LMFDB - Embedded newform 1950.2.i.y.601.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(451,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1950.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.i (of order $3$, 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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.601
Dual form			1950.2.i.y.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-1.36603 + 2.36603i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-1.36603 + 2.36603i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.366025 - 0.633975i) q^{11} +1.00000 q^{12} +(0.232051 - 3.59808i) q^{13} +2.73205 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.23205 + 3.86603i) q^{17} +1.00000 q^{18} +(-0.633975 + 1.09808i) q^{19} +2.73205 q^{21} +(-0.366025 + 0.633975i) q^{22} +(-3.09808 - 5.36603i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.23205 + 1.59808i) q^{26} +1.00000 q^{27} +(-1.36603 - 2.36603i) q^{28} +(3.23205 + 5.59808i) q^{29} +4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.366025 + 0.633975i) q^{33} +4.46410 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-3.96410 - 6.86603i) q^{37} +1.26795 q^{38} +(-3.23205 + 1.59808i) q^{39} +(4.59808 + 7.96410i) q^{41} +(-1.36603 - 2.36603i) q^{42} +(1.63397 - 2.83013i) q^{43} +0.732051 q^{44} +(-3.09808 + 5.36603i) q^{46} +7.66025 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.232051 - 0.401924i) q^{49} +4.46410 q^{51} +(3.00000 + 2.00000i) q^{52} +7.73205 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-1.36603 + 2.36603i) q^{56} +1.26795 q^{57} +(3.23205 - 5.59808i) q^{58} +(6.19615 - 10.7321i) q^{59} +(5.06218 - 8.76795i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-1.36603 - 2.36603i) q^{63} +1.00000 q^{64} +0.732051 q^{66} +(-3.83013 - 6.63397i) q^{67} +(-2.23205 - 3.86603i) q^{68} +(-3.09808 + 5.36603i) q^{69} +(-0.633975 + 1.09808i) q^{71} +(-0.500000 + 0.866025i) q^{72} -4.66025 q^{73} +(-3.96410 + 6.86603i) q^{74} +(-0.633975 - 1.09808i) q^{76} +2.00000 q^{77} +(3.00000 + 2.00000i) q^{78} +12.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(4.59808 - 7.96410i) q^{82} +5.26795 q^{83} +(-1.36603 + 2.36603i) q^{84} -3.26795 q^{86} +(3.23205 - 5.59808i) q^{87} +(-0.366025 - 0.633975i) q^{88} +(2.46410 + 4.26795i) q^{89} +(8.19615 + 5.46410i) q^{91} +6.19615 q^{92} +(-2.00000 - 3.46410i) q^{93} +(-3.83013 - 6.63397i) q^{94} +1.00000 q^{96} +(5.00000 - 8.66025i) q^{97} +(-0.232051 + 0.401924i) q^{98} +0.732051 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + 2 q^{11} + 4 q^{12} - 6 q^{13} + 4 q^{14} - 2 q^{16} - 2 q^{17} + 4 q^{18} - 6 q^{19} + 4 q^{21} + 2 q^{22} - 2 q^{23} - 2 q^{24} - 6 q^{26} + 4 q^{27} - 2 q^{28} + 6 q^{29} + 16 q^{31} - 2 q^{32} + 2 q^{33} + 4 q^{34} - 2 q^{36} - 2 q^{37} + 12 q^{38} - 6 q^{39} + 8 q^{41} - 2 q^{42} + 10 q^{43} - 4 q^{44} - 2 q^{46} - 4 q^{47} - 2 q^{48} + 6 q^{49} + 4 q^{51} + 12 q^{52} + 24 q^{53} - 2 q^{54} - 2 q^{56} + 12 q^{57} + 6 q^{58} + 4 q^{59} - 4 q^{61} - 8 q^{62} - 2 q^{63} + 4 q^{64} - 4 q^{66} + 2 q^{67} - 2 q^{68} - 2 q^{69} - 6 q^{71} - 2 q^{72} + 16 q^{73} - 2 q^{74} - 6 q^{76} + 8 q^{77} + 12 q^{78} + 48 q^{79} - 2 q^{81} + 8 q^{82} + 28 q^{83} - 2 q^{84} - 20 q^{86} + 6 q^{87} + 2 q^{88} - 4 q^{89} + 12 q^{91} + 4 q^{92} - 8 q^{93} + 2 q^{94} + 4 q^{96} + 20 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 + 2 * q^11 + 4 * q^12 - 6 * q^13 + 4 * q^14 - 2 * q^16 - 2 * q^17 + 4 * q^18 - 6 * q^19 + 4 * q^21 + 2 * q^22 - 2 * q^23 - 2 * q^24 - 6 * q^26 + 4 * q^27 - 2 * q^28 + 6 * q^29 + 16 * q^31 - 2 * q^32 + 2 * q^33 + 4 * q^34 - 2 * q^36 - 2 * q^37 + 12 * q^38 - 6 * q^39 + 8 * q^41 - 2 * q^42 + 10 * q^43 - 4 * q^44 - 2 * q^46 - 4 * q^47 - 2 * q^48 + 6 * q^49 + 4 * q^51 + 12 * q^52 + 24 * q^53 - 2 * q^54 - 2 * q^56 + 12 * q^57 + 6 * q^58 + 4 * q^59 - 4 * q^61 - 8 * q^62 - 2 * q^63 + 4 * q^64 - 4 * q^66 + 2 * q^67 - 2 * q^68 - 2 * q^69 - 6 * q^71 - 2 * q^72 + 16 * q^73 - 2 * q^74 - 6 * q^76 + 8 * q^77 + 12 * q^78 + 48 * q^79 - 2 * q^81 + 8 * q^82 + 28 * q^83 - 2 * q^84 - 20 * q^86 + 6 * q^87 + 2 * q^88 - 4 * q^89 + 12 * q^91 + 4 * q^92 - 8 * q^93 + 2 * q^94 + 4 * q^96 + 20 * q^97 + 6 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−1.36603	+	2.36603i	−0.516309	+	0.894274i	0.483512	+	0.875338i	$0.339361\pi$
$7$	−1.36603	+	2.36603i	−0.516309	+	0.894274i	−0.999821	+	0.0189356i	$0.993972\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−0.366025	−	0.633975i	−0.110361	−	0.191151i	0.805555	−	0.592521i	$-0.201867\pi$
$11$	−0.366025	−	0.633975i	−0.110361	−	0.191151i	−0.915916	+	0.401371i	$0.868534\pi$
$12$	1.00000			0.288675
$13$	0.232051	−	3.59808i	0.0643593	−	0.997927i
$13$	0.232051	−	3.59808i	0.0643593	−	0.997927i
$14$	2.73205			0.730171
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.23205	+	3.86603i	−0.541352	+	0.937649i	0.457475	+	0.889223i	$0.348754\pi$
$17$	−2.23205	+	3.86603i	−0.541352	+	0.937649i	−0.998827	+	0.0484264i	$0.984579\pi$
$18$	1.00000			0.235702
$19$	−0.633975	+	1.09808i	−0.145444	+	0.251916i	−0.929538	−	0.368725i	$-0.879794\pi$
$19$	−0.633975	+	1.09808i	−0.145444	+	0.251916i	0.784095	+	0.620641i	$0.213128\pi$
$20$		0			0
$21$	2.73205			0.596182
$22$	−0.366025	+	0.633975i	−0.0780369	+	0.135164i
$23$	−3.09808	−	5.36603i	−0.645994	−	1.11889i	−0.984071	−	0.177775i	$-0.943110\pi$
$23$	−3.09808	−	5.36603i	−0.645994	−	1.11889i	0.338078	−	0.941118i	$-0.390223\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$		0			0
$26$	−3.23205	+	1.59808i	−0.633857	+	0.313409i
$27$	1.00000			0.192450
$28$	−1.36603	−	2.36603i	−0.258155	−	0.447137i
$29$	3.23205	+	5.59808i	0.600177	+	1.03954i	0.992794	+	0.119835i	$0.0382364\pi$
$29$	3.23205	+	5.59808i	0.600177	+	1.03954i	−0.392617	+	0.919702i	$0.628430\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.366025	+	0.633975i	−0.0637168	+	0.110361i
$34$	4.46410			0.765587
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−3.96410	−	6.86603i	−0.651694	−	1.12877i	−0.982712	−	0.185143i	$-0.940725\pi$
$37$	−3.96410	−	6.86603i	−0.651694	−	1.12877i	0.331017	−	0.943625i	$-0.392608\pi$
$38$	1.26795			0.205689
$39$	−3.23205	+	1.59808i	−0.517542	+	0.255897i
$40$		0			0
$41$	4.59808	+	7.96410i	0.718099	+	1.24378i	0.961752	+	0.273921i	$0.0883208\pi$
$41$	4.59808	+	7.96410i	0.718099	+	1.24378i	−0.243653	+	0.969862i	$0.578346\pi$
$42$	−1.36603	−	2.36603i	−0.210782	−	0.365086i
$43$	1.63397	−	2.83013i	0.249179	−	0.431590i	−0.714119	−	0.700024i	$-0.753173\pi$
$43$	1.63397	−	2.83013i	0.249179	−	0.431590i	0.963298	+	0.268434i	$0.0865060\pi$
$44$	0.732051			0.110361
$45$		0			0
$46$	−3.09808	+	5.36603i	−0.456786	+	0.791177i
$47$	7.66025			1.11736			0.558681	−	0.829382i	$-0.311307\pi$
$47$	7.66025			1.11736			0.558681	+	0.829382i	$0.311307\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−0.232051	−	0.401924i	−0.0331501	−	0.0574177i
$50$		0			0
$51$	4.46410			0.625099
$52$	3.00000	+	2.00000i	0.416025	+	0.277350i
$53$	7.73205			1.06208			0.531039	−	0.847347i	$-0.321802\pi$
$53$	7.73205			1.06208			0.531039	+	0.847347i	$0.321802\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$	−1.36603	+	2.36603i	−0.182543	+	0.316173i
$57$	1.26795			0.167944
$58$	3.23205	−	5.59808i	0.424389	−	0.735063i
$59$	6.19615	−	10.7321i	0.806670	−	1.39719i	−0.108487	−	0.994098i	$-0.534601\pi$
$59$	6.19615	−	10.7321i	0.806670	−	1.39719i	0.915158	−	0.403096i	$-0.132066\pi$
$60$		0			0
$61$	5.06218	−	8.76795i	0.648145	−	1.12262i	−0.335420	−	0.942069i	$-0.608878\pi$
$61$	5.06218	−	8.76795i	0.648145	−	1.12262i	0.983565	−	0.180552i	$-0.0577885\pi$
$62$	−2.00000	−	3.46410i	−0.254000	−	0.439941i
$63$	−1.36603	−	2.36603i	−0.172103	−	0.298091i
$64$	1.00000			0.125000
$65$		0			0
$66$	0.732051			0.0901092
$67$	−3.83013	−	6.63397i	−0.467924	−	0.810469i	0.531404	−	0.847119i	$-0.321665\pi$
$67$	−3.83013	−	6.63397i	−0.467924	−	0.810469i	−0.999328	+	0.0366497i	$0.988331\pi$
$68$	−2.23205	−	3.86603i	−0.270676	−	0.468824i
$69$	−3.09808	+	5.36603i	−0.372965	+	0.645994i
$70$		0			0
$71$	−0.633975	+	1.09808i	−0.0752389	+	0.130318i	−0.901190	−	0.433424i	$-0.857305\pi$
$71$	−0.633975	+	1.09808i	−0.0752389	+	0.130318i	0.825951	+	0.563742i	$0.190639\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−4.66025			−0.545441			−0.272721	−	0.962093i	$-0.587924\pi$
$73$	−4.66025			−0.545441			−0.272721	+	0.962093i	$0.587924\pi$
$74$	−3.96410	+	6.86603i	−0.460817	+	0.798159i
$75$		0			0
$76$	−0.633975	−	1.09808i	−0.0727219	−	0.125958i
$77$	2.00000			0.227921
$78$	3.00000	+	2.00000i	0.339683	+	0.226455i
$79$	12.0000			1.35011			0.675053	−	0.737769i	$-0.264121\pi$
$79$	12.0000			1.35011			0.675053	+	0.737769i	$0.264121\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.59808	−	7.96410i	0.507773	−	0.879488i
$83$	5.26795			0.578233			0.289116	−	0.957294i	$-0.406639\pi$
$83$	5.26795			0.578233			0.289116	+	0.957294i	$0.406639\pi$
$84$	−1.36603	+	2.36603i	−0.149046	+	0.258155i
$85$		0			0
$86$	−3.26795			−0.352392
$87$	3.23205	−	5.59808i	0.346512	−	0.600177i
$88$	−0.366025	−	0.633975i	−0.0390184	−	0.0675819i
$89$	2.46410	+	4.26795i	0.261194	+	0.452402i	0.966560	−	0.256442i	$-0.0825504\pi$
$89$	2.46410	+	4.26795i	0.261194	+	0.452402i	−0.705365	+	0.708844i	$0.749217\pi$
$90$		0			0
$91$	8.19615	+	5.46410i	0.859190	+	0.572793i
$92$	6.19615			0.645994
$93$	−2.00000	−	3.46410i	−0.207390	−	0.359211i
$94$	−3.83013	−	6.63397i	−0.395047	−	0.684242i
$95$		0			0
$96$	1.00000			0.102062
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	−0.492287	−	0.870433i	$-0.663839\pi$
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	0.999961	−	0.00888289i	$-0.00282755\pi$
$98$	−0.232051	+	0.401924i	−0.0234407	+	0.0406004i
$99$	0.732051			0.0735739
$100$		0			0
$101$	−6.96410	−	12.0622i	−0.692954	−	1.20023i	−0.970866	−	0.239625i	$-0.922976\pi$
$101$	−6.96410	−	12.0622i	−0.692954	−	1.20023i	0.277912	−	0.960607i	$-0.410358\pi$
$102$	−2.23205	−	3.86603i	−0.221006	−	0.382794i
$103$	9.26795			0.913198			0.456599	−	0.889673i	$-0.349067\pi$
$103$	9.26795			0.913198			0.456599	+	0.889673i	$0.349067\pi$
$104$	0.232051	−	3.59808i	0.0227545	−	0.352820i
$105$		0			0
$106$	−3.86603	−	6.69615i	−0.375502	−	0.650388i
$107$	−0.633975	−	1.09808i	−0.0612886	−	0.106155i	0.833753	−	0.552138i	$-0.186188\pi$
$107$	−0.633975	−	1.09808i	−0.0612886	−	0.106155i	−0.895042	+	0.445983i	$0.852854\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$		0			0
$111$	−3.96410	+	6.86603i	−0.376256	+	0.651694i
$112$	2.73205			0.258155
$113$	−4.50000	+	7.79423i	−0.423324	+	0.733219i	−0.996262	−	0.0863794i	$-0.972470\pi$
$113$	−4.50000	+	7.79423i	−0.423324	+	0.733219i	0.572938	+	0.819599i	$0.305804\pi$
$114$	−0.633975	−	1.09808i	−0.0593772	−	0.102844i
$115$		0			0
$116$	−6.46410			−0.600177
$117$	3.00000	+	2.00000i	0.277350	+	0.184900i
$118$	−12.3923			−1.14080
$119$	−6.09808	−	10.5622i	−0.559010	−	0.968233i
$120$		0			0
$121$	5.23205	−	9.06218i	0.475641	−	0.823834i
$122$	−10.1244			−0.916616
$123$	4.59808	−	7.96410i	0.414595	−	0.718099i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$		0			0
$126$	−1.36603	+	2.36603i	−0.121695	+	0.210782i
$127$	−2.00000	−	3.46410i	−0.177471	−	0.307389i	0.763542	−	0.645758i	$-0.223458\pi$
$127$	−2.00000	−	3.46410i	−0.177471	−	0.307389i	−0.941014	+	0.338368i	$0.890125\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−3.26795			−0.287727
$130$		0			0
$131$	−13.8564			−1.21064			−0.605320	−	0.795982i	$-0.706955\pi$
$131$	−13.8564			−1.21064			−0.605320	+	0.795982i	$0.706955\pi$
$132$	−0.366025	−	0.633975i	−0.0318584	−	0.0551804i
$133$	−1.73205	−	3.00000i	−0.150188	−	0.260133i
$134$	−3.83013	+	6.63397i	−0.330873	+	0.573088i
$135$		0			0
$136$	−2.23205	+	3.86603i	−0.191397	+	0.331509i
$137$	−9.23205	+	15.9904i	−0.788747	+	1.36615i	0.137987	+	0.990434i	$0.455937\pi$
$137$	−9.23205	+	15.9904i	−0.788747	+	1.36615i	−0.926735	+	0.375716i	$0.877397\pi$
$138$	6.19615			0.527452
$139$	0.535898	−	0.928203i	0.0454543	−	0.0787292i	−0.842403	−	0.538848i	$-0.818860\pi$
$139$	0.535898	−	0.928203i	0.0454543	−	0.0787292i	0.887857	+	0.460119i	$0.152193\pi$
$140$		0			0
$141$	−3.83013	−	6.63397i	−0.322555	−	0.558681i
$142$	1.26795			0.106404
$143$	−2.36603	+	1.16987i	−0.197857	+	0.0978297i
$144$	1.00000			0.0833333
$145$		0			0
$146$	2.33013	+	4.03590i	0.192843	+	0.334013i
$147$	−0.232051	+	0.401924i	−0.0191392	+	0.0331501i
$148$	7.92820			0.651694
$149$	−9.96410	+	17.2583i	−0.816291	+	1.41386i	0.0921062	+	0.995749i	$0.470640\pi$
$149$	−9.96410	+	17.2583i	−0.816291	+	1.41386i	−0.908397	+	0.418108i	$0.862693\pi$
$150$		0			0
$151$	−5.12436			−0.417014			−0.208507	−	0.978021i	$-0.566860\pi$
$151$	−5.12436			−0.417014			−0.208507	+	0.978021i	$0.566860\pi$
$152$	−0.633975	+	1.09808i	−0.0514221	+	0.0890657i
$153$	−2.23205	−	3.86603i	−0.180451	−	0.312550i
$154$	−1.00000	−	1.73205i	−0.0805823	−	0.139573i
$155$		0			0
$156$	0.232051	−	3.59808i	0.0185789	−	0.288077i
$157$	9.39230			0.749588			0.374794	−	0.927108i	$-0.377714\pi$
$157$	9.39230			0.749588			0.374794	+	0.927108i	$0.377714\pi$
$158$	−6.00000	−	10.3923i	−0.477334	−	0.826767i
$159$	−3.86603	−	6.69615i	−0.306596	−	0.531039i
$160$		0			0
$161$	16.9282			1.33413
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	6.73205	−	11.6603i	0.527295	−	0.913302i	−0.472199	−	0.881492i	$-0.656540\pi$
$163$	6.73205	−	11.6603i	0.527295	−	0.913302i	0.999494	−	0.0318096i	$-0.0101270\pi$
$164$	−9.19615			−0.718099
$165$		0			0
$166$	−2.63397	−	4.56218i	−0.204436	−	0.354094i
$167$	6.92820	+	12.0000i	0.536120	+	0.928588i	0.999108	+	0.0422232i	$0.0134441\pi$
$167$	6.92820	+	12.0000i	0.536120	+	0.928588i	−0.462988	+	0.886365i	$0.653223\pi$
$168$	2.73205			0.210782
$169$	−12.8923	−	1.66987i	−0.991716	−	0.128452i
$170$		0			0
$171$	−0.633975	−	1.09808i	−0.0484812	−	0.0839720i
$172$	1.63397	+	2.83013i	0.124589	+	0.215795i
$173$	9.39230	−	16.2679i	0.714084	−	1.23683i	−0.249228	−	0.968445i	$-0.580177\pi$
$173$	9.39230	−	16.2679i	0.714084	−	1.23683i	0.963312	−	0.268384i	$-0.0864898\pi$
$174$	−6.46410			−0.490042
$175$		0			0
$176$	−0.366025	+	0.633975i	−0.0275902	+	0.0477876i
$177$	−12.3923			−0.931463
$178$	2.46410	−	4.26795i	0.184692	−	0.319896i
$179$	−9.09808	−	15.7583i	−0.680022	−	1.17783i	−0.974974	−	0.222321i	$-0.928637\pi$
$179$	−9.09808	−	15.7583i	−0.680022	−	1.17783i	0.294951	−	0.955512i	$-0.404697\pi$
$180$		0			0
$181$	−16.1244			−1.19851			−0.599257	−	0.800557i	$-0.704537\pi$
$181$	−16.1244			−1.19851			−0.599257	+	0.800557i	$0.704537\pi$
$182$	0.633975	−	9.83013i	0.0469933	−	0.728657i
$183$	−10.1244			−0.748414
$184$	−3.09808	−	5.36603i	−0.228393	−	0.395589i
$185$		0			0
$186$	−2.00000	+	3.46410i	−0.146647	+	0.254000i
$187$	3.26795			0.238976
$188$	−3.83013	+	6.63397i	−0.279341	+	0.483832i
$189$	−1.36603	+	2.36603i	−0.0993637	+	0.172103i
$190$		0			0
$191$	4.73205	−	8.19615i	0.342399	−	0.593053i	−0.642479	−	0.766304i	$-0.722094\pi$
$191$	4.73205	−	8.19615i	0.342399	−	0.593053i	0.984878	+	0.173251i	$0.0554272\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	5.33013	+	9.23205i	0.383671	+	0.664538i	0.991584	−	0.129466i	$-0.0413264\pi$
$193$	5.33013	+	9.23205i	0.383671	+	0.664538i	−0.607913	+	0.794004i	$0.707993\pi$
$194$	−10.0000			−0.717958
$195$		0			0
$196$	0.464102			0.0331501
$197$	−4.92820	−	8.53590i	−0.351120	−	0.608158i	0.635326	−	0.772244i	$-0.280866\pi$
$197$	−4.92820	−	8.53590i	−0.351120	−	0.608158i	−0.986446	+	0.164086i	$0.947532\pi$
$198$	−0.366025	−	0.633975i	−0.0260123	−	0.0450546i
$199$	14.0263	−	24.2942i	0.994297	−	1.72217i	0.404786	−	0.914411i	$-0.367346\pi$
$199$	14.0263	−	24.2942i	0.994297	−	1.72217i	0.589510	−	0.807761i	$-0.299321\pi$
$200$		0			0
$201$	−3.83013	+	6.63397i	−0.270156	+	0.467924i
$202$	−6.96410	+	12.0622i	−0.489992	+	0.848692i
$203$	−17.6603			−1.23951
$204$	−2.23205	+	3.86603i	−0.156275	+	0.270676i
$205$		0			0
$206$	−4.63397	−	8.02628i	−0.322864	−	0.559217i
$207$	6.19615			0.430662
$208$	−3.23205	+	1.59808i	−0.224102	+	0.110807i
$209$	0.928203			0.0642052
$210$		0			0
$211$	10.7321	+	18.5885i	0.738825	+	1.27968i	0.953025	+	0.302892i	$0.0979523\pi$
$211$	10.7321	+	18.5885i	0.738825	+	1.27968i	−0.214200	+	0.976790i	$0.568714\pi$
$212$	−3.86603	+	6.69615i	−0.265520	+	0.459894i
$213$	1.26795			0.0868784
$214$	−0.633975	+	1.09808i	−0.0433376	+	0.0750629i
$215$		0			0
$216$	1.00000			0.0680414
$217$	−5.46410	+	9.46410i	−0.370927	+	0.642465i
$218$	−5.00000	−	8.66025i	−0.338643	−	0.586546i
$219$	2.33013	+	4.03590i	0.157455	+	0.272721i
$220$		0			0
$221$	13.3923	+	8.92820i	0.900864	+	0.600576i
$222$	7.92820			0.532106
$223$	0.196152	+	0.339746i	0.0131353	+	0.0227511i	0.872518	−	0.488581i	$-0.162485\pi$
$223$	0.196152	+	0.339746i	0.0131353	+	0.0227511i	−0.859383	+	0.511332i	$0.829152\pi$
$224$	−1.36603	−	2.36603i	−0.0912714	−	0.158087i
$225$		0			0
$226$	9.00000			0.598671
$227$	2.09808	−	3.63397i	0.139254	−	0.241195i	−0.787960	−	0.615726i	$-0.788863\pi$
$227$	2.09808	−	3.63397i	0.139254	−	0.241195i	0.927215	+	0.374531i	$0.122196\pi$
$228$	−0.633975	+	1.09808i	−0.0419860	+	0.0727219i
$229$	28.7846			1.90214			0.951070	−	0.308975i	$-0.0999858\pi$
$229$	28.7846			1.90214			0.951070	+	0.308975i	$0.0999858\pi$
$230$		0			0
$231$	−1.00000	−	1.73205i	−0.0657952	−	0.113961i
$232$	3.23205	+	5.59808i	0.212195	+	0.367532i
$233$	12.3923			0.811847			0.405923	−	0.913907i	$-0.366950\pi$
$233$	12.3923			0.811847			0.405923	+	0.913907i	$0.366950\pi$
$234$	0.232051	−	3.59808i	0.0151696	−	0.235214i
$235$		0			0
$236$	6.19615	+	10.7321i	0.403335	+	0.698597i
$237$	−6.00000	−	10.3923i	−0.389742	−	0.675053i
$238$	−6.09808	+	10.5622i	−0.395280	+	0.684644i
$239$	−4.58846			−0.296803			−0.148401	−	0.988927i	$-0.547413\pi$
$239$	−4.58846			−0.296803			−0.148401	+	0.988927i	$0.547413\pi$
$240$		0			0
$241$	4.69615	−	8.13397i	0.302506	−	0.523955i	−0.674197	−	0.738551i	$-0.735510\pi$
$241$	4.69615	−	8.13397i	0.302506	−	0.523955i	0.976703	+	0.214596i	$0.0688435\pi$
$242$	−10.4641			−0.672658
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	5.06218	+	8.76795i	0.324073	+	0.561310i
$245$		0			0
$246$	−9.19615			−0.586325
$247$	3.80385	+	2.53590i	0.242033	+	0.161355i
$248$	4.00000			0.254000
$249$	−2.63397	−	4.56218i	−0.166921	−	0.289116i
$250$		0			0
$251$	10.7321	−	18.5885i	0.677401	−	1.17329i	−0.298360	−	0.954453i	$-0.596440\pi$
$251$	10.7321	−	18.5885i	0.677401	−	1.17329i	0.975761	−	0.218840i	$-0.0702271\pi$
$252$	2.73205			0.172103
$253$	−2.26795	+	3.92820i	−0.142585	+	0.246964i
$254$	−2.00000	+	3.46410i	−0.125491	+	0.217357i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	0.909010	−	0.416775i	$-0.136840\pi$
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	−0.815442	+	0.578838i	$0.803506\pi$
$258$	1.63397	+	2.83013i	0.101727	+	0.176196i
$259$	21.6603			1.34590
$260$		0			0
$261$	−6.46410			−0.400118
$262$	6.92820	+	12.0000i	0.428026	+	0.741362i
$263$	8.56218	+	14.8301i	0.527967	+	0.914465i	0.999468	+	0.0325998i	$0.0103787\pi$
$263$	8.56218	+	14.8301i	0.527967	+	0.914465i	−0.471502	+	0.881865i	$0.656288\pi$
$264$	−0.366025	+	0.633975i	−0.0225273	+	0.0390184i
$265$		0			0
$266$	−1.73205	+	3.00000i	−0.106199	+	0.183942i
$267$	2.46410	−	4.26795i	0.150801	−	0.261194i
$268$	7.66025			0.467924
$269$	−2.19615	+	3.80385i	−0.133902	+	0.231925i	−0.925177	−	0.379535i	$-0.876084\pi$
$269$	−2.19615	+	3.80385i	−0.133902	+	0.231925i	0.791276	+	0.611460i	$0.209417\pi$
$270$		0			0
$271$	−2.92820	−	5.07180i	−0.177876	−	0.308090i	0.763277	−	0.646071i	$-0.223589\pi$
$271$	−2.92820	−	5.07180i	−0.177876	−	0.308090i	−0.941153	+	0.337982i	$0.890256\pi$
$272$	4.46410			0.270676
$273$	0.633975	−	9.83013i	0.0383699	−	0.594946i
$274$	18.4641			1.11546
$275$		0			0
$276$	−3.09808	−	5.36603i	−0.186482	−	0.322997i
$277$	−6.16025	+	10.6699i	−0.370134	+	0.641091i	−0.989586	−	0.143944i	$-0.954021\pi$
$277$	−6.16025	+	10.6699i	−0.370134	+	0.641091i	0.619452	+	0.785034i	$0.287355\pi$
$278$	−1.07180			−0.0642821
$279$	−2.00000	+	3.46410i	−0.119737	+	0.207390i
$280$		0			0
$281$	1.73205			0.103325			0.0516627	−	0.998665i	$-0.483548\pi$
$281$	1.73205			0.103325			0.0516627	+	0.998665i	$0.483548\pi$
$282$	−3.83013	+	6.63397i	−0.228081	+	0.395047i
$283$	−3.83013	−	6.63397i	−0.227677	−	0.394349i	0.729442	−	0.684043i	$-0.239780\pi$
$283$	−3.83013	−	6.63397i	−0.227677	−	0.394349i	−0.957119	+	0.289694i	$0.906447\pi$
$284$	−0.633975	−	1.09808i	−0.0376195	−	0.0651588i
$285$		0			0
$286$	2.19615	+	1.46410i	0.129861	+	0.0865741i
$287$	−25.1244			−1.48304
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−1.46410	−	2.53590i	−0.0861236	−	0.149170i
$290$		0			0
$291$	−10.0000			−0.586210
$292$	2.33013	−	4.03590i	0.136360	−	0.236183i
$293$	−6.86603	+	11.8923i	−0.401117	+	0.694756i	−0.993861	−	0.110635i	$-0.964711\pi$
$293$	−6.86603	+	11.8923i	−0.401117	+	0.694756i	0.592744	+	0.805391i	$0.298045\pi$
$294$	0.464102			0.0270670
$295$		0			0
$296$	−3.96410	−	6.86603i	−0.230409	−	0.399080i
$297$	−0.366025	−	0.633975i	−0.0212389	−	0.0367869i
$298$	19.9282			1.15441
$299$	−20.0263	+	9.90192i	−1.15815	+	0.572643i
$300$		0			0
$301$	4.46410	+	7.73205i	0.257307	+	0.445668i
$302$	2.56218	+	4.43782i	0.147437	+	0.255368i
$303$	−6.96410	+	12.0622i	−0.400077	+	0.692954i
$304$	1.26795			0.0727219
$305$		0			0
$306$	−2.23205	+	3.86603i	−0.127598	+	0.221006i
$307$	−19.2679			−1.09968			−0.549840	−	0.835270i	$-0.685311\pi$
$307$	−19.2679			−1.09968			−0.549840	+	0.835270i	$0.685311\pi$
$308$	−1.00000	+	1.73205i	−0.0569803	+	0.0986928i
$309$	−4.63397	−	8.02628i	−0.263618	−	0.456599i
$310$		0			0
$311$	3.12436			0.177166			0.0885830	−	0.996069i	$-0.471766\pi$
$311$	3.12436			0.177166			0.0885830	+	0.996069i	$0.471766\pi$
$312$	−3.23205	+	1.59808i	−0.182979	+	0.0904732i
$313$	−14.0000			−0.791327			−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000			−0.791327			−0.395663	+	0.918396i	$0.629485\pi$
$314$	−4.69615	−	8.13397i	−0.265019	−	0.459027i
$315$		0			0
$316$	−6.00000	+	10.3923i	−0.337526	+	0.584613i
$317$	29.7321			1.66992			0.834959	−	0.550312i	$-0.185491\pi$
$317$	29.7321			1.66992			0.834959	+	0.550312i	$0.185491\pi$
$318$	−3.86603	+	6.69615i	−0.216796	+	0.375502i
$319$	2.36603	−	4.09808i	0.132472	−	0.229448i
$320$		0			0
$321$	−0.633975	+	1.09808i	−0.0353850	+	0.0612886i
$322$	−8.46410	−	14.6603i	−0.471686	−	0.816984i
$323$	−2.83013	−	4.90192i	−0.157472	−	0.272750i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−13.4641			−0.745708
$327$	−5.00000	−	8.66025i	−0.276501	−	0.478913i
$328$	4.59808	+	7.96410i	0.253886	+	0.439744i
$329$	−10.4641	+	18.1244i	−0.576905	+	0.999228i
$330$		0			0
$331$	14.3923	−	24.9282i	0.791073	−	1.37018i	−0.134231	−	0.990950i	$-0.542856\pi$
$331$	14.3923	−	24.9282i	0.791073	−	1.37018i	0.925303	−	0.379228i	$-0.123810\pi$
$332$	−2.63397	+	4.56218i	−0.144558	+	0.250382i
$333$	7.92820			0.434463
$334$	6.92820	−	12.0000i	0.379094	−	0.656611i
$335$		0			0
$336$	−1.36603	−	2.36603i	−0.0745228	−	0.129077i
$337$	11.0526			0.602071			0.301036	−	0.953613i	$-0.402668\pi$
$337$	11.0526			0.602071			0.301036	+	0.953613i	$0.402668\pi$
$338$	5.00000	+	12.0000i	0.271964	+	0.652714i
$339$	9.00000			0.488813
$340$		0			0
$341$	−1.46410	−	2.53590i	−0.0792855	−	0.137327i
$342$	−0.633975	+	1.09808i	−0.0342814	+	0.0593772i
$343$	−17.8564			−0.964155
$344$	1.63397	−	2.83013i	0.0880980	−	0.152590i
$345$		0			0
$346$	−18.7846			−1.00987
$347$	2.83013	−	4.90192i	0.151929	−	0.263149i	−0.780007	−	0.625770i	$-0.784785\pi$
$347$	2.83013	−	4.90192i	0.151929	−	0.263149i	0.931937	+	0.362621i	$0.118118\pi$
$348$	3.23205	+	5.59808i	0.173256	+	0.300088i
$349$	9.53590	+	16.5167i	0.510445	+	0.884117i	0.999927	+	0.0121031i	$0.00385262\pi$
$349$	9.53590	+	16.5167i	0.510445	+	0.884117i	−0.489482	+	0.872014i	$0.662814\pi$
$350$		0			0
$351$	0.232051	−	3.59808i	0.0123860	−	0.192051i
$352$	0.732051			0.0390184
$353$	12.6244	+	21.8660i	0.671927	+	1.16381i	0.977357	+	0.211597i	$0.0678663\pi$
$353$	12.6244	+	21.8660i	0.671927	+	1.16381i	−0.305430	+	0.952214i	$0.598800\pi$
$354$	6.19615	+	10.7321i	0.329322	+	0.570402i
$355$		0			0
$356$	−4.92820			−0.261194
$357$	−6.09808	+	10.5622i	−0.322744	+	0.559010i
$358$	−9.09808	+	15.7583i	−0.480848	+	0.832854i
$359$	8.87564			0.468439			0.234219	−	0.972184i	$-0.424747\pi$
$359$	8.87564			0.468439			0.234219	+	0.972184i	$0.424747\pi$
$360$		0			0
$361$	8.69615	+	15.0622i	0.457692	+	0.792746i
$362$	8.06218	+	13.9641i	0.423739	+	0.733937i
$363$	−10.4641			−0.549223
$364$	−8.83013	+	4.36603i	−0.462824	+	0.228842i
$365$		0			0
$366$	5.06218	+	8.76795i	0.264604	+	0.458308i
$367$	−16.4904	−	28.5622i	−0.860791	−	1.49093i	−0.871167	−	0.490987i	$-0.836636\pi$
$367$	−16.4904	−	28.5622i	−0.860791	−	1.49093i	0.0103758	−	0.999946i	$-0.496697\pi$
$368$	−3.09808	+	5.36603i	−0.161498	+	0.279723i
$369$	−9.19615			−0.478733
$370$		0			0
$371$	−10.5622	+	18.2942i	−0.548361	+	0.949789i
$372$	4.00000			0.207390
$373$	−11.7679	+	20.3827i	−0.609321	+	1.05538i	0.382031	+	0.924149i	$0.375225\pi$
$373$	−11.7679	+	20.3827i	−0.609321	+	1.05538i	−0.991352	+	0.131226i	$0.958109\pi$
$374$	−1.63397	−	2.83013i	−0.0844908	−	0.146342i
$375$		0			0
$376$	7.66025			0.395047
$377$	20.8923	−	10.3301i	1.07601	−	0.532029i
$378$	2.73205			0.140522
$379$	−13.1244	−	22.7321i	−0.674153	−	1.16767i	−0.976716	−	0.214538i	$-0.931176\pi$
$379$	−13.1244	−	22.7321i	−0.674153	−	1.16767i	0.302563	−	0.953129i	$-0.402158\pi$
$380$		0			0
$381$	−2.00000	+	3.46410i	−0.102463	+	0.177471i
$382$	−9.46410			−0.484226
$383$	−13.4641	+	23.3205i	−0.687983	+	1.19162i	0.284506	+	0.958674i	$0.408171\pi$
$383$	−13.4641	+	23.3205i	−0.687983	+	1.19162i	−0.972489	+	0.232948i	$0.925163\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$		0			0
$386$	5.33013	−	9.23205i	0.271296	−	0.469899i
$387$	1.63397	+	2.83013i	0.0830596	+	0.143863i
$388$	5.00000	+	8.66025i	0.253837	+	0.439658i
$389$	−24.0718			−1.22049			−0.610244	−	0.792213i	$-0.708929\pi$
$389$	−24.0718			−1.22049			−0.610244	+	0.792213i	$0.708929\pi$
$390$		0			0
$391$	27.6603			1.39884
$392$	−0.232051	−	0.401924i	−0.0117203	−	0.0203002i
$393$	6.92820	+	12.0000i	0.349482	+	0.605320i
$394$	−4.92820	+	8.53590i	−0.248279	+	0.430032i
$395$		0			0
$396$	−0.366025	+	0.633975i	−0.0183935	+	0.0318584i
$397$	9.66025	−	16.7321i	0.484834	−	0.839758i	−0.515014	−	0.857182i	$-0.672213\pi$
$397$	9.66025	−	16.7321i	0.484834	−	0.839758i	0.999848	+	0.0174242i	$0.00554659\pi$
$398$	−28.0526			−1.40615
$399$	−1.73205	+	3.00000i	−0.0867110	+	0.150188i
$400$		0			0
$401$	4.52628	+	7.83975i	0.226032	+	0.391498i	0.956628	−	0.291311i	$-0.0940914\pi$
$401$	4.52628	+	7.83975i	0.226032	+	0.391498i	−0.730597	+	0.682809i	$0.760758\pi$
$402$	7.66025			0.382059
$403$	0.928203	−	14.3923i	0.0462371	−	0.716932i
$404$	13.9282			0.692954
$405$		0			0
$406$	8.83013	+	15.2942i	0.438232	+	0.759040i
$407$	−2.90192	+	5.02628i	−0.143843	+	0.249143i
$408$	4.46410			0.221006
$409$	−8.03590	+	13.9186i	−0.397350	+	0.688230i	−0.993398	−	0.114719i	$-0.963403\pi$
$409$	−8.03590	+	13.9186i	−0.397350	+	0.688230i	0.596048	+	0.802949i	$0.296737\pi$
$410$		0			0
$411$	18.4641			0.910767
$412$	−4.63397	+	8.02628i	−0.228300	+	0.395426i
$413$	16.9282	+	29.3205i	0.832982	+	1.44277i
$414$	−3.09808	−	5.36603i	−0.152262	−	0.263726i
$415$		0			0
$416$	3.00000	+	2.00000i	0.147087	+	0.0980581i
$417$	−1.07180			−0.0524861
$418$	−0.464102	−	0.803848i	−0.0227000	−	0.0393175i
$419$	3.26795	+	5.66025i	0.159650	+	0.276522i	0.934742	−	0.355326i	$-0.115630\pi$
$419$	3.26795	+	5.66025i	0.159650	+	0.276522i	−0.775093	+	0.631848i	$0.782297\pi$
$420$		0			0
$421$	17.0526			0.831091			0.415545	−	0.909572i	$-0.363591\pi$
$421$	17.0526			0.831091			0.415545	+	0.909572i	$0.363591\pi$
$422$	10.7321	−	18.5885i	0.522428	−	0.904872i
$423$	−3.83013	+	6.63397i	−0.186227	+	0.322555i
$424$	7.73205			0.375502
$425$		0			0
$426$	−0.633975	−	1.09808i	−0.0307162	−	0.0532020i
$427$	13.8301	+	23.9545i	0.669287	+	1.15924i
$428$	1.26795			0.0612886
$429$	2.19615	+	1.46410i	0.106031	+	0.0706875i
$430$		0			0
$431$	3.90192	+	6.75833i	0.187949	+	0.325537i	0.944566	−	0.328321i	$-0.106483\pi$
$431$	3.90192	+	6.75833i	0.187949	+	0.325537i	−0.756617	+	0.653858i	$0.773149\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	7.40192	−	12.8205i	0.355714	−	0.616114i	−0.631526	−	0.775355i	$-0.717571\pi$
$433$	7.40192	−	12.8205i	0.355714	−	0.616114i	0.987240	+	0.159240i	$0.0509045\pi$
$434$	10.9282			0.524571
$435$		0			0
$436$	−5.00000	+	8.66025i	−0.239457	+	0.414751i
$437$	7.85641			0.375823
$438$	2.33013	−	4.03590i	0.111338	−	0.192843i
$439$	−4.90192	−	8.49038i	−0.233956	−	0.405224i	0.725013	−	0.688735i	$-0.241834\pi$
$439$	−4.90192	−	8.49038i	−0.233956	−	0.405224i	−0.958969	+	0.283512i	$0.908501\pi$
$440$		0			0
$441$	0.464102			0.0221001
$442$	1.03590	−	16.0622i	0.0492727	−	0.764000i
$443$	34.6410			1.64584			0.822922	−	0.568154i	$-0.192342\pi$
$443$	34.6410			1.64584			0.822922	+	0.568154i	$0.192342\pi$
$444$	−3.96410	−	6.86603i	−0.188128	−	0.325847i
$445$		0			0
$446$	0.196152	−	0.339746i	0.00928809	−	0.0160874i
$447$	19.9282			0.942572
$448$	−1.36603	+	2.36603i	−0.0645386	+	0.111784i
$449$	3.92820	−	6.80385i	0.185383	−	0.321093i	−0.758322	−	0.651880i	$-0.773981\pi$
$449$	3.92820	−	6.80385i	0.185383	−	0.321093i	0.943706	+	0.330786i	$0.107314\pi$
$450$		0			0
$451$	3.36603	−	5.83013i	0.158500	−	0.274530i
$452$	−4.50000	−	7.79423i	−0.211662	−	0.366610i
$453$	2.56218	+	4.43782i	0.120382	+	0.208507i
$454$	−4.19615			−0.196935
$455$		0			0
$456$	1.26795			0.0593772
$457$	4.40192	+	7.62436i	0.205913	+	0.356652i	0.950423	−	0.310959i	$-0.100650\pi$
$457$	4.40192	+	7.62436i	0.205913	+	0.356652i	−0.744510	+	0.667611i	$0.767317\pi$
$458$	−14.3923	−	24.9282i	−0.672508	−	1.16482i
$459$	−2.23205	+	3.86603i	−0.104183	+	0.180451i
$460$		0			0
$461$	−13.0359	+	22.5788i	−0.607142	+	1.05160i	0.384567	+	0.923097i	$0.374351\pi$
$461$	−13.0359	+	22.5788i	−0.607142	+	1.05160i	−0.991709	+	0.128504i	$0.958982\pi$
$462$	−1.00000	+	1.73205i	−0.0465242	+	0.0805823i
$463$	−6.33975			−0.294633			−0.147316	−	0.989089i	$-0.547064\pi$
$463$	−6.33975			−0.294633			−0.147316	+	0.989089i	$0.547064\pi$
$464$	3.23205	−	5.59808i	0.150044	−	0.259884i
$465$		0			0
$466$	−6.19615	−	10.7321i	−0.287031	−	0.497153i
$467$	−22.0526			−1.02047			−0.510235	−	0.860035i	$-0.670442\pi$
$467$	−22.0526			−1.02047			−0.510235	+	0.860035i	$0.670442\pi$
$468$	−3.23205	+	1.59808i	−0.149402	+	0.0738711i
$469$	20.9282			0.966375
$470$		0			0
$471$	−4.69615	−	8.13397i	−0.216387	−	0.374794i
$472$	6.19615	−	10.7321i	0.285201	−	0.493983i
$473$	−2.39230			−0.109998
$474$	−6.00000	+	10.3923i	−0.275589	+	0.477334i
$475$		0			0
$476$	12.1962			0.559010
$477$	−3.86603	+	6.69615i	−0.177013	+	0.306596i
$478$	2.29423	+	3.97372i	0.104936	+	0.181754i
$479$	8.00000	+	13.8564i	0.365529	+	0.633115i	0.988861	−	0.148842i	$-0.0475547\pi$
$479$	8.00000	+	13.8564i	0.365529	+	0.633115i	−0.623332	+	0.781958i	$0.714221\pi$
$480$		0			0
$481$	−25.6244	+	12.6699i	−1.16837	+	0.577696i
$482$	−9.39230			−0.427808
$483$	−8.46410	−	14.6603i	−0.385130	−	0.667065i
$484$	5.23205	+	9.06218i	0.237820	+	0.411917i
$485$		0			0
$486$	1.00000			0.0453609
$487$	−19.2224	+	33.2942i	−0.871052	+	1.50871i	−0.0101413	+	0.999949i	$0.503228\pi$
$487$	−19.2224	+	33.2942i	−0.871052	+	1.50871i	−0.860910	+	0.508757i	$0.830105\pi$
$488$	5.06218	−	8.76795i	0.229154	−	0.396906i
$489$	−13.4641			−0.608868
$490$		0			0
$491$	−10.9019	−	18.8827i	−0.491997	−	0.852164i	0.507961	−	0.861380i	$-0.330400\pi$
$491$	−10.9019	−	18.8827i	−0.491997	−	0.852164i	−0.999958	+	0.00921662i	$0.997066\pi$
$492$	4.59808	+	7.96410i	0.207297	+	0.359049i
$493$	−28.8564			−1.29963
$494$	0.294229	−	4.56218i	0.0132380	−	0.205262i
$495$		0			0
$496$	−2.00000	−	3.46410i	−0.0898027	−	0.155543i
$497$	−1.73205	−	3.00000i	−0.0776931	−	0.134568i
$498$	−2.63397	+	4.56218i	−0.118031	+	0.204436i
$499$	40.3923			1.80821			0.904104	−	0.427313i	$-0.140540\pi$
$499$	40.3923			1.80821			0.904104	+	0.427313i	$0.140540\pi$
$500$		0			0
$501$	6.92820	−	12.0000i	0.309529	−	0.536120i
$502$	−21.4641			−0.957990
$503$	−10.9019	+	18.8827i	−0.486093	+	0.841937i	−0.999872	−	0.0159849i	$-0.994912\pi$
$503$	−10.9019	+	18.8827i	−0.486093	+	0.841937i	0.513779	+	0.857922i	$0.328245\pi$
$504$	−1.36603	−	2.36603i	−0.0608476	−	0.105391i
$505$		0			0
$506$	4.53590			0.201645
$507$	5.00000	+	12.0000i	0.222058	+	0.532939i
$508$	4.00000			0.177471
$509$	15.3564	+	26.5981i	0.680661	+	1.17894i	0.974780	+	0.223170i	$0.0716405\pi$
$509$	15.3564	+	26.5981i	0.680661	+	1.17894i	−0.294119	+	0.955769i	$0.595026\pi$
$510$		0			0
$511$	6.36603	−	11.0263i	0.281616	−	0.487774i
$512$	1.00000			0.0441942
$513$	−0.633975	+	1.09808i	−0.0279907	+	0.0484812i
$514$	1.50000	−	2.59808i	0.0661622	−	0.114596i
$515$		0			0
$516$	1.63397	−	2.83013i	0.0719317	−	0.124589i
$517$	−2.80385	−	4.85641i	−0.123313	−	0.213585i
$518$	−10.8301	−	18.7583i	−0.475848	−	0.824194i
$519$	−18.7846			−0.824553
$520$		0			0
$521$	−19.4449			−0.851895			−0.425947	−	0.904748i	$-0.640059\pi$
$521$	−19.4449			−0.851895			−0.425947	+	0.904748i	$0.640059\pi$
$522$	3.23205	+	5.59808i	0.141463	+	0.245021i
$523$	18.2224	+	31.5622i	0.796811	+	1.38012i	0.921683	+	0.387945i	$0.126815\pi$
$523$	18.2224	+	31.5622i	0.796811	+	1.38012i	−0.124871	+	0.992173i	$0.539852\pi$
$524$	6.92820	−	12.0000i	0.302660	−	0.524222i
$525$		0			0
$526$	8.56218	−	14.8301i	0.373329	−	0.646624i
$527$	−8.92820	+	15.4641i	−0.388919	+	0.673627i
$528$	0.732051			0.0318584
$529$	−7.69615	+	13.3301i	−0.334615	+	0.579571i
$530$		0			0
$531$	6.19615	+	10.7321i	0.268890	+	0.465731i
$532$	3.46410			0.150188
$533$	29.7224	−	14.6962i	1.28742	−	0.636561i
$534$	−4.92820			−0.213264
$535$		0			0
$536$	−3.83013	−	6.63397i	−0.165436	−	0.286544i
$537$	−9.09808	+	15.7583i	−0.392611	+	0.680022i
$538$	4.39230			0.189366
$539$	−0.169873	+	0.294229i	−0.00731695	+	0.0126733i
$540$		0			0
$541$	−1.19615			−0.0514266			−0.0257133	−	0.999669i	$-0.508186\pi$
$541$	−1.19615			−0.0514266			−0.0257133	+	0.999669i	$0.508186\pi$
$542$	−2.92820	+	5.07180i	−0.125777	+	0.217852i
$543$	8.06218	+	13.9641i	0.345981	+	0.599257i
$544$	−2.23205	−	3.86603i	−0.0956984	−	0.165754i
$545$		0			0
$546$	−8.83013	+	4.36603i	−0.377895	+	0.186849i
$547$	25.8038			1.10329			0.551646	−	0.834078i	$-0.314000\pi$
$547$	25.8038			1.10329			0.551646	+	0.834078i	$0.314000\pi$
$548$	−9.23205	−	15.9904i	−0.394374	−	0.683075i
$549$	5.06218	+	8.76795i	0.216048	+	0.374207i
$550$		0			0
$551$	−8.19615			−0.349168
$552$	−3.09808	+	5.36603i	−0.131863	+	0.228393i
$553$	−16.3923	+	28.3923i	−0.697072	+	1.20736i
$554$	12.3205			0.523448
$555$		0			0
$556$	0.535898	+	0.928203i	0.0227272	+	0.0393646i
$557$	7.33013	+	12.6962i	0.310587	+	0.537953i	0.978490	−	0.206296i	$-0.0661409\pi$
$557$	7.33013	+	12.6962i	0.310587	+	0.537953i	−0.667902	+	0.744249i	$0.732808\pi$
$558$	4.00000			0.169334
$559$	−9.80385	−	6.53590i	−0.414659	−	0.276439i
$560$		0			0
$561$	−1.63397	−	2.83013i	−0.0689865	−	0.119488i
$562$	−0.866025	−	1.50000i	−0.0365311	−	0.0632737i
$563$	−4.00000	+	6.92820i	−0.168580	+	0.291989i	−0.937921	−	0.346850i	$-0.887251\pi$
$563$	−4.00000	+	6.92820i	−0.168580	+	0.291989i	0.769341	+	0.638838i	$0.220585\pi$
$564$	7.66025			0.322555
$565$		0			0
$566$	−3.83013	+	6.63397i	−0.160992	+	0.278847i
$567$	2.73205			0.114735
$568$	−0.633975	+	1.09808i	−0.0266010	+	0.0460743i
$569$	−9.07180	−	15.7128i	−0.380310	−	0.658715i	0.610797	−	0.791787i	$-0.290849\pi$
$569$	−9.07180	−	15.7128i	−0.380310	−	0.658715i	−0.991106	+	0.133072i	$0.957516\pi$
$570$		0			0
$571$	−25.6603			−1.07385			−0.536924	−	0.843631i	$-0.680414\pi$
$571$	−25.6603			−1.07385			−0.536924	+	0.843631i	$0.680414\pi$
$572$	0.169873	−	2.63397i	0.00710275	−	0.110132i
$573$	−9.46410			−0.395369
$574$	12.5622	+	21.7583i	0.524335	+	0.908175i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	23.9808			0.998332			0.499166	−	0.866506i	$-0.333640\pi$
$577$	23.9808			0.998332			0.499166	+	0.866506i	$0.333640\pi$
$578$	−1.46410	+	2.53590i	−0.0608986	+	0.105479i
$579$	5.33013	−	9.23205i	0.221513	−	0.383671i
$580$		0			0
$581$	−7.19615	+	12.4641i	−0.298547	+	0.517098i
$582$	5.00000	+	8.66025i	0.207257	+	0.358979i
$583$	−2.83013	−	4.90192i	−0.117212	−	0.203017i
$584$	−4.66025			−0.192843
$585$		0			0
$586$	13.7321			0.567266
$587$	−5.07180	−	8.78461i	−0.209335	−	0.362580i	0.742170	−	0.670212i	$-0.233797\pi$
$587$	−5.07180	−	8.78461i	−0.209335	−	0.362580i	−0.951505	+	0.307632i	$0.900463\pi$
$588$	−0.232051	−	0.401924i	−0.00956961	−	0.0165751i
$589$	−2.53590	+	4.39230i	−0.104490	+	0.180982i
$590$		0			0
$591$	−4.92820	+	8.53590i	−0.202719	+	0.351120i
$592$	−3.96410	+	6.86603i	−0.162924	+	0.282192i
$593$	19.3923			0.796347			0.398173	−	0.917310i	$-0.369644\pi$
$593$	19.3923			0.796347			0.398173	+	0.917310i	$0.369644\pi$
$594$	−0.366025	+	0.633975i	−0.0150182	+	0.0260123i
$595$		0			0
$596$	−9.96410	−	17.2583i	−0.408146	−	0.706929i
$597$	−28.0526			−1.14811
$598$	18.5885	+	12.3923i	0.760139	+	0.506759i
$599$	8.78461			0.358929			0.179465	−	0.983764i	$-0.442563\pi$
$599$	8.78461			0.358929			0.179465	+	0.983764i	$0.442563\pi$
$600$		0			0
$601$	−8.50000	−	14.7224i	−0.346722	−	0.600541i	0.638943	−	0.769254i	$-0.279372\pi$
$601$	−8.50000	−	14.7224i	−0.346722	−	0.600541i	−0.985665	+	0.168714i	$0.946039\pi$
$602$	4.46410	−	7.73205i	0.181943	−	0.315135i
$603$	7.66025			0.311950
$604$	2.56218	−	4.43782i	0.104254	−	0.180572i
$605$		0			0
$606$	13.9282			0.565795
$607$	−24.1962	+	41.9090i	−0.982092	+	1.70103i	−0.327883	+	0.944718i	$0.606335\pi$
$607$	−24.1962	+	41.9090i	−0.982092	+	1.70103i	−0.654209	+	0.756314i	$0.726998\pi$
$608$	−0.633975	−	1.09808i	−0.0257111	−	0.0445329i
$609$	8.83013	+	15.2942i	0.357815	+	0.619753i
$610$		0			0
$611$	1.77757	−	27.5622i	0.0719127	−	1.11505i
$612$	4.46410			0.180451
$613$	−10.8923	−	18.8660i	−0.439936	−	0.761992i	0.557748	−	0.830010i	$-0.311666\pi$
$613$	−10.8923	−	18.8660i	−0.439936	−	0.761992i	−0.997684	+	0.0680188i	$0.978332\pi$
$614$	9.63397	+	16.6865i	0.388796	+	0.673414i
$615$		0			0
$616$	2.00000			0.0805823
$617$	16.3564	−	28.3301i	0.658484	−	1.14053i	−0.322524	−	0.946561i	$-0.604531\pi$
$617$	16.3564	−	28.3301i	0.658484	−	1.14053i	0.981008	−	0.193967i	$-0.0621354\pi$
$618$	−4.63397	+	8.02628i	−0.186406	+	0.322864i
$619$	−36.1051			−1.45119			−0.725594	−	0.688123i	$-0.758435\pi$
$619$	−36.1051			−1.45119			−0.725594	+	0.688123i	$0.758435\pi$
$620$		0			0
$621$	−3.09808	−	5.36603i	−0.124322	−	0.215331i
$622$	−1.56218	−	2.70577i	−0.0626376	−	0.108492i
$623$	−13.4641			−0.539428
$624$	3.00000	+	2.00000i	0.120096	+	0.0800641i
$625$		0			0
$626$	7.00000	+	12.1244i	0.279776	+	0.484587i
$627$	−0.464102	−	0.803848i	−0.0185344	−	0.0321026i
$628$	−4.69615	+	8.13397i	−0.187397	+	0.324581i
$629$	35.3923			1.41118
$630$		0			0
$631$	−4.92820	+	8.53590i	−0.196189	+	0.339809i	−0.947290	−	0.320379i	$-0.896190\pi$
$631$	−4.92820	+	8.53590i	−0.196189	+	0.339809i	0.751101	+	0.660187i	$0.229523\pi$
$632$	12.0000			0.477334
$633$	10.7321	−	18.5885i	0.426561	−	0.738825i
$634$	−14.8660	−	25.7487i	−0.590405	−	1.02261i
$635$		0			0
$636$	7.73205			0.306596
$637$	−1.50000	+	0.741670i	−0.0594322	+	0.0293860i
$638$	−4.73205			−0.187344
$639$	−0.633975	−	1.09808i	−0.0250796	−	0.0434392i
$640$		0			0
$641$	−4.52628	+	7.83975i	−0.178777	+	0.309651i	−0.941462	−	0.337119i	$-0.890547\pi$
$641$	−4.52628	+	7.83975i	−0.178777	+	0.309651i	0.762685	+	0.646770i	$0.223881\pi$
$642$	1.26795			0.0500420
$643$	4.39230	−	7.60770i	0.173216	−	0.300018i	−0.766327	−	0.642451i	$-0.777918\pi$
$643$	4.39230	−	7.60770i	0.173216	−	0.300018i	0.939542	+	0.342433i	$0.111251\pi$
$644$	−8.46410	+	14.6603i	−0.333532	+	0.577695i
$645$		0			0
$646$	−2.83013	+	4.90192i	−0.111350	+	0.192864i
$647$	11.6603	+	20.1962i	0.458412	+	0.793993i	0.998877	−	0.0473736i	$-0.0150851\pi$
$647$	11.6603	+	20.1962i	0.458412	+	0.793993i	−0.540465	+	0.841366i	$0.681752\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−9.07180			−0.356099
$650$		0			0
$651$	10.9282			0.428310
$652$	6.73205	+	11.6603i	0.263647	+	0.456651i
$653$	−16.3205	−	28.2679i	−0.638671	−	1.10621i	−0.985725	−	0.168365i	$-0.946151\pi$
$653$	−16.3205	−	28.2679i	−0.638671	−	1.10621i	0.347054	−	0.937845i	$-0.387182\pi$
$654$	−5.00000	+	8.66025i	−0.195515	+	0.338643i
$655$		0			0
$656$	4.59808	−	7.96410i	0.179525	−	0.310946i
$657$	2.33013	−	4.03590i	0.0909069	−	0.157455i
$658$	20.9282			0.815866
$659$	20.7321	−	35.9090i	0.807606	−	1.39881i	−0.106912	−	0.994269i	$-0.534096\pi$
$659$	20.7321	−	35.9090i	0.807606	−	1.39881i	0.914518	−	0.404546i	$-0.132570\pi$
$660$		0			0
$661$	19.2583	+	33.3564i	0.749062	+	1.29741i	0.948273	+	0.317457i	$0.102829\pi$
$661$	19.2583	+	33.3564i	0.749062	+	1.29741i	−0.199210	+	0.979957i	$0.563838\pi$
$662$	−28.7846			−1.11875
$663$	1.03590	−	16.0622i	0.0402310	−	0.623803i
$664$	5.26795			0.204436
$665$		0			0
$666$	−3.96410	−	6.86603i	−0.153606	−	0.266053i
$667$	20.0263	−	34.6865i	0.775421	−	1.34307i
$668$	−13.8564			−0.536120
$669$	0.196152	−	0.339746i	0.00758369	−	0.0131353i
$670$		0			0
$671$	−7.41154			−0.286119
$672$	−1.36603	+	2.36603i	−0.0526956	+	0.0912714i
$673$	−5.13397	−	8.89230i	−0.197900	−	0.342773i	0.749947	−	0.661498i	$-0.230079\pi$
$673$	−5.13397	−	8.89230i	−0.197900	−	0.342773i	−0.947847	+	0.318725i	$0.896746\pi$
$674$	−5.52628	−	9.57180i	−0.212864	−	0.368692i
$675$		0			0
$676$	7.89230	−	10.3301i	0.303550	−	0.397313i
$677$	−48.6410			−1.86943			−0.934713	−	0.355403i	$-0.884344\pi$
$677$	−48.6410			−1.86943			−0.934713	+	0.355403i	$0.884344\pi$
$678$	−4.50000	−	7.79423i	−0.172821	−	0.299336i
$679$	13.6603	+	23.6603i	0.524232	+	0.907997i
$680$		0			0
$681$	−4.19615			−0.160797
$682$	−1.46410	+	2.53590i	−0.0560633	+	0.0971046i
$683$	13.4641	−	23.3205i	0.515190	−	0.892334i	−0.484655	−	0.874705i	$-0.661055\pi$
$683$	13.4641	−	23.3205i	0.515190	−	0.892334i	0.999845	−	0.0176291i	$-0.00561180\pi$
$684$	1.26795			0.0484812
$685$		0			0
$686$	8.92820	+	15.4641i	0.340880	+	0.590422i
$687$	−14.3923	−	24.9282i	−0.549101	−	0.951070i
$688$	−3.26795			−0.124589
$689$	1.79423	−	27.8205i	0.0683547	−	1.05988i
$690$		0			0
$691$	−20.2942	−	35.1506i	−0.772029	−	1.33719i	−0.936449	−	0.350803i	$-0.885909\pi$
$691$	−20.2942	−	35.1506i	−0.772029	−	1.33719i	0.164420	−	0.986390i	$-0.447425\pi$
$692$	9.39230	+	16.2679i	0.357042	+	0.618415i
$693$	−1.00000	+	1.73205i	−0.0379869	+	0.0657952i
$694$	−5.66025			−0.214860
$695$		0			0
$696$	3.23205	−	5.59808i	0.122511	−	0.212195i
$697$	−41.0526			−1.55498
$698$	9.53590	−	16.5167i	0.360939	−	0.625165i
$699$	−6.19615	−	10.7321i	−0.234360	−	0.405923i
$700$		0			0
$701$	−13.4641			−0.508532			−0.254266	−	0.967134i	$-0.581834\pi$
$701$	−13.4641			−0.508532			−0.254266	+	0.967134i	$0.581834\pi$
$702$	−3.23205	+	1.59808i	−0.121986	+	0.0603155i
$703$	10.0526			0.379139
$704$	−0.366025	−	0.633975i	−0.0137951	−	0.0238938i
$705$		0			0
$706$	12.6244	−	21.8660i	0.475124	−	0.822939i
$707$	38.0526			1.43111
$708$	6.19615	−	10.7321i	0.232866	−	0.403335i
$709$	−18.5263	+	32.0885i	−0.695769	+	1.20511i	0.274152	+	0.961686i	$0.411603\pi$
$709$	−18.5263	+	32.0885i	−0.695769	+	1.20511i	−0.969921	+	0.243421i	$0.921730\pi$
$710$		0			0
$711$	−6.00000	+	10.3923i	−0.225018	+	0.389742i
$712$	2.46410	+	4.26795i	0.0923461	+	0.159948i
$713$	−12.3923	−	21.4641i	−0.464095	−	0.803837i
$714$	12.1962			0.456430
$715$		0			0
$716$	18.1962			0.680022
$717$	2.29423	+	3.97372i	0.0856795	+	0.148401i
$718$	−4.43782	−	7.68653i	−0.165618	−	0.286859i
$719$	16.1962	−	28.0526i	0.604015	−	1.04618i	−0.388192	−	0.921579i	$-0.626900\pi$
$719$	16.1962	−	28.0526i	0.604015	−	1.04618i	0.992206	−	0.124605i	$-0.0397665\pi$
$720$		0			0
$721$	−12.6603	+	21.9282i	−0.471492	+	0.816649i
$722$	8.69615	−	15.0622i	0.323637	−	0.560556i
$723$	−9.39230			−0.349304
$724$	8.06218	−	13.9641i	0.299628	−	0.518972i
$725$		0			0
$726$	5.23205	+	9.06218i	0.194180	+	0.336329i
$727$	−13.2679			−0.492081			−0.246040	−	0.969260i	$-0.579130\pi$
$727$	−13.2679			−0.492081			−0.246040	+	0.969260i	$0.579130\pi$
$728$	8.19615	+	5.46410i	0.303770	+	0.202513i
$729$	1.00000			0.0370370
$730$		0			0
$731$	7.29423	+	12.6340i	0.269787	+	0.467284i
$732$	5.06218	−	8.76795i	0.187103	−	0.324073i
$733$	45.3923			1.67660			0.838302	−	0.545207i	$-0.183549\pi$
$733$	45.3923			1.67660			0.838302	+	0.545207i	$0.183549\pi$
$734$	−16.4904	+	28.5622i	−0.608671	+	1.05425i
$735$		0			0
$736$	6.19615			0.228393
$737$	−2.80385	+	4.85641i	−0.103281	+	0.178888i
$738$	4.59808	+	7.96410i	0.169258	+	0.293163i
$739$	−1.07180	−	1.85641i	−0.0394267	−	0.0682890i	0.845639	−	0.533756i	$-0.179220\pi$
$739$	−1.07180	−	1.85641i	−0.0394267	−	0.0682890i	−0.885065	+	0.465467i	$0.845886\pi$
$740$		0			0
$741$	0.294229	−	4.56218i	0.0108088	−	0.167596i
$742$	21.1244			0.775499
$743$	10.7321	+	18.5885i	0.393721	+	0.681944i	0.992937	−	0.118643i	$-0.0378544\pi$
$743$	10.7321	+	18.5885i	0.393721	+	0.681944i	−0.599216	+	0.800587i	$0.704521\pi$
$744$	−2.00000	−	3.46410i	−0.0733236	−	0.127000i
$745$		0			0
$746$	23.5359			0.861710
$747$	−2.63397	+	4.56218i	−0.0963721	+	0.166921i
$748$	−1.63397	+	2.83013i	−0.0597440	+	0.103480i
$749$	3.46410			0.126576
$750$		0			0
$751$	−18.0263	−	31.2224i	−0.657788	−	1.13932i	−0.981187	−	0.193060i	$-0.938159\pi$
$751$	−18.0263	−	31.2224i	−0.657788	−	1.13932i	0.323399	−	0.946263i	$-0.395175\pi$
$752$	−3.83013	−	6.63397i	−0.139670	−	0.241916i
$753$	−21.4641			−0.782195
$754$	−19.3923	−	12.9282i	−0.706226	−	0.470817i
$755$		0			0
$756$	−1.36603	−	2.36603i	−0.0496819	−	0.0860515i
$757$	20.0526	+	34.7321i	0.728823	+	1.26236i	0.957381	+	0.288828i	$0.0932655\pi$
$757$	20.0526	+	34.7321i	0.728823	+	1.26236i	−0.228558	+	0.973530i	$0.573401\pi$
$758$	−13.1244	+	22.7321i	−0.476698	+	0.825665i
$759$	4.53590			0.164643
$760$		0			0
$761$	−11.5359	+	19.9808i	−0.418176	+	0.724302i	−0.995756	−	0.0920320i	$-0.970664\pi$
$761$	−11.5359	+	19.9808i	−0.418176	+	0.724302i	0.577580	+	0.816334i	$0.303997\pi$
$762$	4.00000			0.144905
$763$	−13.6603	+	23.6603i	−0.494534	+	0.856559i
$764$	4.73205	+	8.19615i	0.171200	+	0.296526i
$765$		0			0
$766$	26.9282			0.972956
$767$	−37.1769	−	24.7846i	−1.34238	−	0.894920i
$768$	1.00000			0.0360844
$769$	−22.7321	−	39.3731i	−0.819739	−	1.41983i	−0.905875	−	0.423546i	$-0.860785\pi$
$769$	−22.7321	−	39.3731i	−0.819739	−	1.41983i	0.0861360	−	0.996283i	$-0.472548\pi$
$770$		0			0
$771$	1.50000	−	2.59808i	0.0540212	−	0.0935674i
$772$	−10.6603			−0.383671
$773$	−20.3205	+	35.1962i	−0.730878	+	1.26592i	0.225631	+	0.974213i	$0.427556\pi$
$773$	−20.3205	+	35.1962i	−0.730878	+	1.26592i	−0.956508	+	0.291705i	$0.905778\pi$
$774$	1.63397	−	2.83013i	0.0587320	−	0.101727i
$775$		0			0
$776$	5.00000	−	8.66025i	0.179490	−	0.310885i
$777$	−10.8301	−	18.7583i	−0.388529	−	0.672951i
$778$	12.0359	+	20.8468i	0.431508	+	0.747394i
$779$	−11.6603			−0.417772
$780$		0			0
$781$	0.928203			0.0332137
$782$	−13.8301	−	23.9545i	−0.494564	−	0.856611i
$783$	3.23205	+	5.59808i	0.115504	+	0.200059i
$784$	−0.232051	+	0.401924i	−0.00828753	+	0.0143544i
$785$		0			0
$786$	6.92820	−	12.0000i	0.247121	−	0.428026i
$787$	9.66025	−	16.7321i	0.344351	−	0.596433i	−0.640885	−	0.767637i	$-0.721432\pi$
$787$	9.66025	−	16.7321i	0.344351	−	0.596433i	0.985236	+	0.171204i	$0.0547657\pi$
$788$	9.85641			0.351120
$789$	8.56218	−	14.8301i	0.304822	−	0.527967i
$790$		0			0
$791$	−12.2942	−	21.2942i	−0.437132	−	0.757136i
$792$	0.732051			0.0260123
$793$	−30.3731	−	20.2487i	−1.07858	−	0.719053i
$794$	−19.3205			−0.685659
$795$		0			0
$796$	14.0263	+	24.2942i	0.497148	+	0.861086i
$797$	0.535898	−	0.928203i	0.0189825	−	0.0328786i	−0.856378	−	0.516349i	$-0.827291\pi$
$797$	0.535898	−	0.928203i	0.0189825	−	0.0328786i	0.875361	+	0.483471i	$0.160624\pi$
$798$	3.46410			0.122628
$799$	−17.0981	+	29.6147i	−0.604886	+	1.04769i
$800$		0			0
$801$	−4.92820			−0.174129
$802$	4.52628	−	7.83975i	0.159828	−	0.276831i
$803$	1.70577	+	2.95448i	0.0601954	+	0.104261i
$804$	−3.83013	−	6.63397i	−0.135078	−	0.233962i
$805$		0			0
$806$	−12.9282	+	6.39230i	−0.455377	+	0.225159i
$807$	4.39230			0.154616
$808$	−6.96410	−	12.0622i	−0.244996	−	0.424346i
$809$	−0.990381	−	1.71539i	−0.0348199	−	0.0603099i	0.848090	−	0.529852i	$-0.177752\pi$
$809$	−0.990381	−	1.71539i	−0.0348199	−	0.0603099i	−0.882910	+	0.469542i	$0.844419\pi$
$810$		0			0
$811$	−33.8564			−1.18886			−0.594430	−	0.804148i	$-0.702622\pi$
$811$	−33.8564			−1.18886			−0.594430	+	0.804148i	$0.702622\pi$
$812$	8.83013	−	15.2942i	0.309877	−	0.536722i
$813$	−2.92820	+	5.07180i	−0.102697	+	0.177876i
$814$	5.80385			0.203425
$815$		0			0
$816$	−2.23205	−	3.86603i	−0.0781374	−	0.135338i
$817$	2.07180	+	3.58846i	0.0724830	+	0.125544i
$818$	16.0718			0.561937
$819$	−8.83013	+	4.36603i	−0.308550	+	0.152561i
$820$		0			0
$821$	−5.12436	−	8.87564i	−0.178841	−	0.309762i	0.762643	−	0.646820i	$-0.223902\pi$
$821$	−5.12436	−	8.87564i	−0.178841	−	0.309762i	−0.941484	+	0.337058i	$0.890568\pi$
$822$	−9.23205	−	15.9904i	−0.322005	−	0.557729i
$823$	20.1962	−	34.9808i	0.703994	−	1.21935i	−0.263060	−	0.964780i	$-0.584732\pi$
$823$	20.1962	−	34.9808i	0.703994	−	1.21935i	0.967054	−	0.254573i	$-0.0819350\pi$
$824$	9.26795			0.322864
$825$		0			0
$826$	16.9282	−	29.3205i	0.589008	−	1.02019i
$827$	48.7846			1.69641			0.848204	−	0.529670i	$-0.177684\pi$
$827$	48.7846			1.69641			0.848204	+	0.529670i	$0.177684\pi$
$828$	−3.09808	+	5.36603i	−0.107666	+	0.186482i
$829$	−8.93782	−	15.4808i	−0.310423	−	0.537669i	0.668031	−	0.744134i	$-0.267137\pi$
$829$	−8.93782	−	15.4808i	−0.310423	−	0.537669i	−0.978454	+	0.206465i	$0.933804\pi$
$830$		0			0
$831$	12.3205			0.427394
$832$	0.232051	−	3.59808i	0.00804491	−	0.124741i
$833$	2.07180			0.0717835
$834$	0.535898	+	0.928203i	0.0185566	+	0.0321410i
$835$		0			0
$836$	−0.464102	+	0.803848i	−0.0160513	+	0.0278016i
$837$	4.00000			0.138260
$838$	3.26795	−	5.66025i	0.112889	−	0.195530i
$839$	−24.0526	+	41.6603i	−0.830387	+	1.43827i	0.0673455	+	0.997730i	$0.478547\pi$
$839$	−24.0526	+	41.6603i	−0.830387	+	1.43827i	−0.897732	+	0.440542i	$0.854786\pi$
$840$		0			0
$841$	−6.39230	+	11.0718i	−0.220424	+	0.381786i
$842$	−8.52628	−	14.7679i	−0.293835	−	0.508937i
$843$	−0.866025	−	1.50000i	−0.0298275	−	0.0516627i
$844$	−21.4641			−0.738825
$845$		0			0
$846$	7.66025			0.263365
$847$	14.2942	+	24.7583i	0.491156	+	0.850706i
$848$	−3.86603	−	6.69615i	−0.132760	−	0.229947i
$849$	−3.83013	+	6.63397i	−0.131450	+	0.227677i
$850$		0			0
$851$	−24.5622	+	42.5429i	−0.841981	+	1.45835i
$852$	−0.633975	+	1.09808i	−0.0217196	+	0.0376195i
$853$	−12.0718			−0.413330			−0.206665	−	0.978412i	$-0.566261\pi$
$853$	−12.0718			−0.413330			−0.206665	+	0.978412i	$0.566261\pi$
$854$	13.8301	−	23.9545i	0.473257	−	0.819706i
$855$		0			0
$856$	−0.633975	−	1.09808i	−0.0216688	−	0.0375315i
$857$	3.92820			0.134185			0.0670924	−	0.997747i	$-0.478628\pi$
$857$	3.92820			0.134185			0.0670924	+	0.997747i	$0.478628\pi$
$858$	0.169873	−	2.63397i	0.00579937	−	0.0899224i
$859$	−44.3013			−1.51154			−0.755770	−	0.654837i	$-0.772737\pi$
$859$	−44.3013			−1.51154			−0.755770	+	0.654837i	$0.772737\pi$
$860$		0			0
$861$	12.5622	+	21.7583i	0.428118	+	0.741522i
$862$	3.90192	−	6.75833i	0.132900	−	0.230190i
$863$	21.1244			0.719081			0.359541	−	0.933129i	$-0.382933\pi$
$863$	21.1244			0.719081			0.359541	+	0.933129i	$0.382933\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$		0			0
$866$	−14.8038			−0.503055
$867$	−1.46410	+	2.53590i	−0.0497235	+	0.0861236i
$868$	−5.46410	−	9.46410i	−0.185464	−	0.321233i
$869$	−4.39230	−	7.60770i	−0.148999	−	0.258073i
$870$		0			0
$871$	−24.7583	+	12.2417i	−0.838904	+	0.414793i
$872$	10.0000			0.338643
$873$	5.00000	+	8.66025i	0.169224	+	0.293105i
$874$	−3.92820	−	6.80385i	−0.132873	−	0.230144i
$875$		0			0
$876$	−4.66025			−0.157455
$877$	4.76795	−	8.25833i	0.161002	−	0.278864i	−0.774226	−	0.632909i	$-0.781861\pi$
$877$	4.76795	−	8.25833i	0.161002	−	0.278864i	0.935228	+	0.354045i	$0.115194\pi$
$878$	−4.90192	+	8.49038i	−0.165432	+	0.286536i
$879$	13.7321			0.463171
$880$		0			0
$881$	−8.93782	−	15.4808i	−0.301123	−	0.521560i	0.675268	−	0.737573i	$-0.264028\pi$
$881$	−8.93782	−	15.4808i	−0.301123	−	0.521560i	−0.976391	+	0.216013i	$0.930695\pi$
$882$	−0.232051	−	0.401924i	−0.00781356	−	0.0135335i
$883$	−18.2487			−0.614118			−0.307059	−	0.951690i	$-0.599345\pi$
$883$	−18.2487			−0.614118			−0.307059	+	0.951690i	$0.599345\pi$
$884$	−14.4282	+	7.13397i	−0.485273	+	0.239942i
$885$		0			0
$886$	−17.3205	−	30.0000i	−0.581894	−	1.00787i
$887$	−14.5359	−	25.1769i	−0.488068	−	0.845358i	0.511838	−	0.859082i	$-0.328965\pi$
$887$	−14.5359	−	25.1769i	−0.488068	−	0.845358i	−0.999906	+	0.0137239i	$0.995631\pi$
$888$	−3.96410	+	6.86603i	−0.133027	+	0.230409i
$889$	10.9282			0.366520
$890$		0			0
$891$	−0.366025	+	0.633975i	−0.0122623	+	0.0212389i
$892$	−0.392305			−0.0131353
$893$	−4.85641	+	8.41154i	−0.162513	+	0.281482i
$894$	−9.96410	−	17.2583i	−0.333249	−	0.577205i
$895$		0			0
$896$	2.73205			0.0912714
$897$	18.5885	+	12.3923i	0.620651	+	0.413767i
$898$	−7.85641			−0.262172
$899$	12.9282	+	22.3923i	0.431180	+	0.746825i
$900$		0			0
$901$	−17.2583	+	29.8923i	−0.574958	+	0.995857i
$902$	−6.73205			−0.224153
$903$	4.46410	−	7.73205i	0.148556	−	0.257307i
$904$	−4.50000	+	7.79423i	−0.149668	+	0.259232i
$905$		0			0
$906$	2.56218	−	4.43782i	0.0851227	−	0.147437i
$907$	−3.46410	−	6.00000i	−0.115024	−	0.199227i	0.802766	−	0.596295i	$-0.203361\pi$
$907$	−3.46410	−	6.00000i	−0.115024	−	0.199227i	−0.917789	+	0.397068i	$0.870028\pi$
$908$	2.09808	+	3.63397i	0.0696271	+	0.120598i
$909$	13.9282			0.461969
$910$		0			0
$911$	44.1051			1.46127			0.730634	−	0.682769i	$-0.239225\pi$
$911$	44.1051			1.46127			0.730634	+	0.682769i	$0.239225\pi$
$912$	−0.633975	−	1.09808i	−0.0209930	−	0.0363609i
$913$	−1.92820	−	3.33975i	−0.0638142	−	0.110529i
$914$	4.40192	−	7.62436i	0.145603	−	0.252191i
$915$		0			0
$916$	−14.3923	+	24.9282i	−0.475535	+	0.823651i
$917$	18.9282	−	32.7846i	0.625064	−	1.08264i
$918$	4.46410			0.147337
$919$	28.7321	−	49.7654i	0.947783	−	1.64161i	0.197702	−	0.980262i	$-0.436652\pi$
$919$	28.7321	−	49.7654i	0.947783	−	1.64161i	0.750081	−	0.661346i	$-0.230014\pi$
$920$		0			0
$921$	9.63397	+	16.6865i	0.317450	+	0.549840i
$922$	26.0718			0.858629
$923$	3.80385	+	2.53590i	0.125205	+	0.0834701i
$924$	2.00000			0.0657952
$925$		0			0
$926$	3.16987	+	5.49038i	0.104168	+	0.180425i
$927$	−4.63397	+	8.02628i	−0.152200	+	0.263618i
$928$	−6.46410			−0.212195
$929$	−19.7942	+	34.2846i	−0.649428	+	1.12484i	0.333832	+	0.942633i	$0.391658\pi$
$929$	−19.7942	+	34.2846i	−0.649428	+	1.12484i	−0.983260	+	0.182209i	$0.941675\pi$
$930$		0			0
$931$	0.588457			0.0192859
$932$	−6.19615	+	10.7321i	−0.202962	+	0.351540i
$933$	−1.56218	−	2.70577i	−0.0511434	−	0.0885830i
$934$	11.0263	+	19.0981i	0.360791	+	0.624908i
$935$		0			0
$936$	3.00000	+	2.00000i	0.0980581	+	0.0653720i
$937$	−17.0526			−0.557083			−0.278541	−	0.960424i	$-0.589851\pi$
$937$	−17.0526			−0.557083			−0.278541	+	0.960424i	$0.589851\pi$
$938$	−10.4641	−	18.1244i	−0.341665	−	0.591781i
$939$	7.00000	+	12.1244i	0.228436	+	0.395663i
$940$		0			0
$941$	12.3923			0.403978			0.201989	−	0.979388i	$-0.435260\pi$
$941$	12.3923			0.403978			0.201989	+	0.979388i	$0.435260\pi$
$942$	−4.69615	+	8.13397i	−0.153009	+	0.265019i
$943$	28.4904	−	49.3468i	0.927774	−	1.60695i
$944$	−12.3923			−0.403335
$945$		0			0
$946$	1.19615	+	2.07180i	0.0388903	+	0.0673599i
$947$	−13.8564	−	24.0000i	−0.450273	−	0.779895i	0.548130	−	0.836393i	$-0.315340\pi$
$947$	−13.8564	−	24.0000i	−0.450273	−	0.779895i	−0.998403	+	0.0564979i	$0.982007\pi$
$948$	12.0000			0.389742
$949$	−1.08142	+	16.7679i	−0.0351042	+	0.544311i
$950$		0			0
$951$	−14.8660	−	25.7487i	−0.482064	−	0.834959i
$952$	−6.09808	−	10.5622i	−0.197640	−	0.342322i
$953$	18.8564	−	32.6603i	0.610819	−	1.05797i	−0.380284	−	0.924870i	$-0.624174\pi$
$953$	18.8564	−	32.6603i	0.610819	−	1.05797i	0.991103	−	0.133100i	$-0.0424930\pi$
$954$	7.73205			0.250334
$955$		0			0
$956$	2.29423	−	3.97372i	0.0742007	−	0.128519i
$957$	−4.73205			−0.152965
$958$	8.00000	−	13.8564i	0.258468	−	0.447680i
$959$	−25.2224	−	43.6865i	−0.814475	−	1.41071i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	23.7846	+	15.8564i	0.766847	+	0.511231i
$963$	1.26795			0.0408591
$964$	4.69615	+	8.13397i	0.151253	+	0.261978i
$965$		0			0
$966$	−8.46410	+	14.6603i	−0.272328	+	0.471686i
$967$	−16.5885			−0.533449			−0.266724	−	0.963773i	$-0.585941\pi$
$967$	−16.5885			−0.533449			−0.266724	+	0.963773i	$0.585941\pi$
$968$	5.23205	−	9.06218i	0.168164	−	0.291269i
$969$	−2.83013	+	4.90192i	−0.0909168	+	0.157472i
$970$		0			0
$971$	27.4641	−	47.5692i	0.881365	−	1.52657i	0.0315409	−	0.999502i	$-0.489959\pi$
$971$	27.4641	−	47.5692i	0.881365	−	1.52657i	0.849824	−	0.527066i	$-0.176708\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	1.46410	+	2.53590i	0.0469369	+	0.0812972i
$974$	38.4449			1.23185
$975$		0			0
$976$	−10.1244			−0.324073
$977$	−10.6244	−	18.4019i	−0.339903	−	0.588730i	0.644511	−	0.764595i	$-0.277061\pi$
$977$	−10.6244	−	18.4019i	−0.339903	−	0.588730i	−0.984414	+	0.175865i	$0.943728\pi$
$978$	6.73205	+	11.6603i	0.215267	+	0.372854i
$979$	1.80385	−	3.12436i	0.0576512	−	0.0998548i
$980$		0			0
$981$	−5.00000	+	8.66025i	−0.159638	+	0.276501i
$982$	−10.9019	+	18.8827i	−0.347894	+	0.602571i
$983$	−31.7128			−1.01148			−0.505741	−	0.862685i	$-0.668781\pi$
$983$	−31.7128			−1.01148			−0.505741	+	0.862685i	$0.668781\pi$
$984$	4.59808	−	7.96410i	0.146581	−	0.253886i
$985$		0			0
$986$	14.4282	+	24.9904i	0.459488	+	0.795856i
$987$	20.9282			0.666152
$988$	−4.09808	+	2.02628i	−0.130377	+	0.0644645i
$989$	−20.2487			−0.643872
$990$		0			0
$991$	−4.02628	−	6.97372i	−0.127899	−	0.221528i	0.794963	−	0.606657i	$-0.207490\pi$
$991$	−4.02628	−	6.97372i	−0.127899	−	0.221528i	−0.922862	+	0.385130i	$0.874157\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$	−28.7846			−0.913452
$994$	−1.73205	+	3.00000i	−0.0549373	+	0.0951542i
$995$		0			0
$996$	5.26795			0.166921
$997$	7.96410	−	13.7942i	0.252226	−	0.436868i	−0.711913	−	0.702268i	$-0.752171\pi$
$997$	7.96410	−	13.7942i	0.252226	−	0.436868i	0.964138	+	0.265400i	$0.0855042\pi$
$998$	−20.1962	−	34.9808i	−0.639298	−	1.10730i
$999$	−3.96410	−	6.86603i	−0.125419	−	0.217231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.i.y.601.1		4
5.2	odd	4		390.2.y.b.289.2	yes	4
5.3	odd	4		390.2.y.c.289.1	yes	4
5.4	even	2		1950.2.i.bh.601.2		4
13.9	even	3	inner	1950.2.i.y.451.1		4
15.2	even	4		1170.2.bp.d.289.1		4
15.8	even	4		1170.2.bp.e.289.2		4
65.9	even	6		1950.2.i.bh.451.2		4
65.22	odd	12		390.2.y.c.139.1	yes	4
65.48	odd	12		390.2.y.b.139.2	✓	4
195.113	even	12		1170.2.bp.d.919.1		4
195.152	even	12		1170.2.bp.e.919.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.y.b.139.2	✓	4	65.48	odd	12
390.2.y.b.289.2	yes	4	5.2	odd	4
390.2.y.c.139.1	yes	4	65.22	odd	12
390.2.y.c.289.1	yes	4	5.3	odd	4
1170.2.bp.d.289.1		4	15.2	even	4
1170.2.bp.d.919.1		4	195.113	even	12
1170.2.bp.e.289.2		4	15.8	even	4
1170.2.bp.e.919.2		4	195.152	even	12
1950.2.i.y.451.1		4	13.9	even	3	inner
1950.2.i.y.601.1		4	1.1	even	1	trivial
1950.2.i.bh.451.2		4	65.9	even	6
1950.2.i.bh.601.2		4	5.4	even	2

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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-1.36603 + 2.36603i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-1.36603 + 2.36603i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.366025 - 0.633975i) q^{11} +1.00000 q^{12} +(0.232051 - 3.59808i) q^{13} +2.73205 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.23205 + 3.86603i) q^{17} +1.00000 q^{18} +(-0.633975 + 1.09808i) q^{19} +2.73205 q^{21} +(-0.366025 + 0.633975i) q^{22} +(-3.09808 - 5.36603i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.23205 + 1.59808i) q^{26} +1.00000 q^{27} +(-1.36603 - 2.36603i) q^{28} +(3.23205 + 5.59808i) q^{29} +4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.366025 + 0.633975i) q^{33} +4.46410 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-3.96410 - 6.86603i) q^{37} +1.26795 q^{38} +(-3.23205 + 1.59808i) q^{39} +(4.59808 + 7.96410i) q^{41} +(-1.36603 - 2.36603i) q^{42} +(1.63397 - 2.83013i) q^{43} +0.732051 q^{44} +(-3.09808 + 5.36603i) q^{46} +7.66025 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.232051 - 0.401924i) q^{49} +4.46410 q^{51} +(3.00000 + 2.00000i) q^{52} +7.73205 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-1.36603 + 2.36603i) q^{56} +1.26795 q^{57} +(3.23205 - 5.59808i) q^{58} +(6.19615 - 10.7321i) q^{59} +(5.06218 - 8.76795i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-1.36603 - 2.36603i) q^{63} +1.00000 q^{64} +0.732051 q^{66} +(-3.83013 - 6.63397i) q^{67} +(-2.23205 - 3.86603i) q^{68} +(-3.09808 + 5.36603i) q^{69} +(-0.633975 + 1.09808i) q^{71} +(-0.500000 + 0.866025i) q^{72} -4.66025 q^{73} +(-3.96410 + 6.86603i) q^{74} +(-0.633975 - 1.09808i) q^{76} +2.00000 q^{77} +(3.00000 + 2.00000i) q^{78} +12.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(4.59808 - 7.96410i) q^{82} +5.26795 q^{83} +(-1.36603 + 2.36603i) q^{84} -3.26795 q^{86} +(3.23205 - 5.59808i) q^{87} +(-0.366025 - 0.633975i) q^{88} +(2.46410 + 4.26795i) q^{89} +(8.19615 + 5.46410i) q^{91} +6.19615 q^{92} +(-2.00000 - 3.46410i) q^{93} +(-3.83013 - 6.63397i) q^{94} +1.00000 q^{96} +(5.00000 - 8.66025i) q^{97} +(-0.232051 + 0.401924i) q^{98} +0.732051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + 2 q^{11} + 4 q^{12} - 6 q^{13} + 4 q^{14} - 2 q^{16} - 2 q^{17} + 4 q^{18} - 6 q^{19} + 4 q^{21} + 2 q^{22} - 2 q^{23} - 2 q^{24} - 6 q^{26} + 4 q^{27} - 2 q^{28} + 6 q^{29} + 16 q^{31} - 2 q^{32} + 2 q^{33} + 4 q^{34} - 2 q^{36} - 2 q^{37} + 12 q^{38} - 6 q^{39} + 8 q^{41} - 2 q^{42} + 10 q^{43} - 4 q^{44} - 2 q^{46} - 4 q^{47} - 2 q^{48} + 6 q^{49} + 4 q^{51} + 12 q^{52} + 24 q^{53} - 2 q^{54} - 2 q^{56} + 12 q^{57} + 6 q^{58} + 4 q^{59} - 4 q^{61} - 8 q^{62} - 2 q^{63} + 4 q^{64} - 4 q^{66} + 2 q^{67} - 2 q^{68} - 2 q^{69} - 6 q^{71} - 2 q^{72} + 16 q^{73} - 2 q^{74} - 6 q^{76} + 8 q^{77} + 12 q^{78} + 48 q^{79} - 2 q^{81} + 8 q^{82} + 28 q^{83} - 2 q^{84} - 20 q^{86} + 6 q^{87} + 2 q^{88} - 4 q^{89} + 12 q^{91} + 4 q^{92} - 8 q^{93} + 2 q^{94} + 4 q^{96} + 20 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 + 2 * q^11 + 4 * q^12 - 6 * q^13 + 4 * q^14 - 2 * q^16 - 2 * q^17 + 4 * q^18 - 6 * q^19 + 4 * q^21 + 2 * q^22 - 2 * q^23 - 2 * q^24 - 6 * q^26 + 4 * q^27 - 2 * q^28 + 6 * q^29 + 16 * q^31 - 2 * q^32 + 2 * q^33 + 4 * q^34 - 2 * q^36 - 2 * q^37 + 12 * q^38 - 6 * q^39 + 8 * q^41 - 2 * q^42 + 10 * q^43 - 4 * q^44 - 2 * q^46 - 4 * q^47 - 2 * q^48 + 6 * q^49 + 4 * q^51 + 12 * q^52 + 24 * q^53 - 2 * q^54 - 2 * q^56 + 12 * q^57 + 6 * q^58 + 4 * q^59 - 4 * q^61 - 8 * q^62 - 2 * q^63 + 4 * q^64 - 4 * q^66 + 2 * q^67 - 2 * q^68 - 2 * q^69 - 6 * q^71 - 2 * q^72 + 16 * q^73 - 2 * q^74 - 6 * q^76 + 8 * q^77 + 12 * q^78 + 48 * q^79 - 2 * q^81 + 8 * q^82 + 28 * q^83 - 2 * q^84 - 20 * q^86 + 6 * q^87 + 2 * q^88 - 4 * q^89 + 12 * q^91 + 4 * q^92 - 8 * q^93 + 2 * q^94 + 4 * q^96 + 20 * q^97 + 6 * q^98 - 4 * q^99

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