LMFDB - Embedded newform 1110.2.i.j.121.2

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			121.2
Root			$2.38600 - 4.13267i$ of defining polynomial
Character	$\chi$	$=$	1110.121
Dual form			1110.2.i.j.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(3.88600 - 6.73075i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-2.38600 - 4.13267i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-0.500000 + 0.866025i) q^{22} -2.77200 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{26} -1.00000 q^{27} +0.227998 q^{29} +(0.500000 + 0.866025i) q^{30} +9.54400 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} +(3.88600 + 6.73075i) q^{34} +1.00000 q^{36} +(-4.27200 + 4.33013i) q^{37} +4.77200 q^{38} +(0.500000 - 0.866025i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-2.77200 - 4.80125i) q^{41} +(-0.500000 - 0.866025i) q^{44} +1.00000 q^{45} +(1.38600 - 2.40062i) q^{46} +3.00000 q^{47} -1.00000 q^{48} +(3.50000 - 6.06218i) q^{49} +(-0.500000 - 0.866025i) q^{50} +7.77200 q^{51} +(-0.500000 + 0.866025i) q^{52} +(6.77200 - 11.7295i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.500000 - 0.866025i) q^{55} +(2.38600 - 4.13267i) q^{57} +(-0.113999 + 0.197452i) q^{58} +(6.27200 - 10.8634i) q^{59} -1.00000 q^{60} +(5.00000 + 8.66025i) q^{61} +(-4.77200 + 8.26535i) q^{62} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} -1.00000 q^{66} +(7.65800 + 13.2640i) q^{67} -7.77200 q^{68} +(-1.38600 - 2.40062i) q^{69} +(-1.77200 - 3.06920i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-1.61400 - 5.86473i) q^{74} -1.00000 q^{75} +(-2.38600 + 4.13267i) q^{76} +(0.500000 + 0.866025i) q^{78} +(-2.77200 - 4.80125i) q^{79} +1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} +5.54400 q^{82} +(-4.77200 + 8.26535i) q^{83} -7.77200 q^{85} +(0.113999 + 0.197452i) q^{87} +1.00000 q^{88} +(3.61400 - 6.25963i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(1.38600 + 2.40062i) q^{92} +(4.77200 + 8.26535i) q^{93} +(-1.50000 + 2.59808i) q^{94} +(-2.38600 + 4.13267i) q^{95} +(0.500000 - 0.866025i) q^{96} -0.455996 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
$17$	3.88600	−	6.73075i	0.942494	−	1.63245i	0.181800	−	0.983335i	$-0.441808\pi$
$17$	3.88600	−	6.73075i	0.942494	−	1.63245i	0.760693	−	0.649111i	$-0.224859\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−2.38600	−	4.13267i	−0.547386	−	0.948101i	−0.998453	−	0.0556102i	$-0.982290\pi$
$19$	−2.38600	−	4.13267i	−0.547386	−	0.948101i	0.451066	−	0.892490i	$-0.351044\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	−2.77200			−0.578002			−0.289001	−	0.957329i	$-0.593323\pi$
$23$	−2.77200			−0.578002			−0.289001	+	0.957329i	$0.593323\pi$
$24$	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
$29$	0.227998			0.0423382			0.0211691	−	0.999776i	$-0.493261\pi$
$29$	0.227998			0.0423382			0.0211691	+	0.999776i	$0.493261\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$	9.54400			1.71415			0.857077	−	0.515189i	$-0.172278\pi$
$31$	9.54400			1.71415			0.857077	+	0.515189i	$0.172278\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	3.88600	+	6.73075i	0.666444	+	1.15431i
$35$		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
$38$	4.77200			0.774121
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−2.77200	−	4.80125i	−0.432914	−	0.749829i	0.564209	−	0.825632i	$-0.309181\pi$
$41$	−2.77200	−	4.80125i	−0.432914	−	0.749829i	−0.997123	+	0.0758031i	$0.975848\pi$
$42$		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
$46$	1.38600	−	2.40062i	0.204355	−	0.353953i
$47$	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
$51$	7.77200			1.08830
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	6.77200	−	11.7295i	0.930206	−	1.61116i	0.147239	−	0.989101i	$-0.452961\pi$
$53$	6.77200	−	11.7295i	0.930206	−	1.61116i	0.782967	−	0.622063i	$-0.213705\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−0.500000	−	0.866025i	−0.0674200	−	0.116775i
$56$		0			0
$57$	2.38600	−	4.13267i	0.316034	−	0.547386i
$58$	−0.113999	+	0.197452i	−0.0149688	+	0.0259267i
$59$	6.27200	−	10.8634i	0.816545	−	1.41430i	−0.0916680	−	0.995790i	$-0.529220\pi$
$59$	6.27200	−	10.8634i	0.816545	−	1.41430i	0.908213	−	0.418508i	$-0.137447\pi$
$60$	−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	$0.612191\pi$
$62$	−4.77200	+	8.26535i	−0.606045	+	1.04970i
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$	−1.00000			−0.123091
$67$	7.65800	+	13.2640i	0.935574	+	1.62046i	0.773607	+	0.633665i	$0.218450\pi$
$67$	7.65800	+	13.2640i	0.935574	+	1.62046i	0.161967	+	0.986796i	$0.448216\pi$
$68$	−7.77200			−0.942494
$69$	−1.38600	−	2.40062i	−0.166855	−	0.289001i
$70$		0			0
$71$	−1.77200	−	3.06920i	−0.210298	−	0.364247i	0.741510	−	0.670942i	$-0.234110\pi$
$71$	−1.77200	−	3.06920i	−0.210298	−	0.364247i	−0.951808	+	0.306695i	$0.900777\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	−1.61400	−	5.86473i	−0.187624	−	0.681761i
$75$	−1.00000			−0.115470
$76$	−2.38600	+	4.13267i	−0.273693	+	0.474050i
$77$		0			0
$78$	0.500000	+	0.866025i	0.0566139	+	0.0980581i
$79$	−2.77200	−	4.80125i	−0.311875	−	0.540183i	0.666894	−	0.745153i	$-0.267624\pi$
$79$	−2.77200	−	4.80125i	−0.311875	−	0.540183i	−0.978768	+	0.204970i	$0.934290\pi$
$80$	1.00000			0.111803
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.54400			0.612233
$83$	−4.77200	+	8.26535i	−0.523795	+	0.907240i	0.475821	+	0.879542i	$0.342151\pi$
$83$	−4.77200	+	8.26535i	−0.523795	+	0.907240i	−0.999616	+	0.0276979i	$0.991182\pi$
$84$		0			0
$85$	−7.77200			−0.842992
$86$		0			0
$87$	0.113999	+	0.197452i	0.0122220	+	0.0211691i
$88$	1.00000			0.106600
$89$	3.61400	−	6.25963i	0.383083	−	0.663519i	−0.608418	−	0.793617i	$-0.708196\pi$
$89$	3.61400	−	6.25963i	0.383083	−	0.663519i	0.991501	+	0.130097i	$0.0415289\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$		0			0
$92$	1.38600	+	2.40062i	0.144501	+	0.250282i
$93$	4.77200	+	8.26535i	0.494834	+	0.857077i
$94$	−1.50000	+	2.59808i	−0.154713	+	0.267971i
$95$	−2.38600	+	4.13267i	−0.244799	+	0.424003i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−0.455996			−0.0462994			−0.0231497	−	0.999732i	$-0.507369\pi$
$97$	−0.455996			−0.0462994			−0.0231497	+	0.999732i	$0.507369\pi$
$98$	3.50000	+	6.06218i	0.353553	+	0.612372i
$99$	−0.500000	+	0.866025i	−0.0502519	+	0.0870388i
$100$	1.00000			0.100000
$101$	17.3160			1.72301			0.861503	−	0.507752i	$-0.169523\pi$
$101$	17.3160			1.72301			0.861503	+	0.507752i	$0.169523\pi$
$102$	−3.88600	+	6.73075i	−0.384771	+	0.666444i
$103$	−3.22800			−0.318064			−0.159032	−	0.987273i	$-0.550837\pi$
$103$	−3.22800			−0.318064			−0.159032	+	0.987273i	$0.550837\pi$
$104$	−0.500000	−	0.866025i	−0.0490290	−	0.0849208i
$105$		0			0
$106$	6.77200	+	11.7295i	0.657755	+	1.13927i
$107$	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
$111$	−5.88600	−	1.53460i	−0.558674	−	0.145658i
$112$		0			0
$113$	−0.886001	+	1.53460i	−0.0833480	+	0.144363i	−0.904686	−	0.426079i	$-0.859895\pi$
$113$	−0.886001	+	1.53460i	−0.0833480	+	0.144363i	0.821338	+	0.570442i	$0.193228\pi$
$114$	2.38600	+	4.13267i	0.223469	+	0.387060i
$115$	1.38600	+	2.40062i	0.129245	+	0.223859i
$116$	−0.113999	−	0.197452i	−0.0105845	−	0.0183330i
$117$	1.00000			0.0924500
$118$	6.27200	+	10.8634i	0.577385	+	1.00006i
$119$		0			0
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	−10.0000			−0.909091
$122$	−10.0000			−0.905357
$123$	2.77200	−	4.80125i	0.249943	−	0.432914i
$124$	−4.77200	−	8.26535i	−0.428538	−	0.742250i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−4.61400	+	7.99168i	−0.409426	+	0.709147i	−0.994826	−	0.101598i	$-0.967604\pi$
$127$	−4.61400	+	7.99168i	−0.409426	+	0.709147i	0.585399	+	0.810745i	$0.300938\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−0.500000	−	0.866025i	−0.0438529	−	0.0759555i
$131$	4.88600	−	8.46280i	0.426892	−	0.739398i	−0.569703	−	0.821851i	$-0.692942\pi$
$131$	4.88600	−	8.46280i	0.426892	−	0.739398i	0.996595	+	0.0824521i	$0.0262752\pi$
$132$	0.500000	−	0.866025i	0.0435194	−	0.0753778i
$133$		0			0
$134$	−15.3160			−1.32310
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	3.88600	−	6.73075i	0.333222	−	0.577157i
$137$	−15.3160			−1.30853			−0.654267	−	0.756263i	$-0.727023\pi$
$137$	−15.3160			−1.30853			−0.654267	+	0.756263i	$0.727023\pi$
$138$	2.77200			0.235968
$139$	−3.38600	+	5.86473i	−0.287197	+	0.497440i	−0.973140	−	0.230216i	$-0.926057\pi$
$139$	−3.38600	+	5.86473i	−0.287197	+	0.497440i	0.685943	+	0.727656i	$0.259390\pi$
$140$		0			0
$141$	1.50000	+	2.59808i	0.126323	+	0.218797i
$142$	3.54400			0.297406
$143$	−0.500000	−	0.866025i	−0.0418121	−	0.0724207i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−0.113999	−	0.197452i	−0.00946711	−	0.0163975i
$146$		0			0
$147$	7.00000			0.577350
$148$	5.88600	+	1.53460i	0.483826	+	0.126143i
$149$	−17.3160			−1.41858			−0.709291	−	0.704916i	$-0.750985\pi$
$149$	−17.3160			−1.41858			−0.709291	+	0.704916i	$0.750985\pi$
$150$	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	$0.727796\pi$
$152$	−2.38600	−	4.13267i	−0.193530	−	0.335204i
$153$	3.88600	+	6.73075i	0.314165	+	0.544149i
$154$		0			0
$155$	−4.77200	−	8.26535i	−0.383296	−	0.663889i
$156$	−1.00000			−0.0800641
$157$	−4.27200	+	7.39932i	−0.340943	+	0.590530i	−0.984608	−	0.174777i	$-0.944080\pi$
$157$	−4.27200	+	7.39932i	−0.340943	+	0.590530i	0.643665	+	0.765307i	$0.277413\pi$
$158$	5.54400			0.441057
$159$	13.5440			1.07411
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$		0			0
$162$	1.00000			0.0785674
$163$	−1.88600	+	3.26665i	−0.147723	+	0.255864i	−0.930386	−	0.366583i	$-0.880528\pi$
$163$	−1.88600	+	3.26665i	−0.147723	+	0.255864i	0.782663	+	0.622446i	$0.213861\pi$
$164$	−2.77200	+	4.80125i	−0.216457	+	0.374914i
$165$	0.500000	−	0.866025i	0.0389249	−	0.0674200i
$166$	−4.77200	−	8.26535i	−0.370379	−	0.641516i
$167$	−5.11400	−	8.85771i	−0.395733	−	0.685430i	0.597461	−	0.801898i	$-0.296176\pi$
$167$	−5.11400	−	8.85771i	−0.395733	−	0.685430i	−0.993194	+	0.116468i	$0.962843\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	3.88600	−	6.73075i	0.298043	−	0.516225i
$171$	4.77200			0.364924
$172$		0			0
$173$	2.15800	−	3.73777i	0.164070	−	0.284177i	−0.772255	−	0.635313i	$-0.780871\pi$
$173$	2.15800	−	3.73777i	0.164070	−	0.284177i	0.936325	+	0.351136i	$0.114204\pi$
$174$	−0.227998			−0.0172845
$175$		0			0
$176$	−0.500000	+	0.866025i	−0.0376889	+	0.0652791i
$177$	12.5440			0.942865
$178$	3.61400	+	6.25963i	0.270881	+	0.469179i
$179$	−20.3160			−1.51849			−0.759245	−	0.650805i	$-0.774431\pi$
$179$	−20.3160			−1.51849			−0.759245	+	0.650805i	$0.774431\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	5.77200	+	9.99740i	0.429030	+	0.743101i	0.996787	−	0.0800948i	$-0.0255223\pi$
$181$	5.77200	+	9.99740i	0.429030	+	0.743101i	−0.567758	+	0.823196i	$0.692189\pi$
$182$		0			0
$183$	−5.00000	+	8.66025i	−0.369611	+	0.640184i
$184$	−2.77200			−0.204355
$185$	5.88600	+	1.53460i	0.432747	+	0.112826i
$186$	−9.54400			−0.699800
$187$	3.88600	−	6.73075i	0.284173	−	0.492201i
$188$	−1.50000	−	2.59808i	−0.109399	−	0.189484i
$189$		0			0
$190$	−2.38600	−	4.13267i	−0.173099	−	0.299816i
$191$	21.5440			1.55887			0.779435	−	0.626483i	$-0.215506\pi$
$191$	21.5440			1.55887			0.779435	+	0.626483i	$0.215506\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−19.0880			−1.37398			−0.686992	−	0.726665i	$-0.741069\pi$
$193$	−19.0880			−1.37398			−0.686992	+	0.726665i	$0.741069\pi$
$194$	0.227998	−	0.394904i	0.0163693	−	0.0283525i
$195$	−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
$199$	18.2280			1.29215			0.646074	−	0.763275i	$-0.276410\pi$
$199$	18.2280			1.29215			0.646074	+	0.763275i	$0.276410\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−7.65800	+	13.2640i	−0.540154	+	0.935574i
$202$	−8.65800	+	14.9961i	−0.609175	+	1.05512i
$203$		0			0
$204$	−3.88600	−	6.73075i	−0.272074	−	0.471247i
$205$	−2.77200	+	4.80125i	−0.193605	+	0.335334i
$206$	1.61400	−	2.79553i	0.112453	−	0.194774i
$207$	1.38600	−	2.40062i	0.0963337	−	0.166855i
$208$	1.00000			0.0693375
$209$	−2.38600	−	4.13267i	−0.165043	−	0.285863i
$210$		0			0
$211$	−9.22800			−0.635282			−0.317641	−	0.948211i	$-0.602891\pi$
$211$	−9.22800			−0.635282			−0.317641	+	0.948211i	$0.602891\pi$
$212$	−13.5440			−0.930206
$213$	1.77200	−	3.06920i	0.121416	−	0.210298i
$214$	−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
$221$	−7.77200			−0.522801
$222$	4.27200	−	4.33013i	0.286718	−	0.290619i
$223$	21.8600			1.46385			0.731927	−	0.681383i	$-0.238621\pi$
$223$	21.8600			1.46385			0.731927	+	0.681383i	$0.238621\pi$
$224$		0			0
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	−0.886001	−	1.53460i	−0.0589359	−	0.102080i
$227$	−4.77200	−	8.26535i	−0.316729	−	0.548591i	0.663075	−	0.748553i	$-0.269251\pi$
$227$	−4.77200	−	8.26535i	−0.316729	−	0.548591i	−0.979803	+	0.199963i	$0.935918\pi$
$228$	−4.77200			−0.316034
$229$	−13.7720	−	23.8538i	−0.910080	−	1.57630i	−0.813950	−	0.580935i	$-0.802687\pi$
$229$	−13.7720	−	23.8538i	−0.910080	−	1.57630i	−0.0961296	−	0.995369i	$-0.530646\pi$
$230$	−2.77200			−0.182780
$231$		0			0
$232$	0.227998			0.0149688
$233$	−15.5440			−1.01832			−0.509161	−	0.860671i	$-0.670044\pi$
$233$	−15.5440			−1.01832			−0.509161	+	0.860671i	$0.670044\pi$
$234$	−0.500000	+	0.866025i	−0.0326860	+	0.0566139i
$235$	−1.50000	−	2.59808i	−0.0978492	−	0.169480i
$236$	−12.5440			−0.816545
$237$	2.77200	−	4.80125i	0.180061	−	0.311875i
$238$		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
$241$	−13.2720	−	22.9878i	−0.854925	−	1.48077i	−0.876715	−	0.481011i	$-0.840270\pi$
$241$	−13.2720	−	22.9878i	−0.854925	−	1.48077i	0.0217900	−	0.999763i	$-0.493063\pi$
$242$	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
$246$	2.77200	+	4.80125i	0.176736	+	0.306116i
$247$	−2.38600	+	4.13267i	−0.151818	+	0.262956i
$248$	9.54400			0.606045
$249$	−9.54400			−0.604827
$250$	−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
$253$	−2.77200			−0.174274
$254$	−4.61400	−	7.99168i	−0.289508	−	0.501443i
$255$	−3.88600	−	6.73075i	−0.243351	−	0.421496i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.65800	+	16.7282i	−0.602450	+	1.04347i	0.389999	+	0.920815i	$0.372475\pi$
$257$	−9.65800	+	16.7282i	−0.602450	+	1.04347i	−0.992449	+	0.122658i	$0.960858\pi$
$258$		0			0
$259$		0			0
$260$	1.00000			0.0620174
$261$	−0.113999	+	0.197452i	−0.00705636	+	0.0122220i
$262$	4.88600	+	8.46280i	0.301858	+	0.522834i
$263$	0.158003	+	0.273669i	0.00974287	+	0.0168751i	0.870856	−	0.491539i	$-0.163565\pi$
$263$	0.158003	+	0.273669i	0.00974287	+	0.0168751i	−0.861113	+	0.508414i	$0.830232\pi$
$264$	0.500000	+	0.866025i	0.0307729	+	0.0533002i
$265$	−13.5440			−0.832002
$266$		0			0
$267$	7.22800			0.442346
$268$	7.65800	−	13.2640i	0.467787	−	0.810231i
$269$	−29.0880			−1.77353			−0.886764	−	0.462223i	$-0.847052\pi$
$269$	−29.0880			−1.77353			−0.886764	+	0.462223i	$0.847052\pi$
$270$	−1.00000			−0.0608581
$271$	−6.65800	+	11.5320i	−0.404445	+	0.700519i	−0.994257	−	0.107022i	$-0.965869\pi$
$271$	−6.65800	+	11.5320i	−0.404445	+	0.700519i	0.589812	+	0.807541i	$0.299202\pi$
$272$	3.88600	+	6.73075i	0.235623	+	0.408112i
$273$		0			0
$274$	7.65800	−	13.2640i	0.462637	−	0.801311i
$275$	−0.500000	+	0.866025i	−0.0301511	+	0.0522233i
$276$	−1.38600	+	2.40062i	−0.0834275	+	0.144501i
$277$	5.88600	+	10.1949i	0.353656	+	0.612549i	0.986887	−	0.161413i	$-0.0516052\pi$
$277$	5.88600	+	10.1949i	0.353656	+	0.612549i	−0.633231	+	0.773963i	$0.718272\pi$
$278$	−3.38600	−	5.86473i	−0.203079	−	0.351743i
$279$	−4.77200	+	8.26535i	−0.285692	+	0.494834i
$280$		0			0
$281$	−15.9300	+	27.5916i	−0.950304	+	1.64598i	−0.205539	+	0.978649i	$0.565895\pi$
$281$	−15.9300	+	27.5916i	−0.950304	+	1.64598i	−0.744765	+	0.667327i	$0.767439\pi$
$282$	−3.00000			−0.178647
$283$	13.8860	+	24.0513i	0.825437	+	1.42970i	0.901585	+	0.432602i	$0.142405\pi$
$283$	13.8860	+	24.0513i	0.825437	+	1.42970i	−0.0761477	+	0.997097i	$0.524262\pi$
$284$	−1.77200	+	3.06920i	−0.105149	+	0.182123i
$285$	−4.77200			−0.282669
$286$	1.00000			0.0591312
$287$		0			0
$288$	1.00000			0.0589256
$289$	−21.7020	−	37.5890i	−1.27659	−	2.21112i
$290$	0.227998			0.0133885
$291$	−0.227998	−	0.394904i	−0.0133655	−	0.0231497i
$292$		0			0
$293$	14.7020	+	25.4646i	0.858900	+	1.48766i	0.872979	+	0.487758i	$0.162185\pi$
$293$	14.7020	+	25.4646i	0.858900	+	1.48766i	−0.0140784	+	0.999901i	$0.504481\pi$
$294$	−3.50000	+	6.06218i	−0.204124	+	0.353553i
$295$	−12.5440			−0.730340
$296$	−4.27200	+	4.33013i	−0.248305	+	0.251684i
$297$	−1.00000			−0.0580259
$298$	8.65800	−	14.9961i	0.501545	−	0.868701i
$299$	1.38600	+	2.40062i	0.0801545	+	0.138832i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$		0			0
$302$	−8.00000			−0.460348
$303$	8.65800	+	14.9961i	0.497389	+	0.861503i
$304$	4.77200			0.273693
$305$	5.00000	−	8.66025i	0.286299	−	0.495885i
$306$	−7.77200			−0.444296
$307$	−10.4560			−0.596755			−0.298378	−	0.954448i	$-0.596445\pi$
$307$	−10.4560			−0.596755			−0.298378	+	0.954448i	$0.596445\pi$
$308$		0			0
$309$	−1.61400	−	2.79553i	−0.0918172	−	0.159032i
$310$	9.54400			0.542063
$311$	3.77200	−	6.53330i	0.213891	−	0.370469i	−0.739038	−	0.673664i	$-0.764720\pi$
$311$	3.77200	−	6.53330i	0.213891	−	0.370469i	0.952929	+	0.303194i	$0.0980531\pi$
$312$	0.500000	−	0.866025i	0.0283069	−	0.0490290i
$313$	4.22800	−	7.32311i	0.238981	−	0.413927i	−0.721441	−	0.692475i	$-0.756520\pi$
$313$	4.22800	−	7.32311i	0.238981	−	0.413927i	0.960422	+	0.278549i	$0.0898534\pi$
$314$	−4.27200	−	7.39932i	−0.241083	−	0.417568i
$315$		0			0
$316$	−2.77200	+	4.80125i	−0.155937	+	0.270091i
$317$	4.15800	−	7.20187i	0.233537	−	0.404497i	−0.725310	−	0.688423i	$-0.758303\pi$
$317$	4.15800	−	7.20187i	0.233537	−	0.404497i	0.958846	+	0.283925i	$0.0916368\pi$
$318$	−6.77200	+	11.7295i	−0.379755	+	0.657755i
$319$	0.227998			0.0127654
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−2.00000	+	3.46410i	−0.111629	+	0.193347i
$322$		0			0
$323$	−37.0880			−2.06363
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	1.00000			0.0554700
$326$	−1.88600	−	3.26665i	−0.104456	−	0.180923i
$327$	4.00000			0.221201
$328$	−2.77200	−	4.80125i	−0.153058	−	0.265105i
$329$		0			0
$330$	0.500000	+	0.866025i	0.0275241	+	0.0476731i
$331$	0.386001	−	0.668573i	0.0212165	−	0.0367481i	−0.855222	−	0.518262i	$-0.826579\pi$
$331$	0.386001	−	0.668573i	0.0212165	−	0.0367481i	0.876439	+	0.481513i	$0.159913\pi$
$332$	9.54400			0.523795
$333$	−1.61400	−	5.86473i	−0.0884466	−	0.321385i
$334$	10.2280			0.559651
$335$	7.65800	−	13.2640i	0.418401	−	0.724692i
$336$		0			0
$337$	3.54400	+	6.13839i	0.193054	+	0.334380i	0.946261	−	0.323404i	$-0.104827\pi$
$337$	3.54400	+	6.13839i	0.193054	+	0.334380i	−0.753207	+	0.657784i	$0.771494\pi$
$338$	6.00000	+	10.3923i	0.326357	+	0.565267i
$339$	−1.77200			−0.0962419
$340$	3.88600	+	6.73075i	0.210748	+	0.365026i
$341$	9.54400			0.516837
$342$	−2.38600	+	4.13267i	−0.129020	+	0.223469i
$343$		0			0
$344$		0			0
$345$	−1.38600	+	2.40062i	−0.0746198	+	0.129245i
$346$	2.15800	+	3.73777i	0.116015	+	0.200944i
$347$	−9.08801			−0.487870			−0.243935	−	0.969792i	$-0.578438\pi$
$347$	−9.08801			−0.487870			−0.243935	+	0.969792i	$0.578438\pi$
$348$	0.113999	−	0.197452i	0.00611099	−	0.0105845i
$349$	−11.5440	+	19.9948i	−0.617936	+	1.07030i	0.371925	+	0.928263i	$0.378698\pi$
$349$	−11.5440	+	19.9948i	−0.617936	+	1.07030i	−0.989862	+	0.142035i	$0.954636\pi$
$350$		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	$0.183617\pi$
$354$	−6.27200	+	10.8634i	−0.333353	+	0.577385i
$355$	−1.77200	+	3.06920i	−0.0940481	+	0.162896i
$356$	−7.22800			−0.383083
$357$		0			0
$358$	10.1580	−	17.5942i	0.536867	−	0.929881i
$359$	13.0880			0.690759			0.345379	−	0.938463i	$-0.387750\pi$
$359$	13.0880			0.690759			0.345379	+	0.938463i	$0.387750\pi$
$360$	1.00000			0.0527046
$361$	−1.88600	+	3.26665i	−0.0992632	+	0.171929i
$362$	−11.5440			−0.606739
$363$	−5.00000	−	8.66025i	−0.262432	−	0.454545i
$364$		0			0
$365$		0			0
$366$	−5.00000	−	8.66025i	−0.261354	−	0.452679i
$367$	−8.93000	−	15.4672i	−0.466142	−	0.807382i	0.533110	−	0.846046i	$-0.321023\pi$
$367$	−8.93000	−	15.4672i	−0.466142	−	0.807382i	−0.999252	+	0.0386636i	$0.987690\pi$
$368$	1.38600	−	2.40062i	0.0722503	−	0.125141i
$369$	5.54400			0.288609
$370$	−4.27200	+	4.33013i	−0.222091	+	0.225113i
$371$		0			0
$372$	4.77200	−	8.26535i	0.247417	−	0.428538i
$373$	−1.61400	−	2.79553i	−0.0835697	−	0.144747i	0.821211	−	0.570624i	$-0.193299\pi$
$373$	−1.61400	−	2.79553i	−0.0835697	−	0.144747i	−0.904781	+	0.425877i	$0.859965\pi$
$374$	3.88600	+	6.73075i	0.200940	+	0.348039i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	3.00000			0.154713
$377$	−0.113999	−	0.197452i	−0.00587125	−	0.0101693i
$378$		0			0
$379$	17.5440	−	30.3871i	0.901175	−	1.56088i	0.0752039	−	0.997168i	$-0.476039\pi$
$379$	17.5440	−	30.3871i	0.901175	−	1.56088i	0.825971	−	0.563713i	$-0.190627\pi$
$380$	4.77200			0.244799
$381$	−9.22800			−0.472765
$382$	−10.7720	+	18.6577i	−0.551144	+	0.954609i
$383$	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
$386$	9.54400	−	16.5307i	0.485777	−	0.841390i
$387$		0			0
$388$	0.227998	+	0.394904i	0.0115749	+	0.0200482i
$389$	0.544004	+	0.942242i	0.0275821	+	0.0477736i	0.879487	−	0.475923i	$-0.157886\pi$
$389$	0.544004	+	0.942242i	0.0275821	+	0.0477736i	−0.851905	+	0.523697i	$0.824553\pi$
$390$	0.500000	−	0.866025i	0.0253185	−	0.0438529i
$391$	−10.7720	+	18.6577i	−0.544764	+	0.943558i
$392$	3.50000	−	6.06218i	0.176777	−	0.306186i
$393$	9.77200			0.492932
$394$	7.00000	+	12.1244i	0.352655	+	0.610816i
$395$	−2.77200	+	4.80125i	−0.139475	+	0.241577i
$396$	1.00000			0.0502519
$397$	6.54400			0.328434			0.164217	−	0.986424i	$-0.447490\pi$
$397$	6.54400			0.328434			0.164217	+	0.986424i	$0.447490\pi$
$398$	−9.11400	+	15.7859i	−0.456843	+	0.791276i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	0.316006			0.0157806			0.00789028	−	0.999969i	$-0.497488\pi$
$401$	0.316006			0.0157806			0.00789028	+	0.999969i	$0.497488\pi$
$402$	−7.65800	−	13.2640i	−0.381946	−	0.661551i
$403$	−4.77200	−	8.26535i	−0.237710	−	0.411726i
$404$	−8.65800	−	14.9961i	−0.430752	−	0.746084i
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$		0			0
$407$	−4.27200	+	4.33013i	−0.211755	+	0.214636i
$408$	7.77200			0.384771
$409$	−15.2020	+	26.3306i	−0.751691	+	1.30197i	0.195312	+	0.980741i	$0.437428\pi$
$409$	−15.2020	+	26.3306i	−0.751691	+	1.30197i	−0.947003	+	0.321226i	$0.895905\pi$
$410$	−2.77200	−	4.80125i	−0.136899	−	0.237117i
$411$	−7.65800	−	13.2640i	−0.377741	−	0.654267i
$412$	1.61400	+	2.79553i	0.0795160	+	0.137726i
$413$		0			0
$414$	1.38600	+	2.40062i	0.0681182	+	0.117984i
$415$	9.54400			0.468497
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$	−6.77200			−0.331626
$418$	4.77200			0.233406
$419$	−0.613999	+	1.06348i	−0.0299958	+	0.0519543i	−0.880634	−	0.473798i	$-0.842883\pi$
$419$	−0.613999	+	1.06348i	−0.0299958	+	0.0519543i	0.850638	+	0.525752i	$0.176216\pi$
$420$		0			0
$421$	23.5440			1.14746			0.573732	−	0.819043i	$-0.305495\pi$
$421$	23.5440			1.14746			0.573732	+	0.819043i	$0.305495\pi$
$422$	4.61400	−	7.99168i	0.224606	−	0.389029i
$423$	−1.50000	+	2.59808i	−0.0729325	+	0.126323i
$424$	6.77200	−	11.7295i	0.328877	−	0.569633i
$425$	3.88600	+	6.73075i	0.188499	+	0.326489i
$426$	1.77200	+	3.06920i	0.0858538	+	0.148703i
$427$		0			0
$428$	2.00000	−	3.46410i	0.0966736	−	0.167444i
$429$	0.500000	−	0.866025i	0.0241402	−	0.0418121i
$430$		0			0
$431$	15.7720	+	27.3179i	0.759711	+	1.31586i	0.942998	+	0.332798i	$0.107993\pi$
$431$	15.7720	+	27.3179i	0.759711	+	1.31586i	−0.183288	+	0.983059i	$0.558674\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−29.5440			−1.41979			−0.709897	−	0.704305i	$-0.751259\pi$
$433$	−29.5440			−1.41979			−0.709897	+	0.704305i	$0.751259\pi$
$434$		0			0
$435$	0.113999	−	0.197452i	0.00546584	−	0.00946711i
$436$	−4.00000			−0.191565
$437$	6.61400	+	11.4558i	0.316390	+	0.548004i
$438$		0			0
$439$	−6.43000	−	11.1371i	−0.306887	−	0.531545i	0.670792	−	0.741645i	$-0.265954\pi$
$439$	−6.43000	−	11.1371i	−0.306887	−	0.531545i	−0.977680	+	0.210101i	$0.932621\pi$
$440$	−0.500000	−	0.866025i	−0.0238366	−	0.0412861i
$441$	3.50000	+	6.06218i	0.166667	+	0.288675i
$442$	3.88600	−	6.73075i	0.184838	−	0.320149i
$443$	15.0880			0.716853			0.358426	−	0.933558i	$-0.383313\pi$
$443$	15.0880			0.716853			0.358426	+	0.933558i	$0.383313\pi$
$444$	1.61400	+	5.86473i	0.0765970	+	0.278328i
$445$	−7.22800			−0.342640
$446$	−10.9300	+	18.9313i	−0.517551	+	0.896424i
$447$	−8.65800	−	14.9961i	−0.409509	−	0.709291i
$448$		0			0
$449$	14.3160	+	24.7960i	0.675614	+	1.17020i	0.976289	+	0.216471i	$0.0694547\pi$
$449$	14.3160	+	24.7960i	0.675614	+	1.17020i	−0.300675	+	0.953727i	$0.597212\pi$
$450$	1.00000			0.0471405
$451$	−2.77200	−	4.80125i	−0.130528	−	0.226082i
$452$	1.77200			0.0833480
$453$	−4.00000	+	6.92820i	−0.187936	+	0.325515i
$454$	9.54400			0.447922
$455$		0			0
$456$	2.38600	−	4.13267i	0.111735	−	0.193530i
$457$	13.5440	+	23.4589i	0.633562	+	1.09736i	0.986818	+	0.161835i	$0.0517411\pi$
$457$	13.5440	+	23.4589i	0.633562	+	1.09736i	−0.353256	+	0.935527i	$0.614926\pi$
$458$	27.5440			1.28705
$459$	−3.88600	+	6.73075i	−0.181383	+	0.314165i
$460$	1.38600	−	2.40062i	0.0646226	−	0.111930i
$461$	8.65800	−	14.9961i	0.403243	−	0.698438i	−0.590872	−	0.806765i	$-0.701216\pi$
$461$	8.65800	−	14.9961i	0.403243	−	0.698438i	0.994115	+	0.108327i	$0.0345495\pi$
$462$		0			0
$463$	−15.7720	−	27.3179i	−0.732987	−	1.26957i	−0.955601	−	0.294664i	$-0.904792\pi$
$463$	−15.7720	−	27.3179i	−0.732987	−	1.26957i	0.222614	−	0.974907i	$-0.428541\pi$
$464$	−0.113999	+	0.197452i	−0.00529227	+	0.00916649i
$465$	4.77200	−	8.26535i	0.221296	−	0.383296i
$466$	7.77200	−	13.4615i	0.360031	−	0.623592i
$467$	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
$472$	6.27200	−	10.8634i	0.288692	−	0.500030i
$473$		0			0
$474$	2.77200	+	4.80125i	0.127322	+	0.220529i
$475$	4.77200			0.218954
$476$		0			0
$477$	6.77200	+	11.7295i	0.310069	+	0.537055i
$478$	8.00000	+	13.8564i	0.365911	+	0.633777i
$479$	−8.22800	+	14.2513i	−0.375947	+	0.651159i	−0.990468	−	0.137741i	$-0.956016\pi$
$479$	−8.22800	+	14.2513i	−0.375947	+	0.651159i	0.614521	+	0.788900i	$0.289349\pi$
$480$	−1.00000			−0.0456435
$481$	5.88600	+	1.53460i	0.268379	+	0.0699717i
$482$	26.5440			1.20905
$483$		0			0
$484$	5.00000	+	8.66025i	0.227273	+	0.393648i
$485$	0.227998	+	0.394904i	0.0103529	+	0.0179317i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	22.6320			1.02555			0.512777	−	0.858522i	$-0.328617\pi$
$487$	22.6320			1.02555			0.512777	+	0.858522i	$0.328617\pi$
$488$	5.00000	+	8.66025i	0.226339	+	0.392031i
$489$	−3.77200			−0.170576
$490$	3.50000	−	6.06218i	0.158114	−	0.273861i
$491$	12.3160			0.555814			0.277907	−	0.960608i	$-0.410359\pi$
$491$	12.3160			0.555814			0.277907	+	0.960608i	$0.410359\pi$
$492$	−5.54400			−0.249943
$493$	0.886001	−	1.53460i	0.0399035	−	0.0691148i
$494$	−2.38600	−	4.13267i	−0.107351	−	0.185938i
$495$	1.00000			0.0449467
$496$	−4.77200	+	8.26535i	−0.214269	+	0.371125i
$497$		0			0
$498$	4.77200	−	8.26535i	0.213839	−	0.370379i
$499$	19.7720	+	34.2461i	0.885116	+	1.53307i	0.845580	+	0.533848i	$0.179255\pi$
$499$	19.7720	+	34.2461i	0.885116	+	1.53307i	0.0395361	+	0.999218i	$0.487412\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	5.11400	−	8.85771i	0.228477	−	0.395733i
$502$	−1.50000	+	2.59808i	−0.0669483	+	0.115958i
$503$	8.65800	−	14.9961i	0.386041	−	0.668643i	−0.605872	−	0.795562i	$-0.707176\pi$
$503$	8.65800	−	14.9961i	0.386041	−	0.668643i	0.991913	+	0.126919i	$0.0405089\pi$
$504$		0			0
$505$	−8.65800	−	14.9961i	−0.385276	−	0.667318i
$506$	1.38600	−	2.40062i	0.0616153	−	0.106721i
$507$	12.0000			0.532939
$508$	9.22800			0.409426
$509$	−10.2280	+	17.7154i	−0.453348	+	0.785222i	−0.998592	−	0.0530559i	$-0.983104\pi$
$509$	−10.2280	+	17.7154i	−0.453348	+	0.785222i	0.545243	+	0.838278i	$0.316437\pi$
$510$	7.77200			0.344150
$511$		0			0
$512$	1.00000			0.0441942
$513$	2.38600	+	4.13267i	0.105345	+	0.182462i
$514$	−9.65800	−	16.7282i	−0.425996	−	0.737847i
$515$	1.61400	+	2.79553i	0.0711213	+	0.123186i
$516$		0			0
$517$	3.00000			0.131940
$518$		0			0
$519$	4.31601			0.189452
$520$	−0.500000	+	0.866025i	−0.0219265	+	0.0379777i
$521$	−4.15800	−	7.20187i	−0.182165	−	0.315520i	0.760452	−	0.649394i	$-0.224977\pi$
$521$	−4.15800	−	7.20187i	−0.182165	−	0.315520i	−0.942618	+	0.333874i	$0.891644\pi$
$522$	−0.113999	−	0.197452i	−0.00498960	−	0.00864225i
$523$	17.5440	+	30.3871i	0.767146	+	1.32874i	0.939105	+	0.343631i	$0.111657\pi$
$523$	17.5440	+	30.3871i	0.767146	+	1.32874i	−0.171959	+	0.985104i	$0.555010\pi$
$524$	−9.77200			−0.426892
$525$		0			0
$526$	−0.316006			−0.0137785
$527$	37.0880	−	64.2383i	1.61558	−	2.79826i
$528$	−1.00000			−0.0435194
$529$	−15.3160			−0.665913
$530$	6.77200	−	11.7295i	0.294157	−	0.509495i
$531$	6.27200	+	10.8634i	0.272182	+	0.471433i
$532$		0			0
$533$	−2.77200	+	4.80125i	−0.120069	+	0.207965i
$534$	−3.61400	+	6.25963i	−0.156393	+	0.270881i
$535$	2.00000	−	3.46410i	0.0864675	−	0.149766i
$536$	7.65800	+	13.2640i	0.330775	+	0.572920i
$537$	−10.1580	−	17.5942i	−0.438350	−	0.759245i
$538$	14.5440	−	25.1910i	0.627037	−	1.08606i
$539$	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	$0.373532\pi$
$542$	−6.65800	−	11.5320i	−0.285986	−	0.495342i
$543$	−5.77200	+	9.99740i	−0.247700	+	0.429030i
$544$	−7.77200			−0.333222
$545$	−4.00000			−0.171341
$546$		0			0
$547$	−17.5440			−0.750127			−0.375064	−	0.926999i	$-0.622379\pi$
$547$	−17.5440			−0.750127			−0.375064	+	0.926999i	$0.622379\pi$
$548$	7.65800	+	13.2640i	0.327134	+	0.566612i
$549$	−10.0000			−0.426790
$550$	−0.500000	−	0.866025i	−0.0213201	−	0.0369274i
$551$	−0.544004	−	0.942242i	−0.0231753	−	0.0401409i
$552$	−1.38600	−	2.40062i	−0.0589921	−	0.102177i
$553$		0			0
$554$	−11.7720			−0.500144
$555$	1.61400	+	5.86473i	0.0685104	+	0.248944i
$556$	6.77200			0.287197
$557$	1.15800	−	2.00572i	0.0490662	−	0.0849851i	−0.840449	−	0.541890i	$-0.817709\pi$
$557$	1.15800	−	2.00572i	0.0490662	−	0.0849851i	0.889515	+	0.456905i	$0.151042\pi$
$558$	−4.77200	−	8.26535i	−0.202015	−	0.349900i
$559$		0			0
$560$		0			0
$561$	7.77200			0.328134
$562$	−15.9300	−	27.5916i	−0.671967	−	1.16388i
$563$	−4.45600			−0.187798			−0.0938989	−	0.995582i	$-0.529933\pi$
$563$	−4.45600			−0.187798			−0.0938989	+	0.995582i	$0.529933\pi$
$564$	1.50000	−	2.59808i	0.0631614	−	0.109399i
$565$	1.77200			0.0745487
$566$	−27.7720			−1.16734
$567$		0			0
$568$	−1.77200	−	3.06920i	−0.0743515	−	0.128781i
$569$	43.4040			1.81959			0.909795	−	0.415057i	$-0.136238\pi$
$569$	43.4040			1.81959			0.909795	+	0.415057i	$0.136238\pi$
$570$	2.38600	−	4.13267i	0.0999386	−	0.173099i
$571$	7.15800	−	12.3980i	0.299553	−	0.518841i	−0.676481	−	0.736460i	$-0.736496\pi$
$571$	7.15800	−	12.3980i	0.299553	−	0.518841i	0.976034	+	0.217619i	$0.0698291\pi$
$572$	−0.500000	+	0.866025i	−0.0209061	+	0.0362103i
$573$	10.7720	+	18.6577i	0.450007	+	0.779435i
$574$		0			0
$575$	1.38600	−	2.40062i	0.0578002	−	0.100113i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−5.77200	+	9.99740i	−0.240292	+	0.416197i	−0.960797	−	0.277252i	$-0.910576\pi$
$577$	−5.77200	+	9.99740i	−0.240292	+	0.416197i	0.720506	+	0.693449i	$0.243910\pi$
$578$	43.4040			1.80537
$579$	−9.54400	−	16.5307i	−0.396635	−	0.686992i
$580$	−0.113999	+	0.197452i	−0.00473355	+	0.00819876i
$581$		0			0
$582$	0.455996			0.0189017
$583$	6.77200	−	11.7295i	0.280468	−	0.485784i
$584$		0			0
$585$	−0.500000	−	0.866025i	−0.0206725	−	0.0358057i
$586$	−29.4040			−1.21467
$587$	13.5440	+	23.4589i	0.559021	+	0.968253i	0.997579	+	0.0695495i	$0.0221562\pi$
$587$	13.5440	+	23.4589i	0.559021	+	0.968253i	−0.438558	+	0.898703i	$0.644510\pi$
$588$	−3.50000	−	6.06218i	−0.144338	−	0.250000i
$589$	−22.7720	−	39.4423i	−0.938304	−	1.62519i
$590$	6.27200	−	10.8634i	0.258214	−	0.447240i
$591$	14.0000			0.575883
$592$	−1.61400	−	5.86473i	−0.0663350	−	0.241039i
$593$	−28.4040			−1.16641			−0.583207	−	0.812324i	$-0.698202\pi$
$593$	−28.4040			−1.16641			−0.583207	+	0.812324i	$0.698202\pi$
$594$	0.500000	−	0.866025i	0.0205152	−	0.0355335i
$595$		0			0
$596$	8.65800	+	14.9961i	0.354646	+	0.614264i
$597$	9.11400	+	15.7859i	0.373011	+	0.646074i
$598$	−2.77200			−0.113356
$599$	13.5440	+	23.4589i	0.553393	+	0.958505i	0.998027	+	0.0627922i	$0.0200006\pi$
$599$	13.5440	+	23.4589i	0.553393	+	0.958505i	−0.444634	+	0.895713i	$0.646666\pi$
$600$	−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
$603$	−15.3160			−0.623716
$604$	4.00000	−	6.92820i	0.162758	−	0.281905i
$605$	5.00000	+	8.66025i	0.203279	+	0.352089i
$606$	−17.3160			−0.703415
$607$	6.22800	−	10.7872i	0.252787	−	0.437839i	−0.711505	−	0.702681i	$-0.751986\pi$
$607$	6.22800	−	10.7872i	0.252787	−	0.437839i	0.964292	+	0.264841i	$0.0853196\pi$
$608$	−2.38600	+	4.13267i	−0.0967651	+	0.167602i
$609$		0			0
$610$	5.00000	+	8.66025i	0.202444	+	0.350643i
$611$	−1.50000	−	2.59808i	−0.0606835	−	0.105107i
$612$	3.88600	−	6.73075i	0.157082	−	0.272074i
$613$	−13.2720	+	22.9878i	−0.536051	+	0.928468i	0.463061	+	0.886327i	$0.346751\pi$
$613$	−13.2720	+	22.9878i	−0.536051	+	0.928468i	−0.999112	+	0.0421411i	$0.986582\pi$
$614$	5.22800	−	9.05516i	0.210985	−	0.365436i
$615$	−5.54400			−0.223556
$616$		0			0
$617$	−13.1140	+	22.7141i	−0.527950	+	0.914436i	0.471519	+	0.881856i	$0.343706\pi$
$617$	−13.1140	+	22.7141i	−0.527950	+	0.914436i	−0.999469	+	0.0325801i	$0.989628\pi$
$618$	3.22800			0.129849
$619$	38.1760			1.53442			0.767212	−	0.641394i	$-0.221644\pi$
$619$	38.1760			1.53442			0.767212	+	0.641394i	$0.221644\pi$
$620$	−4.77200	+	8.26535i	−0.191648	+	0.331944i
$621$	2.77200			0.111237
$622$	3.77200	+	6.53330i	0.151243	+	0.261961i
$623$		0			0
$624$	0.500000	+	0.866025i	0.0200160	+	0.0346688i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	4.22800	+	7.32311i	0.168985	+	0.292690i
$627$	2.38600	−	4.13267i	0.0952877	−	0.165043i
$628$	8.54400			0.340943
$629$	12.5440	+	45.5807i	0.500162	+	1.81742i
$630$		0			0
$631$	4.65800	−	8.06790i	0.185432	−	0.321178i	−0.758290	−	0.651917i	$-0.773965\pi$
$631$	4.65800	−	8.06790i	0.185432	−	0.321178i	0.943722	+	0.330740i	$0.107298\pi$
$632$	−2.77200	−	4.80125i	−0.110264	−	0.190983i
$633$	−4.61400	−	7.99168i	−0.183390	−	0.317641i
$634$	4.15800	+	7.20187i	0.165135	+	0.286023i
$635$	9.22800			0.366202
$636$	−6.77200	−	11.7295i	−0.268527	−	0.465103i
$637$	−7.00000			−0.277350
$638$	−0.113999	+	0.197452i	−0.00451327	+	0.00781721i
$639$	3.54400			0.140199
$640$	1.00000			0.0395285
$641$	9.93000	−	17.1993i	0.392212	−	0.679330i	−0.600529	−	0.799603i	$-0.705043\pi$
$641$	9.93000	−	17.1993i	0.392212	−	0.679330i	0.992741	+	0.120272i	$0.0383768\pi$
$642$	−2.00000	−	3.46410i	−0.0789337	−	0.136717i
$643$	−0.227998			−0.00899137			−0.00449568	−	0.999990i	$-0.501431\pi$
$643$	−0.227998			−0.00899137			−0.00449568	+	0.999990i	$0.501431\pi$
$644$		0			0
$645$		0			0
$646$	18.5440	−	32.1192i	0.729604	−	1.26371i
$647$	−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
$649$	6.27200	−	10.8634i	0.246198	−	0.426427i
$650$	−0.500000	+	0.866025i	−0.0196116	+	0.0339683i
$651$		0			0
$652$	3.77200			0.147723
$653$	9.38600	+	16.2570i	0.367303	+	0.636187i	0.989143	−	0.146957i	$-0.0469480\pi$
$653$	9.38600	+	16.2570i	0.367303	+	0.636187i	−0.621840	+	0.783144i	$0.713615\pi$
$654$	−2.00000	+	3.46410i	−0.0782062	+	0.135457i
$655$	−9.77200			−0.381824
$656$	5.54400			0.216457
$657$		0			0
$658$		0			0
$659$	18.0440	+	31.2531i	0.702895	+	1.21745i	0.967446	+	0.253078i	$0.0814428\pi$
$659$	18.0440	+	31.2531i	0.702895	+	1.21745i	−0.264551	+	0.964372i	$0.585224\pi$
$660$	−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	$0.858120\pi$
$662$	0.386001	+	0.668573i	0.0150024	+	0.0259848i
$663$	−3.88600	−	6.73075i	−0.150920	−	0.261401i
$664$	−4.77200	+	8.26535i	−0.185190	+	0.320758i
$665$		0			0
$666$	5.88600	+	1.53460i	0.228078	+	0.0594645i
$667$	−0.632011			−0.0244716
$668$	−5.11400	+	8.85771i	−0.197867	+	0.342715i
$669$	10.9300	+	18.9313i	0.422578	+	0.731927i
$670$	7.65800	+	13.2640i	0.295854	+	0.512435i
$671$	5.00000	+	8.66025i	0.193023	+	0.334325i
$672$		0			0
$673$	−3.54400	−	6.13839i	−0.136611	−	0.236618i	0.789601	−	0.613621i	$-0.210288\pi$
$673$	−3.54400	−	6.13839i	−0.136611	−	0.236618i	−0.926212	+	0.377004i	$0.876954\pi$
$674$	−7.08801			−0.273020
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	−12.0000			−0.461538
$677$	15.8600			0.609550			0.304775	−	0.952424i	$-0.401419\pi$
$677$	15.8600			0.609550			0.304775	+	0.952424i	$0.401419\pi$
$678$	0.886001	−	1.53460i	0.0340267	−	0.0589359i
$679$		0			0
$680$	−7.77200			−0.298043
$681$	4.77200	−	8.26535i	0.182864	−	0.316729i
$682$	−4.77200	+	8.26535i	−0.182729	+	0.316497i
$683$	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	$0.0803543\pi$
$684$	−2.38600	−	4.13267i	−0.0912310	−	0.158017i
$685$	7.65800	+	13.2640i	0.292597	+	0.506793i
$686$		0			0
$687$	13.7720	−	23.8538i	0.525435	−	0.910080i
$688$		0			0
$689$	−13.5440			−0.515985
$690$	−1.38600	−	2.40062i	−0.0527642	−	0.0913902i
$691$	−10.2280	+	17.7154i	−0.389091	+	0.673926i	−0.992328	−	0.123637i	$-0.960544\pi$
$691$	−10.2280	+	17.7154i	−0.389091	+	0.673926i	0.603236	+	0.797563i	$0.293878\pi$
$692$	−4.31601			−0.164070
$693$		0			0
$694$	4.54400	−	7.87045i	0.172488	−	0.298758i
$695$	6.77200			0.256877
$696$	0.113999	+	0.197452i	0.00432112	+	0.00748441i
$697$	−43.0880			−1.63207
$698$	−11.5440	−	19.9948i	−0.436947	−	0.756814i
$699$	−7.77200	−	13.4615i	−0.293964	−	0.509161i
$700$		0			0
$701$	−1.34200	+	2.32441i	−0.0506865	+	0.0877917i	−0.890255	−	0.455461i	$-0.849474\pi$
$701$	−1.34200	+	2.32441i	−0.0506865	+	0.0877917i	0.839569	+	0.543253i	$0.182808\pi$
$702$	−1.00000			−0.0377426
$703$	28.0880	+	7.32311i	1.05936	+	0.276196i
$704$	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
$708$	−6.27200	−	10.8634i	−0.235716	−	0.408273i
$709$	−9.08801			−0.341307			−0.170654	−	0.985331i	$-0.554588\pi$
$709$	−9.08801			−0.341307			−0.170654	+	0.985331i	$0.554588\pi$
$710$	−1.77200	−	3.06920i	−0.0665020	−	0.115185i
$711$	5.54400			0.207916
$712$	3.61400	−	6.25963i	0.135440	−	0.234590i
$713$	−26.4560			−0.990785
$714$		0			0
$715$	−0.500000	+	0.866025i	−0.0186989	+	0.0323875i
$716$	10.1580	+	17.5942i	0.379622	+	0.657525i
$717$	16.0000			0.597531
$718$	−6.54400	+	11.3345i	−0.244220	+	0.423002i
$719$	4.77200	−	8.26535i	0.177966	−	0.308246i	−0.763218	−	0.646141i	$-0.776382\pi$
$719$	4.77200	−	8.26535i	0.177966	−	0.308246i	0.941184	+	0.337896i	$0.109715\pi$
$720$	−0.500000	+	0.866025i	−0.0186339	+	0.0322749i
$721$		0			0
$722$	−1.88600	−	3.26665i	−0.0701897	−	0.121572i
$723$	13.2720	−	22.9878i	0.493591	−	0.854925i
$724$	5.77200	−	9.99740i	0.214515	−	0.371550i
$725$	−0.113999	+	0.197452i	−0.00423382	+	0.00733319i
$726$	10.0000			0.371135
$727$	22.9300	+	39.7159i	0.850427	+	1.47298i	0.880824	+	0.473445i	$0.156990\pi$
$727$	22.9300	+	39.7159i	0.850427	+	1.47298i	−0.0303968	+	0.999538i	$0.509677\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$		0			0
$732$	10.0000			0.369611
$733$	−3.95600	−	6.85199i	−0.146118	−	0.253084i	0.783671	−	0.621176i	$-0.213345\pi$
$733$	−3.95600	−	6.85199i	−0.146118	−	0.253084i	−0.929790	+	0.368092i	$0.880011\pi$
$734$	17.8600			0.659225
$735$	−3.50000	−	6.06218i	−0.129099	−	0.223607i
$736$	1.38600	+	2.40062i	0.0510887	+	0.0884882i
$737$	7.65800	+	13.2640i	0.282086	+	0.488588i
$738$	−2.77200	+	4.80125i	−0.102039	+	0.176736i
$739$	−0.772002			−0.0283985			−0.0141993	−	0.999899i	$-0.504520\pi$
$739$	−0.772002			−0.0283985			−0.0141993	+	0.999899i	$0.504520\pi$
$740$	−1.61400	−	5.86473i	−0.0593318	−	0.215592i
$741$	−4.77200			−0.175304
$742$		0			0
$743$	−15.2720	−	26.4519i	−0.560275	−	0.970425i	−0.997472	−	0.0710595i	$-0.977362\pi$
$743$	−15.2720	−	26.4519i	−0.560275	−	0.970425i	0.437197	−	0.899366i	$-0.355971\pi$
$744$	4.77200	+	8.26535i	0.174950	+	0.303022i
$745$	8.65800	+	14.9961i	0.317205	+	0.549415i
$746$	3.22800			0.118185
$747$	−4.77200	−	8.26535i	−0.174598	−	0.302413i
$748$	−7.77200			−0.284173
$749$		0			0
$750$	−1.00000			−0.0365148
$751$	−1.77200			−0.0646613			−0.0323306	−	0.999477i	$-0.510293\pi$
$751$	−1.77200			−0.0646613			−0.0323306	+	0.999477i	$0.510293\pi$
$752$	−1.50000	+	2.59808i	−0.0546994	+	0.0947421i
$753$	1.50000	+	2.59808i	0.0546630	+	0.0946792i
$754$	0.227998			0.00830320
$755$	4.00000	−	6.92820i	0.145575	−	0.252143i
$756$		0			0
$757$	−20.3860	+	35.3096i	−0.740942	+	1.28335i	0.211125	+	0.977459i	$0.432287\pi$
$757$	−20.3860	+	35.3096i	−0.740942	+	1.28335i	−0.952067	+	0.305890i	$0.901046\pi$
$758$	17.5440	+	30.3871i	0.637227	+	1.10371i
$759$	−1.38600	−	2.40062i	−0.0503086	−	0.0871371i
$760$	−2.38600	+	4.13267i	−0.0865494	+	0.149908i
$761$	23.1580	−	40.1108i	0.839477	−	1.45402i	−0.0508557	−	0.998706i	$-0.516195\pi$
$761$	23.1580	−	40.1108i	0.839477	−	1.45402i	0.890333	−	0.455311i	$-0.150472\pi$
$762$	4.61400	−	7.99168i	0.167148	−	0.289508i
$763$		0			0
$764$	−10.7720	−	18.6577i	−0.389717	−	0.675010i
$765$	3.88600	−	6.73075i	0.140499	−	0.243351i
$766$	−29.0000			−1.04781
$767$	−12.5440			−0.452938
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−37.9480			−1.36844			−0.684220	−	0.729275i	$-0.739857\pi$
$769$	−37.9480			−1.36844			−0.684220	+	0.729275i	$0.739857\pi$
$770$		0			0
$771$	−19.3160			−0.695649
$772$	9.54400	+	16.5307i	0.343496	+	0.594953i
$773$	5.70201	+	9.87617i	0.205087	+	0.355221i	0.950160	−	0.311761i	$-0.100919\pi$
$773$	5.70201	+	9.87617i	0.205087	+	0.355221i	−0.745074	+	0.666982i	$0.767586\pi$
$774$		0			0
$775$	−4.77200	+	8.26535i	−0.171415	+	0.296900i
$776$	−0.455996			−0.0163693
$777$		0			0
$778$	−1.08801			−0.0390070
$779$	−13.2280	+	22.9116i	−0.473942	+	0.820892i
$780$	0.500000	+	0.866025i	0.0179029	+	0.0310087i
$781$	−1.77200	−	3.06920i	−0.0634072	−	0.109825i
$782$	−10.7720	−	18.6577i	−0.385206	−	0.667196i
$783$	−0.227998			−0.00814799
$784$	3.50000	+	6.06218i	0.125000	+	0.216506i
$785$	8.54400			0.304949
$786$	−4.88600	+	8.46280i	−0.174278	+	0.301858i
$787$	−18.2280			−0.649758			−0.324879	−	0.945756i	$-0.605324\pi$
$787$	−18.2280			−0.649758			−0.324879	+	0.945756i	$0.605324\pi$
$788$	−14.0000			−0.498729
$789$	−0.158003	+	0.273669i	−0.00562505	+	0.00974287i
$790$	−2.77200	−	4.80125i	−0.0986234	−	0.170821i
$791$		0			0
$792$	−0.500000	+	0.866025i	−0.0177667	+	0.0307729i
$793$	5.00000	−	8.66025i	0.177555	−	0.307535i
$794$	−3.27200	+	5.66727i	−0.116119	+	0.201124i
$795$	−6.77200	−	11.7295i	−0.240178	−	0.416001i
$796$	−9.11400	−	15.7859i	−0.323037	−	0.559517i
$797$	16.6140	−	28.7763i	0.588498	−	1.01931i	−0.405931	−	0.913904i	$-0.633053\pi$
$797$	16.6140	−	28.7763i	0.588498	−	1.01931i	0.994429	−	0.105405i	$-0.0336139\pi$
$798$		0			0
$799$	11.6580	−	20.1923i	0.412430	−	0.714351i
$800$	1.00000			0.0353553
$801$	3.61400	+	6.25963i	0.127694	+	0.221173i
$802$	−0.158003	+	0.273669i	−0.00557927	+	0.00966358i
$803$		0			0
$804$	15.3160			0.540154
$805$		0			0
$806$	9.54400			0.336173
$807$	−14.5440	−	25.1910i	−0.511973	−	0.886764i
$808$	17.3160			0.609175
$809$	−3.61400	−	6.25963i	−0.127061	−	0.220077i	0.795475	−	0.605986i	$-0.207221\pi$
$809$	−3.61400	−	6.25963i	−0.127061	−	0.220077i	−0.922537	+	0.385909i	$0.873888\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	17.4740	+	30.2659i	0.613595	+	1.06278i	0.990629	+	0.136579i	$0.0436107\pi$
$811$	17.4740	+	30.2659i	0.613595	+	1.06278i	−0.377034	+	0.926200i	$0.623056\pi$
$812$		0			0
$813$	−13.3160			−0.467013
$814$	−1.61400	−	5.86473i	−0.0565706	−	0.205559i
$815$	3.77200			0.132127
$816$	−3.88600	+	6.73075i	−0.136037	+	0.235623i
$817$		0			0
$818$	−15.2020	−	26.3306i	−0.531526	−	0.920630i
$819$		0			0
$820$	5.54400			0.193605
$821$	20.6580	+	35.7807i	0.720969	+	1.24876i	0.960612	+	0.277894i	$0.0896365\pi$
$821$	20.6580	+	35.7807i	0.720969	+	1.24876i	−0.239642	+	0.970861i	$0.577030\pi$
$822$	15.3160			0.534207
$823$	−11.0880	+	19.2050i	−0.386504	+	0.669444i	−0.991977	−	0.126422i	$-0.959651\pi$
$823$	−11.0880	+	19.2050i	−0.386504	+	0.669444i	0.605473	+	0.795866i	$0.292984\pi$
$824$	−3.22800			−0.112453
$825$	−1.00000			−0.0348155
$826$		0			0
$827$	1.45600	+	2.52186i	0.0506300	+	0.0876936i	0.890230	−	0.455512i	$-0.150544\pi$
$827$	1.45600	+	2.52186i	0.0506300	+	0.0876936i	−0.839600	+	0.543206i	$0.817210\pi$
$828$	−2.77200			−0.0963337
$829$	20.7720	−	35.9782i	0.721441	−	1.24957i	−0.238981	−	0.971024i	$-0.576813\pi$
$829$	20.7720	−	35.9782i	0.721441	−	1.24957i	0.960422	−	0.278549i	$-0.0898534\pi$
$830$	−4.77200	+	8.26535i	−0.165639	+	0.286894i
$831$	−5.88600	+	10.1949i	−0.204183	+	0.353656i
$832$	−0.500000	−	0.866025i	−0.0173344	−	0.0300240i
$833$	−27.2020	−	47.1153i	−0.942494	−	1.63245i
$834$	3.38600	−	5.86473i	0.117248	−	0.203079i
$835$	−5.11400	+	8.85771i	−0.176977	+	0.306534i
$836$	−2.38600	+	4.13267i	−0.0825216	+	0.142932i
$837$	−9.54400			−0.329889
$838$	−0.613999	−	1.06348i	−0.0212102	−	0.0367372i
$839$	−21.7720	+	37.7102i	−0.751653	+	1.30190i	0.195368	+	0.980730i	$0.437410\pi$
$839$	−21.7720	+	37.7102i	−0.751653	+	1.30190i	−0.947021	+	0.321171i	$0.895924\pi$
$840$		0			0
$841$	−28.9480			−0.998207
$842$	−11.7720	+	20.3897i	−0.405690	+	0.702676i
$843$	−31.8600			−1.09732
$844$	4.61400	+	7.99168i	0.158820	+	0.275085i
$845$	−12.0000			−0.412813
$846$	−1.50000	−	2.59808i	−0.0515711	−	0.0893237i
$847$		0			0
$848$	6.77200	+	11.7295i	0.232551	+	0.402791i
$849$	−13.8860	+	24.0513i	−0.476566	+	0.825437i
$850$	−7.77200			−0.266577
$851$	11.8420	−	12.0031i	0.405938	−	0.411462i
$852$	−3.54400			−0.121416
$853$	−5.27200	+	9.13138i	−0.180510	+	0.312652i	−0.942054	−	0.335460i	$-0.891108\pi$
$853$	−5.27200	+	9.13138i	−0.180510	+	0.312652i	0.761544	+	0.648113i	$0.224441\pi$
$854$		0			0
$855$	−2.38600	−	4.13267i	−0.0815995	−	0.141334i
$856$	2.00000	+	3.46410i	0.0683586	+	0.118401i
$857$	−5.31601			−0.181591			−0.0907956	−	0.995870i	$-0.528941\pi$
$857$	−5.31601			−0.181591			−0.0907956	+	0.995870i	$0.528941\pi$
$858$	0.500000	+	0.866025i	0.0170697	+	0.0295656i
$859$	−2.13999			−0.0730155			−0.0365078	−	0.999333i	$-0.511623\pi$
$859$	−2.13999			−0.0730155			−0.0365078	+	0.999333i	$0.511623\pi$
$860$		0			0
$861$		0			0
$862$	−31.5440			−1.07439
$863$	−24.1320	+	41.7979i	−0.821463	+	1.42282i	0.0831293	+	0.996539i	$0.473509\pi$
$863$	−24.1320	+	41.7979i	−0.821463	+	1.42282i	−0.904593	+	0.426277i	$0.859825\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−4.31601			−0.146749
$866$	14.7720	−	25.5859i	0.501973	−	0.869443i
$867$	21.7020	−	37.5890i	0.737039	−	1.27659i
$868$		0			0
$869$	−2.77200	−	4.80125i	−0.0940337	−	0.162871i
$870$	0.113999	+	0.197452i	0.00386493	+	0.00669426i
$871$	7.65800	−	13.2640i	0.259482	−	0.449435i
$872$	2.00000	−	3.46410i	0.0677285	−	0.117309i
$873$	0.227998	−	0.394904i	0.00771657	−	0.0133655i
$874$	−13.2280			−0.447444
$875$		0			0
$876$		0			0
$877$	−4.36799			−0.147497			−0.0737483	−	0.997277i	$-0.523496\pi$
$877$	−4.36799			−0.147497			−0.0737483	+	0.997277i	$0.523496\pi$
$878$	12.8600			0.434004
$879$	−14.7020	+	25.4646i	−0.495886	+	0.858900i
$880$	1.00000			0.0337100
$881$	18.4740	+	31.9979i	0.622405	+	1.07804i	0.989037	+	0.147671i	$0.0471777\pi$
$881$	18.4740	+	31.9979i	0.622405	+	1.07804i	−0.366631	+	0.930366i	$0.619489\pi$
$882$	−7.00000			−0.235702
$883$	15.2020	+	26.3306i	0.511588	+	0.886097i	0.999910	+	0.0134331i	$0.00427600\pi$
$883$	15.2020	+	26.3306i	0.511588	+	0.886097i	−0.488322	+	0.872664i	$0.662391\pi$
$884$	3.88600	+	6.73075i	0.130700	+	0.226380i
$885$	−6.27200	−	10.8634i	−0.210831	−	0.365170i
$886$	−7.54400	+	13.0666i	−0.253446	+	0.438981i
$887$	−30.1760			−1.01321			−0.506606	−	0.862178i	$-0.669100\pi$
$887$	−30.1760			−1.01321			−0.506606	+	0.862178i	$0.669100\pi$
$888$	−5.88600	−	1.53460i	−0.197521	−	0.0514978i
$889$		0			0
$890$	3.61400	−	6.25963i	0.121142	−	0.209823i
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$	−10.9300	−	18.9313i	−0.365964	−	0.633868i
$893$	−7.15800	−	12.3980i	−0.239533	−	0.414884i
$894$	17.3160			0.579134
$895$	10.1580	+	17.5942i	0.339545	+	0.588108i
$896$		0			0
$897$	−1.38600	+	2.40062i	−0.0462772	+	0.0801545i
$898$	−28.6320			−0.955463
$899$	2.17601			0.0725742
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−52.6320	−	91.1613i	−1.75343	−	3.03702i
$902$	5.54400			0.184595
$903$		0			0
$904$	−0.886001	+	1.53460i	−0.0294680	+	0.0510400i
$905$	5.77200	−	9.99740i	0.191868	−	0.332325i
$906$	−4.00000	−	6.92820i	−0.132891	−	0.230174i
$907$	−11.2280	−	19.4475i	−0.372820	−	0.645742i	0.617179	−	0.786823i	$-0.288276\pi$
$907$	−11.2280	−	19.4475i	−0.372820	−	0.645742i	−0.989998	+	0.141081i	$0.954942\pi$
$908$	−4.77200	+	8.26535i	−0.158364	+	0.274295i
$909$	−8.65800	+	14.9961i	−0.287168	+	0.497389i
$910$		0			0
$911$	14.0000			0.463841			0.231920	−	0.972735i	$-0.425499\pi$
$911$	14.0000			0.463841			0.231920	+	0.972735i	$0.425499\pi$
$912$	2.38600	+	4.13267i	0.0790084	+	0.136847i
$913$	−4.77200	+	8.26535i	−0.157930	+	0.273543i
$914$	−27.0880			−0.895992
$915$	10.0000			0.330590
$916$	−13.7720	+	23.8538i	−0.455040	+	0.788152i
$917$		0			0
$918$	−3.88600	−	6.73075i	−0.128257	−	0.222148i
$919$	18.8600			0.622134			0.311067	−	0.950388i	$-0.399314\pi$
$919$	18.8600			0.622134			0.311067	+	0.950388i	$0.399314\pi$
$920$	1.38600	+	2.40062i	0.0456951	+	0.0791462i
$921$	−5.22800	−	9.05516i	−0.172268	−	0.298378i
$922$	8.65800	+	14.9961i	0.285136	+	0.493870i
$923$	−1.77200	+	3.06920i	−0.0583262	+	0.101024i
$924$		0			0
$925$	−1.61400	−	5.86473i	−0.0530680	−	0.192831i
$926$	31.5440			1.03660
$927$	1.61400	−	2.79553i	0.0530107	−	0.0918172i
$928$	−0.113999	−	0.197452i	−0.00374220	−	0.00648169i
$929$	−4.61400	−	7.99168i	−0.151380	−	0.262199i	0.780355	−	0.625337i	$-0.215039\pi$
$929$	−4.61400	−	7.99168i	−0.151380	−	0.262199i	−0.931735	+	0.363139i	$0.881705\pi$
$930$	4.77200	+	8.26535i	0.156480	+	0.271031i
$931$	−33.4040			−1.09477
$932$	7.77200	+	13.4615i	0.254580	+	0.440946i
$933$	7.54400			0.246980
$934$	−3.00000	+	5.19615i	−0.0981630	+	0.170023i
$935$	−7.77200			−0.254172
$936$	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
$939$	8.45600			0.275951
$940$	−1.50000	+	2.59808i	−0.0489246	+	0.0847399i
$941$	−18.0880	+	31.3293i	−0.589652	+	1.02131i	0.404626	+	0.914482i	$0.367402\pi$
$941$	−18.0880	+	31.3293i	−0.589652	+	1.02131i	−0.994278	+	0.106825i	$0.965931\pi$
$942$	4.27200	−	7.39932i	0.139189	−	0.241083i
$943$	7.68399	+	13.3091i	0.250225	+	0.433403i
$944$	6.27200	+	10.8634i	0.204136	+	0.353574i
$945$		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	$0.156321\pi$
$948$	−5.54400			−0.180061
$949$		0			0
$950$	−2.38600	+	4.13267i	−0.0774121	+	0.134082i
$951$	8.31601			0.269665
$952$		0			0
$953$	11.3420	−	19.6449i	0.367403	−	0.636361i	−0.621755	−	0.783211i	$-0.713580\pi$
$953$	11.3420	−	19.6449i	0.367403	−	0.636361i	0.989159	+	0.146850i	$0.0469135\pi$
$954$	−13.5440			−0.438503
$955$	−10.7720	−	18.6577i	−0.348574	−	0.603748i
$956$	−16.0000			−0.517477
$957$	0.113999	+	0.197452i	0.00368507	+	0.00638272i
$958$	−8.22800	−	14.2513i	−0.265835	−	0.460439i
$959$		0			0
$960$	0.500000	−	0.866025i	0.0161374	−	0.0279508i
$961$	60.0880			1.93832
$962$	−4.27200	+	4.33013i	−0.137735	+	0.139609i
$963$	−4.00000			−0.128898
$964$	−13.2720	+	22.9878i	−0.427462	+	0.740387i
$965$	9.54400	+	16.5307i	0.307232	+	0.532142i
$966$		0			0
$967$	4.61400	+	7.99168i	0.148376	+	0.256995i	0.930627	−	0.365968i	$-0.119262\pi$
$967$	4.61400	+	7.99168i	0.148376	+	0.256995i	−0.782251	+	0.622963i	$0.785929\pi$
$968$	−10.0000			−0.321412
$969$	−18.5440	−	32.1192i	−0.595719	−	1.03182i
$970$	−0.455996			−0.0146412
$971$	22.6140	−	39.1686i	0.725718	−	1.25698i	−0.232960	−	0.972486i	$-0.574841\pi$
$971$	22.6140	−	39.1686i	0.725718	−	1.25698i	0.958678	−	0.284494i	$-0.0918255\pi$
$972$	−1.00000			−0.0320750
$973$		0			0
$974$	−11.3160	+	19.5999i	−0.362588	+	0.628021i
$975$	0.500000	+	0.866025i	0.0160128	+	0.0277350i
$976$	−10.0000			−0.320092
$977$	22.6580	−	39.2448i	0.724894	−	1.25555i	−0.234124	−	0.972207i	$-0.575222\pi$
$977$	22.6580	−	39.2448i	0.724894	−	1.25555i	0.959018	−	0.283346i	$-0.0914445\pi$
$978$	1.88600	−	3.26665i	0.0603077	−	0.104456i
$979$	3.61400	−	6.25963i	0.115504	−	0.200059i
$980$	3.50000	+	6.06218i	0.111803	+	0.193649i
$981$	2.00000	+	3.46410i	0.0638551	+	0.110600i
$982$	−6.15800	+	10.6660i	−0.196510	+	0.340365i
$983$	−10.9300	+	18.9313i	−0.348613	+	0.603815i	−0.986003	−	0.166726i	$-0.946681\pi$
$983$	−10.9300	+	18.9313i	−0.348613	+	0.603815i	0.637390	+	0.770541i	$0.280014\pi$
$984$	2.77200	−	4.80125i	0.0883682	−	0.153058i
$985$	−14.0000			−0.446077
$986$	0.886001	+	1.53460i	0.0282160	+	0.0488716i
$987$		0			0
$988$	4.77200			0.151818
$989$		0			0
$990$	−0.500000	+	0.866025i	−0.0158910	+	0.0275241i
$991$	55.9480			1.77725			0.888624	−	0.458637i	$-0.151662\pi$
$991$	55.9480			1.77725			0.888624	+	0.458637i	$0.151662\pi$
$992$	−4.77200	−	8.26535i	−0.151511	−	0.262425i
$993$	0.772002			0.0244987
$994$		0			0
$995$	−9.11400	−	15.7859i	−0.288933	−	0.500447i
$996$	4.77200	+	8.26535i	0.151207	+	0.261898i
$997$	12.8160	−	22.1980i	0.405887	−	0.703017i	−0.588537	−	0.808470i	$-0.700296\pi$
$997$	12.8160	−	22.1980i	0.405887	−	0.703017i	0.994424	+	0.105453i	$0.0336293\pi$
$998$	−39.5440			−1.25174
$999$	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.121.2	✓	4
37.26	even	3	inner	1110.2.i.j.211.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.i.j.121.2	✓	4	1.1	even	1	trivial
1110.2.i.j.211.2	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} +(3.88600 - 6.73075i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-2.38600 - 4.13267i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-0.500000 + 0.866025i) q^{22} -2.77200 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{26} -1.00000 q^{27} +0.227998 q^{29} +(0.500000 + 0.866025i) q^{30} +9.54400 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} +(3.88600 + 6.73075i) q^{34} +1.00000 q^{36} +(-4.27200 + 4.33013i) q^{37} +4.77200 q^{38} +(0.500000 - 0.866025i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-2.77200 - 4.80125i) q^{41} +(-0.500000 - 0.866025i) q^{44} +1.00000 q^{45} +(1.38600 - 2.40062i) q^{46} +3.00000 q^{47} -1.00000 q^{48} +(3.50000 - 6.06218i) q^{49} +(-0.500000 - 0.866025i) q^{50} +7.77200 q^{51} +(-0.500000 + 0.866025i) q^{52} +(6.77200 - 11.7295i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.500000 - 0.866025i) q^{55} +(2.38600 - 4.13267i) q^{57} +(-0.113999 + 0.197452i) q^{58} +(6.27200 - 10.8634i) q^{59} -1.00000 q^{60} +(5.00000 + 8.66025i) q^{61} +(-4.77200 + 8.26535i) q^{62} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} -1.00000 q^{66} +(7.65800 + 13.2640i) q^{67} -7.77200 q^{68} +(-1.38600 - 2.40062i) q^{69} +(-1.77200 - 3.06920i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-1.61400 - 5.86473i) q^{74} -1.00000 q^{75} +(-2.38600 + 4.13267i) q^{76} +(0.500000 + 0.866025i) q^{78} +(-2.77200 - 4.80125i) q^{79} +1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} +5.54400 q^{82} +(-4.77200 + 8.26535i) q^{83} -7.77200 q^{85} +(0.113999 + 0.197452i) q^{87} +1.00000 q^{88} +(3.61400 - 6.25963i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(1.38600 + 2.40062i) q^{92} +(4.77200 + 8.26535i) q^{93} +(-1.50000 + 2.59808i) q^{94} +(-2.38600 + 4.13267i) q^{95} +(0.500000 - 0.866025i) q^{96} -0.455996 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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