LMFDB - Embedded newform 1110.2.i.j.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(121,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, 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("1110.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{73})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 19x^{2} + 18x + 324 $ x^4 - x^3 + 19x^2 + 18x + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$-1.88600 + 3.26665i$ of defining polynomial
Character	$\chi$	$=$	1110.121
Dual form			1110.2.i.j.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} +1.00000 q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.386001 + 0.668573i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.88600 + 3.26665i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-0.500000 + 0.866025i) q^{22} +5.77200 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{26} -1.00000 q^{27} +8.77200 q^{29} +(0.500000 + 0.866025i) q^{30} -7.54400 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} +(-0.386001 - 0.668573i) q^{34} +1.00000 q^{36} +(4.27200 + 4.33013i) q^{37} -3.77200 q^{38} +(0.500000 - 0.866025i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(5.77200 + 9.99740i) q^{41} +(-0.500000 - 0.866025i) q^{44} +1.00000 q^{45} +(-2.88600 + 4.99870i) q^{46} +3.00000 q^{47} -1.00000 q^{48} +(3.50000 - 6.06218i) q^{49} +(-0.500000 - 0.866025i) q^{50} -0.772002 q^{51} +(-0.500000 + 0.866025i) q^{52} +(-1.77200 + 3.06920i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.500000 - 0.866025i) q^{55} +(-1.88600 + 3.26665i) q^{57} +(-4.38600 + 7.59678i) q^{58} +(-2.27200 + 3.93522i) q^{59} -1.00000 q^{60} +(5.00000 + 8.66025i) q^{61} +(3.77200 - 6.53330i) q^{62} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} -1.00000 q^{66} +(-5.15800 - 8.93392i) q^{67} +0.772002 q^{68} +(2.88600 + 4.99870i) q^{69} +(6.77200 + 11.7295i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-5.88600 + 1.53460i) q^{74} -1.00000 q^{75} +(1.88600 - 3.26665i) q^{76} +(0.500000 + 0.866025i) q^{78} +(5.77200 + 9.99740i) q^{79} +1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} -11.5440 q^{82} +(3.77200 - 6.53330i) q^{83} +0.772002 q^{85} +(4.38600 + 7.59678i) q^{87} +1.00000 q^{88} +(7.88600 - 13.6590i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-2.88600 - 4.99870i) q^{92} +(-3.77200 - 6.53330i) q^{93} +(-1.50000 + 2.59808i) q^{94} +(1.88600 - 3.26665i) q^{95} +(0.500000 - 0.866025i) q^{96} -17.5440 q^{97} +(3.50000 + 6.06218i) q^{98} +(-0.500000 + 0.866025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 - 2 * q^9	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} - 2 q^{9} + 4 q^{10} + 4 q^{11} + 2 q^{12} - 2 q^{13} + 2 q^{15} - 2 q^{16} + 7 q^{17} - 2 q^{18} - q^{19} - 2 q^{20} - 2 q^{22} + 6 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{26} - 4 q^{27} + 18 q^{29} + 2 q^{30} + 4 q^{31} - 2 q^{32} + 2 q^{33} + 7 q^{34} + 4 q^{36} + 2 q^{38} + 2 q^{39} - 2 q^{40} + 6 q^{41} - 2 q^{44} + 4 q^{45} - 3 q^{46} + 12 q^{47} - 4 q^{48} + 14 q^{49} - 2 q^{50} + 14 q^{51} - 2 q^{52} + 10 q^{53} + 2 q^{54} - 2 q^{55} + q^{57} - 9 q^{58} + 8 q^{59} - 4 q^{60} + 20 q^{61} - 2 q^{62} + 4 q^{64} - 2 q^{65} - 4 q^{66} + 5 q^{67} - 14 q^{68} + 3 q^{69} + 10 q^{71} - 2 q^{72} - 15 q^{74} - 4 q^{75} - q^{76} + 2 q^{78} + 6 q^{79} + 4 q^{80} - 2 q^{81} - 12 q^{82} - 2 q^{83} - 14 q^{85} + 9 q^{87} + 4 q^{88} + 23 q^{89} - 2 q^{90} - 3 q^{92} + 2 q^{93} - 6 q^{94} - q^{95} + 2 q^{96} - 36 q^{97} + 14 q^{98} - 2 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 - 2 * q^9 + 4 * q^10 + 4 * q^11 + 2 * q^12 - 2 * q^13 + 2 * q^15 - 2 * q^16 + 7 * q^17 - 2 * q^18 - q^19 - 2 * q^20 - 2 * q^22 + 6 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^26 - 4 * q^27 + 18 * q^29 + 2 * q^30 + 4 * q^31 - 2 * q^32 + 2 * q^33 + 7 * q^34 + 4 * q^36 + 2 * q^38 + 2 * q^39 - 2 * q^40 + 6 * q^41 - 2 * q^44 + 4 * q^45 - 3 * q^46 + 12 * q^47 - 4 * q^48 + 14 * q^49 - 2 * q^50 + 14 * q^51 - 2 * q^52 + 10 * q^53 + 2 * q^54 - 2 * q^55 + q^57 - 9 * q^58 + 8 * q^59 - 4 * q^60 + 20 * q^61 - 2 * q^62 + 4 * q^64 - 2 * q^65 - 4 * q^66 + 5 * q^67 - 14 * q^68 + 3 * q^69 + 10 * q^71 - 2 * q^72 - 15 * q^74 - 4 * q^75 - q^76 + 2 * q^78 + 6 * q^79 + 4 * q^80 - 2 * q^81 - 12 * q^82 - 2 * q^83 - 14 * q^85 + 9 * q^87 + 4 * q^88 + 23 * q^89 - 2 * q^90 - 3 * q^92 + 2 * q^93 - 6 * q^94 - q^95 + 2 * q^96 - 36 * q^97 + 14 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	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
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.00000			−0.408248
$7$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$7$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000			0.316228
$11$	1.00000			0.301511			0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000			0.301511			0.150756	+	0.988571i	$0.451829\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	0.788320	−	0.615265i	$-0.210951\pi$
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	−0.926995	+	0.375073i	$0.877618\pi$
$14$		0			0
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.386001	+	0.668573i	−0.0936190	+	0.162153i	−0.909031	−	0.416728i	$-0.863177\pi$
$17$	−0.386001	+	0.668573i	−0.0936190	+	0.162153i	0.815412	+	0.578880i	$0.196510\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	1.88600	+	3.26665i	0.432678	+	0.749421i	0.997103	−	0.0760638i	$-0.0242353\pi$
$19$	1.88600	+	3.26665i	0.432678	+	0.749421i	−0.564425	+	0.825485i	$0.690902\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	5.77200			1.20355			0.601773	−	0.798667i	$-0.294461\pi$
$23$	5.77200			1.20355			0.601773	+	0.798667i	$0.294461\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.00000			0.196116
$27$	−1.00000			−0.192450
$28$		0			0
$29$	8.77200			1.62892			0.814460	−	0.580220i	$-0.197033\pi$
$29$	8.77200			1.62892			0.814460	+	0.580220i	$0.197033\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$	−7.54400			−1.35494			−0.677472	−	0.735549i	$-0.736924\pi$
$31$	−7.54400			−1.35494			−0.677472	+	0.735549i	$0.736924\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	−0.386001	−	0.668573i	−0.0661986	−	0.114659i
$35$		0			0
$36$	1.00000			0.166667
$37$	4.27200	+	4.33013i	0.702313	+	0.711868i
$37$	4.27200	+	4.33013i	0.702313	+	0.711868i
$38$	−3.77200			−0.611900
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	5.77200	+	9.99740i	0.901435	+	1.56133i	0.825632	+	0.564209i	$0.190819\pi$
$41$	5.77200	+	9.99740i	0.901435	+	1.56133i	0.0758031	+	0.997123i	$0.475848\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$	1.00000			0.149071
$46$	−2.88600	+	4.99870i	−0.425518	+	0.737018i
$47$	3.00000			0.437595			0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000			0.437595			0.218797	+	0.975770i	$0.429787\pi$
$48$	−1.00000			−0.144338
$49$	3.50000	−	6.06218i	0.500000	−	0.866025i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−0.772002			−0.108102
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	−1.77200	+	3.06920i	−0.243403	+	0.421587i	−0.961681	−	0.274169i	$-0.911597\pi$
$53$	−1.77200	+	3.06920i	−0.243403	+	0.421587i	0.718278	+	0.695756i	$0.244930\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−0.500000	−	0.866025i	−0.0674200	−	0.116775i
$56$		0			0
$57$	−1.88600	+	3.26665i	−0.249807	+	0.432678i
$58$	−4.38600	+	7.59678i	−0.575910	+	0.997506i
$59$	−2.27200	+	3.93522i	−0.295789	+	0.512322i	−0.975168	−	0.221465i	$-0.928916\pi$
$59$	−2.27200	+	3.93522i	−0.295789	+	0.512322i	0.679379	+	0.733788i	$0.262249\pi$
$60$	−1.00000			−0.129099
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	0.985391	+	0.170305i	$0.0544754\pi$
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	−0.345207	+	0.938527i	$0.612191\pi$
$62$	3.77200	−	6.53330i	0.479045	−	0.829730i
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$	−1.00000			−0.123091
$67$	−5.15800	−	8.93392i	−0.630150	−	1.09145i	−0.987521	−	0.157490i	$-0.949660\pi$
$67$	−5.15800	−	8.93392i	−0.630150	−	1.09145i	0.357370	−	0.933963i	$-0.383673\pi$
$68$	0.772002			0.0936190
$69$	2.88600	+	4.99870i	0.347434	+	0.601773i
$70$		0			0
$71$	6.77200	+	11.7295i	0.803689	+	1.39203i	0.917173	+	0.398490i	$0.130466\pi$
$71$	6.77200	+	11.7295i	0.803689	+	1.39203i	−0.113484	+	0.993540i	$0.536201\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	−5.88600	+	1.53460i	−0.684234	+	0.178393i
$75$	−1.00000			−0.115470
$76$	1.88600	−	3.26665i	0.216339	−	0.374710i
$77$		0			0
$78$	0.500000	+	0.866025i	0.0566139	+	0.0980581i
$79$	5.77200	+	9.99740i	0.649401	+	1.12480i	0.983266	+	0.182175i	$0.0583136\pi$
$79$	5.77200	+	9.99740i	0.649401	+	1.12480i	−0.333865	+	0.942621i	$0.608353\pi$
$80$	1.00000			0.111803
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−11.5440			−1.27482
$83$	3.77200	−	6.53330i	0.414031	−	0.717123i	−0.581295	−	0.813693i	$-0.697454\pi$
$83$	3.77200	−	6.53330i	0.414031	−	0.717123i	0.995326	+	0.0965700i	$0.0307872\pi$
$84$		0			0
$85$	0.772002			0.0837354
$86$		0			0
$87$	4.38600	+	7.59678i	0.470229	+	0.814460i
$88$	1.00000			0.106600
$89$	7.88600	−	13.6590i	0.835914	−	1.44785i	−0.0573693	−	0.998353i	$-0.518271\pi$
$89$	7.88600	−	13.6590i	0.835914	−	1.44785i	0.893284	−	0.449493i	$-0.148395\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$		0			0
$92$	−2.88600	−	4.99870i	−0.300886	−	0.521151i
$93$	−3.77200	−	6.53330i	−0.391138	−	0.677472i
$94$	−1.50000	+	2.59808i	−0.154713	+	0.267971i
$95$	1.88600	−	3.26665i	0.193500	−	0.335151i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−17.5440			−1.78132			−0.890662	−	0.454666i	$-0.849759\pi$
$97$	−17.5440			−1.78132			−0.890662	+	0.454666i	$0.849759\pi$
$98$	3.50000	+	6.06218i	0.353553	+	0.612372i
$99$	−0.500000	+	0.866025i	−0.0502519	+	0.0870388i
$100$	1.00000			0.100000
$101$	−8.31601			−0.827473			−0.413737	−	0.910397i	$-0.635777\pi$
$101$	−8.31601			−0.827473			−0.413737	+	0.910397i	$0.635777\pi$
$102$	0.386001	−	0.668573i	0.0382198	−	0.0661986i
$103$	−11.7720			−1.15993			−0.579965	−	0.814641i	$-0.696934\pi$
$103$	−11.7720			−1.15993			−0.579965	+	0.814641i	$0.696934\pi$
$104$	−0.500000	−	0.866025i	−0.0490290	−	0.0849208i
$105$		0			0
$106$	−1.77200	−	3.06920i	−0.172112	−	0.298107i
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	0.946357	−	0.323122i	$-0.104732\pi$
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	−0.753010	+	0.658009i	$0.771399\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	2.00000	−	3.46410i	0.191565	−	0.331801i	−0.754204	−	0.656640i	$-0.771977\pi$
$109$	2.00000	−	3.46410i	0.191565	−	0.331801i	0.945769	+	0.324840i	$0.105310\pi$
$110$	1.00000			0.0953463
$111$	−1.61400	+	5.86473i	−0.153194	+	0.556655i
$112$		0			0
$113$	3.38600	−	5.86473i	0.318528	−	0.551707i	−0.661653	−	0.749810i	$-0.730145\pi$
$113$	3.38600	−	5.86473i	0.318528	−	0.551707i	0.980181	+	0.198103i	$0.0634781\pi$
$114$	−1.88600	−	3.26665i	−0.176640	−	0.305950i
$115$	−2.88600	−	4.99870i	−0.269121	−	0.466131i
$116$	−4.38600	−	7.59678i	−0.407230	−	0.705343i
$117$	1.00000			0.0924500
$118$	−2.27200	−	3.93522i	−0.209155	−	0.362267i
$119$		0			0
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	−10.0000			−0.909091
$122$	−10.0000			−0.905357
$123$	−5.77200	+	9.99740i	−0.520444	+	0.901435i
$124$	3.77200	+	6.53330i	0.338736	+	0.586708i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−8.88600	+	15.3910i	−0.788505	+	1.36573i	0.138378	+	0.990380i	$0.455811\pi$
$127$	−8.88600	+	15.3910i	−0.788505	+	1.36573i	−0.926883	+	0.375351i	$0.877522\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−0.500000	−	0.866025i	−0.0438529	−	0.0759555i
$131$	0.613999	−	1.06348i	0.0536453	−	0.0929165i	−0.837956	−	0.545738i	$-0.816249\pi$
$131$	0.613999	−	1.06348i	0.0536453	−	0.0929165i	0.891601	+	0.452822i	$0.149583\pi$
$132$	0.500000	−	0.866025i	0.0435194	−	0.0753778i
$133$		0			0
$134$	10.3160			0.891167
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	−0.386001	+	0.668573i	−0.0330993	+	0.0573297i
$137$	10.3160			0.881356			0.440678	−	0.897665i	$-0.354738\pi$
$137$	10.3160			0.881356			0.440678	+	0.897665i	$0.354738\pi$
$138$	−5.77200			−0.491345
$139$	0.886001	−	1.53460i	0.0751496	−	0.130163i	−0.826002	−	0.563668i	$-0.809390\pi$
$139$	0.886001	−	1.53460i	0.0751496	−	0.130163i	0.901151	+	0.433505i	$0.142723\pi$
$140$		0			0
$141$	1.50000	+	2.59808i	0.126323	+	0.218797i
$142$	−13.5440			−1.13659
$143$	−0.500000	−	0.866025i	−0.0418121	−	0.0724207i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−4.38600	−	7.59678i	−0.364238	−	0.630878i
$146$		0			0
$147$	7.00000			0.577350
$148$	1.61400	−	5.86473i	0.132670	−	0.482077i
$149$	8.31601			0.681274			0.340637	−	0.940195i	$-0.389357\pi$
$149$	8.31601			0.681274			0.340637	+	0.940195i	$0.389357\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	0.981617	−	0.190864i	$-0.0611289\pi$
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	−0.656101	+	0.754673i	$0.727796\pi$
$152$	1.88600	+	3.26665i	0.152975	+	0.264960i
$153$	−0.386001	−	0.668573i	−0.0312063	−	0.0540509i
$154$		0			0
$155$	3.77200	+	6.53330i	0.302974	+	0.524767i
$156$	−1.00000			−0.0800641
$157$	4.27200	−	7.39932i	0.340943	−	0.590530i	−0.643665	−	0.765307i	$-0.722587\pi$
$157$	4.27200	−	7.39932i	0.340943	−	0.590530i	0.984608	+	0.174777i	$0.0559204\pi$
$158$	−11.5440			−0.918392
$159$	−3.54400			−0.281058
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$		0			0
$162$	1.00000			0.0785674
$163$	2.38600	−	4.13267i	0.186886	−	0.323696i	−0.757324	−	0.653039i	$-0.773494\pi$
$163$	2.38600	−	4.13267i	0.186886	−	0.323696i	0.944210	+	0.329343i	$0.106827\pi$
$164$	5.77200	−	9.99740i	0.450718	−	0.780666i
$165$	0.500000	−	0.866025i	0.0389249	−	0.0674200i
$166$	3.77200	+	6.53330i	0.292764	+	0.507082i
$167$	−9.38600	−	16.2570i	−0.726311	−	1.25801i	−0.958432	−	0.285320i	$-0.907900\pi$
$167$	−9.38600	−	16.2570i	−0.726311	−	1.25801i	0.232122	−	0.972687i	$-0.425433\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	−0.386001	+	0.668573i	−0.0296049	+	0.0512772i
$171$	−3.77200			−0.288452
$172$		0			0
$173$	−10.6580	+	18.4602i	−0.810313	+	1.40350i	0.102332	+	0.994750i	$0.467370\pi$
$173$	−10.6580	+	18.4602i	−0.810313	+	1.40350i	−0.912645	+	0.408753i	$0.865964\pi$
$174$	−8.77200			−0.665004
$175$		0			0
$176$	−0.500000	+	0.866025i	−0.0376889	+	0.0652791i
$177$	−4.54400			−0.341548
$178$	7.88600	+	13.6590i	0.591081	+	1.02378i
$179$	5.31601			0.397337			0.198668	−	0.980067i	$-0.436338\pi$
$179$	5.31601			0.397337			0.198668	+	0.980067i	$0.436338\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	−2.77200	−	4.80125i	−0.206041	−	0.356874i	0.744423	−	0.667709i	$-0.232725\pi$
$181$	−2.77200	−	4.80125i	−0.206041	−	0.356874i	−0.950464	+	0.310835i	$0.899391\pi$
$182$		0			0
$183$	−5.00000	+	8.66025i	−0.369611	+	0.640184i
$184$	5.77200			0.425518
$185$	1.61400	−	5.86473i	0.118664	−	0.431183i
$186$	7.54400			0.553153
$187$	−0.386001	+	0.668573i	−0.0282272	+	0.0488909i
$188$	−1.50000	−	2.59808i	−0.109399	−	0.189484i
$189$		0			0
$190$	1.88600	+	3.26665i	0.136825	+	0.236988i
$191$	4.45600			0.322425			0.161212	−	0.986920i	$-0.448460\pi$
$191$	4.45600			0.322425			0.161212	+	0.986920i	$0.448460\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	15.0880			1.08606			0.543029	−	0.839714i	$-0.317277\pi$
$193$	15.0880			1.08606			0.543029	+	0.839714i	$0.317277\pi$
$194$	8.77200	−	15.1936i	0.629793	−	1.09083i
$195$	−1.00000			−0.0716115
$196$	−7.00000			−0.500000
$197$	7.00000	−	12.1244i	0.498729	−	0.863825i	−0.501270	−	0.865291i	$-0.667133\pi$
$197$	7.00000	−	12.1244i	0.498729	−	0.863825i	0.999999	+	0.00146660i	$0.000466833\pi$
$198$	−0.500000	−	0.866025i	−0.0355335	−	0.0615457i
$199$	26.7720			1.89782			0.948908	−	0.315552i	$-0.102190\pi$
$199$	26.7720			1.89782			0.948908	+	0.315552i	$0.102190\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	5.15800	−	8.93392i	0.363817	−	0.630150i
$202$	4.15800	−	7.20187i	0.292556	−	0.506722i
$203$		0			0
$204$	0.386001	+	0.668573i	0.0270255	+	0.0468095i
$205$	5.77200	−	9.99740i	0.403134	−	0.698249i
$206$	5.88600	−	10.1949i	0.410097	−	0.710309i
$207$	−2.88600	+	4.99870i	−0.200591	+	0.347434i
$208$	1.00000			0.0693375
$209$	1.88600	+	3.26665i	0.130457	+	0.225959i
$210$		0			0
$211$	−17.7720			−1.22348			−0.611738	−	0.791061i	$-0.709529\pi$
$211$	−17.7720			−1.22348			−0.611738	+	0.791061i	$0.709529\pi$
$212$	3.54400			0.243403
$213$	−6.77200	+	11.7295i	−0.464010	+	0.803689i
$214$	−4.00000			−0.273434
$215$		0			0
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	2.00000	+	3.46410i	0.135457	+	0.234619i
$219$		0			0
$220$	−0.500000	+	0.866025i	−0.0337100	+	0.0583874i
$221$	0.772002			0.0519305
$222$	−4.27200	−	4.33013i	−0.286718	−	0.290619i
$223$	−20.8600			−1.39689			−0.698445	−	0.715664i	$-0.746124\pi$
$223$	−20.8600			−1.39689			−0.698445	+	0.715664i	$0.746124\pi$
$224$		0			0
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	3.38600	+	5.86473i	0.225233	+	0.390116i
$227$	3.77200	+	6.53330i	0.250357	+	0.433630i	0.963624	−	0.267262i	$-0.0861188\pi$
$227$	3.77200	+	6.53330i	0.250357	+	0.433630i	−0.713267	+	0.700892i	$0.752785\pi$
$228$	3.77200			0.249807
$229$	−5.22800	−	9.05516i	−0.345476	−	0.598382i	0.639964	−	0.768405i	$-0.278949\pi$
$229$	−5.22800	−	9.05516i	−0.345476	−	0.598382i	−0.985440	+	0.170023i	$0.945616\pi$
$230$	5.77200			0.380595
$231$		0			0
$232$	8.77200			0.575910
$233$	1.54400			0.101151			0.0505755	−	0.998720i	$-0.483894\pi$
$233$	1.54400			0.101151			0.0505755	+	0.998720i	$0.483894\pi$
$234$	−0.500000	+	0.866025i	−0.0326860	+	0.0566139i
$235$	−1.50000	−	2.59808i	−0.0978492	−	0.169480i
$236$	4.54400			0.295789
$237$	−5.77200	+	9.99740i	−0.374932	+	0.649401i
$238$		0			0
$239$	8.00000	−	13.8564i	0.517477	−	0.896296i	−0.482317	−	0.875997i	$-0.660205\pi$
$239$	8.00000	−	13.8564i	0.517477	−	0.896296i	0.999794	−	0.0202996i	$-0.00646202\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	−4.72800	−	8.18913i	−0.304557	−	0.527508i	0.672605	−	0.740001i	$-0.265175\pi$
$241$	−4.72800	−	8.18913i	−0.304557	−	0.527508i	−0.977163	+	0.212493i	$0.931842\pi$
$242$	5.00000	−	8.66025i	0.321412	−	0.556702i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	5.00000	−	8.66025i	0.320092	−	0.554416i
$245$	−7.00000			−0.447214
$246$	−5.77200	−	9.99740i	−0.368009	−	0.637411i
$247$	1.88600	−	3.26665i	0.120003	−	0.207852i
$248$	−7.54400			−0.479045
$249$	7.54400			0.478082
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	3.00000			0.189358			0.0946792	−	0.995508i	$-0.469817\pi$
$251$	3.00000			0.189358			0.0946792	+	0.995508i	$0.469817\pi$
$252$		0			0
$253$	5.77200			0.362883
$254$	−8.88600	−	15.3910i	−0.557557	−	0.965718i
$255$	0.386001	+	0.668573i	0.0241723	+	0.0418677i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.15800	−	5.46982i	0.196991	−	0.341198i	−0.750561	−	0.660802i	$-0.770216\pi$
$257$	3.15800	−	5.46982i	0.196991	−	0.341198i	0.947551	+	0.319604i	$0.103550\pi$
$258$		0			0
$259$		0			0
$260$	1.00000			0.0620174
$261$	−4.38600	+	7.59678i	−0.271487	+	0.470229i
$262$	0.613999	+	1.06348i	0.0379330	+	0.0657019i
$263$	−12.6580	−	21.9243i	−0.780526	−	1.35191i	−0.931636	−	0.363394i	$-0.881618\pi$
$263$	−12.6580	−	21.9243i	−0.780526	−	1.35191i	0.151110	−	0.988517i	$-0.451715\pi$
$264$	0.500000	+	0.866025i	0.0307729	+	0.0533002i
$265$	3.54400			0.217706
$266$		0			0
$267$	15.7720			0.965231
$268$	−5.15800	+	8.93392i	−0.315075	+	0.545726i
$269$	5.08801			0.310221			0.155111	−	0.987897i	$-0.450427\pi$
$269$	5.08801			0.310221			0.155111	+	0.987897i	$0.450427\pi$
$270$	−1.00000			−0.0608581
$271$	6.15800	−	10.6660i	0.374072	−	0.647912i	−0.616116	−	0.787656i	$-0.711295\pi$
$271$	6.15800	−	10.6660i	0.374072	−	0.647912i	0.990188	+	0.139744i	$0.0446279\pi$
$272$	−0.386001	−	0.668573i	−0.0234047	−	0.0405382i
$273$		0			0
$274$	−5.15800	+	8.93392i	−0.311606	+	0.539718i
$275$	−0.500000	+	0.866025i	−0.0301511	+	0.0522233i
$276$	2.88600	−	4.99870i	0.173717	−	0.300886i
$277$	1.61400	+	2.79553i	0.0969758	+	0.167967i	0.910432	−	0.413660i	$-0.135750\pi$
$277$	1.61400	+	2.79553i	0.0969758	+	0.167967i	−0.813456	+	0.581627i	$0.802416\pi$
$278$	0.886001	+	1.53460i	0.0531388	+	0.0920391i
$279$	3.77200	−	6.53330i	0.225824	−	0.391138i
$280$		0			0
$281$	5.43000	−	9.40504i	0.323927	−	0.561058i	−0.657368	−	0.753570i	$-0.728330\pi$
$281$	5.43000	−	9.40504i	0.323927	−	0.561058i	0.981295	+	0.192512i	$0.0616635\pi$
$282$	−3.00000			−0.178647
$283$	9.61400	+	16.6519i	0.571493	+	0.989855i	0.996413	+	0.0846239i	$0.0269689\pi$
$283$	9.61400	+	16.6519i	0.571493	+	0.989855i	−0.424920	+	0.905231i	$0.639698\pi$
$284$	6.77200	−	11.7295i	0.401844	−	0.696015i
$285$	3.77200			0.223434
$286$	1.00000			0.0591312
$287$		0			0
$288$	1.00000			0.0589256
$289$	8.20201	+	14.2063i	0.482471	+	0.835664i
$290$	8.77200			0.515110
$291$	−8.77200	−	15.1936i	−0.514224	−	0.890662i
$292$		0			0
$293$	−15.2020	−	26.3306i	−0.888111	−	1.53825i	−0.842106	−	0.539312i	$-0.818684\pi$
$293$	−15.2020	−	26.3306i	−0.888111	−	1.53825i	−0.0460044	−	0.998941i	$-0.514649\pi$
$294$	−3.50000	+	6.06218i	−0.204124	+	0.353553i
$295$	4.54400			0.264562
$296$	4.27200	+	4.33013i	0.248305	+	0.251684i
$297$	−1.00000			−0.0580259
$298$	−4.15800	+	7.20187i	−0.240867	+	0.417193i
$299$	−2.88600	−	4.99870i	−0.166902	−	0.289082i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$		0			0
$302$	−8.00000			−0.460348
$303$	−4.15800	−	7.20187i	−0.238871	−	0.413737i
$304$	−3.77200			−0.216339
$305$	5.00000	−	8.66025i	0.286299	−	0.495885i
$306$	0.772002			0.0441324
$307$	−27.5440			−1.57202			−0.786010	−	0.618214i	$-0.787856\pi$
$307$	−27.5440			−1.57202			−0.786010	+	0.618214i	$0.787856\pi$
$308$		0			0
$309$	−5.88600	−	10.1949i	−0.334843	−	0.579965i
$310$	−7.54400			−0.428471
$311$	−4.77200	+	8.26535i	−0.270595	+	0.468685i	−0.969014	−	0.247004i	$-0.920554\pi$
$311$	−4.77200	+	8.26535i	−0.270595	+	0.468685i	0.698419	+	0.715689i	$0.253887\pi$
$312$	0.500000	−	0.866025i	0.0283069	−	0.0490290i
$313$	12.7720	−	22.1218i	0.721916	−	1.25040i	−0.238315	−	0.971188i	$-0.576595\pi$
$313$	12.7720	−	22.1218i	0.721916	−	1.25040i	0.960231	−	0.279208i	$-0.0900718\pi$
$314$	4.27200	+	7.39932i	0.241083	+	0.417568i
$315$		0			0
$316$	5.77200	−	9.99740i	0.324700	−	0.562398i
$317$	−8.65800	+	14.9961i	−0.486282	+	0.842265i	−0.999876	−	0.0157685i	$-0.994981\pi$
$317$	−8.65800	+	14.9961i	−0.486282	+	0.842265i	0.513594	+	0.858033i	$0.328314\pi$
$318$	1.77200	−	3.06920i	0.0993689	−	0.172112i
$319$	8.77200			0.491138
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−2.00000	+	3.46410i	−0.111629	+	0.193347i
$322$		0			0
$323$	−2.91199			−0.162028
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	1.00000			0.0554700
$326$	2.38600	+	4.13267i	0.132148	+	0.228888i
$327$	4.00000			0.221201
$328$	5.77200	+	9.99740i	0.318705	+	0.552014i
$329$		0			0
$330$	0.500000	+	0.866025i	0.0275241	+	0.0476731i
$331$	−3.88600	+	6.73075i	−0.213594	+	0.369956i	−0.952837	−	0.303483i	$-0.901850\pi$
$331$	−3.88600	+	6.73075i	−0.213594	+	0.369956i	0.739243	+	0.673439i	$0.235184\pi$
$332$	−7.54400			−0.414031
$333$	−5.88600	+	1.53460i	−0.322551	+	0.0840955i
$334$	18.7720			1.02716
$335$	−5.15800	+	8.93392i	−0.281812	+	0.488112i
$336$		0			0
$337$	−13.5440	−	23.4589i	−0.737789	−	1.27789i	−0.953489	−	0.301428i	$-0.902537\pi$
$337$	−13.5440	−	23.4589i	−0.737789	−	1.27789i	0.215700	−	0.976460i	$-0.430797\pi$
$338$	6.00000	+	10.3923i	0.326357	+	0.565267i
$339$	6.77200			0.367805
$340$	−0.386001	−	0.668573i	−0.0209338	−	0.0362585i
$341$	−7.54400			−0.408531
$342$	1.88600	−	3.26665i	0.101983	−	0.176640i
$343$		0			0
$344$		0			0
$345$	2.88600	−	4.99870i	0.155377	−	0.269121i
$346$	−10.6580	−	18.4602i	−0.572978	−	0.992427i
$347$	25.0880			1.34679			0.673397	−	0.739281i	$-0.264834\pi$
$347$	25.0880			1.34679			0.673397	+	0.739281i	$0.264834\pi$
$348$	4.38600	−	7.59678i	0.235114	−	0.407230i
$349$	5.54400	−	9.60250i	0.296764	−	0.514010i	−0.678630	−	0.734480i	$-0.737426\pi$
$349$	5.54400	−	9.60250i	0.296764	−	0.514010i	0.975394	+	0.220471i	$0.0707593\pi$
$350$		0			0
$351$	0.500000	+	0.866025i	0.0266880	+	0.0462250i
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	−1.00000	+	1.73205i	−0.0532246	+	0.0921878i	−0.891410	−	0.453197i	$-0.850283\pi$
$353$	−1.00000	+	1.73205i	−0.0532246	+	0.0921878i	0.838186	+	0.545385i	$0.183617\pi$
$354$	2.27200	−	3.93522i	0.120756	−	0.209155i
$355$	6.77200	−	11.7295i	0.359421	−	0.622535i
$356$	−15.7720			−0.835914
$357$		0			0
$358$	−2.65800	+	4.60380i	−0.140480	+	0.243318i
$359$	−21.0880			−1.11298			−0.556491	−	0.830853i	$-0.687853\pi$
$359$	−21.0880			−1.11298			−0.556491	+	0.830853i	$0.687853\pi$
$360$	1.00000			0.0527046
$361$	2.38600	−	4.13267i	0.125579	−	0.217509i
$362$	5.54400			0.291386
$363$	−5.00000	−	8.66025i	−0.262432	−	0.454545i
$364$		0			0
$365$		0			0
$366$	−5.00000	−	8.66025i	−0.261354	−	0.452679i
$367$	12.4300	+	21.5294i	0.648841	+	1.12383i	0.983400	+	0.181451i	$0.0580793\pi$
$367$	12.4300	+	21.5294i	0.648841	+	1.12383i	−0.334559	+	0.942375i	$0.608587\pi$
$368$	−2.88600	+	4.99870i	−0.150443	+	0.260575i
$369$	−11.5440			−0.600957
$370$	4.27200	+	4.33013i	0.222091	+	0.225113i
$371$		0			0
$372$	−3.77200	+	6.53330i	−0.195569	+	0.338736i
$373$	−5.88600	−	10.1949i	−0.304766	−	0.527869i	0.672444	−	0.740148i	$-0.265245\pi$
$373$	−5.88600	−	10.1949i	−0.304766	−	0.527869i	−0.977209	+	0.212279i	$0.931911\pi$
$374$	−0.386001	−	0.668573i	−0.0199596	−	0.0345711i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	3.00000			0.154713
$377$	−4.38600	−	7.59678i	−0.225891	−	0.391254i
$378$		0			0
$379$	0.455996	−	0.789809i	0.0234230	−	0.0405697i	−0.854076	−	0.520148i	$-0.825877\pi$
$379$	0.455996	−	0.789809i	0.0234230	−	0.0405697i	0.877499	+	0.479578i	$0.159210\pi$
$380$	−3.77200			−0.193500
$381$	−17.7720			−0.910487
$382$	−2.22800	+	3.85901i	−0.113994	+	0.197444i
$383$	14.5000	+	25.1147i	0.740915	+	1.28330i	0.952079	+	0.305852i	$0.0989414\pi$
$383$	14.5000	+	25.1147i	0.740915	+	1.28330i	−0.211164	+	0.977451i	$0.567725\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−7.54400	+	13.0666i	−0.383980	+	0.665072i
$387$		0			0
$388$	8.77200	+	15.1936i	0.445331	+	0.771336i
$389$	−16.5440	−	28.6551i	−0.838814	−	1.45287i	−0.890887	−	0.454226i	$-0.849916\pi$
$389$	−16.5440	−	28.6551i	−0.838814	−	1.45287i	0.0520724	−	0.998643i	$-0.483417\pi$
$390$	0.500000	−	0.866025i	0.0253185	−	0.0438529i
$391$	−2.22800	+	3.85901i	−0.112675	+	0.195158i
$392$	3.50000	−	6.06218i	0.176777	−	0.306186i
$393$	1.22800			0.0619443
$394$	7.00000	+	12.1244i	0.352655	+	0.610816i
$395$	5.77200	−	9.99740i	0.290421	−	0.503024i
$396$	1.00000			0.0502519
$397$	−10.5440			−0.529188			−0.264594	−	0.964360i	$-0.585238\pi$
$397$	−10.5440			−0.529188			−0.264594	+	0.964360i	$0.585238\pi$
$398$	−13.3860	+	23.1852i	−0.670980	+	1.16217i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−25.3160			−1.26422			−0.632110	−	0.774878i	$-0.717811\pi$
$401$	−25.3160			−1.26422			−0.632110	+	0.774878i	$0.717811\pi$
$402$	5.15800	+	8.93392i	0.257258	+	0.445584i
$403$	3.77200	+	6.53330i	0.187897	+	0.325447i
$404$	4.15800	+	7.20187i	0.206868	+	0.358307i
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$		0			0
$407$	4.27200	+	4.33013i	0.211755	+	0.214636i
$408$	−0.772002			−0.0382198
$409$	14.7020	−	25.4646i	0.726967	−	1.25914i	−0.231192	−	0.972908i	$-0.574262\pi$
$409$	14.7020	−	25.4646i	0.726967	−	1.25914i	0.958159	−	0.286236i	$-0.0924042\pi$
$410$	5.77200	+	9.99740i	0.285059	+	0.493736i
$411$	5.15800	+	8.93392i	0.254426	+	0.440678i
$412$	5.88600	+	10.1949i	0.289982	+	0.502264i
$413$		0			0
$414$	−2.88600	−	4.99870i	−0.141839	−	0.245673i
$415$	−7.54400			−0.370321
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$	1.77200			0.0867753
$418$	−3.77200			−0.184495
$419$	−4.88600	+	8.46280i	−0.238697	+	0.413435i	−0.960341	−	0.278830i	$-0.910054\pi$
$419$	−4.88600	+	8.46280i	−0.238697	+	0.413435i	0.721644	+	0.692265i	$0.243387\pi$
$420$		0			0
$421$	6.45600			0.314646			0.157323	−	0.987547i	$-0.449714\pi$
$421$	6.45600			0.314646			0.157323	+	0.987547i	$0.449714\pi$
$422$	8.88600	−	15.3910i	0.432564	−	0.749222i
$423$	−1.50000	+	2.59808i	−0.0729325	+	0.126323i
$424$	−1.77200	+	3.06920i	−0.0860560	+	0.149053i
$425$	−0.386001	−	0.668573i	−0.0187238	−	0.0324306i
$426$	−6.77200	−	11.7295i	−0.328105	−	0.568294i
$427$		0			0
$428$	2.00000	−	3.46410i	0.0966736	−	0.167444i
$429$	0.500000	−	0.866025i	0.0241402	−	0.0418121i
$430$		0			0
$431$	7.22800	+	12.5193i	0.348160	+	0.603032i	0.985923	−	0.167202i	$-0.0534731\pi$
$431$	7.22800	+	12.5193i	0.348160	+	0.603032i	−0.637762	+	0.770233i	$0.720140\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−12.4560			−0.598597			−0.299298	−	0.954160i	$-0.596753\pi$
$433$	−12.4560			−0.598597			−0.299298	+	0.954160i	$0.596753\pi$
$434$		0			0
$435$	4.38600	−	7.59678i	0.210293	−	0.364238i
$436$	−4.00000			−0.191565
$437$	10.8860	+	18.8551i	0.520748	+	0.901962i
$438$		0			0
$439$	14.9300	+	25.8595i	0.712570	+	1.23421i	0.963889	+	0.266304i	$0.0858024\pi$
$439$	14.9300	+	25.8595i	0.712570	+	1.23421i	−0.251319	+	0.967904i	$0.580864\pi$
$440$	−0.500000	−	0.866025i	−0.0238366	−	0.0412861i
$441$	3.50000	+	6.06218i	0.166667	+	0.288675i
$442$	−0.386001	+	0.668573i	−0.0183602	+	0.0318008i
$443$	−19.0880			−0.906899			−0.453449	−	0.891282i	$-0.649807\pi$
$443$	−19.0880			−0.906899			−0.453449	+	0.891282i	$0.649807\pi$
$444$	5.88600	−	1.53460i	0.279337	−	0.0728288i
$445$	−15.7720			−0.747665
$446$	10.4300	−	18.0653i	0.493875	−	0.855417i
$447$	4.15800	+	7.20187i	0.196667	+	0.340637i
$448$		0			0
$449$	−11.3160	−	19.5999i	−0.534035	−	0.924976i	−0.999209	−	0.0397571i	$-0.987342\pi$
$449$	−11.3160	−	19.5999i	−0.534035	−	0.924976i	0.465174	−	0.885219i	$-0.345992\pi$
$450$	1.00000			0.0471405
$451$	5.77200	+	9.99740i	0.271793	+	0.470759i
$452$	−6.77200			−0.318528
$453$	−4.00000	+	6.92820i	−0.187936	+	0.325515i
$454$	−7.54400			−0.354058
$455$		0			0
$456$	−1.88600	+	3.26665i	−0.0883201	+	0.152975i
$457$	−3.54400	−	6.13839i	−0.165782	−	0.287142i	0.771151	−	0.636652i	$-0.219681\pi$
$457$	−3.54400	−	6.13839i	−0.165782	−	0.287142i	−0.936933	+	0.349510i	$0.886348\pi$
$458$	10.4560			0.488577
$459$	0.386001	−	0.668573i	0.0180170	−	0.0312063i
$460$	−2.88600	+	4.99870i	−0.134560	+	0.233066i
$461$	−4.15800	+	7.20187i	−0.193657	+	0.335425i	−0.946460	−	0.322822i	$-0.895368\pi$
$461$	−4.15800	+	7.20187i	−0.193657	+	0.335425i	0.752802	+	0.658247i	$0.228702\pi$
$462$		0			0
$463$	−7.22800	−	12.5193i	−0.335914	−	0.581819i	0.647746	−	0.761856i	$-0.275712\pi$
$463$	−7.22800	−	12.5193i	−0.335914	−	0.581819i	−0.983660	+	0.180037i	$0.942378\pi$
$464$	−4.38600	+	7.59678i	−0.203615	+	0.352671i
$465$	−3.77200	+	6.53330i	−0.174922	+	0.302974i
$466$	−0.772002	+	1.33715i	−0.0357623	+	0.0619421i
$467$	6.00000			0.277647			0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000			0.277647			0.138823	+	0.990317i	$0.455668\pi$
$468$	−0.500000	−	0.866025i	−0.0231125	−	0.0400320i
$469$		0			0
$470$	3.00000			0.138380
$471$	8.54400			0.393687
$472$	−2.27200	+	3.93522i	−0.104577	+	0.181133i
$473$		0			0
$474$	−5.77200	−	9.99740i	−0.265117	−	0.459196i
$475$	−3.77200			−0.173071
$476$		0			0
$477$	−1.77200	−	3.06920i	−0.0811344	−	0.140529i
$478$	8.00000	+	13.8564i	0.365911	+	0.633777i
$479$	−16.7720	+	29.0500i	−0.766332	+	1.32733i	0.173207	+	0.984885i	$0.444587\pi$
$479$	−16.7720	+	29.0500i	−0.766332	+	1.32733i	−0.939539	+	0.342441i	$0.888746\pi$
$480$	−1.00000			−0.0456435
$481$	1.61400	−	5.86473i	0.0735920	−	0.267408i
$482$	9.45600			0.430709
$483$		0			0
$484$	5.00000	+	8.66025i	0.227273	+	0.393648i
$485$	8.77200	+	15.1936i	0.398316	+	0.689904i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−28.6320			−1.29744			−0.648720	−	0.761027i	$-0.724695\pi$
$487$	−28.6320			−1.29744			−0.648720	+	0.761027i	$0.724695\pi$
$488$	5.00000	+	8.66025i	0.226339	+	0.392031i
$489$	4.77200			0.215797
$490$	3.50000	−	6.06218i	0.158114	−	0.273861i
$491$	−13.3160			−0.600943			−0.300471	−	0.953791i	$-0.597144\pi$
$491$	−13.3160			−0.600943			−0.300471	+	0.953791i	$0.597144\pi$
$492$	11.5440			0.520444
$493$	−3.38600	+	5.86473i	−0.152498	+	0.264134i
$494$	1.88600	+	3.26665i	0.0848552	+	0.146974i
$495$	1.00000			0.0449467
$496$	3.77200	−	6.53330i	0.169368	−	0.293354i
$497$		0			0
$498$	−3.77200	+	6.53330i	−0.169027	+	0.292764i
$499$	11.2280	+	19.4475i	0.502634	+	0.870588i	0.999995	+	0.00304442i	$0.000969070\pi$
$499$	11.2280	+	19.4475i	0.502634	+	0.870588i	−0.497361	+	0.867544i	$0.665698\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	9.38600	−	16.2570i	0.419336	−	0.726311i
$502$	−1.50000	+	2.59808i	−0.0669483	+	0.115958i
$503$	−4.15800	+	7.20187i	−0.185396	+	0.321116i	−0.943710	−	0.330774i	$-0.892690\pi$
$503$	−4.15800	+	7.20187i	−0.185396	+	0.321116i	0.758314	+	0.651890i	$0.226024\pi$
$504$		0			0
$505$	4.15800	+	7.20187i	0.185029	+	0.320479i
$506$	−2.88600	+	4.99870i	−0.128298	+	0.222219i
$507$	12.0000			0.532939
$508$	17.7720			0.788505
$509$	−18.7720	+	32.5141i	−0.832054	+	1.44116i	0.0643520	+	0.997927i	$0.479502\pi$
$509$	−18.7720	+	32.5141i	−0.832054	+	1.44116i	−0.896406	+	0.443233i	$0.853831\pi$
$510$	−0.772002			−0.0341848
$511$		0			0
$512$	1.00000			0.0441942
$513$	−1.88600	−	3.26665i	−0.0832690	−	0.144226i
$514$	3.15800	+	5.46982i	0.139294	+	0.241263i
$515$	5.88600	+	10.1949i	0.259368	+	0.449239i
$516$		0			0
$517$	3.00000			0.131940
$518$		0			0
$519$	−21.3160			−0.935669
$520$	−0.500000	+	0.866025i	−0.0219265	+	0.0379777i
$521$	8.65800	+	14.9961i	0.379314	+	0.656991i	0.990963	−	0.134138i	$-0.0428267\pi$
$521$	8.65800	+	14.9961i	0.379314	+	0.656991i	−0.611649	+	0.791130i	$0.709493\pi$
$522$	−4.38600	−	7.59678i	−0.191970	−	0.332502i
$523$	0.455996	+	0.789809i	0.0199393	+	0.0345359i	0.875823	−	0.482633i	$-0.160319\pi$
$523$	0.455996	+	0.789809i	0.0199393	+	0.0345359i	−0.855884	+	0.517169i	$0.826986\pi$
$524$	−1.22800			−0.0536453
$525$		0			0
$526$	25.3160			1.10383
$527$	2.91199	−	5.04372i	0.126848	−	0.219708i
$528$	−1.00000			−0.0435194
$529$	10.3160			0.448522
$530$	−1.77200	+	3.06920i	−0.0769708	+	0.133317i
$531$	−2.27200	−	3.93522i	−0.0985965	−	0.170774i
$532$		0			0
$533$	5.77200	−	9.99740i	0.250013	−	0.433035i
$534$	−7.88600	+	13.6590i	−0.341261	+	0.591081i
$535$	2.00000	−	3.46410i	0.0864675	−	0.149766i
$536$	−5.15800	−	8.93392i	−0.222792	−	0.385887i
$537$	2.65800	+	4.60380i	0.114701	+	0.198668i
$538$	−2.54400	+	4.40634i	−0.109680	+	0.189971i
$539$	3.50000	−	6.06218i	0.150756	−	0.261116i
$540$	0.500000	−	0.866025i	0.0215166	−	0.0372678i
$541$	18.0000			0.773880			0.386940	−	0.922105i	$-0.373532\pi$
$541$	18.0000			0.773880			0.386940	+	0.922105i	$0.373532\pi$
$542$	6.15800	+	10.6660i	0.264509	+	0.458143i
$543$	2.77200	−	4.80125i	0.118958	−	0.206041i
$544$	0.772002			0.0330993
$545$	−4.00000			−0.171341
$546$		0			0
$547$	−0.455996			−0.0194970			−0.00974850	−	0.999952i	$-0.503103\pi$
$547$	−0.455996			−0.0194970			−0.00974850	+	0.999952i	$0.503103\pi$
$548$	−5.15800	−	8.93392i	−0.220339	−	0.381638i
$549$	−10.0000			−0.426790
$550$	−0.500000	−	0.866025i	−0.0213201	−	0.0369274i
$551$	16.5440	+	28.6551i	0.704798	+	1.22075i
$552$	2.88600	+	4.99870i	0.122836	+	0.212759i
$553$		0			0
$554$	−3.22800			−0.137144
$555$	5.88600	−	1.53460i	0.249847	−	0.0651401i
$556$	−1.77200			−0.0751496
$557$	−11.6580	+	20.1923i	−0.493965	+	0.855573i	−0.999976	−	0.00695416i	$-0.997786\pi$
$557$	−11.6580	+	20.1923i	−0.493965	+	0.855573i	0.506010	+	0.862527i	$0.331120\pi$
$558$	3.77200	+	6.53330i	0.159682	+	0.276577i
$559$		0			0
$560$		0			0
$561$	−0.772002			−0.0325939
$562$	5.43000	+	9.40504i	0.229051	+	0.396728i
$563$	−21.5440			−0.907972			−0.453986	−	0.891009i	$-0.649998\pi$
$563$	−21.5440			−0.907972			−0.453986	+	0.891009i	$0.649998\pi$
$564$	1.50000	−	2.59808i	0.0631614	−	0.109399i
$565$	−6.77200			−0.284900
$566$	−19.2280			−0.808213
$567$		0			0
$568$	6.77200	+	11.7295i	0.284147	+	0.492157i
$569$	−16.4040			−0.687692			−0.343846	−	0.939026i	$-0.611730\pi$
$569$	−16.4040			−0.687692			−0.343846	+	0.939026i	$0.611730\pi$
$570$	−1.88600	+	3.26665i	−0.0789959	+	0.136825i
$571$	−5.65800	+	9.79995i	−0.236780	+	0.410115i	−0.959789	−	0.280724i	$-0.909425\pi$
$571$	−5.65800	+	9.79995i	−0.236780	+	0.410115i	0.723008	+	0.690839i	$0.242759\pi$
$572$	−0.500000	+	0.866025i	−0.0209061	+	0.0362103i
$573$	2.22800	+	3.85901i	0.0930760	+	0.161212i
$574$		0			0
$575$	−2.88600	+	4.99870i	−0.120355	+	0.208460i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	2.77200	−	4.80125i	0.115400	−	0.199879i	−0.802540	−	0.596599i	$-0.796518\pi$
$577$	2.77200	−	4.80125i	0.115400	−	0.199879i	0.917940	+	0.396720i	$0.129852\pi$
$578$	−16.4040			−0.682317
$579$	7.54400	+	13.0666i	0.313518	+	0.543029i
$580$	−4.38600	+	7.59678i	−0.182119	+	0.315439i
$581$		0			0
$582$	17.5440			0.727222
$583$	−1.77200	+	3.06920i	−0.0733888	+	0.127113i
$584$		0			0
$585$	−0.500000	−	0.866025i	−0.0206725	−	0.0358057i
$586$	30.4040			1.25598
$587$	−3.54400	−	6.13839i	−0.146277	−	0.253359i	0.783572	−	0.621301i	$-0.213396\pi$
$587$	−3.54400	−	6.13839i	−0.146277	−	0.253359i	−0.929849	+	0.367943i	$0.880062\pi$
$588$	−3.50000	−	6.06218i	−0.144338	−	0.250000i
$589$	−14.2280	−	24.6436i	−0.586254	−	1.01542i
$590$	−2.27200	+	3.93522i	−0.0935368	+	0.162011i
$591$	14.0000			0.575883
$592$	−5.88600	+	1.53460i	−0.241913	+	0.0630716i
$593$	31.4040			1.28961			0.644804	−	0.764348i	$-0.276939\pi$
$593$	31.4040			1.28961			0.644804	+	0.764348i	$0.276939\pi$
$594$	0.500000	−	0.866025i	0.0205152	−	0.0355335i
$595$		0			0
$596$	−4.15800	−	7.20187i	−0.170318	−	0.295000i
$597$	13.3860	+	23.1852i	0.547853	+	0.948908i
$598$	5.77200			0.236035
$599$	−3.54400	−	6.13839i	−0.144804	−	0.250808i	0.784496	−	0.620134i	$-0.212922\pi$
$599$	−3.54400	−	6.13839i	−0.144804	−	0.250808i	−0.929300	+	0.369326i	$0.879589\pi$
$600$	−1.00000			−0.0408248
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	−0.604601	−	0.796528i	$-0.706668\pi$
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	0.992114	+	0.125336i	$0.0400009\pi$
$602$		0			0
$603$	10.3160			0.420100
$604$	4.00000	−	6.92820i	0.162758	−	0.281905i
$605$	5.00000	+	8.66025i	0.203279	+	0.352089i
$606$	8.31601			0.337815
$607$	14.7720	−	25.5859i	0.599577	−	1.03850i	−0.393306	−	0.919407i	$-0.628669\pi$
$607$	14.7720	−	25.5859i	0.599577	−	1.03850i	0.992883	−	0.119090i	$-0.0379978\pi$
$608$	1.88600	−	3.26665i	0.0764874	−	0.132480i
$609$		0			0
$610$	5.00000	+	8.66025i	0.202444	+	0.350643i
$611$	−1.50000	−	2.59808i	−0.0606835	−	0.105107i
$612$	−0.386001	+	0.668573i	−0.0156032	+	0.0270255i
$613$	−4.72800	+	8.18913i	−0.190962	+	0.330756i	−0.945569	−	0.325421i	$-0.894494\pi$
$613$	−4.72800	+	8.18913i	−0.190962	+	0.330756i	0.754607	+	0.656177i	$0.227827\pi$
$614$	13.7720	−	23.8538i	0.555793	−	0.962661i
$615$	11.5440			0.465499
$616$		0			0
$617$	−17.3860	+	30.1134i	−0.699934	+	1.21232i	0.268555	+	0.963264i	$0.413454\pi$
$617$	−17.3860	+	30.1134i	−0.699934	+	1.21232i	−0.968489	+	0.249057i	$0.919879\pi$
$618$	11.7720			0.473539
$619$	−30.1760			−1.21288			−0.606438	−	0.795131i	$-0.707402\pi$
$619$	−30.1760			−1.21288			−0.606438	+	0.795131i	$0.707402\pi$
$620$	3.77200	−	6.53330i	0.151487	−	0.262384i
$621$	−5.77200			−0.231622
$622$	−4.77200	−	8.26535i	−0.191340	−	0.331410i
$623$		0			0
$624$	0.500000	+	0.866025i	0.0200160	+	0.0346688i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	12.7720	+	22.1218i	0.510472	+	0.884163i
$627$	−1.88600	+	3.26665i	−0.0753196	+	0.130457i
$628$	−8.54400			−0.340943
$629$	−4.54400	+	1.18471i	−0.181181	+	0.0472376i
$630$		0			0
$631$	−8.15800	+	14.1301i	−0.324765	+	0.562509i	−0.981465	−	0.191643i	$-0.938619\pi$
$631$	−8.15800	+	14.1301i	−0.324765	+	0.562509i	0.656700	+	0.754152i	$0.271952\pi$
$632$	5.77200	+	9.99740i	0.229598	+	0.397675i
$633$	−8.88600	−	15.3910i	−0.353187	−	0.611738i
$634$	−8.65800	−	14.9961i	−0.343853	−	0.595571i
$635$	17.7720			0.705260
$636$	1.77200	+	3.06920i	0.0702644	+	0.121702i
$637$	−7.00000			−0.277350
$638$	−4.38600	+	7.59678i	−0.173643	+	0.300759i
$639$	−13.5440			−0.535793
$640$	1.00000			0.0395285
$641$	−11.4300	+	19.7973i	−0.451458	+	0.781948i	−0.998477	−	0.0551720i	$-0.982429\pi$
$641$	−11.4300	+	19.7973i	−0.451458	+	0.781948i	0.547019	+	0.837120i	$0.315763\pi$
$642$	−2.00000	−	3.46410i	−0.0789337	−	0.136717i
$643$	−8.77200			−0.345934			−0.172967	−	0.984928i	$-0.555335\pi$
$643$	−8.77200			−0.345934			−0.172967	+	0.984928i	$0.555335\pi$
$644$		0			0
$645$		0			0
$646$	1.45600	−	2.52186i	0.0572854	−	0.0992212i
$647$	−0.500000	−	0.866025i	−0.0196570	−	0.0340470i	0.856030	−	0.516927i	$-0.172924\pi$
$647$	−0.500000	−	0.866025i	−0.0196570	−	0.0340470i	−0.875687	+	0.482880i	$0.839591\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−2.27200	+	3.93522i	−0.0891839	+	0.154471i
$650$	−0.500000	+	0.866025i	−0.0196116	+	0.0339683i
$651$		0			0
$652$	−4.77200			−0.186886
$653$	5.11400	+	8.85771i	0.200126	+	0.346629i	0.948569	−	0.316571i	$-0.102531\pi$
$653$	5.11400	+	8.85771i	0.200126	+	0.346629i	−0.748443	+	0.663199i	$0.769198\pi$
$654$	−2.00000	+	3.46410i	−0.0782062	+	0.135457i
$655$	−1.22800			−0.0479819
$656$	−11.5440			−0.450718
$657$		0			0
$658$		0			0
$659$	0.955996	+	1.65583i	0.0372403	+	0.0645021i	0.884045	−	0.467402i	$-0.154810\pi$
$659$	0.955996	+	1.65583i	0.0372403	+	0.0645021i	−0.846805	+	0.531904i	$0.821477\pi$
$660$	−1.00000			−0.0389249
$661$	−2.00000	−	3.46410i	−0.0777910	−	0.134738i	0.824506	−	0.565854i	$-0.191453\pi$
$661$	−2.00000	−	3.46410i	−0.0777910	−	0.134738i	−0.902297	+	0.431116i	$0.858120\pi$
$662$	−3.88600	−	6.73075i	−0.151034	−	0.261598i
$663$	0.386001	+	0.668573i	0.0149910	+	0.0259652i
$664$	3.77200	−	6.53330i	0.146382	−	0.253541i
$665$		0			0
$666$	1.61400	−	5.86473i	0.0625412	−	0.227254i
$667$	50.6320			1.96048
$668$	−9.38600	+	16.2570i	−0.363155	+	0.629003i
$669$	−10.4300	−	18.0653i	−0.403247	−	0.698445i
$670$	−5.15800	−	8.93392i	−0.199271	−	0.345148i
$671$	5.00000	+	8.66025i	0.193023	+	0.334325i
$672$		0			0
$673$	13.5440	+	23.4589i	0.522083	+	0.904274i	0.999670	+	0.0256898i	$0.00817821\pi$
$673$	13.5440	+	23.4589i	0.522083	+	0.904274i	−0.477587	+	0.878584i	$0.658488\pi$
$674$	27.0880			1.04339
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	−12.0000			−0.461538
$677$	−26.8600			−1.03231			−0.516157	−	0.856494i	$-0.672638\pi$
$677$	−26.8600			−1.03231			−0.516157	+	0.856494i	$0.672638\pi$
$678$	−3.38600	+	5.86473i	−0.130039	+	0.225233i
$679$		0			0
$680$	0.772002			0.0296049
$681$	−3.77200	+	6.53330i	−0.144543	+	0.250357i
$682$	3.77200	−	6.53330i	0.144437	−	0.250173i
$683$	7.00000	−	12.1244i	0.267848	−	0.463926i	−0.700458	−	0.713693i	$-0.747021\pi$
$683$	7.00000	−	12.1244i	0.267848	−	0.463926i	0.968306	+	0.249768i	$0.0803543\pi$
$684$	1.88600	+	3.26665i	0.0721130	+	0.124903i
$685$	−5.15800	−	8.93392i	−0.197077	−	0.341348i
$686$		0			0
$687$	5.22800	−	9.05516i	0.199461	−	0.345476i
$688$		0			0
$689$	3.54400			0.135016
$690$	2.88600	+	4.99870i	0.109868	+	0.190297i
$691$	−18.7720	+	32.5141i	−0.714121	+	1.23689i	0.249177	+	0.968458i	$0.419840\pi$
$691$	−18.7720	+	32.5141i	−0.714121	+	1.23689i	−0.963298	+	0.268435i	$0.913493\pi$
$692$	21.3160			0.810313
$693$		0			0
$694$	−12.5440	+	21.7269i	−0.476164	+	0.824740i
$695$	−1.77200			−0.0672159
$696$	4.38600	+	7.59678i	0.166251	+	0.287955i
$697$	−8.91199			−0.337566
$698$	5.54400	+	9.60250i	0.209844	+	0.363460i
$699$	0.772002	+	1.33715i	0.0291998	+	0.0505755i
$700$		0			0
$701$	−14.1580	+	24.5224i	−0.534740	+	0.926198i	0.464435	+	0.885607i	$0.346257\pi$
$701$	−14.1580	+	24.5224i	−0.534740	+	0.926198i	−0.999176	+	0.0405906i	$0.987076\pi$
$702$	−1.00000			−0.0377426
$703$	−6.08801	+	22.1218i	−0.229614	+	0.834338i
$704$	1.00000			0.0376889
$705$	1.50000	−	2.59808i	0.0564933	−	0.0978492i
$706$	−1.00000	−	1.73205i	−0.0376355	−	0.0651866i
$707$		0			0
$708$	2.27200	+	3.93522i	0.0853871	+	0.147895i
$709$	25.0880			0.942200			0.471100	−	0.882080i	$-0.343857\pi$
$709$	25.0880			0.942200			0.471100	+	0.882080i	$0.343857\pi$
$710$	6.77200	+	11.7295i	0.254149	+	0.440198i
$711$	−11.5440			−0.432934
$712$	7.88600	−	13.6590i	0.295540	−	0.511891i
$713$	−43.5440			−1.63074
$714$		0			0
$715$	−0.500000	+	0.866025i	−0.0186989	+	0.0323875i
$716$	−2.65800	−	4.60380i	−0.0993342	−	0.172052i
$717$	16.0000			0.597531
$718$	10.5440	−	18.2628i	0.393499	−	0.681560i
$719$	−3.77200	+	6.53330i	−0.140672	+	0.243651i	−0.927750	−	0.373203i	$-0.878260\pi$
$719$	−3.77200	+	6.53330i	−0.140672	+	0.243651i	0.787078	+	0.616854i	$0.211593\pi$
$720$	−0.500000	+	0.866025i	−0.0186339	+	0.0322749i
$721$		0			0
$722$	2.38600	+	4.13267i	0.0887978	+	0.153802i
$723$	4.72800	−	8.18913i	0.175836	−	0.304557i
$724$	−2.77200	+	4.80125i	−0.103021	+	0.178437i
$725$	−4.38600	+	7.59678i	−0.162892	+	0.282137i
$726$	10.0000			0.371135
$727$	1.57000	+	2.71931i	0.0582279	+	0.100854i	0.893670	−	0.448725i	$-0.148122\pi$
$727$	1.57000	+	2.71931i	0.0582279	+	0.100854i	−0.835442	+	0.549579i	$0.814788\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$		0			0
$732$	10.0000			0.369611
$733$	−21.0440	−	36.4493i	−0.777278	−	1.34629i	−0.933505	−	0.358564i	$-0.883267\pi$
$733$	−21.0440	−	36.4493i	−0.777278	−	1.34629i	0.156227	−	0.987721i	$-0.450067\pi$
$734$	−24.8600			−0.917600
$735$	−3.50000	−	6.06218i	−0.129099	−	0.223607i
$736$	−2.88600	−	4.99870i	−0.106379	−	0.184255i
$737$	−5.15800	−	8.93392i	−0.189997	−	0.329085i
$738$	5.77200	−	9.99740i	0.212470	−	0.368009i
$739$	7.77200			0.285898			0.142949	−	0.989730i	$-0.454342\pi$
$739$	7.77200			0.285898			0.142949	+	0.989730i	$0.454342\pi$
$740$	−5.88600	+	1.53460i	−0.216374	+	0.0564130i
$741$	3.77200			0.138568
$742$		0			0
$743$	−6.72800	−	11.6532i	−0.246826	−	0.427516i	0.715817	−	0.698288i	$-0.246054\pi$
$743$	−6.72800	−	11.6532i	−0.246826	−	0.427516i	−0.962644	+	0.270772i	$0.912721\pi$
$744$	−3.77200	−	6.53330i	−0.138288	−	0.239522i
$745$	−4.15800	−	7.20187i	−0.152337	−	0.263856i
$746$	11.7720			0.431004
$747$	3.77200	+	6.53330i	0.138010	+	0.239041i
$748$	0.772002			0.0282272
$749$		0			0
$750$	−1.00000			−0.0365148
$751$	6.77200			0.247114			0.123557	−	0.992337i	$-0.460570\pi$
$751$	6.77200			0.247114			0.123557	+	0.992337i	$0.460570\pi$
$752$	−1.50000	+	2.59808i	−0.0546994	+	0.0947421i
$753$	1.50000	+	2.59808i	0.0546630	+	0.0946792i
$754$	8.77200			0.319457
$755$	4.00000	−	6.92820i	0.145575	−	0.252143i
$756$		0			0
$757$	−16.1140	+	27.9103i	−0.585673	+	1.01442i	0.409118	+	0.912482i	$0.365836\pi$
$757$	−16.1140	+	27.9103i	−0.585673	+	1.01442i	−0.994791	+	0.101934i	$0.967497\pi$
$758$	0.455996	+	0.789809i	0.0165625	+	0.0286871i
$759$	2.88600	+	4.99870i	0.104755	+	0.181441i
$760$	1.88600	−	3.26665i	0.0684124	−	0.118494i
$761$	10.3420	−	17.9129i	0.374897	−	0.649341i	−0.615415	−	0.788204i	$-0.711011\pi$
$761$	10.3420	−	17.9129i	0.374897	−	0.649341i	0.990312	+	0.138863i	$0.0443447\pi$
$762$	8.88600	−	15.3910i	0.321906	−	0.557557i
$763$		0			0
$764$	−2.22800	−	3.85901i	−0.0806061	−	0.139614i
$765$	−0.386001	+	0.668573i	−0.0139559	+	0.0241723i
$766$	−29.0000			−1.04781
$767$	4.54400			0.164074
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	38.9480			1.40450			0.702251	−	0.711930i	$-0.252179\pi$
$769$	38.9480			1.40450			0.702251	+	0.711930i	$0.252179\pi$
$770$		0			0
$771$	6.31601			0.227465
$772$	−7.54400	−	13.0666i	−0.271515	−	0.470277i
$773$	−24.2020	−	41.9191i	−0.870486	−	1.50773i	−0.861495	−	0.507766i	$-0.830472\pi$
$773$	−24.2020	−	41.9191i	−0.870486	−	1.50773i	−0.00899054	−	0.999960i	$-0.502862\pi$
$774$		0			0
$775$	3.77200	−	6.53330i	0.135494	−	0.234683i
$776$	−17.5440			−0.629793
$777$		0			0
$778$	33.0880			1.18626
$779$	−21.7720	+	37.7102i	−0.780063	+	1.35111i
$780$	0.500000	+	0.866025i	0.0179029	+	0.0310087i
$781$	6.77200	+	11.7295i	0.242321	+	0.419713i
$782$	−2.22800	−	3.85901i	−0.0796731	−	0.137998i
$783$	−8.77200			−0.313486
$784$	3.50000	+	6.06218i	0.125000	+	0.216506i
$785$	−8.54400			−0.304949
$786$	−0.613999	+	1.06348i	−0.0219006	+	0.0379330i
$787$	−26.7720			−0.954319			−0.477159	−	0.878817i	$-0.658334\pi$
$787$	−26.7720			−0.954319			−0.477159	+	0.878817i	$0.658334\pi$
$788$	−14.0000			−0.498729
$789$	12.6580	−	21.9243i	0.450637	−	0.780526i
$790$	5.77200	+	9.99740i	0.205359	+	0.355692i
$791$		0			0
$792$	−0.500000	+	0.866025i	−0.0177667	+	0.0307729i
$793$	5.00000	−	8.66025i	0.177555	−	0.307535i
$794$	5.27200	−	9.13138i	0.187096	−	0.324060i
$795$	1.77200	+	3.06920i	0.0628464	+	0.108853i
$796$	−13.3860	−	23.1852i	−0.474454	−	0.821779i
$797$	20.8860	−	36.1756i	0.739820	−	1.28141i	−0.212756	−	0.977105i	$-0.568244\pi$
$797$	20.8860	−	36.1756i	0.739820	−	1.28141i	0.952576	−	0.304301i	$-0.0984227\pi$
$798$		0			0
$799$	−1.15800	+	2.00572i	−0.0409672	+	0.0709573i
$800$	1.00000			0.0353553
$801$	7.88600	+	13.6590i	0.278638	+	0.482615i
$802$	12.6580	−	21.9243i	0.446970	−	0.774174i
$803$		0			0
$804$	−10.3160			−0.363817
$805$		0			0
$806$	−7.54400			−0.265726
$807$	2.54400	+	4.40634i	0.0895532	+	0.155111i
$808$	−8.31601			−0.292556
$809$	−7.88600	−	13.6590i	−0.277257	−	0.480223i	0.693445	−	0.720510i	$-0.256092\pi$
$809$	−7.88600	−	13.6590i	−0.277257	−	0.480223i	−0.970702	+	0.240286i	$0.922759\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	−20.9740	−	36.3280i	−0.736497	−	1.27565i	−0.954063	−	0.299605i	$-0.903145\pi$
$811$	−20.9740	−	36.3280i	−0.736497	−	1.27565i	0.217566	−	0.976046i	$-0.430188\pi$
$812$		0			0
$813$	12.3160			0.431941
$814$	−5.88600	+	1.53460i	−0.206304	+	0.0537877i
$815$	−4.77200			−0.167156
$816$	0.386001	−	0.668573i	0.0135127	−	0.0234047i
$817$		0			0
$818$	14.7020	+	25.4646i	0.514044	+	0.890350i
$819$		0			0
$820$	−11.5440			−0.403134
$821$	7.84200	+	13.5827i	0.273688	+	0.474041i	0.969803	−	0.243889i	$-0.0784232\pi$
$821$	7.84200	+	13.5827i	0.273688	+	0.474041i	−0.696116	+	0.717930i	$0.745090\pi$
$822$	−10.3160			−0.359812
$823$	23.0880	−	39.9896i	0.804797	−	1.39395i	−0.111630	−	0.993750i	$-0.535607\pi$
$823$	23.0880	−	39.9896i	0.804797	−	1.39395i	0.916428	−	0.400200i	$-0.131059\pi$
$824$	−11.7720			−0.410097
$825$	−1.00000			−0.0348155
$826$		0			0
$827$	18.5440	+	32.1192i	0.644838	+	1.11689i	0.984339	+	0.176287i	$0.0564086\pi$
$827$	18.5440	+	32.1192i	0.644838	+	1.11689i	−0.339501	+	0.940606i	$0.610258\pi$
$828$	5.77200			0.200591
$829$	12.2280	−	21.1795i	0.424696	−	0.735595i	−0.571696	−	0.820465i	$-0.693714\pi$
$829$	12.2280	−	21.1795i	0.424696	−	0.735595i	0.996392	+	0.0848706i	$0.0270477\pi$
$830$	3.77200	−	6.53330i	0.130928	−	0.226774i
$831$	−1.61400	+	2.79553i	−0.0559890	+	0.0969758i
$832$	−0.500000	−	0.866025i	−0.0173344	−	0.0300240i
$833$	2.70201	+	4.68001i	0.0936190	+	0.162153i
$834$	−0.886001	+	1.53460i	−0.0306797	+	0.0531388i
$835$	−9.38600	+	16.2570i	−0.324816	+	0.562598i
$836$	1.88600	−	3.26665i	0.0652287	−	0.112979i
$837$	7.54400			0.260759
$838$	−4.88600	−	8.46280i	−0.168784	−	0.292343i
$839$	−13.2280	+	22.9116i	−0.456681	+	0.790995i	−0.998783	−	0.0493177i	$-0.984295\pi$
$839$	−13.2280	+	22.9116i	−0.456681	+	0.790995i	0.542102	+	0.840313i	$0.317629\pi$
$840$		0			0
$841$	47.9480			1.65338
$842$	−3.22800	+	5.59106i	−0.111244	+	0.192681i
$843$	10.8600			0.374039
$844$	8.88600	+	15.3910i	0.305869	+	0.529780i
$845$	−12.0000			−0.412813
$846$	−1.50000	−	2.59808i	−0.0515711	−	0.0893237i
$847$		0			0
$848$	−1.77200	−	3.06920i	−0.0608508	−	0.105397i
$849$	−9.61400	+	16.6519i	−0.329952	+	0.571493i
$850$	0.772002			0.0264794
$851$	24.6580	+	24.9935i	0.845265	+	0.856766i
$852$	13.5440			0.464010
$853$	3.27200	−	5.66727i	0.112031	−	0.194044i	−0.804558	−	0.593874i	$-0.797598\pi$
$853$	3.27200	−	5.66727i	0.112031	−	0.194044i	0.916589	+	0.399830i	$0.130931\pi$
$854$		0			0
$855$	1.88600	+	3.26665i	0.0644999	+	0.111717i
$856$	2.00000	+	3.46410i	0.0683586	+	0.118401i
$857$	20.3160			0.693982			0.346991	−	0.937869i	$-0.387204\pi$
$857$	20.3160			0.693982			0.346991	+	0.937869i	$0.387204\pi$
$858$	0.500000	+	0.866025i	0.0170697	+	0.0295656i
$859$	−44.8600			−1.53060			−0.765302	−	0.643672i	$-0.777410\pi$
$859$	−44.8600			−1.53060			−0.765302	+	0.643672i	$0.777410\pi$
$860$		0			0
$861$		0			0
$862$	−14.4560			−0.492373
$863$	27.1320	−	46.9940i	0.923584	−	1.59970i	0.129762	−	0.991545i	$-0.458579\pi$
$863$	27.1320	−	46.9940i	0.923584	−	1.59970i	0.793822	−	0.608150i	$-0.208088\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	21.3160			0.724766
$866$	6.22800	−	10.7872i	0.211636	−	0.366564i
$867$	−8.20201	+	14.2063i	−0.278555	+	0.482471i
$868$		0			0
$869$	5.77200	+	9.99740i	0.195802	+	0.339139i
$870$	4.38600	+	7.59678i	0.148699	+	0.257555i
$871$	−5.15800	+	8.93392i	−0.174772	+	0.302714i
$872$	2.00000	−	3.46410i	0.0677285	−	0.117309i
$873$	8.77200	−	15.1936i	0.296887	−	0.514224i
$874$	−21.7720			−0.736449
$875$		0			0
$876$		0			0
$877$	−55.6320			−1.87856			−0.939280	−	0.343152i	$-0.888505\pi$
$877$	−55.6320			−1.87856			−0.939280	+	0.343152i	$0.888505\pi$
$878$	−29.8600			−1.00773
$879$	15.2020	−	26.3306i	0.512751	−	0.888111i
$880$	1.00000			0.0337100
$881$	−19.9740	−	34.5960i	−0.672941	−	1.16557i	−0.977066	−	0.212937i	$-0.931697\pi$
$881$	−19.9740	−	34.5960i	−0.672941	−	1.16557i	0.304125	−	0.952632i	$-0.401636\pi$
$882$	−7.00000			−0.235702
$883$	−14.7020	−	25.4646i	−0.494762	−	0.856953i	0.505220	−	0.862991i	$-0.331411\pi$
$883$	−14.7020	−	25.4646i	−0.494762	−	0.856953i	−0.999982	+	0.00603790i	$0.998078\pi$
$884$	−0.386001	−	0.668573i	−0.0129826	−	0.0224866i
$885$	2.27200	+	3.93522i	0.0763725	+	0.132281i
$886$	9.54400	−	16.5307i	0.320637	−	0.555360i
$887$	38.1760			1.28183			0.640913	−	0.767614i	$-0.278556\pi$
$887$	38.1760			1.28183			0.640913	+	0.767614i	$0.278556\pi$
$888$	−1.61400	+	5.86473i	−0.0541623	+	0.196807i
$889$		0			0
$890$	7.88600	−	13.6590i	0.264339	−	0.457849i
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$	10.4300	+	18.0653i	0.349222	+	0.604871i
$893$	5.65800	+	9.79995i	0.189338	+	0.327943i
$894$	−8.31601			−0.278129
$895$	−2.65800	−	4.60380i	−0.0888472	−	0.153888i
$896$		0			0
$897$	2.88600	−	4.99870i	0.0963608	−	0.166902i
$898$	22.6320			0.755240
$899$	−66.1760			−2.20709
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−1.36799	−	2.36943i	−0.0455743	−	0.0789370i
$902$	−11.5440			−0.384373
$903$		0			0
$904$	3.38600	−	5.86473i	0.112617	−	0.195058i
$905$	−2.77200	+	4.80125i	−0.0921445	+	0.159599i
$906$	−4.00000	−	6.92820i	−0.132891	−	0.230174i
$907$	−19.7720	−	34.2461i	−0.656519	−	1.13712i	−0.981511	−	0.191407i	$-0.938695\pi$
$907$	−19.7720	−	34.2461i	−0.656519	−	1.13712i	0.324992	−	0.945717i	$-0.394638\pi$
$908$	3.77200	−	6.53330i	0.125178	−	0.216815i
$909$	4.15800	−	7.20187i	0.137912	−	0.238871i
$910$		0			0
$911$	14.0000			0.463841			0.231920	−	0.972735i	$-0.425499\pi$
$911$	14.0000			0.463841			0.231920	+	0.972735i	$0.425499\pi$
$912$	−1.88600	−	3.26665i	−0.0624517	−	0.108170i
$913$	3.77200	−	6.53330i	0.124835	−	0.216221i
$914$	7.08801			0.234450
$915$	10.0000			0.330590
$916$	−5.22800	+	9.05516i	−0.172738	+	0.299191i
$917$		0			0
$918$	0.386001	+	0.668573i	0.0127399	+	0.0220662i
$919$	−23.8600			−0.787069			−0.393535	−	0.919310i	$-0.628748\pi$
$919$	−23.8600			−0.787069			−0.393535	+	0.919310i	$0.628748\pi$
$920$	−2.88600	−	4.99870i	−0.0951486	−	0.164802i
$921$	−13.7720	−	23.8538i	−0.453803	−	0.786010i
$922$	−4.15800	−	7.20187i	−0.136937	−	0.237181i
$923$	6.77200	−	11.7295i	0.222903	−	0.386080i
$924$		0			0
$925$	−5.88600	+	1.53460i	−0.193531	+	0.0504573i
$926$	14.4560			0.475054
$927$	5.88600	−	10.1949i	0.193322	−	0.334843i
$928$	−4.38600	−	7.59678i	−0.143978	−	0.249376i
$929$	−8.88600	−	15.3910i	−0.291540	−	0.504962i	0.682634	−	0.730761i	$-0.260834\pi$
$929$	−8.88600	−	15.3910i	−0.291540	−	0.504962i	−0.974174	+	0.225798i	$0.927501\pi$
$930$	−3.77200	−	6.53330i	−0.123689	−	0.214235i
$931$	26.4040			0.865357
$932$	−0.772002	−	1.33715i	−0.0252878	−	0.0437997i
$933$	−9.54400			−0.312457
$934$	−3.00000	+	5.19615i	−0.0981630	+	0.170023i
$935$	0.772002			0.0252472
$936$	1.00000			0.0326860
$937$	8.00000	−	13.8564i	0.261349	−	0.452669i	−0.705252	−	0.708957i	$-0.749166\pi$
$937$	8.00000	−	13.8564i	0.261349	−	0.452669i	0.966601	+	0.256288i	$0.0824995\pi$
$938$		0			0
$939$	25.5440			0.833597
$940$	−1.50000	+	2.59808i	−0.0489246	+	0.0847399i
$941$	16.0880	−	27.8652i	0.524454	−	0.908381i	−0.475141	−	0.879910i	$-0.657603\pi$
$941$	16.0880	−	27.8652i	0.524454	−	0.908381i	0.999595	−	0.0284712i	$-0.00906388\pi$
$942$	−4.27200	+	7.39932i	−0.139189	+	0.241083i
$943$	33.3160	+	57.7050i	1.08492	+	1.87913i
$944$	−2.27200	−	3.93522i	−0.0739474	−	0.128081i
$945$		0			0
$946$		0			0
$947$	1.00000	−	1.73205i	0.0324956	−	0.0562841i	−0.849320	−	0.527878i	$-0.822988\pi$
$947$	1.00000	−	1.73205i	0.0324956	−	0.0562841i	0.881816	+	0.471594i	$0.156321\pi$
$948$	11.5440			0.374932
$949$		0			0
$950$	1.88600	−	3.26665i	0.0611900	−	0.105984i
$951$	−17.3160			−0.561510
$952$		0			0
$953$	24.1580	−	41.8429i	0.782554	−	1.35542i	−0.147895	−	0.989003i	$-0.547250\pi$
$953$	24.1580	−	41.8429i	0.782554	−	1.35542i	0.930449	−	0.366421i	$-0.119417\pi$
$954$	3.54400			0.114741
$955$	−2.22800	−	3.85901i	−0.0720963	−	0.124875i
$956$	−16.0000			−0.517477
$957$	4.38600	+	7.59678i	0.141779	+	0.245569i
$958$	−16.7720	−	29.0500i	−0.541879	−	0.938562i
$959$		0			0
$960$	0.500000	−	0.866025i	0.0161374	−	0.0279508i
$961$	25.9120			0.835871
$962$	4.27200	+	4.33013i	0.137735	+	0.139609i
$963$	−4.00000			−0.128898
$964$	−4.72800	+	8.18913i	−0.152279	+	0.263754i
$965$	−7.54400	−	13.0666i	−0.242850	−	0.420629i
$966$		0			0
$967$	8.88600	+	15.3910i	0.285755	+	0.494941i	0.972792	−	0.231681i	$-0.0744225\pi$
$967$	8.88600	+	15.3910i	0.285755	+	0.494941i	−0.687037	+	0.726622i	$0.741089\pi$
$968$	−10.0000			−0.321412
$969$	−1.45600	−	2.52186i	−0.0467733	−	0.0810138i
$970$	−17.5440			−0.563304
$971$	26.8860	−	46.5679i	0.862813	−	1.49444i	−0.00638979	−	0.999980i	$-0.502034\pi$
$971$	26.8860	−	46.5679i	0.862813	−	1.49444i	0.869203	−	0.494456i	$-0.164633\pi$
$972$	−1.00000			−0.0320750
$973$		0			0
$974$	14.3160	−	24.7960i	0.458714	−	0.794517i
$975$	0.500000	+	0.866025i	0.0160128	+	0.0277350i
$976$	−10.0000			−0.320092
$977$	9.84200	−	17.0468i	0.314873	−	0.545377i	−0.664537	−	0.747255i	$-0.731371\pi$
$977$	9.84200	−	17.0468i	0.314873	−	0.545377i	0.979411	+	0.201878i	$0.0647046\pi$
$978$	−2.38600	+	4.13267i	−0.0762959	+	0.132148i
$979$	7.88600	−	13.6590i	0.252038	−	0.436542i
$980$	3.50000	+	6.06218i	0.111803	+	0.193649i
$981$	2.00000	+	3.46410i	0.0638551	+	0.110600i
$982$	6.65800	−	11.5320i	0.212465	−	0.368001i
$983$	10.4300	−	18.0653i	0.332665	−	0.576194i	−0.650368	−	0.759619i	$-0.725385\pi$
$983$	10.4300	−	18.0653i	0.332665	−	0.576194i	0.983034	+	0.183426i	$0.0587187\pi$
$984$	−5.77200	+	9.99740i	−0.184005	+	0.318705i
$985$	−14.0000			−0.446077
$986$	−3.38600	−	5.86473i	−0.107832	−	0.186771i
$987$		0			0
$988$	−3.77200			−0.120003
$989$		0			0
$990$	−0.500000	+	0.866025i	−0.0158910	+	0.0275241i
$991$	−20.9480			−0.665436			−0.332718	−	0.943026i	$-0.607966\pi$
$991$	−20.9480			−0.665436			−0.332718	+	0.943026i	$0.607966\pi$
$992$	3.77200	+	6.53330i	0.119761	+	0.207432i
$993$	−7.77200			−0.246637
$994$		0			0
$995$	−13.3860	−	23.1852i	−0.424365	−	0.735021i
$996$	−3.77200	−	6.53330i	−0.119520	−	0.207015i
$997$	−12.8160	+	22.1980i	−0.405887	+	0.703017i	−0.994424	−	0.105453i	$-0.966371\pi$
$997$	−12.8160	+	22.1980i	−0.405887	+	0.703017i	0.588537	+	0.808470i	$0.299704\pi$
$998$	−22.4560			−0.710832
$999$	−4.27200	−	4.33013i	−0.135160	−	0.136999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.i.j.121.1	✓	4
37.26	even	3	inner	1110.2.i.j.211.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.i.j.121.1	✓	4	1.1	even	1	trivial
1110.2.i.j.211.1	yes	4	37.26	even	3	inner

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} +1.00000 q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.386001 + 0.668573i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.88600 + 3.26665i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-0.500000 + 0.866025i) q^{22} +5.77200 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{26} -1.00000 q^{27} +8.77200 q^{29} +(0.500000 + 0.866025i) q^{30} -7.54400 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} +(-0.386001 - 0.668573i) q^{34} +1.00000 q^{36} +(4.27200 + 4.33013i) q^{37} -3.77200 q^{38} +(0.500000 - 0.866025i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(5.77200 + 9.99740i) q^{41} +(-0.500000 - 0.866025i) q^{44} +1.00000 q^{45} +(-2.88600 + 4.99870i) q^{46} +3.00000 q^{47} -1.00000 q^{48} +(3.50000 - 6.06218i) q^{49} +(-0.500000 - 0.866025i) q^{50} -0.772002 q^{51} +(-0.500000 + 0.866025i) q^{52} +(-1.77200 + 3.06920i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.500000 - 0.866025i) q^{55} +(-1.88600 + 3.26665i) q^{57} +(-4.38600 + 7.59678i) q^{58} +(-2.27200 + 3.93522i) q^{59} -1.00000 q^{60} +(5.00000 + 8.66025i) q^{61} +(3.77200 - 6.53330i) q^{62} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} -1.00000 q^{66} +(-5.15800 - 8.93392i) q^{67} +0.772002 q^{68} +(2.88600 + 4.99870i) q^{69} +(6.77200 + 11.7295i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-5.88600 + 1.53460i) q^{74} -1.00000 q^{75} +(1.88600 - 3.26665i) q^{76} +(0.500000 + 0.866025i) q^{78} +(5.77200 + 9.99740i) q^{79} +1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} -11.5440 q^{82} +(3.77200 - 6.53330i) q^{83} +0.772002 q^{85} +(4.38600 + 7.59678i) q^{87} +1.00000 q^{88} +(7.88600 - 13.6590i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-2.88600 - 4.99870i) q^{92} +(-3.77200 - 6.53330i) q^{93} +(-1.50000 + 2.59808i) q^{94} +(1.88600 - 3.26665i) q^{95} +(0.500000 - 0.866025i) q^{96} -17.5440 q^{97} +(3.50000 + 6.06218i) q^{98} +(-0.500000 + 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} - 2 q^{9} + 4 q^{10} + 4 q^{11} + 2 q^{12} - 2 q^{13} + 2 q^{15} - 2 q^{16} + 7 q^{17} - 2 q^{18} - q^{19} - 2 q^{20} - 2 q^{22} + 6 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{26} - 4 q^{27} + 18 q^{29} + 2 q^{30} + 4 q^{31} - 2 q^{32} + 2 q^{33} + 7 q^{34} + 4 q^{36} + 2 q^{38} + 2 q^{39} - 2 q^{40} + 6 q^{41} - 2 q^{44} + 4 q^{45} - 3 q^{46} + 12 q^{47} - 4 q^{48} + 14 q^{49} - 2 q^{50} + 14 q^{51} - 2 q^{52} + 10 q^{53} + 2 q^{54} - 2 q^{55} + q^{57} - 9 q^{58} + 8 q^{59} - 4 q^{60} + 20 q^{61} - 2 q^{62} + 4 q^{64} - 2 q^{65} - 4 q^{66} + 5 q^{67} - 14 q^{68} + 3 q^{69} + 10 q^{71} - 2 q^{72} - 15 q^{74} - 4 q^{75} - q^{76} + 2 q^{78} + 6 q^{79} + 4 q^{80} - 2 q^{81} - 12 q^{82} - 2 q^{83} - 14 q^{85} + 9 q^{87} + 4 q^{88} + 23 q^{89} - 2 q^{90} - 3 q^{92} + 2 q^{93} - 6 q^{94} - q^{95} + 2 q^{96} - 36 q^{97} + 14 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 - 2 * q^9 + 4 * q^10 + 4 * q^11 + 2 * q^12 - 2 * q^13 + 2 * q^15 - 2 * q^16 + 7 * q^17 - 2 * q^18 - q^19 - 2 * q^20 - 2 * q^22 + 6 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^26 - 4 * q^27 + 18 * q^29 + 2 * q^30 + 4 * q^31 - 2 * q^32 + 2 * q^33 + 7 * q^34 + 4 * q^36 + 2 * q^38 + 2 * q^39 - 2 * q^40 + 6 * q^41 - 2 * q^44 + 4 * q^45 - 3 * q^46 + 12 * q^47 - 4 * q^48 + 14 * q^49 - 2 * q^50 + 14 * q^51 - 2 * q^52 + 10 * q^53 + 2 * q^54 - 2 * q^55 + q^57 - 9 * q^58 + 8 * q^59 - 4 * q^60 + 20 * q^61 - 2 * q^62 + 4 * q^64 - 2 * q^65 - 4 * q^66 + 5 * q^67 - 14 * q^68 + 3 * q^69 + 10 * q^71 - 2 * q^72 - 15 * q^74 - 4 * q^75 - q^76 + 2 * q^78 + 6 * q^79 + 4 * q^80 - 2 * q^81 - 12 * q^82 - 2 * q^83 - 14 * q^85 + 9 * q^87 + 4 * q^88 + 23 * q^89 - 2 * q^90 - 3 * q^92 + 2 * q^93 - 6 * q^94 - q^95 + 2 * q^96 - 36 * q^97 + 14 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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