LMFDB - Embedded newform 1170.2.i.g.451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(451,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, 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("1170.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.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:	$9.34249703649$
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:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1170.451
Dual form			1170.2.i.g.991.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(2.50000 + 4.33013i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(2.50000 + 4.33013i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(-2.50000 + 2.59808i) q^{13} -5.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-4.00000 - 6.92820i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(-2.00000 + 3.46410i) q^{23} +1.00000 q^{25} +(-1.00000 - 3.46410i) q^{26} +(2.50000 - 4.33013i) q^{28} +(-2.00000 + 3.46410i) q^{29} -2.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +8.00000 q^{34} +(2.50000 + 4.33013i) q^{35} +(3.50000 - 6.06218i) q^{37} -5.00000 q^{38} +1.00000 q^{40} +(3.00000 - 5.19615i) q^{41} +(-3.00000 - 5.19615i) q^{43} +3.00000 q^{44} +(-2.00000 - 3.46410i) q^{46} +3.00000 q^{47} +(-9.00000 + 15.5885i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(3.50000 + 0.866025i) q^{52} -1.00000 q^{53} +(-1.50000 + 2.59808i) q^{55} +(2.50000 + 4.33013i) q^{56} +(-2.00000 - 3.46410i) q^{58} +(6.00000 + 10.3923i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(1.00000 - 1.73205i) q^{62} +1.00000 q^{64} +(-2.50000 + 2.59808i) q^{65} +(-4.00000 + 6.92820i) q^{67} +(-4.00000 + 6.92820i) q^{68} -5.00000 q^{70} +(1.00000 + 1.73205i) q^{71} +(3.50000 + 6.06218i) q^{74} +(2.50000 - 4.33013i) q^{76} -15.0000 q^{77} -2.00000 q^{79} +(-0.500000 + 0.866025i) q^{80} +(3.00000 + 5.19615i) q^{82} -8.00000 q^{83} +(-4.00000 - 6.92820i) q^{85} +6.00000 q^{86} +(-1.50000 + 2.59808i) q^{88} +(-5.50000 + 9.52628i) q^{89} +(-17.5000 - 4.33013i) q^{91} +4.00000 q^{92} +(-1.50000 + 2.59808i) q^{94} +(2.50000 + 4.33013i) q^{95} +(-9.00000 - 15.5885i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 2 q^{5} + 5 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 + 2 * q^5 + 5 * q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} + 2 q^{5} + 5 q^{7} + 2 q^{8} - q^{10} - 3 q^{11} - 5 q^{13} - 10 q^{14} - q^{16} - 8 q^{17} + 5 q^{19} - q^{20} - 3 q^{22} - 4 q^{23} + 2 q^{25} - 2 q^{26} + 5 q^{28} - 4 q^{29} - 4 q^{31} - q^{32} + 16 q^{34} + 5 q^{35} + 7 q^{37} - 10 q^{38} + 2 q^{40} + 6 q^{41} - 6 q^{43} + 6 q^{44} - 4 q^{46} + 6 q^{47} - 18 q^{49} - q^{50} + 7 q^{52} - 2 q^{53} - 3 q^{55} + 5 q^{56} - 4 q^{58} + 12 q^{59} - 2 q^{61} + 2 q^{62} + 2 q^{64} - 5 q^{65} - 8 q^{67} - 8 q^{68} - 10 q^{70} + 2 q^{71} + 7 q^{74} + 5 q^{76} - 30 q^{77} - 4 q^{79} - q^{80} + 6 q^{82} - 16 q^{83} - 8 q^{85} + 12 q^{86} - 3 q^{88} - 11 q^{89} - 35 q^{91} + 8 q^{92} - 3 q^{94} + 5 q^{95} - 18 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + 2 * q^5 + 5 * q^7 + 2 * q^8 - q^10 - 3 * q^11 - 5 * q^13 - 10 * q^14 - q^16 - 8 * q^17 + 5 * q^19 - q^20 - 3 * q^22 - 4 * q^23 + 2 * q^25 - 2 * q^26 + 5 * q^28 - 4 * q^29 - 4 * q^31 - q^32 + 16 * q^34 + 5 * q^35 + 7 * q^37 - 10 * q^38 + 2 * q^40 + 6 * q^41 - 6 * q^43 + 6 * q^44 - 4 * q^46 + 6 * q^47 - 18 * q^49 - q^50 + 7 * q^52 - 2 * q^53 - 3 * q^55 + 5 * q^56 - 4 * q^58 + 12 * q^59 - 2 * q^61 + 2 * q^62 + 2 * q^64 - 5 * q^65 - 8 * q^67 - 8 * q^68 - 10 * q^70 + 2 * q^71 + 7 * q^74 + 5 * q^76 - 30 * q^77 - 4 * q^79 - q^80 + 6 * q^82 - 16 * q^83 - 8 * q^85 + 12 * q^86 - 3 * q^88 - 11 * q^89 - 35 * q^91 + 8 * q^92 - 3 * q^94 + 5 * q^95 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	2.50000	+	4.33013i	0.944911	+	1.63663i	0.755929	+	0.654654i	$0.227186\pi$
$7$	2.50000	+	4.33013i	0.944911	+	1.63663i	0.188982	+	0.981981i	$0.439481\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$		0			0
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$14$	−5.00000			−1.33631
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.00000	−	6.92820i	−0.970143	−	1.68034i	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	−4.00000	−	6.92820i	−0.970143	−	1.68034i	−0.275029	−	0.961436i	$-0.588688\pi$
$18$		0			0
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		0			0
$22$	−1.50000	−	2.59808i	−0.319801	−	0.553912i
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−1.00000	−	3.46410i	−0.196116	−	0.679366i
$27$		0			0
$28$	2.50000	−	4.33013i	0.472456	−	0.818317i
$29$	−2.00000	+	3.46410i	−0.371391	+	0.643268i	−0.989780	−	0.142605i	$-0.954452\pi$
$29$	−2.00000	+	3.46410i	−0.371391	+	0.643268i	0.618389	+	0.785872i	$0.287786\pi$
$30$		0			0
$31$	−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
$33$		0			0
$34$	8.00000			1.37199
$35$	2.50000	+	4.33013i	0.422577	+	0.731925i
$36$		0			0
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	−0.420602	−	0.907245i	$-0.638181\pi$
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	0.995998	−	0.0893706i	$-0.0284856\pi$
$38$	−5.00000			−0.811107
$39$		0			0
$40$	1.00000			0.158114
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	−0.530831	−	0.847477i	$-0.678120\pi$
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	0.999353	+	0.0359748i	$0.0114536\pi$
$42$		0			0
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	0.541332	−	0.840809i	$-0.317920\pi$
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	−0.998828	+	0.0484030i	$0.984587\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$	−2.00000	−	3.46410i	−0.294884	−	0.510754i
$47$	3.00000			0.437595			0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000			0.437595			0.218797	+	0.975770i	$0.429787\pi$
$48$		0			0
$49$	−9.00000	+	15.5885i	−1.28571	+	2.22692i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$		0			0
$52$	3.50000	+	0.866025i	0.485363	+	0.120096i
$53$	−1.00000			−0.137361			−0.0686803	−	0.997639i	$-0.521879\pi$
$53$	−1.00000			−0.137361			−0.0686803	+	0.997639i	$0.521879\pi$
$54$		0			0
$55$	−1.50000	+	2.59808i	−0.202260	+	0.350325i
$56$	2.50000	+	4.33013i	0.334077	+	0.578638i
$57$		0			0
$58$	−2.00000	−	3.46410i	−0.262613	−	0.454859i
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	0.931282	+	0.364299i	$0.118692\pi$
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	−0.150148	+	0.988663i	$0.547975\pi$
$60$		0			0
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$	1.00000	−	1.73205i	0.127000	−	0.219971i
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.50000	+	2.59808i	−0.310087	+	0.322252i
$66$		0			0
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$	−4.00000	+	6.92820i	−0.485071	+	0.840168i
$69$		0			0
$70$	−5.00000			−0.597614
$71$	1.00000	+	1.73205i	0.118678	+	0.205557i	0.919244	−	0.393688i	$-0.128801\pi$
$71$	1.00000	+	1.73205i	0.118678	+	0.205557i	−0.800566	+	0.599245i	$0.795468\pi$
$72$		0			0
$73$		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			0
$76$	2.50000	−	4.33013i	0.286770	−	0.496700i
$77$	−15.0000			−1.70941
$78$		0			0
$79$	−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			0
$82$	3.00000	+	5.19615i	0.331295	+	0.573819i
$83$	−8.00000			−0.878114			−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000			−0.878114			−0.439057	+	0.898459i	$0.644687\pi$
$84$		0			0
$85$	−4.00000	−	6.92820i	−0.433861	−	0.751469i
$86$	6.00000			0.646997
$87$		0			0
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$	−5.50000	+	9.52628i	−0.582999	+	1.00978i	0.412123	+	0.911128i	$0.364787\pi$
$89$	−5.50000	+	9.52628i	−0.582999	+	1.00978i	−0.995122	+	0.0986553i	$0.968546\pi$
$90$		0			0
$91$	−17.5000	−	4.33013i	−1.83450	−	0.453921i
$92$	4.00000			0.417029
$93$		0			0
$94$	−1.50000	+	2.59808i	−0.154713	+	0.267971i
$95$	2.50000	+	4.33013i	0.256495	+	0.444262i
$96$		0			0
$97$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$97$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$98$	−9.00000	−	15.5885i	−0.909137	−	1.57467i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−4.00000	+	6.92820i	−0.398015	+	0.689382i	−0.993481	−	0.113998i	$-0.963634\pi$
$101$	−4.00000	+	6.92820i	−0.398015	+	0.689382i	0.595466	+	0.803380i	$0.296967\pi$
$102$		0			0
$103$	−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
$105$		0			0
$106$	0.500000	−	0.866025i	0.0485643	−	0.0841158i
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	−0.973814	−	0.227345i	$-0.926996\pi$
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	0.683793	+	0.729676i	$0.260329\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$	−5.00000			−0.472456
$113$	4.00000	+	6.92820i	0.376288	+	0.651751i	0.990519	−	0.137376i	$-0.0438669\pi$
$113$	4.00000	+	6.92820i	0.376288	+	0.651751i	−0.614231	+	0.789127i	$0.710534\pi$
$114$		0			0
$115$	−2.00000	+	3.46410i	−0.186501	+	0.323029i
$116$	4.00000			0.371391
$117$		0			0
$118$	−12.0000			−1.10469
$119$	20.0000	−	34.6410i	1.83340	−	3.17554i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	2.00000			0.181071
$123$		0			0
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$	1.00000			0.0894427
$126$		0			0
$127$	10.5000	−	18.1865i	0.931724	−	1.61379i	0.151351	−	0.988480i	$-0.451638\pi$
$127$	10.5000	−	18.1865i	0.931724	−	1.61379i	0.780373	−	0.625314i	$-0.215029\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.00000	−	3.46410i	−0.0877058	−	0.303822i
$131$	19.0000			1.66004			0.830019	−	0.557735i	$-0.188330\pi$
$131$	19.0000			1.66004			0.830019	+	0.557735i	$0.188330\pi$
$132$		0			0
$133$	−12.5000	+	21.6506i	−1.08389	+	1.87735i
$134$	−4.00000	−	6.92820i	−0.345547	−	0.598506i
$135$		0			0
$136$	−4.00000	−	6.92820i	−0.342997	−	0.594089i
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$		0			0
$139$	−3.50000	−	6.06218i	−0.296866	−	0.514187i	0.678551	−	0.734553i	$-0.262608\pi$
$139$	−3.50000	−	6.06218i	−0.296866	−	0.514187i	−0.975417	+	0.220366i	$0.929275\pi$
$140$	2.50000	−	4.33013i	0.211289	−	0.365963i
$141$		0			0
$142$	−2.00000			−0.167836
$143$	−3.00000	−	10.3923i	−0.250873	−	0.869048i
$144$		0			0
$145$	−2.00000	+	3.46410i	−0.166091	+	0.287678i
$146$		0			0
$147$		0			0
$148$	−7.00000			−0.575396
$149$	−1.00000	−	1.73205i	−0.0819232	−	0.141895i	0.822153	−	0.569267i	$-0.192773\pi$
$149$	−1.00000	−	1.73205i	−0.0819232	−	0.141895i	−0.904076	+	0.427372i	$0.859440\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$	7.50000	−	12.9904i	0.604367	−	1.04679i
$155$	−2.00000			−0.160644
$156$		0			0
$157$	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			0
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−20.0000			−1.57622
$162$		0			0
$163$	10.0000	+	17.3205i	0.783260	+	1.35665i	0.930033	+	0.367477i	$0.119778\pi$
$163$	10.0000	+	17.3205i	0.783260	+	1.35665i	−0.146772	+	0.989170i	$0.546888\pi$
$164$	−6.00000			−0.468521
$165$		0			0
$166$	4.00000	−	6.92820i	0.310460	−	0.537733i
$167$	−11.5000	+	19.9186i	−0.889897	+	1.54135i	−0.0499004	+	0.998754i	$0.515890\pi$
$167$	−11.5000	+	19.9186i	−0.889897	+	1.54135i	−0.839996	+	0.542592i	$0.817443\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$	8.00000			0.613572
$171$		0			0
$172$	−3.00000	+	5.19615i	−0.228748	+	0.396203i
$173$	2.50000	+	4.33013i	0.190071	+	0.329213i	0.945274	−	0.326278i	$-0.105795\pi$
$173$	2.50000	+	4.33013i	0.190071	+	0.329213i	−0.755202	+	0.655492i	$0.772461\pi$
$174$		0			0
$175$	2.50000	+	4.33013i	0.188982	+	0.327327i
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$		0			0
$178$	−5.50000	−	9.52628i	−0.412242	−	0.714025i
$179$	2.00000	−	3.46410i	0.149487	−	0.258919i	−0.781551	−	0.623841i	$-0.785571\pi$
$179$	2.00000	−	3.46410i	0.149487	−	0.258919i	0.931038	+	0.364922i	$0.118904\pi$
$180$		0			0
$181$	−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
$183$		0			0
$184$	−2.00000	+	3.46410i	−0.147442	+	0.255377i
$185$	3.50000	−	6.06218i	0.257325	−	0.445700i
$186$		0			0
$187$	24.0000			1.75505
$188$	−1.50000	−	2.59808i	−0.109399	−	0.189484i
$189$		0			0
$190$	−5.00000			−0.362738
$191$	1.00000	+	1.73205i	0.0723575	+	0.125327i	0.899934	−	0.436026i	$-0.143614\pi$
$191$	1.00000	+	1.73205i	0.0723575	+	0.125327i	−0.827577	+	0.561353i	$0.810281\pi$
$192$		0			0
$193$	−12.0000	+	20.7846i	−0.863779	+	1.49611i	0.00447566	+	0.999990i	$0.498575\pi$
$193$	−12.0000	+	20.7846i	−0.863779	+	1.49611i	−0.868255	+	0.496119i	$0.834758\pi$
$194$		0			0
$195$		0			0
$196$	18.0000			1.28571
$197$	1.50000	−	2.59808i	0.106871	−	0.185105i	−0.807630	−	0.589689i	$-0.799250\pi$
$197$	1.50000	−	2.59808i	0.106871	−	0.185105i	0.914501	+	0.404584i	$0.132584\pi$
$198$		0			0
$199$	−11.0000	−	19.0526i	−0.779769	−	1.35060i	−0.932075	−	0.362267i	$-0.882003\pi$
$199$	−11.0000	−	19.0526i	−0.779769	−	1.35060i	0.152305	−	0.988334i	$-0.451330\pi$
$200$	1.00000			0.0707107
$201$		0			0
$202$	−4.00000	−	6.92820i	−0.281439	−	0.487467i
$203$	−20.0000			−1.40372
$204$		0			0
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	3.50000	−	6.06218i	0.243857	−	0.422372i
$207$		0			0
$208$	−1.00000	−	3.46410i	−0.0693375	−	0.240192i
$209$	−15.0000			−1.03757
$210$		0			0
$211$	7.50000	−	12.9904i	0.516321	−	0.894295i	−0.483499	−	0.875345i	$-0.660634\pi$
$211$	7.50000	−	12.9904i	0.516321	−	0.894295i	0.999820	−	0.0189499i	$-0.00603229\pi$
$212$	0.500000	+	0.866025i	0.0343401	+	0.0594789i
$213$		0			0
$214$	−3.00000	−	5.19615i	−0.205076	−	0.355202i
$215$	−3.00000	−	5.19615i	−0.204598	−	0.354375i
$216$		0			0
$217$	−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
$222$		0			0
$223$	1.50000	−	2.59808i	0.100447	−	0.173980i	−0.811422	−	0.584461i	$-0.801306\pi$
$223$	1.50000	−	2.59808i	0.100447	−	0.173980i	0.911869	+	0.410481i	$0.134639\pi$
$224$	2.50000	−	4.33013i	0.167038	−	0.289319i
$225$		0			0
$226$	−8.00000			−0.532152
$227$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$227$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$228$		0			0
$229$	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
$231$		0			0
$232$	−2.00000	+	3.46410i	−0.131306	+	0.227429i
$233$	14.0000			0.917170			0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000			0.917170			0.458585	+	0.888650i	$0.348356\pi$
$234$		0			0
$235$	3.00000			0.195698
$236$	6.00000	−	10.3923i	0.390567	−	0.676481i
$237$		0			0
$238$	20.0000	+	34.6410i	1.29641	+	2.24544i
$239$	18.0000			1.16432			0.582162	−	0.813073i	$-0.302207\pi$
$239$	18.0000			1.16432			0.582162	+	0.813073i	$0.302207\pi$
$240$		0			0
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	0.916159	+	0.400815i	$0.131273\pi$
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	−0.110963	+	0.993825i	$0.535394\pi$
$242$	−2.00000			−0.128565
$243$		0			0
$244$	−1.00000	+	1.73205i	−0.0640184	+	0.110883i
$245$	−9.00000	+	15.5885i	−0.574989	+	0.995910i
$246$		0			0
$247$	−17.5000	−	4.33013i	−1.11350	−	0.275519i
$248$	−2.00000			−0.127000
$249$		0			0
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	7.50000	+	12.9904i	0.473396	+	0.819946i	0.999536	−	0.0304521i	$-0.00969471\pi$
$251$	7.50000	+	12.9904i	0.473396	+	0.819946i	−0.526140	+	0.850398i	$0.676361\pi$
$252$		0			0
$253$	−6.00000	−	10.3923i	−0.377217	−	0.653359i
$254$	10.5000	+	18.1865i	0.658829	+	1.14112i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	14.0000	−	24.2487i	0.873296	−	1.51259i	0.0147291	−	0.999892i	$-0.495311\pi$
$257$	14.0000	−	24.2487i	0.873296	−	1.51259i	0.858567	−	0.512702i	$-0.171355\pi$
$258$		0			0
$259$	35.0000			2.17479
$260$	3.50000	+	0.866025i	0.217061	+	0.0537086i
$261$		0			0
$262$	−9.50000	+	16.4545i	−0.586912	+	1.01656i
$263$	−7.50000	+	12.9904i	−0.462470	+	0.801021i	−0.999083	−	0.0428069i	$-0.986370\pi$
$263$	−7.50000	+	12.9904i	−0.462470	+	0.801021i	0.536614	+	0.843828i	$0.319703\pi$
$264$		0			0
$265$	−1.00000			−0.0614295
$266$	−12.5000	−	21.6506i	−0.766424	−	1.32749i
$267$		0			0
$268$	8.00000			0.488678
$269$	2.00000	+	3.46410i	0.121942	+	0.211210i	0.920534	−	0.390664i	$-0.127754\pi$
$269$	2.00000	+	3.46410i	0.121942	+	0.211210i	−0.798591	+	0.601874i	$0.794421\pi$
$270$		0			0
$271$	−2.00000	+	3.46410i	−0.121491	+	0.210429i	−0.920356	−	0.391082i	$-0.872101\pi$
$271$	−2.00000	+	3.46410i	−0.121491	+	0.210429i	0.798865	+	0.601511i	$0.205434\pi$
$272$	8.00000			0.485071
$273$		0			0
$274$	12.0000			0.724947
$275$	−1.50000	+	2.59808i	−0.0904534	+	0.156670i
$276$		0			0
$277$	7.50000	+	12.9904i	0.450631	+	0.780516i	0.998425	−	0.0560969i	$-0.0178656\pi$
$277$	7.50000	+	12.9904i	0.450631	+	0.780516i	−0.547794	+	0.836613i	$0.684532\pi$
$278$	7.00000			0.419832
$279$		0			0
$280$	2.50000	+	4.33013i	0.149404	+	0.258775i
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$		0			0
$283$	5.00000	−	8.66025i	0.297219	−	0.514799i	−0.678280	−	0.734804i	$-0.737274\pi$
$283$	5.00000	−	8.66025i	0.297219	−	0.514799i	0.975499	+	0.220005i	$0.0706075\pi$
$284$	1.00000	−	1.73205i	0.0593391	−	0.102778i
$285$		0			0
$286$	10.5000	+	2.59808i	0.620878	+	0.153627i
$287$	30.0000			1.77084
$288$		0			0
$289$	−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	$-0.251343\pi$
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	−0.967009	+	0.254741i	$0.918010\pi$
$294$		0			0
$295$	6.00000	+	10.3923i	0.349334	+	0.605063i
$296$	3.50000	−	6.06218i	0.203433	−	0.352357i
$297$		0			0
$298$	2.00000			0.115857
$299$	−4.00000	−	13.8564i	−0.231326	−	0.801337i
$300$		0			0
$301$	15.0000	−	25.9808i	0.864586	−	1.49751i
$302$	−11.0000	+	19.0526i	−0.632979	+	1.09635i
$303$		0			0
$304$	−5.00000			−0.286770
$305$	−1.00000	−	1.73205i	−0.0572598	−	0.0991769i
$306$		0			0
$307$	−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
$309$		0			0
$310$	1.00000	−	1.73205i	0.0567962	−	0.0983739i
$311$	12.0000			0.680458			0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000			0.680458			0.340229	+	0.940343i	$0.389495\pi$
$312$		0			0
$313$	−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
$315$		0			0
$316$	1.00000	+	1.73205i	0.0562544	+	0.0974355i
$317$	23.0000			1.29181			0.645904	−	0.763418i	$-0.276480\pi$
$317$	23.0000			1.29181			0.645904	+	0.763418i	$0.276480\pi$
$318$		0			0
$319$	−6.00000	−	10.3923i	−0.335936	−	0.581857i
$320$	1.00000			0.0559017
$321$		0			0
$322$	10.0000	−	17.3205i	0.557278	−	0.965234i
$323$	20.0000	−	34.6410i	1.11283	−	1.92748i
$324$		0			0
$325$	−2.50000	+	2.59808i	−0.138675	+	0.144115i
$326$	−20.0000			−1.10770
$327$		0			0
$328$	3.00000	−	5.19615i	0.165647	−	0.286910i
$329$	7.50000	+	12.9904i	0.413488	+	0.716183i
$330$		0			0
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	0.805812	−	0.592172i	$-0.201729\pi$
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	−0.915742	+	0.401768i	$0.868396\pi$
$332$	4.00000	+	6.92820i	0.219529	+	0.380235i
$333$		0			0
$334$	−11.5000	−	19.9186i	−0.629252	−	1.08990i
$335$	−4.00000	+	6.92820i	−0.218543	+	0.378528i
$336$		0			0
$337$	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
$339$		0			0
$340$	−4.00000	+	6.92820i	−0.216930	+	0.375735i
$341$	3.00000	−	5.19615i	0.162459	−	0.281387i
$342$		0			0
$343$	−55.0000			−2.96972
$344$	−3.00000	−	5.19615i	−0.161749	−	0.280158i
$345$		0			0
$346$	−5.00000			−0.268802
$347$	−8.00000	−	13.8564i	−0.429463	−	0.743851i	0.567363	−	0.823468i	$-0.307964\pi$
$347$	−8.00000	−	13.8564i	−0.429463	−	0.743851i	−0.996826	+	0.0796169i	$0.974630\pi$
$348$		0			0
$349$	−4.00000	+	6.92820i	−0.214115	+	0.370858i	−0.952998	−	0.302975i	$-0.902020\pi$
$349$	−4.00000	+	6.92820i	−0.214115	+	0.370858i	0.738883	+	0.673833i	$0.235353\pi$
$350$	−5.00000			−0.267261
$351$		0			0
$352$	3.00000			0.159901
$353$	8.00000	−	13.8564i	0.425797	−	0.737502i	−0.570697	−	0.821160i	$-0.693327\pi$
$353$	8.00000	−	13.8564i	0.425797	−	0.737502i	0.996495	+	0.0836583i	$0.0266604\pi$
$354$		0			0
$355$	1.00000	+	1.73205i	0.0530745	+	0.0919277i
$356$	11.0000			0.582999
$357$		0			0
$358$	2.00000	+	3.46410i	0.105703	+	0.183083i
$359$	18.0000			0.950004			0.475002	−	0.879985i	$-0.342447\pi$
$359$	18.0000			0.950004			0.475002	+	0.879985i	$0.342447\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	1.00000	−	1.73205i	0.0525588	−	0.0910346i
$363$		0			0
$364$	5.00000	+	17.3205i	0.262071	+	0.907841i
$365$		0			0
$366$		0			0
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	−0.742538	−	0.669804i	$-0.766378\pi$
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	0.951336	+	0.308155i	$0.0997115\pi$
$368$	−2.00000	−	3.46410i	−0.104257	−	0.180579i
$369$		0			0
$370$	3.50000	+	6.06218i	0.181956	+	0.315158i
$371$	−2.50000	−	4.33013i	−0.129794	−	0.224809i
$372$		0			0
$373$	−19.0000	−	32.9090i	−0.983783	−	1.70396i	−0.647225	−	0.762299i	$-0.724071\pi$
$373$	−19.0000	−	32.9090i	−0.983783	−	1.70396i	−0.336557	−	0.941663i	$-0.609263\pi$
$374$	−12.0000	+	20.7846i	−0.620505	+	1.07475i
$375$		0			0
$376$	3.00000			0.154713
$377$	−4.00000	−	13.8564i	−0.206010	−	0.713641i
$378$		0			0
$379$	12.5000	−	21.6506i	0.642082	−	1.11212i	−0.342885	−	0.939377i	$-0.611404\pi$
$379$	12.5000	−	21.6506i	0.642082	−	1.11212i	0.984967	−	0.172741i	$-0.0552624\pi$
$380$	2.50000	−	4.33013i	0.128247	−	0.222131i
$381$		0			0
$382$	−2.00000			−0.102329
$383$	−14.0000	−	24.2487i	−0.715367	−	1.23905i	−0.962818	−	0.270151i	$-0.912926\pi$
$383$	−14.0000	−	24.2487i	−0.715367	−	1.23905i	0.247451	−	0.968900i	$-0.420407\pi$
$384$		0			0
$385$	−15.0000			−0.764471
$386$	−12.0000	−	20.7846i	−0.610784	−	1.05791i
$387$		0			0
$388$		0			0
$389$	32.0000			1.62246			0.811232	−	0.584724i	$-0.198797\pi$
$389$	32.0000			1.62246			0.811232	+	0.584724i	$0.198797\pi$
$390$		0			0
$391$	32.0000			1.61831
$392$	−9.00000	+	15.5885i	−0.454569	+	0.787336i
$393$		0			0
$394$	1.50000	+	2.59808i	0.0755689	+	0.130889i
$395$	−2.00000			−0.100631
$396$		0			0
$397$	−12.5000	−	21.6506i	−0.627357	−	1.08661i	−0.988080	−	0.153941i	$-0.950803\pi$
$397$	−12.5000	−	21.6506i	−0.627357	−	1.08661i	0.360723	−	0.932673i	$-0.382530\pi$
$398$	22.0000			1.10276
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−9.50000	+	16.4545i	−0.474407	+	0.821698i	−0.999571	−	0.0293039i	$-0.990671\pi$
$401$	−9.50000	+	16.4545i	−0.474407	+	0.821698i	0.525163	+	0.851002i	$0.324004\pi$
$402$		0			0
$403$	5.00000	−	5.19615i	0.249068	−	0.258839i
$404$	8.00000			0.398015
$405$		0			0
$406$	10.0000	−	17.3205i	0.496292	−	0.859602i
$407$	10.5000	+	18.1865i	0.520466	+	0.901473i
$408$		0			0
$409$	−12.5000	−	21.6506i	−0.618085	−	1.07056i	−0.989835	−	0.142222i	$-0.954575\pi$
$409$	−12.5000	−	21.6506i	−0.618085	−	1.07056i	0.371750	−	0.928333i	$-0.378758\pi$
$410$	3.00000	+	5.19615i	0.148159	+	0.256620i
$411$		0			0
$412$	3.50000	+	6.06218i	0.172433	+	0.298662i
$413$	−30.0000	+	51.9615i	−1.47620	+	2.55686i
$414$		0			0
$415$	−8.00000			−0.392705
$416$	3.50000	+	0.866025i	0.171602	+	0.0424604i
$417$		0			0
$418$	7.50000	−	12.9904i	0.366837	−	0.635380i
$419$	−6.00000	+	10.3923i	−0.293119	+	0.507697i	−0.974546	−	0.224189i	$-0.928027\pi$
$419$	−6.00000	+	10.3923i	−0.293119	+	0.507697i	0.681426	+	0.731887i	$0.261360\pi$
$420$		0			0
$421$	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
$423$		0			0
$424$	−1.00000			−0.0485643
$425$	−4.00000	−	6.92820i	−0.194029	−	0.336067i
$426$		0			0
$427$	5.00000	−	8.66025i	0.241967	−	0.419099i
$428$	6.00000			0.290021
$429$		0			0
$430$	6.00000			0.289346
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$		0			0
$433$	−8.00000	−	13.8564i	−0.384455	−	0.665896i	0.607238	−	0.794520i	$-0.292277\pi$
$433$	−8.00000	−	13.8564i	−0.384455	−	0.665896i	−0.991693	+	0.128624i	$0.958944\pi$
$434$	10.0000			0.480015
$435$		0			0
$436$	−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	−0.960323	−	0.278889i	$-0.910034\pi$
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	0.721686	+	0.692220i	$0.243367\pi$
$440$	−1.50000	+	2.59808i	−0.0715097	+	0.123858i
$441$		0			0
$442$	−20.0000	+	20.7846i	−0.951303	+	0.988623i
$443$	−6.00000			−0.285069			−0.142534	−	0.989790i	$-0.545525\pi$
$443$	−6.00000			−0.285069			−0.142534	+	0.989790i	$0.545525\pi$
$444$		0			0
$445$	−5.50000	+	9.52628i	−0.260725	+	0.451589i
$446$	1.50000	+	2.59808i	0.0710271	+	0.123022i
$447$		0			0
$448$	2.50000	+	4.33013i	0.118114	+	0.204579i
$449$	−13.5000	−	23.3827i	−0.637104	−	1.10350i	−0.986065	−	0.166360i	$-0.946799\pi$
$449$	−13.5000	−	23.3827i	−0.637104	−	1.10350i	0.348961	−	0.937137i	$-0.386535\pi$
$450$		0			0
$451$	9.00000	+	15.5885i	0.423793	+	0.734032i
$452$	4.00000	−	6.92820i	0.188144	−	0.325875i
$453$		0			0
$454$		0			0
$455$	−17.5000	−	4.33013i	−0.820413	−	0.202999i
$456$		0			0
$457$	−15.0000	+	25.9808i	−0.701670	+	1.21533i	0.266209	+	0.963915i	$0.414229\pi$
$457$	−15.0000	+	25.9808i	−0.701670	+	1.21533i	−0.967880	+	0.251414i	$0.919105\pi$
$458$	−7.00000	+	12.1244i	−0.327089	+	0.566534i
$459$		0			0
$460$	4.00000			0.186501
$461$	4.00000	+	6.92820i	0.186299	+	0.322679i	0.944013	−	0.329907i	$-0.107017\pi$
$461$	4.00000	+	6.92820i	0.186299	+	0.322679i	−0.757715	+	0.652586i	$0.773684\pi$
$462$		0			0
$463$	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
$465$		0			0
$466$	−7.00000	+	12.1244i	−0.324269	+	0.561650i
$467$	24.0000			1.11059			0.555294	−	0.831654i	$-0.312606\pi$
$467$	24.0000			1.11059			0.555294	+	0.831654i	$0.312606\pi$
$468$		0			0
$469$	−40.0000			−1.84703
$470$	−1.50000	+	2.59808i	−0.0691898	+	0.119840i
$471$		0			0
$472$	6.00000	+	10.3923i	0.276172	+	0.478345i
$473$	18.0000			0.827641
$474$		0			0
$475$	2.50000	+	4.33013i	0.114708	+	0.198680i
$476$	−40.0000			−1.83340
$477$		0			0
$478$	−9.00000	+	15.5885i	−0.411650	+	0.712999i
$479$	−14.0000	+	24.2487i	−0.639676	+	1.10795i	0.345827	+	0.938298i	$0.387598\pi$
$479$	−14.0000	+	24.2487i	−0.639676	+	1.10795i	−0.985504	+	0.169654i	$0.945735\pi$
$480$		0			0
$481$	7.00000	+	24.2487i	0.319173	+	1.10565i
$482$	−25.0000			−1.13872
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$		0			0
$486$		0			0
$487$	−18.5000	−	32.0429i	−0.838315	−	1.45200i	−0.891303	−	0.453409i	$-0.850208\pi$
$487$	−18.5000	−	32.0429i	−0.838315	−	1.45200i	0.0529875	−	0.998595i	$-0.483126\pi$
$488$	−1.00000	−	1.73205i	−0.0452679	−	0.0784063i
$489$		0			0
$490$	−9.00000	−	15.5885i	−0.406579	−	0.704215i
$491$	10.5000	−	18.1865i	0.473858	−	0.820747i	−0.525694	−	0.850674i	$-0.676194\pi$
$491$	10.5000	−	18.1865i	0.473858	−	0.820747i	0.999552	+	0.0299272i	$0.00952753\pi$
$492$		0			0
$493$	32.0000			1.44121
$494$	12.5000	−	12.9904i	0.562402	−	0.584465i
$495$		0			0
$496$	1.00000	−	1.73205i	0.0449013	−	0.0777714i
$497$	−5.00000	+	8.66025i	−0.224281	+	0.388465i
$498$		0			0
$499$	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
$501$		0			0
$502$	−15.0000			−0.669483
$503$	−5.50000	−	9.52628i	−0.245233	−	0.424756i	0.716964	−	0.697110i	$-0.245531\pi$
$503$	−5.50000	−	9.52628i	−0.245233	−	0.424756i	−0.962197	+	0.272354i	$0.912198\pi$
$504$		0			0
$505$	−4.00000	+	6.92820i	−0.177998	+	0.308301i
$506$	12.0000			0.533465
$507$		0			0
$508$	−21.0000			−0.931724
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	−0.733679	−	0.679496i	$-0.762199\pi$
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	0.955300	+	0.295637i	$0.0955319\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	14.0000	+	24.2487i	0.617514	+	1.06956i
$515$	−7.00000			−0.308457
$516$		0			0
$517$	−4.50000	+	7.79423i	−0.197910	+	0.342790i
$518$	−17.5000	+	30.3109i	−0.768906	+	1.33178i
$519$		0			0
$520$	−2.50000	+	2.59808i	−0.109632	+	0.113933i
$521$	−5.00000			−0.219054			−0.109527	−	0.993984i	$-0.534934\pi$
$521$	−5.00000			−0.219054			−0.109527	+	0.993984i	$0.534934\pi$
$522$		0			0
$523$	5.00000	−	8.66025i	0.218635	−	0.378686i	−0.735756	−	0.677247i	$-0.763173\pi$
$523$	5.00000	−	8.66025i	0.218635	−	0.378686i	0.954391	+	0.298560i	$0.0965063\pi$
$524$	−9.50000	−	16.4545i	−0.415009	−	0.718817i
$525$		0			0
$526$	−7.50000	−	12.9904i	−0.327016	−	0.566408i
$527$	8.00000	+	13.8564i	0.348485	+	0.603595i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	0.500000	−	0.866025i	0.0217186	−	0.0376177i
$531$		0			0
$532$	25.0000			1.08389
$533$	6.00000	+	20.7846i	0.259889	+	0.900281i
$534$		0			0
$535$	−3.00000	+	5.19615i	−0.129701	+	0.224649i
$536$	−4.00000	+	6.92820i	−0.172774	+	0.299253i
$537$		0			0
$538$	−4.00000			−0.172452
$539$	−27.0000	−	46.7654i	−1.16297	−	2.01433i
$540$		0			0
$541$	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
$543$		0			0
$544$	−4.00000	+	6.92820i	−0.171499	+	0.297044i
$545$	14.0000			0.599694
$546$		0			0
$547$	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
$549$		0			0
$550$	−1.50000	−	2.59808i	−0.0639602	−	0.110782i
$551$	−20.0000			−0.852029
$552$		0			0
$553$	−5.00000	−	8.66025i	−0.212622	−	0.368271i
$554$	−15.0000			−0.637289
$555$		0			0
$556$	−3.50000	+	6.06218i	−0.148433	+	0.257094i
$557$	7.50000	−	12.9904i	0.317785	−	0.550420i	−0.662240	−	0.749291i	$-0.730394\pi$
$557$	7.50000	−	12.9904i	0.317785	−	0.550420i	0.980026	+	0.198871i	$0.0637276\pi$
$558$		0			0
$559$	21.0000	+	5.19615i	0.888205	+	0.219774i
$560$	−5.00000			−0.211289
$561$		0			0
$562$	9.00000	−	15.5885i	0.379642	−	0.657559i
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	0.943560	+	0.331202i	$0.107454\pi$
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	−0.184950	+	0.982748i	$0.559212\pi$
$564$		0			0
$565$	4.00000	+	6.92820i	0.168281	+	0.291472i
$566$	5.00000	+	8.66025i	0.210166	+	0.364018i
$567$		0			0
$568$	1.00000	+	1.73205i	0.0419591	+	0.0726752i
$569$	−7.50000	+	12.9904i	−0.314416	+	0.544585i	−0.979313	−	0.202350i	$-0.935142\pi$
$569$	−7.50000	+	12.9904i	−0.314416	+	0.544585i	0.664897	+	0.746935i	$0.268475\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$	−15.0000	+	25.9808i	−0.626088	+	1.08442i
$575$	−2.00000	+	3.46410i	−0.0834058	+	0.144463i
$576$		0			0
$577$	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
$579$		0			0
$580$	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
$585$		0			0
$586$	9.00000			0.371787
$587$	9.00000	−	15.5885i	0.371470	−	0.643404i	−0.618322	−	0.785925i	$-0.712187\pi$
$587$	9.00000	−	15.5885i	0.371470	−	0.643404i	0.989792	+	0.142520i	$0.0455206\pi$
$588$		0			0
$589$	−5.00000	−	8.66025i	−0.206021	−	0.356840i
$590$	−12.0000			−0.494032
$591$		0			0
$592$	3.50000	+	6.06218i	0.143849	+	0.249154i
$593$	−20.0000			−0.821302			−0.410651	−	0.911793i	$-0.634698\pi$
$593$	−20.0000			−0.821302			−0.410651	+	0.911793i	$0.634698\pi$
$594$		0			0
$595$	20.0000	−	34.6410i	0.819920	−	1.42014i
$596$	−1.00000	+	1.73205i	−0.0409616	+	0.0709476i
$597$		0			0
$598$	14.0000	+	3.46410i	0.572503	+	0.141658i
$599$	−34.0000			−1.38920			−0.694601	−	0.719395i	$-0.744419\pi$
$599$	−34.0000			−1.38920			−0.694601	+	0.719395i	$0.744419\pi$
$600$		0			0
$601$	−18.5000	+	32.0429i	−0.754631	+	1.30706i	0.190927	+	0.981604i	$0.438851\pi$
$601$	−18.5000	+	32.0429i	−0.754631	+	1.30706i	−0.945558	+	0.325455i	$0.894483\pi$
$602$	15.0000	+	25.9808i	0.611354	+	1.05890i
$603$		0			0
$604$	−11.0000	−	19.0526i	−0.447584	−	0.775238i
$605$	1.00000	+	1.73205i	0.0406558	+	0.0704179i
$606$		0			0
$607$	14.5000	+	25.1147i	0.588537	+	1.01938i	0.994424	+	0.105453i	$0.0336291\pi$
$607$	14.5000	+	25.1147i	0.588537	+	1.01938i	−0.405887	+	0.913923i	$0.633038\pi$
$608$	2.50000	−	4.33013i	0.101388	−	0.175610i
$609$		0			0
$610$	2.00000			0.0809776
$611$	−7.50000	+	7.79423i	−0.303418	+	0.315321i
$612$		0			0
$613$	−12.5000	+	21.6506i	−0.504870	+	0.874461i	0.495114	+	0.868828i	$0.335126\pi$
$613$	−12.5000	+	21.6506i	−0.504870	+	0.874461i	−0.999984	+	0.00563283i	$0.998207\pi$
$614$	3.00000	−	5.19615i	0.121070	−	0.209700i
$615$		0			0
$616$	−15.0000			−0.604367
$617$	−7.00000	−	12.1244i	−0.281809	−	0.488108i	0.690021	−	0.723789i	$-0.257601\pi$
$617$	−7.00000	−	12.1244i	−0.281809	−	0.488108i	−0.971830	+	0.235681i	$0.924268\pi$
$618$		0			0
$619$	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
$621$		0			0
$622$	−6.00000	+	10.3923i	−0.240578	+	0.416693i
$623$	−55.0000			−2.20353
$624$		0			0
$625$	1.00000			0.0400000
$626$	3.00000	−	5.19615i	0.119904	−	0.207680i
$627$		0			0
$628$	−7.50000	−	12.9904i	−0.299283	−	0.518373i
$629$	−56.0000			−2.23287
$630$		0			0
$631$	−6.00000	−	10.3923i	−0.238856	−	0.413711i	0.721530	−	0.692383i	$-0.243439\pi$
$631$	−6.00000	−	10.3923i	−0.238856	−	0.413711i	−0.960386	+	0.278672i	$0.910106\pi$
$632$	−2.00000			−0.0795557
$633$		0			0
$634$	−11.5000	+	19.9186i	−0.456723	+	0.791068i
$635$	10.5000	−	18.1865i	0.416680	−	0.721711i
$636$		0			0
$637$	−18.0000	−	62.3538i	−0.713186	−	2.47055i
$638$	12.0000			0.475085
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	13.5000	+	23.3827i	0.533218	+	0.923561i	0.999247	+	0.0387913i	$0.0123508\pi$
$641$	13.5000	+	23.3827i	0.533218	+	0.923561i	−0.466029	+	0.884769i	$0.654316\pi$
$642$		0			0
$643$	22.0000	+	38.1051i	0.867595	+	1.50272i	0.864447	+	0.502724i	$0.167669\pi$
$643$	22.0000	+	38.1051i	0.867595	+	1.50272i	0.00314839	+	0.999995i	$0.498998\pi$
$644$	10.0000	+	17.3205i	0.394055	+	0.682524i
$645$		0			0
$646$	20.0000	+	34.6410i	0.786889	+	1.36293i
$647$	1.50000	−	2.59808i	0.0589711	−	0.102141i	−0.835033	−	0.550200i	$-0.814551\pi$
$647$	1.50000	−	2.59808i	0.0589711	−	0.102141i	0.894004	+	0.448059i	$0.147885\pi$
$648$		0			0
$649$	−36.0000			−1.41312
$650$	−1.00000	−	3.46410i	−0.0392232	−	0.135873i
$651$		0			0
$652$	10.0000	−	17.3205i	0.391630	−	0.678323i
$653$	13.5000	−	23.3827i	0.528296	−	0.915035i	−0.471160	−	0.882048i	$-0.656165\pi$
$653$	13.5000	−	23.3827i	0.528296	−	0.915035i	0.999456	−	0.0329874i	$-0.0105021\pi$
$654$		0			0
$655$	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	0.968052	+	0.250748i	$0.0806766\pi$
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	−0.266872	+	0.963732i	$0.585990\pi$
$660$		0			0
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	−0.752252	−	0.658876i	$-0.771032\pi$
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	0.946729	+	0.322031i	$0.104366\pi$
$662$	4.00000			0.155464
$663$		0			0
$664$	−8.00000			−0.310460
$665$	−12.5000	+	21.6506i	−0.484729	+	0.839576i
$666$		0			0
$667$	−8.00000	−	13.8564i	−0.309761	−	0.536522i
$668$	23.0000			0.889897
$669$		0			0
$670$	−4.00000	−	6.92820i	−0.154533	−	0.267660i
$671$	6.00000			0.231627
$672$		0			0
$673$	16.0000	−	27.7128i	0.616755	−	1.06825i	−0.373319	−	0.927703i	$-0.621780\pi$
$673$	16.0000	−	27.7128i	0.616755	−	1.06825i	0.990074	−	0.140548i	$-0.0448863\pi$
$674$	−7.00000	+	12.1244i	−0.269630	+	0.467013i
$675$		0			0
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$	22.0000			0.845529			0.422764	−	0.906240i	$-0.361060\pi$
$677$	22.0000			0.845529			0.422764	+	0.906240i	$0.361060\pi$
$678$		0			0
$679$		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	0.996154	+	0.0876211i	$0.0279265\pi$
$683$	15.0000	+	25.9808i	0.573959	+	0.994126i	−0.422195	+	0.906505i	$0.638740\pi$
$684$		0			0
$685$	−6.00000	−	10.3923i	−0.229248	−	0.397070i
$686$	27.5000	−	47.6314i	1.04995	−	1.81858i
$687$		0			0
$688$	6.00000			0.228748
$689$	2.50000	−	2.59808i	0.0952424	−	0.0989788i
$690$		0			0
$691$	−8.50000	+	14.7224i	−0.323355	+	0.560068i	−0.981178	−	0.193105i	$-0.938144\pi$
$691$	−8.50000	+	14.7224i	−0.323355	+	0.560068i	0.657823	+	0.753173i	$0.271478\pi$
$692$	2.50000	−	4.33013i	0.0950357	−	0.164607i
$693$		0			0
$694$	16.0000			0.607352
$695$	−3.50000	−	6.06218i	−0.132763	−	0.229952i
$696$		0			0
$697$	−48.0000			−1.81813
$698$	−4.00000	−	6.92820i	−0.151402	−	0.262236i
$699$		0			0
$700$	2.50000	−	4.33013i	0.0944911	−	0.163663i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	35.0000			1.32005
$704$	−1.50000	+	2.59808i	−0.0565334	+	0.0979187i
$705$		0			0
$706$	8.00000	+	13.8564i	0.301084	+	0.521493i
$707$	−40.0000			−1.50435
$708$		0			0
$709$	−16.0000	−	27.7128i	−0.600893	−	1.04078i	−0.992686	−	0.120723i	$-0.961479\pi$
$709$	−16.0000	−	27.7128i	−0.600893	−	1.04078i	0.391794	−	0.920053i	$-0.371855\pi$
$710$	−2.00000			−0.0750587
$711$		0			0
$712$	−5.50000	+	9.52628i	−0.206121	+	0.357012i
$713$	4.00000	−	6.92820i	0.149801	−	0.259463i
$714$		0			0
$715$	−3.00000	−	10.3923i	−0.112194	−	0.388650i
$716$	−4.00000			−0.149487
$717$		0			0
$718$	−9.00000	+	15.5885i	−0.335877	+	0.581756i
$719$	−10.0000	−	17.3205i	−0.372937	−	0.645946i	0.617079	−	0.786901i	$-0.288316\pi$
$719$	−10.0000	−	17.3205i	−0.372937	−	0.645946i	−0.990016	+	0.140955i	$0.954983\pi$
$720$		0			0
$721$	−17.5000	−	30.3109i	−0.651734	−	1.12884i
$722$	−3.00000	−	5.19615i	−0.111648	−	0.193381i
$723$		0			0
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$	−2.00000	+	3.46410i	−0.0742781	+	0.128654i
$726$		0			0
$727$	−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
$729$		0			0
$730$		0			0
$731$	−24.0000	+	41.5692i	−0.887672	+	1.53749i
$732$		0			0
$733$	−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
$735$		0			0
$736$	4.00000			0.147442
$737$	−12.0000	−	20.7846i	−0.442026	−	0.765611i
$738$		0			0
$739$	−9.50000	+	16.4545i	−0.349463	+	0.605288i	−0.986154	−	0.165831i	$-0.946969\pi$
$739$	−9.50000	+	16.4545i	−0.349463	+	0.605288i	0.636691	+	0.771119i	$0.280303\pi$
$740$	−7.00000			−0.257325
$741$		0			0
$742$	5.00000			0.183556
$743$	−8.00000	+	13.8564i	−0.293492	+	0.508342i	−0.974633	−	0.223810i	$-0.928151\pi$
$743$	−8.00000	+	13.8564i	−0.293492	+	0.508342i	0.681141	+	0.732152i	$0.261484\pi$
$744$		0			0
$745$	−1.00000	−	1.73205i	−0.0366372	−	0.0634574i
$746$	38.0000			1.39128
$747$		0			0
$748$	−12.0000	−	20.7846i	−0.438763	−	0.759961i
$749$	−30.0000			−1.09618
$750$		0			0
$751$	4.00000	−	6.92820i	0.145962	−	0.252814i	−0.783769	−	0.621052i	$-0.786706\pi$
$751$	4.00000	−	6.92820i	0.145962	−	0.252814i	0.929731	+	0.368238i	$0.120039\pi$
$752$	−1.50000	+	2.59808i	−0.0546994	+	0.0947421i
$753$		0			0
$754$	14.0000	+	3.46410i	0.509850	+	0.126155i
$755$	22.0000			0.800662
$756$		0			0
$757$	−8.50000	+	14.7224i	−0.308938	+	0.535096i	−0.978130	−	0.207993i	$-0.933307\pi$
$757$	−8.50000	+	14.7224i	−0.308938	+	0.535096i	0.669193	+	0.743089i	$0.266640\pi$
$758$	12.5000	+	21.6506i	0.454020	+	0.786386i
$759$		0			0
$760$	2.50000	+	4.33013i	0.0906845	+	0.157070i
$761$	4.50000	+	7.79423i	0.163125	+	0.282541i	0.935988	−	0.352032i	$-0.114509\pi$
$761$	4.50000	+	7.79423i	0.163125	+	0.282541i	−0.772863	+	0.634573i	$0.781176\pi$
$762$		0			0
$763$	35.0000	+	60.6218i	1.26709	+	2.19466i
$764$	1.00000	−	1.73205i	0.0361787	−	0.0626634i
$765$		0			0
$766$	28.0000			1.01168
$767$	−42.0000	−	10.3923i	−1.51653	−	0.375244i
$768$		0			0
$769$	17.0000	−	29.4449i	0.613036	−	1.06181i	−0.377690	−	0.925932i	$-0.623282\pi$
$769$	17.0000	−	29.4449i	0.613036	−	1.06181i	0.990726	−	0.135877i	$-0.0433852\pi$
$770$	7.50000	−	12.9904i	0.270281	−	0.468141i
$771$		0			0
$772$	24.0000			0.863779
$773$	0.500000	+	0.866025i	0.0179838	+	0.0311488i	0.874877	−	0.484345i	$-0.160942\pi$
$773$	0.500000	+	0.866025i	0.0179838	+	0.0311488i	−0.856893	+	0.515494i	$0.827609\pi$
$774$		0			0
$775$	−2.00000			−0.0718421
$776$		0			0
$777$		0			0
$778$	−16.0000	+	27.7128i	−0.573628	+	0.993552i
$779$	30.0000			1.07486
$780$		0			0
$781$	−6.00000			−0.214697
$782$	−16.0000	+	27.7128i	−0.572159	+	0.991008i
$783$		0			0
$784$	−9.00000	−	15.5885i	−0.321429	−	0.556731i
$785$	15.0000			0.535373
$786$		0			0
$787$	14.0000	+	24.2487i	0.499046	+	0.864373i	0.999999	−	0.00110111i	$-0.000350496\pi$
$787$	14.0000	+	24.2487i	0.499046	+	0.864373i	−0.500953	+	0.865474i	$0.667017\pi$
$788$	−3.00000			−0.106871
$789$		0			0
$790$	1.00000	−	1.73205i	0.0355784	−	0.0616236i
$791$	−20.0000	+	34.6410i	−0.711118	+	1.23169i
$792$		0			0
$793$	7.00000	+	1.73205i	0.248577	+	0.0615069i
$794$	25.0000			0.887217
$795$		0			0
$796$	−11.0000	+	19.0526i	−0.389885	+	0.675300i
$797$	−5.00000	−	8.66025i	−0.177109	−	0.306762i	0.763780	−	0.645477i	$-0.223341\pi$
$797$	−5.00000	−	8.66025i	−0.177109	−	0.306762i	−0.940889	+	0.338715i	$0.890008\pi$
$798$		0			0
$799$	−12.0000	−	20.7846i	−0.424529	−	0.735307i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	−9.50000	−	16.4545i	−0.335457	−	0.581028i
$803$		0			0
$804$		0			0
$805$	−20.0000			−0.704907
$806$	2.00000	+	6.92820i	0.0704470	+	0.244036i
$807$		0			0
$808$	−4.00000	+	6.92820i	−0.140720	+	0.243733i
$809$	−13.0000	+	22.5167i	−0.457056	+	0.791644i	−0.998804	−	0.0488972i	$-0.984429\pi$
$809$	−13.0000	+	22.5167i	−0.457056	+	0.791644i	0.541748	+	0.840541i	$0.317763\pi$
$810$		0			0
$811$	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
$813$		0			0
$814$	−21.0000			−0.736050
$815$	10.0000	+	17.3205i	0.350285	+	0.606711i
$816$		0			0
$817$	15.0000	−	25.9808i	0.524784	−	0.908952i
$818$	25.0000			0.874105
$819$		0			0
$820$	−6.00000			−0.209529
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	−0.991616	−	0.129217i	$-0.958754\pi$
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	0.607714	+	0.794156i	$0.292087\pi$
$822$		0			0
$823$	17.5000	+	30.3109i	0.610012	+	1.05657i	0.991238	+	0.132089i	$0.0421686\pi$
$823$	17.5000	+	30.3109i	0.610012	+	1.05657i	−0.381226	+	0.924482i	$0.624498\pi$
$824$	−7.00000			−0.243857
$825$		0			0
$826$	−30.0000	−	51.9615i	−1.04383	−	1.80797i
$827$	−6.00000			−0.208640			−0.104320	−	0.994544i	$-0.533267\pi$
$827$	−6.00000			−0.208640			−0.104320	+	0.994544i	$0.533267\pi$
$828$		0			0
$829$	8.00000	−	13.8564i	0.277851	−	0.481253i	−0.692999	−	0.720938i	$-0.743711\pi$
$829$	8.00000	−	13.8564i	0.277851	−	0.481253i	0.970851	+	0.239686i	$0.0770444\pi$
$830$	4.00000	−	6.92820i	0.138842	−	0.240481i
$831$		0			0
$832$	−2.50000	+	2.59808i	−0.0866719	+	0.0900721i
$833$	144.000			4.98930
$834$		0			0
$835$	−11.5000	+	19.9186i	−0.397974	+	0.689311i
$836$	7.50000	+	12.9904i	0.259393	+	0.449282i
$837$		0			0
$838$	−6.00000	−	10.3923i	−0.207267	−	0.358996i
$839$	−7.00000	−	12.1244i	−0.241667	−	0.418579i	0.719522	−	0.694469i	$-0.244361\pi$
$839$	−7.00000	−	12.1244i	−0.241667	−	0.418579i	−0.961189	+	0.275890i	$0.911027\pi$
$840$		0			0
$841$	6.50000	+	11.2583i	0.224138	+	0.388218i
$842$	−6.00000	+	10.3923i	−0.206774	+	0.358142i
$843$		0			0
$844$	−15.0000			−0.516321
$845$	−0.500000	−	12.9904i	−0.0172005	−	0.446883i
$846$		0			0
$847$	−5.00000	+	8.66025i	−0.171802	+	0.297570i
$848$	0.500000	−	0.866025i	0.0171701	−	0.0297394i
$849$		0			0
$850$	8.00000			0.274398
$851$	14.0000	+	24.2487i	0.479914	+	0.831235i
$852$		0			0
$853$	−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
$855$		0			0
$856$	−3.00000	+	5.19615i	−0.102538	+	0.177601i
$857$	−38.0000			−1.29806			−0.649028	−	0.760765i	$-0.724824\pi$
$857$	−38.0000			−1.29806			−0.649028	+	0.760765i	$0.724824\pi$
$858$		0			0
$859$	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
$861$		0			0
$862$	6.00000	+	10.3923i	0.204361	+	0.353963i
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$		0			0
$865$	2.50000	+	4.33013i	0.0850026	+	0.147229i
$866$	16.0000			0.543702
$867$		0			0
$868$	−5.00000	+	8.66025i	−0.169711	+	0.293948i
$869$	3.00000	−	5.19615i	0.101768	−	0.176267i
$870$		0			0
$871$	−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	0.811626	+	0.584177i	$0.198583\pi$
$877$	27.0000	+	46.7654i	0.911725	+	1.57915i	0.100099	+	0.994977i	$0.468084\pi$
$878$	−5.00000	−	8.66025i	−0.168742	−	0.292269i
$879$		0			0
$880$	−1.50000	−	2.59808i	−0.0505650	−	0.0875811i
$881$	−7.50000	+	12.9904i	−0.252681	+	0.437657i	−0.964263	−	0.264946i	$-0.914646\pi$
$881$	−7.50000	+	12.9904i	−0.252681	+	0.437657i	0.711582	+	0.702603i	$0.247979\pi$
$882$		0			0
$883$	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
$885$		0			0
$886$	3.00000	−	5.19615i	0.100787	−	0.174568i
$887$	20.5000	−	35.5070i	0.688323	−	1.19221i	−0.284058	−	0.958807i	$-0.591681\pi$
$887$	20.5000	−	35.5070i	0.688323	−	1.19221i	0.972380	−	0.233403i	$-0.0749860\pi$
$888$		0			0
$889$	105.000			3.52159
$890$	−5.50000	−	9.52628i	−0.184360	−	0.319322i
$891$		0			0
$892$	−3.00000			−0.100447
$893$	7.50000	+	12.9904i	0.250978	+	0.434707i
$894$		0			0
$895$	2.00000	−	3.46410i	0.0668526	−	0.115792i
$896$	−5.00000			−0.167038
$897$		0			0
$898$	27.0000			0.901002
$899$	4.00000	−	6.92820i	0.133407	−	0.231069i
$900$		0			0
$901$	4.00000	+	6.92820i	0.133259	+	0.230812i
$902$	−18.0000			−0.599334
$903$		0			0
$904$	4.00000	+	6.92820i	0.133038	+	0.230429i
$905$	−2.00000			−0.0664822
$906$		0			0
$907$	−5.00000	+	8.66025i	−0.166022	+	0.287559i	−0.937018	−	0.349281i	$-0.886426\pi$
$907$	−5.00000	+	8.66025i	−0.166022	+	0.287559i	0.770996	+	0.636841i	$0.219759\pi$
$908$		0			0
$909$		0			0
$910$	12.5000	−	12.9904i	0.414371	−	0.430627i
$911$	20.0000			0.662630			0.331315	−	0.943520i	$-0.392508\pi$
$911$	20.0000			0.662630			0.331315	+	0.943520i	$0.392508\pi$
$912$		0			0
$913$	12.0000	−	20.7846i	0.397142	−	0.687870i
$914$	−15.0000	−	25.9808i	−0.496156	−	0.859367i
$915$		0			0
$916$	−7.00000	−	12.1244i	−0.231287	−	0.400600i
$917$	47.5000	+	82.2724i	1.56859	+	2.71687i
$918$		0			0
$919$	1.00000	+	1.73205i	0.0329870	+	0.0571351i	0.882048	−	0.471160i	$-0.156165\pi$
$919$	1.00000	+	1.73205i	0.0329870	+	0.0571351i	−0.849061	+	0.528295i	$0.822831\pi$
$920$	−2.00000	+	3.46410i	−0.0659380	+	0.114208i
$921$		0			0
$922$	−8.00000			−0.263466
$923$	−7.00000	−	1.73205i	−0.230408	−	0.0570111i
$924$		0			0
$925$	3.50000	−	6.06218i	0.115079	−	0.199323i
$926$	−4.00000	+	6.92820i	−0.131448	+	0.227675i
$927$		0			0
$928$	4.00000			0.131306
$929$	1.00000	+	1.73205i	0.0328089	+	0.0568267i	0.881964	−	0.471317i	$-0.156221\pi$
$929$	1.00000	+	1.73205i	0.0328089	+	0.0568267i	−0.849155	+	0.528144i	$0.822888\pi$
$930$		0			0
$931$	−90.0000			−2.94963
$932$	−7.00000	−	12.1244i	−0.229293	−	0.397146i
$933$		0			0
$934$	−12.0000	+	20.7846i	−0.392652	+	0.680093i
$935$	24.0000			0.784884
$936$		0			0
$937$	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
$939$		0			0
$940$	−1.50000	−	2.59808i	−0.0489246	−	0.0847399i
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$		0			0
$943$	12.0000	+	20.7846i	0.390774	+	0.676840i
$944$	−12.0000			−0.390567
$945$		0			0
$946$	−9.00000	+	15.5885i	−0.292615	+	0.506824i
$947$	29.0000	−	50.2295i	0.942373	−	1.63224i	0.181447	−	0.983401i	$-0.441922\pi$
$947$	29.0000	−	50.2295i	0.942373	−	1.63224i	0.760927	−	0.648838i	$-0.224745\pi$
$948$		0			0
$949$		0			0
$950$	−5.00000			−0.162221
$951$		0			0
$952$	20.0000	−	34.6410i	0.648204	−	1.12272i
$953$	−27.0000	−	46.7654i	−0.874616	−	1.51488i	−0.857171	−	0.515031i	$-0.827780\pi$
$953$	−27.0000	−	46.7654i	−0.874616	−	1.51488i	−0.0174443	−	0.999848i	$-0.505553\pi$
$954$		0			0
$955$	1.00000	+	1.73205i	0.0323592	+	0.0560478i
$956$	−9.00000	−	15.5885i	−0.291081	−	0.504167i
$957$		0			0
$958$	−14.0000	−	24.2487i	−0.452319	−	0.783440i
$959$	30.0000	−	51.9615i	0.968751	−	1.67793i
$960$		0			0
$961$	−27.0000			−0.870968
$962$	−24.5000	−	6.06218i	−0.789912	−	0.195452i
$963$		0			0
$964$	12.5000	−	21.6506i	0.402598	−	0.697320i
$965$	−12.0000	+	20.7846i	−0.386294	+	0.669080i
$966$		0			0
$967$	−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
$969$		0			0
$970$		0			0
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	0.960910	−	0.276861i	$-0.0892941\pi$
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	−0.720224	+	0.693742i	$0.755961\pi$
$972$		0			0
$973$	17.5000	−	30.3109i	0.561024	−	0.971722i
$974$	37.0000			1.18556
$975$		0			0
$976$	2.00000			0.0640184
$977$	10.0000	−	17.3205i	0.319928	−	0.554132i	−0.660544	−	0.750787i	$-0.729674\pi$
$977$	10.0000	−	17.3205i	0.319928	−	0.554132i	0.980473	+	0.196655i	$0.0630078\pi$
$978$		0			0
$979$	−16.5000	−	28.5788i	−0.527342	−	0.913384i
$980$	18.0000			0.574989
$981$		0			0
$982$	10.5000	+	18.1865i	0.335068	+	0.580356i
$983$	−23.0000			−0.733586			−0.366793	−	0.930303i	$-0.619544\pi$
$983$	−23.0000			−0.733586			−0.366793	+	0.930303i	$0.619544\pi$
$984$		0			0
$985$	1.50000	−	2.59808i	0.0477940	−	0.0827816i
$986$	−16.0000	+	27.7128i	−0.509544	+	0.882556i
$987$		0			0
$988$	5.00000	+	17.3205i	0.159071	+	0.551039i
$989$	24.0000			0.763156
$990$		0			0
$991$	−5.00000	+	8.66025i	−0.158830	+	0.275102i	−0.934447	−	0.356102i	$-0.884106\pi$
$991$	−5.00000	+	8.66025i	−0.158830	+	0.275102i	0.775617	+	0.631204i	$0.217439\pi$
$992$	1.00000	+	1.73205i	0.0317500	+	0.0549927i
$993$		0			0
$994$	−5.00000	−	8.66025i	−0.158590	−	0.274687i
$995$	−11.0000	−	19.0526i	−0.348723	−	0.604007i
$996$		0			0
$997$	0.500000	+	0.866025i	0.0158352	+	0.0274273i	0.873834	−	0.486224i	$-0.161626\pi$
$997$	0.500000	+	0.866025i	0.0158352	+	0.0274273i	−0.857999	+	0.513651i	$0.828293\pi$
$998$	−2.00000	+	3.46410i	−0.0633089	+	0.109654i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.i.g.451.1		2
3.2	odd	2		390.2.i.d.61.1	✓	2
13.3	even	3	inner	1170.2.i.g.991.1		2
15.2	even	4		1950.2.z.j.1699.2		4
15.8	even	4		1950.2.z.j.1699.1		4
15.14	odd	2		1950.2.i.i.451.1		2
39.17	odd	6		5070.2.a.x.1.1		1
39.20	even	12		5070.2.b.l.1351.1		2
39.29	odd	6		390.2.i.d.211.1	yes	2
39.32	even	12		5070.2.b.l.1351.2		2
39.35	odd	6		5070.2.a.i.1.1		1
195.29	odd	6		1950.2.i.i.601.1		2
195.68	even	12		1950.2.z.j.1849.2		4
195.107	even	12		1950.2.z.j.1849.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.d.61.1	✓	2	3.2	odd	2
390.2.i.d.211.1	yes	2	39.29	odd	6
1170.2.i.g.451.1		2	1.1	even	1	trivial
1170.2.i.g.991.1		2	13.3	even	3	inner
1950.2.i.i.451.1		2	15.14	odd	2
1950.2.i.i.601.1		2	195.29	odd	6
1950.2.z.j.1699.1		4	15.8	even	4
1950.2.z.j.1699.2		4	15.2	even	4
1950.2.z.j.1849.1		4	195.107	even	12
1950.2.z.j.1849.2		4	195.68	even	12
5070.2.a.i.1.1		1	39.35	odd	6
5070.2.a.x.1.1		1	39.17	odd	6
5070.2.b.l.1351.1		2	39.20	even	12
5070.2.b.l.1351.2		2	39.32	even	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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(2.50000 + 4.33013i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(2.50000 + 4.33013i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(-2.50000 + 2.59808i) q^{13} -5.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-4.00000 - 6.92820i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(-2.00000 + 3.46410i) q^{23} +1.00000 q^{25} +(-1.00000 - 3.46410i) q^{26} +(2.50000 - 4.33013i) q^{28} +(-2.00000 + 3.46410i) q^{29} -2.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +8.00000 q^{34} +(2.50000 + 4.33013i) q^{35} +(3.50000 - 6.06218i) q^{37} -5.00000 q^{38} +1.00000 q^{40} +(3.00000 - 5.19615i) q^{41} +(-3.00000 - 5.19615i) q^{43} +3.00000 q^{44} +(-2.00000 - 3.46410i) q^{46} +3.00000 q^{47} +(-9.00000 + 15.5885i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(3.50000 + 0.866025i) q^{52} -1.00000 q^{53} +(-1.50000 + 2.59808i) q^{55} +(2.50000 + 4.33013i) q^{56} +(-2.00000 - 3.46410i) q^{58} +(6.00000 + 10.3923i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(1.00000 - 1.73205i) q^{62} +1.00000 q^{64} +(-2.50000 + 2.59808i) q^{65} +(-4.00000 + 6.92820i) q^{67} +(-4.00000 + 6.92820i) q^{68} -5.00000 q^{70} +(1.00000 + 1.73205i) q^{71} +(3.50000 + 6.06218i) q^{74} +(2.50000 - 4.33013i) q^{76} -15.0000 q^{77} -2.00000 q^{79} +(-0.500000 + 0.866025i) q^{80} +(3.00000 + 5.19615i) q^{82} -8.00000 q^{83} +(-4.00000 - 6.92820i) q^{85} +6.00000 q^{86} +(-1.50000 + 2.59808i) q^{88} +(-5.50000 + 9.52628i) q^{89} +(-17.5000 - 4.33013i) q^{91} +4.00000 q^{92} +(-1.50000 + 2.59808i) q^{94} +(2.50000 + 4.33013i) q^{95} +(-9.00000 - 15.5885i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 2 q^{5} + 5 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 + 2 * q^5 + 5 * q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} + 2 q^{5} + 5 q^{7} + 2 q^{8} - q^{10} - 3 q^{11} - 5 q^{13} - 10 q^{14} - q^{16} - 8 q^{17} + 5 q^{19} - q^{20} - 3 q^{22} - 4 q^{23} + 2 q^{25} - 2 q^{26} + 5 q^{28} - 4 q^{29} - 4 q^{31} - q^{32} + 16 q^{34} + 5 q^{35} + 7 q^{37} - 10 q^{38} + 2 q^{40} + 6 q^{41} - 6 q^{43} + 6 q^{44} - 4 q^{46} + 6 q^{47} - 18 q^{49} - q^{50} + 7 q^{52} - 2 q^{53} - 3 q^{55} + 5 q^{56} - 4 q^{58} + 12 q^{59} - 2 q^{61} + 2 q^{62} + 2 q^{64} - 5 q^{65} - 8 q^{67} - 8 q^{68} - 10 q^{70} + 2 q^{71} + 7 q^{74} + 5 q^{76} - 30 q^{77} - 4 q^{79} - q^{80} + 6 q^{82} - 16 q^{83} - 8 q^{85} + 12 q^{86} - 3 q^{88} - 11 q^{89} - 35 q^{91} + 8 q^{92} - 3 q^{94} + 5 q^{95} - 18 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + 2 * q^5 + 5 * q^7 + 2 * q^8 - q^10 - 3 * q^11 - 5 * q^13 - 10 * q^14 - q^16 - 8 * q^17 + 5 * q^19 - q^20 - 3 * q^22 - 4 * q^23 + 2 * q^25 - 2 * q^26 + 5 * q^28 - 4 * q^29 - 4 * q^31 - q^32 + 16 * q^34 + 5 * q^35 + 7 * q^37 - 10 * q^38 + 2 * q^40 + 6 * q^41 - 6 * q^43 + 6 * q^44 - 4 * q^46 + 6 * q^47 - 18 * q^49 - q^50 + 7 * q^52 - 2 * q^53 - 3 * q^55 + 5 * q^56 - 4 * q^58 + 12 * q^59 - 2 * q^61 + 2 * q^62 + 2 * q^64 - 5 * q^65 - 8 * q^67 - 8 * q^68 - 10 * q^70 + 2 * q^71 + 7 * q^74 + 5 * q^76 - 30 * q^77 - 4 * q^79 - q^80 + 6 * q^82 - 16 * q^83 - 8 * q^85 + 12 * q^86 - 3 * q^88 - 11 * q^89 - 35 * q^91 + 8 * q^92 - 3 * q^94 + 5 * q^95 - 18 * q^98

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