LMFDB - Embedded newform 546.2.s.d.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(43,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("546.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.s (of order $6$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	546.43
Dual form			546.2.s.d.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.732051i q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.732051i q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.366025 - 0.633975i) q^{10} +(-3.23205 - 1.86603i) q^{11} +1.00000 q^{12} +(-0.866025 - 3.50000i) q^{13} -1.00000 q^{14} +(0.633975 + 0.366025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.133975 + 0.232051i) q^{17} +1.00000i q^{18} +(3.86603 - 2.23205i) q^{19} +(-0.633975 + 0.366025i) q^{20} -1.00000i q^{21} +(1.86603 + 3.23205i) q^{22} +(1.73205 - 3.00000i) q^{23} +(-0.866025 - 0.500000i) q^{24} +4.46410 q^{25} +(-1.00000 + 3.46410i) q^{26} -1.00000 q^{27} +(0.866025 + 0.500000i) q^{28} +(1.50000 - 2.59808i) q^{29} +(-0.366025 - 0.633975i) q^{30} -7.66025i q^{31} +(0.866025 - 0.500000i) q^{32} +(-3.23205 + 1.86603i) q^{33} -0.267949i q^{34} +(0.366025 + 0.633975i) q^{35} +(0.500000 - 0.866025i) q^{36} +(1.09808 + 0.633975i) q^{37} -4.46410 q^{38} +(-3.46410 - 1.00000i) q^{39} +0.732051 q^{40} +(-6.06218 - 3.50000i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(0.366025 + 0.633975i) q^{43} -3.73205i q^{44} +(0.633975 - 0.366025i) q^{45} +(-3.00000 + 1.73205i) q^{46} +4.46410i q^{47} +(0.500000 + 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-3.86603 - 2.23205i) q^{50} +0.267949 q^{51} +(2.59808 - 2.50000i) q^{52} -10.4641 q^{53} +(0.866025 + 0.500000i) q^{54} +(1.36603 - 2.36603i) q^{55} +(-0.500000 - 0.866025i) q^{56} -4.46410i q^{57} +(-2.59808 + 1.50000i) q^{58} +(0.803848 - 0.464102i) q^{59} +0.732051i q^{60} +(5.86603 + 10.1603i) q^{61} +(-3.83013 + 6.63397i) q^{62} +(-0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(2.56218 - 0.633975i) q^{65} +3.73205 q^{66} +(-11.1962 - 6.46410i) q^{67} +(-0.133975 + 0.232051i) q^{68} +(-1.73205 - 3.00000i) q^{69} -0.732051i q^{70} +(1.90192 - 1.09808i) q^{71} +(-0.866025 + 0.500000i) q^{72} +6.53590i q^{73} +(-0.633975 - 1.09808i) q^{74} +(2.23205 - 3.86603i) q^{75} +(3.86603 + 2.23205i) q^{76} -3.73205 q^{77} +(2.50000 + 2.59808i) q^{78} +10.8564 q^{79} +(-0.633975 - 0.366025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.50000 + 6.06218i) q^{82} -5.66025i q^{83} +(0.866025 - 0.500000i) q^{84} +(-0.169873 + 0.0980762i) q^{85} -0.732051i q^{86} +(-1.50000 - 2.59808i) q^{87} +(-1.86603 + 3.23205i) q^{88} +(5.59808 + 3.23205i) q^{89} -0.732051 q^{90} +(-2.50000 - 2.59808i) q^{91} +3.46410 q^{92} +(-6.63397 - 3.83013i) q^{93} +(2.23205 - 3.86603i) q^{94} +(1.63397 + 2.83013i) q^{95} -1.00000i q^{96} +(0.633975 - 0.366025i) q^{97} +(-0.866025 + 0.500000i) q^{98} +3.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9	$ 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{14} + 6 q^{15} - 2 q^{16} + 4 q^{17} + 12 q^{19} - 6 q^{20} + 4 q^{22} + 4 q^{25} - 4 q^{26} - 4 q^{27} + 6 q^{29} + 2 q^{30} - 6 q^{33} - 2 q^{35} + 2 q^{36} - 6 q^{37} - 4 q^{38} - 4 q^{40} - 2 q^{42} - 2 q^{43} + 6 q^{45} - 12 q^{46} + 2 q^{48} + 2 q^{49} - 12 q^{50} + 8 q^{51} - 28 q^{53} + 2 q^{55} - 2 q^{56} + 24 q^{59} + 20 q^{61} + 2 q^{62} - 4 q^{64} - 14 q^{65} + 8 q^{66} - 24 q^{67} - 4 q^{68} + 18 q^{71} - 6 q^{74} + 2 q^{75} + 12 q^{76} - 8 q^{77} + 10 q^{78} - 12 q^{79} - 6 q^{80} - 2 q^{81} + 14 q^{82} - 18 q^{85} - 6 q^{87} - 4 q^{88} + 12 q^{89} + 4 q^{90} - 10 q^{91} - 30 q^{93} + 2 q^{94} + 10 q^{95} + 6 q^{97}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^10 - 6 * q^11 + 4 * q^12 - 4 * q^14 + 6 * q^15 - 2 * q^16 + 4 * q^17 + 12 * q^19 - 6 * q^20 + 4 * q^22 + 4 * q^25 - 4 * q^26 - 4 * q^27 + 6 * q^29 + 2 * q^30 - 6 * q^33 - 2 * q^35 + 2 * q^36 - 6 * q^37 - 4 * q^38 - 4 * q^40 - 2 * q^42 - 2 * q^43 + 6 * q^45 - 12 * q^46 + 2 * q^48 + 2 * q^49 - 12 * q^50 + 8 * q^51 - 28 * q^53 + 2 * q^55 - 2 * q^56 + 24 * q^59 + 20 * q^61 + 2 * q^62 - 4 * q^64 - 14 * q^65 + 8 * q^66 - 24 * q^67 - 4 * q^68 + 18 * q^71 - 6 * q^74 + 2 * q^75 + 12 * q^76 - 8 * q^77 + 10 * q^78 - 12 * q^79 - 6 * q^80 - 2 * q^81 + 14 * q^82 - 18 * q^85 - 6 * q^87 - 4 * q^88 + 12 * q^89 + 4 * q^90 - 10 * q^91 - 30 * q^93 + 2 * q^94 + 10 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$			0.732051i			0.327383i	0.986512	+	0.163692i	$0.0523402\pi$
$5$			0.732051i			0.327383i	−0.986512	+	0.163692i	$0.947660\pi$
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.366025	−	0.633975i	0.115747	−	0.200480i
$11$	−3.23205	−	1.86603i	−0.974500	−	0.562628i	−0.0738948	−	0.997266i	$-0.523543\pi$
$11$	−3.23205	−	1.86603i	−0.974500	−	0.562628i	−0.900605	+	0.434638i	$0.856876\pi$
$12$	1.00000			0.288675
$13$	−0.866025	−	3.50000i	−0.240192	−	0.970725i
$13$	−0.866025	−	3.50000i	−0.240192	−	0.970725i
$14$	−1.00000			−0.267261
$15$	0.633975	+	0.366025i	0.163692	+	0.0945074i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.133975	+	0.232051i	0.0324936	+	0.0562806i	0.881815	−	0.471596i	$-0.156322\pi$
$17$	0.133975	+	0.232051i	0.0324936	+	0.0562806i	−0.849321	+	0.527876i	$0.822988\pi$
$18$			1.00000i			0.235702i
$19$	3.86603	−	2.23205i	0.886927	−	0.512068i	0.0139909	−	0.999902i	$-0.495546\pi$
$19$	3.86603	−	2.23205i	0.886927	−	0.512068i	0.872936	+	0.487835i	$0.162213\pi$
$20$	−0.633975	+	0.366025i	−0.141761	+	0.0818458i
$21$		−	1.00000i		−	0.218218i
$22$	1.86603	+	3.23205i	0.397838	+	0.689076i
$23$	1.73205	−	3.00000i	0.361158	−	0.625543i	−0.626994	−	0.779024i	$-0.715715\pi$
$23$	1.73205	−	3.00000i	0.361158	−	0.625543i	0.988152	+	0.153481i	$0.0490483\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	4.46410			0.892820
$26$	−1.00000	+	3.46410i	−0.196116	+	0.679366i
$27$	−1.00000			−0.192450
$28$	0.866025	+	0.500000i	0.163663	+	0.0944911i
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$	−0.366025	−	0.633975i	−0.0668268	−	0.115747i
$31$		−	7.66025i		−	1.37582i	−0.725795	−	0.687911i	$-0.758528\pi$
$31$		−	7.66025i		−	1.37582i	0.725795	−	0.687911i	$-0.241472\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−3.23205	+	1.86603i	−0.562628	+	0.324833i
$34$		−	0.267949i		−	0.0459529i
$35$	0.366025	+	0.633975i	0.0618696	+	0.107161i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	1.09808	+	0.633975i	0.180523	+	0.104225i	0.587538	−	0.809196i	$-0.300097\pi$
$37$	1.09808	+	0.633975i	0.180523	+	0.104225i	−0.407016	+	0.913421i	$0.633431\pi$
$38$	−4.46410			−0.724173
$39$	−3.46410	−	1.00000i	−0.554700	−	0.160128i
$40$	0.732051			0.115747
$41$	−6.06218	−	3.50000i	−0.946753	−	0.546608i	−0.0546823	−	0.998504i	$-0.517415\pi$
$41$	−6.06218	−	3.50000i	−0.946753	−	0.546608i	−0.892071	+	0.451896i	$0.850748\pi$
$42$	−0.500000	+	0.866025i	−0.0771517	+	0.133631i
$43$	0.366025	+	0.633975i	0.0558184	+	0.0966802i	0.892584	−	0.450880i	$-0.148890\pi$
$43$	0.366025	+	0.633975i	0.0558184	+	0.0966802i	−0.836766	+	0.547561i	$0.815557\pi$
$44$		−	3.73205i		−	0.562628i
$45$	0.633975	−	0.366025i	0.0945074	−	0.0545638i
$46$	−3.00000	+	1.73205i	−0.442326	+	0.255377i
$47$			4.46410i			0.651156i	0.945515	+	0.325578i	$0.105559\pi$
$47$			4.46410i			0.651156i	−0.945515	+	0.325578i	$0.894441\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	−3.86603	−	2.23205i	−0.546739	−	0.315660i
$51$	0.267949			0.0375204
$52$	2.59808	−	2.50000i	0.360288	−	0.346688i
$53$	−10.4641			−1.43735			−0.718677	−	0.695344i	$-0.755252\pi$
$53$	−10.4641			−1.43735			−0.718677	+	0.695344i	$0.755252\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	1.36603	−	2.36603i	0.184195	−	0.319035i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$		−	4.46410i		−	0.591285i
$58$	−2.59808	+	1.50000i	−0.341144	+	0.196960i
$59$	0.803848	−	0.464102i	0.104652	−	0.0604209i	−0.446760	−	0.894654i	$-0.647422\pi$
$59$	0.803848	−	0.464102i	0.104652	−	0.0604209i	0.551413	+	0.834233i	$0.314089\pi$
$60$			0.732051i			0.0945074i
$61$	5.86603	+	10.1603i	0.751068	+	1.30089i	0.947306	+	0.320331i	$0.103794\pi$
$61$	5.86603	+	10.1603i	0.751068	+	1.30089i	−0.196238	+	0.980556i	$0.562873\pi$
$62$	−3.83013	+	6.63397i	−0.486427	+	0.842516i
$63$	−0.866025	−	0.500000i	−0.109109	−	0.0629941i
$64$	−1.00000			−0.125000
$65$	2.56218	−	0.633975i	0.317799	−	0.0786349i
$66$	3.73205			0.459384
$67$	−11.1962	−	6.46410i	−1.36783	−	0.789716i	−0.377177	−	0.926141i	$-0.623105\pi$
$67$	−11.1962	−	6.46410i	−1.36783	−	0.789716i	−0.990650	+	0.136425i	$0.956439\pi$
$68$	−0.133975	+	0.232051i	−0.0162468	+	0.0281403i
$69$	−1.73205	−	3.00000i	−0.208514	−	0.361158i
$70$		−	0.732051i		−	0.0874968i
$71$	1.90192	−	1.09808i	0.225717	−	0.130318i	−0.382878	−	0.923799i	$-0.625067\pi$
$71$	1.90192	−	1.09808i	0.225717	−	0.130318i	0.608595	+	0.793481i	$0.291734\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$			6.53590i			0.764969i	0.923962	+	0.382485i	$0.124931\pi$
$73$			6.53590i			0.764969i	−0.923962	+	0.382485i	$0.875069\pi$
$74$	−0.633975	−	1.09808i	−0.0736980	−	0.127649i
$75$	2.23205	−	3.86603i	0.257735	−	0.446410i
$76$	3.86603	+	2.23205i	0.443464	+	0.256034i
$77$	−3.73205			−0.425307
$78$	2.50000	+	2.59808i	0.283069	+	0.294174i
$79$	10.8564			1.22144			0.610721	−	0.791846i	$-0.290880\pi$
$79$	10.8564			1.22144			0.610721	+	0.791846i	$0.290880\pi$
$80$	−0.633975	−	0.366025i	−0.0708805	−	0.0409229i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.50000	+	6.06218i	0.386510	+	0.669456i
$83$		−	5.66025i		−	0.621294i	−0.950525	−	0.310647i	$-0.899454\pi$
$83$		−	5.66025i		−	0.621294i	0.950525	−	0.310647i	$-0.100546\pi$
$84$	0.866025	−	0.500000i	0.0944911	−	0.0545545i
$85$	−0.169873	+	0.0980762i	−0.0184253	+	0.0106379i
$86$		−	0.732051i		−	0.0789391i
$87$	−1.50000	−	2.59808i	−0.160817	−	0.278543i
$88$	−1.86603	+	3.23205i	−0.198919	+	0.344538i
$89$	5.59808	+	3.23205i	0.593395	+	0.342597i	0.766439	−	0.642317i	$-0.222027\pi$
$89$	5.59808	+	3.23205i	0.593395	+	0.342597i	−0.173044	+	0.984914i	$0.555360\pi$
$90$	−0.732051			−0.0771649
$91$	−2.50000	−	2.59808i	−0.262071	−	0.272352i
$92$	3.46410			0.361158
$93$	−6.63397	−	3.83013i	−0.687911	−	0.397166i
$94$	2.23205	−	3.86603i	0.230218	−	0.398750i
$95$	1.63397	+	2.83013i	0.167642	+	0.290365i
$96$		−	1.00000i		−	0.102062i
$97$	0.633975	−	0.366025i	0.0643704	−	0.0371642i	−0.467469	−	0.884009i	$-0.654834\pi$
$97$	0.633975	−	0.366025i	0.0643704	−	0.0371642i	0.531840	+	0.846845i	$0.321501\pi$
$98$	−0.866025	+	0.500000i	−0.0874818	+	0.0505076i
$99$			3.73205i			0.375085i
$100$	2.23205	+	3.86603i	0.223205	+	0.386603i
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$	−0.232051	−	0.133975i	−0.0229765	−	0.0132655i
$103$	12.1962			1.20172			0.600861	−	0.799353i	$-0.294824\pi$
$103$	12.1962			1.20172			0.600861	+	0.799353i	$0.294824\pi$
$104$	−3.50000	+	0.866025i	−0.343203	+	0.0849208i
$105$	0.732051			0.0714408
$106$	9.06218	+	5.23205i	0.880197	+	0.508182i
$107$	0.767949	−	1.33013i	0.0742405	−	0.128588i	−0.826515	−	0.562914i	$-0.809680\pi$
$107$	0.767949	−	1.33013i	0.0742405	−	0.128588i	0.900756	+	0.434326i	$0.143013\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$		−	3.66025i		−	0.350589i	−0.984516	−	0.175294i	$-0.943912\pi$
$109$		−	3.66025i		−	0.350589i	0.984516	−	0.175294i	$-0.0560877\pi$
$110$	−2.36603	+	1.36603i	−0.225592	+	0.130245i
$111$	1.09808	−	0.633975i	0.104225	−	0.0601742i
$112$			1.00000i			0.0944911i
$113$	5.09808	+	8.83013i	0.479587	+	0.830668i	0.999726	−	0.0234130i	$-0.00745328\pi$
$113$	5.09808	+	8.83013i	0.479587	+	0.830668i	−0.520139	+	0.854081i	$0.674120\pi$
$114$	−2.23205	+	3.86603i	−0.209051	+	0.362086i
$115$	2.19615	+	1.26795i	0.204792	+	0.118237i
$116$	3.00000			0.278543
$117$	−2.59808	+	2.50000i	−0.240192	+	0.231125i
$118$	−0.928203			−0.0854480
$119$	0.232051	+	0.133975i	0.0212721	+	0.0122814i
$120$	0.366025	−	0.633975i	0.0334134	−	0.0578737i
$121$	1.46410	+	2.53590i	0.133100	+	0.230536i
$122$		−	11.7321i		−	1.06217i
$123$	−6.06218	+	3.50000i	−0.546608	+	0.315584i
$124$	6.63397	−	3.83013i	0.595749	−	0.343956i
$125$			6.92820i			0.619677i
$126$	0.500000	+	0.866025i	0.0445435	+	0.0771517i
$127$	−6.26795	+	10.8564i	−0.556191	+	0.963350i	0.441619	+	0.897203i	$0.354404\pi$
$127$	−6.26795	+	10.8564i	−0.556191	+	0.963350i	−0.997810	+	0.0661478i	$0.978929\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	0.732051			0.0644535
$130$	−2.53590	−	0.732051i	−0.222413	−	0.0642051i
$131$	18.9282			1.65376			0.826882	−	0.562375i	$-0.190112\pi$
$131$	18.9282			1.65376			0.826882	+	0.562375i	$0.190112\pi$
$132$	−3.23205	−	1.86603i	−0.281314	−	0.162417i
$133$	2.23205	−	3.86603i	0.193543	−	0.335227i
$134$	6.46410	+	11.1962i	0.558413	+	0.967200i
$135$		−	0.732051i		−	0.0630049i
$136$	0.232051	−	0.133975i	0.0198982	−	0.0114882i
$137$	13.3923	−	7.73205i	1.14418	−	0.660594i	0.196719	−	0.980460i	$-0.436971\pi$
$137$	13.3923	−	7.73205i	1.14418	−	0.660594i	0.947463	+	0.319866i	$0.103638\pi$
$138$			3.46410i			0.294884i
$139$	9.06218	+	15.6962i	0.768644	+	1.33133i	0.938298	+	0.345827i	$0.112401\pi$
$139$	9.06218	+	15.6962i	0.768644	+	1.33133i	−0.169655	+	0.985504i	$0.554265\pi$
$140$	−0.366025	+	0.633975i	−0.0309348	+	0.0535806i
$141$	3.86603	+	2.23205i	0.325578	+	0.187973i
$142$	−2.19615			−0.184297
$143$	−3.73205	+	12.9282i	−0.312090	+	1.08111i
$144$	1.00000			0.0833333
$145$	1.90192	+	1.09808i	0.157946	+	0.0911903i
$146$	3.26795	−	5.66025i	0.270457	−	0.468446i
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$			1.26795i			0.104225i
$149$	−16.3923	+	9.46410i	−1.34291	+	0.775329i	−0.987233	−	0.159280i	$-0.949083\pi$
$149$	−16.3923	+	9.46410i	−1.34291	+	0.775329i	−0.355676	+	0.934609i	$0.615749\pi$
$150$	−3.86603	+	2.23205i	−0.315660	+	0.182246i
$151$			13.1962i			1.07389i	0.843618	+	0.536944i	$0.180421\pi$
$151$			13.1962i			1.07389i	−0.843618	+	0.536944i	$0.819579\pi$
$152$	−2.23205	−	3.86603i	−0.181043	−	0.313576i
$153$	0.133975	−	0.232051i	0.0108312	−	0.0187602i
$154$	3.23205	+	1.86603i	0.260446	+	0.150369i
$155$	5.60770			0.450421
$156$	−0.866025	−	3.50000i	−0.0693375	−	0.280224i
$157$	−15.4641			−1.23417			−0.617085	−	0.786897i	$-0.711686\pi$
$157$	−15.4641			−1.23417			−0.617085	+	0.786897i	$0.711686\pi$
$158$	−9.40192	−	5.42820i	−0.747977	−	0.431845i
$159$	−5.23205	+	9.06218i	−0.414929	+	0.718677i
$160$	0.366025	+	0.633975i	0.0289368	+	0.0501201i
$161$		−	3.46410i		−	0.273009i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	−6.75833	+	3.90192i	−0.529353	+	0.305622i	−0.740753	−	0.671777i	$-0.765531\pi$
$163$	−6.75833	+	3.90192i	−0.529353	+	0.305622i	0.211400	+	0.977400i	$0.432198\pi$
$164$		−	7.00000i		−	0.546608i
$165$	−1.36603	−	2.36603i	−0.106345	−	0.184195i
$166$	−2.83013	+	4.90192i	−0.219660	+	0.380463i
$167$	5.07180	+	2.92820i	0.392467	+	0.226591i	0.683229	−	0.730204i	$-0.260575\pi$
$167$	5.07180	+	2.92820i	0.392467	+	0.226591i	−0.290761	+	0.956796i	$0.593909\pi$
$168$	−1.00000			−0.0771517
$169$	−11.5000	+	6.06218i	−0.884615	+	0.466321i
$170$	0.196152			0.0150442
$171$	−3.86603	−	2.23205i	−0.295642	−	0.170689i
$172$	−0.366025	+	0.633975i	−0.0279092	+	0.0483401i
$173$	10.3660	+	17.9545i	0.788114	+	1.36505i	0.927121	+	0.374763i	$0.122276\pi$
$173$	10.3660	+	17.9545i	0.788114	+	1.36505i	−0.139007	+	0.990291i	$0.544391\pi$
$174$			3.00000i			0.227429i
$175$	3.86603	−	2.23205i	0.292244	−	0.168727i
$176$	3.23205	−	1.86603i	0.243625	−	0.140657i
$177$		−	0.928203i		−	0.0697680i
$178$	−3.23205	−	5.59808i	−0.242252	−	0.419594i
$179$	11.1962	−	19.3923i	0.836840	−	1.44945i	−0.0556840	−	0.998448i	$-0.517734\pi$
$179$	11.1962	−	19.3923i	0.836840	−	1.44945i	0.892524	−	0.451000i	$-0.148933\pi$
$180$	0.633975	+	0.366025i	0.0472537	+	0.0272819i
$181$	−1.19615			−0.0889093			−0.0444547	−	0.999011i	$-0.514155\pi$
$181$	−1.19615			−0.0889093			−0.0444547	+	0.999011i	$0.514155\pi$
$182$	0.866025	+	3.50000i	0.0641941	+	0.259437i
$183$	11.7321			0.867258
$184$	−3.00000	−	1.73205i	−0.221163	−	0.127688i
$185$	−0.464102	+	0.803848i	−0.0341214	+	0.0591000i
$186$	3.83013	+	6.63397i	0.280839	+	0.486427i
$187$		−	1.00000i		−	0.0731272i
$188$	−3.86603	+	2.23205i	−0.281959	+	0.162789i
$189$	−0.866025	+	0.500000i	−0.0629941	+	0.0363696i
$190$		−	3.26795i		−	0.237082i
$191$	2.09808	+	3.63397i	0.151811	+	0.262945i	0.931893	−	0.362732i	$-0.118156\pi$
$191$	2.09808	+	3.63397i	0.151811	+	0.262945i	−0.780082	+	0.625677i	$0.784823\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−14.8923	−	8.59808i	−1.07197	−	0.618903i	−0.143252	−	0.989686i	$-0.545756\pi$
$193$	−14.8923	−	8.59808i	−1.07197	−	0.618903i	−0.928719	+	0.370783i	$0.879089\pi$
$194$	−0.732051			−0.0525582
$195$	0.732051	−	2.53590i	0.0524232	−	0.181599i
$196$	1.00000			0.0714286
$197$	1.96410	+	1.13397i	0.139936	+	0.0807923i	0.568334	−	0.822798i	$-0.307588\pi$
$197$	1.96410	+	1.13397i	0.139936	+	0.0807923i	−0.428397	+	0.903591i	$0.640922\pi$
$198$	1.86603	−	3.23205i	0.132613	−	0.229692i
$199$	−2.09808	−	3.63397i	−0.148729	−	0.257606i	0.782029	−	0.623242i	$-0.214185\pi$
$199$	−2.09808	−	3.63397i	−0.148729	−	0.257606i	−0.930758	+	0.365636i	$0.880851\pi$
$200$		−	4.46410i		−	0.315660i
$201$	−11.1962	+	6.46410i	−0.789716	+	0.455943i
$202$	8.66025	−	5.00000i	0.609333	−	0.351799i
$203$		−	3.00000i		−	0.210559i
$204$	0.133975	+	0.232051i	0.00938010	+	0.0162468i
$205$	2.56218	−	4.43782i	0.178950	−	0.309951i
$206$	−10.5622	−	6.09808i	−0.735902	−	0.424873i
$207$	−3.46410			−0.240772
$208$	3.46410	+	1.00000i	0.240192	+	0.0693375i
$209$	−16.6603			−1.15241
$210$	−0.633975	−	0.366025i	−0.0437484	−	0.0252582i
$211$	7.92820	−	13.7321i	0.545800	−	0.945353i	−0.452756	−	0.891634i	$-0.649559\pi$
$211$	7.92820	−	13.7321i	0.545800	−	0.945353i	0.998556	−	0.0537189i	$-0.0171075\pi$
$212$	−5.23205	−	9.06218i	−0.359339	−	0.622393i
$213$		−	2.19615i		−	0.150478i
$214$	−1.33013	+	0.767949i	−0.0909256	+	0.0524959i
$215$	−0.464102	+	0.267949i	−0.0316515	+	0.0182740i
$216$			1.00000i			0.0680414i
$217$	−3.83013	−	6.63397i	−0.260006	−	0.450344i
$218$	−1.83013	+	3.16987i	−0.123952	+	0.214691i
$219$	5.66025	+	3.26795i	0.382485	+	0.220828i
$220$	2.73205			0.184195
$221$	0.696152	−	0.669873i	0.0468283	−	0.0450605i
$222$	−1.26795			−0.0850992
$223$	7.26795	+	4.19615i	0.486698	+	0.280995i	0.723204	−	0.690635i	$-0.242669\pi$
$223$	7.26795	+	4.19615i	0.486698	+	0.280995i	−0.236506	+	0.971630i	$0.576002\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$	−2.23205	−	3.86603i	−0.148803	−	0.257735i
$226$		−	10.1962i		−	0.678238i
$227$	7.39230	−	4.26795i	0.490645	−	0.283274i	−0.234197	−	0.972189i	$-0.575246\pi$
$227$	7.39230	−	4.26795i	0.490645	−	0.283274i	0.724842	+	0.688915i	$0.241913\pi$
$228$	3.86603	−	2.23205i	0.256034	−	0.147821i
$229$		−	10.3205i		−	0.681998i	−0.940064	−	0.340999i	$-0.889235\pi$
$229$		−	10.3205i		−	0.681998i	0.940064	−	0.340999i	$-0.110765\pi$
$230$	−1.26795	−	2.19615i	−0.0836061	−	0.144810i
$231$	−1.86603	+	3.23205i	−0.122775	+	0.212653i
$232$	−2.59808	−	1.50000i	−0.170572	−	0.0984798i
$233$	−2.19615			−0.143875			−0.0719374	−	0.997409i	$-0.522918\pi$
$233$	−2.19615			−0.143875			−0.0719374	+	0.997409i	$0.522918\pi$
$234$	3.50000	−	0.866025i	0.228802	−	0.0566139i
$235$	−3.26795			−0.213177
$236$	0.803848	+	0.464102i	0.0523260	+	0.0302104i
$237$	5.42820	−	9.40192i	0.352600	−	0.610721i
$238$	−0.133975	−	0.232051i	−0.00868428	−	0.0150416i
$239$		−	13.8038i		−	0.892897i	−0.894809	−	0.446448i	$-0.852689\pi$
$239$		−	13.8038i		−	0.892897i	0.894809	−	0.446448i	$-0.147311\pi$
$240$	−0.633975	+	0.366025i	−0.0409229	+	0.0236268i
$241$	−11.0718	+	6.39230i	−0.713197	+	0.411765i	−0.812244	−	0.583318i	$-0.801754\pi$
$241$	−11.0718	+	6.39230i	−0.713197	+	0.411765i	0.0990466	+	0.995083i	$0.468421\pi$
$242$		−	2.92820i		−	0.188232i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−5.86603	+	10.1603i	−0.375534	+	0.650444i
$245$	0.633975	+	0.366025i	0.0405032	+	0.0233845i
$246$	7.00000			0.446304
$247$	−11.1603	−	11.5981i	−0.710110	−	0.737968i
$248$	−7.66025			−0.486427
$249$	−4.90192	−	2.83013i	−0.310647	−	0.179352i
$250$	3.46410	−	6.00000i	0.219089	−	0.379473i
$251$	9.09808	+	15.7583i	0.574265	+	0.994657i	0.996121	+	0.0879939i	$0.0280456\pi$
$251$	9.09808	+	15.7583i	0.574265	+	0.994657i	−0.421856	+	0.906663i	$0.638621\pi$
$252$		−	1.00000i		−	0.0629941i
$253$	−11.1962	+	6.46410i	−0.703896	+	0.406395i
$254$	10.8564	−	6.26795i	0.681192	−	0.393286i
$255$			0.196152i			0.0122835i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.52628	−	9.57180i	0.344720	−	0.597072i	−0.640583	−	0.767889i	$-0.721307\pi$
$257$	5.52628	−	9.57180i	0.344720	−	0.597072i	0.985303	+	0.170817i	$0.0546406\pi$
$258$	−0.633975	−	0.366025i	−0.0394695	−	0.0227877i
$259$	1.26795			0.0787865
$260$	1.83013	+	1.90192i	0.113500	+	0.117952i
$261$	−3.00000			−0.185695
$262$	−16.3923	−	9.46410i	−1.01272	−	0.584694i
$263$	9.36603	−	16.2224i	0.577534	−	1.00032i	−0.418227	−	0.908342i	$-0.637348\pi$
$263$	9.36603	−	16.2224i	0.577534	−	1.00032i	0.995761	−	0.0919756i	$-0.0293182\pi$
$264$	1.86603	+	3.23205i	0.114846	+	0.198919i
$265$		−	7.66025i		−	0.470566i
$266$	−3.86603	+	2.23205i	−0.237041	+	0.136856i
$267$	5.59808	−	3.23205i	0.342597	−	0.197798i
$268$		−	12.9282i		−	0.789716i
$269$	11.8564	+	20.5359i	0.722898	+	1.25210i	0.959833	+	0.280570i	$0.0905236\pi$
$269$	11.8564	+	20.5359i	0.722898	+	1.25210i	−0.236936	+	0.971525i	$0.576143\pi$
$270$	−0.366025	+	0.633975i	−0.0222756	+	0.0385825i
$271$	18.6340	+	10.7583i	1.13193	+	0.653522i	0.944420	−	0.328740i	$-0.106624\pi$
$271$	18.6340	+	10.7583i	1.13193	+	0.653522i	0.187513	+	0.982262i	$0.439957\pi$
$272$	−0.267949			−0.0162468
$273$	−3.50000	+	0.866025i	−0.211830	+	0.0524142i
$274$	−15.4641			−0.934221
$275$	−14.4282	−	8.33013i	−0.870053	−	0.502326i
$276$	1.73205	−	3.00000i	0.104257	−	0.180579i
$277$	−13.1962	−	22.8564i	−0.792880	−	1.37331i	−0.924177	−	0.381965i	$-0.875247\pi$
$277$	−13.1962	−	22.8564i	−0.792880	−	1.37331i	0.131297	−	0.991343i	$-0.458086\pi$
$278$		−	18.1244i		−	1.08703i
$279$	−6.63397	+	3.83013i	−0.397166	+	0.229304i
$280$	0.633975	−	0.366025i	0.0378872	−	0.0218742i
$281$			18.1962i			1.08549i	0.839897	+	0.542746i	$0.182615\pi$
$281$			18.1962i			1.08549i	−0.839897	+	0.542746i	$0.817385\pi$
$282$	−2.23205	−	3.86603i	−0.132917	−	0.230218i
$283$	−11.4641	+	19.8564i	−0.681470	+	1.18034i	0.293062	+	0.956093i	$0.405326\pi$
$283$	−11.4641	+	19.8564i	−0.681470	+	1.18034i	−0.974532	+	0.224247i	$0.928008\pi$
$284$	1.90192	+	1.09808i	0.112858	+	0.0651588i
$285$	3.26795			0.193577
$286$	9.69615	−	9.33013i	0.573346	−	0.551702i
$287$	−7.00000			−0.413197
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	8.46410	−	14.6603i	0.497888	−	0.862368i
$290$	−1.09808	−	1.90192i	−0.0644813	−	0.111685i
$291$		−	0.732051i		−	0.0429136i
$292$	−5.66025	+	3.26795i	−0.331241	+	0.191242i
$293$	−11.0718	+	6.39230i	−0.646821	+	0.373442i	−0.787237	−	0.616650i	$-0.788489\pi$
$293$	−11.0718	+	6.39230i	−0.646821	+	0.373442i	0.140416	+	0.990093i	$0.455156\pi$
$294$			1.00000i			0.0583212i
$295$	0.339746	+	0.588457i	0.0197808	+	0.0342613i
$296$	0.633975	−	1.09808i	0.0368490	−	0.0638244i
$297$	3.23205	+	1.86603i	0.187543	+	0.108278i
$298$	18.9282			1.09648
$299$	−12.0000	−	3.46410i	−0.693978	−	0.200334i
$300$	4.46410			0.257735
$301$	0.633975	+	0.366025i	0.0365417	+	0.0210974i
$302$	6.59808	−	11.4282i	0.379677	−	0.657619i
$303$	5.00000	+	8.66025i	0.287242	+	0.497519i
$304$			4.46410i			0.256034i
$305$	−7.43782	+	4.29423i	−0.425888	+	0.245887i
$306$	−0.232051	+	0.133975i	−0.0132655	+	0.00765882i
$307$		−	33.7846i		−	1.92819i	−0.265558	−	0.964095i	$-0.585556\pi$
$307$		−	33.7846i		−	1.92819i	0.265558	−	0.964095i	$-0.414444\pi$
$308$	−1.86603	−	3.23205i	−0.106327	−	0.184163i
$309$	6.09808	−	10.5622i	0.346907	−	0.600861i
$310$	−4.85641	−	2.80385i	−0.275825	−	0.159248i
$311$	19.1962			1.08851			0.544257	−	0.838919i	$-0.316812\pi$
$311$	19.1962			1.08851			0.544257	+	0.838919i	$0.316812\pi$
$312$	−1.00000	+	3.46410i	−0.0566139	+	0.196116i
$313$	1.80385			0.101959			0.0509797	−	0.998700i	$-0.483766\pi$
$313$	1.80385			0.101959			0.0509797	+	0.998700i	$0.483766\pi$
$314$	13.3923	+	7.73205i	0.755771	+	0.436345i
$315$	0.366025	−	0.633975i	0.0206232	−	0.0357204i
$316$	5.42820	+	9.40192i	0.305360	+	0.528900i
$317$		−	18.0000i		−	1.01098i	−0.862832	−	0.505490i	$-0.831312\pi$
$317$		−	18.0000i		−	1.01098i	0.862832	−	0.505490i	$-0.168688\pi$
$318$	9.06218	−	5.23205i	0.508182	−	0.293399i
$319$	−9.69615	+	5.59808i	−0.542880	+	0.313432i
$320$		−	0.732051i		−	0.0409229i
$321$	−0.767949	−	1.33013i	−0.0428627	−	0.0742405i
$322$	−1.73205	+	3.00000i	−0.0965234	+	0.167183i
$323$	1.03590	+	0.598076i	0.0576389	+	0.0332779i
$324$	−1.00000			−0.0555556
$325$	−3.86603	−	15.6244i	−0.214449	−	0.866683i
$326$	7.80385			0.432215
$327$	−3.16987	−	1.83013i	−0.175294	−	0.101206i
$328$	−3.50000	+	6.06218i	−0.193255	+	0.334728i
$329$	2.23205	+	3.86603i	0.123057	+	0.213141i
$330$			2.73205i			0.150394i
$331$	−14.6603	+	8.46410i	−0.805800	+	0.465229i	−0.845495	−	0.533983i	$-0.820695\pi$
$331$	−14.6603	+	8.46410i	−0.805800	+	0.465229i	0.0396949	+	0.999212i	$0.487361\pi$
$332$	4.90192	−	2.83013i	0.269028	−	0.155323i
$333$		−	1.26795i		−	0.0694832i
$334$	−2.92820	−	5.07180i	−0.160224	−	0.277516i
$335$	4.73205	−	8.19615i	0.258540	−	0.447804i
$336$	0.866025	+	0.500000i	0.0472456	+	0.0272772i
$337$	−27.7846			−1.51352			−0.756762	−	0.653690i	$-0.773220\pi$
$337$	−27.7846			−1.51352			−0.756762	+	0.653690i	$0.773220\pi$
$338$	12.9904	+	0.500000i	0.706584	+	0.0271964i
$339$	10.1962			0.553779
$340$	−0.169873	−	0.0980762i	−0.00921266	−	0.00531893i
$341$	−14.2942	+	24.7583i	−0.774076	+	1.34074i
$342$	2.23205	+	3.86603i	0.120695	+	0.209051i
$343$		−	1.00000i		−	0.0539949i
$344$	0.633975	−	0.366025i	0.0341816	−	0.0197348i
$345$	2.19615	−	1.26795i	0.118237	−	0.0682641i
$346$		−	20.7321i		−	1.11456i
$347$	−11.4282	−	19.7942i	−0.613498	−	1.06261i	−0.990646	−	0.136457i	$-0.956429\pi$
$347$	−11.4282	−	19.7942i	−0.613498	−	1.06261i	0.377148	−	0.926153i	$-0.376905\pi$
$348$	1.50000	−	2.59808i	0.0804084	−	0.139272i
$349$	20.5359	+	11.8564i	1.09926	+	0.634659i	0.936027	−	0.351928i	$-0.114474\pi$
$349$	20.5359	+	11.8564i	1.09926	+	0.634659i	0.163235	+	0.986587i	$0.447807\pi$
$350$	−4.46410			−0.238616
$351$	0.866025	+	3.50000i	0.0462250	+	0.186816i
$352$	−3.73205			−0.198919
$353$	−1.26795	−	0.732051i	−0.0674861	−	0.0389631i	0.465877	−	0.884849i	$-0.345739\pi$
$353$	−1.26795	−	0.732051i	−0.0674861	−	0.0389631i	−0.533363	+	0.845886i	$0.679072\pi$
$354$	−0.464102	+	0.803848i	−0.0246667	+	0.0427240i
$355$	0.803848	+	1.39230i	0.0426638	+	0.0738959i
$356$			6.46410i			0.342597i
$357$	0.232051	−	0.133975i	0.0122814	−	0.00709069i
$358$	−19.3923	+	11.1962i	−1.02492	+	0.591735i
$359$			15.8038i			0.834095i	0.908885	+	0.417048i	$0.136935\pi$
$359$			15.8038i			0.834095i	−0.908885	+	0.417048i	$0.863065\pi$
$360$	−0.366025	−	0.633975i	−0.0192912	−	0.0334134i
$361$	0.464102	−	0.803848i	0.0244264	−	0.0423078i
$362$	1.03590	+	0.598076i	0.0544456	+	0.0314342i
$363$	2.92820			0.153691
$364$	1.00000	−	3.46410i	0.0524142	−	0.181568i
$365$	−4.78461			−0.250438
$366$	−10.1603	−	5.86603i	−0.531085	−	0.306622i
$367$	−8.12436	+	14.0718i	−0.424088	+	0.734542i	−0.996335	−	0.0855396i	$-0.972739\pi$
$367$	−8.12436	+	14.0718i	−0.424088	+	0.734542i	0.572247	+	0.820081i	$0.306072\pi$
$368$	1.73205	+	3.00000i	0.0902894	+	0.156386i
$369$			7.00000i			0.364405i
$370$	0.803848	−	0.464102i	0.0417900	−	0.0241275i
$371$	−9.06218	+	5.23205i	−0.470485	+	0.271635i
$372$		−	7.66025i		−	0.397166i
$373$	10.2942	+	17.8301i	0.533015	+	0.923209i	0.999257	+	0.0385516i	$0.0122744\pi$
$373$	10.2942	+	17.8301i	0.533015	+	0.923209i	−0.466242	+	0.884657i	$0.654392\pi$
$374$	−0.500000	+	0.866025i	−0.0258544	+	0.0447811i
$375$	6.00000	+	3.46410i	0.309839	+	0.178885i
$376$	4.46410			0.230218
$377$	−10.3923	−	3.00000i	−0.535231	−	0.154508i
$378$	1.00000			0.0514344
$379$	−12.6340	−	7.29423i	−0.648964	−	0.374679i	0.139095	−	0.990279i	$-0.455581\pi$
$379$	−12.6340	−	7.29423i	−0.648964	−	0.374679i	−0.788059	+	0.615600i	$0.788914\pi$
$380$	−1.63397	+	2.83013i	−0.0838211	+	0.145182i
$381$	6.26795	+	10.8564i	0.321117	+	0.556191i
$382$		−	4.19615i		−	0.214694i
$383$	12.6506	−	7.30385i	0.646417	−	0.373209i	−0.140665	−	0.990057i	$-0.544924\pi$
$383$	12.6506	−	7.30385i	0.646417	−	0.373209i	0.787082	+	0.616848i	$0.211591\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$		−	2.73205i		−	0.139238i
$386$	8.59808	+	14.8923i	0.437631	+	0.757998i
$387$	0.366025	−	0.633975i	0.0186061	−	0.0322267i
$388$	0.633975	+	0.366025i	0.0321852	+	0.0185821i
$389$	33.1769			1.68214			0.841068	−	0.540929i	$-0.181927\pi$
$389$	33.1769			1.68214			0.841068	+	0.540929i	$0.181927\pi$
$390$	−1.90192	+	1.83013i	−0.0963077	+	0.0926721i
$391$	0.928203			0.0469413
$392$	−0.866025	−	0.500000i	−0.0437409	−	0.0252538i
$393$	9.46410	−	16.3923i	0.477401	−	0.826882i
$394$	−1.13397	−	1.96410i	−0.0571288	−	0.0989500i
$395$			7.94744i			0.399879i
$396$	−3.23205	+	1.86603i	−0.162417	+	0.0937713i
$397$	−14.2583	+	8.23205i	−0.715605	+	0.413155i	−0.813133	−	0.582078i	$-0.802240\pi$
$397$	−14.2583	+	8.23205i	−0.715605	+	0.413155i	0.0975279	+	0.995233i	$0.468906\pi$
$398$			4.19615i			0.210334i
$399$	−2.23205	−	3.86603i	−0.111742	−	0.193543i
$400$	−2.23205	+	3.86603i	−0.111603	+	0.193301i
$401$	−8.66025	−	5.00000i	−0.432472	−	0.249688i	0.267927	−	0.963439i	$-0.413661\pi$
$401$	−8.66025	−	5.00000i	−0.432472	−	0.249688i	−0.700399	+	0.713751i	$0.746995\pi$
$402$	12.9282			0.644800
$403$	−26.8109	+	6.63397i	−1.33555	+	0.330462i
$404$	−10.0000			−0.497519
$405$	−0.633975	−	0.366025i	−0.0315025	−	0.0181879i
$406$	−1.50000	+	2.59808i	−0.0744438	+	0.128940i
$407$	−2.36603	−	4.09808i	−0.117280	−	0.203134i
$408$		−	0.267949i		−	0.0132655i
$409$	11.4904	−	6.63397i	0.568163	−	0.328029i	−0.188252	−	0.982121i	$-0.560282\pi$
$409$	11.4904	−	6.63397i	0.568163	−	0.328029i	0.756415	+	0.654092i	$0.226949\pi$
$410$	−4.43782	+	2.56218i	−0.219168	+	0.126537i
$411$		−	15.4641i		−	0.762788i
$412$	6.09808	+	10.5622i	0.300431	+	0.520361i
$413$	0.464102	−	0.803848i	0.0228369	−	0.0395548i
$414$	3.00000	+	1.73205i	0.147442	+	0.0851257i
$415$	4.14359			0.203401
$416$	−2.50000	−	2.59808i	−0.122573	−	0.127381i
$417$	18.1244			0.887554
$418$	14.4282	+	8.33013i	0.705706	+	0.407440i
$419$	3.09808	−	5.36603i	0.151351	−	0.262147i	−0.780373	−	0.625314i	$-0.784971\pi$
$419$	3.09808	−	5.36603i	0.151351	−	0.262147i	0.931724	+	0.363166i	$0.118304\pi$
$420$	0.366025	+	0.633975i	0.0178602	+	0.0309348i
$421$		−	14.3923i		−	0.701438i	−0.936481	−	0.350719i	$-0.885937\pi$
$421$		−	14.3923i		−	0.701438i	0.936481	−	0.350719i	$-0.114063\pi$
$422$	−13.7321	+	7.92820i	−0.668466	+	0.385939i
$423$	3.86603	−	2.23205i	0.187973	−	0.108526i
$424$			10.4641i			0.508182i
$425$	0.598076	+	1.03590i	0.0290110	+	0.0502485i
$426$	−1.09808	+	1.90192i	−0.0532020	+	0.0921485i
$427$	10.1603	+	5.86603i	0.491689	+	0.283877i
$428$	1.53590			0.0742405
$429$	9.33013	+	9.69615i	0.450463	+	0.468135i
$430$	0.535898			0.0258433
$431$	18.2942	+	10.5622i	0.881202	+	0.508762i	0.871055	−	0.491186i	$-0.163437\pi$
$431$	18.2942	+	10.5622i	0.881202	+	0.508762i	0.0101474	+	0.999949i	$0.496770\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	4.46410	+	7.73205i	0.214531	+	0.371579i	0.953127	−	0.302569i	$-0.0978444\pi$
$433$	4.46410	+	7.73205i	0.214531	+	0.371579i	−0.738596	+	0.674148i	$0.764511\pi$
$434$			7.66025i			0.367704i
$435$	1.90192	−	1.09808i	0.0911903	−	0.0526487i
$436$	3.16987	−	1.83013i	0.151809	−	0.0876472i
$437$		−	15.4641i		−	0.739748i
$438$	−3.26795	−	5.66025i	−0.156149	−	0.270457i
$439$	−8.19615	+	14.1962i	−0.391181	+	0.677545i	−0.992606	−	0.121384i	$-0.961267\pi$
$439$	−8.19615	+	14.1962i	−0.391181	+	0.677545i	0.601425	+	0.798930i	$0.294600\pi$
$440$	−2.36603	−	1.36603i	−0.112796	−	0.0651227i
$441$	−1.00000			−0.0476190
$442$	−0.937822	+	0.232051i	−0.0446077	+	0.0110375i
$443$	−31.3923			−1.49149			−0.745747	−	0.666230i	$-0.767907\pi$
$443$	−31.3923			−1.49149			−0.745747	+	0.666230i	$0.767907\pi$
$444$	1.09808	+	0.633975i	0.0521124	+	0.0300871i
$445$	−2.36603	+	4.09808i	−0.112160	+	0.194267i
$446$	−4.19615	−	7.26795i	−0.198694	−	0.344147i
$447$			18.9282i			0.895273i
$448$	−0.866025	+	0.500000i	−0.0409159	+	0.0236228i
$449$	−9.29423	+	5.36603i	−0.438622	+	0.253238i	−0.703013	−	0.711177i	$-0.748162\pi$
$449$	−9.29423	+	5.36603i	−0.438622	+	0.253238i	0.264391	+	0.964416i	$0.414829\pi$
$450$			4.46410i			0.210440i
$451$	13.0622	+	22.6244i	0.615074	+	1.06534i
$452$	−5.09808	+	8.83013i	−0.239793	+	0.415334i
$453$	11.4282	+	6.59808i	0.536944	+	0.310005i
$454$	−8.53590			−0.400610
$455$	1.90192	−	1.83013i	0.0891636	−	0.0857977i
$456$	−4.46410			−0.209051
$457$	5.87564	+	3.39230i	0.274851	+	0.158685i	0.631090	−	0.775710i	$-0.282608\pi$
$457$	5.87564	+	3.39230i	0.274851	+	0.158685i	−0.356239	+	0.934395i	$0.615941\pi$
$458$	−5.16025	+	8.93782i	−0.241123	+	0.417637i
$459$	−0.133975	−	0.232051i	−0.00625340	−	0.0108312i
$460$			2.53590i			0.118237i
$461$	−24.0000	+	13.8564i	−1.11779	+	0.645357i	−0.940836	−	0.338862i	$-0.889958\pi$
$461$	−24.0000	+	13.8564i	−1.11779	+	0.645357i	−0.176955	+	0.984219i	$0.556625\pi$
$462$	3.23205	−	1.86603i	0.150369	−	0.0868154i
$463$		−	1.19615i		−	0.0555899i	−0.999614	−	0.0277950i	$-0.991151\pi$
$463$		−	1.19615i		−	0.0555899i	0.999614	−	0.0277950i	$-0.00884855\pi$
$464$	1.50000	+	2.59808i	0.0696358	+	0.120613i
$465$	2.80385	−	4.85641i	0.130025	−	0.225210i
$466$	1.90192	+	1.09808i	0.0881049	+	0.0508674i
$467$	9.85641			0.456100			0.228050	−	0.973649i	$-0.426765\pi$
$467$	9.85641			0.456100			0.228050	+	0.973649i	$0.426765\pi$
$468$	−3.46410	−	1.00000i	−0.160128	−	0.0462250i
$469$	−12.9282			−0.596969
$470$	2.83013	+	1.63397i	0.130544	+	0.0753696i
$471$	−7.73205	+	13.3923i	−0.356274	+	0.617085i
$472$	−0.464102	−	0.803848i	−0.0213620	−	0.0370001i
$473$		−	2.73205i		−	0.125620i
$474$	−9.40192	+	5.42820i	−0.431845	+	0.249326i
$475$	17.2583	−	9.96410i	0.791866	−	0.457184i
$476$			0.267949i			0.0122814i
$477$	5.23205	+	9.06218i	0.239559	+	0.414929i
$478$	−6.90192	+	11.9545i	−0.315687	+	0.546785i
$479$	27.1865	+	15.6962i	1.24218	+	0.717176i	0.969539	−	0.244939i	$-0.0787679\pi$
$479$	27.1865	+	15.6962i	1.24218	+	0.717176i	0.272646	+	0.962114i	$0.412101\pi$
$480$	0.732051			0.0334134
$481$	1.26795	−	4.39230i	0.0578135	−	0.200272i
$482$	12.7846			0.582323
$483$	−3.00000	−	1.73205i	−0.136505	−	0.0788110i
$484$	−1.46410	+	2.53590i	−0.0665501	+	0.115268i
$485$	0.267949	+	0.464102i	0.0121669	+	0.0210738i
$486$		−	1.00000i		−	0.0453609i
$487$	18.3564	−	10.5981i	0.831808	−	0.480245i	−0.0226632	−	0.999743i	$-0.507215\pi$
$487$	18.3564	−	10.5981i	0.831808	−	0.480245i	0.854471	+	0.519498i	$0.173881\pi$
$488$	10.1603	−	5.86603i	0.459933	−	0.265542i
$489$			7.80385i			0.352902i
$490$	−0.366025	−	0.633975i	−0.0165353	−	0.0286401i
$491$	18.1244	−	31.3923i	0.817941	−	1.41671i	−0.0892562	−	0.996009i	$-0.528449\pi$
$491$	18.1244	−	31.3923i	0.817941	−	1.41671i	0.907197	−	0.420706i	$-0.138218\pi$
$492$	−6.06218	−	3.50000i	−0.273304	−	0.157792i
$493$	0.803848			0.0362035
$494$	3.86603	+	15.6244i	0.173941	+	0.702973i
$495$	−2.73205			−0.122797
$496$	6.63397	+	3.83013i	0.297874	+	0.171978i
$497$	1.09808	−	1.90192i	0.0492554	−	0.0853129i
$498$	2.83013	+	4.90192i	0.126821	+	0.219660i
$499$		−	12.9808i		−	0.581099i	−0.956860	−	0.290549i	$-0.906162\pi$
$499$		−	12.9808i		−	0.581099i	0.956860	−	0.290549i	$-0.0938380\pi$
$500$	−6.00000	+	3.46410i	−0.268328	+	0.154919i
$501$	5.07180	−	2.92820i	0.226591	−	0.130822i
$502$		−	18.1962i		−	0.812134i
$503$	11.8564	+	20.5359i	0.528651	+	0.915650i	0.999442	+	0.0334056i	$0.0106353\pi$
$503$	11.8564	+	20.5359i	0.528651	+	0.915650i	−0.470791	+	0.882245i	$0.656031\pi$
$504$	−0.500000	+	0.866025i	−0.0222718	+	0.0385758i
$505$	−6.33975	−	3.66025i	−0.282115	−	0.162879i
$506$	12.9282			0.574729
$507$	−0.500000	+	12.9904i	−0.0222058	+	0.576923i
$508$	−12.5359			−0.556191
$509$	−22.5622	−	13.0263i	−1.00005	−	0.577380i	−0.0917876	−	0.995779i	$-0.529258\pi$
$509$	−22.5622	−	13.0263i	−1.00005	−	0.577380i	−0.908263	+	0.418399i	$0.862591\pi$
$510$	0.0980762	−	0.169873i	0.00434289	−	0.00752210i
$511$	3.26795	+	5.66025i	0.144566	+	0.250395i
$512$			1.00000i			0.0441942i
$513$	−3.86603	+	2.23205i	−0.170689	+	0.0985475i
$514$	−9.57180	+	5.52628i	−0.422194	+	0.243754i
$515$			8.92820i			0.393424i
$516$	0.366025	+	0.633975i	0.0161134	+	0.0279092i
$517$	8.33013	−	14.4282i	0.366359	−	0.634552i
$518$	−1.09808	−	0.633975i	−0.0482467	−	0.0278552i
$519$	20.7321			0.910036
$520$	−0.633975	−	2.56218i	−0.0278016	−	0.112359i
$521$	−2.26795			−0.0993607			−0.0496803	−	0.998765i	$-0.515820\pi$
$521$	−2.26795			−0.0993607			−0.0496803	+	0.998765i	$0.515820\pi$
$522$	2.59808	+	1.50000i	0.113715	+	0.0656532i
$523$	9.40192	−	16.2846i	0.411117	−	0.712076i	−0.583895	−	0.811829i	$-0.698472\pi$
$523$	9.40192	−	16.2846i	0.411117	−	0.712076i	0.995012	+	0.0997531i	$0.0318053\pi$
$524$	9.46410	+	16.3923i	0.413441	+	0.716101i
$525$		−	4.46410i		−	0.194829i
$526$	−16.2224	+	9.36603i	−0.707332	+	0.408378i
$527$	1.77757	−	1.02628i	0.0774321	−	0.0447054i
$528$		−	3.73205i		−	0.162417i
$529$	5.50000	+	9.52628i	0.239130	+	0.414186i
$530$	−3.83013	+	6.63397i	−0.166370	+	0.288161i
$531$	−0.803848	−	0.464102i	−0.0348840	−	0.0201403i
$532$	4.46410			0.193543
$533$	−7.00000	+	24.2487i	−0.303204	+	1.05033i
$534$	−6.46410			−0.279729
$535$	0.973721	+	0.562178i	0.0420976	+	0.0243051i
$536$	−6.46410	+	11.1962i	−0.279207	+	0.483600i
$537$	−11.1962	−	19.3923i	−0.483150	−	0.836840i
$538$		−	23.7128i		−	1.02233i
$539$	−3.23205	+	1.86603i	−0.139214	+	0.0803754i
$540$	0.633975	−	0.366025i	0.0272819	−	0.0157512i
$541$			30.1962i			1.29823i	0.760689	+	0.649117i	$0.224861\pi$
$541$			30.1962i			1.29823i	−0.760689	+	0.649117i	$0.775139\pi$
$542$	−10.7583	−	18.6340i	−0.462110	−	0.800398i
$543$	−0.598076	+	1.03590i	−0.0256659	+	0.0444547i
$544$	0.232051	+	0.133975i	0.00994910	+	0.00574411i
$545$	2.67949			0.114777
$546$	3.46410	+	1.00000i	0.148250	+	0.0427960i
$547$	−12.8756			−0.550523			−0.275261	−	0.961369i	$-0.588764\pi$
$547$	−12.8756			−0.550523			−0.275261	+	0.961369i	$0.588764\pi$
$548$	13.3923	+	7.73205i	0.572091	+	0.330297i
$549$	5.86603	−	10.1603i	0.250356	−	0.433629i
$550$	8.33013	+	14.4282i	0.355198	+	0.615221i
$551$		−	13.3923i		−	0.570531i
$552$	−3.00000	+	1.73205i	−0.127688	+	0.0737210i
$553$	9.40192	−	5.42820i	0.399810	−	0.230831i
$554$			26.3923i			1.12130i
$555$	0.464102	+	0.803848i	0.0197000	+	0.0341214i
$556$	−9.06218	+	15.6962i	−0.384322	+	0.665665i
$557$	31.7487	+	18.3301i	1.34524	+	0.776672i	0.987570	−	0.157177i	$-0.0502394\pi$
$557$	31.7487	+	18.3301i	1.34524	+	0.776672i	0.357666	+	0.933850i	$0.383573\pi$
$558$	7.66025			0.324284
$559$	1.90192	−	1.83013i	0.0804428	−	0.0774061i
$560$	−0.732051			−0.0309348
$561$	−0.866025	−	0.500000i	−0.0365636	−	0.0211100i
$562$	9.09808	−	15.7583i	0.383779	−	0.664725i
$563$	−16.6340	−	28.8109i	−0.701038	−	1.21423i	−0.968102	−	0.250555i	$-0.919387\pi$
$563$	−16.6340	−	28.8109i	−0.701038	−	1.21423i	0.267064	−	0.963679i	$-0.413947\pi$
$564$			4.46410i			0.187973i
$565$	−6.46410	+	3.73205i	−0.271947	+	0.157009i
$566$	19.8564	−	11.4641i	0.834627	−	0.481872i
$567$			1.00000i			0.0419961i
$568$	−1.09808	−	1.90192i	−0.0460743	−	0.0798029i
$569$	11.3660	−	19.6865i	0.476489	−	0.825302i	−0.523149	−	0.852242i	$-0.675243\pi$
$569$	11.3660	−	19.6865i	0.476489	−	0.825302i	0.999637	+	0.0269391i	$0.00857603\pi$
$570$	−2.83013	−	1.63397i	−0.118541	−	0.0684397i
$571$	−19.8038			−0.828765			−0.414383	−	0.910103i	$-0.636002\pi$
$571$	−19.8038			−0.828765			−0.414383	+	0.910103i	$0.636002\pi$
$572$	−13.0622	+	3.23205i	−0.546157	+	0.135139i
$573$	4.19615			0.175297
$574$	6.06218	+	3.50000i	0.253030	+	0.146087i
$575$	7.73205	−	13.3923i	0.322449	−	0.558498i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$		−	13.2679i		−	0.552352i	−0.961107	−	0.276176i	$-0.910933\pi$
$577$		−	13.2679i		−	0.552352i	0.961107	−	0.276176i	$-0.0890673\pi$
$578$	−14.6603	+	8.46410i	−0.609786	+	0.352060i
$579$	−14.8923	+	8.59808i	−0.618903	+	0.357324i
$580$			2.19615i			0.0911903i
$581$	−2.83013	−	4.90192i	−0.117413	−	0.203366i
$582$	−0.366025	+	0.633975i	−0.0151722	+	0.0262791i
$583$	33.8205	+	19.5263i	1.40070	+	0.808696i
$584$	6.53590			0.270457
$585$	−1.83013	−	1.90192i	−0.0756664	−	0.0786349i
$586$	12.7846			0.528127
$587$	−27.1699	−	15.6865i	−1.12142	−	0.647453i	−0.179657	−	0.983729i	$-0.557499\pi$
$587$	−27.1699	−	15.6865i	−1.12142	−	0.647453i	−0.941763	+	0.336277i	$0.890832\pi$
$588$	0.500000	−	0.866025i	0.0206197	−	0.0357143i
$589$	−17.0981	−	29.6147i	−0.704514	−	1.22025i
$590$		−	0.679492i		−	0.0279742i
$591$	1.96410	−	1.13397i	0.0807923	−	0.0466455i
$592$	−1.09808	+	0.633975i	−0.0451307	+	0.0260562i
$593$			13.6795i			0.561749i	0.959744	+	0.280875i	$0.0906245\pi$
$593$			13.6795i			0.561749i	−0.959744	+	0.280875i	$0.909375\pi$
$594$	−1.86603	−	3.23205i	−0.0765639	−	0.132613i
$595$	−0.0980762	+	0.169873i	−0.00402073	+	0.00696411i
$596$	−16.3923	−	9.46410i	−0.671455	−	0.387665i
$597$	−4.19615			−0.171737
$598$	8.66025	+	9.00000i	0.354144	+	0.368037i
$599$	−21.7128			−0.887161			−0.443581	−	0.896234i	$-0.646292\pi$
$599$	−21.7128			−0.887161			−0.443581	+	0.896234i	$0.646292\pi$
$600$	−3.86603	−	2.23205i	−0.157830	−	0.0911231i
$601$	6.43782	−	11.1506i	0.262604	−	0.454844i	−0.704329	−	0.709874i	$-0.748752\pi$
$601$	6.43782	−	11.1506i	0.262604	−	0.454844i	0.966933	+	0.255030i	$0.0820853\pi$
$602$	−0.366025	−	0.633975i	−0.0149181	−	0.0258389i
$603$			12.9282i			0.526477i
$604$	−11.4282	+	6.59808i	−0.465007	+	0.268472i
$605$	−1.85641	+	1.07180i	−0.0754737	+	0.0435747i
$606$		−	10.0000i		−	0.406222i
$607$	−19.9545	−	34.5622i	−0.809927	−	1.40284i	−0.912914	−	0.408153i	$-0.866173\pi$
$607$	−19.9545	−	34.5622i	−0.809927	−	1.40284i	0.102986	−	0.994683i	$-0.467160\pi$
$608$	2.23205	−	3.86603i	0.0905216	−	0.156788i
$609$	−2.59808	−	1.50000i	−0.105279	−	0.0607831i
$610$	8.58846			0.347736
$611$	15.6244	−	3.86603i	0.632094	−	0.156403i
$612$	0.267949			0.0108312
$613$	36.2487	+	20.9282i	1.46407	+	0.845282i	0.999196	−	0.0400938i	$-0.0127657\pi$
$613$	36.2487	+	20.9282i	1.46407	+	0.845282i	0.464876	+	0.885376i	$0.346099\pi$
$614$	−16.8923	+	29.2583i	−0.681718	+	1.18077i
$615$	−2.56218	−	4.43782i	−0.103317	−	0.178950i
$616$			3.73205i			0.150369i
$617$	35.9545	−	20.7583i	1.44747	−	0.835699i	0.449143	−	0.893460i	$-0.351730\pi$
$617$	35.9545	−	20.7583i	1.44747	−	0.835699i	0.998330	+	0.0577612i	$0.0183962\pi$
$618$	−10.5622	+	6.09808i	−0.424873	+	0.245301i
$619$			2.32051i			0.0932691i	0.998912	+	0.0466345i	$0.0148496\pi$
$619$			2.32051i			0.0932691i	−0.998912	+	0.0466345i	$0.985150\pi$
$620$	2.80385	+	4.85641i	0.112605	+	0.195038i
$621$	−1.73205	+	3.00000i	−0.0695048	+	0.120386i
$622$	−16.6244	−	9.59808i	−0.666576	−	0.384848i
$623$	6.46410			0.258979
$624$	2.59808	−	2.50000i	0.104006	−	0.100080i
$625$	17.2487			0.689948
$626$	−1.56218	−	0.901924i	−0.0624372	−	0.0360481i
$627$	−8.33013	+	14.4282i	−0.332673	+	0.576207i
$628$	−7.73205	−	13.3923i	−0.308542	−	0.534411i
$629$			0.339746i			0.0135466i
$630$	−0.633975	+	0.366025i	−0.0252582	+	0.0145828i
$631$	−13.8397	+	7.99038i	−0.550952	+	0.318092i	−0.749506	−	0.661998i	$-0.769709\pi$
$631$	−13.8397	+	7.99038i	−0.550952	+	0.318092i	0.198554	+	0.980090i	$0.436375\pi$
$632$		−	10.8564i		−	0.431845i
$633$	−7.92820	−	13.7321i	−0.315118	−	0.545800i
$634$	−9.00000	+	15.5885i	−0.357436	+	0.619097i
$635$	−7.94744	−	4.58846i	−0.315385	−	0.182087i
$636$	−10.4641			−0.414929
$637$	−3.46410	−	1.00000i	−0.137253	−	0.0396214i
$638$	11.1962			0.443260
$639$	−1.90192	−	1.09808i	−0.0752389	−	0.0434392i
$640$	−0.366025	+	0.633975i	−0.0144684	+	0.0250600i
$641$	−8.12436	−	14.0718i	−0.320893	−	0.555803i	0.659780	−	0.751459i	$-0.270650\pi$
$641$	−8.12436	−	14.0718i	−0.320893	−	0.555803i	−0.980672	+	0.195656i	$0.937316\pi$
$642$			1.53590i			0.0606171i
$643$	1.45448	−	0.839746i	0.0573592	−	0.0331163i	−0.471046	−	0.882109i	$-0.656123\pi$
$643$	1.45448	−	0.839746i	0.0573592	−	0.0331163i	0.528405	+	0.848992i	$0.322790\pi$
$644$	3.00000	−	1.73205i	0.118217	−	0.0682524i
$645$			0.535898i			0.0211010i
$646$	−0.598076	−	1.03590i	−0.0235310	−	0.0407569i
$647$	0.866025	−	1.50000i	0.0340470	−	0.0589711i	−0.848500	−	0.529196i	$-0.822494\pi$
$647$	0.866025	−	1.50000i	0.0340470	−	0.0589711i	0.882547	+	0.470225i	$0.155827\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−3.46410			−0.135978
$650$	−4.46410	+	15.4641i	−0.175096	+	0.606552i
$651$	−7.66025			−0.300229
$652$	−6.75833	−	3.90192i	−0.264677	−	0.152811i
$653$	−5.83975	+	10.1147i	−0.228527	+	0.395820i	−0.957372	−	0.288859i	$-0.906724\pi$
$653$	−5.83975	+	10.1147i	−0.228527	+	0.395820i	0.728845	+	0.684679i	$0.240058\pi$
$654$	1.83013	+	3.16987i	0.0715636	+	0.123952i
$655$			13.8564i			0.541415i
$656$	6.06218	−	3.50000i	0.236688	−	0.136652i
$657$	5.66025	−	3.26795i	0.220828	−	0.127495i
$658$		−	4.46410i		−	0.174029i
$659$	−16.9641	−	29.3827i	−0.660828	−	1.14459i	−0.980399	−	0.197025i	$-0.936872\pi$
$659$	−16.9641	−	29.3827i	−0.660828	−	1.14459i	0.319571	−	0.947562i	$-0.396461\pi$
$660$	1.36603	−	2.36603i	0.0531725	−	0.0920974i
$661$	23.9090	+	13.8038i	0.929951	+	0.536907i	0.886796	−	0.462161i	$-0.152926\pi$
$661$	23.9090	+	13.8038i	0.929951	+	0.536907i	0.0431549	+	0.999068i	$0.486259\pi$
$662$	16.9282			0.657933
$663$	−0.232051	−	0.937822i	−0.00901211	−	0.0364220i
$664$	−5.66025			−0.219660
$665$	2.83013	+	1.63397i	0.109748	+	0.0633628i
$666$	−0.633975	+	1.09808i	−0.0245660	+	0.0425496i
$667$	−5.19615	−	9.00000i	−0.201196	−	0.348481i
$668$			5.85641i			0.226591i
$669$	7.26795	−	4.19615i	0.280995	−	0.162233i
$670$	−8.19615	+	4.73205i	−0.316645	+	0.182815i
$671$		−	43.7846i		−	1.69029i
$672$	−0.500000	−	0.866025i	−0.0192879	−	0.0334077i
$673$	−23.9641	+	41.5070i	−0.923748	+	1.59998i	−0.130186	+	0.991490i	$0.541557\pi$
$673$	−23.9641	+	41.5070i	−0.923748	+	1.59998i	−0.793562	+	0.608489i	$0.791776\pi$
$674$	24.0622	+	13.8923i	0.926840	+	0.535112i
$675$	−4.46410			−0.171823
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	−47.7654			−1.83577			−0.917886	−	0.396844i	$-0.870105\pi$
$677$	−47.7654			−1.83577			−0.917886	+	0.396844i	$0.870105\pi$
$678$	−8.83013	−	5.09808i	−0.339119	−	0.195790i
$679$	0.366025	−	0.633975i	0.0140468	−	0.0243297i
$680$	0.0980762	+	0.169873i	0.00376105	+	0.00651433i
$681$		−	8.53590i		−	0.327096i
$682$	24.7583	−	14.2942i	0.948045	−	0.547354i
$683$	−22.8564	+	13.1962i	−0.874576	+	0.504937i	−0.868866	−	0.495047i	$-0.835151\pi$
$683$	−22.8564	+	13.1962i	−0.874576	+	0.504937i	−0.00570987	+	0.999984i	$0.501818\pi$
$684$		−	4.46410i		−	0.170689i
$685$	5.66025	+	9.80385i	0.216267	+	0.374586i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	−8.93782	−	5.16025i	−0.340999	−	0.196876i
$688$	−0.732051			−0.0279092
$689$	9.06218	+	36.6244i	0.345241	+	1.39528i
$690$	−2.53590			−0.0965400
$691$	35.3205	+	20.3923i	1.34366	+	0.775760i	0.987342	−	0.158607i	$-0.0507002\pi$
$691$	35.3205	+	20.3923i	1.34366	+	0.775760i	0.356314	+	0.934366i	$0.384033\pi$
$692$	−10.3660	+	17.9545i	−0.394057	+	0.682527i
$693$	1.86603	+	3.23205i	0.0708844	+	0.122775i
$694$			22.8564i			0.867617i
$695$	−11.4904	+	6.63397i	−0.435855	+	0.251641i
$696$	−2.59808	+	1.50000i	−0.0984798	+	0.0568574i
$697$		−	1.87564i		−	0.0710451i
$698$	−11.8564	−	20.5359i	−0.448772	−	0.777295i
$699$	−1.09808	+	1.90192i	−0.0415331	+	0.0719374i
$700$	3.86603	+	2.23205i	0.146122	+	0.0843636i
$701$	−14.3205			−0.540878			−0.270439	−	0.962737i	$-0.587169\pi$
$701$	−14.3205			−0.540878			−0.270439	+	0.962737i	$0.587169\pi$
$702$	1.00000	−	3.46410i	0.0377426	−	0.130744i
$703$	5.66025			0.213481
$704$	3.23205	+	1.86603i	0.121812	+	0.0703285i
$705$	−1.63397	+	2.83013i	−0.0615390	+	0.106589i
$706$	0.732051	+	1.26795i	0.0275511	+	0.0477199i
$707$			10.0000i			0.376089i
$708$	0.803848	−	0.464102i	0.0302104	−	0.0174420i
$709$	20.8301	−	12.0263i	0.782292	−	0.451656i	−0.0549501	−	0.998489i	$-0.517500\pi$
$709$	20.8301	−	12.0263i	0.782292	−	0.451656i	0.837242	+	0.546833i	$0.184167\pi$
$710$		−	1.60770i		−	0.0603357i
$711$	−5.42820	−	9.40192i	−0.203574	−	0.352600i
$712$	3.23205	−	5.59808i	0.121126	−	0.209797i
$713$	−22.9808	−	13.2679i	−0.860636	−	0.496889i
$714$	−0.267949			−0.0100277
$715$	−9.46410	−	2.73205i	−0.353937	−	0.102173i
$716$	22.3923			0.836840
$717$	−11.9545	−	6.90192i	−0.446448	−	0.257757i
$718$	7.90192	−	13.6865i	0.294897	−	0.510777i
$719$	1.52628	+	2.64359i	0.0569206	+	0.0985894i	0.893082	−	0.449895i	$-0.148538\pi$
$719$	1.52628	+	2.64359i	0.0569206	+	0.0985894i	−0.836161	+	0.548484i	$0.815205\pi$
$720$			0.732051i			0.0272819i
$721$	10.5622	−	6.09808i	0.393356	−	0.227104i
$722$	−0.803848	+	0.464102i	−0.0299161	+	0.0172721i
$723$			12.7846i			0.475465i
$724$	−0.598076	−	1.03590i	−0.0222273	−	0.0384989i
$725$	6.69615	−	11.5981i	0.248689	−	0.430742i
$726$	−2.53590	−	1.46410i	−0.0941160	−	0.0543379i
$727$	−1.46410			−0.0543005			−0.0271503	−	0.999631i	$-0.508643\pi$
$727$	−1.46410			−0.0543005			−0.0271503	+	0.999631i	$0.508643\pi$
$728$	−2.59808	+	2.50000i	−0.0962911	+	0.0926562i
$729$	1.00000			0.0370370
$730$	4.14359	+	2.39230i	0.153361	+	0.0885432i
$731$	−0.0980762	+	0.169873i	−0.00362748	+	0.00628298i
$732$	5.86603	+	10.1603i	0.216815	+	0.375534i
$733$		−	6.85641i		−	0.253247i	−0.991951	−	0.126624i	$-0.959586\pi$
$733$		−	6.85641i		−	0.253247i	0.991951	−	0.126624i	$-0.0404140\pi$
$734$	14.0718	−	8.12436i	0.519399	−	0.299875i
$735$	0.633975	−	0.366025i	0.0233845	−	0.0135011i
$736$		−	3.46410i		−	0.127688i
$737$	24.1244	+	41.7846i	0.888632	+	1.53916i
$738$	3.50000	−	6.06218i	0.128837	−	0.223152i
$739$	5.53590	+	3.19615i	0.203641	+	0.117572i	0.598353	−	0.801233i	$-0.295822\pi$
$739$	5.53590	+	3.19615i	0.203641	+	0.117572i	−0.394712	+	0.918805i	$0.629155\pi$
$740$	−0.928203			−0.0341214
$741$	−15.6244	+	3.86603i	−0.573975	+	0.142022i
$742$	10.4641			0.384149
$743$	−16.9019	−	9.75833i	−0.620071	−	0.357998i	0.156825	−	0.987626i	$-0.449874\pi$
$743$	−16.9019	−	9.75833i	−0.620071	−	0.357998i	−0.776897	+	0.629628i	$0.783207\pi$
$744$	−3.83013	+	6.63397i	−0.140419	+	0.243213i
$745$	−6.92820	−	12.0000i	−0.253830	−	0.439646i
$746$		−	20.5885i		−	0.753797i
$747$	−4.90192	+	2.83013i	−0.179352	+	0.103549i
$748$	0.866025	−	0.500000i	0.0316650	−	0.0182818i
$749$		−	1.53590i		−	0.0561205i
$750$	−3.46410	−	6.00000i	−0.126491	−	0.219089i
$751$	−3.42820	+	5.93782i	−0.125097	+	0.216674i	−0.921771	−	0.387735i	$-0.873258\pi$
$751$	−3.42820	+	5.93782i	−0.125097	+	0.216674i	0.796674	+	0.604409i	$0.206591\pi$
$752$	−3.86603	−	2.23205i	−0.140979	−	0.0813945i
$753$	18.1962			0.663105
$754$	7.50000	+	7.79423i	0.273134	+	0.283849i
$755$	−9.66025			−0.351573
$756$	−0.866025	−	0.500000i	−0.0314970	−	0.0181848i
$757$	19.0263	−	32.9545i	0.691522	−	1.19775i	−0.279817	−	0.960053i	$-0.590274\pi$
$757$	19.0263	−	32.9545i	0.691522	−	1.19775i	0.971339	−	0.237698i	$-0.0763928\pi$
$758$	7.29423	+	12.6340i	0.264938	+	0.458887i
$759$			12.9282i			0.469264i
$760$	2.83013	−	1.63397i	0.102659	−	0.0592705i
$761$	−0.588457	+	0.339746i	−0.0213316	+	0.0123158i	−0.510628	−	0.859802i	$-0.670587\pi$
$761$	−0.588457	+	0.339746i	−0.0213316	+	0.0123158i	0.489296	+	0.872118i	$0.337254\pi$
$762$		−	12.5359i		−	0.454128i
$763$	−1.83013	−	3.16987i	−0.0662550	−	0.114757i
$764$	−2.09808	+	3.63397i	−0.0759057	+	0.131473i
$765$	0.169873	+	0.0980762i	0.00614177	+	0.00354595i
$766$	−14.6077			−0.527797
$767$	−2.32051	−	2.41154i	−0.0837887	−	0.0870758i
$768$	−1.00000			−0.0360844
$769$	21.1699	+	12.2224i	0.763405	+	0.440752i	0.830517	−	0.556993i	$-0.188045\pi$
$769$	21.1699	+	12.2224i	0.763405	+	0.440752i	−0.0671118	+	0.997745i	$0.521378\pi$
$770$	−1.36603	+	2.36603i	−0.0492281	+	0.0852656i
$771$

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.732051i q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.732051i q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.366025 - 0.633975i) q^{10} +(-3.23205 - 1.86603i) q^{11} +1.00000 q^{12} +(-0.866025 - 3.50000i) q^{13} -1.00000 q^{14} +(0.633975 + 0.366025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.133975 + 0.232051i) q^{17} +1.00000i q^{18} +(3.86603 - 2.23205i) q^{19} +(-0.633975 + 0.366025i) q^{20} -1.00000i q^{21} +(1.86603 + 3.23205i) q^{22} +(1.73205 - 3.00000i) q^{23} +(-0.866025 - 0.500000i) q^{24} +4.46410 q^{25} +(-1.00000 + 3.46410i) q^{26} -1.00000 q^{27} +(0.866025 + 0.500000i) q^{28} +(1.50000 - 2.59808i) q^{29} +(-0.366025 - 0.633975i) q^{30} -7.66025i q^{31} +(0.866025 - 0.500000i) q^{32} +(-3.23205 + 1.86603i) q^{33} -0.267949i q^{34} +(0.366025 + 0.633975i) q^{35} +(0.500000 - 0.866025i) q^{36} +(1.09808 + 0.633975i) q^{37} -4.46410 q^{38} +(-3.46410 - 1.00000i) q^{39} +0.732051 q^{40} +(-6.06218 - 3.50000i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(0.366025 + 0.633975i) q^{43} -3.73205i q^{44} +(0.633975 - 0.366025i) q^{45} +(-3.00000 + 1.73205i) q^{46} +4.46410i q^{47} +(0.500000 + 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-3.86603 - 2.23205i) q^{50} +0.267949 q^{51} +(2.59808 - 2.50000i) q^{52} -10.4641 q^{53} +(0.866025 + 0.500000i) q^{54} +(1.36603 - 2.36603i) q^{55} +(-0.500000 - 0.866025i) q^{56} -4.46410i q^{57} +(-2.59808 + 1.50000i) q^{58} +(0.803848 - 0.464102i) q^{59} +0.732051i q^{60} +(5.86603 + 10.1603i) q^{61} +(-3.83013 + 6.63397i) q^{62} +(-0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(2.56218 - 0.633975i) q^{65} +3.73205 q^{66} +(-11.1962 - 6.46410i) q^{67} +(-0.133975 + 0.232051i) q^{68} +(-1.73205 - 3.00000i) q^{69} -0.732051i q^{70} +(1.90192 - 1.09808i) q^{71} +(-0.866025 + 0.500000i) q^{72} +6.53590i q^{73} +(-0.633975 - 1.09808i) q^{74} +(2.23205 - 3.86603i) q^{75} +(3.86603 + 2.23205i) q^{76} -3.73205 q^{77} +(2.50000 + 2.59808i) q^{78} +10.8564 q^{79} +(-0.633975 - 0.366025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.50000 + 6.06218i) q^{82} -5.66025i q^{83} +(0.866025 - 0.500000i) q^{84} +(-0.169873 + 0.0980762i) q^{85} -0.732051i q^{86} +(-1.50000 - 2.59808i) q^{87} +(-1.86603 + 3.23205i) q^{88} +(5.59808 + 3.23205i) q^{89} -0.732051 q^{90} +(-2.50000 - 2.59808i) q^{91} +3.46410 q^{92} +(-6.63397 - 3.83013i) q^{93} +(2.23205 - 3.86603i) q^{94} +(1.63397 + 2.83013i) q^{95} -1.00000i q^{96} +(0.633975 - 0.366025i) q^{97} +(-0.866025 + 0.500000i) q^{98} +3.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9	\( 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{14} + 6 q^{15} - 2 q^{16} + 4 q^{17} + 12 q^{19} - 6 q^{20} + 4 q^{22} + 4 q^{25} - 4 q^{26} - 4 q^{27} + 6 q^{29} + 2 q^{30} - 6 q^{33} - 2 q^{35} + 2 q^{36} - 6 q^{37} - 4 q^{38} - 4 q^{40} - 2 q^{42} - 2 q^{43} + 6 q^{45} - 12 q^{46} + 2 q^{48} + 2 q^{49} - 12 q^{50} + 8 q^{51} - 28 q^{53} + 2 q^{55} - 2 q^{56} + 24 q^{59} + 20 q^{61} + 2 q^{62} - 4 q^{64} - 14 q^{65} + 8 q^{66} - 24 q^{67} - 4 q^{68} + 18 q^{71} - 6 q^{74} + 2 q^{75} + 12 q^{76} - 8 q^{77} + 10 q^{78} - 12 q^{79} - 6 q^{80} - 2 q^{81} + 14 q^{82} - 18 q^{85} - 6 q^{87} - 4 q^{88} + 12 q^{89} + 4 q^{90} - 10 q^{91} - 30 q^{93} + 2 q^{94} + 10 q^{95} + 6 q^{97}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^10 - 6 * q^11 + 4 * q^12 - 4 * q^14 + 6 * q^15 - 2 * q^16 + 4 * q^17 + 12 * q^19 - 6 * q^20 + 4 * q^22 + 4 * q^25 - 4 * q^26 - 4 * q^27 + 6 * q^29 + 2 * q^30 - 6 * q^33 - 2 * q^35 + 2 * q^36 - 6 * q^37 - 4 * q^38 - 4 * q^40 - 2 * q^42 - 2 * q^43 + 6 * q^45 - 12 * q^46 + 2 * q^48 + 2 * q^49 - 12 * q^50 + 8 * q^51 - 28 * q^53 + 2 * q^55 - 2 * q^56 + 24 * q^59 + 20 * q^61 + 2 * q^62 - 4 * q^64 - 14 * q^65 + 8 * q^66 - 24 * q^67 - 4 * q^68 + 18 * q^71 - 6 * q^74 + 2 * q^75 + 12 * q^76 - 8 * q^77 + 10 * q^78 - 12 * q^79 - 6 * q^80 - 2 * q^81 + 14 * q^82 - 18 * q^85 - 6 * q^87 - 4 * q^88 + 12 * q^89 + 4 * q^90 - 10 * q^91 - 30 * q^93 + 2 * q^94 + 10 * q^95 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more