LMFDB - Embedded newform 735.2.q.b.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(79,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, 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("735.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.q (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:	$5.86900454856$
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 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	735.79
Dual form			735.2.q.b.214.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.23205 - 1.86603i) q^{5} +1.00000 q^{6} +3.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.23205 - 1.86603i) q^{5} +1.00000 q^{6} +3.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.133975 + 2.23205i) q^{10} +(3.00000 + 5.19615i) q^{11} +(0.866025 + 0.500000i) q^{12} +2.00000i 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} -6.00000i q^{22} +(-1.50000 - 2.59808i) q^{24} +(-1.96410 + 4.59808i) q^{25} +(1.00000 - 1.73205i) q^{26} +1.00000i q^{27} +2.00000 q^{29} +(-1.23205 - 1.86603i) q^{30} +(-5.00000 - 8.66025i) q^{31} +(4.33013 - 2.50000i) q^{32} +(-5.19615 - 3.00000i) q^{33} -4.00000 q^{34} -1.00000 q^{36} +(-3.46410 - 2.00000i) q^{37} +(-5.19615 + 3.00000i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(5.59808 - 3.69615i) q^{40} -2.00000 q^{41} -4.00000i q^{43} +(3.00000 - 5.19615i) q^{44} +(-2.23205 + 0.133975i) q^{45} +1.00000i q^{48} +(4.00000 - 3.00000i) q^{50} +(-2.00000 + 3.46410i) q^{51} +(1.73205 - 1.00000i) q^{52} +(5.19615 - 3.00000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(6.00000 - 12.0000i) q^{55} +6.00000i q^{57} +(-1.73205 - 1.00000i) q^{58} +(4.00000 + 6.92820i) q^{59} +(-0.133975 - 2.23205i) q^{60} +(-1.00000 + 1.73205i) q^{61} +10.0000i q^{62} -7.00000 q^{64} +(3.73205 - 2.46410i) q^{65} +(3.00000 + 5.19615i) q^{66} +(13.8564 - 8.00000i) q^{67} +(-3.46410 - 2.00000i) q^{68} +10.0000 q^{71} +(2.59808 + 1.50000i) q^{72} +(5.19615 - 3.00000i) q^{73} +(2.00000 + 3.46410i) q^{74} +(-0.598076 - 4.96410i) q^{75} -6.00000 q^{76} +2.00000i q^{78} +(2.00000 - 3.46410i) q^{79} +(-2.23205 + 0.133975i) 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} +(-1.73205 + 1.00000i) q^{87} +(-15.5885 + 9.00000i) q^{88} +(-3.00000 + 5.19615i) q^{89} +(2.00000 + 1.00000i) q^{90} +(8.66025 + 5.00000i) q^{93} +(-13.3923 + 0.803848i) q^{95} +(-2.50000 + 4.33013i) q^{96} -2.00000i q^{97} +6.00000 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} + 12 q^{11} + 8 q^{15} + 2 q^{16} + 12 q^{19} - 4 q^{20} - 6 q^{24} + 6 q^{25} + 4 q^{26} + 8 q^{29} + 2 q^{30} - 20 q^{31} - 16 q^{34} - 4 q^{36} - 4 q^{39} + 12 q^{40} - 8 q^{41} + 12 q^{44} - 2 q^{45} + 16 q^{50} - 8 q^{51} + 2 q^{54} + 24 q^{55} + 16 q^{59} - 4 q^{60} - 4 q^{61} - 28 q^{64} + 8 q^{65} + 12 q^{66} + 40 q^{71} + 8 q^{74} + 8 q^{75} - 24 q^{76} + 8 q^{79} - 2 q^{80} - 2 q^{81} - 32 q^{85} - 8 q^{86} - 12 q^{89} + 8 q^{90} - 12 q^{95} - 10 q^{96} + 24 q^{99}+O(q^{100}) $ 4 * q - 2 * q^4 + 2 * q^5 + 4 * q^6 + 2 * q^9 + 4 * q^10 + 12 * q^11 + 8 * q^15 + 2 * q^16 + 12 * q^19 - 4 * q^20 - 6 * q^24 + 6 * q^25 + 4 * q^26 + 8 * q^29 + 2 * q^30 - 20 * q^31 - 16 * q^34 - 4 * q^36 - 4 * q^39 + 12 * q^40 - 8 * q^41 + 12 * q^44 - 2 * q^45 + 16 * q^50 - 8 * q^51 + 2 * q^54 + 24 * q^55 + 16 * q^59 - 4 * q^60 - 4 * q^61 - 28 * q^64 + 8 * q^65 + 12 * q^66 + 40 * q^71 + 8 * q^74 + 8 * q^75 - 24 * q^76 + 8 * q^79 - 2 * q^80 - 2 * q^81 - 32 * q^85 - 8 * q^86 - 12 * q^89 + 8 * q^90 - 12 * q^95 - 10 * q^96 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

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	0.161521	−	0.986869i	$-0.448360\pi$
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i	−0.773893	+	0.633316i	$0.781693\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.23205	−	1.86603i	−0.550990	−	0.834512i
$5$	−1.23205	−	1.86603i	−0.550990	−	0.834512i
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$			3.00000i			1.06066i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.133975	+	2.23205i	0.0423665	+	0.705836i
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.821541	+	0.570149i	$0.193114\pi$
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.0829925	+	0.996550i	$0.473552\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$		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
$22$		−	6.00000i		−	1.27920i
$23$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$23$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$24$	−1.50000	−	2.59808i	−0.306186	−	0.530330i
$25$	−1.96410	+	4.59808i	−0.392820	+	0.919615i
$26$	1.00000	−	1.73205i	0.196116	−	0.339683i
$27$			1.00000i			0.192450i
$28$		0			0
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$	−1.23205	−	1.86603i	−0.224941	−	0.340688i
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.830014	−	0.557743i	$-0.811667\pi$
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.0680129	−	0.997684i	$-0.521666\pi$
$32$	4.33013	−	2.50000i	0.765466	−	0.441942i
$33$	−5.19615	−	3.00000i	−0.904534	−	0.522233i
$34$	−4.00000			−0.685994
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−3.46410	−	2.00000i	−0.569495	−	0.328798i	0.187453	−	0.982274i	$-0.439977\pi$
$37$	−3.46410	−	2.00000i	−0.569495	−	0.328798i	−0.756948	+	0.653476i	$0.773310\pi$
$38$	−5.19615	+	3.00000i	−0.842927	+	0.486664i
$39$	−1.00000	−	1.73205i	−0.160128	−	0.277350i
$40$	5.59808	−	3.69615i	0.885134	−	0.584413i
$41$	−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	$-0.0986555\pi$
$44$	3.00000	−	5.19615i	0.452267	−	0.783349i
$45$	−2.23205	+	0.133975i	−0.332734	+	0.0199718i
$46$		0			0
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$			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
$52$	1.73205	−	1.00000i	0.240192	−	0.138675i
$53$	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
$55$	6.00000	−	12.0000i	0.809040	−	1.61808i
$56$		0			0
$57$			6.00000i			0.794719i
$58$	−1.73205	−	1.00000i	−0.227429	−	0.131306i
$59$	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	$0.658984\pi$
$60$	−0.133975	−	2.23205i	−0.0172960	−	0.288157i
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$			10.0000i			1.27000i
$63$		0			0
$64$	−7.00000			−0.875000
$65$	3.73205	−	2.46410i	0.462904	−	0.305634i
$66$	3.00000	+	5.19615i	0.369274	+	0.639602i
$67$	13.8564	−	8.00000i	1.69283	−	0.977356i	0.740613	−	0.671932i	$-0.234535\pi$
$67$	13.8564	−	8.00000i	1.69283	−	0.977356i	0.952217	−	0.305424i	$-0.0987981\pi$
$68$	−3.46410	−	2.00000i	−0.420084	−	0.242536i
$69$		0			0
$70$		0			0
$71$	10.0000			1.18678			0.593391	−	0.804914i	$-0.297789\pi$
$71$	10.0000			1.18678			0.593391	+	0.804914i	$0.297789\pi$
$72$	2.59808	+	1.50000i	0.306186	+	0.176777i
$73$	5.19615	−	3.00000i	0.608164	−	0.351123i	−0.164083	−	0.986447i	$-0.552466\pi$
$73$	5.19615	−	3.00000i	0.608164	−	0.351123i	0.772246	+	0.635323i	$0.219133\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$	−0.598076	−	4.96410i	−0.0690599	−	0.573205i
$76$	−6.00000			−0.688247
$77$		0			0
$78$			2.00000i			0.226455i
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$	−2.23205	+	0.133975i	−0.249551	+	0.0149788i
$81$	−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	$-0.855313\pi$
$83$		−	8.00000i		−	0.878114i	0.898459	−	0.439057i	$-0.144687\pi$
$84$		0			0
$85$	−8.00000	−	4.00000i	−0.867722	−	0.433861i
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$	−1.73205	+	1.00000i	−0.185695	+	0.107211i
$88$	−15.5885	+	9.00000i	−1.66174	+	0.959403i
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$	2.00000	+	1.00000i	0.210819	+	0.105409i
$91$		0			0
$92$		0			0
$93$	8.66025	+	5.00000i	0.898027	+	0.518476i
$94$		0			0
$95$	−13.3923	+	0.803848i	−1.37402	+	0.0824730i
$96$	−2.50000	+	4.33013i	−0.255155	+	0.441942i
$97$		−	2.00000i		−	0.203069i	−0.994832	−	0.101535i	$-0.967625\pi$
$97$		−	2.00000i		−	0.203069i	0.994832	−	0.101535i	$-0.0323753\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$	4.96410	−	0.598076i	0.496410	−	0.0598076i
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$	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
$107$	3.46410	+	2.00000i	0.334887	+	0.193347i	0.658009	−	0.753010i	$-0.271399\pi$
$107$	3.46410	+	2.00000i	0.334887	+	0.193347i	−0.323122	+	0.946357i	$0.604732\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$	−11.1962	+	7.39230i	−1.06751	+	0.704829i
$111$	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
$115$		0			0
$116$	−1.00000	−	1.73205i	−0.0928477	−	0.160817i
$117$	1.73205	+	1.00000i	0.160128	+	0.0924500i
$118$		−	8.00000i		−	0.736460i
$119$		0			0
$120$	−3.00000	+	6.00000i	−0.273861	+	0.547723i
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$	1.73205	−	1.00000i	0.156813	−	0.0905357i
$123$	1.73205	−	1.00000i	0.156174	−	0.0901670i
$124$	−5.00000	+	8.66025i	−0.449013	+	0.777714i
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$		0			0
$127$		−	20.0000i		−	1.77471i	−0.461084	−	0.887357i	$-0.652539\pi$
$127$		−	20.0000i		−	1.77471i	0.461084	−	0.887357i	$-0.347461\pi$
$128$	−2.59808	−	1.50000i	−0.229640	−	0.132583i
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$	−4.46410	+	0.267949i	−0.391528	+	0.0235007i
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	−0.765331	−	0.643637i	$-0.777425\pi$
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	0.940072	+	0.340977i	$0.110758\pi$
$132$			6.00000i			0.522233i
$133$		0			0
$134$	−16.0000			−1.38219
$135$	1.86603	−	1.23205i	0.160602	−	0.106038i
$136$	6.00000	+	10.3923i	0.514496	+	0.891133i
$137$	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	$0.250827\pi$
$138$		0			0
$139$	2.00000			0.169638			0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000			0.169638			0.0848189	+	0.996396i	$0.472969\pi$
$140$		0			0
$141$		0			0
$142$	−8.66025	−	5.00000i	−0.726752	−	0.419591i
$143$	−10.3923	+	6.00000i	−0.869048	+	0.501745i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−2.46410	−	3.73205i	−0.204633	−	0.309930i
$146$	−6.00000			−0.496564
$147$		0			0
$148$			4.00000i			0.328798i
$149$	−7.00000	+	12.1244i	−0.573462	+	0.993266i	0.422744	+	0.906249i	$0.361067\pi$
$149$	−7.00000	+	12.1244i	−0.573462	+	0.993266i	−0.996207	+	0.0870170i	$0.972267\pi$
$150$	−1.96410	+	4.59808i	−0.160368	+	0.375431i
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$	15.5885	+	9.00000i	1.26439	+	0.729996i
$153$		−	4.00000i		−	0.323381i
$154$		0			0
$155$	−10.0000	+	20.0000i	−0.803219	+	1.60644i
$156$	−1.00000	+	1.73205i	−0.0800641	+	0.138675i
$157$	15.5885	−	9.00000i	1.24409	−	0.718278i	0.274169	−	0.961681i	$-0.411597\pi$
$157$	15.5885	−	9.00000i	1.24409	−	0.718278i	0.969925	+	0.243403i	$0.0782638\pi$
$158$	−3.46410	+	2.00000i	−0.275589	+	0.159111i
$159$	−3.00000	+	5.19615i	−0.237915	+	0.412082i
$160$	−10.0000	−	5.00000i	−0.790569	−	0.395285i
$161$		0			0
$162$			1.00000i			0.0785674i
$163$	−3.46410	−	2.00000i	−0.271329	−	0.156652i	0.358162	−	0.933659i	$-0.383403\pi$
$163$	−3.46410	−	2.00000i	−0.271329	−	0.156652i	−0.629492	+	0.777007i	$0.716737\pi$
$164$	1.00000	+	1.73205i	0.0780869	+	0.135250i
$165$	0.803848	+	13.3923i	0.0625794	+	1.04259i
$166$	−4.00000	+	6.92820i	−0.310460	+	0.537733i
$167$			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
$169$	9.00000			0.692308
$170$	4.92820	+	7.46410i	0.377976	+	0.572470i
$171$	−3.00000	−	5.19615i	−0.229416	−	0.397360i
$172$	−3.46410	+	2.00000i	−0.264135	+	0.152499i
$173$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$173$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$174$	2.00000			0.151620
$175$		0			0
$176$	6.00000			0.452267
$177$	−6.92820	−	4.00000i	−0.520756	−	0.300658i
$178$	5.19615	−	3.00000i	0.389468	−	0.224860i
$179$	−7.00000	−	12.1244i	−0.523205	−	0.906217i	−0.999635	−	0.0270049i	$-0.991403\pi$
$179$	−7.00000	−	12.1244i	−0.523205	−	0.906217i	0.476431	−	0.879212i	$-0.341930\pi$
$180$	1.23205	+	1.86603i	0.0918316	+	0.139085i
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$		0			0
$183$		−	2.00000i		−	0.147844i
$184$		0			0
$185$	0.535898	+	8.92820i	0.0394000	+	0.656415i
$186$	−5.00000	−	8.66025i	−0.366618	−	0.635001i
$187$	20.7846	+	12.0000i	1.51992	+	0.877527i
$188$		0			0
$189$		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	$-0.0590746\pi$
$192$	6.06218	−	3.50000i	0.437500	−	0.252591i
$193$	−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	$0.426299\pi$
$194$	−1.00000	+	1.73205i	−0.0717958	+	0.124354i
$195$	−2.00000	+	4.00000i	−0.143223	+	0.286446i
$196$		0			0
$197$		−	2.00000i		−	0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$		−	2.00000i		−	0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$	−5.19615	−	3.00000i	−0.369274	−	0.213201i
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	0.503774	−	0.863836i	$-0.331945\pi$
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	−0.999990	+	0.00436292i	$0.998611\pi$
$200$	−13.7942	−	5.89230i	−0.975399	−	0.416649i
$201$	−8.00000	+	13.8564i	−0.564276	+	0.977356i
$202$			6.00000i			0.422159i
$203$		0			0
$204$	4.00000			0.280056
$205$	2.46410	+	3.73205i	0.172100	+	0.260658i
$206$	−4.00000	−	6.92820i	−0.278693	−	0.482711i
$207$		0			0
$208$	1.73205	+	1.00000i	0.120096	+	0.0693375i
$209$	36.0000			2.49017
$210$		0			0
$211$	−16.0000			−1.10149			−0.550743	−	0.834675i	$-0.685655\pi$
$211$	−16.0000			−1.10149			−0.550743	+	0.834675i	$0.685655\pi$
$212$	−5.19615	−	3.00000i	−0.356873	−	0.206041i
$213$	−8.66025	+	5.00000i	−0.593391	+	0.342594i
$214$	−2.00000	−	3.46410i	−0.136717	−	0.236801i
$215$	−7.46410	+	4.92820i	−0.509048	+	0.336101i
$216$	−3.00000			−0.204124
$217$		0			0
$218$		−	2.00000i		−	0.135457i
$219$	−3.00000	+	5.19615i	−0.202721	+	0.351123i
$220$	−13.3923	+	0.803848i	−0.902909	+	0.0541954i
$221$	4.00000	+	6.92820i	0.269069	+	0.466041i
$222$	−3.46410	−	2.00000i	−0.232495	−	0.134231i
$223$			24.0000i			1.60716i	0.595198	+	0.803579i	$0.297074\pi$
$223$			24.0000i			1.60716i	−0.595198	+	0.803579i	$0.702926\pi$
$224$		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	−0.252136	−	0.967692i	$-0.581133\pi$
$227$	6.92820	−	4.00000i	0.459841	−	0.265489i	0.711977	+	0.702202i	$0.247800\pi$
$228$	5.19615	−	3.00000i	0.344124	−	0.198680i
$229$	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	$0.0594799\pi$
$230$		0			0
$231$		0			0
$232$			6.00000i			0.393919i
$233$	22.5167	+	13.0000i	1.47512	+	0.851658i	0.999606	−	0.0280525i	$-0.00893057\pi$
$233$	22.5167	+	13.0000i	1.47512	+	0.851658i	0.475509	+	0.879711i	$0.342264\pi$
$234$	−1.00000	−	1.73205i	−0.0653720	−	0.113228i
$235$		0			0
$236$	4.00000	−	6.92820i	0.260378	−	0.450988i
$237$			4.00000i			0.259828i
$238$		0			0
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$	1.86603	−	1.23205i	0.120451	−	0.0795285i
$241$	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	$0.582673\pi$
$242$	21.6506	−	12.5000i	1.39176	−	0.803530i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	2.00000			0.128037
$245$		0			0
$246$	−2.00000			−0.127515
$247$	10.3923	+	6.00000i	0.661247	+	0.381771i
$248$	25.9808	−	15.0000i	1.64978	−	0.952501i
$249$	4.00000	+	6.92820i	0.253490	+	0.439057i
$250$	−10.5263	−	3.76795i	−0.665740	−	0.238306i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		0			0
$254$	−10.0000	+	17.3205i	−0.627456	+	1.08679i
$255$	8.92820	−	0.535898i	0.559106	−	0.0335593i
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	−13.8564	−	8.00000i	−0.864339	−	0.499026i	0.00112398	−	0.999999i	$-0.499642\pi$
$257$	−13.8564	−	8.00000i	−0.864339	−	0.499026i	−0.865463	+	0.500973i	$0.832976\pi$
$258$		−	4.00000i		−	0.249029i
$259$		0			0
$260$	−4.00000	−	2.00000i	−0.248069	−	0.124035i
$261$	1.00000	−	1.73205i	0.0618984	−	0.107211i
$262$	−3.46410	+	2.00000i	−0.214013	+	0.123560i
$263$	−20.7846	+	12.0000i	−1.28163	+	0.739952i	−0.977147	−	0.212565i	$-0.931818\pi$
$263$	−20.7846	+	12.0000i	−1.28163	+	0.739952i	−0.304487	+	0.952517i	$0.598485\pi$
$264$	9.00000	−	15.5885i	0.553912	−	0.959403i
$265$	−12.0000	−	6.00000i	−0.737154	−	0.368577i
$266$		0			0
$267$		−	6.00000i		−	0.367194i
$268$	−13.8564	−	8.00000i	−0.846415	−	0.488678i
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	0.996586	−	0.0825561i	$-0.0263084\pi$
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	−0.569789	+	0.821791i	$0.692975\pi$
$270$	−2.23205	+	0.133975i	−0.135838	+	0.00815343i
$271$	−7.00000	+	12.1244i	−0.425220	+	0.736502i	−0.996441	−	0.0842940i	$-0.973137\pi$
$271$	−7.00000	+	12.1244i	−0.425220	+	0.736502i	0.571221	+	0.820796i	$0.306470\pi$
$272$		−	4.00000i		−	0.242536i
$273$		0			0
$274$	−6.00000			−0.362473
$275$	−29.7846	+	3.58846i	−1.79608	+	0.216392i
$276$		0			0
$277$	24.2487	−	14.0000i	1.45696	−	0.841178i	0.458103	−	0.888899i	$-0.348529\pi$
$277$	24.2487	−	14.0000i	1.45696	−	0.841178i	0.998861	+	0.0477206i	$0.0151957\pi$
$278$	−1.73205	−	1.00000i	−0.103882	−	0.0599760i
$279$	−10.0000			−0.598684
$280$		0			0
$281$	−2.00000			−0.119310			−0.0596550	−	0.998219i	$-0.519000\pi$
$281$	−2.00000			−0.119310			−0.0596550	+	0.998219i	$0.519000\pi$
$282$		0			0
$283$	−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	$0.535959\pi$
$284$	−5.00000	−	8.66025i	−0.296695	−	0.513892i
$285$	11.1962	−	7.39230i	0.663203	−	0.437882i
$286$	12.0000			0.709575
$287$		0			0
$288$		−	5.00000i		−	0.294628i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	0.267949	+	4.46410i	0.0157345	+	0.262141i
$291$	1.00000	+	1.73205i	0.0586210	+	0.101535i
$292$	−5.19615	−	3.00000i	−0.304082	−	0.175562i
$293$		−	24.0000i		−	1.40209i	−0.713115	−	0.701047i	$-0.752716\pi$
$293$		−	24.0000i		−	1.40209i	0.713115	−	0.701047i	$-0.247284\pi$
$294$		0			0
$295$	8.00000	−	16.0000i	0.465778	−	0.931556i
$296$	6.00000	−	10.3923i	0.348743	−	0.604040i
$297$	−5.19615	+	3.00000i	−0.301511	+	0.174078i
$298$	12.1244	−	7.00000i	0.702345	−	0.405499i
$299$		0			0
$300$	−4.00000	+	3.00000i	−0.230940	+	0.173205i
$301$		0			0
$302$			8.00000i			0.460348i
$303$	5.19615	+	3.00000i	0.298511	+	0.172345i
$304$	−3.00000	−	5.19615i	−0.172062	−	0.298020i
$305$	4.46410	−	0.267949i	0.255614	−	0.0153427i
$306$	−2.00000	+	3.46410i	−0.114332	+	0.198030i
$307$			4.00000i			0.228292i	0.993464	+	0.114146i	$0.0364132\pi$
$307$			4.00000i			0.228292i	−0.993464	+	0.114146i	$0.963587\pi$
$308$		0			0
$309$	−8.00000			−0.455104
$310$	18.6603	−	12.3205i	1.05983	−	0.699758i
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$	5.19615	−	3.00000i	0.294174	−	0.169842i
$313$	5.19615	+	3.00000i	0.293704	+	0.169570i	0.639611	−	0.768699i	$-0.279095\pi$
$313$	5.19615	+	3.00000i	0.293704	+	0.169570i	−0.345907	+	0.938269i	$0.612429\pi$
$314$	−18.0000			−1.01580
$315$		0			0
$316$	−4.00000			−0.225018
$317$	−15.5885	−	9.00000i	−0.875535	−	0.505490i	−0.00635137	−	0.999980i	$-0.502022\pi$
$317$	−15.5885	−	9.00000i	−0.875535	−	0.505490i	−0.869184	+	0.494489i	$0.835355\pi$
$318$	5.19615	−	3.00000i	0.291386	−	0.168232i
$319$	6.00000	+	10.3923i	0.335936	+	0.581857i
$320$	8.62436	+	13.0622i	0.482116	+	0.730198i
$321$	−4.00000			−0.223258
$322$		0			0
$323$		−	24.0000i		−	1.33540i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−9.19615	−	3.92820i	−0.510111	−	0.217898i
$326$	2.00000	+	3.46410i	0.110770	+	0.191859i
$327$	−1.73205	−	1.00000i	−0.0957826	−	0.0553001i
$328$		−	6.00000i		−	0.331295i
$329$		0			0
$330$	6.00000	−	12.0000i	0.330289	−	0.660578i
$331$	12.0000	−	20.7846i	0.659580	−	1.14243i	−0.321145	−	0.947030i	$-0.604068\pi$
$331$	12.0000	−	20.7846i	0.659580	−	1.14243i	0.980725	−	0.195395i	$-0.0625990\pi$
$332$	−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
$335$	−32.0000	−	16.0000i	−1.74835	−	0.874173i
$336$		0			0
$337$			24.0000i			1.30736i	0.756770	+	0.653682i	$0.226776\pi$
$337$			24.0000i			1.30736i	−0.756770	+	0.653682i	$0.773224\pi$
$338$	−7.79423	−	4.50000i	−0.423950	−	0.244768i
$339$	−3.00000	−	5.19615i	−0.162938	−	0.282216i
$340$	0.535898	+	8.92820i	0.0290632	+	0.484200i
$341$	30.0000	−	51.9615i	1.62459	−	2.81387i
$342$			6.00000i			0.324443i
$343$		0			0
$344$	12.0000			0.646997
$345$		0			0
$346$		0			0
$347$	−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	$0.437721\pi$
$348$	1.73205	+	1.00000i	0.0928477	+	0.0536056i
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$		0			0
$351$	−2.00000			−0.106752
$352$	25.9808	+	15.0000i	1.38478	+	0.799503i
$353$	−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
$355$	−12.3205	−	18.6603i	−0.653905	−	0.990383i
$356$	6.00000			0.317999
$357$		0			0
$358$			14.0000i			0.739923i
$359$	11.0000	−	19.0526i	0.580558	−	1.00556i	−0.414855	−	0.909887i	$-0.636168\pi$
$359$	11.0000	−	19.0526i	0.580558	−	1.00556i	0.995413	−	0.0956683i	$-0.0304988\pi$
$360$	−0.401924	−	6.69615i	−0.0211832	−	0.352918i
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	−5.19615	−	3.00000i	−0.273104	−	0.157676i
$363$		−	25.0000i		−	1.31216i
$364$		0			0
$365$	−12.0000	−	6.00000i	−0.628109	−	0.314054i
$366$	−1.00000	+	1.73205i	−0.0522708	+	0.0905357i
$367$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$367$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$368$		0			0
$369$	−1.00000	+	1.73205i	−0.0520579	+	0.0901670i
$370$	4.00000	−	8.00000i	0.207950	−	0.415900i
$371$		0			0
$372$		−	10.0000i		−	0.518476i
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$	−12.0000	−	20.7846i	−0.620505	−	1.07475i
$375$	−8.52628	+	7.23205i	−0.440295	+	0.373461i
$376$		0			0
$377$			4.00000i			0.206010i
$378$		0			0
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$	7.39230	+	11.1962i	0.379217	+	0.574351i
$381$	10.0000	+	17.3205i	0.512316	+	0.887357i
$382$	−15.5885	+	9.00000i	−0.797575	+	0.460480i
$383$	−17.3205	−	10.0000i	−0.885037	−	0.510976i	−0.0127209	−	0.999919i	$-0.504049\pi$
$383$	−17.3205	−	10.0000i	−0.885037	−	0.510976i	−0.872316	+	0.488943i	$0.837383\pi$
$384$	3.00000			0.153093
$385$		0			0
$386$	8.00000			0.407189
$387$	−3.46410	−	2.00000i	−0.176090	−	0.101666i
$388$	−1.73205	+	1.00000i	−0.0879316	+	0.0507673i
$389$	13.0000	+	22.5167i	0.659126	+	1.14164i	0.980842	+	0.194804i	$0.0624070\pi$
$389$	13.0000	+	22.5167i	0.659126	+	1.14164i	−0.321716	+	0.946836i	$0.604260\pi$
$390$	3.73205	−	2.46410i	0.188980	−	0.124775i
$391$		0			0
$392$		0			0
$393$			4.00000i			0.201773i
$394$	−1.00000	+	1.73205i	−0.0503793	+	0.0872595i
$395$	−8.92820	+	0.535898i	−0.449227	+	0.0269640i
$396$	−3.00000	−	5.19615i	−0.150756	−	0.261116i
$397$	−19.0526	−	11.0000i	−0.956221	−	0.552074i	−0.0612128	−	0.998125i	$-0.519497\pi$
$397$	−19.0526	−	11.0000i	−0.956221	−	0.552074i	−0.895008	+	0.446051i	$0.852830\pi$
$398$			14.0000i			0.701757i
$399$		0			0
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	15.0000	−	25.9808i	0.749064	−	1.29742i	−0.199207	−	0.979957i	$-0.563837\pi$
$401$	15.0000	−	25.9808i	0.749064	−	1.29742i	0.948272	−	0.317460i	$-0.102830\pi$
$402$	13.8564	−	8.00000i	0.691095	−	0.399004i
$403$	17.3205	−	10.0000i	0.862796	−	0.498135i
$404$	−3.00000	+	5.19615i	−0.149256	+	0.258518i
$405$	−1.00000	+	2.00000i	−0.0496904	+	0.0993808i
$406$		0			0
$407$		−	24.0000i		−	1.18964i
$408$	−10.3923	−	6.00000i	−0.514496	−	0.297044i
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	0.998674	+	0.0514740i	$0.0163919\pi$
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	−0.454759	+	0.890614i	$0.650275\pi$
$410$	−0.267949	−	4.46410i	−0.0132331	−	0.220466i
$411$	−3.00000	+	5.19615i	−0.147979	+	0.256307i
$412$		−	8.00000i		−	0.394132i
$413$		0			0
$414$		0			0
$415$	−14.9282	+	9.85641i	−0.732797	+	0.483832i
$416$	5.00000	+	8.66025i	0.245145	+	0.424604i
$417$	−1.73205	+	1.00000i	−0.0848189	+	0.0489702i
$418$	−31.1769	−	18.0000i	−1.52491	−	0.880409i
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	18.0000			0.877266			0.438633	−	0.898666i	$-0.355463\pi$
$421$	18.0000			0.877266			0.438633	+	0.898666i	$0.355463\pi$
$422$	13.8564	+	8.00000i	0.674519	+	0.389434i
$423$		0			0
$424$	9.00000	+	15.5885i	0.437079	+	0.757042i
$425$	2.39230	+	19.8564i	0.116044	+	0.963177i
$426$	10.0000			0.484502
$427$		0			0
$428$		−	4.00000i		−	0.193347i
$429$	6.00000	−	10.3923i	0.289683	−	0.501745i
$430$	8.92820	−	0.535898i	0.430556	−	0.0258433i
$431$	7.00000	+	12.1244i	0.337178	+	0.584010i	0.983901	−	0.178716i	$-0.0571942\pi$
$431$	7.00000	+	12.1244i	0.337178	+	0.584010i	−0.646723	+	0.762725i	$0.723861\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$			34.0000i			1.63394i	0.576683	+	0.816968i	$0.304347\pi$
$433$			34.0000i			1.63394i	−0.576683	+	0.816968i	$0.695653\pi$
$434$		0			0
$435$	4.00000	+	2.00000i	0.191785	+	0.0958927i
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$		0			0
$438$	5.19615	−	3.00000i	0.248282	−	0.143346i
$439$	−3.00000	+	5.19615i	−0.143182	+	0.247999i	−0.928693	−	0.370849i	$-0.879067\pi$
$439$	−3.00000	+	5.19615i	−0.143182	+	0.247999i	0.785511	+	0.618848i	$0.212400\pi$
$440$	36.0000	+	18.0000i	1.71623	+	0.858116i
$441$		0			0
$442$		−	8.00000i		−	0.380521i
$443$	3.46410	+	2.00000i	0.164584	+	0.0950229i	0.580030	−	0.814595i	$-0.303041\pi$
$443$	3.46410	+	2.00000i	0.164584	+	0.0950229i	−0.415445	+	0.909618i	$0.636374\pi$
$444$	−2.00000	−	3.46410i	−0.0949158	−	0.164399i
$445$	13.3923	−	0.803848i	0.634856	−	0.0381060i
$446$	12.0000	−	20.7846i	0.568216	−	0.984180i
$447$		−	14.0000i		−	0.662177i
$448$		0			0
$449$	−10.0000			−0.471929			−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000			−0.471929			−0.235965	+	0.971762i	$0.575825\pi$
$450$	−0.598076	−	4.96410i	−0.0281936	−	0.234010i
$451$	−6.00000	−	10.3923i	−0.282529	−	0.489355i
$452$	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
$456$	−18.0000			−0.842927
$457$	−17.3205	−	10.0000i	−0.810219	−	0.467780i	0.0368128	−	0.999322i	$-0.488279\pi$
$457$	−17.3205	−	10.0000i	−0.810219	−	0.467780i	−0.847032	+	0.531542i	$0.821613\pi$
$458$	−8.66025	+	5.00000i	−0.404667	+	0.233635i
$459$	2.00000	+	3.46410i	0.0933520	+	0.161690i
$460$		0			0
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$		0			0
$463$			36.0000i			1.67306i	0.547920	+	0.836531i	$0.315420\pi$
$463$			36.0000i			1.67306i	−0.547920	+	0.836531i	$0.684580\pi$
$464$	1.00000	−	1.73205i	0.0464238	−	0.0804084i
$465$	−1.33975	−	22.3205i	−0.0621292	−	1.03509i
$466$	−13.0000	−	22.5167i	−0.602213	−	1.04306i
$467$	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	$0.479272\pi$
$468$		−	2.00000i		−	0.0924500i
$469$		0			0
$470$		0			0
$471$	−9.00000	+	15.5885i	−0.414698	+	0.718278i
$472$	−20.7846	+	12.0000i	−0.956689	+	0.552345i
$473$	20.7846	−	12.0000i	0.955677	−	0.551761i
$474$	2.00000	−	3.46410i	0.0918630	−	0.159111i
$475$	18.0000	+	24.0000i	0.825897	+	1.10120i
$476$		0			0
$477$		−	6.00000i		−	0.274721i
$478$	−5.19615	−	3.00000i	−0.237666	−	0.137217i
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	−0.998392	−	0.0566937i	$-0.981944\pi$
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	0.450098	−	0.892979i	$-0.351389\pi$
$480$	11.1603	−	0.669873i	0.509394	−	0.0305754i
$481$	4.00000	−	6.92820i	0.182384	−	0.315899i
$482$		−	22.0000i		−	1.00207i
$483$		0			0
$484$	25.0000			1.13636
$485$	−3.73205	+	2.46410i	−0.169464	+	0.111889i
$486$	−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	$0.420981\pi$
$488$	−5.19615	−	3.00000i	−0.235219	−	0.135804i
$489$	4.00000			0.180886
$490$		0			0
$491$	10.0000			0.451294			0.225647	−	0.974209i	$-0.427550\pi$
$491$	10.0000			0.451294			0.225647	+	0.974209i	$0.427550\pi$
$492$	−1.73205	−	1.00000i	−0.0780869	−	0.0450835i
$493$	6.92820	−	4.00000i	0.312031	−	0.180151i
$494$	−6.00000	−	10.3923i	−0.269953	−	0.467572i
$495$	−7.39230	−	11.1962i	−0.332259	−	0.503230i
$496$	−10.0000			−0.449013
$497$		0			0
$498$		−	8.00000i		−	0.358489i
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	−0.817781	−	0.575529i	$-0.804796\pi$
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	0.907314	+	0.420455i	$0.138129\pi$
$500$	−7.23205	−	8.52628i	−0.323427	−	0.381307i
$501$	−6.00000	−	10.3923i	−0.268060	−	0.464294i
$502$		0			0
$503$			36.0000i			1.60516i	0.596544	+	0.802580i	$0.296540\pi$
$503$			36.0000i			1.60516i	−0.596544	+	0.802580i	$0.703460\pi$
$504$		0			0
$505$	−6.00000	+	12.0000i	−0.266996	+	0.533993i
$506$		0			0
$507$	−7.79423	+	4.50000i	−0.346154	+	0.199852i
$508$	−17.3205	+	10.0000i	−0.768473	+	0.443678i
$509$	−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
$512$		−	11.0000i		−	0.486136i
$513$	5.19615	+	3.00000i	0.229416	+	0.132453i
$514$	8.00000	+	13.8564i	0.352865	+	0.611180i
$515$	−1.07180	−	17.8564i	−0.0472290	−	0.786847i
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$		0			0
$518$		0			0
$519$		0			0
$520$	7.39230	+	11.1962i	0.324174	+	0.490984i
$521$	19.0000	+	32.9090i	0.832405	+	1.44177i	0.896126	+	0.443800i	$0.146370\pi$
$521$	19.0000	+	32.9090i	0.832405	+	1.44177i	−0.0637207	+	0.997968i	$0.520297\pi$
$522$	−1.73205	+	1.00000i	−0.0758098	+	0.0437688i
$523$	17.3205	+	10.0000i	0.757373	+	0.437269i	0.828352	−	0.560208i	$-0.189279\pi$
$523$	17.3205	+	10.0000i	0.757373	+	0.437269i	−0.0709788	+	0.997478i	$0.522612\pi$
$524$	−4.00000			−0.174741
$525$		0			0
$526$	24.0000			1.04645
$527$	−34.6410	−	20.0000i	−1.50899	−	0.871214i
$528$	−5.19615	+	3.00000i	−0.226134	+	0.130558i
$529$	−11.5000	−	19.9186i	−0.500000	−	0.866025i
$530$	7.39230	+	11.1962i	0.321101	+	0.486330i
$531$	8.00000			0.347170
$532$		0			0
$533$		−	4.00000i		−	0.173259i
$534$	−3.00000	+	5.19615i	−0.129823	+	0.224860i
$535$	−0.535898	−	8.92820i	−0.0231689	−	0.386000i
$536$	24.0000	+	41.5692i	1.03664	+	1.79552i
$537$	12.1244	+	7.00000i	0.523205	+	0.302072i
$538$		−	14.0000i		−	0.603583i
$539$		0			0
$540$	−2.00000	−	1.00000i	−0.0860663	−	0.0430331i
$541$	−3.00000	+	5.19615i	−0.128980	+	0.223400i	−0.923282	−	0.384124i	$-0.874504\pi$
$541$	−3.00000	+	5.19615i	−0.128980	+	0.223400i	0.794302	+	0.607524i	$0.207837\pi$
$542$	12.1244	−	7.00000i	0.520786	−	0.300676i
$543$	−5.19615	+	3.00000i	−0.222988	+	0.128742i
$544$	10.0000	−	17.3205i	0.428746	−	0.742611i
$545$	2.00000	−	4.00000i	0.0856706	−	0.171341i
$546$		0			0
$547$			16.0000i			0.684111i	0.939680	+	0.342055i	$0.111123\pi$
$547$			16.0000i			0.684111i	−0.939680	+	0.342055i	$0.888877\pi$
$548$	−5.19615	−	3.00000i	−0.221969	−	0.128154i
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$	27.5885	+	11.7846i	1.17638	+	0.502497i
$551$	6.00000	−	10.3923i	0.255609	−	0.442727i
$552$		0			0
$553$		0			0
$554$	−28.0000			−1.18961
$555$	−4.92820	−	7.46410i	−0.209191	−	0.316833i
$556$	−1.00000	−	1.73205i	−0.0424094	−	0.0734553i
$557$	−32.9090	+	19.0000i	−1.39440	+	0.805056i	−0.993798	−	0.111198i	$-0.964531\pi$
$557$	−32.9090	+	19.0000i	−1.39440	+	0.805056i	−0.400599	+	0.916253i	$0.631198\pi$
$558$	8.66025	+	5.00000i	0.366618	+	0.211667i
$559$	8.00000			0.338364
$560$		0			0
$561$	−24.0000			−1.01328
$562$	1.73205	+	1.00000i	0.0730622	+	0.0421825i
$563$	31.1769	−	18.0000i	1.31395	−	0.758610i	0.331202	−	0.943560i	$-0.392546\pi$
$563$	31.1769	−	18.0000i	1.31395	−	0.758610i	0.982748	+	0.184950i	$0.0592124\pi$
$564$		0			0
$565$	11.1962	−	7.39230i	0.471026	−	0.310997i
$566$	20.0000			0.840663
$567$		0			0
$568$			30.0000i			1.25877i
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	0.358954	+	0.933355i	$0.383134\pi$
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	−0.987786	+	0.155815i	$0.950200\pi$
$570$	−13.3923	+	0.803848i	−0.560942	+	0.0336695i
$571$	−18.0000	−	31.1769i	−0.753277	−	1.30471i	−0.946227	−	0.323505i	$-0.895139\pi$
$571$	−18.0000	−	31.1769i	−0.753277	−	1.30471i	0.192950	−	0.981209i	$-0.438194\pi$
$572$	10.3923	+	6.00000i	0.434524	+	0.250873i
$573$			18.0000i			0.751961i
$574$		0			0
$575$		0			0
$576$	−3.50000	+	6.06218i	−0.145833	+	0.252591i
$577$	12.1244	−	7.00000i	0.504744	−	0.291414i	−0.225927	−	0.974144i	$-0.572541\pi$
$577$	12.1244	−	7.00000i	0.504744	−	0.291414i	0.730670	+	0.682730i	$0.239208\pi$
$578$	0.866025	−	0.500000i	0.0360219	−	0.0207973i
$579$	4.00000	−	6.92820i	0.166234	−	0.287926i
$580$	−2.00000	+	4.00000i	−0.0830455	+	0.166091i
$581$		0			0
$582$		−	2.00000i		−	0.0829027i
$583$	31.1769	+	18.0000i	1.29122	+	0.745484i
$584$	9.00000	+	15.5885i	0.372423	+	0.645055i
$585$	−0.267949	−	4.46410i	−0.0110783	−	0.184568i
$586$	−12.0000	+	20.7846i	−0.495715	+	0.858604i
$587$		−	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
$589$	−60.0000			−2.47226
$590$	−14.9282	+	9.85641i	−0.614584	+	0.405782i
$591$	1.00000	+	1.73205i	0.0411345	+	0.0712470i
$592$	−3.46410	+	2.00000i	−0.142374	+	0.0821995i
$593$	38.1051	+	22.0000i	1.56479	+	0.903432i	0.996761	+	0.0804231i	$0.0256271\pi$
$593$	38.1051	+	22.0000i	1.56479	+	0.903432i	0.568029	+	0.823009i	$0.307706\pi$
$594$	6.00000			0.246183
$595$		0			0
$596$	14.0000			0.573462
$597$	12.1244	+	7.00000i	0.496217	+	0.286491i
$598$		0			0
$599$	−1.00000	−	1.73205i	−0.0408589	−	0.0707697i	0.844873	−	0.534967i	$-0.179676\pi$
$599$	−1.00000	−	1.73205i	−0.0408589	−	0.0707697i	−0.885732	+	0.464198i	$0.846343\pi$
$600$	14.8923	−	1.79423i	0.607976	−	0.0732491i
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$		0			0
$603$		−	16.0000i		−	0.651570i
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	55.8013	−	3.34936i	2.26864	−	0.136171i
$606$	−3.00000	−	5.19615i	−0.121867	−	0.211079i
$607$	−20.7846	−	12.0000i	−0.843621	−	0.487065i	0.0148722	−	0.999889i	$-0.495266\pi$
$607$	−20.7846	−	12.0000i	−0.843621	−	0.487065i	−0.858494	+	0.512824i	$0.828599\pi$
$608$		−	30.0000i		−	1.21666i
$609$		0			0
$610$	−4.00000	−	2.00000i	−0.161955	−	0.0809776i
$611$		0			0
$612$	−3.46410	+	2.00000i	−0.140028	+	0.0808452i
$613$	3.46410	−	2.00000i	0.139914	−	0.0807792i	−0.428409	−	0.903585i	$-0.640926\pi$
$613$	3.46410	−	2.00000i	0.139914	−	0.0807792i	0.568323	+	0.822806i	$0.307592\pi$
$614$	2.00000	−	3.46410i	0.0807134	−	0.139800i
$615$	−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
$619$	−5.00000	−	8.66025i	−0.200967	−	0.348085i	0.747873	−	0.663842i	$-0.231075\pi$
$619$	−5.00000	−	8.66025i	−0.200967	−	0.348085i	−0.948840	+	0.315757i	$0.897742\pi$
$620$	22.3205	−	1.33975i	0.896413	−	0.0538055i
$621$		0			0
$622$			24.0000i			0.962312i
$623$		0			0
$624$	−2.00000			−0.0800641
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$	−3.00000	−	5.19615i	−0.119904	−	0.207680i
$627$	−31.1769	+	18.0000i	−1.24509	+	0.718851i
$628$	−15.5885	−	9.00000i	−0.622047	−	0.359139i
$629$	−16.0000			−0.637962
$630$		0			0
$631$	−20.0000			−0.796187			−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000			−0.796187			−0.398094	+	0.917345i	$0.630328\pi$
$632$	10.3923	+	6.00000i	0.413384	+	0.238667i
$633$	13.8564	−	8.00000i	0.550743	−	0.317971i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	−37.3205	+	24.6410i	−1.48102	+	0.977849i
$636$	6.00000			0.237915
$637$		0			0
$638$		−	12.0000i		−	0.475085i
$639$	5.00000	−	8.66025i	0.197797	−	0.342594i
$640$	0.401924	+	6.69615i	0.0158874	+	0.264689i
$641$	1.00000	+	1.73205i	0.0394976	+	0.0684119i	0.885098	−	0.465404i	$-0.154091\pi$
$641$	1.00000	+	1.73205i	0.0394976	+	0.0684119i	−0.845601	+	0.533816i	$0.820758\pi$
$642$	3.46410	+	2.00000i	0.136717	+	0.0789337i
$643$			20.0000i			0.788723i	0.918955	+	0.394362i	$0.129034\pi$
$643$			20.0000i			0.788723i	−0.918955	+	0.394362i	$0.870966\pi$
$644$		0			0
$645$	4.00000	−	8.00000i	0.157500	−	0.315000i
$646$	−12.0000	+	20.7846i	−0.472134	+	0.817760i
$647$	−17.3205	+	10.0000i	−0.680939	+	0.393141i	−0.800209	−	0.599721i	$-0.795278\pi$
$647$	−17.3205	+	10.0000i	−0.680939	+	0.393141i	0.119269	+	0.992862i	$0.461945\pi$
$648$	2.59808	−	1.50000i	0.102062	−	0.0589256i
$649$	−24.0000	+	41.5692i	−0.942082	+	1.63173i
$650$	6.00000	+	8.00000i	0.235339	+	0.313786i
$651$		0			0
$652$			4.00000i			0.156652i
$653$	−1.73205	−	1.00000i	−0.0677804	−	0.0391330i	0.465727	−	0.884929i	$-0.345793\pi$
$653$	−1.73205	−	1.00000i	−0.0677804	−	0.0391330i	−0.533507	+	0.845796i	$0.679126\pi$
$654$	1.00000	+	1.73205i	0.0391031	+	0.0677285i
$655$	−8.92820	+	0.535898i	−0.348854	+	0.0209393i
$656$	−1.00000	+	1.73205i	−0.0390434	+	0.0676252i
$657$		−	6.00000i		−	0.234082i
$658$		0			0
$659$	18.0000			0.701180			0.350590	−	0.936529i	$-0.385981\pi$
$659$	18.0000			0.701180			0.350590	+	0.936529i	$0.385981\pi$
$660$	11.1962	−	7.39230i	0.435810	−	0.287745i
$661$	−9.00000	−	15.5885i	−0.350059	−	0.606321i	0.636200	−	0.771524i	$-0.280505\pi$
$661$	−9.00000	−	15.5885i	−0.350059	−	0.606321i	−0.986260	+	0.165203i	$0.947172\pi$
$662$	−20.7846	+	12.0000i	−0.807817	+	0.466393i
$663$	−6.92820	−	4.00000i	−0.269069	−	0.155347i
$664$	24.0000			0.931381
$665$		0			0
$666$	4.00000			0.154997
$667$		0			0
$668$	10.3923	−	6.00000i	0.402090	−	0.232147i
$669$	−12.0000	−	20.7846i	−0.463947	−	0.803579i
$670$	19.7128	+	29.8564i	0.761572	+	1.15345i
$671$	−12.0000			−0.463255
$672$		0			0
$673$		−	36.0000i		−	1.38770i	−0.720121	−	0.693849i	$-0.755914\pi$
$673$		−	36.0000i		−	1.38770i	0.720121	−	0.693849i	$-0.244086\pi$
$674$	12.0000	−	20.7846i	0.462223	−	0.800593i
$675$	−4.59808	−	1.96410i	−0.176980	−	0.0755983i
$676$	−4.50000	−	7.79423i	−0.173077	−	0.299778i
$677$	−27.7128	−	16.0000i	−1.06509	−	0.614930i	−0.138254	−	0.990397i	$-0.544149\pi$
$677$	−27.7128	−	16.0000i	−1.06509	−	0.614930i	−0.926836	+	0.375467i	$0.877482\pi$
$678$			6.00000i			0.230429i
$679$		0			0
$680$	12.0000	−	24.0000i	0.460179	−	0.920358i
$681$	−4.00000	+	6.92820i	−0.153280	+	0.265489i
$682$	−51.9615	+	30.0000i	−1.98971	+	1.14876i
$683$	24.2487	−	14.0000i	0.927851	−	0.535695i	0.0417198	−	0.999129i	$-0.486716\pi$
$683$	24.2487	−	14.0000i	0.927851	−	0.535695i	0.886131	+	0.463434i	$0.153383\pi$
$684$	−3.00000	+	5.19615i	−0.114708	+	0.198680i
$685$	−12.0000	−	6.00000i	−0.458496	−	0.229248i
$686$		0			0
$687$			10.0000i			0.381524i
$688$	−3.46410	−	2.00000i	−0.132068	−	0.0762493i
$689$	6.00000	+	10.3923i	0.228582	+	0.395915i
$690$		0			0
$691$	−25.0000	+	43.3013i	−0.951045	+	1.64726i	−0.207875	+	0.978155i	$0.566655\pi$
$691$	−25.0000	+	43.3013i	−0.951045	+	1.64726i	−0.743170	+	0.669102i	$0.766679\pi$
$692$		0			0
$693$		0			0
$694$	12.0000			0.455514
$695$	−2.46410	−	3.73205i	−0.0934687	−	0.141565i
$696$	−3.00000	−	5.19615i	−0.113715	−	0.196960i
$697$	−6.92820	+	4.00000i	−0.262424	+	0.151511i
$698$	1.73205	+	1.00000i	0.0655591	+	0.0378506i
$699$	−26.0000			−0.983410
$700$		0			0
$701$	−10.0000			−0.377695			−0.188847	−	0.982006i	$-0.560475\pi$
$701$	−10.0000			−0.377695			−0.188847	+	0.982006i	$0.560475\pi$
$702$	1.73205	+	1.00000i	0.0653720	+	0.0377426i
$703$	−20.7846	+	12.0000i	−0.783906	+	0.452589i
$704$	−21.0000	−	36.3731i	−0.791467	−	1.37086i
$705$		0			0
$706$	20.0000			0.752710
$707$		0			0
$708$			8.00000i			0.300658i
$709$	13.0000	−	22.5167i	0.488225	−	0.845631i	−0.511683	−	0.859174i	$-0.670978\pi$
$709$	13.0000	−	22.5167i	0.488225	−	0.845631i	0.999908	+	0.0135434i	$0.00431112\pi$
$710$	1.33975	+	22.3205i	0.0502798	+	0.837674i
$711$	−2.00000	−	3.46410i	−0.0750059	−	0.129914i
$712$	−15.5885	−	9.00000i	−0.584202	−	0.337289i
$713$		0			0
$714$		0			0
$715$	24.0000	+	12.0000i	0.897549	+	0.448775i
$716$	−7.00000	+	12.1244i	−0.261602	+	0.453108i
$717$	−5.19615	+	3.00000i	−0.194054	+	0.112037i
$718$	−19.0526	+	11.0000i	−0.711035	+	0.410516i
$719$	−6.00000	+	10.3923i	−0.223762	+	0.387568i	−0.955947	−	0.293538i	$-0.905167\pi$
$719$	−6.00000	+	10.3923i	−0.223762	+	0.387568i	0.732185	+	0.681106i	$0.238501\pi$
$720$	−1.00000	+	2.00000i	−0.0372678	+	0.0745356i
$721$		0			0
$722$			17.0000i			0.632674i
$723$	−19.0526	−	11.0000i	−0.708572	−	0.409094i
$724$	−3.00000	−	5.19615i	−0.111494	−	0.193113i
$725$	−3.92820	+	9.19615i	−0.145890	+	0.341537i
$726$	−12.5000	+	21.6506i	−0.463919	+	0.803530i
$727$		−	40.0000i		−	1.48352i	−0.670667	−	0.741759i	$-0.733992\pi$
$727$		−	40.0000i		−	1.48352i	0.670667	−	0.741759i	$-0.266008\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	7.39230	+	11.1962i	0.273601	+	0.414388i
$731$	−8.00000	−	13.8564i	−0.295891	−	0.512498i
$732$	−1.73205	+	1.00000i	−0.0640184	+	0.0369611i
$733$	19.0526	+	11.0000i	0.703722	+	0.406294i	0.808732	−	0.588177i	$-0.200154\pi$
$733$	19.0526	+	11.0000i	0.703722	+	0.406294i	−0.105010	+	0.994471i	$0.533487\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	83.1384	+	48.0000i	3.06244	+	1.76810i
$738$	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	$-0.466811\pi$
$740$	7.46410	−	4.92820i	0.274386	−	0.181164i
$741$	−12.0000			−0.440831
$742$		0			0
$743$			40.0000i			1.46746i	0.679442	+	0.733729i	$0.262222\pi$
$743$			40.0000i			1.46746i	−0.679442	+	0.733729i	$0.737778\pi$
$744$	−15.0000	+	25.9808i	−0.549927	+	0.952501i
$745$	31.2487	−	1.87564i	1.14486	−	0.0687183i
$746$		0			0
$747$	−6.92820	−	4.00000i	−0.253490	−	0.146352i
$748$		−	24.0000i		−	0.877527i
$749$		0			0
$750$	11.0000	−	2.00000i	0.401663	−	0.0730297i
$751$	6.00000	−	10.3923i	0.218943	−	0.379221i	−0.735542	−	0.677479i	$-0.763072\pi$
$751$	6.00000	−	10.3923i	0.218943	−	0.379221i	0.954485	+	0.298259i	$0.0964058\pi$
$752$		0			0
$753$		0			0
$754$	2.00000	−	3.46410i	0.0728357	−	0.126155i
$755$	−8.00000	+	16.0000i	−0.291150	+	0.582300i
$756$		0			0
$757$			40.0000i			1.45382i	0.686730	+	0.726912i	$0.259045\pi$
$757$			40.0000i			1.45382i	−0.686730	+	0.726912i	$0.740955\pi$
$758$	−24.2487	−	14.0000i	−0.880753	−	0.508503i
$759$		0			0
$760$	−2.41154	−	40.1769i	−0.0874758	−	1.45737i
$761$	−11.0000	+	19.0526i	−0.398750	+	0.690655i	−0.993572	−	0.113203i	$-0.963889\pi$
$761$	−11.0000	+	19.0526i	−0.398750	+	0.690655i	0.594822	+	0.803857i	$0.297222\pi$
$762$		−	20.0000i		−	0.724524i
$763$		0			0
$764$	−18.0000			−0.651217
$765$	−7.46410	+	4.92820i	−0.269865	+	0.178180i
$766$	10.0000	+	17.3205i	0.361315	+	0.625815i
$767$	−13.8564	+	8.00000i	−0.500326	+	0.288863i
$768$	−14.7224	−	8.50000i	−0.531250	−	0.306717i
$769$	−18.0000			−0.649097			−0.324548	−	0.945869i	$-0.605212\pi$
$769$	−18.0000			−0.649097			−0.324548	+	0.945869i	$0.605212\pi$
$770$		0			0
$771$	16.0000			0.576226
$772$	6.92820	+	4.00000i	0.249351	+	0.143963i
$773$	−20.7846	+	12.0000i	−0.747570	+	0.431610i	−0.824815	−	0.565402i	$-0.808721\pi$
$773$	−20.7846	+	12.0000i	−0.747570	+	0.431610i	0.0772449	+	0.997012i	$0.475388\pi$
$774$	2.00000	+	3.46410i	0.0718885	+	0.124515i
$775$	49.6410	−	5.98076i	1.78316	−	0.214835i
$776$	6.00000			0.215387
$777$		0			0
$778$		−	26.0000i		−	0.932145i
$779$	−6.00000	+	10.3923i	−0.214972	+	0.372343i
$780$	4.46410	−	0.267949i	0.159840	−	0.00959412i
$781$	30.0000	+	51.9615i	1.07348	+	1.85933i
$782$		0			0
$783$			2.00000i			0.0714742i
$784$		0			0
$785$	−36.0000	−	18.0000i	−1.28490	−	0.642448i
$786$	2.00000	−	3.46410i	0.0713376	−	0.123560i
$787$	−3.46410	+	2.00000i	−0.123482	+	0.0712923i	−0.560469	−	0.828176i	$-0.689379\pi$
$787$	−3.46410	+	2.00000i	−0.123482	+	0.0712923i	0.436987	+	0.899468i	$0.356046\pi$
$788$	−1.73205	+	1.00000i	−0.0617018	+	0.0356235i
$789$	12.0000	−	20.7846i	0.427211	−	0.739952i
$790$	8.00000	+	4.00000i	0.284627	+	0.142314i
$791$		0			0
$792$			18.0000i			0.639602i
$793$	−3.46410	−	2.00000i	−0.123014	−	0.0710221i
$794$	11.0000	+	19.0526i	0.390375	+	0.676150i
$795$	13.3923	−	0.803848i	0.474976	−	0.0285095i
$796$	−7.00000	+	12.1244i	−0.248108	+	0.429736i
$797$		−	16.0000i		−	0.566749i	−0.959009	−	0.283375i	$-0.908546\pi$
$797$		−	16.0000i		−	0.566749i	0.959009	−	0.283375i	$-0.0914540\pi$
$798$		0			0
$799$		0			0
$800$	2.99038	+	24.8205i	0.105726	+	0.877537i
$801$	3.00000	+	5.19615i	0.106000	+	0.183597i
$802$	−25.9808	+	15.0000i	−0.917413	+	0.529668i
$803$	31.1769	+	18.0000i	1.10021	+	0.635206i
$804$	16.0000			0.564276
$805$		0			0
$806$	−20.0000			−0.704470
$807$	−12.1244	−	7.00000i	−0.426798	−	0.246412i
$808$	15.5885	−	9.00000i	0.548400	−	0.316619i
$809$	−9.00000	−	15.5885i	−0.316423	−	0.548061i	0.663316	−	0.748340i	$-0.269149\pi$
$809$	−9.00000	−	15.5885i	−0.316423	−	0.548061i	−0.979739	+	0.200279i	$0.935815\pi$
$810$	1.86603	−	1.23205i	0.0655654	−	0.0432899i
$811$	−34.0000			−1.19390			−0.596951	−	0.802278i	$-0.703621\pi$
$811$	−34.0000			−1.19390			−0.596951	+	0.802278i	$0.703621\pi$
$812$		0			0
$813$		−	14.0000i		−	0.491001i
$814$	−12.0000	+	20.7846i	−0.420600	+	0.728500i
$815$	0.535898	+	8.92820i	0.0187717	+	0.312741i
$816$	2.00000	+	3.46410i	0.0700140	+	0.121268i
$817$	−20.7846	−	12.0000i	−0.727161	−	0.419827i
$818$		−	22.0000i		−	0.769212i
$819$		0			0
$820$	2.00000	−	4.00000i	0.0698430	−	0.139686i
$821$	1.00000	−	1.73205i	0.0349002	−	0.0604490i	−0.848048	−	0.529920i	$-0.822222\pi$
$821$	1.00000	−	1.73205i	0.0349002	−	0.0604490i	0.882948	+	0.469471i	$0.155555\pi$
$822$	5.19615	−	3.00000i	0.181237	−	0.104637i
$823$	38.1051	−	22.0000i	1.32826	−	0.766872i	0.343230	−	0.939251i	$-0.388479\pi$
$823$	38.1051	−	22.0000i	1.32826	−	0.766872i	0.985031	+	0.172379i	$0.0551455\pi$
$824$	−12.0000	+	20.7846i	−0.418040	+	0.724066i
$825$	24.0000	−	18.0000i	0.835573	−	0.626680i
$826$		0			0
$827$			12.0000i			0.417281i	0.977992	+	0.208640i	$0.0669038\pi$
$827$			12.0000i			0.417281i	−0.977992	+	0.208640i	$0.933096\pi$
$828$		0			0
$829$	3.00000	+	5.19615i	0.104194	+	0.180470i	0.913409	−	0.407044i	$-0.133440\pi$
$829$	3.00000	+	5.19615i	0.104194	+	0.180470i	−0.809214	+	0.587513i	$0.800107\pi$
$830$	17.8564	−	1.07180i	0.619805	−	0.0372026i
$831$	−14.0000	+	24.2487i	−0.485655	+	0.841178i
$832$		−	14.0000i		−	0.485363i
$833$		0			0
$834$	2.00000			0.0692543
$835$	22.3923	−	14.7846i	0.774918	−	0.511643i
$836$	−18.0000	−	31.1769i	−0.622543	−	1.07828i
$837$	8.66025	−	5.00000i	0.299342	−	0.172825i
$838$	10.3923	+	6.00000i	0.358996	+	0.207267i
$839$	12.0000			0.414286			0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000			0.414286			0.207143	+	0.978311i	$0.433583\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	−15.5885	−	9.00000i	−0.537214	−	0.310160i
$843$	1.73205	−	1.00000i	0.0596550	−	0.0344418i
$844$	8.00000	+	13.8564i	0.275371	+	0.476957i
$845$	−11.0885	−	16.7942i	−0.381455	−	0.577739i
$846$		0			0
$847$		0			0
$848$		−	6.00000i		−	0.206041i
$849$	10.0000	−	17.3205i	0.343199	−	0.594438i
$850$	7.85641	−	18.3923i	0.269473	−	0.630851i
$851$		0			0
$852$	8.66025	+	5.00000i	0.296695	+	0.171297i
$853$		−	30.0000i		−	1.02718i	−0.858036	−	0.513590i	$-0.828315\pi$
$853$		−	30.0000i		−	1.02718i	0.858036	−	0.513590i	$-0.171685\pi$
$854$		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	−0.811057	−	0.584967i	$-0.801107\pi$
$857$	−20.7846	+	12.0000i	−0.709989	+	0.409912i	0.101068	+	0.994880i	$0.467774\pi$
$858$	−10.3923	+	6.00000i	−0.354787	+	0.204837i
$859$	13.0000	−	22.5167i	0.443554	−	0.768259i	−0.554396	−	0.832253i	$-0.687051\pi$
$859$	13.0000	−	22.5167i	0.443554	−	0.768259i	0.997950	+	0.0639945i	$0.0203840\pi$
$860$	8.00000	+	4.00000i	0.272798	+	0.136399i
$861$		0			0
$862$		−	14.0000i		−	0.476842i
$863$	20.7846	+	12.0000i	0.707516	+	0.408485i	0.810141	−	0.586235i	$-0.199391\pi$
$863$	20.7846	+	12.0000i	0.707516	+	0.408485i	−0.102624	+	0.994720i	$0.532724\pi$
$864$	2.50000	+	4.33013i	0.0850517	+	0.147314i
$865$		0			0
$866$	17.0000	−	29.4449i	0.577684	−	1.00058i
$867$		−	1.00000i		−	0.0339618i
$868$		0			0
$869$	24.0000			0.814144
$870$	−2.46410	−	3.73205i	−0.0835409	−	0.126528i
$871$	16.0000	+	27.7128i	0.542139	+	0.939013i
$872$	−5.19615	+	3.00000i	−0.175964	+	0.101593i
$873$	−1.73205	−	1.00000i	−0.0586210	−	0.0338449i
$874$		0			0
$875$		0			0
$876$	6.00000			0.202721
$877$	−3.46410	−	2.00000i	−0.116974	−	0.0675352i	0.440371	−	0.897816i	$-0.354847\pi$
$877$	−3.46410	−	2.00000i	−0.116974	−	0.0675352i	−0.557346	+	0.830281i	$0.688180\pi$
$878$	5.19615	−	3.00000i	0.175362	−	0.101245i
$879$	12.0000	+	20.7846i	0.404750	+	0.701047i
$880$	−7.39230	−	11.1962i	−0.249195	−	0.377422i
$881$	−14.0000			−0.471672			−0.235836	−	0.971793i	$-0.575783\pi$
$881$	−14.0000			−0.471672			−0.235836	+	0.971793i	$0.575783\pi$
$882$		0			0
$883$		−	48.0000i		−	1.61533i	−0.589643	−	0.807664i	$-0.700731\pi$
$883$		−	48.0000i		−	1.61533i	0.589643	−	0.807664i	$-0.299269\pi$
$884$	4.00000	−	6.92820i	0.134535	−	0.233021i
$885$	1.07180	+	17.8564i	0.0360281	+	0.600237i
$886$	−2.00000	−	3.46410i	−0.0671913	−	0.116379i
$887$	−6.92820	−	4.00000i	−0.232626	−	0.134307i	0.379157	−	0.925332i	$-0.376214\pi$
$887$	−6.92820	−	4.00000i	−0.232626	−	0.134307i	−0.611783	+	0.791026i	$0.709547\pi$
$888$			12.0000i			0.402694i
$889$		0			0
$890$	−12.0000	−	6.00000i	−0.402241	−	0.201120i
$891$	3.00000	−	5.19615i	0.100504	−	0.174078i
$892$	20.7846	−	12.0000i	0.695920	−	0.401790i
$893$		0			0
$894$	−7.00000	+	12.1244i	−0.234115	+	0.405499i
$895$	−14.0000	+	28.0000i	−0.467968	+	0.935937i
$896$		0			0
$897$		0			0
$898$	8.66025	+	5.00000i	0.288996	+	0.166852i
$899$	−10.0000	−	17.3205i	−0.333519	−	0.577671i
$900$	1.96410	−	4.59808i	0.0654701	−	0.153269i
$901$	12.0000	−	20.7846i	0.399778	−	0.692436i
$902$			12.0000i			0.399556i
$903$		0			0
$904$	−18.0000			−0.598671
$905$	−7.39230	−	11.1962i	−0.245729	−	0.372173i
$906$	−4.00000	−	6.92820i	−0.132891	−	0.230174i
$907$	−13.8564	+	8.00000i	−0.460094	+	0.265636i	−0.712084	−	0.702094i	$-0.752248\pi$
$907$	−13.8564	+	8.00000i	−0.460094	+	0.265636i	0.251990	+	0.967730i	$0.418915\pi$
$908$	−6.92820	−	4.00000i	−0.229920	−	0.132745i
$909$	−6.00000			−0.199007
$910$		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
$913$	41.5692	−	24.0000i	1.37574	−	0.794284i
$914$	10.0000	+	17.3205i	0.330771	+	0.572911i
$915$	−3.73205	+	2.46410i	−0.123378	+	0.0814607i
$916$	−10.0000			−0.330409
$917$		0			0
$918$		−	4.00000i		−	0.132020i
$919$	14.0000	−	24.2487i	0.461817	−	0.799891i	−0.537234	−	0.843433i	$-0.680531\pi$
$919$	14.0000	−	24.2487i	0.461817	−	0.799891i	0.999052	+	0.0435419i	$0.0138642\pi$
$920$		0			0
$921$	−2.00000	−	3.46410i	−0.0659022	−	0.114146i
$922$	25.9808	+	15.0000i	0.855631	+	0.493999i
$923$			20.0000i			0.658308i
$924$		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
$928$	8.66025	−	5.00000i	0.284287	−	0.164133i
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	−0.728046	−	0.685529i	$-0.759571\pi$
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	0.957708	+	0.287742i	$0.0929044\pi$
$930$	−10.0000	+	20.0000i	−0.327913	+	0.655826i
$931$		0			0
$932$		−	26.0000i		−	0.851658i
$933$	20.7846	+	12.0000i	0.680458	+	0.392862i
$934$	−12.0000	−	20.7846i	−0.392652	−	0.680093i
$935$	−3.21539	−	53.5692i	−0.105155	−	1.75190i
$936$	−3.00000	+	5.19615i	−0.0980581	+	0.169842i
$937$			2.00000i			0.0653372i	0.999466	+	0.0326686i	$0.0104006\pi$
$937$			2.00000i			0.0653372i	−0.999466	+	0.0326686i	$0.989599\pi$
$938$		0			0
$939$	−6.00000			−0.195803
$940$		0			0
$941$	−21.0000	−	36.3731i	−0.684580	−	1.18573i	−0.973568	−	0.228395i	$-0.926652\pi$
$941$	−21.0000	−	36.3731i	−0.684580	−	1.18573i	0.288988	−	0.957333i	$-0.406681\pi$
$942$	15.5885	−	9.00000i	0.507899	−	0.293236i
$943$		0			0
$944$	8.00000			0.260378
$945$		0			0
$946$	−24.0000			−0.780307
$947$	−31.1769	−	18.0000i	−1.01311	−	0.584921i	−0.101012	−	0.994885i	$-0.532208\pi$
$947$	−31.1769	−	18.0000i	−1.01311	−	0.584921i	−0.912102	+	0.409964i	$0.865541\pi$
$948$	3.46410	−	2.00000i	0.112509	−	0.0649570i
$949$	6.00000	+	10.3923i	0.194768	+	0.337348i
$950$	−3.58846	−	29.7846i	−0.116425	−	0.966340i
$951$	18.0000			0.583690
$952$		0			0
$953$			6.00000i			0.194359i	0.995267	+	0.0971795i	$0.0309821\pi$
$953$			6.00000i			0.194359i	−0.995267	+	0.0971795i	$0.969018\pi$
$954$	−3.00000	+	5.19615i	−0.0971286	+	0.168232i
$955$	−40.1769	+	2.41154i	−1.30009	+	0.0780357i
$956$	−3.00000	−	5.19615i	−0.0970269	−	0.168056i
$957$	−10.3923	−	6.00000i	−0.335936	−	0.193952i
$958$			24.0000i			0.775405i
$959$		0			0
$960$	−14.0000	−	7.00000i	−0.451848	−	0.225924i
$961$	−34.5000	+	59.7558i	−1.11290	+	1.92760i
$962$	−6.92820	+	4.00000i	−0.223374	+	0.128965i
$963$	3.46410	−	2.00000i	0.111629	−	0.0644491i
$964$	11.0000	−	19.0526i	0.354286	−	0.613642i
$965$	16.0000	+	8.00000i	0.515058	+	0.257529i
$966$		0			0
$967$		−	40.0000i		−	1.28631i	−0.765735	−	0.643157i	$-0.777624\pi$
$967$		−	40.0000i		−	1.28631i	0.765735	−	0.643157i	$-0.222376\pi$
$968$	−64.9519	−	37.5000i	−2.08763	−	1.20530i
$969$	12.0000	+	20.7846i	0.385496	+	0.667698i
$970$	4.46410	−	0.267949i	0.143334	−	0.00860333i
$971$	−4.00000	+	6.92820i	−0.128366	+	0.222337i	−0.923044	−	0.384695i	$-0.874307\pi$
$971$	−4.00000	+	6.92820i	−0.128366	+	0.222337i	0.794678	+	0.607032i	$0.207640\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		0			0
$974$	12.0000			0.384505
$975$	9.92820	−	1.19615i	0.317957	−	0.0383075i
$976$	1.00000	+	1.73205i	0.0320092	+	0.0554416i
$977$	−25.9808	+	15.0000i	−0.831198	+	0.479893i	−0.854263	−	0.519841i	$-0.825991\pi$
$977$	−25.9808	+	15.0000i	−0.831198	+	0.479893i	0.0230645	+	0.999734i	$0.492658\pi$
$978$	−3.46410	−	2.00000i	−0.110770	−	0.0639529i
$979$	−36.0000			−1.15056
$980$		0			0
$981$	2.00000			0.0638551
$982$	−8.66025	−	5.00000i	−0.276360	−	0.159556i
$983$	−20.7846	+	12.0000i	−0.662926	+	0.382741i	−0.793391	−	0.608712i	$-0.791686\pi$
$983$	−20.7846	+	12.0000i	−0.662926	+	0.382741i	0.130465	+	0.991453i	$0.458353\pi$
$984$	3.00000	+	5.19615i	0.0956365	+	0.165647i
$985$	−3.73205	+	2.46410i	−0.118913	+	0.0785128i
$986$	−8.00000			−0.254772
$987$		0			0
$988$		−	12.0000i		−	0.381771i
$989$		0			0
$990$	0.803848	+	13.3923i	0.0255480	+	0.425635i
$991$	−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	$0.853570\pi$
$992$	−43.3013	−	25.0000i	−1.37482	−	0.793751i
$993$			24.0000i			0.761617i
$994$		0			0
$995$	−14.0000	+	28.0000i	−0.443830	+	0.887660i
$996$	4.00000	−	6.92820i	0.126745	−	0.219529i
$997$	12.1244	−	7.00000i	0.383982	−	0.221692i	−0.295567	−	0.955322i	$-0.595509\pi$
$997$	12.1244	−	7.00000i	0.383982	−	0.221692i	0.679549	+	0.733630i	$0.262175\pi$
$998$	−3.46410	+	2.00000i	−0.109654	+	0.0633089i
$999$	2.00000	−	3.46410i	0.0632772	−	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.q.b.79.1		4
5.4	even	2	inner	735.2.q.b.79.2		4
7.2	even	3		735.2.d.a.589.2		2
7.3	odd	6		735.2.q.a.214.2		4
7.4	even	3	inner	735.2.q.b.214.2		4
7.5	odd	6		105.2.d.a.64.2	yes	2
7.6	odd	2		735.2.q.a.79.1		4
21.2	odd	6		2205.2.d.f.1324.1		2
21.5	even	6		315.2.d.c.64.1		2
28.19	even	6		1680.2.t.f.1009.1		2
35.2	odd	12		3675.2.a.d.1.1		1
35.4	even	6	inner	735.2.q.b.214.1		4
35.9	even	6		735.2.d.a.589.1		2
35.12	even	12		525.2.a.b.1.1		1
35.19	odd	6		105.2.d.a.64.1	✓	2
35.23	odd	12		3675.2.a.l.1.1		1
35.24	odd	6		735.2.q.a.214.1		4
35.33	even	12		525.2.a.c.1.1		1
35.34	odd	2		735.2.q.a.79.2		4
84.47	odd	6		5040.2.t.e.1009.2		2
105.44	odd	6		2205.2.d.f.1324.2		2
105.47	odd	12		1575.2.a.i.1.1		1
105.68	odd	12		1575.2.a.e.1.1		1
105.89	even	6		315.2.d.c.64.2		2
140.19	even	6		1680.2.t.f.1009.2		2
140.47	odd	12		8400.2.a.bj.1.1		1
140.103	odd	12		8400.2.a.ch.1.1		1
420.299	odd	6		5040.2.t.e.1009.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.d.a.64.1	✓	2	35.19	odd	6
105.2.d.a.64.2	yes	2	7.5	odd	6
315.2.d.c.64.1		2	21.5	even	6
315.2.d.c.64.2		2	105.89	even	6
525.2.a.b.1.1		1	35.12	even	12
525.2.a.c.1.1		1	35.33	even	12
735.2.d.a.589.1		2	35.9	even	6
735.2.d.a.589.2		2	7.2	even	3
735.2.q.a.79.1		4	7.6	odd	2
735.2.q.a.79.2		4	35.34	odd	2
735.2.q.a.214.1		4	35.24	odd	6
735.2.q.a.214.2		4	7.3	odd	6
735.2.q.b.79.1		4	1.1	even	1	trivial
735.2.q.b.79.2		4	5.4	even	2	inner
735.2.q.b.214.1		4	35.4	even	6	inner
735.2.q.b.214.2		4	7.4	even	3	inner
1575.2.a.e.1.1		1	105.68	odd	12
1575.2.a.i.1.1		1	105.47	odd	12
1680.2.t.f.1009.1		2	28.19	even	6
1680.2.t.f.1009.2		2	140.19	even	6
2205.2.d.f.1324.1		2	21.2	odd	6
2205.2.d.f.1324.2		2	105.44	odd	6
3675.2.a.d.1.1		1	35.2	odd	12
3675.2.a.l.1.1		1	35.23	odd	12
5040.2.t.e.1009.1		2	420.299	odd	6
5040.2.t.e.1009.2		2	84.47	odd	6
8400.2.a.bj.1.1		1	140.47	odd	12
8400.2.a.ch.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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.23205 - 1.86603i) q^{5} +1.00000 q^{6} +3.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.23205 - 1.86603i) q^{5} +1.00000 q^{6} +3.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.133975 + 2.23205i) q^{10} +(3.00000 + 5.19615i) q^{11} +(0.866025 + 0.500000i) q^{12} +2.00000i 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} -6.00000i q^{22} +(-1.50000 - 2.59808i) q^{24} +(-1.96410 + 4.59808i) q^{25} +(1.00000 - 1.73205i) q^{26} +1.00000i q^{27} +2.00000 q^{29} +(-1.23205 - 1.86603i) q^{30} +(-5.00000 - 8.66025i) q^{31} +(4.33013 - 2.50000i) q^{32} +(-5.19615 - 3.00000i) q^{33} -4.00000 q^{34} -1.00000 q^{36} +(-3.46410 - 2.00000i) q^{37} +(-5.19615 + 3.00000i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(5.59808 - 3.69615i) q^{40} -2.00000 q^{41} -4.00000i q^{43} +(3.00000 - 5.19615i) q^{44} +(-2.23205 + 0.133975i) q^{45} +1.00000i q^{48} +(4.00000 - 3.00000i) q^{50} +(-2.00000 + 3.46410i) q^{51} +(1.73205 - 1.00000i) q^{52} +(5.19615 - 3.00000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(6.00000 - 12.0000i) q^{55} +6.00000i q^{57} +(-1.73205 - 1.00000i) q^{58} +(4.00000 + 6.92820i) q^{59} +(-0.133975 - 2.23205i) q^{60} +(-1.00000 + 1.73205i) q^{61} +10.0000i q^{62} -7.00000 q^{64} +(3.73205 - 2.46410i) q^{65} +(3.00000 + 5.19615i) q^{66} +(13.8564 - 8.00000i) q^{67} +(-3.46410 - 2.00000i) q^{68} +10.0000 q^{71} +(2.59808 + 1.50000i) q^{72} +(5.19615 - 3.00000i) q^{73} +(2.00000 + 3.46410i) q^{74} +(-0.598076 - 4.96410i) q^{75} -6.00000 q^{76} +2.00000i q^{78} +(2.00000 - 3.46410i) q^{79} +(-2.23205 + 0.133975i) 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} +(-1.73205 + 1.00000i) q^{87} +(-15.5885 + 9.00000i) q^{88} +(-3.00000 + 5.19615i) q^{89} +(2.00000 + 1.00000i) q^{90} +(8.66025 + 5.00000i) q^{93} +(-13.3923 + 0.803848i) q^{95} +(-2.50000 + 4.33013i) q^{96} -2.00000i q^{97} +6.00000 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	\( 4 q - 2 q^{4} + 2 q^{5} + 4 q^{6} + 2 q^{9} + 4 q^{10} + 12 q^{11} + 8 q^{15} + 2 q^{16} + 12 q^{19} - 4 q^{20} - 6 q^{24} + 6 q^{25} + 4 q^{26} + 8 q^{29} + 2 q^{30} - 20 q^{31} - 16 q^{34} - 4 q^{36} - 4 q^{39} + 12 q^{40} - 8 q^{41} + 12 q^{44} - 2 q^{45} + 16 q^{50} - 8 q^{51} + 2 q^{54} + 24 q^{55} + 16 q^{59} - 4 q^{60} - 4 q^{61} - 28 q^{64} + 8 q^{65} + 12 q^{66} + 40 q^{71} + 8 q^{74} + 8 q^{75} - 24 q^{76} + 8 q^{79} - 2 q^{80} - 2 q^{81} - 32 q^{85} - 8 q^{86} - 12 q^{89} + 8 q^{90} - 12 q^{95} - 10 q^{96} + 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^4 + 2 * q^5 + 4 * q^6 + 2 * q^9 + 4 * q^10 + 12 * q^11 + 8 * q^15 + 2 * q^16 + 12 * q^19 - 4 * q^20 - 6 * q^24 + 6 * q^25 + 4 * q^26 + 8 * q^29 + 2 * q^30 - 20 * q^31 - 16 * q^34 - 4 * q^36 - 4 * q^39 + 12 * q^40 - 8 * q^41 + 12 * q^44 - 2 * q^45 + 16 * q^50 - 8 * q^51 + 2 * q^54 + 24 * q^55 + 16 * q^59 - 4 * q^60 - 4 * q^61 - 28 * q^64 + 8 * q^65 + 12 * q^66 + 40 * q^71 + 8 * q^74 + 8 * q^75 - 24 * q^76 + 8 * q^79 - 2 * q^80 - 2 * q^81 - 32 * q^85 - 8 * q^86 - 12 * q^89 + 8 * q^90 - 12 * q^95 - 10 * q^96 + 24 * q^99

Introduction

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