LMFDB - Embedded newform 1470.2.i.s.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(361,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, 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("1470.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.i (of order $3$, degree $2$, not 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:	$11.7380090971$
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 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1470.961
Dual form			1470.2.i.s.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.500000 - 0.866025i) q^{12} -2.00000 q^{13} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{18} +(4.00000 - 6.92820i) q^{19} -1.00000 q^{20} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{26} -1.00000 q^{27} +6.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(-2.00000 - 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} -6.00000 q^{34} +1.00000 q^{36} +(5.00000 - 8.66025i) q^{37} +(-4.00000 - 6.92820i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(-0.500000 + 0.866025i) q^{40} +6.00000 q^{41} -4.00000 q^{43} +(0.500000 + 0.866025i) q^{45} -1.00000 q^{48} -1.00000 q^{50} +(3.00000 - 5.19615i) q^{51} +(1.00000 + 1.73205i) q^{52} +(3.00000 + 5.19615i) q^{53} +(-0.500000 + 0.866025i) q^{54} +8.00000 q^{57} +(3.00000 - 5.19615i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(-5.00000 + 8.66025i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} +12.0000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-5.00000 - 8.66025i) q^{73} +(-5.00000 - 8.66025i) q^{74} +(0.500000 - 0.866025i) q^{75} -8.00000 q^{76} -2.00000 q^{78} +(-4.00000 + 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} -12.0000 q^{83} -6.00000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(3.00000 + 5.19615i) q^{87} +(-3.00000 + 5.19615i) q^{89} +1.00000 q^{90} +(2.00000 - 3.46410i) q^{93} +(-4.00000 - 6.92820i) q^{95} +(-0.500000 + 0.866025i) q^{96} +10.0000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^8 - q^9	$ 2 q + q^{2} + q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{8} - q^{9} - q^{10} + q^{12} - 4 q^{13} + 2 q^{15} - q^{16} - 6 q^{17} + q^{18} + 8 q^{19} - 2 q^{20} - q^{24} - q^{25} - 2 q^{26} - 2 q^{27} + 12 q^{29} + q^{30} - 4 q^{31} + q^{32} - 12 q^{34} + 2 q^{36} + 10 q^{37} - 8 q^{38} - 2 q^{39} - q^{40} + 12 q^{41} - 8 q^{43} + q^{45} - 2 q^{48} - 2 q^{50} + 6 q^{51} + 2 q^{52} + 6 q^{53} - q^{54} + 16 q^{57} + 6 q^{58} - 12 q^{59} - q^{60} - 10 q^{61} - 8 q^{62} + 2 q^{64} - 2 q^{65} + 4 q^{67} - 6 q^{68} + 24 q^{71} + q^{72} - 10 q^{73} - 10 q^{74} + q^{75} - 16 q^{76} - 4 q^{78} - 8 q^{79} + q^{80} - q^{81} + 6 q^{82} - 24 q^{83} - 12 q^{85} - 4 q^{86} + 6 q^{87} - 6 q^{89} + 2 q^{90} + 4 q^{93} - 8 q^{95} - q^{96} + 20 q^{97}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^8 - q^9 - q^10 + q^12 - 4 * q^13 + 2 * q^15 - q^16 - 6 * q^17 + q^18 + 8 * q^19 - 2 * q^20 - q^24 - q^25 - 2 * q^26 - 2 * q^27 + 12 * q^29 + q^30 - 4 * q^31 + q^32 - 12 * q^34 + 2 * q^36 + 10 * q^37 - 8 * q^38 - 2 * q^39 - q^40 + 12 * q^41 - 8 * q^43 + q^45 - 2 * q^48 - 2 * q^50 + 6 * q^51 + 2 * q^52 + 6 * q^53 - q^54 + 16 * q^57 + 6 * q^58 - 12 * q^59 - q^60 - 10 * q^61 - 8 * q^62 + 2 * q^64 - 2 * q^65 + 4 * q^67 - 6 * q^68 + 24 * q^71 + q^72 - 10 * q^73 - 10 * q^74 + q^75 - 16 * q^76 - 4 * q^78 - 8 * q^79 + q^80 - q^81 + 6 * q^82 - 24 * q^83 - 12 * q^85 - 4 * q^86 + 6 * q^87 - 6 * q^89 + 2 * q^90 + 4 * q^93 - 8 * q^95 - q^96 + 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	4.00000	−	6.92820i	0.917663	−	1.58944i	0.114708	−	0.993399i	$-0.463407\pi$
$19$	4.00000	−	6.92820i	0.917663	−	1.58944i	0.802955	−	0.596040i	$-0.203260\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.00000	+	1.73205i	−0.196116	+	0.339683i
$27$	−1.00000			−0.192450
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−6.00000			−1.02899
$35$		0			0
$36$	1.00000			0.166667
$37$	5.00000	−	8.66025i	0.821995	−	1.42374i	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	5.00000	−	8.66025i	0.821995	−	1.42374i	0.904194	−	0.427121i	$-0.140472\pi$
$38$	−4.00000	−	6.92820i	−0.648886	−	1.12390i
$39$	−1.00000	−	1.73205i	−0.160128	−	0.277350i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$		0			0
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	−1.00000			−0.144338
$49$		0			0
$50$	−1.00000			−0.141421
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$		0			0
$56$		0			0
$57$	8.00000			1.05963
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	−0.931282	−	0.364299i	$-0.881308\pi$
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	0.150148	−	0.988663i	$-0.452025\pi$
$60$	−0.500000	−	0.866025i	−0.0645497	−	0.111803i
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	0.345207	+	0.938527i	$0.387809\pi$
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	−0.985391	+	0.170305i	$0.945525\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.00000	+	1.73205i	−0.124035	+	0.214834i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$		0			0
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−5.00000	−	8.66025i	−0.585206	−	1.01361i	−0.994850	−	0.101361i	$-0.967680\pi$
$73$	−5.00000	−	8.66025i	−0.585206	−	1.01361i	0.409644	−	0.912245i	$-0.365653\pi$
$74$	−5.00000	−	8.66025i	−0.581238	−	1.00673i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$	−8.00000			−0.917663
$77$		0			0
$78$	−2.00000			−0.226455
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	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
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	−6.00000			−0.650791
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$	3.00000	+	5.19615i	0.321634	+	0.557086i
$88$		0			0
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$	1.00000			0.105409
$91$		0			0
$92$		0			0
$93$	2.00000	−	3.46410i	0.207390	−	0.359211i
$94$		0			0
$95$	−4.00000	−	6.92820i	−0.410391	−	0.710819i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	10.0000			1.01535			0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000			1.01535			0.507673	+	0.861550i	$0.330506\pi$
$98$		0			0
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$	−3.00000	−	5.19615i	−0.297044	−	0.514496i
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	−0.598858	−	0.800855i	$-0.704379\pi$
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	0.992990	+	0.118199i	$0.0377120\pi$
$104$	2.00000			0.196116
$105$		0			0
$106$	6.00000			0.582772
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	−0.977769	−	0.209687i	$-0.932756\pi$
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	0.307290	−	0.951616i	$-0.400578\pi$
$110$		0			0
$111$	10.0000			0.949158
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$	4.00000	−	6.92820i	0.374634	−	0.648886i
$115$		0			0
$116$	−3.00000	−	5.19615i	−0.278543	−	0.482451i
$117$	1.00000	−	1.73205i	0.0924500	−	0.160128i
$118$	−12.0000			−1.10469
$119$		0			0
$120$	−1.00000			−0.0912871
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	5.00000	+	8.66025i	0.452679	+	0.784063i
$123$	3.00000	+	5.19615i	0.270501	+	0.468521i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−2.00000	−	3.46410i	−0.176090	−	0.304997i
$130$	1.00000	+	1.73205i	0.0877058	+	0.151911i
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$		0			0
$133$		0			0
$134$	4.00000			0.345547
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	0.708942	−	0.705266i	$-0.249173\pi$
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$138$		0			0
$139$	16.0000			1.35710			0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000			1.35710			0.678551	+	0.734553i	$0.262608\pi$
$140$		0			0
$141$		0			0
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$		0			0
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	3.00000	−	5.19615i	0.249136	−	0.431517i
$146$	−10.0000			−0.827606
$147$		0			0
$148$	−10.0000			−0.821995
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$	−4.00000	+	6.92820i	−0.324443	+	0.561951i
$153$	6.00000			0.485071
$154$		0			0
$155$	−4.00000			−0.321288
$156$	−1.00000	+	1.73205i	−0.0800641	+	0.138675i
$157$	−11.0000	−	19.0526i	−0.877896	−	1.52056i	−0.853646	−	0.520854i	$-0.825614\pi$
$157$	−11.0000	−	19.0526i	−0.877896	−	1.52056i	−0.0242497	−	0.999706i	$-0.507720\pi$
$158$	4.00000	+	6.92820i	0.318223	+	0.551178i
$159$	−3.00000	+	5.19615i	−0.237915	+	0.412082i
$160$	1.00000			0.0790569
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$	−3.00000	−	5.19615i	−0.234261	−	0.405751i
$165$		0			0
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	−3.00000	+	5.19615i	−0.230089	+	0.398527i
$171$	4.00000	+	6.92820i	0.305888	+	0.529813i
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$	6.00000			0.454859
$175$		0			0
$176$		0			0
$177$	6.00000	−	10.3923i	0.450988	−	0.781133i
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	12.0000	+	20.7846i	0.896922	+	1.55351i	0.831408	+	0.555663i	$0.187536\pi$
$179$	12.0000	+	20.7846i	0.896922	+	1.55351i	0.0655145	+	0.997852i	$0.479131\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$		0			0
$183$	−10.0000			−0.739221
$184$		0			0
$185$	−5.00000	−	8.66025i	−0.367607	−	0.636715i
$186$	−2.00000	−	3.46410i	−0.146647	−	0.254000i
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−8.00000			−0.580381
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	0.827788	−	0.561041i	$-0.189599\pi$
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	−0.899770	+	0.436365i	$0.856266\pi$
$194$	5.00000	−	8.66025i	0.358979	−	0.621770i
$195$	−2.00000			−0.143223
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	10.0000	+	17.3205i	0.708881	+	1.22782i	0.965272	+	0.261245i	$0.0841331\pi$
$199$	10.0000	+	17.3205i	0.708881	+	1.22782i	−0.256391	+	0.966573i	$0.582534\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−2.00000	+	3.46410i	−0.141069	+	0.244339i
$202$	6.00000			0.422159
$203$		0			0
$204$	−6.00000			−0.420084
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	−4.00000	−	6.92820i	−0.278693	−	0.482711i
$207$		0			0
$208$	1.00000	−	1.73205i	0.0693375	−	0.120096i
$209$		0			0
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$	3.00000	−	5.19615i	0.206041	−	0.356873i
$213$	6.00000	+	10.3923i	0.411113	+	0.712069i
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	−2.00000	+	3.46410i	−0.136399	+	0.236250i
$216$	1.00000			0.0680414
$217$		0			0
$218$	−14.0000			−0.948200
$219$	5.00000	−	8.66025i	0.337869	−	0.585206i
$220$		0			0
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$	5.00000	−	8.66025i	0.335578	−	0.581238i
$223$	−8.00000			−0.535720			−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000			−0.535720			−0.267860	+	0.963458i	$0.586316\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	3.00000	−	5.19615i	0.199557	−	0.345643i
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	0.993508	−	0.113761i	$-0.0362899\pi$
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	−0.595274	+	0.803523i	$0.702957\pi$
$228$	−4.00000	−	6.92820i	−0.264906	−	0.458831i
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	−0.536515	−	0.843891i	$-0.680260\pi$
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	0.999088	+	0.0426906i	$0.0135930\pi$
$230$		0			0
$231$		0			0
$232$	−6.00000			−0.393919
$233$	−15.0000	+	25.9808i	−0.982683	+	1.70206i	−0.330870	+	0.943676i	$0.607342\pi$
$233$	−15.0000	+	25.9808i	−0.982683	+	1.70206i	−0.651813	+	0.758380i	$0.725991\pi$
$234$	−1.00000	−	1.73205i	−0.0653720	−	0.113228i
$235$		0			0
$236$	−6.00000	+	10.3923i	−0.390567	+	0.676481i
$237$	−8.00000			−0.519656
$238$		0			0
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	13.0000	+	22.5167i	0.837404	+	1.45043i	0.892058	+	0.451920i	$0.149261\pi$
$241$	13.0000	+	22.5167i	0.837404	+	1.45043i	−0.0546547	+	0.998505i	$0.517406\pi$
$242$	−5.50000	−	9.52628i	−0.353553	−	0.612372i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	10.0000			0.640184
$245$		0			0
$246$	6.00000			0.382546
$247$	−8.00000	+	13.8564i	−0.509028	+	0.881662i
$248$	2.00000	+	3.46410i	0.127000	+	0.219971i
$249$	−6.00000	−	10.3923i	−0.380235	−	0.658586i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$		0			0
$254$	4.00000	−	6.92820i	0.250982	−	0.434714i
$255$	−3.00000	−	5.19615i	−0.187867	−	0.325396i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−15.0000	+	25.9808i	−0.935674	+	1.62064i	−0.162247	+	0.986750i	$0.551874\pi$
$257$	−15.0000	+	25.9808i	−0.935674	+	1.62064i	−0.773427	+	0.633885i	$0.781459\pi$
$258$	−4.00000			−0.249029
$259$		0			0
$260$	2.00000			0.124035
$261$	−3.00000	+	5.19615i	−0.185695	+	0.321634i
$262$	6.00000	+	10.3923i	0.370681	+	0.642039i
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	0.952517	+	0.304487i	$0.0984850\pi$
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	−0.212565	+	0.977147i	$0.568182\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$		0			0
$267$	−6.00000			−0.367194
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	−0.998361	−	0.0572259i	$-0.981774\pi$
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	−0.384201	−	0.923249i	$-0.625523\pi$
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	0.991658	−	0.128897i	$-0.0411435\pi$
$272$	6.00000			0.363803
$273$		0			0
$274$	−6.00000			−0.362473
$275$		0			0
$276$		0			0
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	0.976231	−	0.216731i	$-0.0695395\pi$
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	−0.675810	+	0.737075i	$0.736206\pi$
$278$	8.00000	−	13.8564i	0.479808	−	0.831052i
$279$	4.00000			0.239474
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$		0			0
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$	4.00000	−	6.92820i	0.236940	−	0.410391i
$286$		0			0
$287$		0			0
$288$	−1.00000			−0.0589256
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	−3.00000	−	5.19615i	−0.176166	−	0.305129i
$291$	5.00000	+	8.66025i	0.293105	+	0.507673i
$292$	−5.00000	+	8.66025i	−0.292603	+	0.506803i
$293$	−30.0000			−1.75262			−0.876309	−	0.481749i	$-0.840002\pi$
$293$	−30.0000			−1.75262			−0.876309	+	0.481749i	$0.840002\pi$
$294$		0			0
$295$	−12.0000			−0.698667
$296$	−5.00000	+	8.66025i	−0.290619	+	0.503367i
$297$		0			0
$298$	3.00000	+	5.19615i	0.173785	+	0.301005i
$299$		0			0
$300$	−1.00000			−0.0577350
$301$		0			0
$302$	−8.00000			−0.460348
$303$	−3.00000	+	5.19615i	−0.172345	+	0.298511i
$304$	4.00000	+	6.92820i	0.229416	+	0.397360i
$305$	5.00000	+	8.66025i	0.286299	+	0.495885i
$306$	3.00000	−	5.19615i	0.171499	−	0.297044i
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$	−2.00000	+	3.46410i	−0.113592	+	0.196748i
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	0.974841	+	0.222900i	$0.0715523\pi$
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	−0.294384	+	0.955687i	$0.595114\pi$
$312$	1.00000	+	1.73205i	0.0566139	+	0.0980581i
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	−0.597522	−	0.801852i	$-0.703848\pi$
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	0.993186	+	0.116543i	$0.0371814\pi$
$314$	−22.0000			−1.24153
$315$		0			0
$316$	8.00000			0.450035
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	0.494489	+	0.869184i	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$	3.00000	+	5.19615i	0.168232	+	0.291386i
$319$		0			0
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−12.0000			−0.669775
$322$		0			0
$323$	−48.0000			−2.67079
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	1.00000	+	1.73205i	0.0554700	+	0.0960769i
$326$	10.0000	+	17.3205i	0.553849	+	0.959294i
$327$	7.00000	−	12.1244i	0.387101	−	0.670478i
$328$	−6.00000			−0.331295
$329$		0			0
$330$		0			0
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$	6.00000	+	10.3923i	0.329293	+	0.570352i
$333$	5.00000	+	8.66025i	0.273998	+	0.474579i
$334$		0			0
$335$	4.00000			0.218543
$336$		0			0
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$	3.00000	+	5.19615i	0.162938	+	0.282216i
$340$	3.00000	+	5.19615i	0.162698	+	0.281801i
$341$		0			0
$342$	8.00000			0.432590
$343$		0			0
$344$	4.00000			0.215666
$345$		0			0
$346$	−3.00000	−	5.19615i	−0.161281	−	0.279347i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$	3.00000	−	5.19615i	0.160817	−	0.278543i
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$		0			0
$351$	2.00000			0.106752
$352$		0			0
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	0.775077	−	0.631867i	$-0.217711\pi$
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	−0.934751	+	0.355303i	$0.884378\pi$
$354$	−6.00000	−	10.3923i	−0.318896	−	0.552345i
$355$	6.00000	−	10.3923i	0.318447	−	0.551566i
$356$	6.00000			0.317999
$357$		0			0
$358$	24.0000			1.26844
$359$	6.00000	−	10.3923i	0.316668	−	0.548485i	−0.663123	−	0.748511i	$-0.730769\pi$
$359$	6.00000	−	10.3923i	0.316668	−	0.548485i	0.979791	+	0.200026i	$0.0641026\pi$
$360$	−0.500000	−	0.866025i	−0.0263523	−	0.0456435i
$361$	−22.5000	−	38.9711i	−1.18421	−	2.05111i
$362$	5.00000	−	8.66025i	0.262794	−	0.455173i
$363$	11.0000			0.577350
$364$		0			0
$365$	−10.0000			−0.523424
$366$	−5.00000	+	8.66025i	−0.261354	+	0.452679i
$367$	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	$0.766378\pi$
$368$		0			0
$369$	−3.00000	+	5.19615i	−0.156174	+	0.270501i
$370$	−10.0000			−0.519875
$371$		0			0
$372$	−4.00000			−0.207390
$373$	17.0000	−	29.4449i	0.880227	−	1.52460i	0.0291379	−	0.999575i	$-0.490724\pi$
$373$	17.0000	−	29.4449i	0.880227	−	1.52460i	0.851089	−	0.525022i	$-0.175943\pi$
$374$		0			0
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$		0			0
$377$	−12.0000			−0.618031
$378$		0			0
$379$	−4.00000			−0.205466			−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000			−0.205466			−0.102733	+	0.994709i	$0.532759\pi$
$380$	−4.00000	+	6.92820i	−0.205196	+	0.355409i
$381$	4.00000	+	6.92820i	0.204926	+	0.354943i
$382$	6.00000	+	10.3923i	0.306987	+	0.531717i
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	−0.377531	−	0.925997i	$-0.623227\pi$
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	0.990702	−	0.136047i	$-0.0434398\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−2.00000			−0.101797
$387$	2.00000	−	3.46410i	0.101666	−	0.176090i
$388$	−5.00000	−	8.66025i	−0.253837	−	0.439658i
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	0.779895	−	0.625910i	$-0.215272\pi$
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	−0.932002	+	0.362454i	$0.881939\pi$
$390$	−1.00000	+	1.73205i	−0.0506370	+	0.0877058i
$391$		0			0
$392$		0			0
$393$	−12.0000			−0.605320
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$	4.00000	+	6.92820i	0.201262	+	0.348596i
$396$		0			0
$397$	1.00000	−	1.73205i	0.0501886	−	0.0869291i	−0.839840	−	0.542834i	$-0.817351\pi$
$397$	1.00000	−	1.73205i	0.0501886	−	0.0869291i	0.890028	+	0.455905i	$0.150684\pi$
$398$	20.0000			1.00251
$399$		0			0
$400$	1.00000			0.0500000
$401$	15.0000	−	25.9808i	0.749064	−	1.29742i	−0.199207	−	0.979957i	$-0.563837\pi$
$401$	15.0000	−	25.9808i	0.749064	−	1.29742i	0.948272	−	0.317460i	$-0.102830\pi$
$402$	2.00000	+	3.46410i	0.0997509	+	0.172774i
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$	3.00000	−	5.19615i	0.149256	−	0.258518i
$405$	−1.00000			−0.0496904
$406$		0			0
$407$		0			0
$408$	−3.00000	+	5.19615i	−0.148522	+	0.257248i
$409$	13.0000	+	22.5167i	0.642809	+	1.11338i	0.984803	+	0.173675i	$0.0555643\pi$
$409$	13.0000	+	22.5167i	0.642809	+	1.11338i	−0.341994	+	0.939702i	$0.611102\pi$
$410$	−3.00000	−	5.19615i	−0.148159	−	0.256620i
$411$	3.00000	−	5.19615i	0.147979	−	0.256307i
$412$	−8.00000			−0.394132
$413$		0			0
$414$		0			0
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	8.00000	+	13.8564i	0.391762	+	0.678551i
$418$		0			0
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$	38.0000			1.85201			0.926003	−	0.377515i	$-0.123221\pi$
$421$	38.0000			1.85201			0.926003	+	0.377515i	$0.123221\pi$
$422$	−2.00000	+	3.46410i	−0.0973585	+	0.168630i
$423$		0			0
$424$	−3.00000	−	5.19615i	−0.145693	−	0.252347i
$425$	−3.00000	+	5.19615i	−0.145521	+	0.252050i
$426$	12.0000			0.581402
$427$		0			0
$428$	12.0000			0.580042
$429$		0			0
$430$	2.00000	+	3.46410i	0.0964486	+	0.167054i
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	0.973574	−	0.228373i	$-0.0733406\pi$
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	−0.684564	+	0.728953i	$0.740007\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	10.0000			0.480569			0.240285	−	0.970702i	$-0.422759\pi$
$433$	10.0000			0.480569			0.240285	+	0.970702i	$0.422759\pi$
$434$		0			0
$435$	6.00000			0.287678
$436$	−7.00000	+	12.1244i	−0.335239	+	0.580651i
$437$		0			0
$438$	−5.00000	−	8.66025i	−0.238909	−	0.413803i
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	0.310228	+	0.950662i	$0.399595\pi$
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	−0.978412	+	0.206666i	$0.933739\pi$
$440$		0			0
$441$		0			0
$442$	12.0000			0.570782
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	−0.687557	−	0.726130i	$-0.741317\pi$
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	0.972626	+	0.232377i	$0.0746503\pi$
$444$	−5.00000	−	8.66025i	−0.237289	−	0.410997i
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$	−4.00000	+	6.92820i	−0.189405	+	0.328060i
$447$	−6.00000			−0.283790
$448$		0			0
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$	0.500000	−	0.866025i	0.0235702	−	0.0408248i
$451$		0			0
$452$	−3.00000	−	5.19615i	−0.141108	−	0.244406i
$453$	4.00000	−	6.92820i	0.187936	−	0.325515i
$454$	12.0000			0.563188
$455$		0			0
$456$	−8.00000			−0.374634
$457$	−1.00000	+	1.73205i	−0.0467780	+	0.0810219i	−0.888466	−	0.458942i	$-0.848229\pi$
$457$	−1.00000	+	1.73205i	−0.0467780	+	0.0810219i	0.841688	+	0.539964i	$0.181562\pi$
$458$	−7.00000	−	12.1244i	−0.327089	−	0.566534i
$459$	3.00000	+	5.19615i	0.140028	+	0.242536i
$460$		0			0
$461$	18.0000			0.838344			0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$		0			0
$463$	−40.0000			−1.85896			−0.929479	−	0.368875i	$-0.879743\pi$
$463$	−40.0000			−1.85896			−0.929479	+	0.368875i	$0.879743\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	−2.00000	−	3.46410i	−0.0927478	−	0.160644i
$466$	15.0000	+	25.9808i	0.694862	+	1.20354i
$467$	−18.0000	+	31.1769i	−0.832941	+	1.44270i	0.0627555	+	0.998029i	$0.480011\pi$
$467$	−18.0000	+	31.1769i	−0.832941	+	1.44270i	−0.895696	+	0.444667i	$0.853322\pi$
$468$	−2.00000			−0.0924500
$469$		0			0
$470$		0			0
$471$	11.0000	−	19.0526i	0.506853	−	0.877896i
$472$	6.00000	+	10.3923i	0.276172	+	0.478345i
$473$		0			0
$474$	−4.00000	+	6.92820i	−0.183726	+	0.318223i
$475$	−8.00000			−0.367065
$476$		0			0
$477$	−6.00000			−0.274721
$478$	−6.00000	+	10.3923i	−0.274434	+	0.475333i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$	0.500000	+	0.866025i	0.0228218	+	0.0395285i
$481$	−10.0000	+	17.3205i	−0.455961	+	0.789747i
$482$	26.0000			1.18427
$483$		0			0
$484$	−11.0000			−0.500000
$485$	5.00000	−	8.66025i	0.227038	−	0.393242i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−16.0000	−	27.7128i	−0.725029	−	1.25579i	−0.958962	−	0.283535i	$-0.908493\pi$
$487$	−16.0000	−	27.7128i	−0.725029	−	1.25579i	0.233933	−	0.972253i	$-0.424840\pi$
$488$	5.00000	−	8.66025i	0.226339	−	0.392031i
$489$	−20.0000			−0.904431
$490$		0			0
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$	3.00000	−	5.19615i	0.135250	−	0.234261i
$493$	−18.0000	−	31.1769i	−0.810679	−	1.40414i
$494$	8.00000	+	13.8564i	0.359937	+	0.623429i
$495$		0			0
$496$	4.00000			0.179605
$497$		0			0
$498$	−12.0000			−0.537733
$499$	−10.0000	+	17.3205i	−0.447661	+	0.775372i	−0.998233	−	0.0594153i	$-0.981076\pi$
$499$	−10.0000	+	17.3205i	−0.447661	+	0.775372i	0.550572	+	0.834788i	$0.314410\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		0			0
$502$	6.00000	−	10.3923i	0.267793	−	0.463831i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	6.00000			0.266996
$506$		0			0
$507$	−4.50000	−	7.79423i	−0.199852	−	0.346154i
$508$	−4.00000	−	6.92820i	−0.177471	−	0.307389i
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$	−6.00000			−0.265684
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−4.00000	+	6.92820i	−0.176604	+	0.305888i
$514$	15.0000	+	25.9808i	0.661622	+	1.14596i
$515$	−4.00000	−	6.92820i	−0.176261	−	0.305293i
$516$	−2.00000	+	3.46410i	−0.0880451	+	0.152499i
$517$		0			0
$518$		0			0
$519$	6.00000			0.263371
$520$	1.00000	−	1.73205i	0.0438529	−	0.0759555i
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	0.792797	−	0.609486i	$-0.208624\pi$
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	−0.924229	+	0.381839i	$0.875291\pi$
$522$	3.00000	+	5.19615i	0.131306	+	0.227429i
$523$	−14.0000	+	24.2487i	−0.612177	+	1.06032i	0.378695	+	0.925521i	$0.376373\pi$
$523$	−14.0000	+	24.2487i	−0.612177	+	1.06032i	−0.990873	+	0.134801i	$0.956961\pi$
$524$	12.0000			0.524222
$525$		0			0
$526$	24.0000			1.04645
$527$	−12.0000	+	20.7846i	−0.522728	+	0.905392i
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	3.00000	−	5.19615i	0.130312	−	0.225706i
$531$	12.0000			0.520756
$532$		0			0
$533$	−12.0000			−0.519778
$534$	−3.00000	+	5.19615i	−0.129823	+	0.224860i
$535$	6.00000	+	10.3923i	0.259403	+	0.449299i
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$	−12.0000	+	20.7846i	−0.517838	+	0.896922i
$538$	−18.0000			−0.776035
$539$		0			0
$540$	1.00000			0.0430331
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	−0.225617	−	0.974216i	$-0.572440\pi$
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	0.956504	−	0.291718i	$-0.0942267\pi$
$542$	−10.0000	−	17.3205i	−0.429537	−	0.743980i
$543$	5.00000	+	8.66025i	0.214571	+	0.371647i
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$	−14.0000			−0.599694
$546$		0			0
$547$	44.0000			1.88130			0.940652	−	0.339372i	$-0.110215\pi$
$547$	44.0000			1.88130			0.940652	+	0.339372i	$0.110215\pi$
$548$	−3.00000	+	5.19615i	−0.128154	+	0.221969i
$549$	−5.00000	−	8.66025i	−0.213395	−	0.369611i
$550$		0			0
$551$	24.0000	−	41.5692i	1.02243	−	1.77091i
$552$		0			0
$553$		0			0
$554$	10.0000			0.424859
$555$	5.00000	−	8.66025i	0.212238	−	0.367607i
$556$	−8.00000	−	13.8564i	−0.339276	−	0.587643i
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	0.609912	−	0.792469i	$-0.291205\pi$
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	−0.991254	+	0.131965i	$0.957871\pi$
$558$	2.00000	−	3.46410i	0.0846668	−	0.146647i
$559$	8.00000			0.338364
$560$		0			0
$561$		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
$565$	3.00000	−	5.19615i	0.126211	−	0.218604i
$566$	−4.00000			−0.168133
$567$		0			0
$568$	−12.0000			−0.503509
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	0.922032	+	0.387113i	$0.126528\pi$
$570$	−4.00000	−	6.92820i	−0.167542	−	0.290191i
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	0.904835	−	0.425762i	$-0.139994\pi$
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	−0.821138	+	0.570730i	$0.806660\pi$
$572$		0			0
$573$	−12.0000			−0.501307
$574$		0			0
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−5.00000	−	8.66025i	−0.208153	−	0.360531i	0.742980	−	0.669314i	$-0.233412\pi$
$577$	−5.00000	−	8.66025i	−0.208153	−	0.360531i	−0.951133	+	0.308783i	$0.900078\pi$
$578$	9.50000	+	16.4545i	0.395148	+	0.684416i
$579$	1.00000	−	1.73205i	0.0415586	−	0.0719816i
$580$	−6.00000			−0.249136
$581$		0			0
$582$	10.0000			0.414513
$583$		0			0
$584$	5.00000	+	8.66025i	0.206901	+	0.358364i
$585$	−1.00000	−	1.73205i	−0.0413449	−	0.0716115i
$586$	−15.0000	+	25.9808i	−0.619644	+	1.07326i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	−32.0000			−1.31854
$590$	−6.00000	+	10.3923i	−0.247016	+	0.427844i
$591$	9.00000	+	15.5885i	0.370211	+	0.641223i
$592$	5.00000	+	8.66025i	0.205499	+	0.355934i
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	−0.921026	−	0.389501i	$-0.872647\pi$
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	0.797831	+	0.602881i	$0.205981\pi$
$594$		0			0
$595$		0			0
$596$	6.00000			0.245770
$597$	−10.0000	+	17.3205i	−0.409273	+	0.708881i
$598$		0			0
$599$	−18.0000	−	31.1769i	−0.735460	−	1.27385i	−0.954521	−	0.298143i	$-0.903633\pi$
$599$	−18.0000	−	31.1769i	−0.735460	−	1.27385i	0.219061	−	0.975711i	$-0.429701\pi$
$600$	−0.500000	+	0.866025i	−0.0204124	+	0.0353553i
$601$	−2.00000			−0.0815817			−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000			−0.0815817			−0.0407909	+	0.999168i	$0.512988\pi$
$602$		0			0
$603$	−4.00000			−0.162893
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	−5.50000	−	9.52628i	−0.223607	−	0.387298i
$606$	3.00000	+	5.19615i	0.121867	+	0.211079i
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	−0.773358	−	0.633970i	$-0.781424\pi$
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	0.935713	+	0.352763i	$0.114758\pi$
$608$	8.00000			0.324443
$609$		0			0
$610$	10.0000			0.404888
$611$		0			0
$612$	−3.00000	−	5.19615i	−0.121268	−	0.210042i
$613$	−19.0000	−	32.9090i	−0.767403	−	1.32918i	−0.938967	−	0.344008i	$-0.888215\pi$
$613$	−19.0000	−	32.9090i	−0.767403	−	1.32918i	0.171564	−	0.985173i	$-0.445118\pi$
$614$	2.00000	−	3.46410i	0.0807134	−	0.139800i
$615$	6.00000			0.241943
$616$		0			0
$617$	−18.0000			−0.724653			−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000			−0.724653			−0.362326	+	0.932051i	$0.618017\pi$
$618$	4.00000	−	6.92820i	0.160904	−	0.278693i
$619$	16.0000	+	27.7128i	0.643094	+	1.11387i	0.984738	+	0.174042i	$0.0556830\pi$
$619$	16.0000	+	27.7128i	0.643094	+	1.11387i	−0.341644	+	0.939829i	$0.610984\pi$
$620$	2.00000	+	3.46410i	0.0803219	+	0.139122i
$621$		0			0
$622$	24.0000			0.962312
$623$		0			0
$624$	2.00000			0.0800641
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−7.00000	−	12.1244i	−0.279776	−	0.484587i
$627$		0			0
$628$	−11.0000	+	19.0526i	−0.438948	+	0.760280i
$629$	−60.0000			−2.39236
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	4.00000	−	6.92820i	0.159111	−	0.275589i
$633$	−2.00000	−	3.46410i	−0.0794929	−	0.137686i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	4.00000	−	6.92820i	0.158735	−	0.274937i
$636$	6.00000			0.237915
$637$		0			0
$638$		0			0
$639$	−6.00000	+	10.3923i	−0.237356	+	0.411113i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−21.0000	−	36.3731i	−0.829450	−	1.43665i	−0.898470	−	0.439034i	$-0.855321\pi$
$641$	−21.0000	−	36.3731i	−0.829450	−	1.43665i	0.0690201	−	0.997615i	$-0.478013\pi$
$642$	−6.00000	+	10.3923i	−0.236801	+	0.410152i
$643$	4.00000			0.157745			0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000			0.157745			0.0788723	+	0.996885i	$0.474868\pi$
$644$		0			0
$645$	−4.00000			−0.157500
$646$	−24.0000	+	41.5692i	−0.944267	+	1.63552i
$647$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$647$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$		0			0
$650$	2.00000			0.0784465
$651$		0			0
$652$	20.0000			0.783260
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	−0.801337	−	0.598213i	$-0.795878\pi$
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	0.918736	+	0.394872i	$0.129211\pi$
$654$	−7.00000	−	12.1244i	−0.273722	−	0.474100i
$655$	6.00000	+	10.3923i	0.234439	+	0.406061i
$656$	−3.00000	+	5.19615i	−0.117130	+	0.202876i
$657$	10.0000			0.390137
$658$		0			0
$659$	48.0000			1.86981			0.934907	−	0.354892i	$-0.115482\pi$
$659$	48.0000			1.86981			0.934907	+	0.354892i	$0.115482\pi$
$660$		0			0
$661$	−17.0000	−	29.4449i	−0.661223	−	1.14527i	−0.980294	−	0.197542i	$-0.936704\pi$
$661$	−17.0000	−	29.4449i	−0.661223	−	1.14527i	0.319071	−	0.947731i	$-0.396629\pi$
$662$	−14.0000	−	24.2487i	−0.544125	−	0.942453i
$663$	−6.00000	+	10.3923i	−0.233021	+	0.403604i
$664$	12.0000			0.465690
$665$		0			0
$666$	10.0000			0.387492
$667$		0			0
$668$		0			0
$669$	−4.00000	−	6.92820i	−0.154649	−	0.267860i
$670$	2.00000	−	3.46410i	0.0772667	−	0.133830i
$671$		0			0
$672$		0			0
$673$	26.0000			1.00223			0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000			1.00223			0.501113	+	0.865382i	$0.332924\pi$
$674$	1.00000	−	1.73205i	0.0385186	−	0.0667161i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	−0.985517	−	0.169580i	$-0.945759\pi$
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	0.639618	+	0.768693i	$0.279092\pi$
$678$	6.00000			0.230429
$679$		0			0
$680$	6.00000			0.230089
$681$	−6.00000	+	10.3923i	−0.229920	+	0.398234i
$682$		0			0
$683$	−18.0000	−	31.1769i	−0.688751	−	1.19295i	−0.972242	−	0.233977i	$-0.924826\pi$
$683$	−18.0000	−	31.1769i	−0.688751	−	1.19295i	0.283491	−	0.958975i	$-0.408507\pi$
$684$	4.00000	−	6.92820i	0.152944	−	0.264906i
$685$	−6.00000			−0.229248
$686$		0			0
$687$	14.0000			0.534133
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$		0			0
$691$	−8.00000	+	13.8564i	−0.304334	+	0.527123i	−0.977113	−	0.212721i	$-0.931767\pi$
$691$	−8.00000	+	13.8564i	−0.304334	+	0.527123i	0.672779	+	0.739844i	$0.265101\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	12.0000			0.455514
$695$	8.00000	−	13.8564i	0.303457	−	0.525603i
$696$	−3.00000	−	5.19615i	−0.113715	−	0.196960i
$697$	−18.0000	−	31.1769i	−0.681799	−	1.18091i
$698$	5.00000	−	8.66025i	0.189253	−	0.327795i
$699$	−30.0000			−1.13470
$700$		0			0
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$	1.00000	−	1.73205i	0.0377426	−	0.0653720i
$703$	−40.0000	−	69.2820i	−1.50863	−	2.61302i
$704$		0			0
$705$		0			0
$706$	−6.00000			−0.225813
$707$		0			0
$708$	−12.0000			−0.450988
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	−0.756730	−	0.653727i	$-0.773204\pi$
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	0.944509	+	0.328484i	$0.106538\pi$
$710$	−6.00000	−	10.3923i	−0.225176	−	0.390016i
$711$	−4.00000	−	6.92820i	−0.150012	−	0.259828i
$712$	3.00000	−	5.19615i	0.112430	−	0.194734i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	12.0000	−	20.7846i	0.448461	−	0.776757i
$717$	−6.00000	−	10.3923i	−0.224074	−	0.388108i
$718$	−6.00000	−	10.3923i	−0.223918	−	0.387837i
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	−0.998224	−	0.0595683i	$-0.981028\pi$
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	0.550700	+	0.834703i	$0.314361\pi$
$720$	−1.00000			−0.0372678
$721$		0			0
$722$	−45.0000			−1.67473
$723$	−13.0000	+	22.5167i	−0.483475	+	0.837404i
$724$	−5.00000	−	8.66025i	−0.185824	−	0.321856i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	5.50000	−	9.52628i	0.204124	−	0.353553i
$727$	−32.0000			−1.18681			−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000			−1.18681			−0.593407	+	0.804902i	$0.702218\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−5.00000	+	8.66025i	−0.185058	+	0.320530i
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$	5.00000	+	8.66025i	0.184805	+	0.320092i
$733$	1.00000	−	1.73205i	0.0369358	−	0.0639748i	−0.846967	−	0.531646i	$-0.821574\pi$
$733$	1.00000	−	1.73205i	0.0369358	−	0.0639748i	0.883902	+	0.467671i	$0.154907\pi$
$734$	8.00000			0.295285
$735$		0			0
$736$		0			0
$737$		0			0
$738$	3.00000	+	5.19615i	0.110432	+	0.191273i
$739$	14.0000	+	24.2487i	0.514998	+	0.892003i	0.999849	+	0.0174060i	$0.00554079\pi$
$739$	14.0000	+	24.2487i	0.514998	+	0.892003i	−0.484850	+	0.874597i	$0.661126\pi$
$740$	−5.00000	+	8.66025i	−0.183804	+	0.318357i
$741$	−16.0000			−0.587775
$742$		0			0
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$	−2.00000	+	3.46410i	−0.0733236	+	0.127000i
$745$	3.00000	+	5.19615i	0.109911	+	0.190372i
$746$	−17.0000	−	29.4449i	−0.622414	−	1.07805i
$747$	6.00000	−	10.3923i	0.219529	−	0.380235i
$748$		0			0
$749$		0			0
$750$	−1.00000			−0.0365148
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	−0.929731	−	0.368238i	$-0.879961\pi$
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	0.783769	+	0.621052i	$0.213294\pi$
$752$		0			0
$753$	6.00000	+	10.3923i	0.218652	+	0.378717i
$754$	−6.00000	+	10.3923i	−0.218507	+	0.378465i
$755$	−8.00000			−0.291150
$756$		0			0
$757$	−34.0000			−1.23575			−0.617876	−	0.786276i	$-0.712006\pi$
$757$	−34.0000			−1.23575			−0.617876	+	0.786276i	$0.712006\pi$
$758$	−2.00000	+	3.46410i	−0.0726433	+	0.125822i
$759$		0			0
$760$	4.00000	+	6.92820i	0.145095	+	0.251312i
$761$	−3.00000	+	5.19615i	−0.108750	+	0.188360i	−0.915264	−	0.402854i	$-0.868018\pi$
$761$	−3.00000	+	5.19615i	−0.108750	+	0.188360i	0.806514	+	0.591215i	$0.201351\pi$
$762$	8.00000			0.289809
$763$		0			0
$764$	12.0000			0.434145
$765$	3.00000	−	5.19615i	0.108465	−	0.187867i
$766$	−12.0000	−	20.7846i	−0.433578	−	0.750978i
$767$	12.0000	+	20.7846i	0.433295	+	0.750489i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−26.0000			−0.937584			−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000			−0.937584			−0.468792	+	0.883309i	$0.655311\pi$
$770$		0			0
$771$	−30.0000			−1.08042
$772$	−1.00000	+	1.73205i	−0.0359908	+	0.0623379i
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	0.657542	−	0.753418i	$-0.271596\pi$
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	−0.981250	+	0.192740i	$0.938263\pi$
$774$	−2.00000	−	3.46410i	−0.0718885	−	0.124515i
$775$	−2.00000	+	3.46410i	−0.0718421	+	0.124434i
$776$	−10.0000			−0.358979
$777$		0			0
$778$	−6.00000			−0.215110
$779$	24.0000	−	41.5692i	0.859889	−	1.48937i
$780$	1.00000	+	1.73205i	0.0358057	+	0.0620174i
$781$		0			0
$782$		0			0
$783$	−6.00000			−0.214423
$784$		0			0
$785$	−22.0000			−0.785214
$786$	−6.00000	+	10.3923i	−0.214013	+	0.370681i
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	0.828176	−	0.560469i	$-0.189379\pi$
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	−0.899468	+	0.436987i	$0.856046\pi$
$788$	−9.00000	−	15.5885i	−0.320612	−	0.555316i
$789$	−12.0000	+	20.7846i	−0.427211	+	0.739952i
$790$	8.00000			0.284627
$791$		0			0
$792$		0			0
$793$	10.0000	−	17.3205i	0.355110	−	0.615069i
$794$	−1.00000	−	1.73205i	−0.0354887	−	0.0614682i
$795$	3.00000	+	5.19615i	0.106399	+	0.184289i
$796$	10.0000	−	17.3205i	0.354441	−	0.613909i
$797$	42.0000			1.48772			0.743858	−	0.668338i	$-0.232994\pi$
$797$	42.0000			1.48772			0.743858	+	0.668338i	$0.232994\pi$
$798$		0			0
$799$		0			0
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−3.00000	−	5.19615i	−0.106000	−	0.183597i
$802$	−15.0000	−	25.9808i	−0.529668	−	0.917413i
$803$		0			0
$804$	4.00000			0.141069
$805$		0			0
$806$	8.00000			0.281788
$807$	9.00000	−	15.5885i	0.316815	−	0.548740i
$808$	−3.00000	−	5.19615i	−0.105540	−	0.182800i
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	0.999491	+	0.0319002i	$0.0101559\pi$
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	−0.472119	+	0.881535i	$0.656511\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	16.0000			0.561836			0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000			0.561836			0.280918	+	0.959732i	$0.409361\pi$
$812$		0			0
$813$	20.0000			0.701431
$814$		0			0
$815$	10.0000	+	17.3205i	0.350285	+	0.606711i
$816$	3.00000	+	5.19615i	0.105021	+	0.181902i
$817$	−16.0000	+	27.7128i	−0.559769	+	0.969549i
$818$	26.0000			0.909069
$819$		0			0
$820$	−6.00000			−0.209529
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	−0.665144	−	0.746715i	$-0.731630\pi$
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	0.979246	+	0.202674i	$0.0649632\pi$
$822$	−3.00000	−	5.19615i	−0.104637	−	0.181237i
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	−0.997686	−	0.0679910i	$-0.978341\pi$
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	0.439961	−	0.898017i	$-0.354992\pi$
$824$	−4.00000	+	6.92820i	−0.139347	+	0.241355i
$825$		0			0
$826$		0			0
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$		0			0
$829$	−17.0000	−	29.4449i	−0.590434	−	1.02266i	−0.994174	−	0.107788i	$-0.965623\pi$
$829$	−17.0000	−	29.4449i	−0.590434	−	1.02266i	0.403739	−	0.914874i	$-0.367710\pi$
$830$	6.00000	+	10.3923i	0.208263	+	0.360722i
$831$	−5.00000	+	8.66025i	−0.173448	+	0.300421i
$832$	−2.00000			−0.0693375
$833$		0			0
$834$	16.0000			0.554035
$835$		0			0
$836$		0			0
$837$	2.00000	+	3.46410i	0.0691301	+	0.119737i
$838$	6.00000	−	10.3923i	0.207267	−	0.358996i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	19.0000	−	32.9090i	0.654783	−	1.13412i
$843$	9.00000	+	15.5885i	0.309976	+	0.536895i
$844$	2.00000	+	3.46410i	0.0688428	+	0.119239i
$845$	−4.50000	+	7.79423i	−0.154805	+	0.268130i
$846$		0			0
$847$		0			0
$848$	−6.00000			−0.206041
$849$	2.00000	−	3.46410i	0.0686398	−	0.118888i
$850$	3.00000	+	5.19615i	0.102899	+	0.178227i
$851$		0			0
$852$	6.00000	−	10.3923i	0.205557	−	0.356034i
$853$	−26.0000			−0.890223			−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000			−0.890223			−0.445112	+	0.895475i	$0.646836\pi$
$854$		0			0
$855$	8.00000			0.273594
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	−3.00000	−	5.19615i	−0.102478	−	0.177497i	0.810227	−	0.586116i	$-0.199344\pi$
$857$	−3.00000	−	5.19615i	−0.102478	−	0.177497i	−0.912705	+	0.408619i	$0.866010\pi$
$858$		0			0
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	0.291858	+	0.956462i	$0.405727\pi$
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	−0.974249	+	0.225475i	$0.927607\pi$
$860$	4.00000			0.136399
$861$		0			0
$862$	12.0000			0.408722
$863$	12.0000	−	20.7846i	0.408485	−	0.707516i	−0.586235	−	0.810141i	$-0.699391\pi$
$863$	12.0000	−	20.7846i	0.408485	−	0.707516i	0.994720	+	0.102624i	$0.0327240\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−3.00000	−	5.19615i	−0.102003	−	0.176674i
$866$	5.00000	−	8.66025i	0.169907	−	0.294287i
$867$	−19.0000			−0.645274
$868$		0			0
$869$		0			0
$870$	3.00000	−	5.19615i	0.101710	−	0.176166i
$871$	−4.00000	−	6.92820i	−0.135535	−	0.234753i
$872$	7.00000	+	12.1244i	0.237050	+	0.410582i
$873$	−5.00000	+	8.66025i	−0.169224	+	0.293105i
$874$		0			0
$875$		0			0
$876$	−10.0000			−0.337869
$877$	−7.00000	+	12.1244i	−0.236373	+	0.409410i	−0.959671	−	0.281126i	$-0.909292\pi$
$877$	−7.00000	+	12.1244i	−0.236373	+	0.409410i	0.723298	+	0.690536i	$0.242625\pi$
$878$	14.0000	+	24.2487i	0.472477	+	0.818354i
$879$	−15.0000	−	25.9808i	−0.505937	−	0.876309i
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		0			0
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$	6.00000	−	10.3923i	0.201802	−	0.349531i
$885$	−6.00000	−	10.3923i	−0.201688	−	0.349334i
$886$	−6.00000	−	10.3923i	−0.201574	−	0.349136i
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	−0.591156	−	0.806557i	$-0.701328\pi$
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	0.994077	+	0.108678i	$0.0346618\pi$
$888$	−10.0000			−0.335578
$889$		0			0
$890$	6.00000			0.201120
$891$		0			0
$892$	4.00000	+	6.92820i	0.133930	+	0.231973i
$893$		0			0
$894$	−3.00000	+	5.19615i	−0.100335	+	0.173785i
$895$	24.0000			0.802232
$896$		0			0
$897$		0			0
$898$	9.00000	−	15.5885i	0.300334	−	0.520194i
$899$	−12.0000	−	20.7846i	−0.400222	−	0.693206i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	18.0000	−	31.1769i	0.599667	−	1.03865i
$902$		0			0
$903$		0			0
$904$	−6.00000			−0.199557
$905$	5.00000	−	8.66025i	0.166206	−	0.287877i
$906$	−4.00000	−	6.92820i	−0.132891	−	0.230174i
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	0.999195	−	0.0401089i	$-0.0127705\pi$
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	−0.534333	+	0.845274i	$0.679437\pi$
$908$	6.00000	−	10.3923i	0.199117	−	0.344881i
$909$	−6.00000			−0.199007
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	−4.00000	+	6.92820i	−0.132453	+	0.229416i
$913$		0			0
$914$	1.00000	+	1.73205i	0.0330771	+	0.0572911i
$915$	−5.00000	+	8.66025i	−0.165295	+	0.286299i
$916$	−14.0000			−0.462573
$917$		0			0
$918$	6.00000			0.198030
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	0.471684	+	0.881768i	$0.343646\pi$
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	−0.999475	+	0.0323936i	$0.989687\pi$
$920$		0			0
$921$	2.00000	+	3.46410i	0.0659022	+	0.114146i
$922$	9.00000	−	15.5885i	0.296399	−	0.513378i
$923$	−24.0000			−0.789970
$924$		0			0
$925$	−10.0000			−0.328798
$926$	−20.0000	+	34.6410i	−0.657241	+	1.13837i
$927$	4.00000	+	6.92820i	0.131377	+	0.227552i
$928$	3.00000	+	5.19615i	0.0984798	+	0.170572i
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	−0.999959	−	0.00905914i	$-0.997116\pi$
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	0.507825	+	0.861460i	$0.330450\pi$
$930$	−4.00000			−0.131165
$931$		0			0
$932$	30.0000			0.982683
$933$	−12.0000	+	20.7846i	−0.392862	+	0.680458i
$934$	18.0000	+	31.1769i	0.588978	+	1.02014i
$935$		0			0
$936$	−1.00000	+	1.73205i	−0.0326860	+	0.0566139i
$937$	−38.0000			−1.24141			−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000			−1.24141			−0.620703	+	0.784046i	$0.713153\pi$
$938$		0			0
$939$	14.0000			0.456873
$940$		0			0
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	0.681218	−	0.732081i	$-0.261451\pi$
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	−0.974609	+	0.223912i	$0.928117\pi$
$942$	−11.0000	−	19.0526i	−0.358399	−	0.620766i
$943$		0			0
$944$	12.0000			0.390567
$945$		0			0
$946$		0			0
$947$	18.0000	−	31.1769i	0.584921	−	1.01311i	−0.409964	−	0.912102i	$-0.634459\pi$
$947$	18.0000	−	31.1769i	0.584921	−	1.01311i	0.994885	−	0.101012i	$-0.0322080\pi$
$948$	4.00000	+	6.92820i	0.129914	+	0.225018i
$949$	10.0000	+	17.3205i	0.324614	+	0.562247i
$950$	−4.00000	+	6.92820i	−0.129777	+	0.224781i
$951$	−18.0000			−0.583690
$952$		0			0
$953$	30.0000			0.971795			0.485898	−	0.874016i	$-0.338493\pi$
$953$	30.0000			0.971795			0.485898	+	0.874016i	$0.338493\pi$
$954$	−3.00000	+	5.19615i	−0.0971286	+	0.168232i
$955$	6.00000	+	10.3923i	0.194155	+	0.336287i
$956$	6.00000	+	10.3923i	0.194054	+	0.336111i
$957$		0			0
$958$		0			0
$959$		0			0
$960$	1.00000			0.0322749
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	10.0000	+	17.3205i	0.322413	+	0.558436i
$963$	−6.00000	−	10.3923i	−0.193347	−	0.334887i
$964$	13.0000	−	22.5167i	0.418702	−	0.725213i
$965$	−2.00000			−0.0643823
$966$		0			0
$967$	8.00000			0.257263			0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000			0.257263			0.128631	+	0.991692i	$0.458942\pi$
$968$	−5.50000	+	9.52628i	−0.176777	+	0.306186i
$969$	−24.0000	−	41.5692i	−0.770991	−	1.33540i
$970$	−5.00000	−	8.66025i	−0.160540	−	0.278064i
$971$	18.0000	−	31.1769i	0.577647	−	1.00051i	−0.418101	−	0.908401i	$-0.637304\pi$
$971$	18.0000	−	31.1769i	0.577647	−	1.00051i	0.995748	−	0.0921142i	$-0.0293625\pi$
$972$	−1.00000			−0.0320750
$973$		0			0
$974$	−32.0000			−1.02535
$975$	−1.00000	+	1.73205i	−0.0320256	+	0.0554700i
$976$	−5.00000	−	8.66025i	−0.160046	−	0.277208i
$977$	−3.00000	−	5.19615i	−0.0959785	−	0.166240i	0.814038	−	0.580812i	$-0.197265\pi$
$977$	−3.00000	−	5.19615i	−0.0959785	−	0.166240i	−0.910017	+	0.414572i	$0.863931\pi$
$978$	−10.0000	+	17.3205i	−0.319765	+	0.553849i
$979$		0			0
$980$		0			0
$981$	14.0000			0.446986
$982$		0			0
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	0.991453	−	0.130465i	$-0.0416470\pi$
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	−0.608712	+	0.793391i	$0.708314\pi$
$984$	−3.00000	−	5.19615i	−0.0956365	−	0.165647i
$985$	9.00000	−	15.5885i	0.286764	−	0.496690i
$986$	−36.0000			−1.14647
$987$		0			0
$988$	16.0000			0.509028
$989$		0			0
$990$		0			0
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	0.795474	−	0.605988i	$-0.207222\pi$
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	−0.922538	+	0.385906i	$0.873889\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$	28.0000			0.888553
$994$		0			0
$995$	20.0000			0.634043
$996$	−6.00000	+	10.3923i	−0.190117	+	0.329293i
$997$	13.0000	+	22.5167i	0.411714	+	0.713110i	0.995077	−	0.0991016i	$-0.0315969\pi$
$997$	13.0000	+	22.5167i	0.411714	+	0.713110i	−0.583363	+	0.812211i	$0.698264\pi$
$998$	10.0000	+	17.3205i	0.316544	+	0.548271i
$999$	−5.00000	+	8.66025i	−0.158193	+	0.273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.i.s.961.1		2
7.2	even	3		1470.2.a.b.1.1		1
7.3	odd	6		1470.2.i.l.361.1		2
7.4	even	3	inner	1470.2.i.s.361.1		2
7.5	odd	6		210.2.a.b.1.1	✓	1
7.6	odd	2		1470.2.i.l.961.1		2
21.2	odd	6		4410.2.a.bi.1.1		1
21.5	even	6		630.2.a.h.1.1		1
28.19	even	6		1680.2.a.g.1.1		1
35.9	even	6		7350.2.a.cs.1.1		1
35.12	even	12		1050.2.g.c.799.1		2
35.19	odd	6		1050.2.a.k.1.1		1
35.33	even	12		1050.2.g.c.799.2		2
56.5	odd	6		6720.2.a.n.1.1		1
56.19	even	6		6720.2.a.bi.1.1		1
84.47	odd	6		5040.2.a.g.1.1		1
105.47	odd	12		3150.2.g.i.2899.2		2
105.68	odd	12		3150.2.g.i.2899.1		2
105.89	even	6		3150.2.a.f.1.1		1
140.19	even	6		8400.2.a.cm.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.a.b.1.1	✓	1	7.5	odd	6
630.2.a.h.1.1		1	21.5	even	6
1050.2.a.k.1.1		1	35.19	odd	6
1050.2.g.c.799.1		2	35.12	even	12
1050.2.g.c.799.2		2	35.33	even	12
1470.2.a.b.1.1		1	7.2	even	3
1470.2.i.l.361.1		2	7.3	odd	6
1470.2.i.l.961.1		2	7.6	odd	2
1470.2.i.s.361.1		2	7.4	even	3	inner
1470.2.i.s.961.1		2	1.1	even	1	trivial
1680.2.a.g.1.1		1	28.19	even	6
3150.2.a.f.1.1		1	105.89	even	6
3150.2.g.i.2899.1		2	105.68	odd	12
3150.2.g.i.2899.2		2	105.47	odd	12
4410.2.a.bi.1.1		1	21.2	odd	6
5040.2.a.g.1.1		1	84.47	odd	6
6720.2.a.n.1.1		1	56.5	odd	6
6720.2.a.bi.1.1		1	56.19	even	6
7350.2.a.cs.1.1		1	35.9	even	6
8400.2.a.cm.1.1		1	140.19	even	6

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.500000 - 0.866025i) q^{12} -2.00000 q^{13} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{18} +(4.00000 - 6.92820i) q^{19} -1.00000 q^{20} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{26} -1.00000 q^{27} +6.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(-2.00000 - 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} -6.00000 q^{34} +1.00000 q^{36} +(5.00000 - 8.66025i) q^{37} +(-4.00000 - 6.92820i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(-0.500000 + 0.866025i) q^{40} +6.00000 q^{41} -4.00000 q^{43} +(0.500000 + 0.866025i) q^{45} -1.00000 q^{48} -1.00000 q^{50} +(3.00000 - 5.19615i) q^{51} +(1.00000 + 1.73205i) q^{52} +(3.00000 + 5.19615i) q^{53} +(-0.500000 + 0.866025i) q^{54} +8.00000 q^{57} +(3.00000 - 5.19615i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(-5.00000 + 8.66025i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} +12.0000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-5.00000 - 8.66025i) q^{73} +(-5.00000 - 8.66025i) q^{74} +(0.500000 - 0.866025i) q^{75} -8.00000 q^{76} -2.00000 q^{78} +(-4.00000 + 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} -12.0000 q^{83} -6.00000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(3.00000 + 5.19615i) q^{87} +(-3.00000 + 5.19615i) q^{89} +1.00000 q^{90} +(2.00000 - 3.46410i) q^{93} +(-4.00000 - 6.92820i) q^{95} +(-0.500000 + 0.866025i) q^{96} +10.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{8} - q^{9} - q^{10} + q^{12} - 4 q^{13} + 2 q^{15} - q^{16} - 6 q^{17} + q^{18} + 8 q^{19} - 2 q^{20} - q^{24} - q^{25} - 2 q^{26} - 2 q^{27} + 12 q^{29} + q^{30} - 4 q^{31} + q^{32} - 12 q^{34} + 2 q^{36} + 10 q^{37} - 8 q^{38} - 2 q^{39} - q^{40} + 12 q^{41} - 8 q^{43} + q^{45} - 2 q^{48} - 2 q^{50} + 6 q^{51} + 2 q^{52} + 6 q^{53} - q^{54} + 16 q^{57} + 6 q^{58} - 12 q^{59} - q^{60} - 10 q^{61} - 8 q^{62} + 2 q^{64} - 2 q^{65} + 4 q^{67} - 6 q^{68} + 24 q^{71} + q^{72} - 10 q^{73} - 10 q^{74} + q^{75} - 16 q^{76} - 4 q^{78} - 8 q^{79} + q^{80} - q^{81} + 6 q^{82} - 24 q^{83} - 12 q^{85} - 4 q^{86} + 6 q^{87} - 6 q^{89} + 2 q^{90} + 4 q^{93} - 8 q^{95} - q^{96} + 20 q^{97}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^8 - q^9 - q^10 + q^12 - 4 * q^13 + 2 * q^15 - q^16 - 6 * q^17 + q^18 + 8 * q^19 - 2 * q^20 - q^24 - q^25 - 2 * q^26 - 2 * q^27 + 12 * q^29 + q^30 - 4 * q^31 + q^32 - 12 * q^34 + 2 * q^36 + 10 * q^37 - 8 * q^38 - 2 * q^39 - q^40 + 12 * q^41 - 8 * q^43 + q^45 - 2 * q^48 - 2 * q^50 + 6 * q^51 + 2 * q^52 + 6 * q^53 - q^54 + 16 * q^57 + 6 * q^58 - 12 * q^59 - q^60 - 10 * q^61 - 8 * q^62 + 2 * q^64 - 2 * q^65 + 4 * q^67 - 6 * q^68 + 24 * q^71 + q^72 - 10 * q^73 - 10 * q^74 + q^75 - 16 * q^76 - 4 * q^78 - 8 * q^79 + q^80 - q^81 + 6 * q^82 - 24 * q^83 - 12 * q^85 - 4 * q^86 + 6 * q^87 - 6 * q^89 + 2 * q^90 + 4 * q^93 - 8 * q^95 - q^96 + 20 * q^97

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