LMFDB - Embedded newform 1050.2.o.j.499.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(499,1050)]

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([0, 3, 2]))

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

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

chi := DirichletCharacter("1050.499");

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.o (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:	$8.38429221223$
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 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1050.499
Dual form			1050.2.o.j.949.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-1.73205 + 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-1.73205 + 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-0.866025 - 0.500000i) q^{12} -7.00000i q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.46410 + 2.00000i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(0.500000 - 0.866025i) q^{19} +(0.500000 - 2.59808i) q^{21} -1.00000i q^{22} +(0.866025 + 0.500000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.50000 + 6.06218i) q^{26} +1.00000i q^{27} +(-2.59808 - 0.500000i) q^{28} +8.00000 q^{29} +(-3.00000 - 5.19615i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.866025 - 0.500000i) q^{33} +4.00000 q^{34} +1.00000 q^{36} +(2.59808 + 1.50000i) q^{37} +(-0.866025 + 0.500000i) q^{38} +(3.50000 + 6.06218i) q^{39} +9.00000 q^{41} +(-1.73205 + 2.00000i) q^{42} +4.00000i q^{43} +(-0.500000 + 0.866025i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(2.59808 + 1.50000i) q^{47} -1.00000i q^{48} +(-1.00000 - 6.92820i) q^{49} +(2.00000 - 3.46410i) q^{51} +(6.06218 - 3.50000i) q^{52} +(0.866025 - 0.500000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.00000 + 1.73205i) q^{56} +1.00000i q^{57} +(-6.92820 - 4.00000i) q^{58} +(6.00000 + 10.3923i) q^{59} +(2.00000 - 3.46410i) q^{61} +6.00000i q^{62} +(0.866025 + 2.50000i) q^{63} -1.00000 q^{64} +(0.500000 + 0.866025i) q^{66} +(10.3923 - 6.00000i) q^{67} +(-3.46410 - 2.00000i) q^{68} -1.00000 q^{69} -14.0000 q^{71} +(-0.866025 - 0.500000i) q^{72} +(12.1244 - 7.00000i) q^{73} +(-1.50000 - 2.59808i) q^{74} +1.00000 q^{76} +(-2.59808 - 0.500000i) q^{77} -7.00000i q^{78} +(2.00000 - 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-7.79423 - 4.50000i) q^{82} -12.0000i q^{83} +(2.50000 - 0.866025i) q^{84} +(2.00000 - 3.46410i) q^{86} +(-6.92820 + 4.00000i) q^{87} +(0.866025 - 0.500000i) q^{88} +(-1.00000 + 1.73205i) q^{89} +(14.0000 + 12.1244i) q^{91} +1.00000i q^{92} +(5.19615 + 3.00000i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(-0.500000 + 0.866025i) q^{96} -16.0000i q^{97} +(-2.59808 + 6.50000i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9} + 2 q^{11} + 10 q^{14} - 2 q^{16} + 2 q^{19} + 2 q^{21} + 2 q^{24} - 14 q^{26} + 32 q^{29} - 12 q^{31} + 16 q^{34} + 4 q^{36} + 14 q^{39} + 36 q^{41} - 2 q^{44} - 2 q^{46} - 4 q^{49} + 8 q^{51} + 2 q^{54} + 8 q^{56} + 24 q^{59} + 8 q^{61} - 4 q^{64} + 2 q^{66} - 4 q^{69} - 56 q^{71} - 6 q^{74} + 4 q^{76} + 8 q^{79} - 2 q^{81} + 10 q^{84} + 8 q^{86} - 4 q^{89} + 56 q^{91} - 6 q^{94} - 2 q^{96} + 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9 + 2 * q^11 + 10 * q^14 - 2 * q^16 + 2 * q^19 + 2 * q^21 + 2 * q^24 - 14 * q^26 + 32 * q^29 - 12 * q^31 + 16 * q^34 + 4 * q^36 + 14 * q^39 + 36 * q^41 - 2 * q^44 - 2 * q^46 - 4 * q^49 + 8 * q^51 + 2 * q^54 + 8 * q^56 + 24 * q^59 + 8 * q^61 - 4 * q^64 + 2 * q^66 - 4 * q^69 - 56 * q^71 - 6 * q^74 + 4 * q^76 + 8 * q^79 - 2 * q^81 + 10 * q^84 + 8 * q^86 - 4 * q^89 + 56 * q^91 - 6 * q^94 - 2 * q^96 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.00000			0.408248
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$		−	7.00000i		−	1.94145i	−0.240192	−	0.970725i	$-0.577210\pi$
$13$		−	7.00000i		−	1.94145i	0.240192	−	0.970725i	$-0.422790\pi$
$14$	2.50000	−	0.866025i	0.668153	−	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.46410	+	2.00000i	−0.840168	+	0.485071i	−0.857321	−	0.514782i	$-0.827873\pi$
$17$	−3.46410	+	2.00000i	−0.840168	+	0.485071i	0.0171533	+	0.999853i	$0.494540\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$		0			0
$21$	0.500000	−	2.59808i	0.109109	−	0.566947i
$22$		−	1.00000i		−	0.213201i
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i	0.587565	−	0.809177i	$-0.300087\pi$
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i	−0.406986	+	0.913434i	$0.633420\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	−3.50000	+	6.06218i	−0.686406	+	1.18889i
$27$			1.00000i			0.192450i
$28$	−2.59808	−	0.500000i	−0.490990	−	0.0944911i
$29$	8.00000			1.48556			0.742781	−	0.669534i	$-0.233506\pi$
$29$	8.00000			1.48556			0.742781	+	0.669534i	$0.233506\pi$
$30$		0			0
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	−0.998968	−	0.0454165i	$-0.985539\pi$
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	0.460152	−	0.887840i	$-0.347795\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−0.866025	−	0.500000i	−0.150756	−	0.0870388i
$34$	4.00000			0.685994
$35$		0			0
$36$	1.00000			0.166667
$37$	2.59808	+	1.50000i	0.427121	+	0.246598i	0.698119	−	0.715981i	$-0.254020\pi$
$37$	2.59808	+	1.50000i	0.427121	+	0.246598i	−0.270998	+	0.962580i	$0.587354\pi$
$38$	−0.866025	+	0.500000i	−0.140488	+	0.0811107i
$39$	3.50000	+	6.06218i	0.560449	+	0.970725i
$40$		0			0
$41$	9.00000			1.40556			0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000			1.40556			0.702782	+	0.711405i	$0.251941\pi$
$42$	−1.73205	+	2.00000i	−0.267261	+	0.308607i
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$		0			0
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	2.59808	+	1.50000i	0.378968	+	0.218797i	0.677369	−	0.735643i	$-0.263120\pi$
$47$	2.59808	+	1.50000i	0.378968	+	0.218797i	−0.298401	+	0.954441i	$0.596453\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$		0			0
$51$	2.00000	−	3.46410i	0.280056	−	0.485071i
$52$	6.06218	−	3.50000i	0.840673	−	0.485363i
$53$	0.866025	−	0.500000i	0.118958	−	0.0686803i	−0.439340	−	0.898321i	$-0.644788\pi$
$53$	0.866025	−	0.500000i	0.118958	−	0.0686803i	0.558298	+	0.829640i	$0.311454\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	2.00000	+	1.73205i	0.267261	+	0.231455i
$57$			1.00000i			0.132453i
$58$	−6.92820	−	4.00000i	−0.909718	−	0.525226i
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	0.931282	+	0.364299i	$0.118692\pi$
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	−0.150148	+	0.988663i	$0.547975\pi$
$60$		0			0
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	−0.709113	−	0.705095i	$-0.750904\pi$
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	0.965187	+	0.261562i	$0.0842377\pi$
$62$			6.00000i			0.762001i
$63$	0.866025	+	2.50000i	0.109109	+	0.314970i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	0.500000	+	0.866025i	0.0615457	+	0.106600i
$67$	10.3923	−	6.00000i	1.26962	−	0.733017i	0.294706	−	0.955588i	$-0.404778\pi$
$67$	10.3923	−	6.00000i	1.26962	−	0.733017i	0.974916	+	0.222571i	$0.0714450\pi$
$68$	−3.46410	−	2.00000i	−0.420084	−	0.242536i
$69$	−1.00000			−0.120386
$70$		0			0
$71$	−14.0000			−1.66149			−0.830747	−	0.556650i	$-0.812086\pi$
$71$	−14.0000			−1.66149			−0.830747	+	0.556650i	$0.812086\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	12.1244	−	7.00000i	1.41905	−	0.819288i	0.422833	−	0.906208i	$-0.361036\pi$
$73$	12.1244	−	7.00000i	1.41905	−	0.819288i	0.996215	+	0.0869195i	$0.0277023\pi$
$74$	−1.50000	−	2.59808i	−0.174371	−	0.302020i
$75$		0			0
$76$	1.00000			0.114708
$77$	−2.59808	−	0.500000i	−0.296078	−	0.0569803i
$78$		−	7.00000i		−	0.792594i
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−7.79423	−	4.50000i	−0.860729	−	0.496942i
$83$		−	12.0000i		−	1.31717i	−0.752506	−	0.658586i	$-0.771155\pi$
$83$		−	12.0000i		−	1.31717i	0.752506	−	0.658586i	$-0.228845\pi$
$84$	2.50000	−	0.866025i	0.272772	−	0.0944911i
$85$		0			0
$86$	2.00000	−	3.46410i	0.215666	−	0.373544i
$87$	−6.92820	+	4.00000i	−0.742781	+	0.428845i
$88$	0.866025	−	0.500000i	0.0923186	−	0.0533002i
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	−0.914146	−	0.405385i	$-0.867138\pi$
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	0.808146	+	0.588982i	$0.200471\pi$
$90$		0			0
$91$	14.0000	+	12.1244i	1.46760	+	1.27098i
$92$			1.00000i			0.104257i
$93$	5.19615	+	3.00000i	0.538816	+	0.311086i
$94$	−1.50000	−	2.59808i	−0.154713	−	0.267971i
$95$		0			0
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$		−	16.0000i		−	1.62455i	−0.583272	−	0.812277i	$-0.698228\pi$
$97$		−	16.0000i		−	1.62455i	0.583272	−	0.812277i	$-0.301772\pi$
$98$	−2.59808	+	6.50000i	−0.262445	+	0.656599i
$99$	1.00000			0.100504
$100$		0			0
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$	−3.46410	+	2.00000i	−0.342997	+	0.198030i
$103$	13.8564	+	8.00000i	1.36531	+	0.788263i	0.990325	−	0.138767i	$-0.0443138\pi$
$103$	13.8564	+	8.00000i	1.36531	+	0.788263i	0.374987	+	0.927030i	$0.377647\pi$
$104$	−7.00000			−0.686406
$105$		0			0
$106$	−1.00000			−0.0971286
$107$	15.5885	+	9.00000i	1.50699	+	0.870063i	0.999967	+	0.00813215i	$0.00258857\pi$
$107$	15.5885	+	9.00000i	1.50699	+	0.870063i	0.507026	+	0.861931i	$0.330745\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	0.520794	−	0.853682i	$-0.325636\pi$
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	−0.999708	+	0.0241802i	$0.992302\pi$
$110$		0			0
$111$	−3.00000			−0.284747
$112$	−0.866025	−	2.50000i	−0.0818317	−	0.236228i
$113$			6.00000i			0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$	0.500000	−	0.866025i	0.0468293	−	0.0811107i
$115$		0			0
$116$	4.00000	+	6.92820i	0.371391	+	0.643268i
$117$	−6.06218	−	3.50000i	−0.560449	−	0.323575i
$118$		−	12.0000i		−	1.10469i
$119$	2.00000	−	10.3923i	0.183340	−	0.952661i
$120$		0			0
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	−3.46410	+	2.00000i	−0.313625	+	0.181071i
$123$	−7.79423	+	4.50000i	−0.702782	+	0.405751i
$124$	3.00000	−	5.19615i	0.269408	−	0.466628i
$125$		0			0
$126$	0.500000	−	2.59808i	0.0445435	−	0.231455i
$127$			5.00000i			0.443678i	0.975083	+	0.221839i	$0.0712060\pi$
$127$			5.00000i			0.443678i	−0.975083	+	0.221839i	$0.928794\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−2.00000	−	3.46410i	−0.176090	−	0.304997i
$130$		0			0
$131$	6.50000	−	11.2583i	0.567908	−	0.983645i	−0.428865	−	0.903369i	$-0.641086\pi$
$131$	6.50000	−	11.2583i	0.567908	−	0.983645i	0.996773	−	0.0802763i	$-0.0255803\pi$
$132$		−	1.00000i		−	0.0870388i
$133$	0.866025	+	2.50000i	0.0750939	+	0.216777i
$134$	−12.0000			−1.03664
$135$		0			0
$136$	2.00000	+	3.46410i	0.171499	+	0.297044i
$137$	−1.73205	+	1.00000i	−0.147979	+	0.0854358i	−0.572161	−	0.820141i	$-0.693895\pi$
$137$	−1.73205	+	1.00000i	−0.147979	+	0.0854358i	0.424182	+	0.905577i	$0.360562\pi$
$138$	0.866025	+	0.500000i	0.0737210	+	0.0425628i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−3.00000			−0.252646
$142$	12.1244	+	7.00000i	1.01745	+	0.587427i
$143$	6.06218	−	3.50000i	0.506945	−	0.292685i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$		0			0
$146$	−14.0000			−1.15865
$147$	4.33013	+	5.50000i	0.357143	+	0.453632i
$148$			3.00000i			0.246598i
$149$	−2.00000	+	3.46410i	−0.163846	+	0.283790i	−0.936245	−	0.351348i	$-0.885723\pi$
$149$	−2.00000	+	3.46410i	−0.163846	+	0.283790i	0.772399	+	0.635138i	$0.219057\pi$
$150$		0			0
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	0.903842	−	0.427865i	$-0.140734\pi$
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	−0.822464	+	0.568818i	$0.807401\pi$
$152$	−0.866025	−	0.500000i	−0.0702439	−	0.0405554i
$153$			4.00000i			0.323381i
$154$	2.00000	+	1.73205i	0.161165	+	0.139573i
$155$		0			0
$156$	−3.50000	+	6.06218i	−0.280224	+	0.485363i
$157$	12.9904	−	7.50000i	1.03675	−	0.598565i	0.117836	−	0.993033i	$-0.462404\pi$
$157$	12.9904	−	7.50000i	1.03675	−	0.598565i	0.918910	+	0.394468i	$0.129071\pi$
$158$	−3.46410	+	2.00000i	−0.275589	+	0.159111i
$159$	−0.500000	+	0.866025i	−0.0396526	+	0.0686803i
$160$		0			0
$161$	−2.50000	+	0.866025i	−0.197028	+	0.0682524i
$162$			1.00000i			0.0785674i
$163$	6.92820	+	4.00000i	0.542659	+	0.313304i	0.746156	−	0.665771i	$-0.231897\pi$
$163$	6.92820	+	4.00000i	0.542659	+	0.313304i	−0.203497	+	0.979076i	$0.565231\pi$
$164$	4.50000	+	7.79423i	0.351391	+	0.608627i
$165$		0			0
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$		−	5.00000i		−	0.386912i	−0.981109	−	0.193456i	$-0.938030\pi$
$167$		−	5.00000i		−	0.386912i	0.981109	−	0.193456i	$-0.0619696\pi$
$168$	−2.59808	−	0.500000i	−0.200446	−	0.0385758i
$169$	−36.0000			−2.76923
$170$		0			0
$171$	−0.500000	−	0.866025i	−0.0382360	−	0.0662266i
$172$	−3.46410	+	2.00000i	−0.264135	+	0.152499i
$173$	−18.1865	−	10.5000i	−1.38270	−	0.798300i	−0.390218	−	0.920722i	$-0.627601\pi$
$173$	−18.1865	−	10.5000i	−1.38270	−	0.798300i	−0.992478	+	0.122422i	$0.960934\pi$
$174$	8.00000			0.606478
$175$		0			0
$176$	−1.00000			−0.0753778
$177$	−10.3923	−	6.00000i	−0.781133	−	0.450988i
$178$	1.73205	−	1.00000i	0.129823	−	0.0749532i
$179$	6.50000	+	11.2583i	0.485833	+	0.841487i	0.999867	−	0.0162823i	$-0.00518305\pi$
$179$	6.50000	+	11.2583i	0.485833	+	0.841487i	−0.514035	+	0.857769i	$0.671850\pi$
$180$		0			0
$181$	−12.0000			−0.891953			−0.445976	−	0.895045i	$-0.647144\pi$
$181$	−12.0000			−0.891953			−0.445976	+	0.895045i	$0.647144\pi$
$182$	−6.06218	−	17.5000i	−0.449359	−	1.29719i
$183$			4.00000i			0.295689i
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$		0			0
$186$	−3.00000	−	5.19615i	−0.219971	−	0.381000i
$187$	−3.46410	−	2.00000i	−0.253320	−	0.146254i
$188$			3.00000i			0.218797i
$189$	−2.00000	−	1.73205i	−0.145479	−	0.125988i
$190$		0			0
$191$	5.00000	−	8.66025i	0.361787	−	0.626634i	−0.626468	−	0.779447i	$-0.715500\pi$
$191$	5.00000	−	8.66025i	0.361787	−	0.626634i	0.988255	+	0.152813i	$0.0488333\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−22.5167	+	13.0000i	−1.62078	+	0.935760i	−0.634074	+	0.773272i	$0.718619\pi$
$193$	−22.5167	+	13.0000i	−1.62078	+	0.935760i	−0.986710	+	0.162488i	$0.948048\pi$
$194$	−8.00000	+	13.8564i	−0.574367	+	0.994832i
$195$		0			0
$196$	5.50000	−	4.33013i	0.392857	−	0.309295i
$197$		−	3.00000i		−	0.213741i	−0.994273	−	0.106871i	$-0.965917\pi$
$197$		−	3.00000i		−	0.213741i	0.994273	−	0.106871i	$-0.0340831\pi$
$198$	−0.866025	−	0.500000i	−0.0615457	−	0.0355335i
$199$	−6.00000	−	10.3923i	−0.425329	−	0.736691i	0.571122	−	0.820865i	$-0.306508\pi$
$199$	−6.00000	−	10.3923i	−0.425329	−	0.736691i	−0.996451	+	0.0841740i	$0.973175\pi$
$200$		0			0
$201$	−6.00000	+	10.3923i	−0.423207	+	0.733017i
$202$		0			0
$203$	−13.8564	+	16.0000i	−0.972529	+	1.12298i
$204$	4.00000			0.280056
$205$		0			0
$206$	−8.00000	−	13.8564i	−0.557386	−	0.965422i
$207$	0.866025	−	0.500000i	0.0601929	−	0.0347524i
$208$	6.06218	+	3.50000i	0.420336	+	0.242681i
$209$	1.00000			0.0691714
$210$		0			0
$211$	−15.0000			−1.03264			−0.516321	−	0.856395i	$-0.672699\pi$
$211$	−15.0000			−1.03264			−0.516321	+	0.856395i	$0.672699\pi$
$212$	0.866025	+	0.500000i	0.0594789	+	0.0343401i
$213$	12.1244	−	7.00000i	0.830747	−	0.479632i
$214$	−9.00000	−	15.5885i	−0.615227	−	1.06561i
$215$		0			0
$216$	1.00000			0.0680414
$217$	15.5885	+	3.00000i	1.05821	+	0.203653i
$218$			10.0000i			0.677285i
$219$	−7.00000	+	12.1244i	−0.473016	+	0.819288i
$220$		0			0
$221$	14.0000	+	24.2487i	0.941742	+	1.63114i
$222$	2.59808	+	1.50000i	0.174371	+	0.100673i
$223$			4.00000i			0.267860i	0.990991	+	0.133930i	$0.0427597\pi$
$223$			4.00000i			0.267860i	−0.990991	+	0.133930i	$0.957240\pi$
$224$	−0.500000	+	2.59808i	−0.0334077	+	0.173591i
$225$		0			0
$226$	3.00000	−	5.19615i	0.199557	−	0.345643i
$227$	−17.3205	+	10.0000i	−1.14960	+	0.663723i	−0.948790	−	0.315906i	$-0.897691\pi$
$227$	−17.3205	+	10.0000i	−1.14960	+	0.663723i	−0.200812	+	0.979630i	$0.564358\pi$
$228$	−0.866025	+	0.500000i	−0.0573539	+	0.0331133i
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	0.231287	+	0.972886i	$0.425707\pi$
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	−0.958187	+	0.286143i	$0.907627\pi$
$230$		0			0
$231$	2.50000	−	0.866025i	0.164488	−	0.0569803i
$232$		−	8.00000i		−	0.525226i
$233$	22.5167	+	13.0000i	1.47512	+	0.851658i	0.999606	−	0.0280525i	$-0.00893057\pi$
$233$	22.5167	+	13.0000i	1.47512	+	0.851658i	0.475509	+	0.879711i	$0.342264\pi$
$234$	3.50000	+	6.06218i	0.228802	+	0.396297i
$235$		0			0
$236$	−6.00000	+	10.3923i	−0.390567	+	0.676481i
$237$			4.00000i			0.259828i
$238$	−6.92820	+	8.00000i	−0.449089	+	0.518563i
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		0			0
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	0.731001	−	0.682376i	$-0.239053\pi$
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	−0.956456	+	0.291877i	$0.905720\pi$
$242$	−8.66025	+	5.00000i	−0.556702	+	0.321412i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	4.00000			0.256074
$245$		0			0
$246$	9.00000			0.573819
$247$	−6.06218	−	3.50000i	−0.385727	−	0.222700i
$248$	−5.19615	+	3.00000i	−0.329956	+	0.190500i
$249$	6.00000	+	10.3923i	0.380235	+	0.658586i
$250$		0			0
$251$	−3.00000			−0.189358			−0.0946792	−	0.995508i	$-0.530183\pi$
$251$	−3.00000			−0.189358			−0.0946792	+	0.995508i	$0.530183\pi$
$252$	−1.73205	+	2.00000i	−0.109109	+	0.125988i
$253$			1.00000i			0.0628695i
$254$	2.50000	−	4.33013i	0.156864	−	0.271696i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.92820	+	4.00000i	0.432169	+	0.249513i	0.700270	−	0.713878i	$-0.253063\pi$
$257$	6.92820	+	4.00000i	0.432169	+	0.249513i	−0.268101	+	0.963391i	$0.586396\pi$
$258$			4.00000i			0.249029i
$259$	−7.50000	+	2.59808i	−0.466027	+	0.161437i
$260$		0			0
$261$	4.00000	−	6.92820i	0.247594	−	0.428845i
$262$	−11.2583	+	6.50000i	−0.695542	+	0.401571i
$263$	13.8564	−	8.00000i	0.854423	−	0.493301i	−0.00771799	−	0.999970i	$-0.502457\pi$
$263$	13.8564	−	8.00000i	0.854423	−	0.493301i	0.862141	+	0.506669i	$0.169123\pi$
$264$	−0.500000	+	0.866025i	−0.0307729	+	0.0533002i
$265$		0			0
$266$	0.500000	−	2.59808i	0.0306570	−	0.159298i
$267$		−	2.00000i		−	0.122398i
$268$	10.3923	+	6.00000i	0.634811	+	0.366508i
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	−0.999870	−	0.0161307i	$-0.994865\pi$
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	0.513905	+	0.857847i	$0.328199\pi$
$272$		−	4.00000i		−	0.242536i
$273$	−18.1865	−	3.50000i	−1.10070	−	0.211830i
$274$	2.00000			0.120824
$275$		0			0
$276$	−0.500000	−	0.866025i	−0.0300965	−	0.0521286i
$277$	−1.73205	+	1.00000i	−0.104069	+	0.0600842i	−0.551131	−	0.834419i	$-0.685804\pi$
$277$	−1.73205	+	1.00000i	−0.104069	+	0.0600842i	0.447062	+	0.894503i	$0.352470\pi$
$278$	−3.46410	−	2.00000i	−0.207763	−	0.119952i
$279$	−6.00000			−0.359211
$280$		0			0
$281$	3.00000			0.178965			0.0894825	−	0.995988i	$-0.471479\pi$
$281$	3.00000			0.178965			0.0894825	+	0.995988i	$0.471479\pi$
$282$	2.59808	+	1.50000i	0.154713	+	0.0893237i
$283$	1.73205	−	1.00000i	0.102960	−	0.0594438i	−0.447636	−	0.894216i	$-0.647734\pi$
$283$	1.73205	−	1.00000i	0.102960	−	0.0594438i	0.550596	+	0.834772i	$0.314401\pi$
$284$	−7.00000	−	12.1244i	−0.415374	−	0.719448i
$285$		0			0
$286$	−7.00000			−0.413919
$287$	−15.5885	+	18.0000i	−0.920158	+	1.06251i
$288$		−	1.00000i		−	0.0589256i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$		0			0
$291$	8.00000	+	13.8564i	0.468968	+	0.812277i
$292$	12.1244	+	7.00000i	0.709524	+	0.409644i
$293$		−	9.00000i		−	0.525786i	−0.964825	−	0.262893i	$-0.915323\pi$
$293$		−	9.00000i		−	0.525786i	0.964825	−	0.262893i	$-0.0846766\pi$
$294$	−1.00000	−	6.92820i	−0.0583212	−	0.404061i
$295$		0			0
$296$	1.50000	−	2.59808i	0.0871857	−	0.151010i
$297$	−0.866025	+	0.500000i	−0.0502519	+	0.0290129i
$298$	3.46410	−	2.00000i	0.200670	−	0.115857i
$299$	3.50000	−	6.06218i	0.202410	−	0.350585i
$300$		0			0
$301$	−8.00000	−	6.92820i	−0.461112	−	0.399335i
$302$		−	2.00000i		−	0.115087i
$303$		0			0
$304$	0.500000	+	0.866025i	0.0286770	+	0.0496700i
$305$		0			0
$306$	2.00000	−	3.46410i	0.114332	−	0.198030i
$307$			8.00000i			0.456584i	0.973593	+	0.228292i	$0.0733141\pi$
$307$			8.00000i			0.456584i	−0.973593	+	0.228292i	$0.926686\pi$
$308$	−0.866025	−	2.50000i	−0.0493464	−	0.142451i
$309$	−16.0000			−0.910208
$310$		0			0
$311$	−8.00000	−	13.8564i	−0.453638	−	0.785725i	0.544970	−	0.838455i	$-0.316541\pi$
$311$	−8.00000	−	13.8564i	−0.453638	−	0.785725i	−0.998609	+	0.0527306i	$0.983208\pi$
$312$	6.06218	−	3.50000i	0.343203	−	0.198148i
$313$	−20.7846	−	12.0000i	−1.17482	−	0.678280i	−0.220006	−	0.975499i	$-0.570608\pi$
$313$	−20.7846	−	12.0000i	−1.17482	−	0.678280i	−0.954810	+	0.297218i	$0.903941\pi$
$314$	−15.0000			−0.846499
$315$		0			0
$316$	4.00000			0.225018
$317$	−8.66025	−	5.00000i	−0.486408	−	0.280828i	0.236675	−	0.971589i	$-0.423942\pi$
$317$	−8.66025	−	5.00000i	−0.486408	−	0.280828i	−0.723083	+	0.690761i	$0.757276\pi$
$318$	0.866025	−	0.500000i	0.0485643	−	0.0280386i
$319$	4.00000	+	6.92820i	0.223957	+	0.387905i
$320$		0			0
$321$	−18.0000			−1.00466
$322$	2.59808	+	0.500000i	0.144785	+	0.0278639i
$323$			4.00000i			0.222566i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$		0			0
$326$	−4.00000	−	6.92820i	−0.221540	−	0.383718i
$327$	8.66025	+	5.00000i	0.478913	+	0.276501i
$328$		−	9.00000i		−	0.496942i
$329$	−7.50000	+	2.59808i	−0.413488	+	0.143237i
$330$		0			0
$331$	4.50000	−	7.79423i	0.247342	−	0.428410i	−0.715445	−	0.698669i	$-0.753776\pi$
$331$	4.50000	−	7.79423i	0.247342	−	0.428410i	0.962788	+	0.270259i	$0.0871094\pi$
$332$	10.3923	−	6.00000i	0.570352	−	0.329293i
$333$	2.59808	−	1.50000i	0.142374	−	0.0821995i
$334$	−2.50000	+	4.33013i	−0.136794	+	0.236934i
$335$		0			0
$336$	2.00000	+	1.73205i	0.109109	+	0.0944911i
$337$		0			0		1.00000			$0$
$337$		0			0		−1.00000			$\pi$
$338$	31.1769	+	18.0000i	1.69580	+	0.979071i
$339$	−3.00000	−	5.19615i	−0.162938	−	0.282216i
$340$		0			0
$341$	3.00000	−	5.19615i	0.162459	−	0.281387i
$342$			1.00000i			0.0540738i
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$	4.00000			0.215666
$345$		0			0
$346$	10.5000	+	18.1865i	0.564483	+	0.977714i
$347$	−29.4449	+	17.0000i	−1.58068	+	0.912608i	−0.585923	+	0.810366i	$0.699268\pi$
$347$	−29.4449	+	17.0000i	−1.58068	+	0.912608i	−0.994760	+	0.102241i	$0.967399\pi$
$348$	−6.92820	−	4.00000i	−0.371391	−	0.214423i
$349$	28.0000			1.49881			0.749403	−	0.662114i	$-0.230341\pi$
$349$	28.0000			1.49881			0.749403	+	0.662114i	$0.230341\pi$
$350$		0			0
$351$	7.00000			0.373632
$352$	0.866025	+	0.500000i	0.0461593	+	0.0266501i
$353$	6.92820	−	4.00000i	0.368751	−	0.212899i	−0.304162	−	0.952620i	$-0.598376\pi$
$353$	6.92820	−	4.00000i	0.368751	−	0.212899i	0.672913	+	0.739722i	$0.265043\pi$
$354$	6.00000	+	10.3923i	0.318896	+	0.552345i
$355$		0			0
$356$	−2.00000			−0.106000
$357$	3.46410	+	10.0000i	0.183340	+	0.529256i
$358$		−	13.0000i		−	0.687071i
$359$	18.0000	−	31.1769i	0.950004	−	1.64545i	0.204595	−	0.978847i	$-0.434412\pi$
$359$	18.0000	−	31.1769i	0.950004	−	1.64545i	0.745409	−	0.666608i	$-0.232254\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	10.3923	+	6.00000i	0.546207	+	0.315353i
$363$			10.0000i			0.524864i
$364$	−3.50000	+	18.1865i	−0.183450	+	0.953233i
$365$		0			0
$366$	2.00000	−	3.46410i	0.104542	−	0.181071i
$367$	16.4545	−	9.50000i	0.858917	−	0.495896i	−0.00473247	−	0.999989i	$-0.501506\pi$
$367$	16.4545	−	9.50000i	0.858917	−	0.495896i	0.863649	+	0.504093i	$0.168173\pi$
$368$	−0.866025	+	0.500000i	−0.0451447	+	0.0260643i
$369$	4.50000	−	7.79423i	0.234261	−	0.405751i
$370$		0			0
$371$	−0.500000	+	2.59808i	−0.0259587	+	0.134885i
$372$			6.00000i			0.311086i
$373$	22.5167	+	13.0000i	1.16587	+	0.673114i	0.952703	−	0.303902i	$-0.0982894\pi$
$373$	22.5167	+	13.0000i	1.16587	+	0.673114i	0.213165	+	0.977016i	$0.431623\pi$
$374$	2.00000	+	3.46410i	0.103418	+	0.179124i
$375$		0			0
$376$	1.50000	−	2.59808i	0.0773566	−	0.133986i
$377$		−	56.0000i		−	2.88415i
$378$	0.866025	+	2.50000i	0.0445435	+	0.128586i
$379$	−1.00000			−0.0513665			−0.0256833	−	0.999670i	$-0.508176\pi$
$379$	−1.00000			−0.0513665			−0.0256833	+	0.999670i	$0.508176\pi$
$380$		0			0
$381$	−2.50000	−	4.33013i	−0.128079	−	0.221839i
$382$	−8.66025	+	5.00000i	−0.443097	+	0.255822i
$383$	11.2583	+	6.50000i	0.575274	+	0.332134i	0.759253	−	0.650796i	$-0.225565\pi$
$383$	11.2583	+	6.50000i	0.575274	+	0.332134i	−0.183979	+	0.982930i	$0.558898\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	26.0000			1.32337
$387$	3.46410	+	2.00000i	0.176090	+	0.101666i
$388$	13.8564	−	8.00000i	0.703452	−	0.406138i
$389$	−7.00000	−	12.1244i	−0.354914	−	0.614729i	0.632189	−	0.774814i	$-0.282157\pi$
$389$	−7.00000	−	12.1244i	−0.354914	−	0.614729i	−0.987103	+	0.160085i	$0.948823\pi$
$390$		0			0
$391$	−4.00000			−0.202289
$392$	−6.92820	+	1.00000i	−0.349927	+	0.0505076i
$393$			13.0000i			0.655763i
$394$	−1.50000	+	2.59808i	−0.0755689	+	0.130889i
$395$		0			0
$396$	0.500000	+	0.866025i	0.0251259	+	0.0435194i
$397$	−15.5885	−	9.00000i	−0.782362	−	0.451697i	0.0549046	−	0.998492i	$-0.482515\pi$
$397$	−15.5885	−	9.00000i	−0.782362	−	0.451697i	−0.837267	+	0.546795i	$0.815848\pi$
$398$			12.0000i			0.601506i
$399$	−2.00000	−	1.73205i	−0.100125	−	0.0867110i
$400$		0			0
$401$	8.50000	−	14.7224i	0.424470	−	0.735203i	−0.571901	−	0.820323i	$-0.693794\pi$
$401$	8.50000	−	14.7224i	0.424470	−	0.735203i	0.996371	+	0.0851195i	$0.0271272\pi$
$402$	10.3923	−	6.00000i	0.518321	−	0.299253i
$403$	−36.3731	+	21.0000i	−1.81187	+	1.04608i
$404$		0			0
$405$		0			0
$406$	20.0000	−	6.92820i	0.992583	−	0.343841i
$407$			3.00000i			0.148704i
$408$	−3.46410	−	2.00000i	−0.171499	−	0.0990148i
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	0.962757	−	0.270367i	$-0.0871450\pi$
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	−0.715523	+	0.698589i	$0.753812\pi$
$410$		0			0
$411$	1.00000	−	1.73205i	0.0493264	−	0.0854358i
$412$			16.0000i			0.788263i
$413$	−31.1769	−	6.00000i	−1.53412	−	0.295241i
$414$	−1.00000			−0.0491473
$415$		0			0
$416$	−3.50000	−	6.06218i	−0.171602	−	0.297223i
$417$	−3.46410	+	2.00000i	−0.169638	+	0.0979404i
$418$	−0.866025	−	0.500000i	−0.0423587	−	0.0244558i
$419$	−11.0000			−0.537385			−0.268693	−	0.963226i	$-0.586592\pi$
$419$	−11.0000			−0.537385			−0.268693	+	0.963226i	$0.586592\pi$
$420$		0			0
$421$	−14.0000			−0.682318			−0.341159	−	0.940006i	$-0.610819\pi$
$421$	−14.0000			−0.682318			−0.341159	+	0.940006i	$0.610819\pi$
$422$	12.9904	+	7.50000i	0.632362	+	0.365094i
$423$	2.59808	−	1.50000i	0.126323	−	0.0729325i
$424$	−0.500000	−	0.866025i	−0.0242821	−	0.0420579i
$425$		0			0
$426$	−14.0000			−0.678302
$427$	3.46410	+	10.0000i	0.167640	+	0.483934i
$428$			18.0000i			0.870063i
$429$	−3.50000	+	6.06218i	−0.168982	+	0.292685i
$430$		0			0
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	0.973574	−	0.228373i	$-0.0733406\pi$
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	−0.684564	+	0.728953i	$0.740007\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$		−	40.0000i		−	1.92228i	−0.276066	−	0.961139i	$-0.589031\pi$
$433$		−	40.0000i		−	1.92228i	0.276066	−	0.961139i	$-0.410969\pi$
$434$	−12.0000	−	10.3923i	−0.576018	−	0.498847i
$435$		0			0
$436$	5.00000	−	8.66025i	0.239457	−	0.414751i
$437$	0.866025	−	0.500000i	0.0414276	−	0.0239182i
$438$	12.1244	−	7.00000i	0.579324	−	0.334473i
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	−0.609503	−	0.792784i	$-0.708631\pi$
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	0.991322	+	0.131453i	$0.0419644\pi$
$440$		0			0
$441$	−6.50000	−	2.59808i	−0.309524	−	0.123718i
$442$		−	28.0000i		−	1.33182i
$443$	−31.1769	−	18.0000i	−1.48126	−	0.855206i	−0.481486	−	0.876454i	$-0.659903\pi$
$443$	−31.1769	−	18.0000i	−1.48126	−	0.855206i	−0.999774	+	0.0212481i	$0.993236\pi$
$444$	−1.50000	−	2.59808i	−0.0711868	−	0.123299i
$445$		0			0
$446$	2.00000	−	3.46410i	0.0947027	−	0.164030i
$447$		−	4.00000i		−	0.189194i
$448$	1.73205	−	2.00000i	0.0818317	−	0.0944911i
$449$	25.0000			1.17982			0.589911	−	0.807468i	$-0.299163\pi$
$449$	25.0000			1.17982			0.589911	+	0.807468i	$0.299163\pi$
$450$		0			0
$451$	4.50000	+	7.79423i	0.211897	+	0.367016i
$452$	−5.19615	+	3.00000i	−0.244406	+	0.141108i
$453$	−1.73205	−	1.00000i	−0.0813788	−	0.0469841i
$454$	20.0000			0.938647
$455$		0			0
$456$	1.00000			0.0468293
$457$	−8.66025	−	5.00000i	−0.405110	−	0.233890i	0.283577	−	0.958950i	$-0.408479\pi$
$457$	−8.66025	−	5.00000i	−0.405110	−	0.233890i	−0.688686	+	0.725059i	$0.741812\pi$
$458$	19.0526	−	11.0000i	0.890268	−	0.513996i
$459$	−2.00000	−	3.46410i	−0.0933520	−	0.161690i
$460$		0			0
$461$	−28.0000			−1.30409			−0.652045	−	0.758180i	$-0.726089\pi$
$461$	−28.0000			−1.30409			−0.652045	+	0.758180i	$0.726089\pi$
$462$	−2.59808	−	0.500000i	−0.120873	−	0.0232621i
$463$		−	33.0000i		−	1.53364i	−0.641862	−	0.766820i	$-0.721838\pi$
$463$		−	33.0000i		−	1.53364i	0.641862	−	0.766820i	$-0.278162\pi$
$464$	−4.00000	+	6.92820i	−0.185695	+	0.321634i
$465$		0			0
$466$	−13.0000	−	22.5167i	−0.602213	−	1.04306i
$467$	−10.3923	−	6.00000i	−0.480899	−	0.277647i	0.239892	−	0.970799i	$-0.422888\pi$
$467$	−10.3923	−	6.00000i	−0.480899	−	0.277647i	−0.720791	+	0.693153i	$0.756221\pi$
$468$		−	7.00000i		−	0.323575i
$469$	−6.00000	+	31.1769i	−0.277054	+	1.43962i
$470$		0			0
$471$	−7.50000	+	12.9904i	−0.345582	+	0.598565i
$472$	10.3923	−	6.00000i	0.478345	−	0.276172i
$473$	−3.46410	+	2.00000i	−0.159280	+	0.0919601i
$474$	2.00000	−	3.46410i	0.0918630	−	0.159111i
$475$		0			0
$476$	10.0000	−	3.46410i	0.458349	−	0.158777i
$477$		−	1.00000i		−	0.0457869i
$478$	−5.19615	−	3.00000i	−0.237666	−	0.137217i
$479$	13.0000	+	22.5167i	0.593985	+	1.02881i	0.993689	+	0.112168i	$0.0357796\pi$
$479$	13.0000	+	22.5167i	0.593985	+	1.02881i	−0.399704	+	0.916644i	$0.630887\pi$
$480$		0			0
$481$	10.5000	−	18.1865i	0.478759	−	0.829235i
$482$			7.00000i			0.318841i
$483$	1.73205	−	2.00000i	0.0788110	−	0.0910032i
$484$	10.0000			0.454545
$485$		0			0
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−6.92820	+	4.00000i	−0.313947	+	0.181257i	−0.648691	−	0.761052i	$-0.724683\pi$
$487$	−6.92820	+	4.00000i	−0.313947	+	0.181257i	0.334744	+	0.942309i	$0.391350\pi$
$488$	−3.46410	−	2.00000i	−0.156813	−	0.0905357i
$489$	−8.00000			−0.361773
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$	−7.79423	−	4.50000i	−0.351391	−	0.202876i
$493$	−27.7128	+	16.0000i	−1.24812	+	0.720604i
$494$	3.50000	+	6.06218i	0.157472	+	0.272750i
$495$		0			0
$496$	6.00000			0.269408
$497$	24.2487	−	28.0000i	1.08770	−	1.25597i
$498$		−	12.0000i		−	0.537733i
$499$	12.0000	−	20.7846i	0.537194	−	0.930447i	−0.461860	−	0.886953i	$-0.652818\pi$
$499$	12.0000	−	20.7846i	0.537194	−	0.930447i	0.999054	−	0.0434940i	$-0.0138489\pi$
$500$		0			0
$501$	2.50000	+	4.33013i	0.111692	+	0.193456i
$502$	2.59808	+	1.50000i	0.115958	+	0.0669483i
$503$		−	28.0000i		−	1.24846i	−0.781241	−	0.624229i	$-0.785413\pi$
$503$		−	28.0000i		−	1.24846i	0.781241	−	0.624229i	$-0.214587\pi$
$504$	2.50000	−	0.866025i	0.111359	−	0.0385758i
$505$		0			0
$506$	0.500000	−	0.866025i	0.0222277	−	0.0384995i
$507$	31.1769	−	18.0000i	1.38462	−	0.799408i
$508$	−4.33013	+	2.50000i	−0.192118	+	0.110920i
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$		0			0
$511$	−7.00000	+	36.3731i	−0.309662	+	1.60905i
$512$			1.00000i			0.0441942i
$513$	0.866025	+	0.500000i	0.0382360	+	0.0220755i
$514$	−4.00000	−	6.92820i	−0.176432	−	0.305590i
$515$		0			0
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$			3.00000i			0.131940i
$518$	7.79423	+	1.50000i	0.342459	+	0.0659062i
$519$	21.0000			0.921798
$520$		0			0
$521$	10.5000	+	18.1865i	0.460013	+	0.796766i	0.998961	−	0.0455727i	$-0.0145113\pi$
$521$	10.5000	+	18.1865i	0.460013	+	0.796766i	−0.538948	+	0.842339i	$0.681178\pi$
$522$	−6.92820	+	4.00000i	−0.303239	+	0.175075i
$523$	−12.1244	−	7.00000i	−0.530161	−	0.306089i	0.210921	−	0.977503i	$-0.432354\pi$
$523$	−12.1244	−	7.00000i	−0.530161	−	0.306089i	−0.741082	+	0.671414i	$0.765687\pi$
$524$	13.0000			0.567908
$525$		0			0
$526$	−16.0000			−0.697633
$527$	20.7846	+	12.0000i	0.905392	+	0.522728i
$528$	0.866025	−	0.500000i	0.0376889	−	0.0217597i
$529$	−11.0000	−	19.0526i	−0.478261	−	0.828372i
$530$		0			0
$531$	12.0000			0.520756
$532$	−1.73205	+	2.00000i	−0.0750939	+	0.0867110i
$533$		−	63.0000i		−	2.72883i
$534$	−1.00000	+	1.73205i	−0.0432742	+	0.0749532i
$535$		0			0
$536$	−6.00000	−	10.3923i	−0.259161	−	0.448879i
$537$	−11.2583	−	6.50000i	−0.485833	−	0.280496i
$538$		0			0
$539$	5.50000	−	4.33013i	0.236902	−	0.186512i
$540$		0			0
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	−0.886721	−	0.462304i	$-0.847023\pi$
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	0.843728	+	0.536771i	$0.180356\pi$
$542$	13.8564	−	8.00000i	0.595184	−	0.343629i
$543$	10.3923	−	6.00000i	0.445976	−	0.257485i
$544$	−2.00000	+	3.46410i	−0.0857493	+	0.148522i
$545$		0			0
$546$	14.0000	+	12.1244i	0.599145	+	0.518875i
$547$			36.0000i			1.53925i	0.638497	+	0.769624i	$0.279557\pi$
$547$			36.0000i			1.53925i	−0.638497	+	0.769624i	$0.720443\pi$
$548$	−1.73205	−	1.00000i	−0.0739895	−	0.0427179i
$549$	−2.00000	−	3.46410i	−0.0853579	−	0.147844i
$550$		0			0
$551$	4.00000	−	6.92820i	0.170406	−	0.295151i
$552$			1.00000i			0.0425628i
$553$	3.46410	+	10.0000i	0.147309	+	0.425243i
$554$	2.00000			0.0849719
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	38.9711	−	22.5000i	1.65126	−	0.953356i	0.674705	−	0.738087i	$-0.264271\pi$
$557$	38.9711	−	22.5000i	1.65126	−	0.953356i	0.976555	−	0.215268i	$-0.0690627\pi$
$558$	5.19615	+	3.00000i	0.219971	+	0.127000i
$559$	28.0000			1.18427
$560$		0			0
$561$	4.00000			0.168880
$562$	−2.59808	−	1.50000i	−0.109593	−	0.0632737i
$563$	−12.1244	+	7.00000i	−0.510981	+	0.295015i	−0.733237	−	0.679974i	$-0.761991\pi$
$563$	−12.1244	+	7.00000i	−0.510981	+	0.295015i	0.222256	+	0.974988i	$0.428658\pi$
$564$	−1.50000	−	2.59808i	−0.0631614	−	0.109399i
$565$		0			0
$566$	−2.00000			−0.0840663
$567$	2.59808	+	0.500000i	0.109109	+	0.0209980i
$568$			14.0000i			0.587427i
$569$	−18.5000	+	32.0429i	−0.775560	+	1.34331i	0.158919	+	0.987292i	$0.449199\pi$
$569$	−18.5000	+	32.0429i	−0.775560	+	1.34331i	−0.934479	+	0.356018i	$0.884134\pi$
$570$		0			0
$571$	4.00000	+	6.92820i	0.167395	+	0.289936i	0.937503	−	0.347977i	$-0.113131\pi$
$571$	4.00000	+	6.92820i	0.167395	+	0.289936i	−0.770108	+	0.637913i	$0.779798\pi$
$572$	6.06218	+	3.50000i	0.253472	+	0.146342i
$573$			10.0000i			0.417756i
$574$	22.5000	−	7.79423i	0.939132	−	0.325325i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−12.1244	+	7.00000i	−0.504744	+	0.291414i	−0.730670	−	0.682730i	$-0.760792\pi$
$577$	−12.1244	+	7.00000i	−0.504744	+	0.291414i	0.225927	+	0.974144i	$0.427459\pi$
$578$	0.866025	−	0.500000i	0.0360219	−	0.0207973i
$579$	13.0000	−	22.5167i	0.540262	−	0.935760i
$580$		0			0
$581$	24.0000	+	20.7846i	0.995688	+	0.862291i
$582$		−	16.0000i		−	0.663221i
$583$	0.866025	+	0.500000i	0.0358671	+	0.0207079i
$584$	−7.00000	−	12.1244i	−0.289662	−	0.501709i
$585$		0			0
$586$	−4.50000	+	7.79423i	−0.185893	+	0.321977i
$587$			42.0000i			1.73353i	0.498721	+	0.866763i	$0.333803\pi$
$587$			42.0000i			1.73353i	−0.498721	+	0.866763i	$0.666197\pi$
$588$	−2.59808	+	6.50000i	−0.107143	+	0.268055i
$589$	−6.00000			−0.247226
$590$		0			0
$591$	1.50000	+	2.59808i	0.0617018	+	0.106871i
$592$	−2.59808	+	1.50000i	−0.106780	+	0.0616496i
$593$	10.3923	+	6.00000i	0.426761	+	0.246390i	0.697966	−	0.716131i	$-0.254089\pi$
$593$	10.3923	+	6.00000i	0.426761	+	0.246390i	−0.271205	+	0.962522i	$0.587422\pi$
$594$	1.00000			0.0410305
$595$		0			0
$596$	−4.00000			−0.163846
$597$	10.3923	+	6.00000i	0.425329	+	0.245564i
$598$	−6.06218	+	3.50000i	−0.247901	+	0.143126i
$599$	3.00000	+	5.19615i	0.122577	+	0.212309i	0.920783	−	0.390075i	$-0.127551\pi$
$599$	3.00000	+	5.19615i	0.122577	+	0.212309i	−0.798206	+	0.602384i	$0.794218\pi$
$600$		0			0
$601$	22.0000			0.897399			0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000			0.897399			0.448699	+	0.893683i	$0.351887\pi$
$602$	3.46410	+	10.0000i	0.141186	+	0.407570i
$603$		−	12.0000i		−	0.488678i
$604$	−1.00000	+	1.73205i	−0.0406894	+	0.0704761i
$605$		0			0
$606$		0			0
$607$	−21.6506	−	12.5000i	−0.878772	−	0.507359i	−0.00851879	−	0.999964i	$-0.502712\pi$
$607$	−21.6506	−	12.5000i	−0.878772	−	0.507359i	−0.870253	+	0.492604i	$0.836045\pi$
$608$		−	1.00000i		−	0.0405554i
$609$	4.00000	−	20.7846i	0.162088	−	0.842235i
$610$		0			0
$611$	10.5000	−	18.1865i	0.424785	−	0.735748i
$612$	−3.46410	+	2.00000i	−0.140028	+	0.0808452i
$613$	12.9904	−	7.50000i	0.524677	−	0.302922i	−0.214169	−	0.976797i	$-0.568704\pi$
$613$	12.9904	−	7.50000i	0.524677	−	0.302922i	0.738846	+	0.673874i	$0.235371\pi$
$614$	4.00000	−	6.92820i	0.161427	−	0.279600i
$615$		0			0
$616$	−0.500000	+	2.59808i	−0.0201456	+	0.104679i
$617$			8.00000i			0.322068i	0.986949	+	0.161034i	$0.0514829\pi$
$617$			8.00000i			0.322068i	−0.986949	+	0.161034i	$0.948517\pi$
$618$	13.8564	+	8.00000i	0.557386	+	0.321807i
$619$	−3.50000	−	6.06218i	−0.140677	−	0.243659i	0.787075	−	0.616858i	$-0.211595\pi$
$619$	−3.50000	−	6.06218i	−0.140677	−	0.243659i	−0.927752	+	0.373198i	$0.878261\pi$
$620$		0			0
$621$	−0.500000	+	0.866025i	−0.0200643	+	0.0347524i
$622$			16.0000i			0.641542i
$623$	−1.73205	−	5.00000i	−0.0693932	−	0.200321i
$624$	−7.00000			−0.280224
$625$		0			0
$626$	12.0000	+	20.7846i	0.479616	+	0.830720i
$627$	−0.866025	+	0.500000i	−0.0345857	+	0.0199681i
$628$	12.9904	+	7.50000i	0.518373	+	0.299283i
$629$	−12.0000			−0.478471
$630$		0			0
$631$	14.0000			0.557331			0.278666	−	0.960388i	$-0.410108\pi$
$631$	14.0000			0.557331			0.278666	+	0.960388i	$0.410108\pi$
$632$	−3.46410	−	2.00000i	−0.137795	−	0.0795557i
$633$	12.9904	−	7.50000i	0.516321	−	0.298098i
$634$	5.00000	+	8.66025i	0.198575	+	0.343943i
$635$		0			0
$636$	−1.00000			−0.0396526
$637$	−48.4974	+	7.00000i	−1.92154	+	0.277350i
$638$		−	8.00000i		−	0.316723i
$639$	−7.00000	+	12.1244i	−0.276916	+	0.479632i
$640$		0			0
$641$	11.5000	+	19.9186i	0.454223	+	0.786737i	0.998643	−	0.0520757i	$-0.0165837\pi$
$641$	11.5000	+	19.9186i	0.454223	+	0.786737i	−0.544420	+	0.838812i	$0.683250\pi$
$642$	15.5885	+	9.00000i	0.615227	+	0.355202i
$643$		−	26.0000i		−	1.02534i	−0.858586	−	0.512670i	$-0.828656\pi$
$643$		−	26.0000i		−	1.02534i	0.858586	−	0.512670i	$-0.171344\pi$
$644$	−2.00000	−	1.73205i	−0.0788110	−	0.0682524i
$645$		0			0
$646$	2.00000	−	3.46410i	0.0786889	−	0.136293i
$647$	−12.9904	+	7.50000i	−0.510705	+	0.294855i	−0.733123	−	0.680096i	$-0.761938\pi$
$647$	−12.9904	+	7.50000i	−0.510705	+	0.294855i	0.222419	+	0.974951i	$0.428605\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−6.00000	+	10.3923i	−0.235521	+	0.407934i
$650$		0			0
$651$	−15.0000	+	5.19615i	−0.587896	+	0.203653i
$652$			8.00000i			0.313304i
$653$	25.1147	+	14.5000i	0.982816	+	0.567429i	0.903119	−	0.429390i	$-0.141272\pi$
$653$	25.1147	+	14.5000i	0.982816	+	0.567429i	0.0796966	+	0.996819i	$0.474605\pi$
$654$	−5.00000	−	8.66025i	−0.195515	−	0.338643i
$655$		0			0
$656$	−4.50000	+	7.79423i	−0.175695	+	0.304314i
$657$		−	14.0000i		−	0.546192i
$658$	7.79423	+	1.50000i	0.303851	+	0.0584761i
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$	−4.00000	−	6.92820i	−0.155582	−	0.269476i	0.777689	−	0.628649i	$-0.216392\pi$
$661$	−4.00000	−	6.92820i	−0.155582	−	0.269476i	−0.933271	+	0.359174i	$0.883059\pi$
$662$	−7.79423	+	4.50000i	−0.302931	+	0.174897i
$663$	−24.2487	−	14.0000i	−0.941742	−	0.543715i
$664$	−12.0000			−0.465690
$665$		0			0
$666$	−3.00000			−0.116248
$667$	6.92820	+	4.00000i	0.268261	+	0.154881i
$668$	4.33013	−	2.50000i	0.167538	−	0.0967279i
$669$	−2.00000	−	3.46410i	−0.0773245	−	0.133930i
$670$		0			0
$671$	4.00000			0.154418
$672$	−0.866025	−	2.50000i	−0.0334077	−	0.0964396i
$673$			12.0000i			0.462566i	0.972887	+	0.231283i	$0.0742923\pi$
$673$			12.0000i			0.462566i	−0.972887	+	0.231283i	$0.925708\pi$
$674$		0			0
$675$		0			0
$676$	−18.0000	−	31.1769i	−0.692308	−	1.19911i
$677$	−0.866025	−	0.500000i	−0.0332841	−	0.0192166i	0.483266	−	0.875474i	$-0.339451\pi$
$677$	−0.866025	−	0.500000i	−0.0332841	−	0.0192166i	−0.516550	+	0.856257i	$0.672784\pi$
$678$			6.00000i			0.230429i
$679$	32.0000	+	27.7128i	1.22805	+	1.06352i
$680$		0			0
$681$	10.0000	−	17.3205i	0.383201	−	0.663723i
$682$	−5.19615	+	3.00000i	−0.198971	+	0.114876i
$683$	−10.3923	+	6.00000i	−0.397650	+	0.229584i	−0.685470	−	0.728101i	$-0.740403\pi$
$683$	−10.3923	+	6.00000i	−0.397650	+	0.229584i	0.287819	+	0.957685i	$0.407070\pi$
$684$	0.500000	−	0.866025i	0.0191180	−	0.0331133i
$685$		0			0
$686$	−8.50000	−	16.4545i	−0.324532	−	0.628235i
$687$		−	22.0000i		−	0.839352i
$688$	−3.46410	−	2.00000i	−0.132068	−	0.0762493i
$689$	−3.50000	−	6.06218i	−0.133339	−	0.230951i
$690$		0			0
$691$	−6.00000	+	10.3923i	−0.228251	+	0.395342i	−0.957290	−	0.289130i	$-0.906634\pi$
$691$	−6.00000	+	10.3923i	−0.228251	+	0.395342i	0.729039	+	0.684472i	$0.239967\pi$
$692$		−	21.0000i		−	0.798300i
$693$	−1.73205	+	2.00000i	−0.0657952	+	0.0759737i
$694$	34.0000			1.29062
$695$		0			0
$696$	4.00000	+	6.92820i	0.151620	+	0.262613i
$697$	−31.1769	+	18.0000i	−1.18091	+	0.681799i
$698$	−24.2487	−	14.0000i	−0.917827	−	0.529908i
$699$	−26.0000			−0.983410
$700$		0			0
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$	−6.06218	−	3.50000i	−0.228802	−	0.132099i
$703$	2.59808	−	1.50000i	0.0979883	−	0.0565736i
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$		0			0
$706$	−8.00000			−0.301084
$707$		0			0
$708$		−	12.0000i		−	0.450988i
$709$	2.00000	−	3.46410i	0.0751116	−	0.130097i	−0.826023	−	0.563636i	$-0.809402\pi$
$709$	2.00000	−	3.46410i	0.0751116	−	0.130097i	0.901135	+	0.433539i	$0.142735\pi$
$710$		0			0
$711$	−2.00000	−	3.46410i	−0.0750059	−	0.129914i
$712$	1.73205	+	1.00000i	0.0649113	+	0.0374766i
$713$		−	6.00000i		−	0.224702i
$714$	2.00000	−	10.3923i	0.0748481	−	0.388922i
$715$		0			0
$716$	−6.50000	+	11.2583i	−0.242916	+	0.420744i
$717$	−5.19615	+	3.00000i	−0.194054	+	0.112037i
$718$	−31.1769	+	18.0000i	−1.16351	+	0.671754i
$719$	13.0000	−	22.5167i	0.484818	−	0.839730i	−0.515030	−	0.857172i	$-0.672219\pi$
$719$	13.0000	−	22.5167i	0.484818	−	0.839730i	0.999848	+	0.0174426i	$0.00555244\pi$
$720$		0			0
$721$	−40.0000	+	13.8564i	−1.48968	+	0.516040i
$722$		−	18.0000i		−	0.669891i
$723$	6.06218	+	3.50000i	0.225455	+	0.130166i
$724$	−6.00000	−	10.3923i	−0.222988	−	0.386227i
$725$		0			0
$726$	5.00000	−	8.66025i	0.185567	−	0.321412i
$727$			17.0000i			0.630495i	0.949009	+	0.315248i	$0.102088\pi$
$727$			17.0000i			0.630495i	−0.949009	+	0.315248i	$0.897912\pi$
$728$	12.1244	−	14.0000i	0.449359	−	0.518875i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−8.00000	−	13.8564i	−0.295891	−	0.512498i
$732$	−3.46410	+	2.00000i	−0.128037	+	0.0739221i
$733$	32.0429	+	18.5000i	1.18353	+	0.683313i	0.956829	−	0.290651i	$-0.0938717\pi$
$733$	32.0429	+	18.5000i	1.18353	+	0.683313i	0.226704	+	0.973964i	$0.427205\pi$
$734$	−19.0000			−0.701303
$735$		0			0
$736$	1.00000			0.0368605
$737$	10.3923	+	6.00000i	0.382805	+	0.221013i
$738$	−7.79423	+	4.50000i	−0.286910	+	0.165647i
$739$	20.5000	+	35.5070i	0.754105	+	1.30615i	0.945818	+	0.324697i	$0.105262\pi$
$739$	20.5000	+	35.5070i	0.754105	+	1.30615i	−0.191714	+	0.981451i	$0.561404\pi$
$740$		0			0
$741$	7.00000			0.257151
$742$	1.73205	−	2.00000i	0.0635856	−	0.0734223i
$743$			9.00000i			0.330178i	0.986279	+	0.165089i	$0.0527911\pi$
$743$			9.00000i			0.330178i	−0.986279	+	0.165089i	$0.947209\pi$
$744$	3.00000	−	5.19615i	0.109985	−	0.190500i
$745$		0			0
$746$	−13.0000	−	22.5167i	−0.475964	−	0.824394i
$747$	−10.3923	−	6.00000i	−0.380235	−	0.219529i
$748$		−	4.00000i		−	0.146254i
$749$	−45.0000	+	15.5885i	−1.64426	+	0.569590i
$750$		0			0
$751$	13.0000	−	22.5167i	0.474377	−	0.821645i	−0.525193	−	0.850983i	$-0.676007\pi$
$751$	13.0000	−	22.5167i	0.474377	−	0.821645i	0.999570	+	0.0293387i	$0.00934013\pi$
$752$	−2.59808	+	1.50000i	−0.0947421	+	0.0546994i
$753$	2.59808	−	1.50000i	0.0946792	−	0.0546630i
$754$	−28.0000	+	48.4974i	−1.01970	+	1.76617i
$755$		0			0
$756$	0.500000	−	2.59808i	0.0181848	−	0.0944911i
$757$		−	2.00000i		−	0.0726912i	−0.999339	−	0.0363456i	$-0.988428\pi$
$757$		−	2.00000i		−	0.0726912i	0.999339	−	0.0363456i	$-0.0115717\pi$
$758$	0.866025	+	0.500000i	0.0314555	+	0.0181608i
$759$	−0.500000	−	0.866025i	−0.0181489	−	0.0314347i
$760$		0			0
$761$	8.50000	−	14.7224i	0.308125	−	0.533688i	−0.669827	−	0.742517i	$-0.733632\pi$
$761$	8.50000	−	14.7224i	0.308125	−	0.533688i	0.977952	+	0.208829i	$0.0669652\pi$
$762$			5.00000i			0.181131i
$763$	25.9808	+	5.00000i	0.940567	+	0.181012i
$764$	10.0000			0.361787
$765$		0			0
$766$	−6.50000	−	11.2583i	−0.234855	−	0.406780i
$767$	72.7461	−	42.0000i	2.62671	−	1.51653i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	29.0000			1.04577			0.522883	−	0.852404i	$-0.324856\pi$
$769$	29.0000			1.04577			0.522883	+	0.852404i	$0.324856\pi$
$770$		0			0
$771$	−8.00000			−0.288113
$772$	−22.5167	−	13.0000i	−0.810392	−	0.467880i
$773$	−37.2391	+	21.5000i	−1.33940	+	0.773301i	−0.986718	−	0.162443i	$-0.948063\pi$
$773$	−37.2391	+	21.5000i	−1.33940	+	0.773301i	−0.352679	+	0.935744i	$0.614729\pi$
$774$	−2.00000	−	3.46410i	−0.0718885	−	0.124515i
$775$		0			0
$776$	−16.0000			−0.574367
$777$	5.19615	−	6.00000i	0.186411	−	0.215249i
$778$			14.0000i			0.501924i
$779$	4.50000	−	7.79423i	0.161229	−	0.279257i
$780$		0			0
$781$	−7.00000	−	12.1244i	−0.250480	−	0.433844i
$782$	3.46410	+	2.00000i	0.123876	+	0.0715199i
$783$			8.00000i			0.285897i
$784$	6.50000	+	2.59808i	0.232143	+	0.0927884i
$785$		0			0
$786$	6.50000	−	11.2583i	0.231847	−	0.401571i
$787$	−19.0526	+	11.0000i	−0.679150	+	0.392108i	−0.799535	−	0.600620i	$-0.794921\pi$
$787$	−19.0526	+	11.0000i	−0.679150	+	0.392108i	0.120384	+	0.992727i	$0.461587\pi$
$788$	2.59808	−	1.50000i	0.0925526	−	0.0534353i
$789$	−8.00000	+	13.8564i	−0.284808	+	0.493301i
$790$		0			0
$791$	−12.0000	−	10.3923i	−0.426671	−	0.369508i
$792$		−	1.00000i		−	0.0355335i
$793$	−24.2487	−	14.0000i	−0.861097	−	0.497155i
$794$	9.00000	+	15.5885i	0.319398	+	0.553214i
$795$		0			0
$796$	6.00000	−	10.3923i	0.212664	−	0.368345i
$797$		−	6.00000i		−	0.212531i	−0.994338	−	0.106265i	$-0.966111\pi$
$797$		−	6.00000i		−	0.212531i	0.994338	−	0.106265i	$-0.0338893\pi$
$798$	0.866025	+	2.50000i	0.0306570	+	0.0884990i
$799$	−12.0000			−0.424529
$800$		0			0
$801$	1.00000	+	1.73205i	0.0353333	+	0.0611990i
$802$	−14.7224	+	8.50000i	−0.519867	+	0.300145i
$803$	12.1244	+	7.00000i	0.427859	+	0.247025i
$804$	−12.0000			−0.423207
$805$		0			0
$806$	42.0000			1.47939
$807$		0			0
$808$		0			0
$809$	26.5000	+	45.8993i	0.931690	+	1.61374i	0.780432	+	0.625241i	$0.214999\pi$
$809$	26.5000	+	45.8993i	0.931690	+	1.61374i	0.151259	+	0.988494i	$0.451667\pi$
$810$		0			0
$811$	37.0000			1.29925			0.649623	−	0.760257i	$-0.274927\pi$
$811$	37.0000			1.29925			0.649623	+	0.760257i	$0.274927\pi$
$812$	−20.7846	−	4.00000i	−0.729397	−	0.140372i
$813$		−	16.0000i		−	0.561144i
$814$	1.50000	−	2.59808i	0.0525750	−	0.0910625i
$815$		0			0
$816$	2.00000	+	3.46410i	0.0700140	+	0.121268i
$817$	3.46410	+	2.00000i	0.121194	+	0.0699711i
$818$		−	10.0000i		−	0.349642i
$819$	17.5000	−	6.06218i	0.611499	−	0.211830i
$820$		0			0
$821$	−17.0000	+	29.4449i	−0.593304	+	1.02763i	0.400480	+	0.916306i	$0.368843\pi$
$821$	−17.0000	+	29.4449i	−0.593304	+	1.02763i	−0.993784	+	0.111327i	$0.964490\pi$
$822$	−1.73205	+	1.00000i	−0.0604122	+	0.0348790i
$823$	−41.5692	+	24.0000i	−1.44901	+	0.836587i	−0.998423	−	0.0561440i	$-0.982119\pi$
$823$	−41.5692	+	24.0000i	−1.44901	+	0.836587i	−0.450589	+	0.892731i	$0.648786\pi$
$824$	8.00000	−	13.8564i	0.278693	−	0.482711i
$825$		0			0
$826$	24.0000	+	20.7846i	0.835067	+	0.723189i
$827$			10.0000i			0.347734i	0.984769	+	0.173867i	$0.0556263\pi$
$827$			10.0000i			0.347734i	−0.984769	+	0.173867i	$0.944374\pi$
$828$	0.866025	+	0.500000i	0.0300965	+	0.0173762i
$829$	6.00000	+	10.3923i	0.208389	+	0.360940i	0.951207	−	0.308553i	$-0.0998448\pi$
$829$	6.00000	+	10.3923i	0.208389	+	0.360940i	−0.742818	+	0.669493i	$0.766511\pi$
$830$		0			0
$831$	1.00000	−	1.73205i	0.0346896	−	0.0600842i
$832$			7.00000i			0.242681i
$833$	17.3205	+	22.0000i	0.600120	+	0.762255i
$834$	4.00000			0.138509
$835$		0			0
$836$	0.500000	+	0.866025i	0.0172929	+	0.0299521i
$837$	5.19615	−	3.00000i	0.179605	−	0.103695i
$838$	9.52628	+	5.50000i	0.329080	+	0.189994i
$839$	−44.0000			−1.51905			−0.759524	−	0.650479i	$-0.774568\pi$
$839$	−44.0000			−1.51905			−0.759524	+	0.650479i	$0.774568\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$	12.1244	+	7.00000i	0.417833	+	0.241236i
$843$	−2.59808	+	1.50000i	−0.0894825	+	0.0516627i
$844$	−7.50000	−	12.9904i	−0.258161	−	0.447147i
$845$		0			0
$846$	−3.00000			−0.103142
$847$	8.66025	+	25.0000i	0.297570	+	0.859010i
$848$			1.00000i			0.0343401i
$849$	−1.00000	+	1.73205i	−0.0343199	+	0.0594438i
$850$		0			0
$851$	1.50000	+	2.59808i	0.0514193	+	0.0890609i
$852$	12.1244	+	7.00000i	0.415374	+	0.239816i
$853$		−	1.00000i		−	0.0342393i	−0.999853	−	0.0171197i	$-0.994550\pi$
$853$		−	1.00000i		−	0.0342393i	0.999853	−	0.0171197i	$-0.00544963\pi$
$854$	2.00000	−	10.3923i	0.0684386	−	0.355617i
$855$		0			0
$856$	9.00000	−	15.5885i	0.307614	−	0.532803i
$857$	−19.0526	+	11.0000i	−0.650823	+	0.375753i	−0.788771	−	0.614687i	$-0.789283\pi$
$857$	−19.0526	+	11.0000i	−0.650823	+	0.375753i	0.137948	+	0.990439i	$0.455949\pi$
$858$	6.06218	−	3.50000i	0.206959	−	0.119488i
$859$	−10.0000	+	17.3205i	−0.341196	+	0.590968i	−0.984655	−	0.174512i	$-0.944165\pi$
$859$	−10.0000	+	17.3205i	−0.341196	+	0.590968i	0.643459	+	0.765480i	$0.277499\pi$
$860$		0			0
$861$	4.50000	−	23.3827i	0.153360	−	0.796880i
$862$		−	12.0000i		−	0.408722i
$863$	25.1147	+	14.5000i	0.854916	+	0.493586i	0.862306	−	0.506387i	$-0.169019\pi$
$863$	25.1147	+	14.5000i	0.854916	+	0.493586i	−0.00739078	+	0.999973i	$0.502353\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$		0			0
$866$	−20.0000	+	34.6410i	−0.679628	+	1.17715i
$867$		−	1.00000i		−	0.0339618i
$868$	5.19615	+	15.0000i	0.176369	+	0.509133i
$869$	4.00000			0.135691
$870$		0			0
$871$	−42.0000	−	72.7461i	−1.42312	−	2.46491i
$872$	−8.66025	+	5.00000i	−0.293273	+	0.169321i
$873$	−13.8564	−	8.00000i	−0.468968	−	0.270759i
$874$	−1.00000			−0.0338255
$875$		0			0
$876$	−14.0000			−0.473016
$877$	−19.9186	−	11.5000i	−0.672603	−	0.388327i	0.124459	−	0.992225i	$-0.460280\pi$
$877$	−19.9186	−	11.5000i	−0.672603	−	0.388327i	−0.797062	+	0.603897i	$0.793614\pi$
$878$	−13.8564	+	8.00000i	−0.467631	+	0.269987i
$879$	4.50000	+	7.79423i	0.151781	+	0.262893i
$880$		0			0
$881$	−25.0000			−0.842271			−0.421136	−	0.906998i	$-0.638368\pi$
$881$	−25.0000			−0.842271			−0.421136	+	0.906998i	$0.638368\pi$
$882$	4.33013	+	5.50000i	0.145803	+	0.185195i
$883$			58.0000i			1.95186i	0.218094	+	0.975928i	$0.430016\pi$
$883$			58.0000i			1.95186i	−0.218094	+	0.975928i	$0.569984\pi$
$884$	−14.0000	+	24.2487i	−0.470871	+	0.815572i
$885$		0			0
$886$	18.0000	+	31.1769i	0.604722	+	1.04741i
$887$	−17.3205	−	10.0000i	−0.581566	−	0.335767i	0.180190	−	0.983632i	$-0.442329\pi$
$887$	−17.3205	−	10.0000i	−0.581566	−	0.335767i	−0.761755	+	0.647865i	$0.775662\pi$
$888$			3.00000i			0.100673i
$889$	−10.0000	−	8.66025i	−0.335389	−	0.290456i
$890$		0			0
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	−3.46410	+	2.00000i	−0.115987	+	0.0669650i
$893$	2.59808	−	1.50000i	0.0869413	−	0.0501956i
$894$	−2.00000	+	3.46410i	−0.0668900	+	0.115857i
$895$		0			0
$896$	−2.50000	+	0.866025i	−0.0835191	+	0.0289319i
$897$			7.00000i			0.233723i
$898$	−21.6506	−	12.5000i	−0.722491	−	0.417130i
$899$	−24.0000	−	41.5692i	−0.800445	−	1.38641i
$900$		0			0
$901$	−2.00000	+	3.46410i	−0.0666297	+	0.115406i
$902$		−	9.00000i		−	0.299667i
$903$	10.3923	+	2.00000i	0.345834	+	0.0665558i
$904$	6.00000			0.199557
$905$		0			0
$906$	1.00000	+	1.73205i	0.0332228	+	0.0575435i
$907$	39.8372	−	23.0000i	1.32277	−	0.763702i	0.338602	−	0.940930i	$-0.390046\pi$
$907$	39.8372	−	23.0000i	1.32277	−	0.763702i	0.984170	+	0.177227i	$0.0567128\pi$
$908$	−17.3205	−	10.0000i	−0.574801	−	0.331862i
$909$		0			0
$910$		0			0
$911$	−58.0000			−1.92163			−0.960813	−	0.277198i	$-0.910594\pi$
$911$	−58.0000			−1.92163			−0.960813	+	0.277198i	$0.910594\pi$
$912$	−0.866025	−	0.500000i	−0.0286770	−	0.0165567i
$913$	10.3923	−	6.00000i	0.343935	−	0.198571i
$914$	5.00000	+	8.66025i	0.165385	+	0.286456i
$915$		0			0
$916$	−22.0000			−0.726900
$917$	11.2583	+	32.5000i	0.371783	+	1.07324i
$918$			4.00000i			0.132020i
$919$	−22.0000	+	38.1051i	−0.725713	+	1.25697i	0.232967	+	0.972485i	$0.425157\pi$
$919$	−22.0000	+	38.1051i	−0.725713	+	1.25697i	−0.958680	+	0.284487i	$0.908177\pi$
$920$		0			0
$921$	−4.00000	−	6.92820i	−0.131804	−	0.228292i
$922$	24.2487	+	14.0000i	0.798589	+	0.461065i
$923$			98.0000i			3.22571i
$924$	2.00000	+	1.73205i	0.0657952	+	0.0569803i
$925$		0			0
$926$	−16.5000	+	28.5788i	−0.542224	+	0.939159i
$927$	13.8564	−	8.00000i	0.455104	−	0.262754i
$928$	6.92820	−	4.00000i	0.227429	−	0.131306i
$929$	15.5000	−	26.8468i	0.508539	−	0.880815i	−0.491413	−	0.870927i	$-0.663519\pi$
$929$	15.5000	−	26.8468i	0.508539	−	0.880815i	0.999951	−	0.00988764i	$-0.00314738\pi$
$930$		0			0
$931$	−6.50000	−	2.59808i	−0.213029	−	0.0851485i
$932$			26.0000i			0.851658i
$933$	13.8564	+	8.00000i	0.453638	+	0.261908i
$934$	6.00000	+	10.3923i	0.196326	+	0.340047i
$935$		0			0
$936$	−3.50000	+	6.06218i	−0.114401	+	0.198148i
$937$			16.0000i			0.522697i	0.965244	+	0.261349i	$0.0841672\pi$
$937$			16.0000i			0.522697i	−0.965244	+	0.261349i	$0.915833\pi$
$938$	20.7846	−	24.0000i	0.678642	−	0.783628i
$939$	24.0000			0.783210
$940$		0			0
$941$	15.0000	+	25.9808i	0.488986	+	0.846949i	0.999920	−	0.0126715i	$-0.00403357\pi$
$941$	15.0000	+	25.9808i	0.488986	+	0.846949i	−0.510934	+	0.859620i	$0.670700\pi$
$942$	12.9904	−	7.50000i	0.423249	−	0.244363i
$943$	7.79423	+	4.50000i	0.253815	+	0.146540i
$944$	−12.0000			−0.390567
$945$		0			0
$946$	4.00000			0.130051
$947$	−39.8372	−	23.0000i	−1.29453	−	0.747400i	−0.315080	−	0.949065i	$-0.602031\pi$
$947$	−39.8372	−	23.0000i	−1.29453	−	0.747400i	−0.979454	+	0.201666i	$0.935365\pi$
$948$	−3.46410	+	2.00000i	−0.112509	+	0.0649570i
$949$	−49.0000	−	84.8705i	−1.59061	−	2.75501i
$950$		0			0
$951$	10.0000			0.324272
$952$	−10.3923	−	2.00000i	−0.336817	−	0.0648204i
$953$		−	44.0000i		−	1.42530i	−0.701520	−	0.712650i	$-0.747495\pi$
$953$		−	44.0000i		−	1.42530i	0.701520	−	0.712650i	$-0.252505\pi$
$954$	−0.500000	+	0.866025i	−0.0161881	+	0.0280386i
$955$		0			0
$956$	3.00000	+	5.19615i	0.0970269	+	0.168056i
$957$	−6.92820	−	4.00000i	−0.223957	−	0.129302i
$958$		−	26.0000i		−	0.840022i
$959$	1.00000	−	5.19615i	0.0322917	−	0.167793i
$960$		0			0
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	−18.1865	+	10.5000i	−0.586357	+	0.338534i
$963$	15.5885	−	9.00000i	0.502331	−	0.290021i
$964$	3.50000	−	6.06218i	0.112727	−	0.195250i
$965$		0			0
$966$	−2.50000	+	0.866025i	−0.0804362	+	0.0278639i
$967$		−	20.0000i		−	0.643157i	−0.946883	−	0.321578i	$-0.895787\pi$
$967$		−	20.0000i		−	0.643157i	0.946883	−	0.321578i	$-0.104213\pi$
$968$	−8.66025	−	5.00000i	−0.278351	−	0.160706i
$969$	−2.00000	−	3.46410i	−0.0642493	−	0.111283i
$970$		0			0
$971$	−21.5000	+	37.2391i	−0.689968	+	1.19506i	0.281880	+	0.959450i	$0.409042\pi$
$971$	−21.5000	+	37.2391i	−0.689968	+	1.19506i	−0.971848	+	0.235610i	$0.924291\pi$
$972$			1.00000i			0.0320750i
$973$	−6.92820	+	8.00000i	−0.222108	+	0.256468i
$974$	8.00000			0.256337
$975$		0			0
$976$	2.00000	+	3.46410i	0.0640184	+	0.110883i
$977$	15.5885	−	9.00000i	0.498719	−	0.287936i	−0.229465	−	0.973317i	$-0.573698\pi$
$977$	15.5885	−	9.00000i	0.498719	−	0.287936i	0.728184	+	0.685381i	$0.240364\pi$
$978$	6.92820	+	4.00000i	0.221540	+	0.127906i
$979$	−2.00000			−0.0639203
$980$		0			0
$981$	−10.0000			−0.319275
$982$	10.3923	+	6.00000i	0.331632	+	0.191468i
$983$	28.5788	−	16.5000i	0.911523	−	0.526268i	0.0306024	−	0.999532i	$-0.490257\pi$
$983$	28.5788	−	16.5000i	0.911523	−	0.526268i	0.880921	+	0.473263i	$0.156924\pi$
$984$	4.50000	+	7.79423i	0.143455	+	0.248471i
$985$		0			0
$986$	32.0000			1.01909
$987$	5.19615	−	6.00000i	0.165395	−	0.190982i
$988$		−	7.00000i		−	0.222700i
$989$	−2.00000	+	3.46410i	−0.0635963	+	0.110152i
$990$		0			0
$991$	−5.00000	−	8.66025i	−0.158830	−	0.275102i	0.775617	−	0.631204i	$-0.217439\pi$
$991$	−5.00000	−	8.66025i	−0.158830	−	0.275102i	−0.934447	+	0.356102i	$0.884106\pi$
$992$	−5.19615	−	3.00000i	−0.164978	−	0.0952501i
$993$			9.00000i			0.285606i
$994$	−35.0000	+	12.1244i	−1.11013	+	0.384561i
$995$		0			0
$996$	−6.00000	+	10.3923i	−0.190117	+	0.329293i
$997$	8.66025	−	5.00000i	0.274273	−	0.158352i	−0.356555	−	0.934274i	$-0.616049\pi$
$997$	8.66025	−	5.00000i	0.274273	−	0.158352i	0.630828	+	0.775923i	$0.282715\pi$
$998$	−20.7846	+	12.0000i	−0.657925	+	0.379853i
$999$	−1.50000	+	2.59808i	−0.0474579	+	0.0821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.o.j.499.1		4
5.2	odd	4		1050.2.i.s.751.1		2
5.3	odd	4		210.2.i.a.121.1	✓	2
5.4	even	2	inner	1050.2.o.j.499.2		4
7.4	even	3	inner	1050.2.o.j.949.2		4
15.8	even	4		630.2.k.h.541.1		2
20.3	even	4		1680.2.bg.k.961.1		2
35.2	odd	12		7350.2.a.j.1.1		1
35.3	even	12		1470.2.i.i.361.1		2
35.4	even	6	inner	1050.2.o.j.949.1		4
35.12	even	12		7350.2.a.ba.1.1		1
35.13	even	4		1470.2.i.i.961.1		2
35.18	odd	12		210.2.i.a.151.1	yes	2
35.23	odd	12		1470.2.a.r.1.1		1
35.32	odd	12		1050.2.i.s.151.1		2
35.33	even	12		1470.2.a.k.1.1		1
105.23	even	12		4410.2.a.g.1.1		1
105.53	even	12		630.2.k.h.361.1		2
105.68	odd	12		4410.2.a.q.1.1		1
140.123	even	12		1680.2.bg.k.1201.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.i.a.121.1	✓	2	5.3	odd	4
210.2.i.a.151.1	yes	2	35.18	odd	12
630.2.k.h.361.1		2	105.53	even	12
630.2.k.h.541.1		2	15.8	even	4
1050.2.i.s.151.1		2	35.32	odd	12
1050.2.i.s.751.1		2	5.2	odd	4
1050.2.o.j.499.1		4	1.1	even	1	trivial
1050.2.o.j.499.2		4	5.4	even	2	inner
1050.2.o.j.949.1		4	35.4	even	6	inner
1050.2.o.j.949.2		4	7.4	even	3	inner
1470.2.a.k.1.1		1	35.33	even	12
1470.2.a.r.1.1		1	35.23	odd	12
1470.2.i.i.361.1		2	35.3	even	12
1470.2.i.i.961.1		2	35.13	even	4
1680.2.bg.k.961.1		2	20.3	even	4
1680.2.bg.k.1201.1		2	140.123	even	12
4410.2.a.g.1.1		1	105.23	even	12
4410.2.a.q.1.1		1	105.68	odd	12
7350.2.a.j.1.1		1	35.2	odd	12
7350.2.a.ba.1.1		1	35.12	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-1.73205 + 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-1.73205 + 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-0.866025 - 0.500000i) q^{12} -7.00000i q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.46410 + 2.00000i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(0.500000 - 0.866025i) q^{19} +(0.500000 - 2.59808i) q^{21} -1.00000i q^{22} +(0.866025 + 0.500000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.50000 + 6.06218i) q^{26} +1.00000i q^{27} +(-2.59808 - 0.500000i) q^{28} +8.00000 q^{29} +(-3.00000 - 5.19615i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.866025 - 0.500000i) q^{33} +4.00000 q^{34} +1.00000 q^{36} +(2.59808 + 1.50000i) q^{37} +(-0.866025 + 0.500000i) q^{38} +(3.50000 + 6.06218i) q^{39} +9.00000 q^{41} +(-1.73205 + 2.00000i) q^{42} +4.00000i q^{43} +(-0.500000 + 0.866025i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(2.59808 + 1.50000i) q^{47} -1.00000i q^{48} +(-1.00000 - 6.92820i) q^{49} +(2.00000 - 3.46410i) q^{51} +(6.06218 - 3.50000i) q^{52} +(0.866025 - 0.500000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.00000 + 1.73205i) q^{56} +1.00000i q^{57} +(-6.92820 - 4.00000i) q^{58} +(6.00000 + 10.3923i) q^{59} +(2.00000 - 3.46410i) q^{61} +6.00000i q^{62} +(0.866025 + 2.50000i) q^{63} -1.00000 q^{64} +(0.500000 + 0.866025i) q^{66} +(10.3923 - 6.00000i) q^{67} +(-3.46410 - 2.00000i) q^{68} -1.00000 q^{69} -14.0000 q^{71} +(-0.866025 - 0.500000i) q^{72} +(12.1244 - 7.00000i) q^{73} +(-1.50000 - 2.59808i) q^{74} +1.00000 q^{76} +(-2.59808 - 0.500000i) q^{77} -7.00000i q^{78} +(2.00000 - 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-7.79423 - 4.50000i) q^{82} -12.0000i q^{83} +(2.50000 - 0.866025i) q^{84} +(2.00000 - 3.46410i) q^{86} +(-6.92820 + 4.00000i) q^{87} +(0.866025 - 0.500000i) q^{88} +(-1.00000 + 1.73205i) q^{89} +(14.0000 + 12.1244i) q^{91} +1.00000i q^{92} +(5.19615 + 3.00000i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(-0.500000 + 0.866025i) q^{96} -16.0000i q^{97} +(-2.59808 + 6.50000i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9} + 2 q^{11} + 10 q^{14} - 2 q^{16} + 2 q^{19} + 2 q^{21} + 2 q^{24} - 14 q^{26} + 32 q^{29} - 12 q^{31} + 16 q^{34} + 4 q^{36} + 14 q^{39} + 36 q^{41} - 2 q^{44} - 2 q^{46} - 4 q^{49} + 8 q^{51} + 2 q^{54} + 8 q^{56} + 24 q^{59} + 8 q^{61} - 4 q^{64} + 2 q^{66} - 4 q^{69} - 56 q^{71} - 6 q^{74} + 4 q^{76} + 8 q^{79} - 2 q^{81} + 10 q^{84} + 8 q^{86} - 4 q^{89} + 56 q^{91} - 6 q^{94} - 2 q^{96} + 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9 + 2 * q^11 + 10 * q^14 - 2 * q^16 + 2 * q^19 + 2 * q^21 + 2 * q^24 - 14 * q^26 + 32 * q^29 - 12 * q^31 + 16 * q^34 + 4 * q^36 + 14 * q^39 + 36 * q^41 - 2 * q^44 - 2 * q^46 - 4 * q^49 + 8 * q^51 + 2 * q^54 + 8 * q^56 + 24 * q^59 + 8 * q^61 - 4 * q^64 + 2 * q^66 - 4 * q^69 - 56 * q^71 - 6 * q^74 + 4 * q^76 + 8 * q^79 - 2 * q^81 + 10 * q^84 + 8 * q^86 - 4 * q^89 + 56 * q^91 - 6 * q^94 - 2 * q^96 + 4 * q^99

Introduction

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