LMFDB - Embedded newform 189.2.s.a.17.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,2,Mod(17,189)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("189.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	189.17
Dual form			189.2.s.a.89.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(-2.50000 + 0.866025i) q^{7} -1.73205i q^{8} +(4.50000 + 2.59808i) q^{10} +1.73205i q^{11} +(-1.50000 - 0.866025i) q^{13} +(-4.50000 - 0.866025i) q^{14} +(2.50000 - 4.33013i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-4.50000 + 2.59808i) q^{19} +(1.50000 + 2.59808i) q^{20} +(-1.50000 + 2.59808i) q^{22} -5.19615i q^{23} +4.00000 q^{25} +(-1.50000 - 2.59808i) q^{26} +(-2.00000 - 1.73205i) q^{28} +(4.50000 - 2.59808i) q^{29} +(-3.00000 + 1.73205i) q^{31} +(4.50000 - 2.59808i) q^{32} +(-4.50000 + 2.59808i) q^{34} +(-7.50000 + 2.59808i) q^{35} +(-3.50000 - 6.06218i) q^{37} -9.00000 q^{38} -5.19615i q^{40} +(-1.50000 + 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(-1.50000 + 0.866025i) q^{44} +(4.50000 - 7.79423i) q^{46} +(5.50000 - 4.33013i) q^{49} +(6.00000 + 3.46410i) q^{50} -1.73205i q^{52} +(7.50000 + 4.33013i) q^{53} +5.19615i q^{55} +(1.50000 + 4.33013i) q^{56} +9.00000 q^{58} +(12.0000 + 6.92820i) q^{61} -6.00000 q^{62} -1.00000 q^{64} +(-4.50000 - 2.59808i) q^{65} +(2.00000 + 3.46410i) q^{67} -3.00000 q^{68} +(-13.5000 - 2.59808i) q^{70} +3.46410i q^{71} +(-4.50000 - 2.59808i) q^{73} -12.1244i q^{74} +(-4.50000 - 2.59808i) q^{76} +(-1.50000 - 4.33013i) q^{77} +(-4.00000 + 6.92820i) q^{79} +(7.50000 - 12.9904i) q^{80} +(-4.50000 + 2.59808i) q^{82} +(7.50000 + 12.9904i) q^{83} +(-4.50000 + 7.79423i) q^{85} -1.73205i q^{86} +3.00000 q^{88} +(-1.50000 - 2.59808i) q^{89} +(4.50000 + 0.866025i) q^{91} +(4.50000 - 2.59808i) q^{92} +(-13.5000 + 7.79423i) q^{95} +(-1.50000 + 0.866025i) q^{97} +(12.0000 - 1.73205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + q^{4} + 6 q^{5} - 5 q^{7} + 9 q^{10} - 3 q^{13} - 9 q^{14} + 5 q^{16} - 3 q^{17} - 9 q^{19} + 3 q^{20} - 3 q^{22} + 8 q^{25} - 3 q^{26} - 4 q^{28} + 9 q^{29} - 6 q^{31} + 9 q^{32} - 9 q^{34}+ \cdots + 24 q^{98}+O(q^{100}) $ 2 * q + 3 * q^2 + q^4 + 6 * q^5 - 5 * q^7 + 9 * q^10 - 3 * q^13 - 9 * q^14 + 5 * q^16 - 3 * q^17 - 9 * q^19 + 3 * q^20 - 3 * q^22 + 8 * q^25 - 3 * q^26 - 4 * q^28 + 9 * q^29 - 6 * q^31 + 9 * q^32 - 9 * q^34 - 15 * q^35 - 7 * q^37 - 18 * q^38 - 3 * q^41 - q^43 - 3 * q^44 + 9 * q^46 + 11 * q^49 + 12 * q^50 + 15 * q^53 + 3 * q^56 + 18 * q^58 + 24 * q^61 - 12 * q^62 - 2 * q^64 - 9 * q^65 + 4 * q^67 - 6 * q^68 - 27 * q^70 - 9 * q^73 - 9 * q^76 - 3 * q^77 - 8 * q^79 + 15 * q^80 - 9 * q^82 + 15 * q^83 - 9 * q^85 + 6 * q^88 - 3 * q^89 + 9 * q^91 + 9 * q^92 - 27 * q^95 - 3 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.50000	+	0.866025i	1.06066	+	0.612372i	0.925615	−	0.378467i	$-0.123549\pi$
$2$	1.50000	+	0.866025i	1.06066	+	0.612372i	0.135045	+	0.990839i	$0.456882\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	3.00000			1.34164			0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$		0			0
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$		−	1.73205i		−	0.612372i
$9$		0			0
$10$	4.50000	+	2.59808i	1.42302	+	0.821584i
$11$			1.73205i			0.522233i	0.965307	+	0.261116i	$0.0840907\pi$
$11$			1.73205i			0.522233i	−0.965307	+	0.261116i	$0.915909\pi$
$12$		0			0
$13$	−1.50000	−	0.866025i	−0.416025	−	0.240192i	0.277350	−	0.960769i	$-0.410544\pi$
$13$	−1.50000	−	0.866025i	−0.416025	−	0.240192i	−0.693375	+	0.720577i	$0.743877\pi$
$14$	−4.50000	−	0.866025i	−1.20268	−	0.231455i
$15$		0			0
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		0			0
$19$	−4.50000	+	2.59808i	−1.03237	+	0.596040i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−4.50000	+	2.59808i	−1.03237	+	0.596040i	−0.114708	+	0.993399i	$0.536593\pi$
$20$	1.50000	+	2.59808i	0.335410	+	0.580948i
$21$		0			0
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$		−	5.19615i		−	1.08347i	−0.840548	−	0.541736i	$-0.817767\pi$
$23$		−	5.19615i		−	1.08347i	0.840548	−	0.541736i	$-0.182233\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$	−1.50000	−	2.59808i	−0.294174	−	0.509525i
$27$		0			0
$28$	−2.00000	−	1.73205i	−0.377964	−	0.327327i
$29$	4.50000	−	2.59808i	0.835629	−	0.482451i	−0.0201471	−	0.999797i	$-0.506413\pi$
$29$	4.50000	−	2.59808i	0.835629	−	0.482451i	0.855776	+	0.517346i	$0.173080\pi$
$30$		0			0
$31$	−3.00000	+	1.73205i	−0.538816	+	0.311086i	−0.744599	−	0.667512i	$-0.767359\pi$
$31$	−3.00000	+	1.73205i	−0.538816	+	0.311086i	0.205783	+	0.978598i	$0.434026\pi$
$32$	4.50000	−	2.59808i	0.795495	−	0.459279i
$33$		0			0
$34$	−4.50000	+	2.59808i	−0.771744	+	0.445566i
$35$	−7.50000	+	2.59808i	−1.26773	+	0.439155i
$36$		0			0
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	−0.995998	−	0.0893706i	$-0.971514\pi$
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	0.420602	−	0.907245i	$-0.361819\pi$
$38$	−9.00000			−1.45999
$39$		0			0
$40$		−	5.19615i		−	0.821584i
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	0.825380	−	0.564578i	$-0.190961\pi$
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	−0.901629	+	0.432511i	$0.857628\pi$
$44$	−1.50000	+	0.866025i	−0.226134	+	0.130558i
$45$		0			0
$46$	4.50000	−	7.79423i	0.663489	−	1.14920i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	6.00000	+	3.46410i	0.848528	+	0.489898i
$51$		0			0
$52$		−	1.73205i		−	0.240192i
$53$	7.50000	+	4.33013i	1.03020	+	0.594789i	0.917043	−	0.398788i	$-0.130569\pi$
$53$	7.50000	+	4.33013i	1.03020	+	0.594789i	0.113161	+	0.993577i	$0.463902\pi$
$54$		0			0
$55$			5.19615i			0.700649i
$56$	1.50000	+	4.33013i	0.200446	+	0.578638i
$57$		0			0
$58$	9.00000			1.18176
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	12.0000	+	6.92820i	1.53644	+	0.887066i	0.999043	+	0.0437377i	$0.0139266\pi$
$61$	12.0000	+	6.92820i	1.53644	+	0.887066i	0.537400	+	0.843328i	$0.319407\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−4.50000	−	2.59808i	−0.558156	−	0.322252i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	−3.00000			−0.363803
$69$		0			0
$70$	−13.5000	−	2.59808i	−1.61356	−	0.310530i
$71$			3.46410i			0.411113i	0.978645	+	0.205557i	$0.0659005\pi$
$71$			3.46410i			0.411113i	−0.978645	+	0.205557i	$0.934100\pi$
$72$		0			0
$73$	−4.50000	−	2.59808i	−0.526685	−	0.304082i	0.212980	−	0.977056i	$-0.431683\pi$
$73$	−4.50000	−	2.59808i	−0.526685	−	0.304082i	−0.739666	+	0.672975i	$0.765016\pi$
$74$		−	12.1244i		−	1.40943i
$75$		0			0
$76$	−4.50000	−	2.59808i	−0.516185	−	0.298020i
$77$	−1.50000	−	4.33013i	−0.170941	−	0.493464i
$78$		0			0
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	7.50000	−	12.9904i	0.838525	−	1.45237i
$81$		0			0
$82$	−4.50000	+	2.59808i	−0.496942	+	0.286910i
$83$	7.50000	+	12.9904i	0.823232	+	1.42588i	0.903263	+	0.429087i	$0.141165\pi$
$83$	7.50000	+	12.9904i	0.823232	+	1.42588i	−0.0800311	+	0.996792i	$0.525502\pi$
$84$		0			0
$85$	−4.50000	+	7.79423i	−0.488094	+	0.845403i
$86$		−	1.73205i		−	0.186772i
$87$		0			0
$88$	3.00000			0.319801
$89$	−1.50000	−	2.59808i	−0.159000	−	0.275396i	0.775509	−	0.631337i	$-0.217494\pi$
$89$	−1.50000	−	2.59808i	−0.159000	−	0.275396i	−0.934508	+	0.355942i	$0.884160\pi$
$90$		0			0
$91$	4.50000	+	0.866025i	0.471728	+	0.0907841i
$92$	4.50000	−	2.59808i	0.469157	−	0.270868i
$93$		0			0
$94$		0			0
$95$	−13.5000	+	7.79423i	−1.38507	+	0.799671i
$96$		0			0
$97$	−1.50000	+	0.866025i	−0.152302	+	0.0879316i	−0.574214	−	0.818705i	$-0.694692\pi$
$97$	−1.50000	+	0.866025i	−0.152302	+	0.0879316i	0.421912	+	0.906637i	$0.361359\pi$
$98$	12.0000	−	1.73205i	1.21218	−	0.174964i
$99$		0			0
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	3.00000			0.298511			0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000			0.298511			0.149256	+	0.988799i	$0.452312\pi$
$102$		0			0
$103$		−	12.1244i		−	1.19465i	−0.802000	−	0.597324i	$-0.796231\pi$
$103$		−	12.1244i		−	1.19465i	0.802000	−	0.597324i	$-0.203769\pi$
$104$	−1.50000	+	2.59808i	−0.147087	+	0.254762i
$105$		0			0
$106$	7.50000	+	12.9904i	0.728464	+	1.26174i
$107$	7.50000	−	4.33013i	0.725052	−	0.418609i	−0.0915571	−	0.995800i	$-0.529184\pi$
$107$	7.50000	−	4.33013i	0.725052	−	0.418609i	0.816609	+	0.577191i	$0.195851\pi$
$108$		0			0
$109$	−9.50000	+	16.4545i	−0.909935	+	1.57605i	−0.0957826	+	0.995402i	$0.530535\pi$
$109$	−9.50000	+	16.4545i	−0.909935	+	1.57605i	−0.814152	+	0.580651i	$0.802798\pi$
$110$	−4.50000	+	7.79423i	−0.429058	+	0.743151i
$111$		0			0
$112$	−2.50000	+	12.9904i	−0.236228	+	1.22748i
$113$	−1.50000	−	0.866025i	−0.141108	−	0.0814688i	0.427784	−	0.903881i	$-0.359294\pi$
$113$	−1.50000	−	0.866025i	−0.141108	−	0.0814688i	−0.568892	+	0.822412i	$0.692628\pi$
$114$		0			0
$115$		−	15.5885i		−	1.45363i
$116$	4.50000	+	2.59808i	0.417815	+	0.241225i
$117$		0			0
$118$		0			0
$119$	1.50000	−	7.79423i	0.137505	−	0.714496i
$120$		0			0
$121$	8.00000			0.727273
$122$	12.0000	+	20.7846i	1.08643	+	1.88175i
$123$		0			0
$124$	−3.00000	−	1.73205i	−0.269408	−	0.155543i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	20.0000			1.77471			0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000			1.77471			0.887357	+	0.461084i	$0.152539\pi$
$128$	−10.5000	−	6.06218i	−0.928078	−	0.535826i
$129$		0			0
$130$	−4.50000	−	7.79423i	−0.394676	−	0.683599i
$131$	9.00000			0.786334			0.393167	−	0.919467i	$-0.371379\pi$
$131$	9.00000			0.786334			0.393167	+	0.919467i	$0.371379\pi$
$132$		0			0
$133$	9.00000	−	10.3923i	0.780399	−	0.901127i
$134$			6.92820i			0.598506i
$135$		0			0
$136$	4.50000	+	2.59808i	0.385872	+	0.222783i
$137$		−	12.1244i		−	1.03585i	−0.855425	−	0.517927i	$-0.826704\pi$
$137$		−	12.1244i		−	1.03585i	0.855425	−	0.517927i	$-0.173296\pi$
$138$		0			0
$139$	−7.50000	−	4.33013i	−0.636142	−	0.367277i	0.146985	−	0.989139i	$-0.453043\pi$
$139$	−7.50000	−	4.33013i	−0.636142	−	0.367277i	−0.783127	+	0.621862i	$0.786376\pi$
$140$	−6.00000	−	5.19615i	−0.507093	−	0.439155i
$141$		0			0
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	1.50000	−	2.59808i	0.125436	−	0.217262i
$144$		0			0
$145$	13.5000	−	7.79423i	1.12111	−	0.647275i
$146$	−4.50000	−	7.79423i	−0.372423	−	0.645055i
$147$		0			0
$148$	3.50000	−	6.06218i	0.287698	−	0.498308i
$149$		−	1.73205i		−	0.141895i	−0.997480	−	0.0709476i	$-0.977398\pi$
$149$		−	1.73205i		−	0.141895i	0.997480	−	0.0709476i	$-0.0226023\pi$
$150$		0			0
$151$	−17.0000			−1.38344			−0.691720	−	0.722166i	$-0.743147\pi$
$151$	−17.0000			−1.38344			−0.691720	+	0.722166i	$0.743147\pi$
$152$	4.50000	+	7.79423i	0.364998	+	0.632195i
$153$		0			0
$154$	1.50000	−	7.79423i	0.120873	−	0.628077i
$155$	−9.00000	+	5.19615i	−0.722897	+	0.417365i
$156$		0			0
$157$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$157$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$158$	−12.0000	+	6.92820i	−0.954669	+	0.551178i
$159$		0			0
$160$	13.5000	−	7.79423i	1.06727	−	0.616188i
$161$	4.50000	+	12.9904i	0.354650	+	1.02379i
$162$		0			0
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	0.566149	−	0.824303i	$-0.308433\pi$
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	−0.996942	+	0.0781474i	$0.975100\pi$
$164$	−3.00000			−0.234261
$165$		0			0
$166$			25.9808i			2.01650i
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	−0.637713	−	0.770274i	$-0.720119\pi$
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	0.985933	+	0.167139i	$0.0534527\pi$
$168$		0			0
$169$	−5.00000	−	8.66025i	−0.384615	−	0.666173i
$170$	−13.5000	+	7.79423i	−1.03540	+	0.597790i
$171$		0			0
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$	−10.0000	+	3.46410i	−0.755929	+	0.261861i
$176$	7.50000	+	4.33013i	0.565334	+	0.326396i
$177$		0			0
$178$		−	5.19615i		−	0.389468i
$179$	−13.5000	−	7.79423i	−1.00904	−	0.582568i	−0.0981277	−	0.995174i	$-0.531285\pi$
$179$	−13.5000	−	7.79423i	−1.00904	−	0.582568i	−0.910910	+	0.412606i	$0.864619\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	6.00000	+	5.19615i	0.444750	+	0.385164i
$183$		0			0
$184$	−9.00000			−0.663489
$185$	−10.5000	−	18.1865i	−0.771975	−	1.33710i
$186$		0			0
$187$	−4.50000	−	2.59808i	−0.329073	−	0.189990i
$188$		0			0
$189$		0			0
$190$	−27.0000			−1.95879
$191$	15.0000	+	8.66025i	1.08536	+	0.626634i	0.932338	−	0.361588i	$-0.117765\pi$
$191$	15.0000	+	8.66025i	1.08536	+	0.626634i	0.153024	+	0.988222i	$0.451099\pi$
$192$		0			0
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	0.899770	−	0.436365i	$-0.143734\pi$
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	−0.827788	+	0.561041i	$0.810401\pi$
$194$	−3.00000			−0.215387
$195$		0			0
$196$	6.50000	+	2.59808i	0.464286	+	0.185577i
$197$		−	13.8564i		−	0.987228i	−0.869681	−	0.493614i	$-0.835676\pi$
$197$		−	13.8564i		−	0.987228i	0.869681	−	0.493614i	$-0.164324\pi$
$198$		0			0
$199$	−7.50000	−	4.33013i	−0.531661	−	0.306955i	0.210032	−	0.977695i	$-0.432643\pi$
$199$	−7.50000	−	4.33013i	−0.531661	−	0.306955i	−0.741693	+	0.670740i	$0.765977\pi$
$200$		−	6.92820i		−	0.489898i
$201$		0			0
$202$	4.50000	+	2.59808i	0.316619	+	0.182800i
$203$	−9.00000	+	10.3923i	−0.631676	+	0.729397i
$204$		0			0
$205$	−4.50000	+	7.79423i	−0.314294	+	0.544373i
$206$	10.5000	−	18.1865i	0.731570	−	1.26712i
$207$		0			0
$208$	−7.50000	+	4.33013i	−0.520031	+	0.300240i
$209$	−4.50000	−	7.79423i	−0.311272	−	0.539138i
$210$		0			0
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	−0.767049	−	0.641588i	$-0.778276\pi$
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	0.939156	+	0.343490i	$0.111609\pi$
$212$			8.66025i			0.594789i
$213$		0			0
$214$	15.0000			1.02538
$215$	−1.50000	−	2.59808i	−0.102299	−	0.177187i
$216$		0			0
$217$	6.00000	−	6.92820i	0.407307	−	0.470317i
$218$	−28.5000	+	16.4545i	−1.93026	+	1.11444i
$219$		0			0
$220$	−4.50000	+	2.59808i	−0.303390	+	0.175162i
$221$	4.50000	−	2.59808i	0.302703	−	0.174766i
$222$		0			0
$223$	−4.50000	+	2.59808i	−0.301342	+	0.173980i	−0.643046	−	0.765828i	$-0.722329\pi$
$223$	−4.50000	+	2.59808i	−0.301342	+	0.173980i	0.341703	+	0.939808i	$0.388996\pi$
$224$	−9.00000	+	10.3923i	−0.601338	+	0.694365i
$225$		0			0
$226$	−1.50000	−	2.59808i	−0.0997785	−	0.172821i
$227$	−21.0000			−1.39382			−0.696909	−	0.717159i	$-0.745442\pi$
$227$	−21.0000			−1.39382			−0.696909	+	0.717159i	$0.745442\pi$
$228$		0			0
$229$		−	8.66025i		−	0.572286i	−0.958187	−	0.286143i	$-0.907627\pi$
$229$		−	8.66025i		−	0.572286i	0.958187	−	0.286143i	$-0.0923732\pi$
$230$	13.5000	−	23.3827i	0.890164	−	1.54181i
$231$		0			0
$232$	−4.50000	−	7.79423i	−0.295439	−	0.511716i
$233$	−4.50000	+	2.59808i	−0.294805	+	0.170206i	−0.640107	−	0.768286i	$-0.721110\pi$
$233$	−4.50000	+	2.59808i	−0.294805	+	0.170206i	0.345302	+	0.938492i	$0.387777\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	9.00000	−	10.3923i	0.583383	−	0.673633i
$239$	−1.50000	−	0.866025i	−0.0970269	−	0.0560185i	0.450701	−	0.892675i	$-0.351174\pi$
$239$	−1.50000	−	0.866025i	−0.0970269	−	0.0560185i	−0.547728	+	0.836656i	$0.684507\pi$
$240$		0			0
$241$			22.5167i			1.45043i	0.688525	+	0.725213i	$0.258259\pi$
$241$			22.5167i			1.45043i	−0.688525	+	0.725213i	$0.741741\pi$
$242$	12.0000	+	6.92820i	0.771389	+	0.445362i
$243$		0			0
$244$			13.8564i			0.887066i
$245$	16.5000	−	12.9904i	1.05415	−	0.829925i
$246$		0			0
$247$	9.00000			0.572656
$248$	3.00000	+	5.19615i	0.190500	+	0.329956i
$249$		0			0
$250$	−4.50000	−	2.59808i	−0.284605	−	0.164317i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	9.00000			0.565825
$254$	30.0000	+	17.3205i	1.88237	+	1.08679i
$255$		0			0
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	3.00000			0.187135			0.0935674	−	0.995613i	$-0.470173\pi$
$257$	3.00000			0.187135			0.0935674	+	0.995613i	$0.470173\pi$
$258$		0			0
$259$	14.0000	+	12.1244i	0.869918	+	0.753371i
$260$		−	5.19615i		−	0.322252i
$261$		0			0
$262$	13.5000	+	7.79423i	0.834033	+	0.481529i
$263$			22.5167i			1.38844i	0.719764	+	0.694218i	$0.244250\pi$
$263$			22.5167i			1.38844i	−0.719764	+	0.694218i	$0.755750\pi$
$264$		0			0
$265$	22.5000	+	12.9904i	1.38216	+	0.797993i
$266$	22.5000	−	7.79423i	1.37956	−	0.477895i
$267$		0			0
$268$	−2.00000	+	3.46410i	−0.122169	+	0.211604i
$269$	−7.50000	+	12.9904i	−0.457283	+	0.792038i	−0.998816	−	0.0486418i	$-0.984511\pi$
$269$	−7.50000	+	12.9904i	−0.457283	+	0.792038i	0.541533	+	0.840679i	$0.317844\pi$
$270$		0			0
$271$	−10.5000	+	6.06218i	−0.637830	+	0.368251i	−0.783778	−	0.621041i	$-0.786710\pi$
$271$	−10.5000	+	6.06218i	−0.637830	+	0.368251i	0.145948	+	0.989292i	$0.453377\pi$
$272$	7.50000	+	12.9904i	0.454754	+	0.787658i
$273$		0			0
$274$	10.5000	−	18.1865i	0.634328	−	1.09869i
$275$			6.92820i			0.417786i
$276$		0			0
$277$	−1.00000			−0.0600842			−0.0300421	−	0.999549i	$-0.509564\pi$
$277$	−1.00000			−0.0600842			−0.0300421	+	0.999549i	$0.509564\pi$
$278$	−7.50000	−	12.9904i	−0.449820	−	0.779111i
$279$		0			0
$280$	4.50000	+	12.9904i	0.268926	+	0.776324i
$281$	16.5000	−	9.52628i	0.984307	−	0.568290i	0.0807396	−	0.996735i	$-0.474272\pi$
$281$	16.5000	−	9.52628i	0.984307	−	0.568290i	0.903568	+	0.428445i	$0.140938\pi$
$282$		0			0
$283$	3.00000	−	1.73205i	0.178331	−	0.102960i	−0.408177	−	0.912903i	$-0.633835\pi$
$283$	3.00000	−	1.73205i	0.178331	−	0.102960i	0.586509	+	0.809943i	$0.300502\pi$
$284$	−3.00000	+	1.73205i	−0.178017	+	0.102778i
$285$		0			0
$286$	4.50000	−	2.59808i	0.266091	−	0.153627i
$287$	1.50000	−	7.79423i	0.0885422	−	0.460079i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	27.0000			1.58549
$291$		0			0
$292$		−	5.19615i		−	0.304082i
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	−0.704117	−	0.710084i	$-0.748657\pi$
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	0.967009	+	0.254741i	$0.0819901\pi$
$294$		0			0
$295$		0			0
$296$	−10.5000	+	6.06218i	−0.610300	+	0.352357i
$297$		0			0
$298$	1.50000	−	2.59808i	0.0868927	−	0.150503i
$299$	−4.50000	+	7.79423i	−0.260242	+	0.450752i
$300$		0			0
$301$	2.00000	+	1.73205i	0.115278	+	0.0998337i
$302$	−25.5000	−	14.7224i	−1.46736	−	0.847181i
$303$		0			0
$304$			25.9808i			1.49010i
$305$	36.0000	+	20.7846i	2.06135	+	1.19012i
$306$		0			0
$307$		−	24.2487i		−	1.38395i	−0.721923	−	0.691974i	$-0.756741\pi$
$307$		−	24.2487i		−	1.38395i	0.721923	−	0.691974i	$-0.243259\pi$
$308$	3.00000	−	3.46410i	0.170941	−	0.197386i
$309$		0			0
$310$	−18.0000			−1.02233
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	0.974841	+	0.222900i	$0.0715523\pi$
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	−0.294384	+	0.955687i	$0.595114\pi$
$312$		0			0
$313$	−18.0000	−	10.3923i	−1.01742	−	0.587408i	−0.104065	−	0.994571i	$-0.533185\pi$
$313$	−18.0000	−	10.3923i	−1.01742	−	0.587408i	−0.913356	+	0.407163i	$0.866518\pi$
$314$		0			0
$315$		0			0
$316$	−8.00000			−0.450035
$317$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$317$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$318$		0			0
$319$	4.50000	+	7.79423i	0.251952	+	0.436393i
$320$	−3.00000			−0.167705
$321$		0			0
$322$	−4.50000	+	23.3827i	−0.250775	+	1.30307i
$323$		−	15.5885i		−	0.867365i
$324$		0			0
$325$	−6.00000	−	3.46410i	−0.332820	−	0.192154i
$326$		−	19.0526i		−	1.05522i
$327$		0			0
$328$	4.50000	+	2.59808i	0.248471	+	0.143455i
$329$		0			0
$330$		0			0
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	−0.734905	−	0.678170i	$-0.762773\pi$
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	0.954765	+	0.297361i	$0.0961066\pi$
$332$	−7.50000	+	12.9904i	−0.411616	+	0.712940i
$333$		0			0
$334$	13.5000	−	7.79423i	0.738687	−	0.426481i
$335$	6.00000	+	10.3923i	0.327815	+	0.567792i
$336$		0			0
$337$	−9.50000	+	16.4545i	−0.517498	+	0.896333i	0.482295	+	0.876009i	$0.339803\pi$
$337$	−9.50000	+	16.4545i	−0.517498	+	0.896333i	−0.999793	+	0.0203242i	$0.993530\pi$
$338$		−	17.3205i		−	0.942111i
$339$		0			0
$340$	−9.00000			−0.488094
$341$	−3.00000	−	5.19615i	−0.162459	−	0.281387i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−1.50000	+	0.866025i	−0.0808746	+	0.0466930i
$345$		0			0
$346$	9.00000	−	5.19615i	0.483843	−	0.279347i
$347$	3.00000	−	1.73205i	0.161048	−	0.0929814i	−0.417310	−	0.908764i	$-0.637027\pi$
$347$	3.00000	−	1.73205i	0.161048	−	0.0929814i	0.578358	+	0.815783i	$0.303694\pi$
$348$		0			0
$349$	10.5000	−	6.06218i	0.562052	−	0.324501i	−0.191917	−	0.981411i	$-0.561470\pi$
$349$	10.5000	−	6.06218i	0.562052	−	0.324501i	0.753969	+	0.656910i	$0.228137\pi$
$350$	−18.0000	−	3.46410i	−0.962140	−	0.185164i
$351$		0			0
$352$	4.50000	+	7.79423i	0.239851	+	0.415434i
$353$	−21.0000			−1.11772			−0.558859	−	0.829263i	$-0.688761\pi$
$353$	−21.0000			−1.11772			−0.558859	+	0.829263i	$0.688761\pi$
$354$		0			0
$355$			10.3923i			0.551566i
$356$	1.50000	−	2.59808i	0.0794998	−	0.137698i
$357$		0			0
$358$	−13.5000	−	23.3827i	−0.713497	−	1.23581i
$359$	19.5000	−	11.2583i	1.02917	−	0.594192i	0.112424	−	0.993660i	$-0.464139\pi$
$359$	19.5000	−	11.2583i	1.02917	−	0.594192i	0.916747	+	0.399468i	$0.130805\pi$
$360$		0			0
$361$	4.00000	−	6.92820i	0.210526	−	0.364642i
$362$		0			0
$363$		0			0
$364$	1.50000	+	4.33013i	0.0786214	+	0.226960i
$365$	−13.5000	−	7.79423i	−0.706622	−	0.407969i
$366$		0			0
$367$		−	5.19615i		−	0.271237i	−0.990761	−	0.135618i	$-0.956698\pi$
$367$		−	5.19615i		−	0.271237i	0.990761	−	0.135618i	$-0.0433021\pi$
$368$	−22.5000	−	12.9904i	−1.17289	−	0.677170i
$369$		0			0
$370$		−	36.3731i		−	1.89095i
$371$	−22.5000	−	4.33013i	−1.16814	−	0.224809i
$372$		0			0
$373$	−37.0000			−1.91579			−0.957894	−	0.287123i	$-0.907301\pi$
$373$	−37.0000			−1.91579			−0.957894	+	0.287123i	$0.907301\pi$
$374$	−4.50000	−	7.79423i	−0.232689	−	0.403030i
$375$		0			0
$376$		0			0
$377$	−9.00000			−0.463524
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	−13.5000	−	7.79423i	−0.692535	−	0.399835i
$381$		0			0
$382$	15.0000	+	25.9808i	0.767467	+	1.32929i
$383$	9.00000			0.459879			0.229939	−	0.973205i	$-0.426147\pi$
$383$	9.00000			0.459879			0.229939	+	0.973205i	$0.426147\pi$
$384$		0			0
$385$	−4.50000	−	12.9904i	−0.229341	−	0.662051i
$386$			3.46410i			0.176318i
$387$		0			0
$388$	−1.50000	−	0.866025i	−0.0761510	−	0.0439658i
$389$			36.3731i			1.84419i	0.386966	+	0.922094i	$0.373523\pi$
$389$			36.3731i			1.84419i	−0.386966	+	0.922094i	$0.626477\pi$
$390$		0			0
$391$	13.5000	+	7.79423i	0.682724	+	0.394171i
$392$	−7.50000	−	9.52628i	−0.378807	−	0.481150i
$393$		0			0
$394$	12.0000	−	20.7846i	0.604551	−	1.04711i
$395$	−12.0000	+	20.7846i	−0.603786	+	1.04579i
$396$		0			0
$397$	7.50000	−	4.33013i	0.376414	−	0.217323i	−0.299843	−	0.953989i	$-0.596934\pi$
$397$	7.50000	−	4.33013i	0.376414	−	0.217323i	0.676257	+	0.736666i	$0.263601\pi$
$398$	−7.50000	−	12.9904i	−0.375941	−	0.651149i
$399$		0			0
$400$	10.0000	−	17.3205i	0.500000	−	0.866025i
$401$			32.9090i			1.64340i	0.569924	+	0.821698i	$0.306973\pi$
$401$			32.9090i			1.64340i	−0.569924	+	0.821698i	$0.693027\pi$
$402$		0			0
$403$	6.00000			0.298881
$404$	1.50000	+	2.59808i	0.0746278	+	0.129259i
$405$		0			0
$406$	−22.5000	+	7.79423i	−1.11666	+	0.386821i
$407$	10.5000	−	6.06218i	0.520466	−	0.300491i
$408$		0			0
$409$	−6.00000	+	3.46410i	−0.296681	+	0.171289i	−0.640951	−	0.767582i	$-0.721460\pi$
$409$	−6.00000	+	3.46410i	−0.296681	+	0.171289i	0.344270	+	0.938871i	$0.388126\pi$
$410$	−13.5000	+	7.79423i	−0.666717	+	0.384930i
$411$		0			0
$412$	10.5000	−	6.06218i	0.517298	−	0.298662i
$413$		0			0
$414$		0			0
$415$	22.5000	+	38.9711i	1.10448	+	1.91302i
$416$	−9.00000			−0.441261
$417$		0			0
$418$		−	15.5885i		−	0.762456i
$419$	16.5000	−	28.5788i	0.806078	−	1.39617i	−0.109483	−	0.993989i	$-0.534920\pi$
$419$	16.5000	−	28.5788i	0.806078	−	1.39617i	0.915561	−	0.402179i	$-0.131747\pi$
$420$		0			0
$421$	−5.50000	−	9.52628i	−0.268054	−	0.464282i	0.700306	−	0.713843i	$-0.253047\pi$
$421$	−5.50000	−	9.52628i	−0.268054	−	0.464282i	−0.968359	+	0.249561i	$0.919714\pi$
$422$	7.50000	−	4.33013i	0.365094	−	0.210787i
$423$		0			0
$424$	7.50000	−	12.9904i	0.364232	−	0.630869i
$425$	−6.00000	+	10.3923i	−0.291043	+	0.504101i
$426$		0			0
$427$	−36.0000	−	6.92820i	−1.74216	−	0.335279i
$428$	7.50000	+	4.33013i	0.362526	+	0.209305i
$429$		0			0
$430$		−	5.19615i		−	0.250581i
$431$	−13.5000	−	7.79423i	−0.650272	−	0.375435i	0.138288	−	0.990392i	$-0.455840\pi$
$431$	−13.5000	−	7.79423i	−0.650272	−	0.375435i	−0.788560	+	0.614957i	$0.789173\pi$
$432$		0			0
$433$			13.8564i			0.665896i	0.942945	+	0.332948i	$0.108043\pi$
$433$			13.8564i			0.665896i	−0.942945	+	0.332948i	$0.891957\pi$
$434$	15.0000	−	5.19615i	0.720023	−	0.249423i
$435$		0			0
$436$	−19.0000			−0.909935
$437$	13.5000	+	23.3827i	0.645793	+	1.11855i
$438$		0			0
$439$	27.0000	+	15.5885i	1.28864	+	0.743996i	0.978412	−	0.206666i	$-0.0662612\pi$
$439$	27.0000	+	15.5885i	1.28864	+	0.743996i	0.310228	+	0.950662i	$0.399595\pi$
$440$	9.00000			0.429058
$441$		0			0
$442$	9.00000			0.428086
$443$	−27.0000	−	15.5885i	−1.28281	−	0.740630i	−0.305448	−	0.952209i	$-0.598806\pi$
$443$	−27.0000	−	15.5885i	−1.28281	−	0.740630i	−0.977361	+	0.211579i	$0.932139\pi$
$444$		0			0
$445$	−4.50000	−	7.79423i	−0.213320	−	0.369482i
$446$	−9.00000			−0.426162
$447$		0			0
$448$	2.50000	−	0.866025i	0.118114	−	0.0409159i
$449$			34.6410i			1.63481i	0.576063	+	0.817405i	$0.304588\pi$
$449$			34.6410i			1.63481i	−0.576063	+	0.817405i	$0.695412\pi$
$450$		0			0
$451$	−4.50000	−	2.59808i	−0.211897	−	0.122339i
$452$		−	1.73205i		−	0.0814688i
$453$		0			0
$454$	−31.5000	−	18.1865i	−1.47837	−	0.853536i
$455$	13.5000	+	2.59808i	0.632890	+	0.121800i
$456$		0			0
$457$	13.0000	−	22.5167i	0.608114	−	1.05328i	−0.383437	−	0.923567i	$-0.625260\pi$
$457$	13.0000	−	22.5167i	0.608114	−	1.05328i	0.991551	−	0.129718i	$-0.0414071\pi$
$458$	7.50000	−	12.9904i	0.350452	−	0.607001i
$459$		0			0
$460$	13.5000	−	7.79423i	0.629441	−	0.363408i
$461$	−7.50000	−	12.9904i	−0.349310	−	0.605022i	0.636817	−	0.771015i	$-0.280251\pi$
$461$	−7.50000	−	12.9904i	−0.349310	−	0.605022i	−0.986127	+	0.165992i	$0.946917\pi$
$462$		0			0
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	−0.854173	−	0.519989i	$-0.825936\pi$
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	0.877410	+	0.479741i	$0.159269\pi$
$464$		−	25.9808i		−	1.20613i
$465$		0			0
$466$	−9.00000			−0.416917
$467$	−1.50000	−	2.59808i	−0.0694117	−	0.120225i	0.829231	−	0.558906i	$-0.188779\pi$
$467$	−1.50000	−	2.59808i	−0.0694117	−	0.120225i	−0.898642	+	0.438682i	$0.855446\pi$
$468$		0			0
$469$	−8.00000	−	6.92820i	−0.369406	−	0.319915i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.50000	−	0.866025i	0.0689701	−	0.0398199i
$474$		0			0
$475$	−18.0000	+	10.3923i	−0.825897	+	0.476832i
$476$	7.50000	−	2.59808i	0.343762	−	0.119083i
$477$		0			0
$478$	−1.50000	−	2.59808i	−0.0686084	−	0.118833i
$479$	27.0000			1.23366			0.616831	−	0.787096i	$-0.288416\pi$
$479$	27.0000			1.23366			0.616831	+	0.787096i	$0.288416\pi$
$480$		0			0
$481$			12.1244i			0.552823i
$482$	−19.5000	+	33.7750i	−0.888201	+	1.53841i
$483$		0			0
$484$	4.00000	+	6.92820i	0.181818	+	0.314918i
$485$	−4.50000	+	2.59808i	−0.204334	+	0.117973i
$486$		0			0
$487$	11.5000	−	19.9186i	0.521115	−	0.902597i	−0.478584	−	0.878042i	$-0.658850\pi$
$487$	11.5000	−	19.9186i	0.521115	−	0.902597i	0.999698	−	0.0245553i	$-0.00781698\pi$
$488$	12.0000	−	20.7846i	0.543214	−	0.940875i
$489$		0			0
$490$	36.0000	−	5.19615i	1.62631	−	0.234738i
$491$	22.5000	+	12.9904i	1.01541	+	0.586248i	0.912771	−	0.408471i	$-0.133938\pi$
$491$	22.5000	+	12.9904i	1.01541	+	0.586248i	0.102639	+	0.994719i	$0.467271\pi$
$492$		0			0
$493$			15.5885i			0.702069i
$494$	13.5000	+	7.79423i	0.607394	+	0.350679i
$495$		0			0
$496$			17.3205i			0.777714i
$497$	−3.00000	−	8.66025i	−0.134568	−	0.388465i
$498$		0			0
$499$	25.0000			1.11915			0.559577	−	0.828778i	$-0.310964\pi$
$499$	25.0000			1.11915			0.559577	+	0.828778i	$0.310964\pi$
$500$	−1.50000	−	2.59808i	−0.0670820	−	0.116190i
$501$		0			0
$502$	−18.0000	−	10.3923i	−0.803379	−	0.463831i
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$	13.5000	+	7.79423i	0.600148	+	0.346496i
$507$		0			0
$508$	10.0000	+	17.3205i	0.443678	+	0.768473i
$509$	−33.0000			−1.46270			−0.731350	−	0.682003i	$-0.761109\pi$
$509$	−33.0000			−1.46270			−0.731350	+	0.682003i	$0.761109\pi$
$510$		0			0
$511$	13.5000	+	2.59808i	0.597205	+	0.114932i
$512$		−	8.66025i		−	0.382733i
$513$		0			0
$514$	4.50000	+	2.59808i	0.198486	+	0.114596i
$515$		−	36.3731i		−	1.60279i
$516$		0			0
$517$		0			0
$518$	10.5000	+	30.3109i	0.461344	+	1.33178i
$519$		0			0
$520$	−4.50000	+	7.79423i	−0.197338	+	0.341800i
$521$	22.5000	−	38.9711i	0.985743	−	1.70736i	0.347155	−	0.937808i	$-0.387148\pi$
$521$	22.5000	−	38.9711i	0.985743	−	1.70736i	0.638588	−	0.769549i	$-0.279519\pi$
$522$		0			0
$523$	−16.5000	+	9.52628i	−0.721495	+	0.416555i	−0.815303	−	0.579035i	$-0.803429\pi$
$523$	−16.5000	+	9.52628i	−0.721495	+	0.416555i	0.0938079	+	0.995590i	$0.470096\pi$
$524$	4.50000	+	7.79423i	0.196583	+	0.340492i
$525$		0			0
$526$	−19.5000	+	33.7750i	−0.850240	+	1.47266i
$527$		−	10.3923i		−	0.452696i
$528$		0			0
$529$	−4.00000			−0.173913
$530$	22.5000	+	38.9711i	0.977338	+	1.69280i
$531$		0			0
$532$	13.5000	+	2.59808i	0.585299	+	0.112641i
$533$	4.50000	−	2.59808i	0.194917	−	0.112535i
$534$		0			0
$535$	22.5000	−	12.9904i	0.972760	−	0.561623i
$536$	6.00000	−	3.46410i	0.259161	−	0.149626i
$537$		0			0
$538$	−22.5000	+	12.9904i	−0.970044	+	0.560055i
$539$	7.50000	+	9.52628i	0.323048	+	0.410326i
$540$		0			0
$541$	6.50000	+	11.2583i	0.279457	+	0.484033i	0.971250	−	0.238062i	$-0.0765123\pi$
$541$	6.50000	+	11.2583i	0.279457	+	0.484033i	−0.691793	+	0.722096i	$0.743179\pi$
$542$	−21.0000			−0.902027
$543$		0			0
$544$			15.5885i			0.668350i
$545$	−28.5000	+	49.3634i	−1.22081	+	2.11450i
$546$		0			0
$547$	9.50000	+	16.4545i	0.406191	+	0.703543i	0.994459	−	0.105123i	$-0.0335235\pi$
$547$	9.50000	+	16.4545i	0.406191	+	0.703543i	−0.588269	+	0.808666i	$0.700190\pi$
$548$	10.5000	−	6.06218i	0.448538	−	0.258963i
$549$		0			0
$550$	−6.00000	+	10.3923i	−0.255841	+	0.443129i
$551$	−13.5000	+	23.3827i	−0.575119	+	0.996136i
$552$		0			0
$553$	4.00000	−	20.7846i	0.170097	−	0.883852i
$554$	−1.50000	−	0.866025i	−0.0637289	−	0.0367939i
$555$		0			0
$556$		−	8.66025i		−	0.367277i
$557$	−10.5000	−	6.06218i	−0.444899	−	0.256863i	0.260774	−	0.965400i	$-0.416022\pi$
$557$	−10.5000	−	6.06218i	−0.444899	−	0.256863i	−0.705674	+	0.708537i	$0.749355\pi$
$558$		0			0
$559$			1.73205i			0.0732579i
$560$	−7.50000	+	38.9711i	−0.316933	+	1.64683i
$561$		0			0
$562$	33.0000			1.39202
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	−0.943560	−	0.331202i	$-0.892546\pi$
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	0.184950	−	0.982748i	$-0.440788\pi$
$564$		0			0
$565$	−4.50000	−	2.59808i	−0.189316	−	0.109302i
$566$	6.00000			0.252199
$567$		0			0
$568$	6.00000			0.251754
$569$	−6.00000	−	3.46410i	−0.251533	−	0.145223i	0.368933	−	0.929456i	$-0.379723\pi$
$569$	−6.00000	−	3.46410i	−0.251533	−	0.145223i	−0.620466	+	0.784233i	$0.713057\pi$
$570$		0			0
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$	3.00000			0.125436
$573$		0			0
$574$	9.00000	−	10.3923i	0.375653	−	0.433766i
$575$		−	20.7846i		−	0.866778i
$576$		0			0
$577$	−34.5000	−	19.9186i	−1.43625	−	0.829222i	−0.438667	−	0.898650i	$-0.644549\pi$
$577$	−34.5000	−	19.9186i	−1.43625	−	0.829222i	−0.997587	+	0.0694283i	$0.977883\pi$
$578$			13.8564i			0.576351i
$579$		0			0
$580$	13.5000	+	7.79423i	0.560557	+	0.323638i
$581$	−30.0000	−	25.9808i	−1.24461	−	1.07786i
$582$		0			0
$583$	−7.50000	+	12.9904i	−0.310618	+	0.538007i
$584$	−4.50000	+	7.79423i	−0.186211	+	0.322527i
$585$		0			0
$586$	13.5000	−	7.79423i	0.557680	−	0.321977i
$587$	−10.5000	−	18.1865i	−0.433381	−	0.750639i	0.563781	−	0.825925i	$-0.309346\pi$
$587$	−10.5000	−	18.1865i	−0.433381	−	0.750639i	−0.997162	+	0.0752860i	$0.976013\pi$
$588$		0			0
$589$	9.00000	−	15.5885i	0.370839	−	0.642311i
$590$		0			0
$591$		0			0
$592$	−35.0000			−1.43849
$593$	−19.5000	−	33.7750i	−0.800769	−	1.38697i	−0.919111	−	0.394000i	$-0.871091\pi$
$593$	−19.5000	−	33.7750i	−0.800769	−	1.38697i	0.118342	−	0.992973i	$-0.462242\pi$
$594$		0			0
$595$	4.50000	−	23.3827i	0.184482	−	0.958597i
$596$	1.50000	−	0.866025i	0.0614424	−	0.0354738i
$597$		0			0
$598$	−13.5000	+	7.79423i	−0.552056	+	0.318730i
$599$	21.0000	−	12.1244i	0.858037	−	0.495388i	−0.00531761	−	0.999986i	$-0.501693\pi$
$599$	21.0000	−	12.1244i	0.858037	−	0.495388i	0.863354	+	0.504598i	$0.168359\pi$
$600$		0			0
$601$	−25.5000	+	14.7224i	−1.04017	+	0.600541i	−0.919881	−	0.392199i	$-0.871715\pi$
$601$	−25.5000	+	14.7224i	−1.04017	+	0.600541i	−0.120286	+	0.992739i	$0.538381\pi$
$602$	1.50000	+	4.33013i	0.0611354	+	0.176483i
$603$		0			0
$604$	−8.50000	−	14.7224i	−0.345860	−	0.599047i
$605$	24.0000			0.975739
$606$		0			0
$607$			15.5885i			0.632716i	0.948640	+	0.316358i	$0.102460\pi$
$607$			15.5885i			0.632716i	−0.948640	+	0.316358i	$0.897540\pi$
$608$	−13.5000	+	23.3827i	−0.547497	+	0.948293i
$609$		0			0
$610$	36.0000	+	62.3538i	1.45760	+	2.52463i
$611$		0			0
$612$		0			0
$613$	−23.5000	+	40.7032i	−0.949156	+	1.64399i	−0.201948	+	0.979396i	$0.564727\pi$
$613$	−23.5000	+	40.7032i	−0.949156	+	1.64399i	−0.747208	+	0.664590i	$0.768606\pi$
$614$	21.0000	−	36.3731i	0.847491	−	1.46790i
$615$		0			0
$616$	−7.50000	+	2.59808i	−0.302184	+	0.104679i
$617$	4.50000	+	2.59808i	0.181163	+	0.104595i	0.587839	−	0.808978i	$-0.299979\pi$
$617$	4.50000	+	2.59808i	0.181163	+	0.104595i	−0.406676	+	0.913573i	$0.633312\pi$
$618$		0			0
$619$		−	19.0526i		−	0.765787i	−0.923792	−	0.382893i	$-0.874928\pi$
$619$		−	19.0526i		−	0.765787i	0.923792	−	0.382893i	$-0.125072\pi$
$620$	−9.00000	−	5.19615i	−0.361449	−	0.208683i
$621$		0			0
$622$			41.5692i			1.66677i
$623$	6.00000	+	5.19615i	0.240385	+	0.208179i
$624$		0			0
$625$	−29.0000			−1.16000
$626$	−18.0000	−	31.1769i	−0.719425	−	1.24608i
$627$		0			0
$628$		0			0
$629$	21.0000			0.837325
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	12.0000	+	6.92820i	0.477334	+	0.275589i
$633$		0			0
$634$		0			0
$635$	60.0000			2.38103
$636$		0			0
$637$	−12.0000	+	1.73205i	−0.475457	+	0.0686264i
$638$			15.5885i			0.617153i
$639$		0			0
$640$	−31.5000	−	18.1865i	−1.24515	−	0.718886i
$641$		−	12.1244i		−	0.478883i	−0.970911	−	0.239442i	$-0.923036\pi$
$641$		−	12.1244i		−	0.478883i	0.970911	−	0.239442i	$-0.0769644\pi$
$642$		0			0
$643$	10.5000	+	6.06218i	0.414080	+	0.239069i	0.692541	−	0.721378i	$-0.256491\pi$
$643$	10.5000	+	6.06218i	0.414080	+	0.239069i	−0.278462	+	0.960447i	$0.589824\pi$
$644$	−9.00000	+	10.3923i	−0.354650	+	0.409514i
$645$		0			0
$646$	13.5000	−	23.3827i	0.531150	−	0.919979i
$647$	1.50000	−	2.59808i	0.0589711	−	0.102141i	−0.835033	−	0.550200i	$-0.814551\pi$
$647$	1.50000	−	2.59808i	0.0589711	−	0.102141i	0.894004	+	0.448059i	$0.147885\pi$
$648$		0			0
$649$		0			0
$650$	−6.00000	−	10.3923i	−0.235339	−	0.407620i
$651$		0			0
$652$	5.50000	−	9.52628i	0.215397	−	0.373078i
$653$			39.8372i			1.55895i	0.626434	+	0.779474i	$0.284514\pi$
$653$			39.8372i			1.55895i	−0.626434	+	0.779474i	$0.715486\pi$
$654$		0			0
$655$	27.0000			1.05498
$656$	7.50000	+	12.9904i	0.292826	+	0.507189i
$657$		0			0
$658$		0			0
$659$	−10.5000	+	6.06218i	−0.409022	+	0.236149i	−0.690369	−	0.723457i	$-0.742552\pi$
$659$	−10.5000	+	6.06218i	−0.409022	+	0.236149i	0.281347	+	0.959606i	$0.409219\pi$
$660$		0			0
$661$	36.0000	−	20.7846i	1.40024	−	0.808428i	0.405821	−	0.913953i	$-0.366986\pi$
$661$	36.0000	−	20.7846i	1.40024	−	0.808428i	0.994417	+	0.105525i	$0.0336523\pi$
$662$	12.0000	−	6.92820i	0.466393	−	0.269272i
$663$		0			0
$664$	22.5000	−	12.9904i	0.873169	−	0.504125i
$665$	27.0000	−	31.1769i	1.04702	−	1.20899i
$666$		0			0
$667$	−13.5000	−	23.3827i	−0.522722	−	0.905381i
$668$	9.00000			0.348220
$669$		0			0
$670$			20.7846i			0.802980i
$671$	−12.0000	+	20.7846i	−0.463255	+	0.802381i
$672$		0			0
$673$	14.5000	+	25.1147i	0.558934	+	0.968102i	0.997586	+	0.0694449i	$0.0221228\pi$
$673$	14.5000	+	25.1147i	0.558934	+	0.968102i	−0.438652	+	0.898657i	$0.644544\pi$
$674$	−28.5000	+	16.4545i	−1.09778	+	0.633803i
$675$		0			0
$676$	5.00000	−	8.66025i	0.192308	−	0.333087i
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	−0.985517	−	0.169580i	$-0.945759\pi$
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	0.639618	+	0.768693i	$0.279092\pi$
$678$		0			0
$679$	3.00000	−	3.46410i	0.115129	−	0.132940i
$680$	13.5000	+	7.79423i	0.517701	+	0.298895i
$681$		0			0
$682$		−	10.3923i		−	0.397942i
$683$	−7.50000	−	4.33013i	−0.286980	−	0.165688i	0.349599	−	0.936899i	$-0.386318\pi$
$683$	−7.50000	−	4.33013i	−0.286980	−	0.165688i	−0.636579	+	0.771212i	$0.719651\pi$
$684$		0			0
$685$		−	36.3731i		−	1.38974i
$686$	−28.5000	+	14.7224i	−1.08814	+	0.562105i
$687$		0			0
$688$	−5.00000			−0.190623
$689$	−7.50000	−	12.9904i	−0.285727	−	0.494894i
$690$		0			0
$691$	−3.00000	−	1.73205i	−0.114125	−	0.0658903i	0.441851	−	0.897089i	$-0.354322\pi$
$691$	−3.00000	−	1.73205i	−0.114125	−	0.0658903i	−0.555976	+	0.831198i	$0.687655\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	6.00000			0.227757
$695$	−22.5000	−	12.9904i	−0.853474	−	0.492753i
$696$		0			0
$697$	−4.50000	−	7.79423i	−0.170450	−	0.295227i
$698$	21.0000			0.794862
$699$		0			0
$700$	−8.00000	−	6.92820i	−0.302372	−	0.261861i
$701$			34.6410i			1.30837i	0.756333	+	0.654187i	$0.226989\pi$
$701$			34.6410i			1.30837i	−0.756333	+	0.654187i	$0.773011\pi$
$702$		0			0
$703$	31.5000	+	18.1865i	1.18805	+	0.685918i
$704$		−	1.73205i		−	0.0652791i
$705$		0			0
$706$	−31.5000	−	18.1865i	−1.18552	−	0.684459i
$707$	−7.50000	+	2.59808i	−0.282067	+	0.0977107i
$708$		0			0
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	−0.944509	−	0.328484i	$-0.893462\pi$
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	0.756730	+	0.653727i	$0.226796\pi$
$710$	−9.00000	+	15.5885i	−0.337764	+	0.585024i
$711$		0			0
$712$	−4.50000	+	2.59808i	−0.168645	+	0.0973670i
$713$	9.00000	+	15.5885i	0.337053	+	0.583792i
$714$		0			0
$715$	4.50000	−	7.79423i	0.168290	−	0.291488i
$716$		−	15.5885i		−	0.582568i
$717$		0			0
$718$	39.0000			1.45547
$719$	4.50000	+	7.79423i	0.167822	+	0.290676i	0.937654	−	0.347571i	$-0.112993\pi$
$719$	4.50000	+	7.79423i	0.167822	+	0.290676i	−0.769832	+	0.638247i	$0.779660\pi$
$720$		0			0
$721$	10.5000	+	30.3109i	0.391040	+	1.12884i
$722$	12.0000	−	6.92820i	0.446594	−	0.257841i
$723$		0			0
$724$		0			0
$725$	18.0000	−	10.3923i	0.668503	−	0.385961i
$726$		0			0
$727$	−10.5000	+	6.06218i	−0.389423	+	0.224834i	−0.681910	−	0.731436i	$-0.738851\pi$
$727$	−10.5000	+	6.06218i	−0.389423	+	0.224834i	0.292487	+	0.956270i	$0.405517\pi$
$728$	1.50000	−	7.79423i	0.0555937	−	0.288873i
$729$		0			0
$730$	−13.5000	−	23.3827i	−0.499657	−	0.865432i
$731$	3.00000			0.110959
$732$		0			0
$733$		−	43.3013i		−	1.59937i	−0.600420	−	0.799684i	$-0.705000\pi$
$733$		−	43.3013i		−	1.59937i	0.600420	−	0.799684i	$-0.295000\pi$
$734$	4.50000	−	7.79423i	0.166098	−	0.287690i
$735$		0			0
$736$	−13.5000	−	23.3827i	−0.497617	−	0.861897i
$737$	−6.00000	+	3.46410i	−0.221013	+	0.127602i
$738$		0			0
$739$	3.50000	−	6.06218i	0.128750	−	0.223001i	−0.794443	−	0.607339i	$-0.792237\pi$
$739$	3.50000	−	6.06218i	0.128750	−	0.223001i	0.923192	+	0.384338i	$0.125570\pi$
$740$	10.5000	−	18.1865i	0.385988	−	0.668550i
$741$		0			0
$742$	−30.0000	−	25.9808i	−1.10133	−	0.953784i
$743$	10.5000	+	6.06218i	0.385208	+	0.222400i	0.680082	−	0.733136i	$-0.261944\pi$
$743$	10.5000	+	6.06218i	0.385208	+	0.222400i	−0.294874	+	0.955536i	$0.595278\pi$
$744$		0			0
$745$		−	5.19615i		−	0.190372i
$746$	−55.5000	−	32.0429i	−2.03200	−	1.17318i
$747$		0			0
$748$		−	5.19615i		−	0.189990i
$749$	−15.0000	+	17.3205i	−0.548088	+	0.632878i
$750$		0			0
$751$	37.0000			1.35015			0.675075	−	0.737749i	$-0.264111\pi$
$751$	37.0000			1.35015			0.675075	+	0.737749i	$0.264111\pi$
$752$		0			0
$753$		0			0
$754$	−13.5000	−	7.79423i	−0.491641	−	0.283849i
$755$	−51.0000			−1.85608
$756$		0			0
$757$	10.0000			0.363456			0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000			0.363456			0.181728	+	0.983349i	$0.441831\pi$
$758$	−30.0000	−	17.3205i	−1.08965	−	0.629109i
$759$		0			0
$760$	13.5000	+	23.3827i	0.489696	+	0.848179i
$761$	−45.0000			−1.63125			−0.815624	−	0.578582i	$-0.803606\pi$
$761$	−45.0000			−1.63125			−0.815624	+	0.578582i	$0.803606\pi$
$762$		0			0
$763$	9.50000	−	49.3634i	0.343923	−	1.78708i
$764$			17.3205i			0.626634i
$765$		0			0
$766$	13.5000	+	7.79423i	0.487775	+	0.281617i
$767$		0			0
$768$		0			0
$769$	−13.5000	−	7.79423i	−0.486822	−	0.281067i	0.236433	−	0.971648i	$-0.424022\pi$
$769$	−13.5000	−	7.79423i	−0.486822	−	0.281067i	−0.723255	+	0.690581i	$0.757355\pi$
$770$	4.50000	−	23.3827i	0.162169	−	0.842654i
$771$		0			0
$772$	−1.00000	+	1.73205i	−0.0359908	+	0.0623379i
$773$	−25.5000	+	44.1673i	−0.917171	+	1.58859i	−0.113480	+	0.993540i	$0.536200\pi$
$773$	−25.5000	+	44.1673i	−0.917171	+	1.58859i	−0.803691	+	0.595047i	$0.797133\pi$
$774$		0			0
$775$	−12.0000	+	6.92820i	−0.431053	+	0.248868i
$776$	1.50000	+	2.59808i	0.0538469	+	0.0932655i
$777$		0			0
$778$	−31.5000	+	54.5596i	−1.12933	+	1.95606i
$779$		−	15.5885i		−	0.558514i
$780$		0			0
$781$	−6.00000			−0.214697
$782$	13.5000	+	23.3827i	0.482759	+	0.836163i
$783$		0			0
$784$	−5.00000	−	34.6410i	−0.178571	−	1.23718i
$785$		0			0
$786$		0			0
$787$	−33.0000	+	19.0526i	−1.17632	+	0.679150i	−0.955161	−	0.296087i	$-0.904318\pi$
$787$	−33.0000	+	19.0526i	−1.17632	+	0.679150i	−0.221162	+	0.975237i	$0.570985\pi$
$788$	12.0000	−	6.92820i	0.427482	−	0.246807i
$789$		0			0
$790$	−36.0000	+	20.7846i	−1.28082	+	0.739483i
$791$	4.50000	+	0.866025i	0.160002	+	0.0307923i
$792$		0			0
$793$	−12.0000	−	20.7846i	−0.426132	−	0.738083i
$794$	15.0000			0.532330
$795$		0			0
$796$		−	8.66025i		−	0.306955i
$797$	22.5000	−	38.9711i	0.796991	−	1.38043i	−0.124576	−	0.992210i	$-0.539757\pi$
$797$	22.5000	−	38.9711i	0.796991	−	1.38043i	0.921567	−	0.388219i	$-0.126909\pi$
$798$		0			0
$799$		0			0
$800$	18.0000	−	10.3923i	0.636396	−	0.367423i
$801$		0			0
$802$	−28.5000	+	49.3634i	−1.00637	+	1.74308i
$803$	4.50000	−	7.79423i	0.158802	−	0.275052i
$804$		0			0
$805$	13.5000	+	38.9711i	0.475812	+	1.37355i
$806$	9.00000	+	5.19615i	0.317011	+	0.183027i
$807$		0			0
$808$		−	5.19615i		−	0.182800i
$809$	1.50000	+	0.866025i	0.0527372	+	0.0304478i	0.526137	−	0.850400i	$-0.323640\pi$
$809$	1.50000	+	0.866025i	0.0527372	+	0.0304478i	−0.473400	+	0.880848i	$0.656973\pi$
$810$		0			0
$811$		−	10.3923i		−	0.364923i	−0.983213	−	0.182462i	$-0.941593\pi$
$811$		−	10.3923i		−	0.364923i	0.983213	−	0.182462i	$-0.0584065\pi$
$812$	−13.5000	−	2.59808i	−0.473757	−	0.0911746i
$813$		0			0
$814$	21.0000			0.736050
$815$	−16.5000	−	28.5788i	−0.577970	−	1.00107i
$816$		0			0
$817$	4.50000	+	2.59808i	0.157435	+	0.0908952i
$818$	−12.0000			−0.419570
$819$		0			0
$820$	−9.00000			−0.314294
$821$	−6.00000	−	3.46410i	−0.209401	−	0.120898i	0.391632	−	0.920122i	$-0.371911\pi$
$821$	−6.00000	−	3.46410i	−0.209401	−	0.120898i	−0.601033	+	0.799224i	$0.705244\pi$
$822$		0			0
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	0.971102	−	0.238664i	$-0.0767093\pi$
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	−0.692240	+	0.721668i	$0.743376\pi$
$824$	−21.0000			−0.731570
$825$		0			0
$826$		0			0
$827$		−	24.2487i		−	0.843210i	−0.906780	−	0.421605i	$-0.861467\pi$
$827$		−	24.2487i		−	0.843210i	0.906780	−	0.421605i	$-0.138533\pi$
$828$		0			0
$829$	31.5000	+	18.1865i	1.09404	+	0.631644i	0.934649	−	0.355571i	$-0.115714\pi$
$829$	31.5000	+	18.1865i	1.09404	+	0.631644i	0.159391	+	0.987216i	$0.449047\pi$
$830$			77.9423i			2.70542i
$831$		0			0
$832$	1.50000	+	0.866025i	0.0520031	+	0.0300240i
$833$	3.00000	+	20.7846i	0.103944	+	0.720144i
$834$		0			0
$835$	13.5000	−	23.3827i	0.467187	−	0.809191i
$836$	4.50000	−	7.79423i	0.155636	−	0.269569i
$837$		0			0
$838$	49.5000	−	28.5788i	1.70995	−	0.987240i
$839$	19.5000	+	33.7750i	0.673215	+	1.16604i	0.976987	+	0.213298i	$0.0684204\pi$
$839$	19.5000	+	33.7750i	0.673215	+	1.16604i	−0.303773	+	0.952745i	$0.598246\pi$
$840$		0			0
$841$	−1.00000	+	1.73205i	−0.0344828	+	0.0597259i
$842$		−	19.0526i		−	0.656595i
$843$		0			0
$844$	5.00000			0.172107
$845$	−15.0000	−	25.9808i	−0.516016	−	0.893765i
$846$		0			0
$847$	−20.0000	+	6.92820i	−0.687208	+	0.238056i
$848$	37.5000	−	21.6506i	1.28776	−	0.743486i
$849$		0			0
$850$	−18.0000	+	10.3923i	−0.617395	+	0.356453i
$851$	−31.5000	+	18.1865i	−1.07981	+	0.623426i
$852$		0			0
$853$	22.5000	−	12.9904i	0.770385	−	0.444782i	−0.0626267	−	0.998037i	$-0.519948\pi$
$853$	22.5000	−	12.9904i	0.770385	−	0.444782i	0.833012	+	0.553255i	$0.186614\pi$
$854$	−48.0000	−	41.5692i	−1.64253	−	1.42247i
$855$		0			0
$856$	−7.50000	−	12.9904i	−0.256345	−	0.444002i
$857$	27.0000			0.922302			0.461151	−	0.887322i	$-0.347437\pi$
$857$	27.0000			0.922302			0.461151	+	0.887322i	$0.347437\pi$
$858$		0			0
$859$			50.2295i			1.71381i	0.515476	+	0.856904i	$0.327615\pi$
$859$			50.2295i			1.71381i	−0.515476	+	0.856904i	$0.672385\pi$
$860$	1.50000	−	2.59808i	0.0511496	−	0.0885937i
$861$		0			0
$862$	−13.5000	−	23.3827i	−0.459812	−	0.796417i
$863$	37.5000	−	21.6506i	1.27651	−	0.736996i	0.300309	−	0.953842i	$-0.402910\pi$
$863$	37.5000	−	21.6506i	1.27651	−	0.736996i	0.976206	+	0.216846i	$0.0695769\pi$
$864$		0			0
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$	−12.0000	+	20.7846i	−0.407777	+	0.706290i
$867$		0			0
$868$	9.00000	+	1.73205i	0.305480	+	0.0587896i
$869$	−12.0000	−	6.92820i	−0.407072	−	0.235023i
$870$		0			0
$871$		−	6.92820i		−	0.234753i
$872$	28.5000	+	16.4545i	0.965132	+	0.557219i
$873$		0			0
$874$			46.7654i			1.58186i
$875$	7.50000	−	2.59808i	0.253546	−	0.0878310i
$876$		0			0
$877$	23.0000			0.776655			0.388327	−	0.921521i	$-0.373053\pi$
$877$	23.0000			0.776655			0.388327	+	0.921521i	$0.373053\pi$
$878$	27.0000	+	46.7654i	0.911206	+	1.57825i
$879$		0			0
$880$	22.5000	+	12.9904i	0.758475	+	0.437906i
$881$	54.0000			1.81931			0.909653	−	0.415369i	$-0.136347\pi$
$881$	54.0000			1.81931			0.909653	+	0.415369i	$0.136347\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$	4.50000	+	2.59808i	0.151351	+	0.0873828i
$885$		0			0
$886$	−27.0000	−	46.7654i	−0.907083	−	1.57111i
$887$	−15.0000			−0.503651			−0.251825	−	0.967773i	$-0.581031\pi$
$887$	−15.0000			−0.503651			−0.251825	+	0.967773i	$0.581031\pi$
$888$		0			0
$889$	−50.0000	+	17.3205i	−1.67695	+	0.580911i
$890$		−	15.5885i		−	0.522526i
$891$		0			0
$892$	−4.50000	−	2.59808i	−0.150671	−	0.0869900i
$893$		0			0
$894$		0			0
$895$	−40.5000	−	23.3827i	−1.35377	−	0.781597i
$896$	31.5000	+	6.06218i	1.05234	+	0.202523i
$897$		0			0
$898$	−30.0000	+	51.9615i	−1.00111	+	1.73398i
$899$	−9.00000	+	15.5885i	−0.300167	+	0.519904i
$900$		0			0
$901$	−22.5000	+	12.9904i	−0.749584	+	0.432772i
$902$	−4.50000	−	7.79423i	−0.149834	−	0.259519i
$903$		0			0
$904$	−1.50000	+	2.59808i	−0.0498893	+	0.0864107i
$905$		0			0
$906$		0			0
$907$	19.0000			0.630885			0.315442	−	0.948945i	$-0.397847\pi$
$907$	19.0000			0.630885			0.315442	+	0.948945i	$0.397847\pi$
$908$	−10.5000	−	18.1865i	−0.348455	−	0.603541i
$909$		0			0
$910$	18.0000	+	15.5885i	0.596694	+	0.516752i
$911$	−4.50000	+	2.59808i	−0.149092	+	0.0860781i	−0.572690	−	0.819772i	$-0.694100\pi$
$911$	−4.50000	+	2.59808i	−0.149092	+	0.0860781i	0.423598	+	0.905850i	$0.360767\pi$
$912$		0			0
$913$	−22.5000	+	12.9904i	−0.744641	+	0.429919i
$914$	39.0000	−	22.5167i	1.29001	−	0.744785i
$915$		0			0
$916$	7.50000	−	4.33013i	0.247807	−	0.143071i
$917$	−22.5000	+	7.79423i	−0.743015	+	0.257388i
$918$		0			0
$919$	14.5000	+	25.1147i	0.478311	+	0.828459i	0.999691	−	0.0248659i	$-0.00791589\pi$
$919$	14.5000	+	25.1147i	0.478311	+	0.828459i	−0.521380	+	0.853325i	$0.674583\pi$
$920$	−27.0000			−0.890164
$921$		0			0
$922$		−	25.9808i		−	0.855631i
$923$	3.00000	−	5.19615i	0.0987462	−	0.171033i
$924$		0			0
$925$	−14.0000	−	24.2487i	−0.460317	−	0.797293i
$926$	1.50000	−	0.866025i	0.0492931	−	0.0284594i
$927$		0			0
$928$	13.5000	−	23.3827i	0.443159	−	0.767574i
$929$	15.0000	−	25.9808i	0.492134	−	0.852401i	−0.507825	−	0.861460i	$-0.669550\pi$
$929$	15.0000	−	25.9808i	0.492134	−	0.852401i	0.999959	+	0.00905914i	$0.00288365\pi$
$930$		0			0
$931$	−13.5000	+	33.7750i	−0.442445	+	1.10693i
$932$	−4.50000	−	2.59808i	−0.147402	−	0.0851028i
$933$		0			0
$934$		−	5.19615i		−	0.170023i
$935$	−13.5000	−	7.79423i	−0.441497	−	0.254899i
$936$		0			0
$937$			13.8564i			0.452669i	0.974050	+	0.226335i	$0.0726743\pi$
$937$			13.8564i			0.452669i	−0.974050	+	0.226335i	$0.927326\pi$
$938$	−6.00000	−	17.3205i	−0.195907	−	0.565535i
$939$		0			0
$940$		0			0
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	0.681218	−	0.732081i	$-0.261451\pi$
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	−0.974609	+	0.223912i	$0.928117\pi$
$942$		0			0
$943$	13.5000	+	7.79423i	0.439620	+	0.253815i
$944$		0			0
$945$		0			0
$946$	3.00000			0.0975384
$947$	45.0000	+	25.9808i	1.46230	+	0.844261i	0.999118	−	0.0419998i	$-0.0133729\pi$
$947$	45.0000	+	25.9808i	1.46230	+	0.844261i	0.463186	+	0.886261i	$0.346706\pi$
$948$		0			0
$949$	4.50000	+	7.79423i	0.146076	+	0.253011i
$950$	−36.0000			−1.16799
$951$		0			0
$952$	−13.5000	−	2.59808i	−0.437538	−	0.0842041i
$953$			20.7846i			0.673280i	0.941634	+	0.336640i	$0.109290\pi$
$953$			20.7846i			0.673280i	−0.941634	+	0.336640i	$0.890710\pi$
$954$		0			0
$955$	45.0000	+	25.9808i	1.45617	+	0.840718i
$956$		−	1.73205i		−	0.0560185i
$957$		0			0
$958$	40.5000	+	23.3827i	1.30850	+	0.755460i
$959$	10.5000	+	30.3109i	0.339063	+	0.978790i
$960$		0			0
$961$	−9.50000	+	16.4545i	−0.306452	+	0.530790i
$962$	−10.5000	+	18.1865i	−0.338534	+	0.586357i
$963$		0			0
$964$	−19.5000	+	11.2583i	−0.628053	+	0.362606i
$965$	3.00000	+	5.19615i	0.0965734	+	0.167270i
$966$		0			0
$967$	12.5000	−	21.6506i	0.401973	−	0.696237i	−0.591991	−	0.805945i	$-0.701658\pi$
$967$	12.5000	−	21.6506i	0.401973	−	0.696237i	0.993964	+	0.109707i	$0.0349913\pi$
$968$		−	13.8564i		−	0.445362i
$969$		0			0
$970$	−9.00000			−0.288973
$971$	28.5000	+	49.3634i	0.914609	+	1.58415i	0.807473	+	0.589904i	$0.200834\pi$
$971$	28.5000	+	49.3634i	0.914609	+	1.58415i	0.107135	+	0.994244i	$0.465832\pi$
$972$		0			0
$973$	22.5000	+	4.33013i	0.721317	+	0.138817i
$974$	34.5000	−	19.9186i	1.10545	−	0.638233i
$975$		0			0
$976$	60.0000	−	34.6410i	1.92055	−	1.10883i
$977$	36.0000	−	20.7846i	1.15174	−	0.664959i	0.202431	−	0.979297i	$-0.435116\pi$
$977$	36.0000	−	20.7846i	1.15174	−	0.664959i	0.949311	+	0.314338i	$0.101783\pi$
$978$		0			0
$979$	4.50000	−	2.59808i	0.143821	−	0.0830349i
$980$	19.5000	+	7.79423i	0.622905	+	0.248978i
$981$		0			0
$982$	22.5000	+	38.9711i	0.718004	+	1.24362i
$983$	39.0000			1.24391			0.621953	−	0.783054i	$-0.286339\pi$
$983$	39.0000			1.24391			0.621953	+	0.783054i	$0.286339\pi$
$984$		0			0
$985$		−	41.5692i		−	1.32451i
$986$	−13.5000	+	23.3827i	−0.429928	+	0.744656i
$987$		0			0
$988$	4.50000	+	7.79423i	0.143164	+	0.247967i
$989$	−4.50000	+	2.59808i	−0.143092	+	0.0826140i
$990$		0			0
$991$	23.5000	−	40.7032i	0.746502	−	1.29298i	−0.202988	−	0.979181i	$-0.565065\pi$
$991$	23.5000	−	40.7032i	0.746502	−	1.29298i	0.949490	−	0.313798i	$-0.101602\pi$
$992$	−9.00000	+	15.5885i	−0.285750	+	0.494934i
$993$		0			0
$994$	3.00000	−	15.5885i	0.0951542	−	0.494436i
$995$	−22.5000	−	12.9904i	−0.713298	−	0.411823i
$996$		0			0
$997$			8.66025i			0.274273i	0.990552	+	0.137136i	$0.0437899\pi$
$997$			8.66025i			0.274273i	−0.990552	+	0.137136i	$0.956210\pi$
$998$	37.5000	+	21.6506i	1.18704	+	0.685339i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.s.a.17.1		2
3.2	odd	2		63.2.s.a.59.1	yes	2
4.3	odd	2		3024.2.df.a.17.1		2
7.2	even	3		1323.2.i.a.1097.1		2
7.3	odd	6		1323.2.o.b.881.1		2
7.4	even	3		1323.2.o.a.881.1		2
7.5	odd	6		189.2.i.a.152.1		2
7.6	odd	2		1323.2.s.a.962.1		2
9.2	odd	6		189.2.i.a.143.1		2
9.4	even	3		567.2.p.a.80.1		2
9.5	odd	6		567.2.p.b.80.1		2
9.7	even	3		63.2.i.a.38.1	yes	2
12.11	even	2		1008.2.df.a.689.1		2
21.2	odd	6		441.2.i.a.68.1		2
21.5	even	6		63.2.i.a.5.1	✓	2
21.11	odd	6		441.2.o.b.293.1		2
21.17	even	6		441.2.o.a.293.1		2
21.20	even	2		441.2.s.a.374.1		2
28.19	even	6		3024.2.ca.a.2609.1		2
36.7	odd	6		1008.2.ca.a.353.1		2
36.11	even	6		3024.2.ca.a.2033.1		2
63.2	odd	6		1323.2.s.a.656.1		2
63.5	even	6		567.2.p.a.404.1		2
63.11	odd	6		1323.2.o.b.440.1		2
63.16	even	3		441.2.s.a.362.1		2
63.20	even	6		1323.2.i.a.521.1		2
63.25	even	3		441.2.o.a.146.1		2
63.34	odd	6		441.2.i.a.227.1		2
63.38	even	6		1323.2.o.a.440.1		2
63.40	odd	6		567.2.p.b.404.1		2
63.47	even	6	inner	189.2.s.a.89.1		2
63.52	odd	6		441.2.o.b.146.1		2
63.61	odd	6		63.2.s.a.47.1	yes	2
84.47	odd	6		1008.2.ca.a.257.1		2
252.47	odd	6		3024.2.df.a.1601.1		2
252.187	even	6		1008.2.df.a.929.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.a.5.1	✓	2	21.5	even	6
63.2.i.a.38.1	yes	2	9.7	even	3
63.2.s.a.47.1	yes	2	63.61	odd	6
63.2.s.a.59.1	yes	2	3.2	odd	2
189.2.i.a.143.1		2	9.2	odd	6
189.2.i.a.152.1		2	7.5	odd	6
189.2.s.a.17.1		2	1.1	even	1	trivial
189.2.s.a.89.1		2	63.47	even	6	inner
441.2.i.a.68.1		2	21.2	odd	6
441.2.i.a.227.1		2	63.34	odd	6
441.2.o.a.146.1		2	63.25	even	3
441.2.o.a.293.1		2	21.17	even	6
441.2.o.b.146.1		2	63.52	odd	6
441.2.o.b.293.1		2	21.11	odd	6
441.2.s.a.362.1		2	63.16	even	3
441.2.s.a.374.1		2	21.20	even	2
567.2.p.a.80.1		2	9.4	even	3
567.2.p.a.404.1		2	63.5	even	6
567.2.p.b.80.1		2	9.5	odd	6
567.2.p.b.404.1		2	63.40	odd	6
1008.2.ca.a.257.1		2	84.47	odd	6
1008.2.ca.a.353.1		2	36.7	odd	6
1008.2.df.a.689.1		2	12.11	even	2
1008.2.df.a.929.1		2	252.187	even	6
1323.2.i.a.521.1		2	63.20	even	6
1323.2.i.a.1097.1		2	7.2	even	3
1323.2.o.a.440.1		2	63.38	even	6
1323.2.o.a.881.1		2	7.4	even	3
1323.2.o.b.440.1		2	63.11	odd	6
1323.2.o.b.881.1		2	7.3	odd	6
1323.2.s.a.656.1		2	63.2	odd	6
1323.2.s.a.962.1		2	7.6	odd	2
3024.2.ca.a.2033.1		2	36.11	even	6
3024.2.ca.a.2609.1		2	28.19	even	6
3024.2.df.a.17.1		2	4.3	odd	2
3024.2.df.a.1601.1		2	252.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(-2.50000 + 0.866025i) q^{7} -1.73205i q^{8} +(4.50000 + 2.59808i) q^{10} +1.73205i q^{11} +(-1.50000 - 0.866025i) q^{13} +(-4.50000 - 0.866025i) q^{14} +(2.50000 - 4.33013i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-4.50000 + 2.59808i) q^{19} +(1.50000 + 2.59808i) q^{20} +(-1.50000 + 2.59808i) q^{22} -5.19615i q^{23} +4.00000 q^{25} +(-1.50000 - 2.59808i) q^{26} +(-2.00000 - 1.73205i) q^{28} +(4.50000 - 2.59808i) q^{29} +(-3.00000 + 1.73205i) q^{31} +(4.50000 - 2.59808i) q^{32} +(-4.50000 + 2.59808i) q^{34} +(-7.50000 + 2.59808i) q^{35} +(-3.50000 - 6.06218i) q^{37} -9.00000 q^{38} -5.19615i q^{40} +(-1.50000 + 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(-1.50000 + 0.866025i) q^{44} +(4.50000 - 7.79423i) q^{46} +(5.50000 - 4.33013i) q^{49} +(6.00000 + 3.46410i) q^{50} -1.73205i q^{52} +(7.50000 + 4.33013i) q^{53} +5.19615i q^{55} +(1.50000 + 4.33013i) q^{56} +9.00000 q^{58} +(12.0000 + 6.92820i) q^{61} -6.00000 q^{62} -1.00000 q^{64} +(-4.50000 - 2.59808i) q^{65} +(2.00000 + 3.46410i) q^{67} -3.00000 q^{68} +(-13.5000 - 2.59808i) q^{70} +3.46410i q^{71} +(-4.50000 - 2.59808i) q^{73} -12.1244i q^{74} +(-4.50000 - 2.59808i) q^{76} +(-1.50000 - 4.33013i) q^{77} +(-4.00000 + 6.92820i) q^{79} +(7.50000 - 12.9904i) q^{80} +(-4.50000 + 2.59808i) q^{82} +(7.50000 + 12.9904i) q^{83} +(-4.50000 + 7.79423i) q^{85} -1.73205i q^{86} +3.00000 q^{88} +(-1.50000 - 2.59808i) q^{89} +(4.50000 + 0.866025i) q^{91} +(4.50000 - 2.59808i) q^{92} +(-13.5000 + 7.79423i) q^{95} +(-1.50000 + 0.866025i) q^{97} +(12.0000 - 1.73205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + q^{4} + 6 q^{5} - 5 q^{7} + 9 q^{10} - 3 q^{13} - 9 q^{14} + 5 q^{16} - 3 q^{17} - 9 q^{19} + 3 q^{20} - 3 q^{22} + 8 q^{25} - 3 q^{26} - 4 q^{28} + 9 q^{29} - 6 q^{31} + 9 q^{32} - 9 q^{34}+ \cdots + 24 q^{98}+O(q^{100}) \) 2 * q + 3 * q^2 + q^4 + 6 * q^5 - 5 * q^7 + 9 * q^10 - 3 * q^13 - 9 * q^14 + 5 * q^16 - 3 * q^17 - 9 * q^19 + 3 * q^20 - 3 * q^22 + 8 * q^25 - 3 * q^26 - 4 * q^28 + 9 * q^29 - 6 * q^31 + 9 * q^32 - 9 * q^34 - 15 * q^35 - 7 * q^37 - 18 * q^38 - 3 * q^41 - q^43 - 3 * q^44 + 9 * q^46 + 11 * q^49 + 12 * q^50 + 15 * q^53 + 3 * q^56 + 18 * q^58 + 24 * q^61 - 12 * q^62 - 2 * q^64 - 9 * q^65 + 4 * q^67 - 6 * q^68 - 27 * q^70 - 9 * q^73 - 9 * q^76 - 3 * q^77 - 8 * q^79 + 15 * q^80 - 9 * q^82 + 15 * q^83 - 9 * q^85 + 6 * q^88 - 3 * q^89 + 9 * q^91 + 9 * q^92 - 27 * q^95 - 3 * q^97 + 24 * q^98

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