LMFDB - Embedded newform 1950.2.i.z.451.2

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:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.2
Root			$1.28078 + 2.21837i$ of defining polynomial
Character	$\chi$	$=$	1950.451
Dual form			1950.2.i.z.601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(1.78078 + 3.08440i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} +(1.78078 + 3.08440i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.280776 - 0.486319i) q^{11} +1.00000 q^{12} +(2.84233 + 2.21837i) q^{13} -3.56155 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.56155 + 2.70469i) q^{17} +1.00000 q^{18} +(1.21922 + 2.11176i) q^{19} -3.56155 q^{21} +(0.280776 + 0.486319i) q^{22} +(3.84233 - 6.65511i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.34233 + 1.35234i) q^{26} +1.00000 q^{27} +(1.78078 - 3.08440i) q^{28} +(-0.561553 + 0.972638i) q^{29} +4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.280776 + 0.486319i) q^{33} -3.12311 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-0.280776 + 0.486319i) q^{37} -2.43845 q^{38} +(-3.34233 + 1.35234i) q^{39} +(1.56155 - 2.70469i) q^{41} +(1.78078 - 3.08440i) q^{42} +(-0.219224 - 0.379706i) q^{43} -0.561553 q^{44} +(3.84233 + 6.65511i) q^{46} +4.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-2.84233 + 4.92306i) q^{49} -3.12311 q^{51} +(0.500000 - 3.57071i) q^{52} +4.24621 q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.78078 + 3.08440i) q^{56} -2.43845 q^{57} +(-0.561553 - 0.972638i) q^{58} +(5.12311 + 8.87348i) q^{59} +(0.842329 + 1.45896i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(1.78078 - 3.08440i) q^{63} +1.00000 q^{64} -0.561553 q^{66} +(-5.90388 + 10.2258i) q^{67} +(1.56155 - 2.70469i) q^{68} +(3.84233 + 6.65511i) q^{69} +(-6.28078 - 10.8786i) q^{71} +(-0.500000 - 0.866025i) q^{72} +9.00000 q^{73} +(-0.280776 - 0.486319i) q^{74} +(1.21922 - 2.11176i) q^{76} +2.00000 q^{77} +(0.500000 - 3.57071i) q^{78} -15.8078 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.56155 + 2.70469i) q^{82} +6.56155 q^{83} +(1.78078 + 3.08440i) q^{84} +0.438447 q^{86} +(-0.561553 - 0.972638i) q^{87} +(0.280776 - 0.486319i) q^{88} +(-5.12311 + 8.87348i) q^{89} +(-1.78078 + 12.7173i) q^{91} -7.68466 q^{92} +(-2.00000 + 3.46410i) q^{93} +(-2.00000 + 3.46410i) q^{94} +1.00000 q^{96} +(1.40388 + 2.43160i) q^{97} +(-2.84233 - 4.92306i) q^{98} -0.561553 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} + 3 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 + 3 * q^7 + 4 * q^8 - 2 * q^9	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} + 3 q^{7} + 4 q^{8} - 2 q^{9} - 3 q^{11} + 4 q^{12} - q^{13} - 6 q^{14} - 2 q^{16} - 2 q^{17} + 4 q^{18} + 9 q^{19} - 6 q^{21} - 3 q^{22} + 3 q^{23} - 2 q^{24} - q^{26} + 4 q^{27} + 3 q^{28} + 6 q^{29} + 16 q^{31} - 2 q^{32} - 3 q^{33} + 4 q^{34} - 2 q^{36} + 3 q^{37} - 18 q^{38} - q^{39} - 2 q^{41} + 3 q^{42} - 5 q^{43} + 6 q^{44} + 3 q^{46} + 16 q^{47} - 2 q^{48} + q^{49} + 4 q^{51} + 2 q^{52} - 16 q^{53} - 2 q^{54} + 3 q^{56} - 18 q^{57} + 6 q^{58} + 4 q^{59} - 9 q^{61} - 8 q^{62} + 3 q^{63} + 4 q^{64} + 6 q^{66} - 3 q^{67} - 2 q^{68} + 3 q^{69} - 21 q^{71} - 2 q^{72} + 36 q^{73} + 3 q^{74} + 9 q^{76} + 8 q^{77} + 2 q^{78} - 22 q^{79} - 2 q^{81} - 2 q^{82} + 18 q^{83} + 3 q^{84} + 10 q^{86} + 6 q^{87} - 3 q^{88} - 4 q^{89} - 3 q^{91} - 6 q^{92} - 8 q^{93} - 8 q^{94} + 4 q^{96} - 15 q^{97} + q^{98} + 6 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^6 + 3 * q^7 + 4 * q^8 - 2 * q^9 - 3 * q^11 + 4 * q^12 - q^13 - 6 * q^14 - 2 * q^16 - 2 * q^17 + 4 * q^18 + 9 * q^19 - 6 * q^21 - 3 * q^22 + 3 * q^23 - 2 * q^24 - q^26 + 4 * q^27 + 3 * q^28 + 6 * q^29 + 16 * q^31 - 2 * q^32 - 3 * q^33 + 4 * q^34 - 2 * q^36 + 3 * q^37 - 18 * q^38 - q^39 - 2 * q^41 + 3 * q^42 - 5 * q^43 + 6 * q^44 + 3 * q^46 + 16 * q^47 - 2 * q^48 + q^49 + 4 * q^51 + 2 * q^52 - 16 * q^53 - 2 * q^54 + 3 * q^56 - 18 * q^57 + 6 * q^58 + 4 * q^59 - 9 * q^61 - 8 * q^62 + 3 * q^63 + 4 * q^64 + 6 * q^66 - 3 * q^67 - 2 * q^68 + 3 * q^69 - 21 * q^71 - 2 * q^72 + 36 * q^73 + 3 * q^74 + 9 * q^76 + 8 * q^77 + 2 * q^78 - 22 * q^79 - 2 * q^81 - 2 * q^82 + 18 * q^83 + 3 * q^84 + 10 * q^86 + 6 * q^87 - 3 * q^88 - 4 * q^89 - 3 * q^91 - 6 * q^92 - 8 * q^93 - 8 * q^94 + 4 * q^96 - 15 * q^97 + q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$7$	1.78078	+	3.08440i	0.673070	+	1.16579i	0.977029	+	0.213107i	$0.0683582\pi$
$7$	1.78078	+	3.08440i	0.673070	+	1.16579i	−0.303959	+	0.952685i	$0.598308\pi$
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	0.280776	−	0.486319i	0.0846573	−	0.146631i	−0.820588	−	0.571520i	$-0.806354\pi$
$11$	0.280776	−	0.486319i	0.0846573	−	0.146631i	0.905245	+	0.424890i	$0.139687\pi$
$12$	1.00000			0.288675
$13$	2.84233	+	2.21837i	0.788320	+	0.615265i
$13$	2.84233	+	2.21837i	0.788320	+	0.615265i
$14$	−3.56155			−0.951865
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.56155	+	2.70469i	0.378732	+	0.655983i	0.990878	−	0.134761i	$-0.0430268\pi$
$17$	1.56155	+	2.70469i	0.378732	+	0.655983i	−0.612146	+	0.790745i	$0.709693\pi$
$18$	1.00000			0.235702
$19$	1.21922	+	2.11176i	0.279709	+	0.484470i	0.971312	−	0.237807i	$-0.0764287\pi$
$19$	1.21922	+	2.11176i	0.279709	+	0.484470i	−0.691603	+	0.722278i	$0.743095\pi$
$20$		0			0
$21$	−3.56155			−0.777195
$22$	0.280776	+	0.486319i	0.0598617	+	0.103684i
$23$	3.84233	−	6.65511i	0.801181	−	1.38769i	−0.117658	−	0.993054i	$-0.537539\pi$
$23$	3.84233	−	6.65511i	0.801181	−	1.38769i	0.918839	−	0.394632i	$-0.129128\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$		0			0
$26$	−3.34233	+	1.35234i	−0.655485	+	0.265217i
$27$	1.00000			0.192450
$28$	1.78078	−	3.08440i	0.336535	−	0.582896i
$29$	−0.561553	+	0.972638i	−0.104278	+	0.180614i	−0.913443	−	0.406967i	$-0.866586\pi$
$29$	−0.561553	+	0.972638i	−0.104278	+	0.180614i	0.809165	+	0.587581i	$0.199920\pi$
$30$		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
$33$	0.280776	+	0.486319i	0.0488769	+	0.0846573i
$34$	−3.12311			−0.535608
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−0.280776	+	0.486319i	−0.0461594	+	0.0799504i	−0.888182	−	0.459492i	$-0.848032\pi$
$37$	−0.280776	+	0.486319i	−0.0461594	+	0.0799504i	0.842023	+	0.539442i	$0.181365\pi$
$38$	−2.43845			−0.395568
$39$	−3.34233	+	1.35234i	−0.535201	+	0.216548i
$40$		0			0
$41$	1.56155	−	2.70469i	0.243874	−	0.422401i	−0.717941	−	0.696104i	$-0.754915\pi$
$41$	1.56155	−	2.70469i	0.243874	−	0.422401i	0.961814	+	0.273703i	$0.0882485\pi$
$42$	1.78078	−	3.08440i	0.274780	−	0.475933i
$43$	−0.219224	−	0.379706i	−0.0334313	−	0.0579047i	0.848826	−	0.528673i	$-0.177310\pi$
$43$	−0.219224	−	0.379706i	−0.0334313	−	0.0579047i	−0.882257	+	0.470768i	$0.843977\pi$
$44$	−0.561553			−0.0846573
$45$		0			0
$46$	3.84233	+	6.65511i	0.566521	+	0.981242i
$47$	4.00000			0.583460			0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000			0.583460			0.291730	+	0.956501i	$0.405769\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−2.84233	+	4.92306i	−0.406047	+	0.703294i
$50$		0			0
$51$	−3.12311			−0.437322
$52$	0.500000	−	3.57071i	0.0693375	−	0.495169i
$53$	4.24621			0.583262			0.291631	−	0.956531i	$-0.405802\pi$
$53$	4.24621			0.583262			0.291631	+	0.956531i	$0.405802\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$		0			0
$56$	1.78078	+	3.08440i	0.237966	+	0.412170i
$57$	−2.43845			−0.322980
$58$	−0.561553	−	0.972638i	−0.0737355	−	0.127714i
$59$	5.12311	+	8.87348i	0.666972	+	1.15523i	0.978747	+	0.205073i	$0.0657431\pi$
$59$	5.12311	+	8.87348i	0.666972	+	1.15523i	−0.311775	+	0.950156i	$0.600924\pi$
$60$		0			0
$61$	0.842329	+	1.45896i	0.107849	+	0.186800i	0.914899	−	0.403683i	$-0.132270\pi$
$61$	0.842329	+	1.45896i	0.107849	+	0.186800i	−0.807050	+	0.590484i	$0.798937\pi$
$62$	−2.00000	+	3.46410i	−0.254000	+	0.439941i
$63$	1.78078	−	3.08440i	0.224357	−	0.388597i
$64$	1.00000			0.125000
$65$		0			0
$66$	−0.561553			−0.0691224
$67$	−5.90388	+	10.2258i	−0.721274	+	1.24928i	0.239215	+	0.970967i	$0.423110\pi$
$67$	−5.90388	+	10.2258i	−0.721274	+	1.24928i	−0.960489	+	0.278317i	$0.910224\pi$
$68$	1.56155	−	2.70469i	0.189366	−	0.327992i
$69$	3.84233	+	6.65511i	0.462562	+	0.801181i
$70$		0			0
$71$	−6.28078	−	10.8786i	−0.745391	−	1.29106i	−0.950012	−	0.312214i	$-0.898929\pi$
$71$	−6.28078	−	10.8786i	−0.745391	−	1.29106i	0.204621	−	0.978841i	$-0.434404\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	9.00000			1.05337			0.526685	−	0.850060i	$-0.323435\pi$
$73$	9.00000			1.05337			0.526685	+	0.850060i	$0.323435\pi$
$74$	−0.280776	−	0.486319i	−0.0326396	−	0.0565334i
$75$		0			0
$76$	1.21922	−	2.11176i	0.139855	−	0.242235i
$77$	2.00000			0.227921
$78$	0.500000	−	3.57071i	0.0566139	−	0.404304i
$79$	−15.8078			−1.77851			−0.889256	−	0.457409i	$-0.848777\pi$
$79$	−15.8078			−1.77851			−0.889256	+	0.457409i	$0.848777\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.56155	+	2.70469i	0.172445	+	0.298683i
$83$	6.56155			0.720224			0.360112	−	0.932909i	$-0.382738\pi$
$83$	6.56155			0.720224			0.360112	+	0.932909i	$0.382738\pi$
$84$	1.78078	+	3.08440i	0.194299	+	0.336535i
$85$		0			0
$86$	0.438447			0.0472790
$87$	−0.561553	−	0.972638i	−0.0602048	−	0.104278i
$88$	0.280776	−	0.486319i	0.0299309	−	0.0518418i
$89$	−5.12311	+	8.87348i	−0.543048	+	0.940587i	0.455679	+	0.890144i	$0.349397\pi$
$89$	−5.12311	+	8.87348i	−0.543048	+	0.940587i	−0.998727	+	0.0504427i	$0.983937\pi$
$90$		0			0
$91$	−1.78078	+	12.7173i	−0.186676	+	1.33313i
$92$	−7.68466			−0.801181
$93$	−2.00000	+	3.46410i	−0.207390	+	0.359211i
$94$	−2.00000	+	3.46410i	−0.206284	+	0.357295i
$95$		0			0
$96$	1.00000			0.102062
$97$	1.40388	+	2.43160i	0.142543	+	0.246891i	0.928453	−	0.371449i	$-0.121139\pi$
$97$	1.40388	+	2.43160i	0.142543	+	0.246891i	−0.785911	+	0.618340i	$0.787806\pi$
$98$	−2.84233	−	4.92306i	−0.287119	−	0.497304i
$99$	−0.561553			−0.0564382
$100$		0			0
$101$	3.12311	−	5.40938i	0.310761	−	0.538253i	−0.667767	−	0.744371i	$-0.732750\pi$
$101$	3.12311	−	5.40938i	0.310761	−	0.538253i	0.978527	+	0.206118i	$0.0660829\pi$
$102$	1.56155	−	2.70469i	0.154617	−	0.267804i
$103$	−4.43845			−0.437333			−0.218667	−	0.975800i	$-0.570171\pi$
$103$	−4.43845			−0.437333			−0.218667	+	0.975800i	$0.570171\pi$
$104$	2.84233	+	2.21837i	0.278713	+	0.217529i
$105$		0			0
$106$	−2.12311	+	3.67733i	−0.206214	+	0.357174i
$107$	−2.68466	+	4.64996i	−0.259536	+	0.449529i	−0.966118	−	0.258102i	$-0.916903\pi$
$107$	−2.68466	+	4.64996i	−0.259536	+	0.449529i	0.706582	+	0.707631i	$0.250236\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−2.80776			−0.268935			−0.134468	−	0.990918i	$-0.542932\pi$
$109$	−2.80776			−0.268935			−0.134468	+	0.990918i	$0.542932\pi$
$110$		0			0
$111$	−0.280776	−	0.486319i	−0.0266501	−	0.0461594i
$112$	−3.56155			−0.336535
$113$	−2.00000	−	3.46410i	−0.188144	−	0.325875i	0.756487	−	0.654008i	$-0.226914\pi$
$113$	−2.00000	−	3.46410i	−0.188144	−	0.325875i	−0.944632	+	0.328133i	$0.893581\pi$
$114$	1.21922	−	2.11176i	0.114191	−	0.197784i
$115$		0			0
$116$	1.12311			0.104278
$117$	0.500000	−	3.57071i	0.0462250	−	0.330113i
$118$	−10.2462			−0.943240
$119$	−5.56155	+	9.63289i	−0.509827	+	0.883046i
$120$		0			0
$121$	5.34233	+	9.25319i	0.485666	+	0.841199i
$122$	−1.68466			−0.152522
$123$	1.56155	+	2.70469i	0.140800	+	0.243874i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$		0			0
$126$	1.78078	+	3.08440i	0.158644	+	0.274780i
$127$	−10.9039	+	18.8861i	−0.967563	+	1.67587i	−0.264998	+	0.964249i	$0.585371\pi$
$127$	−10.9039	+	18.8861i	−0.967563	+	1.67587i	−0.702565	+	0.711619i	$0.747962\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	0.438447			0.0386031
$130$		0			0
$131$	0.876894			0.0766146			0.0383073	−	0.999266i	$-0.487803\pi$
$131$	0.876894			0.0766146			0.0383073	+	0.999266i	$0.487803\pi$
$132$	0.280776	−	0.486319i	0.0244384	−	0.0423286i
$133$	−4.34233	+	7.52113i	−0.376528	+	0.652165i
$134$	−5.90388	−	10.2258i	−0.510018	−	0.883377i
$135$		0			0
$136$	1.56155	+	2.70469i	0.133902	+	0.231925i
$137$	−8.24621	−	14.2829i	−0.704521	−	1.22027i	−0.966864	−	0.255292i	$-0.917828\pi$
$137$	−8.24621	−	14.2829i	−0.704521	−	1.22027i	0.262343	−	0.964975i	$-0.415505\pi$
$138$	−7.68466			−0.654162
$139$	−10.7808	−	18.6729i	−0.914414	−	1.58381i	−0.807758	−	0.589515i	$-0.799319\pi$
$139$	−10.7808	−	18.6729i	−0.914414	−	1.58381i	−0.106656	−	0.994296i	$-0.534014\pi$
$140$		0			0
$141$	−2.00000	+	3.46410i	−0.168430	+	0.291730i
$142$	12.5616			1.05414
$143$	1.87689	−	0.759413i	0.156954	−	0.0635053i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−4.50000	+	7.79423i	−0.372423	+	0.645055i
$147$	−2.84233	−	4.92306i	−0.234431	−	0.406047i
$148$	0.561553			0.0461594
$149$	5.12311	+	8.87348i	0.419701	+	0.726944i	0.995909	−	0.0903593i	$-0.0288015\pi$
$149$	5.12311	+	8.87348i	0.419701	+	0.726944i	−0.576208	+	0.817303i	$0.695468\pi$
$150$		0			0
$151$	−16.6847			−1.35778			−0.678889	−	0.734241i	$-0.737538\pi$
$151$	−16.6847			−1.35778			−0.678889	+	0.734241i	$0.737538\pi$
$152$	1.21922	+	2.11176i	0.0988921	+	0.171286i
$153$	1.56155	−	2.70469i	0.126244	−	0.218661i
$154$	−1.00000	+	1.73205i	−0.0805823	+	0.139573i
$155$		0			0
$156$	2.84233	+	2.21837i	0.227568	+	0.177612i
$157$	17.2462			1.37640			0.688199	−	0.725522i	$-0.258402\pi$
$157$	17.2462			1.37640			0.688199	+	0.725522i	$0.258402\pi$
$158$	7.90388	−	13.6899i	0.628799	−	1.08911i
$159$	−2.12311	+	3.67733i	−0.168373	+	0.291631i
$160$		0			0
$161$	27.3693			2.15700
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	8.24621	+	14.2829i	0.645893	+	1.11872i	0.984094	+	0.177646i	$0.0568482\pi$
$163$	8.24621	+	14.2829i	0.645893	+	1.11872i	−0.338201	+	0.941074i	$0.609818\pi$
$164$	−3.12311			−0.243874
$165$		0			0
$166$	−3.28078	+	5.68247i	−0.254638	+	0.441045i
$167$	−11.8423	+	20.5115i	−0.916387	+	1.58723i	−0.111529	+	0.993761i	$0.535575\pi$
$167$	−11.8423	+	20.5115i	−0.916387	+	1.58723i	−0.804858	+	0.593468i	$0.797759\pi$
$168$	−3.56155			−0.274780
$169$	3.15767	+	12.6107i	0.242898	+	0.970052i
$170$		0			0
$171$	1.21922	−	2.11176i	0.0932364	−	0.161490i
$172$	−0.219224	+	0.379706i	−0.0167156	+	0.0289523i
$173$	4.43845	+	7.68762i	0.337449	+	0.584479i	0.983952	−	0.178433i	$-0.0571027\pi$
$173$	4.43845	+	7.68762i	0.337449	+	0.584479i	−0.646503	+	0.762911i	$0.723769\pi$
$174$	1.12311			0.0851424
$175$		0			0
$176$	0.280776	+	0.486319i	0.0211643	+	0.0366577i
$177$	−10.2462			−0.770152
$178$	−5.12311	−	8.87348i	−0.383993	−	0.665095i
$179$	7.84233	−	13.5833i	0.586163	−	1.01526i	−0.408566	−	0.912729i	$-0.633971\pi$
$179$	7.84233	−	13.5833i	0.586163	−	1.01526i	0.994729	−	0.102536i	$-0.0326956\pi$
$180$		0			0
$181$	−15.4924			−1.15154			−0.575771	−	0.817611i	$-0.695298\pi$
$181$	−15.4924			−1.15154			−0.575771	+	0.817611i	$0.695298\pi$
$182$	−10.1231	−	7.90084i	−0.750375	−	0.585649i
$183$	−1.68466			−0.124534
$184$	3.84233	−	6.65511i	0.283260	−	0.490621i
$185$		0			0
$186$	−2.00000	−	3.46410i	−0.146647	−	0.254000i
$187$	1.75379			0.128250
$188$	−2.00000	−	3.46410i	−0.145865	−	0.252646i
$189$	1.78078	+	3.08440i	0.129532	+	0.224357i
$190$		0			0
$191$	−7.96543	−	13.7965i	−0.576359	−	0.998282i	−0.995893	−	0.0905428i	$-0.971140\pi$
$191$	−7.96543	−	13.7965i	−0.576359	−	0.998282i	0.419534	−	0.907740i	$-0.362194\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−1.50000	+	2.59808i	−0.107972	+	0.187014i	−0.914949	−	0.403570i	$-0.867769\pi$
$193$	−1.50000	+	2.59808i	−0.107972	+	0.187014i	0.806976	+	0.590584i	$0.201102\pi$
$194$	−2.80776			−0.201586
$195$		0			0
$196$	5.68466			0.406047
$197$	−2.56155	+	4.43674i	−0.182503	+	0.316105i	−0.942732	−	0.333550i	$-0.891753\pi$
$197$	−2.56155	+	4.43674i	−0.182503	+	0.316105i	0.760229	+	0.649655i	$0.225087\pi$
$198$	0.280776	−	0.486319i	0.0199539	−	0.0345612i
$199$	2.21922	+	3.84381i	0.157317	+	0.272480i	0.933900	−	0.357534i	$-0.116382\pi$
$199$	2.21922	+	3.84381i	0.157317	+	0.272480i	−0.776584	+	0.630014i	$0.783049\pi$
$200$		0			0
$201$	−5.90388	−	10.2258i	−0.416428	−	0.721274i
$202$	3.12311	+	5.40938i	0.219741	+	0.380602i
$203$	−4.00000			−0.280745
$204$	1.56155	+	2.70469i	0.109331	+	0.189366i
$205$		0			0
$206$	2.21922	−	3.84381i	0.154621	−	0.267811i
$207$	−7.68466			−0.534121
$208$	−3.34233	+	1.35234i	−0.231749	+	0.0937682i
$209$	1.36932			0.0947176
$210$		0			0
$211$	−0.561553	+	0.972638i	−0.0386589	+	0.0669592i	−0.884707	−	0.466147i	$-0.845642\pi$
$211$	−0.561553	+	0.972638i	−0.0386589	+	0.0669592i	0.846049	+	0.533106i	$0.178975\pi$
$212$	−2.12311	−	3.67733i	−0.145815	−	0.252560i
$213$	12.5616			0.860703
$214$	−2.68466	−	4.64996i	−0.183519	−	0.317865i
$215$		0			0
$216$	1.00000			0.0680414
$217$	7.12311	+	12.3376i	0.483548	+	0.837530i
$218$	1.40388	−	2.43160i	0.0950829	−	0.164688i
$219$	−4.50000	+	7.79423i	−0.304082	+	0.526685i
$220$		0			0
$221$	−1.56155	+	11.1517i	−0.105041	+	0.750146i
$222$	0.561553			0.0376890
$223$	0.219224	−	0.379706i	0.0146803	−	0.0254270i	−0.858592	−	0.512660i	$-0.828660\pi$
$223$	0.219224	−	0.379706i	0.0146803	−	0.0254270i	0.873272	+	0.487233i	$0.161994\pi$
$224$	1.78078	−	3.08440i	0.118983	−	0.206085i
$225$		0			0
$226$	4.00000			0.266076
$227$	−14.8423	−	25.7077i	−0.985120	−	1.70628i	−0.641402	−	0.767205i	$-0.721647\pi$
$227$	−14.8423	−	25.7077i	−0.985120	−	1.70628i	−0.343718	−	0.939073i	$-0.611686\pi$
$228$	1.21922	+	2.11176i	0.0807451	+	0.139855i
$229$	9.49242			0.627277			0.313638	−	0.949542i	$-0.398452\pi$
$229$	9.49242			0.627277			0.313638	+	0.949542i	$0.398452\pi$
$230$		0			0
$231$	−1.00000	+	1.73205i	−0.0657952	+	0.113961i
$232$	−0.561553	+	0.972638i	−0.0368677	+	0.0638568i
$233$	−25.3693			−1.66200			−0.831000	−	0.556273i	$-0.812231\pi$
$233$	−25.3693			−1.66200			−0.831000	+	0.556273i	$0.812231\pi$
$234$	2.84233	+	2.21837i	0.185809	+	0.145019i
$235$		0			0
$236$	5.12311	−	8.87348i	0.333486	−	0.577614i
$237$	7.90388	−	13.6899i	0.513412	−	0.889256i
$238$	−5.56155	−	9.63289i	−0.360502	−	0.624408i
$239$	27.0540			1.74998			0.874988	−	0.484144i	$-0.160869\pi$
$239$	27.0540			1.74998			0.874988	+	0.484144i	$0.160869\pi$
$240$		0			0
$241$	−7.78078	−	13.4767i	−0.501204	−	0.868111i	−0.999999	−	0.00139067i	$-0.999557\pi$
$241$	−7.78078	−	13.4767i	−0.501204	−	0.868111i	0.498795	−	0.866720i	$-0.333776\pi$
$242$	−10.6847			−0.686836
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	0.842329	−	1.45896i	0.0539246	−	0.0934002i
$245$		0			0
$246$	−3.12311			−0.199122
$247$	−1.21922	+	8.70700i	−0.0775773	+	0.554013i
$248$	4.00000			0.254000
$249$	−3.28078	+	5.68247i	−0.207911	+	0.360112i
$250$		0			0
$251$	−11.9654	−	20.7247i	−0.755252	−	1.30813i	−0.945249	−	0.326350i	$-0.894181\pi$
$251$	−11.9654	−	20.7247i	−0.755252	−	1.30813i	0.189998	−	0.981785i	$-0.439152\pi$
$252$	−3.56155			−0.224357
$253$	−2.15767	−	3.73720i	−0.135652	−	0.234955i
$254$	−10.9039	−	18.8861i	−0.684170	−	1.18502i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.80776	−	11.7914i	0.424657	−	0.735527i	−0.571732	−	0.820441i	$-0.693728\pi$
$257$	6.80776	−	11.7914i	0.424657	−	0.735527i	0.996388	+	0.0849138i	$0.0270615\pi$
$258$	−0.219224	+	0.379706i	−0.0136483	+	0.0236395i
$259$	−2.00000			−0.124274
$260$		0			0
$261$	1.12311			0.0695185
$262$	−0.438447	+	0.759413i	−0.0270874	+	0.0469167i
$263$	−3.15767	+	5.46925i	−0.194710	+	0.337248i	−0.946806	−	0.321806i	$-0.895710\pi$
$263$	−3.15767	+	5.46925i	−0.194710	+	0.337248i	0.752095	+	0.659054i	$0.229043\pi$
$264$	0.280776	+	0.486319i	0.0172806	+	0.0299309i
$265$		0			0
$266$	−4.34233	−	7.52113i	−0.266245	−	0.461150i
$267$	−5.12311	−	8.87348i	−0.313529	−	0.543048i
$268$	11.8078			0.721274
$269$	1.68466	+	2.91791i	0.102715	+	0.177908i	0.912803	−	0.408401i	$-0.133914\pi$
$269$	1.68466	+	2.91791i	0.102715	+	0.177908i	−0.810087	+	0.586310i	$0.800580\pi$
$270$		0			0
$271$	−4.46543	+	7.73436i	−0.271256	+	0.469829i	−0.969184	−	0.246339i	$-0.920772\pi$
$271$	−4.46543	+	7.73436i	−0.271256	+	0.469829i	0.697928	+	0.716168i	$0.254106\pi$
$272$	−3.12311			−0.189366
$273$	−10.1231	−	7.90084i	−0.612678	−	0.478181i
$274$	16.4924			0.996344
$275$		0			0
$276$	3.84233	−	6.65511i	0.231281	−	0.400591i
$277$	−2.50000	−	4.33013i	−0.150210	−	0.260172i	0.781094	−	0.624413i	$-0.214662\pi$
$277$	−2.50000	−	4.33013i	−0.150210	−	0.260172i	−0.931305	+	0.364241i	$0.881328\pi$
$278$	21.5616			1.29318
$279$	−2.00000	−	3.46410i	−0.119737	−	0.207390i
$280$		0			0
$281$	−1.75379			−0.104622			−0.0523111	−	0.998631i	$-0.516659\pi$
$281$	−1.75379			−0.104622			−0.0523111	+	0.998631i	$0.516659\pi$
$282$	−2.00000	−	3.46410i	−0.119098	−	0.206284i
$283$	−14.8078	+	25.6478i	−0.880230	+	1.52460i	−0.0291454	+	0.999575i	$0.509279\pi$
$283$	−14.8078	+	25.6478i	−0.880230	+	1.52460i	−0.851085	+	0.525028i	$0.824055\pi$
$284$	−6.28078	+	10.8786i	−0.372696	+	0.645528i
$285$		0			0
$286$	−0.280776	+	2.00514i	−0.0166027	+	0.118567i
$287$	11.1231			0.656576
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	3.62311	−	6.27540i	0.213124	−	0.369141i
$290$		0			0
$291$	−2.80776			−0.164594
$292$	−4.50000	−	7.79423i	−0.263343	−	0.456123i
$293$	−10.1231	−	17.5337i	−0.591398	−	1.02433i	−0.994044	−	0.108976i	$-0.965243\pi$
$293$	−10.1231	−	17.5337i	−0.591398	−	1.02433i	0.402646	−	0.915356i	$-0.368090\pi$
$294$	5.68466			0.331536
$295$		0			0
$296$	−0.280776	+	0.486319i	−0.0163198	+	0.0282667i
$297$	0.280776	−	0.486319i	0.0162923	−	0.0282191i
$298$	−10.2462			−0.593547
$299$	25.6847	−	10.3923i	1.48538	−	0.601003i
$300$		0			0
$301$	0.780776	−	1.35234i	0.0450032	−	0.0779478i
$302$	8.34233	−	14.4493i	0.480047	−	0.831466i
$303$	3.12311	+	5.40938i	0.179418	+	0.310761i
$304$	−2.43845			−0.139855
$305$		0			0
$306$	1.56155	+	2.70469i	0.0892680	+	0.154617i
$307$	22.2462			1.26966			0.634829	−	0.772653i	$-0.281070\pi$
$307$	22.2462			1.26966			0.634829	+	0.772653i	$0.281070\pi$
$308$	−1.00000	−	1.73205i	−0.0569803	−	0.0986928i
$309$	2.21922	−	3.84381i	0.126247	−	0.218667i
$310$		0			0
$311$	−10.3153			−0.584929			−0.292465	−	0.956276i	$-0.594475\pi$
$311$	−10.3153			−0.584929			−0.292465	+	0.956276i	$0.594475\pi$
$312$	−3.34233	+	1.35234i	−0.189222	+	0.0765614i
$313$	31.0000			1.75222			0.876112	−	0.482108i	$-0.160129\pi$
$313$	31.0000			1.75222			0.876112	+	0.482108i	$0.160129\pi$
$314$	−8.62311	+	14.9357i	−0.486630	+	0.842868i
$315$		0			0
$316$	7.90388	+	13.6899i	0.444628	+	0.770118i
$317$	16.2462			0.912478			0.456239	−	0.889857i	$-0.349196\pi$
$317$	16.2462			0.912478			0.456239	+	0.889857i	$0.349196\pi$
$318$	−2.12311	−	3.67733i	−0.119058	−	0.206214i
$319$	0.315342	+	0.546188i	0.0176557	+	0.0305806i
$320$		0			0
$321$	−2.68466	−	4.64996i	−0.149843	−	0.259536i
$322$	−13.6847	+	23.7025i	−0.762616	+	1.32089i
$323$	−3.80776	+	6.59524i	−0.211870	+	0.366969i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−16.4924			−0.913431
$327$	1.40388	−	2.43160i	0.0776349	−	0.134468i
$328$	1.56155	−	2.70469i	0.0862223	−	0.149341i
$329$	7.12311	+	12.3376i	0.392710	+	0.680193i
$330$		0			0
$331$	8.34233	+	14.4493i	0.458536	+	0.794207i	0.998884	−	0.0472342i	$-0.0150407\pi$
$331$	8.34233	+	14.4493i	0.458536	+	0.794207i	−0.540348	+	0.841442i	$0.681707\pi$
$332$	−3.28078	−	5.68247i	−0.180056	−	0.311866i
$333$	0.561553			0.0307729
$334$	−11.8423	−	20.5115i	−0.647983	−	1.12234i
$335$		0			0
$336$	1.78078	−	3.08440i	0.0971493	−	0.168268i
$337$	8.05398			0.438728			0.219364	−	0.975643i	$-0.429602\pi$
$337$	8.05398			0.438728			0.219364	+	0.975643i	$0.429602\pi$
$338$	−12.5000	−	3.57071i	−0.679910	−	0.194221i
$339$	4.00000			0.217250
$340$		0			0
$341$	1.12311	−	1.94528i	0.0608196	−	0.105343i
$342$	1.21922	+	2.11176i	0.0659281	+	0.114191i
$343$	4.68466			0.252948
$344$	−0.219224	−	0.379706i	−0.0118197	−	0.0204724i
$345$		0			0
$346$	−8.87689			−0.477225
$347$	12.4039	+	21.4842i	0.665875	+	1.15333i	0.979047	+	0.203633i	$0.0652751\pi$
$347$	12.4039	+	21.4842i	0.665875	+	1.15333i	−0.313172	+	0.949696i	$0.601392\pi$
$348$	−0.561553	+	0.972638i	−0.0301024	+	0.0521389i
$349$	9.62311	−	16.6677i	0.515113	−	0.892202i	−0.484733	−	0.874662i	$-0.661083\pi$
$349$	9.62311	−	16.6677i	0.515113	−	0.892202i	0.999846	−	0.0175398i	$-0.00558339\pi$
$350$		0			0
$351$	2.84233	+	2.21837i	0.151712	+	0.118408i
$352$	−0.561553			−0.0299309
$353$	−1.12311	+	1.94528i	−0.0597769	+	0.103537i	−0.894365	−	0.447338i	$-0.852372\pi$
$353$	−1.12311	+	1.94528i	−0.0597769	+	0.103537i	0.834588	+	0.550874i	$0.185706\pi$
$354$	5.12311	−	8.87348i	0.272290	−	0.471620i
$355$		0			0
$356$	10.2462			0.543048
$357$	−5.56155	−	9.63289i	−0.294349	−	0.509827i
$358$	7.84233	+	13.5833i	0.414480	+	0.717900i
$359$	−4.87689			−0.257393			−0.128696	−	0.991684i	$-0.541079\pi$
$359$	−4.87689			−0.257393			−0.128696	+	0.991684i	$0.541079\pi$
$360$		0			0
$361$	6.52699	−	11.3051i	0.343526	−	0.595004i
$362$	7.74621	−	13.4168i	0.407132	−	0.705173i
$363$	−10.6847			−0.560799
$364$	11.9039	−	4.81645i	0.623933	−	0.252450i
$365$		0			0
$366$	0.842329	−	1.45896i	0.0440293	−	0.0762609i
$367$	5.09612	−	8.82674i	0.266015	−	0.460752i	−0.701814	−	0.712360i	$-0.747626\pi$
$367$	5.09612	−	8.82674i	0.266015	−	0.460752i	0.967829	+	0.251609i	$0.0809595\pi$
$368$	3.84233	+	6.65511i	0.200295	+	0.346922i
$369$	−3.12311			−0.162582
$370$		0			0
$371$	7.56155	+	13.0970i	0.392576	+	0.679962i
$372$	4.00000			0.207390
$373$	4.74621	+	8.22068i	0.245750	+	0.425651i	0.962342	−	0.271841i	$-0.0876326\pi$
$373$	4.74621	+	8.22068i	0.245750	+	0.425651i	−0.716593	+	0.697492i	$0.754299\pi$
$374$	−0.876894	+	1.51883i	−0.0453431	+	0.0785366i
$375$		0			0
$376$	4.00000			0.206284
$377$	−3.75379	+	1.51883i	−0.193330	+	0.0782235i
$378$	−3.56155			−0.183187
$379$	12.0270	−	20.8314i	0.617785	−	1.07003i	−0.372104	−	0.928191i	$-0.621364\pi$
$379$	12.0270	−	20.8314i	0.617785	−	1.07003i	0.989889	−	0.141844i	$-0.0453031\pi$
$380$		0			0
$381$	−10.9039	−	18.8861i	−0.558623	−	0.967563i
$382$	15.9309			0.815094
$383$	2.71922	+	4.70983i	0.138946	+	0.240661i	0.927098	−	0.374819i	$-0.122295\pi$
$383$	2.71922	+	4.70983i	0.138946	+	0.240661i	−0.788152	+	0.615481i	$0.788962\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$		0			0
$386$	−1.50000	−	2.59808i	−0.0763480	−	0.132239i
$387$	−0.219224	+	0.379706i	−0.0111438	+	0.0193016i
$388$	1.40388	−	2.43160i	0.0712713	−	0.123446i
$389$	11.3693			0.576447			0.288224	−	0.957563i	$-0.406935\pi$
$389$	11.3693			0.576447			0.288224	+	0.957563i	$0.406935\pi$
$390$		0			0
$391$	24.0000			1.21373
$392$	−2.84233	+	4.92306i	−0.143559	+	0.248652i
$393$	−0.438447	+	0.759413i	−0.0221167	+	0.0383073i
$394$	−2.56155	−	4.43674i	−0.129049	−	0.223520i
$395$		0			0
$396$	0.280776	+	0.486319i	0.0141095	+	0.0244384i
$397$	4.90388	+	8.49377i	0.246119	+	0.426290i	0.962446	−	0.271475i	$-0.0875113\pi$
$397$	4.90388	+	8.49377i	0.246119	+	0.426290i	−0.716327	+	0.697765i	$0.754178\pi$
$398$	−4.43845			−0.222479
$399$	−4.34233	−	7.52113i	−0.217388	−	0.376528i
$400$		0			0
$401$	6.31534	−	10.9385i	0.315373	−	0.546242i	−0.664144	−	0.747605i	$-0.731204\pi$
$401$	6.31534	−	10.9385i	0.315373	−	0.546242i	0.979517	+	0.201363i	$0.0645370\pi$
$402$	11.8078			0.588918
$403$	11.3693	+	8.87348i	0.566346	+	0.442019i
$404$	−6.24621			−0.310761
$405$		0			0
$406$	2.00000	−	3.46410i	0.0992583	−	0.171920i
$407$	0.157671	+	0.273094i	0.00781545	+	0.0135368i
$408$	−3.12311			−0.154617
$409$	−8.12311	−	14.0696i	−0.401662	−	0.695699i	0.592265	−	0.805743i	$-0.298234\pi$
$409$	−8.12311	−	14.0696i	−0.401662	−	0.695699i	−0.993927	+	0.110045i	$0.964901\pi$
$410$		0			0
$411$	16.4924			0.813511
$412$	2.21922	+	3.84381i	0.109333	+	0.189371i
$413$	−18.2462	+	31.6034i	−0.897837	+	1.55510i
$414$	3.84233	−	6.65511i	0.188840	−	0.327081i
$415$		0			0
$416$	0.500000	−	3.57071i	0.0245145	−	0.175069i
$417$	21.5616			1.05587
$418$	−0.684658	+	1.18586i	−0.0334877	+	0.0580025i
$419$	5.96543	−	10.3324i	0.291431	−	0.504773i	−0.682718	−	0.730682i	$-0.739202\pi$
$419$	5.96543	−	10.3324i	0.291431	−	0.504773i	0.974148	+	0.225910i	$0.0725354\pi$
$420$		0			0
$421$	31.2462			1.52285			0.761424	−	0.648255i	$-0.224501\pi$
$421$	31.2462			1.52285			0.761424	+	0.648255i	$0.224501\pi$
$422$	−0.561553	−	0.972638i	−0.0273360	−	0.0473473i
$423$	−2.00000	−	3.46410i	−0.0972433	−	0.168430i
$424$	4.24621			0.206214
$425$		0			0
$426$	−6.28078	+	10.8786i	−0.304305	+	0.527071i
$427$	−3.00000	+	5.19615i	−0.145180	+	0.251459i
$428$	5.36932			0.259536
$429$	−0.280776	+	2.00514i	−0.0135560	+	0.0968093i
$430$		0			0
$431$	−9.15767	+	15.8616i	−0.441109	+	0.764024i	−0.997772	−	0.0667146i	$-0.978748\pi$
$431$	−9.15767	+	15.8616i	−0.441109	+	0.764024i	0.556663	+	0.830739i	$0.312082\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	6.84233	+	11.8513i	0.328821	+	0.569535i	0.982278	−	0.187428i	$-0.0600153\pi$
$433$	6.84233	+	11.8513i	0.328821	+	0.569535i	−0.653457	+	0.756964i	$0.726682\pi$
$434$	−14.2462			−0.683840
$435$		0			0
$436$	1.40388	+	2.43160i	0.0672338	+	0.116452i
$437$	18.7386			0.896390
$438$	−4.50000	−	7.79423i	−0.215018	−	0.372423i
$439$	3.46543	−	6.00231i	0.165396	−	0.286475i	−0.771400	−	0.636351i	$-0.780443\pi$
$439$	3.46543	−	6.00231i	0.165396	−	0.286475i	0.936796	+	0.349876i	$0.113776\pi$
$440$		0			0
$441$	5.68466			0.270698
$442$	−8.87689	−	6.92820i	−0.422231	−	0.329541i
$443$	−2.80776			−0.133401			−0.0667004	−	0.997773i	$-0.521247\pi$
$443$	−2.80776			−0.133401			−0.0667004	+	0.997773i	$0.521247\pi$
$444$	−0.280776	+	0.486319i	−0.0133251	+	0.0230797i
$445$		0			0
$446$	0.219224	+	0.379706i	0.0103805	+	0.0179796i
$447$	−10.2462			−0.484629
$448$	1.78078	+	3.08440i	0.0841338	+	0.145724i
$449$	1.56155	+	2.70469i	0.0736942	+	0.127642i	0.900518	−	0.434819i	$-0.143188\pi$
$449$	1.56155	+	2.70469i	0.0736942	+	0.127642i	−0.826823	+	0.562462i	$0.809854\pi$
$450$		0			0
$451$	−0.876894	−	1.51883i	−0.0412913	−	0.0715187i
$452$	−2.00000	+	3.46410i	−0.0940721	+	0.162938i
$453$	8.34233	−	14.4493i	0.391957	−	0.678889i
$454$	29.6847			1.39317
$455$		0			0
$456$	−2.43845			−0.114191
$457$	−2.25379	+	3.90368i	−0.105428	+	0.182606i	−0.913913	−	0.405910i	$-0.866955\pi$
$457$	−2.25379	+	3.90368i	−0.105428	+	0.182606i	0.808485	+	0.588517i	$0.200288\pi$
$458$	−4.74621	+	8.22068i	−0.221776	+	0.384127i
$459$	1.56155	+	2.70469i	0.0728870	+	0.126244i
$460$		0			0
$461$	−5.31534	−	9.20644i	−0.247560	−	0.428787i	0.715288	−	0.698830i	$-0.246295\pi$
$461$	−5.31534	−	9.20644i	−0.247560	−	0.428787i	−0.962848	+	0.270043i	$0.912962\pi$
$462$	−1.00000	−	1.73205i	−0.0465242	−	0.0805823i
$463$	27.8078			1.29234			0.646168	−	0.763195i	$-0.276370\pi$
$463$	27.8078			1.29234			0.646168	+	0.763195i	$0.276370\pi$
$464$	−0.561553	−	0.972638i	−0.0260694	−	0.0451536i
$465$		0			0
$466$	12.6847	−	21.9705i	0.587605	−	1.01776i
$467$	−3.43845			−0.159112			−0.0795562	−	0.996830i	$-0.525350\pi$
$467$	−3.43845			−0.159112			−0.0795562	+	0.996830i	$0.525350\pi$
$468$	−3.34233	+	1.35234i	−0.154499	+	0.0625121i
$469$	−42.0540			−1.94187
$470$		0			0
$471$	−8.62311	+	14.9357i	−0.397332	+	0.688199i
$472$	5.12311	+	8.87348i	0.235810	+	0.408435i
$473$	−0.246211			−0.0113208
$474$	7.90388	+	13.6899i	0.363037	+	0.628799i
$475$		0			0
$476$	11.1231			0.509827
$477$	−2.12311	−	3.67733i	−0.0972103	−	0.168373i
$478$	−13.5270	+	23.4294i	−0.618710	+	1.07164i
$479$	5.80776	−	10.0593i	0.265364	−	0.459623i	−0.702295	−	0.711886i	$-0.747841\pi$
$479$	5.80776	−	10.0593i	0.265364	−	0.459623i	0.967659	+	0.252263i	$0.0811747\pi$
$480$		0			0
$481$	−1.87689	+	0.759413i	−0.0855790	+	0.0346262i
$482$	15.5616			0.708809
$483$	−13.6847	+	23.7025i	−0.622674	+	1.07850i
$484$	5.34233	−	9.25319i	0.242833	−	0.420599i
$485$		0			0
$486$	1.00000			0.0453609
$487$	−21.3423	−	36.9660i	−0.967113	−	1.67509i	−0.703827	−	0.710372i	$-0.748527\pi$
$487$	−21.3423	−	36.9660i	−0.967113	−	1.67509i	−0.263286	−	0.964718i	$-0.584806\pi$
$488$	0.842329	+	1.45896i	0.0381305	+	0.0660439i
$489$	−16.4924			−0.745813
$490$		0			0
$491$	−15.6501	+	27.1068i	−0.706279	+	1.22331i	0.259949	+	0.965622i	$0.416294\pi$
$491$	−15.6501	+	27.1068i	−0.706279	+	1.22331i	−0.966228	+	0.257689i	$0.917039\pi$
$492$	1.56155	−	2.70469i	0.0704002	−	0.121937i
$493$	−3.50758			−0.157973
$494$	−6.93087	−	5.40938i	−0.311835	−	0.243379i
$495$		0			0
$496$	−2.00000	+	3.46410i	−0.0898027	+	0.155543i
$497$	22.3693	−	38.7448i	1.00340	−	1.73794i
$498$	−3.28078	−	5.68247i	−0.147015	−	0.254638i
$499$	6.05398			0.271013			0.135507	−	0.990776i	$-0.456734\pi$
$499$	6.05398			0.271013			0.135507	+	0.990776i	$0.456734\pi$
$500$		0			0
$501$	−11.8423	−	20.5115i	−0.529076	−	0.916387i
$502$	23.9309			1.06809
$503$	12.1577	+	21.0577i	0.542084	+	0.938917i	0.998784	+	0.0492961i	$0.0156978\pi$
$503$	12.1577	+	21.0577i	0.542084	+	0.938917i	−0.456700	+	0.889621i	$0.650969\pi$
$504$	1.78078	−	3.08440i	0.0793221	−	0.137390i
$505$		0			0
$506$	4.31534			0.191840
$507$	−12.5000	−	3.57071i	−0.555144	−	0.158581i
$508$	21.8078			0.967563
$509$	8.12311	−	14.0696i	0.360050	−	0.623625i	−0.627918	−	0.778279i	$-0.716093\pi$
$509$	8.12311	−	14.0696i	0.360050	−	0.623625i	0.987969	+	0.154654i	$0.0494262\pi$
$510$		0			0
$511$	16.0270	+	27.7596i	0.708992	+	1.22801i
$512$	1.00000			0.0441942
$513$	1.21922	+	2.11176i	0.0538300	+	0.0932364i
$514$	6.80776	+	11.7914i	0.300278	+	0.520096i
$515$		0			0
$516$	−0.219224	−	0.379706i	−0.00965078	−	0.0167156i
$517$	1.12311	−	1.94528i	0.0493941	−	0.0855531i
$518$	1.00000	−	1.73205i	0.0439375	−	0.0761019i
$519$	−8.87689			−0.389652
$520$		0			0
$521$	34.7386			1.52193			0.760964	−	0.648795i	$-0.224727\pi$
$521$	34.7386			1.52193			0.760964	+	0.648795i	$0.224727\pi$
$522$	−0.561553	+	0.972638i	−0.0245785	+	0.0425712i
$523$	−12.4654	+	21.5908i	−0.545075	+	0.944098i	0.453527	+	0.891243i	$0.350166\pi$
$523$	−12.4654	+	21.5908i	−0.545075	+	0.944098i	−0.998602	+	0.0528556i	$0.983168\pi$
$524$	−0.438447	−	0.759413i	−0.0191537	−	0.0331751i
$525$		0			0
$526$	−3.15767	−	5.46925i	−0.137681	−	0.238470i
$527$	6.24621	+	10.8188i	0.272089	+	0.471272i
$528$	−0.561553			−0.0244384
$529$	−18.0270	−	31.2237i	−0.783782	−	1.35755i
$530$		0			0
$531$	5.12311	−	8.87348i	0.222324	−	0.385076i
$532$	8.68466			0.376528
$533$	10.4384	−	4.22351i	0.452139	−	0.182941i
$534$	10.2462			0.443397
$535$		0			0
$536$	−5.90388	+	10.2258i	−0.255009	+	0.441688i
$537$	7.84233	+	13.5833i	0.338421	+	0.586163i
$538$	−3.36932			−0.145262
$539$	1.59612	+	2.76456i	0.0687497	+	0.119078i
$540$		0			0
$541$	−22.3153			−0.959411			−0.479706	−	0.877429i	$-0.659257\pi$
$541$	−22.3153			−0.959411			−0.479706	+	0.877429i	$0.659257\pi$
$542$	−4.46543	−	7.73436i	−0.191807	−	0.332219i
$543$	7.74621	−	13.4168i	0.332422	−	0.575771i
$544$	1.56155	−	2.70469i	0.0669510	−	0.115963i
$545$		0			0
$546$	11.9039	−	4.81645i	0.509439	−	0.206125i
$547$	−30.9309			−1.32251			−0.661254	−	0.750162i	$-0.729976\pi$
$547$	−30.9309			−1.32251			−0.661254	+	0.750162i	$0.729976\pi$
$548$	−8.24621	+	14.2829i	−0.352261	+	0.610133i
$549$	0.842329	−	1.45896i	0.0359497	−	0.0622668i
$550$		0			0
$551$	−2.73863			−0.116670
$552$	3.84233	+	6.65511i	0.163540	+	0.283260i
$553$	−28.1501	−	48.7574i	−1.19706	−	2.07338i
$554$	5.00000			0.212430
$555$		0			0
$556$	−10.7808	+	18.6729i	−0.457207	+	0.791905i
$557$	15.8078	−	27.3799i	0.669796	−	1.16012i	−0.308164	−	0.951333i	$-0.599715\pi$
$557$	15.8078	−	27.3799i	0.669796	−	1.16012i	0.977961	−	0.208788i	$-0.0669520\pi$
$558$	4.00000			0.169334
$559$	0.219224	−	1.56557i	0.00927217	−	0.0662165i
$560$		0			0
$561$	−0.876894	+	1.51883i	−0.0370225	+	0.0641249i
$562$	0.876894	−	1.51883i	0.0369896	−	0.0640678i
$563$	−10.4039	−	18.0201i	−0.438471	−	0.759455i	0.559100	−	0.829100i	$-0.311147\pi$
$563$	−10.4039	−	18.0201i	−0.438471	−	0.759455i	−0.997572	+	0.0696453i	$0.977813\pi$
$564$	4.00000			0.168430
$565$		0			0
$566$	−14.8078	−	25.6478i	−0.622417	−	1.07806i
$567$	−3.56155			−0.149571
$568$	−6.28078	−	10.8786i	−0.263536	−	0.456457i
$569$	5.75379	−	9.96585i	0.241211	−	0.417790i	−0.719848	−	0.694131i	$-0.755789\pi$
$569$	5.75379	−	9.96585i	0.241211	−	0.417790i	0.961060	+	0.276341i	$0.0891220\pi$
$570$		0			0
$571$	21.4233			0.896537			0.448268	−	0.893899i	$-0.352041\pi$
$571$	21.4233			0.896537			0.448268	+	0.893899i	$0.352041\pi$
$572$	−1.59612	−	1.24573i	−0.0667370	−	0.0520867i
$573$	15.9309			0.665522
$574$	−5.56155	+	9.63289i	−0.232135	+	0.402069i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	23.0000			0.957503			0.478751	−	0.877951i	$-0.341090\pi$
$577$	23.0000			0.957503			0.478751	+	0.877951i	$0.341090\pi$
$578$	3.62311	+	6.27540i	0.150701	+	0.261022i
$579$	−1.50000	−	2.59808i	−0.0623379	−	0.107972i
$580$		0			0
$581$	11.6847	+	20.2384i	0.484761	+	0.839631i
$582$	1.40388	−	2.43160i	0.0581928	−	0.100793i
$583$	1.19224	−	2.06501i	0.0493774	−	0.0855241i
$584$	9.00000			0.372423
$585$		0			0
$586$	20.2462			0.836363
$587$	8.96543	−	15.5286i	0.370043	−	0.640933i	−0.619529	−	0.784974i	$-0.712676\pi$
$587$	8.96543	−	15.5286i	0.370043	−	0.640933i	0.989572	+	0.144041i	$0.0460096\pi$
$588$	−2.84233	+	4.92306i	−0.117216	+	0.203024i
$589$	4.87689	+	8.44703i	0.200949	+	0.348054i
$590$		0			0
$591$	−2.56155	−	4.43674i	−0.105368	−	0.182503i
$592$	−0.280776	−	0.486319i	−0.0115398	−	0.0199876i
$593$	−38.9848			−1.60092			−0.800458	−	0.599389i	$-0.795410\pi$
$593$	−38.9848			−1.60092			−0.800458	+	0.599389i	$0.795410\pi$
$594$	0.280776	+	0.486319i	0.0115204	+	0.0199539i
$595$		0			0
$596$	5.12311	−	8.87348i	0.209851	−	0.363472i
$597$	−4.43845			−0.181654
$598$	−3.84233	+	27.4397i	−0.157125	+	1.12209i
$599$	−18.3153			−0.748345			−0.374172	−	0.927359i	$-0.622073\pi$
$599$	−18.3153			−0.748345			−0.374172	+	0.927359i	$0.622073\pi$
$600$		0			0
$601$	2.90388	−	5.02967i	0.118452	−	0.205165i	−0.800703	−	0.599062i	$-0.795540\pi$
$601$	2.90388	−	5.02967i	0.118452	−	0.205165i	0.919154	+	0.393898i	$0.128874\pi$
$602$	0.780776	+	1.35234i	0.0318221	+	0.0551174i
$603$	11.8078			0.480849
$604$	8.34233	+	14.4493i	0.339445	+	0.587935i
$605$		0			0
$606$	−6.24621			−0.253735
$607$	19.6847	+	34.0948i	0.798976	+	1.38387i	0.920284	+	0.391252i	$0.127958\pi$
$607$	19.6847	+	34.0948i	0.798976	+	1.38387i	−0.121308	+	0.992615i	$0.538709\pi$
$608$	1.21922	−	2.11176i	0.0494460	−	0.0856431i
$609$	2.00000	−	3.46410i	0.0810441	−	0.140372i
$610$		0			0
$611$	11.3693	+	8.87348i	0.459953	+	0.358983i
$612$	−3.12311			−0.126244
$613$	18.2732	−	31.6501i	0.738048	−	1.27834i	−0.215326	−	0.976542i	$-0.569081\pi$
$613$	18.2732	−	31.6501i	0.738048	−	1.27834i	0.953373	−	0.301794i	$-0.0975853\pi$
$614$	−11.1231	+	19.2658i	−0.448892	+	0.777504i
$615$		0			0
$616$	2.00000			0.0805823
$617$	−23.6847	−	41.0230i	−0.953508	−	1.65153i	−0.737745	−	0.675079i	$-0.764109\pi$
$617$	−23.6847	−	41.0230i	−0.953508	−	1.65153i	−0.215763	−	0.976446i	$-0.569224\pi$
$618$	2.21922	+	3.84381i	0.0892703	+	0.154621i
$619$	−12.3002			−0.494386			−0.247193	−	0.968966i	$-0.579508\pi$
$619$	−12.3002			−0.494386			−0.247193	+	0.968966i	$0.579508\pi$
$620$		0			0
$621$	3.84233	−	6.65511i	0.154187	−	0.267060i
$622$	5.15767	−	8.93335i	0.206804	−	0.358195i
$623$	−36.4924			−1.46204
$624$	0.500000	−	3.57071i	0.0200160	−	0.142943i
$625$		0			0
$626$	−15.5000	+	26.8468i	−0.619505	+	1.07301i
$627$	−0.684658	+	1.18586i	−0.0273426	+	0.0473588i
$628$	−8.62311	−	14.9357i	−0.344099	−	0.595998i
$629$	−1.75379			−0.0699281
$630$		0			0
$631$	−16.4654	−	28.5190i	−0.655479	−	1.13532i	−0.981774	−	0.190054i	$-0.939134\pi$
$631$	−16.4654	−	28.5190i	−0.655479	−	1.13532i	0.326295	−	0.945268i	$-0.394200\pi$
$632$	−15.8078			−0.628799
$633$	−0.561553	−	0.972638i	−0.0223197	−	0.0386589i
$634$	−8.12311	+	14.0696i	−0.322610	+	0.558776i
$635$		0			0
$636$	4.24621			0.168373
$637$	−19.0000	+	7.68762i	−0.752807	+	0.304594i
$638$	−0.630683			−0.0249690
$639$	−6.28078	+	10.8786i	−0.248464	+	0.430352i
$640$		0			0
$641$	−19.1231	−	33.1222i	−0.755317	−	1.30825i	−0.945216	−	0.326444i	$-0.894149\pi$
$641$	−19.1231	−	33.1222i	−0.755317	−	1.30825i	0.189899	−	0.981804i	$-0.439184\pi$
$642$	5.36932			0.211910
$643$	−12.2732	−	21.2578i	−0.484008	−	0.838326i	0.515824	−	0.856695i	$-0.327486\pi$
$643$	−12.2732	−	21.2578i	−0.484008	−	0.838326i	−0.999831	+	0.0183689i	$0.994153\pi$
$644$	−13.6847	−	23.7025i	−0.539251	−	0.934010i
$645$		0			0
$646$	−3.80776	−	6.59524i	−0.149814	−	0.259486i
$647$	−16.2116	+	28.0794i	−0.637346	+	1.10391i	0.348667	+	0.937247i	$0.386634\pi$
$647$	−16.2116	+	28.0794i	−0.637346	+	1.10391i	−0.986013	+	0.166668i	$0.946699\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	5.75379			0.225856
$650$		0			0
$651$	−14.2462			−0.558353
$652$	8.24621	−	14.2829i	0.322947	−	0.559360i
$653$	18.8078	−	32.5760i	0.736005	−	1.27480i	−0.218276	−	0.975887i	$-0.570043\pi$
$653$	18.8078	−	32.5760i	0.736005	−	1.27480i	0.954281	−	0.298911i	$-0.0966232\pi$
$654$	1.40388	+	2.43160i	0.0548961	+	0.0950829i
$655$		0			0
$656$	1.56155	+	2.70469i	0.0609684	+	0.105600i
$657$	−4.50000	−	7.79423i	−0.175562	−	0.304082i
$658$	−14.2462			−0.555375
$659$	−9.15767	−	15.8616i	−0.356732	−	0.617878i	0.630681	−	0.776042i	$-0.282776\pi$
$659$	−9.15767	−	15.8616i	−0.356732	−	0.617878i	−0.987413	+	0.158164i	$0.949442\pi$
$660$		0			0
$661$	24.2732	−	42.0424i	0.944118	−	1.63526i	0.186610	−	0.982434i	$-0.440250\pi$
$661$	24.2732	−	42.0424i	0.944118	−	1.63526i	0.757508	−	0.652826i	$-0.226417\pi$
$662$	−16.6847			−0.648468
$663$	−8.87689	−	6.92820i	−0.344750	−	0.269069i
$664$	6.56155			0.254638
$665$		0			0
$666$	−0.280776	+	0.486319i	−0.0108799	+	0.0188445i
$667$	4.31534	+	7.47439i	0.167091	+	0.289410i
$668$	23.6847			0.916387
$669$	0.219224	+	0.379706i	0.00847567	+	0.0146803i
$670$		0			0
$671$	0.946025			0.0365209
$672$	1.78078	+	3.08440i	0.0686949	+	0.118983i
$673$	−14.3769	+	24.9015i	−0.554189	+	0.959883i	0.443778	+	0.896137i	$0.353638\pi$
$673$	−14.3769	+	24.9015i	−0.554189	+	0.959883i	−0.997966	+	0.0637458i	$0.979695\pi$
$674$	−4.02699	+	6.97495i	−0.155114	+	0.268665i
$675$		0			0
$676$	9.34233	−	9.03996i	0.359320	−	0.347691i
$677$	11.6155			0.446421			0.223211	−	0.974770i	$-0.428346\pi$
$677$	11.6155			0.446421			0.223211	+	0.974770i	$0.428346\pi$
$678$	−2.00000	+	3.46410i	−0.0768095	+	0.133038i
$679$	−5.00000	+	8.66025i	−0.191882	+	0.332350i
$680$		0			0
$681$	29.6847			1.13752
$682$	1.12311	+	1.94528i	0.0430059	+	0.0744885i
$683$	−7.71922	−	13.3701i	−0.295368	−	0.511592i	0.679703	−	0.733488i	$-0.262109\pi$
$683$	−7.71922	−	13.3701i	−0.295368	−	0.511592i	−0.975070	+	0.221896i	$0.928776\pi$
$684$	−2.43845			−0.0932364
$685$		0			0
$686$	−2.34233	+	4.05703i	−0.0894305	+	0.154898i
$687$	−4.74621	+	8.22068i	−0.181079	+	0.313638i
$688$	0.438447			0.0167156
$689$	12.0691	+	9.41967i	0.459797	+	0.358861i
$690$		0			0
$691$	2.41146	−	4.17677i	0.0917362	−	0.158892i	−0.816506	−	0.577338i	$-0.804092\pi$
$691$	2.41146	−	4.17677i	0.0917362	−	0.158892i	0.908242	+	0.418446i	$0.137425\pi$
$692$	4.43845	−	7.68762i	0.168724	−	0.292239i
$693$	−1.00000	−	1.73205i	−0.0379869	−	0.0657952i
$694$	−24.8078			−0.941690
$695$		0			0
$696$	−0.561553	−	0.972638i	−0.0212856	−	0.0368677i
$697$	9.75379			0.369451
$698$	9.62311	+	16.6677i	0.364240	+	0.630882i
$699$	12.6847	−	21.9705i	0.479778	−	0.831000i
$700$		0			0
$701$	−0.876894			−0.0331198			−0.0165599	−	0.999863i	$-0.505271\pi$
$701$	−0.876894			−0.0331198			−0.0165599	+	0.999863i	$0.505271\pi$
$702$	−3.34233	+	1.35234i	−0.126148	+	0.0510410i
$703$	−1.36932			−0.0516448
$704$	0.280776	−	0.486319i	0.0105822	−	0.0183288i
$705$		0			0
$706$	−1.12311	−	1.94528i	−0.0422686	−	0.0732114i
$707$	22.2462			0.836655
$708$	5.12311	+	8.87348i	0.192538	+	0.333486i
$709$	14.3769	+	24.9015i	0.539936	+	0.935196i	0.998907	+	0.0467448i	$0.0148848\pi$
$709$	14.3769	+	24.9015i	0.539936	+	0.935196i	−0.458971	+	0.888451i	$0.651782\pi$
$710$		0			0
$711$	7.90388	+	13.6899i	0.296419	+	0.513412i
$712$	−5.12311	+	8.87348i	−0.191997	+	0.332548i
$713$	15.3693	−	26.6204i	0.575585	−	0.996943i
$714$	11.1231			0.416272
$715$		0			0
$716$	−15.6847			−0.586163
$717$	−13.5270	+	23.4294i	−0.505175	+	0.874988i
$718$	2.43845	−	4.22351i	0.0910020	−	0.157620i
$719$	8.71922	+	15.1021i	0.325172	+	0.563215i	0.981547	−	0.191220i	$-0.0612444\pi$
$719$	8.71922	+	15.1021i	0.325172	+	0.563215i	−0.656375	+	0.754435i	$0.727911\pi$
$720$		0			0
$721$	−7.90388	−	13.6899i	−0.294356	−	0.509839i
$722$	6.52699	+	11.3051i	0.242909	+	0.420731i
$723$	15.5616			0.578740
$724$	7.74621	+	13.4168i	0.287886	+	0.498633i
$725$		0			0
$726$	5.34233	−	9.25319i	0.198272	−	0.343418i
$727$	−50.7926			−1.88379			−0.941897	−	0.335902i	$-0.890959\pi$
$727$	−50.7926			−1.88379			−0.941897	+	0.335902i	$0.890959\pi$
$728$	−1.78078	+	12.7173i	−0.0660000	+	0.471334i
$729$	1.00000			0.0370370
$730$		0			0
$731$	0.684658	−	1.18586i	0.0253230	−	0.0438607i
$732$	0.842329	+	1.45896i	0.0311334	+	0.0539246i
$733$	−47.9848			−1.77236			−0.886180	−	0.463340i	$-0.846651\pi$
$733$	−47.9848			−1.77236			−0.886180	+	0.463340i	$0.846651\pi$
$734$	5.09612	+	8.82674i	0.188101	+	0.325801i
$735$		0			0
$736$	−7.68466			−0.283260
$737$	3.31534	+	5.74234i	0.122122	+	0.211522i
$738$	1.56155	−	2.70469i	0.0574816	−	0.0995610i
$739$	6.56155	−	11.3649i	0.241371	−	0.418066i	−0.719734	−	0.694250i	$-0.755736\pi$
$739$	6.56155	−	11.3649i	0.241371	−	0.418066i	0.961105	+	0.276183i	$0.0890697\pi$
$740$		0			0
$741$	−6.93087	−	5.40938i	−0.254612	−	0.198718i
$742$	−15.1231			−0.555187
$743$	−5.56155	+	9.63289i	−0.204034	+	0.353397i	−0.949824	−	0.312784i	$-0.898739\pi$
$743$	−5.56155	+	9.63289i	−0.204034	+	0.353397i	0.745791	+	0.666180i	$0.232072\pi$
$744$	−2.00000	+	3.46410i	−0.0733236	+	0.127000i
$745$		0			0
$746$	−9.49242			−0.347542
$747$	−3.28078	−	5.68247i	−0.120037	−	0.207911i
$748$	−0.876894	−	1.51883i	−0.0320624	−	0.0555338i
$749$	−19.1231			−0.698743
$750$		0			0
$751$	−25.1231	+	43.5145i	−0.916755	+	1.58787i	−0.112444	+	0.993658i	$0.535868\pi$
$751$	−25.1231	+	43.5145i	−0.916755	+	1.58787i	−0.804311	+	0.594208i	$0.797465\pi$
$752$	−2.00000	+	3.46410i	−0.0729325	+	0.126323i
$753$	23.9309			0.872089
$754$	0.561553	−	4.01029i	0.0204505	−	0.146046i
$755$		0			0
$756$	1.78078	−	3.08440i	0.0647662	−	0.112178i
$757$	15.3423	−	26.5737i	0.557626	−	0.965837i	−0.440068	−	0.897965i	$-0.645046\pi$
$757$	15.3423	−	26.5737i	0.557626	−	0.965837i	0.997694	−	0.0678727i	$-0.0216212\pi$
$758$	12.0270	+	20.8314i	0.436840	+	0.756629i
$759$	4.31534			0.156637
$760$		0			0
$761$	11.4924	+	19.9055i	0.416600	+	0.721572i	0.995595	−	0.0937588i	$-0.0298882\pi$
$761$	11.4924	+	19.9055i	0.416600	+	0.721572i	−0.578995	+	0.815331i	$0.696555\pi$
$762$	21.8078			0.790012
$763$	−5.00000	−	8.66025i	−0.181012	−	0.313522i
$764$	−7.96543	+	13.7965i	−0.288179	+	0.499141i
$765$		0			0
$766$	−5.43845			−0.196499
$767$	−5.12311	+	36.5863i	−0.184985	+	1.32105i
$768$	1.00000			0.0360844
$769$	4.65767	−	8.06732i	0.167960	−	0.290915i	−0.769743	−	0.638354i	$-0.779615\pi$
$769$	4.65767	−	8.06732i	0.167960	−	0.290915i	0.937702	+	0.347439i	$0.112949\pi$
$770$		0			0
$771$	6.80776	+	11.7914i	0.245176	+	0.424657i
$772$	3.00000			0.107972
$773$	14.8078	+	25.6478i	0.532598	+	0.922487i	0.999275	+	0.0380595i	$0.0121177\pi$
$773$	14.8078	+	25.6478i	0.532598	+	0.922487i	−0.466677	+	0.884428i	$0.654549\pi$
$774$	−0.219224	−	0.379706i	−0.00787983	−	0.0136483i
$775$		0			0
$776$	1.40388	+	2.43160i	0.0503964	+	0.0872892i
$777$	1.00000	−	1.73205i	0.0358748	−	0.0621370i
$778$	−5.68466	+	9.84612i	−0.203805	+	0.353000i
$779$	7.61553			0.272855
$780$		0			0
$781$	−7.05398			−0.252411
$782$	−12.0000	+	20.7846i	−0.429119	+	0.743256i
$783$	−0.561553	+	0.972638i	−0.0200683	+	0.0347592i
$784$	−2.84233	−	4.92306i	−0.101512	−	0.175824i
$785$		0			0
$786$	−0.438447	−	0.759413i	−0.0156389	−	0.0270874i
$787$	6.00000	+	10.3923i	0.213877	+	0.370446i	0.952925	−	0.303207i	$-0.0980575\pi$
$787$	6.00000	+	10.3923i	0.213877	+	0.370446i	−0.739048	+	0.673653i	$0.764724\pi$
$788$	5.12311			0.182503
$789$	−3.15767	−	5.46925i	−0.112416	−	0.194710i
$790$		0			0
$791$	7.12311	−	12.3376i	0.253268	−	0.438674i
$792$	−0.561553			−0.0199539
$793$	−0.842329	+	6.01543i	−0.0299120	+	0.213614i
$794$	−9.80776			−0.348065
$795$		0			0
$796$	2.21922	−	3.84381i	0.0786583	−	0.136240i
$797$	13.1231	+	22.7299i	0.464844	+	0.805134i	0.999194	−	0.0401293i	$-0.0127770\pi$
$797$	13.1231	+	22.7299i	0.464844	+	0.805134i	−0.534350	+	0.845263i	$0.679444\pi$
$798$	8.68466			0.307434
$799$	6.24621	+	10.8188i	0.220975	+	0.382740i
$800$		0			0
$801$	10.2462			0.362032
$802$	6.31534	+	10.9385i	0.223002	+	0.386252i
$803$	2.52699	−	4.37687i	0.0891755	−	0.154456i
$804$	−5.90388	+	10.2258i	−0.208214	+	0.360637i
$805$		0			0
$806$	−13.3693	+	5.40938i	−0.470914	+	0.190537i
$807$	−3.36932			−0.118606
$808$	3.12311	−	5.40938i	0.109870	−	0.190301i
$809$	−15.8078	+	27.3799i	−0.555771	+	0.962624i	0.442072	+	0.896980i	$0.354244\pi$
$809$	−15.8078	+	27.3799i	−0.555771	+	0.962624i	−0.997843	+	0.0656446i	$0.979090\pi$
$810$		0			0
$811$	−16.9309			−0.594523			−0.297262	−	0.954796i	$-0.596073\pi$
$811$	−16.9309			−0.594523			−0.297262	+	0.954796i	$0.596073\pi$
$812$	2.00000	+	3.46410i	0.0701862	+	0.121566i
$813$	−4.46543	−	7.73436i	−0.156610	−	0.271256i
$814$	−0.315342			−0.0110527
$815$		0			0
$816$	1.56155	−	2.70469i	0.0546653	−	0.0946830i
$817$	0.534565	−	0.925894i	0.0187021	−	0.0323929i
$818$	16.2462			0.568035
$819$	11.9039	−	4.81645i	0.415955	−	0.168300i
$820$		0			0
$821$	−19.4924	+	33.7619i	−0.680290	+	1.17830i	0.294602	+	0.955620i	$0.404813\pi$
$821$	−19.4924	+	33.7619i	−0.680290	+	1.17830i	−0.974892	+	0.222677i	$0.928520\pi$
$822$	−8.24621	+	14.2829i	−0.287620	+	0.498172i
$823$	−25.3963	−	43.9877i	−0.885260	−	1.53331i	−0.845416	−	0.534109i	$-0.820647\pi$
$823$	−25.3963	−	43.9877i	−0.885260	−	1.53331i	−0.0398436	−	0.999206i	$-0.512686\pi$
$824$	−4.43845			−0.154621
$825$		0			0
$826$	−18.2462	−	31.6034i	−0.634867	−	1.09962i
$827$	6.06913			0.211044			0.105522	−	0.994417i	$-0.466349\pi$
$827$	6.06913			0.211044			0.105522	+	0.994417i	$0.466349\pi$
$828$	3.84233	+	6.65511i	0.133530	+	0.231281i
$829$	−6.27320	+	10.8655i	−0.217877	+	0.377374i	−0.954159	−	0.299301i	$-0.903247\pi$
$829$	−6.27320	+	10.8655i	−0.217877	+	0.377374i	0.736282	+	0.676675i	$0.236580\pi$
$830$		0			0
$831$	5.00000			0.173448
$832$	2.84233	+	2.21837i	0.0985400	+	0.0769081i
$833$	−17.7538			−0.615132
$834$	−10.7808	+	18.6729i	−0.373308	+	0.646588i
$835$		0			0
$836$	−0.684658	−	1.18586i	−0.0236794	−	0.0410139i
$837$	4.00000			0.138260
$838$	5.96543	+	10.3324i	0.206073	+	0.356928i
$839$	−6.84233	−	11.8513i	−0.236223	−	0.409151i	0.723404	−	0.690425i	$-0.242576\pi$
$839$	−6.84233	−	11.8513i	−0.236223	−	0.409151i	−0.959628	+	0.281274i	$0.909243\pi$
$840$		0			0
$841$	13.8693	+	24.0224i	0.478252	+	0.828357i
$842$	−15.6231	+	27.0600i	−0.538408	+	0.932550i
$843$	0.876894	−	1.51883i	0.0302018	−	0.0523111i
$844$	1.12311			0.0386589
$845$		0			0
$846$	4.00000			0.137523
$847$	−19.0270	+	32.9557i	−0.653775	+	1.13237i
$848$	−2.12311	+	3.67733i	−0.0729077	+	0.126280i
$849$	−14.8078	−	25.6478i	−0.508201	−	0.880230i
$850$		0			0
$851$	2.15767	+	3.73720i	0.0739640	+	0.128109i
$852$	−6.28078	−	10.8786i	−0.215176	−	0.372696i
$853$	18.9848			0.650029			0.325014	−	0.945709i	$-0.394631\pi$
$853$	18.9848			0.650029			0.325014	+	0.945709i	$0.394631\pi$
$854$	−3.00000	−	5.19615i	−0.102658	−	0.177809i
$855$		0			0
$856$	−2.68466	+	4.64996i	−0.0917597	+	0.158933i
$857$	−56.2462			−1.92133			−0.960667	−	0.277703i	$-0.910427\pi$
$857$	−56.2462			−1.92133			−0.960667	+	0.277703i	$0.910427\pi$
$858$	−1.59612	−	1.24573i	−0.0544906	−	0.0425286i
$859$	27.4233			0.935671			0.467835	−	0.883816i	$-0.345034\pi$
$859$	27.4233			0.935671			0.467835	+	0.883816i	$0.345034\pi$
$860$		0			0
$861$	−5.56155	+	9.63289i	−0.189537	+	0.328288i
$862$	−9.15767	−	15.8616i	−0.311912	−	0.540247i
$863$	2.06913			0.0704340			0.0352170	−	0.999380i	$-0.488788\pi$
$863$	2.06913			0.0704340			0.0352170	+	0.999380i	$0.488788\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$		0			0
$866$	−13.6847			−0.465024
$867$	3.62311	+	6.27540i	0.123047	+	0.213124i
$868$	7.12311	−	12.3376i	0.241774	−	0.418765i
$869$	−4.43845	+	7.68762i	−0.150564	+	0.260785i
$870$		0			0
$871$	−39.4654	+	15.9682i	−1.33724	+	0.541061i
$872$	−2.80776			−0.0950829
$873$	1.40388	−	2.43160i	0.0475142	−	0.0822970i
$874$	−9.36932	+	16.2281i	−0.316922	+	0.548925i
$875$		0			0
$876$	9.00000			0.304082
$877$	−21.7462	−	37.6655i	−0.734317	−	1.27188i	−0.955022	−	0.296534i	$-0.904169\pi$
$877$	−21.7462	−	37.6655i	−0.734317	−	1.27188i	0.220705	−	0.975341i	$-0.429164\pi$
$878$	3.46543	+	6.00231i	0.116953	+	0.202568i
$879$	20.2462			0.682888
$880$		0			0
$881$	−24.5616	+	42.5419i	−0.827500	+	1.43327i	0.0724940	+	0.997369i	$0.476904\pi$
$881$	−24.5616	+	42.5419i	−0.827500	+	1.43327i	−0.899994	+	0.435903i	$0.856429\pi$
$882$	−2.84233	+	4.92306i	−0.0957062	+	0.165768i
$883$	34.2462			1.15248			0.576238	−	0.817282i	$-0.304520\pi$
$883$	34.2462			1.15248			0.576238	+	0.817282i	$0.304520\pi$
$884$	10.4384	−	4.22351i	0.351083	−	0.142052i
$885$		0			0
$886$	1.40388	−	2.43160i	0.0471643	−	0.0816910i
$887$	20.6847	−	35.8269i	0.694523	−	1.20295i	−0.275818	−	0.961210i	$-0.588949\pi$
$887$	20.6847	−	35.8269i	0.694523	−	1.20295i	0.970341	−	0.241739i	$-0.0777178\pi$
$888$	−0.280776	−	0.486319i	−0.00942224	−	0.0163198i
$889$	−77.6695			−2.60495
$890$		0			0
$891$	0.280776	+	0.486319i	0.00940636	+	0.0162923i
$892$	−0.438447			−0.0146803
$893$	4.87689	+	8.44703i	0.163199	+	0.282669i
$894$	5.12311	−	8.87348i	0.171342	−	0.296774i
$895$		0			0
$896$	−3.56155			−0.118983
$897$	−3.84233	+	27.4397i	−0.128292	+	0.916186i
$898$	−3.12311			−0.104219
$899$	−2.24621	+	3.89055i	−0.0749153	+	0.129757i
$900$		0			0
$901$	6.63068	+	11.4847i	0.220900	+	0.382610i
$902$	1.75379			0.0583948
$903$	0.780776	+	1.35234i	0.0259826	+	0.0450032i
$904$	−2.00000	−	3.46410i	−0.0665190	−	0.115214i
$905$		0			0
$906$	8.34233	+	14.4493i	0.277155	+	0.480047i
$907$	1.93087	−	3.34436i	0.0641135	−	0.111048i	−0.832187	−	0.554495i	$-0.812911\pi$
$907$	1.93087	−	3.34436i	0.0641135	−	0.111048i	0.896300	+	0.443447i	$0.146245\pi$
$908$	−14.8423	+	25.7077i	−0.492560	+	0.853139i
$909$	−6.24621			−0.207174
$910$		0			0
$911$	39.6847			1.31481			0.657406	−	0.753537i	$-0.271654\pi$
$911$	39.6847			1.31481			0.657406	+	0.753537i	$0.271654\pi$
$912$	1.21922	−	2.11176i	0.0403725	−	0.0699273i
$913$	1.84233	−	3.19101i	0.0609722	−	0.105607i
$914$	−2.25379	−	3.90368i	−0.0745487	−	0.129122i
$915$		0			0
$916$	−4.74621	−	8.22068i	−0.156819	−	0.271619i
$917$	1.56155	+	2.70469i	0.0515670	+	0.0893167i
$918$	−3.12311			−0.103078
$919$	−13.6577	−	23.6558i	−0.450525	−	0.780332i	0.547894	−	0.836548i	$-0.315430\pi$
$919$	−13.6577	−	23.6558i	−0.450525	−	0.780332i	−0.998419	+	0.0562158i	$0.982097\pi$
$920$		0			0
$921$	−11.1231	+	19.2658i	−0.366519	+	0.634829i
$922$	10.6307			0.350103
$923$	6.28078	−	44.8537i	0.206734	−	1.47638i
$924$	2.00000			0.0657952
$925$		0			0
$926$	−13.9039	+	24.0822i	−0.456910	+	0.791391i
$927$	2.21922	+	3.84381i	0.0728889	+	0.126247i
$928$	1.12311			0.0368677
$929$	24.9309	+	43.1815i	0.817955	+	1.41674i	0.907186	+	0.420729i	$0.138226\pi$
$929$	24.9309	+	43.1815i	0.817955	+	1.41674i	−0.0892310	+	0.996011i	$0.528441\pi$
$930$		0			0
$931$	−13.8617			−0.454300
$932$	12.6847	+	21.9705i	0.415500	+	0.719667i
$933$	5.15767	−	8.93335i	0.168855	−	0.292465i
$934$	1.71922	−	2.97778i	0.0562547	−	0.0974360i
$935$		0			0
$936$	0.500000	−	3.57071i	0.0163430	−	0.116712i
$937$	−11.2462			−0.367398			−0.183699	−	0.982983i	$-0.558807\pi$
$937$	−11.2462			−0.367398			−0.183699	+	0.982983i	$0.558807\pi$
$938$	21.0270	−	36.4198i	0.686555	−	1.18915i
$939$	−15.5000	+	26.8468i	−0.505823	+	0.876112i
$940$		0			0
$941$	34.6307			1.12893			0.564464	−	0.825458i	$-0.309083\pi$
$941$	34.6307			1.12893			0.564464	+	0.825458i	$0.309083\pi$
$942$	−8.62311	−	14.9357i	−0.280956	−	0.486630i
$943$	−12.0000	−	20.7846i	−0.390774	−	0.676840i
$944$	−10.2462			−0.333486
$945$		0			0
$946$	0.123106	−	0.213225i	0.00400251	−	0.00693255i
$947$	−23.3348	+	40.4170i	−0.758278	+	1.31338i	0.185451	+	0.982654i	$0.440625\pi$
$947$	−23.3348	+	40.4170i	−0.758278	+	1.31338i	−0.943728	+	0.330722i	$0.892708\pi$
$948$	−15.8078			−0.513412
$949$	25.5810	+	19.9653i	0.830393	+	0.648102i
$950$		0			0
$951$	−8.12311	+	14.0696i	−0.263410	+	0.456239i
$952$	−5.56155	+	9.63289i	−0.180251	+	0.312204i
$953$	4.12311	+	7.14143i	0.133560	+	0.231334i	0.925047	−	0.379854i	$-0.124026\pi$
$953$	4.12311	+	7.14143i	0.133560	+	0.231334i	−0.791486	+	0.611187i	$0.790692\pi$
$954$	4.24621			0.137476
$955$		0			0
$956$	−13.5270	−	23.4294i	−0.437494	−	0.757762i
$957$	−0.630683			−0.0203871
$958$	5.80776	+	10.0593i	0.187640	+	0.325003i
$959$	29.3693	−	50.8691i	0.948385	−	1.64265i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	0.280776	−	2.00514i	0.00905259	−	0.0646485i
$963$	5.36932			0.173024
$964$	−7.78078	+	13.4767i	−0.250602	+	0.434055i
$965$		0			0
$966$	−13.6847	−	23.7025i	−0.440297	−	0.762616i
$967$	16.6307			0.534807			0.267403	−	0.963585i	$-0.413834\pi$
$967$	16.6307			0.534807			0.267403	+	0.963585i	$0.413834\pi$
$968$	5.34233	+	9.25319i	0.171709	+	0.297409i
$969$	−3.80776	−	6.59524i	−0.122323	−	0.211870i
$970$		0			0
$971$	−7.31534	−	12.6705i	−0.234760	−	0.406617i	0.724443	−	0.689335i	$-0.242097\pi$
$971$	−7.31534	−	12.6705i	−0.234760	−	0.406617i	−0.959203	+	0.282718i	$0.908764\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	38.3963	−	66.5044i	1.23093	−	2.13203i
$974$	42.6847			1.36770
$975$		0			0
$976$	−1.68466			−0.0539246
$977$	23.1231	−	40.0504i	0.739774	−	1.28133i	−0.212823	−	0.977091i	$-0.568266\pi$
$977$	23.1231	−	40.0504i	0.739774	−	1.28133i	0.952597	−	0.304235i	$-0.0984008\pi$
$978$	8.24621	−	14.2829i	0.263685	−	0.456715i
$979$	2.87689	+	4.98293i	0.0919459	+	0.159255i
$980$		0			0
$981$	1.40388	+	2.43160i	0.0448225	+	0.0776349i
$982$	−15.6501	−	27.1068i	−0.499415	−	0.865011i
$983$	−22.2462			−0.709544			−0.354772	−	0.934953i	$-0.615441\pi$
$983$	−22.2462			−0.709544			−0.354772	+	0.934953i	$0.615441\pi$
$984$	1.56155	+	2.70469i	0.0497805	+	0.0862223i
$985$		0			0
$986$	1.75379	−	3.03765i	0.0558520	−	0.0967385i
$987$	−14.2462			−0.453462
$988$	8.15009	−	3.29762i	0.259289	−	0.104911i
$989$	−3.36932			−0.107138
$990$		0			0
$991$	9.97301	−	17.2738i	0.316803	−	0.548719i	−0.663016	−	0.748605i	$-0.730724\pi$
$991$	9.97301	−	17.2738i	0.316803	−	0.548719i	0.979819	+	0.199886i	$0.0640572\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$	−16.6847			−0.529472
$994$	22.3693	+	38.7448i	0.709512	+	1.22891i
$995$		0			0
$996$	6.56155			0.207911
$997$	−13.8348	−	23.9625i	−0.438151	−	0.758900i	0.559396	−	0.828901i	$-0.311033\pi$
$997$	−13.8348	−	23.9625i	−0.438151	−	0.758900i	−0.997547	+	0.0700008i	$0.977700\pi$
$998$	−3.02699	+	5.24290i	−0.0958176	+	0.165961i
$999$	−0.280776	+	0.486319i	−0.00888337	+	0.0153865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.i.z.451.2	✓	4
5.2	odd	4		1950.2.z.m.1699.1		8
5.3	odd	4		1950.2.z.m.1699.4		8
5.4	even	2		1950.2.i.bg.451.1	yes	4
13.3	even	3	inner	1950.2.i.z.601.2	yes	4
65.3	odd	12		1950.2.z.m.1849.1		8
65.29	even	6		1950.2.i.bg.601.1	yes	4
65.42	odd	12		1950.2.z.m.1849.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.i.z.451.2	✓	4	1.1	even	1	trivial
1950.2.i.z.601.2	yes	4	13.3	even	3	inner
1950.2.i.bg.451.1	yes	4	5.4	even	2
1950.2.i.bg.601.1	yes	4	65.29	even	6
1950.2.z.m.1699.1		8	5.2	odd	4
1950.2.z.m.1699.4		8	5.3	odd	4
1950.2.z.m.1849.1		8	65.3	odd	12
1950.2.z.m.1849.4		8	65.42	odd	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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(1.78078 + 3.08440i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} +(1.78078 + 3.08440i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.280776 - 0.486319i) q^{11} +1.00000 q^{12} +(2.84233 + 2.21837i) q^{13} -3.56155 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.56155 + 2.70469i) q^{17} +1.00000 q^{18} +(1.21922 + 2.11176i) q^{19} -3.56155 q^{21} +(0.280776 + 0.486319i) q^{22} +(3.84233 - 6.65511i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.34233 + 1.35234i) q^{26} +1.00000 q^{27} +(1.78078 - 3.08440i) q^{28} +(-0.561553 + 0.972638i) q^{29} +4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.280776 + 0.486319i) q^{33} -3.12311 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-0.280776 + 0.486319i) q^{37} -2.43845 q^{38} +(-3.34233 + 1.35234i) q^{39} +(1.56155 - 2.70469i) q^{41} +(1.78078 - 3.08440i) q^{42} +(-0.219224 - 0.379706i) q^{43} -0.561553 q^{44} +(3.84233 + 6.65511i) q^{46} +4.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-2.84233 + 4.92306i) q^{49} -3.12311 q^{51} +(0.500000 - 3.57071i) q^{52} +4.24621 q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.78078 + 3.08440i) q^{56} -2.43845 q^{57} +(-0.561553 - 0.972638i) q^{58} +(5.12311 + 8.87348i) q^{59} +(0.842329 + 1.45896i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(1.78078 - 3.08440i) q^{63} +1.00000 q^{64} -0.561553 q^{66} +(-5.90388 + 10.2258i) q^{67} +(1.56155 - 2.70469i) q^{68} +(3.84233 + 6.65511i) q^{69} +(-6.28078 - 10.8786i) q^{71} +(-0.500000 - 0.866025i) q^{72} +9.00000 q^{73} +(-0.280776 - 0.486319i) q^{74} +(1.21922 - 2.11176i) q^{76} +2.00000 q^{77} +(0.500000 - 3.57071i) q^{78} -15.8078 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.56155 + 2.70469i) q^{82} +6.56155 q^{83} +(1.78078 + 3.08440i) q^{84} +0.438447 q^{86} +(-0.561553 - 0.972638i) q^{87} +(0.280776 - 0.486319i) q^{88} +(-5.12311 + 8.87348i) q^{89} +(-1.78078 + 12.7173i) q^{91} -7.68466 q^{92} +(-2.00000 + 3.46410i) q^{93} +(-2.00000 + 3.46410i) q^{94} +1.00000 q^{96} +(1.40388 + 2.43160i) q^{97} +(-2.84233 - 4.92306i) q^{98} -0.561553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} + 3 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^6 + 3 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} + 3 q^{7} + 4 q^{8} - 2 q^{9} - 3 q^{11} + 4 q^{12} - q^{13} - 6 q^{14} - 2 q^{16} - 2 q^{17} + 4 q^{18} + 9 q^{19} - 6 q^{21} - 3 q^{22} + 3 q^{23} - 2 q^{24} - q^{26} + 4 q^{27} + 3 q^{28} + 6 q^{29} + 16 q^{31} - 2 q^{32} - 3 q^{33} + 4 q^{34} - 2 q^{36} + 3 q^{37} - 18 q^{38} - q^{39} - 2 q^{41} + 3 q^{42} - 5 q^{43} + 6 q^{44} + 3 q^{46} + 16 q^{47} - 2 q^{48} + q^{49} + 4 q^{51} + 2 q^{52} - 16 q^{53} - 2 q^{54} + 3 q^{56} - 18 q^{57} + 6 q^{58} + 4 q^{59} - 9 q^{61} - 8 q^{62} + 3 q^{63} + 4 q^{64} + 6 q^{66} - 3 q^{67} - 2 q^{68} + 3 q^{69} - 21 q^{71} - 2 q^{72} + 36 q^{73} + 3 q^{74} + 9 q^{76} + 8 q^{77} + 2 q^{78} - 22 q^{79} - 2 q^{81} - 2 q^{82} + 18 q^{83} + 3 q^{84} + 10 q^{86} + 6 q^{87} - 3 q^{88} - 4 q^{89} - 3 q^{91} - 6 q^{92} - 8 q^{93} - 8 q^{94} + 4 q^{96} - 15 q^{97} + q^{98} + 6 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^6 + 3 * q^7 + 4 * q^8 - 2 * q^9 - 3 * q^11 + 4 * q^12 - q^13 - 6 * q^14 - 2 * q^16 - 2 * q^17 + 4 * q^18 + 9 * q^19 - 6 * q^21 - 3 * q^22 + 3 * q^23 - 2 * q^24 - q^26 + 4 * q^27 + 3 * q^28 + 6 * q^29 + 16 * q^31 - 2 * q^32 - 3 * q^33 + 4 * q^34 - 2 * q^36 + 3 * q^37 - 18 * q^38 - q^39 - 2 * q^41 + 3 * q^42 - 5 * q^43 + 6 * q^44 + 3 * q^46 + 16 * q^47 - 2 * q^48 + q^49 + 4 * q^51 + 2 * q^52 - 16 * q^53 - 2 * q^54 + 3 * q^56 - 18 * q^57 + 6 * q^58 + 4 * q^59 - 9 * q^61 - 8 * q^62 + 3 * q^63 + 4 * q^64 + 6 * q^66 - 3 * q^67 - 2 * q^68 + 3 * q^69 - 21 * q^71 - 2 * q^72 + 36 * q^73 + 3 * q^74 + 9 * q^76 + 8 * q^77 + 2 * q^78 - 22 * q^79 - 2 * q^81 - 2 * q^82 + 18 * q^83 + 3 * q^84 + 10 * q^86 + 6 * q^87 - 3 * q^88 - 4 * q^89 - 3 * q^91 - 6 * q^92 - 8 * q^93 - 8 * q^94 + 4 * q^96 - 15 * q^97 + q^98 + 6 * q^99

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