LMFDB - Embedded newform 900.2.k.g.343.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(307,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("900.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.k (of order $4$, 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			343.1
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	900.343
Dual form			900.2.k.g.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.74238 + 1.74238i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.74238 + 1.74238i) q^{7} +2.82843 q^{8} -2.00000i q^{11} +(4.05317 + 4.05317i) q^{13} +(0.901924 - 3.36603i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-4.24264 + 4.24264i) q^{17} -7.19615 q^{19} +(-2.44949 + 1.41421i) q^{22} +(-0.378937 + 0.378937i) q^{23} +(2.09808 - 7.83013i) q^{26} +(-4.76028 + 1.27551i) q^{28} +7.46410i q^{29} +0.267949i q^{31} +(-2.82843 + 4.89898i) q^{32} +(8.19615 + 2.19615i) q^{34} +(2.07055 - 2.07055i) q^{37} +(5.08845 + 8.81345i) q^{38} +5.46410 q^{41} +(-1.74238 + 1.74238i) q^{43} +(3.46410 + 2.00000i) q^{44} +(0.732051 + 0.196152i) q^{46} +(9.14162 + 9.14162i) q^{47} -0.928203i q^{49} +(-11.0735 + 2.96713i) q^{52} +(-1.03528 - 1.03528i) q^{53} +(4.92820 + 4.92820i) q^{56} +(9.14162 - 5.27792i) q^{58} -4.53590 q^{59} +3.00000 q^{61} +(0.328169 - 0.189469i) q^{62} +8.00000 q^{64} +(8.81345 + 8.81345i) q^{67} +(-3.10583 - 11.5911i) q^{68} +9.46410i q^{71} +(-2.82843 - 2.82843i) q^{73} +(-4.00000 - 1.07180i) q^{74} +(7.19615 - 12.4641i) q^{76} +(3.48477 - 3.48477i) q^{77} -0.535898 q^{79} +(-3.86370 - 6.69213i) q^{82} +(-0.656339 + 0.656339i) q^{83} +(3.36603 + 0.901924i) q^{86} -5.65685i q^{88} -6.92820i q^{89} +14.1244i q^{91} +(-0.277401 - 1.03528i) q^{92} +(4.73205 - 17.6603i) q^{94} +(-4.43211 + 4.43211i) q^{97} +(-1.13681 + 0.656339i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4}+O(q^{10}) $ 8 * q - 8 * q^4	$ 8 q - 8 q^{4} + 28 q^{14} - 16 q^{16} - 16 q^{19} - 4 q^{26} + 24 q^{34} + 16 q^{41} - 8 q^{46} - 16 q^{56} - 64 q^{59} + 24 q^{61} + 64 q^{64} - 32 q^{74} + 16 q^{76} - 32 q^{79} + 20 q^{86} + 24 q^{94}+O(q^{100}) $ 8 * q - 8 * q^4 + 28 * q^14 - 16 * q^16 - 16 * q^19 - 4 * q^26 + 24 * q^34 + 16 * q^41 - 8 * q^46 - 16 * q^56 - 64 * q^59 + 24 * q^61 + 64 * q^64 - 32 * q^74 + 16 * q^76 - 32 * q^79 + 20 * q^86 + 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.707107	−	1.22474i	−0.500000	−	0.866025i
$2$	−0.707107	−	1.22474i	−0.500000	−	0.866025i
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.74238	+	1.74238i	0.658559	+	0.658559i	0.955039	−	0.296480i	$-0.0958129\pi$
$7$	1.74238	+	1.74238i	0.658559	+	0.658559i	−0.296480	+	0.955039i	$0.595813\pi$
$8$	2.82843			1.00000
$9$		0			0
$10$		0			0
$11$		−	2.00000i		−	0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$		0			0
$13$	4.05317	+	4.05317i	1.12415	+	1.12415i	0.991111	+	0.133037i	$0.0424728\pi$
$13$	4.05317	+	4.05317i	1.12415	+	1.12415i	0.133037	+	0.991111i	$0.457527\pi$
$14$	0.901924	−	3.36603i	0.241049	−	0.899608i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	−4.24264	+	4.24264i	−1.02899	+	1.02899i	−0.0294245	+	0.999567i	$0.509367\pi$
$17$	−4.24264	+	4.24264i	−1.02899	+	1.02899i	−0.999567	+	0.0294245i	$0.990633\pi$
$18$		0			0
$19$	−7.19615			−1.65091			−0.825455	−	0.564467i	$-0.809082\pi$
$19$	−7.19615			−1.65091			−0.825455	+	0.564467i	$0.809082\pi$
$20$		0			0
$21$		0			0
$22$	−2.44949	+	1.41421i	−0.522233	+	0.301511i
$23$	−0.378937	+	0.378937i	−0.0790139	+	0.0790139i	−0.745509	−	0.666495i	$-0.767794\pi$
$23$	−0.378937	+	0.378937i	−0.0790139	+	0.0790139i	0.666495	+	0.745509i	$0.267794\pi$
$24$		0			0
$25$		0			0
$26$	2.09808	−	7.83013i	0.411467	−	1.53561i
$27$		0			0
$28$	−4.76028	+	1.27551i	−0.899608	+	0.241049i
$29$			7.46410i			1.38605i	0.720914	+	0.693024i	$0.243722\pi$
$29$			7.46410i			1.38605i	−0.720914	+	0.693024i	$0.756278\pi$
$30$		0			0
$31$			0.267949i			0.0481251i	0.999710	+	0.0240625i	$0.00766009\pi$
$31$			0.267949i			0.0481251i	−0.999710	+	0.0240625i	$0.992340\pi$
$32$	−2.82843	+	4.89898i	−0.500000	+	0.866025i
$33$		0			0
$34$	8.19615	+	2.19615i	1.40563	+	0.376637i
$35$		0			0
$36$		0			0
$37$	2.07055	−	2.07055i	0.340397	−	0.340397i	−0.516120	−	0.856516i	$-0.672624\pi$
$37$	2.07055	−	2.07055i	0.340397	−	0.340397i	0.856516	+	0.516120i	$0.172624\pi$
$38$	5.08845	+	8.81345i	0.825455	+	1.42973i
$39$		0			0
$40$		0			0
$41$	5.46410			0.853349			0.426675	−	0.904405i	$-0.359685\pi$
$41$	5.46410			0.853349			0.426675	+	0.904405i	$0.359685\pi$
$42$		0			0
$43$	−1.74238	+	1.74238i	−0.265711	+	0.265711i	−0.827369	−	0.561658i	$-0.810164\pi$
$43$	−1.74238	+	1.74238i	−0.265711	+	0.265711i	0.561658	+	0.827369i	$0.310164\pi$
$44$	3.46410	+	2.00000i	0.522233	+	0.301511i
$45$		0			0
$46$	0.732051	+	0.196152i	0.107935	+	0.0289211i
$47$	9.14162	+	9.14162i	1.33344	+	1.33344i	0.902269	+	0.431173i	$0.141900\pi$
$47$	9.14162	+	9.14162i	1.33344	+	1.33344i	0.431173	+	0.902269i	$0.358100\pi$
$48$		0			0
$49$		−	0.928203i		−	0.132600i
$50$		0			0
$51$		0			0
$52$	−11.0735	+	2.96713i	−1.53561	+	0.411467i
$53$	−1.03528	−	1.03528i	−0.142206	−	0.142206i	0.632420	−	0.774626i	$-0.282062\pi$
$53$	−1.03528	−	1.03528i	−0.142206	−	0.142206i	−0.774626	+	0.632420i	$0.782062\pi$
$54$		0			0
$55$		0			0
$56$	4.92820	+	4.92820i	0.658559	+	0.658559i
$57$		0			0
$58$	9.14162	−	5.27792i	1.20035	−	0.693024i
$59$	−4.53590			−0.590524			−0.295262	−	0.955416i	$-0.595407\pi$
$59$	−4.53590			−0.590524			−0.295262	+	0.955416i	$0.595407\pi$
$60$		0			0
$61$	3.00000			0.384111			0.192055	−	0.981384i	$-0.438485\pi$
$61$	3.00000			0.384111			0.192055	+	0.981384i	$0.438485\pi$
$62$	0.328169	−	0.189469i	0.0416776	−	0.0240625i
$63$		0			0
$64$	8.00000			1.00000
$65$		0			0
$66$		0			0
$67$	8.81345	+	8.81345i	1.07673	+	1.07673i	0.996800	+	0.0799342i	$0.0254710\pi$
$67$	8.81345	+	8.81345i	1.07673	+	1.07673i	0.0799342	+	0.996800i	$0.474529\pi$
$68$	−3.10583	−	11.5911i	−0.376637	−	1.40563i
$69$		0			0
$70$		0			0
$71$			9.46410i			1.12318i	0.827415	+	0.561591i	$0.189811\pi$
$71$			9.46410i			1.12318i	−0.827415	+	0.561591i	$0.810189\pi$
$72$		0			0
$73$	−2.82843	−	2.82843i	−0.331042	−	0.331042i	0.521940	−	0.852982i	$-0.325209\pi$
$73$	−2.82843	−	2.82843i	−0.331042	−	0.331042i	−0.852982	+	0.521940i	$0.825209\pi$
$74$	−4.00000	−	1.07180i	−0.464991	−	0.124594i
$75$		0			0
$76$	7.19615	−	12.4641i	0.825455	−	1.42973i
$77$	3.48477	−	3.48477i	0.397126	−	0.397126i
$78$		0			0
$79$	−0.535898			−0.0602933			−0.0301466	−	0.999545i	$-0.509597\pi$
$79$	−0.535898			−0.0602933			−0.0301466	+	0.999545i	$0.509597\pi$
$80$		0			0
$81$		0			0
$82$	−3.86370	−	6.69213i	−0.426675	−	0.739022i
$83$	−0.656339	+	0.656339i	−0.0720425	+	0.0720425i	−0.742210	−	0.670167i	$-0.766222\pi$
$83$	−0.656339	+	0.656339i	−0.0720425	+	0.0720425i	0.670167	+	0.742210i	$0.266222\pi$
$84$		0			0
$85$		0			0
$86$	3.36603	+	0.901924i	0.362968	+	0.0972569i
$87$		0			0
$88$		−	5.65685i		−	0.603023i
$89$		−	6.92820i		−	0.734388i	−0.930144	−	0.367194i	$-0.880318\pi$
$89$		−	6.92820i		−	0.734388i	0.930144	−	0.367194i	$-0.119682\pi$
$90$		0			0
$91$			14.1244i			1.48063i
$92$	−0.277401	−	1.03528i	−0.0289211	−	0.107935i
$93$		0			0
$94$	4.73205	−	17.6603i	0.488074	−	1.82152i
$95$		0			0
$96$		0			0
$97$	−4.43211	+	4.43211i	−0.450013	+	0.450013i	−0.895359	−	0.445346i	$-0.853081\pi$
$97$	−4.43211	+	4.43211i	−0.450013	+	0.450013i	0.445346	+	0.895359i	$0.353081\pi$
$98$	−1.13681	+	0.656339i	−0.114835	+	0.0663002i
$99$		0			0
$100$		0			0
$101$	1.46410			0.145684			0.0728418	−	0.997344i	$-0.476793\pi$
$101$	1.46410			0.145684			0.0728418	+	0.997344i	$0.476793\pi$
$102$		0			0
$103$	4.89898	−	4.89898i	0.482711	−	0.482711i	−0.423286	−	0.905996i	$-0.639123\pi$
$103$	4.89898	−	4.89898i	0.482711	−	0.482711i	0.905996	+	0.423286i	$0.139123\pi$
$104$	11.4641	+	11.4641i	1.12415	+	1.12415i
$105$		0			0
$106$	−0.535898	+	2.00000i	−0.0520511	+	0.194257i
$107$	−4.62158	−	4.62158i	−0.446785	−	0.446785i	0.447499	−	0.894284i	$-0.352315\pi$
$107$	−4.62158	−	4.62158i	−0.446785	−	0.446785i	−0.894284	+	0.447499i	$0.852315\pi$
$108$		0			0
$109$			7.00000i			0.670478i	0.942133	+	0.335239i	$0.108817\pi$
$109$			7.00000i			0.670478i	−0.942133	+	0.335239i	$0.891183\pi$
$110$		0			0
$111$		0			0
$112$	2.55103	−	9.52056i	0.241049	−	0.899608i
$113$	9.79796	+	9.79796i	0.921714	+	0.921714i	0.997151	−	0.0754362i	$-0.0240349\pi$
$113$	9.79796	+	9.79796i	0.921714	+	0.921714i	−0.0754362	+	0.997151i	$0.524035\pi$
$114$		0			0
$115$		0			0
$116$	−12.9282	−	7.46410i	−1.20035	−	0.693024i
$117$		0			0
$118$	3.20736	+	5.55532i	0.295262	+	0.511409i
$119$	−14.7846			−1.35530
$120$		0			0
$121$	7.00000			0.636364
$122$	−2.12132	−	3.67423i	−0.192055	−	0.332650i
$123$		0			0
$124$	−0.464102	−	0.267949i	−0.0416776	−	0.0240625i
$125$		0			0
$126$		0			0
$127$	2.07055	+	2.07055i	0.183732	+	0.183732i	0.792980	−	0.609248i	$-0.208529\pi$
$127$	2.07055	+	2.07055i	0.183732	+	0.183732i	−0.609248	+	0.792980i	$0.708529\pi$
$128$	−5.65685	−	9.79796i	−0.500000	−	0.866025i
$129$		0			0
$130$		0			0
$131$		−	9.46410i		−	0.826882i	−0.910531	−	0.413441i	$-0.864327\pi$
$131$		−	9.46410i		−	0.826882i	0.910531	−	0.413441i	$-0.135673\pi$
$132$		0			0
$133$	−12.5385	−	12.5385i	−1.08722	−	1.08722i
$134$	4.56218	−	17.0263i	0.394112	−	1.47085i
$135$		0			0
$136$	−12.0000	+	12.0000i	−1.02899	+	1.02899i
$137$	6.03579	−	6.03579i	0.515672	−	0.515672i	−0.400586	−	0.916259i	$-0.631194\pi$
$137$	6.03579	−	6.03579i	0.515672	−	0.515672i	0.916259	+	0.400586i	$0.131194\pi$
$138$		0			0
$139$	−19.4641			−1.65092			−0.825462	−	0.564458i	$-0.809085\pi$
$139$	−19.4641			−1.65092			−0.825462	+	0.564458i	$0.809085\pi$
$140$		0			0
$141$		0			0
$142$	11.5911	−	6.69213i	0.972704	−	0.561591i
$143$	8.10634	−	8.10634i	0.677887	−	0.677887i
$144$		0			0
$145$		0			0
$146$	−1.46410	+	5.46410i	−0.121170	+	0.452212i
$147$		0			0
$148$	1.51575	+	5.65685i	0.124594	+	0.464991i
$149$		−	15.8564i		−	1.29901i	−0.760358	−	0.649504i	$-0.774977\pi$
$149$		−	15.8564i		−	1.29901i	0.760358	−	0.649504i	$-0.225023\pi$
$150$		0			0
$151$			4.26795i			0.347321i	0.984806	+	0.173660i	$0.0555595\pi$
$151$			4.26795i			0.347321i	−0.984806	+	0.173660i	$0.944440\pi$
$152$	−20.3538			−1.65091
$153$		0			0
$154$	−6.73205	−	1.80385i	−0.542484	−	0.145358i
$155$		0			0
$156$		0			0
$157$	6.88160	−	6.88160i	0.549211	−	0.549211i	−0.377001	−	0.926213i	$-0.623045\pi$
$157$	6.88160	−	6.88160i	0.549211	−	0.549211i	0.926213	+	0.377001i	$0.123045\pi$
$158$	0.378937	+	0.656339i	0.0301466	+	0.0522155i
$159$		0			0
$160$		0			0
$161$	−1.32051			−0.104071
$162$		0			0
$163$	−10.2277	+	10.2277i	−0.801092	+	0.801092i	−0.983266	−	0.182174i	$-0.941687\pi$
$163$	−10.2277	+	10.2277i	−0.801092	+	0.801092i	0.182174	+	0.983266i	$0.441687\pi$
$164$	−5.46410	+	9.46410i	−0.426675	+	0.739022i
$165$		0			0
$166$	1.26795	+	0.339746i	0.0984119	+	0.0263694i
$167$	−3.10583	−	3.10583i	−0.240336	−	0.240336i	0.576653	−	0.816989i	$-0.304358\pi$
$167$	−3.10583	−	3.10583i	−0.240336	−	0.240336i	−0.816989	+	0.576653i	$0.804358\pi$
$168$		0			0
$169$			19.8564i			1.52742i
$170$		0			0
$171$		0			0
$172$	−1.27551	−	4.76028i	−0.0972569	−	0.362968i
$173$	−6.31319	−	6.31319i	−0.479983	−	0.479983i	0.425143	−	0.905126i	$-0.360224\pi$
$173$	−6.31319	−	6.31319i	−0.479983	−	0.479983i	−0.905126	+	0.425143i	$0.860224\pi$
$174$		0			0
$175$		0			0
$176$	−6.92820	+	4.00000i	−0.522233	+	0.301511i
$177$		0			0
$178$	−8.48528	+	4.89898i	−0.635999	+	0.367194i
$179$	25.3205			1.89254			0.946272	−	0.323372i	$-0.104817\pi$
$179$	25.3205			1.89254			0.946272	+	0.323372i	$0.104817\pi$
$180$		0			0
$181$	−13.9282			−1.03528			−0.517638	−	0.855600i	$-0.673188\pi$
$181$	−13.9282			−1.03528			−0.517638	+	0.855600i	$0.673188\pi$
$182$	17.2987	−	9.98743i	1.28227	−	0.740317i
$183$		0			0
$184$	−1.07180	+	1.07180i	−0.0790139	+	0.0790139i
$185$		0			0
$186$		0			0
$187$	8.48528	+	8.48528i	0.620505	+	0.620505i
$188$	−24.9754	+	6.69213i	−1.82152	+	0.488074i
$189$		0			0
$190$		0			0
$191$			16.9282i			1.22488i	0.790516	+	0.612441i	$0.209812\pi$
$191$			16.9282i			1.22488i	−0.790516	+	0.612441i	$0.790188\pi$
$192$		0			0
$193$	9.71003	+	9.71003i	0.698943	+	0.698943i	0.964183	−	0.265240i	$-0.0854510\pi$
$193$	9.71003	+	9.71003i	0.698943	+	0.698943i	−0.265240	+	0.964183i	$0.585451\pi$
$194$	8.56218	+	2.29423i	0.614729	+	0.164716i
$195$		0			0
$196$	1.60770	+	0.928203i	0.114835	+	0.0663002i
$197$	10.1769	−	10.1769i	0.725074	−	0.725074i	−0.244560	−	0.969634i	$-0.578644\pi$
$197$	10.1769	−	10.1769i	0.725074	−	0.725074i	0.969634	+	0.244560i	$0.0786436\pi$
$198$		0			0
$199$	14.1244			1.00125			0.500625	−	0.865665i	$-0.333104\pi$
$199$	14.1244			1.00125			0.500625	+	0.865665i	$0.333104\pi$
$200$		0			0
$201$		0			0
$202$	−1.03528	−	1.79315i	−0.0728418	−	0.126166i
$203$	−13.0053	+	13.0053i	−0.912795	+	0.912795i
$204$		0			0
$205$		0			0
$206$	−9.46410	−	2.53590i	−0.659395	−	0.176684i
$207$		0			0
$208$	5.93426	−	22.1469i	0.411467	−	1.53561i
$209$			14.3923i			0.995537i
$210$		0			0
$211$		−	7.19615i		−	0.495404i	−0.968836	−	0.247702i	$-0.920325\pi$
$211$		−	7.19615i		−	0.495404i	0.968836	−	0.247702i	$-0.0796753\pi$
$212$	2.82843	−	0.757875i	0.194257	−	0.0520511i
$213$		0			0
$214$	−2.39230	+	8.92820i	−0.163535	+	0.610319i
$215$		0			0
$216$		0			0
$217$	−0.466870	+	0.466870i	−0.0316932	+	0.0316932i
$218$	8.57321	−	4.94975i	0.580651	−	0.335239i
$219$		0			0
$220$		0			0
$221$	−34.3923			−2.31348
$222$		0			0
$223$	−8.05558	+	8.05558i	−0.539441	+	0.539441i	−0.923365	−	0.383924i	$-0.874573\pi$
$223$	−8.05558	+	8.05558i	−0.539441	+	0.539441i	0.383924	+	0.923365i	$0.374573\pi$
$224$	−13.4641	+	3.60770i	−0.899608	+	0.241049i
$225$		0			0
$226$	5.07180	−	18.9282i	0.337371	−	1.25909i
$227$	−8.76268	−	8.76268i	−0.581600	−	0.581600i	0.353743	−	0.935343i	$-0.384909\pi$
$227$	−8.76268	−	8.76268i	−0.581600	−	0.581600i	−0.935343	+	0.353743i	$0.884909\pi$
$228$		0			0
$229$		−	24.8564i		−	1.64256i	−0.570527	−	0.821279i	$-0.693261\pi$
$229$		−	24.8564i		−	1.64256i	0.570527	−	0.821279i	$-0.306739\pi$
$230$		0			0
$231$		0			0
$232$			21.1117i			1.38605i
$233$	−8.76268	−	8.76268i	−0.574062	−	0.574062i	0.359199	−	0.933261i	$-0.383050\pi$
$233$	−8.76268	−	8.76268i	−0.574062	−	0.574062i	−0.933261	+	0.359199i	$0.883050\pi$
$234$		0			0
$235$		0			0
$236$	4.53590	−	7.85641i	0.295262	−	0.511409i
$237$		0			0
$238$	10.4543	+	18.1074i	0.677651	+	1.17373i
$239$	−17.4641			−1.12966			−0.564829	−	0.825208i	$-0.691058\pi$
$239$	−17.4641			−1.12966			−0.564829	+	0.825208i	$0.691058\pi$
$240$		0			0
$241$	−14.8564			−0.956985			−0.478493	−	0.878092i	$-0.658817\pi$
$241$	−14.8564			−0.956985			−0.478493	+	0.878092i	$0.658817\pi$
$242$	−4.94975	−	8.57321i	−0.318182	−	0.551107i
$243$		0			0
$244$	−3.00000	+	5.19615i	−0.192055	+	0.332650i
$245$		0			0
$246$		0			0
$247$	−29.1672	−	29.1672i	−1.85587	−	1.85587i
$248$			0.757875i			0.0481251i
$249$		0			0
$250$		0			0
$251$			2.14359i			0.135302i	0.997709	+	0.0676512i	$0.0215505\pi$
$251$			2.14359i			0.135302i	−0.997709	+	0.0676512i	$0.978449\pi$
$252$		0			0
$253$	0.757875	+	0.757875i	0.0476472	+	0.0476472i
$254$	1.07180	−	4.00000i	0.0672505	−	0.250982i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−9.04008	+	9.04008i	−0.563905	+	0.563905i	−0.930414	−	0.366509i	$-0.880553\pi$
$257$	−9.04008	+	9.04008i	−0.563905	+	0.563905i	0.366509	+	0.930414i	$0.380553\pi$
$258$		0			0
$259$	7.21539			0.448343
$260$		0			0
$261$		0			0
$262$	−11.5911	+	6.69213i	−0.716101	+	0.413441i
$263$	−15.1774	+	15.1774i	−0.935879	+	0.935879i	−0.998065	−	0.0621853i	$-0.980193\pi$
$263$	−15.1774	+	15.1774i	−0.935879	+	0.935879i	0.0621853	+	0.998065i	$0.480193\pi$
$264$		0			0
$265$		0			0
$266$	−6.49038	+	24.2224i	−0.397951	+	1.48517i
$267$		0			0
$268$	−24.0788	+	6.45189i	−1.47085	+	0.394112i
$269$		−	1.60770i		−	0.0980229i	−0.998798	−	0.0490115i	$-0.984393\pi$
$269$		−	1.60770i		−	0.0980229i	0.998798	−	0.0490115i	$-0.0156071\pi$
$270$		0			0
$271$		−	24.2487i		−	1.47300i	−0.676435	−	0.736502i	$-0.736476\pi$
$271$		−	24.2487i		−	1.47300i	0.676435	−	0.736502i	$-0.263524\pi$
$272$	23.1822	+	6.21166i	1.40563	+	0.376637i
$273$		0			0
$274$	−11.6603	−	3.12436i	−0.704422	−	0.188749i
$275$		0			0
$276$		0			0
$277$	0.845807	−	0.845807i	0.0508196	−	0.0508196i	−0.681240	−	0.732060i	$-0.738559\pi$
$277$	0.845807	−	0.845807i	0.0508196	−	0.0508196i	0.732060	+	0.681240i	$0.238559\pi$
$278$	13.7632	+	23.8386i	0.825462	+	1.42974i
$279$		0			0
$280$		0			0
$281$	14.3923			0.858573			0.429286	−	0.903168i	$-0.358765\pi$
$281$	14.3923			0.858573			0.429286	+	0.903168i	$0.358765\pi$
$282$		0			0
$283$	15.1266	−	15.1266i	0.899186	−	0.899186i	−0.0961785	−	0.995364i	$-0.530662\pi$
$283$	15.1266	−	15.1266i	0.899186	−	0.899186i	0.995364	+	0.0961785i	$0.0306620\pi$
$284$	−16.3923	−	9.46410i	−0.972704	−	0.561591i
$285$		0			0
$286$	−15.6603	−	4.19615i	−0.926010	−	0.248124i
$287$	9.52056	+	9.52056i	0.561981	+	0.561981i
$288$		0			0
$289$		−	19.0000i		−	1.11765i
$290$		0			0
$291$		0			0
$292$	7.72741	−	2.07055i	0.452212	−	0.121170i
$293$	−8.86422	−	8.86422i	−0.517853	−	0.517853i	0.399068	−	0.916921i	$-0.369334\pi$
$293$	−8.86422	−	8.86422i	−0.517853	−	0.517853i	−0.916921	+	0.399068i	$0.869334\pi$
$294$		0			0
$295$		0			0
$296$	5.85641	−	5.85641i	0.340397	−	0.340397i
$297$		0			0
$298$	−19.4201	+	11.2122i	−1.12497	+	0.649504i
$299$	−3.07180			−0.177647
$300$		0			0
$301$	−6.07180			−0.349973
$302$	5.22715	−	3.01790i	0.300789	−	0.173660i
$303$		0			0
$304$	14.3923	+	24.9282i	0.825455	+	1.42973i
$305$		0			0
$306$		0			0
$307$	−9.46979	−	9.46979i	−0.540469	−	0.540469i	0.383197	−	0.923667i	$-0.374823\pi$
$307$	−9.46979	−	9.46979i	−0.540469	−	0.540469i	−0.923667	+	0.383197i	$0.874823\pi$
$308$	2.55103	+	9.52056i	0.145358	+	0.542484i
$309$		0			0
$310$		0			0
$311$		−	27.4641i		−	1.55735i	−0.627430	−	0.778673i	$-0.715893\pi$
$311$		−	27.4641i		−	1.55735i	0.627430	−	0.778673i	$-0.284107\pi$
$312$		0			0
$313$	5.74479	+	5.74479i	0.324715	+	0.324715i	0.850572	−	0.525858i	$-0.176256\pi$
$313$	5.74479	+	5.74479i	0.324715	+	0.324715i	−0.525858	+	0.850572i	$0.676256\pi$
$314$	−13.2942	−	3.56218i	−0.750237	−	0.201025i
$315$		0			0
$316$	0.535898	−	0.928203i	0.0301466	−	0.0522155i
$317$	4.89898	−	4.89898i	0.275154	−	0.275154i	−0.556017	−	0.831171i	$-0.687671\pi$
$317$	4.89898	−	4.89898i	0.275154	−	0.275154i	0.831171	+	0.556017i	$0.187671\pi$
$318$		0			0
$319$	14.9282			0.835819
$320$		0			0
$321$		0			0
$322$	0.933740	+	1.61729i	0.0520353	+	0.0901278i
$323$	30.5307	−	30.5307i	1.69877	−	1.69877i
$324$		0			0
$325$		0			0
$326$	19.7583	+	5.29423i	1.09431	+	0.293220i
$327$		0			0
$328$	15.4548			0.853349
$329$			31.8564i			1.75630i
$330$		0			0
$331$			2.39230i			0.131493i	0.997836	+	0.0657465i	$0.0209429\pi$
$331$			2.39230i			0.131493i	−0.997836	+	0.0657465i	$0.979057\pi$
$332$	−0.480473	−	1.79315i	−0.0263694	−	0.0984119i
$333$		0			0
$334$	−1.60770	+	6.00000i	−0.0879692	+	0.328305i
$335$		0			0
$336$		0			0
$337$	8.01841	−	8.01841i	0.436791	−	0.436791i	−0.454140	−	0.890930i	$-0.650053\pi$
$337$	8.01841	−	8.01841i	0.436791	−	0.436791i	0.890930	+	0.454140i	$0.150053\pi$
$338$	24.3190	−	14.0406i	1.32278	−	0.763708i
$339$		0			0
$340$		0			0
$341$	0.535898			0.0290205
$342$		0			0
$343$	13.8140	−	13.8140i	0.745884	−	0.745884i
$344$	−4.92820	+	4.92820i	−0.265711	+	0.265711i
$345$		0			0
$346$	−3.26795	+	12.1962i	−0.175686	+	0.655669i
$347$	−7.82894	−	7.82894i	−0.420280	−	0.420280i	0.465020	−	0.885300i	$-0.346047\pi$
$347$	−7.82894	−	7.82894i	−0.420280	−	0.420280i	−0.885300	+	0.465020i	$0.846047\pi$
$348$		0			0
$349$			3.85641i			0.206429i	0.994659	+	0.103214i	$0.0329128\pi$
$349$			3.85641i			0.206429i	−0.994659	+	0.103214i	$0.967087\pi$
$350$		0			0
$351$		0			0
$352$	9.79796	+	5.65685i	0.522233	+	0.301511i
$353$	11.2122	+	11.2122i	0.596764	+	0.596764i	0.939450	−	0.342686i	$-0.111337\pi$
$353$	11.2122	+	11.2122i	0.596764	+	0.596764i	−0.342686	+	0.939450i	$0.611337\pi$
$354$		0			0
$355$		0			0
$356$	12.0000	+	6.92820i	0.635999	+	0.367194i
$357$		0			0
$358$	−17.9043	−	31.0112i	−0.946272	−	1.63899i
$359$	24.3923			1.28738			0.643688	−	0.765288i	$-0.277403\pi$
$359$	24.3923			1.28738			0.643688	+	0.765288i	$0.277403\pi$
$360$		0			0
$361$	32.7846			1.72551
$362$	9.84873	+	17.0585i	0.517638	+	0.896575i
$363$		0			0
$364$	−24.4641	−	14.1244i	−1.28227	−	0.740317i
$365$		0			0
$366$		0			0
$367$	−7.50077	−	7.50077i	−0.391537	−	0.391537i	0.483698	−	0.875235i	$-0.339293\pi$
$367$	−7.50077	−	7.50077i	−0.391537	−	0.391537i	−0.875235	+	0.483698i	$0.839293\pi$
$368$	2.07055	+	0.554803i	0.107935	+	0.0289211i
$369$		0			0
$370$		0			0
$371$		−	3.60770i		−	0.187302i
$372$		0			0
$373$	13.6753	+	13.6753i	0.708078	+	0.708078i	0.966131	−	0.258052i	$-0.0830808\pi$
$373$	13.6753	+	13.6753i	0.708078	+	0.708078i	−0.258052	+	0.966131i	$0.583081\pi$
$374$	4.39230	−	16.3923i	0.227121	−	0.847626i
$375$		0			0
$376$	25.8564	+	25.8564i	1.33344	+	1.33344i
$377$	−30.2533	+	30.2533i	−1.55812	+	1.55812i
$378$		0			0
$379$	15.7321			0.808101			0.404051	−	0.914737i	$-0.367602\pi$
$379$	15.7321			0.808101			0.404051	+	0.914737i	$0.367602\pi$
$380$		0			0
$381$		0			0
$382$	20.7327	−	11.9700i	1.06078	−	0.612441i
$383$	−11.8685	+	11.8685i	−0.606453	+	0.606453i	−0.942017	−	0.335565i	$-0.891073\pi$
$383$	−11.8685	+	11.8685i	−0.606453	+	0.606453i	0.335565	+	0.942017i	$0.391073\pi$
$384$		0			0
$385$		0			0
$386$	5.02628	−	18.7583i	0.255831	−	0.954774i
$387$		0			0
$388$	−3.24453	−	12.1087i	−0.164716	−	0.614729i
$389$		−	14.5359i		−	0.736999i	−0.929628	−	0.368500i	$-0.879872\pi$
$389$		−	14.5359i		−	0.736999i	0.929628	−	0.368500i	$-0.120128\pi$
$390$		0			0
$391$		−	3.21539i		−	0.162609i
$392$		−	2.62536i		−	0.132600i
$393$		0			0
$394$	−19.6603	−	5.26795i	−0.990469	−	0.265395i
$395$		0			0
$396$		0			0
$397$	−13.8511	+	13.8511i	−0.695168	+	0.695168i	−0.963364	−	0.268196i	$-0.913573\pi$
$397$	−13.8511	+	13.8511i	−0.695168	+	0.695168i	0.268196	+	0.963364i	$0.413573\pi$
$398$	−9.98743	−	17.2987i	−0.500625	−	0.867107i
$399$		0			0
$400$		0			0
$401$	33.1769			1.65678			0.828388	−	0.560155i	$-0.189258\pi$
$401$	33.1769			1.65678			0.828388	+	0.560155i	$0.189258\pi$
$402$		0			0
$403$	−1.08604	+	1.08604i	−0.0540997	+	0.0540997i
$404$	−1.46410	+	2.53590i	−0.0728418	+	0.126166i
$405$		0			0
$406$	25.1244	+	6.73205i	1.24690	+	0.334106i
$407$	−4.14110	−	4.14110i	−0.205267	−	0.205267i
$408$		0			0
$409$		−	27.7846i		−	1.37386i	−0.726723	−	0.686930i	$-0.758958\pi$
$409$		−	27.7846i		−	1.37386i	0.726723	−	0.686930i	$-0.241042\pi$
$410$		0			0
$411$		0			0
$412$	3.58630	+	13.3843i	0.176684	+	0.659395i
$413$	−7.90327	−	7.90327i	−0.388895	−	0.388895i
$414$		0			0
$415$		0			0
$416$	−31.3205	+	8.39230i	−1.53561	+	0.411467i
$417$		0			0
$418$	17.6269	−	10.1769i	0.862160	−	0.497768i
$419$	26.5359			1.29636			0.648182	−	0.761486i	$-0.275530\pi$
$419$	26.5359			1.29636			0.648182	+	0.761486i	$0.275530\pi$
$420$		0			0
$421$	6.78461			0.330662			0.165331	−	0.986238i	$-0.447131\pi$
$421$	6.78461			0.330662			0.165331	+	0.986238i	$0.447131\pi$
$422$	−8.81345	+	5.08845i	−0.429032	+	0.247702i
$423$		0			0
$424$	−2.92820	−	2.92820i	−0.142206	−	0.142206i
$425$		0			0
$426$		0			0
$427$	5.22715	+	5.22715i	0.252959	+	0.252959i
$428$	12.6264	−	3.38323i	0.610319	−	0.163535i
$429$		0			0
$430$		0			0
$431$			25.7128i			1.23854i	0.785177	+	0.619271i	$0.212572\pi$
$431$			25.7128i			1.23854i	−0.785177	+	0.619271i	$0.787428\pi$
$432$		0			0
$433$	−3.11943	−	3.11943i	−0.149910	−	0.149910i	0.628168	−	0.778078i	$-0.283805\pi$
$433$	−3.11943	−	3.11943i	−0.149910	−	0.149910i	−0.778078	+	0.628168i	$0.783805\pi$
$434$	0.901924	+	0.241670i	0.0432937	+	0.0116005i
$435$		0			0
$436$	−12.1244	−	7.00000i	−0.580651	−	0.335239i
$437$	2.72689	−	2.72689i	0.130445	−	0.130445i
$438$		0			0
$439$	27.9808			1.33545			0.667724	−	0.744409i	$-0.267268\pi$
$439$	27.9808			1.33545			0.667724	+	0.744409i	$0.267268\pi$
$440$		0			0
$441$		0			0
$442$	24.3190	+	42.1218i	1.15674	+	2.00353i
$443$	9.04008	−	9.04008i	0.429507	−	0.429507i	−0.458953	−	0.888460i	$-0.651775\pi$
$443$	9.04008	−	9.04008i	0.429507	−	0.429507i	0.888460	+	0.458953i	$0.151775\pi$
$444$		0			0
$445$		0			0
$446$	15.5622	+	4.16987i	0.736890	+	0.197449i
$447$		0			0
$448$	13.9391	+	13.9391i	0.658559	+	0.658559i
$449$		−	33.8564i		−	1.59778i	−0.601475	−	0.798891i	$-0.705420\pi$
$449$		−	33.8564i		−	1.59778i	0.601475	−	0.798891i	$-0.294580\pi$
$450$		0			0
$451$		−	10.9282i		−	0.514589i
$452$	−26.7685	+	7.17260i	−1.25909	+	0.337371i
$453$		0			0
$454$	−4.53590	+	16.9282i	−0.212880	+	0.794480i
$455$		0			0
$456$		0			0
$457$	−25.2528	+	25.2528i	−1.18127	+	1.18127i	−0.201861	+	0.979414i	$0.564699\pi$
$457$	−25.2528	+	25.2528i	−1.18127	+	1.18127i	−0.979414	+	0.201861i	$0.935301\pi$
$458$	−30.4428	+	17.5761i	−1.42250	+	0.821279i
$459$		0			0
$460$		0			0
$461$	−15.6077			−0.726923			−0.363461	−	0.931609i	$-0.618405\pi$
$461$	−15.6077			−0.726923			−0.363461	+	0.931609i	$0.618405\pi$
$462$		0			0
$463$	−9.24316	+	9.24316i	−0.429566	+	0.429566i	−0.888480	−	0.458915i	$-0.848238\pi$
$463$	−9.24316	+	9.24316i	−0.429566	+	0.429566i	0.458915	+	0.888480i	$0.348238\pi$
$464$	25.8564	−	14.9282i	1.20035	−	0.693024i
$465$		0			0
$466$	−4.53590	+	16.9282i	−0.210121	+	0.784184i
$467$	−2.44949	−	2.44949i	−0.113349	−	0.113349i	0.648157	−	0.761506i	$-0.275540\pi$
$467$	−2.44949	−	2.44949i	−0.113349	−	0.113349i	−0.761506	+	0.648157i	$0.775540\pi$
$468$		0			0
$469$			30.7128i			1.41819i
$470$		0			0
$471$		0			0
$472$	−12.8295			−0.590524
$473$	3.48477	+	3.48477i	0.160230	+	0.160230i
$474$		0			0
$475$		0			0
$476$	14.7846	−	25.6077i	0.677651	−	1.17373i
$477$		0			0
$478$	12.3490	+	21.3891i	0.564829	+	0.978313i
$479$	13.3205			0.608630			0.304315	−	0.952572i	$-0.401573\pi$
$479$	13.3205			0.608630			0.304315	+	0.952572i	$0.401573\pi$
$480$		0			0
$481$	16.7846			0.765312
$482$	10.5051	+	18.1953i	0.478493	+	0.828774i
$483$		0			0
$484$	−7.00000	+	12.1244i	−0.318182	+	0.551107i
$485$		0			0
$486$		0			0
$487$	15.2282	+	15.2282i	0.690055	+	0.690055i	0.962244	−	0.272189i	$-0.0877476\pi$
$487$	15.2282	+	15.2282i	0.690055	+	0.690055i	−0.272189	+	0.962244i	$0.587748\pi$
$488$	8.48528			0.384111
$489$		0			0
$490$		0			0
$491$		−	34.6410i		−	1.56333i	−0.623700	−	0.781664i	$-0.714371\pi$
$491$		−	34.6410i		−	1.56333i	0.623700	−	0.781664i	$-0.285629\pi$
$492$		0			0
$493$	−31.6675	−	31.6675i	−1.42623	−	1.42623i
$494$	−15.0981	+	56.3468i	−0.679295	+	2.53516i
$495$		0			0
$496$	0.928203	−	0.535898i	0.0416776	−	0.0240625i
$497$	−16.4901	+	16.4901i	−0.739682	+	0.739682i
$498$		0			0
$499$	−5.87564			−0.263030			−0.131515	−	0.991314i	$-0.541984\pi$
$499$	−5.87564			−0.263030			−0.131515	+	0.991314i	$0.541984\pi$
$500$		0			0
$501$		0			0
$502$	2.62536	−	1.51575i	0.117175	−	0.0676512i
$503$	14.4195	−	14.4195i	0.642935	−	0.642935i	−0.308341	−	0.951276i	$-0.599774\pi$
$503$	14.4195	−	14.4195i	0.642935	−	0.642935i	0.951276	+	0.308341i	$0.0997737\pi$
$504$		0			0
$505$		0			0
$506$	0.392305	−	1.46410i	0.0174401	−	0.0650873i
$507$		0			0
$508$	−5.65685	+	1.51575i	−0.250982	+	0.0672505i
$509$			11.0718i			0.490749i	0.969428	+	0.245374i	$0.0789109\pi$
$509$			11.0718i			0.490749i	−0.969428	+	0.245374i	$0.921089\pi$
$510$		0			0
$511$		−	9.85641i		−	0.436022i
$512$	22.6274			1.00000
$513$		0			0
$514$	17.4641	+	4.67949i	0.770309	+	0.206404i
$515$		0			0
$516$		0			0
$517$	18.2832	−	18.2832i	0.804096	−	0.804096i
$518$	−5.10205	−	8.83701i	−0.224171	−	0.388276i
$519$		0			0
$520$		0			0
$521$	17.6077			0.771407			0.385704	−	0.922623i	$-0.373959\pi$
$521$	17.6077			0.771407			0.385704	+	0.922623i	$0.373959\pi$
$522$		0			0
$523$	13.7124	−	13.7124i	0.599603	−	0.599603i	−0.340604	−	0.940207i	$-0.610632\pi$
$523$	13.7124	−	13.7124i	0.599603	−	0.599603i	0.940207	+	0.340604i	$0.110632\pi$
$524$	16.3923	+	9.46410i	0.716101	+	0.413441i
$525$		0			0
$526$	29.3205	+	7.85641i	1.27843	+	0.342556i
$527$	−1.13681	−	1.13681i	−0.0495203	−	0.0495203i
$528$		0			0
$529$			22.7128i			0.987514i
$530$		0			0
$531$		0			0
$532$	34.2557	−	9.17878i	1.48517	−	0.397951i
$533$	22.1469	+	22.1469i	0.959291	+	0.959291i
$534$		0			0
$535$		0			0
$536$	24.9282	+	24.9282i	1.07673	+	1.07673i
$537$		0			0
$538$	−1.96902	+	1.13681i	−0.0848903	+	0.0490115i
$539$	−1.85641			−0.0799611
$540$		0			0
$541$	−33.7846			−1.45251			−0.726257	−	0.687423i	$-0.758742\pi$
$541$	−33.7846			−1.45251			−0.726257	+	0.687423i	$0.758742\pi$
$542$	−29.6985	+	17.1464i	−1.27566	+	0.736502i
$543$		0			0
$544$	−8.78461	−	32.7846i	−0.376637	−	1.40563i
$545$		0			0
$546$		0			0
$547$	−17.5254	−	17.5254i	−0.749331	−	0.749331i	0.225023	−	0.974353i	$-0.427754\pi$
$547$	−17.5254	−	17.5254i	−0.749331	−	0.749331i	−0.974353	+	0.225023i	$0.927754\pi$
$548$	4.41851	+	16.4901i	0.188749	+	0.704422i
$549$		0			0
$550$		0			0
$551$		−	53.7128i		−	2.28824i
$552$		0			0
$553$	−0.933740	−	0.933740i	−0.0397067	−	0.0397067i
$554$	−1.63397	−	0.437822i	−0.0694209	−	0.0186013i
$555$		0			0
$556$	19.4641	−	33.7128i	0.825462	−	1.42974i
$557$	25.6317	−	25.6317i	1.08605	−	1.08605i	0.0901194	−	0.995931i	$-0.471275\pi$
$557$	25.6317	−	25.6317i	1.08605	−	1.08605i	0.995931	−	0.0901194i	$-0.0287249\pi$
$558$		0			0
$559$	−14.1244			−0.597397
$560$		0			0
$561$		0			0
$562$	−10.1769	−	17.6269i	−0.429286	−	0.743546i
$563$	−16.3886	+	16.3886i	−0.690695	+	0.690695i	−0.962385	−	0.271690i	$-0.912418\pi$
$563$	−16.3886	+	16.3886i	−0.690695	+	0.690695i	0.271690	+	0.962385i	$0.412418\pi$
$564$		0			0
$565$		0			0
$566$	−29.2224	−	7.83013i	−1.22831	−	0.329125i
$567$		0			0
$568$			26.7685i			1.12318i
$569$		−	17.3205i		−	0.726113i	−0.931767	−	0.363057i	$-0.881733\pi$
$569$		−	17.3205i		−	0.726113i	0.931767	−	0.363057i	$-0.118267\pi$
$570$		0			0
$571$			16.8038i			0.703219i	0.936147	+	0.351610i	$0.114366\pi$
$571$			16.8038i			0.703219i	−0.936147	+	0.351610i	$0.885634\pi$
$572$	5.93426	+	22.1469i	0.248124	+	0.926010i
$573$		0			0
$574$	4.92820	−	18.3923i	0.205699	−	0.767680i
$575$		0			0
$576$		0			0
$577$	−10.8468	+	10.8468i	−0.451560	+	0.451560i	−0.895872	−	0.444312i	$-0.853448\pi$
$577$	−10.8468	+	10.8468i	−0.451560	+	0.451560i	0.444312	+	0.895872i	$0.353448\pi$
$578$	−23.2702	+	13.4350i	−0.967911	+	0.558824i
$579$		0			0
$580$		0			0
$581$	−2.28719			−0.0948885
$582$		0			0
$583$	−2.07055	+	2.07055i	−0.0857535	+	0.0857535i
$584$	−8.00000	−	8.00000i	−0.331042	−	0.331042i
$585$		0			0
$586$	−4.58846	+	17.1244i	−0.189547	+	0.707401i
$587$	13.6617	+	13.6617i	0.563877	+	0.563877i	0.930406	−	0.366529i	$-0.119454\pi$
$587$	13.6617	+	13.6617i	0.563877	+	0.563877i	−0.366529	+	0.930406i	$0.619454\pi$
$588$		0			0
$589$		−	1.92820i		−	0.0794502i
$590$		0			0
$591$		0			0
$592$	−11.3137	−	3.03150i	−0.464991	−	0.124594i
$593$	22.9048	+	22.9048i	0.940588	+	0.940588i	0.998331	−	0.0577433i	$-0.0183905\pi$
$593$	22.9048	+	22.9048i	0.940588	+	0.940588i	−0.0577433	+	0.998331i	$0.518390\pi$
$594$		0			0
$595$		0			0
$596$	27.4641	+	15.8564i	1.12497	+	0.649504i
$597$		0			0
$598$	2.17209	+	3.76217i	0.0888233	+	0.153846i
$599$	−46.6410			−1.90570			−0.952850	−	0.303441i	$-0.901864\pi$
$599$	−46.6410			−1.90570			−0.952850	+	0.303441i	$0.901864\pi$
$600$		0			0
$601$	−19.7846			−0.807031			−0.403516	−	0.914973i	$-0.632212\pi$
$601$	−19.7846			−0.807031			−0.403516	+	0.914973i	$0.632212\pi$
$602$	4.29341	+	7.43640i	0.174986	+	0.303085i
$603$		0			0
$604$	−7.39230	−	4.26795i	−0.300789	−	0.173660i
$605$		0			0
$606$		0			0
$607$	−13.9391	−	13.9391i	−0.565769	−	0.565769i	0.365171	−	0.930940i	$-0.381010\pi$
$607$	−13.9391	−	13.9391i	−0.565769	−	0.565769i	−0.930940	+	0.365171i	$0.881010\pi$
$608$	20.3538	−	35.2538i	0.825455	−	1.42973i
$609$		0			0
$610$		0			0
$611$			74.1051i			2.99797i
$612$		0			0
$613$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$613$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$614$	−4.90192	+	18.2942i	−0.197826	+	0.738295i
$615$		0			0
$616$	9.85641	−	9.85641i	0.397126	−	0.397126i
$617$	−10.0754	+	10.0754i	−0.405619	+	0.405619i	−0.880208	−	0.474589i	$-0.842597\pi$
$617$	−10.0754	+	10.0754i	−0.405619	+	0.405619i	0.474589	+	0.880208i	$0.342597\pi$
$618$		0			0
$619$	35.9808			1.44619			0.723094	−	0.690749i	$-0.242719\pi$
$619$	35.9808			1.44619			0.723094	+	0.690749i	$0.242719\pi$
$620$		0			0
$621$		0			0
$622$	−33.6365	+	19.4201i	−1.34870	+	0.778673i
$623$	12.0716	−	12.0716i	0.483638	−	0.483638i
$624$		0			0
$625$		0			0
$626$	2.97372	−	11.0981i	0.118854	−	0.443568i
$627$		0			0
$628$	5.03768	+	18.8009i	0.201025	+	0.750237i
$629$			17.5692i			0.700531i
$630$		0			0
$631$			1.58846i			0.0632355i	0.999500	+	0.0316177i	$0.0100659\pi$
$631$			1.58846i			0.0632355i	−0.999500	+	0.0316177i	$0.989934\pi$
$632$	−1.51575			−0.0602933
$633$		0			0
$634$	−9.46410	−	2.53590i	−0.375867	−	0.100713i
$635$		0			0
$636$		0			0
$637$	3.76217	−	3.76217i	0.149062	−	0.149062i
$638$	−10.5558	−	18.2832i	−0.417909	−	0.723840i
$639$		0			0
$640$		0			0
$641$	3.21539			0.127000			0.0635001	−	0.997982i	$-0.479774\pi$
$641$	3.21539			0.127000			0.0635001	+	0.997982i	$0.479774\pi$
$642$		0			0
$643$	−12.0716	+	12.0716i	−0.476057	+	0.476057i	−0.903868	−	0.427811i	$-0.859285\pi$
$643$	−12.0716	+	12.0716i	−0.476057	+	0.476057i	0.427811	+	0.903868i	$0.359285\pi$
$644$	1.32051	−	2.28719i	0.0520353	−	0.0901278i
$645$		0			0
$646$	−58.9808	−	15.8038i	−2.32057	−	0.621794i
$647$	−3.58630	−	3.58630i	−0.140992	−	0.140992i	0.633088	−	0.774080i	$-0.281787\pi$
$647$	−3.58630	−	3.58630i	−0.140992	−	0.140992i	−0.774080	+	0.633088i	$0.781787\pi$
$648$		0			0
$649$			9.07180i			0.356099i
$650$		0			0
$651$		0			0
$652$	−7.48717	−	27.9425i	−0.293220	−	1.09431i
$653$	−7.34847	−	7.34847i	−0.287568	−	0.287568i	0.548550	−	0.836118i	$-0.315180\pi$
$653$	−7.34847	−	7.34847i	−0.287568	−	0.287568i	−0.836118	+	0.548550i	$0.815180\pi$
$654$		0			0
$655$		0			0
$656$	−10.9282	−	18.9282i	−0.426675	−	0.739022i
$657$		0			0
$658$	39.0160	−	22.5259i	1.52100	−	0.878150i
$659$	−14.5359			−0.566238			−0.283119	−	0.959085i	$-0.591369\pi$
$659$	−14.5359			−0.566238			−0.283119	+	0.959085i	$0.591369\pi$
$660$		0			0
$661$	−7.85641			−0.305579			−0.152789	−	0.988259i	$-0.548826\pi$
$661$	−7.85641			−0.305579			−0.152789	+	0.988259i	$0.548826\pi$
$662$	2.92996	−	1.69161i	0.113876	−	0.0657465i
$663$		0			0
$664$	−1.85641	+	1.85641i	−0.0720425	+	0.0720425i
$665$		0			0
$666$		0			0
$667$	−2.82843	−	2.82843i	−0.109517	−	0.109517i
$668$	8.48528	−	2.27362i	0.328305	−	0.0879692i
$669$		0			0
$670$		0			0
$671$		−	6.00000i		−	0.231627i
$672$		0			0
$673$	2.82843	+	2.82843i	0.109028	+	0.109028i	0.759516	−	0.650488i	$-0.225436\pi$
$673$	2.82843	+	2.82843i	0.109028	+	0.109028i	−0.650488	+	0.759516i	$0.725436\pi$
$674$	−15.4904	−	4.15064i	−0.596667	−	0.159876i
$675$		0			0
$676$	−34.3923	−	19.8564i	−1.32278	−	0.763708i
$677$	25.9091	−	25.9091i	0.995768	−	0.995768i	−0.00422306	−	0.999991i	$-0.501344\pi$
$677$	25.9091	−	25.9091i	0.995768	−	0.995768i	0.999991	+	0.00422306i	$0.00134424\pi$
$678$		0			0
$679$	−15.4449			−0.592719
$680$		0			0
$681$		0			0
$682$	−0.378937	−	0.656339i	−0.0145103	−	0.0251325i
$683$	−3.58630	+	3.58630i	−0.137226	+	0.137226i	−0.772383	−	0.635157i	$-0.780935\pi$
$683$	−3.58630	+	3.58630i	−0.137226	+	0.137226i	0.635157	+	0.772383i	$0.280935\pi$
$684$		0			0
$685$		0			0
$686$	−26.6865	−	7.15064i	−1.01890	−	0.273013i
$687$		0			0
$688$	9.52056	+	2.55103i	0.362968	+	0.0972569i
$689$		−	8.39230i		−	0.319721i
$690$		0			0
$691$		−	25.3205i		−	0.963238i	−0.876381	−	0.481619i	$-0.840049\pi$
$691$		−	25.3205i		−	0.963238i	0.876381	−	0.481619i	$-0.159951\pi$
$692$	17.2480	−	4.62158i	0.655669	−	0.175686i
$693$		0			0
$694$	−4.05256	+	15.1244i	−0.153833	+	0.574113i
$695$		0			0
$696$		0			0
$697$	−23.1822	+	23.1822i	−0.878089	+	0.878089i
$698$	4.72311	−	2.72689i	0.178773	−	0.103214i
$699$		0			0
$700$		0			0
$701$	15.4641			0.584071			0.292036	−	0.956407i	$-0.405667\pi$
$701$	15.4641			0.584071			0.292036	+	0.956407i	$0.405667\pi$
$702$		0			0
$703$	−14.9000	+	14.9000i	−0.561965	+	0.561965i
$704$		−	16.0000i		−	0.603023i
$705$		0			0
$706$	5.80385	−	21.6603i	0.218431	−	0.815194i
$707$	2.55103	+	2.55103i	0.0959412	+	0.0959412i
$708$		0			0
$709$		−	24.8564i		−	0.933502i	−0.884389	−	0.466751i	$-0.845424\pi$
$709$		−	24.8564i		−	0.933502i	0.884389	−	0.466751i	$-0.154576\pi$
$710$		0			0
$711$		0			0
$712$		−	19.5959i		−	0.734388i
$713$	−0.101536	−	0.101536i	−0.00380255	−	0.00380255i
$714$		0			0
$715$		0			0
$716$	−25.3205	+	43.8564i	−0.946272	+	1.63899i
$717$		0			0
$718$	−17.2480	−	29.8744i	−0.643688	−	1.11490i
$719$	12.9282			0.482141			0.241070	−	0.970508i	$-0.422502\pi$
$719$	12.9282			0.482141			0.241070	+	0.970508i	$0.422502\pi$
$720$		0			0
$721$	17.0718			0.635787
$722$	−23.1822	−	40.1528i	−0.862753	−	1.49433i
$723$		0			0
$724$	13.9282	−	24.1244i	0.517638	−	0.896575i
$725$		0			0
$726$		0			0
$727$	33.3083	+	33.3083i	1.23534	+	1.23534i	0.961885	+	0.273453i	$0.0881658\pi$
$727$	33.3083	+	33.3083i	1.23534	+	1.23534i	0.273453	+	0.961885i	$0.411834\pi$
$728$			39.9497i			1.48063i
$729$		0			0
$730$		0			0
$731$		−	14.7846i		−	0.546829i
$732$		0			0
$733$	13.9391	+	13.9391i	0.514851	+	0.514851i	0.916009	−	0.401158i	$-0.131392\pi$
$733$	13.9391	+	13.9391i	0.514851	+	0.514851i	−0.401158	+	0.916009i	$0.631392\pi$
$734$	−3.88269	+	14.4904i	−0.143313	+	0.534850i
$735$		0			0
$736$	−0.784610	−	2.92820i	−0.0289211	−	0.107935i
$737$	17.6269	−	17.6269i	0.649295	−	0.649295i
$738$		0			0
$739$	−14.3923			−0.529429			−0.264715	−	0.964327i	$-0.585278\pi$
$739$	−14.3923			−0.529429			−0.264715	+	0.964327i	$0.585278\pi$
$740$		0			0
$741$		0			0
$742$	−4.41851	+	2.55103i	−0.162208	+	0.0936511i
$743$	−21.8695	+	21.8695i	−0.802316	+	0.802316i	−0.983457	−	0.181141i	$-0.942021\pi$
$743$	−21.8695	+	21.8695i	−0.802316	+	0.802316i	0.181141	+	0.983457i	$0.442021\pi$
$744$		0			0
$745$		0			0
$746$	7.07884	−	26.4186i	0.259175	−	0.967253i
$747$		0			0
$748$	−23.1822	+	6.21166i	−0.847626	+	0.227121i
$749$		−	16.1051i		−	0.588468i
$750$		0			0
$751$		−	11.4641i		−	0.418331i	−0.977880	−	0.209166i	$-0.932925\pi$
$751$		−	11.4641i		−	0.418331i	0.977880	−	0.209166i	$-0.0670747\pi$
$752$	13.3843	−	49.9507i	0.488074	−	1.82152i
$753$		0			0
$754$	58.4449	+	15.6603i	2.12844	+	0.570313i
$755$		0			0
$756$		0			0
$757$	20.6448	−	20.6448i	0.750348	−	0.750348i	−0.224196	−	0.974544i	$-0.571976\pi$
$757$	20.6448	−	20.6448i	0.750348	−	0.750348i	0.974544	+	0.224196i	$0.0719756\pi$
$758$	−11.1242	−	19.2677i	−0.404051	−	0.699836i
$759$		0			0
$760$		0			0
$761$	−46.6410			−1.69074			−0.845368	−	0.534185i	$-0.820619\pi$
$761$	−46.6410			−1.69074			−0.845368	+	0.534185i	$0.820619\pi$
$762$		0			0
$763$	−12.1967	+	12.1967i	−0.441549	+	0.441549i
$764$	−29.3205	−	16.9282i	−1.06078	−	0.612441i
$765$		0			0
$766$	22.9282	+	6.14359i	0.828430	+	0.221977i
$767$	−18.3848	−	18.3848i	−0.663836	−	0.663836i
$768$		0			0
$769$			29.9282i			1.07924i	0.841909	+	0.539619i	$0.181432\pi$
$769$			29.9282i			1.07924i	−0.841909	+	0.539619i	$0.818568\pi$
$770$		0			0
$771$		0			0
$772$	−26.5283	+	7.10823i	−0.954774	+	0.255831i
$773$	−23.4596	−	23.4596i	−0.843784	−	0.843784i	0.145565	−	0.989349i	$-0.453500\pi$
$773$	−23.4596	−	23.4596i	−0.843784	−	0.843784i	−0.989349	+	0.145565i	$0.953500\pi$
$774$		0			0
$775$		0			0
$776$	−12.5359	+	12.5359i	−0.450013	+	0.450013i
$777$		0			0
$778$	−17.8028	+	10.2784i	−0.638260	+	0.368500i
$779$	−39.3205			−1.40880
$780$		0			0
$781$	18.9282			0.677304
$782$	−3.93803	+	2.27362i	−0.140824	+	0.0813046i
$783$		0			0
$784$	−3.21539	+	1.85641i	−0.114835	+	0.0663002i
$785$		0			0
$786$		0			0
$787$	10.0246	+	10.0246i	0.357338	+	0.357338i	0.862831	−	0.505493i	$-0.168689\pi$
$787$	10.0246	+	10.0246i	0.357338	+	0.357338i	−0.505493	+	0.862831i	$0.668689\pi$
$788$	7.45001	+	27.8038i	0.265395	+	0.990469i
$789$		0			0
$790$		0			0
$791$			34.1436i			1.21401i
$792$		0			0
$793$	12.1595	+	12.1595i	0.431797	+	0.431797i
$794$	26.7583	+	7.16987i	0.949618	+	0.254449i
$795$		0			0
$796$	−14.1244	+	24.4641i	−0.500625	+	0.867107i
$797$	−9.79796	+	9.79796i	−0.347062	+	0.347062i	−0.859014	−	0.511952i	$-0.828922\pi$
$797$	−9.79796	+	9.79796i	−0.347062	+	0.347062i	0.511952	+	0.859014i	$0.328922\pi$
$798$		0			0
$799$	−77.5692			−2.74420
$800$		0			0
$801$		0			0
$802$	−23.4596	−	40.6333i	−0.828388	−	1.43481i
$803$	−5.65685	+	5.65685i	−0.199626	+	0.199626i
$804$		0			0
$805$		0			0
$806$	2.09808	+	0.562178i	0.0739016	+	0.0198019i
$807$		0			0
$808$	4.14110			0.145684
$809$			49.1769i			1.72897i	0.502660	+	0.864484i	$0.332355\pi$
$809$			49.1769i			1.72897i	−0.502660	+	0.864484i	$0.667645\pi$
$810$		0			0
$811$			26.1244i			0.917350i	0.888604	+	0.458675i	$0.151676\pi$
$811$			26.1244i			0.917350i	−0.888604	+	0.458675i	$0.848324\pi$
$812$	−9.52056	−	35.5312i	−0.334106	−	1.24690i
$813$		0			0
$814$	−2.14359	+	8.00000i	−0.0751329	+	0.280400i
$815$		0			0
$816$		0			0
$817$	12.5385	−	12.5385i	0.438665	−	0.438665i
$818$	−34.0291	+	19.6467i	−1.18980	+	0.686930i
$819$		0			0
$820$		0			0
$821$	−55.5692			−1.93938			−0.969690	−	0.244340i	$-0.921429\pi$
$821$	−55.5692			−1.93938			−0.969690	+	0.244340i	$0.921429\pi$
$822$		0			0
$823$	33.5114	−	33.5114i	1.16813	−	1.16813i	0.185488	−	0.982646i	$-0.440613\pi$
$823$	33.5114	−	33.5114i	1.16813	−	1.16813i	0.982646	−	0.185488i	$-0.0593866\pi$
$824$	13.8564	−	13.8564i	0.482711	−	0.482711i
$825$		0			0
$826$	−4.09103	+	15.2679i	−0.142345	+	0.531240i
$827$	30.0774	+	30.0774i	1.04589	+	1.04589i	0.998895	+	0.0469995i	$0.0149659\pi$
$827$	30.0774	+	30.0774i	1.04589	+	1.04589i	0.0469995	+	0.998895i	$0.485034\pi$
$828$		0			0
$829$		−	17.7128i		−	0.615191i	−0.951517	−	0.307596i	$-0.900476\pi$
$829$		−	17.7128i		−	0.615191i	0.951517	−	0.307596i	$-0.0995244\pi$
$830$		0			0
$831$		0			0
$832$	32.4254	+	32.4254i	1.12415	+	1.12415i
$833$	3.93803	+	3.93803i	0.136445	+	0.136445i
$834$		0			0
$835$		0			0
$836$	−24.9282	−	14.3923i	−0.862160	−	0.497768i
$837$		0			0
$838$	−18.7637	−	32.4997i	−0.648182	−	1.12268i
$839$	40.6410			1.40308			0.701542	−	0.712628i	$-0.252495\pi$
$839$	40.6410			1.40308			0.701542	+	0.712628i	$0.252495\pi$
$840$		0			0
$841$	−26.7128			−0.921131
$842$	−4.79744	−	8.30942i	−0.165331	−	0.286361i
$843$		0			0
$844$	12.4641	+	7.19615i	0.429032	+	0.247702i
$845$		0			0
$846$		0			0
$847$	12.1967	+	12.1967i	0.419083	+	0.419083i
$848$	−1.51575	+	5.65685i	−0.0520511	+	0.194257i
$849$		0			0
$850$		0			0
$851$			1.56922i			0.0537921i
$852$		0			0
$853$	11.0227	+	11.0227i	0.377410	+	0.377410i	0.870167	−	0.492757i	$-0.164011\pi$
$853$	11.0227	+	11.0227i	0.377410	+	0.377410i	−0.492757	+	0.870167i	$0.664011\pi$
$854$	2.70577	−	10.0981i	0.0925896	−	0.345549i
$855$		0			0
$856$	−13.0718	−	13.0718i	−0.446785	−	0.446785i
$857$	−33.7381	+	33.7381i	−1.15247	+	1.15247i	−0.166414	+	0.986056i	$0.553219\pi$
$857$	−33.7381	+	33.7381i	−1.15247	+	1.15247i	−0.986056	+	0.166414i	$0.946781\pi$
$858$		0			0
$859$	−21.6077			−0.737245			−0.368623	−	0.929579i	$-0.620170\pi$
$859$	−21.6077			−0.737245			−0.368623	+	0.929579i	$0.620170\pi$
$860$		0			0
$861$		0			0
$862$	31.4916	−	18.1817i	1.07261	−	0.619271i
$863$	27.3233	−	27.3233i	0.930097	−	0.930097i	−0.0676147	−	0.997712i	$-0.521539\pi$
$863$	27.3233	−	27.3233i	0.930097	−	0.930097i	0.997712	+	0.0676147i	$0.0215389\pi$
$864$		0			0
$865$		0			0
$866$	−1.61474	+	6.02628i	−0.0548710	+	0.204781i
$867$		0			0
$868$	−0.341773	−	1.27551i	−0.0116005	−	0.0432937i
$869$			1.07180i			0.0363582i
$870$		0			0
$871$			71.4449i			2.42082i
$872$			19.7990i			0.670478i
$873$		0			0
$874$	−5.26795	−	1.41154i	−0.178191	−	0.0477461i
$875$		0			0
$876$		0			0
$877$	22.5123	−	22.5123i	0.760186	−	0.760186i	−0.216170	−	0.976356i	$-0.569357\pi$
$877$	22.5123	−	22.5123i	0.760186	−	0.760186i	0.976356	+	0.216170i	$0.0693566\pi$
$878$	−19.7854	−	34.2693i	−0.667724	−	1.15653i
$879$		0			0
$880$		0			0
$881$	50.9282			1.71581			0.857907	−	0.513804i	$-0.171764\pi$
$881$	50.9282			1.71581			0.857907	+	0.513804i	$0.171764\pi$
$882$		0			0
$883$	−21.3383	+	21.3383i	−0.718091	+	0.718091i	−0.968214	−	0.250123i	$-0.919529\pi$
$883$	−21.3383	+	21.3383i	−0.718091	+	0.718091i	0.250123	+	0.968214i	$0.419529\pi$
$884$	34.3923	−	59.5692i	1.15674	−	2.00353i
$885$		0			0
$886$	−17.4641	−	4.67949i	−0.586718	−	0.157211i
$887$	−5.55532	−	5.55532i	−0.186529	−	0.186529i	0.607665	−	0.794194i	$-0.292107\pi$
$887$	−5.55532	−	5.55532i	−0.186529	−	0.186529i	−0.794194	+	0.607665i	$0.792107\pi$
$888$		0			0
$889$			7.21539i			0.241996i
$890$		0			0
$891$		0			0
$892$	−5.89709	−	22.0082i	−0.197449	−	0.736890i
$893$	−65.7845	−	65.7845i	−2.20139	−	2.20139i
$894$		0			0
$895$		0			0
$896$	7.21539	−	26.9282i	0.241049	−	0.899608i
$897$		0			0
$898$	−41.4655	+	23.9401i	−1.38372	+	0.798891i
$899$	−2.00000			−0.0667037
$900$		0			0
$901$	8.78461			0.292658
$902$	−13.3843	+	7.72741i	−0.445647	+	0.257294i
$903$		0			0
$904$	27.7128	+	27.7128i	0.921714	+	0.921714i
$905$		0			0
$906$		0			0
$907$	−6.96953	−	6.96953i	−0.231420	−	0.231420i	0.581866	−	0.813285i	$-0.302323\pi$
$907$	−6.96953	−	6.96953i	−0.231420	−	0.231420i	−0.813285	+	0.581866i	$0.802323\pi$
$908$	23.9401	−	6.41473i	0.794480	−	0.212880i
$909$		0			0
$910$		0			0
$911$			26.3923i			0.874416i	0.899360	+	0.437208i	$0.144033\pi$
$911$			26.3923i			0.874416i	−0.899360	+	0.437208i	$0.855967\pi$
$912$		0			0
$913$	1.31268	+	1.31268i	0.0434433	+	0.0434433i
$914$	48.7846	+	13.0718i	1.61365	+	0.432377i
$915$		0			0
$916$	43.0526	+	24.8564i	1.42250	+	0.821279i
$917$	16.4901	−	16.4901i	0.544551	−	0.544551i
$918$		0			0
$919$	−9.33975			−0.308090			−0.154045	−	0.988064i	$-0.549230\pi$
$919$	−9.33975			−0.308090			−0.154045	+	0.988064i	$0.549230\pi$
$920$		0			0
$921$		0			0
$922$	11.0363	+	19.1154i	0.363461	+	0.629534i
$923$	−38.3596	+	38.3596i	−1.26262	+	1.26262i
$924$		0			0
$925$		0			0
$926$	17.8564	+	4.78461i	0.586798	+	0.157232i
$927$		0			0
$928$	−36.5665	−	21.1117i	−1.20035	−	0.693024i
$929$			7.46410i			0.244889i	0.992475	+	0.122445i	$0.0390734\pi$
$929$			7.46410i			0.244889i	−0.992475	+	0.122445i	$0.960927\pi$
$930$		0			0
$931$			6.67949i			0.218912i
$932$	23.9401	−	6.41473i	0.784184	−	0.210121i
$933$		0			0
$934$	−1.26795	+	4.73205i	−0.0414886	+	0.154837i
$935$		0			0
$936$		0			0
$937$	37.4123	−	37.4123i	1.22221	−	1.22221i	0.255360	−	0.966846i	$-0.417806\pi$
$937$	37.4123	−	37.4123i	1.22221	−	1.22221i	0.966846	−	0.255360i	$-0.0821940\pi$
$938$	37.6154	−	21.7172i	1.22819	−	0.709093i
$939$		0			0
$940$		0			0
$941$	−24.9282			−0.812636			−0.406318	−	0.913732i	$-0.633188\pi$
$941$	−24.9282			−0.812636			−0.406318	+	0.913732i	$0.633188\pi$
$942$		0			0
$943$	−2.07055	+	2.07055i	−0.0674265	+	0.0674265i
$944$	9.07180	+	15.7128i	0.295262	+	0.511409i
$945$		0			0
$946$	1.80385	−	6.73205i	0.0586481	−	0.218878i
$947$	−11.4896	−	11.4896i	−0.373361	−	0.373361i	0.495339	−	0.868700i	$-0.335044\pi$
$947$	−11.4896	−	11.4896i	−0.373361	−	0.373361i	−0.868700	+	0.495339i	$0.835044\pi$
$948$		0			0
$949$		−	22.9282i		−	0.744281i
$950$		0			0
$951$		0			0
$952$	−41.8172			−1.35530
$953$	−11.1106	−	11.1106i	−0.359909	−	0.359909i	0.503870	−	0.863779i	$-0.331909\pi$
$953$	−11.1106	−	11.1106i	−0.359909	−	0.359909i	−0.863779	+	0.503870i	$0.831909\pi$
$954$		0			0
$955$		0			0
$956$	17.4641	−	30.2487i	0.564829	−	0.978313i
$957$		0			0
$958$	−9.41902	−	16.3142i	−0.304315	−	0.527089i
$959$	21.0333			0.679201
$960$		0			0
$961$	30.9282			0.997684
$962$	−11.8685	−	20.5569i	−0.382656	−	0.662780i
$963$		0			0
$964$	14.8564	−	25.7321i	0.478493	−	0.828774i
$965$		0			0
$966$		0			0
$967$	33.9411	+	33.9411i	1.09147	+	1.09147i	0.995372	+	0.0961015i	$0.0306373\pi$
$967$	33.9411	+	33.9411i	1.09147	+	1.09147i	0.0961015	+	0.995372i	$0.469363\pi$
$968$	19.7990			0.636364
$969$		0			0
$970$		0			0
$971$			19.1769i			0.615416i	0.951481	+	0.307708i	$0.0995621\pi$
$971$			19.1769i			0.615416i	−0.951481	+	0.307708i	$0.900438\pi$
$972$		0			0
$973$	−33.9139	−	33.9139i	−1.08723	−	1.08723i
$974$	7.88269	−	29.4186i	0.252578	−	0.942632i
$975$		0			0
$976$	−6.00000	−	10.3923i	−0.192055	−	0.332650i
$977$	27.7023	−	27.7023i	0.886274	−	0.886274i	−0.107889	−	0.994163i	$-0.534409\pi$
$977$	27.7023	−	27.7023i	0.886274	−	0.886274i	0.994163	+	0.107889i	$0.0344091\pi$
$978$		0			0
$979$	−13.8564			−0.442853
$980$		0			0
$981$		0			0
$982$	−42.4264	+	24.4949i	−1.35388	+	0.781664i
$983$	−18.2832	+	18.2832i	−0.583145	+	0.583145i	−0.935766	−	0.352621i	$-0.885290\pi$
$983$	−18.2832	+	18.2832i	−0.583145	+	0.583145i	0.352621	+	0.935766i	$0.385290\pi$
$984$		0			0
$985$		0			0
$986$	−16.3923	+	61.1769i	−0.522037	+	1.94827i
$987$		0			0
$988$	79.6864	−	21.3519i	2.53516	−	0.679295i
$989$		−	1.32051i		−	0.0419897i
$990$		0			0
$991$			57.5885i			1.82936i	0.404181	+	0.914679i	$0.367556\pi$
$991$			57.5885i			1.82936i	−0.404181	+	0.914679i	$0.632444\pi$
$992$	−1.31268	−	0.757875i	−0.0416776	−	0.0240625i
$993$		0			0
$994$	31.8564	+	8.53590i	1.01042	+	0.270742i
$995$		0			0
$996$		0			0
$997$	19.5959	−	19.5959i	0.620609	−	0.620609i	−0.325078	−	0.945687i	$-0.605391\pi$
$997$	19.5959	−	19.5959i	0.620609	−	0.620609i	0.945687	+	0.325078i	$0.105391\pi$
$998$	4.15471	+	7.19617i	0.131515	+	0.227791i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.k.g.343.1		8
3.2	odd	2		300.2.j.a.43.4	yes	8
4.3	odd	2		900.2.k.l.343.4		8
5.2	odd	4		900.2.k.l.307.3		8
5.3	odd	4		900.2.k.l.307.2		8
5.4	even	2	inner	900.2.k.g.343.4		8
12.11	even	2		300.2.j.c.43.1	yes	8
15.2	even	4		300.2.j.c.7.2	yes	8
15.8	even	4		300.2.j.c.7.3	yes	8
15.14	odd	2		300.2.j.a.43.1	yes	8
20.3	even	4	inner	900.2.k.g.307.3		8
20.7	even	4	inner	900.2.k.g.307.2		8
20.19	odd	2		900.2.k.l.343.1		8
60.23	odd	4		300.2.j.a.7.2	✓	8
60.47	odd	4		300.2.j.a.7.3	yes	8
60.59	even	2		300.2.j.c.43.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.j.a.7.2	✓	8	60.23	odd	4
300.2.j.a.7.3	yes	8	60.47	odd	4
300.2.j.a.43.1	yes	8	15.14	odd	2
300.2.j.a.43.4	yes	8	3.2	odd	2
300.2.j.c.7.2	yes	8	15.2	even	4
300.2.j.c.7.3	yes	8	15.8	even	4
300.2.j.c.43.1	yes	8	12.11	even	2
300.2.j.c.43.4	yes	8	60.59	even	2
900.2.k.g.307.2		8	20.7	even	4	inner
900.2.k.g.307.3		8	20.3	even	4	inner
900.2.k.g.343.1		8	1.1	even	1	trivial
900.2.k.g.343.4		8	5.4	even	2	inner
900.2.k.l.307.2		8	5.3	odd	4
900.2.k.l.307.3		8	5.2	odd	4
900.2.k.l.343.1		8	20.19	odd	2
900.2.k.l.343.4		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.74238 + 1.74238i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.74238 + 1.74238i) q^{7} +2.82843 q^{8} -2.00000i q^{11} +(4.05317 + 4.05317i) q^{13} +(0.901924 - 3.36603i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-4.24264 + 4.24264i) q^{17} -7.19615 q^{19} +(-2.44949 + 1.41421i) q^{22} +(-0.378937 + 0.378937i) q^{23} +(2.09808 - 7.83013i) q^{26} +(-4.76028 + 1.27551i) q^{28} +7.46410i q^{29} +0.267949i q^{31} +(-2.82843 + 4.89898i) q^{32} +(8.19615 + 2.19615i) q^{34} +(2.07055 - 2.07055i) q^{37} +(5.08845 + 8.81345i) q^{38} +5.46410 q^{41} +(-1.74238 + 1.74238i) q^{43} +(3.46410 + 2.00000i) q^{44} +(0.732051 + 0.196152i) q^{46} +(9.14162 + 9.14162i) q^{47} -0.928203i q^{49} +(-11.0735 + 2.96713i) q^{52} +(-1.03528 - 1.03528i) q^{53} +(4.92820 + 4.92820i) q^{56} +(9.14162 - 5.27792i) q^{58} -4.53590 q^{59} +3.00000 q^{61} +(0.328169 - 0.189469i) q^{62} +8.00000 q^{64} +(8.81345 + 8.81345i) q^{67} +(-3.10583 - 11.5911i) q^{68} +9.46410i q^{71} +(-2.82843 - 2.82843i) q^{73} +(-4.00000 - 1.07180i) q^{74} +(7.19615 - 12.4641i) q^{76} +(3.48477 - 3.48477i) q^{77} -0.535898 q^{79} +(-3.86370 - 6.69213i) q^{82} +(-0.656339 + 0.656339i) q^{83} +(3.36603 + 0.901924i) q^{86} -5.65685i q^{88} -6.92820i q^{89} +14.1244i q^{91} +(-0.277401 - 1.03528i) q^{92} +(4.73205 - 17.6603i) q^{94} +(-4.43211 + 4.43211i) q^{97} +(-1.13681 + 0.656339i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4}+O(q^{10}) \) 8 * q - 8 * q^4	\( 8 q - 8 q^{4} + 28 q^{14} - 16 q^{16} - 16 q^{19} - 4 q^{26} + 24 q^{34} + 16 q^{41} - 8 q^{46} - 16 q^{56} - 64 q^{59} + 24 q^{61} + 64 q^{64} - 32 q^{74} + 16 q^{76} - 32 q^{79} + 20 q^{86} + 24 q^{94}+O(q^{100}) \) 8 * q - 8 * q^4 + 28 * q^14 - 16 * q^16 - 16 * q^19 - 4 * q^26 + 24 * q^34 + 16 * q^41 - 8 * q^46 - 16 * q^56 - 64 * q^59 + 24 * q^61 + 64 * q^64 - 32 * q^74 + 16 * q^76 - 32 * q^79 + 20 * q^86 + 24 * q^94

Introduction

L-functions

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