LMFDB - Embedded newform 63.2.e.b.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,2,Mod(37,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.e (of order $3$, 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:	$0.503057532734$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.2.e.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(-2.50000 - 0.866025i) q^{7} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(2.00000 - 3.46410i) q^{10} +(-1.00000 + 1.73205i) q^{11} +1.00000 q^{13} +(-1.00000 - 5.19615i) q^{14} +(2.00000 + 3.46410i) q^{16} +(-0.500000 - 0.866025i) q^{19} +4.00000 q^{20} -4.00000 q^{22} +(0.500000 - 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} +(4.00000 - 3.46410i) q^{28} -4.00000 q^{29} +(-4.50000 + 7.79423i) q^{31} +(-4.00000 + 6.92820i) q^{32} +(1.00000 + 5.19615i) q^{35} +(-1.50000 - 2.59808i) q^{37} +(1.00000 - 1.73205i) q^{38} +10.0000 q^{41} +5.00000 q^{43} +(-2.00000 - 3.46410i) q^{44} +(-3.00000 - 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +2.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(6.00000 - 10.3923i) q^{53} +4.00000 q^{55} +(-4.00000 - 6.92820i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(-5.00000 - 8.66025i) q^{61} -18.0000 q^{62} -8.00000 q^{64} +(-1.00000 - 1.73205i) q^{65} +(2.50000 - 4.33013i) q^{67} +(-8.00000 + 6.92820i) q^{70} +6.00000 q^{71} +(1.50000 - 2.59808i) q^{73} +(3.00000 - 5.19615i) q^{74} +2.00000 q^{76} +(4.00000 - 3.46410i) q^{77} +(0.500000 + 0.866025i) q^{79} +(4.00000 - 6.92820i) q^{80} +(10.0000 + 17.3205i) q^{82} -6.00000 q^{83} +(5.00000 + 8.66025i) q^{86} +(8.00000 + 13.8564i) q^{89} +(-2.50000 - 0.866025i) q^{91} +(6.00000 - 10.3923i) q^{94} +(-1.00000 + 1.73205i) q^{95} -6.00000 q^{97} +(-2.00000 + 13.8564i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 5 q^{7}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 5 * q^7	$ 2 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 5 q^{7} + 4 q^{10} - 2 q^{11} + 2 q^{13} - 2 q^{14} + 4 q^{16} - q^{19} + 8 q^{20} - 8 q^{22} + q^{25} + 2 q^{26} + 8 q^{28} - 8 q^{29} - 9 q^{31} - 8 q^{32} + 2 q^{35} - 3 q^{37} + 2 q^{38} + 20 q^{41} + 10 q^{43} - 4 q^{44} - 6 q^{47} + 11 q^{49} + 4 q^{50} - 2 q^{52} + 12 q^{53} + 8 q^{55} - 8 q^{58} - 12 q^{59} - 10 q^{61} - 36 q^{62} - 16 q^{64} - 2 q^{65} + 5 q^{67} - 16 q^{70} + 12 q^{71} + 3 q^{73} + 6 q^{74} + 4 q^{76} + 8 q^{77} + q^{79} + 8 q^{80} + 20 q^{82} - 12 q^{83} + 10 q^{86} + 16 q^{89} - 5 q^{91} + 12 q^{94} - 2 q^{95} - 12 q^{97} - 4 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 5 * q^7 + 4 * q^10 - 2 * q^11 + 2 * q^13 - 2 * q^14 + 4 * q^16 - q^19 + 8 * q^20 - 8 * q^22 + q^25 + 2 * q^26 + 8 * q^28 - 8 * q^29 - 9 * q^31 - 8 * q^32 + 2 * q^35 - 3 * q^37 + 2 * q^38 + 20 * q^41 + 10 * q^43 - 4 * q^44 - 6 * q^47 + 11 * q^49 + 4 * q^50 - 2 * q^52 + 12 * q^53 + 8 * q^55 - 8 * q^58 - 12 * q^59 - 10 * q^61 - 36 * q^62 - 16 * q^64 - 2 * q^65 + 5 * q^67 - 16 * q^70 + 12 * q^71 + 3 * q^73 + 6 * q^74 + 4 * q^76 + 8 * q^77 + q^79 + 8 * q^80 + 20 * q^82 - 12 * q^83 + 10 * q^86 + 16 * q^89 - 5 * q^91 + 12 * q^94 - 2 * q^95 - 12 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.00000	+	1.73205i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$2$	1.00000	+	1.73205i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	0.550990	−	0.834512i	$-0.314250\pi$
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	−0.998203	+	0.0599153i	$0.980917\pi$
$6$		0			0
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$		0			0
$9$		0			0
$10$	2.00000	−	3.46410i	0.632456	−	1.09545i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		0			0
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$	−1.00000	−	5.19615i	−0.267261	−	1.38873i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	4.00000			0.894427
$21$		0			0
$22$	−4.00000			−0.852803
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$		0			0
$28$	4.00000	−	3.46410i	0.755929	−	0.654654i
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$		0			0
$31$	−4.50000	+	7.79423i	−0.808224	+	1.39988i	0.105869	+	0.994380i	$0.466238\pi$
$31$	−4.50000	+	7.79423i	−0.808224	+	1.39988i	−0.914093	+	0.405505i	$0.867096\pi$
$32$	−4.00000	+	6.92820i	−0.707107	+	1.22474i
$33$		0			0
$34$		0			0
$35$	1.00000	+	5.19615i	0.169031	+	0.878310i
$36$		0			0
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	0.715981	−	0.698119i	$-0.245980\pi$
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	−0.962580	+	0.270998i	$0.912646\pi$
$38$	1.00000	−	1.73205i	0.162221	−	0.280976i
$39$		0			0
$40$		0			0
$41$	10.0000			1.56174			0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000			1.56174			0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$	5.00000			0.762493			0.381246	−	0.924473i	$-0.375495\pi$
$43$	5.00000			0.762493			0.381246	+	0.924473i	$0.375495\pi$
$44$	−2.00000	−	3.46410i	−0.301511	−	0.522233i
$45$		0			0
$46$		0			0
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	2.00000			0.282843
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	−0.0783936	−	0.996922i	$-0.524979\pi$
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	0.902557	−	0.430570i	$-0.141688\pi$
$54$		0			0
$55$	4.00000			0.539360
$56$		0			0
$57$		0			0
$58$	−4.00000	−	6.92820i	−0.525226	−	0.909718i
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	0.150148	+	0.988663i	$0.452025\pi$
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	−0.931282	+	0.364299i	$0.881308\pi$
$60$		0			0
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$	−18.0000			−2.28600
$63$		0			0
$64$	−8.00000			−1.00000
$65$	−1.00000	−	1.73205i	−0.124035	−	0.214834i
$66$		0			0
$67$	2.50000	−	4.33013i	0.305424	−	0.529009i	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	2.50000	−	4.33013i	0.305424	−	0.529009i	0.977356	+	0.211604i	$0.0678686\pi$
$68$		0			0
$69$		0			0
$70$	−8.00000	+	6.92820i	−0.956183	+	0.828079i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	1.50000	−	2.59808i	0.175562	−	0.304082i	−0.764794	−	0.644275i	$-0.777159\pi$
$73$	1.50000	−	2.59808i	0.175562	−	0.304082i	0.940356	+	0.340193i	$0.110493\pi$
$74$	3.00000	−	5.19615i	0.348743	−	0.604040i
$75$		0			0
$76$	2.00000			0.229416
$77$	4.00000	−	3.46410i	0.455842	−	0.394771i
$78$		0			0
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$	4.00000	−	6.92820i	0.447214	−	0.774597i
$81$		0			0
$82$	10.0000	+	17.3205i	1.10432	+	1.91273i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		0			0
$85$		0			0
$86$	5.00000	+	8.66025i	0.539164	+	0.933859i
$87$		0			0
$88$		0			0
$89$	8.00000	+	13.8564i	0.847998	+	1.46878i	0.882992	+	0.469389i	$0.155526\pi$
$89$	8.00000	+	13.8564i	0.847998	+	1.46878i	−0.0349934	+	0.999388i	$0.511141\pi$
$90$		0			0
$91$	−2.50000	−	0.866025i	−0.262071	−	0.0907841i
$92$		0			0
$93$		0			0
$94$	6.00000	−	10.3923i	0.618853	−	1.07188i
$95$	−1.00000	+	1.73205i	−0.102598	+	0.177705i
$96$		0			0
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$	−2.00000	+	13.8564i	−0.202031	+	1.39971i
$99$		0			0
$100$	1.00000	+	1.73205i	0.100000	+	0.173205i
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	−0.811976	−	0.583691i	$-0.801608\pi$
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	0.911479	+	0.411346i	$0.134941\pi$
$102$		0			0
$103$	3.50000	+	6.06218i	0.344865	+	0.597324i	0.985329	−	0.170664i	$-0.0545913\pi$
$103$	3.50000	+	6.06218i	0.344865	+	0.597324i	−0.640464	+	0.767988i	$0.721258\pi$
$104$		0			0
$105$		0			0
$106$	24.0000			2.33109
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	0.605308	−	0.795991i	$-0.293050\pi$
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	−0.992003	+	0.126217i	$0.959717\pi$
$108$		0			0
$109$	−4.50000	+	7.79423i	−0.431022	+	0.746552i	−0.996962	−	0.0778949i	$-0.975180\pi$
$109$	−4.50000	+	7.79423i	−0.431022	+	0.746552i	0.565940	+	0.824447i	$0.308513\pi$
$110$	4.00000	+	6.92820i	0.381385	+	0.660578i
$111$		0			0
$112$	−2.00000	−	10.3923i	−0.188982	−	0.981981i
$113$	−10.0000			−0.940721			−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000			−0.940721			−0.470360	+	0.882474i	$0.655876\pi$
$114$		0			0
$115$		0			0
$116$	4.00000	−	6.92820i	0.371391	−	0.643268i
$117$		0			0
$118$	−24.0000			−2.20938
$119$		0			0
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	10.0000	−	17.3205i	0.905357	−	1.56813i
$123$		0			0
$124$	−9.00000	−	15.5885i	−0.808224	−	1.39988i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	−15.0000			−1.33103			−0.665517	−	0.746382i	$-0.731789\pi$
$127$	−15.0000			−1.33103			−0.665517	+	0.746382i	$0.731789\pi$
$128$		0			0
$129$		0			0
$130$	2.00000	−	3.46410i	0.175412	−	0.303822i
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	−0.990972	−	0.134069i	$-0.957196\pi$
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	0.379379	−	0.925241i	$-0.376138\pi$
$132$		0			0
$133$	0.500000	+	2.59808i	0.0433555	+	0.225282i
$134$	10.0000			0.863868
$135$		0			0
$136$		0			0
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$		0			0
$139$	−3.00000			−0.254457			−0.127228	−	0.991873i	$-0.540608\pi$
$139$	−3.00000			−0.254457			−0.127228	+	0.991873i	$0.540608\pi$
$140$	−10.0000	−	3.46410i	−0.845154	−	0.292770i
$141$		0			0
$142$	6.00000	+	10.3923i	0.503509	+	0.872103i
$143$	−1.00000	+	1.73205i	−0.0836242	+	0.144841i
$144$		0			0
$145$	4.00000	+	6.92820i	0.332182	+	0.575356i
$146$	6.00000			0.496564
$147$		0			0
$148$	6.00000			0.493197
$149$	−6.00000	−	10.3923i	−0.491539	−	0.851371i	0.508413	−	0.861113i	$-0.330232\pi$
$149$	−6.00000	−	10.3923i	−0.491539	−	0.851371i	−0.999953	+	0.00974235i	$0.996899\pi$
$150$		0			0
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$		0			0
$153$		0			0
$154$	10.0000	+	3.46410i	0.805823	+	0.279145i
$155$	18.0000			1.44579
$156$		0			0
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	0.997609	−	0.0691164i	$-0.0220180\pi$
$158$	−1.00000	+	1.73205i	−0.0795557	+	0.137795i
$159$		0			0
$160$	16.0000			1.26491
$161$		0			0
$162$		0			0
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	0.777007	−	0.629492i	$-0.216737\pi$
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	−0.933659	+	0.358162i	$0.883403\pi$
$164$	−10.0000	+	17.3205i	−0.780869	+	1.35250i
$165$		0			0
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$	14.0000			1.08335			0.541676	−	0.840587i	$-0.317790\pi$
$167$	14.0000			1.08335			0.541676	+	0.840587i	$0.317790\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$		0			0
$171$		0			0
$172$	−5.00000	+	8.66025i	−0.381246	+	0.660338i
$173$	4.00000	+	6.92820i	0.304114	+	0.526742i	0.977064	−	0.212947i	$-0.0683062\pi$
$173$	4.00000	+	6.92820i	0.304114	+	0.526742i	−0.672949	+	0.739689i	$0.734973\pi$
$174$		0			0
$175$	−2.00000	+	1.73205i	−0.151186	+	0.130931i
$176$	−8.00000			−0.603023
$177$		0			0
$178$	−16.0000	+	27.7128i	−1.19925	+	2.07716i
$179$	1.00000	−	1.73205i	0.0747435	−	0.129460i	−0.826231	−	0.563331i	$-0.809520\pi$
$179$	1.00000	−	1.73205i	0.0747435	−	0.129460i	0.900975	+	0.433872i	$0.142853\pi$
$180$		0			0
$181$	13.0000			0.966282			0.483141	−	0.875542i	$-0.339496\pi$
$181$	13.0000			0.966282			0.483141	+	0.875542i	$0.339496\pi$
$182$	−1.00000	−	5.19615i	−0.0741249	−	0.385164i
$183$		0			0
$184$		0			0
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$		0			0
$187$		0			0
$188$	12.0000			0.875190
$189$		0			0
$190$	−4.00000			−0.290191
$191$	5.00000	+	8.66025i	0.361787	+	0.626634i	0.988255	−	0.152813i	$-0.0488333\pi$
$191$	5.00000	+	8.66025i	0.361787	+	0.626634i	−0.626468	+	0.779447i	$0.715500\pi$
$192$		0			0
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	−0.993215	−	0.116289i	$-0.962900\pi$
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	0.597317	+	0.802005i	$0.296234\pi$
$194$	−6.00000	−	10.3923i	−0.430775	−	0.746124i
$195$		0			0
$196$	−13.0000	+	5.19615i	−0.928571	+	0.371154i
$197$	−16.0000			−1.13995			−0.569976	−	0.821661i	$-0.693048\pi$
$197$	−16.0000			−1.13995			−0.569976	+	0.821661i	$0.693048\pi$
$198$		0			0
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$		0			0
$201$		0			0
$202$	4.00000			0.281439
$203$	10.0000	+	3.46410i	0.701862	+	0.243132i
$204$		0			0
$205$	−10.0000	−	17.3205i	−0.698430	−	1.20972i
$206$	−7.00000	+	12.1244i	−0.487713	+	0.844744i
$207$		0			0
$208$	2.00000	+	3.46410i	0.138675	+	0.240192i
$209$	2.00000			0.138343
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	12.0000	+	20.7846i	0.824163	+	1.42749i
$213$		0			0
$214$	8.00000	−	13.8564i	0.546869	−	0.947204i
$215$	−5.00000	−	8.66025i	−0.340997	−	0.590624i
$216$		0			0
$217$	18.0000	−	15.5885i	1.22192	−	1.05821i
$218$	−18.0000			−1.21911
$219$		0			0
$220$	−4.00000	+	6.92820i	−0.269680	+	0.467099i
$221$		0			0
$222$		0			0
$223$	16.0000			1.07144			0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000			1.07144			0.535720	+	0.844396i	$0.320040\pi$
$224$	16.0000	−	13.8564i	1.06904	−	0.925820i
$225$		0			0
$226$	−10.0000	−	17.3205i	−0.665190	−	1.15214i
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	−0.395860	−	0.918311i	$-0.629553\pi$
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	0.993210	−	0.116331i	$-0.0371134\pi$
$228$		0			0
$229$	9.50000	+	16.4545i	0.627778	+	1.08734i	0.987997	+	0.154475i	$0.0493686\pi$
$229$	9.50000	+	16.4545i	0.627778	+	1.08734i	−0.360219	+	0.932868i	$0.617298\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$		0			0
$235$	−6.00000	+	10.3923i	−0.391397	+	0.677919i
$236$	−12.0000	−	20.7846i	−0.781133	−	1.35296i
$237$		0			0
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	0.547533	+	0.836784i	$0.315567\pi$
$242$	−7.00000	+	12.1244i	−0.449977	+	0.779383i
$243$		0			0
$244$	20.0000			1.28037
$245$	2.00000	−	13.8564i	0.127775	−	0.885253i
$246$		0			0
$247$	−0.500000	−	0.866025i	−0.0318142	−	0.0551039i
$248$		0			0
$249$		0			0
$250$	−12.0000	−	20.7846i	−0.758947	−	1.31453i
$251$	8.00000			0.504956			0.252478	−	0.967603i	$-0.418755\pi$
$251$	8.00000			0.504956			0.252478	+	0.967603i	$0.418755\pi$
$252$		0			0
$253$		0			0
$254$	−15.0000	−	25.9808i	−0.941184	−	1.63018i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	13.0000	+	22.5167i	0.810918	+	1.40455i	0.912222	+	0.409695i	$0.134365\pi$
$257$	13.0000	+	22.5167i	0.810918	+	1.40455i	−0.101305	+	0.994855i	$0.532302\pi$
$258$		0			0
$259$	1.50000	+	7.79423i	0.0932055	+	0.484310i
$260$	4.00000			0.248069
$261$		0			0
$262$	14.0000	−	24.2487i	0.864923	−	1.49809i
$263$	2.00000	−	3.46410i	0.123325	−	0.213606i	−0.797752	−	0.602986i	$-0.793977\pi$
$263$	2.00000	−	3.46410i	0.123325	−	0.213606i	0.921077	+	0.389380i	$0.127311\pi$
$264$		0			0
$265$	−24.0000			−1.47431
$266$	−4.00000	+	3.46410i	−0.245256	+	0.212398i
$267$		0			0
$268$	5.00000	+	8.66025i	0.305424	+	0.529009i
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	−0.759958	−	0.649972i	$-0.774781\pi$
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	0.942871	+	0.333157i	$0.108114\pi$
$270$		0			0
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	0.513905	−	0.857847i	$-0.328199\pi$
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	−0.999870	+	0.0161307i	$0.994865\pi$
$272$		0			0
$273$		0			0
$274$	−24.0000			−1.44989
$275$	1.00000	+	1.73205i	0.0603023	+	0.104447i
$276$		0			0
$277$	−6.50000	+	11.2583i	−0.390547	+	0.676448i	−0.992522	−	0.122068i	$-0.961047\pi$
$277$	−6.50000	+	11.2583i	−0.390547	+	0.676448i	0.601975	+	0.798515i	$0.294381\pi$
$278$	−3.00000	−	5.19615i	−0.179928	−	0.311645i
$279$		0			0
$280$		0			0
$281$	4.00000			0.238620			0.119310	−	0.992857i	$-0.461932\pi$
$281$	4.00000			0.238620			0.119310	+	0.992857i	$0.461932\pi$
$282$		0			0
$283$	5.50000	−	9.52628i	0.326941	−	0.566279i	−0.654962	−	0.755662i	$-0.727315\pi$
$283$	5.50000	−	9.52628i	0.326941	−	0.566279i	0.981903	+	0.189383i	$0.0606488\pi$
$284$	−6.00000	+	10.3923i	−0.356034	+	0.616670i
$285$		0			0
$286$	−4.00000			−0.236525
$287$	−25.0000	−	8.66025i	−1.47570	−	0.511199i
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−8.00000	+	13.8564i	−0.469776	+	0.813676i
$291$		0			0
$292$	3.00000	+	5.19615i	0.175562	+	0.304082i
$293$	−8.00000			−0.467365			−0.233682	−	0.972313i	$-0.575078\pi$
$293$	−8.00000			−0.467365			−0.233682	+	0.972313i	$0.575078\pi$
$294$		0			0
$295$	24.0000			1.39733
$296$		0			0
$297$		0			0
$298$	12.0000	−	20.7846i	0.695141	−	1.20402i
$299$		0			0
$300$		0			0
$301$	−12.5000	−	4.33013i	−0.720488	−	0.249584i
$302$	32.0000			1.84139
$303$		0			0
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$	−10.0000	+	17.3205i	−0.572598	+	0.991769i
$306$		0			0
$307$	−17.0000			−0.970241			−0.485121	−	0.874447i	$-0.661224\pi$
$307$	−17.0000			−0.970241			−0.485121	+	0.874447i	$0.661224\pi$
$308$	2.00000	+	10.3923i	0.113961	+	0.592157i
$309$		0			0
$310$	18.0000	+	31.1769i	1.02233	+	1.77073i
$311$	−3.00000	+	5.19615i	−0.170114	+	0.294647i	−0.938460	−	0.345389i	$-0.887747\pi$
$311$	−3.00000	+	5.19615i	−0.170114	+	0.294647i	0.768345	+	0.640036i	$0.221080\pi$
$312$		0			0
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	0.879810	−	0.475325i	$-0.157669\pi$
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	−0.851549	+	0.524276i	$0.824336\pi$
$314$	28.0000			1.58013
$315$		0			0
$316$	−2.00000			−0.112509
$317$	12.0000	+	20.7846i	0.673987	+	1.16738i	0.976764	+	0.214318i	$0.0687530\pi$
$317$	12.0000	+	20.7846i	0.673987	+	1.16738i	−0.302777	+	0.953062i	$0.597914\pi$
$318$		0			0
$319$	4.00000	−	6.92820i	0.223957	−	0.387905i
$320$	8.00000	+	13.8564i	0.447214	+	0.774597i
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	0.500000	−	0.866025i	0.0277350	−	0.0480384i
$326$	4.00000	−	6.92820i	0.221540	−	0.383718i
$327$		0			0
$328$		0			0
$329$	3.00000	+	15.5885i	0.165395	+	0.859419i
$330$		0			0
$331$	12.5000	+	21.6506i	0.687062	+	1.19003i	0.972784	+	0.231714i	$0.0744333\pi$
$331$	12.5000	+	21.6506i	0.687062	+	1.19003i	−0.285722	+	0.958313i	$0.592233\pi$
$332$	6.00000	−	10.3923i	0.329293	−	0.570352i
$333$		0			0
$334$	14.0000	+	24.2487i	0.766046	+	1.32683i
$335$	−10.0000			−0.546358
$336$		0			0
$337$	13.0000			0.708155			0.354078	−	0.935216i	$-0.384795\pi$
$337$	13.0000			0.708155			0.354078	+	0.935216i	$0.384795\pi$
$338$	−12.0000	−	20.7846i	−0.652714	−	1.13053i
$339$		0			0
$340$		0			0
$341$	−9.00000	−	15.5885i	−0.487377	−	0.844162i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$		0			0
$346$	−8.00000	+	13.8564i	−0.430083	+	0.744925i
$347$	16.0000	−	27.7128i	0.858925	−	1.48770i	−0.0140303	−	0.999902i	$-0.504466\pi$
$347$	16.0000	−	27.7128i	0.858925	−	1.48770i	0.872955	−	0.487800i	$-0.162201\pi$
$348$		0			0
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$	−5.00000	−	1.73205i	−0.267261	−	0.0925820i
$351$		0			0
$352$	−8.00000	−	13.8564i	−0.426401	−	0.738549i
$353$	17.0000	−	29.4449i	0.904819	−	1.56719i	0.0836583	−	0.996495i	$-0.473340\pi$
$353$	17.0000	−	29.4449i	0.904819	−	1.56719i	0.821160	−	0.570697i	$-0.193327\pi$
$354$		0			0
$355$	−6.00000	−	10.3923i	−0.318447	−	0.551566i
$356$	−32.0000			−1.69600
$357$		0			0
$358$	4.00000			0.211407
$359$	10.0000	+	17.3205i	0.527780	+	0.914141i	0.999476	+	0.0323801i	$0.0103087\pi$
$359$	10.0000	+	17.3205i	0.527780	+	0.914141i	−0.471696	+	0.881761i	$0.656358\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	13.0000	+	22.5167i	0.683265	+	1.18345i
$363$		0			0
$364$	4.00000	−	3.46410i	0.209657	−	0.181568i
$365$	−6.00000			−0.314054
$366$		0			0
$367$	4.50000	−	7.79423i	0.234898	−	0.406855i	−0.724345	−	0.689438i	$-0.757858\pi$
$367$	4.50000	−	7.79423i	0.234898	−	0.406855i	0.959243	+	0.282582i	$0.0911910\pi$
$368$		0			0
$369$		0			0
$370$	−12.0000			−0.623850
$371$	−24.0000	+	20.7846i	−1.24602	+	1.07908i
$372$		0			0
$373$	−11.5000	−	19.9186i	−0.595447	−	1.03135i	−0.993484	−	0.113975i	$-0.963641\pi$
$373$	−11.5000	−	19.9186i	−0.595447	−	1.03135i	0.398036	−	0.917370i	$-0.369692\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.00000			−0.206010
$378$		0			0
$379$	3.00000			0.154100			0.0770498	−	0.997027i	$-0.475450\pi$
$379$	3.00000			0.154100			0.0770498	+	0.997027i	$0.475450\pi$
$380$	−2.00000	−	3.46410i	−0.102598	−	0.177705i
$381$		0			0
$382$	−10.0000	+	17.3205i	−0.511645	+	0.886194i
$383$	−6.00000	−	10.3923i	−0.306586	−	0.531022i	0.671027	−	0.741433i	$-0.265853\pi$
$383$	−6.00000	−	10.3923i	−0.306586	−	0.531022i	−0.977613	+	0.210411i	$0.932520\pi$
$384$		0			0
$385$	−10.0000	−	3.46410i	−0.509647	−	0.176547i
$386$	−22.0000			−1.11977
$387$		0			0
$388$	6.00000	−	10.3923i	0.304604	−	0.527589i
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	−0.932002	−	0.362454i	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$	−16.0000	−	27.7128i	−0.806068	−	1.39615i
$395$	1.00000	−	1.73205i	0.0503155	−	0.0871489i
$396$		0			0
$397$	4.50000	+	7.79423i	0.225849	+	0.391181i	0.956574	−	0.291491i	$-0.0941512\pi$
$397$	4.50000	+	7.79423i	0.225849	+	0.391181i	−0.730725	+	0.682672i	$0.760818\pi$
$398$		0			0
$399$		0			0
$400$	4.00000			0.200000
$401$	−18.0000	−	31.1769i	−0.898877	−	1.55690i	−0.828932	−	0.559350i	$-0.811051\pi$
$401$	−18.0000	−	31.1769i	−0.898877	−	1.55690i	−0.0699455	−	0.997551i	$-0.522283\pi$
$402$		0			0
$403$	−4.50000	+	7.79423i	−0.224161	+	0.388258i
$404$	2.00000	+	3.46410i	0.0995037	+	0.172345i
$405$		0			0
$406$	4.00000	+	20.7846i	0.198517	+	1.03152i
$407$	6.00000			0.297409
$408$		0			0
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	−0.921192	−	0.389109i	$-0.872783\pi$
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	0.797574	+	0.603220i	$0.206116\pi$
$410$	20.0000	−	34.6410i	0.987730	−	1.71080i
$411$		0			0
$412$	−14.0000			−0.689730
$413$	24.0000	−	20.7846i	1.18096	−	1.02274i
$414$		0			0
$415$	6.00000	+	10.3923i	0.294528	+	0.510138i
$416$	−4.00000	+	6.92820i	−0.196116	+	0.339683i
$417$		0			0
$418$	2.00000	+	3.46410i	0.0978232	+	0.169435i
$419$	−30.0000			−1.46560			−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000			−1.46560			−0.732798	+	0.680446i	$0.761786\pi$
$420$		0			0
$421$	−7.00000			−0.341159			−0.170580	−	0.985344i	$-0.554564\pi$
$421$	−7.00000			−0.341159			−0.170580	+	0.985344i	$0.554564\pi$
$422$	4.00000	+	6.92820i	0.194717	+	0.337260i
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	5.00000	+	25.9808i	0.241967	+	1.25730i
$428$	16.0000			0.773389
$429$		0			0
$430$	10.0000	−	17.3205i	0.482243	−	0.835269i
$431$	−9.00000	+	15.5885i	−0.433515	+	0.750870i	−0.997173	−	0.0751385i	$-0.976060\pi$
$431$	−9.00000	+	15.5885i	−0.433515	+	0.750870i	0.563658	+	0.826008i	$0.309393\pi$
$432$		0			0
$433$	31.0000			1.48976			0.744882	−	0.667196i	$-0.232506\pi$
$433$	31.0000			1.48976			0.744882	+	0.667196i	$0.232506\pi$
$434$	45.0000	+	15.5885i	2.16007	+	0.748270i
$435$		0			0
$436$	−9.00000	−	15.5885i	−0.431022	−	0.746552i
$437$		0			0
$438$		0			0
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	0.972626	−	0.232377i	$-0.0746503\pi$
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	−0.687557	+	0.726130i	$0.741317\pi$
$444$		0			0
$445$	16.0000	−	27.7128i	0.758473	−	1.31371i
$446$	16.0000	+	27.7128i	0.757622	+	1.31224i
$447$		0			0
$448$	20.0000	+	6.92820i	0.944911	+	0.327327i
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		0			0
$451$	−10.0000	+	17.3205i	−0.470882	+	0.815591i
$452$	10.0000	−	17.3205i	0.470360	−	0.814688i
$453$		0			0
$454$	36.0000			1.68956
$455$	1.00000	+	5.19615i	0.0468807	+	0.243599i
$456$		0			0
$457$	5.50000	+	9.52628i	0.257279	+	0.445621i	0.965512	−	0.260358i	$-0.0838407\pi$
$457$	5.50000	+	9.52628i	0.257279	+	0.445621i	−0.708233	+	0.705979i	$0.750507\pi$
$458$	−19.0000	+	32.9090i	−0.887812	+	1.53773i
$459$		0			0
$460$		0			0
$461$	−20.0000			−0.931493			−0.465746	−	0.884918i	$-0.654214\pi$
$461$	−20.0000			−0.931493			−0.465746	+	0.884918i	$0.654214\pi$
$462$		0			0
$463$	−17.0000			−0.790057			−0.395029	−	0.918669i	$-0.629265\pi$
$463$	−17.0000			−0.790057			−0.395029	+	0.918669i	$0.629265\pi$
$464$	−8.00000	−	13.8564i	−0.371391	−	0.643268i
$465$		0			0
$466$	−6.00000	+	10.3923i	−0.277945	+	0.481414i
$467$	3.00000	+	5.19615i	0.138823	+	0.240449i	0.927052	−	0.374934i	$-0.122335\pi$
$467$	3.00000	+	5.19615i	0.138823	+	0.240449i	−0.788228	+	0.615383i	$0.789001\pi$
$468$		0			0
$469$	−10.0000	+	8.66025i	−0.461757	+	0.399893i
$470$	−24.0000			−1.10704
$471$		0			0
$472$		0			0
$473$	−5.00000	+	8.66025i	−0.229900	+	0.398199i
$474$		0			0
$475$	−1.00000			−0.0458831
$476$		0			0
$477$		0			0
$478$	−6.00000	−	10.3923i	−0.274434	−	0.475333i
$479$	−14.0000	+	24.2487i	−0.639676	+	1.10795i	0.345827	+	0.938298i	$0.387598\pi$
$479$	−14.0000	+	24.2487i	−0.639676	+	1.10795i	−0.985504	+	0.169654i	$0.945735\pi$
$480$		0			0
$481$	−1.50000	−	2.59808i	−0.0683941	−	0.118462i
$482$	−28.0000			−1.27537
$483$		0			0
$484$	−14.0000			−0.636364
$485$	6.00000	+	10.3923i	0.272446	+	0.471890i
$486$		0			0
$487$	−15.5000	+	26.8468i	−0.702372	+	1.21654i	0.265260	+	0.964177i	$0.414542\pi$
$487$	−15.5000	+	26.8468i	−0.702372	+	1.21654i	−0.967632	+	0.252367i	$0.918791\pi$
$488$		0			0
$489$		0			0
$490$	26.0000	−	10.3923i	1.17456	−	0.469476i
$491$	28.0000			1.26362			0.631811	−	0.775122i	$-0.282312\pi$
$491$	28.0000			1.26362			0.631811	+	0.775122i	$0.282312\pi$
$492$		0			0
$493$		0			0
$494$	1.00000	−	1.73205i	0.0449921	−	0.0779287i
$495$		0			0
$496$	−36.0000			−1.61645
$497$	−15.0000	−	5.19615i	−0.672842	−	0.233079i
$498$		0			0
$499$	−18.5000	−	32.0429i	−0.828174	−	1.43444i	−0.899469	−	0.436984i	$-0.856047\pi$
$499$	−18.5000	−	32.0429i	−0.828174	−	1.43444i	0.0712957	−	0.997455i	$-0.477287\pi$
$500$	12.0000	−	20.7846i	0.536656	−	0.929516i
$501$		0			0
$502$	8.00000	+	13.8564i	0.357057	+	0.618442i
$503$	42.0000			1.87269			0.936344	−	0.351085i	$-0.114187\pi$
$503$	42.0000			1.87269			0.936344	+	0.351085i	$0.114187\pi$
$504$		0			0
$505$	−4.00000			−0.177998
$506$		0			0
$507$		0			0
$508$	15.0000	−	25.9808i	0.665517	−	1.15271i
$509$	1.00000	+	1.73205i	0.0443242	+	0.0767718i	0.887336	−	0.461123i	$-0.152553\pi$
$509$	1.00000	+	1.73205i	0.0443242	+	0.0767718i	−0.843012	+	0.537895i	$0.819220\pi$
$510$		0			0
$511$	−6.00000	+	5.19615i	−0.265424	+	0.229864i
$512$	−32.0000			−1.41421
$513$		0			0
$514$	−26.0000	+	45.0333i	−1.14681	+	1.98633i
$515$	7.00000	−	12.1244i	0.308457	−	0.534263i
$516$		0			0
$517$	12.0000			0.527759
$518$	−12.0000	+	10.3923i	−0.527250	+	0.456612i
$519$		0			0
$520$		0			0
$521$	6.00000	−	10.3923i	0.262865	−	0.455295i	−0.704137	−	0.710064i	$-0.748666\pi$
$521$	6.00000	−	10.3923i	0.262865	−	0.455295i	0.967002	+	0.254769i	$0.0819994\pi$
$522$		0			0
$523$	−15.5000	−	26.8468i	−0.677768	−	1.17393i	−0.975652	−	0.219326i	$-0.929614\pi$
$523$	−15.5000	−	26.8468i	−0.677768	−	1.17393i	0.297884	−	0.954602i	$-0.403719\pi$
$524$	28.0000			1.22319
$525$		0			0
$526$	8.00000			0.348817
$527$		0			0
$528$		0			0
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	−24.0000	−	41.5692i	−1.04249	−	1.80565i
$531$		0			0
$532$	−5.00000	−	1.73205i	−0.216777	−	0.0750939i
$533$	10.0000			0.433148
$534$		0			0
$535$	−8.00000	+	13.8564i	−0.345870	+	0.599065i
$536$		0			0
$537$		0			0
$538$	12.0000			0.517357
$539$	−13.0000	+	5.19615i	−0.559950	+	0.223814i
$540$		0			0
$541$	9.50000	+	16.4545i	0.408437	+	0.707433i	0.994715	−	0.102677i	$-0.0327407\pi$
$541$	9.50000	+	16.4545i	0.408437	+	0.707433i	−0.586278	+	0.810110i	$0.699407\pi$
$542$	16.0000	−	27.7128i	0.687259	−	1.19037i
$543$		0			0
$544$		0			0
$545$	18.0000			0.771035
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	−12.0000	−	20.7846i	−0.512615	−	0.887875i
$549$		0			0
$550$	−2.00000	+	3.46410i	−0.0852803	+	0.147710i
$551$	2.00000	+	3.46410i	0.0852029	+	0.147576i
$552$		0			0
$553$	−0.500000	−	2.59808i	−0.0212622	−	0.110481i
$554$	−26.0000			−1.10463
$555$		0			0
$556$	3.00000	−	5.19615i	0.127228	−	0.220366i
$557$	−1.00000	+	1.73205i	−0.0423714	+	0.0733893i	−0.886433	−	0.462856i	$-0.846825\pi$
$557$	−1.00000	+	1.73205i	−0.0423714	+	0.0733893i	0.844062	+	0.536246i	$0.180158\pi$
$558$		0			0
$559$	5.00000			0.211477
$560$	−16.0000	+	13.8564i	−0.676123	+	0.585540i
$561$		0			0
$562$	4.00000	+	6.92820i	0.168730	+	0.292249i
$563$	−13.0000	+	22.5167i	−0.547885	+	0.948964i	0.450535	+	0.892759i	$0.351233\pi$
$563$	−13.0000	+	22.5167i	−0.547885	+	0.948964i	−0.998419	+	0.0562051i	$0.982100\pi$
$564$		0			0
$565$	10.0000	+	17.3205i	0.420703	+	0.728679i
$566$	22.0000			0.924729
$567$		0			0
$568$		0			0
$569$	−13.0000	−	22.5167i	−0.544988	−	0.943948i	−0.998608	−	0.0527519i	$-0.983201\pi$
$569$	−13.0000	−	22.5167i	−0.544988	−	0.943948i	0.453619	−	0.891196i	$-0.350133\pi$
$570$		0			0
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	−0.595862	−	0.803087i	$-0.703189\pi$
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	0.993425	+	0.114488i	$0.0365228\pi$
$572$	−2.00000	−	3.46410i	−0.0836242	−	0.144841i
$573$		0			0
$574$	−10.0000	−	51.9615i	−0.417392	−	2.16883i
$575$		0			0
$576$		0			0
$577$	8.50000	−	14.7224i	0.353860	−	0.612903i	−0.633062	−	0.774101i	$-0.718202\pi$
$577$	8.50000	−	14.7224i	0.353860	−	0.612903i	0.986922	+	0.161198i	$0.0515357\pi$
$578$	−17.0000	+	29.4449i	−0.707107	+	1.22474i
$579$		0			0
$580$	−16.0000			−0.664364
$581$	15.0000	+	5.19615i	0.622305	+	0.215573i
$582$		0			0
$583$	12.0000	+	20.7846i	0.496989	+	0.860811i
$584$		0			0
$585$		0			0
$586$	−8.00000	−	13.8564i	−0.330477	−	0.572403i
$587$	−16.0000			−0.660391			−0.330195	−	0.943913i	$-0.607115\pi$
$587$	−16.0000			−0.660391			−0.330195	+	0.943913i	$0.607115\pi$
$588$		0			0
$589$	9.00000			0.370839
$590$	24.0000	+	41.5692i	0.988064	+	1.71138i
$591$		0			0
$592$	6.00000	−	10.3923i	0.246598	−	0.427121i
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	0.797831	−	0.602881i	$-0.205981\pi$
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	−0.921026	+	0.389501i	$0.872647\pi$
$594$		0			0
$595$		0			0
$596$	24.0000			0.983078
$597$		0			0
$598$		0			0
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	−0.717021	−	0.697051i	$-0.754495\pi$
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	0.962175	+	0.272433i	$0.0878284\pi$
$600$		0			0
$601$	−9.00000			−0.367118			−0.183559	−	0.983009i	$-0.558762\pi$
$601$	−9.00000			−0.367118			−0.183559	+	0.983009i	$0.558762\pi$
$602$	−5.00000	−	25.9808i	−0.203785	−	1.05890i
$603$		0			0
$604$	16.0000	+	27.7128i	0.651031	+	1.12762i
$605$	7.00000	−	12.1244i	0.284590	−	0.492925i
$606$		0			0
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	0.532509	−	0.846424i	$-0.321249\pi$
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	−0.999279	+	0.0379540i	$0.987916\pi$
$608$	8.00000			0.324443
$609$		0			0
$610$	−40.0000			−1.61955
$611$	−3.00000	−	5.19615i	−0.121367	−	0.210214i
$612$		0			0
$613$	−17.0000	+	29.4449i	−0.686624	+	1.18927i	0.286300	+	0.958140i	$0.407575\pi$
$613$	−17.0000	+	29.4449i	−0.686624	+	1.18927i	−0.972924	+	0.231127i	$0.925759\pi$
$614$	−17.0000	−	29.4449i	−0.686064	−	1.18830i
$615$		0			0
$616$		0			0
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$		0			0
$619$	14.5000	−	25.1147i	0.582804	−	1.00945i	−0.412341	−	0.911030i	$-0.635289\pi$
$619$	14.5000	−	25.1147i	0.582804	−	1.00945i	0.995145	−	0.0984169i	$-0.0313779\pi$
$620$	−18.0000	+	31.1769i	−0.722897	+	1.25210i
$621$		0			0
$622$	−12.0000			−0.481156
$623$	−8.00000	−	41.5692i	−0.320513	−	1.66544i
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	−1.00000	+	1.73205i	−0.0399680	+	0.0692267i
$627$		0			0
$628$	14.0000	+	24.2487i	0.558661	+	0.967629i
$629$		0			0
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$		0			0
$633$		0			0
$634$	−24.0000	+	41.5692i	−0.953162	+	1.65092i
$635$	15.0000	+	25.9808i	0.595257	+	1.03102i
$636$		0			0
$637$	5.50000	+	4.33013i	0.217918	+	0.171566i
$638$	16.0000			0.633446
$639$		0			0
$640$		0			0
$641$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$641$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$642$		0			0
$643$	−19.0000			−0.749287			−0.374643	−	0.927169i	$-0.622235\pi$
$643$	−19.0000			−0.749287			−0.374643	+	0.927169i	$0.622235\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.00000	−	1.73205i	0.0393141	−	0.0680939i	−0.845699	−	0.533660i	$-0.820816\pi$
$647$	1.00000	−	1.73205i	0.0393141	−	0.0680939i	0.885013	+	0.465566i	$0.154149\pi$
$648$		0			0
$649$	−12.0000	−	20.7846i	−0.471041	−	0.815867i
$650$	2.00000			0.0784465
$651$		0			0
$652$	8.00000			0.313304
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	0.986634	−	0.162951i	$-0.0521013\pi$
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	−0.634437	+	0.772975i	$0.718768\pi$
$654$		0			0
$655$	−14.0000	+	24.2487i	−0.547025	+	0.947476i
$656$	20.0000	+	34.6410i	0.780869	+	1.35250i
$657$		0			0
$658$	−24.0000	+	20.7846i	−0.935617	+	0.810268i
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$	20.5000	−	35.5070i	0.797358	−	1.38106i	−0.123974	−	0.992286i	$-0.539564\pi$
$661$	20.5000	−	35.5070i	0.797358	−	1.38106i	0.921331	−	0.388778i	$-0.127103\pi$
$662$	−25.0000	+	43.3013i	−0.971653	+	1.68295i
$663$		0			0
$664$		0			0
$665$	4.00000	−	3.46410i	0.155113	−	0.134332i
$666$		0			0
$667$		0			0
$668$	−14.0000	+	24.2487i	−0.541676	+	0.938211i
$669$		0			0
$670$	−10.0000	−	17.3205i	−0.386334	−	0.669150i
$671$	20.0000			0.772091
$672$		0			0
$673$	−41.0000			−1.58043			−0.790217	−	0.612827i	$-0.790032\pi$
$673$	−41.0000			−1.58043			−0.790217	+	0.612827i	$0.790032\pi$
$674$	13.0000	+	22.5167i	0.500741	+	0.867309i
$675$		0			0
$676$	12.0000	−	20.7846i	0.461538	−	0.799408i
$677$	6.00000	+	10.3923i	0.230599	+	0.399409i	0.957984	−	0.286820i	$-0.0925982\pi$
$677$	6.00000	+	10.3923i	0.230599	+	0.399409i	−0.727386	+	0.686229i	$0.759265\pi$
$678$		0			0
$679$	15.0000	+	5.19615i	0.575647	+	0.199410i
$680$		0			0
$681$		0			0
$682$	18.0000	−	31.1769i	0.689256	−	1.19383i
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$		0			0
$685$	24.0000			0.916993
$686$	17.0000	−	32.9090i	0.649063	−	1.25647i
$687$		0			0
$688$	10.0000	+	17.3205i	0.381246	+	0.660338i
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$		0			0
$691$	18.5000	+	32.0429i	0.703773	+	1.21897i	0.967132	+	0.254273i	$0.0818362\pi$
$691$	18.5000	+	32.0429i	0.703773	+	1.21897i	−0.263359	+	0.964698i	$0.584830\pi$
$692$	−16.0000			−0.608229
$693$		0			0
$694$	64.0000			2.42941
$695$	3.00000	+	5.19615i	0.113796	+	0.197101i
$696$		0			0
$697$		0			0
$698$	−14.0000	−	24.2487i	−0.529908	−	0.917827i
$699$		0			0
$700$	−1.00000	−	5.19615i	−0.0377964	−	0.196396i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	−1.50000	+	2.59808i	−0.0565736	+	0.0979883i
$704$	8.00000	−	13.8564i	0.301511	−	0.522233i
$705$		0			0
$706$	68.0000			2.55921
$707$	−4.00000	+	3.46410i	−0.150435	+	0.130281i
$708$		0			0
$709$	−15.0000	−	25.9808i	−0.563337	−	0.975728i	−0.997202	−	0.0747503i	$-0.976184\pi$
$709$	−15.0000	−	25.9808i	−0.563337	−	0.975728i	0.433865	−	0.900978i	$-0.357149\pi$
$710$	12.0000	−	20.7846i	0.450352	−	0.780033i
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$	4.00000			0.149592
$716$	2.00000	+	3.46410i	0.0747435	+	0.129460i
$717$		0			0
$718$	−20.0000	+	34.6410i	−0.746393	+	1.29279i
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	0.647965	−	0.761670i	$-0.275620\pi$
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	−0.983608	+	0.180319i	$0.942287\pi$
$720$		0			0
$721$	−3.50000	−	18.1865i	−0.130347	−	0.677302i
$722$	36.0000			1.33978
$723$		0			0
$724$	−13.0000	+	22.5167i	−0.483141	+	0.836825i
$725$	−2.00000	+	3.46410i	−0.0742781	+	0.128654i
$726$		0			0
$727$	−13.0000			−0.482143			−0.241072	−	0.970507i	$-0.577499\pi$
$727$	−13.0000			−0.482143			−0.241072	+	0.970507i	$0.577499\pi$
$728$		0			0
$729$		0			0
$730$	−6.00000	−	10.3923i	−0.222070	−	0.384636i
$731$		0			0
$732$		0			0
$733$	7.50000	+	12.9904i	0.277019	+	0.479811i	0.970642	−	0.240527i	$-0.0773202\pi$
$733$	7.50000	+	12.9904i	0.277019	+	0.479811i	−0.693624	+	0.720338i	$0.743987\pi$
$734$	18.0000			0.664392
$735$		0			0
$736$		0			0
$737$	5.00000	+	8.66025i	0.184177	+	0.319005i
$738$		0			0
$739$	7.50000	−	12.9904i	0.275892	−	0.477859i	−0.694468	−	0.719524i	$-0.744360\pi$
$739$	7.50000	−	12.9904i	0.275892	−	0.477859i	0.970360	+	0.241665i	$0.0776935\pi$
$740$	−6.00000	−	10.3923i	−0.220564	−	0.382029i
$741$		0			0
$742$	−60.0000	−	20.7846i	−2.20267	−	0.763027i
$743$	−42.0000			−1.54083			−0.770415	−	0.637542i	$-0.779951\pi$
$743$	−42.0000			−1.54083			−0.770415	+	0.637542i	$0.779951\pi$
$744$		0			0
$745$	−12.0000	+	20.7846i	−0.439646	+	0.761489i
$746$	23.0000	−	39.8372i	0.842090	−	1.45854i
$747$		0			0
$748$		0			0
$749$	4.00000	+	20.7846i	0.146157	+	0.759453i
$750$		0			0
$751$	−6.50000	−	11.2583i	−0.237188	−	0.410822i	0.722718	−	0.691143i	$-0.242893\pi$
$751$	−6.50000	−	11.2583i	−0.237188	−	0.410822i	−0.959906	+	0.280321i	$0.909559\pi$
$752$	12.0000	−	20.7846i	0.437595	−	0.757937i
$753$		0			0
$754$	−4.00000	−	6.92820i	−0.145671	−	0.252310i
$755$	−32.0000			−1.16460
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	3.00000	+	5.19615i	0.108965	+	0.188733i
$759$		0			0
$760$		0			0
$761$	−24.0000	−	41.5692i	−0.869999	−	1.50688i	−0.861996	−	0.506915i	$-0.830786\pi$
$761$	−24.0000	−	41.5692i	−0.869999	−	1.50688i	−0.00800331	−	0.999968i	$-0.502548\pi$
$762$		0			0
$763$	18.0000	−	15.5885i	0.651644	−	0.564340i
$764$	−20.0000			−0.723575
$765$		0			0
$766$	12.0000	−	20.7846i	0.433578	−	0.750978i
$767$	−6.00000	+	10.3923i	−0.216647	+	0.375244i
$768$		0			0
$769$	−49.0000			−1.76699			−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−49.0000			−1.76699			−0.883493	+	0.468445i	$0.844814\pi$
$770$	−4.00000	−	20.7846i	−0.144150	−	0.749025i
$771$		0			0
$772$	−11.0000	−	19.0526i	−0.395899	−	0.685717i
$773$	−17.0000	+	29.4449i	−0.611448	+	1.05906i	0.379549	+	0.925172i	$0.376079\pi$
$773$	−17.0000	+	29.4449i	−0.611448	+	1.05906i	−0.990997	+	0.133887i	$0.957254\pi$
$774$		0			0
$775$	4.50000	+	7.79423i	0.161645	+	0.279977i
$776$		0			0
$777$		0			0
$778$	−12.0000			−0.430221
$779$	−5.00000	−	8.66025i	−0.179144	−	0.310286i
$780$		0			0
$781$	−6.00000	+	10.3923i	−0.214697	+	0.371866i
$782$		0			0
$783$		0			0
$784$	−4.00000	+	27.7128i	−0.142857	+	0.989743i
$785$	−28.0000			−0.999363
$786$		0			0
$787$	−20.0000	+	34.6410i	−0.712923	+	1.23482i	0.250832	+	0.968031i	$0.419296\pi$
$787$	−20.0000	+	34.6410i	−0.712923	+	1.23482i	−0.963755	+	0.266788i	$0.914038\pi$
$788$	16.0000	−	27.7128i	0.569976	−	0.987228i
$789$		0			0
$790$	4.00000			0.142314
$791$	25.0000	+	8.66025i	0.888898	+	0.307923i
$792$		0			0
$793$	−5.00000	−	8.66025i	−0.177555	−	0.307535i
$794$	−9.00000	+	15.5885i	−0.319398	+	0.553214i
$795$		0			0
$796$		0			0
$797$	8.00000			0.283375			0.141687	−	0.989911i	$-0.454747\pi$
$797$	8.00000			0.283375			0.141687	+	0.989911i	$0.454747\pi$
$798$		0			0
$799$		0			0
$800$	4.00000	+	6.92820i	0.141421	+	0.244949i
$801$		0			0
$802$	36.0000	−	62.3538i	1.27120	−	2.20179i
$803$	3.00000	+	5.19615i	0.105868	+	0.183368i
$804$		0			0
$805$		0			0
$806$	−18.0000			−0.634023
$807$		0			0
$808$		0			0
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	−0.472119	−	0.881535i	$-0.656511\pi$
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	0.999491	−	0.0319002i	$-0.0101559\pi$
$810$		0			0
$811$	32.0000			1.12367			0.561836	−	0.827249i	$-0.310095\pi$
$811$	32.0000			1.12367			0.561836	+	0.827249i	$0.310095\pi$
$812$	−16.0000	+	13.8564i	−0.561490	+	0.486265i
$813$		0			0
$814$	6.00000	+	10.3923i	0.210300	+	0.364250i
$815$	−4.00000	+	6.92820i	−0.140114	+	0.242684i
$816$		0			0
$817$	−2.50000	−	4.33013i	−0.0874639	−	0.151492i
$818$	−10.0000			−0.349642
$819$		0			0
$820$	40.0000			1.39686
$821$	1.00000	+	1.73205i	0.0349002	+	0.0604490i	0.882948	−	0.469471i	$-0.155555\pi$
$821$	1.00000	+	1.73205i	0.0349002	+	0.0604490i	−0.848048	+	0.529920i	$0.822222\pi$
$822$		0			0
$823$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$823$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$824$		0			0
$825$		0			0
$826$	60.0000	+	20.7846i	2.08767	+	0.723189i
$827$	30.0000			1.04320			0.521601	−	0.853189i	$-0.325335\pi$
$827$	30.0000			1.04320			0.521601	+	0.853189i	$0.325335\pi$
$828$		0			0
$829$	−20.5000	+	35.5070i	−0.711994	+	1.23321i	0.252113	+	0.967698i	$0.418875\pi$
$829$	−20.5000	+	35.5070i	−0.711994	+	1.23321i	−0.964107	+	0.265513i	$0.914459\pi$
$830$	−12.0000	+	20.7846i	−0.416526	+	0.721444i
$831$		0			0
$832$	−8.00000			−0.277350
$833$		0			0
$834$		0			0
$835$	−14.0000	−	24.2487i	−0.484490	−	0.839161i
$836$	−2.00000	+	3.46410i	−0.0691714	+	0.119808i
$837$		0			0
$838$	−30.0000	−	51.9615i	−1.03633	−	1.79498i
$839$	44.0000			1.51905			0.759524	−	0.650479i	$-0.225432\pi$
$839$	44.0000			1.51905			0.759524	+	0.650479i	$0.225432\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	−7.00000	−	12.1244i	−0.241236	−	0.417833i
$843$		0			0
$844$	−4.00000	+	6.92820i	−0.137686	+	0.238479i
$845$	12.0000	+	20.7846i	0.412813	+	0.715012i
$846$		0			0
$847$	−3.50000	−	18.1865i	−0.120261	−	0.624897i
$848$	48.0000			1.64833
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	35.0000			1.19838			0.599189	−	0.800608i	$-0.295490\pi$
$853$	35.0000			1.19838			0.599189	+	0.800608i	$0.295490\pi$
$854$	−40.0000	+	34.6410i	−1.36877	+	1.18539i
$855$		0			0
$856$		0			0
$857$	−16.0000	+	27.7128i	−0.546550	+	0.946652i	0.451958	+	0.892039i	$0.350726\pi$
$857$	−16.0000	+	27.7128i	−0.546550	+	0.946652i	−0.998508	+	0.0546125i	$0.982608\pi$
$858$		0			0
$859$	20.0000	+	34.6410i	0.682391	+	1.18194i	0.974249	+	0.225475i	$0.0723932\pi$
$859$	20.0000	+	34.6410i	0.682391	+	1.18194i	−0.291858	+	0.956462i	$0.594273\pi$
$860$	20.0000			0.681994
$861$		0			0
$862$	−36.0000			−1.22616
$863$	−27.0000	−	46.7654i	−0.919091	−	1.59191i	−0.800799	−	0.598933i	$-0.795592\pi$
$863$	−27.0000	−	46.7654i	−0.919091	−	1.59191i	−0.118291	−	0.992979i	$-0.537742\pi$
$864$		0			0
$865$	8.00000	−	13.8564i	0.272008	−	0.471132i
$866$	31.0000	+	53.6936i	1.05342	+	1.82458i
$867$		0			0
$868$	9.00000	+	46.7654i	0.305480	+	1.58732i
$869$	−2.00000			−0.0678454
$870$		0			0
$871$	2.50000	−	4.33013i	0.0847093	−	0.146721i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	30.0000	+	10.3923i	1.01419	+	0.351324i
$876$		0			0
$877$	19.0000	+	32.9090i	0.641584	+	1.11126i	0.985079	+	0.172102i	$0.0550559\pi$
$877$	19.0000	+	32.9090i	0.641584	+	1.11126i	−0.343495	+	0.939155i	$0.611611\pi$
$878$		0			0
$879$		0			0
$880$	8.00000	+	13.8564i	0.269680	+	0.467099i
$881$	−24.0000			−0.808581			−0.404290	−	0.914631i	$-0.632481\pi$
$881$	−24.0000			−0.808581			−0.404290	+	0.914631i	$0.632481\pi$
$882$		0			0
$883$	−13.0000			−0.437485			−0.218742	−	0.975783i	$-0.570195\pi$
$883$	−13.0000			−0.437485			−0.218742	+	0.975783i	$0.570195\pi$
$884$		0			0
$885$		0			0
$886$	−12.0000	+	20.7846i	−0.403148	+	0.698273i
$887$	−17.0000	−	29.4449i	−0.570804	−	0.988662i	−0.996484	−	0.0837878i	$-0.973298\pi$
$887$	−17.0000	−	29.4449i	−0.570804	−	0.988662i	0.425679	−	0.904874i	$-0.360035\pi$
$888$		0			0
$889$	37.5000	+	12.9904i	1.25771	+	0.435683i
$890$	64.0000			2.14528
$891$		0			0
$892$	−16.0000	+	27.7128i	−0.535720	+	0.927894i
$893$	−3.00000	+	5.19615i	−0.100391	+	0.173883i
$894$		0			0
$895$	−4.00000			−0.133705
$896$		0			0
$897$		0			0
$898$	18.0000	+	31.1769i	0.600668	+	1.04039i
$899$	18.0000	−	31.1769i	0.600334	−	1.03981i
$900$		0			0
$901$		0			0
$902$	−40.0000			−1.33185
$903$		0			0
$904$		0			0
$905$	−13.0000	−	22.5167i	−0.432135	−	0.748479i
$906$		0			0
$907$	18.5000	−	32.0429i	0.614282	−	1.06397i	−0.376228	−	0.926527i	$-0.622779\pi$
$907$	18.5000	−	32.0429i	0.614282	−	1.06397i	0.990510	−	0.137441i	$-0.0438878\pi$
$908$	18.0000	+	31.1769i	0.597351	+	1.03464i
$909$		0			0
$910$	−8.00000	+	6.92820i	−0.265197	+	0.229668i
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$		0			0
$913$	6.00000	−	10.3923i	0.198571	−	0.343935i
$914$	−11.0000	+	19.0526i	−0.363848	+	0.630203i
$915$		0			0
$916$	−38.0000			−1.25556
$917$	7.00000	+	36.3731i	0.231160	+	1.20114i
$918$		0			0
$919$	−11.5000	−	19.9186i	−0.379350	−	0.657053i	0.611618	−	0.791153i	$-0.290519\pi$
$919$	−11.5000	−	19.9186i	−0.379350	−	0.657053i	−0.990968	+	0.134100i	$0.957186\pi$
$920$		0			0
$921$		0			0
$922$	−20.0000	−	34.6410i	−0.658665	−	1.14084i
$923$	6.00000			0.197492
$924$		0			0
$925$	−3.00000			−0.0986394
$926$	−17.0000	−	29.4449i	−0.558655	−	0.967618i
$927$		0			0
$928$	16.0000	−	27.7128i	0.525226	−	0.909718i
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	0.957708	−	0.287742i	$-0.0929044\pi$
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	−0.728046	+	0.685529i	$0.759571\pi$
$930$		0			0
$931$	1.00000	−	6.92820i	0.0327737	−	0.227063i
$932$	−12.0000			−0.393073
$933$		0			0
$934$	−6.00000	+	10.3923i	−0.196326	+	0.340047i
$935$		0			0
$936$		0			0
$937$	15.0000			0.490029			0.245014	−	0.969519i	$-0.421207\pi$
$937$	15.0000			0.490029			0.245014	+	0.969519i	$0.421207\pi$
$938$	−25.0000	−	8.66025i	−0.816279	−	0.282767i
$939$		0			0
$940$	−12.0000	−	20.7846i	−0.391397	−	0.677919i
$941$	−2.00000	+	3.46410i	−0.0651981	+	0.112926i	−0.896782	−	0.442473i	$-0.854101\pi$
$941$	−2.00000	+	3.46410i	−0.0651981	+	0.112926i	0.831584	+	0.555399i	$0.187435\pi$
$942$		0			0
$943$		0			0
$944$	−48.0000			−1.56227
$945$		0			0
$946$	−20.0000			−0.650256
$947$	−5.00000	−	8.66025i	−0.162478	−	0.281420i	0.773279	−	0.634066i	$-0.218615\pi$
$947$	−5.00000	−	8.66025i	−0.162478	−	0.281420i	−0.935757	+	0.352646i	$0.885282\pi$
$948$		0			0
$949$	1.50000	−	2.59808i	0.0486921	−	0.0843371i
$950$	−1.00000	−	1.73205i	−0.0324443	−	0.0561951i
$951$		0			0
$952$		0			0
$953$	−44.0000			−1.42530			−0.712650	−	0.701520i	$-0.752505\pi$
$953$	−44.0000			−1.42530			−0.712650	+	0.701520i	$0.752505\pi$
$954$		0			0
$955$	10.0000	−	17.3205i	0.323592	−	0.560478i
$956$	6.00000	−	10.3923i	0.194054	−	0.336111i
$957$		0			0
$958$	−56.0000			−1.80928
$959$	24.0000	−	20.7846i	0.775000	−	0.671170i
$960$		0			0
$961$	−25.0000	−	43.3013i	−0.806452	−	1.39682i
$962$	3.00000	−	5.19615i	0.0967239	−	0.167531i
$963$		0			0
$964$	−14.0000	−	24.2487i	−0.450910	−	0.780998i
$965$	22.0000			0.708205
$966$		0			0
$967$	19.0000			0.610999			0.305499	−	0.952192i	$-0.401177\pi$
$967$	19.0000			0.610999			0.305499	+	0.952192i	$0.401177\pi$
$968$		0			0
$969$		0			0
$970$	−12.0000	+	20.7846i	−0.385297	+	0.667354i
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	0.995748	+	0.0921142i	$0.0293625\pi$
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	−0.418101	+	0.908401i	$0.637304\pi$
$972$		0			0
$973$	7.50000	+	2.59808i	0.240439	+	0.0832905i
$974$	−62.0000			−1.98661
$975$		0			0
$976$	20.0000	−	34.6410i	0.640184	−	1.10883i
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	−0.973317	−	0.229465i	$-0.926302\pi$
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	0.685381	+	0.728184i	$0.259636\pi$
$978$		0			0
$979$	−32.0000			−1.02272
$980$	22.0000	+	17.3205i	0.702764	+	0.553283i
$981$		0			0
$982$	28.0000	+	48.4974i	0.893516	+	1.54761i
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	−0.422027	−	0.906583i	$-0.638681\pi$
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	0.996138	−	0.0878058i	$-0.0279855\pi$
$984$		0			0
$985$	16.0000	+	27.7128i	0.509802	+	0.883004i
$986$		0			0
$987$		0			0
$988$	2.00000			0.0636285
$989$		0			0
$990$		0			0
$991$	−8.50000	+	14.7224i	−0.270011	+	0.467673i	−0.968864	−	0.247592i	$-0.920361\pi$
$991$	−8.50000	+	14.7224i	−0.270011	+	0.467673i	0.698853	+	0.715265i	$0.253694\pi$
$992$	−36.0000	−	62.3538i	−1.14300	−	1.97974i
$993$		0			0
$994$	−6.00000	−	31.1769i	−0.190308	−	0.988872i
$995$		0			0
$996$		0			0
$997$	−9.50000	+	16.4545i	−0.300868	+	0.521119i	−0.976333	−	0.216274i	$-0.930610\pi$
$997$	−9.50000	+	16.4545i	−0.300868	+	0.521119i	0.675465	+	0.737392i	$0.263943\pi$
$998$	37.0000	−	64.0859i	1.17121	−	2.02860i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.e.b.46.1		2
3.2	odd	2		21.2.e.a.4.1	✓	2
4.3	odd	2		1008.2.s.d.865.1		2
7.2	even	3	inner	63.2.e.b.37.1		2
7.3	odd	6		441.2.a.a.1.1		1
7.4	even	3		441.2.a.b.1.1		1
7.5	odd	6		441.2.e.e.226.1		2
7.6	odd	2		441.2.e.e.361.1		2
9.2	odd	6		567.2.g.a.109.1		2
9.4	even	3		567.2.h.a.298.1		2
9.5	odd	6		567.2.h.f.298.1		2
9.7	even	3		567.2.g.f.109.1		2
12.11	even	2		336.2.q.f.193.1		2
15.2	even	4		525.2.r.e.424.2		4
15.8	even	4		525.2.r.e.424.1		4
15.14	odd	2		525.2.i.e.151.1		2
21.2	odd	6		21.2.e.a.16.1	yes	2
21.5	even	6		147.2.e.a.79.1		2
21.11	odd	6		147.2.a.c.1.1		1
21.17	even	6		147.2.a.b.1.1		1
21.20	even	2		147.2.e.a.67.1		2
24.5	odd	2		1344.2.q.m.193.1		2
24.11	even	2		1344.2.q.c.193.1		2
28.3	even	6		7056.2.a.m.1.1		1
28.11	odd	6		7056.2.a.bp.1.1		1
28.23	odd	6		1008.2.s.d.289.1		2
63.2	odd	6		567.2.h.f.352.1		2
63.16	even	3		567.2.h.a.352.1		2
63.23	odd	6		567.2.g.a.541.1		2
63.58	even	3		567.2.g.f.541.1		2
84.11	even	6		2352.2.a.d.1.1		1
84.23	even	6		336.2.q.f.289.1		2
84.47	odd	6		2352.2.q.c.961.1		2
84.59	odd	6		2352.2.a.w.1.1		1
84.83	odd	2		2352.2.q.c.1537.1		2
105.2	even	12		525.2.r.e.499.1		4
105.23	even	12		525.2.r.e.499.2		4
105.44	odd	6		525.2.i.e.226.1		2
105.59	even	6		3675.2.a.c.1.1		1
105.74	odd	6		3675.2.a.a.1.1		1
168.11	even	6		9408.2.a.cv.1.1		1
168.53	odd	6		9408.2.a.bg.1.1		1
168.59	odd	6		9408.2.a.k.1.1		1
168.101	even	6		9408.2.a.bz.1.1		1
168.107	even	6		1344.2.q.c.961.1		2
168.149	odd	6		1344.2.q.m.961.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.2.e.a.4.1	✓	2	3.2	odd	2
21.2.e.a.16.1	yes	2	21.2	odd	6
63.2.e.b.37.1		2	7.2	even	3	inner
63.2.e.b.46.1		2	1.1	even	1	trivial
147.2.a.b.1.1		1	21.17	even	6
147.2.a.c.1.1		1	21.11	odd	6
147.2.e.a.67.1		2	21.20	even	2
147.2.e.a.79.1		2	21.5	even	6
336.2.q.f.193.1		2	12.11	even	2
336.2.q.f.289.1		2	84.23	even	6
441.2.a.a.1.1		1	7.3	odd	6
441.2.a.b.1.1		1	7.4	even	3
441.2.e.e.226.1		2	7.5	odd	6
441.2.e.e.361.1		2	7.6	odd	2
525.2.i.e.151.1		2	15.14	odd	2
525.2.i.e.226.1		2	105.44	odd	6
525.2.r.e.424.1		4	15.8	even	4
525.2.r.e.424.2		4	15.2	even	4
525.2.r.e.499.1		4	105.2	even	12
525.2.r.e.499.2		4	105.23	even	12
567.2.g.a.109.1		2	9.2	odd	6
567.2.g.a.541.1		2	63.23	odd	6
567.2.g.f.109.1		2	9.7	even	3
567.2.g.f.541.1		2	63.58	even	3
567.2.h.a.298.1		2	9.4	even	3
567.2.h.a.352.1		2	63.16	even	3
567.2.h.f.298.1		2	9.5	odd	6
567.2.h.f.352.1		2	63.2	odd	6
1008.2.s.d.289.1		2	28.23	odd	6
1008.2.s.d.865.1		2	4.3	odd	2
1344.2.q.c.193.1		2	24.11	even	2
1344.2.q.c.961.1		2	168.107	even	6
1344.2.q.m.193.1		2	24.5	odd	2
1344.2.q.m.961.1		2	168.149	odd	6
2352.2.a.d.1.1		1	84.11	even	6
2352.2.a.w.1.1		1	84.59	odd	6
2352.2.q.c.961.1		2	84.47	odd	6
2352.2.q.c.1537.1		2	84.83	odd	2
3675.2.a.a.1.1		1	105.74	odd	6
3675.2.a.c.1.1		1	105.59	even	6
7056.2.a.m.1.1		1	28.3	even	6
7056.2.a.bp.1.1		1	28.11	odd	6
9408.2.a.k.1.1		1	168.59	odd	6
9408.2.a.bg.1.1		1	168.53	odd	6
9408.2.a.bz.1.1		1	168.101	even	6
9408.2.a.cv.1.1		1	168.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(-2.50000 - 0.866025i) q^{7} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(2.00000 - 3.46410i) q^{10} +(-1.00000 + 1.73205i) q^{11} +1.00000 q^{13} +(-1.00000 - 5.19615i) q^{14} +(2.00000 + 3.46410i) q^{16} +(-0.500000 - 0.866025i) q^{19} +4.00000 q^{20} -4.00000 q^{22} +(0.500000 - 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} +(4.00000 - 3.46410i) q^{28} -4.00000 q^{29} +(-4.50000 + 7.79423i) q^{31} +(-4.00000 + 6.92820i) q^{32} +(1.00000 + 5.19615i) q^{35} +(-1.50000 - 2.59808i) q^{37} +(1.00000 - 1.73205i) q^{38} +10.0000 q^{41} +5.00000 q^{43} +(-2.00000 - 3.46410i) q^{44} +(-3.00000 - 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +2.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(6.00000 - 10.3923i) q^{53} +4.00000 q^{55} +(-4.00000 - 6.92820i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(-5.00000 - 8.66025i) q^{61} -18.0000 q^{62} -8.00000 q^{64} +(-1.00000 - 1.73205i) q^{65} +(2.50000 - 4.33013i) q^{67} +(-8.00000 + 6.92820i) q^{70} +6.00000 q^{71} +(1.50000 - 2.59808i) q^{73} +(3.00000 - 5.19615i) q^{74} +2.00000 q^{76} +(4.00000 - 3.46410i) q^{77} +(0.500000 + 0.866025i) q^{79} +(4.00000 - 6.92820i) q^{80} +(10.0000 + 17.3205i) q^{82} -6.00000 q^{83} +(5.00000 + 8.66025i) q^{86} +(8.00000 + 13.8564i) q^{89} +(-2.50000 - 0.866025i) q^{91} +(6.00000 - 10.3923i) q^{94} +(-1.00000 + 1.73205i) q^{95} -6.00000 q^{97} +(-2.00000 + 13.8564i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 5 q^{7}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 5 * q^7	\( 2 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 5 q^{7} + 4 q^{10} - 2 q^{11} + 2 q^{13} - 2 q^{14} + 4 q^{16} - q^{19} + 8 q^{20} - 8 q^{22} + q^{25} + 2 q^{26} + 8 q^{28} - 8 q^{29} - 9 q^{31} - 8 q^{32} + 2 q^{35} - 3 q^{37} + 2 q^{38} + 20 q^{41} + 10 q^{43} - 4 q^{44} - 6 q^{47} + 11 q^{49} + 4 q^{50} - 2 q^{52} + 12 q^{53} + 8 q^{55} - 8 q^{58} - 12 q^{59} - 10 q^{61} - 36 q^{62} - 16 q^{64} - 2 q^{65} + 5 q^{67} - 16 q^{70} + 12 q^{71} + 3 q^{73} + 6 q^{74} + 4 q^{76} + 8 q^{77} + q^{79} + 8 q^{80} + 20 q^{82} - 12 q^{83} + 10 q^{86} + 16 q^{89} - 5 q^{91} + 12 q^{94} - 2 q^{95} - 12 q^{97} - 4 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 5 * q^7 + 4 * q^10 - 2 * q^11 + 2 * q^13 - 2 * q^14 + 4 * q^16 - q^19 + 8 * q^20 - 8 * q^22 + q^25 + 2 * q^26 + 8 * q^28 - 8 * q^29 - 9 * q^31 - 8 * q^32 + 2 * q^35 - 3 * q^37 + 2 * q^38 + 20 * q^41 + 10 * q^43 - 4 * q^44 - 6 * q^47 + 11 * q^49 + 4 * q^50 - 2 * q^52 + 12 * q^53 + 8 * q^55 - 8 * q^58 - 12 * q^59 - 10 * q^61 - 36 * q^62 - 16 * q^64 - 2 * q^65 + 5 * q^67 - 16 * q^70 + 12 * q^71 + 3 * q^73 + 6 * q^74 + 4 * q^76 + 8 * q^77 + q^79 + 8 * q^80 + 20 * q^82 - 12 * q^83 + 10 * q^86 + 16 * q^89 - 5 * q^91 + 12 * q^94 - 2 * q^95 - 12 * q^97 - 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more