97214	−	21.0745i	−0.0755170	−	0.806985i
$683$	3.25735			0.124639			0.0623196	−	0.998056i	$-0.480150\pi$
$683$	3.25735			0.124639			0.0623196	+	0.998056i	$0.480150\pi$
$684$	−1.00000	−	0.726543i	−0.0382360	−	0.0277800i
$685$	−20.3951	+	62.7697i	−0.779258	+	2.39831i
$686$	−6.12868	−	18.8621i	−0.233994	−	0.720159i
$687$	4.09017	−	2.97168i	0.156050	−	0.113377i
$688$	−1.00000	+	0.726543i	−0.0381246	+	0.0276992i
$689$	1.09017	+	3.35520i	0.0415322	+	0.127823i
$690$	1.47214	−	4.53077i	0.0560433	−	0.172483i
$691$	11.0902	+	8.05748i	0.421890	+	0.306521i	0.778398	−	0.627771i	$-0.216033\pi$
$691$	11.0902	+	8.05748i	0.421890	+	0.306521i	−0.356508	+	0.934292i	$0.616033\pi$
$692$	−10.8541			−0.412611
$693$	−4.02786	+	6.79615i	−0.153006	+	0.258165i
$694$	5.14590			0.195336
$695$	27.3262	+	19.8537i	1.03654	+	0.753093i
$696$	0.809017	−	2.48990i	0.0306657	−	0.0943794i
$697$	2.47214	+	7.60845i	0.0936388	+	0.288191i
$698$	7.09017	−	5.15131i	0.268367	−	0.194980i
$699$	7.23607	−	5.25731i	0.273693	−	0.198850i
$700$	7.25329	+	22.3233i	0.274149	+	0.843742i
$701$	5.85410	−	18.0171i	0.221106	−	0.680495i	−0.777557	−	0.628812i	$-0.783541\pi$
$701$	5.85410	−	18.0171i	0.221106	−	0.680495i	0.998664	−	0.0516832i	$-0.0164586\pi$
$702$	1.00000	+	0.726543i	0.0377426	+	0.0274216i
$703$	12.9443			0.488202
$704$	2.19098	+	2.48990i	0.0825758	+	0.0938416i
$705$	−24.9443			−0.939456
$706$	−22.3262	−	16.2210i	−0.840259	−	0.610484i
$707$	−10.7599	+	33.1155i	−0.404666	+	1.24544i
$708$	−0.881966	−	2.71441i	−0.0331463	−	0.102014i
$709$	33.1803	−	24.1069i	1.24611	−	0.905355i	0.248124	−	0.968728i	$-0.420186\pi$
$709$	33.1803	−	24.1069i	1.24611	−	0.905355i	0.997990	+	0.0633736i	$0.0201860\pi$
$710$	11.0000	−	7.99197i	0.412823	−	0.299933i
$711$	1.95492	+	6.01661i	0.0733150	+	0.225640i
$712$	0.527864	−	1.62460i	0.0197825	−	0.0608844i
$713$	−6.38197	−	4.63677i	−0.239007	−	0.173648i
$714$	−15.4164			−0.576945
$715$	15.4164	+	3.46120i	0.576541	+	0.129442i
$716$	−8.61803			−0.322071
$717$	−6.09017	−	4.42477i	−0.227442	−	0.165246i
$718$	5.32624	−	16.3925i	0.198773	−	0.611762i
$719$	−2.14590	−	6.60440i	−0.0800285	−	0.246302i	0.903035	−	0.429567i	$-0.141334\pi$
$719$	−2.14590	−	6.60440i	−0.0800285	−	0.246302i	−0.983064	+	0.183264i	$0.941334\pi$
$720$	3.11803	−	2.26538i	0.116202	−	0.0844259i
$721$	32.8262	−	23.8497i	1.22251	−	0.888208i
$722$	−5.39919	−	16.6170i	−0.200937	−	0.618420i
$723$	6.97214	−	21.4580i	0.259297	−	0.798033i
$724$	6.09017	+	4.42477i	0.226339	+	0.164445i
$725$	−25.7984			−0.958128
$726$	10.8090	−	2.04087i	0.401160	−	0.0757438i
$727$	−23.4164			−0.868466			−0.434233	−	0.900800i	$-0.642981\pi$
$727$	−23.4164			−0.868466			−0.434233	+	0.900800i	$0.642981\pi$
$728$	−2.38197	−	1.73060i	−0.0882815	−	0.0641403i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−5.15248	−	15.8577i	−0.190702	−	0.586919i
$731$	−6.47214	+	4.70228i	−0.239381	+	0.173920i
$732$	−9.09017	+	6.60440i	−0.335982	+	0.244105i
$733$	−9.36068	−	28.8092i	−0.345745	−	1.06409i	−0.961184	−	0.275908i	$-0.911021\pi$
$733$	−9.36068	−	28.8092i	−0.345745	−	1.06409i	0.615439	−	0.788184i	$-0.288979\pi$
$734$	0.156541	−	0.481784i	0.00577804	−	0.0177830i
$735$	4.13525	+	3.00444i	0.152531	+	0.110820i
$736$	1.23607			0.0455621
$737$	−12.9443	−	2.90617i	−0.476808	−	0.107050i
$738$	1.23607			0.0455003
$739$	−26.6525	−	19.3642i	−0.980427	−	0.712322i	−0.0226231	−	0.999744i	$-0.507202\pi$
$739$	−26.6525	−	19.3642i	−0.980427	−	0.712322i	−0.957804	+	0.287422i	$0.907202\pi$
$740$	−12.4721	+	38.3853i	−0.458485	+	1.41107i
$741$	−0.472136	−	1.45309i	−0.0173443	−	0.0533804i
$742$	−5.50000	+	3.99598i	−0.201911	+	0.146697i
$743$	−27.3262	+	19.8537i	−1.00250	+	0.728361i	−0.962623	−	0.270844i	$-0.912697\pi$
$743$	−27.3262	+	19.8537i	−1.00250	+	0.728361i	−0.0398791	+	0.999205i	$0.512697\pi$
$744$	−1.97214	−	6.06961i	−0.0723020	−	0.222523i
$745$	−4.30902	+	13.2618i	−0.157870	+	0.485874i
$746$	14.9443	+	10.8576i	0.547149	+	0.397527i
$747$	−16.3262			−0.597346
$748$	14.1803	+	16.1150i	0.518485	+	0.589221i
$749$	18.1459			0.663037
$750$	−15.1353	−	10.9964i	−0.552661	−	0.401532i
$751$	−14.1803	+	43.6426i	−0.517448	+	1.59254i	0.261335	+	0.965248i	$0.415837\pi$
$751$	−14.1803	+	43.6426i	−0.517448	+	1.59254i	−0.778783	+	0.627293i	$0.784163\pi$
$752$	−2.00000	−	6.15537i	−0.0729325	−	0.224463i
$753$	−2.97214	+	2.15938i	−0.108311	+	0.0786923i
$754$	2.61803	−	1.90211i	0.0953432	−	0.0692709i
$755$	7.53444	+	23.1886i	0.274206	+	0.843921i
$756$	−0.736068	+	2.26538i	−0.0267705	+	0.0823912i
$757$	−29.5623	−	21.4783i	−1.07446	−	0.780641i	−0.0977516	−	0.995211i	$-0.531165\pi$
$757$	−29.5623	−	21.4783i	−1.07446	−	0.780641i	−0.976709	+	0.214570i	$0.931165\pi$
$758$	−9.70820			−0.352618
$759$	2.09017	−	3.52671i	0.0758684	−	0.128012i
$760$	−4.76393			−0.172806
$761$	−19.1803	−	13.9353i	−0.695287	−	0.505155i	0.183107	−	0.983093i	$-0.441385\pi$
$761$	−19.1803	−	13.9353i	−0.695287	−	0.505155i	−0.878394	+	0.477938i	$0.841385\pi$
$762$	−3.70820	+	11.4127i	−0.134334	+	0.413438i
$763$	−6.93112	−	21.3318i	−0.250923	−	0.772262i
$764$	−10.9443	+	7.95148i	−0.395950	+	0.287674i
$765$	20.1803	−	14.6619i	0.729622	−	0.530101i
$766$	2.70820	+	8.33499i	0.0978514	+	0.301156i
$767$	1.09017	−	3.35520i	0.0393638	−	0.121149i
$768$	0.809017	+	0.587785i	0.0291929	+	0.0212099i
$769$	29.2705			1.05552			0.527761	−	0.849393i	$-0.323032\pi$
$769$	29.2705			1.05552			0.527761	+	0.849393i	$0.323032\pi$
$770$	2.83688	+	30.3153i	0.102234	+	1.09249i
$771$	24.1803			0.870834
$772$	12.3992	+	9.00854i	0.446257	+	0.324224i
$773$	−8.80902	+	27.1114i	−0.316838	+	0.975128i	0.658153	+	0.752884i	$0.271338\pi$
$773$	−8.80902	+	27.1114i	−0.316838	+	0.975128i	−0.974991	+	0.222244i	$0.928662\pi$
$774$	0.381966	+	1.17557i	0.0137295	+	0.0422550i
$775$	−50.8779	+	36.9650i	−1.82759	+	1.32782i
$776$	3.50000	−	2.54290i	0.125643	−	0.0912847i
$777$	−7.70820	−	23.7234i	−0.276530	−	0.851073i
$778$	6.50658	−	20.0252i	0.233272	−	0.717938i
$779$	−1.23607	−	0.898056i	−0.0442867	−	0.0321762i
$780$	4.76393			0.170576
$781$	10.7426	−	4.63677i	0.384402	−	0.165917i
$782$	8.00000			0.286079
$783$	−2.11803	−	1.53884i	−0.0756924	−	0.0549937i
$784$	−0.409830	+	1.26133i	−0.0146368	+	0.0450474i
$785$	5.32624	+	16.3925i	0.190102	+	0.585073i
$786$	14.7812	−	10.7391i	0.527226	−	0.383052i
$787$	−38.4164	+	27.9112i	−1.36940	+	0.994925i	−0.371613	+	0.928388i	$0.621195\pi$
$787$	−38.4164	+	27.9112i	−1.36940	+	0.994925i	−0.997784	+	0.0665375i	$0.978805\pi$
$788$	−1.57295	−	4.84104i	−0.0560340	−	0.172455i
$789$	1.76393	−	5.42882i	0.0627976	−	0.193271i
$790$	19.7254	+	14.3314i	0.701799	+	0.509887i
$791$	−8.40325			−0.298785
$792$	3.04508	−	1.31433i	0.108202	−	0.0467026i
$793$	−13.8885			−0.493197
$794$	20.9443	+	15.2169i	0.743284	+	0.540028i
$795$	3.39919	−	10.4616i	0.120557	−	0.371035i
$796$	6.13525	+	18.8824i	0.217458	+	0.669268i
$797$	16.4894	−	11.9802i	0.584083	−	0.424361i	−0.256111	−	0.966647i	$-0.582441\pi$
$797$	16.4894	−	11.9802i	0.584083	−	0.424361i	0.840194	+	0.542286i	$0.182441\pi$
$798$	2.38197	−	1.73060i	0.0843207	−	0.0612626i
$799$	−12.9443	−	39.8384i	−0.457935	−	1.40938i
$800$	3.04508	−	9.37181i	0.107660	−	0.331343i
$801$	−1.38197	−	1.00406i	−0.0488294	−	0.0354766i
$802$	23.7082			0.837166
$803$	−1.33688	−	14.2861i	−0.0471775	−	0.504145i
$804$	−4.00000			−0.141069
$805$	9.18034	+	6.66991i	0.323564	+	0.235083i
$806$	2.43769	−	7.50245i	0.0858641	−	0.264263i
$807$	−4.61803	−	14.2128i	−0.162562	−	0.500316i
$808$	11.8262	−	8.59226i	0.416046	−	0.302275i
$809$	40.6525	−	29.5358i	1.42926	−	1.03842i	0.439112	−	0.898432i	$-0.355293\pi$
$809$	40.6525	−	29.5358i	1.42926	−	1.03842i	0.990153	−	0.139989i	$-0.0447068\pi$
$810$	−1.19098	−	3.66547i	−0.0418469	−	0.128791i
$811$	−13.9787	+	43.0221i	−0.490859	+	1.51071i	0.332453	+	0.943120i	$0.392124\pi$
$811$	−13.9787	+	43.0221i	−0.490859	+	1.51071i	−0.823312	+	0.567589i	$0.807876\pi$
$812$	5.04508	+	3.66547i	0.177048	+	0.128633i
$813$	3.41641			0.119819
$814$	−17.7082	+	29.8788i	−0.620672	+	1.04725i
$815$	−51.7082			−1.81126
$816$	5.23607	+	3.80423i	0.183299	+	0.133175i
$817$	0.472136	−	1.45309i	0.0165179	−	0.0508370i
$818$	−0.281153	−	0.865300i	−0.00983028	−	0.0302545i
$819$	−2.38197	+	1.73060i	−0.0832326	+	0.0604720i
$820$	3.85410	−	2.80017i	0.134591	−	0.0977861i
$821$	3.06231	+	9.42481i	0.106875	+	0.328928i	0.990166	−	0.139897i	$-0.0446773\pi$
$821$	3.06231	+	9.42481i	0.106875	+	0.328928i	−0.883291	+	0.468826i	$0.844677\pi$
$822$	−5.29180	+	16.2865i	−0.184573	+	0.568056i
$823$	−39.0066	−	28.3399i	−1.35968	−	0.987868i	−0.998465	−	0.0553871i	$-0.982361\pi$
$823$	−39.0066	−	28.3399i	−1.35968	−	0.987868i	−0.361219	−	0.932481i	$-0.617639\pi$
$824$	−17.0344			−0.593423
$825$	−21.5902	−	24.5357i	−0.751673	−	0.854224i
$826$	6.79837			0.236546
$827$	40.1976	+	29.2052i	1.39781	+	1.01557i	0.994957	+	0.100299i	$0.0319800\pi$
$827$	40.1976	+	29.2052i	1.39781	+	1.01557i	0.402849	+	0.915267i	$0.368020\pi$
$828$	0.381966	−	1.17557i	0.0132742	−	0.0408539i
$829$	−17.0902	−	52.5981i	−0.593566	−	1.82681i	−0.561738	−	0.827315i	$-0.689867\pi$
$829$	−17.0902	−	52.5981i	−0.593566	−	1.82681i	−0.0318284	−	0.999493i	$-0.510133\pi$
$830$	−50.9058	+	36.9852i	−1.76696	+	1.28378i
$831$	−23.5623	+	17.1190i	−0.817367	+	0.593852i
$832$	0.381966	+	1.17557i	0.0132423	+	0.0407556i
$833$	−2.65248	+	8.16348i	−0.0919028	+	0.282848i
$834$	7.09017	+	5.15131i	0.245513	+	0.178375i
$835$	−10.6525			−0.368644
$836$	−4.00000	−	0.898056i	−0.138343	−	0.0310599i
$837$	−6.38197			−0.220593
$838$	−23.4443	−	17.0333i	−0.809869	−	0.588404i
$839$	11.4721	−	35.3076i	0.396062	−	1.21895i	−0.532069	−	0.846701i	$-0.678585\pi$
$839$	11.4721	−	35.3076i	0.396062	−	1.21895i	0.928131	−	0.372253i	$-0.121415\pi$
$840$	2.83688	+	8.73102i	0.0978817	+	0.301249i
$841$	17.9164	−	13.0170i	0.617807	−	0.448863i
$842$	4.14590	−	3.01217i	0.142877	−	0.103806i
$843$	5.29180	+	16.2865i	0.182259	+	0.560936i
$844$	8.23607	−	25.3480i	0.283497	−	0.872515i
$845$	−35.7705	−	25.9888i	−1.23054	−	0.894042i
$846$	−6.47214			−0.222517
$847$	−3.33282	+	25.9888i	−0.114517	+	0.892986i
$848$	2.85410			0.0980103
$849$	9.61803	+	6.98791i	0.330090	+	0.239824i
$850$	19.7082	−	60.6556i	0.675986	−	2.08047i
$851$	4.00000	+	12.3107i	0.137118	+	0.422007i
$852$	2.85410	−	2.07363i	0.0977799	−	0.0710413i
$853$	−26.6525	+	19.3642i	−0.912563	+	0.663016i	−0.941662	−	0.336560i	$-0.890736\pi$
$853$	−26.6525	+	19.3642i	−0.912563	+	0.663016i	0.0290985	+	0.999577i	$0.490736\pi$
$854$	−8.27051	−	25.4540i	−0.283011	−	0.871018i
$855$	−1.47214	+	4.53077i	−0.0503460	+	0.154949i
$856$	−6.16312	−	4.47777i	−0.210651	−	0.153047i
$857$	13.2361			0.452135			0.226068	−	0.974112i	$-0.427413\pi$
$857$	13.2361			0.452135			0.226068	+	0.974112i	$0.427413\pi$
$858$	4.00000	+	0.898056i	0.136558	+	0.0306591i
$859$	53.5967			1.82870			0.914349	−	0.404928i	$-0.132703\pi$
$859$	53.5967			1.82870			0.914349	+	0.404928i	$0.132703\pi$
$860$	3.85410	+	2.80017i	0.131424	+	0.0954850i
$861$	−0.909830	+	2.80017i	−0.0310069	+	0.0954295i
$862$	−0.854102	−	2.62866i	−0.0290908	−	0.0895324i
$863$	−5.85410	+	4.25325i	−0.199276	+	0.144782i	−0.682948	−	0.730467i	$-0.739303\pi$
$863$	−5.85410	+	4.25325i	−0.199276	+	0.144782i	0.483672	+	0.875249i	$0.339303\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$	12.9271	+	39.7854i	0.439533	+	1.35274i
$866$	−1.02786	+	3.16344i	−0.0349282	+	0.107498i
$867$	20.1353	+	14.6291i	0.683829	+	0.496831i
$868$	15.2016			0.515977
$869$	13.8607	+	15.7517i	0.470191	+	0.534339i
$870$	−10.0902			−0.342089
$871$	−4.00000	−	2.90617i	−0.135535	−	0.0984718i
$872$	−2.90983	+	8.95554i	−0.0985393	+	0.303273i
$873$	−1.33688	−	4.11450i	−0.0452466	−	0.139255i
$874$	−1.23607	+	0.898056i	−0.0418106	+	0.0303772i
$875$	36.0517	−	26.1931i	1.21877	−	0.885487i
$876$	−1.33688	−	4.11450i	−0.0451690	−	0.139016i
$877$	4.43769	−	13.6578i	0.149850	−	0.461192i	−0.847753	−	0.530392i	$-0.822045\pi$
$877$	4.43769	−	13.6578i	0.149850	−	0.461192i	0.997603	+	0.0692003i	$0.0220447\pi$
$878$	10.5451	+	7.66145i	0.355879	+	0.258562i
$879$	23.9787			0.808782
$880$	6.51722	−	10.9964i	0.219695	−	0.370689i
$881$	−25.7082			−0.866131			−0.433066	−	0.901362i	$-0.642568\pi$
$881$	−25.7082			−0.866131			−0.433066	+	0.901362i	$0.642568\pi$
$882$	1.07295	+	0.779543i	0.0361281	+	0.0262486i
$883$	15.5066	−	47.7243i	0.521838	−	1.60605i	−0.248647	−	0.968594i	$-0.579986\pi$
$883$	15.5066	−	47.7243i	0.521838	−	1.60605i	0.770485	−	0.637458i	$-0.220014\pi$
$884$	2.47214	+	7.60845i	0.0831469	+	0.255900i
$885$	−8.89919	+	6.46564i	−0.299143	+	0.217340i
$886$	14.0172	−	10.1841i	0.470918	−	0.342142i
$887$	11.9098	+	36.6547i	0.399893	+	1.23074i	0.925085	+	0.379760i	$0.123994\pi$
$887$	11.9098	+	36.6547i	0.399893	+	1.23074i	−0.525192	+	0.850984i	$0.676006\pi$
$888$	−3.23607	+	9.95959i	−0.108595	+	0.334222i
$889$	−23.1246	−	16.8010i	−0.775575	−	0.563488i
$890$	−6.58359			−0.220683
$891$	−0.309017	−	3.30220i	−0.0103525	−	0.110628i
$892$	−13.0902			−0.438291
$893$	6.47214	+	4.70228i	0.216582	+	0.157356i
$894$	−1.11803	+	3.44095i	−0.0373927	+	0.115083i
$895$	10.2639	+	31.5891i	0.343085	+	1.05591i
$896$	−1.92705	+	1.40008i	−0.0643783	+	0.0467735i
$897$	1.23607	−	0.898056i	0.0412711	−	0.0299852i
$898$	0.0344419	+	0.106001i	0.00114934	+	0.00353730i
$899$	−5.16312	+	15.8904i	−0.172200	+	0.529976i
$900$	−7.97214	−	5.79210i	−0.265738	−	0.193070i
$901$	18.4721			0.615396
$902$	3.76393	−	1.62460i	0.125325	−	0.0540932i
$903$	−2.94427			−0.0979792
$904$	2.85410	+	2.07363i	0.0949260	+	0.0689678i
$905$	8.96556	−	27.5932i	0.298025	−	0.917227i
$906$	1.95492	+	6.01661i	0.0649477	+	0.199888i
$907$	−11.4721	+	8.33499i	−0.380926	+	0.276759i	−0.761727	−	0.647898i	$-0.775648\pi$
$907$	−11.4721	+	8.33499i	−0.380926	+	0.276759i	0.380801	+	0.924657i	$0.375648\pi$
$908$	11.2082	−	8.14324i	0.371957	−	0.270243i
$909$	−4.51722	−	13.9026i	−0.149827	−	0.461119i
$910$	−3.50658	+	10.7921i	−0.116242	+	0.357756i
$911$	−24.5066	−	17.8051i	−0.811939	−	0.589908i	0.102453	−	0.994738i	$-0.467331\pi$
$911$	−24.5066	−	17.8051i	−0.811939	−	0.589908i	−0.914392	+	0.404830i	$0.867331\pi$
$912$	−1.23607			−0.0409303
$913$	−49.7148	+	21.4580i	−1.64532	+	0.710157i
$914$	24.9787			0.826222
$915$	35.0344	+	25.4540i	1.15820	+	0.841484i
$916$	1.56231	−	4.80828i	0.0516200	−	0.158870i
$917$	13.4483	+	41.3897i	0.444103	+	1.36681i
$918$	5.23607	−	3.80423i	0.172816	−	0.125558i
$919$	−13.5344	+	9.83335i	−0.446460	+	0.324372i	−0.788197	−	0.615424i	$-0.788985\pi$
$919$	−13.5344	+	9.83335i	−0.446460	+	0.324372i	0.341737	+	0.939796i	$0.388985\pi$
$920$	−1.47214	−	4.53077i	−0.0485349	−	0.149375i
$921$	−4.52786	+	13.9353i	−0.149198	+	0.459185i
$922$	10.3820	+	7.54294i	0.341912	+	0.248413i
$923$	4.36068			0.143534
$924$	0.736068	+	7.86572i	0.0242149	+	0.258763i
$925$	103.193			3.39298
$926$	−6.39919	−	4.64928i	−0.210290	−	0.152785i
$927$	−5.26393	+	16.2007i	−0.172890	+	0.532101i
$928$	−0.809017	−	2.48990i	−0.0265573	−	0.0817349i
$929$	−13.8541	+	10.0656i	−0.454538	+	0.330241i	−0.791385	−	0.611318i	$-0.790640\pi$
$929$	−13.8541	+	10.0656i	−0.454538	+	0.330241i	0.336847	+	0.941560i	$0.390640\pi$
$930$	−19.8992	+	14.4576i	−0.652520	+	0.474084i
$931$	−0.506578	−	1.55909i	−0.0166024	−	0.0510970i
$932$	2.76393	−	8.50651i	0.0905356	−	0.278640i
$933$	9.61803	+	6.98791i	0.314880	+	0.228774i
$934$	−0.562306			−0.0183992
$935$	42.1803	−	71.1702i	1.37944	−	2.32752i
$936$	1.23607			0.0404021
$937$	23.0172	+	16.7230i	0.751940	+	0.546316i	0.896428	−	0.443190i	$-0.146153\pi$
$937$	23.0172	+	16.7230i	0.751940	+	0.546316i	−0.144488	+	0.989507i	$0.546153\pi$
$938$	2.94427	−	9.06154i	0.0961339	−	0.295870i
$939$	−6.75329	−	20.7845i	−0.220385	−	0.678276i
$940$	−20.1803	+	14.6619i	−0.658210	+	0.478218i
$941$	−36.2705	+	26.3521i	−1.18238	+	0.859053i	−0.992439	−	0.122742i	$-0.960831\pi$
$941$	−36.2705	+	26.3521i	−1.18238	+	0.859053i	−0.189946	+	0.981795i	$0.560831\pi$
$942$	1.38197	+	4.25325i	0.0450269	+	0.138579i
$943$	0.472136	−	1.45309i	0.0153749	−	0.0473190i
$944$	−2.30902	−	1.67760i	−0.0751521	−	0.0546012i
$945$	9.18034			0.298636
$946$	2.70820	+	3.07768i	0.0880513	+	0.100064i
$947$	−13.3262			−0.433045			−0.216522	−	0.976278i	$-0.569471\pi$
$947$	−13.3262			−0.433045			−0.216522	+	0.976278i	$0.569471\pi$
$948$	5.11803	+	3.71847i	0.166226	+	0.120770i
$949$	1.65248	−	5.08580i	0.0536416	−	0.165092i
$950$	3.76393	+	11.5842i	0.122118	+	0.375841i
$951$	12.8541	−	9.33905i	0.416823	−	0.302840i
$952$	−12.4721	+	9.06154i	−0.404224	+	0.293686i
$953$	−12.5836	−	38.7283i	−0.407623	−	1.25453i	−0.918685	−	0.394990i	$-0.870748\pi$
$953$	−12.5836	−	38.7283i	−0.407623	−	1.25453i	0.511063	−	0.859543i	$-0.329252\pi$
$954$	0.881966	−	2.71441i	0.0285547	−	0.0878823i
$955$	42.1803	+	30.6458i	1.36492	+	0.991675i
$956$	−7.52786			−0.243469
$957$	−8.47214	−	1.90211i	−0.273865	−	0.0614866i
$958$	−2.76393			−0.0892986
$959$	−33.0000	−	23.9759i	−1.06563	−	0.774222i
$960$	1.19098	−	3.66547i	0.0384388	−	0.118302i
$961$	3.00658	+	9.25330i	0.0969864	+	0.298493i
$962$	−10.4721	+	7.60845i	−0.337635	+	0.245306i
$963$	−6.16312	+	4.47777i	−0.198604	+	0.144294i
$964$	−6.97214	−	21.4580i	−0.224557	−	0.691117i
$965$	18.2533	−	56.1778i	0.587594	−	1.80843i
$966$	2.38197	+	1.73060i	0.0766385	+	0.0556811i
$967$	−46.6869			−1.50135			−0.750675	−	0.660672i	$-0.770272\pi$
$967$	−46.6869			−1.50135			−0.750675	+	0.660672i	$0.770272\pi$
$968$	7.54508	−	8.00448i	0.242508	−	0.257274i
$969$	−8.00000			−0.256997
$970$	−13.4894	−	9.80059i	−0.433117	−	0.314678i
$971$	16.4721	−	50.6960i	0.528616	−	1.62691i	−0.228437	−	0.973559i	$-0.573361\pi$
$971$	16.4721	−	50.6960i	0.528616	−	1.62691i	0.757053	−	0.653354i	$-0.226639\pi$
$972$	−0.309017	−	0.951057i	−0.00991172	−	0.0305052i
$973$	−16.8885	+	12.2702i	−0.541422	+	0.393366i
$974$	17.7812	−	12.9188i	0.569745	−	0.413944i
$975$	−3.76393	−	11.5842i	−0.120542	−	0.370991i
$976$	−3.47214	+	10.6861i	−0.111140	+	0.342055i
$977$	33.3607	+	24.2380i	1.06730	+	0.775441i	0.975425	−	0.220330i	$-0.0707133\pi$
$977$	33.3607	+	24.2380i	1.06730	+	0.775441i	0.0918772	+	0.995770i	$0.470713\pi$
$978$	−13.4164			−0.429009
$979$	−5.52786	−	1.24108i	−0.176671	−	0.0396652i
$980$	5.11146			0.163279
$981$	7.61803	+	5.53483i	0.243225	+	0.176713i
$982$	−11.8197	+	36.3772i	−0.377181	+	1.16084i
$983$	9.61803	+	29.6013i	0.306768	+	0.944134i	0.979012	+	0.203804i	$0.0653306\pi$
$983$	9.61803	+	29.6013i	0.306768	+	0.944134i	−0.672244	+	0.740330i	$0.734669\pi$
$984$	1.00000	−	0.726543i	0.0318788	−	0.0231613i
$985$	−15.8713	+	11.5312i	−0.505702	+	0.367414i
$986$	−5.23607	−	16.1150i	−0.166750	−	0.513205i
$987$	4.76393	−	14.6619i	0.151638	−	0.466693i
$988$	−1.23607	−	0.898056i	−0.0393246	−	0.0285710i
$989$	1.52786			0.0485833
$990$	−8.44427	−	9.59632i	−0.268377	−	0.304991i
$991$	14.6869			0.466545			0.233273	−	0.972411i	$-0.425057\pi$
$991$	14.6869			0.466545			0.233273	+	0.972411i	$0.425057\pi$
$992$	−5.16312	−	3.75123i	−0.163929	−	0.119102i
$993$	2.76393	−	8.50651i	0.0877107	−	0.269946i
$994$	2.59675	+	7.99197i	0.0823638	+	0.253490i
$995$	61.9058	−	44.9772i	1.96254	−	1.42587i
$996$	−13.2082	+	9.59632i	−0.418518	+	0.304071i
$997$	−11.1115	−	34.1975i	−0.351903	−	1.08305i	−0.957783	−	0.287491i	$-0.907179\pi$
$997$	−11.1115	−	34.1975i	−0.351903	−	1.08305i	0.605880	−	0.795556i	$-0.292821\pi$
$998$	6.00000	−	18.4661i	0.189927	−	0.584534i
$999$	8.47214	+	6.15537i	0.268047	+	0.194747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	66.2.e.a.37.1	yes	4
3.2	odd	2		198.2.f.c.37.1		4
4.3	odd	2		528.2.y.d.433.1		4
11.2	odd	10		726.2.e.n.511.1		4
11.3	even	5	inner	66.2.e.a.25.1	✓	4
11.4	even	5		726.2.e.f.493.1		4
11.5	even	5		726.2.a.l.1.1		2
11.6	odd	10		726.2.a.j.1.1		2
11.7	odd	10		726.2.e.n.493.1		4
11.8	odd	10		726.2.e.r.487.1		4
11.9	even	5		726.2.e.f.511.1		4
11.10	odd	2		726.2.e.r.565.1		4
33.5	odd	10		2178.2.a.t.1.2		2
33.14	odd	10		198.2.f.c.91.1		4
33.17	even	10		2178.2.a.bb.1.2		2
44.3	odd	10		528.2.y.d.289.1		4
44.27	odd	10		5808.2.a.cb.1.1		2
44.39	even	10		5808.2.a.cg.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.e.a.25.1	✓	4	11.3	even	5	inner
66.2.e.a.37.1	yes	4	1.1	even	1	trivial
198.2.f.c.37.1		4	3.2	odd	2
198.2.f.c.91.1		4	33.14	odd	10
528.2.y.d.289.1		4	44.3	odd	10
528.2.y.d.433.1		4	4.3	odd	2
726.2.a.j.1.1		2	11.6	odd	10
726.2.a.l.1.1		2	11.5	even	5
726.2.e.f.493.1		4	11.4	even	5
726.2.e.f.511.1		4	11.9	even	5
726.2.e.n.493.1		4	11.7	odd	10
726.2.e.n.511.1		4	11.2	odd	10
726.2.e.r.487.1		4	11.8	odd	10
726.2.e.r.565.1		4	11.10	odd	2
2178.2.a.t.1.2		2	33.5	odd	10
2178.2.a.bb.1.2		2	33.17	even	10
5808.2.a.cb.1.1		2	44.27	odd	10
5808.2.a.cg.1.1		2	44.39	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	66.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(3.11803 - 2.26538i) q^{5} +(0.809017 - 0.587785i) q^{6} +(0.736068 + 2.26538i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} -3.85410 q^{10} +(-3.23607 - 0.726543i) q^{11} -1.00000 q^{12} +(-1.00000 - 0.726543i) q^{13} +(0.736068 - 2.26538i) q^{14} +(1.19098 + 3.66547i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-5.23607 + 3.80423i) q^{17} +(0.309017 + 0.951057i) q^{18} +(0.381966 - 1.17557i) q^{19} +(3.11803 + 2.26538i) q^{20} -2.38197 q^{21} +(2.19098 + 2.48990i) q^{22} +1.23607 q^{23} +(0.809017 + 0.587785i) q^{24} +(3.04508 - 9.37181i) q^{25} +(0.381966 + 1.17557i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-1.92705 + 1.40008i) q^{28} +(-0.809017 - 2.48990i) q^{29} +(1.19098 - 3.66547i) q^{30} +(-5.16312 - 3.75123i) q^{31} +1.00000 q^{32} +(1.69098 - 2.85317i) q^{33} +6.47214 q^{34} +(7.42705 + 5.39607i) q^{35} +(0.309017 - 0.951057i) q^{36} +(3.23607 + 9.95959i) q^{37} +(-1.00000 + 0.726543i) q^{38} +(1.00000 - 0.726543i) q^{39} +(-1.19098 - 3.66547i) q^{40} +(0.381966 - 1.17557i) q^{41} +(1.92705 + 1.40008i) q^{42} +1.23607 q^{43} +(-0.309017 - 3.30220i) q^{44} -3.85410 q^{45} +(-1.00000 - 0.726543i) q^{46} +(-2.00000 + 6.15537i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(1.07295 - 0.779543i) q^{49} +(-7.97214 + 5.79210i) q^{50} +(-2.00000 - 6.15537i) q^{51} +(0.381966 - 1.17557i) q^{52} +(-2.30902 - 1.67760i) q^{53} -1.00000 q^{54} +(-11.7361 + 5.06555i) q^{55} +2.38197 q^{56} +(1.00000 + 0.726543i) q^{57} +(-0.809017 + 2.48990i) q^{58} +(0.881966 + 2.71441i) q^{59} +(-3.11803 + 2.26538i) q^{60} +(9.09017 - 6.60440i) q^{61} +(1.97214 + 6.06961i) q^{62} +(0.736068 - 2.26538i) q^{63} +(-0.809017 - 0.587785i) q^{64} -4.76393 q^{65} +(-3.04508 + 1.31433i) q^{66} +4.00000 q^{67} +(-5.23607 - 3.80423i) q^{68} +(-0.381966 + 1.17557i) q^{69} +(-2.83688 - 8.73102i) q^{70} +(-2.85410 + 2.07363i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(1.33688 + 4.11450i) q^{73} +(3.23607 - 9.95959i) q^{74} +(7.97214 + 5.79210i) q^{75} +1.23607 q^{76} +(-0.736068 - 7.86572i) q^{77} -1.23607 q^{78} +(-5.11803 - 3.71847i) q^{79} +(-1.19098 + 3.66547i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-1.00000 + 0.726543i) q^{82} +(13.2082 - 9.59632i) q^{83} +(-0.736068 - 2.26538i) q^{84} +(-7.70820 + 23.7234i) q^{85} +(-1.00000 - 0.726543i) q^{86} +2.61803 q^{87} +(-1.69098 + 2.85317i) q^{88} +1.70820 q^{89} +(3.11803 + 2.26538i) q^{90} +(0.909830 - 2.80017i) q^{91} +(0.381966 + 1.17557i) q^{92} +(5.16312 - 3.75123i) q^{93} +(5.23607 - 3.80423i) q^{94} +(-1.47214 - 4.53077i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(3.50000 + 2.54290i) q^{97} -1.32624 q^{98} +(2.19098 + 2.48990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{3} - q^{4} + 8 q^{5} + q^{6} - 6 q^{7} - q^{8} - q^{9} - 2 q^{10} - 4 q^{11} - 4 q^{12} - 4 q^{13} - 6 q^{14} + 7 q^{15} - q^{16} - 12 q^{17} - q^{18} + 6 q^{19} + 8 q^{20} - 14 q^{21}+ \cdots + 11 q^{99}+O(q^{100}) \) 4 * q - q^2 + q^3 - q^4 + 8 * q^5 + q^6 - 6 * q^7 - q^8 - q^9 - 2 * q^10 - 4 * q^11 - 4 * q^12 - 4 * q^13 - 6 * q^14 + 7 * q^15 - q^16 - 12 * q^17 - q^18 + 6 * q^19 + 8 * q^20 - 14 * q^21 + 11 * q^22 - 4 * q^23 + q^24 + q^25 + 6 * q^26 + q^27 - q^28 - q^29 + 7 * q^30 - 5 * q^31 + 4 * q^32 + 9 * q^33 + 8 * q^34 + 23 * q^35 - q^36 + 4 * q^37 - 4 * q^38 + 4 * q^39 - 7 * q^40 + 6 * q^41 + q^42 - 4 * q^43 + q^44 - 2 * q^45 - 4 * q^46 - 8 * q^47 + q^48 + 11 * q^49 - 14 * q^50 - 8 * q^51 + 6 * q^52 - 7 * q^53 - 4 * q^54 - 38 * q^55 + 14 * q^56 + 4 * q^57 - q^58 + 8 * q^59 - 8 * q^60 + 14 * q^61 - 10 * q^62 - 6 * q^63 - q^64 - 28 * q^65 - q^66 + 16 * q^67 - 12 * q^68 - 6 * q^69 - 27 * q^70 + 2 * q^71 - q^72 + 21 * q^73 + 4 * q^74 + 14 * q^75 - 4 * q^76 + 6 * q^77 + 4 * q^78 - 16 * q^79 - 7 * q^80 - q^81 - 4 * q^82 + 26 * q^83 + 6 * q^84 - 4 * q^85 - 4 * q^86 + 6 * q^87 - 9 * q^88 - 20 * q^89 + 8 * q^90 + 26 * q^91 + 6 * q^92 + 5 * q^93 + 12 * q^94 + 12 * q^95 + q^96 + 14 * q^97 + 26 * q^98 + 11 * q^99

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