LMFDB - Embedded newform 432.2.k.a.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(109,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("432.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	432.109
Dual form			432.2.k.a.325.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} -2.00000 q^{4} +(-0.707107 + 0.707107i) q^{5} -3.00000i q^{7} +2.82843i q^{8} +O(q^{10})$	\(q-1.41421i q^{2} -2.00000 q^{4} +(-0.707107 + 0.707107i) q^{5} -3.00000i q^{7} +2.82843i q^{8} +(1.00000 + 1.00000i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(-5.00000 - 5.00000i) q^{13} -4.24264 q^{14} +4.00000 q^{16} -4.24264 q^{17} +(-2.00000 - 2.00000i) q^{19} +(1.41421 - 1.41421i) q^{20} +(1.00000 + 1.00000i) q^{22} +5.65685i q^{23} +4.00000i q^{25} +(-7.07107 + 7.07107i) q^{26} +6.00000i q^{28} +(-5.65685 - 5.65685i) q^{29} -1.00000 q^{31} -5.65685i q^{32} +6.00000i q^{34} +(2.12132 + 2.12132i) q^{35} +(4.00000 - 4.00000i) q^{37} +(-2.82843 + 2.82843i) q^{38} +(-2.00000 - 2.00000i) q^{40} -2.82843i q^{41} +(1.00000 - 1.00000i) q^{43} +(1.41421 - 1.41421i) q^{44} +8.00000 q^{46} +4.24264 q^{47} -2.00000 q^{49} +5.65685 q^{50} +(10.0000 + 10.0000i) q^{52} +(7.77817 - 7.77817i) q^{53} -1.00000i q^{55} +8.48528 q^{56} +(-8.00000 + 8.00000i) q^{58} +(-7.07107 + 7.07107i) q^{59} +(-2.00000 - 2.00000i) q^{61} +1.41421i q^{62} -8.00000 q^{64} +7.07107 q^{65} +(-5.00000 - 5.00000i) q^{67} +8.48528 q^{68} +(3.00000 - 3.00000i) q^{70} +1.41421i q^{71} -3.00000i q^{73} +(-5.65685 - 5.65685i) q^{74} +(4.00000 + 4.00000i) q^{76} +(2.12132 + 2.12132i) q^{77} +14.0000 q^{79} +(-2.82843 + 2.82843i) q^{80} -4.00000 q^{82} +(4.94975 + 4.94975i) q^{83} +(3.00000 - 3.00000i) q^{85} +(-1.41421 - 1.41421i) q^{86} +(-2.00000 - 2.00000i) q^{88} -15.5563i q^{89} +(-15.0000 + 15.0000i) q^{91} -11.3137i q^{92} -6.00000i q^{94} +2.82843 q^{95} +5.00000 q^{97} +2.82843i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{4}+O(q^{10}) $ 4 * q - 8 * q^4	$ 4 q - 8 q^{4} + 4 q^{10} - 20 q^{13} + 16 q^{16} - 8 q^{19} + 4 q^{22} - 4 q^{31} + 16 q^{37} - 8 q^{40} + 4 q^{43} + 32 q^{46} - 8 q^{49} + 40 q^{52} - 32 q^{58} - 8 q^{61} - 32 q^{64} - 20 q^{67} + 12 q^{70} + 16 q^{76} + 56 q^{79} - 16 q^{82} + 12 q^{85} - 8 q^{88} - 60 q^{91} + 20 q^{97}+O(q^{100}) $ 4 * q - 8 * q^4 + 4 * q^10 - 20 * q^13 + 16 * q^16 - 8 * q^19 + 4 * q^22 - 4 * q^31 + 16 * q^37 - 8 * q^40 + 4 * q^43 + 32 * q^46 - 8 * q^49 + 40 * q^52 - 32 * q^58 - 8 * q^61 - 32 * q^64 - 20 * q^67 + 12 * q^70 + 16 * q^76 + 56 * q^79 - 16 * q^82 + 12 * q^85 - 8 * q^88 - 60 * q^91 + 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		−	1.41421i		−	1.00000i
$2$		−	1.41421i		−	1.00000i
$3$		0			0
$3$		0			0
$4$	−2.00000			−1.00000
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i	−0.847316	−	0.531089i	$-0.821783\pi$
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i	0.531089	+	0.847316i	$0.321783\pi$
$6$		0			0
$7$		−	3.00000i		−	1.13389i	−0.823754	−	0.566947i	$-0.808125\pi$
$7$		−	3.00000i		−	1.13389i	0.823754	−	0.566947i	$-0.191875\pi$
$8$			2.82843i			1.00000i
$9$		0			0
$10$	1.00000	+	1.00000i	0.316228	+	0.316228i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i	−0.805626	−	0.592425i	$-0.798171\pi$
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i	0.592425	+	0.805626i	$0.298171\pi$
$12$		0			0
$13$	−5.00000	−	5.00000i	−1.38675	−	1.38675i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−5.00000	−	5.00000i	−1.38675	−	1.38675i	−0.554700	−	0.832050i	$-0.687167\pi$
$14$	−4.24264			−1.13389
$15$		0			0
$16$	4.00000			1.00000
$17$	−4.24264			−1.02899			−0.514496	−	0.857493i	$-0.672021\pi$
$17$	−4.24264			−1.02899			−0.514496	+	0.857493i	$0.672021\pi$
$18$		0			0
$19$	−2.00000	−	2.00000i	−0.458831	−	0.458831i	0.439440	−	0.898272i	$-0.355177\pi$
$19$	−2.00000	−	2.00000i	−0.458831	−	0.458831i	−0.898272	+	0.439440i	$0.855177\pi$
$20$	1.41421	−	1.41421i	0.316228	−	0.316228i
$21$		0			0
$22$	1.00000	+	1.00000i	0.213201	+	0.213201i
$23$			5.65685i			1.17954i	0.807573	+	0.589768i	$0.200781\pi$
$23$			5.65685i			1.17954i	−0.807573	+	0.589768i	$0.799219\pi$
$24$		0			0
$25$			4.00000i			0.800000i
$26$	−7.07107	+	7.07107i	−1.38675	+	1.38675i
$27$		0			0
$28$			6.00000i			1.13389i
$29$	−5.65685	−	5.65685i	−1.05045	−	1.05045i	−0.998658	−	0.0517937i	$-0.983506\pi$
$29$	−5.65685	−	5.65685i	−1.05045	−	1.05045i	−0.0517937	−	0.998658i	$-0.516494\pi$
$30$		0			0
$31$	−1.00000			−0.179605			−0.0898027	−	0.995960i	$-0.528624\pi$
$31$	−1.00000			−0.179605			−0.0898027	+	0.995960i	$0.528624\pi$
$32$		−	5.65685i		−	1.00000i
$33$		0			0
$34$			6.00000i			1.02899i
$35$	2.12132	+	2.12132i	0.358569	+	0.358569i
$36$		0			0
$37$	4.00000	−	4.00000i	0.657596	−	0.657596i	−0.297215	−	0.954811i	$-0.596058\pi$
$37$	4.00000	−	4.00000i	0.657596	−	0.657596i	0.954811	+	0.297215i	$0.0960577\pi$
$38$	−2.82843	+	2.82843i	−0.458831	+	0.458831i
$39$		0			0
$40$	−2.00000	−	2.00000i	−0.316228	−	0.316228i
$41$		−	2.82843i		−	0.441726i	−0.975305	−	0.220863i	$-0.929113\pi$
$41$		−	2.82843i		−	0.441726i	0.975305	−	0.220863i	$-0.0708874\pi$
$42$		0			0
$43$	1.00000	−	1.00000i	0.152499	−	0.152499i	−0.626734	−	0.779233i	$-0.715609\pi$
$43$	1.00000	−	1.00000i	0.152499	−	0.152499i	0.779233	+	0.626734i	$0.215609\pi$
$44$	1.41421	−	1.41421i	0.213201	−	0.213201i
$45$		0			0
$46$	8.00000			1.17954
$47$	4.24264			0.618853			0.309426	−	0.950923i	$-0.399863\pi$
$47$	4.24264			0.618853			0.309426	+	0.950923i	$0.399863\pi$
$48$		0			0
$49$	−2.00000			−0.285714
$50$	5.65685			0.800000
$51$		0			0
$52$	10.0000	+	10.0000i	1.38675	+	1.38675i
$53$	7.77817	−	7.77817i	1.06841	−	1.06841i	0.0709334	−	0.997481i	$-0.477402\pi$
$53$	7.77817	−	7.77817i	1.06841	−	1.06841i	0.997481	−	0.0709334i	$-0.0225978\pi$
$54$		0			0
$55$		−	1.00000i		−	0.134840i
$56$	8.48528			1.13389
$57$		0			0
$58$	−8.00000	+	8.00000i	−1.05045	+	1.05045i
$59$	−7.07107	+	7.07107i	−0.920575	+	0.920575i	−0.997070	−	0.0764953i	$-0.975627\pi$
$59$	−7.07107	+	7.07107i	−0.920575	+	0.920575i	0.0764953	+	0.997070i	$0.475627\pi$
$60$		0			0
$61$	−2.00000	−	2.00000i	−0.256074	−	0.256074i	0.567381	−	0.823455i	$-0.307957\pi$
$61$	−2.00000	−	2.00000i	−0.256074	−	0.256074i	−0.823455	+	0.567381i	$0.807957\pi$
$62$			1.41421i			0.179605i
$63$		0			0
$64$	−8.00000			−1.00000
$65$	7.07107			0.877058
$66$		0			0
$67$	−5.00000	−	5.00000i	−0.610847	−	0.610847i	0.332320	−	0.943167i	$-0.392169\pi$
$67$	−5.00000	−	5.00000i	−0.610847	−	0.610847i	−0.943167	+	0.332320i	$0.892169\pi$
$68$	8.48528			1.02899
$69$		0			0
$70$	3.00000	−	3.00000i	0.358569	−	0.358569i
$71$			1.41421i			0.167836i	0.996473	+	0.0839181i	$0.0267434\pi$
$71$			1.41421i			0.167836i	−0.996473	+	0.0839181i	$0.973257\pi$
$72$		0			0
$73$		−	3.00000i		−	0.351123i	−0.984468	−	0.175562i	$-0.943826\pi$
$73$		−	3.00000i		−	0.351123i	0.984468	−	0.175562i	$-0.0561742\pi$
$74$	−5.65685	−	5.65685i	−0.657596	−	0.657596i
$75$		0			0
$76$	4.00000	+	4.00000i	0.458831	+	0.458831i
$77$	2.12132	+	2.12132i	0.241747	+	0.241747i
$78$		0			0
$79$	14.0000			1.57512			0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000			1.57512			0.787562	+	0.616236i	$0.211343\pi$
$80$	−2.82843	+	2.82843i	−0.316228	+	0.316228i
$81$		0			0
$82$	−4.00000			−0.441726
$83$	4.94975	+	4.94975i	0.543305	+	0.543305i	0.924496	−	0.381191i	$-0.124486\pi$
$83$	4.94975	+	4.94975i	0.543305	+	0.543305i	−0.381191	+	0.924496i	$0.624486\pi$
$84$		0			0
$85$	3.00000	−	3.00000i	0.325396	−	0.325396i
$86$	−1.41421	−	1.41421i	−0.152499	−	0.152499i
$87$		0			0
$88$	−2.00000	−	2.00000i	−0.213201	−	0.213201i
$89$		−	15.5563i		−	1.64897i	−0.565884	−	0.824485i	$-0.691465\pi$
$89$		−	15.5563i		−	1.64897i	0.565884	−	0.824485i	$-0.308535\pi$
$90$		0			0
$91$	−15.0000	+	15.0000i	−1.57243	+	1.57243i
$92$		−	11.3137i		−	1.17954i
$93$		0			0
$94$		−	6.00000i		−	0.618853i
$95$	2.82843			0.290191
$96$		0			0
$97$	5.00000			0.507673			0.253837	−	0.967247i	$-0.418307\pi$
$97$	5.00000			0.507673			0.253837	+	0.967247i	$0.418307\pi$
$98$			2.82843i			0.285714i
$99$		0			0
$100$		−	8.00000i		−	0.800000i
$101$	−4.94975	+	4.94975i	−0.492518	+	0.492518i	−0.909099	−	0.416581i	$-0.863228\pi$
$101$	−4.94975	+	4.94975i	−0.492518	+	0.492518i	0.416581	+	0.909099i	$0.363228\pi$
$102$		0			0
$103$		−	6.00000i		−	0.591198i	−0.955312	−	0.295599i	$-0.904481\pi$
$103$		−	6.00000i		−	0.591198i	0.955312	−	0.295599i	$-0.0955191\pi$
$104$	14.1421	−	14.1421i	1.38675	−	1.38675i
$105$		0			0
$106$	−11.0000	−	11.0000i	−1.06841	−	1.06841i
$107$	12.0208	−	12.0208i	1.16210	−	1.16210i	0.178080	−	0.984016i	$-0.443011\pi$
$107$	12.0208	−	12.0208i	1.16210	−	1.16210i	0.984016	−	0.178080i	$-0.0569886\pi$
$108$		0			0
$109$	−8.00000	−	8.00000i	−0.766261	−	0.766261i	0.211185	−	0.977446i	$-0.432268\pi$
$109$	−8.00000	−	8.00000i	−0.766261	−	0.766261i	−0.977446	+	0.211185i	$0.932268\pi$
$110$	−1.41421			−0.134840
$111$		0			0
$112$		−	12.0000i		−	1.13389i
$113$	−16.9706			−1.59646			−0.798228	−	0.602355i	$-0.794229\pi$
$113$	−16.9706			−1.59646			−0.798228	+	0.602355i	$0.794229\pi$
$114$		0			0
$115$	−4.00000	−	4.00000i	−0.373002	−	0.373002i
$116$	11.3137	+	11.3137i	1.05045	+	1.05045i
$117$		0			0
$118$	10.0000	+	10.0000i	0.920575	+	0.920575i
$119$			12.7279i			1.16677i
$120$		0			0
$121$			10.0000i			0.909091i
$122$	−2.82843	+	2.82843i	−0.256074	+	0.256074i
$123$		0			0
$124$	2.00000			0.179605
$125$	−6.36396	−	6.36396i	−0.569210	−	0.569210i
$126$		0			0
$127$	17.0000			1.50851			0.754253	−	0.656584i	$-0.227999\pi$
$127$	17.0000			1.50851			0.754253	+	0.656584i	$0.227999\pi$
$128$			11.3137i			1.00000i
$129$		0			0
$130$		−	10.0000i		−	0.877058i
$131$	13.4350	+	13.4350i	1.17382	+	1.17382i	0.981290	+	0.192534i	$0.0616704\pi$
$131$	13.4350	+	13.4350i	1.17382	+	1.17382i	0.192534	+	0.981290i	$0.438330\pi$
$132$		0			0
$133$	−6.00000	+	6.00000i	−0.520266	+	0.520266i
$134$	−7.07107	+	7.07107i	−0.610847	+	0.610847i
$135$		0			0
$136$		−	12.0000i		−	1.02899i
$137$			1.41421i			0.120824i	0.998174	+	0.0604122i	$0.0192415\pi$
$137$			1.41421i			0.120824i	−0.998174	+	0.0604122i	$0.980758\pi$
$138$		0			0
$139$	−14.0000	+	14.0000i	−1.18746	+	1.18746i	−0.209698	+	0.977766i	$0.567248\pi$
$139$	−14.0000	+	14.0000i	−1.18746	+	1.18746i	−0.977766	+	0.209698i	$0.932752\pi$
$140$	−4.24264	−	4.24264i	−0.358569	−	0.358569i
$141$		0			0
$142$	2.00000			0.167836
$143$	7.07107			0.591312
$144$		0			0
$145$	8.00000			0.664364
$146$	−4.24264			−0.351123
$147$		0			0
$148$	−8.00000	+	8.00000i	−0.657596	+	0.657596i
$149$	3.53553	−	3.53553i	0.289642	−	0.289642i	−0.547297	−	0.836939i	$-0.684343\pi$
$149$	3.53553	−	3.53553i	0.289642	−	0.289642i	0.836939	+	0.547297i	$0.184343\pi$
$150$		0			0
$151$		−	15.0000i		−	1.22068i	−0.792139	−	0.610341i	$-0.791032\pi$
$151$		−	15.0000i		−	1.22068i	0.792139	−	0.610341i	$-0.208968\pi$
$152$	5.65685	−	5.65685i	0.458831	−	0.458831i
$153$		0			0
$154$	3.00000	−	3.00000i	0.241747	−	0.241747i
$155$	0.707107	−	0.707107i	0.0567962	−	0.0567962i
$156$		0			0
$157$	−2.00000	−	2.00000i	−0.159617	−	0.159617i	0.622780	−	0.782397i	$-0.286003\pi$
$157$	−2.00000	−	2.00000i	−0.159617	−	0.159617i	−0.782397	+	0.622780i	$0.786003\pi$
$158$		−	19.7990i		−	1.57512i
$159$		0			0
$160$	4.00000	+	4.00000i	0.316228	+	0.316228i
$161$	16.9706			1.33747
$162$		0			0
$163$	7.00000	+	7.00000i	0.548282	+	0.548282i	0.925944	−	0.377661i	$-0.123272\pi$
$163$	7.00000	+	7.00000i	0.548282	+	0.548282i	−0.377661	+	0.925944i	$0.623272\pi$
$164$			5.65685i			0.441726i
$165$		0			0
$166$	7.00000	−	7.00000i	0.543305	−	0.543305i
$167$		−	15.5563i		−	1.20379i	−0.798577	−	0.601893i	$-0.794413\pi$
$167$		−	15.5563i		−	1.20379i	0.798577	−	0.601893i	$-0.205587\pi$
$168$		0			0
$169$			37.0000i			2.84615i
$170$	−4.24264	−	4.24264i	−0.325396	−	0.325396i
$171$		0			0
$172$	−2.00000	+	2.00000i	−0.152499	+	0.152499i
$173$	−7.77817	−	7.77817i	−0.591364	−	0.591364i	0.346636	−	0.938000i	$-0.387324\pi$
$173$	−7.77817	−	7.77817i	−0.591364	−	0.591364i	−0.938000	+	0.346636i	$0.887324\pi$
$174$		0			0
$175$	12.0000			0.907115
$176$	−2.82843	+	2.82843i	−0.213201	+	0.213201i
$177$		0			0
$178$	−22.0000			−1.64897
$179$	−12.0208	−	12.0208i	−0.898478	−	0.898478i	0.0968236	−	0.995302i	$-0.469132\pi$
$179$	−12.0208	−	12.0208i	−0.898478	−	0.898478i	−0.995302	+	0.0968236i	$0.969132\pi$
$180$		0			0
$181$	4.00000	−	4.00000i	0.297318	−	0.297318i	−0.542645	−	0.839962i	$-0.682577\pi$
$181$	4.00000	−	4.00000i	0.297318	−	0.297318i	0.839962	+	0.542645i	$0.182577\pi$
$182$	21.2132	+	21.2132i	1.57243	+	1.57243i
$183$		0			0
$184$	−16.0000			−1.17954
$185$			5.65685i			0.415900i
$186$		0			0
$187$	3.00000	−	3.00000i	0.219382	−	0.219382i
$188$	−8.48528			−0.618853
$189$		0			0
$190$		−	4.00000i		−	0.290191i
$191$	−21.2132			−1.53493			−0.767467	−	0.641089i	$-0.778483\pi$
$191$	−21.2132			−1.53493			−0.767467	+	0.641089i	$0.778483\pi$
$192$		0			0
$193$	17.0000			1.22369			0.611843	−	0.790979i	$-0.290428\pi$
$193$	17.0000			1.22369			0.611843	+	0.790979i	$0.290428\pi$
$194$		−	7.07107i		−	0.507673i
$195$		0			0
$196$	4.00000			0.285714
$197$	−9.19239	+	9.19239i	−0.654931	+	0.654931i	−0.954176	−	0.299246i	$-0.903265\pi$
$197$	−9.19239	+	9.19239i	−0.654931	+	0.654931i	0.299246	+	0.954176i	$0.403265\pi$
$198$		0			0
$199$			21.0000i			1.48865i	0.667817	+	0.744325i	$0.267229\pi$
$199$			21.0000i			1.48865i	−0.667817	+	0.744325i	$0.732771\pi$
$200$	−11.3137			−0.800000
$201$		0			0
$202$	7.00000	+	7.00000i	0.492518	+	0.492518i
$203$	−16.9706	+	16.9706i	−1.19110	+	1.19110i
$204$		0			0
$205$	2.00000	+	2.00000i	0.139686	+	0.139686i
$206$	−8.48528			−0.591198
$207$		0			0
$208$	−20.0000	−	20.0000i	−1.38675	−	1.38675i
$209$	2.82843			0.195646
$210$		0			0
$211$	10.0000	+	10.0000i	0.688428	+	0.688428i	0.961884	−	0.273456i	$-0.0881668\pi$
$211$	10.0000	+	10.0000i	0.688428	+	0.688428i	−0.273456	+	0.961884i	$0.588167\pi$
$212$	−15.5563	+	15.5563i	−1.06841	+	1.06841i
$213$		0			0
$214$	−17.0000	−	17.0000i	−1.16210	−	1.16210i
$215$			1.41421i			0.0964486i
$216$		0			0
$217$			3.00000i			0.203653i
$218$	−11.3137	+	11.3137i	−0.766261	+	0.766261i
$219$		0			0
$220$			2.00000i			0.134840i
$221$	21.2132	+	21.2132i	1.42695	+	1.42695i
$222$		0			0
$223$	2.00000			0.133930			0.0669650	−	0.997755i	$-0.478668\pi$
$223$	2.00000			0.133930			0.0669650	+	0.997755i	$0.478668\pi$
$224$	−16.9706			−1.13389
$225$		0			0
$226$			24.0000i			1.59646i
$227$	−9.89949	−	9.89949i	−0.657053	−	0.657053i	0.297629	−	0.954682i	$-0.403804\pi$
$227$	−9.89949	−	9.89949i	−0.657053	−	0.657053i	−0.954682	+	0.297629i	$0.903804\pi$
$228$		0			0
$229$	7.00000	−	7.00000i	0.462573	−	0.462573i	−0.436925	−	0.899498i	$-0.643932\pi$
$229$	7.00000	−	7.00000i	0.462573	−	0.462573i	0.899498	+	0.436925i	$0.143932\pi$
$230$	−5.65685	+	5.65685i	−0.373002	+	0.373002i
$231$		0			0
$232$	16.0000	−	16.0000i	1.05045	−	1.05045i
$233$			1.41421i			0.0926482i	0.998926	+	0.0463241i	$0.0147507\pi$
$233$			1.41421i			0.0926482i	−0.998926	+	0.0463241i	$0.985249\pi$
$234$		0			0
$235$	−3.00000	+	3.00000i	−0.195698	+	0.195698i
$236$	14.1421	−	14.1421i	0.920575	−	0.920575i
$237$		0			0
$238$	18.0000			1.16677
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	−16.0000			−1.03065			−0.515325	−	0.856995i	$-0.672329\pi$
$241$	−16.0000			−1.03065			−0.515325	+	0.856995i	$0.672329\pi$
$242$	14.1421			0.909091
$243$		0			0
$244$	4.00000	+	4.00000i	0.256074	+	0.256074i
$245$	1.41421	−	1.41421i	0.0903508	−	0.0903508i
$246$		0			0
$247$			20.0000i			1.27257i
$248$		−	2.82843i		−	0.179605i
$249$		0			0
$250$	−9.00000	+	9.00000i	−0.569210	+	0.569210i
$251$	−7.07107	+	7.07107i	−0.446322	+	0.446322i	−0.894130	−	0.447808i	$-0.852205\pi$
$251$	−7.07107	+	7.07107i	−0.446322	+	0.446322i	0.447808	+	0.894130i	$0.352205\pi$
$252$		0			0
$253$	−4.00000	−	4.00000i	−0.251478	−	0.251478i
$254$		−	24.0416i		−	1.50851i
$255$		0			0
$256$	16.0000			1.00000
$257$	−21.2132			−1.32324			−0.661622	−	0.749838i	$-0.730131\pi$
$257$	−21.2132			−1.32324			−0.661622	+	0.749838i	$0.730131\pi$
$258$		0			0
$259$	−12.0000	−	12.0000i	−0.745644	−	0.745644i
$260$	−14.1421			−0.877058
$261$		0			0
$262$	19.0000	−	19.0000i	1.17382	−	1.17382i
$263$			14.1421i			0.872041i	0.899937	+	0.436021i	$0.143613\pi$
$263$			14.1421i			0.872041i	−0.899937	+	0.436021i	$0.856387\pi$
$264$		0			0
$265$			11.0000i			0.675725i
$266$	8.48528	+	8.48528i	0.520266	+	0.520266i
$267$		0			0
$268$	10.0000	+	10.0000i	0.610847	+	0.610847i
$269$	−5.65685	−	5.65685i	−0.344904	−	0.344904i	0.513303	−	0.858207i	$-0.328422\pi$
$269$	−5.65685	−	5.65685i	−0.344904	−	0.344904i	−0.858207	+	0.513303i	$0.828422\pi$
$270$		0			0
$271$	−19.0000			−1.15417			−0.577084	−	0.816685i	$-0.695809\pi$
$271$	−19.0000			−1.15417			−0.577084	+	0.816685i	$0.695809\pi$
$272$	−16.9706			−1.02899
$273$		0			0
$274$	2.00000			0.120824
$275$	−2.82843	−	2.82843i	−0.170561	−	0.170561i
$276$		0			0
$277$	−8.00000	+	8.00000i	−0.480673	+	0.480673i	−0.905347	−	0.424673i	$-0.860389\pi$
$277$	−8.00000	+	8.00000i	−0.480673	+	0.480673i	0.424673	+	0.905347i	$0.360389\pi$
$278$	19.7990	+	19.7990i	1.18746	+	1.18746i
$279$		0			0
$280$	−6.00000	+	6.00000i	−0.358569	+	0.358569i
$281$			18.3848i			1.09674i	0.836235	+	0.548372i	$0.184752\pi$
$281$			18.3848i			1.09674i	−0.836235	+	0.548372i	$0.815248\pi$
$282$		0			0
$283$	10.0000	−	10.0000i	0.594438	−	0.594438i	−0.344389	−	0.938827i	$-0.611914\pi$
$283$	10.0000	−	10.0000i	0.594438	−	0.594438i	0.938827	+	0.344389i	$0.111914\pi$
$284$		−	2.82843i		−	0.167836i
$285$		0			0
$286$		−	10.0000i		−	0.591312i
$287$	−8.48528			−0.500870
$288$		0			0
$289$	1.00000			0.0588235
$290$		−	11.3137i		−	0.664364i
$291$		0			0
$292$			6.00000i			0.351123i
$293$	−2.82843	+	2.82843i	−0.165238	+	0.165238i	−0.784883	−	0.619644i	$-0.787277\pi$
$293$	−2.82843	+	2.82843i	−0.165238	+	0.165238i	0.619644	+	0.784883i	$0.287277\pi$
$294$		0			0
$295$		−	10.0000i		−	0.582223i
$296$	11.3137	+	11.3137i	0.657596	+	0.657596i
$297$		0			0
$298$	−5.00000	−	5.00000i	−0.289642	−	0.289642i
$299$	28.2843	−	28.2843i	1.63572	−	1.63572i
$300$		0			0
$301$	−3.00000	−	3.00000i	−0.172917	−	0.172917i
$302$	−21.2132			−1.22068
$303$		0			0
$304$	−8.00000	−	8.00000i	−0.458831	−	0.458831i
$305$	2.82843			0.161955
$306$		0			0
$307$	−5.00000	−	5.00000i	−0.285365	−	0.285365i	0.549879	−	0.835244i	$-0.314674\pi$
$307$	−5.00000	−	5.00000i	−0.285365	−	0.285365i	−0.835244	+	0.549879i	$0.814674\pi$
$308$	−4.24264	−	4.24264i	−0.241747	−	0.241747i
$309$		0			0
$310$	−1.00000	−	1.00000i	−0.0567962	−	0.0567962i
$311$		−	28.2843i		−	1.60385i	−0.597422	−	0.801927i	$-0.703808\pi$
$311$		−	28.2843i		−	1.60385i	0.597422	−	0.801927i	$-0.296192\pi$
$312$		0			0
$313$		−	9.00000i		−	0.508710i	−0.967111	−	0.254355i	$-0.918137\pi$
$313$		−	9.00000i		−	0.508710i	0.967111	−	0.254355i	$-0.0818632\pi$
$314$	−2.82843	+	2.82843i	−0.159617	+	0.159617i
$315$		0			0
$316$	−28.0000			−1.57512
$317$	9.19239	+	9.19239i	0.516296	+	0.516296i	0.916449	−	0.400153i	$-0.131043\pi$
$317$	9.19239	+	9.19239i	0.516296	+	0.516296i	−0.400153	+	0.916449i	$0.631043\pi$
$318$		0			0
$319$	8.00000			0.447914
$320$	5.65685	−	5.65685i	0.316228	−	0.316228i
$321$		0			0
$322$		−	24.0000i		−	1.33747i
$323$	8.48528	+	8.48528i	0.472134	+	0.472134i
$324$		0			0
$325$	20.0000	−	20.0000i	1.10940	−	1.10940i
$326$	9.89949	−	9.89949i	0.548282	−	0.548282i
$327$		0			0
$328$	8.00000			0.441726
$329$		−	12.7279i		−	0.701713i
$330$		0			0
$331$	1.00000	−	1.00000i	0.0549650	−	0.0549650i	−0.679090	−	0.734055i	$-0.737625\pi$
$331$	1.00000	−	1.00000i	0.0549650	−	0.0549650i	0.734055	+	0.679090i	$0.237625\pi$
$332$	−9.89949	−	9.89949i	−0.543305	−	0.543305i
$333$		0			0
$334$	−22.0000			−1.20379
$335$	7.07107			0.386334
$336$		0			0
$337$	8.00000			0.435788			0.217894	−	0.975972i	$-0.430081\pi$
$337$	8.00000			0.435788			0.217894	+	0.975972i	$0.430081\pi$
$338$	52.3259			2.84615
$339$		0			0
$340$	−6.00000	+	6.00000i	−0.325396	+	0.325396i
$341$	0.707107	−	0.707107i	0.0382920	−	0.0382920i
$342$		0			0
$343$		−	15.0000i		−	0.809924i
$344$	2.82843	+	2.82843i	0.152499	+	0.152499i
$345$		0			0
$346$	−11.0000	+	11.0000i	−0.591364	+	0.591364i
$347$	3.53553	−	3.53553i	0.189797	−	0.189797i	−0.605811	−	0.795609i	$-0.707151\pi$
$347$	3.53553	−	3.53553i	0.189797	−	0.189797i	0.795609	+	0.605811i	$0.207151\pi$
$348$		0			0
$349$	−14.0000	−	14.0000i	−0.749403	−	0.749403i	0.224964	−	0.974367i	$-0.427773\pi$
$349$	−14.0000	−	14.0000i	−0.749403	−	0.749403i	−0.974367	+	0.224964i	$0.927773\pi$
$350$		−	16.9706i		−	0.907115i
$351$		0			0
$352$	4.00000	+	4.00000i	0.213201	+	0.213201i
$353$	25.4558			1.35488			0.677439	−	0.735579i	$-0.263090\pi$
$353$	25.4558			1.35488			0.677439	+	0.735579i	$0.263090\pi$
$354$		0			0
$355$	−1.00000	−	1.00000i	−0.0530745	−	0.0530745i
$356$			31.1127i			1.64897i
$357$		0			0
$358$	−17.0000	+	17.0000i	−0.898478	+	0.898478i
$359$		−	24.0416i		−	1.26887i	−0.772977	−	0.634434i	$-0.781233\pi$
$359$		−	24.0416i		−	1.26887i	0.772977	−	0.634434i	$-0.218767\pi$
$360$		0			0
$361$		−	11.0000i		−	0.578947i
$362$	−5.65685	−	5.65685i	−0.297318	−	0.297318i
$363$		0			0
$364$	30.0000	−	30.0000i	1.57243	−	1.57243i
$365$	2.12132	+	2.12132i	0.111035	+	0.111035i
$366$		0			0
$367$	5.00000			0.260998			0.130499	−	0.991448i	$-0.458342\pi$
$367$	5.00000			0.260998			0.130499	+	0.991448i	$0.458342\pi$
$368$			22.6274i			1.17954i
$369$		0			0
$370$	8.00000			0.415900
$371$	−23.3345	−	23.3345i	−1.21147	−	1.21147i
$372$		0			0
$373$	−5.00000	+	5.00000i	−0.258890	+	0.258890i	−0.824603	−	0.565712i	$-0.808601\pi$
$373$	−5.00000	+	5.00000i	−0.258890	+	0.258890i	0.565712	+	0.824603i	$0.308601\pi$
$374$	−4.24264	−	4.24264i	−0.219382	−	0.219382i
$375$		0			0
$376$			12.0000i			0.618853i
$377$			56.5685i			2.91343i
$378$		0			0
$379$	−14.0000	+	14.0000i	−0.719132	+	0.719132i	−0.968427	−	0.249296i	$-0.919801\pi$
$379$	−14.0000	+	14.0000i	−0.719132	+	0.719132i	0.249296	+	0.968427i	$0.419801\pi$
$380$	−5.65685			−0.290191
$381$		0			0
$382$			30.0000i			1.53493i
$383$	21.2132			1.08394			0.541972	−	0.840397i	$-0.317678\pi$
$383$	21.2132			1.08394			0.541972	+	0.840397i	$0.317678\pi$
$384$		0			0
$385$	−3.00000			−0.152894
$386$		−	24.0416i		−	1.22369i
$387$		0			0
$388$	−10.0000			−0.507673
$389$	−0.707107	+	0.707107i	−0.0358517	+	0.0358517i	−0.724805	−	0.688954i	$-0.758070\pi$
$389$	−0.707107	+	0.707107i	−0.0358517	+	0.0358517i	0.688954	+	0.724805i	$0.258070\pi$
$390$		0			0
$391$		−	24.0000i		−	1.21373i
$392$		−	5.65685i		−	0.285714i
$393$		0			0
$394$	13.0000	+	13.0000i	0.654931	+	0.654931i
$395$	−9.89949	+	9.89949i	−0.498098	+	0.498098i
$396$		0			0
$397$	−11.0000	−	11.0000i	−0.552074	−	0.552074i	0.374965	−	0.927039i	$-0.377655\pi$
$397$	−11.0000	−	11.0000i	−0.552074	−	0.552074i	−0.927039	+	0.374965i	$0.877655\pi$
$398$	29.6985			1.48865
$399$		0			0
$400$			16.0000i			0.800000i
$401$	8.48528			0.423735			0.211867	−	0.977298i	$-0.432046\pi$
$401$	8.48528			0.423735			0.211867	+	0.977298i	$0.432046\pi$
$402$		0			0
$403$	5.00000	+	5.00000i	0.249068	+	0.249068i
$404$	9.89949	−	9.89949i	0.492518	−	0.492518i
$405$		0			0
$406$	24.0000	+	24.0000i	1.19110	+	1.19110i
$407$			5.65685i			0.280400i
$408$		0			0
$409$		−	21.0000i		−	1.03838i	−0.854658	−	0.519192i	$-0.826233\pi$
$409$		−	21.0000i		−	1.03838i	0.854658	−	0.519192i	$-0.173767\pi$
$410$	2.82843	−	2.82843i	0.139686	−	0.139686i
$411$		0			0
$412$			12.0000i			0.591198i
$413$	21.2132	+	21.2132i	1.04383	+	1.04383i
$414$		0			0
$415$	−7.00000			−0.343616
$416$	−28.2843	+	28.2843i	−1.38675	+	1.38675i
$417$		0			0
$418$		−	4.00000i		−	0.195646i
$419$	−18.3848	−	18.3848i	−0.898155	−	0.898155i	0.0971178	−	0.995273i	$-0.469038\pi$
$419$	−18.3848	−	18.3848i	−0.898155	−	0.898155i	−0.995273	+	0.0971178i	$0.969038\pi$
$420$		0			0
$421$	−8.00000	+	8.00000i	−0.389896	+	0.389896i	−0.874650	−	0.484754i	$-0.838909\pi$
$421$	−8.00000	+	8.00000i	−0.389896	+	0.389896i	0.484754	+	0.874650i	$0.338909\pi$
$422$	14.1421	−	14.1421i	0.688428	−	0.688428i
$423$		0			0
$424$	22.0000	+	22.0000i	1.06841	+	1.06841i
$425$		−	16.9706i		−	0.823193i
$426$		0			0
$427$	−6.00000	+	6.00000i	−0.290360	+	0.290360i
$428$	−24.0416	+	24.0416i	−1.16210	+	1.16210i
$429$		0			0
$430$	2.00000			0.0964486
$431$	−4.24264			−0.204361			−0.102180	−	0.994766i	$-0.532582\pi$
$431$	−4.24264			−0.204361			−0.102180	+	0.994766i	$0.532582\pi$
$432$		0			0
$433$	17.0000			0.816968			0.408484	−	0.912766i	$-0.366058\pi$
$433$	17.0000			0.816968			0.408484	+	0.912766i	$0.366058\pi$
$434$	4.24264			0.203653
$435$		0			0
$436$	16.0000	+	16.0000i	0.766261	+	0.766261i
$437$	11.3137	−	11.3137i	0.541208	−	0.541208i
$438$		0			0
$439$		−	15.0000i		−	0.715911i	−0.933739	−	0.357955i	$-0.883474\pi$
$439$		−	15.0000i		−	0.715911i	0.933739	−	0.357955i	$-0.116526\pi$
$440$	2.82843			0.134840
$441$		0			0
$442$	30.0000	−	30.0000i	1.42695	−	1.42695i
$443$	18.3848	−	18.3848i	0.873487	−	0.873487i	−0.119364	−	0.992851i	$-0.538085\pi$
$443$	18.3848	−	18.3848i	0.873487	−	0.873487i	0.992851	+	0.119364i	$0.0380854\pi$
$444$		0			0
$445$	11.0000	+	11.0000i	0.521450	+	0.521450i
$446$		−	2.82843i		−	0.133930i
$447$		0			0
$448$			24.0000i			1.13389i
$449$	−8.48528			−0.400445			−0.200223	−	0.979750i	$-0.564167\pi$
$449$	−8.48528			−0.400445			−0.200223	+	0.979750i	$0.564167\pi$
$450$		0			0
$451$	2.00000	+	2.00000i	0.0941763	+	0.0941763i
$452$	33.9411			1.59646
$453$		0			0
$454$	−14.0000	+	14.0000i	−0.657053	+	0.657053i
$455$		−	21.2132i		−	0.994490i
$456$		0			0
$457$		−	15.0000i		−	0.701670i	−0.936437	−	0.350835i	$-0.885898\pi$
$457$		−	15.0000i		−	0.701670i	0.936437	−	0.350835i	$-0.114102\pi$
$458$	−9.89949	−	9.89949i	−0.462573	−	0.462573i
$459$		0			0
$460$	8.00000	+	8.00000i	0.373002	+	0.373002i
$461$	−16.2635	−	16.2635i	−0.757465	−	0.757465i	0.218396	−	0.975860i	$-0.429918\pi$
$461$	−16.2635	−	16.2635i	−0.757465	−	0.757465i	−0.975860	+	0.218396i	$0.929918\pi$
$462$		0			0
$463$	−1.00000			−0.0464739			−0.0232370	−	0.999730i	$-0.507397\pi$
$463$	−1.00000			−0.0464739			−0.0232370	+	0.999730i	$0.507397\pi$
$464$	−22.6274	−	22.6274i	−1.05045	−	1.05045i
$465$		0			0
$466$	2.00000			0.0926482
$467$	9.19239	+	9.19239i	0.425373	+	0.425373i	0.887049	−	0.461676i	$-0.152752\pi$
$467$	9.19239	+	9.19239i	0.425373	+	0.425373i	−0.461676	+	0.887049i	$0.652752\pi$
$468$		0			0
$469$	−15.0000	+	15.0000i	−0.692636	+	0.692636i
$470$	4.24264	+	4.24264i	0.195698	+	0.195698i
$471$		0			0
$472$	−20.0000	−	20.0000i	−0.920575	−	0.920575i
$473$			1.41421i			0.0650256i
$474$		0			0
$475$	8.00000	−	8.00000i	0.367065	−	0.367065i
$476$		−	25.4558i		−	1.16677i
$477$		0			0
$478$		0			0
$479$	−4.24264			−0.193851			−0.0969256	−	0.995292i	$-0.530901\pi$
$479$	−4.24264			−0.193851			−0.0969256	+	0.995292i	$0.530901\pi$
$480$		0			0
$481$	−40.0000			−1.82384
$482$			22.6274i			1.03065i
$483$		0			0
$484$		−	20.0000i		−	0.909091i
$485$	−3.53553	+	3.53553i	−0.160540	+	0.160540i
$486$		0			0
$487$			12.0000i			0.543772i	0.962329	+	0.271886i	$0.0876473\pi$
$487$			12.0000i			0.543772i	−0.962329	+	0.271886i	$0.912353\pi$
$488$	5.65685	−	5.65685i	0.256074	−	0.256074i
$489$		0			0
$490$	−2.00000	−	2.00000i	−0.0903508	−	0.0903508i
$491$	−9.19239	+	9.19239i	−0.414847	+	0.414847i	−0.883423	−	0.468576i	$-0.844767\pi$
$491$	−9.19239	+	9.19239i	−0.414847	+	0.414847i	0.468576	+	0.883423i	$0.344767\pi$
$492$		0			0
$493$	24.0000	+	24.0000i	1.08091	+	1.08091i
$494$	28.2843			1.27257
$495$		0			0
$496$	−4.00000			−0.179605
$497$	4.24264			0.190308
$498$		0			0
$499$	−17.0000	−	17.0000i	−0.761025	−	0.761025i	0.215483	−	0.976508i	$-0.430867\pi$
$499$	−17.0000	−	17.0000i	−0.761025	−	0.761025i	−0.976508	+	0.215483i	$0.930867\pi$
$500$	12.7279	+	12.7279i	0.569210	+	0.569210i
$501$		0			0
$502$	10.0000	+	10.0000i	0.446322	+	0.446322i
$503$			14.1421i			0.630567i	0.948998	+	0.315283i	$0.102100\pi$
$503$			14.1421i			0.630567i	−0.948998	+	0.315283i	$0.897900\pi$
$504$		0			0
$505$		−	7.00000i		−	0.311496i
$506$	−5.65685	+	5.65685i	−0.251478	+	0.251478i
$507$		0			0
$508$	−34.0000			−1.50851
$509$	21.9203	+	21.9203i	0.971601	+	0.971601i	0.999608	−	0.0280071i	$-0.00891609\pi$
$509$	21.9203	+	21.9203i	0.971601	+	0.971601i	−0.0280071	+	0.999608i	$0.508916\pi$
$510$		0			0
$511$	−9.00000			−0.398137
$512$		−	22.6274i		−	1.00000i
$513$		0			0
$514$			30.0000i			1.32324i
$515$	4.24264	+	4.24264i	0.186953	+	0.186953i
$516$		0			0
$517$	−3.00000	+	3.00000i	−0.131940	+	0.131940i
$518$	−16.9706	+	16.9706i	−0.745644	+	0.745644i
$519$		0			0
$520$			20.0000i			0.877058i
$521$		−	15.5563i		−	0.681536i	−0.940147	−	0.340768i	$-0.889313\pi$
$521$		−	15.5563i		−	0.681536i	0.940147	−	0.340768i	$-0.110687\pi$
$522$		0			0
$523$	25.0000	−	25.0000i	1.09317	−	1.09317i	0.0979859	−	0.995188i	$-0.468760\pi$
$523$	25.0000	−	25.0000i	1.09317	−	1.09317i	0.995188	−	0.0979859i	$-0.0312400\pi$
$524$	−26.8701	−	26.8701i	−1.17382	−	1.17382i
$525$		0			0
$526$	20.0000			0.872041
$527$	4.24264			0.184812
$528$		0			0
$529$	−9.00000			−0.391304
$530$	15.5563			0.675725
$531$		0			0
$532$	12.0000	−	12.0000i	0.520266	−	0.520266i
$533$	−14.1421	+	14.1421i	−0.612564	+	0.612564i
$534$		0			0
$535$			17.0000i			0.734974i
$536$	14.1421	−	14.1421i	0.610847	−	0.610847i
$537$		0			0
$538$	−8.00000	+	8.00000i	−0.344904	+	0.344904i
$539$	1.41421	−	1.41421i	0.0609145	−	0.0609145i
$540$		0			0
$541$	22.0000	+	22.0000i	0.945854	+	0.945854i	0.998608	−	0.0527537i	$-0.0167998\pi$
$541$	22.0000	+	22.0000i	0.945854	+	0.945854i	−0.0527537	+	0.998608i	$0.516800\pi$
$542$			26.8701i			1.15417i
$543$		0			0
$544$			24.0000i			1.02899i
$545$	11.3137			0.484626
$546$		0			0
$547$	−5.00000	−	5.00000i	−0.213785	−	0.213785i	0.592088	−	0.805873i	$-0.298304\pi$
$547$	−5.00000	−	5.00000i	−0.213785	−	0.213785i	−0.805873	+	0.592088i	$0.798304\pi$
$548$		−	2.82843i		−	0.120824i
$549$		0			0
$550$	−4.00000	+	4.00000i	−0.170561	+	0.170561i
$551$			22.6274i			0.963960i
$552$		0			0
$553$		−	42.0000i		−	1.78602i
$554$	11.3137	+	11.3137i	0.480673	+	0.480673i
$555$		0			0
$556$	28.0000	−	28.0000i	1.18746	−	1.18746i
$557$	−16.2635	−	16.2635i	−0.689105	−	0.689105i	0.272929	−	0.962034i	$-0.412007\pi$
$557$	−16.2635	−	16.2635i	−0.689105	−	0.689105i	−0.962034	+	0.272929i	$0.912007\pi$
$558$		0			0
$559$	−10.0000			−0.422955
$560$	8.48528	+	8.48528i	0.358569	+	0.358569i
$561$		0			0
$562$	26.0000			1.09674
$563$	13.4350	+	13.4350i	0.566219	+	0.566219i	0.931067	−	0.364848i	$-0.118879\pi$
$563$	13.4350	+	13.4350i	0.566219	+	0.566219i	−0.364848	+	0.931067i	$0.618879\pi$
$564$		0			0
$565$	12.0000	−	12.0000i	0.504844	−	0.504844i
$566$	−14.1421	−	14.1421i	−0.594438	−	0.594438i
$567$		0			0
$568$	−4.00000			−0.167836
$569$			39.5980i			1.66003i	0.557738	+	0.830017i	$0.311669\pi$
$569$			39.5980i			1.66003i	−0.557738	+	0.830017i	$0.688331\pi$
$570$		0			0
$571$	7.00000	−	7.00000i	0.292941	−	0.292941i	−0.545300	−	0.838241i	$-0.683584\pi$
$571$	7.00000	−	7.00000i	0.292941	−	0.292941i	0.838241	+	0.545300i	$0.183584\pi$
$572$	−14.1421			−0.591312
$573$		0			0
$574$			12.0000i			0.500870i
$575$	−22.6274			−0.943629
$576$		0			0
$577$	−28.0000			−1.16566			−0.582828	−	0.812596i	$-0.698054\pi$
$577$	−28.0000			−1.16566			−0.582828	+	0.812596i	$0.698054\pi$
$578$		−	1.41421i		−	0.0588235i
$579$		0			0
$580$	−16.0000			−0.664364
$581$	14.8492	−	14.8492i	0.616050	−	0.616050i
$582$		0			0
$583$			11.0000i			0.455573i
$584$	8.48528			0.351123
$585$		0			0
$586$	4.00000	+	4.00000i	0.165238	+	0.165238i
$587$	−4.94975	+	4.94975i	−0.204298	+	0.204298i	−0.801839	−	0.597541i	$-0.796145\pi$
$587$	−4.94975	+	4.94975i	−0.204298	+	0.204298i	0.597541	+	0.801839i	$0.296145\pi$
$588$		0			0
$589$	2.00000	+	2.00000i	0.0824086	+	0.0824086i
$590$	−14.1421			−0.582223
$591$		0			0
$592$	16.0000	−	16.0000i	0.657596	−	0.657596i
$593$	−4.24264			−0.174224			−0.0871122	−	0.996199i	$-0.527764\pi$
$593$	−4.24264			−0.174224			−0.0871122	+	0.996199i	$0.527764\pi$
$594$		0			0
$595$	−9.00000	−	9.00000i	−0.368964	−	0.368964i
$596$	−7.07107	+	7.07107i	−0.289642	+	0.289642i
$597$		0			0
$598$	−40.0000	−	40.0000i	−1.63572	−	1.63572i
$599$		−	32.5269i		−	1.32901i	−0.747282	−	0.664507i	$-0.768642\pi$
$599$		−	32.5269i		−	1.32901i	0.747282	−	0.664507i	$-0.231358\pi$
$600$		0			0
$601$		−	9.00000i		−	0.367118i	−0.983009	−	0.183559i	$-0.941238\pi$
$601$		−	9.00000i		−	0.367118i	0.983009	−	0.183559i	$-0.0587618\pi$
$602$	−4.24264	+	4.24264i	−0.172917	+	0.172917i
$603$		0			0
$604$			30.0000i			1.22068i
$605$	−7.07107	−	7.07107i	−0.287480	−	0.287480i
$606$		0			0
$607$	−28.0000			−1.13648			−0.568242	−	0.822861i	$-0.692376\pi$
$607$	−28.0000			−1.13648			−0.568242	+	0.822861i	$0.692376\pi$
$608$	−11.3137	+	11.3137i	−0.458831	+	0.458831i
$609$		0			0
$610$		−	4.00000i		−	0.161955i
$611$	−21.2132	−	21.2132i	−0.858194	−	0.858194i
$612$		0			0
$613$	1.00000	−	1.00000i	0.0403896	−	0.0403896i	−0.686624	−	0.727013i	$-0.740908\pi$
$613$	1.00000	−	1.00000i	0.0403896	−	0.0403896i	0.727013	+	0.686624i	$0.240908\pi$
$614$	−7.07107	+	7.07107i	−0.285365	+	0.285365i
$615$		0			0
$616$	−6.00000	+	6.00000i	−0.241747	+	0.241747i
$617$		−	45.2548i		−	1.82189i	−0.412527	−	0.910946i	$-0.635354\pi$
$617$		−	45.2548i		−	1.82189i	0.412527	−	0.910946i	$-0.364646\pi$
$618$		0			0
$619$	25.0000	−	25.0000i	1.00483	−	1.00483i	0.00484658	−	0.999988i	$-0.498457\pi$
$619$	25.0000	−	25.0000i	1.00483	−	1.00483i	0.999988	−	0.00484658i	$-0.00154272\pi$
$620$	−1.41421	+	1.41421i	−0.0567962	+	0.0567962i
$621$		0			0
$622$	−40.0000			−1.60385
$623$	−46.6690			−1.86976
$624$		0			0
$625$	−11.0000			−0.440000
$626$	−12.7279			−0.508710
$627$		0			0
$628$	4.00000	+	4.00000i	0.159617	+	0.159617i
$629$	−16.9706	+	16.9706i	−0.676661	+	0.676661i
$630$		0			0
$631$			15.0000i			0.597141i	0.954388	+	0.298570i	$0.0965097\pi$
$631$			15.0000i			0.597141i	−0.954388	+	0.298570i	$0.903490\pi$
$632$			39.5980i			1.57512i
$633$		0			0
$634$	13.0000	−	13.0000i	0.516296	−	0.516296i
$635$	−12.0208	+	12.0208i	−0.477032	+	0.477032i
$636$		0			0
$637$	10.0000	+	10.0000i	0.396214	+	0.396214i
$638$		−	11.3137i		−	0.447914i
$639$		0			0
$640$	−8.00000	−	8.00000i	−0.316228	−	0.316228i
$641$	16.9706			0.670297			0.335148	−	0.942165i	$-0.391214\pi$
$641$	16.9706			0.670297			0.335148	+	0.942165i	$0.391214\pi$
$642$		0			0
$643$	22.0000	+	22.0000i	0.867595	+	0.867595i	0.992206	−	0.124610i	$-0.0397681\pi$
$643$	22.0000	+	22.0000i	0.867595	+	0.867595i	−0.124610	+	0.992206i	$0.539768\pi$
$644$	−33.9411			−1.33747
$645$		0			0
$646$	12.0000	−	12.0000i	0.472134	−	0.472134i
$647$			39.5980i			1.55676i	0.627795	+	0.778379i	$0.283958\pi$
$647$			39.5980i			1.55676i	−0.627795	+	0.778379i	$0.716042\pi$
$648$		0			0
$649$		−	10.0000i		−	0.392534i
$650$	−28.2843	−	28.2843i	−1.10940	−	1.10940i
$651$		0			0
$652$	−14.0000	−	14.0000i	−0.548282	−	0.548282i
$653$	4.94975	+	4.94975i	0.193699	+	0.193699i	0.797292	−	0.603594i	$-0.206265\pi$
$653$	4.94975	+	4.94975i	0.193699	+	0.193699i	−0.603594	+	0.797292i	$0.706265\pi$
$654$		0			0
$655$	−19.0000			−0.742391
$656$		−	11.3137i		−	0.441726i
$657$		0			0
$658$	−18.0000			−0.701713
$659$	13.4350	+	13.4350i	0.523354	+	0.523354i	0.918583	−	0.395228i	$-0.129335\pi$
$659$	13.4350	+	13.4350i	0.523354	+	0.523354i	−0.395228	+	0.918583i	$0.629335\pi$
$660$		0			0
$661$	−2.00000	+	2.00000i	−0.0777910	+	0.0777910i	−0.744932	−	0.667141i	$-0.767518\pi$
$661$	−2.00000	+	2.00000i	−0.0777910	+	0.0777910i	0.667141	+	0.744932i	$0.267518\pi$
$662$	−1.41421	−	1.41421i	−0.0549650	−	0.0549650i
$663$		0			0
$664$	−14.0000	+	14.0000i	−0.543305	+	0.543305i
$665$		−	8.48528i		−	0.329045i
$666$		0			0
$667$	32.0000	−	32.0000i	1.23904	−	1.23904i
$668$			31.1127i			1.20379i
$669$		0			0
$670$		−	10.0000i		−	0.386334i
$671$	2.82843			0.109190
$672$		0			0
$673$	41.0000			1.58043			0.790217	−	0.612827i	$-0.209968\pi$
$673$	41.0000			1.58043			0.790217	+	0.612827i	$0.209968\pi$
$674$		−	11.3137i		−	0.435788i
$675$		0			0
$676$		−	74.0000i		−	2.84615i
$677$	−19.7990	+	19.7990i	−0.760937	+	0.760937i	−0.976492	−	0.215555i	$-0.930844\pi$
$677$	−19.7990	+	19.7990i	−0.760937	+	0.760937i	0.215555	+	0.976492i	$0.430844\pi$
$678$		0			0
$679$		−	15.0000i		−	0.575647i
$680$	8.48528	+	8.48528i	0.325396	+	0.325396i
$681$		0			0
$682$	−1.00000	−	1.00000i	−0.0382920	−	0.0382920i
$683$	5.65685	−	5.65685i	0.216454	−	0.216454i	−0.590549	−	0.807002i	$-0.701089\pi$
$683$	5.65685	−	5.65685i	0.216454	−	0.216454i	0.807002	+	0.590549i	$0.201089\pi$
$684$		0			0
$685$	−1.00000	−	1.00000i	−0.0382080	−	0.0382080i
$686$	−21.2132			−0.809924
$687$		0			0
$688$	4.00000	−	4.00000i	0.152499	−	0.152499i
$689$	−77.7817			−2.96325
$690$		0			0
$691$	28.0000	+	28.0000i	1.06517	+	1.06517i	0.997723	+	0.0674474i	$0.0214855\pi$
$691$	28.0000	+	28.0000i	1.06517	+	1.06517i	0.0674474	+	0.997723i	$0.478515\pi$
$692$	15.5563	+	15.5563i	0.591364	+	0.591364i
$693$		0			0
$694$	−5.00000	−	5.00000i	−0.189797	−	0.189797i
$695$		−	19.7990i		−	0.751018i
$696$		0			0
$697$			12.0000i			0.454532i
$698$	−19.7990	+	19.7990i	−0.749403	+	0.749403i
$699$		0			0
$700$	−24.0000			−0.907115
$701$	17.6777	+	17.6777i	0.667676	+	0.667676i	0.957178	−	0.289501i	$-0.0934894\pi$
$701$	17.6777	+	17.6777i	0.667676	+	0.667676i	−0.289501	+	0.957178i	$0.593489\pi$
$702$		0			0
$703$	−16.0000			−0.603451
$704$	5.65685	−	5.65685i	0.213201	−	0.213201i
$705$		0			0
$706$		−	36.0000i		−	1.35488i
$707$	14.8492	+	14.8492i	0.558463	+	0.558463i
$708$		0			0
$709$	−14.0000	+	14.0000i	−0.525781	+	0.525781i	−0.919312	−	0.393531i	$-0.871254\pi$
$709$	−14.0000	+	14.0000i	−0.525781	+	0.525781i	0.393531	+	0.919312i	$0.371254\pi$
$710$	−1.41421	+	1.41421i	−0.0530745	+	0.0530745i
$711$		0			0
$712$	44.0000			1.64897
$713$		−	5.65685i		−	0.211851i
$714$		0			0
$715$	−5.00000	+	5.00000i	−0.186989	+	0.186989i
$716$	24.0416	+	24.0416i	0.898478	+	0.898478i
$717$		0			0
$718$	−34.0000			−1.26887
$719$	16.9706			0.632895			0.316448	−	0.948610i	$-0.397510\pi$
$719$	16.9706			0.632895			0.316448	+	0.948610i	$0.397510\pi$
$720$		0			0
$721$	−18.0000			−0.670355
$722$	−15.5563			−0.578947
$723$		0			0
$724$	−8.00000	+	8.00000i	−0.297318	+	0.297318i
$725$	22.6274	−	22.6274i	0.840361	−	0.840361i
$726$		0			0
$727$			45.0000i			1.66896i	0.551040	+	0.834479i	$0.314231\pi$
$727$			45.0000i			1.66896i	−0.551040	+	0.834479i	$0.685769\pi$
$728$	−42.4264	−	42.4264i	−1.57243	−	1.57243i
$729$		0			0
$730$	3.00000	−	3.00000i	0.111035	−	0.111035i
$731$	−4.24264	+	4.24264i	−0.156920	+	0.156920i
$732$		0			0
$733$	4.00000	+	4.00000i	0.147743	+	0.147743i	0.777109	−	0.629366i	$-0.216685\pi$
$733$	4.00000	+	4.00000i	0.147743	+	0.147743i	−0.629366	+	0.777109i	$0.716685\pi$
$734$		−	7.07107i		−	0.260998i
$735$		0			0
$736$	32.0000			1.17954
$737$	7.07107			0.260466
$738$		0			0
$739$	31.0000	+	31.0000i	1.14035	+	1.14035i	0.988385	+	0.151968i	$0.0485611\pi$
$739$	31.0000	+	31.0000i	1.14035	+	1.14035i	0.151968	+	0.988385i	$0.451439\pi$
$740$		−	11.3137i		−	0.415900i
$741$		0			0
$742$	−33.0000	+	33.0000i	−1.21147	+	1.21147i
$743$		−	7.07107i		−	0.259412i	−0.991552	−	0.129706i	$-0.958597\pi$
$743$		−	7.07107i		−	0.259412i	0.991552	−	0.129706i	$-0.0414034\pi$
$744$		0			0
$745$			5.00000i			0.183186i
$746$	7.07107	+	7.07107i	0.258890	+	0.258890i
$747$		0			0
$748$	−6.00000	+	6.00000i	−0.219382	+	0.219382i
$749$	−36.0624	−	36.0624i	−1.31769	−	1.31769i
$750$		0			0
$751$	−43.0000			−1.56909			−0.784546	−	0.620070i	$-0.787104\pi$
$751$	−43.0000			−1.56909			−0.784546	+	0.620070i	$0.787104\pi$
$752$	16.9706			0.618853
$753$		0			0
$754$	80.0000			2.91343
$755$	10.6066	+	10.6066i	0.386014	+	0.386014i
$756$		0			0
$757$	−11.0000	+	11.0000i	−0.399802	+	0.399802i	−0.878163	−	0.478361i	$-0.841231\pi$
$757$	−11.0000	+	11.0000i	−0.399802	+	0.399802i	0.478361	+	0.878163i	$0.341231\pi$
$758$	19.7990	+	19.7990i	0.719132	+	0.719132i
$759$		0			0
$760$			8.00000i			0.290191i
$761$		−	2.82843i		−	0.102530i	−0.998685	−	0.0512652i	$-0.983675\pi$
$761$		−	2.82843i		−	0.102530i	0.998685	−	0.0512652i	$-0.0163254\pi$
$762$		0			0
$763$	−24.0000	+	24.0000i	−0.868858	+	0.868858i
$764$	42.4264			1.53493
$765$		0			0
$766$		−	30.0000i		−	1.08394i
$767$	70.7107			2.55321
$768$		0			0
$769$	35.0000			1.26213			0.631066	−	0.775729i	$-0.282618\pi$
$769$	35.0000			1.26213			0.631066	+	0.775729i	$0.282618\pi$
$770$			4.24264i			0.152894i
$771$		0			0
$772$	−34.0000			−1.22369
$773$	−24.0416	+	24.0416i	−0.864717	+	0.864717i	−0.991882	−	0.127164i	$-0.959412\pi$
$773$	−24.0416	+	24.0416i	−0.864717	+	0.864717i	0.127164	+	0.991882i	$0.459412\pi$
$774$		0			0
$775$		−	4.00000i		−	0.143684i
$776$			14.1421i			0.507673i
$777$		0			0
$778$	1.00000	+	1.00000i	0.0358517	+	0.0358517i
$779$	−5.65685	+	5.65685i	−0.202678	+	0.202678i
$780$		0			0
$781$	−1.00000	−	1.00000i	−0.0357828	−	0.0357828i
$782$	−33.9411			−1.21373
$783$		0			0
$784$	−8.00000			−0.285714
$785$	2.82843			0.100951
$786$		0			0
$787$	−14.0000	−	14.0000i	−0.499046	−	0.499046i	0.412095	−	0.911141i	$-0.364797\pi$
$787$	−14.0000	−	14.0000i	−0.499046	−	0.499046i	−0.911141	+	0.412095i	$0.864797\pi$
$788$	18.3848	−	18.3848i	0.654931	−	0.654931i
$789$		0			0
$790$	14.0000	+	14.0000i	0.498098	+	0.498098i
$791$			50.9117i			1.81021i
$792$		0			0
$793$			20.0000i			0.710221i
$794$	−15.5563	+	15.5563i	−0.552074	+	0.552074i
$795$		0			0
$796$		−	42.0000i		−	1.48865i
$797$	−7.77817	−	7.77817i	−0.275517	−	0.275517i	0.555799	−	0.831316i	$-0.312412\pi$
$797$	−7.77817	−	7.77817i	−0.275517	−	0.275517i	−0.831316	+	0.555799i	$0.812412\pi$
$798$		0			0
$799$	−18.0000			−0.636794
$800$	22.6274			0.800000
$801$		0			0
$802$		−	12.0000i		−	0.423735i
$803$	2.12132	+	2.12132i	0.0748598	+	0.0748598i
$804$		0			0
$805$	−12.0000	+	12.0000i	−0.422944	+	0.422944i
$806$	7.07107	−	7.07107i	0.249068	−	0.249068i
$807$		0			0
$808$	−14.0000	−	14.0000i	−0.492518	−	0.492518i
$809$		−	15.5563i		−	0.546932i	−0.961882	−	0.273466i	$-0.911830\pi$
$809$		−	15.5563i		−	0.546932i	0.961882	−	0.273466i	$-0.0881701\pi$
$810$		0			0
$811$	−8.00000	+	8.00000i	−0.280918	+	0.280918i	−0.833475	−	0.552557i	$-0.813652\pi$
$811$	−8.00000	+	8.00000i	−0.280918	+	0.280918i	0.552557	+	0.833475i	$0.313652\pi$
$812$	33.9411	−	33.9411i	1.19110	−	1.19110i
$813$		0			0
$814$	8.00000			0.280400
$815$	−9.89949			−0.346764
$816$		0			0
$817$	−4.00000			−0.139942
$818$	−29.6985			−1.03838
$819$		0			0
$820$	−4.00000	−	4.00000i	−0.139686	−	0.139686i
$821$	35.3553	−	35.3553i	1.23391	−	1.23391i	0.271460	−	0.962450i	$-0.412493\pi$
$821$	35.3553	−	35.3553i	1.23391	−	1.23391i	0.962450	−	0.271460i	$-0.0875065\pi$
$822$		0			0
$823$			9.00000i			0.313720i	0.987621	+	0.156860i	$0.0501372\pi$
$823$			9.00000i			0.313720i	−0.987621	+	0.156860i	$0.949863\pi$
$824$	16.9706			0.591198
$825$		0			0
$826$	30.0000	−	30.0000i	1.04383	−	1.04383i
$827$	9.89949	−	9.89949i	0.344239	−	0.344239i	−0.513719	−	0.857958i	$-0.671733\pi$
$827$	9.89949	−	9.89949i	0.344239	−	0.344239i	0.857958	+	0.513719i	$0.171733\pi$
$828$		0			0
$829$	13.0000	+	13.0000i	0.451509	+	0.451509i	0.895855	−	0.444346i	$-0.146564\pi$
$829$	13.0000	+	13.0000i	0.451509	+	0.451509i	−0.444346	+	0.895855i	$0.646564\pi$
$830$			9.89949i			0.343616i
$831$		0			0
$832$	40.0000	+	40.0000i	1.38675	+	1.38675i
$833$	8.48528			0.293998
$834$		0			0
$835$	11.0000	+	11.0000i	0.380671	+	0.380671i
$836$	−5.65685			−0.195646
$837$		0			0
$838$	−26.0000	+	26.0000i	−0.898155	+	0.898155i
$839$			9.89949i			0.341769i	0.985291	+	0.170884i	$0.0546624\pi$
$839$			9.89949i			0.341769i	−0.985291	+	0.170884i	$0.945338\pi$
$840$		0			0
$841$			35.0000i			1.20690i
$842$	11.3137	+	11.3137i	0.389896	+	0.389896i
$843$		0			0
$844$	−20.0000	−	20.0000i	−0.688428	−	0.688428i
$845$	−26.1630	−	26.1630i	−0.900033	−	0.900033i
$846$		0			0
$847$	30.0000			1.03081
$848$	31.1127	−	31.1127i	1.06841	−	1.06841i
$849$		0			0
$850$	−24.0000			−0.823193
$851$	22.6274	+	22.6274i	0.775658	+	0.775658i
$852$		0			0
$853$	31.0000	−	31.0000i	1.06142	−	1.06142i	0.0634337	−	0.997986i	$-0.479795\pi$
$853$	31.0000	−	31.0000i	1.06142	−	1.06142i	0.997986	−	0.0634337i	$-0.0202051\pi$
$854$	8.48528	+	8.48528i	0.290360	+	0.290360i
$855$		0			0
$856$	34.0000	+	34.0000i	1.16210	+	1.16210i
$857$		−	24.0416i		−	0.821246i	−0.911805	−	0.410623i	$-0.865311\pi$
$857$		−	24.0416i		−	0.821246i	0.911805	−	0.410623i	$-0.134689\pi$
$858$		0			0
$859$	28.0000	−	28.0000i	0.955348	−	0.955348i	−0.0436972	−	0.999045i	$-0.513914\pi$
$859$	28.0000	−	28.0000i	0.955348	−	0.955348i	0.999045	+	0.0436972i	$0.0139137\pi$
$860$		−	2.82843i		−	0.0964486i
$861$		0			0
$862$			6.00000i			0.204361i
$863$	16.9706			0.577685			0.288842	−	0.957377i	$-0.406730\pi$
$863$	16.9706			0.577685			0.288842	+	0.957377i	$0.406730\pi$
$864$		0			0
$865$	11.0000			0.374011
$866$		−	24.0416i		−	0.816968i
$867$		0			0
$868$		−	6.00000i		−	0.203653i
$869$	−9.89949	+	9.89949i	−0.335817	+	0.335817i
$870$		0			0
$871$			50.0000i			1.69419i
$872$	22.6274	−	22.6274i	0.766261	−	0.766261i
$873$		0			0
$874$	−16.0000	−	16.0000i	−0.541208	−	0.541208i
$875$	−19.0919	+	19.0919i	−0.645423	+	0.645423i
$876$		0			0
$877$	25.0000	+	25.0000i	0.844190	+	0.844190i	0.989401	−	0.145211i	$-0.0463860\pi$
$877$	25.0000	+	25.0000i	0.844190	+	0.844190i	−0.145211	+	0.989401i	$0.546386\pi$
$878$	−21.2132			−0.715911
$879$		0			0
$880$		−	4.00000i		−	0.134840i
$881$	−12.7279			−0.428815			−0.214407	−	0.976744i	$-0.568782\pi$
$881$	−12.7279			−0.428815			−0.214407	+	0.976744i	$0.568782\pi$
$882$		0			0
$883$	28.0000	+	28.0000i	0.942275	+	0.942275i	0.998422	−	0.0561475i	$-0.0178817\pi$
$883$	28.0000	+	28.0000i	0.942275	+	0.942275i	−0.0561475	+	0.998422i	$0.517882\pi$
$884$	−42.4264	−	42.4264i	−1.42695	−	1.42695i
$885$		0			0
$886$	−26.0000	−	26.0000i	−0.873487	−	0.873487i
$887$		−	7.07107i		−	0.237423i	−0.992929	−	0.118712i	$-0.962124\pi$
$887$		−	7.07107i		−	0.237423i	0.992929	−	0.118712i	$-0.0378764\pi$
$888$		0			0
$889$		−	51.0000i		−	1.71049i
$890$	15.5563	−	15.5563i	0.521450	−	0.521450i
$891$		0			0
$892$	−4.00000			−0.133930
$893$	−8.48528	−	8.48528i	−0.283949	−	0.283949i
$894$		0			0
$895$	17.0000			0.568247
$896$	33.9411			1.13389
$897$		0			0
$898$			12.0000i			0.400445i
$899$	5.65685	+	5.65685i	0.188667	+	0.188667i
$900$		0			0
$901$	−33.0000	+	33.0000i	−1.09939	+	1.09939i
$902$	2.82843	−	2.82843i	0.0941763	−	0.0941763i
$903$		0			0
$904$		−	48.0000i		−	1.59646i
$905$			5.65685i			0.188040i
$906$		0			0
$907$	−2.00000	+	2.00000i	−0.0664089	+	0.0664089i	−0.739531	−	0.673122i	$-0.764953\pi$
$907$	−2.00000	+	2.00000i	−0.0664089	+	0.0664089i	0.673122	+	0.739531i	$0.264953\pi$
$908$	19.7990	+	19.7990i	0.657053	+	0.657053i
$909$		0			0
$910$	−30.0000			−0.994490
$911$	−12.7279			−0.421695			−0.210847	−	0.977519i	$-0.567622\pi$
$911$	−12.7279			−0.421695			−0.210847	+	0.977519i	$0.567622\pi$
$912$		0			0
$913$	−7.00000			−0.231666
$914$	−21.2132			−0.701670
$915$		0			0
$916$	−14.0000	+	14.0000i	−0.462573	+	0.462573i
$917$	40.3051	−	40.3051i	1.33099	−	1.33099i
$918$		0			0
$919$		−	21.0000i		−	0.692726i	−0.938101	−	0.346363i	$-0.887417\pi$
$919$		−	21.0000i		−	0.692726i	0.938101	−	0.346363i	$-0.112583\pi$
$920$	11.3137	−	11.3137i	0.373002	−	0.373002i
$921$		0			0
$922$	−23.0000	+	23.0000i	−0.757465	+	0.757465i
$923$	7.07107	−	7.07107i	0.232747	−	0.232747i
$924$		0			0
$925$	16.0000	+	16.0000i	0.526077	+	0.526077i
$926$			1.41421i			0.0464739i
$927$		0			0
$928$	−32.0000	+	32.0000i	−1.05045	+	1.05045i
$929$	59.3970			1.94875			0.974376	−	0.224927i	$-0.0722143\pi$
$929$	59.3970			1.94875			0.974376	+	0.224927i	$0.0722143\pi$
$930$		0			0
$931$	4.00000	+	4.00000i	0.131095	+	0.131095i
$932$		−	2.82843i		−	0.0926482i
$933$		0			0
$934$	13.0000	−	13.0000i	0.425373	−	0.425373i
$935$			4.24264i			0.138749i
$936$		0			0
$937$		−	15.0000i		−	0.490029i	−0.969519	−	0.245014i	$-0.921207\pi$
$937$		−	15.0000i		−	0.490029i	0.969519	−	0.245014i	$-0.0787927\pi$
$938$	21.2132	+	21.2132i	0.692636	+	0.692636i
$939$		0			0
$940$	6.00000	−	6.00000i	0.195698	−	0.195698i
$941$	4.94975	+	4.94975i	0.161357	+	0.161357i	0.783168	−	0.621811i	$-0.213603\pi$
$941$	4.94975	+	4.94975i	0.161357	+	0.161357i	−0.621811	+	0.783168i	$0.713603\pi$
$942$		0			0
$943$	16.0000			0.521032
$944$	−28.2843	+	28.2843i	−0.920575	+	0.920575i
$945$		0			0
$946$	2.00000			0.0650256
$947$	13.4350	+	13.4350i	0.436580	+	0.436580i	0.890859	−	0.454279i	$-0.150103\pi$
$947$	13.4350	+	13.4350i	0.436580	+	0.436580i	−0.454279	+	0.890859i	$0.650103\pi$
$948$		0			0
$949$	−15.0000	+	15.0000i	−0.486921	+	0.486921i
$950$	−11.3137	−	11.3137i	−0.367065	−	0.367065i
$951$		0			0
$952$	−36.0000			−1.16677
$953$			5.65685i			0.183243i	0.995794	+	0.0916217i	$0.0292051\pi$
$953$			5.65685i			0.183243i	−0.995794	+	0.0916217i	$0.970795\pi$
$954$		0			0
$955$	15.0000	−	15.0000i	0.485389	−	0.485389i
$956$		0			0
$957$		0			0
$958$			6.00000i			0.193851i
$959$	4.24264			0.137002
$960$		0			0
$961$	−30.0000			−0.967742
$962$			56.5685i			1.82384i
$963$		0			0
$964$	32.0000			1.03065
$965$	−12.0208	+	12.0208i	−0.386964	+	0.386964i
$966$		0			0
$967$			33.0000i			1.06121i	0.847620	+	0.530604i	$0.178035\pi$
$967$			33.0000i			1.06121i	−0.847620	+	0.530604i	$0.821965\pi$
$968$	−28.2843			−0.909091
$969$		0			0
$970$	5.00000	+	5.00000i	0.160540	+	0.160540i
$971$	−4.94975	+	4.94975i	−0.158845	+	0.158845i	−0.782055	−	0.623210i	$-0.785828\pi$
$971$	−4.94975	+	4.94975i	−0.158845	+	0.158845i	0.623210	+	0.782055i	$0.285828\pi$
$972$		0			0
$973$	42.0000	+	42.0000i	1.34646	+	1.34646i
$974$	16.9706			0.543772
$975$		0			0
$976$	−8.00000	−	8.00000i	−0.256074	−	0.256074i
$977$	−12.7279			−0.407202			−0.203601	−	0.979054i	$-0.565265\pi$
$977$	−12.7279			−0.407202			−0.203601	+	0.979054i	$0.565265\pi$
$978$		0			0
$979$	11.0000	+	11.0000i	0.351562	+	0.351562i
$980$	−2.82843	+	2.82843i	−0.0903508	+	0.0903508i
$981$		0			0
$982$	13.0000	+	13.0000i	0.414847	+	0.414847i
$983$			26.8701i			0.857022i	0.903537	+	0.428511i	$0.140962\pi$
$983$			26.8701i			0.857022i	−0.903537	+	0.428511i	$0.859038\pi$
$984$		0			0
$985$		−	13.0000i		−	0.414214i
$986$	33.9411	−	33.9411i	1.08091	−	1.08091i
$987$		0			0
$988$		−	40.0000i		−	1.27257i
$989$	5.65685	+	5.65685i	0.179878	+	0.179878i
$990$		0			0
$991$	−13.0000			−0.412959			−0.206479	−	0.978451i	$-0.566201\pi$
$991$	−13.0000			−0.412959			−0.206479	+	0.978451i	$0.566201\pi$
$992$			5.65685i			0.179605i
$993$		0			0
$994$		−	6.00000i		−	0.190308i
$995$	−14.8492	−	14.8492i	−0.470753	−	0.470753i
$996$		0			0
$997$	1.00000	−	1.00000i	0.0316703	−	0.0316703i	−0.691094	−	0.722765i	$-0.742871\pi$
$997$	1.00000	−	1.00000i	0.0316703	−	0.0316703i	0.722765	+	0.691094i	$0.242871\pi$
$998$	−24.0416	+	24.0416i	−0.761025	+	0.761025i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.k.a.109.1	✓	4
3.2	odd	2	inner	432.2.k.a.109.2	yes	4
4.3	odd	2		1728.2.k.a.1297.1		4
12.11	even	2		1728.2.k.a.1297.2		4
16.5	even	4	inner	432.2.k.a.325.2	yes	4
16.11	odd	4		1728.2.k.a.433.1		4
48.5	odd	4	inner	432.2.k.a.325.1	yes	4
48.11	even	4		1728.2.k.a.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.k.a.109.1	✓	4	1.1	even	1	trivial
432.2.k.a.109.2	yes	4	3.2	odd	2	inner
432.2.k.a.325.1	yes	4	48.5	odd	4	inner
432.2.k.a.325.2	yes	4	16.5	even	4	inner
1728.2.k.a.433.1		4	16.11	odd	4
1728.2.k.a.433.2		4	48.11	even	4
1728.2.k.a.1297.1		4	4.3	odd	2
1728.2.k.a.1297.2		4	12.11	even	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} -2.00000 q^{4} +(-0.707107 + 0.707107i) q^{5} -3.00000i q^{7} +2.82843i q^{8} +O(q^{10})\)	\(q-1.41421i q^{2} -2.00000 q^{4} +(-0.707107 + 0.707107i) q^{5} -3.00000i q^{7} +2.82843i q^{8} +(1.00000 + 1.00000i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(-5.00000 - 5.00000i) q^{13} -4.24264 q^{14} +4.00000 q^{16} -4.24264 q^{17} +(-2.00000 - 2.00000i) q^{19} +(1.41421 - 1.41421i) q^{20} +(1.00000 + 1.00000i) q^{22} +5.65685i q^{23} +4.00000i q^{25} +(-7.07107 + 7.07107i) q^{26} +6.00000i q^{28} +(-5.65685 - 5.65685i) q^{29} -1.00000 q^{31} -5.65685i q^{32} +6.00000i q^{34} +(2.12132 + 2.12132i) q^{35} +(4.00000 - 4.00000i) q^{37} +(-2.82843 + 2.82843i) q^{38} +(-2.00000 - 2.00000i) q^{40} -2.82843i q^{41} +(1.00000 - 1.00000i) q^{43} +(1.41421 - 1.41421i) q^{44} +8.00000 q^{46} +4.24264 q^{47} -2.00000 q^{49} +5.65685 q^{50} +(10.0000 + 10.0000i) q^{52} +(7.77817 - 7.77817i) q^{53} -1.00000i q^{55} +8.48528 q^{56} +(-8.00000 + 8.00000i) q^{58} +(-7.07107 + 7.07107i) q^{59} +(-2.00000 - 2.00000i) q^{61} +1.41421i q^{62} -8.00000 q^{64} +7.07107 q^{65} +(-5.00000 - 5.00000i) q^{67} +8.48528 q^{68} +(3.00000 - 3.00000i) q^{70} +1.41421i q^{71} -3.00000i q^{73} +(-5.65685 - 5.65685i) q^{74} +(4.00000 + 4.00000i) q^{76} +(2.12132 + 2.12132i) q^{77} +14.0000 q^{79} +(-2.82843 + 2.82843i) q^{80} -4.00000 q^{82} +(4.94975 + 4.94975i) q^{83} +(3.00000 - 3.00000i) q^{85} +(-1.41421 - 1.41421i) q^{86} +(-2.00000 - 2.00000i) q^{88} -15.5563i q^{89} +(-15.0000 + 15.0000i) q^{91} -11.3137i q^{92} -6.00000i q^{94} +2.82843 q^{95} +5.00000 q^{97} +2.82843i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{4}+O(q^{10}) \) 4 * q - 8 * q^4	\( 4 q - 8 q^{4} + 4 q^{10} - 20 q^{13} + 16 q^{16} - 8 q^{19} + 4 q^{22} - 4 q^{31} + 16 q^{37} - 8 q^{40} + 4 q^{43} + 32 q^{46} - 8 q^{49} + 40 q^{52} - 32 q^{58} - 8 q^{61} - 32 q^{64} - 20 q^{67} + 12 q^{70} + 16 q^{76} + 56 q^{79} - 16 q^{82} + 12 q^{85} - 8 q^{88} - 60 q^{91} + 20 q^{97}+O(q^{100}) \) 4 * q - 8 * q^4 + 4 * q^10 - 20 * q^13 + 16 * q^16 - 8 * q^19 + 4 * q^22 - 4 * q^31 + 16 * q^37 - 8 * q^40 + 4 * q^43 + 32 * q^46 - 8 * q^49 + 40 * q^52 - 32 * q^58 - 8 * q^61 - 32 * q^64 - 20 * q^67 + 12 * q^70 + 16 * q^76 + 56 * q^79 - 16 * q^82 + 12 * q^85 - 8 * q^88 - 60 * q^91 + 20 * q^97

Introduction

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