LMFDB - Embedded newform 1470.2.i.o.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1470,2,Mod(361,1470)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [2,1,-1,-1,1,-2,0,-2,-1,-1,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1470.361
Dual form			1470.2.i.o.961.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{12} +2.00000 q^{13} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(0.500000 - 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} -1.00000 q^{20} +(0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} +1.00000 q^{27} -6.00000 q^{29} +(-0.500000 - 0.866025i) q^{30} +(-4.00000 + 6.92820i) q^{31} +(0.500000 - 0.866025i) q^{32} -6.00000 q^{34} +1.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(-0.500000 - 0.866025i) q^{40} -6.00000 q^{41} -4.00000 q^{43} +(0.500000 - 0.866025i) q^{45} +1.00000 q^{48} -1.00000 q^{50} +(-3.00000 - 5.19615i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} +(0.500000 + 0.866025i) q^{54} -4.00000 q^{57} +(-3.00000 - 5.19615i) q^{58} +(0.500000 - 0.866025i) q^{60} +(5.00000 + 8.66025i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(0.500000 + 0.866025i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-0.500000 - 0.866025i) q^{75} -4.00000 q^{76} -2.00000 q^{78} +(-4.00000 - 6.92820i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.00000 - 5.19615i) q^{82} +12.0000 q^{83} -6.00000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(3.00000 - 5.19615i) q^{87} +(-9.00000 - 15.5885i) q^{89} +1.00000 q^{90} +(-4.00000 - 6.92820i) q^{93} +(-2.00000 + 3.46410i) q^{95} +(0.500000 + 0.866025i) q^{96} +2.00000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} + q^{5} - 2 q^{6} - 2 q^{8} - q^{9} - q^{10} - q^{12} + 4 q^{13} - 2 q^{15} - q^{16} - 6 q^{17} + q^{18} + 4 q^{19} - 2 q^{20} + q^{24} - q^{25} + 2 q^{26} + 2 q^{27}+ \cdots + 4 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 + 4 * q^19 - 2 * q^20 + q^24 - q^25 + 2 * q^26 + 2 * q^27 - 12 * q^29 - q^30 - 8 * q^31 + q^32 - 12 * q^34 + 2 * q^36 - 2 * q^37 - 4 * 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 - 8 * q^57 - 6 * q^58 + q^60 + 10 * q^61 - 16 * q^62 + 2 * q^64 + 2 * q^65 + 4 * q^67 - 6 * q^68 + q^72 - 2 * q^73 + 2 * q^74 - q^75 - 8 * 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 - 18 * q^89 + 2 * q^90 - 8 * q^93 - 4 * q^95 + q^96 + 4 * q^97

Character values

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

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		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	0.230285	+	0.973123i	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$		0			0
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	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	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	0.243204	+	0.969975i	$0.421802\pi$
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	−0.961625	+	0.274367i	$0.911532\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−6.00000			−1.02899
$35$		0			0
$36$	1.00000			0.166667
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	−2.00000	+	3.46410i	−0.324443	+	0.561951i
$39$	−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	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		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	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	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	−0.583036	−	0.812447i	$-0.698135\pi$
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	0.995117	+	0.0987002i	$0.0314685\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$		0			0
$57$	−4.00000			−0.529813
$58$	−3.00000	−	5.19615i	−0.393919	−	0.682288i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$	0.500000	−	0.866025i	0.0645497	−	0.111803i
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	0.985391	+	0.170305i	$0.0544754\pi$
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	−0.345207	+	0.938527i	$0.612191\pi$
$62$	−8.00000			−1.01600
$63$		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	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$	−4.00000			−0.458831
$77$		0			0
$78$	−2.00000			−0.226455
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	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	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		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
$89$	−9.00000	−	15.5885i	−0.953998	−	1.65237i	−0.736644	−	0.676280i	$-0.763591\pi$
$89$	−9.00000	−	15.5885i	−0.953998	−	1.65237i	−0.217354	−	0.976093i	$-0.569742\pi$
$90$	1.00000			0.105409
$91$		0			0
$92$		0			0
$93$	−4.00000	−	6.92820i	−0.414781	−	0.718421i
$94$		0			0
$95$	−2.00000	+	3.46410i	−0.205196	+	0.355409i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$		0			0
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.0623905	+	0.998052i	$0.519872\pi$
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.833143	+	0.553058i	$0.813461\pi$
$102$	3.00000	−	5.19615i	0.297044	−	0.514496i
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	0.947576	−	0.319531i	$-0.103525\pi$
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	−0.750510	+	0.660859i	$0.770192\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	6.00000			0.582772
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	0.995474	+	0.0950377i	$0.0302972\pi$
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	−0.415432	+	0.909624i	$0.636370\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$		0			0
$111$	2.00000			0.189832
$112$		0			0
$113$	−18.0000			−1.69330			−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000			−1.69330			−0.846649	+	0.532152i	$0.821383\pi$
$114$	−2.00000	−	3.46410i	−0.187317	−	0.324443i
$115$		0			0
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$	−1.00000	−	1.73205i	−0.0924500	−	0.160128i
$118$		0			0
$119$		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
$124$	−4.00000	−	6.92820i	−0.359211	−	0.622171i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	20.0000			1.77471			0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000			1.77471			0.887357	+	0.461084i	$0.152539\pi$
$128$	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
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$		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	−0.965250	−	0.261329i	$-0.915839\pi$
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	0.708942	+	0.705266i	$0.249173\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−3.00000	−	5.19615i	−0.249136	−	0.431517i
$146$	−2.00000			−0.165521
$147$		0			0
$148$	2.00000			0.164399
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	−0.981617	−	0.190864i	$-0.938871\pi$
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	0.656101	+	0.754673i	$0.272204\pi$
$152$	−2.00000	−	3.46410i	−0.162221	−	0.280976i
$153$	6.00000			0.485071
$154$		0			0
$155$	−8.00000			−0.642575
$156$	−1.00000	−	1.73205i	−0.0800641	−	0.138675i
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	−0.903167	−	0.429289i	$-0.858764\pi$
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	0.823359	+	0.567521i	$0.192098\pi$
$158$	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
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$	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
$171$	2.00000	−	3.46410i	0.152944	−	0.264906i
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	−0.973670	−	0.227964i	$-0.926793\pi$
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	0.289412	−	0.957205i	$-0.406540\pi$
$174$	6.00000			0.454859
$175$		0			0
$176$		0			0
$177$		0			0
$178$	9.00000	−	15.5885i	0.674579	−	1.16840i
$179$	−12.0000	+	20.7846i	−0.896922	+	1.55351i	−0.0655145	+	0.997852i	$0.520869\pi$
$179$	−12.0000	+	20.7846i	−0.896922	+	1.55351i	−0.831408	+	0.555663i	$0.812464\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$		0			0
$183$	−10.0000			−0.739221
$184$		0			0
$185$	1.00000	−	1.73205i	0.0735215	−	0.127343i
$186$	4.00000	−	6.92820i	0.293294	−	0.508001i
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−4.00000			−0.290191
$191$	12.0000	+	20.7846i	0.868290	+	1.50392i	0.863743	+	0.503932i	$0.168114\pi$
$191$	12.0000	+	20.7846i	0.868290	+	1.50392i	0.00454614	+	0.999990i	$0.498553\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	11.0000	−	19.0526i	0.791797	−	1.37143i	−0.133056	−	0.991109i	$-0.542479\pi$
$193$	11.0000	−	19.0526i	0.791797	−	1.37143i	0.924853	−	0.380325i	$-0.124188\pi$
$194$	1.00000	+	1.73205i	0.0717958	+	0.124354i
$195$	−2.00000			−0.143223
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	−0.972257	−	0.233915i	$-0.924846\pi$
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	0.688705	+	0.725042i	$0.258180\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	2.00000	+	3.46410i	0.141069	+	0.244339i
$202$	−18.0000			−1.26648
$203$		0			0
$204$	6.00000			0.420084
$205$	−3.00000	−	5.19615i	−0.209529	−	0.362915i
$206$	−2.00000	+	3.46410i	−0.139347	+	0.241355i
$207$		0			0
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$		0			0
$210$		0			0
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$	3.00000	+	5.19615i	0.206041	+	0.356873i
$213$		0			0
$214$	−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
$218$	10.0000			0.677285
$219$	−1.00000	−	1.73205i	−0.0675737	−	0.117041i
$220$		0			0
$221$	−6.00000	+	10.3923i	−0.403604	+	0.699062i
$222$	1.00000	+	1.73205i	0.0671156	+	0.116248i
$223$	20.0000			1.33930			0.669650	−	0.742677i	$-0.266444\pi$
$223$	20.0000			1.33930			0.669650	+	0.742677i	$0.266444\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	−9.00000	−	15.5885i	−0.598671	−	1.03693i
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	−0.595274	−	0.803523i	$-0.702957\pi$
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	0.993508	+	0.113761i	$0.0362899\pi$
$228$	2.00000	−	3.46410i	0.132453	−	0.229416i
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	0.982592	−	0.185776i	$-0.0594799\pi$
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	−0.652183	+	0.758062i	$0.726147\pi$
$230$		0			0
$231$		0			0
$232$	6.00000			0.393919
$233$	9.00000	+	15.5885i	0.589610	+	1.02123i	0.994283	+	0.106773i	$0.0340517\pi$
$233$	9.00000	+	15.5885i	0.589610	+	1.02123i	−0.404674	+	0.914461i	$0.632615\pi$
$234$	1.00000	−	1.73205i	0.0653720	−	0.113228i
$235$		0			0
$236$		0			0
$237$	8.00000			0.519656
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	−0.896435	−	0.443176i	$-0.853852\pi$
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	0.832019	+	0.554747i	$0.187185\pi$
$242$	−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
$247$	4.00000	+	6.92820i	0.254514	+	0.440831i
$248$	4.00000	−	6.92820i	0.254000	−	0.439941i
$249$	−6.00000	+	10.3923i	−0.380235	+	0.658586i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−24.0000			−1.51487			−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000			−1.51487			−0.757433	+	0.652913i	$0.773547\pi$
$252$		0			0
$253$		0			0
$254$	10.0000	+	17.3205i	0.627456	+	1.08679i
$255$	3.00000	−	5.19615i	0.187867	−	0.325396i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	0.997374	+	0.0724199i	$0.0230722\pi$
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	−0.435970	+	0.899961i	$0.643595\pi$
$258$	4.00000			0.249029
$259$		0			0
$260$	−2.00000			−0.124035
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$		0			0
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$		0			0
$267$	18.0000			1.10158
$268$	2.00000	+	3.46410i	0.122169	+	0.211604i
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	−0.759958	−	0.649972i	$-0.774781\pi$
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	0.942871	+	0.333157i	$0.108114\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$	6.00000			0.363803
$273$		0			0
$274$	−6.00000			−0.362473
$275$		0			0
$276$		0			0
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	−0.894503	−	0.447062i	$-0.852470\pi$
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	0.834419	+	0.551131i	$0.185804\pi$
$278$	−2.00000	−	3.46410i	−0.119952	−	0.207763i
$279$	8.00000			0.478947
$280$		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
$283$	14.0000	−	24.2487i	0.832214	−	1.44144i	−0.0640654	−	0.997946i	$-0.520407\pi$
$283$	14.0000	−	24.2487i	0.832214	−	1.44144i	0.896279	−	0.443491i	$-0.146260\pi$
$284$		0			0
$285$	−2.00000	−	3.46410i	−0.118470	−	0.205196i
$286$		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
$291$	−1.00000	+	1.73205i	−0.0586210	+	0.101535i
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		0			0
$295$		0			0
$296$	1.00000	+	1.73205i	0.0581238	+	0.100673i
$297$		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
$303$	−9.00000	−	15.5885i	−0.517036	−	0.895533i
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$	−5.00000	+	8.66025i	−0.286299	+	0.495885i
$306$	3.00000	+	5.19615i	0.171499	+	0.297044i
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$	−4.00000			−0.227552
$310$	−4.00000	−	6.92820i	−0.227185	−	0.393496i
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$	1.00000	−	1.73205i	0.0566139	−	0.0980581i
$313$	−1.00000	−	1.73205i	−0.0565233	−	0.0979013i	0.836379	−	0.548151i	$-0.184668\pi$
$313$	−1.00000	−	1.73205i	−0.0565233	−	0.0979013i	−0.892903	+	0.450250i	$0.851335\pi$
$314$	−2.00000			−0.112867
$315$		0			0
$316$	8.00000			0.450035
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	−0.999980	−	0.00635137i	$-0.997978\pi$
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	0.494489	−	0.869184i	$-0.335355\pi$
$318$	−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
$323$	−24.0000			−1.33540
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−1.00000	+	1.73205i	−0.0554700	+	0.0960769i
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$	5.00000	+	8.66025i	0.276501	+	0.478913i
$328$	6.00000			0.331295
$329$		0			0
$330$		0			0
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	0.937829	+	0.347097i	$0.112833\pi$
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	−0.168320	+	0.985732i	$0.553834\pi$
$332$	−6.00000	+	10.3923i	−0.329293	+	0.570352i
$333$	−1.00000	+	1.73205i	−0.0547997	+	0.0949158i
$334$		0			0
$335$	4.00000			0.218543
$336$		0			0
$337$	26.0000			1.41631			0.708155	−	0.706057i	$-0.249528\pi$
$337$	26.0000			1.41631			0.708155	+	0.706057i	$0.249528\pi$
$338$	−4.50000	−	7.79423i	−0.244768	−	0.423950i
$339$	9.00000	−	15.5885i	0.488813	−	0.846649i
$340$	3.00000	−	5.19615i	0.162698	−	0.281801i
$341$		0			0
$342$	4.00000			0.216295
$343$		0			0
$344$	4.00000			0.215666
$345$		0			0
$346$	9.00000	−	15.5885i	0.483843	−	0.838041i
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	−0.980921	−	0.194409i	$-0.937721\pi$
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	0.658824	+	0.752297i	$0.271054\pi$
$348$	3.00000	+	5.19615i	0.160817	+	0.278543i
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$		0			0
$351$	2.00000			0.106752
$352$		0			0
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	−0.934751	−	0.355303i	$-0.884378\pi$
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	0.775077	+	0.631867i	$0.217711\pi$
$354$		0			0
$355$		0			0
$356$	18.0000			0.953998
$357$		0			0
$358$	−24.0000			−1.26844
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	0.986865	+	0.161546i	$0.0516481\pi$
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	−0.353529	+	0.935423i	$0.615019\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	7.00000	+	12.1244i	0.367912	+	0.637242i
$363$	−11.0000			−0.577350
$364$		0			0
$365$	−2.00000			−0.104685
$366$	−5.00000	−	8.66025i	−0.261354	−	0.452679i
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	−0.225750	−	0.974185i	$-0.572483\pi$
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	0.956544	−	0.291587i	$-0.0941834\pi$
$368$		0			0
$369$	3.00000	+	5.19615i	0.156174	+	0.270501i
$370$	2.00000			0.103975
$371$		0			0
$372$	8.00000			0.414781
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	−0.977016	−	0.213165i	$-0.931623\pi$
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	0.303902	−	0.952703i	$-0.401711\pi$
$374$		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	$0.532759\pi$
$380$	−2.00000	−	3.46410i	−0.102598	−	0.177705i
$381$	−10.0000	+	17.3205i	−0.512316	+	0.887357i
$382$	−12.0000	+	20.7846i	−0.613973	+	1.06343i
$383$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$383$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	22.0000			1.11977
$387$	2.00000	+	3.46410i	0.101666	+	0.176090i
$388$	−1.00000	+	1.73205i	−0.0507673	+	0.0879316i
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	−0.779895	−	0.625910i	$-0.784728\pi$
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	0.932002	+	0.362454i	$0.118061\pi$
$390$	−1.00000	−	1.73205i	−0.0506370	−	0.0877058i
$391$		0			0
$392$		0			0
$393$		0			0
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$	4.00000	−	6.92820i	0.201262	−	0.348596i
$396$		0			0
$397$	11.0000	+	19.0526i	0.552074	+	0.956221i	0.998125	+	0.0612128i	$0.0194968\pi$
$397$	11.0000	+	19.0526i	0.552074	+	0.956221i	−0.446051	+	0.895008i	$0.647170\pi$
$398$	−8.00000			−0.401004
$399$		0			0
$400$	1.00000			0.0500000
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	0.931158	−	0.364615i	$-0.118800\pi$
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	−0.781345	+	0.624099i	$0.785466\pi$
$402$	−2.00000	+	3.46410i	−0.0997509	+	0.172774i
$403$	−8.00000	+	13.8564i	−0.398508	+	0.690237i
$404$	−9.00000	−	15.5885i	−0.447767	−	0.775555i
$405$	−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	0.341994	+	0.939702i	$0.388898\pi$
$409$	−13.0000	+	22.5167i	−0.642809	+	1.11338i	−0.984803	+	0.173675i	$0.944436\pi$
$410$	3.00000	−	5.19615i	0.148159	−	0.256620i
$411$	−3.00000	−	5.19615i	−0.147979	−	0.256307i
$412$	−4.00000			−0.197066
$413$		0			0
$414$		0			0
$415$	6.00000	+	10.3923i	0.294528	+	0.510138i
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$	2.00000	−	3.46410i	0.0979404	−	0.169638i
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	10.0000	+	17.3205i	0.486792	+	0.843149i
$423$		0			0
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$	−3.00000	−	5.19615i	−0.145521	−	0.252050i
$426$		0			0
$427$		0			0
$428$	−12.0000			−0.580042
$429$		0			0
$430$	2.00000	−	3.46410i	0.0964486	−	0.167054i
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	26.0000			1.24948			0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000			1.24948			0.624740	+	0.780833i	$0.285205\pi$
$434$		0			0
$435$	6.00000			0.287678
$436$	5.00000	+	8.66025i	0.239457	+	0.414751i
$437$		0			0
$438$	1.00000	−	1.73205i	0.0477818	−	0.0827606i
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	0.754642	−	0.656136i	$-0.227810\pi$
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	−0.945552	+	0.325471i	$0.894477\pi$
$440$		0			0
$441$		0			0
$442$	−12.0000			−0.570782
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	0.687557	−	0.726130i	$-0.258683\pi$
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	−0.972626	+	0.232377i	$0.925350\pi$
$444$	−1.00000	+	1.73205i	−0.0474579	+	0.0821995i
$445$	9.00000	−	15.5885i	0.426641	−	0.738964i
$446$	10.0000	+	17.3205i	0.473514	+	0.820150i
$447$	−6.00000			−0.283790
$448$		0			0
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$	0.500000	+	0.866025i	0.0235702	+	0.0408248i
$451$		0			0
$452$	9.00000	−	15.5885i	0.423324	−	0.733219i
$453$	−4.00000	−	6.92820i	−0.187936	−	0.325515i
$454$	12.0000			0.563188
$455$		0			0
$456$	4.00000			0.187317
$457$	−13.0000	−	22.5167i	−0.608114	−	1.05328i	−0.991551	−	0.129718i	$-0.958593\pi$
$457$	−13.0000	−	22.5167i	−0.608114	−	1.05328i	0.383437	−	0.923567i	$-0.374740\pi$
$458$	−5.00000	+	8.66025i	−0.233635	+	0.404667i
$459$	−3.00000	+	5.19615i	−0.140028	+	0.242536i
$460$		0			0
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$		0			0
$463$	−4.00000			−0.185896			−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000			−0.185896			−0.0929479	+	0.995671i	$0.529629\pi$
$464$	3.00000	+	5.19615i	0.139272	+	0.241225i
$465$	4.00000	−	6.92820i	0.185496	−	0.321288i
$466$	−9.00000	+	15.5885i	−0.416917	+	0.722121i
$467$	18.0000	+	31.1769i	0.832941	+	1.44270i	0.895696	+	0.444667i	$0.146678\pi$
$467$	18.0000	+	31.1769i	0.832941	+	1.44270i	−0.0627555	+	0.998029i	$0.519989\pi$
$468$	2.00000			0.0924500
$469$		0			0
$470$		0			0
$471$	−1.00000	−	1.73205i	−0.0460776	−	0.0798087i
$472$		0			0
$473$		0			0
$474$	4.00000	+	6.92820i	0.183726	+	0.318223i
$475$	−4.00000			−0.183533
$476$		0			0
$477$	−6.00000			−0.274721
$478$	12.0000	+	20.7846i	0.548867	+	0.950666i
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$	−0.500000	+	0.866025i	−0.0228218	+	0.0395285i
$481$	−2.00000	−	3.46410i	−0.0911922	−	0.157949i
$482$	−2.00000			−0.0910975
$483$		0			0
$484$	−11.0000			−0.500000
$485$	1.00000	+	1.73205i	0.0454077	+	0.0786484i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	14.0000	−	24.2487i	0.634401	−	1.09881i	−0.352241	−	0.935909i	$-0.614580\pi$
$487$	14.0000	−	24.2487i	0.634401	−	1.09881i	0.986642	−	0.162905i	$-0.0520863\pi$
$488$	−5.00000	−	8.66025i	−0.226339	−	0.392031i
$489$	−4.00000			−0.180886
$490$		0			0
$491$	24.0000			1.08310			0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000			1.08310			0.541552	+	0.840667i	$0.317837\pi$
$492$	3.00000	+	5.19615i	0.135250	+	0.234261i
$493$	18.0000	−	31.1769i	0.810679	−	1.40414i
$494$	−4.00000	+	6.92820i	−0.179969	+	0.311715i
$495$		0			0
$496$	8.00000			0.359211
$497$		0			0
$498$	−12.0000			−0.537733
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	0.907314	−	0.420455i	$-0.138129\pi$
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	−0.817781	+	0.575529i	$0.804796\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$	−12.0000	−	20.7846i	−0.535586	−	0.927663i
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		0			0
$505$	−18.0000			−0.800989
$506$		0			0
$507$	4.50000	−	7.79423i	0.199852	−	0.346154i
$508$	−10.0000	+	17.3205i	−0.443678	+	0.768473i
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$	6.00000			0.265684
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	2.00000	+	3.46410i	0.0883022	+	0.152944i
$514$	−9.00000	+	15.5885i	−0.396973	+	0.687577i
$515$	−2.00000	+	3.46410i	−0.0881305	+	0.152647i
$516$	2.00000	+	3.46410i	0.0880451	+	0.152499i
$517$		0			0
$518$		0			0
$519$	18.0000			0.790112
$520$	−1.00000	−	1.73205i	−0.0438529	−	0.0759555i
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	−0.993011	−	0.118020i	$-0.962345\pi$
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	0.598714	+	0.800963i	$0.295679\pi$
$522$	−3.00000	+	5.19615i	−0.131306	+	0.227429i
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	0.560208	−	0.828352i	$-0.310721\pi$
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	−0.997478	+	0.0709788i	$0.977388\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−24.0000	−	41.5692i	−1.04546	−	1.81078i
$528$		0			0
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	3.00000	+	5.19615i	0.130312	+	0.225706i
$531$		0			0
$532$		0			0
$533$	−12.0000			−0.519778
$534$	9.00000	+	15.5885i	0.389468	+	0.674579i
$535$	−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
$538$	6.00000			0.258678
$539$		0			0
$540$	−1.00000			−0.0430331
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	0.953262	−	0.302144i	$-0.0977023\pi$
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	−0.738296	+	0.674477i	$0.764369\pi$
$542$	−8.00000	+	13.8564i	−0.343629	+	0.595184i
$543$	−7.00000	+	12.1244i	−0.300399	+	0.520306i
$544$	3.00000	+	5.19615i	0.128624	+	0.222783i
$545$	10.0000			0.428353
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	−3.00000	−	5.19615i	−0.128154	−	0.221969i
$549$	5.00000	−	8.66025i	0.213395	−	0.369611i
$550$		0			0
$551$	−12.0000	−	20.7846i	−0.511217	−	0.885454i
$552$		0			0
$553$		0			0
$554$	−2.00000			−0.0849719
$555$	1.00000	+	1.73205i	0.0424476	+	0.0735215i
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	−9.00000	+	15.5885i	−0.381342	+	0.660504i	−0.991254	−	0.131965i	$-0.957871\pi$
$557$	−9.00000	+	15.5885i	−0.381342	+	0.660504i	0.609912	+	0.792469i	$0.291205\pi$
$558$	4.00000	+	6.92820i	0.169334	+	0.293294i
$559$	−8.00000			−0.338364
$560$		0			0
$561$		0			0
$562$	9.00000	+	15.5885i	0.379642	+	0.657559i
$563$	6.00000	−	10.3923i	0.252870	−	0.437983i	−0.711445	−	0.702742i	$-0.751959\pi$
$563$	6.00000	−	10.3923i	0.252870	−	0.437983i	0.964315	+	0.264758i	$0.0852922\pi$
$564$		0			0
$565$	−9.00000	−	15.5885i	−0.378633	−	0.655811i
$566$	28.0000			1.17693
$567$		0			0
$568$		0			0
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	0.613369	−	0.789797i	$-0.289814\pi$
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	−0.990668	+	0.136295i	$0.956481\pi$
$570$	2.00000	−	3.46410i	0.0837708	−	0.145095i
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$		0			0
$573$	−24.0000			−1.00261
$574$		0			0
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−1.00000	+	1.73205i	−0.0416305	+	0.0721062i	−0.886090	−	0.463513i	$-0.846589\pi$
$577$	−1.00000	+	1.73205i	−0.0416305	+	0.0721062i	0.844459	+	0.535620i	$0.179922\pi$
$578$	9.50000	−	16.4545i	0.395148	−	0.684416i
$579$	11.0000	+	19.0526i	0.457144	+	0.791797i
$580$	6.00000			0.249136
$581$		0			0
$582$	−2.00000			−0.0829027
$583$		0			0
$584$	1.00000	−	1.73205i	0.0413803	−	0.0716728i
$585$	1.00000	−	1.73205i	0.0413449	−	0.0716115i
$586$	−3.00000	−	5.19615i	−0.123929	−	0.214651i
$587$	−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
$590$		0			0
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	−15.0000	−	25.9808i	−0.615976	−	1.06690i	−0.990212	−	0.139569i	$-0.955428\pi$
$593$	−15.0000	−	25.9808i	−0.615976	−	1.06690i	0.374236	−	0.927333i	$-0.377905\pi$
$594$		0			0
$595$		0			0
$596$	−6.00000			−0.245770
$597$	−4.00000	−	6.92820i	−0.163709	−	0.283552i
$598$		0			0
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	−0.509631	−	0.860393i	$-0.670218\pi$
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	0.999938	+	0.0111569i	$0.00355143\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$		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
$606$	9.00000	−	15.5885i	0.365600	−	0.633238i
$607$	2.00000	+	3.46410i	0.0811775	+	0.140604i	0.903756	−	0.428048i	$-0.140799\pi$
$607$	2.00000	+	3.46410i	0.0811775	+	0.140604i	−0.822578	+	0.568652i	$0.807465\pi$
$608$	4.00000			0.162221
$609$		0			0
$610$	−10.0000			−0.404888
$611$		0			0
$612$	−3.00000	+	5.19615i	−0.121268	+	0.210042i
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	−0.885514	−	0.464614i	$-0.846193\pi$
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	0.845124	+	0.534570i	$0.179527\pi$
$614$	10.0000	+	17.3205i	0.403567	+	0.698999i
$615$	6.00000			0.241943
$616$		0			0
$617$	30.0000			1.20775			0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000			1.20775			0.603877	+	0.797077i	$0.293622\pi$
$618$	−2.00000	−	3.46410i	−0.0804518	−	0.139347i
$619$	−22.0000	+	38.1051i	−0.884255	+	1.53157i	−0.0376891	+	0.999290i	$0.512000\pi$
$619$	−22.0000	+	38.1051i	−0.884255	+	1.53157i	−0.846566	+	0.532284i	$0.821334\pi$
$620$	4.00000	−	6.92820i	0.160644	−	0.278243i
$621$		0			0
$622$		0			0
$623$		0			0
$624$	2.00000			0.0800641
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	1.00000	−	1.73205i	0.0399680	−	0.0692267i
$627$		0			0
$628$	−1.00000	−	1.73205i	−0.0399043	−	0.0691164i
$629$	12.0000			0.478471
$630$		0			0
$631$	32.0000			1.27390			0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000			1.27390			0.636950	+	0.770905i	$0.280196\pi$
$632$	4.00000	+	6.92820i	0.159111	+	0.275589i
$633$	−10.0000	+	17.3205i	−0.397464	+	0.688428i
$634$	9.00000	−	15.5885i	0.357436	−	0.619097i
$635$	10.0000	+	17.3205i	0.396838	+	0.687343i
$636$	−6.00000			−0.237915
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$	−6.00000	−	10.3923i	−0.236801	−	0.410152i
$643$	−4.00000			−0.157745			−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000			−0.157745			−0.0788723	+	0.996885i	$0.525132\pi$
$644$		0			0
$645$	4.00000			0.157500
$646$	−12.0000	−	20.7846i	−0.472134	−	0.817760i
$647$	−12.0000	+	20.7846i	−0.471769	+	0.817127i	−0.999478	−	0.0322975i	$-0.989718\pi$
$647$	−12.0000	+	20.7846i	−0.471769	+	0.817127i	0.527710	+	0.849425i	$0.323051\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$		0			0
$650$	−2.00000			−0.0784465
$651$		0			0
$652$	−4.00000			−0.156652
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	0.634437	−	0.772975i	$-0.281232\pi$
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	−0.986634	+	0.162951i	$0.947899\pi$
$654$	−5.00000	+	8.66025i	−0.195515	+	0.338643i
$655$		0			0
$656$	3.00000	+	5.19615i	0.117130	+	0.202876i
$657$	2.00000			0.0780274
$658$		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
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$	−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
$666$	−2.00000			−0.0774984
$667$		0			0
$668$		0			0
$669$	−10.0000	+	17.3205i	−0.386622	+	0.669650i
$670$	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	$0.332924\pi$
$674$	13.0000	+	22.5167i	0.500741	+	0.867309i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	0.917899	−	0.396813i	$-0.129884\pi$
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	−0.802600	+	0.596518i	$0.796551\pi$
$678$	18.0000			0.691286
$679$		0			0
$680$	6.00000			0.230089
$681$	6.00000	+	10.3923i	0.229920	+	0.398234i
$682$		0			0
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	−0.728101	−	0.685470i	$-0.759597\pi$
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	0.957685	+	0.287819i	$0.0929302\pi$
$684$	2.00000	+	3.46410i	0.0764719	+	0.132453i
$685$	−6.00000			−0.229248
$686$		0			0
$687$	−10.0000			−0.381524
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$		0			0
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	−0.892458	−	0.451130i	$-0.851021\pi$
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	0.0555386	−	0.998457i	$-0.482312\pi$
$692$	18.0000			0.684257
$693$		0			0
$694$	−12.0000			−0.455514
$695$	−2.00000	−	3.46410i	−0.0758643	−	0.131401i
$696$	−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
$699$	−18.0000			−0.680823
$700$		0			0
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$	1.00000	+	1.73205i	0.0377426	+	0.0653720i
$703$	4.00000	−	6.92820i	0.150863	−	0.261302i
$704$		0			0
$705$		0			0
$706$	−6.00000			−0.225813
$707$		0			0
$708$		0			0
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	−0.963512	−	0.267664i	$-0.913748\pi$
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	0.249952	−	0.968258i	$-0.419585\pi$
$710$		0			0
$711$	−4.00000	+	6.92820i	−0.150012	+	0.259828i
$712$	9.00000	+	15.5885i	0.337289	+	0.584202i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−12.0000	−	20.7846i	−0.448461	−	0.776757i
$717$	−12.0000	+	20.7846i	−0.448148	+	0.776215i
$718$	−12.0000	+	20.7846i	−0.447836	+	0.775675i
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$	−1.00000			−0.0372678
$721$		0			0
$722$	3.00000			0.111648
$723$	−1.00000	−	1.73205i	−0.0371904	−	0.0644157i
$724$	−7.00000	+	12.1244i	−0.260153	+	0.450598i
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$	−5.50000	−	9.52628i	−0.204124	−	0.353553i
$727$	−28.0000			−1.03846			−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000			−1.03846			−0.519231	+	0.854634i	$0.673782\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−1.00000	−	1.73205i	−0.0370117	−	0.0641061i
$731$	12.0000	−	20.7846i	0.443836	−	0.768747i
$732$	5.00000	−	8.66025i	0.184805	−	0.320092i
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	0.994471	−	0.105010i	$-0.0334875\pi$
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	−0.588177	+	0.808732i	$0.700154\pi$
$734$	28.0000			1.03350
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−3.00000	+	5.19615i	−0.110432	+	0.191273i
$739$	26.0000	−	45.0333i	0.956425	−	1.65658i	0.225354	−	0.974277i	$-0.427646\pi$
$739$	26.0000	−	45.0333i	0.956425	−	1.65658i	0.731072	−	0.682300i	$-0.239020\pi$
$740$	1.00000	+	1.73205i	0.0367607	+	0.0636715i
$741$	−8.00000			−0.293887
$742$		0			0
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$	4.00000	+	6.92820i	0.146647	+	0.254000i
$745$	−3.00000	+	5.19615i	−0.109911	+	0.190372i
$746$	13.0000	−	22.5167i	0.475964	−	0.824394i
$747$	−6.00000	−	10.3923i	−0.219529	−	0.380235i
$748$		0			0
$749$		0			0
$750$	1.00000			0.0365148
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	0.956963	+	0.290209i	$0.0937250\pi$
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	−0.227153	+	0.973859i	$0.572942\pi$
$752$		0			0
$753$	12.0000	−	20.7846i	0.437304	−	0.757433i
$754$	−6.00000	−	10.3923i	−0.218507	−	0.378465i
$755$	−8.00000			−0.291150
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−2.00000	−	3.46410i	−0.0726433	−	0.125822i
$759$		0			0
$760$	2.00000	−	3.46410i	0.0725476	−	0.125656i
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	0.655515	−	0.755182i	$-0.272452\pi$
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	−0.981764	+	0.190101i	$0.939118\pi$
$762$	−20.0000			−0.724524
$763$		0			0
$764$	−24.0000			−0.868290
$765$	3.00000	+	5.19615i	0.108465	+	0.187867i
$766$		0			0
$767$		0			0
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	2.00000			0.0721218			0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000			0.0721218			0.0360609	+	0.999350i	$0.488519\pi$
$770$		0			0
$771$	−18.0000			−0.648254
$772$	11.0000	+	19.0526i	0.395899	+	0.685717i
$773$	−21.0000	+	36.3731i	−0.755318	+	1.30825i	0.189899	+	0.981804i	$0.439184\pi$
$773$	−21.0000	+	36.3731i	−0.755318	+	1.30825i	−0.945216	+	0.326445i	$0.894149\pi$
$774$	−2.00000	+	3.46410i	−0.0718885	+	0.124515i
$775$	−4.00000	−	6.92820i	−0.143684	−	0.248868i
$776$	−2.00000			−0.0717958
$777$		0			0
$778$	6.00000			0.215110
$779$	−12.0000	−	20.7846i	−0.429945	−	0.744686i
$780$	1.00000	−	1.73205i	0.0358057	−	0.0620174i
$781$		0			0
$782$		0			0
$783$	−6.00000			−0.214423
$784$		0			0
$785$	−2.00000			−0.0713831
$786$		0			0
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	−0.828176	−	0.560469i	$-0.810621\pi$
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	0.899468	+	0.436987i	$0.143954\pi$
$788$	3.00000	−	5.19615i	0.106871	−	0.185105i
$789$		0			0
$790$	8.00000			0.284627
$791$		0			0
$792$		0			0
$793$	10.0000	+	17.3205i	0.355110	+	0.615069i
$794$	−11.0000	+	19.0526i	−0.390375	+	0.676150i
$795$	−3.00000	+	5.19615i	−0.106399	+	0.184289i
$796$	−4.00000	−	6.92820i	−0.141776	−	0.245564i
$797$	−30.0000			−1.06265			−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000			−1.06265			−0.531327	+	0.847167i	$0.678307\pi$
$798$		0			0
$799$		0			0
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−9.00000	+	15.5885i	−0.317999	+	0.550791i
$802$	−3.00000	+	5.19615i	−0.105934	+	0.183483i
$803$		0			0
$804$	−4.00000			−0.141069
$805$		0			0
$806$	−16.0000			−0.563576
$807$	3.00000	+	5.19615i	0.105605	+	0.182913i
$808$	9.00000	−	15.5885i	0.316619	−	0.548400i
$809$	27.0000	−	46.7654i	0.949269	−	1.64418i	0.202301	−	0.979323i	$-0.435158\pi$
$809$	27.0000	−	46.7654i	0.949269	−	1.64418i	0.746968	−	0.664860i	$-0.231509\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$		0			0
$813$	−16.0000			−0.561144
$814$		0			0
$815$	−2.00000	+	3.46410i	−0.0700569	+	0.121342i
$816$	−3.00000	+	5.19615i	−0.105021	+	0.181902i
$817$	−8.00000	−	13.8564i	−0.279885	−	0.484774i
$818$	−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	$-0.268370\pi$
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	−0.979246	+	0.202674i	$0.935037\pi$
$822$	3.00000	−	5.19615i	0.104637	−	0.181237i
$823$	−10.0000	+	17.3205i	−0.348578	+	0.603755i	−0.985997	−	0.166762i	$-0.946669\pi$
$823$	−10.0000	+	17.3205i	−0.348578	+	0.603755i	0.637419	+	0.770517i	$0.280002\pi$
$824$	−2.00000	−	3.46410i	−0.0696733	−	0.120678i
$825$		0			0
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	−19.0000	+	32.9090i	−0.659897	+	1.14298i	0.320745	+	0.947166i	$0.396067\pi$
$829$	−19.0000	+	32.9090i	−0.659897	+	1.14298i	−0.980642	+	0.195810i	$0.937266\pi$
$830$	−6.00000	+	10.3923i	−0.208263	+	0.360722i
$831$	−1.00000	−	1.73205i	−0.0346896	−	0.0600842i
$832$	2.00000			0.0693375
$833$		0			0
$834$	4.00000			0.138509
$835$		0			0
$836$		0			0
$837$	−4.00000	+	6.92820i	−0.138260	+	0.239474i
$838$		0			0
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	−5.00000	−	8.66025i	−0.172311	−	0.298452i
$843$	−9.00000	+	15.5885i	−0.309976	+	0.536895i
$844$	−10.0000	+	17.3205i	−0.344214	+	0.596196i
$845$	−4.50000	−	7.79423i	−0.154805	−	0.268130i
$846$		0			0
$847$		0			0
$848$	−6.00000			−0.206041
$849$	14.0000	+	24.2487i	0.480479	+	0.832214i
$850$	3.00000	−	5.19615i	0.102899	−	0.178227i
$851$		0			0
$852$		0			0
$853$	−46.0000			−1.57501			−0.787505	−	0.616308i	$-0.788628\pi$
$853$	−46.0000			−1.57501			−0.787505	+	0.616308i	$0.788628\pi$
$854$		0			0
$855$	4.00000			0.136797
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$		0			0
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	0.898126	−	0.439738i	$-0.144929\pi$
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	−0.829887	+	0.557931i	$0.811595\pi$
$860$	4.00000			0.136399
$861$		0			0
$862$		0			0
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	0.586235	−	0.810141i	$-0.300609\pi$
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	−0.994720	+	0.102624i	$0.967276\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$	13.0000	+	22.5167i	0.441758	+	0.765147i
$867$	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
$872$	−5.00000	+	8.66025i	−0.169321	+	0.293273i
$873$	−1.00000	−	1.73205i	−0.0338449	−	0.0586210i
$874$		0			0
$875$		0			0
$876$	2.00000			0.0675737
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	0.848648	−	0.528958i	$-0.177417\pi$
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	−0.882415	+	0.470471i	$0.844084\pi$
$878$	4.00000	−	6.92820i	0.134993	−	0.233816i
$879$	3.00000	−	5.19615i	0.101187	−	0.175262i
$880$		0			0
$881$	−54.0000			−1.81931			−0.909653	−	0.415369i	$-0.863653\pi$
$881$	−54.0000			−1.81931			−0.909653	+	0.415369i	$0.863653\pi$
$882$		0			0
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$	−6.00000	−	10.3923i	−0.201802	−	0.349531i
$885$		0			0
$886$	6.00000	−	10.3923i	0.201574	−	0.349136i
$887$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$887$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$888$	−2.00000			−0.0671156
$889$		0			0
$890$	18.0000			0.603361
$891$		0			0
$892$	−10.0000	+	17.3205i	−0.334825	+	0.579934i
$893$		0			0
$894$	−3.00000	−	5.19615i	−0.100335	−	0.173785i
$895$	−24.0000			−0.802232
$896$		0			0
$897$		0			0
$898$	−3.00000	−	5.19615i	−0.100111	−	0.173398i
$899$	24.0000	−	41.5692i	0.800445	−	1.38641i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	18.0000	+	31.1769i	0.599667	+	1.03865i
$902$		0			0
$903$		0			0
$904$	18.0000			0.598671
$905$	7.00000	+	12.1244i	0.232688	+	0.403027i
$906$	4.00000	−	6.92820i	0.132891	−	0.230174i
$907$	−22.0000	+	38.1051i	−0.730498	+	1.26526i	0.226173	+	0.974087i	$0.427379\pi$
$907$	−22.0000	+	38.1051i	−0.730498	+	1.26526i	−0.956671	+	0.291172i	$0.905955\pi$
$908$	6.00000	+	10.3923i	0.199117	+	0.344881i
$909$	18.0000			0.597022
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$	2.00000	+	3.46410i	0.0662266	+	0.114708i
$913$		0			0
$914$	13.0000	−	22.5167i	0.430002	−	0.744785i
$915$	−5.00000	−	8.66025i	−0.165295	−	0.286299i
$916$	−10.0000			−0.330409
$917$		0			0
$918$	−6.00000			−0.198030
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	0.967274	−	0.253735i	$-0.0816592\pi$
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	−0.703378	+	0.710816i	$0.748326\pi$
$920$		0			0
$921$	−10.0000	+	17.3205i	−0.329511	+	0.570730i
$922$	−15.0000	−	25.9808i	−0.493999	−	0.855631i
$923$		0			0
$924$		0			0
$925$	2.00000			0.0657596
$926$	−2.00000	−	3.46410i	−0.0657241	−	0.113837i
$927$	2.00000	−	3.46410i	0.0656886	−	0.113776i
$928$	−3.00000	+	5.19615i	−0.0984798	+	0.170572i
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	0.911034	−	0.412332i	$-0.135286\pi$
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	−0.812607	+	0.582812i	$0.801952\pi$
$930$	8.00000			0.262330
$931$		0			0
$932$	−18.0000			−0.589610
$933$		0			0
$934$	−18.0000	+	31.1769i	−0.588978	+	1.02014i
$935$		0			0
$936$	1.00000	+	1.73205i	0.0326860	+	0.0566139i
$937$	26.0000			0.849383			0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000			0.849383			0.424691	+	0.905338i	$0.360383\pi$
$938$		0			0
$939$	2.00000			0.0652675
$940$		0			0
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	−0.974609	−	0.223912i	$-0.928117\pi$
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	0.681218	+	0.732081i	$0.261451\pi$
$942$	1.00000	−	1.73205i	0.0325818	−	0.0564333i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−18.0000	−	31.1769i	−0.584921	−	1.01311i	−0.994885	−	0.101012i	$-0.967792\pi$
$947$	−18.0000	−	31.1769i	−0.584921	−	1.01311i	0.409964	−	0.912102i	$-0.365541\pi$
$948$	−4.00000	+	6.92820i	−0.129914	+	0.225018i
$949$	−2.00000	+	3.46410i	−0.0649227	+	0.112449i
$950$	−2.00000	−	3.46410i	−0.0648886	−	0.112390i
$951$	18.0000			0.583690
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$	−3.00000	−	5.19615i	−0.0971286	−	0.168232i
$955$	−12.0000	+	20.7846i	−0.388311	+	0.672574i
$956$	−12.0000	+	20.7846i	−0.388108	+	0.672222i
$957$		0			0
$958$	24.0000			0.775405
$959$		0			0
$960$	−1.00000			−0.0322749
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	2.00000	−	3.46410i	0.0644826	−	0.111687i
$963$	6.00000	−	10.3923i	0.193347	−	0.334887i
$964$	−1.00000	−	1.73205i	−0.0322078	−	0.0557856i
$965$	22.0000			0.708205
$966$		0			0
$967$	−4.00000			−0.128631			−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000			−0.128631			−0.0643157	+	0.997930i	$0.520486\pi$
$968$	−5.50000	−	9.52628i	−0.176777	−	0.306186i
$969$	12.0000	−	20.7846i	0.385496	−	0.667698i
$970$	−1.00000	+	1.73205i	−0.0321081	+	0.0556128i
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	0.606685	−	0.794943i	$-0.292499\pi$
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	−0.991783	+	0.127933i	$0.959166\pi$
$972$	1.00000			0.0320750
$973$		0			0
$974$	28.0000			0.897178
$975$	−1.00000	−	1.73205i	−0.0320256	−	0.0554700i
$976$	5.00000	−	8.66025i	0.160046	−	0.277208i
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	−0.305530	−	0.952183i	$-0.598833\pi$
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	0.977379	−	0.211495i	$-0.0678332\pi$
$978$	−2.00000	−	3.46410i	−0.0639529	−	0.110770i
$979$		0			0
$980$		0			0
$981$	−10.0000			−0.319275
$982$	12.0000	+	20.7846i	0.382935	+	0.663264i
$983$	12.0000	−	20.7846i	0.382741	−	0.662926i	−0.608712	−	0.793391i	$-0.708314\pi$
$983$	12.0000	−	20.7846i	0.382741	−	0.662926i	0.991453	+	0.130465i	$0.0416470\pi$
$984$	−3.00000	+	5.19615i	−0.0956365	+	0.165647i
$985$	−3.00000	−	5.19615i	−0.0955879	−	0.165563i
$986$	36.0000			1.14647
$987$		0			0
$988$	−8.00000			−0.254514
$989$		0			0
$990$		0			0
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	−0.710530	−	0.703667i	$-0.751545\pi$
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	0.964658	+	0.263504i	$0.0848781\pi$
$992$	4.00000	+	6.92820i	0.127000	+	0.219971i
$993$	−28.0000			−0.888553
$994$		0			0
$995$	−8.00000			−0.253617
$996$	−6.00000	−	10.3923i	−0.190117	−	0.329293i
$997$	−13.0000	+	22.5167i	−0.411714	+	0.713110i	−0.995077	−	0.0991016i	$-0.968403\pi$
$997$	−13.0000	+	22.5167i	−0.411714	+	0.713110i	0.583363	+	0.812211i	$0.301736\pi$
$998$	−2.00000	+	3.46410i	−0.0633089	+	0.109654i
$999$	−1.00000	−	1.73205i	−0.0316386	−	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.i.o.361.1		2
7.2	even	3	inner	1470.2.i.o.961.1		2
7.3	odd	6		1470.2.a.d.1.1		1
7.4	even	3		30.2.a.a.1.1	✓	1
7.5	odd	6		1470.2.i.q.961.1		2
7.6	odd	2		1470.2.i.q.361.1		2
21.11	odd	6		90.2.a.c.1.1		1
21.17	even	6		4410.2.a.z.1.1		1
28.11	odd	6		240.2.a.b.1.1		1
35.4	even	6		150.2.a.b.1.1		1
35.18	odd	12		150.2.c.a.49.2		2
35.24	odd	6		7350.2.a.ct.1.1		1
35.32	odd	12		150.2.c.a.49.1		2
56.11	odd	6		960.2.a.p.1.1		1
56.53	even	6		960.2.a.e.1.1		1
63.4	even	3		810.2.e.l.541.1		2
63.11	odd	6		810.2.e.b.271.1		2
63.25	even	3		810.2.e.l.271.1		2
63.32	odd	6		810.2.e.b.541.1		2
77.32	odd	6		3630.2.a.w.1.1		1
84.11	even	6		720.2.a.j.1.1		1
91.18	odd	12		5070.2.b.k.1351.2		2
91.25	even	6		5070.2.a.w.1.1		1
91.60	odd	12		5070.2.b.k.1351.1		2
105.32	even	12		450.2.c.b.199.2		2
105.53	even	12		450.2.c.b.199.1		2
105.74	odd	6		450.2.a.d.1.1		1
112.11	odd	12		3840.2.k.f.1921.2		2
112.53	even	12		3840.2.k.y.1921.1		2
112.67	odd	12		3840.2.k.f.1921.1		2
112.109	even	12		3840.2.k.y.1921.2		2
119.67	even	6		8670.2.a.g.1.1		1
140.39	odd	6		1200.2.a.k.1.1		1
140.67	even	12		1200.2.f.e.49.2		2
140.123	even	12		1200.2.f.e.49.1		2
168.11	even	6		2880.2.a.q.1.1		1
168.53	odd	6		2880.2.a.a.1.1		1
280.53	odd	12		4800.2.f.p.3649.1		2
280.67	even	12		4800.2.f.w.3649.1		2
280.109	even	6		4800.2.a.cq.1.1		1
280.123	even	12		4800.2.f.w.3649.2		2
280.179	odd	6		4800.2.a.d.1.1		1
280.277	odd	12		4800.2.f.p.3649.2		2
420.179	even	6		3600.2.a.f.1.1		1
420.263	odd	12		3600.2.f.i.2449.1		2
420.347	odd	12		3600.2.f.i.2449.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.2.a.a.1.1	✓	1	7.4	even	3
90.2.a.c.1.1		1	21.11	odd	6
150.2.a.b.1.1		1	35.4	even	6
150.2.c.a.49.1		2	35.32	odd	12
150.2.c.a.49.2		2	35.18	odd	12
240.2.a.b.1.1		1	28.11	odd	6
450.2.a.d.1.1		1	105.74	odd	6
450.2.c.b.199.1		2	105.53	even	12
450.2.c.b.199.2		2	105.32	even	12
720.2.a.j.1.1		1	84.11	even	6
810.2.e.b.271.1		2	63.11	odd	6
810.2.e.b.541.1		2	63.32	odd	6
810.2.e.l.271.1		2	63.25	even	3
810.2.e.l.541.1		2	63.4	even	3
960.2.a.e.1.1		1	56.53	even	6
960.2.a.p.1.1		1	56.11	odd	6
1200.2.a.k.1.1		1	140.39	odd	6
1200.2.f.e.49.1		2	140.123	even	12
1200.2.f.e.49.2		2	140.67	even	12
1470.2.a.d.1.1		1	7.3	odd	6
1470.2.i.o.361.1		2	1.1	even	1	trivial
1470.2.i.o.961.1		2	7.2	even	3	inner
1470.2.i.q.361.1		2	7.6	odd	2
1470.2.i.q.961.1		2	7.5	odd	6
2880.2.a.a.1.1		1	168.53	odd	6
2880.2.a.q.1.1		1	168.11	even	6
3600.2.a.f.1.1		1	420.179	even	6
3600.2.f.i.2449.1		2	420.263	odd	12
3600.2.f.i.2449.2		2	420.347	odd	12
3630.2.a.w.1.1		1	77.32	odd	6
3840.2.k.f.1921.1		2	112.67	odd	12
3840.2.k.f.1921.2		2	112.11	odd	12
3840.2.k.y.1921.1		2	112.53	even	12
3840.2.k.y.1921.2		2	112.109	even	12
4410.2.a.z.1.1		1	21.17	even	6
4800.2.a.d.1.1		1	280.179	odd	6
4800.2.a.cq.1.1		1	280.109	even	6
4800.2.f.p.3649.1		2	280.53	odd	12
4800.2.f.p.3649.2		2	280.277	odd	12
4800.2.f.w.3649.1		2	280.67	even	12
4800.2.f.w.3649.2		2	280.123	even	12
5070.2.a.w.1.1		1	91.25	even	6
5070.2.b.k.1351.1		2	91.60	odd	12
5070.2.b.k.1351.2		2	91.18	odd	12
7350.2.a.ct.1.1		1	35.24	odd	6
8670.2.a.g.1.1		1	119.67	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 $\F_{q}$
Belyi maps

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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{12} +2.00000 q^{13} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(0.500000 - 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} -1.00000 q^{20} +(0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} +1.00000 q^{27} -6.00000 q^{29} +(-0.500000 - 0.866025i) q^{30} +(-4.00000 + 6.92820i) q^{31} +(0.500000 - 0.866025i) q^{32} -6.00000 q^{34} +1.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(-0.500000 - 0.866025i) q^{40} -6.00000 q^{41} -4.00000 q^{43} +(0.500000 - 0.866025i) q^{45} +1.00000 q^{48} -1.00000 q^{50} +(-3.00000 - 5.19615i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} +(0.500000 + 0.866025i) q^{54} -4.00000 q^{57} +(-3.00000 - 5.19615i) q^{58} +(0.500000 - 0.866025i) q^{60} +(5.00000 + 8.66025i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(0.500000 + 0.866025i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-0.500000 - 0.866025i) q^{75} -4.00000 q^{76} -2.00000 q^{78} +(-4.00000 - 6.92820i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.00000 - 5.19615i) q^{82} +12.0000 q^{83} -6.00000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(3.00000 - 5.19615i) q^{87} +(-9.00000 - 15.5885i) q^{89} +1.00000 q^{90} +(-4.00000 - 6.92820i) q^{93} +(-2.00000 + 3.46410i) q^{95} +(0.500000 + 0.866025i) q^{96} +2.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} + q^{5} - 2 q^{6} - 2 q^{8} - q^{9} - q^{10} - q^{12} + 4 q^{13} - 2 q^{15} - q^{16} - 6 q^{17} + q^{18} + 4 q^{19} - 2 q^{20} + q^{24} - q^{25} + 2 q^{26} + 2 q^{27}+ \cdots + 4 q^{97}+O(q^{100}) \) 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 + 4 * q^19 - 2 * q^20 + q^24 - q^25 + 2 * q^26 + 2 * q^27 - 12 * q^29 - q^30 - 8 * q^31 + q^32 - 12 * q^34 + 2 * q^36 - 2 * q^37 - 4 * 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 - 8 * q^57 - 6 * q^58 + q^60 + 10 * q^61 - 16 * q^62 + 2 * q^64 + 2 * q^65 + 4 * q^67 - 6 * q^68 + q^72 - 2 * q^73 + 2 * q^74 - q^75 - 8 * 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 - 18 * q^89 + 2 * q^90 - 8 * q^93 - 4 * q^95 + q^96 + 4 * q^97

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