LMFDB - Embedded newform 2184.2.bj.k.841.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2184,2,Mod(841,2184)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2184, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2184.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2184 = 2^{3} \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2184.bj (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.4393278014$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.8248090761.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{6} - 2x^{5} + 41x^{4} - 7x^{3} + 57x^{2} + 8x + 64 $ x^8 + 7x^6 - 2x^5 + 41x^4 - 7x^3 + 57x^2 + 8x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.2
Root			$-0.545220 + 0.944349i$ of defining polynomial
Character	$\chi$	$=$	2184.841
Dual form			2184.2.bj.k.1849.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} -1.09044 q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} -1.09044 q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-0.778358 + 1.34816i) q^{11} +(0.778358 - 3.52053i) q^{13} +(-0.545220 + 0.944349i) q^{15} +(-1.17233 - 2.03054i) q^{17} +(1.59044 + 2.75472i) q^{19} -1.00000 q^{21} +(2.21755 - 3.84091i) q^{23} -3.81094 q^{25} -1.00000 q^{27} +(-0.815029 + 1.41167i) q^{29} +1.24604 q^{31} +(0.778358 + 1.34816i) q^{33} +(0.545220 + 0.944349i) q^{35} +(0.265719 - 0.460239i) q^{37} +(-2.65969 - 2.43434i) q^{39} +(-4.66824 + 8.08563i) q^{41} +(-4.02849 - 6.97755i) q^{43} +(0.545220 + 0.944349i) q^{45} -12.0235 q^{47} +(-0.500000 + 0.866025i) q^{49} -2.34466 q^{51} -2.26012 q^{53} +(0.848753 - 1.47008i) q^{55} +3.18088 q^{57} +(-4.74899 - 8.22549i) q^{59} +(0.220499 + 0.381915i) q^{61} +(-0.500000 + 0.866025i) q^{63} +(-0.848753 + 3.83893i) q^{65} +(0.861392 - 1.49198i) q^{67} +(-2.21755 - 3.84091i) q^{69} +(1.60603 + 2.78172i) q^{71} +1.77106 q^{73} +(-1.90547 + 3.30037i) q^{75} +1.55672 q^{77} -1.02299 q^{79} +(-0.500000 + 0.866025i) q^{81} -15.9561 q^{83} +(1.27836 + 2.21418i) q^{85} +(0.815029 + 1.41167i) q^{87} +(-4.55698 + 7.89293i) q^{89} +(-3.43805 + 1.08619i) q^{91} +(0.623022 - 1.07911i) q^{93} +(-1.73428 - 3.00386i) q^{95} +(-5.68818 - 9.85222i) q^{97} +1.55672 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 4 * q^7 - 4 * q^9	$ 8 q + 4 q^{3} - 4 q^{7} - 4 q^{9} - 3 q^{11} + 3 q^{13} + q^{17} + 4 q^{19} - 8 q^{21} + 3 q^{23} - 12 q^{25} - 8 q^{27} - 6 q^{29} - 38 q^{31} + 3 q^{33} - 12 q^{37} - 9 q^{41} + q^{43} + 28 q^{47} - 4 q^{49} + 2 q^{51} - 16 q^{53} + 4 q^{55} + 8 q^{57} + 5 q^{59} - 8 q^{61} - 4 q^{63} - 4 q^{65} + 15 q^{67} - 3 q^{69} + 20 q^{71} + 48 q^{73} - 6 q^{75} + 6 q^{77} - 4 q^{79} - 4 q^{81} - 8 q^{83} + 7 q^{85} + 6 q^{87} + 30 q^{89} - 3 q^{91} - 19 q^{93} - 28 q^{95} + 9 q^{97} + 6 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 4 * q^7 - 4 * q^9 - 3 * q^11 + 3 * q^13 + q^17 + 4 * q^19 - 8 * q^21 + 3 * q^23 - 12 * q^25 - 8 * q^27 - 6 * q^29 - 38 * q^31 + 3 * q^33 - 12 * q^37 - 9 * q^41 + q^43 + 28 * q^47 - 4 * q^49 + 2 * q^51 - 16 * q^53 + 4 * q^55 + 8 * q^57 + 5 * q^59 - 8 * q^61 - 4 * q^63 - 4 * q^65 + 15 * q^67 - 3 * q^69 + 20 * q^71 + 48 * q^73 - 6 * q^75 + 6 * q^77 - 4 * q^79 - 4 * q^81 - 8 * q^83 + 7 * q^85 + 6 * q^87 + 30 * q^89 - 3 * q^91 - 19 * q^93 - 28 * q^95 + 9 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2184\mathbb{Z}\right)^\times$.

$n$	$1093$	$1249$	$1457$	$1639$	$2017$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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			0
$2$		0			0
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	−1.09044			−0.487660			−0.243830	−	0.969818i	$-0.578404\pi$
$5$	−1.09044			−0.487660			−0.243830	+	0.969818i	$0.578404\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−0.778358	+	1.34816i	−0.234684	+	0.406484i	−0.959181	−	0.282794i	$-0.908739\pi$
$11$	−0.778358	+	1.34816i	−0.234684	+	0.406484i	0.724497	+	0.689278i	$0.242072\pi$
$12$		0			0
$13$	0.778358	−	3.52053i	0.215878	−	0.976420i
$13$	0.778358	−	3.52053i	0.215878	−	0.976420i
$14$		0			0
$15$	−0.545220	+	0.944349i	−0.140775	+	0.243830i
$16$		0			0
$17$	−1.17233	−	2.03054i	−0.284332	−	0.492478i	0.688115	−	0.725602i	$-0.258439\pi$
$17$	−1.17233	−	2.03054i	−0.284332	−	0.492478i	−0.972447	+	0.233124i	$0.925105\pi$
$18$		0			0
$19$	1.59044	+	2.75472i	0.364872	+	0.631977i	0.988756	−	0.149540i	$-0.0477794\pi$
$19$	1.59044	+	2.75472i	0.364872	+	0.631977i	−0.623884	+	0.781517i	$0.714446\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	2.21755	−	3.84091i	0.462392	−	0.800886i	−0.536688	−	0.843781i	$-0.680325\pi$
$23$	2.21755	−	3.84091i	0.462392	−	0.800886i	0.999080	+	0.0428951i	$0.0136581\pi$
$24$		0			0
$25$	−3.81094			−0.762188
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−0.815029	+	1.41167i	−0.151347	+	0.262141i	−0.931723	−	0.363170i	$-0.881694\pi$
$29$	−0.815029	+	1.41167i	−0.151347	+	0.262141i	0.780376	+	0.625311i	$0.215028\pi$
$30$		0			0
$31$	1.24604			0.223796			0.111898	−	0.993720i	$-0.464307\pi$
$31$	1.24604			0.223796			0.111898	+	0.993720i	$0.464307\pi$
$32$		0			0
$33$	0.778358	+	1.34816i	0.135495	+	0.234684i
$34$		0			0
$35$	0.545220	+	0.944349i	0.0921591	+	0.159624i
$36$		0			0
$37$	0.265719	−	0.460239i	0.0436839	−	0.0756628i	−0.843357	−	0.537354i	$-0.819424\pi$
$37$	0.265719	−	0.460239i	0.0436839	−	0.0756628i	0.887041	+	0.461691i	$0.152757\pi$
$38$		0			0
$39$	−2.65969	−	2.43434i	−0.425892	−	0.389807i
$40$		0			0
$41$	−4.66824	+	8.08563i	−0.729057	+	1.26276i	0.228225	+	0.973608i	$0.426708\pi$
$41$	−4.66824	+	8.08563i	−0.729057	+	1.26276i	−0.957282	+	0.289155i	$0.906626\pi$
$42$		0			0
$43$	−4.02849	−	6.97755i	−0.614339	−	1.06407i	−0.990500	−	0.137512i	$-0.956089\pi$
$43$	−4.02849	−	6.97755i	−0.614339	−	1.06407i	0.376161	−	0.926554i	$-0.377244\pi$
$44$		0			0
$45$	0.545220	+	0.944349i	0.0812766	+	0.140775i
$46$		0			0
$47$	−12.0235			−1.75381			−0.876906	−	0.480662i	$-0.840396\pi$
$47$	−12.0235			−1.75381			−0.876906	+	0.480662i	$0.840396\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	−2.34466			−0.328319
$52$		0			0
$53$	−2.26012			−0.310451			−0.155225	−	0.987879i	$-0.549610\pi$
$53$	−2.26012			−0.310451			−0.155225	+	0.987879i	$0.549610\pi$
$54$		0			0
$55$	0.848753	−	1.47008i	0.114446	−	0.198226i
$56$		0			0
$57$	3.18088			0.421318
$58$		0			0
$59$	−4.74899	−	8.22549i	−0.618266	−	1.07087i	−0.989802	−	0.142449i	$-0.954502\pi$
$59$	−4.74899	−	8.22549i	−0.618266	−	1.07087i	0.371536	−	0.928418i	$-0.378831\pi$
$60$		0			0
$61$	0.220499	+	0.381915i	0.0282320	+	0.0488992i	0.879796	−	0.475351i	$-0.157679\pi$
$61$	0.220499	+	0.381915i	0.0282320	+	0.0488992i	−0.851564	+	0.524250i	$0.824346\pi$
$62$		0			0
$63$	−0.500000	+	0.866025i	−0.0629941	+	0.109109i
$64$		0			0
$65$	−0.848753	+	3.83893i	−0.105275	+	0.476161i
$66$		0			0
$67$	0.861392	−	1.49198i	0.105236	−	0.182274i	−0.808599	−	0.588361i	$-0.799774\pi$
$67$	0.861392	−	1.49198i	0.105236	−	0.182274i	0.913835	+	0.406087i	$0.133107\pi$
$68$		0			0
$69$	−2.21755	−	3.84091i	−0.266962	−	0.462392i
$70$		0			0
$71$	1.60603	+	2.78172i	0.190600	+	0.330129i	0.945449	−	0.325769i	$-0.105623\pi$
$71$	1.60603	+	2.78172i	0.190600	+	0.330129i	−0.754849	+	0.655899i	$0.772290\pi$
$72$		0			0
$73$	1.77106			0.207286			0.103643	−	0.994615i	$-0.466950\pi$
$73$	1.77106			0.207286			0.103643	+	0.994615i	$0.466950\pi$
$74$		0			0
$75$	−1.90547	+	3.30037i	−0.220025	+	0.381094i
$76$		0			0
$77$	1.55672			0.177404
$78$		0			0
$79$	−1.02299			−0.115096			−0.0575478	−	0.998343i	$-0.518328\pi$
$79$	−1.02299			−0.115096			−0.0575478	+	0.998343i	$0.518328\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−15.9561			−1.75141			−0.875703	−	0.482849i	$-0.839602\pi$
$83$	−15.9561			−1.75141			−0.875703	+	0.482849i	$0.839602\pi$
$84$		0			0
$85$	1.27836	+	2.21418i	0.138657	+	0.240162i
$86$		0			0
$87$	0.815029	+	1.41167i	0.0873803	+	0.151347i
$88$		0			0
$89$	−4.55698	+	7.89293i	−0.483039	+	0.836648i	−0.999810	−	0.0194751i	$-0.993800\pi$
$89$	−4.55698	+	7.89293i	−0.483039	+	0.836648i	0.516771	+	0.856124i	$0.327134\pi$
$90$		0			0
$91$	−3.43805	+	1.08619i	−0.360406	+	0.113864i
$92$		0			0
$93$	0.623022	−	1.07911i	0.0646043	−	0.111898i
$94$		0			0
$95$	−1.73428	−	3.00386i	−0.177933	−	0.308190i
$96$		0			0
$97$	−5.68818	−	9.85222i	−0.577548	−	1.00034i	−0.995760	−	0.0919924i	$-0.970676\pi$
$97$	−5.68818	−	9.85222i	−0.577548	−	1.00034i	0.418212	−	0.908349i	$-0.362657\pi$
$98$		0			0
$99$	1.55672			0.156456
$100$		0			0
$101$	−2.47178	+	4.28124i	−0.245951	+	0.425999i	−0.962399	−	0.271642i	$-0.912434\pi$
$101$	−2.47178	+	4.28124i	−0.245951	+	0.425999i	0.716448	+	0.697641i	$0.245767\pi$
$102$		0			0
$103$	−1.27361			−0.125492			−0.0627462	−	0.998030i	$-0.519986\pi$
$103$	−1.27361			−0.125492			−0.0627462	+	0.998030i	$0.519986\pi$
$104$		0			0
$105$	1.09044			0.106416
$106$		0			0
$107$	2.34761	−	4.06618i	0.226952	−	0.393092i	−0.729951	−	0.683499i	$-0.760457\pi$
$107$	2.34761	−	4.06618i	0.226952	−	0.393092i	0.956903	+	0.290407i	$0.0937906\pi$
$108$		0			0
$109$	−12.7693			−1.22308			−0.611539	−	0.791215i	$-0.709449\pi$
$109$	−12.7693			−1.22308			−0.611539	+	0.791215i	$0.709449\pi$
$110$		0			0
$111$	−0.265719	−	0.460239i	−0.0252209	−	0.0436839i
$112$		0			0
$113$	−3.99068	−	6.91206i	−0.375411	−	0.650232i	0.614977	−	0.788545i	$-0.289165\pi$
$113$	−3.99068	−	6.91206i	−0.375411	−	0.650232i	−0.990389	+	0.138313i	$0.955832\pi$
$114$		0			0
$115$	−2.41811	+	4.18829i	−0.225490	+	0.390560i
$116$		0			0
$117$	−3.43805	+	1.08619i	−0.317848	+	0.100418i
$118$		0			0
$119$	−1.17233	+	2.03054i	−0.107467	+	0.186139i
$120$		0			0
$121$	4.28832	+	7.42758i	0.389847	+	0.675235i
$122$		0			0
$123$	4.66824	+	8.08563i	0.420921	+	0.729057i
$124$		0			0
$125$	9.60781			0.859348
$126$		0			0
$127$	5.17528	−	8.96385i	0.459232	−	0.795413i	−0.539689	−	0.841865i	$-0.681458\pi$
$127$	5.17528	−	8.96385i	0.459232	−	0.795413i	0.998921	+	0.0464519i	$0.0147914\pi$
$128$		0			0
$129$	−8.05698			−0.709378
$130$		0			0
$131$	2.76288			0.241394			0.120697	−	0.992689i	$-0.461487\pi$
$131$	2.76288			0.241394			0.120697	+	0.992689i	$0.461487\pi$
$132$		0			0
$133$	1.59044	−	2.75472i	0.137909	−	0.238865i
$134$		0			0
$135$	1.09044			0.0938502
$136$		0			0
$137$	1.10079	+	1.90663i	0.0940471	+	0.162894i	0.909211	−	0.416337i	$-0.136686\pi$
$137$	1.10079	+	1.90663i	0.0940471	+	0.162894i	−0.815163	+	0.579231i	$0.803353\pi$
$138$		0			0
$139$	−9.68295	−	16.7714i	−0.821297	−	1.42253i	−0.904717	−	0.426014i	$-0.859917\pi$
$139$	−9.68295	−	16.7714i	−0.821297	−	1.42253i	0.0834194	−	0.996515i	$-0.473416\pi$
$140$		0			0
$141$	−6.01176	+	10.4127i	−0.506282	+	0.876906i
$142$		0			0
$143$	4.14039	+	3.78958i	0.346237	+	0.316901i
$144$		0			0
$145$	0.888741	−	1.53934i	0.0738059	−	0.127836i
$146$		0			0
$147$	0.500000	+	0.866025i	0.0412393	+	0.0714286i
$148$		0			0
$149$	9.97804	+	17.2825i	0.817433	+	1.41584i	0.907568	+	0.419905i	$0.137937\pi$
$149$	9.97804	+	17.2825i	0.817433	+	1.41584i	−0.0901351	+	0.995930i	$0.528730\pi$
$150$		0			0
$151$	23.0887			1.87893			0.939465	−	0.342644i	$-0.111322\pi$
$151$	23.0887			1.87893			0.939465	+	0.342644i	$0.111322\pi$
$152$		0			0
$153$	−1.17233	+	2.03054i	−0.0947774	+	0.164159i
$154$		0			0
$155$	−1.35874			−0.109136
$156$		0			0
$157$	−22.8516			−1.82375			−0.911877	−	0.410464i	$-0.865367\pi$
$157$	−22.8516			−1.82375			−0.911877	+	0.410464i	$0.865367\pi$
$158$		0			0
$159$	−1.13006	+	1.95732i	−0.0896194	+	0.155225i
$160$		0			0
$161$	−4.43510			−0.349535
$162$		0			0
$163$	−2.28396	−	3.95594i	−0.178894	−	0.309853i	0.762608	−	0.646861i	$-0.223918\pi$
$163$	−2.28396	−	3.95594i	−0.178894	−	0.309853i	−0.941502	+	0.337008i	$0.890585\pi$
$164$		0			0
$165$	−0.848753	−	1.47008i	−0.0660754	−	0.114446i
$166$		0			0
$167$	9.77302	−	16.9274i	0.756259	−	1.30988i	−0.188487	−	0.982076i	$-0.560358\pi$
$167$	9.77302	−	16.9274i	0.756259	−	1.30988i	0.944746	−	0.327804i	$-0.106308\pi$
$168$		0			0
$169$	−11.7883	−	5.48047i	−0.906794	−	0.421575i
$170$		0			0
$171$	1.59044	−	2.75472i	0.121624	−	0.210659i
$172$		0			0
$173$	6.49477	+	11.2493i	0.493788	+	0.855266i	0.999974	−	0.00715820i	$-0.00227855\pi$
$173$	6.49477	+	11.2493i	0.493788	+	0.855266i	−0.506186	+	0.862424i	$0.668945\pi$
$174$		0			0
$175$	1.90547	+	3.30037i	0.144040	+	0.249485i
$176$		0			0
$177$	−9.49798			−0.713912
$178$		0			0
$179$	−4.59899	+	7.96568i	−0.343745	+	0.595383i	−0.985125	−	0.171840i	$-0.945029\pi$
$179$	−4.59899	+	7.96568i	−0.343745	+	0.595383i	0.641380	+	0.767223i	$0.278362\pi$
$180$		0			0
$181$	−3.83393			−0.284974			−0.142487	−	0.989797i	$-0.545510\pi$
$181$	−3.83393			−0.284974			−0.142487	+	0.989797i	$0.545510\pi$
$182$		0			0
$183$	0.440997			0.0325995
$184$		0			0
$185$	−0.289751	+	0.501863i	−0.0213029	+	0.0368977i
$186$		0			0
$187$	3.64998			0.266913
$188$		0			0
$189$	0.500000	+	0.866025i	0.0363696	+	0.0629941i
$190$		0			0
$191$	1.38133	+	2.39254i	0.0999499	+	0.173118i	0.911664	−	0.410937i	$-0.134798\pi$
$191$	1.38133	+	2.39254i	0.0999499	+	0.173118i	−0.811714	+	0.584055i	$0.801465\pi$
$192$		0			0
$193$	4.23864	−	7.34154i	0.305104	−	0.528455i	−0.672181	−	0.740387i	$-0.734642\pi$
$193$	4.23864	−	7.34154i	0.305104	−	0.528455i	0.977284	+	0.211932i	$0.0679755\pi$
$194$		0			0
$195$	2.90024	+	2.65451i	0.207690	+	0.190093i
$196$		0			0
$197$	−10.2912	+	17.8248i	−0.733215	+	1.26997i	0.222287	+	0.974981i	$0.428648\pi$
$197$	−10.2912	+	17.8248i	−0.733215	+	1.26997i	−0.955502	+	0.294984i	$0.904686\pi$
$198$		0			0
$199$	2.66530	+	4.61643i	0.188938	+	0.327250i	0.944896	−	0.327370i	$-0.106162\pi$
$199$	2.66530	+	4.61643i	0.188938	+	0.327250i	−0.755959	+	0.654619i	$0.772829\pi$
$200$		0			0
$201$	−0.861392	−	1.49198i	−0.0607579	−	0.105236i
$202$		0			0
$203$	1.63006			0.114408
$204$		0			0
$205$	5.09044	−	8.81690i	0.355532	−	0.615799i
$206$		0			0
$207$	−4.43510			−0.308261
$208$		0			0
$209$	−4.95173			−0.342518
$210$		0			0
$211$	−3.86471	+	6.69387i	−0.266058	+	0.460825i	−0.967840	−	0.251566i	$-0.919054\pi$
$211$	−3.86471	+	6.69387i	−0.266058	+	0.460825i	0.701783	+	0.712391i	$0.252388\pi$
$212$		0			0
$213$	3.21205			0.220086
$214$		0			0
$215$	4.39283	+	7.60861i	0.299589	+	0.518903i
$216$		0			0
$217$	−0.623022	−	1.07911i	−0.0422935	−	0.0732544i
$218$		0			0
$219$	0.885528	−	1.53378i	0.0598384	−	0.103643i
$220$		0			0
$221$	−8.06107	+	2.54675i	−0.542246	+	0.171313i
$222$		0			0
$223$	12.1095	−	20.9743i	0.810913	−	1.40454i	−0.101314	−	0.994855i	$-0.532305\pi$
$223$	12.1095	−	20.9743i	0.810913	−	1.40454i	0.912226	−	0.409687i	$-0.134362\pi$
$224$		0			0
$225$	1.90547	+	3.30037i	0.127031	+	0.220025i
$226$		0			0
$227$	−6.31235	−	10.9333i	−0.418965	−	0.725669i	0.576870	−	0.816836i	$-0.304274\pi$
$227$	−6.31235	−	10.9333i	−0.418965	−	0.725669i	−0.995836	+	0.0911665i	$0.970940\pi$
$228$		0			0
$229$	27.5743			1.82216			0.911082	−	0.412225i	$-0.135248\pi$
$229$	27.5743			1.82216			0.911082	+	0.412225i	$0.135248\pi$
$230$		0			0
$231$	0.778358	−	1.34816i	0.0512122	−	0.0887021i
$232$		0			0
$233$	−16.8791			−1.10579			−0.552894	−	0.833251i	$-0.686477\pi$
$233$	−16.8791			−1.10579			−0.552894	+	0.833251i	$0.686477\pi$
$234$		0			0
$235$	13.1109			0.855263
$236$		0			0
$237$	−0.511496	+	0.885937i	−0.0332252	+	0.0575478i
$238$		0			0
$239$	3.93308			0.254410			0.127205	−	0.991876i	$-0.459399\pi$
$239$	3.93308			0.254410			0.127205	+	0.991876i	$0.459399\pi$
$240$		0			0
$241$	3.48452	+	6.03536i	0.224458	+	0.388772i	0.956157	−	0.292856i	$-0.0946057\pi$
$241$	3.48452	+	6.03536i	0.224458	+	0.388772i	−0.731699	+	0.681628i	$0.761272\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	0.545220	−	0.944349i	0.0348328	−	0.0603323i
$246$		0			0
$247$	10.9360	−	3.45504i	0.695843	−	0.219839i
$248$		0			0
$249$	−7.97804	+	13.8184i	−0.505588	+	0.875703i
$250$		0			0
$251$	−9.31824	−	16.1397i	−0.588162	−	1.01873i	−0.994473	−	0.104992i	$-0.966518\pi$
$251$	−9.31824	−	16.1397i	−0.588162	−	1.01873i	0.406311	−	0.913735i	$-0.366815\pi$
$252$		0			0
$253$	3.45210	+	5.97921i	0.217032	+	0.375910i
$254$		0			0
$255$	2.55672			0.160108
$256$		0			0
$257$	1.83327	−	3.17532i	0.114356	−	0.198071i	−0.803166	−	0.595755i	$-0.796853\pi$
$257$	1.83327	−	3.17532i	0.114356	−	0.198071i	0.917522	+	0.397684i	$0.130186\pi$
$258$		0			0
$259$	−0.531438			−0.0330220
$260$		0			0
$261$	1.63006			0.100898
$262$		0			0
$263$	−1.48441	+	2.57108i	−0.0915329	+	0.158540i	−0.908156	−	0.418631i	$-0.862510\pi$
$263$	−1.48441	+	2.57108i	−0.0915329	+	0.158540i	0.816623	+	0.577171i	$0.195843\pi$
$264$		0			0
$265$	2.46452			0.151394
$266$		0			0
$267$	4.55698	+	7.89293i	0.278883	+	0.483039i
$268$		0			0
$269$	6.80162	+	11.7807i	0.414702	+	0.718285i	0.995397	−	0.0958363i	$-0.0305525\pi$
$269$	6.80162	+	11.7807i	0.414702	+	0.718285i	−0.580695	+	0.814121i	$0.697219\pi$
$270$		0			0
$271$	4.34031	−	7.51763i	0.263655	−	0.456664i	−0.703555	−	0.710640i	$-0.748405\pi$
$271$	4.34031	−	7.51763i	0.263655	−	0.456664i	0.967210	+	0.253977i	$0.0817387\pi$
$272$		0			0
$273$	−0.778358	+	3.52053i	−0.0471084	+	0.213072i
$274$		0			0
$275$	2.96628	−	5.13774i	0.178873	−	0.309817i
$276$		0			0
$277$	−9.05698	−	15.6872i	−0.544181	−	0.942550i	−0.998658	−	0.0517911i	$-0.983507\pi$
$277$	−9.05698	−	15.6872i	−0.544181	−	0.942550i	0.454477	−	0.890759i	$-0.349826\pi$
$278$		0			0
$279$	−0.623022	−	1.07911i	−0.0372993	−	0.0646043i
$280$		0			0
$281$	11.8050			0.704230			0.352115	−	0.935957i	$-0.385463\pi$
$281$	11.8050			0.704230			0.352115	+	0.935957i	$0.385463\pi$
$282$		0			0
$283$	5.30239	−	9.18401i	0.315194	−	0.545933i	−0.664284	−	0.747480i	$-0.731264\pi$
$283$	5.30239	−	9.18401i	0.315194	−	0.545933i	0.979479	+	0.201547i	$0.0645970\pi$
$284$		0			0
$285$	−3.46856			−0.205460
$286$		0			0
$287$	9.33648			0.551115
$288$		0			0
$289$	5.75128	−	9.96150i	0.338310	−	0.585971i
$290$		0			0
$291$	−11.3764			−0.666895
$292$		0			0
$293$	−2.62748	−	4.55093i	−0.153499	−	0.265868i	0.779012	−	0.627009i	$-0.215721\pi$
$293$	−2.62748	−	4.55093i	−0.153499	−	0.265868i	−0.932512	+	0.361140i	$0.882388\pi$
$294$		0			0
$295$	5.17849	+	8.96941i	0.301503	+	0.522219i
$296$		0			0
$297$	0.778358	−	1.34816i	0.0451649	−	0.0782279i
$298$		0			0
$299$	−11.7960	−	10.7966i	−0.682181	−	0.624382i
$300$		0			0
$301$	−4.02849	+	6.97755i	−0.232198	+	0.402179i
$302$		0			0
$303$	2.47178	+	4.28124i	0.142000	+	0.245951i
$304$		0			0
$305$	−0.240441	−	0.416456i	−0.0137676	−	0.0238462i
$306$		0			0
$307$	−13.9709			−0.797361			−0.398680	−	0.917090i	$-0.630532\pi$
$307$	−13.9709			−0.797361			−0.398680	+	0.917090i	$0.630532\pi$
$308$		0			0
$309$	−0.636804	+	1.10298i	−0.0362265	+	0.0627462i
$310$		0			0
$311$	−15.4300			−0.874952			−0.437476	−	0.899230i	$-0.644128\pi$
$311$	−15.4300			−0.874952			−0.437476	+	0.899230i	$0.644128\pi$
$312$		0			0
$313$	−4.45167			−0.251623			−0.125812	−	0.992054i	$-0.540153\pi$
$313$	−4.45167			−0.251623			−0.125812	+	0.992054i	$0.540153\pi$
$314$		0			0
$315$	0.545220	−	0.944349i	0.0307197	−	0.0532081i
$316$		0			0
$317$	−2.89528			−0.162615			−0.0813076	−	0.996689i	$-0.525910\pi$
$317$	−2.89528			−0.162615			−0.0813076	+	0.996689i	$0.525910\pi$
$318$		0			0
$319$	−1.26877	−	2.19757i	−0.0710374	−	0.123040i
$320$		0			0
$321$	−2.34761	−	4.06618i	−0.131031	−	0.226952i
$322$		0			0
$323$	3.72905	−	6.45890i	0.207490	−	0.359383i
$324$		0			0
$325$	−2.96628	+	13.4165i	−0.164539	+	0.744216i
$326$		0			0
$327$	−6.38465	+	11.0585i	−0.353072	+	0.611539i
$328$		0			0
$329$	6.01176	+	10.4127i	0.331439	+	0.574070i
$330$		0			0
$331$	12.5819	+	21.7925i	0.691563	+	1.19782i	0.971326	+	0.237753i	$0.0764110\pi$
$331$	12.5819	+	21.7925i	0.691563	+	1.19782i	−0.279762	+	0.960069i	$0.590256\pi$
$332$		0			0
$333$	−0.531438			−0.0291226
$334$		0			0
$335$	−0.939297	+	1.62691i	−0.0513193	+	0.0888876i
$336$		0			0
$337$	28.5662			1.55610			0.778049	−	0.628203i	$-0.216209\pi$
$337$	28.5662			1.55610			0.778049	+	0.628203i	$0.216209\pi$
$338$		0			0
$339$	−7.98135			−0.433488
$340$		0			0
$341$	−0.969868	+	1.67986i	−0.0525213	+	0.0909696i
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	2.41811	+	4.18829i	0.130187	+	0.225490i
$346$		0			0
$347$	−4.71870	−	8.17302i	−0.253313	−	0.438751i	0.711123	−	0.703068i	$-0.248187\pi$
$347$	−4.71870	−	8.17302i	−0.253313	−	0.438751i	−0.964436	+	0.264317i	$0.914854\pi$
$348$		0			0
$349$	4.65523	−	8.06310i	0.249189	−	0.431608i	−0.714112	−	0.700031i	$-0.753169\pi$
$349$	4.65523	−	8.06310i	0.249189	−	0.431608i	0.963301	+	0.268424i	$0.0865027\pi$
$350$		0			0
$351$	−0.778358	+	3.52053i	−0.0415457	+	0.187912i
$352$		0			0
$353$	−4.40226	+	7.62493i	−0.234308	+	0.405834i	−0.959071	−	0.283164i	$-0.908616\pi$
$353$	−4.40226	+	7.62493i	−0.234308	+	0.405834i	0.724763	+	0.688998i	$0.241949\pi$
$354$		0			0
$355$	−1.75128	−	3.03330i	−0.0929481	−	0.160991i
$356$		0			0
$357$	1.17233	+	2.03054i	0.0620464	+	0.107467i
$358$		0			0
$359$	28.9336			1.52706			0.763529	−	0.645774i	$-0.223465\pi$
$359$	28.9336			1.52706			0.763529	+	0.645774i	$0.223465\pi$
$360$		0			0
$361$	4.44100	−	7.69203i	0.233737	−	0.404844i
$362$		0			0
$363$	8.57663			0.450157
$364$		0			0
$365$	−1.93123			−0.101085
$366$		0			0
$367$	14.2722	−	24.7203i	0.745005	−	1.29039i	−0.205187	−	0.978723i	$-0.565780\pi$
$367$	14.2722	−	24.7203i	0.745005	−	1.29039i	0.950192	−	0.311664i	$-0.100886\pi$
$368$		0			0
$369$	9.33648			0.486038
$370$		0			0
$371$	1.13006	+	1.95732i	0.0586697	+	0.101619i
$372$		0			0
$373$	−5.07676	−	8.79321i	−0.262865	−	0.455295i	0.704137	−	0.710064i	$-0.251334\pi$
$373$	−5.07676	−	8.79321i	−0.262865	−	0.455295i	−0.967002	+	0.254769i	$0.918001\pi$
$374$		0			0
$375$	4.80390	−	8.32060i	0.248072	−	0.429674i
$376$		0			0
$377$	4.33545	+	3.96812i	0.223287	+	0.204369i
$378$		0			0
$379$	−3.81094	+	6.60074i	−0.195755	+	0.339057i	−0.947148	−	0.320798i	$-0.896049\pi$
$379$	−3.81094	+	6.60074i	−0.195755	+	0.339057i	0.751393	+	0.659855i	$0.229382\pi$
$380$		0			0
$381$	−5.17528	−	8.96385i	−0.265138	−	0.459232i
$382$		0			0
$383$	10.7357	+	18.5948i	0.548568	+	0.950148i	0.998373	+	0.0570210i	$0.0181602\pi$
$383$	10.7357	+	18.5948i	0.548568	+	0.950148i	−0.449805	+	0.893127i	$0.648506\pi$
$384$		0			0
$385$	−1.69751			−0.0865130
$386$		0			0
$387$	−4.02849	+	6.97755i	−0.204780	+	0.354689i
$388$		0			0
$389$	−12.6388			−0.640811			−0.320406	−	0.947280i	$-0.603819\pi$
$389$	−12.6388			−0.640811			−0.320406	+	0.947280i	$0.603819\pi$
$390$		0			0
$391$	−10.3988			−0.525891
$392$		0			0
$393$	1.38144	−	2.39272i	0.0696843	−	0.120697i
$394$		0			0
$395$	1.11551			0.0561275
$396$		0			0
$397$	6.65675	+	11.5298i	0.334093	+	0.578665i	0.983310	−	0.181938i	$-0.0582369\pi$
$397$	6.65675	+	11.5298i	0.334093	+	0.578665i	−0.649218	+	0.760603i	$0.724904\pi$
$398$		0			0
$399$	−1.59044	−	2.75472i	−0.0796216	−	0.137909i
$400$		0			0
$401$	5.31949	−	9.21362i	0.265643	−	0.460106i	−0.702089	−	0.712089i	$-0.747749\pi$
$401$	5.31949	−	9.21362i	0.265643	−	0.460106i	0.967732	+	0.251983i	$0.0810826\pi$
$402$		0			0
$403$	0.969868	−	4.38674i	0.0483126	−	0.218519i
$404$		0			0
$405$	0.545220	−	0.944349i	0.0270922	−	0.0469251i
$406$		0			0
$407$	0.413649	+	0.716461i	0.0205038	+	0.0355137i
$408$		0			0
$409$	−11.0259	−	19.0974i	−0.545196	−	0.944308i	−0.998595	−	0.0529997i	$-0.983122\pi$
$409$	−11.0259	−	19.0974i	−0.545196	−	0.944308i	0.453398	−	0.891308i	$-0.350212\pi$
$410$		0			0
$411$	2.20159			0.108596
$412$		0			0
$413$	−4.74899	+	8.22549i	−0.233683	+	0.404750i
$414$		0			0
$415$	17.3992			0.854091
$416$		0			0
$417$	−19.3659			−0.948352
$418$		0			0
$419$	12.2093	−	21.1471i	0.596462	−	1.03310i	−0.396877	−	0.917872i	$-0.629906\pi$
$419$	12.2093	−	21.1471i	0.596462	−	1.03310i	0.993339	−	0.115230i	$-0.0367606\pi$
$420$		0			0
$421$	10.1786			0.496074			0.248037	−	0.968751i	$-0.420214\pi$
$421$	10.1786			0.496074			0.248037	+	0.968751i	$0.420214\pi$
$422$		0			0
$423$	6.01176	+	10.4127i	0.292302	+	0.506282i
$424$		0			0
$425$	4.46769	+	7.73826i	0.216715	+	0.375361i
$426$		0			0
$427$	0.220499	−	0.381915i	0.0106707	−	0.0184822i
$428$		0			0
$429$	5.35207	−	1.69089i	0.258400	−	0.0816368i
$430$		0			0
$431$	7.93423	−	13.7425i	0.382178	−	0.661952i	−0.609195	−	0.793020i	$-0.708507\pi$
$431$	7.93423	−	13.7425i	0.382178	−	0.661952i	0.991373	+	0.131068i	$0.0418407\pi$
$432$		0			0
$433$	−7.35502	−	12.7393i	−0.353460	−	0.612210i	0.633394	−	0.773830i	$-0.281661\pi$
$433$	−7.35502	−	12.7393i	−0.353460	−	0.612210i	−0.986853	+	0.161620i	$0.948328\pi$
$434$		0			0
$435$	−0.888741	−	1.53934i	−0.0426119	−	0.0738059i
$436$		0			0
$437$	14.1075			0.674855
$438$		0			0
$439$	−4.92655	+	8.53304i	−0.235132	+	0.407260i	−0.959311	−	0.282352i	$-0.908885\pi$
$439$	−4.92655	+	8.53304i	−0.235132	+	0.407260i	0.724179	+	0.689612i	$0.242219\pi$
$440$		0			0
$441$	1.00000			0.0476190
$442$		0			0
$443$	6.85332			0.325611			0.162805	−	0.986658i	$-0.447946\pi$
$443$	6.85332			0.325611			0.162805	+	0.986658i	$0.447946\pi$
$444$		0			0
$445$	4.96912	−	8.60677i	0.235559	−	0.408000i
$446$		0			0
$447$	19.9561			0.943890
$448$		0			0
$449$	−8.49487	−	14.7135i	−0.400898	−	0.694375i	0.592937	−	0.805249i	$-0.297968\pi$
$449$	−8.49487	−	14.7135i	−0.400898	−	0.694375i	−0.993834	+	0.110874i	$0.964635\pi$
$450$		0			0
$451$	−7.26713	−	12.5870i	−0.342196	−	0.592700i
$452$		0			0
$453$	11.5443	−	19.9954i	0.542401	−	0.939465i
$454$		0			0
$455$	3.74899	−	1.18442i	0.175755	−	0.0555267i
$456$		0			0
$457$	−8.52005	+	14.7572i	−0.398551	+	0.690310i	−0.993547	−	0.113418i	$-0.963820\pi$
$457$	−8.52005	+	14.7572i	−0.398551	+	0.690310i	0.594996	+	0.803728i	$0.297153\pi$
$458$		0			0
$459$	1.17233	+	2.03054i	0.0547198	+	0.0947774i
$460$		0			0
$461$	1.71346	+	2.96780i	0.0798039	+	0.138224i	0.903165	−	0.429293i	$-0.141237\pi$
$461$	1.71346	+	2.96780i	0.0798039	+	0.138224i	−0.823361	+	0.567517i	$0.807904\pi$
$462$		0			0
$463$	26.4267			1.22815			0.614077	−	0.789246i	$-0.289528\pi$
$463$	26.4267			1.22815			0.614077	+	0.789246i	$0.289528\pi$
$464$		0			0
$465$	−0.679368	+	1.17670i	−0.0315049	+	0.0545682i
$466$		0			0
$467$	−28.5884			−1.32291			−0.661457	−	0.749983i	$-0.730062\pi$
$467$	−28.5884			−1.32291			−0.661457	+	0.749983i	$0.730062\pi$
$468$		0			0
$469$	−1.72278			−0.0795508
$470$		0			0
$471$	−11.4258	+	19.7900i	−0.526472	+	0.911877i
$472$		0			0
$473$	12.5424			0.576702
$474$		0			0
$475$	−6.06107	−	10.4981i	−0.278101	−	0.481685i
$476$		0			0
$477$	1.13006	+	1.95732i	0.0517418	+	0.0896194i
$478$		0			0
$479$	7.90661	−	13.6947i	0.361262	−	0.625725i	−0.626907	−	0.779094i	$-0.715679\pi$
$479$	7.90661	−	13.6947i	0.361262	−	0.625725i	0.988169	+	0.153370i	$0.0490125\pi$
$480$		0			0
$481$	−1.41346	−	1.29370i	−0.0644483	−	0.0589878i
$482$		0			0
$483$	−2.21755	+	3.84091i	−0.100902	+	0.174768i
$484$		0			0
$485$	6.20263	+	10.7433i	0.281647	+	0.487827i
$486$		0			0
$487$	6.94993	+	12.0376i	0.314931	+	0.545477i	0.979423	−	0.201819i	$-0.0646852\pi$
$487$	6.94993	+	12.0376i	0.314931	+	0.545477i	−0.664492	+	0.747296i	$0.731352\pi$
$488$		0			0
$489$	−4.56792			−0.206569
$490$		0			0
$491$	−6.67005	+	11.5529i	−0.301015	+	0.521373i	−0.976366	−	0.216123i	$-0.930659\pi$
$491$	−6.67005	+	11.5529i	−0.301015	+	0.521373i	0.675351	+	0.737496i	$0.263992\pi$
$492$		0			0
$493$	3.82194			0.172131
$494$		0			0
$495$	−1.69751			−0.0762973
$496$		0			0
$497$	1.60603	−	2.78172i	0.0720401	−	0.124777i
$498$		0			0
$499$	8.28156			0.370734			0.185367	−	0.982669i	$-0.440653\pi$
$499$	8.28156			0.370734			0.185367	+	0.982669i	$0.440653\pi$
$500$		0			0
$501$	−9.77302	−	16.9274i	−0.436626	−	0.756259i
$502$		0			0
$503$	−15.4544	−	26.7678i	−0.689077	−	1.19352i	−0.972137	−	0.234414i	$-0.924683\pi$
$503$	−15.4544	−	26.7678i	−0.689077	−	1.19352i	0.283060	−	0.959102i	$-0.408650\pi$
$504$		0			0
$505$	2.69532	−	4.66844i	0.119940	−	0.207743i
$506$		0			0
$507$	−10.6404	+	7.46875i	−0.472556	+	0.331699i
$508$		0			0
$509$	−0.796127	+	1.37893i	−0.0352877	+	0.0611201i	−0.883130	−	0.469129i	$-0.844568\pi$
$509$	−0.796127	+	1.37893i	−0.0352877	+	0.0611201i	0.847842	+	0.530249i	$0.177901\pi$
$510$		0			0
$511$	−0.885528	−	1.53378i	−0.0391734	−	0.0678504i
$512$		0			0
$513$	−1.59044	−	2.75472i	−0.0702197	−	0.121624i
$514$		0			0
$515$	1.38879			0.0611976
$516$		0			0
$517$	9.35861	−	16.2096i	0.411591	−	0.712897i
$518$		0			0
$519$	12.9895			0.570177
$520$		0			0
$521$	17.0383			0.746463			0.373232	−	0.927738i	$-0.378250\pi$
$521$	17.0383			0.746463			0.373232	+	0.927738i	$0.378250\pi$
$522$		0			0
$523$	11.8792	−	20.5753i	0.519439	−	0.899695i	−0.480306	−	0.877101i	$-0.659474\pi$
$523$	11.8792	−	20.5753i	0.519439	−	0.899695i	0.999745	−	0.0225936i	$-0.00719239\pi$
$524$		0			0
$525$	3.81094			0.166323
$526$		0			0
$527$	−1.46078	−	2.53014i	−0.0636324	−	0.110215i
$528$		0			0
$529$	1.66493	+	2.88374i	0.0723881	+	0.125380i
$530$		0			0
$531$	−4.74899	+	8.22549i	−0.206089	+	0.356956i
$532$		0			0
$533$	24.8322	+	22.7282i	1.07560	+	0.984469i
$534$		0			0
$535$	−2.55993	+	4.43393i	−0.110675	+	0.191695i
$536$		0			0
$537$	4.59899	+	7.96568i	0.198461	+	0.343745i
$538$		0			0
$539$	−0.778358	−	1.34816i	−0.0335263	−	0.0580692i
$540$		0			0
$541$	5.60425			0.240945			0.120473	−	0.992717i	$-0.461559\pi$
$541$	5.60425			0.240945			0.120473	+	0.992717i	$0.461559\pi$
$542$		0			0
$543$	−1.91697	+	3.32028i	−0.0822649	+	0.142487i
$544$		0			0
$545$	13.9242			0.596446
$546$		0			0
$547$	−6.22231			−0.266047			−0.133023	−	0.991113i	$-0.542469\pi$
$547$	−6.22231			−0.266047			−0.133023	+	0.991113i	$0.542469\pi$
$548$		0			0
$549$	0.220499	−	0.381915i	0.00941066	−	0.0162997i
$550$		0			0
$551$	−5.18502			−0.220889
$552$		0			0
$553$	0.511496	+	0.885937i	0.0217510	+	0.0376739i
$554$		0			0
$555$	0.289751	+	0.501863i	0.0122992	+	0.0213029i
$556$		0			0
$557$	−14.3495	+	24.8541i	−0.608008	+	1.05310i	0.383561	+	0.923516i	$0.374698\pi$
$557$	−14.3495	+	24.8541i	−0.608008	+	1.05310i	−0.991568	+	0.129584i	$0.958636\pi$
$558$		0			0
$559$	−27.7003	+	8.75141i	−1.17160	+	0.370145i
$560$		0			0
$561$	1.82499	−	3.16097i	0.0770511	−	0.133456i
$562$		0			0
$563$	16.2340	+	28.1182i	0.684183	+	1.18504i	0.973693	+	0.227865i	$0.0731745\pi$
$563$	16.2340	+	28.1182i	0.684183	+	1.18504i	−0.289509	+	0.957175i	$0.593492\pi$
$564$		0			0
$565$	4.35160	+	7.53719i	0.183073	+	0.317092i
$566$		0			0
$567$	1.00000			0.0419961
$568$		0			0
$569$	0.240544	−	0.416635i	0.0100841	−	0.0174662i	−0.860939	−	0.508708i	$-0.830123\pi$
$569$	0.240544	−	0.416635i	0.0100841	−	0.0174662i	0.871023	+	0.491241i	$0.163457\pi$
$570$		0			0
$571$	9.67658			0.404952			0.202476	−	0.979287i	$-0.435101\pi$
$571$	9.67658			0.404952			0.202476	+	0.979287i	$0.435101\pi$
$572$		0			0
$573$	2.76267			0.115412
$574$		0			0
$575$	−8.45096	+	14.6375i	−0.352429	+	0.610425i
$576$		0			0
$577$	−26.1664			−1.08932			−0.544660	−	0.838657i	$-0.683341\pi$
$577$	−26.1664			−1.08932			−0.544660	+	0.838657i	$0.683341\pi$
$578$		0			0
$579$	−4.23864	−	7.34154i	−0.176152	−	0.305104i
$580$		0			0
$581$	7.97804	+	13.8184i	0.330985	+	0.573282i
$582$		0			0
$583$	1.75918	−	3.04699i	0.0728578	−	0.126193i
$584$		0			0
$585$	3.74899	−	1.18442i	0.155002	−	0.0489699i
$586$		0			0
$587$	−4.31845	+	7.47977i	−0.178241	+	0.308723i	−0.941278	−	0.337632i	$-0.890374\pi$
$587$	−4.31845	+	7.47977i	−0.178241	+	0.308723i	0.763037	+	0.646355i	$0.223707\pi$
$588$		0			0
$589$	1.98176	+	3.43251i	0.0816569	+	0.141434i
$590$		0			0
$591$	10.2912	+	17.8248i	0.423322	+	0.733215i
$592$		0			0
$593$	18.8233			0.772979			0.386489	−	0.922294i	$-0.373688\pi$
$593$	18.8233			0.772979			0.386489	+	0.922294i	$0.373688\pi$
$594$		0			0
$595$	1.27836	−	2.21418i	0.0524076	−	0.0907726i
$596$		0			0
$597$	5.33059			0.218167
$598$		0			0
$599$	34.1229			1.39422			0.697112	−	0.716963i	$-0.254468\pi$
$599$	34.1229			1.39422			0.697112	+	0.716963i	$0.254468\pi$
$600$		0			0
$601$	18.0455	−	31.2557i	0.736091	−	1.27495i	−0.218152	−	0.975915i	$-0.570003\pi$
$601$	18.0455	−	31.2557i	0.736091	−	1.27495i	0.954243	−	0.299032i	$-0.0966637\pi$
$602$		0			0
$603$	−1.72278			−0.0701572
$604$		0			0
$605$	−4.67616	−	8.09934i	−0.190113	−	0.329285i
$606$		0			0
$607$	14.8301	+	25.6865i	0.601936	+	1.04258i	0.992528	+	0.122019i	$0.0389369\pi$
$607$	14.8301	+	25.6865i	0.601936	+	1.04258i	−0.390592	+	0.920564i	$0.627730\pi$
$608$		0			0
$609$	0.815029	−	1.41167i	0.0330266	−	0.0572038i
$610$		0			0
$611$	−9.35861	+	42.3292i	−0.378609	+	1.71246i
$612$		0			0
$613$	17.0920	−	29.6042i	0.690340	−	1.19570i	−0.281387	−	0.959594i	$-0.590794\pi$
$613$	17.0920	−	29.6042i	0.690340	−	1.19570i	0.971727	−	0.236109i	$-0.0758722\pi$
$614$		0			0
$615$	−5.09044	−	8.81690i	−0.205266	−	0.355532i
$616$		0			0
$617$	12.5598	+	21.7543i	0.505640	+	0.875793i	0.999979	+	0.00652429i	$0.00207676\pi$
$617$	12.5598	+	21.7543i	0.505640	+	0.875793i	−0.494339	+	0.869269i	$0.664590\pi$
$618$		0			0
$619$	21.3201			0.856928			0.428464	−	0.903559i	$-0.359055\pi$
$619$	21.3201			0.856928			0.428464	+	0.903559i	$0.359055\pi$
$620$		0			0
$621$	−2.21755	+	3.84091i	−0.0889873	+	0.154131i
$622$		0			0
$623$	9.11397			0.365143
$624$		0			0
$625$	8.57796			0.343118
$626$		0			0
$627$	−2.47586	+	4.28832i	−0.0988765	+	0.171259i
$628$		0			0
$629$	−1.24604			−0.0496830
$630$		0			0
$631$	−3.97509	−	6.88506i	−0.158246	−	0.274090i	0.775990	−	0.630745i	$-0.217251\pi$
$631$	−3.97509	−	6.88506i	−0.158246	−	0.274090i	−0.934236	+	0.356655i	$0.883917\pi$
$632$		0			0
$633$	3.86471	+	6.69387i	0.153608	+	0.266058i
$634$		0			0
$635$	−5.64333	+	9.77454i	−0.223949	+	0.387891i
$636$		0			0
$637$	2.65969	+	2.43434i	0.105381	+	0.0964523i
$638$		0			0
$639$	1.60603	−	2.78172i	0.0635334	−	0.110043i
$640$		0			0
$641$	−17.1841	−	29.7637i	−0.678731	−	1.17560i	−0.975363	−	0.220605i	$-0.929197\pi$
$641$	−17.1841	−	29.7637i	−0.678731	−	1.17560i	0.296632	−	0.954992i	$-0.404136\pi$
$642$		0			0
$643$	15.3681	+	26.6184i	0.606060	+	1.04973i	0.991883	+	0.127154i	$0.0405841\pi$
$643$	15.3681	+	26.6184i	0.606060	+	1.04973i	−0.385823	+	0.922573i	$0.626083\pi$
$644$		0			0
$645$	8.78566			0.345935
$646$		0			0
$647$	12.7105	−	22.0153i	0.499702	−	0.865509i	−0.500298	−	0.865853i	$-0.666776\pi$
$647$	12.7105	−	22.0153i	0.499702	−	0.865509i	1.00000		0.000344143i	$0.000109544\pi$
$648$		0			0
$649$	14.7857			0.580388
$650$		0			0
$651$	−1.24604			−0.0488363
$652$		0			0
$653$	0.231704	−	0.401323i	0.00906729	−	0.0157050i	−0.861456	−	0.507832i	$-0.830447\pi$
$653$	0.231704	−	0.401323i	0.00906729	−	0.0157050i	0.870523	+	0.492127i	$0.163780\pi$
$654$		0			0
$655$	−3.01275			−0.117718
$656$		0			0
$657$	−0.885528	−	1.53378i	−0.0345477	−	0.0598384i
$658$		0			0
$659$	1.43815	+	2.49096i	0.0560225	+	0.0970339i	0.892677	−	0.450698i	$-0.148825\pi$
$659$	1.43815	+	2.49096i	0.0560225	+	0.0970339i	−0.836654	+	0.547732i	$0.815491\pi$
$660$		0			0
$661$	−3.00475	+	5.20438i	−0.116871	+	0.202427i	−0.918526	−	0.395360i	$-0.870620\pi$
$661$	−3.00475	+	5.20438i	−0.116871	+	0.202427i	0.801655	+	0.597787i	$0.203953\pi$
$662$		0			0
$663$	−1.82499	+	8.25447i	−0.0708767	+	0.320577i
$664$		0			0
$665$	−1.73428	+	3.00386i	−0.0672525	+	0.116485i
$666$		0			0
$667$	3.61474	+	6.26091i	0.139963	+	0.242423i
$668$		0			0
$669$	−12.1095	−	20.9743i	−0.468181	−	0.810913i
$670$		0			0
$671$	−0.686508			−0.0265023
$672$		0			0
$673$	−7.23938	+	12.5390i	−0.279057	+	0.483342i	−0.971151	−	0.238466i	$-0.923355\pi$
$673$	−7.23938	+	12.5390i	−0.279057	+	0.483342i	0.692093	+	0.721808i	$0.256689\pi$
$674$		0			0
$675$	3.81094			0.146683
$676$		0			0
$677$	−28.9665			−1.11327			−0.556637	−	0.830756i	$-0.687909\pi$
$677$	−28.9665			−1.11327			−0.556637	+	0.830756i	$0.687909\pi$
$678$		0			0
$679$	−5.68818	+	9.85222i	−0.218292	+	0.378094i
$680$		0			0
$681$	−12.6247			−0.483779
$682$		0			0
$683$	−17.6133	−	30.5071i	−0.673954	−	1.16732i	−0.976773	−	0.214275i	$-0.931261\pi$
$683$	−17.6133	−	30.5071i	−0.673954	−	1.16732i	0.302819	−	0.953048i	$-0.402072\pi$
$684$		0			0
$685$	−1.20035	−	2.07907i	−0.0458630	−	0.0794371i
$686$		0			0
$687$	13.7872	−	23.8801i	0.526013	−	0.911082i
$688$		0			0
$689$	−1.75918	+	7.95682i	−0.0670194	+	0.303131i
$690$		0			0
$691$	−14.6925	+	25.4482i	−0.558931	+	0.968096i	0.438655	+	0.898655i	$0.355455\pi$
$691$	−14.6925	+	25.4482i	−0.558931	+	0.968096i	−0.997586	+	0.0694408i	$0.977878\pi$
$692$		0			0
$693$	−0.778358	−	1.34816i	−0.0295674	−	0.0512122i
$694$		0			0
$695$	10.5587	+	18.2882i	0.400514	+	0.693710i
$696$		0			0
$697$	21.8909			0.829178
$698$		0			0
$699$	−8.43956	+	14.6178i	−0.319214	+	0.552894i
$700$		0			0
$701$	31.5677			1.19230			0.596148	−	0.802875i	$-0.296697\pi$
$701$	31.5677			1.19230			0.596148	+	0.802875i	$0.296697\pi$
$702$		0			0
$703$	1.69044			0.0637562
$704$		0			0
$705$	6.55547	−	11.3544i	0.246893	−	0.427632i
$706$		0			0
$707$	4.94355			0.185921
$708$		0			0
$709$	16.2054	+	28.0687i	0.608608	+	1.05414i	0.991470	+	0.130335i	$0.0416052\pi$
$709$	16.2054	+	28.0687i	0.608608	+	1.05414i	−0.382862	+	0.923806i	$0.625061\pi$
$710$		0			0
$711$	0.511496	+	0.885937i	0.0191826	+	0.0332252i
$712$		0			0
$713$	2.76317	−	4.78594i	0.103481	−	0.179235i
$714$		0			0
$715$	−4.51485	−	4.13232i	−0.168846	−	0.154540i
$716$		0			0
$717$	1.96654	−	3.40615i	0.0734419	−	0.127205i
$718$		0			0
$719$	−19.7099	−	34.1386i	−0.735055	−	1.27315i	−0.954699	−	0.297573i	$-0.903823\pi$
$719$	−19.7099	−	34.1386i	−0.735055	−	1.27315i	0.219644	−	0.975580i	$-0.429511\pi$
$720$		0			0
$721$	0.636804	+	1.10298i	0.0237158	+	0.0410770i
$722$		0			0
$723$	6.96904			0.259181
$724$		0			0
$725$	3.10603	−	5.37980i	0.115355	−	0.199801i
$726$		0			0
$727$	−17.6513			−0.654650			−0.327325	−	0.944912i	$-0.606147\pi$
$727$	−17.6513			−0.654650			−0.327325	+	0.944912i	$0.606147\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−9.44546	+	16.3600i	−0.349353	+	0.605097i
$732$		0			0
$733$	37.9452			1.40154			0.700769	−	0.713388i	$-0.252840\pi$
$733$	37.9452			1.40154			0.700769	+	0.713388i	$0.252840\pi$
$734$		0			0
$735$	−0.545220	−	0.944349i	−0.0201108	−	0.0348328i
$736$		0			0
$737$	1.34094	+	2.32258i	0.0493943	+	0.0855534i
$738$		0			0
$739$	9.89641	−	17.1411i	0.364045	−	0.630545i	−0.624577	−	0.780963i	$-0.714729\pi$
$739$	9.89641	−	17.1411i	0.364045	−	0.630545i	0.988622	+	0.150418i	$0.0480619\pi$
$740$		0			0
$741$	2.47586	−	11.1984i	0.0909532	−	0.411383i
$742$		0			0
$743$	−1.43500	+	2.48549i	−0.0526451	+	0.0911839i	−0.891147	−	0.453715i	$-0.850099\pi$
$743$	−1.43500	+	2.48549i	−0.0526451	+	0.0911839i	0.838502	+	0.544899i	$0.183432\pi$
$744$		0			0
$745$	−10.8805	−	18.8455i	−0.398629	−	0.690446i
$746$		0			0
$747$	7.97804	+	13.8184i	0.291901	+	0.505588i
$748$		0			0
$749$	−4.69522			−0.171560
$750$		0			0
$751$	12.6520	−	21.9139i	0.461678	−	0.799649i	−0.537367	−	0.843348i	$-0.680581\pi$
$751$	12.6520	−	21.9139i	0.461678	−	0.799649i	0.999045	+	0.0436994i	$0.0139144\pi$
$752$		0			0
$753$	−18.6365			−0.679151
$754$		0			0
$755$	−25.1768			−0.916279
$756$		0			0
$757$	−5.55101	+	9.61463i	−0.201755	+	0.349450i	−0.949094	−	0.314993i	$-0.897998\pi$
$757$	−5.55101	+	9.61463i	−0.201755	+	0.349450i	0.747339	+	0.664443i	$0.231331\pi$
$758$		0			0
$759$	6.90420			0.250607
$760$		0			0
$761$	12.7362	+	22.0598i	0.461689	+	0.799668i	0.999045	−	0.0436870i	$-0.0139104\pi$
$761$	12.7362	+	22.0598i	0.461689	+	0.799668i	−0.537357	+	0.843355i	$0.680577\pi$
$762$		0			0
$763$	6.38465	+	11.0585i	0.231140	+	0.400346i
$764$		0			0
$765$	1.27836	−	2.21418i	0.0462191	−	0.0800539i
$766$		0			0
$767$	−32.6545	+	10.3166i	−1.17909	+	0.372511i
$768$		0			0
$769$	−22.1415	+	38.3503i	−0.798444	+	1.38295i	0.122185	+	0.992507i	$0.461010\pi$
$769$	−22.1415	+	38.3503i	−0.798444	+	1.38295i	−0.920629	+	0.390438i	$0.872323\pi$
$770$		0			0
$771$	−1.83327	−	3.17532i	−0.0660236	−	0.114356i
$772$		0			0
$773$	−7.47955	−	12.9550i	−0.269021	−	0.465958i	0.699588	−	0.714546i	$-0.253367\pi$
$773$	−7.47955	−	12.9550i	−0.269021	−	0.465958i	−0.968609	+	0.248588i	$0.920033\pi$
$774$		0			0
$775$	−4.74860			−0.170575
$776$		0			0
$777$	−0.265719	+	0.460239i	−0.00953262	+	0.0165110i
$778$		0			0
$779$	−29.6982			−1.06405
$780$		0			0
$781$	−5.00025			−0.178923
$782$		0			0
$783$	0.815029	−	1.41167i	0.0291268	−	0.0504490i
$784$		0			0
$785$	24.9183			0.889371
$786$		0			0
$787$	−9.63697	−	16.6917i	−0.343521	−	0.594995i	0.641563	−	0.767070i	$-0.278286\pi$
$787$	−9.63697	−	16.6917i	−0.343521	−	0.594995i	−0.985084	+	0.172075i	$0.944953\pi$
$788$		0			0
$789$	1.48441	+	2.57108i	0.0528465	+	0.0915329i
$790$		0			0
$791$	−3.99068	+	6.91206i	−0.141892	+	0.245764i
$792$		0			0
$793$	1.51617	−	0.479007i	0.0538408	−	0.0170100i
$794$		0			0
$795$	1.23226	−	2.13434i	0.0437038	−	0.0756972i
$796$		0			0
$797$	−14.9343	−	25.8670i	−0.529001	−	0.916257i	−0.999428	−	0.0338179i	$-0.989233\pi$
$797$	−14.9343	−	25.8670i	−0.529001	−	0.916257i	0.470427	−	0.882439i	$-0.344100\pi$
$798$		0			0
$799$	14.0956	+	24.4142i	0.498665	+	0.863713i
$800$		0			0
$801$	9.11397			0.322026
$802$		0			0
$803$	−1.37852	+	2.38766i	−0.0486467	+	0.0842586i
$804$		0			0
$805$	4.83622			0.170454
$806$		0			0
$807$	13.6032			0.478856
$808$		0			0
$809$	20.7782	−	35.9890i	0.730524	−	1.26530i	−0.226136	−	0.974096i	$-0.572609\pi$
$809$	20.7782	−	35.9890i	0.730524	−	1.26530i	0.956660	−	0.291208i	$-0.0940573\pi$
$810$		0			0
$811$	−42.6317			−1.49700			−0.748501	−	0.663134i	$-0.769226\pi$
$811$	−42.6317			−1.49700			−0.748501	+	0.663134i	$0.769226\pi$
$812$		0			0
$813$	−4.34031	−	7.51763i	−0.152221	−	0.263655i
$814$		0			0
$815$	2.49052	+	4.31371i	0.0872392	+	0.151103i
$816$		0			0
$817$	12.8142	−	22.1948i	0.448310	−	0.776496i
$818$		0			0
$819$	2.65969	+	2.43434i	0.0929372	+	0.0850629i
$820$		0			0
$821$	−18.9682	+	32.8540i	−0.661996	+	1.14661i	0.318094	+	0.948059i	$0.396957\pi$
$821$	−18.9682	+	32.8540i	−0.661996	+	1.14661i	−0.980090	+	0.198552i	$0.936376\pi$
$822$		0			0
$823$	16.0865	+	27.8627i	0.560741	+	0.971231i	0.997432	+	0.0716199i	$0.0228168\pi$
$823$	16.0865	+	27.8627i	0.560741	+	0.971231i	−0.436691	+	0.899611i	$0.643850\pi$
$824$		0			0
$825$	−2.96628	−	5.13774i	−0.103272	−	0.178873i
$826$		0			0
$827$	1.17164			0.0407418			0.0203709	−	0.999792i	$-0.493515\pi$
$827$	1.17164			0.0407418			0.0203709	+	0.999792i	$0.493515\pi$
$828$		0			0
$829$	0.647536	−	1.12157i	0.0224899	−	0.0389536i	−0.854561	−	0.519350i	$-0.826174\pi$
$829$	0.647536	−	1.12157i	0.0224899	−	0.0389536i	0.877051	+	0.480397i	$0.159507\pi$
$830$		0			0
$831$	−18.1140			−0.628367
$832$		0			0
$833$	2.34466			0.0812378
$834$		0			0
$835$	−10.6569	+	18.4583i	−0.368797	+	0.638776i
$836$		0			0
$837$	−1.24604			−0.0430696
$838$		0			0
$839$	−7.40972	−	12.8340i	−0.255812	−	0.443079i	0.709304	−	0.704903i	$-0.249009\pi$
$839$	−7.40972	−	12.8340i	−0.255812	−	0.443079i	−0.965116	+	0.261824i	$0.915676\pi$
$840$		0			0
$841$	13.1715	+	22.8136i	0.454188	+	0.786677i
$842$		0			0
$843$	5.90252	−	10.2235i	0.203294	−	0.352115i
$844$		0			0
$845$	12.8545	+	5.97613i	0.442207	+	0.205585i
$846$		0			0
$847$	4.28832	−	7.42758i	0.147348	−	0.255215i
$848$		0			0
$849$	−5.30239	−	9.18401i	−0.181978	−	0.315194i
$850$		0			0
$851$	−1.17849	−	2.04121i	−0.0403982	−	0.0699717i
$852$		0			0
$853$	−32.5500			−1.11449			−0.557246	−	0.830348i	$-0.688142\pi$
$853$	−32.5500			−1.11449			−0.557246	+	0.830348i	$0.688142\pi$
$854$		0			0
$855$	−1.73428	+	3.00386i	−0.0593112	+	0.102730i
$856$		0			0
$857$	10.2267			0.349336			0.174668	−	0.984627i	$-0.444115\pi$
$857$	10.2267			0.349336			0.174668	+	0.984627i	$0.444115\pi$
$858$		0			0
$859$	−33.1544			−1.13121			−0.565606	−	0.824675i	$-0.691358\pi$
$859$	−33.1544			−1.13121			−0.565606	+	0.824675i	$0.691358\pi$
$860$		0			0
$861$	4.66824	−	8.08563i	0.159093	−	0.275558i
$862$		0			0
$863$	25.9057			0.881841			0.440921	−	0.897546i	$-0.354652\pi$
$863$	25.9057			0.881841			0.440921	+	0.897546i	$0.354652\pi$
$864$		0			0
$865$	−7.08216	−	12.2667i	−0.240801	−	0.417079i
$866$		0			0
$867$	−5.75128	−	9.96150i	−0.195324	−	0.338310i
$868$		0			0
$869$	0.796254	−	1.37915i	0.0270111	−	0.0467846i
$870$		0			0
$871$	−4.58208	−	4.19385i	−0.155258	−	0.142103i
$872$		0			0
$873$	−5.68818	+	9.85222i	−0.192516	+	0.333447i
$874$		0			0
$875$	−4.80390	−	8.32060i	−0.162402	−	0.281288i
$876$		0			0
$877$	−12.4327	−	21.5341i	−0.419823	−	0.727155i	0.576098	−	0.817380i	$-0.304574\pi$
$877$	−12.4327	−	21.5341i	−0.419823	−	0.727155i	−0.995921	+	0.0902257i	$0.971241\pi$
$878$		0			0
$879$	−5.25496			−0.177245
$880$		0			0
$881$	22.1503	−	38.3655i	0.746264	−	1.29257i	−0.203338	−	0.979109i	$-0.565179\pi$
$881$	22.1503	−	38.3655i	0.746264	−	1.29257i	0.949602	−	0.313459i	$-0.101488\pi$
$882$		0			0
$883$	−42.3723			−1.42594			−0.712971	−	0.701193i	$-0.752651\pi$
$883$	−42.3723			−1.42594			−0.712971	+	0.701193i	$0.752651\pi$
$884$		0			0
$885$	10.3570			0.348146
$886$		0			0
$887$	−3.82384	+	6.62309i	−0.128392	+	0.222382i	−0.923054	−	0.384671i	$-0.874315\pi$
$887$	−3.82384	+	6.62309i	−0.128392	+	0.222382i	0.794662	+	0.607053i	$0.207648\pi$
$888$		0			0
$889$	−10.3506			−0.347147
$890$		0			0
$891$	−0.778358	−	1.34816i	−0.0260760	−	0.0451649i
$892$		0			0
$893$	−19.1227	−	33.1215i	−0.639917	−	1.10837i
$894$		0			0
$895$	5.01493	−	8.68611i	0.167630	−	0.290344i
$896$		0			0
$897$	−15.2481	+	4.81736i	−0.509120	+	0.160847i
$898$		0			0
$899$	−1.01556	+	1.75900i	−0.0338709	+	0.0586661i
$900$		0			0
$901$	2.64961	+	4.58925i	0.0882712	+	0.152890i
$902$		0			0
$903$	4.02849	+	6.97755i	0.134060	+	0.232198i
$904$		0			0
$905$	4.18067			0.138970
$906$		0			0
$907$	−0.342087	+	0.592512i	−0.0113588	+	0.0196740i	−0.871649	−	0.490131i	$-0.836949\pi$
$907$	−0.342087	+	0.592512i	−0.0113588	+	0.0196740i	0.860290	+	0.509805i	$0.170282\pi$
$908$		0			0
$909$	4.94355			0.163967
$910$		0			0
$911$	−46.8414			−1.55193			−0.775963	−	0.630779i	$-0.782736\pi$
$911$	−46.8414			−1.55193			−0.775963	+	0.630779i	$0.782736\pi$
$912$		0			0
$913$	12.4195	−	21.5113i	0.411027	−	0.711919i
$914$		0			0
$915$	−0.480882			−0.0158975
$916$		0			0
$917$	−1.38144	−	2.39272i	−0.0456191	−	0.0790146i
$918$		0			0
$919$	10.9571	+	18.9782i	0.361440	+	0.626033i	0.988198	−	0.153181i	$-0.0489518\pi$
$919$	10.9571	+	18.9782i	0.361440	+	0.626033i	−0.626758	+	0.779214i	$0.715618\pi$
$920$		0			0
$921$	−6.98544	+	12.0991i	−0.230178	+	0.398680i
$922$		0			0
$923$	11.0432	−	3.48890i	0.363491	−	0.114838i
$924$		0			0
$925$	−1.01264	+	1.75394i	−0.0332954	+	0.0576693i
$926$		0			0
$927$	0.636804	+	1.10298i	0.0209154	+	0.0362265i
$928$		0			0
$929$	8.27655	+	14.3354i	0.271545	+	0.470330i	0.969258	−	0.246048i	$-0.0791321\pi$
$929$	8.27655	+	14.3354i	0.271545	+	0.470330i	−0.697713	+	0.716378i	$0.745799\pi$
$930$		0			0
$931$	−3.18088			−0.104249
$932$		0			0
$933$	−7.71498	+	13.3627i	−0.252577	+	0.437476i
$934$		0			0
$935$	−3.98008			−0.130163
$936$		0			0
$937$	−21.5208			−0.703053			−0.351526	−	0.936178i	$-0.614337\pi$
$937$	−21.5208			−0.703053			−0.351526	+	0.936178i	$0.614337\pi$
$938$		0			0
$939$	−2.22583	+	3.85526i	−0.0726374	+	0.125812i
$940$		0			0
$941$	−2.98253			−0.0972276			−0.0486138	−	0.998818i	$-0.515480\pi$
$941$	−2.98253			−0.0972276			−0.0486138	+	0.998818i	$0.515480\pi$
$942$		0			0
$943$	20.7041	+	35.8606i	0.674220	+	1.16778i
$944$		0			0
$945$	−0.545220	−	0.944349i	−0.0177360	−	0.0307197i
$946$		0			0
$947$	2.94071	−	5.09345i	0.0955601	−	0.165515i	−0.814282	−	0.580469i	$-0.802869\pi$
$947$	2.94071	−	5.09345i	0.0955601	−	0.165515i	0.909842	+	0.414954i	$0.136202\pi$
$948$		0			0
$949$	1.37852	−	6.23506i	0.0447485	−	0.202399i
$950$		0			0
$951$	−1.44764	+	2.50739i	−0.0469429	+	0.0813076i
$952$		0			0
$953$	13.6661	+	23.6704i	0.442689	+	0.766760i	0.997888	−	0.0649577i	$-0.0206912\pi$
$953$	13.6661	+	23.6704i	0.442689	+	0.766760i	−0.555199	+	0.831718i	$0.687358\pi$
$954$		0			0
$955$	−1.50626	−	2.60892i	−0.0487415	−	0.0844228i
$956$		0			0
$957$	−2.53754			−0.0820270
$958$		0			0
$959$	1.10079	−	1.90663i	0.0355465	−	0.0615683i
$960$		0			0
$961$	−29.4474			−0.949915
$962$		0			0
$963$	−4.69522			−0.151301
$964$		0			0
$965$	−4.62198	+	8.00551i	−0.148787	+	0.257706i
$966$		0			0
$967$	−49.2819			−1.58480			−0.792399	−	0.610003i	$-0.791168\pi$
$967$	−49.2819			−1.58480			−0.792399	+	0.610003i	$0.791168\pi$
$968$		0			0
$969$	−3.72905	−	6.45890i	−0.119794	−	0.207490i
$970$		0			0
$971$	−16.0441	−	27.7893i	−0.514881	−	0.891800i	−0.999851	−	0.0172690i	$-0.994503\pi$
$971$	−16.0441	−	27.7893i	−0.514881	−	0.891800i	0.484970	−	0.874531i	$-0.338831\pi$
$972$		0			0
$973$	−9.68295	+	16.7714i	−0.310421	+	0.537665i
$974$		0			0
$975$	10.1359	+	9.27714i	0.324609	+	0.297106i
$976$		0			0
$977$	−21.8795	+	37.8964i	−0.699988	+	1.21241i	0.268482	+	0.963285i	$0.413478\pi$
$977$	−21.8795	+	37.8964i	−0.699988	+	1.21241i	−0.968470	+	0.249130i	$0.919855\pi$
$978$		0			0
$979$	−7.09393	−	12.2870i	−0.226723	−	0.392696i
$980$		0			0
$981$	6.38465	+	11.0585i	0.203846	+	0.353072i
$982$		0			0
$983$	−10.6523			−0.339754			−0.169877	−	0.985465i	$-0.554337\pi$
$983$	−10.6523			−0.339754			−0.169877	+	0.985465i	$0.554337\pi$
$984$		0			0
$985$	11.2219	−	19.4369i	0.357559	−	0.619311i
$986$		0			0
$987$	12.0235			0.382713
$988$		0			0
$989$	−35.7336			−1.13626
$990$		0			0
$991$	22.4629	−	38.9069i	0.713558	−	1.23592i	−0.249955	−	0.968258i	$-0.580416\pi$
$991$	22.4629	−	38.9069i	0.713558	−	1.23592i	0.963513	−	0.267662i	$-0.0862510\pi$
$992$		0			0
$993$	25.1638			0.798548
$994$		0			0
$995$	−2.90635	−	5.03394i	−0.0921374	−	0.159587i
$996$		0			0
$997$	−17.4626	−	30.2461i	−0.553047	−	0.957905i	−0.998053	−	0.0623772i	$-0.980132\pi$
$997$	−17.4626	−	30.2461i	−0.553047	−	0.957905i	0.445006	−	0.895528i	$-0.353202\pi$
$998$		0			0
$999$	−0.265719	+	0.460239i	−0.00840698	+	0.0145613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2184.2.bj.k.841.2	✓	8
13.3	even	3	inner	2184.2.bj.k.1849.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2184.2.bj.k.841.2	✓	8	1.1	even	1	trivial
2184.2.bj.k.1849.2	yes	8	13.3	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2184 = 2^{3} \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2184.bj (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} -1.09044 q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} -1.09044 q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-0.778358 + 1.34816i) q^{11} +(0.778358 - 3.52053i) q^{13} +(-0.545220 + 0.944349i) q^{15} +(-1.17233 - 2.03054i) q^{17} +(1.59044 + 2.75472i) q^{19} -1.00000 q^{21} +(2.21755 - 3.84091i) q^{23} -3.81094 q^{25} -1.00000 q^{27} +(-0.815029 + 1.41167i) q^{29} +1.24604 q^{31} +(0.778358 + 1.34816i) q^{33} +(0.545220 + 0.944349i) q^{35} +(0.265719 - 0.460239i) q^{37} +(-2.65969 - 2.43434i) q^{39} +(-4.66824 + 8.08563i) q^{41} +(-4.02849 - 6.97755i) q^{43} +(0.545220 + 0.944349i) q^{45} -12.0235 q^{47} +(-0.500000 + 0.866025i) q^{49} -2.34466 q^{51} -2.26012 q^{53} +(0.848753 - 1.47008i) q^{55} +3.18088 q^{57} +(-4.74899 - 8.22549i) q^{59} +(0.220499 + 0.381915i) q^{61} +(-0.500000 + 0.866025i) q^{63} +(-0.848753 + 3.83893i) q^{65} +(0.861392 - 1.49198i) q^{67} +(-2.21755 - 3.84091i) q^{69} +(1.60603 + 2.78172i) q^{71} +1.77106 q^{73} +(-1.90547 + 3.30037i) q^{75} +1.55672 q^{77} -1.02299 q^{79} +(-0.500000 + 0.866025i) q^{81} -15.9561 q^{83} +(1.27836 + 2.21418i) q^{85} +(0.815029 + 1.41167i) q^{87} +(-4.55698 + 7.89293i) q^{89} +(-3.43805 + 1.08619i) q^{91} +(0.623022 - 1.07911i) q^{93} +(-1.73428 - 3.00386i) q^{95} +(-5.68818 - 9.85222i) q^{97} +1.55672 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 4 * q^7 - 4 * q^9	\( 8 q + 4 q^{3} - 4 q^{7} - 4 q^{9} - 3 q^{11} + 3 q^{13} + q^{17} + 4 q^{19} - 8 q^{21} + 3 q^{23} - 12 q^{25} - 8 q^{27} - 6 q^{29} - 38 q^{31} + 3 q^{33} - 12 q^{37} - 9 q^{41} + q^{43} + 28 q^{47} - 4 q^{49} + 2 q^{51} - 16 q^{53} + 4 q^{55} + 8 q^{57} + 5 q^{59} - 8 q^{61} - 4 q^{63} - 4 q^{65} + 15 q^{67} - 3 q^{69} + 20 q^{71} + 48 q^{73} - 6 q^{75} + 6 q^{77} - 4 q^{79} - 4 q^{81} - 8 q^{83} + 7 q^{85} + 6 q^{87} + 30 q^{89} - 3 q^{91} - 19 q^{93} - 28 q^{95} + 9 q^{97} + 6 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^7 - 4 * q^9 - 3 * q^11 + 3 * q^13 + q^17 + 4 * q^19 - 8 * q^21 + 3 * q^23 - 12 * q^25 - 8 * q^27 - 6 * q^29 - 38 * q^31 + 3 * q^33 - 12 * q^37 - 9 * q^41 + q^43 + 28 * q^47 - 4 * q^49 + 2 * q^51 - 16 * q^53 + 4 * q^55 + 8 * q^57 + 5 * q^59 - 8 * q^61 - 4 * q^63 - 4 * q^65 + 15 * q^67 - 3 * q^69 + 20 * q^71 + 48 * q^73 - 6 * q^75 + 6 * q^77 - 4 * q^79 - 4 * q^81 - 8 * q^83 + 7 * q^85 + 6 * q^87 + 30 * q^89 - 3 * q^91 - 19 * q^93 - 28 * q^95 + 9 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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