LMFDB - Embedded newform 1380.2.r.b.1013.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(737,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1380.737");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.r (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:	$11.0193554789$
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:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1013.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1380.1013
Dual form			1380.2.r.b.737.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70711 - 0.292893i) q^{3} +(-2.12132 + 0.707107i) q^{5} +(3.00000 - 3.00000i) q^{7} +(2.82843 + 1.00000i) q^{9} +O(q^{10})$	\(q+(-1.70711 - 0.292893i) q^{3} +(-2.12132 + 0.707107i) q^{5} +(3.00000 - 3.00000i) q^{7} +(2.82843 + 1.00000i) q^{9} +2.82843i q^{11} +(-3.00000 - 3.00000i) q^{13} +(3.82843 - 0.585786i) q^{15} +(1.41421 + 1.41421i) q^{17} +4.00000i q^{19} +(-6.00000 + 4.24264i) q^{21} +(0.707107 - 0.707107i) q^{23} +(4.00000 - 3.00000i) q^{25} +(-4.53553 - 2.53553i) q^{27} +2.82843 q^{29} -4.00000 q^{31} +(0.828427 - 4.82843i) q^{33} +(-4.24264 + 8.48528i) q^{35} +(4.00000 - 4.00000i) q^{37} +(4.24264 + 6.00000i) q^{39} -2.82843i q^{41} +(5.00000 + 5.00000i) q^{43} +(-6.70711 - 0.121320i) q^{45} +(-5.65685 - 5.65685i) q^{47} -11.0000i q^{49} +(-2.00000 - 2.82843i) q^{51} +(-2.00000 - 6.00000i) q^{55} +(1.17157 - 6.82843i) q^{57} -1.41421 q^{59} +2.00000 q^{61} +(11.4853 - 5.48528i) q^{63} +(8.48528 + 4.24264i) q^{65} +(7.00000 - 7.00000i) q^{67} +(-1.41421 + 1.00000i) q^{69} -15.5563i q^{71} +(1.00000 + 1.00000i) q^{73} +(-7.70711 + 3.94975i) q^{75} +(8.48528 + 8.48528i) q^{77} -10.0000i q^{79} +(7.00000 + 5.65685i) q^{81} +(8.48528 - 8.48528i) q^{83} +(-4.00000 - 2.00000i) q^{85} +(-4.82843 - 0.828427i) q^{87} +9.89949 q^{89} -18.0000 q^{91} +(6.82843 + 1.17157i) q^{93} +(-2.82843 - 8.48528i) q^{95} +(12.0000 - 12.0000i) q^{97} +(-2.82843 + 8.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 12 q^{7}+O(q^{10}) $ 4 * q - 4 * q^3 + 12 * q^7	$ 4 q - 4 q^{3} + 12 q^{7} - 12 q^{13} + 4 q^{15} - 24 q^{21} + 16 q^{25} - 4 q^{27} - 16 q^{31} - 8 q^{33} + 16 q^{37} + 20 q^{43} - 24 q^{45} - 8 q^{51} - 8 q^{55} + 16 q^{57} + 8 q^{61} + 12 q^{63} + 28 q^{67} + 4 q^{73} - 28 q^{75} + 28 q^{81} - 16 q^{85} - 8 q^{87} - 72 q^{91} + 16 q^{93} + 48 q^{97}+O(q^{100}) $ 4 * q - 4 * q^3 + 12 * q^7 - 12 * q^13 + 4 * q^15 - 24 * q^21 + 16 * q^25 - 4 * q^27 - 16 * q^31 - 8 * q^33 + 16 * q^37 + 20 * q^43 - 24 * q^45 - 8 * q^51 - 8 * q^55 + 16 * q^57 + 8 * q^61 + 12 * q^63 + 28 * q^67 + 4 * q^73 - 28 * q^75 + 28 * q^81 - 16 * q^85 - 8 * q^87 - 72 * q^91 + 16 * q^93 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.70711	−	0.292893i	−0.985599	−	0.169102i
$3$	−1.70711	−	0.292893i	−0.985599	−	0.169102i
$4$		0			0
$5$	−2.12132	+	0.707107i	−0.948683	+	0.316228i
$5$	−2.12132	+	0.707107i	−0.948683	+	0.316228i
$6$		0			0
$7$	3.00000	−	3.00000i	1.13389	−	1.13389i	0.144370	−	0.989524i	$-0.453885\pi$
$7$	3.00000	−	3.00000i	1.13389	−	1.13389i	0.989524	−	0.144370i	$-0.0461154\pi$
$8$		0			0
$9$	2.82843	+	1.00000i	0.942809	+	0.333333i
$10$		0			0
$11$			2.82843i			0.852803i	0.904534	+	0.426401i	$0.140219\pi$
$11$			2.82843i			0.852803i	−0.904534	+	0.426401i	$0.859781\pi$
$12$		0			0
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	0.155747	−	0.987797i	$-0.450222\pi$
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	−0.987797	+	0.155747i	$0.950222\pi$
$14$		0			0
$15$	3.82843	−	0.585786i	0.988496	−	0.151249i
$16$		0			0
$17$	1.41421	+	1.41421i	0.342997	+	0.342997i	0.857493	−	0.514496i	$-0.172021\pi$
$17$	1.41421	+	1.41421i	0.342997	+	0.342997i	−0.514496	+	0.857493i	$0.672021\pi$
$18$		0			0
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$		0			0
$21$	−6.00000	+	4.24264i	−1.30931	+	0.925820i
$22$		0			0
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$24$		0			0
$25$	4.00000	−	3.00000i	0.800000	−	0.600000i
$26$		0			0
$27$	−4.53553	−	2.53553i	−0.872864	−	0.487964i
$28$		0			0
$29$	2.82843			0.525226			0.262613	−	0.964901i	$-0.415416\pi$
$29$	2.82843			0.525226			0.262613	+	0.964901i	$0.415416\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$		0			0
$33$	0.828427	−	4.82843i	0.144211	−	0.840521i
$34$		0			0
$35$	−4.24264	+	8.48528i	−0.717137	+	1.43427i
$36$		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	$0.0960577\pi$
$38$		0			0
$39$	4.24264	+	6.00000i	0.679366	+	0.960769i
$40$		0			0
$41$		−	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
$43$	5.00000	+	5.00000i	0.762493	+	0.762493i	0.976772	−	0.214280i	$-0.0687403\pi$
$43$	5.00000	+	5.00000i	0.762493	+	0.762493i	−0.214280	+	0.976772i	$0.568740\pi$
$44$		0			0
$45$	−6.70711	−	0.121320i	−0.999836	−	0.0180854i
$46$		0			0
$47$	−5.65685	−	5.65685i	−0.825137	−	0.825137i	0.161703	−	0.986840i	$-0.448301\pi$
$47$	−5.65685	−	5.65685i	−0.825137	−	0.825137i	−0.986840	+	0.161703i	$0.948301\pi$
$48$		0			0
$49$		−	11.0000i		−	1.57143i
$50$		0			0
$51$	−2.00000	−	2.82843i	−0.280056	−	0.396059i
$52$		0			0
$53$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$53$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$54$		0			0
$55$	−2.00000	−	6.00000i	−0.269680	−	0.809040i
$56$		0			0
$57$	1.17157	−	6.82843i	0.155179	−	0.904447i
$58$		0			0
$59$	−1.41421			−0.184115			−0.0920575	−	0.995754i	$-0.529344\pi$
$59$	−1.41421			−0.184115			−0.0920575	+	0.995754i	$0.529344\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$		0			0
$63$	11.4853	−	5.48528i	1.44701	−	0.691080i
$64$		0			0
$65$	8.48528	+	4.24264i	1.05247	+	0.526235i
$66$		0			0
$67$	7.00000	−	7.00000i	0.855186	−	0.855186i	−0.135580	−	0.990766i	$-0.543290\pi$
$67$	7.00000	−	7.00000i	0.855186	−	0.855186i	0.990766	+	0.135580i	$0.0432899\pi$
$68$		0			0
$69$	−1.41421	+	1.00000i	−0.170251	+	0.120386i
$70$		0			0
$71$		−	15.5563i		−	1.84620i	−0.384561	−	0.923099i	$-0.625647\pi$
$71$		−	15.5563i		−	1.84620i	0.384561	−	0.923099i	$-0.374353\pi$
$72$		0			0
$73$	1.00000	+	1.00000i	0.117041	+	0.117041i	0.763202	−	0.646160i	$-0.223626\pi$
$73$	1.00000	+	1.00000i	0.117041	+	0.117041i	−0.646160	+	0.763202i	$0.723626\pi$
$74$		0			0
$75$	−7.70711	+	3.94975i	−0.889940	+	0.456078i
$76$		0			0
$77$	8.48528	+	8.48528i	0.966988	+	0.966988i
$78$		0			0
$79$		−	10.0000i		−	1.12509i	−0.826767	−	0.562544i	$-0.809823\pi$
$79$		−	10.0000i		−	1.12509i	0.826767	−	0.562544i	$-0.190177\pi$
$80$		0			0
$81$	7.00000	+	5.65685i	0.777778	+	0.628539i
$82$		0			0
$83$	8.48528	−	8.48528i	0.931381	−	0.931381i	−0.0664117	−	0.997792i	$-0.521155\pi$
$83$	8.48528	−	8.48528i	0.931381	−	0.931381i	0.997792	+	0.0664117i	$0.0211551\pi$
$84$		0			0
$85$	−4.00000	−	2.00000i	−0.433861	−	0.216930i
$86$		0			0
$87$	−4.82843	−	0.828427i	−0.517662	−	0.0888167i
$88$		0			0
$89$	9.89949			1.04934			0.524672	−	0.851304i	$-0.324188\pi$
$89$	9.89949			1.04934			0.524672	+	0.851304i	$0.324188\pi$
$90$		0			0
$91$	−18.0000			−1.88691
$92$		0			0
$93$	6.82843	+	1.17157i	0.708075	+	0.121486i
$94$		0			0
$95$	−2.82843	−	8.48528i	−0.290191	−	0.870572i
$96$		0			0
$97$	12.0000	−	12.0000i	1.21842	−	1.21842i	0.250229	−	0.968187i	$-0.419494\pi$
$97$	12.0000	−	12.0000i	1.21842	−	1.21842i	0.968187	−	0.250229i	$-0.0805058\pi$
$98$		0			0
$99$	−2.82843	+	8.00000i	−0.284268	+	0.804030i
$100$		0			0
$101$		−	8.48528i		−	0.844317i	−0.906522	−	0.422159i	$-0.861273\pi$
$101$		−	8.48528i		−	0.844317i	0.906522	−	0.422159i	$-0.138727\pi$
$102$		0			0
$103$	−13.0000	−	13.0000i	−1.28093	−	1.28093i	−0.940140	−	0.340788i	$-0.889306\pi$
$103$	−13.0000	−	13.0000i	−1.28093	−	1.28093i	−0.340788	−	0.940140i	$-0.610694\pi$
$104$		0			0
$105$	9.72792	−	13.2426i	0.949348	−	1.29235i
$106$		0			0
$107$	2.82843	+	2.82843i	0.273434	+	0.273434i	0.830481	−	0.557047i	$-0.188066\pi$
$107$	2.82843	+	2.82843i	0.273434	+	0.273434i	−0.557047	+	0.830481i	$0.688066\pi$
$108$		0			0
$109$		−	6.00000i		−	0.574696i	−0.957826	−	0.287348i	$-0.907226\pi$
$109$		−	6.00000i		−	0.574696i	0.957826	−	0.287348i	$-0.0927736\pi$
$110$		0			0
$111$	−8.00000	+	5.65685i	−0.759326	+	0.536925i
$112$		0			0
$113$	1.41421	−	1.41421i	0.133038	−	0.133038i	−0.637452	−	0.770490i	$-0.720012\pi$
$113$	1.41421	−	1.41421i	0.133038	−	0.133038i	0.770490	+	0.637452i	$0.220012\pi$
$114$		0			0
$115$	−1.00000	+	2.00000i	−0.0932505	+	0.186501i
$116$		0			0
$117$	−5.48528	−	11.4853i	−0.507114	−	1.06181i
$118$		0			0
$119$	8.48528			0.777844
$120$		0			0
$121$	3.00000			0.272727
$122$		0			0
$123$	−0.828427	+	4.82843i	−0.0746968	+	0.435365i
$124$		0			0
$125$	−6.36396	+	9.19239i	−0.569210	+	0.822192i
$126$		0			0
$127$	−4.00000	+	4.00000i	−0.354943	+	0.354943i	−0.861945	−	0.507002i	$-0.830754\pi$
$127$	−4.00000	+	4.00000i	−0.354943	+	0.354943i	0.507002	+	0.861945i	$0.330754\pi$
$128$		0			0
$129$	−7.07107	−	10.0000i	−0.622573	−	0.880451i
$130$		0			0
$131$			12.7279i			1.11204i	0.831168	+	0.556022i	$0.187673\pi$
$131$			12.7279i			1.11204i	−0.831168	+	0.556022i	$0.812327\pi$
$132$		0			0
$133$	12.0000	+	12.0000i	1.04053	+	1.04053i
$134$		0			0
$135$	11.4142	+	2.17157i	0.982379	+	0.186899i
$136$		0			0
$137$	11.3137	+	11.3137i	0.966595	+	0.966595i	0.999460	−	0.0328645i	$-0.0104630\pi$
$137$	11.3137	+	11.3137i	0.966595	+	0.966595i	−0.0328645	+	0.999460i	$0.510463\pi$
$138$		0			0
$139$		−	12.0000i		−	1.01783i	−0.860818	−	0.508913i	$-0.830047\pi$
$139$		−	12.0000i		−	1.01783i	0.860818	−	0.508913i	$-0.169953\pi$
$140$		0			0
$141$	8.00000	+	11.3137i	0.673722	+	0.952786i
$142$		0			0
$143$	8.48528	−	8.48528i	0.709575	−	0.709575i
$144$		0			0
$145$	−6.00000	+	2.00000i	−0.498273	+	0.166091i
$146$		0			0
$147$	−3.22183	+	18.7782i	−0.265732	+	1.54880i
$148$		0			0
$149$	−7.07107			−0.579284			−0.289642	−	0.957135i	$-0.593536\pi$
$149$	−7.07107			−0.579284			−0.289642	+	0.957135i	$0.593536\pi$
$150$		0			0
$151$	−12.0000			−0.976546			−0.488273	−	0.872691i	$-0.662373\pi$
$151$	−12.0000			−0.976546			−0.488273	+	0.872691i	$0.662373\pi$
$152$		0			0
$153$	2.58579	+	5.41421i	0.209048	+	0.437713i
$154$		0			0
$155$	8.48528	−	2.82843i	0.681554	−	0.227185i
$156$		0			0
$157$	−6.00000	+	6.00000i	−0.478852	+	0.478852i	−0.904764	−	0.425912i	$-0.859953\pi$
$157$	−6.00000	+	6.00000i	−0.478852	+	0.478852i	0.425912	+	0.904764i	$0.359953\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	4.24264i		−	0.334367i
$162$		0			0
$163$	6.00000	+	6.00000i	0.469956	+	0.469956i	0.901900	−	0.431944i	$-0.142172\pi$
$163$	6.00000	+	6.00000i	0.469956	+	0.469956i	−0.431944	+	0.901900i	$0.642172\pi$
$164$		0			0
$165$	1.65685	+	10.8284i	0.128986	+	0.842992i
$166$		0			0
$167$	−16.9706	−	16.9706i	−1.31322	−	1.31322i	−0.919027	−	0.394195i	$-0.871024\pi$
$167$	−16.9706	−	16.9706i	−1.31322	−	1.31322i	−0.394195	−	0.919027i	$-0.628976\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$		0			0
$171$	−4.00000	+	11.3137i	−0.305888	+	0.865181i
$172$		0			0
$173$	−9.89949	+	9.89949i	−0.752645	+	0.752645i	−0.974972	−	0.222327i	$-0.928635\pi$
$173$	−9.89949	+	9.89949i	−0.752645	+	0.752645i	0.222327	+	0.974972i	$0.428635\pi$
$174$		0			0
$175$	3.00000	−	21.0000i	0.226779	−	1.58745i
$176$		0			0
$177$	2.41421	+	0.414214i	0.181463	+	0.0311342i
$178$		0			0
$179$	−18.3848			−1.37414			−0.687071	−	0.726590i	$-0.741104\pi$
$179$	−18.3848			−1.37414			−0.687071	+	0.726590i	$0.741104\pi$
$180$		0			0
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$		0			0
$183$	−3.41421	−	0.585786i	−0.252386	−	0.0433026i
$184$		0			0
$185$	−5.65685	+	11.3137i	−0.415900	+	0.831800i
$186$		0			0
$187$	−4.00000	+	4.00000i	−0.292509	+	0.292509i
$188$		0			0
$189$	−21.2132	+	6.00000i	−1.54303	+	0.436436i
$190$		0			0
$191$			19.7990i			1.43260i	0.697790	+	0.716302i	$0.254167\pi$
$191$			19.7990i			1.43260i	−0.697790	+	0.716302i	$0.745833\pi$
$192$		0			0
$193$	9.00000	+	9.00000i	0.647834	+	0.647834i	0.952469	−	0.304635i	$-0.0985345\pi$
$193$	9.00000	+	9.00000i	0.647834	+	0.647834i	−0.304635	+	0.952469i	$0.598534\pi$
$194$		0			0
$195$	−13.2426	−	9.72792i	−0.948325	−	0.696631i
$196$		0			0
$197$	−7.07107	−	7.07107i	−0.503793	−	0.503793i	0.408822	−	0.912614i	$-0.365940\pi$
$197$	−7.07107	−	7.07107i	−0.503793	−	0.503793i	−0.912614	+	0.408822i	$0.865940\pi$
$198$		0			0
$199$			22.0000i			1.55954i	0.626067	+	0.779769i	$0.284664\pi$
$199$			22.0000i			1.55954i	−0.626067	+	0.779769i	$0.715336\pi$
$200$		0			0
$201$	−14.0000	+	9.89949i	−0.987484	+	0.698257i
$202$		0			0
$203$	8.48528	−	8.48528i	0.595550	−	0.595550i
$204$		0			0
$205$	2.00000	+	6.00000i	0.139686	+	0.419058i
$206$		0			0
$207$	2.70711	−	1.29289i	0.188157	−	0.0898623i
$208$		0			0
$209$	−11.3137			−0.782586
$210$		0			0
$211$		0			0			−	1.00000i	$-0.5\pi$
$211$		0			0				1.00000i	$0.5\pi$
$212$		0			0
$213$	−4.55635	+	26.5563i	−0.312196	+	1.81961i
$214$		0			0
$215$	−14.1421	−	7.07107i	−0.964486	−	0.482243i
$216$		0			0
$217$	−12.0000	+	12.0000i	−0.814613	+	0.814613i
$218$		0			0
$219$	−1.41421	−	2.00000i	−0.0955637	−	0.135147i
$220$		0			0
$221$		−	8.48528i		−	0.570782i
$222$		0			0
$223$	18.0000	+	18.0000i	1.20537	+	1.20537i	0.972511	+	0.232859i	$0.0748079\pi$
$223$	18.0000	+	18.0000i	1.20537	+	1.20537i	0.232859	+	0.972511i	$0.425192\pi$
$224$		0			0
$225$	14.3137	−	4.48528i	0.954247	−	0.299019i
$226$		0			0
$227$	−16.9706	−	16.9706i	−1.12638	−	1.12638i	−0.990762	−	0.135614i	$-0.956699\pi$
$227$	−16.9706	−	16.9706i	−1.12638	−	1.12638i	−0.135614	−	0.990762i	$-0.543301\pi$
$228$		0			0
$229$		−	22.0000i		−	1.45380i	−0.686743	−	0.726900i	$-0.740960\pi$
$229$		−	22.0000i		−	1.45380i	0.686743	−	0.726900i	$-0.259040\pi$
$230$		0			0
$231$	−12.0000	−	16.9706i	−0.789542	−	1.11658i
$232$		0			0
$233$	21.2132	−	21.2132i	1.38972	−	1.38972i	0.563837	−	0.825886i	$-0.309325\pi$
$233$	21.2132	−	21.2132i	1.38972	−	1.38972i	0.825886	−	0.563837i	$-0.190675\pi$
$234$		0			0
$235$	16.0000	+	8.00000i	1.04372	+	0.521862i
$236$		0			0
$237$	−2.92893	+	17.0711i	−0.190255	+	1.10889i
$238$		0			0
$239$	−9.89949			−0.640345			−0.320173	−	0.947359i	$-0.603741\pi$
$239$	−9.89949			−0.640345			−0.320173	+	0.947359i	$0.603741\pi$
$240$		0			0
$241$	6.00000			0.386494			0.193247	−	0.981150i	$-0.438098\pi$
$241$	6.00000			0.386494			0.193247	+	0.981150i	$0.438098\pi$
$242$		0			0
$243$	−10.2929	−	11.7071i	−0.660289	−	0.751011i
$244$		0			0
$245$	7.77817	+	23.3345i	0.496929	+	1.49079i
$246$		0			0
$247$	12.0000	−	12.0000i	0.763542	−	0.763542i
$248$		0			0
$249$	−16.9706	+	12.0000i	−1.07547	+	0.760469i
$250$		0			0
$251$			2.82843i			0.178529i	0.996008	+	0.0892644i	$0.0284516\pi$
$251$			2.82843i			0.178529i	−0.996008	+	0.0892644i	$0.971548\pi$
$252$		0			0
$253$	2.00000	+	2.00000i	0.125739	+	0.125739i
$254$		0			0
$255$	6.24264	+	4.58579i	0.390929	+	0.287173i
$256$		0			0
$257$	7.07107	+	7.07107i	0.441081	+	0.441081i	0.892375	−	0.451294i	$-0.149037\pi$
$257$	7.07107	+	7.07107i	0.441081	+	0.441081i	−0.451294	+	0.892375i	$0.649037\pi$
$258$		0			0
$259$		−	24.0000i		−	1.49129i
$260$		0			0
$261$	8.00000	+	2.82843i	0.495188	+	0.175075i
$262$		0			0
$263$	11.3137	−	11.3137i	0.697633	−	0.697633i	−0.266266	−	0.963899i	$-0.585790\pi$
$263$	11.3137	−	11.3137i	0.697633	−	0.697633i	0.963899	+	0.266266i	$0.0857901\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−16.8995	−	2.89949i	−1.03423	−	0.177446i
$268$		0			0
$269$	16.9706			1.03471			0.517357	−	0.855770i	$-0.326916\pi$
$269$	16.9706			1.03471			0.517357	+	0.855770i	$0.326916\pi$
$270$		0			0
$271$	12.0000			0.728948			0.364474	−	0.931214i	$-0.381249\pi$
$271$	12.0000			0.728948			0.364474	+	0.931214i	$0.381249\pi$
$272$		0			0
$273$	30.7279	+	5.27208i	1.85974	+	0.319081i
$274$		0			0
$275$	8.48528	+	11.3137i	0.511682	+	0.682242i
$276$		0			0
$277$	21.0000	−	21.0000i	1.26177	−	1.26177i	0.311532	−	0.950236i	$-0.399158\pi$
$277$	21.0000	−	21.0000i	1.26177	−	1.26177i	0.950236	−	0.311532i	$-0.100842\pi$
$278$		0			0
$279$	−11.3137	−	4.00000i	−0.677334	−	0.239474i
$280$		0			0
$281$			26.8701i			1.60293i	0.598040	+	0.801467i	$0.295947\pi$
$281$			26.8701i			1.60293i	−0.598040	+	0.801467i	$0.704053\pi$
$282$		0			0
$283$	15.0000	+	15.0000i	0.891657	+	0.891657i	0.994679	−	0.103022i	$-0.0328511\pi$
$283$	15.0000	+	15.0000i	0.891657	+	0.891657i	−0.103022	+	0.994679i	$0.532851\pi$
$284$		0			0
$285$	2.34315	+	15.3137i	0.138796	+	0.907106i
$286$		0			0
$287$	−8.48528	−	8.48528i	−0.500870	−	0.500870i
$288$		0			0
$289$		−	13.0000i		−	0.764706i
$290$		0			0
$291$	−24.0000	+	16.9706i	−1.40690	+	0.994832i
$292$		0			0
$293$	−8.48528	+	8.48528i	−0.495715	+	0.495715i	−0.910101	−	0.414386i	$-0.863996\pi$
$293$	−8.48528	+	8.48528i	−0.495715	+	0.495715i	0.414386	+	0.910101i	$0.363996\pi$
$294$		0			0
$295$	3.00000	−	1.00000i	0.174667	−	0.0582223i
$296$		0			0
$297$	7.17157	−	12.8284i	0.416137	−	0.744381i
$298$		0			0
$299$	−4.24264			−0.245358
$300$		0			0
$301$	30.0000			1.72917
$302$		0			0
$303$	−2.48528	+	14.4853i	−0.142776	+	0.832158i
$304$		0			0
$305$	−4.24264	+	1.41421i	−0.242933	+	0.0809776i
$306$		0			0
$307$	18.0000	−	18.0000i	1.02731	−	1.02731i	0.0276979	−	0.999616i	$-0.491182\pi$
$307$	18.0000	−	18.0000i	1.02731	−	1.02731i	0.999616	−	0.0276979i	$-0.00881765\pi$
$308$		0			0
$309$	18.3848	+	26.0000i	1.04587	+	1.47909i
$310$		0			0
$311$			15.5563i			0.882120i	0.897478	+	0.441060i	$0.145397\pi$
$311$			15.5563i			0.882120i	−0.897478	+	0.441060i	$0.854603\pi$
$312$		0			0
$313$	4.00000	+	4.00000i	0.226093	+	0.226093i	0.811058	−	0.584965i	$-0.198892\pi$
$313$	4.00000	+	4.00000i	0.226093	+	0.226093i	−0.584965	+	0.811058i	$0.698892\pi$
$314$		0			0
$315$	−20.4853	+	19.7574i	−1.15421	+	1.11320i
$316$		0			0
$317$	4.24264	+	4.24264i	0.238290	+	0.238290i	0.816142	−	0.577851i	$-0.196109\pi$
$317$	4.24264	+	4.24264i	0.238290	+	0.238290i	−0.577851	+	0.816142i	$0.696109\pi$
$318$		0			0
$319$			8.00000i			0.447914i
$320$		0			0
$321$	−4.00000	−	5.65685i	−0.223258	−	0.315735i
$322$		0			0
$323$	−5.65685	+	5.65685i	−0.314756	+	0.314756i
$324$		0			0
$325$	−21.0000	−	3.00000i	−1.16487	−	0.166410i
$326$		0			0
$327$	−1.75736	+	10.2426i	−0.0971822	+	0.566419i
$328$		0			0
$329$	−33.9411			−1.87123
$330$		0			0
$331$	−16.0000			−0.879440			−0.439720	−	0.898135i	$-0.644922\pi$
$331$	−16.0000			−0.879440			−0.439720	+	0.898135i	$0.644922\pi$
$332$		0			0
$333$	15.3137	−	7.31371i	0.839186	−	0.400789i
$334$		0			0
$335$	−9.89949	+	19.7990i	−0.540867	+	1.08173i
$336$		0			0
$337$	−12.0000	+	12.0000i	−0.653682	+	0.653682i	−0.953878	−	0.300196i	$-0.902948\pi$
$337$	−12.0000	+	12.0000i	−0.653682	+	0.653682i	0.300196	+	0.953878i	$0.402948\pi$
$338$		0			0
$339$	−2.82843	+	2.00000i	−0.153619	+	0.108625i
$340$		0			0
$341$		−	11.3137i		−	0.612672i
$342$		0			0
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$		0			0
$345$	2.29289	−	3.12132i	0.123445	−	0.168046i
$346$		0			0
$347$	−8.48528	−	8.48528i	−0.455514	−	0.455514i	0.441666	−	0.897180i	$-0.354388\pi$
$347$	−8.48528	−	8.48528i	−0.455514	−	0.455514i	−0.897180	+	0.441666i	$0.854388\pi$
$348$		0			0
$349$			28.0000i			1.49881i	0.662114	+	0.749403i	$0.269659\pi$
$349$			28.0000i			1.49881i	−0.662114	+	0.749403i	$0.730341\pi$
$350$		0			0
$351$	6.00000	+	21.2132i	0.320256	+	1.13228i
$352$		0			0
$353$	4.24264	−	4.24264i	0.225813	−	0.225813i	−0.585128	−	0.810941i	$-0.698956\pi$
$353$	4.24264	−	4.24264i	0.225813	−	0.225813i	0.810941	+	0.585128i	$0.198956\pi$
$354$		0			0
$355$	11.0000	+	33.0000i	0.583819	+	1.75146i
$356$		0			0
$357$	−14.4853	−	2.48528i	−0.766642	−	0.131535i
$358$		0			0
$359$	5.65685			0.298557			0.149279	−	0.988795i	$-0.452305\pi$
$359$	5.65685			0.298557			0.149279	+	0.988795i	$0.452305\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$		0			0
$363$	−5.12132	−	0.878680i	−0.268800	−	0.0461187i
$364$		0			0
$365$	−2.82843	−	1.41421i	−0.148047	−	0.0740233i
$366$		0			0
$367$	−11.0000	+	11.0000i	−0.574195	+	0.574195i	−0.933298	−	0.359103i	$-0.883083\pi$
$367$	−11.0000	+	11.0000i	−0.574195	+	0.574195i	0.359103	+	0.933298i	$0.383083\pi$
$368$		0			0
$369$	2.82843	−	8.00000i	0.147242	−	0.416463i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−26.0000	−	26.0000i	−1.34623	−	1.34623i	−0.889718	−	0.456511i	$-0.849099\pi$
$373$	−26.0000	−	26.0000i	−1.34623	−	1.34623i	−0.456511	−	0.889718i	$-0.650901\pi$
$374$		0			0
$375$	13.5563	−	13.8284i	0.700047	−	0.714097i
$376$		0			0
$377$	−8.48528	−	8.48528i	−0.437014	−	0.437014i
$378$		0			0
$379$		−	12.0000i		−	0.616399i	−0.951322	−	0.308199i	$-0.900274\pi$
$379$		−	12.0000i		−	0.616399i	0.951322	−	0.308199i	$-0.0997264\pi$
$380$		0			0
$381$	8.00000	−	5.65685i	0.409852	−	0.289809i
$382$		0			0
$383$	16.9706	−	16.9706i	0.867155	−	0.867155i	−0.125001	−	0.992157i	$-0.539894\pi$
$383$	16.9706	−	16.9706i	0.867155	−	0.867155i	0.992157	+	0.125001i	$0.0398935\pi$
$384$		0			0
$385$	−24.0000	−	12.0000i	−1.22315	−	0.611577i
$386$		0			0
$387$	9.14214	+	19.1421i	0.464721	+	0.973049i
$388$		0			0
$389$	−15.5563			−0.788738			−0.394369	−	0.918952i	$-0.629037\pi$
$389$	−15.5563			−0.788738			−0.394369	+	0.918952i	$0.629037\pi$
$390$		0			0
$391$	2.00000			0.101144
$392$		0			0
$393$	3.72792	−	21.7279i	0.188049	−	1.09603i
$394$		0			0
$395$	7.07107	+	21.2132i	0.355784	+	1.06735i
$396$		0			0
$397$	7.00000	−	7.00000i	0.351320	−	0.351320i	−0.509281	−	0.860601i	$-0.670088\pi$
$397$	7.00000	−	7.00000i	0.351320	−	0.351320i	0.860601	+	0.509281i	$0.170088\pi$
$398$		0			0
$399$	−16.9706	−	24.0000i	−0.849591	−	1.20150i
$400$		0			0
$401$		−	15.5563i		−	0.776847i	−0.921481	−	0.388424i	$-0.873020\pi$
$401$		−	15.5563i		−	0.776847i	0.921481	−	0.388424i	$-0.126980\pi$
$402$		0			0
$403$	12.0000	+	12.0000i	0.597763	+	0.597763i
$404$		0			0
$405$	−18.8492	−	7.05025i	−0.936626	−	0.350330i
$406$		0			0
$407$	11.3137	+	11.3137i	0.560800	+	0.560800i
$408$		0			0
$409$			26.0000i			1.28562i	0.766027	+	0.642809i	$0.222231\pi$
$409$			26.0000i			1.28562i	−0.766027	+	0.642809i	$0.777769\pi$
$410$		0			0
$411$	−16.0000	−	22.6274i	−0.789222	−	1.11613i
$412$		0			0
$413$	−4.24264	+	4.24264i	−0.208767	+	0.208767i
$414$		0			0
$415$	−12.0000	+	24.0000i	−0.589057	+	1.17811i
$416$		0			0
$417$	−3.51472	+	20.4853i	−0.172117	+	1.00317i
$418$		0			0
$419$	−28.2843			−1.38178			−0.690889	−	0.722961i	$-0.742780\pi$
$419$	−28.2843			−1.38178			−0.690889	+	0.722961i	$0.742780\pi$
$420$		0			0
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$		0			0
$423$	−10.3431	−	21.6569i	−0.502901	−	1.05299i
$424$		0			0
$425$	9.89949	+	1.41421i	0.480196	+	0.0685994i
$426$		0			0
$427$	6.00000	−	6.00000i	0.290360	−	0.290360i
$428$		0			0
$429$	−16.9706	+	12.0000i	−0.819346	+	0.579365i
$430$		0			0
$431$			5.65685i			0.272481i	0.990676	+	0.136241i	$0.0435020\pi$
$431$			5.65685i			0.272481i	−0.990676	+	0.136241i	$0.956498\pi$
$432$		0			0
$433$	−10.0000	−	10.0000i	−0.480569	−	0.480569i	0.424744	−	0.905313i	$-0.360364\pi$
$433$	−10.0000	−	10.0000i	−0.480569	−	0.480569i	−0.905313	+	0.424744i	$0.860364\pi$
$434$		0			0
$435$	10.8284	−	1.65685i	0.519183	−	0.0794401i
$436$		0			0
$437$	2.82843	+	2.82843i	0.135302	+	0.135302i
$438$		0			0
$439$			20.0000i			0.954548i	0.878755	+	0.477274i	$0.158375\pi$
$439$			20.0000i			0.954548i	−0.878755	+	0.477274i	$0.841625\pi$
$440$		0			0
$441$	11.0000	−	31.1127i	0.523810	−	1.48156i
$442$		0			0
$443$	−2.82843	+	2.82843i	−0.134383	+	0.134383i	−0.771099	−	0.636716i	$-0.780292\pi$
$443$	−2.82843	+	2.82843i	−0.134383	+	0.134383i	0.636716	+	0.771099i	$0.280292\pi$
$444$		0			0
$445$	−21.0000	+	7.00000i	−0.995495	+	0.331832i
$446$		0			0
$447$	12.0711	+	2.07107i	0.570942	+	0.0979581i
$448$		0			0
$449$	5.65685			0.266963			0.133482	−	0.991051i	$-0.457384\pi$
$449$	5.65685			0.266963			0.133482	+	0.991051i	$0.457384\pi$
$450$		0			0
$451$	8.00000			0.376705
$452$		0			0
$453$	20.4853	+	3.51472i	0.962482	+	0.165136i
$454$		0			0
$455$	38.1838	−	12.7279i	1.79008	−	0.596694i
$456$		0			0
$457$	12.0000	−	12.0000i	0.561336	−	0.561336i	−0.368351	−	0.929687i	$-0.620077\pi$
$457$	12.0000	−	12.0000i	0.561336	−	0.561336i	0.929687	+	0.368351i	$0.120077\pi$
$458$		0			0
$459$	−2.82843	−	10.0000i	−0.132020	−	0.466760i
$460$		0			0
$461$		−	28.2843i		−	1.31733i	−0.752436	−	0.658665i	$-0.771121\pi$
$461$		−	28.2843i		−	1.31733i	0.752436	−	0.658665i	$-0.228879\pi$
$462$		0			0
$463$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$463$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$464$		0			0
$465$	−15.3137	+	2.34315i	−0.710156	+	0.108661i
$466$		0			0
$467$	−28.2843	−	28.2843i	−1.30884	−	1.30884i	−0.922253	−	0.386587i	$-0.873654\pi$
$467$	−28.2843	−	28.2843i	−1.30884	−	1.30884i	−0.386587	−	0.922253i	$-0.626346\pi$
$468$		0			0
$469$		−	42.0000i		−	1.93938i
$470$		0			0
$471$	12.0000	−	8.48528i	0.552931	−	0.390981i
$472$		0			0
$473$	−14.1421	+	14.1421i	−0.650256	+	0.650256i
$474$		0			0
$475$	12.0000	+	16.0000i	0.550598	+	0.734130i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	36.7696			1.68004			0.840022	−	0.542553i	$-0.182542\pi$
$479$	36.7696			1.68004			0.840022	+	0.542553i	$0.182542\pi$
$480$		0			0
$481$	−24.0000			−1.09431
$482$		0			0
$483$	−1.24264	+	7.24264i	−0.0565421	+	0.329552i
$484$		0			0
$485$	−16.9706	+	33.9411i	−0.770594	+	1.54119i
$486$		0			0
$487$	−16.0000	+	16.0000i	−0.725029	+	0.725029i	−0.969625	−	0.244596i	$-0.921345\pi$
$487$	−16.0000	+	16.0000i	−0.725029	+	0.725029i	0.244596	+	0.969625i	$0.421345\pi$
$488$		0			0
$489$	−8.48528	−	12.0000i	−0.383718	−	0.542659i
$490$		0			0
$491$		−	32.5269i		−	1.46792i	−0.679193	−	0.733959i	$-0.737670\pi$
$491$		−	32.5269i		−	1.46792i	0.679193	−	0.733959i	$-0.262330\pi$
$492$		0			0
$493$	4.00000	+	4.00000i	0.180151	+	0.180151i
$494$		0			0
$495$	0.343146	−	18.9706i	0.0154233	−	0.852663i
$496$		0			0
$497$	−46.6690	−	46.6690i	−2.09339	−	2.09339i
$498$		0			0
$499$			40.0000i			1.79065i	0.445418	+	0.895323i	$0.353055\pi$
$499$			40.0000i			1.79065i	−0.445418	+	0.895323i	$0.646945\pi$
$500$		0			0
$501$	24.0000	+	33.9411i	1.07224	+	1.51638i
$502$		0			0
$503$	−28.2843	+	28.2843i	−1.26113	+	1.26113i	−0.310589	+	0.950544i	$0.600526\pi$
$503$	−28.2843	+	28.2843i	−1.26113	+	1.26113i	−0.950544	+	0.310589i	$0.899474\pi$
$504$		0			0
$505$	6.00000	+	18.0000i	0.266996	+	0.800989i
$506$		0			0
$507$	1.46447	−	8.53553i	0.0650392	−	0.379076i
$508$		0			0
$509$	42.4264			1.88052			0.940259	−	0.340461i	$-0.110583\pi$
$509$	42.4264			1.88052			0.940259	+	0.340461i	$0.110583\pi$
$510$		0			0
$511$	6.00000			0.265424
$512$		0			0
$513$	10.1421	−	18.1421i	0.447786	−	0.800995i
$514$		0			0
$515$	36.7696	+	18.3848i	1.62026	+	0.810130i
$516$		0			0
$517$	16.0000	−	16.0000i	0.703679	−	0.703679i
$518$		0			0
$519$	19.7990	−	14.0000i	0.869079	−	0.614532i
$520$		0			0
$521$		−	1.41421i		−	0.0619578i	−0.999520	−	0.0309789i	$-0.990138\pi$
$521$		−	1.41421i		−	0.0619578i	0.999520	−	0.0309789i	$-0.00986247\pi$
$522$		0			0
$523$	−9.00000	−	9.00000i	−0.393543	−	0.393543i	0.482405	−	0.875948i	$-0.339763\pi$
$523$	−9.00000	−	9.00000i	−0.393543	−	0.393543i	−0.875948	+	0.482405i	$0.839763\pi$
$524$		0			0
$525$	−11.2721	+	34.9706i	−0.491954	+	1.52624i
$526$		0			0
$527$	−5.65685	−	5.65685i	−0.246416	−	0.246416i
$528$		0			0
$529$		−	1.00000i		−	0.0434783i
$530$		0			0
$531$	−4.00000	−	1.41421i	−0.173585	−	0.0613716i
$532$		0			0
$533$	−8.48528	+	8.48528i	−0.367538	+	0.367538i
$534$		0			0
$535$	−8.00000	−	4.00000i	−0.345870	−	0.172935i
$536$		0			0
$537$	31.3848	+	5.38478i	1.35435	+	0.232370i
$538$		0			0
$539$	31.1127			1.34012
$540$		0			0
$541$	6.00000			0.257960			0.128980	−	0.991647i	$-0.458830\pi$
$541$	6.00000			0.257960			0.128980	+	0.991647i	$0.458830\pi$
$542$		0			0
$543$	−10.2426	−	1.75736i	−0.439554	−	0.0754155i
$544$		0			0
$545$	4.24264	+	12.7279i	0.181735	+	0.545204i
$546$		0			0
$547$	−26.0000	+	26.0000i	−1.11168	+	1.11168i	−0.118756	+	0.992923i	$0.537891\pi$
$547$	−26.0000	+	26.0000i	−1.11168	+	1.11168i	−0.992923	+	0.118756i	$0.962109\pi$
$548$		0			0
$549$	5.65685	+	2.00000i	0.241429	+	0.0853579i
$550$		0			0
$551$			11.3137i			0.481980i
$552$		0			0
$553$	−30.0000	−	30.0000i	−1.27573	−	1.27573i
$554$		0			0
$555$	12.9706	−	17.6569i	0.550570	−	0.749492i
$556$		0			0
$557$	12.7279	+	12.7279i	0.539299	+	0.539299i	0.923323	−	0.384024i	$-0.125462\pi$
$557$	12.7279	+	12.7279i	0.539299	+	0.539299i	−0.384024	+	0.923323i	$0.625462\pi$
$558$		0			0
$559$		−	30.0000i		−	1.26886i
$560$		0			0
$561$	8.00000	−	5.65685i	0.337760	−	0.238833i
$562$		0			0
$563$	−31.1127	+	31.1127i	−1.31124	+	1.31124i	−0.390745	+	0.920499i	$0.627783\pi$
$563$	−31.1127	+	31.1127i	−1.31124	+	1.31124i	−0.920499	+	0.390745i	$0.872217\pi$
$564$		0			0
$565$	−2.00000	+	4.00000i	−0.0841406	+	0.168281i
$566$		0			0
$567$	37.9706	−	4.02944i	1.59461	−	0.169220i
$568$		0			0
$569$	1.41421			0.0592869			0.0296435	−	0.999561i	$-0.490563\pi$
$569$	1.41421			0.0592869			0.0296435	+	0.999561i	$0.490563\pi$
$570$		0			0
$571$	26.0000			1.08807			0.544033	−	0.839064i	$-0.316897\pi$
$571$	26.0000			1.08807			0.544033	+	0.839064i	$0.316897\pi$
$572$		0			0
$573$	5.79899	−	33.7990i	0.242256	−	1.41197i
$574$		0			0
$575$	0.707107	−	4.94975i	0.0294884	−	0.206419i
$576$		0			0
$577$	13.0000	−	13.0000i	0.541197	−	0.541197i	−0.382683	−	0.923880i	$-0.625000\pi$
$577$	13.0000	−	13.0000i	0.541197	−	0.541197i	0.923880	+	0.382683i	$0.125000\pi$
$578$		0			0
$579$	−12.7279	−	18.0000i	−0.528954	−	0.748054i
$580$		0			0
$581$		−	50.9117i		−	2.11217i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	19.7574	+	20.4853i	0.816866	+	0.846962i
$586$		0			0
$587$	−15.5563	−	15.5563i	−0.642079	−	0.642079i	0.308987	−	0.951066i	$-0.400010\pi$
$587$	−15.5563	−	15.5563i	−0.642079	−	0.642079i	−0.951066	+	0.308987i	$0.900010\pi$
$588$		0			0
$589$		−	16.0000i		−	0.659269i
$590$		0			0
$591$	10.0000	+	14.1421i	0.411345	+	0.581730i
$592$		0			0
$593$	−9.89949	+	9.89949i	−0.406524	+	0.406524i	−0.880524	−	0.474001i	$-0.842809\pi$
$593$	−9.89949	+	9.89949i	−0.406524	+	0.406524i	0.474001	+	0.880524i	$0.342809\pi$
$594$		0			0
$595$	−18.0000	+	6.00000i	−0.737928	+	0.245976i
$596$		0			0
$597$	6.44365	−	37.5563i	0.263721	−	1.53708i
$598$		0			0
$599$	35.3553			1.44458			0.722290	−	0.691590i	$-0.243090\pi$
$599$	35.3553			1.44458			0.722290	+	0.691590i	$0.243090\pi$
$600$		0			0
$601$	12.0000			0.489490			0.244745	−	0.969587i	$-0.421296\pi$
$601$	12.0000			0.489490			0.244745	+	0.969587i	$0.421296\pi$
$602$		0			0
$603$	26.7990	−	12.7990i	1.09134	−	0.521215i
$604$		0			0
$605$	−6.36396	+	2.12132i	−0.258732	+	0.0862439i
$606$		0			0
$607$	8.00000	−	8.00000i	0.324710	−	0.324710i	−0.525861	−	0.850571i	$-0.676257\pi$
$607$	8.00000	−	8.00000i	0.324710	−	0.324710i	0.850571	+	0.525861i	$0.176257\pi$
$608$		0			0
$609$	−16.9706	+	12.0000i	−0.687682	+	0.486265i
$610$		0			0
$611$			33.9411i			1.37311i
$612$		0			0
$613$	−10.0000	−	10.0000i	−0.403896	−	0.403896i	0.475707	−	0.879604i	$-0.342192\pi$
$613$	−10.0000	−	10.0000i	−0.403896	−	0.403896i	−0.879604	+	0.475707i	$0.842192\pi$
$614$		0			0
$615$	−1.65685	−	10.8284i	−0.0668108	−	0.436644i
$616$		0			0
$617$	−8.48528	−	8.48528i	−0.341605	−	0.341605i	0.515366	−	0.856970i	$-0.327656\pi$
$617$	−8.48528	−	8.48528i	−0.341605	−	0.341605i	−0.856970	+	0.515366i	$0.827656\pi$
$618$		0			0
$619$			10.0000i			0.401934i	0.979598	+	0.200967i	$0.0644084\pi$
$619$			10.0000i			0.401934i	−0.979598	+	0.200967i	$0.935592\pi$
$620$		0			0
$621$	−5.00000	+	1.41421i	−0.200643	+	0.0567504i
$622$		0			0
$623$	29.6985	−	29.6985i	1.18984	−	1.18984i
$624$		0			0
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$		0			0
$627$	19.3137	+	3.31371i	0.771315	+	0.132337i
$628$		0			0
$629$	11.3137			0.451107
$630$		0			0
$631$	−34.0000			−1.35352			−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000			−1.35352			−0.676759	+	0.736204i	$0.736616\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	5.65685	−	11.3137i	0.224485	−	0.448971i
$636$		0			0
$637$	−33.0000	+	33.0000i	−1.30751	+	1.30751i
$638$		0			0
$639$	15.5563	−	44.0000i	0.615400	−	1.74061i
$640$		0			0
$641$			32.5269i			1.28474i	0.766396	+	0.642368i	$0.222048\pi$
$641$			32.5269i			1.28474i	−0.766396	+	0.642368i	$0.777952\pi$
$642$		0			0
$643$	23.0000	+	23.0000i	0.907031	+	0.907031i	0.996032	−	0.0890002i	$-0.0283672\pi$
$643$	23.0000	+	23.0000i	0.907031	+	0.907031i	−0.0890002	+	0.996032i	$0.528367\pi$
$644$		0			0
$645$	22.0711	+	16.2132i	0.869047	+	0.638394i
$646$		0			0
$647$	16.9706	+	16.9706i	0.667182	+	0.667182i	0.957063	−	0.289881i	$-0.0936157\pi$
$647$	16.9706	+	16.9706i	0.667182	+	0.667182i	−0.289881	+	0.957063i	$0.593616\pi$
$648$		0			0
$649$		−	4.00000i		−	0.157014i
$650$		0			0
$651$	24.0000	−	16.9706i	0.940634	−	0.665129i
$652$		0			0
$653$	−12.7279	+	12.7279i	−0.498082	+	0.498082i	−0.910841	−	0.412758i	$-0.864565\pi$
$653$	−12.7279	+	12.7279i	−0.498082	+	0.498082i	0.412758	+	0.910841i	$0.364565\pi$
$654$		0			0
$655$	−9.00000	−	27.0000i	−0.351659	−	1.05498i
$656$		0			0
$657$	1.82843	+	3.82843i	0.0713337	+	0.149361i
$658$		0			0
$659$	5.65685			0.220360			0.110180	−	0.993912i	$-0.464857\pi$
$659$	5.65685			0.220360			0.110180	+	0.993912i	$0.464857\pi$
$660$		0			0
$661$	2.00000			0.0777910			0.0388955	−	0.999243i	$-0.487616\pi$
$661$	2.00000			0.0777910			0.0388955	+	0.999243i	$0.487616\pi$
$662$		0			0
$663$	−2.48528	+	14.4853i	−0.0965203	+	0.562562i
$664$		0			0
$665$	−33.9411	−	16.9706i	−1.31618	−	0.658090i
$666$		0			0
$667$	2.00000	−	2.00000i	0.0774403	−	0.0774403i
$668$		0			0
$669$	−25.4558	−	36.0000i	−0.984180	−	1.39184i
$670$		0			0
$671$			5.65685i			0.218380i
$672$		0			0
$673$	5.00000	+	5.00000i	0.192736	+	0.192736i	0.796877	−	0.604141i	$-0.206484\pi$
$673$	5.00000	+	5.00000i	0.192736	+	0.192736i	−0.604141	+	0.796877i	$0.706484\pi$
$674$		0			0
$675$	−25.7487	+	3.46447i	−0.991069	+	0.133347i
$676$		0			0
$677$	−2.82843	−	2.82843i	−0.108705	−	0.108705i	0.650662	−	0.759367i	$-0.274491\pi$
$677$	−2.82843	−	2.82843i	−0.108705	−	0.108705i	−0.759367	+	0.650662i	$0.774491\pi$
$678$		0			0
$679$		−	72.0000i		−	2.76311i
$680$		0			0
$681$	24.0000	+	33.9411i	0.919682	+	1.30063i
$682$		0			0
$683$	21.2132	−	21.2132i	0.811701	−	0.811701i	−0.173188	−	0.984889i	$-0.555407\pi$
$683$	21.2132	−	21.2132i	0.811701	−	0.811701i	0.984889	+	0.173188i	$0.0554069\pi$
$684$		0			0
$685$	−32.0000	−	16.0000i	−1.22266	−	0.611329i
$686$		0			0
$687$	−6.44365	+	37.5563i	−0.245841	+	1.43286i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−8.00000			−0.304334			−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000			−0.304334			−0.152167	+	0.988355i	$0.548625\pi$
$692$		0			0
$693$	15.5147	+	32.4853i	0.589355	+	1.23401i
$694$		0			0
$695$	8.48528	+	25.4558i	0.321865	+	0.965595i
$696$		0			0
$697$	4.00000	−	4.00000i	0.151511	−	0.151511i
$698$		0			0
$699$	−42.4264	+	30.0000i	−1.60471	+	1.13470i
$700$		0			0
$701$		−	43.8406i		−	1.65584i	−0.560848	−	0.827919i	$-0.689525\pi$
$701$		−	43.8406i		−	1.65584i	0.560848	−	0.827919i	$-0.310475\pi$
$702$		0			0
$703$	16.0000	+	16.0000i	0.603451	+	0.603451i
$704$		0			0
$705$	−24.9706	−	18.3431i	−0.940446	−	0.690843i
$706$		0			0
$707$	−25.4558	−	25.4558i	−0.957366	−	0.957366i
$708$		0			0
$709$			6.00000i			0.225335i	0.993633	+	0.112667i	$0.0359394\pi$
$709$			6.00000i			0.225335i	−0.993633	+	0.112667i	$0.964061\pi$
$710$		0			0
$711$	10.0000	−	28.2843i	0.375029	−	1.06074i
$712$		0			0
$713$	−2.82843	+	2.82843i	−0.105925	+	0.105925i
$714$		0			0
$715$	−12.0000	+	24.0000i	−0.448775	+	0.897549i
$716$		0			0
$717$	16.8995	+	2.89949i	0.631123	+	0.108284i
$718$		0			0
$719$	−9.89949			−0.369189			−0.184594	−	0.982815i	$-0.559097\pi$
$719$	−9.89949			−0.369189			−0.184594	+	0.982815i	$0.559097\pi$
$720$		0			0
$721$	−78.0000			−2.90487
$722$		0			0
$723$	−10.2426	−	1.75736i	−0.380928	−	0.0653569i
$724$		0			0
$725$	11.3137	−	8.48528i	0.420181	−	0.315135i
$726$		0			0
$727$	−17.0000	+	17.0000i	−0.630495	+	0.630495i	−0.948192	−	0.317697i	$-0.897090\pi$
$727$	−17.0000	+	17.0000i	−0.630495	+	0.630495i	0.317697	+	0.948192i	$0.397090\pi$
$728$		0			0
$729$	14.1421	+	23.0000i	0.523783	+	0.851852i
$730$		0			0
$731$			14.1421i			0.523066i
$732$		0			0
$733$	20.0000	+	20.0000i	0.738717	+	0.738717i	0.972330	−	0.233613i	$-0.0750548\pi$
$733$	20.0000	+	20.0000i	0.738717	+	0.738717i	−0.233613	+	0.972330i	$0.575055\pi$
$734$		0			0
$735$	−6.44365	−	42.1127i	−0.237678	−	1.55335i
$736$		0			0
$737$	19.7990	+	19.7990i	0.729305	+	0.729305i
$738$		0			0
$739$		0			0		1.00000			$0$
$739$		0			0		−1.00000			$\pi$
$740$		0			0
$741$	−24.0000	+	16.9706i	−0.881662	+	0.623429i
$742$		0			0
$743$	2.82843	−	2.82843i	0.103765	−	0.103765i	−0.653318	−	0.757083i	$-0.726624\pi$
$743$	2.82843	−	2.82843i	0.103765	−	0.103765i	0.757083	+	0.653318i	$0.226624\pi$
$744$		0			0
$745$	15.0000	−	5.00000i	0.549557	−	0.183186i
$746$		0			0
$747$	32.4853	−	15.5147i	1.18857	−	0.567654i
$748$		0			0
$749$	16.9706			0.620091
$750$		0			0
$751$	24.0000			0.875772			0.437886	−	0.899030i	$-0.355727\pi$
$751$	24.0000			0.875772			0.437886	+	0.899030i	$0.355727\pi$
$752$		0			0
$753$	0.828427	−	4.82843i	0.0301896	−	0.175958i
$754$		0			0
$755$	25.4558	−	8.48528i	0.926433	−	0.308811i
$756$		0			0
$757$	6.00000	−	6.00000i	0.218074	−	0.218074i	−0.589613	−	0.807686i	$-0.700720\pi$
$757$	6.00000	−	6.00000i	0.218074	−	0.218074i	0.807686	+	0.589613i	$0.200720\pi$
$758$		0			0
$759$	−2.82843	−	4.00000i	−0.102665	−	0.145191i
$760$		0			0
$761$			14.1421i			0.512652i	0.966590	+	0.256326i	$0.0825121\pi$
$761$			14.1421i			0.512652i	−0.966590	+	0.256326i	$0.917488\pi$
$762$		0			0
$763$	−18.0000	−	18.0000i	−0.651644	−	0.651644i
$764$		0			0
$765$	−9.31371	−	9.65685i	−0.336738	−	0.349144i
$766$		0			0
$767$	4.24264	+	4.24264i	0.153193	+	0.153193i
$768$		0			0
$769$			42.0000i			1.51456i	0.653091	+	0.757279i	$0.273472\pi$
$769$			42.0000i			1.51456i	−0.653091	+	0.757279i	$0.726528\pi$
$770$		0			0
$771$	−10.0000	−	14.1421i	−0.360141	−	0.509317i
$772$		0			0
$773$	7.07107	−	7.07107i	0.254329	−	0.254329i	−0.568414	−	0.822743i	$-0.692443\pi$
$773$	7.07107	−	7.07107i	0.254329	−	0.254329i	0.822743	+	0.568414i	$0.192443\pi$
$774$		0			0
$775$	−16.0000	+	12.0000i	−0.574737	+	0.431053i
$776$		0			0
$777$	−7.02944	+	40.9706i	−0.252180	+	1.46981i
$778$		0			0
$779$	11.3137			0.405356
$780$		0			0
$781$	44.0000			1.57444
$782$		0			0
$783$	−12.8284	−	7.17157i	−0.458451	−	0.256291i
$784$		0			0
$785$	8.48528	−	16.9706i	0.302853	−	0.605705i
$786$		0			0
$787$	15.0000	−	15.0000i	0.534692	−	0.534692i	−0.387273	−	0.921965i	$-0.626583\pi$
$787$	15.0000	−	15.0000i	0.534692	−	0.534692i	0.921965	+	0.387273i	$0.126583\pi$
$788$		0			0
$789$	−22.6274	+	16.0000i	−0.805557	+	0.569615i
$790$		0			0
$791$		−	8.48528i		−	0.301702i
$792$		0			0
$793$	−6.00000	−	6.00000i	−0.213066	−	0.213066i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	8.48528	+	8.48528i	0.300564	+	0.300564i	0.841235	−	0.540670i	$-0.181829\pi$
$797$	8.48528	+	8.48528i	0.300564	+	0.300564i	−0.540670	+	0.841235i	$0.681829\pi$
$798$		0			0
$799$		−	16.0000i		−	0.566039i
$800$		0			0
$801$	28.0000	+	9.89949i	0.989331	+	0.349781i
$802$		0			0
$803$	−2.82843	+	2.82843i	−0.0998130	+	0.0998130i
$804$		0			0
$805$	3.00000	+	9.00000i	0.105736	+	0.317208i
$806$		0			0
$807$	−28.9706	−	4.97056i	−1.01981	−	0.174972i
$808$		0			0
$809$	39.5980			1.39219			0.696095	−	0.717949i	$-0.254919\pi$
$809$	39.5980			1.39219			0.696095	+	0.717949i	$0.254919\pi$
$810$		0			0
$811$	16.0000			0.561836			0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000			0.561836			0.280918	+	0.959732i	$0.409361\pi$
$812$		0			0
$813$	−20.4853	−	3.51472i	−0.718450	−	0.123267i
$814$		0			0
$815$	−16.9706	−	8.48528i	−0.594453	−	0.297226i
$816$		0			0
$817$	−20.0000	+	20.0000i	−0.699711	+	0.699711i
$818$		0			0
$819$	−50.9117	−	18.0000i	−1.77900	−	0.628971i
$820$		0			0
$821$			33.9411i			1.18455i	0.805735	+	0.592277i	$0.201771\pi$
$821$			33.9411i			1.18455i	−0.805735	+	0.592277i	$0.798229\pi$
$822$		0			0
$823$	10.0000	+	10.0000i	0.348578	+	0.348578i	0.859580	−	0.511002i	$-0.170725\pi$
$823$	10.0000	+	10.0000i	0.348578	+	0.348578i	−0.511002	+	0.859580i	$0.670725\pi$
$824$		0			0
$825$	−11.1716	−	21.7990i	−0.388944	−	0.758943i
$826$		0			0
$827$	14.1421	+	14.1421i	0.491770	+	0.491770i	0.908864	−	0.417093i	$-0.136951\pi$
$827$	14.1421	+	14.1421i	0.491770	+	0.491770i	−0.417093	+	0.908864i	$0.636951\pi$
$828$		0			0
$829$			2.00000i			0.0694629i	0.999397	+	0.0347314i	$0.0110576\pi$
$829$			2.00000i			0.0694629i	−0.999397	+	0.0347314i	$0.988942\pi$
$830$		0			0
$831$	−42.0000	+	29.6985i	−1.45696	+	1.03023i
$832$		0			0
$833$	15.5563	−	15.5563i	0.538996	−	0.538996i
$834$		0			0
$835$	48.0000	+	24.0000i	1.66111	+	0.830554i
$836$		0			0
$837$	18.1421	+	10.1421i	0.627084	+	0.350563i
$838$		0			0
$839$	−42.4264			−1.46472			−0.732361	−	0.680916i	$-0.761582\pi$
$839$	−42.4264			−1.46472			−0.732361	+	0.680916i	$0.761582\pi$
$840$		0			0
$841$	−21.0000			−0.724138
$842$		0			0
$843$	7.87006	−	45.8701i	0.271059	−	1.57985i
$844$		0			0
$845$	−3.53553	−	10.6066i	−0.121626	−	0.364878i
$846$		0			0
$847$	9.00000	−	9.00000i	0.309244	−	0.309244i
$848$		0			0
$849$	−21.2132	−	30.0000i	−0.728035	−	1.02960i
$850$		0			0
$851$		−	5.65685i		−	0.193914i
$852$		0			0
$853$	−29.0000	−	29.0000i	−0.992941	−	0.992941i	0.00703417	−	0.999975i	$-0.497761\pi$
$853$	−29.0000	−	29.0000i	−0.992941	−	0.992941i	−0.999975	+	0.00703417i	$0.997761\pi$
$854$		0			0
$855$	0.485281	−	26.8284i	0.0165963	−	0.917513i
$856$		0			0
$857$	−26.8701	−	26.8701i	−0.917864	−	0.917864i	0.0790101	−	0.996874i	$-0.474824\pi$
$857$	−26.8701	−	26.8701i	−0.917864	−	0.917864i	−0.996874	+	0.0790101i	$0.974824\pi$
$858$		0			0
$859$			20.0000i			0.682391i	0.939992	+	0.341196i	$0.110832\pi$
$859$			20.0000i			0.682391i	−0.939992	+	0.341196i	$0.889168\pi$
$860$		0			0
$861$	12.0000	+	16.9706i	0.408959	+	0.578355i
$862$		0			0
$863$	−18.3848	+	18.3848i	−0.625825	+	0.625825i	−0.947015	−	0.321190i	$-0.895917\pi$
$863$	−18.3848	+	18.3848i	−0.625825	+	0.625825i	0.321190	+	0.947015i	$0.395917\pi$
$864$		0			0
$865$	14.0000	−	28.0000i	0.476014	−	0.952029i
$866$		0			0
$867$	−3.80761	+	22.1924i	−0.129313	+	0.753693i
$868$		0			0
$869$	28.2843			0.959478
$870$		0			0
$871$	−42.0000			−1.42312
$872$		0			0
$873$	45.9411	−	21.9411i	1.55487	−	0.742595i
$874$		0			0
$875$	8.48528	+	46.6690i	0.286855	+	1.57770i
$876$		0			0
$877$	−35.0000	+	35.0000i	−1.18187	+	1.18187i	−0.202606	+	0.979260i	$0.564941\pi$
$877$	−35.0000	+	35.0000i	−1.18187	+	1.18187i	−0.979260	+	0.202606i	$0.935059\pi$
$878$		0			0
$879$	16.9706	−	12.0000i	0.572403	−	0.404750i
$880$		0			0
$881$		−	41.0122i		−	1.38174i	−0.722981	−	0.690868i	$-0.757229\pi$
$881$		−	41.0122i		−	1.38174i	0.722981	−	0.690868i	$-0.242771\pi$
$882$		0			0
$883$	10.0000	+	10.0000i	0.336527	+	0.336527i	0.855058	−	0.518532i	$-0.173521\pi$
$883$	10.0000	+	10.0000i	0.336527	+	0.336527i	−0.518532	+	0.855058i	$0.673521\pi$
$884$		0			0
$885$	−5.41421	+	0.828427i	−0.181997	+	0.0278473i
$886$		0			0
$887$	−12.7279	−	12.7279i	−0.427362	−	0.427362i	0.460367	−	0.887729i	$-0.347718\pi$
$887$	−12.7279	−	12.7279i	−0.427362	−	0.427362i	−0.887729	+	0.460367i	$0.847718\pi$
$888$		0			0
$889$			24.0000i			0.804934i
$890$		0			0
$891$	−16.0000	+	19.7990i	−0.536020	+	0.663291i
$892$		0			0
$893$	22.6274	−	22.6274i	0.757198	−	0.757198i
$894$		0			0
$895$	39.0000	−	13.0000i	1.30363	−	0.434542i
$896$		0			0
$897$	7.24264	+	1.24264i	0.241825	+	0.0414906i
$898$		0			0
$899$	−11.3137			−0.377333
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−51.2132	−	8.78680i	−1.70427	−	0.292406i
$904$		0			0
$905$	−12.7279	+	4.24264i	−0.423090	+	0.141030i
$906$		0			0
$907$	39.0000	−	39.0000i	1.29497	−	1.29497i	0.363303	−	0.931671i	$-0.381649\pi$
$907$	39.0000	−	39.0000i	1.29497	−	1.29497i	0.931671	−	0.363303i	$-0.118351\pi$
$908$		0			0
$909$	8.48528	−	24.0000i	0.281439	−	0.796030i
$910$		0			0
$911$			42.4264i			1.40565i	0.711363	+	0.702825i	$0.248078\pi$
$911$			42.4264i			1.40565i	−0.711363	+	0.702825i	$0.751922\pi$
$912$		0			0
$913$	24.0000	+	24.0000i	0.794284	+	0.794284i
$914$		0			0
$915$	7.65685	−	1.17157i	0.253128	−	0.0387310i
$916$		0			0
$917$	38.1838	+	38.1838i	1.26094	+	1.26094i
$918$		0			0
$919$			8.00000i			0.263896i	0.991257	+	0.131948i	$0.0421231\pi$
$919$			8.00000i			0.263896i	−0.991257	+	0.131948i	$0.957877\pi$
$920$		0			0
$921$	−36.0000	+	25.4558i	−1.18624	+	0.838799i
$922$		0			0
$923$	−46.6690	+	46.6690i	−1.53613	+	1.53613i
$924$		0			0
$925$	4.00000	−	28.0000i	0.131519	−	0.920634i
$926$		0			0
$927$	−23.7696	−	49.7696i	−0.780695	−	1.63465i
$928$		0			0
$929$	22.6274			0.742381			0.371191	−	0.928557i	$-0.378950\pi$
$929$	22.6274			0.742381			0.371191	+	0.928557i	$0.378950\pi$
$930$		0			0
$931$	44.0000			1.44204
$932$		0			0
$933$	4.55635	−	26.5563i	0.149168	−	0.869416i
$934$		0			0
$935$	5.65685	−	11.3137i	0.184999	−	0.369998i
$936$		0			0
$937$	−36.0000	+	36.0000i	−1.17607	+	1.17607i	−0.195331	+	0.980737i	$0.562578\pi$
$937$	−36.0000	+	36.0000i	−1.17607	+	1.17607i	−0.980737	+	0.195331i	$0.937422\pi$
$938$		0			0
$939$	−5.65685	−	8.00000i	−0.184604	−	0.261070i
$940$		0			0
$941$			15.5563i			0.507122i	0.967319	+	0.253561i	$0.0816019\pi$
$941$			15.5563i			0.507122i	−0.967319	+	0.253561i	$0.918398\pi$
$942$		0			0
$943$	−2.00000	−	2.00000i	−0.0651290	−	0.0651290i
$944$		0			0
$945$	40.7574	−	27.7279i	1.32584	−	0.901989i
$946$		0			0
$947$	−29.6985	−	29.6985i	−0.965071	−	0.965071i	0.0343392	−	0.999410i	$-0.489067\pi$
$947$	−29.6985	−	29.6985i	−0.965071	−	0.965071i	−0.999410	+	0.0343392i	$0.989067\pi$
$948$		0			0
$949$		−	6.00000i		−	0.194768i
$950$		0			0
$951$	−6.00000	−	8.48528i	−0.194563	−	0.275154i
$952$		0			0
$953$	9.89949	−	9.89949i	0.320676	−	0.320676i	−0.528350	−	0.849026i	$-0.677189\pi$
$953$	9.89949	−	9.89949i	0.320676	−	0.320676i	0.849026	+	0.528350i	$0.177189\pi$
$954$		0			0
$955$	−14.0000	−	42.0000i	−0.453029	−	1.35909i
$956$		0			0
$957$	2.34315	−	13.6569i	0.0757431	−	0.441463i
$958$		0			0
$959$	67.8823			2.19203
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	5.17157	+	10.8284i	0.166652	+	0.348941i
$964$		0			0
$965$	−25.4558	−	12.7279i	−0.819453	−	0.409726i
$966$		0			0
$967$	−26.0000	+	26.0000i	−0.836104	+	0.836104i	−0.988344	−	0.152240i	$-0.951351\pi$
$967$	−26.0000	+	26.0000i	−0.836104	+	0.836104i	0.152240	+	0.988344i	$0.451351\pi$
$968$		0			0
$969$	11.3137	−	8.00000i	0.363449	−	0.256997i
$970$		0			0
$971$		−	19.7990i		−	0.635380i	−0.948195	−	0.317690i	$-0.897093\pi$
$971$		−	19.7990i		−	0.635380i	0.948195	−	0.317690i	$-0.102907\pi$
$972$		0			0
$973$	−36.0000	−	36.0000i	−1.15411	−	1.15411i
$974$		0			0
$975$	34.9706	+	11.2721i	1.11995	+	0.360995i
$976$		0			0
$977$	38.1838	+	38.1838i	1.22161	+	1.22161i	0.967061	+	0.254546i	$0.0819261\pi$
$977$	38.1838	+	38.1838i	1.22161	+	1.22161i	0.254546	+	0.967061i	$0.418074\pi$
$978$		0			0
$979$			28.0000i			0.894884i
$980$		0			0
$981$	6.00000	−	16.9706i	0.191565	−	0.541828i
$982$		0			0
$983$	19.7990	−	19.7990i	0.631490	−	0.631490i	−0.316952	−	0.948442i	$-0.602659\pi$
$983$	19.7990	−	19.7990i	0.631490	−	0.631490i	0.948442	+	0.316952i	$0.102659\pi$
$984$		0			0
$985$	20.0000	+	10.0000i	0.637253	+	0.318626i
$986$		0			0
$987$	57.9411	+	9.94113i	1.84429	+	0.316430i
$988$		0			0
$989$	7.07107			0.224847
$990$		0			0
$991$	−20.0000			−0.635321			−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000			−0.635321			−0.317660	+	0.948205i	$0.602897\pi$
$992$		0			0
$993$	27.3137	+	4.68629i	0.866774	+	0.148715i
$994$		0			0
$995$	−15.5563	−	46.6690i	−0.493169	−	1.47951i
$996$		0			0
$997$	39.0000	−	39.0000i	1.23514	−	1.23514i	0.273179	−	0.961963i	$-0.411925\pi$
$997$	39.0000	−	39.0000i	1.23514	−	1.23514i	0.961963	−	0.273179i	$-0.0880752\pi$
$998$		0			0
$999$	−28.2843	+	8.00000i	−0.894875	+	0.253109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.r.b.1013.1	yes	4
3.2	odd	2	inner	1380.2.r.b.1013.2	yes	4
5.2	odd	4	inner	1380.2.r.b.737.2	yes	4
15.2	even	4	inner	1380.2.r.b.737.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.r.b.737.1	✓	4	15.2	even	4	inner
1380.2.r.b.737.2	yes	4	5.2	odd	4	inner
1380.2.r.b.1013.1	yes	4	1.1	even	1	trivial
1380.2.r.b.1013.2	yes	4	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70711 - 0.292893i) q^{3} +(-2.12132 + 0.707107i) q^{5} +(3.00000 - 3.00000i) q^{7} +(2.82843 + 1.00000i) q^{9} +O(q^{10})\)	\(q+(-1.70711 - 0.292893i) q^{3} +(-2.12132 + 0.707107i) q^{5} +(3.00000 - 3.00000i) q^{7} +(2.82843 + 1.00000i) q^{9} +2.82843i q^{11} +(-3.00000 - 3.00000i) q^{13} +(3.82843 - 0.585786i) q^{15} +(1.41421 + 1.41421i) q^{17} +4.00000i q^{19} +(-6.00000 + 4.24264i) q^{21} +(0.707107 - 0.707107i) q^{23} +(4.00000 - 3.00000i) q^{25} +(-4.53553 - 2.53553i) q^{27} +2.82843 q^{29} -4.00000 q^{31} +(0.828427 - 4.82843i) q^{33} +(-4.24264 + 8.48528i) q^{35} +(4.00000 - 4.00000i) q^{37} +(4.24264 + 6.00000i) q^{39} -2.82843i q^{41} +(5.00000 + 5.00000i) q^{43} +(-6.70711 - 0.121320i) q^{45} +(-5.65685 - 5.65685i) q^{47} -11.0000i q^{49} +(-2.00000 - 2.82843i) q^{51} +(-2.00000 - 6.00000i) q^{55} +(1.17157 - 6.82843i) q^{57} -1.41421 q^{59} +2.00000 q^{61} +(11.4853 - 5.48528i) q^{63} +(8.48528 + 4.24264i) q^{65} +(7.00000 - 7.00000i) q^{67} +(-1.41421 + 1.00000i) q^{69} -15.5563i q^{71} +(1.00000 + 1.00000i) q^{73} +(-7.70711 + 3.94975i) q^{75} +(8.48528 + 8.48528i) q^{77} -10.0000i q^{79} +(7.00000 + 5.65685i) q^{81} +(8.48528 - 8.48528i) q^{83} +(-4.00000 - 2.00000i) q^{85} +(-4.82843 - 0.828427i) q^{87} +9.89949 q^{89} -18.0000 q^{91} +(6.82843 + 1.17157i) q^{93} +(-2.82843 - 8.48528i) q^{95} +(12.0000 - 12.0000i) q^{97} +(-2.82843 + 8.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 12 q^{7}+O(q^{10}) \) 4 * q - 4 * q^3 + 12 * q^7	\( 4 q - 4 q^{3} + 12 q^{7} - 12 q^{13} + 4 q^{15} - 24 q^{21} + 16 q^{25} - 4 q^{27} - 16 q^{31} - 8 q^{33} + 16 q^{37} + 20 q^{43} - 24 q^{45} - 8 q^{51} - 8 q^{55} + 16 q^{57} + 8 q^{61} + 12 q^{63} + 28 q^{67} + 4 q^{73} - 28 q^{75} + 28 q^{81} - 16 q^{85} - 8 q^{87} - 72 q^{91} + 16 q^{93} + 48 q^{97}+O(q^{100}) \) 4 * q - 4 * q^3 + 12 * q^7 - 12 * q^13 + 4 * q^15 - 24 * q^21 + 16 * q^25 - 4 * q^27 - 16 * q^31 - 8 * q^33 + 16 * q^37 + 20 * q^43 - 24 * q^45 - 8 * q^51 - 8 * q^55 + 16 * q^57 + 8 * q^61 + 12 * q^63 + 28 * q^67 + 4 * q^73 - 28 * q^75 + 28 * q^81 - 16 * q^85 - 8 * q^87 - 72 * q^91 + 16 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more