LMFDB - Embedded newform 245.2.e.c.116.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,2,Mod(116,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("245.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.e (of order $3$, degree $2$, not 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:	$1.95633484952$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			116.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	245.116
Dual form			245.2.e.c.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} -6.00000 q^{6} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} -6.00000 q^{6} +(-3.00000 - 5.19615i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-3.00000 - 5.19615i) q^{12} +3.00000 q^{13} -3.00000 q^{15} +(2.00000 + 3.46410i) q^{16} +(1.50000 - 2.59808i) q^{17} +(6.00000 - 10.3923i) q^{18} +(-3.00000 - 5.19615i) q^{19} -2.00000 q^{20} -2.00000 q^{22} +(2.00000 + 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(3.00000 + 5.19615i) q^{26} +9.00000 q^{27} -1.00000 q^{29} +(-3.00000 - 5.19615i) q^{30} +(-3.00000 + 5.19615i) q^{31} +(-4.00000 + 6.92820i) q^{32} +(-1.50000 - 2.59808i) q^{33} +6.00000 q^{34} +12.0000 q^{36} +(6.00000 - 10.3923i) q^{38} +(-4.50000 + 7.79423i) q^{39} +6.00000 q^{41} -6.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} +(3.00000 - 5.19615i) q^{45} +(-4.00000 + 6.92820i) q^{46} +(4.50000 + 7.79423i) q^{47} -12.0000 q^{48} -2.00000 q^{50} +(4.50000 + 7.79423i) q^{51} +(-3.00000 + 5.19615i) q^{52} +(5.00000 - 8.66025i) q^{53} +(9.00000 + 15.5885i) q^{54} -1.00000 q^{55} +18.0000 q^{57} +(-1.00000 - 1.73205i) q^{58} +(3.00000 - 5.19615i) q^{59} +(3.00000 - 5.19615i) q^{60} -12.0000 q^{62} -8.00000 q^{64} +(1.50000 + 2.59808i) q^{65} +(3.00000 - 5.19615i) q^{66} +(7.00000 - 12.1244i) q^{67} +(3.00000 + 5.19615i) q^{68} -12.0000 q^{69} -8.00000 q^{71} +(-3.00000 + 5.19615i) q^{73} +(-1.50000 - 2.59808i) q^{75} +12.0000 q^{76} -18.0000 q^{78} +(0.500000 + 0.866025i) q^{79} +(-2.00000 + 3.46410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(6.00000 + 10.3923i) q^{82} +12.0000 q^{83} +3.00000 q^{85} +(-6.00000 - 10.3923i) q^{86} +(1.50000 - 2.59808i) q^{87} +(-6.00000 - 10.3923i) q^{89} +12.0000 q^{90} -8.00000 q^{92} +(-9.00000 - 15.5885i) q^{93} +(-9.00000 + 15.5885i) q^{94} +(3.00000 - 5.19615i) q^{95} +(-12.0000 - 20.7846i) q^{96} -15.0000 q^{97} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{5} - 12 q^{6} - 6 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 + q^5 - 12 * q^6 - 6 * q^9	$ 2 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{5} - 12 q^{6} - 6 q^{9} - 2 q^{10} - q^{11} - 6 q^{12} + 6 q^{13} - 6 q^{15} + 4 q^{16} + 3 q^{17} + 12 q^{18} - 6 q^{19} - 4 q^{20} - 4 q^{22} + 4 q^{23} - q^{25} + 6 q^{26} + 18 q^{27} - 2 q^{29} - 6 q^{30} - 6 q^{31} - 8 q^{32} - 3 q^{33} + 12 q^{34} + 24 q^{36} + 12 q^{38} - 9 q^{39} + 12 q^{41} - 12 q^{43} - 2 q^{44} + 6 q^{45} - 8 q^{46} + 9 q^{47} - 24 q^{48} - 4 q^{50} + 9 q^{51} - 6 q^{52} + 10 q^{53} + 18 q^{54} - 2 q^{55} + 36 q^{57} - 2 q^{58} + 6 q^{59} + 6 q^{60} - 24 q^{62} - 16 q^{64} + 3 q^{65} + 6 q^{66} + 14 q^{67} + 6 q^{68} - 24 q^{69} - 16 q^{71} - 6 q^{73} - 3 q^{75} + 24 q^{76} - 36 q^{78} + q^{79} - 4 q^{80} - 9 q^{81} + 12 q^{82} + 24 q^{83} + 6 q^{85} - 12 q^{86} + 3 q^{87} - 12 q^{89} + 24 q^{90} - 16 q^{92} - 18 q^{93} - 18 q^{94} + 6 q^{95} - 24 q^{96} - 30 q^{97} + 12 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 + q^5 - 12 * q^6 - 6 * q^9 - 2 * q^10 - q^11 - 6 * q^12 + 6 * q^13 - 6 * q^15 + 4 * q^16 + 3 * q^17 + 12 * q^18 - 6 * q^19 - 4 * q^20 - 4 * q^22 + 4 * q^23 - q^25 + 6 * q^26 + 18 * q^27 - 2 * q^29 - 6 * q^30 - 6 * q^31 - 8 * q^32 - 3 * q^33 + 12 * q^34 + 24 * q^36 + 12 * q^38 - 9 * q^39 + 12 * q^41 - 12 * q^43 - 2 * q^44 + 6 * q^45 - 8 * q^46 + 9 * q^47 - 24 * q^48 - 4 * q^50 + 9 * q^51 - 6 * q^52 + 10 * q^53 + 18 * q^54 - 2 * q^55 + 36 * q^57 - 2 * q^58 + 6 * q^59 + 6 * q^60 - 24 * q^62 - 16 * q^64 + 3 * q^65 + 6 * q^66 + 14 * q^67 + 6 * q^68 - 24 * q^69 - 16 * q^71 - 6 * q^73 - 3 * q^75 + 24 * q^76 - 36 * q^78 + q^79 - 4 * q^80 - 9 * q^81 + 12 * q^82 + 24 * q^83 + 6 * q^85 - 12 * q^86 + 3 * q^87 - 12 * q^89 + 24 * q^90 - 16 * q^92 - 18 * q^93 - 18 * q^94 + 6 * q^95 - 24 * q^96 - 30 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.00000	+	1.73205i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$2$	1.00000	+	1.73205i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$3$	−1.50000	+	2.59808i	−0.866025	+	1.50000i			1.00000i	$0.5\pi$
$3$	−1.50000	+	2.59808i	−0.866025	+	1.50000i	−0.866025	+	0.500000i	$0.833333\pi$
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−6.00000			−2.44949
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−3.00000	−	5.19615i	−1.00000	−	1.73205i
$10$	−1.00000	+	1.73205i	−0.316228	+	0.547723i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	−0.931505	−	0.363727i	$-0.881504\pi$
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	0.780750	+	0.624844i	$0.214837\pi$
$12$	−3.00000	−	5.19615i	−0.866025	−	1.50000i
$13$	3.00000			0.832050			0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000			0.832050			0.416025	+	0.909353i	$0.363423\pi$
$14$		0			0
$15$	−3.00000			−0.774597
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	6.00000	−	10.3923i	1.41421	−	2.44949i
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	0.284157	−	0.958778i	$-0.408286\pi$
$20$	−2.00000			−0.447214
$21$		0			0
$22$	−2.00000			−0.426401
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.00000	+	5.19615i	0.588348	+	1.01905i
$27$	9.00000			1.73205
$28$		0			0
$29$	−1.00000			−0.185695			−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000			−0.185695			−0.0928477	+	0.995680i	$0.529597\pi$
$30$	−3.00000	−	5.19615i	−0.547723	−	0.948683i
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	0.460152	+	0.887840i	$0.347795\pi$
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	−0.998968	+	0.0454165i	$0.985539\pi$
$32$	−4.00000	+	6.92820i	−0.707107	+	1.22474i
$33$	−1.50000	−	2.59808i	−0.261116	−	0.452267i
$34$	6.00000			1.02899
$35$		0			0
$36$	12.0000			2.00000
$37$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$37$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$38$	6.00000	−	10.3923i	0.973329	−	1.68585i
$39$	−4.50000	+	7.79423i	−0.720577	+	1.24808i
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	−6.00000			−0.914991			−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000			−0.914991			−0.457496	+	0.889212i	$0.651253\pi$
$44$	−1.00000	−	1.73205i	−0.150756	−	0.261116i
$45$	3.00000	−	5.19615i	0.447214	−	0.774597i
$46$	−4.00000	+	6.92820i	−0.589768	+	1.02151i
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	0.981543	+	0.191243i	$0.0612518\pi$
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	−0.325150	+	0.945662i	$0.605415\pi$
$48$	−12.0000			−1.73205
$49$		0			0
$50$	−2.00000			−0.282843
$51$	4.50000	+	7.79423i	0.630126	+	1.09141i
$52$	−3.00000	+	5.19615i	−0.416025	+	0.720577i
$53$	5.00000	−	8.66025i	0.686803	−	1.18958i	−0.286064	−	0.958211i	$-0.592347\pi$
$53$	5.00000	−	8.66025i	0.686803	−	1.18958i	0.972867	−	0.231367i	$-0.0743197\pi$
$54$	9.00000	+	15.5885i	1.22474	+	2.12132i
$55$	−1.00000			−0.134840
$56$		0			0
$57$	18.0000			2.38416
$58$	−1.00000	−	1.73205i	−0.131306	−	0.227429i
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$	3.00000	−	5.19615i	0.387298	−	0.670820i
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$	−12.0000			−1.52400
$63$		0			0
$64$	−8.00000			−1.00000
$65$	1.50000	+	2.59808i	0.186052	+	0.322252i
$66$	3.00000	−	5.19615i	0.369274	−	0.639602i
$67$	7.00000	−	12.1244i	0.855186	−	1.48123i	−0.0212861	−	0.999773i	$-0.506776\pi$
$67$	7.00000	−	12.1244i	0.855186	−	1.48123i	0.876472	−	0.481452i	$-0.159891\pi$
$68$	3.00000	+	5.19615i	0.363803	+	0.630126i
$69$	−12.0000			−1.44463
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	−3.00000	+	5.19615i	−0.351123	+	0.608164i	−0.986447	−	0.164083i	$-0.947534\pi$
$73$	−3.00000	+	5.19615i	−0.351123	+	0.608164i	0.635323	+	0.772246i	$0.280867\pi$
$74$		0			0
$75$	−1.50000	−	2.59808i	−0.173205	−	0.300000i
$76$	12.0000			1.37649
$77$		0			0
$78$	−18.0000			−2.03810
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$	−2.00000	+	3.46410i	−0.223607	+	0.387298i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	6.00000	+	10.3923i	0.662589	+	1.14764i
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	3.00000			0.325396
$86$	−6.00000	−	10.3923i	−0.646997	−	1.12063i
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$		0			0
$89$	−6.00000	−	10.3923i	−0.635999	−	1.10158i	−0.986303	−	0.164946i	$-0.947255\pi$
$89$	−6.00000	−	10.3923i	−0.635999	−	1.10158i	0.350304	−	0.936636i	$-0.386078\pi$
$90$	12.0000			1.26491
$91$		0			0
$92$	−8.00000			−0.834058
$93$	−9.00000	−	15.5885i	−0.933257	−	1.61645i
$94$	−9.00000	+	15.5885i	−0.928279	+	1.60783i
$95$	3.00000	−	5.19615i	0.307794	−	0.533114i
$96$	−12.0000	−	20.7846i	−1.22474	−	2.12132i
$97$	−15.0000			−1.52302			−0.761510	−	0.648154i	$-0.775541\pi$
$97$	−15.0000			−1.52302			−0.761510	+	0.648154i	$0.775541\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$	−1.00000	−	1.73205i	−0.100000	−	0.173205i
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.0623905	−	0.998052i	$-0.480128\pi$
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.833143	−	0.553058i	$-0.186539\pi$
$102$	−9.00000	+	15.5885i	−0.891133	+	1.54349i
$103$	4.50000	+	7.79423i	0.443398	+	0.767988i	0.997939	−	0.0641683i	$-0.0204394\pi$
$103$	4.50000	+	7.79423i	0.443398	+	0.767988i	−0.554541	+	0.832156i	$0.687106\pi$
$104$		0			0
$105$		0			0
$106$	20.0000			1.94257
$107$	1.00000	+	1.73205i	0.0966736	+	0.167444i	0.910306	−	0.413936i	$-0.135846\pi$
$107$	1.00000	+	1.73205i	0.0966736	+	0.167444i	−0.813632	+	0.581380i	$0.802513\pi$
$108$	−9.00000	+	15.5885i	−0.866025	+	1.50000i
$109$	7.50000	−	12.9904i	0.718370	−	1.24425i	−0.243276	−	0.969957i	$-0.578222\pi$
$109$	7.50000	−	12.9904i	0.718370	−	1.24425i	0.961645	−	0.274296i	$-0.0884447\pi$
$110$	−1.00000	−	1.73205i	−0.0953463	−	0.165145i
$111$		0			0
$112$		0			0
$113$	8.00000			0.752577			0.376288	−	0.926503i	$-0.377200\pi$
$113$	8.00000			0.752577			0.376288	+	0.926503i	$0.377200\pi$
$114$	18.0000	+	31.1769i	1.68585	+	2.91999i
$115$	−2.00000	+	3.46410i	−0.186501	+	0.323029i
$116$	1.00000	−	1.73205i	0.0928477	−	0.160817i
$117$	−9.00000	−	15.5885i	−0.832050	−	1.44115i
$118$	12.0000			1.10469
$119$		0			0
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$		0			0
$123$	−9.00000	+	15.5885i	−0.811503	+	1.40556i
$124$	−6.00000	−	10.3923i	−0.538816	−	0.933257i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−2.00000			−0.177471			−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000			−0.177471			−0.0887357	+	0.996055i	$0.528283\pi$
$128$		0			0
$129$	9.00000	−	15.5885i	0.792406	−	1.37249i
$130$	−3.00000	+	5.19615i	−0.263117	+	0.455733i
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$	6.00000			0.522233
$133$		0			0
$134$	28.0000			2.41883
$135$	4.50000	+	7.79423i	0.387298	+	0.670820i
$136$		0			0
$137$	−4.00000	+	6.92820i	−0.341743	+	0.591916i	−0.984757	−	0.173939i	$-0.944351\pi$
$137$	−4.00000	+	6.92820i	−0.341743	+	0.591916i	0.643013	+	0.765855i	$0.277684\pi$
$138$	−12.0000	−	20.7846i	−1.02151	−	1.76930i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$	−27.0000			−2.27381
$142$	−8.00000	−	13.8564i	−0.671345	−	1.16280i
$143$	−1.50000	+	2.59808i	−0.125436	+	0.217262i
$144$	12.0000	−	20.7846i	1.00000	−	1.73205i
$145$	−0.500000	−	0.866025i	−0.0415227	−	0.0719195i
$146$	−12.0000			−0.993127
$147$		0			0
$148$		0			0
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	0.585231	−	0.810867i	$-0.301004\pi$
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	−0.994847	+	0.101391i	$0.967671\pi$
$150$	3.00000	−	5.19615i	0.244949	−	0.424264i
$151$	−7.50000	+	12.9904i	−0.610341	+	1.05714i	0.380841	+	0.924640i	$0.375634\pi$
$151$	−7.50000	+	12.9904i	−0.610341	+	1.05714i	−0.991183	+	0.132502i	$0.957699\pi$
$152$		0			0
$153$	−18.0000			−1.45521
$154$		0			0
$155$	−6.00000			−0.481932
$156$	−9.00000	−	15.5885i	−0.720577	−	1.24808i
$157$	−9.00000	+	15.5885i	−0.718278	+	1.24409i	0.243403	+	0.969925i	$0.421736\pi$
$157$	−9.00000	+	15.5885i	−0.718278	+	1.24409i	−0.961681	+	0.274169i	$0.911597\pi$
$158$	−1.00000	+	1.73205i	−0.0795557	+	0.137795i
$159$	15.0000	+	25.9808i	1.18958	+	2.06041i
$160$	−8.00000			−0.632456
$161$		0			0
$162$	−18.0000			−1.41421
$163$	−8.00000	−	13.8564i	−0.626608	−	1.08532i	−0.988227	−	0.152992i	$-0.951109\pi$
$163$	−8.00000	−	13.8564i	−0.626608	−	1.08532i	0.361619	−	0.932326i	$-0.382224\pi$
$164$	−6.00000	+	10.3923i	−0.468521	+	0.811503i
$165$	1.50000	−	2.59808i	0.116775	−	0.202260i
$166$	12.0000	+	20.7846i	0.931381	+	1.61320i
$167$	3.00000			0.232147			0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000			0.232147			0.116073	+	0.993241i	$0.462969\pi$
$168$		0			0
$169$	−4.00000			−0.307692
$170$	3.00000	+	5.19615i	0.230089	+	0.398527i
$171$	−18.0000	+	31.1769i	−1.37649	+	2.38416i
$172$	6.00000	−	10.3923i	0.457496	−	0.792406i
$173$	1.50000	+	2.59808i	0.114043	+	0.197528i	0.917397	−	0.397974i	$-0.130287\pi$
$173$	1.50000	+	2.59808i	0.114043	+	0.197528i	−0.803354	+	0.595502i	$0.796953\pi$
$174$	6.00000			0.454859
$175$		0			0
$176$	−4.00000			−0.301511
$177$	9.00000	+	15.5885i	0.676481	+	1.17170i
$178$	12.0000	−	20.7846i	0.899438	−	1.55787i
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	−0.931038	−	0.364922i	$-0.881096\pi$
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	0.781551	+	0.623841i	$0.214429\pi$
$180$	6.00000	+	10.3923i	0.447214	+	0.774597i
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$	18.0000	−	31.1769i	1.31982	−	2.28600i
$187$	1.50000	+	2.59808i	0.109691	+	0.189990i
$188$	−18.0000			−1.31278
$189$		0			0
$190$	12.0000			0.870572
$191$	−8.50000	−	14.7224i	−0.615038	−	1.06528i	−0.990378	−	0.138390i	$-0.955807\pi$
$191$	−8.50000	−	14.7224i	−0.615038	−	1.06528i	0.375339	−	0.926887i	$-0.377526\pi$
$192$	12.0000	−	20.7846i	0.866025	−	1.50000i
$193$	−6.00000	+	10.3923i	−0.431889	+	0.748054i	−0.997036	−	0.0769360i	$-0.975486\pi$
$193$	−6.00000	+	10.3923i	−0.431889	+	0.748054i	0.565147	+	0.824991i	$0.308820\pi$
$194$	−15.0000	−	25.9808i	−1.07694	−	1.86531i
$195$	−9.00000			−0.644503
$196$		0			0
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$	6.00000	+	10.3923i	0.426401	+	0.738549i
$199$	−3.00000	+	5.19615i	−0.212664	+	0.368345i	−0.952548	−	0.304390i	$-0.901547\pi$
$199$	−3.00000	+	5.19615i	−0.212664	+	0.368345i	0.739883	+	0.672735i	$0.234881\pi$
$200$		0			0
$201$	21.0000	+	36.3731i	1.48123	+	2.56556i
$202$	36.0000			2.53295
$203$		0			0
$204$	−18.0000			−1.26025
$205$	3.00000	+	5.19615i	0.209529	+	0.362915i
$206$	−9.00000	+	15.5885i	−0.627060	+	1.08610i
$207$	12.0000	−	20.7846i	0.834058	−	1.44463i
$208$	6.00000	+	10.3923i	0.416025	+	0.720577i
$209$	6.00000			0.415029
$210$		0			0
$211$	15.0000			1.03264			0.516321	−	0.856395i	$-0.327301\pi$
$211$	15.0000			1.03264			0.516321	+	0.856395i	$0.327301\pi$
$212$	10.0000	+	17.3205i	0.686803	+	1.18958i
$213$	12.0000	−	20.7846i	0.822226	−	1.42414i
$214$	−2.00000	+	3.46410i	−0.136717	+	0.236801i
$215$	−3.00000	−	5.19615i	−0.204598	−	0.354375i
$216$		0			0
$217$		0			0
$218$	30.0000			2.03186
$219$	−9.00000	−	15.5885i	−0.608164	−	1.05337i
$220$	1.00000	−	1.73205i	0.0674200	−	0.116775i
$221$	4.50000	−	7.79423i	0.302703	−	0.524297i
$222$		0			0
$223$	3.00000			0.200895			0.100447	−	0.994942i	$-0.467973\pi$
$223$	3.00000			0.200895			0.100447	+	0.994942i	$0.467973\pi$
$224$		0			0
$225$	6.00000			0.400000
$226$	8.00000	+	13.8564i	0.532152	+	0.921714i
$227$	−1.50000	+	2.59808i	−0.0995585	+	0.172440i	−0.911502	−	0.411296i	$-0.865076\pi$
$227$	−1.50000	+	2.59808i	−0.0995585	+	0.172440i	0.811943	+	0.583736i	$0.198410\pi$
$228$	−18.0000	+	31.1769i	−1.19208	+	2.06474i
$229$	3.00000	+	5.19615i	0.198246	+	0.343371i	0.947960	−	0.318390i	$-0.103142\pi$
$229$	3.00000	+	5.19615i	0.198246	+	0.343371i	−0.749714	+	0.661762i	$0.769809\pi$
$230$	−8.00000			−0.527504
$231$		0			0
$232$		0			0
$233$	4.00000	+	6.92820i	0.262049	+	0.453882i	0.966786	−	0.255586i	$-0.0822686\pi$
$233$	4.00000	+	6.92820i	0.262049	+	0.453882i	−0.704737	+	0.709468i	$0.748935\pi$
$234$	18.0000	−	31.1769i	1.17670	−	2.03810i
$235$	−4.50000	+	7.79423i	−0.293548	+	0.508439i
$236$	6.00000	+	10.3923i	0.390567	+	0.676481i
$237$	−3.00000			−0.194871
$238$		0			0
$239$	7.00000			0.452792			0.226396	−	0.974035i	$-0.427306\pi$
$239$	7.00000			0.452792			0.226396	+	0.974035i	$0.427306\pi$
$240$	−6.00000	−	10.3923i	−0.387298	−	0.670820i
$241$	12.0000	−	20.7846i	0.772988	−	1.33885i	−0.162930	−	0.986638i	$-0.552095\pi$
$241$	12.0000	−	20.7846i	0.772988	−	1.33885i	0.935918	−	0.352217i	$-0.114572\pi$
$242$	−10.0000	+	17.3205i	−0.642824	+	1.11340i
$243$		0			0
$244$		0			0
$245$		0			0
$246$	−36.0000			−2.29528
$247$	−9.00000	−	15.5885i	−0.572656	−	0.991870i
$248$		0			0
$249$	−18.0000	+	31.1769i	−1.14070	+	1.97576i
$250$	−1.00000	−	1.73205i	−0.0632456	−	0.109545i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	−4.00000			−0.251478
$254$	−2.00000	−	3.46410i	−0.125491	−	0.217357i
$255$	−4.50000	+	7.79423i	−0.281801	+	0.488094i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$	36.0000			2.24126
$259$		0			0
$260$	−6.00000			−0.372104
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$	12.0000	−	20.7846i	0.741362	−	1.28408i
$263$	5.00000	−	8.66025i	0.308313	−	0.534014i	−0.669680	−	0.742650i	$-0.733569\pi$
$263$	5.00000	−	8.66025i	0.308313	−	0.534014i	0.977993	+	0.208635i	$0.0669022\pi$
$264$		0			0
$265$	10.0000			0.614295
$266$		0			0
$267$	36.0000			2.20316
$268$	14.0000	+	24.2487i	0.855186	+	1.48123i
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	0.224523	+	0.974469i	$0.427917\pi$
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	−0.956176	+	0.292791i	$0.905416\pi$
$270$	−9.00000	+	15.5885i	−0.547723	+	0.948683i
$271$	−12.0000	−	20.7846i	−0.728948	−	1.26258i	−0.957328	−	0.289003i	$-0.906676\pi$
$271$	−12.0000	−	20.7846i	−0.728948	−	1.26258i	0.228380	−	0.973572i	$-0.426657\pi$
$272$	12.0000			0.727607
$273$		0			0
$274$	−16.0000			−0.966595
$275$	−0.500000	−	0.866025i	−0.0301511	−	0.0522233i
$276$	12.0000	−	20.7846i	0.722315	−	1.25109i
$277$	14.0000	−	24.2487i	0.841178	−	1.45696i	−0.0477206	−	0.998861i	$-0.515196\pi$
$277$	14.0000	−	24.2487i	0.841178	−	1.45696i	0.888899	−	0.458103i	$-0.151471\pi$
$278$		0			0
$279$	36.0000			2.15526
$280$		0			0
$281$	−5.00000			−0.298275			−0.149137	−	0.988816i	$-0.547650\pi$
$281$	−5.00000			−0.298275			−0.149137	+	0.988816i	$0.547650\pi$
$282$	−27.0000	−	46.7654i	−1.60783	−	2.78484i
$283$	−10.5000	+	18.1865i	−0.624160	+	1.08108i	0.364542	+	0.931187i	$0.381225\pi$
$283$	−10.5000	+	18.1865i	−0.624160	+	1.08108i	−0.988703	+	0.149890i	$0.952108\pi$
$284$	8.00000	−	13.8564i	0.474713	−	0.822226i
$285$	9.00000	+	15.5885i	0.533114	+	0.923381i
$286$	−6.00000			−0.354787
$287$		0			0
$288$	48.0000			2.82843
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	1.00000	−	1.73205i	0.0587220	−	0.101710i
$291$	22.5000	−	38.9711i	1.31897	−	2.28453i
$292$	−6.00000	−	10.3923i	−0.351123	−	0.608164i
$293$	9.00000			0.525786			0.262893	−	0.964825i	$-0.415323\pi$
$293$	9.00000			0.525786			0.262893	+	0.964825i	$0.415323\pi$
$294$		0			0
$295$	6.00000			0.349334
$296$		0			0
$297$	−4.50000	+	7.79423i	−0.261116	+	0.452267i
$298$	10.0000	−	17.3205i	0.579284	−	1.00335i
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$	6.00000			0.346410
$301$		0			0
$302$	−30.0000			−1.72631
$303$	27.0000	+	46.7654i	1.55111	+	2.68660i
$304$	12.0000	−	20.7846i	0.688247	−	1.19208i
$305$		0			0
$306$	−18.0000	−	31.1769i	−1.02899	−	1.78227i
$307$	−3.00000			−0.171219			−0.0856095	−	0.996329i	$-0.527284\pi$
$307$	−3.00000			−0.171219			−0.0856095	+	0.996329i	$0.527284\pi$
$308$		0			0
$309$	−27.0000			−1.53598
$310$	−6.00000	−	10.3923i	−0.340777	−	0.590243i
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	−0.768345	−	0.640036i	$-0.778920\pi$
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	0.938460	+	0.345389i	$0.112253\pi$
$312$		0			0
$313$	−1.50000	−	2.59808i	−0.0847850	−	0.146852i	0.820515	−	0.571626i	$-0.193687\pi$
$313$	−1.50000	−	2.59808i	−0.0847850	−	0.146852i	−0.905300	+	0.424774i	$0.860354\pi$
$314$	−36.0000			−2.03160
$315$		0			0
$316$	−2.00000			−0.112509
$317$	11.0000	+	19.0526i	0.617822	+	1.07010i	0.989882	+	0.141890i	$0.0453179\pi$
$317$	11.0000	+	19.0526i	0.617822	+	1.07010i	−0.372061	+	0.928208i	$0.621349\pi$
$318$	−30.0000	+	51.9615i	−1.68232	+	2.91386i
$319$	0.500000	−	0.866025i	0.0279946	−	0.0484881i
$320$	−4.00000	−	6.92820i	−0.223607	−	0.387298i
$321$	−6.00000			−0.334887
$322$		0			0
$323$	−18.0000			−1.00155
$324$	−9.00000	−	15.5885i	−0.500000	−	0.866025i
$325$	−1.50000	+	2.59808i	−0.0832050	+	0.144115i
$326$	16.0000	−	27.7128i	0.886158	−	1.53487i
$327$	22.5000	+	38.9711i	1.24425	+	2.15511i
$328$		0			0
$329$		0			0
$330$	6.00000			0.330289
$331$	−6.00000	−	10.3923i	−0.329790	−	0.571213i	0.652680	−	0.757634i	$-0.273645\pi$
$331$	−6.00000	−	10.3923i	−0.329790	−	0.571213i	−0.982470	+	0.186421i	$0.940311\pi$
$332$	−12.0000	+	20.7846i	−0.658586	+	1.14070i
$333$		0			0
$334$	3.00000	+	5.19615i	0.164153	+	0.284321i
$335$	14.0000			0.764902
$336$		0			0
$337$	−24.0000			−1.30736			−0.653682	−	0.756770i	$-0.726776\pi$
$337$	−24.0000			−1.30736			−0.653682	+	0.756770i	$0.726776\pi$
$338$	−4.00000	−	6.92820i	−0.217571	−	0.376845i
$339$	−12.0000	+	20.7846i	−0.651751	+	1.12887i
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$	−3.00000	−	5.19615i	−0.162459	−	0.281387i
$342$	−72.0000			−3.89331
$343$		0			0
$344$		0			0
$345$	−6.00000	−	10.3923i	−0.323029	−	0.559503i
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	−8.00000	+	13.8564i	−0.429463	+	0.743851i	−0.996826	−	0.0796169i	$-0.974630\pi$
$347$	−8.00000	+	13.8564i	−0.429463	+	0.743851i	0.567363	+	0.823468i	$0.307964\pi$
$348$	3.00000	+	5.19615i	0.160817	+	0.278543i
$349$	−30.0000			−1.60586			−0.802932	−	0.596071i	$-0.796728\pi$
$349$	−30.0000			−1.60586			−0.802932	+	0.596071i	$0.796728\pi$
$350$		0			0
$351$	27.0000			1.44115
$352$	−4.00000	−	6.92820i	−0.213201	−	0.369274i
$353$	1.50000	−	2.59808i	0.0798369	−	0.138282i	−0.823343	−	0.567545i	$-0.807893\pi$
$353$	1.50000	−	2.59808i	0.0798369	−	0.138282i	0.903179	+	0.429263i	$0.141227\pi$
$354$	−18.0000	+	31.1769i	−0.956689	+	1.65703i
$355$	−4.00000	−	6.92820i	−0.212298	−	0.367711i
$356$	24.0000			1.27200
$357$		0			0
$358$	−8.00000			−0.422813
$359$	−16.0000	−	27.7128i	−0.844448	−	1.46263i	−0.886100	−	0.463494i	$-0.846596\pi$
$359$	−16.0000	−	27.7128i	−0.844448	−	1.46263i	0.0416523	−	0.999132i	$-0.486738\pi$
$360$		0			0
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	−6.00000	−	10.3923i	−0.315353	−	0.546207i
$363$	−30.0000			−1.57459
$364$		0			0
$365$	−6.00000			−0.314054
$366$		0			0
$367$	16.5000	−	28.5788i	0.861293	−	1.49180i	−0.00938849	−	0.999956i	$-0.502988\pi$
$367$	16.5000	−	28.5788i	0.861293	−	1.49180i	0.870681	−	0.491847i	$-0.163678\pi$
$368$	−8.00000	+	13.8564i	−0.417029	+	0.722315i
$369$	−18.0000	−	31.1769i	−0.937043	−	1.62301i
$370$		0			0
$371$		0			0
$372$	36.0000			1.86651
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	0.809591	−	0.586994i	$-0.199689\pi$
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	−0.913147	+	0.407630i	$0.866355\pi$
$374$	−3.00000	+	5.19615i	−0.155126	+	0.268687i
$375$	1.50000	−	2.59808i	0.0774597	−	0.134164i
$376$		0			0
$377$	−3.00000			−0.154508
$378$		0			0
$379$	−24.0000			−1.23280			−0.616399	−	0.787434i	$-0.711409\pi$
$379$	−24.0000			−1.23280			−0.616399	+	0.787434i	$0.711409\pi$
$380$	6.00000	+	10.3923i	0.307794	+	0.533114i
$381$	3.00000	−	5.19615i	0.153695	−	0.266207i
$382$	17.0000	−	29.4449i	0.869796	−	1.50653i
$383$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$383$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$384$		0			0
$385$		0			0
$386$	−24.0000			−1.22157
$387$	18.0000	+	31.1769i	0.914991	+	1.58481i
$388$	15.0000	−	25.9808i	0.761510	−	1.31897i
$389$	−6.50000	+	11.2583i	−0.329563	+	0.570820i	−0.982425	−	0.186657i	$-0.940235\pi$
$389$	−6.50000	+	11.2583i	−0.329563	+	0.570820i	0.652862	+	0.757477i	$0.273568\pi$
$390$	−9.00000	−	15.5885i	−0.455733	−	0.789352i
$391$	12.0000			0.606866
$392$		0			0
$393$	36.0000			1.81596
$394$	−2.00000	−	3.46410i	−0.100759	−	0.174519i
$395$	−0.500000	+	0.866025i	−0.0251577	+	0.0435745i
$396$	−6.00000	+	10.3923i	−0.301511	+	0.522233i
$397$	−4.50000	−	7.79423i	−0.225849	−	0.391181i	0.730725	−	0.682672i	$-0.239182\pi$
$397$	−4.50000	−	7.79423i	−0.225849	−	0.391181i	−0.956574	+	0.291491i	$0.905849\pi$
$398$	−12.0000			−0.601506
$399$		0			0
$400$	−4.00000			−0.200000
$401$	9.50000	+	16.4545i	0.474407	+	0.821698i	0.999571	−	0.0293039i	$-0.00932905\pi$
$401$	9.50000	+	16.4545i	0.474407	+	0.821698i	−0.525163	+	0.851002i	$0.675996\pi$
$402$	−42.0000	+	72.7461i	−2.09477	+	3.62825i
$403$	−9.00000	+	15.5885i	−0.448322	+	0.776516i
$404$	18.0000	+	31.1769i	0.895533	+	1.55111i
$405$	−9.00000			−0.447214
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−15.0000	+	25.9808i	−0.741702	+	1.28467i	0.210017	+	0.977698i	$0.432648\pi$
$409$	−15.0000	+	25.9808i	−0.741702	+	1.28467i	−0.951720	+	0.306968i	$0.900685\pi$
$410$	−6.00000	+	10.3923i	−0.296319	+	0.513239i
$411$	−12.0000	−	20.7846i	−0.591916	−	1.02523i
$412$	−18.0000			−0.886796
$413$		0			0
$414$	48.0000			2.35907
$415$	6.00000	+	10.3923i	0.294528	+	0.510138i
$416$	−12.0000	+	20.7846i	−0.588348	+	1.01905i
$417$		0			0
$418$	6.00000	+	10.3923i	0.293470	+	0.508304i
$419$	−6.00000			−0.293119			−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000			−0.293119			−0.146560	+	0.989202i	$0.546820\pi$
$420$		0			0
$421$	1.00000			0.0487370			0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000			0.0487370			0.0243685	+	0.999703i	$0.492242\pi$
$422$	15.0000	+	25.9808i	0.730189	+	1.26472i
$423$	27.0000	−	46.7654i	1.31278	−	2.27381i
$424$		0			0
$425$	1.50000	+	2.59808i	0.0727607	+	0.126025i
$426$	48.0000			2.32561
$427$		0			0
$428$	−4.00000			−0.193347
$429$	−4.50000	−	7.79423i	−0.217262	−	0.376309i
$430$	6.00000	−	10.3923i	0.289346	−	0.501161i
$431$	−2.50000	+	4.33013i	−0.120421	+	0.208575i	−0.919934	−	0.392074i	$-0.871758\pi$
$431$	−2.50000	+	4.33013i	−0.120421	+	0.208575i	0.799513	+	0.600649i	$0.205091\pi$
$432$	18.0000	+	31.1769i	0.866025	+	1.50000i
$433$	−30.0000			−1.44171			−0.720854	−	0.693087i	$-0.756250\pi$
$433$	−30.0000			−1.44171			−0.720854	+	0.693087i	$0.756250\pi$
$434$		0			0
$435$	3.00000			0.143839
$436$	15.0000	+	25.9808i	0.718370	+	1.24425i
$437$	12.0000	−	20.7846i	0.574038	−	0.994263i
$438$	18.0000	−	31.1769i	0.860073	−	1.48969i
$439$	−6.00000	−	10.3923i	−0.286364	−	0.495998i	0.686575	−	0.727059i	$-0.259113\pi$
$439$	−6.00000	−	10.3923i	−0.286364	−	0.495998i	−0.972939	+	0.231062i	$0.925780\pi$
$440$		0			0
$441$		0			0
$442$	18.0000			0.856173
$443$	−17.0000	−	29.4449i	−0.807694	−	1.39897i	−0.914457	−	0.404683i	$-0.867382\pi$
$443$	−17.0000	−	29.4449i	−0.807694	−	1.39897i	0.106763	−	0.994285i	$-0.465952\pi$
$444$		0			0
$445$	6.00000	−	10.3923i	0.284427	−	0.492642i
$446$	3.00000	+	5.19615i	0.142054	+	0.246045i
$447$	30.0000			1.41895
$448$		0			0
$449$	23.0000			1.08544			0.542719	−	0.839915i	$-0.317395\pi$
$449$	23.0000			1.08544			0.542719	+	0.839915i	$0.317395\pi$
$450$	6.00000	+	10.3923i	0.282843	+	0.489898i
$451$	−3.00000	+	5.19615i	−0.141264	+	0.244677i
$452$	−8.00000	+	13.8564i	−0.376288	+	0.651751i
$453$	−22.5000	−	38.9711i	−1.05714	−	1.83102i
$454$	−6.00000			−0.281594
$455$		0			0
$456$		0			0
$457$	−3.00000	−	5.19615i	−0.140334	−	0.243066i	0.787288	−	0.616585i	$-0.211484\pi$
$457$	−3.00000	−	5.19615i	−0.140334	−	0.243066i	−0.927622	+	0.373519i	$0.878151\pi$
$458$	−6.00000	+	10.3923i	−0.280362	+	0.485601i
$459$	13.5000	−	23.3827i	0.630126	−	1.09141i
$460$	−4.00000	−	6.92820i	−0.186501	−	0.323029i
$461$	36.0000			1.67669			0.838344	−	0.545142i	$-0.183524\pi$
$461$	36.0000			1.67669			0.838344	+	0.545142i	$0.183524\pi$
$462$		0			0
$463$	−4.00000			−0.185896			−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000			−0.185896			−0.0929479	+	0.995671i	$0.529629\pi$
$464$	−2.00000	−	3.46410i	−0.0928477	−	0.160817i
$465$	9.00000	−	15.5885i	0.417365	−	0.722897i
$466$	−8.00000	+	13.8564i	−0.370593	+	0.641886i
$467$	7.50000	+	12.9904i	0.347059	+	0.601123i	0.985726	−	0.168360i	$-0.0538472\pi$
$467$	7.50000	+	12.9904i	0.347059	+	0.601123i	−0.638667	+	0.769483i	$0.720514\pi$
$468$	36.0000			1.66410
$469$		0			0
$470$	−18.0000			−0.830278
$471$	−27.0000	−	46.7654i	−1.24409	−	2.15483i
$472$		0			0
$473$	3.00000	−	5.19615i	0.137940	−	0.238919i
$474$	−3.00000	−	5.19615i	−0.137795	−	0.238667i
$475$	6.00000			0.275299
$476$		0			0
$477$	−60.0000			−2.74721
$478$	7.00000	+	12.1244i	0.320173	+	0.554555i
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$	12.0000	−	20.7846i	0.547723	−	0.948683i
$481$		0			0
$482$	48.0000			2.18634
$483$		0			0
$484$	−20.0000			−0.909091
$485$	−7.50000	−	12.9904i	−0.340557	−	0.589863i
$486$		0			0
$487$	−18.0000	+	31.1769i	−0.815658	+	1.41276i	0.0931967	+	0.995648i	$0.470291\pi$
$487$	−18.0000	+	31.1769i	−0.815658	+	1.41276i	−0.908855	+	0.417113i	$0.863042\pi$
$488$		0			0
$489$	48.0000			2.17064
$490$		0			0
$491$	23.0000			1.03798			0.518988	−	0.854782i	$-0.326309\pi$
$491$	23.0000			1.03798			0.518988	+	0.854782i	$0.326309\pi$
$492$	−18.0000	−	31.1769i	−0.811503	−	1.40556i
$493$	−1.50000	+	2.59808i	−0.0675566	+	0.117011i
$494$	18.0000	−	31.1769i	0.809858	−	1.40272i
$495$	3.00000	+	5.19615i	0.134840	+	0.233550i
$496$	−24.0000			−1.07763
$497$		0			0
$498$	−72.0000			−3.22640
$499$	13.5000	+	23.3827i	0.604343	+	1.04675i	0.992155	+	0.125014i	$0.0398977\pi$
$499$	13.5000	+	23.3827i	0.604343	+	1.04675i	−0.387812	+	0.921739i	$0.626769\pi$
$500$	1.00000	−	1.73205i	0.0447214	−	0.0774597i
$501$	−4.50000	+	7.79423i	−0.201045	+	0.348220i
$502$	−12.0000	−	20.7846i	−0.535586	−	0.927663i
$503$	9.00000			0.401290			0.200645	−	0.979664i	$-0.435696\pi$
$503$	9.00000			0.401290			0.200645	+	0.979664i	$0.435696\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$	−4.00000	−	6.92820i	−0.177822	−	0.307996i
$507$	6.00000	−	10.3923i	0.266469	−	0.461538i
$508$	2.00000	−	3.46410i	0.0887357	−	0.153695i
$509$	12.0000	+	20.7846i	0.531891	+	0.921262i	0.999307	+	0.0372243i	$0.0118516\pi$
$509$	12.0000	+	20.7846i	0.531891	+	0.921262i	−0.467416	+	0.884037i	$0.654815\pi$
$510$	−18.0000			−0.797053
$511$		0			0
$512$	−32.0000			−1.41421
$513$	−27.0000	−	46.7654i	−1.19208	−	2.06474i
$514$	18.0000	−	31.1769i	0.793946	−	1.37515i
$515$	−4.50000	+	7.79423i	−0.198294	+	0.343455i
$516$	18.0000	+	31.1769i	0.792406	+	1.37249i
$517$	−9.00000			−0.395820
$518$		0			0
$519$	−9.00000			−0.395056
$520$		0			0
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	−0.598714	−	0.800963i	$-0.704321\pi$
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	0.993011	+	0.118020i	$0.0376547\pi$
$522$	−6.00000	+	10.3923i	−0.262613	+	0.454859i
$523$	−12.0000	−	20.7846i	−0.524723	−	0.908848i	−0.999586	−	0.0287874i	$-0.990835\pi$
$523$	−12.0000	−	20.7846i	−0.524723	−	0.908848i	0.474862	−	0.880060i	$-0.342498\pi$
$524$	24.0000			1.04844
$525$		0			0
$526$	20.0000			0.872041
$527$	9.00000	+	15.5885i	0.392046	+	0.679044i
$528$	6.00000	−	10.3923i	0.261116	−	0.452267i
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	10.0000	+	17.3205i	0.434372	+	0.752355i
$531$	−36.0000			−1.56227
$532$		0			0
$533$	18.0000			0.779667
$534$	36.0000	+	62.3538i	1.55787	+	2.69831i
$535$	−1.00000	+	1.73205i	−0.0432338	+	0.0748831i
$536$		0			0
$537$	−6.00000	−	10.3923i	−0.258919	−	0.448461i
$538$	−48.0000			−2.06943
$539$		0			0
$540$	−18.0000			−0.774597
$541$	−5.50000	−	9.52628i	−0.236463	−	0.409567i	0.723234	−	0.690604i	$-0.242655\pi$
$541$	−5.50000	−	9.52628i	−0.236463	−	0.409567i	−0.959697	+	0.281037i	$0.909322\pi$
$542$	24.0000	−	41.5692i	1.03089	−	1.78555i
$543$	9.00000	−	15.5885i	0.386227	−	0.668965i
$544$	12.0000	+	20.7846i	0.514496	+	0.891133i
$545$	15.0000			0.642529
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	−8.00000	−	13.8564i	−0.341743	−	0.591916i
$549$		0			0
$550$	1.00000	−	1.73205i	0.0426401	−	0.0738549i
$551$	3.00000	+	5.19615i	0.127804	+	0.221364i
$552$		0			0
$553$		0			0
$554$	56.0000			2.37921
$555$		0			0
$556$		0			0
$557$	−2.00000	+	3.46410i	−0.0847427	+	0.146779i	−0.905282	−	0.424812i	$-0.860340\pi$
$557$	−2.00000	+	3.46410i	−0.0847427	+	0.146779i	0.820539	+	0.571591i	$0.193674\pi$
$558$	36.0000	+	62.3538i	1.52400	+	2.63965i
$559$	−18.0000			−0.761319
$560$		0			0
$561$	−9.00000			−0.379980
$562$	−5.00000	−	8.66025i	−0.210912	−	0.365311i
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	−0.964315	−	0.264758i	$-0.914708\pi$
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	0.711445	+	0.702742i	$0.248041\pi$
$564$	27.0000	−	46.7654i	1.13691	−	1.96918i
$565$	4.00000	+	6.92820i	0.168281	+	0.291472i
$566$	−42.0000			−1.76539
$567$		0			0
$568$		0			0
$569$	19.0000	+	32.9090i	0.796521	+	1.37962i	0.921869	+	0.387503i	$0.126662\pi$
$569$	19.0000	+	32.9090i	0.796521	+	1.37962i	−0.125347	+	0.992113i	$0.540004\pi$
$570$	−18.0000	+	31.1769i	−0.753937	+	1.30586i
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	−0.904835	−	0.425762i	$-0.860006\pi$
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	0.821138	+	0.570730i	$0.193340\pi$
$572$	−3.00000	−	5.19615i	−0.125436	−	0.217262i
$573$	51.0000			2.13056
$574$		0			0
$575$	−4.00000			−0.166812
$576$	24.0000	+	41.5692i	1.00000	+	1.73205i
$577$	−7.50000	+	12.9904i	−0.312229	+	0.540797i	−0.978845	−	0.204605i	$-0.934409\pi$
$577$	−7.50000	+	12.9904i	−0.312229	+	0.540797i	0.666616	+	0.745402i	$0.267742\pi$
$578$	−8.00000	+	13.8564i	−0.332756	+	0.576351i
$579$	−18.0000	−	31.1769i	−0.748054	−	1.29567i
$580$	2.00000			0.0830455
$581$		0			0
$582$	90.0000			3.73062
$583$	5.00000	+	8.66025i	0.207079	+	0.358671i
$584$		0			0
$585$	9.00000	−	15.5885i	0.372104	−	0.644503i
$586$	9.00000	+	15.5885i	0.371787	+	0.643953i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	36.0000			1.48335
$590$	6.00000	+	10.3923i	0.247016	+	0.427844i
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$		0			0
$593$	22.5000	+	38.9711i	0.923964	+	1.60035i	0.793219	+	0.608937i	$0.208404\pi$
$593$	22.5000	+	38.9711i	0.923964	+	1.60035i	0.130746	+	0.991416i	$0.458263\pi$
$594$	−18.0000			−0.738549
$595$		0			0
$596$	20.0000			0.819232
$597$	−9.00000	−	15.5885i	−0.368345	−	0.637993i
$598$	−12.0000	+	20.7846i	−0.490716	+	0.849946i
$599$	−8.50000	+	14.7224i	−0.347301	+	0.601542i	−0.985769	−	0.168106i	$-0.946235\pi$
$599$	−8.50000	+	14.7224i	−0.347301	+	0.601542i	0.638468	+	0.769648i	$0.279568\pi$
$600$		0			0
$601$	−30.0000			−1.22373			−0.611863	−	0.790964i	$-0.709580\pi$
$601$	−30.0000			−1.22373			−0.611863	+	0.790964i	$0.709580\pi$
$602$		0			0
$603$	−84.0000			−3.42074
$604$	−15.0000	−	25.9808i	−0.610341	−	1.05714i
$605$	−5.00000	+	8.66025i	−0.203279	+	0.352089i
$606$	−54.0000	+	93.5307i	−2.19360	+	3.79943i
$607$	−10.5000	−	18.1865i	−0.426182	−	0.738169i	0.570348	−	0.821403i	$-0.306808\pi$
$607$	−10.5000	−	18.1865i	−0.426182	−	0.738169i	−0.996530	+	0.0832344i	$0.973475\pi$
$608$	48.0000			1.94666
$609$		0			0
$610$		0			0
$611$	13.5000	+	23.3827i	0.546152	+	0.945962i
$612$	18.0000	−	31.1769i	0.727607	−	1.26025i
$613$	1.00000	−	1.73205i	0.0403896	−	0.0699569i	−0.845124	−	0.534570i	$-0.820473\pi$
$613$	1.00000	−	1.73205i	0.0403896	−	0.0699569i	0.885514	+	0.464614i	$0.153807\pi$
$614$	−3.00000	−	5.19615i	−0.121070	−	0.209700i
$615$	−18.0000			−0.725830
$616$		0			0
$617$	4.00000			0.161034			0.0805170	−	0.996753i	$-0.474343\pi$
$617$	4.00000			0.161034			0.0805170	+	0.996753i	$0.474343\pi$
$618$	−27.0000	−	46.7654i	−1.08610	−	1.88118i
$619$	12.0000	−	20.7846i	0.482321	−	0.835404i	−0.517473	−	0.855699i	$-0.673127\pi$
$619$	12.0000	−	20.7846i	0.482321	−	0.835404i	0.999794	+	0.0202954i	$0.00646066\pi$
$620$	6.00000	−	10.3923i	0.240966	−	0.417365i
$621$	18.0000	+	31.1769i	0.722315	+	1.25109i
$622$	12.0000			0.481156
$623$		0			0
$624$	−36.0000			−1.44115
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	3.00000	−	5.19615i	0.119904	−	0.207680i
$627$	−9.00000	+	15.5885i	−0.359425	+	0.622543i
$628$	−18.0000	−	31.1769i	−0.718278	−	1.24409i
$629$		0			0
$630$		0			0
$631$	−11.0000			−0.437903			−0.218952	−	0.975736i	$-0.570264\pi$
$631$	−11.0000			−0.437903			−0.218952	+	0.975736i	$0.570264\pi$
$632$		0			0
$633$	−22.5000	+	38.9711i	−0.894295	+	1.54896i
$634$	−22.0000	+	38.1051i	−0.873732	+	1.51335i
$635$	−1.00000	−	1.73205i	−0.0396838	−	0.0687343i
$636$	−60.0000			−2.37915
$637$		0			0
$638$	2.00000			0.0791808
$639$	24.0000	+	41.5692i	0.949425	+	1.64445i
$640$		0			0
$641$	1.00000	−	1.73205i	0.0394976	−	0.0684119i	−0.845601	−	0.533816i	$-0.820758\pi$
$641$	1.00000	−	1.73205i	0.0394976	−	0.0684119i	0.885098	+	0.465404i	$0.154091\pi$
$642$	−6.00000	−	10.3923i	−0.236801	−	0.410152i
$643$	27.0000			1.06478			0.532388	−	0.846500i	$-0.321295\pi$
$643$	27.0000			1.06478			0.532388	+	0.846500i	$0.321295\pi$
$644$		0			0
$645$	18.0000			0.708749
$646$	−18.0000	−	31.1769i	−0.708201	−	1.22664i
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	−0.959529	−	0.281609i	$-0.909132\pi$
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	0.723645	+	0.690172i	$0.242465\pi$
$648$		0			0
$649$	3.00000	+	5.19615i	0.117760	+	0.203967i
$650$	−6.00000			−0.235339
$651$		0			0
$652$	32.0000			1.25322
$653$	−7.00000	−	12.1244i	−0.273931	−	0.474463i	0.695934	−	0.718106i	$-0.254991\pi$
$653$	−7.00000	−	12.1244i	−0.273931	−	0.474463i	−0.969865	+	0.243643i	$0.921657\pi$
$654$	−45.0000	+	77.9423i	−1.75964	+	3.04778i
$655$	6.00000	−	10.3923i	0.234439	−	0.406061i
$656$	12.0000	+	20.7846i	0.468521	+	0.811503i
$657$	36.0000			1.40449
$658$		0			0
$659$	−19.0000			−0.740135			−0.370067	−	0.929005i	$-0.620665\pi$
$659$	−19.0000			−0.740135			−0.370067	+	0.929005i	$0.620665\pi$
$660$	3.00000	+	5.19615i	0.116775	+	0.202260i
$661$	−6.00000	+	10.3923i	−0.233373	+	0.404214i	−0.958799	−	0.284087i	$-0.908310\pi$
$661$	−6.00000	+	10.3923i	−0.233373	+	0.404214i	0.725426	+	0.688301i	$0.241643\pi$
$662$	12.0000	−	20.7846i	0.466393	−	0.807817i
$663$	13.5000	+	23.3827i	0.524297	+	0.908108i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−2.00000	−	3.46410i	−0.0774403	−	0.134131i
$668$	−3.00000	+	5.19615i	−0.116073	+	0.201045i
$669$	−4.50000	+	7.79423i	−0.173980	+	0.301342i
$670$	14.0000	+	24.2487i	0.540867	+	0.936809i
$671$		0			0
$672$		0			0
$673$	12.0000			0.462566			0.231283	−	0.972887i	$-0.425708\pi$
$673$	12.0000			0.462566			0.231283	+	0.972887i	$0.425708\pi$
$674$	−24.0000	−	41.5692i	−0.924445	−	1.60119i
$675$	−4.50000	+	7.79423i	−0.173205	+	0.300000i
$676$	4.00000	−	6.92820i	0.153846	−	0.266469i
$677$	4.50000	+	7.79423i	0.172949	+	0.299557i	0.939450	−	0.342687i	$-0.111337\pi$
$677$	4.50000	+	7.79423i	0.172949	+	0.299557i	−0.766501	+	0.642244i	$0.778004\pi$
$678$	−48.0000			−1.84343
$679$		0			0
$680$		0			0
$681$	−4.50000	−	7.79423i	−0.172440	−	0.298675i
$682$	6.00000	−	10.3923i	0.229752	−	0.397942i
$683$	−4.00000	+	6.92820i	−0.153056	+	0.265100i	−0.932349	−	0.361559i	$-0.882245\pi$
$683$	−4.00000	+	6.92820i	−0.153056	+	0.265100i	0.779294	+	0.626659i	$0.215578\pi$
$684$	−36.0000	−	62.3538i	−1.37649	−	2.38416i
$685$	−8.00000			−0.305664
$686$		0			0
$687$	−18.0000			−0.686743
$688$	−12.0000	−	20.7846i	−0.457496	−	0.792406i
$689$	15.0000	−	25.9808i	0.571454	−	0.989788i
$690$	12.0000	−	20.7846i	0.456832	−	0.791257i
$691$	−18.0000	−	31.1769i	−0.684752	−	1.18603i	−0.973515	−	0.228625i	$-0.926577\pi$
$691$	−18.0000	−	31.1769i	−0.684752	−	1.18603i	0.288762	−	0.957401i	$-0.406756\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−32.0000			−1.21470
$695$		0			0
$696$		0			0
$697$	9.00000	−	15.5885i	0.340899	−	0.590455i
$698$	−30.0000	−	51.9615i	−1.13552	−	1.96677i
$699$	−24.0000			−0.907763
$700$		0			0
$701$	47.0000			1.77517			0.887583	−	0.460648i	$-0.152383\pi$
$701$	47.0000			1.77517			0.887583	+	0.460648i	$0.152383\pi$
$702$	27.0000	+	46.7654i	1.01905	+	1.76505i
$703$		0			0
$704$	4.00000	−	6.92820i	0.150756	−	0.261116i
$705$	−13.5000	−	23.3827i	−0.508439	−	0.880643i
$706$	6.00000			0.225813
$707$		0			0
$708$	−36.0000			−1.35296
$709$	16.5000	+	28.5788i	0.619671	+	1.07330i	0.989546	+	0.144219i	$0.0460671\pi$
$709$	16.5000	+	28.5788i	0.619671	+	1.07330i	−0.369875	+	0.929081i	$0.620600\pi$
$710$	8.00000	−	13.8564i	0.300235	−	0.520022i
$711$	3.00000	−	5.19615i	0.112509	−	0.194871i
$712$		0			0
$713$	−24.0000			−0.898807
$714$		0			0
$715$	−3.00000			−0.112194
$716$	−4.00000	−	6.92820i	−0.149487	−	0.258919i
$717$	−10.5000	+	18.1865i	−0.392130	+	0.679189i
$718$	32.0000	−	55.4256i	1.19423	−	2.06847i
$719$	18.0000	+	31.1769i	0.671287	+	1.16270i	0.977539	+	0.210752i	$0.0675914\pi$
$719$	18.0000	+	31.1769i	0.671287	+	1.16270i	−0.306253	+	0.951950i	$0.599075\pi$
$720$	24.0000			0.894427
$721$		0			0
$722$	−34.0000			−1.26535
$723$	36.0000	+	62.3538i	1.33885	+	2.31896i
$724$	6.00000	−	10.3923i	0.222988	−	0.386227i
$725$	0.500000	−	0.866025i	0.0185695	−	0.0321634i
$726$	−30.0000	−	51.9615i	−1.11340	−	1.92847i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−6.00000	−	10.3923i	−0.222070	−	0.384636i
$731$	−9.00000	+	15.5885i	−0.332877	+	0.576560i
$732$		0			0
$733$	−7.50000	−	12.9904i	−0.277019	−	0.479811i	0.693624	−	0.720338i	$-0.256013\pi$
$733$	−7.50000	−	12.9904i	−0.277019	−	0.479811i	−0.970642	+	0.240527i	$0.922680\pi$
$734$	66.0000			2.43610
$735$		0			0
$736$	−32.0000			−1.17954
$737$	7.00000	+	12.1244i	0.257848	+	0.446606i
$738$	36.0000	−	62.3538i	1.32518	−	2.29528i
$739$	21.5000	−	37.2391i	0.790890	−	1.36986i	−0.134526	−	0.990910i	$-0.542951\pi$
$739$	21.5000	−	37.2391i	0.790890	−	1.36986i	0.925416	−	0.378952i	$-0.123715\pi$
$740$		0			0
$741$	54.0000			1.98374
$742$		0			0
$743$	−22.0000			−0.807102			−0.403551	−	0.914957i	$-0.632224\pi$
$743$	−22.0000			−0.807102			−0.403551	+	0.914957i	$0.632224\pi$
$744$		0			0
$745$	5.00000	−	8.66025i	0.183186	−	0.317287i
$746$	4.00000	−	6.92820i	0.146450	−	0.253660i
$747$	−36.0000	−	62.3538i	−1.31717	−	2.28141i
$748$	−6.00000			−0.219382
$749$		0			0
$750$	6.00000			0.219089
$751$	−7.50000	−	12.9904i	−0.273679	−	0.474026i	0.696122	−	0.717923i	$-0.254907\pi$
$751$	−7.50000	−	12.9904i	−0.273679	−	0.474026i	−0.969801	+	0.243898i	$0.921574\pi$
$752$	−18.0000	+	31.1769i	−0.656392	+	1.13691i
$753$	18.0000	−	31.1769i	0.655956	−	1.13615i
$754$	−3.00000	−	5.19615i	−0.109254	−	0.189233i
$755$	−15.0000			−0.545906
$756$		0			0
$757$	48.0000			1.74459			0.872295	−	0.488980i	$-0.162631\pi$
$757$	48.0000			1.74459			0.872295	+	0.488980i	$0.162631\pi$
$758$	−24.0000	−	41.5692i	−0.871719	−	1.50986i
$759$	6.00000	−	10.3923i	0.217786	−	0.377217i
$760$		0			0
$761$	−6.00000	−	10.3923i	−0.217500	−	0.376721i	0.736543	−	0.676391i	$-0.236457\pi$
$761$	−6.00000	−	10.3923i	−0.217500	−	0.376721i	−0.954043	+	0.299670i	$0.903123\pi$
$762$	12.0000			0.434714
$763$		0			0
$764$	34.0000			1.23008
$765$	−9.00000	−	15.5885i	−0.325396	−	0.563602i
$766$		0			0
$767$	9.00000	−	15.5885i	0.324971	−	0.562867i
$768$	−24.0000	−	41.5692i	−0.866025	−	1.50000i
$769$	42.0000			1.51456			0.757279	−	0.653091i	$-0.226528\pi$
$769$	42.0000			1.51456			0.757279	+	0.653091i	$0.226528\pi$
$770$		0			0
$771$	54.0000			1.94476
$772$	−12.0000	−	20.7846i	−0.431889	−	0.748054i
$773$	−1.50000	+	2.59808i	−0.0539513	+	0.0934463i	−0.891740	−	0.452549i	$-0.850515\pi$
$773$	−1.50000	+	2.59808i	−0.0539513	+	0.0934463i	0.837788	+	0.545995i	$0.183848\pi$
$774$	−36.0000	+	62.3538i	−1.29399	+	2.24126i
$775$	−3.00000	−	5.19615i	−0.107763	−	0.186651i
$776$		0			0
$777$		0			0
$778$	−26.0000			−0.932145
$779$	−18.0000	−	31.1769i	−0.644917	−	1.11703i
$780$	9.00000	−	15.5885i	0.322252	−	0.558156i
$781$	4.00000	−	6.92820i	0.143131	−	0.247911i
$782$	12.0000	+	20.7846i	0.429119	+	0.743256i
$783$	−9.00000			−0.321634
$784$		0			0
$785$	−18.0000			−0.642448
$786$	36.0000	+	62.3538i	1.28408	+	2.22409i
$787$	−19.5000	+	33.7750i	−0.695100	+	1.20395i	0.275047	+	0.961431i	$0.411307\pi$
$787$	−19.5000	+	33.7750i	−0.695100	+	1.20395i	−0.970147	+	0.242518i	$0.922027\pi$
$788$	2.00000	−	3.46410i	0.0712470	−	0.123404i
$789$	15.0000	+	25.9808i	0.534014	+	0.924940i
$790$	−2.00000			−0.0711568
$791$		0			0
$792$		0			0
$793$		0			0
$794$	9.00000	−	15.5885i	0.319398	−	0.553214i
$795$	−15.0000	+	25.9808i	−0.531995	+	0.921443i
$796$	−6.00000	−	10.3923i	−0.212664	−	0.368345i
$797$	−27.0000			−0.956389			−0.478195	−	0.878254i	$-0.658709\pi$
$797$	−27.0000			−0.956389			−0.478195	+	0.878254i	$0.658709\pi$
$798$		0			0
$799$	27.0000			0.955191
$800$	−4.00000	−	6.92820i	−0.141421	−	0.244949i
$801$	−36.0000	+	62.3538i	−1.27200	+	2.20316i
$802$	−19.0000	+	32.9090i	−0.670913	+	1.16206i
$803$	−3.00000	−	5.19615i	−0.105868	−	0.183368i
$804$	−84.0000			−2.96245
$805$		0			0
$806$	−36.0000			−1.26805
$807$	−36.0000	−	62.3538i	−1.26726	−	2.19496i
$808$		0			0
$809$	17.5000	−	30.3109i	0.615267	−	1.06567i	−0.375070	−	0.926996i	$-0.622381\pi$
$809$	17.5000	−	30.3109i	0.615267	−	1.06567i	0.990338	−	0.138678i	$-0.0442852\pi$
$810$	−9.00000	−	15.5885i	−0.316228	−	0.547723i
$811$	48.0000			1.68551			0.842754	−	0.538299i	$-0.180933\pi$
$811$	48.0000			1.68551			0.842754	+	0.538299i	$0.180933\pi$
$812$		0			0
$813$	72.0000			2.52515
$814$		0			0
$815$	8.00000	−	13.8564i	0.280228	−	0.485369i
$816$	−18.0000	+	31.1769i	−0.630126	+	1.09141i
$817$	18.0000	+	31.1769i	0.629740	+	1.09074i
$818$	−60.0000			−2.09785
$819$		0			0
$820$	−12.0000			−0.419058
$821$	11.5000	+	19.9186i	0.401353	+	0.695163i	0.993889	−	0.110380i	$-0.0352068\pi$
$821$	11.5000	+	19.9186i	0.401353	+	0.695163i	−0.592537	+	0.805543i	$0.701873\pi$
$822$	24.0000	−	41.5692i	0.837096	−	1.44989i
$823$	−25.0000	+	43.3013i	−0.871445	+	1.50939i	−0.0109433	+	0.999940i	$0.503483\pi$
$823$	−25.0000	+	43.3013i	−0.871445	+	1.50939i	−0.860502	+	0.509447i	$0.829850\pi$
$824$		0			0
$825$	3.00000			0.104447
$826$		0			0
$827$	−16.0000			−0.556375			−0.278187	−	0.960527i	$-0.589734\pi$
$827$	−16.0000			−0.556375			−0.278187	+	0.960527i	$0.589734\pi$
$828$	24.0000	+	41.5692i	0.834058	+	1.44463i
$829$	−3.00000	+	5.19615i	−0.104194	+	0.180470i	−0.913409	−	0.407044i	$-0.866560\pi$
$829$	−3.00000	+	5.19615i	−0.104194	+	0.180470i	0.809214	+	0.587513i	$0.199893\pi$
$830$	−12.0000	+	20.7846i	−0.416526	+	0.721444i
$831$	42.0000	+	72.7461i	1.45696	+	2.52354i
$832$	−24.0000			−0.832050
$833$		0			0
$834$		0			0
$835$	1.50000	+	2.59808i	0.0519096	+	0.0899101i
$836$	−6.00000	+	10.3923i	−0.207514	+	0.359425i
$837$	−27.0000	+	46.7654i	−0.933257	+	1.61645i
$838$	−6.00000	−	10.3923i	−0.207267	−	0.358996i
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$	1.00000	+	1.73205i	0.0344623	+	0.0596904i
$843$	7.50000	−	12.9904i	0.258314	−	0.447412i
$844$	−15.0000	+	25.9808i	−0.516321	+	0.894295i
$845$	−2.00000	−	3.46410i	−0.0688021	−	0.119169i
$846$	108.000			3.71312
$847$		0			0
$848$	40.0000			1.37361
$849$	−31.5000	−	54.5596i	−1.08108	−	1.87248i
$850$	−3.00000	+	5.19615i	−0.102899	+	0.178227i
$851$		0			0
$852$	24.0000	+	41.5692i	0.822226	+	1.42414i
$853$	30.0000			1.02718			0.513590	−	0.858036i	$-0.328315\pi$
$853$	30.0000			1.02718			0.513590	+	0.858036i	$0.328315\pi$
$854$		0			0
$855$	−36.0000			−1.23117
$856$		0			0
$857$	−27.0000	+	46.7654i	−0.922302	+	1.59747i	−0.126459	+	0.991972i	$0.540361\pi$
$857$	−27.0000	+	46.7654i	−0.922302	+	1.59747i	−0.795843	+	0.605503i	$0.792972\pi$
$858$	9.00000	−	15.5885i	0.307255	−	0.532181i
$859$	−6.00000	−	10.3923i	−0.204717	−	0.354581i	0.745325	−	0.666701i	$-0.232294\pi$
$859$	−6.00000	−	10.3923i	−0.204717	−	0.354581i	−0.950043	+	0.312120i	$0.898961\pi$
$860$	12.0000			0.409197
$861$		0			0
$862$	−10.0000			−0.340601
$863$	17.0000	+	29.4449i	0.578687	+	1.00231i	0.995630	+	0.0933825i	$0.0297679\pi$
$863$	17.0000	+	29.4449i	0.578687	+	1.00231i	−0.416944	+	0.908932i	$0.636899\pi$
$864$	−36.0000	+	62.3538i	−1.22474	+	2.12132i
$865$	−1.50000	+	2.59808i	−0.0510015	+	0.0883372i
$866$	−30.0000	−	51.9615i	−1.01944	−	1.76572i
$867$	−24.0000			−0.815083
$868$		0			0
$869$	−1.00000			−0.0339227
$870$	3.00000	+	5.19615i	0.101710	+	0.176166i
$871$	21.0000	−	36.3731i	0.711558	−	1.23245i
$872$		0			0
$873$	45.0000	+	77.9423i	1.52302	+	2.63795i
$874$	48.0000			1.62362
$875$		0			0
$876$	36.0000			1.21633
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	0.989788	−	0.142548i	$-0.0455296\pi$
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	−0.618344	+	0.785907i	$0.712196\pi$
$878$	12.0000	−	20.7846i	0.404980	−	0.701447i
$879$	−13.5000	+	23.3827i	−0.455344	+	0.788678i
$880$	−2.00000	−	3.46410i	−0.0674200	−	0.116775i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$	9.00000	+	15.5885i	0.302703	+	0.524297i
$885$	−9.00000	+	15.5885i	−0.302532	+	0.524000i
$886$	34.0000	−	58.8897i	1.14225	−	1.97844i
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	0.994077	−	0.108678i	$-0.0346618\pi$
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	−0.591156	+	0.806557i	$0.701328\pi$
$888$		0			0
$889$		0			0
$890$	24.0000			0.804482
$891$	−4.50000	−	7.79423i	−0.150756	−	0.261116i
$892$	−3.00000	+	5.19615i	−0.100447	+	0.173980i
$893$	27.0000	−	46.7654i	0.903521	−	1.56494i
$894$	30.0000	+	51.9615i	1.00335	+	1.73785i
$895$	−4.00000			−0.133705
$896$		0			0
$897$	−36.0000			−1.20201
$898$	23.0000	+	39.8372i	0.767520	+	1.32938i
$899$	3.00000	−	5.19615i	0.100056	−	0.173301i
$900$	−6.00000	+	10.3923i	−0.200000	+	0.346410i
$901$	−15.0000	−	25.9808i	−0.499722	−	0.865545i
$902$	−12.0000			−0.399556
$903$		0			0
$904$		0			0
$905$	−3.00000	−	5.19615i	−0.0997234	−	0.172726i
$906$	45.0000	−	77.9423i	1.49502	−	2.58946i
$907$	−12.0000	+	20.7846i	−0.398453	+	0.690142i	−0.993535	−	0.113523i	$-0.963786\pi$
$907$	−12.0000	+	20.7846i	−0.398453	+	0.690142i	0.595082	+	0.803665i	$0.297120\pi$
$908$	−3.00000	−	5.19615i	−0.0995585	−	0.172440i
$909$	−108.000			−3.58213
$910$		0			0
$911$	40.0000			1.32526			0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000			1.32526			0.662630	+	0.748947i	$0.269440\pi$
$912$	36.0000	+	62.3538i	1.19208	+	2.06474i
$913$	−6.00000	+	10.3923i	−0.198571	+	0.343935i
$914$	6.00000	−	10.3923i	0.198462	−	0.343747i
$915$		0			0
$916$	−12.0000			−0.396491
$917$		0			0
$918$	54.0000			1.78227
$919$	4.50000	+	7.79423i	0.148441	+	0.257108i	0.930652	−	0.365907i	$-0.119241\pi$
$919$	4.50000	+	7.79423i	0.148441	+	0.257108i	−0.782210	+	0.623015i	$0.785908\pi$
$920$		0			0
$921$	4.50000	−	7.79423i	0.148280	−	0.256829i
$922$	36.0000	+	62.3538i	1.18560	+	2.05351i
$923$	−24.0000			−0.789970
$924$		0			0
$925$		0			0
$926$	−4.00000	−	6.92820i	−0.131448	−	0.227675i
$927$	27.0000	−	46.7654i	0.886796	−	1.53598i
$928$	4.00000	−	6.92820i	0.131306	−	0.227429i
$929$	−21.0000	−	36.3731i	−0.688988	−	1.19336i	−0.972166	−	0.234294i	$-0.924722\pi$
$929$	−21.0000	−	36.3731i	−0.688988	−	1.19336i	0.283178	−	0.959067i	$-0.408611\pi$
$930$	36.0000			1.18049
$931$		0			0
$932$	−16.0000			−0.524097
$933$	9.00000	+	15.5885i	0.294647	+	0.510343i
$934$	−15.0000	+	25.9808i	−0.490815	+	0.850117i
$935$	−1.50000	+	2.59808i	−0.0490552	+	0.0849662i
$936$		0			0
$937$	−27.0000			−0.882052			−0.441026	−	0.897494i	$-0.645385\pi$
$937$	−27.0000			−0.882052			−0.441026	+	0.897494i	$0.645385\pi$
$938$		0			0
$939$	9.00000			0.293704
$940$	−9.00000	−	15.5885i	−0.293548	−	0.508439i
$941$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$941$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$942$	54.0000	−	93.5307i	1.75942	−	3.04740i
$943$	12.0000	+	20.7846i	0.390774	+	0.676840i
$944$	24.0000			0.781133
$945$		0			0
$946$	12.0000			0.390154
$947$	1.00000	+	1.73205i	0.0324956	+	0.0562841i	0.881816	−	0.471594i	$-0.156321\pi$
$947$	1.00000	+	1.73205i	0.0324956	+	0.0562841i	−0.849320	+	0.527878i	$0.822988\pi$
$948$	3.00000	−	5.19615i	0.0974355	−	0.168763i
$949$	−9.00000	+	15.5885i	−0.292152	+	0.506023i
$950$	6.00000	+	10.3923i	0.194666	+	0.337171i
$951$	−66.0000			−2.14020
$952$		0			0
$953$	−38.0000			−1.23094			−0.615470	−	0.788160i	$-0.711034\pi$
$953$	−38.0000			−1.23094			−0.615470	+	0.788160i	$0.711034\pi$
$954$	−60.0000	−	103.923i	−1.94257	−	3.36463i
$955$	8.50000	−	14.7224i	0.275054	−	0.476407i
$956$	−7.00000	+	12.1244i	−0.226396	+	0.392130i
$957$	1.50000	+	2.59808i	0.0484881	+	0.0839839i
$958$	48.0000			1.55081
$959$		0			0
$960$	24.0000			0.774597
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$		0			0
$963$	6.00000	−	10.3923i	0.193347	−	0.334887i
$964$	24.0000	+	41.5692i	0.772988	+	1.33885i
$965$	−12.0000			−0.386294
$966$		0			0
$967$	−22.0000			−0.707472			−0.353736	−	0.935345i	$-0.615089\pi$
$967$	−22.0000			−0.707472			−0.353736	+	0.935345i	$0.615089\pi$
$968$		0			0
$969$	27.0000	−	46.7654i	0.867365	−	1.50232i
$970$	15.0000	−	25.9808i	0.481621	−	0.834192i
$971$	9.00000	+	15.5885i	0.288824	+	0.500257i	0.973529	−	0.228562i	$-0.0734025\pi$
$971$	9.00000	+	15.5885i	0.288824	+	0.500257i	−0.684706	+	0.728820i	$0.740069\pi$
$972$		0			0
$973$		0			0
$974$	−72.0000			−2.30703
$975$	−4.50000	−	7.79423i	−0.144115	−	0.249615i
$976$		0			0
$977$	−17.0000	+	29.4449i	−0.543878	+	0.942025i	0.454798	+	0.890594i	$0.349711\pi$
$977$	−17.0000	+	29.4449i	−0.543878	+	0.942025i	−0.998677	+	0.0514302i	$0.983622\pi$
$978$	48.0000	+	83.1384i	1.53487	+	2.65847i
$979$	12.0000			0.383522
$980$		0			0
$981$	−90.0000			−2.87348
$982$	23.0000	+	39.8372i	0.733959	+	1.27126i
$983$	−22.5000	+	38.9711i	−0.717639	+	1.24299i	0.244294	+	0.969701i	$0.421444\pi$
$983$	−22.5000	+	38.9711i	−0.717639	+	1.24299i	−0.961933	+	0.273285i	$0.911890\pi$
$984$		0			0
$985$	−1.00000	−	1.73205i	−0.0318626	−	0.0551877i
$986$	−6.00000			−0.191079
$987$		0			0
$988$	36.0000			1.14531
$989$	−12.0000	−	20.7846i	−0.381578	−	0.660912i
$990$	−6.00000	+	10.3923i	−0.190693	+	0.330289i
$991$	18.0000	−	31.1769i	0.571789	−	0.990367i	−0.424594	−	0.905384i	$-0.639583\pi$
$991$	18.0000	−	31.1769i	0.571789	−	0.990367i	0.996382	−	0.0849833i	$-0.0270837\pi$
$992$	−24.0000	−	41.5692i	−0.762001	−	1.31982i
$993$	36.0000			1.14243
$994$		0			0
$995$	−6.00000			−0.190213
$996$	−36.0000	−	62.3538i	−1.14070	−	1.97576i
$997$	1.50000	−	2.59808i	0.0475055	−	0.0822819i	−0.841295	−	0.540576i	$-0.818206\pi$
$997$	1.50000	−	2.59808i	0.0475055	−	0.0822819i	0.888800	+	0.458295i	$0.151540\pi$
$998$	−27.0000	+	46.7654i	−0.854670	+	1.48033i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.e.c.116.1		2
7.2	even	3	inner	245.2.e.c.226.1		2
7.3	odd	6		245.2.a.a.1.1	✓	1
7.4	even	3		245.2.a.b.1.1	yes	1
7.5	odd	6		245.2.e.d.226.1		2
7.6	odd	2		245.2.e.d.116.1		2
21.11	odd	6		2205.2.a.l.1.1		1
21.17	even	6		2205.2.a.j.1.1		1
28.3	even	6		3920.2.a.bj.1.1		1
28.11	odd	6		3920.2.a.a.1.1		1
35.3	even	12		1225.2.b.b.99.2		2
35.4	even	6		1225.2.a.h.1.1		1
35.17	even	12		1225.2.b.b.99.1		2
35.18	odd	12		1225.2.b.a.99.2		2
35.24	odd	6		1225.2.a.j.1.1		1
35.32	odd	12		1225.2.b.a.99.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.2.a.a.1.1	✓	1	7.3	odd	6
245.2.a.b.1.1	yes	1	7.4	even	3
245.2.e.c.116.1		2	1.1	even	1	trivial
245.2.e.c.226.1		2	7.2	even	3	inner
245.2.e.d.116.1		2	7.6	odd	2
245.2.e.d.226.1		2	7.5	odd	6
1225.2.a.h.1.1		1	35.4	even	6
1225.2.a.j.1.1		1	35.24	odd	6
1225.2.b.a.99.1		2	35.32	odd	12
1225.2.b.a.99.2		2	35.18	odd	12
1225.2.b.b.99.1		2	35.17	even	12
1225.2.b.b.99.2		2	35.3	even	12
2205.2.a.j.1.1		1	21.17	even	6
2205.2.a.l.1.1		1	21.11	odd	6
3920.2.a.a.1.1		1	28.11	odd	6
3920.2.a.bj.1.1		1	28.3	even	6

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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} -6.00000 q^{6} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} -6.00000 q^{6} +(-3.00000 - 5.19615i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-3.00000 - 5.19615i) q^{12} +3.00000 q^{13} -3.00000 q^{15} +(2.00000 + 3.46410i) q^{16} +(1.50000 - 2.59808i) q^{17} +(6.00000 - 10.3923i) q^{18} +(-3.00000 - 5.19615i) q^{19} -2.00000 q^{20} -2.00000 q^{22} +(2.00000 + 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(3.00000 + 5.19615i) q^{26} +9.00000 q^{27} -1.00000 q^{29} +(-3.00000 - 5.19615i) q^{30} +(-3.00000 + 5.19615i) q^{31} +(-4.00000 + 6.92820i) q^{32} +(-1.50000 - 2.59808i) q^{33} +6.00000 q^{34} +12.0000 q^{36} +(6.00000 - 10.3923i) q^{38} +(-4.50000 + 7.79423i) q^{39} +6.00000 q^{41} -6.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} +(3.00000 - 5.19615i) q^{45} +(-4.00000 + 6.92820i) q^{46} +(4.50000 + 7.79423i) q^{47} -12.0000 q^{48} -2.00000 q^{50} +(4.50000 + 7.79423i) q^{51} +(-3.00000 + 5.19615i) q^{52} +(5.00000 - 8.66025i) q^{53} +(9.00000 + 15.5885i) q^{54} -1.00000 q^{55} +18.0000 q^{57} +(-1.00000 - 1.73205i) q^{58} +(3.00000 - 5.19615i) q^{59} +(3.00000 - 5.19615i) q^{60} -12.0000 q^{62} -8.00000 q^{64} +(1.50000 + 2.59808i) q^{65} +(3.00000 - 5.19615i) q^{66} +(7.00000 - 12.1244i) q^{67} +(3.00000 + 5.19615i) q^{68} -12.0000 q^{69} -8.00000 q^{71} +(-3.00000 + 5.19615i) q^{73} +(-1.50000 - 2.59808i) q^{75} +12.0000 q^{76} -18.0000 q^{78} +(0.500000 + 0.866025i) q^{79} +(-2.00000 + 3.46410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(6.00000 + 10.3923i) q^{82} +12.0000 q^{83} +3.00000 q^{85} +(-6.00000 - 10.3923i) q^{86} +(1.50000 - 2.59808i) q^{87} +(-6.00000 - 10.3923i) q^{89} +12.0000 q^{90} -8.00000 q^{92} +(-9.00000 - 15.5885i) q^{93} +(-9.00000 + 15.5885i) q^{94} +(3.00000 - 5.19615i) q^{95} +(-12.0000 - 20.7846i) q^{96} -15.0000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{5} - 12 q^{6} - 6 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 + q^5 - 12 * q^6 - 6 * q^9	\( 2 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{5} - 12 q^{6} - 6 q^{9} - 2 q^{10} - q^{11} - 6 q^{12} + 6 q^{13} - 6 q^{15} + 4 q^{16} + 3 q^{17} + 12 q^{18} - 6 q^{19} - 4 q^{20} - 4 q^{22} + 4 q^{23} - q^{25} + 6 q^{26} + 18 q^{27} - 2 q^{29} - 6 q^{30} - 6 q^{31} - 8 q^{32} - 3 q^{33} + 12 q^{34} + 24 q^{36} + 12 q^{38} - 9 q^{39} + 12 q^{41} - 12 q^{43} - 2 q^{44} + 6 q^{45} - 8 q^{46} + 9 q^{47} - 24 q^{48} - 4 q^{50} + 9 q^{51} - 6 q^{52} + 10 q^{53} + 18 q^{54} - 2 q^{55} + 36 q^{57} - 2 q^{58} + 6 q^{59} + 6 q^{60} - 24 q^{62} - 16 q^{64} + 3 q^{65} + 6 q^{66} + 14 q^{67} + 6 q^{68} - 24 q^{69} - 16 q^{71} - 6 q^{73} - 3 q^{75} + 24 q^{76} - 36 q^{78} + q^{79} - 4 q^{80} - 9 q^{81} + 12 q^{82} + 24 q^{83} + 6 q^{85} - 12 q^{86} + 3 q^{87} - 12 q^{89} + 24 q^{90} - 16 q^{92} - 18 q^{93} - 18 q^{94} + 6 q^{95} - 24 q^{96} - 30 q^{97} + 12 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 + q^5 - 12 * q^6 - 6 * q^9 - 2 * q^10 - q^11 - 6 * q^12 + 6 * q^13 - 6 * q^15 + 4 * q^16 + 3 * q^17 + 12 * q^18 - 6 * q^19 - 4 * q^20 - 4 * q^22 + 4 * q^23 - q^25 + 6 * q^26 + 18 * q^27 - 2 * q^29 - 6 * q^30 - 6 * q^31 - 8 * q^32 - 3 * q^33 + 12 * q^34 + 24 * q^36 + 12 * q^38 - 9 * q^39 + 12 * q^41 - 12 * q^43 - 2 * q^44 + 6 * q^45 - 8 * q^46 + 9 * q^47 - 24 * q^48 - 4 * q^50 + 9 * q^51 - 6 * q^52 + 10 * q^53 + 18 * q^54 - 2 * q^55 + 36 * q^57 - 2 * q^58 + 6 * q^59 + 6 * q^60 - 24 * q^62 - 16 * q^64 + 3 * q^65 + 6 * q^66 + 14 * q^67 + 6 * q^68 - 24 * q^69 - 16 * q^71 - 6 * q^73 - 3 * q^75 + 24 * q^76 - 36 * q^78 + q^79 - 4 * q^80 - 9 * q^81 + 12 * q^82 + 24 * q^83 + 6 * q^85 - 12 * q^86 + 3 * q^87 - 12 * q^89 + 24 * q^90 - 16 * q^92 - 18 * q^93 - 18 * q^94 + 6 * q^95 - 24 * q^96 - 30 * q^97 + 12 * q^99

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