LMFDB - Embedded newform 338.2.c.d.315.1

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,2,Mod(191,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.191"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(338, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	338.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,1,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.69894358832$
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 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			315.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	338.315
Dual form			338.2.c.d.191.1

$q$-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} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-3.00000 - 5.19615i) q^{11} +1.00000 q^{12} +1.00000 q^{14} +(1.50000 + 2.59808i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +2.00000 q^{18} +(-1.00000 + 1.73205i) q^{19} +(1.50000 - 2.59808i) q^{20} -1.00000 q^{21} +(3.00000 - 5.19615i) q^{22} +(0.500000 + 0.866025i) q^{24} +4.00000 q^{25} -5.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(-3.00000 - 5.19615i) q^{29} +(-1.50000 + 2.59808i) q^{30} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{33} +3.00000 q^{34} +(-1.50000 + 2.59808i) q^{35} +(1.00000 + 1.73205i) q^{36} +(3.50000 + 6.06218i) q^{37} -2.00000 q^{38} +3.00000 q^{40} +(-0.500000 - 0.866025i) q^{42} +(0.500000 - 0.866025i) q^{43} +6.00000 q^{44} +(-3.00000 + 5.19615i) q^{45} +3.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.00000 + 5.19615i) q^{49} +(2.00000 + 3.46410i) q^{50} -3.00000 q^{51} +(-2.50000 - 4.33013i) q^{54} +(9.00000 + 15.5885i) q^{55} +(-0.500000 + 0.866025i) q^{56} +2.00000 q^{57} +(3.00000 - 5.19615i) q^{58} +(3.00000 - 5.19615i) q^{59} -3.00000 q^{60} +(-4.00000 + 6.92820i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-1.00000 - 1.73205i) q^{63} +1.00000 q^{64} -6.00000 q^{66} +(-7.00000 - 12.1244i) q^{67} +(1.50000 + 2.59808i) q^{68} -3.00000 q^{70} +(1.50000 - 2.59808i) q^{71} +(-1.00000 + 1.73205i) q^{72} +2.00000 q^{73} +(-3.50000 + 6.06218i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(-1.00000 - 1.73205i) q^{76} -6.00000 q^{77} +8.00000 q^{79} +(1.50000 + 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} +(0.500000 - 0.866025i) q^{84} +(-4.50000 + 7.79423i) q^{85} +1.00000 q^{86} +(-3.00000 + 5.19615i) q^{87} +(3.00000 + 5.19615i) q^{88} +(3.00000 + 5.19615i) q^{89} -6.00000 q^{90} +(2.00000 + 3.46410i) q^{93} +(1.50000 + 2.59808i) q^{94} +(3.00000 - 5.19615i) q^{95} -1.00000 q^{96} +(5.00000 - 8.66025i) q^{97} +(-3.00000 + 5.19615i) q^{98} -12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} - 6 q^{5} + q^{6} + q^{7} - 2 q^{8} + 2 q^{9} - 3 q^{10} - 6 q^{11} + 2 q^{12} + 2 q^{14} + 3 q^{15} - q^{16} + 3 q^{17} + 4 q^{18} - 2 q^{19} + 3 q^{20} - 2 q^{21} + 6 q^{22}+ \cdots - 24 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 - 6 * q^5 + q^6 + q^7 - 2 * q^8 + 2 * q^9 - 3 * q^10 - 6 * q^11 + 2 * q^12 + 2 * q^14 + 3 * q^15 - q^16 + 3 * q^17 + 4 * q^18 - 2 * q^19 + 3 * q^20 - 2 * q^21 + 6 * q^22 + q^24 + 8 * q^25 - 10 * q^27 + q^28 - 6 * q^29 - 3 * q^30 - 8 * q^31 + q^32 - 6 * q^33 + 6 * q^34 - 3 * q^35 + 2 * q^36 + 7 * q^37 - 4 * q^38 + 6 * q^40 - q^42 + q^43 + 12 * q^44 - 6 * q^45 + 6 * q^47 - q^48 + 6 * q^49 + 4 * q^50 - 6 * q^51 - 5 * q^54 + 18 * q^55 - q^56 + 4 * q^57 + 6 * q^58 + 6 * q^59 - 6 * q^60 - 8 * q^61 - 4 * q^62 - 2 * q^63 + 2 * q^64 - 12 * q^66 - 14 * q^67 + 3 * q^68 - 6 * q^70 + 3 * q^71 - 2 * q^72 + 4 * q^73 - 7 * q^74 - 4 * q^75 - 2 * q^76 - 12 * q^77 + 16 * q^79 + 3 * q^80 - q^81 + 24 * q^83 + q^84 - 9 * q^85 + 2 * q^86 - 6 * q^87 + 6 * q^88 + 6 * q^89 - 12 * q^90 + 4 * q^93 + 3 * q^94 + 6 * q^95 - 2 * q^96 + 10 * q^97 - 6 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−3.00000			−1.34164			−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000			−1.34164			−0.670820	+	0.741620i	$0.734058\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	0.944911	+	0.327327i	$0.106148\pi$
$8$	−1.00000			−0.353553
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.821541	−	0.570149i	$-0.806886\pi$
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.0829925	−	0.996550i	$-0.526448\pi$
$12$	1.00000			0.288675
$13$		0			0
$13$		0			0
$14$	1.00000			0.267261
$15$	1.50000	+	2.59808i	0.387298	+	0.670820i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	2.00000			0.471405
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	1.50000	−	2.59808i	0.335410	−	0.580948i
$21$	−1.00000			−0.218218
$22$	3.00000	−	5.19615i	0.639602	−	1.10782i
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	4.00000			0.800000
$26$		0			0
$27$	−5.00000			−0.962250
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$	−1.50000	+	2.59808i	−0.273861	+	0.474342i
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−3.00000	+	5.19615i	−0.522233	+	0.904534i
$34$	3.00000			0.514496
$35$	−1.50000	+	2.59808i	−0.253546	+	0.439155i
$36$	1.00000	+	1.73205i	0.166667	+	0.288675i
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$	−2.00000			−0.324443
$39$		0			0
$40$	3.00000			0.474342
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$	−0.500000	−	0.866025i	−0.0771517	−	0.133631i
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	6.00000			0.904534
$45$	−3.00000	+	5.19615i	−0.447214	+	0.774597i
$46$		0			0
$47$	3.00000			0.437595			0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000			0.437595			0.218797	+	0.975770i	$0.429787\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$	−3.00000			−0.420084
$52$		0			0
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	−2.50000	−	4.33013i	−0.340207	−	0.589256i
$55$	9.00000	+	15.5885i	1.21356	+	2.10195i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	2.00000			0.264906
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$	−3.00000			−0.387298
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	−2.00000	−	3.46410i	−0.254000	−	0.439941i
$63$	−1.00000	−	1.73205i	−0.125988	−	0.218218i
$64$	1.00000			0.125000
$65$		0			0
$66$	−6.00000			−0.738549
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	−0.876472	−	0.481452i	$-0.840109\pi$
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	0.0212861	−	0.999773i	$-0.493224\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$		0			0
$70$	−3.00000			−0.358569
$71$	1.50000	−	2.59808i	0.178017	−	0.308335i	−0.763184	−	0.646181i	$-0.776365\pi$
$71$	1.50000	−	2.59808i	0.178017	−	0.308335i	0.941201	+	0.337846i	$0.109698\pi$
$72$	−1.00000	+	1.73205i	−0.117851	+	0.204124i
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$	−3.50000	+	6.06218i	−0.406867	+	0.704714i
$75$	−2.00000	−	3.46410i	−0.230940	−	0.400000i
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$	−6.00000			−0.683763
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$	0.500000	−	0.866025i	0.0545545	−	0.0944911i
$85$	−4.50000	+	7.79423i	−0.488094	+	0.845403i
$86$	1.00000			0.107833
$87$	−3.00000	+	5.19615i	−0.321634	+	0.557086i
$88$	3.00000	+	5.19615i	0.319801	+	0.553912i
$89$	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	$0.730322\pi$
$90$	−6.00000			−0.632456
$91$		0			0
$92$		0			0
$93$	2.00000	+	3.46410i	0.207390	+	0.359211i
$94$	1.50000	+	2.59808i	0.154713	+	0.267971i
$95$	3.00000	−	5.19615i	0.307794	−	0.533114i
$96$	−1.00000			−0.102062
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	−0.492287	−	0.870433i	$-0.663839\pi$
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	0.999961	−	0.00888289i	$-0.00282755\pi$
$98$	−3.00000	+	5.19615i	−0.303046	+	0.524891i
$99$	−12.0000			−1.20605
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	0.993258	+	0.115924i	$0.0369830\pi$
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	−0.396236	+	0.918149i	$0.629684\pi$
$102$	−1.50000	−	2.59808i	−0.148522	−	0.257248i
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$		0			0
$105$	3.00000			0.292770
$106$		0			0
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$	2.50000	−	4.33013i	0.240563	−	0.416667i
$109$	−7.00000			−0.670478			−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000			−0.670478			−0.335239	+	0.942133i	$0.608817\pi$
$110$	−9.00000	+	15.5885i	−0.858116	+	1.48630i
$111$	3.50000	−	6.06218i	0.332205	−	0.575396i
$112$	−1.00000			−0.0944911
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	−0.689714	−	0.724082i	$-0.742264\pi$
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	0.971930	+	0.235269i	$0.0755971\pi$
$114$	1.00000	+	1.73205i	0.0936586	+	0.162221i
$115$		0			0
$116$	6.00000			0.557086
$117$		0			0
$118$	6.00000			0.552345
$119$	−1.50000	−	2.59808i	−0.137505	−	0.238165i
$120$	−1.50000	−	2.59808i	−0.136931	−	0.237171i
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$	−8.00000			−0.724286
$123$		0			0
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	3.00000			0.268328
$126$	1.00000	−	1.73205i	0.0890871	−	0.154303i
$127$	−10.0000	−	17.3205i	−0.887357	−	1.53695i	−0.842989	−	0.537931i	$-0.819206\pi$
$127$	−10.0000	−	17.3205i	−0.887357	−	1.53695i	−0.0443678	−	0.999015i	$-0.514127\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−1.00000			−0.0880451
$130$		0			0
$131$	−21.0000			−1.83478			−0.917389	−	0.397991i	$-0.869707\pi$
$131$	−21.0000			−1.83478			−0.917389	+	0.397991i	$0.869707\pi$
$132$	−3.00000	−	5.19615i	−0.261116	−	0.452267i
$133$	1.00000	+	1.73205i	0.0867110	+	0.150188i
$134$	7.00000	−	12.1244i	0.604708	−	1.04738i
$135$	15.0000			1.29099
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$137$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$138$		0			0
$139$	6.50000	−	11.2583i	0.551323	−	0.954919i	−0.446857	−	0.894606i	$-0.647457\pi$
$139$	6.50000	−	11.2583i	0.551323	−	0.954919i	0.998179	−	0.0603135i	$-0.0192101\pi$
$140$	−1.50000	−	2.59808i	−0.126773	−	0.219578i
$141$	−1.50000	−	2.59808i	−0.126323	−	0.218797i
$142$	3.00000			0.251754
$143$		0			0
$144$	−2.00000			−0.166667
$145$	9.00000	+	15.5885i	0.747409	+	1.29455i
$146$	1.00000	+	1.73205i	0.0827606	+	0.143346i
$147$	3.00000	−	5.19615i	0.247436	−	0.428571i
$148$	−7.00000			−0.575396
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	2.00000	−	3.46410i	0.163299	−	0.282843i
$151$	17.0000			1.38344			0.691720	−	0.722166i	$-0.256853\pi$
$151$	17.0000			1.38344			0.691720	+	0.722166i	$0.256853\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$	−3.00000	−	5.19615i	−0.242536	−	0.420084i
$154$	−3.00000	−	5.19615i	−0.241747	−	0.418718i
$155$	12.0000			0.963863
$156$		0			0
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	4.00000	+	6.92820i	0.318223	+	0.551178i
$159$		0			0
$160$	−1.50000	+	2.59808i	−0.118585	+	0.205396i
$161$		0			0
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	−0.361619	−	0.932326i	$-0.617776\pi$
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	0.988227	−	0.152992i	$-0.0488907\pi$
$164$		0			0
$165$	9.00000	−	15.5885i	0.700649	−	1.21356i
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$167$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$168$	1.00000			0.0771517
$169$		0			0
$170$	−9.00000			−0.690268
$171$	2.00000	+	3.46410i	0.152944	+	0.264906i
$172$	0.500000	+	0.866025i	0.0381246	+	0.0660338i
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$	−6.00000			−0.454859
$175$	2.00000	−	3.46410i	0.151186	−	0.261861i
$176$	−3.00000	+	5.19615i	−0.226134	+	0.391675i
$177$	−6.00000			−0.450988
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	0.804508	−	0.593942i	$-0.202429\pi$
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	−0.916623	+	0.399753i	$0.869096\pi$
$180$	−3.00000	−	5.19615i	−0.223607	−	0.387298i
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$		0			0
$183$	8.00000			0.591377
$184$		0			0
$185$	−10.5000	−	18.1865i	−0.771975	−	1.33710i
$186$	−2.00000	+	3.46410i	−0.146647	+	0.254000i
$187$	−18.0000			−1.31629
$188$	−1.50000	+	2.59808i	−0.109399	+	0.189484i
$189$	−2.50000	+	4.33013i	−0.181848	+	0.314970i
$190$	6.00000			0.435286
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	−0.331611	−	0.943416i	$-0.607592\pi$
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	0.982828	−	0.184525i	$-0.0590746\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	0.928986	−	0.370116i	$-0.120682\pi$
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	−0.785022	+	0.619467i	$0.787349\pi$
$194$	10.0000			0.717958
$195$		0			0
$196$	−6.00000			−0.428571
$197$	−1.50000	−	2.59808i	−0.106871	−	0.185105i	0.807630	−	0.589689i	$-0.200750\pi$
$197$	−1.50000	−	2.59808i	−0.106871	−	0.185105i	−0.914501	+	0.404584i	$0.867416\pi$
$198$	−6.00000	−	10.3923i	−0.426401	−	0.738549i
$199$	−1.00000	+	1.73205i	−0.0708881	+	0.122782i	−0.899291	−	0.437351i	$-0.855917\pi$
$199$	−1.00000	+	1.73205i	−0.0708881	+	0.122782i	0.828403	+	0.560133i	$0.189250\pi$
$200$	−4.00000			−0.282843
$201$	−7.00000	+	12.1244i	−0.493742	+	0.855186i
$202$	−6.00000	+	10.3923i	−0.422159	+	0.731200i
$203$	−6.00000			−0.421117
$204$	1.50000	−	2.59808i	0.105021	−	0.181902i
$205$		0			0
$206$	−2.00000	−	3.46410i	−0.139347	−	0.241355i
$207$		0			0
$208$		0			0
$209$	12.0000			0.830057
$210$	1.50000	+	2.59808i	0.103510	+	0.179284i
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	0.998221	−	0.0596196i	$-0.0189888\pi$
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	−0.550743	+	0.834675i	$0.685655\pi$
$212$		0			0
$213$	−3.00000			−0.205557
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$	−1.50000	+	2.59808i	−0.102299	+	0.177187i
$216$	5.00000			0.340207
$217$	−2.00000	+	3.46410i	−0.135769	+	0.235159i
$218$	−3.50000	−	6.06218i	−0.237050	−	0.410582i
$219$	−1.00000	−	1.73205i	−0.0675737	−	0.117041i
$220$	−18.0000			−1.21356
$221$		0			0
$222$	7.00000			0.469809
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	0.986267	+	0.165161i	$0.0528144\pi$
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	−0.350100	+	0.936713i	$0.613852\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	4.00000	−	6.92820i	0.266667	−	0.461880i
$226$	6.00000			0.399114
$227$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$227$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$228$	−1.00000	+	1.73205i	−0.0662266	+	0.114708i
$229$	−13.0000			−0.859064			−0.429532	−	0.903052i	$-0.641321\pi$
$229$	−13.0000			−0.859064			−0.429532	+	0.903052i	$0.641321\pi$
$230$		0			0
$231$	3.00000	+	5.19615i	0.197386	+	0.341882i
$232$	3.00000	+	5.19615i	0.196960	+	0.341144i
$233$	−27.0000			−1.76883			−0.884414	−	0.466702i	$-0.845442\pi$
$233$	−27.0000			−1.76883			−0.884414	+	0.466702i	$0.845442\pi$
$234$		0			0
$235$	−9.00000			−0.587095
$236$	3.00000	+	5.19615i	0.195283	+	0.338241i
$237$	−4.00000	−	6.92820i	−0.259828	−	0.450035i
$238$	1.50000	−	2.59808i	0.0972306	−	0.168408i
$239$	15.0000			0.970269			0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000			0.970269			0.485135	+	0.874439i	$0.338771\pi$
$240$	1.50000	−	2.59808i	0.0968246	−	0.167705i
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$	−25.0000			−1.60706
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$	−4.00000	−	6.92820i	−0.256074	−	0.443533i
$245$	−9.00000	−	15.5885i	−0.574989	−	0.995910i
$246$		0			0
$247$		0			0
$248$	4.00000			0.254000
$249$	−6.00000	−	10.3923i	−0.380235	−	0.658586i
$250$	1.50000	+	2.59808i	0.0948683	+	0.164317i
$251$	−12.0000	+	20.7846i	−0.757433	+	1.31191i	0.186722	+	0.982413i	$0.440214\pi$
$251$	−12.0000	+	20.7846i	−0.757433	+	1.31191i	−0.944156	+	0.329500i	$0.893120\pi$
$252$	2.00000			0.125988
$253$		0			0
$254$	10.0000	−	17.3205i	0.627456	−	1.08679i
$255$	9.00000			0.563602
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.50000	−	7.79423i	−0.280702	−	0.486191i	0.690856	−	0.722993i	$-0.257234\pi$
$257$	−4.50000	−	7.79423i	−0.280702	−	0.486191i	−0.971558	+	0.236802i	$0.923901\pi$
$258$	−0.500000	−	0.866025i	−0.0311286	−	0.0539164i
$259$	7.00000			0.434959
$260$		0			0
$261$	−12.0000			−0.742781
$262$	−10.5000	−	18.1865i	−0.648692	−	1.12357i
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	0.989561	−	0.144112i	$-0.0460326\pi$
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	−0.619586	+	0.784929i	$0.712699\pi$
$264$	3.00000	−	5.19615i	0.184637	−	0.319801i
$265$		0			0
$266$	−1.00000	+	1.73205i	−0.0613139	+	0.106199i
$267$	3.00000	−	5.19615i	0.183597	−	0.317999i
$268$	14.0000			0.855186
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	0.224523	+	0.974469i	$0.427917\pi$
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	−0.956176	+	0.292791i	$0.905416\pi$
$270$	7.50000	+	12.9904i	0.456435	+	0.790569i
$271$	−5.50000	−	9.52628i	−0.334101	−	0.578680i	0.649211	−	0.760609i	$-0.275099\pi$
$271$	−5.50000	−	9.52628i	−0.334101	−	0.578680i	−0.983312	+	0.181928i	$0.941766\pi$
$272$	−3.00000			−0.181902
$273$		0			0
$274$		0			0
$275$	−12.0000	−	20.7846i	−0.723627	−	1.25336i
$276$		0			0
$277$	14.0000	−	24.2487i	0.841178	−	1.45696i	−0.0477206	−	0.998861i	$-0.515196\pi$
$277$	14.0000	−	24.2487i	0.841178	−	1.45696i	0.888899	−	0.458103i	$-0.151471\pi$
$278$	13.0000			0.779688
$279$	−4.00000	+	6.92820i	−0.239474	+	0.414781i
$280$	1.50000	−	2.59808i	0.0896421	−	0.155265i
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$	1.50000	−	2.59808i	0.0893237	−	0.154713i
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	1.50000	+	2.59808i	0.0890086	+	0.154167i
$285$	−6.00000			−0.355409
$286$		0			0
$287$		0			0
$288$	−1.00000	−	1.73205i	−0.0589256	−	0.102062i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−9.00000	+	15.5885i	−0.528498	+	0.915386i
$291$	−10.0000			−0.586210
$292$	−1.00000	+	1.73205i	−0.0585206	+	0.101361i
$293$	−10.5000	+	18.1865i	−0.613417	+	1.06247i	0.377244	+	0.926114i	$0.376872\pi$
$293$	−10.5000	+	18.1865i	−0.613417	+	1.06247i	−0.990660	+	0.136355i	$0.956461\pi$
$294$	6.00000			0.349927
$295$	−9.00000	+	15.5885i	−0.524000	+	0.907595i
$296$	−3.50000	−	6.06218i	−0.203433	−	0.352357i
$297$	15.0000	+	25.9808i	0.870388	+	1.50756i
$298$	6.00000			0.347571
$299$		0			0
$300$	4.00000			0.230940
$301$	−0.500000	−	0.866025i	−0.0288195	−	0.0499169i
$302$	8.50000	+	14.7224i	0.489120	+	0.847181i
$303$	6.00000	−	10.3923i	0.344691	−	0.597022i
$304$	2.00000			0.114708
$305$	12.0000	−	20.7846i	0.687118	−	1.19012i
$306$	3.00000	−	5.19615i	0.171499	−	0.297044i
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$	3.00000	−	5.19615i	0.170941	−	0.296078i
$309$	2.00000	+	3.46410i	0.113776	+	0.197066i
$310$	6.00000	+	10.3923i	0.340777	+	0.590243i
$311$	−30.0000			−1.70114			−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000			−1.70114			−0.850572	+	0.525859i	$0.823744\pi$
$312$		0			0
$313$	−1.00000			−0.0565233			−0.0282617	−	0.999601i	$-0.508997\pi$
$313$	−1.00000			−0.0565233			−0.0282617	+	0.999601i	$0.508997\pi$
$314$	7.00000	+	12.1244i	0.395033	+	0.684217i
$315$	3.00000	+	5.19615i	0.169031	+	0.292770i
$316$	−4.00000	+	6.92820i	−0.225018	+	0.389742i
$317$	−6.00000			−0.336994			−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000			−0.336994			−0.168497	+	0.985702i	$0.553891\pi$
$318$		0			0
$319$	−18.0000	+	31.1769i	−1.00781	+	1.74557i
$320$	−3.00000			−0.167705
$321$	−6.00000	+	10.3923i	−0.334887	+	0.580042i
$322$		0			0
$323$	3.00000	+	5.19615i	0.166924	+	0.289122i
$324$	1.00000			0.0555556
$325$		0			0
$326$	16.0000			0.886158
$327$	3.50000	+	6.06218i	0.193550	+	0.335239i
$328$		0			0
$329$	1.50000	−	2.59808i	0.0826977	−	0.143237i
$330$	18.0000			0.990867
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	−0.954765	−	0.297361i	$-0.903893\pi$
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	0.734905	+	0.678170i	$0.237227\pi$
$332$	−6.00000	+	10.3923i	−0.329293	+	0.570352i
$333$	14.0000			0.767195
$334$		0			0
$335$	21.0000	+	36.3731i	1.14735	+	1.98727i
$336$	0.500000	+	0.866025i	0.0272772	+	0.0472456i
$337$	23.0000			1.25289			0.626445	−	0.779466i	$-0.284509\pi$
$337$	23.0000			1.25289			0.626445	+	0.779466i	$0.284509\pi$
$338$		0			0
$339$	−6.00000			−0.325875
$340$	−4.50000	−	7.79423i	−0.244047	−	0.422701i
$341$	12.0000	+	20.7846i	0.649836	+	1.12555i
$342$	−2.00000	+	3.46410i	−0.108148	+	0.187317i
$343$	13.0000			0.701934
$344$	−0.500000	+	0.866025i	−0.0269582	+	0.0466930i
$345$		0			0
$346$		0			0
$347$	−1.50000	+	2.59808i	−0.0805242	+	0.139472i	−0.903475	−	0.428640i	$-0.858993\pi$
$347$	−1.50000	+	2.59808i	−0.0805242	+	0.139472i	0.822951	+	0.568112i	$0.192326\pi$
$348$	−3.00000	−	5.19615i	−0.160817	−	0.278543i
$349$	9.50000	+	16.4545i	0.508523	+	0.880788i	0.999951	+	0.00987003i	$0.00314178\pi$
$349$	9.50000	+	16.4545i	0.508523	+	0.880788i	−0.491428	+	0.870918i	$0.663525\pi$
$350$	4.00000			0.213809
$351$		0			0
$352$	−6.00000			−0.319801
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	−0.985719	−	0.168397i	$-0.946141\pi$
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	0.347024	−	0.937856i	$-0.387192\pi$
$354$	−3.00000	−	5.19615i	−0.159448	−	0.276172i
$355$	−4.50000	+	7.79423i	−0.238835	+	0.413675i
$356$	−6.00000			−0.317999
$357$	−1.50000	+	2.59808i	−0.0793884	+	0.137505i
$358$	1.50000	−	2.59808i	0.0792775	−	0.137313i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$	3.00000	−	5.19615i	0.158114	−	0.273861i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	10.0000	+	17.3205i	0.525588	+	0.910346i
$363$	25.0000			1.31216
$364$		0			0
$365$	−6.00000			−0.314054
$366$	4.00000	+	6.92820i	0.209083	+	0.362143i
$367$	−13.0000	−	22.5167i	−0.678594	−	1.17536i	−0.975404	−	0.220423i	$-0.929256\pi$
$367$	−13.0000	−	22.5167i	−0.678594	−	1.17536i	0.296810	−	0.954937i	$-0.404077\pi$
$368$		0			0
$369$		0			0
$370$	10.5000	−	18.1865i	0.545869	−	0.945473i
$371$		0			0
$372$	−4.00000			−0.207390
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	−0.809591	−	0.586994i	$-0.800311\pi$
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	0.913147	+	0.407630i	$0.133645\pi$
$374$	−9.00000	−	15.5885i	−0.465379	−	0.806060i
$375$	−1.50000	−	2.59808i	−0.0774597	−	0.134164i
$376$	−3.00000			−0.154713
$377$		0			0
$378$	−5.00000			−0.257172
$379$	−10.0000	−	17.3205i	−0.513665	−	0.889695i	−0.999874	−	0.0158521i	$-0.994954\pi$
$379$	−10.0000	−	17.3205i	−0.513665	−	0.889695i	0.486209	−	0.873843i	$-0.338379\pi$
$380$	3.00000	+	5.19615i	0.153897	+	0.266557i
$381$	−10.0000	+	17.3205i	−0.512316	+	0.887357i
$382$	18.0000			0.920960
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	0.462563	+	0.886586i	$0.346930\pi$
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	−0.999088	+	0.0427020i	$0.986403\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	18.0000			0.917365
$386$	−2.00000	+	3.46410i	−0.101797	+	0.176318i
$387$	−1.00000	−	1.73205i	−0.0508329	−	0.0880451i
$388$	5.00000	+	8.66025i	0.253837	+	0.439658i
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$		0			0
$391$		0			0
$392$	−3.00000	−	5.19615i	−0.151523	−	0.262445i
$393$	10.5000	+	18.1865i	0.529655	+	0.917389i
$394$	1.50000	−	2.59808i	0.0755689	−	0.130889i
$395$	−24.0000			−1.20757
$396$	6.00000	−	10.3923i	0.301511	−	0.522233i
$397$	17.0000	−	29.4449i	0.853206	−	1.47780i	−0.0250943	−	0.999685i	$-0.507989\pi$
$397$	17.0000	−	29.4449i	0.853206	−	1.47780i	0.878300	−	0.478110i	$-0.158678\pi$
$398$	−2.00000			−0.100251
$399$	1.00000	−	1.73205i	0.0500626	−	0.0867110i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−18.0000	−	31.1769i	−0.898877	−	1.55690i	−0.828932	−	0.559350i	$-0.811051\pi$
$401$	−18.0000	−	31.1769i	−0.898877	−	1.55690i	−0.0699455	−	0.997551i	$-0.522283\pi$
$402$	−14.0000			−0.698257
$403$		0			0
$404$	−12.0000			−0.597022
$405$	1.50000	+	2.59808i	0.0745356	+	0.129099i
$406$	−3.00000	−	5.19615i	−0.148888	−	0.257881i
$407$	21.0000	−	36.3731i	1.04093	−	1.80295i
$408$	3.00000			0.148522
$409$	−16.0000	+	27.7128i	−0.791149	+	1.37031i	0.134107	+	0.990967i	$0.457183\pi$
$409$	−16.0000	+	27.7128i	−0.791149	+	1.37031i	−0.925256	+	0.379344i	$0.876150\pi$
$410$		0			0
$411$		0			0
$412$	2.00000	−	3.46410i	0.0985329	−	0.170664i
$413$	−3.00000	−	5.19615i	−0.147620	−	0.255686i
$414$		0			0
$415$	−36.0000			−1.76717
$416$		0			0
$417$	−13.0000			−0.636613
$418$	6.00000	+	10.3923i	0.293470	+	0.508304i
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	0.734919	−	0.678155i	$-0.237220\pi$
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	−0.954759	+	0.297382i	$0.903887\pi$
$420$	−1.50000	+	2.59808i	−0.0731925	+	0.126773i
$421$	17.0000			0.828529			0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000			0.828529			0.414265	+	0.910156i	$0.364039\pi$
$422$	−6.50000	+	11.2583i	−0.316415	+	0.548047i
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$		0			0
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$	−1.50000	−	2.59808i	−0.0726752	−	0.125877i
$427$	4.00000	+	6.92820i	0.193574	+	0.335279i
$428$	12.0000			0.580042
$429$		0			0
$430$	−3.00000			−0.144673
$431$	16.5000	+	28.5788i	0.794777	+	1.37659i	0.922981	+	0.384846i	$0.125746\pi$
$431$	16.5000	+	28.5788i	0.794777	+	1.37659i	−0.128204	+	0.991748i	$0.540921\pi$
$432$	2.50000	+	4.33013i	0.120281	+	0.208333i
$433$	12.5000	−	21.6506i	0.600712	−	1.04046i	−0.392002	−	0.919964i	$-0.628217\pi$
$433$	12.5000	−	21.6506i	0.600712	−	1.04046i	0.992713	−	0.120499i	$-0.0384494\pi$
$434$	−4.00000			−0.192006
$435$	9.00000	−	15.5885i	0.431517	−	0.747409i
$436$	3.50000	−	6.06218i	0.167620	−	0.290326i
$437$		0			0
$438$	1.00000	−	1.73205i	0.0477818	−	0.0827606i
$439$	−13.0000	−	22.5167i	−0.620456	−	1.07466i	−0.989401	−	0.145210i	$-0.953614\pi$
$439$	−13.0000	−	22.5167i	−0.620456	−	1.07466i	0.368945	−	0.929451i	$-0.379719\pi$
$440$	−9.00000	−	15.5885i	−0.429058	−	0.743151i
$441$	12.0000			0.571429
$442$		0			0
$443$	21.0000			0.997740			0.498870	−	0.866677i	$-0.333748\pi$
$443$	21.0000			0.997740			0.498870	+	0.866677i	$0.333748\pi$
$444$	3.50000	+	6.06218i	0.166103	+	0.287698i
$445$	−9.00000	−	15.5885i	−0.426641	−	0.738964i
$446$	−9.50000	+	16.4545i	−0.449838	+	0.779142i
$447$	−6.00000			−0.283790
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	−3.00000	+	5.19615i	−0.141579	+	0.245222i	−0.928091	−	0.372353i	$-0.878551\pi$
$449$	−3.00000	+	5.19615i	−0.141579	+	0.245222i	0.786513	+	0.617574i	$0.211885\pi$
$450$	8.00000			0.377124
$451$		0			0
$452$	3.00000	+	5.19615i	0.141108	+	0.244406i
$453$	−8.50000	−	14.7224i	−0.399365	−	0.691720i
$454$		0			0
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	0.958950	−	0.283577i	$-0.0915211\pi$
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	−0.725059	+	0.688686i	$0.758188\pi$
$458$	−6.50000	−	11.2583i	−0.303725	−	0.526067i
$459$	−7.50000	+	12.9904i	−0.350070	+	0.606339i
$460$		0			0
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	−0.951584	−	0.307388i	$-0.900545\pi$
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	0.741998	+	0.670402i	$0.233878\pi$
$462$	−3.00000	+	5.19615i	−0.139573	+	0.241747i
$463$	−40.0000			−1.85896			−0.929479	−	0.368875i	$-0.879743\pi$
$463$	−40.0000			−1.85896			−0.929479	+	0.368875i	$0.879743\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	−6.00000	−	10.3923i	−0.278243	−	0.481932i
$466$	−13.5000	−	23.3827i	−0.625375	−	1.08318i
$467$	36.0000			1.66588			0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000			1.66588			0.832941	+	0.553362i	$0.186655\pi$
$468$		0			0
$469$	−14.0000			−0.646460
$470$	−4.50000	−	7.79423i	−0.207570	−	0.359521i
$471$	−7.00000	−	12.1244i	−0.322543	−	0.558661i
$472$	−3.00000	+	5.19615i	−0.138086	+	0.239172i
$473$	−6.00000			−0.275880
$474$	4.00000	−	6.92820i	0.183726	−	0.318223i
$475$	−4.00000	+	6.92820i	−0.183533	+	0.317888i
$476$	3.00000			0.137505
$477$		0			0
$478$	7.50000	+	12.9904i	0.343042	+	0.594166i
$479$	10.5000	+	18.1865i	0.479757	+	0.830964i	0.999730	−	0.0232187i	$-0.00739140\pi$
$479$	10.5000	+	18.1865i	0.479757	+	0.830964i	−0.519973	+	0.854183i	$0.674058\pi$
$480$	3.00000			0.136931
$481$		0			0
$482$	10.0000			0.455488
$483$		0			0
$484$	−12.5000	−	21.6506i	−0.568182	−	0.984120i
$485$	−15.0000	+	25.9808i	−0.681115	+	1.17973i
$486$	−16.0000			−0.725775
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	−0.625859	−	0.779936i	$-0.715252\pi$
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	0.988374	+	0.152042i	$0.0485850\pi$
$488$	4.00000	−	6.92820i	0.181071	−	0.313625i
$489$	−16.0000			−0.723545
$490$	9.00000	−	15.5885i	0.406579	−	0.704215i
$491$	4.50000	+	7.79423i	0.203082	+	0.351749i	0.949520	−	0.313707i	$-0.101571\pi$
$491$	4.50000	+	7.79423i	0.203082	+	0.351749i	−0.746438	+	0.665455i	$0.768237\pi$
$492$		0			0
$493$	−18.0000			−0.810679
$494$		0			0
$495$	36.0000			1.61808
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$	−1.50000	−	2.59808i	−0.0672842	−	0.116540i
$498$	6.00000	−	10.3923i	0.268866	−	0.465690i
$499$	−40.0000			−1.79065			−0.895323	−	0.445418i	$-0.853055\pi$
$499$	−40.0000			−1.79065			−0.895323	+	0.445418i	$0.853055\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$		0			0
$502$	−24.0000			−1.07117
$503$	15.0000	−	25.9808i	0.668817	−	1.15842i	−0.309418	−	0.950926i	$-0.600134\pi$
$503$	15.0000	−	25.9808i	0.668817	−	1.15842i	0.978235	−	0.207499i	$-0.0665323\pi$
$504$	1.00000	+	1.73205i	0.0445435	+	0.0771517i
$505$	−18.0000	−	31.1769i	−0.800989	−	1.38735i
$506$		0			0
$507$		0			0
$508$	20.0000			0.887357
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	0.993593	−	0.113020i	$-0.0360525\pi$
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	−0.594675	+	0.803966i	$0.702719\pi$
$510$	4.50000	+	7.79423i	0.199263	+	0.345134i
$511$	1.00000	−	1.73205i	0.0442374	−	0.0766214i
$512$	−1.00000			−0.0441942
$513$	5.00000	−	8.66025i	0.220755	−	0.382360i
$514$	4.50000	−	7.79423i	0.198486	−	0.343789i
$515$	12.0000			0.528783
$516$	0.500000	−	0.866025i	0.0220113	−	0.0381246i
$517$	−9.00000	−	15.5885i	−0.395820	−	0.685580i
$518$	3.50000	+	6.06218i	0.153781	+	0.266357i
$519$		0			0
$520$		0			0
$521$	−9.00000			−0.394297			−0.197149	−	0.980374i	$-0.563168\pi$
$521$	−9.00000			−0.394297			−0.197149	+	0.980374i	$0.563168\pi$
$522$	−6.00000	−	10.3923i	−0.262613	−	0.454859i
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	0.560208	−	0.828352i	$-0.310721\pi$
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	−0.997478	+	0.0709788i	$0.977388\pi$
$524$	10.5000	−	18.1865i	0.458695	−	0.794482i
$525$	−4.00000			−0.174574
$526$	−6.00000	+	10.3923i	−0.261612	+	0.453126i
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$	6.00000			0.261116
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$		0			0
$531$	−6.00000	−	10.3923i	−0.260378	−	0.450988i
$532$	−2.00000			−0.0867110
$533$		0			0
$534$	6.00000			0.259645
$535$	18.0000	+	31.1769i	0.778208	+	1.34790i
$536$	7.00000	+	12.1244i	0.302354	+	0.523692i
$537$	−1.50000	+	2.59808i	−0.0647298	+	0.112115i
$538$	−24.0000			−1.03471
$539$	18.0000	−	31.1769i	0.775315	−	1.34288i
$540$	−7.50000	+	12.9904i	−0.322749	+	0.559017i
$541$	11.0000			0.472927			0.236463	−	0.971640i	$-0.424012\pi$
$541$	11.0000			0.472927			0.236463	+	0.971640i	$0.424012\pi$
$542$	5.50000	−	9.52628i	0.236245	−	0.409189i
$543$	−10.0000	−	17.3205i	−0.429141	−	0.743294i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$	21.0000			0.899541
$546$		0			0
$547$	17.0000			0.726868			0.363434	−	0.931620i	$-0.381604\pi$
$547$	17.0000			0.726868			0.363434	+	0.931620i	$0.381604\pi$
$548$		0			0
$549$	8.00000	+	13.8564i	0.341432	+	0.591377i
$550$	12.0000	−	20.7846i	0.511682	−	0.886259i
$551$	12.0000			0.511217
$552$		0			0
$553$	4.00000	−	6.92820i	0.170097	−	0.294617i
$554$	28.0000			1.18961
$555$	−10.5000	+	18.1865i	−0.445700	+	0.771975i
$556$	6.50000	+	11.2583i	0.275661	+	0.477460i
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	0.832496	−	0.554031i	$-0.186911\pi$
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	−0.896053	+	0.443947i	$0.853578\pi$
$558$	−8.00000			−0.338667
$559$		0			0
$560$	3.00000			0.126773
$561$	9.00000	+	15.5885i	0.379980	+	0.658145i
$562$	−3.00000	−	5.19615i	−0.126547	−	0.219186i
$563$	−19.5000	+	33.7750i	−0.821827	+	1.42345i	0.0824933	+	0.996592i	$0.473712\pi$
$563$	−19.5000	+	33.7750i	−0.821827	+	1.42345i	−0.904320	+	0.426855i	$0.859622\pi$
$564$	3.00000			0.126323
$565$	−9.00000	+	15.5885i	−0.378633	+	0.655811i
$566$	−2.00000	+	3.46410i	−0.0840663	+	0.145607i
$567$	−1.00000			−0.0419961
$568$	−1.50000	+	2.59808i	−0.0629386	+	0.109013i
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	0.664897	−	0.746935i	$-0.268475\pi$
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	−0.979313	+	0.202350i	$0.935142\pi$
$570$	−3.00000	−	5.19615i	−0.125656	−	0.217643i
$571$	5.00000			0.209243			0.104622	−	0.994512i	$-0.466637\pi$
$571$	5.00000			0.209243			0.104622	+	0.994512i	$0.466637\pi$
$572$		0			0
$573$	−18.0000			−0.751961
$574$		0			0
$575$		0			0
$576$	1.00000	−	1.73205i	0.0416667	−	0.0721688i
$577$	38.0000			1.58196			0.790980	−	0.611842i	$-0.209571\pi$
$577$	38.0000			1.58196			0.790980	+	0.611842i	$0.209571\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$	2.00000	−	3.46410i	0.0831172	−	0.143963i
$580$	−18.0000			−0.747409
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	−5.00000	−	8.66025i	−0.207257	−	0.358979i
$583$		0			0
$584$	−2.00000			−0.0827606
$585$		0			0
$586$	−21.0000			−0.867502
$587$	−12.0000	−	20.7846i	−0.495293	−	0.857873i	0.504692	−	0.863299i	$-0.331606\pi$
$587$	−12.0000	−	20.7846i	−0.495293	−	0.857873i	−0.999985	+	0.00542667i	$0.998273\pi$
$588$	3.00000	+	5.19615i	0.123718	+	0.214286i
$589$	4.00000	−	6.92820i	0.164817	−	0.285472i
$590$	−18.0000			−0.741048
$591$	−1.50000	+	2.59808i	−0.0617018	+	0.106871i
$592$	3.50000	−	6.06218i	0.143849	−	0.249154i
$593$	18.0000			0.739171			0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000			0.739171			0.369586	+	0.929197i	$0.379500\pi$
$594$	−15.0000	+	25.9808i	−0.615457	+	1.06600i
$595$	4.50000	+	7.79423i	0.184482	+	0.319532i
$596$	3.00000	+	5.19615i	0.122885	+	0.212843i
$597$	2.00000			0.0818546
$598$		0			0
$599$	6.00000			0.245153			0.122577	−	0.992459i	$-0.460884\pi$
$599$	6.00000			0.245153			0.122577	+	0.992459i	$0.460884\pi$
$600$	2.00000	+	3.46410i	0.0816497	+	0.141421i
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	0.992114	−	0.125336i	$-0.0400009\pi$
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	−0.604601	+	0.796528i	$0.706668\pi$
$602$	0.500000	−	0.866025i	0.0203785	−	0.0352966i
$603$	−28.0000			−1.14025
$604$	−8.50000	+	14.7224i	−0.345860	+	0.599047i
$605$	37.5000	−	64.9519i	1.52459	−	2.64067i
$606$	12.0000			0.487467
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	−0.972396	−	0.233338i	$-0.925035\pi$
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	0.688274	+	0.725450i	$0.258368\pi$
$608$	1.00000	+	1.73205i	0.0405554	+	0.0702439i
$609$	3.00000	+	5.19615i	0.121566	+	0.210559i
$610$	24.0000			0.971732
$611$		0			0
$612$	6.00000			0.242536
$613$	−19.0000	−	32.9090i	−0.767403	−	1.32918i	−0.938967	−	0.344008i	$-0.888215\pi$
$613$	−19.0000	−	32.9090i	−0.767403	−	1.32918i	0.171564	−	0.985173i	$-0.445118\pi$
$614$	1.00000	+	1.73205i	0.0403567	+	0.0698999i
$615$		0			0
$616$	6.00000			0.241747
$617$	12.0000	−	20.7846i	0.483102	−	0.836757i	−0.516710	−	0.856161i	$-0.672843\pi$
$617$	12.0000	−	20.7846i	0.483102	−	0.836757i	0.999812	+	0.0194037i	$0.00617676\pi$
$618$	−2.00000	+	3.46410i	−0.0804518	+	0.139347i
$619$	−28.0000			−1.12542			−0.562708	−	0.826656i	$-0.690240\pi$
$619$	−28.0000			−1.12542			−0.562708	+	0.826656i	$0.690240\pi$
$620$	−6.00000	+	10.3923i	−0.240966	+	0.417365i
$621$		0			0
$622$	−15.0000	−	25.9808i	−0.601445	−	1.04173i
$623$	6.00000			0.240385
$624$		0			0
$625$	−29.0000			−1.16000
$626$	−0.500000	−	0.866025i	−0.0199840	−	0.0346133i
$627$	−6.00000	−	10.3923i	−0.239617	−	0.415029i
$628$	−7.00000	+	12.1244i	−0.279330	+	0.483814i
$629$	21.0000			0.837325
$630$	−3.00000	+	5.19615i	−0.119523	+	0.207020i
$631$	−14.5000	+	25.1147i	−0.577236	+	0.999802i	0.418559	+	0.908190i	$0.362535\pi$
$631$	−14.5000	+	25.1147i	−0.577236	+	0.999802i	−0.995795	+	0.0916122i	$0.970798\pi$
$632$	−8.00000			−0.318223
$633$	6.50000	−	11.2583i	0.258352	−	0.447478i
$634$	−3.00000	−	5.19615i	−0.119145	−	0.206366i
$635$	30.0000	+	51.9615i	1.19051	+	2.06203i
$636$		0			0
$637$		0			0
$638$	−36.0000			−1.42525
$639$	−3.00000	−	5.19615i	−0.118678	−	0.205557i
$640$	−1.50000	−	2.59808i	−0.0592927	−	0.102698i
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	−0.631721	−	0.775196i	$-0.717651\pi$
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	0.987200	+	0.159489i	$0.0509845\pi$
$642$	−12.0000			−0.473602
$643$	−7.00000	+	12.1244i	−0.276053	+	0.478138i	−0.970400	−	0.241502i	$-0.922360\pi$
$643$	−7.00000	+	12.1244i	−0.276053	+	0.478138i	0.694347	+	0.719640i	$0.255693\pi$
$644$		0			0
$645$	3.00000			0.118125
$646$	−3.00000	+	5.19615i	−0.118033	+	0.204440i
$647$	3.00000	+	5.19615i	0.117942	+	0.204282i	0.918952	−	0.394369i	$-0.129037\pi$
$647$	3.00000	+	5.19615i	0.117942	+	0.204282i	−0.801010	+	0.598651i	$0.795704\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−36.0000			−1.41312
$650$		0			0
$651$	4.00000			0.156772
$652$	8.00000	+	13.8564i	0.313304	+	0.542659i
$653$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$653$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$654$	−3.50000	+	6.06218i	−0.136861	+	0.237050i
$655$	63.0000			2.46161
$656$		0			0
$657$	2.00000	−	3.46410i	0.0780274	−	0.135147i
$658$	3.00000			0.116952
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	−0.266872	−	0.963732i	$-0.585990\pi$
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	0.968052	−	0.250748i	$-0.0806766\pi$
$660$	9.00000	+	15.5885i	0.350325	+	0.606780i
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	0.996682	−	0.0813955i	$-0.0259377\pi$
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	−0.568831	+	0.822454i	$0.692604\pi$
$662$	−8.00000			−0.310929
$663$		0			0
$664$	−12.0000			−0.465690
$665$	−3.00000	−	5.19615i	−0.116335	−	0.201498i
$666$	7.00000	+	12.1244i	0.271244	+	0.469809i
$667$		0			0
$668$		0			0
$669$	9.50000	−	16.4545i	0.367291	−	0.636167i
$670$	−21.0000	+	36.3731i	−0.811301	+	1.40521i
$671$	48.0000			1.85302
$672$	−0.500000	+	0.866025i	−0.0192879	+	0.0334077i
$673$	9.50000	+	16.4545i	0.366198	+	0.634274i	0.988968	−	0.148132i	$-0.0473259\pi$
$673$	9.50000	+	16.4545i	0.366198	+	0.634274i	−0.622770	+	0.782405i	$0.713993\pi$
$674$	11.5000	+	19.9186i	0.442963	+	0.767235i
$675$	−20.0000			−0.769800
$676$		0			0
$677$	48.0000			1.84479			0.922395	−	0.386248i	$-0.126229\pi$
$677$	48.0000			1.84479			0.922395	+	0.386248i	$0.126229\pi$
$678$	−3.00000	−	5.19615i	−0.115214	−	0.199557i
$679$	−5.00000	−	8.66025i	−0.191882	−	0.332350i
$680$	4.50000	−	7.79423i	0.172567	−	0.298895i
$681$		0			0
$682$	−12.0000	+	20.7846i	−0.459504	+	0.795884i
$683$	−12.0000	+	20.7846i	−0.459167	+	0.795301i	−0.998917	−	0.0465244i	$-0.985185\pi$
$683$	−12.0000	+	20.7846i	−0.459167	+	0.795301i	0.539750	+	0.841825i	$0.318519\pi$
$684$	−4.00000			−0.152944
$685$		0			0
$686$	6.50000	+	11.2583i	0.248171	+	0.429845i
$687$	6.50000	+	11.2583i	0.247990	+	0.429532i
$688$	−1.00000			−0.0381246
$689$		0			0
$690$		0			0
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$		0			0
$693$	−6.00000	+	10.3923i	−0.227921	+	0.394771i
$694$	−3.00000			−0.113878
$695$	−19.5000	+	33.7750i	−0.739677	+	1.28116i
$696$	3.00000	−	5.19615i	0.113715	−	0.196960i
$697$		0			0
$698$	−9.50000	+	16.4545i	−0.359580	+	0.622811i
$699$	13.5000	+	23.3827i	0.510617	+	0.884414i
$700$	2.00000	+	3.46410i	0.0755929	+	0.130931i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	−14.0000			−0.528020
$704$	−3.00000	−	5.19615i	−0.113067	−	0.195837i
$705$	4.50000	+	7.79423i	0.169480	+	0.293548i
$706$	12.0000	−	20.7846i	0.451626	−	0.782239i
$707$	12.0000			0.451306
$708$	3.00000	−	5.19615i	0.112747	−	0.195283i
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	−0.999908	−	0.0135434i	$-0.995689\pi$
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	0.511683	+	0.859174i	$0.329022\pi$
$710$	−9.00000			−0.337764
$711$	8.00000	−	13.8564i	0.300023	−	0.519656i
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$		0			0
$714$	−3.00000			−0.112272
$715$		0			0
$716$	3.00000			0.112115
$717$	−7.50000	−	12.9904i	−0.280093	−	0.485135i
$718$		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	$0.202354\pi$
$720$	6.00000			0.223607
$721$	−2.00000	+	3.46410i	−0.0744839	+	0.129010i
$722$	−7.50000	+	12.9904i	−0.279121	+	0.483452i
$723$	−10.0000			−0.371904
$724$	−10.0000	+	17.3205i	−0.371647	+	0.643712i
$725$	−12.0000	−	20.7846i	−0.445669	−	0.771921i
$726$	12.5000	+	21.6506i	0.463919	+	0.803530i
$727$	−10.0000			−0.370879			−0.185440	−	0.982656i	$-0.559371\pi$
$727$	−10.0000			−0.370879			−0.185440	+	0.982656i	$0.559371\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	−3.00000	−	5.19615i	−0.111035	−	0.192318i
$731$	−1.50000	−	2.59808i	−0.0554795	−	0.0960933i
$732$	−4.00000	+	6.92820i	−0.147844	+	0.256074i
$733$	23.0000			0.849524			0.424762	−	0.905305i	$-0.360358\pi$
$733$	23.0000			0.849524			0.424762	+	0.905305i	$0.360358\pi$
$734$	13.0000	−	22.5167i	0.479839	−	0.831105i
$735$	−9.00000	+	15.5885i	−0.331970	+	0.574989i
$736$		0			0
$737$	−42.0000	+	72.7461i	−1.54709	+	2.67964i
$738$		0			0
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	0.621374	−	0.783514i	$-0.286575\pi$
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	−0.989230	+	0.146369i	$0.953241\pi$
$740$	21.0000			0.771975
$741$		0			0
$742$		0			0
$743$	4.50000	+	7.79423i	0.165089	+	0.285943i	0.936687	−	0.350168i	$-0.113876\pi$
$743$	4.50000	+	7.79423i	0.165089	+	0.285943i	−0.771598	+	0.636111i	$0.780542\pi$
$744$	−2.00000	−	3.46410i	−0.0733236	−	0.127000i
$745$	−9.00000	+	15.5885i	−0.329734	+	0.571117i
$746$	4.00000			0.146450
$747$	12.0000	−	20.7846i	0.439057	−	0.760469i
$748$	9.00000	−	15.5885i	0.329073	−	0.569970i
$749$	−12.0000			−0.438470
$750$	1.50000	−	2.59808i	0.0547723	−	0.0948683i
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	0.956963	+	0.290209i	$0.0937250\pi$
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	−0.227153	+	0.973859i	$0.572942\pi$
$752$	−1.50000	−	2.59808i	−0.0546994	−	0.0947421i
$753$	24.0000			0.874609
$754$		0			0
$755$	−51.0000			−1.85608
$756$	−2.50000	−	4.33013i	−0.0909241	−	0.157485i
$757$	8.00000	+	13.8564i	0.290765	+	0.503620i	0.973991	−	0.226587i	$-0.0727569\pi$
$757$	8.00000	+	13.8564i	0.290765	+	0.503620i	−0.683226	+	0.730207i	$0.739424\pi$
$758$	10.0000	−	17.3205i	0.363216	−	0.629109i
$759$		0			0
$760$	−3.00000	+	5.19615i	−0.108821	+	0.188484i
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	−0.806514	−	0.591215i	$-0.798649\pi$
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	0.915264	+	0.402854i	$0.131982\pi$
$762$	−20.0000			−0.724524
$763$	−3.50000	+	6.06218i	−0.126709	+	0.219466i
$764$	9.00000	+	15.5885i	0.325609	+	0.563971i
$765$	9.00000	+	15.5885i	0.325396	+	0.563602i
$766$	−21.0000			−0.758761
$767$		0			0
$768$	1.00000			0.0360844
$769$	−16.0000	−	27.7128i	−0.576975	−	0.999350i	−0.995824	−	0.0912938i	$-0.970900\pi$
$769$	−16.0000	−	27.7128i	−0.576975	−	0.999350i	0.418849	−	0.908056i	$-0.362434\pi$
$770$	9.00000	+	15.5885i	0.324337	+	0.561769i
$771$	−4.50000	+	7.79423i	−0.162064	+	0.280702i
$772$	−4.00000			−0.143963
$773$	19.5000	−	33.7750i	0.701366	−	1.21480i	−0.266621	−	0.963802i	$-0.585907\pi$
$773$	19.5000	−	33.7750i	0.701366	−	1.21480i	0.967987	−	0.251000i	$-0.0807596\pi$
$774$	1.00000	−	1.73205i	0.0359443	−	0.0622573i
$775$	−16.0000			−0.574737
$776$	−5.00000	+	8.66025i	−0.179490	+	0.310885i
$777$	−3.50000	−	6.06218i	−0.125562	−	0.217479i
$778$	−3.00000	−	5.19615i	−0.107555	−	0.186291i
$779$		0			0
$780$		0			0
$781$	−18.0000			−0.644091
$782$		0			0
$783$	15.0000	+	25.9808i	0.536056	+	0.928477i
$784$	3.00000	−	5.19615i	0.107143	−	0.185577i
$785$	−42.0000			−1.49904
$786$	−10.5000	+	18.1865i	−0.374523	+	0.648692i
$787$	20.0000	−	34.6410i	0.712923	−	1.23482i	−0.250832	−	0.968031i	$-0.580704\pi$
$787$	20.0000	−	34.6410i	0.712923	−	1.23482i	0.963755	−	0.266788i	$-0.0859624\pi$
$788$	3.00000			0.106871
$789$	6.00000	−	10.3923i	0.213606	−	0.369976i
$790$	−12.0000	−	20.7846i	−0.426941	−	0.739483i
$791$	−3.00000	−	5.19615i	−0.106668	−	0.184754i
$792$	12.0000			0.426401
$793$		0			0
$794$	34.0000			1.20661
$795$		0			0
$796$	−1.00000	−	1.73205i	−0.0354441	−	0.0613909i
$797$	21.0000	−	36.3731i	0.743858	−	1.28840i	−0.206868	−	0.978369i	$-0.566327\pi$
$797$	21.0000	−	36.3731i	0.743858	−	1.28840i	0.950726	−	0.310031i	$-0.100340\pi$
$798$	2.00000			0.0707992
$799$	4.50000	−	7.79423i	0.159199	−	0.275740i
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$	12.0000			0.423999
$802$	18.0000	−	31.1769i	0.635602	−	1.10090i
$803$	−6.00000	−	10.3923i	−0.211735	−	0.366736i
$804$	−7.00000	−	12.1244i	−0.246871	−	0.427593i
$805$		0			0
$806$		0			0
$807$	24.0000			0.844840
$808$	−6.00000	−	10.3923i	−0.211079	−	0.365600i
$809$	16.5000	+	28.5788i	0.580109	+	1.00478i	0.995466	+	0.0951198i	$0.0303234\pi$
$809$	16.5000	+	28.5788i	0.580109	+	1.00478i	−0.415357	+	0.909659i	$0.636343\pi$
$810$	−1.50000	+	2.59808i	−0.0527046	+	0.0912871i
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	3.00000	−	5.19615i	0.105279	−	0.182349i
$813$	−5.50000	+	9.52628i	−0.192893	+	0.334101i
$814$	42.0000			1.47210
$815$	−24.0000	+	41.5692i	−0.840683	+	1.45611i
$816$	1.50000	+	2.59808i	0.0525105	+	0.0909509i
$817$	1.00000	+	1.73205i	0.0349856	+	0.0605968i
$818$	−32.0000			−1.11885
$819$		0			0
$820$		0			0
$821$	1.50000	+	2.59808i	0.0523504	+	0.0906735i	0.891013	−	0.453978i	$-0.149995\pi$
$821$	1.50000	+	2.59808i	0.0523504	+	0.0906735i	−0.838663	+	0.544651i	$0.816662\pi$
$822$		0			0
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	−0.961851	−	0.273573i	$-0.911795\pi$
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	0.717847	+	0.696201i	$0.245128\pi$
$824$	4.00000			0.139347
$825$	−12.0000	+	20.7846i	−0.417786	+	0.723627i
$826$	3.00000	−	5.19615i	0.104383	−	0.180797i
$827$	18.0000			0.625921			0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000			0.625921			0.312961	+	0.949766i	$0.398679\pi$
$828$		0			0
$829$	−19.0000	−	32.9090i	−0.659897	−	1.14298i	−0.980642	−	0.195810i	$-0.937266\pi$
$829$	−19.0000	−	32.9090i	−0.659897	−	1.14298i	0.320745	−	0.947166i	$-0.396067\pi$
$830$	−18.0000	−	31.1769i	−0.624789	−	1.08217i
$831$	−28.0000			−0.971309
$832$		0			0
$833$	18.0000			0.623663
$834$	−6.50000	−	11.2583i	−0.225077	−	0.389844i
$835$		0			0
$836$	−6.00000	+	10.3923i	−0.207514	+	0.359425i
$837$	20.0000			0.691301
$838$	4.50000	−	7.79423i	0.155450	−	0.269247i
$839$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$839$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$840$	−3.00000			−0.103510
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	8.50000	+	14.7224i	0.292929	+	0.507369i
$843$	3.00000	+	5.19615i	0.103325	+	0.178965i
$844$	−13.0000			−0.447478
$845$		0			0
$846$	6.00000			0.206284
$847$	12.5000	+	21.6506i	0.429505	+	0.743925i
$848$		0			0
$849$	2.00000	−	3.46410i	0.0686398	−	0.118888i
$850$	12.0000			0.411597
$851$		0			0
$852$	1.50000	−	2.59808i	0.0513892	−	0.0890086i
$853$	−37.0000			−1.26686			−0.633428	−	0.773802i	$-0.718353\pi$
$853$	−37.0000			−1.26686			−0.633428	+	0.773802i	$0.718353\pi$
$854$	−4.00000	+	6.92820i	−0.136877	+	0.237078i
$855$	−6.00000	−	10.3923i	−0.205196	−	0.355409i
$856$	6.00000	+	10.3923i	0.205076	+	0.355202i
$857$	−42.0000			−1.43469			−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000			−1.43469			−0.717346	+	0.696717i	$0.754643\pi$
$858$		0			0
$859$	−4.00000			−0.136478			−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000			−0.136478			−0.0682391	+	0.997669i	$0.521738\pi$
$860$	−1.50000	−	2.59808i	−0.0511496	−	0.0885937i
$861$		0			0
$862$	−16.5000	+	28.5788i	−0.561992	+	0.973399i
$863$	−45.0000			−1.53182			−0.765909	−	0.642949i	$-0.777711\pi$
$863$	−45.0000			−1.53182			−0.765909	+	0.642949i	$0.777711\pi$
$864$	−2.50000	+	4.33013i	−0.0850517	+	0.147314i
$865$		0			0
$866$	25.0000			0.849535
$867$	4.00000	−	6.92820i	0.135847	−	0.235294i
$868$	−2.00000	−	3.46410i	−0.0678844	−	0.117579i
$869$	−24.0000	−	41.5692i	−0.814144	−	1.41014i
$870$	18.0000			0.610257
$871$		0			0
$872$	7.00000			0.237050
$873$	−10.0000	−	17.3205i	−0.338449	−	0.586210i
$874$		0			0
$875$	1.50000	−	2.59808i	0.0507093	−	0.0878310i
$876$	2.00000			0.0675737
$877$	6.50000	−	11.2583i	0.219489	−	0.380167i	−0.735163	−	0.677891i	$-0.762894\pi$
$877$	6.50000	−	11.2583i	0.219489	−	0.380167i	0.954652	+	0.297724i	$0.0962275\pi$
$878$	13.0000	−	22.5167i	0.438729	−	0.759900i
$879$	21.0000			0.708312
$880$	9.00000	−	15.5885i	0.303390	−	0.525487i
$881$	−10.5000	−	18.1865i	−0.353754	−	0.612720i	0.633150	−	0.774029i	$-0.281762\pi$
$881$	−10.5000	−	18.1865i	−0.353754	−	0.612720i	−0.986904	+	0.161309i	$0.948428\pi$
$882$	6.00000	+	10.3923i	0.202031	+	0.349927i
$883$	29.0000			0.975928			0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000			0.975928			0.487964	+	0.872864i	$0.337740\pi$
$884$		0			0
$885$	18.0000			0.605063
$886$	10.5000	+	18.1865i	0.352754	+	0.610989i
$887$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$887$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$888$	−3.50000	+	6.06218i	−0.117452	+	0.203433i
$889$	−20.0000			−0.670778
$890$	9.00000	−	15.5885i	0.301681	−	0.522526i
$891$	−3.00000	+	5.19615i	−0.100504	+	0.174078i
$892$	−19.0000			−0.636167
$893$	−3.00000	+	5.19615i	−0.100391	+	0.173883i
$894$	−3.00000	−	5.19615i	−0.100335	−	0.173785i
$895$	4.50000	+	7.79423i	0.150418	+	0.260532i
$896$	1.00000			0.0334077
$897$		0			0
$898$	−6.00000			−0.200223
$899$	12.0000	+	20.7846i	0.400222	+	0.693206i
$900$	4.00000	+	6.92820i	0.133333	+	0.230940i
$901$		0			0
$902$		0			0
$903$	−0.500000	+	0.866025i	−0.0166390	+	0.0288195i
$904$	−3.00000	+	5.19615i	−0.0997785	+	0.172821i
$905$	−60.0000			−1.99447
$906$	8.50000	−	14.7224i	0.282394	−	0.489120i
$907$	18.5000	+	32.0429i	0.614282	+	1.06397i	0.990510	+	0.137441i	$0.0438878\pi$
$907$	18.5000	+	32.0429i	0.614282	+	1.06397i	−0.376228	+	0.926527i	$0.622779\pi$
$908$		0			0
$909$	24.0000			0.796030
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$	−1.00000	−	1.73205i	−0.0331133	−	0.0573539i
$913$	−36.0000	−	62.3538i	−1.19143	−	2.06361i
$914$	−5.00000	+	8.66025i	−0.165385	+	0.286456i
$915$	−24.0000			−0.793416
$916$	6.50000	−	11.2583i	0.214766	−	0.371986i
$917$	−10.5000	+	18.1865i	−0.346741	+	0.600572i
$918$	−15.0000			−0.495074
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$		0			0
$921$	−1.00000	−	1.73205i	−0.0329511	−	0.0570730i
$922$	−9.00000			−0.296399
$923$		0			0
$924$	−6.00000			−0.197386
$925$	14.0000	+	24.2487i	0.460317	+	0.797293i
$926$	−20.0000	−	34.6410i	−0.657241	−	1.13837i
$927$	−4.00000	+	6.92820i	−0.131377	+	0.227552i
$928$	−6.00000			−0.196960
$929$	−18.0000	+	31.1769i	−0.590561	+	1.02288i	0.403596	+	0.914937i	$0.367760\pi$
$929$	−18.0000	+	31.1769i	−0.590561	+	1.02288i	−0.994157	+	0.107944i	$0.965573\pi$
$930$	6.00000	−	10.3923i	0.196748	−	0.340777i
$931$	−12.0000			−0.393284
$932$	13.5000	−	23.3827i	0.442207	−	0.765925i
$933$	15.0000	+	25.9808i	0.491078	+	0.850572i
$934$	18.0000	+	31.1769i	0.588978	+	1.02014i
$935$	54.0000			1.76599
$936$		0			0
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$	−7.00000	−	12.1244i	−0.228558	−	0.395874i
$939$	0.500000	+	0.866025i	0.0163169	+	0.0282617i
$940$	4.50000	−	7.79423i	0.146774	−	0.254220i
$941$	−21.0000			−0.684580			−0.342290	−	0.939594i	$-0.611203\pi$
$941$	−21.0000			−0.684580			−0.342290	+	0.939594i	$0.611203\pi$
$942$	7.00000	−	12.1244i	0.228072	−	0.395033i
$943$		0			0
$944$	−6.00000			−0.195283
$945$	7.50000	−	12.9904i	0.243975	−	0.422577i
$946$	−3.00000	−	5.19615i	−0.0975384	−	0.168941i
$947$	−3.00000	−	5.19615i	−0.0974869	−	0.168852i	0.813157	−	0.582045i	$-0.197747\pi$
$947$	−3.00000	−	5.19615i	−0.0974869	−	0.168852i	−0.910644	+	0.413192i	$0.864414\pi$
$948$	8.00000			0.259828
$949$		0			0
$950$	−8.00000			−0.259554
$951$	3.00000	+	5.19615i	0.0972817	+	0.168497i
$952$	1.50000	+	2.59808i	0.0486153	+	0.0842041i
$953$	−7.50000	+	12.9904i	−0.242949	+	0.420800i	−0.961553	−	0.274620i	$-0.911448\pi$
$953$	−7.50000	+	12.9904i	−0.242949	+	0.420800i	0.718604	+	0.695419i	$0.244781\pi$
$954$		0			0
$955$	−27.0000	+	46.7654i	−0.873699	+	1.51329i
$956$	−7.50000	+	12.9904i	−0.242567	+	0.420139i
$957$	36.0000			1.16371
$958$	−10.5000	+	18.1865i	−0.339240	+	0.587580i
$959$		0			0
$960$	1.50000	+	2.59808i	0.0484123	+	0.0838525i
$961$	−15.0000			−0.483871
$962$		0			0
$963$	−24.0000			−0.773389
$964$	5.00000	+	8.66025i	0.161039	+	0.278928i
$965$	−6.00000	−	10.3923i	−0.193147	−	0.334540i
$966$		0			0
$967$	−31.0000			−0.996893			−0.498446	−	0.866921i	$-0.666096\pi$
$967$	−31.0000			−0.996893			−0.498446	+	0.866921i	$0.666096\pi$
$968$	12.5000	−	21.6506i	0.401765	−	0.695878i
$969$	3.00000	−	5.19615i	0.0963739	−	0.166924i
$970$	−30.0000			−0.963242
$971$	1.50000	−	2.59808i	0.0481373	−	0.0833762i	−0.840953	−	0.541108i	$-0.818005\pi$
$971$	1.50000	−	2.59808i	0.0481373	−	0.0833762i	0.889090	+	0.457732i	$0.151338\pi$
$972$	−8.00000	−	13.8564i	−0.256600	−	0.444444i
$973$	−6.50000	−	11.2583i	−0.208380	−	0.360925i
$974$	16.0000			0.512673
$975$		0			0
$976$	8.00000			0.256074
$977$	27.0000	+	46.7654i	0.863807	+	1.49616i	0.868227	+	0.496167i	$0.165259\pi$
$977$	27.0000	+	46.7654i	0.863807	+	1.49616i	−0.00442082	+	0.999990i	$0.501407\pi$
$978$	−8.00000	−	13.8564i	−0.255812	−	0.443079i
$979$	18.0000	−	31.1769i	0.575282	−	0.996419i
$980$	18.0000			0.574989
$981$	−7.00000	+	12.1244i	−0.223493	+	0.387101i
$982$	−4.50000	+	7.79423i	−0.143601	+	0.248724i
$983$	39.0000			1.24391			0.621953	−	0.783054i	$-0.286339\pi$
$983$	39.0000			1.24391			0.621953	+	0.783054i	$0.286339\pi$
$984$		0			0
$985$	4.50000	+	7.79423i	0.143382	+	0.248345i
$986$	−9.00000	−	15.5885i	−0.286618	−	0.496438i
$987$	−3.00000			−0.0954911
$988$		0			0
$989$		0			0
$990$	18.0000	+	31.1769i	0.572078	+	0.990867i
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	0.849705	−	0.527258i	$-0.176780\pi$
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	−0.881471	+	0.472237i	$0.843446\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$	8.00000			0.253872
$994$	1.50000	−	2.59808i	0.0475771	−	0.0824060i
$995$	3.00000	−	5.19615i	0.0951064	−	0.164729i
$996$	12.0000			0.380235
$997$	23.0000	−	39.8372i	0.728417	−	1.26166i	−0.229135	−	0.973395i	$-0.573590\pi$
$997$	23.0000	−	39.8372i	0.728417	−	1.26166i	0.957552	−	0.288261i	$-0.0930771\pi$
$998$	−20.0000	−	34.6410i	−0.633089	−	1.09654i
$999$	−17.5000	−	30.3109i	−0.553675	−	0.958994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.2.c.d.315.1		2
13.2	odd	12		338.2.b.c.337.2		2
13.3	even	3		26.2.a.a.1.1	✓	1
13.4	even	6		338.2.c.a.191.1		2
13.5	odd	4		338.2.e.a.23.2		4
13.6	odd	12		338.2.e.a.147.1		4
13.7	odd	12		338.2.e.a.147.2		4
13.8	odd	4		338.2.e.a.23.1		4
13.9	even	3	inner	338.2.c.d.191.1		2
13.10	even	6		338.2.a.f.1.1		1
13.11	odd	12		338.2.b.c.337.1		2
13.12	even	2		338.2.c.a.315.1		2
39.2	even	12		3042.2.b.a.1351.1		2
39.11	even	12		3042.2.b.a.1351.2		2
39.23	odd	6		3042.2.a.a.1.1		1
39.29	odd	6		234.2.a.e.1.1		1
52.3	odd	6		208.2.a.a.1.1		1
52.11	even	12		2704.2.f.d.337.1		2
52.15	even	12		2704.2.f.d.337.2		2
52.23	odd	6		2704.2.a.f.1.1		1
65.3	odd	12		650.2.b.d.599.2		2
65.29	even	6		650.2.a.j.1.1		1
65.42	odd	12		650.2.b.d.599.1		2
65.49	even	6		8450.2.a.c.1.1		1
91.3	odd	6		1274.2.f.r.79.1		2
91.16	even	3		1274.2.f.p.1145.1		2
91.55	odd	6		1274.2.a.d.1.1		1
91.68	odd	6		1274.2.f.r.1145.1		2
91.81	even	3		1274.2.f.p.79.1		2
104.3	odd	6		832.2.a.i.1.1		1
104.29	even	6		832.2.a.d.1.1		1
117.16	even	3		2106.2.e.ba.1405.1		2
117.29	odd	6		2106.2.e.b.1405.1		2
117.68	odd	6		2106.2.e.b.703.1		2
117.94	even	3		2106.2.e.ba.703.1		2
143.120	odd	6		3146.2.a.n.1.1		1
156.107	even	6		1872.2.a.q.1.1		1
195.29	odd	6		5850.2.a.p.1.1		1
195.68	even	12		5850.2.e.a.5149.1		2
195.107	even	12		5850.2.e.a.5149.2		2
208.3	odd	12		3328.2.b.j.1665.1		2
208.29	even	12		3328.2.b.m.1665.2		2
208.107	odd	12		3328.2.b.j.1665.2		2
208.133	even	12		3328.2.b.m.1665.1		2
221.16	even	6		7514.2.a.c.1.1		1
247.94	odd	6		9386.2.a.j.1.1		1
260.159	odd	6		5200.2.a.x.1.1		1
312.29	odd	6		7488.2.a.g.1.1		1
312.107	even	6		7488.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.2.a.a.1.1	✓	1	13.3	even	3
208.2.a.a.1.1		1	52.3	odd	6
234.2.a.e.1.1		1	39.29	odd	6
338.2.a.f.1.1		1	13.10	even	6
338.2.b.c.337.1		2	13.11	odd	12
338.2.b.c.337.2		2	13.2	odd	12
338.2.c.a.191.1		2	13.4	even	6
338.2.c.a.315.1		2	13.12	even	2
338.2.c.d.191.1		2	13.9	even	3	inner
338.2.c.d.315.1		2	1.1	even	1	trivial
338.2.e.a.23.1		4	13.8	odd	4
338.2.e.a.23.2		4	13.5	odd	4
338.2.e.a.147.1		4	13.6	odd	12
338.2.e.a.147.2		4	13.7	odd	12
650.2.a.j.1.1		1	65.29	even	6
650.2.b.d.599.1		2	65.42	odd	12
650.2.b.d.599.2		2	65.3	odd	12
832.2.a.d.1.1		1	104.29	even	6
832.2.a.i.1.1		1	104.3	odd	6
1274.2.a.d.1.1		1	91.55	odd	6
1274.2.f.p.79.1		2	91.81	even	3
1274.2.f.p.1145.1		2	91.16	even	3
1274.2.f.r.79.1		2	91.3	odd	6
1274.2.f.r.1145.1		2	91.68	odd	6
1872.2.a.q.1.1		1	156.107	even	6
2106.2.e.b.703.1		2	117.68	odd	6
2106.2.e.b.1405.1		2	117.29	odd	6
2106.2.e.ba.703.1		2	117.94	even	3
2106.2.e.ba.1405.1		2	117.16	even	3
2704.2.a.f.1.1		1	52.23	odd	6
2704.2.f.d.337.1		2	52.11	even	12
2704.2.f.d.337.2		2	52.15	even	12
3042.2.a.a.1.1		1	39.23	odd	6
3042.2.b.a.1351.1		2	39.2	even	12
3042.2.b.a.1351.2		2	39.11	even	12
3146.2.a.n.1.1		1	143.120	odd	6
3328.2.b.j.1665.1		2	208.3	odd	12
3328.2.b.j.1665.2		2	208.107	odd	12
3328.2.b.m.1665.1		2	208.133	even	12
3328.2.b.m.1665.2		2	208.29	even	12
5200.2.a.x.1.1		1	260.159	odd	6
5850.2.a.p.1.1		1	195.29	odd	6
5850.2.e.a.5149.1		2	195.68	even	12
5850.2.e.a.5149.2		2	195.107	even	12
7488.2.a.g.1.1		1	312.29	odd	6
7488.2.a.h.1.1		1	312.107	even	6
7514.2.a.c.1.1		1	221.16	even	6
8450.2.a.c.1.1		1	65.49	even	6
9386.2.a.j.1.1		1	247.94	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	338.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-3.00000 - 5.19615i) q^{11} +1.00000 q^{12} +1.00000 q^{14} +(1.50000 + 2.59808i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +2.00000 q^{18} +(-1.00000 + 1.73205i) q^{19} +(1.50000 - 2.59808i) q^{20} -1.00000 q^{21} +(3.00000 - 5.19615i) q^{22} +(0.500000 + 0.866025i) q^{24} +4.00000 q^{25} -5.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(-3.00000 - 5.19615i) q^{29} +(-1.50000 + 2.59808i) q^{30} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{33} +3.00000 q^{34} +(-1.50000 + 2.59808i) q^{35} +(1.00000 + 1.73205i) q^{36} +(3.50000 + 6.06218i) q^{37} -2.00000 q^{38} +3.00000 q^{40} +(-0.500000 - 0.866025i) q^{42} +(0.500000 - 0.866025i) q^{43} +6.00000 q^{44} +(-3.00000 + 5.19615i) q^{45} +3.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.00000 + 5.19615i) q^{49} +(2.00000 + 3.46410i) q^{50} -3.00000 q^{51} +(-2.50000 - 4.33013i) q^{54} +(9.00000 + 15.5885i) q^{55} +(-0.500000 + 0.866025i) q^{56} +2.00000 q^{57} +(3.00000 - 5.19615i) q^{58} +(3.00000 - 5.19615i) q^{59} -3.00000 q^{60} +(-4.00000 + 6.92820i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-1.00000 - 1.73205i) q^{63} +1.00000 q^{64} -6.00000 q^{66} +(-7.00000 - 12.1244i) q^{67} +(1.50000 + 2.59808i) q^{68} -3.00000 q^{70} +(1.50000 - 2.59808i) q^{71} +(-1.00000 + 1.73205i) q^{72} +2.00000 q^{73} +(-3.50000 + 6.06218i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(-1.00000 - 1.73205i) q^{76} -6.00000 q^{77} +8.00000 q^{79} +(1.50000 + 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} +(0.500000 - 0.866025i) q^{84} +(-4.50000 + 7.79423i) q^{85} +1.00000 q^{86} +(-3.00000 + 5.19615i) q^{87} +(3.00000 + 5.19615i) q^{88} +(3.00000 + 5.19615i) q^{89} -6.00000 q^{90} +(2.00000 + 3.46410i) q^{93} +(1.50000 + 2.59808i) q^{94} +(3.00000 - 5.19615i) q^{95} -1.00000 q^{96} +(5.00000 - 8.66025i) q^{97} +(-3.00000 + 5.19615i) q^{98} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} - 6 q^{5} + q^{6} + q^{7} - 2 q^{8} + 2 q^{9} - 3 q^{10} - 6 q^{11} + 2 q^{12} + 2 q^{14} + 3 q^{15} - q^{16} + 3 q^{17} + 4 q^{18} - 2 q^{19} + 3 q^{20} - 2 q^{21} + 6 q^{22}+ \cdots - 24 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 - 6 * q^5 + q^6 + q^7 - 2 * q^8 + 2 * q^9 - 3 * q^10 - 6 * q^11 + 2 * q^12 + 2 * q^14 + 3 * q^15 - q^16 + 3 * q^17 + 4 * q^18 - 2 * q^19 + 3 * q^20 - 2 * q^21 + 6 * q^22 + q^24 + 8 * q^25 - 10 * q^27 + q^28 - 6 * q^29 - 3 * q^30 - 8 * q^31 + q^32 - 6 * q^33 + 6 * q^34 - 3 * q^35 + 2 * q^36 + 7 * q^37 - 4 * q^38 + 6 * q^40 - q^42 + q^43 + 12 * q^44 - 6 * q^45 + 6 * q^47 - q^48 + 6 * q^49 + 4 * q^50 - 6 * q^51 - 5 * q^54 + 18 * q^55 - q^56 + 4 * q^57 + 6 * q^58 + 6 * q^59 - 6 * q^60 - 8 * q^61 - 4 * q^62 - 2 * q^63 + 2 * q^64 - 12 * q^66 - 14 * q^67 + 3 * q^68 - 6 * q^70 + 3 * q^71 - 2 * q^72 + 4 * q^73 - 7 * q^74 - 4 * q^75 - 2 * q^76 - 12 * q^77 + 16 * q^79 + 3 * q^80 - q^81 + 24 * q^83 + q^84 - 9 * q^85 + 2 * q^86 - 6 * q^87 + 6 * q^88 + 6 * q^89 - 12 * q^90 + 4 * q^93 + 3 * q^94 + 6 * q^95 - 2 * q^96 + 10 * q^97 - 6 * q^98 - 24 * q^99

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