LMFDB - Embedded newform 546.2.i.g.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(79,546)]

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, 2, 0]))

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

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

chi := DirichletCharacter("546.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.79
Dual form			546.2.i.g.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +1.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +1.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(-1.50000 - 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{12} -1.00000 q^{13} +(-2.50000 - 0.866025i) q^{14} +2.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{17} +(0.500000 + 0.866025i) q^{18} +(1.50000 - 2.59808i) q^{19} -2.00000 q^{20} +(2.00000 - 1.73205i) q^{21} -3.00000 q^{22} +(-0.500000 - 0.866025i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.500000 + 0.866025i) q^{26} -1.00000 q^{27} +(-2.00000 + 1.73205i) q^{28} +3.00000 q^{29} +(1.00000 - 1.73205i) q^{30} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} -1.00000 q^{34} +(-5.00000 - 1.73205i) q^{35} +1.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(-1.50000 - 2.59808i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(-1.00000 + 1.73205i) q^{40} +2.00000 q^{41} +(-0.500000 - 2.59808i) q^{42} +6.00000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(1.00000 + 1.73205i) q^{45} +(4.50000 - 7.79423i) q^{47} -1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} +1.00000 q^{50} +(0.500000 - 0.866025i) q^{51} +(0.500000 + 0.866025i) q^{52} +(-0.500000 - 0.866025i) q^{53} +(-0.500000 + 0.866025i) q^{54} -6.00000 q^{55} +(0.500000 + 2.59808i) q^{56} +3.00000 q^{57} +(1.50000 - 2.59808i) q^{58} +(-5.50000 - 9.52628i) q^{59} +(-1.00000 - 1.73205i) q^{60} +(-5.50000 + 9.52628i) q^{61} +4.00000 q^{62} +(2.50000 + 0.866025i) q^{63} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(-1.50000 - 2.59808i) q^{66} +(3.50000 + 6.06218i) q^{67} +(-0.500000 + 0.866025i) q^{68} +(-4.00000 + 3.46410i) q^{70} +15.0000 q^{71} +(0.500000 - 0.866025i) q^{72} +(6.00000 + 10.3923i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-0.500000 + 0.866025i) q^{75} -3.00000 q^{76} +(-6.00000 + 5.19615i) q^{77} -1.00000 q^{78} +(-1.00000 + 1.73205i) q^{79} +(1.00000 + 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} +(-2.50000 - 0.866025i) q^{84} -2.00000 q^{85} +(3.00000 - 5.19615i) q^{86} +(1.50000 + 2.59808i) q^{87} +(1.50000 + 2.59808i) q^{88} +(-5.00000 + 8.66025i) q^{89} +2.00000 q^{90} +(0.500000 + 2.59808i) q^{91} +(-2.00000 + 3.46410i) q^{93} +(-4.50000 - 7.79423i) q^{94} +(-3.00000 - 5.19615i) q^{95} +(-0.500000 + 0.866025i) q^{96} -12.0000 q^{97} +(-1.00000 + 6.92820i) q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} + 2 q^{5} + 2 q^{6} - q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 + 2 * q^5 + 2 * q^6 - q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} + q^{3} - q^{4} + 2 q^{5} + 2 q^{6} - q^{7} - 2 q^{8} - q^{9} - 2 q^{10} - 3 q^{11} + q^{12} - 2 q^{13} - 5 q^{14} + 4 q^{15} - q^{16} - q^{17} + q^{18} + 3 q^{19} - 4 q^{20} + 4 q^{21} - 6 q^{22} - q^{24} + q^{25} - q^{26} - 2 q^{27} - 4 q^{28} + 6 q^{29} + 2 q^{30} + 4 q^{31} + q^{32} + 3 q^{33} - 2 q^{34} - 10 q^{35} + 2 q^{36} + 2 q^{37} - 3 q^{38} - q^{39} - 2 q^{40} + 4 q^{41} - q^{42} + 12 q^{43} - 3 q^{44} + 2 q^{45} + 9 q^{47} - 2 q^{48} - 13 q^{49} + 2 q^{50} + q^{51} + q^{52} - q^{53} - q^{54} - 12 q^{55} + q^{56} + 6 q^{57} + 3 q^{58} - 11 q^{59} - 2 q^{60} - 11 q^{61} + 8 q^{62} + 5 q^{63} + 2 q^{64} - 2 q^{65} - 3 q^{66} + 7 q^{67} - q^{68} - 8 q^{70} + 30 q^{71} + q^{72} + 12 q^{73} - 2 q^{74} - q^{75} - 6 q^{76} - 12 q^{77} - 2 q^{78} - 2 q^{79} + 2 q^{80} - q^{81} + 2 q^{82} - 5 q^{84} - 4 q^{85} + 6 q^{86} + 3 q^{87} + 3 q^{88} - 10 q^{89} + 4 q^{90} + q^{91} - 4 q^{93} - 9 q^{94} - 6 q^{95} - q^{96} - 24 q^{97} - 2 q^{98} + 6 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 + 2 * q^5 + 2 * q^6 - q^7 - 2 * q^8 - q^9 - 2 * q^10 - 3 * q^11 + q^12 - 2 * q^13 - 5 * q^14 + 4 * q^15 - q^16 - q^17 + q^18 + 3 * q^19 - 4 * q^20 + 4 * q^21 - 6 * q^22 - q^24 + q^25 - q^26 - 2 * q^27 - 4 * q^28 + 6 * q^29 + 2 * q^30 + 4 * q^31 + q^32 + 3 * q^33 - 2 * q^34 - 10 * q^35 + 2 * q^36 + 2 * q^37 - 3 * q^38 - q^39 - 2 * q^40 + 4 * q^41 - q^42 + 12 * q^43 - 3 * q^44 + 2 * q^45 + 9 * q^47 - 2 * q^48 - 13 * q^49 + 2 * q^50 + q^51 + q^52 - q^53 - q^54 - 12 * q^55 + q^56 + 6 * q^57 + 3 * q^58 - 11 * q^59 - 2 * q^60 - 11 * q^61 + 8 * q^62 + 5 * q^63 + 2 * q^64 - 2 * q^65 - 3 * q^66 + 7 * q^67 - q^68 - 8 * q^70 + 30 * q^71 + q^72 + 12 * q^73 - 2 * q^74 - q^75 - 6 * q^76 - 12 * q^77 - 2 * q^78 - 2 * q^79 + 2 * q^80 - q^81 + 2 * q^82 - 5 * q^84 - 4 * q^85 + 6 * q^86 + 3 * q^87 + 3 * q^88 - 10 * q^89 + 4 * q^90 + q^91 - 4 * q^93 - 9 * q^94 - 6 * q^95 - q^96 - 24 * q^97 - 2 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	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
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	0.998203	+	0.0599153i	$0.0190830\pi$
$6$	1.00000			0.408248
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.00000	−	1.73205i	−0.316228	−	0.547723i
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−2.50000	−	0.866025i	−0.668153	−	0.231455i
$15$	2.00000			0.516398
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i	0.799000	−	0.601331i	$-0.205363\pi$
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i	−0.920268	+	0.391289i	$0.872029\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	1.50000	−	2.59808i	0.344124	−	0.596040i	−0.641071	−	0.767482i	$-0.721509\pi$
$19$	1.50000	−	2.59808i	0.344124	−	0.596040i	0.985194	+	0.171442i	$0.0548427\pi$
$20$	−2.00000			−0.447214
$21$	2.00000	−	1.73205i	0.436436	−	0.377964i
$22$	−3.00000			−0.639602
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$	−1.00000			−0.192450
$28$	−2.00000	+	1.73205i	−0.377964	+	0.327327i
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$	1.00000	−	1.73205i	0.182574	−	0.316228i
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.50000	−	2.59808i	0.261116	−	0.452267i
$34$	−1.00000			−0.171499
$35$	−5.00000	−	1.73205i	−0.845154	−	0.292770i
$36$	1.00000			0.166667
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	−1.50000	−	2.59808i	−0.243332	−	0.421464i
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$	−1.00000	+	1.73205i	−0.158114	+	0.273861i
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$	−0.500000	−	2.59808i	−0.0771517	−	0.400892i
$43$	6.00000			0.914991			0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000			0.914991			0.457496	+	0.889212i	$0.348747\pi$
$44$	−1.50000	+	2.59808i	−0.226134	+	0.391675i
$45$	1.00000	+	1.73205i	0.149071	+	0.258199i
$46$		0			0
$47$	4.50000	−	7.79423i	0.656392	−	1.13691i	−0.325150	−	0.945662i	$-0.605415\pi$
$47$	4.50000	−	7.79423i	0.656392	−	1.13691i	0.981543	−	0.191243i	$-0.0612518\pi$
$48$	−1.00000			−0.144338
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	1.00000			0.141421
$51$	0.500000	−	0.866025i	0.0700140	−	0.121268i
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	−0.500000	−	0.866025i	−0.0686803	−	0.118958i	0.829640	−	0.558298i	$-0.188546\pi$
$53$	−0.500000	−	0.866025i	−0.0686803	−	0.118958i	−0.898321	+	0.439340i	$0.855212\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−6.00000			−0.809040
$56$	0.500000	+	2.59808i	0.0668153	+	0.347183i
$57$	3.00000			0.397360
$58$	1.50000	−	2.59808i	0.196960	−	0.341144i
$59$	−5.50000	−	9.52628i	−0.716039	−	1.24022i	−0.962557	−	0.271078i	$-0.912620\pi$
$59$	−5.50000	−	9.52628i	−0.716039	−	1.24022i	0.246518	−	0.969138i	$-0.420713\pi$
$60$	−1.00000	−	1.73205i	−0.129099	−	0.223607i
$61$	−5.50000	+	9.52628i	−0.704203	+	1.21972i	0.262776	+	0.964857i	$0.415362\pi$
$61$	−5.50000	+	9.52628i	−0.704203	+	1.21972i	−0.966978	+	0.254858i	$0.917971\pi$
$62$	4.00000			0.508001
$63$	2.50000	+	0.866025i	0.314970	+	0.109109i
$64$	1.00000			0.125000
$65$	−1.00000	+	1.73205i	−0.124035	+	0.214834i
$66$	−1.50000	−	2.59808i	−0.184637	−	0.319801i
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	0.996659	−	0.0816792i	$-0.0260283\pi$
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	−0.569066	+	0.822292i	$0.692695\pi$
$68$	−0.500000	+	0.866025i	−0.0606339	+	0.105021i
$69$		0			0
$70$	−4.00000	+	3.46410i	−0.478091	+	0.414039i
$71$	15.0000			1.78017			0.890086	−	0.455792i	$-0.150644\pi$
$71$	15.0000			1.78017			0.890086	+	0.455792i	$0.150644\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	6.00000	+	10.3923i	0.702247	+	1.21633i	0.967676	+	0.252197i	$0.0811531\pi$
$73$	6.00000	+	10.3923i	0.702247	+	1.21633i	−0.265429	+	0.964130i	$0.585514\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	−3.00000			−0.344124
$77$	−6.00000	+	5.19615i	−0.683763	+	0.592157i
$78$	−1.00000			−0.113228
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	−0.916781	−	0.399390i	$-0.869222\pi$
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	0.804272	+	0.594261i	$0.202555\pi$
$80$	1.00000	+	1.73205i	0.111803	+	0.193649i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.00000	−	1.73205i	0.110432	−	0.191273i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	−2.50000	−	0.866025i	−0.272772	−	0.0944911i
$85$	−2.00000			−0.216930
$86$	3.00000	−	5.19615i	0.323498	−	0.560316i
$87$	1.50000	+	2.59808i	0.160817	+	0.278543i
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	0.469389	+	0.882992i	$0.344474\pi$
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	−0.999388	+	0.0349934i	$0.988859\pi$
$90$	2.00000			0.210819
$91$	0.500000	+	2.59808i	0.0524142	+	0.272352i
$92$		0			0
$93$	−2.00000	+	3.46410i	−0.207390	+	0.359211i
$94$	−4.50000	−	7.79423i	−0.464140	−	0.803913i
$95$	−3.00000	−	5.19615i	−0.307794	−	0.533114i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−12.0000			−1.21842			−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000			−1.21842			−0.609208	+	0.793011i	$0.708512\pi$
$98$	−1.00000	+	6.92820i	−0.101015	+	0.699854i
$99$	3.00000			0.301511
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	7.00000	+	12.1244i	0.696526	+	1.20642i	0.969664	+	0.244443i	$0.0786053\pi$
$101$	7.00000	+	12.1244i	0.696526	+	1.20642i	−0.273138	+	0.961975i	$0.588061\pi$
$102$	−0.500000	−	0.866025i	−0.0495074	−	0.0857493i
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	0.282194	+	0.959357i	$0.408938\pi$
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	−0.971925	+	0.235291i	$0.924396\pi$
$104$	1.00000			0.0980581
$105$	−1.00000	−	5.19615i	−0.0975900	−	0.507093i
$106$	−1.00000			−0.0971286
$107$	2.00000	−	3.46410i	0.193347	−	0.334887i	−0.753010	−	0.658009i	$-0.771399\pi$
$107$	2.00000	−	3.46410i	0.193347	−	0.334887i	0.946357	+	0.323122i	$0.104732\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	4.00000	+	6.92820i	0.383131	+	0.663602i	0.991508	−	0.130046i	$-0.0415126\pi$
$109$	4.00000	+	6.92820i	0.383131	+	0.663602i	−0.608377	+	0.793648i	$0.708179\pi$
$110$	−3.00000	+	5.19615i	−0.286039	+	0.495434i
$111$	2.00000			0.189832
$112$	2.50000	+	0.866025i	0.236228	+	0.0818317i
$113$	3.00000			0.282216			0.141108	−	0.989994i	$-0.454933\pi$
$113$	3.00000			0.282216			0.141108	+	0.989994i	$0.454933\pi$
$114$	1.50000	−	2.59808i	0.140488	−	0.243332i
$115$		0			0
$116$	−1.50000	−	2.59808i	−0.139272	−	0.241225i
$117$	0.500000	−	0.866025i	0.0462250	−	0.0800641i
$118$	−11.0000			−1.01263
$119$	−2.00000	+	1.73205i	−0.183340	+	0.158777i
$120$	−2.00000			−0.182574
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	5.50000	+	9.52628i	0.497947	+	0.862469i
$123$	1.00000	+	1.73205i	0.0901670	+	0.156174i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	12.0000			1.07331
$126$	2.00000	−	1.73205i	0.178174	−	0.154303i
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	3.00000	+	5.19615i	0.264135	+	0.457496i
$130$	1.00000	+	1.73205i	0.0877058	+	0.151911i
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	−0.475380	−	0.879781i	$-0.657689\pi$
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	0.999602	−	0.0281993i	$-0.00897729\pi$
$132$	−3.00000			−0.261116
$133$	−7.50000	−	2.59808i	−0.650332	−	0.225282i
$134$	7.00000			0.604708
$135$	−1.00000	+	1.73205i	−0.0860663	+	0.149071i
$136$	0.500000	+	0.866025i	0.0428746	+	0.0742611i
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	−0.938148	−	0.346235i	$-0.887460\pi$
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	0.169226	−	0.985577i	$-0.445873\pi$
$138$		0			0
$139$	−14.0000			−1.18746			−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000			−1.18746			−0.593732	+	0.804663i	$0.702346\pi$
$140$	1.00000	+	5.19615i	0.0845154	+	0.439155i
$141$	9.00000			0.757937
$142$	7.50000	−	12.9904i	0.629386	−	1.09013i
$143$	1.50000	+	2.59808i	0.125436	+	0.217262i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	3.00000	−	5.19615i	0.249136	−	0.431517i
$146$	12.0000			0.993127
$147$	−5.50000	−	4.33013i	−0.453632	−	0.357143i
$148$	−2.00000			−0.164399
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	8.50000	+	14.7224i	0.691720	+	1.19809i	0.971274	+	0.237964i	$0.0764802\pi$
$151$	8.50000	+	14.7224i	0.691720	+	1.19809i	−0.279554	+	0.960130i	$0.590186\pi$
$152$	−1.50000	+	2.59808i	−0.121666	+	0.210732i
$153$	1.00000			0.0808452
$154$	1.50000	+	7.79423i	0.120873	+	0.628077i
$155$	8.00000			0.642575
$156$	−0.500000	+	0.866025i	−0.0400320	+	0.0693375i
$157$	5.50000	+	9.52628i	0.438948	+	0.760280i	0.997609	−	0.0691164i	$-0.0220180\pi$
$157$	5.50000	+	9.52628i	0.438948	+	0.760280i	−0.558661	+	0.829396i	$0.688685\pi$
$158$	1.00000	+	1.73205i	0.0795557	+	0.137795i
$159$	0.500000	−	0.866025i	0.0396526	−	0.0686803i
$160$	2.00000			0.158114
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	12.5000	−	21.6506i	0.979076	−	1.69581i	0.313304	−	0.949653i	$-0.398564\pi$
$163$	12.5000	−	21.6506i	0.979076	−	1.69581i	0.665771	−	0.746156i	$-0.268103\pi$
$164$	−1.00000	−	1.73205i	−0.0780869	−	0.135250i
$165$	−3.00000	−	5.19615i	−0.233550	−	0.404520i
$166$		0			0
$167$	−19.0000			−1.47026			−0.735132	−	0.677924i	$-0.762880\pi$
$167$	−19.0000			−1.47026			−0.735132	+	0.677924i	$0.762880\pi$
$168$	−2.00000	+	1.73205i	−0.154303	+	0.133631i
$169$	1.00000			0.0769231
$170$	−1.00000	+	1.73205i	−0.0766965	+	0.132842i
$171$	1.50000	+	2.59808i	0.114708	+	0.198680i
$172$	−3.00000	−	5.19615i	−0.228748	−	0.396203i
$173$	−3.50000	+	6.06218i	−0.266100	+	0.460899i	−0.967851	−	0.251523i	$-0.919068\pi$
$173$	−3.50000	+	6.06218i	−0.266100	+	0.460899i	0.701751	+	0.712422i	$0.252402\pi$
$174$	3.00000			0.227429
$175$	2.00000	−	1.73205i	0.151186	−	0.130931i
$176$	3.00000			0.226134
$177$	5.50000	−	9.52628i	0.413405	−	0.716039i
$178$	5.00000	+	8.66025i	0.374766	+	0.649113i
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	0.956088	−	0.293079i	$-0.0946798\pi$
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	−0.731858	+	0.681457i	$0.761346\pi$
$180$	1.00000	−	1.73205i	0.0745356	−	0.129099i
$181$	−5.00000			−0.371647			−0.185824	−	0.982583i	$-0.559495\pi$
$181$	−5.00000			−0.371647			−0.185824	+	0.982583i	$0.559495\pi$
$182$	2.50000	+	0.866025i	0.185312	+	0.0641941i
$183$	−11.0000			−0.813143
$184$		0			0
$185$	−2.00000	−	3.46410i	−0.147043	−	0.254686i
$186$	2.00000	+	3.46410i	0.146647	+	0.254000i
$187$	−1.50000	+	2.59808i	−0.109691	+	0.189990i
$188$	−9.00000			−0.656392
$189$	0.500000	+	2.59808i	0.0363696	+	0.188982i
$190$	−6.00000			−0.435286
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	−0.563081	−	0.826402i	$-0.690384\pi$
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	0.997225	+	0.0744412i	$0.0237173\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	0.999990	+	0.00447566i	$0.00142465\pi$
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	−0.496119	+	0.868255i	$0.665242\pi$
$194$	−6.00000	+	10.3923i	−0.430775	+	0.746124i
$195$	−2.00000			−0.143223
$196$	5.50000	+	4.33013i	0.392857	+	0.309295i
$197$	8.00000			0.569976			0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000			0.569976			0.284988	+	0.958531i	$0.408010\pi$
$198$	1.50000	−	2.59808i	0.106600	−	0.184637i
$199$	−6.00000	−	10.3923i	−0.425329	−	0.736691i	0.571122	−	0.820865i	$-0.306508\pi$
$199$	−6.00000	−	10.3923i	−0.425329	−	0.736691i	−0.996451	+	0.0841740i	$0.973175\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−3.50000	+	6.06218i	−0.246871	+	0.427593i
$202$	14.0000			0.985037
$203$	−1.50000	−	7.79423i	−0.105279	−	0.547048i
$204$	−1.00000			−0.0700140
$205$	2.00000	−	3.46410i	0.139686	−	0.241943i
$206$	7.00000	+	12.1244i	0.487713	+	0.844744i
$207$		0			0
$208$	0.500000	−	0.866025i	0.0346688	−	0.0600481i
$209$	−9.00000			−0.622543
$210$	−5.00000	−	1.73205i	−0.345033	−	0.119523i
$211$	−16.0000			−1.10149			−0.550743	−	0.834675i	$-0.685655\pi$
$211$	−16.0000			−1.10149			−0.550743	+	0.834675i	$0.685655\pi$
$212$	−0.500000	+	0.866025i	−0.0343401	+	0.0594789i
$213$	7.50000	+	12.9904i	0.513892	+	0.890086i
$214$	−2.00000	−	3.46410i	−0.136717	−	0.236801i
$215$	6.00000	−	10.3923i	0.409197	−	0.708749i
$216$	1.00000			0.0680414
$217$	8.00000	−	6.92820i	0.543075	−	0.470317i
$218$	8.00000			0.541828
$219$	−6.00000	+	10.3923i	−0.405442	+	0.702247i
$220$	3.00000	+	5.19615i	0.202260	+	0.350325i
$221$	0.500000	+	0.866025i	0.0336336	+	0.0582552i
$222$	1.00000	−	1.73205i	0.0671156	−	0.116248i
$223$	−1.00000			−0.0669650			−0.0334825	−	0.999439i	$-0.510660\pi$
$223$	−1.00000			−0.0669650			−0.0334825	+	0.999439i	$0.510660\pi$
$224$	2.00000	−	1.73205i	0.133631	−	0.115728i
$225$	−1.00000			−0.0666667
$226$	1.50000	−	2.59808i	0.0997785	−	0.172821i
$227$	−4.00000	−	6.92820i	−0.265489	−	0.459841i	0.702202	−	0.711977i	$-0.252200\pi$
$227$	−4.00000	−	6.92820i	−0.265489	−	0.459841i	−0.967692	+	0.252136i	$0.918867\pi$
$228$	−1.50000	−	2.59808i	−0.0993399	−	0.172062i
$229$	1.00000	−	1.73205i	0.0660819	−	0.114457i	−0.831092	−	0.556136i	$-0.812283\pi$
$229$	1.00000	−	1.73205i	0.0660819	−	0.114457i	0.897173	+	0.441679i	$0.145617\pi$
$230$		0			0
$231$	−7.50000	−	2.59808i	−0.493464	−	0.170941i
$232$	−3.00000			−0.196960
$233$	−3.50000	+	6.06218i	−0.229293	+	0.397146i	−0.957599	−	0.288106i	$-0.906975\pi$
$233$	−3.50000	+	6.06218i	−0.229293	+	0.397146i	0.728306	+	0.685252i	$0.240308\pi$
$234$	−0.500000	−	0.866025i	−0.0326860	−	0.0566139i
$235$	−9.00000	−	15.5885i	−0.587095	−	1.01688i
$236$	−5.50000	+	9.52628i	−0.358020	+	0.620108i
$237$	−2.00000			−0.129914
$238$	0.500000	+	2.59808i	0.0324102	+	0.168408i
$239$	−11.0000			−0.711531			−0.355765	−	0.934575i	$-0.615780\pi$
$239$	−11.0000			−0.711531			−0.355765	+	0.934575i	$0.615780\pi$
$240$	−1.00000	+	1.73205i	−0.0645497	+	0.111803i
$241$	−6.00000	−	10.3923i	−0.386494	−	0.669427i	0.605481	−	0.795860i	$-0.292981\pi$
$241$	−6.00000	−	10.3923i	−0.386494	−	0.669427i	−0.991975	+	0.126432i	$0.959647\pi$
$242$	−1.00000	−	1.73205i	−0.0642824	−	0.111340i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	11.0000			0.704203
$245$	−2.00000	+	13.8564i	−0.127775	+	0.885253i
$246$	2.00000			0.127515
$247$	−1.50000	+	2.59808i	−0.0954427	+	0.165312i
$248$	−2.00000	−	3.46410i	−0.127000	−	0.219971i
$249$		0			0
$250$	6.00000	−	10.3923i	0.379473	−	0.657267i
$251$	−10.0000			−0.631194			−0.315597	−	0.948893i	$-0.602205\pi$
$251$	−10.0000			−0.631194			−0.315597	+	0.948893i	$0.602205\pi$
$252$	−0.500000	−	2.59808i	−0.0314970	−	0.163663i
$253$		0			0
$254$	4.00000	−	6.92820i	0.250982	−	0.434714i
$255$	−1.00000	−	1.73205i	−0.0626224	−	0.108465i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	13.0000	−	22.5167i	0.810918	−	1.40455i	−0.101305	−	0.994855i	$-0.532302\pi$
$257$	13.0000	−	22.5167i	0.810918	−	1.40455i	0.912222	−	0.409695i	$-0.134365\pi$
$258$	6.00000			0.373544
$259$	−5.00000	−	1.73205i	−0.310685	−	0.107624i
$260$	2.00000			0.124035
$261$	−1.50000	+	2.59808i	−0.0928477	+	0.160817i
$262$	−6.00000	−	10.3923i	−0.370681	−	0.642039i
$263$	−5.00000	−	8.66025i	−0.308313	−	0.534014i	0.669680	−	0.742650i	$-0.266431\pi$
$263$	−5.00000	−	8.66025i	−0.308313	−	0.534014i	−0.977993	+	0.208635i	$0.933098\pi$
$264$	−1.50000	+	2.59808i	−0.0923186	+	0.159901i
$265$	−2.00000			−0.122859
$266$	−6.00000	+	5.19615i	−0.367884	+	0.318597i
$267$	−10.0000			−0.611990
$268$	3.50000	−	6.06218i	0.213797	−	0.370306i
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	0.985389	+	0.170321i	$0.0544803\pi$
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	−0.345192	+	0.938532i	$0.612186\pi$
$270$	1.00000	+	1.73205i	0.0608581	+	0.105409i
$271$	−7.50000	+	12.9904i	−0.455593	+	0.789109i	−0.998722	−	0.0505395i	$-0.983906\pi$
$271$	−7.50000	+	12.9904i	−0.455593	+	0.789109i	0.543130	+	0.839649i	$0.317239\pi$
$272$	1.00000			0.0606339
$273$	−2.00000	+	1.73205i	−0.121046	+	0.104828i
$274$	−18.0000			−1.08742
$275$	1.50000	−	2.59808i	0.0904534	−	0.156670i
$276$		0			0
$277$	−2.50000	−	4.33013i	−0.150210	−	0.260172i	0.781094	−	0.624413i	$-0.214662\pi$
$277$	−2.50000	−	4.33013i	−0.150210	−	0.260172i	−0.931305	+	0.364241i	$0.881328\pi$
$278$	−7.00000	+	12.1244i	−0.419832	+	0.727171i
$279$	−4.00000			−0.239474
$280$	5.00000	+	1.73205i	0.298807	+	0.103510i
$281$	−24.0000			−1.43172			−0.715860	−	0.698244i	$-0.753965\pi$
$281$	−24.0000			−1.43172			−0.715860	+	0.698244i	$0.753965\pi$
$282$	4.50000	−	7.79423i	0.267971	−	0.464140i
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	−7.50000	−	12.9904i	−0.445043	−	0.770837i
$285$	3.00000	−	5.19615i	0.177705	−	0.307794i
$286$	3.00000			0.177394
$287$	−1.00000	−	5.19615i	−0.0590281	−	0.306719i
$288$	−1.00000			−0.0589256
$289$	8.00000	−	13.8564i	0.470588	−	0.815083i
$290$	−3.00000	−	5.19615i	−0.176166	−	0.305129i
$291$	−6.00000	−	10.3923i	−0.351726	−	0.609208i
$292$	6.00000	−	10.3923i	0.351123	−	0.608164i
$293$	−12.0000			−0.701047			−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000			−0.701047			−0.350524	+	0.936554i	$0.613996\pi$
$294$	−6.50000	+	2.59808i	−0.379088	+	0.151523i
$295$	−22.0000			−1.28089
$296$	−1.00000	+	1.73205i	−0.0581238	+	0.100673i
$297$	1.50000	+	2.59808i	0.0870388	+	0.150756i
$298$		0			0
$299$		0			0
$300$	1.00000			0.0577350
$301$	−3.00000	−	15.5885i	−0.172917	−	0.898504i
$302$	17.0000			0.978240
$303$	−7.00000	+	12.1244i	−0.402139	+	0.696526i
$304$	1.50000	+	2.59808i	0.0860309	+	0.149010i
$305$	11.0000	+	19.0526i	0.629858	+	1.09095i
$306$	0.500000	−	0.866025i	0.0285831	−	0.0495074i
$307$	−15.0000			−0.856095			−0.428048	−	0.903756i	$-0.640798\pi$
$307$	−15.0000			−0.856095			−0.428048	+	0.903756i	$0.640798\pi$
$308$	7.50000	+	2.59808i	0.427352	+	0.148039i
$309$	−14.0000			−0.796432
$310$	4.00000	−	6.92820i	0.227185	−	0.393496i
$311$	−7.00000	−	12.1244i	−0.396934	−	0.687509i	0.596412	−	0.802678i	$-0.296592\pi$
$311$	−7.00000	−	12.1244i	−0.396934	−	0.687509i	−0.993346	+	0.115169i	$0.963259\pi$
$312$	0.500000	+	0.866025i	0.0283069	+	0.0490290i
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	−0.597522	−	0.801852i	$-0.703848\pi$
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	0.993186	+	0.116543i	$0.0371814\pi$
$314$	11.0000			0.620766
$315$	4.00000	−	3.46410i	0.225374	−	0.195180i
$316$	2.00000			0.112509
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	0.494489	+	0.869184i	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$	−0.500000	−	0.866025i	−0.0280386	−	0.0485643i
$319$	−4.50000	−	7.79423i	−0.251952	−	0.436393i
$320$	1.00000	−	1.73205i	0.0559017	−	0.0968246i
$321$	4.00000			0.223258
$322$		0			0
$323$	−3.00000			−0.166924
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−0.500000	−	0.866025i	−0.0277350	−	0.0480384i
$326$	−12.5000	−	21.6506i	−0.692311	−	1.19912i
$327$	−4.00000	+	6.92820i	−0.221201	+	0.383131i
$328$	−2.00000			−0.110432
$329$	−22.5000	−	7.79423i	−1.24047	−	0.429710i
$330$	−6.00000			−0.330289
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$		0			0
$333$	1.00000	+	1.73205i	0.0547997	+	0.0949158i
$334$	−9.50000	+	16.4545i	−0.519817	+	0.900349i
$335$	14.0000			0.764902
$336$	0.500000	+	2.59808i	0.0272772	+	0.141737i
$337$	7.00000			0.381314			0.190657	−	0.981657i	$-0.438938\pi$
$337$	7.00000			0.381314			0.190657	+	0.981657i	$0.438938\pi$
$338$	0.500000	−	0.866025i	0.0271964	−	0.0471056i
$339$	1.50000	+	2.59808i	0.0814688	+	0.141108i
$340$	1.00000	+	1.73205i	0.0542326	+	0.0939336i
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$	3.00000			0.162221
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−6.00000			−0.323498
$345$		0			0
$346$	3.50000	+	6.06218i	0.188161	+	0.325905i
$347$	−1.00000	−	1.73205i	−0.0536828	−	0.0929814i	0.837935	−	0.545770i	$-0.183763\pi$
$347$	−1.00000	−	1.73205i	−0.0536828	−	0.0929814i	−0.891618	+	0.452788i	$0.850429\pi$
$348$	1.50000	−	2.59808i	0.0804084	−	0.139272i
$349$	20.0000			1.07058			0.535288	−	0.844670i	$-0.320203\pi$
$349$	20.0000			1.07058			0.535288	+	0.844670i	$0.320203\pi$
$350$	−0.500000	−	2.59808i	−0.0267261	−	0.138873i
$351$	1.00000			0.0533761
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	0.999711	−	0.0240566i	$-0.00765819\pi$
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	−0.520689	+	0.853746i	$0.674325\pi$
$354$	−5.50000	−	9.52628i	−0.292322	−	0.506316i
$355$	15.0000	−	25.9808i	0.796117	−	1.37892i
$356$	10.0000			0.529999
$357$	−2.50000	−	0.866025i	−0.132314	−	0.0458349i
$358$	6.00000			0.317110
$359$	−8.00000	+	13.8564i	−0.422224	+	0.731313i	−0.996157	−	0.0875892i	$-0.972084\pi$
$359$	−8.00000	+	13.8564i	−0.422224	+	0.731313i	0.573933	+	0.818902i	$0.305417\pi$
$360$	−1.00000	−	1.73205i	−0.0527046	−	0.0912871i
$361$	5.00000	+	8.66025i	0.263158	+	0.455803i
$362$	−2.50000	+	4.33013i	−0.131397	+	0.227586i
$363$	2.00000			0.104973
$364$	2.00000	−	1.73205i	0.104828	−	0.0907841i
$365$	24.0000			1.25622
$366$	−5.50000	+	9.52628i	−0.287490	+	0.497947i
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	0.529607	−	0.848243i	$-0.322339\pi$
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	−0.999404	+	0.0345320i	$0.989006\pi$
$368$		0			0
$369$	−1.00000	+	1.73205i	−0.0520579	+	0.0901670i
$370$	−4.00000			−0.207950
$371$	−2.00000	+	1.73205i	−0.103835	+	0.0899236i
$372$	4.00000			0.207390
$373$	5.50000	−	9.52628i	0.284779	−	0.493252i	−0.687776	−	0.725923i	$-0.741413\pi$
$373$	5.50000	−	9.52628i	0.284779	−	0.493252i	0.972556	+	0.232671i	$0.0747464\pi$
$374$	1.50000	+	2.59808i	0.0775632	+	0.134343i
$375$	6.00000	+	10.3923i	0.309839	+	0.536656i
$376$	−4.50000	+	7.79423i	−0.232070	+	0.401957i
$377$	−3.00000			−0.154508
$378$	2.50000	+	0.866025i	0.128586	+	0.0445435i
$379$	36.0000			1.84920			0.924598	−	0.380945i	$-0.124401\pi$
$379$	36.0000			1.84920			0.924598	+	0.380945i	$0.124401\pi$
$380$	−3.00000	+	5.19615i	−0.153897	+	0.266557i
$381$	4.00000	+	6.92820i	0.204926	+	0.354943i
$382$	−6.00000	−	10.3923i	−0.306987	−	0.531717i
$383$	16.0000	−	27.7128i	0.817562	−	1.41606i	−0.0899119	−	0.995950i	$-0.528659\pi$
$383$	16.0000	−	27.7128i	0.817562	−	1.41606i	0.907474	−	0.420109i	$-0.138008\pi$
$384$	1.00000			0.0510310
$385$	3.00000	+	15.5885i	0.152894	+	0.794461i
$386$	14.0000			0.712581
$387$	−3.00000	+	5.19615i	−0.152499	+	0.264135i
$388$	6.00000	+	10.3923i	0.304604	+	0.527589i
$389$	−6.50000	−	11.2583i	−0.329563	−	0.570820i	0.652862	−	0.757477i	$-0.273568\pi$
$389$	−6.50000	−	11.2583i	−0.329563	−	0.570820i	−0.982425	+	0.186657i	$0.940235\pi$
$390$	−1.00000	+	1.73205i	−0.0506370	+	0.0877058i
$391$		0			0
$392$	6.50000	−	2.59808i	0.328300	−	0.131223i
$393$	12.0000			0.605320
$394$	4.00000	−	6.92820i	0.201517	−	0.349038i
$395$	2.00000	+	3.46410i	0.100631	+	0.174298i
$396$	−1.50000	−	2.59808i	−0.0753778	−	0.130558i
$397$	10.0000	−	17.3205i	0.501886	−	0.869291i	−0.498112	−	0.867113i	$-0.665973\pi$
$397$	10.0000	−	17.3205i	0.501886	−	0.869291i	0.999998	−	0.00217869i	$-0.000693499\pi$
$398$	−12.0000			−0.601506
$399$	−1.50000	−	7.79423i	−0.0750939	−	0.390199i
$400$	−1.00000			−0.0500000
$401$	−6.00000	+	10.3923i	−0.299626	+	0.518967i	−0.976050	−	0.217545i	$-0.930195\pi$
$401$	−6.00000	+	10.3923i	−0.299626	+	0.518967i	0.676425	+	0.736512i	$0.263528\pi$
$402$	3.50000	+	6.06218i	0.174564	+	0.302354i
$403$	−2.00000	−	3.46410i	−0.0996271	−	0.172559i
$404$	7.00000	−	12.1244i	0.348263	−	0.603209i
$405$	−2.00000			−0.0993808
$406$	−7.50000	−	2.59808i	−0.372219	−	0.128940i
$407$	−6.00000			−0.297409
$408$	−0.500000	+	0.866025i	−0.0247537	+	0.0428746i
$409$	19.0000	+	32.9090i	0.939490	+	1.62724i	0.766426	+	0.642333i	$0.222033\pi$
$409$	19.0000	+	32.9090i	0.939490	+	1.62724i	0.173064	+	0.984911i	$0.444633\pi$
$410$	−2.00000	−	3.46410i	−0.0987730	−	0.171080i
$411$	9.00000	−	15.5885i	0.443937	−	0.768922i
$412$	14.0000			0.689730
$413$	−22.0000	+	19.0526i	−1.08255	+	0.937515i
$414$		0			0
$415$		0			0
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	−7.00000	−	12.1244i	−0.342791	−	0.593732i
$418$	−4.50000	+	7.79423i	−0.220102	+	0.381228i
$419$	−6.00000			−0.293119			−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000			−0.293119			−0.146560	+	0.989202i	$0.546820\pi$
$420$	−4.00000	+	3.46410i	−0.195180	+	0.169031i
$421$		0			0			−	1.00000i	$-0.5\pi$
$421$		0			0				1.00000i	$0.5\pi$
$422$	−8.00000	+	13.8564i	−0.389434	+	0.674519i
$423$	4.50000	+	7.79423i	0.218797	+	0.378968i
$424$	0.500000	+	0.866025i	0.0242821	+	0.0420579i
$425$	0.500000	−	0.866025i	0.0242536	−	0.0420084i
$426$	15.0000			0.726752
$427$	27.5000	+	9.52628i	1.33082	+	0.461009i
$428$	−4.00000			−0.193347
$429$	−1.50000	+	2.59808i	−0.0724207	+	0.125436i
$430$	−6.00000	−	10.3923i	−0.289346	−	0.501161i
$431$	20.0000	+	34.6410i	0.963366	+	1.66860i	0.713942	+	0.700205i	$0.246908\pi$
$431$	20.0000	+	34.6410i	0.963366	+	1.66860i	0.249424	+	0.968394i	$0.419759\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−11.0000			−0.528626			−0.264313	−	0.964437i	$-0.585145\pi$
$433$	−11.0000			−0.528626			−0.264313	+	0.964437i	$0.585145\pi$
$434$	−2.00000	−	10.3923i	−0.0960031	−	0.498847i
$435$	6.00000			0.287678
$436$	4.00000	−	6.92820i	0.191565	−	0.331801i
$437$		0			0
$438$	6.00000	+	10.3923i	0.286691	+	0.496564i
$439$	−8.00000	+	13.8564i	−0.381819	+	0.661330i	−0.991322	−	0.131453i	$-0.958036\pi$
$439$	−8.00000	+	13.8564i	−0.381819	+	0.661330i	0.609503	+	0.792784i	$0.291369\pi$
$440$	6.00000			0.286039
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$	1.00000			0.0475651
$443$	−3.00000	+	5.19615i	−0.142534	+	0.246877i	−0.928450	−	0.371457i	$-0.878858\pi$
$443$	−3.00000	+	5.19615i	−0.142534	+	0.246877i	0.785916	+	0.618333i	$0.212192\pi$
$444$	−1.00000	−	1.73205i	−0.0474579	−	0.0821995i
$445$	10.0000	+	17.3205i	0.474045	+	0.821071i
$446$	−0.500000	+	0.866025i	−0.0236757	+	0.0410075i
$447$		0			0
$448$	−0.500000	−	2.59808i	−0.0236228	−	0.122748i
$449$	−40.0000			−1.88772			−0.943858	−	0.330350i	$-0.892833\pi$
$449$	−40.0000			−1.88772			−0.943858	+	0.330350i	$0.892833\pi$
$450$	−0.500000	+	0.866025i	−0.0235702	+	0.0408248i
$451$	−3.00000	−	5.19615i	−0.141264	−	0.244677i
$452$	−1.50000	−	2.59808i	−0.0705541	−	0.122203i
$453$	−8.50000	+	14.7224i	−0.399365	+	0.691720i
$454$	−8.00000			−0.375459
$455$	5.00000	+	1.73205i	0.234404	+	0.0811998i
$456$	−3.00000			−0.140488
$457$	16.0000	−	27.7128i	0.748448	−	1.29635i	−0.200118	−	0.979772i	$-0.564132\pi$
$457$	16.0000	−	27.7128i	0.748448	−	1.29635i	0.948566	−	0.316579i	$-0.102534\pi$
$458$	−1.00000	−	1.73205i	−0.0467269	−	0.0809334i
$459$	0.500000	+	0.866025i	0.0233380	+	0.0404226i
$460$		0			0
$461$	−20.0000			−0.931493			−0.465746	−	0.884918i	$-0.654214\pi$
$461$	−20.0000			−0.931493			−0.465746	+	0.884918i	$0.654214\pi$
$462$	−6.00000	+	5.19615i	−0.279145	+	0.241747i
$463$	−32.0000			−1.48717			−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000			−1.48717			−0.743583	+	0.668644i	$0.766875\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$	4.00000	+	6.92820i	0.185496	+	0.321288i
$466$	3.50000	+	6.06218i	0.162134	+	0.280825i
$467$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$467$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$468$	−1.00000			−0.0462250
$469$	14.0000	−	12.1244i	0.646460	−	0.559851i
$470$	−18.0000			−0.830278
$471$	−5.50000	+	9.52628i	−0.253427	+	0.438948i
$472$	5.50000	+	9.52628i	0.253158	+	0.438483i
$473$	−9.00000	−	15.5885i	−0.413820	−	0.716758i
$474$	−1.00000	+	1.73205i	−0.0459315	+	0.0795557i
$475$	3.00000			0.137649
$476$	2.50000	+	0.866025i	0.114587	+	0.0396942i
$477$	1.00000			0.0457869
$478$	−5.50000	+	9.52628i	−0.251564	+	0.435722i
$479$	−7.50000	−	12.9904i	−0.342684	−	0.593546i	0.642246	−	0.766498i	$-0.278003\pi$
$479$	−7.50000	−	12.9904i	−0.342684	−	0.593546i	−0.984930	+	0.172953i	$0.944669\pi$
$480$	1.00000	+	1.73205i	0.0456435	+	0.0790569i
$481$	−1.00000	+	1.73205i	−0.0455961	+	0.0789747i
$482$	−12.0000			−0.546585
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	−12.0000	+	20.7846i	−0.544892	+	0.943781i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	16.5000	+	28.5788i	0.747686	+	1.29503i	0.948929	+	0.315489i	$0.102169\pi$
$487$	16.5000	+	28.5788i	0.747686	+	1.29503i	−0.201243	+	0.979541i	$0.564498\pi$
$488$	5.50000	−	9.52628i	0.248973	−	0.431234i
$489$	25.0000			1.13054
$490$	11.0000	+	8.66025i	0.496929	+	0.391230i
$491$	22.0000			0.992846			0.496423	−	0.868081i	$-0.334646\pi$
$491$	22.0000			0.992846			0.496423	+	0.868081i	$0.334646\pi$
$492$	1.00000	−	1.73205i	0.0450835	−	0.0780869i
$493$	−1.50000	−	2.59808i	−0.0675566	−	0.117011i
$494$	1.50000	+	2.59808i	0.0674882	+	0.116893i
$495$	3.00000	−	5.19615i	0.134840	−	0.233550i
$496$	−4.00000			−0.179605
$497$	−7.50000	−	38.9711i	−0.336421	−	1.74809i
$498$		0			0
$499$	−14.0000	+	24.2487i	−0.626726	+	1.08552i	0.361478	+	0.932381i	$0.382272\pi$
$499$	−14.0000	+	24.2487i	−0.626726	+	1.08552i	−0.988204	+	0.153141i	$0.951061\pi$
$500$	−6.00000	−	10.3923i	−0.268328	−	0.464758i
$501$	−9.50000	−	16.4545i	−0.424429	−	0.735132i
$502$	−5.00000	+	8.66025i	−0.223161	+	0.386526i
$503$	−20.0000			−0.891756			−0.445878	−	0.895094i	$-0.647108\pi$
$503$	−20.0000			−0.891756			−0.445878	+	0.895094i	$0.647108\pi$
$504$	−2.50000	−	0.866025i	−0.111359	−	0.0385758i
$505$	28.0000			1.24598
$506$		0			0
$507$	0.500000	+	0.866025i	0.0222058	+	0.0384615i
$508$	−4.00000	−	6.92820i	−0.177471	−	0.307389i
$509$	−6.00000	+	10.3923i	−0.265945	+	0.460631i	−0.967811	−	0.251679i	$-0.919017\pi$
$509$	−6.00000	+	10.3923i	−0.265945	+	0.460631i	0.701866	+	0.712309i	$0.252351\pi$
$510$	−2.00000			−0.0885615
$511$	24.0000	−	20.7846i	1.06170	−	0.919457i
$512$	−1.00000			−0.0441942
$513$	−1.50000	+	2.59808i	−0.0662266	+	0.114708i
$514$	−13.0000	−	22.5167i	−0.573405	−	0.993167i
$515$	14.0000	+	24.2487i	0.616914	+	1.06853i
$516$	3.00000	−	5.19615i	0.132068	−	0.228748i
$517$	−27.0000			−1.18746
$518$	−4.00000	+	3.46410i	−0.175750	+	0.152204i
$519$	−7.00000			−0.307266
$520$	1.00000	−	1.73205i	0.0438529	−	0.0759555i
$521$	19.0000	+	32.9090i	0.832405	+	1.44177i	0.896126	+	0.443800i	$0.146370\pi$
$521$	19.0000	+	32.9090i	0.832405	+	1.44177i	−0.0637207	+	0.997968i	$0.520297\pi$
$522$	1.50000	+	2.59808i	0.0656532	+	0.113715i
$523$	−3.00000	+	5.19615i	−0.131181	+	0.227212i	−0.924132	−	0.382073i	$-0.875210\pi$
$523$	−3.00000	+	5.19615i	−0.131181	+	0.227212i	0.792951	+	0.609285i	$0.208544\pi$
$524$	−12.0000			−0.524222
$525$	2.50000	+	0.866025i	0.109109	+	0.0377964i
$526$	−10.0000			−0.436021
$527$	2.00000	−	3.46410i	0.0871214	−	0.150899i
$528$	1.50000	+	2.59808i	0.0652791	+	0.113067i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	−1.00000	+	1.73205i	−0.0434372	+	0.0752355i
$531$	11.0000			0.477359
$532$	1.50000	+	7.79423i	0.0650332	+	0.337923i
$533$	−2.00000			−0.0866296
$534$	−5.00000	+	8.66025i	−0.216371	+	0.374766i
$535$	−4.00000	−	6.92820i	−0.172935	−	0.299532i
$536$	−3.50000	−	6.06218i	−0.151177	−	0.261846i
$537$	−3.00000	+	5.19615i	−0.129460	+	0.224231i
$538$	21.0000			0.905374
$539$	16.5000	+	12.9904i	0.710705	+	0.559535i
$540$	2.00000			0.0860663
$541$	−11.0000	+	19.0526i	−0.472927	+	0.819133i	−0.999520	−	0.0309841i	$-0.990136\pi$
$541$	−11.0000	+	19.0526i	−0.472927	+	0.819133i	0.526593	+	0.850118i	$0.323469\pi$
$542$	7.50000	+	12.9904i	0.322153	+	0.557985i
$543$	−2.50000	−	4.33013i	−0.107285	−	0.185824i
$544$	0.500000	−	0.866025i	0.0214373	−	0.0371305i
$545$	16.0000			0.685365
$546$	0.500000	+	2.59808i	0.0213980	+	0.111187i
$547$	44.0000			1.88130			0.940652	−	0.339372i	$-0.110215\pi$
$547$	44.0000			1.88130			0.940652	+	0.339372i	$0.110215\pi$
$548$	−9.00000	+	15.5885i	−0.384461	+	0.665906i
$549$	−5.50000	−	9.52628i	−0.234734	−	0.406572i
$550$	−1.50000	−	2.59808i	−0.0639602	−	0.110782i
$551$	4.50000	−	7.79423i	0.191706	−	0.332045i
$552$		0			0
$553$	5.00000	+	1.73205i	0.212622	+	0.0736543i
$554$	−5.00000			−0.212430
$555$	2.00000	−	3.46410i	0.0848953	−	0.147043i
$556$	7.00000	+	12.1244i	0.296866	+	0.514187i
$557$	11.0000	+	19.0526i	0.466085	+	0.807283i	0.999250	−	0.0387286i	$-0.0123308\pi$
$557$	11.0000	+	19.0526i	0.466085	+	0.807283i	−0.533165	+	0.846011i	$0.678997\pi$
$558$	−2.00000	+	3.46410i	−0.0846668	+	0.146647i
$559$	−6.00000			−0.253773
$560$	4.00000	−	3.46410i	0.169031	−	0.146385i
$561$	−3.00000			−0.126660
$562$	−12.0000	+	20.7846i	−0.506189	+	0.876746i
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	−0.999978	−	0.00664037i	$-0.997886\pi$
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	0.494238	−	0.869326i	$-0.335447\pi$
$564$	−4.50000	−	7.79423i	−0.189484	−	0.328196i
$565$	3.00000	−	5.19615i	0.126211	−	0.218604i
$566$	4.00000			0.168133
$567$	−2.00000	+	1.73205i	−0.0839921	+	0.0727393i
$568$	−15.0000			−0.629386
$569$	−19.5000	+	33.7750i	−0.817483	+	1.41592i	0.0900490	+	0.995937i	$0.471298\pi$
$569$	−19.5000	+	33.7750i	−0.817483	+	1.41592i	−0.907532	+	0.419984i	$0.862036\pi$
$570$	−3.00000	−	5.19615i	−0.125656	−	0.217643i
$571$	−22.0000	−	38.1051i	−0.920671	−	1.59465i	−0.798379	−	0.602155i	$-0.794309\pi$
$571$	−22.0000	−	38.1051i	−0.920671	−	1.59465i	−0.122292	−	0.992494i	$-0.539025\pi$
$572$	1.50000	−	2.59808i	0.0627182	−	0.108631i
$573$	12.0000			0.501307
$574$	−5.00000	−	1.73205i	−0.208696	−	0.0722944i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	9.00000	+	15.5885i	0.374675	+	0.648956i	0.990278	−	0.139100i	$-0.0444210\pi$
$577$	9.00000	+	15.5885i	0.374675	+	0.648956i	−0.615603	+	0.788056i	$0.711088\pi$
$578$	−8.00000	−	13.8564i	−0.332756	−	0.576351i
$579$	−7.00000	+	12.1244i	−0.290910	+	0.503871i
$580$	−6.00000			−0.249136
$581$		0			0
$582$	−12.0000			−0.497416
$583$	−1.50000	+	2.59808i	−0.0621237	+	0.107601i
$584$	−6.00000	−	10.3923i	−0.248282	−	0.430037i
$585$	−1.00000	−	1.73205i	−0.0413449	−	0.0716115i
$586$	−6.00000	+	10.3923i	−0.247858	+	0.429302i
$587$	39.0000			1.60970			0.804851	−	0.593477i	$-0.202245\pi$
$587$	39.0000			1.60970			0.804851	+	0.593477i	$0.202245\pi$
$588$	−1.00000	+	6.92820i	−0.0412393	+	0.285714i
$589$	12.0000			0.494451
$590$	−11.0000	+	19.0526i	−0.452863	+	0.784381i
$591$	4.00000	+	6.92820i	0.164538	+	0.284988i
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	17.0000	−	29.4449i	0.698106	−	1.20916i	−0.271016	−	0.962575i	$-0.587360\pi$
$593$	17.0000	−	29.4449i	0.698106	−	1.20916i	0.969122	−	0.246581i	$-0.0793071\pi$
$594$	3.00000			0.123091
$595$	1.00000	+	5.19615i	0.0409960	+	0.213021i
$596$		0			0
$597$	6.00000	−	10.3923i	0.245564	−	0.425329i
$598$		0			0
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	0.990752	+	0.135686i	$0.0433238\pi$
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	−0.377869	+	0.925859i	$0.623343\pi$
$600$	0.500000	−	0.866025i	0.0204124	−	0.0353553i
$601$	−35.0000			−1.42768			−0.713840	−	0.700309i	$-0.753046\pi$
$601$	−35.0000			−1.42768			−0.713840	+	0.700309i	$0.753046\pi$
$602$	−15.0000	−	5.19615i	−0.611354	−	0.211779i
$603$	−7.00000			−0.285062
$604$	8.50000	−	14.7224i	0.345860	−	0.599047i
$605$	−2.00000	−	3.46410i	−0.0813116	−	0.140836i
$606$	7.00000	+	12.1244i	0.284356	+	0.492518i
$607$	−14.0000	+	24.2487i	−0.568242	+	0.984225i	0.428497	+	0.903543i	$0.359043\pi$
$607$	−14.0000	+	24.2487i	−0.568242	+	0.984225i	−0.996740	+	0.0806818i	$0.974290\pi$
$608$	3.00000			0.121666
$609$	6.00000	−	5.19615i	0.243132	−	0.210559i
$610$	22.0000			0.890754
$611$	−4.50000	+	7.79423i	−0.182051	+	0.315321i
$612$	−0.500000	−	0.866025i	−0.0202113	−	0.0350070i
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$	−7.50000	+	12.9904i	−0.302675	+	0.524249i
$615$	4.00000			0.161296
$616$	6.00000	−	5.19615i	0.241747	−	0.209359i
$617$	−14.0000			−0.563619			−0.281809	−	0.959470i	$-0.590935\pi$
$617$	−14.0000			−0.563619			−0.281809	+	0.959470i	$0.590935\pi$
$618$	−7.00000	+	12.1244i	−0.281581	+	0.487713i
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	0.592025	−	0.805919i	$-0.298329\pi$
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	−0.993959	+	0.109749i	$0.964995\pi$
$620$	−4.00000	−	6.92820i	−0.160644	−	0.278243i
$621$		0			0
$622$	−14.0000			−0.561349
$623$	25.0000	+	8.66025i	1.00160	+	0.346966i
$624$	1.00000			0.0400320
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	−7.00000	−	12.1244i	−0.279776	−	0.484587i
$627$	−4.50000	−	7.79423i	−0.179713	−	0.311272i
$628$	5.50000	−	9.52628i	0.219474	−	0.380140i
$629$	−2.00000			−0.0797452
$630$	−1.00000	−	5.19615i	−0.0398410	−	0.207020i
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$	1.00000	−	1.73205i	0.0397779	−	0.0688973i
$633$	−8.00000	−	13.8564i	−0.317971	−	0.550743i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	8.00000	−	13.8564i	0.317470	−	0.549875i
$636$	−1.00000			−0.0396526
$637$	6.50000	−	2.59808i	0.257539	−	0.102940i
$638$	−9.00000			−0.356313
$639$	−7.50000	+	12.9904i	−0.296695	+	0.513892i
$640$	−1.00000	−	1.73205i	−0.0395285	−	0.0684653i
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	0.987200	−	0.159489i	$-0.0509845\pi$
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	−0.631721	+	0.775196i	$0.717651\pi$
$642$	2.00000	−	3.46410i	0.0789337	−	0.136717i
$643$	1.00000			0.0394362			0.0197181	−	0.999806i	$-0.493723\pi$
$643$	1.00000			0.0394362			0.0197181	+	0.999806i	$0.493723\pi$
$644$		0			0
$645$	12.0000			0.472500
$646$	−1.50000	+	2.59808i	−0.0590167	+	0.102220i
$647$	3.00000	+	5.19615i	0.117942	+	0.204282i	0.918952	−	0.394369i	$-0.129037\pi$
$647$	3.00000	+	5.19615i	0.117942	+	0.204282i	−0.801010	+	0.598651i	$0.795704\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−16.5000	+	28.5788i	−0.647682	+	1.12182i
$650$	−1.00000			−0.0392232
$651$	10.0000	+	3.46410i	0.391931	+	0.135769i
$652$	−25.0000			−0.979076
$653$	15.0000	−	25.9808i	0.586995	−	1.01671i	−0.407628	−	0.913148i	$-0.633644\pi$
$653$	15.0000	−	25.9808i	0.586995	−	1.01671i	0.994623	−	0.103558i	$-0.0330227\pi$
$654$	4.00000	+	6.92820i	0.156412	+	0.270914i
$655$	−12.0000	−	20.7846i	−0.468879	−	0.812122i
$656$	−1.00000	+	1.73205i	−0.0390434	+	0.0676252i
$657$	−12.0000			−0.468165
$658$	−18.0000	+	15.5885i	−0.701713	+	0.607701i
$659$	30.0000			1.16863			0.584317	−	0.811525i	$-0.301362\pi$
$659$	30.0000			1.16863			0.584317	+	0.811525i	$0.301362\pi$
$660$	−3.00000	+	5.19615i	−0.116775	+	0.202260i
$661$	−19.0000	−	32.9090i	−0.739014	−	1.28001i	−0.952940	−	0.303160i	$-0.901958\pi$
$661$	−19.0000	−	32.9090i	−0.739014	−	1.28001i	0.213925	−	0.976850i	$-0.431375\pi$
$662$	−14.0000	−	24.2487i	−0.544125	−	0.942453i
$663$	−0.500000	+	0.866025i	−0.0194184	+	0.0336336i
$664$		0			0
$665$	−12.0000	+	10.3923i	−0.465340	+	0.402996i
$666$	2.00000			0.0774984
$667$		0			0
$668$	9.50000	+	16.4545i	0.367566	+	0.636643i
$669$	−0.500000	−	0.866025i	−0.0193311	−	0.0334825i
$670$	7.00000	−	12.1244i	0.270434	−	0.468405i
$671$	33.0000			1.27395
$672$	2.50000	+	0.866025i	0.0964396	+	0.0334077i
$673$	−34.0000			−1.31060			−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000			−1.31060			−0.655302	+	0.755367i	$0.727459\pi$
$674$	3.50000	−	6.06218i	0.134815	−	0.233506i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−0.500000	+	0.866025i	−0.0192166	+	0.0332841i	−0.875474	−	0.483266i	$-0.839451\pi$
$677$	−0.500000	+	0.866025i	−0.0192166	+	0.0332841i	0.856257	+	0.516550i	$0.172784\pi$
$678$	3.00000			0.115214
$679$	6.00000	+	31.1769i	0.230259	+	1.19646i
$680$	2.00000			0.0766965
$681$	4.00000	−	6.92820i	0.153280	−	0.265489i
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	22.0000	+	38.1051i	0.841807	+	1.45805i	0.888366	+	0.459136i	$0.151841\pi$
$683$	22.0000	+	38.1051i	0.841807	+	1.45805i	−0.0465592	+	0.998916i	$0.514826\pi$
$684$	1.50000	−	2.59808i	0.0573539	−	0.0993399i
$685$	−36.0000			−1.37549
$686$	18.5000	−	0.866025i	0.706333	−	0.0330650i
$687$	2.00000			0.0763048
$688$	−3.00000	+	5.19615i	−0.114374	+	0.198101i
$689$	0.500000	+	0.866025i	0.0190485	+	0.0329929i
$690$		0			0
$691$	−17.5000	+	30.3109i	−0.665731	+	1.15308i	0.313355	+	0.949636i	$0.398547\pi$
$691$	−17.5000	+	30.3109i	−0.665731	+	1.15308i	−0.979086	+	0.203445i	$0.934786\pi$
$692$	7.00000			0.266100
$693$	−1.50000	−	7.79423i	−0.0569803	−	0.296078i
$694$	−2.00000			−0.0759190
$695$	−14.0000	+	24.2487i	−0.531050	+	0.919806i
$696$	−1.50000	−	2.59808i	−0.0568574	−	0.0984798i
$697$	−1.00000	−	1.73205i	−0.0378777	−	0.0656061i
$698$	10.0000	−	17.3205i	0.378506	−	0.655591i
$699$	−7.00000			−0.264764
$700$	−2.50000	−	0.866025i	−0.0944911	−	0.0327327i
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$	0.500000	−	0.866025i	0.0188713	−	0.0326860i
$703$	−3.00000	−	5.19615i	−0.113147	−	0.195977i
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$	9.00000	−	15.5885i	0.338960	−	0.587095i
$706$	18.0000			0.677439
$707$	28.0000	−	24.2487i	1.05305	−	0.911967i
$708$	−11.0000			−0.413405
$709$	10.0000	−	17.3205i	0.375558	−	0.650485i	−0.614852	−	0.788642i	$-0.710784\pi$
$709$	10.0000	−	17.3205i	0.375558	−	0.650485i	0.990410	+	0.138157i	$0.0441178\pi$
$710$	−15.0000	−	25.9808i	−0.562940	−	0.975041i
$711$	−1.00000	−	1.73205i	−0.0375029	−	0.0649570i
$712$	5.00000	−	8.66025i	0.187383	−	0.324557i
$713$		0			0
$714$	−2.00000	+	1.73205i	−0.0748481	+	0.0648204i
$715$	6.00000			0.224387
$716$	3.00000	−	5.19615i	0.112115	−	0.194189i
$717$	−5.50000	−	9.52628i	−0.205401	−	0.355765i
$718$	8.00000	+	13.8564i	0.298557	+	0.517116i
$719$	−19.0000	+	32.9090i	−0.708580	+	1.22730i	0.256803	+	0.966464i	$0.417331\pi$
$719$	−19.0000	+	32.9090i	−0.708580	+	1.22730i	−0.965384	+	0.260834i	$0.916003\pi$
$720$	−2.00000			−0.0745356
$721$	35.0000	+	12.1244i	1.30347	+	0.451535i
$722$	10.0000			0.372161
$723$	6.00000	−	10.3923i	0.223142	−	0.386494i
$724$	2.50000	+	4.33013i	0.0929118	+	0.160928i
$725$	1.50000	+	2.59808i	0.0557086	+	0.0964901i
$726$	1.00000	−	1.73205i	0.0371135	−	0.0642824i
$727$	−12.0000			−0.445055			−0.222528	−	0.974926i	$-0.571431\pi$
$727$	−12.0000			−0.445055			−0.222528	+	0.974926i	$0.571431\pi$
$728$	−0.500000	−	2.59808i	−0.0185312	−	0.0962911i
$729$	1.00000			0.0370370
$730$	12.0000	−	20.7846i	0.444140	−	0.769273i
$731$	−3.00000	−	5.19615i	−0.110959	−	0.192187i
$732$	5.50000	+	9.52628i	0.203286	+	0.352101i
$733$	4.00000	−	6.92820i	0.147743	−	0.255899i	−0.782650	−	0.622462i	$-0.786132\pi$
$733$	4.00000	−	6.92820i	0.147743	−	0.255899i	0.930393	+	0.366563i	$0.119466\pi$
$734$	−18.0000			−0.664392
$735$	−13.0000	+	5.19615i	−0.479512	+	0.191663i
$736$		0			0
$737$	10.5000	−	18.1865i	0.386772	−	0.669910i
$738$	1.00000	+	1.73205i	0.0368105	+	0.0637577i
$739$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$739$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$740$	−2.00000	+	3.46410i	−0.0735215	+	0.127343i
$741$	−3.00000			−0.110208
$742$	0.500000	+	2.59808i	0.0183556	+	0.0953784i
$743$	−35.0000			−1.28403			−0.642013	−	0.766694i	$-0.721900\pi$
$743$	−35.0000			−1.28403			−0.642013	+	0.766694i	$0.721900\pi$
$744$	2.00000	−	3.46410i	0.0733236	−	0.127000i
$745$		0			0
$746$	−5.50000	−	9.52628i	−0.201369	−	0.348782i
$747$		0			0
$748$	3.00000			0.109691
$749$	−10.0000	−	3.46410i	−0.365392	−	0.126576i
$750$	12.0000			0.438178
$751$	−14.0000	+	24.2487i	−0.510867	+	0.884848i	0.489053	+	0.872254i	$0.337342\pi$
$751$	−14.0000	+	24.2487i	−0.510867	+	0.884848i	−0.999921	+	0.0125942i	$0.995991\pi$
$752$	4.50000	+	7.79423i	0.164098	+	0.284226i
$753$	−5.00000	−	8.66025i	−0.182210	−	0.315597i
$754$	−1.50000	+	2.59808i	−0.0546268	+	0.0946164i
$755$	34.0000			1.23739
$756$	2.00000	−	1.73205i	0.0727393	−	0.0629941i
$757$	19.0000			0.690567			0.345283	−	0.938498i	$-0.387783\pi$
$757$	19.0000			0.690567			0.345283	+	0.938498i	$0.387783\pi$
$758$	18.0000	−	31.1769i	0.653789	−	1.13240i
$759$		0			0
$760$	3.00000	+	5.19615i	0.108821	+	0.188484i
$761$	−14.0000	+	24.2487i	−0.507500	+	0.879015i	0.492463	+	0.870334i	$0.336097\pi$
$761$	−14.0000	+	24.2487i	−0.507500	+	0.879015i	−0.999962	+	0.00868155i	$0.997237\pi$
$762$	8.00000			0.289809
$763$	16.0000	−	13.8564i	0.579239	−	0.501636i
$764$	−12.0000			−0.434145
$765$	1.00000	−	1.73205i	0.0361551	−	0.0626224i
$766$	−16.0000	−	27.7128i	−0.578103	−	1.00130i
$767$	5.50000	+	9.52628i	0.198593	+	0.343974i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−4.00000			−0.144244			−0.0721218	−	0.997396i	$-0.522977\pi$
$769$	−4.00000			−0.144244			−0.0721218	+	0.997396i	$0.522977\pi$
$770$	15.0000	+	5.19615i	0.540562	+	0.187256i
$771$	26.0000			0.936367
$772$	7.00000	−	12.1244i	0.251936	−	0.436365i
$773$	−21.0000

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +1.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +1.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(-1.50000 - 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{12} -1.00000 q^{13} +(-2.50000 - 0.866025i) q^{14} +2.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{17} +(0.500000 + 0.866025i) q^{18} +(1.50000 - 2.59808i) q^{19} -2.00000 q^{20} +(2.00000 - 1.73205i) q^{21} -3.00000 q^{22} +(-0.500000 - 0.866025i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.500000 + 0.866025i) q^{26} -1.00000 q^{27} +(-2.00000 + 1.73205i) q^{28} +3.00000 q^{29} +(1.00000 - 1.73205i) q^{30} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} -1.00000 q^{34} +(-5.00000 - 1.73205i) q^{35} +1.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(-1.50000 - 2.59808i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(-1.00000 + 1.73205i) q^{40} +2.00000 q^{41} +(-0.500000 - 2.59808i) q^{42} +6.00000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(1.00000 + 1.73205i) q^{45} +(4.50000 - 7.79423i) q^{47} -1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} +1.00000 q^{50} +(0.500000 - 0.866025i) q^{51} +(0.500000 + 0.866025i) q^{52} +(-0.500000 - 0.866025i) q^{53} +(-0.500000 + 0.866025i) q^{54} -6.00000 q^{55} +(0.500000 + 2.59808i) q^{56} +3.00000 q^{57} +(1.50000 - 2.59808i) q^{58} +(-5.50000 - 9.52628i) q^{59} +(-1.00000 - 1.73205i) q^{60} +(-5.50000 + 9.52628i) q^{61} +4.00000 q^{62} +(2.50000 + 0.866025i) q^{63} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(-1.50000 - 2.59808i) q^{66} +(3.50000 + 6.06218i) q^{67} +(-0.500000 + 0.866025i) q^{68} +(-4.00000 + 3.46410i) q^{70} +15.0000 q^{71} +(0.500000 - 0.866025i) q^{72} +(6.00000 + 10.3923i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-0.500000 + 0.866025i) q^{75} -3.00000 q^{76} +(-6.00000 + 5.19615i) q^{77} -1.00000 q^{78} +(-1.00000 + 1.73205i) q^{79} +(1.00000 + 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} +(-2.50000 - 0.866025i) q^{84} -2.00000 q^{85} +(3.00000 - 5.19615i) q^{86} +(1.50000 + 2.59808i) q^{87} +(1.50000 + 2.59808i) q^{88} +(-5.00000 + 8.66025i) q^{89} +2.00000 q^{90} +(0.500000 + 2.59808i) q^{91} +(-2.00000 + 3.46410i) q^{93} +(-4.50000 - 7.79423i) q^{94} +(-3.00000 - 5.19615i) q^{95} +(-0.500000 + 0.866025i) q^{96} -12.0000 q^{97} +(-1.00000 + 6.92820i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} + 2 q^{5} + 2 q^{6} - q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 + 2 * q^5 + 2 * q^6 - q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} + 2 q^{5} + 2 q^{6} - q^{7} - 2 q^{8} - q^{9} - 2 q^{10} - 3 q^{11} + q^{12} - 2 q^{13} - 5 q^{14} + 4 q^{15} - q^{16} - q^{17} + q^{18} + 3 q^{19} - 4 q^{20} + 4 q^{21} - 6 q^{22} - q^{24} + q^{25} - q^{26} - 2 q^{27} - 4 q^{28} + 6 q^{29} + 2 q^{30} + 4 q^{31} + q^{32} + 3 q^{33} - 2 q^{34} - 10 q^{35} + 2 q^{36} + 2 q^{37} - 3 q^{38} - q^{39} - 2 q^{40} + 4 q^{41} - q^{42} + 12 q^{43} - 3 q^{44} + 2 q^{45} + 9 q^{47} - 2 q^{48} - 13 q^{49} + 2 q^{50} + q^{51} + q^{52} - q^{53} - q^{54} - 12 q^{55} + q^{56} + 6 q^{57} + 3 q^{58} - 11 q^{59} - 2 q^{60} - 11 q^{61} + 8 q^{62} + 5 q^{63} + 2 q^{64} - 2 q^{65} - 3 q^{66} + 7 q^{67} - q^{68} - 8 q^{70} + 30 q^{71} + q^{72} + 12 q^{73} - 2 q^{74} - q^{75} - 6 q^{76} - 12 q^{77} - 2 q^{78} - 2 q^{79} + 2 q^{80} - q^{81} + 2 q^{82} - 5 q^{84} - 4 q^{85} + 6 q^{86} + 3 q^{87} + 3 q^{88} - 10 q^{89} + 4 q^{90} + q^{91} - 4 q^{93} - 9 q^{94} - 6 q^{95} - q^{96} - 24 q^{97} - 2 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + 2 * q^5 + 2 * q^6 - q^7 - 2 * q^8 - q^9 - 2 * q^10 - 3 * q^11 + q^12 - 2 * q^13 - 5 * q^14 + 4 * q^15 - q^16 - q^17 + q^18 + 3 * q^19 - 4 * q^20 + 4 * q^21 - 6 * q^22 - q^24 + q^25 - q^26 - 2 * q^27 - 4 * q^28 + 6 * q^29 + 2 * q^30 + 4 * q^31 + q^32 + 3 * q^33 - 2 * q^34 - 10 * q^35 + 2 * q^36 + 2 * q^37 - 3 * q^38 - q^39 - 2 * q^40 + 4 * q^41 - q^42 + 12 * q^43 - 3 * q^44 + 2 * q^45 + 9 * q^47 - 2 * q^48 - 13 * q^49 + 2 * q^50 + q^51 + q^52 - q^53 - q^54 - 12 * q^55 + q^56 + 6 * q^57 + 3 * q^58 - 11 * q^59 - 2 * q^60 - 11 * q^61 + 8 * q^62 + 5 * q^63 + 2 * q^64 - 2 * q^65 - 3 * q^66 + 7 * q^67 - q^68 - 8 * q^70 + 30 * q^71 + q^72 + 12 * q^73 - 2 * q^74 - q^75 - 6 * q^76 - 12 * q^77 - 2 * q^78 - 2 * q^79 + 2 * q^80 - q^81 + 2 * q^82 - 5 * q^84 - 4 * q^85 + 6 * q^86 + 3 * q^87 + 3 * q^88 - 10 * q^89 + 4 * q^90 + q^91 - 4 * q^93 - 9 * q^94 - 6 * q^95 - q^96 - 24 * q^97 - 2 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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