LMFDB - Embedded newform 1078.2.e.u.177.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(67,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("1078.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.e (of order $3$, degree $2$, not 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:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1078.177
Dual form			1078.2.e.u.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.41421 + 2.44949i) q^{5} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.41421 + 2.44949i) q^{5} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(1.41421 + 2.44949i) q^{10} +(-0.500000 - 0.866025i) q^{11} -5.65685 q^{13} +(-0.500000 + 0.866025i) q^{16} +(1.41421 + 2.44949i) q^{17} +(-1.50000 - 2.59808i) q^{18} +(4.24264 - 7.34847i) q^{19} +2.82843 q^{20} -1.00000 q^{22} +(4.00000 - 6.92820i) q^{23} +(-1.50000 - 2.59808i) q^{25} +(-2.82843 + 4.89898i) q^{26} -6.00000 q^{29} +(-4.24264 - 7.34847i) q^{31} +(0.500000 + 0.866025i) q^{32} +2.82843 q^{34} -3.00000 q^{36} +(3.00000 - 5.19615i) q^{37} +(-4.24264 - 7.34847i) q^{38} +(1.41421 - 2.44949i) q^{40} +8.48528 q^{41} -4.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(4.24264 + 7.34847i) q^{45} +(-4.00000 - 6.92820i) q^{46} +(-1.41421 + 2.44949i) q^{47} -3.00000 q^{50} +(2.82843 + 4.89898i) q^{52} +(-3.00000 - 5.19615i) q^{53} +2.82843 q^{55} +(-3.00000 + 5.19615i) q^{58} +(-2.82843 - 4.89898i) q^{59} +(-2.82843 + 4.89898i) q^{61} -8.48528 q^{62} +1.00000 q^{64} +(8.00000 - 13.8564i) q^{65} +(2.00000 + 3.46410i) q^{67} +(1.41421 - 2.44949i) q^{68} +(-1.50000 + 2.59808i) q^{72} +(-4.24264 - 7.34847i) q^{73} +(-3.00000 - 5.19615i) q^{74} -8.48528 q^{76} +(-1.41421 - 2.44949i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(4.24264 - 7.34847i) q^{82} +2.82843 q^{83} -8.00000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(0.500000 + 0.866025i) q^{88} +(5.65685 - 9.79796i) q^{89} +8.48528 q^{90} -8.00000 q^{92} +(1.41421 + 2.44949i) q^{94} +(12.0000 + 20.7846i) q^{95} -11.3137 q^{97} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 + 6 * q^9	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 6 q^{9} - 2 q^{11} - 2 q^{16} - 6 q^{18} - 4 q^{22} + 16 q^{23} - 6 q^{25} - 24 q^{29} + 2 q^{32} - 12 q^{36} + 12 q^{37} - 16 q^{43} - 2 q^{44} - 16 q^{46} - 12 q^{50} - 12 q^{53} - 12 q^{58} + 4 q^{64} + 32 q^{65} + 8 q^{67} - 6 q^{72} - 12 q^{74} - 18 q^{81} - 32 q^{85} - 8 q^{86} + 2 q^{88} - 32 q^{92} + 48 q^{95} - 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 + 6 * q^9 - 2 * q^11 - 2 * q^16 - 6 * q^18 - 4 * q^22 + 16 * q^23 - 6 * q^25 - 24 * q^29 + 2 * q^32 - 12 * q^36 + 12 * q^37 - 16 * q^43 - 2 * q^44 - 16 * q^46 - 12 * q^50 - 12 * q^53 - 12 * q^58 + 4 * q^64 + 32 * q^65 + 8 * q^67 - 6 * q^72 - 12 * q^74 - 18 * q^81 - 32 * q^85 - 8 * q^86 + 2 * q^88 - 32 * q^92 + 48 * q^95 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$3$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.41421	+	2.44949i	−0.632456	+	1.09545i	0.354593	+	0.935021i	$0.384620\pi$
$5$	−1.41421	+	2.44949i	−0.632456	+	1.09545i	−0.987048	+	0.160424i	$0.948714\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	1.41421	+	2.44949i	0.447214	+	0.774597i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	−5.65685			−1.56893			−0.784465	−	0.620174i	$-0.787062\pi$
$13$	−5.65685			−1.56893			−0.784465	+	0.620174i	$0.787062\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.41421	+	2.44949i	0.342997	+	0.594089i	0.984988	−	0.172624i	$-0.0552245\pi$
$17$	1.41421	+	2.44949i	0.342997	+	0.594089i	−0.641991	+	0.766712i	$0.721891\pi$
$18$	−1.50000	−	2.59808i	−0.353553	−	0.612372i
$19$	4.24264	−	7.34847i	0.973329	−	1.68585i	0.287984	−	0.957635i	$-0.407015\pi$
$19$	4.24264	−	7.34847i	0.973329	−	1.68585i	0.685344	−	0.728219i	$-0.259652\pi$
$20$	2.82843			0.632456
$21$		0			0
$22$	−1.00000			−0.213201
$23$	4.00000	−	6.92820i	0.834058	−	1.44463i	−0.0607377	−	0.998154i	$-0.519345\pi$
$23$	4.00000	−	6.92820i	0.834058	−	1.44463i	0.894795	−	0.446476i	$-0.147321\pi$
$24$		0			0
$25$	−1.50000	−	2.59808i	−0.300000	−	0.519615i
$26$	−2.82843	+	4.89898i	−0.554700	+	0.960769i
$27$		0			0
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	−4.24264	−	7.34847i	−0.762001	−	1.31982i	−0.941818	−	0.336124i	$-0.890884\pi$
$31$	−4.24264	−	7.34847i	−0.762001	−	1.31982i	0.179817	−	0.983700i	$-0.442449\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	2.82843			0.485071
$35$		0			0
$36$	−3.00000			−0.500000
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	−0.506772	−	0.862080i	$-0.669162\pi$
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	0.999969	+	0.00783774i	$0.00249486\pi$
$38$	−4.24264	−	7.34847i	−0.688247	−	1.19208i
$39$		0			0
$40$	1.41421	−	2.44949i	0.223607	−	0.387298i
$41$	8.48528			1.32518			0.662589	−	0.748983i	$-0.269458\pi$
$41$	8.48528			1.32518			0.662589	+	0.748983i	$0.269458\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$	4.24264	+	7.34847i	0.632456	+	1.09545i
$46$	−4.00000	−	6.92820i	−0.589768	−	1.02151i
$47$	−1.41421	+	2.44949i	−0.206284	+	0.357295i	−0.950541	−	0.310599i	$-0.899470\pi$
$47$	−1.41421	+	2.44949i	−0.206284	+	0.357295i	0.744257	+	0.667893i	$0.232804\pi$
$48$		0			0
$49$		0			0
$50$	−3.00000			−0.424264
$51$		0			0
$52$	2.82843	+	4.89898i	0.392232	+	0.679366i
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$		0			0
$55$	2.82843			0.381385
$56$		0			0
$57$		0			0
$58$	−3.00000	+	5.19615i	−0.393919	+	0.682288i
$59$	−2.82843	−	4.89898i	−0.368230	−	0.637793i	0.621059	−	0.783764i	$-0.286703\pi$
$59$	−2.82843	−	4.89898i	−0.368230	−	0.637793i	−0.989289	+	0.145971i	$0.953369\pi$
$60$		0			0
$61$	−2.82843	+	4.89898i	−0.362143	+	0.627250i	−0.988313	−	0.152436i	$-0.951288\pi$
$61$	−2.82843	+	4.89898i	−0.362143	+	0.627250i	0.626170	+	0.779686i	$0.284621\pi$
$62$	−8.48528			−1.07763
$63$		0			0
$64$	1.00000			0.125000
$65$	8.00000	−	13.8564i	0.992278	−	1.71868i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	1.41421	−	2.44949i	0.171499	−	0.297044i
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	−1.50000	+	2.59808i	−0.176777	+	0.306186i
$73$	−4.24264	−	7.34847i	−0.496564	−	0.860073i	0.503429	−	0.864037i	$-0.332072\pi$
$73$	−4.24264	−	7.34847i	−0.496564	−	0.860073i	−0.999992	+	0.00396356i	$0.998738\pi$
$74$	−3.00000	−	5.19615i	−0.348743	−	0.604040i
$75$		0			0
$76$	−8.48528			−0.973329
$77$		0			0
$78$		0			0
$79$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$79$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$80$	−1.41421	−	2.44949i	−0.158114	−	0.273861i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	4.24264	−	7.34847i	0.468521	−	0.811503i
$83$	2.82843			0.310460			0.155230	−	0.987878i	$-0.450388\pi$
$83$	2.82843			0.310460			0.155230	+	0.987878i	$0.450388\pi$
$84$		0			0
$85$	−8.00000			−0.867722
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$		0			0
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	5.65685	−	9.79796i	0.599625	−	1.03858i	−0.393251	−	0.919431i	$-0.628650\pi$
$89$	5.65685	−	9.79796i	0.599625	−	1.03858i	0.992876	−	0.119150i	$-0.0380171\pi$
$90$	8.48528			0.894427
$91$		0			0
$92$	−8.00000			−0.834058
$93$		0			0
$94$	1.41421	+	2.44949i	0.145865	+	0.252646i
$95$	12.0000	+	20.7846i	1.23117	+	2.13246i
$96$		0			0
$97$	−11.3137			−1.14873			−0.574367	−	0.818598i	$-0.694752\pi$
$97$	−11.3137			−1.14873			−0.574367	+	0.818598i	$0.694752\pi$
$98$		0			0
$99$	−3.00000			−0.301511
$100$	−1.50000	+	2.59808i	−0.150000	+	0.259808i
$101$	5.65685	+	9.79796i	0.562878	+	0.974933i	0.997244	+	0.0741967i	$0.0236393\pi$
$101$	5.65685	+	9.79796i	0.562878	+	0.974933i	−0.434366	+	0.900737i	$0.643027\pi$
$102$		0			0
$103$	−7.07107	+	12.2474i	−0.696733	+	1.20678i	0.272860	+	0.962054i	$0.412030\pi$
$103$	−7.07107	+	12.2474i	−0.696733	+	1.20678i	−0.969593	+	0.244723i	$0.921303\pi$
$104$	5.65685			0.554700
$105$		0			0
$106$	−6.00000			−0.582772
$107$	−2.00000	+	3.46410i	−0.193347	+	0.334887i	−0.946357	−	0.323122i	$-0.895268\pi$
$107$	−2.00000	+	3.46410i	−0.193347	+	0.334887i	0.753010	+	0.658009i	$0.228601\pi$
$108$		0			0
$109$	7.00000	+	12.1244i	0.670478	+	1.16130i	0.977769	+	0.209687i	$0.0672444\pi$
$109$	7.00000	+	12.1244i	0.670478	+	1.16130i	−0.307290	+	0.951616i	$0.599422\pi$
$110$	1.41421	−	2.44949i	0.134840	−	0.233550i
$111$		0			0
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$	11.3137	+	19.5959i	1.05501	+	1.82733i
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$	−8.48528	+	14.6969i	−0.784465	+	1.35873i
$118$	−5.65685			−0.520756
$119$		0			0
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	2.82843	+	4.89898i	0.256074	+	0.443533i
$123$		0			0
$124$	−4.24264	+	7.34847i	−0.381000	+	0.659912i
$125$	−5.65685			−0.505964
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−8.00000	−	13.8564i	−0.701646	−	1.21529i
$131$	1.41421	−	2.44949i	0.123560	−	0.214013i	−0.797609	−	0.603175i	$-0.793902\pi$
$131$	1.41421	−	2.44949i	0.123560	−	0.214013i	0.921169	+	0.389162i	$0.127235\pi$
$132$		0			0
$133$		0			0
$134$	4.00000			0.345547
$135$		0			0
$136$	−1.41421	−	2.44949i	−0.121268	−	0.210042i
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	0.938148	+	0.346235i	$0.112540\pi$
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	−0.169226	+	0.985577i	$0.554127\pi$
$138$		0			0
$139$	8.48528			0.719712			0.359856	−	0.933008i	$-0.382826\pi$
$139$	8.48528			0.719712			0.359856	+	0.933008i	$0.382826\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.82843	+	4.89898i	0.236525	+	0.409673i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	8.48528	−	14.6969i	0.704664	−	1.22051i
$146$	−8.48528			−0.702247
$147$		0			0
$148$	−6.00000			−0.493197
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$		0			0
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$	−4.24264	+	7.34847i	−0.344124	+	0.596040i
$153$	8.48528			0.685994
$154$		0			0
$155$	24.0000			1.92773
$156$		0			0
$157$	−9.89949	−	17.1464i	−0.790066	−	1.36843i	−0.925926	−	0.377706i	$-0.876713\pi$
$157$	−9.89949	−	17.1464i	−0.790066	−	1.36843i	0.135860	−	0.990728i	$-0.456620\pi$
$158$		0			0
$159$		0			0
$160$	−2.82843			−0.223607
$161$		0			0
$162$	−9.00000			−0.707107
$163$	−6.00000	+	10.3923i	−0.469956	+	0.813988i	−0.999410	−	0.0343508i	$-0.989064\pi$
$163$	−6.00000	+	10.3923i	−0.469956	+	0.813988i	0.529454	+	0.848339i	$0.322397\pi$
$164$	−4.24264	−	7.34847i	−0.331295	−	0.573819i
$165$		0			0
$166$	1.41421	−	2.44949i	0.109764	−	0.190117i
$167$	5.65685			0.437741			0.218870	−	0.975754i	$-0.429763\pi$
$167$	5.65685			0.437741			0.218870	+	0.975754i	$0.429763\pi$
$168$		0			0
$169$	19.0000			1.46154
$170$	−4.00000	+	6.92820i	−0.306786	+	0.531369i
$171$	−12.7279	−	22.0454i	−0.973329	−	1.68585i
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	2.82843	−	4.89898i	0.215041	−	0.372463i	−0.738244	−	0.674534i	$-0.764345\pi$
$173$	2.82843	−	4.89898i	0.215041	−	0.372463i	0.953285	+	0.302071i	$0.0976780\pi$
$174$		0			0
$175$		0			0
$176$	1.00000			0.0753778
$177$		0			0
$178$	−5.65685	−	9.79796i	−0.423999	−	0.734388i
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$	4.24264	−	7.34847i	0.316228	−	0.547723i
$181$	−8.48528			−0.630706			−0.315353	−	0.948974i	$-0.602123\pi$
$181$	−8.48528			−0.630706			−0.315353	+	0.948974i	$0.602123\pi$
$182$		0			0
$183$		0			0
$184$	−4.00000	+	6.92820i	−0.294884	+	0.510754i
$185$	8.48528	+	14.6969i	0.623850	+	1.08054i
$186$		0			0
$187$	1.41421	−	2.44949i	0.103418	−	0.179124i
$188$	2.82843			0.206284
$189$		0			0
$190$	24.0000			1.74114
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	−0.684244	−	0.729253i	$-0.739868\pi$
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	0.973674	+	0.227946i	$0.0732010\pi$
$192$		0			0
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	0.999990	+	0.00447566i	$0.00142465\pi$
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	−0.496119	+	0.868255i	$0.665242\pi$
$194$	−5.65685	+	9.79796i	−0.406138	+	0.703452i
$195$		0			0
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	−1.50000	+	2.59808i	−0.106600	+	0.184637i
$199$	−7.07107	−	12.2474i	−0.501255	−	0.868199i	−0.999999	−	0.00144942i	$-0.999539\pi$
$199$	−7.07107	−	12.2474i	−0.501255	−	0.868199i	0.498744	−	0.866749i	$-0.333795\pi$
$200$	1.50000	+	2.59808i	0.106066	+	0.183712i
$201$		0			0
$202$	11.3137			0.796030
$203$		0			0
$204$		0			0
$205$	−12.0000	+	20.7846i	−0.838116	+	1.45166i
$206$	7.07107	+	12.2474i	0.492665	+	0.853320i
$207$	−12.0000	−	20.7846i	−0.834058	−	1.44463i
$208$	2.82843	−	4.89898i	0.196116	−	0.339683i
$209$	−8.48528			−0.586939
$210$		0			0
$211$	28.0000			1.92760			0.963800	−	0.266627i	$-0.0859092\pi$
$211$	28.0000			1.92760			0.963800	+	0.266627i	$0.0859092\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$		0			0
$214$	2.00000	+	3.46410i	0.136717	+	0.236801i
$215$	5.65685	−	9.79796i	0.385794	−	0.668215i
$216$		0			0
$217$		0			0
$218$	14.0000			0.948200
$219$		0			0
$220$	−1.41421	−	2.44949i	−0.0953463	−	0.165145i
$221$	−8.00000	−	13.8564i	−0.538138	−	0.932083i
$222$		0			0
$223$	−2.82843			−0.189405			−0.0947027	−	0.995506i	$-0.530190\pi$
$223$	−2.82843			−0.189405			−0.0947027	+	0.995506i	$0.530190\pi$
$224$		0			0
$225$	−9.00000			−0.600000
$226$	−3.00000	+	5.19615i	−0.199557	+	0.345643i
$227$	1.41421	+	2.44949i	0.0938647	+	0.162578i	0.909134	−	0.416503i	$-0.136745\pi$
$227$	1.41421	+	2.44949i	0.0938647	+	0.162578i	−0.815270	+	0.579082i	$0.803411\pi$
$228$		0			0
$229$	−7.07107	+	12.2474i	−0.467269	+	0.809334i	−0.999301	−	0.0373904i	$-0.988095\pi$
$229$	−7.07107	+	12.2474i	−0.467269	+	0.809334i	0.532031	+	0.846725i	$0.321429\pi$
$230$	22.6274			1.49201
$231$		0			0
$232$	6.00000			0.393919
$233$	13.0000	−	22.5167i	0.851658	−	1.47512i	−0.0280525	−	0.999606i	$-0.508931\pi$
$233$	13.0000	−	22.5167i	0.851658	−	1.47512i	0.879711	−	0.475509i	$-0.157736\pi$
$234$	8.48528	+	14.6969i	0.554700	+	0.960769i
$235$	−4.00000	−	6.92820i	−0.260931	−	0.451946i
$236$	−2.82843	+	4.89898i	−0.184115	+	0.318896i
$237$		0			0
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	1.41421	+	2.44949i	0.0910975	+	0.157786i	0.907973	−	0.419028i	$-0.137629\pi$
$241$	1.41421	+	2.44949i	0.0910975	+	0.157786i	−0.816876	+	0.576814i	$0.804296\pi$
$242$	0.500000	+	0.866025i	0.0321412	+	0.0556702i
$243$		0			0
$244$	5.65685			0.362143
$245$		0			0
$246$		0			0
$247$	−24.0000	+	41.5692i	−1.52708	+	2.64499i
$248$	4.24264	+	7.34847i	0.269408	+	0.466628i
$249$		0			0
$250$	−2.82843	+	4.89898i	−0.178885	+	0.309839i
$251$	5.65685			0.357057			0.178529	−	0.983935i	$-0.442866\pi$
$251$	5.65685			0.357057			0.178529	+	0.983935i	$0.442866\pi$
$252$		0			0
$253$	−8.00000			−0.502956
$254$	4.00000	−	6.92820i	0.250982	−	0.434714i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.65685	−	9.79796i	0.352865	−	0.611180i	−0.633885	−	0.773427i	$-0.718541\pi$
$257$	5.65685	−	9.79796i	0.352865	−	0.611180i	0.986750	+	0.162247i	$0.0518742\pi$
$258$		0			0
$259$		0			0
$260$	−16.0000			−0.992278
$261$	−9.00000	+	15.5885i	−0.557086	+	0.964901i
$262$	−1.41421	−	2.44949i	−0.0873704	−	0.151330i
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	0.999970	−	0.00771799i	$-0.00245674\pi$
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	−0.506669	+	0.862141i	$0.669123\pi$
$264$		0			0
$265$	16.9706			1.04249
$266$		0			0
$267$		0			0
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	−12.7279	−	22.0454i	−0.776035	−	1.34413i	−0.934211	−	0.356721i	$-0.883895\pi$
$269$	−12.7279	−	22.0454i	−0.776035	−	1.34413i	0.158176	−	0.987411i	$-0.449439\pi$
$270$		0			0
$271$	14.1421	−	24.4949i	0.859074	−	1.48796i	−0.0137402	−	0.999906i	$-0.504374\pi$
$271$	14.1421	−	24.4949i	0.859074	−	1.48796i	0.872814	−	0.488053i	$-0.162293\pi$
$272$	−2.82843			−0.171499
$273$		0			0
$274$	18.0000			1.08742
$275$	−1.50000	+	2.59808i	−0.0904534	+	0.156670i
$276$		0			0
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	0.976231	−	0.216731i	$-0.0695395\pi$
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	−0.675810	+	0.737075i	$0.736206\pi$
$278$	4.24264	−	7.34847i	0.254457	−	0.440732i
$279$	−25.4558			−1.52400
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	7.07107	+	12.2474i	0.420331	+	0.728035i	0.995972	−	0.0896677i	$-0.0285805\pi$
$283$	7.07107	+	12.2474i	0.420331	+	0.728035i	−0.575640	+	0.817703i	$0.695247\pi$
$284$		0			0
$285$		0			0
$286$	5.65685			0.334497
$287$		0			0
$288$	3.00000			0.176777
$289$	4.50000	−	7.79423i	0.264706	−	0.458484i
$290$	−8.48528	−	14.6969i	−0.498273	−	0.863034i
$291$		0			0
$292$	−4.24264	+	7.34847i	−0.248282	+	0.430037i
$293$	−5.65685			−0.330477			−0.165238	−	0.986254i	$-0.552839\pi$
$293$	−5.65685			−0.330477			−0.165238	+	0.986254i	$0.552839\pi$
$294$		0			0
$295$	16.0000			0.931556
$296$	−3.00000	+	5.19615i	−0.174371	+	0.302020i
$297$		0			0
$298$	−5.00000	−	8.66025i	−0.289642	−	0.501675i
$299$	−22.6274	+	39.1918i	−1.30858	+	2.26652i
$300$		0			0
$301$		0			0
$302$	−8.00000			−0.460348
$303$		0			0
$304$	4.24264	+	7.34847i	0.243332	+	0.421464i
$305$	−8.00000	−	13.8564i	−0.458079	−	0.793416i
$306$	4.24264	−	7.34847i	0.242536	−	0.420084i
$307$	−14.1421			−0.807134			−0.403567	−	0.914950i	$-0.632230\pi$
$307$	−14.1421			−0.807134			−0.403567	+	0.914950i	$0.632230\pi$
$308$		0			0
$309$		0			0
$310$	12.0000	−	20.7846i	0.681554	−	1.18049i
$311$	7.07107	+	12.2474i	0.400963	+	0.694489i	0.993842	−	0.110802i	$-0.0353421\pi$
$311$	7.07107	+	12.2474i	0.400963	+	0.694489i	−0.592879	+	0.805292i	$0.702009\pi$
$312$		0			0
$313$	−8.48528	+	14.6969i	−0.479616	+	0.830720i	−0.999727	−	0.0233791i	$-0.992558\pi$
$313$	−8.48528	+	14.6969i	−0.479616	+	0.830720i	0.520110	+	0.854099i	$0.325891\pi$
$314$	−19.7990			−1.11732
$315$		0			0
$316$		0			0
$317$	1.00000	−	1.73205i	0.0561656	−	0.0972817i	−0.836576	−	0.547852i	$-0.815446\pi$
$317$	1.00000	−	1.73205i	0.0561656	−	0.0972817i	0.892741	+	0.450570i	$0.148779\pi$
$318$		0			0
$319$	3.00000	+	5.19615i	0.167968	+	0.290929i
$320$	−1.41421	+	2.44949i	−0.0790569	+	0.136931i
$321$		0			0
$322$		0			0
$323$	24.0000			1.33540
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	8.48528	+	14.6969i	0.470679	+	0.815239i
$326$	6.00000	+	10.3923i	0.332309	+	0.575577i
$327$		0			0
$328$	−8.48528			−0.468521
$329$		0			0
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	−1.41421	−	2.44949i	−0.0776151	−	0.134433i
$333$	−9.00000	−	15.5885i	−0.493197	−	0.854242i
$334$	2.82843	−	4.89898i	0.154765	−	0.268060i
$335$	−11.3137			−0.618134
$336$		0			0
$337$	−18.0000			−0.980522			−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000			−0.980522			−0.490261	+	0.871576i	$0.663099\pi$
$338$	9.50000	−	16.4545i	0.516732	−	0.895006i
$339$		0			0
$340$	4.00000	+	6.92820i	0.216930	+	0.375735i
$341$	−4.24264	+	7.34847i	−0.229752	+	0.397942i
$342$	−25.4558			−1.37649
$343$		0			0
$344$	4.00000			0.215666
$345$		0			0
$346$	−2.82843	−	4.89898i	−0.152057	−	0.263371i
$347$	2.00000	+	3.46410i	0.107366	+	0.185963i	0.914702	−	0.404128i	$-0.132425\pi$
$347$	2.00000	+	3.46410i	0.107366	+	0.185963i	−0.807337	+	0.590091i	$0.799092\pi$
$348$		0			0
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$		0			0
$351$		0			0
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$353$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$354$		0			0
$355$		0			0
$356$	−11.3137			−0.599625
$357$		0			0
$358$	12.0000			0.634220
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	0.353529	+	0.935423i	$0.384981\pi$
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	−0.986865	+	0.161546i	$0.948352\pi$
$360$	−4.24264	−	7.34847i	−0.223607	−	0.387298i
$361$	−26.5000	−	45.8993i	−1.39474	−	2.41576i
$362$	−4.24264	+	7.34847i	−0.222988	+	0.386227i
$363$		0			0
$364$		0			0
$365$	24.0000			1.25622
$366$		0			0
$367$	12.7279	+	22.0454i	0.664392	+	1.15076i	0.979450	+	0.201688i	$0.0646428\pi$
$367$	12.7279	+	22.0454i	0.664392	+	1.15076i	−0.315058	+	0.949073i	$0.602024\pi$
$368$	4.00000	+	6.92820i	0.208514	+	0.361158i
$369$	12.7279	−	22.0454i	0.662589	−	1.14764i
$370$	16.9706			0.882258
$371$		0			0
$372$		0			0
$373$	1.00000	−	1.73205i	0.0517780	−	0.0896822i	−0.838975	−	0.544170i	$-0.816844\pi$
$373$	1.00000	−	1.73205i	0.0517780	−	0.0896822i	0.890753	+	0.454488i	$0.150178\pi$
$374$	−1.41421	−	2.44949i	−0.0731272	−	0.126660i
$375$		0			0
$376$	1.41421	−	2.44949i	0.0729325	−	0.126323i
$377$	33.9411			1.74806
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$	12.0000	−	20.7846i	0.615587	−	1.06623i
$381$		0			0
$382$	−4.00000	−	6.92820i	−0.204658	−	0.354478i
$383$	7.07107	−	12.2474i	0.361315	−	0.625815i	−0.626863	−	0.779130i	$-0.715661\pi$
$383$	7.07107	−	12.2474i	0.361315	−	0.625815i	0.988177	+	0.153314i	$0.0489947\pi$
$384$		0			0
$385$		0			0
$386$	14.0000			0.712581
$387$	−6.00000	+	10.3923i	−0.304997	+	0.528271i
$388$	5.65685	+	9.79796i	0.287183	+	0.497416i
$389$	−5.00000	−	8.66025i	−0.253510	−	0.439092i	0.710980	−	0.703213i	$-0.248252\pi$
$389$	−5.00000	−	8.66025i	−0.253510	−	0.439092i	−0.964490	+	0.264120i	$0.914918\pi$
$390$		0			0
$391$	22.6274			1.14432
$392$		0			0
$393$		0			0
$394$	−9.00000	+	15.5885i	−0.453413	+	0.785335i
$395$		0			0
$396$	1.50000	+	2.59808i	0.0753778	+	0.130558i
$397$	−4.24264	+	7.34847i	−0.212932	+	0.368809i	−0.952631	−	0.304129i	$-0.901635\pi$
$397$	−4.24264	+	7.34847i	−0.212932	+	0.368809i	0.739699	+	0.672938i	$0.234968\pi$
$398$	−14.1421			−0.708881
$399$		0			0
$400$	3.00000			0.150000
$401$	5.00000	−	8.66025i	0.249688	−	0.432472i	−0.713751	−	0.700399i	$-0.753005\pi$
$401$	5.00000	−	8.66025i	0.249688	−	0.432472i	0.963439	+	0.267927i	$0.0863386\pi$
$402$		0			0
$403$	24.0000	+	41.5692i	1.19553	+	2.07071i
$404$	5.65685	−	9.79796i	0.281439	−	0.487467i
$405$	25.4558			1.26491
$406$		0			0
$407$	−6.00000			−0.297409
$408$		0			0
$409$	4.24264	+	7.34847i	0.209785	+	0.363358i	0.951647	−	0.307195i	$-0.0993902\pi$
$409$	4.24264	+	7.34847i	0.209785	+	0.363358i	−0.741862	+	0.670553i	$0.766057\pi$
$410$	12.0000	+	20.7846i	0.592638	+	1.02648i
$411$		0			0
$412$	14.1421			0.696733
$413$		0			0
$414$	−24.0000			−1.17954
$415$	−4.00000	+	6.92820i	−0.196352	+	0.340092i
$416$	−2.82843	−	4.89898i	−0.138675	−	0.240192i
$417$		0			0
$418$	−4.24264	+	7.34847i	−0.207514	+	0.359425i
$419$	−22.6274			−1.10542			−0.552711	−	0.833373i	$-0.686407\pi$
$419$	−22.6274			−1.10542			−0.552711	+	0.833373i	$0.686407\pi$
$420$		0			0
$421$	−26.0000			−1.26716			−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000			−1.26716			−0.633581	+	0.773676i	$0.718416\pi$
$422$	14.0000	−	24.2487i	0.681509	−	1.18041i
$423$	4.24264	+	7.34847i	0.206284	+	0.357295i
$424$	3.00000	+	5.19615i	0.145693	+	0.252347i
$425$	4.24264	−	7.34847i	0.205798	−	0.356453i
$426$		0			0
$427$		0			0
$428$	4.00000			0.193347
$429$		0			0
$430$	−5.65685	−	9.79796i	−0.272798	−	0.472500i
$431$	−8.00000	−	13.8564i	−0.385346	−	0.667440i	0.606471	−	0.795106i	$-0.292585\pi$
$431$	−8.00000	−	13.8564i	−0.385346	−	0.667440i	−0.991817	+	0.127666i	$0.959251\pi$
$432$		0			0
$433$	33.9411			1.63111			0.815553	−	0.578682i	$-0.196433\pi$
$433$	33.9411			1.63111			0.815553	+	0.578682i	$0.196433\pi$
$434$		0			0
$435$		0			0
$436$	7.00000	−	12.1244i	0.335239	−	0.580651i
$437$	−33.9411	−	58.7878i	−1.62362	−	2.81220i
$438$		0			0
$439$	−14.1421	+	24.4949i	−0.674967	+	1.16908i	0.301511	+	0.953463i	$0.402509\pi$
$439$	−14.1421	+	24.4949i	−0.674967	+	1.16908i	−0.976478	+	0.215615i	$0.930824\pi$
$440$	−2.82843			−0.134840
$441$		0			0
$442$	−16.0000			−0.761042
$443$	10.0000	−	17.3205i	0.475114	−	0.822922i	−0.524479	−	0.851423i	$-0.675740\pi$
$443$	10.0000	−	17.3205i	0.475114	−	0.822922i	0.999594	+	0.0285009i	$0.00907336\pi$
$444$		0			0
$445$	16.0000	+	27.7128i	0.758473	+	1.31371i
$446$	−1.41421	+	2.44949i	−0.0669650	+	0.115987i
$447$		0			0
$448$		0			0
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$	−4.50000	+	7.79423i	−0.212132	+	0.367423i
$451$	−4.24264	−	7.34847i	−0.199778	−	0.346026i
$452$	3.00000	+	5.19615i	0.141108	+	0.244406i
$453$		0			0
$454$	2.82843			0.132745
$455$		0			0
$456$		0			0
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	0.725059	+	0.688686i	$0.241812\pi$
$458$	7.07107	+	12.2474i	0.330409	+	0.572286i
$459$		0			0
$460$	11.3137	−	19.5959i	0.527504	−	0.913664i
$461$	−11.3137			−0.526932			−0.263466	−	0.964669i	$-0.584866\pi$
$461$	−11.3137			−0.526932			−0.263466	+	0.964669i	$0.584866\pi$
$462$		0			0
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$	3.00000	−	5.19615i	0.139272	−	0.241225i
$465$		0			0
$466$	−13.0000	−	22.5167i	−0.602213	−	1.04306i
$467$	16.9706	−	29.3939i	0.785304	−	1.36019i	−0.143513	−	0.989648i	$-0.545840\pi$
$467$	16.9706	−	29.3939i	0.785304	−	1.36019i	0.928817	−	0.370538i	$-0.120827\pi$
$468$	16.9706			0.784465
$469$		0			0
$470$	−8.00000			−0.369012
$471$		0			0
$472$	2.82843	+	4.89898i	0.130189	+	0.225494i
$473$	2.00000	+	3.46410i	0.0919601	+	0.159280i
$474$		0			0
$475$	−25.4558			−1.16799
$476$		0			0
$477$	−18.0000			−0.824163
$478$	12.0000	−	20.7846i	0.548867	−	0.950666i
$479$	5.65685	+	9.79796i	0.258468	+	0.447680i	0.965832	−	0.259170i	$-0.0834489\pi$
$479$	5.65685	+	9.79796i	0.258468	+	0.447680i	−0.707364	+	0.706850i	$0.750116\pi$
$480$		0			0
$481$	−16.9706	+	29.3939i	−0.773791	+	1.34025i
$482$	2.82843			0.128831
$483$		0			0
$484$	1.00000			0.0454545
$485$	16.0000	−	27.7128i	0.726523	−	1.25837i
$486$		0			0
$487$	−4.00000	−	6.92820i	−0.181257	−	0.313947i	0.761052	−	0.648691i	$-0.224683\pi$
$487$	−4.00000	−	6.92820i	−0.181257	−	0.313947i	−0.942309	+	0.334744i	$0.891350\pi$
$488$	2.82843	−	4.89898i	0.128037	−	0.221766i
$489$		0			0
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$		0			0
$493$	−8.48528	−	14.6969i	−0.382158	−	0.661917i
$494$	24.0000	+	41.5692i	1.07981	+	1.87029i
$495$	4.24264	−	7.34847i	0.190693	−	0.330289i
$496$	8.48528			0.381000
$497$		0			0
$498$		0			0
$499$	−22.0000	+	38.1051i	−0.984855	+	1.70582i	−0.342277	+	0.939599i	$0.611198\pi$
$499$	−22.0000	+	38.1051i	−0.984855	+	1.70582i	−0.642578	+	0.766220i	$0.722135\pi$
$500$	2.82843	+	4.89898i	0.126491	+	0.219089i
$501$		0			0
$502$	2.82843	−	4.89898i	0.126239	−	0.218652i
$503$	5.65685			0.252227			0.126113	−	0.992016i	$-0.459750\pi$
$503$	5.65685			0.252227			0.126113	+	0.992016i	$0.459750\pi$
$504$		0			0
$505$	−32.0000			−1.42398
$506$	−4.00000	+	6.92820i	−0.177822	+	0.307996i
$507$		0			0
$508$	−4.00000	−	6.92820i	−0.177471	−	0.307389i
$509$	15.5563	−	26.9444i	0.689523	−	1.19429i	−0.282469	−	0.959276i	$-0.591154\pi$
$509$	15.5563	−	26.9444i	0.689523	−	1.19429i	0.971992	−	0.235013i	$-0.0755131\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−5.65685	−	9.79796i	−0.249513	−	0.432169i
$515$	−20.0000	−	34.6410i	−0.881305	−	1.52647i
$516$		0			0
$517$	2.82843			0.124394
$518$		0			0
$519$		0			0
$520$	−8.00000	+	13.8564i	−0.350823	+	0.607644i
$521$	5.65685	+	9.79796i	0.247831	+	0.429256i	0.962924	−	0.269773i	$-0.0869488\pi$
$521$	5.65685	+	9.79796i	0.247831	+	0.429256i	−0.715093	+	0.699030i	$0.753615\pi$
$522$	9.00000	+	15.5885i	0.393919	+	0.682288i
$523$	−15.5563	+	26.9444i	−0.680232	+	1.17820i	0.294678	+	0.955596i	$0.404787\pi$
$523$	−15.5563	+	26.9444i	−0.680232	+	1.17820i	−0.974910	+	0.222599i	$0.928546\pi$
$524$	−2.82843			−0.123560
$525$		0			0
$526$	16.0000			0.697633
$527$	12.0000	−	20.7846i	0.522728	−	0.905392i
$528$		0			0
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$	8.48528	−	14.6969i	0.368577	−	0.638394i
$531$	−16.9706			−0.736460
$532$		0			0
$533$	−48.0000			−2.07911
$534$		0			0
$535$	−5.65685	−	9.79796i	−0.244567	−	0.423603i
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$		0			0
$538$	−25.4558			−1.09748
$539$		0			0
$540$		0			0
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	−0.738296	−	0.674477i	$-0.764369\pi$
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$542$	−14.1421	−	24.4949i	−0.607457	−	1.05215i
$543$		0			0
$544$	−1.41421	+	2.44949i	−0.0606339	+	0.105021i
$545$	−39.5980			−1.69619
$546$		0			0
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$	9.00000	−	15.5885i	0.384461	−	0.665906i
$549$	8.48528	+	14.6969i	0.362143	+	0.627250i
$550$	1.50000	+	2.59808i	0.0639602	+	0.110782i
$551$	−25.4558	+	44.0908i	−1.08446	+	1.87833i
$552$		0			0
$553$		0			0
$554$	10.0000			0.424859
$555$		0			0
$556$	−4.24264	−	7.34847i	−0.179928	−	0.311645i
$557$	21.0000	+	36.3731i	0.889799	+	1.54118i	0.840113	+	0.542411i	$0.182489\pi$
$557$	21.0000	+	36.3731i	0.889799	+	1.54118i	0.0496855	+	0.998765i	$0.484178\pi$
$558$	−12.7279	+	22.0454i	−0.538816	+	0.933257i
$559$	22.6274			0.957038
$560$		0			0
$561$		0			0
$562$	3.00000	−	5.19615i	0.126547	−	0.219186i
$563$	−9.89949	−	17.1464i	−0.417214	−	0.722636i	0.578444	−	0.815722i	$-0.303660\pi$
$563$	−9.89949	−	17.1464i	−0.417214	−	0.722636i	−0.995658	+	0.0930862i	$0.970327\pi$
$564$		0			0
$565$	8.48528	−	14.6969i	0.356978	−	0.618305i
$566$	14.1421			0.594438
$567$		0			0
$568$		0			0
$569$	−11.0000	+	19.0526i	−0.461144	+	0.798725i	−0.999018	−	0.0443003i	$-0.985894\pi$
$569$	−11.0000	+	19.0526i	−0.461144	+	0.798725i	0.537874	+	0.843025i	$0.319228\pi$
$570$		0			0
$571$	−6.00000	−	10.3923i	−0.251092	−	0.434904i	0.712735	−	0.701434i	$-0.247456\pi$
$571$	−6.00000	−	10.3923i	−0.251092	−	0.434904i	−0.963827	+	0.266529i	$0.914123\pi$
$572$	2.82843	−	4.89898i	0.118262	−	0.204837i
$573$		0			0
$574$		0			0
$575$	−24.0000			−1.00087
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	8.48528	+	14.6969i	0.353247	+	0.611842i	0.986816	−	0.161844i	$-0.0517442\pi$
$577$	8.48528	+	14.6969i	0.353247	+	0.611842i	−0.633569	+	0.773686i	$0.718411\pi$
$578$	−4.50000	−	7.79423i	−0.187175	−	0.324197i
$579$		0			0
$580$	−16.9706			−0.704664
$581$		0			0
$582$		0			0
$583$	−3.00000	+	5.19615i	−0.124247	+	0.215203i
$584$	4.24264	+	7.34847i	0.175562	+	0.304082i
$585$	−24.0000	−	41.5692i	−0.992278	−	1.71868i
$586$	−2.82843	+	4.89898i	−0.116841	+	0.202375i
$587$	39.5980			1.63438			0.817192	−	0.576366i	$-0.195530\pi$
$587$	39.5980			1.63438			0.817192	+	0.576366i	$0.195530\pi$
$588$		0			0
$589$	−72.0000			−2.96671
$590$	8.00000	−	13.8564i	0.329355	−	0.570459i
$591$		0			0
$592$	3.00000	+	5.19615i	0.123299	+	0.213561i
$593$	18.3848	−	31.8434i	0.754972	−	1.30765i	−0.190416	−	0.981704i	$-0.560984\pi$
$593$	18.3848	−	31.8434i	0.754972	−	1.30765i	0.945388	−	0.325947i	$-0.105683\pi$
$594$		0			0
$595$		0			0
$596$	−10.0000			−0.409616
$597$		0			0
$598$	22.6274	+	39.1918i	0.925304	+	1.60267i
$599$	8.00000	+	13.8564i	0.326871	+	0.566157i	0.981889	−	0.189456i	$-0.0606724\pi$
$599$	8.00000	+	13.8564i	0.326871	+	0.566157i	−0.655018	+	0.755613i	$0.727339\pi$
$600$		0			0
$601$	−19.7990			−0.807618			−0.403809	−	0.914843i	$-0.632314\pi$
$601$	−19.7990			−0.807618			−0.403809	+	0.914843i	$0.632314\pi$
$602$		0			0
$603$	12.0000			0.488678
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	−1.41421	−	2.44949i	−0.0574960	−	0.0995859i
$606$		0			0
$607$	16.9706	−	29.3939i	0.688814	−	1.19306i	−0.283408	−	0.958999i	$-0.591465\pi$
$607$	16.9706	−	29.3939i	0.688814	−	1.19306i	0.972222	−	0.234061i	$-0.0752016\pi$
$608$	8.48528			0.344124
$609$		0			0
$610$	−16.0000			−0.647821
$611$	8.00000	−	13.8564i	0.323645	−	0.560570i
$612$	−4.24264	−	7.34847i	−0.171499	−	0.297044i
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$	−7.07107	+	12.2474i	−0.285365	+	0.494267i
$615$		0			0
$616$		0			0
$617$	38.0000			1.52982			0.764911	−	0.644136i	$-0.222783\pi$
$617$	38.0000			1.52982			0.764911	+	0.644136i	$0.222783\pi$
$618$		0			0
$619$	5.65685	+	9.79796i	0.227368	+	0.393813i	0.957027	−	0.289998i	$-0.0936546\pi$
$619$	5.65685	+	9.79796i	0.227368	+	0.393813i	−0.729659	+	0.683811i	$0.760321\pi$
$620$	−12.0000	−	20.7846i	−0.481932	−	0.834730i
$621$		0			0
$622$	14.1421			0.567048
$623$		0			0
$624$		0			0
$625$	15.5000	−	26.8468i	0.620000	−	1.07387i
$626$	8.48528	+	14.6969i	0.339140	+	0.587408i
$627$		0			0
$628$	−9.89949	+	17.1464i	−0.395033	+	0.684217i
$629$	16.9706			0.676661
$630$		0			0
$631$	32.0000			1.27390			0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000			1.27390			0.636950	+	0.770905i	$0.280196\pi$
$632$		0			0
$633$		0			0
$634$	−1.00000	−	1.73205i	−0.0397151	−	0.0687885i
$635$	−11.3137	+	19.5959i	−0.448971	+	0.777640i
$636$		0			0
$637$		0			0
$638$	6.00000			0.237542
$639$		0			0
$640$	1.41421	+	2.44949i	0.0559017	+	0.0968246i
$641$	−23.0000	−	39.8372i	−0.908445	−	1.57347i	−0.816224	−	0.577735i	$-0.803937\pi$
$641$	−23.0000	−	39.8372i	−0.908445	−	1.57347i	−0.0922210	−	0.995739i	$-0.529397\pi$
$642$		0			0
$643$	5.65685			0.223085			0.111542	−	0.993760i	$-0.464421\pi$
$643$	5.65685			0.223085			0.111542	+	0.993760i	$0.464421\pi$
$644$		0			0
$645$		0			0
$646$	12.0000	−	20.7846i	0.472134	−	0.817760i
$647$	18.3848	+	31.8434i	0.722780	+	1.25189i	0.959881	+	0.280407i	$0.0904694\pi$
$647$	18.3848	+	31.8434i	0.722780	+	1.25189i	−0.237101	+	0.971485i	$0.576197\pi$
$648$	4.50000	+	7.79423i	0.176777	+	0.306186i
$649$	−2.82843	+	4.89898i	−0.111025	+	0.192302i
$650$	16.9706			0.665640
$651$		0			0
$652$	12.0000			0.469956
$653$	15.0000	−	25.9808i	0.586995	−	1.01671i	−0.407628	−	0.913148i	$-0.633644\pi$
$653$	15.0000	−	25.9808i	0.586995	−	1.01671i	0.994623	−	0.103558i	$-0.0330227\pi$
$654$		0			0
$655$	4.00000	+	6.92820i	0.156293	+	0.270707i
$656$	−4.24264	+	7.34847i	−0.165647	+	0.286910i
$657$	−25.4558			−0.993127
$658$		0			0
$659$	4.00000			0.155818			0.0779089	−	0.996960i	$-0.475176\pi$
$659$	4.00000			0.155818			0.0779089	+	0.996960i	$0.475176\pi$
$660$		0			0
$661$	4.24264	+	7.34847i	0.165020	+	0.285822i	0.936662	−	0.350234i	$-0.113898\pi$
$661$	4.24264	+	7.34847i	0.165020	+	0.285822i	−0.771643	+	0.636056i	$0.780565\pi$
$662$	−2.00000	−	3.46410i	−0.0777322	−	0.134636i
$663$		0			0
$664$	−2.82843			−0.109764
$665$		0			0
$666$	−18.0000			−0.697486
$667$	−24.0000	+	41.5692i	−0.929284	+	1.60957i
$668$	−2.82843	−	4.89898i	−0.109435	−	0.189547i
$669$		0			0
$670$	−5.65685	+	9.79796i	−0.218543	+	0.378528i
$671$	5.65685			0.218380
$672$		0			0
$673$	14.0000			0.539660			0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000			0.539660			0.269830	+	0.962908i	$0.413032\pi$
$674$	−9.00000	+	15.5885i	−0.346667	+	0.600445i
$675$		0			0
$676$	−9.50000	−	16.4545i	−0.365385	−	0.632865i
$677$	−14.1421	+	24.4949i	−0.543526	+	0.941415i	0.455172	+	0.890404i	$0.349578\pi$
$677$	−14.1421	+	24.4949i	−0.543526	+	0.941415i	−0.998698	+	0.0510117i	$0.983755\pi$
$678$		0			0
$679$		0			0
$680$	8.00000			0.306786
$681$		0			0
$682$	4.24264	+	7.34847i	0.162459	+	0.281387i
$683$	10.0000	+	17.3205i	0.382639	+	0.662751i	0.991439	−	0.130573i	$-0.0416818\pi$
$683$	10.0000	+	17.3205i	0.382639	+	0.662751i	−0.608799	+	0.793324i	$0.708349\pi$
$684$	−12.7279	+	22.0454i	−0.486664	+	0.842927i
$685$	−50.9117			−1.94524
$686$		0			0
$687$		0			0
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	16.9706	+	29.3939i	0.646527	+	1.11982i
$690$		0			0
$691$	25.4558	−	44.0908i	0.968386	−	1.67729i	0.268157	−	0.963375i	$-0.413585\pi$
$691$	25.4558	−	44.0908i	0.968386	−	1.67729i	0.700229	−	0.713918i	$-0.253081\pi$
$692$	−5.65685			−0.215041
$693$		0			0
$694$	4.00000			0.151838
$695$	−12.0000	+	20.7846i	−0.455186	+	0.788405i
$696$		0			0
$697$	12.0000	+	20.7846i	0.454532	+	0.787273i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	2.00000			0.0755390			0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000			0.0755390			0.0377695	+	0.999286i	$0.487975\pi$
$702$		0			0
$703$	−25.4558	−	44.0908i	−0.960085	−	1.66292i
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	−0.944509	−	0.328484i	$-0.893462\pi$
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	0.756730	+	0.653727i	$0.226796\pi$
$710$		0			0
$711$		0			0
$712$	−5.65685	+	9.79796i	−0.212000	+	0.367194i
$713$	−67.8823			−2.54221
$714$		0			0
$715$	−16.0000			−0.598366
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$		0			0
$718$	12.0000	+	20.7846i	0.447836	+	0.775675i
$719$	12.7279	−	22.0454i	0.474671	−	0.822155i	−0.524908	−	0.851159i	$-0.675900\pi$
$719$	12.7279	−	22.0454i	0.474671	−	0.822155i	0.999579	+	0.0290041i	$0.00923357\pi$
$720$	−8.48528			−0.316228
$721$		0			0
$722$	−53.0000			−1.97246
$723$		0			0
$724$	4.24264	+	7.34847i	0.157676	+	0.273104i
$725$	9.00000	+	15.5885i	0.334252	+	0.578941i
$726$		0			0
$727$	−14.1421			−0.524503			−0.262251	−	0.965000i	$-0.584465\pi$
$727$	−14.1421			−0.524503			−0.262251	+	0.965000i	$0.584465\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	12.0000	−	20.7846i	0.444140	−	0.769273i
$731$	−5.65685	−	9.79796i	−0.209226	−	0.362391i
$732$		0			0
$733$	8.48528	−	14.6969i	0.313411	−	0.542844i	−0.665687	−	0.746231i	$-0.731862\pi$
$733$	8.48528	−	14.6969i	0.313411	−	0.542844i	0.979098	+	0.203387i	$0.0651949\pi$
$734$	25.4558			0.939592
$735$		0			0
$736$	8.00000			0.294884
$737$	2.00000	−	3.46410i	0.0736709	−	0.127602i
$738$	−12.7279	−	22.0454i	−0.468521	−	0.811503i
$739$	−18.0000	−	31.1769i	−0.662141	−	1.14686i	−0.980052	−	0.198741i	$-0.936315\pi$
$739$	−18.0000	−	31.1769i	−0.662141	−	1.14686i	0.317911	−	0.948120i	$-0.397019\pi$
$740$	8.48528	−	14.6969i	0.311925	−	0.540270i
$741$		0			0
$742$		0			0
$743$	16.0000			0.586983			0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000			0.586983			0.293492	+	0.955962i	$0.405183\pi$
$744$		0			0
$745$	14.1421	+	24.4949i	0.518128	+	0.897424i
$746$	−1.00000	−	1.73205i	−0.0366126	−	0.0634149i
$747$	4.24264	−	7.34847i	0.155230	−	0.268866i
$748$	−2.82843			−0.103418
$749$		0			0
$750$		0			0
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	−0.682341	−	0.731034i	$-0.739038\pi$
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	0.974265	+	0.225407i	$0.0723712\pi$
$752$	−1.41421	−	2.44949i	−0.0515711	−	0.0893237i
$753$		0			0
$754$	16.9706	−	29.3939i	0.618031	−	1.07046i
$755$	22.6274			0.823496
$756$		0			0
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$	−14.0000	+	24.2487i	−0.508503	+	0.880753i
$759$		0			0
$760$	−12.0000	−	20.7846i	−0.435286	−	0.753937i
$761$	−1.41421	+	2.44949i	−0.0512652	+	0.0887939i	−0.890519	−	0.454946i	$-0.849659\pi$
$761$	−1.41421	+	2.44949i	−0.0512652	+	0.0887939i	0.839254	+	0.543740i	$0.182992\pi$
$762$		0			0
$763$		0			0
$764$	−8.00000			−0.289430
$765$	−12.0000	+	20.7846i	−0.433861	+	0.751469i
$766$	−7.07107	−	12.2474i	−0.255488	−	0.442518i
$767$	16.0000	+	27.7128i	0.577727	+	1.00065i
$768$		0			0
$769$	36.7696			1.32594			0.662972	−	0.748644i	$-0.269295\pi$
$769$	36.7696			1.32594			0.662972	+	0.748644i	$0.269295\pi$
$770$		0			0
$771$		0			0
$772$	7.00000	−	12.1244i	0.251936	−	0.436365i
$773$	1.41421	+	2.44949i	0.0508657	+	0.0881020i	0.890337	−	0.455302i	$-0.150469\pi$
$773$	1.41421	+	2.44949i	0.0508657	+	0.0881020i	−0.839471	+	0.543404i	$0.817135\pi$
$774$	6.00000	+	10.3923i	0.215666	+	0.373544i
$775$	−12.7279	+	22.0454i	−0.457200	+	0.791894i
$776$	11.3137			0.406138
$777$		0			0
$778$	−10.0000			−0.358517
$779$	36.0000	−	62.3538i	1.28983	−	2.23406i
$780$		0			0
$781$		0			0
$782$	11.3137	−	19.5959i	0.404577	−	0.700749i
$783$		0			0
$784$		0			0
$785$	56.0000			1.99873
$786$		0			0
$787$	−12.7279	−	22.0454i	−0.453701	−	0.785834i	0.544911	−	0.838494i	$-0.316563\pi$
$787$	−12.7279	−	22.0454i	−0.453701	−	0.785834i	−0.998613	+	0.0526599i	$0.983230\pi$
$788$	9.00000	+	15.5885i	0.320612	+	0.555316i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	3.00000			0.106600
$793$	16.0000	−	27.7128i	0.568177	−	0.984111i
$794$	4.24264	+	7.34847i	0.150566	+	0.260787i
$795$		0			0
$796$	−7.07107	+	12.2474i	−0.250627	+	0.434099i
$797$	19.7990			0.701316			0.350658	−	0.936504i	$-0.385958\pi$
$797$	19.7990			0.701316			0.350658	+	0.936504i	$0.385958\pi$
$798$		0			0
$799$	−8.00000			−0.283020
$800$	1.50000	−	2.59808i	0.0530330	−	0.0918559i
$801$	−16.9706	−	29.3939i	−0.599625	−	1.03858i
$802$	−5.00000	−	8.66025i	−0.176556	−	0.305804i
$803$	−4.24264	+	7.34847i	−0.149720	+	0.259322i
$804$		0			0
$805$		0			0
$806$	48.0000			1.69073
$807$		0			0
$808$	−5.65685	−	9.79796i	−0.199007	−	0.344691i
$809$	−13.0000	−	22.5167i	−0.457056	−	0.791644i	0.541748	−	0.840541i	$-0.317763\pi$
$809$	−13.0000	−	22.5167i	−0.457056	−	0.791644i	−0.998804	+	0.0488972i	$0.984429\pi$
$810$	12.7279	−	22.0454i	0.447214	−	0.774597i
$811$	8.48528			0.297959			0.148979	−	0.988840i	$-0.452401\pi$
$811$	8.48528			0.297959			0.148979	+	0.988840i	$0.452401\pi$
$812$		0			0
$813$		0			0
$814$	−3.00000	+	5.19615i	−0.105150	+	0.182125i
$815$	−16.9706	−	29.3939i	−0.594453	−	1.02962i
$816$		0			0
$817$	−16.9706	+	29.3939i	−0.593725	+	1.02836i
$818$	8.48528			0.296681
$819$		0			0
$820$	24.0000			0.838116
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	−0.991616	−	0.129217i	$-0.958754\pi$
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	0.607714	+	0.794156i	$0.292087\pi$
$822$		0			0
$823$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$823$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$824$	7.07107	−	12.2474i	0.246332	−	0.426660i
$825$		0			0
$826$		0			0
$827$	20.0000			0.695468			0.347734	−	0.937593i	$-0.386951\pi$
$827$	20.0000			0.695468			0.347734	+	0.937593i	$0.386951\pi$
$828$	−12.0000	+	20.7846i	−0.417029	+	0.722315i
$829$	−12.7279	−	22.0454i	−0.442059	−	0.765669i	0.555783	−	0.831327i	$-0.312418\pi$
$829$	−12.7279	−	22.0454i	−0.442059	−	0.765669i	−0.997842	+	0.0656587i	$0.979085\pi$
$830$	4.00000	+	6.92820i	0.138842	+	0.240481i
$831$		0			0
$832$	−5.65685			−0.196116
$833$		0			0
$834$		0			0
$835$	−8.00000	+	13.8564i	−0.276851	+	0.479521i
$836$	4.24264	+	7.34847i	0.146735	+	0.254152i
$837$		0			0
$838$	−11.3137	+	19.5959i	−0.390826	+	0.676930i
$839$	53.7401			1.85531			0.927657	−	0.373432i	$-0.121819\pi$
$839$	53.7401			1.85531			0.927657	+	0.373432i	$0.121819\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	−13.0000	+	22.5167i	−0.448010	+	0.775975i
$843$		0			0
$844$	−14.0000	−	24.2487i	−0.481900	−	0.834675i
$845$	−26.8701	+	46.5403i	−0.924358	+	1.60104i
$846$	8.48528			0.291730
$847$		0			0
$848$	6.00000			0.206041
$849$		0			0
$850$	−4.24264	−	7.34847i	−0.145521	−	0.252050i
$851$	−24.0000	−	41.5692i	−0.822709	−	1.42497i
$852$		0			0
$853$	50.9117			1.74318			0.871592	−	0.490233i	$-0.163088\pi$
$853$	50.9117			1.74318			0.871592	+	0.490233i	$0.163088\pi$
$854$		0			0
$855$	72.0000			2.46235
$856$	2.00000	−	3.46410i	0.0683586	−	0.118401i
$857$	−1.41421	−	2.44949i	−0.0483086	−	0.0836730i	0.840860	−	0.541253i	$-0.182050\pi$
$857$	−1.41421	−	2.44949i	−0.0483086	−	0.0836730i	−0.889169	+	0.457580i	$0.848716\pi$
$858$		0			0
$859$	19.7990	−	34.2929i	0.675533	−	1.17006i	−0.300780	−	0.953694i	$-0.597247\pi$
$859$	19.7990	−	34.2929i	0.675533	−	1.17006i	0.976313	−	0.216364i	$-0.0694197\pi$
$860$	−11.3137			−0.385794
$861$		0			0
$862$	−16.0000			−0.544962
$863$	12.0000	−	20.7846i	0.408485	−	0.707516i	−0.586235	−	0.810141i	$-0.699391\pi$
$863$	12.0000	−	20.7846i	0.408485	−	0.707516i	0.994720	+	0.102624i	$0.0327240\pi$
$864$		0			0
$865$	8.00000	+	13.8564i	0.272008	+	0.471132i
$866$	16.9706	−	29.3939i	0.576683	−	0.998845i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−11.3137	−	19.5959i	−0.383350	−	0.663982i
$872$	−7.00000	−	12.1244i	−0.237050	−	0.410582i
$873$	−16.9706	+	29.3939i	−0.574367	+	0.994832i
$874$	−67.8823			−2.29615
$875$		0			0
$876$		0			0
$877$	7.00000	−	12.1244i	0.236373	−	0.409410i	−0.723298	−	0.690536i	$-0.757375\pi$
$877$	7.00000	−	12.1244i	0.236373	−	0.409410i	0.959671	+	0.281126i	$0.0907079\pi$
$878$	14.1421	+	24.4949i	0.477274	+	0.826663i
$879$		0			0
$880$	−1.41421	+	2.44949i	−0.0476731	+	0.0825723i
$881$	−5.65685			−0.190584			−0.0952921	−	0.995449i	$-0.530379\pi$
$881$	−5.65685			−0.190584			−0.0952921	+	0.995449i	$0.530379\pi$
$882$		0			0
$883$	−28.0000			−0.942275			−0.471138	−	0.882060i	$-0.656156\pi$
$883$	−28.0000			−0.942275			−0.471138	+	0.882060i	$0.656156\pi$
$884$	−8.00000	+	13.8564i	−0.269069	+	0.466041i
$885$		0			0
$886$	−10.0000	−	17.3205i	−0.335957	−	0.581894i
$887$	−22.6274	+	39.1918i	−0.759754	+	1.31593i	0.183221	+	0.983072i	$0.441347\pi$
$887$	−22.6274	+	39.1918i	−0.759754	+	1.31593i	−0.942976	+	0.332861i	$0.891986\pi$
$888$		0			0
$889$		0			0
$890$	32.0000			1.07264
$891$	−4.50000	+	7.79423i	−0.150756	+	0.261116i
$892$	1.41421	+	2.44949i	0.0473514	+	0.0820150i
$893$	12.0000	+	20.7846i	0.401565	+	0.695530i
$894$		0			0
$895$	−33.9411			−1.13453
$896$		0			0
$897$		0			0
$898$	−3.00000	+	5.19615i	−0.100111	+	0.173398i
$899$	25.4558	+	44.0908i	0.849000	+	1.47051i
$900$	4.50000	+	7.79423i	0.150000	+	0.259808i
$901$	8.48528	−	14.6969i	0.282686	−	0.489626i
$902$	−8.48528			−0.282529
$903$		0			0
$904$	6.00000			0.199557
$905$	12.0000	−	20.7846i	0.398893	−	0.690904i
$906$		0			0
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	0.948278	−	0.317441i	$-0.102824\pi$
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	−0.749051	+	0.662512i	$0.769490\pi$
$908$	1.41421	−	2.44949i	0.0469323	−	0.0812892i
$909$	33.9411			1.12576
$910$		0			0
$911$	32.0000			1.06021			0.530104	−	0.847933i	$-0.322153\pi$
$911$	32.0000			1.06021			0.530104	+	0.847933i	$0.322153\pi$
$912$		0			0
$913$	−1.41421	−	2.44949i	−0.0468036	−	0.0810663i
$914$	5.00000	+	8.66025i	0.165385	+	0.286456i
$915$		0			0
$916$	14.1421			0.467269
$917$		0			0
$918$		0			0
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$	−11.3137	−	19.5959i	−0.373002	−	0.646058i
$921$		0			0
$922$	−5.65685	+	9.79796i	−0.186299	+	0.322679i
$923$		0			0
$924$		0			0
$925$	−18.0000			−0.591836
$926$	−12.0000	+	20.7846i	−0.394344	+	0.683025i
$927$	21.2132	+	36.7423i	0.696733	+	1.20678i
$928$	−3.00000	−	5.19615i	−0.0984798	−	0.170572i
$929$	−5.65685	+	9.79796i	−0.185595	+	0.321461i	−0.943777	−	0.330583i	$-0.892755\pi$
$929$	−5.65685	+	9.79796i	−0.185595	+	0.321461i	0.758182	+	0.652043i	$0.226088\pi$
$930$		0			0
$931$		0			0
$932$	−26.0000			−0.851658
$933$		0			0
$934$	−16.9706	−	29.3939i	−0.555294	−	0.961797i
$935$	4.00000	+	6.92820i	0.130814	+	0.226576i
$936$	8.48528	−	14.6969i	0.277350	−	0.480384i
$937$	19.7990			0.646805			0.323402	−	0.946262i	$-0.395173\pi$
$937$	19.7990			0.646805			0.323402	+	0.946262i	$0.395173\pi$
$938$		0			0
$939$		0			0
$940$	−4.00000	+	6.92820i	−0.130466	+	0.225973i
$941$	25.4558	+	44.0908i	0.829837	+	1.43732i	0.898166	+	0.439657i	$0.144900\pi$
$941$	25.4558	+	44.0908i	0.829837	+	1.43732i	−0.0683291	+	0.997663i	$0.521767\pi$
$942$		0			0
$943$	33.9411	−	58.7878i	1.10528	−	1.91439i
$944$	5.65685			0.184115
$945$		0			0
$946$	4.00000			0.130051
$947$	−26.0000	+	45.0333i	−0.844886	+	1.46339i	0.0408333	+	0.999166i	$0.486999\pi$
$947$	−26.0000	+	45.0333i	−0.844886	+	1.46339i	−0.885720	+	0.464220i	$0.846335\pi$
$948$		0			0
$949$	24.0000	+	41.5692i	0.779073	+	1.34939i
$950$	−12.7279	+	22.0454i	−0.412948	+	0.715247i
$951$		0			0
$952$		0			0
$953$	42.0000			1.36051			0.680257	−	0.732974i	$-0.261868\pi$
$953$	42.0000			1.36051			0.680257	+	0.732974i	$0.261868\pi$
$954$	−9.00000	+	15.5885i	−0.291386	+	0.504695i
$955$	11.3137	+	19.5959i	0.366103	+	0.634109i
$956$	−12.0000	−	20.7846i	−0.388108	−	0.672222i
$957$		0			0
$958$	11.3137			0.365529
$959$		0			0
$960$		0			0
$961$	−20.5000	+	35.5070i	−0.661290	+	1.14539i
$962$	16.9706	+	29.3939i	0.547153	+	0.947697i
$963$	6.00000	+	10.3923i	0.193347	+	0.334887i
$964$	1.41421	−	2.44949i	0.0455488	−	0.0788928i
$965$	−39.5980			−1.27470
$966$		0			0
$967$	−40.0000			−1.28631			−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000			−1.28631			−0.643157	+	0.765735i	$0.722376\pi$
$968$	0.500000	−	0.866025i	0.0160706	−	0.0278351i
$969$		0			0
$970$	−16.0000	−	27.7128i	−0.513729	−	0.889805i
$971$	5.65685	−	9.79796i	0.181537	−	0.314431i	−0.760867	−	0.648908i	$-0.775226\pi$
$971$	5.65685	−	9.79796i	0.181537	−	0.314431i	0.942404	+	0.334476i	$0.108559\pi$
$972$		0			0
$973$		0			0
$974$	−8.00000			−0.256337
$975$		0			0
$976$	−2.82843	−	4.89898i	−0.0905357	−	0.156813i
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	0.973317	−	0.229465i	$-0.0736978\pi$
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	−0.685381	+	0.728184i	$0.740364\pi$
$978$		0			0
$979$	−11.3137			−0.361588
$980$		0			0
$981$	42.0000			1.34096
$982$	−6.00000	+	10.3923i	−0.191468	+	0.331632i
$983$	−24.0416	−	41.6413i	−0.766809	−	1.32815i	−0.939285	−	0.343138i	$-0.888510\pi$
$983$	−24.0416	−	41.6413i	−0.766809	−	1.32815i	0.172476	−	0.985014i	$-0.444823\pi$
$984$		0			0
$985$	25.4558	−	44.0908i	0.811091	−	1.40485i
$986$	−16.9706			−0.540453
$987$		0			0
$988$	48.0000			1.52708
$989$	−16.0000	+	27.7128i	−0.508770	+	0.881216i
$990$	−4.24264	−	7.34847i	−0.134840	−	0.233550i
$991$	−12.0000	−	20.7846i	−0.381193	−	0.660245i	0.610040	−	0.792370i	$-0.291153\pi$
$991$	−12.0000	−	20.7846i	−0.381193	−	0.660245i	−0.991233	+	0.132125i	$0.957820\pi$
$992$	4.24264	−	7.34847i	0.134704	−	0.233314i
$993$		0			0
$994$		0			0
$995$	40.0000			1.26809
$996$		0			0
$997$	5.65685	+	9.79796i	0.179154	+	0.310304i	0.941591	−	0.336758i	$-0.109331\pi$
$997$	5.65685	+	9.79796i	0.179154	+	0.310304i	−0.762437	+	0.647063i	$0.775997\pi$
$998$	22.0000	+	38.1051i	0.696398	+	1.20620i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.e.u.177.1		4
7.2	even	3		1078.2.a.o.1.2	yes	2
7.3	odd	6	inner	1078.2.e.u.67.2		4
7.4	even	3	inner	1078.2.e.u.67.1		4
7.5	odd	6		1078.2.a.o.1.1	✓	2
7.6	odd	2	inner	1078.2.e.u.177.2		4
21.2	odd	6		9702.2.a.dk.1.1		2
21.5	even	6		9702.2.a.dk.1.2		2
28.19	even	6		8624.2.a.bo.1.1		2
28.23	odd	6		8624.2.a.bo.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1078.2.a.o.1.1	✓	2	7.5	odd	6
1078.2.a.o.1.2	yes	2	7.2	even	3
1078.2.e.u.67.1		4	7.4	even	3	inner
1078.2.e.u.67.2		4	7.3	odd	6	inner
1078.2.e.u.177.1		4	1.1	even	1	trivial
1078.2.e.u.177.2		4	7.6	odd	2	inner
8624.2.a.bo.1.1		2	28.19	even	6
8624.2.a.bo.1.2		2	28.23	odd	6
9702.2.a.dk.1.1		2	21.2	odd	6
9702.2.a.dk.1.2		2	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.41421 + 2.44949i) q^{5} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.41421 + 2.44949i) q^{5} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(1.41421 + 2.44949i) q^{10} +(-0.500000 - 0.866025i) q^{11} -5.65685 q^{13} +(-0.500000 + 0.866025i) q^{16} +(1.41421 + 2.44949i) q^{17} +(-1.50000 - 2.59808i) q^{18} +(4.24264 - 7.34847i) q^{19} +2.82843 q^{20} -1.00000 q^{22} +(4.00000 - 6.92820i) q^{23} +(-1.50000 - 2.59808i) q^{25} +(-2.82843 + 4.89898i) q^{26} -6.00000 q^{29} +(-4.24264 - 7.34847i) q^{31} +(0.500000 + 0.866025i) q^{32} +2.82843 q^{34} -3.00000 q^{36} +(3.00000 - 5.19615i) q^{37} +(-4.24264 - 7.34847i) q^{38} +(1.41421 - 2.44949i) q^{40} +8.48528 q^{41} -4.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(4.24264 + 7.34847i) q^{45} +(-4.00000 - 6.92820i) q^{46} +(-1.41421 + 2.44949i) q^{47} -3.00000 q^{50} +(2.82843 + 4.89898i) q^{52} +(-3.00000 - 5.19615i) q^{53} +2.82843 q^{55} +(-3.00000 + 5.19615i) q^{58} +(-2.82843 - 4.89898i) q^{59} +(-2.82843 + 4.89898i) q^{61} -8.48528 q^{62} +1.00000 q^{64} +(8.00000 - 13.8564i) q^{65} +(2.00000 + 3.46410i) q^{67} +(1.41421 - 2.44949i) q^{68} +(-1.50000 + 2.59808i) q^{72} +(-4.24264 - 7.34847i) q^{73} +(-3.00000 - 5.19615i) q^{74} -8.48528 q^{76} +(-1.41421 - 2.44949i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(4.24264 - 7.34847i) q^{82} +2.82843 q^{83} -8.00000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(0.500000 + 0.866025i) q^{88} +(5.65685 - 9.79796i) q^{89} +8.48528 q^{90} -8.00000 q^{92} +(1.41421 + 2.44949i) q^{94} +(12.0000 + 20.7846i) q^{95} -11.3137 q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 + 6 * q^9	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 6 q^{9} - 2 q^{11} - 2 q^{16} - 6 q^{18} - 4 q^{22} + 16 q^{23} - 6 q^{25} - 24 q^{29} + 2 q^{32} - 12 q^{36} + 12 q^{37} - 16 q^{43} - 2 q^{44} - 16 q^{46} - 12 q^{50} - 12 q^{53} - 12 q^{58} + 4 q^{64} + 32 q^{65} + 8 q^{67} - 6 q^{72} - 12 q^{74} - 18 q^{81} - 32 q^{85} - 8 q^{86} + 2 q^{88} - 32 q^{92} + 48 q^{95} - 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 + 6 * q^9 - 2 * q^11 - 2 * q^16 - 6 * q^18 - 4 * q^22 + 16 * q^23 - 6 * q^25 - 24 * q^29 + 2 * q^32 - 12 * q^36 + 12 * q^37 - 16 * q^43 - 2 * q^44 - 16 * q^46 - 12 * q^50 - 12 * q^53 - 12 * q^58 + 4 * q^64 + 32 * q^65 + 8 * q^67 - 6 * q^72 - 12 * q^74 - 18 * q^81 - 32 * q^85 - 8 * q^86 + 2 * q^88 - 32 * q^92 + 48 * q^95 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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