LMFDB - Embedded newform 570.2.c.c.569.5

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			569.5
Root			$0.500000 + 2.41267i$ of defining polynomial
Character	$\chi$	$=$	570.569
Dual form			570.2.c.c.569.3

$q$-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} +(-0.964508 + 3.75096i) 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} +(-3.75096 - 0.964508i) 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} +(6.70252 - 0.276026i) 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} +(3.16259 + 6.85551i) q^{57} -8.25629i q^{58} +5.64214 q^{59} +(0.964508 - 3.75096i) 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} +(6.18957 - 6.05716i) 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} +(0.276026 + 6.70252i) 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	$0.225548\pi$
$11$			4.31662i			1.30151i	−0.759287	+	0.650756i	$0.774452\pi$
$12$	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
$15$	−0.964508	+	3.75096i	−0.249035	+	0.968495i
$16$	1.00000			0.250000
$17$	−3.21974			−0.780903			−0.390451	−	0.920624i	$-0.627681\pi$
$17$	−3.21974			−0.780903			−0.390451	+	0.920624i	$0.627681\pi$
$18$	−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	$-0.762584\pi$
$23$	−7.04509			−1.46900			−0.734501	+	0.678608i	$0.762584\pi$
$24$	−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	$-0.778042\pi$
$29$	−8.25629			−1.53315			−0.766577	+	0.642153i	$0.778042\pi$
$30$	−3.75096	−	0.964508i	−0.684829	−	0.176094i
$31$			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	$-0.146369\pi$
$41$	11.4760			1.79225			0.896127	+	0.443797i	$0.146369\pi$
$42$	−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
$45$	6.70252	−	0.276026i	0.999153	−	0.0411475i
$46$		−	7.04509i		−	1.03874i
$47$	−8.86188			−1.29264			−0.646319	−	0.763067i	$-0.723693\pi$
$47$	−8.86188			−1.29264			−0.646319	+	0.763067i	$0.723693\pi$
$48$	−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	$0.0218788\pi$
$53$			1.00000i			0.137361i	−0.997639	+	0.0686803i	$0.978121\pi$
$54$	−3.31662	+	4.00000i	−0.451335	+	0.544331i
$55$	5.00000	−	8.25629i	0.674200	−	1.11328i
$56$	−3.21974			−0.430256
$57$	3.16259	+	6.85551i	0.418895	+	0.908035i
$58$		−	8.25629i		−	1.08410i
$59$	5.64214			0.734544			0.367272	−	0.930114i	$-0.380292\pi$
$59$	5.64214			0.734544			0.367272	+	0.930114i	$0.380292\pi$
$60$	0.964508	−	3.75096i	0.124517	−	0.484247i
$61$	−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	$-0.708471\pi$
$71$	−10.2648			−1.21821			−0.609106	+	0.793089i	$0.708471\pi$
$72$	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
$75$	6.18957	−	6.05716i	0.714710	−	0.699420i
$76$	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	$-0.385021\pi$
$83$	6.43949			0.706826			0.353413	+	0.935467i	$0.385021\pi$
$84$	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	$-0.544244\pi$
$89$	−2.61414			−0.277099			−0.138549	+	0.990356i	$0.544244\pi$
$90$	0.276026	+	6.70252i	0.0290957	+	0.706508i
$91$		−	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	$-0.747663\pi$
$101$		−	14.3166i		−	1.42456i	0.701897	−	0.712279i	$-0.252337\pi$
$102$	−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
$105$	12.0771	+	3.10547i	1.17861	+	0.303063i
$106$	−1.00000			−0.0971286
$107$			0.0501256i			0.00484583i	0.999997	+	0.00242291i	$0.000771238\pi$
$107$			0.0501256i			0.00484583i	−0.999997	+	0.00242291i	$0.999229\pi$
$108$	−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	$0.0252300\pi$
$113$			1.68338i			0.158359i	−0.996860	+	0.0791793i	$0.974770\pi$
$114$	−6.85551	+	3.16259i	−0.642078	+	0.296203i
$115$	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
$120$	3.75096	+	0.964508i	0.342415	+	0.0880471i
$121$	−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	$-0.856093\pi$
$131$		−	10.0000i		−	0.873704i	0.899533	−	0.436852i	$-0.143907\pi$
$132$	−7.15831	+	2.15831i	−0.623051	+	0.187857i
$133$	1.94987	+	13.8984i	0.169076	+	1.20515i
$134$		−	7.00000i		−	0.604708i
$135$	−3.80900	−	10.9769i	−0.327826	−	0.944738i
$136$			3.21974i			0.276091i
$137$	−3.21974			−0.275081			−0.137541	−	0.990496i	$-0.543920\pi$
$137$	−3.21974			−0.275081			−0.137541	+	0.990496i	$0.543920\pi$
$138$	−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	$0.0523901\pi$
$149$			4.00000i			0.327693i	−0.986486	+	0.163846i	$0.947610\pi$
$150$	6.05716	+	6.18957i	0.494565	+	0.505377i
$151$		−	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
$165$	−16.1915	−	4.16342i	−1.26051	−	0.324122i
$166$			6.43949i			0.499801i
$167$		−	24.9499i		−	1.93068i	−0.260997	−	0.965340i	$-0.584051\pi$
$167$		−	24.9499i		−	1.93068i	0.260997	−	0.965340i	$-0.415949\pi$
$168$	1.60987	+	5.33934i	0.124204	+	0.411939i
$169$	−2.00000			−0.153846
$170$	−3.72947	+	6.15831i	−0.286037	+	0.472321i
$171$	9.78729	−	8.67231i	0.748453	−	0.663188i
$172$			3.82534i			0.291680i
$173$			13.2665i			1.00863i	0.863519	+	0.504317i	$0.168256\pi$
$173$			13.2665i			1.00863i	−0.863519	+	0.504317i	$0.831744\pi$
$174$	−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	$-0.288306\pi$
$179$	16.5126			1.23421			0.617104	+	0.786882i	$0.288306\pi$
$180$	−6.70252	+	0.276026i	−0.499577	+	0.0205738i
$181$			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	$-0.942101\pi$
$191$		−	5.00000i		−	0.361787i	0.983503	−	0.180894i	$-0.0578990\pi$
$192$	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
$195$	−3.19891	+	12.4405i	−0.229079	+	0.890885i
$196$	3.36675			0.240482
$197$	5.03654			0.358839			0.179419	−	0.983773i	$-0.442578\pi$
$197$	5.03654			0.358839			0.179419	+	0.983773i	$0.442578\pi$
$198$	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
$210$	−3.10547	+	12.0771i	−0.214298	+	0.833402i
$211$			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
$225$	−13.1394	−	7.23567i	−0.875963	−	0.482378i
$226$	−1.68338			−0.111976
$227$		−	19.9499i		−	1.32412i	−0.749451	−	0.662060i	$-0.769682\pi$
$227$		−	19.9499i		−	1.32412i	0.749451	−	0.662060i	$-0.230318\pi$
$228$	−3.16259	−	6.85551i	−0.209447	−	0.454017i
$229$		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	$-0.836426\pi$
$233$	−26.5857			−1.74168			−0.870842	+	0.491563i	$0.836426\pi$
$234$	−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	$-0.781006\pi$
$239$		−	19.6332i		−	1.26997i	0.772525	−	0.634985i	$-0.218994\pi$
$240$	−0.964508	+	3.75096i	−0.0622587	+	0.242124i
$241$			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	$0.474348\pi$
$251$			31.5831i			1.99351i	−0.0805007	+	0.996755i	$0.525652\pi$
$252$	−5.33934	−	8.04936i	−0.336347	−	0.507062i
$253$		−	30.4110i		−	1.91192i
$254$			16.6332i			1.04366i
$255$	3.10547	−	12.0771i	0.194472	−	0.756300i
$256$	1.00000			0.0625000
$257$		−	4.94987i		−	0.308765i	−0.988011	−	0.154382i	$-0.950661\pi$
$257$		−	4.94987i		−	0.308765i	0.988011	−	0.154382i	$-0.0493388\pi$
$258$	−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	$-0.718159\pi$
$263$	−20.5297			−1.26591			−0.632957	+	0.774187i	$0.718159\pi$
$264$	−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	$-0.269376\pi$
$269$	21.7409			1.32556			0.662782	+	0.748813i	$0.269376\pi$
$270$	10.9769	−	3.80900i	0.668031	−	0.231808i
$271$	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	$-0.440333\pi$
$281$	6.24774			0.372709			0.186354	+	0.982483i	$0.440333\pi$
$282$	−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
$285$	1.89184	−	16.7756i	0.112063	−	0.993701i
$286$	−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	$0.179150\pi$
$293$			18.2665i			1.06714i	−0.845756	+	0.533570i	$0.820850\pi$
$294$	−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
$300$	−6.18957	+	6.05716i	−0.357355	+	0.349710i
$301$	−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	$-0.798118\pi$
$311$		−	20.8997i		−	1.18512i	0.805528	−	0.592558i	$-0.201882\pi$
$312$	−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
$315$	−0.888733	−	21.5804i	−0.0500744	−	1.21592i
$316$			15.3014i			0.860769i
$317$		−	17.0000i		−	0.954815i	−0.878682	−	0.477408i	$-0.841577\pi$
$317$		−	17.0000i		−	0.954815i	0.878682	−	0.477408i	$-0.158423\pi$
$318$	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
$330$	4.16342	−	16.1915i	0.229189	−	0.891313i
$331$		−	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
$342$	8.67231	+	9.78729i	0.468945	+	0.529236i
$343$		−	11.6981i		−	0.631640i
$344$	−3.82534			−0.206249
$345$	6.79504	−	26.4259i	0.365833	−	1.42272i
$346$	−13.2665			−0.713211
$347$	−20.1462			−1.08150			−0.540751	−	0.841182i	$-0.681860\pi$
$347$	−20.1462			−1.08150			−0.540751	+	0.841182i	$0.681860\pi$
$348$	−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	$-0.286393\pi$
$353$	23.3659			1.24364			0.621821	+	0.783159i	$0.286393\pi$
$354$	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	$0.0412728\pi$
$359$			4.89975i			0.258599i	−0.991606	+	0.129299i	$0.958727\pi$
$360$	−0.276026	−	6.70252i	−0.0145478	−	0.353254i
$361$	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
$375$	−18.8547	+	4.41589i	−0.973653	+	0.228036i
$376$			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	$0.0620617\pi$
$383$			7.58312i			0.387480i	−0.981053	+	0.193740i	$0.937938\pi$
$384$	−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	$-0.865144\pi$
$389$		−	16.2164i		−	0.822203i	0.911590	−	0.411101i	$-0.134856\pi$
$390$	−12.4405	−	3.19891i	−0.629951	−	0.161983i
$391$	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
$399$	22.0730	−	10.1827i	1.10503	−	0.509773i
$400$	2.31662	+	4.43094i	0.115831	+	0.221547i
$401$	−21.5491			−1.07611			−0.538056	−	0.842909i	$-0.680841\pi$
$401$	−21.5491			−1.07611			−0.538056	+	0.842909i	$0.680841\pi$
$402$	−11.6082	+	3.50000i	−0.578964	+	0.174564i
$403$			8.67014i			0.431890i
$404$			14.3166i			0.712279i
$405$	−16.2986	+	11.8049i	−0.809882	+	0.586592i
$406$	−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	$-0.976263\pi$
$419$		−	3.05013i		−	0.149008i	0.997221	−	0.0745042i	$-0.0237374\pi$
$420$	−12.0771	−	3.10547i	−0.589304	−	0.151531i
$421$			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	$-0.361243\pi$
$431$	17.5320			0.844488			0.422244	+	0.906482i	$0.361243\pi$
$432$	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
$435$	7.96325	−	30.9690i	0.381809	−	1.48485i
$436$		−	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	$-0.597452\pi$
$443$	−12.6872			−0.602788			−0.301394	+	0.953500i	$0.597452\pi$
$444$	−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	$-0.719567\pi$
$449$	−26.9691			−1.27275			−0.636376	+	0.771379i	$0.719567\pi$
$450$	7.23567	−	13.1394i	0.341093	−	0.619400i
$451$			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
$456$	6.85551	−	3.16259i	0.321039	−	0.148102i
$457$			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	$0.167628\pi$
$461$			21.5831i			1.00523i	−0.864511	+	0.502613i	$0.832372\pi$
$462$	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
$465$	−9.80556	−	2.52136i	−0.454722	−	0.116925i
$466$		−	26.5857i		−	1.23156i
$467$	26.7774			1.23911			0.619555	−	0.784953i	$-0.287313\pi$
$467$	26.7774			1.23911			0.619555	+	0.784953i	$0.287313\pi$
$468$	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	$0.103629\pi$
$479$			14.0000i			0.639676i	−0.947472	+	0.319838i	$0.896371\pi$
$480$	−3.75096	−	0.964508i	−0.171207	−	0.0440236i
$481$	−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	$0.0608242\pi$
$491$			8.41688i			0.379848i	−0.981799	+	0.189924i	$0.939176\pi$
$492$	5.73801	+	19.0308i	0.258690	+	0.857977i
$493$	26.5831			1.19724
$494$	−2.00855	−	14.3166i	−0.0903687	−	0.644135i
$495$	1.19150	+	28.9323i	0.0535540	+	1.30041i
$496$			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	$-0.633994\pi$
$503$	−18.3294			−0.817266			−0.408633	+	0.912699i	$0.633994\pi$
$504$	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	$-0.463034\pi$
$509$	5.22829			0.231740			0.115870	+	0.993264i	$0.463034\pi$
$510$	12.0771	+	3.10547i	0.534785	+	0.137512i
$511$	5.84962			0.258772
$512$			1.00000i			0.0441942i
$513$	−19.2750	−	11.8942i	−0.851014	−	0.525143i
$514$	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	$-0.394036\pi$
$521$	14.9179			0.653564			0.326782	+	0.945100i	$0.394036\pi$
$522$	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
$525$	−19.5025	−	19.9288i	−0.851159	−	0.869766i
$526$		−	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
$540$	3.80900	+	10.9769i	0.163913	+	0.472369i
$541$	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
$555$	1.92902	−	7.50193i	0.0818822	−	0.318439i
$556$	10.0000			0.424094
$557$	13.7067			0.580771			0.290385	−	0.956910i	$-0.406217\pi$
$557$	13.7067			0.580771			0.290385	+	0.956910i	$0.406217\pi$
$558$	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	$-0.783029\pi$
$563$		−	29.8997i		−	1.26012i	0.776545	−	0.630062i	$-0.216971\pi$
$564$	−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	$-0.465046\pi$
$569$	5.22829			0.219181			0.109591	+	0.993977i	$0.465046\pi$
$570$	16.7756	+	1.89184i	0.702653	+	0.0792404i
$571$	−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
$585$	22.2298	−	0.915474i	0.919087	−	0.0378502i
$586$	−18.2665			−0.754582
$587$	16.3208			0.673632			0.336816	−	0.941570i	$-0.390650\pi$
$587$	16.3208			0.673632			0.336816	+	0.941570i	$0.390650\pi$
$588$	−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	$-0.638505\pi$
$593$	−20.5297			−0.843052			−0.421526	+	0.906816i	$0.638505\pi$
$594$	−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	$-0.366346\pi$
$599$	19.9544			0.815315			0.407658	+	0.913135i	$0.366346\pi$
$600$	−6.05716	−	6.18957i	−0.247282	−	0.252688i
$601$		−	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
$615$	−11.0687	+	43.0462i	−0.446334	+	1.73579i
$616$		−	13.8984i		−	0.559984i
$617$	18.9350			0.762293			0.381147	−	0.924515i	$-0.375529\pi$
$617$	18.9350			0.762293			0.381147	+	0.924515i	$0.375529\pi$
$618$	−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
$627$	−29.5927	+	13.6517i	−1.18182	+	0.545196i
$628$		−	7.65069i		−	0.305296i
$629$	6.43949			0.256759
$630$	21.5804	−	0.888733i	0.859784	−	0.0354080i
$631$	−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	$-0.498795\pi$
$641$	0.191748			0.00757358			0.00378679	+	0.999993i	$0.498795\pi$
$642$	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
$645$	14.3487	+	3.68957i	0.564980	+	0.145277i
$646$	1.94987	+	13.8984i	0.0767168	+	0.546826i
$647$	−0.605599			−0.0238086			−0.0119043	−	0.999929i	$-0.503789\pi$
$647$	−0.605599			−0.0238086			−0.0119043	+	0.999929i	$0.503789\pi$
$648$	−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	$-0.426684\pi$
$653$	11.6678			0.456595			0.228298	+	0.973591i	$0.426684\pi$
$654$	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	$-0.642020\pi$
$659$	−22.1547			−0.863025			−0.431513	+	0.902107i	$0.642020\pi$
$660$	16.1915	+	4.16342i	0.630253	+	0.162061i
$661$		−	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
$675$	−5.42927	+	25.4071i	−0.208973	+	0.977921i
$676$	2.00000			0.0769231
$677$			46.1662i			1.77431i	0.461469	+	0.887157i	$0.347323\pi$
$677$			46.1662i			1.77431i	−0.461469	+	0.887157i	$0.652677\pi$
$678$	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	$-0.848148\pi$
$683$		−	24.0000i		−	0.918334i	0.888350	−	0.459167i	$-0.151852\pi$
$684$	−9.78729	+	8.67231i	−0.374226	+	0.331594i
$685$	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
$690$	26.4259	+	6.79504i	1.00602	+	0.258683i
$691$	−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	$-0.751499\pi$
$701$		−	37.2665i		−	1.40754i	0.710430	−	0.703768i	$-0.248501\pi$
$702$	−11.0000	+	13.2665i	−0.415168	+	0.500712i
$703$	8.63325	−	1.21120i	0.325609	−	0.0456812i
$704$		−	4.31662i		−	0.162689i
$705$	8.54736	−	33.2406i	0.321912	−	1.25191i
$706$			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	$0.225554\pi$
$719$			34.8997i			1.30154i	−0.759274	+	0.650771i	$0.774446\pi$
$720$	6.70252	−	0.276026i	0.249788	−	0.0102869i
$721$			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
$735$	3.24726	−	12.6286i	0.119777	−	0.465811i
$736$		−	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
$741$	10.4891	+	22.7372i	0.385327	+	0.835271i
$742$			3.21974i			0.118201i
$743$			44.8496i			1.64537i	0.568495	+	0.822687i	$0.307526\pi$
$743$			44.8496i			1.64537i	−0.568495	+	0.822687i	$0.692474\pi$
$744$	−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
$750$	−4.41589	−	18.8547i	−0.161246	−	0.688476i
$751$		−	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	$-0.937972\pi$
$761$		−	10.6834i		−	0.387272i	0.981073	−	0.193636i	$-0.0620281\pi$
$762$	27.5831	−	8.31662i	0.999231	−	0.301280i
$763$	22.0660			0.798843
$764$			5.00000i			0.180894i
$765$	−21.5804	+	0.888733i	−0.780241	+	0.0321322i
$766$	−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	$0.143110\pi$
$773$			24.1662i			0.869200i	−0.900624	+	0.434600i	$0.856890\pi$
$774$	−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
$780$	3.19891	−	12.4405i	0.114539	−	0.445443i
$781$		−	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
$795$	−3.75096	−	0.964508i	−0.133033	−	0.0342076i
$796$	25.2164			0.893771
$797$			31.6332i			1.12051i	0.828321	+	0.560254i	$0.189296\pi$
$797$			31.6332i			1.12051i	−0.828321	+	0.560254i	$0.810704\pi$
$798$	10.1827	+	22.0730i	0.360464	+	0.781376i
$799$	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	$0.0109128\pi$
$809$			1.94987i			0.0685539i	−0.999412	+	0.0342770i	$0.989087\pi$
$810$	−11.8049	−	16.2986i	−0.414783	−	0.572673i
$811$			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	$-0.824625\pi$
$821$		−	30.0000i		−	1.04701i	0.852023	−	0.523504i	$-0.175375\pi$
$822$	−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
$825$	26.1465	+	26.7181i	0.910304	+	0.930204i
$826$	18.1662			0.632085
$827$		−	8.58312i		−	0.298464i	−0.988802	−	0.149232i	$-0.952320\pi$
$827$		−	8.58312i		−	0.298464i	0.988802	−	0.149232i	$-0.0476802\pi$
$828$	−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	$-0.533336\pi$
$839$	−6.05599			−0.209076			−0.104538	+	0.994521i	$0.533336\pi$
$840$	3.10547	−	12.0771i	0.107149	−	0.416701i
$841$	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
$855$	−28.7651	+	5.25054i	−0.983746	+	0.179565i
$856$	0.0501256			0.00171326
$857$		−	12.0000i		−	0.409912i	−0.978771	−	0.204956i	$-0.934295\pi$
$857$		−	12.0000i		−	0.409912i	0.978771	−	0.204956i	$-0.0657052\pi$
$858$	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	$0.0637217\pi$
$863$			11.6834i			0.397707i	−0.980029	+	0.198853i	$0.936278\pi$
$864$	−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
$870$	30.9690	+	7.96325i	1.04995	+	0.269980i
$871$	−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	$0.0863092\pi$
$881$			15.8997i			0.535676i	−0.963464	+	0.267838i	$0.913691\pi$
$882$	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
$885$	−5.44189	+	21.1635i	−0.182927	+	0.711402i
$886$		−	12.6872i		−	0.426236i
$887$		−	33.5831i		−	1.12761i	−0.825908	−	0.563805i	$-0.809337\pi$
$887$		−	33.5831i		−	1.12761i	0.825908	−	0.563805i	$-0.190663\pi$
$888$	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
$900$	13.1394	+	7.23567i	0.437982	+	0.241189i
$901$		−	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	$-0.631088\pi$
$911$	−24.1633			−0.800564			−0.400282	+	0.916392i	$0.631088\pi$
$912$	3.16259	+	6.85551i	0.104724	+	0.227009i
$913$			27.7969i			0.919942i
$914$	−27.1913			−0.899407
$915$	2.23440	−	8.68957i	0.0738671	−	0.287268i
$916$		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	$-0.904313\pi$
$929$		−	18.0501i		−	0.592205i	0.955156	−	0.296103i	$-0.0956871\pi$
$930$	2.52136	−	9.80556i	0.0826788	−	0.321537i
$931$	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	$-0.469686\pi$
$941$	5.83389			0.190179			0.0950897	+	0.995469i	$0.469686\pi$
$942$	3.82534	+	12.6872i	0.124636	+	0.413372i
$943$	−80.8496			−2.63283
$944$	5.64214			0.183636
$945$	−35.3427	+	12.2640i	−1.14970	+	0.398948i
$946$			16.5126i			0.536870i
$947$	18.9350			0.615304			0.307652	−	0.951499i	$-0.400457\pi$
$947$	18.9350			0.615304			0.307652	+	0.951499i	$0.400457\pi$
$948$	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	$-0.987537\pi$
$953$		−	2.41688i		−	0.0782903i	0.999234	−	0.0391451i	$-0.0124635\pi$
$954$	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
$960$	0.964508	−	3.75096i	0.0311294	−	0.121062i
$961$	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
$969$	−10.1827	−	22.0730i	−0.327116	−	0.709087i
$970$	−3.89975	+	6.43949i	−0.125213	+	0.206759i
$971$	8.03418			0.257829			0.128915	−	0.991656i	$-0.458851\pi$
$971$	8.03418			0.257829			0.128915	+	0.991656i	$0.458851\pi$
$972$	15.5000	+	1.65831i	0.497163	+	0.0531904i
$973$			32.1974i			1.03220i
$974$		−	36.5330i		−	1.17059i
$975$	20.5285	−	20.0893i	0.657438	−	0.643373i
$976$	−2.31662			−0.0741534
$977$			29.5831i			0.946448i	0.880942	+	0.473224i	$0.156910\pi$
$977$			29.5831i			0.946448i	−0.880942	+	0.473224i	$0.843090\pi$
$978$	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	$-0.857372\pi$
$983$		−	27.1662i		−	0.866469i	0.901281	−	0.433234i	$-0.142628\pi$
$984$	−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
$990$	−28.9323	+	1.19150i	−0.919528	+	0.0378684i
$991$		−	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.569.5	yes	8
3.2	odd	2	inner	570.2.c.c.569.4	yes	8
5.4	even	2		570.2.c.f.569.4	yes	8
15.14	odd	2		570.2.c.f.569.5	yes	8
19.18	odd	2		570.2.c.f.569.3	yes	8
57.56	even	2		570.2.c.f.569.6	yes	8
95.94	odd	2	inner	570.2.c.c.569.6	yes	8
285.284	even	2	inner	570.2.c.c.569.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.c.c.569.3	✓	8	285.284	even	2	inner
570.2.c.c.569.4	yes	8	3.2	odd	2	inner
570.2.c.c.569.5	yes	8	1.1	even	1	trivial
570.2.c.c.569.6	yes	8	95.94	odd	2	inner
570.2.c.f.569.3	yes	8	19.18	odd	2
570.2.c.f.569.4	yes	8	5.4	even	2
570.2.c.f.569.5	yes	8	15.14	odd	2
570.2.c.f.569.6	yes	8	57.56	even	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} +(-0.964508 + 3.75096i) 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} +(-3.75096 - 0.964508i) 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} +(6.70252 - 0.276026i) 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} +(3.16259 + 6.85551i) q^{57} -8.25629i q^{58} +5.64214 q^{59} +(0.964508 - 3.75096i) 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} +(6.18957 - 6.05716i) 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} +(0.276026 + 6.70252i) 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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