LMFDB - Embedded newform 1380.2.r.b.1013.2

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			1013.2
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1380.1013
Dual form			1380.2.r.b.737.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.292893 - 1.70711i) q^{3} +(2.12132 - 0.707107i) q^{5} +(3.00000 - 3.00000i) q^{7} +(-2.82843 + 1.00000i) q^{9} +O(q^{10})$	\(q+(-0.292893 - 1.70711i) q^{3} +(2.12132 - 0.707107i) q^{5} +(3.00000 - 3.00000i) q^{7} +(-2.82843 + 1.00000i) q^{9} -2.82843i q^{11} +(-3.00000 - 3.00000i) q^{13} +(-1.82843 - 3.41421i) q^{15} +(-1.41421 - 1.41421i) q^{17} +4.00000i q^{19} +(-6.00000 - 4.24264i) q^{21} +(-0.707107 + 0.707107i) q^{23} +(4.00000 - 3.00000i) q^{25} +(2.53553 + 4.53553i) q^{27} -2.82843 q^{29} -4.00000 q^{31} +(-4.82843 + 0.828427i) q^{33} +(4.24264 - 8.48528i) q^{35} +(4.00000 - 4.00000i) q^{37} +(-4.24264 + 6.00000i) q^{39} +2.82843i q^{41} +(5.00000 + 5.00000i) q^{43} +(-5.29289 + 4.12132i) q^{45} +(5.65685 + 5.65685i) q^{47} -11.0000i q^{49} +(-2.00000 + 2.82843i) q^{51} +(-2.00000 - 6.00000i) q^{55} +(6.82843 - 1.17157i) q^{57} +1.41421 q^{59} +2.00000 q^{61} +(-5.48528 + 11.4853i) q^{63} +(-8.48528 - 4.24264i) q^{65} +(7.00000 - 7.00000i) q^{67} +(1.41421 + 1.00000i) q^{69} +15.5563i q^{71} +(1.00000 + 1.00000i) q^{73} +(-6.29289 - 5.94975i) q^{75} +(-8.48528 - 8.48528i) q^{77} -10.0000i q^{79} +(7.00000 - 5.65685i) q^{81} +(-8.48528 + 8.48528i) q^{83} +(-4.00000 - 2.00000i) q^{85} +(0.828427 + 4.82843i) q^{87} -9.89949 q^{89} -18.0000 q^{91} +(1.17157 + 6.82843i) q^{93} +(2.82843 + 8.48528i) q^{95} +(12.0000 - 12.0000i) q^{97} +(2.82843 + 8.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.292893	−	1.70711i	−0.169102	−	0.985599i
$3$	−0.292893	−	1.70711i	−0.169102	−	0.985599i
$4$		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	$-0.859781\pi$
$11$		−	2.82843i		−	0.852803i	0.904534	−	0.426401i	$-0.140219\pi$
$12$		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
$15$	−1.82843	−	3.41421i	−0.472098	−	0.881546i
$16$		0			0
$17$	−1.41421	−	1.41421i	−0.342997	−	0.342997i	0.514496	−	0.857493i	$-0.327979\pi$
$17$	−1.41421	−	1.41421i	−0.342997	−	0.342997i	−0.857493	+	0.514496i	$0.827979\pi$
$18$		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
$27$	2.53553	+	4.53553i	0.487964	+	0.872864i
$28$		0			0
$29$	−2.82843			−0.525226			−0.262613	−	0.964901i	$-0.584584\pi$
$29$	−2.82843			−0.525226			−0.262613	+	0.964901i	$0.584584\pi$
$30$		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
$33$	−4.82843	+	0.828427i	−0.840521	+	0.144211i
$34$		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	$0.0708874\pi$
$41$			2.82843i			0.441726i	−0.975305	+	0.220863i	$0.929113\pi$
$42$		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
$45$	−5.29289	+	4.12132i	−0.789018	+	0.614370i
$46$		0			0
$47$	5.65685	+	5.65685i	0.825137	+	0.825137i	0.986840	−	0.161703i	$-0.0516985\pi$
$47$	5.65685	+	5.65685i	0.825137	+	0.825137i	−0.161703	+	0.986840i	$0.551699\pi$
$48$		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
$57$	6.82843	−	1.17157i	0.904447	−	0.155179i
$58$		0			0
$59$	1.41421			0.184115			0.0920575	−	0.995754i	$-0.470656\pi$
$59$	1.41421			0.184115			0.0920575	+	0.995754i	$0.470656\pi$
$60$		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
$63$	−5.48528	+	11.4853i	−0.691080	+	1.44701i
$64$		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	$0.374353\pi$
$71$			15.5563i			1.84620i	−0.384561	+	0.923099i	$0.625647\pi$
$72$		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
$75$	−6.29289	−	5.94975i	−0.726641	−	0.687018i
$76$		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	−0.997792	−	0.0664117i	$-0.978845\pi$
$83$	−8.48528	+	8.48528i	−0.931381	+	0.931381i	0.0664117	+	0.997792i	$0.478845\pi$
$84$		0			0
$85$	−4.00000	−	2.00000i	−0.433861	−	0.216930i
$86$		0			0
$87$	0.828427	+	4.82843i	0.0888167	+	0.517662i
$88$		0			0
$89$	−9.89949			−1.04934			−0.524672	−	0.851304i	$-0.675812\pi$
$89$	−9.89949			−1.04934			−0.524672	+	0.851304i	$0.675812\pi$
$90$		0			0
$91$	−18.0000			−1.88691
$92$		0			0
$93$	1.17157	+	6.82843i	0.121486	+	0.708075i
$94$		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	$0.138727\pi$
$101$			8.48528i			0.844317i	−0.906522	+	0.422159i	$0.861273\pi$
$102$		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
$105$	−15.7279	−	4.75736i	−1.53489	−	0.464271i
$106$		0			0
$107$	−2.82843	−	2.82843i	−0.273434	−	0.273434i	0.557047	−	0.830481i	$-0.311934\pi$
$107$	−2.82843	−	2.82843i	−0.273434	−	0.273434i	−0.830481	+	0.557047i	$0.811934\pi$
$108$		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	−0.770490	−	0.637452i	$-0.779988\pi$
$113$	−1.41421	+	1.41421i	−0.133038	+	0.133038i	0.637452	+	0.770490i	$0.279988\pi$
$114$		0			0
$115$	−1.00000	+	2.00000i	−0.0932505	+	0.186501i
$116$		0			0
$117$	11.4853	+	5.48528i	1.06181	+	0.507114i
$118$		0			0
$119$	−8.48528			−0.777844
$120$		0			0
$121$	3.00000			0.272727
$122$		0			0
$123$	4.82843	−	0.828427i	0.435365	−	0.0746968i
$124$		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	$-0.812327\pi$
$131$		−	12.7279i		−	1.11204i	0.831168	−	0.556022i	$-0.187673\pi$
$132$		0			0
$133$	12.0000	+	12.0000i	1.04053	+	1.04053i
$134$		0			0
$135$	8.58579	+	7.82843i	0.738947	+	0.673764i
$136$		0			0
$137$	−11.3137	−	11.3137i	−0.966595	−	0.966595i	0.0328645	−	0.999460i	$-0.489537\pi$
$137$	−11.3137	−	11.3137i	−0.966595	−	0.966595i	−0.999460	+	0.0328645i	$0.989537\pi$
$138$		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
$147$	−18.7782	+	3.22183i	−1.54880	+	0.265732i
$148$		0			0
$149$	7.07107			0.579284			0.289642	−	0.957135i	$-0.406464\pi$
$149$	7.07107			0.579284			0.289642	+	0.957135i	$0.406464\pi$
$150$		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
$153$	5.41421	+	2.58579i	0.437713	+	0.209048i
$154$		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
$165$	−9.65685	+	5.17157i	−0.751785	+	0.402606i
$166$		0			0
$167$	16.9706	+	16.9706i	1.31322	+	1.31322i	0.919027	+	0.394195i	$0.128976\pi$
$167$	16.9706	+	16.9706i	1.31322	+	1.31322i	0.394195	+	0.919027i	$0.371024\pi$
$168$		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	−0.222327	−	0.974972i	$-0.571365\pi$
$173$	9.89949	−	9.89949i	0.752645	−	0.752645i	0.974972	+	0.222327i	$0.0713654\pi$
$174$		0			0
$175$	3.00000	−	21.0000i	0.226779	−	1.58745i
$176$		0			0
$177$	−0.414214	−	2.41421i	−0.0311342	−	0.181463i
$178$		0			0
$179$	18.3848			1.37414			0.687071	−	0.726590i	$-0.258896\pi$
$179$	18.3848			1.37414			0.687071	+	0.726590i	$0.258896\pi$
$180$		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
$183$	−0.585786	−	3.41421i	−0.0433026	−	0.252386i
$184$		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	$-0.745833\pi$
$191$		−	19.7990i		−	1.43260i	0.697790	−	0.716302i	$-0.254167\pi$
$192$		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
$195$	−4.75736	+	15.7279i	−0.340682	+	1.12630i
$196$		0			0
$197$	7.07107	+	7.07107i	0.503793	+	0.503793i	0.912614	−	0.408822i	$-0.134060\pi$
$197$	7.07107	+	7.07107i	0.503793	+	0.503793i	−0.408822	+	0.912614i	$0.634060\pi$
$198$		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
$207$	1.29289	−	2.70711i	0.0898623	−	0.188157i
$208$		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
$213$	26.5563	−	4.55635i	1.81961	−	0.312196i
$214$		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
$225$	−8.31371	+	12.4853i	−0.554247	+	0.832352i
$226$		0			0
$227$	16.9706	+	16.9706i	1.12638	+	1.12638i	0.990762	+	0.135614i	$0.0433007\pi$
$227$	16.9706	+	16.9706i	1.12638	+	1.12638i	0.135614	+	0.990762i	$0.456699\pi$
$228$		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	$0.690675\pi$
$233$	−21.2132	+	21.2132i	−1.38972	+	1.38972i	−0.825886	+	0.563837i	$0.809325\pi$
$234$		0			0
$235$	16.0000	+	8.00000i	1.04372	+	0.521862i
$236$		0			0
$237$	−17.0711	+	2.92893i	−1.10889	+	0.190255i
$238$		0			0
$239$	9.89949			0.640345			0.320173	−	0.947359i	$-0.396259\pi$
$239$	9.89949			0.640345			0.320173	+	0.947359i	$0.396259\pi$
$240$		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
$243$	−11.7071	−	10.2929i	−0.751011	−	0.660289i
$244$		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	$-0.971548\pi$
$251$		−	2.82843i		−	0.178529i	0.996008	−	0.0892644i	$-0.0284516\pi$
$252$		0			0
$253$	2.00000	+	2.00000i	0.125739	+	0.125739i
$254$		0			0
$255$	−2.24264	+	7.41421i	−0.140440	+	0.464296i
$256$		0			0
$257$	−7.07107	−	7.07107i	−0.441081	−	0.441081i	0.451294	−	0.892375i	$-0.350963\pi$
$257$	−7.07107	−	7.07107i	−0.441081	−	0.441081i	−0.892375	+	0.451294i	$0.850963\pi$
$258$		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	−0.963899	−	0.266266i	$-0.914210\pi$
$263$	−11.3137	+	11.3137i	−0.697633	+	0.697633i	0.266266	+	0.963899i	$0.414210\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	2.89949	+	16.8995i	0.177446	+	1.03423i
$268$		0			0
$269$	−16.9706			−1.03471			−0.517357	−	0.855770i	$-0.673084\pi$
$269$	−16.9706			−1.03471			−0.517357	+	0.855770i	$0.673084\pi$
$270$		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
$273$	5.27208	+	30.7279i	0.319081	+	1.85974i
$274$		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	$-0.704053\pi$
$281$		−	26.8701i		−	1.60293i	0.598040	−	0.801467i	$-0.295947\pi$
$282$		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
$285$	13.6569	−	7.31371i	0.808962	−	0.433227i
$286$		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	−0.414386	−	0.910101i	$-0.636004\pi$
$293$	8.48528	−	8.48528i	0.495715	−	0.495715i	0.910101	+	0.414386i	$0.136004\pi$
$294$		0			0
$295$	3.00000	−	1.00000i	0.174667	−	0.0582223i
$296$		0			0
$297$	12.8284	−	7.17157i	0.744381	−	0.416137i
$298$		0			0
$299$	4.24264			0.245358
$300$		0			0
$301$	30.0000			1.72917
$302$		0			0
$303$	14.4853	−	2.48528i	0.832158	−	0.142776i
$304$		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	$-0.854603\pi$
$311$		−	15.5563i		−	0.882120i	0.897478	−	0.441060i	$-0.145397\pi$
$312$		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
$315$	−3.51472	+	28.2426i	−0.198032	+	1.59129i
$316$		0			0
$317$	−4.24264	−	4.24264i	−0.238290	−	0.238290i	0.577851	−	0.816142i	$-0.303891\pi$
$317$	−4.24264	−	4.24264i	−0.238290	−	0.238290i	−0.816142	+	0.577851i	$0.803891\pi$
$318$		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
$327$	−10.2426	+	1.75736i	−0.566419	+	0.0971822i
$328$		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
$333$	−7.31371	+	15.3137i	−0.400789	+	0.839186i
$334$		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
$345$	3.70711	+	1.12132i	0.199584	+	0.0603699i
$346$		0			0
$347$	8.48528	+	8.48528i	0.455514	+	0.455514i	0.897180	−	0.441666i	$-0.145612\pi$
$347$	8.48528	+	8.48528i	0.455514	+	0.455514i	−0.441666	+	0.897180i	$0.645612\pi$
$348$		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	−0.810941	−	0.585128i	$-0.801044\pi$
$353$	−4.24264	+	4.24264i	−0.225813	+	0.225813i	0.585128	+	0.810941i	$0.301044\pi$
$354$		0			0
$355$	11.0000	+	33.0000i	0.583819	+	1.75146i
$356$		0			0
$357$	2.48528	+	14.4853i	0.131535	+	0.766642i
$358$		0			0
$359$	−5.65685			−0.298557			−0.149279	−	0.988795i	$-0.547695\pi$
$359$	−5.65685			−0.298557			−0.149279	+	0.988795i	$0.547695\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$		0			0
$363$	−0.878680	−	5.12132i	−0.0461187	−	0.268800i
$364$		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
$375$	−17.5563	−	8.17157i	−0.906606	−	0.421978i
$376$		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	−0.992157	−	0.125001i	$-0.960106\pi$
$383$	−16.9706	+	16.9706i	−0.867155	+	0.867155i	0.125001	+	0.992157i	$0.460106\pi$
$384$		0			0
$385$	−24.0000	−	12.0000i	−1.22315	−	0.611577i
$386$		0			0
$387$	−19.1421	−	9.14214i	−0.973049	−	0.464721i
$388$		0			0
$389$	15.5563			0.788738			0.394369	−	0.918952i	$-0.370963\pi$
$389$	15.5563			0.788738			0.394369	+	0.918952i	$0.370963\pi$
$390$		0			0
$391$	2.00000			0.101144
$392$		0			0
$393$	−21.7279	+	3.72792i	−1.09603	+	0.188049i
$394$		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	$0.126980\pi$
$401$			15.5563i			0.776847i	−0.921481	+	0.388424i	$0.873020\pi$
$402$		0			0
$403$	12.0000	+	12.0000i	0.597763	+	0.597763i
$404$		0			0
$405$	10.8492	−	16.9497i	0.539103	−	0.842240i
$406$		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
$417$	−20.4853	+	3.51472i	−1.00317	+	0.172117i
$418$		0			0
$419$	28.2843			1.38178			0.690889	−	0.722961i	$-0.257220\pi$
$419$	28.2843			1.38178			0.690889	+	0.722961i	$0.257220\pi$
$420$		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
$423$	−21.6569	−	10.3431i	−1.05299	−	0.502901i
$424$		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	$-0.956498\pi$
$431$		−	5.65685i		−	0.272481i	0.990676	−	0.136241i	$-0.0435020\pi$
$432$		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
$435$	5.17157	+	9.65685i	0.247958	+	0.463011i
$436$		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	−0.636716	−	0.771099i	$-0.719708\pi$
$443$	2.82843	−	2.82843i	0.134383	−	0.134383i	0.771099	+	0.636716i	$0.219708\pi$
$444$		0			0
$445$	−21.0000	+	7.00000i	−0.995495	+	0.331832i
$446$		0			0
$447$	−2.07107	−	12.0711i	−0.0979581	−	0.570942i
$448$		0			0
$449$	−5.65685			−0.266963			−0.133482	−	0.991051i	$-0.542616\pi$
$449$	−5.65685			−0.266963			−0.133482	+	0.991051i	$0.542616\pi$
$450$		0			0
$451$	8.00000			0.376705
$452$		0			0
$453$	3.51472	+	20.4853i	0.165136	+	0.962482i
$454$		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	$0.228879\pi$
$461$			28.2843i			1.31733i	−0.752436	+	0.658665i	$0.771121\pi$
$462$		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
$465$	7.31371	+	13.6569i	0.339165	+	0.633321i
$466$		0			0
$467$	28.2843	+	28.2843i	1.30884	+	1.30884i	0.922253	+	0.386587i	$0.126346\pi$
$467$	28.2843	+	28.2843i	1.30884	+	1.30884i	0.386587	+	0.922253i	$0.373654\pi$
$468$		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	$-0.817458\pi$
$479$	−36.7696			−1.68004			−0.840022	+	0.542553i	$0.817458\pi$
$480$		0			0
$481$	−24.0000			−1.09431
$482$		0			0
$483$	7.24264	−	1.24264i	0.329552	−	0.0565421i
$484$		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	$0.262330\pi$
$491$			32.5269i			1.46792i	−0.679193	+	0.733959i	$0.737670\pi$
$492$		0			0
$493$	4.00000	+	4.00000i	0.180151	+	0.180151i
$494$		0			0
$495$	11.6569	+	14.9706i	0.523937	+	0.672877i
$496$		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	$-0.399474\pi$
$503$	28.2843	−	28.2843i	1.26113	−	1.26113i	0.950544	−	0.310589i	$-0.100526\pi$
$504$		0			0
$505$	6.00000	+	18.0000i	0.266996	+	0.800989i
$506$		0			0
$507$	8.53553	−	1.46447i	0.379076	−	0.0650392i
$508$		0			0
$509$	−42.4264			−1.88052			−0.940259	−	0.340461i	$-0.889417\pi$
$509$	−42.4264			−1.88052			−0.940259	+	0.340461i	$0.889417\pi$
$510$		0			0
$511$	6.00000			0.265424
$512$		0			0
$513$	−18.1421	+	10.1421i	−0.800995	+	0.447786i
$514$		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	$0.00986247\pi$
$521$			1.41421i			0.0619578i	−0.999520	+	0.0309789i	$0.990138\pi$
$522$		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
$525$	−36.7279	+	1.02944i	−1.60294	+	0.0449283i
$526$		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
$537$	−5.38478	−	31.3848i	−0.232370	−	1.35435i
$538$		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
$543$	−1.75736	−	10.2426i	−0.0754155	−	0.439554i
$544$		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
$555$	−20.9706	−	6.34315i	−0.890151	−	0.269252i
$556$		0			0
$557$	−12.7279	−	12.7279i	−0.539299	−	0.539299i	0.384024	−	0.923323i	$-0.374538\pi$
$557$	−12.7279	−	12.7279i	−0.539299	−	0.539299i	−0.923323	+	0.384024i	$0.874538\pi$
$558$		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	$-0.372217\pi$
$563$	31.1127	−	31.1127i	1.31124	−	1.31124i	0.920499	−	0.390745i	$-0.127783\pi$
$564$		0			0
$565$	−2.00000	+	4.00000i	−0.0841406	+	0.168281i
$566$		0			0
$567$	4.02944	−	37.9706i	0.169220	−	1.59461i
$568$		0			0
$569$	−1.41421			−0.0592869			−0.0296435	−	0.999561i	$-0.509437\pi$
$569$	−1.41421			−0.0592869			−0.0296435	+	0.999561i	$0.509437\pi$
$570$		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
$573$	−33.7990	+	5.79899i	−1.41197	+	0.242256i
$574$		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
$585$	28.2426	+	3.51472i	1.16769	+	0.145316i
$586$		0			0
$587$	15.5563	+	15.5563i	0.642079	+	0.642079i	0.951066	−	0.308987i	$-0.0999900\pi$
$587$	15.5563	+	15.5563i	0.642079	+	0.642079i	−0.308987	+	0.951066i	$0.599990\pi$
$588$		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	−0.474001	−	0.880524i	$-0.657191\pi$
$593$	9.89949	−	9.89949i	0.406524	−	0.406524i	0.880524	+	0.474001i	$0.157191\pi$
$594$		0			0
$595$	−18.0000	+	6.00000i	−0.737928	+	0.245976i
$596$		0			0
$597$	37.5563	−	6.44365i	1.53708	−	0.263721i
$598$		0			0
$599$	−35.3553			−1.44458			−0.722290	−	0.691590i	$-0.756910\pi$
$599$	−35.3553			−1.44458			−0.722290	+	0.691590i	$0.756910\pi$
$600$		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
$603$	−12.7990	+	26.7990i	−0.521215	+	1.09134i
$604$		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
$615$	9.65685	−	5.17157i	0.389402	−	0.208538i
$616$		0			0
$617$	8.48528	+	8.48528i	0.341605	+	0.341605i	0.856970	−	0.515366i	$-0.172344\pi$
$617$	8.48528	+	8.48528i	0.341605	+	0.341605i	−0.515366	+	0.856970i	$0.672344\pi$
$618$		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
$627$	−3.31371	−	19.3137i	−0.132337	−	0.771315i
$628$		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	$-0.777952\pi$
$641$		−	32.5269i		−	1.28474i	0.766396	−	0.642368i	$-0.222048\pi$
$642$		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
$645$	7.92893	−	26.2132i	0.312201	−	1.03214i
$646$		0			0
$647$	−16.9706	−	16.9706i	−0.667182	−	0.667182i	0.289881	−	0.957063i	$-0.406384\pi$
$647$	−16.9706	−	16.9706i	−0.667182	−	0.667182i	−0.957063	+	0.289881i	$0.906384\pi$
$648$		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	−0.412758	−	0.910841i	$-0.635435\pi$
$653$	12.7279	−	12.7279i	0.498082	−	0.498082i	0.910841	+	0.412758i	$0.135435\pi$
$654$		0			0
$655$	−9.00000	−	27.0000i	−0.351659	−	1.05498i
$656$		0			0
$657$	−3.82843	−	1.82843i	−0.149361	−	0.0713337i
$658$		0			0
$659$	−5.65685			−0.220360			−0.110180	−	0.993912i	$-0.535143\pi$
$659$	−5.65685			−0.220360			−0.110180	+	0.993912i	$0.535143\pi$
$660$		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
$663$	14.4853	−	2.48528i	0.562562	−	0.0965203i
$664$		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
$675$	23.7487	+	10.5355i	0.914089	+	0.405513i
$676$		0			0
$677$	2.82843	+	2.82843i	0.108705	+	0.108705i	0.759367	−	0.650662i	$-0.225509\pi$
$677$	2.82843	+	2.82843i	0.108705	+	0.108705i	−0.650662	+	0.759367i	$0.725509\pi$
$678$		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	−0.984889	−	0.173188i	$-0.944593\pi$
$683$	−21.2132	+	21.2132i	−0.811701	+	0.811701i	0.173188	+	0.984889i	$0.444593\pi$
$684$		0			0
$685$	−32.0000	−	16.0000i	−1.22266	−	0.611329i
$686$		0			0
$687$	−37.5563	+	6.44365i	−1.43286	+	0.245841i
$688$		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
$693$	32.4853	+	15.5147i	1.23401	+	0.589355i
$694$		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	$0.310475\pi$
$701$			43.8406i			1.65584i	−0.560848	+	0.827919i	$0.689525\pi$
$702$		0			0
$703$	16.0000	+	16.0000i	0.603451	+	0.603451i
$704$		0			0
$705$	8.97056	−	29.6569i	0.337851	−	1.11694i
$706$		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
$717$	−2.89949	−	16.8995i	−0.108284	−	0.631123i
$718$		0			0
$719$	9.89949			0.369189			0.184594	−	0.982815i	$-0.440903\pi$
$719$	9.89949			0.369189			0.184594	+	0.982815i	$0.440903\pi$
$720$		0			0
$721$	−78.0000			−2.90487
$722$		0			0
$723$	−1.75736	−	10.2426i	−0.0653569	−	0.380928i
$724$		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
$735$	−37.5563	+	20.1127i	−1.38529	+	0.741868i
$736$		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	−0.757083	−	0.653318i	$-0.773376\pi$
$743$	−2.82843	+	2.82843i	−0.103765	+	0.103765i	0.653318	+	0.757083i	$0.273376\pi$
$744$		0			0
$745$	15.0000	−	5.00000i	0.549557	−	0.183186i
$746$		0			0
$747$	15.5147	−	32.4853i	0.567654	−	1.18857i
$748$		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
$753$	−4.82843	+	0.828427i	−0.175958	+	0.0301896i
$754$		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	$-0.917488\pi$
$761$		−	14.1421i		−	0.512652i	0.966590	−	0.256326i	$-0.0825121\pi$
$762$		0			0
$763$	−18.0000	−	18.0000i	−0.651644	−	0.651644i
$764$		0			0
$765$	13.3137	+	1.65685i	0.481358	+	0.0599037i
$766$		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	−0.822743	−	0.568414i	$-0.807557\pi$
$773$	−7.07107	+	7.07107i	−0.254329	+	0.254329i	0.568414	+	0.822743i	$0.307557\pi$
$774$		0			0
$775$	−16.0000	+	12.0000i	−0.574737	+	0.431053i
$776$		0			0
$777$	−40.9706	+	7.02944i	−1.46981	+	0.252180i
$778$		0			0
$779$	−11.3137			−0.405356
$780$		0			0
$781$	44.0000			1.57444
$782$		0			0
$783$	−7.17157	−	12.8284i	−0.256291	−	0.458451i
$784$		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	0.540670	−	0.841235i	$-0.318171\pi$
$797$	−8.48528	−	8.48528i	−0.300564	−	0.300564i	−0.841235	+	0.540670i	$0.818171\pi$
$798$		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
$807$	4.97056	+	28.9706i	0.174972	+	1.01981i
$808$		0			0
$809$	−39.5980			−1.39219			−0.696095	−	0.717949i	$-0.745081\pi$
$809$	−39.5980			−1.39219			−0.696095	+	0.717949i	$0.745081\pi$
$810$		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
$813$	−3.51472	−	20.4853i	−0.123267	−	0.718450i
$814$		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	$-0.798229\pi$
$821$		−	33.9411i		−	1.18455i	0.805735	−	0.592277i	$-0.201771\pi$
$822$		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
$825$	−16.8284	+	17.7990i	−0.585891	+	0.619681i
$826$		0			0
$827$	−14.1421	−	14.1421i	−0.491770	−	0.491770i	0.417093	−	0.908864i	$-0.363049\pi$
$827$	−14.1421	−	14.1421i	−0.491770	−	0.491770i	−0.908864	+	0.417093i	$0.863049\pi$
$828$		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
$837$	−10.1421	−	18.1421i	−0.350563	−	0.627084i
$838$		0			0
$839$	42.4264			1.46472			0.732361	−	0.680916i	$-0.238418\pi$
$839$	42.4264			1.46472			0.732361	+	0.680916i	$0.238418\pi$
$840$		0			0
$841$	−21.0000			−0.724138
$842$		0			0
$843$	−45.8701	+	7.87006i	−1.57985	+	0.271059i
$844$		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
$855$	−16.4853	−	21.1716i	−0.563785	−	0.724053i
$856$		0			0
$857$	26.8701	+	26.8701i	0.917864	+	0.917864i	0.996874	−	0.0790101i	$-0.0251759\pi$
$857$	26.8701	+	26.8701i	0.917864	+	0.917864i	−0.0790101	+	0.996874i	$0.525176\pi$
$858$		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	−0.321190	−	0.947015i	$-0.604083\pi$
$863$	18.3848	−	18.3848i	0.625825	−	0.625825i	0.947015	+	0.321190i	$0.104083\pi$
$864$		0			0
$865$	14.0000	−	28.0000i	0.476014	−	0.952029i
$866$		0			0
$867$	−22.1924	+	3.80761i	−0.753693	+	0.129313i
$868$		0			0
$869$	−28.2843			−0.959478
$870$		0			0
$871$	−42.0000			−1.42312
$872$		0			0
$873$	−21.9411	+	45.9411i	−0.742595	+	1.55487i
$874$		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	$0.242771\pi$
$881$			41.0122i			1.38174i	−0.722981	+	0.690868i	$0.757229\pi$
$882$		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
$885$	−2.58579	−	4.82843i	−0.0869203	−	0.162306i
$886$		0			0
$887$	12.7279	+	12.7279i	0.427362	+	0.427362i	0.887729	−	0.460367i	$-0.152282\pi$
$887$	12.7279	+	12.7279i	0.427362	+	0.427362i	−0.460367	+	0.887729i	$0.652282\pi$
$888$		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
$897$	−1.24264	−	7.24264i	−0.0414906	−	0.241825i
$898$		0			0
$899$	11.3137			0.377333
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−8.78680	−	51.2132i	−0.292406	−	1.70427i
$904$		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	$-0.751922\pi$
$911$		−	42.4264i		−	1.40565i	0.711363	−	0.702825i	$-0.248078\pi$
$912$		0			0
$913$	24.0000	+	24.0000i	0.794284	+	0.794284i
$914$		0			0
$915$	−3.65685	−	6.82843i	−0.120892	−	0.225741i
$916$		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
$927$	49.7696	+	23.7696i	1.63465	+	0.780695i
$928$		0			0
$929$	−22.6274			−0.742381			−0.371191	−	0.928557i	$-0.621050\pi$
$929$	−22.6274			−0.742381			−0.371191	+	0.928557i	$0.621050\pi$
$930$		0			0
$931$	44.0000			1.44204
$932$		0			0
$933$	−26.5563	+	4.55635i	−0.869416	+	0.149168i
$934$		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	$-0.918398\pi$
$941$		−	15.5563i		−	0.507122i	0.967319	−	0.253561i	$-0.0816019\pi$
$942$		0			0
$943$	−2.00000	−	2.00000i	−0.0651290	−	0.0651290i
$944$		0			0
$945$	49.2426	−	2.27208i	1.60186	−	0.0739107i
$946$		0			0
$947$	29.6985	+	29.6985i	0.965071	+	0.965071i	0.999410	−	0.0343392i	$-0.0109326\pi$
$947$	29.6985	+	29.6985i	0.965071	+	0.965071i	−0.0343392	+	0.999410i	$0.510933\pi$
$948$		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	−0.849026	−	0.528350i	$-0.822811\pi$
$953$	−9.89949	+	9.89949i	−0.320676	+	0.320676i	0.528350	+	0.849026i	$0.322811\pi$
$954$		0			0
$955$	−14.0000	−	42.0000i	−0.453029	−	1.35909i
$956$		0			0
$957$	13.6569	−	2.34315i	0.441463	−	0.0757431i
$958$		0			0
$959$	−67.8823			−2.19203
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	10.8284	+	5.17157i	0.348941	+	0.166652i
$964$		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	$0.102907\pi$
$971$			19.7990i			0.635380i	−0.948195	+	0.317690i	$0.897093\pi$
$972$		0			0
$973$	−36.0000	−	36.0000i	−1.15411	−	1.15411i
$974$		0			0
$975$	1.02944	+	36.7279i	0.0329684	+	1.17623i
$976$		0			0
$977$	−38.1838	−	38.1838i	−1.22161	−	1.22161i	−0.967061	−	0.254546i	$-0.918074\pi$
$977$	−38.1838	−	38.1838i	−1.22161	−	1.22161i	−0.254546	−	0.967061i	$-0.581926\pi$
$978$		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	−0.948442	−	0.316952i	$-0.897341\pi$
$983$	−19.7990	+	19.7990i	−0.631490	+	0.631490i	0.316952	+	0.948442i	$0.397341\pi$
$984$		0			0
$985$	20.0000	+	10.0000i	0.637253	+	0.318626i
$986$		0			0
$987$	−9.94113	−	57.9411i	−0.316430	−	1.84429i
$988$		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
$993$	4.68629	+	27.3137i	0.148715	+	0.866774i
$994$		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.1013.2	yes	4
3.2	odd	2	inner	1380.2.r.b.1013.1	yes	4
5.2	odd	4	inner	1380.2.r.b.737.1	✓	4
15.2	even	4	inner	1380.2.r.b.737.2	yes	4

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

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)

\(f(q)\)	\(=\)	\(q+(-0.292893 - 1.70711i) q^{3} +(2.12132 - 0.707107i) q^{5} +(3.00000 - 3.00000i) q^{7} +(-2.82843 + 1.00000i) q^{9} +O(q^{10})\)	\(q+(-0.292893 - 1.70711i) q^{3} +(2.12132 - 0.707107i) q^{5} +(3.00000 - 3.00000i) q^{7} +(-2.82843 + 1.00000i) q^{9} -2.82843i q^{11} +(-3.00000 - 3.00000i) q^{13} +(-1.82843 - 3.41421i) q^{15} +(-1.41421 - 1.41421i) q^{17} +4.00000i q^{19} +(-6.00000 - 4.24264i) q^{21} +(-0.707107 + 0.707107i) q^{23} +(4.00000 - 3.00000i) q^{25} +(2.53553 + 4.53553i) q^{27} -2.82843 q^{29} -4.00000 q^{31} +(-4.82843 + 0.828427i) q^{33} +(4.24264 - 8.48528i) q^{35} +(4.00000 - 4.00000i) q^{37} +(-4.24264 + 6.00000i) q^{39} +2.82843i q^{41} +(5.00000 + 5.00000i) q^{43} +(-5.29289 + 4.12132i) q^{45} +(5.65685 + 5.65685i) q^{47} -11.0000i q^{49} +(-2.00000 + 2.82843i) q^{51} +(-2.00000 - 6.00000i) q^{55} +(6.82843 - 1.17157i) q^{57} +1.41421 q^{59} +2.00000 q^{61} +(-5.48528 + 11.4853i) q^{63} +(-8.48528 - 4.24264i) q^{65} +(7.00000 - 7.00000i) q^{67} +(1.41421 + 1.00000i) q^{69} +15.5563i q^{71} +(1.00000 + 1.00000i) q^{73} +(-6.29289 - 5.94975i) q^{75} +(-8.48528 - 8.48528i) q^{77} -10.0000i q^{79} +(7.00000 - 5.65685i) q^{81} +(-8.48528 + 8.48528i) q^{83} +(-4.00000 - 2.00000i) q^{85} +(0.828427 + 4.82843i) q^{87} -9.89949 q^{89} -18.0000 q^{91} +(1.17157 + 6.82843i) q^{93} +(2.82843 + 8.48528i) q^{95} +(12.0000 - 12.0000i) q^{97} +(2.82843 + 8.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 12 q^{7}+O(q^{10}) \) 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

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Representations

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Database

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