LMFDB - Embedded newform 390.2.i.d.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(61,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("390.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.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:	$3.11416567883$
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			211.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	390.211
Dual form			390.2.i.d.61.1

$q$-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 q^{5} +(0.500000 - 0.866025i) q^{6} +(2.50000 - 4.33013i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} +1.00000 q^{12} +(-2.50000 - 2.59808i) q^{13} +5.00000 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.00000 - 6.92820i) q^{17} -1.00000 q^{18} +(2.50000 - 4.33013i) q^{19} +(0.500000 - 0.866025i) q^{20} -5.00000 q^{21} +(-1.50000 + 2.59808i) q^{22} +(2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{24} +1.00000 q^{25} +(1.00000 - 3.46410i) q^{26} +1.00000 q^{27} +(2.50000 + 4.33013i) q^{28} +(2.00000 + 3.46410i) q^{29} +(-0.500000 + 0.866025i) q^{30} -2.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +8.00000 q^{34} +(-2.50000 + 4.33013i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(3.50000 + 6.06218i) q^{37} +5.00000 q^{38} +(-1.00000 + 3.46410i) q^{39} +1.00000 q^{40} +(-3.00000 - 5.19615i) q^{41} +(-2.50000 - 4.33013i) q^{42} +(-3.00000 + 5.19615i) q^{43} -3.00000 q^{44} +(0.500000 - 0.866025i) q^{45} +(-2.00000 + 3.46410i) q^{46} -3.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-9.00000 - 15.5885i) q^{49} +(0.500000 + 0.866025i) q^{50} -8.00000 q^{51} +(3.50000 - 0.866025i) q^{52} +1.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.50000 - 2.59808i) q^{55} +(-2.50000 + 4.33013i) q^{56} -5.00000 q^{57} +(-2.00000 + 3.46410i) q^{58} +(-6.00000 + 10.3923i) q^{59} -1.00000 q^{60} +(-1.00000 + 1.73205i) q^{61} +(-1.00000 - 1.73205i) q^{62} +(2.50000 + 4.33013i) q^{63} +1.00000 q^{64} +(2.50000 + 2.59808i) q^{65} +3.00000 q^{66} +(-4.00000 - 6.92820i) q^{67} +(4.00000 + 6.92820i) q^{68} +(2.00000 - 3.46410i) q^{69} -5.00000 q^{70} +(-1.00000 + 1.73205i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-3.50000 + 6.06218i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(2.50000 + 4.33013i) q^{76} +15.0000 q^{77} +(-3.50000 + 0.866025i) q^{78} -2.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} +8.00000 q^{83} +(2.50000 - 4.33013i) q^{84} +(-4.00000 + 6.92820i) q^{85} -6.00000 q^{86} +(2.00000 - 3.46410i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(5.50000 + 9.52628i) q^{89} +1.00000 q^{90} +(-17.5000 + 4.33013i) q^{91} -4.00000 q^{92} +(1.00000 + 1.73205i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(-2.50000 + 4.33013i) q^{95} -1.00000 q^{96} +(9.00000 - 15.5885i) q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} - 2 q^{5} + q^{6} + 5 q^{7} - 2 q^{8} - q^{9} - q^{10} + 3 q^{11} + 2 q^{12} - 5 q^{13} + 10 q^{14} + q^{15} - q^{16} + 8 q^{17} - 2 q^{18} + 5 q^{19} + q^{20} - 10 q^{21}+ \cdots - 6 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 - 2 * q^5 + q^6 + 5 * q^7 - 2 * q^8 - q^9 - q^10 + 3 * q^11 + 2 * q^12 - 5 * q^13 + 10 * q^14 + q^15 - q^16 + 8 * q^17 - 2 * q^18 + 5 * q^19 + q^20 - 10 * q^21 - 3 * q^22 + 4 * q^23 + q^24 + 2 * q^25 + 2 * q^26 + 2 * q^27 + 5 * q^28 + 4 * q^29 - q^30 - 4 * q^31 + q^32 + 3 * q^33 + 16 * q^34 - 5 * q^35 - q^36 + 7 * q^37 + 10 * q^38 - 2 * q^39 + 2 * q^40 - 6 * q^41 - 5 * q^42 - 6 * q^43 - 6 * q^44 + q^45 - 4 * q^46 - 6 * q^47 - q^48 - 18 * q^49 + q^50 - 16 * q^51 + 7 * q^52 + 2 * q^53 + q^54 - 3 * q^55 - 5 * q^56 - 10 * q^57 - 4 * q^58 - 12 * q^59 - 2 * q^60 - 2 * q^61 - 2 * q^62 + 5 * q^63 + 2 * q^64 + 5 * q^65 + 6 * q^66 - 8 * q^67 + 8 * q^68 + 4 * q^69 - 10 * q^70 - 2 * q^71 + q^72 - 7 * q^74 - q^75 + 5 * q^76 + 30 * q^77 - 7 * q^78 - 4 * q^79 + q^80 - q^81 + 6 * q^82 + 16 * q^83 + 5 * q^84 - 8 * q^85 - 12 * q^86 + 4 * q^87 - 3 * q^88 + 11 * q^89 + 2 * q^90 - 35 * q^91 - 8 * q^92 + 2 * q^93 - 3 * q^94 - 5 * q^95 - 2 * q^96 + 18 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	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			−0.447214
$5$	−1.00000			−0.447214
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	2.50000	−	4.33013i	0.944911	−	1.63663i	0.188982	−	0.981981i	$-0.439481\pi$
$7$	2.50000	−	4.33013i	0.944911	−	1.63663i	0.755929	−	0.654654i	$-0.227186\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$	1.00000			0.288675
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$14$	5.00000			1.33631
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.00000	−	6.92820i	0.970143	−	1.68034i	0.275029	−	0.961436i	$-0.411312\pi$
$17$	4.00000	−	6.92820i	0.970143	−	1.68034i	0.695113	−	0.718900i	$-0.255354\pi$
$18$	−1.00000			−0.235702
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	−0.422659	−	0.906289i	$-0.638903\pi$
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	0.996199	−	0.0871106i	$-0.0277634\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−5.00000			−1.09109
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	1.00000			0.200000
$26$	1.00000	−	3.46410i	0.196116	−	0.679366i
$27$	1.00000			0.192450
$28$	2.50000	+	4.33013i	0.472456	+	0.818317i
$29$	2.00000	+	3.46410i	0.371391	+	0.643268i	0.989780	−	0.142605i	$-0.0455477\pi$
$29$	2.00000	+	3.46410i	0.371391	+	0.643268i	−0.618389	+	0.785872i	$0.712214\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.50000	−	2.59808i	0.261116	−	0.452267i
$34$	8.00000			1.37199
$35$	−2.50000	+	4.33013i	−0.422577	+	0.731925i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$	5.00000			0.811107
$39$	−1.00000	+	3.46410i	−0.160128	+	0.554700i
$40$	1.00000			0.158114
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	0.530831	−	0.847477i	$-0.321880\pi$
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	−0.999353	+	0.0359748i	$0.988546\pi$
$42$	−2.50000	−	4.33013i	−0.385758	−	0.668153i
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	−0.998828	−	0.0484030i	$-0.984587\pi$
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	0.541332	+	0.840809i	$0.317920\pi$
$44$	−3.00000			−0.452267
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$	−2.00000	+	3.46410i	−0.294884	+	0.510754i
$47$	−3.00000			−0.437595			−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000			−0.437595			−0.218797	+	0.975770i	$0.570213\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−9.00000	−	15.5885i	−1.28571	−	2.22692i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−8.00000			−1.12022
$52$	3.50000	−	0.866025i	0.485363	−	0.120096i
$53$	1.00000			0.137361			0.0686803	−	0.997639i	$-0.478121\pi$
$53$	1.00000			0.137361			0.0686803	+	0.997639i	$0.478121\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−1.50000	−	2.59808i	−0.202260	−	0.350325i
$56$	−2.50000	+	4.33013i	−0.334077	+	0.578638i
$57$	−5.00000			−0.662266
$58$	−2.00000	+	3.46410i	−0.262613	+	0.454859i
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	0.150148	+	0.988663i	$0.452025\pi$
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	−0.931282	+	0.364299i	$0.881308\pi$
$60$	−1.00000			−0.129099
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$	−1.00000	−	1.73205i	−0.127000	−	0.219971i
$63$	2.50000	+	4.33013i	0.314970	+	0.545545i
$64$	1.00000			0.125000
$65$	2.50000	+	2.59808i	0.310087	+	0.322252i
$66$	3.00000			0.369274
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	4.00000	+	6.92820i	0.485071	+	0.840168i
$69$	2.00000	−	3.46410i	0.240772	−	0.417029i
$70$	−5.00000			−0.597614
$71$	−1.00000	+	1.73205i	−0.118678	+	0.205557i	−0.919244	−	0.393688i	$-0.871199\pi$
$71$	−1.00000	+	1.73205i	−0.118678	+	0.205557i	0.800566	+	0.599245i	$0.204532\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	−3.50000	+	6.06218i	−0.406867	+	0.704714i
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$	2.50000	+	4.33013i	0.286770	+	0.496700i
$77$	15.0000			1.70941
$78$	−3.50000	+	0.866025i	−0.396297	+	0.0980581i
$79$	−2.00000			−0.225018			−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000			−0.225018			−0.112509	+	0.993651i	$0.535889\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.00000	−	5.19615i	0.331295	−	0.573819i
$83$	8.00000			0.878114			0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000			0.878114			0.439057	+	0.898459i	$0.355313\pi$
$84$	2.50000	−	4.33013i	0.272772	−	0.472456i
$85$	−4.00000	+	6.92820i	−0.433861	+	0.751469i
$86$	−6.00000			−0.646997
$87$	2.00000	−	3.46410i	0.214423	−	0.371391i
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	5.50000	+	9.52628i	0.582999	+	1.00978i	0.995122	+	0.0986553i	$0.0314541\pi$
$89$	5.50000	+	9.52628i	0.582999	+	1.00978i	−0.412123	+	0.911128i	$0.635213\pi$
$90$	1.00000			0.105409
$91$	−17.5000	+	4.33013i	−1.83450	+	0.453921i
$92$	−4.00000			−0.417029
$93$	1.00000	+	1.73205i	0.103695	+	0.179605i
$94$	−1.50000	−	2.59808i	−0.154713	−	0.267971i
$95$	−2.50000	+	4.33013i	−0.256495	+	0.444262i
$96$	−1.00000			−0.102062
$97$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$97$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$98$	9.00000	−	15.5885i	0.909137	−	1.57467i
$99$	−3.00000			−0.301511
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	4.00000	+	6.92820i	0.398015	+	0.689382i	0.993481	−	0.113998i	$-0.0363659\pi$
$101$	4.00000	+	6.92820i	0.398015	+	0.689382i	−0.595466	+	0.803380i	$0.703033\pi$
$102$	−4.00000	−	6.92820i	−0.396059	−	0.685994i
$103$	−7.00000			−0.689730			−0.344865	−	0.938652i	$-0.612075\pi$
$103$	−7.00000			−0.689730			−0.344865	+	0.938652i	$0.612075\pi$
$104$	2.50000	+	2.59808i	0.245145	+	0.254762i
$105$	5.00000			0.487950
$106$	0.500000	+	0.866025i	0.0485643	+	0.0841158i
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	0.973814	−	0.227345i	$-0.0730044\pi$
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	−0.683793	+	0.729676i	$0.739671\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$	1.50000	−	2.59808i	0.143019	−	0.247717i
$111$	3.50000	−	6.06218i	0.332205	−	0.575396i
$112$	−5.00000			−0.472456
$113$	−4.00000	+	6.92820i	−0.376288	+	0.651751i	−0.990519	−	0.137376i	$-0.956133\pi$
$113$	−4.00000	+	6.92820i	−0.376288	+	0.651751i	0.614231	+	0.789127i	$0.289466\pi$
$114$	−2.50000	−	4.33013i	−0.234146	−	0.405554i
$115$	−2.00000	−	3.46410i	−0.186501	−	0.323029i
$116$	−4.00000			−0.371391
$117$	3.50000	−	0.866025i	0.323575	−	0.0800641i
$118$	−12.0000			−1.10469
$119$	−20.0000	−	34.6410i	−1.83340	−	3.17554i
$120$	−0.500000	−	0.866025i	−0.0456435	−	0.0790569i
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−2.00000			−0.181071
$123$	−3.00000	+	5.19615i	−0.270501	+	0.468521i
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$	−1.00000			−0.0894427
$126$	−2.50000	+	4.33013i	−0.222718	+	0.385758i
$127$	10.5000	+	18.1865i	0.931724	+	1.61379i	0.780373	+	0.625314i	$0.215029\pi$
$127$	10.5000	+	18.1865i	0.931724	+	1.61379i	0.151351	+	0.988480i	$0.451638\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	6.00000			0.528271
$130$	−1.00000	+	3.46410i	−0.0877058	+	0.303822i
$131$	−19.0000			−1.66004			−0.830019	−	0.557735i	$-0.811670\pi$
$131$	−19.0000			−1.66004			−0.830019	+	0.557735i	$0.811670\pi$
$132$	1.50000	+	2.59808i	0.130558	+	0.226134i
$133$	−12.5000	−	21.6506i	−1.08389	−	1.87735i
$134$	4.00000	−	6.92820i	0.345547	−	0.598506i
$135$	−1.00000			−0.0860663
$136$	−4.00000	+	6.92820i	−0.342997	+	0.594089i
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$	4.00000			0.340503
$139$	−3.50000	+	6.06218i	−0.296866	+	0.514187i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$	−3.50000	+	6.06218i	−0.296866	+	0.514187i	0.678551	+	0.734553i	$0.262608\pi$
$140$	−2.50000	−	4.33013i	−0.211289	−	0.365963i
$141$	1.50000	+	2.59808i	0.126323	+	0.218797i
$142$	−2.00000			−0.167836
$143$	3.00000	−	10.3923i	0.250873	−	0.869048i
$144$	1.00000			0.0833333
$145$	−2.00000	−	3.46410i	−0.166091	−	0.287678i
$146$		0			0
$147$	−9.00000	+	15.5885i	−0.742307	+	1.28571i
$148$	−7.00000			−0.575396
$149$	1.00000	−	1.73205i	0.0819232	−	0.141895i	−0.822153	−	0.569267i	$-0.807227\pi$
$149$	1.00000	−	1.73205i	0.0819232	−	0.141895i	0.904076	+	0.427372i	$0.140560\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	22.0000			1.79033			0.895167	−	0.445730i	$-0.147056\pi$
$151$	22.0000			1.79033			0.895167	+	0.445730i	$0.147056\pi$
$152$	−2.50000	+	4.33013i	−0.202777	+	0.351220i
$153$	4.00000	+	6.92820i	0.323381	+	0.560112i
$154$	7.50000	+	12.9904i	0.604367	+	1.04679i
$155$	2.00000			0.160644
$156$	−2.50000	−	2.59808i	−0.200160	−	0.208013i
$157$	15.0000			1.19713			0.598565	−	0.801074i	$-0.295738\pi$
$157$	15.0000			1.19713			0.598565	+	0.801074i	$0.295738\pi$
$158$	−1.00000	−	1.73205i	−0.0795557	−	0.137795i
$159$	−0.500000	−	0.866025i	−0.0396526	−	0.0686803i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	20.0000			1.57622
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	10.0000	−	17.3205i	0.783260	−	1.35665i	−0.146772	−	0.989170i	$-0.546888\pi$
$163$	10.0000	−	17.3205i	0.783260	−	1.35665i	0.930033	−	0.367477i	$-0.119778\pi$
$164$	6.00000			0.468521
$165$	−1.50000	+	2.59808i	−0.116775	+	0.202260i
$166$	4.00000	+	6.92820i	0.310460	+	0.537733i
$167$	11.5000	+	19.9186i	0.889897	+	1.54135i	0.839996	+	0.542592i	$0.182557\pi$
$167$	11.5000	+	19.9186i	0.889897	+	1.54135i	0.0499004	+	0.998754i	$0.484110\pi$
$168$	5.00000			0.385758
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$	−8.00000			−0.613572
$171$	2.50000	+	4.33013i	0.191180	+	0.331133i
$172$	−3.00000	−	5.19615i	−0.228748	−	0.396203i
$173$	−2.50000	+	4.33013i	−0.190071	+	0.329213i	−0.945274	−	0.326278i	$-0.894205\pi$
$173$	−2.50000	+	4.33013i	−0.190071	+	0.329213i	0.755202	+	0.655492i	$0.227539\pi$
$174$	4.00000			0.303239
$175$	2.50000	−	4.33013i	0.188982	−	0.327327i
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$	12.0000			0.901975
$178$	−5.50000	+	9.52628i	−0.412242	+	0.714025i
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	0.781551	−	0.623841i	$-0.214429\pi$
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	−0.931038	+	0.364922i	$0.881096\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$	−12.5000	−	12.9904i	−0.926562	−	0.962911i
$183$	2.00000			0.147844
$184$	−2.00000	−	3.46410i	−0.147442	−	0.255377i
$185$	−3.50000	−	6.06218i	−0.257325	−	0.445700i
$186$	−1.00000	+	1.73205i	−0.0733236	+	0.127000i
$187$	24.0000			1.75505
$188$	1.50000	−	2.59808i	0.109399	−	0.189484i
$189$	2.50000	−	4.33013i	0.181848	−	0.314970i
$190$	−5.00000			−0.362738
$191$	−1.00000	+	1.73205i	−0.0723575	+	0.125327i	−0.899934	−	0.436026i	$-0.856386\pi$
$191$	−1.00000	+	1.73205i	−0.0723575	+	0.125327i	0.827577	+	0.561353i	$0.189719\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−12.0000	−	20.7846i	−0.863779	−	1.49611i	−0.868255	−	0.496119i	$-0.834758\pi$
$193$	−12.0000	−	20.7846i	−0.863779	−	1.49611i	0.00447566	−	0.999990i	$-0.498575\pi$
$194$		0			0
$195$	1.00000	−	3.46410i	0.0716115	−	0.248069i
$196$	18.0000			1.28571
$197$	−1.50000	−	2.59808i	−0.106871	−	0.185105i	0.807630	−	0.589689i	$-0.200750\pi$
$197$	−1.50000	−	2.59808i	−0.106871	−	0.185105i	−0.914501	+	0.404584i	$0.867416\pi$
$198$	−1.50000	−	2.59808i	−0.106600	−	0.184637i
$199$	−11.0000	+	19.0526i	−0.779769	+	1.35060i	0.152305	+	0.988334i	$0.451330\pi$
$199$	−11.0000	+	19.0526i	−0.779769	+	1.35060i	−0.932075	+	0.362267i	$0.882003\pi$
$200$	−1.00000			−0.0707107
$201$	−4.00000	+	6.92820i	−0.282138	+	0.488678i
$202$	−4.00000	+	6.92820i	−0.281439	+	0.487467i
$203$	20.0000			1.40372
$204$	4.00000	−	6.92820i	0.280056	−	0.485071i
$205$	3.00000	+	5.19615i	0.209529	+	0.362915i
$206$	−3.50000	−	6.06218i	−0.243857	−	0.422372i
$207$	−4.00000			−0.278019
$208$	−1.00000	+	3.46410i	−0.0693375	+	0.240192i
$209$	15.0000			1.03757
$210$	2.50000	+	4.33013i	0.172516	+	0.298807i
$211$	7.50000	+	12.9904i	0.516321	+	0.894295i	0.999820	+	0.0189499i	$0.00603229\pi$
$211$	7.50000	+	12.9904i	0.516321	+	0.894295i	−0.483499	+	0.875345i	$0.660634\pi$
$212$	−0.500000	+	0.866025i	−0.0343401	+	0.0594789i
$213$	2.00000			0.137038
$214$	−3.00000	+	5.19615i	−0.205076	+	0.355202i
$215$	3.00000	−	5.19615i	0.204598	−	0.354375i
$216$	−1.00000			−0.0680414
$217$	−5.00000	+	8.66025i	−0.339422	+	0.587896i
$218$	7.00000	+	12.1244i	0.474100	+	0.821165i
$219$		0			0
$220$	3.00000			0.202260
$221$	−28.0000	+	6.92820i	−1.88348	+	0.466041i
$222$	7.00000			0.469809
$223$	1.50000	+	2.59808i	0.100447	+	0.173980i	0.911869	−	0.410481i	$-0.134639\pi$
$223$	1.50000	+	2.59808i	0.100447	+	0.173980i	−0.811422	+	0.584461i	$0.801306\pi$
$224$	−2.50000	−	4.33013i	−0.167038	−	0.289319i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	−8.00000			−0.532152
$227$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$227$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$228$	2.50000	−	4.33013i	0.165567	−	0.286770i
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$	2.00000	−	3.46410i	0.131876	−	0.228416i
$231$	−7.50000	−	12.9904i	−0.493464	−	0.854704i
$232$	−2.00000	−	3.46410i	−0.131306	−	0.227429i
$233$	−14.0000			−0.917170			−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000			−0.917170			−0.458585	+	0.888650i	$0.651644\pi$
$234$	2.50000	+	2.59808i	0.163430	+	0.169842i
$235$	3.00000			0.195698
$236$	−6.00000	−	10.3923i	−0.390567	−	0.676481i
$237$	1.00000	+	1.73205i	0.0649570	+	0.112509i
$238$	20.0000	−	34.6410i	1.29641	−	2.24544i
$239$	−18.0000			−1.16432			−0.582162	−	0.813073i	$-0.697793\pi$
$239$	−18.0000			−1.16432			−0.582162	+	0.813073i	$0.697793\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	−0.110963	−	0.993825i	$-0.535394\pi$
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	0.916159	−	0.400815i	$-0.131273\pi$
$242$	2.00000			0.128565
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−1.00000	−	1.73205i	−0.0640184	−	0.110883i
$245$	9.00000	+	15.5885i	0.574989	+	0.995910i
$246$	−6.00000			−0.382546
$247$	−17.5000	+	4.33013i	−1.11350	+	0.275519i
$248$	2.00000			0.127000
$249$	−4.00000	−	6.92820i	−0.253490	−	0.439057i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−7.50000	+	12.9904i	−0.473396	+	0.819946i	−0.999536	−	0.0304521i	$-0.990305\pi$
$251$	−7.50000	+	12.9904i	−0.473396	+	0.819946i	0.526140	+	0.850398i	$0.323639\pi$
$252$	−5.00000			−0.314970
$253$	−6.00000	+	10.3923i	−0.377217	+	0.653359i
$254$	−10.5000	+	18.1865i	−0.658829	+	1.14112i
$255$	8.00000			0.500979
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−14.0000	−	24.2487i	−0.873296	−	1.51259i	−0.858567	−	0.512702i	$-0.828645\pi$
$257$	−14.0000	−	24.2487i	−0.873296	−	1.51259i	−0.0147291	−	0.999892i	$-0.504689\pi$
$258$	3.00000	+	5.19615i	0.186772	+	0.323498i
$259$	35.0000			2.17479
$260$	−3.50000	+	0.866025i	−0.217061	+	0.0537086i
$261$	−4.00000			−0.247594
$262$	−9.50000	−	16.4545i	−0.586912	−	1.01656i
$263$	7.50000	+	12.9904i	0.462470	+	0.801021i	0.999083	−	0.0428069i	$-0.0136300\pi$
$263$	7.50000	+	12.9904i	0.462470	+	0.801021i	−0.536614	+	0.843828i	$0.680297\pi$
$264$	−1.50000	+	2.59808i	−0.0923186	+	0.159901i
$265$	−1.00000			−0.0614295
$266$	12.5000	−	21.6506i	0.766424	−	1.32749i
$267$	5.50000	−	9.52628i	0.336595	−	0.582999i
$268$	8.00000			0.488678
$269$	−2.00000	+	3.46410i	−0.121942	+	0.211210i	−0.920534	−	0.390664i	$-0.872246\pi$
$269$	−2.00000	+	3.46410i	−0.121942	+	0.211210i	0.798591	+	0.601874i	$0.205579\pi$
$270$	−0.500000	−	0.866025i	−0.0304290	−	0.0527046i
$271$	−2.00000	−	3.46410i	−0.121491	−	0.210429i	0.798865	−	0.601511i	$-0.205434\pi$
$271$	−2.00000	−	3.46410i	−0.121491	−	0.210429i	−0.920356	+	0.391082i	$0.872101\pi$
$272$	−8.00000			−0.485071
$273$	12.5000	+	12.9904i	0.756534	+	0.786214i
$274$	12.0000			0.724947
$275$	1.50000	+	2.59808i	0.0904534	+	0.156670i
$276$	2.00000	+	3.46410i	0.120386	+	0.208514i
$277$	7.50000	−	12.9904i	0.450631	−	0.780516i	−0.547794	−	0.836613i	$-0.684532\pi$
$277$	7.50000	−	12.9904i	0.450631	−	0.780516i	0.998425	+	0.0560969i	$0.0178656\pi$
$278$	−7.00000			−0.419832
$279$	1.00000	−	1.73205i	0.0598684	−	0.103695i
$280$	2.50000	−	4.33013i	0.149404	−	0.258775i
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$	−1.50000	+	2.59808i	−0.0893237	+	0.154713i
$283$	5.00000	+	8.66025i	0.297219	+	0.514799i	0.975499	−	0.220005i	$-0.0706075\pi$
$283$	5.00000	+	8.66025i	0.297219	+	0.514799i	−0.678280	+	0.734804i	$0.737274\pi$
$284$	−1.00000	−	1.73205i	−0.0593391	−	0.102778i
$285$	5.00000			0.296174
$286$	10.5000	−	2.59808i	0.620878	−	0.153627i
$287$	−30.0000			−1.77084
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−23.5000	−	40.7032i	−1.38235	−	2.39431i
$290$	2.00000	−	3.46410i	0.117444	−	0.203419i
$291$		0			0
$292$		0			0
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	−0.704117	−	0.710084i	$-0.748657\pi$
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	0.967009	+	0.254741i	$0.0819901\pi$
$294$	−18.0000			−1.04978
$295$	6.00000	−	10.3923i	0.349334	−	0.605063i
$296$	−3.50000	−	6.06218i	−0.203433	−	0.352357i
$297$	1.50000	+	2.59808i	0.0870388	+	0.150756i
$298$	2.00000			0.115857
$299$	4.00000	−	13.8564i	0.231326	−	0.801337i
$300$	1.00000			0.0577350
$301$	15.0000	+	25.9808i	0.864586	+	1.49751i
$302$	11.0000	+	19.0526i	0.632979	+	1.09635i
$303$	4.00000	−	6.92820i	0.229794	−	0.398015i
$304$	−5.00000			−0.286770
$305$	1.00000	−	1.73205i	0.0572598	−	0.0991769i
$306$	−4.00000	+	6.92820i	−0.228665	+	0.396059i
$307$	−6.00000			−0.342438			−0.171219	−	0.985233i	$-0.554771\pi$
$307$	−6.00000			−0.342438			−0.171219	+	0.985233i	$0.554771\pi$
$308$	−7.50000	+	12.9904i	−0.427352	+	0.740196i
$309$	3.50000	+	6.06218i	0.199108	+	0.344865i
$310$	1.00000	+	1.73205i	0.0567962	+	0.0983739i
$311$	−12.0000			−0.680458			−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000			−0.680458			−0.340229	+	0.940343i	$0.610505\pi$
$312$	1.00000	−	3.46410i	0.0566139	−	0.196116i
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	7.50000	+	12.9904i	0.423249	+	0.733090i
$315$	−2.50000	−	4.33013i	−0.140859	−	0.243975i
$316$	1.00000	−	1.73205i	0.0562544	−	0.0974355i
$317$	−23.0000			−1.29181			−0.645904	−	0.763418i	$-0.723520\pi$
$317$	−23.0000			−1.29181			−0.645904	+	0.763418i	$0.723520\pi$
$318$	0.500000	−	0.866025i	0.0280386	−	0.0485643i
$319$	−6.00000	+	10.3923i	−0.335936	+	0.581857i
$320$	−1.00000			−0.0559017
$321$	3.00000	−	5.19615i	0.167444	−	0.290021i
$322$	10.0000	+	17.3205i	0.557278	+	0.965234i
$323$	−20.0000	−	34.6410i	−1.11283	−	1.92748i
$324$	1.00000			0.0555556
$325$	−2.50000	−	2.59808i	−0.138675	−	0.144115i
$326$	20.0000			1.10770
$327$	−7.00000	−	12.1244i	−0.387101	−	0.670478i
$328$	3.00000	+	5.19615i	0.165647	+	0.286910i
$329$	−7.50000	+	12.9904i	−0.413488	+	0.716183i
$330$	−3.00000			−0.165145
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	−0.915742	−	0.401768i	$-0.868396\pi$
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	0.805812	+	0.592172i	$0.201729\pi$
$332$	−4.00000	+	6.92820i	−0.219529	+	0.380235i
$333$	−7.00000			−0.383598
$334$	−11.5000	+	19.9186i	−0.629252	+	1.08990i
$335$	4.00000	+	6.92820i	0.218543	+	0.378528i
$336$	2.50000	+	4.33013i	0.136386	+	0.236228i
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	−11.5000	+	6.06218i	−0.625518	+	0.329739i
$339$	8.00000			0.434500
$340$	−4.00000	−	6.92820i	−0.216930	−	0.375735i
$341$	−3.00000	−	5.19615i	−0.162459	−	0.281387i
$342$	−2.50000	+	4.33013i	−0.135185	+	0.234146i
$343$	−55.0000			−2.96972
$344$	3.00000	−	5.19615i	0.161749	−	0.280158i
$345$	−2.00000	+	3.46410i	−0.107676	+	0.186501i
$346$	−5.00000			−0.268802
$347$	8.00000	−	13.8564i	0.429463	−	0.743851i	−0.567363	−	0.823468i	$-0.692036\pi$
$347$	8.00000	−	13.8564i	0.429463	−	0.743851i	0.996826	+	0.0796169i	$0.0253697\pi$
$348$	2.00000	+	3.46410i	0.107211	+	0.185695i
$349$	−4.00000	−	6.92820i	−0.214115	−	0.370858i	0.738883	−	0.673833i	$-0.235353\pi$
$349$	−4.00000	−	6.92820i	−0.214115	−	0.370858i	−0.952998	+	0.302975i	$0.902020\pi$
$350$	5.00000			0.267261
$351$	−2.50000	−	2.59808i	−0.133440	−	0.138675i
$352$	3.00000			0.159901
$353$	−8.00000	−	13.8564i	−0.425797	−	0.737502i	0.570697	−	0.821160i	$-0.306673\pi$
$353$	−8.00000	−	13.8564i	−0.425797	−	0.737502i	−0.996495	+	0.0836583i	$0.973340\pi$
$354$	6.00000	+	10.3923i	0.318896	+	0.552345i
$355$	1.00000	−	1.73205i	0.0530745	−	0.0919277i
$356$	−11.0000			−0.582999
$357$	−20.0000	+	34.6410i	−1.05851	+	1.83340i
$358$	2.00000	−	3.46410i	0.105703	−	0.183083i
$359$	−18.0000			−0.950004			−0.475002	−	0.879985i	$-0.657553\pi$
$359$	−18.0000			−0.950004			−0.475002	+	0.879985i	$0.657553\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	−1.00000	−	1.73205i	−0.0525588	−	0.0910346i
$363$	−2.00000			−0.104973
$364$	5.00000	−	17.3205i	0.262071	−	0.907841i
$365$		0			0
$366$	1.00000	+	1.73205i	0.0522708	+	0.0905357i
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	0.951336	−	0.308155i	$-0.0997115\pi$
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	−0.742538	+	0.669804i	$0.766378\pi$
$368$	2.00000	−	3.46410i	0.104257	−	0.180579i
$369$	6.00000			0.312348
$370$	3.50000	−	6.06218i	0.181956	−	0.315158i
$371$	2.50000	−	4.33013i	0.129794	−	0.224809i
$372$	−2.00000			−0.103695
$373$	−19.0000	+	32.9090i	−0.983783	+	1.70396i	−0.336557	+	0.941663i	$0.609263\pi$
$373$	−19.0000	+	32.9090i	−0.983783	+	1.70396i	−0.647225	+	0.762299i	$0.724071\pi$
$374$	12.0000	+	20.7846i	0.620505	+	1.07475i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	3.00000			0.154713
$377$	4.00000	−	13.8564i	0.206010	−	0.713641i
$378$	5.00000			0.257172
$379$	12.5000	+	21.6506i	0.642082	+	1.11212i	0.984967	+	0.172741i	$0.0552624\pi$
$379$	12.5000	+	21.6506i	0.642082	+	1.11212i	−0.342885	+	0.939377i	$0.611404\pi$
$380$	−2.50000	−	4.33013i	−0.128247	−	0.222131i
$381$	10.5000	−	18.1865i	0.537931	−	0.931724i
$382$	−2.00000			−0.102329
$383$	14.0000	−	24.2487i	0.715367	−	1.23905i	−0.247451	−	0.968900i	$-0.579593\pi$
$383$	14.0000	−	24.2487i	0.715367	−	1.23905i	0.962818	−	0.270151i	$-0.0870736\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	−15.0000			−0.764471
$386$	12.0000	−	20.7846i	0.610784	−	1.05791i
$387$	−3.00000	−	5.19615i	−0.152499	−	0.264135i
$388$		0			0
$389$	−32.0000			−1.62246			−0.811232	−	0.584724i	$-0.801203\pi$
$389$	−32.0000			−1.62246			−0.811232	+	0.584724i	$0.801203\pi$
$390$	3.50000	−	0.866025i	0.177229	−	0.0438529i
$391$	32.0000			1.61831
$392$	9.00000	+	15.5885i	0.454569	+	0.787336i
$393$	9.50000	+	16.4545i	0.479212	+	0.830019i
$394$	1.50000	−	2.59808i	0.0755689	−	0.130889i
$395$	2.00000			0.100631
$396$	1.50000	−	2.59808i	0.0753778	−	0.130558i
$397$	−12.5000	+	21.6506i	−0.627357	+	1.08661i	0.360723	+	0.932673i	$0.382530\pi$
$397$	−12.5000	+	21.6506i	−0.627357	+	1.08661i	−0.988080	+	0.153941i	$0.950803\pi$
$398$	−22.0000			−1.10276
$399$	−12.5000	+	21.6506i	−0.625783	+	1.08389i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	9.50000	+	16.4545i	0.474407	+	0.821698i	0.999571	−	0.0293039i	$-0.00932905\pi$
$401$	9.50000	+	16.4545i	0.474407	+	0.821698i	−0.525163	+	0.851002i	$0.675996\pi$
$402$	−8.00000			−0.399004
$403$	5.00000	+	5.19615i	0.249068	+	0.258839i
$404$	−8.00000			−0.398015
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$	10.0000	+	17.3205i	0.496292	+	0.859602i
$407$	−10.5000	+	18.1865i	−0.520466	+	0.901473i
$408$	8.00000			0.396059
$409$	−12.5000	+	21.6506i	−0.618085	+	1.07056i	0.371750	+	0.928333i	$0.378758\pi$
$409$	−12.5000	+	21.6506i	−0.618085	+	1.07056i	−0.989835	+	0.142222i	$0.954575\pi$
$410$	−3.00000	+	5.19615i	−0.148159	+	0.256620i
$411$	−12.0000			−0.591916
$412$	3.50000	−	6.06218i	0.172433	−	0.298662i
$413$	30.0000	+	51.9615i	1.47620	+	2.55686i
$414$	−2.00000	−	3.46410i	−0.0982946	−	0.170251i
$415$	−8.00000			−0.392705
$416$	−3.50000	+	0.866025i	−0.171602	+	0.0424604i
$417$	7.00000			0.342791
$418$	7.50000	+	12.9904i	0.366837	+	0.635380i
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	0.974546	−	0.224189i	$-0.0719734\pi$
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	−0.681426	+	0.731887i	$0.738640\pi$
$420$	−2.50000	+	4.33013i	−0.121988	+	0.211289i
$421$	12.0000			0.584844			0.292422	−	0.956289i	$-0.405539\pi$
$421$	12.0000			0.584844			0.292422	+	0.956289i	$0.405539\pi$
$422$	−7.50000	+	12.9904i	−0.365094	+	0.632362i
$423$	1.50000	−	2.59808i	0.0729325	−	0.126323i
$424$	−1.00000			−0.0485643
$425$	4.00000	−	6.92820i	0.194029	−	0.336067i
$426$	1.00000	+	1.73205i	0.0484502	+	0.0839181i
$427$	5.00000	+	8.66025i	0.241967	+	0.419099i
$428$	−6.00000			−0.290021
$429$	−10.5000	+	2.59808i	−0.506945	+	0.125436i
$430$	6.00000			0.289346
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−8.00000	+	13.8564i	−0.384455	+	0.665896i	−0.991693	−	0.128624i	$-0.958944\pi$
$433$	−8.00000	+	13.8564i	−0.384455	+	0.665896i	0.607238	+	0.794520i	$0.292277\pi$
$434$	−10.0000			−0.480015
$435$	−2.00000	+	3.46410i	−0.0958927	+	0.166091i
$436$	−7.00000	+	12.1244i	−0.335239	+	0.580651i
$437$	20.0000			0.956730
$438$		0			0
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	0.721686	−	0.692220i	$-0.243367\pi$
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	−0.960323	+	0.278889i	$0.910034\pi$
$440$	1.50000	+	2.59808i	0.0715097	+	0.123858i
$441$	18.0000			0.857143
$442$	−20.0000	−	20.7846i	−0.951303	−	0.988623i
$443$	6.00000			0.285069			0.142534	−	0.989790i	$-0.454475\pi$
$443$	6.00000			0.285069			0.142534	+	0.989790i	$0.454475\pi$
$444$	3.50000	+	6.06218i	0.166103	+	0.287698i
$445$	−5.50000	−	9.52628i	−0.260725	−	0.451589i
$446$	−1.50000	+	2.59808i	−0.0710271	+	0.123022i
$447$	−2.00000			−0.0945968
$448$	2.50000	−	4.33013i	0.118114	−	0.204579i
$449$	13.5000	−	23.3827i	0.637104	−	1.10350i	−0.348961	−	0.937137i	$-0.613465\pi$
$449$	13.5000	−	23.3827i	0.637104	−	1.10350i	0.986065	−	0.166360i	$-0.0532013\pi$
$450$	−1.00000			−0.0471405
$451$	9.00000	−	15.5885i	0.423793	−	0.734032i
$452$	−4.00000	−	6.92820i	−0.188144	−	0.325875i
$453$	−11.0000	−	19.0526i	−0.516825	−	0.895167i
$454$		0			0
$455$	17.5000	−	4.33013i	0.820413	−	0.202999i
$456$	5.00000			0.234146
$457$	−15.0000	−	25.9808i	−0.701670	−	1.21533i	−0.967880	−	0.251414i	$-0.919105\pi$
$457$	−15.0000	−	25.9808i	−0.701670	−	1.21533i	0.266209	−	0.963915i	$-0.414229\pi$
$458$	7.00000	+	12.1244i	0.327089	+	0.566534i
$459$	4.00000	−	6.92820i	0.186704	−	0.323381i
$460$	4.00000			0.186501
$461$	−4.00000	+	6.92820i	−0.186299	+	0.322679i	−0.944013	−	0.329907i	$-0.892983\pi$
$461$	−4.00000	+	6.92820i	−0.186299	+	0.322679i	0.757715	+	0.652586i	$0.226316\pi$
$462$	7.50000	−	12.9904i	0.348932	−	0.604367i
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$	2.00000	−	3.46410i	0.0928477	−	0.160817i
$465$	−1.00000	−	1.73205i	−0.0463739	−	0.0803219i
$466$	−7.00000	−	12.1244i	−0.324269	−	0.561650i
$467$	−24.0000			−1.11059			−0.555294	−	0.831654i	$-0.687394\pi$
$467$	−24.0000			−1.11059			−0.555294	+	0.831654i	$0.687394\pi$
$468$	−1.00000	+	3.46410i	−0.0462250	+	0.160128i
$469$	−40.0000			−1.84703
$470$	1.50000	+	2.59808i	0.0691898	+	0.119840i
$471$	−7.50000	−	12.9904i	−0.345582	−	0.598565i
$472$	6.00000	−	10.3923i	0.276172	−	0.478345i
$473$	−18.0000			−0.827641
$474$	−1.00000	+	1.73205i	−0.0459315	+	0.0795557i
$475$	2.50000	−	4.33013i	0.114708	−	0.198680i
$476$	40.0000			1.83340
$477$	−0.500000	+	0.866025i	−0.0228934	+	0.0396526i
$478$	−9.00000	−	15.5885i	−0.411650	−	0.712999i
$479$	14.0000	+	24.2487i	0.639676	+	1.10795i	0.985504	+	0.169654i	$0.0542649\pi$
$479$	14.0000	+	24.2487i	0.639676	+	1.10795i	−0.345827	+	0.938298i	$0.612402\pi$
$480$	1.00000			0.0456435
$481$	7.00000	−	24.2487i	0.319173	−	1.10565i
$482$	25.0000			1.13872
$483$	−10.0000	−	17.3205i	−0.455016	−	0.788110i
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$		0			0
$486$	−1.00000			−0.0453609
$487$	−18.5000	+	32.0429i	−0.838315	+	1.45200i	0.0529875	+	0.998595i	$0.483126\pi$
$487$	−18.5000	+	32.0429i	−0.838315	+	1.45200i	−0.891303	+	0.453409i	$0.850208\pi$
$488$	1.00000	−	1.73205i	0.0452679	−	0.0784063i
$489$	−20.0000			−0.904431
$490$	−9.00000	+	15.5885i	−0.406579	+	0.704215i
$491$	−10.5000	−	18.1865i	−0.473858	−	0.820747i	0.525694	−	0.850674i	$-0.323806\pi$
$491$	−10.5000	−	18.1865i	−0.473858	−	0.820747i	−0.999552	+	0.0299272i	$0.990472\pi$
$492$	−3.00000	−	5.19615i	−0.135250	−	0.234261i
$493$	32.0000			1.44121
$494$	−12.5000	−	12.9904i	−0.562402	−	0.584465i
$495$	3.00000			0.134840
$496$	1.00000	+	1.73205i	0.0449013	+	0.0777714i
$497$	5.00000	+	8.66025i	0.224281	+	0.388465i
$498$	4.00000	−	6.92820i	0.179244	−	0.310460i
$499$	4.00000			0.179065			0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000			0.179065			0.0895323	+	0.995984i	$0.471463\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	11.5000	−	19.9186i	0.513782	−	0.889897i
$502$	−15.0000			−0.669483
$503$	5.50000	−	9.52628i	0.245233	−	0.424756i	−0.716964	−	0.697110i	$-0.754469\pi$
$503$	5.50000	−	9.52628i	0.245233	−	0.424756i	0.962197	+	0.272354i	$0.0878022\pi$
$504$	−2.50000	−	4.33013i	−0.111359	−	0.192879i
$505$	−4.00000	−	6.92820i	−0.177998	−	0.308301i
$506$	−12.0000			−0.533465
$507$	11.5000	−	6.06218i	0.510733	−	0.269231i
$508$	−21.0000			−0.931724
$509$	−5.00000	−	8.66025i	−0.221621	−	0.383859i	0.733679	−	0.679496i	$-0.237801\pi$
$509$	−5.00000	−	8.66025i	−0.221621	−	0.383859i	−0.955300	+	0.295637i	$0.904468\pi$
$510$	4.00000	+	6.92820i	0.177123	+	0.306786i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	2.50000	−	4.33013i	0.110378	−	0.191180i
$514$	14.0000	−	24.2487i	0.617514	−	1.06956i
$515$	7.00000			0.308457
$516$	−3.00000	+	5.19615i	−0.132068	+	0.228748i
$517$	−4.50000	−	7.79423i	−0.197910	−	0.342790i
$518$	17.5000	+	30.3109i	0.768906	+	1.33178i
$519$	5.00000			0.219476
$520$	−2.50000	−	2.59808i	−0.109632	−	0.113933i
$521$	5.00000			0.219054			0.109527	−	0.993984i	$-0.465066\pi$
$521$	5.00000			0.219054			0.109527	+	0.993984i	$0.465066\pi$
$522$	−2.00000	−	3.46410i	−0.0875376	−	0.151620i
$523$	5.00000	+	8.66025i	0.218635	+	0.378686i	0.954391	−	0.298560i	$-0.0965063\pi$
$523$	5.00000	+	8.66025i	0.218635	+	0.378686i	−0.735756	+	0.677247i	$0.763173\pi$
$524$	9.50000	−	16.4545i	0.415009	−	0.718817i
$525$	−5.00000			−0.218218
$526$	−7.50000	+	12.9904i	−0.327016	+	0.566408i
$527$	−8.00000	+	13.8564i	−0.348485	+	0.603595i
$528$	−3.00000			−0.130558
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	−0.500000	−	0.866025i	−0.0217186	−	0.0376177i
$531$	−6.00000	−	10.3923i	−0.260378	−	0.450988i
$532$	25.0000			1.08389
$533$	−6.00000	+	20.7846i	−0.259889	+	0.900281i
$534$	11.0000			0.476017
$535$	−3.00000	−	5.19615i	−0.129701	−	0.224649i
$536$	4.00000	+	6.92820i	0.172774	+	0.299253i
$537$	−2.00000	+	3.46410i	−0.0863064	+	0.149487i
$538$	−4.00000			−0.172452
$539$	27.0000	−	46.7654i	1.16297	−	2.01433i
$540$	0.500000	−	0.866025i	0.0215166	−	0.0372678i
$541$	34.0000			1.46177			0.730887	−	0.682498i	$-0.239107\pi$
$541$	34.0000			1.46177			0.730887	+	0.682498i	$0.239107\pi$
$542$	2.00000	−	3.46410i	0.0859074	−	0.148796i
$543$	1.00000	+	1.73205i	0.0429141	+	0.0743294i
$544$	−4.00000	−	6.92820i	−0.171499	−	0.297044i
$545$	−14.0000			−0.599694
$546$	−5.00000	+	17.3205i	−0.213980	+	0.741249i
$547$	6.00000			0.256541			0.128271	−	0.991739i	$-0.459057\pi$
$547$	6.00000			0.256541			0.128271	+	0.991739i	$0.459057\pi$
$548$	6.00000	+	10.3923i	0.256307	+	0.443937i
$549$	−1.00000	−	1.73205i	−0.0426790	−	0.0739221i
$550$	−1.50000	+	2.59808i	−0.0639602	+	0.110782i
$551$	20.0000			0.852029
$552$	−2.00000	+	3.46410i	−0.0851257	+	0.147442i
$553$	−5.00000	+	8.66025i	−0.212622	+	0.368271i
$554$	15.0000			0.637289
$555$	−3.50000	+	6.06218i	−0.148567	+	0.257325i
$556$	−3.50000	−	6.06218i	−0.148433	−	0.257094i
$557$	−7.50000	−	12.9904i	−0.317785	−	0.550420i	0.662240	−	0.749291i	$-0.269606\pi$
$557$	−7.50000	−	12.9904i	−0.317785	−	0.550420i	−0.980026	+	0.198871i	$0.936272\pi$
$558$	2.00000			0.0846668
$559$	21.0000	−	5.19615i	0.888205	−	0.219774i
$560$	5.00000			0.211289
$561$	−12.0000	−	20.7846i	−0.506640	−	0.877527i
$562$	9.00000	+	15.5885i	0.379642	+	0.657559i
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	0.184950	+	0.982748i	$0.440788\pi$
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	−0.943560	+	0.331202i	$0.892546\pi$
$564$	−3.00000			−0.126323
$565$	4.00000	−	6.92820i	0.168281	−	0.291472i
$566$	−5.00000	+	8.66025i	−0.210166	+	0.364018i
$567$	−5.00000			−0.209980
$568$	1.00000	−	1.73205i	0.0419591	−	0.0726752i
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	0.979313	−	0.202350i	$-0.0648579\pi$
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	−0.664897	+	0.746935i	$0.731525\pi$
$570$	2.50000	+	4.33013i	0.104713	+	0.181369i
$571$	−33.0000			−1.38101			−0.690504	−	0.723329i	$-0.742611\pi$
$571$	−33.0000			−1.38101			−0.690504	+	0.723329i	$0.742611\pi$
$572$	7.50000	+	7.79423i	0.313591	+	0.325893i
$573$	2.00000			0.0835512
$574$	−15.0000	−	25.9808i	−0.626088	−	1.08442i
$575$	2.00000	+	3.46410i	0.0834058	+	0.144463i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$	23.5000	−	40.7032i	0.977471	−	1.69303i
$579$	−12.0000	+	20.7846i	−0.498703	+	0.863779i
$580$	4.00000			0.166091
$581$	20.0000	−	34.6410i	0.829740	−	1.43715i
$582$		0			0
$583$	1.50000	+	2.59808i	0.0621237	+	0.107601i
$584$		0			0
$585$	−3.50000	+	0.866025i	−0.144707	+	0.0358057i
$586$	9.00000			0.371787
$587$	−9.00000	−	15.5885i	−0.371470	−	0.643404i	0.618322	−	0.785925i	$-0.287813\pi$
$587$	−9.00000	−	15.5885i	−0.371470	−	0.643404i	−0.989792	+	0.142520i	$0.954479\pi$
$588$	−9.00000	−	15.5885i	−0.371154	−	0.642857i
$589$	−5.00000	+	8.66025i	−0.206021	+	0.356840i
$590$	12.0000			0.494032
$591$	−1.50000	+	2.59808i	−0.0617018	+	0.106871i
$592$	3.50000	−	6.06218i	0.143849	−	0.249154i
$593$	20.0000			0.821302			0.410651	−	0.911793i	$-0.365302\pi$
$593$	20.0000			0.821302			0.410651	+	0.911793i	$0.365302\pi$
$594$	−1.50000	+	2.59808i	−0.0615457	+	0.106600i
$595$	20.0000	+	34.6410i	0.819920	+	1.42014i
$596$	1.00000	+	1.73205i	0.0409616	+	0.0709476i
$597$	22.0000			0.900400
$598$	14.0000	−	3.46410i	0.572503	−	0.141658i
$599$	34.0000			1.38920			0.694601	−	0.719395i	$-0.255581\pi$
$599$	34.0000			1.38920			0.694601	+	0.719395i	$0.255581\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	−18.5000	−	32.0429i	−0.754631	−	1.30706i	−0.945558	−	0.325455i	$-0.894483\pi$
$601$	−18.5000	−	32.0429i	−0.754631	−	1.30706i	0.190927	−	0.981604i	$-0.438851\pi$
$602$	−15.0000	+	25.9808i	−0.611354	+	1.05890i
$603$	8.00000			0.325785
$604$	−11.0000	+	19.0526i	−0.447584	+	0.775238i
$605$	−1.00000	+	1.73205i	−0.0406558	+	0.0704179i
$606$	8.00000			0.324978
$607$	14.5000	−	25.1147i	0.588537	−	1.01938i	−0.405887	−	0.913923i	$-0.633038\pi$
$607$	14.5000	−	25.1147i	0.588537	−	1.01938i	0.994424	−	0.105453i	$-0.0336291\pi$
$608$	−2.50000	−	4.33013i	−0.101388	−	0.175610i
$609$	−10.0000	−	17.3205i	−0.405220	−	0.701862i
$610$	2.00000			0.0809776
$611$	7.50000	+	7.79423i	0.303418	+	0.315321i
$612$	−8.00000			−0.323381
$613$	−12.5000	−	21.6506i	−0.504870	−	0.874461i	−0.999984	−	0.00563283i	$-0.998207\pi$
$613$	−12.5000	−	21.6506i	−0.504870	−	0.874461i	0.495114	−	0.868828i	$-0.335126\pi$
$614$	−3.00000	−	5.19615i	−0.121070	−	0.209700i
$615$	3.00000	−	5.19615i	0.120972	−	0.209529i
$616$	−15.0000			−0.604367
$617$	7.00000	−	12.1244i	0.281809	−	0.488108i	−0.690021	−	0.723789i	$-0.742399\pi$
$617$	7.00000	−	12.1244i	0.281809	−	0.488108i	0.971830	+	0.235681i	$0.0757321\pi$
$618$	−3.50000	+	6.06218i	−0.140791	+	0.243857i
$619$	17.0000			0.683288			0.341644	−	0.939829i	$-0.389016\pi$
$619$	17.0000			0.683288			0.341644	+	0.939829i	$0.389016\pi$
$620$	−1.00000	+	1.73205i	−0.0401610	+	0.0695608i
$621$	2.00000	+	3.46410i	0.0802572	+	0.139010i
$622$	−6.00000	−	10.3923i	−0.240578	−	0.416693i
$623$	55.0000			2.20353
$624$	3.50000	−	0.866025i	0.140112	−	0.0346688i
$625$	1.00000			0.0400000
$626$	−3.00000	−	5.19615i	−0.119904	−	0.207680i
$627$	−7.50000	−	12.9904i	−0.299521	−	0.518786i
$628$	−7.50000	+	12.9904i	−0.299283	+	0.518373i
$629$	56.0000			2.23287
$630$	2.50000	−	4.33013i	0.0996024	−	0.172516i
$631$	−6.00000	+	10.3923i	−0.238856	+	0.413711i	−0.960386	−	0.278672i	$-0.910106\pi$
$631$	−6.00000	+	10.3923i	−0.238856	+	0.413711i	0.721530	+	0.692383i	$0.243439\pi$
$632$	2.00000			0.0795557
$633$	7.50000	−	12.9904i	0.298098	−	0.516321i
$634$	−11.5000	−	19.9186i	−0.456723	−	0.791068i
$635$	−10.5000	−	18.1865i	−0.416680	−	0.721711i
$636$	1.00000			0.0396526
$637$	−18.0000	+	62.3538i	−0.713186	+	2.47055i
$638$	−12.0000			−0.475085
$639$	−1.00000	−	1.73205i	−0.0395594	−	0.0685189i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	0.466029	+	0.884769i	$0.345684\pi$
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	−0.999247	+	0.0387913i	$0.987649\pi$
$642$	6.00000			0.236801
$643$	22.0000	−	38.1051i	0.867595	−	1.50272i	0.00314839	−	0.999995i	$-0.498998\pi$
$643$	22.0000	−	38.1051i	0.867595	−	1.50272i	0.864447	−	0.502724i	$-0.167669\pi$
$644$	−10.0000	+	17.3205i	−0.394055	+	0.682524i
$645$	−6.00000			−0.236250
$646$	20.0000	−	34.6410i	0.786889	−	1.36293i
$647$	−1.50000	−	2.59808i	−0.0589711	−	0.102141i	0.835033	−	0.550200i	$-0.185449\pi$
$647$	−1.50000	−	2.59808i	−0.0589711	−	0.102141i	−0.894004	+	0.448059i	$0.852115\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−36.0000			−1.41312
$650$	1.00000	−	3.46410i	0.0392232	−	0.135873i
$651$	10.0000			0.391931
$652$	10.0000	+	17.3205i	0.391630	+	0.678323i
$653$	−13.5000	−	23.3827i	−0.528296	−	0.915035i	−0.999456	−	0.0329874i	$-0.989498\pi$
$653$	−13.5000	−	23.3827i	−0.528296	−	0.915035i	0.471160	−	0.882048i	$-0.343835\pi$
$654$	7.00000	−	12.1244i	0.273722	−	0.474100i
$655$	19.0000			0.742391
$656$	−3.00000	+	5.19615i	−0.117130	+	0.202876i
$657$		0			0
$658$	−15.0000			−0.584761
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	0.266872	+	0.963732i	$0.414010\pi$
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	−0.968052	+	0.250748i	$0.919323\pi$
$660$	−1.50000	−	2.59808i	−0.0583874	−	0.101130i
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	0.946729	−	0.322031i	$-0.104366\pi$
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	−0.752252	+	0.658876i	$0.771032\pi$
$662$	−4.00000			−0.155464
$663$	20.0000	+	20.7846i	0.776736	+	0.807207i
$664$	−8.00000			−0.310460
$665$	12.5000	+	21.6506i	0.484729	+	0.839576i
$666$	−3.50000	−	6.06218i	−0.135622	−	0.234905i
$667$	−8.00000	+	13.8564i	−0.309761	+	0.536522i
$668$	−23.0000			−0.889897
$669$	1.50000	−	2.59808i	0.0579934	−	0.100447i
$670$	−4.00000	+	6.92820i	−0.154533	+	0.267660i
$671$	−6.00000			−0.231627
$672$	−2.50000	+	4.33013i	−0.0964396	+	0.167038i
$673$	16.0000	+	27.7128i	0.616755	+	1.06825i	0.990074	+	0.140548i	$0.0448863\pi$
$673$	16.0000	+	27.7128i	0.616755	+	1.06825i	−0.373319	+	0.927703i	$0.621780\pi$
$674$	7.00000	+	12.1244i	0.269630	+	0.467013i
$675$	1.00000			0.0384900
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	−22.0000			−0.845529			−0.422764	−	0.906240i	$-0.638940\pi$
$677$	−22.0000			−0.845529			−0.422764	+	0.906240i	$0.638940\pi$
$678$	4.00000	+	6.92820i	0.153619	+	0.266076i
$679$		0			0
$680$	4.00000	−	6.92820i	0.153393	−	0.265684i
$681$		0			0
$682$	3.00000	−	5.19615i	0.114876	−	0.198971i
$683$	−15.0000	+	25.9808i	−0.573959	+	0.994126i	0.422195	+	0.906505i	$0.361260\pi$
$683$	−15.0000	+	25.9808i	−0.573959	+	0.994126i	−0.996154	+	0.0876211i	$0.972074\pi$
$684$	−5.00000			−0.191180
$685$	−6.00000	+	10.3923i	−0.229248	+	0.397070i
$686$	−27.5000	−	47.6314i	−1.04995	−	1.81858i
$687$	−7.00000	−	12.1244i	−0.267067	−	0.462573i
$688$	6.00000			0.228748
$689$	−2.50000	−	2.59808i	−0.0952424	−	0.0989788i
$690$	−4.00000			−0.152277
$691$	−8.50000	−	14.7224i	−0.323355	−	0.560068i	0.657823	−	0.753173i	$-0.271478\pi$
$691$	−8.50000	−	14.7224i	−0.323355	−	0.560068i	−0.981178	+	0.193105i	$0.938144\pi$
$692$	−2.50000	−	4.33013i	−0.0950357	−	0.164607i
$693$	−7.50000	+	12.9904i	−0.284901	+	0.493464i
$694$	16.0000			0.607352
$695$	3.50000	−	6.06218i	0.132763	−	0.229952i
$696$	−2.00000	+	3.46410i	−0.0758098	+	0.131306i
$697$	−48.0000			−1.81813
$698$	4.00000	−	6.92820i	0.151402	−	0.262236i
$699$	7.00000	+	12.1244i	0.264764	+	0.458585i
$700$	2.50000	+	4.33013i	0.0944911	+	0.163663i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	1.00000	−	3.46410i	0.0377426	−	0.130744i
$703$	35.0000			1.32005
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$	−1.50000	−	2.59808i	−0.0564933	−	0.0978492i
$706$	8.00000	−	13.8564i	0.301084	−	0.521493i
$707$	40.0000			1.50435
$708$	−6.00000	+	10.3923i	−0.225494	+	0.390567i
$709$	−16.0000	+	27.7128i	−0.600893	+	1.04078i	0.391794	+	0.920053i	$0.371855\pi$
$709$	−16.0000	+	27.7128i	−0.600893	+	1.04078i	−0.992686	+	0.120723i	$0.961479\pi$
$710$	2.00000			0.0750587
$711$	1.00000	−	1.73205i	0.0375029	−	0.0649570i
$712$	−5.50000	−	9.52628i	−0.206121	−	0.357012i
$713$	−4.00000	−	6.92820i	−0.149801	−	0.259463i
$714$	−40.0000			−1.49696
$715$	−3.00000	+	10.3923i	−0.112194	+	0.388650i
$716$	4.00000			0.149487
$717$	9.00000	+	15.5885i	0.336111	+	0.582162i
$718$	−9.00000	−	15.5885i	−0.335877	−	0.581756i
$719$	10.0000	−	17.3205i	0.372937	−	0.645946i	−0.617079	−	0.786901i	$-0.711684\pi$
$719$	10.0000	−	17.3205i	0.372937	−	0.645946i	0.990016	+	0.140955i	$0.0450174\pi$
$720$	−1.00000			−0.0372678
$721$	−17.5000	+	30.3109i	−0.651734	+	1.12884i
$722$	3.00000	−	5.19615i	0.111648	−	0.193381i
$723$	−25.0000			−0.929760
$724$	1.00000	−	1.73205i	0.0371647	−	0.0643712i
$725$	2.00000	+	3.46410i	0.0742781	+	0.128654i
$726$	−1.00000	−	1.73205i	−0.0371135	−	0.0642824i
$727$	−11.0000			−0.407967			−0.203984	−	0.978974i	$-0.565389\pi$
$727$	−11.0000			−0.407967			−0.203984	+	0.978974i	$0.565389\pi$
$728$	17.5000	−	4.33013i	0.648593	−	0.160485i
$729$	1.00000			0.0370370
$730$		0			0
$731$	24.0000	+	41.5692i	0.887672	+	1.53749i
$732$	−1.00000	+	1.73205i	−0.0369611	+	0.0640184i
$733$	−43.0000			−1.58824			−0.794121	−	0.607760i	$-0.792068\pi$
$733$	−43.0000			−1.58824			−0.794121	+	0.607760i	$0.792068\pi$
$734$	−4.00000	+	6.92820i	−0.147643	+	0.255725i
$735$	9.00000	−	15.5885i	0.331970	−	0.574989i
$736$	4.00000			0.147442
$737$	12.0000	−	20.7846i	0.442026	−	0.765611i
$738$	3.00000	+	5.19615i	0.110432	+	0.191273i
$739$	−9.50000	−	16.4545i	−0.349463	−	0.605288i	0.636691	−	0.771119i	$-0.280303\pi$
$739$	−9.50000	−	16.4545i	−0.349463	−	0.605288i	−0.986154	+	0.165831i	$0.946969\pi$
$740$	7.00000			0.257325
$741$	12.5000	+	12.9904i	0.459199	+	0.477214i
$742$	5.00000			0.183556
$743$	8.00000	+	13.8564i	0.293492	+	0.508342i	0.974633	−	0.223810i	$-0.0718494\pi$
$743$	8.00000	+	13.8564i	0.293492	+	0.508342i	−0.681141	+	0.732152i	$0.738516\pi$
$744$	−1.00000	−	1.73205i	−0.0366618	−	0.0635001i
$745$	−1.00000	+	1.73205i	−0.0366372	+	0.0634574i
$746$	−38.0000			−1.39128
$747$	−4.00000	+	6.92820i	−0.146352	+	0.253490i
$748$	−12.0000	+	20.7846i	−0.438763	+	0.759961i
$749$	30.0000			1.09618
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	4.00000	+	6.92820i	0.145962	+	0.252814i	0.929731	−	0.368238i	$-0.120039\pi$
$751$	4.00000	+	6.92820i	0.145962	+	0.252814i	−0.783769	+	0.621052i	$0.786706\pi$
$752$	1.50000	+	2.59808i	0.0546994	+	0.0947421i
$753$	15.0000			0.546630
$754$	14.0000	−	3.46410i	0.509850	−	0.126155i
$755$	−22.0000			−0.800662
$756$	2.50000	+	4.33013i	0.0909241	+	0.157485i
$757$	−8.50000	−	14.7224i	−0.308938	−	0.535096i	0.669193	−	0.743089i	$-0.266640\pi$
$757$	−8.50000	−	14.7224i	−0.308938	−	0.535096i	−0.978130	+	0.207993i	$0.933307\pi$
$758$	−12.5000	+	21.6506i	−0.454020	+	0.786386i
$759$	12.0000			0.435572
$760$	2.50000	−	4.33013i	0.0906845	−	0.157070i
$761$	−4.50000	+	7.79423i	−0.163125	+	0.282541i	−0.935988	−	0.352032i	$-0.885491\pi$
$761$	−4.50000	+	7.79423i	−0.163125	+	0.282541i	0.772863	+	0.634573i	$0.218824\pi$
$762$	21.0000			0.760750
$763$	35.0000	−	60.6218i	1.26709	−	2.19466i
$764$	−1.00000	−	1.73205i	−0.0361787	−	0.0626634i
$765$	−4.00000	−	6.92820i	−0.144620	−	0.250490i
$766$	28.0000			1.01168
$767$	42.0000	−	10.3923i	1.51653	−	0.375244i
$768$	1.00000			0.0360844
$769$	17.0000	+	29.4449i	0.613036	+	1.06181i	0.990726	+	0.135877i	$0.0433852\pi$
$769$	17.0000	+	29.4449i	0.613036	+	1.06181i	−0.377690	+	0.925932i	$0.623282\pi$
$770$	−7.50000	−	12.9904i	−0.270281	−	0.468141i
$771$	−14.0000	+	24.2487i	−0.504198	+	0.873296i
$772$	24.0000			0.863779
$773$	−0.500000	+	0.866025i	−0.0179838	+	0.0311488i	−0.874877	−	0.484345i	$-0.839058\pi$
$773$	−0.500000	+	0.866025i	−0.0179838	+	0.0311488i	0.856893	+	0.515494i	$0.172391\pi$
$774$	3.00000	−	5.19615i	0.107833	−	0.186772i
$775$	−2.00000			−0.0718421
$776$		0			0
$777$	−17.5000	−	30.3109i	−0.627809	−	1.08740i
$778$	−16.0000	−	27.7128i	−0.573628	−	0.993552i
$779$	−30.0000			−1.07486
$780$	2.50000	+	2.59808i	0.0895144	+	0.0930261i
$781$	−6.00000			−0.214697
$782$	16.0000	+	27.7128i	0.572159	+	0.991008i
$783$	2.00000	+	3.46410i	0.0714742	+	0.123797i
$784$	−9.00000	+	15.5885i	−0.321429	+	0.556731i
$785$	−15.0000			−0.535373
$786$	−9.50000	+	16.4545i	−0.338854	+	0.586912i
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	−0.500953	−	0.865474i	$-0.667017\pi$
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	0.999999	+	0.00110111i	$0.000350496\pi$
$788$	3.00000			0.106871
$789$	7.50000	−	12.9904i	0.267007	−	0.462470i
$790$	1.00000	+	1.73205i	0.0355784	+	0.0616236i
$791$	20.0000	+	34.6410i	0.711118	+	1.23169i
$792$	3.00000			0.106600
$793$	7.00000	−	1.73205i	0.248577	−	0.0615069i
$794$	−25.0000			−0.887217
$795$	0.500000	+	0.866025i	0.0177332	+	0.0307148i
$796$	−11.0000	−	19.0526i	−0.389885	−	0.675300i
$797$	5.00000	−	8.66025i	0.177109	−	0.306762i	−0.763780	−	0.645477i	$-0.776659\pi$
$797$	5.00000	−	8.66025i	0.177109	−	0.306762i	0.940889	+	0.338715i	$0.109992\pi$
$798$	−25.0000			−0.884990
$799$	−12.0000	+	20.7846i	−0.424529	+	0.735307i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−11.0000			−0.388666
$802$	−9.50000	+	16.4545i	−0.335457	+	0.581028i
$803$		0			0
$804$	−4.00000	−	6.92820i	−0.141069	−	0.244339i
$805$	−20.0000			−0.704907
$806$	−2.00000	+	6.92820i	−0.0704470	+	0.244036i
$807$	4.00000			0.140807
$808$	−4.00000	−	6.92820i	−0.140720	−	0.243733i
$809$	13.0000	+	22.5167i	0.457056	+	0.791644i	0.998804	−	0.0488972i	$-0.0155707\pi$
$809$	13.0000	+	22.5167i	0.457056	+	0.791644i	−0.541748	+	0.840541i	$0.682237\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	25.0000			0.877869			0.438934	−	0.898519i	$-0.355356\pi$
$811$	25.0000			0.877869			0.438934	+	0.898519i	$0.355356\pi$
$812$	−10.0000	+	17.3205i	−0.350931	+	0.607831i
$813$	−2.00000	+	3.46410i	−0.0701431	+	0.121491i
$814$	−21.0000			−0.736050
$815$	−10.0000	+	17.3205i	−0.350285	+	0.606711i
$816$	4.00000	+	6.92820i	0.140028	+	0.242536i
$817$	15.0000	+	25.9808i	0.524784	+	0.908952i
$818$	−25.0000			−0.874105
$819$	5.00000	−	17.3205i	0.174714	−	0.605228i
$820$	−6.00000			−0.209529
$821$	11.0000	+	19.0526i	0.383903	+	0.664939i	0.991616	−	0.129217i	$-0.0412465\pi$
$821$	11.0000	+	19.0526i	0.383903	+	0.664939i	−0.607714	+	0.794156i	$0.707913\pi$
$822$	−6.00000	−	10.3923i	−0.209274	−	0.362473i
$823$	17.5000	−	30.3109i	0.610012	−	1.05657i	−0.381226	−	0.924482i	$-0.624498\pi$
$823$	17.5000	−	30.3109i	0.610012	−	1.05657i	0.991238	−	0.132089i	$-0.0421686\pi$
$824$	7.00000			0.243857
$825$	1.50000	−	2.59808i	0.0522233	−	0.0904534i
$826$	−30.0000	+	51.9615i	−1.04383	+	1.80797i
$827$	6.00000			0.208640			0.104320	−	0.994544i	$-0.466733\pi$
$827$	6.00000			0.208640			0.104320	+	0.994544i	$0.466733\pi$
$828$	2.00000	−	3.46410i	0.0695048	−	0.120386i
$829$	8.00000	+	13.8564i	0.277851	+	0.481253i	0.970851	−	0.239686i	$-0.0770444\pi$
$829$	8.00000	+	13.8564i	0.277851	+	0.481253i	−0.692999	+	0.720938i	$0.743711\pi$
$830$	−4.00000	−	6.92820i	−0.138842	−	0.240481i
$831$	−15.0000			−0.520344
$832$	−2.50000	−	2.59808i	−0.0866719	−	0.0900721i
$833$	−144.000			−4.98930
$834$	3.50000	+	6.06218i	0.121195	+	0.209916i
$835$	−11.5000	−	19.9186i	−0.397974	−	0.689311i
$836$	−7.50000	+	12.9904i	−0.259393	+	0.449282i
$837$	−2.00000			−0.0691301
$838$	−6.00000	+	10.3923i	−0.207267	+	0.358996i
$839$	7.00000	−	12.1244i	0.241667	−	0.418579i	−0.719522	−	0.694469i	$-0.755639\pi$
$839$	7.00000	−	12.1244i	0.241667	−	0.418579i	0.961189	+	0.275890i	$0.0889726\pi$
$840$	−5.00000			−0.172516
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$	6.00000	+	10.3923i	0.206774	+	0.358142i
$843$	−9.00000	−	15.5885i	−0.309976	−	0.536895i
$844$	−15.0000			−0.516321
$845$	0.500000	−	12.9904i	0.0172005	−	0.446883i
$846$	3.00000			0.103142
$847$	−5.00000	−	8.66025i	−0.171802	−	0.297570i
$848$	−0.500000	−	0.866025i	−0.0171701	−	0.0297394i
$849$	5.00000	−	8.66025i	0.171600	−	0.297219i
$850$	8.00000			0.274398
$851$	−14.0000	+	24.2487i	−0.479914	+	0.831235i
$852$	−1.00000	+	1.73205i	−0.0342594	+	0.0593391i
$853$	−26.0000			−0.890223			−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000			−0.890223			−0.445112	+	0.895475i	$0.646836\pi$
$854$	−5.00000	+	8.66025i	−0.171096	+	0.296348i
$855$	−2.50000	−	4.33013i	−0.0854982	−	0.148087i
$856$	−3.00000	−	5.19615i	−0.102538	−	0.177601i
$857$	38.0000			1.29806			0.649028	−	0.760765i	$-0.275176\pi$
$857$	38.0000			1.29806			0.649028	+	0.760765i	$0.275176\pi$
$858$	−7.50000	−	7.79423i	−0.256046	−	0.266091i
$859$	3.00000			0.102359			0.0511793	−	0.998689i	$-0.483702\pi$
$859$	3.00000			0.102359			0.0511793	+	0.998689i	$0.483702\pi$
$860$	3.00000	+	5.19615i	0.102299	+	0.177187i
$861$	15.0000	+	25.9808i	0.511199	+	0.885422i
$862$	6.00000	−	10.3923i	0.204361	−	0.353963i
$863$	−24.0000			−0.816970			−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	2.50000	−	4.33013i	0.0850026	−	0.147229i
$866$	−16.0000			−0.543702
$867$	−23.5000	+	40.7032i	−0.798102	+	1.38235i
$868$	−5.00000	−	8.66025i	−0.169711	−	0.293948i
$869$	−3.00000	−	5.19615i	−0.101768	−	0.176267i
$870$	−4.00000			−0.135613
$871$	−8.00000	+	27.7128i	−0.271070	+	0.939013i
$872$	−14.0000			−0.474100
$873$		0			0
$874$	10.0000	+	17.3205i	0.338255	+	0.585875i
$875$	−2.50000	+	4.33013i	−0.0845154	+	0.146385i
$876$		0			0
$877$	27.0000	−	46.7654i	0.911725	−	1.57915i	0.100099	−	0.994977i	$-0.468084\pi$
$877$	27.0000	−	46.7654i	0.911725	−	1.57915i	0.811626	−	0.584177i	$-0.198583\pi$
$878$	5.00000	−	8.66025i	0.168742	−	0.292269i
$879$	−9.00000			−0.303562
$880$	−1.50000	+	2.59808i	−0.0505650	+	0.0875811i
$881$	7.50000	+	12.9904i	0.252681	+	0.437657i	0.964263	−	0.264946i	$-0.0853542\pi$
$881$	7.50000	+	12.9904i	0.252681	+	0.437657i	−0.711582	+	0.702603i	$0.752021\pi$
$882$	9.00000	+	15.5885i	0.303046	+	0.524891i
$883$	30.0000			1.00958			0.504790	−	0.863242i	$-0.331570\pi$
$883$	30.0000			1.00958			0.504790	+	0.863242i	$0.331570\pi$
$884$	8.00000	−	27.7128i	0.269069	−	0.932083i
$885$	−12.0000			−0.403376
$886$	3.00000	+	5.19615i	0.100787	+	0.174568i
$887$	−20.5000	−	35.5070i	−0.688323	−	1.19221i	−0.972380	−	0.233403i	$-0.925014\pi$
$887$	−20.5000	−	35.5070i	−0.688323	−	1.19221i	0.284058	−	0.958807i	$-0.408319\pi$
$888$	−3.50000	+	6.06218i	−0.117452	+	0.203433i
$889$	105.000			3.52159
$890$	5.50000	−	9.52628i	0.184360	−	0.319322i
$891$	1.50000	−	2.59808i	0.0502519	−	0.0870388i
$892$	−3.00000			−0.100447
$893$	−7.50000	+	12.9904i	−0.250978	+	0.434707i
$894$	−1.00000	−	1.73205i	−0.0334450	−	0.0579284i
$895$	2.00000	+	3.46410i	0.0668526	+	0.115792i
$896$	5.00000			0.167038
$897$	−14.0000	+	3.46410i	−0.467446	+	0.115663i
$898$	27.0000			0.901002
$899$	−4.00000	−	6.92820i	−0.133407	−	0.231069i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	4.00000	−	6.92820i	0.133259	−	0.230812i
$902$	18.0000			0.599334
$903$	15.0000	−	25.9808i	0.499169	−	0.864586i
$904$	4.00000	−	6.92820i	0.133038	−	0.230429i
$905$	2.00000			0.0664822
$906$	11.0000	−	19.0526i	0.365451	−	0.632979i
$907$	−5.00000	−	8.66025i	−0.166022	−	0.287559i	0.770996	−	0.636841i	$-0.219759\pi$
$907$	−5.00000	−	8.66025i	−0.166022	−	0.287559i	−0.937018	+	0.349281i	$0.886426\pi$
$908$		0			0
$909$	−8.00000			−0.265343
$910$	12.5000	+	12.9904i	0.414371	+	0.430627i
$911$	−20.0000			−0.662630			−0.331315	−	0.943520i	$-0.607492\pi$
$911$	−20.0000			−0.662630			−0.331315	+	0.943520i	$0.607492\pi$
$912$	2.50000	+	4.33013i	0.0827833	+	0.143385i
$913$	12.0000	+	20.7846i	0.397142	+	0.687870i
$914$	15.0000	−	25.9808i	0.496156	−	0.859367i
$915$	−2.00000			−0.0661180
$916$	−7.00000	+	12.1244i	−0.231287	+	0.400600i
$917$	−47.5000	+	82.2724i	−1.56859	+	2.71687i
$918$	8.00000			0.264039
$919$	1.00000	−	1.73205i	0.0329870	−	0.0571351i	−0.849061	−	0.528295i	$-0.822831\pi$
$919$	1.00000	−	1.73205i	0.0329870	−	0.0571351i	0.882048	+	0.471160i	$0.156165\pi$
$920$	2.00000	+	3.46410i	0.0659380	+	0.114208i
$921$	3.00000	+	5.19615i	0.0988534	+	0.171219i
$922$	−8.00000			−0.263466
$923$	7.00000	−	1.73205i	0.230408	−	0.0570111i
$924$	15.0000			0.493464
$925$	3.50000	+	6.06218i	0.115079	+	0.199323i
$926$	4.00000	+	6.92820i	0.131448	+	0.227675i
$927$	3.50000	−	6.06218i	0.114955	−	0.199108i
$928$	4.00000			0.131306
$929$	−1.00000	+	1.73205i	−0.0328089	+	0.0568267i	−0.881964	−	0.471317i	$-0.843779\pi$
$929$	−1.00000	+	1.73205i	−0.0328089	+	0.0568267i	0.849155	+	0.528144i	$0.177112\pi$
$930$	1.00000	−	1.73205i	0.0327913	−	0.0567962i
$931$	−90.0000			−2.94963
$932$	7.00000	−	12.1244i	0.229293	−	0.397146i
$933$	6.00000	+	10.3923i	0.196431	+	0.340229i
$934$	−12.0000	−	20.7846i	−0.392652	−	0.680093i
$935$	−24.0000			−0.784884
$936$	−3.50000	+	0.866025i	−0.114401	+	0.0283069i
$937$	30.0000			0.980057			0.490029	−	0.871706i	$-0.336986\pi$
$937$	30.0000			0.980057			0.490029	+	0.871706i	$0.336986\pi$
$938$	−20.0000	−	34.6410i	−0.653023	−	1.13107i
$939$	3.00000	+	5.19615i	0.0979013	+	0.169570i
$940$	−1.50000	+	2.59808i	−0.0489246	+	0.0847399i
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$	7.50000	−	12.9904i	0.244363	−	0.423249i
$943$	12.0000	−	20.7846i	0.390774	−	0.676840i
$944$	12.0000			0.390567
$945$	−2.50000	+	4.33013i	−0.0813250	+	0.140859i
$946$	−9.00000	−	15.5885i	−0.292615	−	0.506824i
$947$	−29.0000	−	50.2295i	−0.942373	−	1.63224i	−0.760927	−	0.648838i	$-0.775255\pi$
$947$	−29.0000	−	50.2295i	−0.942373	−	1.63224i	−0.181447	−	0.983401i	$-0.558078\pi$
$948$	−2.00000			−0.0649570
$949$		0			0
$950$	5.00000			0.162221
$951$	11.5000	+	19.9186i	0.372913	+	0.645904i
$952$	20.0000	+	34.6410i	0.648204	+	1.12272i
$953$	27.0000	−	46.7654i	0.874616	−	1.51488i	0.0174443	−	0.999848i	$-0.494447\pi$
$953$	27.0000	−	46.7654i	0.874616	−	1.51488i	0.857171	−	0.515031i	$-0.172220\pi$
$954$	−1.00000			−0.0323762
$955$	1.00000	−	1.73205i	0.0323592	−	0.0560478i
$956$	9.00000	−	15.5885i	0.291081	−	0.504167i
$957$	12.0000			0.387905
$958$	−14.0000	+	24.2487i	−0.452319	+	0.783440i
$959$	−30.0000	−	51.9615i	−0.968751	−	1.67793i
$960$	0.500000	+	0.866025i	0.0161374	+	0.0279508i
$961$	−27.0000			−0.870968
$962$	24.5000	−	6.06218i	0.789912	−	0.195452i
$963$	−6.00000			−0.193347
$964$	12.5000	+	21.6506i	0.402598	+	0.697320i
$965$	12.0000	+	20.7846i	0.386294	+	0.669080i
$966$	10.0000	−	17.3205i	0.321745	−	0.557278i
$967$	−31.0000			−0.996893			−0.498446	−	0.866921i	$-0.666096\pi$
$967$	−31.0000			−0.996893			−0.498446	+	0.866921i	$0.666096\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$	−20.0000	+	34.6410i	−0.642493	+	1.11283i
$970$		0			0
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	−0.960910	−	0.276861i	$-0.910706\pi$
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	0.720224	+	0.693742i	$0.244039\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	17.5000	+	30.3109i	0.561024	+	0.971722i
$974$	−37.0000			−1.18556
$975$	−1.00000	+	3.46410i	−0.0320256	+	0.110940i
$976$	2.00000			0.0640184
$977$	−10.0000	−	17.3205i	−0.319928	−	0.554132i	0.660544	−	0.750787i	$-0.270326\pi$
$977$	−10.0000	−	17.3205i	−0.319928	−	0.554132i	−0.980473	+	0.196655i	$0.936992\pi$
$978$	−10.0000	−	17.3205i	−0.319765	−	0.553849i
$979$	−16.5000	+	28.5788i	−0.527342	+	0.913384i
$980$	−18.0000			−0.574989
$981$	−7.00000	+	12.1244i	−0.223493	+	0.387101i
$982$	10.5000	−	18.1865i	0.335068	−	0.580356i
$983$	23.0000			0.733586			0.366793	−	0.930303i	$-0.380456\pi$
$983$	23.0000			0.733586			0.366793	+	0.930303i	$0.380456\pi$
$984$	3.00000	−	5.19615i	0.0956365	−	0.165647i
$985$	1.50000	+	2.59808i	0.0477940	+	0.0827816i
$986$	16.0000	+	27.7128i	0.509544	+	0.882556i
$987$	15.0000			0.477455
$988$	5.00000	−	17.3205i	0.159071	−	0.551039i
$989$	−24.0000			−0.763156
$990$	1.50000	+	2.59808i	0.0476731	+	0.0825723i
$991$	−5.00000	−	8.66025i	−0.158830	−	0.275102i	0.775617	−	0.631204i	$-0.217439\pi$
$991$	−5.00000	−	8.66025i	−0.158830	−	0.275102i	−0.934447	+	0.356102i	$0.884106\pi$
$992$	−1.00000	+	1.73205i	−0.0317500	+	0.0549927i
$993$	4.00000			0.126936
$994$	−5.00000	+	8.66025i	−0.158590	+	0.274687i
$995$	11.0000	−	19.0526i	0.348723	−	0.604007i
$996$	8.00000			0.253490
$997$	0.500000	−	0.866025i	0.0158352	−	0.0274273i	−0.857999	−	0.513651i	$-0.828293\pi$
$997$	0.500000	−	0.866025i	0.0158352	−	0.0274273i	0.873834	+	0.486224i	$0.161626\pi$
$998$	2.00000	+	3.46410i	0.0633089	+	0.109654i
$999$	3.50000	+	6.06218i	0.110735	+	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.i.d.211.1	yes	2
3.2	odd	2		1170.2.i.g.991.1		2
5.2	odd	4		1950.2.z.j.1849.1		4
5.3	odd	4		1950.2.z.j.1849.2		4
5.4	even	2		1950.2.i.i.601.1		2
13.2	odd	12		5070.2.b.l.1351.2		2
13.3	even	3		5070.2.a.i.1.1		1
13.9	even	3	inner	390.2.i.d.61.1	✓	2
13.10	even	6		5070.2.a.x.1.1		1
13.11	odd	12		5070.2.b.l.1351.1		2
39.35	odd	6		1170.2.i.g.451.1		2
65.9	even	6		1950.2.i.i.451.1		2
65.22	odd	12		1950.2.z.j.1699.2		4
65.48	odd	12		1950.2.z.j.1699.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.d.61.1	✓	2	13.9	even	3	inner
390.2.i.d.211.1	yes	2	1.1	even	1	trivial
1170.2.i.g.451.1		2	39.35	odd	6
1170.2.i.g.991.1		2	3.2	odd	2
1950.2.i.i.451.1		2	65.9	even	6
1950.2.i.i.601.1		2	5.4	even	2
1950.2.z.j.1699.1		4	65.48	odd	12
1950.2.z.j.1699.2		4	65.22	odd	12
1950.2.z.j.1849.1		4	5.2	odd	4
1950.2.z.j.1849.2		4	5.3	odd	4
5070.2.a.i.1.1		1	13.3	even	3
5070.2.a.x.1.1		1	13.10	even	6
5070.2.b.l.1351.1		2	13.11	odd	12
5070.2.b.l.1351.2		2	13.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.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 q^{5} +(0.500000 - 0.866025i) q^{6} +(2.50000 - 4.33013i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} +1.00000 q^{12} +(-2.50000 - 2.59808i) q^{13} +5.00000 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.00000 - 6.92820i) q^{17} -1.00000 q^{18} +(2.50000 - 4.33013i) q^{19} +(0.500000 - 0.866025i) q^{20} -5.00000 q^{21} +(-1.50000 + 2.59808i) q^{22} +(2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{24} +1.00000 q^{25} +(1.00000 - 3.46410i) q^{26} +1.00000 q^{27} +(2.50000 + 4.33013i) q^{28} +(2.00000 + 3.46410i) q^{29} +(-0.500000 + 0.866025i) q^{30} -2.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +8.00000 q^{34} +(-2.50000 + 4.33013i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(3.50000 + 6.06218i) q^{37} +5.00000 q^{38} +(-1.00000 + 3.46410i) q^{39} +1.00000 q^{40} +(-3.00000 - 5.19615i) q^{41} +(-2.50000 - 4.33013i) q^{42} +(-3.00000 + 5.19615i) q^{43} -3.00000 q^{44} +(0.500000 - 0.866025i) q^{45} +(-2.00000 + 3.46410i) q^{46} -3.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-9.00000 - 15.5885i) q^{49} +(0.500000 + 0.866025i) q^{50} -8.00000 q^{51} +(3.50000 - 0.866025i) q^{52} +1.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.50000 - 2.59808i) q^{55} +(-2.50000 + 4.33013i) q^{56} -5.00000 q^{57} +(-2.00000 + 3.46410i) q^{58} +(-6.00000 + 10.3923i) q^{59} -1.00000 q^{60} +(-1.00000 + 1.73205i) q^{61} +(-1.00000 - 1.73205i) q^{62} +(2.50000 + 4.33013i) q^{63} +1.00000 q^{64} +(2.50000 + 2.59808i) q^{65} +3.00000 q^{66} +(-4.00000 - 6.92820i) q^{67} +(4.00000 + 6.92820i) q^{68} +(2.00000 - 3.46410i) q^{69} -5.00000 q^{70} +(-1.00000 + 1.73205i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-3.50000 + 6.06218i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(2.50000 + 4.33013i) q^{76} +15.0000 q^{77} +(-3.50000 + 0.866025i) q^{78} -2.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} +8.00000 q^{83} +(2.50000 - 4.33013i) q^{84} +(-4.00000 + 6.92820i) q^{85} -6.00000 q^{86} +(2.00000 - 3.46410i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(5.50000 + 9.52628i) q^{89} +1.00000 q^{90} +(-17.5000 + 4.33013i) q^{91} -4.00000 q^{92} +(1.00000 + 1.73205i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(-2.50000 + 4.33013i) q^{95} -1.00000 q^{96} +(9.00000 - 15.5885i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{5} + q^{6} + 5 q^{7} - 2 q^{8} - q^{9} - q^{10} + 3 q^{11} + 2 q^{12} - 5 q^{13} + 10 q^{14} + q^{15} - q^{16} + 8 q^{17} - 2 q^{18} + 5 q^{19} + q^{20} - 10 q^{21}+ \cdots - 6 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 - 2 * q^5 + q^6 + 5 * q^7 - 2 * q^8 - q^9 - q^10 + 3 * q^11 + 2 * q^12 - 5 * q^13 + 10 * q^14 + q^15 - q^16 + 8 * q^17 - 2 * q^18 + 5 * q^19 + q^20 - 10 * q^21 - 3 * q^22 + 4 * q^23 + q^24 + 2 * q^25 + 2 * q^26 + 2 * q^27 + 5 * q^28 + 4 * q^29 - q^30 - 4 * q^31 + q^32 + 3 * q^33 + 16 * q^34 - 5 * q^35 - q^36 + 7 * q^37 + 10 * q^38 - 2 * q^39 + 2 * q^40 - 6 * q^41 - 5 * q^42 - 6 * q^43 - 6 * q^44 + q^45 - 4 * q^46 - 6 * q^47 - q^48 - 18 * q^49 + q^50 - 16 * q^51 + 7 * q^52 + 2 * q^53 + q^54 - 3 * q^55 - 5 * q^56 - 10 * q^57 - 4 * q^58 - 12 * q^59 - 2 * q^60 - 2 * q^61 - 2 * q^62 + 5 * q^63 + 2 * q^64 + 5 * q^65 + 6 * q^66 - 8 * q^67 + 8 * q^68 + 4 * q^69 - 10 * q^70 - 2 * q^71 + q^72 - 7 * q^74 - q^75 + 5 * q^76 + 30 * q^77 - 7 * q^78 - 4 * q^79 + q^80 - q^81 + 6 * q^82 + 16 * q^83 + 5 * q^84 - 8 * q^85 - 12 * q^86 + 4 * q^87 - 3 * q^88 + 11 * q^89 + 2 * q^90 - 35 * q^91 - 8 * q^92 + 2 * q^93 - 3 * q^94 - 5 * q^95 - 2 * q^96 + 18 * q^98 - 6 * q^99

Introduction

L-functions

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