LMFDB - Embedded newform 28.2.f.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [28,2,Mod(3,28)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(28, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("28.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 28 = 2^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	28.f (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:	$0.223581125660$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			3.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	28.3
Dual form			28.2.f.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 - 0.366025i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(-1.73205 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.36603 - 0.366025i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(-1.73205 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.36603 - 0.633975i) q^{10} +(0.866025 + 0.500000i) q^{11} +(3.00000 - 1.73205i) q^{12} -3.46410i q^{13} +(3.09808 - 2.09808i) q^{14} +3.00000i q^{15} +(2.00000 + 3.46410i) q^{16} +(-1.50000 - 0.866025i) q^{17} +(-2.59808 - 4.50000i) q^{19} -3.46410 q^{20} +(1.50000 + 4.33013i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(0.866025 - 0.500000i) q^{23} +(-4.73205 + 1.26795i) q^{24} +(-1.00000 + 1.73205i) q^{25} +(-1.26795 + 4.73205i) q^{26} +5.19615 q^{27} +(-5.00000 + 1.73205i) q^{28} +4.00000 q^{29} +(1.09808 - 4.09808i) q^{30} +(-0.866025 + 1.50000i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(1.50000 - 0.866025i) q^{33} +(1.73205 + 1.73205i) q^{34} +(0.866025 - 4.50000i) q^{35} +(-1.50000 - 2.59808i) q^{37} +(1.90192 + 7.09808i) q^{38} +(-5.19615 - 3.00000i) q^{39} +(4.73205 + 1.26795i) q^{40} +3.46410i q^{41} +(-0.464102 - 6.46410i) q^{42} +2.00000i q^{43} +(1.00000 + 1.73205i) q^{44} +(-1.36603 + 0.366025i) q^{46} +(4.33013 + 7.50000i) q^{47} +6.92820 q^{48} +(-1.00000 - 6.92820i) q^{49} +(2.00000 - 2.00000i) q^{50} +(-2.59808 + 1.50000i) q^{51} +(3.46410 - 6.00000i) q^{52} +(0.500000 - 0.866025i) q^{53} +(-7.09808 - 1.90192i) q^{54} -1.73205 q^{55} +(7.46410 - 0.535898i) q^{56} -9.00000 q^{57} +(-5.46410 - 1.46410i) q^{58} +(-2.59808 + 4.50000i) q^{59} +(-3.00000 + 5.19615i) q^{60} +(-4.50000 + 2.59808i) q^{61} +(1.73205 - 1.73205i) q^{62} +8.00000i q^{64} +(3.00000 + 5.19615i) q^{65} +(-2.36603 + 0.633975i) q^{66} +(2.59808 + 1.50000i) q^{67} +(-1.73205 - 3.00000i) q^{68} -1.73205i q^{69} +(-2.83013 + 5.83013i) q^{70} -14.0000i q^{71} +(7.50000 + 4.33013i) q^{73} +(1.09808 + 4.09808i) q^{74} +(1.73205 + 3.00000i) q^{75} -10.3923i q^{76} +(-2.50000 + 0.866025i) q^{77} +(6.00000 + 6.00000i) q^{78} +(7.79423 - 4.50000i) q^{79} +(-6.00000 - 3.46410i) q^{80} +(4.50000 - 7.79423i) q^{81} +(1.26795 - 4.73205i) q^{82} -13.8564 q^{83} +(-1.73205 + 9.00000i) q^{84} +3.00000 q^{85} +(0.732051 - 2.73205i) q^{86} +(3.46410 - 6.00000i) q^{87} +(-0.732051 - 2.73205i) q^{88} +(13.5000 - 7.79423i) q^{89} +(6.92820 + 6.00000i) q^{91} +2.00000 q^{92} +(1.50000 + 2.59808i) q^{93} +(-3.16987 - 11.8301i) q^{94} +(7.79423 + 4.50000i) q^{95} +(-9.46410 - 2.53590i) q^{96} +17.3205i q^{97} +(-1.16987 + 9.83013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 6 q^{5} - 8 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 6 * q^5 - 8 * q^8	$ 4 q - 2 q^{2} - 6 q^{5} - 8 q^{8} + 6 q^{10} + 12 q^{12} + 2 q^{14} + 8 q^{16} - 6 q^{17} + 6 q^{21} - 4 q^{22} - 12 q^{24} - 4 q^{25} - 12 q^{26} - 20 q^{28} + 16 q^{29} - 6 q^{30} + 8 q^{32} + 6 q^{33} - 6 q^{37} + 18 q^{38} + 12 q^{40} + 12 q^{42} + 4 q^{44} - 2 q^{46} - 4 q^{49} + 8 q^{50} + 2 q^{53} - 18 q^{54} + 16 q^{56} - 36 q^{57} - 8 q^{58} - 12 q^{60} - 18 q^{61} + 12 q^{65} - 6 q^{66} + 6 q^{70} + 30 q^{73} - 6 q^{74} - 10 q^{77} + 24 q^{78} - 24 q^{80} + 18 q^{81} + 12 q^{82} + 12 q^{85} - 4 q^{86} + 4 q^{88} + 54 q^{89} + 8 q^{92} + 6 q^{93} - 30 q^{94} - 24 q^{96} - 22 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 6 * q^5 - 8 * q^8 + 6 * q^10 + 12 * q^12 + 2 * q^14 + 8 * q^16 - 6 * q^17 + 6 * q^21 - 4 * q^22 - 12 * q^24 - 4 * q^25 - 12 * q^26 - 20 * q^28 + 16 * q^29 - 6 * q^30 + 8 * q^32 + 6 * q^33 - 6 * q^37 + 18 * q^38 + 12 * q^40 + 12 * q^42 + 4 * q^44 - 2 * q^46 - 4 * q^49 + 8 * q^50 + 2 * q^53 - 18 * q^54 + 16 * q^56 - 36 * q^57 - 8 * q^58 - 12 * q^60 - 18 * q^61 + 12 * q^65 - 6 * q^66 + 6 * q^70 + 30 * q^73 - 6 * q^74 - 10 * q^77 + 24 * q^78 - 24 * q^80 + 18 * q^81 + 12 * q^82 + 12 * q^85 - 4 * q^86 + 4 * q^88 + 54 * q^89 + 8 * q^92 + 6 * q^93 - 30 * q^94 - 24 * q^96 - 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i	1.00000			$0$
$4$	1.73205	+	1.00000i	0.866025	+	0.500000i
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	−0.796387	−	0.604787i	$-0.793258\pi$
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	0.125567	+	0.992085i	$0.459925\pi$
$6$	−1.73205	+	1.73205i	−0.707107	+	0.707107i
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$		0			0
$10$	2.36603	−	0.633975i	0.748203	−	0.200480i
$11$	0.866025	+	0.500000i	0.261116	+	0.150756i	0.624844	−	0.780750i	$-0.285163\pi$
$11$	0.866025	+	0.500000i	0.261116	+	0.150756i	−0.363727	+	0.931505i	$0.618496\pi$
$12$	3.00000	−	1.73205i	0.866025	−	0.500000i
$13$		−	3.46410i		−	0.960769i	−0.877058	−	0.480384i	$-0.840497\pi$
$13$		−	3.46410i		−	0.960769i	0.877058	−	0.480384i	$-0.159503\pi$
$14$	3.09808	−	2.09808i	0.827996	−	0.560734i
$15$			3.00000i			0.774597i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−1.50000	−	0.866025i	−0.363803	−	0.210042i	0.306944	−	0.951727i	$-0.400693\pi$
$17$	−1.50000	−	0.866025i	−0.363803	−	0.210042i	−0.670748	+	0.741685i	$0.734027\pi$
$18$		0			0
$19$	−2.59808	−	4.50000i	−0.596040	−	1.03237i	−0.993399	−	0.114708i	$-0.963407\pi$
$19$	−2.59808	−	4.50000i	−0.596040	−	1.03237i	0.397360	−	0.917663i	$-0.369927\pi$
$20$	−3.46410			−0.774597
$21$	1.50000	+	4.33013i	0.327327	+	0.944911i
$22$	−1.00000	−	1.00000i	−0.213201	−	0.213201i
$23$	0.866025	−	0.500000i	0.180579	−	0.104257i	−0.406986	−	0.913434i	$-0.633420\pi$
$23$	0.866025	−	0.500000i	0.180579	−	0.104257i	0.587565	+	0.809177i	$0.300087\pi$
$24$	−4.73205	+	1.26795i	−0.965926	+	0.258819i
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$	−1.26795	+	4.73205i	−0.248665	+	0.928032i
$27$	5.19615			1.00000
$28$	−5.00000	+	1.73205i	−0.944911	+	0.327327i
$29$	4.00000			0.742781			0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000			0.742781			0.371391	+	0.928477i	$0.378881\pi$
$30$	1.09808	−	4.09808i	0.200480	−	0.748203i
$31$	−0.866025	+	1.50000i	−0.155543	+	0.269408i	−0.933257	−	0.359211i	$-0.883046\pi$
$31$	−0.866025	+	1.50000i	−0.155543	+	0.269408i	0.777714	+	0.628619i	$0.216379\pi$
$32$	−1.46410	−	5.46410i	−0.258819	−	0.965926i
$33$	1.50000	−	0.866025i	0.261116	−	0.150756i
$34$	1.73205	+	1.73205i	0.297044	+	0.297044i
$35$	0.866025	−	4.50000i	0.146385	−	0.760639i
$36$		0			0
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	0.715981	−	0.698119i	$-0.245980\pi$
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	−0.962580	+	0.270998i	$0.912646\pi$
$38$	1.90192	+	7.09808i	0.308533	+	1.15146i
$39$	−5.19615	−	3.00000i	−0.832050	−	0.480384i
$40$	4.73205	+	1.26795i	0.748203	+	0.200480i
$41$			3.46410i			0.541002i	0.962720	+	0.270501i	$0.0871893\pi$
$41$			3.46410i			0.541002i	−0.962720	+	0.270501i	$0.912811\pi$
$42$	−0.464102	−	6.46410i	−0.0716124	−	0.997433i
$43$			2.00000i			0.304997i	0.988304	+	0.152499i	$0.0487319\pi$
$43$			2.00000i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$		0			0
$46$	−1.36603	+	0.366025i	−0.201409	+	0.0539675i
$47$	4.33013	+	7.50000i	0.631614	+	1.09399i	0.987222	+	0.159352i	$0.0509405\pi$
$47$	4.33013	+	7.50000i	0.631614	+	1.09399i	−0.355608	+	0.934635i	$0.615726\pi$
$48$	6.92820			1.00000
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$	2.00000	−	2.00000i	0.282843	−	0.282843i
$51$	−2.59808	+	1.50000i	−0.363803	+	0.210042i
$52$	3.46410	−	6.00000i	0.480384	−	0.832050i
$53$	0.500000	−	0.866025i	0.0686803	−	0.118958i	−0.829640	−	0.558298i	$-0.811454\pi$
$53$	0.500000	−	0.866025i	0.0686803	−	0.118958i	0.898321	+	0.439340i	$0.144788\pi$
$54$	−7.09808	−	1.90192i	−0.965926	−	0.258819i
$55$	−1.73205			−0.233550
$56$	7.46410	−	0.535898i	0.997433	−	0.0716124i
$57$	−9.00000			−1.19208
$58$	−5.46410	−	1.46410i	−0.717472	−	0.192246i
$59$	−2.59808	+	4.50000i	−0.338241	+	0.585850i	−0.984102	−	0.177605i	$-0.943165\pi$
$59$	−2.59808	+	4.50000i	−0.338241	+	0.585850i	0.645861	+	0.763455i	$0.276498\pi$
$60$	−3.00000	+	5.19615i	−0.387298	+	0.670820i
$61$	−4.50000	+	2.59808i	−0.576166	+	0.332650i	−0.759608	−	0.650381i	$-0.774609\pi$
$61$	−4.50000	+	2.59808i	−0.576166	+	0.332650i	0.183442	+	0.983030i	$0.441276\pi$
$62$	1.73205	−	1.73205i	0.219971	−	0.219971i
$63$		0			0
$64$			8.00000i			1.00000i
$65$	3.00000	+	5.19615i	0.372104	+	0.644503i
$66$	−2.36603	+	0.633975i	−0.291238	+	0.0780369i
$67$	2.59808	+	1.50000i	0.317406	+	0.183254i	0.650236	−	0.759733i	$-0.274670\pi$
$67$	2.59808	+	1.50000i	0.317406	+	0.183254i	−0.332830	+	0.942987i	$0.608004\pi$
$68$	−1.73205	−	3.00000i	−0.210042	−	0.363803i
$69$		−	1.73205i		−	0.208514i
$70$	−2.83013	+	5.83013i	−0.338265	+	0.696833i
$71$		−	14.0000i		−	1.66149i	−0.556650	−	0.830747i	$-0.687914\pi$
$71$		−	14.0000i		−	1.66149i	0.556650	−	0.830747i	$-0.312086\pi$
$72$		0			0
$73$	7.50000	+	4.33013i	0.877809	+	0.506803i	0.869935	−	0.493166i	$-0.164160\pi$
$73$	7.50000	+	4.33013i	0.877809	+	0.506803i	0.00787336	+	0.999969i	$0.497494\pi$
$74$	1.09808	+	4.09808i	0.127649	+	0.476392i
$75$	1.73205	+	3.00000i	0.200000	+	0.346410i
$76$		−	10.3923i		−	1.19208i
$77$	−2.50000	+	0.866025i	−0.284901	+	0.0986928i
$78$	6.00000	+	6.00000i	0.679366	+	0.679366i
$79$	7.79423	−	4.50000i	0.876919	−	0.506290i	0.00727784	−	0.999974i	$-0.497683\pi$
$79$	7.79423	−	4.50000i	0.876919	−	0.506290i	0.869641	+	0.493684i	$0.164350\pi$
$80$	−6.00000	−	3.46410i	−0.670820	−	0.387298i
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$	1.26795	−	4.73205i	0.140022	−	0.522568i
$83$	−13.8564			−1.52094			−0.760469	−	0.649374i	$-0.775031\pi$
$83$	−13.8564			−1.52094			−0.760469	+	0.649374i	$0.775031\pi$
$84$	−1.73205	+	9.00000i	−0.188982	+	0.981981i
$85$	3.00000			0.325396
$86$	0.732051	−	2.73205i	0.0789391	−	0.294605i
$87$	3.46410	−	6.00000i	0.371391	−	0.643268i
$88$	−0.732051	−	2.73205i	−0.0780369	−	0.291238i
$89$	13.5000	−	7.79423i	1.43100	−	0.826187i	0.433800	−	0.901009i	$-0.357172\pi$
$89$	13.5000	−	7.79423i	1.43100	−	0.826187i	0.997197	+	0.0748225i	$0.0238390\pi$
$90$		0			0
$91$	6.92820	+	6.00000i	0.726273	+	0.628971i
$92$	2.00000			0.208514
$93$	1.50000	+	2.59808i	0.155543	+	0.269408i
$94$	−3.16987	−	11.8301i	−0.326947	−	1.22018i
$95$	7.79423	+	4.50000i	0.799671	+	0.461690i
$96$	−9.46410	−	2.53590i	−0.965926	−	0.258819i
$97$			17.3205i			1.75863i	0.476240	+	0.879316i	$0.342000\pi$
$97$			17.3205i			1.75863i	−0.476240	+	0.879316i	$0.658000\pi$
$98$	−1.16987	+	9.83013i	−0.118175	+	0.992993i
$99$		0			0
$100$	−3.46410	+	2.00000i	−0.346410	+	0.200000i
$101$	−7.50000	−	4.33013i	−0.746278	−	0.430864i	0.0780696	−	0.996948i	$-0.475124\pi$
$101$	−7.50000	−	4.33013i	−0.746278	−	0.430864i	−0.824347	+	0.566084i	$0.808458\pi$
$102$	4.09808	−	1.09808i	0.405770	−	0.108726i
$103$	−4.33013	−	7.50000i	−0.426660	−	0.738997i	0.569914	−	0.821705i	$-0.306977\pi$
$103$	−4.33013	−	7.50000i	−0.426660	−	0.738997i	−0.996574	+	0.0827075i	$0.973643\pi$
$104$	−6.92820	+	6.92820i	−0.679366	+	0.679366i
$105$	−6.00000	−	5.19615i	−0.585540	−	0.507093i
$106$	−1.00000	+	1.00000i	−0.0971286	+	0.0971286i
$107$	−11.2583	+	6.50000i	−1.08838	+	0.628379i	−0.933146	−	0.359498i	$-0.882948\pi$
$107$	−11.2583	+	6.50000i	−1.08838	+	0.628379i	−0.155238	+	0.987877i	$0.549614\pi$
$108$	9.00000	+	5.19615i	0.866025	+	0.500000i
$109$	−4.50000	+	7.79423i	−0.431022	+	0.746552i	−0.996962	−	0.0778949i	$-0.975180\pi$
$109$	−4.50000	+	7.79423i	−0.431022	+	0.746552i	0.565940	+	0.824447i	$0.308513\pi$
$110$	2.36603	+	0.633975i	0.225592	+	0.0604471i
$111$	−5.19615			−0.493197
$112$	−10.3923	−	2.00000i	−0.981981	−	0.188982i
$113$	−16.0000			−1.50515			−0.752577	−	0.658505i	$-0.771189\pi$
$113$	−16.0000			−1.50515			−0.752577	+	0.658505i	$0.771189\pi$
$114$	12.2942	+	3.29423i	1.15146	+	0.308533i
$115$	−0.866025	+	1.50000i	−0.0807573	+	0.139876i
$116$	6.92820	+	4.00000i	0.643268	+	0.371391i
$117$		0			0
$118$	5.19615	−	5.19615i	0.478345	−	0.478345i
$119$	4.33013	−	1.50000i	0.396942	−	0.137505i
$120$	6.00000	−	6.00000i	0.547723	−	0.547723i
$121$	−5.00000	−	8.66025i	−0.454545	−	0.787296i
$122$	7.09808	−	1.90192i	0.642630	−	0.172192i
$123$	5.19615	+	3.00000i	0.468521	+	0.270501i
$124$	−3.00000	+	1.73205i	−0.269408	+	0.155543i
$125$		−	12.1244i		−	1.08444i
$126$		0			0
$127$			6.00000i			0.532414i	0.963916	+	0.266207i	$0.0857705\pi$
$127$			6.00000i			0.532414i	−0.963916	+	0.266207i	$0.914230\pi$
$128$	2.92820	−	10.9282i	0.258819	−	0.965926i
$129$	3.00000	+	1.73205i	0.264135	+	0.152499i
$130$	−2.19615	−	8.19615i	−0.192615	−	0.718850i
$131$	2.59808	+	4.50000i	0.226995	+	0.393167i	0.956916	−	0.290365i	$-0.0937766\pi$
$131$	2.59808	+	4.50000i	0.226995	+	0.393167i	−0.729921	+	0.683531i	$0.760443\pi$
$132$	3.46410			0.301511
$133$	13.5000	+	2.59808i	1.17060	+	0.225282i
$134$	−3.00000	−	3.00000i	−0.259161	−	0.259161i
$135$	−7.79423	+	4.50000i	−0.670820	+	0.387298i
$136$	1.26795	+	4.73205i	0.108726	+	0.405770i
$137$	−0.500000	+	0.866025i	−0.0427179	+	0.0739895i	−0.886594	−	0.462549i	$-0.846935\pi$
$137$	−0.500000	+	0.866025i	−0.0427179	+	0.0739895i	0.843876	+	0.536538i	$0.180268\pi$
$138$	−0.633975	+	2.36603i	−0.0539675	+	0.201409i
$139$	6.92820			0.587643			0.293821	−	0.955860i	$-0.405073\pi$
$139$	6.92820			0.587643			0.293821	+	0.955860i	$0.405073\pi$
$140$	6.00000	−	6.92820i	0.507093	−	0.585540i
$141$	15.0000			1.26323
$142$	−5.12436	+	19.1244i	−0.430026	+	1.60488i
$143$	1.73205	−	3.00000i	0.144841	−	0.250873i
$144$		0			0
$145$	−6.00000	+	3.46410i	−0.498273	+	0.287678i
$146$	−8.66025	−	8.66025i	−0.716728	−	0.716728i
$147$	−11.2583	−	4.50000i	−0.928571	−	0.371154i
$148$		−	6.00000i		−	0.493197i
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	0.844818	−	0.535054i	$-0.179709\pi$
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	−0.885779	+	0.464107i	$0.846375\pi$
$150$	−1.26795	−	4.73205i	−0.103528	−	0.386370i
$151$	−6.06218	−	3.50000i	−0.493333	−	0.284826i	0.232623	−	0.972567i	$-0.425269\pi$
$151$	−6.06218	−	3.50000i	−0.493333	−	0.284826i	−0.725956	+	0.687741i	$0.758602\pi$
$152$	−3.80385	+	14.1962i	−0.308533	+	1.15146i
$153$		0			0
$154$	3.73205	−	0.267949i	0.300737	−	0.0215920i
$155$		−	3.00000i		−	0.240966i
$156$	−6.00000	−	10.3923i	−0.480384	−	0.832050i
$157$	1.50000	+	0.866025i	0.119713	+	0.0691164i	0.558661	−	0.829396i	$-0.311315\pi$
$157$	1.50000	+	0.866025i	0.119713	+	0.0691164i	−0.438948	+	0.898513i	$0.644649\pi$
$158$	−12.2942	+	3.29423i	−0.978076	+	0.262075i
$159$	−0.866025	−	1.50000i	−0.0686803	−	0.118958i
$160$	6.92820	+	6.92820i	0.547723	+	0.547723i
$161$	−0.500000	+	2.59808i	−0.0394055	+	0.204757i
$162$	−9.00000	+	9.00000i	−0.707107	+	0.707107i
$163$	18.1865	−	10.5000i	1.42448	−	0.822423i	0.427802	−	0.903873i	$-0.359288\pi$
$163$	18.1865	−	10.5000i	1.42448	−	0.822423i	0.996678	+	0.0814491i	$0.0259548\pi$
$164$	−3.46410	+	6.00000i	−0.270501	+	0.468521i
$165$	−1.50000	+	2.59808i	−0.116775	+	0.202260i
$166$	18.9282	+	5.07180i	1.46911	+	0.393648i
$167$	17.3205			1.34030			0.670151	−	0.742225i	$-0.266230\pi$
$167$	17.3205			1.34030			0.670151	+	0.742225i	$0.266230\pi$
$168$	5.66025	−	11.6603i	0.436698	−	0.899608i
$169$	1.00000			0.0769231
$170$	−4.09808	−	1.09808i	−0.314308	−	0.0842186i
$171$		0			0
$172$	−2.00000	+	3.46410i	−0.152499	+	0.264135i
$173$	−10.5000	+	6.06218i	−0.798300	+	0.460899i	−0.842876	−	0.538107i	$-0.819140\pi$
$173$	−10.5000	+	6.06218i	−0.798300	+	0.460899i	0.0445762	+	0.999006i	$0.485806\pi$
$174$	−6.92820	+	6.92820i	−0.525226	+	0.525226i
$175$	−1.73205	−	5.00000i	−0.130931	−	0.377964i
$176$			4.00000i			0.301511i
$177$	4.50000	+	7.79423i	0.338241	+	0.585850i
$178$	−21.2942	+	5.70577i	−1.59607	+	0.427666i
$179$	−16.4545	−	9.50000i	−1.22987	−	0.710063i	−0.262864	−	0.964833i	$-0.584667\pi$
$179$	−16.4545	−	9.50000i	−1.22987	−	0.710063i	−0.967002	+	0.254770i	$0.918000\pi$
$180$		0			0
$181$		−	6.92820i		−	0.514969i	−0.966282	−	0.257485i	$-0.917106\pi$
$181$		−	6.92820i		−	0.514969i	0.966282	−	0.257485i	$-0.0828937\pi$
$182$	−7.26795	−	10.7321i	−0.538736	−	0.795513i
$183$			9.00000i			0.665299i
$184$	−2.73205	−	0.732051i	−0.201409	−	0.0539675i
$185$	4.50000	+	2.59808i	0.330847	+	0.191014i
$186$	−1.09808	−	4.09808i	−0.0805149	−	0.300486i
$187$	−0.866025	−	1.50000i	−0.0633300	−	0.109691i
$188$			17.3205i			1.26323i
$189$	−9.00000	+	10.3923i	−0.654654	+	0.755929i
$190$	−9.00000	−	9.00000i	−0.652929	−	0.652929i
$191$	−0.866025	+	0.500000i	−0.0626634	+	0.0361787i	−0.531004	−	0.847369i	$-0.678185\pi$
$191$	−0.866025	+	0.500000i	−0.0626634	+	0.0361787i	0.468341	+	0.883548i	$0.344852\pi$
$192$	12.0000	+	6.92820i	0.866025	+	0.500000i
$193$	7.50000	−	12.9904i	0.539862	−	0.935068i	−0.459049	−	0.888411i	$-0.651810\pi$
$193$	7.50000	−	12.9904i	0.539862	−	0.935068i	0.998911	−	0.0466572i	$-0.0148568\pi$
$194$	6.33975	−	23.6603i	0.455167	−	1.69871i
$195$	10.3923			0.744208
$196$	5.19615	−	13.0000i	0.371154	−	0.928571i
$197$	16.0000			1.13995			0.569976	−	0.821661i	$-0.306952\pi$
$197$	16.0000			1.13995			0.569976	+	0.821661i	$0.306952\pi$
$198$		0			0
$199$	−11.2583	+	19.5000i	−0.798082	+	1.38232i	0.122782	+	0.992434i	$0.460818\pi$
$199$	−11.2583	+	19.5000i	−0.798082	+	1.38232i	−0.920864	+	0.389885i	$0.872515\pi$
$200$	5.46410	−	1.46410i	0.386370	−	0.103528i
$201$	4.50000	−	2.59808i	0.317406	−	0.183254i
$202$	8.66025	+	8.66025i	0.609333	+	0.609333i
$203$	−6.92820	+	8.00000i	−0.486265	+	0.561490i
$204$	−6.00000			−0.420084
$205$	−3.00000	−	5.19615i	−0.209529	−	0.362915i
$206$	3.16987	+	11.8301i	0.220856	+	0.824244i
$207$		0			0
$208$	12.0000	−	6.92820i	0.832050	−	0.480384i
$209$		−	5.19615i		−	0.359425i
$210$	6.29423	+	9.29423i	0.434343	+	0.641363i
$211$			10.0000i			0.688428i	0.938891	+	0.344214i	$0.111855\pi$
$211$			10.0000i			0.688428i	−0.938891	+	0.344214i	$0.888145\pi$
$212$	1.73205	−	1.00000i	0.118958	−	0.0686803i
$213$	−21.0000	−	12.1244i	−1.43890	−	0.830747i
$214$	17.7583	−	4.75833i	1.21393	−	0.325273i
$215$	−1.73205	−	3.00000i	−0.118125	−	0.204598i
$216$	−10.3923	−	10.3923i	−0.707107	−	0.707107i
$217$	−1.50000	−	4.33013i	−0.101827	−	0.293948i
$218$	9.00000	−	9.00000i	0.609557	−	0.609557i
$219$	12.9904	−	7.50000i	0.877809	−	0.506803i
$220$	−3.00000	−	1.73205i	−0.202260	−	0.116775i
$221$	−3.00000	+	5.19615i	−0.201802	+	0.349531i
$222$	7.09808	+	1.90192i	0.476392	+	0.127649i
$223$	−6.92820			−0.463947			−0.231973	−	0.972722i	$-0.574518\pi$
$223$	−6.92820			−0.463947			−0.231973	+	0.972722i	$0.574518\pi$
$224$	13.4641	+	6.53590i	0.899608	+	0.436698i
$225$		0			0
$226$	21.8564	+	5.85641i	1.45387	+	0.389562i
$227$	9.52628	−	16.5000i	0.632281	−	1.09514i	−0.354803	−	0.934941i	$-0.615452\pi$
$227$	9.52628	−	16.5000i	0.632281	−	1.09514i	0.987084	−	0.160202i	$-0.0512147\pi$
$228$	−15.5885	−	9.00000i	−1.03237	−	0.596040i
$229$	−13.5000	+	7.79423i	−0.892105	+	0.515057i	−0.874630	−	0.484790i	$-0.838896\pi$
$229$	−13.5000	+	7.79423i	−0.892105	+	0.515057i	−0.0174746	+	0.999847i	$0.505563\pi$
$230$	1.73205	−	1.73205i	0.114208	−	0.114208i
$231$	−0.866025	+	4.50000i	−0.0569803	+	0.296078i
$232$	−8.00000	−	8.00000i	−0.525226	−	0.525226i
$233$	3.50000	+	6.06218i	0.229293	+	0.397146i	0.957599	−	0.288106i	$-0.0930254\pi$
$233$	3.50000	+	6.06218i	0.229293	+	0.397146i	−0.728306	+	0.685252i	$0.759692\pi$
$234$		0			0
$235$	−12.9904	−	7.50000i	−0.847399	−	0.489246i
$236$	−9.00000	+	5.19615i	−0.585850	+	0.338241i
$237$		−	15.5885i		−	1.01258i
$238$	−6.46410	+	0.464102i	−0.419005	+	0.0300832i
$239$			20.0000i			1.29369i	0.762620	+	0.646846i	$0.223912\pi$
$239$			20.0000i			1.29369i	−0.762620	+	0.646846i	$0.776088\pi$
$240$	−10.3923	+	6.00000i	−0.670820	+	0.387298i
$241$	−4.50000	−	2.59808i	−0.289870	−	0.167357i	0.348013	−	0.937490i	$-0.386857\pi$
$241$	−4.50000	−	2.59808i	−0.289870	−	0.167357i	−0.637883	+	0.770133i	$0.720190\pi$
$242$	3.66025	+	13.6603i	0.235290	+	0.878114i
$243$		0			0
$244$	−10.3923			−0.665299
$245$	7.50000	+	9.52628i	0.479157	+	0.608612i
$246$	−6.00000	−	6.00000i	−0.382546	−	0.382546i
$247$	−15.5885	+	9.00000i	−0.991870	+	0.572656i
$248$	4.73205	−	1.26795i	0.300486	−	0.0805149i
$249$	−12.0000	+	20.7846i	−0.760469	+	1.31717i
$250$	−4.43782	+	16.5622i	−0.280673	+	1.04748i
$251$	3.46410			0.218652			0.109326	−	0.994006i	$-0.465131\pi$
$251$	3.46410			0.218652			0.109326	+	0.994006i	$0.465131\pi$
$252$		0			0
$253$	1.00000			0.0628695
$254$	2.19615	−	8.19615i	0.137799	−	0.514272i
$255$	2.59808	−	4.50000i	0.162698	−	0.281801i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	4.50000	−	2.59808i	0.280702	−	0.162064i	−0.353039	−	0.935609i	$-0.614852\pi$
$257$	4.50000	−	2.59808i	0.280702	−	0.162064i	0.633741	+	0.773545i	$0.281518\pi$
$258$	−3.46410	−	3.46410i	−0.215666	−	0.215666i
$259$	7.79423	+	1.50000i	0.484310	+	0.0932055i
$260$			12.0000i			0.744208i
$261$		0			0
$262$	−1.90192	−	7.09808i	−0.117501	−	0.438521i
$263$	19.9186	+	11.5000i	1.22823	+	0.709120i	0.966660	−	0.256063i	$-0.0824256\pi$
$263$	19.9186	+	11.5000i	1.22823	+	0.709120i	0.261573	+	0.965184i	$0.415759\pi$
$264$	−4.73205	−	1.26795i	−0.291238	−	0.0780369i
$265$			1.73205i			0.106399i
$266$	−17.4904	−	8.49038i	−1.07240	−	0.520579i
$267$		−	27.0000i		−	1.65237i
$268$	3.00000	+	5.19615i	0.183254	+	0.317406i
$269$	19.5000	+	11.2583i	1.18894	+	0.686433i	0.958065	−	0.286552i	$-0.0925091\pi$
$269$	19.5000	+	11.2583i	1.18894	+	0.686433i	0.230871	+	0.972984i	$0.425842\pi$
$270$	12.2942	−	3.29423i	0.748203	−	0.200480i
$271$	−7.79423	−	13.5000i	−0.473466	−	0.820067i	0.526073	−	0.850439i	$-0.323664\pi$
$271$	−7.79423	−	13.5000i	−0.473466	−	0.820067i	−0.999539	+	0.0303728i	$0.990331\pi$
$272$		−	6.92820i		−	0.420084i
$273$	15.0000	−	5.19615i	0.907841	−	0.314485i
$274$	1.00000	−	1.00000i	0.0604122	−	0.0604122i
$275$	−1.73205	+	1.00000i	−0.104447	+	0.0603023i
$276$	1.73205	−	3.00000i	0.104257	−	0.180579i
$277$	6.50000	−	11.2583i	0.390547	−	0.676448i	−0.601975	−	0.798515i	$-0.705619\pi$
$277$	6.50000	−	11.2583i	0.390547	−	0.676448i	0.992522	+	0.122068i	$0.0389525\pi$
$278$	−9.46410	−	2.53590i	−0.567619	−	0.152093i
$279$		0			0
$280$	−10.7321	+	7.26795i	−0.641363	+	0.434343i
$281$	−4.00000			−0.238620			−0.119310	−	0.992857i	$-0.538068\pi$
$281$	−4.00000			−0.238620			−0.119310	+	0.992857i	$0.538068\pi$
$282$	−20.4904	−	5.49038i	−1.22018	−	0.326947i
$283$	6.06218	−	10.5000i	0.360359	−	0.624160i	−0.627661	−	0.778487i	$-0.715988\pi$
$283$	6.06218	−	10.5000i	0.360359	−	0.624160i	0.988020	+	0.154327i	$0.0493208\pi$
$284$	14.0000	−	24.2487i	0.830747	−	1.43890i
$285$	13.5000	−	7.79423i	0.799671	−	0.461690i
$286$	−3.46410	+	3.46410i	−0.204837	+	0.204837i
$287$	−6.92820	−	6.00000i	−0.408959	−	0.354169i
$288$		0			0
$289$	−7.00000	−	12.1244i	−0.411765	−	0.713197i
$290$	9.46410	−	2.53590i	0.555751	−	0.148913i
$291$	25.9808	+	15.0000i	1.52302	+	0.879316i
$292$	8.66025	+	15.0000i	0.506803	+	0.877809i
$293$			20.7846i			1.21425i	0.794606	+	0.607125i	$0.207677\pi$
$293$			20.7846i			1.21425i	−0.794606	+	0.607125i	$0.792323\pi$
$294$	13.7321	+	10.2679i	0.800869	+	0.598839i
$295$		−	9.00000i		−	0.524000i
$296$	−2.19615	+	8.19615i	−0.127649	+	0.476392i
$297$	4.50000	+	2.59808i	0.261116	+	0.150756i
$298$	0.366025	+	1.36603i	0.0212033	+	0.0791317i
$299$	−1.73205	−	3.00000i	−0.100167	−	0.173494i
$300$			6.92820i			0.400000i
$301$	−4.00000	−	3.46410i	−0.230556	−	0.199667i
$302$	7.00000	+	7.00000i	0.402805	+	0.402805i
$303$	−12.9904	+	7.50000i	−0.746278	+	0.430864i
$304$	10.3923	−	18.0000i	0.596040	−	1.03237i
$305$	4.50000	−	7.79423i	0.257669	−	0.446296i
$306$		0			0
$307$	−20.7846			−1.18624			−0.593120	−	0.805114i	$-0.702104\pi$
$307$	−20.7846			−1.18624			−0.593120	+	0.805114i	$0.702104\pi$
$308$	−5.19615	−	1.00000i	−0.296078	−	0.0569803i
$309$	−15.0000			−0.853320
$310$	−1.09808	+	4.09808i	−0.0623665	+	0.232755i
$311$	4.33013	−	7.50000i	0.245539	−	0.425286i	−0.716744	−	0.697336i	$-0.754368\pi$
$311$	4.33013	−	7.50000i	0.245539	−	0.425286i	0.962283	+	0.272050i	$0.0877017\pi$
$312$	4.39230	+	16.3923i	0.248665	+	0.928032i
$313$	1.50000	−	0.866025i	0.0847850	−	0.0489506i	−0.457008	−	0.889463i	$-0.651079\pi$
$313$	1.50000	−	0.866025i	0.0847850	−	0.0489506i	0.541793	+	0.840512i	$0.317746\pi$
$314$	−1.73205	−	1.73205i	−0.0977453	−	0.0977453i
$315$		0			0
$316$	18.0000			1.01258
$317$	−5.50000	−	9.52628i	−0.308911	−	0.535049i	0.669214	−	0.743070i	$-0.266631\pi$
$317$	−5.50000	−	9.52628i	−0.308911	−	0.535049i	−0.978124	+	0.208021i	$0.933298\pi$
$318$	0.633975	+	2.36603i	0.0355515	+	0.132680i
$319$	3.46410	+	2.00000i	0.193952	+	0.111979i
$320$	−6.92820	−	12.0000i	−0.387298	−	0.670820i
$321$			22.5167i			1.25676i
$322$	1.63397	−	3.36603i	0.0910578	−	0.187581i
$323$			9.00000i			0.500773i
$324$	15.5885	−	9.00000i	0.866025	−	0.500000i
$325$	6.00000	+	3.46410i	0.332820	+	0.192154i
$326$	−28.6865	+	7.68653i	−1.58880	+	0.425718i
$327$	7.79423	+	13.5000i	0.431022	+	0.746552i
$328$	6.92820	−	6.92820i	0.382546	−	0.382546i
$329$	−22.5000	−	4.33013i	−1.24047	−	0.238728i
$330$	3.00000	−	3.00000i	0.165145	−	0.165145i
$331$	−6.06218	+	3.50000i	−0.333207	+	0.192377i	−0.657264	−	0.753660i	$-0.728286\pi$
$331$	−6.06218	+	3.50000i	−0.333207	+	0.192377i	0.324057	+	0.946038i	$0.394953\pi$
$332$	−24.0000	−	13.8564i	−1.31717	−	0.760469i
$333$		0			0
$334$	−23.6603	−	6.33975i	−1.29463	−	0.346895i
$335$	−5.19615			−0.283896
$336$	−12.0000	+	13.8564i	−0.654654	+	0.755929i
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	−1.36603	−	0.366025i	−0.0743020	−	0.0199092i
$339$	−13.8564	+	24.0000i	−0.752577	+	1.30350i
$340$	5.19615	+	3.00000i	0.281801	+	0.162698i
$341$	−1.50000	+	0.866025i	−0.0812296	+	0.0468979i
$342$		0			0
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$	4.00000	−	4.00000i	0.215666	−	0.215666i
$345$	1.50000	+	2.59808i	0.0807573	+	0.139876i
$346$	16.5622	−	4.43782i	0.890388	−	0.238579i
$347$	−11.2583	−	6.50000i	−0.604379	−	0.348938i	0.166383	−	0.986061i	$-0.446791\pi$
$347$	−11.2583	−	6.50000i	−0.604379	−	0.348938i	−0.770762	+	0.637123i	$0.780124\pi$
$348$	12.0000	−	6.92820i	0.643268	−	0.371391i
$349$		−	10.3923i		−	0.556287i	−0.960539	−	0.278144i	$-0.910281\pi$
$349$		−	10.3923i		−	0.556287i	0.960539	−	0.278144i	$-0.0897191\pi$
$350$	0.535898	+	7.46410i	0.0286450	+	0.398973i
$351$		−	18.0000i		−	0.960769i
$352$	1.46410	−	5.46410i	0.0780369	−	0.291238i
$353$	−25.5000	−	14.7224i	−1.35723	−	0.783596i	−0.367979	−	0.929834i	$-0.619950\pi$
$353$	−25.5000	−	14.7224i	−1.35723	−	0.783596i	−0.989249	+	0.146238i	$0.953283\pi$
$354$	−3.29423	−	12.2942i	−0.175086	−	0.653431i
$355$	12.1244	+	21.0000i	0.643494	+	1.11456i
$356$	31.1769			1.65237
$357$	1.50000	−	7.79423i	0.0793884	−	0.412514i
$358$	19.0000	+	19.0000i	1.00418	+	1.00418i
$359$	19.9186	−	11.5000i	1.05126	−	0.606947i	0.128260	−	0.991741i	$-0.459061\pi$
$359$	19.9186	−	11.5000i	1.05126	−	0.606947i	0.923003	+	0.384794i	$0.125727\pi$
$360$		0			0
$361$	−4.00000	+	6.92820i	−0.210526	+	0.364642i
$362$	−2.53590	+	9.46410i	−0.133284	+	0.497422i
$363$	−17.3205			−0.909091
$364$	6.00000	+	17.3205i	0.314485	+	0.907841i
$365$	−15.0000			−0.785136
$366$	3.29423	−	12.2942i	0.172192	−	0.642630i
$367$	0.866025	−	1.50000i	0.0452062	−	0.0782994i	−0.842537	−	0.538639i	$-0.818939\pi$
$367$	0.866025	−	1.50000i	0.0452062	−	0.0782994i	0.887743	+	0.460339i	$0.152272\pi$
$368$	3.46410	+	2.00000i	0.180579	+	0.104257i
$369$		0			0
$370$	−5.19615	−	5.19615i	−0.270135	−	0.270135i
$371$	0.866025	+	2.50000i	0.0449618	+	0.129794i
$372$			6.00000i			0.311086i
$373$	14.5000	+	25.1147i	0.750782	+	1.30039i	0.947444	+	0.319921i	$0.103656\pi$
$373$	14.5000	+	25.1147i	0.750782	+	1.30039i	−0.196663	+	0.980471i	$0.563010\pi$
$374$	0.633975	+	2.36603i	0.0327820	+	0.122344i
$375$	−18.1865	−	10.5000i	−0.939149	−	0.542218i
$376$	6.33975	−	23.6603i	0.326947	−	1.22018i
$377$		−	13.8564i		−	0.713641i
$378$	16.0981	−	10.9019i	0.827996	−	0.560734i
$379$		−	8.00000i		−	0.410932i	−0.978664	−	0.205466i	$-0.934129\pi$
$379$		−	8.00000i		−	0.410932i	0.978664	−	0.205466i	$-0.0658711\pi$
$380$	9.00000	+	15.5885i	0.461690	+	0.799671i
$381$	9.00000	+	5.19615i	0.461084	+	0.266207i
$382$	1.36603	−	0.366025i	0.0698919	−	0.0187275i
$383$	−2.59808	−	4.50000i	−0.132755	−	0.229939i	0.791982	−	0.610544i	$-0.209049\pi$
$383$	−2.59808	−	4.50000i	−0.132755	−	0.229939i	−0.924738	+	0.380605i	$0.875716\pi$
$384$	−13.8564	−	13.8564i	−0.707107	−	0.707107i
$385$	3.00000	−	3.46410i	0.152894	−	0.176547i
$386$	−15.0000	+	15.0000i	−0.763480	+	0.763480i
$387$		0			0
$388$	−17.3205	+	30.0000i	−0.879316	+	1.52302i
$389$	9.50000	−	16.4545i	0.481669	−	0.834275i	−0.518110	−	0.855314i	$-0.673364\pi$
$389$	9.50000	−	16.4545i	0.481669	−	0.834275i	0.999779	+	0.0210389i	$0.00669738\pi$
$390$	−14.1962	−	3.80385i	−0.718850	−	0.192615i
$391$	−1.73205			−0.0875936
$392$	−11.8564	+	15.8564i	−0.598839	+	0.800869i
$393$	9.00000			0.453990
$394$	−21.8564	−	5.85641i	−1.10111	−	0.295041i
$395$	−7.79423	+	13.5000i	−0.392170	+	0.679259i
$396$		0			0
$397$	16.5000	−	9.52628i	0.828111	−	0.478110i	−0.0250943	−	0.999685i	$-0.507989\pi$
$397$	16.5000	−	9.52628i	0.828111	−	0.478110i	0.853206	+	0.521575i	$0.174655\pi$
$398$	22.5167	−	22.5167i	1.12866	−	1.12866i
$399$	15.5885	−	18.0000i	0.780399	−	0.901127i
$400$	−8.00000			−0.400000
$401$	11.5000	+	19.9186i	0.574283	+	0.994687i	0.996119	+	0.0880147i	$0.0280523\pi$
$401$	11.5000	+	19.9186i	0.574283	+	0.994687i	−0.421837	+	0.906672i	$0.638614\pi$
$402$	−7.09808	+	1.90192i	−0.354020	+	0.0948593i
$403$	5.19615	+	3.00000i	0.258839	+	0.149441i
$404$	−8.66025	−	15.0000i	−0.430864	−	0.746278i
$405$			15.5885i			0.774597i
$406$	12.3923	−	8.39230i	0.615020	−	0.416503i
$407$		−	3.00000i		−	0.148704i
$408$	8.19615	+	2.19615i	0.405770	+	0.108726i
$409$	22.5000	+	12.9904i	1.11255	+	0.642333i	0.939490	−	0.342578i	$-0.111300\pi$
$409$	22.5000	+	12.9904i	1.11255	+	0.642333i	0.173064	+	0.984911i	$0.444633\pi$
$410$	2.19615	+	8.19615i	0.108460	+	0.404779i
$411$	0.866025	+	1.50000i	0.0427179	+	0.0739895i
$412$		−	17.3205i		−	0.853320i
$413$	−4.50000	−	12.9904i	−0.221431	−	0.639215i
$414$		0			0
$415$	20.7846	−	12.0000i	1.02028	−	0.589057i
$416$	−18.9282	+	5.07180i	−0.928032	+	0.248665i
$417$	6.00000	−	10.3923i	0.293821	−	0.508913i
$418$	−1.90192	+	7.09808i	−0.0930261	+	0.347178i
$419$	20.7846			1.01539			0.507697	−	0.861536i	$-0.330497\pi$
$419$	20.7846			1.01539			0.507697	+	0.861536i	$0.330497\pi$
$420$	−5.19615	−	15.0000i	−0.253546	−	0.731925i
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$	3.66025	−	13.6603i	0.178178	−	0.664971i
$423$		0			0
$424$	−2.73205	+	0.732051i	−0.132680	+	0.0355515i
$425$	3.00000	−	1.73205i	0.145521	−	0.0840168i
$426$	24.2487	+	24.2487i	1.17485	+	1.17485i
$427$	2.59808	−	13.5000i	0.125730	−	0.653311i
$428$	−26.0000			−1.25676
$429$	−3.00000	−	5.19615i	−0.144841	−	0.250873i
$430$	1.26795	+	4.73205i	0.0611459	+	0.228200i
$431$	−19.9186	−	11.5000i	−0.959444	−	0.553936i	−0.0634424	−	0.997985i	$-0.520208\pi$
$431$	−19.9186	−	11.5000i	−0.959444	−	0.553936i	−0.896002	+	0.444050i	$0.853541\pi$
$432$	10.3923	+	18.0000i	0.500000	+	0.866025i
$433$			10.3923i			0.499422i	0.968320	+	0.249711i	$0.0803357\pi$
$433$			10.3923i			0.499422i	−0.968320	+	0.249711i	$0.919664\pi$
$434$	0.464102	+	6.46410i	0.0222776	+	0.310287i
$435$			12.0000i			0.575356i
$436$	−15.5885	+	9.00000i	−0.746552	+	0.431022i
$437$	−4.50000	−	2.59808i	−0.215264	−	0.124283i
$438$	−20.4904	+	5.49038i	−0.979068	+	0.262341i
$439$	11.2583	+	19.5000i	0.537331	+	0.930684i	0.999047	+	0.0436563i	$0.0139007\pi$
$439$	11.2583	+	19.5000i	0.537331	+	0.930684i	−0.461716	+	0.887028i	$0.652766\pi$
$440$	3.46410	+	3.46410i	0.165145	+	0.165145i
$441$		0			0
$442$	6.00000	−	6.00000i	0.285391	−	0.285391i
$443$	−14.7224	+	8.50000i	−0.699484	+	0.403847i	−0.807155	−	0.590339i	$-0.798994\pi$
$443$	−14.7224	+	8.50000i	−0.699484	+	0.403847i	0.107671	+	0.994187i	$0.465661\pi$
$444$	−9.00000	−	5.19615i	−0.427121	−	0.246598i
$445$	−13.5000	+	23.3827i	−0.639961	+	1.10845i
$446$	9.46410	+	2.53590i	0.448138	+	0.120078i
$447$	−1.73205			−0.0819232
$448$	−16.0000	−	13.8564i	−0.755929	−	0.654654i
$449$	8.00000			0.377543			0.188772	−	0.982021i	$-0.439549\pi$
$449$	8.00000			0.377543			0.188772	+	0.982021i	$0.439549\pi$
$450$		0			0
$451$	−1.73205	+	3.00000i	−0.0815591	+	0.141264i
$452$	−27.7128	−	16.0000i	−1.30350	−	0.752577i
$453$	−10.5000	+	6.06218i	−0.493333	+	0.284826i
$454$	−19.0526	+	19.0526i	−0.894181	+	0.894181i
$455$	−15.5885	−	3.00000i	−0.730798	−	0.140642i
$456$	18.0000	+	18.0000i	0.842927	+	0.842927i
$457$	−7.50000	−	12.9904i	−0.350835	−	0.607664i	0.635561	−	0.772051i	$-0.280769\pi$
$457$	−7.50000	−	12.9904i	−0.350835	−	0.607664i	−0.986396	+	0.164386i	$0.947436\pi$
$458$	21.2942	−	5.70577i	0.995014	−	0.266613i
$459$	−7.79423	−	4.50000i	−0.363803	−	0.210042i
$460$	−3.00000	+	1.73205i	−0.139876	+	0.0807573i
$461$			17.3205i			0.806696i	0.915047	+	0.403348i	$0.132154\pi$
$461$			17.3205i			0.806696i	−0.915047	+	0.403348i	$0.867846\pi$
$462$	2.83013	−	5.83013i	0.131669	−	0.271242i
$463$		−	30.0000i		−	1.39422i	−0.716965	−	0.697109i	$-0.754469\pi$
$463$		−	30.0000i		−	1.39422i	0.716965	−	0.697109i	$-0.245531\pi$
$464$	8.00000	+	13.8564i	0.371391	+	0.643268i
$465$	−4.50000	−	2.59808i	−0.208683	−	0.120483i
$466$	−2.56218	−	9.56218i	−0.118691	−	0.442959i
$467$	−4.33013	−	7.50000i	−0.200374	−	0.347059i	0.748275	−	0.663389i	$-0.230883\pi$
$467$	−4.33013	−	7.50000i	−0.200374	−	0.347059i	−0.948649	+	0.316330i	$0.897549\pi$
$468$		0			0
$469$	−7.50000	+	2.59808i	−0.346318	+	0.119968i
$470$	15.0000	+	15.0000i	0.691898	+	0.691898i
$471$	2.59808	−	1.50000i	0.119713	−	0.0691164i
$472$	14.1962	−	3.80385i	0.653431	−	0.175086i
$473$	−1.00000	+	1.73205i	−0.0459800	+	0.0796398i
$474$	−5.70577	+	21.2942i	−0.262075	+	0.978076i
$475$	10.3923			0.476832
$476$	9.00000	+	1.73205i	0.412514	+	0.0793884i
$477$		0			0
$478$	7.32051	−	27.3205i	0.334832	−	1.24961i
$479$	−6.06218	+	10.5000i	−0.276988	+	0.479757i	−0.970635	−	0.240558i	$-0.922670\pi$
$479$	−6.06218	+	10.5000i	−0.276988	+	0.479757i	0.693647	+	0.720315i	$0.256003\pi$
$480$	16.3923	−	4.39230i	0.748203	−	0.200480i
$481$	−9.00000	+	5.19615i	−0.410365	+	0.236924i
$482$	5.19615	+	5.19615i	0.236678	+	0.236678i
$483$	3.46410	+	3.00000i	0.157622	+	0.136505i
$484$		−	20.0000i		−	0.909091i
$485$	−15.0000	−	25.9808i	−0.681115	−	1.17973i
$486$		0			0
$487$	26.8468	+	15.5000i	1.21654	+	0.702372i	0.964177	−	0.265260i	$-0.0854576\pi$
$487$	26.8468	+	15.5000i	1.21654	+	0.702372i	0.252367	+	0.967632i	$0.418791\pi$
$488$	14.1962	+	3.80385i	0.642630	+	0.172192i
$489$		−	36.3731i		−	1.64485i
$490$	−6.75833	−	15.7583i	−0.305310	−	0.711889i
$491$			32.0000i			1.44414i	0.691820	+	0.722070i	$0.256809\pi$
$491$			32.0000i			1.44414i	−0.691820	+	0.722070i	$0.743191\pi$
$492$	6.00000	+	10.3923i	0.270501	+	0.468521i
$493$	−6.00000	−	3.46410i	−0.270226	−	0.156015i
$494$	24.5885	−	6.58846i	1.10629	−	0.296429i
$495$		0			0
$496$	−6.92820			−0.311086
$497$	28.0000	+	24.2487i	1.25597	+	1.08770i
$498$	24.0000	−	24.0000i	1.07547	−	1.07547i
$499$	−30.3109	+	17.5000i	−1.35690	+	0.783408i	−0.989205	−	0.146538i	$-0.953187\pi$
$499$	−30.3109	+	17.5000i	−1.35690	+	0.783408i	−0.367697	+	0.929946i	$0.619854\pi$
$500$	12.1244	−	21.0000i	0.542218	−	0.939149i
$501$	15.0000	−	25.9808i	0.670151	−	1.16073i
$502$	−4.73205	−	1.26795i	−0.211202	−	0.0565913i
$503$	6.92820			0.308913			0.154457	−	0.988000i	$-0.450637\pi$
$503$	6.92820			0.308913			0.154457	+	0.988000i	$0.450637\pi$
$504$		0			0
$505$	15.0000			0.667491
$506$	−1.36603	−	0.366025i	−0.0607272	−	0.0162718i
$507$	0.866025	−	1.50000i	0.0384615	−	0.0666173i
$508$	−6.00000	+	10.3923i	−0.266207	+	0.461084i
$509$	10.5000	−	6.06218i	0.465404	−	0.268701i	−0.248910	−	0.968527i	$-0.580072\pi$
$509$	10.5000	−	6.06218i	0.465404	−	0.268701i	0.714314	+	0.699825i	$0.246739\pi$
$510$	−5.19615	+	5.19615i	−0.230089	+	0.230089i
$511$	−21.6506	+	7.50000i	−0.957768	+	0.331780i
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$	−13.5000	−	23.3827i	−0.596040	−	1.03237i
$514$	−7.09808	+	1.90192i	−0.313083	+	0.0838903i
$515$	12.9904	+	7.50000i	0.572425	+	0.330489i
$516$	3.46410	+	6.00000i	0.152499	+	0.264135i
$517$			8.66025i			0.380878i
$518$	−10.0981	−	4.90192i	−0.443684	−	0.215378i
$519$			21.0000i			0.921798i
$520$	4.39230	−	16.3923i	0.192615	−	0.718850i
$521$	1.50000	+	0.866025i	0.0657162	+	0.0379413i	0.532498	−	0.846431i	$-0.321253\pi$
$521$	1.50000	+	0.866025i	0.0657162	+	0.0379413i	−0.466782	+	0.884372i	$0.654587\pi$
$522$		0			0
$523$	−12.9904	−	22.5000i	−0.568030	−	0.983856i	−0.996761	−	0.0804241i	$-0.974373\pi$
$523$	−12.9904	−	22.5000i	−0.568030	−	0.983856i	0.428731	−	0.903432i	$-0.358961\pi$
$524$			10.3923i			0.453990i
$525$	−9.00000	−	1.73205i	−0.392792	−	0.0755929i
$526$	−23.0000	−	23.0000i	−1.00285	−	1.00285i
$527$	2.59808	−	1.50000i	0.113174	−	0.0653410i
$528$	6.00000	+	3.46410i	0.261116	+	0.150756i
$529$	−11.0000	+	19.0526i	−0.478261	+	0.828372i
$530$	0.633975	−	2.36603i	0.0275381	−	0.102774i
$531$		0			0
$532$	20.7846	+	18.0000i	0.901127	+	0.780399i
$533$	12.0000			0.519778
$534$	−9.88269	+	36.8827i	−0.427666	+	1.59607i
$535$	11.2583	−	19.5000i	0.486740	−	0.843059i
$536$	−2.19615	−	8.19615i	−0.0948593	−	0.354020i
$537$	−28.5000	+	16.4545i	−1.22987	+	0.710063i
$538$	−22.5167	−	22.5167i	−0.970762	−	0.970762i
$539$	2.59808	−	6.50000i	0.111907	−	0.279975i
$540$	−18.0000			−0.774597
$541$	9.50000	+	16.4545i	0.408437	+	0.707433i	0.994715	−	0.102677i	$-0.0327407\pi$
$541$	9.50000	+	16.4545i	0.408437	+	0.707433i	−0.586278	+	0.810110i	$0.699407\pi$
$542$	5.70577	+	21.2942i	0.245084	+	0.914665i
$543$	−10.3923	−	6.00000i	−0.445976	−	0.257485i
$544$	−2.53590	+	9.46410i	−0.108726	+	0.405770i
$545$		−	15.5885i		−	0.667736i
$546$	−22.3923	+	1.60770i	−0.958302	+	0.0688030i
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$	−1.73205	+	1.00000i	−0.0739895	+	0.0427179i
$549$		0			0
$550$	2.73205	−	0.732051i	0.116495	−	0.0312148i
$551$	−10.3923	−	18.0000i	−0.442727	−	0.766826i
$552$	−3.46410	+	3.46410i	−0.147442	+	0.147442i
$553$	−4.50000	+	23.3827i	−0.191359	+	0.994333i
$554$	−13.0000	+	13.0000i	−0.552317	+	0.552317i
$555$	7.79423	−	4.50000i	0.330847	−	0.191014i
$556$	12.0000	+	6.92820i	0.508913	+	0.293821i
$557$	−18.5000	+	32.0429i	−0.783870	+	1.35770i	0.145802	+	0.989314i	$0.453424\pi$
$557$	−18.5000	+	32.0429i	−0.783870	+	1.35770i	−0.929672	+	0.368389i	$0.879909\pi$
$558$		0			0
$559$	6.92820			0.293032
$560$	17.3205	−	6.00000i	0.731925	−	0.253546i
$561$	−3.00000			−0.126660
$562$	5.46410	+	1.46410i	0.230489	+	0.0617594i
$563$	11.2583	−	19.5000i	0.474482	−	0.821827i	−0.525091	−	0.851046i	$-0.675969\pi$
$563$	11.2583	−	19.5000i	0.474482	−	0.821827i	0.999573	+	0.0292191i	$0.00930205\pi$
$564$	25.9808	+	15.0000i	1.09399	+	0.631614i
$565$	24.0000	−	13.8564i	1.00969	−	0.582943i
$566$	−12.1244	+	12.1244i	−0.509625	+	0.509625i
$567$	7.79423	+	22.5000i	0.327327	+	0.944911i
$568$	−28.0000	+	28.0000i	−1.17485	+	1.17485i
$569$	6.50000	+	11.2583i	0.272494	+	0.471974i	0.969500	−	0.245092i	$-0.0788181\pi$
$569$	6.50000	+	11.2583i	0.272494	+	0.471974i	−0.697006	+	0.717066i	$0.745485\pi$
$570$	−21.2942	+	5.70577i	−0.891917	+	0.238988i
$571$	18.1865	+	10.5000i	0.761083	+	0.439411i	0.829684	−	0.558233i	$-0.188520\pi$
$571$	18.1865	+	10.5000i	0.761083	+	0.439411i	−0.0686016	+	0.997644i	$0.521854\pi$
$572$	6.00000	−	3.46410i	0.250873	−	0.144841i
$573$			1.73205i			0.0723575i
$574$	7.26795	+	10.7321i	0.303358	+	0.447947i
$575$			2.00000i			0.0834058i
$576$		0			0
$577$	−28.5000	−	16.4545i	−1.18647	−	0.685009i	−0.228968	−	0.973434i	$-0.573535\pi$
$577$	−28.5000	−	16.4545i	−1.18647	−	0.685009i	−0.957503	+	0.288425i	$0.906868\pi$
$578$	5.12436	+	19.1244i	0.213145	+	0.795468i
$579$	−12.9904	−	22.5000i	−0.539862	−	0.935068i
$580$	−13.8564			−0.575356
$581$	24.0000	−	27.7128i	0.995688	−	1.14972i
$582$	−30.0000	−	30.0000i	−1.24354	−	1.24354i
$583$	0.866025	−	0.500000i	0.0358671	−	0.0207079i
$584$	−6.33975	−	23.6603i	−0.262341	−	0.979068i
$585$		0			0
$586$	7.60770	−	28.3923i	0.314271	−	1.17288i
$587$	−6.92820			−0.285958			−0.142979	−	0.989726i	$-0.545668\pi$
$587$	−6.92820			−0.285958			−0.142979	+	0.989726i	$0.545668\pi$
$588$	−15.0000	−	19.0526i	−0.618590	−	0.785714i
$589$	9.00000			0.370839
$590$	−3.29423	+	12.2942i	−0.135621	+	0.506145i
$591$	13.8564	−	24.0000i	0.569976	−	0.987228i
$592$	6.00000	−	10.3923i	0.246598	−	0.427121i
$593$	−13.5000	+	7.79423i	−0.554379	+	0.320071i	−0.750886	−	0.660432i	$-0.770373\pi$
$593$	−13.5000	+	7.79423i	−0.554379	+	0.320071i	0.196508	+	0.980502i	$0.437040\pi$
$594$	−5.19615	−	5.19615i	−0.213201	−	0.213201i
$595$	−5.19615	+	6.00000i	−0.213021	+	0.245976i
$596$		−	2.00000i		−	0.0819232i
$597$	19.5000	+	33.7750i	0.798082	+	1.38232i
$598$	1.26795	+	4.73205i	0.0518503	+	0.193508i
$599$	−14.7224	−	8.50000i	−0.601542	−	0.347301i	0.168106	−	0.985769i	$-0.446235\pi$
$599$	−14.7224	−	8.50000i	−0.601542	−	0.347301i	−0.769648	+	0.638468i	$0.779568\pi$
$600$	2.53590	−	9.46410i	0.103528	−	0.386370i
$601$		−	38.1051i		−	1.55434i	−0.629291	−	0.777170i	$-0.716654\pi$
$601$		−	38.1051i		−	1.55434i	0.629291	−	0.777170i	$-0.283346\pi$
$602$	4.19615	+	6.19615i	0.171022	+	0.252536i
$603$		0			0
$604$	−7.00000	−	12.1244i	−0.284826	−	0.493333i
$605$	15.0000	+	8.66025i	0.609837	+	0.352089i
$606$	20.4904	−	5.49038i	0.832365	−	0.223031i
$607$	7.79423	+	13.5000i	0.316358	+	0.547948i	0.979725	−	0.200346i	$-0.0642066\pi$
$607$	7.79423	+	13.5000i	0.316358	+	0.547948i	−0.663367	+	0.748294i	$0.730873\pi$
$608$	−20.7846	+	20.7846i	−0.842927	+	0.842927i
$609$	6.00000	+	17.3205i	0.243132	+	0.701862i
$610$	−9.00000	+	9.00000i	−0.364399	+	0.364399i
$611$	25.9808	−	15.0000i	1.05107	−	0.606835i
$612$		0			0
$613$	15.5000	−	26.8468i	0.626039	−	1.08433i	−0.362300	−	0.932062i	$-0.618008\pi$
$613$	15.5000	−	26.8468i	0.626039	−	1.08433i	0.988339	−	0.152270i	$-0.0486583\pi$
$614$	28.3923	+	7.60770i	1.14582	+	0.307022i
$615$	−10.3923			−0.419058
$616$	6.73205	+	3.26795i	0.271242	+	0.131669i
$617$	20.0000			0.805170			0.402585	−	0.915383i	$-0.368112\pi$
$617$	20.0000			0.805170			0.402585	+	0.915383i	$0.368112\pi$
$618$	20.4904	+	5.49038i	0.824244	+	0.220856i
$619$	7.79423	−	13.5000i	0.313276	−	0.542611i	−0.665793	−	0.746136i	$-0.731907\pi$
$619$	7.79423	−	13.5000i	0.313276	−	0.542611i	0.979070	+	0.203526i	$0.0652400\pi$
$620$	3.00000	−	5.19615i	0.120483	−	0.208683i
$621$	4.50000	−	2.59808i	0.180579	−	0.104257i
$622$	−8.66025	+	8.66025i	−0.347245	+	0.347245i
$623$	−7.79423	+	40.5000i	−0.312269	+	1.62260i
$624$		−	24.0000i		−	0.960769i
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	−2.36603	+	0.633975i	−0.0945654	+	0.0253387i
$627$	−7.79423	−	4.50000i	−0.311272	−	0.179713i
$628$	1.73205	+	3.00000i	0.0691164	+	0.119713i
$629$			5.19615i			0.207184i
$630$		0			0
$631$			30.0000i			1.19428i	0.802137	+	0.597141i	$0.203697\pi$
$631$			30.0000i			1.19428i	−0.802137	+	0.597141i	$0.796303\pi$
$632$	−24.5885	−	6.58846i	−0.978076	−	0.262075i
$633$	15.0000	+	8.66025i	0.596196	+	0.344214i
$634$	4.02628	+	15.0263i	0.159904	+	0.596770i
$635$	−5.19615	−	9.00000i	−0.206203	−	0.357154i
$636$		−	3.46410i		−	0.137361i
$637$	−24.0000	+	3.46410i	−0.950915	+	0.137253i
$638$	−4.00000	−	4.00000i	−0.158362	−	0.158362i
$639$		0			0
$640$	5.07180	+	18.9282i	0.200480	+	0.748203i
$641$	6.50000	−	11.2583i	0.256735	−	0.444677i	−0.708631	−	0.705580i	$-0.750687\pi$
$641$	6.50000	−	11.2583i	0.256735	−	0.444677i	0.965365	+	0.260902i	$0.0840201\pi$
$642$	8.24167	−	30.7583i	0.325273	−	1.21393i
$643$	13.8564			0.546443			0.273222	−	0.961951i	$-0.411911\pi$
$643$	13.8564			0.546443			0.273222	+	0.961951i	$0.411911\pi$
$644$	−3.46410	+	4.00000i	−0.136505	+	0.157622i
$645$	−6.00000			−0.236250
$646$	3.29423	−	12.2942i	0.129610	−	0.483710i
$647$	−16.4545	+	28.5000i	−0.646892	+	1.12045i	0.336968	+	0.941516i	$0.390598\pi$
$647$	−16.4545	+	28.5000i	−0.646892	+	1.12045i	−0.983861	+	0.178935i	$0.942735\pi$
$648$	−24.5885	+	6.58846i	−0.965926	+	0.258819i
$649$	−4.50000	+	2.59808i	−0.176640	+	0.101983i
$650$	−6.92820	−	6.92820i	−0.271746	−	0.271746i
$651$	−7.79423	−	1.50000i	−0.305480	−	0.0587896i
$652$	42.0000			1.64485
$653$	−15.5000	−	26.8468i	−0.606562	−	1.05060i	−0.991803	−	0.127780i	$-0.959215\pi$
$653$	−15.5000	−	26.8468i	−0.606562	−	1.05060i	0.385241	−	0.922816i	$-0.374118\pi$
$654$	−5.70577	−	21.2942i	−0.223113	−	0.832670i
$655$	−7.79423	−	4.50000i	−0.304546	−	0.175830i
$656$	−12.0000	+	6.92820i	−0.468521	+	0.270501i
$657$		0			0
$658$	29.1506	+	14.1506i	1.13641	+	0.551649i
$659$		−	38.0000i		−	1.48027i	−0.672458	−	0.740135i	$-0.734762\pi$
$659$		−	38.0000i		−	1.48027i	0.672458	−	0.740135i	$-0.265238\pi$
$660$	−5.19615	+	3.00000i	−0.202260	+	0.116775i
$661$	−34.5000	−	19.9186i	−1.34189	−	0.774743i	−0.354809	−	0.934939i	$-0.615454\pi$
$661$	−34.5000	−	19.9186i	−1.34189	−	0.774743i	−0.987085	+	0.160196i	$0.948788\pi$
$662$	9.56218	−	2.56218i	0.371645	−	0.0995819i
$663$	5.19615	+	9.00000i	0.201802	+	0.349531i
$664$	27.7128	+	27.7128i	1.07547	+	1.07547i
$665$	−22.5000	+	7.79423i	−0.872513	+	0.302247i
$666$		0			0
$667$	3.46410	−	2.00000i	0.134131	−	0.0774403i
$668$	30.0000	+	17.3205i	1.16073	+	0.670151i
$669$	−6.00000	+	10.3923i	−0.231973	+	0.401790i
$670$	7.09808	+	1.90192i	0.274223	+	0.0734777i
$671$	−5.19615			−0.200595
$672$	21.4641	−	14.5359i	0.827996	−	0.560734i
$673$	24.0000			0.925132			0.462566	−	0.886585i	$-0.346929\pi$
$673$	24.0000			0.925132			0.462566	+	0.886585i	$0.346929\pi$
$674$		0			0
$675$	−5.19615	+	9.00000i	−0.200000	+	0.346410i
$676$	1.73205	+	1.00000i	0.0666173	+	0.0384615i
$677$	−37.5000	+	21.6506i	−1.44124	+	0.832102i	−0.997933	−	0.0642672i	$-0.979529\pi$
$677$	−37.5000	+	21.6506i	−1.44124	+	0.832102i	−0.443309	+	0.896369i	$0.646196\pi$
$678$	27.7128	−	27.7128i	1.06430	−	1.06430i
$679$	−34.6410	−	30.0000i	−1.32940	−	1.15129i
$680$	−6.00000	−	6.00000i	−0.230089	−	0.230089i
$681$	−16.5000	−	28.5788i	−0.632281	−	1.09514i
$682$	2.36603	−	0.633975i	0.0905998	−	0.0242761i
$683$	21.6506	+	12.5000i	0.828439	+	0.478299i	0.853318	−	0.521391i	$-0.174587\pi$
$683$	21.6506	+	12.5000i	0.828439	+	0.478299i	−0.0248792	+	0.999690i	$0.507920\pi$
$684$		0			0
$685$		−	1.73205i		−	0.0661783i
$686$	−17.6340	−	19.3660i	−0.673268	−	0.739398i
$687$			27.0000i			1.03011i
$688$	−6.92820	+	4.00000i	−0.264135	+	0.152499i
$689$	−3.00000	−	1.73205i	−0.114291	−	0.0659859i
$690$	−1.09808	−	4.09808i	−0.0418030	−	0.156011i
$691$	6.06218	+	10.5000i	0.230616	+	0.399439i	0.957990	−	0.286803i	$-0.0925925\pi$
$691$	6.06218	+	10.5000i	0.230616	+	0.399439i	−0.727373	+	0.686242i	$0.759259\pi$
$692$	−24.2487			−0.921798
$693$		0			0
$694$	13.0000	+	13.0000i	0.493473	+	0.493473i
$695$	−10.3923	+	6.00000i	−0.394203	+	0.227593i
$696$	−18.9282	+	5.07180i	−0.717472	+	0.192246i
$697$	3.00000	−	5.19615i	0.113633	−	0.196818i
$698$	−3.80385	+	14.1962i	−0.143978	+	0.537332i
$699$	12.1244			0.458585
$700$	2.00000	−	10.3923i	0.0755929	−	0.392792i
$701$	−26.0000			−0.982006			−0.491003	−	0.871158i	$-0.663370\pi$
$701$	−26.0000			−0.982006			−0.491003	+	0.871158i	$0.663370\pi$
$702$	−6.58846	+	24.5885i	−0.248665	+	0.928032i
$703$	−7.79423	+	13.5000i	−0.293965	+	0.509162i
$704$	−4.00000	+	6.92820i	−0.150756	+	0.261116i
$705$	−22.5000	+	12.9904i	−0.847399	+	0.489246i
$706$	29.4449	+	29.4449i	1.10817	+	1.10817i
$707$	21.6506	−	7.50000i	0.814256	−	0.282067i
$708$			18.0000i			0.676481i
$709$	4.50000	+	7.79423i	0.169001	+	0.292718i	0.938069	−	0.346449i	$-0.112613\pi$
$709$	4.50000	+	7.79423i	0.169001	+	0.292718i	−0.769068	+	0.639167i	$0.779279\pi$
$710$	−8.87564	−	33.1244i	−0.333097	−	1.24313i
$711$		0			0
$712$	−42.5885	−	11.4115i	−1.59607	−	0.427666i
$713$			1.73205i			0.0648658i
$714$	−4.90192	+	10.0981i	−0.183450	+	0.377911i
$715$			6.00000i			0.224387i
$716$	−19.0000	−	32.9090i	−0.710063	−	1.22987i
$717$	30.0000	+	17.3205i	1.12037	+	0.646846i
$718$	−31.4186	+	8.41858i	−1.17253	+	0.314179i
$719$	12.9904	+	22.5000i	0.484459	+	0.839108i	0.999841	−	0.0178527i	$-0.00568298\pi$
$719$	12.9904	+	22.5000i	0.484459	+	0.839108i	−0.515381	+	0.856961i	$0.672350\pi$
$720$		0			0
$721$	22.5000	+	4.33013i	0.837944	+	0.161262i
$722$	8.00000	−	8.00000i	0.297729	−	0.297729i
$723$	−7.79423	+	4.50000i	−0.289870	+	0.167357i
$724$	6.92820	−	12.0000i	0.257485	−	0.445976i
$725$	−4.00000	+	6.92820i	−0.148556	+	0.257307i
$726$	23.6603	+	6.33975i	0.878114	+	0.235290i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	−1.85641	−	25.8564i	−0.0688030	−	0.958302i
$729$	27.0000			1.00000
$730$	20.4904	+	5.49038i	0.758383	+	0.203208i
$731$	1.73205	−	3.00000i	0.0640622	−	0.110959i
$732$	−9.00000	+	15.5885i	−0.332650	+	0.576166i
$733$	37.5000	−	21.6506i	1.38509	−	0.799684i	0.392337	−	0.919822i	$-0.371667\pi$
$733$	37.5000	−	21.6506i	1.38509	−	0.799684i	0.992757	+	0.120137i	$0.0383334\pi$
$734$	−1.73205	+	1.73205i	−0.0639312	+	0.0639312i
$735$	20.7846	−	3.00000i	0.766652	−	0.110657i
$736$	−4.00000	−	4.00000i	−0.147442	−	0.147442i
$737$	1.50000	+	2.59808i	0.0552532	+	0.0957014i
$738$		0			0
$739$	−44.1673	−	25.5000i	−1.62472	−	0.938033i	−0.985634	−	0.168898i	$-0.945979\pi$
$739$	−44.1673	−	25.5000i	−1.62472	−	0.938033i	−0.639087	−	0.769135i	$-0.720687\pi$
$740$	5.19615	+	9.00000i	0.191014	+	0.330847i
$741$			31.1769i			1.14531i
$742$	−0.267949	−	3.73205i	−0.00983672	−	0.137008i
$743$		−	34.0000i		−	1.24734i	−0.781688	−	0.623670i	$-0.785641\pi$
$743$		−	34.0000i		−	1.24734i	0.781688	−	0.623670i	$-0.214359\pi$
$744$	2.19615	−	8.19615i	0.0805149	−	0.300486i
$745$	1.50000	+	0.866025i	0.0549557	+	0.0317287i
$746$	−10.6147	−	39.6147i	−0.388633	−	1.45040i
$747$		0			0
$748$		−	3.46410i		−	0.126660i
$749$	6.50000	−	33.7750i	0.237505	−	1.23411i
$750$	21.0000	+	21.0000i	0.766812	+	0.766812i
$751$	−21.6506	+	12.5000i	−0.790043	+	0.456131i	−0.839978	−	0.542621i	$-0.817432\pi$
$751$	−21.6506	+	12.5000i	−0.790043	+	0.456131i	0.0499348	+	0.998752i	$0.484099\pi$
$752$	−17.3205	+	30.0000i	−0.631614	+	1.09399i
$753$	3.00000	−	5.19615i	0.109326	−	0.189358i
$754$	−5.07180	+	18.9282i	−0.184704	+	0.689325i
$755$	12.1244			0.441250
$756$	−25.9808	+	9.00000i	−0.944911	+	0.327327i
$757$	−48.0000			−1.74459			−0.872295	−	0.488980i	$-0.837369\pi$
$757$	−48.0000			−1.74459			−0.872295	+	0.488980i	$0.837369\pi$
$758$	−2.92820	+	10.9282i	−0.106357	+	0.396930i
$759$	0.866025	−	1.50000i	0.0314347	−	0.0544466i
$760$	−6.58846	−	24.5885i	−0.238988	−	0.891917i
$761$	16.5000	−	9.52628i	0.598125	−	0.345327i	−0.170179	−	0.985413i	$-0.554435\pi$
$761$	16.5000	−	9.52628i	0.598125	−	0.345327i	0.768303	+	0.640086i	$0.221101\pi$
$762$	−10.3923	−	10.3923i	−0.376473	−	0.376473i
$763$	−7.79423	−	22.5000i	−0.282170	−	0.814555i
$764$	−2.00000			−0.0723575
$765$		0			0
$766$	1.90192	+	7.09808i	0.0687193	+	0.256464i
$767$	15.5885	+	9.00000i	0.562867	+	0.324971i
$768$	13.8564	+	24.0000i	0.500000	+	0.866025i
$769$			3.46410i			0.124919i	0.998048	+	0.0624593i	$0.0198944\pi$
$769$			3.46410i			0.124919i	−0.998048	+	0.0624593i	$0.980106\pi$
$770$

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:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	28.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 0.366025i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(-1.73205 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.36603 - 0.366025i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(-1.73205 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.36603 - 0.633975i) q^{10} +(0.866025 + 0.500000i) q^{11} +(3.00000 - 1.73205i) q^{12} -3.46410i q^{13} +(3.09808 - 2.09808i) q^{14} +3.00000i q^{15} +(2.00000 + 3.46410i) q^{16} +(-1.50000 - 0.866025i) q^{17} +(-2.59808 - 4.50000i) q^{19} -3.46410 q^{20} +(1.50000 + 4.33013i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(0.866025 - 0.500000i) q^{23} +(-4.73205 + 1.26795i) q^{24} +(-1.00000 + 1.73205i) q^{25} +(-1.26795 + 4.73205i) q^{26} +5.19615 q^{27} +(-5.00000 + 1.73205i) q^{28} +4.00000 q^{29} +(1.09808 - 4.09808i) q^{30} +(-0.866025 + 1.50000i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(1.50000 - 0.866025i) q^{33} +(1.73205 + 1.73205i) q^{34} +(0.866025 - 4.50000i) q^{35} +(-1.50000 - 2.59808i) q^{37} +(1.90192 + 7.09808i) q^{38} +(-5.19615 - 3.00000i) q^{39} +(4.73205 + 1.26795i) q^{40} +3.46410i q^{41} +(-0.464102 - 6.46410i) q^{42} +2.00000i q^{43} +(1.00000 + 1.73205i) q^{44} +(-1.36603 + 0.366025i) q^{46} +(4.33013 + 7.50000i) q^{47} +6.92820 q^{48} +(-1.00000 - 6.92820i) q^{49} +(2.00000 - 2.00000i) q^{50} +(-2.59808 + 1.50000i) q^{51} +(3.46410 - 6.00000i) q^{52} +(0.500000 - 0.866025i) q^{53} +(-7.09808 - 1.90192i) q^{54} -1.73205 q^{55} +(7.46410 - 0.535898i) q^{56} -9.00000 q^{57} +(-5.46410 - 1.46410i) q^{58} +(-2.59808 + 4.50000i) q^{59} +(-3.00000 + 5.19615i) q^{60} +(-4.50000 + 2.59808i) q^{61} +(1.73205 - 1.73205i) q^{62} +8.00000i q^{64} +(3.00000 + 5.19615i) q^{65} +(-2.36603 + 0.633975i) q^{66} +(2.59808 + 1.50000i) q^{67} +(-1.73205 - 3.00000i) q^{68} -1.73205i q^{69} +(-2.83013 + 5.83013i) q^{70} -14.0000i q^{71} +(7.50000 + 4.33013i) q^{73} +(1.09808 + 4.09808i) q^{74} +(1.73205 + 3.00000i) q^{75} -10.3923i q^{76} +(-2.50000 + 0.866025i) q^{77} +(6.00000 + 6.00000i) q^{78} +(7.79423 - 4.50000i) q^{79} +(-6.00000 - 3.46410i) q^{80} +(4.50000 - 7.79423i) q^{81} +(1.26795 - 4.73205i) q^{82} -13.8564 q^{83} +(-1.73205 + 9.00000i) q^{84} +3.00000 q^{85} +(0.732051 - 2.73205i) q^{86} +(3.46410 - 6.00000i) q^{87} +(-0.732051 - 2.73205i) q^{88} +(13.5000 - 7.79423i) q^{89} +(6.92820 + 6.00000i) q^{91} +2.00000 q^{92} +(1.50000 + 2.59808i) q^{93} +(-3.16987 - 11.8301i) q^{94} +(7.79423 + 4.50000i) q^{95} +(-9.46410 - 2.53590i) q^{96} +17.3205i q^{97} +(-1.16987 + 9.83013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{5} - 8 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 6 * q^5 - 8 * q^8	\( 4 q - 2 q^{2} - 6 q^{5} - 8 q^{8} + 6 q^{10} + 12 q^{12} + 2 q^{14} + 8 q^{16} - 6 q^{17} + 6 q^{21} - 4 q^{22} - 12 q^{24} - 4 q^{25} - 12 q^{26} - 20 q^{28} + 16 q^{29} - 6 q^{30} + 8 q^{32} + 6 q^{33} - 6 q^{37} + 18 q^{38} + 12 q^{40} + 12 q^{42} + 4 q^{44} - 2 q^{46} - 4 q^{49} + 8 q^{50} + 2 q^{53} - 18 q^{54} + 16 q^{56} - 36 q^{57} - 8 q^{58} - 12 q^{60} - 18 q^{61} + 12 q^{65} - 6 q^{66} + 6 q^{70} + 30 q^{73} - 6 q^{74} - 10 q^{77} + 24 q^{78} - 24 q^{80} + 18 q^{81} + 12 q^{82} + 12 q^{85} - 4 q^{86} + 4 q^{88} + 54 q^{89} + 8 q^{92} + 6 q^{93} - 30 q^{94} - 24 q^{96} - 22 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 6 * q^5 - 8 * q^8 + 6 * q^10 + 12 * q^12 + 2 * q^14 + 8 * q^16 - 6 * q^17 + 6 * q^21 - 4 * q^22 - 12 * q^24 - 4 * q^25 - 12 * q^26 - 20 * q^28 + 16 * q^29 - 6 * q^30 + 8 * q^32 + 6 * q^33 - 6 * q^37 + 18 * q^38 + 12 * q^40 + 12 * q^42 + 4 * q^44 - 2 * q^46 - 4 * q^49 + 8 * q^50 + 2 * q^53 - 18 * q^54 + 16 * q^56 - 36 * q^57 - 8 * q^58 - 12 * q^60 - 18 * q^61 + 12 * q^65 - 6 * q^66 + 6 * q^70 + 30 * q^73 - 6 * q^74 - 10 * q^77 + 24 * q^78 - 24 * q^80 + 18 * q^81 + 12 * q^82 + 12 * q^85 - 4 * q^86 + 4 * q^88 + 54 * q^89 + 8 * q^92 + 6 * q^93 - 30 * q^94 - 24 * q^96 - 22 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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