LMFDB - Embedded newform 2184.2.bj.h.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:	8.0.8548296849.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 9x^{6} + 8x^{5} + 25x^{4} + 3x^{3} + 11x^{2} + 2x + 4 $ x^8 - 2x^7 + 9x^6 + 8x^5 + 25x^4 + 3x^3 + 11x^2 + 2*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.2
Root			$-0.320522 + 0.555160i$ of defining polynomial
Character	$\chi$	$=$	2184.841
Dual form			2184.2.bj.h.1849.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} -0.306978 q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} -0.306978 q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.71345 + 2.96778i) q^{11} +(-2.04751 - 2.96778i) q^{13} +(0.153489 - 0.265850i) q^{15} +(-0.248118 - 0.429753i) q^{17} +(2.28585 + 3.95921i) q^{19} -1.00000 q^{21} +(0.901607 - 1.56163i) q^{23} -4.90576 q^{25} +1.00000 q^{27} +(2.66703 - 4.61944i) q^{29} -7.38464 q^{31} +(-1.71345 - 2.96778i) q^{33} +(-0.153489 - 0.265850i) q^{35} +(-0.460466 + 0.797551i) q^{37} +(3.59393 - 0.289309i) q^{39} +(-3.70476 + 6.41684i) q^{41} +(-3.52529 - 6.10597i) q^{43} +(0.153489 + 0.265850i) q^{45} +8.55433 q^{47} +(-0.500000 + 0.866025i) q^{49} +0.496237 q^{51} -1.32434 q^{53} +(0.525990 - 0.911041i) q^{55} -4.57170 q^{57} +(-5.31114 - 9.19916i) q^{59} +(-4.90200 - 8.49052i) q^{61} +(0.500000 - 0.866025i) q^{63} +(0.628540 + 0.911041i) q^{65} +(-0.269246 + 0.466348i) q^{67} +(0.901607 + 1.56163i) q^{69} +(0.175715 + 0.304347i) q^{71} -13.4103 q^{73} +(2.45288 - 4.24852i) q^{75} -3.42689 q^{77} -6.02489 q^{79} +(-0.500000 + 0.866025i) q^{81} +3.58906 q^{83} +(0.0761667 + 0.131925i) q^{85} +(2.66703 + 4.61944i) q^{87} +(-0.328106 + 0.568296i) q^{89} +(1.54641 - 3.25709i) q^{91} +(3.69232 - 6.39528i) q^{93} +(-0.701705 - 1.21539i) q^{95} +(3.87938 + 6.71928i) q^{97} +3.42689 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9	$ 8 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9} + q^{11} + q^{13} - 2 q^{15} - 3 q^{17} - 2 q^{19} - 8 q^{21} + 5 q^{23} + 4 q^{25} + 8 q^{27} + 20 q^{29} - 2 q^{31} + q^{33} + 2 q^{35} + 6 q^{37} - 2 q^{39} - 7 q^{41} - q^{43} - 2 q^{45} + 12 q^{47} - 4 q^{49} + 6 q^{51} - 20 q^{53} + 12 q^{55} + 4 q^{57} + 5 q^{59} + 2 q^{61} + 4 q^{63} - 26 q^{65} - 17 q^{67} + 5 q^{69} + 8 q^{71} + 16 q^{73} - 2 q^{75} + 2 q^{77} - 60 q^{79} - 4 q^{81} + 4 q^{83} - 7 q^{85} + 20 q^{87} - 10 q^{89} - q^{91} + q^{93} - 20 q^{95} + 19 q^{97} - 2 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9 + q^11 + q^13 - 2 * q^15 - 3 * q^17 - 2 * q^19 - 8 * q^21 + 5 * q^23 + 4 * q^25 + 8 * q^27 + 20 * q^29 - 2 * q^31 + q^33 + 2 * q^35 + 6 * q^37 - 2 * q^39 - 7 * q^41 - q^43 - 2 * q^45 + 12 * q^47 - 4 * q^49 + 6 * q^51 - 20 * q^53 + 12 * q^55 + 4 * q^57 + 5 * q^59 + 2 * q^61 + 4 * q^63 - 26 * q^65 - 17 * q^67 + 5 * q^69 + 8 * q^71 + 16 * q^73 - 2 * q^75 + 2 * q^77 - 60 * q^79 - 4 * q^81 + 4 * q^83 - 7 * q^85 + 20 * q^87 - 10 * q^89 - q^91 + q^93 - 20 * q^95 + 19 * q^97 - 2 * 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
$5$	−0.306978			−0.137285			−0.0686423	−	0.997641i	$-0.521867\pi$
$5$	−0.306978			−0.137285			−0.0686423	+	0.997641i	$0.521867\pi$
$6$		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
$11$	−1.71345	+	2.96778i	−0.516624	+	0.894818i	0.483190	+	0.875515i	$0.339478\pi$
$11$	−1.71345	+	2.96778i	−0.516624	+	0.894818i	−0.999814	+	0.0193028i	$0.993855\pi$
$12$		0			0
$13$	−2.04751	−	2.96778i	−0.567878	−	0.823113i
$13$	−2.04751	−	2.96778i	−0.567878	−	0.823113i
$14$		0			0
$15$	0.153489	−	0.265850i	0.0396306	−	0.0686423i
$16$		0			0
$17$	−0.248118	−	0.429753i	−0.0601775	−	0.104231i	0.834367	−	0.551209i	$-0.185833\pi$
$17$	−0.248118	−	0.429753i	−0.0601775	−	0.104231i	−0.894545	+	0.446979i	$0.852500\pi$
$18$		0			0
$19$	2.28585	+	3.95921i	0.524410	+	0.908305i	0.999596	+	0.0284193i	$0.00904736\pi$
$19$	2.28585	+	3.95921i	0.524410	+	0.908305i	−0.475186	+	0.879885i	$0.657619\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	0.901607	−	1.56163i	0.187998	−	0.325622i	−0.756585	−	0.653896i	$-0.773133\pi$
$23$	0.901607	−	1.56163i	0.187998	−	0.325622i	0.944583	+	0.328274i	$0.106467\pi$
$24$		0			0
$25$	−4.90576			−0.981153
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	2.66703	−	4.61944i	0.495256	−	0.857808i	−0.504729	−	0.863278i	$-0.668408\pi$
$29$	2.66703	−	4.61944i	0.495256	−	0.857808i	0.999985	+	0.00546979i	$0.00174110\pi$
$30$		0			0
$31$	−7.38464			−1.32632			−0.663160	−	0.748478i	$-0.730785\pi$
$31$	−7.38464			−1.32632			−0.663160	+	0.748478i	$0.730785\pi$
$32$		0			0
$33$	−1.71345	−	2.96778i	−0.298273	−	0.516624i
$34$		0			0
$35$	−0.153489	−	0.265850i	−0.0259443	−	0.0449369i
$36$		0			0
$37$	−0.460466	+	0.797551i	−0.0757002	+	0.131117i	−0.901391	−	0.433007i	$-0.857453\pi$
$37$	−0.460466	+	0.797551i	−0.0757002	+	0.131117i	0.825690	+	0.564124i	$0.190786\pi$
$38$		0			0
$39$	3.59393	−	0.289309i	0.575489	−	0.0463265i
$40$		0			0
$41$	−3.70476	+	6.41684i	−0.578587	+	1.00214i	0.417055	+	0.908881i	$0.363062\pi$
$41$	−3.70476	+	6.41684i	−0.578587	+	1.00214i	−0.995642	+	0.0932606i	$0.970271\pi$
$42$		0			0
$43$	−3.52529	−	6.10597i	−0.537601	−	0.931152i	−0.999033	−	0.0439765i	$-0.985997\pi$
$43$	−3.52529	−	6.10597i	−0.537601	−	0.931152i	0.461432	−	0.887176i	$-0.347336\pi$
$44$		0			0
$45$	0.153489	+	0.265850i	0.0228808	+	0.0396306i
$46$		0			0
$47$	8.55433			1.24778			0.623889	−	0.781513i	$-0.285552\pi$
$47$	8.55433			1.24778			0.623889	+	0.781513i	$0.285552\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	0.496237			0.0694870
$52$		0			0
$53$	−1.32434			−0.181912			−0.0909562	−	0.995855i	$-0.528992\pi$
$53$	−1.32434			−0.181912			−0.0909562	+	0.995855i	$0.528992\pi$
$54$		0			0
$55$	0.525990	−	0.911041i	0.0709244	−	0.122845i
$56$		0			0
$57$	−4.57170			−0.605536
$58$		0			0
$59$	−5.31114	−	9.19916i	−0.691451	−	1.19763i	−0.971363	−	0.237602i	$-0.923638\pi$
$59$	−5.31114	−	9.19916i	−0.691451	−	1.19763i	0.279912	−	0.960026i	$-0.409695\pi$
$60$		0			0
$61$	−4.90200	−	8.49052i	−0.627637	−	1.08710i	−0.988025	−	0.154296i	$-0.950689\pi$
$61$	−4.90200	−	8.49052i	−0.627637	−	1.08710i	0.360388	−	0.932803i	$-0.382644\pi$
$62$		0			0
$63$	0.500000	−	0.866025i	0.0629941	−	0.109109i
$64$		0			0
$65$	0.628540	+	0.911041i	0.0779608	+	0.113001i
$66$		0			0
$67$	−0.269246	+	0.466348i	−0.0328937	+	0.0569735i	−0.882004	−	0.471243i	$-0.843806\pi$
$67$	−0.269246	+	0.466348i	−0.0328937	+	0.0569735i	0.849110	+	0.528216i	$0.177139\pi$
$68$		0			0
$69$	0.901607	+	1.56163i	0.108541	+	0.187998i
$70$		0			0
$71$	0.175715	+	0.304347i	0.0208535	+	0.0361194i	0.876264	−	0.481832i	$-0.160028\pi$
$71$	0.175715	+	0.304347i	0.0208535	+	0.0361194i	−0.855410	+	0.517951i	$0.826695\pi$
$72$		0			0
$73$	−13.4103			−1.56956			−0.784779	−	0.619775i	$-0.787224\pi$
$73$	−13.4103			−1.56956			−0.784779	+	0.619775i	$0.787224\pi$
$74$		0			0
$75$	2.45288	−	4.24852i	0.283234	−	0.490576i
$76$		0			0
$77$	−3.42689			−0.390531
$78$		0			0
$79$	−6.02489			−0.677853			−0.338927	−	0.940813i	$-0.610064\pi$
$79$	−6.02489			−0.677853			−0.338927	+	0.940813i	$0.610064\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	3.58906			0.393951			0.196975	−	0.980408i	$-0.436888\pi$
$83$	3.58906			0.393951			0.196975	+	0.980408i	$0.436888\pi$
$84$		0			0
$85$	0.0761667	+	0.131925i	0.00826144	+	0.0143092i
$86$		0			0
$87$	2.66703	+	4.61944i	0.285936	+	0.495256i
$88$		0			0
$89$	−0.328106	+	0.568296i	−0.0347791	+	0.0602392i	−0.882891	−	0.469578i	$-0.844406\pi$
$89$	−0.328106	+	0.568296i	−0.0347791	+	0.0602392i	0.848112	+	0.529817i	$0.177739\pi$
$90$		0			0
$91$	1.54641	−	3.25709i	0.162108	−	0.341435i
$92$		0			0
$93$	3.69232	−	6.39528i	0.382876	−	0.663160i
$94$		0			0
$95$	−0.701705	−	1.21539i	−0.0719934	−	0.124696i
$96$		0			0
$97$	3.87938	+	6.71928i	0.393891	+	0.682240i	0.992959	−	0.118458i	$-0.0377953\pi$
$97$	3.87938	+	6.71928i	0.393891	+	0.682240i	−0.599068	+	0.800698i	$0.704462\pi$
$98$		0			0
$99$	3.42689			0.344416
$100$		0			0
$101$	2.71454	−	4.70173i	0.270107	−	0.467840i	−0.698782	−	0.715335i	$-0.746274\pi$
$101$	2.71454	−	4.70173i	0.270107	−	0.467840i	0.968889	+	0.247495i	$0.0796075\pi$
$102$		0			0
$103$	9.07766			0.894448			0.447224	−	0.894422i	$-0.352413\pi$
$103$	9.07766			0.894448			0.447224	+	0.894422i	$0.352413\pi$
$104$		0			0
$105$	0.306978			0.0299579
$106$		0			0
$107$	3.52152	−	6.09946i	0.340438	−	0.589657i	−0.644076	−	0.764962i	$-0.722758\pi$
$107$	3.52152	−	6.09946i	0.340438	−	0.589657i	0.984514	+	0.175305i	$0.0560912\pi$
$108$		0			0
$109$	−5.06794			−0.485420			−0.242710	−	0.970099i	$-0.578036\pi$
$109$	−5.06794			−0.485420			−0.242710	+	0.970099i	$0.578036\pi$
$110$		0			0
$111$	−0.460466	−	0.797551i	−0.0437055	−	0.0757002i
$112$		0			0
$113$	−6.42619	−	11.1305i	−0.604525	−	1.04707i	−0.992126	−	0.125241i	$-0.960030\pi$
$113$	−6.42619	−	11.1305i	−0.604525	−	1.04707i	0.387601	−	0.921827i	$-0.373304\pi$
$114$		0			0
$115$	−0.276773	+	0.479385i	−0.0258092	+	0.0447029i
$116$		0			0
$117$	−1.54641	+	3.25709i	−0.142966	+	0.301118i
$118$		0			0
$119$	0.248118	−	0.429753i	0.0227450	−	0.0393954i
$120$		0			0
$121$	−0.371797	−	0.643971i	−0.0337997	−	0.0585428i
$122$		0			0
$123$	−3.70476	−	6.41684i	−0.334047	−	0.578587i
$124$		0			0
$125$	3.04085			0.271982
$126$		0			0
$127$	2.96643	−	5.13800i	0.263228	−	0.455924i	−0.703870	−	0.710329i	$-0.748546\pi$
$127$	2.96643	−	5.13800i	0.263228	−	0.455924i	0.967098	+	0.254405i	$0.0818796\pi$
$128$		0			0
$129$	7.05057			0.620768
$130$		0			0
$131$	−20.1683			−1.76211			−0.881056	−	0.473012i	$-0.843167\pi$
$131$	−20.1683			−1.76211			−0.881056	+	0.473012i	$0.843167\pi$
$132$		0			0
$133$	−2.28585	+	3.95921i	−0.198208	+	0.343307i
$134$		0			0
$135$	−0.306978			−0.0264204
$136$		0			0
$137$	−2.96713	−	5.13922i	−0.253499	−	0.439073i	0.710988	−	0.703204i	$-0.248248\pi$
$137$	−2.96713	−	5.13922i	−0.253499	−	0.439073i	−0.964487	+	0.264131i	$0.914915\pi$
$138$		0			0
$139$	1.02599	+	1.77707i	0.0870233	+	0.150729i	0.906252	−	0.422739i	$-0.138931\pi$
$139$	1.02599	+	1.77707i	0.0870233	+	0.150729i	−0.819228	+	0.573468i	$0.805598\pi$
$140$		0			0
$141$	−4.27717	+	7.40827i	−0.360202	+	0.623889i
$142$		0			0
$143$	12.3160	−	0.991432i	1.02992	−	0.0829077i
$144$		0			0
$145$	−0.818719	+	1.41806i	−0.0679909	+	0.117764i
$146$		0			0
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$		0			0
$149$	−8.98991	−	15.5710i	−0.736482	−	1.27562i	−0.954070	−	0.299584i	$-0.903152\pi$
$149$	−8.98991	−	15.5710i	−0.736482	−	1.27562i	0.217588	−	0.976041i	$-0.430181\pi$
$150$		0			0
$151$	−7.78805			−0.633782			−0.316891	−	0.948462i	$-0.602639\pi$
$151$	−7.78805			−0.633782			−0.316891	+	0.948462i	$0.602639\pi$
$152$		0			0
$153$	−0.248118	+	0.429753i	−0.0200592	+	0.0347435i
$154$		0			0
$155$	2.26692			0.182083
$156$		0			0
$157$	−20.4783			−1.63434			−0.817171	−	0.576395i	$-0.804459\pi$
$157$	−20.4783			−1.63434			−0.817171	+	0.576395i	$0.804459\pi$
$158$		0			0
$159$	0.662171	−	1.14691i	0.0525136	−	0.0909562i
$160$		0			0
$161$	1.80321			0.142113
$162$		0			0
$163$	−5.67391	−	9.82751i	−0.444415	−	0.769750i	0.553596	−	0.832785i	$-0.313255\pi$
$163$	−5.67391	−	9.82751i	−0.444415	−	0.769750i	−0.998011	+	0.0630357i	$0.979922\pi$
$164$		0			0
$165$	0.525990	+	0.911041i	0.0409482	+	0.0709244i
$166$		0			0
$167$	−1.23185	+	2.13363i	−0.0953236	+	0.165105i	−0.909744	−	0.415171i	$-0.863722\pi$
$167$	−1.23185	+	2.13363i	−0.0953236	+	0.165105i	0.814420	+	0.580276i	$0.197055\pi$
$168$		0			0
$169$	−4.61539	+	12.1531i	−0.355030	+	0.934855i
$170$		0			0
$171$	2.28585	−	3.95921i	0.174803	−	0.302768i
$172$		0			0
$173$	−9.38879	−	16.2619i	−0.713817	−	1.23637i	−0.963414	−	0.268017i	$-0.913632\pi$
$173$	−9.38879	−	16.2619i	−0.713817	−	1.23637i	0.249597	−	0.968350i	$-0.419702\pi$
$174$		0			0
$175$	−2.45288	−	4.24852i	−0.185420	−	0.321158i
$176$		0			0
$177$	10.6223			0.798419
$178$		0			0
$179$	5.06482	−	8.77252i	0.378562	−	0.655689i	−0.612291	−	0.790633i	$-0.709752\pi$
$179$	5.06482	−	8.77252i	0.378562	−	0.655689i	0.990853	+	0.134943i	$0.0430852\pi$
$180$		0			0
$181$	−13.3486			−0.992195			−0.496097	−	0.868267i	$-0.665234\pi$
$181$	−13.3486			−0.992195			−0.496097	+	0.868267i	$0.665234\pi$
$182$		0			0
$183$	9.80400			0.724733
$184$		0			0
$185$	0.141353	−	0.244830i	0.0103925	−	0.0180003i
$186$		0			0
$187$	1.70055			0.124356
$188$		0			0
$189$	0.500000	+	0.866025i	0.0363696	+	0.0629941i
$190$		0			0
$191$	12.1512	+	21.0464i	0.879227	+	1.52287i	0.852191	+	0.523232i	$0.175274\pi$
$191$	12.1512	+	21.0464i	0.879227	+	1.52287i	0.0270366	+	0.999634i	$0.491393\pi$
$192$		0			0
$193$	−0.451841	+	0.782612i	−0.0325242	+	0.0563336i	−0.881829	−	0.471569i	$-0.843688\pi$
$193$	−0.451841	+	0.782612i	−0.0325242	+	0.0563336i	0.849305	+	0.527902i	$0.177021\pi$
$194$		0			0
$195$	−1.10325	+	0.0888114i	−0.0790057	+	0.00635992i
$196$		0			0
$197$	7.09322	−	12.2858i	0.505371	−	0.875328i	−0.494610	−	0.869115i	$-0.664689\pi$
$197$	7.09322	−	12.2858i	0.505371	−	0.875328i	0.999981	−	0.00621316i	$-0.00197772\pi$
$198$		0			0
$199$	−0.644864	−	1.11694i	−0.0457132	−	0.0791775i	0.842263	−	0.539066i	$-0.181223\pi$
$199$	−0.644864	−	1.11694i	−0.0457132	−	0.0791775i	−0.887977	+	0.459889i	$0.847889\pi$
$200$		0			0
$201$	−0.269246	−	0.466348i	−0.0189912	−	0.0328937i
$202$		0			0
$203$	5.33407			0.374378
$204$		0			0
$205$	1.13728	−	1.96983i	0.0794311	−	0.137579i
$206$		0			0
$207$	−1.80321			−0.125332
$208$		0			0
$209$	−15.6667			−1.08369
$210$		0			0
$211$	6.62031	−	11.4667i	0.455761	−	0.789401i	−0.542971	−	0.839752i	$-0.682701\pi$
$211$	6.62031	−	11.4667i	0.455761	−	0.789401i	0.998732	+	0.0503506i	$0.0160339\pi$
$212$		0			0
$213$	−0.351430			−0.0240796
$214$		0			0
$215$	1.08218	+	1.87440i	0.0738043	+	0.127833i
$216$		0			0
$217$	−3.69232	−	6.39528i	−0.250651	−	0.434140i
$218$		0			0
$219$	6.70516	−	11.6137i	0.453093	−	0.784779i
$220$		0			0
$221$	−0.767387	+	1.61628i	−0.0516200	+	0.108723i
$222$		0			0
$223$	−3.63166	+	6.29021i	−0.243194	+	0.421224i	−0.961622	−	0.274377i	$-0.911528\pi$
$223$	−3.63166	+	6.29021i	−0.243194	+	0.421224i	0.718428	+	0.695601i	$0.244862\pi$
$224$		0			0
$225$	2.45288	+	4.24852i	0.163525	+	0.283234i
$226$		0			0
$227$	11.2369	+	19.4629i	0.745821	+	1.29180i	0.949810	+	0.312827i	$0.101276\pi$
$227$	11.2369	+	19.4629i	0.745821	+	1.29180i	−0.203989	+	0.978973i	$0.565391\pi$
$228$		0			0
$229$	−18.8386			−1.24489			−0.622445	−	0.782663i	$-0.713861\pi$
$229$	−18.8386			−1.24489			−0.622445	+	0.782663i	$0.713861\pi$
$230$		0			0
$231$	1.71345	−	2.96778i	0.112736	−	0.195265i
$232$		0			0
$233$	17.9314			1.17473			0.587364	−	0.809323i	$-0.300166\pi$
$233$	17.9314			1.17473			0.587364	+	0.809323i	$0.300166\pi$
$234$		0			0
$235$	−2.62599			−0.171301
$236$		0			0
$237$	3.01245	−	5.21771i	0.195679	−	0.338927i
$238$		0			0
$239$	9.03944			0.584713			0.292356	−	0.956309i	$-0.405561\pi$
$239$	9.03944			0.584713			0.292356	+	0.956309i	$0.405561\pi$
$240$		0			0
$241$	−4.90647	−	8.49825i	−0.316053	−	0.547421i	0.663607	−	0.748081i	$-0.269025\pi$
$241$	−4.90647	−	8.49825i	−0.316053	−	0.547421i	−0.979661	+	0.200660i	$0.935691\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	0.153489	−	0.265850i	0.00980604	−	0.0169846i
$246$		0			0
$247$	7.06974	−	14.8904i	0.449837	−	0.947454i
$248$		0			0
$249$	−1.79453	+	3.10822i	−0.113724	+	0.196975i
$250$		0			0
$251$	7.30627	+	12.6548i	0.461168	+	0.798766i	0.999019	−	0.0442733i	$-0.0140972\pi$
$251$	7.30627	+	12.6548i	0.461168	+	0.798766i	−0.537852	+	0.843040i	$0.680764\pi$
$252$		0			0
$253$	3.08971	+	5.35154i	0.194248	+	0.336448i
$254$		0			0
$255$	−0.152333			−0.00953949
$256$		0			0
$257$	−2.94763	+	5.10544i	−0.183868	+	0.318469i	−0.943194	−	0.332241i	$-0.892195\pi$
$257$	−2.94763	+	5.10544i	−0.183868	+	0.318469i	0.759327	+	0.650710i	$0.225529\pi$
$258$		0			0
$259$	−0.920933			−0.0572240
$260$		0			0
$261$	−5.33407			−0.330170
$262$		0			0
$263$	−5.03922	+	8.72819i	−0.310732	+	0.538203i	−0.978521	−	0.206147i	$-0.933907\pi$
$263$	−5.03922	+	8.72819i	−0.310732	+	0.538203i	0.667789	+	0.744350i	$0.267241\pi$
$264$		0			0
$265$	0.406543			0.0249738
$266$		0			0
$267$	−0.328106	−	0.568296i	−0.0200797	−	0.0347791i
$268$		0			0
$269$	8.71941	+	15.1025i	0.531632	+	0.920813i	0.999318	+	0.0369186i	$0.0117542\pi$
$269$	8.71941	+	15.1025i	0.531632	+	0.920813i	−0.467687	+	0.883894i	$0.654912\pi$
$270$		0			0
$271$	6.85033	−	11.8651i	0.416128	−	0.720755i	−0.579418	−	0.815030i	$-0.696720\pi$
$271$	6.85033	−	11.8651i	0.416128	−	0.720755i	0.995546	+	0.0942756i	$0.0300535\pi$
$272$		0			0
$273$	2.04751	+	2.96778i	0.123921	+	0.179618i
$274$		0			0
$275$	8.40576	−	14.5592i	0.506887	−	0.877953i
$276$		0			0
$277$	13.5183	+	23.4144i	0.812237	+	1.40684i	0.911295	+	0.411754i	$0.135084\pi$
$277$	13.5183	+	23.4144i	0.812237	+	1.40684i	−0.0990586	+	0.995082i	$0.531583\pi$
$278$		0			0
$279$	3.69232	+	6.39528i	0.221053	+	0.382876i
$280$		0			0
$281$	10.0333			0.598538			0.299269	−	0.954169i	$-0.403257\pi$
$281$	10.0333			0.598538			0.299269	+	0.954169i	$0.403257\pi$
$282$		0			0
$283$	−9.66764	+	16.7448i	−0.574682	+	0.995378i	0.421394	+	0.906877i	$0.361541\pi$
$283$	−9.66764	+	16.7448i	−0.574682	+	0.995378i	−0.996076	+	0.0885005i	$0.971793\pi$
$284$		0			0
$285$	1.40341			0.0831308
$286$		0			0
$287$	−7.40953			−0.437371
$288$		0			0
$289$	8.37687	−	14.5092i	0.492757	−	0.853481i
$290$		0			0
$291$	−7.75876			−0.454827
$292$		0			0
$293$	14.6469	+	25.3692i	0.855682	+	1.48208i	0.876011	+	0.482291i	$0.160195\pi$
$293$	14.6469	+	25.3692i	0.855682	+	1.48208i	−0.0203297	+	0.999793i	$0.506472\pi$
$294$		0			0
$295$	1.63040	+	2.82393i	0.0949255	+	0.164416i
$296$		0			0
$297$	−1.71345	+	2.96778i	−0.0994242	+	0.172208i
$298$		0			0
$299$	−6.48062	+	0.521686i	−0.374784	+	0.0301699i
$300$		0			0
$301$	3.52529	−	6.10597i	0.203194	−	0.351942i
$302$		0			0
$303$	2.71454	+	4.70173i	0.155947	+	0.270107i
$304$		0			0
$305$	1.50480	+	2.60640i	0.0861649	+	0.149242i
$306$		0			0
$307$	−13.6750			−0.780476			−0.390238	−	0.920714i	$-0.627607\pi$
$307$	−13.6750			−0.780476			−0.390238	+	0.920714i	$0.627607\pi$
$308$		0			0
$309$	−4.53883	+	7.86148i	−0.258205	+	0.447224i
$310$		0			0
$311$	−22.4117			−1.27085			−0.635426	−	0.772162i	$-0.719176\pi$
$311$	−22.4117			−1.27085			−0.635426	+	0.772162i	$0.719176\pi$
$312$		0			0
$313$	−16.0368			−0.906454			−0.453227	−	0.891395i	$-0.649727\pi$
$313$	−16.0368			−0.906454			−0.453227	+	0.891395i	$0.649727\pi$
$314$		0			0
$315$	−0.153489	+	0.265850i	−0.00864811	+	0.0149790i
$316$		0			0
$317$	1.60110			0.0899266			0.0449633	−	0.998989i	$-0.485683\pi$
$317$	1.60110			0.0899266			0.0449633	+	0.998989i	$0.485683\pi$
$318$		0			0
$319$	9.13964	+	15.8303i	0.511721	+	0.886327i
$320$		0			0
$321$	3.52152	+	6.09946i	0.196552	+	0.340438i
$322$		0			0
$323$	1.13432	−	1.96470i	0.0631154	−	0.109319i
$324$		0			0
$325$	10.0446	+	14.5592i	0.557175	+	0.807600i
$326$		0			0
$327$	2.53397	−	4.38896i	0.140129	−	0.242710i
$328$		0			0
$329$	4.27717	+	7.40827i	0.235808	+	0.408431i
$330$		0			0
$331$	−2.53616	−	4.39277i	−0.139400	−	0.241448i	0.787870	−	0.615842i	$-0.211184\pi$
$331$	−2.53616	−	4.39277i	−0.139400	−	0.241448i	−0.927270	+	0.374394i	$0.877851\pi$
$332$		0			0
$333$	0.920933			0.0504668
$334$		0			0
$335$	0.0826526	−	0.143158i	0.00451579	−	0.00782158i
$336$		0			0
$337$	−30.1082			−1.64010			−0.820048	−	0.572295i	$-0.806053\pi$
$337$	−30.1082			−1.64010			−0.820048	+	0.572295i	$0.806053\pi$
$338$		0			0
$339$	12.8524			0.698045
$340$		0			0
$341$	12.6532	−	21.9159i	0.685208	−	1.18682i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	−0.276773	−	0.479385i	−0.0149010	−	0.0258092i
$346$		0			0
$347$	−4.64073	−	8.03799i	−0.249128	−	0.431502i	0.714156	−	0.699986i	$-0.246811\pi$
$347$	−4.64073	−	8.03799i	−0.249128	−	0.431502i	−0.963284	+	0.268484i	$0.913477\pi$
$348$		0			0
$349$	−7.88399	+	13.6555i	−0.422020	+	0.730961i	−0.996137	−	0.0878129i	$-0.972012\pi$
$349$	−7.88399	+	13.6555i	−0.422020	+	0.730961i	0.574117	+	0.818773i	$0.305346\pi$
$350$		0			0
$351$	−2.04751	−	2.96778i	−0.109288	−	0.158408i
$352$		0			0
$353$	−11.1214	+	19.2628i	−0.591933	+	1.02526i	0.402039	+	0.915623i	$0.368302\pi$
$353$	−11.1214	+	19.2628i	−0.591933	+	1.02526i	−0.993972	+	0.109635i	$0.965032\pi$
$354$		0			0
$355$	−0.0539406	−	0.0934278i	−0.00286287	−	0.00495863i
$356$		0			0
$357$	0.248118	+	0.429753i	0.0131318	+	0.0227450i
$358$		0			0
$359$	13.6925			0.722663			0.361332	−	0.932437i	$-0.382322\pi$
$359$	13.6925			0.722663			0.361332	+	0.932437i	$0.382322\pi$
$360$		0			0
$361$	−0.950217	+	1.64582i	−0.0500114	+	0.0866223i
$362$		0			0
$363$	0.743594			0.0390285
$364$		0			0
$365$	4.11667			0.215476
$366$		0			0
$367$	2.22583	−	3.85526i	0.116188	−	0.201243i	−0.802066	−	0.597235i	$-0.796266\pi$
$367$	2.22583	−	3.85526i	0.116188	−	0.201243i	0.918254	+	0.395992i	$0.129599\pi$
$368$		0			0
$369$	7.40953			0.385725
$370$		0			0
$371$	−0.662171	−	1.14691i	−0.0343782	−	0.0595448i
$372$		0			0
$373$	8.32709	+	14.4229i	0.431160	+	0.746792i	0.996974	−	0.0777417i	$-0.0247710\pi$
$373$	8.32709	+	14.4229i	0.431160	+	0.746792i	−0.565813	+	0.824534i	$0.691438\pi$
$374$		0			0
$375$	−1.52042	+	2.63345i	−0.0785144	+	0.135991i
$376$		0			0
$377$	−19.1702	+	1.54319i	−0.987317	+	0.0794785i
$378$		0			0
$379$	5.73607	−	9.93516i	0.294642	−	0.510335i	−0.680260	−	0.732971i	$-0.738133\pi$
$379$	5.73607	−	9.93516i	0.294642	−	0.510335i	0.974902	+	0.222636i	$0.0714663\pi$
$380$		0			0
$381$	2.96643	+	5.13800i	0.151975	+	0.263228i
$382$		0			0
$383$	17.1650	+	29.7306i	0.877089	+	1.51916i	0.854520	+	0.519418i	$0.173851\pi$
$383$	17.1650	+	29.7306i	0.877089	+	1.51916i	0.0225692	+	0.999745i	$0.492815\pi$
$384$		0			0
$385$	1.05198			0.0536138
$386$		0			0
$387$	−3.52529	+	6.10597i	−0.179200	+	0.310384i
$388$		0			0
$389$	7.31682			0.370977			0.185489	−	0.982646i	$-0.440613\pi$
$389$	7.31682			0.370977			0.185489	+	0.982646i	$0.440613\pi$
$390$		0			0
$391$	−0.894821			−0.0452530
$392$		0			0
$393$	10.0841	−	17.4663i	0.508678	−	0.881056i
$394$		0			0
$395$	1.84951			0.0930588
$396$		0			0
$397$	−6.99553	−	12.1166i	−0.351096	−	0.608116i	0.635346	−	0.772228i	$-0.280857\pi$
$397$	−6.99553	−	12.1166i	−0.351096	−	0.608116i	−0.986442	+	0.164112i	$0.947524\pi$
$398$		0			0
$399$	−2.28585	−	3.95921i	−0.114436	−	0.198208i
$400$		0			0
$401$	6.20210	−	10.7424i	0.309718	−	0.536447i	−0.668583	−	0.743638i	$-0.733099\pi$
$401$	6.20210	−	10.7424i	0.309718	−	0.536447i	0.978301	+	0.207191i	$0.0664320\pi$
$402$		0			0
$403$	15.1201	+	21.9159i	0.753187	+	1.09171i
$404$		0			0
$405$	0.153489	−	0.265850i	0.00762692	−	0.0132102i
$406$		0			0
$407$	−1.57797	−	2.73312i	−0.0782170	−	0.135476i
$408$		0			0
$409$	9.25811	+	16.0355i	0.457784	+	0.792906i	0.998844	−	0.0480788i	$-0.0153099\pi$
$409$	9.25811	+	16.0355i	0.457784	+	0.792906i	−0.541059	+	0.840984i	$0.681977\pi$
$410$		0			0
$411$	5.93426			0.292715
$412$		0			0
$413$	5.31114	−	9.19916i	0.261344	−	0.452661i
$414$		0			0
$415$	−1.10176			−0.0540834
$416$		0			0
$417$	−2.05198			−0.100486
$418$		0			0
$419$	−4.57285	+	7.92042i	−0.223399	+	0.386938i	−0.955838	−	0.293895i	$-0.905048\pi$
$419$	−4.57285	+	7.92042i	−0.223399	+	0.386938i	0.732439	+	0.680832i	$0.238382\pi$
$420$		0			0
$421$	−3.95970			−0.192984			−0.0964919	−	0.995334i	$-0.530762\pi$
$421$	−3.95970			−0.192984			−0.0964919	+	0.995334i	$0.530762\pi$
$422$		0			0
$423$	−4.27717	−	7.40827i	−0.207963	−	0.360202i
$424$		0			0
$425$	1.21721	+	2.10827i	0.0590433	+	0.102266i
$426$		0			0
$427$	4.90200	−	8.49052i	0.237224	−	0.410885i
$428$		0			0
$429$	−5.29939	+	11.1617i	−0.255857	+	0.538891i
$430$		0			0
$431$	−12.3244	+	21.3465i	−0.593647	+	1.02823i	0.400090	+	0.916476i	$0.368979\pi$
$431$	−12.3244	+	21.3465i	−0.593647	+	1.02823i	−0.993736	+	0.111750i	$0.964354\pi$
$432$		0			0
$433$	6.39042	+	11.0685i	0.307104	+	0.531920i	0.977728	−	0.209878i	$-0.0673067\pi$
$433$	6.39042	+	11.0685i	0.307104	+	0.531920i	−0.670624	+	0.741798i	$0.733973\pi$
$434$		0			0
$435$	−0.818719	−	1.41806i	−0.0392546	−	0.0679909i
$436$		0			0
$437$	8.24375			0.394352
$438$		0			0
$439$	−12.7067	+	22.0086i	−0.606455	+	1.05041i	0.385364	+	0.922765i	$0.374076\pi$
$439$	−12.7067	+	22.0086i	−0.606455	+	1.05041i	−0.991820	+	0.127647i	$0.959258\pi$
$440$		0			0
$441$	1.00000			0.0476190
$442$		0			0
$443$	−4.26264			−0.202524			−0.101262	−	0.994860i	$-0.532288\pi$
$443$	−4.26264			−0.202524			−0.101262	+	0.994860i	$0.532288\pi$
$444$		0			0
$445$	0.100721	−	0.174454i	0.00477464	−	0.00826991i
$446$		0			0
$447$	17.9798			0.850416
$448$		0			0
$449$	−7.21519	−	12.4971i	−0.340506	−	0.589774i	0.644021	−	0.765008i	$-0.277265\pi$
$449$	−7.21519	−	12.4971i	−0.340506	−	0.589774i	−0.984527	+	0.175234i	$0.943932\pi$
$450$		0			0
$451$	−12.6958	−	21.9898i	−0.597823	−	1.03546i
$452$		0			0
$453$	3.89402	−	6.74465i	0.182957	−	0.316891i
$454$		0			0
$455$	−0.474714	+	0.999852i	−0.0222550	+	0.0468738i
$456$		0			0
$457$	−19.1671	+	33.1984i	−0.896600	+	1.55296i	−0.0647880	+	0.997899i	$0.520637\pi$
$457$	−19.1671	+	33.1984i	−0.896600	+	1.55296i	−0.831812	+	0.555058i	$0.812696\pi$
$458$		0			0
$459$	−0.248118	−	0.429753i	−0.0115812	−	0.0200592i
$460$		0			0
$461$	−0.751825	−	1.30220i	−0.0350160	−	0.0606494i	0.847986	−	0.530018i	$-0.177815\pi$
$461$	−0.751825	−	1.30220i	−0.0350160	−	0.0606494i	−0.883002	+	0.469369i	$0.844482\pi$
$462$		0			0
$463$	11.5841			0.538357			0.269178	−	0.963090i	$-0.413248\pi$
$463$	11.5841			0.538357			0.269178	+	0.963090i	$0.413248\pi$
$464$		0			0
$465$	−1.13346	+	1.96321i	−0.0525629	+	0.0910416i
$466$		0			0
$467$	12.8253			0.593484			0.296742	−	0.954958i	$-0.404100\pi$
$467$	12.8253			0.593484			0.296742	+	0.954958i	$0.404100\pi$
$468$		0			0
$469$	−0.538492			−0.0248653
$470$		0			0
$471$	10.2391	−	17.7347i	0.471794	−	0.817171i
$472$		0			0
$473$	24.1616			1.11095
$474$		0			0
$475$	−11.2138	−	19.4229i	−0.514526	−	0.891186i
$476$		0			0
$477$	0.662171	+	1.14691i	0.0303187	+	0.0525136i
$478$		0			0
$479$	9.48460	−	16.4278i	0.433362	−	0.750605i	−0.563798	−	0.825913i	$-0.690660\pi$
$479$	9.48460	−	16.4278i	0.433362	−	0.750605i	0.997160	+	0.0753072i	$0.0239937\pi$
$480$		0			0
$481$	3.30976	−	0.266434i	0.150912	−	0.0121484i
$482$		0			0
$483$	−0.901607	+	1.56163i	−0.0410245	+	0.0710566i
$484$		0			0
$485$	−1.19088	−	2.06267i	−0.0540752	−	0.0936610i
$486$		0			0
$487$	15.4280	+	26.7221i	0.699109	+	1.21089i	0.968776	+	0.247939i	$0.0797531\pi$
$487$	15.4280	+	26.7221i	0.699109	+	1.21089i	−0.269667	+	0.962954i	$0.586914\pi$
$488$		0			0
$489$	11.3478			0.513166
$490$		0			0
$491$	−0.786770	+	1.36273i	−0.0355064	+	0.0614989i	−0.883233	−	0.468935i	$-0.844638\pi$
$491$	−0.786770	+	1.36273i	−0.0355064	+	0.0614989i	0.847726	+	0.530434i	$0.177971\pi$
$492$		0			0
$493$	−2.64696			−0.119213
$494$		0			0
$495$	−1.05198			−0.0472830
$496$		0			0
$497$	−0.175715	+	0.304347i	−0.00788189	+	0.0136518i
$498$		0			0
$499$	4.43802			0.198673			0.0993366	−	0.995054i	$-0.468328\pi$
$499$	4.43802			0.198673			0.0993366	+	0.995054i	$0.468328\pi$
$500$		0			0
$501$	−1.23185	−	2.13363i	−0.0550351	−	0.0953236i
$502$		0			0
$503$	21.3837	+	37.0376i	0.953451	+	1.65143i	0.737873	+	0.674939i	$0.235830\pi$
$503$	21.3837	+	37.0376i	0.953451	+	1.65143i	0.215578	+	0.976487i	$0.430837\pi$
$504$		0			0
$505$	−0.833304	+	1.44333i	−0.0370816	+	0.0642271i
$506$		0			0
$507$	−8.21721	−	10.0736i	−0.364939	−	0.447384i
$508$		0			0
$509$	12.6169	−	21.8532i	0.559236	−	0.968625i	−0.438324	−	0.898817i	$-0.644428\pi$
$509$	12.6169	−	21.8532i	0.559236	−	0.968625i	0.997560	−	0.0698084i	$-0.0222388\pi$
$510$		0			0
$511$	−6.70516	−	11.6137i	−0.296619	−	0.513759i
$512$		0			0
$513$	2.28585	+	3.95921i	0.100923	+	0.174803i
$514$		0			0
$515$	−2.78664			−0.122794
$516$		0			0
$517$	−14.6574	+	25.3874i	−0.644631	+	1.11653i
$518$		0			0
$519$	18.7776			0.824245
$520$		0			0
$521$	13.7098			0.600636			0.300318	−	0.953839i	$-0.402907\pi$
$521$	13.7098			0.600636			0.300318	+	0.953839i	$0.402907\pi$
$522$		0			0
$523$	−18.5502	+	32.1299i	−0.811144	+	1.40494i	0.100920	+	0.994895i	$0.467821\pi$
$523$	−18.5502	+	32.1299i	−0.811144	+	1.40494i	−0.912064	+	0.410048i	$0.865512\pi$
$524$		0			0
$525$	4.90576			0.214105
$526$		0			0
$527$	1.83226	+	3.17357i	0.0798146	+	0.138243i
$528$		0			0
$529$	9.87421	+	17.1026i	0.429313	+	0.743593i
$530$		0			0
$531$	−5.31114	+	9.19916i	−0.230484	+	0.399209i
$532$		0			0
$533$	26.6293	−	2.14364i	1.15344	−	0.0928516i
$534$		0			0
$535$	−1.08103	+	1.87240i	−0.0467369	+	0.0809507i
$536$		0			0
$537$	5.06482	+	8.77252i	0.218563	+	0.378562i
$538$		0			0
$539$	−1.71345	−	2.96778i	−0.0738034	−	0.127831i
$540$		0			0
$541$	34.2699			1.47338			0.736689	−	0.676232i	$-0.236388\pi$
$541$	34.2699			1.47338			0.736689	+	0.676232i	$0.236388\pi$
$542$		0			0
$543$	6.67431	−	11.5602i	0.286422	−	0.496097i
$544$		0			0
$545$	1.55574			0.0666407
$546$		0			0
$547$	−17.5120			−0.748758			−0.374379	−	0.927276i	$-0.622144\pi$
$547$	−17.5120			−0.748758			−0.374379	+	0.927276i	$0.622144\pi$
$548$		0			0
$549$	−4.90200	+	8.49052i	−0.209212	+	0.362366i
$550$		0			0
$551$	24.3857			1.03887
$552$		0			0
$553$	−3.01245	−	5.21771i	−0.128102	−	0.221880i
$554$		0			0
$555$	0.141353	+	0.244830i	0.00600010	+	0.0103925i
$556$		0			0
$557$	−0.114780	+	0.198805i	−0.00486339	+	0.00842365i	−0.868447	−	0.495782i	$-0.834881\pi$
$557$	−0.114780	+	0.198805i	−0.00486339	+	0.00842365i	0.863583	+	0.504206i	$0.168215\pi$
$558$		0			0
$559$	−10.9031	+	22.9643i	−0.461152	+	0.971287i
$560$		0			0
$561$	−0.850275	+	1.47272i	−0.0358986	+	0.0621782i
$562$		0			0
$563$	−14.6077	−	25.3013i	−0.615641	−	1.06632i	−0.990272	−	0.139147i	$-0.955564\pi$
$563$	−14.6077	−	25.3013i	−0.615641	−	1.06632i	0.374631	−	0.927174i	$-0.377769\pi$
$564$		0			0
$565$	1.97270	+	3.41681i	0.0829919	+	0.143746i
$566$		0			0
$567$	−1.00000			−0.0419961
$568$		0			0
$569$	−5.80737	+	10.0587i	−0.243458	+	0.421681i	−0.961697	−	0.274115i	$-0.911615\pi$
$569$	−5.80737	+	10.0587i	−0.243458	+	0.421681i	0.718239	+	0.695796i	$0.244948\pi$
$570$		0			0
$571$	−43.2195			−1.80868			−0.904341	−	0.426811i	$-0.859637\pi$
$571$	−43.2195			−1.80868			−0.904341	+	0.426811i	$0.859637\pi$
$572$		0			0
$573$	−24.3023			−1.01524
$574$		0			0
$575$	−4.42307	+	7.66099i	−0.184455	+	0.319485i
$576$		0			0
$577$	−3.35963			−0.139863			−0.0699316	−	0.997552i	$-0.522278\pi$
$577$	−3.35963			−0.139863			−0.0699316	+	0.997552i	$0.522278\pi$
$578$		0			0
$579$	−0.451841	−	0.782612i	−0.0187779	−	0.0325242i
$580$		0			0
$581$	1.79453	+	3.10822i	0.0744497	+	0.128951i
$582$		0			0
$583$	2.26919	−	3.93035i	0.0939802	−	0.162779i
$584$		0			0
$585$	0.474714	−	0.999852i	0.0196270	−	0.0413388i
$586$		0			0
$587$	−7.85528	+	13.6057i	−0.324222	+	0.561569i	−0.981355	−	0.192206i	$-0.938436\pi$
$587$	−7.85528	+	13.6057i	−0.324222	+	0.561569i	0.657133	+	0.753775i	$0.271769\pi$
$588$		0			0
$589$	−16.8802	−	29.2373i	−0.695535	−	1.20470i
$590$		0			0
$591$	7.09322	+	12.2858i	0.291776	+	0.505371i
$592$		0			0
$593$	−23.8910			−0.981087			−0.490543	−	0.871417i	$-0.663202\pi$
$593$	−23.8910			−0.981087			−0.490543	+	0.871417i	$0.663202\pi$
$594$		0			0
$595$	−0.0761667	+	0.131925i	−0.00312253	+	0.00540838i
$596$		0			0
$597$	1.28973			0.0527850
$598$		0			0
$599$	−26.7505			−1.09300			−0.546498	−	0.837460i	$-0.684039\pi$
$599$	−26.7505			−1.09300			−0.546498	+	0.837460i	$0.684039\pi$
$600$		0			0
$601$	−5.00104	+	8.66206i	−0.203997	+	0.353333i	−0.949813	−	0.312819i	$-0.898727\pi$
$601$	−5.00104	+	8.66206i	−0.203997	+	0.353333i	0.745816	+	0.666152i	$0.232060\pi$
$602$		0			0
$603$	0.538492			0.0219291
$604$		0			0
$605$	0.114133	+	0.197685i	0.00464018	+	0.00803703i
$606$		0			0
$607$	5.11102	+	8.85254i	0.207450	+	0.359314i	0.950910	−	0.309466i	$-0.100150\pi$
$607$	5.11102	+	8.85254i	0.207450	+	0.359314i	−0.743461	+	0.668780i	$0.766817\pi$
$608$		0			0
$609$	−2.66703	+	4.61944i	−0.108074	+	0.187189i
$610$		0			0
$611$	−17.5151	−	25.3874i	−0.708585	−	1.02706i
$612$		0			0
$613$	−5.99571	+	10.3849i	−0.242164	+	0.419441i	−0.961331	−	0.275397i	$-0.911191\pi$
$613$	−5.99571	+	10.3849i	−0.242164	+	0.419441i	0.719166	+	0.694838i	$0.244524\pi$
$614$		0			0
$615$	1.13728	+	1.96983i	0.0458595	+	0.0794311i
$616$		0			0
$617$	−10.5270	−	18.2333i	−0.423801	−	0.734045i	0.572507	−	0.819900i	$-0.305971\pi$
$617$	−10.5270	−	18.2333i	−0.423801	−	0.734045i	−0.996308	+	0.0858554i	$0.972638\pi$
$618$		0			0
$619$	44.1485			1.77448			0.887238	−	0.461311i	$-0.152621\pi$
$619$	44.1485			1.77448			0.887238	+	0.461311i	$0.152621\pi$
$620$		0			0
$621$	0.901607	−	1.56163i	0.0361802	−	0.0626660i
$622$		0			0
$623$	−0.656211			−0.0262905
$624$		0			0
$625$	23.5954			0.943814
$626$		0			0
$627$	7.83336	−	13.5678i	0.312834	−	0.541845i
$628$		0			0
$629$	0.457000			0.0182218
$630$		0			0
$631$	6.95710	+	12.0500i	0.276958	+	0.479705i	0.970627	−	0.240589i	$-0.0773405\pi$
$631$	6.95710	+	12.0500i	0.276958	+	0.479705i	−0.693669	+	0.720293i	$0.744007\pi$
$632$		0			0
$633$	6.62031	+	11.4667i	0.263134	+	0.455761i
$634$		0			0
$635$	−0.910626	+	1.57725i	−0.0361371	+	0.0625913i
$636$		0			0
$637$	3.59393	−	0.289309i	0.142397	−	0.0114628i
$638$		0			0
$639$	0.175715	−	0.304347i	0.00695118	−	0.0120398i
$640$		0			0
$641$	−11.2169	−	19.4282i	−0.443041	−	0.767369i	0.554873	−	0.831935i	$-0.312767\pi$
$641$	−11.2169	−	19.4282i	−0.443041	−	0.767369i	−0.997913	+	0.0645660i	$0.979434\pi$
$642$		0			0
$643$	8.38008	+	14.5147i	0.330478	+	0.572405i	0.982606	−	0.185704i	$-0.0594566\pi$
$643$	8.38008	+	14.5147i	0.330478	+	0.572405i	−0.652127	+	0.758109i	$0.726123\pi$
$644$		0			0
$645$	−2.16437			−0.0852219
$646$		0			0
$647$	−15.4674	+	26.7904i	−0.608087	+	1.05324i	0.383468	+	0.923554i	$0.374730\pi$
$647$	−15.4674	+	26.7904i	−0.608087	+	1.05324i	−0.991555	+	0.129684i	$0.958604\pi$
$648$		0			0
$649$	36.4014			1.42888
$650$		0			0
$651$	7.38464			0.289427
$652$		0			0
$653$	21.9762	−	38.0638i	0.859994	−	1.48955i	−0.0119394	−	0.999929i	$-0.503801\pi$
$653$	21.9762	−	38.0638i	0.859994	−	1.48955i	0.871933	−	0.489625i	$-0.162866\pi$
$654$		0			0
$655$	6.19121			0.241911
$656$		0			0
$657$	6.70516	+	11.6137i	0.261593	+	0.453093i
$658$		0			0
$659$	15.2335	+	26.3852i	0.593413	+	1.02782i	0.993769	+	0.111462i	$0.0355532\pi$
$659$	15.2335	+	26.3852i	0.593413	+	1.02782i	−0.400356	+	0.916360i	$0.631113\pi$
$660$		0			0
$661$	−1.64578	+	2.85058i	−0.0640136	+	0.110875i	−0.896256	−	0.443537i	$-0.853723\pi$
$661$	−1.64578	+	2.85058i	−0.0640136	+	0.110875i	0.832242	+	0.554412i	$0.187057\pi$
$662$		0			0
$663$	−1.01605	−	1.47272i	−0.0394601	−	0.0571957i
$664$		0			0
$665$	0.701705	−	1.21539i	0.0272109	−	0.0471307i
$666$		0			0
$667$	−4.80923	−	8.32983i	−0.186214	−	0.322532i
$668$		0			0
$669$	−3.63166	−	6.29021i	−0.140408	−	0.243194i
$670$		0			0
$671$	33.5973			1.29701
$672$		0			0
$673$	19.9647	−	34.5799i	0.769583	−	1.33296i	−0.168206	−	0.985752i	$-0.553797\pi$
$673$	19.9647	−	34.5799i	0.769583	−	1.33296i	0.937789	−	0.347205i	$-0.112869\pi$
$674$		0			0
$675$	−4.90576			−0.188823
$676$		0			0
$677$	−3.86597			−0.148581			−0.0742906	−	0.997237i	$-0.523669\pi$
$677$	−3.86597			−0.148581			−0.0742906	+	0.997237i	$0.523669\pi$
$678$		0			0
$679$	−3.87938	+	6.71928i	−0.148877	+	0.257862i
$680$		0			0
$681$	−22.4739			−0.861200
$682$		0			0
$683$	−1.39784	−	2.42114i	−0.0534870	−	0.0926422i	0.838042	−	0.545605i	$-0.183700\pi$
$683$	−1.39784	−	2.42114i	−0.0534870	−	0.0926422i	−0.891529	+	0.452963i	$0.850367\pi$
$684$		0			0
$685$	0.910843	+	1.57763i	0.0348015	+	0.0602780i
$686$		0			0
$687$	9.41931	−	16.3147i	0.359369	−	0.622445i
$688$		0			0
$689$	2.71161	+	3.93035i	0.103304	+	0.149734i
$690$		0			0
$691$	10.1067	−	17.5053i	0.384477	−	0.665934i	−0.607219	−	0.794534i	$-0.707715\pi$
$691$	10.1067	−	17.5053i	0.384477	−	0.665934i	0.991697	+	0.128600i	$0.0410484\pi$
$692$		0			0
$693$	1.71345	+	2.96778i	0.0650884	+	0.112736i
$694$		0			0
$695$	−0.314956	−	0.545520i	−0.0119470	−	0.0206927i
$696$		0			0
$697$	3.67688			0.139272
$698$		0			0
$699$	−8.96572	+	15.5291i	−0.339115	+	0.587364i
$700$		0			0
$701$	7.74889			0.292672			0.146336	−	0.989235i	$-0.453252\pi$
$701$	7.74889			0.292672			0.146336	+	0.989235i	$0.453252\pi$
$702$		0			0
$703$	−4.21023			−0.158792
$704$		0			0
$705$	1.31299	−	2.27417i	0.0494502	−	0.0856503i
$706$		0			0
$707$	5.42909			0.204182
$708$		0			0
$709$	−24.0183	−	41.6008i	−0.902024	−	1.56235i	−0.824862	−	0.565334i	$-0.808747\pi$
$709$	−24.0183	−	41.6008i	−0.902024	−	1.56235i	−0.0771622	−	0.997019i	$-0.524586\pi$
$710$		0			0
$711$	3.01245	+	5.21771i	0.112976	+	0.195679i
$712$		0			0
$713$	−6.65804	+	11.5321i	−0.249346	+	0.431879i
$714$		0			0
$715$	−3.78074	+	0.304347i	−0.141391	+	0.0113819i
$716$		0			0
$717$	−4.51972	+	7.82838i	−0.168792	+	0.292356i
$718$		0			0
$719$	13.0843	+	22.6626i	0.487962	+	0.845174i	0.999904	−	0.0138455i	$-0.00440729\pi$
$719$	13.0843	+	22.6626i	0.487962	+	0.845174i	−0.511943	+	0.859020i	$0.671074\pi$
$720$		0			0
$721$	4.53883	+	7.86148i	0.169035	+	0.292777i
$722$		0			0
$723$	9.81294			0.364947
$724$		0			0
$725$	−13.0838	+	22.6619i	−0.485921	+	0.841641i
$726$		0			0
$727$	−1.53097			−0.0567804			−0.0283902	−	0.999597i	$-0.509038\pi$
$727$	−1.53097			−0.0567804			−0.0283902	+	0.999597i	$0.509038\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−1.74938	+	3.03001i	−0.0647030	+	0.112069i
$732$		0			0
$733$	24.5131			0.905412			0.452706	−	0.891660i	$-0.350459\pi$
$733$	24.5131			0.905412			0.452706	+	0.891660i	$0.350459\pi$
$734$		0			0
$735$	0.153489	+	0.265850i	0.00566152	+	0.00980604i
$736$		0			0
$737$	−0.922678	−	1.59813i	−0.0339873	−	0.0588677i
$738$		0			0
$739$	6.92430	−	11.9932i	0.254715	−	0.441179i	−0.710103	−	0.704097i	$-0.751352\pi$
$739$	6.92430	−	11.9932i	0.254715	−	0.441179i	0.964818	+	0.262919i	$0.0846852\pi$
$740$		0			0
$741$	9.36061	+	13.5678i	0.343871	+	0.498425i
$742$		0			0
$743$	1.17281	−	2.03137i	0.0430264	−	0.0745239i	−0.843710	−	0.536799i	$-0.819633\pi$
$743$	1.17281	−	2.03137i	0.0430264	−	0.0745239i	0.886737	+	0.462275i	$0.152967\pi$
$744$		0			0
$745$	2.75970	+	4.77994i	0.101108	+	0.175124i
$746$		0			0
$747$	−1.79453	−	3.10822i	−0.0656585	−	0.113724i
$748$		0			0
$749$	7.04304			0.257347
$750$		0			0
$751$	23.1008	−	40.0118i	0.842961	−	1.46005i	−0.0444186	−	0.999013i	$-0.514144\pi$
$751$	23.1008	−	40.0118i	0.842961	−	1.46005i	0.887380	−	0.461039i	$-0.152523\pi$
$752$		0			0
$753$	−14.6125			−0.532511
$754$		0			0
$755$	2.39076			0.0870085
$756$		0			0
$757$	19.2031	−	33.2608i	0.697950	−	1.20888i	−0.271226	−	0.962516i	$-0.587429\pi$
$757$	19.2031	−	33.2608i	0.697950	−	1.20888i	0.969176	−	0.246369i	$-0.0792376\pi$
$758$		0			0
$759$	−6.17942			−0.224299
$760$		0			0
$761$	−25.7770	−	44.6471i	−0.934415	−	1.61846i	−0.775673	−	0.631135i	$-0.782589\pi$
$761$	−25.7770	−	44.6471i	−0.934415	−	1.61846i	−0.158743	−	0.987320i	$-0.550744\pi$
$762$		0			0
$763$	−2.53397	−	4.38896i	−0.0917358	−	0.158891i
$764$		0			0
$765$	0.0761667	−	0.131925i	0.00275381	−	0.00476975i
$766$		0			0
$767$	−16.4264	+	34.5976i	−0.593124	+	1.24925i
$768$		0			0
$769$	13.3424	−	23.1097i	0.481139	−	0.833356i	−0.518627	−	0.855000i	$-0.673557\pi$
$769$	13.3424	−	23.1097i	0.481139	−	0.833356i	0.999766	+	0.0216441i	$0.00689006\pi$
$770$		0			0
$771$	−2.94763	−	5.10544i	−0.106156	−	0.183868i
$772$		0			0
$773$	15.4983	+	26.8438i	0.557434	+	0.965505i	0.997710	+	0.0676419i	$0.0215475\pi$
$773$	15.4983	+	26.8438i	0.557434	+	0.965505i	−0.440275	+	0.897863i	$0.645119\pi$
$774$		0			0
$775$	36.2273			1.30132
$776$		0			0
$777$	0.460466	−	0.797551i	0.0165191	−	0.0286120i
$778$		0			0
$779$	−33.8741			−1.21367
$780$		0			0
$781$	−1.20431			−0.0430937
$782$		0			0
$783$	2.66703	−	4.61944i	0.0953120	−	0.165085i
$784$		0			0
$785$	6.28636			0.224370
$786$		0			0
$787$	−26.6816	−	46.2139i	−0.951096	−	1.64735i	−0.743060	−	0.669225i	$-0.766626\pi$
$787$	−26.6816	−	46.2139i	−0.951096	−	1.64735i	−0.208036	−	0.978121i	$-0.566707\pi$
$788$		0			0
$789$	−5.03922	−	8.72819i	−0.179401	−	0.310732i
$790$		0			0
$791$	6.42619	−	11.1305i	0.228489	−	0.395754i
$792$		0			0
$793$	−15.1610	+	31.9325i	−0.538384	+	1.13396i
$794$		0			0
$795$	−0.203272	+	0.352077i	−0.00720930	+	0.0124869i
$796$		0			0
$797$	7.89002	+	13.6659i	0.279479	+	0.484072i	0.971255	−	0.238040i	$-0.0765049\pi$
$797$	7.89002	+	13.6659i	0.279479	+	0.484072i	−0.691776	+	0.722112i	$0.743172\pi$
$798$		0			0
$799$	−2.12249	−	3.67625i	−0.0750882	−	0.130057i
$800$		0			0
$801$	0.656211			0.0231861
$802$		0			0
$803$	22.9779	−	39.7988i	0.810871	−	1.40447i
$804$		0			0
$805$	−0.553546			−0.0195099
$806$		0			0
$807$	−17.4388			−0.613875
$808$		0			0
$809$	12.9106	−	22.3619i	0.453913	−	0.786201i	−0.544712	−	0.838623i	$-0.683361\pi$
$809$	12.9106	−	22.3619i	0.453913	−	0.786201i	0.998625	+	0.0524223i	$0.0166942\pi$
$810$		0			0
$811$	−45.8649			−1.61053			−0.805267	−	0.592912i	$-0.797978\pi$
$811$	−45.8649			−1.61053			−0.805267	+	0.592912i	$0.797978\pi$
$812$		0			0
$813$	6.85033	+	11.8651i	0.240252	+	0.416128i
$814$		0			0
$815$	1.74176	+	3.01682i	0.0610113	+	0.105675i
$816$		0			0
$817$	16.1165	−	27.9147i	0.563847	−	0.976611i
$818$		0			0
$819$	−3.59393	+	0.289309i	−0.125582	+	0.0101093i
$820$		0			0
$821$	7.55714	−	13.0894i	0.263746	−	0.456822i	−0.703488	−	0.710707i	$-0.748375\pi$
$821$	7.55714	−	13.0894i	0.263746	−	0.456822i	0.967234	+	0.253885i	$0.0817086\pi$
$822$		0			0
$823$	−15.2816	−	26.4686i	−0.532684	−	0.922636i	−0.999272	−	0.0381611i	$-0.987850\pi$
$823$	−15.2816	−	26.4686i	−0.532684	−	0.922636i	0.466587	−	0.884475i	$-0.345483\pi$
$824$		0			0
$825$	8.40576	+	14.5592i	0.292651	+	0.506887i
$826$		0			0
$827$	−28.0432			−0.975158			−0.487579	−	0.873079i	$-0.662120\pi$
$827$	−28.0432			−0.975158			−0.487579	+	0.873079i	$0.662120\pi$
$828$		0			0
$829$	1.69724	−	2.93970i	0.0589475	−	0.102100i	−0.835046	−	0.550181i	$-0.814559\pi$
$829$	1.69724	−	2.93970i	0.0589475	−	0.102100i	0.893993	+	0.448081i	$0.147892\pi$
$830$		0			0
$831$	−27.0366			−0.937890
$832$		0			0
$833$	0.496237			0.0171936
$834$		0			0
$835$	0.378151	−	0.654977i	0.0130865	−	0.0226664i
$836$		0			0
$837$	−7.38464			−0.255250
$838$		0			0
$839$	8.94973	+	15.5014i	0.308979	+	0.535167i	0.978139	−	0.207951i	$-0.0666794\pi$
$839$	8.94973	+	15.5014i	0.308979	+	0.535167i	−0.669160	+	0.743118i	$0.733346\pi$
$840$		0			0
$841$	0.273873	+	0.474361i	0.00944389	+	0.0163573i
$842$		0			0
$843$	−5.01666	+	8.68911i	−0.172783	+	0.299269i
$844$		0			0
$845$	1.41682	−	3.73073i	0.0487401	−	0.128341i
$846$		0			0
$847$	0.371797	−	0.643971i	0.0127751	−	0.0221271i
$848$		0			0
$849$	−9.66764	−	16.7448i	−0.331793	−	0.574682i
$850$		0			0
$851$	0.830320	+	1.43816i	0.0284630	+	0.0492993i
$852$		0			0
$853$	−30.6013			−1.04777			−0.523884	−	0.851790i	$-0.675517\pi$
$853$	−30.6013			−1.04777			−0.523884	+	0.851790i	$0.675517\pi$
$854$		0			0
$855$	−0.701705	+	1.21539i	−0.0239978	+	0.0415654i
$856$		0			0
$857$	16.1652			0.552194			0.276097	−	0.961130i	$-0.410959\pi$
$857$	16.1652			0.552194			0.276097	+	0.961130i	$0.410959\pi$
$858$		0			0
$859$	10.9576			0.373867			0.186934	−	0.982373i	$-0.440145\pi$
$859$	10.9576			0.373867			0.186934	+	0.982373i	$0.440145\pi$
$860$		0			0
$861$	3.70476	−	6.41684i	0.126258	−	0.218685i
$862$		0			0
$863$	−21.9282			−0.746444			−0.373222	−	0.927742i	$-0.621747\pi$
$863$	−21.9282			−0.746444			−0.373222	+	0.927742i	$0.621747\pi$
$864$		0			0
$865$	2.88215	+	4.99203i	0.0979960	+	0.169734i
$866$		0			0
$867$	8.37687	+	14.5092i	0.284494	+	0.492757i
$868$		0			0
$869$	10.3233	−	17.8805i	0.350195	−	0.606555i
$870$		0			0
$871$	1.93530	−	0.155791i	0.0655752	−	0.00527877i
$872$		0			0
$873$	3.87938	−	6.71928i	0.131297	−	0.227413i
$874$		0			0
$875$	1.52042	+	2.63345i	0.0513997	+	0.0890269i
$876$		0			0
$877$	14.1071	+	24.4342i	0.476362	+	0.825083i	0.999633	−	0.0270829i	$-0.00862182\pi$
$877$	14.1071	+	24.4342i	0.476362	+	0.825083i	−0.523271	+	0.852166i	$0.675288\pi$
$878$		0			0
$879$	−29.2938			−0.988056
$880$		0			0
$881$	−4.42158	+	7.65840i	−0.148967	+	0.258018i	−0.930846	−	0.365412i	$-0.880928\pi$
$881$	−4.42158	+	7.65840i	−0.148967	+	0.258018i	0.781879	+	0.623430i	$0.214261\pi$
$882$		0			0
$883$	−44.1842			−1.48692			−0.743459	−	0.668781i	$-0.766816\pi$
$883$	−44.1842			−1.48692			−0.743459	+	0.668781i	$0.766816\pi$
$884$		0			0
$885$	−3.26080			−0.109611
$886$		0			0
$887$	5.34569	−	9.25901i	0.179491	−	0.310887i	−0.762215	−	0.647323i	$-0.775888\pi$
$887$	5.34569	−	9.25901i	0.179491	−	0.310887i	0.941706	+	0.336436i	$0.109222\pi$
$888$		0			0
$889$	5.93285			0.198981
$890$		0			0
$891$	−1.71345	−	2.96778i	−0.0574026	−	0.0994242i
$892$		0			0
$893$	19.5539	+	33.8684i	0.654347	+	1.13336i
$894$		0			0
$895$	−1.55479	+	2.69297i	−0.0519708	+	0.0900160i
$896$		0			0
$897$	2.78851	−	5.87322i	0.0931058	−	0.196101i
$898$		0			0
$899$	−19.6951	+	34.1129i	−0.656867	+	1.13773i
$900$		0			0
$901$	0.328593	+	0.569141i	0.0109470	+	0.0189608i
$902$		0			0
$903$	3.52529	+	6.10597i	0.117314	+	0.203194i
$904$		0			0
$905$	4.09773			0.136213
$906$		0			0
$907$	0.495195	−	0.857704i	0.0164427	−	0.0284796i	−0.857687	−	0.514172i	$-0.828099\pi$
$907$	0.495195	−	0.857704i	0.0164427	−	0.0284796i	0.874130	+	0.485693i	$0.161433\pi$
$908$		0			0
$909$	−5.42909			−0.180072
$910$		0			0
$911$	−22.2711			−0.737873			−0.368937	−	0.929455i	$-0.620278\pi$
$911$	−22.2711			−0.737873			−0.368937	+	0.929455i	$0.620278\pi$
$912$		0			0
$913$	−6.14967	+	10.6515i	−0.203524	+	0.352514i
$914$		0			0
$915$	−3.00961			−0.0994946
$916$		0			0
$917$	−10.0841	−	17.4663i	−0.333008	−	0.576786i
$918$		0			0
$919$	1.82679	+	3.16410i	0.0602603	+	0.104374i	0.894582	−	0.446904i	$-0.147474\pi$
$919$	1.82679	+	3.16410i	0.0602603	+	0.104374i	−0.834321	+	0.551278i	$0.814140\pi$
$920$		0			0
$921$	6.83752	−	11.8429i	0.225304	−	0.390238i
$922$		0			0
$923$	0.543456	−	1.14464i	0.0178881	−	0.0376762i
$924$		0			0
$925$	2.25894	−	3.91260i	0.0742735	−	0.128645i
$926$		0			0
$927$	−4.53883	−	7.86148i	−0.149075	−	0.258205i
$928$		0			0
$929$	−12.8736	−	22.2978i	−0.422370	−	0.731566i	0.573801	−	0.818995i	$-0.305468\pi$
$929$	−12.8736	−	22.2978i	−0.422370	−	0.731566i	−0.996171	+	0.0874286i	$0.972135\pi$
$930$		0			0
$931$	−4.57170			−0.149831
$932$		0			0
$933$	11.2059	−	19.4091i	0.366863	−	0.635426i
$934$		0			0
$935$	−0.522031			−0.0170722
$936$		0			0
$937$	−26.2674			−0.858117			−0.429058	−	0.903277i	$-0.641155\pi$
$937$	−26.2674			−0.858117			−0.429058	+	0.903277i	$0.641155\pi$
$938$		0			0
$939$	8.01841	−	13.8883i	0.261671	−	0.453227i
$940$		0			0
$941$	−8.49106			−0.276800			−0.138400	−	0.990376i	$-0.544196\pi$
$941$	−8.49106			−0.276800			−0.138400	+	0.990376i	$0.544196\pi$
$942$		0			0
$943$	6.68048	+	11.5709i	0.217546	+	0.376802i
$944$		0			0
$945$	−0.153489	−	0.265850i	−0.00499299	−	0.00864811i
$946$		0			0
$947$	−22.6831	+	39.2883i	−0.737101	+	1.27670i	0.216694	+	0.976240i	$0.430473\pi$
$947$	−22.6831	+	39.2883i	−0.737101	+	1.27670i	−0.953795	+	0.300457i	$0.902861\pi$
$948$		0			0
$949$	27.4578	+	39.7988i	0.891317	+	1.29192i
$950$		0			0
$951$	−0.800549	+	1.38659i	−0.0259596	+	0.0449633i
$952$		0			0
$953$	18.0382	+	31.2430i	0.584314	+	1.01206i	0.994961	+	0.100267i	$0.0319697\pi$
$953$	18.0382	+	31.2430i	0.584314	+	1.01206i	−0.410647	+	0.911795i	$0.634697\pi$
$954$		0			0
$955$	−3.73013	−	6.46078i	−0.120704	−	0.209066i
$956$		0			0
$957$	−18.2793			−0.590885
$958$		0			0
$959$	2.96713	−	5.13922i	0.0958136	−	0.165954i
$960$		0			0
$961$	23.5329			0.759125
$962$		0			0
$963$	−7.04304			−0.226959
$964$		0			0
$965$	0.138705	−	0.240244i	0.00446508	−	0.00773374i
$966$		0			0
$967$	52.6509			1.69314			0.846570	−	0.532277i	$-0.178664\pi$
$967$	52.6509			1.69314			0.846570	+	0.532277i	$0.178664\pi$
$968$		0			0
$969$	1.13432	+	1.96470i	0.0364397	+	0.0631154i
$970$		0			0
$971$	−9.29838	−	16.1053i	−0.298399	−	0.516843i	0.677371	−	0.735642i	$-0.263119\pi$
$971$	−9.29838	−	16.1053i	−0.298399	−	0.516843i	−0.975770	+	0.218799i	$0.929786\pi$
$972$		0			0
$973$	−1.02599	+	1.77707i	−0.0328917	+	0.0569701i
$974$		0			0
$975$	−17.6310	+	1.41928i	−0.564642	+	0.0454534i
$976$		0			0
$977$	−2.26460	+	3.92240i	−0.0724510	+	0.125489i	−0.899975	−	0.435942i	$-0.856415\pi$
$977$	−2.26460	+	3.92240i	−0.0724510	+	0.125489i	0.827524	+	0.561430i	$0.189749\pi$
$978$		0			0
$979$	−1.12438	−	1.94749i	−0.0359354	−	0.0622420i
$980$		0			0
$981$	2.53397	+	4.38896i	0.0809034	+	0.140129i
$982$		0			0
$983$	−17.3450			−0.553220			−0.276610	−	0.960982i	$-0.589211\pi$
$983$	−17.3450			−0.553220			−0.276610	+	0.960982i	$0.589211\pi$
$984$		0			0
$985$	−2.17746	+	3.77147i	−0.0693796	+	0.120169i
$986$		0			0
$987$	−8.55433			−0.272287
$988$		0			0
$989$	−12.7137			−0.404272
$990$		0			0
$991$	−27.4057	+	47.4681i	−0.870572	+	1.50787i	−0.00916523	+	0.999958i	$0.502917\pi$
$991$	−27.4057	+	47.4681i	−0.870572	+	1.50787i	−0.861406	+	0.507916i	$0.830416\pi$
$992$		0			0
$993$	5.07233			0.160965
$994$		0			0
$995$	0.197959	+	0.342875i	0.00627571	+	0.0108699i
$996$		0			0
$997$	−28.8601	−	49.9871i	−0.914008	−	1.58311i	−0.808347	−	0.588706i	$-0.799638\pi$
$997$	−28.8601	−	49.9871i	−0.914008	−	1.58311i	−0.105661	−	0.994402i	$-0.533696\pi$
$998$		0			0
$999$	−0.460466	+	0.797551i	−0.0145685	+	0.0252334i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2184.2.bj.h.841.2	✓	8	1.1	even	1	trivial
2184.2.bj.h.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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} -0.306978 q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} -0.306978 q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.71345 + 2.96778i) q^{11} +(-2.04751 - 2.96778i) q^{13} +(0.153489 - 0.265850i) q^{15} +(-0.248118 - 0.429753i) q^{17} +(2.28585 + 3.95921i) q^{19} -1.00000 q^{21} +(0.901607 - 1.56163i) q^{23} -4.90576 q^{25} +1.00000 q^{27} +(2.66703 - 4.61944i) q^{29} -7.38464 q^{31} +(-1.71345 - 2.96778i) q^{33} +(-0.153489 - 0.265850i) q^{35} +(-0.460466 + 0.797551i) q^{37} +(3.59393 - 0.289309i) q^{39} +(-3.70476 + 6.41684i) q^{41} +(-3.52529 - 6.10597i) q^{43} +(0.153489 + 0.265850i) q^{45} +8.55433 q^{47} +(-0.500000 + 0.866025i) q^{49} +0.496237 q^{51} -1.32434 q^{53} +(0.525990 - 0.911041i) q^{55} -4.57170 q^{57} +(-5.31114 - 9.19916i) q^{59} +(-4.90200 - 8.49052i) q^{61} +(0.500000 - 0.866025i) q^{63} +(0.628540 + 0.911041i) q^{65} +(-0.269246 + 0.466348i) q^{67} +(0.901607 + 1.56163i) q^{69} +(0.175715 + 0.304347i) q^{71} -13.4103 q^{73} +(2.45288 - 4.24852i) q^{75} -3.42689 q^{77} -6.02489 q^{79} +(-0.500000 + 0.866025i) q^{81} +3.58906 q^{83} +(0.0761667 + 0.131925i) q^{85} +(2.66703 + 4.61944i) q^{87} +(-0.328106 + 0.568296i) q^{89} +(1.54641 - 3.25709i) q^{91} +(3.69232 - 6.39528i) q^{93} +(-0.701705 - 1.21539i) q^{95} +(3.87938 + 6.71928i) q^{97} +3.42689 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9	\( 8 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9} + q^{11} + q^{13} - 2 q^{15} - 3 q^{17} - 2 q^{19} - 8 q^{21} + 5 q^{23} + 4 q^{25} + 8 q^{27} + 20 q^{29} - 2 q^{31} + q^{33} + 2 q^{35} + 6 q^{37} - 2 q^{39} - 7 q^{41} - q^{43} - 2 q^{45} + 12 q^{47} - 4 q^{49} + 6 q^{51} - 20 q^{53} + 12 q^{55} + 4 q^{57} + 5 q^{59} + 2 q^{61} + 4 q^{63} - 26 q^{65} - 17 q^{67} + 5 q^{69} + 8 q^{71} + 16 q^{73} - 2 q^{75} + 2 q^{77} - 60 q^{79} - 4 q^{81} + 4 q^{83} - 7 q^{85} + 20 q^{87} - 10 q^{89} - q^{91} + q^{93} - 20 q^{95} + 19 q^{97} - 2 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9 + q^11 + q^13 - 2 * q^15 - 3 * q^17 - 2 * q^19 - 8 * q^21 + 5 * q^23 + 4 * q^25 + 8 * q^27 + 20 * q^29 - 2 * q^31 + q^33 + 2 * q^35 + 6 * q^37 - 2 * q^39 - 7 * q^41 - q^43 - 2 * q^45 + 12 * q^47 - 4 * q^49 + 6 * q^51 - 20 * q^53 + 12 * q^55 + 4 * q^57 + 5 * q^59 + 2 * q^61 + 4 * q^63 - 26 * q^65 - 17 * q^67 + 5 * q^69 + 8 * q^71 + 16 * q^73 - 2 * q^75 + 2 * q^77 - 60 * q^79 - 4 * q^81 + 4 * q^83 - 7 * q^85 + 20 * q^87 - 10 * q^89 - q^91 + q^93 - 20 * q^95 + 19 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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