LMFDB - Embedded newform 105.2.b.d.41.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [105,2,Mod(41,105)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(105, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("105.41"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,1,-6,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.838429221223$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			41.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	105.41
Dual form			105.2.b.d.41.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.52434i q^{2} +(1.68614 - 0.396143i) q^{3} -4.37228 q^{4} +1.00000 q^{5} +(-1.00000 - 4.25639i) q^{6} +(-2.00000 + 1.73205i) q^{7} +5.98844i q^{8} +(2.68614 - 1.33591i) q^{9} -2.52434i q^{10} -0.792287i q^{11} +(-7.37228 + 1.73205i) q^{12} +5.84096i q^{13} +(4.37228 + 5.04868i) q^{14} +(1.68614 - 0.396143i) q^{15} +6.37228 q^{16} -1.37228 q^{17} +(-3.37228 - 6.78073i) q^{18} -3.46410i q^{19} -4.37228 q^{20} +(-2.68614 + 3.71277i) q^{21} -2.00000 q^{22} -1.87953i q^{23} +(2.37228 + 10.0974i) q^{24} +1.00000 q^{25} +14.7446 q^{26} +(4.00000 - 3.31662i) q^{27} +(8.74456 - 7.57301i) q^{28} -4.25639i q^{29} +(-1.00000 - 4.25639i) q^{30} +3.46410i q^{31} -4.10891i q^{32} +(-0.313859 - 1.33591i) q^{33} +3.46410i q^{34} +(-2.00000 + 1.73205i) q^{35} +(-11.7446 + 5.84096i) q^{36} +4.74456 q^{37} -8.74456 q^{38} +(2.31386 + 9.84868i) q^{39} +5.98844i q^{40} -6.00000 q^{41} +(9.37228 + 6.78073i) q^{42} -6.74456 q^{43} +3.46410i q^{44} +(2.68614 - 1.33591i) q^{45} -4.74456 q^{46} -7.37228 q^{47} +(10.7446 - 2.52434i) q^{48} +(1.00000 - 6.92820i) q^{49} -2.52434i q^{50} +(-2.31386 + 0.543620i) q^{51} -25.5383i q^{52} +8.51278i q^{53} +(-8.37228 - 10.0974i) q^{54} -0.792287i q^{55} +(-10.3723 - 11.9769i) q^{56} +(-1.37228 - 5.84096i) q^{57} -10.7446 q^{58} +2.74456 q^{59} +(-7.37228 + 1.73205i) q^{60} +6.92820i q^{61} +8.74456 q^{62} +(-3.05842 + 7.32435i) q^{63} +2.37228 q^{64} +5.84096i q^{65} +(-3.37228 + 0.792287i) q^{66} -6.74456 q^{67} +6.00000 q^{68} +(-0.744563 - 3.16915i) q^{69} +(4.37228 + 5.04868i) q^{70} -13.5615i q^{71} +(8.00000 + 16.0858i) q^{72} +6.92820i q^{73} -11.9769i q^{74} +(1.68614 - 0.396143i) q^{75} +15.1460i q^{76} +(1.37228 + 1.58457i) q^{77} +(24.8614 - 5.84096i) q^{78} +3.37228 q^{79} +6.37228 q^{80} +(5.43070 - 7.17687i) q^{81} +15.1460i q^{82} +5.48913 q^{83} +(11.7446 - 16.2333i) q^{84} -1.37228 q^{85} +17.0256i q^{86} +(-1.68614 - 7.17687i) q^{87} +4.74456 q^{88} +3.25544 q^{89} +(-3.37228 - 6.78073i) q^{90} +(-10.1168 - 11.6819i) q^{91} +8.21782i q^{92} +(1.37228 + 5.84096i) q^{93} +18.6101i q^{94} -3.46410i q^{95} +(-1.62772 - 6.92820i) q^{96} -1.08724i q^{97} +(-17.4891 - 2.52434i) q^{98} +(-1.05842 - 2.12819i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} - 6 q^{4} + 4 q^{5} - 4 q^{6} - 8 q^{7} + 5 q^{9} - 18 q^{12} + 6 q^{14} + q^{15} + 14 q^{16} + 6 q^{17} - 2 q^{18} - 6 q^{20} - 5 q^{21} - 8 q^{22} - 2 q^{24} + 4 q^{25} + 36 q^{26} + 16 q^{27}+ \cdots + 13 q^{99}+O(q^{100}) $ 4 * q + q^3 - 6 * q^4 + 4 * q^5 - 4 * q^6 - 8 * q^7 + 5 * q^9 - 18 * q^12 + 6 * q^14 + q^15 + 14 * q^16 + 6 * q^17 - 2 * q^18 - 6 * q^20 - 5 * q^21 - 8 * q^22 - 2 * q^24 + 4 * q^25 + 36 * q^26 + 16 * q^27 + 12 * q^28 - 4 * q^30 - 7 * q^33 - 8 * q^35 - 24 * q^36 - 4 * q^37 - 12 * q^38 + 15 * q^39 - 24 * q^41 + 26 * q^42 - 4 * q^43 + 5 * q^45 + 4 * q^46 - 18 * q^47 + 20 * q^48 + 4 * q^49 - 15 * q^51 - 22 * q^54 - 30 * q^56 + 6 * q^57 - 20 * q^58 - 12 * q^59 - 18 * q^60 + 12 * q^62 + 5 * q^63 - 2 * q^64 - 2 * q^66 - 4 * q^67 + 24 * q^68 + 20 * q^69 + 6 * q^70 + 32 * q^72 + q^75 - 6 * q^77 + 42 * q^78 + 2 * q^79 + 14 * q^80 - 7 * q^81 - 24 * q^83 + 24 * q^84 + 6 * q^85 - q^87 - 4 * q^88 + 36 * q^89 - 2 * q^90 - 6 * q^91 - 6 * q^93 - 18 * q^96 - 24 * q^98 + 13 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	2.52434i		−	1.78498i	−0.451071	−	0.892488i	$-0.648958\pi$
$2$		−	2.52434i		−	1.78498i	0.451071	−	0.892488i	$-0.351042\pi$
$3$	1.68614	−	0.396143i	0.973494	−	0.228714i
$3$	1.68614	−	0.396143i	0.973494	−	0.228714i
$4$	−4.37228			−2.18614
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.00000	−	4.25639i	−0.408248	−	1.73766i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$			5.98844i			2.11723i
$9$	2.68614	−	1.33591i	0.895380	−	0.445302i
$10$		−	2.52434i		−	0.798266i
$11$		−	0.792287i		−	0.238884i	−0.992841	−	0.119442i	$-0.961890\pi$
$11$		−	0.792287i		−	0.238884i	0.992841	−	0.119442i	$-0.0381105\pi$
$12$	−7.37228	+	1.73205i	−2.12819	+	0.500000i
$13$			5.84096i			1.61999i	0.586436	+	0.809996i	$0.300531\pi$
$13$			5.84096i			1.61999i	−0.586436	+	0.809996i	$0.699469\pi$
$14$	4.37228	+	5.04868i	1.16854	+	1.34932i
$15$	1.68614	−	0.396143i	0.435360	−	0.102284i
$16$	6.37228			1.59307
$17$	−1.37228			−0.332827			−0.166414	−	0.986056i	$-0.553219\pi$
$17$	−1.37228			−0.332827			−0.166414	+	0.986056i	$0.553219\pi$
$18$	−3.37228	−	6.78073i	−0.794854	−	1.59823i
$19$		−	3.46410i		−	0.794719i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$		−	3.46410i		−	0.794719i	0.917663	−	0.397360i	$-0.130073\pi$
$20$	−4.37228			−0.977672
$21$	−2.68614	+	3.71277i	−0.586164	+	0.810192i
$22$	−2.00000			−0.426401
$23$		−	1.87953i		−	0.391909i	−0.980613	−	0.195954i	$-0.937220\pi$
$23$		−	1.87953i		−	0.391909i	0.980613	−	0.195954i	$-0.0627804\pi$
$24$	2.37228	+	10.0974i	0.484240	+	2.06111i
$25$	1.00000			0.200000
$26$	14.7446			2.89165
$27$	4.00000	−	3.31662i	0.769800	−	0.638285i
$28$	8.74456	−	7.57301i	1.65257	−	1.43117i
$29$		−	4.25639i		−	0.790392i	−0.918597	−	0.395196i	$-0.870677\pi$
$29$		−	4.25639i		−	0.790392i	0.918597	−	0.395196i	$-0.129323\pi$
$30$	−1.00000	−	4.25639i	−0.182574	−	0.777107i
$31$			3.46410i			0.622171i	0.950382	+	0.311086i	$0.100693\pi$
$31$			3.46410i			0.622171i	−0.950382	+	0.311086i	$0.899307\pi$
$32$		−	4.10891i		−	0.726360i
$33$	−0.313859	−	1.33591i	−0.0546359	−	0.232552i
$34$			3.46410i			0.594089i
$35$	−2.00000	+	1.73205i	−0.338062	+	0.292770i
$36$	−11.7446	+	5.84096i	−1.95743	+	0.973494i
$37$	4.74456			0.780001			0.390001	−	0.920815i	$-0.372475\pi$
$37$	4.74456			0.780001			0.390001	+	0.920815i	$0.372475\pi$
$38$	−8.74456			−1.41856
$39$	2.31386	+	9.84868i	0.370514	+	1.57705i
$40$			5.98844i			0.946855i
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$	9.37228	+	6.78073i	1.44617	+	1.04629i
$43$	−6.74456			−1.02854			−0.514268	−	0.857629i	$-0.671936\pi$
$43$	−6.74456			−1.02854			−0.514268	+	0.857629i	$0.671936\pi$
$44$			3.46410i			0.522233i
$45$	2.68614	−	1.33591i	0.400426	−	0.199145i
$46$	−4.74456			−0.699548
$47$	−7.37228			−1.07536			−0.537679	−	0.843150i	$-0.680699\pi$
$47$	−7.37228			−1.07536			−0.537679	+	0.843150i	$0.680699\pi$
$48$	10.7446	−	2.52434i	1.55084	−	0.364357i
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		−	2.52434i		−	0.356995i
$51$	−2.31386	+	0.543620i	−0.324005	+	0.0761221i
$52$		−	25.5383i		−	3.54153i
$53$			8.51278i			1.16932i	0.811278	+	0.584660i	$0.198772\pi$
$53$			8.51278i			1.16932i	−0.811278	+	0.584660i	$0.801228\pi$
$54$	−8.37228	−	10.0974i	−1.13932	−	1.37408i
$55$		−	0.792287i		−	0.106832i
$56$	−10.3723	−	11.9769i	−1.38605	−	1.60048i
$57$	−1.37228	−	5.84096i	−0.181763	−	0.773654i
$58$	−10.7446			−1.41083
$59$	2.74456			0.357312			0.178656	−	0.983912i	$-0.442825\pi$
$59$	2.74456			0.357312			0.178656	+	0.983912i	$0.442825\pi$
$60$	−7.37228	+	1.73205i	−0.951757	+	0.223607i
$61$			6.92820i			0.887066i	0.896258	+	0.443533i	$0.146275\pi$
$61$			6.92820i			0.887066i	−0.896258	+	0.443533i	$0.853725\pi$
$62$	8.74456			1.11056
$63$	−3.05842	+	7.32435i	−0.385325	+	0.922781i
$64$	2.37228			0.296535
$65$			5.84096i			0.724482i
$66$	−3.37228	+	0.792287i	−0.415099	+	0.0975238i
$67$	−6.74456			−0.823979			−0.411990	−	0.911188i	$-0.635166\pi$
$67$	−6.74456			−0.823979			−0.411990	+	0.911188i	$0.635166\pi$
$68$	6.00000			0.727607
$69$	−0.744563	−	3.16915i	−0.0896348	−	0.381521i
$70$	4.37228	+	5.04868i	0.522588	+	0.603432i
$71$		−	13.5615i		−	1.60945i	−0.593649	−	0.804724i	$-0.702313\pi$
$71$		−	13.5615i		−	1.60945i	0.593649	−	0.804724i	$-0.297687\pi$
$72$	8.00000	+	16.0858i	0.942809	+	1.89573i
$73$			6.92820i			0.810885i	0.914121	+	0.405442i	$0.132883\pi$
$73$			6.92820i			0.810885i	−0.914121	+	0.405442i	$0.867117\pi$
$74$		−	11.9769i		−	1.39228i
$75$	1.68614	−	0.396143i	0.194699	−	0.0457427i
$76$			15.1460i			1.73737i
$77$	1.37228	+	1.58457i	0.156386	+	0.180579i
$78$	24.8614	−	5.84096i	2.81500	−	0.661359i
$79$	3.37228			0.379411			0.189706	−	0.981841i	$-0.439247\pi$
$79$	3.37228			0.379411			0.189706	+	0.981841i	$0.439247\pi$
$80$	6.37228			0.712443
$81$	5.43070	−	7.17687i	0.603411	−	0.797430i
$82$			15.1460i			1.67260i
$83$	5.48913			0.602510			0.301255	−	0.953544i	$-0.402594\pi$
$83$	5.48913			0.602510			0.301255	+	0.953544i	$0.402594\pi$
$84$	11.7446	−	16.2333i	1.28144	−	1.77119i
$85$	−1.37228			−0.148845
$86$			17.0256i			1.83591i
$87$	−1.68614	−	7.17687i	−0.180773	−	0.769441i
$88$	4.74456			0.505772
$89$	3.25544			0.345076			0.172538	−	0.985003i	$-0.444803\pi$
$89$	3.25544			0.345076			0.172538	+	0.985003i	$0.444803\pi$
$90$	−3.37228	−	6.78073i	−0.355470	−	0.714751i
$91$	−10.1168	−	11.6819i	−1.06053	−	1.22460i
$92$			8.21782i			0.856767i
$93$	1.37228	+	5.84096i	0.142299	+	0.605680i
$94$			18.6101i			1.91949i
$95$		−	3.46410i		−	0.355409i
$96$	−1.62772	−	6.92820i	−0.166128	−	0.707107i
$97$		−	1.08724i		−	0.110393i	−0.998476	−	0.0551963i	$-0.982422\pi$
$97$		−	1.08724i		−	0.110393i	0.998476	−	0.0551963i	$-0.0175785\pi$
$98$	−17.4891	−	2.52434i	−1.76667	−	0.254997i
$99$	−1.05842	−	2.12819i	−0.106375	−	0.213892i
$100$	−4.37228			−0.437228
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$	1.37228	+	5.84096i	0.135876	+	0.578341i
$103$		−	16.2333i		−	1.59951i	−0.600326	−	0.799756i	$-0.704962\pi$
$103$		−	16.2333i		−	1.59951i	0.600326	−	0.799756i	$-0.295038\pi$
$104$	−34.9783			−3.42990
$105$	−2.68614	+	3.71277i	−0.262140	+	0.362329i
$106$	21.4891			2.08721
$107$		−	6.63325i		−	0.641260i	−0.947204	−	0.320630i	$-0.896105\pi$
$107$		−	6.63325i		−	0.641260i	0.947204	−	0.320630i	$-0.103895\pi$
$108$	−17.4891	+	14.5012i	−1.68289	+	1.39538i
$109$	0.116844			0.0111916			0.00559581	−	0.999984i	$-0.498219\pi$
$109$	0.116844			0.0111916			0.00559581	+	0.999984i	$0.498219\pi$
$110$	−2.00000			−0.190693
$111$	8.00000	−	1.87953i	0.759326	−	0.178397i
$112$	−12.7446	+	11.0371i	−1.20425	+	1.04291i
$113$		−	10.0974i		−	0.949879i	−0.880018	−	0.474939i	$-0.842470\pi$
$113$		−	10.0974i		−	0.949879i	0.880018	−	0.474939i	$-0.157530\pi$
$114$	−14.7446	+	3.46410i	−1.38095	+	0.324443i
$115$		−	1.87953i		−	0.175267i
$116$			18.6101i			1.72791i
$117$	7.80298	+	15.6896i	0.721386	+	1.45051i
$118$		−	6.92820i		−	0.637793i
$119$	2.74456	−	2.37686i	0.251594	−	0.217886i
$120$	2.37228	+	10.0974i	0.216559	+	0.921758i
$121$	10.3723			0.942935
$122$	17.4891			1.58339
$123$	−10.1168	+	2.37686i	−0.912205	+	0.214314i
$124$		−	15.1460i		−	1.36015i
$125$	1.00000			0.0894427
$126$	18.4891	+	7.72049i	1.64714	+	0.687796i
$127$	10.7446			0.953426			0.476713	−	0.879059i	$-0.341828\pi$
$127$	10.7446			0.953426			0.476713	+	0.879059i	$0.341828\pi$
$128$		−	14.2063i		−	1.25567i
$129$	−11.3723	+	2.67181i	−1.00127	+	0.235240i
$130$	14.7446			1.29318
$131$	−17.4891			−1.52803			−0.764016	−	0.645197i	$-0.776775\pi$
$131$	−17.4891			−1.52803			−0.764016	+	0.645197i	$0.776775\pi$
$132$	1.37228	+	5.84096i	0.119442	+	0.508391i
$133$	6.00000	+	6.92820i	0.520266	+	0.600751i
$134$			17.0256i			1.47078i
$135$	4.00000	−	3.31662i	0.344265	−	0.285450i
$136$		−	8.21782i		−	0.704673i
$137$			13.2665i			1.13343i	0.823913	+	0.566717i	$0.191787\pi$
$137$			13.2665i			1.13343i	−0.823913	+	0.566717i	$0.808213\pi$
$138$	−8.00000	+	1.87953i	−0.681005	+	0.159996i
$139$		−	1.28962i		−	0.109384i	−0.998503	−	0.0546921i	$-0.982582\pi$
$139$		−	1.28962i		−	0.109384i	0.998503	−	0.0546921i	$-0.0174177\pi$
$140$	8.74456	−	7.57301i	0.739050	−	0.640036i
$141$	−12.4307	+	2.92048i	−1.04685	+	0.245949i
$142$	−34.2337			−2.87283
$143$	4.62772			0.386989
$144$	17.1168	−	8.51278i	1.42640	−	0.709398i
$145$		−	4.25639i		−	0.353474i
$146$	17.4891			1.44741
$147$	−1.05842	−	12.0781i	−0.0872972	−	0.996182i
$148$	−20.7446			−1.70519
$149$		−	10.0974i		−	0.827207i	−0.910457	−	0.413604i	$-0.864270\pi$
$149$		−	10.0974i		−	0.827207i	0.910457	−	0.413604i	$-0.135730\pi$
$150$	−1.00000	−	4.25639i	−0.0816497	−	0.347533i
$151$	3.37228			0.274432			0.137216	−	0.990541i	$-0.456184\pi$
$151$	3.37228			0.274432			0.137216	+	0.990541i	$0.456184\pi$
$152$	20.7446			1.68261
$153$	−3.68614	+	1.83324i	−0.298007	+	0.148209i
$154$	4.00000	−	3.46410i	0.322329	−	0.279145i
$155$			3.46410i			0.278243i
$156$	−10.1168	−	43.0612i	−0.809996	−	3.44766i
$157$		0			0		1.00000			$0$
$157$		0			0		−1.00000			$\pi$
$158$		−	8.51278i		−	0.677240i
$159$	3.37228	+	14.3537i	0.267439	+	1.13833i
$160$		−	4.10891i		−	0.324838i
$161$	3.25544	+	3.75906i	0.256564	+	0.296255i
$162$	−18.1168	−	13.7089i	−1.42339	−	1.07708i
$163$	8.00000			0.626608			0.313304	−	0.949653i	$-0.398564\pi$
$163$	8.00000			0.626608			0.313304	+	0.949653i	$0.398564\pi$
$164$	26.2337			2.04851
$165$	−0.313859	−	1.33591i	−0.0244339	−	0.104000i
$166$		−	13.8564i		−	1.07547i
$167$	−22.1168			−1.71145			−0.855726	−	0.517429i	$-0.826889\pi$
$167$	−22.1168			−1.71145			−0.855726	+	0.517429i	$0.826889\pi$
$168$	−22.2337	−	16.0858i	−1.71537	−	1.24105i
$169$	−21.1168			−1.62437
$170$			3.46410i			0.265684i
$171$	−4.62772	−	9.30506i	−0.353890	−	0.711576i
$172$	29.4891			2.24852
$173$	16.1168			1.22534			0.612670	−	0.790338i	$-0.290095\pi$
$173$	16.1168			1.22534			0.612670	+	0.790338i	$0.290095\pi$
$174$	−18.1168	+	4.25639i	−1.37343	+	0.322676i
$175$	−2.00000	+	1.73205i	−0.151186	+	0.130931i
$176$		−	5.04868i		−	0.380558i
$177$	4.62772	−	1.08724i	0.347841	−	0.0817220i
$178$		−	8.21782i		−	0.615952i
$179$		−	6.63325i		−	0.495792i	−0.968787	−	0.247896i	$-0.920261\pi$
$179$		−	6.63325i		−	0.495792i	0.968787	−	0.247896i	$-0.0797392\pi$
$180$	−11.7446	+	5.84096i	−0.875388	+	0.435360i
$181$		−	18.6101i		−	1.38328i	−0.722242	−	0.691640i	$-0.756889\pi$
$181$		−	18.6101i		−	1.38328i	0.722242	−	0.691640i	$-0.243111\pi$
$182$	−29.4891	+	25.5383i	−2.18588	+	1.89303i
$183$	2.74456	+	11.6819i	0.202884	+	0.863553i
$184$	11.2554			0.829762
$185$	4.74456			0.348827
$186$	14.7446	−	3.46410i	1.08112	−	0.254000i
$187$			1.08724i			0.0795069i
$188$	32.2337			2.35088
$189$	−2.25544	+	13.5615i	−0.164059	+	0.986451i
$190$	−8.74456			−0.634397
$191$			15.6434i			1.13191i	0.824435	+	0.565957i	$0.191493\pi$
$191$			15.6434i			1.13191i	−0.824435	+	0.565957i	$0.808507\pi$
$192$	4.00000	−	0.939764i	0.288675	−	0.0678216i
$193$	22.2337			1.60042			0.800208	−	0.599723i	$-0.204722\pi$
$193$	22.2337			1.60042			0.800208	+	0.599723i	$0.204722\pi$
$194$	−2.74456			−0.197048
$195$	2.31386	+	9.84868i	0.165699	+	0.705279i
$196$	−4.37228	+	30.2921i	−0.312306	+	2.16372i
$197$			22.3692i			1.59374i	0.604152	+	0.796869i	$0.293512\pi$
$197$			22.3692i			1.59374i	−0.604152	+	0.796869i	$0.706488\pi$
$198$	−5.37228	+	2.67181i	−0.381791	+	0.189878i
$199$			12.9715i			0.919528i	0.888041	+	0.459764i	$0.152066\pi$
$199$			12.9715i			0.919528i	−0.888041	+	0.459764i	$0.847934\pi$
$200$			5.98844i			0.423447i
$201$	−11.3723	+	2.67181i	−0.802139	+	0.188455i
$202$		−	15.1460i		−	1.06567i
$203$	7.37228	+	8.51278i	0.517433	+	0.597480i
$204$	10.1168	−	2.37686i	0.708321	−	0.166414i
$205$	−6.00000			−0.419058
$206$	−40.9783			−2.85509
$207$	−2.51087	−	5.04868i	−0.174518	−	0.350907i
$208$			37.2203i			2.58076i
$209$	−2.74456			−0.189845
$210$	9.37228	+	6.78073i	0.646749	+	0.467915i
$211$	6.11684			0.421101			0.210550	−	0.977583i	$-0.432474\pi$
$211$	6.11684			0.421101			0.210550	+	0.977583i	$0.432474\pi$
$212$		−	37.2203i		−	2.55630i
$213$	−5.37228	−	22.8665i	−0.368103	−	1.56679i
$214$	−16.7446			−1.14463
$215$	−6.74456			−0.459975
$216$	19.8614	+	23.9538i	1.35140	+	1.62985i
$217$	−6.00000	−	6.92820i	−0.407307	−	0.470317i
$218$		−	0.294954i		−	0.0199768i
$219$	2.74456	+	11.6819i	0.185460	+	0.789391i
$220$			3.46410i			0.233550i
$221$		−	8.01544i		−	0.539177i
$222$	−4.74456	−	20.1947i	−0.318434	−	1.35538i
$223$			20.9870i			1.40539i	0.711490	+	0.702696i	$0.248021\pi$
$223$			20.9870i			1.40539i	−0.711490	+	0.702696i	$0.751979\pi$
$224$	7.11684	+	8.21782i	0.475514	+	0.549076i
$225$	2.68614	−	1.33591i	0.179076	−	0.0890605i
$226$	−25.4891			−1.69551
$227$	−15.6060			−1.03580			−0.517902	−	0.855440i	$-0.673287\pi$
$227$	−15.6060			−1.03580			−0.517902	+	0.855440i	$0.673287\pi$
$228$	6.00000	+	25.5383i	0.397360	+	1.69132i
$229$		−	4.75372i		−	0.314135i	−0.987588	−	0.157067i	$-0.949796\pi$
$229$		−	4.75372i		−	0.314135i	0.987588	−	0.157067i	$-0.0502040\pi$
$230$	−4.74456			−0.312847
$231$	2.94158	+	2.12819i	0.193542	+	0.140025i
$232$	25.4891			1.67344
$233$			3.75906i			0.246264i	0.992390	+	0.123132i	$0.0392938\pi$
$233$			3.75906i			0.246264i	−0.992390	+	0.123132i	$0.960706\pi$
$234$	39.6060	−	19.6974i	2.58912	−	1.28766i
$235$	−7.37228			−0.480915
$236$	−12.0000			−0.781133
$237$	5.68614	−	1.33591i	0.369355	−	0.0867765i
$238$	−6.00000	−	6.92820i	−0.388922	−	0.449089i
$239$			15.6434i			1.01188i	0.862567	+	0.505942i	$0.168855\pi$
$239$			15.6434i			1.01188i	−0.862567	+	0.505942i	$0.831145\pi$
$240$	10.7446	−	2.52434i	0.693559	−	0.162945i
$241$			23.3639i			1.50500i	0.658593	+	0.752499i	$0.271152\pi$
$241$			23.3639i			1.50500i	−0.658593	+	0.752499i	$0.728848\pi$
$242$		−	26.1831i		−	1.68312i
$243$	6.31386	−	14.2525i	0.405034	−	0.914302i
$244$		−	30.2921i		−	1.93925i
$245$	1.00000	−	6.92820i	0.0638877	−	0.442627i
$246$	6.00000	+	25.5383i	0.382546	+	1.62826i
$247$	20.2337			1.28744
$248$	−20.7446			−1.31728
$249$	9.25544	−	2.17448i	0.586540	−	0.137802i
$250$		−	2.52434i		−	0.159653i
$251$	17.4891			1.10390			0.551952	−	0.833876i	$-0.313883\pi$
$251$	17.4891			1.10390			0.551952	+	0.833876i	$0.313883\pi$
$252$	13.3723	−	32.0241i	0.842375	−	2.01733i
$253$	−1.48913			−0.0936205
$254$		−	27.1229i		−	1.70184i
$255$	−2.31386	+	0.543620i	−0.144899	+	0.0340428i
$256$	−31.1168			−1.94480
$257$	23.4891			1.46521			0.732606	−	0.680653i	$-0.238304\pi$
$257$	23.4891			1.46521			0.732606	+	0.680653i	$0.238304\pi$
$258$	6.74456	+	28.7075i	0.419898	+	1.78725i
$259$	−9.48913	+	8.21782i	−0.589626	+	0.510631i
$260$		−	25.5383i		−	1.58382i
$261$	−5.68614	−	11.4333i	−0.351963	−	0.707701i
$262$			44.1485i			2.72750i
$263$		−	13.5615i		−	0.836235i	−0.908393	−	0.418118i	$-0.862690\pi$
$263$		−	13.5615i		−	0.836235i	0.908393	−	0.418118i	$-0.137310\pi$
$264$	8.00000	−	1.87953i	0.492366	−	0.115677i
$265$			8.51278i			0.522936i
$266$	17.4891	−	15.1460i	1.07233	−	0.928662i
$267$	5.48913	−	1.28962i	0.335929	−	0.0789235i
$268$	29.4891			1.80134
$269$	−8.74456			−0.533165			−0.266583	−	0.963812i	$-0.585895\pi$
$269$	−8.74456			−0.533165			−0.266583	+	0.963812i	$0.585895\pi$
$270$	−8.37228	−	10.0974i	−0.509521	−	0.614505i
$271$			15.1460i			0.920056i	0.887905	+	0.460028i	$0.152161\pi$
$271$			15.1460i			0.920056i	−0.887905	+	0.460028i	$0.847839\pi$
$272$	−8.74456			−0.530217
$273$	−21.6861	−	15.6896i	−1.31250	−	0.949581i
$274$	33.4891			2.02315
$275$		−	0.792287i		−	0.0477767i
$276$	3.25544	+	13.8564i	0.195954	+	0.834058i
$277$	−6.23369			−0.374546			−0.187273	−	0.982308i	$-0.559965\pi$
$277$	−6.23369			−0.374546			−0.187273	+	0.982308i	$0.559965\pi$
$278$	−3.25544			−0.195248
$279$	4.62772	+	9.30506i	0.277054	+	0.557080i
$280$	−10.3723	−	11.9769i	−0.619862	−	0.715755i
$281$			4.84630i			0.289106i	0.989497	+	0.144553i	$0.0461744\pi$
$281$			4.84630i			0.289106i	−0.989497	+	0.144553i	$0.953826\pi$
$282$	7.37228	+	31.3793i	0.439013	+	1.86861i
$283$		−	9.30506i		−	0.553129i	−0.960995	−	0.276564i	$-0.910804\pi$
$283$		−	9.30506i		−	0.553129i	0.960995	−	0.276564i	$-0.0891959\pi$
$284$			59.2945i			3.51848i
$285$	−1.37228	−	5.84096i	−0.0812869	−	0.345989i
$286$		−	11.6819i		−	0.690767i
$287$	12.0000	−	10.3923i	0.708338	−	0.613438i
$288$	−5.48913	−	11.0371i	−0.323450	−	0.650368i
$289$	−15.1168			−0.889226
$290$	−10.7446			−0.630942
$291$	−0.430703	−	1.83324i	−0.0252483	−	0.107466i
$292$		−	30.2921i		−	1.77271i
$293$	−28.1168			−1.64260			−0.821302	−	0.570494i	$-0.806752\pi$
$293$	−28.1168			−1.64260			−0.821302	+	0.570494i	$0.806752\pi$
$294$	−30.4891	+	2.67181i	−1.77816	+	0.155823i
$295$	2.74456			0.159795
$296$			28.4125i			1.65144i
$297$	−2.62772	−	3.16915i	−0.152476	−	0.183893i
$298$	−25.4891			−1.47655
$299$	10.9783			0.634889
$300$	−7.37228	+	1.73205i	−0.425639	+	0.100000i
$301$	13.4891	−	11.6819i	0.777500	−	0.673335i
$302$		−	8.51278i		−	0.489855i
$303$	10.1168	−	2.37686i	0.581198	−	0.136547i
$304$		−	22.0742i		−	1.26604i
$305$			6.92820i			0.396708i
$306$	4.62772	+	9.30506i	0.264549	+	0.531935i
$307$		−	7.13058i		−	0.406964i	−0.979079	−	0.203482i	$-0.934774\pi$
$307$		−	7.13058i		−	0.406964i	0.979079	−	0.203482i	$-0.0652258\pi$
$308$	−6.00000	−	6.92820i	−0.341882	−	0.394771i
$309$	−6.43070	−	27.3716i	−0.365830	−	1.55711i
$310$	8.74456			0.496658
$311$	20.2337			1.14735			0.573674	−	0.819084i	$-0.305518\pi$
$311$	20.2337			1.14735			0.573674	+	0.819084i	$0.305518\pi$
$312$	−58.9783	+	13.8564i	−3.33899	+	0.784465i
$313$		−	24.4511i		−	1.38206i	−0.722827	−	0.691029i	$-0.757158\pi$
$313$		−	24.4511i		−	1.38206i	0.722827	−	0.691029i	$-0.242842\pi$
$314$		0			0
$315$	−3.05842	+	7.32435i	−0.172323	+	0.412680i
$316$	−14.7446			−0.829446
$317$			8.51278i			0.478125i	0.971004	+	0.239063i	$0.0768401\pi$
$317$			8.51278i			0.478125i	−0.971004	+	0.239063i	$0.923160\pi$
$318$	36.2337	−	8.51278i	2.03188	−	0.477373i
$319$	−3.37228			−0.188812
$320$	2.37228			0.132615
$321$	−2.62772	−	11.1846i	−0.146665	−	0.624263i
$322$	9.48913	−	8.21782i	0.528808	−	0.457961i
$323$			4.75372i			0.264504i
$324$	−23.7446	+	31.3793i	−1.31914	+	1.74329i
$325$			5.84096i			0.323998i
$326$		−	20.1947i		−	1.11848i
$327$	0.197015	−	0.0462870i	0.0108950	−	0.00255968i
$328$		−	35.9306i		−	1.98394i
$329$	14.7446	−	12.7692i	0.812894	−	0.703987i
$330$	−3.37228	+	0.792287i	−0.185638	+	0.0436140i
$331$	−4.00000			−0.219860			−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000			−0.219860			−0.109930	+	0.993939i	$0.535063\pi$
$332$	−24.0000			−1.31717
$333$	12.7446	−	6.33830i	0.698398	−	0.347336i
$334$			55.8304i			3.05490i
$335$	−6.74456			−0.368495
$336$	−17.1168	+	23.6588i	−0.933800	+	1.29069i
$337$	−18.2337			−0.993252			−0.496626	−	0.867965i	$-0.665428\pi$
$337$	−18.2337			−0.993252			−0.496626	+	0.867965i	$0.665428\pi$
$338$			53.3060i			2.89947i
$339$	−4.00000	−	17.0256i	−0.217250	−	0.924701i
$340$	6.00000			0.325396
$341$	2.74456			0.148626
$342$	−23.4891	+	11.6819i	−1.27015	+	0.631686i
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		−	40.3894i		−	2.17765i
$345$	−0.744563	−	3.16915i	−0.0400859	−	0.170621i
$346$		−	40.6844i		−	2.18720i
$347$		−	18.3152i		−	0.983210i	−0.870818	−	0.491605i	$-0.836410\pi$
$347$		−	18.3152i		−	0.983210i	0.870818	−	0.491605i	$-0.163590\pi$
$348$	7.37228	+	31.3793i	0.395196	+	1.68211i
$349$			4.75372i			0.254461i	0.991873	+	0.127230i	$0.0406088\pi$
$349$			4.75372i			0.254461i	−0.991873	+	0.127230i	$0.959391\pi$
$350$	4.37228	+	5.04868i	0.233708	+	0.269863i
$351$	19.3723	+	23.3639i	1.03402	+	1.24707i
$352$	−3.25544			−0.173515
$353$	7.88316			0.419578			0.209789	−	0.977747i	$-0.432722\pi$
$353$	7.88316			0.419578			0.209789	+	0.977747i	$0.432722\pi$
$354$	−2.74456	−	11.6819i	−0.145872	−	0.620887i
$355$		−	13.5615i		−	0.719767i
$356$	−14.2337			−0.754384
$357$	3.68614	−	5.09496i	0.195091	−	0.269654i
$358$	−16.7446			−0.884978
$359$			9.80240i			0.517351i	0.965964	+	0.258675i	$0.0832860\pi$
$359$			9.80240i			0.517351i	−0.965964	+	0.258675i	$0.916714\pi$
$360$	8.00000	+	16.0858i	0.421637	+	0.847796i
$361$	7.00000			0.368421
$362$	−46.9783			−2.46912
$363$	17.4891	−	4.10891i	0.917941	−	0.215662i
$364$	44.2337	+	51.0767i	2.31848	+	2.67714i
$365$			6.92820i			0.362639i
$366$	29.4891	−	6.92820i	1.54142	−	0.362143i
$367$			25.3360i			1.32253i	0.750154	+	0.661263i	$0.229979\pi$
$367$			25.3360i			1.32253i	−0.750154	+	0.661263i	$0.770021\pi$
$368$		−	11.9769i		−	0.624338i
$369$	−16.1168	+	8.01544i	−0.839009	+	0.417267i
$370$		−	11.9769i		−	0.622648i
$371$	−14.7446	−	17.0256i	−0.765500	−	0.883923i
$372$	−6.00000	−	25.5383i	−0.311086	−	1.32410i
$373$	−24.7446			−1.28122			−0.640612	−	0.767864i	$-0.721319\pi$
$373$	−24.7446			−1.28122			−0.640612	+	0.767864i	$0.721319\pi$
$374$	2.74456			0.141918
$375$	1.68614	−	0.396143i	0.0870719	−	0.0204568i
$376$		−	44.1485i		−	2.27678i
$377$	24.8614			1.28043
$378$	34.2337	+	5.69349i	1.76079	+	0.292841i
$379$	1.48913			0.0764912			0.0382456	−	0.999268i	$-0.487823\pi$
$379$	1.48913			0.0764912			0.0382456	+	0.999268i	$0.487823\pi$
$380$			15.1460i			0.776975i
$381$	18.1168	−	4.25639i	0.928154	−	0.218061i
$382$	39.4891			2.02044
$383$	−17.4891			−0.893653			−0.446826	−	0.894621i	$-0.647446\pi$
$383$	−17.4891			−0.893653			−0.446826	+	0.894621i	$0.647446\pi$
$384$	−5.62772	−	23.9538i	−0.287188	−	1.22239i
$385$	1.37228	+	1.58457i	0.0699379	+	0.0807574i
$386$		−	56.1253i		−	2.85670i
$387$	−18.1168	+	9.01011i	−0.920931	+	0.458010i
$388$			4.75372i			0.241334i
$389$		−	13.7638i		−	0.697854i	−0.937150	−	0.348927i	$-0.886546\pi$
$389$		−	13.7638i		−	0.697854i	0.937150	−	0.348927i	$-0.113454\pi$
$390$	24.8614	−	5.84096i	1.25891	−	0.295769i
$391$			2.57924i			0.130438i
$392$	41.4891	+	5.98844i	2.09552	+	0.302462i
$393$	−29.4891	+	6.92820i	−1.48753	+	0.349482i
$394$	56.4674			2.84479
$395$	3.37228			0.169678
$396$	4.62772	+	9.30506i	0.232552	+	0.467597i
$397$			3.66648i			0.184015i	0.995758	+	0.0920077i	$0.0293284\pi$
$397$			3.66648i			0.184015i	−0.995758	+	0.0920077i	$0.970672\pi$
$398$	32.7446			1.64134
$399$	12.8614	+	9.30506i	0.643876	+	0.465836i
$400$	6.37228			0.318614
$401$			2.67181i			0.133424i	0.997772	+	0.0667120i	$0.0212509\pi$
$401$			2.67181i			0.133424i	−0.997772	+	0.0667120i	$0.978749\pi$
$402$	6.74456	+	28.7075i	0.336388	+	1.43180i
$403$	−20.2337			−1.00791
$404$	−26.2337			−1.30517
$405$	5.43070	−	7.17687i	0.269854	−	0.356622i
$406$	21.4891	−	18.6101i	1.06649	−	0.923605i
$407$		−	3.75906i		−	0.186329i
$408$	−3.25544	−	13.8564i	−0.161168	−	0.685994i
$409$		−	35.0458i		−	1.73290i	−0.499262	−	0.866451i	$-0.666396\pi$
$409$		−	35.0458i		−	1.73290i	0.499262	−	0.866451i	$-0.333604\pi$
$410$			15.1460i			0.748009i
$411$	5.25544	+	22.3692i	0.259232	+	1.10339i
$412$			70.9764i			3.49676i
$413$	−5.48913	+	4.75372i	−0.270102	+	0.233915i
$414$	−12.7446	+	6.33830i	−0.626361	+	0.311510i
$415$	5.48913			0.269451
$416$	24.0000			1.17670
$417$	−0.510875	−	2.17448i	−0.0250176	−	0.106485i
$418$			6.92820i			0.338869i
$419$	−2.74456			−0.134081			−0.0670403	−	0.997750i	$-0.521356\pi$
$419$	−2.74456			−0.134081			−0.0670403	+	0.997750i	$0.521356\pi$
$420$	11.7446	−	16.2333i	0.573076	−	0.792102i
$421$	−25.6060			−1.24796			−0.623979	−	0.781441i	$-0.714485\pi$
$421$	−25.6060			−1.24796			−0.623979	+	0.781441i	$0.714485\pi$
$422$		−	15.4410i		−	0.751655i
$423$	−19.8030	+	9.84868i	−0.962854	+	0.478859i
$424$	−50.9783			−2.47572
$425$	−1.37228			−0.0665654
$426$	−57.7228	+	13.5615i	−2.79668	+	0.657055i
$427$	−12.0000	−	13.8564i	−0.580721	−	0.670559i
$428$			29.0024i			1.40189i
$429$	7.80298	−	1.83324i	0.376732	−	0.0885097i
$430$			17.0256i			0.821045i
$431$			31.6742i			1.52569i	0.646579	+	0.762847i	$0.276199\pi$
$431$			31.6742i			1.52569i	−0.646579	+	0.762847i	$0.723801\pi$
$432$	25.4891	−	21.1345i	1.22635	−	1.01683i
$433$		−	2.57924i		−	0.123950i	−0.998078	−	0.0619752i	$-0.980260\pi$
$433$		−	2.57924i		−	0.123950i	0.998078	−	0.0619752i	$-0.0197400\pi$
$434$	−17.4891	+	15.1460i	−0.839505	+	0.727033i
$435$	−1.68614	−	7.17687i	−0.0808443	−	0.344105i
$436$	−0.510875			−0.0244665
$437$	−6.51087			−0.311457
$438$	29.4891	−	6.92820i	1.40904	−	0.331042i
$439$			1.28962i			0.0615502i	0.999526	+	0.0307751i	$0.00979757\pi$
$439$			1.28962i			0.0615502i	−0.999526	+	0.0307751i	$0.990202\pi$
$440$	4.74456			0.226188
$441$	−6.56930	−	19.9460i	−0.312824	−	0.949811i
$442$	−20.2337			−0.962418
$443$		−	6.63325i		−	0.315155i	−0.987507	−	0.157578i	$-0.949632\pi$
$443$		−	6.63325i		−	0.315155i	0.987507	−	0.157578i	$-0.0503684\pi$
$444$	−34.9783	+	8.21782i	−1.65999	+	0.390001i
$445$	3.25544			0.154323
$446$	52.9783			2.50859
$447$	−4.00000	−	17.0256i	−0.189194	−	0.805281i
$448$	−4.74456	+	4.10891i	−0.224160	+	0.194128i
$449$			28.2101i			1.33132i	0.746256	+	0.665660i	$0.231850\pi$
$449$			28.2101i			1.33132i	−0.746256	+	0.665660i	$0.768150\pi$
$450$	−3.37228	−	6.78073i	−0.158971	−	0.319647i
$451$			4.75372i			0.223844i
$452$			44.1485i			2.07657i
$453$	5.68614	−	1.33591i	0.267158	−	0.0627664i
$454$			39.3947i			1.84889i
$455$	−10.1168	−	11.6819i	−0.474285	−	0.547657i
$456$	34.9783	−	8.21782i	1.63801	−	0.384835i
$457$	−32.9783			−1.54266			−0.771329	−	0.636437i	$-0.780408\pi$
$457$	−32.9783			−1.54266			−0.771329	+	0.636437i	$0.780408\pi$
$458$	−12.0000			−0.560723
$459$	−5.48913	+	4.55134i	−0.256210	+	0.212438i
$460$			8.21782i			0.383158i
$461$	−8.74456			−0.407275			−0.203637	−	0.979046i	$-0.565276\pi$
$461$	−8.74456			−0.407275			−0.203637	+	0.979046i	$0.565276\pi$
$462$	5.37228	−	7.42554i	0.249941	−	0.345467i
$463$	36.4674			1.69478			0.847391	−	0.530969i	$-0.178172\pi$
$463$	36.4674			1.69478			0.847391	+	0.530969i	$0.178172\pi$
$464$		−	27.1229i		−	1.25915i
$465$	1.37228	+	5.84096i	0.0636380	+	0.270868i
$466$	9.48913			0.439575
$467$	−13.8832			−0.642436			−0.321218	−	0.947005i	$-0.604092\pi$
$467$	−13.8832			−0.642436			−0.321218	+	0.947005i	$0.604092\pi$
$468$	−34.1168	−	68.5996i	−1.57705	−	3.17102i
$469$	13.4891	−	11.6819i	0.622870	−	0.539421i
$470$			18.6101i			0.858421i
$471$		0			0
$472$			16.4356i			0.756512i
$473$			5.34363i			0.245700i
$474$	−3.37228	−	14.3537i	−0.154894	−	0.659289i
$475$		−	3.46410i		−	0.158944i
$476$	−12.0000	+	10.3923i	−0.550019	+	0.476331i
$477$	11.3723	+	22.8665i	0.520701	+	1.04699i
$478$	39.4891			1.80619
$479$	18.5109			0.845783			0.422892	−	0.906180i	$-0.361015\pi$
$479$	18.5109			0.845783			0.422892	+	0.906180i	$0.361015\pi$
$480$	−1.62772	−	6.92820i	−0.0742949	−	0.316228i
$481$			27.7128i			1.26360i
$482$	58.9783			2.68639
$483$	6.97825	+	5.04868i	0.317521	+	0.229723i
$484$	−45.3505			−2.06139
$485$		−	1.08724i		−	0.0493691i
$486$	−35.9783	−	15.9383i	−1.63201	−	0.722977i
$487$	14.5109			0.657550			0.328775	−	0.944408i	$-0.393364\pi$
$487$	14.5109			0.657550			0.328775	+	0.944408i	$0.393364\pi$
$488$	−41.4891			−1.87812
$489$	13.4891	−	3.16915i	0.609999	−	0.143314i
$490$	−17.4891	−	2.52434i	−0.790078	−	0.114038i
$491$			10.8896i			0.491442i	0.969341	+	0.245721i	$0.0790248\pi$
$491$			10.8896i			0.491442i	−0.969341	+	0.245721i	$0.920975\pi$
$492$	44.2337	−	10.3923i	1.99421	−	0.468521i
$493$			5.84096i			0.263064i
$494$		−	51.0767i		−	2.29805i
$495$	−1.05842	−	2.12819i	−0.0475725	−	0.0956552i
$496$			22.0742i			0.991162i
$497$	23.4891	+	27.1229i	1.05363	+	1.21663i
$498$	−5.48913	−	23.3639i	−0.245974	−	1.04696i
$499$	−10.3505			−0.463353			−0.231677	−	0.972793i	$-0.574421\pi$
$499$	−10.3505			−0.463353			−0.231677	+	0.972793i	$0.574421\pi$
$500$	−4.37228			−0.195534
$501$	−37.2921	+	8.76144i	−1.66609	+	0.391432i
$502$		−	44.1485i		−	1.97044i
$503$	−27.6060			−1.23089			−0.615445	−	0.788180i	$-0.711024\pi$
$503$	−27.6060			−1.23089			−0.615445	+	0.788180i	$0.711024\pi$
$504$	−43.8614	−	18.3152i	−1.95374	−	0.815823i
$505$	6.00000			0.266996
$506$			3.75906i			0.167110i
$507$	−35.6060	+	8.36530i	−1.58132	+	0.371516i
$508$	−46.9783			−2.08432
$509$	−38.2337			−1.69468			−0.847339	−	0.531052i	$-0.821797\pi$
$509$	−38.2337			−1.69468			−0.847339	+	0.531052i	$0.821797\pi$
$510$	1.37228	+	5.84096i	0.0607656	+	0.258642i
$511$	−12.0000	−	13.8564i	−0.530849	−	0.612971i
$512$			50.1369i			2.21576i
$513$	−11.4891	−	13.8564i	−0.507257	−	0.611775i
$514$		−	59.2945i		−	2.61537i
$515$		−	16.2333i		−	0.715323i
$516$	49.7228	−	11.6819i	2.18892	−	0.514268i
$517$			5.84096i			0.256885i
$518$	20.7446	+	23.9538i	0.911464	+	1.05247i
$519$	27.1753	−	6.38458i	1.19286	−	0.280252i
$520$	−34.9783			−1.53390
$521$	34.4674			1.51004			0.755022	−	0.655700i	$-0.227626\pi$
$521$	34.4674			1.51004			0.755022	+	0.655700i	$0.227626\pi$
$522$	−28.8614	+	14.3537i	−1.26323	+	0.628246i
$523$			10.3923i			0.454424i	0.973845	+	0.227212i	$0.0729610\pi$
$523$			10.3923i			0.454424i	−0.973845	+	0.227212i	$0.927039\pi$
$524$	76.4674			3.34049
$525$	−2.68614	+	3.71277i	−0.117233	+	0.162038i
$526$	−34.2337			−1.49266
$527$		−	4.75372i		−	0.207075i
$528$	−2.00000	−	8.51278i	−0.0870388	−	0.370471i
$529$	19.4674			0.846408
$530$	21.4891			0.933428
$531$	7.37228	−	3.66648i	0.319930	−	0.159112i
$532$	−26.2337	−	30.2921i	−1.13737	−	1.31333i
$533$		−	35.0458i		−	1.51800i
$534$	−3.25544	−	13.8564i	−0.140877	−	0.599625i
$535$		−	6.63325i		−	0.286780i
$536$		−	40.3894i		−	1.74456i
$537$	−2.62772	−	11.1846i	−0.113394	−	0.482651i
$538$			22.0742i			0.951688i
$539$	−5.48913	−	0.792287i	−0.236433	−	0.0341262i
$540$	−17.4891	+	14.5012i	−0.752612	+	0.624033i
$541$	18.6277			0.800868			0.400434	−	0.916326i	$-0.368859\pi$
$541$	18.6277			0.800868			0.400434	+	0.916326i	$0.368859\pi$
$542$	38.2337			1.64228
$543$	−7.37228	−	31.3793i	−0.316375	−	1.34661i
$544$			5.63858i			0.241752i
$545$	0.116844			0.00500505
$546$	−39.6060	+	54.7431i	−1.69498	+	2.34279i
$547$	42.9783			1.83762			0.918809	−	0.394703i	$-0.129153\pi$
$547$	42.9783			1.83762			0.918809	+	0.394703i	$0.129153\pi$
$548$		−	58.0049i		−	2.47785i
$549$	9.25544	+	18.6101i	0.395012	+	0.794261i
$550$	−2.00000			−0.0852803
$551$	−14.7446			−0.628139
$552$	18.9783	−	4.45877i	0.807768	−	0.189778i
$553$	−6.74456	+	5.84096i	−0.286808	+	0.248383i
$554$			15.7359i			0.668556i
$555$	8.00000	−	1.87953i	0.339581	−	0.0797815i
$556$			5.63858i			0.239129i
$557$		−	30.8820i		−	1.30851i	−0.756274	−	0.654255i	$-0.772982\pi$
$557$		−	30.8820i		−	1.30851i	0.756274	−	0.654255i	$-0.227018\pi$
$558$	23.4891	−	11.6819i	0.994374	−	0.494535i
$559$		−	39.3947i		−	1.66622i
$560$	−12.7446	+	11.0371i	−0.538556	+	0.466403i
$561$	0.430703	+	1.83324i	0.0181843	+	0.0773995i
$562$	12.2337			0.516047
$563$	5.48913			0.231339			0.115670	−	0.993288i	$-0.463099\pi$
$563$	5.48913			0.231339			0.115670	+	0.993288i	$0.463099\pi$
$564$	54.3505	−	12.7692i	2.28857	−	0.537679i
$565$		−	10.0974i		−	0.424799i
$566$	−23.4891			−0.987322
$567$	1.56930	+	23.7600i	0.0659043	+	0.997826i
$568$	81.2119			3.40758
$569$			10.6873i			0.448033i	0.974585	+	0.224017i	$0.0719170\pi$
$569$			10.6873i			0.448033i	−0.974585	+	0.224017i	$0.928083\pi$
$570$	−14.7446	+	3.46410i	−0.617582	+	0.145095i
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$	−20.2337			−0.846013
$573$	6.19702	+	26.3769i	0.258884	+	1.10191i
$574$	−26.2337	−	30.2921i	−1.09497	−	1.26437i
$575$		−	1.87953i		−	0.0783817i
$576$	6.37228	−	3.16915i	0.265512	−	0.132048i
$577$		−	12.7692i		−	0.531587i	−0.964030	−	0.265794i	$-0.914366\pi$
$577$		−	12.7692i		−	0.531587i	0.964030	−	0.265794i	$-0.0856340\pi$
$578$			38.1600i			1.58725i
$579$	37.4891	−	8.80773i	1.55799	−	0.366037i
$580$			18.6101i			0.772744i
$581$	−10.9783	+	9.50744i	−0.455455	+	0.394435i
$582$	−4.62772	+	1.08724i	−0.191825	+	0.0450676i
$583$	6.74456			0.279331
$584$	−41.4891			−1.71683
$585$	7.80298	+	15.6896i	0.322614	+	0.648687i
$586$			70.9764i			2.93201i
$587$	−5.48913			−0.226560			−0.113280	−	0.993563i	$-0.536136\pi$
$587$	−5.48913			−0.226560			−0.113280	+	0.993563i	$0.536136\pi$
$588$	4.62772	+	52.8087i	0.190844	+	2.17779i
$589$	12.0000			0.494451
$590$		−	6.92820i		−	0.285230i
$591$	8.86141	+	37.7176i	0.364510	+	1.55149i
$592$	30.2337			1.24260
$593$	−1.37228			−0.0563528			−0.0281764	−	0.999603i	$-0.508970\pi$
$593$	−1.37228			−0.0563528			−0.0281764	+	0.999603i	$0.508970\pi$
$594$	−8.00000	+	6.63325i	−0.328244	+	0.272166i
$595$	2.74456	−	2.37686i	0.112516	−	0.0974418i
$596$			44.1485i			1.80839i
$597$	5.13859	+	21.8719i	0.210309	+	0.895155i
$598$		−	27.7128i		−	1.13326i
$599$			1.78695i			0.0730129i	0.999333	+	0.0365065i	$0.0116230\pi$
$599$			1.78695i			0.0730129i	−0.999333	+	0.0365065i	$0.988377\pi$
$600$	2.37228	+	10.0974i	0.0968480	+	0.412223i
$601$			2.17448i			0.0886989i	0.999016	+	0.0443495i	$0.0141215\pi$
$601$			2.17448i			0.0886989i	−0.999016	+	0.0443495i	$0.985878\pi$
$602$	−29.4891	−	34.0511i	−1.20189	−	1.38782i
$603$	−18.1168	+	9.01011i	−0.737775	+	0.366920i
$604$	−14.7446			−0.599948
$605$	10.3723			0.421693
$606$	−6.00000	−	25.5383i	−0.243733	−	1.03742i
$607$			20.9870i			0.851836i	0.904762	+	0.425918i	$0.140049\pi$
$607$			20.9870i			0.851836i	−0.904762	+	0.425918i	$0.859951\pi$
$608$	−14.2337			−0.577252
$609$	15.8030	+	11.4333i	0.640369	+	0.463299i
$610$	17.4891			0.708114
$611$		−	43.0612i		−	1.74207i
$612$	16.1168	−	8.01544i	0.651485	−	0.324005i
$613$	−4.51087			−0.182193			−0.0910963	−	0.995842i	$-0.529037\pi$
$613$	−4.51087			−0.182193			−0.0910963	+	0.995842i	$0.529037\pi$
$614$	−18.0000			−0.726421
$615$	−10.1168	+	2.37686i	−0.407951	+	0.0958443i
$616$	−9.48913	+	8.21782i	−0.382328	+	0.331106i
$617$		−	37.8102i		−	1.52218i	−0.648646	−	0.761090i	$-0.724665\pi$
$617$		−	37.8102i		−	1.52218i	0.648646	−	0.761090i	$-0.275335\pi$
$618$	−69.0951	+	16.2333i	−2.77941	+	0.652998i
$619$		−	1.28962i		−	0.0518342i	−0.999664	−	0.0259171i	$-0.991749\pi$
$619$		−	1.28962i		−	0.0518342i	0.999664	−	0.0259171i	$-0.00825060\pi$
$620$		−	15.1460i		−	0.608279i
$621$	−6.23369	−	7.51811i	−0.250149	−	0.301691i
$622$		−	51.0767i		−	2.04799i
$623$	−6.51087	+	5.63858i	−0.260853	+	0.225905i
$624$	14.7446	+	62.7586i	0.590255	+	2.51235i
$625$	1.00000			0.0400000
$626$	−61.7228			−2.46694
$627$	−4.62772	+	1.08724i	−0.184813	+	0.0434202i
$628$		0			0
$629$	−6.51087			−0.259606
$630$	18.4891	+	7.72049i	0.736624	+	0.307592i
$631$	−5.88316			−0.234205			−0.117102	−	0.993120i	$-0.537361\pi$
$631$	−5.88316			−0.234205			−0.117102	+	0.993120i	$0.537361\pi$
$632$			20.1947i			0.803302i
$633$	10.3139	−	2.42315i	0.409939	−	0.0963115i
$634$	21.4891			0.853442
$635$	10.7446			0.426385
$636$	−14.7446	−	62.7586i	−0.584660	−	2.48854i
$637$	40.4674	+	5.84096i	1.60338	+	0.231427i
$638$			8.51278i			0.337024i
$639$	−18.1168	−	36.4280i	−0.716691	−	1.44107i
$640$		−	14.2063i		−	0.561552i
$641$			29.7021i			1.17316i	0.809890	+	0.586582i	$0.199527\pi$
$641$			29.7021i			1.17316i	−0.809890	+	0.586582i	$0.800473\pi$
$642$	−28.2337	+	6.63325i	−1.11429	+	0.261793i
$643$			39.5971i			1.56156i	0.624807	+	0.780779i	$0.285178\pi$
$643$			39.5971i			1.56156i	−0.624807	+	0.780779i	$0.714822\pi$
$644$	−14.2337	−	16.4356i	−0.560886	−	0.647655i
$645$	−11.3723	+	2.67181i	−0.447783	+	0.105203i
$646$	12.0000			0.472134
$647$	12.0000			0.471769			0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000			0.471769			0.235884	+	0.971781i	$0.424201\pi$
$648$	42.9783	+	32.5214i	1.68835	+	1.27756i
$649$		−	2.17448i		−	0.0853559i
$650$	14.7446			0.578329
$651$	−12.8614	−	9.30506i	−0.504078	−	0.364694i
$652$	−34.9783			−1.36985
$653$		−	33.0564i		−	1.29360i	−0.762660	−	0.646799i	$-0.776107\pi$
$653$		−	33.0564i		−	1.29360i	0.762660	−	0.646799i	$-0.223893\pi$
$654$	−0.116844	−	0.497333i	−0.00456896	−	0.0194473i
$655$	−17.4891			−0.683357
$656$	−38.2337			−1.49277
$657$	9.25544	+	18.6101i	0.361089	+	0.726050i
$658$	−32.2337	−	37.2203i	−1.25660	−	1.45100i
$659$			20.3971i			0.794558i	0.917698	+	0.397279i	$0.130045\pi$
$659$			20.3971i			0.794558i	−0.917698	+	0.397279i	$0.869955\pi$
$660$	1.37228	+	5.84096i	0.0534160	+	0.227359i
$661$		−	6.92820i		−	0.269476i	−0.990881	−	0.134738i	$-0.956981\pi$
$661$		−	6.92820i		−	0.269476i	0.990881	−	0.134738i	$-0.0430193\pi$
$662$			10.0974i			0.392445i
$663$	−3.17527	−	13.5152i	−0.123317	−	0.524886i
$664$			32.8713i			1.27565i
$665$	6.00000	+	6.92820i	0.232670	+	0.268664i
$666$	−16.0000	−	32.1716i	−0.619987	−	1.24662i
$667$	−8.00000			−0.309761
$668$	96.7011			3.74148
$669$	8.31386	+	35.3870i	0.321432	+	1.36814i
$670$			17.0256i			0.657755i
$671$	5.48913			0.211905
$672$	15.2554	+	11.0371i	0.588491	+	0.425766i
$673$	22.2337			0.857046			0.428523	−	0.903531i	$-0.359034\pi$
$673$	22.2337			0.857046			0.428523	+	0.903531i	$0.359034\pi$
$674$			46.0280i			1.77293i
$675$	4.00000	−	3.31662i	0.153960	−	0.127657i
$676$	92.3288			3.55111
$677$	21.6060			0.830385			0.415192	−	0.909734i	$-0.363714\pi$
$677$	21.6060			0.830385			0.415192	+	0.909734i	$0.363714\pi$
$678$	−42.9783	+	10.0974i	−1.65057	+	0.387786i
$679$	1.88316	+	2.17448i	0.0722689	+	0.0834489i
$680$		−	8.21782i		−	0.315139i
$681$	−26.3139	+	6.18220i	−1.00835	+	0.236903i
$682$		−	6.92820i		−	0.265295i
$683$			51.7764i			1.98117i	0.136906	+	0.990584i	$0.456284\pi$
$683$			51.7764i			1.98117i	−0.136906	+	0.990584i	$0.543716\pi$
$684$	20.2337	+	40.6844i	0.773654	+	1.55561i
$685$			13.2665i			0.506887i
$686$	39.3505	−	25.2434i	1.50241	−	0.963797i
$687$	−1.88316	−	8.01544i	−0.0718469	−	0.305808i
$688$	−42.9783			−1.63853
$689$	−49.7228			−1.89429
$690$	−8.00000	+	1.87953i	−0.304555	+	0.0715524i
$691$		−	38.5099i		−	1.46498i	−0.680775	−	0.732492i	$-0.738357\pi$
$691$		−	38.5099i		−	1.46498i	0.680775	−	0.732492i	$-0.261643\pi$
$692$	−70.4674			−2.67877
$693$	5.80298	+	2.42315i	0.220437	+	0.0920478i
$694$	−46.2337			−1.75501
$695$		−	1.28962i		−	0.0489181i
$696$	42.9783	−	10.0974i	1.62909	−	0.382739i
$697$	8.23369			0.311873
$698$	12.0000			0.454207
$699$	1.48913	+	6.33830i	0.0563239	+	0.239736i
$700$	8.74456	−	7.57301i	0.330513	−	0.286233i
$701$		−	45.8256i		−	1.73081i	−0.501074	−	0.865405i	$-0.667061\pi$
$701$		−	45.8256i		−	1.73081i	0.501074	−	0.865405i	$-0.332939\pi$
$702$	58.9783	−	48.9022i	2.22599	−	1.84569i
$703$		−	16.4356i		−	0.619882i
$704$		−	1.87953i		−	0.0708374i
$705$	−12.4307	+	2.92048i	−0.468167	+	0.109992i
$706$		−	19.8997i		−	0.748937i
$707$	−12.0000	+	10.3923i	−0.451306	+	0.390843i
$708$	−20.2337	+	4.75372i	−0.760429	+	0.178656i
$709$	24.1168			0.905727			0.452864	−	0.891580i	$-0.350402\pi$
$709$	24.1168			0.905727			0.452864	+	0.891580i	$0.350402\pi$
$710$	−34.2337			−1.28477
$711$	9.05842	−	4.50506i	0.339717	−	0.168953i
$712$			19.4950i			0.730606i
$713$	6.51087			0.243834
$714$	−12.8614	−	9.30506i	−0.481326	−	0.348233i
$715$	4.62772			0.173067
$716$			29.0024i			1.08387i
$717$	6.19702	+	26.3769i	0.231432	+	0.985064i
$718$	24.7446			0.923459
$719$	40.4674			1.50918			0.754589	−	0.656197i	$-0.227836\pi$
$719$	40.4674			1.50918			0.754589	+	0.656197i	$0.227836\pi$
$720$	17.1168	−	8.51278i	0.637907	−	0.317252i
$721$	28.1168	+	32.4665i	1.04713	+	1.20912i
$722$		−	17.6704i		−	0.657623i
$723$	9.25544	+	39.3947i	0.344213	+	1.46511i
$724$			81.3687i			3.02404i
$725$		−	4.25639i		−	0.158078i
$726$	−10.3723	−	44.1485i	−0.384951	−	1.63850i
$727$			3.46410i			0.128476i	0.997935	+	0.0642382i	$0.0204617\pi$
$727$			3.46410i			0.128476i	−0.997935	+	0.0642382i	$0.979538\pi$
$728$	69.9565	−	60.5841i	2.59276	−	2.24540i
$729$	5.00000	−	26.5330i	0.185185	−	0.982704i
$730$	17.4891			0.647302
$731$	9.25544			0.342325
$732$	−12.0000	−	51.0767i	−0.443533	−	1.88785i
$733$		−	10.1899i		−	0.376373i	−0.982133	−	0.188187i	$-0.939739\pi$
$733$		−	10.1899i		−	0.376373i	0.982133	−	0.188187i	$-0.0602610\pi$
$734$	63.9565			2.36068
$735$	−1.05842	−	12.0781i	−0.0390405	−	0.445506i
$736$	−7.72281			−0.284667
$737$			5.34363i			0.196835i
$738$	20.2337	+	40.6844i	0.744812	+	1.49761i
$739$	−8.62772			−0.317376			−0.158688	−	0.987329i	$-0.550726\pi$
$739$	−8.62772			−0.317376			−0.158688	+	0.987329i	$0.550726\pi$
$740$	−20.7446			−0.762585
$741$	34.1168	−	8.01544i	1.25331	−	0.294455i
$742$	−42.9783	+	37.2203i	−1.57778	+	1.36640i
$743$		−	36.9253i		−	1.35466i	−0.735680	−	0.677329i	$-0.763137\pi$
$743$		−	36.9253i		−	1.35466i	0.735680	−	0.677329i	$-0.236863\pi$
$744$	−34.9783	+	8.21782i	−1.28236	+	0.301280i
$745$		−	10.0974i		−	0.369938i
$746$			62.4636i			2.28696i
$747$	14.7446	−	7.33296i	0.539475	−	0.268299i
$748$		−	4.75372i		−	0.173813i
$749$	11.4891	+	13.2665i	0.419804	+	0.484747i
$750$	−1.00000	−	4.25639i	−0.0365148	−	0.155421i
$751$	−22.3505			−0.815582			−0.407791	−	0.913075i	$-0.633701\pi$
$751$	−22.3505			−0.815582			−0.407791	+	0.913075i	$0.633701\pi$
$752$	−46.9783			−1.71312
$753$	29.4891	−	6.92820i	1.07464	−	0.252478i
$754$		−	62.7586i		−	2.28553i
$755$	3.37228			0.122730
$756$	9.86141	−	59.2945i	0.358656	−	2.15652i
$757$	−54.2337			−1.97116			−0.985578	−	0.169219i	$-0.945875\pi$
$757$	−54.2337			−1.97116			−0.985578	+	0.169219i	$0.945875\pi$
$758$		−	3.75906i		−	0.136535i
$759$	−2.51087	+	0.589907i	−0.0911390	+	0.0214123i
$760$	20.7446			0.752484
$761$	−26.2337			−0.950970			−0.475485	−	0.879724i	$-0.657727\pi$
$761$	−26.2337			−0.950970			−0.475485	+	0.879724i	$0.657727\pi$
$762$	−10.7446	−	45.7330i	−0.389234	−	1.65673i
$763$	−0.233688	+	0.202380i	−0.00846007	+	0.00732664i
$764$		−	68.3972i		−	2.47452i
$765$	−3.68614	+	1.83324i	−0.133273	+	0.0662810i
$766$			44.1485i			1.59515i
$767$			16.0309i			0.578842i
$768$	−52.4674	+	12.3267i	−1.89325	+	0.444803i
$769$			21.1894i			0.764108i	0.924140	+	0.382054i	$0.124783\pi$
$769$			21.1894i			0.764108i	−0.924140	+	0.382054i	$0.875217\pi$
$770$	4.00000	−	3.46410i	0.144150	−	0.124838i
$771$	39.6060	−	9.30506i	1.42637	−	0.335114i
$772$	−97.2119			−3.49873
$773$	−46.6277			−1.67708			−0.838541	−	0.544838i	$-0.816591\pi$
$773$	−46.6277			−1.67708			−0.838541	+	0.544838i	$0.816591\pi$
$774$	22.7446	+	45.7330i	0.817536	+	1.64384i
$775$			3.46410i			0.124434i
$776$	6.51087			0.233727
$777$	−12.7446	+	17.6155i	−0.457209	+	0.631951i
$778$	−34.7446			−1.24565
$779$			20.7846i			0.744686i
$780$	−10.1168	−	43.0612i	−0.362241	−	1.54184i
$781$	−10.7446			−0.384471
$782$	6.51087			0.232828
$783$	−14.1168	−	17.0256i	−0.504495	−	0.608444i
$784$	6.37228	−	44.1485i	0.227581	−	1.57673i
$785$		0			0
$786$	17.4891	+	74.4405i	0.623816	+	2.65521i
$787$		−	46.5253i		−	1.65845i	−0.558916	−	0.829224i	$-0.688783\pi$
$787$		−	46.5253i		−	1.65845i	0.558916	−	0.829224i	$-0.311217\pi$
$788$		−	97.8044i		−	3.48414i
$789$	−5.37228	−	22.8665i	−0.191258	−	0.814070i
$790$		−	8.51278i		−	0.302871i
$791$	17.4891	+	20.1947i	0.621842	+	0.718041i
$792$	12.7446	−	6.33830i	0.452858	−	0.225222i
$793$	−40.4674			−1.43704
$794$	9.25544			0.328463
$795$	3.37228	+	14.3537i	0.119602	+	0.509075i
$796$		−	56.7152i		−	2.01022i
$797$	−42.8614			−1.51823			−0.759114	−	0.650957i	$-0.774368\pi$
$797$	−42.8614			−1.51823			−0.759114	+	0.650957i	$0.774368\pi$
$798$	23.4891	−	32.4665i	0.831506	−	1.14930i
$799$	10.1168			0.357908
$800$		−	4.10891i		−	0.145272i
$801$	8.74456	−	4.34896i	0.308974	−	0.153663i
$802$	6.74456			0.238159
$803$	5.48913			0.193707
$804$	49.7228	−	11.6819i	1.75359	−	0.411990i
$805$	3.25544	+	3.75906i	0.114739	+	0.132489i
$806$			51.0767i			1.79910i
$807$	−14.7446	+	3.46410i	−0.519033	+	0.121942i
$808$			35.9306i			1.26404i
$809$		−	36.7229i		−	1.29111i	−0.763714	−	0.645555i	$-0.776626\pi$
$809$		−	36.7229i		−	1.29111i	0.763714	−	0.645555i	$-0.223374\pi$
$810$	−18.1168	−	13.7089i	−0.636561	−	0.481683i
$811$		−	1.28962i		−	0.0452847i	−0.999744	−	0.0226423i	$-0.992792\pi$
$811$		−	1.28962i		−	0.0452847i	0.999744	−	0.0226423i	$-0.00720790\pi$
$812$	−32.2337	−	37.2203i	−1.13118	−	1.30617i
$813$	6.00000	+	25.5383i	0.210429	+	0.895668i
$814$	−9.48913			−0.332594
$815$	8.00000			0.280228
$816$	−14.7446	+	3.46410i	−0.516163	+	0.121268i
$817$			23.3639i			0.817398i
$818$	−88.4674			−3.09319
$819$	−42.7812	−	17.8641i	−1.49490	−	0.624223i
$820$	26.2337			0.916120
$821$			11.7745i			0.410933i	0.978664	+	0.205466i	$0.0658711\pi$
$821$			11.7745i			0.410933i	−0.978664	+	0.205466i	$0.934129\pi$
$822$	56.4674	−	13.2665i	1.96953	−	0.462722i
$823$	−48.2337			−1.68132			−0.840660	−	0.541563i	$-0.817833\pi$
$823$	−48.2337			−1.68132			−0.840660	+	0.541563i	$0.817833\pi$
$824$	97.2119			3.38654
$825$	−0.313859	−	1.33591i	−0.0109272	−	0.0465103i
$826$	12.0000	+	13.8564i	0.417533	+	0.482126i
$827$		−	18.3152i		−	0.636881i	−0.947943	−	0.318441i	$-0.896841\pi$
$827$		−	18.3152i		−	0.636881i	0.947943	−	0.318441i	$-0.103159\pi$
$828$	10.9783	+	22.0742i	0.381521	+	0.767133i
$829$			32.4665i			1.12761i	0.825908	+	0.563805i	$0.190663\pi$
$829$			32.4665i			1.12761i	−0.825908	+	0.563805i	$0.809337\pi$
$830$		−	13.8564i		−	0.480963i
$831$	−10.5109	+	2.46943i	−0.364618	+	0.0856637i
$832$			13.8564i			0.480384i
$833$	−1.37228	+	9.50744i	−0.0475467	+	0.329413i
$834$	−5.48913	+	1.28962i	−0.190073	+	0.0446559i
$835$	−22.1168			−0.765385
$836$	12.0000			0.415029
$837$	11.4891	+	13.8564i	0.397122	+	0.478947i
$838$			6.92820i			0.239331i
$839$	−53.4891			−1.84665			−0.923325	−	0.384020i	$-0.874539\pi$
$839$	−53.4891			−1.84665			−0.923325	+	0.384020i	$0.874539\pi$
$840$	−22.2337	−	16.0858i	−0.767135	−	0.555013i
$841$	10.8832			0.375281
$842$			64.6381i			2.22758i
$843$	1.91983	+	8.17154i	0.0661224	+	0.281443i
$844$	−26.7446			−0.920586
$845$	−21.1168			−0.726442
$846$	24.8614	+	49.9894i	0.854753	+	1.71867i
$847$	−20.7446	+	17.9653i	−0.712792	+	0.617296i
$848$			54.2458i			1.86281i
$849$	−3.68614	−	15.6896i	−0.126508	−	0.538467i
$850$			3.46410i			0.118818i
$851$		−	8.91754i		−	0.305689i
$852$	23.4891	+	99.9788i	0.804724	+	3.42522i
$853$		−	46.7277i		−	1.59993i	−0.600049	−	0.799963i	$-0.704852\pi$
$853$		−	46.7277i		−	1.59993i	0.600049	−	0.799963i	$-0.295148\pi$
$854$	−34.9783	+	30.2921i	−1.19693	+	1.03657i
$855$	−4.62772	−	9.30506i	−0.158265	−	0.318226i
$856$	39.7228			1.35770
$857$	−22.4674			−0.767471			−0.383735	−	0.923443i	$-0.625363\pi$
$857$	−22.4674			−0.767471			−0.383735	+	0.923443i	$0.625363\pi$
$858$	−4.62772	−	19.6974i	−0.157988	−	0.672457i
$859$			45.4381i			1.55033i	0.631760	+	0.775164i	$0.282333\pi$
$859$			45.4381i			1.55033i	−0.631760	+	0.775164i	$0.717667\pi$
$860$	29.4891			1.00557
$861$	16.1168	−	22.2766i	0.549261	−	0.759185i
$862$	79.9565			2.72333
$863$			28.0078i			0.953395i	0.879067	+	0.476698i	$0.158166\pi$
$863$			28.0078i			0.953395i	−0.879067	+	0.476698i	$0.841834\pi$
$864$	−13.6277	−	16.4356i	−0.463624	−	0.559152i
$865$	16.1168			0.547989
$866$	−6.51087			−0.221249
$867$	−25.4891	+	5.98844i	−0.865656	+	0.203378i
$868$	26.2337	+	30.2921i	0.890429	+	1.02818i
$869$		−	2.67181i		−	0.0906351i
$870$	−18.1168	+	4.25639i	−0.614219	+	0.144305i
$871$		−	39.3947i		−	1.33484i
$872$			0.699713i			0.0236953i
$873$	−1.45245	−	2.92048i	−0.0491581	−	0.0988433i
$874$			16.4356i			0.555944i
$875$	−2.00000	+	1.73205i	−0.0676123	+	0.0585540i
$876$	−12.0000	−	51.0767i	−0.405442	−	1.72572i
$877$	30.4674			1.02881			0.514405	−	0.857547i	$-0.328013\pi$
$877$	30.4674			1.02881			0.514405	+	0.857547i	$0.328013\pi$
$878$	3.25544			0.109866
$879$	−47.4090	+	11.1383i	−1.59906	+	0.375686i
$880$		−	5.04868i		−	0.170191i
$881$	−2.23369			−0.0752549			−0.0376274	−	0.999292i	$-0.511980\pi$
$881$	−2.23369			−0.0752549			−0.0376274	+	0.999292i	$0.511980\pi$
$882$	−50.3505	+	16.5831i	−1.69539	+	0.558383i
$883$	26.5109			0.892162			0.446081	−	0.894993i	$-0.352819\pi$
$883$	26.5109			0.892162			0.446081	+	0.894993i	$0.352819\pi$
$884$			35.0458i			1.17872i
$885$	4.62772	−	1.08724i	0.155559	−	0.0365472i
$886$	−16.7446			−0.562545
$887$	41.4891			1.39307			0.696534	−	0.717524i	$-0.254724\pi$
$887$	41.4891			1.39307			0.696534	+	0.717524i	$0.254724\pi$
$888$	11.2554	+	47.9075i	0.377708	+	1.60767i
$889$	−21.4891	+	18.6101i	−0.720722	+	0.624164i
$890$		−	8.21782i		−	0.275462i
$891$	−5.68614	−	4.30268i	−0.190493	−	0.144145i
$892$		−	91.7610i		−	3.07239i
$893$			25.5383i			0.854608i
$894$	−42.9783	+	10.0974i	−1.43741	+	0.337706i
$895$		−	6.63325i		−	0.221725i
$896$	24.6060	+	28.4125i	0.822028	+	0.949196i
$897$	18.5109	−	4.34896i	0.618060	−	0.145208i
$898$	71.2119			2.37637
$899$	14.7446			0.491759
$900$	−11.7446	+	5.84096i	−0.391485	+	0.194699i
$901$		−	11.6819i		−	0.389181i
$902$	12.0000			0.399556
$903$	18.1168	−	25.0410i	0.602891	−	0.833312i
$904$	60.4674			2.01112
$905$		−	18.6101i		−	0.618622i
$906$	−3.37228	−	14.3537i	−0.112037	−	0.476871i
$907$	8.00000			0.265636			0.132818	−	0.991140i	$-0.457597\pi$
$907$	8.00000			0.265636			0.132818	+	0.991140i	$0.457597\pi$
$908$	68.2337			2.26441
$909$	16.1168	−	8.01544i	0.534562	−	0.265855i
$910$	−29.4891	+	25.5383i	−0.977555	+	0.846587i
$911$			23.6588i			0.783851i	0.919997	+	0.391926i	$0.128191\pi$
$911$			23.6588i			0.783851i	−0.919997	+	0.391926i	$0.871809\pi$
$912$	−8.74456	−	37.2203i	−0.289561	−	1.23249i
$913$		−	4.34896i		−	0.143930i
$914$			83.2482i			2.75361i
$915$	2.74456	+	11.6819i	0.0907324	+	0.386193i
$916$			20.7846i			0.686743i
$917$	34.9783	−	30.2921i	1.15508	−	1.00033i
$918$	11.4891	+	13.8564i	0.379198	+	0.457330i
$919$	−11.3723			−0.375137			−0.187568	−	0.982252i	$-0.560061\pi$
$919$	−11.3723			−0.375137			−0.187568	+	0.982252i	$0.560061\pi$
$920$	11.2554			0.371081
$921$	−2.82473	−	12.0232i	−0.0930782	−	0.396177i
$922$			22.0742i			0.726976i
$923$	79.2119			2.60729
$924$	−12.8614	−	9.30506i	−0.423109	−	0.306114i
$925$	4.74456			0.156000
$926$		−	92.0560i		−	3.02515i
$927$	−21.6861	−	43.6048i	−0.712266	−	1.43217i
$928$	−17.4891			−0.574109
$929$	7.02175			0.230376			0.115188	−	0.993344i	$-0.463253\pi$
$929$	7.02175			0.230376			0.115188	+	0.993344i	$0.463253\pi$
$930$	14.7446	−	3.46410i	0.483493	−	0.113592i
$931$	−24.0000	−	3.46410i	−0.786568	−	0.113531i
$932$		−	16.4356i		−	0.538368i
$933$	34.1168	−	8.01544i	1.11694	−	0.262414i
$934$			35.0458i			1.14673i
$935$			1.08724i			0.0355566i
$936$	−93.9565	+	46.7277i	−3.07106	+	1.52734i
$937$		−	49.9894i		−	1.63308i	−0.577287	−	0.816542i	$-0.695888\pi$
$937$		−	49.9894i		−	1.63308i	0.577287	−	0.816542i	$-0.304112\pi$
$938$	−29.4891	−	34.0511i	−0.962854	−	1.11181i
$939$	−9.68614	−	41.2280i	−0.316095	−	1.34542i
$940$	32.2337			1.05135
$941$	−27.2554			−0.888502			−0.444251	−	0.895902i	$-0.646530\pi$
$941$	−27.2554			−0.888502			−0.444251	+	0.895902i	$0.646530\pi$
$942$		0			0
$943$			11.2772i			0.367235i
$944$	17.4891			0.569223
$945$	−2.25544	+	13.5615i	−0.0733694	+	0.441154i
$946$	13.4891			0.438569
$947$		−	48.2025i		−	1.56637i	−0.621789	−	0.783185i	$-0.713594\pi$
$947$		−	48.2025i		−	1.56637i	0.621789	−	0.783185i	$-0.286406\pi$
$948$	−24.8614	+	5.84096i	−0.807461	+	0.189706i
$949$	−40.4674			−1.31363
$950$	−8.74456			−0.283711
$951$	3.37228	+	14.3537i	0.109354	+	0.465452i
$952$	14.2337	+	16.4356i	0.461316	+	0.532682i
$953$			38.8048i			1.25701i	0.777805	+	0.628506i	$0.216333\pi$
$953$			38.8048i			1.25701i	−0.777805	+	0.628506i	$0.783667\pi$
$954$	57.7228	−	28.7075i	1.86885	−	0.929439i
$955$			15.6434i			0.506207i
$956$		−	68.3972i		−	2.21212i
$957$	−5.68614	+	1.33591i	−0.183807	+	0.0431838i
$958$		−	46.7277i		−	1.50970i
$959$	−22.9783	−	26.5330i	−0.742006	−	0.856795i
$960$	4.00000	−	0.939764i	0.129099	−	0.0303307i
$961$	19.0000			0.612903
$962$	69.9565			2.25549
$963$	−8.86141	−	17.8178i	−0.285555	−	0.574172i
$964$		−	102.153i		−	3.29014i
$965$	22.2337			0.715728
$966$	12.7446	−	17.6155i	0.410050	−	0.566768i
$967$	−24.2337			−0.779303			−0.389651	−	0.920962i	$-0.627405\pi$
$967$	−24.2337			−0.779303			−0.389651	+	0.920962i	$0.627405\pi$
$968$			62.1138i			1.99641i
$969$	1.88316	+	8.01544i	0.0604957	+	0.257493i
$970$	−2.74456			−0.0881226
$971$	−43.2119			−1.38674			−0.693369	−	0.720583i	$-0.743874\pi$
$971$	−43.2119			−1.38674			−0.693369	+	0.720583i	$0.743874\pi$
$972$	−27.6060	+	62.3162i	−0.885462	+	1.99879i
$973$	2.23369	+	2.57924i	0.0716087	+	0.0826867i
$974$		−	36.6303i		−	1.17371i
$975$	2.31386	+	9.84868i	0.0741028	+	0.315410i
$976$			44.1485i			1.41316i
$977$			38.8048i			1.24148i	0.784018	+	0.620738i	$0.213167\pi$
$977$			38.8048i			1.24148i	−0.784018	+	0.620738i	$0.786833\pi$
$978$	−8.00000	−	34.0511i	−0.255812	−	1.08883i
$979$		−	2.57924i		−	0.0824329i
$980$	−4.37228	+	30.2921i	−0.139667	+	0.967644i
$981$	0.313859	−	0.156093i	0.0100208	−	0.00498366i
$982$	27.4891			0.877213
$983$	11.1386			0.355266			0.177633	−	0.984097i	$-0.443156\pi$
$983$	11.1386			0.355266			0.177633	+	0.984097i	$0.443156\pi$
$984$	−14.2337	−	60.5841i	−0.453753	−	1.93135i
$985$			22.3692i			0.712741i
$986$	14.7446			0.469563
$987$	19.8030	−	27.3716i	0.630336	−	0.871247i
$988$	−88.4674			−2.81452
$989$			12.6766i			0.403092i
$990$	−5.37228	+	2.67181i	−0.170742	+	0.0849158i
$991$	2.51087			0.0797606			0.0398803	−	0.999204i	$-0.487302\pi$
$991$	2.51087			0.0797606			0.0398803	+	0.999204i	$0.487302\pi$
$992$	14.2337			0.451920
$993$	−6.74456	+	1.58457i	−0.214032	+	0.0502849i
$994$	68.4674	−	59.2945i	2.17165	−	1.88071i
$995$			12.9715i			0.411226i
$996$	−40.4674	+	9.50744i	−1.28226	+	0.301255i
$997$		−	21.8719i		−	0.692688i	−0.938107	−	0.346344i	$-0.887423\pi$
$997$		−	21.8719i		−	0.692688i	0.938107	−	0.346344i	$-0.112577\pi$
$998$			26.1282i			0.827075i
$999$	18.9783	−	15.7359i	0.600445	−	0.497863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.b.d.41.1	yes	4
3.2	odd	2		105.2.b.c.41.4	yes	4
4.3	odd	2		1680.2.f.g.881.2		4
5.2	odd	4		525.2.g.d.524.7		8
5.3	odd	4		525.2.g.d.524.2		8
5.4	even	2		525.2.b.e.251.4		4
7.2	even	3		735.2.s.g.521.1		4
7.3	odd	6		735.2.s.i.656.2		4
7.4	even	3		735.2.s.j.656.2		4
7.5	odd	6		735.2.s.h.521.1		4
7.6	odd	2		105.2.b.c.41.1	✓	4
12.11	even	2		1680.2.f.h.881.4		4
15.2	even	4		525.2.g.e.524.2		8
15.8	even	4		525.2.g.e.524.7		8
15.14	odd	2		525.2.b.g.251.1		4
21.2	odd	6		735.2.s.i.521.2		4
21.5	even	6		735.2.s.j.521.2		4
21.11	odd	6		735.2.s.h.656.1		4
21.17	even	6		735.2.s.g.656.1		4
21.20	even	2	inner	105.2.b.d.41.4	yes	4
28.27	even	2		1680.2.f.h.881.3		4
35.13	even	4		525.2.g.e.524.1		8
35.27	even	4		525.2.g.e.524.8		8
35.34	odd	2		525.2.b.g.251.4		4
84.83	odd	2		1680.2.f.g.881.1		4
105.62	odd	4		525.2.g.d.524.1		8
105.83	odd	4		525.2.g.d.524.8		8
105.104	even	2		525.2.b.e.251.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.b.c.41.1	✓	4	7.6	odd	2
105.2.b.c.41.4	yes	4	3.2	odd	2
105.2.b.d.41.1	yes	4	1.1	even	1	trivial
105.2.b.d.41.4	yes	4	21.20	even	2	inner
525.2.b.e.251.1		4	105.104	even	2
525.2.b.e.251.4		4	5.4	even	2
525.2.b.g.251.1		4	15.14	odd	2
525.2.b.g.251.4		4	35.34	odd	2
525.2.g.d.524.1		8	105.62	odd	4
525.2.g.d.524.2		8	5.3	odd	4
525.2.g.d.524.7		8	5.2	odd	4
525.2.g.d.524.8		8	105.83	odd	4
525.2.g.e.524.1		8	35.13	even	4
525.2.g.e.524.2		8	15.2	even	4
525.2.g.e.524.7		8	15.8	even	4
525.2.g.e.524.8		8	35.27	even	4
735.2.s.g.521.1		4	7.2	even	3
735.2.s.g.656.1		4	21.17	even	6
735.2.s.h.521.1		4	7.5	odd	6
735.2.s.h.656.1		4	21.11	odd	6
735.2.s.i.521.2		4	21.2	odd	6
735.2.s.i.656.2		4	7.3	odd	6
735.2.s.j.521.2		4	21.5	even	6
735.2.s.j.656.2		4	7.4	even	3
1680.2.f.g.881.1		4	84.83	odd	2
1680.2.f.g.881.2		4	4.3	odd	2
1680.2.f.h.881.3		4	28.27	even	2
1680.2.f.h.881.4		4	12.11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.52434i q^{2} +(1.68614 - 0.396143i) q^{3} -4.37228 q^{4} +1.00000 q^{5} +(-1.00000 - 4.25639i) q^{6} +(-2.00000 + 1.73205i) q^{7} +5.98844i q^{8} +(2.68614 - 1.33591i) q^{9} -2.52434i q^{10} -0.792287i q^{11} +(-7.37228 + 1.73205i) q^{12} +5.84096i q^{13} +(4.37228 + 5.04868i) q^{14} +(1.68614 - 0.396143i) q^{15} +6.37228 q^{16} -1.37228 q^{17} +(-3.37228 - 6.78073i) q^{18} -3.46410i q^{19} -4.37228 q^{20} +(-2.68614 + 3.71277i) q^{21} -2.00000 q^{22} -1.87953i q^{23} +(2.37228 + 10.0974i) q^{24} +1.00000 q^{25} +14.7446 q^{26} +(4.00000 - 3.31662i) q^{27} +(8.74456 - 7.57301i) q^{28} -4.25639i q^{29} +(-1.00000 - 4.25639i) q^{30} +3.46410i q^{31} -4.10891i q^{32} +(-0.313859 - 1.33591i) q^{33} +3.46410i q^{34} +(-2.00000 + 1.73205i) q^{35} +(-11.7446 + 5.84096i) q^{36} +4.74456 q^{37} -8.74456 q^{38} +(2.31386 + 9.84868i) q^{39} +5.98844i q^{40} -6.00000 q^{41} +(9.37228 + 6.78073i) q^{42} -6.74456 q^{43} +3.46410i q^{44} +(2.68614 - 1.33591i) q^{45} -4.74456 q^{46} -7.37228 q^{47} +(10.7446 - 2.52434i) q^{48} +(1.00000 - 6.92820i) q^{49} -2.52434i q^{50} +(-2.31386 + 0.543620i) q^{51} -25.5383i q^{52} +8.51278i q^{53} +(-8.37228 - 10.0974i) q^{54} -0.792287i q^{55} +(-10.3723 - 11.9769i) q^{56} +(-1.37228 - 5.84096i) q^{57} -10.7446 q^{58} +2.74456 q^{59} +(-7.37228 + 1.73205i) q^{60} +6.92820i q^{61} +8.74456 q^{62} +(-3.05842 + 7.32435i) q^{63} +2.37228 q^{64} +5.84096i q^{65} +(-3.37228 + 0.792287i) q^{66} -6.74456 q^{67} +6.00000 q^{68} +(-0.744563 - 3.16915i) q^{69} +(4.37228 + 5.04868i) q^{70} -13.5615i q^{71} +(8.00000 + 16.0858i) q^{72} +6.92820i q^{73} -11.9769i q^{74} +(1.68614 - 0.396143i) q^{75} +15.1460i q^{76} +(1.37228 + 1.58457i) q^{77} +(24.8614 - 5.84096i) q^{78} +3.37228 q^{79} +6.37228 q^{80} +(5.43070 - 7.17687i) q^{81} +15.1460i q^{82} +5.48913 q^{83} +(11.7446 - 16.2333i) q^{84} -1.37228 q^{85} +17.0256i q^{86} +(-1.68614 - 7.17687i) q^{87} +4.74456 q^{88} +3.25544 q^{89} +(-3.37228 - 6.78073i) q^{90} +(-10.1168 - 11.6819i) q^{91} +8.21782i q^{92} +(1.37228 + 5.84096i) q^{93} +18.6101i q^{94} -3.46410i q^{95} +(-1.62772 - 6.92820i) q^{96} -1.08724i q^{97} +(-17.4891 - 2.52434i) q^{98} +(-1.05842 - 2.12819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - 6 q^{4} + 4 q^{5} - 4 q^{6} - 8 q^{7} + 5 q^{9} - 18 q^{12} + 6 q^{14} + q^{15} + 14 q^{16} + 6 q^{17} - 2 q^{18} - 6 q^{20} - 5 q^{21} - 8 q^{22} - 2 q^{24} + 4 q^{25} + 36 q^{26} + 16 q^{27}+ \cdots + 13 q^{99}+O(q^{100}) \) 4 * q + q^3 - 6 * q^4 + 4 * q^5 - 4 * q^6 - 8 * q^7 + 5 * q^9 - 18 * q^12 + 6 * q^14 + q^15 + 14 * q^16 + 6 * q^17 - 2 * q^18 - 6 * q^20 - 5 * q^21 - 8 * q^22 - 2 * q^24 + 4 * q^25 + 36 * q^26 + 16 * q^27 + 12 * q^28 - 4 * q^30 - 7 * q^33 - 8 * q^35 - 24 * q^36 - 4 * q^37 - 12 * q^38 + 15 * q^39 - 24 * q^41 + 26 * q^42 - 4 * q^43 + 5 * q^45 + 4 * q^46 - 18 * q^47 + 20 * q^48 + 4 * q^49 - 15 * q^51 - 22 * q^54 - 30 * q^56 + 6 * q^57 - 20 * q^58 - 12 * q^59 - 18 * q^60 + 12 * q^62 + 5 * q^63 - 2 * q^64 - 2 * q^66 - 4 * q^67 + 24 * q^68 + 20 * q^69 + 6 * q^70 + 32 * q^72 + q^75 - 6 * q^77 + 42 * q^78 + 2 * q^79 + 14 * q^80 - 7 * q^81 - 24 * q^83 + 24 * q^84 + 6 * q^85 - q^87 - 4 * q^88 + 36 * q^89 - 2 * q^90 - 6 * q^91 - 6 * q^93 - 18 * q^96 - 24 * q^98 + 13 * q^99

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