LMFDB - Embedded newform 546.2.g.d.209.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(209,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("546.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.g (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 4x^{10} - 8x^{8} + 26x^{7} - 50x^{6} + 78x^{5} - 72x^{4} + 324x^{2} - 486x + 729 $ x^12 - 2x^11 + 4x^10 - 8x^8 + 26x^7 - 50x^6 + 78x^5 - 72x^4 + 324x^2 - 486*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			209.6
Root			$0.146987 + 1.72580i$ of defining polynomial
Character	$\chi$	$=$	546.209
Dual form			546.2.g.d.209.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.72580 + 0.146987i) q^{3} -1.00000 q^{4} -3.83276 q^{5} +(0.146987 - 1.72580i) q^{6} +(-0.655092 + 2.56337i) q^{7} +1.00000i q^{8} +(2.95679 + 0.507343i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.72580 + 0.146987i) q^{3} -1.00000 q^{4} -3.83276 q^{5} +(0.146987 - 1.72580i) q^{6} +(-0.655092 + 2.56337i) q^{7} +1.00000i q^{8} +(2.95679 + 0.507343i) q^{9} +3.83276i q^{10} +3.53879i q^{11} +(-1.72580 - 0.146987i) q^{12} +1.00000i q^{13} +(2.56337 + 0.655092i) q^{14} +(-6.61459 - 0.563368i) q^{15} +1.00000 q^{16} -6.47987 q^{17} +(0.507343 - 2.95679i) q^{18} +1.55008i q^{19} +3.83276 q^{20} +(-1.50734 + 4.32758i) q^{21} +3.53879 q^{22} +3.87495i q^{23} +(-0.146987 + 1.72580i) q^{24} +9.69005 q^{25} +1.00000 q^{26} +(5.02826 + 1.31018i) q^{27} +(0.655092 - 2.56337i) q^{28} -6.70339i q^{29} +(-0.563368 + 6.61459i) q^{30} +9.76102i q^{31} -1.00000i q^{32} +(-0.520157 + 6.10725i) q^{33} +6.47987i q^{34} +(2.51081 - 9.82477i) q^{35} +(-2.95679 - 0.507343i) q^{36} -0.597183 q^{37} +1.55008 q^{38} +(-0.146987 + 1.72580i) q^{39} -3.83276i q^{40} +11.0403 q^{41} +(4.32758 + 1.50734i) q^{42} -0.604159 q^{43} -3.53879i q^{44} +(-11.3327 - 1.94452i) q^{45} +3.87495 q^{46} -12.5799 q^{47} +(1.72580 + 0.146987i) q^{48} +(-6.14171 - 3.35848i) q^{49} -9.69005i q^{50} +(-11.1830 - 0.952459i) q^{51} -1.00000i q^{52} -6.84142i q^{53} +(1.31018 - 5.02826i) q^{54} -13.5633i q^{55} +(-2.56337 - 0.655092i) q^{56} +(-0.227842 + 2.67513i) q^{57} -6.70339 q^{58} -1.74126 q^{59} +(6.61459 + 0.563368i) q^{60} +5.28005i q^{61} +9.76102 q^{62} +(-3.23748 + 7.24698i) q^{63} -1.00000 q^{64} -3.83276i q^{65} +(6.10725 + 0.520157i) q^{66} +5.39566 q^{67} +6.47987 q^{68} +(-0.569569 + 6.68740i) q^{69} +(-9.82477 - 2.51081i) q^{70} +9.18326i q^{71} +(-0.507343 + 2.95679i) q^{72} -11.6727i q^{73} +0.597183i q^{74} +(16.7231 + 1.42432i) q^{75} -1.55008i q^{76} +(-9.07121 - 2.31823i) q^{77} +(1.72580 + 0.146987i) q^{78} -3.29905 q^{79} -3.83276 q^{80} +(8.48521 + 3.00021i) q^{81} -11.0403i q^{82} -2.06179 q^{83} +(1.50734 - 4.32758i) q^{84} +24.8358 q^{85} +0.604159i q^{86} +(0.985315 - 11.5687i) q^{87} -3.53879 q^{88} -1.46706 q^{89} +(-1.94452 + 11.3327i) q^{90} +(-2.56337 - 0.655092i) q^{91} -3.87495i q^{92} +(-1.43475 + 16.8456i) q^{93} +12.5799i q^{94} -5.94108i q^{95} +(0.146987 - 1.72580i) q^{96} -10.3490i q^{97} +(-3.35848 + 6.14171i) q^{98} +(-1.79538 + 10.4634i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} - 12 q^{4} - 4 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9}+O(q^{10}) $ 12 * q + 2 * q^3 - 12 * q^4 - 4 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9	$ 12 q + 2 q^{3} - 12 q^{4} - 4 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9} - 2 q^{12} + 10 q^{14} + 4 q^{15} + 12 q^{16} + 12 q^{17} + 8 q^{18} + 4 q^{20} - 20 q^{21} - 2 q^{24} + 20 q^{25} + 12 q^{26} + 8 q^{27} + 8 q^{28} + 14 q^{30} + 46 q^{33} - 22 q^{35} - 4 q^{36} + 16 q^{37} - 8 q^{38} - 2 q^{39} + 28 q^{41} + 4 q^{42} - 8 q^{43} + 24 q^{46} - 68 q^{47} + 2 q^{48} + 26 q^{49} - 50 q^{51} + 16 q^{54} - 10 q^{56} - 28 q^{57} - 24 q^{58} + 8 q^{59} - 4 q^{60} + 16 q^{62} - 2 q^{63} - 12 q^{64} - 12 q^{66} + 8 q^{67} - 12 q^{68} - 24 q^{69} - 28 q^{70} - 8 q^{72} + 92 q^{75} - 8 q^{77} + 2 q^{78} + 36 q^{79} - 4 q^{80} + 16 q^{81} - 32 q^{83} + 20 q^{84} + 8 q^{87} - 48 q^{89} + 2 q^{90} - 10 q^{91} + 8 q^{93} + 2 q^{96} + 16 q^{98}+O(q^{100}) $ 12 * q + 2 * q^3 - 12 * q^4 - 4 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9 - 2 * q^12 + 10 * q^14 + 4 * q^15 + 12 * q^16 + 12 * q^17 + 8 * q^18 + 4 * q^20 - 20 * q^21 - 2 * q^24 + 20 * q^25 + 12 * q^26 + 8 * q^27 + 8 * q^28 + 14 * q^30 + 46 * q^33 - 22 * q^35 - 4 * q^36 + 16 * q^37 - 8 * q^38 - 2 * q^39 + 28 * q^41 + 4 * q^42 - 8 * q^43 + 24 * q^46 - 68 * q^47 + 2 * q^48 + 26 * q^49 - 50 * q^51 + 16 * q^54 - 10 * q^56 - 28 * q^57 - 24 * q^58 + 8 * q^59 - 4 * q^60 + 16 * q^62 - 2 * q^63 - 12 * q^64 - 12 * q^66 + 8 * q^67 - 12 * q^68 - 24 * q^69 - 28 * q^70 - 8 * q^72 + 92 * q^75 - 8 * q^77 + 2 * q^78 + 36 * q^79 - 4 * q^80 + 16 * q^81 - 32 * q^83 + 20 * q^84 + 8 * q^87 - 48 * q^89 + 2 * q^90 - 10 * q^91 + 8 * q^93 + 2 * q^96 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$1$

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
$3$	1.72580	+	0.146987i	0.996393	+	0.0848633i
$3$	1.72580	+	0.146987i	0.996393	+	0.0848633i
$4$	−1.00000			−0.500000
$5$	−3.83276			−1.71406			−0.857031	−	0.515264i	$-0.827694\pi$
$5$	−3.83276			−1.71406			−0.857031	+	0.515264i	$0.827694\pi$
$6$	0.146987	−	1.72580i	0.0600074	−	0.704556i
$7$	−0.655092	+	2.56337i	−0.247602	+	0.968862i
$7$	−0.655092	+	2.56337i	−0.247602	+	0.968862i
$8$			1.00000i			0.353553i
$9$	2.95679	+	0.507343i	0.985596	+	0.169114i
$10$			3.83276i			1.21203i
$11$			3.53879i			1.06698i	0.845805	+	0.533492i	$0.179121\pi$
$11$			3.53879i			1.06698i	−0.845805	+	0.533492i	$0.820879\pi$
$12$	−1.72580	−	0.146987i	−0.498196	−	0.0424316i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	2.56337	+	0.655092i	0.685089	+	0.175081i
$15$	−6.61459	−	0.563368i	−1.70788	−	0.145461i
$16$	1.00000			0.250000
$17$	−6.47987			−1.57160			−0.785799	−	0.618482i	$-0.787748\pi$
$17$	−6.47987			−1.57160			−0.785799	+	0.618482i	$0.787748\pi$
$18$	0.507343	−	2.95679i	0.119582	−	0.696922i
$19$			1.55008i			0.355612i	0.984066	+	0.177806i	$0.0569000\pi$
$19$			1.55008i			0.355612i	−0.984066	+	0.177806i	$0.943100\pi$
$20$	3.83276			0.857031
$21$	−1.50734	+	4.32758i	−0.328929	+	0.944355i
$22$	3.53879			0.754472
$23$			3.87495i			0.807983i	0.914763	+	0.403991i	$0.132377\pi$
$23$			3.87495i			0.807983i	−0.914763	+	0.403991i	$0.867623\pi$
$24$	−0.146987	+	1.72580i	−0.0300037	+	0.352278i
$25$	9.69005			1.93801
$26$	1.00000			0.196116
$27$	5.02826	+	1.31018i	0.967689	+	0.252145i
$28$	0.655092	−	2.56337i	0.123801	−	0.484431i
$29$		−	6.70339i		−	1.24479i	−0.782704	−	0.622394i	$-0.786160\pi$
$29$		−	6.70339i		−	1.24479i	0.782704	−	0.622394i	$-0.213840\pi$
$30$	−0.563368	+	6.61459i	−0.102856	+	1.20765i
$31$			9.76102i			1.75313i	0.481282	+	0.876566i	$0.340171\pi$
$31$			9.76102i			1.75313i	−0.481282	+	0.876566i	$0.659829\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.520157	+	6.10725i	−0.0905477	+	1.06313i
$34$			6.47987i			1.11129i
$35$	2.51081	−	9.82477i	0.424405	−	1.66069i
$36$	−2.95679	−	0.507343i	−0.492798	−	0.0845571i
$37$	−0.597183			−0.0981763			−0.0490882	−	0.998794i	$-0.515632\pi$
$37$	−0.597183			−0.0981763			−0.0490882	+	0.998794i	$0.515632\pi$
$38$	1.55008			0.251456
$39$	−0.146987	+	1.72580i	−0.0235368	+	0.276350i
$40$		−	3.83276i		−	0.606013i
$41$	11.0403			1.72421			0.862104	−	0.506732i	$-0.169147\pi$
$41$	11.0403			1.72421			0.862104	+	0.506732i	$0.169147\pi$
$42$	4.32758	+	1.50734i	0.667760	+	0.232588i
$43$	−0.604159			−0.0921334			−0.0460667	−	0.998938i	$-0.514669\pi$
$43$	−0.604159			−0.0921334			−0.0460667	+	0.998938i	$0.514669\pi$
$44$		−	3.53879i		−	0.533492i
$45$	−11.3327	−	1.94452i	−1.68937	−	0.289872i
$46$	3.87495			0.571330
$47$	−12.5799			−1.83496			−0.917481	−	0.397780i	$-0.869781\pi$
$47$	−12.5799			−1.83496			−0.917481	+	0.397780i	$0.869781\pi$
$48$	1.72580	+	0.146987i	0.249098	+	0.0212158i
$49$	−6.14171	−	3.35848i	−0.877387	−	0.479783i
$50$		−	9.69005i		−	1.37038i
$51$	−11.1830	−	0.952459i	−1.56593	−	0.133371i
$52$		−	1.00000i		−	0.138675i
$53$		−	6.84142i		−	0.939741i	−0.882735	−	0.469871i	$-0.844301\pi$
$53$		−	6.84142i		−	0.939741i	0.882735	−	0.469871i	$-0.155699\pi$
$54$	1.31018	−	5.02826i	0.178294	−	0.684260i
$55$		−	13.5633i		−	1.82888i
$56$	−2.56337	−	0.655092i	−0.342544	−	0.0875404i
$57$	−0.227842	+	2.67513i	−0.0301784	+	0.354330i
$58$	−6.70339			−0.880199
$59$	−1.74126			−0.226693			−0.113347	−	0.993556i	$-0.536157\pi$
$59$	−1.74126			−0.226693			−0.113347	+	0.993556i	$0.536157\pi$
$60$	6.61459	+	0.563368i	0.853940	+	0.0727305i
$61$			5.28005i			0.676041i	0.941139	+	0.338020i	$0.109757\pi$
$61$			5.28005i			0.676041i	−0.941139	+	0.338020i	$0.890243\pi$
$62$	9.76102			1.23965
$63$	−3.23748	+	7.24698i	−0.407884	+	0.913034i
$64$	−1.00000			−0.125000
$65$		−	3.83276i		−	0.475395i
$66$	6.10725	+	0.520157i	0.751750	+	0.0640269i
$67$	5.39566			0.659184			0.329592	−	0.944123i	$-0.393089\pi$
$67$	5.39566			0.659184			0.329592	+	0.944123i	$0.393089\pi$
$68$	6.47987			0.785799
$69$	−0.569569	+	6.68740i	−0.0685680	+	0.805068i
$70$	−9.82477	−	2.51081i	−1.17429	−	0.300099i
$71$			9.18326i			1.08985i	0.838484	+	0.544926i	$0.183442\pi$
$71$			9.18326i			1.08985i	−0.838484	+	0.544926i	$0.816558\pi$
$72$	−0.507343	+	2.95679i	−0.0597909	+	0.348461i
$73$		−	11.6727i		−	1.36619i	−0.730329	−	0.683095i	$-0.760633\pi$
$73$		−	11.6727i		−	1.36619i	0.730329	−	0.683095i	$-0.239367\pi$
$74$			0.597183i			0.0694211i
$75$	16.7231	+	1.42432i	1.93102	+	0.164466i
$76$		−	1.55008i		−	0.177806i
$77$	−9.07121	−	2.31823i	−1.03376	−	0.264187i
$78$	1.72580	+	0.146987i	0.195409	+	0.0166431i
$79$	−3.29905			−0.371172			−0.185586	−	0.982628i	$-0.559418\pi$
$79$	−3.29905			−0.371172			−0.185586	+	0.982628i	$0.559418\pi$
$80$	−3.83276			−0.428516
$81$	8.48521	+	3.00021i	0.942801	+	0.333357i
$82$		−	11.0403i		−	1.21920i
$83$	−2.06179			−0.226311			−0.113155	−	0.993577i	$-0.536096\pi$
$83$	−2.06179			−0.226311			−0.113155	+	0.993577i	$0.536096\pi$
$84$	1.50734	−	4.32758i	0.164465	−	0.472177i
$85$	24.8358			2.69382
$86$			0.604159i			0.0651482i
$87$	0.985315	−	11.5687i	0.105637	−	1.24030i
$88$	−3.53879			−0.377236
$89$	−1.46706			−0.155508			−0.0777538	−	0.996973i	$-0.524775\pi$
$89$	−1.46706			−0.155508			−0.0777538	+	0.996973i	$0.524775\pi$
$90$	−1.94452	+	11.3327i	−0.204971	+	1.19457i
$91$	−2.56337	−	0.655092i	−0.268714	−	0.0686723i
$92$		−	3.87495i		−	0.403991i
$93$	−1.43475	+	16.8456i	−0.148776	+	1.74681i
$94$			12.5799i			1.29751i
$95$		−	5.94108i		−	0.609542i
$96$	0.146987	−	1.72580i	0.0150018	−	0.176139i
$97$		−	10.3490i		−	1.05078i	−0.850862	−	0.525390i	$-0.823920\pi$
$97$		−	10.3490i		−	1.05078i	0.850862	−	0.525390i	$-0.176080\pi$
$98$	−3.35848	+	6.14171i	−0.339258	+	0.620406i
$99$	−1.79538	+	10.4634i	−0.180442	+	1.05162i
$100$	−9.69005			−0.969005
$101$	10.9143			1.08602			0.543009	−	0.839727i	$-0.317285\pi$
$101$	10.9143			1.08602			0.543009	+	0.839727i	$0.317285\pi$
$102$	−0.952459	+	11.1830i	−0.0943075	+	1.10728i
$103$			0.598318i			0.0589540i	0.999565	+	0.0294770i	$0.00938419\pi$
$103$			0.598318i			0.0589540i	−0.999565	+	0.0294770i	$0.990616\pi$
$104$	−1.00000			−0.0980581
$105$	5.77728	−	16.5866i	0.563805	−	1.61868i
$106$	−6.84142			−0.664498
$107$			12.7010i			1.22785i	0.789364	+	0.613926i	$0.210411\pi$
$107$			12.7010i			1.22785i	−0.789364	+	0.613926i	$0.789589\pi$
$108$	−5.02826	−	1.31018i	−0.483845	−	0.126073i
$109$	−5.62257			−0.538545			−0.269272	−	0.963064i	$-0.586783\pi$
$109$	−5.62257			−0.538545			−0.269272	+	0.963064i	$0.586783\pi$
$110$	−13.5633			−1.29321
$111$	−1.03062	−	0.0877784i	−0.0978221	−	0.00833156i
$112$	−0.655092	+	2.56337i	−0.0619004	+	0.242215i
$113$			10.6609i			1.00289i	0.865190	+	0.501445i	$0.167198\pi$
$113$			10.6609i			1.00289i	−0.865190	+	0.501445i	$0.832802\pi$
$114$	2.67513	+	0.227842i	0.250549	+	0.0213394i
$115$		−	14.8518i		−	1.38493i
$116$			6.70339i			0.622394i
$117$	−0.507343	+	2.95679i	−0.0469038	+	0.273355i
$118$			1.74126i			0.160296i
$119$	4.24491	−	16.6103i	0.389130	−	1.52266i
$120$	0.563368	−	6.61459i	0.0514282	−	0.603827i
$121$	−1.52300			−0.138455
$122$	5.28005			0.478033
$123$	19.0534	+	1.62279i	1.71799	+	0.146322i
$124$		−	9.76102i		−	0.876566i
$125$	−17.9759			−1.60781
$126$	7.24698	+	3.23748i	0.645612	+	0.288417i
$127$	4.95442			0.439634			0.219817	−	0.975541i	$-0.429454\pi$
$127$	4.95442			0.439634			0.219817	+	0.975541i	$0.429454\pi$
$128$			1.00000i			0.0883883i
$129$	−1.04266	−	0.0888038i	−0.0918011	−	0.00781874i
$130$	−3.83276			−0.336155
$131$	9.02449			0.788474			0.394237	−	0.919009i	$-0.371009\pi$
$131$	9.02449			0.788474			0.394237	+	0.919009i	$0.371009\pi$
$132$	0.520157	−	6.10725i	0.0452739	−	0.531567i
$133$	−3.97342	−	1.01544i	−0.344539	−	0.0880502i
$134$		−	5.39566i		−	0.466114i
$135$	−19.2721	−	5.02162i	−1.65868	−	0.432192i
$136$		−	6.47987i		−	0.555644i
$137$		−	4.15721i		−	0.355174i	−0.984105	−	0.177587i	$-0.943171\pi$
$137$		−	4.15721i		−	0.355174i	0.984105	−	0.177587i	$-0.0568292\pi$
$138$	6.68740	+	0.569569i	0.569269	+	0.0484849i
$139$		−	0.0159714i		−	0.00135467i	−1.00000		0.000677337i	$-0.999784\pi$
$139$		−	0.0159714i		−	0.00135467i	1.00000		0.000677337i	$-0.000215603\pi$
$140$	−2.51081	+	9.82477i	−0.212202	+	0.830345i
$141$	−21.7104	−	1.84908i	−1.82834	−	0.155721i
$142$	9.18326			0.770642
$143$	−3.53879			−0.295928
$144$	2.95679	+	0.507343i	0.246399	+	0.0422786i
$145$			25.6925i			2.13365i
$146$	−11.6727			−0.966042
$147$	−10.1057	−	6.69884i	−0.833506	−	0.552511i
$148$	0.597183			0.0490882
$149$			10.5043i			0.860548i	0.902698	+	0.430274i	$0.141583\pi$
$149$			10.5043i			0.860548i	−0.902698	+	0.430274i	$0.858417\pi$
$150$	1.42432	−	16.7231i	0.116295	−	1.36544i
$151$	−7.95857			−0.647659			−0.323830	−	0.946115i	$-0.604970\pi$
$151$	−7.95857			−0.647659			−0.323830	+	0.946115i	$0.604970\pi$
$152$	−1.55008			−0.125728
$153$	−19.1596	−	3.28751i	−1.54896	−	0.265780i
$154$	−2.31823	+	9.07121i	−0.186808	+	0.730979i
$155$		−	37.4117i		−	3.00498i
$156$	0.146987	−	1.72580i	0.0117684	−	0.138175i
$157$			4.29431i			0.342723i	0.985208	+	0.171362i	$0.0548167\pi$
$157$			4.29431i			0.342723i	−0.985208	+	0.171362i	$0.945183\pi$
$158$			3.29905i			0.262458i
$159$	1.00560	−	11.8069i	0.0797495	−	0.936351i
$160$			3.83276i			0.303006i
$161$	−9.93292	−	2.53845i	−0.782824	−	0.200058i
$162$	3.00021	−	8.48521i	0.235719	−	0.666661i
$163$	18.5687			1.45442			0.727208	−	0.686418i	$-0.240818\pi$
$163$	18.5687			1.45442			0.727208	+	0.686418i	$0.240818\pi$
$164$	−11.0403			−0.862104
$165$	1.99364	−	23.4076i	0.155204	−	1.82228i
$166$			2.06179i			0.160026i
$167$	10.6873			0.827005			0.413503	−	0.910503i	$-0.364305\pi$
$167$	10.6873			0.827005			0.413503	+	0.910503i	$0.364305\pi$
$168$	−4.32758	−	1.50734i	−0.333880	−	0.116294i
$169$	−1.00000			−0.0769231
$170$		−	24.8358i		−	1.90482i
$171$	−0.786421	+	4.58326i	−0.0601391	+	0.350490i
$172$	0.604159			0.0460667
$173$	13.4395			1.02179			0.510894	−	0.859644i	$-0.329314\pi$
$173$	13.4395			1.02179			0.510894	+	0.859644i	$0.329314\pi$
$174$	−11.5687	−	0.985315i	−0.877023	−	0.0746965i
$175$	−6.34788	+	24.8392i	−0.479854	+	1.87766i
$176$			3.53879i			0.266746i
$177$	−3.00508	−	0.255944i	−0.225875	−	0.0192379i
$178$			1.46706i			0.109960i
$179$			6.55533i			0.489969i	0.969527	+	0.244984i	$0.0787828\pi$
$179$			6.55533i			0.489969i	−0.969527	+	0.244984i	$0.921217\pi$
$180$	11.3327	+	1.94452i	0.844687	+	0.144936i
$181$		−	17.1646i		−	1.27583i	−0.770106	−	0.637916i	$-0.779797\pi$
$181$		−	17.1646i		−	1.27583i	0.770106	−	0.637916i	$-0.220203\pi$
$182$	−0.655092	+	2.56337i	−0.0485587	+	0.190009i
$183$	−0.776101	+	9.11232i	−0.0573710	+	0.673602i
$184$	−3.87495			−0.285665
$185$	2.28886			0.168280
$186$	16.8456	+	1.43475i	1.23518	+	0.105201i
$187$		−	22.9309i		−	1.67687i
$188$	12.5799			0.917481
$189$	−6.65246	+	12.0310i	−0.483895	+	0.875126i
$190$	−5.94108			−0.431011
$191$		−	9.04802i		−	0.654692i	−0.944905	−	0.327346i	$-0.893846\pi$
$191$		−	9.04802i		−	0.654692i	0.944905	−	0.327346i	$-0.106154\pi$
$192$	−1.72580	−	0.146987i	−0.124549	−	0.0106079i
$193$	−6.04974			−0.435470			−0.217735	−	0.976008i	$-0.569867\pi$
$193$	−6.04974			−0.435470			−0.217735	+	0.976008i	$0.569867\pi$
$194$	−10.3490			−0.743013
$195$	0.563368	−	6.61459i	0.0403436	−	0.473681i
$196$	6.14171	+	3.35848i	0.438693	+	0.239892i
$197$			1.88643i			0.134402i	0.997739	+	0.0672011i	$0.0214069\pi$
$197$			1.88643i			0.134402i	−0.997739	+	0.0672011i	$0.978593\pi$
$198$	10.4634	+	1.79538i	0.743605	+	0.127592i
$199$			11.4529i			0.811877i	0.913900	+	0.405939i	$0.133055\pi$
$199$			11.4529i			0.811877i	−0.913900	+	0.405939i	$0.866945\pi$
$200$			9.69005i			0.685190i
$201$	9.31184	+	0.793094i	0.656806	+	0.0559405i
$202$		−	10.9143i		−	0.767930i
$203$	17.1833	+	4.39134i	1.20603	+	0.308212i
$204$	11.1830	+	0.952459i	0.782965	+	0.0666855i
$205$	−42.3149			−2.95540
$206$	0.598318			0.0416868
$207$	−1.96593	+	11.4574i	−0.136641	+	0.796345i
$208$			1.00000i			0.0693375i
$209$	−5.48540			−0.379433
$210$	−16.5866	−	5.77728i	−1.14458	−	0.398670i
$211$	16.5318			1.13810			0.569048	−	0.822305i	$-0.307312\pi$
$211$	16.5318			1.13810			0.569048	+	0.822305i	$0.307312\pi$
$212$			6.84142i			0.469871i
$213$	−1.34982	+	15.8485i	−0.0924884	+	1.08592i
$214$	12.7010			0.868222
$215$	2.31560			0.157922
$216$	−1.31018	+	5.02826i	−0.0891468	+	0.342130i
$217$	−25.0211	−	6.39437i	−1.69854	−	0.434078i
$218$			5.62257i			0.380809i
$219$	1.71575	−	20.1448i	0.115939	−	1.36126i
$220$			13.5633i			0.914439i
$221$		−	6.47987i		−	0.435883i
$222$	−0.0877784	+	1.03062i	−0.00589130	+	0.0691707i
$223$			10.9849i			0.735601i	0.929905	+	0.367800i	$0.119889\pi$
$223$			10.9849i			0.735601i	−0.929905	+	0.367800i	$0.880111\pi$
$224$	2.56337	+	0.655092i	0.171272	+	0.0437702i
$225$	28.6514	+	4.91618i	1.91010	+	0.327745i
$226$	10.6609			0.709150
$227$	18.3687			1.21918			0.609588	−	0.792718i	$-0.291335\pi$
$227$	18.3687			1.21918			0.609588	+	0.792718i	$0.291335\pi$
$228$	0.227842	−	2.67513i	0.0150892	−	0.177165i
$229$			8.77152i			0.579638i	0.957081	+	0.289819i	$0.0935952\pi$
$229$			8.77152i			0.579638i	−0.957081	+	0.289819i	$0.906405\pi$
$230$	−14.8518			−0.979295
$231$	−15.3144	−	5.33416i	−1.00761	−	0.350962i
$232$	6.70339			0.440099
$233$			25.7318i			1.68574i	0.538114	+	0.842872i	$0.319137\pi$
$233$			25.7318i			1.68574i	−0.538114	+	0.842872i	$0.680863\pi$
$234$	2.95679	+	0.507343i	0.193291	+	0.0331660i
$235$	48.2156			3.14524
$236$	1.74126			0.113347
$237$	−5.69351	−	0.484919i	−0.369833	−	0.0314989i
$238$	−16.6103	−	4.24491i	−1.07668	−	0.275157i
$239$			12.7421i			0.824221i	0.911134	+	0.412111i	$0.135208\pi$
$239$			12.7421i			0.824221i	−0.911134	+	0.412111i	$0.864792\pi$
$240$	−6.61459	−	0.563368i	−0.426970	−	0.0363652i
$241$		−	13.1363i		−	0.846184i	−0.906087	−	0.423092i	$-0.860945\pi$
$241$		−	13.1363i		−	0.846184i	0.906087	−	0.423092i	$-0.139055\pi$
$242$			1.52300i			0.0979024i
$243$	14.2028	+	6.42499i	0.911110	+	0.412163i
$244$		−	5.28005i		−	0.338020i
$245$	23.5397	+	12.8723i	1.50390	+	0.822379i
$246$	1.62279	−	19.0534i	0.103465	−	1.21480i
$247$	−1.55008			−0.0986292
$248$	−9.76102			−0.619826
$249$	−3.55824	−	0.303057i	−0.225494	−	0.0192055i
$250$			17.9759i			1.13689i
$251$	20.8113			1.31359			0.656797	−	0.754067i	$-0.271911\pi$
$251$	20.8113			1.31359			0.656797	+	0.754067i	$0.271911\pi$
$252$	3.23748	−	7.24698i	0.203942	−	0.456517i
$253$	−13.7126			−0.862105
$254$		−	4.95442i		−	0.310868i
$255$	42.8617	+	3.65055i	2.68410	+	0.228606i
$256$	1.00000			0.0625000
$257$	−14.9960			−0.935424			−0.467712	−	0.883881i	$-0.654922\pi$
$257$	−14.9960			−0.935424			−0.467712	+	0.883881i	$0.654922\pi$
$258$	−0.0888038	+	1.04266i	−0.00552869	+	0.0649132i
$259$	0.391210	−	1.53080i	0.0243086	−	0.0951193i
$260$			3.83276i			0.237698i
$261$	3.40092	−	19.8205i	0.210511	−	1.22686i
$262$		−	9.02449i		−	0.557535i
$263$		−	11.2324i		−	0.692621i	−0.938120	−	0.346310i	$-0.887434\pi$
$263$		−	11.2324i		−	0.692621i	0.938120	−	0.346310i	$-0.112566\pi$
$264$	−6.10725	−	0.520157i	−0.375875	−	0.0320135i
$265$			26.2215i			1.61078i
$266$	−1.01544	+	3.97342i	−0.0622609	+	0.243626i
$267$	−2.53185	−	0.215639i	−0.154947	−	0.0131969i
$268$	−5.39566			−0.329592
$269$	0.548970			0.0334713			0.0167356	−	0.999860i	$-0.494673\pi$
$269$	0.548970			0.0334713			0.0167356	+	0.999860i	$0.494673\pi$
$270$	−5.02162	+	19.2721i	−0.305606	+	1.17286i
$271$		−	17.9616i		−	1.09109i	−0.838082	−	0.545545i	$-0.816323\pi$
$271$		−	17.9616i		−	1.09109i	0.838082	−	0.545545i	$-0.183677\pi$
$272$	−6.47987			−0.392900
$273$	−4.32758	−	1.50734i	−0.261917	−	0.0912285i
$274$	−4.15721			−0.251146
$275$			34.2910i			2.06783i
$276$	0.569569	−	6.68740i	0.0342840	−	0.402534i
$277$	−9.40678			−0.565199			−0.282599	−	0.959238i	$-0.591197\pi$
$277$	−9.40678			−0.565199			−0.282599	+	0.959238i	$0.591197\pi$
$278$	−0.0159714			−0.000957899
$279$	−4.95218	+	28.8613i	−0.296480	+	1.72788i
$280$	9.82477	+	2.51081i	0.587143	+	0.150050i
$281$			28.3782i			1.69290i	0.532467	+	0.846451i	$0.321265\pi$
$281$			28.3782i			1.69290i	−0.532467	+	0.846451i	$0.678735\pi$
$282$	−1.84908	+	21.7104i	−0.110111	+	1.29283i
$283$			21.3006i			1.26619i	0.774075	+	0.633094i	$0.218215\pi$
$283$			21.3006i			1.26619i	−0.774075	+	0.633094i	$0.781785\pi$
$284$		−	9.18326i		−	0.544926i
$285$	0.873264	−	10.2531i	0.0517277	−	0.607343i
$286$			3.53879i			0.209253i
$287$	−7.23242	+	28.3004i	−0.426916	+	1.67052i
$288$	0.507343	−	2.95679i	0.0298955	−	0.174230i
$289$	24.9887			1.46992
$290$	25.6925			1.50872
$291$	1.52117	−	17.8603i	0.0891725	−	1.04699i
$292$			11.6727i			0.683095i
$293$	10.8691			0.634978			0.317489	−	0.948262i	$-0.397160\pi$
$293$	10.8691			0.634978			0.317489	+	0.948262i	$0.397160\pi$
$294$	−6.69884	+	10.1057i	−0.390684	+	0.589378i
$295$	6.67384			0.388566
$296$		−	0.597183i		−	0.0347106i
$297$	−4.63646	+	17.7939i	−0.269035	+	1.03251i
$298$	10.5043			0.608499
$299$	−3.87495			−0.224094
$300$	−16.7231	−	1.42432i	−0.965510	−	0.0822329i
$301$	0.395780	−	1.54868i	0.0228124	−	0.0892646i
$302$			7.95857i			0.457964i
$303$	18.8360	+	1.60427i	1.08210	+	0.0921630i
$304$			1.55008i			0.0889031i
$305$		−	20.2372i		−	1.15878i
$306$	−3.28751	+	19.1596i	−0.187935	+	1.09528i
$307$		−	8.05501i		−	0.459723i	−0.973223	−	0.229862i	$-0.926173\pi$
$307$		−	8.05501i		−	0.459723i	0.973223	−	0.229862i	$-0.0738274\pi$
$308$	9.07121	+	2.31823i	0.516880	+	0.132093i
$309$	−0.0879453	+	1.03258i	−0.00500303	+	0.0587414i
$310$	−37.4117			−2.12484
$311$	−2.09862			−0.119002			−0.0595009	−	0.998228i	$-0.518951\pi$
$311$	−2.09862			−0.119002			−0.0595009	+	0.998228i	$0.518951\pi$
$312$	−1.72580	−	0.146987i	−0.0977043	−	0.00832153i
$313$			16.8977i			0.955117i	0.878600	+	0.477559i	$0.158478\pi$
$313$			16.8977i			0.955117i	−0.878600	+	0.477559i	$0.841522\pi$
$314$	4.29431			0.242342
$315$	12.4085	−	27.7759i	0.699138	−	1.56500i
$316$	3.29905			0.185586
$317$		−	32.7364i		−	1.83866i	−0.393491	−	0.919328i	$-0.628733\pi$
$317$		−	32.7364i		−	1.83866i	0.393491	−	0.919328i	$-0.371267\pi$
$318$	−11.8069	−	1.00560i	−0.662100	−	0.0563914i
$319$	23.7219			1.32817
$320$	3.83276			0.214258
$321$	−1.86689	+	21.9194i	−0.104199	+	1.22342i
$322$	−2.53845	+	9.93292i	−0.141462	+	0.553540i
$323$		−	10.0443i		−	0.558880i
$324$	−8.48521	−	3.00021i	−0.471400	−	0.166678i
$325$			9.69005i			0.537507i
$326$		−	18.5687i		−	1.02843i
$327$	−9.70345	−	0.826448i	−0.536602	−	0.0457027i
$328$			11.0403i			0.609599i
$329$	8.24097	−	32.2468i	0.454339	−	1.77782i
$330$	−23.4076	−	1.99364i	−1.28855	−	0.109746i
$331$	−13.6138			−0.748283			−0.374142	−	0.927372i	$-0.622063\pi$
$331$	−13.6138			−0.748283			−0.374142	+	0.927372i	$0.622063\pi$
$332$	2.06179			0.113155
$333$	−1.76574	−	0.302977i	−0.0967622	−	0.0166030i
$334$		−	10.6873i		−	0.584781i
$335$	−20.6803			−1.12988
$336$	−1.50734	+	4.32758i	−0.0822323	+	0.236089i
$337$	−0.276737			−0.0150748			−0.00753740	−	0.999972i	$-0.502399\pi$
$337$	−0.276737			−0.0150748			−0.00753740	+	0.999972i	$0.502399\pi$
$338$			1.00000i			0.0543928i
$339$	−1.56701	+	18.3986i	−0.0851085	+	0.999272i
$340$	−24.8358			−1.34691
$341$	−34.5422			−1.87056
$342$	4.58326	+	0.786421i	0.247834	+	0.0425248i
$343$	12.6324	−	13.5433i	0.682086	−	0.731272i
$344$		−	0.604159i		−	0.0325741i
$345$	2.18302	−	25.6312i	0.117530	−	1.37994i
$346$		−	13.4395i		−	0.722513i
$347$			2.85298i			0.153156i	0.997064	+	0.0765780i	$0.0243994\pi$
$347$			2.85298i			0.153156i	−0.997064	+	0.0765780i	$0.975601\pi$
$348$	−0.985315	+	11.5687i	−0.0528184	+	0.620149i
$349$			9.55389i			0.511408i	0.966755	+	0.255704i	$0.0823073\pi$
$349$			9.55389i			0.511408i	−0.966755	+	0.255704i	$0.917693\pi$
$350$	24.8392	+	6.34788i	1.32771	+	0.339308i
$351$	−1.31018	+	5.02826i	−0.0699325	+	0.268389i
$352$	3.53879			0.188618
$353$	−10.7608			−0.572742			−0.286371	−	0.958119i	$-0.592449\pi$
$353$	−10.7608			−0.572742			−0.286371	+	0.958119i	$0.592449\pi$
$354$	−0.255944	+	3.00508i	−0.0136033	+	0.159718i
$355$		−	35.1972i		−	1.86808i
$356$	1.46706			0.0777538
$357$	9.76738	−	28.0421i	0.516945	−	1.48415i
$358$	6.55533			0.346460
$359$		−	24.5118i		−	1.29368i	−0.762624	−	0.646842i	$-0.776089\pi$
$359$		−	24.5118i		−	1.29368i	0.762624	−	0.646842i	$-0.223911\pi$
$360$	1.94452	−	11.3327i	0.102485	−	0.597284i
$361$	16.5973			0.873540
$362$	−17.1646			−0.902150
$363$	−2.62840	−	0.223862i	−0.137955	−	0.0117497i
$364$	2.56337	+	0.655092i	0.134357	+	0.0343362i
$365$			44.7388i			2.34174i
$366$	9.11232	+	0.776101i	0.476309	+	0.0405674i
$367$		−	18.6513i		−	0.973588i	−0.873517	−	0.486794i	$-0.838166\pi$
$367$		−	18.6513i		−	0.973588i	0.873517	−	0.486794i	$-0.161834\pi$
$368$			3.87495i			0.201996i
$369$	32.6439	+	5.60122i	1.69937	+	0.291588i
$370$		−	2.28886i		−	0.118992i
$371$	17.5371	+	4.48176i	0.910480	+	0.232681i
$372$	1.43475	−	16.8456i	0.0743882	−	0.873404i
$373$	4.55264			0.235727			0.117863	−	0.993030i	$-0.462396\pi$
$373$	4.55264			0.235727			0.117863	+	0.993030i	$0.462396\pi$
$374$	−22.9309			−1.18573
$375$	−31.0228	−	2.64223i	−1.60201	−	0.136444i
$376$		−	12.5799i		−	0.648757i
$377$	6.70339			0.345242
$378$	12.0310	+	6.65246i	0.618807	+	0.342166i
$379$	−14.4380			−0.741629			−0.370815	−	0.928707i	$-0.620922\pi$
$379$	−14.4380			−0.741629			−0.370815	+	0.928707i	$0.620922\pi$
$380$			5.94108i			0.304771i
$381$	8.55035	+	0.728238i	0.438048	+	0.0373087i
$382$	−9.04802			−0.462937
$383$	−19.0301			−0.972391			−0.486196	−	0.873850i	$-0.661616\pi$
$383$	−19.0301			−0.972391			−0.486196	+	0.873850i	$0.661616\pi$
$384$	−0.146987	+	1.72580i	−0.00750092	+	0.0880695i
$385$	34.7678	+	8.88522i	1.77193	+	0.452833i
$386$			6.04974i			0.307924i
$387$	−1.78637	−	0.306516i	−0.0908064	−	0.0155811i
$388$			10.3490i			0.525390i
$389$			1.06894i			0.0541973i	0.999633	+	0.0270986i	$0.00862682\pi$
$389$			1.06894i			0.0541973i	−0.999633	+	0.0270986i	$0.991373\pi$
$390$	−6.61459	−	0.563368i	−0.334943	−	0.0285272i
$391$		−	25.1092i		−	1.26982i
$392$	3.35848	−	6.14171i	0.169629	−	0.310203i
$393$	15.5745	+	1.32649i	0.785629	+	0.0669124i
$394$	1.88643			0.0950368
$395$	12.6445			0.636213
$396$	1.79538	−	10.4634i	0.0902211	−	0.525808i
$397$		−	5.70472i		−	0.286312i	−0.989700	−	0.143156i	$-0.954275\pi$
$397$		−	5.70472i		−	0.286312i	0.989700	−	0.143156i	$-0.0457250\pi$
$398$	11.4529			0.574084
$399$	−6.70809	−	2.33650i	−0.335824	−	0.116971i
$400$	9.69005			0.484503
$401$			25.1273i			1.25480i	0.778698	+	0.627399i	$0.215880\pi$
$401$			25.1273i			1.25480i	−0.778698	+	0.627399i	$0.784120\pi$
$402$	0.793094	−	9.31184i	0.0395559	−	0.464432i
$403$	−9.76102			−0.486231
$404$	−10.9143			−0.543009
$405$	−32.5218	−	11.4991i	−1.61602	−	0.571394i
$406$	4.39134	−	17.1833i	0.217939	−	0.852791i
$407$		−	2.11330i		−	0.104753i
$408$	0.952459	−	11.1830i	0.0471538	−	0.553640i
$409$		−	10.6907i		−	0.528619i	−0.964438	−	0.264310i	$-0.914856\pi$
$409$		−	10.6907i		−	0.528619i	0.964438	−	0.264310i	$-0.0851441\pi$
$410$			42.3149i			2.08978i
$411$	0.611058	−	7.17452i	0.0301412	−	0.353893i
$412$		−	0.598318i		−	0.0294770i
$413$	1.14069	−	4.46350i	0.0561296	−	0.219634i
$414$	11.4574	+	1.96593i	0.563101	+	0.0966200i
$415$	7.90235			0.387911
$416$	1.00000			0.0490290
$417$	0.00234759	−	0.0275634i	0.000114962	−	0.00134979i
$418$			5.48540i			0.268300i
$419$	11.5531			0.564406			0.282203	−	0.959355i	$-0.408935\pi$
$419$	11.5531			0.564406			0.282203	+	0.959355i	$0.408935\pi$
$420$	−5.77728	+	16.5866i	−0.281903	+	0.809341i
$421$	−4.18647			−0.204036			−0.102018	−	0.994783i	$-0.532530\pi$
$421$	−4.18647			−0.204036			−0.102018	+	0.994783i	$0.532530\pi$
$422$		−	16.5318i		−	0.804755i
$423$	−37.1960	−	6.38230i	−1.80853	−	0.310318i
$424$	6.84142			0.332249
$425$	−62.7903			−3.04577
$426$	15.8485	+	1.34982i	0.767862	+	0.0653992i
$427$	−13.5347	−	3.45892i	−0.654990	−	0.167389i
$428$		−	12.7010i		−	0.613926i
$429$	−6.10725	−	0.520157i	−0.294861	−	0.0251134i
$430$		−	2.31560i		−	0.111668i
$431$			30.3437i			1.46160i	0.682590	+	0.730802i	$0.260854\pi$
$431$			30.3437i			1.46160i	−0.682590	+	0.730802i	$0.739146\pi$
$432$	5.02826	+	1.31018i	0.241922	+	0.0630363i
$433$		−	7.90187i		−	0.379740i	−0.981809	−	0.189870i	$-0.939193\pi$
$433$		−	7.90187i		−	0.379740i	0.981809	−	0.189870i	$-0.0608066\pi$
$434$	−6.39437	+	25.0211i	−0.306940	+	1.20105i
$435$	−3.77647	+	44.3402i	−0.181068	+	2.12595i
$436$	5.62257			0.269272
$437$	−6.00648			−0.287329
$438$	−20.1448	−	1.71575i	−0.962558	−	0.0819815i
$439$			38.0804i			1.81748i	0.417364	+	0.908739i	$0.362954\pi$
$439$			38.0804i			1.81748i	−0.417364	+	0.908739i	$0.637046\pi$
$440$	13.5633			0.646606
$441$	−16.4558	−	13.0463i	−0.783611	−	0.621252i
$442$	−6.47987			−0.308216
$443$		−	4.75228i		−	0.225788i	−0.993607	−	0.112894i	$-0.963988\pi$
$443$		−	4.75228i		−	0.225788i	0.993607	−	0.112894i	$-0.0360120\pi$
$444$	1.03062	+	0.0877784i	0.0489111	+	0.00416578i
$445$	5.62287			0.266550
$446$	10.9849			0.520148
$447$	−1.54400	+	18.1284i	−0.0730289	+	0.857443i
$448$	0.655092	−	2.56337i	0.0309502	−	0.121108i
$449$		−	18.2285i		−	0.860257i	−0.902768	−	0.430129i	$-0.858468\pi$
$449$		−	18.2285i		−	0.860257i	0.902768	−	0.430129i	$-0.141532\pi$
$450$	4.91618	−	28.6514i	0.231751	−	1.35064i
$451$			39.0693i			1.83970i
$452$		−	10.6609i		−	0.501445i
$453$	−13.7349	−	1.16981i	−0.645323	−	0.0549625i
$454$		−	18.3687i		−	0.862088i
$455$	9.82477	+	2.51081i	0.460593	+	0.117709i
$456$	−2.67513	−	0.227842i	−0.125274	−	0.0106697i
$457$	−20.6866			−0.967677			−0.483838	−	0.875157i	$-0.660758\pi$
$457$	−20.6866			−0.967677			−0.483838	+	0.875157i	$0.660758\pi$
$458$	8.77152			0.409866
$459$	−32.5825	−	8.48982i	−1.52082	−	0.396271i
$460$			14.8518i			0.692466i
$461$	39.2144			1.82640			0.913198	−	0.407516i	$-0.133605\pi$
$461$	39.2144			1.82640			0.913198	+	0.407516i	$0.133605\pi$
$462$	−5.33416	+	15.3144i	−0.248168	+	0.712489i
$463$	−8.05138			−0.374179			−0.187090	−	0.982343i	$-0.559906\pi$
$463$	−8.05138			−0.374179			−0.187090	+	0.982343i	$0.559906\pi$
$464$		−	6.70339i		−	0.311197i
$465$	5.49905	−	64.5652i	0.255012	−	2.99414i
$466$	25.7318			1.19200
$467$	−5.39494			−0.249648			−0.124824	−	0.992179i	$-0.539837\pi$
$467$	−5.39494			−0.249648			−0.124824	+	0.992179i	$0.539837\pi$
$468$	0.507343	−	2.95679i	0.0234519	−	0.136678i
$469$	−3.53465	+	13.8311i	−0.163215	+	0.638659i
$470$		−	48.2156i		−	2.22402i
$471$	−0.631210	+	7.41114i	−0.0290846	+	0.341487i
$472$		−	1.74126i		−	0.0801481i
$473$		−	2.13799i		−	0.0983049i
$474$	−0.484919	+	5.69351i	−0.0222731	+	0.261512i
$475$			15.0203i			0.689181i
$476$	−4.24491	+	16.6103i	−0.194565	+	0.761331i
$477$	3.47094	−	20.2286i	0.158924	−	0.926206i
$478$	12.7421			0.582812
$479$	−20.6008			−0.941275			−0.470638	−	0.882327i	$-0.655976\pi$
$479$	−20.6008			−0.941275			−0.470638	+	0.882327i	$0.655976\pi$
$480$	−0.563368	+	6.61459i	−0.0257141	+	0.301913i
$481$		−	0.597183i		−	0.0272292i
$482$	−13.1363			−0.598343
$483$	−16.7691	−	5.84088i	−0.763022	−	0.265769i
$484$	1.52300			0.0692275
$485$			39.6651i			1.80110i
$486$	6.42499	−	14.2028i	0.291444	−	0.644252i
$487$	−15.7925			−0.715625			−0.357813	−	0.933793i	$-0.616477\pi$
$487$	−15.7925			−0.715625			−0.357813	+	0.933793i	$0.616477\pi$
$488$	−5.28005			−0.239017
$489$	32.0460	+	2.72937i	1.44917	+	0.123426i
$490$	12.8723	−	23.5397i	0.581510	−	1.06342i
$491$			20.4861i			0.924524i	0.886743	+	0.462262i	$0.152962\pi$
$491$			20.4861i			0.924524i	−0.886743	+	0.462262i	$0.847038\pi$
$492$	−19.0534	−	1.62279i	−0.858994	−	0.0731609i
$493$			43.4371i			1.95631i
$494$			1.55008i			0.0697413i
$495$	6.88125	−	40.1039i	0.309289	−	1.80254i
$496$			9.76102i			0.438283i
$497$	−23.5401	−	6.01588i	−1.05592	−	0.269849i
$498$	−0.303057	+	3.55824i	−0.0135803	+	0.159449i
$499$	−31.3034			−1.40133			−0.700667	−	0.713488i	$-0.747114\pi$
$499$	−31.3034			−1.40133			−0.700667	+	0.713488i	$0.747114\pi$
$500$	17.9759			0.803905
$501$	18.4441	+	1.57089i	0.824022	+	0.0701823i
$502$		−	20.8113i		−	0.928852i
$503$	12.1873			0.543404			0.271702	−	0.962381i	$-0.412414\pi$
$503$	12.1873			0.543404			0.271702	+	0.962381i	$0.412414\pi$
$504$	−7.24698	−	3.23748i	−0.322806	−	0.144209i
$505$	−41.8320			−1.86150
$506$			13.7126i			0.609600i
$507$	−1.72580	−	0.146987i	−0.0766456	−	0.00652794i
$508$	−4.95442			−0.219817
$509$	32.4560			1.43859			0.719293	−	0.694706i	$-0.244466\pi$
$509$	32.4560			1.43859			0.719293	+	0.694706i	$0.244466\pi$
$510$	3.65055	−	42.8617i	0.161649	−	1.89795i
$511$	29.9215	+	7.64672i	1.32365	+	0.338271i
$512$		−	1.00000i		−	0.0441942i
$513$	−2.03089	+	7.79420i	−0.0896659	+	0.344122i
$514$			14.9960i			0.661445i
$515$		−	2.29321i		−	0.101051i
$516$	1.04266	+	0.0888038i	0.0459005	+	0.00390937i
$517$		−	44.5174i		−	1.95787i
$518$	−1.53080	−	0.391210i	−0.0672595	−	0.0171888i
$519$	23.1940	+	1.97544i	1.01810	+	0.0867123i
$520$	3.83276			0.168078
$521$	−23.3355			−1.02235			−0.511174	−	0.859477i	$-0.670789\pi$
$521$	−23.3355			−1.02235			−0.511174	+	0.859477i	$0.670789\pi$
$522$	−19.8205	−	3.40092i	−0.867521	−	0.148854i
$523$		−	5.32316i		−	0.232765i	−0.993204	−	0.116383i	$-0.962870\pi$
$523$		−	5.32316i		−	0.232765i	0.993204	−	0.116383i	$-0.0371299\pi$
$524$	−9.02449			−0.394237
$525$	−14.6062	+	41.9344i	−0.637468	+	1.83017i
$526$	−11.2324			−0.489757
$527$		−	63.2501i		−	2.75522i
$528$	−0.520157	+	6.10725i	−0.0226369	+	0.265784i
$529$	7.98477			0.347164
$530$	26.2215			1.13899
$531$	−5.14855	−	0.883417i	−0.223428	−	0.0383370i
$532$	3.97342	+	1.01544i	0.172270	+	0.0440251i
$533$			11.0403i			0.478209i
$534$	−0.215639	+	2.53185i	−0.00933160	+	0.109564i
$535$		−	48.6799i		−	2.10461i
$536$			5.39566i			0.233057i
$537$	−0.963552	+	11.3132i	−0.0415803	+	0.488201i
$538$		−	0.548970i		−	0.0236678i
$539$	11.8850	−	21.7342i	0.511921	−	0.936158i
$540$	19.2721	+	5.02162i	0.829340	+	0.216096i
$541$	2.28504			0.0982415			0.0491207	−	0.998793i	$-0.484358\pi$
$541$	2.28504			0.0982415			0.0491207	+	0.998793i	$0.484358\pi$
$542$	−17.9616			−0.771517
$543$	2.52298	−	29.6227i	0.108271	−	1.27123i
$544$			6.47987i			0.277822i
$545$	21.5500			0.923100
$546$	−1.50734	+	4.32758i	−0.0645083	+	0.185203i
$547$	−3.40027			−0.145385			−0.0726925	−	0.997354i	$-0.523159\pi$
$547$	−3.40027			−0.145385			−0.0726925	+	0.997354i	$0.523159\pi$
$548$			4.15721i			0.177587i
$549$	−2.67879	+	15.6120i	−0.114328	+	0.666304i
$550$	34.2910			1.46217
$551$	10.3908			0.442662
$552$	−6.68740	−	0.569569i	−0.284634	−	0.0242425i
$553$	2.16118	−	8.45668i	0.0919028	−	0.359615i
$554$			9.40678i			0.399656i
$555$	3.95012	+	0.336434i	0.167673	+	0.0142808i
$556$			0.0159714i			0.000677337i
$557$			26.1294i			1.10714i	0.832804	+	0.553568i	$0.186734\pi$
$557$			26.1294i			1.10714i	−0.832804	+	0.553568i	$0.813266\pi$
$558$	28.8613	+	4.95218i	1.22180	+	0.209643i
$559$		−	0.604159i		−	0.0255532i
$560$	2.51081	−	9.82477i	0.106101	−	0.415173i
$561$	3.37055	−	39.5741i	0.142305	−	1.67082i
$562$	28.3782			1.19706
$563$	−33.5979			−1.41598			−0.707992	−	0.706220i	$-0.750399\pi$
$563$	−33.5979			−1.41598			−0.707992	+	0.706220i	$0.750399\pi$
$564$	21.7104	+	1.84908i	0.914171	+	0.0778604i
$565$		−	40.8606i		−	1.71902i
$566$	21.3006			0.895330
$567$	−13.2492	+	19.7853i	−0.556416	+	0.830904i
$568$	−9.18326			−0.385321
$569$		−	20.2598i		−	0.849336i	−0.905349	−	0.424668i	$-0.860391\pi$
$569$		−	20.2598i		−	0.849336i	0.905349	−	0.424668i	$-0.139609\pi$
$570$	−10.2531	−	0.873264i	−0.429457	−	0.0365770i
$571$	−2.55199			−0.106797			−0.0533987	−	0.998573i	$-0.517005\pi$
$571$	−2.55199			−0.106797			−0.0533987	+	0.998573i	$0.517005\pi$
$572$	3.53879			0.147964
$573$	1.32995	−	15.6151i	0.0555593	−	0.652330i
$574$	28.3004	+	7.23242i	1.18124	+	0.301876i
$575$			37.5485i			1.56588i
$576$	−2.95679	−	0.507343i	−0.123200	−	0.0211393i
$577$		−	29.0022i		−	1.20738i	−0.797220	−	0.603689i	$-0.793697\pi$
$577$		−	29.0022i		−	1.20738i	0.797220	−	0.603689i	$-0.206303\pi$
$578$		−	24.9887i		−	1.03939i
$579$	−10.4407	−	0.889236i	−0.433899	−	0.0369554i
$580$		−	25.6925i		−	1.06682i
$581$	1.35066	−	5.28512i	0.0560349	−	0.219264i
$582$	−17.8603	−	1.52117i	−0.740333	−	0.0630545i
$583$	24.2103			1.00269
$584$	11.6727			0.483021
$585$	1.94452	−	11.3327i	0.0803961	−	0.468548i
$586$		−	10.8691i		−	0.448997i
$587$	4.97590			0.205378			0.102689	−	0.994714i	$-0.467255\pi$
$587$	4.97590			0.205378			0.102689	+	0.994714i	$0.467255\pi$
$588$	10.1057	+	6.69884i	0.416753	+	0.276255i
$589$	−15.1304			−0.623436
$590$		−	6.67384i		−	0.274758i
$591$	−0.277281	+	3.25560i	−0.0114058	+	0.133917i
$592$	−0.597183			−0.0245441
$593$	−2.09710			−0.0861176			−0.0430588	−	0.999073i	$-0.513710\pi$
$593$	−2.09710			−0.0861176			−0.0430588	+	0.999073i	$0.513710\pi$
$594$	17.7939	+	4.63646i	0.730094	+	0.190236i
$595$	−16.2697	+	63.6632i	−0.666994	+	2.60994i
$596$		−	10.5043i		−	0.430274i
$597$	−1.68344	+	19.7655i	−0.0688986	+	0.808949i
$598$			3.87495i			0.158458i
$599$			18.5175i			0.756606i	0.925682	+	0.378303i	$0.123492\pi$
$599$			18.5175i			0.756606i	−0.925682	+	0.378303i	$0.876508\pi$
$600$	−1.42432	+	16.7231i	−0.0581475	+	0.682719i
$601$			37.7166i			1.53849i	0.638953	+	0.769246i	$0.279368\pi$
$601$			37.7166i			1.53849i	−0.638953	+	0.769246i	$0.720632\pi$
$602$	−1.54868	−	0.395780i	−0.0631196	−	0.0161308i
$603$	15.9538	+	2.73745i	0.649690	+	0.111477i
$604$	7.95857			0.323830
$605$	5.83731			0.237320
$606$	1.60427	−	18.8360i	0.0651690	−	0.765160i
$607$		−	14.2872i		−	0.579899i	−0.957042	−	0.289950i	$-0.906361\pi$
$607$		−	14.2872i		−	0.579899i	0.957042	−	0.289950i	$-0.0936386\pi$
$608$	1.55008			0.0628640
$609$	29.0094	+	10.1043i	1.17552	+	0.409447i
$610$	−20.2372			−0.819379
$611$		−	12.5799i		−	0.508927i
$612$	19.1596	+	3.28751i	0.774481	+	0.132890i
$613$	19.1299			0.772651			0.386325	−	0.922363i	$-0.373744\pi$
$613$	19.1299			0.772651			0.386325	+	0.922363i	$0.373744\pi$
$614$	−8.05501			−0.325074
$615$	−73.0271	−	6.21976i	−2.94474	−	0.250805i
$616$	2.31823	−	9.07121i	0.0934042	−	0.365489i
$617$			32.8876i			1.32400i	0.749502	+	0.662002i	$0.230293\pi$
$617$			32.8876i			1.32400i	−0.749502	+	0.662002i	$0.769707\pi$
$618$	1.03258	+	0.0879453i	0.0415364	+	0.00353768i
$619$		−	33.2924i		−	1.33814i	−0.743201	−	0.669068i	$-0.766693\pi$
$619$		−	33.2924i		−	1.33814i	0.743201	−	0.669068i	$-0.233307\pi$
$620$			37.4117i			1.50249i
$621$	−5.07690	+	19.4843i	−0.203729	+	0.781876i
$622$			2.09862i			0.0841470i
$623$	0.961057	−	3.76060i	0.0385039	−	0.150665i
$624$	−0.146987	+	1.72580i	−0.00588421	+	0.0690874i
$625$	20.4469			0.817875
$626$	16.8977			0.675370
$627$	−9.46671	−	0.806285i	−0.378064	−	0.0321999i
$628$		−	4.29431i		−	0.171362i
$629$	3.86967			0.154294
$630$	−27.7759	−	12.4085i	−1.10662	−	0.494365i
$631$	−20.4297			−0.813292			−0.406646	−	0.913586i	$-0.633302\pi$
$631$	−20.4297			−0.813292			−0.406646	+	0.913586i	$0.633302\pi$
$632$		−	3.29905i		−	0.131229i
$633$	28.5306	+	2.42997i	1.13399	+	0.0965824i
$634$	−32.7364			−1.30013
$635$	−18.9891			−0.753560
$636$	−1.00560	+	11.8069i	−0.0398748	+	0.468176i
$637$	3.35848	−	6.14171i	0.133068	−	0.243343i
$638$		−	23.7219i		−	0.939158i
$639$	−4.65906	+	27.1530i	−0.184310	+	1.07415i
$640$		−	3.83276i		−	0.151503i
$641$		−	22.3785i		−	0.883898i	−0.897040	−	0.441949i	$-0.854287\pi$
$641$		−	22.3785i		−	0.883898i	0.897040	−	0.441949i	$-0.145713\pi$
$642$	21.9194	+	1.86689i	0.865090	+	0.0736802i
$643$		−	41.9210i		−	1.65320i	−0.562788	−	0.826602i	$-0.690271\pi$
$643$		−	41.9210i		−	1.65320i	0.562788	−	0.826602i	$-0.309729\pi$
$644$	9.93292	+	2.53845i	0.391412	+	0.100029i
$645$	3.99626	+	0.340364i	0.157353	+	0.0134018i
$646$	−10.0443			−0.395188
$647$	−0.0109042			−0.000428690			−0.000214345	−	1.00000i	$-0.500068\pi$
$647$	−0.0109042			−0.000428690			−0.000214345		1.00000i	$0.500068\pi$
$648$	−3.00021	+	8.48521i	−0.117859	+	0.333330i
$649$		−	6.16196i		−	0.241878i
$650$	9.69005			0.380075
$651$	−42.2416	−	14.7132i	−1.65558	−	0.576656i
$652$	−18.5687			−0.727208
$653$		−	10.1915i		−	0.398824i	−0.979916	−	0.199412i	$-0.936097\pi$
$653$		−	10.1915i		−	0.398824i	0.979916	−	0.199412i	$-0.0639033\pi$
$654$	−0.826448	+	9.70345i	−0.0323167	+	0.379435i
$655$	−34.5887			−1.35149
$656$	11.0403			0.431052
$657$	5.92208	−	34.5138i	0.231042	−	1.34651i
$658$	−32.2468	−	8.24097i	−1.25711	−	0.321266i
$659$			7.10895i			0.276925i	0.990368	+	0.138463i	$0.0442161\pi$
$659$			7.10895i			0.276925i	−0.990368	+	0.138463i	$0.955784\pi$
$660$	−1.99364	+	23.4076i	−0.0776022	+	0.911140i
$661$			20.4994i			0.797334i	0.917096	+	0.398667i	$0.130527\pi$
$661$			20.4994i			0.797334i	−0.917096	+	0.398667i	$0.869473\pi$
$662$			13.6138i			0.529116i
$663$	0.952459	−	11.1830i	0.0369905	−	0.434311i
$664$		−	2.06179i		−	0.0800130i
$665$	15.2292	+	3.89196i	0.590562	+	0.150924i
$666$	−0.302977	+	1.76574i	−0.0117401	+	0.0684212i
$667$	25.9753			1.00577
$668$	−10.6873			−0.413503
$669$	−1.61464	+	18.9577i	−0.0624255	+	0.732947i
$670$			20.6803i			0.798948i
$671$	−18.6850			−0.721325
$672$	4.32758	+	1.50734i	0.166940	+	0.0581470i
$673$	−26.9039			−1.03707			−0.518534	−	0.855057i	$-0.673522\pi$
$673$	−26.9039			−1.03707			−0.518534	+	0.855057i	$0.673522\pi$
$674$			0.276737i			0.0106595i
$675$	48.7241	+	12.6958i	1.87539	+	0.488660i
$676$	1.00000			0.0384615
$677$	28.4525			1.09352			0.546759	−	0.837290i	$-0.315861\pi$
$677$	28.4525			1.09352			0.546759	+	0.837290i	$0.315861\pi$
$678$	18.3986	+	1.56701i	0.706592	+	0.0601808i
$679$	26.5282	+	6.77953i	1.01806	+	0.260175i
$680$			24.8358i			0.952409i
$681$	31.7008	+	2.69997i	1.21478	+	0.103463i
$682$			34.5422i			1.32269i
$683$		−	0.283408i		−	0.0108443i	−0.999985	−	0.00542215i	$-0.998274\pi$
$683$		−	0.283408i		−	0.0108443i	0.999985	−	0.00542215i	$-0.00172593\pi$
$684$	0.786421	−	4.58326i	0.0300696	−	0.175245i
$685$			15.9336i			0.608791i
$686$	−13.5433	−	12.6324i	−0.517087	−	0.482308i
$687$	−1.28930	+	15.1379i	−0.0491900	+	0.577547i
$688$	−0.604159			−0.0230334
$689$	6.84142			0.260637
$690$	−25.6312	−	2.18302i	−0.975763	−	0.0831062i
$691$			3.14189i			0.119523i	0.998213	+	0.0597615i	$0.0190340\pi$
$691$			3.14189i			0.119523i	−0.998213	+	0.0597615i	$0.980966\pi$
$692$	−13.4395			−0.510894
$693$	−25.6455	−	11.4567i	−0.974193	−	0.435205i
$694$	2.85298			0.108298
$695$			0.0612144i			0.00232199i
$696$	11.5687	+	0.985315i	0.438512	+	0.0373483i
$697$	−71.5398			−2.70976
$698$	9.55389			0.361620
$699$	−3.78225	+	44.4080i	−0.143058	+	1.67966i
$700$	6.34788	−	24.8392i	0.239927	−	0.938832i
$701$		−	41.4916i		−	1.56712i	−0.621318	−	0.783559i	$-0.713402\pi$
$701$		−	41.4916i		−	1.56712i	0.621318	−	0.783559i	$-0.286598\pi$
$702$	5.02826	+	1.31018i	0.189780	+	0.0494497i
$703$		−	0.925681i		−	0.0349127i
$704$		−	3.53879i		−	0.133373i
$705$	83.2106	+	7.08709i	3.13389	+	0.266915i
$706$			10.7608i			0.404990i
$707$	−7.14990	+	27.9775i	−0.268900	+	1.05220i
$708$	3.00508	+	0.255944i	0.112938	+	0.00961896i
$709$	−1.50518			−0.0565282			−0.0282641	−	0.999600i	$-0.508998\pi$
$709$	−1.50518			−0.0565282			−0.0282641	+	0.999600i	$0.508998\pi$
$710$	−35.1972			−1.32093
$711$	−9.75460	−	1.67375i	−0.365826	−	0.0627705i
$712$		−	1.46706i		−	0.0549802i
$713$	−37.8235			−1.41650
$714$	−28.0421	−	9.76738i	−1.04945	−	0.365535i
$715$	13.5633			0.507239
$716$		−	6.55533i		−	0.244984i
$717$	−1.87294	+	21.9904i	−0.0699461	+	0.821248i
$718$	−24.5118			−0.914773
$719$	27.9526			1.04245			0.521227	−	0.853418i	$-0.325474\pi$
$719$	27.9526			1.04245			0.521227	+	0.853418i	$0.325474\pi$
$720$	−11.3327	−	1.94452i	−0.422344	−	0.0724681i
$721$	−1.53371	−	0.391954i	−0.0571183	−	0.0145971i
$722$		−	16.5973i		−	0.617686i
$723$	1.93087	−	22.6707i	0.0718100	−	0.843132i
$724$			17.1646i			0.637916i
$725$		−	64.9562i		−	2.41241i
$726$	−0.223862	+	2.62840i	−0.00830832	+	0.0975492i
$727$			18.3871i			0.681938i	0.940075	+	0.340969i	$0.110755\pi$
$727$			18.3871i			0.681938i	−0.940075	+	0.340969i	$0.889245\pi$
$728$	0.655092	−	2.56337i	0.0242793	−	0.0950047i
$729$	23.5668	+	13.1759i	0.872846	+	0.487996i
$730$	44.7388			1.65586
$731$	3.91487			0.144797
$732$	0.776101	−	9.11232i	0.0286855	−	0.336801i
$733$			5.48224i			0.202491i	0.994861	+	0.101246i	$0.0322828\pi$
$733$			5.48224i			0.202491i	−0.994861	+	0.101246i	$0.967717\pi$
$734$	−18.6513			−0.688430
$735$	38.7328	+	25.6750i	1.42868	+	0.947038i
$736$	3.87495			0.142833
$737$			19.0941i			0.703339i
$738$	5.60122	−	32.6439i	0.206184	−	1.20164i
$739$	−49.9723			−1.83826			−0.919130	−	0.393955i	$-0.871106\pi$
$739$	−49.9723			−1.83826			−0.919130	+	0.393955i	$0.871106\pi$
$740$	−2.28886			−0.0841402
$741$	−2.67513	−	0.227842i	−0.0982734	−	0.00836999i
$742$	4.48176	−	17.5371i	0.164531	−	0.643806i
$743$		−	13.7626i		−	0.504900i	−0.967610	−	0.252450i	$-0.918764\pi$
$743$		−	13.7626i		−	0.504900i	0.967610	−	0.252450i	$-0.0812363\pi$
$744$	−16.8456	−	1.43475i	−0.617590	−	0.0526004i
$745$		−	40.2606i		−	1.47503i
$746$		−	4.55264i		−	0.166684i
$747$	−6.09628	−	1.04603i	−0.223051	−	0.0382724i
$748$			22.9309i			0.838435i
$749$	−32.5573	−	8.32032i	−1.18962	−	0.304018i
$750$	−2.64223	+	31.0228i	−0.0964804	+	1.13279i
$751$	19.3636			0.706587			0.353294	−	0.935512i	$-0.385062\pi$
$751$	19.3636			0.706587			0.353294	+	0.935512i	$0.385062\pi$
$752$	−12.5799			−0.458740
$753$	35.9161	+	3.05899i	1.30886	+	0.111476i
$754$		−	6.70339i		−	0.244123i
$755$	30.5033			1.11013
$756$	6.65246	−	12.0310i	0.241948	−	0.437563i
$757$	−11.2207			−0.407822			−0.203911	−	0.978989i	$-0.565365\pi$
$757$	−11.2207			−0.407822			−0.203911	+	0.978989i	$0.565365\pi$
$758$			14.4380i			0.524411i
$759$	−23.6653	−	2.01558i	−0.858995	−	0.0731610i
$760$	5.94108			0.215506
$761$	−6.07389			−0.220178			−0.110089	−	0.993922i	$-0.535114\pi$
$761$	−6.07389			−0.220178			−0.110089	+	0.993922i	$0.535114\pi$
$762$	0.728238	−	8.55035i	0.0263813	−	0.309747i
$763$	3.68330	−	14.4127i	0.133345	−	0.521776i
$764$			9.04802i			0.327346i
$765$	73.4342	+	12.6003i	2.65502	+	0.455563i
$766$			19.0301i			0.687584i
$767$		−	1.74126i		−	0.0628734i
$768$	1.72580	+	0.146987i	0.0622745	+	0.00530395i
$769$			53.3703i			1.92458i	0.272022	+	0.962291i	$0.412308\pi$
$769$			53.3703i			1.92458i	−0.272022	+	0.962291i	$0.587692\pi$
$770$	8.88522	−	34.7678i	0.320201	−	1.25294i
$771$	−25.8801	−	2.20422i	−0.932050	−	0.0793831i
$772$	6.04974			0.217735
$773$	−26.8657			−0.966291			−0.483145	−	0.875540i	$-0.660506\pi$
$773$	−26.8657			−0.966291			−0.483145	+	0.875540i	$0.660506\pi$
$774$	−0.306516	+	1.78637i	−0.0110175	+	0.0642098i
$775$			94.5849i			3.39759i
$776$	10.3490			0.371507
$777$	0.900160	−	2.58436i	0.0322930	−	0.0927132i
$778$	1.06894			0.0383232
$779$			17.1134i			0.613150i
$780$	−0.563368	+	6.61459i	−0.0201718	+	0.236840i
$781$	−32.4976			−1.16286
$782$	−25.1092			−0.897901
$783$	8.78268	−	33.7064i	0.313867	−	1.20457i
$784$	−6.14171	−	3.35848i	−0.219347	−	0.119946i
$785$		−	16.4591i		−	0.587449i
$786$	1.32649	−	15.5745i	0.0473142	−	0.555524i
$787$		−	34.2164i		−	1.21968i	−0.792524	−	0.609841i	$-0.791233\pi$
$787$		−	34.2164i		−	1.21968i	0.792524	−	0.609841i	$-0.208767\pi$
$788$		−	1.88643i		−	0.0672011i
$789$	1.65103	−	19.3849i	0.0587781	−	0.690122i
$790$		−	12.6445i		−	0.449870i
$791$	−27.3277	−	6.98385i	−0.971662	−	0.248317i
$792$	−10.4634	−	1.79538i	−0.371802	−	0.0637959i
$793$	−5.28005			−0.187500
$794$	−5.70472			−0.202453
$795$	−3.85424	+	45.2532i	−0.136696	+	1.60496i
$796$		−	11.4529i		−	0.405939i
$797$	−3.09513			−0.109635			−0.0548175	−	0.998496i	$-0.517458\pi$
$797$	−3.09513			−0.109635			−0.0548175	+	0.998496i	$0.517458\pi$
$798$	−2.33650	+	6.70809i	−0.0827112	+	0.237464i
$799$	81.5159			2.88382
$800$		−	9.69005i		−	0.342595i
$801$	−4.33777	−	0.744300i	−0.153268	−	0.0262985i
$802$	25.1273			0.887276
$803$	41.3073			1.45770
$804$	−9.31184	−	0.793094i	−0.328403	−	0.0279703i
$805$	38.0705	+	9.72927i	1.34181	+	0.342912i
$806$			9.76102i			0.343817i
$807$	0.947414	+	0.0806917i	0.0333505	+	0.00284048i
$808$			10.9143i			0.383965i
$809$		−	34.5753i		−	1.21560i	−0.794089	−	0.607802i	$-0.792051\pi$
$809$		−	34.5753i		−	1.21560i	0.794089	−	0.607802i	$-0.207949\pi$
$810$	−11.4991	+	32.5218i	−0.404037	+	1.14270i
$811$		−	18.2511i		−	0.640884i	−0.947268	−	0.320442i	$-0.896169\pi$
$811$		−	18.2511i		−	0.640884i	0.947268	−	0.320442i	$-0.103831\pi$
$812$	−17.1833	−	4.39134i	−0.603014	−	0.154106i
$813$	2.64013	−	30.9982i	0.0925934	−	1.08715i
$814$	−2.11330			−0.0740712
$815$	−71.1695			−2.49296
$816$	−11.1830	−	0.952459i	−0.391482	−	0.0333427i
$817$		−	0.936495i		−	0.0327638i
$818$	−10.6907			−0.373790
$819$	−7.24698	−	3.23748i	−0.253230	−	0.113127i
$820$	42.3149			1.47770
$821$		−	12.4344i		−	0.433964i	−0.976176	−	0.216982i	$-0.930379\pi$
$821$		−	12.4344i		−	0.433964i	0.976176	−	0.216982i	$-0.0696214\pi$
$822$	−7.17452	−	0.611058i	−0.250240	−	0.0213131i
$823$	−1.74146			−0.0607034			−0.0303517	−	0.999539i	$-0.509663\pi$
$823$	−1.74146			−0.0607034			−0.0303517	+	0.999539i	$0.509663\pi$
$824$	−0.598318			−0.0208434
$825$	−5.04035	+	59.1795i	−0.175482	+	2.06037i
$826$	−4.46350	−	1.14069i	−0.155305	−	0.0396896i
$827$		−	39.4093i		−	1.37039i	−0.728358	−	0.685197i	$-0.759716\pi$
$827$		−	39.4093i		−	1.37039i	0.728358	−	0.685197i	$-0.240284\pi$
$828$	1.96593	−	11.4574i	0.0683207	−	0.398172i
$829$		−	43.3524i		−	1.50569i	−0.658198	−	0.752845i	$-0.728681\pi$
$829$		−	43.3524i		−	1.50569i	0.658198	−	0.752845i	$-0.271319\pi$
$830$		−	7.90235i		−	0.274294i
$831$	−16.2343	−	1.38268i	−0.563160	−	0.0479646i
$832$		−	1.00000i		−	0.0346688i
$833$	39.7975	+	21.7625i	1.37890	+	0.754027i
$834$	−0.0275634	−	0.00234759i	−0.000954443	−	8.12904e-5i
$835$	−40.9617			−1.41754
$836$	5.48540			0.189716
$837$	−12.7887	+	49.0810i	−0.442044	+	1.69649i
$838$		−	11.5531i		−	0.399095i
$839$	12.9744			0.447927			0.223964	−	0.974598i	$-0.428100\pi$
$839$	12.9744			0.447927			0.223964	+	0.974598i	$0.428100\pi$
$840$	16.5866	+	5.77728i	0.572291	+	0.199335i
$841$	−15.9355			−0.549499
$842$			4.18647i			0.144275i
$843$	−4.17124	+	48.9752i	−0.143665	+	1.68679i
$844$	−16.5318			−0.569048
$845$	3.83276			0.131851
$846$	−6.38230	+	37.1960i	−0.219428	+	1.27883i
$847$	0.997708	−	3.90402i	0.0342817	−	0.134144i
$848$		−	6.84142i		−	0.234935i
$849$	−3.13092	+	36.7606i	−0.107453	+	1.26162i
$850$			62.7903i			2.15369i
$851$		−	2.31405i		−	0.0793247i
$852$	1.34982	−	15.8485i	0.0462442	−	0.542960i
$853$			24.7116i			0.846110i	0.906104	+	0.423055i	$0.139042\pi$
$853$			24.7116i			0.846110i	−0.906104	+	0.423055i	$0.860958\pi$
$854$	−3.45892	+	13.5347i	−0.118362	+	0.463148i
$855$	3.01416	−	17.5665i	0.103082	−	0.600763i
$856$	−12.7010			−0.434111
$857$	−38.6969			−1.32186			−0.660930	−	0.750447i	$-0.729838\pi$
$857$	−38.6969			−1.32186			−0.660930	+	0.750447i	$0.729838\pi$
$858$	−0.520157	+	6.10725i	−0.0177579	+	0.208498i
$859$			26.6914i			0.910699i	0.890313	+	0.455350i	$0.150486\pi$
$859$			26.6914i			0.910699i	−0.890313	+	0.455350i	$0.849514\pi$
$860$	−2.31560			−0.0789612
$861$	−16.6415	+	47.7778i	−0.567142	+	1.62826i
$862$	30.3437			1.03351
$863$		−	16.4748i		−	0.560808i	−0.959882	−	0.280404i	$-0.909532\pi$
$863$		−	16.4748i		−	0.560808i	0.959882	−	0.280404i	$-0.0904684\pi$
$864$	1.31018	−	5.02826i	0.0445734	−	0.171065i
$865$	−51.5105			−1.75141
$866$	−7.90187			−0.268516
$867$	43.1255	+	3.67302i	1.46462	+	0.124742i
$868$	25.0211	+	6.39437i	0.849271	+	0.217039i
$869$		−	11.6746i		−	0.396035i
$870$	44.3402	+	3.77647i	1.50327	+	0.128034i
$871$			5.39566i			0.182825i
$872$		−	5.62257i		−	0.190404i
$873$	5.25048	−	30.5997i	0.177702	−	1.03564i
$874$			6.00648i			0.203172i
$875$	11.7758	−	46.0787i	0.398096	−	1.55775i
$876$	−1.71575	+	20.1448i	−0.0579697	+	0.680631i
$877$	34.4149			1.16211			0.581055	−	0.813864i	$-0.302640\pi$
$877$	34.4149			1.16211			0.581055	+	0.813864i	$0.302640\pi$
$878$	38.0804			1.28515
$879$	18.7579	+	1.59762i	0.632687	+	0.0538863i
$880$		−	13.5633i		−	0.457219i
$881$	−10.6765			−0.359699			−0.179850	−	0.983694i	$-0.557561\pi$
$881$	−10.6765			−0.359699			−0.179850	+	0.983694i	$0.557561\pi$
$882$	−13.0463	+	16.4558i	−0.439291	+	0.554097i
$883$	−38.0731			−1.28126			−0.640630	−	0.767850i	$-0.721327\pi$
$883$	−38.0731			−1.28126			−0.640630	+	0.767850i	$0.721327\pi$
$884$			6.47987i			0.217942i
$885$	11.5177	+	0.980971i	0.387165	+	0.0329750i
$886$	−4.75228			−0.159656
$887$	−22.9996			−0.772251			−0.386126	−	0.922446i	$-0.626187\pi$
$887$	−22.9996			−0.772251			−0.386126	+	0.922446i	$0.626187\pi$
$888$	0.0877784	−	1.03062i	0.00294565	−	0.0345853i
$889$	−3.24560	+	12.7000i	−0.108854	+	0.425944i
$890$		−	5.62287i		−	0.188479i
$891$	−10.6171	+	30.0273i	−0.355686	+	1.00595i
$892$		−	10.9849i		−	0.367800i
$893$		−	19.4998i		−	0.652535i
$894$	18.1284	+	1.54400i	0.606304	+	0.0516392i
$895$		−	25.1250i		−	0.839837i
$896$	−2.56337	−	0.655092i	−0.0856361	−	0.0218851i
$897$	−6.68740	−	0.569569i	−0.223286	−	0.0190174i
$898$	−18.2285			−0.608294
$899$	65.4320			2.18228
$900$	−28.6514	−	4.91618i	−0.955048	−	0.163873i
$901$			44.3315i			1.47690i
$902$	39.0693			1.30087
$903$	0.910675	−	2.61455i	0.0303054	−	0.0870066i
$904$	−10.6609			−0.354575
$905$			65.7877i			2.18686i
$906$	−1.16981	+	13.7349i	−0.0388643	+	0.456312i
$907$	30.9557			1.02787			0.513934	−	0.857830i	$-0.328188\pi$
$907$	30.9557			1.02787			0.513934	+	0.857830i	$0.328188\pi$
$908$	−18.3687			−0.609588
$909$	32.2714	+	5.53731i	1.07037	+	0.183661i
$910$	2.51081	−	9.82477i	0.0832326	−	0.325688i
$911$			40.8374i			1.35300i	0.736440	+	0.676502i	$0.236505\pi$
$911$			40.8374i			1.35300i	−0.736440	+	0.676502i	$0.763495\pi$
$912$	−0.227842	+	2.67513i	−0.00754461	+	0.0885824i
$913$		−	7.29623i		−	0.241470i
$914$			20.6866i			0.684251i
$915$	2.97461	−	34.9253i	0.0983375	−	1.15460i
$916$		−	8.77152i		−	0.289819i
$917$	−5.91188	+	23.1331i	−0.195227	+	0.763922i
$918$	−8.48982	+	32.5825i	−0.280206	+	1.07538i
$919$	29.3642			0.968636			0.484318	−	0.874892i	$-0.339068\pi$
$919$	29.3642			0.968636			0.484318	+	0.874892i	$0.339068\pi$
$920$	14.8518			0.489648
$921$	1.18398	−	13.9013i	0.0390136	−	0.458065i
$922$		−	39.2144i		−	1.29146i
$923$	−9.18326			−0.302271
$924$	15.3144	+	5.33416i	0.503806	+	0.175481i
$925$	−5.78674			−0.190267
$926$			8.05138i			0.264585i
$927$	−0.303552	+	1.76910i	−0.00996997	+	0.0581049i
$928$	−6.70339			−0.220050
$929$	−49.5474			−1.62560			−0.812799	−	0.582544i	$-0.802057\pi$
$929$	−49.5474			−1.62560			−0.812799	+	0.582544i	$0.802057\pi$
$930$	−64.5652	−	5.49905i	−2.11717	−	0.180321i
$931$	5.20592	−	9.52013i	0.170617	−	0.312010i
$932$		−	25.7318i		−	0.842872i
$933$	−3.62180	−	0.308471i	−0.118572	−	0.0100989i
$934$			5.39494i			0.176528i
$935$			87.8885i			2.87426i
$936$	−2.95679	−	0.507343i	−0.0966457	−	0.0165830i
$937$			56.8532i			1.85731i	0.370939	+	0.928657i	$0.379036\pi$
$937$			56.8532i			1.85731i	−0.370939	+	0.928657i	$0.620964\pi$
$938$	13.8311	+	3.53465i	0.451600	+	0.115410i
$939$	−2.48376	+	29.1622i	−0.0810543	+	0.951672i
$940$	−48.2156			−1.57262
$941$	48.8828			1.59353			0.796766	−	0.604287i	$-0.206542\pi$
$941$	48.8828			1.59353			0.796766	+	0.604287i	$0.206542\pi$
$942$	7.41114	+	0.631210i	0.241468	+	0.0205659i
$943$			42.7807i			1.39313i
$944$	−1.74126			−0.0566733
$945$	25.4973	−	46.1119i	0.829427	−	1.50002i
$946$	−2.13799			−0.0695121
$947$		−	48.7459i		−	1.58403i	−0.610501	−	0.792015i	$-0.709032\pi$
$947$		−	48.7459i		−	1.58403i	0.610501	−	0.792015i	$-0.290968\pi$
$948$	5.69351	+	0.484919i	0.184917	+	0.0157494i
$949$	11.6727			0.378913
$950$	15.0203			0.487324
$951$	4.81183	−	56.4965i	0.156034	−	1.83202i
$952$	16.6103	+	4.24491i	0.538342	+	0.137578i
$953$		−	2.16214i		−	0.0700385i	−0.999387	−	0.0350192i	$-0.988851\pi$
$953$		−	2.16214i		−	0.0700385i	0.999387	−	0.0350192i	$-0.0111493\pi$
$954$	−20.2286	−	3.47094i	−0.654926	−	0.112376i
$955$			34.6789i			1.12218i
$956$		−	12.7421i		−	0.412111i
$957$	40.9393	+	3.48682i	1.32338	+	0.112713i
$958$			20.6008i			0.665582i
$959$	10.6565	+	2.72335i	0.344115	+	0.0879417i
$960$	6.61459	+	0.563368i	0.213485	+	0.0181826i
$961$	−64.2776			−2.07347
$962$	−0.597183			−0.0192540
$963$	−6.44376	+	37.5542i	−0.207647	+	1.21017i
$964$			13.1363i			0.423092i
$965$	23.1872			0.746422
$966$	−5.84088	+	16.7691i	−0.187927	+	0.539538i
$967$	8.43003			0.271091			0.135546	−	0.990771i	$-0.456721\pi$
$967$	8.43003			0.271091			0.135546	+	0.990771i	$0.456721\pi$
$968$		−	1.52300i		−	0.0489512i
$969$	1.47639	−	17.3345i	0.0474284	−	0.556864i
$970$	39.6651			1.27357
$971$	−30.8086			−0.988695			−0.494348	−	0.869264i	$-0.664593\pi$
$971$	−30.8086			−0.988695			−0.494348	+	0.869264i	$0.664593\pi$
$972$	−14.2028	−	6.42499i	−0.455555	−	0.206082i
$973$	0.0409405	+	0.0104627i	0.00131249	+	0.000335419i
$974$			15.7925i			0.506023i
$975$	−1.42432	+	16.7231i	−0.0456146	+	0.535568i
$976$			5.28005i			0.169010i
$977$		−	60.6092i		−	1.93906i	−0.244970	−	0.969531i	$-0.578778\pi$
$977$		−	60.6092i		−	1.93906i	0.244970	−	0.969531i	$-0.421222\pi$
$978$	2.72937	−	32.0460i	0.0872757	−	1.02472i
$979$		−	5.19159i		−	0.165924i
$980$	−23.5397	−	12.8723i	−0.751948	−	0.411189i
$981$	−16.6248	−	2.85257i	−0.530788	−	0.0910756i
$982$	20.4861			0.653737
$983$	−57.7943			−1.84335			−0.921676	−	0.387960i	$-0.873180\pi$
$983$	−57.7943			−1.84335			−0.921676	+	0.387960i	$0.873180\pi$
$984$	−1.62279	+	19.0534i	−0.0517326	+	0.607400i
$985$		−	7.23022i		−	0.230374i
$986$	43.4371			1.38332
$987$	18.9622	−	54.4403i	0.603572	−	1.73285i
$988$	1.55008			0.0493146
$989$		−	2.34109i		−	0.0744422i
$990$	−40.1039	−	6.88125i	−1.27458	−	0.218700i
$991$	35.9463			1.14187			0.570935	−	0.820995i	$-0.306581\pi$
$991$	35.9463			1.14187			0.570935	+	0.820995i	$0.306581\pi$
$992$	9.76102			0.309913
$993$	−23.4948	−	2.00106i	−0.745584	−	0.0635017i
$994$	−6.01588	+	23.5401i	−0.190812	+	0.746646i
$995$		−	43.8964i		−	1.39161i
$996$	3.55824	+	0.303057i	0.112747	+	0.00960274i
$997$			9.91463i			0.313999i	0.987599	+	0.157000i	$0.0501822\pi$
$997$			9.91463i			0.313999i	−0.987599	+	0.157000i	$0.949818\pi$
$998$			31.3034i			0.990893i
$999$	−3.00279	−	0.782420i	−0.0950042	−	0.0247547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.g.d.209.6	yes	12
3.2	odd	2		546.2.g.c.209.7	yes	12
7.6	odd	2		546.2.g.c.209.1	✓	12
21.20	even	2	inner	546.2.g.d.209.12	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.g.c.209.1	✓	12	7.6	odd	2
546.2.g.c.209.7	yes	12	3.2	odd	2
546.2.g.d.209.6	yes	12	1.1	even	1	trivial
546.2.g.d.209.12	yes	12	21.20	even	2	inner

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.72580 + 0.146987i) q^{3} -1.00000 q^{4} -3.83276 q^{5} +(0.146987 - 1.72580i) q^{6} +(-0.655092 + 2.56337i) q^{7} +1.00000i q^{8} +(2.95679 + 0.507343i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.72580 + 0.146987i) q^{3} -1.00000 q^{4} -3.83276 q^{5} +(0.146987 - 1.72580i) q^{6} +(-0.655092 + 2.56337i) q^{7} +1.00000i q^{8} +(2.95679 + 0.507343i) q^{9} +3.83276i q^{10} +3.53879i q^{11} +(-1.72580 - 0.146987i) q^{12} +1.00000i q^{13} +(2.56337 + 0.655092i) q^{14} +(-6.61459 - 0.563368i) q^{15} +1.00000 q^{16} -6.47987 q^{17} +(0.507343 - 2.95679i) q^{18} +1.55008i q^{19} +3.83276 q^{20} +(-1.50734 + 4.32758i) q^{21} +3.53879 q^{22} +3.87495i q^{23} +(-0.146987 + 1.72580i) q^{24} +9.69005 q^{25} +1.00000 q^{26} +(5.02826 + 1.31018i) q^{27} +(0.655092 - 2.56337i) q^{28} -6.70339i q^{29} +(-0.563368 + 6.61459i) q^{30} +9.76102i q^{31} -1.00000i q^{32} +(-0.520157 + 6.10725i) q^{33} +6.47987i q^{34} +(2.51081 - 9.82477i) q^{35} +(-2.95679 - 0.507343i) q^{36} -0.597183 q^{37} +1.55008 q^{38} +(-0.146987 + 1.72580i) q^{39} -3.83276i q^{40} +11.0403 q^{41} +(4.32758 + 1.50734i) q^{42} -0.604159 q^{43} -3.53879i q^{44} +(-11.3327 - 1.94452i) q^{45} +3.87495 q^{46} -12.5799 q^{47} +(1.72580 + 0.146987i) q^{48} +(-6.14171 - 3.35848i) q^{49} -9.69005i q^{50} +(-11.1830 - 0.952459i) q^{51} -1.00000i q^{52} -6.84142i q^{53} +(1.31018 - 5.02826i) q^{54} -13.5633i q^{55} +(-2.56337 - 0.655092i) q^{56} +(-0.227842 + 2.67513i) q^{57} -6.70339 q^{58} -1.74126 q^{59} +(6.61459 + 0.563368i) q^{60} +5.28005i q^{61} +9.76102 q^{62} +(-3.23748 + 7.24698i) q^{63} -1.00000 q^{64} -3.83276i q^{65} +(6.10725 + 0.520157i) q^{66} +5.39566 q^{67} +6.47987 q^{68} +(-0.569569 + 6.68740i) q^{69} +(-9.82477 - 2.51081i) q^{70} +9.18326i q^{71} +(-0.507343 + 2.95679i) q^{72} -11.6727i q^{73} +0.597183i q^{74} +(16.7231 + 1.42432i) q^{75} -1.55008i q^{76} +(-9.07121 - 2.31823i) q^{77} +(1.72580 + 0.146987i) q^{78} -3.29905 q^{79} -3.83276 q^{80} +(8.48521 + 3.00021i) q^{81} -11.0403i q^{82} -2.06179 q^{83} +(1.50734 - 4.32758i) q^{84} +24.8358 q^{85} +0.604159i q^{86} +(0.985315 - 11.5687i) q^{87} -3.53879 q^{88} -1.46706 q^{89} +(-1.94452 + 11.3327i) q^{90} +(-2.56337 - 0.655092i) q^{91} -3.87495i q^{92} +(-1.43475 + 16.8456i) q^{93} +12.5799i q^{94} -5.94108i q^{95} +(0.146987 - 1.72580i) q^{96} -10.3490i q^{97} +(-3.35848 + 6.14171i) q^{98} +(-1.79538 + 10.4634i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} - 12 q^{4} - 4 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9}+O(q^{10}) \) 12 * q + 2 * q^3 - 12 * q^4 - 4 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9	\( 12 q + 2 q^{3} - 12 q^{4} - 4 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9} - 2 q^{12} + 10 q^{14} + 4 q^{15} + 12 q^{16} + 12 q^{17} + 8 q^{18} + 4 q^{20} - 20 q^{21} - 2 q^{24} + 20 q^{25} + 12 q^{26} + 8 q^{27} + 8 q^{28} + 14 q^{30} + 46 q^{33} - 22 q^{35} - 4 q^{36} + 16 q^{37} - 8 q^{38} - 2 q^{39} + 28 q^{41} + 4 q^{42} - 8 q^{43} + 24 q^{46} - 68 q^{47} + 2 q^{48} + 26 q^{49} - 50 q^{51} + 16 q^{54} - 10 q^{56} - 28 q^{57} - 24 q^{58} + 8 q^{59} - 4 q^{60} + 16 q^{62} - 2 q^{63} - 12 q^{64} - 12 q^{66} + 8 q^{67} - 12 q^{68} - 24 q^{69} - 28 q^{70} - 8 q^{72} + 92 q^{75} - 8 q^{77} + 2 q^{78} + 36 q^{79} - 4 q^{80} + 16 q^{81} - 32 q^{83} + 20 q^{84} + 8 q^{87} - 48 q^{89} + 2 q^{90} - 10 q^{91} + 8 q^{93} + 2 q^{96} + 16 q^{98}+O(q^{100}) \) 12 * q + 2 * q^3 - 12 * q^4 - 4 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9 - 2 * q^12 + 10 * q^14 + 4 * q^15 + 12 * q^16 + 12 * q^17 + 8 * q^18 + 4 * q^20 - 20 * q^21 - 2 * q^24 + 20 * q^25 + 12 * q^26 + 8 * q^27 + 8 * q^28 + 14 * q^30 + 46 * q^33 - 22 * q^35 - 4 * q^36 + 16 * q^37 - 8 * q^38 - 2 * q^39 + 28 * q^41 + 4 * q^42 - 8 * q^43 + 24 * q^46 - 68 * q^47 + 2 * q^48 + 26 * q^49 - 50 * q^51 + 16 * q^54 - 10 * q^56 - 28 * q^57 - 24 * q^58 + 8 * q^59 - 4 * q^60 + 16 * q^62 - 2 * q^63 - 12 * q^64 - 12 * q^66 + 8 * q^67 - 12 * q^68 - 24 * q^69 - 28 * q^70 - 8 * q^72 + 92 * q^75 - 8 * q^77 + 2 * q^78 + 36 * q^79 - 4 * q^80 + 16 * q^81 - 32 * q^83 + 20 * q^84 + 8 * q^87 - 48 * q^89 + 2 * q^90 - 10 * q^91 + 8 * q^93 + 2 * q^96 + 16 * q^98

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