LMFDB - Embedded newform 1470.2.n.a.79.1

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			79.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1470.79
Dual form			1470.2.n.a.949.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.133975 + 2.23205i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.23205 - 1.86603i) 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} +(-4.96410 - 0.598076i) q^{25} +(-3.00000 + 5.19615i) q^{26} -1.00000i q^{27} +(0.133975 - 2.23205i) 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} +(2.23205 + 0.133975i) q^{40} -2.00000 q^{41} -4.00000i q^{43} +(1.00000 - 1.73205i) q^{44} +(1.86603 + 1.23205i) 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} +(-1.23205 + 1.86603i) q^{60} +(1.00000 - 1.73205i) q^{61} +8.00000i q^{62} -1.00000 q^{64} +(13.3923 + 0.803848i) 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} +(-4.59808 + 1.96410i) q^{75} +6.00000i q^{78} +(-1.86603 - 1.23205i) 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
$5$	−0.133975	+	2.23205i	−0.0599153	+	0.998203i
$5$	−0.133975	+	2.23205i	−0.0599153	+	0.998203i
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.23205	−	1.86603i	0.389609	−	0.590089i
$11$	−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	0.815604	−	0.578610i	$-0.196405\pi$
$23$	3.46410	+	2.00000i	0.722315	+	0.417029i	−0.0932891	+	0.995639i	$0.529738\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−4.96410	−	0.598076i	−0.992820	−	0.119615i
$26$	−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	$0.5\pi$
$30$	0.133975	−	2.23205i	0.0244603	−	0.407515i
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$	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	0.635571	−	0.772043i	$-0.280765\pi$
$37$	1.73205	+	1.00000i	0.284747	+	0.164399i	−0.350823	+	0.936442i	$0.614098\pi$
$38$		0			0
$39$	−3.00000	−	5.19615i	−0.480384	−	0.832050i
$40$	2.23205	+	0.133975i	0.352918	+	0.0211832i
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$	1.00000	−	1.73205i	0.150756	−	0.261116i
$45$	1.86603	+	1.23205i	0.278171	+	0.183663i
$46$	−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	−0.0987002	−	0.995117i	$-0.531468\pi$
$53$	5.19615	−	3.00000i	0.713746	−	0.412082i	0.812447	+	0.583036i	$0.198135\pi$
$54$	−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	$-0.941040\pi$
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	0.331949	−	0.943297i	$-0.392294\pi$
$60$	−1.23205	+	1.86603i	−0.159057	+	0.240903i
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$			8.00000i			1.01600i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	13.3923	+	0.803848i	1.66111	+	0.0997050i
$66$	1.00000	+	1.73205i	0.123091	+	0.213201i
$67$	6.92820	−	4.00000i	0.846415	−	0.488678i	−0.0130248	−	0.999915i	$-0.504146\pi$
$67$	6.92820	−	4.00000i	0.846415	−	0.488678i	0.859440	+	0.511237i	$0.170813\pi$
$68$	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
$75$	−4.59808	+	1.96410i	−0.530940	+	0.226795i
$76$		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	$0.166667\pi$
$80$	−1.86603	−	1.23205i	−0.208628	−	0.137747i
$81$	−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	$-0.655526\pi$
$89$	5.00000	−	8.66025i	0.529999	−	0.917985i	0.999388	−	0.0349934i	$-0.0111410\pi$
$90$	−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
$100$	−1.96410	−	4.59808i	−0.196410	−	0.459808i
$101$	−4.00000	−	6.92820i	−0.398015	−	0.689382i	0.595466	−	0.803380i	$-0.296967\pi$
$101$	−4.00000	−	6.92820i	−0.398015	−	0.689382i	−0.993481	+	0.113998i	$0.963634\pi$
$102$	−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	0.909624	−	0.415432i	$-0.136370\pi$
$107$	10.3923	+	6.00000i	1.00466	+	0.580042i	0.0950377	+	0.995474i	$0.469703\pi$
$108$	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	$0.674364\pi$
$110$	−4.46410	−	0.267949i	−0.425635	−	0.0255480i
$111$	2.00000			0.189832
$112$		0			0
$113$			6.00000i			0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$		0			0
$115$	−4.92820	+	7.46410i	−0.459557	+	0.696031i
$116$		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	$-0.971717\pi$
$127$		−	2.00000i		−	0.177471i	0.996055	−	0.0887357i	$-0.0282826\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−2.00000	−	3.46410i	−0.176090	−	0.304997i
$130$	−11.1962	−	7.39230i	−0.981968	−	0.648348i
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	0.141865	+	0.989886i	$0.454690\pi$
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	−0.928199	+	0.372084i	$0.878643\pi$
$132$		−	2.00000i		−	0.174078i
$133$		0			0
$134$	−8.00000			−0.691095
$135$	2.23205	+	0.133975i	0.192104	+	0.0115307i
$136$	−1.00000	−	1.73205i	−0.0857493	−	0.148522i
$137$	15.5885	−	9.00000i	1.33181	−	0.768922i	0.346235	−	0.938148i	$-0.387460\pi$
$137$	15.5885	−	9.00000i	1.33181	−	0.768922i	0.985577	+	0.169226i	$0.0541268\pi$
$138$	−3.46410	−	2.00000i	−0.294884	−	0.170251i
$139$	−20.0000			−1.69638			−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000			−1.69638			−0.848189	+	0.529694i	$0.822307\pi$
$140$		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	$0.861067\pi$
$150$	4.96410	+	0.598076i	0.405317	+	0.0488327i
$151$	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	−0.152992	−	0.988227i	$-0.548891\pi$
$163$	−13.8564	−	8.00000i	−1.08532	−	0.626608i	−0.932326	+	0.361619i	$0.882224\pi$
$164$	−1.00000	−	1.73205i	−0.0780869	−	0.135250i
$165$	2.46410	−	3.73205i	0.191830	−	0.290540i
$166$	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
$170$	0.267949	−	4.46410i	0.0205508	−	0.342381i
$171$		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	$0.711416\pi$
$180$	−0.133975	+	2.23205i	−0.00998588	+	0.166367i
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$		−	2.00000i		−	0.147844i
$184$	2.00000	−	3.46410i	0.147442	−	0.255377i
$185$	−2.46410	+	3.73205i	−0.181164	+	0.274386i
$186$	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	−0.619467	−	0.785022i	$-0.712651\pi$
$193$	−3.46410	+	2.00000i	−0.249351	+	0.143963i	0.370116	+	0.928986i	$0.379318\pi$
$194$	−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	$-0.713321\pi$
$197$		−	22.0000i		−	1.56744i	0.621117	−	0.783718i	$-0.286679\pi$
$198$	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	$0.833333\pi$
$200$	−0.598076	+	4.96410i	−0.0422904	+	0.351015i
$201$	4.00000	−	6.92820i	0.282138	−	0.488678i
$202$			8.00000i			0.562878i
$203$		0			0
$204$	2.00000			0.140028
$205$	0.267949	−	4.46410i	0.0187144	−	0.311786i
$206$	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
$215$	8.92820	+	0.535898i	0.608898	+	0.0365480i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$		−	10.0000i		−	0.677285i
$219$	2.00000	−	3.46410i	0.135147	−	0.234082i
$220$	3.73205	+	2.46410i	0.251615	+	0.166130i
$221$	−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	−0.652183	−	0.758062i	$-0.726147\pi$
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	0.982592	+	0.185776i	$0.0594799\pi$
$230$	8.00000	−	4.00000i	0.527504	−	0.263752i
$231$		0			0
$232$		0			0
$233$	12.1244	+	7.00000i	0.794293	+	0.458585i	0.841472	−	0.540301i	$-0.181690\pi$
$233$	12.1244	+	7.00000i	0.794293	+	0.458585i	−0.0471787	+	0.998886i	$0.515023\pi$
$234$	3.00000	+	5.19615i	0.196116	+	0.339683i
$235$	−9.85641	+	14.9282i	−0.642961	+	0.973809i
$236$	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	$0.723912\pi$
$240$	−2.23205	−	0.133975i	−0.144078	−	0.00864802i
$241$	11.0000	+	19.0526i	0.708572	+	1.22728i	0.965387	+	0.260822i	$0.0839937\pi$
$241$	11.0000	+	19.0526i	0.708572	+	1.22728i	−0.256814	+	0.966461i	$0.582673\pi$
$242$	−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
$250$	−7.23205	+	8.52628i	−0.457395	+	0.539249i
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$		0			0
$253$		−	8.00000i		−	0.502956i
$254$	−1.00000	+	1.73205i	−0.0627456	+	0.108679i
$255$	3.73205	+	2.46410i	0.233710	+	0.154308i
$256$	−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	−0.602986	−	0.797752i	$-0.706023\pi$
$263$	−3.46410	+	2.00000i	−0.213606	+	0.123325i	0.389380	+	0.921077i	$0.372689\pi$
$264$	−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	$0.833333\pi$
$270$	−1.86603	−	1.23205i	−0.113563	−	0.0749802i
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	−0.961563	−	0.274586i	$-0.911459\pi$
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	0.718580	+	0.695444i	$0.244792\pi$
$272$			2.00000i			0.121268i
$273$		0			0
$274$	−18.0000			−1.08742
$275$	3.92820	+	9.19615i	0.236880	+	0.554549i
$276$	2.00000	+	3.46410i	0.120386	+	0.208514i
$277$	−1.73205	+	1.00000i	−0.104069	+	0.0600842i	−0.551131	−	0.834419i	$-0.685804\pi$
$277$	−1.73205	+	1.00000i	−0.104069	+	0.0600842i	0.447062	+	0.894503i	$0.352470\pi$
$278$	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
$305$	3.73205	+	2.46410i	0.213697	+	0.141094i
$306$	−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
$310$	−17.8564	−	1.07180i	−1.01418	−	0.0608740i
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	0.984475	−	0.175525i	$-0.0561621\pi$
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	−0.644246	+	0.764818i	$0.722829\pi$
$312$	−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	0.547852	−	0.836576i	$-0.315446\pi$
$317$	1.73205	+	1.00000i	0.0972817	+	0.0561656i	−0.450570	+	0.892741i	$0.648779\pi$
$318$	−5.19615	+	3.00000i	−0.291386	+	0.168232i
$319$		0			0
$320$	0.133975	−	2.23205i	0.00748941	−	0.124775i
$321$	12.0000			0.669775
$322$		0			0
$323$		0			0
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−3.58846	+	29.7846i	−0.199052	+	1.65215i
$326$	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	$0.276092\pi$
$337$			28.0000i			1.52526i	−0.646837	+	0.762629i	$0.723908\pi$
$338$	19.9186	+	11.5000i	1.08343	+	0.625518i
$339$	3.00000	+	5.19615i	0.162938	+	0.282216i
$340$	−2.46410	+	3.73205i	−0.133635	+	0.202399i
$341$	−8.00000	+	13.8564i	−0.433224	+	0.750366i
$342$		0			0
$343$		0			0
$344$	−4.00000			−0.215666
$345$	−0.535898	+	8.92820i	−0.0288518	+	0.480678i
$346$	7.00000	+	12.1244i	0.376322	+	0.651809i
$347$	−10.3923	+	6.00000i	−0.557888	+	0.322097i	−0.752297	−	0.658824i	$-0.771054\pi$
$347$	−10.3923	+	6.00000i	−0.557888	+	0.322097i	0.194409	+	0.980921i	$0.437721\pi$
$348$		0			0
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$		0			0
$351$	−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
$355$	−1.60770	+	26.7846i	−0.0853276	+	1.42158i
$356$	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	$0.166667\pi$
$360$	1.23205	−	1.86603i	0.0649348	−	0.0983482i
$361$	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	0.359408	−	0.933181i	$-0.382979\pi$
$373$	−5.19615	−	3.00000i	−0.269047	−	0.155334i	−0.628454	+	0.777847i	$0.716312\pi$
$374$	2.00000	+	3.46410i	0.103418	+	0.179124i
$375$	−3.76795	−	10.5263i	−0.194576	−	0.543575i
$376$	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	$0.664080\pi$
$390$	−13.3923	−	0.803848i	−0.678146	−	0.0407044i
$391$	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	0.962757	−	0.270367i	$-0.0871450\pi$
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	−0.715523	+	0.698589i	$0.753812\pi$
$410$	−2.46410	+	3.73205i	−0.121693	+	0.184313i
$411$	9.00000	−	15.5885i	0.443937	−	0.768922i
$412$		−	14.0000i		−	0.689730i
$413$		0			0
$414$	−4.00000			−0.196589
$415$	−8.92820	−	0.535898i	−0.438268	−	0.0263062i
$416$	−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	$-0.578547\pi$
$419$	−10.0000			−0.488532			−0.244266	+	0.969708i	$0.578547\pi$
$420$		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
$425$	−9.19615	+	3.92820i	−0.446079	+	0.190546i
$426$	−12.0000			−0.581402
$427$		0			0
$428$			12.0000i			0.580042i
$429$	−6.00000	+	10.3923i	−0.289683	+	0.501745i
$430$	−7.46410	−	4.92820i	−0.359951	−	0.237659i
$431$	−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	−0.481486	−	0.876454i	$-0.659903\pi$
$443$	−31.1769	−	18.0000i	−1.48126	−	0.855206i	−0.999774	+	0.0212481i	$0.993236\pi$
$444$	1.00000	+	1.73205i	0.0474579	+	0.0821995i
$445$	18.6603	+	12.3205i	0.884581	+	0.584048i
$446$	−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	$0.750354\pi$
$450$	4.59808	−	1.96410i	0.216755	−	0.0925886i
$451$	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	0.979772	−	0.200118i	$-0.0641325\pi$
$457$	27.7128	+	16.0000i	1.29635	+	0.748448i	0.316579	+	0.948566i	$0.397466\pi$
$458$	−8.66025	+	5.00000i	−0.404667	+	0.233635i
$459$	−1.00000	−	1.73205i	−0.0466760	−	0.0808452i
$460$	−8.92820	−	0.535898i	−0.416280	−	0.0249864i
$461$	−12.0000			−0.558896			−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000			−0.558896			−0.279448	+	0.960161i	$0.590151\pi$
$462$		0			0
$463$			6.00000i			0.278844i	0.990233	+	0.139422i	$0.0445244\pi$
$463$			6.00000i			0.278844i	−0.990233	+	0.139422i	$0.955476\pi$
$464$		0			0
$465$	9.85641	−	14.9282i	0.457080	−	0.692279i
$466$	−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	0.541884	−	0.840453i	$-0.317711\pi$
$479$	−10.0000	−	17.3205i	−0.456912	−	0.791394i	−0.998796	+	0.0490589i	$0.984378\pi$
$480$	1.86603	+	1.23205i	0.0851720	+	0.0562352i
$481$	6.00000	−	10.3923i	0.273576	−	0.473848i
$482$		−	22.0000i		−	1.00207i
$483$		0			0
$484$	7.00000			0.318182
$485$	17.8564	+	1.07180i	0.810818	+	0.0486678i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	15.5885	−	9.00000i	0.706380	−	0.407829i	−0.103339	−	0.994646i	$-0.532953\pi$
$487$	15.5885	−	9.00000i	0.706380	−	0.407829i	0.809719	+	0.586817i	$0.199619\pi$
$488$	−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
$495$	0.267949	−	4.46410i	0.0120434	−	0.200646i
$496$	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	$0.166667\pi$
$500$	10.5263	−	3.76795i	0.470750	−	0.168508i
$501$	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
$515$	17.2487	−	26.1244i	0.760069	−	1.15118i
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$		−	16.0000i		−	0.703679i
$518$		0			0
$519$	−14.0000			−0.614532
$520$	0.803848	−	13.3923i	0.0352510	−	0.587291i
$521$	11.0000	+	19.0526i	0.481919	+	0.834708i	0.999785	−	0.0207541i	$-0.00660670\pi$
$521$	11.0000	+	19.0526i	0.481919	+	0.834708i	−0.517866	+	0.855462i	$0.673273\pi$
$522$		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
$530$	0.803848	−	13.3923i	0.0349169	−	0.581725i
$531$	−10.0000			−0.433963
$532$		0			0
$533$			12.0000i			0.519778i
$534$	−5.00000	+	8.66025i	−0.216371	+	0.374766i
$535$	−14.7846	+	22.3923i	−0.639194	+	0.968104i
$536$	−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	$0.204275\pi$
$547$			28.0000i			1.19719i	−0.801050	+	0.598597i	$0.795725\pi$
$548$	15.5885	+	9.00000i	0.665906	+	0.384461i
$549$	−1.00000	−	1.73205i	−0.0426790	−	0.0739221i
$550$	1.19615	−	9.92820i	0.0510041	−	0.423340i
$551$		0			0
$552$		−	4.00000i		−	0.170251i
$553$		0			0
$554$	2.00000			0.0849719
$555$	−0.267949	+	4.46410i	−0.0113738	+	0.189491i
$556$	−10.0000	−	17.3205i	−0.424094	−	0.734553i
$557$	15.5885	−	9.00000i	0.660504	−	0.381342i	−0.131965	−	0.991254i	$-0.542129\pi$
$557$	15.5885	−	9.00000i	0.660504	−	0.381342i	0.792469	+	0.609912i	$0.208795\pi$
$558$	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
$565$	−13.3923	−	0.803848i	−0.563418	−	0.0338181i
$566$	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
$585$	7.39230	−	11.1962i	0.305634	−	0.462904i
$586$	−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
$590$	−22.3205	−	1.33975i	−0.918921	−	0.0551565i
$591$	−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	$0.833333\pi$
$600$	1.96410	+	4.59808i	0.0801841	+	0.187716i
$601$	−2.00000			−0.0815817			−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000			−0.0815817			−0.0407909	+	0.999168i	$0.512988\pi$
$602$		0			0
$603$		−	8.00000i		−	0.325785i
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	13.0622	+	8.62436i	0.531053	+	0.350630i
$606$	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	0.0291886	−	0.999574i	$-0.490708\pi$
$613$	22.5167	−	13.0000i	0.909439	−	0.525065i	0.880251	+	0.474509i	$0.157374\pi$
$614$	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	$-0.987182\pi$
$617$		−	2.00000i		−	0.0805170i	0.999189	−	0.0402585i	$-0.0128181\pi$
$618$	12.1244	+	7.00000i	0.487713	+	0.281581i
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	0.592025	−	0.805919i	$-0.298329\pi$
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	−0.993959	+	0.109749i	$0.964995\pi$
$620$	14.9282	+	9.85641i	0.599531	+	0.395843i
$621$	2.00000	−	3.46410i	0.0802572	−	0.139010i
$622$		−	12.0000i		−	0.481156i
$623$		0			0
$624$	6.00000			0.240192
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$	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
$635$	4.46410	+	0.267949i	0.177152	+	0.0106332i
$636$	6.00000			0.237915
$637$		0			0
$638$		0			0
$639$	6.00000	−	10.3923i	0.237356	−	0.411113i
$640$	−1.23205	+	1.86603i	−0.0487011	+	0.0737611i
$641$	−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	−0.0101092	−	0.999949i	$-0.503218\pi$
$653$	−22.5167	−	13.0000i	−0.881145	−	0.508729i	−0.871036	+	0.491220i	$0.836551\pi$
$654$	−5.00000	−	8.66025i	−0.195515	−	0.338643i
$655$	−33.5885	−	22.1769i	−1.31241	−	0.866524i
$656$	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	$0.0729380\pi$
$660$	4.46410	+	0.267949i	0.173765	+	0.0104299i
$661$	1.00000	+	1.73205i	0.0388955	+	0.0673690i	0.884818	−	0.465937i	$-0.154283\pi$
$661$	1.00000	+	1.73205i	0.0388955	+	0.0673690i	−0.845922	+	0.533306i	$0.820949\pi$
$662$	−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
$670$	1.07180	−	17.8564i	0.0414071	−	0.689853i
$671$	−4.00000			−0.154418
$672$		0			0
$673$			36.0000i			1.38770i	0.720121	+	0.693849i	$0.244086\pi$
$673$			36.0000i			1.38770i	−0.720121	+	0.693849i	$0.755914\pi$
$674$	14.0000	−	24.2487i	0.539260	−	0.934025i
$675$	−0.598076	+	4.96410i	−0.0230200	+	0.191068i
$676$	−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	−0.564809	−	0.825222i	$-0.691050\pi$
$683$	−3.46410	+	2.00000i	−0.132550	+	0.0765279i	0.432259	+	0.901750i	$0.357717\pi$
$684$		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
$690$	4.92820	−	7.46410i	0.187613	−	0.284153i
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	0.779857	+	0.625958i	$0.215292\pi$
$692$		−	14.0000i		−	0.532200i
$693$		0			0
$694$	12.0000			0.455514
$695$	2.67949	−	44.6410i	0.101639	−	1.69333i
$696$		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
$705$	−1.07180	+	17.8564i	−0.0403662	+	0.672511i
$706$	−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	$-0.0238160\pi$
$710$	14.7846	−	22.3923i	0.554857	−	0.840368i
$711$		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	$-0.565365\pi$
$719$	20.0000	−	34.6410i	0.745874	−	1.29189i	0.949785	−	0.312903i	$-0.101301\pi$
$720$	−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
$730$	0.535898	−	8.92820i	0.0198345	−	0.330448i
$731$	−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	$0.570181\pi$
$740$	−4.46410	−	0.267949i	−0.164104	−	0.00985001i
$741$		0			0
$742$		0			0
$743$		−	24.0000i		−	0.880475i	−0.897881	−	0.440237i	$-0.854894\pi$
$743$		−	24.0000i		−	0.880475i	0.897881	−	0.440237i	$-0.145106\pi$
$744$	−4.00000	+	6.92820i	−0.146647	+	0.254000i
$745$	−37.3205	−	24.6410i	−1.36732	−	0.902777i
$746$	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	$-0.988428\pi$
$757$		−	2.00000i		−	0.0726912i	0.999339	−	0.0363456i	$-0.0115717\pi$
$758$	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	−0.981764	−	0.190101i	$-0.939118\pi$
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	0.655515	+	0.755182i	$0.272452\pi$
$762$			2.00000i			0.0724524i
$763$		0			0
$764$	−12.0000			−0.434145
$765$	4.46410	+	0.267949i	0.161400	+	0.00968772i
$766$	−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	$-0.681921\pi$
$769$	−30.0000			−1.08183			−0.540914	+	0.841078i	$0.681921\pi$
$770$		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
$775$	15.7128	+	36.7846i	0.564421	+	1.32134i
$776$	−8.00000			−0.287183
$777$		0			0
$778$		−	20.0000i		−	0.717035i
$779$		0			0
$780$	11.1962	+	7.39230i	0.400887	+	0.264687i
$781$	−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
$795$	11.1962	+	7.39230i	0.397087	+	0.262178i
$796$		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
$800$	−4.59808	+	1.96410i	−0.162567	+	0.0694415i
$801$	−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	$-0.343489\pi$
$810$	−2.23205	−	0.133975i	−0.0784263	−	0.00470739i
$811$	−52.0000			−1.82597			−0.912983	−	0.407997i	$-0.866228\pi$
$811$	−52.0000			−1.82597			−0.912983	+	0.407997i	$0.866228\pi$
$812$		0			0
$813$			8.00000i			0.280572i
$814$	−2.00000	+	3.46410i	−0.0701000	+	0.121417i
$815$	19.7128	−	29.8564i	0.690510	−	1.04582i
$816$	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	−0.406695	−	0.913564i	$-0.633319\pi$
$823$	5.19615	−	3.00000i	0.181126	−	0.104573i	0.587822	+	0.808990i	$0.299986\pi$
$824$	−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	$0.161846\pi$
$827$			28.0000i			0.973655i	−0.873498	+	0.486828i	$0.838154\pi$
$828$	3.46410	+	2.00000i	0.120386	+	0.0695048i
$829$	15.0000	+	25.9808i	0.520972	+	0.902349i	0.999703	+	0.0243876i	$0.00776357\pi$
$829$	15.0000	+	25.9808i	0.520972	+	0.902349i	−0.478731	+	0.877962i	$0.658903\pi$
$830$	7.46410	+	4.92820i	0.259083	+	0.171060i
$831$	−1.00000	+	1.73205i	−0.0346896	+	0.0600842i
$832$			6.00000i			0.208013i
$833$		0			0
$834$	20.0000			0.692543
$835$	−26.7846	−	1.60770i	−0.926920	−	0.0556366i
$836$		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	$-0.257401\pi$
$839$	40.0000			1.38095			0.690477	+	0.723355i	$0.257401\pi$
$840$		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
$845$	3.08142	−	51.3372i	0.106004	−	1.76605i
$846$	−8.00000			−0.275046
$847$		0			0
$848$			6.00000i			0.206041i
$849$	−8.00000	+	13.8564i	−0.274559	+	0.475551i
$850$	9.92820	+	1.19615i	0.340535	+	0.0410277i
$851$	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	−0.984655	−	0.174512i	$-0.944165\pi$
$859$	−10.0000	+	17.3205i	−0.341196	+	0.590968i	0.643459	+	0.765480i	$0.277499\pi$
$860$	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	−0.135490	−	0.990779i	$-0.543261\pi$
$863$	−31.1769	−	18.0000i	−1.06127	−	0.612727i	−0.925785	+	0.378052i	$0.876594\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	17.2487	−	26.1244i	0.586474	−	0.888255i
$866$	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	0.785907	−	0.618344i	$-0.212196\pi$
$877$	19.0526	+	11.0000i	0.643359	+	0.371444i	−0.142548	+	0.989788i	$0.545530\pi$
$878$		0			0
$879$	−3.00000	−	5.19615i	−0.101187	−	0.175262i
$880$	−0.267949	+	4.46410i	−0.00903257	+	0.150485i
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$		0			0
$883$		−	24.0000i		−	0.807664i	−0.914833	−	0.403832i	$-0.867678\pi$
$883$		−	24.0000i		−	0.807664i	0.914833	−	0.403832i	$-0.132322\pi$
$884$	6.00000	−	10.3923i	0.201802	−	0.349531i
$885$	12.3205	−	18.6603i	0.414149	−	0.627258i
$886$	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
$900$	−4.96410	−	0.598076i	−0.165470	−	0.0199359i
$901$	6.00000	−	10.3923i	0.199889	−	0.346218i
$902$		−	4.00000i		−	0.133185i
$903$		0			0
$904$	6.00000			0.199557
$905$	0.267949	−	4.46410i	0.00890693	−	0.148392i
$906$	−4.00000	−	6.92820i	−0.132891	−	0.230174i
$907$	−10.3923	+	6.00000i	−0.345071	+	0.199227i	−0.662512	−	0.749051i	$-0.730510\pi$
$907$	−10.3923	+	6.00000i	−0.345071	+	0.199227i	0.317441	+	0.948278i	$0.397176\pi$
$908$	−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
$915$	4.46410	+	0.267949i	0.147579	+	0.00885813i
$916$	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	$0.166667\pi$
$920$	7.46410	+	4.92820i	0.246084	+	0.162478i
$921$	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	−0.999959	−	0.00905914i	$-0.997116\pi$
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	0.507825	+	0.861460i	$0.330450\pi$
$930$	−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
$935$	4.92820	−	7.46410i	0.161169	−	0.244102i
$936$	−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
$940$	−17.8564	−	1.07180i	−0.582412	−	0.0349582i
$941$	−14.0000	−	24.2487i	−0.456387	−	0.790485i	0.542380	−	0.840133i	$-0.317523\pi$
$941$	−14.0000	−	24.2487i	−0.456387	−	0.790485i	−0.998767	+	0.0496480i	$0.984190\pi$
$942$	−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	0.659256	−	0.751918i	$-0.270871\pi$
$947$	10.3923	+	6.00000i	0.337705	+	0.194974i	−0.321552	+	0.946892i	$0.604204\pi$
$948$		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	$0.267571\pi$
$953$			46.0000i			1.49009i	−0.667016	+	0.745043i	$0.732429\pi$
$954$	−3.00000	+	5.19615i	−0.0971286	+	0.168232i
$955$	−22.3923	−	14.7846i	−0.724598	−	0.478419i
$956$	−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	$0.209232\pi$
$967$			38.0000i			1.22200i	−0.791632	+	0.610999i	$0.790768\pi$
$968$	−6.06218	−	3.50000i	−0.194846	−	0.112494i
$969$		0			0
$970$	−14.9282	−	9.85641i	−0.479316	−	0.316470i
$971$	−9.00000	+	15.5885i	−0.288824	+	0.500257i	−0.973529	−	0.228562i	$-0.926597\pi$
$971$	−9.00000	+	15.5885i	−0.288824	+	0.500257i	0.684706	+	0.728820i	$0.259931\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		0			0
$974$	−18.0000			−0.576757
$975$	11.7846	+	27.5885i	0.377410	+	0.883538i
$976$	1.00000	+	1.73205i	0.0320092	+	0.0554416i
$977$	−36.3731	+	21.0000i	−1.16368	+	0.671850i	−0.952183	−	0.305530i	$-0.901167\pi$
$977$	−36.3731	+	21.0000i	−1.16368	+	0.671850i	−0.211495	+	0.977379i	$0.567833\pi$
$978$	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
$985$	49.1051	+	2.94744i	1.56462	+	0.0939133i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	8.00000	−	13.8564i	0.254385	−	0.440608i
$990$	−2.46410	+	3.73205i	−0.0783143	+	0.118612i
$991$	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.a.79.1		4
5.4	even	2	inner	1470.2.n.a.79.2		4
7.2	even	3		1470.2.g.g.589.2		2
7.3	odd	6		1470.2.n.h.949.2		4
7.4	even	3	inner	1470.2.n.a.949.2		4
7.5	odd	6		30.2.c.a.19.2	yes	2
7.6	odd	2		1470.2.n.h.79.1		4
21.5	even	6		90.2.c.a.19.1		2
28.19	even	6		240.2.f.a.49.2		2
35.2	odd	12		7350.2.a.bg.1.1		1
35.4	even	6	inner	1470.2.n.a.949.1		4
35.9	even	6		1470.2.g.g.589.1		2
35.12	even	12		150.2.a.a.1.1		1
35.19	odd	6		30.2.c.a.19.1	✓	2
35.23	odd	12		7350.2.a.cc.1.1		1
35.24	odd	6		1470.2.n.h.949.1		4
35.33	even	12		150.2.a.c.1.1		1
35.34	odd	2		1470.2.n.h.79.2		4
56.5	odd	6		960.2.f.h.769.2		2
56.19	even	6		960.2.f.i.769.1		2
63.5	even	6		810.2.i.b.379.2		4
63.40	odd	6		810.2.i.e.379.1		4
63.47	even	6		810.2.i.b.109.1		4
63.61	odd	6		810.2.i.e.109.2		4
84.47	odd	6		720.2.f.f.289.1		2
105.47	odd	12		450.2.a.f.1.1		1
105.68	odd	12		450.2.a.b.1.1		1
105.89	even	6		90.2.c.a.19.2		2
112.5	odd	12		3840.2.d.g.2689.1		2
112.19	even	12		3840.2.d.j.2689.2		2
112.61	odd	12		3840.2.d.y.2689.2		2
112.75	even	12		3840.2.d.x.2689.1		2
140.19	even	6		240.2.f.a.49.1		2
140.47	odd	12		1200.2.a.m.1.1		1
140.103	odd	12		1200.2.a.g.1.1		1
168.5	even	6		2880.2.f.e.1729.2		2
168.131	odd	6		2880.2.f.c.1729.2		2
280.19	even	6		960.2.f.i.769.2		2
280.117	even	12		4800.2.a.cg.1.1		1
280.173	even	12		4800.2.a.l.1.1		1
280.187	odd	12		4800.2.a.m.1.1		1
280.229	odd	6		960.2.f.h.769.1		2
280.243	odd	12		4800.2.a.cj.1.1		1
315.124	odd	6		810.2.i.e.109.1		4
315.194	even	6		810.2.i.b.379.1		4
315.229	odd	6		810.2.i.e.379.2		4
315.299	even	6		810.2.i.b.109.2		4
420.47	even	12		3600.2.a.o.1.1		1
420.299	odd	6		720.2.f.f.289.2		2
420.383	even	12		3600.2.a.bg.1.1		1
560.19	even	12		3840.2.d.x.2689.2		2
560.229	odd	12		3840.2.d.y.2689.1		2
560.299	even	12		3840.2.d.j.2689.1		2
560.509	odd	12		3840.2.d.g.2689.2		2
840.299	odd	6		2880.2.f.c.1729.1		2
840.509	even	6		2880.2.f.e.1729.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.2.c.a.19.1	✓	2	35.19	odd	6
30.2.c.a.19.2	yes	2	7.5	odd	6
90.2.c.a.19.1		2	21.5	even	6
90.2.c.a.19.2		2	105.89	even	6
150.2.a.a.1.1		1	35.12	even	12
150.2.a.c.1.1		1	35.33	even	12
240.2.f.a.49.1		2	140.19	even	6
240.2.f.a.49.2		2	28.19	even	6
450.2.a.b.1.1		1	105.68	odd	12
450.2.a.f.1.1		1	105.47	odd	12
720.2.f.f.289.1		2	84.47	odd	6
720.2.f.f.289.2		2	420.299	odd	6
810.2.i.b.109.1		4	63.47	even	6
810.2.i.b.109.2		4	315.299	even	6
810.2.i.b.379.1		4	315.194	even	6
810.2.i.b.379.2		4	63.5	even	6
810.2.i.e.109.1		4	315.124	odd	6
810.2.i.e.109.2		4	63.61	odd	6
810.2.i.e.379.1		4	63.40	odd	6
810.2.i.e.379.2		4	315.229	odd	6
960.2.f.h.769.1		2	280.229	odd	6
960.2.f.h.769.2		2	56.5	odd	6
960.2.f.i.769.1		2	56.19	even	6
960.2.f.i.769.2		2	280.19	even	6
1200.2.a.g.1.1		1	140.103	odd	12
1200.2.a.m.1.1		1	140.47	odd	12
1470.2.g.g.589.1		2	35.9	even	6
1470.2.g.g.589.2		2	7.2	even	3
1470.2.n.a.79.1		4	1.1	even	1	trivial
1470.2.n.a.79.2		4	5.4	even	2	inner
1470.2.n.a.949.1		4	35.4	even	6	inner
1470.2.n.a.949.2		4	7.4	even	3	inner
1470.2.n.h.79.1		4	7.6	odd	2
1470.2.n.h.79.2		4	35.34	odd	2
1470.2.n.h.949.1		4	35.24	odd	6
1470.2.n.h.949.2		4	7.3	odd	6
2880.2.f.c.1729.1		2	840.299	odd	6
2880.2.f.c.1729.2		2	168.131	odd	6
2880.2.f.e.1729.1		2	840.509	even	6
2880.2.f.e.1729.2		2	168.5	even	6
3600.2.a.o.1.1		1	420.47	even	12
3600.2.a.bg.1.1		1	420.383	even	12
3840.2.d.g.2689.1		2	112.5	odd	12
3840.2.d.g.2689.2		2	560.509	odd	12
3840.2.d.j.2689.1		2	560.299	even	12
3840.2.d.j.2689.2		2	112.19	even	12
3840.2.d.x.2689.1		2	112.75	even	12
3840.2.d.x.2689.2		2	560.19	even	12
3840.2.d.y.2689.1		2	560.229	odd	12
3840.2.d.y.2689.2		2	112.61	odd	12
4800.2.a.l.1.1		1	280.173	even	12
4800.2.a.m.1.1		1	280.187	odd	12
4800.2.a.cg.1.1		1	280.117	even	12
4800.2.a.cj.1.1		1	280.243	odd	12
7350.2.a.bg.1.1		1	35.2	odd	12
7350.2.a.cc.1.1		1	35.23	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
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} +(-0.133975 + 2.23205i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.23205 - 1.86603i) 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} +(-4.96410 - 0.598076i) q^{25} +(-3.00000 + 5.19615i) q^{26} -1.00000i q^{27} +(0.133975 - 2.23205i) 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} +(2.23205 + 0.133975i) q^{40} -2.00000 q^{41} -4.00000i q^{43} +(1.00000 - 1.73205i) q^{44} +(1.86603 + 1.23205i) 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} +(-1.23205 + 1.86603i) q^{60} +(1.00000 - 1.73205i) q^{61} +8.00000i q^{62} -1.00000 q^{64} +(13.3923 + 0.803848i) 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} +(-4.59808 + 1.96410i) q^{75} +6.00000i q^{78} +(-1.86603 - 1.23205i) 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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