LMFDB - Embedded newform 2184.2.bj.k.841.4

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			841.4
Root			$1.10962 - 1.92192i$ of defining polynomial
Character	$\chi$	$=$	2184.841
Dual form			2184.2.bj.k.1849.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +2.21924 q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +2.21924 q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(2.45150 - 4.24612i) q^{11} +(-2.45150 - 2.64389i) q^{13} +(1.10962 - 1.92192i) q^{15} +(-0.879352 - 1.52308i) q^{17} +(-1.71924 - 2.97782i) q^{19} -1.00000 q^{21} +(0.269730 - 0.467186i) q^{23} -0.0749542 q^{25} -1.00000 q^{27} +(-2.25672 + 3.90876i) q^{29} -6.38559 q^{31} +(-2.45150 - 4.24612i) q^{33} +(-1.10962 - 1.92192i) q^{35} +(-1.81542 + 3.14441i) q^{37} +(-3.51543 + 0.801113i) q^{39} +(0.802415 - 1.38982i) q^{41} +(1.65532 + 2.86709i) q^{43} +(-1.10962 - 1.92192i) q^{45} +7.40202 q^{47} +(-0.500000 + 0.866025i) q^{49} -1.75870 q^{51} -8.02689 q^{53} +(5.44047 - 9.42317i) q^{55} -3.43849 q^{57} +(1.36112 + 2.35752i) q^{59} +(-0.205801 - 0.356458i) q^{61} +(-0.500000 + 0.866025i) q^{63} +(-5.44047 - 5.86744i) q^{65} +(4.30440 - 7.45544i) q^{67} +(-0.269730 - 0.467186i) q^{69} +(-1.33085 - 2.30510i) q^{71} -3.25010 q^{73} +(-0.0374771 + 0.0649122i) q^{75} -4.90299 q^{77} +8.58674 q^{79} +(-0.500000 + 0.866025i) q^{81} +9.76952 q^{83} +(-1.95150 - 3.38009i) q^{85} +(2.25672 + 3.90876i) q^{87} +(6.81063 - 11.7964i) q^{89} +(-1.06393 + 3.44500i) q^{91} +(-3.19279 + 5.53008i) q^{93} +(-3.81542 - 6.60851i) q^{95} +(-0.860110 - 1.48975i) q^{97} -4.90299 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.21924			0.992476			0.496238	−	0.868186i	$-0.334714\pi$
$5$	2.21924			0.992476			0.496238	+	0.868186i	$0.334714\pi$
$6$		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
$11$	2.45150	−	4.24612i	0.739154	−	1.28025i	−0.213722	−	0.976894i	$-0.568559\pi$
$11$	2.45150	−	4.24612i	0.739154	−	1.28025i	0.952877	−	0.303358i	$-0.0981079\pi$
$12$		0			0
$13$	−2.45150	−	2.64389i	−0.679923	−	0.733284i
$13$	−2.45150	−	2.64389i	−0.679923	−	0.733284i
$14$		0			0
$15$	1.10962	−	1.92192i	0.286503	−	0.496238i
$16$		0			0
$17$	−0.879352	−	1.52308i	−0.213274	−	0.369402i	0.739463	−	0.673197i	$-0.235079\pi$
$17$	−0.879352	−	1.52308i	−0.213274	−	0.369402i	−0.952737	+	0.303795i	$0.901746\pi$
$18$		0			0
$19$	−1.71924	−	2.97782i	−0.394422	−	0.683158i	0.598605	−	0.801044i	$-0.295722\pi$
$19$	−1.71924	−	2.97782i	−0.394422	−	0.683158i	−0.993027	+	0.117886i	$0.962388\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	0.269730	−	0.467186i	0.0562426	−	0.0974150i	−0.836533	−	0.547916i	$-0.815421\pi$
$23$	0.269730	−	0.467186i	0.0562426	−	0.0974150i	0.892776	+	0.450501i	$0.148755\pi$
$24$		0			0
$25$	−0.0749542			−0.0149908
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−2.25672	+	3.90876i	−0.419063	+	0.725838i	−0.995845	−	0.0910597i	$-0.970975\pi$
$29$	−2.25672	+	3.90876i	−0.419063	+	0.725838i	0.576783	+	0.816898i	$0.304308\pi$
$30$		0			0
$31$	−6.38559			−1.14689			−0.573443	−	0.819246i	$-0.694392\pi$
$31$	−6.38559			−1.14689			−0.573443	+	0.819246i	$0.694392\pi$
$32$		0			0
$33$	−2.45150	−	4.24612i	−0.426751	−	0.739154i
$34$		0			0
$35$	−1.10962	−	1.92192i	−0.187560	−	0.324864i
$36$		0			0
$37$	−1.81542	+	3.14441i	−0.298454	+	0.516937i	−0.975782	−	0.218743i	$-0.929804\pi$
$37$	−1.81542	+	3.14441i	−0.298454	+	0.516937i	0.677329	+	0.735681i	$0.263138\pi$
$38$		0			0
$39$	−3.51543	+	0.801113i	−0.562919	+	0.128281i
$40$		0			0
$41$	0.802415	−	1.38982i	0.125316	−	0.217054i	−0.796540	−	0.604585i	$-0.793339\pi$
$41$	0.802415	−	1.38982i	0.125316	−	0.217054i	0.921857	+	0.387531i	$0.126672\pi$
$42$		0			0
$43$	1.65532	+	2.86709i	0.252433	+	0.437227i	0.964195	−	0.265193i	$-0.0854358\pi$
$43$	1.65532	+	2.86709i	0.252433	+	0.437227i	−0.711762	+	0.702421i	$0.752102\pi$
$44$		0			0
$45$	−1.10962	−	1.92192i	−0.165413	−	0.286503i
$46$		0			0
$47$	7.40202			1.07970			0.539848	−	0.841763i	$-0.318482\pi$
$47$	7.40202			1.07970			0.539848	+	0.841763i	$0.318482\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	−1.75870			−0.246268
$52$		0			0
$53$	−8.02689			−1.10258			−0.551289	−	0.834314i	$-0.685864\pi$
$53$	−8.02689			−1.10258			−0.551289	+	0.834314i	$0.685864\pi$
$54$		0			0
$55$	5.44047	−	9.42317i	0.733593	−	1.27062i
$56$		0			0
$57$	−3.43849			−0.455439
$58$		0			0
$59$	1.36112	+	2.35752i	0.177202	+	0.306924i	0.940921	−	0.338625i	$-0.109962\pi$
$59$	1.36112	+	2.35752i	0.177202	+	0.306924i	−0.763719	+	0.645549i	$0.776629\pi$
$60$		0			0
$61$	−0.205801	−	0.356458i	−0.0263502	−	0.0456398i	0.852550	−	0.522646i	$-0.175055\pi$
$61$	−0.205801	−	0.356458i	−0.0263502	−	0.0456398i	−0.878900	+	0.477006i	$0.841722\pi$
$62$		0			0
$63$	−0.500000	+	0.866025i	−0.0629941	+	0.109109i
$64$		0			0
$65$	−5.44047	−	5.86744i	−0.674807	−	0.727767i
$66$		0			0
$67$	4.30440	−	7.45544i	0.525866	−	0.910826i	−0.473680	−	0.880697i	$-0.657075\pi$
$67$	4.30440	−	7.45544i	0.525866	−	0.910826i	0.999546	−	0.0301295i	$-0.00959196\pi$
$68$		0			0
$69$	−0.269730	−	0.467186i	−0.0324717	−	0.0562426i
$70$		0			0
$71$	−1.33085	−	2.30510i	−0.157943	−	0.273565i	0.776184	−	0.630507i	$-0.217153\pi$
$71$	−1.33085	−	2.30510i	−0.157943	−	0.273565i	−0.934127	+	0.356942i	$0.883819\pi$
$72$		0			0
$73$	−3.25010			−0.380395			−0.190197	−	0.981746i	$-0.560913\pi$
$73$	−3.25010			−0.380395			−0.190197	+	0.981746i	$0.560913\pi$
$74$		0			0
$75$	−0.0374771	+	0.0649122i	−0.00432748	+	0.00749542i
$76$		0			0
$77$	−4.90299			−0.558748
$78$		0			0
$79$	8.58674			0.966084			0.483042	−	0.875597i	$-0.339532\pi$
$79$	8.58674			0.966084			0.483042	+	0.875597i	$0.339532\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	9.76952			1.07234			0.536172	−	0.844109i	$-0.319870\pi$
$83$	9.76952			1.07234			0.536172	+	0.844109i	$0.319870\pi$
$84$		0			0
$85$	−1.95150	−	3.38009i	−0.211670	−	0.366622i
$86$		0			0
$87$	2.25672	+	3.90876i	0.241946	+	0.419063i
$88$		0			0
$89$	6.81063	−	11.7964i	0.721926	−	1.25041i	−0.238301	−	0.971191i	$-0.576591\pi$
$89$	6.81063	−	11.7964i	0.721926	−	1.25041i	0.960227	−	0.279220i	$-0.0900760\pi$
$90$		0			0
$91$	−1.06393	+	3.44500i	−0.111530	+	0.361135i
$92$		0			0
$93$	−3.19279	+	5.53008i	−0.331077	+	0.573443i
$94$		0			0
$95$	−3.81542	−	6.60851i	−0.391454	−	0.678019i
$96$		0			0
$97$	−0.860110	−	1.48975i	−0.0873309	−	0.151262i	0.819051	−	0.573720i	$-0.194500\pi$
$97$	−0.860110	−	1.48975i	−0.0873309	−	0.151262i	−0.906382	+	0.422459i	$0.861167\pi$
$98$		0			0
$99$	−4.90299			−0.492769
$100$		0			0
$101$	−3.24768	+	5.62514i	−0.323156	+	0.559723i	−0.981137	−	0.193311i	$-0.938077\pi$
$101$	−3.24768	+	5.62514i	−0.323156	+	0.559723i	0.657981	+	0.753034i	$0.271411\pi$
$102$		0			0
$103$	1.34314			0.132343			0.0661716	−	0.997808i	$-0.478922\pi$
$103$	1.34314			0.132343			0.0661716	+	0.997808i	$0.478922\pi$
$104$		0			0
$105$	−2.21924			−0.216576
$106$		0			0
$107$	3.28317	−	5.68662i	0.317396	−	0.549747i	−0.662548	−	0.749020i	$-0.730525\pi$
$107$	3.28317	−	5.68662i	0.317396	−	0.549747i	0.979944	+	0.199273i	$0.0638581\pi$
$108$		0			0
$109$	9.37997			0.898438			0.449219	−	0.893422i	$-0.351702\pi$
$109$	9.37997			0.898438			0.449219	+	0.893422i	$0.351702\pi$
$110$		0			0
$111$	1.81542	+	3.14441i	0.172312	+	0.298454i
$112$		0			0
$113$	10.0208	+	17.3566i	0.942681	+	1.63277i	0.760330	+	0.649537i	$0.225037\pi$
$113$	10.0208	+	17.3566i	0.942681	+	1.63277i	0.182351	+	0.983233i	$0.441629\pi$
$114$		0			0
$115$	0.598597	−	1.03680i	0.0558194	−	0.0966821i
$116$		0			0
$117$	−1.06393	+	3.44500i	−0.0983602	+	0.318491i
$118$		0			0
$119$	−0.879352	+	1.52308i	−0.0806101	+	0.139621i
$120$		0			0
$121$	−6.51968	−	11.2924i	−0.592698	−	1.02658i
$122$		0			0
$123$	−0.802415	−	1.38982i	−0.0723513	−	0.125316i
$124$		0			0
$125$	−11.2626			−1.00735
$126$		0			0
$127$	6.40382	−	11.0917i	0.568247	−	0.984233i	−0.428492	−	0.903545i	$-0.640955\pi$
$127$	6.40382	−	11.0917i	0.568247	−	0.984233i	0.996739	−	0.0806876i	$-0.0257116\pi$
$128$		0			0
$129$	3.31063			0.291485
$130$		0			0
$131$	−12.6136			−1.10206			−0.551029	−	0.834486i	$-0.685765\pi$
$131$	−12.6136			−1.10206			−0.551029	+	0.834486i	$0.685765\pi$
$132$		0			0
$133$	−1.71924	+	2.97782i	−0.149077	+	0.258210i
$134$		0			0
$135$	−2.21924			−0.191002
$136$		0			0
$137$	−10.6699	−	18.4808i	−0.911592	−	1.57892i	−0.811815	−	0.583915i	$-0.801520\pi$
$137$	−10.6699	−	18.4808i	−0.911592	−	1.57892i	−0.0997772	−	0.995010i	$-0.531813\pi$
$138$		0			0
$139$	3.97896	+	6.89175i	0.337491	+	0.584551i	0.983960	−	0.178389i	$-0.0570885\pi$
$139$	3.97896	+	6.89175i	0.337491	+	0.584551i	−0.646469	+	0.762940i	$0.723755\pi$
$140$		0			0
$141$	3.70101	−	6.41034i	0.311681	−	0.539848i
$142$		0			0
$143$	−17.2361	+	3.92785i	−1.44136	+	0.328464i
$144$		0			0
$145$	−5.00822	+	8.67449i	−0.415910	+	0.720377i
$146$		0			0
$147$	0.500000	+	0.866025i	0.0412393	+	0.0714286i
$148$		0			0
$149$	−2.88476	−	4.99655i	−0.236329	−	0.409333i	0.723329	−	0.690503i	$-0.242611\pi$
$149$	−2.88476	−	4.99655i	−0.236329	−	0.409333i	−0.959658	+	0.281170i	$0.909278\pi$
$150$		0			0
$151$	2.65088			0.215726			0.107863	−	0.994166i	$-0.465599\pi$
$151$	2.65088			0.215726			0.107863	+	0.994166i	$0.465599\pi$
$152$		0			0
$153$	−0.879352	+	1.52308i	−0.0710914	+	0.123134i
$154$		0			0
$155$	−14.1712			−1.13826
$156$		0			0
$157$	12.9627			1.03454			0.517270	−	0.855822i	$-0.326948\pi$
$157$	12.9627			1.03454			0.517270	+	0.855822i	$0.326948\pi$
$158$		0			0
$159$	−4.01344	+	6.95149i	−0.318287	+	0.551289i
$160$		0			0
$161$	−0.539460			−0.0425154
$162$		0			0
$163$	8.79381	+	15.2313i	0.688784	+	1.19301i	0.972231	+	0.234021i	$0.0751885\pi$
$163$	8.79381	+	15.2313i	0.688784	+	1.19301i	−0.283447	+	0.958988i	$0.591478\pi$
$164$		0			0
$165$	−5.44047	−	9.42317i	−0.423540	−	0.733593i
$166$		0			0
$167$	9.48317	−	16.4253i	0.733830	−	1.27103i	−0.221405	−	0.975182i	$-0.571064\pi$
$167$	9.48317	−	16.4253i	0.733830	−	1.27103i	0.955235	−	0.295849i	$-0.0956025\pi$
$168$		0			0
$169$	−0.980323	+	12.9630i	−0.0754095	+	0.997153i
$170$		0			0
$171$	−1.71924	+	2.97782i	−0.131474	+	0.227719i
$172$		0			0
$173$	−2.33907	−	4.05138i	−0.177836	−	0.308021i	0.763303	−	0.646040i	$-0.223576\pi$
$173$	−2.33907	−	4.05138i	−0.177836	−	0.308021i	−0.941139	+	0.338020i	$0.890243\pi$
$174$		0			0
$175$	0.0374771	+	0.0649122i	0.00283300	+	0.00490690i
$176$		0			0
$177$	2.72223			0.204616
$178$		0			0
$179$	5.03709	−	8.72449i	0.376489	−	0.652099i	−0.614059	−	0.789260i	$-0.710464\pi$
$179$	5.03709	−	8.72449i	0.376489	−	0.652099i	0.990549	+	0.137161i	$0.0437978\pi$
$180$		0			0
$181$	9.51179			0.707006			0.353503	−	0.935433i	$-0.384990\pi$
$181$	9.51179			0.707006			0.353503	+	0.935433i	$0.384990\pi$
$182$		0			0
$183$	−0.411603			−0.0304266
$184$		0			0
$185$	−4.02887	+	6.97821i	−0.296208	+	0.513048i
$186$		0			0
$187$	−8.62292			−0.630570
$188$		0			0
$189$	0.500000	+	0.866025i	0.0363696	+	0.0629941i
$190$		0			0
$191$	5.46692	+	9.46899i	0.395573	+	0.685152i	0.993174	−	0.116641i	$-0.0372128\pi$
$191$	5.46692	+	9.46899i	0.395573	+	0.685152i	−0.597601	+	0.801793i	$0.703879\pi$
$192$		0			0
$193$	6.58955	−	11.4134i	0.474326	−	0.821557i	−0.525241	−	0.850953i	$-0.676025\pi$
$193$	6.58955	−	11.4134i	0.474326	−	0.821557i	0.999568	+	0.0293958i	$0.00935831\pi$
$194$		0			0
$195$	−7.80159	+	1.77787i	−0.558683	+	0.127316i
$196$		0			0
$197$	−12.7785	+	22.1331i	−0.910433	+	1.57692i	−0.0969783	+	0.995286i	$0.530918\pi$
$197$	−12.7785	+	22.1331i	−0.910433	+	1.57692i	−0.813454	+	0.581629i	$0.802416\pi$
$198$		0			0
$199$	−4.32688	−	7.49438i	−0.306725	−	0.531263i	0.670919	−	0.741531i	$-0.265900\pi$
$199$	−4.32688	−	7.49438i	−0.306725	−	0.531263i	−0.977644	+	0.210268i	$0.932566\pi$
$200$		0			0
$201$	−4.30440	−	7.45544i	−0.303609	−	0.525866i
$202$		0			0
$203$	4.51344			0.316782
$204$		0			0
$205$	1.78076	−	3.08436i	0.124373	−	0.215421i
$206$		0			0
$207$	−0.539460			−0.0374950
$208$		0			0
$209$	−16.8589			−1.16615
$210$		0			0
$211$	7.85251	−	13.6009i	0.540589	−	0.936328i	−0.458281	−	0.888807i	$-0.651535\pi$
$211$	7.85251	−	13.6009i	0.540589	−	0.936328i	0.998870	−	0.0475204i	$-0.0151319\pi$
$212$		0			0
$213$	−2.66170			−0.182377
$214$		0			0
$215$	3.67355	+	6.36278i	0.250534	+	0.433938i
$216$		0			0
$217$	3.19279	+	5.53008i	0.216741	+	0.375406i
$218$		0			0
$219$	−1.62505	+	2.81467i	−0.109811	+	0.190197i
$220$		0			0
$221$	−1.87114	+	6.05874i	−0.125866	+	0.407555i
$222$		0			0
$223$	0.878344	−	1.52134i	0.0588183	−	0.101876i	−0.835117	−	0.550072i	$-0.814600\pi$
$223$	0.878344	−	1.52134i	0.0588183	−	0.101876i	0.893935	+	0.448196i	$0.147933\pi$
$224$		0			0
$225$	0.0374771	+	0.0649122i	0.00249847	+	0.00432748i
$226$		0			0
$227$	−1.32462	−	2.29430i	−0.0879178	−	0.152278i	0.818713	−	0.574203i	$-0.194688\pi$
$227$	−1.32462	−	2.29430i	−0.0879178	−	0.152278i	−0.906631	+	0.421925i	$0.861355\pi$
$228$		0			0
$229$	−1.35395			−0.0894716			−0.0447358	−	0.998999i	$-0.514245\pi$
$229$	−1.35395			−0.0894716			−0.0447358	+	0.998999i	$0.514245\pi$
$230$		0			0
$231$	−2.45150	+	4.24612i	−0.161297	+	0.279374i
$232$		0			0
$233$	13.9203			0.911949			0.455974	−	0.889993i	$-0.349291\pi$
$233$	13.9203			0.911949			0.455974	+	0.889993i	$0.349291\pi$
$234$		0			0
$235$	16.4269			1.07157
$236$		0			0
$237$	4.29337	−	7.43634i	0.278884	−	0.483042i
$238$		0			0
$239$	−12.1828			−0.788038			−0.394019	−	0.919102i	$-0.628916\pi$
$239$	−12.1828			−0.788038			−0.394019	+	0.919102i	$0.628916\pi$
$240$		0			0
$241$	−8.66213	−	15.0033i	−0.557977	−	0.966445i	−0.997665	−	0.0682941i	$-0.978244\pi$
$241$	−8.66213	−	15.0033i	−0.557977	−	0.966445i	0.439688	−	0.898150i	$-0.355089\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	−1.10962	+	1.92192i	−0.0708912	+	0.122787i
$246$		0			0
$247$	−3.65831	+	11.8456i	−0.232772	+	0.753718i
$248$		0			0
$249$	4.88476	−	8.46065i	0.309559	−	0.536172i
$250$		0			0
$251$	−7.37355	−	12.7714i	−0.465415	−	0.806122i	0.533806	−	0.845607i	$-0.320761\pi$
$251$	−7.37355	−	12.7714i	−0.465415	−	0.806122i	−0.999220	+	0.0394856i	$0.987428\pi$
$252$		0			0
$253$	−1.32248	−	2.29061i	−0.0831439	−	0.144009i
$254$		0			0
$255$	−3.90299			−0.244415
$256$		0			0
$257$	−5.72166	+	9.91021i	−0.356907	+	0.618182i	−0.987442	−	0.157979i	$-0.949502\pi$
$257$	−5.72166	+	9.91021i	−0.356907	+	0.618182i	0.630535	+	0.776161i	$0.282836\pi$
$258$		0			0
$259$	3.63085			0.225610
$260$		0			0
$261$	4.51344			0.279375
$262$		0			0
$263$	−1.11160	+	1.92536i	−0.0685445	+	0.118723i	−0.898261	−	0.439463i	$-0.855169\pi$
$263$	−1.11160	+	1.92536i	−0.0685445	+	0.118723i	0.829716	+	0.558185i	$0.188502\pi$
$264$		0			0
$265$	−17.8136			−1.09428
$266$		0			0
$267$	−6.81063	−	11.7964i	−0.416804	−	0.721926i
$268$		0			0
$269$	−10.9459	−	18.9588i	−0.667382	−	1.15594i	−0.978634	−	0.205612i	$-0.934082\pi$
$269$	−10.9459	−	18.9588i	−0.667382	−	1.15594i	0.311252	−	0.950328i	$-0.399252\pi$
$270$		0			0
$271$	3.48457	−	6.03546i	0.211673	−	0.366628i	−0.740565	−	0.671984i	$-0.765442\pi$
$271$	3.48457	−	6.03546i	0.211673	−	0.366628i	0.952238	+	0.305356i	$0.0987755\pi$
$272$		0			0
$273$	2.45150	+	2.64389i	0.148371	+	0.160016i
$274$		0			0
$275$	−0.183750	+	0.318264i	−0.0110805	+	0.0191921i
$276$		0			0
$277$	2.31063	+	4.00213i	0.138832	+	0.240465i	0.927055	−	0.374926i	$-0.122332\pi$
$277$	2.31063	+	4.00213i	0.138832	+	0.240465i	−0.788223	+	0.615390i	$0.788998\pi$
$278$		0			0
$279$	3.19279	+	5.53008i	0.191148	+	0.331077i
$280$		0			0
$281$	5.02602			0.299827			0.149914	−	0.988699i	$-0.452100\pi$
$281$	5.02602			0.299827			0.149914	+	0.988699i	$0.452100\pi$
$282$		0			0
$283$	7.89280	−	13.6707i	0.469178	−	0.812640i	−0.530201	−	0.847872i	$-0.677884\pi$
$283$	7.89280	−	13.6707i	0.469178	−	0.812640i	0.999379	+	0.0352318i	$0.0112169\pi$
$284$		0			0
$285$	−7.63085			−0.452012
$286$		0			0
$287$	−1.60483			−0.0947301
$288$		0			0
$289$	6.95348	−	12.0438i	0.409028	−	0.708458i
$290$		0			0
$291$	−1.72022			−0.100841
$292$		0			0
$293$	12.6924	+	21.9839i	0.741498	+	1.28431i	0.951813	+	0.306679i	$0.0992177\pi$
$293$	12.6924	+	21.9839i	0.741498	+	1.28431i	−0.210315	+	0.977634i	$0.567449\pi$
$294$		0			0
$295$	3.02065	+	5.23192i	0.175869	+	0.304614i
$296$		0			0
$297$	−2.45150	+	4.24612i	−0.142250	+	0.246385i
$298$		0			0
$299$	−1.89643	+	0.432168i	−0.109673	+	0.0249929i
$300$		0			0
$301$	1.65532	−	2.86709i	0.0954108	−	0.165256i
$302$		0			0
$303$	3.24768	+	5.62514i	0.186574	+	0.323156i
$304$		0			0
$305$	−0.456724	−	0.791068i	−0.0261519	−	0.0452964i
$306$		0			0
$307$	31.7198			1.81034			0.905172	−	0.425045i	$-0.139742\pi$
$307$	31.7198			1.81034			0.905172	+	0.425045i	$0.139742\pi$
$308$		0			0
$309$	0.671568	−	1.16319i	0.0382042	−	0.0661716i
$310$		0			0
$311$	24.8722			1.41037			0.705187	−	0.709021i	$-0.250863\pi$
$311$	24.8722			1.41037			0.705187	+	0.709021i	$0.250863\pi$
$312$		0			0
$313$	2.28095			0.128927			0.0644634	−	0.997920i	$-0.479466\pi$
$313$	2.28095			0.128927			0.0644634	+	0.997920i	$0.479466\pi$
$314$		0			0
$315$	−1.10962	+	1.92192i	−0.0625201	+	0.108288i
$316$		0			0
$317$	−16.3542			−0.918546			−0.459273	−	0.888295i	$-0.651890\pi$
$317$	−16.3542			−0.918546			−0.459273	+	0.888295i	$0.651890\pi$
$318$		0			0
$319$	11.0647	+	19.1646i	0.619504	+	1.07301i
$320$		0			0
$321$	−3.28317	−	5.68662i	−0.183249	−	0.317396i
$322$		0			0
$323$	−3.02364	+	5.23710i	−0.168240	+	0.291400i
$324$		0			0
$325$	0.183750	+	0.198171i	0.0101926	+	0.0109925i
$326$		0			0
$327$	4.68998	−	8.12329i	0.259357	−	0.449219i
$328$		0			0
$329$	−3.70101	−	6.41034i	−0.204043	−	0.353413i
$330$		0			0
$331$	15.5986	+	27.0176i	0.857376	+	1.48502i	0.874423	+	0.485165i	$0.161240\pi$
$331$	15.5986	+	27.0176i	0.857376	+	1.48502i	−0.0170463	+	0.999855i	$0.505426\pi$
$332$		0			0
$333$	3.63085			0.198969
$334$		0			0
$335$	9.55251	−	16.5454i	0.521909	−	0.903974i
$336$		0			0
$337$	−10.7175			−0.583819			−0.291909	−	0.956446i	$-0.594291\pi$
$337$	−10.7175			−0.583819			−0.291909	+	0.956446i	$0.594291\pi$
$338$		0			0
$339$	20.0417			1.08851
$340$		0			0
$341$	−15.6542	+	27.1140i	−0.847725	+	1.46830i
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	−0.598597	−	1.03680i	−0.0322274	−	0.0558194i
$346$		0			0
$347$	−6.42703	−	11.1319i	−0.345021	−	0.597594i	0.640337	−	0.768094i	$-0.278795\pi$
$347$	−6.42703	−	11.1319i	−0.345021	−	0.597594i	−0.985358	+	0.170501i	$0.945462\pi$
$348$		0			0
$349$	17.0150	−	29.4709i	0.910794	−	1.57754i	0.0978485	−	0.995201i	$-0.468804\pi$
$349$	17.0150	−	29.4709i	0.910794	−	1.57754i	0.812945	−	0.582340i	$-0.197863\pi$
$350$		0			0
$351$	2.45150	+	2.64389i	0.130851	+	0.141120i
$352$		0			0
$353$	−5.92065	+	10.2549i	−0.315124	+	0.545811i	−0.979464	−	0.201620i	$-0.935380\pi$
$353$	−5.92065	+	10.2549i	−0.315124	+	0.545811i	0.664340	+	0.747431i	$0.268713\pi$
$354$		0			0
$355$	−2.95348	−	5.11558i	−0.156754	−	0.271507i
$356$		0			0
$357$	0.879352	+	1.52308i	0.0465402	+	0.0806101i
$358$		0			0
$359$	3.00195			0.158437			0.0792184	−	0.996857i	$-0.474758\pi$
$359$	3.00195			0.158437			0.0792184	+	0.996857i	$0.474758\pi$
$360$		0			0
$361$	3.58840	−	6.21529i	0.188863	−	0.327120i
$362$		0			0
$363$	−13.0394			−0.684389
$364$		0			0
$365$	−7.21276			−0.377533
$366$		0			0
$367$	−6.35550	+	11.0080i	−0.331754	+	0.574615i	−0.982856	−	0.184375i	$-0.940974\pi$
$367$	−6.35550	+	11.0080i	−0.331754	+	0.574615i	0.651102	+	0.758991i	$0.274307\pi$
$368$		0			0
$369$	−1.60483			−0.0835441
$370$		0			0
$371$	4.01344	+	6.95149i	0.208368	+	0.360903i
$372$		0			0
$373$	12.5142	+	21.6752i	0.647961	+	1.12230i	0.983609	+	0.180314i	$0.0577114\pi$
$373$	12.5142	+	21.6752i	0.647961	+	1.12230i	−0.335648	+	0.941987i	$0.608955\pi$
$374$		0			0
$375$	−5.63128	+	9.75367i	−0.290798	+	0.503677i
$376$		0			0
$377$	15.8667	−	3.61578i	0.817175	−	0.186222i
$378$		0			0
$379$	−0.0749542	+	0.129824i	−0.00385014	+	0.00666863i	−0.867944	−	0.496662i	$-0.834559\pi$
$379$	−0.0749542	+	0.129824i	−0.00385014	+	0.00666863i	0.864094	+	0.503331i	$0.167892\pi$
$380$		0			0
$381$	−6.40382	−	11.0917i	−0.328078	−	0.568247i
$382$		0			0
$383$	11.5651	+	20.0313i	0.590948	+	1.02355i	0.994105	+	0.108421i	$0.0345796\pi$
$383$	11.5651	+	20.0313i	0.590948	+	1.02355i	−0.403157	+	0.915131i	$0.632087\pi$
$384$		0			0
$385$	−10.8809			−0.554544
$386$		0			0
$387$	1.65532	−	2.86709i	0.0841444	−	0.145742i
$388$		0			0
$389$	−16.0617			−0.814361			−0.407180	−	0.913348i	$-0.633488\pi$
$389$	−16.0617			−0.814361			−0.407180	+	0.913348i	$0.633488\pi$
$390$		0			0
$391$	−0.948750			−0.0479804
$392$		0			0
$393$	−6.30682	+	10.9237i	−0.318137	+	0.551029i
$394$		0			0
$395$	19.0561			0.958816
$396$		0			0
$397$	5.99096	+	10.3766i	0.300678	+	0.520789i	0.976290	−	0.216469i	$-0.0694539\pi$
$397$	5.99096	+	10.3766i	0.300678	+	0.520789i	−0.675612	+	0.737257i	$0.736121\pi$
$398$		0			0
$399$	1.71924	+	2.97782i	0.0860699	+	0.149077i
$400$		0			0
$401$	−4.74289	+	8.21492i	−0.236848	+	0.410234i	−0.959808	−	0.280657i	$-0.909448\pi$
$401$	−4.74289	+	8.21492i	−0.236848	+	0.410234i	0.722960	+	0.690890i	$0.242781\pi$
$402$		0			0
$403$	15.6542	+	16.8828i	0.779794	+	0.840992i
$404$		0			0
$405$	−1.10962	+	1.92192i	−0.0551376	+	0.0955011i
$406$		0			0
$407$	8.90101	+	15.4170i	0.441207	+	0.764193i
$408$		0			0
$409$	12.8612	+	22.2762i	0.635943	+	1.10149i	0.986314	+	0.164875i	$0.0527222\pi$
$409$	12.8612	+	22.2762i	0.635943	+	1.10149i	−0.350371	+	0.936611i	$0.613944\pi$
$410$		0			0
$411$	−21.3398			−1.05262
$412$		0			0
$413$	1.36112	−	2.35752i	0.0669762	−	0.116006i
$414$		0			0
$415$	21.6810			1.06428
$416$		0			0
$417$	7.95791			0.389701
$418$		0			0
$419$	11.6799	−	20.2302i	0.570602	−	0.988312i	−0.425902	−	0.904769i	$-0.640043\pi$
$419$	11.6799	−	20.2302i	0.570602	−	0.988312i	0.996504	−	0.0835426i	$-0.0266235\pi$
$420$		0			0
$421$	−3.75309			−0.182914			−0.0914571	−	0.995809i	$-0.529152\pi$
$421$	−3.75309			−0.182914			−0.0914571	+	0.995809i	$0.529152\pi$
$422$		0			0
$423$	−3.70101	−	6.41034i	−0.179949	−	0.311681i
$424$		0			0
$425$	0.0659111	+	0.114161i	0.00319716	+	0.00553764i
$426$		0			0
$427$	−0.205801	+	0.356458i	−0.00995943	+	0.0172502i
$428$		0			0
$429$	−5.21644	+	16.8908i	−0.251852	+	0.815497i
$430$		0			0
$431$	−4.52548	+	7.83835i	−0.217985	+	0.377560i	−0.954192	−	0.299196i	$-0.903282\pi$
$431$	−4.52548	+	7.83835i	−0.217985	+	0.377560i	0.736207	+	0.676756i	$0.236615\pi$
$432$		0			0
$433$	1.69197	+	2.93057i	0.0813107	+	0.140834i	0.903813	−	0.427927i	$-0.140756\pi$
$433$	1.69197	+	2.93057i	0.0813107	+	0.140834i	−0.822502	+	0.568762i	$0.807423\pi$
$434$		0			0
$435$	5.00822	+	8.67449i	0.240126	+	0.415910i
$436$		0			0
$437$	−1.85493			−0.0887332
$438$		0			0
$439$	−7.35730	+	12.7432i	−0.351145	+	0.608201i	−0.986450	−	0.164060i	$-0.947541\pi$
$439$	−7.35730	+	12.7432i	−0.351145	+	0.608201i	0.635306	+	0.772261i	$0.280874\pi$
$440$		0			0
$441$	1.00000			0.0476190
$442$		0			0
$443$	−11.8329			−0.562197			−0.281098	−	0.959679i	$-0.590699\pi$
$443$	−11.8329			−0.562197			−0.281098	+	0.959679i	$0.590699\pi$
$444$		0			0
$445$	15.1145	−	26.1790i	0.716494	−	1.24100i
$446$		0			0
$447$	−5.76952			−0.272889
$448$		0			0
$449$	12.1128	+	20.9800i	0.571639	+	0.990107i	0.996398	+	0.0848007i	$0.0270254\pi$
$449$	12.1128	+	20.9800i	0.571639	+	0.990107i	−0.424759	+	0.905306i	$0.639641\pi$
$450$		0			0
$451$	−3.93424	−	6.81430i	−0.185256	−	0.320873i
$452$		0			0
$453$	1.32544	−	2.29573i	0.0622747	−	0.107863i
$454$		0			0
$455$	−2.36112	+	7.64531i	−0.110691	+	0.358418i
$456$		0			0
$457$	2.61121	−	4.52275i	0.122147	−	0.211565i	−0.798467	−	0.602039i	$-0.794355\pi$
$457$	2.61121	−	4.52275i	0.122147	−	0.211565i	0.920614	+	0.390473i	$0.127689\pi$
$458$		0			0
$459$	0.879352	+	1.52308i	0.0410446	+	0.0710914i
$460$		0			0
$461$	−5.41204	−	9.37392i	−0.252064	−	0.436587i	0.712030	−	0.702149i	$-0.247776\pi$
$461$	−5.41204	−	9.37392i	−0.252064	−	0.436587i	−0.964094	+	0.265562i	$0.914443\pi$
$462$		0			0
$463$	35.7234			1.66021			0.830104	−	0.557609i	$-0.188281\pi$
$463$	35.7234			1.66021			0.830104	+	0.557609i	$0.188281\pi$
$464$		0			0
$465$	−7.08559	+	12.2726i	−0.328586	+	0.569128i
$466$		0			0
$467$	−13.0585			−0.604276			−0.302138	−	0.953264i	$-0.597700\pi$
$467$	−13.0585			−0.604276			−0.302138	+	0.953264i	$0.597700\pi$
$468$		0			0
$469$	−8.60880			−0.397517
$470$		0			0
$471$	6.48137	−	11.2261i	0.298646	−	0.517270i
$472$		0			0
$473$	16.2320			0.746349
$474$		0			0
$475$	0.128865	+	0.223200i	0.00591271	+	0.0102411i
$476$		0			0
$477$	4.01344	+	6.95149i	0.183763	+	0.318287i
$478$		0			0
$479$	9.69478	−	16.7918i	0.442966	−	0.767239i	−0.554942	−	0.831889i	$-0.687260\pi$
$479$	9.69478	−	16.7918i	0.442966	−	0.767239i	0.997908	+	0.0646498i	$0.0205930\pi$
$480$		0			0
$481$	12.7640	−	2.90872i	0.581987	−	0.132626i
$482$		0			0
$483$	−0.269730	+	0.467186i	−0.0122731	+	0.0212577i
$484$		0			0
$485$	−1.90879	−	3.30613i	−0.0866739	−	0.150124i
$486$		0			0
$487$	20.9917	+	36.3587i	0.951226	+	1.64757i	0.742778	+	0.669538i	$0.233508\pi$
$487$	20.9917	+	36.3587i	0.951226	+	1.64757i	0.208448	+	0.978034i	$0.433159\pi$
$488$		0			0
$489$	17.5876			0.795339
$490$		0			0
$491$	0.935245	−	1.61989i	0.0422070	−	0.0731047i	−0.844150	−	0.536107i	$-0.819894\pi$
$491$	0.935245	−	1.61989i	0.0422070	−	0.0731047i	0.886357	+	0.463002i	$0.153228\pi$
$492$		0			0
$493$	7.93781			0.357501
$494$		0			0
$495$	−10.8809			−0.489062
$496$		0			0
$497$	−1.33085	+	2.30510i	−0.0596967	+	0.103398i
$498$		0			0
$499$	−36.2372			−1.62220			−0.811100	−	0.584907i	$-0.801131\pi$
$499$	−36.2372			−1.62220			−0.811100	+	0.584907i	$0.801131\pi$
$500$		0			0
$501$	−9.48317	−	16.4253i	−0.423677	−	0.733830i
$502$		0			0
$503$	19.9104	+	34.4859i	0.887762	+	1.53765i	0.842515	+	0.538673i	$0.181074\pi$
$503$	19.9104	+	34.4859i	0.887762	+	1.53765i	0.0452473	+	0.998976i	$0.485592\pi$
$504$		0			0
$505$	−7.20739	+	12.4836i	−0.320725	+	0.555512i
$506$		0			0
$507$	10.7361	+	7.33048i	0.476807	+	0.325558i
$508$		0			0
$509$	−17.0252	+	29.4886i	−0.754630	+	1.30706i	0.190928	+	0.981604i	$0.438850\pi$
$509$	−17.0252	+	29.4886i	−0.754630	+	1.30706i	−0.945558	+	0.325454i	$0.894483\pi$
$510$		0			0
$511$	1.62505	+	2.81467i	0.0718879	+	0.124513i
$512$		0			0
$513$	1.71924	+	2.97782i	0.0759065	+	0.131474i
$514$		0			0
$515$	2.98075			0.131347
$516$		0			0
$517$	18.1460	−	31.4298i	0.798061	−	1.38228i
$518$		0			0
$519$	−4.67813			−0.205347
$520$		0			0
$521$	−22.3523			−0.979272			−0.489636	−	0.871927i	$-0.662870\pi$
$521$	−22.3523			−0.979272			−0.489636	+	0.871927i	$0.662870\pi$
$522$		0			0
$523$	−3.12141	+	5.40644i	−0.136490	+	0.236407i	−0.926166	−	0.377117i	$-0.876915\pi$
$523$	−3.12141	+	5.40644i	−0.136490	+	0.236407i	0.789676	+	0.613524i	$0.210249\pi$
$524$		0			0
$525$	0.0749542			0.00327127
$526$		0			0
$527$	5.61518	+	9.72577i	0.244601	+	0.423661i
$528$		0			0
$529$	11.3545	+	19.6666i	0.493674	+	0.855068i
$530$		0			0
$531$	1.36112	−	2.35752i	0.0590675	−	0.102308i
$532$		0			0
$533$	−5.64166	+	1.28565i	−0.244368	+	0.0556877i
$534$		0			0
$535$	7.28616	−	12.6200i	0.315008	−	0.545610i
$536$		0			0
$537$	−5.03709	−	8.72449i	−0.217366	−	0.376489i
$538$		0			0
$539$	2.45150	+	4.24612i	0.105593	+	0.182893i
$540$		0			0
$541$	20.6009			0.885700			0.442850	−	0.896596i	$-0.353967\pi$
$541$	20.6009			0.885700			0.442850	+	0.896596i	$0.353967\pi$
$542$		0			0
$543$	4.75590	−	8.23745i	0.204095	−	0.353503i
$544$		0			0
$545$	20.8164			0.891678
$546$		0			0
$547$	−41.5639			−1.77714			−0.888572	−	0.458737i	$-0.848302\pi$
$547$	−41.5639			−1.77714			−0.888572	+	0.458737i	$0.848302\pi$
$548$		0			0
$549$	−0.205801	+	0.356458i	−0.00878339	+	0.0152133i
$550$		0			0
$551$	15.5194			0.661150
$552$		0			0
$553$	−4.29337	−	7.43634i	−0.182573	−	0.316225i
$554$		0			0
$555$	4.02887	+	6.97821i	0.171016	+	0.296208i
$556$		0			0
$557$	14.4223	−	24.9801i	0.611092	−	1.05844i	−0.379965	−	0.925001i	$-0.624064\pi$
$557$	14.4223	−	24.9801i	0.611092	−	1.05844i	0.991057	−	0.133441i	$-0.0426026\pi$
$558$		0			0
$559$	3.52228	−	11.4051i	0.148976	−	0.482386i
$560$		0			0
$561$	−4.31146	+	7.46766i	−0.182030	+	0.315285i
$562$		0			0
$563$	−11.8385	−	20.5049i	−0.498934	−	0.864180i	0.501065	−	0.865410i	$-0.332942\pi$
$563$	−11.8385	−	20.5049i	−0.498934	−	0.864180i	−0.999999	+	0.00123005i	$0.999608\pi$
$564$		0			0
$565$	22.2387	+	38.5185i	0.935588	+	1.62049i
$566$		0			0
$567$	1.00000			0.0419961
$568$		0			0
$569$	−11.3170	+	19.6016i	−0.474434	+	0.821744i	−0.999571	−	0.0292737i	$-0.990681\pi$
$569$	−11.3170	+	19.6016i	−0.474434	+	0.821744i	0.525138	+	0.851017i	$0.324014\pi$
$570$		0			0
$571$	−16.4753			−0.689471			−0.344735	−	0.938700i	$-0.612031\pi$
$571$	−16.4753			−0.689471			−0.344735	+	0.938700i	$0.612031\pi$
$572$		0			0
$573$	10.9338			0.456768
$574$		0			0
$575$	−0.0202174	+	0.0350175i	−0.000843123	+	0.00146033i
$576$		0			0
$577$	22.5611			0.939230			0.469615	−	0.882871i	$-0.344393\pi$
$577$	22.5611			0.939230			0.469615	+	0.882871i	$0.344393\pi$
$578$		0			0
$579$	−6.58955	−	11.4134i	−0.273852	−	0.474326i
$580$		0			0
$581$	−4.88476	−	8.46065i	−0.202654	−	0.351007i
$582$		0			0
$583$	−19.6779	+	34.0831i	−0.814975	+	1.41158i
$584$		0			0
$585$	−2.36112	+	7.64531i	−0.0976202	+	0.316095i
$586$		0			0
$587$	21.1739	−	36.6743i	0.873941	−	1.51371i	0.0160551	−	0.999871i	$-0.494889\pi$
$587$	21.1739	−	36.6743i	0.873941	−	1.51371i	0.857886	−	0.513840i	$-0.171777\pi$
$588$		0			0
$589$	10.9784	+	19.0151i	0.452356	+	0.783504i
$590$		0			0
$591$	12.7785	+	22.1331i	0.525638	+	0.910433i
$592$		0			0
$593$	11.3576			0.466399			0.233199	−	0.972429i	$-0.425081\pi$
$593$	11.3576			0.466399			0.233199	+	0.972429i	$0.425081\pi$
$594$		0			0
$595$	−1.95150	+	3.38009i	−0.0800036	+	0.138570i
$596$		0			0
$597$	−8.65377			−0.354175
$598$		0			0
$599$	−11.6205			−0.474800			−0.237400	−	0.971412i	$-0.576295\pi$
$599$	−11.6205			−0.474800			−0.237400	+	0.971412i	$0.576295\pi$
$600$		0			0
$601$	11.4827	−	19.8887i	0.468391	−	0.811277i	−0.530957	−	0.847399i	$-0.678167\pi$
$601$	11.4827	−	19.8887i	0.468391	−	0.811277i	0.999347	+	0.0361224i	$0.0115006\pi$
$602$		0			0
$603$	−8.60880			−0.350577
$604$		0			0
$605$	−14.4688	−	25.0606i	−0.588239	−	1.01886i
$606$		0			0
$607$	−8.60120	−	14.8977i	−0.349112	−	0.604679i	0.636980	−	0.770880i	$-0.280183\pi$
$607$	−8.60120	−	14.8977i	−0.349112	−	0.604679i	−0.986092	+	0.166201i	$0.946850\pi$
$608$		0			0
$609$	2.25672	−	3.90876i	0.0914470	−	0.158391i
$610$		0			0
$611$	−18.1460	−	19.5701i	−0.734110	−	0.791723i
$612$		0			0
$613$	−18.5060	+	32.0534i	−0.747451	+	1.29462i	0.201589	+	0.979470i	$0.435389\pi$
$613$	−18.5060	+	32.0534i	−0.747451	+	1.29462i	−0.949041	+	0.315153i	$0.897944\pi$
$614$		0			0
$615$	−1.78076	−	3.08436i	−0.0718070	−	0.124373i
$616$		0			0
$617$	14.4876	+	25.0932i	0.583248	+	1.01021i	0.995091	+	0.0989603i	$0.0315517\pi$
$617$	14.4876	+	25.0932i	0.583248	+	1.01021i	−0.411844	+	0.911255i	$0.635115\pi$
$618$		0			0
$619$	−10.3319			−0.415274			−0.207637	−	0.978206i	$-0.566577\pi$
$619$	−10.3319			−0.415274			−0.207637	+	0.978206i	$0.566577\pi$
$620$		0			0
$621$	−0.269730	+	0.467186i	−0.0108239	+	0.0187475i
$622$		0			0
$623$	−13.6213			−0.545724
$624$		0			0
$625$	−24.6196			−0.984784
$626$		0			0
$627$	−8.42945	+	14.6002i	−0.336640	+	0.583077i
$628$		0			0
$629$	6.38559			0.254610
$630$		0			0
$631$	10.4092	+	18.0293i	0.414385	+	0.717736i	0.995364	−	0.0961831i	$-0.0306634\pi$
$631$	10.4092	+	18.0293i	0.414385	+	0.717736i	−0.580979	+	0.813919i	$0.697330\pi$
$632$		0			0
$633$	−7.85251	−	13.6009i	−0.312109	−	0.540589i
$634$		0			0
$635$	14.2116	−	24.6153i	0.563972	−	0.976828i
$636$		0			0
$637$	3.51543	−	0.801113i	0.139286	−	0.0317413i
$638$		0			0
$639$	−1.33085	+	2.30510i	−0.0526476	+	0.0911883i
$640$		0			0
$641$	−7.17834	−	12.4333i	−0.283527	−	0.491084i	0.688724	−	0.725024i	$-0.258171\pi$
$641$	−7.17834	−	12.4333i	−0.283527	−	0.491084i	−0.972251	+	0.233940i	$0.924838\pi$
$642$		0			0
$643$	−23.2832	−	40.3276i	−0.918198	−	1.59037i	−0.802151	−	0.597122i	$-0.796311\pi$
$643$	−23.2832	−	40.3276i	−0.918198	−	1.59037i	−0.116047	−	0.993244i	$-0.537022\pi$
$644$		0			0
$645$	7.34710			0.289292
$646$		0			0
$647$	4.06349	−	7.03818i	0.159752	−	0.276699i	−0.775027	−	0.631928i	$-0.782264\pi$
$647$	4.06349	−	7.03818i	0.159752	−	0.276699i	0.934779	+	0.355229i	$0.115597\pi$
$648$		0			0
$649$	13.3471			0.523920
$650$		0			0
$651$	6.38559			0.250271
$652$		0			0
$653$	−15.8904	+	27.5230i	−0.621840	+	1.07706i	0.367303	+	0.930101i	$0.380281\pi$
$653$	−15.8904	+	27.5230i	−0.621840	+	1.07706i	−0.989143	+	0.146957i	$0.953052\pi$
$654$		0			0
$655$	−27.9927			−1.09377
$656$		0			0
$657$	1.62505	+	2.81467i	0.0633992	+	0.109811i
$658$		0			0
$659$	−12.7098	−	22.0140i	−0.495104	−	0.857545i	0.504880	−	0.863189i	$-0.331537\pi$
$659$	−12.7098	−	22.0140i	−0.495104	−	0.857545i	−0.999984	+	0.00564434i	$0.998203\pi$
$660$		0			0
$661$	−2.39164	+	4.14244i	−0.0930240	+	0.161122i	−0.908782	−	0.417271i	$-0.862987\pi$
$661$	−2.39164	+	4.14244i	−0.0930240	+	0.161122i	0.815758	+	0.578393i	$0.196320\pi$
$662$		0			0
$663$	4.31146	+	4.64982i	0.167443	+	0.180584i
$664$		0			0
$665$	−3.81542	+	6.60851i	−0.147956	+	0.256267i
$666$		0			0
$667$	1.21741	+	2.10862i	0.0471383	+	0.0816460i
$668$		0			0
$669$	−0.878344	−	1.52134i	−0.0339588	−	0.0588183i
$670$		0			0
$671$	−2.01809			−0.0779074
$672$		0			0
$673$	23.7732	−	41.1764i	0.916389	−	1.58723i	0.111535	−	0.993760i	$-0.464423\pi$
$673$	23.7732	−	41.1764i	0.916389	−	1.58723i	0.804854	−	0.593473i	$-0.202243\pi$
$674$		0			0
$675$	0.0749542			0.00288499
$676$		0			0
$677$	−20.9086			−0.803583			−0.401792	−	0.915731i	$-0.631612\pi$
$677$	−20.9086			−0.803583			−0.401792	+	0.915731i	$0.631612\pi$
$678$		0			0
$679$	−0.860110	+	1.48975i	−0.0330080	+	0.0571715i
$680$		0			0
$681$	−2.64923			−0.101519
$682$		0			0
$683$	−0.668865	−	1.15851i	−0.0255934	−	0.0443291i	0.852945	−	0.522001i	$-0.174814\pi$
$683$	−0.668865	−	1.15851i	−0.0255934	−	0.0443291i	−0.878538	+	0.477672i	$0.841481\pi$
$684$		0			0
$685$	−23.6791	−	41.0135i	−0.904734	−	1.56704i
$686$		0			0
$687$	−0.676976	+	1.17256i	−0.0258282	+	0.0447358i
$688$		0			0
$689$	19.6779	+	21.2222i	0.749668	+	0.808502i
$690$		0			0
$691$	−10.1342	+	17.5530i	−0.385525	+	0.667748i	−0.991842	−	0.127475i	$-0.959313\pi$
$691$	−10.1342	+	17.5530i	−0.385525	+	0.667748i	0.606317	+	0.795223i	$0.292646\pi$
$692$		0			0
$693$	2.45150	+	4.24612i	0.0931247	+	0.161297i
$694$		0			0
$695$	8.83028	+	15.2945i	0.334951	+	0.580153i
$696$		0			0
$697$	−2.82242			−0.106907
$698$		0			0
$699$	6.96015	−	12.0553i	0.263257	−	0.455974i
$700$		0			0
$701$	32.9599			1.24488			0.622438	−	0.782669i	$-0.286142\pi$
$701$	32.9599			1.24488			0.622438	+	0.782669i	$0.286142\pi$
$702$		0			0
$703$	12.4846			0.470867
$704$		0			0
$705$	8.21345	−	14.2261i	0.309336	−	0.535786i
$706$		0			0
$707$	6.49536			0.244283
$708$		0			0
$709$	5.59053	+	9.68308i	0.209957	+	0.363656i	0.951701	−	0.307028i	$-0.0993344\pi$
$709$	5.59053	+	9.68308i	0.209957	+	0.363656i	−0.741744	+	0.670683i	$0.766001\pi$
$710$		0			0
$711$	−4.29337	−	7.43634i	−0.161014	−	0.278884i
$712$		0			0
$713$	−1.72238	+	2.98326i	−0.0645038	+	0.111724i
$714$		0			0
$715$	−38.2511	+	8.71687i	−1.43051	+	0.325992i
$716$		0			0
$717$	−6.09139	+	10.5506i	−0.227487	+	0.394019i
$718$		0			0
$719$	2.40908	+	4.17265i	0.0898435	+	0.155614i	0.907445	−	0.420171i	$-0.138030\pi$
$719$	2.40908	+	4.17265i	0.0898435	+	0.155614i	−0.817601	+	0.575785i	$0.804697\pi$
$720$		0			0
$721$	−0.671568	−	1.16319i	−0.0250105	−	0.0433195i
$722$		0			0
$723$	−17.3243			−0.644296
$724$		0			0
$725$	0.169151	−	0.292978i	0.00628210	−	0.0108809i
$726$		0			0
$727$	6.20317			0.230063			0.115031	−	0.993362i	$-0.463303\pi$
$727$	6.20317			0.230063			0.115031	+	0.993362i	$0.463303\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	2.91121	−	5.04237i	0.107675	−	0.186499i
$732$		0			0
$733$	41.6473			1.53828			0.769139	−	0.639081i	$-0.220685\pi$
$733$	41.6473			1.53828			0.769139	+	0.639081i	$0.220685\pi$
$734$		0			0
$735$	1.10962	+	1.92192i	0.0409290	+	0.0708912i
$736$		0			0
$737$	−21.1044	−	36.5540i	−0.777392	−	1.34648i
$738$		0			0
$739$	−10.8910	+	18.8638i	−0.400632	+	0.693914i	−0.993802	−	0.111162i	$-0.964543\pi$
$739$	−10.8910	+	18.8638i	−0.400632	+	0.693914i	0.593171	+	0.805077i	$0.297876\pi$
$740$		0			0
$741$	8.42945	+	9.09099i	0.309663	+	0.333966i
$742$		0			0
$743$	−9.31320	+	16.1309i	−0.341668	+	0.591786i	−0.984743	−	0.174017i	$-0.944325\pi$
$743$	−9.31320	+	16.1309i	−0.341668	+	0.591786i	0.643075	+	0.765804i	$0.277659\pi$
$744$		0			0
$745$	−6.40199	−	11.0886i	−0.234551	−	0.406254i
$746$		0			0
$747$	−4.88476	−	8.46065i	−0.178724	−	0.309559i
$748$		0			0
$749$	−6.56635			−0.239929
$750$		0			0
$751$	−25.3032	+	43.8265i	−0.923328	+	1.59925i	−0.129099	+	0.991632i	$0.541208\pi$
$751$	−25.3032	+	43.8265i	−0.923328	+	1.59925i	−0.794229	+	0.607619i	$0.792125\pi$
$752$		0			0
$753$	−14.7471			−0.537414
$754$		0			0
$755$	5.88296			0.214103
$756$		0			0
$757$	−18.7131	+	32.4120i	−0.680137	+	1.17803i	0.294801	+	0.955559i	$0.404747\pi$
$757$	−18.7131	+	32.4120i	−0.680137	+	1.17803i	−0.974939	+	0.222474i	$0.928587\pi$
$758$		0			0
$759$	−2.64497			−0.0960063
$760$		0			0
$761$	19.5487	+	33.8593i	0.708640	+	1.22740i	0.965362	+	0.260915i	$0.0840241\pi$
$761$	19.5487	+	33.8593i	0.708640	+	1.22740i	−0.256722	+	0.966485i	$0.582643\pi$
$762$		0			0
$763$	−4.68998	−	8.12329i	−0.169789	−	0.294083i
$764$		0			0
$765$	−1.95150	+	3.38009i	−0.0705565	+	0.122207i
$766$		0			0
$767$	2.89626	−	9.37811i	0.104578	−	0.338624i
$768$		0			0
$769$	−4.42119	+	7.65772i	−0.159432	+	0.276144i	−0.934664	−	0.355532i	$-0.884300\pi$
$769$	−4.42119	+	7.65772i	−0.159432	+	0.276144i	0.775232	+	0.631677i	$0.217633\pi$
$770$		0			0
$771$	5.72166	+	9.91021i	0.206061	+	0.356907i
$772$		0			0
$773$	18.4088	+	31.8850i	0.662120	+	1.14683i	0.980058	+	0.198714i	$0.0636764\pi$
$773$	18.4088	+	31.8850i	0.662120	+	1.14683i	−0.317938	+	0.948112i	$0.602990\pi$
$774$		0			0
$775$	0.478626			0.0171928
$776$		0			0
$777$	1.81542	−	3.14441i	0.0651280	−	0.112805i
$778$		0			0
$779$	−5.51819			−0.197710
$780$		0			0
$781$	−13.0503			−0.466976
$782$		0			0
$783$	2.25672	−	3.90876i	0.0806486	−	0.139688i
$784$		0			0
$785$	28.7675			1.02676
$786$		0			0
$787$	−15.1945	−	26.3177i	−0.541627	−	0.938125i	−0.998811	−	0.0487528i	$-0.984475\pi$
$787$	−15.1945	−	26.3177i	−0.541627	−	0.938125i	0.457184	−	0.889372i	$-0.348858\pi$
$788$		0			0
$789$	1.11160	+	1.92536i	0.0395742	+	0.0685445i
$790$		0			0
$791$	10.0208	−	17.3566i	0.356300	−	0.617129i
$792$		0			0
$793$	−0.437916	+	1.41797i	−0.0155509	+	0.0503537i
$794$		0			0
$795$	−8.90681	+	15.4270i	−0.315892	+	0.547141i
$796$		0			0
$797$	9.29921	+	16.1067i	0.329395	+	0.570529i	0.982392	−	0.186832i	$-0.0598219\pi$
$797$	9.29921	+	16.1067i	0.329395	+	0.570529i	−0.652997	+	0.757361i	$0.726489\pi$
$798$		0			0
$799$	−6.50898	−	11.2739i	−0.230271	−	0.398841i
$800$		0			0
$801$	−13.6213			−0.481284
$802$		0			0
$803$	−7.96760	+	13.8003i	−0.281171	+	0.487002i
$804$		0			0
$805$	−1.19719			−0.0421955
$806$		0			0
$807$	−21.8918			−0.770626
$808$		0			0
$809$	13.5234	−	23.4231i	0.475456	−	0.823514i	−0.524149	−	0.851627i	$-0.675616\pi$
$809$	13.5234	−	23.4231i	0.475456	−	0.823514i	0.999605	+	0.0281129i	$0.00894980\pi$
$810$		0			0
$811$	−47.6654			−1.67376			−0.836879	−	0.547388i	$-0.815622\pi$
$811$	−47.6654			−1.67376			−0.836879	+	0.547388i	$0.815622\pi$
$812$		0			0
$813$	−3.48457	−	6.03546i	−0.122209	−	0.211673i
$814$		0			0
$815$	19.5156	+	33.8020i	0.683602	+	1.18403i
$816$		0			0
$817$	5.69179	−	9.85846i	0.199130	−	0.344904i
$818$		0			0
$819$	3.51543	−	0.801113i	0.122839	−	0.0279932i
$820$		0			0
$821$	−20.5495	+	35.5928i	−0.717183	+	1.24220i	0.244928	+	0.969541i	$0.421236\pi$
$821$	−20.5495	+	35.5928i	−0.717183	+	1.24220i	−0.962111	+	0.272657i	$0.912098\pi$
$822$		0			0
$823$	14.4651	+	25.0543i	0.504221	+	0.873337i	0.999988	+	0.00488122i	$0.00155375\pi$
$823$	14.4651	+	25.0543i	0.504221	+	0.873337i	−0.495767	+	0.868456i	$0.665113\pi$
$824$		0			0
$825$	0.183750	+	0.318264i	0.00639735	+	0.0110805i
$826$		0			0
$827$	3.82853			0.133131			0.0665655	−	0.997782i	$-0.478796\pi$
$827$	3.82853			0.133131			0.0665655	+	0.997782i	$0.478796\pi$
$828$		0			0
$829$	12.0989	−	20.9560i	0.420213	−	0.727830i	−0.575747	−	0.817628i	$-0.695289\pi$
$829$	12.0989	−	20.9560i	0.420213	−	0.727830i	0.995960	+	0.0897975i	$0.0286220\pi$
$830$		0			0
$831$	4.62126			0.160310
$832$		0			0
$833$	1.75870			0.0609355
$834$		0			0
$835$	21.0455	−	36.4518i	0.728309	−	1.26147i
$836$		0			0
$837$	6.38559			0.220718
$838$		0			0
$839$	−17.5853	−	30.4587i	−0.607114	−	1.05155i	−0.991714	−	0.128468i	$-0.958994\pi$
$839$	−17.5853	−	30.4587i	−0.607114	−	1.05155i	0.384600	−	0.923083i	$-0.374339\pi$
$840$		0			0
$841$	4.31442	+	7.47279i	0.148773	+	0.257682i
$842$		0			0
$843$	2.51301	−	4.35266i	0.0865526	−	0.149914i
$844$		0			0
$845$	−2.17558	+	28.7680i	−0.0748421	+	0.989650i
$846$		0			0
$847$	−6.51968	+	11.2924i	−0.224019	+	0.388012i
$848$		0			0
$849$	−7.89280	−	13.6707i	−0.270880	−	0.469178i
$850$		0			0
$851$	0.979348	+	1.69628i	0.0335716	+	0.0581477i
$852$		0			0
$853$	50.9920			1.74593			0.872967	−	0.487779i	$-0.162193\pi$
$853$	50.9920			1.74593			0.872967	+	0.487779i	$0.162193\pi$
$854$		0			0
$855$	−3.81542	+	6.60851i	−0.130485	+	0.226006i
$856$		0			0
$857$	7.93550			0.271071			0.135536	−	0.990772i	$-0.456724\pi$
$857$	7.93550			0.271071			0.135536	+	0.990772i	$0.456724\pi$
$858$		0			0
$859$	−1.88851			−0.0644352			−0.0322176	−	0.999481i	$-0.510257\pi$
$859$	−1.88851			−0.0644352			−0.0322176	+	0.999481i	$0.510257\pi$
$860$		0			0
$861$	−0.802415	+	1.38982i	−0.0273462	+	0.0473651i
$862$		0			0
$863$	−18.7727			−0.639030			−0.319515	−	0.947581i	$-0.603520\pi$
$863$	−18.7727			−0.639030			−0.319515	+	0.947581i	$0.603520\pi$
$864$		0			0
$865$	−5.19096	−	8.99100i	−0.176498	−	0.305703i
$866$		0			0
$867$	−6.95348	−	12.0438i	−0.236153	−	0.409028i
$868$		0			0
$869$	21.0504	−	36.4603i	0.714085	−	1.23683i
$870$		0			0
$871$	−30.2636	+	6.89662i	−1.02544	+	0.233683i
$872$		0			0
$873$	−0.860110	+	1.48975i	−0.0291103	+	0.0504205i
$874$		0			0
$875$	5.63128	+	9.75367i	0.190372	+	0.329734i
$876$		0			0
$877$	−12.9986	−	22.5142i	−0.438932	−	0.760252i	0.558676	−	0.829386i	$-0.311310\pi$
$877$	−12.9986	−	22.5142i	−0.438932	−	0.760252i	−0.997607	+	0.0691344i	$0.977976\pi$
$878$		0			0
$879$	25.3848			0.856208
$880$		0			0
$881$	−6.80429	+	11.7854i	−0.229242	+	0.397060i	−0.957584	−	0.288155i	$-0.906958\pi$
$881$	−6.80429	+	11.7854i	−0.229242	+	0.397060i	0.728341	+	0.685214i	$0.240292\pi$
$882$		0			0
$883$	−8.27575			−0.278501			−0.139251	−	0.990257i	$-0.544469\pi$
$883$	−8.27575			−0.278501			−0.139251	+	0.990257i	$0.544469\pi$
$884$		0			0
$885$	6.04130			0.203076
$886$		0			0
$887$	5.96876	−	10.3382i	0.200411	−	0.347122i	−0.748250	−	0.663417i	$-0.769106\pi$
$887$	5.96876	−	10.3382i	0.200411	−	0.347122i	0.948661	+	0.316295i	$0.102439\pi$
$888$		0			0
$889$	−12.8076			−0.429555
$890$		0			0
$891$	2.45150	+	4.24612i	0.0821282	+	0.142250i
$892$		0			0
$893$	−12.7259	−	22.0419i	−0.425855	−	0.737603i
$894$		0			0
$895$	11.1785	−	19.3618i	0.373657	−	0.647193i
$896$		0			0
$897$	−0.573947	+	1.85844i	−0.0191635	+	0.0620515i
$898$		0			0
$899$	14.4105	−	24.9597i	0.480617	−	0.832453i
$900$		0			0
$901$	7.05846	+	12.2256i	0.235151	+	0.407294i
$902$		0			0
$903$	−1.65532	−	2.86709i	−0.0550855	−	0.0954108i
$904$		0			0
$905$	21.1090			0.701686
$906$		0			0
$907$	18.4471	−	31.9514i	0.612527	−	1.06093i	−0.378286	−	0.925689i	$-0.623486\pi$
$907$	18.4471	−	31.9514i	0.612527	−	1.06093i	0.990813	−	0.135239i	$-0.0431804\pi$
$908$		0			0
$909$	6.49536			0.215437
$910$		0			0
$911$	−7.09132			−0.234946			−0.117473	−	0.993076i	$-0.537479\pi$
$911$	−7.09132			−0.234946			−0.117473	+	0.993076i	$0.537479\pi$
$912$		0			0
$913$	23.9499	−	41.4825i	0.792628	−	1.37287i
$914$		0			0
$915$	−0.913447			−0.0301976
$916$		0			0
$917$	6.30682	+	10.9237i	0.208269	+	0.360733i
$918$		0			0
$919$	19.9242	+	34.5098i	0.657239	+	1.13837i	0.981327	+	0.192345i	$0.0616093\pi$
$919$	19.9242	+	34.5098i	0.657239	+	1.13837i	−0.324088	+	0.946027i	$0.605057\pi$
$920$		0			0
$921$	15.8599	−	27.4702i	0.522601	−	0.905172i
$922$		0			0
$923$	−2.83186	+	9.16956i	−0.0932117	+	0.301820i
$924$		0			0
$925$	0.136074	−	0.235686i	0.00447407	−	0.00774932i
$926$		0			0
$927$	−0.671568	−	1.16319i	−0.0220572	−	0.0382042i
$928$		0			0
$929$	7.18133	+	12.4384i	0.235612	+	0.408092i	0.959450	−	0.281878i	$-0.0909573\pi$
$929$	7.18133	+	12.4384i	0.235612	+	0.408092i	−0.723838	+	0.689969i	$0.757624\pi$
$930$		0			0
$931$	3.43849			0.112692
$932$		0			0
$933$	12.4361	−	21.5400i	0.407140	−	0.705187i
$934$		0			0
$935$	−19.1364			−0.625826
$936$		0			0
$937$	−23.2385			−0.759169			−0.379584	−	0.925157i	$-0.623933\pi$
$937$	−23.2385			−0.759169			−0.379584	+	0.925157i	$0.623933\pi$
$938$		0			0
$939$	1.14047	−	1.97536i	0.0372179	−	0.0644634i
$940$		0			0
$941$	29.6943			0.968006			0.484003	−	0.875066i	$-0.339182\pi$
$941$	29.6943			0.968006			0.484003	+	0.875066i	$0.339182\pi$
$942$		0			0
$943$	−0.432871	−	0.749754i	−0.0140962	−	0.0244154i
$944$		0			0
$945$	1.10962	+	1.92192i	0.0360960	+	0.0625201i
$946$		0			0
$947$	−8.80285	+	15.2470i	−0.286054	+	0.495460i	−0.972864	−	0.231377i	$-0.925677\pi$
$947$	−8.80285	+	15.2470i	−0.286054	+	0.495460i	0.686810	+	0.726837i	$0.259010\pi$
$948$		0			0
$949$	7.96760	+	8.59290i	0.258639	+	0.278937i
$950$		0			0
$951$	−8.17712	+	14.1632i	−0.265161	+	0.459273i
$952$		0			0
$953$	7.74909	+	13.4218i	0.251018	+	0.434775i	0.963806	−	0.266604i	$-0.0859015\pi$
$953$	7.74909	+	13.4218i	0.251018	+	0.434775i	−0.712789	+	0.701379i	$0.752568\pi$
$954$		0			0
$955$	12.1324	+	21.0140i	0.392596	+	0.679997i
$956$		0			0
$957$	22.1294			0.715341
$958$		0			0
$959$	−10.6699	+	18.4808i	−0.344550	+	0.596777i
$960$		0			0
$961$	9.77571			0.315345
$962$		0			0
$963$	−6.56635			−0.211598
$964$		0			0
$965$	14.6238	−	25.3292i	0.470758	−	0.815376i
$966$		0			0
$967$	−18.4950			−0.594759			−0.297379	−	0.954759i	$-0.596113\pi$
$967$	−18.4950			−0.594759			−0.297379	+	0.954759i	$0.596113\pi$
$968$		0			0
$969$	3.02364	+	5.23710i	0.0971334	+	0.168240i
$970$		0			0
$971$	−29.3729	−	50.8754i	−0.942622	−	1.63267i	−0.760444	−	0.649403i	$-0.775019\pi$
$971$	−29.3729	−	50.8754i	−0.942622	−	1.63267i	−0.182178	−	0.983266i	$-0.558315\pi$
$972$		0			0
$973$	3.97896	−	6.89175i	0.127559	−	0.220939i
$974$		0			0
$975$	0.263496	−	0.0600468i	0.00843862	−	0.00192304i
$976$		0			0
$977$	9.80279	−	16.9789i	0.313619	−	0.543204i	−0.665524	−	0.746376i	$-0.731792\pi$
$977$	9.80279	−	16.9789i	0.313619	−	0.543204i	0.979143	+	0.203172i	$0.0651252\pi$
$978$		0			0
$979$	−33.3925	−	57.8375i	−1.06723	−	1.84849i
$980$		0			0
$981$	−4.68998	−	8.12329i	−0.149740	−	0.259357i
$982$		0			0
$983$	−5.69168			−0.181536			−0.0907682	−	0.995872i	$-0.528932\pi$
$983$	−5.69168			−0.181536			−0.0907682	+	0.995872i	$0.528932\pi$
$984$		0			0
$985$	−28.3587	+	49.1187i	−0.903583	+	1.56505i
$986$		0			0
$987$	−7.40202			−0.235609
$988$		0			0
$989$	1.78595			0.0567900
$990$		0			0
$991$	−19.2283	+	33.3043i	−0.610806	+	1.05795i	0.380299	+	0.924864i	$0.375821\pi$
$991$	−19.2283	+	33.3043i	−0.610806	+	1.05795i	−0.991105	+	0.133083i	$0.957512\pi$
$992$		0			0
$993$	31.1972			0.990013
$994$		0			0
$995$	−9.60241	−	16.6319i	−0.304417	−	0.527266i
$996$		0			0
$997$	−11.0929	−	19.2135i	−0.351317	−	0.608499i	0.635163	−	0.772378i	$-0.280933\pi$
$997$	−11.0929	−	19.2135i	−0.351317	−	0.608499i	−0.986480	+	0.163879i	$0.947599\pi$
$998$		0			0
$999$	1.81542	−	3.14441i	0.0574375	−	0.0994846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2184.2.bj.k.841.4	✓	8
13.3	even	3	inner	2184.2.bj.k.1849.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2184.2.bj.k.841.4	✓	8	1.1	even	1	trivial
2184.2.bj.k.1849.4	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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +2.21924 q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +2.21924 q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(2.45150 - 4.24612i) q^{11} +(-2.45150 - 2.64389i) q^{13} +(1.10962 - 1.92192i) q^{15} +(-0.879352 - 1.52308i) q^{17} +(-1.71924 - 2.97782i) q^{19} -1.00000 q^{21} +(0.269730 - 0.467186i) q^{23} -0.0749542 q^{25} -1.00000 q^{27} +(-2.25672 + 3.90876i) q^{29} -6.38559 q^{31} +(-2.45150 - 4.24612i) q^{33} +(-1.10962 - 1.92192i) q^{35} +(-1.81542 + 3.14441i) q^{37} +(-3.51543 + 0.801113i) q^{39} +(0.802415 - 1.38982i) q^{41} +(1.65532 + 2.86709i) q^{43} +(-1.10962 - 1.92192i) q^{45} +7.40202 q^{47} +(-0.500000 + 0.866025i) q^{49} -1.75870 q^{51} -8.02689 q^{53} +(5.44047 - 9.42317i) q^{55} -3.43849 q^{57} +(1.36112 + 2.35752i) q^{59} +(-0.205801 - 0.356458i) q^{61} +(-0.500000 + 0.866025i) q^{63} +(-5.44047 - 5.86744i) q^{65} +(4.30440 - 7.45544i) q^{67} +(-0.269730 - 0.467186i) q^{69} +(-1.33085 - 2.30510i) q^{71} -3.25010 q^{73} +(-0.0374771 + 0.0649122i) q^{75} -4.90299 q^{77} +8.58674 q^{79} +(-0.500000 + 0.866025i) q^{81} +9.76952 q^{83} +(-1.95150 - 3.38009i) q^{85} +(2.25672 + 3.90876i) q^{87} +(6.81063 - 11.7964i) q^{89} +(-1.06393 + 3.44500i) q^{91} +(-3.19279 + 5.53008i) q^{93} +(-3.81542 - 6.60851i) q^{95} +(-0.860110 - 1.48975i) q^{97} -4.90299 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 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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