LMFDB - Embedded newform 1470.2.n.h.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(79,1470)]

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, 3, 2]))

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

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

chi := DirichletCharacter("1470.79");

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.n (of order $6$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1470.79
Dual form			1470.2.n.h.949.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.86603 - 1.23205i) q^{5} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.23205 - 0.133975i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(0.866025 + 0.500000i) q^{12} -6.00000i q^{13} +(1.00000 - 2.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.73205 - 1.00000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(2.00000 + 1.00000i) q^{20} -2.00000i q^{22} +(-3.46410 - 2.00000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.96410 - 4.59808i) q^{25} +(3.00000 - 5.19615i) q^{26} -1.00000i q^{27} +(1.86603 - 1.23205i) q^{30} +(4.00000 + 6.92820i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.73205 - 1.00000i) q^{33} +2.00000 q^{34} +1.00000 q^{36} +(-1.73205 - 1.00000i) q^{37} +(-3.00000 - 5.19615i) q^{39} +(1.23205 + 1.86603i) q^{40} +2.00000 q^{41} +4.00000i q^{43} +(1.00000 - 1.73205i) q^{44} +(-0.133975 - 2.23205i) q^{45} +(-2.00000 - 3.46410i) q^{46} +(6.92820 + 4.00000i) q^{47} +1.00000i q^{48} +(4.00000 - 3.00000i) q^{50} +(1.00000 - 1.73205i) q^{51} +(5.19615 - 3.00000i) q^{52} +(-5.19615 + 3.00000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-4.00000 - 2.00000i) q^{55} +(5.00000 + 8.66025i) q^{59} +(2.23205 - 0.133975i) q^{60} +(-1.00000 + 1.73205i) q^{61} +8.00000i q^{62} -1.00000 q^{64} +(-7.39230 - 11.1962i) q^{65} +(-1.00000 - 1.73205i) q^{66} +(-6.92820 + 4.00000i) q^{67} +(1.73205 + 1.00000i) q^{68} -4.00000 q^{69} +12.0000 q^{71} +(0.866025 + 0.500000i) q^{72} +(3.46410 - 2.00000i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-0.598076 - 4.96410i) q^{75} -6.00000i q^{78} +(0.133975 + 2.23205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.73205 + 1.00000i) q^{82} +4.00000i q^{83} +(2.00000 - 4.00000i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(1.73205 - 1.00000i) q^{88} +(-5.00000 + 8.66025i) q^{89} +(1.00000 - 2.00000i) q^{90} -4.00000i q^{92} +(6.92820 + 4.00000i) q^{93} +(4.00000 + 6.92820i) q^{94} +(-0.500000 + 0.866025i) q^{96} -8.00000i q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 4 q^{5} + 4 q^{6} + 2 q^{9} + 2 q^{10} - 4 q^{11} + 4 q^{15} - 2 q^{16} + 8 q^{20} + 2 q^{24} - 6 q^{25} + 12 q^{26} + 4 q^{30} + 16 q^{31} + 8 q^{34} + 4 q^{36} - 12 q^{39} - 2 q^{40} + 8 q^{41}+ \cdots - 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 4 * q^5 + 4 * q^6 + 2 * q^9 + 2 * q^10 - 4 * q^11 + 4 * q^15 - 2 * q^16 + 8 * q^20 + 2 * q^24 - 6 * q^25 + 12 * q^26 + 4 * q^30 + 16 * q^31 + 8 * q^34 + 4 * q^36 - 12 * q^39 - 2 * q^40 + 8 * q^41 + 4 * q^44 - 4 * q^45 - 8 * q^46 + 16 * q^50 + 4 * q^51 + 2 * q^54 - 16 * q^55 + 20 * q^59 + 2 * q^60 - 4 * q^61 - 4 * q^64 + 12 * q^65 - 4 * q^66 - 16 * q^69 + 48 * q^71 - 4 * q^74 + 8 * q^75 + 4 * q^80 - 2 * q^81 + 8 * q^85 - 8 * q^86 - 20 * q^89 + 4 * q^90 + 16 * q^94 - 2 * q^96 - 8 * q^99

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.86603	−	1.23205i	0.834512	−	0.550990i
$5$	1.86603	−	1.23205i	0.834512	−	0.550990i
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	2.23205	−	0.133975i	0.705836	−	0.0423665i
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$		−	6.00000i		−	1.66410i	−0.554700	−	0.832050i	$-0.687167\pi$
$13$		−	6.00000i		−	1.66410i	0.554700	−	0.832050i	$-0.312833\pi$
$14$		0			0
$15$	1.00000	−	2.00000i	0.258199	−	0.516398i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.73205	−	1.00000i	0.420084	−	0.242536i	−0.275029	−	0.961436i	$-0.588688\pi$
$17$	1.73205	−	1.00000i	0.420084	−	0.242536i	0.695113	+	0.718900i	$0.255354\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$	2.00000	+	1.00000i	0.447214	+	0.223607i
$21$		0			0
$22$		−	2.00000i		−	0.426401i
$23$	−3.46410	−	2.00000i	−0.722315	−	0.417029i	0.0932891	−	0.995639i	$-0.470262\pi$
$23$	−3.46410	−	2.00000i	−0.722315	−	0.417029i	−0.815604	+	0.578610i	$0.803595\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	1.96410	−	4.59808i	0.392820	−	0.919615i
$26$	3.00000	−	5.19615i	0.588348	−	1.01905i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	1.86603	−	1.23205i	0.340688	−	0.224941i
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884683\pi$
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−1.73205	−	1.00000i	−0.301511	−	0.174078i
$34$	2.00000			0.342997
$35$		0			0
$36$	1.00000			0.166667
$37$	−1.73205	−	1.00000i	−0.284747	−	0.164399i	0.350823	−	0.936442i	$-0.385902\pi$
$37$	−1.73205	−	1.00000i	−0.284747	−	0.164399i	−0.635571	+	0.772043i	$0.719235\pi$
$38$		0			0
$39$	−3.00000	−	5.19615i	−0.480384	−	0.832050i
$40$	1.23205	+	1.86603i	0.194804	+	0.295045i
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$		0			0
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$	1.00000	−	1.73205i	0.150756	−	0.261116i
$45$	−0.133975	−	2.23205i	−0.0199718	−	0.332734i
$46$	−2.00000	−	3.46410i	−0.294884	−	0.510754i
$47$	6.92820	+	4.00000i	1.01058	+	0.583460i	0.911362	−	0.411606i	$-0.135032\pi$
$47$	6.92820	+	4.00000i	1.01058	+	0.583460i	0.0992202	+	0.995066i	$0.468365\pi$
$48$			1.00000i			0.144338i
$49$		0			0
$50$	4.00000	−	3.00000i	0.565685	−	0.424264i
$51$	1.00000	−	1.73205i	0.140028	−	0.242536i
$52$	5.19615	−	3.00000i	0.720577	−	0.416025i
$53$	−5.19615	+	3.00000i	−0.713746	+	0.412082i	−0.812447	−	0.583036i	$-0.801865\pi$
$53$	−5.19615	+	3.00000i	−0.713746	+	0.412082i	0.0987002	+	0.995117i	$0.468532\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−4.00000	−	2.00000i	−0.539360	−	0.269680i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.00000	+	8.66025i	0.650945	+	1.12747i	0.982894	+	0.184172i	$0.0589603\pi$
$59$	5.00000	+	8.66025i	0.650945	+	1.12747i	−0.331949	+	0.943297i	$0.607706\pi$
$60$	2.23205	−	0.133975i	0.288157	−	0.0172960i
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$			8.00000i			1.01600i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−7.39230	−	11.1962i	−0.916903	−	1.38871i
$66$	−1.00000	−	1.73205i	−0.123091	−	0.213201i
$67$	−6.92820	+	4.00000i	−0.846415	+	0.488678i	−0.859440	−	0.511237i	$-0.829187\pi$
$67$	−6.92820	+	4.00000i	−0.846415	+	0.488678i	0.0130248	+	0.999915i	$0.495854\pi$
$68$	1.73205	+	1.00000i	0.210042	+	0.121268i
$69$	−4.00000			−0.481543
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	3.46410	−	2.00000i	0.405442	−	0.234082i	−0.283387	−	0.959006i	$-0.591458\pi$
$73$	3.46410	−	2.00000i	0.405442	−	0.234082i	0.688830	+	0.724923i	$0.258125\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$	−0.598076	−	4.96410i	−0.0690599	−	0.573205i
$76$		0			0
$77$		0			0
$78$		−	6.00000i		−	0.679366i
$79$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$79$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$80$	0.133975	+	2.23205i	0.0149788	+	0.249551i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.73205	+	1.00000i	0.191273	+	0.110432i
$83$			4.00000i			0.439057i	0.975606	+	0.219529i	$0.0704519\pi$
$83$			4.00000i			0.439057i	−0.975606	+	0.219529i	$0.929548\pi$
$84$		0			0
$85$	2.00000	−	4.00000i	0.216930	−	0.433861i
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$		0			0
$88$	1.73205	−	1.00000i	0.184637	−	0.106600i
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	0.469389	+	0.882992i	$0.344474\pi$
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	−0.999388	+	0.0349934i	$0.988859\pi$
$90$	1.00000	−	2.00000i	0.105409	−	0.210819i
$91$		0			0
$92$		−	4.00000i		−	0.417029i
$93$	6.92820	+	4.00000i	0.718421	+	0.414781i
$94$	4.00000	+	6.92820i	0.412568	+	0.714590i
$95$		0			0
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$		−	8.00000i		−	0.812277i	−0.913812	−	0.406138i	$-0.866875\pi$
$97$		−	8.00000i		−	0.812277i	0.913812	−	0.406138i	$-0.133125\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$	4.96410	−	0.598076i	0.496410	−	0.0598076i
$101$	4.00000	+	6.92820i	0.398015	+	0.689382i	0.993481	−	0.113998i	$-0.0363659\pi$
$101$	4.00000	+	6.92820i	0.398015	+	0.689382i	−0.595466	+	0.803380i	$0.703033\pi$
$102$	1.73205	−	1.00000i	0.171499	−	0.0990148i
$103$	−12.1244	−	7.00000i	−1.19465	−	0.689730i	−0.235291	−	0.971925i	$-0.575604\pi$
$103$	−12.1244	−	7.00000i	−1.19465	−	0.689730i	−0.959357	+	0.282194i	$0.908938\pi$
$104$	6.00000			0.588348
$105$		0			0
$106$	−6.00000			−0.582772
$107$	−10.3923	−	6.00000i	−1.00466	−	0.580042i	−0.0950377	−	0.995474i	$-0.530297\pi$
$107$	−10.3923	−	6.00000i	−1.00466	−	0.580042i	−0.909624	+	0.415432i	$0.863630\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	0.999708	−	0.0241802i	$-0.00769755\pi$
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	−0.520794	+	0.853682i	$0.674364\pi$
$110$	−2.46410	−	3.73205i	−0.234943	−	0.355837i
$111$	−2.00000			−0.189832
$112$		0			0
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$		0			0
$115$	−8.92820	+	0.535898i	−0.832559	+	0.0499728i
$116$		0			0
$117$	−5.19615	−	3.00000i	−0.480384	−	0.277350i
$118$			10.0000i			0.920575i
$119$		0			0
$120$	2.00000	+	1.00000i	0.182574	+	0.0912871i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−1.73205	+	1.00000i	−0.156813	+	0.0905357i
$123$	1.73205	−	1.00000i	0.156174	−	0.0901670i
$124$	−4.00000	+	6.92820i	−0.359211	+	0.622171i
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$			2.00000i			0.177471i	0.996055	+	0.0887357i	$0.0282826\pi$
$127$			2.00000i			0.177471i	−0.996055	+	0.0887357i	$0.971717\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$	−0.803848	−	13.3923i	−0.0705021	−	1.17458i
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	−0.141865	−	0.989886i	$-0.545310\pi$
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	0.928199	−	0.372084i	$-0.121357\pi$
$132$		−	2.00000i		−	0.174078i
$133$		0			0
$134$	−8.00000			−0.691095
$135$	−1.23205	−	1.86603i	−0.106038	−	0.160602i
$136$	1.00000	+	1.73205i	0.0857493	+	0.148522i
$137$	−15.5885	+	9.00000i	−1.33181	+	0.768922i	−0.985577	−	0.169226i	$-0.945873\pi$
$137$	−15.5885	+	9.00000i	−1.33181	+	0.768922i	−0.346235	+	0.938148i	$0.612540\pi$
$138$	−3.46410	−	2.00000i	−0.294884	−	0.170251i
$139$	20.0000			1.69638			0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000			1.69638			0.848189	+	0.529694i	$0.177693\pi$
$140$		0			0
$141$	8.00000			0.673722
$142$	10.3923	+	6.00000i	0.872103	+	0.503509i
$143$	−10.3923	+	6.00000i	−0.869048	+	0.501745i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$		0			0
$146$	4.00000			0.331042
$147$		0			0
$148$		−	2.00000i		−	0.164399i
$149$	−10.0000	+	17.3205i	−0.819232	+	1.41895i	0.0870170	+	0.996207i	$0.472267\pi$
$149$	−10.0000	+	17.3205i	−0.819232	+	1.41895i	−0.906249	+	0.422744i	$0.861067\pi$
$150$	1.96410	−	4.59808i	0.160368	−	0.375431i
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	0.981617	−	0.190864i	$-0.0611289\pi$
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	−0.656101	+	0.754673i	$0.727796\pi$
$152$		0			0
$153$		−	2.00000i		−	0.161690i
$154$		0			0
$155$	16.0000	+	8.00000i	1.28515	+	0.642575i
$156$	3.00000	−	5.19615i	0.240192	−	0.416025i
$157$	19.0526	−	11.0000i	1.52056	−	0.877896i	0.520854	−	0.853646i	$-0.325614\pi$
$157$	19.0526	−	11.0000i	1.52056	−	0.877896i	0.999706	−	0.0242497i	$-0.00771967\pi$
$158$		0			0
$159$	−3.00000	+	5.19615i	−0.237915	+	0.412082i
$160$	−1.00000	+	2.00000i	−0.0790569	+	0.158114i
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	13.8564	+	8.00000i	1.08532	+	0.626608i	0.932326	−	0.361619i	$-0.117776\pi$
$163$	13.8564	+	8.00000i	1.08532	+	0.626608i	0.152992	+	0.988227i	$0.451109\pi$
$164$	1.00000	+	1.73205i	0.0780869	+	0.135250i
$165$	−4.46410	+	0.267949i	−0.347530	+	0.0208598i
$166$	−2.00000	+	3.46410i	−0.155230	+	0.268866i
$167$			12.0000i			0.928588i	0.885681	+	0.464294i	$0.153692\pi$
$167$			12.0000i			0.928588i	−0.885681	+	0.464294i	$0.846308\pi$
$168$		0			0
$169$	−23.0000			−1.76923
$170$	3.73205	−	2.46410i	0.286235	−	0.188988i
$171$		0			0
$172$	−3.46410	+	2.00000i	−0.264135	+	0.152499i
$173$	−12.1244	−	7.00000i	−0.921798	−	0.532200i	−0.0375896	−	0.999293i	$-0.511968\pi$
$173$	−12.1244	−	7.00000i	−0.921798	−	0.532200i	−0.884208	+	0.467093i	$0.845301\pi$
$174$		0			0
$175$		0			0
$176$	2.00000			0.150756
$177$	8.66025	+	5.00000i	0.650945	+	0.375823i
$178$	−8.66025	+	5.00000i	−0.649113	+	0.374766i
$179$	5.00000	+	8.66025i	0.373718	+	0.647298i	0.990134	−	0.140122i	$-0.0447496\pi$
$179$	5.00000	+	8.66025i	0.373718	+	0.647298i	−0.616417	+	0.787420i	$0.711416\pi$
$180$	1.86603	−	1.23205i	0.139085	−	0.0918316i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$			2.00000i			0.147844i
$184$	2.00000	−	3.46410i	0.147442	−	0.255377i
$185$	−4.46410	+	0.267949i	−0.328207	+	0.0197000i
$186$	4.00000	+	6.92820i	0.293294	+	0.508001i
$187$	−3.46410	−	2.00000i	−0.253320	−	0.146254i
$188$			8.00000i			0.583460i
$189$		0			0
$190$		0			0
$191$	−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	$0.309616\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	3.46410	−	2.00000i	0.249351	−	0.143963i	−0.370116	−	0.928986i	$-0.620682\pi$
$193$	3.46410	−	2.00000i	0.249351	−	0.143963i	0.619467	+	0.785022i	$0.287349\pi$
$194$	4.00000	−	6.92820i	0.287183	−	0.497416i
$195$	−12.0000	−	6.00000i	−0.859338	−	0.429669i
$196$		0			0
$197$			22.0000i			1.56744i	0.621117	+	0.783718i	$0.286679\pi$
$197$			22.0000i			1.56744i	−0.621117	+	0.783718i	$0.713321\pi$
$198$	−1.73205	−	1.00000i	−0.123091	−	0.0710669i
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$	4.59808	+	1.96410i	0.325133	+	0.138883i
$201$	−4.00000	+	6.92820i	−0.282138	+	0.488678i
$202$			8.00000i			0.562878i
$203$		0			0
$204$	2.00000			0.140028
$205$	3.73205	−	2.46410i	0.260658	−	0.172100i
$206$	−7.00000	−	12.1244i	−0.487713	−	0.844744i
$207$	−3.46410	+	2.00000i	−0.240772	+	0.139010i
$208$	5.19615	+	3.00000i	0.360288	+	0.208013i
$209$		0			0
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$	−5.19615	−	3.00000i	−0.356873	−	0.206041i
$213$	10.3923	−	6.00000i	0.712069	−	0.411113i
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	4.92820	+	7.46410i	0.336101	+	0.509048i
$216$	1.00000			0.0680414
$217$		0			0
$218$			10.0000i			0.677285i
$219$	2.00000	−	3.46410i	0.135147	−	0.234082i
$220$	−0.267949	−	4.46410i	−0.0180651	−	0.300970i
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$	−1.73205	−	1.00000i	−0.116248	−	0.0671156i
$223$		−	26.0000i		−	1.74109i	−0.492090	−	0.870544i	$-0.663767\pi$
$223$		−	26.0000i		−	1.74109i	0.492090	−	0.870544i	$-0.336233\pi$
$224$		0			0
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$	3.00000	−	5.19615i	0.199557	−	0.345643i
$227$	−24.2487	+	14.0000i	−1.60944	+	0.929213i	−0.619949	+	0.784642i	$0.712847\pi$
$227$	−24.2487	+	14.0000i	−1.60944	+	0.929213i	−0.989494	+	0.144571i	$0.953820\pi$
$228$		0			0
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	−0.982592	−	0.185776i	$-0.940520\pi$
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	0.652183	+	0.758062i	$0.273853\pi$
$230$	−8.00000	−	4.00000i	−0.527504	−	0.263752i
$231$		0			0
$232$		0			0
$233$	−12.1244	−	7.00000i	−0.794293	−	0.458585i	0.0471787	−	0.998886i	$-0.484977\pi$
$233$	−12.1244	−	7.00000i	−0.794293	−	0.458585i	−0.841472	+	0.540301i	$0.818310\pi$
$234$	−3.00000	−	5.19615i	−0.196116	−	0.339683i
$235$	17.8564	−	1.07180i	1.16482	−	0.0699163i
$236$	−5.00000	+	8.66025i	−0.325472	+	0.563735i
$237$		0			0
$238$		0			0
$239$	−20.0000			−1.29369			−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000			−1.29369			−0.646846	+	0.762620i	$0.723912\pi$
$240$	1.23205	+	1.86603i	0.0795285	+	0.120451i
$241$	−11.0000	−	19.0526i	−0.708572	−	1.22728i	−0.965387	−	0.260822i	$-0.916006\pi$
$241$	−11.0000	−	19.0526i	−0.708572	−	1.22728i	0.256814	−	0.966461i	$-0.417327\pi$
$242$	6.06218	−	3.50000i	0.389692	−	0.224989i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−2.00000			−0.128037
$245$		0			0
$246$	2.00000			0.127515
$247$		0			0
$248$	−6.92820	+	4.00000i	−0.439941	+	0.254000i
$249$	2.00000	+	3.46410i	0.126745	+	0.219529i
$250$	3.76795	−	10.5263i	0.238306	−	0.665740i
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$		0			0
$253$			8.00000i			0.502956i
$254$	−1.00000	+	1.73205i	−0.0627456	+	0.108679i
$255$	−0.267949	−	4.46410i	−0.0167796	−	0.279553i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.5885	+	9.00000i	0.972381	+	0.561405i	0.899961	−	0.435970i	$-0.143595\pi$
$257$	15.5885	+	9.00000i	0.972381	+	0.561405i	0.0724199	+	0.997374i	$0.476928\pi$
$258$			4.00000i			0.249029i
$259$		0			0
$260$	6.00000	−	12.0000i	0.372104	−	0.744208i
$261$		0			0
$262$	15.5885	−	9.00000i	0.963058	−	0.556022i
$263$	3.46410	−	2.00000i	0.213606	−	0.123325i	−0.389380	−	0.921077i	$-0.627311\pi$
$263$	3.46410	−	2.00000i	0.213606	−	0.123325i	0.602986	+	0.797752i	$0.293977\pi$
$264$	1.00000	−	1.73205i	0.0615457	−	0.106600i
$265$	−6.00000	+	12.0000i	−0.368577	+	0.737154i
$266$		0			0
$267$			10.0000i			0.611990i
$268$	−6.92820	−	4.00000i	−0.423207	−	0.244339i
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$	−0.133975	−	2.23205i	−0.00815343	−	0.135838i
$271$	4.00000	−	6.92820i	0.242983	−	0.420858i	−0.718580	−	0.695444i	$-0.755208\pi$
$271$	4.00000	−	6.92820i	0.242983	−	0.420858i	0.961563	+	0.274586i	$0.0885408\pi$
$272$			2.00000i			0.121268i
$273$		0			0
$274$	−18.0000			−1.08742
$275$	−9.92820	+	1.19615i	−0.598693	+	0.0721307i
$276$	−2.00000	−	3.46410i	−0.120386	−	0.208514i
$277$	1.73205	−	1.00000i	0.104069	−	0.0600842i	−0.447062	−	0.894503i	$-0.647530\pi$
$277$	1.73205	−	1.00000i	0.104069	−	0.0600842i	0.551131	+	0.834419i	$0.314196\pi$
$278$	17.3205	+	10.0000i	1.03882	+	0.599760i
$279$	8.00000			0.478947
$280$		0			0
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$	6.92820	+	4.00000i	0.412568	+	0.238197i
$283$	−13.8564	+	8.00000i	−0.823678	+	0.475551i	−0.851683	−	0.524057i	$-0.824418\pi$
$283$	−13.8564	+	8.00000i	−0.823678	+	0.475551i	0.0280052	+	0.999608i	$0.491084\pi$
$284$	6.00000	+	10.3923i	0.356034	+	0.616670i
$285$		0			0
$286$	−12.0000			−0.709575
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	−6.50000	+	11.2583i	−0.382353	+	0.662255i
$290$		0			0
$291$	−4.00000	−	6.92820i	−0.234484	−	0.406138i
$292$	3.46410	+	2.00000i	0.202721	+	0.117041i
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$		0			0
$295$	20.0000	+	10.0000i	1.16445	+	0.582223i
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$	−1.73205	+	1.00000i	−0.100504	+	0.0580259i
$298$	−17.3205	+	10.0000i	−1.00335	+	0.579284i
$299$	−12.0000	+	20.7846i	−0.693978	+	1.20201i
$300$	4.00000	−	3.00000i	0.230940	−	0.173205i
$301$		0			0
$302$			8.00000i			0.460348i
$303$	6.92820	+	4.00000i	0.398015	+	0.229794i
$304$		0			0
$305$	0.267949	+	4.46410i	0.0153427	+	0.255614i
$306$	1.00000	−	1.73205i	0.0571662	−	0.0990148i
$307$			12.0000i			0.684876i	0.939540	+	0.342438i	$0.111253\pi$
$307$			12.0000i			0.684876i	−0.939540	+	0.342438i	$0.888747\pi$
$308$		0			0
$309$	−14.0000			−0.796432
$310$	9.85641	+	14.9282i	0.559806	+	0.847865i
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	0.644246	−	0.764818i	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$	5.19615	−	3.00000i	0.294174	−	0.169842i
$313$	−3.46410	−	2.00000i	−0.195803	−	0.113047i	0.398894	−	0.916997i	$-0.369394\pi$
$313$	−3.46410	−	2.00000i	−0.195803	−	0.113047i	−0.594696	+	0.803951i	$0.702728\pi$
$314$	22.0000			1.24153
$315$		0			0
$316$		0			0
$317$	−1.73205	−	1.00000i	−0.0972817	−	0.0561656i	0.450570	−	0.892741i	$-0.351221\pi$
$317$	−1.73205	−	1.00000i	−0.0972817	−	0.0561656i	−0.547852	+	0.836576i	$0.684554\pi$
$318$	−5.19615	+	3.00000i	−0.291386	+	0.168232i
$319$		0			0
$320$	−1.86603	+	1.23205i	−0.104314	+	0.0688737i
$321$	−12.0000			−0.669775
$322$		0			0
$323$		0			0
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−27.5885	−	11.7846i	−1.53033	−	0.653693i
$326$	8.00000	+	13.8564i	0.443079	+	0.767435i
$327$	8.66025	+	5.00000i	0.478913	+	0.276501i
$328$			2.00000i			0.110432i
$329$		0			0
$330$	−4.00000	−	2.00000i	−0.220193	−	0.110096i
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	−0.734905	−	0.678170i	$-0.762773\pi$
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	0.954765	+	0.297361i	$0.0961066\pi$
$332$	−3.46410	+	2.00000i	−0.190117	+	0.109764i
$333$	−1.73205	+	1.00000i	−0.0949158	+	0.0547997i
$334$	−6.00000	+	10.3923i	−0.328305	+	0.568642i
$335$	−8.00000	+	16.0000i	−0.437087	+	0.874173i
$336$		0			0
$337$		−	28.0000i		−	1.52526i	−0.646837	−	0.762629i	$-0.723908\pi$
$337$		−	28.0000i		−	1.52526i	0.646837	−	0.762629i	$-0.276092\pi$
$338$	−19.9186	−	11.5000i	−1.08343	−	0.625518i
$339$	−3.00000	−	5.19615i	−0.162938	−	0.282216i
$340$	4.46410	−	0.267949i	0.242100	−	0.0145316i
$341$	8.00000	−	13.8564i	0.433224	−	0.750366i
$342$		0			0
$343$		0			0
$344$	−4.00000			−0.215666
$345$	−7.46410	+	4.92820i	−0.401854	+	0.265326i
$346$	−7.00000	−	12.1244i	−0.376322	−	0.651809i
$347$	10.3923	−	6.00000i	0.557888	−	0.322097i	−0.194409	−	0.980921i	$-0.562279\pi$
$347$	10.3923	−	6.00000i	0.557888	−	0.322097i	0.752297	+	0.658824i	$0.228946\pi$
$348$		0			0
$349$	−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
$351$	−6.00000			−0.320256
$352$	1.73205	+	1.00000i	0.0923186	+	0.0533002i
$353$	12.1244	−	7.00000i	0.645314	−	0.372572i	−0.141344	−	0.989960i	$-0.545142\pi$
$353$	12.1244	−	7.00000i	0.645314	−	0.372572i	0.786659	+	0.617388i	$0.211809\pi$
$354$	5.00000	+	8.66025i	0.265747	+	0.460287i
$355$	22.3923	−	14.7846i	1.18846	−	0.784686i
$356$	−10.0000			−0.529999
$357$		0			0
$358$			10.0000i			0.528516i
$359$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$359$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$360$	2.23205	−	0.133975i	0.117639	−	0.00706108i
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$	1.73205	+	1.00000i	0.0910346	+	0.0525588i
$363$		−	7.00000i		−	0.367405i
$364$		0			0
$365$	4.00000	−	8.00000i	0.209370	−	0.418739i
$366$	−1.00000	+	1.73205i	−0.0522708	+	0.0905357i
$367$	1.73205	−	1.00000i	0.0904123	−	0.0521996i	−0.454112	−	0.890945i	$-0.650043\pi$
$367$	1.73205	−	1.00000i	0.0904123	−	0.0521996i	0.544524	+	0.838745i	$0.316710\pi$
$368$	3.46410	−	2.00000i	0.180579	−	0.104257i
$369$	1.00000	−	1.73205i	0.0520579	−	0.0901670i
$370$	−4.00000	−	2.00000i	−0.207950	−	0.103975i
$371$		0			0
$372$			8.00000i			0.414781i
$373$	5.19615	+	3.00000i	0.269047	+	0.155334i	0.628454	−	0.777847i	$-0.283688\pi$
$373$	5.19615	+	3.00000i	0.269047	+	0.155334i	−0.359408	+	0.933181i	$0.617021\pi$
$374$	−2.00000	−	3.46410i	−0.103418	−	0.179124i
$375$	−7.23205	−	8.52628i	−0.373461	−	0.440295i
$376$	−4.00000	+	6.92820i	−0.206284	+	0.357295i
$377$		0			0
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$		0			0
$381$	1.00000	+	1.73205i	0.0512316	+	0.0887357i
$382$	−10.3923	+	6.00000i	−0.531717	+	0.306987i
$383$	13.8564	+	8.00000i	0.708029	+	0.408781i	0.810331	−	0.585973i	$-0.199287\pi$
$383$	13.8564	+	8.00000i	0.708029	+	0.408781i	−0.102302	+	0.994753i	$0.532621\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	4.00000			0.203595
$387$	3.46410	+	2.00000i	0.176090	+	0.101666i
$388$	6.92820	−	4.00000i	0.351726	−	0.203069i
$389$	10.0000	+	17.3205i	0.507020	+	0.878185i	0.999967	+	0.00812520i	$0.00258636\pi$
$389$	10.0000	+	17.3205i	0.507020	+	0.878185i	−0.492947	+	0.870059i	$0.664080\pi$
$390$	−7.39230	−	11.1962i	−0.374324	−	0.566939i
$391$	−8.00000			−0.404577
$392$		0			0
$393$		−	18.0000i		−	0.907980i
$394$	−11.0000	+	19.0526i	−0.554172	+	0.959854i
$395$		0			0
$396$	−1.00000	−	1.73205i	−0.0502519	−	0.0870388i
$397$	−1.73205	−	1.00000i	−0.0869291	−	0.0501886i	0.455905	−	0.890028i	$-0.349316\pi$
$397$	−1.73205	−	1.00000i	−0.0869291	−	0.0501886i	−0.542834	+	0.839840i	$0.682649\pi$
$398$		0			0
$399$		0			0
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	−11.0000	+	19.0526i	−0.549314	+	0.951439i	0.449008	+	0.893528i	$0.351777\pi$
$401$	−11.0000	+	19.0526i	−0.549314	+	0.951439i	−0.998322	+	0.0579116i	$0.981556\pi$
$402$	−6.92820	+	4.00000i	−0.345547	+	0.199502i
$403$	41.5692	−	24.0000i	2.07071	−	1.19553i
$404$	−4.00000	+	6.92820i	−0.199007	+	0.344691i
$405$	−2.00000	−	1.00000i	−0.0993808	−	0.0496904i
$406$		0			0
$407$			4.00000i			0.198273i
$408$	1.73205	+	1.00000i	0.0857493	+	0.0495074i
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	0.715523	−	0.698589i	$-0.246188\pi$
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	−0.962757	+	0.270367i	$0.912855\pi$
$410$	4.46410	−	0.267949i	0.220466	−	0.0132331i
$411$	−9.00000	+	15.5885i	−0.443937	+	0.768922i
$412$		−	14.0000i		−	0.689730i
$413$		0			0
$414$	−4.00000			−0.196589
$415$	4.92820	+	7.46410i	0.241916	+	0.366398i
$416$	3.00000	+	5.19615i	0.147087	+	0.254762i
$417$	17.3205	−	10.0000i	0.848189	−	0.489702i
$418$		0			0
$419$	10.0000			0.488532			0.244266	−	0.969708i	$-0.421453\pi$
$419$	10.0000			0.488532			0.244266	+	0.969708i	$0.421453\pi$
$420$		0			0
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$	10.3923	+	6.00000i	0.505889	+	0.292075i
$423$	6.92820	−	4.00000i	0.336861	−	0.194487i
$424$	−3.00000	−	5.19615i	−0.145693	−	0.252347i
$425$	−1.19615	−	9.92820i	−0.0580219	−	0.481589i
$426$	12.0000			0.581402
$427$		0			0
$428$		−	12.0000i		−	0.580042i
$429$	−6.00000	+	10.3923i	−0.289683	+	0.501745i
$430$	0.535898	+	8.92820i	0.0258433	+	0.430556i
$431$	−16.0000	−	27.7128i	−0.770693	−	1.33488i	−0.937184	−	0.348836i	$-0.886577\pi$
$431$	−16.0000	−	27.7128i	−0.770693	−	1.33488i	0.166491	−	0.986043i	$-0.446756\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$			4.00000i			0.192228i	0.995370	+	0.0961139i	$0.0306413\pi$
$433$			4.00000i			0.192228i	−0.995370	+	0.0961139i	$0.969359\pi$
$434$		0			0
$435$		0			0
$436$	−5.00000	+	8.66025i	−0.239457	+	0.414751i
$437$		0			0
$438$	3.46410	−	2.00000i	0.165521	−	0.0955637i
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$	2.00000	−	4.00000i	0.0953463	−	0.190693i
$441$		0			0
$442$		−	12.0000i		−	0.570782i
$443$	31.1769	+	18.0000i	1.48126	+	0.855206i	0.999774	−	0.0212481i	$-0.00676401\pi$
$443$	31.1769	+	18.0000i	1.48126	+	0.855206i	0.481486	+	0.876454i	$0.340097\pi$
$444$	−1.00000	−	1.73205i	−0.0474579	−	0.0821995i
$445$	1.33975	+	22.3205i	0.0635100	+	1.05809i
$446$	13.0000	−	22.5167i	0.615568	−	1.06619i
$447$			20.0000i			0.945968i
$448$		0			0
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$	−0.598076	−	4.96410i	−0.0281936	−	0.234010i
$451$	−2.00000	−	3.46410i	−0.0941763	−	0.163118i
$452$	5.19615	−	3.00000i	0.244406	−	0.141108i
$453$	6.92820	+	4.00000i	0.325515	+	0.187936i
$454$	−28.0000			−1.31411
$455$		0			0
$456$		0			0
$457$	−27.7128	−	16.0000i	−1.29635	−	0.748448i	−0.316579	−	0.948566i	$-0.602534\pi$
$457$	−27.7128	−	16.0000i	−1.29635	−	0.748448i	−0.979772	+	0.200118i	$0.935868\pi$
$458$	−8.66025	+	5.00000i	−0.404667	+	0.233635i
$459$	−1.00000	−	1.73205i	−0.0466760	−	0.0808452i
$460$	−4.92820	−	7.46410i	−0.229779	−	0.348016i
$461$	12.0000			0.558896			0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000			0.558896			0.279448	+	0.960161i	$0.409849\pi$
$462$		0			0
$463$		−	6.00000i		−	0.278844i	−0.990233	−	0.139422i	$-0.955476\pi$
$463$		−	6.00000i		−	0.278844i	0.990233	−	0.139422i	$-0.0445244\pi$
$464$		0			0
$465$	17.8564	−	1.07180i	0.828071	−	0.0497034i
$466$	−7.00000	−	12.1244i	−0.324269	−	0.561650i
$467$	−10.3923	−	6.00000i	−0.480899	−	0.277647i	0.239892	−	0.970799i	$-0.422888\pi$
$467$	−10.3923	−	6.00000i	−0.480899	−	0.277647i	−0.720791	+	0.693153i	$0.756221\pi$
$468$		−	6.00000i		−	0.277350i
$469$		0			0
$470$	16.0000	+	8.00000i	0.738025	+	0.369012i
$471$	11.0000	−	19.0526i	0.506853	−	0.877896i
$472$	−8.66025	+	5.00000i	−0.398621	+	0.230144i
$473$	6.92820	−	4.00000i	0.318559	−	0.183920i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			6.00000i			0.274721i
$478$	−17.3205	−	10.0000i	−0.792222	−	0.457389i
$479$	10.0000	+	17.3205i	0.456912	+	0.791394i	0.998796	−	0.0490589i	$-0.0156222\pi$
$479$	10.0000	+	17.3205i	0.456912	+	0.791394i	−0.541884	+	0.840453i	$0.682289\pi$
$480$	0.133975	+	2.23205i	0.00611508	+	0.101879i
$481$	−6.00000	+	10.3923i	−0.273576	+	0.473848i
$482$		−	22.0000i		−	1.00207i
$483$		0			0
$484$	7.00000			0.318182
$485$	−9.85641	−	14.9282i	−0.447556	−	0.677855i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−15.5885	+	9.00000i	−0.706380	+	0.407829i	−0.809719	−	0.586817i	$-0.800381\pi$
$487$	−15.5885	+	9.00000i	−0.706380	+	0.407829i	0.103339	+	0.994646i	$0.467047\pi$
$488$	−1.73205	−	1.00000i	−0.0784063	−	0.0452679i
$489$	16.0000			0.723545
$490$		0			0
$491$	−18.0000			−0.812329			−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000			−0.812329			−0.406164	+	0.913800i	$0.633134\pi$
$492$	1.73205	+	1.00000i	0.0780869	+	0.0450835i
$493$		0			0
$494$		0			0
$495$	−3.73205	+	2.46410i	−0.167743	+	0.110753i
$496$	−8.00000			−0.359211
$497$		0			0
$498$			4.00000i			0.179244i
$499$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$499$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$500$	8.52628	−	7.23205i	0.381307	−	0.323427i
$501$	6.00000	+	10.3923i	0.268060	+	0.464294i
$502$	−15.5885	−	9.00000i	−0.695747	−	0.401690i
$503$			24.0000i			1.07011i	0.844818	+	0.535054i	$0.179709\pi$
$503$			24.0000i			1.07011i	−0.844818	+	0.535054i	$0.820291\pi$
$504$		0			0
$505$	16.0000	+	8.00000i	0.711991	+	0.355995i
$506$	−4.00000	+	6.92820i	−0.177822	+	0.307996i
$507$	−19.9186	+	11.5000i	−0.884615	+	0.510733i
$508$	−1.73205	+	1.00000i	−0.0768473	+	0.0443678i
$509$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$509$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$510$	2.00000	−	4.00000i	0.0885615	−	0.177123i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	9.00000	+	15.5885i	0.396973	+	0.687577i
$515$	−31.2487	+	1.87564i	−1.37698	+	0.0826508i
$516$	−2.00000	+	3.46410i	−0.0880451	+	0.152499i
$517$		−	16.0000i		−	0.703679i
$518$		0			0
$519$	−14.0000			−0.614532
$520$	11.1962	−	7.39230i	0.490984	−	0.324174i
$521$	−11.0000	−	19.0526i	−0.481919	−	0.834708i	0.517866	−	0.855462i	$-0.326727\pi$
$521$	−11.0000	−	19.0526i	−0.481919	−	0.834708i	−0.999785	+	0.0207541i	$0.993393\pi$
$522$		0			0
$523$	13.8564	+	8.00000i	0.605898	+	0.349816i	0.771358	−	0.636401i	$-0.219578\pi$
$523$	13.8564	+	8.00000i	0.605898	+	0.349816i	−0.165460	+	0.986216i	$0.552911\pi$
$524$	18.0000			0.786334
$525$		0			0
$526$	4.00000			0.174408
$527$	13.8564	+	8.00000i	0.603595	+	0.348485i
$528$	1.73205	−	1.00000i	0.0753778	−	0.0435194i
$529$	−3.50000	−	6.06218i	−0.152174	−	0.263573i
$530$	−11.1962	+	7.39230i	−0.486330	+	0.321101i
$531$	10.0000			0.433963
$532$		0			0
$533$		−	12.0000i		−	0.519778i
$534$	−5.00000	+	8.66025i	−0.216371	+	0.374766i
$535$	−26.7846	+	1.60770i	−1.15800	+	0.0695067i
$536$	−4.00000	−	6.92820i	−0.172774	−	0.299253i
$537$	8.66025	+	5.00000i	0.373718	+	0.215766i
$538$		0			0
$539$		0			0
$540$	1.00000	−	2.00000i	0.0430331	−	0.0860663i
$541$	19.0000	−	32.9090i	0.816874	−	1.41487i	−0.0911008	−	0.995842i	$-0.529039\pi$
$541$	19.0000	−	32.9090i	0.816874	−	1.41487i	0.907975	−	0.419025i	$-0.137628\pi$
$542$	6.92820	−	4.00000i	0.297592	−	0.171815i
$543$	1.73205	−	1.00000i	0.0743294	−	0.0429141i
$544$	−1.00000	+	1.73205i	−0.0428746	+	0.0742611i
$545$	20.0000	+	10.0000i	0.856706	+	0.428353i
$546$		0			0
$547$		−	28.0000i		−	1.19719i	−0.801050	−	0.598597i	$-0.795725\pi$
$547$		−	28.0000i		−	1.19719i	0.801050	−	0.598597i	$-0.204275\pi$
$548$	−15.5885	−	9.00000i	−0.665906	−	0.384461i
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$	−9.19615	−	3.92820i	−0.392125	−	0.167499i
$551$		0			0
$552$		−	4.00000i		−	0.170251i
$553$		0			0
$554$	2.00000			0.0849719
$555$	−3.73205	+	2.46410i	−0.158417	+	0.104595i
$556$	10.0000	+	17.3205i	0.424094	+	0.734553i
$557$	−15.5885	+	9.00000i	−0.660504	+	0.381342i	−0.792469	−	0.609912i	$-0.791205\pi$
$557$	−15.5885	+	9.00000i	−0.660504	+	0.381342i	0.131965	+	0.991254i	$0.457871\pi$
$558$	6.92820	+	4.00000i	0.293294	+	0.169334i
$559$	24.0000			1.01509
$560$		0			0
$561$	−4.00000			−0.168880
$562$	−15.5885	−	9.00000i	−0.657559	−	0.379642i
$563$	38.1051	−	22.0000i	1.60594	−	0.927189i	0.615673	−	0.788002i	$-0.288884\pi$
$563$	38.1051	−	22.0000i	1.60594	−	0.927189i	0.990266	−	0.139188i	$-0.0444492\pi$
$564$	4.00000	+	6.92820i	0.168430	+	0.291730i
$565$	−7.39230	−	11.1962i	−0.310997	−	0.471026i
$566$	−16.0000			−0.672530
$567$		0			0
$568$			12.0000i			0.503509i
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	−0.951592	−	0.307364i	$-0.900553\pi$
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	0.741981	+	0.670421i	$0.233886\pi$
$570$		0			0
$571$	4.00000	+	6.92820i	0.167395	+	0.289936i	0.937503	−	0.347977i	$-0.113131\pi$
$571$	4.00000	+	6.92820i	0.167395	+	0.289936i	−0.770108	+	0.637913i	$0.779798\pi$
$572$	−10.3923	−	6.00000i	−0.434524	−	0.250873i
$573$			12.0000i			0.501307i
$574$		0			0
$575$	−16.0000	+	12.0000i	−0.667246	+	0.500435i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	27.7128	−	16.0000i	1.15370	−	0.666089i	0.203913	−	0.978989i	$-0.434634\pi$
$577$	27.7128	−	16.0000i	1.15370	−	0.666089i	0.949786	+	0.312900i	$0.101301\pi$
$578$	−11.2583	+	6.50000i	−0.468285	+	0.270364i
$579$	2.00000	−	3.46410i	0.0831172	−	0.143963i
$580$		0			0
$581$		0			0
$582$		−	8.00000i		−	0.331611i
$583$	10.3923	+	6.00000i	0.430405	+	0.248495i
$584$	2.00000	+	3.46410i	0.0827606	+	0.143346i
$585$	−13.3923	+	0.803848i	−0.553704	+	0.0332350i
$586$	3.00000	−	5.19615i	0.123929	−	0.214651i
$587$			12.0000i			0.495293i	0.968850	+	0.247647i	$0.0796572\pi$
$587$			12.0000i			0.495293i	−0.968850	+	0.247647i	$0.920343\pi$
$588$		0			0
$589$		0			0
$590$	12.3205	+	18.6603i	0.507227	+	0.768231i
$591$	11.0000	+	19.0526i	0.452480	+	0.783718i
$592$	1.73205	−	1.00000i	0.0711868	−	0.0410997i
$593$	5.19615	+	3.00000i	0.213380	+	0.123195i	0.602881	−	0.797831i	$-0.294019\pi$
$593$	5.19615	+	3.00000i	0.213380	+	0.123195i	−0.389501	+	0.921026i	$0.627353\pi$
$594$	−2.00000			−0.0820610
$595$		0			0
$596$	−20.0000			−0.819232
$597$		0			0
$598$	−20.7846	+	12.0000i	−0.849946	+	0.490716i
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$	4.96410	−	0.598076i	0.202659	−	0.0244164i
$601$	2.00000			0.0815817			0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000			0.0815817			0.0407909	+	0.999168i	$0.487012\pi$
$602$		0			0
$603$			8.00000i			0.325785i
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	−0.937822	−	15.6244i	−0.0381279	−	0.635220i
$606$	4.00000	+	6.92820i	0.162489	+	0.281439i
$607$	−19.0526	−	11.0000i	−0.773320	−	0.446476i	0.0607380	−	0.998154i	$-0.480655\pi$
$607$	−19.0526	−	11.0000i	−0.773320	−	0.446476i	−0.834058	+	0.551678i	$0.813988\pi$
$608$		0			0
$609$		0			0
$610$	−2.00000	+	4.00000i	−0.0809776	+	0.161955i
$611$	24.0000	−	41.5692i	0.970936	−	1.68171i
$612$	1.73205	−	1.00000i	0.0700140	−	0.0404226i
$613$	−22.5167	+	13.0000i	−0.909439	+	0.525065i	−0.880251	−	0.474509i	$-0.842626\pi$
$613$	−22.5167	+	13.0000i	−0.909439	+	0.525065i	−0.0291886	+	0.999574i	$0.509292\pi$
$614$	−6.00000	+	10.3923i	−0.242140	+	0.419399i
$615$	2.00000	−	4.00000i	0.0806478	−	0.161296i
$616$		0			0
$617$			2.00000i			0.0805170i	0.999189	+	0.0402585i	$0.0128181\pi$
$617$			2.00000i			0.0805170i	−0.999189	+	0.0402585i	$0.987182\pi$
$618$	−12.1244	−	7.00000i	−0.487713	−	0.281581i
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	0.993959	−	0.109749i	$-0.0350048\pi$
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	−0.592025	+	0.805919i	$0.701671\pi$
$620$	1.07180	+	17.8564i	0.0430444	+	0.717131i
$621$	−2.00000	+	3.46410i	−0.0802572	+	0.139010i
$622$		−	12.0000i		−	0.481156i
$623$		0			0
$624$	6.00000			0.240192
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$	−2.00000	−	3.46410i	−0.0799361	−	0.138453i
$627$		0			0
$628$	19.0526	+	11.0000i	0.760280	+	0.438948i
$629$	−4.00000			−0.159490
$630$		0			0
$631$	32.0000			1.27390			0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000			1.27390			0.636950	+	0.770905i	$0.280196\pi$
$632$		0			0
$633$	10.3923	−	6.00000i	0.413057	−	0.238479i
$634$	−1.00000	−	1.73205i	−0.0397151	−	0.0687885i
$635$	2.46410	+	3.73205i	0.0977849	+	0.148102i
$636$	−6.00000			−0.237915
$637$		0			0
$638$		0			0
$639$	6.00000	−	10.3923i	0.237356	−	0.411113i
$640$	−2.23205	+	0.133975i	−0.0882296	+	0.00529581i
$641$	−1.00000	−	1.73205i	−0.0394976	−	0.0684119i	0.845601	−	0.533816i	$-0.179242\pi$
$641$	−1.00000	−	1.73205i	−0.0394976	−	0.0684119i	−0.885098	+	0.465404i	$0.845909\pi$
$642$	−10.3923	−	6.00000i	−0.410152	−	0.236801i
$643$			24.0000i			0.946468i	0.880937	+	0.473234i	$0.156913\pi$
$643$			24.0000i			0.946468i	−0.880937	+	0.473234i	$0.843087\pi$
$644$		0			0
$645$	8.00000	+	4.00000i	0.315000	+	0.157500i
$646$		0			0
$647$	−41.5692	+	24.0000i	−1.63425	+	0.943537i	−0.651494	+	0.758654i	$0.725858\pi$
$647$	−41.5692	+	24.0000i	−1.63425	+	0.943537i	−0.982760	+	0.184884i	$0.940809\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	10.0000	−	17.3205i	0.392534	−	0.679889i
$650$	−18.0000	−	24.0000i	−0.706018	−	0.941357i
$651$		0			0
$652$			16.0000i			0.626608i
$653$	22.5167	+	13.0000i	0.881145	+	0.508729i	0.871036	−	0.491220i	$-0.163449\pi$
$653$	22.5167	+	13.0000i	0.881145	+	0.508729i	0.0101092	+	0.999949i	$0.496782\pi$
$654$	5.00000	+	8.66025i	0.195515	+	0.338643i
$655$	−2.41154	−	40.1769i	−0.0942268	−	1.56984i
$656$	−1.00000	+	1.73205i	−0.0390434	+	0.0676252i
$657$		−	4.00000i		−	0.156055i
$658$		0			0
$659$	50.0000			1.94772			0.973862	−	0.227142i	$-0.0729380\pi$
$659$	50.0000			1.94772			0.973862	+	0.227142i	$0.0729380\pi$
$660$	−2.46410	−	3.73205i	−0.0959150	−	0.145270i
$661$	−1.00000	−	1.73205i	−0.0388955	−	0.0673690i	0.845922	−	0.533306i	$-0.179051\pi$
$661$	−1.00000	−	1.73205i	−0.0388955	−	0.0673690i	−0.884818	+	0.465937i	$0.845717\pi$
$662$	6.92820	−	4.00000i	0.269272	−	0.155464i
$663$	−10.3923	−	6.00000i	−0.403604	−	0.233021i
$664$	−4.00000			−0.155230
$665$		0			0
$666$	−2.00000			−0.0774984
$667$		0			0
$668$	−10.3923	+	6.00000i	−0.402090	+	0.232147i
$669$	−13.0000	−	22.5167i	−0.502609	−	0.870544i
$670$	−14.9282	+	9.85641i	−0.576727	+	0.380786i
$671$	4.00000			0.154418
$672$		0			0
$673$		−	36.0000i		−	1.38770i	−0.720121	−	0.693849i	$-0.755914\pi$
$673$		−	36.0000i		−	1.38770i	0.720121	−	0.693849i	$-0.244086\pi$
$674$	14.0000	−	24.2487i	0.539260	−	0.934025i
$675$	−4.59808	−	1.96410i	−0.176980	−	0.0755983i
$676$	−11.5000	−	19.9186i	−0.442308	−	0.766099i
$677$	−1.73205	−	1.00000i	−0.0665681	−	0.0384331i	0.466347	−	0.884602i	$-0.345570\pi$
$677$	−1.73205	−	1.00000i	−0.0665681	−	0.0384331i	−0.532915	+	0.846169i	$0.678903\pi$
$678$		−	6.00000i		−	0.230429i
$679$		0			0
$680$	4.00000	+	2.00000i	0.153393	+	0.0766965i
$681$	−14.0000	+	24.2487i	−0.536481	+	0.929213i
$682$	13.8564	−	8.00000i	0.530589	−	0.306336i
$683$	3.46410	−	2.00000i	0.132550	−	0.0765279i	−0.432259	−	0.901750i	$-0.642283\pi$
$683$	3.46410	−	2.00000i	0.132550	−	0.0765279i	0.564809	+	0.825222i	$0.308950\pi$
$684$		0			0
$685$	−18.0000	+	36.0000i	−0.687745	+	1.37549i
$686$		0			0
$687$			10.0000i			0.381524i
$688$	−3.46410	−	2.00000i	−0.132068	−	0.0762493i
$689$	18.0000	+	31.1769i	0.685745	+	1.18775i
$690$	−8.92820	+	0.535898i	−0.339891	+	0.0204013i
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	−0.779857	−	0.625958i	$-0.784708\pi$
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	0.932024	+	0.362397i	$0.118041\pi$
$692$		−	14.0000i		−	0.532200i
$693$		0			0
$694$	12.0000			0.455514
$695$	37.3205	−	24.6410i	1.41565	−	0.934687i
$696$		0			0
$697$	3.46410	−	2.00000i	0.131212	−	0.0757554i
$698$	−8.66025	−	5.00000i	−0.327795	−	0.189253i
$699$	−14.0000			−0.529529
$700$		0			0
$701$	32.0000			1.20862			0.604312	−	0.796748i	$-0.293448\pi$
$701$	32.0000			1.20862			0.604312	+	0.796748i	$0.293448\pi$
$702$	−5.19615	−	3.00000i	−0.196116	−	0.113228i
$703$		0			0
$704$	1.00000	+	1.73205i	0.0376889	+	0.0652791i
$705$	14.9282	−	9.85641i	0.562229	−	0.371214i
$706$	14.0000			0.526897
$707$		0			0
$708$			10.0000i			0.375823i
$709$	15.0000	−	25.9808i	0.563337	−	0.975728i	−0.433865	−	0.900978i	$-0.642851\pi$
$709$	15.0000	−	25.9808i	0.563337	−	0.975728i	0.997202	−	0.0747503i	$-0.0238160\pi$
$710$	26.7846	−	1.60770i	1.00521	−	0.0603357i
$711$		0			0
$712$	−8.66025	−	5.00000i	−0.324557	−	0.187383i
$713$		−	32.0000i		−	1.19841i
$714$		0			0
$715$	−12.0000	+	24.0000i	−0.448775	+	0.897549i
$716$	−5.00000	+	8.66025i	−0.186859	+	0.323649i
$717$	−17.3205	+	10.0000i	−0.646846	+	0.373457i
$718$		0			0
$719$	−20.0000	+	34.6410i	−0.745874	+	1.29189i	0.203911	+	0.978989i	$0.434635\pi$
$719$	−20.0000	+	34.6410i	−0.745874	+	1.29189i	−0.949785	+	0.312903i	$0.898699\pi$
$720$	2.00000	+	1.00000i	0.0745356	+	0.0372678i
$721$		0			0
$722$			19.0000i			0.707107i
$723$	−19.0526	−	11.0000i	−0.708572	−	0.409094i
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$		0			0
$726$	3.50000	−	6.06218i	0.129897	−	0.224989i
$727$		−	18.0000i		−	0.667583i	−0.942647	−	0.333792i	$-0.891672\pi$
$727$		−	18.0000i		−	0.667583i	0.942647	−	0.333792i	$-0.108328\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	7.46410	−	4.92820i	0.276259	−	0.182401i
$731$	4.00000	+	6.92820i	0.147945	+	0.256249i
$732$	−1.73205	+	1.00000i	−0.0640184	+	0.0369611i
$733$	−12.1244	−	7.00000i	−0.447823	−	0.258551i	0.259087	−	0.965854i	$-0.416578\pi$
$733$	−12.1244	−	7.00000i	−0.447823	−	0.258551i	−0.706910	+	0.707303i	$0.749912\pi$
$734$	2.00000			0.0738213
$735$		0			0
$736$	4.00000			0.147442
$737$	13.8564	+	8.00000i	0.510407	+	0.294684i
$738$	1.73205	−	1.00000i	0.0637577	−	0.0368105i
$739$	20.0000	+	34.6410i	0.735712	+	1.27429i	0.954410	+	0.298498i	$0.0964856\pi$
$739$	20.0000	+	34.6410i	0.735712	+	1.27429i	−0.218698	+	0.975793i	$0.570181\pi$
$740$	−2.46410	−	3.73205i	−0.0905822	−	0.137193i
$741$		0			0
$742$		0			0
$743$			24.0000i			0.880475i	0.897881	+	0.440237i	$0.145106\pi$
$743$			24.0000i			0.880475i	−0.897881	+	0.440237i	$0.854894\pi$
$744$	−4.00000	+	6.92820i	−0.146647	+	0.254000i
$745$	2.67949	+	44.6410i	0.0981690	+	1.63552i
$746$	3.00000	+	5.19615i	0.109838	+	0.190245i
$747$	3.46410	+	2.00000i	0.126745	+	0.0731762i
$748$		−	4.00000i		−	0.146254i
$749$		0			0
$750$	−2.00000	−	11.0000i	−0.0730297	−	0.401663i
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	0.411170	+	0.911559i	$0.365120\pi$
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	−0.995018	+	0.0996961i	$0.968213\pi$
$752$	−6.92820	+	4.00000i	−0.252646	+	0.145865i
$753$	−15.5885	+	9.00000i	−0.568075	+	0.327978i
$754$		0			0
$755$	16.0000	+	8.00000i	0.582300	+	0.291150i
$756$		0			0
$757$			2.00000i			0.0726912i	0.999339	+	0.0363456i	$0.0115717\pi$
$757$			2.00000i			0.0726912i	−0.999339	+	0.0363456i	$0.988428\pi$
$758$	−17.3205	−	10.0000i	−0.629109	−	0.363216i
$759$	4.00000	+	6.92820i	0.145191	+	0.251478i
$760$		0			0
$761$	9.00000	−	15.5885i	0.326250	−	0.565081i	−0.655515	−	0.755182i	$-0.727548\pi$
$761$	9.00000	−	15.5885i	0.326250	−	0.565081i	0.981764	+	0.190101i	$0.0608816\pi$
$762$			2.00000i			0.0724524i
$763$		0			0
$764$	−12.0000			−0.434145
$765$	−2.46410	−	3.73205i	−0.0890898	−	0.134933i
$766$	8.00000	+	13.8564i	0.289052	+	0.500652i
$767$	51.9615	−	30.0000i	1.87622	−	1.08324i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	30.0000			1.08183			0.540914	−	0.841078i	$-0.318079\pi$
$769$	30.0000			1.08183			0.540914	+	0.841078i	$0.318079\pi$
$770$		0			0
$771$	18.0000			0.648254
$772$	3.46410	+	2.00000i	0.124676	+	0.0719816i
$773$	46.7654	−	27.0000i	1.68203	−	0.971123i	0.721726	−	0.692179i	$-0.243349\pi$
$773$	46.7654	−	27.0000i	1.68203	−	0.971123i	0.960307	−	0.278944i	$-0.0899843\pi$
$774$	2.00000	+	3.46410i	0.0718885	+	0.124515i
$775$	39.7128	−	4.78461i	1.42653	−	0.171868i
$776$	8.00000			0.287183
$777$		0			0
$778$			20.0000i			0.717035i
$779$		0			0
$780$	−0.803848	−	13.3923i	−0.0287824	−	0.479521i
$781$	−12.0000	−	20.7846i	−0.429394	−	0.743732i
$782$	−6.92820	−	4.00000i	−0.247752	−	0.143040i
$783$		0			0
$784$		0			0
$785$	22.0000	−	44.0000i	0.785214	−	1.57043i
$786$	9.00000	−	15.5885i	0.321019	−	0.556022i
$787$	27.7128	−	16.0000i	0.987855	−	0.570338i	0.0832226	−	0.996531i	$-0.473479\pi$
$787$	27.7128	−	16.0000i	0.987855	−	0.570338i	0.904632	+	0.426193i	$0.140145\pi$
$788$	−19.0526	+	11.0000i	−0.678719	+	0.391859i
$789$	2.00000	−	3.46410i	0.0712019	−	0.123325i
$790$		0			0
$791$		0			0
$792$		−	2.00000i		−	0.0710669i
$793$	10.3923	+	6.00000i	0.369042	+	0.213066i
$794$	−1.00000	−	1.73205i	−0.0354887	−	0.0614682i
$795$	0.803848	+	13.3923i	0.0285095	+	0.474976i
$796$		0			0
$797$			2.00000i			0.0708436i	0.999372	+	0.0354218i	$0.0112775\pi$
$797$			2.00000i			0.0708436i	−0.999372	+	0.0354218i	$0.988723\pi$
$798$		0			0
$799$	16.0000			0.566039
$800$	0.598076	+	4.96410i	0.0211452	+	0.175507i
$801$	5.00000	+	8.66025i	0.176666	+	0.305995i
$802$	−19.0526	+	11.0000i	−0.672769	+	0.388424i
$803$	−6.92820	−	4.00000i	−0.244491	−	0.141157i
$804$	−8.00000			−0.282138
$805$		0			0
$806$	48.0000			1.69073
$807$		0			0
$808$	−6.92820	+	4.00000i	−0.243733	+	0.140720i
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	−0.999491	−	0.0319002i	$-0.989844\pi$
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	0.472119	−	0.881535i	$-0.343489\pi$
$810$	−1.23205	−	1.86603i	−0.0432899	−	0.0655654i
$811$	52.0000			1.82597			0.912983	−	0.407997i	$-0.133772\pi$
$811$	52.0000			1.82597			0.912983	+	0.407997i	$0.133772\pi$
$812$		0			0
$813$		−	8.00000i		−	0.280572i
$814$	−2.00000	+	3.46410i	−0.0701000	+	0.121417i
$815$	35.7128	−	2.14359i	1.25097	−	0.0750868i
$816$	1.00000	+	1.73205i	0.0350070	+	0.0606339i
$817$		0			0
$818$		−	10.0000i		−	0.349642i
$819$		0			0
$820$	4.00000	+	2.00000i	0.139686	+	0.0698430i
$821$	4.00000	−	6.92820i	0.139601	−	0.241796i	−0.787745	−	0.616002i	$-0.788751\pi$
$821$	4.00000	−	6.92820i	0.139601	−	0.241796i	0.927346	+	0.374206i	$0.122085\pi$
$822$	−15.5885	+	9.00000i	−0.543710	+	0.313911i
$823$	−5.19615	+	3.00000i	−0.181126	+	0.104573i	−0.587822	−	0.808990i	$-0.700014\pi$
$823$	−5.19615	+	3.00000i	−0.181126	+	0.104573i	0.406695	+	0.913564i	$0.366681\pi$
$824$	7.00000	−	12.1244i	0.243857	−	0.422372i
$825$	−8.00000	+	6.00000i	−0.278524	+	0.208893i
$826$		0			0
$827$		−	28.0000i		−	0.973655i	−0.873498	−	0.486828i	$-0.838154\pi$
$827$		−	28.0000i		−	0.973655i	0.873498	−	0.486828i	$-0.161846\pi$
$828$	−3.46410	−	2.00000i	−0.120386	−	0.0695048i
$829$	−15.0000	−	25.9808i	−0.520972	−	0.902349i	−0.999703	−	0.0243876i	$-0.992236\pi$
$829$	−15.0000	−	25.9808i	−0.520972	−	0.902349i	0.478731	−	0.877962i	$-0.341097\pi$
$830$	0.535898	+	8.92820i	0.0186013	+	0.309902i
$831$	1.00000	−	1.73205i	0.0346896	−	0.0600842i
$832$			6.00000i			0.208013i
$833$		0			0
$834$	20.0000			0.692543
$835$	14.7846	+	22.3923i	0.511643	+	0.774918i
$836$		0			0
$837$	6.92820	−	4.00000i	0.239474	−	0.138260i
$838$	8.66025	+	5.00000i	0.299164	+	0.172722i
$839$	−40.0000			−1.38095			−0.690477	−	0.723355i	$-0.742599\pi$
$839$	−40.0000			−1.38095			−0.690477	+	0.723355i	$0.742599\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	19.0526	+	11.0000i	0.656595	+	0.379085i
$843$	−15.5885	+	9.00000i	−0.536895	+	0.309976i
$844$	6.00000	+	10.3923i	0.206529	+	0.357718i
$845$	−42.9186	+	28.3372i	−1.47644	+	0.974828i
$846$	8.00000			0.275046
$847$		0			0
$848$		−	6.00000i		−	0.206041i
$849$	−8.00000	+	13.8564i	−0.274559	+	0.475551i
$850$	3.92820	−	9.19615i	0.134736	−	0.315425i
$851$	4.00000	+	6.92820i	0.137118	+	0.237496i
$852$	10.3923	+	6.00000i	0.356034	+	0.205557i
$853$			14.0000i			0.479351i	0.970853	+	0.239675i	$0.0770410\pi$
$853$			14.0000i			0.479351i	−0.970853	+	0.239675i	$0.922959\pi$
$854$		0			0
$855$		0			0
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	36.3731	−	21.0000i	1.24248	−	0.717346i	0.272882	−	0.962048i	$-0.412023\pi$
$857$	36.3731	−	21.0000i	1.24248	−	0.717346i	0.969599	+	0.244701i	$0.0786899\pi$
$858$	−10.3923	+	6.00000i	−0.354787	+	0.204837i
$859$	10.0000	−	17.3205i	0.341196	−	0.590968i	−0.643459	−	0.765480i	$-0.722501\pi$
$859$	10.0000	−	17.3205i	0.341196	−	0.590968i	0.984655	+	0.174512i	$0.0558348\pi$
$860$	−4.00000	+	8.00000i	−0.136399	+	0.272798i
$861$		0			0
$862$		−	32.0000i		−	1.08992i
$863$	31.1769	+	18.0000i	1.06127	+	0.612727i	0.925785	−	0.378052i	$-0.123406\pi$
$863$	31.1769	+	18.0000i	1.06127	+	0.612727i	0.135490	+	0.990779i	$0.456739\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−31.2487	+	1.87564i	−1.06249	+	0.0637738i
$866$	−2.00000	+	3.46410i	−0.0679628	+	0.117715i
$867$			13.0000i			0.441503i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	24.0000	+	41.5692i	0.813209	+	1.40852i
$872$	−8.66025	+	5.00000i	−0.293273	+	0.169321i
$873$	−6.92820	−	4.00000i	−0.234484	−	0.135379i
$874$		0			0
$875$		0			0
$876$	4.00000			0.135147
$877$	−19.0526	−	11.0000i	−0.643359	−	0.371444i	0.142548	−	0.989788i	$-0.454470\pi$
$877$	−19.0526	−	11.0000i	−0.643359	−	0.371444i	−0.785907	+	0.618344i	$0.787804\pi$
$878$		0			0
$879$	−3.00000	−	5.19615i	−0.101187	−	0.175262i
$880$	3.73205	−	2.46410i	0.125807	−	0.0830648i
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$			24.0000i			0.807664i	0.914833	+	0.403832i	$0.132322\pi$
$883$			24.0000i			0.807664i	−0.914833	+	0.403832i	$0.867678\pi$
$884$	6.00000	−	10.3923i	0.201802	−	0.349531i
$885$	22.3205	−	1.33975i	0.750296	−	0.0450351i
$886$	18.0000	+	31.1769i	0.604722	+	1.04741i
$887$	−10.3923	−	6.00000i	−0.348939	−	0.201460i	0.315279	−	0.948999i	$-0.397902\pi$
$887$	−10.3923	−	6.00000i	−0.348939	−	0.201460i	−0.664218	+	0.747539i	$0.731235\pi$
$888$		−	2.00000i		−	0.0671156i
$889$		0			0
$890$	−10.0000	+	20.0000i	−0.335201	+	0.670402i
$891$	−1.00000	+	1.73205i	−0.0335013	+	0.0580259i
$892$	22.5167	−	13.0000i	0.753914	−	0.435272i
$893$		0			0
$894$	−10.0000	+	17.3205i	−0.334450	+	0.579284i
$895$	20.0000	+	10.0000i	0.668526	+	0.334263i
$896$		0			0
$897$			24.0000i			0.801337i
$898$	−25.9808	−	15.0000i	−0.866989	−	0.500556i
$899$		0			0
$900$	1.96410	−	4.59808i	0.0654701	−	0.153269i
$901$	−6.00000	+	10.3923i	−0.199889	+	0.346218i
$902$		−	4.00000i		−	0.133185i
$903$		0			0
$904$	6.00000			0.199557
$905$	3.73205	−	2.46410i	0.124058	−	0.0819095i
$906$	4.00000	+	6.92820i	0.132891	+	0.230174i
$907$	10.3923	−	6.00000i	0.345071	−	0.199227i	−0.317441	−	0.948278i	$-0.602824\pi$
$907$	10.3923	−	6.00000i	0.345071	−	0.199227i	0.662512	+	0.749051i	$0.269490\pi$
$908$	−24.2487	−	14.0000i	−0.804722	−	0.464606i
$909$	8.00000			0.265343
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		0			0
$913$	6.92820	−	4.00000i	0.229290	−	0.132381i
$914$	−16.0000	−	27.7128i	−0.529233	−	0.916658i
$915$	2.46410	+	3.73205i	0.0814607	+	0.123378i
$916$	−10.0000			−0.330409
$917$		0			0
$918$		−	2.00000i		−	0.0660098i
$919$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$919$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$920$	−0.535898	−	8.92820i	−0.0176680	−	0.294354i
$921$	6.00000	+	10.3923i	0.197707	+	0.342438i
$922$	10.3923	+	6.00000i	0.342252	+	0.197599i
$923$		−	72.0000i		−	2.36991i
$924$		0			0
$925$	−8.00000	+	6.00000i	−0.263038	+	0.197279i
$926$	3.00000	−	5.19615i	0.0985861	−	0.170756i
$927$	−12.1244	+	7.00000i	−0.398216	+	0.229910i
$928$		0			0
$929$	15.0000	−	25.9808i	0.492134	−	0.852401i	−0.507825	−	0.861460i	$-0.669550\pi$
$929$	15.0000	−	25.9808i	0.492134	−	0.852401i	0.999959	+	0.00905914i	$0.00288365\pi$
$930$	16.0000	+	8.00000i	0.524661	+	0.262330i
$931$		0			0
$932$		−	14.0000i		−	0.458585i
$933$	−10.3923	−	6.00000i	−0.340229	−	0.196431i
$934$	−6.00000	−	10.3923i	−0.196326	−	0.340047i
$935$	−8.92820	+	0.535898i	−0.291983	+	0.0175258i
$936$	3.00000	−	5.19615i	0.0980581	−	0.169842i
$937$		−	8.00000i		−	0.261349i	−0.991425	−	0.130674i	$-0.958286\pi$
$937$		−	8.00000i		−	0.261349i	0.991425	−	0.130674i	$-0.0417142\pi$
$938$		0			0
$939$	−4.00000			−0.130535
$940$	9.85641	+	14.9282i	0.321481	+	0.486904i
$941$	14.0000	+	24.2487i	0.456387	+	0.790485i	0.998767	−	0.0496480i	$-0.0158099\pi$
$941$	14.0000	+	24.2487i	0.456387	+	0.790485i	−0.542380	+	0.840133i	$0.682477\pi$
$942$	19.0526	−	11.0000i	0.620766	−	0.358399i
$943$	−6.92820	−	4.00000i	−0.225613	−	0.130258i
$944$	−10.0000			−0.325472
$945$		0			0
$946$	8.00000			0.260102
$947$	−10.3923	−	6.00000i	−0.337705	−	0.194974i	0.321552	−	0.946892i	$-0.395796\pi$
$947$	−10.3923	−	6.00000i	−0.337705	−	0.194974i	−0.659256	+	0.751918i	$0.729129\pi$
$948$		0			0
$949$	−12.0000	−	20.7846i	−0.389536	−	0.674697i
$950$		0			0
$951$	−2.00000			−0.0648544
$952$		0			0
$953$		−	46.0000i		−	1.49009i	−0.667016	−	0.745043i	$-0.732429\pi$
$953$		−	46.0000i		−	1.49009i	0.667016	−	0.745043i	$-0.267571\pi$
$954$	−3.00000	+	5.19615i	−0.0971286	+	0.168232i
$955$	1.60770	+	26.7846i	0.0520238	+	0.866730i
$956$	−10.0000	−	17.3205i	−0.323423	−	0.560185i
$957$		0			0
$958$			20.0000i			0.646171i
$959$		0			0
$960$	−1.00000	+	2.00000i	−0.0322749	+	0.0645497i
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	−10.3923	+	6.00000i	−0.335061	+	0.193448i
$963$	−10.3923	+	6.00000i	−0.334887	+	0.193347i
$964$	11.0000	−	19.0526i	0.354286	−	0.613642i
$965$	4.00000	−	8.00000i	0.128765	−	0.257529i
$966$		0			0
$967$		−	38.0000i		−	1.22200i	−0.791632	−	0.610999i	$-0.790768\pi$
$967$		−	38.0000i		−	1.22200i	0.791632	−	0.610999i	$-0.209232\pi$
$968$	6.06218	+	3.50000i	0.194846	+	0.112494i
$969$		0			0
$970$	−1.07180	−	17.8564i	−0.0344133	−	0.573335i
$971$	9.00000	−	15.5885i	0.288824	−	0.500257i	−0.684706	−	0.728820i	$-0.740069\pi$
$971$	9.00000	−	15.5885i	0.288824	−	0.500257i	0.973529	+	0.228562i	$0.0734025\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		0			0
$974$	−18.0000			−0.576757
$975$	−29.7846	+	3.58846i	−0.953871	+	0.114923i
$976$	−1.00000	−	1.73205i	−0.0320092	−	0.0554416i
$977$	36.3731	−	21.0000i	1.16368	−	0.671850i	0.211495	−	0.977379i	$-0.432167\pi$
$977$	36.3731	−	21.0000i	1.16368	−	0.671850i	0.952183	+	0.305530i	$0.0988335\pi$
$978$	13.8564	+	8.00000i	0.443079	+	0.255812i
$979$	20.0000			0.639203
$980$		0			0
$981$	10.0000			0.319275
$982$	−15.5885	−	9.00000i	−0.497448	−	0.287202i
$983$	−13.8564	+	8.00000i	−0.441951	+	0.255160i	−0.704425	−	0.709779i	$-0.748795\pi$
$983$	−13.8564	+	8.00000i	−0.441951	+	0.255160i	0.262474	+	0.964939i	$0.415462\pi$
$984$	1.00000	+	1.73205i	0.0318788	+	0.0552158i
$985$	27.1051	+	41.0526i	0.863641	+	1.30804i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	8.00000	−	13.8564i	0.254385	−	0.440608i
$990$	−4.46410	+	0.267949i	−0.141878	+	0.00851598i
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	0.922538	−	0.385906i	$-0.126111\pi$
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	−0.795474	+	0.605988i	$0.792778\pi$
$992$	−6.92820	−	4.00000i	−0.219971	−	0.127000i
$993$		−	8.00000i		−	0.253872i
$994$		0			0
$995$		0			0
$996$	−2.00000	+	3.46410i	−0.0633724	+	0.109764i
$997$	−15.5885	+	9.00000i	−0.493691	+	0.285033i	−0.726105	−	0.687584i	$-0.758671\pi$
$997$	−15.5885	+	9.00000i	−0.493691	+	0.285033i	0.232413	+	0.972617i	$0.425338\pi$
$998$		0			0
$999$	−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.n.h.79.2		4
5.4	even	2	inner	1470.2.n.h.79.1		4
7.2	even	3		30.2.c.a.19.1	✓	2
7.3	odd	6		1470.2.n.a.949.1		4
7.4	even	3	inner	1470.2.n.h.949.1		4
7.5	odd	6		1470.2.g.g.589.1		2
7.6	odd	2		1470.2.n.a.79.2		4
21.2	odd	6		90.2.c.a.19.2		2
28.23	odd	6		240.2.f.a.49.1		2
35.2	odd	12		150.2.a.c.1.1		1
35.4	even	6	inner	1470.2.n.h.949.2		4
35.9	even	6		30.2.c.a.19.2	yes	2
35.12	even	12		7350.2.a.cc.1.1		1
35.19	odd	6		1470.2.g.g.589.2		2
35.23	odd	12		150.2.a.a.1.1		1
35.24	odd	6		1470.2.n.a.949.2		4
35.33	even	12		7350.2.a.bg.1.1		1
35.34	odd	2		1470.2.n.a.79.1		4
56.37	even	6		960.2.f.h.769.1		2
56.51	odd	6		960.2.f.i.769.2		2
63.2	odd	6		810.2.i.b.109.2		4
63.16	even	3		810.2.i.e.109.1		4
63.23	odd	6		810.2.i.b.379.1		4
63.58	even	3		810.2.i.e.379.2		4
84.23	even	6		720.2.f.f.289.2		2
105.2	even	12		450.2.a.b.1.1		1
105.23	even	12		450.2.a.f.1.1		1
105.44	odd	6		90.2.c.a.19.1		2
112.37	even	12		3840.2.d.y.2689.1		2
112.51	odd	12		3840.2.d.x.2689.2		2
112.93	even	12		3840.2.d.g.2689.2		2
112.107	odd	12		3840.2.d.j.2689.1		2
140.23	even	12		1200.2.a.m.1.1		1
140.79	odd	6		240.2.f.a.49.2		2
140.107	even	12		1200.2.a.g.1.1		1
168.107	even	6		2880.2.f.c.1729.1		2
168.149	odd	6		2880.2.f.e.1729.1		2
280.37	odd	12		4800.2.a.l.1.1		1
280.93	odd	12		4800.2.a.cg.1.1		1
280.107	even	12		4800.2.a.cj.1.1		1
280.149	even	6		960.2.f.h.769.2		2
280.163	even	12		4800.2.a.m.1.1		1
280.219	odd	6		960.2.f.i.769.1		2
315.79	even	6		810.2.i.e.109.2		4
315.149	odd	6		810.2.i.b.379.2		4
315.184	even	6		810.2.i.e.379.1		4
315.254	odd	6		810.2.i.b.109.1		4
420.23	odd	12		3600.2.a.o.1.1		1
420.107	odd	12		3600.2.a.bg.1.1		1
420.359	even	6		720.2.f.f.289.1		2
560.149	even	12		3840.2.d.g.2689.1		2
560.219	odd	12		3840.2.d.x.2689.1		2
560.429	even	12		3840.2.d.y.2689.2		2
560.499	odd	12		3840.2.d.j.2689.2		2
840.149	odd	6		2880.2.f.e.1729.2		2
840.779	even	6		2880.2.f.c.1729.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.2.c.a.19.1	✓	2	7.2	even	3
30.2.c.a.19.2	yes	2	35.9	even	6
90.2.c.a.19.1		2	105.44	odd	6
90.2.c.a.19.2		2	21.2	odd	6
150.2.a.a.1.1		1	35.23	odd	12
150.2.a.c.1.1		1	35.2	odd	12
240.2.f.a.49.1		2	28.23	odd	6
240.2.f.a.49.2		2	140.79	odd	6
450.2.a.b.1.1		1	105.2	even	12
450.2.a.f.1.1		1	105.23	even	12
720.2.f.f.289.1		2	420.359	even	6
720.2.f.f.289.2		2	84.23	even	6
810.2.i.b.109.1		4	315.254	odd	6
810.2.i.b.109.2		4	63.2	odd	6
810.2.i.b.379.1		4	63.23	odd	6
810.2.i.b.379.2		4	315.149	odd	6
810.2.i.e.109.1		4	63.16	even	3
810.2.i.e.109.2		4	315.79	even	6
810.2.i.e.379.1		4	315.184	even	6
810.2.i.e.379.2		4	63.58	even	3
960.2.f.h.769.1		2	56.37	even	6
960.2.f.h.769.2		2	280.149	even	6
960.2.f.i.769.1		2	280.219	odd	6
960.2.f.i.769.2		2	56.51	odd	6
1200.2.a.g.1.1		1	140.107	even	12
1200.2.a.m.1.1		1	140.23	even	12
1470.2.g.g.589.1		2	7.5	odd	6
1470.2.g.g.589.2		2	35.19	odd	6
1470.2.n.a.79.1		4	35.34	odd	2
1470.2.n.a.79.2		4	7.6	odd	2
1470.2.n.a.949.1		4	7.3	odd	6
1470.2.n.a.949.2		4	35.24	odd	6
1470.2.n.h.79.1		4	5.4	even	2	inner
1470.2.n.h.79.2		4	1.1	even	1	trivial
1470.2.n.h.949.1		4	7.4	even	3	inner
1470.2.n.h.949.2		4	35.4	even	6	inner
2880.2.f.c.1729.1		2	168.107	even	6
2880.2.f.c.1729.2		2	840.779	even	6
2880.2.f.e.1729.1		2	168.149	odd	6
2880.2.f.e.1729.2		2	840.149	odd	6
3600.2.a.o.1.1		1	420.23	odd	12
3600.2.a.bg.1.1		1	420.107	odd	12
3840.2.d.g.2689.1		2	560.149	even	12
3840.2.d.g.2689.2		2	112.93	even	12
3840.2.d.j.2689.1		2	112.107	odd	12
3840.2.d.j.2689.2		2	560.499	odd	12
3840.2.d.x.2689.1		2	560.219	odd	12
3840.2.d.x.2689.2		2	112.51	odd	12
3840.2.d.y.2689.1		2	112.37	even	12
3840.2.d.y.2689.2		2	560.429	even	12
4800.2.a.l.1.1		1	280.37	odd	12
4800.2.a.m.1.1		1	280.163	even	12
4800.2.a.cg.1.1		1	280.93	odd	12
4800.2.a.cj.1.1		1	280.107	even	12
7350.2.a.bg.1.1		1	35.33	even	12
7350.2.a.cc.1.1		1	35.12	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.86603 - 1.23205i) q^{5} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.23205 - 0.133975i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(0.866025 + 0.500000i) q^{12} -6.00000i q^{13} +(1.00000 - 2.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.73205 - 1.00000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(2.00000 + 1.00000i) q^{20} -2.00000i q^{22} +(-3.46410 - 2.00000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.96410 - 4.59808i) q^{25} +(3.00000 - 5.19615i) q^{26} -1.00000i q^{27} +(1.86603 - 1.23205i) q^{30} +(4.00000 + 6.92820i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.73205 - 1.00000i) q^{33} +2.00000 q^{34} +1.00000 q^{36} +(-1.73205 - 1.00000i) q^{37} +(-3.00000 - 5.19615i) q^{39} +(1.23205 + 1.86603i) q^{40} +2.00000 q^{41} +4.00000i q^{43} +(1.00000 - 1.73205i) q^{44} +(-0.133975 - 2.23205i) q^{45} +(-2.00000 - 3.46410i) q^{46} +(6.92820 + 4.00000i) q^{47} +1.00000i q^{48} +(4.00000 - 3.00000i) q^{50} +(1.00000 - 1.73205i) q^{51} +(5.19615 - 3.00000i) q^{52} +(-5.19615 + 3.00000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-4.00000 - 2.00000i) q^{55} +(5.00000 + 8.66025i) q^{59} +(2.23205 - 0.133975i) q^{60} +(-1.00000 + 1.73205i) q^{61} +8.00000i q^{62} -1.00000 q^{64} +(-7.39230 - 11.1962i) q^{65} +(-1.00000 - 1.73205i) q^{66} +(-6.92820 + 4.00000i) q^{67} +(1.73205 + 1.00000i) q^{68} -4.00000 q^{69} +12.0000 q^{71} +(0.866025 + 0.500000i) q^{72} +(3.46410 - 2.00000i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-0.598076 - 4.96410i) q^{75} -6.00000i q^{78} +(0.133975 + 2.23205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.73205 + 1.00000i) q^{82} +4.00000i q^{83} +(2.00000 - 4.00000i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(1.73205 - 1.00000i) q^{88} +(-5.00000 + 8.66025i) q^{89} +(1.00000 - 2.00000i) q^{90} -4.00000i q^{92} +(6.92820 + 4.00000i) q^{93} +(4.00000 + 6.92820i) q^{94} +(-0.500000 + 0.866025i) q^{96} -8.00000i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 4 q^{5} + 4 q^{6} + 2 q^{9} + 2 q^{10} - 4 q^{11} + 4 q^{15} - 2 q^{16} + 8 q^{20} + 2 q^{24} - 6 q^{25} + 12 q^{26} + 4 q^{30} + 16 q^{31} + 8 q^{34} + 4 q^{36} - 12 q^{39} - 2 q^{40} + 8 q^{41}+ \cdots - 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 4 * q^5 + 4 * q^6 + 2 * q^9 + 2 * q^10 - 4 * q^11 + 4 * q^15 - 2 * q^16 + 8 * q^20 + 2 * q^24 - 6 * q^25 + 12 * q^26 + 4 * q^30 + 16 * q^31 + 8 * q^34 + 4 * q^36 - 12 * q^39 - 2 * q^40 + 8 * q^41 + 4 * q^44 - 4 * q^45 - 8 * q^46 + 16 * q^50 + 4 * q^51 + 2 * q^54 - 16 * q^55 + 20 * q^59 + 2 * q^60 - 4 * q^61 - 4 * q^64 + 12 * q^65 - 4 * q^66 - 16 * q^69 + 48 * q^71 - 4 * q^74 + 8 * q^75 + 4 * q^80 - 2 * q^81 + 8 * q^85 - 8 * q^86 - 20 * q^89 + 4 * q^90 + 16 * q^94 - 2 * q^96 - 8 * q^99

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