LMFDB - Embedded newform 570.2.c.c.569.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(569,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("570.569");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.c (of order $2$, degree $1$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1499238400.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 59x^{4} - 66x^{3} + 54x^{2} - 26x + 5 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 59x^4 - 66x^3 + 54x^2 - 26*x + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			569.4
Root			$0.500000 + 1.41267i$ of defining polynomial
Character	$\chi$	$=$	570.569
Dual form			570.2.c.c.569.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.500000 + 1.65831i) q^{3} -1.00000 q^{4} +(1.91267 + 1.15831i) q^{5} +(1.65831 + 0.500000i) q^{6} -3.21974i q^{7} +1.00000i q^{8} +(-2.50000 - 1.65831i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.500000 + 1.65831i) q^{3} -1.00000 q^{4} +(1.91267 + 1.15831i) q^{5} +(1.65831 + 0.500000i) q^{6} -3.21974i q^{7} +1.00000i q^{8} +(-2.50000 - 1.65831i) q^{9} +(1.15831 - 1.91267i) q^{10} -4.31662i q^{11} +(0.500000 - 1.65831i) q^{12} +3.31662 q^{13} -3.21974 q^{14} +(-2.87718 + 2.59265i) q^{15} +1.00000 q^{16} +3.21974 q^{17} +(-1.65831 + 2.50000i) q^{18} +(-4.31662 + 0.605599i) q^{19} +(-1.91267 - 1.15831i) q^{20} +(5.33934 + 1.60987i) q^{21} -4.31662 q^{22} +7.04509 q^{23} +(-1.65831 - 0.500000i) q^{24} +(2.31662 + 4.43094i) q^{25} -3.31662i q^{26} +(4.00000 - 3.31662i) q^{27} +3.21974i q^{28} +8.25629 q^{29} +(2.59265 + 2.87718i) q^{30} +2.61414i q^{31} -1.00000i q^{32} +(7.15831 + 2.15831i) q^{33} -3.21974i q^{34} +(3.72947 - 6.15831i) q^{35} +(2.50000 + 1.65831i) q^{36} -2.00000 q^{37} +(0.605599 + 4.31662i) q^{38} +(-1.65831 + 5.50000i) q^{39} +(-1.15831 + 1.91267i) q^{40} -11.4760 q^{41} +(1.60987 - 5.33934i) q^{42} -3.82534i q^{43} +4.31662i q^{44} +(-2.86084 - 6.06759i) q^{45} -7.04509i q^{46} +8.86188 q^{47} +(-0.500000 + 1.65831i) q^{48} -3.36675 q^{49} +(4.43094 - 2.31662i) q^{50} +(-1.60987 + 5.33934i) q^{51} -3.31662 q^{52} -1.00000i q^{53} +(-3.31662 - 4.00000i) q^{54} +(5.00000 - 8.25629i) q^{55} +3.21974 q^{56} +(1.15404 - 7.46111i) q^{57} -8.25629i q^{58} -5.64214 q^{59} +(2.87718 - 2.59265i) q^{60} -2.31662 q^{61} +2.61414 q^{62} +(-5.33934 + 8.04936i) q^{63} -1.00000 q^{64} +(6.34361 + 3.84169i) q^{65} +(2.15831 - 7.15831i) q^{66} -7.00000 q^{67} -3.21974 q^{68} +(-3.52254 + 11.6830i) q^{69} +(-6.15831 - 3.72947i) q^{70} +10.2648 q^{71} +(1.65831 - 2.50000i) q^{72} +1.81680i q^{73} +2.00000i q^{74} +(-8.50620 + 1.62622i) q^{75} +(4.31662 - 0.605599i) q^{76} -13.8984 q^{77} +(5.50000 + 1.65831i) q^{78} -15.3014i q^{79} +(1.91267 + 1.15831i) q^{80} +(3.50000 + 8.29156i) q^{81} +11.4760i q^{82} -6.43949 q^{83} +(-5.33934 - 1.60987i) q^{84} +(6.15831 + 3.72947i) q^{85} -3.82534 q^{86} +(-4.12814 + 13.6915i) q^{87} +4.31662 q^{88} +2.61414 q^{89} +(-6.06759 + 2.86084i) q^{90} -10.6787i q^{91} -7.04509 q^{92} +(-4.33507 - 1.30707i) q^{93} -8.86188i q^{94} +(-8.95776 - 3.84169i) q^{95} +(1.65831 + 0.500000i) q^{96} -3.36675 q^{97} +3.36675i q^{98} +(-7.15831 + 10.7916i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 8 q^{4} - 20 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 - 8 * q^4 - 20 * q^9	$ 8 q - 4 q^{3} - 8 q^{4} - 20 q^{9} - 4 q^{10} + 4 q^{12} - 22 q^{15} + 8 q^{16} - 8 q^{19} - 8 q^{22} - 8 q^{25} + 32 q^{27} + 2 q^{30} + 44 q^{33} + 20 q^{36} - 16 q^{37} + 4 q^{40} + 22 q^{45} - 4 q^{48} - 80 q^{49} + 40 q^{55} + 4 q^{57} + 22 q^{60} + 8 q^{61} - 8 q^{64} + 4 q^{66} - 56 q^{67} - 36 q^{70} + 4 q^{75} + 8 q^{76} + 44 q^{78} + 28 q^{81} + 36 q^{85} + 8 q^{88} + 10 q^{90} - 80 q^{97} - 44 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 8 * q^4 - 20 * q^9 - 4 * q^10 + 4 * q^12 - 22 * q^15 + 8 * q^16 - 8 * q^19 - 8 * q^22 - 8 * q^25 + 32 * q^27 + 2 * q^30 + 44 * q^33 + 20 * q^36 - 16 * q^37 + 4 * q^40 + 22 * q^45 - 4 * q^48 - 80 * q^49 + 40 * q^55 + 4 * q^57 + 22 * q^60 + 8 * q^61 - 8 * q^64 + 4 * q^66 - 56 * q^67 - 36 * q^70 + 4 * q^75 + 8 * q^76 + 44 * q^78 + 28 * q^81 + 36 * q^85 + 8 * q^88 + 10 * q^90 - 80 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.500000	+	1.65831i	−0.288675	+	0.957427i
$3$	−0.500000	+	1.65831i	−0.288675	+	0.957427i
$4$	−1.00000			−0.500000
$5$	1.91267	+	1.15831i	0.855373	+	0.518013i
$5$	1.91267	+	1.15831i	0.855373	+	0.518013i
$6$	1.65831	+	0.500000i	0.677003	+	0.204124i
$7$		−	3.21974i		−	1.21695i	−0.793574	−	0.608474i	$-0.791782\pi$
$7$		−	3.21974i		−	1.21695i	0.793574	−	0.608474i	$-0.208218\pi$
$8$			1.00000i			0.353553i
$9$	−2.50000	−	1.65831i	−0.833333	−	0.552771i
$10$	1.15831	−	1.91267i	0.366291	−	0.604840i
$11$		−	4.31662i		−	1.30151i	−0.759287	−	0.650756i	$-0.774452\pi$
$11$		−	4.31662i		−	1.30151i	0.759287	−	0.650756i	$-0.225548\pi$
$12$	0.500000	−	1.65831i	0.144338	−	0.478714i
$13$	3.31662			0.919866			0.459933	−	0.887954i	$-0.347873\pi$
$13$	3.31662			0.919866			0.459933	+	0.887954i	$0.347873\pi$
$14$	−3.21974			−0.860513
$15$	−2.87718	+	2.59265i	−0.742885	+	0.669420i
$16$	1.00000			0.250000
$17$	3.21974			0.780903			0.390451	−	0.920624i	$-0.372319\pi$
$17$	3.21974			0.780903			0.390451	+	0.920624i	$0.372319\pi$
$18$	−1.65831	+	2.50000i	−0.390868	+	0.589256i
$19$	−4.31662	+	0.605599i	−0.990302	+	0.138934i
$19$	−4.31662	+	0.605599i	−0.990302	+	0.138934i
$20$	−1.91267	−	1.15831i	−0.427686	−	0.259007i
$21$	5.33934	+	1.60987i	1.16514	+	0.351303i
$22$	−4.31662			−0.920307
$23$	7.04509			1.46900			0.734501	−	0.678608i	$-0.237416\pi$
$23$	7.04509			1.46900			0.734501	+	0.678608i	$0.237416\pi$
$24$	−1.65831	−	0.500000i	−0.338502	−	0.102062i
$25$	2.31662	+	4.43094i	0.463325	+	0.886188i
$26$		−	3.31662i		−	0.650444i
$27$	4.00000	−	3.31662i	0.769800	−	0.638285i
$28$			3.21974i			0.608474i
$29$	8.25629			1.53315			0.766577	−	0.642153i	$-0.221958\pi$
$29$	8.25629			1.53315			0.766577	+	0.642153i	$0.221958\pi$
$30$	2.59265	+	2.87718i	0.473351	+	0.525299i
$31$			2.61414i			0.469514i	0.972054	+	0.234757i	$0.0754295\pi$
$31$			2.61414i			0.469514i	−0.972054	+	0.234757i	$0.924571\pi$
$32$		−	1.00000i		−	0.176777i
$33$	7.15831	+	2.15831i	1.24610	+	0.375714i
$34$		−	3.21974i		−	0.552182i
$35$	3.72947	−	6.15831i	0.630395	−	1.04094i
$36$	2.50000	+	1.65831i	0.416667	+	0.276385i
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	0.605599	+	4.31662i	0.0982412	+	0.700249i
$39$	−1.65831	+	5.50000i	−0.265543	+	0.880705i
$40$	−1.15831	+	1.91267i	−0.183145	+	0.302420i
$41$	−11.4760			−1.79225			−0.896127	−	0.443797i	$-0.853631\pi$
$41$	−11.4760			−1.79225			−0.896127	+	0.443797i	$0.853631\pi$
$42$	1.60987	−	5.33934i	0.248409	−	0.823878i
$43$		−	3.82534i		−	0.583359i	−0.956516	−	0.291680i	$-0.905786\pi$
$43$		−	3.82534i		−	0.583359i	0.956516	−	0.291680i	$-0.0942141\pi$
$44$			4.31662i			0.650756i
$45$	−2.86084	−	6.06759i	−0.426468	−	0.904503i
$46$		−	7.04509i		−	1.03874i
$47$	8.86188			1.29264			0.646319	−	0.763067i	$-0.276307\pi$
$47$	8.86188			1.29264			0.646319	+	0.763067i	$0.276307\pi$
$48$	−0.500000	+	1.65831i	−0.0721688	+	0.239357i
$49$	−3.36675			−0.480964
$50$	4.43094	−	2.31662i	0.626630	−	0.327620i
$51$	−1.60987	+	5.33934i	−0.225427	+	0.747657i
$52$	−3.31662			−0.459933
$53$		−	1.00000i		−	0.137361i	−0.997639	−	0.0686803i	$-0.978121\pi$
$53$		−	1.00000i		−	0.137361i	0.997639	−	0.0686803i	$-0.0218788\pi$
$54$	−3.31662	−	4.00000i	−0.451335	−	0.544331i
$55$	5.00000	−	8.25629i	0.674200	−	1.11328i
$56$	3.21974			0.430256
$57$	1.15404	−	7.46111i	0.152856	−	0.988248i
$58$		−	8.25629i		−	1.08410i
$59$	−5.64214			−0.734544			−0.367272	−	0.930114i	$-0.619708\pi$
$59$	−5.64214			−0.734544			−0.367272	+	0.930114i	$0.619708\pi$
$60$	2.87718	−	2.59265i	0.371442	−	0.334710i
$61$	−2.31662			−0.296613			−0.148307	−	0.988941i	$-0.547382\pi$
$61$	−2.31662			−0.296613			−0.148307	+	0.988941i	$0.547382\pi$
$62$	2.61414			0.331997
$63$	−5.33934	+	8.04936i	−0.672694	+	1.01412i
$64$	−1.00000			−0.125000
$65$	6.34361	+	3.84169i	0.786828	+	0.476503i
$66$	2.15831	−	7.15831i	0.265670	−	0.881127i
$67$	−7.00000			−0.855186			−0.427593	−	0.903971i	$-0.640638\pi$
$67$	−7.00000			−0.855186			−0.427593	+	0.903971i	$0.640638\pi$
$68$	−3.21974			−0.390451
$69$	−3.52254	+	11.6830i	−0.424064	+	1.40646i
$70$	−6.15831	−	3.72947i	−0.736059	−	0.445757i
$71$	10.2648			1.21821			0.609106	−	0.793089i	$-0.291529\pi$
$71$	10.2648			1.21821			0.609106	+	0.793089i	$0.291529\pi$
$72$	1.65831	−	2.50000i	0.195434	−	0.294628i
$73$			1.81680i			0.212640i	0.994332	+	0.106320i	$0.0339068\pi$
$73$			1.81680i			0.212640i	−0.994332	+	0.106320i	$0.966093\pi$
$74$			2.00000i			0.232495i
$75$	−8.50620	+	1.62622i	−0.982211	+	0.187779i
$76$	4.31662	−	0.605599i	0.495151	−	0.0694670i
$77$	−13.8984			−1.58387
$78$	5.50000	+	1.65831i	0.622752	+	0.187767i
$79$		−	15.3014i		−	1.72154i	−0.508995	−	0.860769i	$-0.669983\pi$
$79$		−	15.3014i		−	1.72154i	0.508995	−	0.860769i	$-0.330017\pi$
$80$	1.91267	+	1.15831i	0.213843	+	0.129503i
$81$	3.50000	+	8.29156i	0.388889	+	0.921285i
$82$			11.4760i			1.26732i
$83$	−6.43949			−0.706826			−0.353413	−	0.935467i	$-0.614979\pi$
$83$	−6.43949			−0.706826			−0.353413	+	0.935467i	$0.614979\pi$
$84$	−5.33934	−	1.60987i	−0.582570	−	0.175651i
$85$	6.15831	+	3.72947i	0.667963	+	0.404518i
$86$	−3.82534			−0.412497
$87$	−4.12814	+	13.6915i	−0.442583	+	1.46788i
$88$	4.31662			0.460154
$89$	2.61414			0.277099			0.138549	−	0.990356i	$-0.455756\pi$
$89$	2.61414			0.277099			0.138549	+	0.990356i	$0.455756\pi$
$90$	−6.06759	+	2.86084i	−0.639580	+	0.301558i
$91$		−	10.6787i		−	1.11943i
$92$	−7.04509			−0.734501
$93$	−4.33507	−	1.30707i	−0.449526	−	0.135537i
$94$		−	8.86188i		−	0.914034i
$95$	−8.95776	−	3.84169i	−0.919047	−	0.394149i
$96$	1.65831	+	0.500000i	0.169251	+	0.0510310i
$97$	−3.36675			−0.341842			−0.170921	−	0.985285i	$-0.554674\pi$
$97$	−3.36675			−0.341842			−0.170921	+	0.985285i	$0.554674\pi$
$98$			3.36675i			0.340093i
$99$	−7.15831	+	10.7916i	−0.719437	+	1.08459i
$100$	−2.31662	−	4.43094i	−0.231662	−	0.443094i
$101$			14.3166i			1.42456i	0.701897	+	0.712279i	$0.252337\pi$
$101$			14.3166i			1.42456i	−0.701897	+	0.712279i	$0.747663\pi$
$102$	5.33934	+	1.60987i	0.528674	+	0.159401i
$103$	−17.5831			−1.73252			−0.866258	−	0.499596i	$-0.833482\pi$
$103$	−17.5831			−1.73252			−0.866258	+	0.499596i	$0.833482\pi$
$104$			3.31662i			0.325222i
$105$	8.34767	+	9.26378i	0.814649	+	0.904052i
$106$	−1.00000			−0.0971286
$107$		−	0.0501256i		−	0.00484583i	−0.999997	−	0.00242291i	$-0.999229\pi$
$107$		−	0.0501256i		−	0.00484583i	0.999997	−	0.00242291i	$-0.000771238\pi$
$108$	−4.00000	+	3.31662i	−0.384900	+	0.319142i
$109$			6.85334i			0.656431i	0.944603	+	0.328215i	$0.106447\pi$
$109$			6.85334i			0.656431i	−0.944603	+	0.328215i	$0.893553\pi$
$110$	−8.25629	−	5.00000i	−0.787206	−	0.476731i
$111$	1.00000	−	3.31662i	0.0949158	−	0.314800i
$112$		−	3.21974i		−	0.304237i
$113$		−	1.68338i		−	0.158359i	−0.996860	−	0.0791793i	$-0.974770\pi$
$113$		−	1.68338i		−	0.158359i	0.996860	−	0.0791793i	$-0.0252300\pi$
$114$	−7.46111	−	1.15404i	−0.698797	−	0.108086i
$115$	13.4749	+	8.16041i	1.25654	+	0.760962i
$116$	−8.25629			−0.766577
$117$	−8.29156	−	5.50000i	−0.766555	−	0.508475i
$118$			5.64214i			0.519401i
$119$		−	10.3668i		−	0.950318i
$120$	−2.59265	−	2.87718i	−0.236676	−	0.262649i
$121$	−7.63325			−0.693932
$122$			2.31662i			0.209737i
$123$	5.73801	−	19.0308i	0.517379	−	1.71595i
$124$		−	2.61414i		−	0.234757i
$125$	−0.701473	+	11.1583i	−0.0627417	+	0.998030i
$126$	8.04936	+	5.33934i	0.717094	+	0.475666i
$127$	16.6332			1.47596			0.737981	−	0.674821i	$-0.235779\pi$
$127$	16.6332			1.47596			0.737981	+	0.674821i	$0.235779\pi$
$128$			1.00000i			0.0883883i
$129$	6.34361	+	1.91267i	0.558524	+	0.168401i
$130$	3.84169	−	6.34361i	0.336938	−	0.556372i
$131$			10.0000i			0.873704i	0.899533	+	0.436852i	$0.143907\pi$
$131$			10.0000i			0.873704i	−0.899533	+	0.436852i	$0.856093\pi$
$132$	−7.15831	−	2.15831i	−0.623051	−	0.187857i
$133$	1.94987	+	13.8984i	0.169076	+	1.20515i
$134$			7.00000i			0.604708i
$135$	11.4924	−	1.71036i	0.989106	−	0.147205i
$136$			3.21974i			0.276091i
$137$	3.21974			0.275081			0.137541	−	0.990496i	$-0.456080\pi$
$137$	3.21974			0.275081			0.137541	+	0.990496i	$0.456080\pi$
$138$	11.6830	+	3.52254i	0.994519	+	0.299859i
$139$	−10.0000			−0.848189			−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000			−0.848189			−0.424094	+	0.905618i	$0.639408\pi$
$140$	−3.72947	+	6.15831i	−0.315198	+	0.520472i
$141$	−4.43094	+	14.6958i	−0.373153	+	1.23761i
$142$		−	10.2648i		−	0.861405i
$143$		−	14.3166i		−	1.19722i
$144$	−2.50000	−	1.65831i	−0.208333	−	0.138193i
$145$	15.7916	+	9.56336i	1.31142	+	0.794194i
$146$	1.81680			0.150359
$147$	1.68338	−	5.58312i	0.138842	−	0.460488i
$148$	2.00000			0.164399
$149$		−	4.00000i		−	0.327693i	−0.986486	−	0.163846i	$-0.947610\pi$
$149$		−	4.00000i		−	0.327693i	0.986486	−	0.163846i	$-0.0523901\pi$
$150$	1.62622	+	8.50620i	0.132780	+	0.694528i
$151$		−	16.5126i		−	1.34377i	−0.740654	−	0.671887i	$-0.765484\pi$
$151$		−	16.5126i		−	1.34377i	0.740654	−	0.671887i	$-0.234516\pi$
$152$	−0.605599	−	4.31662i	−0.0491206	−	0.350125i
$153$	−8.04936	−	5.33934i	−0.650752	−	0.431660i
$154$			13.8984i			1.11997i
$155$	−3.02800	+	5.00000i	−0.243215	+	0.401610i
$156$	1.65831	−	5.50000i	0.132771	−	0.440352i
$157$			7.65069i			0.610591i	0.952258	+	0.305296i	$0.0987553\pi$
$157$			7.65069i			0.610591i	−0.952258	+	0.305296i	$0.901245\pi$
$158$	−15.3014			−1.21731
$159$	1.65831	+	0.500000i	0.131513	+	0.0396526i
$160$	1.15831	−	1.91267i	0.0915726	−	0.151210i
$161$		−	22.6834i		−	1.78770i
$162$	8.29156	−	3.50000i	0.651447	−	0.274986i
$163$			1.40295i			0.109887i	0.998489	+	0.0549436i	$0.0174979\pi$
$163$			1.40295i			0.109887i	−0.998489	+	0.0549436i	$0.982502\pi$
$164$	11.4760			0.896127
$165$	11.1915	+	12.4197i	0.871257	+	0.966873i
$166$			6.43949i			0.499801i
$167$			24.9499i			1.93068i	0.260997	+	0.965340i	$0.415949\pi$
$167$			24.9499i			1.93068i	−0.260997	+	0.965340i	$0.584051\pi$
$168$	−1.60987	+	5.33934i	−0.124204	+	0.411939i
$169$	−2.00000			−0.153846
$170$	3.72947	−	6.15831i	0.286037	−	0.472321i
$171$	11.7958	+	5.64431i	0.902050	+	0.431632i
$172$			3.82534i			0.291680i
$173$		−	13.2665i		−	1.00863i	−0.863519	−	0.504317i	$-0.831744\pi$
$173$		−	13.2665i		−	1.00863i	0.863519	−	0.504317i	$-0.168256\pi$
$174$	13.6915	+	4.12814i	1.03795	+	0.312954i
$175$	14.2665	−	7.45894i	1.07845	−	0.563843i
$176$		−	4.31662i		−	0.325378i
$177$	2.82107	−	9.35643i	0.212045	−	0.703272i
$178$		−	2.61414i		−	0.195938i
$179$	−16.5126			−1.23421			−0.617104	−	0.786882i	$-0.711694\pi$
$179$	−16.5126			−1.23421			−0.617104	+	0.786882i	$0.711694\pi$
$180$	2.86084	+	6.06759i	0.213234	+	0.452251i
$181$			16.5126i			1.22737i	0.789551	+	0.613685i	$0.210313\pi$
$181$			16.5126i			1.22737i	−0.789551	+	0.613685i	$0.789687\pi$
$182$	−10.6787			−0.791557
$183$	1.15831	−	3.84169i	0.0856249	−	0.283986i
$184$			7.04509i			0.519371i
$185$	−3.82534	−	2.31662i	−0.281245	−	0.170322i
$186$	−1.30707	+	4.33507i	−0.0958392	+	0.317863i
$187$		−	13.8984i		−	1.01635i
$188$	−8.86188			−0.646319
$189$	−10.6787	−	12.8790i	−0.776760	−	0.936808i
$190$	−3.84169	+	8.95776i	−0.278705	+	0.649864i
$191$			5.00000i			0.361787i	0.983503	+	0.180894i	$0.0578990\pi$
$191$			5.00000i			0.361787i	−0.983503	+	0.180894i	$0.942101\pi$
$192$	0.500000	−	1.65831i	0.0360844	−	0.119678i
$193$	−6.00000			−0.431889			−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000			−0.431889			−0.215945	+	0.976406i	$0.569283\pi$
$194$			3.36675i			0.241719i
$195$	−9.54253	+	8.59885i	−0.683354	+	0.615776i
$196$	3.36675			0.240482
$197$	−5.03654			−0.358839			−0.179419	−	0.983773i	$-0.557422\pi$
$197$	−5.03654			−0.358839			−0.179419	+	0.983773i	$0.557422\pi$
$198$	10.7916	+	7.15831i	0.766923	+	0.508719i
$199$	−25.2164			−1.78754			−0.893771	−	0.448524i	$-0.851950\pi$
$199$	−25.2164			−1.78754			−0.893771	+	0.448524i	$0.851950\pi$
$200$	−4.43094	+	2.31662i	−0.313315	+	0.163810i
$201$	3.50000	−	11.6082i	0.246871	−	0.818778i
$202$	14.3166			1.00731
$203$		−	26.5831i		−	1.86577i
$204$	1.60987	−	5.33934i	0.112714	−	0.373829i
$205$	−21.9499	−	13.2928i	−1.53305	−	0.928411i
$206$			17.5831i			1.22507i
$207$	−17.6127	−	11.6830i	−1.22417	−	0.812022i
$208$	3.31662			0.229967
$209$	2.61414	+	18.6332i	0.180824	+	1.28889i
$210$	9.26378	−	8.34767i	0.639262	−	0.576044i
$211$			3.02800i			0.208456i	0.994553	+	0.104228i	$0.0332371\pi$
$211$			3.02800i			0.208456i	−0.994553	+	0.104228i	$0.966763\pi$
$212$			1.00000i			0.0686803i
$213$	−5.13242	+	17.0223i	−0.351667	+	1.16635i
$214$	−0.0501256			−0.00342652
$215$	4.43094	−	7.31662i	0.302188	−	0.498990i
$216$	3.31662	+	4.00000i	0.225668	+	0.272166i
$217$	8.41688			0.571375
$218$	6.85334			0.464167
$219$	−3.01282	−	0.908399i	−0.203587	−	0.0613839i
$220$	−5.00000	+	8.25629i	−0.337100	+	0.556639i
$221$	10.6787			0.718326
$222$	−3.31662	−	1.00000i	−0.222597	−	0.0671156i
$223$	−3.26650			−0.218741			−0.109370	−	0.994001i	$-0.534883\pi$
$223$	−3.26650			−0.218741			−0.109370	+	0.994001i	$0.534883\pi$
$224$	−3.21974			−0.215128
$225$	1.55632	−	14.9190i	0.103755	−	0.994603i
$226$	−1.68338			−0.111976
$227$			19.9499i			1.32412i	0.749451	+	0.662060i	$0.230318\pi$
$227$			19.9499i			1.32412i	−0.749451	+	0.662060i	$0.769682\pi$
$228$	−1.15404	+	7.46111i	−0.0764281	+	0.494124i
$229$		0			0			−	1.00000i	$-0.5\pi$
$229$		0			0				1.00000i	$0.5\pi$
$230$	8.16041	−	13.4749i	0.538082	−	0.888511i
$231$	6.94921	−	23.0479i	0.457225	−	1.51644i
$232$			8.25629i			0.542052i
$233$	26.5857			1.74168			0.870842	−	0.491563i	$-0.163574\pi$
$233$	26.5857			1.74168			0.870842	+	0.491563i	$0.163574\pi$
$234$	−5.50000	+	8.29156i	−0.359546	+	0.542036i
$235$	16.9499	+	10.2648i	1.10569	+	0.669604i
$236$	5.64214			0.367272
$237$	25.3745	+	7.65069i	1.64825	+	0.496965i
$238$	−10.3668			−0.671977
$239$			19.6332i			1.26997i	0.772525	+	0.634985i	$0.218994\pi$
$239$			19.6332i			1.26997i	−0.772525	+	0.634985i	$0.781006\pi$
$240$	−2.87718	+	2.59265i	−0.185721	+	0.167355i
$241$			5.22829i			0.336784i	0.985720	+	0.168392i	$0.0538574\pi$
$241$			5.22829i			0.336784i	−0.985720	+	0.168392i	$0.946143\pi$
$242$			7.63325i			0.490684i
$243$	−15.5000	+	1.65831i	−0.994325	+	0.106381i
$244$	2.31662			0.148307
$245$	−6.43949	−	3.89975i	−0.411404	−	0.249146i
$246$	−19.0308	−	5.73801i	−1.21336	−	0.365842i
$247$	−14.3166	+	2.00855i	−0.910945	+	0.127801i
$248$	−2.61414			−0.165998
$249$	3.21974	−	10.6787i	0.204043	−	0.676734i
$250$	11.1583	+	0.701473i	0.705714	+	0.0443651i
$251$		−	31.5831i		−	1.99351i	−0.0805007	−	0.996755i	$-0.525652\pi$
$251$		−	31.5831i		−	1.99351i	0.0805007	−	0.996755i	$-0.474348\pi$
$252$	5.33934	−	8.04936i	0.336347	−	0.507062i
$253$		−	30.4110i		−	1.91192i
$254$		−	16.6332i		−	1.04366i
$255$	−9.26378	+	8.34767i	−0.580120	+	0.522751i
$256$	1.00000			0.0625000
$257$			4.94987i			0.308765i	0.988011	+	0.154382i	$0.0493388\pi$
$257$			4.94987i			0.308765i	−0.988011	+	0.154382i	$0.950661\pi$
$258$	1.91267	−	6.34361i	0.119078	−	0.394936i
$259$			6.43949i			0.400130i
$260$	−6.34361	−	3.84169i	−0.393414	−	0.238251i
$261$	−20.6407	−	13.6915i	−1.27763	−	0.847483i
$262$	10.0000			0.617802
$263$	20.5297			1.26591			0.632957	−	0.774187i	$-0.281841\pi$
$263$	20.5297			1.26591			0.632957	+	0.774187i	$0.281841\pi$
$264$	−2.15831	+	7.15831i	−0.132835	+	0.440564i
$265$	1.15831	−	1.91267i	0.0711546	−	0.117494i
$266$	13.8984	−	1.94987i	0.852167	−	0.119554i
$267$	−1.30707	+	4.33507i	−0.0799915	+	0.265302i
$268$	7.00000			0.427593
$269$	−21.7409			−1.32556			−0.662782	−	0.748813i	$-0.730624\pi$
$269$	−21.7409			−1.32556			−0.662782	+	0.748813i	$0.730624\pi$
$270$	−1.71036	−	11.4924i	−0.104089	−	0.699404i
$271$	2.68338			0.163003			0.0815017	−	0.996673i	$-0.474028\pi$
$271$	2.68338			0.163003			0.0815017	+	0.996673i	$0.474028\pi$
$272$	3.21974			0.195226
$273$	17.7086	+	5.33934i	1.07177	+	0.323152i
$274$		−	3.21974i		−	0.194512i
$275$	19.1267	−	10.0000i	1.15338	−	0.603023i
$276$	3.52254	−	11.6830i	0.212032	−	0.703231i
$277$		−	14.0902i		−	0.846596i	−0.905990	−	0.423298i	$-0.860872\pi$
$277$		−	14.0902i		−	0.846596i	0.905990	−	0.423298i	$-0.139128\pi$
$278$			10.0000i			0.599760i
$279$	4.33507	−	6.53536i	0.259534	−	0.391262i
$280$	6.15831	+	3.72947i	0.368030	+	0.222878i
$281$	−6.24774			−0.372709			−0.186354	−	0.982483i	$-0.559667\pi$
$281$	−6.24774			−0.372709			−0.186354	+	0.982483i	$0.559667\pi$
$282$	14.6958	+	4.43094i	0.875121	+	0.263859i
$283$			26.5857i			1.58035i	0.612879	+	0.790177i	$0.290011\pi$
$283$			26.5857i			1.58035i	−0.612879	+	0.790177i	$0.709989\pi$
$284$	−10.2648			−0.609106
$285$	10.8496	−	12.9339i	0.642675	−	0.766139i
$286$	−14.3166			−0.846560
$287$			36.9499i			2.18108i
$288$	−1.65831	+	2.50000i	−0.0977170	+	0.147314i
$289$	−6.63325			−0.390191
$290$	9.56336	−	15.7916i	0.561580	−	0.927312i
$291$	1.68338	−	5.58312i	0.0986812	−	0.327289i
$292$		−	1.81680i		−	0.106320i
$293$		−	18.2665i		−	1.06714i	−0.845756	−	0.533570i	$-0.820850\pi$
$293$		−	18.2665i		−	1.06714i	0.845756	−	0.533570i	$-0.179150\pi$
$294$	−5.58312	−	1.68338i	−0.325614	−	0.0981764i
$295$	−10.7916	−	6.53536i	−0.628309	−	0.380503i
$296$		−	2.00000i		−	0.116248i
$297$	−14.3166	−	17.2665i	−0.830735	−	1.00190i
$298$	−4.00000			−0.231714
$299$	23.3659			1.35129
$300$	8.50620	−	1.62622i	0.491106	−	0.0938897i
$301$	−12.3166			−0.709918
$302$	−16.5126			−0.950192
$303$	−23.7414	−	7.15831i	−1.36391	−	0.411234i
$304$	−4.31662	+	0.605599i	−0.247575	+	0.0347335i
$305$	−4.43094	−	2.68338i	−0.253715	−	0.153650i
$306$	−5.33934	+	8.04936i	−0.305230	+	0.460151i
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$	13.8984			0.791936
$309$	8.79156	−	29.1583i	0.500134	−	1.65876i
$310$	5.00000	+	3.02800i	0.283981	+	0.171979i
$311$			20.8997i			1.18512i	0.805528	+	0.592558i	$0.201882\pi$
$311$			20.8997i			1.18512i	−0.805528	+	0.592558i	$0.798118\pi$
$312$	−5.50000	−	1.65831i	−0.311376	−	0.0938835i
$313$		−	20.7518i		−	1.17296i	−0.809964	−	0.586480i	$-0.800513\pi$
$313$		−	20.7518i		−	1.17296i	0.809964	−	0.586480i	$-0.199487\pi$
$314$	7.65069			0.431753
$315$	−19.5361	+	9.21116i	−1.10073	+	0.518990i
$316$			15.3014i			0.860769i
$317$			17.0000i			0.954815i	0.878682	+	0.477408i	$0.158423\pi$
$317$			17.0000i			0.954815i	−0.878682	+	0.477408i	$0.841577\pi$
$318$	0.500000	−	1.65831i	0.0280386	−	0.0929935i
$319$		−	35.6393i		−	1.99542i
$320$	−1.91267	−	1.15831i	−0.106922	−	0.0647516i
$321$	0.0831240	+	0.0250628i	0.00463953	+	0.00139887i
$322$	−22.6834			−1.26410
$323$	−13.8984	+	1.94987i	−0.773329	+	0.108494i
$324$	−3.50000	−	8.29156i	−0.194444	−	0.460642i
$325$	7.68338	+	14.6958i	0.426197	+	0.815175i
$326$	1.40295			0.0777020
$327$	−11.3650	−	3.42667i	−0.628485	−	0.189495i
$328$		−	11.4760i		−	0.633658i
$329$		−	28.5330i		−	1.57308i
$330$	12.4197	−	11.1915i	0.683682	−	0.616072i
$331$		−	13.4846i		−	0.741179i	−0.928797	−	0.370590i	$-0.879156\pi$
$331$		−	13.4846i		−	0.741179i	0.928797	−	0.370590i	$-0.120844\pi$
$332$	6.43949			0.353413
$333$	5.00000	+	3.31662i	0.273998	+	0.181750i
$334$	24.9499			1.36520
$335$	−13.3887	−	8.10819i	−0.731503	−	0.442998i
$336$	5.33934	+	1.60987i	0.291285	+	0.0878257i
$337$	28.2164			1.53704			0.768522	−	0.639823i	$-0.220993\pi$
$337$	28.2164			1.53704			0.768522	+	0.639823i	$0.220993\pi$
$338$			2.00000i			0.108786i
$339$	2.79156	+	0.841688i	0.151617	+	0.0457142i
$340$	−6.15831	−	3.72947i	−0.333981	−	0.202259i
$341$	11.2843			0.611078
$342$	5.64431	−	11.7958i	0.305210	−	0.637846i
$343$		−	11.6981i		−	0.631640i
$344$	3.82534			0.206249
$345$	−20.2700	+	18.2654i	−1.09130	+	0.983379i
$346$	−13.2665			−0.713211
$347$	20.1462			1.08150			0.540751	−	0.841182i	$-0.318140\pi$
$347$	20.1462			1.08150			0.540751	+	0.841182i	$0.318140\pi$
$348$	4.12814	−	13.6915i	0.221292	−	0.733941i
$349$	8.63325			0.462127			0.231064	−	0.972939i	$-0.425779\pi$
$349$	8.63325			0.462127			0.231064	+	0.972939i	$0.425779\pi$
$350$	−7.45894	−	14.2665i	−0.398697	−	0.762576i
$351$	13.2665	−	11.0000i	0.708113	−	0.587137i
$352$	−4.31662			−0.230077
$353$	−23.3659			−1.24364			−0.621821	−	0.783159i	$-0.713607\pi$
$353$	−23.3659			−1.24364			−0.621821	+	0.783159i	$0.713607\pi$
$354$	−9.35643	−	2.82107i	−0.497289	−	0.149938i
$355$	19.6332	+	11.8899i	1.04202	+	0.631049i
$356$	−2.61414			−0.138549
$357$	17.1913	+	5.18338i	0.909861	+	0.274333i
$358$			16.5126i			0.872716i
$359$		−	4.89975i		−	0.258599i	−0.991606	−	0.129299i	$-0.958727\pi$
$359$		−	4.89975i		−	0.258599i	0.991606	−	0.129299i	$-0.0412728\pi$
$360$	6.06759	−	2.86084i	0.319790	−	0.150779i
$361$	18.2665	−	5.22829i	0.961395	−	0.275173i
$362$	16.5126			0.867881
$363$	3.81662	−	12.6583i	0.200321	−	0.664389i
$364$			10.6787i			0.559715i
$365$	−2.10442	+	3.47494i	−0.110150	+	0.181887i
$366$	−3.84169	−	1.15831i	−0.200808	−	0.0605460i
$367$			7.65069i			0.399363i	0.979861	+	0.199681i	$0.0639907\pi$
$367$			7.65069i			0.399363i	−0.979861	+	0.199681i	$0.936009\pi$
$368$	7.04509			0.367251
$369$	28.6901	+	19.0308i	1.49355	+	0.990706i
$370$	−2.31662	+	3.82534i	−0.120436	+	0.198870i
$371$	−3.21974			−0.167161
$372$	4.33507	+	1.30707i	0.224763	+	0.0677685i
$373$	23.3166			1.20729			0.603645	−	0.797254i	$-0.293715\pi$
$373$	23.3166			1.20729			0.603645	+	0.797254i	$0.293715\pi$
$374$	−13.8984			−0.718671
$375$	−18.1532	−	6.74242i	−0.937429	−	0.348177i
$376$			8.86188i			0.457017i
$377$	27.3830			1.41030
$378$	−12.8790	+	10.6787i	−0.662423	+	0.549252i
$379$			36.4366i			1.87162i	0.352499	+	0.935812i	$0.385332\pi$
$379$			36.4366i			1.87162i	−0.352499	+	0.935812i	$0.614668\pi$
$380$	8.95776	+	3.84169i	0.459523	+	0.197074i
$381$	−8.31662	+	27.5831i	−0.426074	+	1.41313i
$382$	5.00000			0.255822
$383$		−	7.58312i		−	0.387480i	−0.981053	−	0.193740i	$-0.937938\pi$
$383$		−	7.58312i		−	0.387480i	0.981053	−	0.193740i	$-0.0620617\pi$
$384$	−1.65831	−	0.500000i	−0.0846254	−	0.0255155i
$385$	−26.5831	−	16.0987i	−1.35480	−	0.820467i
$386$			6.00000i			0.305392i
$387$	−6.34361	+	9.56336i	−0.322464	+	0.486133i
$388$	3.36675			0.170921
$389$			16.2164i			0.822203i	0.911590	+	0.411101i	$0.134856\pi$
$389$			16.2164i			0.822203i	−0.911590	+	0.411101i	$0.865144\pi$
$390$	8.59885	+	9.54253i	0.435420	+	0.483205i
$391$	22.6834			1.14715
$392$		−	3.36675i		−	0.170047i
$393$	−16.5831	−	5.00000i	−0.836508	−	0.252217i
$394$			5.03654i			0.253737i
$395$	17.7238	−	29.2665i	0.891780	−	1.47256i
$396$	7.15831	−	10.7916i	0.359719	−	0.542296i
$397$			29.3915i			1.47512i	0.675282	+	0.737560i	$0.264022\pi$
$397$			29.3915i			1.47512i	−0.675282	+	0.737560i	$0.735978\pi$
$398$			25.2164i			1.26398i
$399$	−24.0229	−	3.71571i	−1.20265	−	0.186018i
$400$	2.31662	+	4.43094i	0.115831	+	0.221547i
$401$	21.5491			1.07611			0.538056	−	0.842909i	$-0.319159\pi$
$401$	21.5491			1.07611			0.538056	+	0.842909i	$0.319159\pi$
$402$	−11.6082	−	3.50000i	−0.578964	−	0.174564i
$403$			8.67014i			0.431890i
$404$		−	14.3166i		−	0.712279i
$405$	−2.90987	+	19.9131i	−0.144593	+	0.989491i
$406$	−26.5831			−1.31930
$407$			8.63325i			0.427934i
$408$	−5.33934	−	1.60987i	−0.264337	−	0.0797005i
$409$			3.82534i			0.189151i	0.995518	+	0.0945755i	$0.0301494\pi$
$409$			3.82534i			0.189151i	−0.995518	+	0.0945755i	$0.969851\pi$
$410$	−13.2928	+	21.9499i	−0.656486	+	1.08403i
$411$	−1.60987	+	5.33934i	−0.0794091	+	0.263370i
$412$	17.5831			0.866258
$413$			18.1662i			0.893903i
$414$	−11.6830	+	17.6127i	−0.574186	+	0.865618i
$415$	−12.3166	−	7.45894i	−0.604599	−	0.366145i
$416$		−	3.31662i		−	0.162611i
$417$	5.00000	−	16.5831i	0.244851	−	0.812079i
$418$	18.6332	−	2.61414i	0.911382	−	0.127862i
$419$			3.05013i			0.149008i	0.997221	+	0.0745042i	$0.0237374\pi$
$419$			3.05013i			0.149008i	−0.997221	+	0.0745042i	$0.976263\pi$
$420$	−8.34767	−	9.26378i	−0.407325	−	0.452026i
$421$			16.0987i			0.784604i	0.919837	+	0.392302i	$0.128321\pi$
$421$			16.0987i			0.784604i	−0.919837	+	0.392302i	$0.871679\pi$
$422$	3.02800			0.147401
$423$	−22.1547	−	14.6958i	−1.07720	−	0.714533i
$424$	1.00000			0.0485643
$425$	7.45894	+	14.2665i	0.361812	+	0.692027i
$426$	17.0223	+	5.13242i	0.824733	+	0.248666i
$427$			7.45894i			0.360963i
$428$			0.0501256i			0.00242291i
$429$	23.7414	+	7.15831i	1.14625	+	0.345607i
$430$	−7.31662	−	4.43094i	−0.352839	−	0.213679i
$431$	−17.5320			−0.844488			−0.422244	−	0.906482i	$-0.638757\pi$
$431$	−17.5320			−0.844488			−0.422244	+	0.906482i	$0.638757\pi$
$432$	4.00000	−	3.31662i	0.192450	−	0.159571i
$433$	−1.68338			−0.0808978			−0.0404489	−	0.999182i	$-0.512879\pi$
$433$	−1.68338			−0.0808978			−0.0404489	+	0.999182i	$0.512879\pi$
$434$		−	8.41688i		−	0.404023i
$435$	−23.7548	+	21.4057i	−1.13896	+	1.02632i
$436$		−	6.85334i		−	0.328215i
$437$	−30.4110	+	4.26650i	−1.45476	+	0.204094i
$438$	−0.908399	+	3.01282i	−0.0434050	+	0.143958i
$439$			3.82534i			0.182574i	0.995825	+	0.0912868i	$0.0290980\pi$
$439$			3.82534i			0.182574i	−0.995825	+	0.0912868i	$0.970902\pi$
$440$	8.25629	+	5.00000i	0.393603	+	0.238366i
$441$	8.41688	+	5.58312i	0.400804	+	0.265863i
$442$		−	10.6787i		−	0.507933i
$443$	12.6872			0.602788			0.301394	−	0.953500i	$-0.402548\pi$
$443$	12.6872			0.602788			0.301394	+	0.953500i	$0.402548\pi$
$444$	−1.00000	+	3.31662i	−0.0474579	+	0.157400i
$445$	5.00000	+	3.02800i	0.237023	+	0.143541i
$446$			3.26650i			0.154673i
$447$	6.63325	+	2.00000i	0.313742	+	0.0945968i
$448$			3.21974i			0.152119i
$449$	26.9691			1.27275			0.636376	−	0.771379i	$-0.280433\pi$
$449$	26.9691			1.27275			0.636376	+	0.771379i	$0.280433\pi$
$450$	−14.9190	−	1.55632i	−0.703290	−	0.0733658i
$451$			49.5377i			2.33264i
$452$			1.68338i			0.0791793i
$453$	27.3830	+	8.25629i	1.28657	+	0.387914i
$454$	19.9499			0.936294
$455$	12.3693	−	20.4248i	0.579879	−	0.957530i
$456$	7.46111	+	1.15404i	0.349399	+	0.0540429i
$457$			27.1913i			1.27195i	0.771708	+	0.635977i	$0.219403\pi$
$457$			27.1913i			1.27195i	−0.771708	+	0.635977i	$0.780597\pi$
$458$		0			0
$459$	12.8790	−	10.6787i	0.601139	−	0.498438i
$460$	−13.4749	−	8.16041i	−0.628272	−	0.380481i
$461$		−	21.5831i		−	1.00523i	−0.864511	−	0.502613i	$-0.832372\pi$
$461$		−	21.5831i		−	1.00523i	0.864511	−	0.502613i	$-0.167628\pi$
$462$	−23.0479	−	6.94921i	−1.07229	−	0.323307i
$463$			15.3014i			0.711115i	0.934654	+	0.355558i	$0.115709\pi$
$463$			15.3014i			0.711115i	−0.934654	+	0.355558i	$0.884291\pi$
$464$	8.25629			0.383288
$465$	−6.77756	−	7.52136i	−0.314302	−	0.348795i
$466$		−	26.5857i		−	1.23156i
$467$	−26.7774			−1.23911			−0.619555	−	0.784953i	$-0.712687\pi$
$467$	−26.7774			−1.23911			−0.619555	+	0.784953i	$0.712687\pi$
$468$	8.29156	+	5.50000i	0.383278	+	0.254238i
$469$			22.5382i			1.04072i
$470$	10.2648	−	16.9499i	0.473481	−	0.781839i
$471$	−12.6872	−	3.82534i	−0.584597	−	0.176263i
$472$		−	5.64214i		−	0.259701i
$473$	−16.5126			−0.759249
$474$	7.65069	−	25.3745i	0.351408	−	1.16549i
$475$	−12.6834	−	17.7238i	−0.581953	−	0.813222i
$476$			10.3668i			0.475159i
$477$	−1.65831	+	2.50000i	−0.0759289	+	0.114467i
$478$	19.6332			0.898004
$479$		−	14.0000i		−	0.639676i	−0.947472	−	0.319838i	$-0.896371\pi$
$479$		−	14.0000i		−	0.639676i	0.947472	−	0.319838i	$-0.103629\pi$
$480$	2.59265	+	2.87718i	0.118338	+	0.131325i
$481$	−6.63325			−0.302450
$482$	5.22829			0.238142
$483$	37.6161	+	11.3417i	1.71159	+	0.516065i
$484$	7.63325			0.346966
$485$	−6.43949	−	3.89975i	−0.292402	−	0.177078i
$486$	1.65831	+	15.5000i	0.0752226	+	0.703094i
$487$	−36.5330			−1.65547			−0.827734	−	0.561121i	$-0.810370\pi$
$487$	−36.5330			−1.65547			−0.827734	+	0.561121i	$0.810370\pi$
$488$		−	2.31662i		−	0.104869i
$489$	−2.32652	−	0.701473i	−0.105209	−	0.0317217i
$490$	−3.89975	+	6.43949i	−0.176173	+	0.290906i
$491$		−	8.41688i		−	0.379848i	−0.981799	−	0.189924i	$-0.939176\pi$
$491$		−	8.41688i		−	0.379848i	0.981799	−	0.189924i	$-0.0608242\pi$
$492$	−5.73801	+	19.0308i	−0.258690	+	0.857977i
$493$	26.5831			1.19724
$494$	2.00855	+	14.3166i	0.0903687	+	0.644135i
$495$	−26.1915	+	12.3492i	−1.17722	+	0.555053i
$496$			2.61414i			0.117379i
$497$		−	33.0501i		−	1.48250i
$498$	−10.6787	−	3.21974i	−0.478523	−	0.144280i
$499$	8.41688			0.376791			0.188396	−	0.982093i	$-0.439671\pi$
$499$	8.41688			0.376791			0.188396	+	0.982093i	$0.439671\pi$
$500$	0.701473	−	11.1583i	0.0313708	−	0.499015i
$501$	−41.3747	−	12.4749i	−1.84848	−	0.557339i
$502$	−31.5831			−1.40962
$503$	18.3294			0.817266			0.408633	−	0.912699i	$-0.366006\pi$
$503$	18.3294			0.817266			0.408633	+	0.912699i	$0.366006\pi$
$504$	−8.04936	−	5.33934i	−0.358547	−	0.237833i
$505$	−16.5831	+	27.3830i	−0.737939	+	1.21853i
$506$	−30.4110			−1.35193
$507$	1.00000	−	3.31662i	0.0444116	−	0.147296i
$508$	−16.6332			−0.737981
$509$	−5.22829			−0.231740			−0.115870	−	0.993264i	$-0.536966\pi$
$509$	−5.22829			−0.231740			−0.115870	+	0.993264i	$0.536966\pi$
$510$	8.34767	+	9.26378i	0.369641	+	0.410207i
$511$	5.84962			0.258772
$512$		−	1.00000i		−	0.0441942i
$513$	−15.2580	+	16.7390i	−0.673655	+	0.739046i
$514$	4.94987			0.218330
$515$	−33.6307	−	20.3668i	−1.48195	−	0.897466i
$516$	−6.34361	−	1.91267i	−0.279262	−	0.0842007i
$517$		−	38.2534i		−	1.68238i
$518$	6.43949			0.282935
$519$	22.0000	+	6.63325i	0.965693	+	0.291167i
$520$	−3.84169	+	6.34361i	−0.168469	+	0.278186i
$521$	−14.9179			−0.653564			−0.326782	−	0.945100i	$-0.605964\pi$
$521$	−14.9179			−0.653564			−0.326782	+	0.945100i	$0.605964\pi$
$522$	−13.6915	+	20.6407i	−0.599261	+	0.903419i
$523$	29.0000			1.26808			0.634041	−	0.773300i	$-0.281395\pi$
$523$	29.0000			1.26808			0.634041	+	0.773300i	$0.281395\pi$
$524$		−	10.0000i		−	0.436852i
$525$	5.23600	+	27.3878i	0.228518	+	1.19530i
$526$		−	20.5297i		−	0.895136i
$527$			8.41688i			0.366645i
$528$	7.15831	+	2.15831i	0.311526	+	0.0939285i
$529$	26.6332			1.15797
$530$	−1.91267	−	1.15831i	−0.0830811	−	0.0503139i
$531$	14.1054	+	9.35643i	0.612120	+	0.406035i
$532$	−1.94987	−	13.8984i	−0.0845378	−	0.602573i
$533$	−38.0617			−1.64863
$534$	4.33507	+	1.30707i	0.187597	+	0.0565626i
$535$	0.0580611	−	0.0958739i	0.00251020	−	0.00414499i
$536$		−	7.00000i		−	0.302354i
$537$	8.25629	−	27.3830i	0.356285	−	1.18166i
$538$			21.7409i			0.937315i
$539$			14.5330i			0.625981i
$540$	−11.4924	+	1.71036i	−0.494553	+	0.0736024i
$541$	30.8496			1.32633			0.663164	−	0.748474i	$-0.269213\pi$
$541$	30.8496			1.32633			0.663164	+	0.748474i	$0.269213\pi$
$542$		−	2.68338i		−	0.115261i
$543$	−27.3830	−	8.25629i	−1.17512	−	0.354311i
$544$		−	3.21974i		−	0.138045i
$545$	−7.93831	+	13.1082i	−0.340040	+	0.561493i
$546$	5.33934	−	17.7086i	0.228503	−	0.757858i
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$	−3.21974			−0.137541
$549$	5.79156	+	3.84169i	0.247178	+	0.163959i
$550$	−10.0000	−	19.1267i	−0.426401	−	0.815566i
$551$	−35.6393	+	5.00000i	−1.51828	+	0.213007i
$552$	−11.6830	−	3.52254i	−0.497260	−	0.149929i
$553$	−49.2665			−2.09502
$554$	−14.0902			−0.598634
$555$	5.75436	−	5.18530i	0.244259	−	0.220104i
$556$	10.0000			0.424094
$557$	−13.7067			−0.580771			−0.290385	−	0.956910i	$-0.593783\pi$
$557$	−13.7067			−0.580771			−0.290385	+	0.956910i	$0.593783\pi$
$558$	−6.53536	−	4.33507i	−0.276664	−	0.183518i
$559$		−	12.6872i		−	0.536613i
$560$	3.72947	−	6.15831i	0.157599	−	0.260236i
$561$	23.0479	+	6.94921i	0.973084	+	0.293396i
$562$			6.24774i			0.263545i
$563$			29.8997i			1.26012i	0.776545	+	0.630062i	$0.216971\pi$
$563$			29.8997i			1.26012i	−0.776545	+	0.630062i	$0.783029\pi$
$564$	4.43094	−	14.6958i	0.186576	−	0.618804i
$565$	1.94987	−	3.21974i	0.0820318	−	0.135456i
$566$	26.5857			1.11748
$567$	26.6967	−	11.2691i	1.12116	−	0.473258i
$568$			10.2648i			0.430703i
$569$	−5.22829			−0.219181			−0.109591	−	0.993977i	$-0.534954\pi$
$569$	−5.22829			−0.219181			−0.109591	+	0.993977i	$0.534954\pi$
$570$	−12.9339	−	10.8496i	−0.541742	−	0.454440i
$571$	−32.3166			−1.35241			−0.676204	−	0.736714i	$-0.736376\pi$
$571$	−32.3166			−1.35241			−0.676204	+	0.736714i	$0.736376\pi$
$572$			14.3166i			0.598608i
$573$	−8.29156	−	2.50000i	−0.346385	−	0.104439i
$574$	36.9499			1.54226
$575$	16.3208	+	31.2164i	0.680625	+	1.30181i
$576$	2.50000	+	1.65831i	0.104167	+	0.0690963i
$577$		−	17.1182i		−	0.712639i	−0.934364	−	0.356319i	$-0.884032\pi$
$577$		−	17.1182i		−	0.712639i	0.934364	−	0.356319i	$-0.115968\pi$
$578$			6.63325i			0.275907i
$579$	3.00000	−	9.94987i	0.124676	−	0.413503i
$580$	−15.7916	−	9.56336i	−0.655709	−	0.397097i
$581$			20.7335i			0.860171i
$582$	−5.58312	−	1.68338i	−0.231428	−	0.0697781i
$583$	−4.31662			−0.178776
$584$	−1.81680			−0.0751796
$585$	−9.48832	−	20.1239i	−0.392294	−	0.832021i
$586$	−18.2665			−0.754582
$587$	−16.3208			−0.673632			−0.336816	−	0.941570i	$-0.609350\pi$
$587$	−16.3208			−0.673632			−0.336816	+	0.941570i	$0.609350\pi$
$588$	−1.68338	+	5.58312i	−0.0694212	+	0.230244i
$589$	−1.58312	−	11.2843i	−0.0652315	−	0.464961i
$590$	−6.53536	+	10.7916i	−0.269057	+	0.444282i
$591$	2.51827	−	8.35216i	0.103588	−	0.343562i
$592$	−2.00000			−0.0821995
$593$	20.5297			0.843052			0.421526	−	0.906816i	$-0.361495\pi$
$593$	20.5297			0.843052			0.421526	+	0.906816i	$0.361495\pi$
$594$	−17.2665	+	14.3166i	−0.708453	+	0.587418i
$595$	12.0079	−	19.8282i	0.492277	−	0.812876i
$596$			4.00000i			0.163846i
$597$	12.6082	−	41.8166i	0.516019	−	1.71144i
$598$		−	23.3659i		−	0.955503i
$599$	−19.9544			−0.815315			−0.407658	−	0.913135i	$-0.633654\pi$
$599$	−19.9544			−0.815315			−0.407658	+	0.913135i	$0.633654\pi$
$600$	−1.62622	−	8.50620i	−0.0663900	−	0.347264i
$601$		−	24.3550i		−	0.993461i	−0.867905	−	0.496731i	$-0.834534\pi$
$601$		−	24.3550i		−	0.993461i	0.867905	−	0.496731i	$-0.165466\pi$
$602$			12.3166i			0.501988i
$603$	17.5000	+	11.6082i	0.712655	+	0.472722i
$604$			16.5126i			0.671887i
$605$	−14.5999	−	8.84169i	−0.593570	−	0.359466i
$606$	−7.15831	+	23.7414i	−0.290787	+	0.964430i
$607$	36.6332			1.48690			0.743449	−	0.668793i	$-0.233189\pi$
$607$	36.6332			1.48690			0.743449	+	0.668793i	$0.233189\pi$
$608$	0.605599	+	4.31662i	0.0245603	+	0.175062i
$609$	44.0831	+	13.2916i	1.78634	+	0.538601i
$610$	−2.68338	+	4.43094i	−0.108647	+	0.179404i
$611$	29.3915			1.18905
$612$	8.04936	+	5.33934i	0.325376	+	0.215830i
$613$			17.9155i			0.723601i	0.932256	+	0.361800i	$0.117838\pi$
$613$			17.9155i			0.723601i	−0.932256	+	0.361800i	$0.882162\pi$
$614$			2.00000i			0.0807134i
$615$	33.0186	−	29.7533i	1.33144	−	1.19977i
$616$		−	13.8984i		−	0.559984i
$617$	−18.9350			−0.762293			−0.381147	−	0.924515i	$-0.624471\pi$
$617$	−18.9350			−0.762293			−0.381147	+	0.924515i	$0.624471\pi$
$618$	−29.1583	−	8.79156i	−1.17292	−	0.353648i
$619$	1.58312			0.0636311			0.0318156	−	0.999494i	$-0.489871\pi$
$619$	1.58312			0.0636311			0.0318156	+	0.999494i	$0.489871\pi$
$620$	3.02800	−	5.00000i	0.121607	−	0.200805i
$621$	28.1803	−	23.3659i	1.13084	−	0.937642i
$622$	20.8997			0.838004
$623$		−	8.41688i		−	0.337215i
$624$	−1.65831	+	5.50000i	−0.0663856	+	0.220176i
$625$	−14.2665	+	20.5297i	−0.570660	+	0.821186i
$626$	−20.7518			−0.829407
$627$	−32.2068	−	4.98156i	−1.28622	−	0.198944i
$628$		−	7.65069i		−	0.305296i
$629$	−6.43949			−0.256759
$630$	9.21116	+	19.5361i	0.366981	+	0.778336i
$631$	−23.8997			−0.951434			−0.475717	−	0.879598i	$-0.657811\pi$
$631$	−23.8997			−0.951434			−0.475717	+	0.879598i	$0.657811\pi$
$632$	15.3014			0.608656
$633$	−5.02136	−	1.51400i	−0.199581	−	0.0601760i
$634$	17.0000			0.675156
$635$	31.8139	+	19.2665i	1.26250	+	0.764568i
$636$	−1.65831	−	0.500000i	−0.0657564	−	0.0198263i
$637$	−11.1662			−0.442423
$638$	−35.6393			−1.41097
$639$	−25.6621	−	17.0223i	−1.01518	−	0.673392i
$640$	−1.15831	+	1.91267i	−0.0457863	+	0.0756050i
$641$	−0.191748			−0.00757358			−0.00378679	−	0.999993i	$-0.501205\pi$
$641$	−0.191748			−0.00757358			−0.00378679	+	0.999993i	$0.501205\pi$
$642$	0.0250628	−	0.0831240i	0.000989150	−	0.00328064i
$643$		−	0.383495i		−	0.0151236i	−0.999971	−	0.00756179i	$-0.997593\pi$
$643$		−	0.383495i		−	0.0151236i	0.999971	−	0.00756179i	$-0.00240702\pi$
$644$			22.6834i			0.893850i
$645$	9.91778	+	11.0062i	0.390512	+	0.433369i
$646$	1.94987	+	13.8984i	0.0767168	+	0.546826i
$647$	0.605599			0.0238086			0.0119043	−	0.999929i	$-0.496211\pi$
$647$	0.605599			0.0238086			0.0119043	+	0.999929i	$0.496211\pi$
$648$	−8.29156	+	3.50000i	−0.325723	+	0.137493i
$649$			24.3550i			0.956018i
$650$	14.6958	−	7.68338i	0.576416	−	0.301367i
$651$	−4.20844	+	13.9578i	−0.164942	+	0.547050i
$652$		−	1.40295i		−	0.0549436i
$653$	−11.6678			−0.456595			−0.228298	−	0.973591i	$-0.573316\pi$
$653$	−11.6678			−0.456595			−0.228298	+	0.973591i	$0.573316\pi$
$654$	−3.42667	+	11.3650i	−0.133993	+	0.444406i
$655$	−11.5831	+	19.1267i	−0.452590	+	0.747343i
$656$	−11.4760			−0.448064
$657$	3.01282	−	4.54199i	0.117541	−	0.177200i
$658$	−28.5330			−1.11233
$659$	22.1547			0.863025			0.431513	−	0.902107i	$-0.357980\pi$
$659$	22.1547			0.863025			0.431513	+	0.902107i	$0.357980\pi$
$660$	−11.1915	−	12.4197i	−0.435629	−	0.483436i
$661$		−	32.6113i		−	1.26843i	−0.773156	−	0.634216i	$-0.781323\pi$
$661$		−	32.6113i		−	1.26843i	0.773156	−	0.634216i	$-0.218677\pi$
$662$	−13.4846			−0.524093
$663$	−5.33934	+	17.7086i	−0.207363	+	0.687745i
$664$		−	6.43949i		−	0.249901i
$665$	−12.3693	+	28.8417i	−0.479659	+	1.11843i
$666$	3.31662	−	5.00000i	0.128517	−	0.193746i
$667$	58.1662			2.25221
$668$		−	24.9499i		−	0.965340i
$669$	1.63325	−	5.41688i	0.0631451	−	0.209429i
$670$	−8.10819	+	13.3887i	−0.313247	+	0.517251i
$671$			10.0000i			0.386046i
$672$	1.60987	−	5.33934i	0.0621022	−	0.205970i
$673$	−13.2665			−0.511386			−0.255693	−	0.966758i	$-0.582304\pi$
$673$	−13.2665			−0.511386			−0.255693	+	0.966758i	$0.582304\pi$
$674$		−	28.2164i		−	1.08685i
$675$	23.9623	+	10.0404i	0.922308	+	0.386455i
$676$	2.00000			0.0769231
$677$		−	46.1662i		−	1.77431i	−0.461469	−	0.887157i	$-0.652677\pi$
$677$		−	46.1662i		−	1.77431i	0.461469	−	0.887157i	$-0.347323\pi$
$678$	0.841688	−	2.79156i	0.0323248	−	0.107209i
$679$			10.8401i			0.416004i
$680$	−3.72947	+	6.15831i	−0.143019	+	0.236160i
$681$	−33.0831	−	9.97494i	−1.26775	−	0.382240i
$682$		−	11.2843i		−	0.432097i
$683$			24.0000i			0.918334i	0.888350	+	0.459167i	$0.151852\pi$
$683$			24.0000i			0.918334i	−0.888350	+	0.459167i	$0.848148\pi$
$684$	−11.7958	−	5.64431i	−0.451025	−	0.215816i
$685$	6.15831	+	3.72947i	0.235297	+	0.142496i
$686$	−11.6981			−0.446637
$687$		0			0
$688$		−	3.82534i		−	0.145840i
$689$		−	3.31662i		−	0.126353i
$690$	18.2654	+	20.2700i	0.695354	+	0.771665i
$691$	−13.8997			−0.528771			−0.264386	−	0.964417i	$-0.585169\pi$
$691$	−13.8997			−0.528771			−0.264386	+	0.964417i	$0.585169\pi$
$692$			13.2665i			0.504317i
$693$	34.7461	+	23.0479i	1.31989	+	0.875519i
$694$		−	20.1462i		−	0.764738i
$695$	−19.1267	−	11.5831i	−0.725518	−	0.439373i
$696$	−13.6915	−	4.12814i	−0.518975	−	0.156477i
$697$	−36.9499			−1.39958
$698$		−	8.63325i		−	0.326773i
$699$	−13.2928	+	44.0873i	−0.502781	+	1.66754i
$700$	−14.2665	+	7.45894i	−0.539223	+	0.281921i
$701$			37.2665i			1.40754i	0.710430	+	0.703768i	$0.248501\pi$
$701$			37.2665i			1.40754i	−0.710430	+	0.703768i	$0.751499\pi$
$702$	−11.0000	−	13.2665i	−0.415168	−	0.500712i
$703$	8.63325	−	1.21120i	0.325609	−	0.0456812i
$704$			4.31662i			0.162689i
$705$	−25.4972	+	22.9758i	−0.960281	+	0.865318i
$706$			23.3659i			0.879388i
$707$	46.0959			1.73361
$708$	−2.82107	+	9.35643i	−0.106022	+	0.351636i
$709$	28.6332			1.07534			0.537672	−	0.843154i	$-0.319304\pi$
$709$	28.6332			1.07534			0.537672	+	0.843154i	$0.319304\pi$
$710$	11.8899	−	19.6332i	0.446219	−	0.736823i
$711$	−25.3745	+	38.2534i	−0.951616	+	1.43462i
$712$			2.61414i			0.0979692i
$713$			18.4169i			0.689717i
$714$	5.18338	−	17.1913i	0.193983	−	0.643369i
$715$	16.5831	−	27.3830i	0.620174	−	1.02407i
$716$	16.5126			0.617104
$717$	−32.5581	−	9.81662i	−1.21590	−	0.366609i
$718$	−4.89975			−0.182857
$719$		−	34.8997i		−	1.30154i	−0.759274	−	0.650771i	$-0.774446\pi$
$719$		−	34.8997i		−	1.30154i	0.759274	−	0.650771i	$-0.225554\pi$
$720$	−2.86084	−	6.06759i	−0.106617	−	0.226126i
$721$			56.6132i			2.10838i
$722$	−5.22829	−	18.2665i	−0.194577	−	0.679809i
$723$	−8.67014	−	2.61414i	−0.322446	−	0.0972211i
$724$		−	16.5126i		−	0.613685i
$725$	19.1267	+	36.5831i	0.710348	+	1.35866i
$726$	−12.6583	−	3.81662i	−0.469794	−	0.141648i
$727$			13.2928i			0.493004i	0.969142	+	0.246502i	$0.0792811\pi$
$727$			13.2928i			0.493004i	−0.969142	+	0.246502i	$0.920719\pi$
$728$	10.6787			0.395778
$729$	5.00000	−	26.5330i	0.185185	−	0.982704i
$730$	3.47494	+	2.10442i	0.128613	+	0.0778881i
$731$		−	12.3166i		−	0.455547i
$732$	−1.15831	+	3.84169i	−0.0428125	+	0.141993i
$733$		−	6.43949i		−	0.237848i	−0.992903	−	0.118924i	$-0.962056\pi$
$733$		−	6.43949i		−	0.237848i	0.992903	−	0.118924i	$-0.0379445\pi$
$734$	7.65069			0.282392
$735$	9.68675	−	8.72881i	0.357301	−	0.321967i
$736$		−	7.04509i		−	0.259685i
$737$			30.2164i			1.11303i
$738$	19.0308	−	28.6901i	0.700535	−	1.05610i
$739$	−10.2164			−0.375815			−0.187908	−	0.982187i	$-0.560171\pi$
$739$	−10.2164			−0.375815			−0.187908	+	0.982187i	$0.560171\pi$
$740$	3.82534	+	2.31662i	0.140622	+	0.0851608i
$741$	3.82752	−	24.7457i	0.140607	−	0.909056i
$742$			3.21974i			0.118201i
$743$		−	44.8496i		−	1.64537i	−0.568495	−	0.822687i	$-0.692474\pi$
$743$		−	44.8496i		−	1.64537i	0.568495	−	0.822687i	$-0.307526\pi$
$744$	1.30707	−	4.33507i	0.0479196	−	0.158931i
$745$	4.63325	−	7.65069i	0.169749	−	0.280299i
$746$		−	23.3166i		−	0.853682i
$747$	16.0987	+	10.6787i	0.589021	+	0.390713i
$748$			13.8984i			0.508177i
$749$	−0.161392			−0.00589712
$750$	−6.74242	+	18.1532i	−0.246198	+	0.662862i
$751$		−	24.3550i		−	0.888727i	−0.895847	−	0.444363i	$-0.853430\pi$
$751$		−	24.3550i		−	0.888727i	0.895847	−	0.444363i	$-0.146570\pi$
$752$	8.86188			0.323160
$753$	52.3747	+	15.7916i	1.90864	+	0.575477i
$754$		−	27.3830i		−	0.997230i
$755$	19.1267	−	31.5831i	0.696092	−	1.14943i
$756$	10.6787	+	12.8790i	0.388380	+	0.468404i
$757$			12.8790i			0.468094i	0.972225	+	0.234047i	$0.0751970\pi$
$757$			12.8790i			0.468094i	−0.972225	+	0.234047i	$0.924803\pi$
$758$	36.4366			1.32344
$759$	50.4309	+	15.2055i	1.83053	+	0.551925i
$760$	3.84169	−	8.95776i	0.139353	−	0.324932i
$761$			10.6834i			0.387272i	0.981073	+	0.193636i	$0.0620281\pi$
$761$			10.6834i			0.387272i	−0.981073	+	0.193636i	$0.937972\pi$
$762$	27.5831	+	8.31662i	0.999231	+	0.301280i
$763$	22.0660			0.798843
$764$		−	5.00000i		−	0.180894i
$765$	−9.21116	−	19.5361i	−0.333030	−	0.706328i
$766$	−7.58312			−0.273989
$767$	−18.7129			−0.675682
$768$	−0.500000	+	1.65831i	−0.0180422	+	0.0598392i
$769$	−48.1662			−1.73692			−0.868460	−	0.495760i	$-0.834890\pi$
$769$	−48.1662			−1.73692			−0.868460	+	0.495760i	$0.834890\pi$
$770$	−16.0987	+	26.5831i	−0.580158	+	0.957989i
$771$	−8.20844	−	2.47494i	−0.295620	−	0.0891327i
$772$	6.00000			0.215945
$773$		−	24.1662i		−	0.869200i	−0.900624	−	0.434600i	$-0.856890\pi$
$773$		−	24.1662i		−	0.869200i	0.900624	−	0.434600i	$-0.143110\pi$
$774$	9.56336	+	6.34361i	0.343748	+	0.228016i
$775$	−11.5831	+	6.05599i	−0.416078	+	0.217538i
$776$		−	3.36675i		−	0.120859i
$777$	−10.6787	−	3.21974i	−0.383096	−	0.115508i
$778$	16.2164			0.581385
$779$	49.5377	−	6.94987i	1.77487	−	0.249005i
$780$	9.54253	−	8.59885i	0.341677	−	0.307888i
$781$		−	44.3094i		−	1.58552i
$782$		−	22.6834i		−	0.811156i
$783$	33.0251	−	27.3830i	1.18022	−	0.978589i
$784$	−3.36675			−0.120241
$785$	−8.86188	+	14.6332i	−0.316294	+	0.522283i
$786$	−5.00000	+	16.5831i	−0.178344	+	0.591500i
$787$	−8.36675			−0.298242			−0.149121	−	0.988819i	$-0.547644\pi$
$787$	−8.36675			−0.298242			−0.149121	+	0.988819i	$0.547644\pi$
$788$	5.03654			0.179419
$789$	−10.2648	+	34.0446i	−0.365438	+	1.21202i
$790$	−29.2665	−	17.7238i	−1.04126	−	0.630583i
$791$	−5.42004			−0.192714
$792$	−10.7916	−	7.15831i	−0.383461	−	0.254360i
$793$	−7.68338			−0.272845
$794$	29.3915			1.04307
$795$	2.59265	+	2.87718i	0.0919518	+	0.102043i
$796$	25.2164			0.893771
$797$		−	31.6332i		−	1.12051i	−0.828321	−	0.560254i	$-0.810704\pi$
$797$		−	31.6332i		−	1.12051i	0.828321	−	0.560254i	$-0.189296\pi$
$798$	−3.71571	+	24.0229i	−0.131535	+	0.850400i
$799$	28.5330			1.00942
$800$	4.43094	−	2.31662i	0.156657	−	0.0819051i
$801$	−6.53536	−	4.33507i	−0.230916	−	0.153172i
$802$		−	21.5491i		−	0.760926i
$803$	7.84243			0.276753
$804$	−3.50000	+	11.6082i	−0.123435	+	0.409389i
$805$	26.2744	−	43.3858i	0.926052	−	1.52915i
$806$	8.67014			0.305393
$807$	10.8704	−	36.0531i	0.382657	−	1.26913i
$808$	−14.3166			−0.503657
$809$		−	1.94987i		−	0.0685539i	−0.999412	−	0.0342770i	$-0.989087\pi$
$809$		−	1.94987i		−	0.0685539i	0.999412	−	0.0342770i	$-0.0109128\pi$
$810$	19.9131	+	2.90987i	0.699676	+	0.102242i
$811$			41.2814i			1.44959i	0.688966	+	0.724793i	$0.258065\pi$
$811$			41.2814i			1.44959i	−0.688966	+	0.724793i	$0.741935\pi$
$812$			26.5831i			0.932885i
$813$	−1.34169	+	4.44987i	−0.0470550	+	0.156064i
$814$	8.63325			0.302595
$815$	−1.62505	+	2.68338i	−0.0569230	+	0.0939945i
$816$	−1.60987	+	5.33934i	−0.0563568	+	0.186914i
$817$	2.31662	+	16.5126i	0.0810484	+	0.577702i
$818$	3.82534			0.133750
$819$	−17.7086	+	26.6967i	−0.618788	+	0.932858i
$820$	21.9499	+	13.2928i	0.766523	+	0.464206i
$821$			30.0000i			1.04701i	0.852023	+	0.523504i	$0.175375\pi$
$821$			30.0000i			1.04701i	−0.852023	+	0.523504i	$0.824625\pi$
$822$	5.33934	+	1.60987i	0.186231	+	0.0561507i
$823$		−	17.3099i		−	0.603386i	−0.953405	−	0.301693i	$-0.902448\pi$
$823$		−	17.3099i		−	0.603386i	0.953405	−	0.301693i	$-0.0975517\pi$
$824$		−	17.5831i		−	0.612537i
$825$	7.01977	+	36.7181i	0.244397	+	1.27836i
$826$	18.1662			0.632085
$827$			8.58312i			0.298464i	0.988802	+	0.149232i	$0.0476802\pi$
$827$			8.58312i			0.298464i	−0.988802	+	0.149232i	$0.952320\pi$
$828$	17.6127	+	11.6830i	0.612084	+	0.406011i
$829$		−	31.4001i		−	1.09057i	−0.838251	−	0.545285i	$-0.816421\pi$
$829$		−	31.4001i		−	1.09057i	0.838251	−	0.545285i	$-0.183579\pi$
$830$	−7.45894	+	12.3166i	−0.258904	+	0.427516i
$831$	23.3659	+	7.04509i	0.810554	+	0.244391i
$832$	−3.31662			−0.114983
$833$	−10.8401			−0.375586
$834$	−16.5831	−	5.00000i	−0.574227	−	0.173136i
$835$	−28.8997	+	47.7209i	−1.00012	+	1.65145i
$836$	−2.61414	−	18.6332i	−0.0904121	−	0.644444i
$837$	8.67014	+	10.4566i	0.299684	+	0.361432i
$838$	3.05013			0.105365
$839$	6.05599			0.209076			0.104538	−	0.994521i	$-0.466664\pi$
$839$	6.05599			0.209076			0.104538	+	0.994521i	$0.466664\pi$
$840$	−9.26378	+	8.34767i	−0.319631	+	0.288022i
$841$	39.1662			1.35056
$842$	16.0987			0.554799
$843$	3.12387	−	10.3607i	0.107592	−	0.356842i
$844$		−	3.02800i		−	0.104228i
$845$	−3.82534	−	2.31662i	−0.131596	−	0.0796943i
$846$	−14.6958	+	22.1547i	−0.505251	+	0.761695i
$847$			24.5771i			0.844479i
$848$		−	1.00000i		−	0.0343401i
$849$	−44.0873	−	13.2928i	−1.51307	−	0.456209i
$850$	14.2665	−	7.45894i	0.489337	−	0.255839i
$851$	−14.0902			−0.483005
$852$	5.13242	−	17.0223i	0.175834	−	0.583174i
$853$		−	49.9212i		−	1.70927i	−0.519230	−	0.854635i	$-0.673781\pi$
$853$		−	49.9212i		−	1.70927i	0.519230	−	0.854635i	$-0.326219\pi$
$854$	7.45894			0.255240
$855$	16.0237	+	24.4590i	0.547998	+	0.836479i
$856$	0.0501256			0.00171326
$857$			12.0000i			0.409912i	0.978771	+	0.204956i	$0.0657052\pi$
$857$			12.0000i			0.409912i	−0.978771	+	0.204956i	$0.934295\pi$
$858$	7.15831	−	23.7414i	0.244381	−	0.810519i
$859$	2.94987			0.100648			0.0503242	−	0.998733i	$-0.483975\pi$
$859$	2.94987			0.100648			0.0503242	+	0.998733i	$0.483975\pi$
$860$	−4.43094	+	7.31662i	−0.151094	+	0.249495i
$861$	−61.2744	−	18.4749i	−2.08823	−	0.629624i
$862$			17.5320i			0.597143i
$863$		−	11.6834i		−	0.397707i	−0.980029	−	0.198853i	$-0.936278\pi$
$863$		−	11.6834i		−	0.397707i	0.980029	−	0.198853i	$-0.0637217\pi$
$864$	−3.31662	−	4.00000i	−0.112834	−	0.136083i
$865$	15.3668	−	25.3745i	0.522485	−	0.862757i
$866$			1.68338i			0.0572034i
$867$	3.31662	−	11.0000i	0.112638	−	0.373580i
$868$	−8.41688			−0.285687
$869$	−66.0503			−2.24060
$870$	21.4057	+	23.7548i	0.725720	+	0.805364i
$871$	−23.2164			−0.786657
$872$	−6.85334			−0.232083
$873$	8.41688	+	5.58312i	0.284868	+	0.188960i
$874$	4.26650	+	30.4110i	0.144316	+	1.02867i
$875$	35.9269	+	2.25856i	1.21455	+	0.0763534i
$876$	3.01282	+	0.908399i	0.101794	+	0.0306920i
$877$	−19.9499			−0.673659			−0.336830	−	0.941566i	$-0.609355\pi$
$877$	−19.9499			−0.673659			−0.336830	+	0.941566i	$0.609355\pi$
$878$	3.82534			0.129099
$879$	30.2916	+	9.13325i	1.02171	+	0.308057i
$880$	5.00000	−	8.25629i	0.168550	−	0.278319i
$881$		−	15.8997i		−	0.535676i	−0.963464	−	0.267838i	$-0.913691\pi$
$881$		−	15.8997i		−	0.535676i	0.963464	−	0.267838i	$-0.0863092\pi$
$882$	5.58312	−	8.41688i	0.187994	−	0.283411i
$883$		−	0.383495i		−	0.0129056i	−0.999979	−	0.00645282i	$-0.997946\pi$
$883$		−	0.383495i		−	0.0129056i	0.999979	−	0.00645282i	$-0.00205401\pi$
$884$	−10.6787			−0.359163
$885$	16.2335	−	14.6281i	0.545682	−	0.491718i
$886$		−	12.6872i		−	0.426236i
$887$			33.5831i			1.12761i	0.825908	+	0.563805i	$0.190663\pi$
$887$			33.5831i			1.12761i	−0.825908	+	0.563805i	$0.809337\pi$
$888$	3.31662	+	1.00000i	0.111299	+	0.0335578i
$889$		−	53.5548i		−	1.79617i
$890$	3.02800	−	5.00000i	0.101499	−	0.167600i
$891$	35.7916	−	15.1082i	1.19906	−	0.506143i
$892$	3.26650			0.109370
$893$	−38.2534	+	5.36675i	−1.28010	+	0.179591i
$894$	2.00000	−	6.63325i	0.0668900	−	0.221849i
$895$	−31.5831	−	19.1267i	−1.05571	−	0.639336i
$896$	3.21974			0.107564
$897$	−11.6830	+	38.7480i	−0.390083	+	1.29376i
$898$		−	26.9691i		−	0.899972i
$899$			21.5831i			0.719837i
$900$	−1.55632	+	14.9190i	−0.0518775	+	0.497301i
$901$		−	3.21974i		−	0.107265i
$902$	49.5377			1.64943
$903$	6.15831	−	20.4248i	0.204936	−	0.679695i
$904$	1.68338			0.0559882
$905$	−19.1267	+	31.5831i	−0.635794	+	1.04986i
$906$	8.25629	−	27.3830i	0.274297	−	0.909739i
$907$	6.16625			0.204747			0.102373	−	0.994746i	$-0.467356\pi$
$907$	6.16625			0.204747			0.102373	+	0.994746i	$0.467356\pi$
$908$		−	19.9499i		−	0.662060i
$909$	23.7414	−	35.7916i	0.787454	−	1.18713i
$910$	−20.4248	−	12.3693i	−0.677076	−	0.410037i
$911$	24.1633			0.800564			0.400282	−	0.916392i	$-0.368912\pi$
$911$	24.1633			0.800564			0.400282	+	0.916392i	$0.368912\pi$
$912$	1.15404	−	7.46111i	0.0382141	−	0.247062i
$913$			27.7969i			0.919942i
$914$	27.1913			0.899407
$915$	6.66535	−	6.00620i	0.220350	−	0.198559i
$916$		0			0
$917$	32.1974			1.06325
$918$	−10.6787	−	12.8790i	−0.352449	−	0.425070i
$919$	−17.9499			−0.592112			−0.296056	−	0.955171i	$-0.595671\pi$
$919$	−17.9499			−0.592112			−0.296056	+	0.955171i	$0.595671\pi$
$920$	−8.16041	+	13.4749i	−0.269041	+	0.444256i
$921$	1.00000	−	3.31662i	0.0329511	−	0.109287i
$922$	−21.5831			−0.710802
$923$	34.0446			1.12059
$924$	−6.94921	+	23.0479i	−0.228612	+	0.758221i
$925$	−4.63325	−	8.86188i	−0.152340	−	0.291377i
$926$	15.3014			0.502834
$927$	43.9578	+	29.1583i	1.44376	+	0.957685i
$928$		−	8.25629i		−	0.271026i
$929$			18.0501i			0.592205i	0.955156	+	0.296103i	$0.0956871\pi$
$929$			18.0501i			0.592205i	−0.955156	+	0.296103i	$0.904313\pi$
$930$	−7.52136	+	6.77756i	−0.246635	+	0.222245i
$931$	14.5330	−	2.03890i	0.476300	−	0.0668223i
$932$	−26.5857			−0.870842
$933$	−34.6583	−	10.4499i	−1.13466	−	0.342114i
$934$			26.7774i			0.876183i
$935$	16.0987	−	26.5831i	0.526484	−	0.869361i
$936$	5.50000	−	8.29156i	0.179773	−	0.271018i
$937$			15.0793i			0.492618i	0.969191	+	0.246309i	$0.0792178\pi$
$937$			15.0793i			0.492618i	−0.969191	+	0.246309i	$0.920782\pi$
$938$	22.5382			0.735899
$939$	34.4129	+	10.3759i	1.12302	+	0.338604i
$940$	−16.9499	−	10.2648i	−0.552844	−	0.334802i
$941$	−5.83389			−0.190179			−0.0950897	−	0.995469i	$-0.530314\pi$
$941$	−5.83389			−0.190179			−0.0950897	+	0.995469i	$0.530314\pi$
$942$	−3.82534	+	12.6872i	−0.124636	+	0.413372i
$943$	−80.8496			−2.63283
$944$	−5.64214			−0.183636
$945$	−5.50693	−	37.0025i	−0.179141	−	1.20369i
$946$			16.5126i			0.536870i
$947$	−18.9350			−0.615304			−0.307652	−	0.951499i	$-0.599543\pi$
$947$	−18.9350			−0.615304			−0.307652	+	0.951499i	$0.599543\pi$
$948$	−25.3745	−	7.65069i	−0.824124	−	0.248483i
$949$			6.02564i			0.195600i
$950$	−17.7238	+	12.6834i	−0.575035	+	0.411503i
$951$	−28.1913	−	8.50000i	−0.914166	−	0.275631i
$952$	10.3668			0.335988
$953$			2.41688i			0.0782903i	0.999234	+	0.0391451i	$0.0124635\pi$
$953$			2.41688i			0.0782903i	−0.999234	+	0.0391451i	$0.987537\pi$
$954$	2.50000	+	1.65831i	0.0809405	+	0.0536898i
$955$	−5.79156	+	9.56336i	−0.187411	+	0.309463i
$956$		−	19.6332i		−	0.634985i
$957$	59.1011	+	17.8196i	1.91047	+	0.576027i
$958$	−14.0000			−0.452319
$959$		−	10.3668i		−	0.334760i
$960$	2.87718	−	2.59265i	0.0928606	−	0.0836774i
$961$	24.1662			0.779556
$962$			6.63325i			0.213865i
$963$	−0.0831240	+	0.125314i	−0.00267863	+	0.00403819i
$964$		−	5.22829i		−	0.168392i
$965$	−11.4760	−	6.94987i	−0.369426	−	0.223724i
$966$	11.3417	−	37.6161i	0.364913	−	1.21028i
$967$		−	35.8310i		−	1.15225i	−0.817362	−	0.576124i	$-0.804564\pi$
$967$		−	35.8310i		−	1.15225i	0.817362	−	0.576124i	$-0.195436\pi$
$968$		−	7.63325i		−	0.245342i
$969$	3.71571	−	24.0229i	0.119366	−	0.771726i
$970$	−3.89975	+	6.43949i	−0.125213	+	0.206759i
$971$	−8.03418			−0.257829			−0.128915	−	0.991656i	$-0.541149\pi$
$971$	−8.03418			−0.257829			−0.128915	+	0.991656i	$0.541149\pi$
$972$	15.5000	−	1.65831i	0.497163	−	0.0531904i
$973$			32.1974i			1.03220i
$974$			36.5330i			1.17059i
$975$	−28.2119	+	5.39355i	−0.903503	+	0.172732i
$976$	−2.31662			−0.0741534
$977$		−	29.5831i		−	0.946448i	−0.880942	−	0.473224i	$-0.843090\pi$
$977$		−	29.5831i		−	0.946448i	0.880942	−	0.473224i	$-0.156910\pi$
$978$	−0.701473	+	2.32652i	−0.0224306	+	0.0743940i
$979$		−	11.2843i		−	0.360647i
$980$	6.43949	+	3.89975i	0.205702	+	0.124573i
$981$	11.3650	−	17.1333i	0.362856	−	0.547026i
$982$	−8.41688			−0.268593
$983$			27.1662i			0.866469i	0.901281	+	0.433234i	$0.142628\pi$
$983$			27.1662i			0.866469i	−0.901281	+	0.433234i	$0.857372\pi$
$984$	19.0308	+	5.73801i	0.606681	+	0.182921i
$985$	−9.63325	−	5.83389i	−0.306941	−	0.185883i
$986$		−	26.5831i		−	0.846579i
$987$	47.3166	+	14.2665i	1.50610	+	0.454108i
$988$	14.3166	−	2.00855i	0.455473	−	0.0639003i
$989$		−	26.9499i		−	0.856956i
$990$	12.3492	+	26.1915i	0.392482	+	0.832421i
$991$		−	30.4110i		−	0.966037i	−0.875610	−	0.483019i	$-0.839540\pi$
$991$		−	30.4110i		−	0.966037i	0.875610	−	0.483019i	$-0.160460\pi$
$992$	2.61414			0.0829992
$993$	22.3616	+	6.74229i	0.709625	+	0.213960i
$994$	−33.0501			−1.04829
$995$	−48.2306	−	29.2084i	−1.52901	−	0.925970i
$996$	−3.21974	+	10.6787i	−0.102021	+	0.338367i
$997$		−	33.2169i		−	1.05199i	−0.850488	−	0.525995i	$-0.823693\pi$
$997$		−	33.2169i		−	1.05199i	0.850488	−	0.525995i	$-0.176307\pi$
$998$		−	8.41688i		−	0.266432i
$999$	−8.00000	+	6.63325i	−0.253109	+	0.209867i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.c.c.569.4	yes	8
3.2	odd	2	inner	570.2.c.c.569.5	yes	8
5.4	even	2		570.2.c.f.569.5	yes	8
15.14	odd	2		570.2.c.f.569.4	yes	8
19.18	odd	2		570.2.c.f.569.6	yes	8
57.56	even	2		570.2.c.f.569.3	yes	8
95.94	odd	2	inner	570.2.c.c.569.3	✓	8
285.284	even	2	inner	570.2.c.c.569.6	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.c.c.569.3	✓	8	95.94	odd	2	inner
570.2.c.c.569.4	yes	8	1.1	even	1	trivial
570.2.c.c.569.5	yes	8	3.2	odd	2	inner
570.2.c.c.569.6	yes	8	285.284	even	2	inner
570.2.c.f.569.3	yes	8	57.56	even	2
570.2.c.f.569.4	yes	8	15.14	odd	2
570.2.c.f.569.5	yes	8	5.4	even	2
570.2.c.f.569.6	yes	8	19.18	odd	2

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.500000 + 1.65831i) q^{3} -1.00000 q^{4} +(1.91267 + 1.15831i) q^{5} +(1.65831 + 0.500000i) q^{6} -3.21974i q^{7} +1.00000i q^{8} +(-2.50000 - 1.65831i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.500000 + 1.65831i) q^{3} -1.00000 q^{4} +(1.91267 + 1.15831i) q^{5} +(1.65831 + 0.500000i) q^{6} -3.21974i q^{7} +1.00000i q^{8} +(-2.50000 - 1.65831i) q^{9} +(1.15831 - 1.91267i) q^{10} -4.31662i q^{11} +(0.500000 - 1.65831i) q^{12} +3.31662 q^{13} -3.21974 q^{14} +(-2.87718 + 2.59265i) q^{15} +1.00000 q^{16} +3.21974 q^{17} +(-1.65831 + 2.50000i) q^{18} +(-4.31662 + 0.605599i) q^{19} +(-1.91267 - 1.15831i) q^{20} +(5.33934 + 1.60987i) q^{21} -4.31662 q^{22} +7.04509 q^{23} +(-1.65831 - 0.500000i) q^{24} +(2.31662 + 4.43094i) q^{25} -3.31662i q^{26} +(4.00000 - 3.31662i) q^{27} +3.21974i q^{28} +8.25629 q^{29} +(2.59265 + 2.87718i) q^{30} +2.61414i q^{31} -1.00000i q^{32} +(7.15831 + 2.15831i) q^{33} -3.21974i q^{34} +(3.72947 - 6.15831i) q^{35} +(2.50000 + 1.65831i) q^{36} -2.00000 q^{37} +(0.605599 + 4.31662i) q^{38} +(-1.65831 + 5.50000i) q^{39} +(-1.15831 + 1.91267i) q^{40} -11.4760 q^{41} +(1.60987 - 5.33934i) q^{42} -3.82534i q^{43} +4.31662i q^{44} +(-2.86084 - 6.06759i) q^{45} -7.04509i q^{46} +8.86188 q^{47} +(-0.500000 + 1.65831i) q^{48} -3.36675 q^{49} +(4.43094 - 2.31662i) q^{50} +(-1.60987 + 5.33934i) q^{51} -3.31662 q^{52} -1.00000i q^{53} +(-3.31662 - 4.00000i) q^{54} +(5.00000 - 8.25629i) q^{55} +3.21974 q^{56} +(1.15404 - 7.46111i) q^{57} -8.25629i q^{58} -5.64214 q^{59} +(2.87718 - 2.59265i) q^{60} -2.31662 q^{61} +2.61414 q^{62} +(-5.33934 + 8.04936i) q^{63} -1.00000 q^{64} +(6.34361 + 3.84169i) q^{65} +(2.15831 - 7.15831i) q^{66} -7.00000 q^{67} -3.21974 q^{68} +(-3.52254 + 11.6830i) q^{69} +(-6.15831 - 3.72947i) q^{70} +10.2648 q^{71} +(1.65831 - 2.50000i) q^{72} +1.81680i q^{73} +2.00000i q^{74} +(-8.50620 + 1.62622i) q^{75} +(4.31662 - 0.605599i) q^{76} -13.8984 q^{77} +(5.50000 + 1.65831i) q^{78} -15.3014i q^{79} +(1.91267 + 1.15831i) q^{80} +(3.50000 + 8.29156i) q^{81} +11.4760i q^{82} -6.43949 q^{83} +(-5.33934 - 1.60987i) q^{84} +(6.15831 + 3.72947i) q^{85} -3.82534 q^{86} +(-4.12814 + 13.6915i) q^{87} +4.31662 q^{88} +2.61414 q^{89} +(-6.06759 + 2.86084i) q^{90} -10.6787i q^{91} -7.04509 q^{92} +(-4.33507 - 1.30707i) q^{93} -8.86188i q^{94} +(-8.95776 - 3.84169i) q^{95} +(1.65831 + 0.500000i) q^{96} -3.36675 q^{97} +3.36675i q^{98} +(-7.15831 + 10.7916i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 8 q^{4} - 20 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 - 8 * q^4 - 20 * q^9	\( 8 q - 4 q^{3} - 8 q^{4} - 20 q^{9} - 4 q^{10} + 4 q^{12} - 22 q^{15} + 8 q^{16} - 8 q^{19} - 8 q^{22} - 8 q^{25} + 32 q^{27} + 2 q^{30} + 44 q^{33} + 20 q^{36} - 16 q^{37} + 4 q^{40} + 22 q^{45} - 4 q^{48} - 80 q^{49} + 40 q^{55} + 4 q^{57} + 22 q^{60} + 8 q^{61} - 8 q^{64} + 4 q^{66} - 56 q^{67} - 36 q^{70} + 4 q^{75} + 8 q^{76} + 44 q^{78} + 28 q^{81} + 36 q^{85} + 8 q^{88} + 10 q^{90} - 80 q^{97} - 44 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 8 * q^4 - 20 * q^9 - 4 * q^10 + 4 * q^12 - 22 * q^15 + 8 * q^16 - 8 * q^19 - 8 * q^22 - 8 * q^25 + 32 * q^27 + 2 * q^30 + 44 * q^33 + 20 * q^36 - 16 * q^37 + 4 * q^40 + 22 * q^45 - 4 * q^48 - 80 * q^49 + 40 * q^55 + 4 * q^57 + 22 * q^60 + 8 * q^61 - 8 * q^64 + 4 * q^66 - 56 * q^67 - 36 * q^70 + 4 * q^75 + 8 * q^76 + 44 * q^78 + 28 * q^81 + 36 * q^85 + 8 * q^88 + 10 * q^90 - 80 * q^97 - 44 * q^99

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