LMFDB - Embedded newform 1050.2.s.b.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(101,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("1050.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.38429221223$
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			101.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1050.101
Dual form			1050.2.s.b.551.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.73205i q^{6} +(2.50000 - 0.866025i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.73205i q^{6} +(2.50000 - 0.866025i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-2.59808 - 1.50000i) q^{11} +(0.866025 + 1.50000i) q^{12} -3.46410i q^{13} +(1.73205 - 2.00000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.73205 - 3.00000i) q^{17} +(-2.59808 - 1.50000i) q^{18} +(3.00000 - 1.73205i) q^{19} +(-0.866025 + 4.50000i) q^{21} -3.00000 q^{22} +(-5.19615 + 3.00000i) q^{23} +(1.50000 + 0.866025i) q^{24} +(-1.73205 - 3.00000i) q^{26} +5.19615 q^{27} +(0.500000 - 2.59808i) q^{28} -3.00000i q^{29} +(-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} +6.92820 q^{41} +(1.50000 + 4.33013i) q^{42} +8.00000 q^{43} +(-2.59808 + 1.50000i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(-3.46410 - 6.00000i) q^{47} +1.73205 q^{48} +(5.50000 - 4.33013i) q^{49} +(3.00000 + 5.19615i) q^{51} +(-3.00000 - 1.73205i) q^{52} +(7.79423 + 4.50000i) q^{53} +(4.50000 - 2.59808i) q^{54} +(-0.866025 - 2.50000i) q^{56} +6.00000i q^{57} +(-1.50000 - 2.59808i) q^{58} +(-0.866025 + 1.50000i) q^{59} -1.73205 q^{62} +(-6.00000 - 5.19615i) q^{63} -1.00000 q^{64} +(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} -3.46410i q^{76} +(-7.79423 - 1.50000i) q^{77} +6.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(6.00000 - 3.46410i) q^{82} +8.66025 q^{83} +(3.46410 + 3.00000i) q^{84} +(6.92820 - 4.00000i) q^{86} +(4.50000 + 2.59808i) q^{87} +(-1.50000 + 2.59808i) q^{88} +(-5.19615 - 9.00000i) q^{89} +(-3.00000 - 8.66025i) q^{91} +6.00000i q^{92} +(2.59808 - 1.50000i) q^{93} +(-6.00000 - 3.46410i) q^{94} +(1.50000 - 0.866025i) q^{96} -5.19615i q^{97} +(2.59808 - 6.50000i) q^{98} +9.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 10 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 10 * q^7 - 6 * q^9	$ 4 q + 2 q^{4} + 10 q^{7} - 6 q^{9} - 2 q^{16} + 12 q^{19} - 12 q^{22} + 6 q^{24} + 2 q^{28} - 6 q^{31} + 18 q^{33} - 12 q^{36} - 4 q^{37} + 6 q^{42} + 32 q^{43} - 12 q^{46} + 22 q^{49} + 12 q^{51} - 12 q^{52} + 18 q^{54} - 6 q^{58} - 24 q^{63} - 4 q^{64} + 4 q^{67} - 24 q^{73} + 24 q^{78} + 2 q^{79} - 18 q^{81} + 24 q^{82} + 18 q^{87} - 6 q^{88} - 12 q^{91} - 24 q^{94} + 6 q^{96}+O(q^{100}) $ 4 * q + 2 * q^4 + 10 * q^7 - 6 * q^9 - 2 * q^16 + 12 * q^19 - 12 * q^22 + 6 * q^24 + 2 * q^28 - 6 * q^31 + 18 * q^33 - 12 * q^36 - 4 * q^37 + 6 * q^42 + 32 * q^43 - 12 * q^46 + 22 * q^49 + 12 * q^51 - 12 * q^52 + 18 * q^54 - 6 * q^58 - 24 * q^63 - 4 * q^64 + 4 * q^67 - 24 * q^73 + 24 * q^78 + 2 * q^79 - 18 * q^81 + 24 * q^82 + 18 * q^87 - 6 * q^88 - 12 * q^91 - 24 * q^94 + 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	−	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			0
$5$		0			0
$6$			1.73205i			0.707107i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$		−	1.00000i		−	0.353553i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$		0			0
$11$	−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	$-0.159503\pi$
$14$	1.73205	−	2.00000i	0.462910	−	0.534522i
$15$		0			0
$16$	−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	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.00000	−	1.73205i	0.688247	−	0.397360i	0.802955	+	0.596040i	$0.203260\pi$
$20$		0			0
$21$	−0.866025	+	4.50000i	−0.188982	+	0.981981i
$22$	−3.00000			−0.639602
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.931831	−	0.362892i	$-0.881789\pi$
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.151642	+	0.988436i	$0.548456\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$		0			0
$26$	−1.73205	−	3.00000i	−0.339683	−	0.588348i
$27$	5.19615			1.00000
$28$	0.500000	−	2.59808i	0.0944911	−	0.490990i
$29$		−	3.00000i		−	0.557086i	−0.960424	−	0.278543i	$-0.910149\pi$
$29$		−	3.00000i		−	0.557086i	0.960424	−	0.278543i	$-0.0898515\pi$
$30$		0			0
$31$	−1.50000	−	0.866025i	−0.269408	−	0.155543i	0.359211	−	0.933257i	$-0.383046\pi$
$31$	−1.50000	−	0.866025i	−0.269408	−	0.155543i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−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	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	1.73205	−	3.00000i	0.280976	−	0.486664i
$39$	5.19615	+	3.00000i	0.832050	+	0.480384i
$40$		0			0
$41$	6.92820			1.08200			0.541002	−	0.841021i	$-0.318045\pi$
$41$	6.92820			1.08200			0.541002	+	0.841021i	$0.318045\pi$
$42$	1.50000	+	4.33013i	0.231455	+	0.668153i
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$	−2.59808	+	1.50000i	−0.391675	+	0.226134i
$45$		0			0
$46$	−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
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$		0			0
$51$	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	0.928351	−	0.371706i	$-0.121227\pi$
$53$	7.79423	+	4.50000i	1.07062	+	0.618123i	0.142269	+	0.989828i	$0.454560\pi$
$54$	4.50000	−	2.59808i	0.612372	−	0.353553i
$55$		0			0
$56$	−0.866025	−	2.50000i	−0.115728	−	0.334077i
$57$			6.00000i			0.794719i
$58$	−1.50000	−	2.59808i	−0.196960	−	0.341144i
$59$	−0.866025	+	1.50000i	−0.112747	+	0.195283i	−0.916877	−	0.399170i	$-0.869298\pi$
$59$	−0.866025	+	1.50000i	−0.112747	+	0.195283i	0.804130	+	0.594454i	$0.202632\pi$
$60$		0			0
$61$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$61$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$62$	−1.73205			−0.219971
$63$	−6.00000	−	5.19615i	−0.755929	−	0.654654i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	2.59808	−	4.50000i	0.319801	−	0.553912i
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$	−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
$75$		0			0
$76$		−	3.46410i		−	0.397360i
$77$	−7.79423	−	1.50000i	−0.888235	−	0.170941i
$78$	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			0
$81$	−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	$0.342342\pi$
$84$	3.46410	+	3.00000i	0.377964	+	0.327327i
$85$		0			0
$86$	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	$-0.980993\pi$
$89$	−5.19615	−	9.00000i	−0.550791	−	0.953998i	0.447427	−	0.894321i	$-0.352341\pi$
$90$		0			0
$91$	−3.00000	−	8.66025i	−0.314485	−	0.907841i
$92$			6.00000i			0.625543i
$93$	2.59808	−	1.50000i	0.269408	−	0.155543i
$94$	−6.00000	−	3.46410i	−0.618853	−	0.357295i
$95$		0			0
$96$	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	$-0.0849741\pi$
$98$	2.59808	−	6.50000i	0.262445	−	0.656599i
$99$			9.00000i			0.904534i
$100$		0			0
$101$		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	−0.620298	−	0.784366i	$-0.712988\pi$
$107$	−2.59808	+	1.50000i	−0.251166	+	0.145010i	0.369132	+	0.929377i	$0.379655\pi$
$108$	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	$0.136131\pi$
$110$		0			0
$111$	3.46410			0.328798
$112$	−2.00000	−	1.73205i	−0.188982	−	0.163663i
$113$			12.0000i			1.12887i	0.825479	+	0.564433i	$0.190905\pi$
$113$			12.0000i			1.12887i	−0.825479	+	0.564433i	$0.809095\pi$
$114$	3.00000	+	5.19615i	0.280976	+	0.486664i
$115$		0			0
$116$	−2.59808	−	1.50000i	−0.241225	−	0.139272i
$117$	−9.00000	+	5.19615i	−0.832050	+	0.480384i
$118$			1.73205i			0.159448i
$119$	1.73205	−	9.00000i	0.158777	−	0.825029i
$120$		0			0
$121$	−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
$125$		0			0
$126$	−7.79423	−	1.50000i	−0.694365	−	0.133631i
$127$	−11.0000			−0.976092			−0.488046	−	0.872818i	$-0.662290\pi$
$127$	−11.0000			−0.976092			−0.488046	+	0.872818i	$0.662290\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−6.92820	+	12.0000i	−0.609994	+	1.05654i
$130$		0			0
$131$	−2.59808	−	4.50000i	−0.226995	−	0.393167i	0.729921	−	0.683531i	$-0.239557\pi$
$131$	−2.59808	−	4.50000i	−0.226995	−	0.393167i	−0.956916	+	0.290365i	$0.906223\pi$
$132$		−	5.19615i		−	0.452267i
$133$	6.00000	−	6.92820i	0.520266	−	0.600751i
$134$		−	2.00000i		−	0.172774i
$135$		0			0
$136$	−3.00000	−	1.73205i	−0.257248	−	0.148522i
$137$	−15.5885	−	9.00000i	−1.33181	−	0.768922i	−0.346235	−	0.938148i	$-0.612540\pi$
$137$	−15.5885	−	9.00000i	−1.33181	−	0.768922i	−0.985577	+	0.169226i	$0.945873\pi$
$138$	−5.19615	−	9.00000i	−0.442326	−	0.766131i
$139$			17.3205i			1.46911i	0.678551	+	0.734553i	$0.262608\pi$
$139$			17.3205i			1.46911i	−0.678551	+	0.734553i	$0.737392\pi$
$140$		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
$145$		0			0
$146$	−6.92820			−0.573382
$147$	1.73205	+	12.0000i	0.142857	+	0.989743i
$148$	−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	$0.597237\pi$
$150$		0			0
$151$	−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
$154$	−7.50000	+	2.59808i	−0.604367	+	0.209359i
$155$		0			0
$156$	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
$160$		0			0
$161$	−10.3923	+	12.0000i	−0.819028	+	0.945732i
$162$			9.00000i			0.707107i
$163$	7.00000	+	12.1244i	0.548282	+	0.949653i	0.998392	+	0.0566798i	$0.0180514\pi$
$163$	7.00000	+	12.1244i	0.548282	+	0.949653i	−0.450110	+	0.892973i	$0.648615\pi$
$164$	3.46410	−	6.00000i	0.270501	−	0.468521i
$165$		0			0
$166$	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	$0.266230\pi$
$168$	4.50000	+	0.866025i	0.347183	+	0.0668153i
$169$	1.00000			0.0769231
$170$		0			0
$171$	−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	$0.518639\pi$
$180$		0			0
$181$			6.92820i			0.514969i	0.966282	+	0.257485i	$0.0828937\pi$
$181$			6.92820i			0.514969i	−0.966282	+	0.257485i	$0.917106\pi$
$182$	−6.92820	−	6.00000i	−0.513553	−	0.444750i
$183$		0			0
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$		0			0
$186$	1.50000	−	2.59808i	0.109985	−	0.190500i
$187$	−9.00000	+	5.19615i	−0.658145	+	0.379980i
$188$	−6.92820			−0.505291
$189$	12.9904	−	4.50000i	0.944911	−	0.327327i
$190$		0			0
$191$		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	$0.477068\pi$
$193$	−11.5000	+	19.9186i	−0.827788	+	1.43377i	−0.899770	+	0.436365i	$0.856266\pi$
$194$	−2.59808	−	4.50000i	−0.186531	−	0.323081i
$195$		0			0
$196$	−1.00000	−	6.92820i	−0.0714286	−	0.494872i
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$	4.50000	+	7.79423i	0.319801	+	0.553912i
$199$	9.00000	+	5.19615i	0.637993	+	0.368345i	0.783841	−	0.620962i	$-0.213258\pi$
$199$	9.00000	+	5.19615i	0.637993	+	0.368345i	−0.145848	+	0.989307i	$0.546591\pi$
$200$		0			0
$201$	1.73205	+	3.00000i	0.122169	+	0.211604i
$202$		0			0
$203$	−2.59808	−	7.50000i	−0.182349	−	0.526397i
$204$	6.00000			0.420084
$205$		0			0
$206$	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
$215$		0			0
$216$		−	5.19615i		−	0.353553i
$217$	−4.50000	−	0.866025i	−0.305480	−	0.0587896i
$218$		−	2.00000i		−	0.135457i
$219$	10.3923	−	6.00000i	0.702247	−	0.405442i
$220$		0			0
$221$	−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	$0.664183\pi$
$224$	−2.59808	−	0.500000i	−0.173591	−	0.0334077i
$225$		0			0
$226$	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	−0.841011	−	0.541017i	$-0.818039\pi$
$229$	−12.0000	+	6.92820i	−0.792982	+	0.457829i	0.0480291	+	0.998846i	$0.484706\pi$
$230$		0			0
$231$	9.00000	−	10.3923i	0.592157	−	0.683763i
$232$	−3.00000			−0.196960
$233$	−15.5885	+	9.00000i	−1.02123	+	0.589610i	−0.914461	−	0.404674i	$-0.867385\pi$
$233$	−15.5885	+	9.00000i	−1.02123	+	0.589610i	−0.106773	+	0.994283i	$0.534052\pi$
$234$	−5.19615	+	9.00000i	−0.339683	+	0.588348i
$235$		0			0
$236$	0.866025	+	1.50000i	0.0563735	+	0.0976417i
$237$	−1.73205			−0.112509
$238$	−3.00000	−	8.66025i	−0.194461	−	0.561361i
$239$		−	6.00000i		−	0.388108i	−0.980991	−	0.194054i	$-0.937836\pi$
$239$		−	6.00000i		−	0.388108i	0.980991	−	0.194054i	$-0.0621637\pi$
$240$		0			0
$241$	−22.5000	−	12.9904i	−1.44935	−	0.836784i	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−22.5000	−	12.9904i	−1.44935	−	0.836784i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	−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
$250$		0			0
$251$	19.0526			1.20259			0.601293	−	0.799028i	$-0.294652\pi$
$251$	19.0526			1.20259			0.601293	+	0.799028i	$0.294652\pi$
$252$	−7.50000	+	2.59808i	−0.472456	+	0.163663i
$253$	18.0000			1.13165
$254$	−9.52628	+	5.50000i	−0.597732	+	0.345101i
$255$		0			0
$256$	−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
$259$	−4.00000	−	3.46410i	−0.248548	−	0.215249i
$260$		0			0
$261$	−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
$265$		0			0
$266$	1.73205	−	9.00000i	0.106199	−	0.551825i
$267$	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	$-0.478612\pi$
$269$	14.7224	−	25.5000i	0.897643	−	1.55476i	0.830500	−	0.557019i	$-0.188055\pi$
$270$		0			0
$271$	4.50000	−	2.59808i	0.273356	−	0.157822i	−0.357056	−	0.934083i	$-0.616219\pi$
$271$	4.50000	−	2.59808i	0.273356	−	0.157822i	0.630412	+	0.776261i	$0.282886\pi$
$272$	−3.46410			−0.210042
$273$	15.5885	+	3.00000i	0.943456	+	0.181568i
$274$	−18.0000			−1.08742
$275$		0			0
$276$	−9.00000	−	5.19615i	−0.541736	−	0.312772i
$277$	4.00000	−	6.92820i	0.240337	−	0.416275i	−0.720473	−	0.693482i	$-0.756075\pi$
$277$	4.00000	−	6.92820i	0.240337	−	0.416275i	0.960810	+	0.277207i	$0.0894088\pi$
$278$	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
$285$		0			0
$286$			10.3923i			0.614510i
$287$	17.3205	−	6.00000i	1.02240	−	0.354169i
$288$			3.00000i			0.176777i
$289$	2.50000	+	4.33013i	0.147059	+	0.254713i
$290$		0			0
$291$	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	$0.312132\pi$
$294$	7.50000	+	9.52628i	0.437409	+	0.555584i
$295$		0			0
$296$	−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
$300$		0			0
$301$	20.0000	−	6.92820i	1.15278	−	0.399335i
$302$			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	$0.756741\pi$
$308$	−5.19615	+	6.00000i	−0.296078	+	0.341882i
$309$			6.00000i			0.341328i
$310$		0			0
$311$	−6.92820	+	12.0000i	−0.392862	+	0.680458i	−0.992826	−	0.119570i	$-0.961848\pi$
$311$	−6.92820	+	12.0000i	−0.392862	+	0.680458i	0.599963	+	0.800027i	$0.295182\pi$
$312$	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	−0.818280	−	0.574819i	$-0.805072\pi$
$317$	−12.9904	+	7.50000i	−0.729612	+	0.421242i	0.0886679	+	0.996061i	$0.471739\pi$
$318$	−7.79423	+	13.5000i	−0.437079	+	0.757042i
$319$	−4.50000	+	7.79423i	−0.251952	+	0.436393i
$320$		0			0
$321$		−	5.19615i		−	0.290021i
$322$	−3.00000	+	15.5885i	−0.167183	+	0.868711i
$323$		−	12.0000i		−	0.667698i
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$		0			0
$326$	12.1244	+	7.00000i	0.671506	+	0.387694i
$327$	1.73205	+	3.00000i	0.0957826	+	0.165900i
$328$		−	6.92820i		−	0.382546i
$329$	−13.8564	−	12.0000i	−0.763928	−	0.661581i
$330$		0			0
$331$	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
$335$		0			0
$336$	4.33013	−	1.50000i	0.236228	−	0.0818317i
$337$	−13.0000			−0.708155			−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000			−0.708155			−0.354078	+	0.935216i	$0.615205\pi$
$338$	0.866025	−	0.500000i	0.0471056	−	0.0271964i
$339$	−18.0000	−	10.3923i	−0.977626	−	0.564433i
$340$		0			0
$341$	2.59808	+	4.50000i	0.140694	+	0.243689i
$342$	−10.3923			−0.561951
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$		−	8.00000i		−	0.431331i
$345$		0			0
$346$		0			0
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	0.752297	−	0.658824i	$-0.228946\pi$
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	−0.194409	+	0.980921i	$0.562279\pi$
$348$	4.50000	−	2.59808i	0.241225	−	0.139272i
$349$			10.3923i			0.556287i	0.960539	+	0.278144i	$0.0897191\pi$
$349$			10.3923i			0.556287i	−0.960539	+	0.278144i	$0.910281\pi$
$350$		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
$355$		0			0
$356$	−10.3923			−0.550791
$357$	12.0000	+	10.3923i	0.635107	+	0.550019i
$358$	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	$0.383946\pi$
$360$		0			0
$361$	−3.50000	+	6.06218i	−0.184211	+	0.319062i
$362$	3.46410	+	6.00000i	0.182069	+	0.315353i
$363$	3.46410			0.181818
$364$	−9.00000	−	1.73205i	−0.471728	−	0.0907841i
$365$		0			0
$366$		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
$370$		0			0
$371$	23.3827	+	4.50000i	1.21397	+	0.233628i
$372$		−	3.00000i		−	0.155543i
$373$	16.0000	+	27.7128i	0.828449	+	1.43492i	0.899255	+	0.437425i	$0.144109\pi$
$373$	16.0000	+	27.7128i	0.828449	+	1.43492i	−0.0708063	+	0.997490i	$0.522557\pi$
$374$	−5.19615	+	9.00000i	−0.268687	+	0.465379i
$375$		0			0
$376$	−6.00000	+	3.46410i	−0.309426	+	0.178647i
$377$	−10.3923			−0.535231
$378$	9.00000	−	10.3923i	0.462910	−	0.534522i
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$		0			0
$381$	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	$0.817499\pi$
$390$		0			0
$391$			20.7846i			1.05112i
$392$	−4.33013	−	5.50000i	−0.218704	−	0.277792i
$393$	9.00000			0.453990
$394$	−9.00000	−	15.5885i	−0.453413	−	0.785335i
$395$		0			0
$396$	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
$399$	5.19615	+	15.0000i	0.260133	+	0.750939i
$400$		0			0
$401$	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
$405$		0			0
$406$	−6.00000	−	5.19615i	−0.297775	−	0.257881i
$407$			6.00000i			0.297409i
$408$	5.19615	−	3.00000i	0.257248	−	0.148522i
$409$	7.50000	+	4.33013i	0.370851	+	0.214111i	0.673830	−	0.738886i	$-0.264648\pi$
$409$	7.50000	+	4.33013i	0.370851	+	0.214111i	−0.302979	+	0.952997i	$0.597981\pi$
$410$		0			0
$411$	27.0000	−	15.5885i	1.33181	−	0.768922i
$412$		−	3.46410i		−	0.170664i
$413$	−0.866025	+	4.50000i	−0.0426143	+	0.221431i
$414$	18.0000			0.884652
$415$		0			0
$416$	−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	$-0.298215\pi$
$419$	24.2487			1.18463			0.592314	+	0.805708i	$0.298215\pi$
$420$		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
$425$		0			0
$426$	−20.7846			−1.00702
$427$		0			0
$428$			3.00000i			0.145010i
$429$	−9.00000	−	15.5885i	−0.434524	−	0.752618i
$430$		0			0
$431$	−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	$-0.313017\pi$
$434$	−4.33013	+	1.50000i	−0.207853	+	0.0720023i
$435$		0			0
$436$	−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	$-0.332075\pi$
$439$	31.5000	−	18.1865i	1.50341	−	0.867996i	0.999992	−	0.00395451i	$-0.00125876\pi$
$440$		0			0
$441$	−19.5000	−	7.79423i	−0.928571	−	0.371154i
$442$	−12.0000			−0.570782
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	−0.303281	−	0.952901i	$-0.598082\pi$
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	0.673596	+	0.739100i	$0.264749\pi$
$444$	1.73205	−	3.00000i	0.0821995	−	0.142374i
$445$		0			0
$446$	12.9904	+	22.5000i	0.615112	+	1.06541i
$447$		−	31.1769i		−	1.47462i
$448$	−2.50000	+	0.866025i	−0.118114	+	0.0409159i
$449$			30.0000i			1.41579i	0.706319	+	0.707894i	$0.250354\pi$
$449$			30.0000i			1.41579i	−0.706319	+	0.707894i	$0.749646\pi$
$450$		0			0
$451$	−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	0.801611	−	0.597847i	$-0.203977\pi$
$457$	−2.50000	−	4.33013i	−0.116945	−	0.202555i	−0.918556	+	0.395292i	$0.870643\pi$
$458$	−6.92820	+	12.0000i	−0.323734	+	0.560723i
$459$	9.00000	−	15.5885i	0.420084	−	0.727607i
$460$		0			0
$461$	−13.8564			−0.645357			−0.322679	−	0.946509i	$-0.604583\pi$
$461$	−13.8564			−0.645357			−0.322679	+	0.946509i	$0.604583\pi$
$462$	2.59808	−	13.5000i	0.120873	−	0.628077i
$463$	4.00000			0.185896			0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000			0.185896			0.0929479	+	0.995671i	$0.470371\pi$
$464$	−2.59808	+	1.50000i	−0.120613	+	0.0696358i
$465$		0			0
$466$	−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
$469$	1.00000	−	5.19615i	0.0461757	−	0.239936i
$470$		0			0
$471$	−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
$475$		0			0
$476$	−6.92820	−	6.00000i	−0.317554	−	0.275010i
$477$		−	27.0000i		−	1.23625i
$478$	−3.00000	−	5.19615i	−0.137217	−	0.237666i
$479$	−3.46410	+	6.00000i	−0.158279	+	0.274147i	−0.934248	−	0.356624i	$-0.883928\pi$
$479$	−3.46410	+	6.00000i	−0.158279	+	0.274147i	0.775969	+	0.630771i	$0.217261\pi$
$480$		0			0
$481$	−6.00000	+	3.46410i	−0.273576	+	0.157949i
$482$	−25.9808			−1.18339
$483$	−9.00000	−	25.9808i	−0.409514	−	1.18217i
$484$	−2.00000			−0.0909091
$485$		0			0
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	0.500000	−	0.866025i	0.0226572	−	0.0392434i	−0.854475	−	0.519493i	$-0.826121\pi$
$487$	0.500000	−	0.866025i	0.0226572	−	0.0392434i	0.877132	+	0.480250i	$0.159454\pi$
$488$		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
$495$		0			0
$496$			1.73205i			0.0777714i
$497$	10.3923	+	30.0000i	0.466159	+	1.34568i
$498$			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	$0.997224\pi$
$500$		0			0
$501$	−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	$0.823103\pi$
$504$	−5.19615	+	6.00000i	−0.231455	+	0.267261i
$505$		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	0.996159	−	0.0875661i	$-0.0279089\pi$
$509$	9.52628	+	16.5000i	0.422245	+	0.731350i	−0.573914	+	0.818916i	$0.694576\pi$
$510$		0			0
$511$	−18.0000	−	3.46410i	−0.796273	−	0.153243i
$512$			1.00000i			0.0441942i
$513$	15.5885	−	9.00000i	0.688247	−	0.397360i
$514$	−9.00000	−	5.19615i	−0.396973	−	0.229192i
$515$		0			0
$516$	6.92820	+	12.0000i	0.304997	+	0.528271i
$517$			20.7846i			0.914106i
$518$	−5.19615	−	1.00000i	−0.228306	−	0.0439375i
$519$		0			0
$520$		0			0
$521$	−13.8564	+	24.0000i	−0.607060	+	1.05146i	0.384662	+	0.923057i	$0.374318\pi$
$521$	−13.8564	+	24.0000i	−0.607060	+	1.05146i	−0.991722	+	0.128402i	$0.959015\pi$
$522$	−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
$530$		0			0
$531$	5.19615			0.225494
$532$	−3.00000	−	8.66025i	−0.130066	−	0.375470i
$533$		−	24.0000i		−	1.03956i
$534$	15.5885	−	9.00000i	0.674579	−	0.389468i
$535$		0			0
$536$	−1.73205	−	1.00000i	−0.0748132	−	0.0431934i
$537$	−18.0000	+	10.3923i	−0.776757	+	0.448461i
$538$		−	29.4449i		−	1.26946i
$539$	−20.7846	+	3.00000i	−0.895257	+	0.129219i
$540$		0			0
$541$	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
$545$		0			0
$546$	15.0000	−	5.19615i	0.641941	−	0.222375i
$547$	−2.00000			−0.0855138			−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000			−0.0855138			−0.0427569	+	0.999086i	$0.513614\pi$
$548$	−15.5885	+	9.00000i	−0.665906	+	0.384461i
$549$		0			0
$550$		0			0
$551$	−5.19615	−	9.00000i	−0.221364	−	0.383413i
$552$	−10.3923			−0.442326
$553$	2.00000	+	1.73205i	0.0850487	+	0.0736543i
$554$		−	8.00000i		−	0.339887i
$555$		0			0
$556$	15.0000	+	8.66025i	0.636142	+	0.367277i
$557$	2.59808	+	1.50000i	0.110084	+	0.0635570i	0.554031	−	0.832496i	$-0.313089\pi$
$557$	2.59808	+	1.50000i	0.110084	+	0.0635570i	−0.443947	+	0.896053i	$0.646422\pi$
$558$	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
$565$		0			0
$566$	−27.7128			−1.16486
$567$	−4.50000	+	23.3827i	−0.188982	+	0.981981i
$568$	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	$0.293194\pi$
$570$		0			0
$571$	−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
$574$	12.0000	−	13.8564i	0.500870	−	0.578355i
$575$		0			0
$576$	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
$580$		0			0
$581$	21.6506	−	7.50000i	0.898220	−	0.311152i
$582$	9.00000			0.373062
$583$	−13.5000	−	23.3827i	−0.559113	−	0.968412i
$584$	−3.46410	+	6.00000i	−0.143346	+	0.248282i
$585$		0			0
$586$	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	$0.395745\pi$
$588$	11.2583	+	4.50000i	0.464286	+	0.185577i
$589$	−6.00000			−0.247226
$590$		0			0
$591$	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	$0.456676\pi$
$600$		0			0
$601$		−	29.4449i		−	1.20108i	−0.799594	−	0.600541i	$-0.794952\pi$
$601$		−	29.4449i		−	1.20108i	0.799594	−	0.600541i	$-0.205048\pi$
$602$	13.8564	−	16.0000i	0.564745	−	0.652111i
$603$	−6.00000			−0.244339
$604$	3.50000	+	6.06218i	0.142413	+	0.246667i
$605$		0			0
$606$		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
$609$	13.5000	+	2.59808i	0.547048	+	0.105279i
$610$		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	−0.845124	−	0.534570i	$-0.820473\pi$
$613$	1.00000	−	1.73205i	0.0403896	−	0.0699569i	0.885514	+	0.464614i	$0.153807\pi$
$614$	12.1244	+	21.0000i	0.489299	+	0.847491i
$615$		0			0
$616$	−1.50000	+	7.79423i	−0.0604367	+	0.314038i
$617$		−	12.0000i		−	0.483102i	−0.970388	−	0.241551i	$-0.922344\pi$
$617$		−	12.0000i		−	0.483102i	0.970388	−	0.241551i	$-0.0776561\pi$
$618$	3.00000	+	5.19615i	0.120678	+	0.209020i
$619$	6.00000	+	3.46410i	0.241160	+	0.139234i	0.615710	−	0.787973i	$-0.288869\pi$
$619$	6.00000	+	3.46410i	0.241160	+	0.139234i	−0.374550	+	0.927207i	$0.622203\pi$
$620$		0			0
$621$	−27.0000	+	15.5885i	−1.08347	+	0.625543i
$622$			13.8564i			0.555591i
$623$	−20.7846	−	18.0000i	−0.832718	−	0.721155i
$624$		−	6.00000i		−	0.240192i
$625$		0			0
$626$	−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
$635$		0			0
$636$			15.5885i			0.618123i
$637$	−15.0000	−	19.0526i	−0.594322	−	0.754890i
$638$			9.00000i			0.356313i
$639$	31.1769	−	18.0000i	1.23334	−	0.712069i
$640$		0			0
$641$	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	$0.889056\pi$
$644$	5.19615	+	15.0000i	0.204757	+	0.591083i
$645$		0			0
$646$	−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
$650$		0			0
$651$	5.19615	−	6.00000i	0.203653	−	0.235159i
$652$	14.0000			0.548282
$653$	−2.59808	+	1.50000i	−0.101671	+	0.0586995i	−0.549973	−	0.835182i	$-0.685362\pi$
$653$	−2.59808	+	1.50000i	−0.101671	+	0.0586995i	0.448303	+	0.893882i	$0.352029\pi$
$654$	3.00000	+	1.73205i	0.117309	+	0.0677285i
$655$		0			0
$656$	−3.46410	−	6.00000i	−0.135250	−	0.234261i
$657$			20.7846i			0.810885i
$658$	−18.0000	−	3.46410i	−0.701713	−	0.135045i
$659$		−	12.0000i		−	0.467454i	−0.972302	−	0.233727i	$-0.924908\pi$
$659$		−	12.0000i		−	0.467454i	0.972302	−	0.233727i	$-0.0750921\pi$
$660$		0			0
$661$	−6.00000	−	3.46410i	−0.233373	−	0.134738i	0.378754	−	0.925497i	$-0.376353\pi$
$661$	−6.00000	−	3.46410i	−0.233373	−	0.134738i	−0.612127	+	0.790759i	$0.709686\pi$
$662$	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
$670$		0			0
$671$		0			0
$672$	3.00000	−	3.46410i	0.115728	−	0.133631i
$673$	41.0000			1.58043			0.790217	−	0.612827i	$-0.209968\pi$
$673$	41.0000			1.58043			0.790217	+	0.612827i	$0.209968\pi$
$674$	−11.2583	+	6.50000i	−0.433655	+	0.250371i
$675$		0			0
$676$	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
$679$	−4.50000	−	12.9904i	−0.172694	−	0.498525i
$680$		0			0
$681$	−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	0.805814	−	0.592168i	$-0.201728\pi$
$683$	18.1865	+	10.5000i	0.695888	+	0.401771i	−0.109926	+	0.993940i	$0.535061\pi$
$684$	−9.00000	+	5.19615i	−0.344124	+	0.198680i
$685$		0			0
$686$	0.866025	−	18.5000i	0.0330650	−	0.706333i
$687$		−	24.0000i		−	0.915657i
$688$	−4.00000	−	6.92820i	−0.152499	−	0.264135i
$689$	15.5885	−	27.0000i	0.593873	−	1.02862i
$690$		0			0
$691$	−6.00000	+	3.46410i	−0.228251	+	0.131781i	−0.609765	−	0.792582i	$-0.708736\pi$
$691$	−6.00000	+	3.46410i	−0.228251	+	0.131781i	0.381514	+	0.924363i	$0.375403\pi$
$692$		0			0
$693$	7.79423	+	22.5000i	0.296078	+	0.854704i
$694$	12.0000			0.455514
$695$		0			0
$696$	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
$705$		0			0
$706$		−	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	$0.580415\pi$
$710$		0			0
$711$	1.50000	−	2.59808i	0.0562544	−	0.0974355i
$712$	−9.00000	+	5.19615i	−0.337289	+	0.194734i
$713$	10.3923			0.389195
$714$	15.5885	+	3.00000i	0.583383	+	0.112272i
$715$		0			0
$716$	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	$0.150620\pi$
$719$	22.5167	+	39.0000i	0.839730	+	1.45445i	−0.0503909	+	0.998730i	$0.516047\pi$
$720$		0			0
$721$	6.00000	−	6.92820i	0.223452	−	0.258020i
$722$			7.00000i			0.260513i
$723$	38.9711	−	22.5000i	1.44935	−	0.836784i
$724$	6.00000	+	3.46410i	0.222988	+	0.128742i
$725$		0			0
$726$	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	$-0.183860\pi$
$728$	−8.66025	+	3.00000i	−0.320970	+	0.111187i
$729$	27.0000			1.00000
$730$		0			0
$731$	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	$0.107785\pi$
$740$		0			0
$741$	20.7846			0.763542
$742$	22.5000	−	7.79423i	0.826001	−	0.286135i
$743$		−	18.0000i		−	0.660356i	−0.943919	−	0.330178i	$-0.892891\pi$
$743$		−	18.0000i		−	0.660356i	0.943919	−	0.330178i	$-0.107109\pi$
$744$	−1.50000	−	2.59808i	−0.0549927	−	0.0952501i
$745$		0			0
$746$	27.7128	+	16.0000i	1.01464	+	0.585802i
$747$	−12.9904	−	22.5000i	−0.475293	−	0.823232i
$748$			10.3923i			0.379980i
$749$	−5.19615	+	6.00000i	−0.189863	+	0.219235i
$750$		0			0
$751$	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
$755$		0			0
$756$	2.59808	−	13.5000i	0.0944911	−	0.490990i
$757$	−4.00000			−0.145382			−0.0726912	−	0.997354i	$-0.523159\pi$
$757$	−4.00000			−0.145382			−0.0726912	+	0.997354i	$0.523159\pi$
$758$	13.8564	−	8.00000i	0.503287	−	0.290573i
$759$	−15.5885	+	27.0000i	−0.565825	+	0.980038i
$760$		0			0
$761$	−8.66025	−	15.0000i	−0.313934	−	0.543750i	0.665276	−	0.746597i	$-0.268314\pi$
$761$	−8.66025	−	15.0000i	−0.313934	−	0.543750i	−0.979210	+	0.202848i	$0.934980\pi$
$762$		−	19.0526i		−	0.690201i
$763$	1.00000	−	5.19615i	0.0362024	−	0.188113i
$764$		0			0
$765$		0			0
$766$	−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	$0.111621\pi$
$769$			19.0526i			0.687053i	−0.939143	+	0.343526i	$0.888379\pi$
$770$		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
$775$		0			0
$776$	−5.19615			−0.186531
$777$	8.66025	−	3.00000i	0.310685	−	0.107624i
$778$	−18.0000			−0.645331
$779$	20.7846	−	12.0000i	0.744686	−	0.429945i
$780$		0			0
$781$	18.0000	−	31.1769i	0.644091	−	1.11560i
$782$	10.3923	+	18.0000i	0.371628	+	0.643679i
$783$		−	15.5885i		−	0.557086i
$784$	−6.50000	−	2.59808i	−0.232143	−	0.0927884i
$785$		0			0
$786$	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
$790$		0			0
$791$	10.3923	+	30.0000i	0.369508	+	1.06668i
$792$	9.00000			0.319801
$793$		0			0
$794$	13.8564	−	24.0000i	0.491745	−	0.851728i
$795$		0			0
$796$	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	$0.347798\pi$
$798$	12.0000	+	10.3923i	0.424795	+	0.367884i
$799$	−24.0000			−0.849059
$800$		0			0
$801$	−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	$0.666667\pi$
$810$		0			0
$811$			31.1769i			1.09477i	0.836881	+	0.547385i	$0.184377\pi$
$811$			31.1769i			1.09477i	−0.836881	+	0.547385i	$0.815623\pi$
$812$	−7.79423	−	1.50000i	−0.273524	−	0.0526397i
$813$			9.00000i			0.315644i
$814$	3.00000	+	5.19615i	0.105150	+	0.182125i
$815$		0			0
$816$	3.00000	−	5.19615i	0.105021	−	0.181902i
$817$	24.0000	−	13.8564i	0.839654	−	0.484774i
$818$	8.66025			0.302799
$819$	−18.0000	+	20.7846i	−0.628971	+	0.726273i
$820$		0			0
$821$	−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	−0.787850	−	0.615867i	$-0.788806\pi$
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	0.927281	+	0.374365i	$0.122139\pi$
$824$	−1.73205	−	3.00000i	−0.0603388	−	0.104510i
$825$		0			0
$826$	1.50000	+	4.33013i	0.0521917	+	0.150664i
$827$		−	9.00000i		−	0.312961i	−0.987681	−	0.156480i	$-0.949985\pi$
$827$		−	9.00000i		−	0.312961i	0.987681	−	0.156480i	$-0.0500148\pi$
$828$	15.5885	−	9.00000i	0.541736	−	0.312772i
$829$	−15.0000	−	8.66025i	−0.520972	−	0.300783i	0.216361	−	0.976314i	$-0.430581\pi$
$829$	−15.0000	−	8.66025i	−0.520972	−	0.300783i	−0.737332	+	0.675530i	$0.763915\pi$
$830$		0			0
$831$	6.92820	+	12.0000i	0.240337	+	0.416275i
$832$			3.46410i			0.120096i
$833$	−3.46410	−	24.0000i	−0.120024	−	0.831551i
$834$	−30.0000			−1.03882
$835$		0			0
$836$	−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	$-0.480955\pi$
$839$	3.46410			0.119594			0.0597970	+	0.998211i	$0.480955\pi$
$840$		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			0
$846$			20.7846i			0.714590i
$847$	−4.00000	−	3.46410i	−0.137442	−	0.119028i
$848$		−	9.00000i		−	0.309061i
$849$	41.5692	−	24.0000i	1.42665	−	0.823678i
$850$		0			0
$851$	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
$855$		0			0
$856$	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	−0.774589	−	0.632465i	$-0.782043\pi$
$859$	−18.0000	+	10.3923i	−0.614152	+	0.354581i	0.160437	+	0.987046i	$0.448710\pi$
$860$		0			0
$861$	−6.00000	+	31.1769i	−0.204479	+	1.06251i
$862$	−24.0000			−0.817443
$863$	−46.7654	+	27.0000i	−1.59191	+	0.919091i	−0.598933	+	0.800799i	$0.704408\pi$
$863$	−46.7654	+	27.0000i	−1.59191	+	0.919091i	−0.992979	+	0.118291i	$0.962258\pi$
$864$	−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
$868$	−3.00000	+	3.46410i	−0.101827	+	0.117579i
$869$		−	3.00000i		−	0.101768i
$870$		0			0
$871$	−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	$0.0998775\pi$
$877$	22.0000	+	38.1051i	0.742887	+	1.28672i	−0.208288	+	0.978068i	$0.566789\pi$
$878$	18.1865	−	31.5000i	0.613766	−	1.06307i
$879$	−16.5000	+	28.5788i	−0.556531	+	0.963940i
$880$		0			0
$881$	10.3923			0.350126			0.175063	−	0.984557i	$-0.443987\pi$
$881$	10.3923			0.350126			0.175063	+	0.984557i	$0.443987\pi$
$882$	−20.7846	+	3.00000i	−0.699854	+	0.101015i
$883$	−52.0000			−1.74994			−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000			−1.74994			−0.874970	+	0.484178i	$0.839119\pi$
$884$	−10.3923	+	6.00000i	−0.349531	+	0.201802i
$885$		0			0
$886$	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
$889$	−27.5000	+	9.52628i	−0.922320	+	0.319501i
$890$		0			0
$891$	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
$895$		0			0
$896$	−1.73205	+	2.00000i	−0.0578638	+	0.0668153i
$897$	−36.0000			−1.20201
$898$	15.0000	+	25.9808i	0.500556	+	0.866989i
$899$	−2.59808	+	4.50000i	−0.0866507	+	0.150083i
$900$		0			0
$901$	27.0000	−	15.5885i	0.899500	−	0.519327i
$902$	−20.7846			−0.692052
$903$	−6.92820	+	36.0000i	−0.230556	+	1.19800i
$904$	12.0000			0.399114
$905$		0			0
$906$	−10.5000	−	6.06218i	−0.348839	−	0.201402i
$907$	−13.0000	+	22.5167i	−0.431658	+	0.747653i	−0.997016	−	0.0771920i	$-0.975405\pi$
$907$	−13.0000	+	22.5167i	−0.431658	+	0.747653i	0.565358	+	0.824845i	$0.308738\pi$
$908$	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
$917$	−10.3923	−	9.00000i	−0.343184	−	0.297206i
$918$		−	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	$0.726329\pi$
$920$		0			0
$921$	−36.3731	−	21.0000i	−1.19853	−	0.691974i
$922$	−12.0000	+	6.92820i	−0.395199	+	0.228168i
$923$	41.5692			1.36827
$924$	−4.50000	−	12.9904i	−0.148039	−	0.427352i
$925$		0			0
$926$	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	$0.126164\pi$
$929$	24.2487	+	42.0000i	0.795574	+	1.37798i	−0.126899	+	0.991916i	$0.540503\pi$
$930$		0			0
$931$	9.00000	−	22.5167i	0.294963	−	0.737954i
$932$			18.0000i			0.589610i
$933$	−12.0000	−	20.7846i	−0.392862	−	0.680458i
$934$	27.0000	+	15.5885i	0.883467	+	0.510070i
$935$		0			0
$936$	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	$-0.119887\pi$
$938$	−1.73205	−	5.00000i	−0.0565535	−	0.163256i
$939$		−	3.00000i		−	0.0979013i
$940$		0			0
$941$	−16.4545	+	28.5000i	−0.536401	+	0.929073i	0.462693	+	0.886518i	$0.346883\pi$
$941$	−16.4545	+	28.5000i	−0.536401	+	0.929073i	−0.999094	+	0.0425550i	$0.986450\pi$
$942$	−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	−0.659256	−	0.751918i	$-0.729129\pi$
$947$	−10.3923	+	6.00000i	−0.337705	+	0.194974i	0.321552	+	0.946892i	$0.395796\pi$
$948$	−0.866025	+	1.50000i	−0.0281272	+	0.0487177i
$949$	−12.0000	+	20.7846i	−0.389536	+	0.674697i
$950$		0			0
$951$		−	25.9808i		−	0.842484i
$952$	−9.00000	−	1.73205i	−0.291692	−	0.0561361i
$953$			24.0000i			0.777436i	0.921357	+	0.388718i	$0.127082\pi$
$953$			24.0000i			0.777436i	−0.921357	+	0.388718i	$0.872918\pi$
$954$	−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
$959$	−46.7654	−	9.00000i	−1.51013	−	0.290625i
$960$		0			0
$961$	−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
$965$		0			0
$966$	−20.7846	−	18.0000i	−0.668734	−	0.579141i
$967$	7.00000			0.225105			0.112552	−	0.993646i	$-0.464097\pi$
$967$	7.00000			0.225105			0.112552	+	0.993646i	$0.464097\pi$
$968$	−1.73205	+	1.00000i	−0.0556702	+	0.0321412i
$969$	18.0000	+	10.3923i	0.578243	+	0.333849i
$970$		0			0
$971$	4.33013	+	7.50000i	0.138960	+	0.240686i	0.927103	−	0.374806i	$-0.122291\pi$
$971$	4.33013	+	7.50000i	0.138960	+	0.240686i	−0.788143	+	0.615492i	$0.788957\pi$
$972$	−15.5885			−0.500000
$973$	15.0000	+	43.3013i	0.480878	+	1.38817i
$974$		−	1.00000i		−	0.0320421i
$975$		0			0
$976$		0			0
$977$	20.7846	+	12.0000i	0.664959	+	0.383914i	0.794164	−	0.607704i	$-0.207909\pi$
$977$	20.7846	+	12.0000i	0.664959	+	0.383914i	−0.129205	+	0.991618i	$0.541243\pi$
$978$	−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
$985$		0			0
$986$	−10.3923			−0.330958
$987$	30.0000	−	10.3923i	0.954911	−	0.330791i
$988$	−12.0000			−0.381771
$989$	−41.5692	+	24.0000i	−1.32182	+	0.763156i
$990$		0			0
$991$	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
$994$	24.0000	+	20.7846i	0.761234	+	0.659248i
$995$		0			0
$996$	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	1050.2.s.b.101.2		4
3.2	odd	2	inner	1050.2.s.b.101.1		4
5.2	odd	4		1050.2.u.d.899.2		4
5.3	odd	4		1050.2.u.a.899.1		4
5.4	even	2		42.2.f.a.17.1	yes	4
7.5	odd	6	inner	1050.2.s.b.551.1		4
15.2	even	4		1050.2.u.a.899.2		4
15.8	even	4		1050.2.u.d.899.1		4
15.14	odd	2		42.2.f.a.17.2	yes	4
20.19	odd	2		336.2.bc.e.17.1		4
21.5	even	6	inner	1050.2.s.b.551.2		4
35.4	even	6		294.2.d.a.293.1		4
35.9	even	6		294.2.f.a.215.2		4
35.12	even	12		1050.2.u.d.299.1		4
35.19	odd	6		42.2.f.a.5.2	yes	4
35.24	odd	6		294.2.d.a.293.2		4
35.33	even	12		1050.2.u.a.299.2		4
35.34	odd	2		294.2.f.a.227.1		4
45.4	even	6		1134.2.l.c.269.1		4
45.14	odd	6		1134.2.l.c.269.2		4
45.29	odd	6		1134.2.t.d.1025.1		4
45.34	even	6		1134.2.t.d.1025.2		4
60.59	even	2		336.2.bc.e.17.2		4
105.44	odd	6		294.2.f.a.215.1		4
105.47	odd	12		1050.2.u.a.299.1		4
105.59	even	6		294.2.d.a.293.3		4
105.68	odd	12		1050.2.u.d.299.2		4
105.74	odd	6		294.2.d.a.293.4		4
105.89	even	6		42.2.f.a.5.1	✓	4
105.104	even	2		294.2.f.a.227.2		4
140.19	even	6		336.2.bc.e.257.2		4
140.39	odd	6		2352.2.k.e.881.3		4
140.59	even	6		2352.2.k.e.881.1		4
315.124	odd	6		1134.2.l.c.215.1		4
315.194	even	6		1134.2.t.d.593.2		4
315.229	odd	6		1134.2.t.d.593.1		4
315.299	even	6		1134.2.l.c.215.2		4
420.59	odd	6		2352.2.k.e.881.4		4
420.179	even	6		2352.2.k.e.881.2		4
420.299	odd	6		336.2.bc.e.257.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.f.a.5.1	✓	4	105.89	even	6
42.2.f.a.5.2	yes	4	35.19	odd	6
42.2.f.a.17.1	yes	4	5.4	even	2
42.2.f.a.17.2	yes	4	15.14	odd	2
294.2.d.a.293.1		4	35.4	even	6
294.2.d.a.293.2		4	35.24	odd	6
294.2.d.a.293.3		4	105.59	even	6
294.2.d.a.293.4		4	105.74	odd	6
294.2.f.a.215.1		4	105.44	odd	6
294.2.f.a.215.2		4	35.9	even	6
294.2.f.a.227.1		4	35.34	odd	2
294.2.f.a.227.2		4	105.104	even	2
336.2.bc.e.17.1		4	20.19	odd	2
336.2.bc.e.17.2		4	60.59	even	2
336.2.bc.e.257.1		4	420.299	odd	6
336.2.bc.e.257.2		4	140.19	even	6
1050.2.s.b.101.1		4	3.2	odd	2	inner
1050.2.s.b.101.2		4	1.1	even	1	trivial
1050.2.s.b.551.1		4	7.5	odd	6	inner
1050.2.s.b.551.2		4	21.5	even	6	inner
1050.2.u.a.299.1		4	105.47	odd	12
1050.2.u.a.299.2		4	35.33	even	12
1050.2.u.a.899.1		4	5.3	odd	4
1050.2.u.a.899.2		4	15.2	even	4
1050.2.u.d.299.1		4	35.12	even	12
1050.2.u.d.299.2		4	105.68	odd	12
1050.2.u.d.899.1		4	15.8	even	4
1050.2.u.d.899.2		4	5.2	odd	4
1134.2.l.c.215.1		4	315.124	odd	6
1134.2.l.c.215.2		4	315.299	even	6
1134.2.l.c.269.1		4	45.4	even	6
1134.2.l.c.269.2		4	45.14	odd	6
1134.2.t.d.593.1		4	315.229	odd	6
1134.2.t.d.593.2		4	315.194	even	6
1134.2.t.d.1025.1		4	45.29	odd	6
1134.2.t.d.1025.2		4	45.34	even	6
2352.2.k.e.881.1		4	140.59	even	6
2352.2.k.e.881.2		4	420.179	even	6
2352.2.k.e.881.3		4	140.39	odd	6
2352.2.k.e.881.4		4	420.59	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.73205i q^{6} +(2.50000 - 0.866025i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.73205i q^{6} +(2.50000 - 0.866025i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-2.59808 - 1.50000i) q^{11} +(0.866025 + 1.50000i) q^{12} -3.46410i q^{13} +(1.73205 - 2.00000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.73205 - 3.00000i) q^{17} +(-2.59808 - 1.50000i) q^{18} +(3.00000 - 1.73205i) q^{19} +(-0.866025 + 4.50000i) q^{21} -3.00000 q^{22} +(-5.19615 + 3.00000i) q^{23} +(1.50000 + 0.866025i) q^{24} +(-1.73205 - 3.00000i) q^{26} +5.19615 q^{27} +(0.500000 - 2.59808i) q^{28} -3.00000i q^{29} +(-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} +6.92820 q^{41} +(1.50000 + 4.33013i) q^{42} +8.00000 q^{43} +(-2.59808 + 1.50000i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(-3.46410 - 6.00000i) q^{47} +1.73205 q^{48} +(5.50000 - 4.33013i) q^{49} +(3.00000 + 5.19615i) q^{51} +(-3.00000 - 1.73205i) q^{52} +(7.79423 + 4.50000i) q^{53} +(4.50000 - 2.59808i) q^{54} +(-0.866025 - 2.50000i) q^{56} +6.00000i q^{57} +(-1.50000 - 2.59808i) q^{58} +(-0.866025 + 1.50000i) q^{59} -1.73205 q^{62} +(-6.00000 - 5.19615i) q^{63} -1.00000 q^{64} +(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} -3.46410i q^{76} +(-7.79423 - 1.50000i) q^{77} +6.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(6.00000 - 3.46410i) q^{82} +8.66025 q^{83} +(3.46410 + 3.00000i) q^{84} +(6.92820 - 4.00000i) q^{86} +(4.50000 + 2.59808i) q^{87} +(-1.50000 + 2.59808i) q^{88} +(-5.19615 - 9.00000i) q^{89} +(-3.00000 - 8.66025i) q^{91} +6.00000i q^{92} +(2.59808 - 1.50000i) q^{93} +(-6.00000 - 3.46410i) q^{94} +(1.50000 - 0.866025i) q^{96} -5.19615i q^{97} +(2.59808 - 6.50000i) q^{98} +9.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 10 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 10 * q^7 - 6 * q^9	\( 4 q + 2 q^{4} + 10 q^{7} - 6 q^{9} - 2 q^{16} + 12 q^{19} - 12 q^{22} + 6 q^{24} + 2 q^{28} - 6 q^{31} + 18 q^{33} - 12 q^{36} - 4 q^{37} + 6 q^{42} + 32 q^{43} - 12 q^{46} + 22 q^{49} + 12 q^{51} - 12 q^{52} + 18 q^{54} - 6 q^{58} - 24 q^{63} - 4 q^{64} + 4 q^{67} - 24 q^{73} + 24 q^{78} + 2 q^{79} - 18 q^{81} + 24 q^{82} + 18 q^{87} - 6 q^{88} - 12 q^{91} - 24 q^{94} + 6 q^{96}+O(q^{100}) \) 4 * q + 2 * q^4 + 10 * q^7 - 6 * q^9 - 2 * q^16 + 12 * q^19 - 12 * q^22 + 6 * q^24 + 2 * q^28 - 6 * q^31 + 18 * q^33 - 12 * q^36 - 4 * q^37 + 6 * q^42 + 32 * q^43 - 12 * q^46 + 22 * q^49 + 12 * q^51 - 12 * q^52 + 18 * q^54 - 6 * q^58 - 24 * q^63 - 4 * q^64 + 4 * q^67 - 24 * q^73 + 24 * q^78 + 2 * q^79 - 18 * q^81 + 24 * q^82 + 18 * q^87 - 6 * q^88 - 12 * q^91 - 24 * q^94 + 6 * q^96

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