LMFDB - Embedded newform 1014.3.f.h.775.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,3,Mod(577,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1014.577");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1014.f (of order $4$, degree $2$, 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:	$27.6294988061$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 82x^{5} + 5053x^{4} - 6736x^{3} + 6728x^{2} + 275384x + 5635876 $ x^8 - 2x^7 + 2x^6 + 82x^5 + 5053x^4 - 6736x^3 + 6728x^2 + 275384*x + 5635876
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			775.2
Root			$-5.39181 - 5.39181i$ of defining polynomial
Character	$\chi$	$=$	1014.775
Dual form			1014.3.f.h.577.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} -1.73205 q^{3} +2.00000i q^{4} +(4.02578 + 4.02578i) q^{5} +(1.73205 + 1.73205i) q^{6} +(3.65976 - 3.65976i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} -1.73205 q^{3} +2.00000i q^{4} +(4.02578 + 4.02578i) q^{5} +(1.73205 + 1.73205i) q^{6} +(3.65976 - 3.65976i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} -8.05157i q^{10} +(-9.31952 + 9.31952i) q^{11} -3.46410i q^{12} -7.31952 q^{14} +(-6.97286 - 6.97286i) q^{15} -4.00000 q^{16} -18.8551i q^{17} +(-3.00000 - 3.00000i) q^{18} +(-21.4627 - 21.4627i) q^{19} +(-8.05157 + 8.05157i) q^{20} +(-6.33889 + 6.33889i) q^{21} +18.6390 q^{22} +12.1058i q^{23} +(-3.46410 + 3.46410i) q^{24} +7.41388i q^{25} -5.19615 q^{27} +(7.31952 + 7.31952i) q^{28} -36.9444 q^{29} +13.9457i q^{30} +(-6.48248 - 6.48248i) q^{31} +(4.00000 + 4.00000i) q^{32} +(16.1419 - 16.1419i) q^{33} +(-18.8551 + 18.8551i) q^{34} +29.4668 q^{35} +6.00000i q^{36} +(37.1815 - 37.1815i) q^{37} +42.9255i q^{38} +16.1031 q^{40} +(4.67087 + 4.67087i) q^{41} +12.6778 q^{42} +13.6054i q^{43} +(-18.6390 - 18.6390i) q^{44} +(12.0774 + 12.0774i) q^{45} +(12.1058 - 12.1058i) q^{46} +(61.6060 - 61.6060i) q^{47} +6.92820 q^{48} +22.2123i q^{49} +(7.41388 - 7.41388i) q^{50} +32.6579i q^{51} +4.64409 q^{53} +(5.19615 + 5.19615i) q^{54} -75.0367 q^{55} -14.6390i q^{56} +(37.1746 + 37.1746i) q^{57} +(36.9444 + 36.9444i) q^{58} +(-17.6437 + 17.6437i) q^{59} +(13.9457 - 13.9457i) q^{60} +38.5426 q^{61} +12.9650i q^{62} +(10.9793 - 10.9793i) q^{63} -8.00000i q^{64} -32.2838 q^{66} +(-67.2276 - 67.2276i) q^{67} +37.7101 q^{68} -20.9679i q^{69} +(-29.4668 - 29.4668i) q^{70} +(28.7155 + 28.7155i) q^{71} +(6.00000 - 6.00000i) q^{72} +(60.4486 - 60.4486i) q^{73} -74.3630 q^{74} -12.8412i q^{75} +(42.9255 - 42.9255i) q^{76} +68.2144i q^{77} -94.2854 q^{79} +(-16.1031 - 16.1031i) q^{80} +9.00000 q^{81} -9.34174i q^{82} +(-63.4890 - 63.4890i) q^{83} +(-12.6778 - 12.6778i) q^{84} +(75.9064 - 75.9064i) q^{85} +(13.6054 - 13.6054i) q^{86} +63.9895 q^{87} +37.2781i q^{88} +(110.281 - 110.281i) q^{89} -24.1547i q^{90} -24.2117 q^{92} +(11.2280 + 11.2280i) q^{93} -123.212 q^{94} -172.809i q^{95} +(-6.92820 - 6.92820i) q^{96} +(-107.297 - 107.297i) q^{97} +(22.2123 - 22.2123i) q^{98} +(-27.9586 + 27.9586i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 6 q^{5} - 2 q^{7} + 16 q^{8} + 24 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 6 * q^5 - 2 * q^7 + 16 * q^8 + 24 * q^9	$ 8 q - 8 q^{2} - 6 q^{5} - 2 q^{7} + 16 q^{8} + 24 q^{9} - 12 q^{11} + 4 q^{14} + 6 q^{15} - 32 q^{16} - 24 q^{18} - 44 q^{19} + 12 q^{20} + 18 q^{21} + 24 q^{22} - 4 q^{28} - 72 q^{29} - 94 q^{31} + 32 q^{32} - 36 q^{33} + 60 q^{34} + 408 q^{35} - 46 q^{37} - 24 q^{40} - 30 q^{41} - 36 q^{42} - 24 q^{44} - 18 q^{45} + 144 q^{46} + 300 q^{47} + 208 q^{50} + 84 q^{53} - 792 q^{55} + 24 q^{57} + 72 q^{58} - 12 q^{59} - 12 q^{60} + 180 q^{61} - 6 q^{63} + 72 q^{66} - 74 q^{67} - 120 q^{68} - 408 q^{70} + 156 q^{71} + 48 q^{72} + 16 q^{73} + 92 q^{74} + 88 q^{76} - 96 q^{79} + 24 q^{80} + 72 q^{81} + 36 q^{84} + 234 q^{85} + 168 q^{86} - 60 q^{87} + 228 q^{89} - 288 q^{92} - 198 q^{93} - 600 q^{94} + 2 q^{97} - 32 q^{98} - 36 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 - 6 * q^5 - 2 * q^7 + 16 * q^8 + 24 * q^9 - 12 * q^11 + 4 * q^14 + 6 * q^15 - 32 * q^16 - 24 * q^18 - 44 * q^19 + 12 * q^20 + 18 * q^21 + 24 * q^22 - 4 * q^28 - 72 * q^29 - 94 * q^31 + 32 * q^32 - 36 * q^33 + 60 * q^34 + 408 * q^35 - 46 * q^37 - 24 * q^40 - 30 * q^41 - 36 * q^42 - 24 * q^44 - 18 * q^45 + 144 * q^46 + 300 * q^47 + 208 * q^50 + 84 * q^53 - 792 * q^55 + 24 * q^57 + 72 * q^58 - 12 * q^59 - 12 * q^60 + 180 * q^61 - 6 * q^63 + 72 * q^66 - 74 * q^67 - 120 * q^68 - 408 * q^70 + 156 * q^71 + 48 * q^72 + 16 * q^73 + 92 * q^74 + 88 * q^76 - 96 * q^79 + 24 * q^80 + 72 * q^81 + 36 * q^84 + 234 * q^85 + 168 * q^86 - 60 * q^87 + 228 * q^89 - 288 * q^92 - 198 * q^93 - 600 * q^94 + 2 * q^97 - 32 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$			2.00000i			0.500000i
$5$	4.02578	+	4.02578i	0.805157	+	0.805157i	0.983896	−	0.178740i	$-0.0572019\pi$
$5$	4.02578	+	4.02578i	0.805157	+	0.805157i	−0.178740	+	0.983896i	$0.557202\pi$
$6$	1.73205	+	1.73205i	0.288675	+	0.288675i
$7$	3.65976	−	3.65976i	0.522823	−	0.522823i	−0.395600	−	0.918423i	$-0.629463\pi$
$7$	3.65976	−	3.65976i	0.522823	−	0.522823i	0.918423	+	0.395600i	$0.129463\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$	3.00000			0.333333
$10$		−	8.05157i		−	0.805157i
$11$	−9.31952	+	9.31952i	−0.847229	+	0.847229i	−0.989787	−	0.142558i	$-0.954467\pi$
$11$	−9.31952	+	9.31952i	−0.847229	+	0.847229i	0.142558	+	0.989787i	$0.454467\pi$
$12$		−	3.46410i		−	0.288675i
$13$		0			0
$13$		0			0
$14$	−7.31952			−0.522823
$15$	−6.97286	−	6.97286i	−0.464858	−	0.464858i
$16$	−4.00000			−0.250000
$17$		−	18.8551i		−	1.10912i	−0.832143	−	0.554560i	$-0.812886\pi$
$17$		−	18.8551i		−	1.10912i	0.832143	−	0.554560i	$-0.187114\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$	−21.4627	−	21.4627i	−1.12962	−	1.12962i	−0.990239	−	0.139379i	$-0.955489\pi$
$19$	−21.4627	−	21.4627i	−1.12962	−	1.12962i	−0.139379	−	0.990239i	$-0.544511\pi$
$20$	−8.05157	+	8.05157i	−0.402578	+	0.402578i
$21$	−6.33889	+	6.33889i	−0.301852	+	0.301852i
$22$	18.6390			0.847229
$23$			12.1058i			0.526341i	0.964749	+	0.263170i	$0.0847682\pi$
$23$			12.1058i			0.526341i	−0.964749	+	0.263170i	$0.915232\pi$
$24$	−3.46410	+	3.46410i	−0.144338	+	0.144338i
$25$			7.41388i			0.296555i
$26$		0			0
$27$	−5.19615			−0.192450
$28$	7.31952	+	7.31952i	0.261411	+	0.261411i
$29$	−36.9444			−1.27394			−0.636972	−	0.770887i	$-0.719813\pi$
$29$	−36.9444			−1.27394			−0.636972	+	0.770887i	$0.719813\pi$
$30$			13.9457i			0.464858i
$31$	−6.48248	−	6.48248i	−0.209112	−	0.209112i	0.594778	−	0.803890i	$-0.297240\pi$
$31$	−6.48248	−	6.48248i	−0.209112	−	0.209112i	−0.803890	+	0.594778i	$0.797240\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	16.1419	−	16.1419i	0.489148	−	0.489148i
$34$	−18.8551	+	18.8551i	−0.554560	+	0.554560i
$35$	29.4668			0.841909
$36$			6.00000i			0.166667i
$37$	37.1815	−	37.1815i	1.00490	−	1.00490i	0.00491701	−	0.999988i	$-0.498435\pi$
$37$	37.1815	−	37.1815i	1.00490	−	1.00490i	0.999988	−	0.00491701i	$-0.00156514\pi$
$38$			42.9255i			1.12962i
$39$		0			0
$40$	16.1031			0.402578
$41$	4.67087	+	4.67087i	0.113924	+	0.113924i	0.761771	−	0.647847i	$-0.224330\pi$
$41$	4.67087	+	4.67087i	0.113924	+	0.113924i	−0.647847	+	0.761771i	$0.724330\pi$
$42$	12.6778			0.301852
$43$			13.6054i			0.316404i	0.987407	+	0.158202i	$0.0505696\pi$
$43$			13.6054i			0.316404i	−0.987407	+	0.158202i	$0.949430\pi$
$44$	−18.6390	−	18.6390i	−0.423614	−	0.423614i
$45$	12.0774	+	12.0774i	0.268386	+	0.268386i
$46$	12.1058	−	12.1058i	0.263170	−	0.263170i
$47$	61.6060	−	61.6060i	1.31077	−	1.31077i	0.389914	−	0.920851i	$-0.372505\pi$
$47$	61.6060	−	61.6060i	1.31077	−	1.31077i	0.920851	−	0.389914i	$-0.127495\pi$
$48$	6.92820			0.144338
$49$			22.2123i			0.453313i
$50$	7.41388	−	7.41388i	0.148278	−	0.148278i
$51$			32.6579i			0.640351i
$52$		0			0
$53$	4.64409			0.0876244			0.0438122	−	0.999040i	$-0.486050\pi$
$53$	4.64409			0.0876244			0.0438122	+	0.999040i	$0.486050\pi$
$54$	5.19615	+	5.19615i	0.0962250	+	0.0962250i
$55$	−75.0367			−1.36430
$56$		−	14.6390i		−	0.261411i
$57$	37.1746	+	37.1746i	0.652185	+	0.652185i
$58$	36.9444	+	36.9444i	0.636972	+	0.636972i
$59$	−17.6437	+	17.6437i	−0.299046	+	0.299046i	−0.840640	−	0.541594i	$-0.817821\pi$
$59$	−17.6437	+	17.6437i	−0.299046	+	0.299046i	0.541594	+	0.840640i	$0.317821\pi$
$60$	13.9457	−	13.9457i	0.232429	−	0.232429i
$61$	38.5426			0.631845			0.315923	−	0.948785i	$-0.397686\pi$
$61$	38.5426			0.631845			0.315923	+	0.948785i	$0.397686\pi$
$62$			12.9650i			0.209112i
$63$	10.9793	−	10.9793i	0.174274	−	0.174274i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	−32.2838			−0.489148
$67$	−67.2276	−	67.2276i	−1.00340	−	1.00340i	−0.999994	−	0.00340321i	$-0.998917\pi$
$67$	−67.2276	−	67.2276i	−1.00340	−	1.00340i	−0.00340321	−	0.999994i	$-0.501083\pi$
$68$	37.7101			0.554560
$69$		−	20.9679i		−	0.303883i
$70$	−29.4668	−	29.4668i	−0.420954	−	0.420954i
$71$	28.7155	+	28.7155i	0.404444	+	0.404444i	0.879796	−	0.475352i	$-0.157679\pi$
$71$	28.7155	+	28.7155i	0.404444	+	0.404444i	−0.475352	+	0.879796i	$0.657679\pi$
$72$	6.00000	−	6.00000i	0.0833333	−	0.0833333i
$73$	60.4486	−	60.4486i	0.828063	−	0.828063i	−0.159186	−	0.987249i	$-0.550887\pi$
$73$	60.4486	−	60.4486i	0.828063	−	0.828063i	0.987249	+	0.159186i	$0.0508869\pi$
$74$	−74.3630			−1.00490
$75$		−	12.8412i		−	0.171216i
$76$	42.9255	−	42.9255i	0.564809	−	0.564809i
$77$			68.2144i			0.885901i
$78$		0			0
$79$	−94.2854			−1.19349			−0.596743	−	0.802433i	$-0.703539\pi$
$79$	−94.2854			−1.19349			−0.596743	+	0.802433i	$0.703539\pi$
$80$	−16.1031	−	16.1031i	−0.201289	−	0.201289i
$81$	9.00000			0.111111
$82$		−	9.34174i		−	0.113924i
$83$	−63.4890	−	63.4890i	−0.764928	−	0.764928i	0.212281	−	0.977209i	$-0.431911\pi$
$83$	−63.4890	−	63.4890i	−0.764928	−	0.764928i	−0.977209	+	0.212281i	$0.931911\pi$
$84$	−12.6778	−	12.6778i	−0.150926	−	0.150926i
$85$	75.9064	−	75.9064i	0.893016	−	0.893016i
$86$	13.6054	−	13.6054i	0.158202	−	0.158202i
$87$	63.9895			0.735512
$88$			37.2781i			0.423614i
$89$	110.281	−	110.281i	1.23911	−	1.23911i	0.278743	−	0.960366i	$-0.410082\pi$
$89$	110.281	−	110.281i	1.23911	−	1.23911i	0.960366	−	0.278743i	$-0.0899178\pi$
$90$		−	24.1547i		−	0.268386i
$91$		0			0
$92$	−24.2117			−0.263170
$93$	11.2280	+	11.2280i	0.120731	+	0.120731i
$94$	−123.212			−1.31077
$95$		−	172.809i		−	1.81904i
$96$	−6.92820	−	6.92820i	−0.0721688	−	0.0721688i
$97$	−107.297	−	107.297i	−1.10616	−	1.10616i	−0.993651	−	0.112507i	$-0.964112\pi$
$97$	−107.297	−	107.297i	−1.10616	−	1.10616i	−0.112507	−	0.993651i	$-0.535888\pi$
$98$	22.2123	−	22.2123i	0.226656	−	0.226656i
$99$	−27.9586	+	27.9586i	−0.282410	+	0.282410i
$100$	−14.8278			−0.148278
$101$		−	45.9730i		−	0.455178i	−0.973757	−	0.227589i	$-0.926916\pi$
$101$		−	45.9730i		−	0.455178i	0.973757	−	0.227589i	$-0.0730843\pi$
$102$	32.6579	−	32.6579i	0.320176	−	0.320176i
$103$			92.8099i			0.901067i	0.892759	+	0.450534i	$0.148766\pi$
$103$			92.8099i			0.901067i	−0.892759	+	0.450534i	$0.851234\pi$
$104$		0			0
$105$	−51.0380			−0.486076
$106$	−4.64409	−	4.64409i	−0.0438122	−	0.0438122i
$107$	75.2403			0.703181			0.351590	−	0.936154i	$-0.385641\pi$
$107$	75.2403			0.703181			0.351590	+	0.936154i	$0.385641\pi$
$108$		−	10.3923i		−	0.0962250i
$109$	−46.0551	−	46.0551i	−0.422524	−	0.422524i	0.463548	−	0.886072i	$-0.346576\pi$
$109$	−46.0551	−	46.0551i	−0.422524	−	0.422524i	−0.886072	+	0.463548i	$0.846576\pi$
$110$	75.0367	+	75.0367i	0.682152	+	0.682152i
$111$	−64.4002	+	64.4002i	−0.580182	+	0.580182i
$112$	−14.6390	+	14.6390i	−0.130706	+	0.130706i
$113$	156.493			1.38490			0.692449	−	0.721467i	$-0.256532\pi$
$113$	156.493			1.38490			0.692449	+	0.721467i	$0.256532\pi$
$114$		−	74.3491i		−	0.652185i
$115$	−48.7355	+	48.7355i	−0.423787	+	0.423787i
$116$		−	73.8888i		−	0.636972i
$117$		0			0
$118$	35.2875			0.299046
$119$	−69.0050	−	69.0050i	−0.579874	−	0.579874i
$120$	−27.8915			−0.232429
$121$		−	52.7068i		−	0.435594i
$122$	−38.5426	−	38.5426i	−0.315923	−	0.315923i
$123$	−8.09018	−	8.09018i	−0.0657738	−	0.0657738i
$124$	12.9650	−	12.9650i	0.104556	−	0.104556i
$125$	70.7979	−	70.7979i	0.566383	−	0.566383i
$126$	−21.9586			−0.174274
$127$		−	183.377i		−	1.44391i	−0.691938	−	0.721957i	$-0.743243\pi$
$127$		−	183.377i		−	1.44391i	0.691938	−	0.721957i	$-0.256757\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		−	23.5652i		−	0.182676i
$130$		0			0
$131$	−151.996			−1.16027			−0.580137	−	0.814519i	$-0.697001\pi$
$131$	−151.996			−1.16027			−0.580137	+	0.814519i	$0.697001\pi$
$132$	32.2838	+	32.2838i	0.244574	+	0.244574i
$133$	−157.097			−1.18118
$134$			134.455i			1.00340i
$135$	−20.9186	−	20.9186i	−0.154953	−	0.154953i
$136$	−37.7101	−	37.7101i	−0.277280	−	0.277280i
$137$	−170.039	+	170.039i	−1.24116	+	1.24116i	−0.281642	+	0.959520i	$0.590879\pi$
$137$	−170.039	+	170.039i	−1.24116	+	1.24116i	−0.959520	+	0.281642i	$0.909121\pi$
$138$	−20.9679	+	20.9679i	−0.151942	+	0.151942i
$139$	−185.463			−1.33426			−0.667132	−	0.744940i	$-0.732478\pi$
$139$	−185.463			−1.33426			−0.667132	+	0.744940i	$0.732478\pi$
$140$			58.9336i			0.420954i
$141$	−106.705	+	106.705i	−0.756771	+	0.756771i
$142$		−	57.4311i		−	0.404444i
$143$		0			0
$144$	−12.0000			−0.0833333
$145$	−148.730	−	148.730i	−1.02572	−	1.02572i
$146$	−120.897			−0.828063
$147$		−	38.4729i		−	0.261720i
$148$	74.3630	+	74.3630i	0.502452	+	0.502452i
$149$	−12.7760	−	12.7760i	−0.0857449	−	0.0857449i	0.662933	−	0.748678i	$-0.269311\pi$
$149$	−12.7760	−	12.7760i	−0.0857449	−	0.0857449i	−0.748678	+	0.662933i	$0.769311\pi$
$150$	−12.8412	+	12.8412i	−0.0856082	+	0.0856082i
$151$	−95.4196	+	95.4196i	−0.631918	+	0.631918i	−0.948549	−	0.316631i	$-0.897448\pi$
$151$	−95.4196	+	95.4196i	−0.631918	+	0.631918i	0.316631	+	0.948549i	$0.397448\pi$
$152$	−85.8510			−0.564809
$153$		−	56.5652i		−	0.369707i
$154$	68.2144	−	68.2144i	0.442951	−	0.442951i
$155$		−	52.1942i		−	0.336736i
$156$		0			0
$157$	−195.116			−1.24278			−0.621389	−	0.783502i	$-0.713431\pi$
$157$	−195.116			−1.24278			−0.621389	+	0.783502i	$0.713431\pi$
$158$	94.2854	+	94.2854i	0.596743	+	0.596743i
$159$	−8.04381			−0.0505900
$160$			32.2063i			0.201289i
$161$	44.3045	+	44.3045i	0.275183	+	0.275183i
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	87.5027	−	87.5027i	0.536826	−	0.536826i	−0.385769	−	0.922595i	$-0.626064\pi$
$163$	87.5027	−	87.5027i	0.536826	−	0.536826i	0.922595	+	0.385769i	$0.126064\pi$
$164$	−9.34174	+	9.34174i	−0.0569618	+	0.0569618i
$165$	129.967			0.787682
$166$			126.978i			0.764928i
$167$	87.8436	−	87.8436i	0.526010	−	0.526010i	−0.393371	−	0.919380i	$-0.628691\pi$
$167$	87.8436	−	87.8436i	0.526010	−	0.526010i	0.919380	+	0.393371i	$0.128691\pi$
$168$			25.3556i			0.150926i
$169$		0			0
$170$	−151.813			−0.893016
$171$	−64.3882	−	64.3882i	−0.376539	−	0.376539i
$172$	−27.2107			−0.158202
$173$			119.181i			0.688908i	0.938803	+	0.344454i	$0.111936\pi$
$173$			119.181i			0.688908i	−0.938803	+	0.344454i	$0.888064\pi$
$174$	−63.9895	−	63.9895i	−0.367756	−	0.367756i
$175$	27.1330	+	27.1330i	0.155046	+	0.155046i
$176$	37.2781	−	37.2781i	0.211807	−	0.211807i
$177$	30.5598	−	30.5598i	0.172654	−	0.172654i
$178$	−220.561			−1.23911
$179$			214.511i			1.19838i	0.800605	+	0.599192i	$0.204512\pi$
$179$			214.511i			1.19838i	−0.800605	+	0.599192i	$0.795488\pi$
$180$	−24.1547	+	24.1547i	−0.134193	+	0.134193i
$181$		−	343.720i		−	1.89901i	−0.313755	−	0.949504i	$-0.601587\pi$
$181$		−	343.720i		−	1.89901i	0.313755	−	0.949504i	$-0.398413\pi$
$182$		0			0
$183$	−66.7577			−0.364796
$184$	24.2117	+	24.2117i	0.131585	+	0.131585i
$185$	299.369			1.61821
$186$		−	22.4560i		−	0.120731i
$187$	175.720	+	175.720i	0.939679	+	0.939679i
$188$	123.212	+	123.212i	0.655383	+	0.655383i
$189$	−19.0167	+	19.0167i	−0.100617	+	0.100617i
$190$	−172.809	+	172.809i	−0.909520	+	0.909520i
$191$	249.718			1.30742			0.653712	−	0.756743i	$-0.273211\pi$
$191$	249.718			1.30742			0.653712	+	0.756743i	$0.273211\pi$
$192$			13.8564i			0.0721688i
$193$	95.8199	−	95.8199i	0.496476	−	0.496476i	−0.413863	−	0.910339i	$-0.635821\pi$
$193$	95.8199	−	95.8199i	0.496476	−	0.496476i	0.910339	+	0.413863i	$0.135821\pi$
$194$			214.595i			1.10616i
$195$		0			0
$196$	−44.4246			−0.226656
$197$	2.48643	+	2.48643i	0.0126215	+	0.0126215i	0.713389	−	0.700768i	$-0.247159\pi$
$197$	2.48643	+	2.48643i	0.0126215	+	0.0126215i	−0.700768	+	0.713389i	$0.747159\pi$
$198$	55.9171			0.282410
$199$		−	265.195i		−	1.33264i	−0.745666	−	0.666319i	$-0.767869\pi$
$199$		−	265.195i		−	1.33264i	0.745666	−	0.666319i	$-0.232131\pi$
$200$	14.8278	+	14.8278i	0.0741388	+	0.0741388i
$201$	116.442	+	116.442i	0.579312	+	0.579312i
$202$	−45.9730	+	45.9730i	−0.227589	+	0.227589i
$203$	−135.208	+	135.208i	−0.666047	+	0.666047i
$204$	−65.3158			−0.320176
$205$			37.6078i			0.183453i
$206$	92.8099	−	92.8099i	0.450534	−	0.450534i
$207$			36.3175i			0.175447i
$208$		0			0
$209$	400.045			1.91409
$210$	51.0380	+	51.0380i	0.243038	+	0.243038i
$211$	−13.7413			−0.0651248			−0.0325624	−	0.999470i	$-0.510367\pi$
$211$	−13.7413			−0.0651248			−0.0325624	+	0.999470i	$0.510367\pi$
$212$			9.28819i			0.0438122i
$213$	−49.7368	−	49.7368i	−0.233506	−	0.233506i
$214$	−75.2403	−	75.2403i	−0.351590	−	0.351590i
$215$	−54.7722	+	54.7722i	−0.254755	+	0.254755i
$216$	−10.3923	+	10.3923i	−0.0481125	+	0.0481125i
$217$	−47.4487			−0.218657
$218$			92.1103i			0.422524i
$219$	−104.700	+	104.700i	−0.478082	+	0.478082i
$220$		−	150.073i		−	0.682152i
$221$		0			0
$222$	128.800			0.580182
$223$	−72.3147	−	72.3147i	−0.324281	−	0.324281i	0.526126	−	0.850407i	$-0.323644\pi$
$223$	−72.3147	−	72.3147i	−0.324281	−	0.324281i	−0.850407	+	0.526126i	$0.823644\pi$
$224$	29.2781			0.130706
$225$			22.2417i			0.0988518i
$226$	−156.493	−	156.493i	−0.692449	−	0.692449i
$227$	−163.921	−	163.921i	−0.722119	−	0.722119i	0.246917	−	0.969037i	$-0.420582\pi$
$227$	−163.921	−	163.921i	−0.722119	−	0.722119i	−0.969037	+	0.246917i	$0.920582\pi$
$228$	−74.3491	+	74.3491i	−0.326093	+	0.326093i
$229$	306.032	−	306.032i	1.33639	−	1.33639i	0.436854	−	0.899533i	$-0.356093\pi$
$229$	306.032	−	306.032i	1.33639	−	1.33639i	0.899533	−	0.436854i	$-0.143907\pi$
$230$	97.4710			0.423787
$231$		−	118.151i		−	0.511475i
$232$	−73.8888	+	73.8888i	−0.318486	+	0.318486i
$233$			156.892i			0.673356i	0.941620	+	0.336678i	$0.109303\pi$
$233$			156.892i			0.673356i	−0.941620	+	0.336678i	$0.890697\pi$
$234$		0			0
$235$	496.025			2.11074
$236$	−35.2875	−	35.2875i	−0.149523	−	0.149523i
$237$	163.307			0.689059
$238$			138.010i			0.579874i
$239$	10.5731	+	10.5731i	0.0442390	+	0.0442390i	0.728880	−	0.684641i	$-0.240041\pi$
$239$	10.5731	+	10.5731i	0.0442390	+	0.0442390i	−0.684641	+	0.728880i	$0.740041\pi$
$240$	27.8915	+	27.8915i	0.116214	+	0.116214i
$241$	166.546	−	166.546i	0.691062	−	0.691062i	−0.271403	−	0.962466i	$-0.587488\pi$
$241$	166.546	−	166.546i	0.691062	−	0.691062i	0.962466	+	0.271403i	$0.0874877\pi$
$242$	−52.7068	+	52.7068i	−0.217797	+	0.217797i
$243$	−15.5885			−0.0641500
$244$			77.0851i			0.315923i
$245$	−89.4220	+	89.4220i	−0.364988	+	0.364988i
$246$			16.1804i			0.0657738i
$247$		0			0
$248$	−25.9299			−0.104556
$249$	109.966	+	109.966i	0.441631	+	0.441631i
$250$	−141.596			−0.566383
$251$			76.9248i			0.306473i	0.988190	+	0.153237i	$0.0489697\pi$
$251$			76.9248i			0.306473i	−0.988190	+	0.153237i	$0.951030\pi$
$252$	21.9586	+	21.9586i	0.0871371	+	0.0871371i
$253$	−112.821	−	112.821i	−0.445931	−	0.445931i
$254$	−183.377	+	183.377i	−0.721957	+	0.721957i
$255$	−131.474	+	131.474i	−0.515583	+	0.515583i
$256$	16.0000			0.0625000
$257$		−	63.5214i		−	0.247165i	−0.992334	−	0.123583i	$-0.960562\pi$
$257$		−	63.5214i		−	0.247165i	0.992334	−	0.123583i	$-0.0394384\pi$
$258$	−23.5652	+	23.5652i	−0.0913378	+	0.0913378i
$259$		−	272.151i		−	1.05077i
$260$		0			0
$261$	−110.833			−0.424648
$262$	151.996	+	151.996i	0.580137	+	0.580137i
$263$	225.177			0.856188			0.428094	−	0.903734i	$-0.359185\pi$
$263$	225.177			0.856188			0.428094	+	0.903734i	$0.359185\pi$
$264$		−	64.5675i		−	0.244574i
$265$	18.6961	+	18.6961i	0.0705514	+	0.0705514i
$266$	157.097	+	157.097i	0.590590	+	0.590590i
$267$	−191.012	+	191.012i	−0.715400	+	0.715400i
$268$	134.455	−	134.455i	0.501699	−	0.501699i
$269$	22.1441			0.0823200			0.0411600	−	0.999153i	$-0.486895\pi$
$269$	22.1441			0.0823200			0.0411600	+	0.999153i	$0.486895\pi$
$270$			41.8372i			0.154953i
$271$	−105.317	+	105.317i	−0.388623	+	0.388623i	−0.874196	−	0.485573i	$-0.838611\pi$
$271$	−105.317	+	105.317i	−0.388623	+	0.388623i	0.485573	+	0.874196i	$0.338611\pi$
$272$			75.4202i			0.277280i
$273$		0			0
$274$	340.078			1.24116
$275$	−69.0938	−	69.0938i	−0.251250	−	0.251250i
$276$	41.9359			0.151942
$277$			202.590i			0.731373i	0.930738	+	0.365687i	$0.119166\pi$
$277$			202.590i			0.731373i	−0.930738	+	0.365687i	$0.880834\pi$
$278$	185.463	+	185.463i	0.667132	+	0.667132i
$279$	−19.4474	−	19.4474i	−0.0697041	−	0.0697041i
$280$	58.9336	−	58.9336i	0.210477	−	0.210477i
$281$	44.0655	−	44.0655i	0.156817	−	0.156817i	−0.624338	−	0.781154i	$-0.714631\pi$
$281$	44.0655	−	44.0655i	0.156817	−	0.156817i	0.781154	+	0.624338i	$0.214631\pi$
$282$	213.409			0.756771
$283$			140.882i			0.497817i	0.968527	+	0.248909i	$0.0800719\pi$
$283$			140.882i			0.497817i	−0.968527	+	0.248909i	$0.919928\pi$
$284$	−57.4311	+	57.4311i	−0.202222	+	0.202222i
$285$			299.314i			1.05022i
$286$		0			0
$287$	34.1885			0.119124
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$	−66.5131			−0.230149
$290$			297.460i			1.02572i
$291$	185.844	+	185.844i	0.638641	+	0.638641i
$292$	120.897	+	120.897i	0.414031	+	0.414031i
$293$	121.000	−	121.000i	0.412970	−	0.412970i	−0.469802	−	0.882772i	$-0.655675\pi$
$293$	121.000	−	121.000i	0.412970	−	0.412970i	0.882772	+	0.469802i	$0.155675\pi$
$294$	−38.4729	+	38.4729i	−0.130860	+	0.130860i
$295$	−142.060			−0.481558
$296$		−	148.726i		−	0.502452i
$297$	48.4256	−	48.4256i	0.163049	−	0.163049i
$298$			25.5520i			0.0857449i
$299$		0			0
$300$	25.6824			0.0856082
$301$	49.7923	+	49.7923i	0.165423	+	0.165423i
$302$	190.839			0.631918
$303$			79.6276i			0.262797i
$304$	85.8510	+	85.8510i	0.282405	+	0.282405i
$305$	155.164	+	155.164i	0.508735	+	0.508735i
$306$	−56.5652	+	56.5652i	−0.184853	+	0.184853i
$307$	−252.758	+	252.758i	−0.823317	+	0.823317i	−0.986582	−	0.163265i	$-0.947797\pi$
$307$	−252.758	+	252.758i	−0.823317	+	0.823317i	0.163265	+	0.986582i	$0.447797\pi$
$308$	−136.429			−0.442951
$309$		−	160.752i		−	0.520231i
$310$	−52.1942	+	52.1942i	−0.168368	+	0.168368i
$311$		−	209.742i		−	0.674411i	−0.941431	−	0.337206i	$-0.890518\pi$
$311$		−	209.742i		−	0.674411i	0.941431	−	0.337206i	$-0.109482\pi$
$312$		0			0
$313$	386.143			1.23368			0.616842	−	0.787087i	$-0.288412\pi$
$313$	386.143			1.23368			0.616842	+	0.787087i	$0.288412\pi$
$314$	195.116	+	195.116i	0.621389	+	0.621389i
$315$	88.4004			0.280636
$316$		−	188.571i		−	0.596743i
$317$	−114.759	−	114.759i	−0.362016	−	0.362016i	0.502538	−	0.864555i	$-0.332400\pi$
$317$	−114.759	−	114.759i	−0.362016	−	0.362016i	−0.864555	+	0.502538i	$0.832400\pi$
$318$	8.04381	+	8.04381i	0.0252950	+	0.0252950i
$319$	344.304	−	344.304i	1.07932	−	1.07932i
$320$	32.2063	−	32.2063i	0.100645	−	0.100645i
$321$	−130.320			−0.405982
$322$		−	88.6089i		−	0.275183i
$323$	−404.681	+	404.681i	−1.25288	+	1.25288i
$324$			18.0000i			0.0555556i
$325$		0			0
$326$	−175.005			−0.536826
$327$	79.7698	+	79.7698i	0.243944	+	0.243944i
$328$	18.6835			0.0569618
$329$		−	450.926i		−	1.37060i
$330$	−129.967	−	129.967i	−0.393841	−	0.393841i
$331$	−258.146	−	258.146i	−0.779898	−	0.779898i	0.199916	−	0.979813i	$-0.435933\pi$
$331$	−258.146	−	258.146i	−0.779898	−	0.779898i	−0.979813	+	0.199916i	$0.935933\pi$
$332$	126.978	−	126.978i	0.382464	−	0.382464i
$333$	111.544	−	111.544i	0.334968	−	0.334968i
$334$	−175.687			−0.526010
$335$		−	541.288i		−	1.61578i
$336$	25.3556	−	25.3556i	0.0754630	−	0.0754630i
$337$			385.355i			1.14349i	0.820432	+	0.571744i	$0.193733\pi$
$337$			385.355i			1.14349i	−0.820432	+	0.571744i	$0.806267\pi$
$338$		0			0
$339$	−271.055			−0.799571
$340$	151.813	+	151.813i	0.446508	+	0.446508i
$341$	120.827			0.354332
$342$			128.776i			0.376539i
$343$	260.620	+	260.620i	0.759825	+	0.759825i
$344$	27.2107	+	27.2107i	0.0791009	+	0.0791009i
$345$	84.4124	−	84.4124i	0.244674	−	0.244674i
$346$	119.181	−	119.181i	0.344454	−	0.344454i
$347$	−23.8673			−0.0687819			−0.0343909	−	0.999408i	$-0.510949\pi$
$347$	−23.8673			−0.0687819			−0.0343909	+	0.999408i	$0.510949\pi$
$348$			127.979i			0.367756i
$349$	−220.406	+	220.406i	−0.631536	+	0.631536i	−0.948453	−	0.316917i	$-0.897352\pi$
$349$	−220.406	+	220.406i	−0.631536	+	0.631536i	0.316917	+	0.948453i	$0.397352\pi$
$350$		−	54.2661i		−	0.155046i
$351$		0			0
$352$	−74.5561			−0.211807
$353$	400.332	+	400.332i	1.13409	+	1.13409i	0.989491	+	0.144594i	$0.0461877\pi$
$353$	400.332	+	400.332i	1.13409	+	1.13409i	0.144594	+	0.989491i	$0.453812\pi$
$354$	−61.1197			−0.172654
$355$			231.205i			0.651282i
$356$	220.561	+	220.561i	0.619554	+	0.619554i
$357$	119.520	+	119.520i	0.334790	+	0.334790i
$358$	214.511	−	214.511i	0.599192	−	0.599192i
$359$	−30.3760	+	30.3760i	−0.0846129	+	0.0846129i	−0.748146	−	0.663534i	$-0.769056\pi$
$359$	−30.3760	+	30.3760i	−0.0846129	+	0.0846129i	0.663534	+	0.748146i	$0.269056\pi$
$360$	48.3094			0.134193
$361$			560.299i			1.55208i
$362$	−343.720	+	343.720i	−0.949504	+	0.949504i
$363$			91.2909i			0.251490i
$364$		0			0
$365$	486.706			1.33344
$366$	66.7577	+	66.7577i	0.182398	+	0.182398i
$367$	−453.012			−1.23436			−0.617182	−	0.786820i	$-0.711726\pi$
$367$	−453.012			−1.23436			−0.617182	+	0.786820i	$0.711726\pi$
$368$		−	48.4234i		−	0.131585i
$369$	14.0126	+	14.0126i	0.0379745	+	0.0379745i
$370$	−299.369	−	299.369i	−0.809106	−	0.809106i
$371$	16.9963	−	16.9963i	0.0458120	−	0.0458120i
$372$	−22.4560	+	22.4560i	−0.0603655	+	0.0603655i
$373$	−407.309			−1.09198			−0.545991	−	0.837791i	$-0.683847\pi$
$373$	−407.309			−1.09198			−0.545991	+	0.837791i	$0.683847\pi$
$374$		−	351.440i		−	0.939679i
$375$	−122.626	+	122.626i	−0.327002	+	0.327002i
$376$		−	246.424i		−	0.655383i
$377$		0			0
$378$	38.0333			0.100617
$379$	7.46065	+	7.46065i	0.0196851	+	0.0196851i	0.716881	−	0.697196i	$-0.245569\pi$
$379$	7.46065	+	7.46065i	0.0196851	+	0.0196851i	−0.697196	+	0.716881i	$0.745569\pi$
$380$	345.618			0.909520
$381$			317.619i			0.833644i
$382$	−249.718	−	249.718i	−0.653712	−	0.653712i
$383$	−348.183	−	348.183i	−0.909093	−	0.909093i	0.0871059	−	0.996199i	$-0.472238\pi$
$383$	−348.183	−	348.183i	−0.909093	−	0.909093i	−0.996199	+	0.0871059i	$0.972238\pi$
$384$	13.8564	−	13.8564i	0.0360844	−	0.0360844i
$385$	−274.616	+	274.616i	−0.713289	+	0.713289i
$386$	−191.640			−0.496476
$387$			40.8161i			0.105468i
$388$	214.595	−	214.595i	0.553079	−	0.553079i
$389$		−	61.5695i		−	0.158276i	−0.996864	−	0.0791382i	$-0.974783\pi$
$389$		−	61.5695i		−	0.158276i	0.996864	−	0.0791382i	$-0.0252168\pi$
$390$		0			0
$391$	228.256			0.583776
$392$	44.4246	+	44.4246i	0.113328	+	0.113328i
$393$	263.265			0.669884
$394$		−	4.97285i		−	0.0126215i
$395$	−379.573	−	379.573i	−0.960943	−	0.960943i
$396$	−55.9171	−	55.9171i	−0.141205	−	0.141205i
$397$	−143.539	+	143.539i	−0.361560	+	0.361560i	−0.864387	−	0.502827i	$-0.832293\pi$
$397$	−143.539	+	143.539i	−0.361560	+	0.361560i	0.502827	+	0.864387i	$0.332293\pi$
$398$	−265.195	+	265.195i	−0.666319	+	0.666319i
$399$	272.100			0.681955
$400$		−	29.6555i		−	0.0741388i
$401$	−194.215	+	194.215i	−0.484326	+	0.484326i	−0.906510	−	0.422184i	$-0.861264\pi$
$401$	−194.215	+	194.215i	−0.484326	+	0.484326i	0.422184	+	0.906510i	$0.361264\pi$
$402$		−	232.883i		−	0.579312i
$403$		0			0
$404$	91.9460			0.227589
$405$	36.2321	+	36.2321i	0.0894619	+	0.0894619i
$406$	270.415			0.666047
$407$			693.027i			1.70277i
$408$	65.3158	+	65.3158i	0.160088	+	0.160088i
$409$	−154.552	−	154.552i	−0.377877	−	0.377877i	0.492459	−	0.870336i	$-0.336098\pi$
$409$	−154.552	−	154.552i	−0.377877	−	0.377877i	−0.870336	+	0.492459i	$0.836098\pi$
$410$	37.6078	−	37.6078i	0.0917264	−	0.0917264i
$411$	294.516	−	294.516i	0.716585	−	0.716585i
$412$	−185.620			−0.450534
$413$			129.144i			0.312696i
$414$	36.3175	−	36.3175i	0.0877235	−	0.0877235i
$415$		−	511.186i		−	1.23177i
$416$		0			0
$417$	321.231			0.770337
$418$	−400.045	−	400.045i	−0.957045	−	0.957045i
$419$	−427.811			−1.02103			−0.510514	−	0.859869i	$-0.670545\pi$
$419$	−427.811			−1.02103			−0.510514	+	0.859869i	$0.670545\pi$
$420$		−	102.076i		−	0.243038i
$421$	275.833	+	275.833i	0.655185	+	0.655185i	0.954237	−	0.299052i	$-0.0966703\pi$
$421$	275.833	+	275.833i	0.655185	+	0.655185i	−0.299052	+	0.954237i	$0.596670\pi$
$422$	13.7413	+	13.7413i	0.0325624	+	0.0325624i
$423$	184.818	−	184.818i	0.436922	−	0.436922i
$424$	9.28819	−	9.28819i	0.0219061	−	0.0219061i
$425$	139.789			0.328916
$426$			99.4735i			0.233506i
$427$	141.057	−	141.057i	0.330343	−	0.330343i
$428$			150.481i			0.351590i
$429$		0			0
$430$	109.544			0.254755
$431$	392.465	+	392.465i	0.910591	+	0.910591i	0.996319	−	0.0857274i	$-0.0273214\pi$
$431$	392.465	+	392.465i	0.910591	+	0.910591i	−0.0857274	+	0.996319i	$0.527321\pi$
$432$	20.7846			0.0481125
$433$			673.789i			1.55610i	0.628205	+	0.778048i	$0.283790\pi$
$433$			673.789i			1.55610i	−0.628205	+	0.778048i	$0.716210\pi$
$434$	47.4487	+	47.4487i	0.109329	+	0.109329i
$435$	257.608	+	257.608i	0.592203	+	0.592203i
$436$	92.1103	−	92.1103i	0.211262	−	0.211262i
$437$	259.825	−	259.825i	0.594564	−	0.594564i
$438$	209.400			0.478082
$439$		−	574.138i		−	1.30783i	−0.756567	−	0.653916i	$-0.773125\pi$
$439$		−	574.138i		−	1.30783i	0.756567	−	0.653916i	$-0.226875\pi$
$440$	−150.073	+	150.073i	−0.341076	+	0.341076i
$441$			66.6370i			0.151104i
$442$		0			0
$443$	−365.652			−0.825399			−0.412700	−	0.910867i	$-0.635414\pi$
$443$	−365.652			−0.825399			−0.412700	+	0.910867i	$0.635414\pi$
$444$	−128.800	−	128.800i	−0.290091	−	0.290091i
$445$	887.933			1.99535
$446$			144.629i			0.324281i
$447$	22.1287	+	22.1287i	0.0495048	+	0.0495048i
$448$	−29.2781	−	29.2781i	−0.0653528	−	0.0653528i
$449$	−580.110	+	580.110i	−1.29200	+	1.29200i	−0.358458	+	0.933546i	$0.616697\pi$
$449$	−580.110	+	580.110i	−1.29200	+	1.29200i	−0.933546	+	0.358458i	$0.883303\pi$
$450$	22.2417	−	22.2417i	0.0494259	−	0.0494259i
$451$	−87.0605			−0.193039
$452$			312.987i			0.692449i
$453$	165.272	−	165.272i	0.364838	−	0.364838i
$454$			327.842i			0.722119i
$455$		0			0
$456$	148.698			0.326093
$457$	−139.768	−	139.768i	−0.305838	−	0.305838i	0.537455	−	0.843293i	$-0.319386\pi$
$457$	−139.768	−	139.768i	−0.305838	−	0.305838i	−0.843293	+	0.537455i	$0.819386\pi$
$458$	−612.065			−1.33639
$459$			97.9737i			0.213450i
$460$	−97.4710	−	97.4710i	−0.211894	−	0.211894i
$461$	−71.5746	−	71.5746i	−0.155259	−	0.155259i	0.625203	−	0.780462i	$-0.285016\pi$
$461$	−71.5746	−	71.5746i	−0.155259	−	0.155259i	−0.780462	+	0.625203i	$0.785016\pi$
$462$	−118.151	+	118.151i	−0.255738	+	0.255738i
$463$	177.994	−	177.994i	0.384435	−	0.384435i	−0.488262	−	0.872697i	$-0.662369\pi$
$463$	177.994	−	177.994i	0.384435	−	0.384435i	0.872697	+	0.488262i	$0.162369\pi$
$464$	147.778			0.318486
$465$			90.4029i			0.194415i
$466$	156.892	−	156.892i	0.336678	−	0.336678i
$467$		−	104.162i		−	0.223044i	−0.993762	−	0.111522i	$-0.964427\pi$
$467$		−	104.162i		−	0.223044i	0.993762	−	0.111522i	$-0.0355726\pi$
$468$		0			0
$469$	−492.074			−1.04920
$470$	−496.025	−	496.025i	−1.05537	−	1.05537i
$471$	337.951			0.717519
$472$			70.5749i			0.149523i
$473$	−126.795	−	126.795i	−0.268066	−	0.268066i
$474$	−163.307	−	163.307i	−0.344530	−	0.344530i
$475$	159.122	−	159.122i	0.334994	−	0.334994i
$476$	138.010	−	138.010i	0.289937	−	0.289937i
$477$	13.9323			0.0292081
$478$		−	21.1462i		−	0.0442390i
$479$	52.2191	−	52.2191i	0.109017	−	0.109017i	−0.650494	−	0.759511i	$-0.725438\pi$
$479$	52.2191	−	52.2191i	0.109017	−	0.109017i	0.759511	+	0.650494i	$0.225438\pi$
$480$		−	55.7829i		−	0.116214i
$481$		0			0
$482$	−333.092			−0.691062
$483$	−76.7376	−	76.7376i	−0.158877	−	0.158877i
$484$	105.414			0.217797
$485$		−	863.912i		−	1.78126i
$486$	15.5885	+	15.5885i	0.0320750	+	0.0320750i
$487$	464.187	+	464.187i	0.953157	+	0.953157i	0.998951	−	0.0457942i	$-0.0145818\pi$
$487$	464.187	+	464.187i	0.953157	+	0.953157i	−0.0457942	+	0.998951i	$0.514582\pi$
$488$	77.0851	−	77.0851i	0.157961	−	0.157961i
$489$	−151.559	+	151.559i	−0.309937	+	0.309937i
$490$	178.844			0.364988
$491$		−	451.726i		−	0.920012i	−0.887916	−	0.460006i	$-0.847847\pi$
$491$		−	451.726i		−	0.920012i	0.887916	−	0.460006i	$-0.152153\pi$
$492$	16.1804	−	16.1804i	0.0328869	−	0.0328869i
$493$			696.588i			1.41296i
$494$		0			0
$495$	−225.110			−0.454768
$496$	25.9299	+	25.9299i	0.0522781	+	0.0522781i
$497$	210.184			0.422905
$498$		−	219.932i		−	0.441631i
$499$	−126.721	−	126.721i	−0.253950	−	0.253950i	0.568638	−	0.822588i	$-0.307471\pi$
$499$	−126.721	−	126.721i	−0.253950	−	0.253950i	−0.822588	+	0.568638i	$0.807471\pi$
$500$	141.596	+	141.596i	0.283192	+	0.283192i
$501$	−152.150	+	152.150i	−0.303692	+	0.303692i
$502$	76.9248	−	76.9248i	0.153237	−	0.153237i
$503$	−347.883			−0.691616			−0.345808	−	0.938305i	$-0.612395\pi$
$503$	−347.883			−0.691616			−0.345808	+	0.938305i	$0.612395\pi$
$504$		−	43.9171i		−	0.0871371i
$505$	185.077	−	185.077i	0.366490	−	0.366490i
$506$			225.641i			0.445931i
$507$		0			0
$508$	366.754			0.721957
$509$	127.161	+	127.161i	0.249826	+	0.249826i	0.820899	−	0.571073i	$-0.193473\pi$
$509$	127.161	+	127.161i	0.249826	+	0.249826i	−0.571073	+	0.820899i	$0.693473\pi$
$510$	262.947			0.515583
$511$		−	442.454i		−	0.865860i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	111.524	+	111.524i	0.217395	+	0.217395i
$514$	−63.5214	+	63.5214i	−0.123583	+	0.123583i
$515$	−373.633	+	373.633i	−0.725501	+	0.725501i
$516$	47.1303			0.0913378
$517$			1148.28i			2.22104i
$518$	−272.151	+	272.151i	−0.525387	+	0.525387i
$519$		−	206.428i		−	0.397741i
$520$		0			0
$521$	−107.588			−0.206503			−0.103251	−	0.994655i	$-0.532925\pi$
$521$	−107.588			−0.206503			−0.103251	+	0.994655i	$0.532925\pi$
$522$	110.833	+	110.833i	0.212324	+	0.212324i
$523$	−601.633			−1.15035			−0.575175	−	0.818031i	$-0.695066\pi$
$523$	−601.633			−1.15035			−0.575175	+	0.818031i	$0.695066\pi$
$524$		−	303.992i		−	0.580137i
$525$	−46.9958	−	46.9958i	−0.0895158	−	0.0895158i
$526$	−225.177	−	225.177i	−0.428094	−	0.428094i
$527$	−122.228	+	122.228i	−0.231931	+	0.231931i
$528$	−64.5675	+	64.5675i	−0.122287	+	0.122287i
$529$	382.449			0.722965
$530$		−	37.3923i		−	0.0705514i
$531$	−52.9312	+	52.9312i	−0.0996821	+	0.0996821i
$532$		−	314.194i		−	0.590590i
$533$		0			0
$534$	382.023			0.715400
$535$	302.901	+	302.901i	0.566171	+	0.566171i
$536$	−268.911			−0.501699
$537$		−	371.544i		−	0.691888i
$538$	−22.1441	−	22.1441i	−0.0411600	−	0.0411600i
$539$	−207.008	−	207.008i	−0.384060	−	0.384060i
$540$	41.8372	−	41.8372i	0.0774763	−	0.0774763i
$541$	212.291	−	212.291i	0.392405	−	0.392405i	−0.483139	−	0.875544i	$-0.660503\pi$
$541$	212.291	−	212.291i	0.392405	−	0.392405i	0.875544	+	0.483139i	$0.160503\pi$
$542$	210.634			0.388623
$543$			595.341i			1.09639i
$544$	75.4202	−	75.4202i	0.138640	−	0.138640i
$545$		−	370.816i		−	0.680397i
$546$		0			0
$547$	−709.928			−1.29786			−0.648929	−	0.760849i	$-0.724783\pi$
$547$	−709.928			−1.29786			−0.648929	+	0.760849i	$0.724783\pi$
$548$	−340.078	−	340.078i	−0.620581	−	0.620581i
$549$	115.628			0.210615
$550$			138.188i			0.251250i
$551$	792.928	+	792.928i	1.43907	+	1.43907i
$552$	−41.9359	−	41.9359i	−0.0759708	−	0.0759708i
$553$	−345.062	+	345.062i	−0.623982	+	0.623982i
$554$	202.590	−	202.590i	0.365687	−	0.365687i
$555$	−518.523			−0.934275
$556$		−	370.925i		−	0.667132i
$557$	504.916	−	504.916i	0.906492	−	0.906492i	−0.0894957	−	0.995987i	$-0.528526\pi$
$557$	504.916	−	504.916i	0.906492	−	0.906492i	0.995987	+	0.0894957i	$0.0285255\pi$
$558$			38.8949i			0.0697041i
$559$		0			0
$560$	−117.867			−0.210477
$561$	−304.356	−	304.356i	−0.542524	−	0.542524i
$562$	−88.1310			−0.156817
$563$		−	184.650i		−	0.327975i	−0.986462	−	0.163988i	$-0.947564\pi$
$563$		−	184.650i		−	0.327975i	0.986462	−	0.163988i	$-0.0524357\pi$
$564$	−213.409	−	213.409i	−0.378385	−	0.378385i
$565$	630.009	+	630.009i	1.11506	+	1.11506i
$566$	140.882	−	140.882i	0.248909	−	0.248909i
$567$	32.9378	−	32.9378i	0.0580914	−	0.0580914i
$568$	114.862			0.202222
$569$			934.094i			1.64164i	0.571186	+	0.820820i	$0.306483\pi$
$569$			934.094i			1.64164i	−0.571186	+	0.820820i	$0.693517\pi$
$570$	299.314	−	299.314i	0.525112	−	0.525112i
$571$			235.631i			0.412664i	0.978482	+	0.206332i	$0.0661527\pi$
$571$			235.631i			0.412664i	−0.978482	+	0.206332i	$0.933847\pi$
$572$		0			0
$573$	−432.524			−0.754842
$574$	−34.1885	−	34.1885i	−0.0595619	−	0.0595619i
$575$	−89.7513			−0.156089
$576$		−	24.0000i		−	0.0416667i
$577$	−213.174	−	213.174i	−0.369452	−	0.369452i	0.497826	−	0.867277i	$-0.334132\pi$
$577$	−213.174	−	213.174i	−0.369452	−	0.369452i	−0.867277	+	0.497826i	$0.834132\pi$
$578$	66.5131	+	66.5131i	0.115075	+	0.115075i
$579$	−165.965	+	165.965i	−0.286641	+	0.286641i
$580$	297.460	−	297.460i	0.512862	−	0.512862i
$581$	−464.709			−0.799844
$582$		−	371.689i		−	0.638641i
$583$	−43.2807	+	43.2807i	−0.0742380	+	0.0742380i
$584$		−	241.794i		−	0.414031i
$585$		0			0
$586$	−242.001			−0.412970
$587$	354.401	+	354.401i	0.603750	+	0.603750i	0.941305	−	0.337556i	$-0.109600\pi$
$587$	354.401	+	354.401i	0.603750	+	0.603750i	−0.337556	+	0.941305i	$0.609600\pi$
$588$	76.9457			0.130860
$589$			278.264i			0.472434i
$590$	142.060	+	142.060i	0.240779	+	0.240779i
$591$	−4.30662	−	4.30662i	−0.00728700	−	0.00728700i
$592$	−148.726	+	148.726i	−0.251226	+	0.251226i
$593$	−456.457	+	456.457i	−0.769743	+	0.769743i	−0.978061	−	0.208319i	$-0.933201\pi$
$593$	−456.457	+	456.457i	−0.769743	+	0.769743i	0.208319	+	0.978061i	$0.433201\pi$
$594$	−96.8513			−0.163049
$595$		−	555.598i		−	0.933779i
$596$	25.5520	−	25.5520i	0.0428724	−	0.0428724i
$597$			459.331i			0.769399i
$598$		0			0
$599$	409.720			0.684007			0.342003	−	0.939699i	$-0.388895\pi$
$599$	409.720			0.684007			0.342003	+	0.939699i	$0.388895\pi$
$600$	−25.6824	−	25.6824i	−0.0428041	−	0.0428041i
$601$	−708.630			−1.17909			−0.589543	−	0.807737i	$-0.700692\pi$
$601$	−708.630			−1.17909			−0.589543	+	0.807737i	$0.700692\pi$
$602$		−	99.5846i		−	0.165423i
$603$	−201.683	−	201.683i	−0.334466	−	0.334466i
$604$	−190.839	−	190.839i	−0.315959	−	0.315959i
$605$	212.186	−	212.186i	0.350721	−	0.350721i
$606$	79.6276	−	79.6276i	0.131399	−	0.131399i
$607$	467.364			0.769957			0.384978	−	0.922926i	$-0.374209\pi$
$607$	467.364			0.769957			0.384978	+	0.922926i	$0.374209\pi$
$608$		−	171.702i		−	0.282405i
$609$	234.186	−	234.186i	0.384542	−	0.384542i
$610$		−	310.328i		−	0.508735i
$611$		0			0
$612$	113.130			0.184853
$613$	−704.485	−	704.485i	−1.14924	−	1.14924i	−0.986702	−	0.162540i	$-0.948031\pi$
$613$	−704.485	−	704.485i	−1.14924	−	1.14924i	−0.162540	−	0.986702i	$-0.551969\pi$
$614$	505.517			0.823317
$615$		−	65.1387i		−	0.105917i
$616$	136.429	+	136.429i	0.221475	+	0.221475i
$617$	220.953	+	220.953i	0.358108	+	0.358108i	0.863115	−	0.505007i	$-0.168510\pi$
$617$	220.953	+	220.953i	0.358108	+	0.358108i	−0.505007	+	0.863115i	$0.668510\pi$
$618$	−160.752	+	160.752i	−0.260116	+	0.260116i
$619$	−459.215	+	459.215i	−0.741865	+	0.741865i	−0.972937	−	0.231071i	$-0.925777\pi$
$619$	−459.215	+	459.215i	−0.741865	+	0.741865i	0.231071	+	0.972937i	$0.425777\pi$
$620$	104.388			0.168368
$621$		−	62.9038i		−	0.101294i
$622$	−209.742	+	209.742i	−0.337206	+	0.337206i
$623$		−	807.201i		−	1.29567i
$624$		0			0
$625$	755.381			1.20861
$626$	−386.143	−	386.143i	−0.616842	−	0.616842i
$627$	−692.898			−1.10510
$628$		−	390.233i		−	0.621389i
$629$	−701.059	−	701.059i	−1.11456	−	1.11456i
$630$	−88.4004	−	88.4004i	−0.140318	−	0.140318i
$631$	−189.565	+	189.565i	−0.300420	+	0.300420i	−0.841178	−	0.540758i	$-0.818137\pi$
$631$	−189.565	+	189.565i	−0.300420	+	0.300420i	0.540758	+	0.841178i	$0.318137\pi$
$632$	−188.571	+	188.571i	−0.298371	+	0.298371i
$633$	23.8007			0.0375998
$634$			229.518i			0.362016i
$635$	738.237	−	738.237i	1.16258	−	1.16258i
$636$		−	16.0876i		−	0.0252950i
$637$		0			0
$638$	−688.608			−1.07932
$639$	86.1466	+	86.1466i	0.134815	+	0.134815i
$640$	−64.4126			−0.100645
$641$		−	172.486i		−	0.269089i	−0.990908	−	0.134545i	$-0.957043\pi$
$641$		−	172.486i		−	0.269089i	0.990908	−	0.134545i	$-0.0429572\pi$
$642$	130.320	+	130.320i	0.202991	+	0.202991i
$643$	672.617	+	672.617i	1.04606	+	1.04606i	0.998887	+	0.0471735i	$0.0150214\pi$
$643$	672.617	+	672.617i	1.04606	+	1.04606i	0.0471735	+	0.998887i	$0.484979\pi$
$644$	−88.6089	+	88.6089i	−0.137592	+	0.137592i
$645$	94.8683	−	94.8683i	0.147083	−	0.147083i
$646$	809.363			1.25288
$647$		−	739.211i		−	1.14252i	−0.820769	−	0.571260i	$-0.806455\pi$
$647$		−	739.211i		−	1.14252i	0.820769	−	0.571260i	$-0.193545\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$		−	328.862i		−	0.506721i
$650$		0			0
$651$	82.1835			0.126242
$652$	175.005	+	175.005i	0.268413	+	0.268413i
$653$	−1122.68			−1.71926			−0.859632	−	0.510914i	$-0.829307\pi$
$653$	−1122.68			−1.71926			−0.859632	+	0.510914i	$0.829307\pi$
$654$		−	159.540i		−	0.243944i
$655$	−611.903	−	611.903i	−0.934202	−	0.934202i
$656$	−18.6835	−	18.6835i	−0.0284809	−	0.0284809i
$657$	181.346	−	181.346i	0.276021	−	0.276021i
$658$	−450.926	+	450.926i	−0.685298	+	0.685298i
$659$	349.019			0.529619			0.264810	−	0.964301i	$-0.414691\pi$
$659$	349.019			0.529619			0.264810	+	0.964301i	$0.414691\pi$
$660$			259.935i			0.393841i
$661$	566.931	−	566.931i	0.857686	−	0.857686i	−0.133379	−	0.991065i	$-0.542583\pi$
$661$	566.931	−	566.931i	0.857686	−	0.857686i	0.991065	+	0.133379i	$0.0425827\pi$
$662$			516.292i			0.779898i
$663$		0			0
$664$	−253.956			−0.382464
$665$	−632.439	−	632.439i	−0.951036	−	0.951036i
$666$	−223.089			−0.334968
$667$		−	447.243i		−	0.670529i
$668$	175.687	+	175.687i	0.263005	+	0.263005i
$669$	125.253	+	125.253i	0.187224	+	0.187224i
$670$	−541.288	+	541.288i	−0.807892	+	0.807892i
$671$	−359.198	+	359.198i	−0.535318	+	0.535318i
$672$	−50.7111			−0.0754630
$673$		−	104.897i		−	0.155865i	−0.996959	−	0.0779323i	$-0.975168\pi$
$673$		−	104.897i		−	0.155865i	0.996959	−	0.0779323i	$-0.0248318\pi$
$674$	385.355	−	385.355i	0.571744	−	0.571744i
$675$		−	38.5237i		−	0.0570721i
$676$		0			0
$677$	−71.7517			−0.105985			−0.0529924	−	0.998595i	$-0.516876\pi$
$677$	−71.7517			−0.105985			−0.0529924	+	0.998595i	$0.516876\pi$
$678$	271.055	+	271.055i	0.399785	+	0.399785i
$679$	−785.365			−1.15665
$680$		−	303.626i		−	0.446508i
$681$	283.920	+	283.920i	0.416916	+	0.416916i
$682$	−120.827	−	120.827i	−0.177166	−	0.177166i
$683$	526.610	−	526.610i	0.771024	−	0.771024i	−0.207261	−	0.978286i	$-0.566455\pi$
$683$	526.610	−	526.610i	0.771024	−	0.771024i	0.978286	+	0.207261i	$0.0664550\pi$
$684$	128.776	−	128.776i	0.188270	−	0.188270i
$685$	−1369.08			−1.99866
$686$		−	521.240i		−	0.759825i
$687$	−530.064	+	530.064i	−0.771563	+	0.771563i
$688$		−	54.4214i		−	0.0791009i
$689$		0			0
$690$	−168.825			−0.244674
$691$	403.147	+	403.147i	0.583425	+	0.583425i	0.935843	−	0.352418i	$-0.114640\pi$
$691$	403.147	+	403.147i	0.583425	+	0.583425i	−0.352418	+	0.935843i	$0.614640\pi$
$692$	−238.362			−0.344454
$693$			204.643i			0.295300i
$694$	23.8673	+	23.8673i	0.0343909	+	0.0343909i
$695$	−746.632	−	746.632i	−1.07429	−	1.07429i
$696$	127.979	−	127.979i	0.183878	−	0.183878i
$697$	88.0695	−	88.0695i	0.126355	−	0.126355i
$698$	440.812			0.631536
$699$		−	271.745i		−	0.388762i
$700$	−54.2661	+	54.2661i	−0.0775229	+	0.0775229i
$701$			234.275i			0.334201i	0.985940	+	0.167101i	$0.0534405\pi$
$701$			234.275i			0.334201i	−0.985940	+	0.167101i	$0.946559\pi$
$702$		0			0
$703$	−1596.03			−2.27032
$704$	74.5561	+	74.5561i	0.105904	+	0.105904i
$705$	−859.140			−1.21864
$706$		−	800.664i		−	1.13409i
$707$	−168.250	−	168.250i	−0.237978	−	0.237978i
$708$	61.1197	+	61.1197i	0.0863272	+	0.0863272i
$709$	−16.8626	+	16.8626i	−0.0237837	+	0.0237837i	−0.718899	−	0.695115i	$-0.755353\pi$
$709$	−16.8626	+	16.8626i	−0.0237837	+	0.0237837i	0.695115	+	0.718899i	$0.255353\pi$
$710$	231.205	−	231.205i	0.325641	−	0.325641i
$711$	−282.856			−0.397829
$712$		−	441.123i		−	0.619554i
$713$	78.4759	−	78.4759i	0.110064	−	0.110064i
$714$		−	239.040i		−	0.334790i
$715$		0			0
$716$	−429.022			−0.599192
$717$	−18.3132	−	18.3132i	−0.0255414	−	0.0255414i
$718$	60.7520			0.0846129
$719$			755.495i			1.05076i	0.850868	+	0.525379i	$0.176076\pi$
$719$			755.495i			1.05076i	−0.850868	+	0.525379i	$0.823924\pi$
$720$	−48.3094	−	48.3094i	−0.0670964	−	0.0670964i
$721$	339.662	+	339.662i	0.471098	+	0.471098i
$722$	560.299	−	560.299i	0.776038	−	0.776038i
$723$	−288.466	+	288.466i	−0.398985	+	0.398985i
$724$	687.441			0.949504
$725$		−	273.901i		−	0.377795i
$726$	91.2909	−	91.2909i	0.125745	−	0.125745i
$727$			686.041i			0.943660i	0.881689	+	0.471830i	$0.156406\pi$
$727$			686.041i			0.943660i	−0.881689	+	0.471830i	$0.843594\pi$
$728$		0			0
$729$	27.0000			0.0370370
$730$	−486.706	−	486.706i	−0.666720	−	0.666720i
$731$	256.530			0.350930
$732$		−	133.515i		−	0.182398i
$733$	−173.245	−	173.245i	−0.236351	−	0.236351i	0.578986	−	0.815337i	$-0.303448\pi$
$733$	−173.245	−	173.245i	−0.236351	−	0.236351i	−0.815337	+	0.578986i	$0.803448\pi$
$734$	453.012	+	453.012i	0.617182	+	0.617182i
$735$	154.884	−	154.884i	0.210726	−	0.210726i
$736$	−48.4234	+	48.4234i	−0.0657926	+	0.0657926i
$737$	1253.06			1.70021
$738$		−	28.0252i		−	0.0379745i
$739$	−70.1524	+	70.1524i	−0.0949289	+	0.0949289i	−0.752976	−	0.658048i	$-0.771383\pi$
$739$	−70.1524	+	70.1524i	−0.0949289	+	0.0949289i	0.658048	+	0.752976i	$0.271383\pi$
$740$			598.739i			0.809106i
$741$		0			0
$742$	−33.9925			−0.0458120
$743$	−882.457	−	882.457i	−1.18769	−	1.18769i	−0.977703	−	0.209992i	$-0.932656\pi$
$743$	−882.457	−	882.457i	−1.18769	−	1.18769i	−0.209992	−	0.977703i	$-0.567344\pi$
$744$	44.9120			0.0603655
$745$		−	102.867i		−	0.138076i
$746$	407.309	+	407.309i	0.545991	+	0.545991i
$747$	−190.467	−	190.467i	−0.254976	−	0.254976i
$748$	−351.440	+	351.440i	−0.469840	+	0.469840i
$749$	275.361	−	275.361i	0.367639	−	0.367639i
$750$	245.251			0.327002
$751$		−	209.378i		−	0.278798i	−0.990236	−	0.139399i	$-0.955483\pi$
$751$		−	209.378i		−	0.278798i	0.990236	−	0.139399i	$-0.0445171\pi$
$752$	−246.424	+	246.424i	−0.327691	+	0.327691i
$753$		−	133.238i		−	0.176942i
$754$		0			0
$755$	−768.277			−1.01759
$756$	−38.0333	−	38.0333i	−0.0503086	−	0.0503086i
$757$	1283.14			1.69503			0.847515	−	0.530771i	$-0.178098\pi$
$757$	1283.14			1.69503			0.847515	+	0.530771i	$0.178098\pi$
$758$		−	14.9213i		−	0.0196851i
$759$	195.411	+	195.411i	0.257459	+	0.257459i
$760$	−345.618	−	345.618i	−0.454760	−	0.454760i
$761$	328.989	−	328.989i	0.432311	−	0.432311i	−0.457103	−	0.889414i	$-0.651113\pi$
$761$	328.989	−	328.989i	0.432311	−	0.432311i	0.889414	+	0.457103i	$0.151113\pi$
$762$	317.619	−	317.619i	0.416822	−	0.416822i
$763$	−337.101			−0.441811
$764$			499.436i			0.653712i
$765$	227.719	−	227.719i	0.297672	−	0.297672i
$766$			696.365i			0.909093i
$767$		0			0
$768$	−27.7128			−0.0360844
$769$	591.777	+	591.777i	0.769541	+	0.769541i	0.978026	−	0.208485i	$-0.0668532\pi$
$769$	591.777	+	591.777i	0.769541	+	0.769541i	−0.208485	+	0.978026i	$0.566853\pi$
$770$	549.233			0.713289
$771$			110.022i			0.142701i
$772$	191.640	+	191.640i	0.248238	+	0.248238i
$773$	442.913	+	442.913i	0.572979	+	0.572979i	0.932960	−	0.359981i	$-0.117217\pi$
$773$	442.913	+	442.913i	0.572979	+	0.572979i	−0.359981	+	0.932960i	$0.617217\pi$
$774$	40.8161	−	40.8161i	0.0527339	−	0.0527339i
$775$	48.0604	−	48.0604i	0.0620134	−	0.0620134i
$776$	−429.189			−0.553079
$777$			471.379i			0.606665i
$778$	−61.5695	+	61.5695i	−0.0791382	+	0.0791382i
$779$		−	200.499i		−	0.257380i
$780$		0			0
$781$	−535.230			−0.685313
$782$	−228.256	−	228.256i	−0.291888	−	0.291888i
$783$	191.969			0.245171
$784$		−	88.8493i		−	0.113328i
$785$	−785.496	−	785.496i	−1.00063	−	1.00063i
$786$	−263.265	−	263.265i	−0.334942	−	0.334942i
$787$	91.4093	−	91.4093i	0.116149	−	0.116149i	−0.646643	−	0.762792i	$-0.723828\pi$
$787$	91.4093	−	91.4093i	0.116149	−	0.116149i	0.762792	+	0.646643i	$0.223828\pi$
$788$	−4.97285	+	4.97285i	−0.00631073	+	0.00631073i
$789$	−390.019			−0.494320
$790$			759.145i			0.960943i
$791$	572.728	−	572.728i	0.724056	−	0.724056i
$792$			111.834i			0.141205i
$793$		0			0
$794$	287.078			0.361560
$795$	−32.3826	−	32.3826i	−0.0407329	−	0.0407329i
$796$	530.390			0.666319
$797$			926.956i			1.16306i	0.813526	+	0.581528i	$0.197545\pi$
$797$			926.956i			1.16306i	−0.813526	+	0.581528i	$0.802455\pi$
$798$	−272.100	−	272.100i	−0.340977	−	0.340977i
$799$	−1161.58	−	1161.58i	−1.45380	−	1.45380i
$800$	−29.6555	+	29.6555i	−0.0370694	+	0.0370694i
$801$	330.842	−	330.842i	0.413036	−	0.413036i
$802$	388.430			0.484326
$803$			1126.70i			1.40312i
$804$	−232.883	+	232.883i	−0.289656	+	0.289656i
$805$			356.720i			0.443131i
$806$		0			0
$807$	−38.3547			−0.0475275
$808$	−91.9460	−	91.9460i	−0.113795	−	0.113795i
$809$	−754.553			−0.932698			−0.466349	−	0.884601i	$-0.654431\pi$
$809$	−754.553			−0.932698			−0.466349	+	0.884601i	$0.654431\pi$
$810$		−	72.4641i		−	0.0894619i
$811$	398.188	+	398.188i	0.490984	+	0.490984i	0.908616	−	0.417632i	$-0.137140\pi$
$811$	398.188	+	398.188i	0.490984	+	0.490984i	−0.417632	+	0.908616i	$0.637140\pi$
$812$	−270.415	−	270.415i	−0.333023	−	0.333023i
$813$	182.414	−	182.414i	0.224372	−	0.224372i
$814$	693.027	−	693.027i	0.851385	−	0.851385i
$815$	704.534			0.864459
$816$		−	130.632i		−	0.160088i
$817$	292.008	−	292.008i	0.357415	−	0.357415i
$818$			309.104i			0.377877i
$819$		0			0
$820$	−75.2156			−0.0917264
$821$	497.803	+	497.803i	0.606337	+	0.606337i	0.941987	−	0.335650i	$-0.108956\pi$
$821$	497.803	+	497.803i	0.606337	+	0.606337i	−0.335650	+	0.941987i	$0.608956\pi$
$822$	−589.033			−0.716585
$823$		−	506.914i		−	0.615934i	−0.951397	−	0.307967i	$-0.900351\pi$
$823$		−	506.914i		−	0.615934i	0.951397	−	0.307967i	$-0.0996486\pi$
$824$	185.620	+	185.620i	0.225267	+	0.225267i
$825$	119.674	+	119.674i	0.145059	+	0.145059i
$826$	129.144	−	129.144i	0.156348	−	0.156348i
$827$	31.7310	−	31.7310i	0.0383689	−	0.0383689i	−0.687662	−	0.726031i	$-0.741363\pi$
$827$	31.7310	−	31.7310i	0.0383689	−	0.0383689i	0.726031	+	0.687662i	$0.241363\pi$
$828$	−72.6351			−0.0877235
$829$		−	150.237i		−	0.181226i	−0.995886	−	0.0906131i	$-0.971117\pi$
$829$		−	150.237i		−	0.181226i	0.995886	−	0.0906131i	$-0.0288827\pi$
$830$	−511.186	+	511.186i	−0.615887	+	0.615887i
$831$		−	350.897i		−	0.422259i
$832$		0			0
$833$	418.815			0.502779
$834$	−321.231	−	321.231i	−0.385169	−	0.385169i
$835$	707.279			0.847040
$836$			800.090i			0.957045i
$837$	33.6840	+	33.6840i	0.0402437	+	0.0402437i
$838$	427.811	+	427.811i	0.510514	+	0.510514i
$839$	150.327	−	150.327i	0.179174	−	0.179174i	−0.611822	−	0.790996i	$-0.709563\pi$
$839$	150.327	−	150.327i	0.179174	−	0.179174i	0.790996	+	0.611822i	$0.209563\pi$
$840$	−102.076	+	102.076i	−0.121519	+	0.121519i
$841$	523.887			0.622933
$842$		−	551.666i		−	0.655185i
$843$	−76.3237	+	76.3237i	−0.0905382	+	0.0905382i
$844$		−	27.4826i		−	0.0325624i
$845$		0			0
$846$	−369.636			−0.436922
$847$	−192.894	−	192.894i	−0.227738	−	0.227738i
$848$	−18.5764			−0.0219061
$849$		−	244.015i		−	0.287415i
$850$	−139.789	−	139.789i	−0.164458	−	0.164458i
$851$	450.113	+	450.113i	0.528923	+	0.528923i
$852$	99.4735	−	99.4735i	0.116753	−	0.116753i
$853$	753.994	−	753.994i	0.883932	−	0.883932i	−0.110000	−	0.993932i	$-0.535085\pi$
$853$	753.994	−	753.994i	0.883932	−	0.883932i	0.993932	+	0.110000i	$0.0350851\pi$
$854$	−282.113			−0.330343
$855$		−	518.426i		−	0.606347i
$856$	150.481	−	150.481i	0.175795	−	0.175795i
$857$		−	844.995i		−	0.985992i	−0.870031	−	0.492996i	$-0.835902\pi$
$857$		−	844.995i		−	0.985992i	0.870031	−	0.492996i	$-0.164098\pi$
$858$		0			0
$859$	721.635			0.840087			0.420044	−	0.907504i	$-0.362015\pi$
$859$	721.635			0.840087			0.420044	+	0.907504i	$0.362015\pi$
$860$	−109.544	−	109.544i	−0.127377	−	0.127377i
$861$	−59.2162			−0.0687761
$862$		−	784.930i		−	0.910591i
$863$	124.534	+	124.534i	0.144304	+	0.144304i	0.775568	−	0.631264i	$-0.217464\pi$
$863$	124.534	+	124.534i	0.144304	+	0.144304i	−0.631264	+	0.775568i	$0.717464\pi$
$864$	−20.7846	−	20.7846i	−0.0240563	−	0.0240563i
$865$	−479.797	+	479.797i	−0.554679	+	0.554679i
$866$	673.789	−	673.789i	0.778048	−	0.778048i
$867$	115.204			0.132877
$868$		−	94.8973i		−	0.109329i
$869$	878.694	−	878.694i	1.01116	−	1.01116i
$870$		−	515.216i		−	0.592203i
$871$		0			0
$872$	−184.221			−0.211262
$873$	−321.892	−	321.892i	−0.368719	−	0.368719i
$874$	−519.649			−0.594564
$875$		−	518.207i		−	0.592236i
$876$	−209.400	−	209.400i	−0.239041	−	0.239041i
$877$	−22.5917	−	22.5917i	−0.0257602	−	0.0257602i	0.694109	−	0.719870i	$-0.255798\pi$
$877$	−22.5917	−	22.5917i	−0.0257602	−	0.0257602i	−0.719870	+	0.694109i	$0.755798\pi$
$878$	−574.138	+	574.138i	−0.653916	+	0.653916i
$879$	−209.579	+	209.579i	−0.238428	+	0.238428i
$880$	300.147			0.341076
$881$			1019.09i			1.15674i	0.815773	+	0.578372i	$0.196312\pi$
$881$			1019.09i			1.15674i	−0.815773	+	0.578372i	$0.803688\pi$
$882$	66.6370	−	66.6370i	0.0755521	−	0.0755521i
$883$			1092.31i			1.23705i	0.785767	+	0.618523i	$0.212268\pi$
$883$			1092.31i			1.23705i	−0.785767	+	0.618523i	$0.787732\pi$
$884$		0			0
$885$	246.055			0.278028
$886$	365.652	+	365.652i	0.412700	+	0.412700i
$887$	−677.300			−0.763585			−0.381792	−	0.924248i	$-0.624693\pi$
$887$	−677.300			−0.763585			−0.381792	+	0.924248i	$0.624693\pi$
$888$			257.601i			0.290091i
$889$	−671.116	−	671.116i	−0.754911	−	0.754911i
$890$	−887.933	−	887.933i	−0.997677	−	0.997677i
$891$	−83.8757	+	83.8757i	−0.0941366	+	0.0941366i
$892$	144.629	−	144.629i	0.162141	−	0.162141i
$893$	−2644.47			−2.96133
$894$		−	44.2573i		−	0.0495048i
$895$	−863.574	+	863.574i	−0.964888	+	0.964888i
$896$			58.5561i			0.0653528i
$897$		0			0
$898$	1160.22			1.29200
$899$	239.491	+	239.491i	0.266397	+	0.266397i
$900$	−44.4833			−0.0494259
$901$		−	87.5647i		−	0.0971861i
$902$	87.0605	+	87.0605i	0.0965194	+	0.0965194i
$903$	−86.2428	−	86.2428i	−0.0955070	−	0.0955070i
$904$	312.987	−	312.987i	0.346224	−	0.346224i
$905$	1383.74	−	1383.74i	1.52900	−	1.52900i
$906$	−330.543			−0.364838
$907$		−	1105.90i		−	1.21930i	−0.792672	−	0.609649i	$-0.791311\pi$
$907$		−	1105.90i		−	1.21930i	0.792672	−	0.609649i	$-0.208689\pi$
$908$	327.842	−	327.842i	0.361060	−	0.361060i
$909$		−	137.919i		−	0.151726i
$910$		0			0
$911$	1389.83			1.52560			0.762802	−	0.646632i	$-0.223823\pi$
$911$	1389.83			1.52560			0.762802	+	0.646632i	$0.223823\pi$
$912$	−148.698	−	148.698i	−0.163046	−	0.163046i
$913$	1183.37			1.29614
$914$			279.536i			0.305838i
$915$	−268.752	−	268.752i	−0.293718	−	0.293718i
$916$	612.065	+	612.065i	0.668193	+	0.668193i
$917$	−556.268	+	556.268i	−0.606617	+	0.606617i
$918$	97.9737	−	97.9737i	0.106725	−	0.106725i
$919$	871.246			0.948037			0.474019	−	0.880515i	$-0.342803\pi$
$919$	871.246			0.948037			0.474019	+	0.880515i	$0.342803\pi$
$920$			194.942i			0.211894i
$921$	437.790	−	437.790i	0.475342	−	0.475342i
$922$			143.149i			0.155259i
$923$		0			0
$924$	236.302			0.255738
$925$	275.659	+	275.659i	0.298010	+	0.298010i
$926$	−355.987			−0.384435
$927$			278.430i			0.300356i
$928$	−147.778	−	147.778i	−0.159243	−	0.159243i
$929$	−425.936	−	425.936i	−0.458488	−	0.458488i	0.439671	−	0.898159i	$-0.355095\pi$
$929$	−425.936	−	425.936i	−0.458488	−	0.458488i	−0.898159	+	0.439671i	$0.855095\pi$
$930$	90.4029	−	90.4029i	0.0972075	−	0.0972075i
$931$	476.738	−	476.738i	0.512070	−	0.512070i
$932$	−313.784			−0.336678
$933$			363.284i			0.389372i
$934$	−104.162	+	104.162i	−0.111522	+	0.111522i
$935$			1414.82i			1.51318i
$936$		0			0
$937$	−905.621			−0.966511			−0.483255	−	0.875479i	$-0.660546\pi$
$937$	−905.621			−0.966511			−0.483255	+	0.875479i	$0.660546\pi$
$938$	492.074	+	492.074i	0.524599	+	0.524599i
$939$	−668.819			−0.712268
$940$			992.050i			1.05537i
$941$	−429.149	−	429.149i	−0.456057	−	0.456057i	0.441302	−	0.897359i	$-0.354517\pi$
$941$	−429.149	−	429.149i	−0.456057	−	0.456057i	−0.897359	+	0.441302i	$0.854517\pi$
$942$	−337.951	−	337.951i	−0.358759	−	0.358759i
$943$	−56.5448	+	56.5448i	−0.0599627	+	0.0599627i
$944$	70.5749	−	70.5749i	0.0747616	−	0.0747616i
$945$	−153.114			−0.162025
$946$			253.591i			0.268066i
$947$	−719.464	+	719.464i	−0.759729	+	0.759729i	−0.976273	−	0.216544i	$-0.930522\pi$
$947$	−719.464	+	719.464i	−0.759729	+	0.759729i	0.216544	+	0.976273i	$0.430522\pi$
$948$			326.614i			0.344530i
$949$		0			0
$950$	−318.245			−0.334994
$951$	198.769	+	198.769i	0.209010	+	0.209010i
$952$	−276.020			−0.289937
$953$		−	895.474i		−	0.939637i	−0.882763	−	0.469819i	$-0.844319\pi$
$953$		−	895.474i		−	0.939637i	0.882763	−	0.469819i	$-0.155681\pi$
$954$	−13.9323	−	13.9323i	−0.0146041	−	0.0146041i
$955$	1005.31	+	1005.31i	1.05268	+	1.05268i
$956$	−21.1462	+	21.1462i	−0.0221195	+	0.0221195i
$957$	−596.352	+	596.352i	−0.623147	+	0.623147i
$958$	−104.438			−0.109017
$959$			1244.60i			1.29782i
$960$	−55.7829	+	55.7829i	−0.0581072	+	0.0581072i
$961$		−	876.955i		−	0.912544i
$962$		0			0
$963$	225.721			0.234394
$964$	333.092	+	333.092i	0.345531	+	0.345531i
$965$	771.501			0.799483
$966$			153.475i			0.158877i
$967$	−299.780	−	299.780i	−0.310010	−	0.310010i	0.534903	−	0.844913i	$-0.320348\pi$
$967$	−299.780	−	299.780i	−0.310010	−	0.310010i	−0.844913	+	0.534903i	$0.820348\pi$
$968$	−105.414	−	105.414i	−0.108898	−	0.108898i
$969$	700.929	−	700.929i	0.723353	−	0.723353i
$970$	−863.912	+	863.912i	−0.890631	+	0.890631i
$971$	645.587			0.664868			0.332434	−	0.943126i	$-0.392130\pi$
$971$	645.587			0.664868			0.332434	+	0.943126i	$0.392130\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	−678.748	+	678.748i	−0.697583	+	0.697583i
$974$		−	928.375i		−	0.953157i
$975$		0			0
$976$	−154.170			−0.157961
$977$	696.201	+	696.201i	0.712591	+	0.712591i	0.967076	−	0.254486i	$-0.0819063\pi$
$977$	696.201	+	696.201i	0.712591	+	0.712591i	−0.254486	+	0.967076i	$0.581906\pi$
$978$	303.118			0.309937
$979$			2055.53i			2.09962i
$980$	−178.844	−	178.844i	−0.182494	−	0.182494i
$981$	−138.165	−	138.165i	−0.140841	−	0.140841i
$982$	−451.726	+	451.726i	−0.460006	+	0.460006i
$983$	−525.791	+	525.791i	−0.534884	+	0.534884i	−0.922022	−	0.387138i	$-0.873464\pi$
$983$	−525.791	+	525.791i	−0.534884	+	0.534884i	0.387138	+	0.922022i	$0.373464\pi$
$984$	−32.3607			−0.0328869
$985$			20.0196i			0.0203245i
$986$	696.588	−	696.588i	0.706479	−	0.706479i
$987$			781.027i			0.791314i
$988$		0			0
$989$	−164.704			−0.166536
$990$	225.110	+	225.110i	0.227384	+	0.227384i
$991$	493.770			0.498255			0.249127	−	0.968471i	$-0.419856\pi$
$991$	493.770			0.498255			0.249127	+	0.968471i	$0.419856\pi$
$992$		−	51.8599i		−	0.0522781i
$993$	447.122	+	447.122i	0.450274	+	0.450274i
$994$	−210.184	−	210.184i	−0.211453	−	0.211453i
$995$	1067.62	−	1067.62i	1.07298	−	1.07298i
$996$	−219.932	+	219.932i	−0.220816	+	0.220816i
$997$	1216.46			1.22012			0.610059	−	0.792356i	$-0.291146\pi$
$997$	1216.46			1.22012			0.610059	+	0.792356i	$0.291146\pi$
$998$			253.442i			0.253950i
$999$	−193.201	+	193.201i	−0.193394	+	0.193394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.3.f.h.775.2		8
13.3	even	3		78.3.l.c.7.2	✓	8
13.5	odd	4	inner	1014.3.f.h.577.2		8
13.6	odd	12		78.3.l.c.67.2	yes	8
13.8	odd	4		1014.3.f.j.577.1		8
13.12	even	2		1014.3.f.j.775.1		8
39.29	odd	6		234.3.bb.d.163.1		8
39.32	even	12		234.3.bb.d.145.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.l.c.7.2	✓	8	13.3	even	3
78.3.l.c.67.2	yes	8	13.6	odd	12
234.3.bb.d.145.1		8	39.32	even	12
234.3.bb.d.163.1		8	39.29	odd	6
1014.3.f.h.577.2		8	13.5	odd	4	inner
1014.3.f.h.775.2		8	1.1	even	1	trivial
1014.3.f.j.577.1		8	13.8	odd	4
1014.3.f.j.775.1		8	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1014.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} -1.73205 q^{3} +2.00000i q^{4} +(4.02578 + 4.02578i) q^{5} +(1.73205 + 1.73205i) q^{6} +(3.65976 - 3.65976i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} -1.73205 q^{3} +2.00000i q^{4} +(4.02578 + 4.02578i) q^{5} +(1.73205 + 1.73205i) q^{6} +(3.65976 - 3.65976i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} -8.05157i q^{10} +(-9.31952 + 9.31952i) q^{11} -3.46410i q^{12} -7.31952 q^{14} +(-6.97286 - 6.97286i) q^{15} -4.00000 q^{16} -18.8551i q^{17} +(-3.00000 - 3.00000i) q^{18} +(-21.4627 - 21.4627i) q^{19} +(-8.05157 + 8.05157i) q^{20} +(-6.33889 + 6.33889i) q^{21} +18.6390 q^{22} +12.1058i q^{23} +(-3.46410 + 3.46410i) q^{24} +7.41388i q^{25} -5.19615 q^{27} +(7.31952 + 7.31952i) q^{28} -36.9444 q^{29} +13.9457i q^{30} +(-6.48248 - 6.48248i) q^{31} +(4.00000 + 4.00000i) q^{32} +(16.1419 - 16.1419i) q^{33} +(-18.8551 + 18.8551i) q^{34} +29.4668 q^{35} +6.00000i q^{36} +(37.1815 - 37.1815i) q^{37} +42.9255i q^{38} +16.1031 q^{40} +(4.67087 + 4.67087i) q^{41} +12.6778 q^{42} +13.6054i q^{43} +(-18.6390 - 18.6390i) q^{44} +(12.0774 + 12.0774i) q^{45} +(12.1058 - 12.1058i) q^{46} +(61.6060 - 61.6060i) q^{47} +6.92820 q^{48} +22.2123i q^{49} +(7.41388 - 7.41388i) q^{50} +32.6579i q^{51} +4.64409 q^{53} +(5.19615 + 5.19615i) q^{54} -75.0367 q^{55} -14.6390i q^{56} +(37.1746 + 37.1746i) q^{57} +(36.9444 + 36.9444i) q^{58} +(-17.6437 + 17.6437i) q^{59} +(13.9457 - 13.9457i) q^{60} +38.5426 q^{61} +12.9650i q^{62} +(10.9793 - 10.9793i) q^{63} -8.00000i q^{64} -32.2838 q^{66} +(-67.2276 - 67.2276i) q^{67} +37.7101 q^{68} -20.9679i q^{69} +(-29.4668 - 29.4668i) q^{70} +(28.7155 + 28.7155i) q^{71} +(6.00000 - 6.00000i) q^{72} +(60.4486 - 60.4486i) q^{73} -74.3630 q^{74} -12.8412i q^{75} +(42.9255 - 42.9255i) q^{76} +68.2144i q^{77} -94.2854 q^{79} +(-16.1031 - 16.1031i) q^{80} +9.00000 q^{81} -9.34174i q^{82} +(-63.4890 - 63.4890i) q^{83} +(-12.6778 - 12.6778i) q^{84} +(75.9064 - 75.9064i) q^{85} +(13.6054 - 13.6054i) q^{86} +63.9895 q^{87} +37.2781i q^{88} +(110.281 - 110.281i) q^{89} -24.1547i q^{90} -24.2117 q^{92} +(11.2280 + 11.2280i) q^{93} -123.212 q^{94} -172.809i q^{95} +(-6.92820 - 6.92820i) q^{96} +(-107.297 - 107.297i) q^{97} +(22.2123 - 22.2123i) q^{98} +(-27.9586 + 27.9586i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 6 q^{5} - 2 q^{7} + 16 q^{8} + 24 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 6 * q^5 - 2 * q^7 + 16 * q^8 + 24 * q^9	\( 8 q - 8 q^{2} - 6 q^{5} - 2 q^{7} + 16 q^{8} + 24 q^{9} - 12 q^{11} + 4 q^{14} + 6 q^{15} - 32 q^{16} - 24 q^{18} - 44 q^{19} + 12 q^{20} + 18 q^{21} + 24 q^{22} - 4 q^{28} - 72 q^{29} - 94 q^{31} + 32 q^{32} - 36 q^{33} + 60 q^{34} + 408 q^{35} - 46 q^{37} - 24 q^{40} - 30 q^{41} - 36 q^{42} - 24 q^{44} - 18 q^{45} + 144 q^{46} + 300 q^{47} + 208 q^{50} + 84 q^{53} - 792 q^{55} + 24 q^{57} + 72 q^{58} - 12 q^{59} - 12 q^{60} + 180 q^{61} - 6 q^{63} + 72 q^{66} - 74 q^{67} - 120 q^{68} - 408 q^{70} + 156 q^{71} + 48 q^{72} + 16 q^{73} + 92 q^{74} + 88 q^{76} - 96 q^{79} + 24 q^{80} + 72 q^{81} + 36 q^{84} + 234 q^{85} + 168 q^{86} - 60 q^{87} + 228 q^{89} - 288 q^{92} - 198 q^{93} - 600 q^{94} + 2 q^{97} - 32 q^{98} - 36 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 6 * q^5 - 2 * q^7 + 16 * q^8 + 24 * q^9 - 12 * q^11 + 4 * q^14 + 6 * q^15 - 32 * q^16 - 24 * q^18 - 44 * q^19 + 12 * q^20 + 18 * q^21 + 24 * q^22 - 4 * q^28 - 72 * q^29 - 94 * q^31 + 32 * q^32 - 36 * q^33 + 60 * q^34 + 408 * q^35 - 46 * q^37 - 24 * q^40 - 30 * q^41 - 36 * q^42 - 24 * q^44 - 18 * q^45 + 144 * q^46 + 300 * q^47 + 208 * q^50 + 84 * q^53 - 792 * q^55 + 24 * q^57 + 72 * q^58 - 12 * q^59 - 12 * q^60 + 180 * q^61 - 6 * q^63 + 72 * q^66 - 74 * q^67 - 120 * q^68 - 408 * q^70 + 156 * q^71 + 48 * q^72 + 16 * q^73 + 92 * q^74 + 88 * q^76 - 96 * q^79 + 24 * q^80 + 72 * q^81 + 36 * q^84 + 234 * q^85 + 168 * q^86 - 60 * q^87 + 228 * q^89 - 288 * q^92 - 198 * q^93 - 600 * q^94 + 2 * q^97 - 32 * q^98 - 36 * q^99

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