LMFDB - Embedded newform 1148.2.ba.a.113.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(113,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("1148.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.ba (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			113.4
Character	$\chi$	$=$	1148.113
Dual form			1148.2.ba.a.701.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.09016i q^{3} +(-0.164331 - 0.505760i) q^{5} +(0.587785 + 0.809017i) q^{7} -1.36876 q^{9} +O(q^{10})$	\(q-2.09016i q^{3} +(-0.164331 - 0.505760i) q^{5} +(0.587785 + 0.809017i) q^{7} -1.36876 q^{9} +(4.19378 + 1.36264i) q^{11} +(0.411006 - 0.565701i) q^{13} +(-1.05712 + 0.343479i) q^{15} +(4.23116 + 1.37479i) q^{17} +(0.594887 + 0.818792i) q^{19} +(1.69097 - 1.22856i) q^{21} +(1.12468 + 0.817130i) q^{23} +(3.81630 - 2.77270i) q^{25} -3.40954i q^{27} +(-1.04111 + 0.338276i) q^{29} +(0.770024 - 2.36989i) q^{31} +(2.84814 - 8.76566i) q^{33} +(0.312577 - 0.430225i) q^{35} +(2.00349 + 6.16611i) q^{37} +(-1.18240 - 0.859067i) q^{39} +(-6.15241 + 1.77421i) q^{41} +(-6.05702 - 4.40069i) q^{43} +(0.224931 + 0.692266i) q^{45} +(4.37284 - 6.01869i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(2.87352 - 8.84379i) q^{51} +(-4.69734 + 1.52626i) q^{53} -2.34497i q^{55} +(1.71140 - 1.24341i) q^{57} +(1.18992 + 0.864530i) q^{59} +(3.97038 - 2.88465i) q^{61} +(-0.804539 - 1.10735i) q^{63} +(-0.353650 - 0.114908i) q^{65} +(7.41978 - 2.41083i) q^{67} +(1.70793 - 2.35077i) q^{69} +(-8.51336 - 2.76616i) q^{71} -11.9718 q^{73} +(-5.79539 - 7.97667i) q^{75} +(1.36264 + 4.19378i) q^{77} +7.66283i q^{79} -11.2328 q^{81} +12.3013 q^{83} -2.36587i q^{85} +(0.707050 + 2.17608i) q^{87} +(-6.03248 - 8.30300i) q^{89} +0.699244 q^{91} +(-4.95345 - 1.60947i) q^{93} +(0.316354 - 0.435423i) q^{95} +(-4.10362 + 1.33335i) q^{97} +(-5.74029 - 1.86513i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) $ 80 * q - 4 * q^5 - 60 * q^9	$ 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) $ 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{10}\right)$

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			0
$2$		0			0
$3$		−	2.09016i		−	1.20675i	−0.797456	−	0.603377i	$-0.793821\pi$
$3$		−	2.09016i		−	1.20675i	0.797456	−	0.603377i	$-0.206179\pi$
$4$		0			0
$5$	−0.164331	−	0.505760i	−0.0734913	−	0.226183i	0.907563	−	0.419916i	$-0.137940\pi$
$5$	−0.164331	−	0.505760i	−0.0734913	−	0.226183i	−0.981054	+	0.193733i	$0.937940\pi$
$6$		0			0
$7$	0.587785	+	0.809017i	0.222162	+	0.305780i
$7$	0.587785	+	0.809017i	0.222162	+	0.305780i
$8$		0			0
$9$	−1.36876			−0.456255
$10$		0			0
$11$	4.19378	+	1.36264i	1.26447	+	0.410852i	0.863086	−	0.505057i	$-0.168529\pi$
$11$	4.19378	+	1.36264i	1.26447	+	0.410852i	0.401386	+	0.915909i	$0.368529\pi$
$12$		0			0
$13$	0.411006	−	0.565701i	0.113992	−	0.156897i	−0.748208	−	0.663464i	$-0.769086\pi$
$13$	0.411006	−	0.565701i	0.113992	−	0.156897i	0.862201	+	0.506567i	$0.169086\pi$
$14$		0			0
$15$	−1.05712	+	0.343479i	−0.272947	+	0.0886859i
$16$		0			0
$17$	4.23116	+	1.37479i	1.02621	+	0.333435i	0.773289	−	0.634053i	$-0.218610\pi$
$17$	4.23116	+	1.37479i	1.02621	+	0.333435i	0.252917	+	0.967488i	$0.418610\pi$
$18$		0			0
$19$	0.594887	+	0.818792i	0.136476	+	0.187844i	0.871785	−	0.489889i	$-0.162963\pi$
$19$	0.594887	+	0.818792i	0.136476	+	0.187844i	−0.735308	+	0.677733i	$0.762963\pi$
$20$		0			0
$21$	1.69097	−	1.22856i	0.369001	−	0.268095i
$22$		0			0
$23$	1.12468	+	0.817130i	0.234513	+	0.170383i	0.698835	−	0.715283i	$-0.253702\pi$
$23$	1.12468	+	0.817130i	0.234513	+	0.170383i	−0.464322	+	0.885666i	$0.653702\pi$
$24$		0			0
$25$	3.81630	−	2.77270i	0.763259	−	0.554540i
$26$		0			0
$27$		−	3.40954i		−	0.656167i
$28$		0			0
$29$	−1.04111	+	0.338276i	−0.193329	+	0.0628162i	−0.404081	−	0.914723i	$-0.632409\pi$
$29$	−1.04111	+	0.338276i	−0.193329	+	0.0628162i	0.210752	+	0.977539i	$0.432409\pi$
$30$		0			0
$31$	0.770024	−	2.36989i	0.138300	−	0.425645i	−0.857788	−	0.514003i	$-0.828162\pi$
$31$	0.770024	−	2.36989i	0.138300	−	0.425645i	0.996089	+	0.0883582i	$0.0281620\pi$
$32$		0			0
$33$	2.84814	−	8.76566i	0.495797	−	1.52591i
$34$		0			0
$35$	0.312577	−	0.430225i	0.0528352	−	0.0727214i
$36$		0			0
$37$	2.00349	+	6.16611i	0.329372	+	1.01370i	0.969428	+	0.245374i	$0.0789109\pi$
$37$	2.00349	+	6.16611i	0.329372	+	1.01370i	−0.640057	+	0.768328i	$0.721089\pi$
$38$		0			0
$39$	−1.18240	−	0.859067i	−0.189336	−	0.137561i
$40$		0			0
$41$	−6.15241	+	1.77421i	−0.960845	+	0.277086i
$41$	−6.15241	+	1.77421i	−0.960845	+	0.277086i
$42$		0			0
$43$	−6.05702	−	4.40069i	−0.923688	−	0.671098i	0.0207516	−	0.999785i	$-0.493394\pi$
$43$	−6.05702	−	4.40069i	−0.923688	−	0.671098i	−0.944439	+	0.328686i	$0.893394\pi$
$44$		0			0
$45$	0.224931	+	0.692266i	0.0335307	+	0.103197i
$46$		0			0
$47$	4.37284	−	6.01869i	0.637844	−	0.877917i	−0.360654	−	0.932699i	$-0.617447\pi$
$47$	4.37284	−	6.01869i	0.637844	−	0.877917i	0.998498	+	0.0547828i	$0.0174466\pi$
$48$		0			0
$49$	−0.309017	+	0.951057i	−0.0441453	+	0.135865i
$50$		0			0
$51$	2.87352	−	8.84379i	0.402373	−	1.23838i
$52$		0			0
$53$	−4.69734	+	1.52626i	−0.645229	+	0.209648i	−0.613309	−	0.789843i	$-0.710162\pi$
$53$	−4.69734	+	1.52626i	−0.645229	+	0.209648i	−0.0319198	+	0.999490i	$0.510162\pi$
$54$		0			0
$55$		−	2.34497i		−	0.316196i
$56$		0			0
$57$	1.71140	−	1.24341i	0.226681	−	0.164693i
$58$		0			0
$59$	1.18992	+	0.864530i	0.154915	+	0.112552i	0.662542	−	0.749024i	$-0.269477\pi$
$59$	1.18992	+	0.864530i	0.154915	+	0.112552i	−0.507628	+	0.861577i	$0.669477\pi$
$60$		0			0
$61$	3.97038	−	2.88465i	0.508356	−	0.369342i	−0.303844	−	0.952722i	$-0.598270\pi$
$61$	3.97038	−	2.88465i	0.508356	−	0.369342i	0.812199	+	0.583380i	$0.198270\pi$
$62$		0			0
$63$	−0.804539	−	1.10735i	−0.101362	−	0.139513i
$64$		0			0
$65$	−0.353650	−	0.114908i	−0.0438649	−	0.0142526i
$66$		0			0
$67$	7.41978	−	2.41083i	0.906470	−	0.294530i	0.181565	−	0.983379i	$-0.441884\pi$
$67$	7.41978	−	2.41083i	0.906470	−	0.294530i	0.724905	+	0.688849i	$0.241884\pi$
$68$		0			0
$69$	1.70793	−	2.35077i	0.205611	−	0.282999i
$70$		0			0
$71$	−8.51336	−	2.76616i	−1.01035	−	0.328283i	−0.243356	−	0.969937i	$-0.578248\pi$
$71$	−8.51336	−	2.76616i	−1.01035	−	0.328283i	−0.766994	+	0.641654i	$0.778248\pi$
$72$		0			0
$73$	−11.9718			−1.40119			−0.700597	−	0.713558i	$-0.747083\pi$
$73$	−11.9718			−1.40119			−0.700597	+	0.713558i	$0.747083\pi$
$74$		0			0
$75$	−5.79539	−	7.97667i	−0.669194	−	0.921066i
$76$		0			0
$77$	1.36264	+	4.19378i	0.155287	+	0.477925i
$78$		0			0
$79$			7.66283i			0.862135i	0.902320	+	0.431068i	$0.141863\pi$
$79$			7.66283i			0.862135i	−0.902320	+	0.431068i	$0.858137\pi$
$80$		0			0
$81$	−11.2328			−1.24809
$82$		0			0
$83$	12.3013			1.35025			0.675123	−	0.737705i	$-0.264091\pi$
$83$	12.3013			1.35025			0.675123	+	0.737705i	$0.264091\pi$
$84$		0			0
$85$		−	2.36587i		−	0.256615i
$86$		0			0
$87$	0.707050	+	2.17608i	0.0758037	+	0.233300i
$88$		0			0
$89$	−6.03248	−	8.30300i	−0.639442	−	0.880116i	0.359144	−	0.933282i	$-0.383069\pi$
$89$	−6.03248	−	8.30300i	−0.639442	−	0.880116i	−0.998586	+	0.0531661i	$0.983069\pi$
$90$		0			0
$91$	0.699244			0.0733007
$92$		0			0
$93$	−4.95345	−	1.60947i	−0.513648	−	0.166894i
$94$		0			0
$95$	0.316354	−	0.435423i	0.0324572	−	0.0446735i
$96$		0			0
$97$	−4.10362	+	1.33335i	−0.416660	+	0.135381i	−0.509842	−	0.860268i	$-0.670296\pi$
$97$	−4.10362	+	1.33335i	−0.416660	+	0.135381i	0.0931822	+	0.995649i	$0.470296\pi$
$98$		0			0
$99$	−5.74029	−	1.86513i	−0.576921	−	0.187453i
$100$		0			0
$101$	−5.84818	−	8.04933i	−0.581915	−	0.800938i	0.411988	−	0.911189i	$-0.364834\pi$
$101$	−5.84818	−	8.04933i	−0.581915	−	0.800938i	−0.993904	+	0.110251i	$0.964834\pi$
$102$		0			0
$103$	3.24756	−	2.35949i	0.319991	−	0.232487i	−0.416181	−	0.909282i	$-0.636632\pi$
$103$	3.24756	−	2.35949i	0.319991	−	0.232487i	0.736172	+	0.676795i	$0.236632\pi$
$104$		0			0
$105$	−0.899239	−	0.653336i	−0.0877568	−	0.0637590i
$106$		0			0
$107$	5.50446	−	3.99923i	0.532136	−	0.386620i	−0.289020	−	0.957323i	$-0.593329\pi$
$107$	5.50446	−	3.99923i	0.532136	−	0.386620i	0.821156	+	0.570703i	$0.193329\pi$
$108$		0			0
$109$			13.9941i			1.34039i	0.742183	+	0.670197i	$0.233790\pi$
$109$			13.9941i			1.34039i	−0.742183	+	0.670197i	$0.766210\pi$
$110$		0			0
$111$	12.8882	−	4.18761i	1.22329	−	0.397471i
$112$		0			0
$113$	−1.03197	+	3.17609i	−0.0970798	+	0.298781i	−0.987790	−	0.155790i	$-0.950208\pi$
$113$	−1.03197	+	3.17609i	−0.0970798	+	0.298781i	0.890710	+	0.454571i	$0.150208\pi$
$114$		0			0
$115$	0.228451	−	0.703101i	0.0213032	−	0.0655645i
$116$		0			0
$117$	−0.562570	+	0.774311i	−0.0520096	+	0.0715850i
$118$		0			0
$119$	1.37479	+	4.23116i	0.126026	+	0.387869i
$120$		0			0
$121$	6.83180	+	4.96359i	0.621072	+	0.451235i
$122$		0			0
$123$	3.70839	+	12.8595i	0.334374	+	1.15950i
$124$		0			0
$125$	−4.18059	−	3.03737i	−0.373923	−	0.271671i
$126$		0			0
$127$	0.157532	+	0.484833i	0.0139787	+	0.0430220i	0.957803	−	0.287427i	$-0.0927999\pi$
$127$	0.157532	+	0.484833i	0.0139787	+	0.0430220i	−0.943824	+	0.330449i	$0.892800\pi$
$128$		0			0
$129$	−9.19813	+	12.6601i	−0.809850	+	1.11466i
$130$		0			0
$131$	5.27596	−	16.2377i	0.460963	−	1.41870i	−0.403027	−	0.915188i	$-0.632042\pi$
$131$	5.27596	−	16.2377i	0.460963	−	1.41870i	0.863989	−	0.503510i	$-0.167958\pi$
$132$		0			0
$133$	−0.312751	+	0.962547i	−0.0271189	+	0.0834634i
$134$		0			0
$135$	−1.72441	+	0.560295i	−0.148414	+	0.0482225i
$136$		0			0
$137$			3.21400i			0.274590i	0.990530	+	0.137295i	$0.0438409\pi$
$137$			3.21400i			0.274590i	−0.990530	+	0.137295i	$0.956159\pi$
$138$		0			0
$139$	9.22169	−	6.69995i	0.782174	−	0.568282i	−0.123457	−	0.992350i	$-0.539398\pi$
$139$	9.22169	−	6.69995i	0.782174	−	0.568282i	0.905631	+	0.424067i	$0.139398\pi$
$140$		0			0
$141$	−12.5800	−	9.13992i	−1.05943	−	0.769720i
$142$		0			0
$143$	2.49451	−	1.81237i	0.208602	−	0.151558i
$144$		0			0
$145$	0.342173	+	0.470961i	0.0284159	+	0.0391112i
$146$		0			0
$147$	1.98786	+	0.645895i	0.163956	+	0.0532725i
$148$		0			0
$149$	11.9970	−	3.89807i	0.982835	−	0.319343i	0.226849	−	0.973930i	$-0.427158\pi$
$149$	11.9970	−	3.89807i	0.982835	−	0.319343i	0.755986	+	0.654587i	$0.227158\pi$
$150$		0			0
$151$	−9.73931	+	13.4050i	−0.792574	+	1.09088i	0.201209	+	0.979548i	$0.435513\pi$
$151$	−9.73931	+	13.4050i	−0.792574	+	1.09088i	−0.993783	+	0.111336i	$0.964487\pi$
$152$		0			0
$153$	−5.79145	−	1.88176i	−0.468211	−	0.152131i
$154$		0			0
$155$	−1.32514			−0.106437
$156$		0			0
$157$	5.36817	+	7.38865i	0.428426	+	0.589678i	0.967591	−	0.252522i	$-0.0812600\pi$
$157$	5.36817	+	7.38865i	0.428426	+	0.589678i	−0.539165	+	0.842200i	$0.681260\pi$
$158$		0			0
$159$	3.19012	+	9.81819i	0.252993	+	0.778633i
$160$		0			0
$161$			1.39019i			0.109562i
$162$		0			0
$163$	4.18387			0.327706			0.163853	−	0.986485i	$-0.447608\pi$
$163$	4.18387			0.327706			0.163853	+	0.986485i	$0.447608\pi$
$164$		0			0
$165$	−4.90136			−0.381571
$166$		0			0
$167$		−	6.71271i		−	0.519445i	−0.965683	−	0.259722i	$-0.916369\pi$
$167$		−	6.71271i		−	0.519445i	0.965683	−	0.259722i	$-0.0836311\pi$
$168$		0			0
$169$	3.86613	+	11.8987i	0.297395	+	0.915286i
$170$		0			0
$171$	−0.814260	−	1.12073i	−0.0622680	−	0.0857045i
$172$		0			0
$173$	2.19087			0.166569			0.0832843	−	0.996526i	$-0.473459\pi$
$173$	2.19087			0.166569			0.0832843	+	0.996526i	$0.473459\pi$
$174$		0			0
$175$	4.48633	+	1.45770i	0.339134	+	0.110191i
$176$		0			0
$177$	1.80701	−	2.48713i	0.135823	−	0.186944i
$178$		0			0
$179$	13.6309	−	4.42894i	1.01882	−	0.331035i	0.248459	−	0.968642i	$-0.420076\pi$
$179$	13.6309	−	4.42894i	1.01882	−	0.331035i	0.770361	+	0.637608i	$0.220076\pi$
$180$		0			0
$181$	9.10874	+	2.95961i	0.677047	+	0.219986i	0.627302	−	0.778776i	$-0.284159\pi$
$181$	9.10874	+	2.95961i	0.677047	+	0.219986i	0.0497450	+	0.998762i	$0.484159\pi$
$182$		0			0
$183$	−6.02938	−	8.29873i	−0.445705	−	0.613460i
$184$		0			0
$185$	2.78934	−	2.02657i	0.205076	−	0.148997i
$186$		0			0
$187$	15.8712	+	11.5311i	1.16062	+	0.843237i
$188$		0			0
$189$	2.75838	−	2.00408i	0.200642	−	0.145775i
$190$		0			0
$191$			7.99148i			0.578243i	0.957292	+	0.289122i	$0.0933632\pi$
$191$			7.99148i			0.578243i	−0.957292	+	0.289122i	$0.906637\pi$
$192$		0			0
$193$	−16.2471	+	5.27900i	−1.16949	+	0.379991i	−0.828453	−	0.560059i	$-0.810779\pi$
$193$	−16.2471	+	5.27900i	−1.16949	+	0.379991i	−0.341038	+	0.940049i	$0.610779\pi$
$194$		0			0
$195$	−0.240176	+	0.739185i	−0.0171993	+	0.0529341i
$196$		0			0
$197$	−5.29217	+	16.2876i	−0.377052	+	1.16045i	0.565032	+	0.825069i	$0.308864\pi$
$197$	−5.29217	+	16.2876i	−0.377052	+	1.16045i	−0.942084	+	0.335377i	$0.891136\pi$
$198$		0			0
$199$	−10.3393	+	14.2308i	−0.732935	+	1.00880i	0.266059	+	0.963957i	$0.414278\pi$
$199$	−10.3393	+	14.2308i	−0.732935	+	1.00880i	−0.998994	+	0.0448414i	$0.985722\pi$
$200$		0			0
$201$	−5.03902	−	15.5085i	−0.355425	−	1.09389i
$202$		0			0
$203$	−0.885618	−	0.643439i	−0.0621582	−	0.0451606i
$204$		0			0
$205$	1.90836	+	2.82009i	0.133286	+	0.196963i
$206$		0			0
$207$	−1.53943	−	1.11846i	−0.106998	−	0.0777382i
$208$		0			0
$209$	1.37910	+	4.24445i	0.0953947	+	0.293595i
$210$		0			0
$211$	−7.28537	+	10.0274i	−0.501545	+	0.690318i	−0.982465	−	0.186447i	$-0.940303\pi$
$211$	−7.28537	+	10.0274i	−0.501545	+	0.690318i	0.480920	+	0.876765i	$0.340303\pi$
$212$		0			0
$213$	−5.78171	+	17.7943i	−0.396156	+	1.21924i
$214$		0			0
$215$	−1.23033	+	3.78657i	−0.0839080	+	0.258242i
$216$		0			0
$217$	2.36989	−	0.770024i	0.160879	−	0.0522726i
$218$		0			0
$219$			25.0230i			1.69090i
$220$		0			0
$221$	2.51675	−	1.82852i	0.169295	−	0.123000i
$222$		0			0
$223$	3.09436	+	2.24818i	0.207213	+	0.150549i	0.686552	−	0.727081i	$-0.259123\pi$
$223$	3.09436	+	2.24818i	0.207213	+	0.150549i	−0.479339	+	0.877630i	$0.659123\pi$
$224$		0			0
$225$	−5.22361	+	3.79517i	−0.348241	+	0.253012i
$226$		0			0
$227$	9.86346	+	13.5759i	0.654661	+	0.901063i	0.999290	−	0.0376759i	$-0.0119954\pi$
$227$	9.86346	+	13.5759i	0.654661	+	0.901063i	−0.344629	+	0.938739i	$0.611995\pi$
$228$		0			0
$229$	−21.7245	−	7.05873i	−1.43560	−	0.466454i	−0.515076	−	0.857145i	$-0.672236\pi$
$229$	−21.7245	−	7.05873i	−1.43560	−	0.466454i	−0.920522	+	0.390690i	$0.872236\pi$
$230$		0			0
$231$	8.76566	−	2.84814i	0.576738	−	0.187394i
$232$		0			0
$233$	11.9022	−	16.3820i	0.779741	−	1.07322i	−0.215569	−	0.976489i	$-0.569161\pi$
$233$	11.9022	−	16.3820i	0.779741	−	1.07322i	0.995310	−	0.0967330i	$-0.0308393\pi$
$234$		0			0
$235$	−3.76261	−	1.22255i	−0.245446	−	0.0797501i
$236$		0			0
$237$	16.0165			1.04039
$238$		0			0
$239$	−13.6842	−	18.8347i	−0.885157	−	1.21831i	−0.974966	−	0.222356i	$-0.928625\pi$
$239$	−13.6842	−	18.8347i	−0.885157	−	1.21831i	0.0898083	−	0.995959i	$-0.471375\pi$
$240$		0			0
$241$	3.44438	+	10.6007i	0.221872	+	0.682852i	0.998594	+	0.0530085i	$0.0168811\pi$
$241$	3.44438	+	10.6007i	0.221872	+	0.682852i	−0.776722	+	0.629844i	$0.783119\pi$
$242$		0			0
$243$			13.2497i			0.849966i
$244$		0			0
$245$	0.531788			0.0339747
$246$		0			0
$247$	0.707693			0.0450294
$248$		0			0
$249$		−	25.7117i		−	1.62941i
$250$		0			0
$251$	2.94175	+	9.05378i	0.185682	+	0.571469i	0.999959	−	0.00900608i	$-0.00286676\pi$
$251$	2.94175	+	9.05378i	0.185682	+	0.571469i	−0.814278	+	0.580475i	$0.802867\pi$
$252$		0			0
$253$	3.60322	+	4.95940i	0.226532	+	0.311795i
$254$		0			0
$255$	−4.94505			−0.309671
$256$		0			0
$257$	15.7402	+	5.11431i	0.981848	+	0.319022i	0.755590	−	0.655045i	$-0.227351\pi$
$257$	15.7402	+	5.11431i	0.981848	+	0.319022i	0.226259	+	0.974067i	$0.427351\pi$
$258$		0			0
$259$	−3.81087	+	5.24521i	−0.236796	+	0.325921i
$260$		0			0
$261$	1.42503	−	0.463020i	0.0882070	−	0.0286602i
$262$		0			0
$263$	3.99739	+	1.29883i	0.246489	+	0.0800892i	0.429656	−	0.902993i	$-0.358635\pi$
$263$	3.99739	+	1.29883i	0.246489	+	0.0800892i	−0.183167	+	0.983082i	$0.558635\pi$
$264$		0			0
$265$	1.54384	+	2.12492i	0.0948374	+	0.130533i
$266$		0			0
$267$	−17.3546	+	12.6088i	−1.06208	+	0.771649i
$268$		0			0
$269$	−7.16162	−	5.20322i	−0.436652	−	0.317246i	0.347651	−	0.937624i	$-0.386979\pi$
$269$	−7.16162	−	5.20322i	−0.436652	−	0.317246i	−0.784303	+	0.620378i	$0.786979\pi$
$270$		0			0
$271$	−11.8355	+	8.59903i	−0.718958	+	0.522354i	−0.886051	−	0.463587i	$-0.846562\pi$
$271$	−11.8355	+	8.59903i	−0.718958	+	0.522354i	0.167093	+	0.985941i	$0.446562\pi$
$272$		0			0
$273$		−	1.46153i		−	0.0884559i
$274$		0			0
$275$	19.7829	−	6.42785i	1.19295	−	0.387614i
$276$		0			0
$277$	−8.58916	+	26.4347i	−0.516072	+	1.58831i	0.265250	+	0.964180i	$0.414545\pi$
$277$	−8.58916	+	26.4347i	−0.516072	+	1.58831i	−0.781322	+	0.624128i	$0.785455\pi$
$278$		0			0
$279$	−1.05398	+	3.24382i	−0.0631002	+	0.194202i
$280$		0			0
$281$	−1.79500	+	2.47060i	−0.107081	+	0.147384i	−0.859194	−	0.511650i	$-0.829035\pi$
$281$	−1.79500	+	2.47060i	−0.107081	+	0.147384i	0.752113	+	0.659034i	$0.229035\pi$
$282$		0			0
$283$	−3.91798	−	12.0583i	−0.232900	−	0.716791i	−0.997393	−	0.0721598i	$-0.977011\pi$
$283$	−3.91798	−	12.0583i	−0.232900	−	0.716791i	0.764494	−	0.644631i	$-0.222989\pi$
$284$		0			0
$285$	−0.910104	−	0.661229i	−0.0539099	−	0.0391678i
$286$		0			0
$287$	−5.05167	−	3.93455i	−0.298190	−	0.232249i
$288$		0			0
$289$	2.25936	+	1.64152i	0.132903	+	0.0965599i
$290$		0			0
$291$	2.78691	+	8.57722i	0.163371	+	0.502806i
$292$		0			0
$293$	−11.4707	+	15.7881i	−0.670126	+	0.922349i	−0.999763	−	0.0217584i	$-0.993074\pi$
$293$	−11.4707	+	15.7881i	−0.670126	+	0.922349i	0.329637	+	0.944108i	$0.393074\pi$
$294$		0			0
$295$	0.241703	−	0.743886i	0.0140725	−	0.0433107i
$296$		0			0
$297$	4.64598	−	14.2989i	0.269587	−	0.829704i
$298$		0			0
$299$	0.924502	−	0.300389i	0.0534654	−	0.0173719i
$300$		0			0
$301$		−	7.48689i		−	0.431537i
$302$		0			0
$303$	−16.8244	+	12.2236i	−0.966535	+	0.702229i
$304$		0			0
$305$	−2.11140	−	1.53402i	−0.120899	−	0.0878379i
$306$		0			0
$307$	18.8431	−	13.6903i	1.07543	−	0.781347i	0.0985514	−	0.995132i	$-0.468579\pi$
$307$	18.8431	−	13.6903i	1.07543	−	0.781347i	0.976881	+	0.213785i	$0.0685791\pi$
$308$		0			0
$309$	−4.93170	−	6.78791i	−0.280555	−	0.386151i
$310$		0			0
$311$	−24.8796	−	8.08388i	−1.41079	−	0.458395i	−0.498129	−	0.867103i	$-0.665979\pi$
$311$	−24.8796	−	8.08388i	−1.41079	−	0.458395i	−0.912665	+	0.408709i	$0.865979\pi$
$312$		0			0
$313$	1.22612	−	0.398391i	0.0693045	−	0.0225184i	−0.274160	−	0.961684i	$-0.588400\pi$
$313$	1.22612	−	0.398391i	0.0693045	−	0.0225184i	0.343464	+	0.939166i	$0.388400\pi$
$314$		0			0
$315$	−0.427844	+	0.588877i	−0.0241063	+	0.0331795i
$316$		0			0
$317$	−20.1245	−	6.53885i	−1.13031	−	0.367258i	−0.316613	−	0.948555i	$-0.602546\pi$
$317$	−20.1245	−	6.53885i	−1.13031	−	0.367258i	−0.813692	+	0.581296i	$0.802546\pi$
$318$		0			0
$319$	−4.82712			−0.270267
$320$		0			0
$321$	−8.35902	−	11.5052i	−0.466555	−	0.642158i
$322$		0			0
$323$	1.39140	+	4.28228i	0.0774194	+	0.238272i
$324$		0			0
$325$		−	3.29848i		−	0.182967i
$326$		0			0
$327$	29.2500			1.61753
$328$		0			0
$329$	7.43951			0.410154
$330$		0			0
$331$		−	12.8541i		−	0.706524i	−0.935524	−	0.353262i	$-0.885072\pi$
$331$		−	12.8541i		−	0.706524i	0.935524	−	0.353262i	$-0.114928\pi$
$332$		0			0
$333$	−2.74231	−	8.43995i	−0.150277	−	0.462506i
$334$		0			0
$335$	−2.43861	−	3.35645i	−0.133235	−	0.183383i
$336$		0			0
$337$	−21.6746			−1.18069			−0.590345	−	0.807151i	$-0.701008\pi$
$337$	−21.6746			−1.18069			−0.590345	+	0.807151i	$0.701008\pi$
$338$		0			0
$339$	6.63852	+	2.15699i	0.360555	+	0.117151i
$340$		0			0
$341$	6.45862	−	8.88953i	0.349754	−	0.481395i
$342$		0			0
$343$	−0.951057	+	0.309017i	−0.0513522	+	0.0166853i
$344$		0			0
$345$	−1.46959	−	0.477499i	−0.0791202	−	0.0257077i
$346$		0			0
$347$	9.04223	+	12.4456i	0.485412	+	0.668113i	0.979534	−	0.201280i	$-0.0645102\pi$
$347$	9.04223	+	12.4456i	0.485412	+	0.668113i	−0.494121	+	0.869393i	$0.664510\pi$
$348$		0			0
$349$	−20.8550	+	15.1521i	−1.11634	+	0.811072i	−0.983651	−	0.180085i	$-0.942363\pi$
$349$	−20.8550	+	15.1521i	−1.11634	+	0.811072i	−0.132693	+	0.991157i	$0.542363\pi$
$350$		0			0
$351$	−1.92878	−	1.40134i	−0.102951	−	0.0747981i
$352$		0			0
$353$	−7.73167	+	5.61739i	−0.411515	+	0.298984i	−0.774215	−	0.632923i	$-0.781855\pi$
$353$	−7.73167	+	5.61739i	−0.411515	+	0.298984i	0.362700	+	0.931906i	$0.381855\pi$
$354$		0			0
$355$			4.76029i			0.252650i
$356$		0			0
$357$	8.84379	−	2.87352i	0.468063	−	0.152083i
$358$		0			0
$359$	−7.94406	+	24.4493i	−0.419272	+	1.29039i	0.489102	+	0.872226i	$0.337324\pi$
$359$	−7.94406	+	24.4493i	−0.419272	+	1.29039i	−0.908374	+	0.418159i	$0.862676\pi$
$360$		0			0
$361$	5.55479	−	17.0959i	0.292358	−	0.899784i
$362$		0			0
$363$	10.3747	−	14.2795i	0.544530	−	0.749481i
$364$		0			0
$365$	1.96734	+	6.05486i	0.102975	+	0.316926i
$366$		0			0
$367$	1.10730	+	0.804498i	0.0578004	+	0.0419944i	0.616310	−	0.787503i	$-0.288627\pi$
$367$	1.10730	+	0.804498i	0.0578004	+	0.0419944i	−0.558510	+	0.829498i	$0.688627\pi$
$368$		0			0
$369$	8.42120	−	2.42848i	0.438390	−	0.126422i
$370$		0			0
$371$	−3.99580	−	2.90312i	−0.207451	−	0.150722i
$372$		0			0
$373$	2.47578	+	7.61967i	0.128191	+	0.394532i	0.994469	−	0.105031i	$-0.0334941\pi$
$373$	2.47578	+	7.61967i	0.128191	+	0.394532i	−0.866278	+	0.499563i	$0.833494\pi$
$374$		0			0
$375$	−6.34859	+	8.73809i	−0.327840	+	0.451233i
$376$		0			0
$377$	−0.236538	+	0.727988i	−0.0121823	+	0.0374933i
$378$		0			0
$379$	−9.16044	+	28.1929i	−0.470540	+	1.44817i	0.381339	+	0.924435i	$0.375463\pi$
$379$	−9.16044	+	28.1929i	−0.470540	+	1.44817i	−0.851879	+	0.523739i	$0.824537\pi$
$380$		0			0
$381$	1.01338	−	0.329267i	0.0519170	−	0.0168688i
$382$		0			0
$383$			3.25043i			0.166089i	0.996546	+	0.0830446i	$0.0264644\pi$
$383$			3.25043i			0.166089i	−0.996546	+	0.0830446i	$0.973536\pi$
$384$		0			0
$385$	1.89712	−	1.37834i	0.0966863	−	0.0702467i
$386$		0			0
$387$	8.29064	+	6.02350i	0.421437	+	0.306192i
$388$		0			0
$389$	−10.2799	+	7.46881i	−0.521213	+	0.378683i	−0.817061	−	0.576552i	$-0.804398\pi$
$389$	−10.2799	+	7.46881i	−0.521213	+	0.378683i	0.295848	+	0.955235i	$0.404398\pi$
$390$		0			0
$391$	3.63533	+	5.00361i	0.183847	+	0.253043i
$392$		0			0
$393$	−33.9395	−	11.0276i	−1.71202	−	0.556269i
$394$		0			0
$395$	3.87555	−	1.25924i	0.195000	−	0.0633594i
$396$		0			0
$397$	4.62509	−	6.36589i	0.232127	−	0.319495i	−0.677025	−	0.735960i	$-0.736731\pi$
$397$	4.62509	−	6.36589i	0.232127	−	0.319495i	0.909152	+	0.416465i	$0.136731\pi$
$398$		0			0
$399$	2.01188	+	0.653698i	0.100720	+	0.0327259i
$400$		0			0
$401$	−25.2325			−1.26005			−0.630026	−	0.776574i	$-0.716956\pi$
$401$	−25.2325			−1.26005			−0.630026	+	0.776574i	$0.716956\pi$
$402$		0			0
$403$	−1.02416	−	1.40964i	−0.0510172	−	0.0702192i
$404$		0			0
$405$	1.84590	+	5.68109i	0.0917234	+	0.282296i
$406$		0			0
$407$			28.5893i			1.41712i
$408$		0			0
$409$	−17.5735			−0.868953			−0.434477	−	0.900683i	$-0.643067\pi$
$409$	−17.5735			−0.868953			−0.434477	+	0.900683i	$0.643067\pi$
$410$		0			0
$411$	6.71776			0.331363
$412$		0			0
$413$			1.47083i			0.0723746i
$414$		0			0
$415$	−2.02150	−	6.22152i	−0.0992313	−	0.305403i
$416$		0			0
$417$	−14.0040	−	19.2748i	−0.685777	−	0.943891i
$418$		0			0
$419$	−6.93588			−0.338840			−0.169420	−	0.985544i	$-0.554189\pi$
$419$	−6.93588			−0.338840			−0.169420	+	0.985544i	$0.554189\pi$
$420$		0			0
$421$	11.7676	+	3.82354i	0.573520	+	0.186348i	0.581396	−	0.813621i	$-0.302507\pi$
$421$	11.7676	+	3.82354i	0.573520	+	0.186348i	−0.00787556	+	0.999969i	$0.502507\pi$
$422$		0			0
$423$	−5.98538	+	8.23817i	−0.291019	+	0.400554i
$424$		0			0
$425$	19.9592	−	6.48514i	0.968164	−	0.314576i
$426$		0			0
$427$	4.66747	+	1.51655i	0.225875	+	0.0733911i
$428$		0			0
$429$	−3.78814	−	5.21393i	−0.182893	−	0.251731i
$430$		0			0
$431$	25.4754	−	18.5090i	1.22711	−	0.891546i	0.230438	−	0.973087i	$-0.425984\pi$
$431$	25.4754	−	18.5090i	1.22711	−	0.891546i	0.996670	+	0.0815412i	$0.0259842\pi$
$432$		0			0
$433$	16.0501	+	11.6611i	0.771319	+	0.560396i	0.902361	−	0.430981i	$-0.141832\pi$
$433$	16.0501	+	11.6611i	0.771319	+	0.560396i	−0.131042	+	0.991377i	$0.541832\pi$
$434$		0			0
$435$	0.984383	−	0.715196i	0.0471975	−	0.0342910i
$436$		0			0
$437$			1.40698i			0.0673051i
$438$		0			0
$439$	−17.2285	+	5.59789i	−0.822273	+	0.267173i	−0.689787	−	0.724012i	$-0.742296\pi$
$439$	−17.2285	+	5.59789i	−0.822273	+	0.267173i	−0.132486	+	0.991185i	$0.542296\pi$
$440$		0			0
$441$	0.422971	−	1.30177i	0.0201415	−	0.0619891i
$442$		0			0
$443$	4.01693	−	12.3628i	0.190850	−	0.587376i	−0.809150	−	0.587602i	$-0.800072\pi$
$443$	4.01693	−	12.3628i	0.190850	−	0.587376i	1.00000		0.000226160i	$7.19891e-5\pi$
$444$		0			0
$445$	−3.20800	+	4.41543i	−0.152074	+	0.209312i
$446$		0			0
$447$	−8.14759	−	25.0757i	−0.385368	−	1.18604i
$448$		0			0
$449$	−13.4620	−	9.78070i	−0.635310	−	0.461580i	0.222926	−	0.974835i	$-0.428439\pi$
$449$	−13.4620	−	9.78070i	−0.635310	−	0.461580i	−0.858236	+	0.513256i	$0.828439\pi$
$450$		0			0
$451$	−28.2195	−	0.942866i	−1.32880	−	0.0443978i
$452$		0			0
$453$	28.0186	+	20.3567i	1.31643	+	0.956441i
$454$		0			0
$455$	−0.114908	−	0.353650i	−0.00538696	−	0.0165794i
$456$		0			0
$457$	14.3086	−	19.6941i	0.669330	−	0.921253i	−0.330415	−	0.943836i	$-0.607189\pi$
$457$	14.3086	−	19.6941i	0.669330	−	0.921253i	0.999745	+	0.0225822i	$0.00718876\pi$
$458$		0			0
$459$	4.68739	−	14.4263i	0.218789	−	0.673362i
$460$		0			0
$461$	−2.75637	+	8.48323i	−0.128377	+	0.395103i	−0.994501	−	0.104725i	$-0.966604\pi$
$461$	−2.75637	+	8.48323i	−0.128377	+	0.395103i	0.866124	+	0.499829i	$0.166604\pi$
$462$		0			0
$463$	−9.07556	+	2.94883i	−0.421777	+	0.137044i	−0.512213	−	0.858859i	$-0.671174\pi$
$463$	−9.07556	+	2.94883i	−0.421777	+	0.137044i	0.0904356	+	0.995902i	$0.471174\pi$
$464$		0			0
$465$			2.76974i			0.128444i
$466$		0			0
$467$	30.4857	−	22.1491i	1.41071	−	1.02494i	0.417490	−	0.908682i	$-0.362910\pi$
$467$	30.4857	−	22.1491i	1.41071	−	1.02494i	0.993219	−	0.116258i	$-0.0370900\pi$
$468$		0			0
$469$	6.31164	+	4.58567i	0.291444	+	0.211747i
$470$		0			0
$471$	15.4434	−	11.2203i	0.711597	−	0.517005i
$472$		0			0
$473$	−19.4053	−	26.7090i	−0.892255	−	1.22808i
$474$		0			0
$475$	4.54053	+	1.47531i	0.208334	+	0.0676918i
$476$		0			0
$477$	6.42955	−	2.08909i	0.294389	−	0.0956527i
$478$		0			0
$479$	19.6091	−	26.9896i	0.895962	−	1.23319i	−0.0757763	−	0.997125i	$-0.524144\pi$
$479$	19.6091	−	26.9896i	0.895962	−	1.23319i	0.971738	−	0.236061i	$-0.0758565\pi$
$480$		0			0
$481$	4.31162	+	1.40093i	0.196593	+	0.0638769i
$482$		0			0
$483$	2.90571			0.132214
$484$		0			0
$485$	1.34871	+	1.85634i	0.0612417	+	0.0842920i
$486$		0			0
$487$	1.82102	+	5.60453i	0.0825184	+	0.253965i	0.983800	−	0.179267i	$-0.0573727\pi$
$487$	1.82102	+	5.60453i	0.0825184	+	0.253965i	−0.901282	+	0.433233i	$0.857373\pi$
$488$		0			0
$489$		−	8.74495i		−	0.395460i
$490$		0			0
$491$	−6.77176			−0.305605			−0.152803	−	0.988257i	$-0.548830\pi$
$491$	−6.77176			−0.305605			−0.152803	+	0.988257i	$0.548830\pi$
$492$		0			0
$493$	−4.87014			−0.219340
$494$		0			0
$495$			3.20971i			0.144266i
$496$		0			0
$497$	−2.76616	−	8.51336i	−0.124079	−	0.381877i
$498$		0			0
$499$	−5.37442	−	7.39726i	−0.240592	−	0.331147i	0.671597	−	0.740917i	$-0.265609\pi$
$499$	−5.37442	−	7.39726i	−0.240592	−	0.331147i	−0.912189	+	0.409770i	$0.865609\pi$
$500$		0			0
$501$	−14.0306			−0.626842
$502$		0			0
$503$	6.73154	+	2.18721i	0.300145	+	0.0975229i	0.455218	−	0.890380i	$-0.349561\pi$
$503$	6.73154	+	2.18721i	0.300145	+	0.0975229i	−0.155073	+	0.987903i	$0.549561\pi$
$504$		0			0
$505$	−3.10999	+	4.28053i	−0.138393	+	0.190481i
$506$		0			0
$507$	24.8702	−	8.08082i	1.10453	−	0.358882i
$508$		0			0
$509$	28.7873	+	9.35357i	1.27598	+	0.414590i	0.867161	−	0.498028i	$-0.165942\pi$
$509$	28.7873	+	9.35357i	1.27598	+	0.414590i	0.408815	+	0.912617i	$0.365942\pi$
$510$		0			0
$511$	−7.03685	−	9.68539i	−0.311292	−	0.428456i
$512$		0			0
$513$	2.79170	−	2.02829i	0.123257	−	0.0895513i
$514$		0			0
$515$	−1.72701	−	1.25475i	−0.0761012	−	0.0552907i
$516$		0			0
$517$	26.5400	−	19.2825i	1.16723	−	0.848042i
$518$		0			0
$519$		−	4.57926i		−	0.201007i
$520$		0			0
$521$	0.387709	−	0.125974i	0.0169858	−	0.00551903i	−0.300512	−	0.953778i	$-0.597157\pi$
$521$	0.387709	−	0.125974i	0.0169858	−	0.00551903i	0.317498	+	0.948259i	$0.397157\pi$
$522$		0			0
$523$	−6.29917	+	19.3868i	−0.275443	+	0.847727i	0.713659	+	0.700494i	$0.247037\pi$
$523$	−6.29917	+	19.3868i	−0.275443	+	0.847727i	−0.989102	+	0.147233i	$0.952963\pi$
$524$		0			0
$525$	3.04682	−	9.37713i	0.132974	−	0.409252i
$526$		0			0
$527$	6.51618	−	8.96876i	0.283849	−	0.390685i
$528$		0			0
$529$	−6.51018	−	20.0363i	−0.283051	−	0.871142i
$530$		0			0
$531$	−1.62872	−	1.18334i	−0.0706806	−	0.0513525i
$532$		0			0
$533$	−1.52500	+	4.20964i	−0.0660551	+	0.182340i
$534$		0			0
$535$	−2.92721	−	2.12674i	−0.126554	−	0.0919470i
$536$		0			0
$537$	−9.25720	−	28.4907i	−0.399478	−	1.22947i
$538$		0			0
$539$	−2.59190	+	3.56744i	−0.111641	+	0.153661i
$540$		0			0
$541$	0.447995	−	1.37879i	0.0192608	−	0.0592786i	−0.940964	−	0.338506i	$-0.890078\pi$
$541$	0.447995	−	1.37879i	0.0192608	−	0.0592786i	0.960225	+	0.279228i	$0.0900784\pi$
$542$		0			0
$543$	6.18605	−	19.0387i	0.265469	−	0.817029i
$544$		0			0
$545$	7.07767	−	2.29968i	0.303174	−	0.0985073i
$546$		0			0
$547$			0.0935609i			0.00400037i	0.999998	+	0.00200019i	$0.000636680\pi$
$547$			0.0935609i			0.00400037i	−0.999998	+	0.00200019i	$0.999363\pi$
$548$		0			0
$549$	−5.43452	+	3.94841i	−0.231940	+	0.168514i
$550$		0			0
$551$	−0.896318	−	0.651213i	−0.0381844	−	0.0277426i
$552$		0			0
$553$	−6.19936	+	4.50410i	−0.263624	+	0.191534i
$554$		0			0
$555$	−4.23586	−	5.83016i	−0.179802	−	0.247476i
$556$		0			0
$557$	1.07533	+	0.349397i	0.0455634	+	0.0148044i	0.331710	−	0.943381i	$-0.392374\pi$
$557$	1.07533	+	0.349397i	0.0455634	+	0.0148044i	−0.286147	+	0.958186i	$0.592374\pi$
$558$		0			0
$559$	−4.97894	+	1.61776i	−0.210587	+	0.0684238i
$560$		0			0
$561$	24.1018	−	33.1733i	1.01758	−	1.40058i
$562$		0			0
$563$	−22.0557	−	7.16634i	−0.929537	−	0.302025i	−0.195164	−	0.980771i	$-0.562524\pi$
$563$	−22.0557	−	7.16634i	−0.929537	−	0.302025i	−0.734373	+	0.678746i	$0.762524\pi$
$564$		0			0
$565$	1.77592			0.0747137
$566$		0			0
$567$	−6.60246	−	9.08751i	−0.277277	−	0.381639i
$568$		0			0
$569$	−4.32450	−	13.3094i	−0.181293	−	0.557961i	0.818572	−	0.574404i	$-0.194766\pi$
$569$	−4.32450	−	13.3094i	−0.181293	−	0.557961i	−0.999865	+	0.0164425i	$0.994766\pi$
$570$		0			0
$571$			14.7350i			0.616642i	0.951282	+	0.308321i	$0.0997671\pi$
$571$			14.7350i			0.616642i	−0.951282	+	0.308321i	$0.900233\pi$
$572$		0			0
$573$	16.7035			0.697797
$574$		0			0
$575$	6.55778			0.273479
$576$		0			0
$577$			15.1732i			0.631669i	0.948814	+	0.315834i	$0.102284\pi$
$577$			15.1732i			0.631669i	−0.948814	+	0.315834i	$0.897716\pi$
$578$		0			0
$579$	11.0339	+	33.9590i	0.458555	+	1.41129i
$580$		0			0
$581$	7.23054	+	9.95198i	0.299973	+	0.412878i
$582$		0			0
$583$	−21.7793			−0.902008
$584$		0			0
$585$	0.484063	+	0.157282i	0.0200136	+	0.00650280i
$586$		0			0
$587$	6.22978	−	8.57456i	0.257131	−	0.353910i	−0.660862	−	0.750507i	$-0.729809\pi$
$587$	6.22978	−	8.57456i	0.257131	−	0.353910i	0.917993	+	0.396597i	$0.129809\pi$
$588$		0			0
$589$	2.39852	−	0.779327i	0.0988294	−	0.0321116i
$590$		0			0
$591$	34.0437	+	11.0615i	1.40037	+	0.455009i
$592$		0			0
$593$	20.9159	+	28.7883i	0.858915	+	1.18219i	0.981827	+	0.189777i	$0.0607765\pi$
$593$	20.9159	+	28.7883i	0.858915	+	1.18219i	−0.122913	+	0.992418i	$0.539223\pi$
$594$		0			0
$595$	1.91403	−	1.39062i	0.0784676	−	0.0570100i
$596$		0			0
$597$	29.7447	+	21.6108i	1.21737	+	0.884472i
$598$		0			0
$599$	13.7616	−	9.99837i	0.562282	−	0.408522i	−0.270011	−	0.962857i	$-0.587027\pi$
$599$	13.7616	−	9.99837i	0.562282	−	0.408522i	0.832294	+	0.554335i	$0.187027\pi$
$600$		0			0
$601$			32.9144i			1.34261i	0.741182	+	0.671304i	$0.234265\pi$
$601$			32.9144i			1.34261i	−0.741182	+	0.671304i	$0.765735\pi$
$602$		0			0
$603$	−10.1559	+	3.29986i	−0.413581	+	0.134381i
$604$		0			0
$605$	1.38771	−	4.27093i	0.0564183	−	0.173638i
$606$		0			0
$607$	−6.99221	+	21.5198i	−0.283805	+	0.873462i	0.702949	+	0.711240i	$0.251866\pi$
$607$	−6.99221	+	21.5198i	−0.283805	+	0.873462i	−0.986754	+	0.162222i	$0.948134\pi$
$608$		0			0
$609$	−1.34489	+	1.85108i	−0.0544977	+	0.0750096i
$610$		0			0
$611$	−1.60752	−	4.94743i	−0.0650332	−	0.200152i
$612$		0			0
$613$	33.3841	+	24.2549i	1.34837	+	0.979648i	0.999091	+	0.0426293i	$0.0135734\pi$
$613$	33.3841	+	24.2549i	1.34837	+	0.979648i	0.349279	+	0.937019i	$0.386427\pi$
$614$		0			0
$615$	5.89443	−	3.98878i	0.237686	−	0.160843i
$616$		0			0
$617$	−14.2542	−	10.3563i	−0.573853	−	0.416928i	0.262650	−	0.964891i	$-0.415404\pi$
$617$	−14.2542	−	10.3563i	−0.573853	−	0.416928i	−0.836503	+	0.547963i	$0.815404\pi$
$618$		0			0
$619$	−6.76569	−	20.8227i	−0.271936	−	0.836933i	−0.990014	−	0.140970i	$-0.954978\pi$
$619$	−6.76569	−	20.8227i	−0.271936	−	0.836933i	0.718078	−	0.695963i	$-0.245022\pi$
$620$		0			0
$621$	2.78604	−	3.83466i	0.111800	−	0.153879i
$622$		0			0
$623$	3.17146	−	9.76076i	0.127062	−	0.391057i
$624$		0			0
$625$	6.43930	−	19.8181i	0.257572	−	0.792725i
$626$		0			0
$627$	8.87157	−	2.88255i	0.354296	−	0.115118i
$628$		0			0
$629$			28.8441i			1.15009i
$630$		0			0
$631$	−20.4817	+	14.8809i	−0.815365	+	0.592397i	−0.915381	−	0.402588i	$-0.868111\pi$
$631$	−20.4817	+	14.8809i	−0.815365	+	0.592397i	0.100016	+	0.994986i	$0.468111\pi$
$632$		0			0
$633$	20.9590	+	15.2276i	0.833044	+	0.605242i
$634$		0			0
$635$	0.219322	−	0.159347i	0.00870353	−	0.00632348i
$636$		0			0
$637$	0.411006	+	0.565701i	0.0162846	+	0.0224139i
$638$		0			0
$639$	11.6528	+	3.78622i	0.460977	+	0.149781i
$640$		0			0
$641$	0.770926	−	0.250489i	0.0304497	−	0.00989372i	−0.293753	−	0.955882i	$-0.594904\pi$
$641$	0.770926	−	0.250489i	0.0304497	−	0.00989372i	0.324202	+	0.945988i	$0.394904\pi$
$642$		0			0
$643$	21.1758	−	29.1460i	0.835093	−	1.14941i	−0.151861	−	0.988402i	$-0.548527\pi$
$643$	21.1758	−	29.1460i	0.835093	−	1.14941i	0.986954	−	0.161005i	$-0.0514734\pi$
$644$		0			0
$645$	7.91454	+	2.57159i	0.311635	+	0.101256i
$646$		0			0
$647$	−19.6981			−0.774411			−0.387206	−	0.921993i	$-0.626560\pi$
$647$	−19.6981			−0.774411			−0.387206	+	0.921993i	$0.626560\pi$
$648$		0			0
$649$	3.81223	+	5.24709i	0.149643	+	0.205966i
$650$		0			0
$651$	−1.60947	−	4.95345i	−0.0630802	−	0.194141i
$652$		0			0
$653$		−	40.1395i		−	1.57078i	−0.619001	−	0.785390i	$-0.712462\pi$
$653$		−	40.1395i		−	1.57078i	0.619001	−	0.785390i	$-0.287538\pi$
$654$		0			0
$655$	−9.07941			−0.354762
$656$		0			0
$657$	16.3866			0.639301
$658$		0			0
$659$			15.0449i			0.586067i	0.956102	+	0.293033i	$0.0946647\pi$
$659$			15.0449i			0.586067i	−0.956102	+	0.293033i	$0.905335\pi$
$660$		0			0
$661$	−11.2617	−	34.6601i	−0.438031	−	1.34812i	−0.889948	−	0.456061i	$-0.849260\pi$
$661$	−11.2617	−	34.6601i	−0.438031	−	1.34812i	0.451917	−	0.892060i	$-0.350740\pi$
$662$		0			0
$663$	−3.82190	−	5.26040i	−0.148430	−	0.204297i
$664$		0			0
$665$	0.538213			0.0208710
$666$		0			0
$667$	−1.44733	−	0.470266i	−0.0560409	−	0.0182088i
$668$		0			0
$669$	4.69905	−	6.46769i	0.181676	−	0.250055i
$670$		0			0
$671$	20.5817	−	6.68739i	0.794546	−	0.258164i
$672$		0			0
$673$	12.5685	+	4.08377i	0.484482	+	0.157418i	0.541066	−	0.840980i	$-0.318021\pi$
$673$	12.5685	+	4.08377i	0.484482	+	0.157418i	−0.0565843	+	0.998398i	$0.518021\pi$
$674$		0			0
$675$	−9.45364	−	13.0118i	−0.363871	−	0.500825i
$676$		0			0
$677$	−31.8299	+	23.1257i	−1.22332	+	0.888795i	−0.996371	−	0.0851119i	$-0.972875\pi$
$677$	−31.8299	+	23.1257i	−1.22332	+	0.888795i	−0.226949	+	0.973907i	$0.572875\pi$
$678$		0			0
$679$	−3.49075	−	2.53618i	−0.133963	−	0.0973296i
$680$		0			0
$681$	28.3757	−	20.6162i	1.08736	−	0.790014i
$682$		0			0
$683$			2.45943i			0.0941076i	0.998892	+	0.0470538i	$0.0149832\pi$
$683$			2.45943i			0.0941076i	−0.998892	+	0.0470538i	$0.985017\pi$
$684$		0			0
$685$	1.62551	−	0.528161i	0.0621076	−	0.0201800i
$686$		0			0
$687$	−14.7539	+	45.4077i	−0.562895	+	1.73241i
$688$		0			0
$689$	−1.06723	+	3.28459i	−0.0406581	+	0.125133i
$690$		0			0
$691$	2.64271	−	3.63737i	0.100533	−	0.138372i	−0.755787	−	0.654818i	$-0.772745\pi$
$691$	2.64271	−	3.63737i	0.100533	−	0.138372i	0.856320	+	0.516446i	$0.172745\pi$
$692$		0			0
$693$	−1.86513	−	5.74029i	−0.0708506	−	0.218056i
$694$		0			0
$695$	−4.90398	−	3.56295i	−0.186019	−	0.135150i
$696$		0			0
$697$	−28.4710	−	0.951269i	−1.07842	−	0.0360319i
$698$		0			0
$699$	−34.2410	−	24.8776i	−1.29511	−	0.940956i
$700$		0			0
$701$	−6.52158	−	20.0714i	−0.246317	−	0.758085i	−0.995417	−	0.0956285i	$-0.969514\pi$
$701$	−6.52158	−	20.0714i	−0.246317	−	0.758085i	0.749100	−	0.662457i	$-0.230486\pi$
$702$		0			0
$703$	−3.85691	+	5.30858i	−0.145466	+	0.200217i
$704$		0			0
$705$	−2.55532	+	7.86445i	−0.0962388	+	0.296192i
$706$		0			0
$707$	3.07457	−	9.46255i	0.115631	−	0.355876i
$708$		0			0
$709$	36.0307	−	11.7071i	1.35316	−	0.439669i	0.459407	−	0.888226i	$-0.348062\pi$
$709$	36.0307	−	11.7071i	1.35316	−	0.439669i	0.893754	+	0.448557i	$0.148062\pi$
$710$		0			0
$711$		−	10.4886i		−	0.393353i
$712$		0			0
$713$	2.80254	−	2.03617i	0.104956	−	0.0762550i
$714$		0			0
$715$	−1.32655	−	0.963796i	−0.0496102	−	0.0360439i
$716$		0			0
$717$	−39.3675	+	28.6022i	−1.47021	+	1.06817i
$718$		0			0
$719$	−15.0307	−	20.6880i	−0.560551	−	0.771532i	0.430846	−	0.902426i	$-0.358215\pi$
$719$	−15.0307	−	20.6880i	−0.560551	−	0.771532i	−0.991396	+	0.130894i	$0.958215\pi$
$720$		0			0
$721$	3.81773	+	1.24046i	0.142180	+	0.0461970i
$722$		0			0
$723$	22.1572	−	7.19930i	0.824034	−	0.267745i
$724$		0			0
$725$	−3.03523	+	4.17764i	−0.112726	+	0.155154i
$726$		0			0
$727$	16.5801	+	5.38722i	0.614924	+	0.199801i	0.599885	−	0.800086i	$-0.295213\pi$
$727$	16.5801	+	5.38722i	0.614924	+	0.199801i	0.0150385	+	0.999887i	$0.495213\pi$
$728$		0			0
$729$	−6.00444			−0.222387
$730$		0			0
$731$	−19.5782	−	26.9471i	−0.724126	−	0.996674i
$732$		0			0
$733$	6.33860	+	19.5082i	0.234122	+	0.720552i	0.997237	+	0.0742897i	$0.0236690\pi$
$733$	6.33860	+	19.5082i	0.234122	+	0.720552i	−0.763115	+	0.646263i	$0.776331\pi$
$734$		0			0
$735$		−	1.11152i		−	0.0409991i
$736$		0			0
$737$	34.4020			1.26721
$738$		0			0
$739$	−49.3409			−1.81504			−0.907518	−	0.420014i	$-0.862025\pi$
$739$	−49.3409			−1.81504			−0.907518	+	0.420014i	$0.862025\pi$
$740$		0			0
$741$		−	1.47919i		−	0.0543394i
$742$		0			0
$743$	−3.63097	−	11.1750i	−0.133207	−	0.409970i	0.862099	−	0.506739i	$-0.169149\pi$
$743$	−3.63097	−	11.1750i	−0.133207	−	0.409970i	−0.995307	+	0.0967688i	$0.969149\pi$
$744$		0			0
$745$	−3.94298	−	5.42705i	−0.144460	−	0.198832i
$746$		0			0
$747$	−16.8376			−0.616056
$748$		0			0
$749$	6.47088	+	2.10252i	0.236441	+	0.0768243i
$750$		0			0
$751$	9.60141	−	13.2152i	0.350361	−	0.482230i	−0.597071	−	0.802188i	$-0.703669\pi$
$751$	9.60141	−	13.2152i	0.350361	−	0.482230i	0.947432	+	0.319958i	$0.103669\pi$
$752$		0			0
$753$	18.9238	−	6.14872i	0.689623	−	0.224072i
$754$		0			0
$755$	8.38020	+	2.72289i	0.304987	+	0.0990961i
$756$		0			0
$757$	26.4147	+	36.3567i	0.960058	+	1.32141i	0.946912	+	0.321493i	$0.104185\pi$
$757$	26.4147	+	36.3567i	0.960058	+	1.32141i	0.0131457	+	0.999914i	$0.495815\pi$
$758$		0			0
$759$	10.3659	−	7.53130i	0.376260	−	0.273369i
$760$		0			0
$761$	−21.5650	−	15.6679i	−0.781732	−	0.567961i	0.123767	−	0.992311i	$-0.460503\pi$
$761$	−21.5650	−	15.6679i	−0.781732	−	0.567961i	−0.905498	+	0.424350i	$0.860503\pi$
$762$		0			0
$763$	−11.3215	+	8.22554i	−0.409865	+	0.297785i
$764$		0			0
$765$			3.23832i			0.117082i
$766$		0			0
$767$	0.978130	−	0.317814i	0.0353182	−	0.0114756i
$768$		0			0
$769$	−11.1258	+	34.2418i	−0.401208	+	1.23479i	0.522812	+	0.852448i	$0.324883\pi$
$769$	−11.1258	+	34.2418i	−0.401208	+	1.23479i	−0.924020	+	0.382344i	$0.875117\pi$
$770$		0			0
$771$	10.6897	−	32.8996i	0.384981	−	1.18485i
$772$		0			0
$773$	20.4452	−	28.1405i	0.735364	−	1.01214i	−0.263508	−	0.964657i	$-0.584879\pi$
$773$	20.4452	−	28.1405i	0.735364	−	1.01214i	0.998872	−	0.0474849i	$-0.0151206\pi$
$774$		0			0
$775$	−3.63236	−	11.1792i	−0.130478	−	0.401570i
$776$		0			0
$777$	10.9633	+	7.96531i	0.393307	+	0.285754i
$778$		0			0
$779$	−5.11270	−	3.98209i	−0.183182	−	0.142673i
$780$		0			0
$781$	−31.9339	−	23.2013i	−1.14268	−	0.830208i
$782$		0			0
$783$	1.15337	+	3.54970i	0.0412179	+	0.126856i
$784$		0			0
$785$	2.85473	−	3.92919i	0.101890	−	0.140239i
$786$		0			0
$787$	−0.116039	+	0.357133i	−0.00413636	+	0.0127304i	−0.953103	−	0.302645i	$-0.902130\pi$
$787$	−0.116039	+	0.357133i	−0.00413636	+	0.0127304i	0.948967	+	0.315375i	$0.102130\pi$
$788$		0			0
$789$	2.71476	−	8.35517i	0.0966480	−	0.297452i
$790$		0			0
$791$	−3.17609	+	1.03197i	−0.112929	+	0.0366927i
$792$		0			0
$793$		−	3.43166i		−	0.121862i
$794$		0			0
$795$	4.44141	−	3.22687i	0.157521	−	0.114445i
$796$		0			0
$797$	1.10487	+	0.802735i	0.0391365	+	0.0284343i	0.607182	−	0.794563i	$-0.292300\pi$
$797$	1.10487	+	0.802735i	0.0391365	+	0.0284343i	−0.568045	+	0.822997i	$0.692300\pi$
$798$		0			0
$799$	26.7766	−	19.4543i	0.947287	−	0.688244i
$800$		0			0
$801$	8.25704	+	11.3648i	0.291748	+	0.401557i
$802$		0			0
$803$	−50.2071	−	16.3133i	−1.77177	−	0.575683i
$804$		0			0
$805$	0.703101	−	0.228451i	0.0247810	−	0.00805185i
$806$		0			0
$807$	−10.8756	+	14.9689i	−0.382838	+	0.526931i
$808$		0			0
$809$	0.348652	+	0.113284i	0.0122580	+	0.00398285i	0.315140	−	0.949045i	$-0.397949\pi$
$809$	0.348652	+	0.113284i	0.0122580	+	0.00398285i	−0.302882	+	0.953028i	$0.597949\pi$
$810$		0			0
$811$	−25.9279			−0.910451			−0.455226	−	0.890376i	$-0.650441\pi$
$811$	−25.9279			−0.910451			−0.455226	+	0.890376i	$0.650441\pi$
$812$		0			0
$813$	17.9733	+	24.7382i	0.630352	+	0.867605i
$814$		0			0
$815$	−0.687541	−	2.11603i	−0.0240835	−	0.0741214i
$816$		0			0
$817$		−	7.57735i		−	0.265098i
$818$		0			0
$819$	−0.957101			−0.0334438
$820$		0			0
$821$	−39.4843			−1.37801			−0.689006	−	0.724756i	$-0.741953\pi$
$821$	−39.4843			−1.37801			−0.689006	+	0.724756i	$0.741953\pi$
$822$		0			0
$823$		−	9.22379i		−	0.321521i	−0.986993	−	0.160761i	$-0.948605\pi$
$823$		−	9.22379i		−	0.321521i	0.986993	−	0.160761i	$-0.0513947\pi$
$824$		0			0
$825$	−13.4352	−	41.3494i	−0.467755	−	1.43960i
$826$		0			0
$827$	1.99769	+	2.74959i	0.0694665	+	0.0956125i	0.842337	−	0.538952i	$-0.181180\pi$
$827$	1.99769	+	2.74959i	0.0694665	+	0.0956125i	−0.772870	+	0.634564i	$0.781180\pi$
$828$		0			0
$829$	−27.8880			−0.968590			−0.484295	−	0.874905i	$-0.660924\pi$
$829$	−27.8880			−0.968590			−0.484295	+	0.874905i	$0.660924\pi$
$830$		0			0
$831$	55.2527	+	17.9527i	1.91670	+	0.622772i
$832$		0			0
$833$	−2.61500	+	3.59924i	−0.0906043	+	0.124706i
$834$		0			0
$835$	−3.39502	+	1.10311i	−0.117490	+	0.0381747i
$836$		0			0
$837$	−8.08024	−	2.62543i	−0.279294	−	0.0907481i
$838$		0			0
$839$	−15.3297	−	21.0995i	−0.529240	−	0.728437i	0.457774	−	0.889068i	$-0.348647\pi$
$839$	−15.3297	−	21.0995i	−0.529240	−	0.728437i	−0.987014	+	0.160632i	$0.948647\pi$
$840$		0			0
$841$	−22.4920	+	16.3414i	−0.775587	+	0.563497i
$842$		0			0
$843$	5.16395	+	3.75183i	0.177856	+	0.129220i
$844$		0			0
$845$	5.38257	−	3.91067i	0.185166	−	0.134531i
$846$		0			0
$847$			8.44456i			0.290159i
$848$		0			0
$849$	−25.2037	+	8.18919i	−0.864990	+	0.281052i
$850$		0			0
$851$	−2.78522	+	8.57204i	−0.0954762	+	0.293846i
$852$		0			0
$853$	−16.7248	+	51.4737i	−0.572647	+	1.76243i	0.0714076	+	0.997447i	$0.477251\pi$
$853$	−16.7248	+	51.4737i	−0.572647	+	1.76243i	−0.644055	+	0.764979i	$0.722749\pi$
$854$		0			0
$855$	−0.433013	+	0.595992i	−0.0148087	+	0.0203825i
$856$		0			0
$857$	−0.497904	−	1.53239i	−0.0170081	−	0.0523455i	0.942192	−	0.335073i	$-0.108761\pi$
$857$	−0.497904	−	1.53239i	−0.0170081	−	0.0523455i	−0.959200	+	0.282727i	$0.908761\pi$
$858$		0			0
$859$	14.8193	+	10.7668i	0.505627	+	0.367360i	0.811162	−	0.584821i	$-0.198835\pi$
$859$	14.8193	+	10.7668i	0.505627	+	0.367360i	−0.305535	+	0.952181i	$0.598835\pi$
$860$		0			0
$861$	−8.22383	+	10.5588i	−0.280267	+	0.359842i
$862$		0			0
$863$	−43.5242	−	31.6222i	−1.48158	−	1.07643i	−0.977043	−	0.213043i	$-0.931663\pi$
$863$	−43.5242	−	31.6222i	−1.48158	−	1.07643i	−0.504539	−	0.863389i	$-0.668337\pi$
$864$		0			0
$865$	−0.360029	−	1.10805i	−0.0122413	−	0.0376750i
$866$		0			0
$867$	3.43103	−	4.72241i	0.116524	−	0.160382i
$868$		0			0
$869$	−10.4417	+	32.1362i	−0.354210	+	1.09015i
$870$		0			0
$871$	1.68576	−	5.18824i	0.0571198	−	0.175797i
$872$		0			0
$873$	5.61689	−	1.82504i	0.190103	−	0.0617682i
$874$		0			0
$875$		−	5.16749i		−	0.174693i
$876$		0			0
$877$	−22.8489	+	16.6007i	−0.771554	+	0.560566i	−0.902432	−	0.430832i	$-0.858220\pi$
$877$	−22.8489	+	16.6007i	−0.771554	+	0.560566i	0.130879	+	0.991398i	$0.458220\pi$
$878$		0			0
$879$	32.9996	+	23.9756i	1.11305	+	0.808677i
$880$		0			0
$881$	14.2632	−	10.3629i	0.480541	−	0.349133i	−0.320994	−	0.947081i	$-0.604017\pi$
$881$	14.2632	−	10.3629i	0.480541	−	0.349133i	0.801535	+	0.597948i	$0.204017\pi$
$882$		0			0
$883$	−25.5982	−	35.2328i	−0.861447	−	1.18568i	−0.981223	−	0.192879i	$-0.938218\pi$
$883$	−25.5982	−	35.2328i	−0.861447	−	1.18568i	0.119776	−	0.992801i	$-0.461782\pi$
$884$		0			0
$885$	−1.55484	−	0.505198i	−0.0522653	−	0.0169820i
$886$		0			0
$887$	−19.1660	+	6.22741i	−0.643531	+	0.209096i	−0.612560	−	0.790424i	$-0.709860\pi$
$887$	−19.1660	+	6.22741i	−0.643531	+	0.209096i	−0.0309715	+	0.999520i	$0.509860\pi$
$888$		0			0
$889$	−0.299644	+	0.412424i	−0.0100497	+	0.0138323i
$890$		0			0
$891$	−47.1078	−	15.3062i	−1.57817	−	0.512778i
$892$		0			0
$893$	7.52940			0.251962
$894$		0			0
$895$	−4.47997	−	6.16615i	−0.149749	−	0.206112i
$896$		0			0
$897$	−0.627861	−	1.93236i	−0.0209637	−	0.0645195i
$898$		0			0
$899$			2.72779i			0.0909768i
$900$		0			0
$901$	−21.9735			−0.732042
$902$		0			0
$903$	−15.6488			−0.520759
$904$		0			0
$905$		−	5.09319i		−	0.169304i
$906$		0			0
$907$	5.04884	+	15.5387i	0.167644	+	0.515955i	0.999221	−	0.0394536i	$-0.0125617\pi$
$907$	5.04884	+	15.5387i	0.167644	+	0.515955i	−0.831577	+	0.555409i	$0.812562\pi$
$908$		0			0
$909$	8.00477	+	11.0176i	0.265502	+	0.365432i
$910$		0			0
$911$	0.269773			0.00893799			0.00446900	−	0.999990i	$-0.498577\pi$
$911$	0.269773			0.00893799			0.00446900	+	0.999990i	$0.498577\pi$
$912$		0			0
$913$	51.5890	+	16.7623i	1.70735	+	0.554751i
$914$		0			0
$915$	−3.20635	+	4.41317i	−0.105999	+	0.145895i
$916$		0			0
$917$	16.2377	−	5.27596i	0.536217	−	0.174228i
$918$		0			0
$919$	26.2256	+	8.52123i	0.865104	+	0.281089i	0.707759	−	0.706454i	$-0.249706\pi$
$919$	26.2256	+	8.52123i	0.865104	+	0.281089i	0.157345	+	0.987544i	$0.449706\pi$
$920$		0			0
$921$	−28.6149	−	39.3851i	−0.942894	−	1.29778i
$922$		0			0
$923$	−5.06386	+	3.67911i	−0.166679	+	0.121099i
$924$		0			0
$925$	24.7427	+	17.9766i	0.813535	+	0.591068i
$926$		0			0
$927$	−4.44514	+	3.22958i	−0.145997	+	0.106073i
$928$		0			0
$929$			32.3452i			1.06121i	0.847619	+	0.530606i	$0.178036\pi$
$929$			32.3452i			1.06121i	−0.847619	+	0.530606i	$0.821964\pi$
$930$		0			0
$931$	−0.962547	+	0.312751i	−0.0315462	+	0.0102500i
$932$		0			0
$933$	−16.8966	+	52.0023i	−0.553169	+	1.70248i
$934$		0			0
$935$	3.22383	−	9.92194i	0.105431	−	0.324482i
$936$		0			0
$937$	−1.91693	+	2.63843i	−0.0626234	+	0.0861938i	−0.839180	−	0.543854i	$-0.816965\pi$
$937$	−1.91693	+	2.63843i	−0.0626234	+	0.0861938i	0.776557	+	0.630048i	$0.216965\pi$
$938$		0			0
$939$	−0.832700	−	2.56279i	−0.0271741	−	0.0836334i
$940$		0			0
$941$	22.6916	+	16.4864i	0.739724	+	0.537441i	0.892625	−	0.450801i	$-0.148861\pi$
$941$	22.6916	+	16.4864i	0.739724	+	0.537441i	−0.152901	+	0.988242i	$0.548861\pi$
$942$		0			0
$943$	−8.36928	−	3.03189i	−0.272541	−	0.0987320i
$944$		0			0
$945$	−1.46687	−	1.06574i	−0.0477173	−	0.0346687i
$946$		0			0
$947$	15.3784	+	47.3297i	0.499730	+	1.53801i	0.809454	+	0.587183i	$0.199763\pi$
$947$	15.3784	+	47.3297i	0.499730	+	1.53801i	−0.309725	+	0.950826i	$0.600237\pi$
$948$		0			0
$949$	−4.92048	+	6.77245i	−0.159725	+	0.219843i
$950$		0			0
$951$	−13.6672	+	42.0634i	−0.443191	+	1.36400i
$952$		0			0
$953$	3.88774	−	11.9652i	0.125936	−	0.387592i	−0.868134	−	0.496329i	$-0.834681\pi$
$953$	3.88774	−	11.9652i	0.125936	−	0.387592i	0.994070	+	0.108738i	$0.0346809\pi$
$954$		0			0
$955$	4.04177	−	1.31325i	0.130789	−	0.0424958i
$956$		0			0
$957$			10.0894i			0.326145i
$958$		0			0
$959$	−2.60018	+	1.88914i	−0.0839641	+	0.0610035i
$960$		0			0
$961$	20.0561	+	14.5716i	0.646971	+	0.470052i
$962$		0			0
$963$	−7.53431	+	5.47399i	−0.242790	+	0.176397i
$964$		0			0
$965$	5.33982	+	7.34963i	0.171895	+	0.236593i
$966$		0			0
$967$	−16.6049	−	5.39526i	−0.533978	−	0.173500i	0.0296015	−	0.999562i	$-0.490576\pi$
$967$	−16.6049	−	5.39526i	−0.533978	−	0.173500i	−0.563580	+	0.826062i	$0.690576\pi$
$968$		0			0
$969$	8.95064	−	2.90824i	0.287536	−	0.0934261i
$970$		0			0
$971$	1.24947	−	1.71975i	0.0400974	−	0.0551893i	−0.788498	−	0.615038i	$-0.789141\pi$
$971$	1.24947	−	1.71975i	0.0400974	−	0.0551893i	0.828595	+	0.559849i	$0.189141\pi$
$972$		0			0
$973$	10.8407	+	3.52237i	0.347538	+	0.112922i
$974$		0			0
$975$	−6.89434			−0.220796
$976$		0			0
$977$	1.44770	+	1.99259i	0.0463161	+	0.0637487i	0.831547	−	0.555455i	$-0.187456\pi$
$977$	1.44770	+	1.99259i	0.0463161	+	0.0637487i	−0.785231	+	0.619203i	$0.787456\pi$
$978$		0			0
$979$	−13.9849	−	43.0410i	−0.446959	−	1.37560i
$980$		0			0
$981$		−	19.1547i		−	0.611561i
$982$		0			0
$983$	6.12473			0.195349			0.0976743	−	0.995218i	$-0.468860\pi$
$983$	6.12473			0.195349			0.0976743	+	0.995218i	$0.468860\pi$
$984$		0			0
$985$	9.10731			0.290183
$986$		0			0
$987$		−	15.5498i		−	0.494955i
$988$		0			0
$989$	−3.21630	−	9.89876i	−0.102272	−	0.314762i
$990$		0			0
$991$	33.8965	+	46.6546i	1.07676	+	1.48203i	0.863040	+	0.505136i	$0.168558\pi$
$991$	33.8965	+	46.6546i	1.07676	+	1.48203i	0.213719	+	0.976895i	$0.431442\pi$
$992$		0			0
$993$	−26.8671			−0.852600
$994$		0			0
$995$	8.89647	+	2.89064i	0.282037	+	0.0916394i
$996$		0			0
$997$	18.2821	−	25.1632i	0.579001	−	0.796926i	−0.414585	−	0.910011i	$-0.636073\pi$
$997$	18.2821	−	25.1632i	0.579001	−	0.796926i	0.993585	+	0.113085i	$0.0360731\pi$
$998$		0			0
$999$	21.0236	−	6.83099i	0.665158	−	0.216123i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.ba.a.113.4	✓	80
41.4	even	10	inner	1148.2.ba.a.701.17	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.ba.a.113.4	✓	80	1.1	even	1	trivial
1148.2.ba.a.701.17	yes	80	41.4	even	10	inner

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-2.09016i q^{3} +(-0.164331 - 0.505760i) q^{5} +(0.587785 + 0.809017i) q^{7} -1.36876 q^{9} +O(q^{10})\)	\(q-2.09016i q^{3} +(-0.164331 - 0.505760i) q^{5} +(0.587785 + 0.809017i) q^{7} -1.36876 q^{9} +(4.19378 + 1.36264i) q^{11} +(0.411006 - 0.565701i) q^{13} +(-1.05712 + 0.343479i) q^{15} +(4.23116 + 1.37479i) q^{17} +(0.594887 + 0.818792i) q^{19} +(1.69097 - 1.22856i) q^{21} +(1.12468 + 0.817130i) q^{23} +(3.81630 - 2.77270i) q^{25} -3.40954i q^{27} +(-1.04111 + 0.338276i) q^{29} +(0.770024 - 2.36989i) q^{31} +(2.84814 - 8.76566i) q^{33} +(0.312577 - 0.430225i) q^{35} +(2.00349 + 6.16611i) q^{37} +(-1.18240 - 0.859067i) q^{39} +(-6.15241 + 1.77421i) q^{41} +(-6.05702 - 4.40069i) q^{43} +(0.224931 + 0.692266i) q^{45} +(4.37284 - 6.01869i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(2.87352 - 8.84379i) q^{51} +(-4.69734 + 1.52626i) q^{53} -2.34497i q^{55} +(1.71140 - 1.24341i) q^{57} +(1.18992 + 0.864530i) q^{59} +(3.97038 - 2.88465i) q^{61} +(-0.804539 - 1.10735i) q^{63} +(-0.353650 - 0.114908i) q^{65} +(7.41978 - 2.41083i) q^{67} +(1.70793 - 2.35077i) q^{69} +(-8.51336 - 2.76616i) q^{71} -11.9718 q^{73} +(-5.79539 - 7.97667i) q^{75} +(1.36264 + 4.19378i) q^{77} +7.66283i q^{79} -11.2328 q^{81} +12.3013 q^{83} -2.36587i q^{85} +(0.707050 + 2.17608i) q^{87} +(-6.03248 - 8.30300i) q^{89} +0.699244 q^{91} +(-4.95345 - 1.60947i) q^{93} +(0.316354 - 0.435423i) q^{95} +(-4.10362 + 1.33335i) q^{97} +(-5.74029 - 1.86513i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) \) 80 * q - 4 * q^5 - 60 * q^9	\( 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) \) 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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