LMFDB - Embedded newform 1078.2.e.h.177.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(67,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("1078.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.e (of order $3$, 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:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1078.177
Dual form			1078.2.e.h.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.00000 + 1.73205i) q^{12} -4.00000 q^{13} +4.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{18} +(-2.00000 + 3.46410i) q^{19} +2.00000 q^{20} -1.00000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(1.00000 + 1.73205i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-2.00000 + 3.46410i) q^{26} -4.00000 q^{27} +2.00000 q^{29} +(2.00000 - 3.46410i) q^{30} +(5.00000 + 8.66025i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{33} +1.00000 q^{36} +(3.00000 - 5.19615i) q^{37} +(2.00000 + 3.46410i) q^{38} +(4.00000 + 6.92820i) q^{39} +(1.00000 - 1.73205i) q^{40} -4.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-1.00000 - 1.73205i) q^{45} +(2.00000 + 3.46410i) q^{46} +(-5.00000 + 8.66025i) q^{47} +2.00000 q^{48} +1.00000 q^{50} +(2.00000 + 3.46410i) q^{52} +(7.00000 + 12.1244i) q^{53} +(-2.00000 + 3.46410i) q^{54} +2.00000 q^{55} +8.00000 q^{57} +(1.00000 - 1.73205i) q^{58} +(-5.00000 - 8.66025i) q^{59} +(-2.00000 - 3.46410i) q^{60} +(4.00000 - 6.92820i) q^{61} +10.0000 q^{62} +1.00000 q^{64} +(4.00000 - 6.92820i) q^{65} +(1.00000 + 1.73205i) q^{66} +(-4.00000 - 6.92820i) q^{67} +8.00000 q^{69} -4.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-2.00000 - 3.46410i) q^{73} +(-3.00000 - 5.19615i) q^{74} +(1.00000 - 1.73205i) q^{75} +4.00000 q^{76} +8.00000 q^{78} +(-8.00000 + 13.8564i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(5.50000 + 9.52628i) q^{81} +4.00000 q^{83} +(-2.00000 + 3.46410i) q^{86} +(-2.00000 - 3.46410i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-5.00000 + 8.66025i) q^{89} -2.00000 q^{90} +4.00000 q^{92} +(10.0000 - 17.3205i) q^{93} +(5.00000 + 8.66025i) q^{94} +(-4.00000 - 6.92820i) q^{95} +(1.00000 - 1.73205i) q^{96} +6.00000 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 4 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - 4 * q^6 - 2 * q^8 - q^9	$ 2 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 4 q^{6} - 2 q^{8} - q^{9} + 2 q^{10} - q^{11} - 2 q^{12} - 8 q^{13} + 8 q^{15} - q^{16} + q^{18} - 4 q^{19} + 4 q^{20} - 2 q^{22} - 4 q^{23} + 2 q^{24} + q^{25} - 4 q^{26} - 8 q^{27} + 4 q^{29} + 4 q^{30} + 10 q^{31} + q^{32} - 2 q^{33} + 2 q^{36} + 6 q^{37} + 4 q^{38} + 8 q^{39} + 2 q^{40} - 8 q^{43} - q^{44} - 2 q^{45} + 4 q^{46} - 10 q^{47} + 4 q^{48} + 2 q^{50} + 4 q^{52} + 14 q^{53} - 4 q^{54} + 4 q^{55} + 16 q^{57} + 2 q^{58} - 10 q^{59} - 4 q^{60} + 8 q^{61} + 20 q^{62} + 2 q^{64} + 8 q^{65} + 2 q^{66} - 8 q^{67} + 16 q^{69} - 8 q^{71} + q^{72} - 4 q^{73} - 6 q^{74} + 2 q^{75} + 8 q^{76} + 16 q^{78} - 16 q^{79} - 2 q^{80} + 11 q^{81} + 8 q^{83} - 4 q^{86} - 4 q^{87} + q^{88} - 10 q^{89} - 4 q^{90} + 8 q^{92} + 20 q^{93} + 10 q^{94} - 8 q^{95} + 2 q^{96} + 12 q^{97} + 2 q^{99}+O(q^{100}) $ 2 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - 4 * q^6 - 2 * q^8 - q^9 + 2 * q^10 - q^11 - 2 * q^12 - 8 * q^13 + 8 * q^15 - q^16 + q^18 - 4 * q^19 + 4 * q^20 - 2 * q^22 - 4 * q^23 + 2 * q^24 + q^25 - 4 * q^26 - 8 * q^27 + 4 * q^29 + 4 * q^30 + 10 * q^31 + q^32 - 2 * q^33 + 2 * q^36 + 6 * q^37 + 4 * q^38 + 8 * q^39 + 2 * q^40 - 8 * q^43 - q^44 - 2 * q^45 + 4 * q^46 - 10 * q^47 + 4 * q^48 + 2 * q^50 + 4 * q^52 + 14 * q^53 - 4 * q^54 + 4 * q^55 + 16 * q^57 + 2 * q^58 - 10 * q^59 - 4 * q^60 + 8 * q^61 + 20 * q^62 + 2 * q^64 + 8 * q^65 + 2 * q^66 - 8 * q^67 + 16 * q^69 - 8 * q^71 + q^72 - 4 * q^73 - 6 * q^74 + 2 * q^75 + 8 * q^76 + 16 * q^78 - 16 * q^79 - 2 * q^80 + 11 * q^81 + 8 * q^83 - 4 * q^86 - 4 * q^87 + q^88 - 10 * q^89 - 4 * q^90 + 8 * q^92 + 20 * q^93 + 10 * q^94 - 8 * q^95 + 2 * q^96 + 12 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	−0.995782	−	0.0917517i	$-0.970753\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	0.418432	−	0.908248i	$-0.362580\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	0.550990	+	0.834512i	$0.314250\pi$
$6$	−2.00000			−0.816497
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	−1.00000	+	1.73205i	−0.288675	+	0.500000i
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$		0			0
$15$	4.00000			1.03280
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	−0.998899	−	0.0469020i	$-0.985065\pi$
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	0.540068	+	0.841621i	$0.318398\pi$
$20$	2.00000			0.447214
$21$		0			0
$22$	−1.00000			−0.213201
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$	1.00000	+	1.73205i	0.204124	+	0.353553i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−2.00000	+	3.46410i	−0.392232	+	0.679366i
$27$	−4.00000			−0.769800
$28$		0			0
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$	2.00000	−	3.46410i	0.365148	−	0.632456i
$31$	5.00000	+	8.66025i	0.898027	+	1.55543i	0.830014	+	0.557743i	$0.188333\pi$
$31$	5.00000	+	8.66025i	0.898027	+	1.55543i	0.0680129	+	0.997684i	$0.478334\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$		0			0
$35$		0			0
$36$	1.00000			0.166667
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	−0.506772	−	0.862080i	$-0.669162\pi$
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	0.999969	+	0.00783774i	$0.00249486\pi$
$38$	2.00000	+	3.46410i	0.324443	+	0.561951i
$39$	4.00000	+	6.92820i	0.640513	+	1.10940i
$40$	1.00000	−	1.73205i	0.158114	−	0.273861i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$	−1.00000	−	1.73205i	−0.149071	−	0.258199i
$46$	2.00000	+	3.46410i	0.294884	+	0.510754i
$47$	−5.00000	+	8.66025i	−0.729325	+	1.26323i	0.227844	+	0.973698i	$0.426832\pi$
$47$	−5.00000	+	8.66025i	−0.729325	+	1.26323i	−0.957169	+	0.289530i	$0.906501\pi$
$48$	2.00000			0.288675
$49$		0			0
$50$	1.00000			0.141421
$51$		0			0
$52$	2.00000	+	3.46410i	0.277350	+	0.480384i
$53$	7.00000	+	12.1244i	0.961524	+	1.66541i	0.718677	+	0.695344i	$0.244748\pi$
$53$	7.00000	+	12.1244i	0.961524	+	1.66541i	0.242846	+	0.970065i	$0.421919\pi$
$54$	−2.00000	+	3.46410i	−0.272166	+	0.471405i
$55$	2.00000			0.269680
$56$		0			0
$57$	8.00000			1.05963
$58$	1.00000	−	1.73205i	0.131306	−	0.227429i
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	−0.982894	−	0.184172i	$-0.941040\pi$
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	0.331949	−	0.943297i	$-0.392294\pi$
$60$	−2.00000	−	3.46410i	−0.258199	−	0.447214i
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	−0.487753	−	0.872982i	$-0.662183\pi$
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	0.999901	−	0.0140840i	$-0.00448323\pi$
$62$	10.0000			1.27000
$63$		0			0
$64$	1.00000			0.125000
$65$	4.00000	−	6.92820i	0.496139	−	0.859338i
$66$	1.00000	+	1.73205i	0.123091	+	0.213201i
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$		0			0
$69$	8.00000			0.963087
$70$		0			0
$71$	−4.00000			−0.474713			−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000			−0.474713			−0.237356	+	0.971423i	$0.576281\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−2.00000	−	3.46410i	−0.234082	−	0.405442i	0.724923	−	0.688830i	$-0.241875\pi$
$73$	−2.00000	−	3.46410i	−0.234082	−	0.405442i	−0.959006	+	0.283387i	$0.908542\pi$
$74$	−3.00000	−	5.19615i	−0.348743	−	0.604040i
$75$	1.00000	−	1.73205i	0.115470	−	0.200000i
$76$	4.00000			0.458831
$77$		0			0
$78$	8.00000			0.905822
$79$	−8.00000	+	13.8564i	−0.900070	+	1.55897i	−0.0726692	+	0.997356i	$0.523152\pi$
$79$	−8.00000	+	13.8564i	−0.900070	+	1.55897i	−0.827401	+	0.561611i	$0.810182\pi$
$80$	−1.00000	−	1.73205i	−0.111803	−	0.193649i
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$		0			0
$83$	4.00000			0.439057			0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000			0.439057			0.219529	+	0.975606i	$0.429548\pi$
$84$		0			0
$85$		0			0
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$	−2.00000	−	3.46410i	−0.214423	−	0.371391i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	0.469389	+	0.882992i	$0.344474\pi$
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	−0.999388	+	0.0349934i	$0.988859\pi$
$90$	−2.00000			−0.210819
$91$		0			0
$92$	4.00000			0.417029
$93$	10.0000	−	17.3205i	1.03695	−	1.79605i
$94$	5.00000	+	8.66025i	0.515711	+	0.893237i
$95$	−4.00000	−	6.92820i	−0.410391	−	0.710819i
$96$	1.00000	−	1.73205i	0.102062	−	0.176777i
$97$	6.00000			0.609208			0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000			0.609208			0.304604	+	0.952479i	$0.401476\pi$
$98$		0			0
$99$	1.00000			0.100504
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	−0.993258	−	0.115924i	$-0.963017\pi$
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	0.396236	−	0.918149i	$-0.370316\pi$
$102$		0			0
$103$	−1.00000	+	1.73205i	−0.0985329	+	0.170664i	−0.911078	−	0.412235i	$-0.864748\pi$
$103$	−1.00000	+	1.73205i	−0.0985329	+	0.170664i	0.812545	+	0.582899i	$0.198082\pi$
$104$	4.00000			0.392232
$105$		0			0
$106$	14.0000			1.35980
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	−0.415432	−	0.909624i	$-0.636370\pi$
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	0.995474	−	0.0950377i	$-0.0302972\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$	7.00000	+	12.1244i	0.670478	+	1.16130i	0.977769	+	0.209687i	$0.0672444\pi$
$109$	7.00000	+	12.1244i	0.670478	+	1.16130i	−0.307290	+	0.951616i	$0.599422\pi$
$110$	1.00000	−	1.73205i	0.0953463	−	0.165145i
$111$	−12.0000			−1.13899
$112$		0			0
$113$	−14.0000			−1.31701			−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000			−1.31701			−0.658505	+	0.752577i	$0.728811\pi$
$114$	4.00000	−	6.92820i	0.374634	−	0.648886i
$115$	−4.00000	−	6.92820i	−0.373002	−	0.646058i
$116$	−1.00000	−	1.73205i	−0.0928477	−	0.160817i
$117$	2.00000	−	3.46410i	0.184900	−	0.320256i
$118$	−10.0000			−0.920575
$119$		0			0
$120$	−4.00000			−0.365148
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−4.00000	−	6.92820i	−0.362143	−	0.627250i
$123$		0			0
$124$	5.00000	−	8.66025i	0.449013	−	0.777714i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	4.00000	+	6.92820i	0.352180	+	0.609994i
$130$	−4.00000	−	6.92820i	−0.350823	−	0.607644i
$131$	−4.00000	+	6.92820i	−0.349482	+	0.605320i	−0.986157	−	0.165812i	$-0.946976\pi$
$131$	−4.00000	+	6.92820i	−0.349482	+	0.605320i	0.636676	+	0.771132i	$0.280309\pi$
$132$	2.00000			0.174078
$133$		0			0
$134$	−8.00000			−0.691095
$135$	4.00000	−	6.92820i	0.344265	−	0.596285i
$136$		0			0
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	0.708942	−	0.705266i	$-0.249173\pi$
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$138$	4.00000	−	6.92820i	0.340503	−	0.589768i
$139$	20.0000			1.69638			0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000			1.69638			0.848189	+	0.529694i	$0.177693\pi$
$140$		0			0
$141$	20.0000			1.68430
$142$	−2.00000	+	3.46410i	−0.167836	+	0.290701i
$143$	2.00000	+	3.46410i	0.167248	+	0.289683i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−2.00000	+	3.46410i	−0.166091	+	0.287678i
$146$	−4.00000			−0.331042
$147$		0			0
$148$	−6.00000			−0.493197
$149$	−11.0000	+	19.0526i	−0.901155	+	1.56085i	−0.0751583	+	0.997172i	$0.523946\pi$
$149$	−11.0000	+	19.0526i	−0.901155	+	1.56085i	−0.825997	+	0.563675i	$0.809387\pi$
$150$	−1.00000	−	1.73205i	−0.0816497	−	0.141421i
$151$	−8.00000	−	13.8564i	−0.651031	−	1.12762i	−0.982873	−	0.184284i	$-0.941004\pi$
$151$	−8.00000	−	13.8564i	−0.651031	−	1.12762i	0.331842	−	0.943335i	$-0.392330\pi$
$152$	2.00000	−	3.46410i	0.162221	−	0.280976i
$153$		0			0
$154$		0			0
$155$	−20.0000			−1.60644
$156$	4.00000	−	6.92820i	0.320256	−	0.554700i
$157$	−5.00000	−	8.66025i	−0.399043	−	0.691164i	0.594565	−	0.804048i	$-0.297324\pi$
$157$	−5.00000	−	8.66025i	−0.399043	−	0.691164i	−0.993608	+	0.112884i	$0.963991\pi$
$158$	8.00000	+	13.8564i	0.636446	+	1.10236i
$159$	14.0000	−	24.2487i	1.11027	−	1.92305i
$160$	−2.00000			−0.158114
$161$		0			0
$162$	11.0000			0.864242
$163$	−12.0000	+	20.7846i	−0.939913	+	1.62798i	−0.174282	+	0.984696i	$0.555760\pi$
$163$	−12.0000	+	20.7846i	−0.939913	+	1.62798i	−0.765631	+	0.643280i	$0.777573\pi$
$164$		0			0
$165$	−2.00000	−	3.46410i	−0.155700	−	0.269680i
$166$	2.00000	−	3.46410i	0.155230	−	0.268866i
$167$	−8.00000			−0.619059			−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000			−0.619059			−0.309529	+	0.950890i	$0.600171\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$	−2.00000	−	3.46410i	−0.152944	−	0.264906i
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	−2.00000	+	3.46410i	−0.152057	+	0.263371i	−0.931984	−	0.362500i	$-0.881923\pi$
$173$	−2.00000	+	3.46410i	−0.152057	+	0.263371i	0.779926	+	0.625871i	$0.215256\pi$
$174$	−4.00000			−0.303239
$175$		0			0
$176$	1.00000			0.0753778
$177$	−10.0000	+	17.3205i	−0.751646	+	1.30189i
$178$	5.00000	+	8.66025i	0.374766	+	0.649113i
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	0.549825	−	0.835280i	$-0.314694\pi$
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	−0.998286	+	0.0585225i	$0.981361\pi$
$180$	−1.00000	+	1.73205i	−0.0745356	+	0.129099i
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$		0			0
$183$	−16.0000			−1.18275
$184$	2.00000	−	3.46410i	0.147442	−	0.255377i
$185$	6.00000	+	10.3923i	0.441129	+	0.764057i
$186$	−10.0000	−	17.3205i	−0.733236	−	1.27000i
$187$		0			0
$188$	10.0000			0.729325
$189$		0			0
$190$	−8.00000			−0.580381
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	−0.973674	−	0.227946i	$-0.926799\pi$
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	0.684244	+	0.729253i	$0.260132\pi$
$192$	−1.00000	−	1.73205i	−0.0721688	−	0.125000i
$193$	3.00000	+	5.19615i	0.215945	+	0.374027i	0.953564	−	0.301189i	$-0.0973836\pi$
$193$	3.00000	+	5.19615i	0.215945	+	0.374027i	−0.737620	+	0.675216i	$0.764050\pi$
$194$	3.00000	−	5.19615i	0.215387	−	0.373062i
$195$	−16.0000			−1.14578
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	0.500000	−	0.866025i	0.0355335	−	0.0615457i
$199$	7.00000	+	12.1244i	0.496217	+	0.859473i	0.999990	−	0.00436292i	$-0.00138876\pi$
$199$	7.00000	+	12.1244i	0.496217	+	0.859473i	−0.503774	+	0.863836i	$0.668055\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−8.00000	+	13.8564i	−0.564276	+	0.977356i
$202$	−12.0000			−0.844317
$203$		0			0
$204$		0			0
$205$		0			0
$206$	1.00000	+	1.73205i	0.0696733	+	0.120678i
$207$	−2.00000	−	3.46410i	−0.139010	−	0.240772i
$208$	2.00000	−	3.46410i	0.138675	−	0.240192i
$209$	4.00000			0.276686
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$	7.00000	−	12.1244i	0.480762	−	0.832704i
$213$	4.00000	+	6.92820i	0.274075	+	0.474713i
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	4.00000	−	6.92820i	0.272798	−	0.472500i
$216$	4.00000			0.272166
$217$		0			0
$218$	14.0000			0.948200
$219$	−4.00000	+	6.92820i	−0.270295	+	0.468165i
$220$	−1.00000	−	1.73205i	−0.0674200	−	0.116775i
$221$		0			0
$222$	−6.00000	+	10.3923i	−0.402694	+	0.697486i
$223$	−14.0000			−0.937509			−0.468755	−	0.883328i	$-0.655297\pi$
$223$	−14.0000			−0.937509			−0.468755	+	0.883328i	$0.655297\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$	−7.00000	+	12.1244i	−0.465633	+	0.806500i
$227$	−4.00000	−	6.92820i	−0.265489	−	0.459841i	0.702202	−	0.711977i	$-0.252200\pi$
$227$	−4.00000	−	6.92820i	−0.265489	−	0.459841i	−0.967692	+	0.252136i	$0.918867\pi$
$228$	−4.00000	−	6.92820i	−0.264906	−	0.458831i
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	−0.652183	−	0.758062i	$-0.726147\pi$
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	0.982592	+	0.185776i	$0.0594799\pi$
$230$	−8.00000			−0.527504
$231$		0			0
$232$	−2.00000			−0.131306
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$	−2.00000	−	3.46410i	−0.130744	−	0.226455i
$235$	−10.0000	−	17.3205i	−0.652328	−	1.12987i
$236$	−5.00000	+	8.66025i	−0.325472	+	0.563735i
$237$	32.0000			2.07862
$238$		0			0
$239$	−8.00000			−0.517477			−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000			−0.517477			−0.258738	+	0.965947i	$0.583307\pi$
$240$	−2.00000	+	3.46410i	−0.129099	+	0.223607i
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	0.707953	−	0.706260i	$-0.249619\pi$
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	−0.965615	+	0.259975i	$0.916286\pi$
$242$	0.500000	+	0.866025i	0.0321412	+	0.0556702i
$243$	5.00000	−	8.66025i	0.320750	−	0.555556i
$244$	−8.00000			−0.512148
$245$		0			0
$246$		0			0
$247$	8.00000	−	13.8564i	0.509028	−	0.881662i
$248$	−5.00000	−	8.66025i	−0.317500	−	0.549927i
$249$	−4.00000	−	6.92820i	−0.253490	−	0.439057i
$250$	−6.00000	+	10.3923i	−0.379473	+	0.657267i
$251$	−26.0000			−1.64111			−0.820553	−	0.571571i	$-0.806334\pi$
$251$	−26.0000			−1.64111			−0.820553	+	0.571571i	$0.806334\pi$
$252$		0			0
$253$	4.00000			0.251478
$254$	−8.00000	+	13.8564i	−0.501965	+	0.869428i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	−0.895528	−	0.445005i	$-0.853202\pi$
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	0.833150	+	0.553047i	$0.186535\pi$
$258$	8.00000			0.498058
$259$		0			0
$260$	−8.00000			−0.496139
$261$	−1.00000	+	1.73205i	−0.0618984	+	0.107211i
$262$	4.00000	+	6.92820i	0.247121	+	0.428026i
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	0.952517	+	0.304487i	$0.0984850\pi$
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	−0.212565	+	0.977147i	$0.568182\pi$
$264$	1.00000	−	1.73205i	0.0615457	−	0.106600i
$265$	−28.0000			−1.72003
$266$		0			0
$267$	20.0000			1.22398
$268$	−4.00000	+	6.92820i	−0.244339	+	0.423207i
$269$	−7.00000	−	12.1244i	−0.426798	−	0.739235i	0.569789	−	0.821791i	$-0.307025\pi$
$269$	−7.00000	−	12.1244i	−0.426798	−	0.739235i	−0.996586	+	0.0825561i	$0.973692\pi$
$270$	−4.00000	−	6.92820i	−0.243432	−	0.421637i
$271$	14.0000	−	24.2487i	0.850439	−	1.47300i	−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	14.0000	−	24.2487i	0.850439	−	1.47300i	0.880812	−	0.473466i	$-0.156997\pi$
$272$		0			0
$273$		0			0
$274$	−6.00000			−0.362473
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	−4.00000	−	6.92820i	−0.240772	−	0.417029i
$277$	−3.00000	−	5.19615i	−0.180253	−	0.312207i	0.761714	−	0.647913i	$-0.224358\pi$
$277$	−3.00000	−	5.19615i	−0.180253	−	0.312207i	−0.941966	+	0.335707i	$0.891025\pi$
$278$	10.0000	−	17.3205i	0.599760	−	1.03882i
$279$	−10.0000			−0.598684
$280$		0			0
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$	10.0000	−	17.3205i	0.595491	−	1.03142i
$283$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$283$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$284$	2.00000	+	3.46410i	0.118678	+	0.205557i
$285$	−8.00000	+	13.8564i	−0.473879	+	0.820783i
$286$	4.00000			0.236525
$287$		0			0
$288$	−1.00000			−0.0589256
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	2.00000	+	3.46410i	0.117444	+	0.203419i
$291$	−6.00000	−	10.3923i	−0.351726	−	0.609208i
$292$	−2.00000	+	3.46410i	−0.117041	+	0.202721i
$293$		0			0			−	1.00000i	$-0.5\pi$
$293$		0			0				1.00000i	$0.5\pi$
$294$		0			0
$295$	20.0000			1.16445
$296$	−3.00000	+	5.19615i	−0.174371	+	0.302020i
$297$	2.00000	+	3.46410i	0.116052	+	0.201008i
$298$	11.0000	+	19.0526i	0.637213	+	1.10369i
$299$	8.00000	−	13.8564i	0.462652	−	0.801337i
$300$	−2.00000			−0.115470
$301$		0			0
$302$	−16.0000			−0.920697
$303$	−12.0000	+	20.7846i	−0.689382	+	1.19404i
$304$	−2.00000	−	3.46410i	−0.114708	−	0.198680i
$305$	8.00000	+	13.8564i	0.458079	+	0.793416i
$306$		0			0
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$		0			0
$309$	4.00000			0.227552
$310$	−10.0000	+	17.3205i	−0.567962	+	0.983739i
$311$	3.00000	+	5.19615i	0.170114	+	0.294647i	0.938460	−	0.345389i	$-0.112253\pi$
$311$	3.00000	+	5.19615i	0.170114	+	0.294647i	−0.768345	+	0.640036i	$0.778920\pi$
$312$	−4.00000	−	6.92820i	−0.226455	−	0.392232i
$313$	3.00000	−	5.19615i	0.169570	−	0.293704i	−0.768699	−	0.639611i	$-0.779095\pi$
$313$	3.00000	−	5.19615i	0.169570	−	0.293704i	0.938269	+	0.345907i	$0.112429\pi$
$314$	−10.0000			−0.564333
$315$		0			0
$316$	16.0000			0.900070
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$	−14.0000	−	24.2487i	−0.785081	−	1.35980i
$319$	−1.00000	−	1.73205i	−0.0559893	−	0.0969762i
$320$	−1.00000	+	1.73205i	−0.0559017	+	0.0968246i
$321$	−24.0000			−1.33955
$322$		0			0
$323$		0			0
$324$	5.50000	−	9.52628i	0.305556	−	0.529238i
$325$	−2.00000	−	3.46410i	−0.110940	−	0.192154i
$326$	12.0000	+	20.7846i	0.664619	+	1.15115i
$327$	14.0000	−	24.2487i	0.774202	−	1.34096i
$328$		0			0
$329$		0			0
$330$	−4.00000			−0.220193
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	−0.448649	−	0.893708i	$-0.648095\pi$
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	0.998298	−	0.0583130i	$-0.0185721\pi$
$332$	−2.00000	−	3.46410i	−0.109764	−	0.190117i
$333$	3.00000	+	5.19615i	0.164399	+	0.284747i
$334$	−4.00000	+	6.92820i	−0.218870	+	0.379094i
$335$	16.0000			0.874173
$336$		0			0
$337$	−34.0000			−1.85210			−0.926049	−	0.377403i	$-0.876817\pi$
$337$	−34.0000			−1.85210			−0.926049	+	0.377403i	$0.876817\pi$
$338$	1.50000	−	2.59808i	0.0815892	−	0.141317i
$339$	14.0000	+	24.2487i	0.760376	+	1.31701i
$340$		0			0
$341$	5.00000	−	8.66025i	0.270765	−	0.468979i
$342$	−4.00000			−0.216295
$343$		0			0
$344$	4.00000			0.215666
$345$	−8.00000	+	13.8564i	−0.430706	+	0.746004i
$346$	2.00000	+	3.46410i	0.107521	+	0.186231i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$	−2.00000	+	3.46410i	−0.107211	+	0.185695i
$349$	32.0000			1.71292			0.856460	−	0.516213i	$-0.172659\pi$
$349$	32.0000			1.71292			0.856460	+	0.516213i	$0.172659\pi$
$350$		0			0
$351$	16.0000			0.854017
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	−1.00000	−	1.73205i	−0.0532246	−	0.0921878i	0.838186	−	0.545385i	$-0.183617\pi$
$353$	−1.00000	−	1.73205i	−0.0532246	−	0.0921878i	−0.891410	+	0.453197i	$0.850283\pi$
$354$	10.0000	+	17.3205i	0.531494	+	0.920575i
$355$	4.00000	−	6.92820i	0.212298	−	0.367711i
$356$	10.0000			0.529999
$357$		0			0
$358$	−12.0000			−0.634220
$359$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$359$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$360$	1.00000	+	1.73205i	0.0527046	+	0.0912871i
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	7.00000	−	12.1244i	0.367912	−	0.637242i
$363$	2.00000			0.104973
$364$		0			0
$365$	8.00000			0.418739
$366$	−8.00000	+	13.8564i	−0.418167	+	0.724286i
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	0.529607	−	0.848243i	$-0.322339\pi$
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	−0.999404	+	0.0345320i	$0.989006\pi$
$368$	−2.00000	−	3.46410i	−0.104257	−	0.180579i
$369$		0			0
$370$	12.0000			0.623850
$371$		0			0
$372$	−20.0000			−1.03695
$373$	17.0000	−	29.4449i	0.880227	−	1.52460i	0.0291379	−	0.999575i	$-0.490724\pi$
$373$	17.0000	−	29.4449i	0.880227	−	1.52460i	0.851089	−	0.525022i	$-0.175943\pi$
$374$		0			0
$375$	12.0000	+	20.7846i	0.619677	+	1.07331i
$376$	5.00000	−	8.66025i	0.257855	−	0.446619i
$377$	−8.00000			−0.412021
$378$		0			0
$379$	8.00000			0.410932			0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000			0.410932			0.205466	+	0.978664i	$0.434129\pi$
$380$	−4.00000	+	6.92820i	−0.205196	+	0.355409i
$381$	16.0000	+	27.7128i	0.819705	+	1.41977i
$382$	4.00000	+	6.92820i	0.204658	+	0.354478i
$383$	−7.00000	+	12.1244i	−0.357683	+	0.619526i	−0.987573	−	0.157159i	$-0.949767\pi$
$383$	−7.00000	+	12.1244i	−0.357683	+	0.619526i	0.629890	+	0.776684i	$0.283100\pi$
$384$	−2.00000			−0.102062
$385$		0			0
$386$	6.00000			0.305392
$387$	2.00000	−	3.46410i	0.101666	−	0.176090i
$388$	−3.00000	−	5.19615i	−0.152302	−	0.263795i
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	0.998763	−	0.0497253i	$-0.0158346\pi$
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	−0.542445	+	0.840091i	$0.682501\pi$
$390$	−8.00000	+	13.8564i	−0.405096	+	0.701646i
$391$		0			0
$392$		0			0
$393$	16.0000			0.807093
$394$	−9.00000	+	15.5885i	−0.453413	+	0.785335i
$395$	−16.0000	−	27.7128i	−0.805047	−	1.39438i
$396$	−0.500000	−	0.866025i	−0.0251259	−	0.0435194i
$397$	−9.00000	+	15.5885i	−0.451697	+	0.782362i	−0.998492	−	0.0549046i	$-0.982515\pi$
$397$	−9.00000	+	15.5885i	−0.451697	+	0.782362i	0.546795	+	0.837267i	$0.315848\pi$
$398$	14.0000			0.701757
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	−5.00000	+	8.66025i	−0.249688	+	0.432472i	−0.963439	−	0.267927i	$-0.913661\pi$
$401$	−5.00000	+	8.66025i	−0.249688	+	0.432472i	0.713751	+	0.700399i	$0.246995\pi$
$402$	8.00000	+	13.8564i	0.399004	+	0.691095i
$403$	−20.0000	−	34.6410i	−0.996271	−	1.72559i
$404$	−6.00000	+	10.3923i	−0.298511	+	0.517036i
$405$	−22.0000			−1.09319
$406$		0			0
$407$	−6.00000			−0.297409
$408$		0			0
$409$	2.00000	+	3.46410i	0.0988936	+	0.171289i	0.911227	−	0.411905i	$-0.135136\pi$
$409$	2.00000	+	3.46410i	0.0988936	+	0.171289i	−0.812333	+	0.583193i	$0.801803\pi$
$410$		0			0
$411$	−6.00000	+	10.3923i	−0.295958	+	0.512615i
$412$	2.00000			0.0985329
$413$		0			0
$414$	−4.00000			−0.196589
$415$	−4.00000	+	6.92820i	−0.196352	+	0.340092i
$416$	−2.00000	−	3.46410i	−0.0980581	−	0.169842i
$417$	−20.0000	−	34.6410i	−0.979404	−	1.69638i
$418$	2.00000	−	3.46410i	0.0978232	−	0.169435i
$419$	−30.0000			−1.46560			−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000			−1.46560			−0.732798	+	0.680446i	$0.761786\pi$
$420$		0			0
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$	−2.00000	+	3.46410i	−0.0973585	+	0.168630i
$423$	−5.00000	−	8.66025i	−0.243108	−	0.421076i
$424$	−7.00000	−	12.1244i	−0.339950	−	0.588811i
$425$		0			0
$426$	8.00000			0.387601
$427$		0			0
$428$	−12.0000			−0.580042
$429$	4.00000	−	6.92820i	0.193122	−	0.334497i
$430$	−4.00000	−	6.92820i	−0.192897	−	0.334108i
$431$	8.00000	+	13.8564i	0.385346	+	0.667440i	0.991817	−	0.127666i	$-0.0407486\pi$
$431$	8.00000	+	13.8564i	0.385346	+	0.667440i	−0.606471	+	0.795106i	$0.707415\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	−10.0000			−0.480569			−0.240285	−	0.970702i	$-0.577241\pi$
$433$	−10.0000			−0.480569			−0.240285	+	0.970702i	$0.577241\pi$
$434$		0			0
$435$	8.00000			0.383571
$436$	7.00000	−	12.1244i	0.335239	−	0.580651i
$437$	−8.00000	−	13.8564i	−0.382692	−	0.662842i
$438$	4.00000	+	6.92820i	0.191127	+	0.331042i
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	−0.310228	−	0.950662i	$-0.600405\pi$
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	0.978412	−	0.206666i	$-0.0662612\pi$
$440$	−2.00000			−0.0953463
$441$		0			0
$442$		0			0
$443$	−2.00000	+	3.46410i	−0.0950229	+	0.164584i	−0.909618	−	0.415445i	$-0.863626\pi$
$443$	−2.00000	+	3.46410i	−0.0950229	+	0.164584i	0.814595	+	0.580030i	$0.196959\pi$
$444$	6.00000	+	10.3923i	0.284747	+	0.493197i
$445$	−10.0000	−	17.3205i	−0.474045	−	0.821071i
$446$	−7.00000	+	12.1244i	−0.331460	+	0.574105i
$447$	44.0000			2.08113
$448$		0			0
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	−0.500000	+	0.866025i	−0.0235702	+	0.0408248i
$451$		0			0
$452$	7.00000	+	12.1244i	0.329252	+	0.570282i
$453$	−16.0000	+	27.7128i	−0.751746	+	1.30206i
$454$	−8.00000			−0.375459
$455$		0			0
$456$	−8.00000			−0.374634
$457$	19.0000	−	32.9090i	0.888783	−	1.53942i	0.0474665	−	0.998873i	$-0.484885\pi$
$457$	19.0000	−	32.9090i	0.888783	−	1.53942i	0.841316	−	0.540544i	$-0.181781\pi$
$458$	−5.00000	−	8.66025i	−0.233635	−	0.404667i
$459$		0			0
$460$	−4.00000	+	6.92820i	−0.186501	+	0.323029i
$461$	32.0000			1.49039			0.745194	−	0.666847i	$-0.232357\pi$
$461$	32.0000			1.49039			0.745194	+	0.666847i	$0.232357\pi$
$462$		0			0
$463$	12.0000			0.557687			0.278844	−	0.960337i	$-0.410049\pi$
$463$	12.0000			0.557687			0.278844	+	0.960337i	$0.410049\pi$
$464$	−1.00000	+	1.73205i	−0.0464238	+	0.0804084i
$465$	20.0000	+	34.6410i	0.927478	+	1.60644i
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	−7.00000	+	12.1244i	−0.323921	+	0.561048i	−0.981293	−	0.192518i	$-0.938335\pi$
$467$	−7.00000	+	12.1244i	−0.323921	+	0.561048i	0.657372	+	0.753566i	$0.271668\pi$
$468$	−4.00000			−0.184900
$469$		0			0
$470$	−20.0000			−0.922531
$471$	−10.0000	+	17.3205i	−0.460776	+	0.798087i
$472$	5.00000	+	8.66025i	0.230144	+	0.398621i
$473$	2.00000	+	3.46410i	0.0919601	+	0.159280i
$474$	16.0000	−	27.7128i	0.734904	−	1.27289i
$475$	−4.00000			−0.183533
$476$		0			0
$477$	−14.0000			−0.641016
$478$	−4.00000	+	6.92820i	−0.182956	+	0.316889i
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	0.695773	−	0.718262i	$-0.255062\pi$
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	−0.969920	+	0.243426i	$0.921729\pi$
$480$	2.00000	+	3.46410i	0.0912871	+	0.158114i
$481$	−12.0000	+	20.7846i	−0.547153	+	0.947697i
$482$	−8.00000			−0.364390
$483$		0			0
$484$	1.00000			0.0454545
$485$	−6.00000	+	10.3923i	−0.272446	+	0.471890i
$486$	−5.00000	−	8.66025i	−0.226805	−	0.392837i
$487$	−6.00000	−	10.3923i	−0.271886	−	0.470920i	0.697459	−	0.716625i	$-0.254314\pi$
$487$	−6.00000	−	10.3923i	−0.271886	−	0.470920i	−0.969345	+	0.245705i	$0.920981\pi$
$488$	−4.00000	+	6.92820i	−0.181071	+	0.313625i
$489$	48.0000			2.17064
$490$		0			0
$491$	−28.0000			−1.26362			−0.631811	−	0.775122i	$-0.717688\pi$
$491$	−28.0000			−1.26362			−0.631811	+	0.775122i	$0.717688\pi$
$492$		0			0
$493$		0			0
$494$	−8.00000	−	13.8564i	−0.359937	−	0.623429i
$495$	−1.00000	+	1.73205i	−0.0449467	+	0.0778499i
$496$	−10.0000			−0.449013
$497$		0			0
$498$	−8.00000			−0.358489
$499$	8.00000	−	13.8564i	0.358129	−	0.620298i	−0.629519	−	0.776985i	$-0.716748\pi$
$499$	8.00000	−	13.8564i	0.358129	−	0.620298i	0.987648	+	0.156687i	$0.0500814\pi$
$500$	6.00000	+	10.3923i	0.268328	+	0.464758i
$501$	8.00000	+	13.8564i	0.357414	+	0.619059i
$502$	−13.0000	+	22.5167i	−0.580218	+	1.00497i
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	24.0000			1.06799
$506$	2.00000	−	3.46410i	0.0889108	−	0.153998i
$507$	−3.00000	−	5.19615i	−0.133235	−	0.230769i
$508$	8.00000	+	13.8564i	0.354943	+	0.614779i
$509$	−19.0000	+	32.9090i	−0.842160	+	1.45866i	0.0459045	+	0.998946i	$0.485383\pi$
$509$	−19.0000	+	32.9090i	−0.842160	+	1.45866i	−0.888065	+	0.459718i	$0.847950\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	8.00000	−	13.8564i	0.353209	−	0.611775i
$514$	1.00000	+	1.73205i	0.0441081	+	0.0763975i
$515$	−2.00000	−	3.46410i	−0.0881305	−	0.152647i
$516$	4.00000	−	6.92820i	0.176090	−	0.304997i
$517$	10.0000			0.439799
$518$		0			0
$519$	8.00000			0.351161
$520$	−4.00000	+	6.92820i	−0.175412	+	0.303822i
$521$	21.0000	+	36.3731i	0.920027	+	1.59353i	0.799370	+	0.600839i	$0.205167\pi$
$521$	21.0000	+	36.3731i	0.920027	+	1.59353i	0.120656	+	0.992694i	$0.461500\pi$
$522$	1.00000	+	1.73205i	0.0437688	+	0.0758098i
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	−0.986216	−	0.165460i	$-0.947089\pi$
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	0.636401	+	0.771358i	$0.280422\pi$
$524$	8.00000			0.349482
$525$		0			0
$526$	24.0000			1.04645
$527$		0			0
$528$	−1.00000	−	1.73205i	−0.0435194	−	0.0753778i
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	−14.0000	+	24.2487i	−0.608121	+	1.05330i
$531$	10.0000			0.433963
$532$		0			0
$533$		0			0
$534$	10.0000	−	17.3205i	0.432742	−	0.749532i
$535$	12.0000	+	20.7846i	0.518805	+	0.898597i
$536$	4.00000	+	6.92820i	0.172774	+	0.299253i
$537$	−12.0000	+	20.7846i	−0.517838	+	0.896922i
$538$	−14.0000			−0.603583
$539$		0			0
$540$	−8.00000			−0.344265
$541$	1.00000	−	1.73205i	0.0429934	−	0.0744667i	−0.843728	−	0.536771i	$-0.819644\pi$
$541$	1.00000	−	1.73205i	0.0429934	−	0.0744667i	0.886721	+	0.462304i	$0.152977\pi$
$542$	−14.0000	−	24.2487i	−0.601351	−	1.04157i
$543$	−14.0000	−	24.2487i	−0.600798	−	1.04061i
$544$		0			0
$545$	−28.0000			−1.19939
$546$		0			0
$547$	4.00000			0.171028			0.0855138	−	0.996337i	$-0.472747\pi$
$547$	4.00000			0.171028			0.0855138	+	0.996337i	$0.472747\pi$
$548$	−3.00000	+	5.19615i	−0.128154	+	0.221969i
$549$	4.00000	+	6.92820i	0.170716	+	0.295689i
$550$	−0.500000	−	0.866025i	−0.0213201	−	0.0369274i
$551$	−4.00000	+	6.92820i	−0.170406	+	0.295151i
$552$	−8.00000			−0.340503
$553$		0			0
$554$	−6.00000			−0.254916
$555$	12.0000	−	20.7846i	0.509372	−	0.882258i
$556$	−10.0000	−	17.3205i	−0.424094	−	0.734553i
$557$	−15.0000	−	25.9808i	−0.635570	−	1.10084i	−0.986394	−	0.164399i	$-0.947432\pi$
$557$	−15.0000	−	25.9808i	−0.635570	−	1.10084i	0.350824	−	0.936442i	$-0.385902\pi$
$558$	−5.00000	+	8.66025i	−0.211667	+	0.366618i
$559$	16.0000			0.676728
$560$		0			0
$561$		0			0
$562$	15.0000	−	25.9808i	0.632737	−	1.09593i
$563$	−6.00000	−	10.3923i	−0.252870	−	0.437983i	0.711445	−	0.702742i	$-0.248041\pi$
$563$	−6.00000	−	10.3923i	−0.252870	−	0.437983i	−0.964315	+	0.264758i	$0.914708\pi$
$564$	−10.0000	−	17.3205i	−0.421076	−	0.729325i
$565$	14.0000	−	24.2487i	0.588984	−	1.02015i
$566$		0			0
$567$		0			0
$568$	4.00000			0.167836
$569$	−7.00000	+	12.1244i	−0.293455	+	0.508279i	−0.974624	−	0.223847i	$-0.928139\pi$
$569$	−7.00000	+	12.1244i	−0.293455	+	0.508279i	0.681169	+	0.732126i	$0.261472\pi$
$570$	8.00000	+	13.8564i	0.335083	+	0.580381i
$571$	14.0000	+	24.2487i	0.585882	+	1.01478i	0.994765	+	0.102190i	$0.0325850\pi$
$571$	14.0000	+	24.2487i	0.585882	+	1.01478i	−0.408883	+	0.912587i	$0.634082\pi$
$572$	2.00000	−	3.46410i	0.0836242	−	0.144841i
$573$	16.0000			0.668410
$574$		0			0
$575$	−4.00000			−0.166812
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	21.0000	+	36.3731i	0.874241	+	1.51423i	0.857569	+	0.514370i	$0.171974\pi$
$577$	21.0000	+	36.3731i	0.874241	+	1.51423i	0.0166728	+	0.999861i	$0.494693\pi$
$578$	−8.50000	−	14.7224i	−0.353553	−	0.612372i
$579$	6.00000	−	10.3923i	0.249351	−	0.431889i
$580$	4.00000			0.166091
$581$		0			0
$582$	−12.0000			−0.497416
$583$	7.00000	−	12.1244i	0.289910	−	0.502140i
$584$	2.00000	+	3.46410i	0.0827606	+	0.143346i
$585$	4.00000	+	6.92820i	0.165380	+	0.286446i
$586$		0			0
$587$	−42.0000			−1.73353			−0.866763	−	0.498721i	$-0.833803\pi$
$587$	−42.0000			−1.73353			−0.866763	+	0.498721i	$0.833803\pi$
$588$		0			0
$589$	−40.0000			−1.64817
$590$	10.0000	−	17.3205i	0.411693	−	0.713074i
$591$	18.0000	+	31.1769i	0.740421	+	1.28245i
$592$	3.00000	+	5.19615i	0.123299	+	0.213561i
$593$	−6.00000	+	10.3923i	−0.246390	+	0.426761i	−0.962522	−	0.271205i	$-0.912578\pi$
$593$	−6.00000	+	10.3923i	−0.246390	+	0.426761i	0.716131	+	0.697966i	$0.245911\pi$
$594$	4.00000			0.164122
$595$		0			0
$596$	22.0000			0.901155
$597$	14.0000	−	24.2487i	0.572982	−	0.992434i
$598$	−8.00000	−	13.8564i	−0.327144	−	0.566631i
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	0.962175	−	0.272433i	$-0.0878284\pi$
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	−0.717021	+	0.697051i	$0.754495\pi$
$600$	−1.00000	+	1.73205i	−0.0408248	+	0.0707107i
$601$	−24.0000			−0.978980			−0.489490	−	0.872009i	$-0.662817\pi$
$601$	−24.0000			−0.978980			−0.489490	+	0.872009i	$0.662817\pi$
$602$		0			0
$603$	8.00000			0.325785
$604$	−8.00000	+	13.8564i	−0.325515	+	0.563809i
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$	12.0000	+	20.7846i	0.487467	+	0.844317i
$607$	12.0000	−	20.7846i	0.487065	−	0.843621i	−0.512824	−	0.858494i	$-0.671401\pi$
$607$	12.0000	−	20.7846i	0.487065	−	0.843621i	0.999889	+	0.0148722i	$0.00473415\pi$
$608$	−4.00000			−0.162221
$609$		0			0
$610$	16.0000			0.647821
$611$	20.0000	−	34.6410i	0.809113	−	1.40143i
$612$		0			0
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$	8.00000	−	13.8564i	0.322854	−	0.559199i
$615$		0			0
$616$		0			0
$617$	38.0000			1.52982			0.764911	−	0.644136i	$-0.222783\pi$
$617$	38.0000			1.52982			0.764911	+	0.644136i	$0.222783\pi$
$618$	2.00000	−	3.46410i	0.0804518	−	0.139347i
$619$	1.00000	+	1.73205i	0.0401934	+	0.0696170i	0.885422	−	0.464787i	$-0.153869\pi$
$619$	1.00000	+	1.73205i	0.0401934	+	0.0696170i	−0.845229	+	0.534404i	$0.820536\pi$
$620$	10.0000	+	17.3205i	0.401610	+	0.695608i
$621$	8.00000	−	13.8564i	0.321029	−	0.556038i
$622$	6.00000			0.240578
$623$		0			0
$624$	−8.00000			−0.320256
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	−3.00000	−	5.19615i	−0.119904	−	0.207680i
$627$	−4.00000	−	6.92820i	−0.159745	−	0.276686i
$628$	−5.00000	+	8.66025i	−0.199522	+	0.345582i
$629$		0			0
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	8.00000	−	13.8564i	0.318223	−	0.551178i
$633$	4.00000	+	6.92820i	0.158986	+	0.275371i
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$	16.0000	−	27.7128i	0.634941	−	1.09975i
$636$	−28.0000			−1.11027
$637$		0			0
$638$	−2.00000			−0.0791808
$639$	2.00000	−	3.46410i	0.0791188	−	0.137038i
$640$	1.00000	+	1.73205i	0.0395285	+	0.0684653i
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	0.987200	−	0.159489i	$-0.0509845\pi$
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	−0.631721	+	0.775196i	$0.717651\pi$
$642$	−12.0000	+	20.7846i	−0.473602	+	0.820303i
$643$	22.0000			0.867595			0.433798	−	0.901010i	$-0.357173\pi$
$643$	22.0000			0.867595			0.433798	+	0.901010i	$0.357173\pi$
$644$		0			0
$645$	−16.0000			−0.629999
$646$		0			0
$647$	−3.00000	−	5.19615i	−0.117942	−	0.204282i	0.801010	−	0.598651i	$-0.204296\pi$
$647$	−3.00000	−	5.19615i	−0.117942	−	0.204282i	−0.918952	+	0.394369i	$0.870963\pi$
$648$	−5.50000	−	9.52628i	−0.216060	−	0.374228i
$649$	−5.00000	+	8.66025i	−0.196267	+	0.339945i
$650$	−4.00000			−0.156893
$651$		0			0
$652$	24.0000			0.939913
$653$	−23.0000	+	39.8372i	−0.900060	+	1.55895i	−0.0726446	+	0.997358i	$0.523144\pi$
$653$	−23.0000	+	39.8372i	−0.900060	+	1.55895i	−0.827415	+	0.561591i	$0.810189\pi$
$654$	−14.0000	−	24.2487i	−0.547443	−	0.948200i
$655$	−8.00000	−	13.8564i	−0.312586	−	0.541415i
$656$		0			0
$657$	4.00000			0.156055
$658$		0			0
$659$	20.0000			0.779089			0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000			0.779089			0.389545	+	0.921008i	$0.372632\pi$
$660$	−2.00000	+	3.46410i	−0.0778499	+	0.134840i
$661$	19.0000	+	32.9090i	0.739014	+	1.28001i	0.952940	+	0.303160i	$0.0980418\pi$
$661$	19.0000	+	32.9090i	0.739014	+	1.28001i	−0.213925	+	0.976850i	$0.568625\pi$
$662$	−10.0000	−	17.3205i	−0.388661	−	0.673181i
$663$		0			0
$664$	−4.00000			−0.155230
$665$		0			0
$666$	6.00000			0.232495
$667$	−4.00000	+	6.92820i	−0.154881	+	0.268261i
$668$	4.00000	+	6.92820i	0.154765	+	0.268060i
$669$	14.0000	+	24.2487i	0.541271	+	0.937509i
$670$	8.00000	−	13.8564i	0.309067	−	0.535320i
$671$	−8.00000			−0.308837
$672$		0			0
$673$	−10.0000			−0.385472			−0.192736	−	0.981251i	$-0.561736\pi$
$673$	−10.0000			−0.385472			−0.192736	+	0.981251i	$0.561736\pi$
$674$	−17.0000	+	29.4449i	−0.654816	+	1.13417i
$675$	−2.00000	−	3.46410i	−0.0769800	−	0.133333i
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	−6.00000	+	10.3923i	−0.230599	+	0.399409i	−0.957984	−	0.286820i	$-0.907402\pi$
$677$	−6.00000	+	10.3923i	−0.230599	+	0.399409i	0.727386	+	0.686229i	$0.240735\pi$
$678$	28.0000			1.07533
$679$		0			0
$680$		0			0
$681$	−8.00000	+	13.8564i	−0.306561	+	0.530979i
$682$	−5.00000	−	8.66025i	−0.191460	−	0.331618i
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	0.728101	−	0.685470i	$-0.240403\pi$
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	−0.957685	+	0.287819i	$0.907070\pi$
$684$	−2.00000	+	3.46410i	−0.0764719	+	0.132453i
$685$	12.0000			0.458496
$686$		0			0
$687$	−20.0000			−0.763048
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	−28.0000	−	48.4974i	−1.06672	−	1.84760i
$690$	8.00000	+	13.8564i	0.304555	+	0.527504i
$691$	−21.0000	+	36.3731i	−0.798878	+	1.38370i	0.121470	+	0.992595i	$0.461239\pi$
$691$	−21.0000	+	36.3731i	−0.798878	+	1.38370i	−0.920348	+	0.391102i	$0.872094\pi$
$692$	4.00000			0.152057
$693$		0			0
$694$	12.0000			0.455514
$695$	−20.0000	+	34.6410i	−0.758643	+	1.31401i
$696$	2.00000	+	3.46410i	0.0758098	+	0.131306i
$697$		0			0
$698$	16.0000	−	27.7128i	0.605609	−	1.04895i
$699$	12.0000			0.453882
$700$		0			0
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$	8.00000	−	13.8564i	0.301941	−	0.522976i
$703$	12.0000	+	20.7846i	0.452589	+	0.783906i
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$	−20.0000	+	34.6410i	−0.753244	+	1.30466i
$706$	−2.00000			−0.0752710
$707$		0			0
$708$	20.0000			0.751646
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	−0.756730	−	0.653727i	$-0.773204\pi$
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	0.944509	+	0.328484i	$0.106538\pi$
$710$	−4.00000	−	6.92820i	−0.150117	−	0.260011i
$711$	−8.00000	−	13.8564i	−0.300023	−	0.519656i
$712$	5.00000	−	8.66025i	0.187383	−	0.324557i
$713$	−40.0000			−1.49801
$714$		0			0
$715$	−8.00000			−0.299183
$716$	−6.00000	+	10.3923i	−0.224231	+	0.388379i
$717$	8.00000	+	13.8564i	0.298765	+	0.517477i
$718$		0			0
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	−0.916529	−	0.399969i	$-0.869021\pi$
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	0.804648	+	0.593753i	$0.202354\pi$
$720$	2.00000			0.0745356
$721$		0			0
$722$	3.00000			0.111648
$723$	−8.00000	+	13.8564i	−0.297523	+	0.515325i
$724$	−7.00000	−	12.1244i	−0.260153	−	0.450598i
$725$	1.00000	+	1.73205i	0.0371391	+	0.0643268i
$726$	1.00000	−	1.73205i	0.0371135	−	0.0642824i
$727$	46.0000			1.70605			0.853023	−	0.521874i	$-0.174767\pi$
$727$	46.0000			1.70605			0.853023	+	0.521874i	$0.174767\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	4.00000	−	6.92820i	0.148047	−	0.256424i
$731$		0			0
$732$	8.00000	+	13.8564i	0.295689	+	0.512148i
$733$	4.00000	−	6.92820i	0.147743	−	0.255899i	−0.782650	−	0.622462i	$-0.786132\pi$
$733$	4.00000	−	6.92820i	0.147743	−	0.255899i	0.930393	+	0.366563i	$0.119466\pi$
$734$	−18.0000			−0.664392
$735$		0			0
$736$	−4.00000			−0.147442
$737$	−4.00000	+	6.92820i	−0.147342	+	0.255204i
$738$		0			0
$739$	26.0000	+	45.0333i	0.956425	+	1.65658i	0.731072	+	0.682300i	$0.239020\pi$
$739$	26.0000	+	45.0333i	0.956425	+	1.65658i	0.225354	+	0.974277i	$0.427646\pi$
$740$	6.00000	−	10.3923i	0.220564	−	0.382029i
$741$	−32.0000			−1.17555
$742$		0			0
$743$	16.0000			0.586983			0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000			0.586983			0.293492	+	0.955962i	$0.405183\pi$
$744$	−10.0000	+	17.3205i	−0.366618	+	0.635001i
$745$	−22.0000	−	38.1051i	−0.806018	−	1.39606i
$746$	−17.0000	−	29.4449i	−0.622414	−	1.07805i
$747$	−2.00000	+	3.46410i	−0.0731762	+	0.126745i
$748$		0			0
$749$		0			0
$750$	24.0000			0.876356
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	−0.988761	−	0.149505i	$-0.952232\pi$
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	0.623856	+	0.781540i	$0.285565\pi$
$752$	−5.00000	−	8.66025i	−0.182331	−	0.315807i
$753$	26.0000	+	45.0333i	0.947493	+	1.64111i
$754$	−4.00000	+	6.92820i	−0.145671	+	0.252310i
$755$	32.0000			1.16460
$756$		0			0
$757$	30.0000			1.09037			0.545184	−	0.838316i	$-0.316460\pi$
$757$	30.0000			1.09037			0.545184	+	0.838316i	$0.316460\pi$
$758$	4.00000	−	6.92820i	0.145287	−	0.251644i
$759$	−4.00000	−	6.92820i	−0.145191	−	0.251478i
$760$	4.00000	+	6.92820i	0.145095	+	0.251312i
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	−0.736543	−	0.676391i	$-0.763543\pi$
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	0.954043	+	0.299670i	$0.0968765\pi$
$762$	32.0000			1.15924
$763$		0			0
$764$	8.00000			0.289430
$765$		0			0
$766$	7.00000	+	12.1244i	0.252920	+	0.438071i
$767$	20.0000	+	34.6410i	0.722158	+	1.25081i
$768$	−1.00000	+	1.73205i	−0.0360844	+	0.0625000i
$769$	4.00000			0.144244			0.0721218	−	0.997396i	$-0.477023\pi$
$769$	4.00000			0.144244			0.0721218	+	0.997396i	$0.477023\pi$
$770$		0			0
$771$	4.00000			0.144056
$772$	3.00000	−	5.19615i	0.107972	−	0.187014i
$773$	17.0000	+	29.4449i	0.611448	+	1.05906i	0.990997	+	0.133887i	$0.0427458\pi$
$773$	17.0000	+	29.4449i	0.611448	+	1.05906i	−0.379549	+	0.925172i	$0.623921\pi$
$774$	−2.00000	−	3.46410i	−0.0718885	−	0.124515i
$775$	−5.00000	+	8.66025i	−0.179605	+	0.311086i
$776$	−6.00000			−0.215387
$777$		0			0
$778$	18.0000			0.645331
$779$		0			0
$780$	8.00000	+	13.8564i	0.286446	+	0.496139i
$781$	2.00000	+	3.46410i	0.0715656	+	0.123955i
$782$		0			0
$783$	−8.00000			−0.285897
$784$		0			0
$785$	20.0000			0.713831
$786$	8.00000	−	13.8564i	0.285351	−	0.494242i
$787$	−10.0000	−	17.3205i	−0.356462	−	0.617409i	0.630905	−	0.775860i	$-0.282684\pi$
$787$	−10.0000	−	17.3205i	−0.356462	−	0.617409i	−0.987367	+	0.158450i	$0.949350\pi$
$788$	9.00000	+	15.5885i	0.320612	+	0.555316i
$789$	24.0000	−	41.5692i	0.854423	−	1.47990i
$790$	−32.0000			−1.13851
$791$		0			0
$792$	−1.00000			−0.0355335
$793$	−16.0000	+	27.7128i	−0.568177	+	0.984111i
$794$	9.00000	+	15.5885i	0.319398	+	0.553214i
$795$	28.0000	+	48.4974i	0.993058	+	1.72003i
$796$	7.00000	−	12.1244i	0.248108	−	0.429736i
$797$	26.0000			0.920967			0.460484	−	0.887668i	$-0.347676\pi$
$797$	26.0000			0.920967			0.460484	+	0.887668i	$0.347676\pi$
$798$		0			0
$799$		0			0
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−5.00000	−	8.66025i	−0.176666	−	0.305995i
$802$	5.00000	+	8.66025i	0.176556	+	0.305804i
$803$	−2.00000	+	3.46410i	−0.0705785	+	0.122245i
$804$	16.0000			0.564276
$805$		0			0
$806$	−40.0000			−1.40894
$807$	−14.0000	+	24.2487i	−0.492823	+	0.853595i
$808$	6.00000	+	10.3923i	0.211079	+	0.365600i
$809$	−13.0000	−	22.5167i	−0.457056	−	0.791644i	0.541748	−	0.840541i	$-0.317763\pi$
$809$	−13.0000	−	22.5167i	−0.457056	−	0.791644i	−0.998804	+	0.0488972i	$0.984429\pi$
$810$	−11.0000	+	19.0526i	−0.386501	+	0.669439i
$811$	−40.0000			−1.40459			−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000			−1.40459			−0.702295	+	0.711886i	$0.747841\pi$
$812$		0			0
$813$	−56.0000			−1.96401
$814$	−3.00000	+	5.19615i	−0.105150	+	0.182125i
$815$	−24.0000	−	41.5692i	−0.840683	−	1.45611i
$816$		0			0
$817$	8.00000	−	13.8564i	0.279885	−	0.484774i
$818$	4.00000			0.139857
$819$		0			0
$820$		0			0
$821$	25.0000	−	43.3013i	0.872506	−	1.51122i	0.0131101	−	0.999914i	$-0.495827\pi$
$821$	25.0000	−	43.3013i	0.872506	−	1.51122i	0.859396	−	0.511311i	$-0.170840\pi$
$822$	6.00000	+	10.3923i	0.209274	+	0.362473i
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	0.787850	−	0.615867i	$-0.211194\pi$
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	−0.927281	+	0.374365i	$0.877861\pi$
$824$	1.00000	−	1.73205i	0.0348367	−	0.0603388i
$825$	−2.00000			−0.0696311
$826$		0			0
$827$	−20.0000			−0.695468			−0.347734	−	0.937593i	$-0.613049\pi$
$827$	−20.0000			−0.695468			−0.347734	+	0.937593i	$0.613049\pi$
$828$	−2.00000	+	3.46410i	−0.0695048	+	0.120386i
$829$	7.00000	+	12.1244i	0.243120	+	0.421096i	0.961601	−	0.274450i	$-0.0884958\pi$
$829$	7.00000	+	12.1244i	0.243120	+	0.421096i	−0.718481	+	0.695546i	$0.755162\pi$
$830$	4.00000	+	6.92820i	0.138842	+	0.240481i
$831$	−6.00000	+	10.3923i	−0.208138	+	0.360505i
$832$	−4.00000			−0.138675
$833$		0			0
$834$	−40.0000			−1.38509
$835$	8.00000	−	13.8564i	0.276851	−	0.479521i
$836$	−2.00000	−	3.46410i	−0.0691714	−	0.119808i
$837$	−20.0000	−	34.6410i	−0.691301	−	1.19737i
$838$	−15.0000	+	25.9808i	−0.518166	+	0.897491i
$839$	30.0000			1.03572			0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000			1.03572			0.517858	+	0.855467i	$0.326730\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	5.00000	−	8.66025i	0.172311	−	0.298452i
$843$	−30.0000	−	51.9615i	−1.03325	−	1.78965i
$844$	2.00000	+	3.46410i	0.0688428	+	0.119239i
$845$	−3.00000	+	5.19615i	−0.103203	+	0.178753i
$846$	−10.0000			−0.343807
$847$		0			0
$848$	−14.0000			−0.480762
$849$		0			0
$850$		0			0
$851$	12.0000	+	20.7846i	0.411355	+	0.712487i
$852$	4.00000	−	6.92820i	0.137038	−	0.237356i
$853$	4.00000			0.136957			0.0684787	−	0.997653i	$-0.478185\pi$
$853$	4.00000			0.136957			0.0684787	+	0.997653i	$0.478185\pi$
$854$		0			0
$855$	8.00000			0.273594
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$	−6.00000	−	10.3923i	−0.204956	−	0.354994i	0.745163	−	0.666883i	$-0.232372\pi$
$857$	−6.00000	−	10.3923i	−0.204956	−	0.354994i	−0.950119	+	0.311888i	$0.899038\pi$
$858$	−4.00000	−	6.92820i	−0.136558	−	0.236525i
$859$	−7.00000	+	12.1244i	−0.238837	+	0.413678i	−0.960381	−	0.278691i	$-0.910099\pi$
$859$	−7.00000	+	12.1244i	−0.238837	+	0.413678i	0.721544	+	0.692369i	$0.243433\pi$
$860$	−8.00000			−0.272798
$861$		0			0
$862$	16.0000			0.544962
$863$	−20.0000	+	34.6410i	−0.680808	+	1.17919i	0.293927	+	0.955828i	$0.405038\pi$
$863$	−20.0000	+	34.6410i	−0.680808	+	1.17919i	−0.974735	+	0.223366i	$0.928296\pi$
$864$	−2.00000	−	3.46410i	−0.0680414	−	0.117851i
$865$	−4.00000	−	6.92820i	−0.136004	−	0.235566i
$866$	−5.00000	+	8.66025i	−0.169907	+	0.294287i
$867$	−34.0000			−1.15470
$868$		0			0
$869$	16.0000			0.542763
$870$	4.00000	−	6.92820i	0.135613	−	0.234888i
$871$	16.0000	+	27.7128i	0.542139	+	0.939013i
$872$	−7.00000	−	12.1244i	−0.237050	−	0.410582i
$873$	−3.00000	+	5.19615i	−0.101535	+	0.175863i
$874$	−16.0000			−0.541208
$875$		0			0
$876$	8.00000			0.270295
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$	−14.0000	−	24.2487i	−0.472477	−	0.818354i
$879$		0			0
$880$	−1.00000	+	1.73205i	−0.0337100	+	0.0583874i
$881$	−42.0000			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$		0			0
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$		0			0
$885$	−20.0000	−	34.6410i	−0.672293	−	1.16445i
$886$	2.00000	+	3.46410i	0.0671913	+	0.116379i
$887$	14.0000	−	24.2487i	0.470074	−	0.814192i	−0.529340	−	0.848410i	$-0.677561\pi$
$887$	14.0000	−	24.2487i	0.470074	−	0.814192i	0.999414	+	0.0342175i	$0.0108939\pi$
$888$	12.0000			0.402694
$889$		0			0
$890$	−20.0000			−0.670402
$891$	5.50000	−	9.52628i	0.184257	−	0.319142i
$892$	7.00000	+	12.1244i	0.234377	+	0.405953i
$893$	−20.0000	−	34.6410i	−0.669274	−	1.15922i
$894$	22.0000	−	38.1051i	0.735790	−	1.27443i
$895$	24.0000			0.802232
$896$		0			0
$897$	−32.0000			−1.06845
$898$	3.00000	−	5.19615i	0.100111	−	0.173398i
$899$	10.0000	+	17.3205i	0.333519	+	0.577671i
$900$	0.500000	+	0.866025i	0.0166667	+	0.0288675i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	14.0000			0.465633
$905$	−14.0000	+	24.2487i	−0.465376	+	0.806054i
$906$	16.0000	+	27.7128i	0.531564	+	0.920697i
$907$	−24.0000	−	41.5692i	−0.796907	−	1.38028i	−0.921621	−	0.388091i	$-0.873135\pi$
$907$	−24.0000	−	41.5692i	−0.796907	−	1.38028i	0.124714	−	0.992193i	$-0.460199\pi$
$908$	−4.00000	+	6.92820i	−0.132745	+	0.229920i
$909$	12.0000			0.398015
$910$		0			0
$911$	−4.00000			−0.132526			−0.0662630	−	0.997802i	$-0.521108\pi$
$911$	−4.00000			−0.132526			−0.0662630	+	0.997802i	$0.521108\pi$
$912$	−4.00000	+	6.92820i	−0.132453	+	0.229416i
$913$	−2.00000	−	3.46410i	−0.0661903	−	0.114645i
$914$	−19.0000	−	32.9090i	−0.628464	−	1.08853i
$915$	16.0000	−	27.7128i	0.528944	−	0.916157i
$916$	−10.0000			−0.330409
$917$		0			0
$918$		0			0
$919$	28.0000	−	48.4974i	0.923635	−	1.59978i	0.129893	−	0.991528i	$-0.458537\pi$
$919$	28.0000	−	48.4974i	0.923635	−	1.59978i	0.793742	−	0.608254i	$-0.208130\pi$
$920$	4.00000	+	6.92820i	0.131876	+	0.228416i
$921$	−16.0000	−	27.7128i	−0.527218	−	0.913168i
$922$	16.0000	−	27.7128i	0.526932	−	0.912673i
$923$	16.0000			0.526646
$924$		0			0
$925$	6.00000			0.197279
$926$	6.00000	−	10.3923i	0.197172	−	0.341512i
$927$	−1.00000	−	1.73205i	−0.0328443	−	0.0568880i
$928$	1.00000	+	1.73205i	0.0328266	+	0.0568574i
$929$	5.00000	−	8.66025i	0.164045	−	0.284134i	−0.772271	−	0.635293i	$-0.780879\pi$
$929$	5.00000	−	8.66025i	0.164045	−	0.284134i	0.936316	+	0.351160i	$0.114213\pi$
$930$	40.0000			1.31165
$931$		0			0
$932$	6.00000			0.196537
$933$	6.00000	−	10.3923i	0.196431	−	0.340229i
$934$	7.00000	+	12.1244i	0.229047	+	0.396721i
$935$		0			0
$936$	−2.00000	+	3.46410i	−0.0653720	+	0.113228i
$937$	−52.0000			−1.69877			−0.849383	−	0.527777i	$-0.823026\pi$
$937$	−52.0000			−1.69877			−0.849383	+	0.527777i	$0.823026\pi$
$938$		0			0
$939$	−12.0000			−0.391605
$940$	−10.0000	+	17.3205i	−0.326164	+	0.564933i
$941$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$941$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$942$	10.0000	+	17.3205i	0.325818	+	0.564333i
$943$		0			0
$944$	10.0000			0.325472
$945$		0			0
$946$	4.00000			0.130051
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	−0.946892	−	0.321552i	$-0.895796\pi$
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	0.751918	+	0.659256i	$0.229129\pi$
$948$	−16.0000	−	27.7128i	−0.519656	−	0.900070i
$949$	8.00000	+	13.8564i	0.259691	+	0.449798i
$950$	−2.00000	+	3.46410i	−0.0648886	+	0.112390i
$951$	−36.0000			−1.16738
$952$		0			0
$953$	34.0000			1.10137			0.550684	−	0.834714i	$-0.314367\pi$
$953$	34.0000			1.10137			0.550684	+	0.834714i	$0.314367\pi$
$954$	−7.00000	+	12.1244i	−0.226633	+	0.392541i
$955$	−8.00000	−	13.8564i	−0.258874	−	0.448383i
$956$	4.00000	+	6.92820i	0.129369	+	0.224074i
$957$	−2.00000	+	3.46410i	−0.0646508	+	0.111979i
$958$	−12.0000			−0.387702
$959$		0			0
$960$	4.00000			0.129099
$961$	−34.5000	+	59.7558i	−1.11290	+	1.92760i
$962$	12.0000	+	20.7846i	0.386896	+	0.670123i
$963$	6.00000	+	10.3923i	0.193347	+	0.334887i
$964$	−4.00000	+	6.92820i	−0.128831	+	0.223142i
$965$	−12.0000			−0.386294
$966$		0			0
$967$	−24.0000			−0.771788			−0.385894	−	0.922543i	$-0.626107\pi$
$967$	−24.0000			−0.771788			−0.385894	+	0.922543i	$0.626107\pi$
$968$	0.500000	−	0.866025i	0.0160706	−	0.0278351i
$969$		0			0
$970$	6.00000	+	10.3923i	0.192648	+	0.333677i
$971$	−15.0000	+	25.9808i	−0.481373	+	0.833762i	−0.999771	−	0.0213768i	$-0.993195\pi$
$971$	−15.0000	+	25.9808i	−0.481373	+	0.833762i	0.518399	+	0.855139i	$0.326528\pi$
$972$	−10.0000			−0.320750
$973$		0			0
$974$	−12.0000			−0.384505
$975$	−4.00000	+	6.92820i	−0.128103	+	0.221880i
$976$	4.00000	+	6.92820i	0.128037	+	0.221766i
$977$	11.0000	+	19.0526i	0.351921	+	0.609545i	0.986586	−	0.163242i	$-0.0521952\pi$
$977$	11.0000	+	19.0526i	0.351921	+	0.609545i	−0.634665	+	0.772787i	$0.718862\pi$
$978$	24.0000	−	41.5692i	0.767435	−	1.32924i
$979$	10.0000			0.319601
$980$		0			0
$981$	−14.0000			−0.446986
$982$	−14.0000	+	24.2487i	−0.446758	+	0.773807i
$983$	−13.0000	−	22.5167i	−0.414636	−	0.718170i	0.580755	−	0.814079i	$-0.302758\pi$
$983$	−13.0000	−	22.5167i	−0.414636	−	0.718170i	−0.995390	+	0.0959088i	$0.969424\pi$
$984$		0			0
$985$	18.0000	−	31.1769i	0.573528	−	0.993379i
$986$		0			0
$987$		0			0
$988$	−16.0000			−0.509028
$989$	8.00000	−	13.8564i	0.254385	−	0.440608i
$990$	1.00000	+	1.73205i	0.0317821	+	0.0550482i
$991$	2.00000	+	3.46410i	0.0635321	+	0.110041i	0.896042	−	0.443969i	$-0.146430\pi$
$991$	2.00000	+	3.46410i	0.0635321	+	0.110041i	−0.832510	+	0.554010i	$0.813097\pi$
$992$	−5.00000	+	8.66025i	−0.158750	+	0.274963i
$993$	−40.0000			−1.26936
$994$		0			0
$995$	−28.0000			−0.887660
$996$	−4.00000	+	6.92820i	−0.126745	+	0.219529i
$997$	−18.0000	−	31.1769i	−0.570066	−	0.987383i	−0.996559	−	0.0828918i	$-0.973584\pi$
$997$	−18.0000	−	31.1769i	−0.570066	−	0.987383i	0.426493	−	0.904491i	$-0.359749\pi$
$998$	−8.00000	−	13.8564i	−0.253236	−	0.438617i
$999$	−12.0000	+	20.7846i	−0.379663	+	0.657596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.e.h.177.1		2
7.2	even	3		154.2.a.b.1.1	✓	1
7.3	odd	6		1078.2.e.l.67.1		2
7.4	even	3	inner	1078.2.e.h.67.1		2
7.5	odd	6		1078.2.a.b.1.1		1
7.6	odd	2		1078.2.e.l.177.1		2
21.2	odd	6		1386.2.a.f.1.1		1
21.5	even	6		9702.2.a.bz.1.1		1
28.19	even	6		8624.2.a.z.1.1		1
28.23	odd	6		1232.2.a.c.1.1		1
35.2	odd	12		3850.2.c.d.1849.1		2
35.9	even	6		3850.2.a.o.1.1		1
35.23	odd	12		3850.2.c.d.1849.2		2
56.37	even	6		4928.2.a.d.1.1		1
56.51	odd	6		4928.2.a.bf.1.1		1
77.65	odd	6		1694.2.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.a.b.1.1	✓	1	7.2	even	3
1078.2.a.b.1.1		1	7.5	odd	6
1078.2.e.h.67.1		2	7.4	even	3	inner
1078.2.e.h.177.1		2	1.1	even	1	trivial
1078.2.e.l.67.1		2	7.3	odd	6
1078.2.e.l.177.1		2	7.6	odd	2
1232.2.a.c.1.1		1	28.23	odd	6
1386.2.a.f.1.1		1	21.2	odd	6
1694.2.a.i.1.1		1	77.65	odd	6
3850.2.a.o.1.1		1	35.9	even	6
3850.2.c.d.1849.1		2	35.2	odd	12
3850.2.c.d.1849.2		2	35.23	odd	12
4928.2.a.d.1.1		1	56.37	even	6
4928.2.a.bf.1.1		1	56.51	odd	6
8624.2.a.z.1.1		1	28.19	even	6
9702.2.a.bz.1.1		1	21.5	even	6

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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.00000 + 1.73205i) q^{12} -4.00000 q^{13} +4.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{18} +(-2.00000 + 3.46410i) q^{19} +2.00000 q^{20} -1.00000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(1.00000 + 1.73205i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-2.00000 + 3.46410i) q^{26} -4.00000 q^{27} +2.00000 q^{29} +(2.00000 - 3.46410i) q^{30} +(5.00000 + 8.66025i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{33} +1.00000 q^{36} +(3.00000 - 5.19615i) q^{37} +(2.00000 + 3.46410i) q^{38} +(4.00000 + 6.92820i) q^{39} +(1.00000 - 1.73205i) q^{40} -4.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-1.00000 - 1.73205i) q^{45} +(2.00000 + 3.46410i) q^{46} +(-5.00000 + 8.66025i) q^{47} +2.00000 q^{48} +1.00000 q^{50} +(2.00000 + 3.46410i) q^{52} +(7.00000 + 12.1244i) q^{53} +(-2.00000 + 3.46410i) q^{54} +2.00000 q^{55} +8.00000 q^{57} +(1.00000 - 1.73205i) q^{58} +(-5.00000 - 8.66025i) q^{59} +(-2.00000 - 3.46410i) q^{60} +(4.00000 - 6.92820i) q^{61} +10.0000 q^{62} +1.00000 q^{64} +(4.00000 - 6.92820i) q^{65} +(1.00000 + 1.73205i) q^{66} +(-4.00000 - 6.92820i) q^{67} +8.00000 q^{69} -4.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-2.00000 - 3.46410i) q^{73} +(-3.00000 - 5.19615i) q^{74} +(1.00000 - 1.73205i) q^{75} +4.00000 q^{76} +8.00000 q^{78} +(-8.00000 + 13.8564i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(5.50000 + 9.52628i) q^{81} +4.00000 q^{83} +(-2.00000 + 3.46410i) q^{86} +(-2.00000 - 3.46410i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-5.00000 + 8.66025i) q^{89} -2.00000 q^{90} +4.00000 q^{92} +(10.0000 - 17.3205i) q^{93} +(5.00000 + 8.66025i) q^{94} +(-4.00000 - 6.92820i) q^{95} +(1.00000 - 1.73205i) q^{96} +6.00000 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 4 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - 4 * q^6 - 2 * q^8 - q^9	\( 2 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 4 q^{6} - 2 q^{8} - q^{9} + 2 q^{10} - q^{11} - 2 q^{12} - 8 q^{13} + 8 q^{15} - q^{16} + q^{18} - 4 q^{19} + 4 q^{20} - 2 q^{22} - 4 q^{23} + 2 q^{24} + q^{25} - 4 q^{26} - 8 q^{27} + 4 q^{29} + 4 q^{30} + 10 q^{31} + q^{32} - 2 q^{33} + 2 q^{36} + 6 q^{37} + 4 q^{38} + 8 q^{39} + 2 q^{40} - 8 q^{43} - q^{44} - 2 q^{45} + 4 q^{46} - 10 q^{47} + 4 q^{48} + 2 q^{50} + 4 q^{52} + 14 q^{53} - 4 q^{54} + 4 q^{55} + 16 q^{57} + 2 q^{58} - 10 q^{59} - 4 q^{60} + 8 q^{61} + 20 q^{62} + 2 q^{64} + 8 q^{65} + 2 q^{66} - 8 q^{67} + 16 q^{69} - 8 q^{71} + q^{72} - 4 q^{73} - 6 q^{74} + 2 q^{75} + 8 q^{76} + 16 q^{78} - 16 q^{79} - 2 q^{80} + 11 q^{81} + 8 q^{83} - 4 q^{86} - 4 q^{87} + q^{88} - 10 q^{89} - 4 q^{90} + 8 q^{92} + 20 q^{93} + 10 q^{94} - 8 q^{95} + 2 q^{96} + 12 q^{97} + 2 q^{99}+O(q^{100}) \) 2 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - 4 * q^6 - 2 * q^8 - q^9 + 2 * q^10 - q^11 - 2 * q^12 - 8 * q^13 + 8 * q^15 - q^16 + q^18 - 4 * q^19 + 4 * q^20 - 2 * q^22 - 4 * q^23 + 2 * q^24 + q^25 - 4 * q^26 - 8 * q^27 + 4 * q^29 + 4 * q^30 + 10 * q^31 + q^32 - 2 * q^33 + 2 * q^36 + 6 * q^37 + 4 * q^38 + 8 * q^39 + 2 * q^40 - 8 * q^43 - q^44 - 2 * q^45 + 4 * q^46 - 10 * q^47 + 4 * q^48 + 2 * q^50 + 4 * q^52 + 14 * q^53 - 4 * q^54 + 4 * q^55 + 16 * q^57 + 2 * q^58 - 10 * q^59 - 4 * q^60 + 8 * q^61 + 20 * q^62 + 2 * q^64 + 8 * q^65 + 2 * q^66 - 8 * q^67 + 16 * q^69 - 8 * q^71 + q^72 - 4 * q^73 - 6 * q^74 + 2 * q^75 + 8 * q^76 + 16 * q^78 - 16 * q^79 - 2 * q^80 + 11 * q^81 + 8 * q^83 - 4 * q^86 - 4 * q^87 + q^88 - 10 * q^89 - 4 * q^90 + 8 * q^92 + 20 * q^93 + 10 * q^94 - 8 * q^95 + 2 * q^96 + 12 * q^97 + 2 * q^99

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