LMFDB - Embedded newform 38.2.c.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,2,Mod(7,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("38.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	38.c (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:	$0.303431527681$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	38.11
Dual form			38.2.c.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} -4.00000 q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} -4.00000 q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +3.00000 q^{11} +1.00000 q^{12} +(-1.00000 - 1.73205i) q^{13} +(-2.00000 + 3.46410i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +2.00000 q^{18} +(-3.50000 - 2.59808i) q^{19} +(2.00000 - 3.46410i) q^{21} +(1.50000 - 2.59808i) q^{22} +(3.00000 + 5.19615i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} -2.00000 q^{26} -5.00000 q^{27} +(2.00000 + 3.46410i) q^{28} +2.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +(-3.00000 - 5.19615i) q^{34} +(1.00000 - 1.73205i) q^{36} -10.0000 q^{37} +(-4.00000 + 1.73205i) q^{38} +2.00000 q^{39} +(-4.50000 + 7.79423i) q^{41} +(-2.00000 - 3.46410i) q^{42} +(2.00000 - 3.46410i) q^{43} +(-1.50000 - 2.59808i) q^{44} +6.00000 q^{46} +(-0.500000 - 0.866025i) q^{48} +9.00000 q^{49} +5.00000 q^{50} +(3.00000 + 5.19615i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(-2.50000 + 4.33013i) q^{54} +4.00000 q^{56} +(4.00000 - 1.73205i) q^{57} +(4.50000 - 7.79423i) q^{59} +(2.00000 + 3.46410i) q^{61} +(1.00000 - 1.73205i) q^{62} +(-4.00000 - 6.92820i) q^{63} +1.00000 q^{64} +(1.50000 + 2.59808i) q^{66} +(3.50000 + 6.06218i) q^{67} -6.00000 q^{68} -6.00000 q^{69} +(3.00000 - 5.19615i) q^{71} +(-1.00000 - 1.73205i) q^{72} +(0.500000 - 0.866025i) q^{73} +(-5.00000 + 8.66025i) q^{74} -5.00000 q^{75} +(-0.500000 + 4.33013i) q^{76} -12.0000 q^{77} +(1.00000 - 1.73205i) q^{78} +(2.00000 - 3.46410i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.50000 + 7.79423i) q^{82} +3.00000 q^{83} -4.00000 q^{84} +(-2.00000 - 3.46410i) q^{86} -3.00000 q^{88} +(-3.00000 - 5.19615i) q^{89} +(4.00000 + 6.92820i) q^{91} +(3.00000 - 5.19615i) q^{92} +(-1.00000 + 1.73205i) q^{93} -1.00000 q^{96} +(-8.50000 + 14.7224i) q^{97} +(4.50000 - 7.79423i) q^{98} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} + q^{6} - 8 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 + q^6 - 8 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q + q^{2} - q^{3} - q^{4} + q^{6} - 8 q^{7} - 2 q^{8} + 2 q^{9} + 6 q^{11} + 2 q^{12} - 2 q^{13} - 4 q^{14} - q^{16} + 6 q^{17} + 4 q^{18} - 7 q^{19} + 4 q^{21} + 3 q^{22} + 6 q^{23} + q^{24} + 5 q^{25} - 4 q^{26} - 10 q^{27} + 4 q^{28} + 4 q^{31} + q^{32} - 3 q^{33} - 6 q^{34} + 2 q^{36} - 20 q^{37} - 8 q^{38} + 4 q^{39} - 9 q^{41} - 4 q^{42} + 4 q^{43} - 3 q^{44} + 12 q^{46} - q^{48} + 18 q^{49} + 10 q^{50} + 6 q^{51} - 2 q^{52} - 6 q^{53} - 5 q^{54} + 8 q^{56} + 8 q^{57} + 9 q^{59} + 4 q^{61} + 2 q^{62} - 8 q^{63} + 2 q^{64} + 3 q^{66} + 7 q^{67} - 12 q^{68} - 12 q^{69} + 6 q^{71} - 2 q^{72} + q^{73} - 10 q^{74} - 10 q^{75} - q^{76} - 24 q^{77} + 2 q^{78} + 4 q^{79} - q^{81} + 9 q^{82} + 6 q^{83} - 8 q^{84} - 4 q^{86} - 6 q^{88} - 6 q^{89} + 8 q^{91} + 6 q^{92} - 2 q^{93} - 2 q^{96} - 17 q^{97} + 9 q^{98} + 6 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 + q^6 - 8 * q^7 - 2 * q^8 + 2 * q^9 + 6 * q^11 + 2 * q^12 - 2 * q^13 - 4 * q^14 - q^16 + 6 * q^17 + 4 * q^18 - 7 * q^19 + 4 * q^21 + 3 * q^22 + 6 * q^23 + q^24 + 5 * q^25 - 4 * q^26 - 10 * q^27 + 4 * q^28 + 4 * q^31 + q^32 - 3 * q^33 - 6 * q^34 + 2 * q^36 - 20 * q^37 - 8 * q^38 + 4 * q^39 - 9 * q^41 - 4 * q^42 + 4 * q^43 - 3 * q^44 + 12 * q^46 - q^48 + 18 * q^49 + 10 * q^50 + 6 * q^51 - 2 * q^52 - 6 * q^53 - 5 * q^54 + 8 * q^56 + 8 * q^57 + 9 * q^59 + 4 * q^61 + 2 * q^62 - 8 * q^63 + 2 * q^64 + 3 * q^66 + 7 * q^67 - 12 * q^68 - 12 * q^69 + 6 * q^71 - 2 * q^72 + q^73 - 10 * q^74 - 10 * q^75 - q^76 - 24 * q^77 + 2 * q^78 + 4 * q^79 - q^81 + 9 * q^82 + 6 * q^83 - 8 * q^84 - 4 * q^86 - 6 * q^88 - 6 * q^89 + 8 * q^91 + 6 * q^92 - 2 * q^93 - 2 * q^96 - 17 * q^97 + 9 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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	−0.973494	−	0.228714i	$-0.926548\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	0.684819	+	0.728714i	$0.259881\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−4.00000			−1.51186			−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000			−1.51186			−0.755929	+	0.654654i	$0.772814\pi$
$8$	−1.00000			−0.353553
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$		0			0
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$	1.00000			0.288675
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−2.00000	+	3.46410i	−0.534522	+	0.925820i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$	2.00000			0.471405
$19$	−3.50000	−	2.59808i	−0.802955	−	0.596040i
$19$	−3.50000	−	2.59808i	−0.802955	−	0.596040i
$20$		0			0
$21$	2.00000	−	3.46410i	0.436436	−	0.755929i
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$	−2.00000			−0.392232
$27$	−5.00000			−0.962250
$28$	2.00000	+	3.46410i	0.377964	+	0.654654i
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$		0			0
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$	−3.00000	−	5.19615i	−0.514496	−	0.891133i
$35$		0			0
$36$	1.00000	−	1.73205i	0.166667	−	0.288675i
$37$	−10.0000			−1.64399			−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000			−1.64399			−0.821995	+	0.569495i	$0.807139\pi$
$38$	−4.00000	+	1.73205i	−0.648886	+	0.280976i
$39$	2.00000			0.320256
$40$		0			0
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	0.264704	+	0.964330i	$0.414726\pi$
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	−0.967486	+	0.252924i	$0.918608\pi$
$42$	−2.00000	−	3.46410i	−0.308607	−	0.534522i
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	−0.672264	−	0.740312i	$-0.734678\pi$
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	0.977261	+	0.212041i	$0.0680112\pi$
$44$	−1.50000	−	2.59808i	−0.226134	−	0.391675i
$45$		0			0
$46$	6.00000			0.884652
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	9.00000			1.28571
$50$	5.00000			0.707107
$51$	3.00000	+	5.19615i	0.420084	+	0.727607i
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$	−2.50000	+	4.33013i	−0.340207	+	0.589256i
$55$		0			0
$56$	4.00000			0.534522
$57$	4.00000	−	1.73205i	0.529813	−	0.229416i
$58$		0			0
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	−0.408919	−	0.912571i	$-0.634094\pi$
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	0.994769	−	0.102151i	$-0.0325726\pi$
$60$		0			0
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	0.965187	−	0.261562i	$-0.0842377\pi$
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	−0.709113	+	0.705095i	$0.750904\pi$
$62$	1.00000	−	1.73205i	0.127000	−	0.219971i
$63$	−4.00000	−	6.92820i	−0.503953	−	0.872872i
$64$	1.00000			0.125000
$65$		0			0
$66$	1.50000	+	2.59808i	0.184637	+	0.319801i
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	0.996659	−	0.0816792i	$-0.0260283\pi$
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	−0.569066	+	0.822292i	$0.692695\pi$
$68$	−6.00000			−0.727607
$69$	−6.00000			−0.722315
$70$		0			0
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$	−1.00000	−	1.73205i	−0.117851	−	0.204124i
$73$	0.500000	−	0.866025i	0.0585206	−	0.101361i	−0.835281	−	0.549823i	$-0.814695\pi$
$73$	0.500000	−	0.866025i	0.0585206	−	0.101361i	0.893801	+	0.448463i	$0.148028\pi$
$74$	−5.00000	+	8.66025i	−0.581238	+	1.00673i
$75$	−5.00000			−0.577350
$76$	−0.500000	+	4.33013i	−0.0573539	+	0.496700i
$77$	−12.0000			−1.36753
$78$	1.00000	−	1.73205i	0.113228	−	0.196116i
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.50000	+	7.79423i	0.496942	+	0.860729i
$83$	3.00000			0.329293			0.164646	−	0.986353i	$-0.447352\pi$
$83$	3.00000			0.329293			0.164646	+	0.986353i	$0.447352\pi$
$84$	−4.00000			−0.436436
$85$		0			0
$86$	−2.00000	−	3.46410i	−0.215666	−	0.373544i
$87$		0			0
$88$	−3.00000			−0.319801
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$	4.00000	+	6.92820i	0.419314	+	0.726273i
$92$	3.00000	−	5.19615i	0.312772	−	0.541736i
$93$	−1.00000	+	1.73205i	−0.103695	+	0.179605i
$94$		0			0
$95$		0			0
$96$	−1.00000			−0.102062
$97$	−8.50000	+	14.7224i	−0.863044	+	1.49484i	0.00593185	+	0.999982i	$0.498112\pi$
$97$	−8.50000	+	14.7224i	−0.863044	+	1.49484i	−0.868976	+	0.494854i	$0.835222\pi$
$98$	4.50000	−	7.79423i	0.454569	−	0.787336i
$99$	3.00000	+	5.19615i	0.301511	+	0.522233i
$100$	2.50000	−	4.33013i	0.250000	−	0.433013i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$	6.00000			0.594089
$103$	2.00000			0.197066			0.0985329	−	0.995134i	$-0.468585\pi$
$103$	2.00000			0.197066			0.0985329	+	0.995134i	$0.468585\pi$
$104$	1.00000	+	1.73205i	0.0980581	+	0.169842i
$105$		0			0
$106$	−6.00000			−0.582772
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$	2.50000	+	4.33013i	0.240563	+	0.416667i
$109$	8.00000	−	13.8564i	0.766261	−	1.32720i	−0.173316	−	0.984866i	$-0.555448\pi$
$109$	8.00000	−	13.8564i	0.766261	−	1.32720i	0.939577	−	0.342337i	$-0.111218\pi$
$110$		0			0
$111$	5.00000	−	8.66025i	0.474579	−	0.821995i
$112$	2.00000	−	3.46410i	0.188982	−	0.327327i
$113$	15.0000			1.41108			0.705541	−	0.708669i	$-0.250704\pi$
$113$	15.0000			1.41108			0.705541	+	0.708669i	$0.250704\pi$
$114$	0.500000	−	4.33013i	0.0468293	−	0.405554i
$115$		0			0
$116$		0			0
$117$	2.00000	−	3.46410i	0.184900	−	0.320256i
$118$	−4.50000	−	7.79423i	−0.414259	−	0.717517i
$119$	−12.0000	+	20.7846i	−1.10004	+	1.90532i
$120$		0			0
$121$	−2.00000			−0.181818
$122$	4.00000			0.362143
$123$	−4.50000	−	7.79423i	−0.405751	−	0.702782i
$124$	−1.00000	−	1.73205i	−0.0898027	−	0.155543i
$125$		0			0
$126$	−8.00000			−0.712697
$127$	−1.00000	−	1.73205i	−0.0887357	−	0.153695i	0.818241	−	0.574875i	$-0.194949\pi$
$127$	−1.00000	−	1.73205i	−0.0887357	−	0.153695i	−0.906977	+	0.421180i	$0.861616\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$		0			0
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	−0.992865	−	0.119241i	$-0.961954\pi$
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	0.599699	+	0.800226i	$0.295287\pi$
$132$	3.00000			0.261116
$133$	14.0000	+	10.3923i	1.21395	+	0.901127i
$134$	7.00000			0.604708
$135$		0			0
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	0.607233	−	0.794524i	$-0.292279\pi$
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	−0.991694	+	0.128618i	$0.958946\pi$
$138$	−3.00000	+	5.19615i	−0.255377	+	0.442326i
$139$	−5.50000	−	9.52628i	−0.466504	−	0.808008i	0.532764	−	0.846264i	$-0.321153\pi$
$139$	−5.50000	−	9.52628i	−0.466504	−	0.808008i	−0.999268	+	0.0382553i	$0.987820\pi$
$140$		0			0
$141$		0			0
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	−3.00000	−	5.19615i	−0.250873	−	0.434524i
$144$	−2.00000			−0.166667
$145$		0			0
$146$	−0.500000	−	0.866025i	−0.0413803	−	0.0716728i
$147$	−4.50000	+	7.79423i	−0.371154	+	0.642857i
$148$	5.00000	+	8.66025i	0.410997	+	0.711868i
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	0.216394	+	0.976306i	$0.430570\pi$
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	−0.953703	+	0.300750i	$0.902763\pi$
$150$	−2.50000	+	4.33013i	−0.204124	+	0.353553i
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$	3.50000	+	2.59808i	0.283887	+	0.210732i
$153$	12.0000			0.970143
$154$	−6.00000	+	10.3923i	−0.483494	+	0.837436i
$155$		0			0
$156$	−1.00000	−	1.73205i	−0.0800641	−	0.138675i
$157$	8.00000	−	13.8564i	0.638470	−	1.10586i	−0.347299	−	0.937754i	$-0.612901\pi$
$157$	8.00000	−	13.8564i	0.638470	−	1.10586i	0.985769	−	0.168107i	$-0.0537655\pi$
$158$	−2.00000	−	3.46410i	−0.159111	−	0.275589i
$159$	6.00000			0.475831
$160$		0			0
$161$	−12.0000	−	20.7846i	−0.945732	−	1.63806i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−19.0000			−1.48819			−0.744097	−	0.668071i	$-0.767120\pi$
$163$	−19.0000			−1.48819			−0.744097	+	0.668071i	$0.767120\pi$
$164$	9.00000			0.702782
$165$		0			0
$166$	1.50000	−	2.59808i	0.116423	−	0.201650i
$167$	12.0000	+	20.7846i	0.928588	+	1.60836i	0.785687	+	0.618624i	$0.212310\pi$
$167$	12.0000	+	20.7846i	0.928588	+	1.60836i	0.142901	+	0.989737i	$0.454357\pi$
$168$	−2.00000	+	3.46410i	−0.154303	+	0.267261i
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$	1.00000	−	8.66025i	0.0764719	−	0.662266i
$172$	−4.00000			−0.304997
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		0			0
$175$	−10.0000	−	17.3205i	−0.755929	−	1.30931i
$176$	−1.50000	+	2.59808i	−0.113067	+	0.195837i
$177$	4.50000	+	7.79423i	0.338241	+	0.585850i
$178$	−6.00000			−0.449719
$179$	9.00000			0.672692			0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000			0.672692			0.336346	+	0.941739i	$0.390809\pi$
$180$		0			0
$181$	−1.00000	−	1.73205i	−0.0743294	−	0.128742i	0.826465	−	0.562988i	$-0.190348\pi$
$181$	−1.00000	−	1.73205i	−0.0743294	−	0.128742i	−0.900794	+	0.434246i	$0.857015\pi$
$182$	8.00000			0.592999
$183$	−4.00000			−0.295689
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$		0			0
$186$	1.00000	+	1.73205i	0.0733236	+	0.127000i
$187$	9.00000	−	15.5885i	0.658145	−	1.13994i
$188$		0			0
$189$	20.0000			1.45479
$190$		0			0
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	0.827788	+	0.561041i	$0.189599\pi$
$194$	8.50000	+	14.7224i	0.610264	+	1.05701i
$195$		0			0
$196$	−4.50000	−	7.79423i	−0.321429	−	0.556731i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	6.00000			0.426401
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	0.987022	−	0.160585i	$-0.0513380\pi$
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	−0.632581	+	0.774494i	$0.718005\pi$
$200$	−2.50000	−	4.33013i	−0.176777	−	0.306186i
$201$	−7.00000			−0.493742
$202$		0			0
$203$		0			0
$204$	3.00000	−	5.19615i	0.210042	−	0.363803i
$205$		0			0
$206$	1.00000	−	1.73205i	0.0696733	−	0.120678i
$207$	−6.00000	+	10.3923i	−0.417029	+	0.722315i
$208$	2.00000			0.138675
$209$	−10.5000	−	7.79423i	−0.726300	−	0.539138i
$210$		0			0
$211$	−10.0000	+	17.3205i	−0.688428	+	1.19239i	0.283918	+	0.958849i	$0.408366\pi$
$211$	−10.0000	+	17.3205i	−0.688428	+	1.19239i	−0.972346	+	0.233544i	$0.924968\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$	3.00000	+	5.19615i	0.205557	+	0.356034i
$214$		0			0
$215$		0			0
$216$	5.00000			0.340207
$217$	−8.00000			−0.543075
$218$	−8.00000	−	13.8564i	−0.541828	−	0.938474i
$219$	0.500000	+	0.866025i	0.0337869	+	0.0585206i
$220$		0			0
$221$	−12.0000			−0.807207
$222$	−5.00000	−	8.66025i	−0.335578	−	0.581238i
$223$	−7.00000	+	12.1244i	−0.468755	+	0.811907i	−0.999362	−	0.0357107i	$-0.988630\pi$
$223$	−7.00000	+	12.1244i	−0.468755	+	0.811907i	0.530607	+	0.847618i	$0.321964\pi$
$224$	−2.00000	−	3.46410i	−0.133631	−	0.231455i
$225$	−5.00000	+	8.66025i	−0.333333	+	0.577350i
$226$	7.50000	−	12.9904i	0.498893	−	0.864107i
$227$	3.00000			0.199117			0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000			0.199117			0.0995585	+	0.995032i	$0.468257\pi$
$228$	−3.50000	−	2.59808i	−0.231793	−	0.172062i
$229$	−16.0000			−1.05731			−0.528655	−	0.848837i	$-0.677303\pi$
$229$	−16.0000			−1.05731			−0.528655	+	0.848837i	$0.677303\pi$
$230$		0			0
$231$	6.00000	−	10.3923i	0.394771	−	0.683763i
$232$		0			0
$233$	−1.50000	+	2.59808i	−0.0982683	+	0.170206i	−0.910968	−	0.412477i	$-0.864664\pi$
$233$	−1.50000	+	2.59808i	−0.0982683	+	0.170206i	0.812700	+	0.582683i	$0.197997\pi$
$234$	−2.00000	−	3.46410i	−0.130744	−	0.226455i
$235$		0			0
$236$	−9.00000			−0.585850
$237$	2.00000	+	3.46410i	0.129914	+	0.225018i
$238$	12.0000	+	20.7846i	0.777844	+	1.34727i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	−2.50000	−	4.33013i	−0.161039	−	0.278928i	0.774202	−	0.632938i	$-0.218151\pi$
$241$	−2.50000	−	4.33013i	−0.161039	−	0.278928i	−0.935242	+	0.354010i	$0.884818\pi$
$242$	−1.00000	+	1.73205i	−0.0642824	+	0.111340i
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$	2.00000	−	3.46410i	0.128037	−	0.221766i
$245$		0			0
$246$	−9.00000			−0.573819
$247$	−1.00000	+	8.66025i	−0.0636285	+	0.551039i
$248$	−2.00000			−0.127000
$249$	−1.50000	+	2.59808i	−0.0950586	+	0.164646i
$250$		0			0
$251$	1.50000	+	2.59808i	0.0946792	+	0.163989i	0.909475	−	0.415759i	$-0.136484\pi$
$251$	1.50000	+	2.59808i	0.0946792	+	0.163989i	−0.814795	+	0.579748i	$0.803151\pi$
$252$	−4.00000	+	6.92820i	−0.251976	+	0.436436i
$253$	9.00000	+	15.5885i	0.565825	+	0.980038i
$254$	−2.00000			−0.125491
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	0.815442	−	0.578838i	$-0.196494\pi$
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	−0.909010	+	0.416775i	$0.863160\pi$
$258$	4.00000			0.249029
$259$	40.0000			2.48548
$260$		0			0
$261$		0			0
$262$	4.50000	+	7.79423i	0.278011	+	0.481529i
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	−0.619586	−	0.784929i	$-0.712699\pi$
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	0.989561	+	0.144112i	$0.0460326\pi$
$264$	1.50000	−	2.59808i	0.0923186	−	0.159901i
$265$		0			0
$266$	16.0000	−	6.92820i	0.981023	−	0.424795i
$267$	6.00000			0.367194
$268$	3.50000	−	6.06218i	0.213797	−	0.370306i
$269$	−6.00000	+	10.3923i	−0.365826	+	0.633630i	−0.988908	−	0.148527i	$-0.952547\pi$
$269$	−6.00000	+	10.3923i	−0.365826	+	0.633630i	0.623082	+	0.782157i	$0.285880\pi$
$270$		0			0
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$	3.00000	+	5.19615i	0.181902	+	0.315063i
$273$	−8.00000			−0.484182
$274$	−9.00000			−0.543710
$275$	7.50000	+	12.9904i	0.452267	+	0.783349i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	8.00000			0.480673			0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000			0.480673			0.240337	+	0.970690i	$0.422742\pi$
$278$	−11.0000			−0.659736
$279$	2.00000	+	3.46410i	0.119737	+	0.207390i
$280$		0			0
$281$	−13.5000	−	23.3827i	−0.805342	−	1.39489i	−0.916060	−	0.401042i	$-0.868648\pi$
$281$	−13.5000	−	23.3827i	−0.805342	−	1.39489i	0.110717	−	0.993852i	$-0.464685\pi$
$282$		0			0
$283$	−2.50000	+	4.33013i	−0.148610	+	0.257399i	−0.930714	−	0.365748i	$-0.880813\pi$
$283$	−2.50000	+	4.33013i	−0.148610	+	0.257399i	0.782104	+	0.623148i	$0.214146\pi$
$284$	−6.00000			−0.356034
$285$		0			0
$286$	−6.00000			−0.354787
$287$	18.0000	−	31.1769i	1.06251	−	1.84032i
$288$	−1.00000	+	1.73205i	−0.0589256	+	0.102062i
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$		0			0
$291$	−8.50000	−	14.7224i	−0.498279	−	0.863044i
$292$	−1.00000			−0.0585206
$293$	24.0000			1.40209			0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000			1.40209			0.701047	+	0.713115i	$0.252716\pi$
$294$	4.50000	+	7.79423i	0.262445	+	0.454569i
$295$		0			0
$296$	10.0000			0.581238
$297$	−15.0000			−0.870388
$298$	9.00000	+	15.5885i	0.521356	+	0.903015i
$299$	6.00000	−	10.3923i	0.346989	−	0.601003i
$300$	2.50000	+	4.33013i	0.144338	+	0.250000i
$301$	−8.00000	+	13.8564i	−0.461112	+	0.798670i
$302$	−5.00000	+	8.66025i	−0.287718	+	0.498342i
$303$		0			0
$304$	4.00000	−	1.73205i	0.229416	−	0.0993399i
$305$		0			0
$306$	6.00000	−	10.3923i	0.342997	−	0.594089i
$307$	3.50000	−	6.06218i	0.199756	−	0.345987i	−0.748694	−	0.662916i	$-0.769319\pi$
$307$	3.50000	−	6.06218i	0.199756	−	0.345987i	0.948449	+	0.316929i	$0.102652\pi$
$308$	6.00000	+	10.3923i	0.341882	+	0.592157i
$309$	−1.00000	+	1.73205i	−0.0568880	+	0.0985329i
$310$		0			0
$311$	−30.0000			−1.70114			−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000			−1.70114			−0.850572	+	0.525859i	$0.823744\pi$
$312$	−2.00000			−0.113228
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	0.999065	+	0.0432311i	$0.0137652\pi$
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	−0.462093	+	0.886831i	$0.652902\pi$
$314$	−8.00000	−	13.8564i	−0.451466	−	0.781962i
$315$		0			0
$316$	−4.00000			−0.225018
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	0.999980	+	0.00635137i	$0.00202172\pi$
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	−0.494489	+	0.869184i	$0.664645\pi$
$318$	3.00000	−	5.19615i	0.168232	−	0.291386i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	−24.0000			−1.33747
$323$	−24.0000	+	10.3923i	−1.33540	+	0.578243i
$324$	1.00000			0.0555556
$325$	5.00000	−	8.66025i	0.277350	−	0.480384i
$326$	−9.50000	+	16.4545i	−0.526156	+	0.911330i
$327$	8.00000	+	13.8564i	0.442401	+	0.766261i
$328$	4.50000	−	7.79423i	0.248471	−	0.430364i
$329$		0			0
$330$		0			0
$331$	5.00000			0.274825			0.137412	−	0.990514i	$-0.456121\pi$
$331$	5.00000			0.274825			0.137412	+	0.990514i	$0.456121\pi$
$332$	−1.50000	−	2.59808i	−0.0823232	−	0.142588i
$333$	−10.0000	−	17.3205i	−0.547997	−	0.949158i
$334$	24.0000			1.31322
$335$		0			0
$336$	2.00000	+	3.46410i	0.109109	+	0.188982i
$337$	−5.50000	+	9.52628i	−0.299604	+	0.518930i	−0.976045	−	0.217567i	$-0.930188\pi$
$337$	−5.50000	+	9.52628i	−0.299604	+	0.518930i	0.676441	+	0.736497i	$0.263521\pi$
$338$	−4.50000	−	7.79423i	−0.244768	−	0.423950i
$339$	−7.50000	+	12.9904i	−0.407344	+	0.705541i
$340$		0			0
$341$	6.00000			0.324918
$342$	−7.00000	−	5.19615i	−0.378517	−	0.280976i
$343$	−8.00000			−0.431959
$344$	−2.00000	+	3.46410i	−0.107833	+	0.186772i
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	4.50000	−	7.79423i	0.241573	−	0.418416i	−0.719590	−	0.694399i	$-0.755670\pi$
$347$	4.50000	−	7.79423i	0.241573	−	0.418416i	0.961162	+	0.275983i	$0.0890035\pi$
$348$		0			0
$349$	−4.00000			−0.214115			−0.107058	−	0.994253i	$-0.534143\pi$
$349$	−4.00000			−0.214115			−0.107058	+	0.994253i	$0.534143\pi$
$350$	−20.0000			−1.06904
$351$	5.00000	+	8.66025i	0.266880	+	0.462250i
$352$	1.50000	+	2.59808i	0.0799503	+	0.138478i
$353$	3.00000			0.159674			0.0798369	−	0.996808i	$-0.474560\pi$
$353$	3.00000			0.159674			0.0798369	+	0.996808i	$0.474560\pi$
$354$	9.00000			0.478345
$355$		0			0
$356$	−3.00000	+	5.19615i	−0.159000	+	0.275396i
$357$	−12.0000	−	20.7846i	−0.635107	−	1.10004i
$358$	4.50000	−	7.79423i	0.237832	−	0.411938i
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	−0.775934	−	0.630814i	$-0.782721\pi$
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	0.934268	+	0.356572i	$0.116054\pi$
$360$		0			0
$361$	5.50000	+	18.1865i	0.289474	+	0.957186i
$362$	−2.00000			−0.105118
$363$	1.00000	−	1.73205i	0.0524864	−	0.0909091i
$364$	4.00000	−	6.92820i	0.209657	−	0.363137i
$365$		0			0
$366$	−2.00000	+	3.46410i	−0.104542	+	0.181071i
$367$	11.0000	+	19.0526i	0.574195	+	0.994535i	0.996129	+	0.0879086i	$0.0280183\pi$
$367$	11.0000	+	19.0526i	0.574195	+	0.994535i	−0.421933	+	0.906627i	$0.638648\pi$
$368$	−6.00000			−0.312772
$369$	−18.0000			−0.937043
$370$		0			0
$371$	12.0000	+	20.7846i	0.623009	+	1.07908i
$372$	2.00000			0.103695
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$	−9.00000	−	15.5885i	−0.465379	−	0.806060i
$375$		0			0
$376$		0			0
$377$		0			0
$378$	10.0000	−	17.3205i	0.514344	−	0.890871i
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$		0			0
$381$	2.00000			0.102463
$382$	6.00000	−	10.3923i	0.306987	−	0.531717i
$383$	18.0000	−	31.1769i	0.919757	−	1.59307i	0.119974	−	0.992777i	$-0.461719\pi$
$383$	18.0000	−	31.1769i	0.919757	−	1.59307i	0.799783	−	0.600289i	$-0.204948\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$		0			0
$386$	1.00000	+	1.73205i	0.0508987	+	0.0881591i
$387$	8.00000			0.406663
$388$	17.0000			0.863044
$389$	18.0000	+	31.1769i	0.912636	+	1.58073i	0.810326	+	0.585980i	$0.199290\pi$
$389$	18.0000	+	31.1769i	0.912636	+	1.58073i	0.102311	+	0.994753i	$0.467376\pi$
$390$		0			0
$391$	36.0000			1.82060
$392$	−9.00000			−0.454569
$393$	−4.50000	−	7.79423i	−0.226995	−	0.393167i
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$		0			0
$396$	3.00000	−	5.19615i	0.150756	−	0.261116i
$397$	5.00000	−	8.66025i	0.250943	−	0.434646i	−0.712843	−	0.701324i	$-0.752593\pi$
$397$	5.00000	−	8.66025i	0.250943	−	0.434646i	0.963786	+	0.266678i	$0.0859261\pi$
$398$	10.0000			0.501255
$399$	−16.0000	+	6.92820i	−0.801002	+	0.346844i
$400$	−5.00000			−0.250000
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	−0.302556	−	0.953131i	$-0.597840\pi$
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	0.976714	−	0.214544i	$-0.0688266\pi$
$402$	−3.50000	+	6.06218i	−0.174564	+	0.302354i
$403$	−2.00000	−	3.46410i	−0.0996271	−	0.172559i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−30.0000			−1.48704
$408$	−3.00000	−	5.19615i	−0.148522	−	0.257248i
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	0.797574	−	0.603220i	$-0.206116\pi$
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	−0.921192	+	0.389109i	$0.872783\pi$
$410$		0			0
$411$	9.00000			0.443937
$412$	−1.00000	−	1.73205i	−0.0492665	−	0.0853320i
$413$	−18.0000	+	31.1769i	−0.885722	+	1.53412i
$414$	6.00000	+	10.3923i	0.294884	+	0.510754i
$415$		0			0
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$	11.0000			0.538672
$418$	−12.0000	+	5.19615i	−0.586939	+	0.254152i
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	−0.718076	−	0.695965i	$-0.754977\pi$
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	0.961761	+	0.273890i	$0.0883103\pi$
$422$	10.0000	+	17.3205i	0.486792	+	0.843149i
$423$		0			0
$424$	3.00000	+	5.19615i	0.145693	+	0.252347i
$425$	30.0000			1.45521
$426$	6.00000			0.290701
$427$	−8.00000	−	13.8564i	−0.387147	−	0.670559i
$428$		0			0
$429$	6.00000			0.289683
$430$		0			0
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	0.959985	+	0.280052i	$0.0903517\pi$
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	−0.237460	+	0.971397i	$0.576315\pi$
$432$	2.50000	−	4.33013i	0.120281	−	0.208333i
$433$	−13.0000	−	22.5167i	−0.624740	−	1.08208i	−0.988591	−	0.150624i	$-0.951872\pi$
$433$	−13.0000	−	22.5167i	−0.624740	−	1.08208i	0.363851	−	0.931457i	$-0.381462\pi$
$434$	−4.00000	+	6.92820i	−0.192006	+	0.332564i
$435$		0			0
$436$	−16.0000			−0.766261
$437$	3.00000	−	25.9808i	0.143509	−	1.24283i
$438$	1.00000			0.0477818
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	−0.983310	−	0.181938i	$-0.941763\pi$
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	0.649218	+	0.760602i	$0.275096\pi$
$440$		0			0
$441$	9.00000	+	15.5885i	0.428571	+	0.742307i
$442$	−6.00000	+	10.3923i	−0.285391	+	0.494312i
$443$	−4.50000	−	7.79423i	−0.213801	−	0.370315i	0.739100	−	0.673596i	$-0.235251\pi$
$443$	−4.50000	−	7.79423i	−0.213801	−	0.370315i	−0.952901	+	0.303281i	$0.901918\pi$
$444$	−10.0000			−0.474579
$445$		0			0
$446$	7.00000	+	12.1244i	0.331460	+	0.574105i
$447$	−9.00000	−	15.5885i	−0.425685	−	0.737309i
$448$	−4.00000			−0.188982
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$	5.00000	+	8.66025i	0.235702	+	0.408248i
$451$	−13.5000	+	23.3827i	−0.635690	+	1.10105i
$452$	−7.50000	−	12.9904i	−0.352770	−	0.611016i
$453$	5.00000	−	8.66025i	0.234920	−	0.406894i
$454$	1.50000	−	2.59808i	0.0703985	−	0.121934i
$455$		0			0
$456$	−4.00000	+	1.73205i	−0.187317	+	0.0811107i
$457$	5.00000			0.233890			0.116945	−	0.993138i	$-0.462690\pi$
$457$	5.00000			0.233890			0.116945	+	0.993138i	$0.462690\pi$
$458$	−8.00000	+	13.8564i	−0.373815	+	0.647467i
$459$	−15.0000	+	25.9808i	−0.700140	+	1.21268i
$460$		0			0
$461$	−3.00000	+	5.19615i	−0.139724	+	0.242009i	−0.927392	−	0.374091i	$-0.877955\pi$
$461$	−3.00000	+	5.19615i	−0.139724	+	0.242009i	0.787668	+	0.616100i	$0.211288\pi$
$462$	−6.00000	−	10.3923i	−0.279145	−	0.483494i
$463$	−34.0000			−1.58011			−0.790057	−	0.613033i	$-0.789949\pi$
$463$	−34.0000			−1.58011			−0.790057	+	0.613033i	$0.789949\pi$
$464$		0			0
$465$		0			0
$466$	1.50000	+	2.59808i	0.0694862	+	0.120354i
$467$	−27.0000			−1.24941			−0.624705	−	0.780860i	$-0.714781\pi$
$467$	−27.0000			−1.24941			−0.624705	+	0.780860i	$0.714781\pi$
$468$	−4.00000			−0.184900
$469$	−14.0000	−	24.2487i	−0.646460	−	1.11970i
$470$		0			0
$471$	8.00000	+	13.8564i	0.368621	+	0.638470i
$472$	−4.50000	+	7.79423i	−0.207129	+	0.358758i
$473$	6.00000	−	10.3923i	0.275880	−	0.477839i
$474$	4.00000			0.183726
$475$	2.50000	−	21.6506i	0.114708	−	0.993399i
$476$	24.0000			1.10004
$477$	6.00000	−	10.3923i	0.274721	−	0.475831i
$478$	−6.00000	+	10.3923i	−0.274434	+	0.475333i
$479$	−18.0000	−	31.1769i	−0.822441	−	1.42451i	−0.903859	−	0.427830i	$-0.859278\pi$
$479$	−18.0000	−	31.1769i	−0.822441	−	1.42451i	0.0814184	−	0.996680i	$-0.474055\pi$
$480$		0			0
$481$	10.0000	+	17.3205i	0.455961	+	0.789747i
$482$	−5.00000			−0.227744
$483$	24.0000			1.09204
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$		0			0
$486$	−16.0000			−0.725775
$487$	2.00000			0.0906287			0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000			0.0906287			0.0453143	+	0.998973i	$0.485571\pi$
$488$	−2.00000	−	3.46410i	−0.0905357	−	0.156813i
$489$	9.50000	−	16.4545i	0.429605	−	0.744097i
$490$		0			0
$491$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$	−4.50000	+	7.79423i	−0.202876	+	0.351391i
$493$		0			0
$494$	7.00000	+	5.19615i	0.314945	+	0.233786i
$495$		0			0
$496$	−1.00000	+	1.73205i	−0.0449013	+	0.0777714i
$497$	−12.0000	+	20.7846i	−0.538274	+	0.932317i
$498$	1.50000	+	2.59808i	0.0672166	+	0.116423i
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	−0.437955	−	0.898997i	$-0.644297\pi$
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	0.997532	−	0.0702185i	$-0.0223697\pi$
$500$		0			0
$501$	−24.0000			−1.07224
$502$	3.00000			0.133897
$503$	−3.00000	−	5.19615i	−0.133763	−	0.231685i	0.791361	−	0.611349i	$-0.209373\pi$
$503$	−3.00000	−	5.19615i	−0.133763	−	0.231685i	−0.925124	+	0.379664i	$0.876040\pi$
$504$	4.00000	+	6.92820i	0.178174	+	0.308607i
$505$		0			0
$506$	18.0000			0.800198
$507$	4.50000	+	7.79423i	0.199852	+	0.346154i
$508$	−1.00000	+	1.73205i	−0.0443678	+	0.0768473i
$509$	12.0000	+	20.7846i	0.531891	+	0.921262i	0.999307	+	0.0372243i	$0.0118516\pi$
$509$	12.0000	+	20.7846i	0.531891	+	0.921262i	−0.467416	+	0.884037i	$0.654815\pi$
$510$		0			0
$511$	−2.00000	+	3.46410i	−0.0884748	+	0.153243i
$512$	−1.00000			−0.0441942
$513$	17.5000	+	12.9904i	0.772644	+	0.573539i
$514$	−3.00000			−0.132324
$515$		0			0
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$		0			0
$518$	20.0000	−	34.6410i	0.878750	−	1.52204i
$519$	−3.00000	−	5.19615i	−0.131685	−	0.228086i
$520$		0			0
$521$	9.00000			0.394297			0.197149	−	0.980374i	$-0.436832\pi$
$521$	9.00000			0.394297			0.197149	+	0.980374i	$0.436832\pi$
$522$		0			0
$523$	14.0000	+	24.2487i	0.612177	+	1.06032i	0.990873	+	0.134801i	$0.0430394\pi$
$523$	14.0000	+	24.2487i	0.612177	+	1.06032i	−0.378695	+	0.925521i	$0.623627\pi$
$524$	9.00000			0.393167
$525$	20.0000			0.872872
$526$	−6.00000	−	10.3923i	−0.261612	−	0.453126i
$527$	6.00000	−	10.3923i	0.261364	−	0.452696i
$528$	−1.50000	−	2.59808i	−0.0652791	−	0.113067i
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$	18.0000			0.781133
$532$	2.00000	−	17.3205i	0.0867110	−	0.750939i
$533$	18.0000			0.779667
$534$	3.00000	−	5.19615i	0.129823	−	0.224860i
$535$		0			0
$536$	−3.50000	−	6.06218i	−0.151177	−	0.261846i
$537$	−4.50000	+	7.79423i	−0.194189	+	0.336346i
$538$	6.00000	+	10.3923i	0.258678	+	0.448044i
$539$	27.0000			1.16297
$540$		0			0
$541$	−22.0000	−	38.1051i	−0.945854	−	1.63827i	−0.754032	−	0.656837i	$-0.771894\pi$
$541$	−22.0000	−	38.1051i	−0.945854	−	1.63827i	−0.191821	−	0.981430i	$-0.561439\pi$
$542$	−8.00000	−	13.8564i	−0.343629	−	0.595184i
$543$	2.00000			0.0858282
$544$	6.00000			0.257248
$545$		0			0
$546$	−4.00000	+	6.92820i	−0.171184	+	0.296500i
$547$	2.00000	+	3.46410i	0.0855138	+	0.148114i	0.905610	−	0.424111i	$-0.139413\pi$
$547$	2.00000	+	3.46410i	0.0855138	+	0.148114i	−0.820096	+	0.572226i	$0.806080\pi$
$548$	−4.50000	+	7.79423i	−0.192230	+	0.332953i
$549$	−4.00000	+	6.92820i	−0.170716	+	0.295689i
$550$	15.0000			0.639602
$551$		0			0
$552$	6.00000			0.255377
$553$	−8.00000	+	13.8564i	−0.340195	+	0.589234i
$554$	4.00000	−	6.92820i	0.169944	−	0.294351i
$555$		0			0
$556$	−5.50000	+	9.52628i	−0.233252	+	0.404004i
$557$	−12.0000	−	20.7846i	−0.508456	−	0.880672i	−0.999952	−	0.00979220i	$-0.996883\pi$
$557$	−12.0000	−	20.7846i	−0.508456	−	0.880672i	0.491496	−	0.870880i	$-0.336450\pi$
$558$	4.00000			0.169334
$559$	−8.00000			−0.338364
$560$		0			0
$561$	9.00000	+	15.5885i	0.379980	+	0.658145i
$562$	−27.0000			−1.13893
$563$	−21.0000			−0.885044			−0.442522	−	0.896758i	$-0.645916\pi$
$563$	−21.0000			−0.885044			−0.442522	+	0.896758i	$0.645916\pi$
$564$		0			0
$565$		0			0
$566$	2.50000	+	4.33013i	0.105083	+	0.182009i
$567$	2.00000	−	3.46410i	0.0839921	−	0.145479i
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$		0			0
$571$	−7.00000			−0.292941			−0.146470	−	0.989215i	$-0.546791\pi$
$571$	−7.00000			−0.292941			−0.146470	+	0.989215i	$0.546791\pi$
$572$	−3.00000	+	5.19615i	−0.125436	+	0.217262i
$573$	−6.00000	+	10.3923i	−0.250654	+	0.434145i
$574$	−18.0000	−	31.1769i	−0.751305	−	1.30130i
$575$	−15.0000	+	25.9808i	−0.625543	+	1.08347i
$576$	1.00000	+	1.73205i	0.0416667	+	0.0721688i
$577$	11.0000			0.457936			0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000			0.457936			0.228968	+	0.973434i	$0.426465\pi$
$578$	−19.0000			−0.790296
$579$	−1.00000	−	1.73205i	−0.0415586	−	0.0719816i
$580$		0			0
$581$	−12.0000			−0.497844
$582$	−17.0000			−0.704673
$583$	−9.00000	−	15.5885i	−0.372742	−	0.645608i
$584$	−0.500000	+	0.866025i	−0.0206901	+	0.0358364i
$585$		0			0
$586$	12.0000	−	20.7846i	0.495715	−	0.858604i
$587$	6.00000	−	10.3923i	0.247647	−	0.428936i	−0.715226	−	0.698893i	$-0.753676\pi$
$587$	6.00000	−	10.3923i	0.247647	−	0.428936i	0.962872	+	0.269957i	$0.0870095\pi$
$588$	9.00000			0.371154
$589$	−7.00000	−	5.19615i	−0.288430	−	0.214104i
$590$		0			0
$591$	−9.00000	+	15.5885i	−0.370211	+	0.641223i
$592$	5.00000	−	8.66025i	0.205499	−	0.355934i
$593$	10.5000	+	18.1865i	0.431183	+	0.746831i	0.996976	−	0.0777165i	$-0.0247629\pi$
$593$	10.5000	+	18.1865i	0.431183	+	0.746831i	−0.565792	+	0.824548i	$0.691430\pi$
$594$	−7.50000	+	12.9904i	−0.307729	+	0.533002i
$595$		0			0
$596$	18.0000			0.737309
$597$	−10.0000			−0.409273
$598$	−6.00000	−	10.3923i	−0.245358	−	0.424973i
$599$	3.00000	+	5.19615i	0.122577	+	0.212309i	0.920783	−	0.390075i	$-0.127551\pi$
$599$	3.00000	+	5.19615i	0.122577	+	0.212309i	−0.798206	+	0.602384i	$0.794218\pi$
$600$	5.00000			0.204124
$601$	−13.0000			−0.530281			−0.265141	−	0.964210i	$-0.585418\pi$
$601$	−13.0000			−0.530281			−0.265141	+	0.964210i	$0.585418\pi$
$602$	8.00000	+	13.8564i	0.326056	+	0.564745i
$603$	−7.00000	+	12.1244i	−0.285062	+	0.493742i
$604$	5.00000	+	8.66025i	0.203447	+	0.352381i
$605$		0			0
$606$		0			0
$607$	20.0000			0.811775			0.405887	−	0.913923i	$-0.366962\pi$
$607$	20.0000			0.811775			0.405887	+	0.913923i	$0.366962\pi$
$608$	0.500000	−	4.33013i	0.0202777	−	0.175610i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−6.00000	−	10.3923i	−0.242536	−	0.420084i
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	−0.885514	−	0.464614i	$-0.846193\pi$
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	0.845124	+	0.534570i	$0.179527\pi$
$614$	−3.50000	−	6.06218i	−0.141249	−	0.244650i
$615$		0			0
$616$	12.0000			0.483494
$617$	−1.50000	−	2.59808i	−0.0603877	−	0.104595i	0.834251	−	0.551385i	$-0.185900\pi$
$617$	−1.50000	−	2.59808i	−0.0603877	−	0.104595i	−0.894639	+	0.446790i	$0.852567\pi$
$618$	1.00000	+	1.73205i	0.0402259	+	0.0696733i
$619$	−4.00000			−0.160774			−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000			−0.160774			−0.0803868	+	0.996764i	$0.525616\pi$
$620$		0			0
$621$	−15.0000	−	25.9808i	−0.601929	−	1.04257i
$622$	−15.0000	+	25.9808i	−0.601445	+	1.04173i
$623$	12.0000	+	20.7846i	0.480770	+	0.832718i
$624$	−1.00000	+	1.73205i	−0.0400320	+	0.0693375i
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	19.0000			0.759393
$627$	12.0000	−	5.19615i	0.479234	−	0.207514i
$628$	−16.0000			−0.638470
$629$	−30.0000	+	51.9615i	−1.19618	+	2.07184i
$630$		0			0
$631$	14.0000	+	24.2487i	0.557331	+	0.965326i	0.997718	+	0.0675178i	$0.0215080\pi$
$631$	14.0000	+	24.2487i	0.557331	+	0.965326i	−0.440387	+	0.897808i	$0.645159\pi$
$632$	−2.00000	+	3.46410i	−0.0795557	+	0.137795i
$633$	−10.0000	−	17.3205i	−0.397464	−	0.688428i
$634$	18.0000			0.714871
$635$		0			0
$636$	−3.00000	−	5.19615i	−0.118958	−	0.206041i
$637$	−9.00000	−	15.5885i	−0.356593	−	0.617637i
$638$		0			0
$639$	12.0000			0.474713
$640$		0			0
$641$	19.5000	−	33.7750i	0.770204	−	1.33403i	−0.167247	−	0.985915i	$-0.553488\pi$
$641$	19.5000	−	33.7750i	0.770204	−	1.33403i	0.937451	−	0.348117i	$-0.113179\pi$
$642$		0			0
$643$	21.5000	−	37.2391i	0.847877	−	1.46857i	−0.0352216	−	0.999380i	$-0.511214\pi$
$643$	21.5000	−	37.2391i	0.847877	−	1.46857i	0.883099	−	0.469187i	$-0.155453\pi$
$644$	−12.0000	+	20.7846i	−0.472866	+	0.819028i
$645$		0			0
$646$	−3.00000	+	25.9808i	−0.118033	+	1.02220i
$647$	18.0000			0.707653			0.353827	−	0.935311i	$-0.384880\pi$
$647$	18.0000			0.707653			0.353827	+	0.935311i	$0.384880\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	13.5000	−	23.3827i	0.529921	−	0.917851i
$650$	−5.00000	−	8.66025i	−0.196116	−	0.339683i
$651$	4.00000	−	6.92820i	0.156772	−	0.271538i
$652$	9.50000	+	16.4545i	0.372049	+	0.644407i
$653$	−12.0000			−0.469596			−0.234798	−	0.972044i	$-0.575443\pi$
$653$	−12.0000			−0.469596			−0.234798	+	0.972044i	$0.575443\pi$
$654$	16.0000			0.625650
$655$		0			0
$656$	−4.50000	−	7.79423i	−0.175695	−	0.304314i
$657$	2.00000			0.0780274
$658$		0			0
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	−0.968052	−	0.250748i	$-0.919323\pi$
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	0.266872	−	0.963732i	$-0.414010\pi$
$660$		0			0
$661$	20.0000	+	34.6410i	0.777910	+	1.34738i	0.933144	+	0.359502i	$0.117053\pi$
$661$	20.0000	+	34.6410i	0.777910	+	1.34738i	−0.155235	+	0.987878i	$0.549613\pi$
$662$	2.50000	−	4.33013i	0.0971653	−	0.168295i
$663$	6.00000	−	10.3923i	0.233021	−	0.403604i
$664$	−3.00000			−0.116423
$665$		0			0
$666$	−20.0000			−0.774984
$667$		0			0
$668$	12.0000	−	20.7846i	0.464294	−	0.804181i
$669$	−7.00000	−	12.1244i	−0.270636	−	0.468755i
$670$		0			0
$671$	6.00000	+	10.3923i	0.231627	+	0.401190i
$672$	4.00000			0.154303
$673$	14.0000			0.539660			0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000			0.539660			0.269830	+	0.962908i	$0.413032\pi$
$674$	5.50000	+	9.52628i	0.211852	+	0.366939i
$675$	−12.5000	−	21.6506i	−0.481125	−	0.833333i
$676$	−9.00000			−0.346154
$677$	−42.0000			−1.61419			−0.807096	−	0.590421i	$-0.798962\pi$
$677$	−42.0000			−1.61419			−0.807096	+	0.590421i	$0.798962\pi$
$678$	7.50000	+	12.9904i	0.288036	+	0.498893i
$679$	34.0000	−	58.8897i	1.30480	−	2.25998i
$680$		0			0
$681$	−1.50000	+	2.59808i	−0.0574801	+	0.0995585i
$682$	3.00000	−	5.19615i	0.114876	−	0.198971i
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$	−8.00000	+	3.46410i	−0.305888	+	0.132453i
$685$		0			0
$686$	−4.00000	+	6.92820i	−0.152721	+	0.264520i
$687$	8.00000	−	13.8564i	0.305219	−	0.528655i
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	44.0000			1.67384			0.836919	−	0.547326i	$-0.184354\pi$
$691$	44.0000			1.67384			0.836919	+	0.547326i	$0.184354\pi$
$692$	6.00000			0.228086
$693$	−12.0000	−	20.7846i	−0.455842	−	0.789542i
$694$	−4.50000	−	7.79423i	−0.170818	−	0.295865i
$695$		0			0
$696$		0			0
$697$	27.0000	+	46.7654i	1.02270	+	1.77136i
$698$	−2.00000	+	3.46410i	−0.0757011	+	0.131118i
$699$	−1.50000	−	2.59808i	−0.0567352	−	0.0982683i
$700$	−10.0000	+	17.3205i	−0.377964	+	0.654654i
$701$	12.0000	−	20.7846i	0.453234	−	0.785024i	−0.545351	−	0.838208i	$-0.683604\pi$
$701$	12.0000	−	20.7846i	0.453234	−	0.785024i	0.998585	+	0.0531839i	$0.0169370\pi$
$702$	10.0000			0.377426
$703$	35.0000	+	25.9808i	1.32005	+	0.979883i
$704$	3.00000			0.113067
$705$		0			0
$706$	1.50000	−	2.59808i	0.0564532	−	0.0977799i
$707$		0			0
$708$	4.50000	−	7.79423i	0.169120	−	0.292925i
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	0.704118	−	0.710083i	$-0.251342\pi$
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	−0.967009	+	0.254743i	$0.918009\pi$
$710$		0			0
$711$	8.00000			0.300023
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$	6.00000	+	10.3923i	0.224702	+	0.389195i
$714$	−24.0000			−0.898177
$715$		0			0
$716$	−4.50000	−	7.79423i	−0.168173	−	0.291284i
$717$	6.00000	−	10.3923i	0.224074	−	0.388108i
$718$	−3.00000	−	5.19615i	−0.111959	−	0.193919i
$719$	−15.0000	+	25.9808i	−0.559406	+	0.968919i	0.438141	+	0.898906i	$0.355637\pi$
$719$	−15.0000	+	25.9808i	−0.559406	+	0.968919i	−0.997546	+	0.0700124i	$0.977696\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$	18.5000	+	4.33013i	0.688499	+	0.161151i
$723$	5.00000			0.185952
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$		0			0
$726$	−1.00000	−	1.73205i	−0.0371135	−	0.0642824i
$727$	−16.0000	+	27.7128i	−0.593407	+	1.02781i	0.400362	+	0.916357i	$0.368884\pi$
$727$	−16.0000	+	27.7128i	−0.593407	+	1.02781i	−0.993770	+	0.111454i	$0.964449\pi$
$728$	−4.00000	−	6.92820i	−0.148250	−	0.256776i
$729$	13.0000			0.481481
$730$		0			0
$731$	−12.0000	−	20.7846i	−0.443836	−	0.768747i
$732$	2.00000	+	3.46410i	0.0739221	+	0.128037i
$733$	−22.0000			−0.812589			−0.406294	−	0.913742i	$-0.633179\pi$
$733$	−22.0000			−0.812589			−0.406294	+	0.913742i	$0.633179\pi$
$734$	22.0000			0.812035
$735$		0			0
$736$	−3.00000	+	5.19615i	−0.110581	+	0.191533i
$737$	10.5000	+	18.1865i	0.386772	+	0.669910i
$738$	−9.00000	+	15.5885i	−0.331295	+	0.573819i
$739$	−17.5000	+	30.3109i	−0.643748	+	1.11500i	0.340841	+	0.940121i	$0.389288\pi$
$739$	−17.5000	+	30.3109i	−0.643748	+	1.11500i	−0.984589	+	0.174883i	$0.944045\pi$
$740$		0			0
$741$	−7.00000	−	5.19615i	−0.257151	−	0.190885i
$742$	24.0000			0.881068
$743$	9.00000	−	15.5885i	0.330178	−	0.571885i	−0.652369	−	0.757902i	$-0.726225\pi$
$743$	9.00000	−	15.5885i	0.330178	−	0.571885i	0.982547	+	0.186017i	$0.0595579\pi$
$744$	1.00000	−	1.73205i	0.0366618	−	0.0635001i
$745$		0			0
$746$	−2.00000	+	3.46410i	−0.0732252	+	0.126830i
$747$	3.00000	+	5.19615i	0.109764	+	0.190117i
$748$	−18.0000			−0.658145
$749$		0			0
$750$		0			0
$751$	−19.0000	−	32.9090i	−0.693320	−	1.20087i	−0.970744	−	0.240118i	$-0.922814\pi$
$751$	−19.0000	−	32.9090i	−0.693320	−	1.20087i	0.277424	−	0.960748i	$-0.410519\pi$
$752$		0			0
$753$	−3.00000			−0.109326
$754$		0			0
$755$		0			0
$756$	−10.0000	−	17.3205i	−0.363696	−	0.629941i
$757$	5.00000	−	8.66025i	0.181728	−	0.314762i	−0.760741	−	0.649056i	$-0.775164\pi$
$757$	5.00000	−	8.66025i	0.181728	−	0.314762i	0.942469	+	0.334293i	$0.108498\pi$
$758$	−14.0000	+	24.2487i	−0.508503	+	0.880753i
$759$	−18.0000			−0.653359
$760$		0			0
$761$	−39.0000			−1.41375			−0.706874	−	0.707339i	$-0.749895\pi$
$761$	−39.0000			−1.41375			−0.706874	+	0.707339i	$0.749895\pi$
$762$	1.00000	−	1.73205i	0.0362262	−	0.0627456i
$763$	−32.0000	+	55.4256i	−1.15848	+	2.00654i
$764$	−6.00000	−	10.3923i	−0.217072	−	0.375980i
$765$		0			0
$766$	−18.0000	−	31.1769i	−0.650366	−	1.12647i
$767$	−18.0000			−0.649942
$768$	1.00000			0.0360844
$769$	−1.00000	−	1.73205i	−0.0360609	−	0.0624593i	0.847432	−	0.530904i	$-0.178148\pi$
$769$	−1.00000	−	1.73205i	−0.0360609	−	0.0624593i	−0.883493	+	0.468445i	$0.844814\pi$
$770$		0			0
$771$	3.00000			0.108042
$772$	2.00000			0.0719816
$773$	24.0000	+	41.5692i	0.863220	+	1.49514i	0.868804	+	0.495156i	$0.164889\pi$
$773$	24.0000	+	41.5692i	0.863220	+	1.49514i	−0.00558380	+	0.999984i	$0.501777\pi$
$774$	4.00000	−	6.92820i	0.143777	−	0.249029i
$775$	5.00000	+	8.66025i	0.179605	+	0.311086i
$776$	8.50000	−	14.7224i	0.305132	−	0.528505i
$777$	−20.0000	+	34.6410i	−0.717496	+	1.24274i
$778$

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} -4.00000 q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} -4.00000 q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +3.00000 q^{11} +1.00000 q^{12} +(-1.00000 - 1.73205i) q^{13} +(-2.00000 + 3.46410i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +2.00000 q^{18} +(-3.50000 - 2.59808i) q^{19} +(2.00000 - 3.46410i) q^{21} +(1.50000 - 2.59808i) q^{22} +(3.00000 + 5.19615i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} -2.00000 q^{26} -5.00000 q^{27} +(2.00000 + 3.46410i) q^{28} +2.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +(-3.00000 - 5.19615i) q^{34} +(1.00000 - 1.73205i) q^{36} -10.0000 q^{37} +(-4.00000 + 1.73205i) q^{38} +2.00000 q^{39} +(-4.50000 + 7.79423i) q^{41} +(-2.00000 - 3.46410i) q^{42} +(2.00000 - 3.46410i) q^{43} +(-1.50000 - 2.59808i) q^{44} +6.00000 q^{46} +(-0.500000 - 0.866025i) q^{48} +9.00000 q^{49} +5.00000 q^{50} +(3.00000 + 5.19615i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(-2.50000 + 4.33013i) q^{54} +4.00000 q^{56} +(4.00000 - 1.73205i) q^{57} +(4.50000 - 7.79423i) q^{59} +(2.00000 + 3.46410i) q^{61} +(1.00000 - 1.73205i) q^{62} +(-4.00000 - 6.92820i) q^{63} +1.00000 q^{64} +(1.50000 + 2.59808i) q^{66} +(3.50000 + 6.06218i) q^{67} -6.00000 q^{68} -6.00000 q^{69} +(3.00000 - 5.19615i) q^{71} +(-1.00000 - 1.73205i) q^{72} +(0.500000 - 0.866025i) q^{73} +(-5.00000 + 8.66025i) q^{74} -5.00000 q^{75} +(-0.500000 + 4.33013i) q^{76} -12.0000 q^{77} +(1.00000 - 1.73205i) q^{78} +(2.00000 - 3.46410i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.50000 + 7.79423i) q^{82} +3.00000 q^{83} -4.00000 q^{84} +(-2.00000 - 3.46410i) q^{86} -3.00000 q^{88} +(-3.00000 - 5.19615i) q^{89} +(4.00000 + 6.92820i) q^{91} +(3.00000 - 5.19615i) q^{92} +(-1.00000 + 1.73205i) q^{93} -1.00000 q^{96} +(-8.50000 + 14.7224i) q^{97} +(4.50000 - 7.79423i) q^{98} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} + q^{6} - 8 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 + q^6 - 8 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q + q^{2} - q^{3} - q^{4} + q^{6} - 8 q^{7} - 2 q^{8} + 2 q^{9} + 6 q^{11} + 2 q^{12} - 2 q^{13} - 4 q^{14} - q^{16} + 6 q^{17} + 4 q^{18} - 7 q^{19} + 4 q^{21} + 3 q^{22} + 6 q^{23} + q^{24} + 5 q^{25} - 4 q^{26} - 10 q^{27} + 4 q^{28} + 4 q^{31} + q^{32} - 3 q^{33} - 6 q^{34} + 2 q^{36} - 20 q^{37} - 8 q^{38} + 4 q^{39} - 9 q^{41} - 4 q^{42} + 4 q^{43} - 3 q^{44} + 12 q^{46} - q^{48} + 18 q^{49} + 10 q^{50} + 6 q^{51} - 2 q^{52} - 6 q^{53} - 5 q^{54} + 8 q^{56} + 8 q^{57} + 9 q^{59} + 4 q^{61} + 2 q^{62} - 8 q^{63} + 2 q^{64} + 3 q^{66} + 7 q^{67} - 12 q^{68} - 12 q^{69} + 6 q^{71} - 2 q^{72} + q^{73} - 10 q^{74} - 10 q^{75} - q^{76} - 24 q^{77} + 2 q^{78} + 4 q^{79} - q^{81} + 9 q^{82} + 6 q^{83} - 8 q^{84} - 4 q^{86} - 6 q^{88} - 6 q^{89} + 8 q^{91} + 6 q^{92} - 2 q^{93} - 2 q^{96} - 17 q^{97} + 9 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 + q^6 - 8 * q^7 - 2 * q^8 + 2 * q^9 + 6 * q^11 + 2 * q^12 - 2 * q^13 - 4 * q^14 - q^16 + 6 * q^17 + 4 * q^18 - 7 * q^19 + 4 * q^21 + 3 * q^22 + 6 * q^23 + q^24 + 5 * q^25 - 4 * q^26 - 10 * q^27 + 4 * q^28 + 4 * q^31 + q^32 - 3 * q^33 - 6 * q^34 + 2 * q^36 - 20 * q^37 - 8 * q^38 + 4 * q^39 - 9 * q^41 - 4 * q^42 + 4 * q^43 - 3 * q^44 + 12 * q^46 - q^48 + 18 * q^49 + 10 * q^50 + 6 * q^51 - 2 * q^52 - 6 * q^53 - 5 * q^54 + 8 * q^56 + 8 * q^57 + 9 * q^59 + 4 * q^61 + 2 * q^62 - 8 * q^63 + 2 * q^64 + 3 * q^66 + 7 * q^67 - 12 * q^68 - 12 * q^69 + 6 * q^71 - 2 * q^72 + q^73 - 10 * q^74 - 10 * q^75 - q^76 - 24 * q^77 + 2 * q^78 + 4 * q^79 - q^81 + 9 * q^82 + 6 * q^83 - 8 * q^84 - 4 * q^86 - 6 * q^88 - 6 * q^89 + 8 * q^91 + 6 * q^92 - 2 * q^93 - 2 * q^96 - 17 * q^97 + 9 * q^98 + 6 * q^99

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