LMFDB - Embedded newform 546.2.s.d.127.1

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			127.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	546.127
Dual form			546.2.s.d.43.1

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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	$-0.947660\pi$
$5$		−	0.732051i		−	0.327383i	0.986512	−	0.163692i	$-0.0523402\pi$
$6$	−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	−0.900605	−	0.434638i	$-0.856876\pi$
$11$	−3.23205	+	1.86603i	−0.974500	+	0.562628i	−0.0738948	+	0.997266i	$0.523543\pi$
$12$	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	−0.849321	−	0.527876i	$-0.822988\pi$
$17$	0.133975	−	0.232051i	0.0324936	−	0.0562806i	0.881815	+	0.471596i	$0.156322\pi$
$18$		−	1.00000i		−	0.235702i
$19$	3.86603	+	2.23205i	0.886927	+	0.512068i	0.872936	−	0.487835i	$-0.162213\pi$
$19$	3.86603	+	2.23205i	0.886927	+	0.512068i	0.0139909	+	0.999902i	$0.495546\pi$
$20$	−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	0.988152	−	0.153481i	$-0.0490483\pi$
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	−0.626994	+	0.779024i	$0.715715\pi$
$24$	−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	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$	−0.366025	+	0.633975i	−0.0668268	+	0.115747i
$31$			7.66025i			1.37582i	0.725795	+	0.687911i	$0.241472\pi$
$31$			7.66025i			1.37582i	−0.725795	+	0.687911i	$0.758528\pi$
$32$	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	−0.407016	−	0.913421i	$-0.633431\pi$
$37$	1.09808	−	0.633975i	0.180523	−	0.104225i	0.587538	+	0.809196i	$0.300097\pi$
$38$	−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	−0.892071	−	0.451896i	$-0.850748\pi$
$41$	−6.06218	+	3.50000i	−0.946753	+	0.546608i	−0.0546823	+	0.998504i	$0.517415\pi$
$42$	−0.500000	−	0.866025i	−0.0771517	−	0.133631i
$43$	0.366025	−	0.633975i	0.0558184	−	0.0966802i	−0.836766	−	0.547561i	$-0.815557\pi$
$43$	0.366025	−	0.633975i	0.0558184	−	0.0966802i	0.892584	+	0.450880i	$0.148890\pi$
$44$			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	$-0.894441\pi$
$47$		−	4.46410i		−	0.651156i	0.945515	−	0.325578i	$-0.105559\pi$
$48$	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	0.551413	−	0.834233i	$-0.314089\pi$
$59$	0.803848	+	0.464102i	0.104652	+	0.0604209i	−0.446760	+	0.894654i	$0.647422\pi$
$60$		−	0.732051i		−	0.0945074i
$61$	5.86603	−	10.1603i	0.751068	−	1.30089i	−0.196238	−	0.980556i	$-0.562873\pi$
$61$	5.86603	−	10.1603i	0.751068	−	1.30089i	0.947306	−	0.320331i	$-0.103794\pi$
$62$	−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	−0.990650	−	0.136425i	$-0.956439\pi$
$67$	−11.1962	+	6.46410i	−1.36783	+	0.789716i	−0.377177	+	0.926141i	$0.623105\pi$
$68$	−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	0.608595	−	0.793481i	$-0.291734\pi$
$71$	1.90192	+	1.09808i	0.225717	+	0.130318i	−0.382878	+	0.923799i	$0.625067\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$		−	6.53590i		−	0.764969i	−0.923962	−	0.382485i	$-0.875069\pi$
$73$		−	6.53590i		−	0.764969i	0.923962	−	0.382485i	$-0.124931\pi$
$74$	−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	$0.100546\pi$
$83$			5.66025i			0.621294i	−0.950525	+	0.310647i	$0.899454\pi$
$84$	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	−0.173044	−	0.984914i	$-0.555360\pi$
$89$	5.59808	−	3.23205i	0.593395	−	0.342597i	0.766439	+	0.642317i	$0.222027\pi$
$90$	−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	0.531840	−	0.846845i	$-0.321501\pi$
$97$	0.633975	+	0.366025i	0.0643704	+	0.0371642i	−0.467469	+	0.884009i	$0.654834\pi$
$98$	−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	0.502477	−	0.864590i	$-0.332422\pi$
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	−0.999996	+	0.00286291i	$0.999089\pi$
$102$	−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	0.900756	−	0.434326i	$-0.143013\pi$
$107$	0.767949	+	1.33013i	0.0742405	+	0.128588i	−0.826515	+	0.562914i	$0.809680\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$			3.66025i			0.350589i	0.984516	+	0.175294i	$0.0560877\pi$
$109$			3.66025i			0.350589i	−0.984516	+	0.175294i	$0.943912\pi$
$110$	−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	−0.520139	−	0.854081i	$-0.674120\pi$
$113$	5.09808	−	8.83013i	0.479587	−	0.830668i	0.999726	+	0.0234130i	$0.00745328\pi$
$114$	−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	−0.997810	−	0.0661478i	$-0.978929\pi$
$127$	−6.26795	−	10.8564i	−0.556191	−	0.963350i	0.441619	−	0.897203i	$-0.354404\pi$
$128$	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	0.947463	−	0.319866i	$-0.103638\pi$
$137$	13.3923	+	7.73205i	1.14418	+	0.660594i	0.196719	+	0.980460i	$0.436971\pi$
$138$		−	3.46410i		−	0.294884i
$139$	9.06218	−	15.6962i	0.768644	−	1.33133i	−0.169655	−	0.985504i	$-0.554265\pi$
$139$	9.06218	−	15.6962i	0.768644	−	1.33133i	0.938298	−	0.345827i	$-0.112401\pi$
$140$	−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	−0.355676	−	0.934609i	$-0.615749\pi$
$149$	−16.3923	−	9.46410i	−1.34291	−	0.775329i	−0.987233	+	0.159280i	$0.949083\pi$
$150$	−3.86603	−	2.23205i	−0.315660	−	0.182246i
$151$		−	13.1962i		−	1.07389i	−0.843618	−	0.536944i	$-0.819579\pi$
$151$		−	13.1962i		−	1.07389i	0.843618	−	0.536944i	$-0.180421\pi$
$152$	−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	0.211400	−	0.977400i	$-0.432198\pi$
$163$	−6.75833	−	3.90192i	−0.529353	−	0.305622i	−0.740753	+	0.671777i	$0.765531\pi$
$164$			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	−0.290761	−	0.956796i	$-0.593909\pi$
$167$	5.07180	−	2.92820i	0.392467	−	0.226591i	0.683229	+	0.730204i	$0.260575\pi$
$168$	−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	−0.139007	−	0.990291i	$-0.544391\pi$
$173$	10.3660	−	17.9545i	0.788114	−	1.36505i	0.927121	−	0.374763i	$-0.122276\pi$
$174$		−	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	0.892524	+	0.451000i	$0.148933\pi$
$179$	11.1962	+	19.3923i	0.836840	+	1.44945i	−0.0556840	+	0.998448i	$0.517734\pi$
$180$	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	−0.780082	−	0.625677i	$-0.784823\pi$
$191$	2.09808	−	3.63397i	0.151811	−	0.262945i	0.931893	+	0.362732i	$0.118156\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−14.8923	+	8.59808i	−1.07197	+	0.618903i	−0.928719	−	0.370783i	$-0.879089\pi$
$193$	−14.8923	+	8.59808i	−1.07197	+	0.618903i	−0.143252	+	0.989686i	$0.545756\pi$
$194$	−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	−0.428397	−	0.903591i	$-0.640922\pi$
$197$	1.96410	−	1.13397i	0.139936	−	0.0807923i	0.568334	+	0.822798i	$0.307588\pi$
$198$	1.86603	+	3.23205i	0.132613	+	0.229692i
$199$	−2.09808	+	3.63397i	−0.148729	+	0.257606i	−0.930758	−	0.365636i	$-0.880851\pi$
$199$	−2.09808	+	3.63397i	−0.148729	+	0.257606i	0.782029	+	0.623242i	$0.214185\pi$
$200$			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	0.998556	+	0.0537189i	$0.0171075\pi$
$211$	7.92820	+	13.7321i	0.545800	+	0.945353i	−0.452756	+	0.891634i	$0.649559\pi$
$212$	−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	−0.236506	−	0.971630i	$-0.576002\pi$
$223$	7.26795	−	4.19615i	0.486698	−	0.280995i	0.723204	+	0.690635i	$0.242669\pi$
$224$	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	0.724842	−	0.688915i	$-0.241913\pi$
$227$	7.39230	+	4.26795i	0.490645	+	0.283274i	−0.234197	+	0.972189i	$0.575246\pi$
$228$	3.86603	+	2.23205i	0.256034	+	0.147821i
$229$			10.3205i			0.681998i	0.940064	+	0.340999i	$0.110765\pi$
$229$			10.3205i			0.681998i	−0.940064	+	0.340999i	$0.889235\pi$
$230$	−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	$0.147311\pi$
$239$			13.8038i			0.892897i	−0.894809	+	0.446448i	$0.852689\pi$
$240$	−0.633975	−	0.366025i	−0.0409229	−	0.0236268i
$241$	−11.0718	−	6.39230i	−0.713197	−	0.411765i	0.0990466	−	0.995083i	$-0.468421\pi$
$241$	−11.0718	−	6.39230i	−0.713197	−	0.411765i	−0.812244	+	0.583318i	$0.801754\pi$
$242$			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	−0.421856	−	0.906663i	$-0.638621\pi$
$251$	9.09808	−	15.7583i	0.574265	−	0.994657i	0.996121	−	0.0879939i	$-0.0280456\pi$
$252$			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	0.985303	−	0.170817i	$-0.0546406\pi$
$257$	5.52628	+	9.57180i	0.344720	+	0.597072i	−0.640583	+	0.767889i	$0.721307\pi$
$258$	−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	0.995761	+	0.0919756i	$0.0293182\pi$
$263$	9.36603	+	16.2224i	0.577534	+	1.00032i	−0.418227	+	0.908342i	$0.637348\pi$
$264$	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	−0.236936	−	0.971525i	$-0.576143\pi$
$269$	11.8564	−	20.5359i	0.722898	−	1.25210i	0.959833	−	0.280570i	$-0.0905236\pi$
$270$	−0.366025	−	0.633975i	−0.0222756	−	0.0385825i
$271$	18.6340	−	10.7583i	1.13193	−	0.653522i	0.187513	−	0.982262i	$-0.439957\pi$
$271$	18.6340	−	10.7583i	1.13193	−	0.653522i	0.944420	+	0.328740i	$0.106624\pi$
$272$	−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	0.131297	+	0.991343i	$0.458086\pi$
$277$	−13.1962	+	22.8564i	−0.792880	+	1.37331i	−0.924177	+	0.381965i	$0.875247\pi$
$278$			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	$-0.817385\pi$
$281$		−	18.1962i		−	1.08549i	0.839897	−	0.542746i	$-0.182615\pi$
$282$	−2.23205	+	3.86603i	−0.132917	+	0.230218i
$283$	−11.4641	−	19.8564i	−0.681470	−	1.18034i	−0.974532	−	0.224247i	$-0.928008\pi$
$283$	−11.4641	−	19.8564i	−0.681470	−	1.18034i	0.293062	−	0.956093i	$-0.405326\pi$
$284$	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	0.140416	−	0.990093i	$-0.455156\pi$
$293$	−11.0718	−	6.39230i	−0.646821	−	0.373442i	−0.787237	+	0.616650i	$0.788489\pi$
$294$		−	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	$0.414444\pi$
$307$			33.7846i			1.92819i	−0.265558	+	0.964095i	$0.585556\pi$
$308$	−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	$0.168688\pi$
$317$			18.0000i			1.01098i	−0.862832	+	0.505490i	$0.831312\pi$
$318$	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	0.0396949	−	0.999212i	$-0.487361\pi$
$331$	−14.6603	−	8.46410i	−0.805800	−	0.465229i	−0.845495	+	0.533983i	$0.820695\pi$
$332$	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	0.377148	+	0.926153i	$0.376905\pi$
$347$	−11.4282	+	19.7942i	−0.613498	+	1.06261i	−0.990646	+	0.136457i	$0.956429\pi$
$348$	1.50000	+	2.59808i	0.0804084	+	0.139272i
$349$	20.5359	−	11.8564i	1.09926	−	0.634659i	0.163235	−	0.986587i	$-0.447807\pi$
$349$	20.5359	−	11.8564i	1.09926	−	0.634659i	0.936027	+	0.351928i	$0.114474\pi$
$350$	−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	−0.533363	−	0.845886i	$-0.679072\pi$
$353$	−1.26795	+	0.732051i	−0.0674861	+	0.0389631i	0.465877	+	0.884849i	$0.345739\pi$
$354$	−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	$-0.863065\pi$
$359$		−	15.8038i		−	0.834095i	0.908885	−	0.417048i	$-0.136935\pi$
$360$	−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	0.572247	−	0.820081i	$-0.306072\pi$
$367$	−8.12436	−	14.0718i	−0.424088	−	0.734542i	−0.996335	+	0.0855396i	$0.972739\pi$
$368$	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	−0.466242	−	0.884657i	$-0.654392\pi$
$373$	10.2942	−	17.8301i	0.533015	−	0.923209i	0.999257	−	0.0385516i	$-0.0122744\pi$
$374$	−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	−0.788059	−	0.615600i	$-0.788914\pi$
$379$	−12.6340	+	7.29423i	−0.648964	+	0.374679i	0.139095	+	0.990279i	$0.455581\pi$
$380$	−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	0.787082	−	0.616848i	$-0.211591\pi$
$383$	12.6506	+	7.30385i	0.646417	+	0.373209i	−0.140665	+	0.990057i	$0.544924\pi$
$384$	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	0.0975279	−	0.995233i	$-0.468906\pi$
$397$	−14.2583	−	8.23205i	−0.715605	−	0.413155i	−0.813133	+	0.582078i	$0.802240\pi$
$398$		−	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	−0.700399	−	0.713751i	$-0.746995\pi$
$401$	−8.66025	+	5.00000i	−0.432472	+	0.249688i	0.267927	+	0.963439i	$0.413661\pi$
$402$	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	0.756415	−	0.654092i	$-0.226949\pi$
$409$	11.4904	+	6.63397i	0.568163	+	0.328029i	−0.188252	+	0.982121i	$0.560282\pi$
$410$	−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	0.931724	−	0.363166i	$-0.118304\pi$
$419$	3.09808	+	5.36603i	0.151351	+	0.262147i	−0.780373	+	0.625314i	$0.784971\pi$
$420$	0.366025	−	0.633975i	0.0178602	−	0.0309348i
$421$			14.3923i			0.701438i	0.936481	+	0.350719i	$0.114063\pi$
$421$			14.3923i			0.701438i	−0.936481	+	0.350719i	$0.885937\pi$
$422$	−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	0.0101474	−	0.999949i	$-0.496770\pi$
$431$	18.2942	−	10.5622i	0.881202	−	0.508762i	0.871055	+	0.491186i	$0.163437\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	4.46410	−	7.73205i	0.214531	−	0.371579i	−0.738596	−	0.674148i	$-0.764511\pi$
$433$	4.46410	−	7.73205i	0.214531	−	0.371579i	0.953127	+	0.302569i	$0.0978444\pi$
$434$		−	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	0.601425	−	0.798930i	$-0.294600\pi$
$439$	−8.19615	−	14.1962i	−0.391181	−	0.677545i	−0.992606	+	0.121384i	$0.961267\pi$
$440$	−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	0.264391	−	0.964416i	$-0.414829\pi$
$449$	−9.29423	−	5.36603i	−0.438622	−	0.253238i	−0.703013	+	0.711177i	$0.748162\pi$
$450$		−	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	−0.356239	−	0.934395i	$-0.615941\pi$
$457$	5.87564	−	3.39230i	0.274851	−	0.158685i	0.631090	+	0.775710i	$0.282608\pi$
$458$	−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	−0.176955	−	0.984219i	$-0.556625\pi$
$461$	−24.0000	−	13.8564i	−1.11779	−	0.645357i	−0.940836	+	0.338862i	$0.889958\pi$
$462$	3.23205	+	1.86603i	0.150369	+	0.0868154i
$463$			1.19615i			0.0555899i	0.999614	+	0.0277950i	$0.00884855\pi$
$463$			1.19615i			0.0555899i	−0.999614	+	0.0277950i	$0.991151\pi$
$464$	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	0.272646	−	0.962114i	$-0.412101\pi$
$479$	27.1865	−	15.6962i	1.24218	−	0.717176i	0.969539	+	0.244939i	$0.0787679\pi$
$480$	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	0.854471	−	0.519498i	$-0.173881\pi$
$487$	18.3564	+	10.5981i	0.831808	+	0.480245i	−0.0226632	+	0.999743i	$0.507215\pi$
$488$	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	0.907197	+	0.420706i	$0.138218\pi$
$491$	18.1244	+	31.3923i	0.817941	+	1.41671i	−0.0892562	+	0.996009i	$0.528449\pi$
$492$	−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	$0.0938380\pi$
$499$			12.9808i			0.581099i	−0.956860	+	0.290549i	$0.906162\pi$
$500$	−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	−0.470791	−	0.882245i	$-0.656031\pi$
$503$	11.8564	−	20.5359i	0.528651	−	0.915650i	0.999442	−	0.0334056i	$-0.0106353\pi$
$504$	−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	−0.908263	−	0.418399i	$-0.862591\pi$
$509$	−22.5622	+	13.0263i	−1.00005	+	0.577380i	−0.0917876	+	0.995779i	$0.529258\pi$
$510$	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	0.995012	−	0.0997531i	$-0.0318053\pi$
$523$	9.40192	+	16.2846i	0.411117	+	0.712076i	−0.583895	+	0.811829i	$0.698472\pi$
$524$	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	$-0.775139\pi$
$541$		−	30.1962i		−	1.29823i	0.760689	−	0.649117i	$-0.224861\pi$
$542$	−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	0.357666	−	0.933850i	$-0.383573\pi$
$557$	31.7487	−	18.3301i	1.34524	−	0.776672i	0.987570	+	0.157177i	$0.0502394\pi$
$558$	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	0.267064	+	0.963679i	$0.413947\pi$
$563$	−16.6340	+	28.8109i	−0.701038	+	1.21423i	−0.968102	+	0.250555i	$0.919387\pi$
$564$		−	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	0.999637	−	0.0269391i	$-0.00857603\pi$
$569$	11.3660	+	19.6865i	0.476489	+	0.825302i	−0.523149	+	0.852242i	$0.675243\pi$
$570$	−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	$0.0890673\pi$
$577$			13.2679i			0.552352i	−0.961107	+	0.276176i	$0.910933\pi$
$578$	−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	−0.941763	−	0.336277i	$-0.890832\pi$
$587$	−27.1699	+	15.6865i	−1.12142	+	0.647453i	−0.179657	+	0.983729i	$0.557499\pi$
$588$	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	$-0.909375\pi$
$593$		−	13.6795i		−	0.561749i	0.959744	−	0.280875i	$-0.0906245\pi$
$594$	−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	0.966933	−	0.255030i	$-0.0820853\pi$
$601$	6.43782	+	11.1506i	0.262604	+	0.454844i	−0.704329	+	0.709874i	$0.748752\pi$
$602$	−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	0.102986	+	0.994683i	$0.467160\pi$
$607$	−19.9545	+	34.5622i	−0.809927	+	1.40284i	−0.912914	+	0.408153i	$0.866173\pi$
$608$	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	0.464876	−	0.885376i	$-0.346099\pi$
$613$	36.2487	−	20.9282i	1.46407	−	0.845282i	0.999196	+	0.0400938i	$0.0127657\pi$
$614$	−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	0.998330	−	0.0577612i	$-0.0183962\pi$
$617$	35.9545	+	20.7583i	1.44747	+	0.835699i	0.449143	+	0.893460i	$0.351730\pi$
$618$	−10.5622	−	6.09808i	−0.424873	−	0.245301i
$619$		−	2.32051i		−	0.0932691i	−0.998912	−	0.0466345i	$-0.985150\pi$
$619$		−	2.32051i		−	0.0932691i	0.998912	−	0.0466345i	$-0.0148496\pi$
$620$	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	0.198554	−	0.980090i	$-0.436375\pi$
$631$	−13.8397	−	7.99038i	−0.550952	−	0.318092i	−0.749506	+	0.661998i	$0.769709\pi$
$632$			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	−0.980672	−	0.195656i	$-0.937316\pi$
$641$	−8.12436	+	14.0718i	−0.320893	+	0.555803i	0.659780	+	0.751459i	$0.270650\pi$
$642$		−	1.53590i		−	0.0606171i
$643$	1.45448	+	0.839746i	0.0573592	+	0.0331163i	0.528405	−	0.848992i	$-0.322790\pi$
$643$	1.45448	+	0.839746i	0.0573592	+	0.0331163i	−0.471046	+	0.882109i	$0.656123\pi$
$644$	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	0.882547	−	0.470225i	$-0.155827\pi$
$647$	0.866025	+	1.50000i	0.0340470	+	0.0589711i	−0.848500	+	0.529196i	$0.822494\pi$
$648$	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	0.728845	−	0.684679i	$-0.240058\pi$
$653$	−5.83975	−	10.1147i	−0.228527	−	0.395820i	−0.957372	+	0.288859i	$0.906724\pi$
$654$	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	0.319571	+	0.947562i	$0.396461\pi$
$659$	−16.9641	+	29.3827i	−0.660828	+	1.14459i	−0.980399	+	0.197025i	$0.936872\pi$
$660$	1.36603	+	2.36603i	0.0531725	+	0.0920974i
$661$	23.9090	−	13.8038i	0.929951	−	0.536907i	0.0431549	−	0.999068i	$-0.486259\pi$
$661$	23.9090	−	13.8038i	0.929951	−	0.536907i	0.886796	+	0.462161i	$0.152926\pi$
$662$	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	−0.793562	−	0.608489i	$-0.791776\pi$
$673$	−23.9641	−	41.5070i	−0.923748	−	1.59998i	−0.130186	−	0.991490i	$-0.541557\pi$
$674$	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	−0.00570987	−	0.999984i	$-0.501818\pi$
$683$	−22.8564	−	13.1962i	−0.874576	−	0.504937i	−0.868866	+	0.495047i	$0.835151\pi$
$684$			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	0.356314	−	0.934366i	$-0.384033\pi$
$691$	35.3205	−	20.3923i	1.34366	−	0.775760i	0.987342	+	0.158607i	$0.0507002\pi$
$692$	−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	0.837242	−	0.546833i	$-0.184167\pi$
$709$	20.8301	+	12.0263i	0.782292	+	0.451656i	−0.0549501	+	0.998489i	$0.517500\pi$
$710$			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	−0.836161	−	0.548484i	$-0.815205\pi$
$719$	1.52628	−	2.64359i	0.0569206	−	0.0985894i	0.893082	+	0.449895i	$0.148538\pi$
$720$		−	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	$0.0404140\pi$
$733$			6.85641i			0.253247i	−0.991951	+	0.126624i	$0.959586\pi$
$734$	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	−0.394712	−	0.918805i	$-0.629155\pi$
$739$	5.53590	−	3.19615i	0.203641	−	0.117572i	0.598353	+	0.801233i	$0.295822\pi$
$740$	−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	−0.776897	−	0.629628i	$-0.783207\pi$
$743$	−16.9019	+	9.75833i	−0.620071	+	0.357998i	0.156825	+	0.987626i	$0.449874\pi$
$744$	−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	0.796674	−	0.604409i	$-0.206591\pi$
$751$	−3.42820	−	5.93782i	−0.125097	−	0.216674i	−0.921771	+	0.387735i	$0.873258\pi$
$752$	−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	0.971339	+	0.237698i	$0.0763928\pi$
$757$	19.0263	+	32.9545i	0.691522	+	1.19775i	−0.279817	+	0.960053i	$0.590274\pi$
$758$	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	0.489296	−	0.872118i	$-0.337254\pi$
$761$	−0.588457	−	0.339746i	−0.0213316	−	0.0123158i	−0.510628	+	0.859802i	$0.670587\pi$
$762$			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	−0.0671118	−	0.997745i	$-0.521378\pi$
$769$	21.1699	−	12.2224i	0.763405	−	0.440752i	0.830517	+	0.556993i	$0.188045\pi$
$770$	−1.36603	−	2.36603i	−0.0492281	−	0.0852656i
$771$	−5.52628	+	9.57180i	−0.199024	+	0.344720i
$772$			17.1962i			0.618903i
$773$	36.7128	+	21.1962i	1.32047	+	0.762373i	0.983803	−	0.179252i	$-0.0573677\pi$
$773$	36.7128	+	21.1962i	1.32047	+	0.762373i	0.336665	+	0.941625i	$0.390701\pi$
$774$	−0.633975	−	0.366025i	−0.0227877	−	0.0131565i
$775$			34.1962i			1.22836i
$776$	−0.366025	+	0.633975i	−0.0131395	+	0.0227584i
$777$	0.633975	+	1.09808i	0.0227437	+	0.0393933i
$778$	−28.7321	+	16.5885i	−1.03009	+	0.594725i
$779$	−31.2487			−1.11960
$780$	2.56218	+	0.633975i	0.0917407	+	0.0226999i
$781$	−8.19615			−0.293281
$782$	−0.803848	+	0.464102i	−0.0287455	+	0.0165962i
$783$	−1.50000	−	2.59808i	−0.0536056	−	0.0928477i
$784$	0.500000	−	0.866025i	0.0178571	−	0.0309295i
$785$			11.3205i			0.404046i
$786$	−16.3923	−	9.46410i	−0.584694	−	0.337573i
$787$	−48.3109	−	27.8923i	−1.72210	−	0.994253i	−0.914575	−	0.404416i	$-0.867475\pi$
$787$	−48.3109	−	27.8923i	−1.72210	−	0.994253i	−0.807522	−	0.589837i	$-0.799192\pi$
$788$		−	2.26795i		−	0.0807923i
$789$	−9.36603	+	16.2224i	−0.333439	+	0.577534i
$790$	3.97372	+	6.88269i	0.141379	+	0.244875i
$791$	8.83013	−	5.09808i	0.313963	−	0.181267i
$792$	3.73205			0.132613
$793$	30.4808	+	29.3301i	1.08240	+	1.04154i
$794$	16.4641			0.584289
$795$	−6.63397	+	3.83013i	−0.235283	+	0.135841i
$796$	2.09808	+	3.63397i	0.0743643	+	0.128803i
$797$	−0.366025	+	0.633975i	−0.0129653	+	0.0224565i	−0.872435	−	0.488730i	$-0.837460\pi$
$797$	−0.366025	+	0.633975i	−0.0129653	+	0.0224565i	0.859470	+	0.511186i	$0.170794\pi$
$798$		−	4.46410i		−	0.158027i
$799$	−1.03590	−	0.598076i	−0.0366475	−	0.0211584i
$800$	3.86603	+	2.23205i	0.136685	+	0.0789149i
$801$			6.46410i			0.228398i
$802$	5.00000	−	8.66025i	0.176556	−	0.305804i
$803$	12.1962	+	21.1244i	0.430393	+	0.745462i
$804$	−11.1962	+	6.46410i	−0.394858	+	0.227971i
$805$	2.53590			0.0893787
$806$	26.5359	−	7.66025i	0.934687	−	0.269821i
$807$	23.7128			0.834731
$808$	8.66025	−	5.00000i	0.304667	−	0.175899i
$809$	0.0980762	+	0.169873i	0.00344818	+	0.00597242i	0.867744	−	0.497011i	$-0.165569\pi$
$809$	0.0980762	+	0.169873i	0.00344818	+	0.00597242i	−0.864296	+	0.502983i	$0.832236\pi$
$810$	0.366025	−	0.633975i	0.0128608	−	0.0222756i
$811$			15.4641i			0.543018i	0.962436	+	0.271509i	$0.0875227\pi$
$811$			15.4641i			0.543018i	−0.962436	+	0.271509i	$0.912477\pi$
$812$	2.59808	+	1.50000i	0.0911746	+	0.0526397i
$813$	18.6340	+	10.7583i	0.653522	+	0.377311i
$814$		−	4.73205i		−	0.165858i
$815$	−2.85641	+	4.94744i	−0.100056	+	0.173301i
$816$	−0.133975	−	0.232051i	−0.00469005	−	0.00812340i
$817$	2.83013	−	1.63397i	0.0990136	−	0.0571655i
$818$	−13.2679			−0.463903
$819$	−1.00000	−	3.46410i	−0.0349428	−	0.121046i
$820$	5.12436			0.178950
$821$	−39.4808	+	22.7942i	−1.37789	+	0.795524i	−0.991905	−	0.126982i	$-0.959471\pi$
$821$	−39.4808	+	22.7942i	−1.37789	+	0.795524i	−0.385983	+	0.922506i	$0.626138\pi$
$822$	−7.73205	−	13.3923i	−0.269686	−	0.467110i
$823$	3.53590	−	6.12436i	0.123254	−	0.213482i	−0.797795	−	0.602928i	$-0.794000\pi$
$823$	3.53590	−	6.12436i	0.123254	−	0.213482i	0.921049	+	0.389447i	$0.127334\pi$
$824$			12.1962i			0.424873i
$825$	−14.4282	−	8.33013i	−0.502326	−	0.290018i
$826$	−0.803848	−	0.464102i	−0.0279694	−	0.0161482i
$827$			19.6077i			0.681826i	0.940095	+	0.340913i	$0.110736\pi$
$827$			19.6077i			0.681826i	−0.940095	+	0.340913i	$0.889264\pi$
$828$	−1.73205	+	3.00000i	−0.0601929	+	0.104257i
$829$	8.33013	+	14.4282i	0.289317	+	0.501112i	0.973647	−	0.228061i	$-0.0732384\pi$
$829$	8.33013	+	14.4282i	0.289317	+	0.501112i	−0.684330	+	0.729173i	$0.739905\pi$
$830$	−3.58846	+	2.07180i	−0.124557	+	0.0719131i
$831$	−26.3923			−0.915539
$832$	0.866025	−	3.50000i	0.0300240	−	0.121341i
$833$	0.267949			0.00928389
$834$	−15.6962	+	9.06218i	−0.543513	+	0.313798i
$835$	−2.14359	−	3.71281i	−0.0741821	−	0.128487i
$836$	−8.33013	+	14.4282i	−0.288103	+	0.499010i
$837$		−	7.66025i		−	0.264777i
$838$	−5.36603	−	3.09808i	−0.185366	−	0.107021i
$839$	5.53590	+	3.19615i	0.191120	+	0.110343i	0.592507	−	0.805565i	$-0.298138\pi$
$839$	5.53590	+	3.19615i	0.191120	+	0.110343i	−0.401387	+	0.915909i	$0.631472\pi$
$840$			0.732051i			0.0252582i
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−7.19615	−	12.4641i	−0.247996	−	0.429541i
$843$	15.7583	−	9.09808i	0.542746	−	0.313354i
$844$	15.8564			0.545800
$845$	−4.43782	+	8.41858i	−0.152666	+	0.289608i
$846$	−4.46410			−0.153479
$847$	2.53590	−	1.46410i	0.0871345	−	0.0503071i
$848$	5.23205	+	9.06218i	0.179669	+	0.311196i
$849$	11.4641	−	19.8564i	0.393447	−	0.681470i
$850$			1.19615i			0.0410277i
$851$	3.80385	+	2.19615i	0.130394	+	0.0752831i
$852$	1.90192	+	1.09808i	0.0651588	+	0.0376195i
$853$		−	12.6077i		−	0.431679i	−0.976429	−	0.215840i	$-0.930751\pi$
$853$		−	12.6077i		−	0.431679i	0.976429	−	0.215840i	$-0.0692488\pi$
$854$	−5.86603	+	10.1603i	−0.200731	+	0.347677i
$855$	1.63397	+	2.83013i	0.0558808	+	0.0967883i
$856$	−1.33013	+	0.767949i	−0.0454628	+	0.0262480i
$857$	42.3923			1.44809			0.724047	−	0.689751i	$-0.242280\pi$
$857$	42.3923			1.44809			0.724047	+	0.689751i	$0.242280\pi$
$858$	−3.23205	+	13.0622i	−0.110340	+	0.445935i
$859$	−6.94744			−0.237044			−0.118522	−	0.992951i	$-0.537816\pi$
$859$	−6.94744			−0.237044			−0.118522	+	0.992951i	$0.537816\pi$
$860$	−0.464102	+	0.267949i	−0.0158257	+	0.00913699i
$861$	−3.50000	−	6.06218i	−0.119280	−	0.206598i
$862$	−10.5622	+	18.2942i	−0.359749	+	0.623104i
$863$		−	40.6410i		−	1.38344i	−0.722168	−	0.691718i	$-0.756854\pi$
$863$		−	40.6410i		−	1.38344i	0.722168	−	0.691718i	$-0.243146\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	−13.1436	−	7.58846i	−0.446896	−	0.258015i
$866$			8.92820i			0.303393i
$867$	−8.46410	+	14.6603i	−0.287456	+	0.497888i
$868$	3.83013	+	6.63397i	0.130003	+	0.225172i
$869$	−35.0885	+	20.2583i	−1.19029	+	0.687217i
$870$	−2.19615			−0.0744565
$871$	−12.9282	−	44.7846i	−0.438055	−	1.51747i
$872$	−3.66025			−0.123952
$873$	−0.633975	+	0.366025i	−0.0214568	+	0.0123881i
$874$	−7.73205	−	13.3923i	−0.261541	−	0.453001i
$875$	3.46410	−	6.00000i	0.117108	−	0.202837i
$876$		−	6.53590i		−	0.220828i
$877$	43.5622	+	25.1506i	1.47099	+	0.849277i	0.999469	−	0.0325782i	$-0.0103718\pi$
$877$	43.5622	+	25.1506i	1.47099	+	0.849277i	0.471521	+	0.881855i	$0.343705\pi$
$878$	14.1962	+	8.19615i	0.479097	+	0.276607i
$879$		−	12.7846i		−	0.431214i
$880$	1.36603	−	2.36603i	0.0460487	−	0.0797587i
$881$	7.46410	+	12.9282i	0.251472	+	0.435562i	0.963931	−	0.266151i	$-0.0857520\pi$
$881$	7.46410	+	12.9282i	0.251472	+	0.435562i	−0.712459	+	0.701713i	$0.752419\pi$
$882$	0.866025	−	0.500000i	0.0291606	−	0.0168359i
$883$	24.4449			0.822635			0.411318	−	0.911492i	$-0.365069\pi$
$883$	24.4449			0.822635			0.411318	+	0.911492i	$0.365069\pi$
$884$	0.928203	−	0.267949i	0.0312189	−	0.00901211i
$885$	0.679492			0.0228409
$886$	27.1865	−	15.6962i	0.913349	−	0.527323i
$887$	−3.47372	−	6.01666i	−0.116636	−	0.202020i	0.801796	−	0.597597i	$-0.203878\pi$
$887$	−3.47372	−	6.01666i	−0.116636	−	0.202020i	−0.918433	+	0.395578i	$0.870544\pi$
$888$	−0.633975	+	1.09808i	−0.0212748	+	0.0368490i
$889$		−	12.5359i		−	0.420441i
$890$	4.09808	+	2.36603i	0.137368	+	0.0793094i
$891$	3.23205	+	1.86603i	0.108278	+	0.0625142i
$892$		−	8.39230i		−	0.280995i
$893$	9.96410	−	17.2583i	0.333436	−	0.577528i
$894$	9.46410	+	16.3923i	0.316527	+	0.548241i
$895$	14.1962	−	8.19615i	0.474525	−	0.273967i
$896$	1.00000			0.0334077
$897$	−9.00000	−	8.66025i	−0.300501	−	0.289157i
$898$	10.7321			0.358133
$899$	−19.9019	+	11.4904i	−0.663766	+	0.383226i
$900$	2.23205	+	3.86603i	0.0744017	+	0.128868i
$901$	−1.40192	+	2.42820i	−0.0467049	+	0.0808952i
$902$			26.1244i			0.869846i
$903$	0.633975	+	0.366025i	0.0210974	+	0.0121806i
$904$	8.83013	+	5.09808i	0.293686	+	0.169559i
$905$			0.875644i			0.0291074i
$906$	−6.59808	+	11.4282i	−0.219206	+	0.379677i
$907$	−10.2679	−	17.7846i	−0.340942	−	0.590528i	0.643666	−	0.765306i	$-0.277413\pi$
$907$	−10.2679	−	17.7846i	−0.340942	−	0.590528i	−0.984608	+	0.174778i	$0.944079\pi$
$908$	7.39230	−	4.26795i	0.245322	−	0.141637i
$909$	10.0000			0.331679
$910$	−2.56218	−	0.633975i	−0.0849354	−	0.0210161i
$911$	38.0526			1.26074			0.630369	−	0.776296i	$-0.282904\pi$
$911$	38.0526			1.26074			0.630369	+	0.776296i	$0.282904\pi$
$912$	3.86603	−	2.23205i	0.128017	−	0.0739106i
$913$	−10.5622	−	18.2942i	−0.349557	−	0.605451i
$914$	−3.39230	+	5.87564i	−0.112207	+	0.194349i
$915$		−	8.58846i		−	0.283926i
$916$	8.93782	+	5.16025i	0.295314	+	0.170500i
$917$	16.3923	+	9.46410i	0.541322	+	0.312532i
$918$		−	0.267949i		−	0.00884364i
$919$	13.8205	−	23.9378i	0.455896	−	0.789636i	−0.542843	−	0.839834i	$-0.682652\pi$
$919$	13.8205	−	23.9378i	0.455896	−	0.789636i	0.998739	+	0.0501985i	$0.0159854\pi$
$920$	1.26795	+	2.19615i	0.0418030	+	0.0724050i
$921$	−29.2583	+	16.8923i	−0.964095	+	0.556620i
$922$	27.7128			0.912673
$923$	−5.49038	+	5.70577i	−0.180718	+	0.187808i
$924$	−3.73205			−0.122775
$925$	4.90192	−	2.83013i	0.161174	−	0.0930540i
$926$	−0.598076	−	1.03590i	−0.0196540	−	0.0340417i
$927$	−6.09808	+	10.5622i	−0.200287	+	0.346907i
$928$			3.00000i			0.0984798i
$929$	43.7032	+	25.2321i	1.43386	+	0.827837i	0.997412	−	0.0718951i	$-0.0229047\pi$
$929$	43.7032	+	25.2321i	1.43386	+	0.827837i	0.436443	+	0.899732i	$0.356238\pi$
$930$	−4.85641	−	2.80385i	−0.159248	−	0.0919418i
$931$			4.46410i			0.146305i
$932$	−1.09808	+	1.90192i	−0.0359687	+	0.0622996i
$933$	9.59808	+	16.6244i	0.314227	+	0.544257i
$934$	−8.53590	+	4.92820i	−0.279303	+	0.161256i
$935$	0.732051			0.0239406
$936$	2.50000	−	2.59808i	0.0817151	−	0.0849208i
$937$	−37.5692			−1.22733			−0.613666	−	0.789565i	$-0.710306\pi$
$937$	−37.5692			−1.22733			−0.613666	+	0.789565i	$0.710306\pi$
$938$	11.1962	−	6.46410i	0.365567	−	0.211060i
$939$	0.901924	+	1.56218i	0.0294332	+	0.0509797i
$940$	−1.63397	+	2.83013i	−0.0532944	+	0.0923086i
$941$		−	13.1769i		−	0.429555i	−0.976663	−	0.214778i	$-0.931097\pi$
$941$		−	13.1769i		−	0.429555i	0.976663	−	0.214778i	$-0.0689027\pi$
$942$	13.3923	+	7.73205i	0.436345	+	0.251924i
$943$	−21.0000	−	12.1244i	−0.683854	−	0.394823i
$944$		−	0.928203i		−	0.0302104i
$945$	−0.366025	+	0.633975i	−0.0119068	+	0.0206232i
$946$	−1.36603	−	2.36603i	−0.0444133	−	0.0769261i
$947$	−44.2128	+	25.5263i	−1.43672	+	0.829493i	−0.997621	−	0.0689442i	$-0.978037\pi$
$947$	−44.2128	+	25.5263i	−1.43672	+	0.829493i	−0.439103	+	0.898437i	$0.644704\pi$
$948$	10.8564			0.352600
$949$	22.8756	+	5.66025i	0.742575	+	0.183740i
$950$	−19.9282			−0.646556
$951$	−15.5885	+	9.00000i	−0.505490	+	0.291845i
$952$	0.133975	+	0.232051i	0.00434214	+	0.00752081i
$953$	25.6865	−	44.4904i	0.832068	−	1.44118i	−0.0643267	−	0.997929i	$-0.520490\pi$
$953$	25.6865	−	44.4904i	0.832068	−	1.44118i	0.896395	−	0.443256i	$-0.146177\pi$
$954$			10.4641i			0.338788i
$955$	−2.66025	−	1.53590i	−0.0860838	−	0.0497005i
$956$	11.9545	+	6.90192i	0.386636	+	0.223224i
$957$		−	11.1962i		−	0.361920i
$958$	−15.6962	+	27.1865i	−0.507120	+	0.878357i
$959$	7.73205	+	13.3923i	0.249681	+	0.432460i
$960$	−0.633975	+	0.366025i	−0.0204614	+	0.0118134i
$961$	−27.6795			−0.892887
$962$	−3.29423	−	3.16987i	−0.106210	−	0.102201i
$963$	−1.53590			−0.0494936
$964$	−11.0718	+	6.39230i	−0.356599	+	0.205882i
$965$	6.29423	+	10.9019i	0.202618	+	0.350945i
$966$	1.73205	−	3.00000i	0.0557278	−	0.0965234i
$967$		−	36.0000i		−	1.15768i	−0.815440	−	0.578841i	$-0.803505\pi$
$967$		−	36.0000i		−	1.15768i	0.815440	−	0.578841i	$-0.196495\pi$
$968$	2.53590	+	1.46410i	0.0815069	+	0.0470580i
$969$	1.03590	+	0.598076i	0.0332779	+	0.0192130i
$970$			0.535898i			0.0172067i
$971$	−22.1244	+	38.3205i	−0.710004	+	1.22976i	0.254851	+	0.966980i	$0.417974\pi$
$971$	−22.1244	+	38.3205i	−0.710004	+	1.22976i	−0.964855	+	0.262783i	$0.915360\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	15.6962	−	9.06218i	0.503196	−	0.290520i
$974$	−21.1962			−0.679169
$975$	−15.4641	+	4.46410i	−0.495248	+	0.142966i
$976$	−11.7321			−0.375534
$977$	15.8038	−	9.12436i	0.505610	−	0.291914i	−0.225417	−	0.974262i	$-0.572375\pi$
$977$	15.8038	−	9.12436i	0.505610	−	0.291914i	0.731027	+	0.682348i	$0.239041\pi$
$978$	3.90192	+	6.75833i	0.124770	+	0.216108i
$979$	−12.0622	+	20.8923i	−0.385509	+	0.667721i
$980$		−	0.732051i		−	0.0233845i
$981$	−3.16987	−	1.83013i	−0.101206	−	0.0584315i
$982$	−31.3923	−	18.1244i	−1.00177	−	0.578371i
$983$			28.1436i			0.897641i	0.893622	+	0.448821i	$0.148156\pi$
$983$			28.1436i			0.897641i	−0.893622	+	0.448821i	$0.851844\pi$
$984$	3.50000	−	6.06218i	0.111576	−	0.193255i
$985$	−0.830127	−	1.43782i	−0.0264500	−	0.0458128i
$986$	−0.696152	+	0.401924i	−0.0221700	+	0.0127999i
$987$	4.46410			0.142094
$988$	4.46410	+	15.4641i	0.142022	+	0.491979i
$989$	2.53590			0.0806369
$990$	2.36603	−	1.36603i	0.0751972	−	0.0434151i
$991$	2.30385	+	3.99038i	0.0731841	+	0.126759i	0.900295	−	0.435280i	$-0.143351\pi$
$991$	2.30385	+	3.99038i	0.0731841	+	0.126759i	−0.827111	+	0.562039i	$0.810017\pi$
$992$	−3.83013	+	6.63397i	−0.121607	+	0.210629i
$993$		−	16.9282i		−	0.537200i
$994$	−1.90192	−	1.09808i	−0.0603254	−	0.0348289i
$995$	2.66025	+	1.53590i	0.0843357	+	0.0486913i
$996$			5.66025i			0.179352i
$997$	−21.1147	+	36.5718i	−0.668710	+	1.15824i	0.309555	+	0.950882i	$0.399820\pi$
$997$	−21.1147	+	36.5718i	−0.668710	+	1.15824i	−0.978265	+	0.207359i	$0.933513\pi$
$998$	−6.49038	−	11.2417i	−0.205449	−	0.355849i
$999$	−1.09808	+	0.633975i	−0.0347416	+	0.0200581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.s.d.127.1	yes	4
3.2	odd	2		1638.2.bj.d.127.2		4
13.2	odd	12		7098.2.a.bj.1.1		2
13.4	even	6	inner	546.2.s.d.43.1	✓	4
13.11	odd	12		7098.2.a.bs.1.2		2
39.17	odd	6		1638.2.bj.d.1135.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.d.43.1	✓	4	13.4	even	6	inner
546.2.s.d.127.1	yes	4	1.1	even	1	trivial
1638.2.bj.d.127.2		4	3.2	odd	2
1638.2.bj.d.1135.2		4	39.17	odd	6
7098.2.a.bj.1.1		2	13.2	odd	12
7098.2.a.bs.1.2		2	13.11	odd	12

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