LMFDB - Embedded newform 1470.2.n.f.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 210)
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.f.949.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.23205 + 0.133975i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.23205 + 0.133975i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.86603 + 1.23205i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(-0.866025 - 0.500000i) q^{12} -6.00000i q^{13} +(-2.00000 + 1.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.46410 - 2.00000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(3.00000 - 5.19615i) q^{19} +(1.00000 + 2.00000i) q^{20} -2.00000i q^{22} +(6.92820 + 4.00000i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(4.96410 + 0.598076i) q^{25} +(3.00000 - 5.19615i) q^{26} +1.00000i q^{27} -6.00000 q^{29} +(-2.23205 - 0.133975i) q^{30} +(-1.00000 - 1.73205i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.73205 + 1.00000i) q^{33} +4.00000 q^{34} +1.00000 q^{36} +(3.46410 + 2.00000i) q^{37} +(5.19615 - 3.00000i) q^{38} +(3.00000 + 5.19615i) q^{39} +(-0.133975 + 2.23205i) q^{40} -2.00000 q^{41} +4.00000i q^{43} +(1.00000 - 1.73205i) q^{44} +(1.23205 - 1.86603i) q^{45} +(4.00000 + 6.92820i) q^{46} +(-6.92820 - 4.00000i) q^{47} -1.00000i q^{48} +(4.00000 + 3.00000i) q^{50} +(-2.00000 + 3.46410i) q^{51} +(5.19615 - 3.00000i) q^{52} +(5.19615 - 3.00000i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.00000 - 4.00000i) q^{55} +6.00000i q^{57} +(-5.19615 - 3.00000i) q^{58} +(4.00000 + 6.92820i) q^{59} +(-1.86603 - 1.23205i) q^{60} +(-5.00000 + 8.66025i) q^{61} -2.00000i q^{62} -1.00000 q^{64} +(0.803848 - 13.3923i) q^{65} +(1.00000 + 1.73205i) q^{66} +(-6.92820 + 4.00000i) q^{67} +(3.46410 + 2.00000i) q^{68} -8.00000 q^{69} -6.00000 q^{71} +(0.866025 + 0.500000i) q^{72} +(12.1244 - 7.00000i) q^{73} +(2.00000 + 3.46410i) q^{74} +(-4.59808 + 1.96410i) q^{75} +6.00000 q^{76} +6.00000i q^{78} +(-6.00000 + 10.3923i) q^{79} +(-1.23205 + 1.86603i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.73205 - 1.00000i) q^{82} +8.00000i q^{83} +(8.00000 - 4.00000i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(5.19615 - 3.00000i) q^{87} +(1.73205 - 1.00000i) q^{88} +(5.00000 - 8.66025i) q^{89} +(2.00000 - 1.00000i) q^{90} +8.00000i q^{92} +(1.73205 + 1.00000i) q^{93} +(-4.00000 - 6.92820i) q^{94} +(7.39230 - 11.1962i) q^{95} +(0.500000 - 0.866025i) q^{96} -10.0000i q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9} + 4 q^{10} - 4 q^{11} - 8 q^{15} - 2 q^{16} + 12 q^{19} + 4 q^{20} - 2 q^{24} + 6 q^{25} + 12 q^{26} - 24 q^{29} - 2 q^{30} - 4 q^{31} + 16 q^{34} + 4 q^{36} + 12 q^{39} - 4 q^{40} - 8 q^{41} + 4 q^{44} - 2 q^{45} + 16 q^{46} + 16 q^{50} - 8 q^{51} - 2 q^{54} - 8 q^{55} + 16 q^{59} - 4 q^{60} - 20 q^{61} - 4 q^{64} + 24 q^{65} + 4 q^{66} - 32 q^{69} - 24 q^{71} + 8 q^{74} - 8 q^{75} + 24 q^{76} - 24 q^{79} + 2 q^{80} - 2 q^{81} + 32 q^{85} - 8 q^{86} + 20 q^{89} + 8 q^{90} - 16 q^{94} - 12 q^{95} + 2 q^{96} - 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9 + 4 * q^10 - 4 * q^11 - 8 * q^15 - 2 * q^16 + 12 * q^19 + 4 * q^20 - 2 * q^24 + 6 * q^25 + 12 * q^26 - 24 * q^29 - 2 * q^30 - 4 * q^31 + 16 * q^34 + 4 * q^36 + 12 * q^39 - 4 * q^40 - 8 * q^41 + 4 * q^44 - 2 * q^45 + 16 * q^46 + 16 * q^50 - 8 * q^51 - 2 * q^54 - 8 * q^55 + 16 * q^59 - 4 * q^60 - 20 * q^61 - 4 * q^64 + 24 * q^65 + 4 * q^66 - 32 * q^69 - 24 * q^71 + 8 * q^74 - 8 * q^75 + 24 * q^76 - 24 * q^79 + 2 * q^80 - 2 * q^81 + 32 * q^85 - 8 * q^86 + 20 * q^89 + 8 * q^90 - 16 * q^94 - 12 * q^95 + 2 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.866025	+	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
$5$	2.23205	+	0.133975i	0.998203	+	0.0599153i
$5$	2.23205	+	0.133975i	0.998203	+	0.0599153i
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.86603	+	1.23205i	0.590089	+	0.389609i
$11$	−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
$15$	−2.00000	+	1.00000i	−0.516398	+	0.258199i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.46410	−	2.00000i	0.840168	−	0.485071i	−0.0171533	−	0.999853i	$-0.505460\pi$
$17$	3.46410	−	2.00000i	0.840168	−	0.485071i	0.857321	+	0.514782i	$0.172127\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	−0.284157	−	0.958778i	$-0.591714\pi$
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	0.972404	−	0.233301i	$-0.0749529\pi$
$20$	1.00000	+	2.00000i	0.223607	+	0.447214i
$21$		0			0
$22$		−	2.00000i		−	0.426401i
$23$	6.92820	+	4.00000i	1.44463	+	0.834058i	0.998154	−	0.0607377i	$-0.0193453\pi$
$23$	6.92820	+	4.00000i	1.44463	+	0.834058i	0.446476	+	0.894795i	$0.352679\pi$
$24$	−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
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$	−2.23205	−	0.133975i	−0.407515	−	0.0244603i
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	1.73205	+	1.00000i	0.301511	+	0.174078i
$34$	4.00000			0.685994
$35$		0			0
$36$	1.00000			0.166667
$37$	3.46410	+	2.00000i	0.569495	+	0.328798i	0.756948	−	0.653476i	$-0.226690\pi$
$37$	3.46410	+	2.00000i	0.569495	+	0.328798i	−0.187453	+	0.982274i	$0.560023\pi$
$38$	5.19615	−	3.00000i	0.842927	−	0.486664i
$39$	3.00000	+	5.19615i	0.480384	+	0.832050i
$40$	−0.133975	+	2.23205i	−0.0211832	+	0.352918i
$41$	−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	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$	1.00000	−	1.73205i	0.150756	−	0.261116i
$45$	1.23205	−	1.86603i	0.183663	−	0.278171i
$46$	4.00000	+	6.92820i	0.589768	+	1.02151i
$47$	−6.92820	−	4.00000i	−1.01058	−	0.583460i	−0.0992202	−	0.995066i	$-0.531635\pi$
$47$	−6.92820	−	4.00000i	−1.01058	−	0.583460i	−0.911362	+	0.411606i	$0.864968\pi$
$48$		−	1.00000i		−	0.144338i
$49$		0			0
$50$	4.00000	+	3.00000i	0.565685	+	0.424264i
$51$	−2.00000	+	3.46410i	−0.280056	+	0.485071i
$52$	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
$55$	−2.00000	−	4.00000i	−0.269680	−	0.539360i
$56$		0			0
$57$			6.00000i			0.794719i
$58$	−5.19615	−	3.00000i	−0.682288	−	0.393919i
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	0.999709	+	0.0241347i	$0.00768307\pi$
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	−0.478953	+	0.877841i	$0.658984\pi$
$60$	−1.86603	−	1.23205i	−0.240903	−	0.159057i
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	0.345207	+	0.938527i	$0.387809\pi$
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	−0.985391	+	0.170305i	$0.945525\pi$
$62$		−	2.00000i		−	0.254000i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.803848	−	13.3923i	0.0997050	−	1.66111i
$66$	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	$0.495854\pi$
$68$	3.46410	+	2.00000i	0.420084	+	0.242536i
$69$	−8.00000			−0.963087
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	12.1244	−	7.00000i	1.41905	−	0.819288i	0.422833	−	0.906208i	$-0.361036\pi$
$73$	12.1244	−	7.00000i	1.41905	−	0.819288i	0.996215	+	0.0869195i	$0.0277023\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$	−4.59808	+	1.96410i	−0.530940	+	0.226795i
$76$	6.00000			0.688247
$77$		0			0
$78$			6.00000i			0.679366i
$79$	−6.00000	+	10.3923i	−0.675053	+	1.16923i	0.301401	+	0.953498i	$0.402546\pi$
$79$	−6.00000	+	10.3923i	−0.675053	+	1.16923i	−0.976453	+	0.215728i	$0.930788\pi$
$80$	−1.23205	+	1.86603i	−0.137747	+	0.208628i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.73205	−	1.00000i	−0.191273	−	0.110432i
$83$			8.00000i			0.878114i	0.898459	+	0.439057i	$0.144687\pi$
$83$			8.00000i			0.878114i	−0.898459	+	0.439057i	$0.855313\pi$
$84$		0			0
$85$	8.00000	−	4.00000i	0.867722	−	0.433861i
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$	5.19615	−	3.00000i	0.557086	−	0.321634i
$88$	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	$-0.0111410\pi$
$90$	2.00000	−	1.00000i	0.210819	−	0.105409i
$91$		0			0
$92$			8.00000i			0.834058i
$93$	1.73205	+	1.00000i	0.179605	+	0.103695i
$94$	−4.00000	−	6.92820i	−0.412568	−	0.714590i
$95$	7.39230	−	11.1962i	0.758434	−	1.14870i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$		−	10.0000i		−	1.01535i	−0.861550	−	0.507673i	$-0.830506\pi$
$97$		−	10.0000i		−	1.01535i	0.861550	−	0.507673i	$-0.169494\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$	1.96410	+	4.59808i	0.196410	+	0.459808i
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	0.999996	−	0.00286291i	$-0.000911295\pi$
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	−0.502477	+	0.864590i	$0.667578\pi$
$102$	−3.46410	+	2.00000i	−0.342997	+	0.198030i
$103$	6.92820	+	4.00000i	0.682656	+	0.394132i	0.800855	−	0.598858i	$-0.204379\pi$
$103$	6.92820	+	4.00000i	0.682656	+	0.394132i	−0.118199	+	0.992990i	$0.537712\pi$
$104$	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
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	−0.977769	−	0.209687i	$-0.932756\pi$
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	0.307290	−	0.951616i	$-0.400578\pi$
$110$	0.267949	−	4.46410i	0.0255480	−	0.425635i
$111$	−4.00000			−0.379663
$112$		0			0
$113$			6.00000i			0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$	−3.00000	+	5.19615i	−0.280976	+	0.486664i
$115$	14.9282	+	9.85641i	1.39206	+	0.919115i
$116$	−3.00000	−	5.19615i	−0.278543	−	0.482451i
$117$	−5.19615	−	3.00000i	−0.480384	−	0.277350i
$118$			8.00000i			0.736460i
$119$		0			0
$120$	−1.00000	−	2.00000i	−0.0912871	−	0.182574i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−8.66025	+	5.00000i	−0.784063	+	0.452679i
$123$	1.73205	−	1.00000i	0.156174	−	0.0901670i
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$		0			0
$127$		−	4.00000i		−	0.354943i	−0.984126	−	0.177471i	$-0.943208\pi$
$127$		−	4.00000i		−	0.354943i	0.984126	−	0.177471i	$-0.0567917\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−2.00000	−	3.46410i	−0.176090	−	0.304997i
$130$	7.39230	−	11.1962i	0.648348	−	0.981968i
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$			2.00000i			0.174078i
$133$		0			0
$134$	−8.00000			−0.691095
$135$	−0.133975	+	2.23205i	−0.0115307	+	0.192104i
$136$	2.00000	+	3.46410i	0.171499	+	0.297044i
$137$	5.19615	−	3.00000i	0.443937	−	0.256307i	−0.261329	−	0.965250i	$-0.584161\pi$
$137$	5.19615	−	3.00000i	0.443937	−	0.256307i	0.705266	+	0.708942i	$0.250827\pi$
$138$	−6.92820	−	4.00000i	−0.589768	−	0.340503i
$139$	−14.0000			−1.18746			−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000			−1.18746			−0.593732	+	0.804663i	$0.702346\pi$
$140$		0			0
$141$	8.00000			0.673722
$142$	−5.19615	−	3.00000i	−0.436051	−	0.251754i
$143$	−10.3923	+	6.00000i	−0.869048	+	0.501745i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−13.3923	−	0.803848i	−1.11217	−	0.0667559i
$146$	14.0000			1.15865
$147$		0			0
$148$			4.00000i			0.328798i
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$	−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	$0.727796\pi$
$152$	5.19615	+	3.00000i	0.421464	+	0.243332i
$153$		−	4.00000i		−	0.323381i
$154$		0			0
$155$	−2.00000	−	4.00000i	−0.160644	−	0.321288i
$156$	−3.00000	+	5.19615i	−0.240192	+	0.416025i
$157$	−19.0526	+	11.0000i	−1.52056	+	0.877896i	−0.520854	+	0.853646i	$0.674386\pi$
$157$	−19.0526	+	11.0000i	−1.52056	+	0.877896i	−0.999706	+	0.0242497i	$0.992280\pi$
$158$	−10.3923	+	6.00000i	−0.826767	+	0.477334i
$159$	−3.00000	+	5.19615i	−0.237915	+	0.412082i
$160$	−2.00000	+	1.00000i	−0.158114	+	0.0790569i
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	0.629492	−	0.777007i	$-0.283263\pi$
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	−0.358162	+	0.933659i	$0.616597\pi$
$164$	−1.00000	−	1.73205i	−0.0780869	−	0.135250i
$165$	3.73205	+	2.46410i	0.290540	+	0.191830i
$166$	−4.00000	+	6.92820i	−0.310460	+	0.537733i
$167$		−	12.0000i		−	0.928588i	−0.885681	−	0.464294i	$-0.846308\pi$
$167$		−	12.0000i		−	0.928588i	0.885681	−	0.464294i	$-0.153692\pi$
$168$		0			0
$169$	−23.0000			−1.76923
$170$	8.92820	+	0.535898i	0.684762	+	0.0411015i
$171$	−3.00000	−	5.19615i	−0.229416	−	0.397360i
$172$	−3.46410	+	2.00000i	−0.264135	+	0.152499i
$173$	6.92820	+	4.00000i	0.526742	+	0.304114i	0.739689	−	0.672949i	$-0.234973\pi$
$173$	6.92820	+	4.00000i	0.526742	+	0.304114i	−0.212947	+	0.977064i	$0.568306\pi$
$174$	6.00000			0.454859
$175$		0			0
$176$	2.00000			0.150756
$177$	−6.92820	−	4.00000i	−0.520756	−	0.300658i
$178$	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	$0.711416\pi$
$180$	2.23205	+	0.133975i	0.166367	+	0.00998588i
$181$	−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
$183$		−	10.0000i		−	0.739221i
$184$	−4.00000	+	6.92820i	−0.294884	+	0.510754i
$185$	7.46410	+	4.92820i	0.548772	+	0.362329i
$186$	1.00000	+	1.73205i	0.0733236	+	0.127000i
$187$	−6.92820	−	4.00000i	−0.506640	−	0.292509i
$188$		−	8.00000i		−	0.583460i
$189$		0			0
$190$	12.0000	−	6.00000i	0.870572	−	0.435286i
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	−0.331611	−	0.943416i	$-0.607592\pi$
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	0.982828	−	0.184525i	$-0.0590746\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−6.92820	+	4.00000i	−0.498703	+	0.287926i	−0.728178	−	0.685388i	$-0.759632\pi$
$193$	−6.92820	+	4.00000i	−0.498703	+	0.287926i	0.229475	+	0.973315i	$0.426299\pi$
$194$	5.00000	−	8.66025i	0.358979	−	0.621770i
$195$	6.00000	+	12.0000i	0.429669	+	0.859338i
$196$		0			0
$197$		−	2.00000i		−	0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$		−	2.00000i		−	0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$	−1.73205	−	1.00000i	−0.123091	−	0.0710669i
$199$	−3.00000	−	5.19615i	−0.212664	−	0.368345i	0.739883	−	0.672735i	$-0.234881\pi$
$199$	−3.00000	−	5.19615i	−0.212664	−	0.368345i	−0.952548	+	0.304390i	$0.901547\pi$
$200$	−0.598076	+	4.96410i	−0.0422904	+	0.351015i
$201$	4.00000	−	6.92820i	0.282138	−	0.488678i
$202$			10.0000i			0.703598i
$203$		0			0
$204$	−4.00000			−0.280056
$205$	−4.46410	−	0.267949i	−0.311786	−	0.0187144i
$206$	4.00000	+	6.92820i	0.278693	+	0.482711i
$207$	6.92820	−	4.00000i	0.481543	−	0.278019i
$208$	5.19615	+	3.00000i	0.360288	+	0.208013i
$209$	−12.0000			−0.830057
$210$		0			0
$211$		0			0			−	1.00000i	$-0.5\pi$
$211$		0			0				1.00000i	$0.5\pi$
$212$	5.19615	+	3.00000i	0.356873	+	0.206041i
$213$	5.19615	−	3.00000i	0.356034	−	0.205557i
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	−0.535898	+	8.92820i	−0.0365480	+	0.608898i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$		−	14.0000i		−	0.948200i
$219$	−7.00000	+	12.1244i	−0.473016	+	0.819288i
$220$	2.46410	−	3.73205i	0.166130	−	0.251615i
$221$	−12.0000	−	20.7846i	−0.807207	−	1.39812i
$222$	−3.46410	−	2.00000i	−0.232495	−	0.134231i
$223$			8.00000i			0.535720i	0.963458	+	0.267860i	$0.0863164\pi$
$223$			8.00000i			0.535720i	−0.963458	+	0.267860i	$0.913684\pi$
$224$		0			0
$225$	3.00000	−	4.00000i	0.200000	−	0.266667i
$226$	−3.00000	+	5.19615i	−0.199557	+	0.345643i
$227$	−6.92820	+	4.00000i	−0.459841	+	0.265489i	−0.711977	−	0.702202i	$-0.752200\pi$
$227$	−6.92820	+	4.00000i	−0.459841	+	0.265489i	0.252136	+	0.967692i	$0.418867\pi$
$228$	−5.19615	+	3.00000i	−0.344124	+	0.198680i
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	−0.999088	−	0.0426906i	$-0.986407\pi$
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	0.536515	+	0.843891i	$0.319740\pi$
$230$	8.00000	+	16.0000i	0.527504	+	1.05501i
$231$		0			0
$232$		−	6.00000i		−	0.393919i
$233$	8.66025	+	5.00000i	0.567352	+	0.327561i	0.756091	−	0.654466i	$-0.227107\pi$
$233$	8.66025	+	5.00000i	0.567352	+	0.327561i	−0.188739	+	0.982027i	$0.560440\pi$
$234$	−3.00000	−	5.19615i	−0.196116	−	0.339683i
$235$	−14.9282	−	9.85641i	−0.973809	−	0.642961i
$236$	−4.00000	+	6.92820i	−0.260378	+	0.450988i
$237$		−	12.0000i		−	0.779484i
$238$		0			0
$239$	−26.0000			−1.68180			−0.840900	−	0.541190i	$-0.817974\pi$
$239$	−26.0000			−1.68180			−0.840900	+	0.541190i	$0.817974\pi$
$240$	0.133975	−	2.23205i	0.00864802	−	0.144078i
$241$	−13.0000	−	22.5167i	−0.837404	−	1.45043i	−0.892058	−	0.451920i	$-0.850739\pi$
$241$	−13.0000	−	22.5167i	−0.837404	−	1.45043i	0.0546547	−	0.998505i	$-0.482594\pi$
$242$	6.06218	−	3.50000i	0.389692	−	0.224989i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−10.0000			−0.640184
$245$		0			0
$246$	2.00000			0.127515
$247$	−31.1769	−	18.0000i	−1.98374	−	1.14531i
$248$	1.73205	−	1.00000i	0.109985	−	0.0635001i
$249$	−4.00000	−	6.92820i	−0.253490	−	0.439057i
$250$	8.52628	+	7.23205i	0.539249	+	0.457395i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		−	16.0000i		−	1.00591i
$254$	2.00000	−	3.46410i	0.125491	−	0.217357i
$255$	−4.92820	+	7.46410i	−0.308616	+	0.467420i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$257$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$258$		−	4.00000i		−	0.249029i
$259$		0			0
$260$	12.0000	−	6.00000i	0.744208	−	0.372104i
$261$	−3.00000	+	5.19615i	−0.185695	+	0.321634i
$262$	−10.3923	+	6.00000i	−0.642039	+	0.370681i
$263$	13.8564	−	8.00000i	0.854423	−	0.493301i	−0.00771799	−	0.999970i	$-0.502457\pi$
$263$	13.8564	−	8.00000i	0.854423	−	0.493301i	0.862141	+	0.506669i	$0.169123\pi$
$264$	−1.00000	+	1.73205i	−0.0615457	+	0.106600i
$265$	12.0000	−	6.00000i	0.737154	−	0.368577i
$266$		0			0
$267$			10.0000i			0.611990i
$268$	−6.92820	−	4.00000i	−0.423207	−	0.244339i
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	−0.998361	−	0.0572259i	$-0.981774\pi$
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$270$	−1.23205	+	1.86603i	−0.0749802	+	0.113563i
$271$	5.00000	−	8.66025i	0.303728	−	0.526073i	−0.673249	−	0.739416i	$-0.735102\pi$
$271$	5.00000	−	8.66025i	0.303728	−	0.526073i	0.976977	+	0.213343i	$0.0684351\pi$
$272$			4.00000i			0.242536i
$273$		0			0
$274$	6.00000			0.362473
$275$	−3.92820	−	9.19615i	−0.236880	−	0.554549i
$276$	−4.00000	−	6.92820i	−0.240772	−	0.417029i
$277$	−24.2487	+	14.0000i	−1.45696	+	0.841178i	−0.998861	−	0.0477206i	$-0.984804\pi$
$277$	−24.2487	+	14.0000i	−1.45696	+	0.841178i	−0.458103	+	0.888899i	$0.651471\pi$
$278$	−12.1244	−	7.00000i	−0.727171	−	0.419832i
$279$	−2.00000			−0.119737
$280$		0			0
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$	6.92820	+	4.00000i	0.412568	+	0.238197i
$283$	−17.3205	+	10.0000i	−1.02960	+	0.594438i	−0.916869	−	0.399188i	$-0.869292\pi$
$283$	−17.3205	+	10.0000i	−1.02960	+	0.594438i	−0.112728	+	0.993626i	$0.535959\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$	−0.803848	+	13.3923i	−0.0476158	+	0.793292i
$286$	−12.0000			−0.709575
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	−11.1962	−	7.39230i	−0.657461	−	0.434091i
$291$	5.00000	+	8.66025i	0.293105	+	0.507673i
$292$	12.1244	+	7.00000i	0.709524	+	0.409644i
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$		0			0
$295$	8.00000	+	16.0000i	0.465778	+	0.931556i
$296$	−2.00000	+	3.46410i	−0.116248	+	0.201347i
$297$	1.73205	−	1.00000i	0.100504	−	0.0580259i
$298$	8.66025	−	5.00000i	0.501675	−	0.289642i
$299$	24.0000	−	41.5692i	1.38796	−	2.40401i
$300$	−4.00000	−	3.00000i	−0.230940	−	0.173205i
$301$		0			0
$302$			8.00000i			0.460348i
$303$	−8.66025	−	5.00000i	−0.497519	−	0.287242i
$304$	3.00000	+	5.19615i	0.172062	+	0.298020i
$305$	−12.3205	+	18.6603i	−0.705470	+	1.06848i
$306$	2.00000	−	3.46410i	0.114332	−	0.198030i
$307$		−	12.0000i		−	0.684876i	−0.939540	−	0.342438i	$-0.888747\pi$
$307$		−	12.0000i		−	0.684876i	0.939540	−	0.342438i	$-0.111253\pi$
$308$		0			0
$309$	−8.00000			−0.455104
$310$	0.267949	−	4.46410i	0.0152185	−	0.253544i
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	0.974841	+	0.222900i	$0.0715523\pi$
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	−0.294384	+	0.955687i	$0.595114\pi$
$312$	−5.19615	+	3.00000i	−0.294174	+	0.169842i
$313$	−1.73205	−	1.00000i	−0.0979013	−	0.0565233i	0.450250	−	0.892903i	$-0.351335\pi$
$313$	−1.73205	−	1.00000i	−0.0979013	−	0.0565233i	−0.548151	+	0.836379i	$0.684668\pi$
$314$	−22.0000			−1.24153
$315$		0			0
$316$	−12.0000			−0.675053
$317$	−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
$319$	6.00000	+	10.3923i	0.335936	+	0.581857i
$320$	−2.23205	−	0.133975i	−0.124775	−	0.00748941i
$321$	−12.0000			−0.669775
$322$		0			0
$323$		−	24.0000i		−	1.33540i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	3.58846	−	29.7846i	0.199052	−	1.65215i
$326$	2.00000	+	3.46410i	0.110770	+	0.191859i
$327$	12.1244	+	7.00000i	0.670478	+	0.387101i
$328$		−	2.00000i		−	0.110432i
$329$		0			0
$330$	2.00000	+	4.00000i	0.110096	+	0.220193i
$331$	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	$0.0961066\pi$
$332$	−6.92820	+	4.00000i	−0.380235	+	0.219529i
$333$	3.46410	−	2.00000i	0.189832	−	0.109599i
$334$	6.00000	−	10.3923i	0.328305	−	0.568642i
$335$	−16.0000	+	8.00000i	−0.874173	+	0.437087i
$336$		0			0
$337$			8.00000i			0.435788i	0.975972	+	0.217894i	$0.0699187\pi$
$337$			8.00000i			0.435788i	−0.975972	+	0.217894i	$0.930081\pi$
$338$	−19.9186	−	11.5000i	−1.08343	−	0.625518i
$339$	−3.00000	−	5.19615i	−0.162938	−	0.282216i
$340$	7.46410	+	4.92820i	0.404798	+	0.267269i
$341$	−2.00000	+	3.46410i	−0.108306	+	0.187592i
$342$		−	6.00000i		−	0.324443i
$343$		0			0
$344$	−4.00000			−0.215666
$345$	−17.8564	−	1.07180i	−0.961357	−	0.0577036i
$346$	4.00000	+	6.92820i	0.215041	+	0.372463i
$347$	−31.1769	+	18.0000i	−1.67366	+	0.966291i	−0.708105	+	0.706107i	$0.750450\pi$
$347$	−31.1769	+	18.0000i	−1.67366	+	0.966291i	−0.965559	+	0.260184i	$0.916217\pi$
$348$	5.19615	+	3.00000i	0.278543	+	0.160817i
$349$	−26.0000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$350$		0			0
$351$	6.00000			0.320256
$352$	1.73205	+	1.00000i	0.0923186	+	0.0533002i
$353$	−17.3205	+	10.0000i	−0.921878	+	0.532246i	−0.884234	−	0.467045i	$-0.845319\pi$
$353$	−17.3205	+	10.0000i	−0.921878	+	0.532246i	−0.0376440	+	0.999291i	$0.511985\pi$
$354$	−4.00000	−	6.92820i	−0.212598	−	0.368230i
$355$	−13.3923	−	0.803848i	−0.710790	−	0.0426638i
$356$	10.0000			0.529999
$357$		0			0
$358$			10.0000i			0.528516i
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	−0.775934	−	0.630814i	$-0.782721\pi$
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	0.934268	+	0.356572i	$0.116054\pi$
$360$	1.86603	+	1.23205i	0.0983482	+	0.0649348i
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	−1.73205	−	1.00000i	−0.0910346	−	0.0525588i
$363$			7.00000i			0.367405i
$364$		0			0
$365$	28.0000	−	14.0000i	1.46559	−	0.732793i
$366$	5.00000	−	8.66025i	0.261354	−	0.452679i
$367$	−27.7128	+	16.0000i	−1.44660	+	0.835193i	−0.998277	−	0.0586798i	$-0.981311\pi$
$367$	−27.7128	+	16.0000i	−1.44660	+	0.835193i	−0.448320	+	0.893873i	$0.647978\pi$
$368$	−6.92820	+	4.00000i	−0.361158	+	0.208514i
$369$	−1.00000	+	1.73205i	−0.0520579	+	0.0901670i
$370$	4.00000	+	8.00000i	0.207950	+	0.415900i
$371$		0			0
$372$			2.00000i			0.103695i
$373$	20.7846	+	12.0000i	1.07619	+	0.621336i	0.929865	−	0.367901i	$-0.119923\pi$
$373$	20.7846	+	12.0000i	1.07619	+	0.621336i	0.146321	+	0.989237i	$0.453257\pi$
$374$	−4.00000	−	6.92820i	−0.206835	−	0.358249i
$375$	−10.5263	+	3.76795i	−0.543575	+	0.194576i
$376$	4.00000	−	6.92820i	0.206284	−	0.357295i
$377$			36.0000i			1.85409i
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	13.3923	+	0.803848i	0.687011	+	0.0412365i
$381$	2.00000	+	3.46410i	0.102463	+	0.177471i
$382$	15.5885	−	9.00000i	0.797575	−	0.460480i
$383$	17.3205	+	10.0000i	0.885037	+	0.510976i	0.872316	−	0.488943i	$-0.162617\pi$
$383$	17.3205	+	10.0000i	0.885037	+	0.510976i	0.0127209	+	0.999919i	$0.495951\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−8.00000			−0.407189
$387$	3.46410	+	2.00000i	0.176090	+	0.101666i
$388$	8.66025	−	5.00000i	0.439658	−	0.253837i
$389$	1.00000	+	1.73205i	0.0507020	+	0.0878185i	0.890263	−	0.455448i	$-0.150521\pi$
$389$	1.00000	+	1.73205i	0.0507020	+	0.0878185i	−0.839561	+	0.543266i	$0.817187\pi$
$390$	−0.803848	+	13.3923i	−0.0407044	+	0.678146i
$391$	32.0000			1.61831
$392$		0			0
$393$		−	12.0000i		−	0.605320i
$394$	1.00000	−	1.73205i	0.0503793	−	0.0872595i
$395$	−14.7846	+	22.3923i	−0.743894	+	1.12668i
$396$	−1.00000	−	1.73205i	−0.0502519	−	0.0870388i
$397$	1.73205	+	1.00000i	0.0869291	+	0.0501886i	0.542834	−	0.839840i	$-0.317351\pi$
$397$	1.73205	+	1.00000i	0.0869291	+	0.0501886i	−0.455905	+	0.890028i	$0.650684\pi$
$398$		−	6.00000i		−	0.300753i
$399$		0			0
$400$	−3.00000	+	4.00000i	−0.150000	+	0.200000i
$401$	7.00000	−	12.1244i	0.349563	−	0.605461i	−0.636609	−	0.771187i	$-0.719663\pi$
$401$	7.00000	−	12.1244i	0.349563	−	0.605461i	0.986172	+	0.165726i	$0.0529966\pi$
$402$	6.92820	−	4.00000i	0.345547	−	0.199502i
$403$	−10.3923	+	6.00000i	−0.517678	+	0.298881i
$404$	−5.00000	+	8.66025i	−0.248759	+	0.430864i
$405$	−1.00000	−	2.00000i	−0.0496904	−	0.0993808i
$406$		0			0
$407$		−	8.00000i		−	0.396545i
$408$	−3.46410	−	2.00000i	−0.171499	−	0.0990148i
$409$	−13.0000	−	22.5167i	−0.642809	−	1.11338i	−0.984803	−	0.173675i	$-0.944436\pi$
$409$	−13.0000	−	22.5167i	−0.642809	−	1.11338i	0.341994	−	0.939702i	$-0.388898\pi$
$410$	−3.73205	−	2.46410i	−0.184313	−	0.121693i
$411$	−3.00000	+	5.19615i	−0.147979	+	0.256307i
$412$			8.00000i			0.394132i
$413$		0			0
$414$	8.00000			0.393179
$415$	−1.07180	+	17.8564i	−0.0526124	+	0.876537i
$416$	3.00000	+	5.19615i	0.147087	+	0.254762i
$417$	12.1244	−	7.00000i	0.593732	−	0.342791i
$418$	−10.3923	−	6.00000i	−0.508304	−	0.293470i
$419$	20.0000			0.977064			0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000			0.977064			0.488532	+	0.872546i	$0.337533\pi$
$420$		0			0
$421$	34.0000			1.65706			0.828529	−	0.559946i	$-0.189178\pi$
$421$	34.0000			1.65706			0.828529	+	0.559946i	$0.189178\pi$
$422$		0			0
$423$	−6.92820	+	4.00000i	−0.336861	+	0.194487i
$424$	3.00000	+	5.19615i	0.145693	+	0.252347i
$425$	18.3923	−	7.85641i	0.892158	−	0.381092i
$426$	6.00000			0.290701
$427$		0			0
$428$			12.0000i			0.580042i
$429$	6.00000	−	10.3923i	0.289683	−	0.501745i
$430$	−4.92820	+	7.46410i	−0.237659	+	0.359951i
$431$	−1.00000	−	1.73205i	−0.0481683	−	0.0834300i	0.840936	−	0.541135i	$-0.182005\pi$
$431$	−1.00000	−	1.73205i	−0.0481683	−	0.0834300i	−0.889104	+	0.457705i	$0.848672\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$			26.0000i			1.24948i	0.780833	+	0.624740i	$0.214795\pi$
$433$			26.0000i			1.24948i	−0.780833	+	0.624740i	$0.785205\pi$
$434$		0			0
$435$	12.0000	−	6.00000i	0.575356	−	0.287678i
$436$	7.00000	−	12.1244i	0.335239	−	0.580651i
$437$	41.5692	−	24.0000i	1.98853	−	1.14808i
$438$	−12.1244	+	7.00000i	−0.579324	+	0.334473i
$439$	9.00000	−	15.5885i	0.429547	−	0.743996i	−0.567286	−	0.823521i	$-0.692007\pi$
$439$	9.00000	−	15.5885i	0.429547	−	0.743996i	0.996833	+	0.0795241i	$0.0253401\pi$
$440$	4.00000	−	2.00000i	0.190693	−	0.0953463i
$441$		0			0
$442$		−	24.0000i		−	1.14156i
$443$	10.3923	+	6.00000i	0.493753	+	0.285069i	0.726130	−	0.687557i	$-0.241317\pi$
$443$	10.3923	+	6.00000i	0.493753	+	0.285069i	−0.232377	+	0.972626i	$0.574650\pi$
$444$	−2.00000	−	3.46410i	−0.0949158	−	0.164399i
$445$	12.3205	−	18.6603i	0.584048	−	0.884581i
$446$	−4.00000	+	6.92820i	−0.189405	+	0.328060i
$447$			10.0000i			0.472984i
$448$		0			0
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	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
$454$	−8.00000			−0.375459
$455$		0			0
$456$	−6.00000			−0.280976
$457$	24.2487	+	14.0000i	1.13431	+	0.654892i	0.945015	−	0.327028i	$-0.106047\pi$
$457$	24.2487	+	14.0000i	1.13431	+	0.654892i	0.189292	+	0.981921i	$0.439381\pi$
$458$	−12.1244	+	7.00000i	−0.566534	+	0.327089i
$459$	2.00000	+	3.46410i	0.0933520	+	0.161690i
$460$	−1.07180	+	17.8564i	−0.0499728	+	0.832559i
$461$	18.0000			0.838344			0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$		0			0
$463$			36.0000i			1.67306i	0.547920	+	0.836531i	$0.315420\pi$
$463$			36.0000i			1.67306i	−0.547920	+	0.836531i	$0.684580\pi$
$464$	3.00000	−	5.19615i	0.139272	−	0.241225i
$465$	3.73205	+	2.46410i	0.173070	+	0.114270i
$466$	5.00000	+	8.66025i	0.231621	+	0.401179i
$467$	20.7846	+	12.0000i	0.961797	+	0.555294i	0.896726	−	0.442587i	$-0.145939\pi$
$467$	20.7846	+	12.0000i	0.961797	+	0.555294i	0.0650714	+	0.997881i	$0.479272\pi$
$468$		−	6.00000i		−	0.277350i
$469$		0			0
$470$	−8.00000	−	16.0000i	−0.369012	−	0.738025i
$471$	11.0000	−	19.0526i	0.506853	−	0.877896i
$472$	−6.92820	+	4.00000i	−0.318896	+	0.184115i
$473$	6.92820	−	4.00000i	0.318559	−	0.183920i
$474$	6.00000	−	10.3923i	0.275589	−	0.477334i
$475$	18.0000	−	24.0000i	0.825897	−	1.10120i
$476$		0			0
$477$		−	6.00000i		−	0.274721i
$478$	−22.5167	−	13.0000i	−1.02989	−	0.594606i
$479$	−4.00000	−	6.92820i	−0.182765	−	0.316558i	0.760056	−	0.649857i	$-0.225171\pi$
$479$	−4.00000	−	6.92820i	−0.182765	−	0.316558i	−0.942821	+	0.333300i	$0.891838\pi$
$480$	1.23205	−	1.86603i	0.0562352	−	0.0851720i
$481$	12.0000	−	20.7846i	0.547153	−	0.947697i
$482$		−	26.0000i		−	1.18427i
$483$		0			0
$484$	7.00000			0.318182
$485$	1.33975	−	22.3205i	0.0608347	−	1.01352i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−10.3923	+	6.00000i	−0.470920	+	0.271886i	−0.716625	−	0.697459i	$-0.754314\pi$
$487$	−10.3923	+	6.00000i	−0.470920	+	0.271886i	0.245705	+	0.969345i	$0.420981\pi$
$488$	−8.66025	−	5.00000i	−0.392031	−	0.226339i
$489$	−4.00000			−0.180886
$490$		0			0
$491$	−30.0000			−1.35388			−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000			−1.35388			−0.676941	+	0.736038i	$0.736695\pi$
$492$	1.73205	+	1.00000i	0.0780869	+	0.0450835i
$493$	−20.7846	+	12.0000i	−0.936092	+	0.540453i
$494$	−18.0000	−	31.1769i	−0.809858	−	1.40272i
$495$	−4.46410	−	0.267949i	−0.200646	−	0.0120434i
$496$	2.00000			0.0898027
$497$		0			0
$498$		−	8.00000i		−	0.358489i
$499$	−6.00000	+	10.3923i	−0.268597	+	0.465223i	−0.968500	−	0.249015i	$-0.919893\pi$
$499$	−6.00000	+	10.3923i	−0.268597	+	0.465223i	0.699903	+	0.714238i	$0.253227\pi$
$500$	3.76795	+	10.5263i	0.168508	+	0.470750i
$501$	6.00000	+	10.3923i	0.268060	+	0.464294i
$502$		0			0
$503$			12.0000i			0.535054i	0.963550	+	0.267527i	$0.0862064\pi$
$503$			12.0000i			0.535054i	−0.963550	+	0.267527i	$0.913794\pi$
$504$		0			0
$505$	10.0000	+	20.0000i	0.444994	+	0.889988i
$506$	8.00000	−	13.8564i	0.355643	−	0.615992i
$507$	19.9186	−	11.5000i	0.884615	−	0.510733i
$508$	3.46410	−	2.00000i	0.153695	−	0.0887357i
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	0.314459	+	0.949271i	$0.398177\pi$
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	−0.979322	+	0.202306i	$0.935156\pi$
$510$	−8.00000	+	4.00000i	−0.354246	+	0.177123i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	5.19615	+	3.00000i	0.229416	+	0.132453i
$514$		0			0
$515$	14.9282	+	9.85641i	0.657815	+	0.434325i
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$			16.0000i			0.703679i
$518$		0			0
$519$	−8.00000			−0.351161
$520$	13.3923	+	0.803848i	0.587291	+	0.0352510i
$521$	−13.0000	−	22.5167i	−0.569540	−	0.986473i	−0.996611	−	0.0822547i	$-0.973788\pi$
$521$	−13.0000	−	22.5167i	−0.569540	−	0.986473i	0.427071	−	0.904218i	$-0.359545\pi$
$522$	−5.19615	+	3.00000i	−0.227429	+	0.131306i
$523$	−24.2487	−	14.0000i	−1.06032	−	0.612177i	−0.134801	−	0.990873i	$-0.543039\pi$
$523$	−24.2487	−	14.0000i	−1.06032	−	0.612177i	−0.925521	+	0.378695i	$0.876373\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$	16.0000			0.697633
$527$	−6.92820	−	4.00000i	−0.301797	−	0.174243i
$528$	−1.73205	+	1.00000i	−0.0753778	+	0.0435194i
$529$	20.5000	+	35.5070i	0.891304	+	1.54378i
$530$	13.3923	+	0.803848i	0.581725	+	0.0349169i
$531$	8.00000			0.347170
$532$		0			0
$533$			12.0000i			0.519778i
$534$	−5.00000	+	8.66025i	−0.216371	+	0.374766i
$535$	22.3923	+	14.7846i	0.968104	+	0.639194i
$536$	−4.00000	−	6.92820i	−0.172774	−	0.299253i
$537$	−8.66025	−	5.00000i	−0.373718	−	0.215766i
$538$		−	18.0000i		−	0.776035i
$539$		0			0
$540$	−2.00000	+	1.00000i	−0.0860663	+	0.0430331i
$541$	−11.0000	+	19.0526i	−0.472927	+	0.819133i	−0.999520	−	0.0309841i	$-0.990136\pi$
$541$	−11.0000	+	19.0526i	−0.472927	+	0.819133i	0.526593	+	0.850118i	$0.323469\pi$
$542$	8.66025	−	5.00000i	0.371990	−	0.214768i
$543$	1.73205	−	1.00000i	0.0743294	−	0.0429141i
$544$	−2.00000	+	3.46410i	−0.0857493	+	0.148522i
$545$	−14.0000	−	28.0000i	−0.599694	−	1.19939i
$546$		0			0
$547$		−	40.0000i		−	1.71028i	−0.518400	−	0.855138i	$-0.673472\pi$
$547$		−	40.0000i		−	1.71028i	0.518400	−	0.855138i	$-0.326528\pi$
$548$	5.19615	+	3.00000i	0.221969	+	0.128154i
$549$	5.00000	+	8.66025i	0.213395	+	0.369611i
$550$	1.19615	−	9.92820i	0.0510041	−	0.423340i
$551$	−18.0000	+	31.1769i	−0.766826	+	1.32818i
$552$		−	8.00000i		−	0.340503i
$553$		0			0
$554$	−28.0000			−1.18961
$555$	−8.92820	−	0.535898i	−0.378981	−	0.0227476i
$556$	−7.00000	−	12.1244i	−0.296866	−	0.514187i
$557$	36.3731	−	21.0000i	1.54118	−	0.889799i	0.542411	−	0.840113i	$-0.317511\pi$
$557$	36.3731	−	21.0000i	1.54118	−	0.889799i	0.998765	−	0.0496855i	$-0.0158219\pi$
$558$	−1.73205	−	1.00000i	−0.0733236	−	0.0423334i
$559$	24.0000			1.01509
$560$		0			0
$561$	8.00000			0.337760
$562$	25.9808	+	15.0000i	1.09593	+	0.632737i
$563$	3.46410	−	2.00000i	0.145994	−	0.0842900i	−0.425223	−	0.905088i	$-0.639804\pi$
$563$	3.46410	−	2.00000i	0.145994	−	0.0842900i	0.571218	+	0.820798i	$0.306471\pi$
$564$	4.00000	+	6.92820i	0.168430	+	0.291730i
$565$	−0.803848	+	13.3923i	−0.0338181	+	0.563418i
$566$	−20.0000			−0.840663
$567$		0			0
$568$		−	6.00000i		−	0.251754i
$569$	−23.0000	+	39.8372i	−0.964210	+	1.67006i	−0.252488	+	0.967600i	$0.581249\pi$
$569$	−23.0000	+	39.8372i	−0.964210	+	1.67006i	−0.711722	+	0.702461i	$0.752085\pi$
$570$	−7.39230	+	11.1962i	−0.309630	+	0.468955i
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	0.821138	−	0.570730i	$-0.193340\pi$
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	−0.904835	+	0.425762i	$0.860006\pi$
$572$	−10.3923	−	6.00000i	−0.434524	−	0.250873i
$573$			18.0000i			0.751961i
$574$		0			0
$575$	32.0000	+	24.0000i	1.33449	+	1.00087i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−22.5167	+	13.0000i	−0.937381	+	0.541197i	−0.889138	−	0.457639i	$-0.848695\pi$
$577$	−22.5167	+	13.0000i	−0.937381	+	0.541197i	−0.0482425	+	0.998836i	$0.515362\pi$
$578$	−0.866025	+	0.500000i	−0.0360219	+	0.0207973i
$579$	4.00000	−	6.92820i	0.166234	−	0.287926i
$580$	−6.00000	−	12.0000i	−0.249136	−	0.498273i
$581$		0			0
$582$			10.0000i			0.414513i
$583$	−10.3923	−	6.00000i	−0.430405	−	0.248495i
$584$	7.00000	+	12.1244i	0.289662	+	0.501709i
$585$	−11.1962	−	7.39230i	−0.462904	−	0.305634i
$586$		0			0
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$		0			0
$589$	−12.0000			−0.494451
$590$	−1.07180	+	17.8564i	−0.0441252	+	0.735137i
$591$	1.00000	+	1.73205i	0.0411345	+	0.0712470i
$592$	−3.46410	+	2.00000i	−0.142374	+	0.0821995i
$593$	10.3923	+	6.00000i	0.426761	+	0.246390i	0.697966	−	0.716131i	$-0.254089\pi$
$593$	10.3923	+	6.00000i	0.426761	+	0.246390i	−0.271205	+	0.962522i	$0.587422\pi$
$594$	2.00000			0.0820610
$595$		0			0
$596$	10.0000			0.409616
$597$	5.19615	+	3.00000i	0.212664	+	0.122782i
$598$	41.5692	−	24.0000i	1.69989	−	0.981433i
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	0.990752	+	0.135686i	$0.0433238\pi$
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	−0.377869	+	0.925859i	$0.623343\pi$
$600$	−1.96410	−	4.59808i	−0.0801841	−	0.187716i
$601$	−38.0000			−1.55005			−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000			−1.55005			−0.775026	+	0.631929i	$0.782263\pi$
$602$		0			0
$603$			8.00000i			0.325785i
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	8.62436	−	13.0622i	0.350630	−	0.531053i
$606$	−5.00000	−	8.66025i	−0.203111	−	0.351799i
$607$	−6.92820	−	4.00000i	−0.281207	−	0.162355i	0.352763	−	0.935713i	$-0.385242\pi$
$607$	−6.92820	−	4.00000i	−0.281207	−	0.162355i	−0.633970	+	0.773358i	$0.718576\pi$
$608$			6.00000i			0.243332i
$609$		0			0
$610$	−20.0000	+	10.0000i	−0.809776	+	0.404888i
$611$	−24.0000	+	41.5692i	−0.970936	+	1.68171i
$612$	3.46410	−	2.00000i	0.140028	−	0.0808452i
$613$	24.2487	−	14.0000i	0.979396	−	0.565455i	0.0773084	−	0.997007i	$-0.475367\pi$
$613$	24.2487	−	14.0000i	0.979396	−	0.565455i	0.902088	+	0.431553i	$0.142034\pi$
$614$	6.00000	−	10.3923i	0.242140	−	0.419399i
$615$	4.00000	−	2.00000i	0.161296	−	0.0806478i
$616$		0			0
$617$			26.0000i			1.04672i	0.852111	+	0.523360i	$0.175322\pi$
$617$			26.0000i			1.04672i	−0.852111	+	0.523360i	$0.824678\pi$
$618$	−6.92820	−	4.00000i	−0.278693	−	0.160904i
$619$	11.0000	+	19.0526i	0.442127	+	0.765787i	0.997847	−	0.0655827i	$-0.0208906\pi$
$619$	11.0000	+	19.0526i	0.442127	+	0.765787i	−0.555720	+	0.831370i	$0.687557\pi$
$620$	2.46410	−	3.73205i	0.0989607	−	0.149883i
$621$	−4.00000	+	6.92820i	−0.160514	+	0.278019i
$622$			24.0000i			0.962312i
$623$		0			0
$624$	−6.00000			−0.240192
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$	−1.00000	−	1.73205i	−0.0399680	−	0.0692267i
$627$	10.3923	−	6.00000i	0.415029	−	0.239617i
$628$	−19.0526	−	11.0000i	−0.760280	−	0.438948i
$629$	16.0000			0.637962
$630$		0			0
$631$	−4.00000			−0.159237			−0.0796187	−	0.996825i	$-0.525370\pi$
$631$	−4.00000			−0.159237			−0.0796187	+	0.996825i	$0.525370\pi$
$632$	−10.3923	−	6.00000i	−0.413384	−	0.238667i
$633$		0			0
$634$	−1.00000	−	1.73205i	−0.0397151	−	0.0687885i
$635$	0.535898	−	8.92820i	0.0212665	−	0.354305i
$636$	−6.00000			−0.237915
$637$		0			0
$638$			12.0000i			0.475085i
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$	−1.86603	−	1.23205i	−0.0737611	−	0.0487011i
$641$	−7.00000	−	12.1244i	−0.276483	−	0.478883i	0.694025	−	0.719951i	$-0.255836\pi$
$641$	−7.00000	−	12.1244i	−0.276483	−	0.478883i	−0.970508	+	0.241068i	$0.922502\pi$
$642$	−10.3923	−	6.00000i	−0.410152	−	0.236801i
$643$		−	12.0000i		−	0.473234i	−0.971603	−	0.236617i	$-0.923961\pi$
$643$		−	12.0000i		−	0.473234i	0.971603	−	0.236617i	$-0.0760386\pi$
$644$		0			0
$645$	−4.00000	−	8.00000i	−0.157500	−	0.315000i
$646$	12.0000	−	20.7846i	0.472134	−	0.817760i
$647$	31.1769	−	18.0000i	1.22569	−	0.707653i	0.259565	−	0.965726i	$-0.416421\pi$
$647$	31.1769	−	18.0000i	1.22569	−	0.707653i	0.966126	+	0.258073i	$0.0830873\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	8.00000	−	13.8564i	0.314027	−	0.543912i
$650$	18.0000	−	24.0000i	0.706018	−	0.941357i
$651$		0			0
$652$			4.00000i			0.156652i
$653$	−29.4449	−	17.0000i	−1.15227	−	0.665261i	−0.202828	−	0.979214i	$-0.565013\pi$
$653$	−29.4449	−	17.0000i	−1.15227	−	0.665261i	−0.949439	+	0.313953i	$0.898347\pi$
$654$	7.00000	+	12.1244i	0.273722	+	0.474100i
$655$	−14.7846	+	22.3923i	−0.577683	+	0.874940i
$656$	1.00000	−	1.73205i	0.0390434	−	0.0676252i
$657$		−	14.0000i		−	0.546192i
$658$		0			0
$659$	26.0000			1.01282			0.506408	−	0.862294i	$-0.330973\pi$
$659$	26.0000			1.01282			0.506408	+	0.862294i	$0.330973\pi$
$660$	−0.267949	+	4.46410i	−0.0104299	+	0.173765i
$661$	19.0000	+	32.9090i	0.739014	+	1.28001i	0.952940	+	0.303160i	$0.0980418\pi$
$661$	19.0000	+	32.9090i	0.739014	+	1.28001i	−0.213925	+	0.976850i	$0.568625\pi$
$662$	6.92820	−	4.00000i	0.269272	−	0.155464i
$663$	20.7846	+	12.0000i	0.807207	+	0.466041i
$664$	−8.00000			−0.310460
$665$		0			0
$666$	4.00000			0.154997
$667$	−41.5692	−	24.0000i	−1.60957	−	0.929284i
$668$	10.3923	−	6.00000i	0.402090	−	0.232147i
$669$	−4.00000	−	6.92820i	−0.154649	−	0.267860i
$670$	−17.8564	−	1.07180i	−0.689853	−	0.0414071i
$671$	20.0000			0.772091
$672$		0			0
$673$			12.0000i			0.462566i	0.972887	+	0.231283i	$0.0742923\pi$
$673$			12.0000i			0.462566i	−0.972887	+	0.231283i	$0.925708\pi$
$674$	−4.00000	+	6.92820i	−0.154074	+	0.266864i
$675$	−0.598076	+	4.96410i	−0.0230200	+	0.191068i
$676$	−11.5000	−	19.9186i	−0.442308	−	0.766099i
$677$	−34.6410	−	20.0000i	−1.33136	−	0.768662i	−0.345854	−	0.938288i	$-0.612411\pi$
$677$	−34.6410	−	20.0000i	−1.33136	−	0.768662i	−0.985509	+	0.169626i	$0.945744\pi$
$678$		−	6.00000i		−	0.230429i
$679$		0			0
$680$	4.00000	+	8.00000i	0.153393	+	0.306786i
$681$	4.00000	−	6.92820i	0.153280	−	0.265489i
$682$	−3.46410	+	2.00000i	−0.132647	+	0.0765840i
$683$	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	$0.308950\pi$
$684$	3.00000	−	5.19615i	0.114708	−	0.198680i
$685$	12.0000	−	6.00000i	0.458496	−	0.229248i
$686$		0			0
$687$		−	14.0000i		−	0.534133i
$688$	−3.46410	−	2.00000i	−0.132068	−	0.0762493i
$689$	−18.0000	−	31.1769i	−0.685745	−	1.18775i
$690$	−14.9282	−	9.85641i	−0.568307	−	0.375227i
$691$	−1.00000	+	1.73205i	−0.0380418	+	0.0658903i	−0.884419	−	0.466693i	$-0.845445\pi$
$691$	−1.00000	+	1.73205i	−0.0380418	+	0.0658903i	0.846378	+	0.532583i	$0.178779\pi$
$692$			8.00000i			0.304114i
$693$		0			0
$694$	−36.0000			−1.36654
$695$	−31.2487	−	1.87564i	−1.18533	−	0.0711472i
$696$	3.00000	+	5.19615i	0.113715	+	0.196960i
$697$	−6.92820	+	4.00000i	−0.262424	+	0.151511i
$698$	−22.5167	−	13.0000i	−0.852268	−	0.492057i
$699$	−10.0000			−0.378235
$700$		0			0
$701$	−34.0000			−1.28416			−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000			−1.28416			−0.642081	+	0.766637i	$0.721929\pi$
$702$	5.19615	+	3.00000i	0.196116	+	0.113228i
$703$	20.7846	−	12.0000i	0.783906	−	0.452589i
$704$	1.00000	+	1.73205i	0.0376889	+	0.0652791i
$705$	17.8564	+	1.07180i	0.672511	+	0.0403662i
$706$	−20.0000			−0.752710
$707$		0			0
$708$		−	8.00000i		−	0.300658i
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	−0.916845	−	0.399244i	$-0.869273\pi$
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	0.804178	+	0.594389i	$0.202606\pi$
$710$	−11.1962	−	7.39230i	−0.420184	−	0.277428i
$711$	6.00000	+	10.3923i	0.225018	+	0.389742i
$712$	8.66025	+	5.00000i	0.324557	+	0.187383i
$713$		−	16.0000i		−	0.599205i
$714$		0			0
$715$	−24.0000	+	12.0000i	−0.897549	+	0.448775i
$716$	−5.00000	+	8.66025i	−0.186859	+	0.323649i
$717$	22.5167	−	13.0000i	0.840900	−	0.485494i
$718$	5.19615	−	3.00000i	0.193919	−	0.111959i
$719$	2.00000	−	3.46410i	0.0745874	−	0.129189i	−0.826319	−	0.563202i	$-0.809569\pi$
$719$	2.00000	−	3.46410i	0.0745874	−	0.129189i	0.900907	+	0.434013i	$0.142903\pi$
$720$	1.00000	+	2.00000i	0.0372678	+	0.0745356i
$721$		0			0
$722$		−	17.0000i		−	0.632674i
$723$	22.5167	+	13.0000i	0.837404	+	0.483475i
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$	−29.7846	−	3.58846i	−1.10617	−	0.133272i
$726$	−3.50000	+	6.06218i	−0.129897	+	0.224989i
$727$			24.0000i			0.890111i	0.895503	+	0.445055i	$0.146816\pi$
$727$			24.0000i			0.890111i	−0.895503	+	0.445055i	$0.853184\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	31.2487	+	1.87564i	1.15657	+	0.0694207i
$731$	8.00000	+	13.8564i	0.295891	+	0.512498i
$732$	8.66025	−	5.00000i	0.320092	−	0.184805i
$733$	12.1244	+	7.00000i	0.447823	+	0.258551i	0.706910	−	0.707303i	$-0.250088\pi$
$733$	12.1244	+	7.00000i	0.447823	+	0.258551i	−0.259087	+	0.965854i	$0.583422\pi$
$734$	−32.0000			−1.18114
$735$		0			0
$736$	−8.00000			−0.294884
$737$	13.8564	+	8.00000i	0.510407	+	0.294684i
$738$	−1.73205	+	1.00000i	−0.0637577	+	0.0368105i
$739$	−22.0000	−	38.1051i	−0.809283	−	1.40172i	−0.913361	−	0.407150i	$-0.866523\pi$
$739$	−22.0000	−	38.1051i	−0.809283	−	1.40172i	0.104078	−	0.994569i	$-0.466811\pi$
$740$	−0.535898	+	8.92820i	−0.0197000	+	0.328207i
$741$	36.0000			1.32249
$742$		0			0
$743$		−	48.0000i		−	1.76095i	−0.474093	−	0.880475i	$-0.657224\pi$
$743$		−	48.0000i		−	1.76095i	0.474093	−	0.880475i	$-0.342776\pi$
$744$	−1.00000	+	1.73205i	−0.0366618	+	0.0635001i
$745$	12.3205	−	18.6603i	0.451388	−	0.683659i
$746$	12.0000	+	20.7846i	0.439351	+	0.760979i
$747$	6.92820	+	4.00000i	0.253490	+	0.146352i
$748$		−	8.00000i		−	0.292509i
$749$		0			0
$750$	−11.0000	−	2.00000i	−0.401663	−	0.0730297i
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	−0.988761	−	0.149505i	$-0.952232\pi$
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	0.623856	+	0.781540i	$0.285565\pi$
$752$	6.92820	−	4.00000i	0.252646	−	0.145865i
$753$		0			0
$754$	−18.0000	+	31.1769i	−0.655521	+	1.13540i
$755$	8.00000	+	16.0000i	0.291150	+	0.582300i
$756$		0			0
$757$			32.0000i			1.16306i	0.813525	+	0.581530i	$0.197546\pi$
$757$			32.0000i			1.16306i	−0.813525	+	0.581530i	$0.802454\pi$
$758$	−17.3205	−	10.0000i	−0.629109	−	0.363216i
$759$	8.00000	+	13.8564i	0.290382	+	0.502956i
$760$	11.1962	+	7.39230i	0.406127	+	0.268147i
$761$	−3.00000	+	5.19615i	−0.108750	+	0.188360i	−0.915264	−	0.402854i	$-0.868018\pi$
$761$	−3.00000	+	5.19615i	−0.108750	+	0.188360i	0.806514	+	0.591215i	$0.201351\pi$
$762$			4.00000i			0.144905i
$763$		0			0
$764$	18.0000			0.651217
$765$	0.535898	−	8.92820i	0.0193754	−	0.322800i
$766$	10.0000	+	17.3205i	0.361315	+	0.625815i
$767$	41.5692	−	24.0000i	1.50098	−	0.866590i
$768$	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
$771$		0			0
$772$	−6.92820	−	4.00000i	−0.249351	−	0.143963i
$773$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$773$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$774$	2.00000	+	3.46410i	0.0718885	+	0.124515i
$775$	−3.92820	−	9.19615i	−0.141105	−	0.330336i
$776$	10.0000			0.358979
$777$		0			0
$778$			2.00000i			0.0717035i
$779$	−6.00000	+	10.3923i	−0.214972	+	0.372343i
$780$	−7.39230	+	11.1962i	−0.264687	+	0.400887i
$781$	6.00000	+	10.3923i	0.214697	+	0.371866i
$782$	27.7128	+	16.0000i	0.991008	+	0.572159i
$783$		−	6.00000i		−	0.214423i
$784$		0			0
$785$	−44.0000	+	22.0000i	−1.57043	+	0.785214i
$786$	6.00000	−	10.3923i	0.214013	−	0.370681i
$787$	24.2487	−	14.0000i	0.864373	−	0.499046i	−0.00110111	−	0.999999i	$-0.500350\pi$
$787$	24.2487	−	14.0000i	0.864373	−	0.499046i	0.865474	+	0.500953i	$0.167017\pi$
$788$	1.73205	−	1.00000i	0.0617018	−	0.0356235i
$789$	−8.00000	+	13.8564i	−0.284808	+	0.493301i
$790$	−24.0000	+	12.0000i	−0.853882	+	0.426941i
$791$		0			0
$792$		−	2.00000i		−	0.0710669i
$793$	51.9615	+	30.0000i	1.84521	+	1.06533i
$794$	1.00000	+	1.73205i	0.0354887	+	0.0614682i
$795$	−7.39230	+	11.1962i	−0.262178	+	0.397087i
$796$	3.00000	−	5.19615i	0.106332	−	0.184173i
$797$		−	8.00000i		−	0.283375i	−0.989911	−	0.141687i	$-0.954747\pi$
$797$		−	8.00000i		−	0.283375i	0.989911	−	0.141687i	$-0.0452527\pi$
$798$		0			0
$799$	−32.0000			−1.13208
$800$	−4.59808	+	1.96410i	−0.162567	+	0.0694415i
$801$	−5.00000	−	8.66025i	−0.176666	−	0.305995i
$802$	12.1244	−	7.00000i	0.428126	−	0.247179i
$803$	−24.2487	−	14.0000i	−0.855718	−	0.494049i
$804$	8.00000			0.282138
$805$		0			0
$806$	−12.0000			−0.422682
$807$	15.5885	+	9.00000i	0.548740	+	0.316815i
$808$	−8.66025	+	5.00000i	−0.304667	+	0.175899i
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	0.999491	+	0.0319002i	$0.0101559\pi$
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	−0.472119	+	0.881535i	$0.656511\pi$
$810$	0.133975	−	2.23205i	0.00470739	−	0.0784263i
$811$	14.0000			0.491606			0.245803	−	0.969320i	$-0.420948\pi$
$811$	14.0000			0.491606			0.245803	+	0.969320i	$0.420948\pi$
$812$		0			0
$813$			10.0000i			0.350715i
$814$	4.00000	−	6.92820i	0.140200	−	0.242833i
$815$	7.46410	+	4.92820i	0.261456	+	0.172627i
$816$	−2.00000	−	3.46410i	−0.0700140	−	0.121268i
$817$	20.7846	+	12.0000i	0.727161	+	0.419827i
$818$		−	26.0000i		−	0.909069i
$819$		0			0
$820$	−2.00000	−	4.00000i	−0.0698430	−	0.139686i
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	−0.991616	−	0.129217i	$-0.958754\pi$
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	0.607714	+	0.794156i	$0.292087\pi$
$822$	−5.19615	+	3.00000i	−0.181237	+	0.104637i
$823$	10.3923	−	6.00000i	0.362253	−	0.209147i	−0.307816	−	0.951446i	$-0.599598\pi$
$823$	10.3923	−	6.00000i	0.362253	−	0.209147i	0.670069	+	0.742299i	$0.266265\pi$
$824$	−4.00000	+	6.92820i	−0.139347	+	0.241355i
$825$	8.00000	+	6.00000i	0.278524	+	0.208893i
$826$		0			0
$827$			20.0000i			0.695468i	0.937593	+	0.347734i	$0.113049\pi$
$827$			20.0000i			0.695468i	−0.937593	+	0.347734i	$0.886951\pi$
$828$	6.92820	+	4.00000i	0.240772	+	0.139010i
$829$	−9.00000	−	15.5885i	−0.312583	−	0.541409i	0.666338	−	0.745650i	$-0.267861\pi$
$829$	−9.00000	−	15.5885i	−0.312583	−	0.541409i	−0.978921	+	0.204240i	$0.934528\pi$
$830$	−9.85641	+	14.9282i	−0.342121	+	0.518165i
$831$	14.0000	−	24.2487i	0.485655	−	0.841178i
$832$			6.00000i			0.208013i
$833$		0			0
$834$	14.0000			0.484780
$835$	1.60770	−	26.7846i	0.0556366	−	0.926920i
$836$	−6.00000	−	10.3923i	−0.207514	−	0.359425i
$837$	1.73205	−	1.00000i	0.0598684	−	0.0345651i
$838$	17.3205	+	10.0000i	0.598327	+	0.345444i
$839$	−20.0000			−0.690477			−0.345238	−	0.938515i	$-0.612202\pi$
$839$	−20.0000			−0.690477			−0.345238	+	0.938515i	$0.612202\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	29.4449	+	17.0000i	1.01474	+	0.585859i
$843$	−25.9808	+	15.0000i	−0.894825	+	0.516627i
$844$		0			0
$845$	−51.3372	−	3.08142i	−1.76605	−	0.106004i
$846$	−8.00000			−0.275046
$847$		0			0
$848$			6.00000i			0.206041i
$849$	10.0000	−	17.3205i	0.343199	−	0.594438i
$850$	19.8564	+	2.39230i	0.681069	+	0.0820554i
$851$	16.0000	+	27.7128i	0.548473	+	0.949983i
$852$	5.19615	+	3.00000i	0.178017	+	0.102778i
$853$		−	38.0000i		−	1.30110i	−0.759465	−	0.650548i	$-0.774539\pi$
$853$		−	38.0000i		−	1.30110i	0.759465	−	0.650548i	$-0.225461\pi$
$854$		0			0
$855$	−6.00000	−	12.0000i	−0.205196	−	0.410391i
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$	20.7846	−	12.0000i	0.709989	−	0.409912i	−0.101068	−	0.994880i	$-0.532226\pi$
$857$	20.7846	−	12.0000i	0.709989	−	0.409912i	0.811057	+	0.584967i	$0.198893\pi$
$858$	10.3923	−	6.00000i	0.354787	−	0.204837i
$859$	5.00000	−	8.66025i	0.170598	−	0.295484i	−0.768031	−	0.640412i	$-0.778763\pi$
$859$	5.00000	−	8.66025i	0.170598	−	0.295484i	0.938629	+	0.344928i	$0.112097\pi$
$860$	−8.00000	+	4.00000i	−0.272798	+	0.136399i
$861$		0			0
$862$		−	2.00000i		−	0.0681203i
$863$	41.5692	+	24.0000i	1.41503	+	0.816970i	0.995857	−	0.0909355i	$-0.0289857\pi$
$863$	41.5692	+	24.0000i	1.41503	+	0.816970i	0.419176	+	0.907905i	$0.362319\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	14.9282	+	9.85641i	0.507574	+	0.335128i
$866$	−13.0000	+	22.5167i	−0.441758	+	0.765147i
$867$		−	1.00000i		−	0.0339618i
$868$		0			0
$869$	24.0000			0.814144
$870$	13.3923	+	0.803848i	0.454042	+	0.0272530i
$871$	24.0000	+	41.5692i	0.813209	+	1.40852i
$872$	12.1244	−	7.00000i	0.410582	−	0.237050i
$873$	−8.66025	−	5.00000i	−0.293105	−	0.169224i
$874$	48.0000			1.62362
$875$		0			0
$876$	−14.0000			−0.473016
$877$	−24.2487	−	14.0000i	−0.818821	−	0.472746i	0.0311889	−	0.999514i	$-0.490071\pi$
$877$	−24.2487	−	14.0000i	−0.818821	−	0.472746i	−0.850010	+	0.526767i	$0.823404\pi$
$878$	15.5885	−	9.00000i	0.526085	−	0.303735i
$879$		0			0
$880$	4.46410	+	0.267949i	0.150485	+	0.00903257i
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		0			0
$883$			24.0000i			0.807664i	0.914833	+	0.403832i	$0.132322\pi$
$883$			24.0000i			0.807664i	−0.914833	+	0.403832i	$0.867678\pi$
$884$	12.0000	−	20.7846i	0.403604	−	0.699062i
$885$	−14.9282	−	9.85641i	−0.501806	−	0.331319i
$886$	6.00000	+	10.3923i	0.201574	+	0.349136i
$887$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$887$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$888$		−	4.00000i		−	0.134231i
$889$		0			0
$890$	20.0000	−	10.0000i	0.670402	−	0.335201i
$891$	−1.00000	+	1.73205i	−0.0335013	+	0.0580259i
$892$	−6.92820	+	4.00000i	−0.231973	+	0.133930i
$893$	−41.5692	+	24.0000i	−1.39106	+	0.803129i
$894$	−5.00000	+	8.66025i	−0.167225	+	0.289642i
$895$	10.0000	+	20.0000i	0.334263	+	0.668526i
$896$		0			0
$897$			48.0000i			1.60267i
$898$	5.19615	+	3.00000i	0.173398	+	0.100111i
$899$	6.00000	+	10.3923i	0.200111	+	0.346603i
$900$	4.96410	+	0.598076i	0.165470	+	0.0199359i
$901$	12.0000	−	20.7846i	0.399778	−	0.692436i
$902$			4.00000i			0.133185i
$903$		0			0
$904$	−6.00000			−0.199557
$905$	−4.46410	−	0.267949i	−0.148392	−	0.00890693i
$906$	−4.00000	−	6.92820i	−0.132891	−	0.230174i
$907$	−20.7846	+	12.0000i	−0.690142	+	0.398453i	−0.803665	−	0.595082i	$-0.797120\pi$
$907$	−20.7846	+	12.0000i	−0.690142	+	0.398453i	0.113523	+	0.993535i	$0.463786\pi$
$908$	−6.92820	−	4.00000i	−0.229920	−	0.132745i
$909$	10.0000			0.331679
$910$		0			0
$911$	6.00000			0.198789			0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000			0.198789			0.0993944	+	0.995048i	$0.468309\pi$
$912$	−5.19615	−	3.00000i	−0.172062	−	0.0993399i
$913$	13.8564	−	8.00000i	0.458580	−	0.264761i
$914$	14.0000	+	24.2487i	0.463079	+	0.802076i
$915$	1.33975	−	22.3205i	0.0442906	−	0.737893i
$916$	−14.0000			−0.462573
$917$		0			0
$918$			4.00000i			0.132020i
$919$	30.0000	−	51.9615i	0.989609	−	1.71405i	0.370281	−	0.928920i	$-0.379261\pi$
$919$	30.0000	−	51.9615i	0.989609	−	1.71405i	0.619327	−	0.785133i	$-0.287405\pi$
$920$	−9.85641	+	14.9282i	−0.324956	+	0.492168i
$921$	6.00000	+	10.3923i	0.197707	+	0.342438i
$922$	15.5885	+	9.00000i	0.513378	+	0.296399i
$923$			36.0000i			1.18495i
$924$		0			0
$925$	16.0000	+	12.0000i	0.526077	+	0.394558i
$926$	−18.0000	+	31.1769i	−0.591517	+	1.02454i
$927$	6.92820	−	4.00000i	0.227552	−	0.131377i
$928$	5.19615	−	3.00000i	0.170572	−	0.0984798i
$929$	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	$0.00288365\pi$
$930$	2.00000	+	4.00000i	0.0655826	+	0.131165i
$931$		0			0
$932$			10.0000i			0.327561i
$933$	−20.7846	−	12.0000i	−0.680458	−	0.392862i
$934$	12.0000	+	20.7846i	0.392652	+	0.680093i
$935$	−14.9282	−	9.85641i	−0.488204	−	0.322339i
$936$	3.00000	−	5.19615i	0.0980581	−	0.169842i
$937$			26.0000i			0.849383i	0.905338	+	0.424691i	$0.139617\pi$
$937$			26.0000i			0.849383i	−0.905338	+	0.424691i	$0.860383\pi$
$938$		0			0
$939$	2.00000			0.0652675
$940$	1.07180	−	17.8564i	0.0349582	−	0.582412i
$941$	−5.00000	−	8.66025i	−0.162995	−	0.282316i	0.772946	−	0.634472i	$-0.218782\pi$
$941$	−5.00000	−	8.66025i	−0.162995	−	0.282316i	−0.935942	+	0.352155i	$0.885449\pi$
$942$	19.0526	−	11.0000i	0.620766	−	0.358399i
$943$	−13.8564	−	8.00000i	−0.451227	−	0.260516i
$944$	−8.00000			−0.260378
$945$		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	$0.729129\pi$
$948$	10.3923	−	6.00000i	0.337526	−	0.194871i
$949$	−42.0000	−	72.7461i	−1.36338	−	2.36144i
$950$	27.5885	−	11.7846i	0.895088	−	0.382343i
$951$	2.00000			0.0648544
$952$		0			0
$953$		−	10.0000i		−	0.323932i	−0.986796	−	0.161966i	$-0.948217\pi$
$953$		−	10.0000i		−	0.323932i	0.986796	−	0.161966i	$-0.0517835\pi$
$954$	3.00000	−	5.19615i	0.0971286	−	0.168232i
$955$	22.1769	−	33.5885i	0.717628	−	1.08690i
$956$	−13.0000	−	22.5167i	−0.420450	−	0.728241i
$957$	−10.3923	−	6.00000i	−0.335936	−	0.193952i
$958$		−	8.00000i		−	0.258468i
$959$		0			0
$960$	2.00000	−	1.00000i	0.0645497	−	0.0322749i
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	20.7846	−	12.0000i	0.670123	−	0.386896i
$963$	10.3923	−	6.00000i	0.334887	−	0.193347i
$964$	13.0000	−	22.5167i	0.418702	−	0.725213i
$965$	−16.0000	+	8.00000i	−0.515058	+	0.257529i
$966$		0			0
$967$		−	56.0000i		−	1.80084i	−0.435023	−	0.900419i	$-0.643260\pi$
$967$		−	56.0000i		−	1.80084i	0.435023	−	0.900419i	$-0.356740\pi$
$968$	6.06218	+	3.50000i	0.194846	+	0.112494i
$969$	12.0000	+	20.7846i	0.385496	+	0.667698i
$970$	12.3205	−	18.6603i	0.395588	−	0.599145i
$971$	−12.0000	+	20.7846i	−0.385098	+	0.667010i	−0.991783	−	0.127933i	$-0.959166\pi$
$971$	−12.0000	+	20.7846i	−0.385098	+	0.667010i	0.606685	+	0.794943i	$0.292499\pi$
$972$			1.00000i			0.0320750i
$973$		0			0
$974$	−12.0000			−0.384505
$975$	11.7846	+	27.5885i	0.377410	+	0.883538i
$976$	−5.00000	−	8.66025i	−0.160046	−	0.277208i
$977$	15.5885	−	9.00000i	0.498719	−	0.287936i	−0.229465	−	0.973317i	$-0.573698\pi$
$977$	15.5885	−	9.00000i	0.498719	−	0.287936i	0.728184	+	0.685381i	$0.240364\pi$
$978$	−3.46410	−	2.00000i	−0.110770	−	0.0639529i
$979$	−20.0000			−0.639203
$980$		0			0
$981$	−14.0000			−0.446986
$982$	−25.9808	−	15.0000i	−0.829079	−	0.478669i
$983$	13.8564	−	8.00000i	0.441951	−	0.255160i	−0.262474	−	0.964939i	$-0.584538\pi$
$983$	13.8564	−	8.00000i	0.441951	−	0.255160i	0.704425	+	0.709779i	$0.251205\pi$
$984$	1.00000	+	1.73205i	0.0318788	+	0.0552158i
$985$	0.267949	−	4.46410i	0.00853757	−	0.142238i
$986$	−24.0000			−0.764316
$987$		0			0
$988$		−	36.0000i		−	1.14531i
$989$	−16.0000	+	27.7128i	−0.508770	+	0.881216i
$990$	−3.73205	−	2.46410i	−0.118612	−	0.0783143i
$991$	−2.00000	−	3.46410i	−0.0635321	−	0.110041i	0.832510	−	0.554010i	$-0.186903\pi$
$991$	−2.00000	−	3.46410i	−0.0635321	−	0.110041i	−0.896042	+	0.443969i	$0.853570\pi$
$992$	1.73205	+	1.00000i	0.0549927	+	0.0317500i
$993$			8.00000i			0.253872i
$994$		0			0
$995$	−6.00000	−	12.0000i	−0.190213	−	0.380426i
$996$	4.00000	−	6.92820i	0.126745	−	0.219529i
$997$	−36.3731	+	21.0000i	−1.15195	+	0.665077i	−0.949361	−	0.314188i	$-0.898268\pi$
$997$	−36.3731	+	21.0000i	−1.15195	+	0.665077i	−0.202586	+	0.979265i	$0.564934\pi$
$998$	−10.3923	+	6.00000i	−0.328963	+	0.189927i
$999$	−2.00000	+	3.46410i	−0.0632772	+	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.n.f.79.2		4
5.4	even	2	inner	1470.2.n.f.79.1		4
7.2	even	3		1470.2.g.b.589.1		2
7.3	odd	6		1470.2.n.b.949.1		4
7.4	even	3	inner	1470.2.n.f.949.1		4
7.5	odd	6		210.2.g.b.169.1	✓	2
7.6	odd	2		1470.2.n.b.79.2		4
21.5	even	6		630.2.g.c.379.2		2
28.19	even	6		1680.2.t.e.1009.1		2
35.2	odd	12		7350.2.a.bz.1.1		1
35.4	even	6	inner	1470.2.n.f.949.2		4
35.9	even	6		1470.2.g.b.589.2		2
35.12	even	12		1050.2.a.p.1.1		1
35.19	odd	6		210.2.g.b.169.2	yes	2
35.23	odd	12		7350.2.a.bk.1.1		1
35.24	odd	6		1470.2.n.b.949.2		4
35.33	even	12		1050.2.a.d.1.1		1
35.34	odd	2		1470.2.n.b.79.1		4
84.47	odd	6		5040.2.t.h.1009.1		2
105.47	odd	12		3150.2.a.d.1.1		1
105.68	odd	12		3150.2.a.bk.1.1		1
105.89	even	6		630.2.g.c.379.1		2
140.19	even	6		1680.2.t.e.1009.2		2
140.47	odd	12		8400.2.a.w.1.1		1
140.103	odd	12		8400.2.a.bp.1.1		1
420.299	odd	6		5040.2.t.h.1009.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.g.b.169.1	✓	2	7.5	odd	6
210.2.g.b.169.2	yes	2	35.19	odd	6
630.2.g.c.379.1		2	105.89	even	6
630.2.g.c.379.2		2	21.5	even	6
1050.2.a.d.1.1		1	35.33	even	12
1050.2.a.p.1.1		1	35.12	even	12
1470.2.g.b.589.1		2	7.2	even	3
1470.2.g.b.589.2		2	35.9	even	6
1470.2.n.b.79.1		4	35.34	odd	2
1470.2.n.b.79.2		4	7.6	odd	2
1470.2.n.b.949.1		4	7.3	odd	6
1470.2.n.b.949.2		4	35.24	odd	6
1470.2.n.f.79.1		4	5.4	even	2	inner
1470.2.n.f.79.2		4	1.1	even	1	trivial
1470.2.n.f.949.1		4	7.4	even	3	inner
1470.2.n.f.949.2		4	35.4	even	6	inner
1680.2.t.e.1009.1		2	28.19	even	6
1680.2.t.e.1009.2		2	140.19	even	6
3150.2.a.d.1.1		1	105.47	odd	12
3150.2.a.bk.1.1		1	105.68	odd	12
5040.2.t.h.1009.1		2	84.47	odd	6
5040.2.t.h.1009.2		2	420.299	odd	6
7350.2.a.bk.1.1		1	35.23	odd	12
7350.2.a.bz.1.1		1	35.2	odd	12
8400.2.a.w.1.1		1	140.47	odd	12
8400.2.a.bp.1.1		1	140.103	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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.23205 + 0.133975i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.23205 + 0.133975i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.86603 + 1.23205i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(-0.866025 - 0.500000i) q^{12} -6.00000i q^{13} +(-2.00000 + 1.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.46410 - 2.00000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(3.00000 - 5.19615i) q^{19} +(1.00000 + 2.00000i) q^{20} -2.00000i q^{22} +(6.92820 + 4.00000i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(4.96410 + 0.598076i) q^{25} +(3.00000 - 5.19615i) q^{26} +1.00000i q^{27} -6.00000 q^{29} +(-2.23205 - 0.133975i) q^{30} +(-1.00000 - 1.73205i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.73205 + 1.00000i) q^{33} +4.00000 q^{34} +1.00000 q^{36} +(3.46410 + 2.00000i) q^{37} +(5.19615 - 3.00000i) q^{38} +(3.00000 + 5.19615i) q^{39} +(-0.133975 + 2.23205i) q^{40} -2.00000 q^{41} +4.00000i q^{43} +(1.00000 - 1.73205i) q^{44} +(1.23205 - 1.86603i) q^{45} +(4.00000 + 6.92820i) q^{46} +(-6.92820 - 4.00000i) q^{47} -1.00000i q^{48} +(4.00000 + 3.00000i) q^{50} +(-2.00000 + 3.46410i) q^{51} +(5.19615 - 3.00000i) q^{52} +(5.19615 - 3.00000i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.00000 - 4.00000i) q^{55} +6.00000i q^{57} +(-5.19615 - 3.00000i) q^{58} +(4.00000 + 6.92820i) q^{59} +(-1.86603 - 1.23205i) q^{60} +(-5.00000 + 8.66025i) q^{61} -2.00000i q^{62} -1.00000 q^{64} +(0.803848 - 13.3923i) q^{65} +(1.00000 + 1.73205i) q^{66} +(-6.92820 + 4.00000i) q^{67} +(3.46410 + 2.00000i) q^{68} -8.00000 q^{69} -6.00000 q^{71} +(0.866025 + 0.500000i) q^{72} +(12.1244 - 7.00000i) q^{73} +(2.00000 + 3.46410i) q^{74} +(-4.59808 + 1.96410i) q^{75} +6.00000 q^{76} +6.00000i q^{78} +(-6.00000 + 10.3923i) q^{79} +(-1.23205 + 1.86603i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.73205 - 1.00000i) q^{82} +8.00000i q^{83} +(8.00000 - 4.00000i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(5.19615 - 3.00000i) q^{87} +(1.73205 - 1.00000i) q^{88} +(5.00000 - 8.66025i) q^{89} +(2.00000 - 1.00000i) q^{90} +8.00000i q^{92} +(1.73205 + 1.00000i) q^{93} +(-4.00000 - 6.92820i) q^{94} +(7.39230 - 11.1962i) q^{95} +(0.500000 - 0.866025i) q^{96} -10.0000i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9} + 4 q^{10} - 4 q^{11} - 8 q^{15} - 2 q^{16} + 12 q^{19} + 4 q^{20} - 2 q^{24} + 6 q^{25} + 12 q^{26} - 24 q^{29} - 2 q^{30} - 4 q^{31} + 16 q^{34} + 4 q^{36} + 12 q^{39} - 4 q^{40} - 8 q^{41} + 4 q^{44} - 2 q^{45} + 16 q^{46} + 16 q^{50} - 8 q^{51} - 2 q^{54} - 8 q^{55} + 16 q^{59} - 4 q^{60} - 20 q^{61} - 4 q^{64} + 24 q^{65} + 4 q^{66} - 32 q^{69} - 24 q^{71} + 8 q^{74} - 8 q^{75} + 24 q^{76} - 24 q^{79} + 2 q^{80} - 2 q^{81} + 32 q^{85} - 8 q^{86} + 20 q^{89} + 8 q^{90} - 16 q^{94} - 12 q^{95} + 2 q^{96} - 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9 + 4 * q^10 - 4 * q^11 - 8 * q^15 - 2 * q^16 + 12 * q^19 + 4 * q^20 - 2 * q^24 + 6 * q^25 + 12 * q^26 - 24 * q^29 - 2 * q^30 - 4 * q^31 + 16 * q^34 + 4 * q^36 + 12 * q^39 - 4 * q^40 - 8 * q^41 + 4 * q^44 - 2 * q^45 + 16 * q^46 + 16 * q^50 - 8 * q^51 - 2 * q^54 - 8 * q^55 + 16 * q^59 - 4 * q^60 - 20 * q^61 - 4 * q^64 + 24 * q^65 + 4 * q^66 - 32 * q^69 - 24 * q^71 + 8 * q^74 - 8 * q^75 + 24 * q^76 - 24 * q^79 + 2 * q^80 - 2 * q^81 + 32 * q^85 - 8 * q^86 + 20 * q^89 + 8 * q^90 - 16 * q^94 - 12 * q^95 + 2 * q^96 - 8 * q^99

Introduction

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