LMFDB - Embedded newform 111.2.j.a.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [111,2,Mod(64,111)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(111, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("111.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 111 = 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	111.j (of order $6$, 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:	$0.886339462436$
Analytic rank:	$1$
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:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	111.85
Dual form			111.2.j.a.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.00000 - 1.73205i) q^{5} -1.73205i q^{6} +(-0.500000 + 0.866025i) q^{7} -1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.00000 - 1.73205i) q^{5} -1.73205i q^{6} +(-0.500000 + 0.866025i) q^{7} -1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +6.00000 q^{10} +(0.500000 + 0.866025i) q^{12} +(-4.50000 - 2.59808i) q^{13} -1.73205i q^{14} +(3.00000 - 1.73205i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-3.00000 + 1.73205i) q^{17} +(1.50000 + 0.866025i) q^{18} +(-3.00000 - 1.73205i) q^{19} +(-3.00000 + 1.73205i) q^{20} +(-0.500000 - 0.866025i) q^{21} +6.92820i q^{23} +(1.50000 + 0.866025i) q^{24} +(3.50000 + 6.06218i) q^{25} +9.00000 q^{26} +1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +6.92820i q^{29} +(-3.00000 + 5.19615i) q^{30} -5.19615i q^{31} +(-4.50000 - 2.59808i) q^{32} +(3.00000 - 5.19615i) q^{34} +(3.00000 - 1.73205i) q^{35} -1.00000 q^{36} +(-5.00000 + 3.46410i) q^{37} +6.00000 q^{38} +(4.50000 - 2.59808i) q^{39} +(-3.00000 + 5.19615i) q^{40} +(3.00000 - 5.19615i) q^{41} +(1.50000 + 0.866025i) q^{42} -5.19615i q^{43} +3.46410i q^{45} +(-6.00000 - 10.3923i) q^{46} -6.00000 q^{47} -5.00000 q^{48} +(3.00000 + 5.19615i) q^{49} +(-10.5000 - 6.06218i) q^{50} -3.46410i q^{51} +(-4.50000 + 2.59808i) q^{52} +(-6.00000 - 10.3923i) q^{53} +(-1.50000 + 0.866025i) q^{54} +(1.50000 + 0.866025i) q^{56} +(3.00000 - 1.73205i) q^{57} +(-6.00000 - 10.3923i) q^{58} +(12.0000 - 6.92820i) q^{59} -3.46410i q^{60} +(4.50000 + 7.79423i) q^{62} +1.00000 q^{63} -1.00000 q^{64} +(9.00000 + 15.5885i) q^{65} +(-3.50000 + 6.06218i) q^{67} +3.46410i q^{68} +(-6.00000 - 3.46410i) q^{69} +(-3.00000 + 5.19615i) q^{70} +(3.00000 - 5.19615i) q^{71} +(-1.50000 + 0.866025i) q^{72} +7.00000 q^{73} +(4.50000 - 9.52628i) q^{74} -7.00000 q^{75} +(-3.00000 + 1.73205i) q^{76} +(-4.50000 + 7.79423i) q^{78} +(-4.50000 - 2.59808i) q^{79} -17.3205i q^{80} +(-0.500000 + 0.866025i) q^{81} +10.3923i q^{82} +(3.00000 + 5.19615i) q^{83} -1.00000 q^{84} +12.0000 q^{85} +(4.50000 + 7.79423i) q^{86} +(-6.00000 - 3.46410i) q^{87} +(-12.0000 + 6.92820i) q^{89} +(-3.00000 - 5.19615i) q^{90} +(4.50000 - 2.59808i) q^{91} +(6.00000 + 3.46410i) q^{92} +(4.50000 + 2.59808i) q^{93} +(9.00000 - 5.19615i) q^{94} +(6.00000 + 10.3923i) q^{95} +(4.50000 - 2.59808i) q^{96} +15.5885i q^{97} +(-9.00000 - 5.19615i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - q^{3} + q^{4} - 6 q^{5} - q^{7} - q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 - q^3 + q^4 - 6 * q^5 - q^7 - q^9	$ 2 q - 3 q^{2} - q^{3} + q^{4} - 6 q^{5} - q^{7} - q^{9} + 12 q^{10} + q^{12} - 9 q^{13} + 6 q^{15} + 5 q^{16} - 6 q^{17} + 3 q^{18} - 6 q^{19} - 6 q^{20} - q^{21} + 3 q^{24} + 7 q^{25} + 18 q^{26} + 2 q^{27} + q^{28} - 6 q^{30} - 9 q^{32} + 6 q^{34} + 6 q^{35} - 2 q^{36} - 10 q^{37} + 12 q^{38} + 9 q^{39} - 6 q^{40} + 6 q^{41} + 3 q^{42} - 12 q^{46} - 12 q^{47} - 10 q^{48} + 6 q^{49} - 21 q^{50} - 9 q^{52} - 12 q^{53} - 3 q^{54} + 3 q^{56} + 6 q^{57} - 12 q^{58} + 24 q^{59} + 9 q^{62} + 2 q^{63} - 2 q^{64} + 18 q^{65} - 7 q^{67} - 12 q^{69} - 6 q^{70} + 6 q^{71} - 3 q^{72} + 14 q^{73} + 9 q^{74} - 14 q^{75} - 6 q^{76} - 9 q^{78} - 9 q^{79} - q^{81} + 6 q^{83} - 2 q^{84} + 24 q^{85} + 9 q^{86} - 12 q^{87} - 24 q^{89} - 6 q^{90} + 9 q^{91} + 12 q^{92} + 9 q^{93} + 18 q^{94} + 12 q^{95} + 9 q^{96} - 18 q^{98}+O(q^{100}) $ 2 * q - 3 * q^2 - q^3 + q^4 - 6 * q^5 - q^7 - q^9 + 12 * q^10 + q^12 - 9 * q^13 + 6 * q^15 + 5 * q^16 - 6 * q^17 + 3 * q^18 - 6 * q^19 - 6 * q^20 - q^21 + 3 * q^24 + 7 * q^25 + 18 * q^26 + 2 * q^27 + q^28 - 6 * q^30 - 9 * q^32 + 6 * q^34 + 6 * q^35 - 2 * q^36 - 10 * q^37 + 12 * q^38 + 9 * q^39 - 6 * q^40 + 6 * q^41 + 3 * q^42 - 12 * q^46 - 12 * q^47 - 10 * q^48 + 6 * q^49 - 21 * q^50 - 9 * q^52 - 12 * q^53 - 3 * q^54 + 3 * q^56 + 6 * q^57 - 12 * q^58 + 24 * q^59 + 9 * q^62 + 2 * q^63 - 2 * q^64 + 18 * q^65 - 7 * q^67 - 12 * q^69 - 6 * q^70 + 6 * q^71 - 3 * q^72 + 14 * q^73 + 9 * q^74 - 14 * q^75 - 6 * q^76 - 9 * q^78 - 9 * q^79 - q^81 + 6 * q^83 - 2 * q^84 + 24 * q^85 + 9 * q^86 - 12 * q^87 - 24 * q^89 - 6 * q^90 + 9 * q^91 + 12 * q^92 + 9 * q^93 + 18 * q^94 + 12 * q^95 + 9 * q^96 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/111\mathbb{Z}\right)^\times$.

$n$	$38$	$76$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.50000	+	0.866025i	−1.06066	+	0.612372i	−0.925615	−	0.378467i	$-0.876451\pi$
$2$	−1.50000	+	0.866025i	−1.06066	+	0.612372i	−0.135045	+	0.990839i	$0.543118\pi$
$3$	−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
$5$	−3.00000	−	1.73205i	−1.34164	−	0.774597i	−0.354593	−	0.935021i	$-0.615380\pi$
$5$	−3.00000	−	1.73205i	−1.34164	−	0.774597i	−0.987048	+	0.160424i	$0.948714\pi$
$6$		−	1.73205i		−	0.707107i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i	0.755929	+	0.654654i	$0.227186\pi$
$8$		−	1.73205i		−	0.612372i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	6.00000			1.89737
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−4.50000	−	2.59808i	−1.24808	−	0.720577i	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−4.50000	−	2.59808i	−1.24808	−	0.720577i	−0.970725	+	0.240192i	$0.922790\pi$
$14$		−	1.73205i		−	0.462910i
$15$	3.00000	−	1.73205i	0.774597	−	0.447214i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	−3.00000	+	1.73205i	−0.727607	+	0.420084i	−0.817546	−	0.575863i	$-0.804666\pi$
$17$	−3.00000	+	1.73205i	−0.727607	+	0.420084i	0.0899392	+	0.995947i	$0.471333\pi$
$18$	1.50000	+	0.866025i	0.353553	+	0.204124i
$19$	−3.00000	−	1.73205i	−0.688247	−	0.397360i	0.114708	−	0.993399i	$-0.463407\pi$
$19$	−3.00000	−	1.73205i	−0.688247	−	0.397360i	−0.802955	+	0.596040i	$0.796740\pi$
$20$	−3.00000	+	1.73205i	−0.670820	+	0.387298i
$21$	−0.500000	−	0.866025i	−0.109109	−	0.188982i
$22$		0			0
$23$			6.92820i			1.44463i	0.691564	+	0.722315i	$0.256922\pi$
$23$			6.92820i			1.44463i	−0.691564	+	0.722315i	$0.743078\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	3.50000	+	6.06218i	0.700000	+	1.21244i
$26$	9.00000			1.76505
$27$	1.00000			0.192450
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$			6.92820i			1.28654i	0.765641	+	0.643268i	$0.222422\pi$
$29$			6.92820i			1.28654i	−0.765641	+	0.643268i	$0.777578\pi$
$30$	−3.00000	+	5.19615i	−0.547723	+	0.948683i
$31$		−	5.19615i		−	0.933257i	−0.884454	−	0.466628i	$-0.845469\pi$
$31$		−	5.19615i		−	0.933257i	0.884454	−	0.466628i	$-0.154531\pi$
$32$	−4.50000	−	2.59808i	−0.795495	−	0.459279i
$33$		0			0
$34$	3.00000	−	5.19615i	0.514496	−	0.891133i
$35$	3.00000	−	1.73205i	0.507093	−	0.292770i
$36$	−1.00000			−0.166667
$37$	−5.00000	+	3.46410i	−0.821995	+	0.569495i
$37$	−5.00000	+	3.46410i	−0.821995	+	0.569495i
$38$	6.00000			0.973329
$39$	4.50000	−	2.59808i	0.720577	−	0.416025i
$40$	−3.00000	+	5.19615i	−0.474342	+	0.821584i
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	−0.530831	−	0.847477i	$-0.678120\pi$
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	0.999353	+	0.0359748i	$0.0114536\pi$
$42$	1.50000	+	0.866025i	0.231455	+	0.133631i
$43$		−	5.19615i		−	0.792406i	−0.918163	−	0.396203i	$-0.870328\pi$
$43$		−	5.19615i		−	0.792406i	0.918163	−	0.396203i	$-0.129672\pi$
$44$		0			0
$45$			3.46410i			0.516398i
$46$	−6.00000	−	10.3923i	−0.884652	−	1.53226i
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	−5.00000			−0.721688
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$	−10.5000	−	6.06218i	−1.48492	−	0.857321i
$51$		−	3.46410i		−	0.485071i
$52$	−4.50000	+	2.59808i	−0.624038	+	0.360288i
$53$	−6.00000	−	10.3923i	−0.824163	−	1.42749i	−0.902557	−	0.430570i	$-0.858312\pi$
$53$	−6.00000	−	10.3923i	−0.824163	−	1.42749i	0.0783936	−	0.996922i	$-0.475021\pi$
$54$	−1.50000	+	0.866025i	−0.204124	+	0.117851i
$55$		0			0
$56$	1.50000	+	0.866025i	0.200446	+	0.115728i
$57$	3.00000	−	1.73205i	0.397360	−	0.229416i
$58$	−6.00000	−	10.3923i	−0.787839	−	1.36458i
$59$	12.0000	−	6.92820i	1.56227	−	0.901975i	0.565240	−	0.824927i	$-0.308784\pi$
$59$	12.0000	−	6.92820i	1.56227	−	0.901975i	0.997027	−	0.0770484i	$-0.0245496\pi$
$60$		−	3.46410i		−	0.447214i
$61$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$61$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$62$	4.50000	+	7.79423i	0.571501	+	0.989868i
$63$	1.00000			0.125988
$64$	−1.00000			−0.125000
$65$	9.00000	+	15.5885i	1.11631	+	1.93351i
$66$		0			0
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	−0.996659	−	0.0816792i	$-0.973972\pi$
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	0.569066	+	0.822292i	$0.307305\pi$
$68$			3.46410i			0.420084i
$69$	−6.00000	−	3.46410i	−0.722315	−	0.417029i
$70$	−3.00000	+	5.19615i	−0.358569	+	0.621059i
$71$	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	$0.0507952\pi$
$72$	−1.50000	+	0.866025i	−0.176777	+	0.102062i
$73$	7.00000			0.819288			0.409644	−	0.912245i	$-0.365653\pi$
$73$	7.00000			0.819288			0.409644	+	0.912245i	$0.365653\pi$
$74$	4.50000	−	9.52628i	0.523114	−	1.10741i
$75$	−7.00000			−0.808290
$76$	−3.00000	+	1.73205i	−0.344124	+	0.198680i
$77$		0			0
$78$	−4.50000	+	7.79423i	−0.509525	+	0.882523i
$79$	−4.50000	−	2.59808i	−0.506290	−	0.292306i	0.225018	−	0.974355i	$-0.427756\pi$
$79$	−4.50000	−	2.59808i	−0.506290	−	0.292306i	−0.731307	+	0.682048i	$0.761089\pi$
$80$		−	17.3205i		−	1.93649i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$			10.3923i			1.14764i
$83$	3.00000	+	5.19615i	0.329293	+	0.570352i	0.982372	−	0.186938i	$-0.0598564\pi$
$83$	3.00000	+	5.19615i	0.329293	+	0.570352i	−0.653079	+	0.757290i	$0.726523\pi$
$84$	−1.00000			−0.109109
$85$	12.0000			1.30158
$86$	4.50000	+	7.79423i	0.485247	+	0.840473i
$87$	−6.00000	−	3.46410i	−0.643268	−	0.371391i
$88$		0			0
$89$	−12.0000	+	6.92820i	−1.27200	+	0.734388i	−0.975364	−	0.220603i	$-0.929197\pi$
$89$	−12.0000	+	6.92820i	−1.27200	+	0.734388i	−0.296634	+	0.954991i	$0.595864\pi$
$90$	−3.00000	−	5.19615i	−0.316228	−	0.547723i
$91$	4.50000	−	2.59808i	0.471728	−	0.272352i
$92$	6.00000	+	3.46410i	0.625543	+	0.361158i
$93$	4.50000	+	2.59808i	0.466628	+	0.269408i
$94$	9.00000	−	5.19615i	0.928279	−	0.535942i
$95$	6.00000	+	10.3923i	0.615587	+	1.06623i
$96$	4.50000	−	2.59808i	0.459279	−	0.265165i
$97$			15.5885i			1.58277i	0.611319	+	0.791384i	$0.290639\pi$
$97$			15.5885i			1.58277i	−0.611319	+	0.791384i	$0.709361\pi$
$98$	−9.00000	−	5.19615i	−0.909137	−	0.524891i
$99$		0			0
$100$	7.00000			0.700000
$101$	−12.0000			−1.19404			−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000			−1.19404			−0.597022	+	0.802225i	$0.703650\pi$
$102$	3.00000	+	5.19615i	0.297044	+	0.514496i
$103$		−	10.3923i		−	1.02398i	−0.858990	−	0.511992i	$-0.828908\pi$
$103$		−	10.3923i		−	1.02398i	0.858990	−	0.511992i	$-0.171092\pi$
$104$	−4.50000	+	7.79423i	−0.441261	+	0.764287i
$105$			3.46410i			0.338062i
$106$	18.0000	+	10.3923i	1.74831	+	1.00939i
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	1.50000	−	0.866025i	0.143674	−	0.0829502i	−0.426440	−	0.904516i	$-0.640232\pi$
$109$	1.50000	−	0.866025i	0.143674	−	0.0829502i	0.570114	+	0.821566i	$0.306899\pi$
$110$		0			0
$111$	−0.500000	−	6.06218i	−0.0474579	−	0.575396i
$112$	−5.00000			−0.472456
$113$	3.00000	−	1.73205i	0.282216	−	0.162938i	−0.352210	−	0.935921i	$-0.614570\pi$
$113$	3.00000	−	1.73205i	0.282216	−	0.162938i	0.634426	+	0.772983i	$0.281236\pi$
$114$	−3.00000	+	5.19615i	−0.280976	+	0.486664i
$115$	12.0000	−	20.7846i	1.11901	−	1.93817i
$116$	6.00000	+	3.46410i	0.557086	+	0.321634i
$117$			5.19615i			0.480384i
$118$	−12.0000	+	20.7846i	−1.10469	+	1.91338i
$119$		−	3.46410i		−	0.317554i
$120$	−3.00000	−	5.19615i	−0.273861	−	0.474342i
$121$	−11.0000			−1.00000
$122$		0			0
$123$	3.00000	+	5.19615i	0.270501	+	0.468521i
$124$	−4.50000	−	2.59808i	−0.404112	−	0.233314i
$125$		−	6.92820i		−	0.619677i
$126$	−1.50000	+	0.866025i	−0.133631	+	0.0771517i
$127$	3.50000	+	6.06218i	0.310575	+	0.537931i	0.978487	−	0.206309i	$-0.0661452\pi$
$127$	3.50000	+	6.06218i	0.310575	+	0.537931i	−0.667912	+	0.744240i	$0.732812\pi$
$128$	10.5000	−	6.06218i	0.928078	−	0.535826i
$129$	4.50000	+	2.59808i	0.396203	+	0.228748i
$130$	−27.0000	−	15.5885i	−2.36806	−	1.36720i
$131$	6.00000	−	3.46410i	0.524222	−	0.302660i	−0.214438	−	0.976738i	$-0.568792\pi$
$131$	6.00000	−	3.46410i	0.524222	−	0.302660i	0.738661	+	0.674078i	$0.235459\pi$
$132$		0			0
$133$	3.00000	−	1.73205i	0.260133	−	0.150188i
$134$		−	12.1244i		−	1.04738i
$135$	−3.00000	−	1.73205i	−0.258199	−	0.149071i
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$	12.0000			1.02151
$139$	−9.50000	−	16.4545i	−0.805779	−	1.39565i	−0.915764	−	0.401718i	$-0.868413\pi$
$139$	−9.50000	−	16.4545i	−0.805779	−	1.39565i	0.109984	−	0.993933i	$-0.464920\pi$
$140$		−	3.46410i		−	0.292770i
$141$	3.00000	−	5.19615i	0.252646	−	0.437595i
$142$			10.3923i			0.872103i
$143$		0			0
$144$	2.50000	−	4.33013i	0.208333	−	0.360844i
$145$	12.0000	−	20.7846i	0.996546	−	1.72607i
$146$	−10.5000	+	6.06218i	−0.868986	+	0.501709i
$147$	−6.00000			−0.494872
$148$	0.500000	+	6.06218i	0.0410997	+	0.498308i
$149$	−12.0000			−0.983078			−0.491539	−	0.870855i	$-0.663566\pi$
$149$	−12.0000			−0.983078			−0.491539	+	0.870855i	$0.663566\pi$
$150$	10.5000	−	6.06218i	0.857321	−	0.494975i
$151$	−8.50000	+	14.7224i	−0.691720	+	1.19809i	0.279554	+	0.960130i	$0.409814\pi$
$151$	−8.50000	+	14.7224i	−0.691720	+	1.19809i	−0.971274	+	0.237964i	$0.923520\pi$
$152$	−3.00000	+	5.19615i	−0.243332	+	0.421464i
$153$	3.00000	+	1.73205i	0.242536	+	0.140028i
$154$		0			0
$155$	−9.00000	+	15.5885i	−0.722897	+	1.25210i
$156$		−	5.19615i		−	0.416025i
$157$	−6.50000	−	11.2583i	−0.518756	−	0.898513i	−0.999762	−	0.0217953i	$-0.993062\pi$
$157$	−6.50000	−	11.2583i	−0.518756	−	0.898513i	0.481006	−	0.876717i	$-0.340272\pi$
$158$	9.00000			0.716002
$159$	12.0000			0.951662
$160$	9.00000	+	15.5885i	0.711512	+	1.23238i
$161$	−6.00000	−	3.46410i	−0.472866	−	0.273009i
$162$		−	1.73205i		−	0.136083i
$163$	−3.00000	+	1.73205i	−0.234978	+	0.135665i	−0.612866	−	0.790186i	$-0.709984\pi$
$163$	−3.00000	+	1.73205i	−0.234978	+	0.135665i	0.377888	+	0.925851i	$0.376650\pi$
$164$	−3.00000	−	5.19615i	−0.234261	−	0.405751i
$165$		0			0
$166$	−9.00000	−	5.19615i	−0.698535	−	0.403300i
$167$	−3.00000	−	1.73205i	−0.232147	−	0.134030i	0.379415	−	0.925227i	$-0.376125\pi$
$167$	−3.00000	−	1.73205i	−0.232147	−	0.134030i	−0.611562	+	0.791196i	$0.709459\pi$
$168$	−1.50000	+	0.866025i	−0.115728	+	0.0668153i
$169$	7.00000	+	12.1244i	0.538462	+	0.932643i
$170$	−18.0000	+	10.3923i	−1.38054	+	0.797053i
$171$			3.46410i			0.264906i
$172$	−4.50000	−	2.59808i	−0.343122	−	0.198101i
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$	12.0000			0.909718
$175$	−7.00000			−0.529150
$176$		0			0
$177$			13.8564i			1.04151i
$178$	12.0000	−	20.7846i	0.899438	−	1.55787i
$179$			13.8564i			1.03568i	0.855479	+	0.517838i	$0.173263\pi$
$179$			13.8564i			1.03568i	−0.855479	+	0.517838i	$0.826737\pi$
$180$	3.00000	+	1.73205i	0.223607	+	0.129099i
$181$	−3.50000	+	6.06218i	−0.260153	+	0.450598i	−0.966282	−	0.257485i	$-0.917106\pi$
$181$	−3.50000	+	6.06218i	−0.260153	+	0.450598i	0.706129	+	0.708083i	$0.250440\pi$
$182$	−4.50000	+	7.79423i	−0.333562	+	0.577747i
$183$		0			0
$184$	12.0000			0.884652
$185$	21.0000	−	1.73205i	1.54395	−	0.127343i
$186$	−9.00000			−0.659912
$187$		0			0
$188$	−3.00000	+	5.19615i	−0.218797	+	0.378968i
$189$	−0.500000	+	0.866025i	−0.0363696	+	0.0629941i
$190$	−18.0000	−	10.3923i	−1.30586	−	0.753937i
$191$		−	10.3923i		−	0.751961i	−0.926628	−	0.375980i	$-0.877306\pi$
$191$		−	10.3923i		−	0.751961i	0.926628	−	0.375980i	$-0.122694\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$		−	19.0526i		−	1.37143i	−0.727869	−	0.685717i	$-0.759489\pi$
$193$		−	19.0526i		−	1.37143i	0.727869	−	0.685717i	$-0.240511\pi$
$194$	−13.5000	−	23.3827i	−0.969244	−	1.67878i
$195$	−18.0000			−1.28901
$196$	6.00000			0.428571
$197$	−12.0000	−	20.7846i	−0.854965	−	1.48084i	−0.876678	−	0.481078i	$-0.840245\pi$
$197$	−12.0000	−	20.7846i	−0.854965	−	1.48084i	0.0217133	−	0.999764i	$-0.493088\pi$
$198$		0			0
$199$			22.5167i			1.59616i	0.602549	+	0.798082i	$0.294152\pi$
$199$			22.5167i			1.59616i	−0.602549	+	0.798082i	$0.705848\pi$
$200$	10.5000	−	6.06218i	0.742462	−	0.428661i
$201$	−3.50000	−	6.06218i	−0.246871	−	0.427593i
$202$	18.0000	−	10.3923i	1.26648	−	0.731200i
$203$	−6.00000	−	3.46410i	−0.421117	−	0.243132i
$204$	−3.00000	−	1.73205i	−0.210042	−	0.121268i
$205$	−18.0000	+	10.3923i	−1.25717	+	0.725830i
$206$	9.00000	+	15.5885i	0.627060	+	1.08610i
$207$	6.00000	−	3.46410i	0.417029	−	0.240772i
$208$		−	25.9808i		−	1.80144i
$209$		0			0
$210$	−3.00000	−	5.19615i	−0.207020	−	0.358569i
$211$	23.0000			1.58339			0.791693	−	0.610920i	$-0.209200\pi$
$211$	23.0000			1.58339			0.791693	+	0.610920i	$0.209200\pi$
$212$	−12.0000			−0.824163
$213$	3.00000	+	5.19615i	0.205557	+	0.356034i
$214$		0			0
$215$	−9.00000	+	15.5885i	−0.613795	+	1.06312i
$216$		−	1.73205i		−	0.117851i
$217$	4.50000	+	2.59808i	0.305480	+	0.176369i
$218$	−1.50000	+	2.59808i	−0.101593	+	0.175964i
$219$	−3.50000	+	6.06218i	−0.236508	+	0.409644i
$220$		0			0
$221$	18.0000			1.21081
$222$	6.00000	+	8.66025i	0.402694	+	0.581238i
$223$	17.0000			1.13840			0.569202	−	0.822198i	$-0.307252\pi$
$223$	17.0000			1.13840			0.569202	+	0.822198i	$0.307252\pi$
$224$	4.50000	−	2.59808i	0.300669	−	0.173591i
$225$	3.50000	−	6.06218i	0.233333	−	0.404145i
$226$	−3.00000	+	5.19615i	−0.199557	+	0.345643i
$227$	−9.00000	−	5.19615i	−0.597351	−	0.344881i	0.170648	−	0.985332i	$-0.445414\pi$
$227$	−9.00000	−	5.19615i	−0.597351	−	0.344881i	−0.767999	+	0.640451i	$0.778747\pi$
$228$		−	3.46410i		−	0.229416i
$229$	−2.50000	+	4.33013i	−0.165205	+	0.286143i	−0.936728	−	0.350058i	$-0.886162\pi$
$229$	−2.50000	+	4.33013i	−0.165205	+	0.286143i	0.771523	+	0.636201i	$0.219495\pi$
$230$			41.5692i			2.74099i
$231$		0			0
$232$	12.0000			0.787839
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$	−4.50000	−	7.79423i	−0.294174	−	0.509525i
$235$	18.0000	+	10.3923i	1.17419	+	0.677919i
$236$		−	13.8564i		−	0.901975i
$237$	4.50000	−	2.59808i	0.292306	−	0.168763i
$238$	3.00000	+	5.19615i	0.194461	+	0.336817i
$239$	9.00000	−	5.19615i	0.582162	−	0.336111i	−0.179830	−	0.983698i	$-0.557555\pi$
$239$	9.00000	−	5.19615i	0.582162	−	0.336111i	0.761992	+	0.647586i	$0.224222\pi$
$240$	15.0000	+	8.66025i	0.968246	+	0.559017i
$241$	−19.5000	−	11.2583i	−1.25611	−	0.725213i	−0.283790	−	0.958886i	$-0.591592\pi$
$241$	−19.5000	−	11.2583i	−1.25611	−	0.725213i	−0.972315	+	0.233674i	$0.924925\pi$
$242$	16.5000	−	9.52628i	1.06066	−	0.612372i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$		−	20.7846i		−	1.32788i
$246$	−9.00000	−	5.19615i	−0.573819	−	0.331295i
$247$	9.00000	+	15.5885i	0.572656	+	0.991870i
$248$	−9.00000			−0.571501
$249$	−6.00000			−0.380235
$250$	6.00000	+	10.3923i	0.379473	+	0.657267i
$251$			10.3923i			0.655956i	0.944685	+	0.327978i	$0.106367\pi$
$251$			10.3923i			0.655956i	−0.944685	+	0.327978i	$0.893633\pi$
$252$	0.500000	−	0.866025i	0.0314970	−	0.0545545i
$253$		0			0
$254$	−10.5000	−	6.06218i	−0.658829	−	0.380375i
$255$	−6.00000	+	10.3923i	−0.375735	+	0.650791i
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	−6.00000	+	3.46410i	−0.374270	+	0.216085i	−0.675322	−	0.737523i	$-0.735995\pi$
$257$	−6.00000	+	3.46410i	−0.374270	+	0.216085i	0.301052	+	0.953608i	$0.402662\pi$
$258$	−9.00000			−0.560316
$259$	−0.500000	−	6.06218i	−0.0310685	−	0.376685i
$260$	18.0000			1.11631
$261$	6.00000	−	3.46410i	0.371391	−	0.214423i
$262$	−6.00000	+	10.3923i	−0.370681	+	0.642039i
$263$	3.00000	−	5.19615i	0.184988	−	0.320408i	−0.758585	−	0.651575i	$-0.774109\pi$
$263$	3.00000	−	5.19615i	0.184988	−	0.320408i	0.943572	+	0.331166i	$0.107442\pi$
$264$		0			0
$265$			41.5692i			2.55358i
$266$	−3.00000	+	5.19615i	−0.183942	+	0.318597i
$267$		−	13.8564i		−	0.847998i
$268$	3.50000	+	6.06218i	0.213797	+	0.370306i
$269$	6.00000			0.365826			0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000			0.365826			0.182913	+	0.983129i	$0.441447\pi$
$270$	6.00000			0.365148
$271$	−3.50000	−	6.06218i	−0.212610	−	0.368251i	0.739921	−	0.672694i	$-0.234863\pi$
$271$	−3.50000	−	6.06218i	−0.212610	−	0.368251i	−0.952531	+	0.304443i	$0.901530\pi$
$272$	−15.0000	−	8.66025i	−0.909509	−	0.525105i
$273$			5.19615i			0.314485i
$274$		0			0
$275$		0			0
$276$	−6.00000	+	3.46410i	−0.361158	+	0.208514i
$277$	6.00000	+	3.46410i	0.360505	+	0.208138i	0.669302	−	0.742990i	$-0.266593\pi$
$277$	6.00000	+	3.46410i	0.360505	+	0.208138i	−0.308797	+	0.951128i	$0.599926\pi$
$278$	28.5000	+	16.4545i	1.70932	+	0.986874i
$279$	−4.50000	+	2.59808i	−0.269408	+	0.155543i
$280$	−3.00000	−	5.19615i	−0.179284	−	0.310530i
$281$	9.00000	−	5.19615i	0.536895	−	0.309976i	−0.206925	−	0.978357i	$-0.566345\pi$
$281$	9.00000	−	5.19615i	0.536895	−	0.309976i	0.743820	+	0.668380i	$0.233012\pi$
$282$			10.3923i			0.618853i
$283$	−10.5000	−	6.06218i	−0.624160	−	0.360359i	0.154327	−	0.988020i	$-0.450679\pi$
$283$	−10.5000	−	6.06218i	−0.624160	−	0.360359i	−0.778487	+	0.627661i	$0.784012\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$	−12.0000			−0.710819
$286$		0			0
$287$	3.00000	+	5.19615i	0.177084	+	0.306719i
$288$			5.19615i			0.306186i
$289$	−2.50000	+	4.33013i	−0.147059	+	0.254713i
$290$			41.5692i			2.44103i
$291$	−13.5000	−	7.79423i	−0.791384	−	0.456906i
$292$	3.50000	−	6.06218i	0.204822	−	0.354762i
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	−0.940252	−	0.340480i	$-0.889411\pi$
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	0.764990	+	0.644042i	$0.222744\pi$
$294$	9.00000	−	5.19615i	0.524891	−	0.303046i
$295$	−48.0000			−2.79467
$296$	6.00000	+	8.66025i	0.348743	+	0.503367i
$297$		0			0
$298$	18.0000	−	10.3923i	1.04271	−	0.602010i
$299$	18.0000	−	31.1769i	1.04097	−	1.80301i
$300$	−3.50000	+	6.06218i	−0.202073	+	0.350000i
$301$	4.50000	+	2.59808i	0.259376	+	0.149751i
$302$		−	29.4449i		−	1.69436i
$303$	6.00000	−	10.3923i	0.344691	−	0.597022i
$304$		−	17.3205i		−	0.993399i
$305$		0			0
$306$	−6.00000			−0.342997
$307$	11.0000			0.627803			0.313902	−	0.949456i	$-0.398364\pi$
$307$	11.0000			0.627803			0.313902	+	0.949456i	$0.398364\pi$
$308$		0			0
$309$	9.00000	+	5.19615i	0.511992	+	0.295599i
$310$		−	31.1769i		−	1.77073i
$311$	−18.0000	+	10.3923i	−1.02069	+	0.589294i	−0.914303	−	0.405032i	$-0.867261\pi$
$311$	−18.0000	+	10.3923i	−1.02069	+	0.589294i	−0.106384	+	0.994325i	$0.533927\pi$
$312$	−4.50000	−	7.79423i	−0.254762	−	0.441261i
$313$	−7.50000	+	4.33013i	−0.423925	+	0.244753i	−0.696755	−	0.717309i	$-0.745374\pi$
$313$	−7.50000	+	4.33013i	−0.423925	+	0.244753i	0.272830	+	0.962062i	$0.412040\pi$
$314$	19.5000	+	11.2583i	1.10045	+	0.635344i
$315$	−3.00000	−	1.73205i	−0.169031	−	0.0975900i
$316$	−4.50000	+	2.59808i	−0.253145	+	0.146153i
$317$	−12.0000	−	20.7846i	−0.673987	−	1.16738i	−0.976764	−	0.214318i	$-0.931247\pi$
$317$	−12.0000	−	20.7846i	−0.673987	−	1.16738i	0.302777	−	0.953062i	$-0.402086\pi$
$318$	−18.0000	+	10.3923i	−1.00939	+	0.582772i
$319$		0			0
$320$	3.00000	+	1.73205i	0.167705	+	0.0968246i
$321$		0			0
$322$	12.0000			0.668734
$323$	12.0000			0.667698
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$		−	36.3731i		−	2.01761i
$326$	3.00000	−	5.19615i	0.166155	−	0.287788i
$327$			1.73205i			0.0957826i
$328$	−9.00000	−	5.19615i	−0.496942	−	0.286910i
$329$	3.00000	−	5.19615i	0.165395	−	0.286473i
$330$		0			0
$331$	−19.5000	+	11.2583i	−1.07182	+	0.618814i	−0.928677	−	0.370889i	$-0.879053\pi$
$331$	−19.5000	+	11.2583i	−1.07182	+	0.618814i	−0.143140	+	0.989703i	$0.545720\pi$
$332$	6.00000			0.329293
$333$	5.50000	+	2.59808i	0.301398	+	0.142374i
$334$	6.00000			0.328305
$335$	21.0000	−	12.1244i	1.14735	−	0.662424i
$336$	2.50000	−	4.33013i	0.136386	−	0.236228i
$337$	3.50000	−	6.06218i	0.190657	−	0.330228i	−0.754811	−	0.655942i	$-0.772271\pi$
$337$	3.50000	−	6.06218i	0.190657	−	0.330228i	0.945468	+	0.325714i	$0.105605\pi$
$338$	−21.0000	−	12.1244i	−1.14225	−	0.659478i
$339$			3.46410i			0.188144i
$340$	6.00000	−	10.3923i	0.325396	−	0.563602i
$341$		0			0
$342$	−3.00000	−	5.19615i	−0.162221	−	0.280976i
$343$	−13.0000			−0.701934
$344$	−9.00000			−0.485247
$345$	12.0000	+	20.7846i	0.646058	+	1.11901i
$346$	−9.00000	−	5.19615i	−0.483843	−	0.279347i
$347$			10.3923i			0.557888i	0.960307	+	0.278944i	$0.0899844\pi$
$347$			10.3923i			0.557888i	−0.960307	+	0.278944i	$0.910016\pi$
$348$	−6.00000	+	3.46410i	−0.321634	+	0.185695i
$349$	−11.0000	−	19.0526i	−0.588817	−	1.01986i	−0.994388	−	0.105797i	$-0.966261\pi$
$349$	−11.0000	−	19.0526i	−0.588817	−	1.01986i	0.405571	−	0.914063i	$-0.367073\pi$
$350$	10.5000	−	6.06218i	0.561249	−	0.324037i
$351$	−4.50000	−	2.59808i	−0.240192	−	0.138675i
$352$		0			0
$353$	−9.00000	+	5.19615i	−0.479022	+	0.276563i	−0.720009	−	0.693965i	$-0.755862\pi$
$353$	−9.00000	+	5.19615i	−0.479022	+	0.276563i	0.240987	+	0.970528i	$0.422529\pi$
$354$	−12.0000	−	20.7846i	−0.637793	−	1.10469i
$355$	−18.0000	+	10.3923i	−0.955341	+	0.551566i
$356$			13.8564i			0.734388i
$357$	3.00000	+	1.73205i	0.158777	+	0.0916698i
$358$	−12.0000	−	20.7846i	−0.634220	−	1.09850i
$359$	−12.0000			−0.633336			−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000			−0.633336			−0.316668	+	0.948536i	$0.602564\pi$
$360$	6.00000			0.316228
$361$	−3.50000	−	6.06218i	−0.184211	−	0.319062i
$362$		−	12.1244i		−	0.637242i
$363$	5.50000	−	9.52628i	0.288675	−	0.500000i
$364$		−	5.19615i		−	0.272352i
$365$	−21.0000	−	12.1244i	−1.09919	−	0.634618i
$366$		0			0
$367$	9.50000	−	16.4545i	0.495896	−	0.858917i	−0.504093	−	0.863649i	$-0.668173\pi$
$367$	9.50000	−	16.4545i	0.495896	−	0.858917i	0.999989	+	0.00473247i	$0.00150640\pi$
$368$	−30.0000	+	17.3205i	−1.56386	+	0.902894i
$369$	−6.00000			−0.312348
$370$	−30.0000	+	20.7846i	−1.55963	+	1.08054i
$371$	12.0000			0.623009
$372$	4.50000	−	2.59808i	0.233314	−	0.134704i
$373$	−6.50000	+	11.2583i	−0.336557	+	0.582934i	−0.983783	−	0.179364i	$-0.942596\pi$
$373$	−6.50000	+	11.2583i	−0.336557	+	0.582934i	0.647225	+	0.762299i	$0.275929\pi$
$374$		0			0
$375$	6.00000	+	3.46410i	0.309839	+	0.178885i
$376$			10.3923i			0.535942i
$377$	18.0000	−	31.1769i	0.927047	−	1.60569i
$378$		−	1.73205i		−	0.0890871i
$379$	10.0000	+	17.3205i	0.513665	+	0.889695i	0.999874	+	0.0158521i	$0.00504609\pi$
$379$	10.0000	+	17.3205i	0.513665	+	0.889695i	−0.486209	+	0.873843i	$0.661621\pi$
$380$	12.0000			0.615587
$381$	−7.00000			−0.358621
$382$	9.00000	+	15.5885i	0.460480	+	0.797575i
$383$	30.0000	+	17.3205i	1.53293	+	0.885037i	0.999225	+	0.0393649i	$0.0125335\pi$
$383$	30.0000	+	17.3205i	1.53293	+	0.885037i	0.533703	+	0.845672i	$0.320800\pi$
$384$			12.1244i			0.618718i
$385$		0			0
$386$	16.5000	+	28.5788i	0.839828	+	1.45462i
$387$	−4.50000	+	2.59808i	−0.228748	+	0.132068i
$388$	13.5000	+	7.79423i	0.685359	+	0.395692i
$389$	24.0000	+	13.8564i	1.21685	+	0.702548i	0.964242	−	0.265022i	$-0.0853791\pi$
$389$	24.0000	+	13.8564i	1.21685	+	0.702548i	0.252606	+	0.967569i	$0.418712\pi$
$390$	27.0000	−	15.5885i	1.36720	−	0.789352i
$391$	−12.0000	−	20.7846i	−0.606866	−	1.05112i
$392$	9.00000	−	5.19615i	0.454569	−	0.262445i
$393$			6.92820i			0.349482i
$394$	36.0000	+	20.7846i	1.81365	+	1.04711i
$395$	9.00000	+	15.5885i	0.452839	+	0.784340i
$396$		0			0
$397$	13.0000			0.652451			0.326226	−	0.945292i	$-0.394223\pi$
$397$	13.0000			0.652451			0.326226	+	0.945292i	$0.394223\pi$
$398$	−19.5000	−	33.7750i	−0.977447	−	1.69299i
$399$			3.46410i			0.173422i
$400$	−17.5000	+	30.3109i	−0.875000	+	1.51554i
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$	10.5000	+	6.06218i	0.523692	+	0.302354i
$403$	−13.5000	+	23.3827i	−0.672483	+	1.16477i
$404$	−6.00000	+	10.3923i	−0.298511	+	0.517036i
$405$	3.00000	−	1.73205i	0.149071	−	0.0860663i
$406$	12.0000			0.595550
$407$		0			0
$408$	−6.00000			−0.297044
$409$	−16.5000	+	9.52628i	−0.815872	+	0.471044i	−0.848991	−	0.528407i	$-0.822789\pi$
$409$	−16.5000	+	9.52628i	−0.815872	+	0.471044i	0.0331186	+	0.999451i	$0.489456\pi$
$410$	18.0000	−	31.1769i	0.888957	−	1.53972i
$411$		0			0
$412$	−9.00000	−	5.19615i	−0.443398	−	0.255996i
$413$			13.8564i			0.681829i
$414$	−6.00000	+	10.3923i	−0.294884	+	0.510754i
$415$		−	20.7846i		−	1.02028i
$416$	13.5000	+	23.3827i	0.661892	+	1.14643i
$417$	19.0000			0.930434
$418$		0			0
$419$	15.0000	+	25.9808i	0.732798	+	1.26924i	0.955683	+	0.294398i	$0.0951193\pi$
$419$	15.0000	+	25.9808i	0.732798	+	1.26924i	−0.222885	+	0.974845i	$0.571547\pi$
$420$	3.00000	+	1.73205i	0.146385	+	0.0845154i
$421$			13.8564i			0.675320i	0.941268	+	0.337660i	$0.109635\pi$
$421$			13.8564i			0.675320i	−0.941268	+	0.337660i	$0.890365\pi$
$422$	−34.5000	+	19.9186i	−1.67943	+	0.969622i
$423$	3.00000	+	5.19615i	0.145865	+	0.252646i
$424$	−18.0000	+	10.3923i	−0.874157	+	0.504695i
$425$	−21.0000	−	12.1244i	−1.01865	−	0.588118i
$426$	−9.00000	−	5.19615i	−0.436051	−	0.251754i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		−	31.1769i		−	1.50348i
$431$	−15.0000	−	8.66025i	−0.722525	−	0.417150i	0.0931566	−	0.995651i	$-0.470304\pi$
$431$	−15.0000	−	8.66025i	−0.722525	−	0.417150i	−0.815681	+	0.578502i	$0.803638\pi$
$432$	2.50000	+	4.33013i	0.120281	+	0.208333i
$433$	10.0000			0.480569			0.240285	−	0.970702i	$-0.422759\pi$
$433$	10.0000			0.480569			0.240285	+	0.970702i	$0.422759\pi$
$434$	−9.00000			−0.432014
$435$	12.0000	+	20.7846i	0.575356	+	0.996546i
$436$		−	1.73205i		−	0.0829502i
$437$	12.0000	−	20.7846i	0.574038	−	0.994263i
$438$		−	12.1244i		−	0.579324i
$439$	28.5000	+	16.4545i	1.36023	+	0.785330i	0.989654	−	0.143472i	$-0.0458268\pi$
$439$	28.5000	+	16.4545i	1.36023	+	0.785330i	0.370576	+	0.928802i	$0.379160\pi$
$440$		0			0
$441$	3.00000	−	5.19615i	0.142857	−	0.247436i
$442$	−27.0000	+	15.5885i	−1.28426	+	0.741467i
$443$	6.00000			0.285069			0.142534	−	0.989790i	$-0.454475\pi$
$443$	6.00000			0.285069			0.142534	+	0.989790i	$0.454475\pi$
$444$	−5.50000	−	2.59808i	−0.261018	−	0.123299i
$445$	48.0000			2.27542
$446$	−25.5000	+	14.7224i	−1.20746	+	0.697127i
$447$	6.00000	−	10.3923i	0.283790	−	0.491539i
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$449$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$450$			12.1244i			0.571548i
$451$		0			0
$452$		−	3.46410i		−	0.162938i
$453$	−8.50000	−	14.7224i	−0.399365	−	0.691720i
$454$	18.0000			0.844782
$455$	−18.0000			−0.843853
$456$	−3.00000	−	5.19615i	−0.140488	−	0.243332i
$457$	30.0000	+	17.3205i	1.40334	+	0.810219i	0.994734	−	0.102491i	$-0.0326814\pi$
$457$	30.0000	+	17.3205i	1.40334	+	0.810219i	0.408607	+	0.912710i	$0.366015\pi$
$458$		−	8.66025i		−	0.404667i
$459$	−3.00000	+	1.73205i	−0.140028	+	0.0808452i
$460$	−12.0000	−	20.7846i	−0.559503	−	0.969087i
$461$	−15.0000	+	8.66025i	−0.698620	+	0.403348i	−0.806833	−	0.590779i	$-0.798820\pi$
$461$	−15.0000	+	8.66025i	−0.698620	+	0.403348i	0.108213	+	0.994128i	$0.465487\pi$
$462$		0			0
$463$	34.5000	+	19.9186i	1.60335	+	0.925695i	0.990811	+	0.135256i	$0.0431856\pi$
$463$	34.5000	+	19.9186i	1.60335	+	0.925695i	0.612540	+	0.790439i	$0.290148\pi$
$464$	−30.0000	+	17.3205i	−1.39272	+	0.804084i
$465$	−9.00000	−	15.5885i	−0.417365	−	0.722897i
$466$	9.00000	−	5.19615i	0.416917	−	0.240707i
$467$			13.8564i			0.641198i	0.947215	+	0.320599i	$0.103884\pi$
$467$			13.8564i			0.641198i	−0.947215	+	0.320599i	$0.896116\pi$
$468$	4.50000	+	2.59808i	0.208013	+	0.120096i
$469$	−3.50000	−	6.06218i	−0.161615	−	0.279925i
$470$	−36.0000			−1.66056
$471$	13.0000			0.599008
$472$	−12.0000	−	20.7846i	−0.552345	−	0.956689i
$473$		0			0
$474$	−4.50000	+	7.79423i	−0.206692	+	0.358001i
$475$		−	24.2487i		−	1.11261i
$476$	−3.00000	−	1.73205i	−0.137505	−	0.0793884i
$477$	−6.00000	+	10.3923i	−0.274721	+	0.475831i
$478$	−9.00000	+	15.5885i	−0.411650	+	0.712999i
$479$	15.0000	−	8.66025i	0.685367	−	0.395697i	−0.116507	−	0.993190i	$-0.537170\pi$
$479$	15.0000	−	8.66025i	0.685367	−	0.395697i	0.801874	+	0.597493i	$0.203836\pi$
$480$	−18.0000			−0.821584
$481$	31.5000	−	2.59808i	1.43628	−	0.118462i
$482$	39.0000			1.77640
$483$	6.00000	−	3.46410i	0.273009	−	0.157622i
$484$	−5.50000	+	9.52628i	−0.250000	+	0.433013i
$485$	27.0000	−	46.7654i	1.22601	−	2.12351i
$486$	1.50000	+	0.866025i	0.0680414	+	0.0392837i
$487$		−	24.2487i		−	1.09881i	−0.835555	−	0.549407i	$-0.814854\pi$
$487$		−	24.2487i		−	1.09881i	0.835555	−	0.549407i	$-0.185146\pi$
$488$		0			0
$489$		−	3.46410i		−	0.156652i
$490$	18.0000	+	31.1769i	0.813157	+	1.40843i
$491$	−18.0000			−0.812329			−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000			−0.812329			−0.406164	+	0.913800i	$0.633134\pi$
$492$	6.00000			0.270501
$493$	−12.0000	−	20.7846i	−0.540453	−	0.936092i
$494$	−27.0000	−	15.5885i	−1.21479	−	0.701358i
$495$		0			0
$496$	22.5000	−	12.9904i	1.01028	−	0.583285i
$497$	3.00000	+	5.19615i	0.134568	+	0.233079i
$498$	9.00000	−	5.19615i	0.403300	−	0.232845i
$499$	−27.0000	−	15.5885i	−1.20869	−	0.697835i	−0.246214	−	0.969216i	$-0.579187\pi$
$499$	−27.0000	−	15.5885i	−1.20869	−	0.697835i	−0.962472	+	0.271380i	$0.912520\pi$
$500$	−6.00000	−	3.46410i	−0.268328	−	0.154919i
$501$	3.00000	−	1.73205i	0.134030	−	0.0773823i
$502$	−9.00000	−	15.5885i	−0.401690	−	0.695747i
$503$	−21.0000	+	12.1244i	−0.936344	+	0.540598i	−0.888812	−	0.458271i	$-0.848469\pi$
$503$	−21.0000	+	12.1244i	−0.936344	+	0.540598i	−0.0475314	+	0.998870i	$0.515135\pi$
$504$		−	1.73205i		−	0.0771517i
$505$	36.0000	+	20.7846i	1.60198	+	0.924903i
$506$		0			0
$507$	−14.0000			−0.621762
$508$	7.00000			0.310575
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$		−	20.7846i		−	0.920358i
$511$	−3.50000	+	6.06218i	−0.154831	+	0.268175i
$512$		−	8.66025i		−	0.382733i
$513$	−3.00000	−	1.73205i	−0.132453	−	0.0764719i
$514$	6.00000	−	10.3923i	0.264649	−	0.458385i
$515$	−18.0000	+	31.1769i	−0.793175	+	1.37382i
$516$	4.50000	−	2.59808i	0.198101	−	0.114374i
$517$		0			0
$518$	6.00000	+	8.66025i	0.263625	+	0.380510i
$519$	−6.00000			−0.263371
$520$	27.0000	−	15.5885i	1.18403	−	0.683599i
$521$	−6.00000	+	10.3923i	−0.262865	+	0.455295i	−0.967002	−	0.254769i	$-0.918001\pi$
$521$	−6.00000	+	10.3923i	−0.262865	+	0.455295i	0.704137	+	0.710064i	$0.251334\pi$
$522$	−6.00000	+	10.3923i	−0.262613	+	0.454859i
$523$	−7.50000	−	4.33013i	−0.327952	−	0.189343i	0.326979	−	0.945031i	$-0.393969\pi$
$523$	−7.50000	−	4.33013i	−0.327952	−	0.189343i	−0.654932	+	0.755688i	$0.727303\pi$
$524$		−	6.92820i		−	0.302660i
$525$	3.50000	−	6.06218i	0.152753	−	0.264575i
$526$			10.3923i			0.453126i
$527$	9.00000	+	15.5885i	0.392046	+	0.679044i
$528$		0			0
$529$	−25.0000			−1.08696
$530$	−36.0000	−	62.3538i	−1.56374	−	2.70848i
$531$	−12.0000	−	6.92820i	−0.520756	−	0.300658i
$532$		−	3.46410i		−	0.150188i
$533$	−27.0000	+	15.5885i	−1.16950	+	0.675211i
$534$	12.0000	+	20.7846i	0.519291	+	0.899438i
$535$		0			0
$536$	10.5000	+	6.06218i	0.453531	+	0.261846i
$537$	−12.0000	−	6.92820i	−0.517838	−	0.298974i
$538$	−9.00000	+	5.19615i	−0.388018	+	0.224022i
$539$		0			0
$540$	−3.00000	+	1.73205i	−0.129099	+	0.0745356i
$541$		−	22.5167i		−	0.968067i	−0.875050	−	0.484033i	$-0.839171\pi$
$541$		−	22.5167i		−	0.968067i	0.875050	−	0.484033i	$-0.160829\pi$
$542$	10.5000	+	6.06218i	0.451014	+	0.260393i
$543$	−3.50000	−	6.06218i	−0.150199	−	0.260153i
$544$	18.0000			0.771744
$545$	−6.00000			−0.257012
$546$	−4.50000	−	7.79423i	−0.192582	−	0.333562i
$547$			22.5167i			0.962743i	0.876517	+	0.481371i	$0.159861\pi$
$547$			22.5167i			0.962743i	−0.876517	+	0.481371i	$0.840139\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	12.0000	−	20.7846i	0.511217	−	0.885454i
$552$	−6.00000	+	10.3923i	−0.255377	+	0.442326i
$553$	4.50000	−	2.59808i	0.191359	−	0.110481i
$554$	−12.0000			−0.509831
$555$	−9.00000	+	19.0526i	−0.382029	+	0.808736i
$556$	−19.0000			−0.805779
$557$	−15.0000	+	8.66025i	−0.635570	+	0.366947i	−0.782906	−	0.622140i	$-0.786264\pi$
$557$	−15.0000	+	8.66025i	−0.635570	+	0.366947i	0.147336	+	0.989087i	$0.452930\pi$
$558$	4.50000	−	7.79423i	0.190500	−	0.329956i
$559$	−13.5000	+	23.3827i	−0.570989	+	0.988982i
$560$	15.0000	+	8.66025i	0.633866	+	0.365963i
$561$		0			0
$562$	−9.00000	+	15.5885i	−0.379642	+	0.657559i
$563$		−	10.3923i		−	0.437983i	−0.975727	−	0.218992i	$-0.929723\pi$
$563$		−	10.3923i		−	0.437983i	0.975727	−	0.218992i	$-0.0702768\pi$
$564$	−3.00000	−	5.19615i	−0.126323	−	0.218797i
$565$	−12.0000			−0.504844
$566$	21.0000			0.882696
$567$	−0.500000	−	0.866025i	−0.0209980	−	0.0363696i
$568$	−9.00000	−	5.19615i	−0.377632	−	0.218026i
$569$		−	13.8564i		−	0.580891i	−0.956892	−	0.290445i	$-0.906197\pi$
$569$		−	13.8564i		−	0.580891i	0.956892	−	0.290445i	$-0.0938035\pi$
$570$	18.0000	−	10.3923i	0.753937	−	0.435286i
$571$	2.50000	+	4.33013i	0.104622	+	0.181210i	0.913584	−	0.406651i	$-0.133303\pi$
$571$	2.50000	+	4.33013i	0.104622	+	0.181210i	−0.808962	+	0.587861i	$0.799970\pi$
$572$		0			0
$573$	9.00000	+	5.19615i	0.375980	+	0.217072i
$574$	−9.00000	−	5.19615i	−0.375653	−	0.216883i
$575$	−42.0000	+	24.2487i	−1.75152	+	1.01124i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$577$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$578$		−	8.66025i		−	0.360219i
$579$	16.5000	+	9.52628i	0.685717	+	0.395899i
$580$	−12.0000	−	20.7846i	−0.498273	−	0.863034i
$581$	−6.00000			−0.248922
$582$	27.0000			1.11919
$583$		0			0
$584$		−	12.1244i		−	0.501709i
$585$	9.00000	−	15.5885i	0.372104	−	0.644503i
$586$		−	10.3923i		−	0.429302i
$587$	−18.0000	−	10.3923i	−0.742940	−	0.428936i	0.0801976	−	0.996779i	$-0.474445\pi$
$587$	−18.0000	−	10.3923i	−0.742940	−	0.428936i	−0.823137	+	0.567843i	$0.807778\pi$
$588$	−3.00000	+	5.19615i	−0.123718	+	0.214286i
$589$	−9.00000	+	15.5885i	−0.370839	+	0.642311i
$590$	72.0000	−	41.5692i	2.96419	−	1.71138i
$591$	24.0000			0.987228
$592$	−27.5000	−	12.9904i	−1.13024	−	0.533901i
$593$	−6.00000			−0.246390			−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000			−0.246390			−0.123195	+	0.992382i	$0.539314\pi$
$594$		0			0
$595$	−6.00000	+	10.3923i	−0.245976	+	0.426043i
$596$	−6.00000	+	10.3923i	−0.245770	+	0.425685i
$597$	−19.5000	−	11.2583i	−0.798082	−	0.460773i
$598$			62.3538i			2.54984i
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	−0.999938	−	0.0111569i	$-0.996449\pi$
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	0.509631	+	0.860393i	$0.329782\pi$
$600$			12.1244i			0.494975i
$601$	−18.5000	−	32.0429i	−0.754631	−	1.30706i	−0.945558	−	0.325455i	$-0.894483\pi$
$601$	−18.5000	−	32.0429i	−0.754631	−	1.30706i	0.190927	−	0.981604i	$-0.438851\pi$
$602$	−9.00000			−0.366813
$603$	7.00000			0.285062
$604$	8.50000	+	14.7224i	0.345860	+	0.599047i
$605$	33.0000	+	19.0526i	1.34164	+	0.774597i
$606$			20.7846i			0.844317i
$607$	39.0000	−	22.5167i	1.58296	−	0.913923i	0.588537	−	0.808470i	$-0.299704\pi$
$607$	39.0000	−	22.5167i	1.58296	−	0.913923i	0.994424	−	0.105453i	$-0.0336291\pi$
$608$	9.00000	+	15.5885i	0.364998	+	0.632195i
$609$	6.00000	−	3.46410i	0.243132	−	0.140372i
$610$		0			0
$611$	27.0000	+	15.5885i	1.09230	+	0.630641i
$612$	3.00000	−	1.73205i	0.121268	−	0.0700140i
$613$	11.0000	+	19.0526i	0.444286	+	0.769526i	0.998002	−	0.0631797i	$-0.0201241\pi$
$613$	11.0000	+	19.0526i	0.444286	+	0.769526i	−0.553716	+	0.832705i	$0.686791\pi$
$614$	−16.5000	+	9.52628i	−0.665886	+	0.384449i
$615$		−	20.7846i		−	0.838116i
$616$		0			0
$617$	−3.00000	−	5.19615i	−0.120775	−	0.209189i	0.799298	−	0.600935i	$-0.205205\pi$
$617$	−3.00000	−	5.19615i	−0.120775	−	0.209189i	−0.920074	+	0.391745i	$0.871871\pi$
$618$	−18.0000			−0.724066
$619$	−1.00000			−0.0401934			−0.0200967	−	0.999798i	$-0.506397\pi$
$619$	−1.00000			−0.0401934			−0.0200967	+	0.999798i	$0.506397\pi$
$620$	9.00000	+	15.5885i	0.361449	+	0.626048i
$621$			6.92820i			0.278019i
$622$	18.0000	−	31.1769i	0.721734	−	1.25008i
$623$		−	13.8564i		−	0.555145i
$624$	22.5000	+	12.9904i	0.900721	+	0.520031i
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	7.50000	−	12.9904i	0.299760	−	0.519200i
$627$		0			0
$628$	−13.0000			−0.518756
$629$	9.00000	−	19.0526i	0.358854	−	0.759675i
$630$	6.00000			0.239046
$631$	4.50000	−	2.59808i	0.179142	−	0.103428i	−0.407747	−	0.913095i	$-0.633686\pi$
$631$	4.50000	−	2.59808i	0.179142	−	0.103428i	0.586890	+	0.809667i	$0.300352\pi$
$632$	−4.50000	+	7.79423i	−0.179000	+	0.310038i
$633$	−11.5000	+	19.9186i	−0.457084	+	0.791693i
$634$	36.0000	+	20.7846i	1.42974	+	0.825462i
$635$		−	24.2487i		−	0.962281i
$636$	6.00000	−	10.3923i	0.237915	−	0.412082i
$637$		−	31.1769i		−	1.23527i
$638$		0			0
$639$	−6.00000			−0.237356
$640$	−42.0000			−1.66020
$641$	12.0000	+	20.7846i	0.473972	+	0.820943i	0.999556	−	0.0297987i	$-0.00948663\pi$
$641$	12.0000	+	20.7846i	0.473972	+	0.820943i	−0.525584	+	0.850741i	$0.676153\pi$
$642$		0			0
$643$			12.1244i			0.478138i	0.971003	+	0.239069i	$0.0768422\pi$
$643$			12.1244i			0.478138i	−0.971003	+	0.239069i	$0.923158\pi$
$644$	−6.00000	+	3.46410i	−0.236433	+	0.136505i
$645$	−9.00000	−	15.5885i	−0.354375	−	0.613795i
$646$	−18.0000	+	10.3923i	−0.708201	+	0.408880i
$647$	−39.0000	−	22.5167i	−1.53325	−	0.885221i	−0.999209	−	0.0397614i	$-0.987340\pi$
$647$	−39.0000	−	22.5167i	−1.53325	−	0.885221i	−0.534039	−	0.845460i	$-0.679326\pi$
$648$	1.50000	+	0.866025i	0.0589256	+	0.0340207i
$649$		0			0
$650$	31.5000	+	54.5596i	1.23553	+	2.14000i
$651$	−4.50000	+	2.59808i	−0.176369	+	0.101827i
$652$			3.46410i			0.135665i
$653$	−6.00000	−	3.46410i	−0.234798	−	0.135561i	0.377985	−	0.925812i	$-0.376617\pi$
$653$	−6.00000	−	3.46410i	−0.234798	−	0.135561i	−0.612784	+	0.790251i	$0.709950\pi$
$654$	−1.50000	−	2.59808i	−0.0586546	−	0.101593i
$655$	−24.0000			−0.937758
$656$	30.0000			1.17130
$657$	−3.50000	−	6.06218i	−0.136548	−	0.236508i
$658$			10.3923i			0.405134i
$659$	15.0000	−	25.9808i	0.584317	−	1.01207i	−0.410643	−	0.911796i	$-0.634696\pi$
$659$	15.0000	−	25.9808i	0.584317	−	1.01207i	0.994960	−	0.100271i	$-0.0319709\pi$
$660$		0			0
$661$	−19.5000	−	11.2583i	−0.758462	−	0.437898i	0.0702812	−	0.997527i	$-0.477610\pi$
$661$	−19.5000	−	11.2583i	−0.758462	−	0.437898i	−0.828743	+	0.559629i	$0.810944\pi$
$662$	19.5000	−	33.7750i	0.757889	−	1.31270i
$663$	−9.00000	+	15.5885i	−0.349531	+	0.605406i
$664$	9.00000	−	5.19615i	0.349268	−	0.201650i
$665$	−12.0000			−0.465340
$666$	−10.5000	+	0.866025i	−0.406867	+	0.0335578i
$667$	−48.0000			−1.85857
$668$	−3.00000	+	1.73205i	−0.116073	+	0.0670151i
$669$	−8.50000	+	14.7224i	−0.328629	+	0.569202i
$670$	−21.0000	+	36.3731i	−0.811301	+	1.40521i
$671$		0			0
$672$			5.19615i			0.200446i
$673$	7.00000	−	12.1244i	0.269830	−	0.467360i	−0.698988	−	0.715134i	$-0.746366\pi$
$673$	7.00000	−	12.1244i	0.269830	−	0.467360i	0.968818	+	0.247774i	$0.0796991\pi$
$674$			12.1244i			0.467013i
$675$	3.50000	+	6.06218i	0.134715	+	0.233333i
$676$	14.0000			0.538462
$677$		0			0			−	1.00000i	$-0.5\pi$
$677$		0			0				1.00000i	$0.5\pi$
$678$	−3.00000	−	5.19615i	−0.115214	−	0.199557i
$679$	−13.5000	−	7.79423i	−0.518082	−	0.299115i
$680$		−	20.7846i		−	0.797053i
$681$	9.00000	−	5.19615i	0.344881	−	0.199117i
$682$		0			0
$683$	33.0000	−	19.0526i	1.26271	−	0.729026i	0.289112	−	0.957295i	$-0.406640\pi$
$683$	33.0000	−	19.0526i	1.26271	−	0.729026i	0.973598	+	0.228269i	$0.0733067\pi$
$684$	3.00000	+	1.73205i	0.114708	+	0.0662266i
$685$		0			0
$686$	19.5000	−	11.2583i	0.744513	−	0.429845i
$687$	−2.50000	−	4.33013i	−0.0953809	−	0.165205i
$688$	22.5000	−	12.9904i	0.857804	−	0.495254i
$689$			62.3538i			2.37549i
$690$	−36.0000	−	20.7846i	−1.37050	−	0.791257i
$691$	−18.5000	−	32.0429i	−0.703773	−	1.21897i	−0.967132	−	0.254273i	$-0.918164\pi$
$691$	−18.5000	−	32.0429i	−0.703773	−	1.21897i	0.263359	−	0.964698i	$-0.415170\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−9.00000	−	15.5885i	−0.341635	−	0.591730i
$695$			65.8179i			2.49662i
$696$	−6.00000	+	10.3923i	−0.227429	+	0.393919i
$697$			20.7846i			0.787273i
$698$	33.0000	+	19.0526i	1.24907	+	0.721150i
$699$	3.00000	−	5.19615i	0.113470	−	0.196537i
$700$	−3.50000	+	6.06218i	−0.132288	+	0.229129i
$701$	−18.0000	+	10.3923i	−0.679851	+	0.392512i	−0.799799	−	0.600268i	$-0.795061\pi$
$701$	−18.0000	+	10.3923i	−0.679851	+	0.392512i	0.119948	+	0.992780i	$0.461727\pi$
$702$	9.00000			0.339683
$703$	21.0000	−	1.73205i	0.792030	−	0.0653255i
$704$		0			0
$705$	−18.0000	+	10.3923i	−0.677919	+	0.391397i
$706$	9.00000	−	15.5885i	0.338719	−	0.586679i
$707$	6.00000	−	10.3923i	0.225653	−	0.390843i
$708$	12.0000	+	6.92820i	0.450988	+	0.260378i
$709$		−	15.5885i		−	0.585437i	−0.956199	−	0.292718i	$-0.905440\pi$
$709$		−	15.5885i		−	0.585437i	0.956199	−	0.292718i	$-0.0945598\pi$
$710$	18.0000	−	31.1769i	0.675528	−	1.17005i
$711$			5.19615i			0.194871i
$712$	12.0000	+	20.7846i	0.449719	+	0.778936i
$713$	36.0000			1.34821
$714$	−6.00000			−0.224544
$715$		0			0
$716$	12.0000	+	6.92820i	0.448461	+	0.258919i
$717$			10.3923i			0.388108i
$718$	18.0000	−	10.3923i	0.671754	−	0.387837i
$719$	−15.0000	−	25.9808i	−0.559406	−	0.968919i	−0.997546	−	0.0700124i	$-0.977696\pi$
$719$	−15.0000	−	25.9808i	−0.559406	−	0.968919i	0.438141	−	0.898906i	$-0.355637\pi$
$720$	−15.0000	+	8.66025i	−0.559017	+	0.322749i
$721$	9.00000	+	5.19615i	0.335178	+	0.193515i
$722$	10.5000	+	6.06218i	0.390770	+	0.225611i
$723$	19.5000	−	11.2583i	0.725213	−	0.418702i
$724$	3.50000	+	6.06218i	0.130076	+	0.225299i
$725$	−42.0000	+	24.2487i	−1.55984	+	0.900575i
$726$			19.0526i			0.707107i
$727$	−7.50000	−	4.33013i	−0.278160	−	0.160596i	0.354430	−	0.935082i	$-0.384675\pi$
$727$	−7.50000	−	4.33013i	−0.278160	−	0.160596i	−0.632590	+	0.774487i	$0.718008\pi$
$728$	−4.50000	−	7.79423i	−0.166781	−	0.288873i
$729$	1.00000			0.0370370
$730$	42.0000			1.55449
$731$	9.00000	+	15.5885i	0.332877	+	0.576560i
$732$		0			0
$733$	−8.50000	+	14.7224i	−0.313955	+	0.543785i	−0.979215	−	0.202826i	$-0.934987\pi$
$733$	−8.50000	+	14.7224i	−0.313955	+	0.543785i	0.665260	+	0.746612i	$0.268321\pi$
$734$			32.9090i			1.21469i
$735$	18.0000	+	10.3923i	0.663940	+	0.383326i
$736$	18.0000	−	31.1769i	0.663489	−	1.14920i
$737$		0			0
$738$	9.00000	−	5.19615i	0.331295	−	0.191273i
$739$	−16.0000			−0.588570			−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−16.0000			−0.588570			−0.294285	+	0.955718i	$0.595081\pi$
$740$	9.00000	−	19.0526i	0.330847	−	0.700386i
$741$	−18.0000			−0.661247
$742$	−18.0000	+	10.3923i	−0.660801	+	0.381514i
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	−0.320166	−	0.947361i	$-0.603739\pi$
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	0.980522	−	0.196409i	$-0.0629279\pi$
$744$	4.50000	−	7.79423i	0.164978	−	0.285750i
$745$	36.0000	+	20.7846i	1.31894	+	0.761489i
$746$		−	22.5167i		−	0.824394i
$747$	3.00000	−	5.19615i	0.109764	−	0.190117i
$748$		0			0
$749$		0			0
$750$	−12.0000			−0.438178
$751$	31.0000			1.13121			0.565603	−	0.824678i	$-0.308643\pi$
$751$	31.0000			1.13121			0.565603	+	0.824678i	$0.308643\pi$
$752$	−15.0000	−	25.9808i	−0.546994	−	0.947421i
$753$	−9.00000	−	5.19615i	−0.327978	−	0.189358i
$754$			62.3538i			2.27079i
$755$	51.0000	−	29.4449i	1.85608	−	1.07161i
$756$	0.500000	+	0.866025i	0.0181848	+	0.0314970i
$757$	−25.5000	+	14.7224i	−0.926813	+	0.535096i	−0.885802	−	0.464063i	$-0.846391\pi$
$757$	−25.5000	+	14.7224i	−0.926813	+	0.535096i	−0.0410110	+	0.999159i	$0.513058\pi$
$758$	−30.0000	−	17.3205i	−1.08965	−	0.629109i
$759$		0			0
$760$	18.0000	−	10.3923i	0.652929	−	0.376969i
$761$	9.00000	+	15.5885i	0.326250	+	0.565081i	0.981764	−	0.190101i	$-0.0608816\pi$
$761$	9.00000	+	15.5885i	0.326250	+	0.565081i	−0.655515	+	0.755182i	$0.727548\pi$
$762$	10.5000	−	6.06218i	0.380375	−	0.219610i
$763$			1.73205i			0.0627044i
$764$	−9.00000	−	5.19615i	−0.325609	−	0.187990i
$765$	−6.00000	−	10.3923i	−0.216930	−	0.375735i
$766$	−60.0000			−2.16789
$767$	−72.0000			−2.59977
$768$	−9.50000	−	16.4545i	−0.342802	−	0.593750i
$769$		−	29.4449i		−	1.06181i	−0.847432	−	0.530904i	$-0.821852\pi$
$769$		−	29.4449i		−	1.06181i	0.847432	−	0.530904i	$-0.178148\pi$
$770$		0			0
$771$		−	6.92820i		−	0.249513i
$772$	−16.5000	−	9.52628i	−0.593848	−	0.342858i
$773$	−24.0000	+	41.5692i	−0.863220	+	1.49514i	0.00558380	+	0.999984i	$0.498223\pi$
$773$	−24.0000	+	41.5692i	−0.863220	+	1.49514i	−0.868804	+	0.495156i	$0.835111\pi$
$774$	4.50000	−	7.79423i	0.161749	−	0.280158i
$775$	31.5000	−	18.1865i	1.13151	−	0.653280i
$776$	27.0000			0.969244
$777$	5.50000	+	2.59808i	0.197311	+	0.0932055i
$778$	−48.0000			−1.72088
$779$	−18.0000	+	10.3923i	−0.644917	+	0.372343i
$780$	−9.00000	+	15.5885i	−0.322252	+	0.558156i
$781$		0			0
$782$	36.0000	+	20.7846i	1.28736	+	0.743256i
$783$			6.92820i			0.247594i
$784$	−15.0000	+	25.9808i	−0.535714	+	0.927884i
$785$			45.0333i			1.60731i
$786$	−6.00000	−	10.3923i	−0.214013	−	0.370681i
$787$	−7.00000			−0.249523			−0.124762	−	0.992187i	$-0.539817\pi$
$787$	−7.00000			−0.249523			−0.124762	+	0.992187i	$0.539817\pi$
$788$	−24.0000			−0.854965
$789$	3.00000	+	5.19615i	0.106803	+	0.184988i
$790$	−27.0000	−	15.5885i	−0.960617	−	0.554612i
$791$			3.46410i			0.123169i
$792$		0			0
$793$		0			0
$794$	−19.5000	+	11.2583i	−0.692029	+	0.399543i
$795$	−36.0000	−	20.7846i	−1.27679	−	0.737154i
$796$	19.5000	+	11.2583i	0.691159	+	0.399041i
$797$	6.00000	−	3.46410i	0.212531	−	0.122705i	−0.389956	−	0.920833i	$-0.627510\pi$
$797$	6.00000	−	3.46410i	0.212531	−	0.122705i	0.602487	+	0.798129i	$0.294177\pi$
$798$	−3.00000	−	5.19615i	−0.106199	−	0.183942i
$799$	18.0000	−	10.3923i	0.636794	−	0.367653i
$800$		−	36.3731i		−	1.28598i
$801$	12.0000	+	6.92820i	0.423999	+	0.244796i
$802$		0			0
$803$		0			0
$804$	−7.00000			−0.246871
$805$	12.0000	+	20.7846i	0.422944	+	0.732561i
$806$		−	46.7654i		−	1.64724i
$807$	−3.00000	+	5.19615i	−0.105605	+	0.182913i
$808$			20.7846i			0.731200i
$809$	21.0000	+	12.1244i	0.738321	+	0.426270i	0.821458	−	0.570268i	$-0.193161\pi$
$809$	21.0000	+	12.1244i	0.738321	+	0.426270i	−0.0831377	+	0.996538i	$0.526494\pi$
$810$	−3.00000	+	5.19615i	−0.105409	+	0.182574i
$811$	10.0000	−	17.3205i	0.351147	−	0.608205i	−0.635303	−	0.772263i	$-0.719125\pi$
$811$	10.0000	−	17.3205i	0.351147	−	0.608205i	0.986451	+	0.164057i	$0.0524582\pi$
$812$	−6.00000	+	3.46410i	−0.210559	+	0.121566i
$813$	7.00000			0.245501
$814$		0			0
$815$	12.0000			0.420342
$816$	15.0000	−	8.66025i	0.525105	−	0.303170i
$817$	−9.00000	+	15.5885i	−0.314870	+	0.545371i
$818$	16.5000	−	28.5788i	0.576909	−	0.999236i
$819$	−4.50000	−	2.59808i	−0.157243	−	0.0907841i
$820$			20.7846i			0.725830i
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	−0.808915	−	0.587925i	$-0.799945\pi$
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	0.913616	+	0.406578i	$0.133278\pi$
$822$		0			0
$823$	9.50000	+	16.4545i	0.331149	+	0.573567i	0.982737	−	0.185006i	$-0.0592303\pi$
$823$	9.50000	+	16.4545i	0.331149	+	0.573567i	−0.651588	+	0.758573i	$0.725897\pi$
$824$	−18.0000			−0.627060
$825$		0			0
$826$	−12.0000	−	20.7846i	−0.417533	−	0.723189i
$827$	30.0000	+	17.3205i	1.04320	+	0.602293i	0.920739	−	0.390180i	$-0.127587\pi$
$827$	30.0000	+	17.3205i	1.04320	+	0.602293i	0.122464	+	0.992473i	$0.460921\pi$
$828$		−	6.92820i		−	0.240772i
$829$	−19.5000	+	11.2583i	−0.677263	+	0.391018i	−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−19.5000	+	11.2583i	−0.677263	+	0.391018i	0.121560	+	0.992584i	$0.461210\pi$
$830$	18.0000	+	31.1769i	0.624789	+	1.08217i
$831$	−6.00000	+	3.46410i	−0.208138	+	0.120168i
$832$	4.50000	+	2.59808i	0.156009	+	0.0900721i
$833$	−18.0000	−	10.3923i	−0.623663	−	0.360072i
$834$	−28.5000	+	16.4545i	−0.986874	+	0.569772i
$835$	6.00000	+	10.3923i	0.207639	+	0.359641i
$836$		0			0
$837$		−	5.19615i		−	0.179605i
$838$	−45.0000	−	25.9808i	−1.55450	−	0.897491i
$839$	−15.0000	−	25.9808i	−0.517858	−	0.896956i	−0.999785	−	0.0207443i	$-0.993396\pi$
$839$	−15.0000	−	25.9808i	−0.517858	−	0.896956i	0.481927	−	0.876211i	$-0.339937\pi$
$840$	6.00000			0.207020
$841$	−19.0000			−0.655172
$842$	−12.0000	−	20.7846i	−0.413547	−	0.716285i
$843$			10.3923i			0.357930i
$844$	11.5000	−	19.9186i	0.395846	−	0.685626i
$845$		−	48.4974i		−	1.66836i
$846$	−9.00000	−	5.19615i	−0.309426	−	0.178647i
$847$	5.50000	−	9.52628i	0.188982	−	0.327327i
$848$	30.0000	−	51.9615i	1.03020	−	1.78437i
$849$	10.5000	−	6.06218i	0.360359	−	0.208053i
$850$	42.0000			1.44059
$851$	−24.0000	−	34.6410i	−0.822709	−	1.18748i
$852$	6.00000			0.205557
$853$	−36.0000	+	20.7846i	−1.23262	+	0.711651i	−0.967575	−	0.252585i	$-0.918719\pi$
$853$	−36.0000	+	20.7846i	−1.23262	+	0.711651i	−0.265042	+	0.964237i	$0.585386\pi$
$854$		0			0
$855$	6.00000	−	10.3923i	0.205196	−	0.355409i
$856$		0			0
$857$			20.7846i			0.709989i	0.934868	+	0.354994i	$0.115517\pi$
$857$			20.7846i			0.709989i	−0.934868	+	0.354994i	$0.884483\pi$
$858$		0			0
$859$		−	5.19615i		−	0.177290i	−0.996063	−	0.0886452i	$-0.971746\pi$
$859$		−	5.19615i		−	0.177290i	0.996063	−	0.0886452i	$-0.0282537\pi$
$860$	9.00000	+	15.5885i	0.306897	+	0.531562i
$861$	−6.00000			−0.204479
$862$	30.0000			1.02180
$863$	−3.00000	−	5.19615i	−0.102121	−	0.176879i	0.810437	−	0.585826i	$-0.199230\pi$
$863$	−3.00000	−	5.19615i	−0.102121	−	0.176879i	−0.912558	+	0.408946i	$0.865896\pi$
$864$	−4.50000	−	2.59808i	−0.153093	−	0.0883883i
$865$		−	20.7846i		−	0.706698i
$866$	−15.0000	+	8.66025i	−0.509721	+	0.294287i
$867$	−2.50000	−	4.33013i	−0.0849045	−	0.147059i
$868$	4.50000	−	2.59808i	0.152740	−	0.0881845i
$869$		0			0
$870$	−36.0000	−	20.7846i	−1.22051	−	0.704664i
$871$	31.5000	−	18.1865i	1.06734	−	0.616227i
$872$	−1.50000	−	2.59808i	−0.0507964	−	0.0879820i
$873$	13.5000	−	7.79423i	0.456906	−	0.263795i
$874$			41.5692i			1.40610i
$875$	6.00000	+	3.46410i	0.202837	+	0.117108i
$876$	3.50000	+	6.06218i	0.118254	+	0.204822i
$877$	13.0000			0.438979			0.219489	−	0.975615i	$-0.429561\pi$
$877$	13.0000			0.438979			0.219489	+	0.975615i	$0.429561\pi$
$878$	−57.0000			−1.92366
$879$	−3.00000	−	5.19615i	−0.101187	−	0.175262i
$880$		0			0
$881$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$881$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$882$			10.3923i			0.349927i
$883$	39.0000	+	22.5167i	1.31245	+	0.757746i	0.982502	−	0.186252i	$-0.0596340\pi$
$883$	39.0000	+	22.5167i	1.31245	+	0.757746i	0.329952	+	0.943998i	$0.392967\pi$
$884$	9.00000	−	15.5885i	0.302703	−	0.524297i
$885$	24.0000	−	41.5692i	0.806751	−	1.39733i
$886$	−9.00000	+	5.19615i	−0.302361	+	0.174568i
$887$	−18.0000			−0.604381			−0.302190	−	0.953248i	$-0.597718\pi$
$887$	−18.0000			−0.604381			−0.302190	+	0.953248i	$0.597718\pi$
$888$	−10.5000	+	0.866025i	−0.352357	+	0.0290619i
$889$	−7.00000			−0.234772
$890$	−72.0000	+	41.5692i	−2.41345	+	1.39340i
$891$		0			0
$892$	8.50000	−	14.7224i	0.284601	−	0.492943i
$893$	18.0000	+	10.3923i	0.602347	+	0.347765i
$894$			20.7846i			0.695141i
$895$	24.0000	−	41.5692i	0.802232	−	1.38951i
$896$			12.1244i			0.405046i
$897$	18.0000	+	31.1769i	0.601003	+	1.04097i
$898$		0			0
$899$	36.0000			1.20067
$900$	−3.50000	−	6.06218i	−0.116667	−	0.202073i
$901$	36.0000	+	20.7846i	1.19933	+	0.692436i
$902$		0			0
$903$	−4.50000	+	2.59808i	−0.149751	+	0.0864586i
$904$	−3.00000	−	5.19615i	−0.0997785	−	0.172821i
$905$	21.0000	−	12.1244i	0.698064	−	0.403027i
$906$	25.5000	+	14.7224i	0.847181	+	0.489120i
$907$	−7.50000	−	4.33013i	−0.249033	−	0.143780i	0.370288	−	0.928917i	$-0.379259\pi$
$907$	−7.50000	−	4.33013i	−0.249033	−	0.143780i	−0.619322	+	0.785137i	$0.712592\pi$
$908$	−9.00000	+	5.19615i	−0.298675	+	0.172440i
$909$	6.00000	+	10.3923i	0.199007	+	0.344691i
$910$	27.0000	−	15.5885i	0.895041	−	0.516752i
$911$		−	6.92820i		−	0.229542i	−0.993392	−	0.114771i	$-0.963387\pi$
$911$		−	6.92820i		−	0.229542i	0.993392	−	0.114771i	$-0.0366134\pi$
$912$	15.0000	+	8.66025i	0.496700	+	0.286770i
$913$		0			0
$914$	−60.0000			−1.98462
$915$		0			0
$916$	2.50000	+	4.33013i	0.0826023	+	0.143071i
$917$			6.92820i			0.228789i
$918$	3.00000	−	5.19615i	0.0990148	−	0.171499i
$919$		−	43.3013i		−	1.42838i	−0.699953	−	0.714189i	$-0.746796\pi$
$919$		−	43.3013i		−	1.42838i	0.699953	−	0.714189i	$-0.253204\pi$
$920$	−36.0000	−	20.7846i	−1.18688	−	0.685248i
$921$	−5.50000	+	9.52628i	−0.181231	+	0.313902i
$922$	15.0000	−	25.9808i	0.493999	−	0.855631i
$923$	−27.0000	+	15.5885i	−0.888716	+	0.513100i
$924$		0			0
$925$	−38.5000	−	18.1865i	−1.26587	−	0.597970i
$926$	−69.0000			−2.26748
$927$	−9.00000	+	5.19615i	−0.295599	+	0.170664i
$928$	18.0000	−	31.1769i	0.590879	−	1.02343i
$929$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$929$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$930$	27.0000	+	15.5885i	0.885365	+	0.511166i
$931$		−	20.7846i		−	0.681188i
$932$	−3.00000	+	5.19615i	−0.0982683	+	0.170206i
$933$		−	20.7846i		−	0.680458i
$934$	−12.0000	−	20.7846i	−0.392652	−	0.680093i
$935$		0			0
$936$	9.00000			0.294174
$937$	−11.5000	−	19.9186i	−0.375689	−	0.650712i	0.614741	−	0.788729i	$-0.289260\pi$
$937$	−11.5000	−	19.9186i	−0.375689	−	0.650712i	−0.990430	+	0.138017i	$0.955927\pi$
$938$	10.5000	+	6.06218i	0.342837	+	0.197937i
$939$		−	8.66025i		−	0.282617i
$940$	18.0000	−	10.3923i	0.587095	−	0.338960i
$941$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$941$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$942$	−19.5000	+	11.2583i	−0.635344	+	0.366816i
$943$	36.0000	+	20.7846i	1.17232	+	0.676840i
$944$	60.0000	+	34.6410i	1.95283	+	1.12747i
$945$	3.00000	−	1.73205i	0.0975900	−	0.0563436i
$946$		0			0
$947$	42.0000	−	24.2487i	1.36482	−	0.787977i	0.374556	−	0.927204i	$-0.377795\pi$
$947$	42.0000	−	24.2487i	1.36482	−	0.787977i	0.990260	+	0.139227i	$0.0444618\pi$
$948$		−	5.19615i		−	0.168763i
$949$	−31.5000	−	18.1865i	−1.02253	−	0.590360i
$950$	21.0000	+	36.3731i	0.681330	+	1.18010i
$951$	24.0000			0.778253
$952$	−6.00000			−0.194461
$953$	−9.00000	−	15.5885i	−0.291539	−	0.504960i	0.682635	−	0.730759i	$-0.260834\pi$
$953$	−9.00000	−	15.5885i	−0.291539	−	0.504960i	−0.974174	+	0.225800i	$0.927501\pi$
$954$		−	20.7846i		−	0.672927i
$955$	−18.0000	+	31.1769i	−0.582466	+	1.00886i
$956$		−	10.3923i		−	0.336111i
$957$		0			0
$958$	−15.0000	+	25.9808i	−0.484628	+	0.839400i
$959$		0			0
$960$	−3.00000	+	1.73205i	−0.0968246	+	0.0559017i
$961$	4.00000			0.129032
$962$	−45.0000	+	31.1769i	−1.45086	+	1.00518i
$963$		0			0
$964$	−19.5000	+	11.2583i	−0.628053	+	0.362606i
$965$	−33.0000	+	57.1577i	−1.06231	+	1.83997i
$966$	−6.00000	+	10.3923i	−0.193047	+	0.334367i
$967$	−1.50000	−	0.866025i	−0.0482367	−	0.0278495i	0.475688	−	0.879614i	$-0.342199\pi$
$967$	−1.50000	−	0.866025i	−0.0482367	−	0.0278495i	−0.523924	+	0.851765i	$0.675533\pi$
$968$			19.0526i			0.612372i
$969$	−6.00000	+	10.3923i	−0.192748	+	0.333849i
$970$			93.5307i			3.00309i
$971$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$971$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$972$	−1.00000			−0.0320750
$973$	19.0000			0.609112
$974$	21.0000	+	36.3731i	0.672883	+	1.16547i
$975$	31.5000	+	18.1865i	1.00881	+	0.582435i
$976$		0			0
$977$	45.0000	−	25.9808i	1.43968	−	0.831198i	0.441851	−	0.897089i	$-0.354322\pi$
$977$	45.0000	−	25.9808i	1.43968	−	0.831198i	0.997827	+	0.0658904i	$0.0209888\pi$
$978$	3.00000	+	5.19615i	0.0959294	+	0.166155i
$979$		0			0
$980$	−18.0000	−	10.3923i	−0.574989	−	0.331970i
$981$	−1.50000	−	0.866025i	−0.0478913	−	0.0276501i
$982$	27.0000	−	15.5885i	0.861605	−	0.497448i
$983$	3.00000	+	5.19615i	0.0956851	+	0.165732i	0.909894	−	0.414840i	$-0.136162\pi$
$983$	3.00000	+	5.19615i	0.0956851	+	0.165732i	−0.814209	+	0.580572i	$0.802829\pi$
$984$	9.00000	−	5.19615i	0.286910	−	0.165647i
$985$			83.1384i			2.64901i
$986$	36.0000	+	20.7846i	1.14647	+	0.661917i
$987$	3.00000	+	5.19615i	0.0954911	+	0.165395i
$988$	18.0000			0.572656
$989$	36.0000			1.14473
$990$		0			0
$991$			51.9615i			1.65061i	0.564686	+	0.825306i	$0.308997\pi$
$991$			51.9615i			1.65061i	−0.564686	+	0.825306i	$0.691003\pi$
$992$	−13.5000	+	23.3827i	−0.428625	+	0.742401i
$993$		−	22.5167i		−	0.714545i
$994$	−9.00000	−	5.19615i	−0.285463	−	0.164812i
$995$	39.0000	−	67.5500i	1.23638	−	2.14148i
$996$	−3.00000	+	5.19615i	−0.0950586	+	0.164646i
$997$	36.0000	−	20.7846i	1.14013	−	0.658255i	0.193668	−	0.981067i	$-0.437961\pi$
$997$	36.0000	−	20.7846i	1.14013	−	0.658255i	0.946463	+	0.322812i	$0.104628\pi$
$998$	54.0000			1.70934
$999$	−5.00000	+	3.46410i	−0.158193	+	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	111.2.j.a.85.1	yes	2
3.2	odd	2		333.2.s.a.307.1		2
4.3	odd	2		1776.2.bz.b.529.1		2
37.8	odd	12		4107.2.a.c.1.1		2
37.27	even	6	inner	111.2.j.a.64.1	✓	2
37.29	odd	12		4107.2.a.c.1.2		2
111.101	odd	6		333.2.s.a.64.1		2
148.27	odd	6		1776.2.bz.b.1729.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.2.j.a.64.1	✓	2	37.27	even	6	inner
111.2.j.a.85.1	yes	2	1.1	even	1	trivial
333.2.s.a.64.1		2	111.101	odd	6
333.2.s.a.307.1		2	3.2	odd	2
1776.2.bz.b.529.1		2	4.3	odd	2
1776.2.bz.b.1729.1		2	148.27	odd	6
4107.2.a.c.1.1		2	37.8	odd	12
4107.2.a.c.1.2		2	37.29	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 111 = 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	111.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.00000 - 1.73205i) q^{5} -1.73205i q^{6} +(-0.500000 + 0.866025i) q^{7} -1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.00000 - 1.73205i) q^{5} -1.73205i q^{6} +(-0.500000 + 0.866025i) q^{7} -1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +6.00000 q^{10} +(0.500000 + 0.866025i) q^{12} +(-4.50000 - 2.59808i) q^{13} -1.73205i q^{14} +(3.00000 - 1.73205i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-3.00000 + 1.73205i) q^{17} +(1.50000 + 0.866025i) q^{18} +(-3.00000 - 1.73205i) q^{19} +(-3.00000 + 1.73205i) q^{20} +(-0.500000 - 0.866025i) q^{21} +6.92820i q^{23} +(1.50000 + 0.866025i) q^{24} +(3.50000 + 6.06218i) q^{25} +9.00000 q^{26} +1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +6.92820i q^{29} +(-3.00000 + 5.19615i) q^{30} -5.19615i q^{31} +(-4.50000 - 2.59808i) q^{32} +(3.00000 - 5.19615i) q^{34} +(3.00000 - 1.73205i) q^{35} -1.00000 q^{36} +(-5.00000 + 3.46410i) q^{37} +6.00000 q^{38} +(4.50000 - 2.59808i) q^{39} +(-3.00000 + 5.19615i) q^{40} +(3.00000 - 5.19615i) q^{41} +(1.50000 + 0.866025i) q^{42} -5.19615i q^{43} +3.46410i q^{45} +(-6.00000 - 10.3923i) q^{46} -6.00000 q^{47} -5.00000 q^{48} +(3.00000 + 5.19615i) q^{49} +(-10.5000 - 6.06218i) q^{50} -3.46410i q^{51} +(-4.50000 + 2.59808i) q^{52} +(-6.00000 - 10.3923i) q^{53} +(-1.50000 + 0.866025i) q^{54} +(1.50000 + 0.866025i) q^{56} +(3.00000 - 1.73205i) q^{57} +(-6.00000 - 10.3923i) q^{58} +(12.0000 - 6.92820i) q^{59} -3.46410i q^{60} +(4.50000 + 7.79423i) q^{62} +1.00000 q^{63} -1.00000 q^{64} +(9.00000 + 15.5885i) q^{65} +(-3.50000 + 6.06218i) q^{67} +3.46410i q^{68} +(-6.00000 - 3.46410i) q^{69} +(-3.00000 + 5.19615i) q^{70} +(3.00000 - 5.19615i) q^{71} +(-1.50000 + 0.866025i) q^{72} +7.00000 q^{73} +(4.50000 - 9.52628i) q^{74} -7.00000 q^{75} +(-3.00000 + 1.73205i) q^{76} +(-4.50000 + 7.79423i) q^{78} +(-4.50000 - 2.59808i) q^{79} -17.3205i q^{80} +(-0.500000 + 0.866025i) q^{81} +10.3923i q^{82} +(3.00000 + 5.19615i) q^{83} -1.00000 q^{84} +12.0000 q^{85} +(4.50000 + 7.79423i) q^{86} +(-6.00000 - 3.46410i) q^{87} +(-12.0000 + 6.92820i) q^{89} +(-3.00000 - 5.19615i) q^{90} +(4.50000 - 2.59808i) q^{91} +(6.00000 + 3.46410i) q^{92} +(4.50000 + 2.59808i) q^{93} +(9.00000 - 5.19615i) q^{94} +(6.00000 + 10.3923i) q^{95} +(4.50000 - 2.59808i) q^{96} +15.5885i q^{97} +(-9.00000 - 5.19615i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - q^{3} + q^{4} - 6 q^{5} - q^{7} - q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 - q^3 + q^4 - 6 * q^5 - q^7 - q^9	\( 2 q - 3 q^{2} - q^{3} + q^{4} - 6 q^{5} - q^{7} - q^{9} + 12 q^{10} + q^{12} - 9 q^{13} + 6 q^{15} + 5 q^{16} - 6 q^{17} + 3 q^{18} - 6 q^{19} - 6 q^{20} - q^{21} + 3 q^{24} + 7 q^{25} + 18 q^{26} + 2 q^{27} + q^{28} - 6 q^{30} - 9 q^{32} + 6 q^{34} + 6 q^{35} - 2 q^{36} - 10 q^{37} + 12 q^{38} + 9 q^{39} - 6 q^{40} + 6 q^{41} + 3 q^{42} - 12 q^{46} - 12 q^{47} - 10 q^{48} + 6 q^{49} - 21 q^{50} - 9 q^{52} - 12 q^{53} - 3 q^{54} + 3 q^{56} + 6 q^{57} - 12 q^{58} + 24 q^{59} + 9 q^{62} + 2 q^{63} - 2 q^{64} + 18 q^{65} - 7 q^{67} - 12 q^{69} - 6 q^{70} + 6 q^{71} - 3 q^{72} + 14 q^{73} + 9 q^{74} - 14 q^{75} - 6 q^{76} - 9 q^{78} - 9 q^{79} - q^{81} + 6 q^{83} - 2 q^{84} + 24 q^{85} + 9 q^{86} - 12 q^{87} - 24 q^{89} - 6 q^{90} + 9 q^{91} + 12 q^{92} + 9 q^{93} + 18 q^{94} + 12 q^{95} + 9 q^{96} - 18 q^{98}+O(q^{100}) \) 2 * q - 3 * q^2 - q^3 + q^4 - 6 * q^5 - q^7 - q^9 + 12 * q^10 + q^12 - 9 * q^13 + 6 * q^15 + 5 * q^16 - 6 * q^17 + 3 * q^18 - 6 * q^19 - 6 * q^20 - q^21 + 3 * q^24 + 7 * q^25 + 18 * q^26 + 2 * q^27 + q^28 - 6 * q^30 - 9 * q^32 + 6 * q^34 + 6 * q^35 - 2 * q^36 - 10 * q^37 + 12 * q^38 + 9 * q^39 - 6 * q^40 + 6 * q^41 + 3 * q^42 - 12 * q^46 - 12 * q^47 - 10 * q^48 + 6 * q^49 - 21 * q^50 - 9 * q^52 - 12 * q^53 - 3 * q^54 + 3 * q^56 + 6 * q^57 - 12 * q^58 + 24 * q^59 + 9 * q^62 + 2 * q^63 - 2 * q^64 + 18 * q^65 - 7 * q^67 - 12 * q^69 - 6 * q^70 + 6 * q^71 - 3 * q^72 + 14 * q^73 + 9 * q^74 - 14 * q^75 - 6 * q^76 - 9 * q^78 - 9 * q^79 - q^81 + 6 * q^83 - 2 * q^84 + 24 * q^85 + 9 * q^86 - 12 * q^87 - 24 * q^89 - 6 * q^90 + 9 * q^91 + 12 * q^92 + 9 * q^93 + 18 * q^94 + 12 * q^95 + 9 * q^96 - 18 * q^98

Introduction

L-functions

Modular forms

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Database

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