LMFDB - Embedded newform 735.2.q.a.214.2

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			214.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	735.214
Dual form			735.2.q.a.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.23205 + 0.133975i) q^{5} -1.00000 q^{6} +3.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.23205 + 0.133975i) q^{5} -1.00000 q^{6} +3.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.86603 + 1.23205i) 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} +(4.96410 - 0.598076i) q^{25} +(-1.00000 - 1.73205i) q^{26} -1.00000i q^{27} +2.00000 q^{29} +(2.23205 - 0.133975i) 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} +(-0.401924 - 6.69615i) q^{40} +2.00000 q^{41} -4.00000i q^{43} +(3.00000 + 5.19615i) q^{44} +(-1.23205 - 1.86603i) 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} +(-1.86603 + 1.23205i) q^{60} +(1.00000 + 1.73205i) q^{61} -10.0000i q^{62} -7.00000 q^{64} +(0.267949 + 4.46410i) 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} +(-4.59808 - 1.96410i) q^{75} +6.00000 q^{76} +2.00000i q^{78} +(2.00000 + 3.46410i) 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} +(-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} +(7.39230 + 11.1962i) 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 $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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	$-0.551640\pi$
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i	0.773893	+	0.633316i	$0.218307\pi$
$3$	−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
$5$	−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
$8$			3.00000i			1.06066i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.86603	+	1.23205i	−0.590089	+	0.389609i
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.0829925	−	0.996550i	$-0.473552\pi$
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.821541	−	0.570149i	$-0.193114\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$		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	0.857321	−	0.514782i	$-0.172127\pi$
$17$	3.46410	+	2.00000i	0.840168	+	0.485071i	−0.0171533	+	0.999853i	$0.505460\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	0.284157	−	0.958778i	$-0.408286\pi$
$20$	1.00000	−	2.00000i	0.223607	−	0.447214i
$21$		0			0
$22$		−	6.00000i		−	1.27920i
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$	1.50000	−	2.59808i	0.306186	−	0.530330i
$25$	4.96410	−	0.598076i	0.992820	−	0.119615i
$26$	−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	$0.440546\pi$
$30$	2.23205	−	0.133975i	0.407515	−	0.0244603i
$31$	5.00000	−	8.66025i	0.898027	−	1.55543i	0.0680129	−	0.997684i	$-0.478334\pi$
$31$	5.00000	−	8.66025i	0.898027	−	1.55543i	0.830014	−	0.557743i	$-0.188333\pi$
$32$	−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	$-0.560023\pi$
$37$	3.46410	−	2.00000i	0.569495	−	0.328798i	0.756948	+	0.653476i	$0.226690\pi$
$38$	−5.19615	−	3.00000i	−0.842927	−	0.486664i
$39$	−1.00000	+	1.73205i	−0.160128	+	0.277350i
$40$	−0.401924	−	6.69615i	−0.0635497	−	1.05875i
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$		0			0
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$	3.00000	+	5.19615i	0.452267	+	0.783349i
$45$	−1.23205	−	1.86603i	−0.183663	−	0.278171i
$46$		0			0
$47$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$47$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$48$		−	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	$-0.468532\pi$
$53$	−5.19615	−	3.00000i	−0.713746	−	0.412082i	−0.812447	+	0.583036i	$0.801865\pi$
$54$	−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	0.478953	+	0.877841i	$0.341016\pi$
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	−0.999709	+	0.0241347i	$0.992317\pi$
$60$	−1.86603	+	1.23205i	−0.240903	+	0.159057i
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$		−	10.0000i		−	1.27000i
$63$		0			0
$64$	−7.00000			−0.875000
$65$	0.267949	+	4.46410i	0.0332350	+	0.553704i
$66$	−3.00000	+	5.19615i	−0.369274	+	0.639602i
$67$	−13.8564	−	8.00000i	−1.69283	−	0.977356i	−0.952217	−	0.305424i	$-0.901202\pi$
$67$	−13.8564	−	8.00000i	−1.69283	−	0.977356i	−0.740613	−	0.671932i	$-0.765465\pi$
$68$	−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	0.772246	−	0.635323i	$-0.219133\pi$
$73$	5.19615	+	3.00000i	0.608164	+	0.351123i	−0.164083	+	0.986447i	$0.552466\pi$
$74$	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
$78$			2.00000i			0.226455i
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$	−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
$87$	−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	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$	−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
$95$	7.39230	+	11.1962i	0.758434	+	1.14870i
$96$	2.50000	+	4.33013i	0.255155	+	0.441942i
$97$			2.00000i			0.203069i	0.994832	+	0.101535i	$0.0323753\pi$
$97$			2.00000i			0.203069i	−0.994832	+	0.101535i	$0.967625\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$	−1.96410	+	4.59808i	−0.196410	+	0.459808i
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$	−3.46410	−	2.00000i	−0.342997	−	0.198030i
$103$	6.92820	−	4.00000i	0.682656	−	0.394132i	−0.118199	−	0.992990i	$-0.537712\pi$
$103$	6.92820	−	4.00000i	0.682656	−	0.394132i	0.800855	+	0.598858i	$0.204379\pi$
$104$	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	$-0.728601\pi$
$107$	−3.46410	+	2.00000i	−0.334887	+	0.193347i	0.323122	+	0.946357i	$0.395268\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$	0.803848	+	13.3923i	0.0766439	+	1.27691i
$111$	−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
$130$	2.46410	+	3.73205i	0.216116	+	0.327323i
$131$	−2.00000	−	3.46410i	−0.174741	−	0.302660i	0.765331	−	0.643637i	$-0.222575\pi$
$131$	−2.00000	−	3.46410i	−0.174741	−	0.302660i	−0.940072	+	0.340977i	$0.889242\pi$
$132$		−	6.00000i		−	0.522233i
$133$		0			0
$134$	−16.0000			−1.38219
$135$	0.133975	+	2.23205i	0.0115307	+	0.192104i
$136$	−6.00000	+	10.3923i	−0.514496	+	0.891133i
$137$	−5.19615	−	3.00000i	−0.443937	−	0.256307i	0.261329	−	0.965250i	$-0.415839\pi$
$137$	−5.19615	−	3.00000i	−0.443937	−	0.256307i	−0.705266	+	0.708942i	$0.749173\pi$
$138$		0			0
$139$	−2.00000			−0.169638			−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000			−0.169638			−0.0848189	+	0.996396i	$0.527031\pi$
$140$		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
$145$	−4.46410	+	0.267949i	−0.370723	+	0.0222520i
$146$	6.00000			0.496564
$147$		0			0
$148$			4.00000i			0.328798i
$149$	−7.00000	−	12.1244i	−0.573462	−	0.993266i	−0.996207	−	0.0870170i	$-0.972267\pi$
$149$	−7.00000	−	12.1244i	−0.573462	−	0.993266i	0.422744	−	0.906249i	$-0.361067\pi$
$150$	−4.96410	+	0.598076i	−0.405317	+	0.0488327i
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	−0.981617	−	0.190864i	$-0.938871\pi$
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	0.656101	+	0.754673i	$0.272204\pi$
$152$	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	0.969925	−	0.243403i	$-0.0782638\pi$
$157$	15.5885	+	9.00000i	1.24409	+	0.718278i	0.274169	+	0.961681i	$0.411597\pi$
$158$	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	$-0.616597\pi$
$163$	3.46410	−	2.00000i	0.271329	−	0.156652i	0.629492	+	0.777007i	$0.283263\pi$
$164$	−1.00000	+	1.73205i	−0.0780869	+	0.135250i
$165$	11.1962	−	7.39230i	0.871619	−	0.575490i
$166$	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
$169$	9.00000			0.692308
$170$	−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
$173$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$173$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$174$	−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	0.476431	+	0.879212i	$0.341930\pi$
$179$	−7.00000	+	12.1244i	−0.523205	+	0.906217i	−0.999635	+	0.0270049i	$0.991403\pi$
$180$	2.23205	−	0.133975i	0.166367	−	0.00998588i
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$		0			0
$183$		−	2.00000i		−	0.147844i
$184$		0			0
$185$	−7.46410	+	4.92820i	−0.548772	+	0.362329i
$186$	−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	0.982828	+	0.184525i	$0.0590746\pi$
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	−0.331611	+	0.943416i	$0.607592\pi$
$192$	6.06218	+	3.50000i	0.437500	+	0.252591i
$193$	6.92820	+	4.00000i	0.498703	+	0.287926i	0.728178	−	0.685388i	$-0.240368\pi$
$193$	6.92820	+	4.00000i	0.498703	+	0.287926i	−0.229475	+	0.973315i	$0.573701\pi$
$194$	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	$-0.668055\pi$
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	0.999990	+	0.00436292i	$0.00138876\pi$
$200$	1.79423	+	14.8923i	0.126871	+	1.05304i
$201$	8.00000	+	13.8564i	0.564276	+	0.977356i
$202$		−	6.00000i		−	0.422159i
$203$		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
$207$		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
$215$	0.535898	+	8.92820i	0.0365480	+	0.608898i
$216$	3.00000			0.204124
$217$		0			0
$218$		−	2.00000i		−	0.135457i
$219$	−3.00000	−	5.19615i	−0.202721	−	0.351123i
$220$	−7.39230	−	11.1962i	−0.498389	−	0.754844i
$221$	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	$-0.702926\pi$
$223$		−	24.0000i		−	1.60716i	0.595198	−	0.803579i	$-0.297074\pi$
$224$		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	$-0.247800\pi$
$227$	6.92820	+	4.00000i	0.459841	+	0.265489i	−0.252136	+	0.967692i	$0.581133\pi$
$228$	−5.19615	−	3.00000i	−0.344124	−	0.198680i
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	0.652183	−	0.758062i	$-0.273853\pi$
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	−0.982592	+	0.185776i	$0.940520\pi$
$230$		0			0
$231$		0			0
$232$			6.00000i			0.393919i
$233$	−22.5167	+	13.0000i	−1.47512	+	0.851658i	−0.999606	−	0.0280525i	$-0.991069\pi$
$233$	−22.5167	+	13.0000i	−1.47512	+	0.851658i	−0.475509	+	0.879711i	$0.657736\pi$
$234$	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	$0.437836\pi$
$240$	0.133975	+	2.23205i	0.00864802	+	0.144078i
$241$	−11.0000	+	19.0526i	−0.708572	+	1.22728i	0.256814	+	0.966461i	$0.417327\pi$
$241$	−11.0000	+	19.0526i	−0.708572	+	1.22728i	−0.965387	+	0.260822i	$0.916006\pi$
$242$	−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
$250$	−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
$253$		0			0
$254$	−10.0000	−	17.3205i	−0.627456	−	1.08679i
$255$	4.92820	+	7.46410i	0.308616	+	0.467420i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−13.8564	+	8.00000i	−0.864339	+	0.499026i	−0.865463	−	0.500973i	$-0.832976\pi$
$257$	−13.8564	+	8.00000i	−0.864339	+	0.499026i	0.00112398	+	0.999999i	$0.499642\pi$
$258$			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	$-0.0681817\pi$
$263$	20.7846	+	12.0000i	1.28163	+	0.739952i	0.304487	+	0.952517i	$0.401515\pi$
$264$	−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	$-0.973692\pi$
$269$	−7.00000	+	12.1244i	−0.426798	+	0.739235i	0.569789	+	0.821791i	$0.307025\pi$
$270$	1.23205	+	1.86603i	0.0749802	+	0.113563i
$271$	7.00000	+	12.1244i	0.425220	+	0.736502i	0.996441	−	0.0842940i	$-0.0268635\pi$
$271$	7.00000	+	12.1244i	0.425220	+	0.736502i	−0.571221	+	0.820796i	$0.693530\pi$
$272$			4.00000i			0.242536i
$273$		0			0
$274$	−6.00000			−0.362473
$275$	11.7846	−	27.5885i	0.710639	−	1.66365i
$276$		0			0
$277$	−24.2487	−	14.0000i	−1.45696	−	0.841178i	−0.458103	−	0.888899i	$-0.651471\pi$
$277$	−24.2487	−	14.0000i	−1.45696	−	0.841178i	−0.998861	+	0.0477206i	$0.984804\pi$
$278$	−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	−0.112728	−	0.993626i	$-0.535959\pi$
$283$	−17.3205	−	10.0000i	−1.02960	−	0.594438i	−0.916869	+	0.399188i	$0.869292\pi$
$284$	−5.00000	+	8.66025i	−0.296695	+	0.513892i
$285$	−0.803848	−	13.3923i	−0.0476158	−	0.793292i
$286$	−12.0000			−0.709575
$287$		0			0
$288$		−	5.00000i		−	0.294628i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	−3.73205	+	2.46410i	−0.219154	+	0.144697i
$291$	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	$0.247284\pi$
$293$			24.0000i			1.40209i	−0.713115	+	0.701047i	$0.752716\pi$
$294$		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
$305$	−2.46410	−	3.73205i	−0.141094	−	0.213697i
$306$	2.00000	+	3.46410i	0.114332	+	0.198030i
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$		0			0
$309$	−8.00000			−0.455104
$310$	1.33975	+	22.3205i	0.0760925	+	1.26772i
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	−0.294384	−	0.955687i	$-0.595114\pi$
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	0.974841	−	0.222900i	$-0.0715523\pi$
$312$	−5.19615	−	3.00000i	−0.294174	−	0.169842i
$313$	5.19615	−	3.00000i	0.293704	−	0.169570i	−0.345907	−	0.938269i	$-0.612429\pi$
$313$	5.19615	−	3.00000i	0.293704	−	0.169570i	0.639611	+	0.768699i	$0.279095\pi$
$314$	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	$-0.497978\pi$
$317$	15.5885	−	9.00000i	0.875535	−	0.505490i	0.869184	+	0.494489i	$0.164645\pi$
$318$	5.19615	+	3.00000i	0.291386	+	0.168232i
$319$	6.00000	−	10.3923i	0.335936	−	0.581857i
$320$	15.6244	−	0.937822i	0.873428	−	0.0524259i
$321$	4.00000			0.223258
$322$		0			0
$323$		−	24.0000i		−	1.33540i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−1.19615	−	9.92820i	−0.0663506	−	0.550718i
$326$	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	0.980725	+	0.195395i	$0.0625990\pi$
$331$	12.0000	+	20.7846i	0.659580	+	1.14243i	−0.321145	+	0.947030i	$0.604068\pi$
$332$	−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
$340$	7.46410	−	4.92820i	0.404798	−	0.267269i
$341$	−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	$-0.228946\pi$
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	−0.194409	+	0.980921i	$0.562279\pi$
$348$	1.73205	−	1.00000i	0.0928477	−	0.0536056i
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$		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	−0.0376440	−	0.999291i	$-0.511985\pi$
$353$	−17.3205	−	10.0000i	−0.921878	−	0.532246i	−0.884234	+	0.467045i	$0.845319\pi$
$354$	4.00000	−	6.92820i	0.212598	−	0.368230i
$355$	−22.3205	+	1.33975i	−1.18465	+	0.0711063i
$356$	−6.00000			−0.317999
$357$		0			0
$358$			14.0000i			0.739923i
$359$	11.0000	+	19.0526i	0.580558	+	1.00556i	0.995413	+	0.0956683i	$0.0304988\pi$
$359$	11.0000	+	19.0526i	0.580558	+	1.00556i	−0.414855	+	0.909887i	$0.636168\pi$
$360$	5.59808	−	3.69615i	0.295045	−	0.194804i
$361$	−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	$-0.333333\pi$
$367$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$368$		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	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$	12.0000	−	20.7846i	0.620505	−	1.07475i
$375$	10.5263	+	3.76795i	0.543575	+	0.194576i
$376$		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	$0.244540\pi$
$380$	−13.3923	+	0.803848i	−0.687011	+	0.0412365i
$381$	−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	−0.872316	−	0.488943i	$-0.837383\pi$
$383$	−17.3205	+	10.0000i	−0.885037	+	0.510976i	−0.0127209	+	0.999919i	$0.504049\pi$
$384$	−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	−0.321716	−	0.946836i	$-0.604260\pi$
$389$	13.0000	−	22.5167i	0.659126	−	1.14164i	0.980842	−	0.194804i	$-0.0624070\pi$
$390$	−0.267949	−	4.46410i	−0.0135681	−	0.226049i
$391$		0			0
$392$		0			0
$393$			4.00000i			0.201773i
$394$	−1.00000	−	1.73205i	−0.0503793	−	0.0872595i
$395$	−4.92820	−	7.46410i	−0.247965	−	0.375560i
$396$	−3.00000	+	5.19615i	−0.150756	+	0.261116i
$397$	−19.0526	+	11.0000i	−0.956221	+	0.552074i	−0.895008	−	0.446051i	$-0.852830\pi$
$397$	−19.0526	+	11.0000i	−0.956221	+	0.552074i	−0.0612128	+	0.998125i	$0.519497\pi$
$398$		−	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	0.948272	+	0.317460i	$0.102830\pi$
$401$	15.0000	+	25.9808i	0.749064	+	1.29742i	−0.199207	+	0.979957i	$0.563837\pi$
$402$	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	0.454759	+	0.890614i	$0.349725\pi$
$409$	−11.0000	+	19.0526i	−0.543915	+	0.942088i	−0.998674	+	0.0514740i	$0.983608\pi$
$410$	−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
$414$		0			0
$415$	−1.07180	−	17.8564i	−0.0526124	−	0.876537i
$416$	−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	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		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
$425$	18.3923	+	7.85641i	0.892158	+	0.381092i
$426$	−10.0000			−0.484502
$427$		0			0
$428$		−	4.00000i		−	0.193347i
$429$	6.00000	+	10.3923i	0.289683	+	0.501745i
$430$	4.92820	+	7.46410i	0.237659	+	0.359951i
$431$	7.00000	−	12.1244i	0.337178	−	0.584010i	−0.646723	−	0.762725i	$-0.723861\pi$
$431$	7.00000	−	12.1244i	0.337178	−	0.584010i	0.983901	+	0.178716i	$0.0571942\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$		−	34.0000i		−	1.63394i	−0.576683	−	0.816968i	$-0.695653\pi$
$433$		−	34.0000i		−	1.63394i	0.576683	−	0.816968i	$-0.304347\pi$
$434$		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	$-0.120933\pi$
$439$	3.00000	+	5.19615i	0.143182	+	0.247999i	−0.785511	+	0.618848i	$0.787600\pi$
$440$	−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	$-0.696959\pi$
$443$	−3.46410	+	2.00000i	−0.164584	+	0.0950229i	0.415445	+	0.909618i	$0.363626\pi$
$444$	2.00000	−	3.46410i	0.0949158	−	0.164399i
$445$	−7.39230	−	11.1962i	−0.350429	−	0.530749i
$446$	−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	$0.575825\pi$
$450$	4.59808	+	1.96410i	0.216755	+	0.0925886i
$451$	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	$-0.511721\pi$
$457$	17.3205	−	10.0000i	0.810219	−	0.467780i	0.847032	+	0.531542i	$0.178387\pi$
$458$	−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	$-0.253798\pi$
$461$	30.0000			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$462$		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
$465$	18.6603	−	12.3205i	0.865349	−	0.571350i
$466$	−13.0000	+	22.5167i	−0.602213	+	1.04306i
$467$	20.7846	−	12.0000i	0.961797	−	0.555294i	0.0650714	−	0.997881i	$-0.479272\pi$
$467$	20.7846	−	12.0000i	0.961797	−	0.555294i	0.896726	+	0.442587i	$0.145939\pi$
$468$			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	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$	−6.16025	−	9.33013i	−0.281176	−	0.425860i
$481$	−4.00000	−	6.92820i	−0.182384	−	0.315899i
$482$			22.0000i			1.00207i
$483$		0			0
$484$	25.0000			1.13636
$485$	−0.267949	−	4.46410i	−0.0121669	−	0.202704i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	10.3923	+	6.00000i	0.470920	+	0.271886i	0.716625	−	0.697459i	$-0.245686\pi$
$487$	10.3923	+	6.00000i	0.470920	+	0.271886i	−0.245705	+	0.969345i	$0.579019\pi$
$488$	−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
$495$	−13.3923	+	0.803848i	−0.601939	+	0.0361303i
$496$	10.0000			0.449013
$497$		0			0
$498$		−	8.00000i		−	0.358489i
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	0.907314	−	0.420455i	$-0.138129\pi$
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	−0.817781	+	0.575529i	$0.804796\pi$
$500$	3.76795	−	10.5263i	0.168508	−	0.470750i
$501$	−6.00000	+	10.3923i	−0.268060	+	0.464294i
$502$		0			0
$503$		−	36.0000i		−	1.60516i	−0.596544	−	0.802580i	$-0.703460\pi$
$503$		−	36.0000i		−	1.60516i	0.596544	−	0.802580i	$-0.296540\pi$
$504$		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	0.979322	+	0.202306i	$0.0648436\pi$
$509$	15.0000	+	25.9808i	0.664863	+	1.15158i	−0.314459	+	0.949271i	$0.601823\pi$
$510$	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
$515$	−14.9282	+	9.85641i	−0.657815	+	0.434325i
$516$	−2.00000	−	3.46410i	−0.0880451	−	0.152499i
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−13.3923	+	0.803848i	−0.587291	+	0.0352510i
$521$	−19.0000	+	32.9090i	−0.832405	+	1.44177i	0.0637207	+	0.997968i	$0.479703\pi$
$521$	−19.0000	+	32.9090i	−0.832405	+	1.44177i	−0.896126	+	0.443800i	$0.853630\pi$
$522$	1.73205	+	1.00000i	0.0758098	+	0.0437688i
$523$	17.3205	−	10.0000i	0.757373	−	0.437269i	−0.0709788	−	0.997478i	$-0.522612\pi$
$523$	17.3205	−	10.0000i	0.757373	−	0.437269i	0.828352	+	0.560208i	$0.189279\pi$
$524$	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
$530$	13.3923	−	0.803848i	0.581725	−	0.0349169i
$531$	−8.00000			−0.347170
$532$		0			0
$533$		−	4.00000i		−	0.173259i
$534$	−3.00000	−	5.19615i	−0.129823	−	0.224860i
$535$	7.46410	−	4.92820i	0.322701	−	0.213065i
$536$	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	0.794302	−	0.607524i	$-0.207837\pi$
$541$	−3.00000	−	5.19615i	−0.128980	−	0.223400i	−0.923282	+	0.384124i	$0.874504\pi$
$542$	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
$550$	−3.58846	−	29.7846i	−0.153012	−	1.27002i
$551$	−6.00000	−	10.3923i	−0.255609	−	0.442727i
$552$		0			0
$553$		0			0
$554$	−28.0000			−1.18961
$555$	8.92820	−	0.535898i	0.378981	−	0.0227476i
$556$	1.00000	−	1.73205i	0.0424094	−	0.0734553i
$557$	32.9090	+	19.0000i	1.39440	+	0.805056i	0.993798	−	0.111198i	$-0.0354686\pi$
$557$	32.9090	+	19.0000i	1.39440	+	0.805056i	0.400599	+	0.916253i	$0.368802\pi$
$558$	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	0.982748	−	0.184950i	$-0.0592124\pi$
$563$	31.1769	+	18.0000i	1.31395	+	0.758610i	0.331202	+	0.943560i	$0.392546\pi$
$564$		0			0
$565$	−0.803848	−	13.3923i	−0.0338181	−	0.563418i
$566$	−20.0000			−0.840663
$567$		0			0
$568$			30.0000i			1.25877i
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	−0.987786	−	0.155815i	$-0.950200\pi$
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	0.358954	−	0.933355i	$-0.383134\pi$
$570$	−7.39230	−	11.1962i	−0.309630	−	0.468955i
$571$	−18.0000	+	31.1769i	−0.753277	+	1.30471i	0.192950	+	0.981209i	$0.438194\pi$
$571$	−18.0000	+	31.1769i	−0.753277	+	1.30471i	−0.946227	+	0.323505i	$0.895139\pi$
$572$	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	0.730670	−	0.682730i	$-0.239208\pi$
$577$	12.1244	+	7.00000i	0.504744	+	0.291414i	−0.225927	+	0.974144i	$0.572541\pi$
$578$	−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
$585$	−3.73205	+	2.46410i	−0.154301	+	0.101878i
$586$	12.0000	+	20.7846i	0.495715	+	0.858604i
$587$			12.0000i			0.495293i	0.968850	+	0.247647i	$0.0796572\pi$
$587$			12.0000i			0.495293i	−0.968850	+	0.247647i	$0.920343\pi$
$588$		0			0
$589$	−60.0000			−2.47226
$590$	−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
$593$	38.1051	−	22.0000i	1.56479	−	0.903432i	0.568029	−	0.823009i	$-0.307706\pi$
$593$	38.1051	−	22.0000i	1.56479	−	0.903432i	0.996761	−	0.0804231i	$-0.0256271\pi$
$594$	−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	−0.885732	−	0.464198i	$-0.846343\pi$
$599$	−1.00000	+	1.73205i	−0.0408589	+	0.0707697i	0.844873	+	0.534967i	$0.179676\pi$
$600$	5.89230	−	13.7942i	0.240552	−	0.563147i
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$		0			0
$603$		−	16.0000i		−	0.651570i
$604$	−4.00000	−	6.92820i	−0.162758	−	0.281905i
$605$	30.8013	+	46.6506i	1.25225	+	1.89662i
$606$	−3.00000	+	5.19615i	−0.121867	+	0.211079i
$607$	−20.7846	+	12.0000i	−0.843621	+	0.487065i	−0.858494	−	0.512824i	$-0.828599\pi$
$607$	−20.7846	+	12.0000i	−0.843621	+	0.487065i	0.0148722	+	0.999889i	$0.495266\pi$
$608$			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	$-0.359074\pi$
$613$	−3.46410	−	2.00000i	−0.139914	−	0.0807792i	−0.568323	+	0.822806i	$0.692408\pi$
$614$	−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	$-0.768925\pi$
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	0.948840	+	0.315757i	$0.102258\pi$
$620$	−12.3205	−	18.6603i	−0.494804	−	0.749414i
$621$		0			0
$622$		−	24.0000i		−	0.962312i
$623$		0			0
$624$	−2.00000			−0.0800641
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	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
$635$	2.67949	+	44.6410i	0.106332	+	1.77152i
$636$	−6.00000			−0.237915
$637$		0			0
$638$		−	12.0000i		−	0.475085i
$639$	5.00000	+	8.66025i	0.197797	+	0.342594i
$640$	−5.59808	+	3.69615i	−0.221283	+	0.146103i
$641$	1.00000	−	1.73205i	0.0394976	−	0.0684119i	−0.845601	−	0.533816i	$-0.820758\pi$
$641$	1.00000	−	1.73205i	0.0394976	−	0.0684119i	0.885098	+	0.465404i	$0.154091\pi$
$642$	3.46410	−	2.00000i	0.136717	−	0.0789337i
$643$		−	20.0000i		−	0.788723i	−0.918955	−	0.394362i	$-0.870966\pi$
$643$		−	20.0000i		−	0.788723i	0.918955	−	0.394362i	$-0.129034\pi$
$644$		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	0.119269	−	0.992862i	$-0.461945\pi$
$647$	−17.3205	−	10.0000i	−0.680939	−	0.393141i	−0.800209	+	0.599721i	$0.795278\pi$
$648$	−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	$-0.654207\pi$
$653$	1.73205	−	1.00000i	0.0677804	−	0.0391330i	0.533507	+	0.845796i	$0.320874\pi$
$654$	−1.00000	+	1.73205i	−0.0391031	+	0.0677285i
$655$	4.92820	+	7.46410i	0.192561	+	0.291647i
$656$	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	$0.385981\pi$
$660$	0.803848	+	13.3923i	0.0312897	+	0.521295i
$661$	9.00000	−	15.5885i	0.350059	−	0.606321i	−0.636200	−	0.771524i	$-0.719495\pi$
$661$	9.00000	−	15.5885i	0.350059	−	0.606321i	0.986260	+	0.165203i	$0.0528281\pi$
$662$	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
$670$	35.7128	−	2.14359i	1.37971	−	0.0828142i
$671$	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
$675$	−0.598076	−	4.96410i	−0.0230200	−	0.191068i
$676$	−4.50000	+	7.79423i	−0.173077	+	0.299778i
$677$	−27.7128	+	16.0000i	−1.06509	+	0.614930i	−0.926836	−	0.375467i	$-0.877482\pi$
$677$	−27.7128	+	16.0000i	−1.06509	+	0.614930i	−0.138254	+	0.990397i	$0.544149\pi$
$678$		−	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	$-0.513284\pi$
$683$	−24.2487	−	14.0000i	−0.927851	−	0.535695i	−0.886131	+	0.463434i	$0.846617\pi$
$684$	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	0.743170	+	0.669102i	$0.233321\pi$
$691$	25.0000	+	43.3013i	0.951045	+	1.64726i	0.207875	+	0.978155i	$0.433345\pi$
$692$		0			0
$693$		0			0
$694$	12.0000			0.455514
$695$	4.46410	−	0.267949i	0.169333	−	0.0101639i
$696$	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	0.999908	−	0.0135434i	$-0.00431112\pi$
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	−0.511683	+	0.859174i	$0.670978\pi$
$710$	−18.6603	+	12.3205i	−0.700307	+	0.462380i
$711$	−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	$-0.0948328\pi$
$719$	6.00000	+	10.3923i	0.223762	+	0.387568i	−0.732185	+	0.681106i	$0.761499\pi$
$720$	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
$725$	9.92820	−	1.19615i	0.368724	−	0.0444240i
$726$	12.5000	+	21.6506i	0.463919	+	0.803530i
$727$			40.0000i			1.48352i	0.670667	+	0.741759i	$0.266008\pi$
$727$			40.0000i			1.48352i	−0.670667	+	0.741759i	$0.733992\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−13.3923	+	0.803848i	−0.495671	+	0.0297517i
$731$	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	−0.105010	−	0.994471i	$-0.533487\pi$
$733$	19.0526	−	11.0000i	0.703722	−	0.406294i	0.808732	+	0.588177i	$0.200154\pi$
$734$		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	0.104078	+	0.994569i	$0.466811\pi$
$739$	−22.0000	+	38.1051i	−0.809283	+	1.40172i	−0.913361	+	0.407150i	$0.866523\pi$
$740$	−0.535898	−	8.92820i	−0.0197000	−	0.328207i
$741$	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
$745$	17.2487	+	26.1244i	0.631944	+	0.957122i
$746$		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	0.954485	−	0.298259i	$-0.0964058\pi$
$751$	6.00000	+	10.3923i	0.218943	+	0.379221i	−0.735542	+	0.677479i	$0.763072\pi$
$752$		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
$760$	−33.5885	+	22.1769i	−1.21838	+	0.804441i
$761$	11.0000	+	19.0526i	0.398750	+	0.690655i	0.993572	−	0.113203i	$-0.0361109\pi$
$761$	11.0000	+	19.0526i	0.398750	+	0.690655i	−0.594822	+	0.803857i	$0.702778\pi$
$762$			20.0000i			0.724524i
$763$		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
$767$	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	$-0.394788\pi$
$769$	18.0000			0.649097			0.324548	+	0.945869i	$0.394788\pi$
$770$		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	0.0772449	−	0.997012i	$-0.475388\pi$
$773$	−20.7846	−	12.0000i	−0.747570	−	0.431610i	−0.824815	+	0.565402i	$0.808721\pi$
$774$	2.00000	−	3.46410i	0.0718885	−	0.124515i
$775$	19.6410	−	45.9808i	0.705526	−	1.65168i
$776$	−6.00000			−0.215387
$777$		0			0
$778$		−	26.0000i		−	0.932145i
$779$	−6.00000	−	10.3923i	−0.214972	−	0.372343i
$780$	2.46410	+	3.73205i	0.0882290	+	0.133629i
$781$	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	0.436987	−	0.899468i	$-0.356046\pi$
$787$	−3.46410	−	2.00000i	−0.123482	−	0.0712923i	−0.560469	+	0.828176i	$0.689379\pi$
$788$	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
$795$	−7.39230	−	11.1962i	−0.262178	−	0.397087i
$796$	7.00000	+	12.1244i	0.248108	+	0.429736i
$797$			16.0000i			0.566749i	0.959009	+	0.283375i	$0.0914540\pi$
$797$			16.0000i			0.566749i	−0.959009	+	0.283375i	$0.908546\pi$
$798$		0			0
$799$		0			0
$800$	−22.9904	−	9.82051i	−0.812833	−	0.347207i
$801$	−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	−0.979739	−	0.200279i	$-0.935815\pi$
$809$	−9.00000	+	15.5885i	−0.316423	+	0.548061i	0.663316	+	0.748340i	$0.269149\pi$
$810$	−0.133975	−	2.23205i	−0.00470739	−	0.0784263i
$811$	34.0000			1.19390			0.596951	−	0.802278i	$-0.296379\pi$
$811$	34.0000			1.19390			0.596951	+	0.802278i	$0.296379\pi$
$812$		0			0
$813$		−	14.0000i		−	0.491001i
$814$	−12.0000	−	20.7846i	−0.420600	−	0.728500i
$815$	−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
$818$			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	0.882948	−	0.469471i	$-0.155555\pi$
$821$	1.00000	+	1.73205i	0.0349002	+	0.0604490i	−0.848048	+	0.529920i	$0.822222\pi$
$822$	5.19615	+	3.00000i	0.181237	+	0.104637i
$823$	−38.1051	−	22.0000i	−1.32826	−	0.766872i	−0.343230	−	0.939251i	$-0.611521\pi$
$823$	−38.1051	−	22.0000i	−1.32826	−	0.766872i	−0.985031	+	0.172379i	$0.944854\pi$
$824$	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	$-0.866560\pi$
$829$	−3.00000	+	5.19615i	−0.104194	+	0.180470i	0.809214	+	0.587513i	$0.199893\pi$
$830$	−9.85641	−	14.9282i	−0.342121	−	0.518165i
$831$	14.0000	+	24.2487i	0.485655	+	0.841178i
$832$			14.0000i			0.485363i
$833$		0			0
$834$	2.00000			0.0692543
$835$	1.60770	+	26.7846i	0.0556366	+	0.926920i
$836$	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	$-0.566417\pi$
$839$	−12.0000			−0.414286			−0.207143	+	0.978311i	$0.566417\pi$
$840$		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
$845$	−20.0885	+	1.20577i	−0.691064	+	0.0414798i
$846$		0			0
$847$		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
$851$		0			0
$852$	8.66025	−	5.00000i	0.296695	−	0.171297i
$853$			30.0000i			1.02718i	0.858036	+	0.513590i	$0.171685\pi$
$853$			30.0000i			1.02718i	−0.858036	+	0.513590i	$0.828315\pi$
$854$		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	$-0.467774\pi$
$857$	−20.7846	−	12.0000i	−0.709989	−	0.409912i	−0.811057	+	0.584967i	$0.801107\pi$
$858$	10.3923	+	6.00000i	0.354787	+	0.204837i
$859$	−13.0000	−	22.5167i	−0.443554	−	0.768259i	0.554396	−	0.832253i	$-0.312949\pi$
$859$	−13.0000	−	22.5167i	−0.443554	−	0.768259i	−0.997950	+	0.0639945i	$0.979616\pi$
$860$	−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	$-0.800609\pi$
$863$	−20.7846	+	12.0000i	−0.707516	+	0.408485i	0.102624	+	0.994720i	$0.467276\pi$
$864$	−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
$870$	4.46410	−	0.267949i	0.151347	−	0.00908433i
$871$	−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	$-0.645153\pi$
$877$	3.46410	−	2.00000i	0.116974	−	0.0675352i	0.557346	+	0.830281i	$0.311820\pi$
$878$	5.19615	+	3.00000i	0.175362	+	0.101245i
$879$	12.0000	−	20.7846i	0.404750	−	0.701047i
$880$	−13.3923	+	0.803848i	−0.451455	+	0.0270977i
$881$	14.0000			0.471672			0.235836	−	0.971793i	$-0.424217\pi$
$881$	14.0000			0.471672			0.235836	+	0.971793i	$0.424217\pi$
$882$		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
$885$	−14.9282	+	9.85641i	−0.501806	+	0.331319i
$886$	−2.00000	+	3.46410i	−0.0671913	+	0.116379i
$887$	−6.92820	+	4.00000i	−0.232626	+	0.134307i	−0.611783	−	0.791026i	$-0.709547\pi$
$887$	−6.92820	+	4.00000i	−0.232626	+	0.134307i	0.379157	+	0.925332i	$0.376214\pi$
$888$		−	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
$900$	−4.96410	+	0.598076i	−0.165470	+	0.0199359i
$901$	−12.0000	−	20.7846i	−0.399778	−	0.692436i
$902$		−	12.0000i		−	0.399556i
$903$		0			0
$904$	−18.0000			−0.598671
$905$	13.3923	−	0.803848i	0.445175	−	0.0267208i
$906$	4.00000	−	6.92820i	0.132891	−	0.230174i
$907$	13.8564	+	8.00000i	0.460094	+	0.265636i	0.712084	−	0.702094i	$-0.247752\pi$
$907$	13.8564	+	8.00000i	0.460094	+	0.265636i	−0.251990	+	0.967730i	$0.581085\pi$
$908$	−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
$915$	0.267949	+	4.46410i	0.00885813	+	0.147579i
$916$	10.0000			0.330409
$917$		0			0
$918$		−	4.00000i		−	0.132020i
$919$	14.0000	+	24.2487i	0.461817	+	0.799891i	0.999052	−	0.0435419i	$-0.0138642\pi$
$919$	14.0000	+	24.2487i	0.461817	+	0.799891i	−0.537234	+	0.843433i	$0.680531\pi$
$920$		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	$-0.240429\pi$
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	−0.957708	+	0.287742i	$0.907096\pi$
$930$	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
$935$	−44.7846	+	29.5692i	−1.46461	+	0.967017i
$936$	3.00000	+	5.19615i	0.0980581	+	0.169842i
$937$		−	2.00000i		−	0.0653372i	−0.999466	−	0.0326686i	$-0.989599\pi$
$937$		−	2.00000i		−	0.0653372i	0.999466	−	0.0326686i	$-0.0104006\pi$
$938$		0			0
$939$	−6.00000			−0.195803
$940$		0			0
$941$	21.0000	−	36.3731i	0.684580	−	1.18573i	−0.288988	−	0.957333i	$-0.593319\pi$
$941$	21.0000	−	36.3731i	0.684580	−	1.18573i	0.973568	−	0.228395i	$-0.0733479\pi$
$942$	−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	$-0.467792\pi$
$947$	31.1769	−	18.0000i	1.01311	−	0.584921i	0.912102	+	0.409964i	$0.134459\pi$
$948$	3.46410	+	2.00000i	0.112509	+	0.0649570i
$949$	6.00000	−	10.3923i	0.194768	−	0.337348i
$950$	−27.5885	−	11.7846i	−0.895088	−	0.382343i
$951$	−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
$955$	−22.1769	−	33.5885i	−0.717628	−	1.08690i
$956$	−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
$970$	−2.46410	−	3.73205i	−0.0791175	−	0.119829i
$971$	4.00000	+	6.92820i	0.128366	+	0.222337i	0.923044	−	0.384695i	$-0.125693\pi$
$971$	4.00000	+	6.92820i	0.128366	+	0.222337i	−0.794678	+	0.607032i	$0.792360\pi$
$972$			1.00000i			0.0320750i
$973$		0			0
$974$	12.0000			0.384505
$975$	−3.92820	+	9.19615i	−0.125803	+	0.294513i
$976$	−1.00000	+	1.73205i	−0.0320092	+	0.0554416i
$977$	25.9808	+	15.0000i	0.831198	+	0.479893i	0.854263	−	0.519841i	$-0.174009\pi$
$977$	25.9808	+	15.0000i	0.831198	+	0.479893i	−0.0230645	+	0.999734i	$0.507342\pi$
$978$	−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	0.130465	−	0.991453i	$-0.458353\pi$
$983$	−20.7846	−	12.0000i	−0.662926	−	0.382741i	−0.793391	+	0.608712i	$0.791686\pi$
$984$	3.00000	−	5.19615i	0.0956365	−	0.165647i
$985$	0.267949	+	4.46410i	0.00853757	+	0.142238i
$986$	8.00000			0.254772
$987$		0			0
$988$		−	12.0000i		−	0.381771i
$989$		0			0
$990$	−11.1962	+	7.39230i	−0.355837	+	0.234943i
$991$	−2.00000	+	3.46410i	−0.0635321	+	0.110041i	−0.896042	−	0.443969i	$-0.853570\pi$
$991$	−2.00000	+	3.46410i	−0.0635321	+	0.110041i	0.832510	+	0.554010i	$0.186903\pi$
$992$	−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	0.679549	−	0.733630i	$-0.262175\pi$
$997$	12.1244	+	7.00000i	0.383982	+	0.221692i	−0.295567	+	0.955322i	$0.595509\pi$
$998$	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.a.214.2		4
5.4	even	2	inner	735.2.q.a.214.1		4
7.2	even	3	inner	735.2.q.a.79.1		4
7.3	odd	6		735.2.d.a.589.2		2
7.4	even	3		105.2.d.a.64.2	yes	2
7.5	odd	6		735.2.q.b.79.1		4
7.6	odd	2		735.2.q.b.214.2		4
21.11	odd	6		315.2.d.c.64.1		2
21.17	even	6		2205.2.d.f.1324.1		2
28.11	odd	6		1680.2.t.f.1009.1		2
35.3	even	12		3675.2.a.l.1.1		1
35.4	even	6		105.2.d.a.64.1	✓	2
35.9	even	6	inner	735.2.q.a.79.2		4
35.17	even	12		3675.2.a.d.1.1		1
35.18	odd	12		525.2.a.c.1.1		1
35.19	odd	6		735.2.q.b.79.2		4
35.24	odd	6		735.2.d.a.589.1		2
35.32	odd	12		525.2.a.b.1.1		1
35.34	odd	2		735.2.q.b.214.1		4
84.11	even	6		5040.2.t.e.1009.2		2
105.32	even	12		1575.2.a.i.1.1		1
105.53	even	12		1575.2.a.e.1.1		1
105.59	even	6		2205.2.d.f.1324.2		2
105.74	odd	6		315.2.d.c.64.2		2
140.39	odd	6		1680.2.t.f.1009.2		2
140.67	even	12		8400.2.a.bj.1.1		1
140.123	even	12		8400.2.a.ch.1.1		1
420.179	even	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	35.4	even	6
105.2.d.a.64.2	yes	2	7.4	even	3
315.2.d.c.64.1		2	21.11	odd	6
315.2.d.c.64.2		2	105.74	odd	6
525.2.a.b.1.1		1	35.32	odd	12
525.2.a.c.1.1		1	35.18	odd	12
735.2.d.a.589.1		2	35.24	odd	6
735.2.d.a.589.2		2	7.3	odd	6
735.2.q.a.79.1		4	7.2	even	3	inner
735.2.q.a.79.2		4	35.9	even	6	inner
735.2.q.a.214.1		4	5.4	even	2	inner
735.2.q.a.214.2		4	1.1	even	1	trivial
735.2.q.b.79.1		4	7.5	odd	6
735.2.q.b.79.2		4	35.19	odd	6
735.2.q.b.214.1		4	35.34	odd	2
735.2.q.b.214.2		4	7.6	odd	2
1575.2.a.e.1.1		1	105.53	even	12
1575.2.a.i.1.1		1	105.32	even	12
1680.2.t.f.1009.1		2	28.11	odd	6
1680.2.t.f.1009.2		2	140.39	odd	6
2205.2.d.f.1324.1		2	21.17	even	6
2205.2.d.f.1324.2		2	105.59	even	6
3675.2.a.d.1.1		1	35.17	even	12
3675.2.a.l.1.1		1	35.3	even	12
5040.2.t.e.1009.1		2	420.179	even	6
5040.2.t.e.1009.2		2	84.11	even	6
8400.2.a.bj.1.1		1	140.67	even	12
8400.2.a.ch.1.1		1	140.123	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.23205 + 0.133975i) q^{5} -1.00000 q^{6} +3.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.23205 + 0.133975i) q^{5} -1.00000 q^{6} +3.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.86603 + 1.23205i) 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} +(4.96410 - 0.598076i) q^{25} +(-1.00000 - 1.73205i) q^{26} -1.00000i q^{27} +2.00000 q^{29} +(2.23205 - 0.133975i) 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} +(-0.401924 - 6.69615i) q^{40} +2.00000 q^{41} -4.00000i q^{43} +(3.00000 + 5.19615i) q^{44} +(-1.23205 - 1.86603i) 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} +(-1.86603 + 1.23205i) q^{60} +(1.00000 + 1.73205i) q^{61} -10.0000i q^{62} -7.00000 q^{64} +(0.267949 + 4.46410i) 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} +(-4.59808 - 1.96410i) q^{75} +6.00000 q^{76} +2.00000i q^{78} +(2.00000 + 3.46410i) 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} +(-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} +(7.39230 + 11.1962i) 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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