LMFDB - Embedded newform 1014.3.f.j.775.1

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			775.1
Root			$-5.39181 - 5.39181i$ of defining polynomial
Character	$\chi$	$=$	1014.775
Dual form			1014.3.f.j.577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} -1.73205 q^{3} +2.00000i q^{4} +(-4.02578 - 4.02578i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(-3.65976 + 3.65976i) q^{7} +(-2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(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	0.178740	−	0.983896i	$-0.442798\pi$
$5$	−4.02578	−	4.02578i	−0.805157	−	0.805157i	−0.983896	+	0.178740i	$0.942798\pi$
$6$	−1.73205	−	1.73205i	−0.288675	−	0.288675i
$7$	−3.65976	+	3.65976i	−0.522823	+	0.522823i	−0.918423	−	0.395600i	$-0.870537\pi$
$7$	−3.65976	+	3.65976i	−0.522823	+	0.522823i	0.395600	+	0.918423i	$0.370537\pi$
$8$	−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	−0.142558	−	0.989787i	$-0.545533\pi$
$11$	9.31952	−	9.31952i	0.847229	−	0.847229i	0.989787	+	0.142558i	$0.0455326\pi$
$12$		−	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	$0.0445107\pi$
$19$	21.4627	+	21.4627i	1.12962	+	1.12962i	0.139379	+	0.990239i	$0.455489\pi$
$20$	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	0.803890	−	0.594778i	$-0.202760\pi$
$31$	6.48248	+	6.48248i	0.209112	+	0.209112i	−0.594778	+	0.803890i	$0.702760\pi$
$32$	−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	$0.501565\pi$
$37$	−37.1815	+	37.1815i	−1.00490	+	1.00490i	−0.999988	+	0.00491701i	$0.998435\pi$
$38$			42.9255i			1.12962i
$39$		0			0
$40$	16.1031			0.402578
$41$	−4.67087	−	4.67087i	−0.113924	−	0.113924i	0.647847	−	0.761771i	$-0.275670\pi$
$41$	−4.67087	−	4.67087i	−0.113924	−	0.113924i	−0.761771	+	0.647847i	$0.775670\pi$
$42$	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	$0.627495\pi$
$47$	−61.6060	+	61.6060i	−1.31077	+	1.31077i	−0.920851	+	0.389914i	$0.872505\pi$
$48$	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	−0.541594	−	0.840640i	$-0.682179\pi$
$59$	17.6437	−	17.6437i	0.299046	−	0.299046i	0.840640	+	0.541594i	$0.182179\pi$
$60$	−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	$0.00108328\pi$
$67$	67.2276	+	67.2276i	1.00340	+	1.00340i	0.00340321	+	0.999994i	$0.498917\pi$
$68$	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	0.475352	−	0.879796i	$-0.342321\pi$
$71$	−28.7155	−	28.7155i	−0.404444	−	0.404444i	−0.879796	+	0.475352i	$0.842321\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	−60.4486	+	60.4486i	−0.828063	+	0.828063i	−0.987249	−	0.159186i	$-0.949113\pi$
$73$	−60.4486	+	60.4486i	−0.828063	+	0.828063i	0.159186	+	0.987249i	$0.449113\pi$
$74$	−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	0.977209	−	0.212281i	$-0.0680891\pi$
$83$	63.4890	+	63.4890i	0.764928	+	0.764928i	−0.212281	+	0.977209i	$0.568089\pi$
$84$	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	$0.589918\pi$
$89$	−110.281	+	110.281i	−1.23911	+	1.23911i	−0.960366	+	0.278743i	$0.910082\pi$
$90$		−	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	$0.0358882\pi$
$97$	107.297	+	107.297i	1.10616	+	1.10616i	0.112507	+	0.993651i	$0.464112\pi$
$98$	−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	0.886072	−	0.463548i	$-0.153424\pi$
$109$	46.0551	+	46.0551i	0.422524	+	0.422524i	−0.463548	+	0.886072i	$0.653424\pi$
$110$	−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	$-0.409121\pi$
$137$	170.039	−	170.039i	1.24116	−	1.24116i	0.959520	−	0.281642i	$-0.0908791\pi$
$138$	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	0.748678	−	0.662933i	$-0.230689\pi$
$149$	12.7760	+	12.7760i	0.0857449	+	0.0857449i	−0.662933	+	0.748678i	$0.730689\pi$
$150$	12.8412	−	12.8412i	0.0856082	−	0.0856082i
$151$	95.4196	−	95.4196i	0.631918	−	0.631918i	−0.316631	−	0.948549i	$-0.602552\pi$
$151$	95.4196	−	95.4196i	0.631918	−	0.631918i	0.948549	+	0.316631i	$0.102552\pi$
$152$	−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	−0.922595	−	0.385769i	$-0.873936\pi$
$163$	−87.5027	+	87.5027i	−0.536826	+	0.536826i	0.385769	+	0.922595i	$0.373936\pi$
$164$	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	−0.919380	−	0.393371i	$-0.871309\pi$
$167$	−87.8436	+	87.8436i	−0.526010	+	0.526010i	0.393371	+	0.919380i	$0.371309\pi$
$168$			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	−0.910339	−	0.413863i	$-0.864179\pi$
$193$	−95.8199	+	95.8199i	−0.496476	+	0.496476i	0.413863	+	0.910339i	$0.364179\pi$
$194$			214.595i			1.10616i
$195$		0			0
$196$	−44.4246			−0.226656
$197$	−2.48643	−	2.48643i	−0.0126215	−	0.0126215i	0.700768	−	0.713389i	$-0.252841\pi$
$197$	−2.48643	−	2.48643i	−0.0126215	−	0.0126215i	−0.713389	+	0.700768i	$0.752841\pi$
$198$	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	0.850407	−	0.526126i	$-0.176356\pi$
$223$	72.3147	+	72.3147i	0.324281	+	0.324281i	−0.526126	+	0.850407i	$0.676356\pi$
$224$	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	0.969037	−	0.246917i	$-0.0794176\pi$
$227$	163.921	+	163.921i	0.722119	+	0.722119i	−0.246917	+	0.969037i	$0.579418\pi$
$228$	74.3491	−	74.3491i	0.326093	−	0.326093i
$229$	−306.032	+	306.032i	−1.33639	+	1.33639i	−0.436854	+	0.899533i	$0.643907\pi$
$229$	−306.032	+	306.032i	−1.33639	+	1.33639i	−0.899533	+	0.436854i	$0.856093\pi$
$230$	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	0.684641	−	0.728880i	$-0.259959\pi$
$239$	−10.5731	−	10.5731i	−0.0442390	−	0.0442390i	−0.728880	+	0.684641i	$0.759959\pi$
$240$	−27.8915	−	27.8915i	−0.116214	−	0.116214i
$241$	−166.546	+	166.546i	−0.691062	+	0.691062i	−0.962466	−	0.271403i	$-0.912512\pi$
$241$	−166.546	+	166.546i	−0.691062	+	0.691062i	0.271403	+	0.962466i	$0.412512\pi$
$242$	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	−0.485573	−	0.874196i	$-0.661389\pi$
$271$	105.317	−	105.317i	0.388623	−	0.388623i	0.874196	+	0.485573i	$0.161389\pi$
$272$			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	−0.781154	−	0.624338i	$-0.785369\pi$
$281$	−44.0655	+	44.0655i	−0.156817	+	0.156817i	0.624338	+	0.781154i	$0.285369\pi$
$282$	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	−0.882772	−	0.469802i	$-0.844325\pi$
$293$	−121.000	+	121.000i	−0.412970	+	0.412970i	0.469802	+	0.882772i	$0.344325\pi$
$294$	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	−0.163265	−	0.986582i	$-0.552203\pi$
$307$	252.758	−	252.758i	0.823317	−	0.823317i	0.986582	+	0.163265i	$0.0522026\pi$
$308$	−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	0.864555	−	0.502538i	$-0.167600\pi$
$317$	114.759	+	114.759i	0.362016	+	0.362016i	−0.502538	+	0.864555i	$0.667600\pi$
$318$	−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	0.979813	−	0.199916i	$-0.0640668\pi$
$331$	258.146	+	258.146i	0.779898	+	0.779898i	−0.199916	+	0.979813i	$0.564067\pi$
$332$	−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	−0.316917	−	0.948453i	$-0.602648\pi$
$349$	220.406	−	220.406i	0.631536	−	0.631536i	0.948453	+	0.316917i	$0.102648\pi$
$350$		−	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	$-0.953812\pi$
$353$	−400.332	−	400.332i	−1.13409	−	1.13409i	−0.144594	−	0.989491i	$-0.546188\pi$
$354$	−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	−0.663534	−	0.748146i	$-0.730944\pi$
$359$	30.3760	−	30.3760i	0.0846129	−	0.0846129i	0.748146	+	0.663534i	$0.230944\pi$
$360$	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	0.697196	−	0.716881i	$-0.254431\pi$
$379$	−7.46065	−	7.46065i	−0.0196851	−	0.0196851i	−0.716881	+	0.697196i	$0.754431\pi$
$380$	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	0.996199	−	0.0871059i	$-0.0277619\pi$
$383$	348.183	+	348.183i	0.909093	+	0.909093i	−0.0871059	+	0.996199i	$0.527762\pi$
$384$	−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	−0.502827	−	0.864387i	$-0.667707\pi$
$397$	143.539	−	143.539i	0.361560	−	0.361560i	0.864387	+	0.502827i	$0.167707\pi$
$398$	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	−0.422184	−	0.906510i	$-0.638736\pi$
$401$	194.215	−	194.215i	0.484326	−	0.484326i	0.906510	+	0.422184i	$0.138736\pi$
$402$		−	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	0.870336	−	0.492459i	$-0.163902\pi$
$409$	154.552	+	154.552i	0.377877	+	0.377877i	−0.492459	+	0.870336i	$0.663902\pi$
$410$	−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	0.299052	−	0.954237i	$-0.403330\pi$
$421$	−275.833	−	275.833i	−0.655185	−	0.655185i	−0.954237	+	0.299052i	$0.903330\pi$
$422$	−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	0.0857274	−	0.996319i	$-0.472679\pi$
$431$	−392.465	−	392.465i	−0.910591	−	0.910591i	−0.996319	+	0.0857274i	$0.972679\pi$
$432$	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	$-0.383303\pi$
$449$	580.110	−	580.110i	1.29200	−	1.29200i	0.933546	−	0.358458i	$-0.116697\pi$
$450$	−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	0.843293	−	0.537455i	$-0.180614\pi$
$457$	139.768	+	139.768i	0.305838	+	0.305838i	−0.537455	+	0.843293i	$0.680614\pi$
$458$	−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	0.780462	−	0.625203i	$-0.214984\pi$
$461$	71.5746	+	71.5746i	0.155259	+	0.155259i	−0.625203	+	0.780462i	$0.714984\pi$
$462$	118.151	−	118.151i	0.255738	−	0.255738i
$463$	−177.994	+	177.994i	−0.384435	+	0.384435i	−0.872697	−	0.488262i	$-0.837631\pi$
$463$	−177.994	+	177.994i	−0.384435	+	0.384435i	0.488262	+	0.872697i	$0.337631\pi$
$464$	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	−0.759511	−	0.650494i	$-0.774562\pi$
$479$	−52.2191	+	52.2191i	−0.109017	+	0.109017i	0.650494	+	0.759511i	$0.274562\pi$
$480$		−	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	0.0457942	−	0.998951i	$-0.485418\pi$
$487$	−464.187	−	464.187i	−0.953157	−	0.953157i	−0.998951	+	0.0457942i	$0.985418\pi$
$488$	−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	0.822588	−	0.568638i	$-0.192529\pi$
$499$	126.721	+	126.721i	0.253950	+	0.253950i	−0.568638	+	0.822588i	$0.692529\pi$
$500$	−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	0.571073	−	0.820899i	$-0.306527\pi$
$509$	−127.161	−	127.161i	−0.249826	−	0.249826i	−0.820899	+	0.571073i	$0.806527\pi$
$510$	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	−0.875544	−	0.483139i	$-0.839497\pi$
$541$	−212.291	+	212.291i	−0.392405	+	0.392405i	0.483139	+	0.875544i	$0.339497\pi$
$542$	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	−0.995987	−	0.0894957i	$-0.971474\pi$
$557$	−504.916	+	504.916i	−0.906492	+	0.906492i	0.0894957	+	0.995987i	$0.471474\pi$
$558$			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	0.867277	−	0.497826i	$-0.165868\pi$
$577$	213.174	+	213.174i	0.369452	+	0.369452i	−0.497826	+	0.867277i	$0.665868\pi$
$578$	−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	0.337556	−	0.941305i	$-0.390400\pi$
$587$	−354.401	−	354.401i	−0.603750	−	0.603750i	−0.941305	+	0.337556i	$0.890400\pi$
$588$	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	−0.208319	−	0.978061i	$-0.566799\pi$
$593$	456.457	−	456.457i	0.769743	−	0.769743i	0.978061	+	0.208319i	$0.0667991\pi$
$594$	−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	$0.0519685\pi$
$613$	704.485	+	704.485i	1.14924	+	1.14924i	0.162540	+	0.986702i	$0.448031\pi$
$614$	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	0.505007	−	0.863115i	$-0.331490\pi$
$617$	−220.953	−	220.953i	−0.358108	−	0.358108i	−0.863115	+	0.505007i	$0.831490\pi$
$618$	160.752	−	160.752i	0.260116	−	0.260116i
$619$	459.215	−	459.215i	0.741865	−	0.741865i	−0.231071	−	0.972937i	$-0.574223\pi$
$619$	459.215	−	459.215i	0.741865	−	0.741865i	0.972937	+	0.231071i	$0.0742231\pi$
$620$	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	−0.540758	−	0.841178i	$-0.681863\pi$
$631$	189.565	−	189.565i	0.300420	−	0.300420i	0.841178	+	0.540758i	$0.181863\pi$
$632$	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	$-0.984979\pi$
$643$	−672.617	−	672.617i	−1.04606	−	1.04606i	−0.0471735	−	0.998887i	$-0.515021\pi$
$644$	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	−0.991065	−	0.133379i	$-0.957417\pi$
$661$	−566.931	+	566.931i	−0.857686	+	0.857686i	0.133379	+	0.991065i	$0.457417\pi$
$662$			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	−0.978286	−	0.207261i	$-0.933545\pi$
$683$	−526.610	+	526.610i	−0.771024	+	0.771024i	0.207261	+	0.978286i	$0.433545\pi$
$684$	−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	0.352418	−	0.935843i	$-0.385360\pi$
$691$	−403.147	−	403.147i	−0.583425	−	0.583425i	−0.935843	+	0.352418i	$0.885360\pi$
$692$	−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	−0.695115	−	0.718899i	$-0.744647\pi$
$709$	16.8626	−	16.8626i	0.0237837	−	0.0237837i	0.718899	+	0.695115i	$0.244647\pi$
$710$	−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	0.815337	−	0.578986i	$-0.196552\pi$
$733$	173.245	+	173.245i	0.236351	+	0.236351i	−0.578986	+	0.815337i	$0.696552\pi$
$734$	−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	−0.658048	−	0.752976i	$-0.728617\pi$
$739$	70.1524	−	70.1524i	0.0949289	−	0.0949289i	0.752976	+	0.658048i	$0.228617\pi$
$740$			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	$0.0673437\pi$
$743$	882.457	+	882.457i	1.18769	+	1.18769i	0.209992	+	0.977703i	$0.432656\pi$
$744$	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	−0.889414	−	0.457103i	$-0.848887\pi$
$761$	−328.989	+	328.989i	−0.432311	+	0.432311i	0.457103	+	0.889414i	$0.348887\pi$
$762$	−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	0.208485	−	0.978026i	$-0.433147\pi$
$769$	−591.777	−	591.777i	−0.769541	−	0.769541i	−0.978026	+	0.208485i	$0.933147\pi$
$770$	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	0.359981	−	0.932960i	$-0.382783\pi$
$773$	−442.913	−	442.913i	−0.572979	−	0.572979i	−0.932960	+	0.359981i	$0.882783\pi$
$774$	−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	−0.762792	−	0.646643i	$-0.776172\pi$
$787$	−91.4093	+	91.4093i	−0.116149	+	0.116149i	0.646643	+	0.762792i	$0.276172\pi$
$788$	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	0.417632	−	0.908616i	$-0.362860\pi$
$811$	−398.188	−	398.188i	−0.490984	−	0.490984i	−0.908616	+	0.417632i	$0.862860\pi$
$812$	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	0.335650	−	0.941987i	$-0.391044\pi$
$821$	−497.803	−	497.803i	−0.606337	−	0.606337i	−0.941987	+	0.335650i	$0.891044\pi$
$822$	−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	−0.726031	−	0.687662i	$-0.758637\pi$
$827$	−31.7310	+	31.7310i	−0.0383689	+	0.0383689i	0.687662	+	0.726031i	$0.258637\pi$
$828$	−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	−0.790996	−	0.611822i	$-0.790437\pi$
$839$	−150.327	+	150.327i	−0.179174	+	0.179174i	0.611822	+	0.790996i	$0.290437\pi$
$840$	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	−0.993932	−	0.110000i	$-0.964915\pi$
$853$	−753.994	+	753.994i	−0.883932	+	0.883932i	0.110000	+	0.993932i	$0.464915\pi$
$854$	−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	0.631264	−	0.775568i	$-0.282536\pi$
$863$	−124.534	−	124.534i	−0.144304	−	0.144304i	−0.775568	+	0.631264i	$0.782536\pi$
$864$	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	0.719870	−	0.694109i	$-0.244202\pi$
$877$	22.5917	+	22.5917i	0.0257602	+	0.0257602i	−0.694109	+	0.719870i	$0.744202\pi$
$878$	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	0.898159	−	0.439671i	$-0.144905\pi$
$929$	425.936	+	425.936i	0.458488	+	0.458488i	−0.439671	+	0.898159i	$0.644905\pi$
$930$	−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	0.897359	−	0.441302i	$-0.145483\pi$
$941$	429.149	+	429.149i	0.456057	+	0.456057i	−0.441302	+	0.897359i	$0.645483\pi$
$942$	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	−0.216544	−	0.976273i	$-0.569478\pi$
$947$	719.464	−	719.464i	0.759729	−	0.759729i	0.976273	+	0.216544i	$0.0694784\pi$
$948$			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	0.844913	−	0.534903i	$-0.179652\pi$
$967$	299.780	+	299.780i	0.310010	+	0.310010i	−0.534903	+	0.844913i	$0.679652\pi$
$968$	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	0.254486	−	0.967076i	$-0.418094\pi$
$977$	−696.201	−	696.201i	−0.712591	−	0.712591i	−0.967076	+	0.254486i	$0.918094\pi$
$978$	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	−0.387138	−	0.922022i	$-0.626536\pi$
$983$	525.791	−	525.791i	0.534884	−	0.534884i	0.922022	+	0.387138i	$0.126536\pi$
$984$	−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.j.775.1		8
13.5	odd	4	inner	1014.3.f.j.577.1		8
13.7	odd	12		78.3.l.c.67.2	yes	8
13.8	odd	4		1014.3.f.h.577.2		8
13.10	even	6		78.3.l.c.7.2	✓	8
13.12	even	2		1014.3.f.h.775.2		8
39.20	even	12		234.3.bb.d.145.1		8
39.23	odd	6		234.3.bb.d.163.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.l.c.7.2	✓	8	13.10	even	6
78.3.l.c.67.2	yes	8	13.7	odd	12
234.3.bb.d.145.1		8	39.20	even	12
234.3.bb.d.163.1		8	39.23	odd	6
1014.3.f.h.577.2		8	13.8	odd	4
1014.3.f.h.775.2		8	13.12	even	2
1014.3.f.j.577.1		8	13.5	odd	4	inner
1014.3.f.j.775.1		8	1.1	even	1	trivial

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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