LMFDB - Embedded newform 882.2.m.c.293.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(293,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("882.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.m (of order $6$, degree $2$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.19
Character	$\chi$	$=$	882.293
Dual form			882.2.m.c.587.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.0537332 - 1.73122i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.99341 + 3.45268i) q^{5} +(-0.819074 - 1.52614i) q^{6} -1.00000i q^{8} +(-2.99423 - 0.186048i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.0537332 - 1.73122i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.99341 + 3.45268i) q^{5} +(-0.819074 - 1.52614i) q^{6} -1.00000i q^{8} +(-2.99423 - 0.186048i) q^{9} +3.98682i q^{10} +(-1.43438 + 0.828141i) q^{11} +(-1.47241 - 0.912143i) q^{12} +(-2.60834 - 1.50592i) q^{13} +(5.87023 + 3.63655i) q^{15} +(-0.500000 - 0.866025i) q^{16} -7.45640 q^{17} +(-2.68610 + 1.33599i) q^{18} +4.57324i q^{19} +(1.99341 + 3.45268i) q^{20} +(-0.828141 + 1.43438i) q^{22} +(-0.253614 - 0.146424i) q^{23} +(-1.73122 - 0.0537332i) q^{24} +(-5.44735 - 9.43509i) q^{25} -3.01185 q^{26} +(-0.482978 + 5.17366i) q^{27} +(-3.18684 + 1.83992i) q^{29} +(6.90204 + 0.214224i) q^{30} +(4.08317 + 2.35742i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.35662 + 2.52773i) q^{33} +(-6.45743 + 3.72820i) q^{34} +(-1.65823 + 2.50005i) q^{36} +6.01391 q^{37} +(2.28662 + 3.96054i) q^{38} +(-2.74723 + 4.43468i) q^{39} +(3.45268 + 1.99341i) q^{40} +(-4.88630 + 8.46333i) q^{41} +(-1.29961 - 2.25100i) q^{43} +1.65628i q^{44} +(6.61108 - 9.96725i) q^{45} -0.292848 q^{46} +(-6.80622 - 11.7887i) q^{47} +(-1.52614 + 0.819074i) q^{48} +(-9.43509 - 5.44735i) q^{50} +(-0.400656 + 12.9086i) q^{51} +(-2.60834 + 1.50592i) q^{52} -0.916164i q^{53} +(2.16856 + 4.72201i) q^{54} -6.60330i q^{55} +(7.91727 + 0.245735i) q^{57} +(-1.83992 + 3.18684i) q^{58} +(3.53337 - 6.11998i) q^{59} +(6.08446 - 3.26550i) q^{60} +(5.75611 - 3.32329i) q^{61} +4.71484 q^{62} -1.00000 q^{64} +(10.3990 - 6.00384i) q^{65} +(2.43873 + 1.51077i) q^{66} +(-2.02838 + 3.51326i) q^{67} +(-3.72820 + 6.45743i) q^{68} +(-0.267120 + 0.431193i) q^{69} +13.9437i q^{71} +(-0.186048 + 2.99423i) q^{72} -4.44068i q^{73} +(5.20820 - 3.00695i) q^{74} +(-16.6269 + 8.92357i) q^{75} +(3.96054 + 2.28662i) q^{76} +(-0.161836 + 5.21416i) q^{78} +(-1.42365 - 2.46583i) q^{79} +3.98682 q^{80} +(8.93077 + 1.11414i) q^{81} +9.77261i q^{82} +(2.59432 + 4.49349i) q^{83} +(14.8636 - 25.7446i) q^{85} +(-2.25100 - 1.29961i) q^{86} +(3.01407 + 5.61597i) q^{87} +(0.828141 + 1.43438i) q^{88} +11.0173 q^{89} +(0.741738 - 11.9374i) q^{90} +(-0.253614 + 0.146424i) q^{92} +(4.30061 - 6.94219i) q^{93} +(-11.7887 - 6.80622i) q^{94} +(-15.7899 - 9.11633i) q^{95} +(-0.912143 + 1.47241i) q^{96} +(-2.51510 + 1.45209i) q^{97} +(4.44894 - 2.21278i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} - 32 q^{9}+O(q^{10}) $ 48 * q + 24 * q^4 - 32 * q^9	$ 48 q + 24 q^{4} - 32 q^{9} + 48 q^{11} + 48 q^{15} - 24 q^{16} + 16 q^{18} + 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} - 64 q^{39} - 48 q^{50} - 80 q^{57} - 48 q^{64} + 32 q^{72} + 32 q^{78} + 48 q^{79} + 48 q^{85} + 96 q^{86} + 48 q^{92} + 96 q^{93} - 192 q^{95} + 104 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 - 32 * q^9 + 48 * q^11 + 48 * q^15 - 24 * q^16 + 16 * q^18 + 48 * q^23 - 24 * q^25 - 16 * q^30 - 16 * q^36 - 64 * q^39 - 48 * q^50 - 80 * q^57 - 48 * q^64 + 32 * q^72 + 32 * q^78 + 48 * q^79 + 48 * q^85 + 96 * q^86 + 48 * q^92 + 96 * q^93 - 192 * q^95 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	0.0537332	−	1.73122i	0.0310229	−	0.999519i
$3$	0.0537332	−	1.73122i	0.0310229	−	0.999519i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.99341	+	3.45268i	−0.891479	+	1.54409i	−0.0533767	+	0.998574i	$0.516998\pi$
$5$	−1.99341	+	3.45268i	−0.891479	+	1.54409i	−0.838102	+	0.545513i	$0.816335\pi$
$6$	−0.819074	−	1.52614i	−0.334386	−	0.623046i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−2.99423	−	0.186048i	−0.998075	−	0.0620159i
$10$			3.98682i			1.26074i
$11$	−1.43438	+	0.828141i	−0.432483	+	0.249694i	−0.700404	−	0.713747i	$-0.746997\pi$
$11$	−1.43438	+	0.828141i	−0.432483	+	0.249694i	0.267921	+	0.963441i	$0.413663\pi$
$12$	−1.47241	−	0.912143i	−0.425049	−	0.263313i
$13$	−2.60834	−	1.50592i	−0.723422	−	0.417668i	0.0925888	−	0.995704i	$-0.470486\pi$
$13$	−2.60834	−	1.50592i	−0.723422	−	0.417668i	−0.816011	+	0.578036i	$0.803819\pi$
$14$		0			0
$15$	5.87023	+	3.63655i	1.51569	+	0.938952i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−7.45640			−1.80844			−0.904221	−	0.427065i	$-0.859548\pi$
$17$	−7.45640			−1.80844			−0.904221	+	0.427065i	$0.859548\pi$
$18$	−2.68610	+	1.33599i	−0.633120	+	0.314896i
$19$			4.57324i			1.04917i	0.851357	+	0.524586i	$0.175780\pi$
$19$			4.57324i			1.04917i	−0.851357	+	0.524586i	$0.824220\pi$
$20$	1.99341	+	3.45268i	0.445740	+	0.772044i
$21$		0			0
$22$	−0.828141	+	1.43438i	−0.176560	+	0.305811i
$23$	−0.253614	−	0.146424i	−0.0528822	−	0.0305316i	0.473326	−	0.880887i	$-0.343053\pi$
$23$	−0.253614	−	0.146424i	−0.0528822	−	0.0305316i	−0.526208	+	0.850356i	$0.676387\pi$
$24$	−1.73122	−	0.0537332i	−0.353383	−	0.0109682i
$25$	−5.44735	−	9.43509i	−1.08947	−	1.88702i
$26$	−3.01185			−0.590672
$27$	−0.482978	+	5.17366i	−0.0929492	+	0.995671i
$28$		0			0
$29$	−3.18684	+	1.83992i	−0.591781	+	0.341665i	−0.765801	−	0.643077i	$-0.777657\pi$
$29$	−3.18684	+	1.83992i	−0.591781	+	0.341665i	0.174020	+	0.984742i	$0.444324\pi$
$30$	6.90204	+	0.214224i	1.26014	+	0.0391119i
$31$	4.08317	+	2.35742i	0.733360	+	0.423405i	0.819650	−	0.572865i	$-0.194168\pi$
$31$	4.08317	+	2.35742i	0.733360	+	0.423405i	−0.0862903	+	0.996270i	$0.527501\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	1.35662	+	2.52773i	0.236157	+	0.440021i
$34$	−6.45743	+	3.72820i	−1.10744	+	0.639381i
$35$		0			0
$36$	−1.65823	+	2.50005i	−0.276372	+	0.416675i
$37$	6.01391			0.988680			0.494340	−	0.869269i	$-0.335410\pi$
$37$	6.01391			0.988680			0.494340	+	0.869269i	$0.335410\pi$
$38$	2.28662	+	3.96054i	0.370939	+	0.642484i
$39$	−2.74723	+	4.43468i	−0.439910	+	0.710117i
$40$	3.45268	+	1.99341i	0.545917	+	0.315185i
$41$	−4.88630	+	8.46333i	−0.763113	+	1.32175i	0.178126	+	0.984008i	$0.442996\pi$
$41$	−4.88630	+	8.46333i	−0.763113	+	1.32175i	−0.941239	+	0.337742i	$0.890337\pi$
$42$		0			0
$43$	−1.29961	−	2.25100i	−0.198189	−	0.343274i	0.749752	−	0.661719i	$-0.230173\pi$
$43$	−1.29961	−	2.25100i	−0.198189	−	0.343274i	−0.947941	+	0.318445i	$0.896839\pi$
$44$			1.65628i			0.249694i
$45$	6.61108	−	9.96725i	0.985521	−	1.48583i
$46$	−0.292848			−0.0431782
$47$	−6.80622	−	11.7887i	−0.992789	−	1.71956i	−0.600210	−	0.799843i	$-0.704916\pi$
$47$	−6.80622	−	11.7887i	−0.992789	−	1.71956i	−0.392579	−	0.919718i	$-0.628417\pi$
$48$	−1.52614	+	0.819074i	−0.220280	+	0.118223i
$49$		0			0
$50$	−9.43509	−	5.44735i	−1.33432	−	0.770372i
$51$	−0.400656	+	12.9086i	−0.0561031	+	1.80757i
$52$	−2.60834	+	1.50592i	−0.361711	+	0.208834i
$53$		−	0.916164i		−	0.125845i	−0.998018	−	0.0629224i	$-0.979958\pi$
$53$		−	0.916164i		−	0.125845i	0.998018	−	0.0629224i	$-0.0200421\pi$
$54$	2.16856	+	4.72201i	0.295103	+	0.642584i
$55$		−	6.60330i		−	0.890388i
$56$		0			0
$57$	7.91727	+	0.245735i	1.04867	+	0.0325484i
$58$	−1.83992	+	3.18684i	−0.241594	+	0.418452i
$59$	3.53337	−	6.11998i	0.460006	−	0.796753i	−0.538955	−	0.842335i	$-0.681181\pi$
$59$	3.53337	−	6.11998i	0.460006	−	0.796753i	0.998961	+	0.0455815i	$0.0145141\pi$
$60$	6.08446	−	3.26550i	0.785500	−	0.421574i
$61$	5.75611	−	3.32329i	0.736995	−	0.425504i	−0.0839809	−	0.996467i	$-0.526763\pi$
$61$	5.75611	−	3.32329i	0.736995	−	0.425504i	0.820976	+	0.570963i	$0.193430\pi$
$62$	4.71484			0.598786
$63$		0			0
$64$	−1.00000			−0.125000
$65$	10.3990	−	6.00384i	1.28983	−	0.744685i
$66$	2.43873	+	1.51077i	0.300187	+	0.185963i
$67$	−2.02838	+	3.51326i	−0.247806	+	0.429213i	−0.962917	−	0.269798i	$-0.913043\pi$
$67$	−2.02838	+	3.51326i	−0.247806	+	0.429213i	0.715111	+	0.699011i	$0.246376\pi$
$68$	−3.72820	+	6.45743i	−0.452111	+	0.783078i
$69$	−0.267120	+	0.431193i	−0.0321574	+	0.0519096i
$70$		0			0
$71$			13.9437i			1.65481i	0.561605	+	0.827406i	$0.310184\pi$
$71$			13.9437i			1.65481i	−0.561605	+	0.827406i	$0.689816\pi$
$72$	−0.186048	+	2.99423i	−0.0219259	+	0.352873i
$73$		−	4.44068i		−	0.519742i	−0.965643	−	0.259871i	$-0.916320\pi$
$73$		−	4.44068i		−	0.519742i	0.965643	−	0.259871i	$-0.0836801\pi$
$74$	5.20820	−	3.00695i	0.605441	−	0.349551i
$75$	−16.6269	+	8.92357i	−1.91991	+	1.03041i
$76$	3.96054	+	2.28662i	0.454305	+	0.262293i
$77$		0			0
$78$	−0.161836	+	5.21416i	−0.0183243	+	0.590387i
$79$	−1.42365	−	2.46583i	−0.160173	−	0.277428i	0.774758	−	0.632258i	$-0.217872\pi$
$79$	−1.42365	−	2.46583i	−0.160173	−	0.277428i	−0.934931	+	0.354831i	$0.884539\pi$
$80$	3.98682			0.445740
$81$	8.93077	+	1.11414i	0.992308	+	0.123793i
$82$			9.77261i			1.07920i
$83$	2.59432	+	4.49349i	0.284763	+	0.493224i	0.972552	−	0.232687i	$-0.0747517\pi$
$83$	2.59432	+	4.49349i	0.284763	+	0.493224i	−0.687789	+	0.725911i	$0.741418\pi$
$84$		0			0
$85$	14.8636	−	25.7446i	1.61219	−	2.79239i
$86$	−2.25100	−	1.29961i	−0.242731	−	0.140141i
$87$	3.01407	+	5.61597i	0.323142	+	0.602096i
$88$	0.828141	+	1.43438i	0.0882802	+	0.152906i
$89$	11.0173			1.16783			0.583917	−	0.811814i	$-0.301519\pi$
$89$	11.0173			1.16783			0.583917	+	0.811814i	$0.301519\pi$
$90$	0.741738	−	11.9374i	0.0781861	−	1.25832i
$91$		0			0
$92$	−0.253614	+	0.146424i	−0.0264411	+	0.0152658i
$93$	4.30061	−	6.94219i	0.445953	−	0.719871i
$94$	−11.7887	−	6.80622i	−1.21591	−	0.702008i
$95$	−15.7899	−	9.11633i	−1.62001	−	0.935316i
$96$	−0.912143	+	1.47241i	−0.0930952	+	0.150277i
$97$	−2.51510	+	1.45209i	−0.255369	+	0.147438i	−0.622220	−	0.782842i	$-0.713769\pi$
$97$	−2.51510	+	1.45209i	−0.255369	+	0.147438i	0.366851	+	0.930280i	$0.380436\pi$
$98$		0			0
$99$	4.44894	−	2.21278i	0.447135	−	0.222393i
$100$	−10.8947			−1.08947
$101$	0.129291	+	0.223938i	0.0128649	+	0.0222827i	0.872386	−	0.488817i	$-0.162572\pi$
$101$	0.129291	+	0.223938i	0.0128649	+	0.0222827i	−0.859521	+	0.511100i	$0.829238\pi$
$102$	6.10734	+	11.3795i	0.604717	+	1.12674i
$103$	−5.89979	−	3.40625i	−0.581324	−	0.335627i	0.180336	−	0.983605i	$-0.442282\pi$
$103$	−5.89979	−	3.40625i	−0.581324	−	0.335627i	−0.761659	+	0.647978i	$0.775615\pi$
$104$	−1.50592	+	2.60834i	−0.147668	+	0.255768i
$105$		0			0
$106$	−0.458082	−	0.793421i	−0.0444928	−	0.0770639i
$107$			10.6382i			1.02844i	0.857659	+	0.514219i	$0.171918\pi$
$107$			10.6382i			1.02844i	−0.857659	+	0.514219i	$0.828082\pi$
$108$	4.23903	+	3.00510i	0.407901	+	0.289166i
$109$	−4.51775			−0.432721			−0.216361	−	0.976313i	$-0.569419\pi$
$109$	−4.51775			−0.432721			−0.216361	+	0.976313i	$0.569419\pi$
$110$	−3.30165	−	5.71862i	−0.314800	−	0.545249i
$111$	0.323147	−	10.4114i	0.0306717	−	0.988204i
$112$		0			0
$113$	−1.47530	−	0.851764i	−0.138784	−	0.0801272i	0.429000	−	0.903304i	$-0.358866\pi$
$113$	−1.47530	−	0.851764i	−0.138784	−	0.0801272i	−0.567785	+	0.823177i	$0.692199\pi$
$114$	6.97942	−	3.74582i	0.653683	−	0.350828i
$115$	1.01111	−	0.583767i	0.0942868	−	0.0544365i
$116$			3.67984i			0.341665i
$117$	7.52977	+	4.99435i	0.696128	+	0.461728i
$118$		−	7.06674i		−	0.650546i
$119$		0			0
$120$	3.63655	−	5.87023i	0.331970	−	0.535877i
$121$	−4.12836	+	7.15054i	−0.375306	+	0.650049i
$122$	3.32329	−	5.75611i	0.300877	−	0.521134i
$123$	14.3893	+	8.91402i	1.29744	+	0.803750i
$124$	4.08317	−	2.35742i	0.366680	−	0.211703i
$125$	23.5011			2.10200
$126$		0			0
$127$	−4.93203			−0.437647			−0.218823	−	0.975765i	$-0.570222\pi$
$127$	−4.93203			−0.437647			−0.218823	+	0.975765i	$0.570222\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−3.96680	+	2.12896i	−0.349257	+	0.187445i
$130$	6.00384	−	10.3990i	0.526572	−	0.912049i
$131$	10.8056	−	18.7158i	0.944088	−	1.63521i	0.186520	−	0.982451i	$-0.440279\pi$
$131$	10.8056	−	18.7158i	0.944088	−	1.63521i	0.757567	−	0.652757i	$-0.226388\pi$
$132$	2.86739	+	0.0889974i	0.249574	+	0.00774623i
$133$		0			0
$134$			4.05676i			0.350451i
$135$	−16.9002	−	11.9808i	−1.45454	−	1.03114i
$136$			7.45640i			0.639381i
$137$	−5.93663	+	3.42752i	−0.507201	+	0.292832i	−0.731682	−	0.681646i	$-0.761264\pi$
$137$	−5.93663	+	3.42752i	−0.507201	+	0.292832i	0.224482	+	0.974478i	$0.427931\pi$
$138$	−0.0157357	+	0.506984i	−0.00133951	+	0.0431574i
$139$	−13.9583	−	8.05882i	−1.18393	−	0.683540i	−0.227007	−	0.973893i	$-0.572894\pi$
$139$	−13.9583	−	8.05882i	−1.18393	−	0.683540i	−0.956920	+	0.290353i	$0.906227\pi$
$140$		0			0
$141$	−20.7745	+	11.1496i	−1.74953	+	0.938965i
$142$	6.97184	+	12.0756i	0.585064	+	1.01336i
$143$	4.98847			0.417157
$144$	1.33599	+	2.68610i	0.111333	+	0.223842i
$145$		−	14.6709i		−	1.21835i
$146$	−2.22034	−	3.84574i	−0.183757	−	0.318276i
$147$		0			0
$148$	3.00695	−	5.20820i	0.247170	−	0.428111i
$149$	1.05460	+	0.608875i	0.0863964	+	0.0498810i	0.542576	−	0.840007i	$-0.317449\pi$
$149$	1.05460	+	0.608875i	0.0863964	+	0.0498810i	−0.456179	+	0.889888i	$0.650782\pi$
$150$	−9.93753	+	16.0415i	−0.811396	+	1.30978i
$151$	−7.01991	−	12.1588i	−0.571272	−	0.989472i	−0.996436	−	0.0843554i	$-0.973117\pi$
$151$	−7.01991	−	12.1588i	−0.571272	−	0.989472i	0.425164	−	0.905116i	$-0.360216\pi$
$152$	4.57324			0.370939
$153$	22.3261	+	1.38725i	1.80496	+	0.112152i
$154$		0			0
$155$	−16.2789	+	9.39861i	−1.30755	+	0.754914i
$156$	2.46693	+	4.59651i	0.197512	+	0.368016i
$157$	−20.4334	−	11.7972i	−1.63076	−	0.941520i	−0.983859	−	0.178947i	$-0.942731\pi$
$157$	−20.4334	−	11.7972i	−1.63076	−	0.941520i	−0.646902	−	0.762573i	$-0.723936\pi$
$158$	−2.46583	−	1.42365i	−0.196171	−	0.113259i
$159$	−1.58608	−	0.0492284i	−0.125784	−	0.00390407i
$160$	3.45268	−	1.99341i	0.272959	−	0.157593i
$161$		0			0
$162$	8.29134	−	3.50051i	0.651430	−	0.275026i
$163$	0.599226			0.0469350			0.0234675	−	0.999725i	$-0.492529\pi$
$163$	0.599226			0.0469350			0.0234675	+	0.999725i	$0.492529\pi$
$164$	4.88630	+	8.46333i	0.381556	+	0.660875i
$165$	−11.4317	−	0.354816i	−0.889960	−	0.0276224i
$166$	4.49349	+	2.59432i	0.348762	+	0.201358i
$167$	−2.67267	+	4.62919i	−0.206817	+	0.358218i	−0.950710	−	0.310081i	$-0.899644\pi$
$167$	−2.67267	+	4.62919i	−0.206817	+	0.358218i	0.743893	+	0.668299i	$0.232977\pi$
$168$		0			0
$169$	−1.96439	−	3.40242i	−0.151107	−	0.261725i
$170$		−	29.7273i		−	2.27998i
$171$	0.850840	−	13.6933i	0.0650654	−	1.04715i
$172$	−2.59923			−0.198189
$173$	−6.06176	−	10.4993i	−0.460867	−	0.798245i	0.538137	−	0.842857i	$-0.319128\pi$
$173$	−6.06176	−	10.4993i	−0.460867	−	0.798245i	−0.999004	+	0.0446121i	$0.985795\pi$
$174$	5.41824	+	3.35654i	0.410756	+	0.254459i
$175$		0			0
$176$	1.43438	+	0.828141i	0.108121	+	0.0624235i
$177$	−10.4051	−	6.44588i	−0.782099	−	0.484502i
$178$	9.54128	−	5.50866i	0.715149	−	0.412891i
$179$			5.56124i			0.415667i	0.978164	+	0.207833i	$0.0666412\pi$
$179$			5.56124i			0.415667i	−0.978164	+	0.207833i	$0.933359\pi$
$180$	−5.32635	−	10.7090i	−0.397003	−	0.798201i
$181$			12.5545i			0.933167i	0.884477	+	0.466583i	$0.154515\pi$
$181$			12.5545i			0.933167i	−0.884477	+	0.466583i	$0.845485\pi$
$182$		0			0
$183$	−5.44405	−	10.1437i	−0.402436	−	0.749840i
$184$	−0.146424	+	0.253614i	−0.0107945	+	0.0186967i
$185$	−11.9882	+	20.7641i	−0.881388	+	1.52661i
$186$	0.253344	−	8.16242i	0.0185761	−	0.598497i
$187$	10.6953	−	6.17495i	0.782120	−	0.451557i
$188$	−13.6124			−0.992789
$189$		0			0
$190$	−18.2327			−1.32274
$191$	−16.3982	+	9.46751i	−1.18653	+	0.685045i	−0.957517	−	0.288378i	$-0.906884\pi$
$191$	−16.3982	+	9.46751i	−1.18653	+	0.685045i	−0.229016	+	0.973423i	$0.573551\pi$
$192$	−0.0537332	+	1.73122i	−0.00387786	+	0.124940i
$193$	−3.80733	+	6.59448i	−0.274057	+	0.474681i	−0.969897	−	0.243516i	$-0.921699\pi$
$193$	−3.80733	+	6.59448i	−0.274057	+	0.474681i	0.695840	+	0.718197i	$0.255032\pi$
$194$	−1.45209	+	2.51510i	−0.104254	+	0.180573i
$195$	−9.83518	−	18.3255i	−0.704312	−	1.31231i
$196$		0			0
$197$		−	6.04895i		−	0.430970i	−0.976507	−	0.215485i	$-0.930867\pi$
$197$		−	6.04895i		−	0.430970i	0.976507	−	0.215485i	$-0.0691332\pi$
$198$	2.74651	−	4.14079i	0.195186	−	0.294273i
$199$			22.8893i			1.62258i	0.584646	+	0.811289i	$0.301233\pi$
$199$			22.8893i			1.62258i	−0.584646	+	0.811289i	$0.698767\pi$
$200$	−9.43509	+	5.44735i	−0.667162	+	0.385186i
$201$	5.97322	+	3.70035i	0.421318	+	0.261002i
$202$	0.223938	+	0.129291i	0.0157562	+	0.00909687i
$203$		0			0
$204$	10.9789	+	6.80130i	0.768676	+	0.476186i
$205$	−19.4808	−	33.7417i	−1.36060	−	2.35662i
$206$	−6.81249			−0.474649
$207$	0.732136	+	0.485612i	0.0508870	+	0.0337523i
$208$			3.01185i			0.208834i
$209$	−3.78729	−	6.55977i	−0.261972	−	0.453749i
$210$		0			0
$211$	3.36942	−	5.83601i	0.231961	−	0.401768i	−0.726424	−	0.687246i	$-0.758819\pi$
$211$	3.36942	−	5.83601i	0.231961	−	0.401768i	0.958385	+	0.285479i	$0.0921526\pi$
$212$	−0.793421	−	0.458082i	−0.0544924	−	0.0314612i
$213$	24.1396	+	0.749239i	1.65401	+	0.0513370i
$214$	5.31912	+	9.21299i	0.363608	+	0.629787i
$215$	10.3626			0.706727
$216$	5.17366	+	0.482978i	0.352023	+	0.0328625i
$217$		0			0
$218$	−3.91248	+	2.25887i	−0.264987	+	0.152990i
$219$	−7.68778	−	0.238612i	−0.519492	−	0.0161239i
$220$	−5.71862	−	3.30165i	−0.385549	−	0.222597i
$221$	19.4488	+	11.2288i	1.30827	+	0.755328i
$222$	−4.92584	−	9.17809i	−0.330600	−	0.615993i
$223$	−7.85930	+	4.53757i	−0.526298	+	0.303858i	−0.739507	−	0.673148i	$-0.764942\pi$
$223$	−7.85930	+	4.53757i	−0.526298	+	0.303858i	0.213210	+	0.977006i	$0.431608\pi$
$224$		0			0
$225$	14.5552	+	29.2643i	0.970348	+	1.95095i
$226$	−1.70353			−0.113317
$227$	−0.313680	−	0.543310i	−0.0208197	−	0.0360607i	0.855428	−	0.517922i	$-0.173294\pi$
$227$	−0.313680	−	0.543310i	−0.0208197	−	0.0360607i	−0.876248	+	0.481861i	$0.839961\pi$
$228$	4.17145	−	6.73369i	0.276261	−	0.445949i
$229$	16.0593	+	9.27182i	1.06123	+	0.612699i	0.925771	−	0.378084i	$-0.123417\pi$
$229$	16.0593	+	9.27182i	1.06123	+	0.612699i	0.135455	+	0.990784i	$0.456750\pi$
$230$	0.583767	−	1.01111i	0.0384924	−	0.0666708i
$231$		0			0
$232$	1.83992	+	3.18684i	0.120797	+	0.209226i
$233$			10.4237i			0.682877i	0.939904	+	0.341438i	$0.110914\pi$
$233$			10.4237i			0.682877i	−0.939904	+	0.341438i	$0.889086\pi$
$234$	9.01815	+	0.560347i	0.589535	+	0.0366310i
$235$	54.2703			3.54020
$236$	−3.53337	−	6.11998i	−0.230003	−	0.398377i
$237$	−4.34539	+	2.33215i	−0.282263	+	0.151489i
$238$		0			0
$239$	5.88865	+	3.39981i	0.380905	+	0.219915i	0.678212	−	0.734866i	$-0.262755\pi$
$239$	5.88865	+	3.39981i	0.380905	+	0.219915i	−0.297307	+	0.954782i	$0.596089\pi$
$240$	0.214224	−	6.90204i	0.0138281	−	0.445525i
$241$	16.3106	−	9.41695i	1.05066	−	0.606599i	0.127826	−	0.991797i	$-0.459200\pi$
$241$	16.3106	−	9.41695i	1.05066	−	0.606599i	0.922834	+	0.385197i	$0.125867\pi$
$242$			8.25673i			0.530763i
$243$	2.40869	−	15.4012i	0.154518	−	0.987990i
$244$		−	6.64659i		−	0.425504i
$245$		0			0
$246$	16.9185	+	0.525114i	1.07868	+	0.0334800i
$247$	6.88694	−	11.9285i	0.438206	−	0.758995i
$248$	2.35742	−	4.08317i	0.149696	−	0.259282i
$249$	7.91860	−	4.24988i	0.501821	−	0.269325i
$250$	20.3525	−	11.7505i	1.28721	−	0.743170i
$251$	−0.0465190			−0.00293625			−0.00146813	−	0.999999i	$-0.500467\pi$
$251$	−0.0465190			−0.00293625			−0.00146813	+	0.999999i	$0.500467\pi$
$252$		0			0
$253$	0.485040			0.0304942
$254$	−4.27126	+	2.46601i	−0.268003	+	0.154731i
$255$	−43.7708	−	27.1155i	−2.74103	−	1.69804i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.60276	+	13.1684i	−0.474247	+	0.821420i	−0.999565	−	0.0294859i	$-0.990613\pi$
$257$	−7.60276	+	13.1684i	−0.474247	+	0.821420i	0.525318	+	0.850906i	$0.323946\pi$
$258$	−2.37087	+	3.82713i	−0.147604	+	0.238267i
$259$		0			0
$260$		−	12.0077i		−	0.744685i
$261$	9.88442	−	4.91624i	0.611831	−	0.304307i
$262$		−	21.6112i		−	1.33514i
$263$	1.69410	−	0.978086i	0.104462	−	0.0603114i	−0.446859	−	0.894605i	$-0.647457\pi$
$263$	1.69410	−	0.978086i	0.104462	−	0.0603114i	0.551321	+	0.834293i	$0.314124\pi$
$264$	2.52773	−	1.35662i	0.155571	−	0.0834941i
$265$	3.16322	+	1.82629i	0.194315	+	0.112188i
$266$		0			0
$267$	0.591996	−	19.0734i	0.0362296	−	1.16727i
$268$	2.02838	+	3.51326i	0.123903	+	0.214606i
$269$	5.45872			0.332824			0.166412	−	0.986056i	$-0.446782\pi$
$269$	5.45872			0.332824			0.166412	+	0.986056i	$0.446782\pi$
$270$	−20.6264	−	1.92555i	−1.25528	−	0.117185i
$271$			14.7969i			0.898846i	0.893319	+	0.449423i	$0.148370\pi$
$271$			14.7969i			0.898846i	−0.893319	+	0.449423i	$0.851630\pi$
$272$	3.72820	+	6.45743i	0.226055	+	0.391539i
$273$		0			0
$274$	−3.42752	+	5.93663i	−0.207064	+	0.358645i
$275$	15.6272	+	9.02236i	0.942354	+	0.544068i
$276$	0.239865	+	0.446929i	0.0144382	+	0.0269020i
$277$	5.23636	+	9.06963i	0.314622	+	0.544941i	0.979357	−	0.202138i	$-0.0647889\pi$
$277$	5.23636	+	9.06963i	0.314622	+	0.544941i	−0.664735	+	0.747079i	$0.731456\pi$
$278$	−16.1176			−0.966672
$279$	−11.7873	−	7.81832i	−0.705690	−	0.468070i
$280$		0			0
$281$	1.02488	−	0.591716i	0.0611394	−	0.0352988i	−0.469119	−	0.883135i	$-0.655428\pi$
$281$	1.02488	−	0.591716i	0.0611394	−	0.0352988i	0.530258	+	0.847836i	$0.322095\pi$
$282$	−12.4165	+	20.0431i	−0.739391	+	1.19355i
$283$	25.6238	+	14.7939i	1.52318	+	0.879408i	0.999624	+	0.0274160i	$0.00872789\pi$
$283$	25.6238	+	14.7939i	1.52318	+	0.879408i	0.523555	+	0.851992i	$0.324605\pi$
$284$	12.0756	+	6.97184i	0.716554	+	0.413703i
$285$	−16.6308	+	26.8460i	−0.985123	+	1.59022i
$286$	4.32014	−	2.49423i	0.255455	−	0.147487i
$287$		0			0
$288$	2.50005	+	1.65823i	0.147317	+	0.0977124i
$289$	38.5979			2.27046
$290$	−7.33543	−	12.7053i	−0.430751	−	0.746083i
$291$	2.37874	+	4.43221i	0.139444	+	0.259821i
$292$	−3.84574	−	2.22034i	−0.225055	−	0.129936i
$293$	6.64419	−	11.5081i	0.388158	−	0.672309i	−0.604044	−	0.796951i	$-0.706445\pi$
$293$	6.64419	−	11.5081i	0.388158	−	0.672309i	0.992202	+	0.124642i	$0.0397782\pi$
$294$		0			0
$295$	14.0869	+	24.3992i	0.820171	+	1.42058i
$296$		−	6.01391i		−	0.349551i
$297$	−3.59174	−	7.82098i	−0.208414	−	0.453819i
$298$	1.21775			0.0705424
$299$	0.441007	+	0.763847i	0.0255041	+	0.0441744i
$300$	−0.585407	+	18.8611i	−0.0337985	+	1.08895i
$301$		0			0
$302$	−12.1588	−	7.01991i	−0.699662	−	0.403950i
$303$	0.394633	−	0.211798i	0.0226711	−	0.0121675i
$304$	3.96054	−	2.28662i	0.227153	−	0.131147i
$305$			26.4987i			1.51731i
$306$	20.0286	−	9.96168i	1.14496	−	0.569471i
$307$			3.34549i			0.190937i	0.995432	+	0.0954686i	$0.0304350\pi$
$307$			3.34549i			0.190937i	−0.995432	+	0.0954686i	$0.969565\pi$
$308$		0			0
$309$	−6.21397	+	10.0308i	−0.353500	+	0.570632i
$310$	−9.39861	+	16.2789i	−0.533805	+	0.924577i
$311$	−11.3917	+	19.7310i	−0.645964	+	1.11884i	0.338114	+	0.941105i	$0.390211\pi$
$311$	−11.3917	+	19.7310i	−0.645964	+	1.11884i	−0.984078	+	0.177737i	$0.943122\pi$
$312$	4.43468	+	2.74723i	0.251064	+	0.155532i
$313$	1.01182	−	0.584177i	0.0571917	−	0.0330196i	−0.471132	−	0.882063i	$-0.656154\pi$
$313$	1.01182	−	0.584177i	0.0571917	−	0.0330196i	0.528323	+	0.849043i	$0.322821\pi$
$314$	−23.5944			−1.33151
$315$		0			0
$316$	−2.84730			−0.160173
$317$	−18.8828	+	10.9020i	−1.06056	+	0.612316i	−0.925588	−	0.378533i	$-0.876429\pi$
$317$	−18.8828	+	10.9020i	−1.06056	+	0.612316i	−0.134974	+	0.990849i	$0.543095\pi$
$318$	−1.39820	+	0.750406i	−0.0784071	+	0.0420807i
$319$	3.04743	−	5.27831i	0.170623	−	0.295528i
$320$	1.99341	−	3.45268i	0.111435	−	0.193011i
$321$	18.4171	+	0.571627i	1.02794	+	0.0319051i
$322$		0			0
$323$		−	34.0999i		−	1.89737i
$324$	5.43026	−	7.17721i	0.301681	−	0.398734i
$325$			32.8132i			1.82015i
$326$	0.518945	−	0.299613i	0.0287417	−	0.0165940i
$327$	−0.242753	+	7.82120i	−0.0134243	+	0.432513i
$328$	8.46333	+	4.88630i	0.467309	+	0.269801i
$329$		0			0
$330$	−10.0776	+	5.40859i	−0.554753	+	0.297733i
$331$	13.9427	+	24.1494i	0.766359	+	1.32737i	0.939525	+	0.342480i	$0.111267\pi$
$331$	13.9427	+	24.1494i	0.766359	+	1.32737i	−0.173166	+	0.984893i	$0.555400\pi$
$332$	5.18863			0.284763
$333$	−18.0070	−	1.11887i	−0.986777	−	0.0613139i
$334$			5.34533i			0.292484i
$335$	−8.08678	−	14.0067i	−0.441828	−	0.765268i
$336$		0			0
$337$	0.00328349	−	0.00568717i	0.000178863	−	0.000309800i	−0.865936	−	0.500155i	$-0.833276\pi$
$337$	0.00328349	−	0.00568717i	0.000178863	−	0.000309800i	0.866115	+	0.499845i	$0.166610\pi$
$338$	−3.40242	−	1.96439i	−0.185067	−	0.106849i
$339$	−1.55386	+	2.50829i	−0.0843941	+	0.136232i
$340$	−14.8636	−	25.7446i	−0.806094	−	1.39620i
$341$	−7.80911			−0.422887
$342$	−6.10980	−	12.2842i	−0.330380	−	0.664252i
$343$		0			0
$344$	−2.25100	+	1.29961i	−0.121366	+	0.0700705i
$345$	−0.956296	−	1.78182i	−0.0514853	−	0.0959302i
$346$	−10.4993	−	6.06176i	−0.564445	−	0.325882i
$347$	−17.7497	−	10.2478i	−0.952856	−	0.550132i	−0.0588892	−	0.998265i	$-0.518756\pi$
$347$	−17.7497	−	10.2478i	−0.952856	−	0.550132i	−0.893967	+	0.448133i	$0.852089\pi$
$348$	6.37061	+	0.197730i	0.341500	+	0.0105994i
$349$	−7.24341	+	4.18198i	−0.387731	+	0.223856i	−0.681176	−	0.732119i	$-0.738531\pi$
$349$	−7.24341	+	4.18198i	−0.387731	+	0.223856i	0.293446	+	0.955976i	$0.405198\pi$
$350$		0			0
$351$	9.05090	−	12.7673i	0.483101	−	0.681468i
$352$	1.65628			0.0882802
$353$	−3.07430	−	5.32484i	−0.163628	−	0.283413i	0.772539	−	0.634967i	$-0.218986\pi$
$353$	−3.07430	−	5.32484i	−0.163628	−	0.283413i	−0.936167	+	0.351555i	$0.885653\pi$
$354$	−12.2341	−	0.379719i	−0.650233	−	0.0201818i
$355$	−48.1431	−	27.7955i	−2.55517	−	1.47523i
$356$	5.50866	−	9.54128i	0.291958	−	0.505687i
$357$		0			0
$358$	2.78062	+	4.81618i	0.146960	+	0.254543i
$359$		−	5.80473i		−	0.306362i	−0.988198	−	0.153181i	$-0.951048\pi$
$359$		−	5.80473i		−	0.306362i	0.988198	−	0.153181i	$-0.0489517\pi$
$360$	−9.96725	−	6.61108i	−0.525320	−	0.348434i
$361$	−1.91450			−0.100763
$362$	6.27724	+	10.8725i	0.329924	+	0.571446i
$363$	12.1573	+	7.53131i	0.638093	+	0.395292i
$364$		0			0
$365$	15.3323	+	8.85209i	0.802527	+	0.463339i
$366$	−9.78651	−	6.06264i	−0.511549	−	0.316899i
$367$	5.16659	−	2.98293i	0.269694	−	0.155708i	−0.359055	−	0.933317i	$-0.616901\pi$
$367$	5.16659	−	2.98293i	0.269694	−	0.155708i	0.628748	+	0.777609i	$0.283568\pi$
$368$			0.292848i			0.0152658i
$369$	16.2053	−	24.4320i	0.843613	−	1.27188i
$370$			23.9763i			1.24647i
$371$		0			0
$372$	−3.86181	−	7.19553i	−0.200225	−	0.373071i
$373$	9.43291	−	16.3383i	0.488418	−	0.845964i	−0.511494	−	0.859287i	$-0.670908\pi$
$373$	9.43291	−	16.3383i	0.488418	−	0.845964i	0.999911	+	0.0133229i	$0.00424093\pi$
$374$	6.17495	−	10.6953i	0.319299	−	0.553042i
$375$	1.26279	−	40.6855i	0.0652102	−	2.10099i
$376$	−11.7887	+	6.80622i	−0.607957	+	0.351004i
$377$	11.0831			0.570810
$378$		0			0
$379$	−12.5331			−0.643784			−0.321892	−	0.946776i	$-0.604319\pi$
$379$	−12.5331			−0.643784			−0.321892	+	0.946776i	$0.604319\pi$
$380$	−15.7899	+	9.11633i	−0.810007	+	0.467658i
$381$	−0.265014	+	8.53841i	−0.0135771	+	0.437436i
$382$	−9.46751	+	16.3982i	−0.484400	+	0.839005i
$383$	0.0844724	−	0.146310i	0.00431634	−	0.00747612i	−0.863859	−	0.503733i	$-0.831959\pi$
$383$	0.0844724	−	0.146310i	0.00431634	−	0.00747612i	0.868176	+	0.496257i	$0.165293\pi$
$384$	0.819074	+	1.52614i	0.0417982	+	0.0778807i
$385$		0			0
$386$			7.61465i			0.387576i
$387$	3.47255	+	6.98179i	0.176519	+	0.354904i
$388$			2.90418i			0.147438i
$389$	7.24937	−	4.18543i	0.367558	−	0.212210i	−0.304833	−	0.952406i	$-0.598601\pi$
$389$	7.24937	−	4.18543i	0.367558	−	0.212210i	0.672391	+	0.740196i	$0.265267\pi$
$390$	−17.6802	−	10.9527i	−0.895274	−	0.554612i
$391$	1.89105	+	1.09180i	0.0956344	+	0.0552146i
$392$		0			0
$393$	−31.8205	−	19.7125i	−1.60513	−	0.994362i
$394$	−3.02447	−	5.23854i	−0.152371	−	0.263914i
$395$	11.3516			0.571163
$396$	0.308148	−	4.95928i	0.0154850	−	0.249213i
$397$			6.23465i			0.312908i	0.987685	+	0.156454i	$0.0500064\pi$
$397$			6.23465i			0.312908i	−0.987685	+	0.156454i	$0.949994\pi$
$398$	11.4446	+	19.8227i	0.573668	+	0.993622i
$399$		0			0
$400$	−5.44735	+	9.43509i	−0.272368	+	0.471754i
$401$	28.8079	+	16.6322i	1.43860	+	0.830573i	0.997752	−	0.0670106i	$-0.0213461\pi$
$401$	28.8079	+	16.6322i	1.43860	+	0.830573i	0.440843	+	0.897584i	$0.354679\pi$
$402$	7.02313	+	0.217983i	0.350282	+	0.0108720i
$403$	−7.10019	−	12.2979i	−0.353686	−	0.612602i
$404$	0.258582			0.0128649
$405$	−21.6494	+	28.6142i	−1.07577	+	1.42185i
$406$		0			0
$407$	−8.62625	+	4.98037i	−0.427587	+	0.246868i
$408$	12.9086	+	0.400656i	0.639073	+	0.0198354i
$409$	−17.5931	−	10.1574i	−0.869920	−	0.502249i	−0.00259864	−	0.999997i	$-0.500827\pi$
$409$	−17.5931	−	10.1574i	−0.869920	−	0.502249i	−0.867322	+	0.497748i	$0.834161\pi$
$410$	−33.7417	−	19.4808i	−1.66639	−	0.962088i
$411$	5.61478	+	10.4618i	0.276957	+	0.516041i
$412$	−5.89979	+	3.40625i	−0.290662	+	0.167814i
$413$		0			0
$414$	0.876854	+	0.0544838i	0.0430950	+	0.00267773i
$415$	−20.6861			−1.01544
$416$	1.50592	+	2.60834i	0.0738340	+	0.127884i
$417$	−14.7016	+	23.7318i	−0.719940	+	1.16215i
$418$	−6.55977	−	3.78729i	−0.320849	−	0.185242i
$419$	−15.4796	+	26.8115i	−0.756229	+	1.30983i	0.188533	+	0.982067i	$0.439627\pi$
$419$	−15.4796	+	26.8115i	−0.756229	+	1.30983i	−0.944761	+	0.327759i	$0.893706\pi$
$420$		0			0
$421$	−8.92724	−	15.4624i	−0.435087	−	0.753593i	0.562216	−	0.826991i	$-0.309949\pi$
$421$	−8.92724	−	15.4624i	−0.435087	−	0.753593i	−0.997303	+	0.0733980i	$0.976616\pi$
$422$		−	6.73884i		−	0.328042i
$423$	18.1861	+	36.5644i	0.884238	+	1.77782i
$424$	−0.916164			−0.0444928
$425$	40.6176	+	70.3518i	1.97024	+	3.41256i
$426$	21.2801	−	11.4209i	1.03102	−	0.553345i
$427$		0			0
$428$	9.21299	+	5.31912i	0.445327	+	0.257110i
$429$	0.268047	−	8.63612i	0.0129414	−	0.416956i
$430$	8.97432	−	5.18132i	0.432780	−	0.249866i
$431$		−	26.6173i		−	1.28211i	−0.767494	−	0.641056i	$-0.778497\pi$
$431$		−	26.6173i		−	1.28211i	0.767494	−	0.641056i	$-0.221503\pi$
$432$	4.72201	−	2.16856i	0.227188	−	0.104335i
$433$		−	12.8312i		−	0.616628i	−0.951285	−	0.308314i	$-0.900235\pi$
$433$		−	12.8312i		−	0.616628i	0.951285	−	0.308314i	$-0.0997648\pi$
$434$		0			0
$435$	−25.3984	−	0.788312i	−1.21776	−	0.0377967i
$436$	−2.25887	+	3.91248i	−0.108180	+	0.187374i
$437$	0.669633	−	1.15984i	0.0320329	−	0.0554826i
$438$	−6.77712	+	3.63725i	−0.323823	+	0.173794i
$439$	−20.2960	+	11.7179i	−0.968678	+	0.559266i	−0.898833	−	0.438292i	$-0.855584\pi$
$439$	−20.2960	+	11.7179i	−0.968678	+	0.559266i	−0.0698448	+	0.997558i	$0.522250\pi$
$440$	−6.60330			−0.314800
$441$		0			0
$442$	22.4575			1.06820
$443$	16.0962	−	9.29315i	0.764754	−	0.441531i	−0.0662462	−	0.997803i	$-0.521102\pi$
$443$	16.0962	−	9.29315i	0.764754	−	0.441531i	0.831000	+	0.556273i	$0.187769\pi$
$444$	−8.85495	−	5.48554i	−0.420237	−	0.260332i
$445$	−21.9620	+	38.0393i	−1.04110	+	1.80324i
$446$	−4.53757	+	7.85930i	−0.214860	+	0.372149i
$447$	1.11076	−	1.79303i	0.0525372	−	0.0848074i
$448$		0			0
$449$			22.7518i			1.07372i	0.843670	+	0.536862i	$0.180390\pi$
$449$			22.7518i			1.07372i	−0.843670	+	0.536862i	$0.819610\pi$
$450$	27.2373	+	18.0660i	1.28398	+	0.851638i
$451$		−	16.1862i		−	0.762179i
$452$	−1.47530	+	0.851764i	−0.0693922	+	0.0400636i
$453$	−21.4268	+	11.4996i	−1.00672	+	0.540301i
$454$	−0.543310	−	0.313680i	−0.0254988	−	0.0147217i
$455$		0			0
$456$	0.245735	−	7.91727i	0.0115076	−	0.370760i
$457$	13.2531	+	22.9550i	0.619952	+	1.07379i	0.989494	+	0.144574i	$0.0461812\pi$
$457$	13.2531	+	22.9550i	0.619952	+	1.07379i	−0.369542	+	0.929214i	$0.620485\pi$
$458$	18.5436			0.866487
$459$	3.60128	−	38.5769i	0.168093	−	1.80061i
$460$		−	1.16753i		−	0.0544365i
$461$	−9.87220	−	17.0992i	−0.459794	−	0.796387i	0.539156	−	0.842206i	$-0.318744\pi$
$461$	−9.87220	−	17.0992i	−0.459794	−	0.796387i	−0.998950	+	0.0458193i	$0.985410\pi$
$462$		0			0
$463$	−1.87477	+	3.24719i	−0.0871278	+	0.150910i	−0.906296	−	0.422644i	$-0.861102\pi$
$463$	−1.87477	+	3.24719i	−0.0871278	+	0.150910i	0.819168	+	0.573553i	$0.194436\pi$
$464$	3.18684	+	1.83992i	0.147945	+	0.0854162i
$465$	15.3963	+	28.6873i	0.713987	+	1.33034i
$466$	5.21183	+	9.02716i	0.241433	+	0.418175i
$467$	−19.9950			−0.925257			−0.462628	−	0.886552i	$-0.653094\pi$
$467$	−19.9950			−0.925257			−0.462628	+	0.886552i	$0.653094\pi$
$468$	8.09012	−	4.02380i	0.373966	−	0.186000i
$469$		0			0
$470$	46.9994	−	27.1351i	2.16792	−	1.25165i
$471$	−21.5215	+	34.7407i	−0.991658	+	1.60077i
$472$	−6.11998	−	3.53337i	−0.281695	−	0.162637i
$473$	3.72829	+	2.15253i	0.171427	+	0.0989734i
$474$	−2.59714	+	4.19239i	−0.119291	+	0.192563i
$475$	43.1489	−	24.9120i	1.97981	−	1.14304i
$476$		0			0
$477$	−0.170450	+	2.74320i	−0.00780438	+	0.125603i
$478$	6.79962			0.311007
$479$	−5.33187	−	9.23507i	−0.243619	−	0.421961i	0.718123	−	0.695916i	$-0.245001\pi$
$479$	−5.33187	−	9.23507i	−0.243619	−	0.421961i	−0.961743	+	0.273955i	$0.911668\pi$
$480$	−3.26550	−	6.08446i	−0.149049	−	0.277716i
$481$	−15.6863	−	9.05648i	−0.715233	−	0.412940i
$482$	9.41695	−	16.3106i	0.428930	−	0.742929i
$483$		0			0
$484$	4.12836	+	7.15054i	0.187653	+	0.325024i
$485$		−	11.5785i		−	0.525750i
$486$	−5.61463	−	14.5422i	−0.254685	−	0.659648i
$487$	−16.9233			−0.766867			−0.383434	−	0.923568i	$-0.625258\pi$
$487$	−16.9233			−0.766867			−0.383434	+	0.923568i	$0.625258\pi$
$488$	−3.32329	−	5.75611i	−0.150438	−	0.260567i
$489$	0.0321984	−	1.03739i	0.00145606	−	0.0469124i
$490$		0			0
$491$	20.4285	+	11.7944i	0.921927	+	0.532275i	0.884249	−	0.467015i	$-0.154671\pi$
$491$	20.4285	+	11.7944i	0.921927	+	0.532275i	0.0376778	+	0.999290i	$0.488004\pi$
$492$	14.9144	−	8.00449i	0.672394	−	0.360870i
$493$	23.7623	−	13.7192i	1.07020	−	0.617881i
$494$		−	13.7739i		−	0.619717i
$495$	−1.22853	+	19.7718i	−0.0552182	+	0.888674i
$496$		−	4.71484i		−	0.211703i
$497$		0			0
$498$	4.73277	−	7.63980i	0.212081	−	0.342348i
$499$	3.37814	−	5.85111i	0.151226	−	0.261932i	−0.780452	−	0.625215i	$-0.785011\pi$
$499$	3.37814	−	5.85111i	0.151226	−	0.261932i	0.931679	+	0.363284i	$0.118344\pi$
$500$	11.7505	−	20.3525i	0.525501	−	0.910194i
$501$	7.87053	+	4.87571i	0.351629	+	0.217830i
$502$	−0.0402866	+	0.0232595i	−0.00179808	+	0.00103812i
$503$	−12.7667			−0.569240			−0.284620	−	0.958640i	$-0.591867\pi$
$503$	−12.7667			−0.569240			−0.284620	+	0.958640i	$0.591867\pi$
$504$		0			0
$505$	−1.03092			−0.0458752
$506$	0.420057	−	0.242520i	0.0186738	−	0.0107813i
$507$	−5.99589	+	3.21796i	−0.266287	+	0.142915i
$508$	−2.46601	+	4.27126i	−0.109412	+	0.189507i
$509$	−2.13873	+	3.70438i	−0.0947974	+	0.164194i	−0.909524	−	0.415651i	$-0.863554\pi$
$509$	−2.13873	+	3.70438i	−0.0947974	+	0.164194i	0.814727	+	0.579845i	$0.196887\pi$
$510$	−51.4644	−	1.59734i	−2.27888	−	0.0707315i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	−23.6604	−	2.20877i	−1.04463	−	0.0975198i
$514$			15.2055i			0.670687i
$515$	23.5214	−	13.5801i	1.03648	−	0.598410i
$516$	−0.139665	+	4.49983i	−0.00614841	+	0.198094i
$517$	19.5254	+	11.2730i	0.858728	+	0.495787i
$518$		0			0
$519$	−18.5022	+	9.93006i	−0.812158	+	0.435881i
$520$	−6.00384	−	10.3990i	−0.263286	−	0.456024i
$521$	8.08028			0.354004			0.177002	−	0.984211i	$-0.443360\pi$
$521$	8.08028			0.354004			0.177002	+	0.984211i	$0.443360\pi$
$522$	6.10204	−	9.19980i	0.267079	−	0.402664i
$523$			32.9016i			1.43869i	0.694654	+	0.719344i	$0.255558\pi$
$523$			32.9016i			1.43869i	−0.694654	+	0.719344i	$0.744442\pi$
$524$	−10.8056	−	18.7158i	−0.472044	−	0.817604i
$525$		0			0
$526$	0.978086	−	1.69410i	0.0426466	−	0.0738661i
$527$	−30.4458	−	17.5779i	−1.32624	−	0.765704i
$528$	1.51077	−	2.43873i	0.0657477	−	0.106132i
$529$	−11.4571	−	19.8443i	−0.498136	−	0.862796i
$530$	3.65258			0.158658
$531$	−11.7183	+	17.6672i	−0.508531	+	0.766692i
$532$		0			0
$533$	25.4902	−	14.7168i	1.10410	−	0.637455i
$534$	−9.02400	−	16.8140i	−0.390507	−	0.727614i
$535$	−36.7305	−	21.2064i	−1.58800	−	0.916831i
$536$	3.51326	+	2.02838i	0.151750	+	0.0876127i
$537$	9.62772	+	0.298824i	0.415467	+	0.0128952i
$538$	4.72739	−	2.72936i	0.203812	−	0.117671i
$539$		0			0
$540$	−18.8258	+	8.64564i	−0.810132	+	0.372049i
$541$	−8.79277			−0.378031			−0.189015	−	0.981974i	$-0.560530\pi$
$541$	−8.79277			−0.378031			−0.189015	+	0.981974i	$0.560530\pi$
$542$	7.39843	+	12.8145i	0.317790	+	0.550428i
$543$	21.7345	+	0.674592i	0.932718	+	0.0289495i
$544$	6.45743	+	3.72820i	0.276860	+	0.159845i
$545$	9.00571	−	15.5983i	0.385762	−	0.668160i
$546$		0			0
$547$	15.2530	+	26.4189i	0.652170	+	1.12959i	0.982595	+	0.185760i	$0.0594747\pi$
$547$	15.2530	+	26.4189i	0.652170	+	1.12959i	−0.330425	+	0.943832i	$0.607192\pi$
$548$			6.85503i			0.292832i
$549$	−17.8534	+	8.87978i	−0.761964	+	0.378980i
$550$	18.0447			0.769429
$551$	−8.41440	−	14.5742i	−0.358465	−	0.620880i
$552$	0.431193	+	0.267120i	0.0183528	+	0.0113694i
$553$		0			0
$554$	9.06963	+	5.23636i	0.385332	+	0.222471i
$555$	35.3030	+	21.8698i	1.49853	+	0.928323i
$556$	−13.9583	+	8.05882i	−0.591963	+	0.341770i
$557$		−	41.7898i		−	1.77069i	−0.464934	−	0.885345i	$-0.653922\pi$
$557$		−	41.7898i		−	1.77069i	0.464934	−	0.885345i	$-0.346078\pi$
$558$	−14.1173	−	0.877186i	−0.597633	−	0.0371342i
$559$			7.82848i			0.331109i
$560$		0			0
$561$	−10.1155	−	18.8477i	−0.427076	−	0.795752i
$562$	0.591716	−	1.02488i	0.0249600	−	0.0432321i
$563$	4.63202	−	8.02289i	0.195216	−	0.338124i	−0.751755	−	0.659442i	$-0.770792\pi$
$563$	4.63202	−	8.02289i	0.195216	−	0.338124i	0.946971	+	0.321318i	$0.104126\pi$
$564$	−0.731440	+	23.5661i	−0.0307992	+	0.992311i
$565$	5.88174	−	3.39583i	0.247447	−	0.142863i
$566$	29.5879			1.24367
$567$		0			0
$568$	13.9437			0.585064
$569$	11.5055	−	6.64272i	0.482337	−	0.278477i	−0.239053	−	0.971007i	$-0.576837\pi$
$569$	11.5055	−	6.64272i	0.482337	−	0.278477i	0.721390	+	0.692529i	$0.243504\pi$
$570$	−0.979699	+	31.5647i	−0.0410351	+	1.32210i
$571$	−16.2394	+	28.1274i	−0.679596	+	1.17709i	0.295507	+	0.955341i	$0.404511\pi$
$571$	−16.2394	+	28.1274i	−0.679596	+	1.17709i	−0.975103	+	0.221754i	$0.928822\pi$
$572$	2.49423	−	4.32014i	0.104289	−	0.180634i
$573$	15.5092	+	28.8976i	0.647905	+	1.20721i
$574$		0			0
$575$			3.19050i			0.133053i
$576$	2.99423	+	0.186048i	0.124759	+	0.00775199i
$577$			20.3193i			0.845905i	0.906152	+	0.422952i	$0.139006\pi$
$577$			20.3193i			0.845905i	−0.906152	+	0.422952i	$0.860994\pi$
$578$	33.4267	−	19.2989i	1.39037	−	0.802730i
$579$	11.2119	+	6.94565i	0.465951	+	0.288651i
$580$	−12.7053	−	7.33543i	−0.527560	−	0.304587i
$581$		0			0
$582$	4.27615	+	2.64903i	0.177252	+	0.109806i
$583$	0.758713	+	1.31413i	0.0314227	+	0.0544257i
$584$	−4.44068			−0.183757
$585$	−32.2538	+	16.0421i	−1.33353	+	0.663261i
$586$		−	13.2884i		−	0.548938i
$587$	−8.67362	−	15.0232i	−0.357999	−	0.620072i	0.629628	−	0.776897i	$-0.283207\pi$
$587$	−8.67362	−	15.0232i	−0.357999	−	0.620072i	−0.987626	+	0.156825i	$0.949874\pi$
$588$		0			0
$589$	−10.7810	+	18.6733i	−0.444225	+	0.769421i
$590$	24.3992	+	14.0869i	1.00450	+	0.579948i
$591$	−10.4720	−	0.325029i	−0.430762	−	0.0133699i
$592$	−3.00695	−	5.20820i	−0.123585	−	0.214056i
$593$	29.1394			1.19661			0.598307	−	0.801267i	$-0.295840\pi$
$593$	29.1394			1.19661			0.598307	+	0.801267i	$0.295840\pi$
$594$	−7.02103	−	4.97730i	−0.288076	−	0.204221i
$595$		0			0
$596$	1.05460	−	0.608875i	0.0431982	−	0.0249405i
$597$	39.6263	+	1.22991i	1.62180	+	0.0503370i
$598$	0.763847	+	0.441007i	0.0312360	+	0.0180341i
$599$	31.9668	+	18.4560i	1.30613	+	0.754092i	0.981447	−	0.191732i	$-0.0614104\pi$
$599$	31.9668	+	18.4560i	1.30613	+	0.754092i	0.324679	+	0.945824i	$0.394744\pi$
$600$	8.92357	+	16.6269i	0.364303	+	0.678790i
$601$	−33.3809	+	19.2725i	−1.36164	+	0.786141i	−0.989842	−	0.142174i	$-0.954591\pi$
$601$	−33.3809	+	19.2725i	−1.36164	+	0.786141i	−0.371795	+	0.928315i	$0.621257\pi$
$602$		0			0
$603$	6.72706	−	10.1421i	0.273947	−	0.413019i
$604$	−14.0398			−0.571272
$605$	−16.4590	−	28.5079i	−0.669155	−	1.15901i
$606$	0.235863	−	0.380739i	0.00958130	−	0.0154664i
$607$	−21.2299	−	12.2571i	−0.861696	−	0.497500i	0.00288390	−	0.999996i	$-0.499082\pi$
$607$	−21.2299	−	12.2571i	−0.861696	−	0.497500i	−0.864580	+	0.502495i	$0.832415\pi$
$608$	2.28662	−	3.96054i	0.0927346	−	0.160621i
$609$		0			0
$610$	13.2494	+	22.9486i	0.536451	+	0.929160i
$611$			40.9986i			1.65862i
$612$	12.3645	−	18.6414i	0.499804	−	0.753533i
$613$	−26.2552			−1.06044			−0.530219	−	0.847861i	$-0.677890\pi$
$613$	−26.2552			−1.06044			−0.530219	+	0.847861i	$0.677890\pi$
$614$	1.67275	+	2.89728i	0.0675065	+	0.116925i
$615$	−59.4610	+	31.9124i	−2.39770	+	1.28683i
$616$		0			0
$617$	32.4708	+	18.7470i	1.30723	+	0.754727i	0.981632	−	0.190783i	$-0.0611026\pi$
$617$	32.4708	+	18.7470i	1.30723	+	0.754727i	0.325593	+	0.945510i	$0.394436\pi$
$618$	−0.366057	+	11.7939i	−0.0147250	+	0.474420i
$619$	17.1863	−	9.92249i	0.690774	−	0.398819i	−0.113128	−	0.993580i	$-0.536087\pi$
$619$	17.1863	−	9.92249i	0.690774	−	0.398819i	0.803902	+	0.594762i	$0.202754\pi$
$620$			18.7972i			0.754914i
$621$	0.880039	−	1.24139i	0.0353147	−	0.0498154i
$622$			22.7834i			0.913531i
$623$		0			0
$624$	5.21416	+	0.161836i	0.208733	+	0.00647863i
$625$	−19.6105	+	33.9664i	−0.784421	+	1.35866i
$626$	0.584177	−	1.01182i	0.0233484	−	0.0404406i
$627$	−11.5599	+	6.20414i	−0.461658	+	0.247769i
$628$	−20.4334	+	11.7972i	−0.815380	+	0.470760i
$629$	−44.8421			−1.78797
$630$		0			0
$631$	−26.3099			−1.04738			−0.523691	−	0.851908i	$-0.675445\pi$
$631$	−26.3099			−1.04738			−0.523691	+	0.851908i	$0.675445\pi$
$632$	−2.46583	+	1.42365i	−0.0980855	+	0.0566297i
$633$	−9.92235	−	6.14679i	−0.394378	−	0.244313i
$634$	−10.9020	+	18.8828i	−0.432973	+	0.749930i
$635$	9.83154	−	17.0287i	0.390153	−	0.675765i
$636$	−0.835672	+	1.34897i	−0.0331366	+	0.0534901i
$637$		0			0
$638$		−	6.09486i		−	0.241298i
$639$	2.59419	−	41.7505i	0.102625	−	1.65163i
$640$		−	3.98682i		−	0.157593i
$641$	−19.6930	+	11.3697i	−0.777826	+	0.449078i	−0.835659	−	0.549248i	$-0.814914\pi$
$641$	−19.6930	+	11.3697i	−0.777826	+	0.449078i	0.0578333	+	0.998326i	$0.481581\pi$
$642$	16.2355	−	8.71351i	0.640764	−	0.343895i
$643$	42.7821	+	24.7003i	1.68716	+	0.974084i	0.956675	+	0.291158i	$0.0940406\pi$
$643$	42.7821	+	24.7003i	1.68716	+	0.974084i	0.730488	+	0.682926i	$0.239293\pi$
$644$		0			0
$645$	0.556818	−	17.9400i	0.0219247	−	0.706386i
$646$	−17.0499	−	29.5314i	−0.670821	−	1.16190i
$647$	−45.4633			−1.78735			−0.893674	−	0.448718i	$-0.851881\pi$
$647$	−45.4633			−1.78735			−0.893674	+	0.448718i	$0.851881\pi$
$648$	1.11414	−	8.93077i	0.0437675	−	0.350834i
$649$			11.7045i			0.459443i
$650$	16.4066	+	28.4170i	0.643519	+	1.11461i
$651$		0			0
$652$	0.299613	−	0.518945i	0.0117338	−	0.0203235i
$653$	−32.1371	−	18.5543i	−1.25762	−	0.726088i	−0.285009	−	0.958525i	$-0.591997\pi$
$653$	−32.1371	−	18.5543i	−1.25762	−	0.726088i	−0.972611	+	0.232437i	$0.925330\pi$
$654$	3.70037	+	6.89473i	0.144696	+	0.269605i
$655$	43.0799	+	74.6165i	1.68327	+	2.91551i
$656$	9.77261			0.381556
$657$	−0.826178	+	13.2964i	−0.0322323	+	0.518742i
$658$		0			0
$659$	−37.9735	+	21.9240i	−1.47924	+	0.854039i	−0.999724	−	0.0234944i	$-0.992521\pi$
$659$	−37.9735	+	21.9240i	−1.47924	+	0.854039i	−0.479515	+	0.877534i	$0.659187\pi$
$660$	−6.02315	+	9.72277i	−0.234451	+	0.378458i
$661$	21.1370	+	12.2034i	0.822133	+	0.474659i	0.851151	−	0.524920i	$-0.175905\pi$
$661$	21.1370	+	12.2034i	0.822133	+	0.474659i	−0.0290185	+	0.999579i	$0.509238\pi$
$662$	24.1494	+	13.9427i	0.938594	+	0.541898i
$663$	20.4845	−	33.0667i	0.795551	−	1.28421i
$664$	4.49349	−	2.59432i	0.174381	−	0.100679i
$665$		0			0
$666$	−16.1540	+	8.03452i	−0.625953	+	0.311331i
$667$	1.07764			0.0417263
$668$	2.67267	+	4.62919i	0.103409	+	0.179109i
$669$	7.43321	+	13.8500i	0.287385	+	0.535471i
$670$	−14.0067	−	8.08678i	−0.541127	−	0.312420i
$671$	−5.50431	+	9.53375i	−0.212492	+	0.368046i
$672$		0			0
$673$	−5.68953	−	9.85456i	−0.219315	−	0.379865i	0.735284	−	0.677760i	$-0.237049\pi$
$673$	−5.68953	−	9.85456i	−0.219315	−	0.379865i	−0.954599	+	0.297894i	$0.903716\pi$
$674$		−	0.00656698i		−	0.000252951i
$675$	51.4449	−	23.6258i	1.98011	−	0.909357i
$676$	−3.92878			−0.151107
$677$	−10.9756	−	19.0103i	−0.421826	−	0.730623i	0.574293	−	0.818650i	$-0.305277\pi$
$677$	−10.9756	−	19.0103i	−0.421826	−	0.730623i	−0.996118	+	0.0880268i	$0.971944\pi$
$678$	−0.0915360	+	2.94918i	−0.00351542	+	0.113262i
$679$		0			0
$680$	−25.7446	−	14.8636i	−0.987260	−	0.569995i
$681$	−0.957442	+	0.513854i	−0.0366893	+	0.0196909i
$682$	−6.76289	+	3.90456i	−0.258964	+	0.149513i
$683$		−	9.58203i		−	0.366646i	−0.983053	−	0.183323i	$-0.941315\pi$
$683$		−	9.58203i		−	0.366646i	0.983053	−	0.183323i	$-0.0586854\pi$
$684$	−11.4333	−	7.58350i	−0.437164	−	0.289962i
$685$		−	27.3298i		−	1.04422i
$686$		0			0
$687$	16.9145	−	27.3039i	0.645327	−	1.04171i
$688$	−1.29961	+	2.25100i	−0.0495473	+	0.0858185i
$689$	−1.37967	+	2.38966i	−0.0525613	+	0.0910389i
$690$	−1.71909	−	1.06496i	−0.0654446	−	0.0405422i
$691$	−0.379952	+	0.219366i	−0.0144541	+	0.00834506i	−0.507210	−	0.861823i	$-0.669323\pi$
$691$	−0.379952	+	0.219366i	−0.0144541	+	0.00834506i	0.492756	+	0.870168i	$0.335990\pi$
$692$	−12.1235			−0.460867
$693$		0			0
$694$	−20.4956			−0.778004
$695$	55.6491	−	32.1290i	2.11089	−	1.21872i
$696$	5.61597	−	3.01407i	0.212873	−	0.114248i
$697$	36.4342	−	63.1059i	1.38004	−	2.39031i
$698$	−4.18198	+	7.24341i	−0.158290	+	0.274167i
$699$	18.0456	+	0.560097i	0.682548	+	0.0211848i
$700$		0			0
$701$		−	29.7259i		−	1.12273i	−0.827568	−	0.561366i	$-0.810276\pi$
$701$		−	29.7259i		−	1.12273i	0.827568	−	0.561366i	$-0.189724\pi$
$702$	1.45466	−	15.5823i	0.0549025	−	0.588115i
$703$			27.5030i			1.03730i
$704$	1.43438	−	0.828141i	0.0540603	−	0.0312118i
$705$	2.91612	−	93.9536i	0.109827	−	3.53850i
$706$	−5.32484	−	3.07430i	−0.200403	−	0.115703i
$707$		0			0
$708$	−10.7849	+	5.78818i	−0.405320	+	0.217533i
$709$	−12.2356	−	21.1928i	−0.459519	−	0.795910i	0.539416	−	0.842039i	$-0.318645\pi$
$709$	−12.2356	−	21.1928i	−0.459519	−	0.795910i	−0.998936	+	0.0461287i	$0.985312\pi$
$710$	−55.5909			−2.08629
$711$	3.80396	+	7.64812i	0.142660	+	0.286827i
$712$		−	11.0173i		−	0.412891i
$713$	−0.690367	−	1.19575i	−0.0258545	−	0.0447812i
$714$		0			0
$715$	−9.94406	+	17.2236i	−0.371887	+	0.644126i
$716$	4.81618	+	2.78062i	0.179989	+	0.103917i
$717$	6.20223	−	10.0118i	0.231626	−	0.373899i
$718$	−2.90236	−	5.02704i	−0.108315	−	0.187608i
$719$	−16.2523			−0.606109			−0.303054	−	0.952973i	$-0.598006\pi$
$719$	−16.2523			−0.606109			−0.303054	+	0.952973i	$0.598006\pi$
$720$	−11.9374	−	0.741738i	−0.444882	−	0.0276429i
$721$		0			0
$722$	−1.65801	+	0.957250i	−0.0617046	+	0.0356252i
$723$	−15.4264	−	28.7433i	−0.573713	−	1.06897i
$724$	10.8725	+	6.27724i	0.404073	+	0.233292i
$725$	34.7197	+	20.0454i	1.28946	+	0.744468i
$726$	14.2942	+	0.443660i	0.530507	+	0.0164658i
$727$	25.4656	−	14.7026i	0.944468	−	0.545289i	0.0531099	−	0.998589i	$-0.483087\pi$
$727$	25.4656	−	14.7026i	0.944468	−	0.545289i	0.891358	+	0.453300i	$0.149753\pi$
$728$		0			0
$729$	−26.5335	−	4.99753i	−0.982721	−	0.185094i
$730$	17.7042			0.655261
$731$	9.69044	+	16.7843i	0.358414	+	0.620791i
$732$	−11.5067	−	0.357142i	−0.425299	−	0.0132004i
$733$	31.9175	+	18.4276i	1.17890	+	0.680638i	0.955760	−	0.294149i	$-0.0950361\pi$
$733$	31.9175	+	18.4276i	1.17890	+	0.680638i	0.223139	+	0.974787i	$0.428369\pi$
$734$	2.98293	−	5.16659i	0.110102	−	0.190702i
$735$		0			0
$736$	0.146424	+	0.253614i	0.00539727	+	0.00934834i
$737$		−	6.71914i		−	0.247503i
$738$	1.81817	−	29.2614i	0.0669278	−	1.07713i
$739$	−43.2260			−1.59010			−0.795048	−	0.606547i	$-0.792554\pi$
$739$	−43.2260			−1.59010			−0.795048	+	0.606547i	$0.792554\pi$
$740$	11.9882	+	20.7641i	0.440694	+	0.763304i
$741$	−20.2808	−	12.5638i	−0.745035	−	0.461541i
$742$		0			0
$743$	−28.2201	−	16.2929i	−1.03530	−	0.597729i	−0.116799	−	0.993156i	$-0.537263\pi$
$743$	−28.2201	−	16.2929i	−1.03530	−	0.597729i	−0.918497	+	0.395427i	$0.870597\pi$
$744$	−6.94219	−	4.30061i	−0.254513	−	0.157668i
$745$	−4.20451	+	2.42747i	−0.154041	+	0.0889357i
$746$		−	18.8658i		−	0.690727i
$747$	−6.93196	−	13.9372i	−0.253627	−	0.509935i
$748$		−	12.3499i		−	0.451557i
$749$		0			0
$750$	−19.2491	−	35.8661i	−0.702879	−	1.30964i
$751$	17.4592	−	30.2402i	0.637095	−	1.10348i	−0.348972	−	0.937133i	$-0.613469\pi$
$751$	17.4592	−	30.2402i	0.637095	−	1.10348i	0.986067	−	0.166348i	$-0.0531976\pi$
$752$	−6.80622	+	11.7887i	−0.248197	+	0.429890i
$753$	−0.00249962	+	0.0805345i	−9.10911e−5	+	0.00293484i
$754$	9.59827	−	5.54156i	0.349548	−	0.201812i
$755$	55.9741			2.03711
$756$		0			0
$757$	−26.0470			−0.946693			−0.473346	−	0.880876i	$-0.656954\pi$
$757$	−26.0470			−0.946693			−0.473346	+	0.880876i	$0.656954\pi$
$758$	−10.8540	+	6.26657i	−0.394236	+	0.227612i
$759$	0.0260628	−	0.839709i	0.000946018	−	0.0304795i
$760$	−9.11633	+	15.7899i	−0.330684	+	0.572761i
$761$	−17.1005	+	29.6189i	−0.619893	+	1.07369i	0.369612	+	0.929186i	$0.379491\pi$
$761$	−17.1005	+	29.6189i	−0.619893	+	1.07369i	−0.989505	+	0.144500i	$0.953843\pi$
$762$	4.03970	+	7.52699i	0.146343	+	0.272674i
$763$		0			0
$764$			18.9350i			0.685045i
$765$	−49.2948	+	74.3198i	−1.78226	+	2.68704i
$766$		−	0.168945i		−	0.00610422i
$767$	−18.4324	+	10.6420i	−0.665556	+	0.384259i
$768$	1.47241	+	0.912143i	0.0531311	+	0.0329141i
$769$	−28.9909	−	16.7379i	−1.04544	−	0.603585i	−0.124071	−	0.992273i	$-0.539595\pi$
$769$	−28.9909	−	16.7379i	−1.04544	−	0.603585i	−0.921369	+	0.388688i	$0.872928\pi$
$770$		0			0
$771$	22.3888	+	13.8696i	0.806312	+	0.499502i
$772$	3.80733	+	6.59448i	0.137029	+	0.237341i
$773$	11.4744			0.412704			0.206352	−	0.978478i	$-0.433841\pi$
$773$	11.4744			0.412704			0.206352	+	0.978478i	$0.433841\pi$
$774$	6.49821	+	4.31013i	0.233573	+	0.154924i
$775$		−	51.3668i		−	1.84515i
$776$	1.45209	+	2.51510i	0.0521271	+	0.0902867i
$777$		0			0
$778$	4.18543	−	7.24937i	0.150055	−	0.259903i
$779$	−38.7048	−	22.3462i	−1.38674	−	0.800637i
$780$	−20.7879	−	0.645211i	−0.744326	−	0.0231023i
$781$	−11.5473	−	20.0006i	−0.413196	−	0.715677i
$782$	2.18359			0.0780852
$783$	−7.97995	−	17.3763i	−0.285180	−	0.620977i
$784$		0			0
$785$	81.4641	−	47.0333i	2.90758	−	1.67869i
$786$	−37.4136	−	1.16124i	−1.33450	−	0.0414200i
$787$	−5.20750	−	3.00655i	−0.185627	−	0.107172i	0.404307	−	0.914623i	$-0.367513\pi$
$787$	−5.20750	−	3.00655i	−0.185627	−	0.107172i	−0.589934	+	0.807452i	$0.700846\pi$
$788$	−5.23854	−	3.02447i	−0.186615	−	0.107742i
$789$	−1.60225	−	2.98540i	−0.0570416	−	0.106283i
$790$	9.83081	−	5.67582i	0.349765	−	0.201937i
$791$		0			0
$792$	−2.21278	−	4.44894i	−0.0786277	−	0.158086i
$793$	−20.0185			−0.710878
$794$	3.11733	+	5.39937i	0.110630	+	0.191616i
$795$	3.33167	−	5.37809i	0.118162	−	0.190741i
$796$	19.8227	+	11.4446i	0.702597	+	0.405644i
$797$	1.19594	−	2.07142i	0.0423623	−	0.0733736i	−0.844067	−	0.536238i	$-0.819845\pi$
$797$	1.19594	−	2.07142i	0.0423623	−	0.0733736i	0.886429	+	0.462864i	$0.153178\pi$
$798$		0			0
$799$	50.7499	+	87.9014i	1.79540	+	3.10973i
$800$			10.8947i			0.385186i
$801$	−32.9883	−	2.04975i	−1.16559	−	0.0724243i
$802$	33.2644			1.17461
$803$	3.67751	+	6.36964i	0.129777	+	0.224780i
$804$	6.19120	−	3.32279i	0.218347	−	0.117186i
$805$		0			0
$806$	−12.2979	−	7.10019i	−0.433175	−	0.250094i
$807$	0.293314	−	9.45023i	0.0103252	−	0.332664i
$808$	0.223938	−	0.129291i	0.00787812	−	0.00454844i
$809$			3.38060i			0.118856i	0.998233	+	0.0594278i	$0.0189276\pi$
$809$			3.38060i			0.118856i	−0.998233	+	0.0594278i	$0.981072\pi$
$810$	−4.44186	+	35.6053i	−0.156071	+	1.25104i
$811$		−	38.2801i		−	1.34419i	−0.740463	−	0.672097i	$-0.765394\pi$
$811$		−	38.2801i		−	1.34419i	0.740463	−	0.672097i	$-0.234606\pi$
$812$		0			0
$813$	25.6166	+	0.795083i	0.898413	+	0.0278848i
$814$	−4.98037	+	8.62625i	−0.174562	+	0.302350i
$815$	−1.19450	+	2.06894i	−0.0418416	+	0.0724718i
$816$	11.3795	−	6.10734i	0.398364	−	0.213800i
$817$	10.2943	−	5.94344i	0.360154	−	0.207935i
$818$	−20.3147			−0.710287
$819$		0			0
$820$	−38.9616			−1.36060
$821$	28.1666	−	16.2620i	0.983021	−	0.567547i	0.0798401	−	0.996808i	$-0.474559\pi$
$821$	28.1666	−	16.2620i	0.983021	−	0.567547i	0.903181	+	0.429260i	$0.141226\pi$
$822$	10.0934	+	6.25277i	0.352049	+	0.218090i
$823$	0.406649	−	0.704337i	0.0141749	−	0.0245516i	−0.858851	−	0.512226i	$-0.828821\pi$
$823$	0.406649	−	0.704337i	0.0141749	−	0.0245516i	0.873026	+	0.487674i	$0.162155\pi$
$824$	−3.40625	+	5.89979i	−0.118662	+	0.205529i
$825$	16.4594	−	26.5692i	0.573041	−	0.925022i
$826$		0			0
$827$		−	26.0812i		−	0.906933i	−0.891273	−	0.453466i	$-0.850187\pi$
$827$		−	26.0812i		−	0.906933i	0.891273	−	0.453466i	$-0.149813\pi$
$828$	0.786620	−	0.391243i	0.0273369	−	0.0135966i
$829$			20.7245i			0.719791i	0.932993	+	0.359896i	$0.117188\pi$
$829$			20.7245i			0.719791i	−0.932993	+	0.359896i	$0.882812\pi$
$830$	−17.9147	+	10.3431i	−0.621829	+	0.359013i
$831$	15.9829	−	8.57793i	0.554440	−	0.297565i
$832$	2.60834	+	1.50592i	0.0904278	+	0.0522085i
$833$		0			0
$834$	−0.866053	+	27.9031i	−0.0299890	+	0.966207i
$835$	−10.6554	−	18.4557i	−0.368746	−	0.638687i
$836$	−7.57457			−0.261972
$837$	−14.1686	+	19.9864i	−0.489738	+	0.690830i
$838$			30.9592i			1.06947i
$839$	6.41783	+	11.1160i	0.221568	+	0.383767i	0.955284	−	0.295689i	$-0.0955492\pi$
$839$	6.41783	+	11.1160i	0.221568	+	0.383767i	−0.733716	+	0.679456i	$0.762216\pi$
$840$		0			0
$841$	−7.72938	+	13.3877i	−0.266530	+	0.461644i
$842$	−15.4624	−	8.92724i	−0.532870	−	0.307653i
$843$	−0.969319	−	1.80609i	−0.0333851	−	0.0622050i
$844$	−3.36942	−	5.83601i	−0.115980	−	0.200884i
$845$	15.6633			0.538835
$846$	34.0318	+	22.5726i	1.17004	+	0.776062i
$847$		0			0
$848$	−0.793421	+	0.458082i	−0.0272462	+	0.0157306i
$849$	26.9884	−	43.5655i	0.926238	−	1.49516i
$850$	70.3518	+	40.6176i	2.41305	+	1.39317i
$851$	−1.52521	−	0.880582i	−0.0522836	−	0.0301860i
$852$	12.7186	−	20.5308i	0.435733	−	0.703375i
$853$	30.3664	−	17.5321i	1.03973	−	0.600287i	0.119971	−	0.992777i	$-0.461720\pi$
$853$	30.3664	−	17.5321i	1.03973	−	0.600287i	0.919756	+	0.392490i	$0.128386\pi$
$854$		0			0
$855$	45.5826	+	30.2340i	1.55889	+	1.03398i
$856$	10.6382			0.363608
$857$	−13.6238	−	23.5972i	−0.465382	−	0.806065i	0.533837	−	0.845587i	$-0.320750\pi$
$857$	−13.6238	−	23.5972i	−0.465382	−	0.806065i	−0.999219	+	0.0395226i	$0.987416\pi$
$858$	−4.08593	−	7.61313i	−0.139491	−	0.259908i
$859$	6.42983	+	3.71226i	0.219383	+	0.126661i	0.605664	−	0.795720i	$-0.292907\pi$
$859$	6.42983	+	3.71226i	0.219383	+	0.126661i	−0.386282	+	0.922381i	$0.626241\pi$
$860$	5.18132	−	8.97432i	0.176682	−	0.306022i
$861$		0			0
$862$	−13.3087	−	23.0513i	−0.453295	−	0.785130i
$863$			33.4882i			1.13995i	0.821661	+	0.569977i	$0.193048\pi$
$863$			33.4882i			1.13995i	−0.821661	+	0.569977i	$0.806952\pi$
$864$	3.00510	−	4.23903i	0.102236	−	0.144215i
$865$	48.3342			1.64341
$866$	−6.41560	−	11.1121i	−0.218011	−	0.377606i
$867$	2.07399	−	66.8213i	0.0704363	−	2.26937i
$868$		0			0
$869$	4.08411	+	2.35796i	0.138544	+	0.0799885i
$870$	−22.3899	+	12.0165i	−0.759087	+	0.407398i
$871$	10.5814	−	6.10917i	0.358537	−	0.207001i
$872$			4.51775i			0.152990i
$873$	7.80093	−	3.87996i	0.264021	−	0.131317i
$874$		−	1.33927i		−	0.0453013i
$875$		0			0
$876$	−4.05053	+	6.53851i	−0.136855	+	0.220916i
$877$	−9.77904	+	16.9378i	−0.330215	+	0.571948i	−0.982554	−	0.185979i	$-0.940454\pi$
$877$	−9.77904	+	16.9378i	−0.330215	+	0.571948i	0.652339	+	0.757927i	$0.273788\pi$
$878$	−11.7179	+	20.2960i	−0.395461	+	0.684959i
$879$	−19.5660	−	12.1209i	−0.659944	−	0.408828i
$880$	−5.71862	+	3.30165i	−0.192775	+	0.111299i
$881$	30.1681			1.01639			0.508195	−	0.861242i	$-0.330313\pi$
$881$	30.1681			1.01639			0.508195	+	0.861242i	$0.330313\pi$
$882$		0			0
$883$	44.0654			1.48292			0.741459	−	0.670998i	$-0.234134\pi$
$883$	44.0654			1.48292			0.741459	+	0.670998i	$0.234134\pi$
$884$	19.4488	−	11.2288i	0.654134	−	0.377664i
$885$	42.9973	−	23.0764i	1.44534	−	0.775706i
$886$	9.29315	−	16.0962i	0.312209	−	0.540763i
$887$	−5.21456	+	9.03188i	−0.175088	+	0.303261i	−0.940192	−	0.340646i	$-0.889354\pi$
$887$	−5.21456	+	9.03188i	−0.175088	+	0.303261i	0.765104	+	0.643907i	$0.222688\pi$
$888$	−10.4114	−	0.323147i	−0.349383	−	0.0108441i
$889$		0			0
$890$			43.9240i			1.47234i
$891$	−13.7328	+	5.79784i	−0.460067	+	0.194235i
$892$			9.07514i			0.303858i
$893$	53.9126	−	31.1264i	1.80412	−	1.04161i
$894$	0.0654336	−	2.10819i	0.00218843	−	0.0705084i
$895$	−19.2012	−	11.0858i	−0.641826	−	0.370558i
$896$		0			0
$897$	1.34608	−	0.722435i	0.0449444	−	0.0241214i
$898$	11.3759	+	19.7036i	0.379619	+	0.657519i
$899$	−17.3499			−0.578651
$900$	32.6212	+	2.02693i	1.08737	+	0.0675645i
$901$			6.83128i			0.227583i
$902$	−8.09310	−	14.0177i	−0.269471	−	0.466737i
$903$		0			0
$904$	−0.851764	+	1.47530i	−0.0283292	+	0.0490677i
$905$	−43.3466	−	25.0262i	−1.44089	−	0.831899i
$906$	−12.8063	+	20.6724i	−0.425461	+	0.686794i
$907$	−11.2709	−	19.5218i	−0.374246	−	0.648212i	0.615968	−	0.787771i	$-0.288765\pi$
$907$	−11.2709	−	19.5218i	−0.374246	−	0.648212i	−0.990214	+	0.139559i	$0.955432\pi$
$908$	−0.627360			−0.0208197
$909$	−0.345463	−	0.694576i	−0.0114583	−	0.0230376i
$910$		0			0
$911$	6.57136	−	3.79398i	0.217719	−	0.125700i	−0.387175	−	0.922006i	$-0.626549\pi$
$911$	6.57136	−	3.79398i	0.217719	−	0.125700i	0.604894	+	0.796306i	$0.293216\pi$
$912$	−3.74582	−	6.97942i	−0.124037	−	0.231112i
$913$	−7.44249	−	4.29692i	−0.246310	−	0.142207i
$914$	22.9550	+	13.2531i	0.759283	+	0.438372i
$915$	45.8750	+	1.42386i	1.51658	+	0.0470714i
$916$	16.0593	−	9.27182i	0.530613	−	0.306350i
$917$		0			0
$918$	−16.1696	−	35.2092i	−0.533677	−	1.16208i
$919$	−49.0302			−1.61736			−0.808679	−	0.588250i	$-0.799817\pi$
$919$	−49.0302			−1.61736			−0.808679	+	0.588250i	$0.799817\pi$
$920$	−0.583767	−	1.01111i	−0.0192462	−	0.0333354i
$921$	5.79177	+	0.179764i	0.190845	+	0.00592342i
$922$	−17.0992	−	9.87220i	−0.563131	−	0.325124i
$923$	20.9981	−	36.3698i	0.691162	−	1.19713i
$924$		0			0
$925$	−32.7599	−	56.7418i	−1.07714	−	1.86566i
$926$			3.74953i			0.123217i
$927$	17.0316	+	11.2967i	0.559391	+	0.371033i
$928$	3.67984			0.120797
$929$	−13.6132	−	23.5788i	−0.446636	−	0.773595i	0.551529	−	0.834156i	$-0.314045\pi$
$929$	−13.6132	−	23.5788i	−0.446636	−	0.773595i	−0.998165	+	0.0605602i	$0.980711\pi$
$930$	27.6772	+	17.1457i	0.907572	+	0.562231i
$931$		0			0
$932$	9.02716	+	5.21183i	0.295694	+	0.170719i
$933$	33.5465	+	20.7817i	1.09826	+	0.680363i
$934$	−17.3161	+	9.99748i	−0.566602	+	0.327128i
$935$			49.2368i			1.61022i
$936$	4.99435	−	7.52977i	0.163245	−	0.246118i
$937$			51.0665i			1.66827i	0.551562	+	0.834134i	$0.314032\pi$
$937$			51.0665i			1.66827i	−0.551562	+	0.834134i	$0.685968\pi$
$938$		0			0
$939$	−0.956968	−	1.78308i	−0.0312295	−	0.0581885i
$940$	27.1351	−	46.9994i	0.885051	−	1.53295i
$941$	23.2152	−	40.2098i	0.756793	−	1.31080i	−0.187686	−	0.982229i	$-0.560099\pi$
$941$	23.2152	−	40.2098i	0.756793	−	1.31080i	0.944478	−	0.328574i	$-0.106568\pi$
$942$	−1.26780	+	40.8471i	−0.0413073	+	1.33087i
$943$	2.47847	−	1.43095i	0.0807102	−	0.0465980i
$944$	−7.06674			−0.230003
$945$		0			0
$946$	4.30506			0.139970
$947$	−30.7556	+	17.7567i	−0.999422	+	0.577016i	−0.908077	−	0.418803i	$-0.862450\pi$
$947$	−30.7556	+	17.7567i	−0.999422	+	0.577016i	−0.0913445	+	0.995819i	$0.529116\pi$
$948$	−0.152994	+	4.92929i	−0.00496903	+	0.160096i
$949$	−6.68732	+	11.5828i	−0.217080	+	0.375993i
$950$	24.9120	−	43.1489i	0.808253	−	1.39994i
$951$	17.8590	+	33.2760i	0.579119	+	1.07905i
$952$		0			0
$953$			10.1647i			0.329268i	0.986355	+	0.164634i	$0.0526443\pi$
$953$			10.1647i			0.329268i	−0.986355	+	0.164634i	$0.947356\pi$
$954$	1.22399	+	2.46091i	0.0396280	+	0.0796748i
$955$		−	75.4904i		−	2.44281i
$956$	5.88865	−	3.39981i	0.190452	−	0.109958i
$957$	−8.97414	−	5.55938i	−0.290093	−	0.179709i
$958$	−9.23507	−	5.33187i	−0.298371	−	0.172265i
$959$		0			0
$960$	−5.87023	−	3.63655i	−0.189461	−	0.117369i
$961$	−4.38513	−	7.59526i	−0.141456	−	0.245009i
$962$	−18.1130			−0.583985
$963$	1.97922	−	31.8533i	0.0637795	−	1.02646i
$964$		−	18.8339i		−	0.606599i
$965$	−15.1791	−	26.2910i	−0.488633	−	0.846337i
$966$		0			0
$967$	15.5961	−	27.0132i	0.501536	−	0.868686i	−0.498462	−	0.866911i	$-0.666102\pi$
$967$	15.5961	−	27.0132i	0.501536	−	0.868686i	0.999998	−	0.00177474i	$-0.000564917\pi$
$968$	7.15054	+	4.12836i	0.229827	+	0.132691i
$969$	−59.0343	−	1.83230i	−1.89645	−	0.0588618i
$970$	−5.78923	−	10.0272i	−0.185881	−	0.321955i
$971$	−28.6629			−0.919836			−0.459918	−	0.887961i	$-0.652121\pi$
$971$	−28.6629			−0.919836			−0.459918	+	0.887961i	$0.652121\pi$
$972$	−12.1335	−	9.78661i	−0.389183	−	0.313906i
$973$		0			0
$974$	−14.6560	+	8.46164i	−0.469608	+	0.271128i
$975$	56.8067	+	1.76316i	1.81927	+	0.0564662i
$976$	−5.75611	−	3.32329i	−0.184249	−	0.106376i
$977$	−25.4631	−	14.7011i	−0.814636	−	0.470330i	0.0339271	−	0.999424i	$-0.489199\pi$
$977$	−25.4631	−	14.7011i	−0.814636	−	0.470330i	−0.848563	+	0.529094i	$0.822532\pi$
$978$	−0.490811	−	0.914506i	−0.0156944	−	0.0292427i
$979$	−15.8031	+	9.12390i	−0.505068	+	0.291601i
$980$		0			0
$981$	13.5271	+	0.840516i	0.431889	+	0.0268356i
$982$	23.5888			0.752750
$983$	14.7425	+	25.5348i	0.470214	+	0.814434i	0.999420	−	0.0340593i	$-0.0108435\pi$
$983$	14.7425	+	25.5348i	0.470214	+	0.814434i	−0.529206	+	0.848493i	$0.677510\pi$
$984$	8.91402	−	14.3893i	0.284168	−	0.458714i
$985$	20.8851	+	12.0580i	0.665455	+	0.384200i
$986$	13.7192	−	23.7623i	0.436908	−	0.756747i
$987$		0			0
$988$	−6.88694	−	11.9285i	−0.219103	−	0.379497i
$989$			0.761180i			0.0242041i
$990$	8.82194	+	17.7371i	0.280380	+	0.563722i
$991$	−13.6643			−0.434061			−0.217030	−	0.976165i	$-0.569637\pi$
$991$	−13.6643			−0.434061			−0.217030	+	0.976165i	$0.569637\pi$
$992$	−2.35742	−	4.08317i	−0.0748482	−	0.129641i
$993$	42.5571	−	22.8402i	1.35051	−	0.724811i
$994$		0			0
$995$	−79.0294	−	45.6277i	−2.50540	−	1.44649i
$996$	0.278802	−	8.98265i	0.00883418	−	0.284626i
$997$	−29.1701	+	16.8414i	−0.923828	+	0.533372i	−0.884854	−	0.465868i	$-0.845742\pi$
$997$	−29.1701	+	16.8414i	−0.923828	+	0.533372i	−0.0389734	+	0.999240i	$0.512409\pi$
$998$		−	6.75628i		−	0.213866i
$999$	−2.90459	+	31.1139i	−0.0918971	+	0.984400i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.m.c.293.19	yes	48
3.2	odd	2		2646.2.m.c.881.2		48
7.2	even	3		882.2.t.c.815.10		48
7.3	odd	6		882.2.l.c.509.22		48
7.4	even	3		882.2.l.c.509.15		48
7.5	odd	6		882.2.t.c.815.3		48
7.6	odd	2	inner	882.2.m.c.293.18	✓	48
9.2	odd	6	inner	882.2.m.c.587.18	yes	48
9.7	even	3		2646.2.m.c.1763.1		48
21.2	odd	6		2646.2.t.c.2285.13		48
21.5	even	6		2646.2.t.c.2285.14		48
21.11	odd	6		2646.2.l.c.1097.2		48
21.17	even	6		2646.2.l.c.1097.1		48
21.20	even	2		2646.2.m.c.881.1		48
63.2	odd	6		882.2.l.c.227.10		48
63.11	odd	6		882.2.t.c.803.3		48
63.16	even	3		2646.2.l.c.521.1		48
63.20	even	6	inner	882.2.m.c.587.19	yes	48
63.25	even	3		2646.2.t.c.1979.14		48
63.34	odd	6		2646.2.m.c.1763.2		48
63.38	even	6		882.2.t.c.803.10		48
63.47	even	6		882.2.l.c.227.3		48
63.52	odd	6		2646.2.t.c.1979.13		48
63.61	odd	6		2646.2.l.c.521.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.l.c.227.3		48	63.47	even	6
882.2.l.c.227.10		48	63.2	odd	6
882.2.l.c.509.15		48	7.4	even	3
882.2.l.c.509.22		48	7.3	odd	6
882.2.m.c.293.18	✓	48	7.6	odd	2	inner
882.2.m.c.293.19	yes	48	1.1	even	1	trivial
882.2.m.c.587.18	yes	48	9.2	odd	6	inner
882.2.m.c.587.19	yes	48	63.20	even	6	inner
882.2.t.c.803.3		48	63.11	odd	6
882.2.t.c.803.10		48	63.38	even	6
882.2.t.c.815.3		48	7.5	odd	6
882.2.t.c.815.10		48	7.2	even	3
2646.2.l.c.521.1		48	63.16	even	3
2646.2.l.c.521.2		48	63.61	odd	6
2646.2.l.c.1097.1		48	21.17	even	6
2646.2.l.c.1097.2		48	21.11	odd	6
2646.2.m.c.881.1		48	21.20	even	2
2646.2.m.c.881.2		48	3.2	odd	2
2646.2.m.c.1763.1		48	9.7	even	3
2646.2.m.c.1763.2		48	63.34	odd	6
2646.2.t.c.1979.13		48	63.52	odd	6
2646.2.t.c.1979.14		48	63.25	even	3
2646.2.t.c.2285.13		48	21.2	odd	6
2646.2.t.c.2285.14		48	21.5	even	6

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.0537332 - 1.73122i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.99341 + 3.45268i) q^{5} +(-0.819074 - 1.52614i) q^{6} -1.00000i q^{8} +(-2.99423 - 0.186048i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.0537332 - 1.73122i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.99341 + 3.45268i) q^{5} +(-0.819074 - 1.52614i) q^{6} -1.00000i q^{8} +(-2.99423 - 0.186048i) q^{9} +3.98682i q^{10} +(-1.43438 + 0.828141i) q^{11} +(-1.47241 - 0.912143i) q^{12} +(-2.60834 - 1.50592i) q^{13} +(5.87023 + 3.63655i) q^{15} +(-0.500000 - 0.866025i) q^{16} -7.45640 q^{17} +(-2.68610 + 1.33599i) q^{18} +4.57324i q^{19} +(1.99341 + 3.45268i) q^{20} +(-0.828141 + 1.43438i) q^{22} +(-0.253614 - 0.146424i) q^{23} +(-1.73122 - 0.0537332i) q^{24} +(-5.44735 - 9.43509i) q^{25} -3.01185 q^{26} +(-0.482978 + 5.17366i) q^{27} +(-3.18684 + 1.83992i) q^{29} +(6.90204 + 0.214224i) q^{30} +(4.08317 + 2.35742i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.35662 + 2.52773i) q^{33} +(-6.45743 + 3.72820i) q^{34} +(-1.65823 + 2.50005i) q^{36} +6.01391 q^{37} +(2.28662 + 3.96054i) q^{38} +(-2.74723 + 4.43468i) q^{39} +(3.45268 + 1.99341i) q^{40} +(-4.88630 + 8.46333i) q^{41} +(-1.29961 - 2.25100i) q^{43} +1.65628i q^{44} +(6.61108 - 9.96725i) q^{45} -0.292848 q^{46} +(-6.80622 - 11.7887i) q^{47} +(-1.52614 + 0.819074i) q^{48} +(-9.43509 - 5.44735i) q^{50} +(-0.400656 + 12.9086i) q^{51} +(-2.60834 + 1.50592i) q^{52} -0.916164i q^{53} +(2.16856 + 4.72201i) q^{54} -6.60330i q^{55} +(7.91727 + 0.245735i) q^{57} +(-1.83992 + 3.18684i) q^{58} +(3.53337 - 6.11998i) q^{59} +(6.08446 - 3.26550i) q^{60} +(5.75611 - 3.32329i) q^{61} +4.71484 q^{62} -1.00000 q^{64} +(10.3990 - 6.00384i) q^{65} +(2.43873 + 1.51077i) q^{66} +(-2.02838 + 3.51326i) q^{67} +(-3.72820 + 6.45743i) q^{68} +(-0.267120 + 0.431193i) q^{69} +13.9437i q^{71} +(-0.186048 + 2.99423i) q^{72} -4.44068i q^{73} +(5.20820 - 3.00695i) q^{74} +(-16.6269 + 8.92357i) q^{75} +(3.96054 + 2.28662i) q^{76} +(-0.161836 + 5.21416i) q^{78} +(-1.42365 - 2.46583i) q^{79} +3.98682 q^{80} +(8.93077 + 1.11414i) q^{81} +9.77261i q^{82} +(2.59432 + 4.49349i) q^{83} +(14.8636 - 25.7446i) q^{85} +(-2.25100 - 1.29961i) q^{86} +(3.01407 + 5.61597i) q^{87} +(0.828141 + 1.43438i) q^{88} +11.0173 q^{89} +(0.741738 - 11.9374i) q^{90} +(-0.253614 + 0.146424i) q^{92} +(4.30061 - 6.94219i) q^{93} +(-11.7887 - 6.80622i) q^{94} +(-15.7899 - 9.11633i) q^{95} +(-0.912143 + 1.47241i) q^{96} +(-2.51510 + 1.45209i) q^{97} +(4.44894 - 2.21278i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} - 32 q^{9}+O(q^{10}) \) 48 * q + 24 * q^4 - 32 * q^9	\( 48 q + 24 q^{4} - 32 q^{9} + 48 q^{11} + 48 q^{15} - 24 q^{16} + 16 q^{18} + 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} - 64 q^{39} - 48 q^{50} - 80 q^{57} - 48 q^{64} + 32 q^{72} + 32 q^{78} + 48 q^{79} + 48 q^{85} + 96 q^{86} + 48 q^{92} + 96 q^{93} - 192 q^{95} + 104 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 - 32 * q^9 + 48 * q^11 + 48 * q^15 - 24 * q^16 + 16 * q^18 + 48 * q^23 - 24 * q^25 - 16 * q^30 - 16 * q^36 - 64 * q^39 - 48 * q^50 - 80 * q^57 - 48 * q^64 + 32 * q^72 + 32 * q^78 + 48 * q^79 + 48 * q^85 + 96 * q^86 + 48 * q^92 + 96 * q^93 - 192 * q^95 + 104 * q^99

Introduction

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