LMFDB - Embedded newform 1134.2.m.g.755.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(377,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("1134.377");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.m (of order $6$, 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:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			755.3
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1134.755
Dual form			1134.2.m.g.377.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.22474 - 2.12132i) q^{5} +(-1.62132 - 2.09077i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.22474 - 2.12132i) q^{5} +(-1.62132 - 2.09077i) q^{7} +1.00000i q^{8} -2.44949i q^{10} +(-2.12132 + 1.22474i) q^{13} +(-0.358719 - 2.62132i) q^{14} +(-0.500000 + 0.866025i) q^{16} -4.89898 q^{17} +2.44949i q^{19} +(1.22474 - 2.12132i) q^{20} +(-5.19615 + 3.00000i) q^{23} +(-0.500000 + 0.866025i) q^{25} -2.44949 q^{26} +(1.00000 - 2.44949i) q^{28} +(-5.19615 - 3.00000i) q^{29} +(-0.866025 + 0.500000i) q^{32} +(-4.24264 - 2.44949i) q^{34} +(-2.44949 + 6.00000i) q^{35} -2.00000 q^{37} +(-1.22474 + 2.12132i) q^{38} +(2.12132 - 1.22474i) q^{40} +(-2.44949 - 4.24264i) q^{41} +(-2.00000 + 3.46410i) q^{43} -6.00000 q^{46} +(2.44949 - 4.24264i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-2.12132 - 1.22474i) q^{52} -6.00000i q^{53} +(2.09077 - 1.62132i) q^{56} +(-3.00000 - 5.19615i) q^{58} +(-6.12372 - 10.6066i) q^{59} +(10.6066 + 6.12372i) q^{61} -1.00000 q^{64} +(5.19615 + 3.00000i) q^{65} +(-4.00000 - 6.92820i) q^{67} +(-2.44949 - 4.24264i) q^{68} +(-5.12132 + 3.97141i) q^{70} +9.79796i q^{73} +(-1.73205 - 1.00000i) q^{74} +(-2.12132 + 1.22474i) q^{76} +(5.00000 - 8.66025i) q^{79} +2.44949 q^{80} -4.89898i q^{82} +(1.22474 - 2.12132i) q^{83} +(6.00000 + 10.3923i) q^{85} +(-3.46410 + 2.00000i) q^{86} +(6.00000 + 2.44949i) q^{91} +(-5.19615 - 3.00000i) q^{92} +(4.24264 - 2.44949i) q^{94} +(5.19615 - 3.00000i) q^{95} +(-4.24264 - 2.44949i) q^{97} +(-4.89898 + 5.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^4 + 4 * q^7	$ 8 q + 4 q^{4} + 4 q^{7} - 4 q^{16} - 4 q^{25} + 8 q^{28} - 16 q^{37} - 16 q^{43} - 48 q^{46} + 20 q^{49} - 24 q^{58} - 8 q^{64} - 32 q^{67} - 24 q^{70} + 40 q^{79} + 48 q^{85} + 48 q^{91}+O(q^{100}) $ 8 * q + 4 * q^4 + 4 * q^7 - 4 * q^16 - 4 * q^25 + 8 * q^28 - 16 * q^37 - 16 * q^43 - 48 * q^46 + 20 * q^49 - 24 * q^58 - 8 * q^64 - 32 * q^67 - 24 * q^70 + 40 * q^79 + 48 * q^85 + 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.22474	−	2.12132i	−0.547723	−	0.948683i	−0.998430	−	0.0560116i	$-0.982162\pi$
$5$	−1.22474	−	2.12132i	−0.547723	−	0.948683i	0.450708	−	0.892672i	$-0.351172\pi$
$6$		0			0
$7$	−1.62132	−	2.09077i	−0.612801	−	0.790237i
$7$	−1.62132	−	2.09077i	−0.612801	−	0.790237i
$8$			1.00000i			0.353553i
$9$		0			0
$10$		−	2.44949i		−	0.774597i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$		0			0
$13$	−2.12132	+	1.22474i	−0.588348	+	0.339683i	−0.764444	−	0.644690i	$-0.776986\pi$
$13$	−2.12132	+	1.22474i	−0.588348	+	0.339683i	0.176096	+	0.984373i	$0.443653\pi$
$14$	−0.358719	−	2.62132i	−0.0958718	−	0.700577i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.89898			−1.18818			−0.594089	−	0.804400i	$-0.702487\pi$
$17$	−4.89898			−1.18818			−0.594089	+	0.804400i	$0.702487\pi$
$18$		0			0
$19$			2.44949i			0.561951i	0.959715	+	0.280976i	$0.0906580\pi$
$19$			2.44949i			0.561951i	−0.959715	+	0.280976i	$0.909342\pi$
$20$	1.22474	−	2.12132i	0.273861	−	0.474342i
$21$		0			0
$22$		0			0
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.931831	−	0.362892i	$-0.881789\pi$
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.151642	+	0.988436i	$0.548456\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.44949			−0.480384
$27$		0			0
$28$	1.00000	−	2.44949i	0.188982	−	0.462910i
$29$	−5.19615	−	3.00000i	−0.964901	−	0.557086i	−0.0672232	−	0.997738i	$-0.521414\pi$
$29$	−5.19615	−	3.00000i	−0.964901	−	0.557086i	−0.897678	+	0.440652i	$0.854747\pi$
$30$		0			0
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−4.24264	−	2.44949i	−0.727607	−	0.420084i
$35$	−2.44949	+	6.00000i	−0.414039	+	1.01419i
$36$		0			0
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	−1.22474	+	2.12132i	−0.198680	+	0.344124i
$39$		0			0
$40$	2.12132	−	1.22474i	0.335410	−	0.193649i
$41$	−2.44949	−	4.24264i	−0.382546	−	0.662589i	0.608879	−	0.793263i	$-0.291619\pi$
$41$	−2.44949	−	4.24264i	−0.382546	−	0.662589i	−0.991425	+	0.130674i	$0.958286\pi$
$42$		0			0
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	−0.977261	−	0.212041i	$-0.931989\pi$
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	0.672264	+	0.740312i	$0.265322\pi$
$44$		0			0
$45$		0			0
$46$	−6.00000			−0.884652
$47$	2.44949	−	4.24264i	0.357295	−	0.618853i	−0.630213	−	0.776422i	$-0.717032\pi$
$47$	2.44949	−	4.24264i	0.357295	−	0.618853i	0.987508	+	0.157569i	$0.0503658\pi$
$48$		0			0
$49$	−1.74264	+	6.77962i	−0.248949	+	0.968517i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		0			0
$52$	−2.12132	−	1.22474i	−0.294174	−	0.169842i
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$		0			0
$55$		0			0
$56$	2.09077	−	1.62132i	0.279391	−	0.216658i
$57$		0			0
$58$	−3.00000	−	5.19615i	−0.393919	−	0.682288i
$59$	−6.12372	−	10.6066i	−0.797241	−	1.38086i	−0.921406	−	0.388600i	$-0.872959\pi$
$59$	−6.12372	−	10.6066i	−0.797241	−	1.38086i	0.124165	−	0.992262i	$-0.460375\pi$
$60$		0			0
$61$	10.6066	+	6.12372i	1.35804	+	0.784063i	0.989359	−	0.145495i	$-0.0464774\pi$
$61$	10.6066	+	6.12372i	1.35804	+	0.784063i	0.368677	+	0.929557i	$0.379811\pi$
$62$		0			0
$63$		0			0
$64$	−1.00000			−0.125000
$65$	5.19615	+	3.00000i	0.644503	+	0.372104i
$66$		0			0
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	−2.44949	−	4.24264i	−0.297044	−	0.514496i
$69$		0			0
$70$	−5.12132	+	3.97141i	−0.612115	+	0.474674i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$			9.79796i			1.14676i	0.819288	+	0.573382i	$0.194369\pi$
$73$			9.79796i			1.14676i	−0.819288	+	0.573382i	$0.805631\pi$
$74$	−1.73205	−	1.00000i	−0.201347	−	0.116248i
$75$		0			0
$76$	−2.12132	+	1.22474i	−0.243332	+	0.140488i
$77$		0			0
$78$		0			0
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	−0.434730	−	0.900561i	$-0.643156\pi$
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	0.997274	−	0.0737937i	$-0.0235106\pi$
$80$	2.44949			0.273861
$81$		0			0
$82$		−	4.89898i		−	0.541002i
$83$	1.22474	−	2.12132i	0.134433	−	0.232845i	−0.790948	−	0.611884i	$-0.790412\pi$
$83$	1.22474	−	2.12132i	0.134433	−	0.232845i	0.925381	+	0.379039i	$0.123745\pi$
$84$		0			0
$85$	6.00000	+	10.3923i	0.650791	+	1.12720i
$86$	−3.46410	+	2.00000i	−0.373544	+	0.215666i
$87$		0			0
$88$		0			0
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$		0			0
$91$	6.00000	+	2.44949i	0.628971	+	0.256776i
$92$	−5.19615	−	3.00000i	−0.541736	−	0.312772i
$93$		0			0
$94$	4.24264	−	2.44949i	0.437595	−	0.252646i
$95$	5.19615	−	3.00000i	0.533114	−	0.307794i
$96$		0			0
$97$	−4.24264	−	2.44949i	−0.430775	−	0.248708i	0.268902	−	0.963168i	$-0.413339\pi$
$97$	−4.24264	−	2.44949i	−0.430775	−	0.248708i	−0.699677	+	0.714460i	$0.746673\pi$
$98$	−4.89898	+	5.00000i	−0.494872	+	0.505076i
$99$		0			0
$100$	−1.00000			−0.100000
$101$	3.67423	−	6.36396i	0.365600	−	0.633238i	−0.623272	−	0.782005i	$-0.714197\pi$
$101$	3.67423	−	6.36396i	0.365600	−	0.633238i	0.988872	+	0.148767i	$0.0475305\pi$
$102$		0			0
$103$	8.48528	−	4.89898i	0.836080	−	0.482711i	−0.0198501	−	0.999803i	$-0.506319\pi$
$103$	8.48528	−	4.89898i	0.836080	−	0.482711i	0.855930	+	0.517092i	$0.172986\pi$
$104$	−1.22474	−	2.12132i	−0.120096	−	0.208013i
$105$		0			0
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$			12.0000i			1.16008i	0.814587	+	0.580042i	$0.196964\pi$
$107$			12.0000i			1.16008i	−0.814587	+	0.580042i	$0.803036\pi$
$108$		0			0
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$		0			0
$111$		0			0
$112$	2.62132	−	0.358719i	0.247691	−	0.0338958i
$113$	−5.19615	+	3.00000i	−0.488813	+	0.282216i	−0.724082	−	0.689714i	$-0.757736\pi$
$113$	−5.19615	+	3.00000i	−0.488813	+	0.282216i	0.235269	+	0.971930i	$0.424403\pi$
$114$		0			0
$115$	12.7279	+	7.34847i	1.18688	+	0.685248i
$116$		−	6.00000i		−	0.557086i
$117$		0			0
$118$		−	12.2474i		−	1.12747i
$119$	7.94282	+	10.2426i	0.728117	+	0.938941i
$120$		0			0
$121$	−5.50000	−	9.52628i	−0.500000	−	0.866025i
$122$	6.12372	+	10.6066i	0.554416	+	0.960277i
$123$		0			0
$124$		0			0
$125$	−9.79796			−0.876356
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	3.00000	+	5.19615i	0.263117	+	0.455733i
$131$	3.67423	+	6.36396i	0.321019	+	0.556022i	0.980699	−	0.195525i	$-0.0626412\pi$
$131$	3.67423	+	6.36396i	0.321019	+	0.556022i	−0.659679	+	0.751547i	$0.729308\pi$
$132$		0			0
$133$	5.12132	−	3.97141i	0.444075	−	0.344365i
$134$		−	8.00000i		−	0.691095i
$135$		0			0
$136$		−	4.89898i		−	0.420084i
$137$	−10.3923	−	6.00000i	−0.887875	−	0.512615i	−0.0146279	−	0.999893i	$-0.504656\pi$
$137$	−10.3923	−	6.00000i	−0.887875	−	0.512615i	−0.873247	+	0.487278i	$0.837990\pi$
$138$		0			0
$139$	2.12132	−	1.22474i	0.179928	−	0.103882i	−0.407331	−	0.913281i	$-0.633540\pi$
$139$	2.12132	−	1.22474i	0.179928	−	0.103882i	0.587259	+	0.809399i	$0.300207\pi$
$140$	−6.42090	+	0.878680i	−0.542665	+	0.0742620i
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$			14.6969i			1.22051i
$146$	−4.89898	+	8.48528i	−0.405442	+	0.702247i
$147$		0			0
$148$	−1.00000	−	1.73205i	−0.0821995	−	0.142374i
$149$	5.19615	−	3.00000i	0.425685	−	0.245770i	−0.271821	−	0.962348i	$-0.587626\pi$
$149$	5.19615	−	3.00000i	0.425685	−	0.245770i	0.697507	+	0.716578i	$0.254293\pi$
$150$		0			0
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	0.981617	+	0.190864i	$0.0611289\pi$
$152$	−2.44949			−0.198680
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−6.36396	+	3.67423i	−0.507899	+	0.293236i	−0.731970	−	0.681337i	$-0.761399\pi$
$157$	−6.36396	+	3.67423i	−0.507899	+	0.293236i	0.224070	+	0.974573i	$0.428065\pi$
$158$	8.66025	−	5.00000i	0.688973	−	0.397779i
$159$		0			0
$160$	2.12132	+	1.22474i	0.167705	+	0.0968246i
$161$	14.6969	+	6.00000i	1.15828	+	0.472866i
$162$		0			0
$163$	−16.0000			−1.25322			−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000			−1.25322			−0.626608	+	0.779334i	$0.715557\pi$
$164$	2.44949	−	4.24264i	0.191273	−	0.331295i
$165$		0			0
$166$	2.12132	−	1.22474i	0.164646	−	0.0950586i
$167$	2.44949	+	4.24264i	0.189547	+	0.328305i	0.945099	−	0.326783i	$-0.105965\pi$
$167$	2.44949	+	4.24264i	0.189547	+	0.328305i	−0.755552	+	0.655089i	$0.772631\pi$
$168$		0			0
$169$	−3.50000	+	6.06218i	−0.269231	+	0.466321i
$170$			12.0000i			0.920358i
$171$		0			0
$172$	−4.00000			−0.304997
$173$	−11.0227	+	19.0919i	−0.838041	+	1.45153i	0.0534899	+	0.998568i	$0.482966\pi$
$173$	−11.0227	+	19.0919i	−0.838041	+	1.45153i	−0.891531	+	0.452961i	$0.850368\pi$
$174$		0			0
$175$	2.62132	−	0.358719i	0.198153	−	0.0271166i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	24.0000i		−	1.79384i	−0.442189	−	0.896922i	$-0.645798\pi$
$179$		−	24.0000i		−	1.79384i	0.442189	−	0.896922i	$-0.354202\pi$
$180$		0			0
$181$			12.2474i			0.910346i	0.890403	+	0.455173i	$0.150423\pi$
$181$			12.2474i			0.910346i	−0.890403	+	0.455173i	$0.849577\pi$
$182$	3.97141	+	5.12132i	0.294380	+	0.379618i
$183$		0			0
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$	2.44949	+	4.24264i	0.180090	+	0.311925i
$186$		0			0
$187$		0			0
$188$	4.89898			0.357295
$189$		0			0
$190$	6.00000			0.435286
$191$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$191$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$192$		0			0
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	0.785022	−	0.619467i	$-0.212651\pi$
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	−0.928986	+	0.370116i	$0.879318\pi$
$194$	−2.44949	−	4.24264i	−0.175863	−	0.304604i
$195$		0			0
$196$	−6.74264	+	1.88064i	−0.481617	+	0.134331i
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$		0			0
$199$		−	9.79796i		−	0.694559i	−0.937762	−	0.347279i	$-0.887106\pi$
$199$		−	9.79796i		−	0.694559i	0.937762	−	0.347279i	$-0.112894\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$		0			0
$202$	6.36396	−	3.67423i	0.447767	−	0.258518i
$203$	2.15232	+	15.7279i	0.151063	+	1.10388i
$204$		0			0
$205$	−6.00000	+	10.3923i	−0.419058	+	0.725830i
$206$	9.79796			0.682656
$207$		0			0
$208$		−	2.44949i		−	0.169842i
$209$		0			0
$210$		0			0
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	0.970229	−	0.242190i	$-0.0778659\pi$
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	−0.694857	+	0.719148i	$0.744533\pi$
$212$	5.19615	−	3.00000i	0.356873	−	0.206041i
$213$		0			0
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$	9.79796			0.668215
$216$		0			0
$217$		0			0
$218$	8.66025	+	5.00000i	0.586546	+	0.338643i
$219$		0			0
$220$		0			0
$221$	10.3923	−	6.00000i	0.699062	−	0.403604i
$222$		0			0
$223$	12.7279	+	7.34847i	0.852325	+	0.492090i	0.861435	−	0.507869i	$-0.169566\pi$
$223$	12.7279	+	7.34847i	0.852325	+	0.492090i	−0.00910984	+	0.999959i	$0.502900\pi$
$224$	2.44949	+	1.00000i	0.163663	+	0.0668153i
$225$		0			0
$226$	−6.00000			−0.399114
$227$	−3.67423	+	6.36396i	−0.243868	+	0.422391i	−0.961813	−	0.273709i	$-0.911750\pi$
$227$	−3.67423	+	6.36396i	−0.243868	+	0.422391i	0.717945	+	0.696100i	$0.245083\pi$
$228$		0			0
$229$	−19.0919	+	11.0227i	−1.26163	+	0.728401i	−0.973389	−	0.229158i	$-0.926403\pi$
$229$	−19.0919	+	11.0227i	−1.26163	+	0.728401i	−0.288238	+	0.957559i	$0.593069\pi$
$230$	7.34847	+	12.7279i	0.484544	+	0.839254i
$231$		0			0
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$			24.0000i			1.57229i	0.618041	+	0.786146i	$0.287927\pi$
$233$			24.0000i			1.57229i	−0.618041	+	0.786146i	$0.712073\pi$
$234$		0			0
$235$	−12.0000			−0.782794
$236$	6.12372	−	10.6066i	0.398621	−	0.690431i
$237$		0			0
$238$	1.75736	+	12.8418i	0.113913	+	0.832410i
$239$	5.19615	−	3.00000i	0.336111	−	0.194054i	−0.322440	−	0.946590i	$-0.604503\pi$
$239$	5.19615	−	3.00000i	0.336111	−	0.194054i	0.658551	+	0.752536i	$0.271170\pi$
$240$		0			0
$241$	−21.2132	−	12.2474i	−1.36646	−	0.788928i	−0.375988	−	0.926624i	$-0.622697\pi$
$241$	−21.2132	−	12.2474i	−1.36646	−	0.788928i	−0.990474	+	0.137697i	$0.956030\pi$
$242$		−	11.0000i		−	0.707107i
$243$		0			0
$244$			12.2474i			0.784063i
$245$	16.5160	−	4.60660i	1.05517	−	0.294305i
$246$		0			0
$247$	−3.00000	−	5.19615i	−0.190885	−	0.330623i
$248$		0			0
$249$		0			0
$250$	−8.48528	−	4.89898i	−0.536656	−	0.309839i
$251$	17.1464			1.08227			0.541136	−	0.840935i	$-0.317994\pi$
$251$	17.1464			1.08227			0.541136	+	0.840935i	$0.317994\pi$
$252$		0			0
$253$		0			0
$254$	6.92820	+	4.00000i	0.434714	+	0.250982i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	14.6969	+	25.4558i	0.916770	+	1.58789i	0.804289	+	0.594238i	$0.202546\pi$
$257$	14.6969	+	25.4558i	0.916770	+	1.58789i	0.112481	+	0.993654i	$0.464120\pi$
$258$		0			0
$259$	3.24264	+	4.18154i	0.201488	+	0.259828i
$260$			6.00000i			0.372104i
$261$		0			0
$262$			7.34847i			0.453990i
$263$	−20.7846	−	12.0000i	−1.28163	−	0.739952i	−0.304487	−	0.952517i	$-0.598485\pi$
$263$	−20.7846	−	12.0000i	−1.28163	−	0.739952i	−0.977147	+	0.212565i	$0.931818\pi$
$264$		0			0
$265$	−12.7279	+	7.34847i	−0.781870	+	0.451413i
$266$	6.42090	−	0.878680i	0.393690	−	0.0538753i
$267$		0			0
$268$	4.00000	−	6.92820i	0.244339	−	0.423207i
$269$	12.2474			0.746740			0.373370	−	0.927682i	$-0.378202\pi$
$269$	12.2474			0.746740			0.373370	+	0.927682i	$0.378202\pi$
$270$		0			0
$271$		−	24.4949i		−	1.48796i	−0.668202	−	0.743980i	$-0.732936\pi$
$271$		−	24.4949i		−	1.48796i	0.668202	−	0.743980i	$-0.267064\pi$
$272$	2.44949	−	4.24264i	0.148522	−	0.257248i
$273$		0			0
$274$	−6.00000	−	10.3923i	−0.362473	−	0.627822i
$275$		0			0
$276$		0			0
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	−0.319447	−	0.947604i	$-0.603497\pi$
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	0.980373	−	0.197153i	$-0.0631696\pi$
$278$	2.44949			0.146911
$279$		0			0
$280$	−6.00000	−	2.44949i	−0.358569	−	0.146385i
$281$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$281$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$282$		0			0
$283$	19.0919	−	11.0227i	1.13489	−	0.655232i	0.189733	−	0.981836i	$-0.439238\pi$
$283$	19.0919	−	11.0227i	1.13489	−	0.655232i	0.945161	+	0.326604i	$0.105904\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.89898	+	12.0000i	−0.289178	+	0.708338i
$288$		0			0
$289$	7.00000			0.411765
$290$	−7.34847	+	12.7279i	−0.431517	+	0.747409i
$291$		0			0
$292$	−8.48528	+	4.89898i	−0.496564	+	0.286691i
$293$	1.22474	+	2.12132i	0.0715504	+	0.123929i	0.899581	−	0.436754i	$-0.143872\pi$
$293$	1.22474	+	2.12132i	0.0715504	+	0.123929i	−0.828031	+	0.560683i	$0.810539\pi$
$294$		0			0
$295$	−15.0000	+	25.9808i	−0.873334	+	1.51266i
$296$		−	2.00000i		−	0.116248i
$297$		0			0
$298$	6.00000			0.347571
$299$	7.34847	−	12.7279i	0.424973	−	0.736075i
$300$		0			0
$301$	10.4853	−	1.43488i	0.604362	−	0.0827050i
$302$	6.92820	−	4.00000i	0.398673	−	0.230174i
$303$		0			0
$304$	−2.12132	−	1.22474i	−0.121666	−	0.0702439i
$305$		−	30.0000i		−	1.71780i
$306$		0			0
$307$		−	7.34847i		−	0.419399i	−0.977766	−	0.209700i	$-0.932751\pi$
$307$		−	7.34847i		−	0.419399i	0.977766	−	0.209700i	$-0.0672486\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	9.79796	+	16.9706i	0.555591	+	0.962312i	0.997857	+	0.0654284i	$0.0208414\pi$
$311$	9.79796	+	16.9706i	0.555591	+	0.962312i	−0.442266	+	0.896884i	$0.645825\pi$
$312$		0			0
$313$	−29.6985	−	17.1464i	−1.67866	−	0.969173i	−0.962519	−	0.271216i	$-0.912574\pi$
$313$	−29.6985	−	17.1464i	−1.67866	−	0.969173i	−0.716139	−	0.697958i	$-0.754092\pi$
$314$	−7.34847			−0.414698
$315$		0			0
$316$	10.0000			0.562544
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.869184	−	0.494489i	$-0.164645\pi$
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.00635137	+	0.999980i	$0.497978\pi$
$318$		0			0
$319$		0			0
$320$	1.22474	+	2.12132i	0.0684653	+	0.118585i
$321$		0			0
$322$	9.72792	+	12.5446i	0.542116	+	0.699084i
$323$		−	12.0000i		−	0.667698i
$324$		0			0
$325$		−	2.44949i		−	0.135873i
$326$	−13.8564	−	8.00000i	−0.767435	−	0.443079i
$327$		0			0
$328$	4.24264	−	2.44949i	0.234261	−	0.135250i
$329$	−12.8418	+	1.75736i	−0.707991	+	0.0968864i
$330$		0			0
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	−0.734905	−	0.678170i	$-0.762773\pi$
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	0.954765	+	0.297361i	$0.0961066\pi$
$332$	2.44949			0.134433
$333$		0			0
$334$			4.89898i			0.268060i
$335$	−9.79796	+	16.9706i	−0.535320	+	0.927201i
$336$		0			0
$337$	16.0000	+	27.7128i	0.871576	+	1.50961i	0.860366	+	0.509676i	$0.170235\pi$
$337$	16.0000	+	27.7128i	0.871576	+	1.50961i	0.0112091	+	0.999937i	$0.496432\pi$
$338$	−6.06218	+	3.50000i	−0.329739	+	0.190375i
$339$		0			0
$340$	−6.00000	+	10.3923i	−0.325396	+	0.563602i
$341$		0			0
$342$		0			0
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$	−3.46410	−	2.00000i	−0.186772	−	0.107833i
$345$		0			0
$346$	−19.0919	+	11.0227i	−1.02639	+	0.592584i
$347$	10.3923	−	6.00000i	0.557888	−	0.322097i	−0.194409	−	0.980921i	$-0.562279\pi$
$347$	10.3923	−	6.00000i	0.557888	−	0.322097i	0.752297	+	0.658824i	$0.228946\pi$
$348$		0			0
$349$	−2.12132	−	1.22474i	−0.113552	−	0.0655591i	0.442149	−	0.896942i	$-0.354216\pi$
$349$	−2.12132	−	1.22474i	−0.113552	−	0.0655591i	−0.555700	+	0.831383i	$0.687550\pi$
$350$	2.44949	+	1.00000i	0.130931	+	0.0534522i
$351$		0			0
$352$		0			0
$353$	−4.89898	+	8.48528i	−0.260746	+	0.451626i	−0.966440	−	0.256891i	$-0.917302\pi$
$353$	−4.89898	+	8.48528i	−0.260746	+	0.451626i	0.705694	+	0.708517i	$0.250635\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	12.0000	−	20.7846i	0.634220	−	1.09850i
$359$			6.00000i			0.316668i	0.987386	+	0.158334i	$0.0506123\pi$
$359$			6.00000i			0.316668i	−0.987386	+	0.158334i	$0.949388\pi$
$360$		0			0
$361$	13.0000			0.684211
$362$	−6.12372	+	10.6066i	−0.321856	+	0.557471i
$363$		0			0
$364$	0.878680	+	6.42090i	0.0460553	+	0.336546i
$365$	20.7846	−	12.0000i	1.08792	−	0.628109i
$366$		0			0
$367$	−4.24264	−	2.44949i	−0.221464	−	0.127862i	0.385164	−	0.922848i	$-0.374145\pi$
$367$	−4.24264	−	2.44949i	−0.221464	−	0.127862i	−0.606628	+	0.794986i	$0.707478\pi$
$368$		−	6.00000i		−	0.312772i
$369$		0			0
$370$			4.89898i			0.254686i
$371$	−12.5446	+	9.72792i	−0.651284	+	0.505049i
$372$		0			0
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	0.625917	−	0.779890i	$-0.284725\pi$
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	−0.988363	+	0.152115i	$0.951392\pi$
$374$		0			0
$375$		0			0
$376$	4.24264	+	2.44949i	0.218797	+	0.126323i
$377$	14.6969			0.756931
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	5.19615	+	3.00000i	0.266557	+	0.153897i
$381$		0			0
$382$		0			0
$383$	−17.1464	−	29.6985i	−0.876142	−	1.51752i	−0.855542	−	0.517734i	$-0.826776\pi$
$383$	−17.1464	−	29.6985i	−0.876142	−	1.51752i	−0.0205998	−	0.999788i	$-0.506558\pi$
$384$		0			0
$385$		0			0
$386$		−	4.00000i		−	0.203595i
$387$		0			0
$388$		−	4.89898i		−	0.248708i
$389$	−5.19615	−	3.00000i	−0.263455	−	0.152106i	0.362454	−	0.932002i	$-0.381939\pi$
$389$	−5.19615	−	3.00000i	−0.263455	−	0.152106i	−0.625910	+	0.779895i	$0.715272\pi$
$390$		0			0
$391$	25.4558	−	14.6969i	1.28736	−	0.743256i
$392$	−6.77962	−	1.74264i	−0.342422	−	0.0880166i
$393$		0			0
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$	−24.4949			−1.23247
$396$		0			0
$397$		−	7.34847i		−	0.368809i	−0.982850	−	0.184405i	$-0.940964\pi$
$397$		−	7.34847i		−	0.368809i	0.982850	−	0.184405i	$-0.0590357\pi$
$398$	4.89898	−	8.48528i	0.245564	−	0.425329i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−25.9808	+	15.0000i	−1.29742	+	0.749064i	−0.979957	−	0.199207i	$-0.936163\pi$
$401$	−25.9808	+	15.0000i	−1.29742	+	0.749064i	−0.317460	+	0.948272i	$0.602830\pi$
$402$		0			0
$403$		0			0
$404$	7.34847			0.365600
$405$		0			0
$406$	−6.00000	+	14.6969i	−0.297775	+	0.729397i
$407$		0			0
$408$		0			0
$409$	−29.6985	+	17.1464i	−1.46850	+	0.847836i	−0.999377	−	0.0352988i	$-0.988762\pi$
$409$	−29.6985	+	17.1464i	−1.46850	+	0.847836i	−0.469119	+	0.883135i	$0.655428\pi$
$410$	−10.3923	+	6.00000i	−0.513239	+	0.296319i
$411$		0			0
$412$	8.48528	+	4.89898i	0.418040	+	0.241355i
$413$	−12.2474	+	30.0000i	−0.602658	+	1.47620i
$414$		0			0
$415$	−6.00000			−0.294528
$416$	1.22474	−	2.12132i	0.0600481	−	0.104006i
$417$		0			0
$418$		0			0
$419$	6.12372	+	10.6066i	0.299164	+	0.518166i	0.975945	−	0.218018i	$-0.0699591\pi$
$419$	6.12372	+	10.6066i	0.299164	+	0.518166i	−0.676781	+	0.736184i	$0.736626\pi$
$420$		0			0
$421$	−1.00000	+	1.73205i	−0.0487370	+	0.0844150i	−0.889365	−	0.457198i	$-0.848853\pi$
$421$	−1.00000	+	1.73205i	−0.0487370	+	0.0844150i	0.840628	+	0.541613i	$0.182186\pi$
$422$			8.00000i			0.389434i
$423$		0			0
$424$	6.00000			0.291386
$425$	2.44949	−	4.24264i	0.118818	−	0.205798i
$426$		0			0
$427$	−4.39340	−	32.1045i	−0.212611	−	1.55364i
$428$	−10.3923	+	6.00000i	−0.502331	+	0.290021i
$429$		0			0
$430$	8.48528	+	4.89898i	0.409197	+	0.236250i
$431$		−	30.0000i		−	1.44505i	−0.691345	−	0.722525i	$-0.742982\pi$
$431$		−	30.0000i		−	1.44505i	0.691345	−	0.722525i	$-0.257018\pi$
$432$		0			0
$433$		−	14.6969i		−	0.706290i	−0.935569	−	0.353145i	$-0.885112\pi$
$433$		−	14.6969i		−	0.706290i	0.935569	−	0.353145i	$-0.114888\pi$
$434$		0			0
$435$		0			0
$436$	5.00000	+	8.66025i	0.239457	+	0.414751i
$437$	−7.34847	−	12.7279i	−0.351525	−	0.608859i
$438$		0			0
$439$	−12.7279	−	7.34847i	−0.607471	−	0.350723i	0.164504	−	0.986376i	$-0.447398\pi$
$439$	−12.7279	−	7.34847i	−0.607471	−	0.350723i	−0.771975	+	0.635653i	$0.780731\pi$
$440$		0			0
$441$		0			0
$442$	12.0000			0.570782
$443$	31.1769	+	18.0000i	1.48126	+	0.855206i	0.999774	−	0.0212481i	$-0.00676401\pi$
$443$	31.1769	+	18.0000i	1.48126	+	0.855206i	0.481486	+	0.876454i	$0.340097\pi$
$444$		0			0
$445$		0			0
$446$	7.34847	+	12.7279i	0.347960	+	0.602685i
$447$		0			0
$448$	1.62132	+	2.09077i	0.0766002	+	0.0987796i
$449$			36.0000i			1.69895i	0.527633	+	0.849473i	$0.323080\pi$
$449$			36.0000i			1.69895i	−0.527633	+	0.849473i	$0.676920\pi$
$450$		0			0
$451$		0			0
$452$	−5.19615	−	3.00000i	−0.244406	−	0.141108i
$453$		0			0
$454$	−6.36396	+	3.67423i	−0.298675	+	0.172440i
$455$	−2.15232	−	15.7279i	−0.100902	−	0.737336i
$456$		0			0
$457$	−14.0000	+	24.2487i	−0.654892	+	1.13431i	0.327028	+	0.945015i	$0.393953\pi$
$457$	−14.0000	+	24.2487i	−0.654892	+	1.13431i	−0.981921	+	0.189292i	$0.939381\pi$
$458$	−22.0454			−1.03011
$459$		0			0
$460$			14.6969i			0.685248i
$461$	15.9217	−	27.5772i	0.741547	−	1.28440i	−0.210244	−	0.977649i	$-0.567426\pi$
$461$	15.9217	−	27.5772i	0.741547	−	1.28440i	0.951791	−	0.306748i	$-0.0992408\pi$
$462$		0			0
$463$	−7.00000	−	12.1244i	−0.325318	−	0.563467i	0.656259	−	0.754536i	$-0.272138\pi$
$463$	−7.00000	−	12.1244i	−0.325318	−	0.563467i	−0.981577	+	0.191069i	$0.938805\pi$
$464$	5.19615	−	3.00000i	0.241225	−	0.139272i
$465$		0			0
$466$	−12.0000	+	20.7846i	−0.555889	+	0.962828i
$467$	7.34847			0.340047			0.170023	−	0.985440i	$-0.445616\pi$
$467$	7.34847			0.340047			0.170023	+	0.985440i	$0.445616\pi$
$468$		0			0
$469$	−8.00000	+	19.5959i	−0.369406	+	0.904855i
$470$	−10.3923	−	6.00000i	−0.479361	−	0.276759i
$471$		0			0
$472$	10.6066	−	6.12372i	0.488208	−	0.281867i
$473$		0			0
$474$		0			0
$475$	−2.12132	−	1.22474i	−0.0973329	−	0.0561951i
$476$	−4.89898	+	12.0000i	−0.224544	+	0.550019i
$477$		0			0
$478$	6.00000			0.274434
$479$	12.2474	−	21.2132i	0.559600	−	0.969256i	−0.437929	−	0.899009i	$-0.644288\pi$
$479$	12.2474	−	21.2132i	0.559600	−	0.969256i	0.997530	−	0.0702467i	$-0.0223786\pi$
$480$		0			0
$481$	4.24264	−	2.44949i	0.193448	−	0.111687i
$482$	−12.2474	−	21.2132i	−0.557856	−	0.966235i
$483$		0			0
$484$	5.50000	−	9.52628i	0.250000	−	0.433013i
$485$			12.0000i			0.544892i
$486$		0			0
$487$	−32.0000			−1.45006			−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000			−1.45006			−0.725029	+	0.688718i	$0.758174\pi$
$488$	−6.12372	+	10.6066i	−0.277208	+	0.480138i
$489$		0			0
$490$	16.6066	+	4.26858i	0.750210	+	0.192835i
$491$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$491$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$492$		0			0
$493$	25.4558	+	14.6969i	1.14647	+	0.661917i
$494$		−	6.00000i		−	0.269953i
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	0.998233	−	0.0594153i	$-0.0189236\pi$
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	−0.550572	+	0.834788i	$0.685590\pi$
$500$	−4.89898	−	8.48528i	−0.219089	−	0.379473i
$501$		0			0
$502$	14.8492	+	8.57321i	0.662754	+	0.382641i
$503$	−39.1918			−1.74748			−0.873739	−	0.486395i	$-0.838311\pi$
$503$	−39.1918			−1.74748			−0.873739	+	0.486395i	$0.838311\pi$
$504$		0			0
$505$	−18.0000			−0.800989
$506$		0			0
$507$		0			0
$508$	4.00000	+	6.92820i	0.177471	+	0.307389i
$509$	−6.12372	−	10.6066i	−0.271429	−	0.470129i	0.697799	−	0.716294i	$-0.254163\pi$
$509$	−6.12372	−	10.6066i	−0.271429	−	0.470129i	−0.969228	+	0.246165i	$0.920830\pi$
$510$		0			0
$511$	20.4853	−	15.8856i	0.906215	−	0.702739i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$			29.3939i			1.29651i
$515$	−20.7846	−	12.0000i	−0.915879	−	0.528783i
$516$		0			0
$517$		0			0
$518$	0.717439	+	5.24264i	0.0315225	+	0.230348i
$519$		0			0
$520$	−3.00000	+	5.19615i	−0.131559	+	0.227866i
$521$	4.89898			0.214628			0.107314	−	0.994225i	$-0.465775\pi$
$521$	4.89898			0.214628			0.107314	+	0.994225i	$0.465775\pi$
$522$		0			0
$523$		−	2.44949i		−	0.107109i	−0.998565	−	0.0535544i	$-0.982945\pi$
$523$		−	2.44949i		−	0.107109i	0.998565	−	0.0535544i	$-0.0170550\pi$
$524$	−3.67423	+	6.36396i	−0.160510	+	0.278011i
$525$		0			0
$526$	−12.0000	−	20.7846i	−0.523225	−	0.906252i
$527$		0			0
$528$		0			0
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$	−14.6969			−0.638394
$531$		0			0
$532$	6.00000	+	2.44949i	0.260133	+	0.106199i
$533$	10.3923	+	6.00000i	0.450141	+	0.259889i
$534$		0			0
$535$	25.4558	−	14.6969i	1.10055	−	0.635404i
$536$	6.92820	−	4.00000i	0.299253	−	0.172774i
$537$		0			0
$538$	10.6066	+	6.12372i	0.457283	+	0.264013i
$539$		0			0
$540$		0			0
$541$	2.00000			0.0859867			0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000			0.0859867			0.0429934	+	0.999075i	$0.486311\pi$
$542$	12.2474	−	21.2132i	0.526073	−	0.911185i
$543$		0			0
$544$	4.24264	−	2.44949i	0.181902	−	0.105021i
$545$	−12.2474	−	21.2132i	−0.524623	−	0.908674i
$546$		0			0
$547$	−4.00000	+	6.92820i	−0.171028	+	0.296229i	−0.938779	−	0.344519i	$-0.888042\pi$
$547$	−4.00000	+	6.92820i	−0.171028	+	0.296229i	0.767752	+	0.640747i	$0.221375\pi$
$548$		−	12.0000i		−	0.512615i
$549$		0			0
$550$		0			0
$551$	7.34847	−	12.7279i	0.313055	−	0.542228i
$552$		0			0
$553$	−26.2132	+	3.58719i	−1.11470	+	0.152543i
$554$	19.0526	−	11.0000i	0.809466	−	0.467345i
$555$		0			0
$556$	2.12132	+	1.22474i	0.0899640	+	0.0519408i
$557$		−	18.0000i		−	0.762684i	−0.924434	−	0.381342i	$-0.875462\pi$
$557$		−	18.0000i		−	0.762684i	0.924434	−	0.381342i	$-0.124538\pi$
$558$		0			0
$559$		−	9.79796i		−	0.414410i
$560$	−3.97141	−	5.12132i	−0.167823	−	0.216415i
$561$		0			0
$562$		0			0
$563$	−11.0227	−	19.0919i	−0.464552	−	0.804627i	0.534630	−	0.845087i	$-0.320451\pi$
$563$	−11.0227	−	19.0919i	−0.464552	−	0.804627i	−0.999181	+	0.0404596i	$0.987118\pi$
$564$		0			0
$565$	12.7279	+	7.34847i	0.535468	+	0.309152i
$566$	22.0454			0.926638
$567$		0			0
$568$		0			0
$569$	−5.19615	−	3.00000i	−0.217834	−	0.125767i	0.387113	−	0.922032i	$-0.373472\pi$
$569$	−5.19615	−	3.00000i	−0.217834	−	0.125767i	−0.604947	+	0.796266i	$0.706806\pi$
$570$		0			0
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$		0			0
$573$		0			0
$574$	−10.2426	+	7.94282i	−0.427520	+	0.331527i
$575$		−	6.00000i		−	0.250217i
$576$		0			0
$577$		−	19.5959i		−	0.815789i	−0.913029	−	0.407894i	$-0.866263\pi$
$577$		−	19.5959i		−	0.815789i	0.913029	−	0.407894i	$-0.133737\pi$
$578$	6.06218	+	3.50000i	0.252153	+	0.145581i
$579$		0			0
$580$	−12.7279	+	7.34847i	−0.528498	+	0.305129i
$581$	−6.42090	+	0.878680i	−0.266384	+	0.0364538i
$582$		0			0
$583$		0			0
$584$	−9.79796			−0.405442
$585$		0			0
$586$			2.44949i			0.101187i
$587$	−3.67423	+	6.36396i	−0.151652	+	0.262669i	−0.931835	−	0.362883i	$-0.881793\pi$
$587$	−3.67423	+	6.36396i	−0.151652	+	0.262669i	0.780183	+	0.625551i	$0.215126\pi$
$588$		0			0
$589$		0			0
$590$	−25.9808	+	15.0000i	−1.06961	+	0.617540i
$591$		0			0
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	−39.1918			−1.60942			−0.804708	−	0.593671i	$-0.797678\pi$
$593$	−39.1918			−1.60942			−0.804708	+	0.593671i	$0.797678\pi$
$594$		0			0
$595$	12.0000	−	29.3939i	0.491952	−	1.20503i
$596$	5.19615	+	3.00000i	0.212843	+	0.122885i
$597$		0			0
$598$	12.7279	−	7.34847i	0.520483	−	0.300501i
$599$	−20.7846	+	12.0000i	−0.849236	+	0.490307i	−0.860393	−	0.509631i	$-0.829782\pi$
$599$	−20.7846	+	12.0000i	−0.849236	+	0.490307i	0.0111569	+	0.999938i	$0.496449\pi$
$600$		0			0
$601$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$601$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$602$	9.79796	+	4.00000i	0.399335	+	0.163028i
$603$		0			0
$604$	8.00000			0.325515
$605$	−13.4722	+	23.3345i	−0.547723	+	0.948683i
$606$		0			0
$607$	4.24264	−	2.44949i	0.172203	−	0.0994217i	−0.411421	−	0.911445i	$-0.634967\pi$
$607$	4.24264	−	2.44949i	0.172203	−	0.0994217i	0.583624	+	0.812024i	$0.301634\pi$
$608$	−1.22474	−	2.12132i	−0.0496700	−	0.0860309i
$609$		0			0
$610$	15.0000	−	25.9808i	0.607332	−	1.05193i
$611$			12.0000i			0.485468i
$612$		0			0
$613$	14.0000			0.565455			0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000			0.565455			0.282727	+	0.959200i	$0.408761\pi$
$614$	3.67423	−	6.36396i	0.148280	−	0.256829i
$615$		0			0
$616$		0			0
$617$	−15.5885	+	9.00000i	−0.627568	+	0.362326i	−0.779809	−	0.626017i	$-0.784684\pi$
$617$	−15.5885	+	9.00000i	−0.627568	+	0.362326i	0.152242	+	0.988343i	$0.451351\pi$
$618$		0			0
$619$	−23.3345	−	13.4722i	−0.937894	−	0.541493i	−0.0485943	−	0.998819i	$-0.515474\pi$
$619$	−23.3345	−	13.4722i	−0.937894	−	0.541493i	−0.889299	+	0.457325i	$0.848807\pi$
$620$		0			0
$621$		0			0
$622$			19.5959i			0.785725i
$623$		0			0
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−17.1464	−	29.6985i	−0.685309	−	1.18699i
$627$		0			0
$628$	−6.36396	−	3.67423i	−0.253950	−	0.146618i
$629$	9.79796			0.390670
$630$		0			0
$631$	2.00000			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$632$	8.66025	+	5.00000i	0.344486	+	0.198889i
$633$		0			0
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	−9.79796	−	16.9706i	−0.388820	−	0.673456i
$636$		0			0
$637$	−4.60660	−	16.5160i	−0.182520	−	0.654389i
$638$		0			0
$639$		0			0
$640$			2.44949i			0.0968246i
$641$	−25.9808	−	15.0000i	−1.02618	−	0.592464i	−0.110291	−	0.993899i	$-0.535178\pi$
$641$	−25.9808	−	15.0000i	−1.02618	−	0.592464i	−0.915888	+	0.401435i	$0.868512\pi$
$642$		0			0
$643$	19.0919	−	11.0227i	0.752910	−	0.434693i	−0.0738342	−	0.997271i	$-0.523524\pi$
$643$	19.0919	−	11.0227i	0.752910	−	0.434693i	0.826745	+	0.562578i	$0.190190\pi$
$644$	2.15232	+	15.7279i	0.0848132	+	0.619767i
$645$		0			0
$646$	6.00000	−	10.3923i	0.236067	−	0.408880i
$647$	44.0908			1.73339			0.866694	−	0.498839i	$-0.166240\pi$
$647$	44.0908			1.73339			0.866694	+	0.498839i	$0.166240\pi$
$648$		0			0
$649$		0			0
$650$	1.22474	−	2.12132i	0.0480384	−	0.0832050i
$651$		0			0
$652$	−8.00000	−	13.8564i	−0.313304	−	0.542659i
$653$	−5.19615	+	3.00000i	−0.203341	+	0.117399i	−0.598213	−	0.801337i	$-0.704122\pi$
$653$	−5.19615	+	3.00000i	−0.203341	+	0.117399i	0.394872	+	0.918736i	$0.370789\pi$
$654$		0			0
$655$	9.00000	−	15.5885i	0.351659	−	0.609091i
$656$	4.89898			0.191273
$657$		0			0
$658$	−12.0000	−	4.89898i	−0.467809	−	0.190982i
$659$	−31.1769	−	18.0000i	−1.21448	−	0.701180i	−0.250748	−	0.968052i	$-0.580677\pi$
$659$	−31.1769	−	18.0000i	−1.21448	−	0.701180i	−0.963732	+	0.266872i	$0.914010\pi$
$660$		0			0
$661$	10.6066	−	6.12372i	0.412549	−	0.238185i	−0.279335	−	0.960194i	$-0.590114\pi$
$661$	10.6066	−	6.12372i	0.412549	−	0.238185i	0.691884	+	0.722008i	$0.256781\pi$
$662$	6.92820	−	4.00000i	0.269272	−	0.155464i
$663$		0			0
$664$	2.12132	+	1.22474i	0.0823232	+	0.0475293i
$665$	−14.6969	−	6.00000i	−0.569923	−	0.232670i
$666$		0			0
$667$	36.0000			1.39393
$668$	−2.44949	+	4.24264i	−0.0947736	+	0.164153i
$669$		0			0
$670$	−16.9706	+	9.79796i	−0.655630	+	0.378528i
$671$		0			0
$672$		0			0
$673$	−17.0000	+	29.4449i	−0.655302	+	1.13502i	0.326516	+	0.945192i	$0.394125\pi$
$673$	−17.0000	+	29.4449i	−0.655302	+	1.13502i	−0.981818	+	0.189824i	$0.939208\pi$
$674$			32.0000i			1.23259i
$675$		0			0
$676$	−7.00000			−0.269231
$677$	−3.67423	+	6.36396i	−0.141212	+	0.244587i	−0.927953	−	0.372696i	$-0.878433\pi$
$677$	−3.67423	+	6.36396i	−0.141212	+	0.244587i	0.786741	+	0.617283i	$0.211767\pi$
$678$		0			0
$679$	1.75736	+	12.8418i	0.0674413	+	0.492823i
$680$	−10.3923	+	6.00000i	−0.398527	+	0.230089i
$681$		0			0
$682$		0			0
$683$			24.0000i			0.918334i	0.888350	+	0.459167i	$0.151852\pi$
$683$			24.0000i			0.918334i	−0.888350	+	0.459167i	$0.848148\pi$
$684$		0			0
$685$			29.3939i			1.12308i
$686$	18.3967	+	2.13604i	0.702388	+	0.0815543i
$687$		0			0
$688$	−2.00000	−	3.46410i	−0.0762493	−	0.132068i
$689$	7.34847	+	12.7279i	0.279954	+	0.484895i
$690$		0			0
$691$	31.8198	+	18.3712i	1.21048	+	0.698872i	0.962864	−	0.269985i	$-0.0870189\pi$
$691$	31.8198	+	18.3712i	1.21048	+	0.698872i	0.247618	+	0.968858i	$0.420352\pi$
$692$	−22.0454			−0.838041
$693$		0			0
$694$	12.0000			0.455514
$695$	−5.19615	−	3.00000i	−0.197101	−	0.113796i
$696$		0			0
$697$	12.0000	+	20.7846i	0.454532	+	0.787273i
$698$	−1.22474	−	2.12132i	−0.0463573	−	0.0802932i
$699$		0			0
$700$	1.62132	+	2.09077i	0.0612801	+	0.0790237i
$701$		−	30.0000i		−	1.13308i	−0.824033	−	0.566542i	$-0.808281\pi$
$701$		−	30.0000i		−	1.13308i	0.824033	−	0.566542i	$-0.191719\pi$
$702$		0			0
$703$		−	4.89898i		−	0.184769i
$704$		0			0
$705$		0			0
$706$	−8.48528	+	4.89898i	−0.319348	+	0.184376i
$707$	−19.2627	+	2.63604i	−0.724448	+	0.0991384i
$708$		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
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	20.7846	−	12.0000i	0.776757	−	0.448461i
$717$		0			0
$718$	−3.00000	+	5.19615i	−0.111959	+	0.193919i
$719$	−24.4949			−0.913506			−0.456753	−	0.889594i	$-0.650988\pi$
$719$	−24.4949			−0.913506			−0.456753	+	0.889594i	$0.650988\pi$
$720$		0			0
$721$	−24.0000	−	9.79796i	−0.893807	−	0.364895i
$722$	11.2583	+	6.50000i	0.418992	+	0.241905i
$723$		0			0
$724$	−10.6066	+	6.12372i	−0.394191	+	0.227586i
$725$	5.19615	−	3.00000i	0.192980	−	0.111417i
$726$		0			0
$727$	−25.4558	−	14.6969i	−0.944105	−	0.545079i	−0.0528602	−	0.998602i	$-0.516834\pi$
$727$	−25.4558	−	14.6969i	−0.944105	−	0.545079i	−0.891245	+	0.453523i	$0.850167\pi$
$728$	−2.44949	+	6.00000i	−0.0907841	+	0.222375i
$729$		0			0
$730$	24.0000			0.888280
$731$	9.79796	−	16.9706i	0.362391	−	0.627679i
$732$		0			0
$733$	19.0919	−	11.0227i	0.705175	−	0.407133i	−0.104097	−	0.994567i	$-0.533195\pi$
$733$	19.0919	−	11.0227i	0.705175	−	0.407133i	0.809272	+	0.587434i	$0.199862\pi$
$734$	−2.44949	−	4.24264i	−0.0904123	−	0.156599i
$735$		0			0
$736$	3.00000	−	5.19615i	0.110581	−	0.191533i
$737$		0			0
$738$		0			0
$739$	20.0000			0.735712			0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000			0.735712			0.367856	+	0.929883i	$0.380092\pi$
$740$	−2.44949	+	4.24264i	−0.0900450	+	0.155963i
$741$		0			0
$742$	−15.7279	+	2.15232i	−0.577390	+	0.0790140i
$743$	−5.19615	+	3.00000i	−0.190628	+	0.110059i	−0.592277	−	0.805735i	$-0.701771\pi$
$743$	−5.19615	+	3.00000i	−0.190628	+	0.110059i	0.401648	+	0.915794i	$0.368437\pi$
$744$		0			0
$745$	−12.7279	−	7.34847i	−0.466315	−	0.269227i
$746$		−	14.0000i		−	0.512576i
$747$		0			0
$748$		0			0
$749$	25.0892	−	19.4558i	0.916741	−	0.710901i
$750$		0			0
$751$	4.00000	+	6.92820i	0.145962	+	0.252814i	0.929731	−	0.368238i	$-0.120039\pi$
$751$	4.00000	+	6.92820i	0.145962	+	0.252814i	−0.783769	+	0.621052i	$0.786706\pi$
$752$	2.44949	+	4.24264i	0.0893237	+	0.154713i
$753$		0			0
$754$	12.7279	+	7.34847i	0.463524	+	0.267615i
$755$	−19.5959			−0.713168
$756$		0			0
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$	−17.3205	−	10.0000i	−0.629109	−	0.363216i
$759$		0			0
$760$	3.00000	+	5.19615i	0.108821	+	0.188484i
$761$	−2.44949	−	4.24264i	−0.0887939	−	0.153796i	0.818208	−	0.574923i	$-0.194968\pi$
$761$	−2.44949	−	4.24264i	−0.0887939	−	0.153796i	−0.907002	+	0.421127i	$0.861635\pi$
$762$		0			0
$763$	−16.2132	−	20.9077i	−0.586957	−	0.756910i
$764$		0			0
$765$		0			0
$766$		−	34.2929i		−	1.23905i
$767$	25.9808	+	15.0000i	0.938111	+	0.541619i
$768$		0			0
$769$	−29.6985	+	17.1464i	−1.07095	+	0.618316i	−0.928442	−	0.371477i	$-0.878851\pi$
$769$	−29.6985	+	17.1464i	−1.07095	+	0.618316i	−0.142513	+	0.989793i	$0.545518\pi$
$770$		0			0
$771$		0			0
$772$	2.00000	−	3.46410i	0.0719816	−	0.124676i
$773$	−26.9444			−0.969122			−0.484561	−	0.874757i	$-0.661021\pi$
$773$	−26.9444			−0.969122			−0.484561	+	0.874757i	$0.661021\pi$
$774$		0			0
$775$		0			0
$776$	2.44949	−	4.24264i	0.0879316	−	0.152302i
$777$		0			0
$778$	−3.00000	−	5.19615i	−0.107555	−	0.186291i
$779$	10.3923	−	6.00000i	0.372343	−	0.214972i
$780$		0			0
$781$		0			0
$782$	29.3939			1.05112
$783$		0			0
$784$	−5.00000	−	4.89898i	−0.178571	−	0.174964i
$785$	15.5885	+	9.00000i	0.556376	+	0.321224i
$786$		0			0
$787$	−27.5772	+	15.9217i	−0.983020	+	0.567547i	−0.903180	−	0.429261i	$-0.858774\pi$
$787$	−27.5772	+	15.9217i	−0.983020	+	0.567547i	−0.0798393	+	0.996808i	$0.525441\pi$
$788$	15.5885	−	9.00000i	0.555316	−	0.320612i
$789$		0			0
$790$	−21.2132	−	12.2474i	−0.754732	−	0.435745i
$791$	14.6969	+	6.00000i	0.522563	+	0.213335i
$792$		0			0
$793$	−30.0000			−1.06533
$794$	3.67423	−	6.36396i	0.130394	−	0.225849i
$795$		0			0
$796$	8.48528	−	4.89898i	0.300753	−	0.173640i
$797$	−3.67423	−	6.36396i	−0.130148	−	0.225423i	0.793585	−	0.608459i	$-0.208212\pi$
$797$	−3.67423	−	6.36396i	−0.130148	−	0.225423i	−0.923734	+	0.383036i	$0.874879\pi$
$798$		0			0
$799$	−12.0000	+	20.7846i	−0.424529	+	0.735307i
$800$		−	1.00000i		−	0.0353553i
$801$		0			0
$802$	−30.0000			−1.05934
$803$		0			0
$804$		0			0
$805$	−5.27208	−	38.5254i	−0.185816	−	1.35784i
$806$		0			0
$807$		0			0
$808$	6.36396	+	3.67423i	0.223883	+	0.129259i
$809$			6.00000i			0.210949i	0.994422	+	0.105474i	$0.0336361\pi$
$809$			6.00000i			0.210949i	−0.994422	+	0.105474i	$0.966364\pi$
$810$		0			0
$811$		−	36.7423i		−	1.29020i	−0.764099	−	0.645099i	$-0.776816\pi$
$811$		−	36.7423i		−	1.29020i	0.764099	−	0.645099i	$-0.223184\pi$
$812$	−12.5446	+	9.72792i	−0.440230	+	0.341383i
$813$		0			0
$814$		0			0
$815$	19.5959	+	33.9411i	0.686415	+	1.18891i
$816$		0			0
$817$	−8.48528	−	4.89898i	−0.296862	−	0.171394i
$818$	−34.2929			−1.19902
$819$		0			0
$820$	−12.0000			−0.419058
$821$	−25.9808	−	15.0000i	−0.906735	−	0.523504i	−0.0273557	−	0.999626i	$-0.508709\pi$
$821$	−25.9808	−	15.0000i	−0.906735	−	0.523504i	−0.879379	+	0.476122i	$0.842042\pi$
$822$		0			0
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	0.717847	−	0.696201i	$-0.245128\pi$
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	−0.961851	+	0.273573i	$0.911795\pi$
$824$	4.89898	+	8.48528i	0.170664	+	0.295599i
$825$		0			0
$826$	−25.6066	+	19.8570i	−0.890968	+	0.690915i
$827$			12.0000i			0.417281i	0.977992	+	0.208640i	$0.0669038\pi$
$827$			12.0000i			0.417281i	−0.977992	+	0.208640i	$0.933096\pi$
$828$		0			0
$829$			26.9444i			0.935817i	0.883777	+	0.467909i	$0.154992\pi$
$829$			26.9444i			0.935817i	−0.883777	+	0.467909i	$0.845008\pi$
$830$	−5.19615	−	3.00000i	−0.180361	−	0.104132i
$831$		0			0
$832$	2.12132	−	1.22474i	0.0735436	−	0.0424604i
$833$	8.53716	−	33.2132i	0.295795	−	1.15077i
$834$		0			0
$835$	6.00000	−	10.3923i	0.207639	−	0.359641i
$836$		0			0
$837$		0			0
$838$			12.2474i			0.423081i
$839$	−12.2474	+	21.2132i	−0.422829	+	0.732361i	−0.996215	−	0.0869242i	$-0.972296\pi$
$839$	−12.2474	+	21.2132i	−0.422829	+	0.732361i	0.573386	+	0.819285i	$0.305630\pi$
$840$		0			0
$841$	3.50000	+	6.06218i	0.120690	+	0.209041i
$842$	−1.73205	+	1.00000i	−0.0596904	+	0.0344623i
$843$		0			0
$844$	−4.00000	+	6.92820i	−0.137686	+	0.238479i
$845$	17.1464			0.589855
$846$		0			0
$847$	−11.0000	+	26.9444i	−0.377964	+	0.925820i
$848$	5.19615	+	3.00000i	0.178437	+	0.103020i
$849$		0			0
$850$	4.24264	−	2.44949i	0.145521	−	0.0840168i
$851$	10.3923	−	6.00000i	0.356244	−	0.205677i
$852$		0			0
$853$	2.12132	+	1.22474i	0.0726326	+	0.0419345i	0.535876	−	0.844296i	$-0.319981\pi$
$853$	2.12132	+	1.22474i	0.0726326	+	0.0419345i	−0.463244	+	0.886231i	$0.653315\pi$
$854$	12.2474	−	30.0000i	0.419099	−	1.02658i
$855$		0			0
$856$	−12.0000			−0.410152
$857$	2.44949	−	4.24264i	0.0836730	−	0.144926i	−0.821152	−	0.570710i	$-0.806668\pi$
$857$	2.44949	−	4.24264i	0.0836730	−	0.144926i	0.904825	+	0.425784i	$0.140002\pi$
$858$		0			0
$859$	23.3345	−	13.4722i	0.796164	−	0.459665i	−0.0459643	−	0.998943i	$-0.514636\pi$
$859$	23.3345	−	13.4722i	0.796164	−	0.459665i	0.842128	+	0.539278i	$0.181303\pi$
$860$	4.89898	+	8.48528i	0.167054	+	0.289346i
$861$		0			0
$862$	15.0000	−	25.9808i	0.510902	−	0.884908i
$863$			24.0000i			0.816970i	0.912765	+	0.408485i	$0.133943\pi$
$863$			24.0000i			0.816970i	−0.912765	+	0.408485i	$0.866057\pi$
$864$		0			0
$865$	54.0000			1.83606
$866$	7.34847	−	12.7279i	0.249711	−	0.432512i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	16.9706	+	9.79796i	0.575026	+	0.331991i
$872$			10.0000i			0.338643i
$873$		0			0
$874$		−	14.6969i		−	0.497131i
$875$	15.8856	+	20.4853i	0.537032	+	0.692529i
$876$		0			0
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	0.989788	−	0.142548i	$-0.0455296\pi$
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	−0.618344	+	0.785907i	$0.712196\pi$
$878$	−7.34847	−	12.7279i	−0.247999	−	0.429547i
$879$		0			0
$880$		0			0
$881$	29.3939			0.990305			0.495152	−	0.868806i	$-0.335112\pi$
$881$	29.3939			0.990305			0.495152	+	0.868806i	$0.335112\pi$
$882$		0			0
$883$	−56.0000			−1.88455			−0.942275	−	0.334840i	$-0.891318\pi$
$883$	−56.0000			−1.88455			−0.942275	+	0.334840i	$0.891318\pi$
$884$	10.3923	+	6.00000i	0.349531	+	0.201802i
$885$		0			0
$886$	18.0000	+	31.1769i	0.604722	+	1.04741i
$887$	2.44949	+	4.24264i	0.0822458	+	0.142454i	0.904214	−	0.427079i	$-0.140457\pi$
$887$	2.44949	+	4.24264i	0.0822458	+	0.142454i	−0.821968	+	0.569533i	$0.807124\pi$
$888$		0			0
$889$	−12.9706	−	16.7262i	−0.435019	−	0.560977i
$890$		0			0
$891$		0			0
$892$			14.6969i			0.492090i
$893$	10.3923	+	6.00000i	0.347765	+	0.200782i
$894$		0			0
$895$	−50.9117	+	29.3939i	−1.70179	+	0.982529i
$896$	0.358719	+	2.62132i	0.0119840	+	0.0875722i
$897$		0			0
$898$	−18.0000	+	31.1769i	−0.600668	+	1.04039i
$899$		0			0
$900$		0			0
$901$			29.3939i			0.979252i
$902$		0			0
$903$		0			0
$904$	−3.00000	−	5.19615i	−0.0997785	−	0.172821i
$905$	25.9808	−	15.0000i	0.863630	−	0.498617i
$906$		0			0
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	−0.999195	−	0.0401089i	$-0.987230\pi$
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	0.534333	+	0.845274i	$0.320563\pi$
$908$	−7.34847			−0.243868
$909$		0			0
$910$	6.00000	−	14.6969i	0.198898	−	0.487199i
$911$	25.9808	+	15.0000i	0.860781	+	0.496972i	0.864274	−	0.503022i	$-0.167778\pi$
$911$	25.9808	+	15.0000i	0.860781	+	0.496972i	−0.00349271	+	0.999994i	$0.501112\pi$
$912$		0			0
$913$		0			0
$914$	−24.2487	+	14.0000i	−0.802076	+	0.463079i
$915$		0			0
$916$	−19.0919	−	11.0227i	−0.630814	−	0.364200i
$917$	7.34847	−	18.0000i	0.242668	−	0.594412i
$918$		0			0
$919$	10.0000			0.329870			0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000			0.329870			0.164935	+	0.986304i	$0.447259\pi$
$920$	−7.34847	+	12.7279i	−0.242272	+	0.419627i
$921$		0			0
$922$	27.5772	−	15.9217i	0.908206	−	0.524353i
$923$		0			0
$924$		0			0
$925$	1.00000	−	1.73205i	0.0328798	−	0.0569495i
$926$		−	14.0000i		−	0.460069i
$927$		0			0
$928$	6.00000			0.196960
$929$	−12.2474	+	21.2132i	−0.401826	+	0.695983i	−0.993946	−	0.109867i	$-0.964958\pi$
$929$	−12.2474	+	21.2132i	−0.401826	+	0.695983i	0.592121	+	0.805849i	$0.298291\pi$
$930$		0			0
$931$	−16.6066	−	4.26858i	−0.544259	−	0.139897i
$932$	−20.7846	+	12.0000i	−0.680823	+	0.393073i
$933$		0			0
$934$	6.36396	+	3.67423i	0.208235	+	0.120225i
$935$		0			0
$936$		0			0
$937$		−	19.5959i		−	0.640171i	−0.947389	−	0.320085i	$-0.896288\pi$
$937$		−	19.5959i		−	0.640171i	0.947389	−	0.320085i	$-0.103712\pi$
$938$	−16.7262	+	12.9706i	−0.546129	+	0.423504i
$939$		0			0
$940$	−6.00000	−	10.3923i	−0.195698	−	0.338960i
$941$	15.9217	+	27.5772i	0.519032	+	0.898990i	0.999755	+	0.0221175i	$0.00704081\pi$
$941$	15.9217	+	27.5772i	0.519032	+	0.898990i	−0.480723	+	0.876872i	$0.659626\pi$
$942$		0			0
$943$	25.4558	+	14.6969i	0.828956	+	0.478598i
$944$	12.2474			0.398621
$945$		0			0
$946$		0			0
$947$	−10.3923	−	6.00000i	−0.337705	−	0.194974i	0.321552	−	0.946892i	$-0.395796\pi$
$947$	−10.3923	−	6.00000i	−0.337705	−	0.194974i	−0.659256	+	0.751918i	$0.729129\pi$
$948$		0			0
$949$	−12.0000	−	20.7846i	−0.389536	−	0.674697i
$950$	−1.22474	−	2.12132i	−0.0397360	−	0.0688247i
$951$		0			0
$952$	−10.2426	+	7.94282i	−0.331966	+	0.257428i
$953$		−	36.0000i		−	1.16615i	−0.812417	−	0.583077i	$-0.801849\pi$
$953$		−	36.0000i		−	1.16615i	0.812417	−	0.583077i	$-0.198151\pi$
$954$		0			0
$955$		0			0
$956$	5.19615	+	3.00000i	0.168056	+	0.0970269i
$957$		0			0
$958$	21.2132	−	12.2474i	0.685367	−	0.395697i
$959$	4.30463	+	31.4558i	0.139004	+	1.01576i
$960$		0			0
$961$	−15.5000	+	26.8468i	−0.500000	+	0.866025i
$962$	4.89898			0.157949
$963$		0			0
$964$		−	24.4949i		−	0.788928i
$965$	−4.89898	+	8.48528i	−0.157704	+	0.273151i
$966$		0			0
$967$	−4.00000	−	6.92820i	−0.128631	−	0.222796i	0.794515	−	0.607244i	$-0.207725\pi$
$967$	−4.00000	−	6.92820i	−0.128631	−	0.222796i	−0.923147	+	0.384448i	$0.874392\pi$
$968$	9.52628	−	5.50000i	0.306186	−	0.176777i
$969$		0			0
$970$	−6.00000	+	10.3923i	−0.192648	+	0.333677i
$971$	41.6413			1.33633			0.668167	−	0.744011i	$-0.267079\pi$
$971$	41.6413			1.33633			0.668167	+	0.744011i	$0.267079\pi$
$972$		0			0
$973$	−6.00000	−	2.44949i	−0.192351	−	0.0785270i
$974$	−27.7128	−	16.0000i	−0.887976	−	0.512673i
$975$		0			0
$976$	−10.6066	+	6.12372i	−0.339509	+	0.196016i
$977$	10.3923	−	6.00000i	0.332479	−	0.191957i	−0.324462	−	0.945899i	$-0.605183\pi$
$977$	10.3923	−	6.00000i	0.332479	−	0.191957i	0.656941	+	0.753942i	$0.271850\pi$
$978$		0			0
$979$		0			0
$980$	12.2474	+	12.0000i	0.391230	+	0.383326i
$981$		0			0
$982$		0			0
$983$	−17.1464	+	29.6985i	−0.546886	+	0.947235i	0.451599	+	0.892221i	$0.350854\pi$
$983$	−17.1464	+	29.6985i	−0.546886	+	0.947235i	−0.998486	+	0.0550138i	$0.982480\pi$
$984$		0			0
$985$	−38.1838	+	22.0454i	−1.21664	+	0.702425i
$986$	14.6969	+	25.4558i	0.468046	+	0.810679i
$987$		0			0
$988$	3.00000	−	5.19615i	0.0954427	−	0.165312i
$989$		−	24.0000i		−	0.763156i
$990$		0			0
$991$	−38.0000			−1.20711			−0.603555	−	0.797321i	$-0.706250\pi$
$991$	−38.0000			−1.20711			−0.603555	+	0.797321i	$0.706250\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−20.7846	+	12.0000i	−0.658916	+	0.380426i
$996$		0			0
$997$	6.36396	+	3.67423i	0.201549	+	0.116364i	0.597378	−	0.801960i	$-0.296209\pi$
$997$	6.36396	+	3.67423i	0.201549	+	0.116364i	−0.395829	+	0.918324i	$0.629543\pi$
$998$			20.0000i			0.633089i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.m.g.755.3		8
3.2	odd	2	inner	1134.2.m.g.755.2		8
7.6	odd	2	inner	1134.2.m.g.755.4		8
9.2	odd	6		42.2.d.a.41.4	yes	4
9.4	even	3	inner	1134.2.m.g.377.1		8
9.5	odd	6	inner	1134.2.m.g.377.4		8
9.7	even	3		42.2.d.a.41.1	✓	4
21.20	even	2	inner	1134.2.m.g.755.1		8
36.7	odd	6		336.2.k.b.209.4		4
36.11	even	6		336.2.k.b.209.2		4
45.2	even	12		1050.2.d.b.1049.1		4
45.7	odd	12		1050.2.d.e.1049.2		4
45.29	odd	6		1050.2.b.b.251.1		4
45.34	even	6		1050.2.b.b.251.4		4
45.38	even	12		1050.2.d.e.1049.4		4
45.43	odd	12		1050.2.d.b.1049.3		4
63.2	odd	6		294.2.f.b.227.4		8
63.11	odd	6		294.2.f.b.215.1		8
63.13	odd	6	inner	1134.2.m.g.377.2		8
63.16	even	3		294.2.f.b.227.2		8
63.20	even	6		42.2.d.a.41.3	yes	4
63.25	even	3		294.2.f.b.215.3		8
63.34	odd	6		42.2.d.a.41.2	yes	4
63.38	even	6		294.2.f.b.215.2		8
63.41	even	6	inner	1134.2.m.g.377.3		8
63.47	even	6		294.2.f.b.227.3		8
63.52	odd	6		294.2.f.b.215.4		8
63.61	odd	6		294.2.f.b.227.1		8
72.11	even	6		1344.2.k.d.1217.3		4
72.29	odd	6		1344.2.k.c.1217.2		4
72.43	odd	6		1344.2.k.d.1217.1		4
72.61	even	6		1344.2.k.c.1217.4		4
252.83	odd	6		336.2.k.b.209.3		4
252.223	even	6		336.2.k.b.209.1		4
315.34	odd	6		1050.2.b.b.251.3		4
315.83	odd	12		1050.2.d.e.1049.1		4
315.97	even	12		1050.2.d.e.1049.3		4
315.209	even	6		1050.2.b.b.251.2		4
315.223	even	12		1050.2.d.b.1049.2		4
315.272	odd	12		1050.2.d.b.1049.4		4
504.83	odd	6		1344.2.k.d.1217.2		4
504.349	odd	6		1344.2.k.c.1217.1		4
504.461	even	6		1344.2.k.c.1217.3		4
504.475	even	6		1344.2.k.d.1217.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.d.a.41.1	✓	4	9.7	even	3
42.2.d.a.41.2	yes	4	63.34	odd	6
42.2.d.a.41.3	yes	4	63.20	even	6
42.2.d.a.41.4	yes	4	9.2	odd	6
294.2.f.b.215.1		8	63.11	odd	6
294.2.f.b.215.2		8	63.38	even	6
294.2.f.b.215.3		8	63.25	even	3
294.2.f.b.215.4		8	63.52	odd	6
294.2.f.b.227.1		8	63.61	odd	6
294.2.f.b.227.2		8	63.16	even	3
294.2.f.b.227.3		8	63.47	even	6
294.2.f.b.227.4		8	63.2	odd	6
336.2.k.b.209.1		4	252.223	even	6
336.2.k.b.209.2		4	36.11	even	6
336.2.k.b.209.3		4	252.83	odd	6
336.2.k.b.209.4		4	36.7	odd	6
1050.2.b.b.251.1		4	45.29	odd	6
1050.2.b.b.251.2		4	315.209	even	6
1050.2.b.b.251.3		4	315.34	odd	6
1050.2.b.b.251.4		4	45.34	even	6
1050.2.d.b.1049.1		4	45.2	even	12
1050.2.d.b.1049.2		4	315.223	even	12
1050.2.d.b.1049.3		4	45.43	odd	12
1050.2.d.b.1049.4		4	315.272	odd	12
1050.2.d.e.1049.1		4	315.83	odd	12
1050.2.d.e.1049.2		4	45.7	odd	12
1050.2.d.e.1049.3		4	315.97	even	12
1050.2.d.e.1049.4		4	45.38	even	12
1134.2.m.g.377.1		8	9.4	even	3	inner
1134.2.m.g.377.2		8	63.13	odd	6	inner
1134.2.m.g.377.3		8	63.41	even	6	inner
1134.2.m.g.377.4		8	9.5	odd	6	inner
1134.2.m.g.755.1		8	21.20	even	2	inner
1134.2.m.g.755.2		8	3.2	odd	2	inner
1134.2.m.g.755.3		8	1.1	even	1	trivial
1134.2.m.g.755.4		8	7.6	odd	2	inner
1344.2.k.c.1217.1		4	504.349	odd	6
1344.2.k.c.1217.2		4	72.29	odd	6
1344.2.k.c.1217.3		4	504.461	even	6
1344.2.k.c.1217.4		4	72.61	even	6
1344.2.k.d.1217.1		4	72.43	odd	6
1344.2.k.d.1217.2		4	504.83	odd	6
1344.2.k.d.1217.3		4	72.11	even	6
1344.2.k.d.1217.4		4	504.475	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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.22474 - 2.12132i) q^{5} +(-1.62132 - 2.09077i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.22474 - 2.12132i) q^{5} +(-1.62132 - 2.09077i) q^{7} +1.00000i q^{8} -2.44949i q^{10} +(-2.12132 + 1.22474i) q^{13} +(-0.358719 - 2.62132i) q^{14} +(-0.500000 + 0.866025i) q^{16} -4.89898 q^{17} +2.44949i q^{19} +(1.22474 - 2.12132i) q^{20} +(-5.19615 + 3.00000i) q^{23} +(-0.500000 + 0.866025i) q^{25} -2.44949 q^{26} +(1.00000 - 2.44949i) q^{28} +(-5.19615 - 3.00000i) q^{29} +(-0.866025 + 0.500000i) q^{32} +(-4.24264 - 2.44949i) q^{34} +(-2.44949 + 6.00000i) q^{35} -2.00000 q^{37} +(-1.22474 + 2.12132i) q^{38} +(2.12132 - 1.22474i) q^{40} +(-2.44949 - 4.24264i) q^{41} +(-2.00000 + 3.46410i) q^{43} -6.00000 q^{46} +(2.44949 - 4.24264i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-2.12132 - 1.22474i) q^{52} -6.00000i q^{53} +(2.09077 - 1.62132i) q^{56} +(-3.00000 - 5.19615i) q^{58} +(-6.12372 - 10.6066i) q^{59} +(10.6066 + 6.12372i) q^{61} -1.00000 q^{64} +(5.19615 + 3.00000i) q^{65} +(-4.00000 - 6.92820i) q^{67} +(-2.44949 - 4.24264i) q^{68} +(-5.12132 + 3.97141i) q^{70} +9.79796i q^{73} +(-1.73205 - 1.00000i) q^{74} +(-2.12132 + 1.22474i) q^{76} +(5.00000 - 8.66025i) q^{79} +2.44949 q^{80} -4.89898i q^{82} +(1.22474 - 2.12132i) q^{83} +(6.00000 + 10.3923i) q^{85} +(-3.46410 + 2.00000i) q^{86} +(6.00000 + 2.44949i) q^{91} +(-5.19615 - 3.00000i) q^{92} +(4.24264 - 2.44949i) q^{94} +(5.19615 - 3.00000i) q^{95} +(-4.24264 - 2.44949i) q^{97} +(-4.89898 + 5.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^4 + 4 * q^7	\( 8 q + 4 q^{4} + 4 q^{7} - 4 q^{16} - 4 q^{25} + 8 q^{28} - 16 q^{37} - 16 q^{43} - 48 q^{46} + 20 q^{49} - 24 q^{58} - 8 q^{64} - 32 q^{67} - 24 q^{70} + 40 q^{79} + 48 q^{85} + 48 q^{91}+O(q^{100}) \) 8 * q + 4 * q^4 + 4 * q^7 - 4 * q^16 - 4 * q^25 + 8 * q^28 - 16 * q^37 - 16 * q^43 - 48 * q^46 + 20 * q^49 - 24 * q^58 - 8 * q^64 - 32 * q^67 - 24 * q^70 + 40 * q^79 + 48 * q^85 + 48 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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