LMFDB - Embedded newform 294.2.f.a.227.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(215,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("294.215");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.f (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			227.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	294.227
Dual form			294.2.f.a.215.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} -1.73205i q^{6} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} -1.73205i q^{6} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(1.50000 + 0.866025i) q^{10} +(-2.59808 - 1.50000i) q^{11} +(0.866025 + 1.50000i) q^{12} -3.46410i q^{13} +3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.73205 - 3.00000i) q^{17} +(2.59808 + 1.50000i) q^{18} +(-3.00000 + 1.73205i) q^{19} -1.73205 q^{20} +3.00000 q^{22} +(5.19615 - 3.00000i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(1.00000 - 1.73205i) q^{25} +(1.73205 + 3.00000i) q^{26} +5.19615 q^{27} -3.00000i q^{29} +(-2.59808 + 1.50000i) q^{30} +(1.50000 + 0.866025i) q^{31} +(0.866025 + 0.500000i) q^{32} +(4.50000 - 2.59808i) q^{33} +3.46410i q^{34} -3.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(1.73205 - 3.00000i) q^{38} +(5.19615 + 3.00000i) q^{39} +(1.50000 - 0.866025i) q^{40} -6.92820 q^{41} -8.00000 q^{43} +(-2.59808 + 1.50000i) q^{44} +(-2.59808 + 4.50000i) q^{45} +(-3.00000 + 5.19615i) q^{46} +(-3.46410 - 6.00000i) q^{47} +1.73205 q^{48} +2.00000i q^{50} +(3.00000 + 5.19615i) q^{51} +(-3.00000 - 1.73205i) q^{52} +(-7.79423 - 4.50000i) q^{53} +(-4.50000 + 2.59808i) q^{54} +5.19615i q^{55} -6.00000i q^{57} +(1.50000 + 2.59808i) q^{58} +(0.866025 - 1.50000i) q^{59} +(1.50000 - 2.59808i) q^{60} -1.73205 q^{62} -1.00000 q^{64} +(-5.19615 + 3.00000i) q^{65} +(-2.59808 + 4.50000i) q^{66} +(-1.00000 + 1.73205i) q^{67} +(-1.73205 - 3.00000i) q^{68} +10.3923i q^{69} +12.0000i q^{71} +(2.59808 - 1.50000i) q^{72} +(-6.00000 - 3.46410i) q^{73} +(-1.73205 - 1.00000i) q^{74} +(1.73205 + 3.00000i) q^{75} +3.46410i q^{76} -6.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(-0.866025 + 1.50000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(6.00000 - 3.46410i) q^{82} +8.66025 q^{83} -6.00000 q^{85} +(6.92820 - 4.00000i) q^{86} +(4.50000 + 2.59808i) q^{87} +(1.50000 - 2.59808i) q^{88} +(5.19615 + 9.00000i) q^{89} -5.19615i q^{90} -6.00000i q^{92} +(-2.59808 + 1.50000i) q^{93} +(6.00000 + 3.46410i) q^{94} +(5.19615 + 3.00000i) q^{95} +(-1.50000 + 0.866025i) q^{96} -5.19615i q^{97} +9.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 6 * q^9	$ 4 q + 2 q^{4} - 6 q^{9} + 6 q^{10} + 12 q^{15} - 2 q^{16} - 12 q^{19} + 12 q^{22} - 6 q^{24} + 4 q^{25} + 6 q^{31} + 18 q^{33} - 12 q^{36} + 4 q^{37} + 6 q^{40} - 32 q^{43} - 12 q^{46} + 12 q^{51} - 12 q^{52} - 18 q^{54} + 6 q^{58} + 6 q^{60} - 4 q^{64} - 4 q^{67} - 24 q^{73} - 24 q^{78} + 2 q^{79} - 18 q^{81} + 24 q^{82} - 24 q^{85} + 18 q^{87} + 6 q^{88} + 24 q^{94} - 6 q^{96}+O(q^{100}) $ 4 * q + 2 * q^4 - 6 * q^9 + 6 * q^10 + 12 * q^15 - 2 * q^16 - 12 * q^19 + 12 * q^22 - 6 * q^24 + 4 * q^25 + 6 * q^31 + 18 * q^33 - 12 * q^36 + 4 * q^37 + 6 * q^40 - 32 * q^43 - 12 * q^46 + 12 * q^51 - 12 * q^52 - 18 * q^54 + 6 * q^58 + 6 * q^60 - 4 * q^64 - 4 * q^67 - 24 * q^73 - 24 * q^78 + 2 * q^79 - 18 * q^81 + 24 * q^82 - 24 * q^85 + 18 * q^87 + 6 * q^88 + 24 * q^94 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.866025	−	1.50000i	−0.387298	−	0.670820i	0.604787	−	0.796387i	$-0.293258\pi$
$5$	−0.866025	−	1.50000i	−0.387298	−	0.670820i	−0.992085	+	0.125567i	$0.959925\pi$
$6$		−	1.73205i		−	0.707107i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$	1.50000	+	0.866025i	0.474342	+	0.273861i
$11$	−2.59808	−	1.50000i	−0.783349	−	0.452267i	0.0542666	−	0.998526i	$-0.482718\pi$
$11$	−2.59808	−	1.50000i	−0.783349	−	0.452267i	−0.837616	+	0.546259i	$0.816051\pi$
$12$	0.866025	+	1.50000i	0.250000	+	0.433013i
$13$		−	3.46410i		−	0.960769i	−0.877058	−	0.480384i	$-0.840497\pi$
$13$		−	3.46410i		−	0.960769i	0.877058	−	0.480384i	$-0.159503\pi$
$14$		0			0
$15$	3.00000			0.774597
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.73205	−	3.00000i	0.420084	−	0.727607i	−0.575863	−	0.817546i	$-0.695334\pi$
$17$	1.73205	−	3.00000i	0.420084	−	0.727607i	0.995947	+	0.0899392i	$0.0286673\pi$
$18$	2.59808	+	1.50000i	0.612372	+	0.353553i
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	0.114708	+	0.993399i	$0.463407\pi$
$20$	−1.73205			−0.387298
$21$		0			0
$22$	3.00000			0.639602
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.151642	−	0.988436i	$-0.451544\pi$
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.931831	+	0.362892i	$0.118211\pi$
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$	1.00000	−	1.73205i	0.200000	−	0.346410i
$26$	1.73205	+	3.00000i	0.339683	+	0.588348i
$27$	5.19615			1.00000
$28$		0			0
$29$		−	3.00000i		−	0.557086i	−0.960424	−	0.278543i	$-0.910149\pi$
$29$		−	3.00000i		−	0.557086i	0.960424	−	0.278543i	$-0.0898515\pi$
$30$	−2.59808	+	1.50000i	−0.474342	+	0.273861i
$31$	1.50000	+	0.866025i	0.269408	+	0.155543i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	1.50000	+	0.866025i	0.269408	+	0.155543i	−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	4.50000	−	2.59808i	0.783349	−	0.452267i
$34$			3.46410i			0.594089i
$35$		0			0
$36$	−3.00000			−0.500000
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$	1.73205	−	3.00000i	0.280976	−	0.486664i
$39$	5.19615	+	3.00000i	0.832050	+	0.480384i
$40$	1.50000	−	0.866025i	0.237171	−	0.136931i
$41$	−6.92820			−1.08200			−0.541002	−	0.841021i	$-0.681955\pi$
$41$	−6.92820			−1.08200			−0.541002	+	0.841021i	$0.681955\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$	−2.59808	+	1.50000i	−0.391675	+	0.226134i
$45$	−2.59808	+	4.50000i	−0.387298	+	0.670820i
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$	−3.46410	−	6.00000i	−0.505291	−	0.875190i	−0.999981	−	0.00612051i	$-0.998052\pi$
$47$	−3.46410	−	6.00000i	−0.505291	−	0.875190i	0.494690	−	0.869069i	$-0.335282\pi$
$48$	1.73205			0.250000
$49$		0			0
$50$			2.00000i			0.282843i
$51$	3.00000	+	5.19615i	0.420084	+	0.727607i
$52$	−3.00000	−	1.73205i	−0.416025	−	0.240192i
$53$	−7.79423	−	4.50000i	−1.07062	−	0.618123i	−0.142269	−	0.989828i	$-0.545440\pi$
$53$	−7.79423	−	4.50000i	−1.07062	−	0.618123i	−0.928351	+	0.371706i	$0.878773\pi$
$54$	−4.50000	+	2.59808i	−0.612372	+	0.353553i
$55$			5.19615i			0.700649i
$56$		0			0
$57$		−	6.00000i		−	0.794719i
$58$	1.50000	+	2.59808i	0.196960	+	0.341144i
$59$	0.866025	−	1.50000i	0.112747	−	0.195283i	−0.804130	−	0.594454i	$-0.797368\pi$
$59$	0.866025	−	1.50000i	0.112747	−	0.195283i	0.916877	+	0.399170i	$0.130702\pi$
$60$	1.50000	−	2.59808i	0.193649	−	0.335410i
$61$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$61$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$62$	−1.73205			−0.219971
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−5.19615	+	3.00000i	−0.644503	+	0.372104i
$66$	−2.59808	+	4.50000i	−0.319801	+	0.553912i
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$	−1.73205	−	3.00000i	−0.210042	−	0.363803i
$69$			10.3923i			1.25109i
$70$		0			0
$71$			12.0000i			1.42414i	0.702109	+	0.712069i	$0.252242\pi$
$71$			12.0000i			1.42414i	−0.702109	+	0.712069i	$0.747758\pi$
$72$	2.59808	−	1.50000i	0.306186	−	0.176777i
$73$	−6.00000	−	3.46410i	−0.702247	−	0.405442i	0.105937	−	0.994373i	$-0.466216\pi$
$73$	−6.00000	−	3.46410i	−0.702247	−	0.405442i	−0.808184	+	0.588930i	$0.799549\pi$
$74$	−1.73205	−	1.00000i	−0.201347	−	0.116248i
$75$	1.73205	+	3.00000i	0.200000	+	0.346410i
$76$			3.46410i			0.397360i
$77$		0			0
$78$	−6.00000			−0.679366
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$	−0.866025	+	1.50000i	−0.0968246	+	0.167705i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	6.00000	−	3.46410i	0.662589	−	0.382546i
$83$	8.66025			0.950586			0.475293	−	0.879827i	$-0.342342\pi$
$83$	8.66025			0.950586			0.475293	+	0.879827i	$0.342342\pi$
$84$		0			0
$85$	−6.00000			−0.650791
$86$	6.92820	−	4.00000i	0.747087	−	0.431331i
$87$	4.50000	+	2.59808i	0.482451	+	0.278543i
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	5.19615	+	9.00000i	0.550791	+	0.953998i	0.998218	+	0.0596775i	$0.0190072\pi$
$89$	5.19615	+	9.00000i	0.550791	+	0.953998i	−0.447427	+	0.894321i	$0.647659\pi$
$90$		−	5.19615i		−	0.547723i
$91$		0			0
$92$		−	6.00000i		−	0.625543i
$93$	−2.59808	+	1.50000i	−0.269408	+	0.155543i
$94$	6.00000	+	3.46410i	0.618853	+	0.357295i
$95$	5.19615	+	3.00000i	0.533114	+	0.307794i
$96$	−1.50000	+	0.866025i	−0.153093	+	0.0883883i
$97$		−	5.19615i		−	0.527589i	−0.964579	−	0.263795i	$-0.915026\pi$
$97$		−	5.19615i		−	0.527589i	0.964579	−	0.263795i	$-0.0849741\pi$
$98$		0			0
$99$			9.00000i			0.904534i
$100$	−1.00000	−	1.73205i	−0.100000	−	0.173205i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$	−5.19615	−	3.00000i	−0.514496	−	0.297044i
$103$	3.00000	−	1.73205i	0.295599	−	0.170664i	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	3.00000	−	1.73205i	0.295599	−	0.170664i	0.640464	+	0.767988i	$0.278742\pi$
$104$	3.46410			0.339683
$105$		0			0
$106$	9.00000			0.874157
$107$	2.59808	−	1.50000i	0.251166	−	0.145010i	−0.369132	−	0.929377i	$-0.620345\pi$
$107$	2.59808	−	1.50000i	0.251166	−	0.145010i	0.620298	+	0.784366i	$0.287012\pi$
$108$	2.59808	−	4.50000i	0.250000	−	0.433013i
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$	−2.59808	−	4.50000i	−0.247717	−	0.429058i
$111$	−3.46410			−0.328798
$112$		0			0
$113$		−	12.0000i		−	1.12887i	−0.825479	−	0.564433i	$-0.809095\pi$
$113$		−	12.0000i		−	1.12887i	0.825479	−	0.564433i	$-0.190905\pi$
$114$	3.00000	+	5.19615i	0.280976	+	0.486664i
$115$	−9.00000	−	5.19615i	−0.839254	−	0.484544i
$116$	−2.59808	−	1.50000i	−0.241225	−	0.139272i
$117$	−9.00000	+	5.19615i	−0.832050	+	0.480384i
$118$			1.73205i			0.159448i
$119$		0			0
$120$			3.00000i			0.273861i
$121$	−1.00000	−	1.73205i	−0.0909091	−	0.157459i
$122$		0			0
$123$	6.00000	−	10.3923i	0.541002	−	0.937043i
$124$	1.50000	−	0.866025i	0.134704	−	0.0777714i
$125$	−12.1244			−1.08444
$126$		0			0
$127$	11.0000			0.976092			0.488046	−	0.872818i	$-0.337710\pi$
$127$	11.0000			0.976092			0.488046	+	0.872818i	$0.337710\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	6.92820	−	12.0000i	0.609994	−	1.05654i
$130$	3.00000	−	5.19615i	0.263117	−	0.455733i
$131$	2.59808	+	4.50000i	0.226995	+	0.393167i	0.956916	−	0.290365i	$-0.0937766\pi$
$131$	2.59808	+	4.50000i	0.226995	+	0.393167i	−0.729921	+	0.683531i	$0.760443\pi$
$132$		−	5.19615i		−	0.452267i
$133$		0			0
$134$		−	2.00000i		−	0.172774i
$135$	−4.50000	−	7.79423i	−0.387298	−	0.670820i
$136$	3.00000	+	1.73205i	0.257248	+	0.148522i
$137$	15.5885	+	9.00000i	1.33181	+	0.768922i	0.985577	−	0.169226i	$-0.0541268\pi$
$137$	15.5885	+	9.00000i	1.33181	+	0.768922i	0.346235	+	0.938148i	$0.387460\pi$
$138$	−5.19615	−	9.00000i	−0.442326	−	0.766131i
$139$		−	17.3205i		−	1.46911i	−0.678551	−	0.734553i	$-0.737392\pi$
$139$		−	17.3205i		−	1.46911i	0.678551	−	0.734553i	$-0.262608\pi$
$140$		0			0
$141$	12.0000			1.01058
$142$	−6.00000	−	10.3923i	−0.503509	−	0.872103i
$143$	−5.19615	+	9.00000i	−0.434524	+	0.752618i
$144$	−1.50000	+	2.59808i	−0.125000	+	0.216506i
$145$	−4.50000	+	2.59808i	−0.373705	+	0.215758i
$146$	6.92820			0.573382
$147$		0			0
$148$	2.00000			0.164399
$149$	−15.5885	+	9.00000i	−1.27706	+	0.737309i	−0.976306	−	0.216394i	$-0.930570\pi$
$149$	−15.5885	+	9.00000i	−1.27706	+	0.737309i	−0.300750	+	0.953703i	$0.597237\pi$
$150$	−3.00000	−	1.73205i	−0.244949	−	0.141421i
$151$	−3.50000	+	6.06218i	−0.284826	+	0.493333i	−0.972567	−	0.232623i	$-0.925269\pi$
$151$	−3.50000	+	6.06218i	−0.284826	+	0.493333i	0.687741	+	0.725956i	$0.258602\pi$
$152$	−1.73205	−	3.00000i	−0.140488	−	0.243332i
$153$	−10.3923			−0.840168
$154$		0			0
$155$		−	3.00000i		−	0.240966i
$156$	5.19615	−	3.00000i	0.416025	−	0.240192i
$157$	18.0000	+	10.3923i	1.43656	+	0.829396i	0.997609	−	0.0691164i	$-0.0220180\pi$
$157$	18.0000	+	10.3923i	1.43656	+	0.829396i	0.438948	+	0.898513i	$0.355351\pi$
$158$	−0.866025	−	0.500000i	−0.0688973	−	0.0397779i
$159$	13.5000	−	7.79423i	1.07062	−	0.618123i
$160$		−	1.73205i		−	0.136931i
$161$		0			0
$162$		−	9.00000i		−	0.707107i
$163$	−7.00000	−	12.1244i	−0.548282	−	0.949653i	−0.998392	−	0.0566798i	$-0.981949\pi$
$163$	−7.00000	−	12.1244i	−0.548282	−	0.949653i	0.450110	−	0.892973i	$-0.351385\pi$
$164$	−3.46410	+	6.00000i	−0.270501	+	0.468521i
$165$	−7.79423	−	4.50000i	−0.606780	−	0.350325i
$166$	−7.50000	+	4.33013i	−0.582113	+	0.336083i
$167$	17.3205			1.34030			0.670151	−	0.742225i	$-0.266230\pi$
$167$	17.3205			1.34030			0.670151	+	0.742225i	$0.266230\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	5.19615	−	3.00000i	0.398527	−	0.230089i
$171$	9.00000	+	5.19615i	0.688247	+	0.397360i
$172$	−4.00000	+	6.92820i	−0.304997	+	0.528271i
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$	−5.19615			−0.393919
$175$		0			0
$176$			3.00000i			0.226134i
$177$	1.50000	+	2.59808i	0.112747	+	0.195283i
$178$	−9.00000	−	5.19615i	−0.674579	−	0.389468i
$179$	10.3923	+	6.00000i	0.776757	+	0.448461i	0.835280	−	0.549825i	$-0.185306\pi$
$179$	10.3923	+	6.00000i	0.776757	+	0.448461i	−0.0585225	+	0.998286i	$0.518639\pi$
$180$	2.59808	+	4.50000i	0.193649	+	0.335410i
$181$		−	6.92820i		−	0.514969i	−0.966282	−	0.257485i	$-0.917106\pi$
$181$		−	6.92820i		−	0.514969i	0.966282	−	0.257485i	$-0.0828937\pi$
$182$		0			0
$183$		0			0
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$	1.73205	−	3.00000i	0.127343	−	0.220564i
$186$	1.50000	−	2.59808i	0.109985	−	0.190500i
$187$	−9.00000	+	5.19615i	−0.658145	+	0.379980i
$188$	−6.92820			−0.505291
$189$		0			0
$190$	−6.00000			−0.435286
$191$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$191$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$192$	0.866025	−	1.50000i	0.0625000	−	0.108253i
$193$	11.5000	−	19.9186i	0.827788	−	1.43377i	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	11.5000	−	19.9186i	0.827788	−	1.43377i	0.899770	−	0.436365i	$-0.143734\pi$
$194$	2.59808	+	4.50000i	0.186531	+	0.323081i
$195$		−	10.3923i		−	0.744208i
$196$		0			0
$197$			18.0000i			1.28245i	0.767354	+	0.641223i	$0.221573\pi$
$197$			18.0000i			1.28245i	−0.767354	+	0.641223i	$0.778427\pi$
$198$	−4.50000	−	7.79423i	−0.319801	−	0.553912i
$199$	−9.00000	−	5.19615i	−0.637993	−	0.368345i	0.145848	−	0.989307i	$-0.453409\pi$
$199$	−9.00000	−	5.19615i	−0.637993	−	0.368345i	−0.783841	+	0.620962i	$0.786742\pi$
$200$	1.73205	+	1.00000i	0.122474	+	0.0707107i
$201$	−1.73205	−	3.00000i	−0.122169	−	0.211604i
$202$		0			0
$203$		0			0
$204$	6.00000			0.420084
$205$	6.00000	+	10.3923i	0.419058	+	0.725830i
$206$	−1.73205	+	3.00000i	−0.120678	+	0.209020i
$207$	−15.5885	−	9.00000i	−1.08347	−	0.625543i
$208$	−3.00000	+	1.73205i	−0.208013	+	0.120096i
$209$	10.3923			0.718851
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	−7.79423	+	4.50000i	−0.535310	+	0.309061i
$213$	−18.0000	−	10.3923i	−1.23334	−	0.712069i
$214$	−1.50000	+	2.59808i	−0.102538	+	0.177601i
$215$	6.92820	+	12.0000i	0.472500	+	0.818393i
$216$			5.19615i			0.353553i
$217$		0			0
$218$			2.00000i			0.135457i
$219$	10.3923	−	6.00000i	0.702247	−	0.405442i
$220$	4.50000	+	2.59808i	0.303390	+	0.175162i
$221$	−10.3923	−	6.00000i	−0.699062	−	0.403604i
$222$	3.00000	−	1.73205i	0.201347	−	0.116248i
$223$			25.9808i			1.73980i	0.493228	+	0.869900i	$0.335817\pi$
$223$			25.9808i			1.73980i	−0.493228	+	0.869900i	$0.664183\pi$
$224$		0			0
$225$	−6.00000			−0.400000
$226$	6.00000	+	10.3923i	0.399114	+	0.691286i
$227$	−2.59808	+	4.50000i	−0.172440	+	0.298675i	−0.939272	−	0.343172i	$-0.888499\pi$
$227$	−2.59808	+	4.50000i	−0.172440	+	0.298675i	0.766832	+	0.641848i	$0.221832\pi$
$228$	−5.19615	−	3.00000i	−0.344124	−	0.198680i
$229$	12.0000	−	6.92820i	0.792982	−	0.457829i	−0.0480291	−	0.998846i	$-0.515294\pi$
$229$	12.0000	−	6.92820i	0.792982	−	0.457829i	0.841011	+	0.541017i	$0.181961\pi$
$230$	10.3923			0.685248
$231$		0			0
$232$	3.00000			0.196960
$233$	15.5885	−	9.00000i	1.02123	−	0.589610i	0.106773	−	0.994283i	$-0.465948\pi$
$233$	15.5885	−	9.00000i	1.02123	−	0.589610i	0.914461	+	0.404674i	$0.132615\pi$
$234$	5.19615	−	9.00000i	0.339683	−	0.588348i
$235$	−6.00000	+	10.3923i	−0.391397	+	0.677919i
$236$	−0.866025	−	1.50000i	−0.0563735	−	0.0976417i
$237$	−1.73205			−0.112509
$238$		0			0
$239$		−	6.00000i		−	0.388108i	−0.980991	−	0.194054i	$-0.937836\pi$
$239$		−	6.00000i		−	0.388108i	0.980991	−	0.194054i	$-0.0621637\pi$
$240$	−1.50000	−	2.59808i	−0.0968246	−	0.167705i
$241$	22.5000	+	12.9904i	1.44935	+	0.836784i	0.998443	−	0.0557856i	$-0.0177663\pi$
$241$	22.5000	+	12.9904i	1.44935	+	0.836784i	0.450910	+	0.892570i	$0.351100\pi$
$242$	1.73205	+	1.00000i	0.111340	+	0.0642824i
$243$	−7.79423	−	13.5000i	−0.500000	−	0.866025i
$244$		0			0
$245$		0			0
$246$			12.0000i			0.765092i
$247$	6.00000	+	10.3923i	0.381771	+	0.661247i
$248$	−0.866025	+	1.50000i	−0.0549927	+	0.0952501i
$249$	−7.50000	+	12.9904i	−0.475293	+	0.823232i
$250$	10.5000	−	6.06218i	0.664078	−	0.383406i
$251$	−19.0526			−1.20259			−0.601293	−	0.799028i	$-0.705348\pi$
$251$	−19.0526			−1.20259			−0.601293	+	0.799028i	$0.705348\pi$
$252$		0			0
$253$	−18.0000			−1.13165
$254$	−9.52628	+	5.50000i	−0.597732	+	0.345101i
$255$	5.19615	−	9.00000i	0.325396	−	0.563602i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.19615	−	9.00000i	−0.324127	−	0.561405i	0.657208	−	0.753709i	$-0.271737\pi$
$257$	−5.19615	−	9.00000i	−0.324127	−	0.561405i	−0.981335	+	0.192304i	$0.938404\pi$
$258$			13.8564i			0.862662i
$259$		0			0
$260$			6.00000i			0.372104i
$261$	−7.79423	+	4.50000i	−0.482451	+	0.278543i
$262$	−4.50000	−	2.59808i	−0.278011	−	0.160510i
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$	2.59808	+	4.50000i	0.159901	+	0.276956i
$265$			15.5885i			0.957591i
$266$		0			0
$267$	−18.0000			−1.10158
$268$	1.00000	+	1.73205i	0.0610847	+	0.105802i
$269$	−14.7224	+	25.5000i	−0.897643	+	1.55476i	−0.0671428	+	0.997743i	$0.521388\pi$
$269$	−14.7224	+	25.5000i	−0.897643	+	1.55476i	−0.830500	+	0.557019i	$0.811945\pi$
$270$	7.79423	+	4.50000i	0.474342	+	0.273861i
$271$	−4.50000	+	2.59808i	−0.273356	+	0.157822i	−0.630412	−	0.776261i	$-0.717114\pi$
$271$	−4.50000	+	2.59808i	−0.273356	+	0.157822i	0.357056	+	0.934083i	$0.383781\pi$
$272$	−3.46410			−0.210042
$273$		0			0
$274$	−18.0000			−1.08742
$275$	−5.19615	+	3.00000i	−0.313340	+	0.180907i
$276$	9.00000	+	5.19615i	0.541736	+	0.312772i
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$	8.66025	+	15.0000i	0.519408	+	0.899640i
$279$		−	5.19615i		−	0.311086i
$280$		0			0
$281$		−	30.0000i		−	1.78965i	−0.446417	−	0.894825i	$-0.647300\pi$
$281$		−	30.0000i		−	1.78965i	0.446417	−	0.894825i	$-0.352700\pi$
$282$	−10.3923	+	6.00000i	−0.618853	+	0.357295i
$283$	−24.0000	−	13.8564i	−1.42665	−	0.823678i	−0.429797	−	0.902926i	$-0.641415\pi$
$283$	−24.0000	−	13.8564i	−1.42665	−	0.823678i	−0.996855	+	0.0792477i	$0.974748\pi$
$284$	10.3923	+	6.00000i	0.616670	+	0.356034i
$285$	−9.00000	+	5.19615i	−0.533114	+	0.307794i
$286$		−	10.3923i		−	0.614510i
$287$		0			0
$288$		−	3.00000i		−	0.176777i
$289$	2.50000	+	4.33013i	0.147059	+	0.254713i
$290$	2.59808	−	4.50000i	0.152564	−	0.264249i
$291$	7.79423	+	4.50000i	0.456906	+	0.263795i
$292$	−6.00000	+	3.46410i	−0.351123	+	0.202721i
$293$	19.0526			1.11306			0.556531	−	0.830827i	$-0.312132\pi$
$293$	19.0526			1.11306			0.556531	+	0.830827i	$0.312132\pi$
$294$		0			0
$295$	−3.00000			−0.174667
$296$	−1.73205	+	1.00000i	−0.100673	+	0.0581238i
$297$	−13.5000	−	7.79423i	−0.783349	−	0.452267i
$298$	9.00000	−	15.5885i	0.521356	−	0.903015i
$299$	−10.3923	−	18.0000i	−0.601003	−	1.04097i
$300$	3.46410			0.200000
$301$		0			0
$302$		−	7.00000i		−	0.402805i
$303$		0			0
$304$	3.00000	+	1.73205i	0.172062	+	0.0993399i
$305$		0			0
$306$	9.00000	−	5.19615i	0.514496	−	0.297044i
$307$			24.2487i			1.38395i	0.721923	+	0.691974i	$0.243259\pi$
$307$			24.2487i			1.38395i	−0.721923	+	0.691974i	$0.756741\pi$
$308$		0			0
$309$			6.00000i			0.341328i
$310$	1.50000	+	2.59808i	0.0851943	+	0.147561i
$311$	6.92820	−	12.0000i	0.392862	−	0.680458i	−0.599963	−	0.800027i	$-0.704818\pi$
$311$	6.92820	−	12.0000i	0.392862	−	0.680458i	0.992826	+	0.119570i	$0.0381515\pi$
$312$	−3.00000	+	5.19615i	−0.169842	+	0.294174i
$313$	−1.50000	+	0.866025i	−0.0847850	+	0.0489506i	−0.541793	−	0.840512i	$-0.682254\pi$
$313$	−1.50000	+	0.866025i	−0.0847850	+	0.0489506i	0.457008	+	0.889463i	$0.348921\pi$
$314$	−20.7846			−1.17294
$315$		0			0
$316$	1.00000			0.0562544
$317$	12.9904	−	7.50000i	0.729612	−	0.421242i	−0.0886679	−	0.996061i	$-0.528261\pi$
$317$	12.9904	−	7.50000i	0.729612	−	0.421242i	0.818280	+	0.574819i	$0.194928\pi$
$318$	−7.79423	+	13.5000i	−0.437079	+	0.757042i
$319$	−4.50000	+	7.79423i	−0.251952	+	0.436393i
$320$	0.866025	+	1.50000i	0.0484123	+	0.0838525i
$321$			5.19615i			0.290021i
$322$		0			0
$323$			12.0000i			0.667698i
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$	−6.00000	−	3.46410i	−0.332820	−	0.192154i
$326$	12.1244	+	7.00000i	0.671506	+	0.387694i
$327$	1.73205	+	3.00000i	0.0957826	+	0.165900i
$328$		−	6.92820i		−	0.382546i
$329$		0			0
$330$	9.00000			0.495434
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	0.954765	−	0.297361i	$-0.0961066\pi$
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	−0.734905	+	0.678170i	$0.762773\pi$
$332$	4.33013	−	7.50000i	0.237647	−	0.411616i
$333$	3.00000	−	5.19615i	0.164399	−	0.284747i
$334$	−15.0000	+	8.66025i	−0.820763	+	0.473868i
$335$	3.46410			0.189264
$336$		0			0
$337$	13.0000			0.708155			0.354078	−	0.935216i	$-0.384795\pi$
$337$	13.0000			0.708155			0.354078	+	0.935216i	$0.384795\pi$
$338$	−0.866025	+	0.500000i	−0.0471056	+	0.0271964i
$339$	18.0000	+	10.3923i	0.977626	+	0.564433i
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$	−2.59808	−	4.50000i	−0.140694	−	0.243689i
$342$	−10.3923			−0.561951
$343$		0			0
$344$		−	8.00000i		−	0.431331i
$345$	15.5885	−	9.00000i	0.839254	−	0.484544i
$346$		0			0
$347$	−10.3923	−	6.00000i	−0.557888	−	0.322097i	0.194409	−	0.980921i	$-0.437721\pi$
$347$	−10.3923	−	6.00000i	−0.557888	−	0.322097i	−0.752297	+	0.658824i	$0.771054\pi$
$348$	4.50000	−	2.59808i	0.241225	−	0.139272i
$349$		−	10.3923i		−	0.556287i	−0.960539	−	0.278144i	$-0.910281\pi$
$349$		−	10.3923i		−	0.556287i	0.960539	−	0.278144i	$-0.0897191\pi$
$350$		0			0
$351$		−	18.0000i		−	0.960769i
$352$	−1.50000	−	2.59808i	−0.0799503	−	0.138478i
$353$	17.3205	−	30.0000i	0.921878	−	1.59674i	0.125370	−	0.992110i	$-0.459988\pi$
$353$	17.3205	−	30.0000i	0.921878	−	1.59674i	0.796507	−	0.604629i	$-0.206679\pi$
$354$	−2.59808	−	1.50000i	−0.138086	−	0.0797241i
$355$	18.0000	−	10.3923i	0.955341	−	0.551566i
$356$	10.3923			0.550791
$357$		0			0
$358$	−12.0000			−0.634220
$359$	−5.19615	+	3.00000i	−0.274242	+	0.158334i	−0.630814	−	0.775934i	$-0.717279\pi$
$359$	−5.19615	+	3.00000i	−0.274242	+	0.158334i	0.356572	+	0.934268i	$0.383946\pi$
$360$	−4.50000	−	2.59808i	−0.237171	−	0.136931i
$361$	−3.50000	+	6.06218i	−0.184211	+	0.319062i
$362$	3.46410	+	6.00000i	0.182069	+	0.315353i
$363$	3.46410			0.181818
$364$		0			0
$365$			12.0000i			0.628109i
$366$		0			0
$367$	19.5000	+	11.2583i	1.01789	+	0.587680i	0.913493	−	0.406855i	$-0.133375\pi$
$367$	19.5000	+	11.2583i	1.01789	+	0.587680i	0.104399	+	0.994535i	$0.466708\pi$
$368$	−5.19615	−	3.00000i	−0.270868	−	0.156386i
$369$	10.3923	+	18.0000i	0.541002	+	0.937043i
$370$			3.46410i			0.180090i
$371$		0			0
$372$			3.00000i			0.155543i
$373$	−16.0000	−	27.7128i	−0.828449	−	1.43492i	−0.899255	−	0.437425i	$-0.855891\pi$
$373$	−16.0000	−	27.7128i	−0.828449	−	1.43492i	0.0708063	−	0.997490i	$-0.477443\pi$
$374$	5.19615	−	9.00000i	0.268687	−	0.465379i
$375$	10.5000	−	18.1865i	0.542218	−	0.939149i
$376$	6.00000	−	3.46410i	0.309426	−	0.178647i
$377$	−10.3923			−0.535231
$378$		0			0
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$	5.19615	−	3.00000i	0.266557	−	0.153897i
$381$	−9.52628	+	16.5000i	−0.488046	+	0.845321i
$382$		0			0
$383$	−1.73205	−	3.00000i	−0.0885037	−	0.153293i	0.818375	−	0.574684i	$-0.194875\pi$
$383$	−1.73205	−	3.00000i	−0.0885037	−	0.153293i	−0.906879	+	0.421392i	$0.861542\pi$
$384$			1.73205i			0.0883883i
$385$		0			0
$386$			23.0000i			1.17067i
$387$	12.0000	+	20.7846i	0.609994	+	1.05654i
$388$	−4.50000	−	2.59808i	−0.228453	−	0.131897i
$389$	−15.5885	−	9.00000i	−0.790366	−	0.456318i	0.0497253	−	0.998763i	$-0.484165\pi$
$389$	−15.5885	−	9.00000i	−0.790366	−	0.456318i	−0.840091	+	0.542445i	$0.817499\pi$
$390$	5.19615	+	9.00000i	0.263117	+	0.455733i
$391$		−	20.7846i		−	1.05112i
$392$		0			0
$393$	−9.00000			−0.453990
$394$	−9.00000	−	15.5885i	−0.453413	−	0.785335i
$395$	0.866025	−	1.50000i	0.0435745	−	0.0754732i
$396$	7.79423	+	4.50000i	0.391675	+	0.226134i
$397$	24.0000	−	13.8564i	1.20453	−	0.695433i	0.242967	−	0.970034i	$-0.421879\pi$
$397$	24.0000	−	13.8564i	1.20453	−	0.695433i	0.961558	+	0.274601i	$0.0885459\pi$
$398$	10.3923			0.520919
$399$		0			0
$400$	−2.00000			−0.100000
$401$	10.3923	−	6.00000i	0.518967	−	0.299626i	−0.217545	−	0.976050i	$-0.569805\pi$
$401$	10.3923	−	6.00000i	0.518967	−	0.299626i	0.736512	+	0.676425i	$0.236472\pi$
$402$	3.00000	+	1.73205i	0.149626	+	0.0863868i
$403$	3.00000	−	5.19615i	0.149441	−	0.258839i
$404$		0			0
$405$	15.5885			0.774597
$406$		0			0
$407$		−	6.00000i		−	0.297409i
$408$	−5.19615	+	3.00000i	−0.257248	+	0.148522i
$409$	−7.50000	−	4.33013i	−0.370851	−	0.214111i	0.302979	−	0.952997i	$-0.402019\pi$
$409$	−7.50000	−	4.33013i	−0.370851	−	0.214111i	−0.673830	+	0.738886i	$0.735352\pi$
$410$	−10.3923	−	6.00000i	−0.513239	−	0.296319i
$411$	−27.0000	+	15.5885i	−1.33181	+	0.768922i
$412$		−	3.46410i		−	0.170664i
$413$		0			0
$414$	18.0000			0.884652
$415$	−7.50000	−	12.9904i	−0.368161	−	0.637673i
$416$	1.73205	−	3.00000i	0.0849208	−	0.147087i
$417$	25.9808	+	15.0000i	1.27228	+	0.734553i
$418$	−9.00000	+	5.19615i	−0.440204	+	0.254152i
$419$	−24.2487			−1.18463			−0.592314	−	0.805708i	$-0.701785\pi$
$419$	−24.2487			−1.18463			−0.592314	+	0.805708i	$0.701785\pi$
$420$		0			0
$421$	32.0000			1.55958			0.779792	−	0.626038i	$-0.215325\pi$
$421$	32.0000			1.55958			0.779792	+	0.626038i	$0.215325\pi$
$422$	−3.46410	+	2.00000i	−0.168630	+	0.0973585i
$423$	−10.3923	+	18.0000i	−0.505291	+	0.875190i
$424$	4.50000	−	7.79423i	0.218539	−	0.378521i
$425$	−3.46410	−	6.00000i	−0.168034	−	0.291043i
$426$	20.7846			1.00702
$427$		0			0
$428$		−	3.00000i		−	0.145010i
$429$	−9.00000	−	15.5885i	−0.434524	−	0.752618i
$430$	−12.0000	−	6.92820i	−0.578691	−	0.334108i
$431$	−20.7846	−	12.0000i	−1.00116	−	0.578020i	−0.0925683	−	0.995706i	$-0.529508\pi$
$431$	−20.7846	−	12.0000i	−1.00116	−	0.578020i	−0.908591	+	0.417687i	$0.862841\pi$
$432$	−2.59808	−	4.50000i	−0.125000	−	0.216506i
$433$		−	34.6410i		−	1.66474i	−0.554220	−	0.832370i	$-0.686983\pi$
$433$		−	34.6410i		−	1.66474i	0.554220	−	0.832370i	$-0.313017\pi$
$434$		0			0
$435$		−	9.00000i		−	0.431517i
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$	−10.3923	+	18.0000i	−0.497131	+	0.861057i
$438$	−6.00000	+	10.3923i	−0.286691	+	0.496564i
$439$	−31.5000	+	18.1865i	−1.50341	+	0.867996i	−0.503421	+	0.864041i	$0.667925\pi$
$439$	−31.5000	+	18.1865i	−1.50341	+	0.867996i	−0.999992	+	0.00395451i	$0.998741\pi$
$440$	−5.19615			−0.247717
$441$		0			0
$442$	12.0000			0.570782
$443$	−7.79423	+	4.50000i	−0.370315	+	0.213801i	−0.673596	−	0.739100i	$-0.735251\pi$
$443$	−7.79423	+	4.50000i	−0.370315	+	0.213801i	0.303281	+	0.952901i	$0.401918\pi$
$444$	−1.73205	+	3.00000i	−0.0821995	+	0.142374i
$445$	9.00000	−	15.5885i	0.426641	−	0.738964i
$446$	−12.9904	−	22.5000i	−0.615112	−	1.06541i
$447$		−	31.1769i		−	1.47462i
$448$		0			0
$449$			30.0000i			1.41579i	0.706319	+	0.707894i	$0.250354\pi$
$449$			30.0000i			1.41579i	−0.706319	+	0.707894i	$0.749646\pi$
$450$	5.19615	−	3.00000i	0.244949	−	0.141421i
$451$	18.0000	+	10.3923i	0.847587	+	0.489355i
$452$	−10.3923	−	6.00000i	−0.488813	−	0.282216i
$453$	−6.06218	−	10.5000i	−0.284826	−	0.493333i
$454$		−	5.19615i		−	0.243868i
$455$		0			0
$456$	6.00000			0.280976
$457$	2.50000	+	4.33013i	0.116945	+	0.202555i	0.918556	−	0.395292i	$-0.129357\pi$
$457$	2.50000	+	4.33013i	0.116945	+	0.202555i	−0.801611	+	0.597847i	$0.796023\pi$
$458$	−6.92820	+	12.0000i	−0.323734	+	0.560723i
$459$	9.00000	−	15.5885i	0.420084	−	0.727607i
$460$	−9.00000	+	5.19615i	−0.419627	+	0.242272i
$461$	13.8564			0.645357			0.322679	−	0.946509i	$-0.395417\pi$
$461$	13.8564			0.645357			0.322679	+	0.946509i	$0.395417\pi$
$462$		0			0
$463$	−4.00000			−0.185896			−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000			−0.185896			−0.0929479	+	0.995671i	$0.529629\pi$
$464$	−2.59808	+	1.50000i	−0.120613	+	0.0696358i
$465$	4.50000	+	2.59808i	0.208683	+	0.120483i
$466$	−9.00000	+	15.5885i	−0.416917	+	0.722121i
$467$	15.5885	+	27.0000i	0.721348	+	1.24941i	0.960460	+	0.278419i	$0.0898104\pi$
$467$	15.5885	+	27.0000i	0.721348	+	1.24941i	−0.239112	+	0.970992i	$0.576856\pi$
$468$			10.3923i			0.480384i
$469$		0			0
$470$		−	12.0000i		−	0.553519i
$471$	−31.1769	+	18.0000i	−1.43656	+	0.829396i
$472$	1.50000	+	0.866025i	0.0690431	+	0.0398621i
$473$	20.7846	+	12.0000i	0.955677	+	0.551761i
$474$	1.50000	−	0.866025i	0.0688973	−	0.0397779i
$475$			6.92820i			0.317888i
$476$		0			0
$477$			27.0000i			1.23625i
$478$	3.00000	+	5.19615i	0.137217	+	0.237666i
$479$	3.46410	−	6.00000i	0.158279	−	0.274147i	−0.775969	−	0.630771i	$-0.782739\pi$
$479$	3.46410	−	6.00000i	0.158279	−	0.274147i	0.934248	+	0.356624i	$0.116072\pi$
$480$	2.59808	+	1.50000i	0.118585	+	0.0684653i
$481$	6.00000	−	3.46410i	0.273576	−	0.157949i
$482$	−25.9808			−1.18339
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	−7.79423	+	4.50000i	−0.353918	+	0.204334i
$486$	13.5000	+	7.79423i	0.612372	+	0.353553i
$487$	−0.500000	+	0.866025i	−0.0226572	+	0.0392434i	−0.877132	−	0.480250i	$-0.840546\pi$
$487$	−0.500000	+	0.866025i	−0.0226572	+	0.0392434i	0.854475	+	0.519493i	$0.173879\pi$
$488$		0			0
$489$	24.2487			1.09656
$490$		0			0
$491$		−	33.0000i		−	1.48927i	−0.667472	−	0.744635i	$-0.732624\pi$
$491$		−	33.0000i		−	1.48927i	0.667472	−	0.744635i	$-0.267376\pi$
$492$	−6.00000	−	10.3923i	−0.270501	−	0.468521i
$493$	−9.00000	−	5.19615i	−0.405340	−	0.234023i
$494$	−10.3923	−	6.00000i	−0.467572	−	0.269953i
$495$	13.5000	−	7.79423i	0.606780	−	0.350325i
$496$		−	1.73205i		−	0.0777714i
$497$		0			0
$498$		−	15.0000i		−	0.672166i
$499$	−11.0000	−	19.0526i	−0.492428	−	0.852910i	0.507534	−	0.861632i	$-0.330557\pi$
$499$	−11.0000	−	19.0526i	−0.492428	−	0.852910i	−0.999962	+	0.00872186i	$0.997224\pi$
$500$	−6.06218	+	10.5000i	−0.271109	+	0.469574i
$501$	−15.0000	+	25.9808i	−0.670151	+	1.16073i
$502$	16.5000	−	9.52628i	0.736431	−	0.425179i
$503$	−38.1051			−1.69902			−0.849512	−	0.527570i	$-0.823103\pi$
$503$	−38.1051			−1.69902			−0.849512	+	0.527570i	$0.823103\pi$
$504$		0			0
$505$		0			0
$506$	15.5885	−	9.00000i	0.692991	−	0.400099i
$507$	−0.866025	+	1.50000i	−0.0384615	+	0.0666173i
$508$	5.50000	−	9.52628i	0.244023	−	0.422660i
$509$	−9.52628	−	16.5000i	−0.422245	−	0.731350i	0.573914	−	0.818916i	$-0.305424\pi$
$509$	−9.52628	−	16.5000i	−0.422245	−	0.731350i	−0.996159	+	0.0875661i	$0.972091\pi$
$510$			10.3923i			0.460179i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−15.5885	+	9.00000i	−0.688247	+	0.397360i
$514$	9.00000	+	5.19615i	0.396973	+	0.229192i
$515$	−5.19615	−	3.00000i	−0.228970	−	0.132196i
$516$	−6.92820	−	12.0000i	−0.304997	−	0.528271i
$517$			20.7846i			0.914106i
$518$		0			0
$519$		0			0
$520$	−3.00000	−	5.19615i	−0.131559	−	0.227866i
$521$	13.8564	−	24.0000i	0.607060	−	1.05146i	−0.384662	−	0.923057i	$-0.625682\pi$
$521$	13.8564	−	24.0000i	0.607060	−	1.05146i	0.991722	−	0.128402i	$-0.0409847\pi$
$522$	4.50000	−	7.79423i	0.196960	−	0.341144i
$523$	33.0000	−	19.0526i	1.44299	−	0.833110i	0.444941	−	0.895560i	$-0.353225\pi$
$523$	33.0000	−	19.0526i	1.44299	−	0.833110i	0.998048	+	0.0624496i	$0.0198913\pi$
$524$	5.19615			0.226995
$525$		0			0
$526$		0			0
$527$	5.19615	−	3.00000i	0.226348	−	0.130682i
$528$	−4.50000	−	2.59808i	−0.195837	−	0.113067i
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$	−7.79423	−	13.5000i	−0.338560	−	0.586403i
$531$	−5.19615			−0.225494
$532$		0			0
$533$			24.0000i			1.03956i
$534$	15.5885	−	9.00000i	0.674579	−	0.389468i
$535$	−4.50000	−	2.59808i	−0.194552	−	0.112325i
$536$	−1.73205	−	1.00000i	−0.0748132	−	0.0431934i
$537$	−18.0000	+	10.3923i	−0.776757	+	0.448461i
$538$		−	29.4449i		−	1.26946i
$539$		0			0
$540$	−9.00000			−0.387298
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	0.985162	−	0.171628i	$-0.0549027\pi$
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	−0.641215	+	0.767361i	$0.721569\pi$
$542$	2.59808	−	4.50000i	0.111597	−	0.193292i
$543$	10.3923	+	6.00000i	0.445976	+	0.257485i
$544$	3.00000	−	1.73205i	0.128624	−	0.0742611i
$545$	−3.46410			−0.148386
$546$		0			0
$547$	2.00000			0.0855138			0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000			0.0855138			0.0427569	+	0.999086i	$0.486386\pi$
$548$	15.5885	−	9.00000i	0.665906	−	0.384461i
$549$		0			0
$550$	3.00000	−	5.19615i	0.127920	−	0.221565i
$551$	5.19615	+	9.00000i	0.221364	+	0.383413i
$552$	−10.3923			−0.442326
$553$		0			0
$554$		−	8.00000i		−	0.339887i
$555$	3.00000	+	5.19615i	0.127343	+	0.220564i
$556$	−15.0000	−	8.66025i	−0.636142	−	0.367277i
$557$	−2.59808	−	1.50000i	−0.110084	−	0.0635570i	0.443947	−	0.896053i	$-0.353578\pi$
$557$	−2.59808	−	1.50000i	−0.110084	−	0.0635570i	−0.554031	+	0.832496i	$0.686911\pi$
$558$	2.59808	+	4.50000i	0.109985	+	0.190500i
$559$			27.7128i			1.17213i
$560$		0			0
$561$		−	18.0000i		−	0.759961i
$562$	15.0000	+	25.9808i	0.632737	+	1.09593i
$563$	12.9904	−	22.5000i	0.547479	−	0.948262i	−0.450967	−	0.892541i	$-0.648921\pi$
$563$	12.9904	−	22.5000i	0.547479	−	0.948262i	0.998446	−	0.0557214i	$-0.0177458\pi$
$564$	6.00000	−	10.3923i	0.252646	−	0.437595i
$565$	−18.0000	+	10.3923i	−0.757266	+	0.437208i
$566$	27.7128			1.16486
$567$		0			0
$568$	−12.0000			−0.503509
$569$	5.19615	−	3.00000i	0.217834	−	0.125767i	−0.387113	−	0.922032i	$-0.626528\pi$
$569$	5.19615	−	3.00000i	0.217834	−	0.125767i	0.604947	+	0.796266i	$0.293194\pi$
$570$	5.19615	−	9.00000i	0.217643	−	0.376969i
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$	5.19615	+	9.00000i	0.217262	+	0.376309i
$573$		0			0
$574$		0			0
$575$		−	12.0000i		−	0.500435i
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	1.50000	+	0.866025i	0.0624458	+	0.0360531i	0.530898	−	0.847436i	$-0.321855\pi$
$577$	1.50000	+	0.866025i	0.0624458	+	0.0360531i	−0.468452	+	0.883489i	$0.655188\pi$
$578$	−4.33013	−	2.50000i	−0.180110	−	0.103986i
$579$	19.9186	+	34.5000i	0.827788	+	1.43377i
$580$			5.19615i			0.215758i
$581$		0			0
$582$	−9.00000			−0.373062
$583$	13.5000	+	23.3827i	0.559113	+	0.968412i
$584$	3.46410	−	6.00000i	0.143346	−	0.248282i
$585$	15.5885	+	9.00000i	0.644503	+	0.372104i
$586$	−16.5000	+	9.52628i	−0.681609	+	0.393527i
$587$	15.5885			0.643404			0.321702	−	0.946841i	$-0.395745\pi$
$587$	15.5885			0.643404			0.321702	+	0.946841i	$0.395745\pi$
$588$		0			0
$589$	−6.00000			−0.247226
$590$	2.59808	−	1.50000i	0.106961	−	0.0617540i
$591$	−27.0000	−	15.5885i	−1.11063	−	0.641223i
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	19.0526	+	33.0000i	0.782395	+	1.35515i	0.930543	+	0.366182i	$0.119335\pi$
$593$	19.0526	+	33.0000i	0.782395	+	1.35515i	−0.148148	+	0.988965i	$0.547331\pi$
$594$	15.5885			0.639602
$595$		0			0
$596$			18.0000i			0.737309i
$597$	15.5885	−	9.00000i	0.637993	−	0.368345i
$598$	18.0000	+	10.3923i	0.736075	+	0.424973i
$599$	25.9808	+	15.0000i	1.06155	+	0.612883i	0.925859	−	0.377869i	$-0.123343\pi$
$599$	25.9808	+	15.0000i	1.06155	+	0.612883i	0.135686	+	0.990752i	$0.456676\pi$
$600$	−3.00000	+	1.73205i	−0.122474	+	0.0707107i
$601$			29.4449i			1.20108i	0.799594	+	0.600541i	$0.205048\pi$
$601$			29.4449i			1.20108i	−0.799594	+	0.600541i	$0.794952\pi$
$602$		0			0
$603$	6.00000			0.244339
$604$	3.50000	+	6.06218i	0.142413	+	0.246667i
$605$	−1.73205	+	3.00000i	−0.0704179	+	0.121967i
$606$		0			0
$607$	−19.5000	+	11.2583i	−0.791481	+	0.456962i	−0.840484	−	0.541837i	$-0.817729\pi$
$607$	−19.5000	+	11.2583i	−0.791481	+	0.456962i	0.0490029	+	0.998799i	$0.484396\pi$
$608$	−3.46410			−0.140488
$609$		0			0
$610$		0			0
$611$	−20.7846	+	12.0000i	−0.840855	+	0.485468i
$612$	−5.19615	+	9.00000i	−0.210042	+	0.363803i
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	−0.885514	−	0.464614i	$-0.846193\pi$
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	0.845124	+	0.534570i	$0.179527\pi$
$614$	−12.1244	−	21.0000i	−0.489299	−	0.847491i
$615$	−20.7846			−0.838116
$616$		0			0
$617$			12.0000i			0.483102i	0.970388	+	0.241551i	$0.0776561\pi$
$617$			12.0000i			0.483102i	−0.970388	+	0.241551i	$0.922344\pi$
$618$	−3.00000	−	5.19615i	−0.120678	−	0.209020i
$619$	−6.00000	−	3.46410i	−0.241160	−	0.139234i	0.374550	−	0.927207i	$-0.377797\pi$
$619$	−6.00000	−	3.46410i	−0.241160	−	0.139234i	−0.615710	+	0.787973i	$0.711131\pi$
$620$	−2.59808	−	1.50000i	−0.104341	−	0.0602414i
$621$	27.0000	−	15.5885i	1.08347	−	0.625543i
$622$			13.8564i			0.555591i
$623$		0			0
$624$		−	6.00000i		−	0.240192i
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	0.866025	−	1.50000i	0.0346133	−	0.0599521i
$627$	−9.00000	+	15.5885i	−0.359425	+	0.622543i
$628$	18.0000	−	10.3923i	0.718278	−	0.414698i
$629$	6.92820			0.276246
$630$		0			0
$631$	−31.0000			−1.23409			−0.617045	−	0.786928i	$-0.711670\pi$
$631$	−31.0000			−1.23409			−0.617045	+	0.786928i	$0.711670\pi$
$632$	−0.866025	+	0.500000i	−0.0344486	+	0.0198889i
$633$	−3.46410	+	6.00000i	−0.137686	+	0.238479i
$634$	−7.50000	+	12.9904i	−0.297863	+	0.515914i
$635$	−9.52628	−	16.5000i	−0.378039	−	0.654783i
$636$		−	15.5885i		−	0.618123i
$637$		0			0
$638$		−	9.00000i		−	0.356313i
$639$	31.1769	−	18.0000i	1.23334	−	0.712069i
$640$	−1.50000	−	0.866025i	−0.0592927	−	0.0342327i
$641$	20.7846	+	12.0000i	0.820943	+	0.473972i	0.850741	−	0.525584i	$-0.176153\pi$
$641$	20.7846	+	12.0000i	0.820943	+	0.473972i	−0.0297987	+	0.999556i	$0.509487\pi$
$642$	−2.59808	−	4.50000i	−0.102538	−	0.177601i
$643$			17.3205i			0.683054i	0.939872	+	0.341527i	$0.110944\pi$
$643$			17.3205i			0.683054i	−0.939872	+	0.341527i	$0.889056\pi$
$644$		0			0
$645$	−24.0000			−0.944999
$646$	−6.00000	−	10.3923i	−0.236067	−	0.408880i
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$	−7.79423	−	4.50000i	−0.306186	−	0.176777i
$649$	−4.50000	+	2.59808i	−0.176640	+	0.101983i
$650$	6.92820			0.271746
$651$		0			0
$652$	−14.0000			−0.548282
$653$	2.59808	−	1.50000i	0.101671	−	0.0586995i	−0.448303	−	0.893882i	$-0.647971\pi$
$653$	2.59808	−	1.50000i	0.101671	−	0.0586995i	0.549973	+	0.835182i	$0.314638\pi$
$654$	−3.00000	−	1.73205i	−0.117309	−	0.0677285i
$655$	4.50000	−	7.79423i	0.175830	−	0.304546i
$656$	3.46410	+	6.00000i	0.135250	+	0.234261i
$657$			20.7846i			0.810885i
$658$		0			0
$659$		−	12.0000i		−	0.467454i	−0.972302	−	0.233727i	$-0.924908\pi$
$659$		−	12.0000i		−	0.467454i	0.972302	−	0.233727i	$-0.0750921\pi$
$660$	−7.79423	+	4.50000i	−0.303390	+	0.175162i
$661$	6.00000	+	3.46410i	0.233373	+	0.134738i	0.612127	−	0.790759i	$-0.290314\pi$
$661$	6.00000	+	3.46410i	0.233373	+	0.134738i	−0.378754	+	0.925497i	$0.623647\pi$
$662$	−6.92820	−	4.00000i	−0.269272	−	0.155464i
$663$	18.0000	−	10.3923i	0.699062	−	0.403604i
$664$			8.66025i			0.336083i
$665$		0			0
$666$			6.00000i			0.232495i
$667$	−9.00000	−	15.5885i	−0.348481	−	0.603587i
$668$	8.66025	−	15.0000i	0.335075	−	0.580367i
$669$	−38.9711	−	22.5000i	−1.50671	−	0.869900i
$670$	−3.00000	+	1.73205i	−0.115900	+	0.0669150i
$671$		0			0
$672$		0			0
$673$	−41.0000			−1.58043			−0.790217	−	0.612827i	$-0.790032\pi$
$673$	−41.0000			−1.58043			−0.790217	+	0.612827i	$0.790032\pi$
$674$	−11.2583	+	6.50000i	−0.433655	+	0.250371i
$675$	5.19615	−	9.00000i	0.200000	−	0.346410i
$676$	0.500000	−	0.866025i	0.0192308	−	0.0333087i
$677$	2.59808	+	4.50000i	0.0998522	+	0.172949i	0.911623	−	0.411027i	$-0.134830\pi$
$677$	2.59808	+	4.50000i	0.0998522	+	0.172949i	−0.811771	+	0.583976i	$0.801496\pi$
$678$	−20.7846			−0.798228
$679$		0			0
$680$		−	6.00000i		−	0.230089i
$681$	−4.50000	−	7.79423i	−0.172440	−	0.298675i
$682$	4.50000	+	2.59808i	0.172314	+	0.0994855i
$683$	−18.1865	−	10.5000i	−0.695888	−	0.401771i	0.109926	−	0.993940i	$-0.464939\pi$
$683$	−18.1865	−	10.5000i	−0.695888	−	0.401771i	−0.805814	+	0.592168i	$0.798272\pi$
$684$	9.00000	−	5.19615i	0.344124	−	0.198680i
$685$		−	31.1769i		−	1.19121i
$686$		0			0
$687$			24.0000i			0.915657i
$688$	4.00000	+	6.92820i	0.152499	+	0.264135i
$689$	−15.5885	+	27.0000i	−0.593873	+	1.02862i
$690$	−9.00000	+	15.5885i	−0.342624	+	0.593442i
$691$	6.00000	−	3.46410i	0.228251	−	0.131781i	−0.381514	−	0.924363i	$-0.624597\pi$
$691$	6.00000	−	3.46410i	0.228251	−	0.131781i	0.609765	+	0.792582i	$0.291264\pi$
$692$		0			0
$693$		0			0
$694$	12.0000			0.455514
$695$	−25.9808	+	15.0000i	−0.985506	+	0.568982i
$696$	−2.59808	+	4.50000i	−0.0984798	+	0.170572i
$697$	−12.0000	+	20.7846i	−0.454532	+	0.787273i
$698$	5.19615	+	9.00000i	0.196677	+	0.340655i
$699$			31.1769i			1.17922i
$700$		0			0
$701$			3.00000i			0.113308i	0.998394	+	0.0566542i	$0.0180433\pi$
$701$			3.00000i			0.113308i	−0.998394	+	0.0566542i	$0.981957\pi$
$702$	9.00000	+	15.5885i	0.339683	+	0.588348i
$703$	−6.00000	−	3.46410i	−0.226294	−	0.130651i
$704$	2.59808	+	1.50000i	0.0979187	+	0.0565334i
$705$	−10.3923	−	18.0000i	−0.391397	−	0.677919i
$706$			34.6410i			1.30373i
$707$		0			0
$708$	3.00000			0.112747
$709$	19.0000	+	32.9090i	0.713560	+	1.23592i	0.963512	+	0.267664i	$0.0862517\pi$
$709$	19.0000	+	32.9090i	0.713560	+	1.23592i	−0.249952	+	0.968258i	$0.580415\pi$
$710$	−10.3923	+	18.0000i	−0.390016	+	0.675528i
$711$	1.50000	−	2.59808i	0.0562544	−	0.0974355i
$712$	−9.00000	+	5.19615i	−0.337289	+	0.194734i
$713$	10.3923			0.389195
$714$		0			0
$715$	18.0000			0.673162
$716$	10.3923	−	6.00000i	0.388379	−	0.224231i
$717$	9.00000	+	5.19615i	0.336111	+	0.194054i
$718$	3.00000	−	5.19615i	0.111959	−	0.193919i
$719$	−22.5167	−	39.0000i	−0.839730	−	1.45445i	−0.890121	−	0.455725i	$-0.849380\pi$
$719$	−22.5167	−	39.0000i	−0.839730	−	1.45445i	0.0503909	−	0.998730i	$-0.483953\pi$
$720$	5.19615			0.193649
$721$		0			0
$722$		−	7.00000i		−	0.260513i
$723$	−38.9711	+	22.5000i	−1.44935	+	0.836784i
$724$	−6.00000	−	3.46410i	−0.222988	−	0.128742i
$725$	−5.19615	−	3.00000i	−0.192980	−	0.111417i
$726$	−3.00000	+	1.73205i	−0.111340	+	0.0642824i
$727$		−	29.4449i		−	1.09205i	−0.837769	−	0.546025i	$-0.816140\pi$
$727$		−	29.4449i		−	1.09205i	0.837769	−	0.546025i	$-0.183860\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$	−6.00000	−	10.3923i	−0.222070	−	0.384636i
$731$	−13.8564	+	24.0000i	−0.512498	+	0.887672i
$732$		0			0
$733$	−30.0000	+	17.3205i	−1.10808	+	0.639748i	−0.938330	−	0.345740i	$-0.887628\pi$
$733$	−30.0000	+	17.3205i	−1.10808	+	0.639748i	−0.169745	+	0.985488i	$0.554294\pi$
$734$	−22.5167			−0.831105
$735$		0			0
$736$	6.00000			0.221163
$737$	5.19615	−	3.00000i	0.191403	−	0.110506i
$738$	−18.0000	−	10.3923i	−0.662589	−	0.382546i
$739$	5.00000	−	8.66025i	0.183928	−	0.318573i	−0.759287	−	0.650756i	$-0.774452\pi$
$739$	5.00000	−	8.66025i	0.183928	−	0.318573i	0.943215	+	0.332184i	$0.107785\pi$
$740$	−1.73205	−	3.00000i	−0.0636715	−	0.110282i
$741$	−20.7846			−0.763542
$742$		0			0
$743$			18.0000i			0.660356i	0.943919	+	0.330178i	$0.107109\pi$
$743$			18.0000i			0.660356i	−0.943919	+	0.330178i	$0.892891\pi$
$744$	−1.50000	−	2.59808i	−0.0549927	−	0.0952501i
$745$	27.0000	+	15.5885i	0.989203	+	0.571117i
$746$	27.7128	+	16.0000i	1.01464	+	0.585802i
$747$	−12.9904	−	22.5000i	−0.475293	−	0.823232i
$748$			10.3923i			0.379980i
$749$		0			0
$750$			21.0000i			0.766812i
$751$	5.50000	+	9.52628i	0.200698	+	0.347619i	0.948753	−	0.316017i	$-0.102346\pi$
$751$	5.50000	+	9.52628i	0.200698	+	0.347619i	−0.748056	+	0.663636i	$0.769012\pi$
$752$	−3.46410	+	6.00000i	−0.126323	+	0.218797i
$753$	16.5000	−	28.5788i	0.601293	−	1.04147i
$754$	9.00000	−	5.19615i	0.327761	−	0.189233i
$755$	12.1244			0.441250
$756$		0			0
$757$	4.00000			0.145382			0.0726912	−	0.997354i	$-0.476841\pi$
$757$	4.00000			0.145382			0.0726912	+	0.997354i	$0.476841\pi$
$758$	−13.8564	+	8.00000i	−0.503287	+	0.290573i
$759$	15.5885	−	27.0000i	0.565825	−	0.980038i
$760$	−3.00000	+	5.19615i	−0.108821	+	0.188484i
$761$	8.66025	+	15.0000i	0.313934	+	0.543750i	0.979210	−	0.202848i	$-0.0650196\pi$
$761$	8.66025	+	15.0000i	0.313934	+	0.543750i	−0.665276	+	0.746597i	$0.731686\pi$
$762$		−	19.0526i		−	0.690201i
$763$		0			0
$764$		0			0
$765$	9.00000	+	15.5885i	0.325396	+	0.563602i
$766$	3.00000	+	1.73205i	0.108394	+	0.0625815i
$767$	−5.19615	−	3.00000i	−0.187622	−	0.108324i
$768$	−0.866025	−	1.50000i	−0.0312500	−	0.0541266i
$769$		−	19.0526i		−	0.687053i	−0.939143	−	0.343526i	$-0.888379\pi$
$769$		−	19.0526i		−	0.687053i	0.939143	−	0.343526i	$-0.111621\pi$
$770$		0			0
$771$	18.0000			0.648254
$772$	−11.5000	−	19.9186i	−0.413894	−	0.716886i
$773$	−13.8564	+	24.0000i	−0.498380	+	0.863220i	−0.999998	−	0.00186926i	$-0.999405\pi$
$773$	−13.8564	+	24.0000i	−0.498380	+	0.863220i	0.501618	+	0.865089i	$0.332738\pi$
$774$	−20.7846	−	12.0000i	−0.747087	−	0.431331i
$775$	3.00000	−	1.73205i	0.107763	−	0.0622171i
$776$	5.19615			0.186531
$777$		0			0
$778$	18.0000			0.645331
$779$	20.7846	−	12.0000i	0.744686	−	0.429945i
$780$	−9.00000	−	5.19615i	−0.322252	−	0.186052i
$781$	18.0000	−	31.1769i	0.644091	−	1.11560i
$782$	10.3923	+	18.0000i	0.371628	+	0.643679i
$783$		−	15.5885i		−	0.557086i
$784$		0			0
$785$		−	36.0000i		−	1.28490i
$786$	7.79423	−	4.50000i	0.278011	−	0.160510i
$787$	−36.0000	−	20.7846i	−1.28326	−	0.740891i	−0.305818	−	0.952090i	$-0.598930\pi$
$787$	−36.0000	−	20.7846i	−1.28326	−	0.740891i	−0.977443	+	0.211199i	$0.932263\pi$
$788$	15.5885	+	9.00000i	0.555316	+	0.320612i
$789$		0			0
$790$			1.73205i			0.0616236i
$791$		0			0
$792$	−9.00000			−0.319801
$793$		0			0
$794$	−13.8564	+	24.0000i	−0.491745	+	0.851728i
$795$	−23.3827	−	13.5000i	−0.829298	−	0.478796i
$796$	−9.00000	+	5.19615i	−0.318997	+	0.184173i
$797$	25.9808			0.920286			0.460143	−	0.887845i	$-0.347798\pi$
$797$	25.9808			0.920286			0.460143	+	0.887845i	$0.347798\pi$
$798$		0			0
$799$	−24.0000			−0.849059
$800$	1.73205	−	1.00000i	0.0612372	−	0.0353553i
$801$	15.5885	−	27.0000i	0.550791	−	0.953998i
$802$	−6.00000	+	10.3923i	−0.211867	+	0.366965i
$803$	10.3923	+	18.0000i	0.366736	+	0.635206i
$804$	−3.46410			−0.122169
$805$		0			0
$806$			6.00000i			0.211341i
$807$	−25.5000	−	44.1673i	−0.897643	−	1.55476i
$808$		0			0
$809$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$809$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$810$	−13.5000	+	7.79423i	−0.474342	+	0.273861i
$811$		−	31.1769i		−	1.09477i	−0.836881	−	0.547385i	$-0.815623\pi$
$811$		−	31.1769i		−	1.09477i	0.836881	−	0.547385i	$-0.184377\pi$
$812$		0			0
$813$		−	9.00000i		−	0.315644i
$814$	3.00000	+	5.19615i	0.105150	+	0.182125i
$815$	−12.1244	+	21.0000i	−0.424698	+	0.735598i
$816$	3.00000	−	5.19615i	0.105021	−	0.181902i
$817$	24.0000	−	13.8564i	0.839654	−	0.484774i
$818$	8.66025			0.302799
$819$		0			0
$820$	12.0000			0.419058
$821$	−2.59808	+	1.50000i	−0.0906735	+	0.0523504i	−0.544651	−	0.838663i	$-0.683338\pi$
$821$	−2.59808	+	1.50000i	−0.0906735	+	0.0523504i	0.453978	+	0.891013i	$0.350005\pi$
$822$	15.5885	−	27.0000i	0.543710	−	0.941733i
$823$	−4.00000	+	6.92820i	−0.139431	+	0.241502i	−0.927281	−	0.374365i	$-0.877861\pi$
$823$	−4.00000	+	6.92820i	−0.139431	+	0.241502i	0.787850	+	0.615867i	$0.211194\pi$
$824$	1.73205	+	3.00000i	0.0603388	+	0.104510i
$825$		−	10.3923i		−	0.361814i
$826$		0			0
$827$			9.00000i			0.312961i	0.987681	+	0.156480i	$0.0500148\pi$
$827$			9.00000i			0.312961i	−0.987681	+	0.156480i	$0.949985\pi$
$828$	−15.5885	+	9.00000i	−0.541736	+	0.312772i
$829$	15.0000	+	8.66025i	0.520972	+	0.300783i	0.737332	−	0.675530i	$-0.236085\pi$
$829$	15.0000	+	8.66025i	0.520972	+	0.300783i	−0.216361	+	0.976314i	$0.569419\pi$
$830$	12.9904	+	7.50000i	0.450903	+	0.260329i
$831$	−6.92820	−	12.0000i	−0.240337	−	0.416275i
$832$			3.46410i			0.120096i
$833$		0			0
$834$	−30.0000			−1.03882
$835$	−15.0000	−	25.9808i	−0.519096	−	0.899101i
$836$	5.19615	−	9.00000i	0.179713	−	0.311272i
$837$	7.79423	+	4.50000i	0.269408	+	0.155543i
$838$	21.0000	−	12.1244i	0.725433	−	0.418829i
$839$	−3.46410			−0.119594			−0.0597970	−	0.998211i	$-0.519045\pi$
$839$	−3.46410			−0.119594			−0.0597970	+	0.998211i	$0.519045\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$	−27.7128	+	16.0000i	−0.955047	+	0.551396i
$843$	45.0000	+	25.9808i	1.54988	+	0.894825i
$844$	2.00000	−	3.46410i	0.0688428	−	0.119239i
$845$	−0.866025	−	1.50000i	−0.0297922	−	0.0516016i
$846$		−	20.7846i		−	0.714590i
$847$		0			0
$848$			9.00000i			0.309061i
$849$	41.5692	−	24.0000i	1.42665	−	0.823678i
$850$	6.00000	+	3.46410i	0.205798	+	0.118818i
$851$	10.3923	+	6.00000i	0.356244	+	0.205677i
$852$	−18.0000	+	10.3923i	−0.616670	+	0.356034i
$853$			24.2487i			0.830260i	0.909762	+	0.415130i	$0.136264\pi$
$853$			24.2487i			0.830260i	−0.909762	+	0.415130i	$0.863736\pi$
$854$		0			0
$855$		−	18.0000i		−	0.615587i
$856$	1.50000	+	2.59808i	0.0512689	+	0.0888004i
$857$	6.92820	−	12.0000i	0.236663	−	0.409912i	−0.723092	−	0.690752i	$-0.757280\pi$
$857$	6.92820	−	12.0000i	0.236663	−	0.409912i	0.959755	+	0.280840i	$0.0906130\pi$
$858$	15.5885	+	9.00000i	0.532181	+	0.307255i
$859$	18.0000	−	10.3923i	0.614152	−	0.354581i	−0.160437	−	0.987046i	$-0.551290\pi$
$859$	18.0000	−	10.3923i	0.614152	−	0.354581i	0.774589	+	0.632465i	$0.217957\pi$
$860$	13.8564			0.472500
$861$		0			0
$862$	24.0000			0.817443
$863$	46.7654	−	27.0000i	1.59191	−	0.919091i	0.598933	−	0.800799i	$-0.295592\pi$
$863$	46.7654	−	27.0000i	1.59191	−	0.919091i	0.992979	−	0.118291i	$-0.0377417\pi$
$864$	4.50000	+	2.59808i	0.153093	+	0.0883883i
$865$		0			0
$866$	17.3205	+	30.0000i	0.588575	+	1.01944i
$867$	−8.66025			−0.294118
$868$		0			0
$869$		−	3.00000i		−	0.101768i
$870$	4.50000	+	7.79423i	0.152564	+	0.264249i
$871$	6.00000	+	3.46410i	0.203302	+	0.117377i
$872$	1.73205	+	1.00000i	0.0586546	+	0.0338643i
$873$	−13.5000	+	7.79423i	−0.456906	+	0.263795i
$874$		−	20.7846i		−	0.703050i
$875$		0			0
$876$		−	12.0000i		−	0.405442i
$877$	−22.0000	−	38.1051i	−0.742887	−	1.28672i	−0.951175	−	0.308651i	$-0.900123\pi$
$877$	−22.0000	−	38.1051i	−0.742887	−	1.28672i	0.208288	−	0.978068i	$-0.433211\pi$
$878$	18.1865	−	31.5000i	0.613766	−	1.06307i
$879$	−16.5000	+	28.5788i	−0.556531	+	0.963940i
$880$	4.50000	−	2.59808i	0.151695	−	0.0875811i
$881$	−10.3923			−0.350126			−0.175063	−	0.984557i	$-0.556013\pi$
$881$	−10.3923			−0.350126			−0.175063	+	0.984557i	$0.556013\pi$
$882$		0			0
$883$	52.0000			1.74994			0.874970	−	0.484178i	$-0.160881\pi$
$883$	52.0000			1.74994			0.874970	+	0.484178i	$0.160881\pi$
$884$	−10.3923	+	6.00000i	−0.349531	+	0.201802i
$885$	2.59808	−	4.50000i	0.0873334	−	0.151266i
$886$	4.50000	−	7.79423i	0.151180	−	0.261852i
$887$	12.1244	+	21.0000i	0.407096	+	0.705111i	0.994563	−	0.104137i	$-0.0332081\pi$
$887$	12.1244	+	21.0000i	0.407096	+	0.705111i	−0.587467	+	0.809248i	$0.699875\pi$
$888$		−	3.46410i		−	0.116248i
$889$		0			0
$890$			18.0000i			0.603361i
$891$	23.3827	−	13.5000i	0.783349	−	0.452267i
$892$	22.5000	+	12.9904i	0.753356	+	0.434950i
$893$	20.7846	+	12.0000i	0.695530	+	0.401565i
$894$	15.5885	+	27.0000i	0.521356	+	0.903015i
$895$		−	20.7846i		−	0.694753i
$896$		0			0
$897$	36.0000			1.20201
$898$	−15.0000	−	25.9808i	−0.500556	−	0.866989i
$899$	2.59808	−	4.50000i	0.0866507	−	0.150083i
$900$	−3.00000	+	5.19615i	−0.100000	+	0.173205i
$901$	−27.0000	+	15.5885i	−0.899500	+	0.519327i
$902$	−20.7846			−0.692052
$903$		0			0
$904$	12.0000			0.399114
$905$	−10.3923	+	6.00000i	−0.345452	+	0.199447i
$906$	10.5000	+	6.06218i	0.348839	+	0.201402i
$907$	13.0000	−	22.5167i	0.431658	−	0.747653i	−0.565358	−	0.824845i	$-0.691262\pi$
$907$	13.0000	−	22.5167i	0.431658	−	0.747653i	0.997016	+	0.0771920i	$0.0245954\pi$
$908$	2.59808	+	4.50000i	0.0862202	+	0.149338i
$909$		0			0
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$	−5.19615	+	3.00000i	−0.172062	+	0.0993399i
$913$	−22.5000	−	12.9904i	−0.744641	−	0.429919i
$914$	−4.33013	−	2.50000i	−0.143228	−	0.0826927i
$915$		0			0
$916$		−	13.8564i		−	0.457829i
$917$		0			0
$918$			18.0000i			0.594089i
$919$	10.0000	+	17.3205i	0.329870	+	0.571351i	0.982486	−	0.186338i	$-0.0596619\pi$
$919$	10.0000	+	17.3205i	0.329870	+	0.571351i	−0.652616	+	0.757689i	$0.726329\pi$
$920$	5.19615	−	9.00000i	0.171312	−	0.296721i
$921$	−36.3731	−	21.0000i	−1.19853	−	0.691974i
$922$	−12.0000	+	6.92820i	−0.395199	+	0.228168i
$923$	41.5692			1.36827
$924$		0			0
$925$	4.00000			0.131519
$926$	3.46410	−	2.00000i	0.113837	−	0.0657241i
$927$	−9.00000	−	5.19615i	−0.295599	−	0.170664i
$928$	1.50000	−	2.59808i	0.0492399	−	0.0852860i
$929$	−24.2487	−	42.0000i	−0.795574	−	1.37798i	−0.922474	−	0.386060i	$-0.873836\pi$
$929$	−24.2487	−	42.0000i	−0.795574	−	1.37798i	0.126899	−	0.991916i	$-0.459497\pi$
$930$	−5.19615			−0.170389
$931$		0			0
$932$		−	18.0000i		−	0.589610i
$933$	12.0000	+	20.7846i	0.392862	+	0.680458i
$934$	−27.0000	−	15.5885i	−0.883467	−	0.510070i
$935$	15.5885	+	9.00000i	0.509797	+	0.294331i
$936$	−5.19615	−	9.00000i	−0.169842	−	0.294174i
$937$		−	22.5167i		−	0.735587i	−0.929907	−	0.367794i	$-0.880113\pi$
$937$		−	22.5167i		−	0.735587i	0.929907	−	0.367794i	$-0.119887\pi$
$938$		0			0
$939$		−	3.00000i		−	0.0979013i
$940$	6.00000	+	10.3923i	0.195698	+	0.338960i
$941$	16.4545	−	28.5000i	0.536401	−	0.929073i	−0.462693	−	0.886518i	$-0.653117\pi$
$941$	16.4545	−	28.5000i	0.536401	−	0.929073i	0.999094	−	0.0425550i	$-0.0135498\pi$
$942$	18.0000	−	31.1769i	0.586472	−	1.01580i
$943$	−36.0000	+	20.7846i	−1.17232	+	0.676840i
$944$	−1.73205			−0.0563735
$945$		0			0
$946$	−24.0000			−0.780307
$947$	10.3923	−	6.00000i	0.337705	−	0.194974i	−0.321552	−	0.946892i	$-0.604204\pi$
$947$	10.3923	−	6.00000i	0.337705	−	0.194974i	0.659256	+	0.751918i	$0.270871\pi$
$948$	−0.866025	+	1.50000i	−0.0281272	+	0.0487177i
$949$	−12.0000	+	20.7846i	−0.389536	+	0.674697i
$950$	−3.46410	−	6.00000i	−0.112390	−	0.194666i
$951$			25.9808i			0.842484i
$952$		0			0
$953$		−	24.0000i		−	0.777436i	−0.921357	−	0.388718i	$-0.872918\pi$
$953$		−	24.0000i		−	0.777436i	0.921357	−	0.388718i	$-0.127082\pi$
$954$	−13.5000	−	23.3827i	−0.437079	−	0.757042i
$955$		0			0
$956$	−5.19615	−	3.00000i	−0.168056	−	0.0970269i
$957$	−7.79423	−	13.5000i	−0.251952	−	0.436393i
$958$			6.92820i			0.223840i
$959$		0			0
$960$	−3.00000			−0.0968246
$961$	−14.0000	−	24.2487i	−0.451613	−	0.782216i
$962$	−3.46410	+	6.00000i	−0.111687	+	0.193448i
$963$	−7.79423	−	4.50000i	−0.251166	−	0.145010i
$964$	22.5000	−	12.9904i	0.724676	−	0.418392i
$965$	−39.8372			−1.28240
$966$		0			0
$967$	−7.00000			−0.225105			−0.112552	−	0.993646i	$-0.535903\pi$
$967$	−7.00000			−0.225105			−0.112552	+	0.993646i	$0.535903\pi$
$968$	1.73205	−	1.00000i	0.0556702	−	0.0321412i
$969$	−18.0000	−	10.3923i	−0.578243	−	0.333849i
$970$	4.50000	−	7.79423i	0.144486	−	0.250258i
$971$	−4.33013	−	7.50000i	−0.138960	−	0.240686i	0.788143	−	0.615492i	$-0.211043\pi$
$971$	−4.33013	−	7.50000i	−0.138960	−	0.240686i	−0.927103	+	0.374806i	$0.877709\pi$
$972$	−15.5885			−0.500000
$973$		0			0
$974$		−	1.00000i		−	0.0320421i
$975$	10.3923	−	6.00000i	0.332820	−	0.192154i
$976$		0			0
$977$	−20.7846	−	12.0000i	−0.664959	−	0.383914i	0.129205	−	0.991618i	$-0.458757\pi$
$977$	−20.7846	−	12.0000i	−0.664959	−	0.383914i	−0.794164	+	0.607704i	$0.792091\pi$
$978$	−21.0000	+	12.1244i	−0.671506	+	0.387694i
$979$		−	31.1769i		−	0.996419i
$980$		0			0
$981$	−6.00000			−0.191565
$982$	16.5000	+	28.5788i	0.526536	+	0.911987i
$983$	−6.92820	+	12.0000i	−0.220975	+	0.382741i	−0.955104	−	0.296269i	$-0.904257\pi$
$983$	−6.92820	+	12.0000i	−0.220975	+	0.382741i	0.734129	+	0.679010i	$0.237591\pi$
$984$	10.3923	+	6.00000i	0.331295	+	0.191273i
$985$	27.0000	−	15.5885i	0.860292	−	0.496690i
$986$	10.3923			0.330958
$987$		0			0
$988$	12.0000			0.381771
$989$	−41.5692	+	24.0000i	−1.32182	+	0.763156i
$990$	−7.79423	+	13.5000i	−0.247717	+	0.429058i
$991$	23.5000	−	40.7032i	0.746502	−	1.29298i	−0.202988	−	0.979181i	$-0.565065\pi$
$991$	23.5000	−	40.7032i	0.746502	−	1.29298i	0.949490	−	0.313798i	$-0.101602\pi$
$992$	0.866025	+	1.50000i	0.0274963	+	0.0476250i
$993$	−13.8564			−0.439720
$994$		0			0
$995$			18.0000i			0.570638i
$996$	7.50000	+	12.9904i	0.237647	+	0.411616i
$997$	−15.0000	−	8.66025i	−0.475055	−	0.274273i	0.243299	−	0.969951i	$-0.421771\pi$
$997$	−15.0000	−	8.66025i	−0.475055	−	0.274273i	−0.718353	+	0.695678i	$0.755104\pi$
$998$	19.0526	+	11.0000i	0.603098	+	0.348199i
$999$	5.19615	+	9.00000i	0.164399	+	0.284747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.f.a.227.1		4
3.2	odd	2	inner	294.2.f.a.227.2		4
7.2	even	3		42.2.f.a.5.2	yes	4
7.3	odd	6		294.2.d.a.293.1		4
7.4	even	3		294.2.d.a.293.2		4
7.5	odd	6	inner	294.2.f.a.215.2		4
7.6	odd	2		42.2.f.a.17.1	yes	4
21.2	odd	6		42.2.f.a.5.1	✓	4
21.5	even	6	inner	294.2.f.a.215.1		4
21.11	odd	6		294.2.d.a.293.3		4
21.17	even	6		294.2.d.a.293.4		4
21.20	even	2		42.2.f.a.17.2	yes	4
28.3	even	6		2352.2.k.e.881.3		4
28.11	odd	6		2352.2.k.e.881.1		4
28.23	odd	6		336.2.bc.e.257.2		4
28.27	even	2		336.2.bc.e.17.1		4
35.2	odd	12		1050.2.u.a.299.2		4
35.9	even	6		1050.2.s.b.551.1		4
35.13	even	4		1050.2.u.d.899.2		4
35.23	odd	12		1050.2.u.d.299.1		4
35.27	even	4		1050.2.u.a.899.1		4
35.34	odd	2		1050.2.s.b.101.2		4
63.2	odd	6		1134.2.l.c.215.2		4
63.13	odd	6		1134.2.l.c.269.1		4
63.16	even	3		1134.2.l.c.215.1		4
63.20	even	6		1134.2.t.d.1025.1		4
63.23	odd	6		1134.2.t.d.593.2		4
63.34	odd	6		1134.2.t.d.1025.2		4
63.41	even	6		1134.2.l.c.269.2		4
63.58	even	3		1134.2.t.d.593.1		4
84.11	even	6		2352.2.k.e.881.4		4
84.23	even	6		336.2.bc.e.257.1		4
84.59	odd	6		2352.2.k.e.881.2		4
84.83	odd	2		336.2.bc.e.17.2		4
105.2	even	12		1050.2.u.d.299.2		4
105.23	even	12		1050.2.u.a.299.1		4
105.44	odd	6		1050.2.s.b.551.2		4
105.62	odd	4		1050.2.u.d.899.1		4
105.83	odd	4		1050.2.u.a.899.2		4
105.104	even	2		1050.2.s.b.101.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.f.a.5.1	✓	4	21.2	odd	6
42.2.f.a.5.2	yes	4	7.2	even	3
42.2.f.a.17.1	yes	4	7.6	odd	2
42.2.f.a.17.2	yes	4	21.20	even	2
294.2.d.a.293.1		4	7.3	odd	6
294.2.d.a.293.2		4	7.4	even	3
294.2.d.a.293.3		4	21.11	odd	6
294.2.d.a.293.4		4	21.17	even	6
294.2.f.a.215.1		4	21.5	even	6	inner
294.2.f.a.215.2		4	7.5	odd	6	inner
294.2.f.a.227.1		4	1.1	even	1	trivial
294.2.f.a.227.2		4	3.2	odd	2	inner
336.2.bc.e.17.1		4	28.27	even	2
336.2.bc.e.17.2		4	84.83	odd	2
336.2.bc.e.257.1		4	84.23	even	6
336.2.bc.e.257.2		4	28.23	odd	6
1050.2.s.b.101.1		4	105.104	even	2
1050.2.s.b.101.2		4	35.34	odd	2
1050.2.s.b.551.1		4	35.9	even	6
1050.2.s.b.551.2		4	105.44	odd	6
1050.2.u.a.299.1		4	105.23	even	12
1050.2.u.a.299.2		4	35.2	odd	12
1050.2.u.a.899.1		4	35.27	even	4
1050.2.u.a.899.2		4	105.83	odd	4
1050.2.u.d.299.1		4	35.23	odd	12
1050.2.u.d.299.2		4	105.2	even	12
1050.2.u.d.899.1		4	105.62	odd	4
1050.2.u.d.899.2		4	35.13	even	4
1134.2.l.c.215.1		4	63.16	even	3
1134.2.l.c.215.2		4	63.2	odd	6
1134.2.l.c.269.1		4	63.13	odd	6
1134.2.l.c.269.2		4	63.41	even	6
1134.2.t.d.593.1		4	63.58	even	3
1134.2.t.d.593.2		4	63.23	odd	6
1134.2.t.d.1025.1		4	63.20	even	6
1134.2.t.d.1025.2		4	63.34	odd	6
2352.2.k.e.881.1		4	28.11	odd	6
2352.2.k.e.881.2		4	84.59	odd	6
2352.2.k.e.881.3		4	28.3	even	6
2352.2.k.e.881.4		4	84.11	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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} -1.73205i q^{6} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} -1.73205i q^{6} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(1.50000 + 0.866025i) q^{10} +(-2.59808 - 1.50000i) q^{11} +(0.866025 + 1.50000i) q^{12} -3.46410i q^{13} +3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.73205 - 3.00000i) q^{17} +(2.59808 + 1.50000i) q^{18} +(-3.00000 + 1.73205i) q^{19} -1.73205 q^{20} +3.00000 q^{22} +(5.19615 - 3.00000i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(1.00000 - 1.73205i) q^{25} +(1.73205 + 3.00000i) q^{26} +5.19615 q^{27} -3.00000i q^{29} +(-2.59808 + 1.50000i) q^{30} +(1.50000 + 0.866025i) q^{31} +(0.866025 + 0.500000i) q^{32} +(4.50000 - 2.59808i) q^{33} +3.46410i q^{34} -3.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(1.73205 - 3.00000i) q^{38} +(5.19615 + 3.00000i) q^{39} +(1.50000 - 0.866025i) q^{40} -6.92820 q^{41} -8.00000 q^{43} +(-2.59808 + 1.50000i) q^{44} +(-2.59808 + 4.50000i) q^{45} +(-3.00000 + 5.19615i) q^{46} +(-3.46410 - 6.00000i) q^{47} +1.73205 q^{48} +2.00000i q^{50} +(3.00000 + 5.19615i) q^{51} +(-3.00000 - 1.73205i) q^{52} +(-7.79423 - 4.50000i) q^{53} +(-4.50000 + 2.59808i) q^{54} +5.19615i q^{55} -6.00000i q^{57} +(1.50000 + 2.59808i) q^{58} +(0.866025 - 1.50000i) q^{59} +(1.50000 - 2.59808i) q^{60} -1.73205 q^{62} -1.00000 q^{64} +(-5.19615 + 3.00000i) q^{65} +(-2.59808 + 4.50000i) q^{66} +(-1.00000 + 1.73205i) q^{67} +(-1.73205 - 3.00000i) q^{68} +10.3923i q^{69} +12.0000i q^{71} +(2.59808 - 1.50000i) q^{72} +(-6.00000 - 3.46410i) q^{73} +(-1.73205 - 1.00000i) q^{74} +(1.73205 + 3.00000i) q^{75} +3.46410i q^{76} -6.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(-0.866025 + 1.50000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(6.00000 - 3.46410i) q^{82} +8.66025 q^{83} -6.00000 q^{85} +(6.92820 - 4.00000i) q^{86} +(4.50000 + 2.59808i) q^{87} +(1.50000 - 2.59808i) q^{88} +(5.19615 + 9.00000i) q^{89} -5.19615i q^{90} -6.00000i q^{92} +(-2.59808 + 1.50000i) q^{93} +(6.00000 + 3.46410i) q^{94} +(5.19615 + 3.00000i) q^{95} +(-1.50000 + 0.866025i) q^{96} -5.19615i q^{97} +9.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 6 * q^9	\( 4 q + 2 q^{4} - 6 q^{9} + 6 q^{10} + 12 q^{15} - 2 q^{16} - 12 q^{19} + 12 q^{22} - 6 q^{24} + 4 q^{25} + 6 q^{31} + 18 q^{33} - 12 q^{36} + 4 q^{37} + 6 q^{40} - 32 q^{43} - 12 q^{46} + 12 q^{51} - 12 q^{52} - 18 q^{54} + 6 q^{58} + 6 q^{60} - 4 q^{64} - 4 q^{67} - 24 q^{73} - 24 q^{78} + 2 q^{79} - 18 q^{81} + 24 q^{82} - 24 q^{85} + 18 q^{87} + 6 q^{88} + 24 q^{94} - 6 q^{96}+O(q^{100}) \) 4 * q + 2 * q^4 - 6 * q^9 + 6 * q^10 + 12 * q^15 - 2 * q^16 - 12 * q^19 + 12 * q^22 - 6 * q^24 + 4 * q^25 + 6 * q^31 + 18 * q^33 - 12 * q^36 + 4 * q^37 + 6 * q^40 - 32 * q^43 - 12 * q^46 + 12 * q^51 - 12 * q^52 - 18 * q^54 + 6 * q^58 + 6 * q^60 - 4 * q^64 - 4 * q^67 - 24 * q^73 - 24 * q^78 + 2 * q^79 - 18 * q^81 + 24 * q^82 - 24 * q^85 + 18 * q^87 + 6 * q^88 + 24 * q^94 - 6 * q^96

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