LMFDB - Embedded newform 900.2.k.h.307.1

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:	8.0.157351936.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{4} + 16 $ x^8 + x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{49}]$
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			307.1
Root			$-1.28897 - 0.581861i$ of defining polynomial
Character	$\chi$	$=$	900.307
Dual form			900.2.k.h.343.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28897 - 0.581861i) q^{2} +(1.32288 + 1.50000i) q^{4} +(1.41421 - 1.41421i) q^{7} +(-0.832353 - 2.70318i) q^{8} +O(q^{10})$	\(q+(-1.28897 - 0.581861i) q^{2} +(1.32288 + 1.50000i) q^{4} +(1.41421 - 1.41421i) q^{7} +(-0.832353 - 2.70318i) q^{8} +5.29150i q^{11} +(-3.74166 + 3.74166i) q^{13} +(-2.64575 + 1.00000i) q^{14} +(-0.500000 + 3.96863i) q^{16} -5.29150 q^{19} +(3.07892 - 6.82058i) q^{22} +(-2.82843 - 2.82843i) q^{23} +(7.00000 - 2.64575i) q^{26} +(3.99215 + 0.250492i) q^{28} +8.00000i q^{29} -5.29150i q^{31} +(2.95367 - 4.82450i) q^{32} +(3.74166 + 3.74166i) q^{37} +(6.82058 + 3.07892i) q^{38} +2.00000 q^{41} +(-5.65685 - 5.65685i) q^{43} +(-7.93725 + 7.00000i) q^{44} +(2.00000 + 5.29150i) q^{46} +3.00000i q^{49} +(-10.5622 - 0.662739i) q^{52} +(-7.48331 + 7.48331i) q^{53} +(-5.00000 - 2.64575i) q^{56} +(4.65489 - 10.3117i) q^{58} -5.29150 q^{59} +6.00000 q^{61} +(-3.07892 + 6.82058i) q^{62} +(-6.61438 + 4.50000i) q^{64} +(-8.48528 + 8.48528i) q^{67} +(-7.48331 + 7.48331i) q^{73} +(-2.64575 - 7.00000i) q^{74} +(-7.00000 - 7.93725i) q^{76} +(7.48331 + 7.48331i) q^{77} +5.29150 q^{79} +(-2.57794 - 1.16372i) q^{82} +(8.48528 + 8.48528i) q^{83} +(4.00000 + 10.5830i) q^{86} +(14.3039 - 4.40440i) q^{88} -6.00000i q^{89} +10.5830i q^{91} +(0.500983 - 7.98430i) q^{92} +(7.48331 + 7.48331i) q^{97} +(1.74558 - 3.86690i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 4 q^{16} + 56 q^{26} + 16 q^{41} + 16 q^{46} - 40 q^{56} + 48 q^{61} - 56 q^{76} + 32 q^{86}+O(q^{100}) $ 8 * q - 4 * q^16 + 56 * q^26 + 16 * q^41 + 16 * q^46 - 40 * q^56 + 48 * q^61 - 56 * q^76 + 32 * q^86

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.28897	−	0.581861i	−0.911438	−	0.411438i
$2$	−1.28897	−	0.581861i	−0.911438	−	0.411438i
$3$		0			0
$3$		0			0
$4$	1.32288	+	1.50000i	0.661438	+	0.750000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.41421	−	1.41421i	0.534522	−	0.534522i	−0.387392	−	0.921915i	$-0.626624\pi$
$7$	1.41421	−	1.41421i	0.534522	−	0.534522i	0.921915	+	0.387392i	$0.126624\pi$
$8$	−0.832353	−	2.70318i	−0.294281	−	0.955719i
$9$		0			0
$10$		0			0
$11$			5.29150i			1.59545i	0.603023	+	0.797724i	$0.293963\pi$
$11$			5.29150i			1.59545i	−0.603023	+	0.797724i	$0.706037\pi$
$12$		0			0
$13$	−3.74166	+	3.74166i	−1.03775	+	1.03775i	−0.0384901	+	0.999259i	$0.512255\pi$
$13$	−3.74166	+	3.74166i	−1.03775	+	1.03775i	−0.999259	+	0.0384901i	$0.987745\pi$
$14$	−2.64575	+	1.00000i	−0.707107	+	0.267261i
$15$		0			0
$16$	−0.500000	+	3.96863i	−0.125000	+	0.992157i
$17$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$17$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$18$		0			0
$19$	−5.29150			−1.21395			−0.606977	−	0.794719i	$-0.707618\pi$
$19$	−5.29150			−1.21395			−0.606977	+	0.794719i	$0.707618\pi$
$20$		0			0
$21$		0			0
$22$	3.07892	−	6.82058i	0.656428	−	1.45415i
$23$	−2.82843	−	2.82843i	−0.589768	−	0.589768i	0.347801	−	0.937568i	$-0.386929\pi$
$23$	−2.82843	−	2.82843i	−0.589768	−	0.589768i	−0.937568	+	0.347801i	$0.886929\pi$
$24$		0			0
$25$		0			0
$26$	7.00000	−	2.64575i	1.37281	−	0.518875i
$27$		0			0
$28$	3.99215	+	0.250492i	0.754445	+	0.0473385i
$29$			8.00000i			1.48556i	0.669534	+	0.742781i	$0.266494\pi$
$29$			8.00000i			1.48556i	−0.669534	+	0.742781i	$0.733506\pi$
$30$		0			0
$31$		−	5.29150i		−	0.950382i	−0.879883	−	0.475191i	$-0.842379\pi$
$31$		−	5.29150i		−	0.950382i	0.879883	−	0.475191i	$-0.157621\pi$
$32$	2.95367	−	4.82450i	0.522141	−	0.852859i
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.74166	+	3.74166i	0.615125	+	0.615125i	0.944277	−	0.329152i	$-0.106763\pi$
$37$	3.74166	+	3.74166i	0.615125	+	0.615125i	−0.329152	+	0.944277i	$0.606763\pi$
$38$	6.82058	+	3.07892i	1.10644	+	0.499467i
$39$		0			0
$40$		0			0
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$		0			0
$43$	−5.65685	−	5.65685i	−0.862662	−	0.862662i	0.128984	−	0.991647i	$-0.458828\pi$
$43$	−5.65685	−	5.65685i	−0.862662	−	0.862662i	−0.991647	+	0.128984i	$0.958828\pi$
$44$	−7.93725	+	7.00000i	−1.19659	+	1.05529i
$45$		0			0
$46$	2.00000	+	5.29150i	0.294884	+	0.780189i
$47$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$47$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$48$		0			0
$49$			3.00000i			0.428571i
$50$		0			0
$51$		0			0
$52$	−10.5622	−	0.662739i	−1.46472	−	0.0919053i
$53$	−7.48331	+	7.48331i	−1.02791	+	1.02791i	−0.0283132	+	0.999599i	$0.509014\pi$
$53$	−7.48331	+	7.48331i	−1.02791	+	1.02791i	−0.999599	+	0.0283132i	$0.990986\pi$
$54$		0			0
$55$		0			0
$56$	−5.00000	−	2.64575i	−0.668153	−	0.353553i
$57$		0			0
$58$	4.65489	−	10.3117i	0.611217	−	1.35400i
$59$	−5.29150			−0.688895			−0.344447	−	0.938806i	$-0.611934\pi$
$59$	−5.29150			−0.688895			−0.344447	+	0.938806i	$0.611934\pi$
$60$		0			0
$61$	6.00000			0.768221			0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000			0.768221			0.384111	+	0.923287i	$0.374508\pi$
$62$	−3.07892	+	6.82058i	−0.391023	+	0.866214i
$63$		0			0
$64$	−6.61438	+	4.50000i	−0.826797	+	0.562500i
$65$		0			0
$66$		0			0
$67$	−8.48528	+	8.48528i	−1.03664	+	1.03664i	−0.0373395	+	0.999303i	$0.511888\pi$
$67$	−8.48528	+	8.48528i	−1.03664	+	1.03664i	−0.999303	+	0.0373395i	$0.988112\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$	−7.48331	+	7.48331i	−0.875856	+	0.875856i	−0.993103	−	0.117247i	$-0.962593\pi$
$73$	−7.48331	+	7.48331i	−0.875856	+	0.875856i	0.117247	+	0.993103i	$0.462593\pi$
$74$	−2.64575	−	7.00000i	−0.307562	−	0.813733i
$75$		0			0
$76$	−7.00000	−	7.93725i	−0.802955	−	0.910465i
$77$	7.48331	+	7.48331i	0.852803	+	0.852803i
$78$		0			0
$79$	5.29150			0.595341			0.297670	−	0.954669i	$-0.403790\pi$
$79$	5.29150			0.595341			0.297670	+	0.954669i	$0.403790\pi$
$80$		0			0
$81$		0			0
$82$	−2.57794	−	1.16372i	−0.284685	−	0.128512i
$83$	8.48528	+	8.48528i	0.931381	+	0.931381i	0.997792	−	0.0664117i	$-0.0211551\pi$
$83$	8.48528	+	8.48528i	0.931381	+	0.931381i	−0.0664117	+	0.997792i	$0.521155\pi$
$84$		0			0
$85$		0			0
$86$	4.00000	+	10.5830i	0.431331	+	1.14119i
$87$		0			0
$88$	14.3039	−	4.40440i	1.52480	−	0.469510i
$89$		−	6.00000i		−	0.635999i	−0.948091	−	0.317999i	$-0.896989\pi$
$89$		−	6.00000i		−	0.635999i	0.948091	−	0.317999i	$-0.103011\pi$
$90$		0			0
$91$			10.5830i			1.10940i
$92$	0.500983	−	7.98430i	0.0522311	−	0.832421i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	7.48331	+	7.48331i	0.759815	+	0.759815i	0.976289	−	0.216473i	$-0.0694554\pi$
$97$	7.48331	+	7.48331i	0.759815	+	0.759815i	−0.216473	+	0.976289i	$0.569455\pi$
$98$	1.74558	−	3.86690i	0.176330	−	0.390616i
$99$		0			0
$100$		0			0
$101$	4.00000			0.398015			0.199007	−	0.979998i	$-0.436228\pi$
$101$	4.00000			0.398015			0.199007	+	0.979998i	$0.436228\pi$
$102$		0			0
$103$	4.24264	+	4.24264i	0.418040	+	0.418040i	0.884528	−	0.466488i	$-0.154481\pi$
$103$	4.24264	+	4.24264i	0.418040	+	0.418040i	−0.466488	+	0.884528i	$0.654481\pi$
$104$	13.2288	+	7.00000i	1.29719	+	0.686406i
$105$		0			0
$106$	14.0000	−	5.29150i	1.35980	−	0.513956i
$107$	−2.82843	+	2.82843i	−0.273434	+	0.273434i	−0.830481	−	0.557047i	$-0.811934\pi$
$107$	−2.82843	+	2.82843i	−0.273434	+	0.273434i	0.557047	+	0.830481i	$0.311934\pi$
$108$		0			0
$109$			2.00000i			0.191565i	0.995402	+	0.0957826i	$0.0305354\pi$
$109$			2.00000i			0.191565i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$		0			0
$111$		0			0
$112$	4.90538	+	6.31959i	0.463515	+	0.597145i
$113$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$113$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$114$		0			0
$115$		0			0
$116$	−12.0000	+	10.5830i	−1.11417	+	0.982607i
$117$		0			0
$118$	6.82058	+	3.07892i	0.627885	+	0.283437i
$119$		0			0
$120$		0			0
$121$	−17.0000			−1.54545
$122$	−7.73381	−	3.49117i	−0.700186	−	0.316075i
$123$		0			0
$124$	7.93725	−	7.00000i	0.712786	−	0.628619i
$125$		0			0
$126$		0			0
$127$	1.41421	−	1.41421i	0.125491	−	0.125491i	−0.641572	−	0.767063i	$-0.721717\pi$
$127$	1.41421	−	1.41421i	0.125491	−	0.125491i	0.767063	+	0.641572i	$0.221717\pi$
$128$	11.1441	−	1.95171i	0.985008	−	0.172508i
$129$		0			0
$130$		0			0
$131$		−	15.8745i		−	1.38696i	−0.720475	−	0.693481i	$-0.756076\pi$
$131$		−	15.8745i		−	1.38696i	0.720475	−	0.693481i	$-0.243924\pi$
$132$		0			0
$133$	−7.48331	+	7.48331i	−0.648886	+	0.648886i
$134$	15.8745	−	6.00000i	1.37135	−	0.518321i
$135$		0			0
$136$		0			0
$137$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$137$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$138$		0			0
$139$	5.29150			0.448819			0.224410	−	0.974495i	$-0.427955\pi$
$139$	5.29150			0.448819			0.224410	+	0.974495i	$0.427955\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−19.7990	−	19.7990i	−1.65567	−	1.65567i
$144$		0			0
$145$		0			0
$146$	14.0000	−	5.29150i	1.15865	−	0.437928i
$147$		0			0
$148$	−0.662739	+	10.5622i	−0.0544768	+	0.868210i
$149$		−	4.00000i		−	0.327693i	−0.986486	−	0.163846i	$-0.947610\pi$
$149$		−	4.00000i		−	0.327693i	0.986486	−	0.163846i	$-0.0523901\pi$
$150$		0			0
$151$			15.8745i			1.29185i	0.763401	+	0.645925i	$0.223528\pi$
$151$			15.8745i			1.29185i	−0.763401	+	0.645925i	$0.776472\pi$
$152$	4.40440	+	14.3039i	0.357244	+	1.16020i
$153$		0			0
$154$	−5.29150	−	14.0000i	−0.426401	−	1.12815i
$155$		0			0
$156$		0			0
$157$	3.74166	+	3.74166i	0.298617	+	0.298617i	0.840472	−	0.541855i	$-0.182278\pi$
$157$	3.74166	+	3.74166i	0.298617	+	0.298617i	−0.541855	+	0.840472i	$0.682278\pi$
$158$	−6.82058	−	3.07892i	−0.542616	−	0.244946i
$159$		0			0
$160$		0			0
$161$	−8.00000			−0.630488
$162$		0			0
$163$	−5.65685	−	5.65685i	−0.443079	−	0.443079i	0.449966	−	0.893045i	$-0.351436\pi$
$163$	−5.65685	−	5.65685i	−0.443079	−	0.443079i	−0.893045	+	0.449966i	$0.851436\pi$
$164$	2.64575	+	3.00000i	0.206598	+	0.234261i
$165$		0			0
$166$	−6.00000	−	15.8745i	−0.465690	−	1.23210i
$167$	−8.48528	+	8.48528i	−0.656611	+	0.656611i	−0.954577	−	0.297966i	$-0.903692\pi$
$167$	−8.48528	+	8.48528i	−0.656611	+	0.656611i	0.297966	+	0.954577i	$0.403692\pi$
$168$		0			0
$169$		−	15.0000i		−	1.15385i
$170$		0			0
$171$		0			0
$172$	1.00197	−	15.9686i	0.0763992	−	1.21759i
$173$	7.48331	−	7.48331i	0.568946	−	0.568946i	−0.362887	−	0.931833i	$-0.618209\pi$
$173$	7.48331	−	7.48331i	0.568946	−	0.568946i	0.931833	+	0.362887i	$0.118209\pi$
$174$		0			0
$175$		0			0
$176$	−21.0000	−	2.64575i	−1.58293	−	0.199431i
$177$		0			0
$178$	−3.49117	+	7.73381i	−0.261674	+	0.579673i
$179$	5.29150			0.395505			0.197753	−	0.980252i	$-0.436636\pi$
$179$	5.29150			0.395505			0.197753	+	0.980252i	$0.436636\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	6.15784	−	13.6412i	0.456449	−	1.01115i
$183$		0			0
$184$	−5.29150	+	10.0000i	−0.390095	+	0.737210i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	10.5830i		−	0.765759i	−0.923798	−	0.382880i	$-0.874932\pi$
$191$		−	10.5830i		−	0.765759i	0.923798	−	0.382880i	$-0.125068\pi$
$192$		0			0
$193$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$193$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$194$	−5.29150	−	14.0000i	−0.379908	−	1.00514i
$195$		0			0
$196$	−4.50000	+	3.96863i	−0.321429	+	0.283473i
$197$	−14.9666	−	14.9666i	−1.06633	−	1.06633i	−0.997638	−	0.0686902i	$-0.978118\pi$
$197$	−14.9666	−	14.9666i	−1.06633	−	1.06633i	−0.0686902	−	0.997638i	$-0.521882\pi$
$198$		0			0
$199$	5.29150			0.375105			0.187552	−	0.982255i	$-0.439945\pi$
$199$	5.29150			0.375105			0.187552	+	0.982255i	$0.439945\pi$
$200$		0			0
$201$		0			0
$202$	−5.15587	−	2.32744i	−0.362766	−	0.163758i
$203$	11.3137	+	11.3137i	0.794067	+	0.794067i
$204$		0			0
$205$		0			0
$206$	−3.00000	−	7.93725i	−0.209020	−	0.553015i
$207$		0			0
$208$	−12.9784	−	16.7201i	−0.899891	−	1.15933i
$209$		−	28.0000i		−	1.93680i
$210$		0			0
$211$		−	26.4575i		−	1.82141i	−0.413057	−	0.910705i	$-0.635539\pi$
$211$		−	26.4575i		−	1.82141i	0.413057	−	0.910705i	$-0.364461\pi$
$212$	−21.1245	−	1.32548i	−1.45083	−	0.0910341i
$213$		0			0
$214$	5.29150	−	2.00000i	0.361720	−	0.136717i
$215$		0			0
$216$		0			0
$217$	−7.48331	−	7.48331i	−0.508001	−	0.508001i
$218$	1.16372	−	2.57794i	0.0788172	−	0.174600i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	9.89949	+	9.89949i	0.662919	+	0.662919i	0.956067	−	0.293148i	$-0.0947028\pi$
$223$	9.89949	+	9.89949i	0.662919	+	0.662919i	−0.293148	+	0.956067i	$0.594703\pi$
$224$	−2.64575	−	11.0000i	−0.176777	−	0.734968i
$225$		0			0
$226$		0			0
$227$	19.7990	−	19.7990i	1.31411	−	1.31411i	0.395744	−	0.918361i	$-0.370487\pi$
$227$	19.7990	−	19.7990i	1.31411	−	1.31411i	0.918361	−	0.395744i	$-0.129513\pi$
$228$		0			0
$229$			14.0000i			0.925146i	0.886581	+	0.462573i	$0.153074\pi$
$229$			14.0000i			0.925146i	−0.886581	+	0.462573i	$0.846926\pi$
$230$		0			0
$231$		0			0
$232$	21.6255	−	6.65882i	1.41978	−	0.437173i
$233$	−14.9666	+	14.9666i	−0.980497	+	0.980497i	−0.999813	−	0.0193169i	$-0.993851\pi$
$233$	−14.9666	+	14.9666i	−0.980497	+	0.980497i	0.0193169	+	0.999813i	$0.493851\pi$
$234$		0			0
$235$		0			0
$236$	−7.00000	−	7.93725i	−0.455661	−	0.516671i
$237$		0			0
$238$		0			0
$239$	10.5830			0.684558			0.342279	−	0.939598i	$-0.388801\pi$
$239$	10.5830			0.684558			0.342279	+	0.939598i	$0.388801\pi$
$240$		0			0
$241$	14.0000			0.901819			0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000			0.901819			0.450910	+	0.892570i	$0.351100\pi$
$242$	21.9125	+	9.89164i	1.40859	+	0.635858i
$243$		0			0
$244$	7.93725	+	9.00000i	0.508131	+	0.576166i
$245$		0			0
$246$		0			0
$247$	19.7990	−	19.7990i	1.25978	−	1.25978i
$248$	−14.3039	+	4.40440i	−0.908298	+	0.279679i
$249$		0			0
$250$		0			0
$251$			5.29150i			0.333997i	0.985957	+	0.166998i	$0.0534075\pi$
$251$			5.29150i			0.333997i	−0.985957	+	0.166998i	$0.946593\pi$
$252$		0			0
$253$	14.9666	−	14.9666i	0.940944	−	0.940944i
$254$	−2.64575	+	1.00000i	−0.166009	+	0.0627456i
$255$		0			0
$256$	−15.5000	−	3.96863i	−0.968750	−	0.248039i
$257$	14.9666	+	14.9666i	0.933593	+	0.933593i	0.997928	−	0.0643356i	$-0.0204928\pi$
$257$	14.9666	+	14.9666i	0.933593	+	0.933593i	−0.0643356	+	0.997928i	$0.520493\pi$
$258$		0			0
$259$	10.5830			0.657596
$260$		0			0
$261$		0			0
$262$	−9.23676	+	20.4617i	−0.570649	+	1.26413i
$263$	8.48528	+	8.48528i	0.523225	+	0.523225i	0.918544	−	0.395319i	$-0.129366\pi$
$263$	8.48528	+	8.48528i	0.523225	+	0.523225i	−0.395319	+	0.918544i	$0.629366\pi$
$264$		0			0
$265$		0			0
$266$	14.0000	−	5.29150i	0.858395	−	0.324443i
$267$		0			0
$268$	−23.9529	−	1.50295i	−1.46316	−	0.0918073i
$269$			24.0000i			1.46331i	0.681677	+	0.731653i	$0.261251\pi$
$269$			24.0000i			1.46331i	−0.681677	+	0.731653i	$0.738749\pi$
$270$		0			0
$271$		−	15.8745i		−	0.964308i	−0.876087	−	0.482154i	$-0.839855\pi$
$271$		−	15.8745i		−	0.964308i	0.876087	−	0.482154i	$-0.160145\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−18.7083	−	18.7083i	−1.12407	−	1.12407i	−0.991123	−	0.132949i	$-0.957555\pi$
$277$	−18.7083	−	18.7083i	−1.12407	−	1.12407i	−0.132949	−	0.991123i	$-0.542445\pi$
$278$	−6.82058	−	3.07892i	−0.409071	−	0.184661i
$279$		0			0
$280$		0			0
$281$	−26.0000			−1.55103			−0.775515	−	0.631329i	$-0.782510\pi$
$281$	−26.0000			−1.55103			−0.775515	+	0.631329i	$0.782510\pi$
$282$		0			0
$283$	−19.7990	−	19.7990i	−1.17693	−	1.17693i	−0.980523	−	0.196405i	$-0.937073\pi$
$283$	−19.7990	−	19.7990i	−1.17693	−	1.17693i	−0.196405	−	0.980523i	$-0.562927\pi$
$284$		0			0
$285$		0			0
$286$	14.0000	+	37.0405i	0.827837	+	2.19025i
$287$	2.82843	−	2.82843i	0.166957	−	0.166957i
$288$		0			0
$289$		−	17.0000i		−	1.00000i
$290$		0			0
$291$		0			0
$292$	−21.1245	−	1.32548i	−1.23622	−	0.0775677i
$293$	14.9666	−	14.9666i	0.874360	−	0.874360i	−0.118584	−	0.992944i	$-0.537836\pi$
$293$	14.9666	−	14.9666i	0.874360	−	0.874360i	0.992944	+	0.118584i	$0.0378355\pi$
$294$		0			0
$295$		0			0
$296$	7.00000	−	13.2288i	0.406867	−	0.768906i
$297$		0			0
$298$	−2.32744	+	5.15587i	−0.134825	+	0.298672i
$299$	21.1660			1.22406
$300$		0			0
$301$	−16.0000			−0.922225
$302$	9.23676	−	20.4617i	0.531516	−	1.17744i
$303$		0			0
$304$	2.64575	−	21.0000i	0.151744	−	1.20443i
$305$		0			0
$306$		0			0
$307$	−8.48528	+	8.48528i	−0.484281	+	0.484281i	−0.906496	−	0.422215i	$-0.861253\pi$
$307$	−8.48528	+	8.48528i	−0.484281	+	0.484281i	0.422215	+	0.906496i	$0.361253\pi$
$308$	−1.32548	+	21.1245i	−0.0755261	+	1.20368i
$309$		0			0
$310$		0			0
$311$			31.7490i			1.80032i	0.435558	+	0.900161i	$0.356551\pi$
$311$			31.7490i			1.80032i	−0.435558	+	0.900161i	$0.643449\pi$
$312$		0			0
$313$	14.9666	−	14.9666i	0.845964	−	0.845964i	−0.143663	−	0.989627i	$-0.545888\pi$
$313$	14.9666	−	14.9666i	0.845964	−	0.845964i	0.989627	+	0.143663i	$0.0458881\pi$
$314$	−2.64575	−	7.00000i	−0.149308	−	0.395033i
$315$		0			0
$316$	7.00000	+	7.93725i	0.393781	+	0.446505i
$317$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$317$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$318$		0			0
$319$	−42.3320			−2.37014
$320$		0			0
$321$		0			0
$322$	10.3117	+	4.65489i	0.574651	+	0.259407i
$323$		0			0
$324$		0			0
$325$		0			0
$326$	4.00000	+	10.5830i	0.221540	+	0.586138i
$327$		0			0
$328$	−1.66471	−	5.40636i	−0.0919180	−	0.298516i
$329$		0			0
$330$		0			0
$331$			5.29150i			0.290847i	0.989369	+	0.145424i	$0.0464545\pi$
$331$			5.29150i			0.290847i	−0.989369	+	0.145424i	$0.953545\pi$
$332$	−1.50295	+	23.9529i	−0.0824851	+	1.31459i
$333$		0			0
$334$	15.8745	−	6.00000i	0.868614	−	0.328305i
$335$		0			0
$336$		0			0
$337$	−7.48331	−	7.48331i	−0.407642	−	0.407642i	0.473273	−	0.880916i	$-0.343072\pi$
$337$	−7.48331	−	7.48331i	−0.407642	−	0.407642i	−0.880916	+	0.473273i	$0.843072\pi$
$338$	−8.72791	+	19.3345i	−0.474736	+	1.05166i
$339$		0			0
$340$		0			0
$341$	28.0000			1.51629
$342$		0			0
$343$	14.1421	+	14.1421i	0.763604	+	0.763604i
$344$	−10.5830	+	20.0000i	−0.570597	+	1.07833i
$345$		0			0
$346$	−14.0000	+	5.29150i	−0.752645	+	0.284473i
$347$	−8.48528	+	8.48528i	−0.455514	+	0.455514i	−0.897180	−	0.441666i	$-0.854388\pi$
$347$	−8.48528	+	8.48528i	−0.455514	+	0.455514i	0.441666	+	0.897180i	$0.354388\pi$
$348$		0			0
$349$		−	2.00000i		−	0.107058i	−0.998566	−	0.0535288i	$-0.982953\pi$
$349$		−	2.00000i		−	0.107058i	0.998566	−	0.0535288i	$-0.0170469\pi$
$350$		0			0
$351$		0			0
$352$	25.5289	+	15.6294i	1.36069	+	0.833048i
$353$	14.9666	−	14.9666i	0.796593	−	0.796593i	−0.185963	−	0.982557i	$-0.559541\pi$
$353$	14.9666	−	14.9666i	0.796593	−	0.796593i	0.982557	+	0.185963i	$0.0595406\pi$
$354$		0			0
$355$		0			0
$356$	9.00000	−	7.93725i	0.476999	−	0.420674i
$357$		0			0
$358$	−6.82058	−	3.07892i	−0.360479	−	0.162726i
$359$	−10.5830			−0.558550			−0.279275	−	0.960211i	$-0.590094\pi$
$359$	−10.5830			−0.558550			−0.279275	+	0.960211i	$0.590094\pi$
$360$		0			0
$361$	9.00000			0.473684
$362$	−2.57794	−	1.16372i	−0.135493	−	0.0611639i
$363$		0			0
$364$	−15.8745	+	14.0000i	−0.832050	+	0.733799i
$365$		0			0
$366$		0			0
$367$	−12.7279	+	12.7279i	−0.664392	+	0.664392i	−0.956412	−	0.292020i	$-0.905673\pi$
$367$	−12.7279	+	12.7279i	−0.664392	+	0.664392i	0.292020	+	0.956412i	$0.405673\pi$
$368$	12.6392	−	9.81076i	0.658863	−	0.511421i
$369$		0			0
$370$		0			0
$371$			21.1660i			1.09888i
$372$		0			0
$373$	18.7083	−	18.7083i	0.968678	−	0.968678i	−0.0308458	−	0.999524i	$-0.509820\pi$
$373$	18.7083	−	18.7083i	0.968678	−	0.968678i	0.999524	+	0.0308458i	$0.00982007\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−29.9333	−	29.9333i	−1.54164	−	1.54164i
$378$		0			0
$379$	5.29150			0.271806			0.135903	−	0.990722i	$-0.456606\pi$
$379$	5.29150			0.271806			0.135903	+	0.990722i	$0.456606\pi$
$380$		0			0
$381$		0			0
$382$	−6.15784	+	13.6412i	−0.315062	+	0.697942i
$383$	−5.65685	−	5.65685i	−0.289052	−	0.289052i	0.547653	−	0.836705i	$-0.315521\pi$
$383$	−5.65685	−	5.65685i	−0.289052	−	0.289052i	−0.836705	+	0.547653i	$0.815521\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$	−1.32548	+	21.1245i	−0.0672909	+	1.07243i
$389$			24.0000i			1.21685i	0.793612	+	0.608424i	$0.208198\pi$
$389$			24.0000i			1.21685i	−0.793612	+	0.608424i	$0.791802\pi$
$390$		0			0
$391$		0			0
$392$	8.10954	−	2.49706i	0.409594	−	0.126120i
$393$		0			0
$394$	10.5830	+	28.0000i	0.533164	+	1.41062i
$395$		0			0
$396$		0			0
$397$	3.74166	+	3.74166i	0.187788	+	0.187788i	0.794739	−	0.606951i	$-0.207608\pi$
$397$	3.74166	+	3.74166i	0.187788	+	0.187788i	−0.606951	+	0.794739i	$0.707608\pi$
$398$	−6.82058	−	3.07892i	−0.341885	−	0.154332i
$399$		0			0
$400$		0			0
$401$	−10.0000			−0.499376			−0.249688	−	0.968326i	$-0.580328\pi$
$401$	−10.0000			−0.499376			−0.249688	+	0.968326i	$0.580328\pi$
$402$		0			0
$403$	19.7990	+	19.7990i	0.986258	+	0.986258i
$404$	5.29150	+	6.00000i	0.263262	+	0.298511i
$405$		0			0
$406$	−8.00000	−	21.1660i	−0.397033	−	1.05045i
$407$	−19.7990	+	19.7990i	−0.981399	+	0.981399i
$408$		0			0
$409$			10.0000i			0.494468i	0.968956	+	0.247234i	$0.0795217\pi$
$409$			10.0000i			0.494468i	−0.968956	+	0.247234i	$0.920478\pi$
$410$		0			0
$411$		0			0
$412$	−0.751475	+	11.9764i	−0.0370225	+	0.590037i
$413$	−7.48331	+	7.48331i	−0.368230	+	0.368230i
$414$		0			0
$415$		0			0
$416$	7.00000	+	29.1033i	0.343203	+	1.42690i
$417$		0			0
$418$	−16.2921	+	36.0911i	−0.796873	+	1.76527i
$419$	−15.8745			−0.775520			−0.387760	−	0.921760i	$-0.626751\pi$
$419$	−15.8745			−0.775520			−0.387760	+	0.921760i	$0.626751\pi$
$420$		0			0
$421$	34.0000			1.65706			0.828529	−	0.559946i	$-0.189178\pi$
$421$	34.0000			1.65706			0.828529	+	0.559946i	$0.189178\pi$
$422$	−15.3946	+	34.1029i	−0.749397	+	1.66010i
$423$		0			0
$424$	26.4575	+	14.0000i	1.28489	+	0.679900i
$425$		0			0
$426$		0			0
$427$	8.48528	−	8.48528i	0.410632	−	0.410632i
$428$	−7.98430	−	0.500983i	−0.385936	−	0.0242159i
$429$		0			0
$430$		0			0
$431$		−	10.5830i		−	0.509765i	−0.966972	−	0.254883i	$-0.917963\pi$
$431$		−	10.5830i		−	0.509765i	0.966972	−	0.254883i	$-0.0820369\pi$
$432$		0			0
$433$	7.48331	−	7.48331i	0.359625	−	0.359625i	−0.504050	−	0.863675i	$-0.668157\pi$
$433$	7.48331	−	7.48331i	0.359625	−	0.359625i	0.863675	+	0.504050i	$0.168157\pi$
$434$	5.29150	+	14.0000i	0.254000	+	0.672022i
$435$		0			0
$436$	−3.00000	+	2.64575i	−0.143674	+	0.126709i
$437$	14.9666	+	14.9666i	0.715951	+	0.715951i
$438$		0			0
$439$	5.29150			0.252550			0.126275	−	0.991995i	$-0.459698\pi$
$439$	5.29150			0.252550			0.126275	+	0.991995i	$0.459698\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.82843	+	2.82843i	0.134383	+	0.134383i	0.771099	−	0.636716i	$-0.219708\pi$
$443$	2.82843	+	2.82843i	0.134383	+	0.134383i	−0.636716	+	0.771099i	$0.719708\pi$
$444$		0			0
$445$		0			0
$446$	−7.00000	−	18.5203i	−0.331460	−	0.876960i
$447$		0			0
$448$	−2.99018	+	15.7181i	−0.141273	+	0.742611i
$449$		−	22.0000i		−	1.03824i	−0.854700	−	0.519122i	$-0.826259\pi$
$449$		−	22.0000i		−	1.03824i	0.854700	−	0.519122i	$-0.173741\pi$
$450$		0			0
$451$			10.5830i			0.498334i
$452$		0			0
$453$		0			0
$454$	−37.0405	+	14.0000i	−1.73840	+	0.657053i
$455$		0			0
$456$		0			0
$457$	7.48331	+	7.48331i	0.350055	+	0.350055i	0.860130	−	0.510075i	$-0.170382\pi$
$457$	7.48331	+	7.48331i	0.350055	+	0.350055i	−0.510075	+	0.860130i	$0.670382\pi$
$458$	8.14605	−	18.0455i	0.380640	−	0.843213i
$459$		0			0
$460$		0			0
$461$	28.0000			1.30409			0.652045	−	0.758180i	$-0.273911\pi$
$461$	28.0000			1.30409			0.652045	+	0.758180i	$0.273911\pi$
$462$		0			0
$463$	24.0416	+	24.0416i	1.11731	+	1.11731i	0.992135	+	0.125175i	$0.0399491\pi$
$463$	24.0416	+	24.0416i	1.11731	+	1.11731i	0.125175	+	0.992135i	$0.460051\pi$
$464$	−31.7490	−	4.00000i	−1.47391	−	0.185695i
$465$		0			0
$466$	28.0000	−	10.5830i	1.29707	−	0.490248i
$467$	25.4558	−	25.4558i	1.17796	−	1.17796i	0.197692	−	0.980264i	$-0.436655\pi$
$467$	25.4558	−	25.4558i	1.17796	−	1.17796i	0.980264	−	0.197692i	$-0.0633445\pi$
$468$		0			0
$469$			24.0000i			1.10822i
$470$		0			0
$471$		0			0
$472$	4.40440	+	14.3039i	0.202729	+	0.658390i
$473$	29.9333	−	29.9333i	1.37633	−	1.37633i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−13.6412	−	6.15784i	−0.623932	−	0.281653i
$479$	−42.3320			−1.93420			−0.967100	−	0.254398i	$-0.918123\pi$
$479$	−42.3320			−1.93420			−0.967100	+	0.254398i	$0.918123\pi$
$480$		0			0
$481$	−28.0000			−1.27669
$482$	−18.0455	−	8.14605i	−0.821952	−	0.371043i
$483$		0			0
$484$	−22.4889	−	25.5000i	−1.02222	−	1.15909i
$485$		0			0
$486$		0			0
$487$	7.07107	−	7.07107i	0.320421	−	0.320421i	−0.528508	−	0.848928i	$-0.677248\pi$
$487$	7.07107	−	7.07107i	0.320421	−	0.320421i	0.848928	+	0.528508i	$0.177248\pi$
$488$	−4.99412	−	16.2191i	−0.226073	−	0.734204i
$489$		0			0
$490$		0			0
$491$		−	15.8745i		−	0.716407i	−0.933644	−	0.358203i	$-0.883389\pi$
$491$		−	15.8745i		−	0.716407i	0.933644	−	0.358203i	$-0.116611\pi$
$492$		0			0
$493$		0			0
$494$	−37.0405	+	14.0000i	−1.66653	+	0.629890i
$495$		0			0
$496$	21.0000	+	2.64575i	0.942928	+	0.118798i
$497$		0			0
$498$		0			0
$499$	−15.8745			−0.710641			−0.355320	−	0.934745i	$-0.615628\pi$
$499$	−15.8745			−0.710641			−0.355320	+	0.934745i	$0.615628\pi$
$500$		0			0
$501$		0			0
$502$	3.07892	−	6.82058i	0.137419	−	0.304417i
$503$	11.3137	+	11.3137i	0.504453	+	0.504453i	0.912819	−	0.408365i	$-0.133901\pi$
$503$	11.3137	+	11.3137i	0.504453	+	0.504453i	−0.408365	+	0.912819i	$0.633901\pi$
$504$		0			0
$505$		0			0
$506$	−28.0000	+	10.5830i	−1.24475	+	0.470472i
$507$		0			0
$508$	3.99215	+	0.250492i	0.177123	+	0.0111138i
$509$			36.0000i			1.59567i	0.602875	+	0.797836i	$0.294022\pi$
$509$			36.0000i			1.59567i	−0.602875	+	0.797836i	$0.705978\pi$
$510$		0			0
$511$			21.1660i			0.936329i
$512$	17.6698	+	14.1343i	0.780903	+	0.624653i
$513$		0			0
$514$	−10.5830	−	28.0000i	−0.466796	−	1.23503i
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−13.6412	−	6.15784i	−0.599358	−	0.270560i
$519$		0			0
$520$		0			0
$521$	−14.0000			−0.613351			−0.306676	−	0.951814i	$-0.599217\pi$
$521$	−14.0000			−0.613351			−0.306676	+	0.951814i	$0.599217\pi$
$522$		0			0
$523$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$523$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$524$	23.8118	−	21.0000i	1.04022	−	0.917389i
$525$		0			0
$526$	−6.00000	−	15.8745i	−0.261612	−	0.692161i
$527$		0			0
$528$		0			0
$529$		−	7.00000i		−	0.304348i
$530$		0			0
$531$		0			0
$532$	−21.1245	−	1.32548i	−0.915862	−	0.0574667i
$533$	−7.48331	+	7.48331i	−0.324138	+	0.324138i
$534$		0			0
$535$		0			0
$536$	30.0000	+	15.8745i	1.29580	+	0.685674i
$537$		0			0
$538$	13.9647	−	30.9352i	0.602059	−	1.33371i
$539$	−15.8745			−0.683763
$540$		0			0
$541$	−10.0000			−0.429934			−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000			−0.429934			−0.214967	+	0.976621i	$0.568964\pi$
$542$	−9.23676	+	20.4617i	−0.396753	+	0.878906i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	5.65685	−	5.65685i	0.241870	−	0.241870i	−0.575754	−	0.817623i	$-0.695291\pi$
$547$	5.65685	−	5.65685i	0.241870	−	0.241870i	0.817623	+	0.575754i	$0.195291\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	42.3320i		−	1.80340i
$552$		0			0
$553$	7.48331	−	7.48331i	0.318223	−	0.318223i
$554$	13.2288	+	35.0000i	0.562036	+	1.48701i
$555$		0			0
$556$	7.00000	+	7.93725i	0.296866	+	0.336615i
$557$	−22.4499	−	22.4499i	−0.951235	−	0.951235i	0.0476304	−	0.998865i	$-0.484833\pi$
$557$	−22.4499	−	22.4499i	−0.951235	−	0.951235i	−0.998865	+	0.0476304i	$0.984833\pi$
$558$		0			0
$559$	42.3320			1.79045
$560$		0			0
$561$		0			0
$562$	33.5132	+	15.1284i	1.41367	+	0.638152i
$563$	−2.82843	−	2.82843i	−0.119204	−	0.119204i	0.644988	−	0.764192i	$-0.276862\pi$
$563$	−2.82843	−	2.82843i	−0.119204	−	0.119204i	−0.764192	+	0.644988i	$0.776862\pi$
$564$		0			0
$565$		0			0
$566$	14.0000	+	37.0405i	0.588464	+	1.55693i
$567$		0			0
$568$		0			0
$569$			6.00000i			0.251533i	0.992060	+	0.125767i	$0.0401390\pi$
$569$			6.00000i			0.251533i	−0.992060	+	0.125767i	$0.959861\pi$
$570$		0			0
$571$			5.29150i			0.221442i	0.993852	+	0.110721i	$0.0353161\pi$
$571$			5.29150i			0.221442i	−0.993852	+	0.110721i	$0.964684\pi$
$572$	3.50688	−	55.8901i	0.146630	−	2.33688i
$573$		0			0
$574$	−5.29150	+	2.00000i	−0.220863	+	0.0834784i
$575$		0			0
$576$		0			0
$577$	−22.4499	−	22.4499i	−0.934603	−	0.934603i	0.0633857	−	0.997989i	$-0.479810\pi$
$577$	−22.4499	−	22.4499i	−0.934603	−	0.934603i	−0.997989	+	0.0633857i	$0.979810\pi$
$578$	−9.89164	+	21.9125i	−0.411438	+	0.911438i
$579$		0			0
$580$		0			0
$581$	24.0000			0.995688
$582$		0			0
$583$	−39.5980	−	39.5980i	−1.63998	−	1.63998i
$584$	26.4575	+	14.0000i	1.09482	+	0.579324i
$585$		0			0
$586$	−28.0000	+	10.5830i	−1.15667	+	0.437180i
$587$	−19.7990	+	19.7990i	−0.817192	+	0.817192i	−0.985700	−	0.168508i	$-0.946105\pi$
$587$	−19.7990	+	19.7990i	−0.817192	+	0.817192i	0.168508	+	0.985700i	$0.446105\pi$
$588$		0			0
$589$			28.0000i			1.15372i
$590$		0			0
$591$		0			0
$592$	−16.7201	+	12.9784i	−0.687191	+	0.533410i
$593$	−14.9666	+	14.9666i	−0.614606	+	0.614606i	−0.944143	−	0.329537i	$-0.893107\pi$
$593$	−14.9666	+	14.9666i	−0.614606	+	0.614606i	0.329537	+	0.944143i	$0.393107\pi$
$594$		0			0
$595$		0			0
$596$	6.00000	−	5.29150i	0.245770	−	0.216748i
$597$		0			0
$598$	−27.2823	−	12.3157i	−1.11566	−	0.503625i
$599$	31.7490			1.29723			0.648615	−	0.761117i	$-0.275349\pi$
$599$	31.7490			1.29723			0.648615	+	0.761117i	$0.275349\pi$
$600$		0			0
$601$	−14.0000			−0.571072			−0.285536	−	0.958368i	$-0.592172\pi$
$601$	−14.0000			−0.571072			−0.285536	+	0.958368i	$0.592172\pi$
$602$	20.6235	+	9.30978i	0.840550	+	0.379438i
$603$		0			0
$604$	−23.8118	+	21.0000i	−0.968887	+	0.854478i
$605$		0			0
$606$		0			0
$607$	−24.0416	+	24.0416i	−0.975820	+	0.975820i	−0.999714	−	0.0238948i	$-0.992393\pi$
$607$	−24.0416	+	24.0416i	−0.975820	+	0.975820i	0.0238948	+	0.999714i	$0.492393\pi$
$608$	−15.6294	+	25.5289i	−0.633855	+	1.03533i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−11.2250	+	11.2250i	−0.453372	+	0.453372i	−0.896472	−	0.443100i	$-0.853879\pi$
$613$	−11.2250	+	11.2250i	−0.453372	+	0.453372i	0.443100	+	0.896472i	$0.353879\pi$
$614$	15.8745	−	6.00000i	0.640643	−	0.242140i
$615$		0			0
$616$	14.0000	−	26.4575i	0.564076	−	1.06600i
$617$	29.9333	+	29.9333i	1.20507	+	1.20507i	0.972605	+	0.232462i	$0.0746782\pi$
$617$	29.9333	+	29.9333i	1.20507	+	1.20507i	0.232462	+	0.972605i	$0.425322\pi$
$618$		0			0
$619$	−5.29150			−0.212683			−0.106342	−	0.994330i	$-0.533914\pi$
$619$	−5.29150			−0.212683			−0.106342	+	0.994330i	$0.533914\pi$
$620$		0			0
$621$		0			0
$622$	18.4735	−	40.9235i	0.740720	−	1.64088i
$623$	−8.48528	−	8.48528i	−0.339956	−	0.339956i
$624$		0			0
$625$		0			0
$626$	−28.0000	+	10.5830i	−1.11911	+	0.422982i
$627$		0			0
$628$	−0.662739	+	10.5622i	−0.0264461	+	0.421479i
$629$		0			0
$630$		0			0
$631$			5.29150i			0.210651i	0.994438	+	0.105326i	$0.0335885\pi$
$631$			5.29150i			0.210651i	−0.994438	+	0.105326i	$0.966411\pi$
$632$	−4.40440	−	14.3039i	−0.175197	−	0.568978i
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−11.2250	−	11.2250i	−0.444750	−	0.444750i
$638$	54.5646	+	24.6314i	2.16023	+	0.975164i
$639$		0			0
$640$		0			0
$641$	30.0000			1.18493			0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000			1.18493			0.592464	+	0.805597i	$0.298155\pi$
$642$		0			0
$643$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$643$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$644$	−10.5830	−	12.0000i	−0.417029	−	0.472866i
$645$		0			0
$646$		0			0
$647$	16.9706	−	16.9706i	0.667182	−	0.667182i	−0.289881	−	0.957063i	$-0.593616\pi$
$647$	16.9706	−	16.9706i	0.667182	−	0.667182i	0.957063	+	0.289881i	$0.0936157\pi$
$648$		0			0
$649$		−	28.0000i		−	1.09910i
$650$		0			0
$651$		0			0
$652$	1.00197	−	15.9686i	0.0392400	−	0.625378i
$653$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$653$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$654$		0			0
$655$		0			0
$656$	−1.00000	+	7.93725i	−0.0390434	+	0.309898i
$657$		0			0
$658$		0			0
$659$	−15.8745			−0.618383			−0.309192	−	0.951000i	$-0.600058\pi$
$659$	−15.8745			−0.618383			−0.309192	+	0.951000i	$0.600058\pi$
$660$		0			0
$661$	18.0000			0.700119			0.350059	−	0.936727i	$-0.386161\pi$
$661$	18.0000			0.700119			0.350059	+	0.936727i	$0.386161\pi$
$662$	3.07892	−	6.82058i	0.119666	−	0.265089i
$663$		0			0
$664$	15.8745	−	30.0000i	0.616050	−	1.16423i
$665$		0			0
$666$		0			0
$667$	22.6274	−	22.6274i	0.876137	−	0.876137i
$668$	−23.9529	−	1.50295i	−0.926765	−	0.0581509i
$669$		0			0
$670$		0			0
$671$			31.7490i			1.22566i
$672$		0			0
$673$	7.48331	−	7.48331i	0.288461	−	0.288461i	−0.548011	−	0.836471i	$-0.684615\pi$
$673$	7.48331	−	7.48331i	0.288461	−	0.288461i	0.836471	+	0.548011i	$0.184615\pi$
$674$	5.29150	+	14.0000i	0.203821	+	0.539260i
$675$		0			0
$676$	22.5000	−	19.8431i	0.865385	−	0.763197i
$677$	14.9666	+	14.9666i	0.575214	+	0.575214i	0.933581	−	0.358367i	$-0.116666\pi$
$677$	14.9666	+	14.9666i	0.575214	+	0.575214i	−0.358367	+	0.933581i	$0.616666\pi$
$678$		0			0
$679$	21.1660			0.812277
$680$		0			0
$681$		0			0
$682$	−36.0911	−	16.2921i	−1.38200	−	0.623857i
$683$	−8.48528	−	8.48528i	−0.324680	−	0.324680i	0.525879	−	0.850559i	$-0.323736\pi$
$683$	−8.48528	−	8.48528i	−0.324680	−	0.324680i	−0.850559	+	0.525879i	$0.823736\pi$
$684$		0			0
$685$		0			0
$686$	−10.0000	−	26.4575i	−0.381802	−	1.01015i
$687$		0			0
$688$	25.2784	−	19.6215i	0.963729	−	0.748063i
$689$		−	56.0000i		−	2.13343i
$690$		0			0
$691$			37.0405i			1.40909i	0.709660	+	0.704544i	$0.248848\pi$
$691$			37.0405i			1.40909i	−0.709660	+	0.704544i	$0.751152\pi$
$692$	21.1245	+	1.32548i	0.803032	+	0.0503871i
$693$		0			0
$694$	15.8745	−	6.00000i	0.602588	−	0.227757i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−1.16372	+	2.57794i	−0.0440475	+	0.0975763i
$699$		0			0
$700$		0			0
$701$	−36.0000			−1.35970			−0.679851	−	0.733351i	$-0.737955\pi$
$701$	−36.0000			−1.35970			−0.679851	+	0.733351i	$0.737955\pi$
$702$		0			0
$703$	−19.7990	−	19.7990i	−0.746733	−	0.746733i
$704$	−23.8118	−	35.0000i	−0.897440	−	1.31911i
$705$		0			0
$706$	−28.0000	+	10.5830i	−1.05379	+	0.398297i
$707$	5.65685	−	5.65685i	0.212748	−	0.212748i
$708$		0			0
$709$		−	10.0000i		−	0.375558i	−0.982211	−	0.187779i	$-0.939871\pi$
$709$		−	10.0000i		−	0.375558i	0.982211	−	0.187779i	$-0.0601289\pi$
$710$		0			0
$711$		0			0
$712$	−16.2191	+	4.99412i	−0.607836	+	0.187162i
$713$	−14.9666	+	14.9666i	−0.560505	+	0.560505i
$714$		0			0
$715$		0			0
$716$	7.00000	+	7.93725i	0.261602	+	0.296629i
$717$		0			0
$718$	13.6412	+	6.15784i	0.509083	+	0.229808i
$719$	31.7490			1.18404			0.592019	−	0.805924i	$-0.298331\pi$
$719$	31.7490			1.18404			0.592019	+	0.805924i	$0.298331\pi$
$720$		0			0
$721$	12.0000			0.446903
$722$	−11.6007	−	5.23675i	−0.431734	−	0.194892i
$723$		0			0
$724$	2.64575	+	3.00000i	0.0983286	+	0.111494i
$725$		0			0
$726$		0			0
$727$	21.2132	−	21.2132i	0.786754	−	0.786754i	−0.194207	−	0.980961i	$-0.562213\pi$
$727$	21.2132	−	21.2132i	0.786754	−	0.786754i	0.980961	+	0.194207i	$0.0622132\pi$
$728$	28.6078	−	8.80879i	1.06027	−	0.326476i
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−26.1916	+	26.1916i	−0.967409	+	0.967409i	−0.999485	−	0.0320765i	$-0.989788\pi$
$733$	−26.1916	+	26.1916i	−0.967409	+	0.967409i	0.0320765	+	0.999485i	$0.489788\pi$
$734$	23.8118	−	9.00000i	0.878908	−	0.332196i
$735$		0			0
$736$	−22.0000	+	5.29150i	−0.810931	+	0.195047i
$737$	−44.8999	−	44.8999i	−1.65391	−	1.65391i
$738$		0			0
$739$	−26.4575			−0.973255			−0.486628	−	0.873609i	$-0.661773\pi$
$739$	−26.4575			−0.973255			−0.486628	+	0.873609i	$0.661773\pi$
$740$		0			0
$741$		0			0
$742$	12.3157	−	27.2823i	0.452123	−	1.00156i
$743$	33.9411	+	33.9411i	1.24518	+	1.24518i	0.957824	+	0.287355i	$0.0927759\pi$
$743$	33.9411	+	33.9411i	1.24518	+	1.24518i	0.287355	+	0.957824i	$0.407224\pi$
$744$		0			0
$745$		0			0
$746$	−35.0000	+	13.2288i	−1.28144	+	0.484339i
$747$		0			0
$748$		0			0
$749$			8.00000i			0.292314i
$750$		0			0
$751$		−	26.4575i		−	0.965448i	−0.875772	−	0.482724i	$-0.839647\pi$
$751$		−	26.4575i		−	0.965448i	0.875772	−	0.482724i	$-0.160353\pi$
$752$		0			0
$753$		0			0
$754$	21.1660	+	56.0000i	0.770821	+	2.03940i
$755$		0			0
$756$		0			0
$757$	33.6749	+	33.6749i	1.22394	+	1.22394i	0.966221	+	0.257715i	$0.0829694\pi$
$757$	33.6749	+	33.6749i	1.22394	+	1.22394i	0.257715	+	0.966221i	$0.417031\pi$
$758$	−6.82058	−	3.07892i	−0.247734	−	0.111831i
$759$		0			0
$760$		0			0
$761$	−42.0000			−1.52250			−0.761249	−	0.648459i	$-0.775414\pi$
$761$	−42.0000			−1.52250			−0.761249	+	0.648459i	$0.775414\pi$
$762$		0			0
$763$	2.82843	+	2.82843i	0.102396	+	0.102396i
$764$	15.8745	−	14.0000i	0.574320	−	0.506502i
$765$		0			0
$766$	4.00000	+	10.5830i	0.144526	+	0.382380i
$767$	19.7990	−	19.7990i	0.714900	−	0.714900i
$768$		0			0
$769$		−	14.0000i		−	0.504853i	−0.967616	−	0.252426i	$-0.918771\pi$
$769$		−	14.0000i		−	0.504853i	0.967616	−	0.252426i	$-0.0812286\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−14.9666	+	14.9666i	−0.538312	+	0.538312i	−0.923033	−	0.384721i	$-0.874298\pi$
$773$	−14.9666	+	14.9666i	−0.538312	+	0.538312i	0.384721	+	0.923033i	$0.374298\pi$
$774$		0			0
$775$		0			0
$776$	14.0000	−	26.4575i	0.502571	−	0.949769i
$777$		0			0
$778$	13.9647	−	30.9352i	0.500657	−	1.10908i
$779$	−10.5830			−0.379176
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−11.9059	−	1.50000i	−0.425210	−	0.0535714i
$785$		0			0
$786$		0			0
$787$	−22.6274	+	22.6274i	−0.806580	+	0.806580i	−0.984115	−	0.177534i	$-0.943188\pi$
$787$	−22.6274	+	22.6274i	−0.806580	+	0.806580i	0.177534	+	0.984115i	$0.443188\pi$
$788$	2.65095	−	42.2489i	0.0944363	−	1.50506i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−22.4499	+	22.4499i	−0.797221	+	0.797221i
$794$	−2.64575	−	7.00000i	−0.0938942	−	0.248421i
$795$		0			0
$796$	7.00000	+	7.93725i	0.248108	+	0.281329i
$797$	22.4499	+	22.4499i	0.795218	+	0.795218i	0.982337	−	0.187119i	$-0.0599151\pi$
$797$	22.4499	+	22.4499i	0.795218	+	0.795218i	−0.187119	+	0.982337i	$0.559915\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$	12.8897	+	5.81861i	0.455150	+	0.205462i
$803$	−39.5980	−	39.5980i	−1.39738	−	1.39738i
$804$		0			0
$805$		0			0
$806$	−14.0000	−	37.0405i	−0.493129	−	1.30470i
$807$		0			0
$808$	−3.32941	−	10.8127i	−0.117128	−	0.380390i
$809$		−	30.0000i		−	1.05474i	−0.849635	−	0.527372i	$-0.823177\pi$
$809$		−	30.0000i		−	1.05474i	0.849635	−	0.527372i	$-0.176823\pi$
$810$		0			0
$811$		−	37.0405i		−	1.30067i	−0.759648	−	0.650334i	$-0.774629\pi$
$811$		−	37.0405i		−	1.30067i	0.759648	−	0.650334i	$-0.225371\pi$
$812$	−2.00393	+	31.9372i	−0.0703243	+	1.12078i
$813$		0			0
$814$	37.0405	−	14.0000i	1.29827	−	0.490700i
$815$		0			0
$816$		0			0
$817$	29.9333	+	29.9333i	1.04723	+	1.04723i
$818$	5.81861	−	12.8897i	0.203443	−	0.450677i
$819$		0			0
$820$		0			0
$821$	−8.00000			−0.279202			−0.139601	−	0.990208i	$-0.544582\pi$
$821$	−8.00000			−0.279202			−0.139601	+	0.990208i	$0.544582\pi$
$822$		0			0
$823$	−1.41421	−	1.41421i	−0.0492964	−	0.0492964i	0.682029	−	0.731325i	$-0.261098\pi$
$823$	−1.41421	−	1.41421i	−0.0492964	−	0.0492964i	−0.731325	+	0.682029i	$0.761098\pi$
$824$	7.93725	−	15.0000i	0.276507	−	0.522550i
$825$		0			0
$826$	14.0000	−	5.29150i	0.487122	−	0.184115i
$827$	−14.1421	+	14.1421i	−0.491770	+	0.491770i	−0.908864	−	0.417093i	$-0.863049\pi$
$827$	−14.1421	+	14.1421i	−0.491770	+	0.491770i	0.417093	+	0.908864i	$0.363049\pi$
$828$		0			0
$829$			14.0000i			0.486240i	0.969996	+	0.243120i	$0.0781709\pi$
$829$			14.0000i			0.486240i	−0.969996	+	0.243120i	$0.921829\pi$
$830$		0			0
$831$		0			0
$832$	7.91128	−	41.5862i	0.274274	−	1.44174i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	42.0000	−	37.0405i	1.45260	−	1.28107i
$837$		0			0
$838$	20.4617	+	9.23676i	0.706839	+	0.319078i
$839$	31.7490			1.09610			0.548049	−	0.836446i	$-0.315371\pi$
$839$	31.7490			1.09610			0.548049	+	0.836446i	$0.315371\pi$
$840$		0			0
$841$	−35.0000			−1.20690
$842$	−43.8249	−	19.7833i	−1.51031	−	0.681777i
$843$		0			0
$844$	39.6863	−	35.0000i	1.36606	−	1.20475i
$845$		0			0
$846$		0			0
$847$	−24.0416	+	24.0416i	−0.826080	+	0.826080i
$848$	−25.9568	−	33.4401i	−0.891361	−	1.14834i
$849$		0			0
$850$		0			0
$851$		−	21.1660i		−	0.725561i
$852$		0			0
$853$	−11.2250	+	11.2250i	−0.384336	+	0.384336i	−0.872661	−	0.488326i	$-0.837608\pi$
$853$	−11.2250	+	11.2250i	−0.384336	+	0.384336i	0.488326	+	0.872661i	$0.337608\pi$
$854$	−15.8745	+	6.00000i	−0.543214	+	0.205316i
$855$		0			0
$856$	10.0000	+	5.29150i	0.341793	+	0.180860i
$857$	29.9333	+	29.9333i	1.02250	+	1.02250i	0.999741	+	0.0227597i	$0.00724526\pi$
$857$	29.9333	+	29.9333i	1.02250	+	1.02250i	0.0227597	+	0.999741i	$0.492755\pi$
$858$		0			0
$859$	−5.29150			−0.180544			−0.0902719	−	0.995917i	$-0.528774\pi$
$859$	−5.29150			−0.180544			−0.0902719	+	0.995917i	$0.528774\pi$
$860$		0			0
$861$		0			0
$862$	−6.15784	+	13.6412i	−0.209737	+	0.464619i
$863$	2.82843	+	2.82843i	0.0962808	+	0.0962808i	0.753607	−	0.657326i	$-0.228312\pi$
$863$	2.82843	+	2.82843i	0.0962808	+	0.0962808i	−0.657326	+	0.753607i	$0.728312\pi$
$864$		0			0
$865$		0			0
$866$	−14.0000	+	5.29150i	−0.475739	+	0.179813i
$867$		0			0
$868$	1.32548	−	21.1245i	0.0449896	−	0.717011i
$869$			28.0000i			0.949835i
$870$		0			0
$871$		−	63.4980i		−	2.15155i
$872$	5.40636	−	1.66471i	0.183083	−	0.0563740i
$873$		0			0
$874$	−10.5830	−	28.0000i	−0.357975	−	0.947114i
$875$		0			0
$876$		0			0
$877$	−3.74166	−	3.74166i	−0.126347	−	0.126347i	0.641106	−	0.767453i	$-0.278476\pi$
$877$	−3.74166	−	3.74166i	−0.126347	−	0.126347i	−0.767453	+	0.641106i	$0.778476\pi$
$878$	−6.82058	−	3.07892i	−0.230183	−	0.103908i
$879$		0			0
$880$		0			0
$881$	2.00000			0.0673817			0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000			0.0673817			0.0336909	+	0.999432i	$0.489274\pi$
$882$		0			0
$883$	28.2843	+	28.2843i	0.951842	+	0.951842i	0.998892	−	0.0470510i	$-0.0149823\pi$
$883$	28.2843	+	28.2843i	0.951842	+	0.951842i	−0.0470510	+	0.998892i	$0.514982\pi$
$884$		0			0
$885$		0			0
$886$	−2.00000	−	5.29150i	−0.0671913	−	0.177772i
$887$	−25.4558	+	25.4558i	−0.854724	+	0.854724i	−0.990711	−	0.135987i	$-0.956579\pi$
$887$	−25.4558	+	25.4558i	−0.854724	+	0.854724i	0.135987	+	0.990711i	$0.456579\pi$
$888$		0			0
$889$		−	4.00000i		−	0.134156i
$890$		0			0
$891$		0			0
$892$	−1.75344	+	27.9450i	−0.0587096	+	0.935669i
$893$		0			0
$894$		0			0
$895$		0			0
$896$	13.0000	−	18.5203i	0.434300	−	0.618718i
$897$		0			0
$898$	−12.8009	+	28.3573i	−0.427173	+	0.946295i
$899$	42.3320			1.41185
$900$		0			0
$901$		0			0
$902$	6.15784	−	13.6412i	0.205034	−	0.454201i
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	11.3137	−	11.3137i	0.375666	−	0.375666i	−0.493870	−	0.869536i	$-0.664418\pi$
$907$	11.3137	−	11.3137i	0.375666	−	0.375666i	0.869536	+	0.493870i	$0.164418\pi$
$908$	55.8901	+	3.50688i	1.85478	+	0.116380i
$909$		0			0
$910$		0			0
$911$			21.1660i			0.701261i	0.936514	+	0.350631i	$0.114033\pi$
$911$			21.1660i			0.701261i	−0.936514	+	0.350631i	$0.885967\pi$
$912$		0			0
$913$	−44.8999	+	44.8999i	−1.48597	+	1.48597i
$914$	−5.29150	−	14.0000i	−0.175027	−	0.463079i
$915$		0			0
$916$	−21.0000	+	18.5203i	−0.693860	+	0.611927i
$917$	−22.4499	−	22.4499i	−0.741362	−	0.741362i
$918$		0			0
$919$	−47.6235			−1.57096			−0.785478	−	0.618890i	$-0.787583\pi$
$919$	−47.6235			−1.57096			−0.785478	+	0.618890i	$0.787583\pi$
$920$		0			0
$921$		0			0
$922$	−36.0911	−	16.2921i	−1.18860	−	0.536552i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−17.0000	−	44.9778i	−0.558655	−	1.47806i
$927$		0			0
$928$	38.5960	+	23.6294i	1.26698	+	0.775673i
$929$		−	22.0000i		−	0.721797i	−0.932605	−	0.360898i	$-0.882470\pi$
$929$		−	22.0000i		−	0.721797i	0.932605	−	0.360898i	$-0.117530\pi$
$930$		0			0
$931$		−	15.8745i		−	0.520266i
$932$	−42.2489	−	2.65095i	−1.38391	−	0.0868349i
$933$		0			0
$934$	−47.6235	+	18.0000i	−1.55829	+	0.588978i
$935$		0			0
$936$		0			0
$937$	14.9666	+	14.9666i	0.488938	+	0.488938i	0.907971	−	0.419033i	$-0.137631\pi$
$937$	14.9666	+	14.9666i	0.488938	+	0.488938i	−0.419033	+	0.907971i	$0.637631\pi$
$938$	13.9647	−	30.9352i	0.455962	−	1.01007i
$939$		0			0
$940$		0			0
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$		0			0
$943$	−5.65685	−	5.65685i	−0.184213	−	0.184213i
$944$	2.64575	−	21.0000i	0.0861119	−	0.683492i
$945$		0			0
$946$	−56.0000	+	21.1660i	−1.82072	+	0.688166i
$947$	−36.7696	+	36.7696i	−1.19485	+	1.19485i	−0.219161	+	0.975689i	$0.570332\pi$
$947$	−36.7696	+	36.7696i	−1.19485	+	1.19485i	−0.975689	+	0.219161i	$0.929668\pi$
$948$		0			0
$949$		−	56.0000i		−	1.81784i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$953$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$954$		0			0
$955$		0			0
$956$	14.0000	+	15.8745i	0.452792	+	0.513418i
$957$		0			0
$958$	54.5646	+	24.6314i	1.76290	+	0.795803i
$959$		0			0
$960$		0			0
$961$	3.00000			0.0967742
$962$	36.0911	+	16.2921i	1.16362	+	0.525279i
$963$		0			0
$964$	18.5203	+	21.0000i	0.596497	+	0.676364i
$965$		0			0
$966$		0			0
$967$	−4.24264	+	4.24264i	−0.136434	+	0.136434i	−0.772026	−	0.635591i	$-0.780756\pi$
$967$	−4.24264	+	4.24264i	−0.136434	+	0.136434i	0.635591	+	0.772026i	$0.280756\pi$
$968$	14.1500	+	45.9541i	0.454798	+	1.47702i
$969$		0			0
$970$		0			0
$971$			15.8745i			0.509437i	0.967015	+	0.254719i	$0.0819828\pi$
$971$			15.8745i			0.509437i	−0.967015	+	0.254719i	$0.918017\pi$
$972$		0			0
$973$	7.48331	−	7.48331i	0.239904	−	0.239904i
$974$	−13.2288	+	5.00000i	−0.423877	+	0.160210i
$975$		0			0
$976$	−3.00000	+	23.8118i	−0.0960277	+	0.762196i
$977$	14.9666	+	14.9666i	0.478825	+	0.478825i	0.904756	−	0.425931i	$-0.140053\pi$
$977$	14.9666	+	14.9666i	0.478825	+	0.478825i	−0.425931	+	0.904756i	$0.640053\pi$
$978$		0			0
$979$	31.7490			1.01470
$980$		0			0
$981$		0			0
$982$	−9.23676	+	20.4617i	−0.294757	+	0.652960i
$983$	−16.9706	−	16.9706i	−0.541277	−	0.541277i	0.382626	−	0.923903i	$-0.375020\pi$
$983$	−16.9706	−	16.9706i	−0.541277	−	0.541277i	−0.923903	+	0.382626i	$0.875020\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	55.8901	+	3.50688i	1.77810	+	0.111569i
$989$			32.0000i			1.01754i
$990$		0			0
$991$			47.6235i			1.51281i	0.654103	+	0.756406i	$0.273046\pi$
$991$			47.6235i			1.51281i	−0.654103	+	0.756406i	$0.726954\pi$
$992$	−25.5289	−	15.6294i	−0.810542	−	0.496233i
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	11.2250	+	11.2250i	0.355498	+	0.355498i	0.862151	−	0.506652i	$-0.169117\pi$
$997$	11.2250	+	11.2250i	0.355498	+	0.355498i	−0.506652	+	0.862151i	$0.669117\pi$
$998$	20.4617	+	9.23676i	0.647705	+	0.292384i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.k.h.307.1		8
3.2	odd	2		300.2.j.b.7.4	yes	8
4.3	odd	2	inner	900.2.k.h.307.2		8
5.2	odd	4	inner	900.2.k.h.343.3		8
5.3	odd	4	inner	900.2.k.h.343.2		8
5.4	even	2	inner	900.2.k.h.307.4		8
12.11	even	2		300.2.j.b.7.3	yes	8
15.2	even	4		300.2.j.b.43.2	yes	8
15.8	even	4		300.2.j.b.43.3	yes	8
15.14	odd	2		300.2.j.b.7.1	✓	8
20.3	even	4	inner	900.2.k.h.343.1		8
20.7	even	4	inner	900.2.k.h.343.4		8
20.19	odd	2	inner	900.2.k.h.307.3		8
60.23	odd	4		300.2.j.b.43.4	yes	8
60.47	odd	4		300.2.j.b.43.1	yes	8
60.59	even	2		300.2.j.b.7.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.j.b.7.1	✓	8	15.14	odd	2
300.2.j.b.7.2	yes	8	60.59	even	2
300.2.j.b.7.3	yes	8	12.11	even	2
300.2.j.b.7.4	yes	8	3.2	odd	2
300.2.j.b.43.1	yes	8	60.47	odd	4
300.2.j.b.43.2	yes	8	15.2	even	4
300.2.j.b.43.3	yes	8	15.8	even	4
300.2.j.b.43.4	yes	8	60.23	odd	4
900.2.k.h.307.1		8	1.1	even	1	trivial
900.2.k.h.307.2		8	4.3	odd	2	inner
900.2.k.h.307.3		8	20.19	odd	2	inner
900.2.k.h.307.4		8	5.4	even	2	inner
900.2.k.h.343.1		8	20.3	even	4	inner
900.2.k.h.343.2		8	5.3	odd	4	inner
900.2.k.h.343.3		8	5.2	odd	4	inner
900.2.k.h.343.4		8	20.7	even	4	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28897 - 0.581861i) q^{2} +(1.32288 + 1.50000i) q^{4} +(1.41421 - 1.41421i) q^{7} +(-0.832353 - 2.70318i) q^{8} +O(q^{10})\)	\(q+(-1.28897 - 0.581861i) q^{2} +(1.32288 + 1.50000i) q^{4} +(1.41421 - 1.41421i) q^{7} +(-0.832353 - 2.70318i) q^{8} +5.29150i q^{11} +(-3.74166 + 3.74166i) q^{13} +(-2.64575 + 1.00000i) q^{14} +(-0.500000 + 3.96863i) q^{16} -5.29150 q^{19} +(3.07892 - 6.82058i) q^{22} +(-2.82843 - 2.82843i) q^{23} +(7.00000 - 2.64575i) q^{26} +(3.99215 + 0.250492i) q^{28} +8.00000i q^{29} -5.29150i q^{31} +(2.95367 - 4.82450i) q^{32} +(3.74166 + 3.74166i) q^{37} +(6.82058 + 3.07892i) q^{38} +2.00000 q^{41} +(-5.65685 - 5.65685i) q^{43} +(-7.93725 + 7.00000i) q^{44} +(2.00000 + 5.29150i) q^{46} +3.00000i q^{49} +(-10.5622 - 0.662739i) q^{52} +(-7.48331 + 7.48331i) q^{53} +(-5.00000 - 2.64575i) q^{56} +(4.65489 - 10.3117i) q^{58} -5.29150 q^{59} +6.00000 q^{61} +(-3.07892 + 6.82058i) q^{62} +(-6.61438 + 4.50000i) q^{64} +(-8.48528 + 8.48528i) q^{67} +(-7.48331 + 7.48331i) q^{73} +(-2.64575 - 7.00000i) q^{74} +(-7.00000 - 7.93725i) q^{76} +(7.48331 + 7.48331i) q^{77} +5.29150 q^{79} +(-2.57794 - 1.16372i) q^{82} +(8.48528 + 8.48528i) q^{83} +(4.00000 + 10.5830i) q^{86} +(14.3039 - 4.40440i) q^{88} -6.00000i q^{89} +10.5830i q^{91} +(0.500983 - 7.98430i) q^{92} +(7.48331 + 7.48331i) q^{97} +(1.74558 - 3.86690i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 4 q^{16} + 56 q^{26} + 16 q^{41} + 16 q^{46} - 40 q^{56} + 48 q^{61} - 56 q^{76} + 32 q^{86}+O(q^{100}) \) 8 * q - 4 * q^16 + 56 * q^26 + 16 * q^41 + 16 * q^46 - 40 * q^56 + 48 * q^61 - 56 * q^76 + 32 * q^86

Introduction

L-functions

Modular forms

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Database

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