LMFDB - Embedded newform 10.3.c.a.3.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [10,3,Mod(3,10)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("10.3"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	10.c (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.272480264360$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	10.3
Dual form			10.3.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+(-1.00000 + 1.00000i) q^{2} +(-2.00000 - 2.00000i) q^{3} -2.00000i q^{4} +5.00000i q^{5} +4.00000 q^{6} +(2.00000 - 2.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} -1.00000i q^{9} +(-5.00000 - 5.00000i) q^{10} -8.00000 q^{11} +(-4.00000 + 4.00000i) q^{12} +(3.00000 + 3.00000i) q^{13} +4.00000i q^{14} +(10.0000 - 10.0000i) q^{15} -4.00000 q^{16} +(7.00000 - 7.00000i) q^{17} +(1.00000 + 1.00000i) q^{18} +20.0000i q^{19} +10.0000 q^{20} -8.00000 q^{21} +(8.00000 - 8.00000i) q^{22} +(-2.00000 - 2.00000i) q^{23} -8.00000i q^{24} -25.0000 q^{25} -6.00000 q^{26} +(-20.0000 + 20.0000i) q^{27} +(-4.00000 - 4.00000i) q^{28} -40.0000i q^{29} +20.0000i q^{30} +52.0000 q^{31} +(4.00000 - 4.00000i) q^{32} +(16.0000 + 16.0000i) q^{33} +14.0000i q^{34} +(10.0000 + 10.0000i) q^{35} -2.00000 q^{36} +(-3.00000 + 3.00000i) q^{37} +(-20.0000 - 20.0000i) q^{38} -12.0000i q^{39} +(-10.0000 + 10.0000i) q^{40} -8.00000 q^{41} +(8.00000 - 8.00000i) q^{42} +(-42.0000 - 42.0000i) q^{43} +16.0000i q^{44} +5.00000 q^{45} +4.00000 q^{46} +(-18.0000 + 18.0000i) q^{47} +(8.00000 + 8.00000i) q^{48} +41.0000i q^{49} +(25.0000 - 25.0000i) q^{50} -28.0000 q^{51} +(6.00000 - 6.00000i) q^{52} +(53.0000 + 53.0000i) q^{53} -40.0000i q^{54} -40.0000i q^{55} +8.00000 q^{56} +(40.0000 - 40.0000i) q^{57} +(40.0000 + 40.0000i) q^{58} +20.0000i q^{59} +(-20.0000 - 20.0000i) q^{60} -48.0000 q^{61} +(-52.0000 + 52.0000i) q^{62} +(-2.00000 - 2.00000i) q^{63} +8.00000i q^{64} +(-15.0000 + 15.0000i) q^{65} -32.0000 q^{66} +(62.0000 - 62.0000i) q^{67} +(-14.0000 - 14.0000i) q^{68} +8.00000i q^{69} -20.0000 q^{70} -28.0000 q^{71} +(2.00000 - 2.00000i) q^{72} +(-47.0000 - 47.0000i) q^{73} -6.00000i q^{74} +(50.0000 + 50.0000i) q^{75} +40.0000 q^{76} +(-16.0000 + 16.0000i) q^{77} +(12.0000 + 12.0000i) q^{78} -20.0000i q^{80} +71.0000 q^{81} +(8.00000 - 8.00000i) q^{82} +(18.0000 + 18.0000i) q^{83} +16.0000i q^{84} +(35.0000 + 35.0000i) q^{85} +84.0000 q^{86} +(-80.0000 + 80.0000i) q^{87} +(-16.0000 - 16.0000i) q^{88} -80.0000i q^{89} +(-5.00000 + 5.00000i) q^{90} +12.0000 q^{91} +(-4.00000 + 4.00000i) q^{92} +(-104.000 - 104.000i) q^{93} -36.0000i q^{94} -100.000 q^{95} -16.0000 q^{96} +(-63.0000 + 63.0000i) q^{97} +(-41.0000 - 41.0000i) q^{98} +8.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{3} + 8 q^{6} + 4 q^{7} + 4 q^{8} - 10 q^{10} - 16 q^{11} - 8 q^{12} + 6 q^{13} + 20 q^{15} - 8 q^{16} + 14 q^{17} + 2 q^{18} + 20 q^{20} - 16 q^{21} + 16 q^{22} - 4 q^{23} - 50 q^{25}+ \cdots - 82 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 4 * q^3 + 8 * q^6 + 4 * q^7 + 4 * q^8 - 10 * q^10 - 16 * q^11 - 8 * q^12 + 6 * q^13 + 20 * q^15 - 8 * q^16 + 14 * q^17 + 2 * q^18 + 20 * q^20 - 16 * q^21 + 16 * q^22 - 4 * q^23 - 50 * q^25 - 12 * q^26 - 40 * q^27 - 8 * q^28 + 104 * q^31 + 8 * q^32 + 32 * q^33 + 20 * q^35 - 4 * q^36 - 6 * q^37 - 40 * q^38 - 20 * q^40 - 16 * q^41 + 16 * q^42 - 84 * q^43 + 10 * q^45 + 8 * q^46 - 36 * q^47 + 16 * q^48 + 50 * q^50 - 56 * q^51 + 12 * q^52 + 106 * q^53 + 16 * q^56 + 80 * q^57 + 80 * q^58 - 40 * q^60 - 96 * q^61 - 104 * q^62 - 4 * q^63 - 30 * q^65 - 64 * q^66 + 124 * q^67 - 28 * q^68 - 40 * q^70 - 56 * q^71 + 4 * q^72 - 94 * q^73 + 100 * q^75 + 80 * q^76 - 32 * q^77 + 24 * q^78 + 142 * q^81 + 16 * q^82 + 36 * q^83 + 70 * q^85 + 168 * q^86 - 160 * q^87 - 32 * q^88 - 10 * q^90 + 24 * q^91 - 8 * q^92 - 208 * q^93 - 200 * q^95 - 32 * q^96 - 126 * q^97 - 82 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	−2.00000	−	2.00000i	−0.666667	−	0.666667i	0.290276	−	0.956943i	$-0.406253\pi$
$3$	−2.00000	−	2.00000i	−0.666667	−	0.666667i	−0.956943	+	0.290276i	$0.906253\pi$
$4$		−	2.00000i		−	0.500000i
$5$			5.00000i			1.00000i
$5$			5.00000i			1.00000i
$6$	4.00000			0.666667
$7$	2.00000	−	2.00000i	0.285714	−	0.285714i	−0.549669	−	0.835383i	$-0.685246\pi$
$7$	2.00000	−	2.00000i	0.285714	−	0.285714i	0.835383	+	0.549669i	$0.185246\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$		−	1.00000i		−	0.111111i
$10$	−5.00000	−	5.00000i	−0.500000	−	0.500000i
$11$	−8.00000			−0.727273			−0.363636	−	0.931541i	$-0.618465\pi$
$11$	−8.00000			−0.727273			−0.363636	+	0.931541i	$0.618465\pi$
$12$	−4.00000	+	4.00000i	−0.333333	+	0.333333i
$13$	3.00000	+	3.00000i	0.230769	+	0.230769i	0.813014	−	0.582245i	$-0.197825\pi$
$13$	3.00000	+	3.00000i	0.230769	+	0.230769i	−0.582245	+	0.813014i	$0.697825\pi$
$14$			4.00000i			0.285714i
$15$	10.0000	−	10.0000i	0.666667	−	0.666667i
$16$	−4.00000			−0.250000
$17$	7.00000	−	7.00000i	0.411765	−	0.411765i	−0.470588	−	0.882353i	$-0.655958\pi$
$17$	7.00000	−	7.00000i	0.411765	−	0.411765i	0.882353	+	0.470588i	$0.155958\pi$
$18$	1.00000	+	1.00000i	0.0555556	+	0.0555556i
$19$			20.0000i			1.05263i	0.850289	+	0.526316i	$0.176427\pi$
$19$			20.0000i			1.05263i	−0.850289	+	0.526316i	$0.823573\pi$
$20$	10.0000			0.500000
$21$	−8.00000			−0.380952
$22$	8.00000	−	8.00000i	0.363636	−	0.363636i
$23$	−2.00000	−	2.00000i	−0.0869565	−	0.0869565i	0.662291	−	0.749247i	$-0.269584\pi$
$23$	−2.00000	−	2.00000i	−0.0869565	−	0.0869565i	−0.749247	+	0.662291i	$0.769584\pi$
$24$		−	8.00000i		−	0.333333i
$25$	−25.0000			−1.00000
$26$	−6.00000			−0.230769
$27$	−20.0000	+	20.0000i	−0.740741	+	0.740741i
$28$	−4.00000	−	4.00000i	−0.142857	−	0.142857i
$29$		−	40.0000i		−	1.37931i	−0.724138	−	0.689655i	$-0.757762\pi$
$29$		−	40.0000i		−	1.37931i	0.724138	−	0.689655i	$-0.242238\pi$
$30$			20.0000i			0.666667i
$31$	52.0000			1.67742			0.838710	−	0.544579i	$-0.183310\pi$
$31$	52.0000			1.67742			0.838710	+	0.544579i	$0.183310\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	16.0000	+	16.0000i	0.484848	+	0.484848i
$34$			14.0000i			0.411765i
$35$	10.0000	+	10.0000i	0.285714	+	0.285714i
$36$	−2.00000			−0.0555556
$37$	−3.00000	+	3.00000i	−0.0810811	+	0.0810811i	−0.746484	−	0.665403i	$-0.768260\pi$
$37$	−3.00000	+	3.00000i	−0.0810811	+	0.0810811i	0.665403	+	0.746484i	$0.268260\pi$
$38$	−20.0000	−	20.0000i	−0.526316	−	0.526316i
$39$		−	12.0000i		−	0.307692i
$40$	−10.0000	+	10.0000i	−0.250000	+	0.250000i
$41$	−8.00000			−0.195122			−0.0975610	−	0.995230i	$-0.531104\pi$
$41$	−8.00000			−0.195122			−0.0975610	+	0.995230i	$0.531104\pi$
$42$	8.00000	−	8.00000i	0.190476	−	0.190476i
$43$	−42.0000	−	42.0000i	−0.976744	−	0.976744i	0.0229915	−	0.999736i	$-0.492681\pi$
$43$	−42.0000	−	42.0000i	−0.976744	−	0.976744i	−0.999736	+	0.0229915i	$0.992681\pi$
$44$			16.0000i			0.363636i
$45$	5.00000			0.111111
$46$	4.00000			0.0869565
$47$	−18.0000	+	18.0000i	−0.382979	+	0.382979i	−0.872174	−	0.489195i	$-0.837290\pi$
$47$	−18.0000	+	18.0000i	−0.382979	+	0.382979i	0.489195	+	0.872174i	$0.337290\pi$
$48$	8.00000	+	8.00000i	0.166667	+	0.166667i
$49$			41.0000i			0.836735i
$50$	25.0000	−	25.0000i	0.500000	−	0.500000i
$51$	−28.0000			−0.549020
$52$	6.00000	−	6.00000i	0.115385	−	0.115385i
$53$	53.0000	+	53.0000i	1.00000	+	1.00000i	1.00000			$0$
$53$	53.0000	+	53.0000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$54$		−	40.0000i		−	0.740741i
$55$		−	40.0000i		−	0.727273i
$56$	8.00000			0.142857
$57$	40.0000	−	40.0000i	0.701754	−	0.701754i
$58$	40.0000	+	40.0000i	0.689655	+	0.689655i
$59$			20.0000i			0.338983i	0.985532	+	0.169492i	$0.0542125\pi$
$59$			20.0000i			0.338983i	−0.985532	+	0.169492i	$0.945787\pi$
$60$	−20.0000	−	20.0000i	−0.333333	−	0.333333i
$61$	−48.0000			−0.786885			−0.393443	−	0.919349i	$-0.628716\pi$
$61$	−48.0000			−0.786885			−0.393443	+	0.919349i	$0.628716\pi$
$62$	−52.0000	+	52.0000i	−0.838710	+	0.838710i
$63$	−2.00000	−	2.00000i	−0.0317460	−	0.0317460i
$64$			8.00000i			0.125000i
$65$	−15.0000	+	15.0000i	−0.230769	+	0.230769i
$66$	−32.0000			−0.484848
$67$	62.0000	−	62.0000i	0.925373	−	0.925373i	−0.0720294	−	0.997403i	$-0.522948\pi$
$67$	62.0000	−	62.0000i	0.925373	−	0.925373i	0.997403	+	0.0720294i	$0.0229475\pi$
$68$	−14.0000	−	14.0000i	−0.205882	−	0.205882i
$69$			8.00000i			0.115942i
$70$	−20.0000			−0.285714
$71$	−28.0000			−0.394366			−0.197183	−	0.980367i	$-0.563179\pi$
$71$	−28.0000			−0.394366			−0.197183	+	0.980367i	$0.563179\pi$
$72$	2.00000	−	2.00000i	0.0277778	−	0.0277778i
$73$	−47.0000	−	47.0000i	−0.643836	−	0.643836i	0.307661	−	0.951496i	$-0.400454\pi$
$73$	−47.0000	−	47.0000i	−0.643836	−	0.643836i	−0.951496	+	0.307661i	$0.900454\pi$
$74$		−	6.00000i		−	0.0810811i
$75$	50.0000	+	50.0000i	0.666667	+	0.666667i
$76$	40.0000			0.526316
$77$	−16.0000	+	16.0000i	−0.207792	+	0.207792i
$78$	12.0000	+	12.0000i	0.153846	+	0.153846i
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$		−	20.0000i		−	0.250000i
$81$	71.0000			0.876543
$82$	8.00000	−	8.00000i	0.0975610	−	0.0975610i
$83$	18.0000	+	18.0000i	0.216867	+	0.216867i	0.807177	−	0.590310i	$-0.200994\pi$
$83$	18.0000	+	18.0000i	0.216867	+	0.216867i	−0.590310	+	0.807177i	$0.700994\pi$
$84$			16.0000i			0.190476i
$85$	35.0000	+	35.0000i	0.411765	+	0.411765i
$86$	84.0000			0.976744
$87$	−80.0000	+	80.0000i	−0.919540	+	0.919540i
$88$	−16.0000	−	16.0000i	−0.181818	−	0.181818i
$89$		−	80.0000i		−	0.898876i	−0.893311	−	0.449438i	$-0.851624\pi$
$89$		−	80.0000i		−	0.898876i	0.893311	−	0.449438i	$-0.148376\pi$
$90$	−5.00000	+	5.00000i	−0.0555556	+	0.0555556i
$91$	12.0000			0.131868
$92$	−4.00000	+	4.00000i	−0.0434783	+	0.0434783i
$93$	−104.000	−	104.000i	−1.11828	−	1.11828i
$94$		−	36.0000i		−	0.382979i
$95$	−100.000			−1.05263
$96$	−16.0000			−0.166667
$97$	−63.0000	+	63.0000i	−0.649485	+	0.649485i	−0.952868	−	0.303384i	$-0.901884\pi$
$97$	−63.0000	+	63.0000i	−0.649485	+	0.649485i	0.303384	+	0.952868i	$0.401884\pi$
$98$	−41.0000	−	41.0000i	−0.418367	−	0.418367i
$99$			8.00000i			0.0808081i
$100$			50.0000i			0.500000i
$101$	62.0000			0.613861			0.306931	−	0.951732i	$-0.400698\pi$
$101$	62.0000			0.613861			0.306931	+	0.951732i	$0.400698\pi$
$102$	28.0000	−	28.0000i	0.274510	−	0.274510i
$103$	118.000	+	118.000i	1.14563	+	1.14563i	0.987403	+	0.158229i	$0.0505783\pi$
$103$	118.000	+	118.000i	1.14563	+	1.14563i	0.158229	+	0.987403i	$0.449422\pi$
$104$			12.0000i			0.115385i
$105$		−	40.0000i		−	0.380952i
$106$	−106.000			−1.00000
$107$	142.000	−	142.000i	1.32710	−	1.32710i	0.419217	−	0.907886i	$-0.362305\pi$
$107$	142.000	−	142.000i	1.32710	−	1.32710i	0.907886	−	0.419217i	$-0.137695\pi$
$108$	40.0000	+	40.0000i	0.370370	+	0.370370i
$109$			10.0000i			0.0917431i	0.998947	+	0.0458716i	$0.0146065\pi$
$109$			10.0000i			0.0917431i	−0.998947	+	0.0458716i	$0.985394\pi$
$110$	40.0000	+	40.0000i	0.363636	+	0.363636i
$111$	12.0000			0.108108
$112$	−8.00000	+	8.00000i	−0.0714286	+	0.0714286i
$113$	23.0000	+	23.0000i	0.203540	+	0.203540i	0.801515	−	0.597975i	$-0.204028\pi$
$113$	23.0000	+	23.0000i	0.203540	+	0.203540i	−0.597975	+	0.801515i	$0.704028\pi$
$114$			80.0000i			0.701754i
$115$	10.0000	−	10.0000i	0.0869565	−	0.0869565i
$116$	−80.0000			−0.689655
$117$	3.00000	−	3.00000i	0.0256410	−	0.0256410i
$118$	−20.0000	−	20.0000i	−0.169492	−	0.169492i
$119$		−	28.0000i		−	0.235294i
$120$	40.0000			0.333333
$121$	−57.0000			−0.471074
$122$	48.0000	−	48.0000i	0.393443	−	0.393443i
$123$	16.0000	+	16.0000i	0.130081	+	0.130081i
$124$		−	104.000i		−	0.838710i
$125$		−	125.000i		−	1.00000i
$126$	4.00000			0.0317460
$127$	−118.000	+	118.000i	−0.929134	+	0.929134i	−0.997650	−	0.0685161i	$-0.978174\pi$
$127$	−118.000	+	118.000i	−0.929134	+	0.929134i	0.0685161	+	0.997650i	$0.478174\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			168.000i			1.30233i
$130$		−	30.0000i		−	0.230769i
$131$	−128.000			−0.977099			−0.488550	−	0.872536i	$-0.662474\pi$
$131$	−128.000			−0.977099			−0.488550	+	0.872536i	$0.662474\pi$
$132$	32.0000	−	32.0000i	0.242424	−	0.242424i
$133$	40.0000	+	40.0000i	0.300752	+	0.300752i
$134$			124.000i			0.925373i
$135$	−100.000	−	100.000i	−0.740741	−	0.740741i
$136$	28.0000			0.205882
$137$	−63.0000	+	63.0000i	−0.459854	+	0.459854i	−0.898607	−	0.438753i	$-0.855420\pi$
$137$	−63.0000	+	63.0000i	−0.459854	+	0.459854i	0.438753	+	0.898607i	$0.355420\pi$
$138$	−8.00000	−	8.00000i	−0.0579710	−	0.0579710i
$139$		−	140.000i		−	1.00719i	−0.863939	−	0.503597i	$-0.832010\pi$
$139$		−	140.000i		−	1.00719i	0.863939	−	0.503597i	$-0.167990\pi$
$140$	20.0000	−	20.0000i	0.142857	−	0.142857i
$141$	72.0000			0.510638
$142$	28.0000	−	28.0000i	0.197183	−	0.197183i
$143$	−24.0000	−	24.0000i	−0.167832	−	0.167832i
$144$			4.00000i			0.0277778i
$145$	200.000			1.37931
$146$	94.0000			0.643836
$147$	82.0000	−	82.0000i	0.557823	−	0.557823i
$148$	6.00000	+	6.00000i	0.0405405	+	0.0405405i
$149$			150.000i			1.00671i	0.864079	+	0.503356i	$0.167901\pi$
$149$			150.000i			1.00671i	−0.864079	+	0.503356i	$0.832099\pi$
$150$	−100.000			−0.666667
$151$	52.0000			0.344371			0.172185	−	0.985065i	$-0.444917\pi$
$151$	52.0000			0.344371			0.172185	+	0.985065i	$0.444917\pi$
$152$	−40.0000	+	40.0000i	−0.263158	+	0.263158i
$153$	−7.00000	−	7.00000i	−0.0457516	−	0.0457516i
$154$		−	32.0000i		−	0.207792i
$155$			260.000i			1.67742i
$156$	−24.0000			−0.153846
$157$	27.0000	−	27.0000i	0.171975	−	0.171975i	−0.615872	−	0.787846i	$-0.711196\pi$
$157$	27.0000	−	27.0000i	0.171975	−	0.171975i	0.787846	+	0.615872i	$0.211196\pi$
$158$		0			0
$159$		−	212.000i		−	1.33333i
$160$	20.0000	+	20.0000i	0.125000	+	0.125000i
$161$	−8.00000			−0.0496894
$162$	−71.0000	+	71.0000i	−0.438272	+	0.438272i
$163$	−82.0000	−	82.0000i	−0.503067	−	0.503067i	0.409322	−	0.912390i	$-0.365765\pi$
$163$	−82.0000	−	82.0000i	−0.503067	−	0.503067i	−0.912390	+	0.409322i	$0.865765\pi$
$164$			16.0000i			0.0975610i
$165$	−80.0000	+	80.0000i	−0.484848	+	0.484848i
$166$	−36.0000			−0.216867
$167$	62.0000	−	62.0000i	0.371257	−	0.371257i	−0.496678	−	0.867935i	$-0.665447\pi$
$167$	62.0000	−	62.0000i	0.371257	−	0.371257i	0.867935	+	0.496678i	$0.165447\pi$
$168$	−16.0000	−	16.0000i	−0.0952381	−	0.0952381i
$169$		−	151.000i		−	0.893491i
$170$	−70.0000			−0.411765
$171$	20.0000			0.116959
$172$	−84.0000	+	84.0000i	−0.488372	+	0.488372i
$173$	−107.000	−	107.000i	−0.618497	−	0.618497i	0.326649	−	0.945146i	$-0.394081\pi$
$173$	−107.000	−	107.000i	−0.618497	−	0.618497i	−0.945146	+	0.326649i	$0.894081\pi$
$174$		−	160.000i		−	0.919540i
$175$	−50.0000	+	50.0000i	−0.285714	+	0.285714i
$176$	32.0000			0.181818
$177$	40.0000	−	40.0000i	0.225989	−	0.225989i
$178$	80.0000	+	80.0000i	0.449438	+	0.449438i
$179$			220.000i			1.22905i	0.788897	+	0.614525i	$0.210652\pi$
$179$			220.000i			1.22905i	−0.788897	+	0.614525i	$0.789348\pi$
$180$		−	10.0000i		−	0.0555556i
$181$	2.00000			0.0110497			0.00552486	−	0.999985i	$-0.498241\pi$
$181$	2.00000			0.0110497			0.00552486	+	0.999985i	$0.498241\pi$
$182$	−12.0000	+	12.0000i	−0.0659341	+	0.0659341i
$183$	96.0000	+	96.0000i	0.524590	+	0.524590i
$184$		−	8.00000i		−	0.0434783i
$185$	−15.0000	−	15.0000i	−0.0810811	−	0.0810811i
$186$	208.000			1.11828
$187$	−56.0000	+	56.0000i	−0.299465	+	0.299465i
$188$	36.0000	+	36.0000i	0.191489	+	0.191489i
$189$			80.0000i			0.423280i
$190$	100.000	−	100.000i	0.526316	−	0.526316i
$191$	212.000			1.10995			0.554974	−	0.831868i	$-0.312728\pi$
$191$	212.000			1.10995			0.554974	+	0.831868i	$0.312728\pi$
$192$	16.0000	−	16.0000i	0.0833333	−	0.0833333i
$193$	−57.0000	−	57.0000i	−0.295337	−	0.295337i	0.543847	−	0.839184i	$-0.316967\pi$
$193$	−57.0000	−	57.0000i	−0.295337	−	0.295337i	−0.839184	+	0.543847i	$0.816967\pi$
$194$		−	126.000i		−	0.649485i
$195$	60.0000			0.307692
$196$	82.0000			0.418367
$197$	−3.00000	+	3.00000i	−0.0152284	+	0.0152284i	−0.714680	−	0.699452i	$-0.753428\pi$
$197$	−3.00000	+	3.00000i	−0.0152284	+	0.0152284i	0.699452	+	0.714680i	$0.253428\pi$
$198$	−8.00000	−	8.00000i	−0.0404040	−	0.0404040i
$199$			120.000i			0.603015i	0.953464	+	0.301508i	$0.0974898\pi$
$199$			120.000i			0.603015i	−0.953464	+	0.301508i	$0.902510\pi$
$200$	−50.0000	−	50.0000i	−0.250000	−	0.250000i
$201$	−248.000			−1.23383
$202$	−62.0000	+	62.0000i	−0.306931	+	0.306931i
$203$	−80.0000	−	80.0000i	−0.394089	−	0.394089i
$204$			56.0000i			0.274510i
$205$		−	40.0000i		−	0.195122i
$206$	−236.000			−1.14563
$207$	−2.00000	+	2.00000i	−0.00966184	+	0.00966184i
$208$	−12.0000	−	12.0000i	−0.0576923	−	0.0576923i
$209$		−	160.000i		−	0.765550i
$210$	40.0000	+	40.0000i	0.190476	+	0.190476i
$211$	−328.000			−1.55450			−0.777251	−	0.629190i	$-0.783387\pi$
$211$	−328.000			−1.55450			−0.777251	+	0.629190i	$0.783387\pi$
$212$	106.000	−	106.000i	0.500000	−	0.500000i
$213$	56.0000	+	56.0000i	0.262911	+	0.262911i
$214$			284.000i			1.32710i
$215$	210.000	−	210.000i	0.976744	−	0.976744i
$216$	−80.0000			−0.370370
$217$	104.000	−	104.000i	0.479263	−	0.479263i
$218$	−10.0000	−	10.0000i	−0.0458716	−	0.0458716i
$219$			188.000i			0.858447i
$220$	−80.0000			−0.363636
$221$	42.0000			0.190045
$222$	−12.0000	+	12.0000i	−0.0540541	+	0.0540541i
$223$	138.000	+	138.000i	0.618834	+	0.618834i	0.945232	−	0.326398i	$-0.105835\pi$
$223$	138.000	+	138.000i	0.618834	+	0.618834i	−0.326398	+	0.945232i	$0.605835\pi$
$224$		−	16.0000i		−	0.0714286i
$225$			25.0000i			0.111111i
$226$	−46.0000			−0.203540
$227$	2.00000	−	2.00000i	0.00881057	−	0.00881057i	−0.702688	−	0.711498i	$-0.748017\pi$
$227$	2.00000	−	2.00000i	0.00881057	−	0.00881057i	0.711498	+	0.702688i	$0.248017\pi$
$228$	−80.0000	−	80.0000i	−0.350877	−	0.350877i
$229$		−	120.000i		−	0.524017i	−0.965066	−	0.262009i	$-0.915615\pi$
$229$		−	120.000i		−	0.524017i	0.965066	−	0.262009i	$-0.0843849\pi$
$230$			20.0000i			0.0869565i
$231$	64.0000			0.277056
$232$	80.0000	−	80.0000i	0.344828	−	0.344828i
$233$	183.000	+	183.000i	0.785408	+	0.785408i	0.980738	−	0.195330i	$-0.0625777\pi$
$233$	183.000	+	183.000i	0.785408	+	0.785408i	−0.195330	+	0.980738i	$0.562578\pi$
$234$			6.00000i			0.0256410i
$235$	−90.0000	−	90.0000i	−0.382979	−	0.382979i
$236$	40.0000			0.169492
$237$		0			0
$238$	28.0000	+	28.0000i	0.117647	+	0.117647i
$239$		−	120.000i		−	0.502092i	−0.967975	−	0.251046i	$-0.919225\pi$
$239$		−	120.000i		−	0.502092i	0.967975	−	0.251046i	$-0.0807746\pi$
$240$	−40.0000	+	40.0000i	−0.166667	+	0.166667i
$241$	232.000			0.962656			0.481328	−	0.876541i	$-0.340155\pi$
$241$	232.000			0.962656			0.481328	+	0.876541i	$0.340155\pi$
$242$	57.0000	−	57.0000i	0.235537	−	0.235537i
$243$	38.0000	+	38.0000i	0.156379	+	0.156379i
$244$			96.0000i			0.393443i
$245$	−205.000			−0.836735
$246$	−32.0000			−0.130081
$247$	−60.0000	+	60.0000i	−0.242915	+	0.242915i
$248$	104.000	+	104.000i	0.419355	+	0.419355i
$249$		−	72.0000i		−	0.289157i
$250$	125.000	+	125.000i	0.500000	+	0.500000i
$251$	−48.0000			−0.191235			−0.0956175	−	0.995418i	$-0.530483\pi$
$251$	−48.0000			−0.191235			−0.0956175	+	0.995418i	$0.530483\pi$
$252$	−4.00000	+	4.00000i	−0.0158730	+	0.0158730i
$253$	16.0000	+	16.0000i	0.0632411	+	0.0632411i
$254$		−	236.000i		−	0.929134i
$255$		−	140.000i		−	0.549020i
$256$	16.0000			0.0625000
$257$	−313.000	+	313.000i	−1.21790	+	1.21790i	−0.249532	+	0.968366i	$0.580277\pi$
$257$	−313.000	+	313.000i	−1.21790	+	1.21790i	−0.968366	+	0.249532i	$0.919723\pi$
$258$	−168.000	−	168.000i	−0.651163	−	0.651163i
$259$			12.0000i			0.0463320i
$260$	30.0000	+	30.0000i	0.115385	+	0.115385i
$261$	−40.0000			−0.153257
$262$	128.000	−	128.000i	0.488550	−	0.488550i
$263$	−262.000	−	262.000i	−0.996198	−	0.996198i	0.00379508	−	0.999993i	$-0.498792\pi$
$263$	−262.000	−	262.000i	−0.996198	−	0.996198i	−0.999993	+	0.00379508i	$0.998792\pi$
$264$			64.0000i			0.242424i
$265$	−265.000	+	265.000i	−1.00000	+	1.00000i
$266$	−80.0000			−0.300752
$267$	−160.000	+	160.000i	−0.599251	+	0.599251i
$268$	−124.000	−	124.000i	−0.462687	−	0.462687i
$269$		−	10.0000i		−	0.0371747i	−0.999827	−	0.0185874i	$-0.994083\pi$
$269$		−	10.0000i		−	0.0371747i	0.999827	−	0.0185874i	$-0.00591688\pi$
$270$	200.000			0.740741
$271$	252.000			0.929889			0.464945	−	0.885340i	$-0.346074\pi$
$271$	252.000			0.929889			0.464945	+	0.885340i	$0.346074\pi$
$272$	−28.0000	+	28.0000i	−0.102941	+	0.102941i
$273$	−24.0000	−	24.0000i	−0.0879121	−	0.0879121i
$274$		−	126.000i		−	0.459854i
$275$	200.000			0.727273
$276$	16.0000			0.0579710
$277$	267.000	−	267.000i	0.963899	−	0.963899i	−0.0354718	−	0.999371i	$-0.511293\pi$
$277$	267.000	−	267.000i	0.963899	−	0.963899i	0.999371	+	0.0354718i	$0.0112934\pi$
$278$	140.000	+	140.000i	0.503597	+	0.503597i
$279$		−	52.0000i		−	0.186380i
$280$			40.0000i			0.142857i
$281$	312.000			1.11032			0.555160	−	0.831743i	$-0.312657\pi$
$281$	312.000			1.11032			0.555160	+	0.831743i	$0.312657\pi$
$282$	−72.0000	+	72.0000i	−0.255319	+	0.255319i
$283$	−262.000	−	262.000i	−0.925795	−	0.925795i	0.0716358	−	0.997431i	$-0.477178\pi$
$283$	−262.000	−	262.000i	−0.925795	−	0.925795i	−0.997431	+	0.0716358i	$0.977178\pi$
$284$			56.0000i			0.197183i
$285$	200.000	+	200.000i	0.701754	+	0.701754i
$286$	48.0000			0.167832
$287$	−16.0000	+	16.0000i	−0.0557491	+	0.0557491i
$288$	−4.00000	−	4.00000i	−0.0138889	−	0.0138889i
$289$			191.000i			0.660900i
$290$	−200.000	+	200.000i	−0.689655	+	0.689655i
$291$	252.000			0.865979
$292$	−94.0000	+	94.0000i	−0.321918	+	0.321918i
$293$	243.000	+	243.000i	0.829352	+	0.829352i	0.987427	−	0.158075i	$-0.0505289\pi$
$293$	243.000	+	243.000i	0.829352	+	0.829352i	−0.158075	+	0.987427i	$0.550529\pi$
$294$			164.000i			0.557823i
$295$	−100.000			−0.338983
$296$	−12.0000			−0.0405405
$297$	160.000	−	160.000i	0.538721	−	0.538721i
$298$	−150.000	−	150.000i	−0.503356	−	0.503356i
$299$		−	12.0000i		−	0.0401338i
$300$	100.000	−	100.000i	0.333333	−	0.333333i
$301$	−168.000			−0.558140
$302$	−52.0000	+	52.0000i	−0.172185	+	0.172185i
$303$	−124.000	−	124.000i	−0.409241	−	0.409241i
$304$		−	80.0000i		−	0.263158i
$305$		−	240.000i		−	0.786885i
$306$	14.0000			0.0457516
$307$	−18.0000	+	18.0000i	−0.0586319	+	0.0586319i	−0.735815	−	0.677183i	$-0.763201\pi$
$307$	−18.0000	+	18.0000i	−0.0586319	+	0.0586319i	0.677183	+	0.735815i	$0.263201\pi$
$308$	32.0000	+	32.0000i	0.103896	+	0.103896i
$309$		−	472.000i		−	1.52751i
$310$	−260.000	−	260.000i	−0.838710	−	0.838710i
$311$	−388.000			−1.24759			−0.623794	−	0.781589i	$-0.714410\pi$
$311$	−388.000			−1.24759			−0.623794	+	0.781589i	$0.714410\pi$
$312$	24.0000	−	24.0000i	0.0769231	−	0.0769231i
$313$	183.000	+	183.000i	0.584665	+	0.584665i	0.936182	−	0.351517i	$-0.114334\pi$
$313$	183.000	+	183.000i	0.584665	+	0.584665i	−0.351517	+	0.936182i	$0.614334\pi$
$314$			54.0000i			0.171975i
$315$	10.0000	−	10.0000i	0.0317460	−	0.0317460i
$316$		0			0
$317$	−213.000	+	213.000i	−0.671924	+	0.671924i	−0.958159	−	0.286235i	$-0.907596\pi$
$317$	−213.000	+	213.000i	−0.671924	+	0.671924i	0.286235	+	0.958159i	$0.407596\pi$
$318$	212.000	+	212.000i	0.666667	+	0.666667i
$319$			320.000i			1.00313i
$320$	−40.0000			−0.125000
$321$	−568.000			−1.76947
$322$	8.00000	−	8.00000i	0.0248447	−	0.0248447i
$323$	140.000	+	140.000i	0.433437	+	0.433437i
$324$		−	142.000i		−	0.438272i
$325$	−75.0000	−	75.0000i	−0.230769	−	0.230769i
$326$	164.000			0.503067
$327$	20.0000	−	20.0000i	0.0611621	−	0.0611621i
$328$	−16.0000	−	16.0000i	−0.0487805	−	0.0487805i
$329$			72.0000i			0.218845i
$330$		−	160.000i		−	0.484848i
$331$	232.000			0.700906			0.350453	−	0.936580i	$-0.386028\pi$
$331$	232.000			0.700906			0.350453	+	0.936580i	$0.386028\pi$
$332$	36.0000	−	36.0000i	0.108434	−	0.108434i
$333$	3.00000	+	3.00000i	0.00900901	+	0.00900901i
$334$			124.000i			0.371257i
$335$	310.000	+	310.000i	0.925373	+	0.925373i
$336$	32.0000			0.0952381
$337$	417.000	−	417.000i	1.23739	−	1.23739i	0.276324	−	0.961064i	$-0.410884\pi$
$337$	417.000	−	417.000i	1.23739	−	1.23739i	0.961064	−	0.276324i	$-0.0891164\pi$
$338$	151.000	+	151.000i	0.446746	+	0.446746i
$339$		−	92.0000i		−	0.271386i
$340$	70.0000	−	70.0000i	0.205882	−	0.205882i
$341$	−416.000			−1.21994
$342$	−20.0000	+	20.0000i	−0.0584795	+	0.0584795i
$343$	180.000	+	180.000i	0.524781	+	0.524781i
$344$		−	168.000i		−	0.488372i
$345$	−40.0000			−0.115942
$346$	214.000			0.618497
$347$	202.000	−	202.000i	0.582133	−	0.582133i	−0.353356	−	0.935489i	$-0.614960\pi$
$347$	202.000	−	202.000i	0.582133	−	0.582133i	0.935489	+	0.353356i	$0.114960\pi$
$348$	160.000	+	160.000i	0.459770	+	0.459770i
$349$			440.000i			1.26074i	0.776293	+	0.630372i	$0.217098\pi$
$349$			440.000i			1.26074i	−0.776293	+	0.630372i	$0.782902\pi$
$350$		−	100.000i		−	0.285714i
$351$	−120.000			−0.341880
$352$	−32.0000	+	32.0000i	−0.0909091	+	0.0909091i
$353$	−447.000	−	447.000i	−1.26629	−	1.26629i	−0.947991	−	0.318298i	$-0.896889\pi$
$353$	−447.000	−	447.000i	−1.26629	−	1.26629i	−0.318298	−	0.947991i	$-0.603111\pi$
$354$			80.0000i			0.225989i
$355$		−	140.000i		−	0.394366i
$356$	−160.000			−0.449438
$357$	−56.0000	+	56.0000i	−0.156863	+	0.156863i
$358$	−220.000	−	220.000i	−0.614525	−	0.614525i
$359$			400.000i			1.11421i	0.830443	+	0.557103i	$0.188087\pi$
$359$			400.000i			1.11421i	−0.830443	+	0.557103i	$0.811913\pi$
$360$	10.0000	+	10.0000i	0.0277778	+	0.0277778i
$361$	−39.0000			−0.108033
$362$	−2.00000	+	2.00000i	−0.00552486	+	0.00552486i
$363$	114.000	+	114.000i	0.314050	+	0.314050i
$364$		−	24.0000i		−	0.0659341i
$365$	235.000	−	235.000i	0.643836	−	0.643836i
$366$	−192.000			−0.524590
$367$	−118.000	+	118.000i	−0.321526	+	0.321526i	−0.849352	−	0.527826i	$-0.823007\pi$
$367$	−118.000	+	118.000i	−0.321526	+	0.321526i	0.527826	+	0.849352i	$0.323007\pi$
$368$	8.00000	+	8.00000i	0.0217391	+	0.0217391i
$369$			8.00000i			0.0216802i
$370$	30.0000			0.0810811
$371$	212.000			0.571429
$372$	−208.000	+	208.000i	−0.559140	+	0.559140i
$373$	−107.000	−	107.000i	−0.286863	−	0.286863i	0.548975	−	0.835839i	$-0.315018\pi$
$373$	−107.000	−	107.000i	−0.286863	−	0.286863i	−0.835839	+	0.548975i	$0.815018\pi$
$374$		−	112.000i		−	0.299465i
$375$	−250.000	+	250.000i	−0.666667	+	0.666667i
$376$	−72.0000			−0.191489
$377$	120.000	−	120.000i	0.318302	−	0.318302i
$378$	−80.0000	−	80.0000i	−0.211640	−	0.211640i
$379$		−	340.000i		−	0.897098i	−0.893758	−	0.448549i	$-0.851941\pi$
$379$		−	340.000i		−	0.897098i	0.893758	−	0.448549i	$-0.148059\pi$
$380$			200.000i			0.526316i
$381$	472.000			1.23885
$382$	−212.000	+	212.000i	−0.554974	+	0.554974i
$383$	−342.000	−	342.000i	−0.892950	−	0.892950i	0.101849	−	0.994800i	$-0.467524\pi$
$383$	−342.000	−	342.000i	−0.892950	−	0.892950i	−0.994800	+	0.101849i	$0.967524\pi$
$384$			32.0000i			0.0833333i
$385$	−80.0000	−	80.0000i	−0.207792	−	0.207792i
$386$	114.000			0.295337
$387$	−42.0000	+	42.0000i	−0.108527	+	0.108527i
$388$	126.000	+	126.000i	0.324742	+	0.324742i
$389$		−	390.000i		−	1.00257i	−0.865282	−	0.501285i	$-0.832861\pi$
$389$		−	390.000i		−	1.00257i	0.865282	−	0.501285i	$-0.167139\pi$
$390$	−60.0000	+	60.0000i	−0.153846	+	0.153846i
$391$	−28.0000			−0.0716113
$392$	−82.0000	+	82.0000i	−0.209184	+	0.209184i
$393$	256.000	+	256.000i	0.651399	+	0.651399i
$394$		−	6.00000i		−	0.0152284i
$395$		0			0
$396$	16.0000			0.0404040
$397$	−323.000	+	323.000i	−0.813602	+	0.813602i	−0.985172	−	0.171570i	$-0.945116\pi$
$397$	−323.000	+	323.000i	−0.813602	+	0.813602i	0.171570	+	0.985172i	$0.445116\pi$
$398$	−120.000	−	120.000i	−0.301508	−	0.301508i
$399$		−	160.000i		−	0.401003i
$400$	100.000			0.250000
$401$	642.000			1.60100			0.800499	−	0.599334i	$-0.204568\pi$
$401$	642.000			1.60100			0.800499	+	0.599334i	$0.204568\pi$
$402$	248.000	−	248.000i	0.616915	−	0.616915i
$403$	156.000	+	156.000i	0.387097	+	0.387097i
$404$		−	124.000i		−	0.306931i
$405$			355.000i			0.876543i
$406$	160.000			0.394089
$407$	24.0000	−	24.0000i	0.0589681	−	0.0589681i
$408$	−56.0000	−	56.0000i	−0.137255	−	0.137255i
$409$			150.000i			0.366748i	0.983043	+	0.183374i	$0.0587020\pi$
$409$			150.000i			0.366748i	−0.983043	+	0.183374i	$0.941298\pi$
$410$	40.0000	+	40.0000i	0.0975610	+	0.0975610i
$411$	252.000			0.613139
$412$	236.000	−	236.000i	0.572816	−	0.572816i
$413$	40.0000	+	40.0000i	0.0968523	+	0.0968523i
$414$		−	4.00000i		−	0.00966184i
$415$	−90.0000	+	90.0000i	−0.216867	+	0.216867i
$416$	24.0000			0.0576923
$417$	−280.000	+	280.000i	−0.671463	+	0.671463i
$418$	160.000	+	160.000i	0.382775	+	0.382775i
$419$		−	300.000i		−	0.715990i	−0.933723	−	0.357995i	$-0.883460\pi$
$419$		−	300.000i		−	0.715990i	0.933723	−	0.357995i	$-0.116540\pi$
$420$	−80.0000			−0.190476
$421$	−208.000			−0.494062			−0.247031	−	0.969008i	$-0.579455\pi$
$421$	−208.000			−0.494062			−0.247031	+	0.969008i	$0.579455\pi$
$422$	328.000	−	328.000i	0.777251	−	0.777251i
$423$	18.0000	+	18.0000i	0.0425532	+	0.0425532i
$424$			212.000i			0.500000i
$425$	−175.000	+	175.000i	−0.411765	+	0.411765i
$426$	−112.000			−0.262911
$427$	−96.0000	+	96.0000i	−0.224824	+	0.224824i
$428$	−284.000	−	284.000i	−0.663551	−	0.663551i
$429$			96.0000i			0.223776i
$430$			420.000i			0.976744i
$431$	−788.000			−1.82831			−0.914153	−	0.405369i	$-0.867143\pi$
$431$	−788.000			−1.82831			−0.914153	+	0.405369i	$0.867143\pi$
$432$	80.0000	−	80.0000i	0.185185	−	0.185185i
$433$	−367.000	−	367.000i	−0.847575	−	0.847575i	0.142255	−	0.989830i	$-0.454565\pi$
$433$	−367.000	−	367.000i	−0.847575	−	0.847575i	−0.989830	+	0.142255i	$0.954565\pi$
$434$			208.000i			0.479263i
$435$	−400.000	−	400.000i	−0.919540	−	0.919540i
$436$	20.0000			0.0458716
$437$	40.0000	−	40.0000i	0.0915332	−	0.0915332i
$438$	−188.000	−	188.000i	−0.429224	−	0.429224i
$439$		−	560.000i		−	1.27563i	−0.770191	−	0.637813i	$-0.779839\pi$
$439$		−	560.000i		−	1.27563i	0.770191	−	0.637813i	$-0.220161\pi$
$440$	80.0000	−	80.0000i	0.181818	−	0.181818i
$441$	41.0000			0.0929705
$442$	−42.0000	+	42.0000i	−0.0950226	+	0.0950226i
$443$	378.000	+	378.000i	0.853273	+	0.853273i	0.990535	−	0.137262i	$-0.0438301\pi$
$443$	378.000	+	378.000i	0.853273	+	0.853273i	−0.137262	+	0.990535i	$0.543830\pi$
$444$		−	24.0000i		−	0.0540541i
$445$	400.000			0.898876
$446$	−276.000			−0.618834
$447$	300.000	−	300.000i	0.671141	−	0.671141i
$448$	16.0000	+	16.0000i	0.0357143	+	0.0357143i
$449$			410.000i			0.913140i	0.889687	+	0.456570i	$0.150922\pi$
$449$			410.000i			0.913140i	−0.889687	+	0.456570i	$0.849078\pi$
$450$	−25.0000	−	25.0000i	−0.0555556	−	0.0555556i
$451$	64.0000			0.141907
$452$	46.0000	−	46.0000i	0.101770	−	0.101770i
$453$	−104.000	−	104.000i	−0.229581	−	0.229581i
$454$			4.00000i			0.00881057i
$455$			60.0000i			0.131868i
$456$	160.000			0.350877
$457$	−393.000	+	393.000i	−0.859956	+	0.859956i	−0.991333	−	0.131376i	$-0.958060\pi$
$457$	−393.000	+	393.000i	−0.859956	+	0.859956i	0.131376	+	0.991333i	$0.458060\pi$
$458$	120.000	+	120.000i	0.262009	+	0.262009i
$459$			280.000i			0.610022i
$460$	−20.0000	−	20.0000i	−0.0434783	−	0.0434783i
$461$	622.000			1.34924			0.674620	−	0.738165i	$-0.264307\pi$
$461$	622.000			1.34924			0.674620	+	0.738165i	$0.264307\pi$
$462$	−64.0000	+	64.0000i	−0.138528	+	0.138528i
$463$	278.000	+	278.000i	0.600432	+	0.600432i	0.940427	−	0.339995i	$-0.110425\pi$
$463$	278.000	+	278.000i	0.600432	+	0.600432i	−0.339995	+	0.940427i	$0.610425\pi$
$464$			160.000i			0.344828i
$465$	520.000	−	520.000i	1.11828	−	1.11828i
$466$	−366.000			−0.785408
$467$	−38.0000	+	38.0000i	−0.0813704	+	0.0813704i	−0.746621	−	0.665250i	$-0.768325\pi$
$467$	−38.0000	+	38.0000i	−0.0813704	+	0.0813704i	0.665250	+	0.746621i	$0.268325\pi$
$468$	−6.00000	−	6.00000i	−0.0128205	−	0.0128205i
$469$		−	248.000i		−	0.528785i
$470$	180.000			0.382979
$471$	−108.000			−0.229299
$472$	−40.0000	+	40.0000i	−0.0847458	+	0.0847458i
$473$	336.000	+	336.000i	0.710359	+	0.710359i
$474$		0			0
$475$		−	500.000i		−	1.05263i
$476$	−56.0000			−0.117647
$477$	53.0000	−	53.0000i	0.111111	−	0.111111i
$478$	120.000	+	120.000i	0.251046	+	0.251046i
$479$			440.000i			0.918580i	0.888286	+	0.459290i	$0.151896\pi$
$479$			440.000i			0.918580i	−0.888286	+	0.459290i	$0.848104\pi$
$480$		−	80.0000i		−	0.166667i
$481$	−18.0000			−0.0374220
$482$	−232.000	+	232.000i	−0.481328	+	0.481328i
$483$	16.0000	+	16.0000i	0.0331263	+	0.0331263i
$484$			114.000i			0.235537i
$485$	−315.000	−	315.000i	−0.649485	−	0.649485i
$486$	−76.0000			−0.156379
$487$	522.000	−	522.000i	1.07187	−	1.07187i	0.0746595	−	0.997209i	$-0.476213\pi$
$487$	522.000	−	522.000i	1.07187	−	1.07187i	0.997209	−	0.0746595i	$-0.0237870\pi$
$488$	−96.0000	−	96.0000i	−0.196721	−	0.196721i
$489$			328.000i			0.670757i
$490$	205.000	−	205.000i	0.418367	−	0.418367i
$491$	−328.000			−0.668024			−0.334012	−	0.942569i	$-0.608403\pi$
$491$	−328.000			−0.668024			−0.334012	+	0.942569i	$0.608403\pi$
$492$	32.0000	−	32.0000i	0.0650407	−	0.0650407i
$493$	−280.000	−	280.000i	−0.567951	−	0.567951i
$494$		−	120.000i		−	0.242915i
$495$	−40.0000			−0.0808081
$496$	−208.000			−0.419355
$497$	−56.0000	+	56.0000i	−0.112676	+	0.112676i
$498$	72.0000	+	72.0000i	0.144578	+	0.144578i
$499$		−	380.000i		−	0.761523i	−0.924673	−	0.380762i	$-0.875662\pi$
$499$		−	380.000i		−	0.761523i	0.924673	−	0.380762i	$-0.124338\pi$
$500$	−250.000			−0.500000
$501$	−248.000			−0.495010
$502$	48.0000	−	48.0000i	0.0956175	−	0.0956175i
$503$	−42.0000	−	42.0000i	−0.0834990	−	0.0834990i	0.664124	−	0.747623i	$-0.268805\pi$
$503$	−42.0000	−	42.0000i	−0.0834990	−	0.0834990i	−0.747623	+	0.664124i	$0.768805\pi$
$504$		−	8.00000i		−	0.0158730i
$505$			310.000i			0.613861i
$506$	−32.0000			−0.0632411
$507$	−302.000	+	302.000i	−0.595661	+	0.595661i
$508$	236.000	+	236.000i	0.464567	+	0.464567i
$509$			440.000i			0.864440i	0.901768	+	0.432220i	$0.142270\pi$
$509$			440.000i			0.864440i	−0.901768	+	0.432220i	$0.857730\pi$
$510$	140.000	+	140.000i	0.274510	+	0.274510i
$511$	−188.000			−0.367906
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−400.000	−	400.000i	−0.779727	−	0.779727i
$514$		−	626.000i		−	1.21790i
$515$	−590.000	+	590.000i	−1.14563	+	1.14563i
$516$	336.000			0.651163
$517$	144.000	−	144.000i	0.278530	−	0.278530i
$518$	−12.0000	−	12.0000i	−0.0231660	−	0.0231660i
$519$			428.000i			0.824663i
$520$	−60.0000			−0.115385
$521$	−258.000			−0.495202			−0.247601	−	0.968862i	$-0.579642\pi$
$521$	−258.000			−0.495202			−0.247601	+	0.968862i	$0.579642\pi$
$522$	40.0000	−	40.0000i	0.0766284	−	0.0766284i
$523$	258.000	+	258.000i	0.493308	+	0.493308i	0.909347	−	0.416039i	$-0.136582\pi$
$523$	258.000	+	258.000i	0.493308	+	0.493308i	−0.416039	+	0.909347i	$0.636582\pi$
$524$			256.000i			0.488550i
$525$	200.000			0.380952
$526$	524.000			0.996198
$527$	364.000	−	364.000i	0.690702	−	0.690702i
$528$	−64.0000	−	64.0000i	−0.121212	−	0.121212i
$529$		−	521.000i		−	0.984877i
$530$		−	530.000i		−	1.00000i
$531$	20.0000			0.0376648
$532$	80.0000	−	80.0000i	0.150376	−	0.150376i
$533$	−24.0000	−	24.0000i	−0.0450281	−	0.0450281i
$534$		−	320.000i		−	0.599251i
$535$	710.000	+	710.000i	1.32710	+	1.32710i
$536$	248.000			0.462687
$537$	440.000	−	440.000i	0.819367	−	0.819367i
$538$	10.0000	+	10.0000i	0.0185874	+	0.0185874i
$539$		−	328.000i		−	0.608534i
$540$	−200.000	+	200.000i	−0.370370	+	0.370370i
$541$	−338.000			−0.624769			−0.312384	−	0.949956i	$-0.601128\pi$
$541$	−338.000			−0.624769			−0.312384	+	0.949956i	$0.601128\pi$
$542$	−252.000	+	252.000i	−0.464945	+	0.464945i
$543$	−4.00000	−	4.00000i	−0.00736648	−	0.00736648i
$544$		−	56.0000i		−	0.102941i
$545$	−50.0000			−0.0917431
$546$	48.0000			0.0879121
$547$	−558.000	+	558.000i	−1.02011	+	1.02011i	−0.0203161	+	0.999794i	$0.506467\pi$
$547$	−558.000	+	558.000i	−1.02011	+	1.02011i	−0.999794	+	0.0203161i	$0.993533\pi$
$548$	126.000	+	126.000i	0.229927	+	0.229927i
$549$			48.0000i			0.0874317i
$550$	−200.000	+	200.000i	−0.363636	+	0.363636i
$551$	800.000			1.45191
$552$	−16.0000	+	16.0000i	−0.0289855	+	0.0289855i
$553$		0			0
$554$			534.000i			0.963899i
$555$			60.0000i			0.108108i
$556$	−280.000			−0.503597
$557$	−3.00000	+	3.00000i	−0.00538600	+	0.00538600i	−0.709795	−	0.704409i	$-0.751212\pi$
$557$	−3.00000	+	3.00000i	−0.00538600	+	0.00538600i	0.704409	+	0.709795i	$0.251212\pi$
$558$	52.0000	+	52.0000i	0.0931900	+	0.0931900i
$559$		−	252.000i		−	0.450805i
$560$	−40.0000	−	40.0000i	−0.0714286	−	0.0714286i
$561$	224.000			0.399287
$562$	−312.000	+	312.000i	−0.555160	+	0.555160i
$563$	−42.0000	−	42.0000i	−0.0746004	−	0.0746004i	0.668822	−	0.743422i	$-0.266799\pi$
$563$	−42.0000	−	42.0000i	−0.0746004	−	0.0746004i	−0.743422	+	0.668822i	$0.766799\pi$
$564$		−	144.000i		−	0.255319i
$565$	−115.000	+	115.000i	−0.203540	+	0.203540i
$566$	524.000			0.925795
$567$	142.000	−	142.000i	0.250441	−	0.250441i
$568$	−56.0000	−	56.0000i	−0.0985915	−	0.0985915i
$569$		−	950.000i		−	1.66960i	−0.550557	−	0.834798i	$-0.685584\pi$
$569$		−	950.000i		−	1.66960i	0.550557	−	0.834798i	$-0.314416\pi$
$570$	−400.000			−0.701754
$571$	392.000			0.686515			0.343257	−	0.939241i	$-0.388470\pi$
$571$	392.000			0.686515			0.343257	+	0.939241i	$0.388470\pi$
$572$	−48.0000	+	48.0000i	−0.0839161	+	0.0839161i
$573$	−424.000	−	424.000i	−0.739965	−	0.739965i
$574$		−	32.0000i		−	0.0557491i
$575$	50.0000	+	50.0000i	0.0869565	+	0.0869565i
$576$	8.00000			0.0138889
$577$	−473.000	+	473.000i	−0.819757	+	0.819757i	−0.986073	−	0.166315i	$-0.946813\pi$
$577$	−473.000	+	473.000i	−0.819757	+	0.819757i	0.166315	+	0.986073i	$0.446813\pi$
$578$	−191.000	−	191.000i	−0.330450	−	0.330450i
$579$			228.000i			0.393782i
$580$		−	400.000i		−	0.689655i
$581$	72.0000			0.123924
$582$	−252.000	+	252.000i	−0.432990	+	0.432990i
$583$	−424.000	−	424.000i	−0.727273	−	0.727273i
$584$		−	188.000i		−	0.321918i
$585$	15.0000	+	15.0000i	0.0256410	+	0.0256410i
$586$	−486.000			−0.829352
$587$	−198.000	+	198.000i	−0.337308	+	0.337308i	−0.855353	−	0.518045i	$-0.826660\pi$
$587$	−198.000	+	198.000i	−0.337308	+	0.337308i	0.518045	+	0.855353i	$0.326660\pi$
$588$	−164.000	−	164.000i	−0.278912	−	0.278912i
$589$			1040.00i			1.76570i
$590$	100.000	−	100.000i	0.169492	−	0.169492i
$591$	12.0000			0.0203046
$592$	12.0000	−	12.0000i	0.0202703	−	0.0202703i
$593$	−47.0000	−	47.0000i	−0.0792580	−	0.0792580i	0.666366	−	0.745624i	$-0.267849\pi$
$593$	−47.0000	−	47.0000i	−0.0792580	−	0.0792580i	−0.745624	+	0.666366i	$0.767849\pi$
$594$			320.000i			0.538721i
$595$	140.000			0.235294
$596$	300.000			0.503356
$597$	240.000	−	240.000i	0.402010	−	0.402010i
$598$	12.0000	+	12.0000i	0.0200669	+	0.0200669i
$599$		−	520.000i		−	0.868114i	−0.900886	−	0.434057i	$-0.857082\pi$
$599$		−	520.000i		−	0.868114i	0.900886	−	0.434057i	$-0.142918\pi$
$600$			200.000i			0.333333i
$601$	−328.000			−0.545757			−0.272879	−	0.962048i	$-0.587976\pi$
$601$	−328.000			−0.545757			−0.272879	+	0.962048i	$0.587976\pi$
$602$	168.000	−	168.000i	0.279070	−	0.279070i
$603$	−62.0000	−	62.0000i	−0.102819	−	0.102819i
$604$		−	104.000i		−	0.172185i
$605$		−	285.000i		−	0.471074i
$606$	248.000			0.409241
$607$	462.000	−	462.000i	0.761120	−	0.761120i	−0.215405	−	0.976525i	$-0.569107\pi$
$607$	462.000	−	462.000i	0.761120	−	0.761120i	0.976525	+	0.215405i	$0.0691070\pi$
$608$	80.0000	+	80.0000i	0.131579	+	0.131579i
$609$			320.000i			0.525452i
$610$	240.000	+	240.000i	0.393443	+	0.393443i
$611$	−108.000			−0.176759
$612$	−14.0000	+	14.0000i	−0.0228758	+	0.0228758i
$613$	723.000	+	723.000i	1.17945	+	1.17945i	0.979886	+	0.199560i	$0.0639512\pi$
$613$	723.000	+	723.000i	1.17945	+	1.17945i	0.199560	+	0.979886i	$0.436049\pi$
$614$		−	36.0000i		−	0.0586319i
$615$	−80.0000	+	80.0000i	−0.130081	+	0.130081i
$616$	−64.0000			−0.103896
$617$	327.000	−	327.000i	0.529984	−	0.529984i	−0.390584	−	0.920567i	$-0.627727\pi$
$617$	327.000	−	327.000i	0.529984	−	0.529984i	0.920567	+	0.390584i	$0.127727\pi$
$618$	472.000	+	472.000i	0.763754	+	0.763754i
$619$			660.000i			1.06624i	0.846041	+	0.533118i	$0.178980\pi$
$619$			660.000i			1.06624i	−0.846041	+	0.533118i	$0.821020\pi$
$620$	520.000			0.838710
$621$	80.0000			0.128824
$622$	388.000	−	388.000i	0.623794	−	0.623794i
$623$	−160.000	−	160.000i	−0.256822	−	0.256822i
$624$			48.0000i			0.0769231i
$625$	625.000			1.00000
$626$	−366.000			−0.584665
$627$	−320.000	+	320.000i	−0.510367	+	0.510367i
$628$	−54.0000	−	54.0000i	−0.0859873	−	0.0859873i
$629$			42.0000i			0.0667727i
$630$			20.0000i			0.0317460i
$631$	−548.000			−0.868463			−0.434231	−	0.900801i	$-0.642980\pi$
$631$	−548.000			−0.868463			−0.434231	+	0.900801i	$0.642980\pi$
$632$		0			0
$633$	656.000	+	656.000i	1.03633	+	1.03633i
$634$		−	426.000i		−	0.671924i
$635$	−590.000	−	590.000i	−0.929134	−	0.929134i
$636$	−424.000			−0.666667
$637$	−123.000	+	123.000i	−0.193093	+	0.193093i
$638$	−320.000	−	320.000i	−0.501567	−	0.501567i
$639$			28.0000i			0.0438185i
$640$	40.0000	−	40.0000i	0.0625000	−	0.0625000i
$641$	−568.000			−0.886115			−0.443058	−	0.896493i	$-0.646106\pi$
$641$	−568.000			−0.886115			−0.443058	+	0.896493i	$0.646106\pi$
$642$	568.000	−	568.000i	0.884735	−	0.884735i
$643$	−342.000	−	342.000i	−0.531882	−	0.531882i	0.389250	−	0.921132i	$-0.372734\pi$
$643$	−342.000	−	342.000i	−0.531882	−	0.531882i	−0.921132	+	0.389250i	$0.872734\pi$
$644$			16.0000i			0.0248447i
$645$	−840.000			−1.30233
$646$	−280.000			−0.433437
$647$	−118.000	+	118.000i	−0.182380	+	0.182380i	−0.792392	−	0.610012i	$-0.791165\pi$
$647$	−118.000	+	118.000i	−0.182380	+	0.182380i	0.610012	+	0.792392i	$0.291165\pi$
$648$	142.000	+	142.000i	0.219136	+	0.219136i
$649$		−	160.000i		−	0.246533i
$650$	150.000			0.230769
$651$	−416.000			−0.639017
$652$	−164.000	+	164.000i	−0.251534	+	0.251534i
$653$	453.000	+	453.000i	0.693721	+	0.693721i	0.963049	−	0.269327i	$-0.0868014\pi$
$653$	453.000	+	453.000i	0.693721	+	0.693721i	−0.269327	+	0.963049i	$0.586801\pi$
$654$			40.0000i			0.0611621i
$655$		−	640.000i		−	0.977099i
$656$	32.0000			0.0487805
$657$	−47.0000	+	47.0000i	−0.0715373	+	0.0715373i
$658$	−72.0000	−	72.0000i	−0.109422	−	0.109422i
$659$		−	140.000i		−	0.212443i	−0.994342	−	0.106222i	$-0.966125\pi$
$659$		−	140.000i		−	0.212443i	0.994342	−	0.106222i	$-0.0338753\pi$
$660$	160.000	+	160.000i	0.242424	+	0.242424i
$661$	512.000			0.774584			0.387292	−	0.921957i	$-0.373411\pi$
$661$	512.000			0.774584			0.387292	+	0.921957i	$0.373411\pi$
$662$	−232.000	+	232.000i	−0.350453	+	0.350453i
$663$	−84.0000	−	84.0000i	−0.126697	−	0.126697i
$664$			72.0000i			0.108434i
$665$	−200.000	+	200.000i	−0.300752	+	0.300752i
$666$	−6.00000			−0.00900901
$667$	−80.0000	+	80.0000i	−0.119940	+	0.119940i
$668$	−124.000	−	124.000i	−0.185629	−	0.185629i
$669$		−	552.000i		−	0.825112i
$670$	−620.000			−0.925373
$671$	384.000			0.572280
$672$	−32.0000	+	32.0000i	−0.0476190	+	0.0476190i
$673$	193.000	+	193.000i	0.286776	+	0.286776i	0.835804	−	0.549028i	$-0.185002\pi$
$673$	193.000	+	193.000i	0.286776	+	0.286776i	−0.549028	+	0.835804i	$0.685002\pi$
$674$			834.000i			1.23739i
$675$	500.000	−	500.000i	0.740741	−	0.740741i
$676$	−302.000			−0.446746
$677$	157.000	−	157.000i	0.231905	−	0.231905i	−0.581582	−	0.813488i	$-0.697566\pi$
$677$	157.000	−	157.000i	0.231905	−	0.231905i	0.813488	+	0.581582i	$0.197566\pi$
$678$	92.0000	+	92.0000i	0.135693	+	0.135693i
$679$			252.000i			0.371134i
$680$			140.000i			0.205882i
$681$	−8.00000			−0.0117474
$682$	416.000	−	416.000i	0.609971	−	0.609971i
$683$	438.000	+	438.000i	0.641288	+	0.641288i	0.950872	−	0.309584i	$-0.100190\pi$
$683$	438.000	+	438.000i	0.641288	+	0.641288i	−0.309584	+	0.950872i	$0.600190\pi$
$684$		−	40.0000i		−	0.0584795i
$685$	−315.000	−	315.000i	−0.459854	−	0.459854i
$686$	−360.000			−0.524781
$687$	−240.000	+	240.000i	−0.349345	+	0.349345i
$688$	168.000	+	168.000i	0.244186	+	0.244186i
$689$			318.000i			0.461538i
$690$	40.0000	−	40.0000i	0.0579710	−	0.0579710i
$691$	1032.00			1.49349			0.746744	−	0.665112i	$-0.231616\pi$
$691$	1032.00			1.49349			0.746744	+	0.665112i	$0.231616\pi$
$692$	−214.000	+	214.000i	−0.309249	+	0.309249i
$693$	16.0000	+	16.0000i	0.0230880	+	0.0230880i
$694$			404.000i			0.582133i
$695$	700.000			1.00719
$696$	−320.000			−0.459770
$697$	−56.0000	+	56.0000i	−0.0803443	+	0.0803443i
$698$	−440.000	−	440.000i	−0.630372	−	0.630372i
$699$		−	732.000i		−	1.04721i
$700$	100.000	+	100.000i	0.142857	+	0.142857i
$701$	−128.000			−0.182596			−0.0912981	−	0.995824i	$-0.529102\pi$
$701$	−128.000			−0.182596			−0.0912981	+	0.995824i	$0.529102\pi$
$702$	120.000	−	120.000i	0.170940	−	0.170940i
$703$	−60.0000	−	60.0000i	−0.0853485	−	0.0853485i
$704$		−	64.0000i		−	0.0909091i
$705$			360.000i			0.510638i
$706$	894.000			1.26629
$707$	124.000	−	124.000i	0.175389	−	0.175389i
$708$	−80.0000	−	80.0000i	−0.112994	−	0.112994i
$709$		−	760.000i		−	1.07193i	−0.844239	−	0.535966i	$-0.819947\pi$
$709$		−	760.000i		−	1.07193i	0.844239	−	0.535966i	$-0.180053\pi$
$710$	140.000	+	140.000i	0.197183	+	0.197183i
$711$		0			0
$712$	160.000	−	160.000i	0.224719	−	0.224719i
$713$	−104.000	−	104.000i	−0.145863	−	0.145863i
$714$		−	112.000i		−	0.156863i
$715$	120.000	−	120.000i	0.167832	−	0.167832i
$716$	440.000			0.614525
$717$	−240.000	+	240.000i	−0.334728	+	0.334728i
$718$	−400.000	−	400.000i	−0.557103	−	0.557103i
$719$			1160.00i			1.61335i	0.590994	+	0.806676i	$0.298736\pi$
$719$			1160.00i			1.61335i	−0.590994	+	0.806676i	$0.701264\pi$
$720$	−20.0000			−0.0277778
$721$	472.000			0.654646
$722$	39.0000	−	39.0000i	0.0540166	−	0.0540166i
$723$	−464.000	−	464.000i	−0.641770	−	0.641770i
$724$		−	4.00000i		−	0.00552486i
$725$			1000.00i			1.37931i
$726$	−228.000			−0.314050
$727$	−558.000	+	558.000i	−0.767538	+	0.767538i	−0.977672	−	0.210135i	$-0.932610\pi$
$727$	−558.000	+	558.000i	−0.767538	+	0.767538i	0.210135	+	0.977672i	$0.432610\pi$
$728$	24.0000	+	24.0000i	0.0329670	+	0.0329670i
$729$		−	791.000i		−	1.08505i
$730$			470.000i			0.643836i
$731$	−588.000			−0.804378
$732$	192.000	−	192.000i	0.262295	−	0.262295i
$733$	−827.000	−	827.000i	−1.12824	−	1.12824i	−0.990463	−	0.137777i	$-0.956004\pi$
$733$	−827.000	−	827.000i	−1.12824	−	1.12824i	−0.137777	−	0.990463i	$-0.543996\pi$
$734$		−	236.000i		−	0.321526i
$735$	410.000	+	410.000i	0.557823	+	0.557823i
$736$	−16.0000			−0.0217391
$737$	−496.000	+	496.000i	−0.672999	+	0.672999i
$738$	−8.00000	−	8.00000i	−0.0108401	−	0.0108401i
$739$			700.000i			0.947226i	0.880733	+	0.473613i	$0.157050\pi$
$739$			700.000i			0.947226i	−0.880733	+	0.473613i	$0.842950\pi$
$740$	−30.0000	+	30.0000i	−0.0405405	+	0.0405405i
$741$	240.000			0.323887
$742$	−212.000	+	212.000i	−0.285714	+	0.285714i
$743$	−382.000	−	382.000i	−0.514132	−	0.514132i	0.401658	−	0.915790i	$-0.368434\pi$
$743$	−382.000	−	382.000i	−0.514132	−	0.514132i	−0.915790	+	0.401658i	$0.868434\pi$
$744$		−	416.000i		−	0.559140i
$745$	−750.000			−1.00671
$746$	214.000			0.286863
$747$	18.0000	−	18.0000i	0.0240964	−	0.0240964i
$748$	112.000	+	112.000i	0.149733	+	0.149733i
$749$		−	568.000i		−	0.758344i
$750$		−	500.000i		−	0.666667i
$751$	−588.000			−0.782956			−0.391478	−	0.920187i	$-0.628036\pi$
$751$	−588.000			−0.782956			−0.391478	+	0.920187i	$0.628036\pi$
$752$	72.0000	−	72.0000i	0.0957447	−	0.0957447i
$753$	96.0000	+	96.0000i	0.127490	+	0.127490i
$754$			240.000i			0.318302i
$755$			260.000i			0.344371i
$756$	160.000			0.211640
$757$	987.000	−	987.000i	1.30383	−	1.30383i	0.378043	−	0.925788i	$-0.376597\pi$
$757$	987.000	−	987.000i	1.30383	−	1.30383i	0.925788	−	0.378043i	$-0.123403\pi$
$758$	340.000	+	340.000i	0.448549	+	0.448549i
$759$		−	64.0000i		−	0.0843215i
$760$	−200.000	−	200.000i	−0.263158	−	0.263158i
$761$	−158.000			−0.207622			−0.103811	−	0.994597i	$-0.533104\pi$
$761$	−158.000			−0.207622			−0.103811	+	0.994597i	$0.533104\pi$
$762$	−472.000	+	472.000i	−0.619423	+	0.619423i
$763$	20.0000	+	20.0000i	0.0262123	+	0.0262123i
$764$		−	424.000i		−	0.554974i
$765$	35.0000	−	35.0000i	0.0457516	−	0.0457516i
$766$	684.000			0.892950
$767$	−60.0000	+	60.0000i	−0.0782269	+	0.0782269i
$768$	−32.0000	−	32.0000i	−0.0416667	−	0.0416667i
$769$		−	80.0000i		−	0.104031i	−0.998646	−	0.0520156i	$-0.983435\pi$
$769$		−	80.0000i		−	0.104031i	0.998646	−	0.0520156i	$-0.0165646\pi$
$770$	160.000			0.207792
$771$	1252.00			1.62387
$772$	−114.000	+	114.000i	−0.147668	+	0.147668i
$773$	243.000	+	243.000i	0.314360	+	0.314360i	0.846596	−	0.532236i	$-0.178648\pi$
$773$	243.000	+	243.000i	0.314360	+	0.314360i	−0.532236	+	0.846596i	$0.678648\pi$
$774$		−	84.0000i		−	0.108527i
$775$	−1300.00			−1.67742
$776$	−252.000			−0.324742
$777$	24.0000	−	24.0000i	0.0308880	−	0.0308880i
$778$	390.000	+	390.000i	0.501285	+	0.501285i
$779$		−	160.000i		−	0.205392i
$780$		−	120.000i		−	0.153846i
$781$	224.000			0.286812
$782$	28.0000	−	28.0000i	0.0358056	−	0.0358056i
$783$	800.000	+	800.000i	1.02171	+	1.02171i
$784$		−	164.000i		−	0.209184i
$785$	135.000	+	135.000i	0.171975	+	0.171975i
$786$	−512.000			−0.651399
$787$	262.000	−	262.000i	0.332910	−	0.332910i	−0.520781	−	0.853690i	$-0.674359\pi$
$787$	262.000	−	262.000i	0.332910	−	0.332910i	0.853690	+	0.520781i	$0.174359\pi$
$788$	6.00000	+	6.00000i	0.00761421	+	0.00761421i
$789$			1048.00i			1.32826i
$790$		0			0
$791$	92.0000			0.116308
$792$	−16.0000	+	16.0000i	−0.0202020	+	0.0202020i
$793$	−144.000	−	144.000i	−0.181589	−	0.181589i
$794$		−	646.000i		−	0.813602i
$795$	1060.00			1.33333
$796$	240.000			0.301508
$797$	267.000	−	267.000i	0.335006	−	0.335006i	−0.519478	−	0.854484i	$-0.673873\pi$
$797$	267.000	−	267.000i	0.335006	−	0.335006i	0.854484	+	0.519478i	$0.173873\pi$
$798$	160.000	+	160.000i	0.200501	+	0.200501i
$799$			252.000i			0.315394i
$800$	−100.000	+	100.000i	−0.125000	+	0.125000i
$801$	−80.0000			−0.0998752
$802$	−642.000	+	642.000i	−0.800499	+	0.800499i
$803$	376.000	+	376.000i	0.468244	+	0.468244i
$804$			496.000i			0.616915i
$805$		−	40.0000i		−	0.0496894i
$806$	−312.000			−0.387097
$807$	−20.0000	+	20.0000i	−0.0247831	+	0.0247831i
$808$	124.000	+	124.000i	0.153465	+	0.153465i
$809$		−	560.000i		−	0.692213i	−0.938195	−	0.346106i	$-0.887504\pi$
$809$		−	560.000i		−	0.692213i	0.938195	−	0.346106i	$-0.112496\pi$
$810$	−355.000	−	355.000i	−0.438272	−	0.438272i
$811$	−208.000			−0.256473			−0.128237	−	0.991744i	$-0.540932\pi$
$811$	−208.000			−0.256473			−0.128237	+	0.991744i	$0.540932\pi$
$812$	−160.000	+	160.000i	−0.197044	+	0.197044i
$813$	−504.000	−	504.000i	−0.619926	−	0.619926i
$814$			48.0000i			0.0589681i
$815$	410.000	−	410.000i	0.503067	−	0.503067i
$816$	112.000			0.137255
$817$	840.000	−	840.000i	1.02815	−	1.02815i
$818$	−150.000	−	150.000i	−0.183374	−	0.183374i
$819$		−	12.0000i		−	0.0146520i
$820$	−80.0000			−0.0975610
$821$	−1568.00			−1.90987			−0.954933	−	0.296821i	$-0.904073\pi$
$821$	−1568.00			−1.90987			−0.954933	+	0.296821i	$0.904073\pi$
$822$	−252.000	+	252.000i	−0.306569	+	0.306569i
$823$	−562.000	−	562.000i	−0.682868	−	0.682868i	0.277778	−	0.960645i	$-0.410402\pi$
$823$	−562.000	−	562.000i	−0.682868	−	0.682868i	−0.960645	+	0.277778i	$0.910402\pi$
$824$			472.000i			0.572816i
$825$	−400.000	−	400.000i	−0.484848	−	0.484848i
$826$	−80.0000			−0.0968523
$827$	762.000	−	762.000i	0.921403	−	0.921403i	−0.0757260	−	0.997129i	$-0.524127\pi$
$827$	762.000	−	762.000i	0.921403	−	0.921403i	0.997129	+	0.0757260i	$0.0241274\pi$
$828$	4.00000	+	4.00000i	0.00483092	+	0.00483092i
$829$		−	170.000i		−	0.205066i	−0.994730	−	0.102533i	$-0.967305\pi$
$829$		−	170.000i		−	0.205066i	0.994730	−	0.102533i	$-0.0326948\pi$
$830$		−	180.000i		−	0.216867i
$831$	−1068.00			−1.28520
$832$	−24.0000	+	24.0000i	−0.0288462	+	0.0288462i
$833$	287.000	+	287.000i	0.344538	+	0.344538i
$834$		−	560.000i		−	0.671463i
$835$	310.000	+	310.000i	0.371257	+	0.371257i
$836$	−320.000			−0.382775
$837$	−1040.00	+	1040.00i	−1.24253	+	1.24253i
$838$	300.000	+	300.000i	0.357995	+	0.357995i
$839$			280.000i			0.333731i	0.985980	+	0.166865i	$0.0533645\pi$
$839$			280.000i			0.333731i	−0.985980	+	0.166865i	$0.946635\pi$
$840$	80.0000	−	80.0000i	0.0952381	−	0.0952381i
$841$	−759.000			−0.902497
$842$	208.000	−	208.000i	0.247031	−	0.247031i
$843$	−624.000	−	624.000i	−0.740214	−	0.740214i
$844$			656.000i			0.777251i
$845$	755.000			0.893491
$846$	−36.0000			−0.0425532
$847$	−114.000	+	114.000i	−0.134593	+	0.134593i
$848$	−212.000	−	212.000i	−0.250000	−	0.250000i
$849$			1048.00i			1.23439i
$850$		−	350.000i		−	0.411765i
$851$	12.0000			0.0141011
$852$	112.000	−	112.000i	0.131455	−	0.131455i
$853$	1123.00	+	1123.00i	1.31653	+	1.31653i	0.916504	+	0.400026i	$0.130999\pi$
$853$	1123.00	+	1123.00i	1.31653	+	1.31653i	0.400026	+	0.916504i	$0.369001\pi$
$854$		−	192.000i		−	0.224824i
$855$			100.000i			0.116959i
$856$	568.000			0.663551
$857$	417.000	−	417.000i	0.486581	−	0.486581i	−0.420644	−	0.907226i	$-0.638196\pi$
$857$	417.000	−	417.000i	0.486581	−	0.486581i	0.907226	+	0.420644i	$0.138196\pi$
$858$	−96.0000	−	96.0000i	−0.111888	−	0.111888i
$859$			1300.00i			1.51339i	0.653769	+	0.756694i	$0.273187\pi$
$859$			1300.00i			1.51339i	−0.653769	+	0.756694i	$0.726813\pi$
$860$	−420.000	−	420.000i	−0.488372	−	0.488372i
$861$	64.0000			0.0743322
$862$	788.000	−	788.000i	0.914153	−	0.914153i
$863$	−242.000	−	242.000i	−0.280417	−	0.280417i	0.552858	−	0.833275i	$-0.313537\pi$
$863$	−242.000	−	242.000i	−0.280417	−	0.280417i	−0.833275	+	0.552858i	$0.813537\pi$
$864$			160.000i			0.185185i
$865$	535.000	−	535.000i	0.618497	−	0.618497i
$866$	734.000			0.847575
$867$	382.000	−	382.000i	0.440600	−	0.440600i
$868$	−208.000	−	208.000i	−0.239631	−	0.239631i
$869$		0			0
$870$	800.000			0.919540
$871$	372.000			0.427095
$872$	−20.0000	+	20.0000i	−0.0229358	+	0.0229358i
$873$	63.0000	+	63.0000i	0.0721649	+	0.0721649i
$874$			80.0000i			0.0915332i
$875$	−250.000	−	250.000i	−0.285714	−	0.285714i
$876$	376.000			0.429224
$877$	−453.000	+	453.000i	−0.516534	+	0.516534i	−0.916521	−	0.399987i	$-0.869015\pi$
$877$	−453.000	+	453.000i	−0.516534	+	0.516534i	0.399987	+	0.916521i	$0.369015\pi$
$878$	560.000	+	560.000i	0.637813	+	0.637813i
$879$		−	972.000i		−	1.10580i
$880$			160.000i			0.181818i
$881$	712.000			0.808173			0.404086	−	0.914721i	$-0.367590\pi$
$881$	712.000			0.808173			0.404086	+	0.914721i	$0.367590\pi$
$882$	−41.0000	+	41.0000i	−0.0464853	+	0.0464853i
$883$	118.000	+	118.000i	0.133635	+	0.133635i	0.770760	−	0.637125i	$-0.219877\pi$
$883$	118.000	+	118.000i	0.133635	+	0.133635i	−0.637125	+	0.770760i	$0.719877\pi$
$884$		−	84.0000i		−	0.0950226i
$885$	200.000	+	200.000i	0.225989	+	0.225989i
$886$	−756.000			−0.853273
$887$	−1158.00	+	1158.00i	−1.30552	+	1.30552i	−0.380914	+	0.924611i	$0.624390\pi$
$887$	−1158.00	+	1158.00i	−1.30552	+	1.30552i	−0.924611	+	0.380914i	$0.875610\pi$
$888$	24.0000	+	24.0000i	0.0270270	+	0.0270270i
$889$			472.000i			0.530934i
$890$	−400.000	+	400.000i	−0.449438	+	0.449438i
$891$	−568.000			−0.637486
$892$	276.000	−	276.000i	0.309417	−	0.309417i
$893$	−360.000	−	360.000i	−0.403135	−	0.403135i
$894$			600.000i			0.671141i
$895$	−1100.00			−1.22905
$896$	−32.0000			−0.0357143
$897$	−24.0000	+	24.0000i	−0.0267559	+	0.0267559i
$898$	−410.000	−	410.000i	−0.456570	−	0.456570i
$899$		−	2080.00i		−	2.31368i
$900$	50.0000			0.0555556
$901$	742.000			0.823529
$902$	−64.0000	+	64.0000i	−0.0709534	+	0.0709534i
$903$	336.000	+	336.000i	0.372093	+	0.372093i
$904$			92.0000i			0.101770i
$905$			10.0000i			0.0110497i
$906$	208.000			0.229581
$907$	142.000	−	142.000i	0.156560	−	0.156560i	−0.624480	−	0.781040i	$-0.714689\pi$
$907$	142.000	−	142.000i	0.156560	−	0.156560i	0.781040	+	0.624480i	$0.214689\pi$
$908$	−4.00000	−	4.00000i	−0.00440529	−	0.00440529i
$909$		−	62.0000i		−	0.0682068i
$910$	−60.0000	−	60.0000i	−0.0659341	−	0.0659341i
$911$	1172.00			1.28650			0.643249	−	0.765657i	$-0.277586\pi$
$911$	1172.00			1.28650			0.643249	+	0.765657i	$0.277586\pi$
$912$	−160.000	+	160.000i	−0.175439	+	0.175439i
$913$	−144.000	−	144.000i	−0.157722	−	0.157722i
$914$		−	786.000i		−	0.859956i
$915$	−480.000	+	480.000i	−0.524590	+	0.524590i
$916$	−240.000			−0.262009
$917$	−256.000	+	256.000i	−0.279171	+	0.279171i
$918$	−280.000	−	280.000i	−0.305011	−	0.305011i
$919$		−	920.000i		−	1.00109i	−0.865711	−	0.500544i	$-0.833133\pi$
$919$		−	920.000i		−	1.00109i	0.865711	−	0.500544i	$-0.166867\pi$
$920$	40.0000			0.0434783
$921$	72.0000			0.0781759
$922$	−622.000	+	622.000i	−0.674620	+	0.674620i
$923$	−84.0000	−	84.0000i	−0.0910076	−	0.0910076i
$924$		−	128.000i		−	0.138528i
$925$	75.0000	−	75.0000i	0.0810811	−	0.0810811i
$926$	−556.000			−0.600432
$927$	118.000	−	118.000i	0.127292	−	0.127292i
$928$	−160.000	−	160.000i	−0.172414	−	0.172414i
$929$			1190.00i			1.28095i	0.767980	+	0.640474i	$0.221262\pi$
$929$			1190.00i			1.28095i	−0.767980	+	0.640474i	$0.778738\pi$
$930$			1040.00i			1.11828i
$931$	−820.000			−0.880773
$932$	366.000	−	366.000i	0.392704	−	0.392704i
$933$	776.000	+	776.000i	0.831726	+	0.831726i
$934$		−	76.0000i		−	0.0813704i
$935$	−280.000	−	280.000i	−0.299465	−	0.299465i
$936$	12.0000			0.0128205
$937$	−233.000	+	233.000i	−0.248666	+	0.248666i	−0.820423	−	0.571757i	$-0.806262\pi$
$937$	−233.000	+	233.000i	−0.248666	+	0.248666i	0.571757	+	0.820423i	$0.306262\pi$
$938$	248.000	+	248.000i	0.264392	+	0.264392i
$939$		−	732.000i		−	0.779553i
$940$	−180.000	+	180.000i	−0.191489	+	0.191489i
$941$	−78.0000			−0.0828905			−0.0414453	−	0.999141i	$-0.513196\pi$
$941$	−78.0000			−0.0828905			−0.0414453	+	0.999141i	$0.513196\pi$
$942$	108.000	−	108.000i	0.114650	−	0.114650i
$943$	16.0000	+	16.0000i	0.0169671	+	0.0169671i
$944$		−	80.0000i		−	0.0847458i
$945$	−400.000			−0.423280
$946$	−672.000			−0.710359
$947$	62.0000	−	62.0000i	0.0654699	−	0.0654699i	−0.673614	−	0.739084i	$-0.735259\pi$
$947$	62.0000	−	62.0000i	0.0654699	−	0.0654699i	0.739084	+	0.673614i	$0.235259\pi$
$948$		0			0
$949$		−	282.000i		−	0.297155i
$950$	500.000	+	500.000i	0.526316	+	0.526316i
$951$	852.000			0.895899
$952$	56.0000	−	56.0000i	0.0588235	−	0.0588235i
$953$	−1017.00	−	1017.00i	−1.06716	−	1.06716i	−0.997576	−	0.0695800i	$-0.977834\pi$
$953$	−1017.00	−	1017.00i	−1.06716	−	1.06716i	−0.0695800	−	0.997576i	$-0.522166\pi$
$954$			106.000i			0.111111i
$955$			1060.00i			1.10995i
$956$	−240.000			−0.251046
$957$	640.000	−	640.000i	0.668757	−	0.668757i
$958$	−440.000	−	440.000i	−0.459290	−	0.459290i
$959$			252.000i			0.262774i
$960$	80.0000	+	80.0000i	0.0833333	+	0.0833333i
$961$	1743.00			1.81374
$962$	18.0000	−	18.0000i	0.0187110	−	0.0187110i
$963$	−142.000	−	142.000i	−0.147456	−	0.147456i
$964$		−	464.000i		−	0.481328i
$965$	285.000	−	285.000i	0.295337	−	0.295337i
$966$	−32.0000			−0.0331263
$967$	502.000	−	502.000i	0.519131	−	0.519131i	−0.398177	−	0.917309i	$-0.630357\pi$
$967$	502.000	−	502.000i	0.519131	−	0.519131i	0.917309	+	0.398177i	$0.130357\pi$
$968$	−114.000	−	114.000i	−0.117769	−	0.117769i
$969$		−	560.000i		−	0.577915i
$970$	630.000			0.649485
$971$	992.000			1.02163			0.510814	−	0.859691i	$-0.329344\pi$
$971$	992.000			1.02163			0.510814	+	0.859691i	$0.329344\pi$
$972$	76.0000	−	76.0000i	0.0781893	−	0.0781893i
$973$	−280.000	−	280.000i	−0.287770	−	0.287770i
$974$			1044.00i			1.07187i
$975$			300.000i			0.307692i
$976$	192.000			0.196721
$977$	−783.000	+	783.000i	−0.801433	+	0.801433i	−0.983320	−	0.181887i	$-0.941780\pi$
$977$	−783.000	+	783.000i	−0.801433	+	0.801433i	0.181887	+	0.983320i	$0.441780\pi$
$978$	−328.000	−	328.000i	−0.335378	−	0.335378i
$979$			640.000i			0.653728i
$980$			410.000i			0.418367i
$981$	10.0000			0.0101937
$982$	328.000	−	328.000i	0.334012	−	0.334012i
$983$	1058.00	+	1058.00i	1.07630	+	1.07630i	0.996838	+	0.0794589i	$0.0253192\pi$
$983$	1058.00	+	1058.00i	1.07630	+	1.07630i	0.0794589	+	0.996838i	$0.474681\pi$
$984$			64.0000i			0.0650407i
$985$	−15.0000	−	15.0000i	−0.0152284	−	0.0152284i
$986$	560.000			0.567951
$987$	144.000	−	144.000i	0.145897	−	0.145897i
$988$	120.000	+	120.000i	0.121457	+	0.121457i
$989$			168.000i			0.169869i
$990$	40.0000	−	40.0000i	0.0404040	−	0.0404040i
$991$	−68.0000			−0.0686176			−0.0343088	−	0.999411i	$-0.510923\pi$
$991$	−68.0000			−0.0686176			−0.0343088	+	0.999411i	$0.510923\pi$
$992$	208.000	−	208.000i	0.209677	−	0.209677i
$993$	−464.000	−	464.000i	−0.467271	−	0.467271i
$994$		−	112.000i		−	0.112676i
$995$	−600.000			−0.603015
$996$	−144.000			−0.144578
$997$	−773.000	+	773.000i	−0.775326	+	0.775326i	−0.979032	−	0.203706i	$-0.934701\pi$
$997$	−773.000	+	773.000i	−0.775326	+	0.775326i	0.203706	+	0.979032i	$0.434701\pi$
$998$	380.000	+	380.000i	0.380762	+	0.380762i
$999$		−	120.000i		−	0.120120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.3.c.a.3.1	✓	2
3.2	odd	2		90.3.g.b.73.1		2
4.3	odd	2		80.3.p.c.33.1		2
5.2	odd	4	inner	10.3.c.a.7.1	yes	2
5.3	odd	4		50.3.c.c.7.1		2
5.4	even	2		50.3.c.c.43.1		2
7.6	odd	2		490.3.f.b.393.1		2
8.3	odd	2		320.3.p.a.193.1		2
8.5	even	2		320.3.p.h.193.1		2
12.11	even	2		720.3.bh.c.433.1		2
15.2	even	4		90.3.g.b.37.1		2
15.8	even	4		450.3.g.b.307.1		2
15.14	odd	2		450.3.g.b.343.1		2
20.3	even	4		400.3.p.b.257.1		2
20.7	even	4		80.3.p.c.17.1		2
20.19	odd	2		400.3.p.b.193.1		2
35.27	even	4		490.3.f.b.197.1		2
40.27	even	4		320.3.p.a.257.1		2
40.37	odd	4		320.3.p.h.257.1		2
60.47	odd	4		720.3.bh.c.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.3.c.a.3.1	✓	2	1.1	even	1	trivial
10.3.c.a.7.1	yes	2	5.2	odd	4	inner
50.3.c.c.7.1		2	5.3	odd	4
50.3.c.c.43.1		2	5.4	even	2
80.3.p.c.17.1		2	20.7	even	4
80.3.p.c.33.1		2	4.3	odd	2
90.3.g.b.37.1		2	15.2	even	4
90.3.g.b.73.1		2	3.2	odd	2
320.3.p.a.193.1		2	8.3	odd	2
320.3.p.a.257.1		2	40.27	even	4
320.3.p.h.193.1		2	8.5	even	2
320.3.p.h.257.1		2	40.37	odd	4
400.3.p.b.193.1		2	20.19	odd	2
400.3.p.b.257.1		2	20.3	even	4
450.3.g.b.307.1		2	15.8	even	4
450.3.g.b.343.1		2	15.14	odd	2
490.3.f.b.197.1		2	35.27	even	4
490.3.f.b.393.1		2	7.6	odd	2
720.3.bh.c.433.1		2	12.11	even	2
720.3.bh.c.577.1		2	60.47	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-2.00000 - 2.00000i) q^{3} -2.00000i q^{4} +5.00000i q^{5} +4.00000 q^{6} +(2.00000 - 2.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} -1.00000i q^{9} +(-5.00000 - 5.00000i) q^{10} -8.00000 q^{11} +(-4.00000 + 4.00000i) q^{12} +(3.00000 + 3.00000i) q^{13} +4.00000i q^{14} +(10.0000 - 10.0000i) q^{15} -4.00000 q^{16} +(7.00000 - 7.00000i) q^{17} +(1.00000 + 1.00000i) q^{18} +20.0000i q^{19} +10.0000 q^{20} -8.00000 q^{21} +(8.00000 - 8.00000i) q^{22} +(-2.00000 - 2.00000i) q^{23} -8.00000i q^{24} -25.0000 q^{25} -6.00000 q^{26} +(-20.0000 + 20.0000i) q^{27} +(-4.00000 - 4.00000i) q^{28} -40.0000i q^{29} +20.0000i q^{30} +52.0000 q^{31} +(4.00000 - 4.00000i) q^{32} +(16.0000 + 16.0000i) q^{33} +14.0000i q^{34} +(10.0000 + 10.0000i) q^{35} -2.00000 q^{36} +(-3.00000 + 3.00000i) q^{37} +(-20.0000 - 20.0000i) q^{38} -12.0000i q^{39} +(-10.0000 + 10.0000i) q^{40} -8.00000 q^{41} +(8.00000 - 8.00000i) q^{42} +(-42.0000 - 42.0000i) q^{43} +16.0000i q^{44} +5.00000 q^{45} +4.00000 q^{46} +(-18.0000 + 18.0000i) q^{47} +(8.00000 + 8.00000i) q^{48} +41.0000i q^{49} +(25.0000 - 25.0000i) q^{50} -28.0000 q^{51} +(6.00000 - 6.00000i) q^{52} +(53.0000 + 53.0000i) q^{53} -40.0000i q^{54} -40.0000i q^{55} +8.00000 q^{56} +(40.0000 - 40.0000i) q^{57} +(40.0000 + 40.0000i) q^{58} +20.0000i q^{59} +(-20.0000 - 20.0000i) q^{60} -48.0000 q^{61} +(-52.0000 + 52.0000i) q^{62} +(-2.00000 - 2.00000i) q^{63} +8.00000i q^{64} +(-15.0000 + 15.0000i) q^{65} -32.0000 q^{66} +(62.0000 - 62.0000i) q^{67} +(-14.0000 - 14.0000i) q^{68} +8.00000i q^{69} -20.0000 q^{70} -28.0000 q^{71} +(2.00000 - 2.00000i) q^{72} +(-47.0000 - 47.0000i) q^{73} -6.00000i q^{74} +(50.0000 + 50.0000i) q^{75} +40.0000 q^{76} +(-16.0000 + 16.0000i) q^{77} +(12.0000 + 12.0000i) q^{78} -20.0000i q^{80} +71.0000 q^{81} +(8.00000 - 8.00000i) q^{82} +(18.0000 + 18.0000i) q^{83} +16.0000i q^{84} +(35.0000 + 35.0000i) q^{85} +84.0000 q^{86} +(-80.0000 + 80.0000i) q^{87} +(-16.0000 - 16.0000i) q^{88} -80.0000i q^{89} +(-5.00000 + 5.00000i) q^{90} +12.0000 q^{91} +(-4.00000 + 4.00000i) q^{92} +(-104.000 - 104.000i) q^{93} -36.0000i q^{94} -100.000 q^{95} -16.0000 q^{96} +(-63.0000 + 63.0000i) q^{97} +(-41.0000 - 41.0000i) q^{98} +8.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{3} + 8 q^{6} + 4 q^{7} + 4 q^{8} - 10 q^{10} - 16 q^{11} - 8 q^{12} + 6 q^{13} + 20 q^{15} - 8 q^{16} + 14 q^{17} + 2 q^{18} + 20 q^{20} - 16 q^{21} + 16 q^{22} - 4 q^{23} - 50 q^{25}+ \cdots - 82 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^3 + 8 * q^6 + 4 * q^7 + 4 * q^8 - 10 * q^10 - 16 * q^11 - 8 * q^12 + 6 * q^13 + 20 * q^15 - 8 * q^16 + 14 * q^17 + 2 * q^18 + 20 * q^20 - 16 * q^21 + 16 * q^22 - 4 * q^23 - 50 * q^25 - 12 * q^26 - 40 * q^27 - 8 * q^28 + 104 * q^31 + 8 * q^32 + 32 * q^33 + 20 * q^35 - 4 * q^36 - 6 * q^37 - 40 * q^38 - 20 * q^40 - 16 * q^41 + 16 * q^42 - 84 * q^43 + 10 * q^45 + 8 * q^46 - 36 * q^47 + 16 * q^48 + 50 * q^50 - 56 * q^51 + 12 * q^52 + 106 * q^53 + 16 * q^56 + 80 * q^57 + 80 * q^58 - 40 * q^60 - 96 * q^61 - 104 * q^62 - 4 * q^63 - 30 * q^65 - 64 * q^66 + 124 * q^67 - 28 * q^68 - 40 * q^70 - 56 * q^71 + 4 * q^72 - 94 * q^73 + 100 * q^75 + 80 * q^76 - 32 * q^77 + 24 * q^78 + 142 * q^81 + 16 * q^82 + 36 * q^83 + 70 * q^85 + 168 * q^86 - 160 * q^87 - 32 * q^88 - 10 * q^90 + 24 * q^91 - 8 * q^92 - 208 * q^93 - 200 * q^95 - 32 * q^96 - 126 * q^97 - 82 * q^98

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