LMFDB - Embedded newform 189.2.h.b.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(37,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

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

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

chi := DirichletCharacter("189.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.1
Root			$-1.02682 - 1.77851i$ of defining polynomial
Character	$\chi$	$=$	189.46
Dual form			189.2.h.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.05365 q^{2} +2.21746 q^{4} +(-0.0731228 + 0.126652i) q^{5} +(-2.33035 + 1.25278i) q^{7} -0.446582 q^{8} +O(q^{10})$	\(q-2.05365 q^{2} +2.21746 q^{4} +(-0.0731228 + 0.126652i) q^{5} +(-2.33035 + 1.25278i) q^{7} -0.446582 q^{8} +(0.150168 - 0.260099i) q^{10} +(0.832020 + 1.44110i) q^{11} +(0.0999454 + 0.173111i) q^{13} +(4.78572 - 2.57276i) q^{14} -3.51780 q^{16} +(-3.13555 + 5.43093i) q^{17} +(3.45879 + 5.99080i) q^{19} +(-0.162147 + 0.280847i) q^{20} +(-1.70867 - 2.95951i) q^{22} +(-3.09092 + 5.35363i) q^{23} +(2.48931 + 4.31160i) q^{25} +(-0.205252 - 0.355508i) q^{26} +(-5.16746 + 2.77798i) q^{28} +(2.46757 - 4.27396i) q^{29} -2.51780 q^{31} +8.11747 q^{32} +(6.43931 - 11.1532i) q^{34} +(0.0117348 - 0.386752i) q^{35} +(-3.50023 - 6.06257i) q^{37} +(-7.10312 - 12.3030i) q^{38} +(0.0326554 - 0.0565608i) q^{40} +(-1.15895 - 2.00736i) q^{41} +(-0.940993 + 1.62985i) q^{43} +(1.84497 + 3.19558i) q^{44} +(6.34765 - 10.9944i) q^{46} +1.81177 q^{47} +(3.86110 - 5.83883i) q^{49} +(-5.11215 - 8.85451i) q^{50} +(0.221625 + 0.383865i) q^{52} +(2.67307 - 4.62989i) q^{53} -0.243359 q^{55} +(1.04069 - 0.559468i) q^{56} +(-5.06752 + 8.77720i) q^{58} +4.57099 q^{59} -0.678276 q^{61} +5.17066 q^{62} -9.63481 q^{64} -0.0292332 q^{65} -6.18684 q^{67} +(-6.95296 + 12.0429i) q^{68} +(-0.0240991 + 0.794251i) q^{70} -1.27749 q^{71} +(-0.778603 + 1.34858i) q^{73} +(7.18823 + 12.4504i) q^{74} +(7.66972 + 13.2843i) q^{76} +(-3.74428 - 2.31594i) q^{77} +12.7957 q^{79} +(0.257231 - 0.445537i) q^{80} +(2.38008 + 4.12241i) q^{82} +(-3.75687 + 6.50709i) q^{83} +(-0.458561 - 0.794251i) q^{85} +(1.93247 - 3.34713i) q^{86} +(-0.371566 - 0.643571i) q^{88} +(-4.53394 - 7.85301i) q^{89} +(-0.449777 - 0.278199i) q^{91} +(-6.85398 + 11.8714i) q^{92} -3.72074 q^{94} -1.01167 q^{95} +(-3.98514 + 6.90246i) q^{97} +(-7.92933 + 11.9909i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) $ 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8	$ 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8} - 7 q^{10} - 4 q^{11} - 8 q^{13} + 20 q^{14} - 4 q^{16} - 12 q^{17} + q^{19} - 5 q^{20} - q^{22} - 3 q^{23} - q^{25} - 11 q^{26} - 2 q^{28} - 7 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{34} - 5 q^{35} - 20 q^{38} - 3 q^{40} - 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} + 54 q^{47} - 8 q^{49} - 19 q^{50} - 10 q^{52} + 21 q^{53} + 4 q^{55} - 18 q^{56} - 10 q^{58} + 60 q^{59} + 28 q^{61} + 12 q^{62} - 50 q^{64} - 22 q^{65} + 4 q^{67} - 27 q^{68} + 40 q^{70} + 6 q^{71} + 15 q^{73} + 36 q^{74} + 5 q^{76} - 11 q^{77} + 8 q^{79} - 20 q^{80} - 5 q^{82} - 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} - 28 q^{89} - 4 q^{91} - 27 q^{92} + 6 q^{94} - 28 q^{95} - 12 q^{97} - 59 q^{98}+O(q^{100}) $ 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8 - 7 * q^10 - 4 * q^11 - 8 * q^13 + 20 * q^14 - 4 * q^16 - 12 * q^17 + q^19 - 5 * q^20 - q^22 - 3 * q^23 - q^25 - 11 * q^26 - 2 * q^28 - 7 * q^29 + 6 * q^31 - 4 * q^32 + 3 * q^34 - 5 * q^35 - 20 * q^38 - 3 * q^40 - 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 + 54 * q^47 - 8 * q^49 - 19 * q^50 - 10 * q^52 + 21 * q^53 + 4 * q^55 - 18 * q^56 - 10 * q^58 + 60 * q^59 + 28 * q^61 + 12 * q^62 - 50 * q^64 - 22 * q^65 + 4 * q^67 - 27 * q^68 + 40 * q^70 + 6 * q^71 + 15 * q^73 + 36 * q^74 + 5 * q^76 - 11 * q^77 + 8 * q^79 - 20 * q^80 - 5 * q^82 - 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 - 28 * q^89 - 4 * q^91 - 27 * q^92 + 6 * q^94 - 28 * q^95 - 12 * q^97 - 59 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.05365			−1.45215			−0.726073	−	0.687617i	$-0.758657\pi$
$2$	−2.05365			−1.45215			−0.726073	+	0.687617i	$0.758657\pi$
$3$		0			0
$3$		0			0
$4$	2.21746			1.10873
$5$	−0.0731228	+	0.126652i	−0.0327015	+	0.0566407i	−0.881913	−	0.471412i	$-0.843744\pi$
$5$	−0.0731228	+	0.126652i	−0.0327015	+	0.0566407i	0.849211	+	0.528053i	$0.177078\pi$
$6$		0			0
$7$	−2.33035	+	1.25278i	−0.880791	+	0.473505i
$7$	−2.33035	+	1.25278i	−0.880791	+	0.473505i
$8$	−0.446582			−0.157891
$9$		0			0
$10$	0.150168	−	0.260099i	0.0474874	−	0.0822506i
$11$	0.832020	+	1.44110i	0.250864	+	0.434508i	0.963764	−	0.266757i	$-0.0859521\pi$
$11$	0.832020	+	1.44110i	0.250864	+	0.434508i	−0.712900	+	0.701265i	$0.752619\pi$
$12$		0			0
$13$	0.0999454	+	0.173111i	0.0277199	+	0.0480122i	0.879553	−	0.475802i	$-0.157842\pi$
$13$	0.0999454	+	0.173111i	0.0277199	+	0.0480122i	−0.851833	+	0.523814i	$0.824509\pi$
$14$	4.78572	−	2.57276i	1.27904	−	0.687599i
$15$		0			0
$16$	−3.51780			−0.879449
$17$	−3.13555	+	5.43093i	−0.760483	+	1.31720i	0.182119	+	0.983277i	$0.441704\pi$
$17$	−3.13555	+	5.43093i	−0.760483	+	1.31720i	−0.942602	+	0.333919i	$0.891629\pi$
$18$		0			0
$19$	3.45879	+	5.99080i	0.793500	+	1.37438i	0.923787	+	0.382907i	$0.125077\pi$
$19$	3.45879	+	5.99080i	0.793500	+	1.37438i	−0.130287	+	0.991476i	$0.541590\pi$
$20$	−0.162147	+	0.280847i	−0.0362571	+	0.0627992i
$21$		0			0
$22$	−1.70867	−	2.95951i	−0.364291	−	0.630970i
$23$	−3.09092	+	5.35363i	−0.644501	+	1.11631i	0.339916	+	0.940456i	$0.389601\pi$
$23$	−3.09092	+	5.35363i	−0.644501	+	1.11631i	−0.984417	+	0.175852i	$0.943732\pi$
$24$		0			0
$25$	2.48931	+	4.31160i	0.497861	+	0.862321i
$26$	−0.205252	−	0.355508i	−0.0402533	−	0.0697208i
$27$		0			0
$28$	−5.16746	+	2.77798i	−0.976559	+	0.524989i
$29$	2.46757	−	4.27396i	0.458217	−	0.793655i	−0.540650	−	0.841248i	$-0.681822\pi$
$29$	2.46757	−	4.27396i	0.458217	−	0.793655i	0.998867	+	0.0475930i	$0.0151551\pi$
$30$		0			0
$31$	−2.51780			−0.452209			−0.226105	−	0.974103i	$-0.572599\pi$
$31$	−2.51780			−0.452209			−0.226105	+	0.974103i	$0.572599\pi$
$32$	8.11747			1.43498
$33$		0			0
$34$	6.43931	−	11.1532i	1.10433	−	1.91276i
$35$	0.0117348	−	0.386752i	0.00198354	−	0.0653730i
$36$		0			0
$37$	−3.50023	−	6.06257i	−0.575434	−	0.996681i	−0.995994	−	0.0894162i	$-0.971500\pi$
$37$	−3.50023	−	6.06257i	−0.575434	−	0.996681i	0.420560	−	0.907264i	$-0.361833\pi$
$38$	−7.10312	−	12.3030i	−1.15228	−	1.99581i
$39$		0			0
$40$	0.0326554	−	0.0565608i	0.00516327	−	0.00894304i
$41$	−1.15895	−	2.00736i	−0.180998	−	0.313498i	0.761223	−	0.648491i	$-0.224599\pi$
$41$	−1.15895	−	2.00736i	−0.180998	−	0.313498i	−0.942221	+	0.334993i	$0.891266\pi$
$42$		0			0
$43$	−0.940993	+	1.62985i	−0.143500	+	0.248550i	−0.928812	−	0.370550i	$-0.879169\pi$
$43$	−0.940993	+	1.62985i	−0.143500	+	0.248550i	0.785312	+	0.619100i	$0.212502\pi$
$44$	1.84497	+	3.19558i	0.278140	+	0.481752i
$45$		0			0
$46$	6.34765	−	10.9944i	0.935910	−	1.62104i
$47$	1.81177			0.264275			0.132137	−	0.991231i	$-0.457816\pi$
$47$	1.81177			0.264275			0.132137	+	0.991231i	$0.457816\pi$
$48$		0			0
$49$	3.86110	−	5.83883i	0.551586	−	0.834118i
$50$	−5.11215	−	8.85451i	−0.722967	−	1.25222i
$51$		0			0
$52$	0.221625	+	0.383865i	0.0307338	+	0.0532325i
$53$	2.67307	−	4.62989i	0.367174	−	0.635964i	−0.621948	−	0.783058i	$-0.713659\pi$
$53$	2.67307	−	4.62989i	0.367174	−	0.635964i	0.989123	+	0.147094i	$0.0469920\pi$
$54$		0			0
$55$	−0.243359			−0.0328145
$56$	1.04069	−	0.559468i	0.139069	−	0.0747621i
$57$		0			0
$58$	−5.06752	+	8.77720i	−0.665398	+	1.15250i
$59$	4.57099			0.595092			0.297546	−	0.954708i	$-0.403832\pi$
$59$	4.57099			0.595092			0.297546	+	0.954708i	$0.403832\pi$
$60$		0			0
$61$	−0.678276			−0.0868443			−0.0434221	−	0.999057i	$-0.513826\pi$
$61$	−0.678276			−0.0868443			−0.0434221	+	0.999057i	$0.513826\pi$
$62$	5.17066			0.656674
$63$		0			0
$64$	−9.63481			−1.20435
$65$	−0.0292332			−0.00362593
$66$		0			0
$67$	−6.18684			−0.755842			−0.377921	−	0.925838i	$-0.623361\pi$
$67$	−6.18684			−0.755842			−0.377921	+	0.925838i	$0.623361\pi$
$68$	−6.95296	+	12.0429i	−0.843170	+	1.46041i
$69$		0			0
$70$	−0.0240991	+	0.794251i	−0.00288039	+	0.0949311i
$71$	−1.27749			−0.151611			−0.0758053	−	0.997123i	$-0.524153\pi$
$71$	−1.27749			−0.151611			−0.0758053	+	0.997123i	$0.524153\pi$
$72$		0			0
$73$	−0.778603	+	1.34858i	−0.0911286	+	0.157839i	−0.907986	−	0.419000i	$-0.862381\pi$
$73$	−0.778603	+	1.34858i	−0.0911286	+	0.157839i	0.816858	+	0.576839i	$0.195714\pi$
$74$	7.18823	+	12.4504i	0.835614	+	1.44733i
$75$		0			0
$76$	7.66972	+	13.2843i	0.879777	+	1.52382i
$77$	−3.74428	−	2.31594i	−0.426700	−	0.263926i
$78$		0			0
$79$	12.7957			1.43963			0.719817	−	0.694164i	$-0.244226\pi$
$79$	12.7957			1.43963			0.719817	+	0.694164i	$0.244226\pi$
$80$	0.257231	−	0.445537i	0.0287593	−	0.0498126i
$81$		0			0
$82$	2.38008	+	4.12241i	0.262835	+	0.455244i
$83$	−3.75687	+	6.50709i	−0.412370	+	0.714246i	−0.995148	−	0.0983854i	$-0.968632\pi$
$83$	−3.75687	+	6.50709i	−0.412370	+	0.714246i	0.582778	+	0.812631i	$0.301966\pi$
$84$		0			0
$85$	−0.458561	−	0.794251i	−0.0497379	−	0.0861486i
$86$	1.93247	−	3.34713i	0.208383	−	0.360930i
$87$		0			0
$88$	−0.371566	−	0.643571i	−0.0396090	−	0.0686048i
$89$	−4.53394	−	7.85301i	−0.480597	−	0.832418i	0.519155	−	0.854680i	$-0.326247\pi$
$89$	−4.53394	−	7.85301i	−0.480597	−	0.832418i	−0.999752	+	0.0222619i	$0.992913\pi$
$90$		0			0
$91$	−0.449777	−	0.278199i	−0.0471494	−	0.0291632i
$92$	−6.85398	+	11.8714i	−0.714577	+	1.23768i
$93$		0			0
$94$	−3.72074			−0.383765
$95$	−1.01167			−0.103795
$96$		0			0
$97$	−3.98514	+	6.90246i	−0.404630	+	0.700839i	−0.994278	−	0.106821i	$-0.965933\pi$
$97$	−3.98514	+	6.90246i	−0.404630	+	0.700839i	0.589649	+	0.807660i	$0.299266\pi$
$98$	−7.92933	+	11.9909i	−0.800983	+	1.21126i
$99$		0			0
$100$	5.51993	+	9.56080i	0.551993	+	0.956080i
$101$	7.42150	+	12.8544i	0.738467	+	1.27906i	0.953186	+	0.302386i	$0.0977832\pi$
$101$	7.42150	+	12.8544i	0.738467	+	1.27906i	−0.214719	+	0.976676i	$0.568883\pi$
$102$		0			0
$103$	0.101974	−	0.176624i	0.0100478	−	0.0174033i	−0.860958	−	0.508676i	$-0.830135\pi$
$103$	0.101974	−	0.176624i	0.0100478	−	0.0174033i	0.871006	+	0.491273i	$0.163468\pi$
$104$	−0.0446339	−	0.0773081i	−0.00437671	−	0.00758068i
$105$		0			0
$106$	−5.48953	+	9.50815i	−0.533191	+	0.923513i
$107$	−3.48444	−	6.03524i	−0.336854	−	0.583448i	0.646985	−	0.762503i	$-0.276030\pi$
$107$	−3.48444	−	6.03524i	−0.336854	−	0.583448i	−0.983839	+	0.179054i	$0.942696\pi$
$108$		0			0
$109$	3.33058	−	5.76874i	0.319012	−	0.552545i	−0.661270	−	0.750148i	$-0.729982\pi$
$109$	3.33058	−	5.76874i	0.319012	−	0.552545i	0.980282	+	0.197603i	$0.0633157\pi$
$110$	0.499772			0.0476514
$111$		0			0
$112$	8.19771	−	4.40701i	0.774611	−	0.416424i
$113$	0.0193234	+	0.0334691i	0.00181779	+	0.00314851i	0.866933	−	0.498425i	$-0.166088\pi$
$113$	0.0193234	+	0.0334691i	0.00181779	+	0.00314851i	−0.865115	+	0.501573i	$0.832755\pi$
$114$		0			0
$115$	−0.452033	−	0.782945i	−0.0421523	−	0.0730100i
$116$	5.47174	−	9.47733i	0.508038	−	0.879948i
$117$		0			0
$118$	−9.38718			−0.864160
$119$	0.503195	−	16.5841i	0.0461278	−	1.52027i
$120$		0			0
$121$	4.11548	−	7.12823i	0.374135	−	0.648021i
$122$	1.39294			0.126111
$123$		0			0
$124$	−5.58311			−0.501378
$125$	−1.45933			−0.130526
$126$		0			0
$127$	13.4788			1.19605			0.598027	−	0.801476i	$-0.295952\pi$
$127$	13.4788			1.19605			0.598027	+	0.801476i	$0.295952\pi$
$128$	3.55154			0.313915
$129$		0			0
$130$	0.0600345			0.00526538
$131$	−9.91665	+	17.1761i	−0.866422	+	1.50069i	−0.000793988		1.00000i	$0.500253\pi$
$131$	−9.91665	+	17.1761i	−0.866422	+	1.50069i	−0.865628	+	0.500687i	$0.833081\pi$
$132$		0			0
$133$	−15.5653	−	9.62759i	−1.34969	−	0.834818i
$134$	12.7056			1.09759
$135$		0			0
$136$	1.40028	−	2.42536i	0.120073	−	0.207973i
$137$	−3.22255	−	5.58162i	−0.275321	−	0.476870i	0.694895	−	0.719111i	$-0.255451\pi$
$137$	−3.22255	−	5.58162i	−0.275321	−	0.476870i	−0.970216	+	0.242241i	$0.922117\pi$
$138$		0			0
$139$	6.26527	+	10.8518i	0.531413	+	0.920435i	0.999328	+	0.0366611i	$0.0116722\pi$
$139$	6.26527	+	10.8518i	0.531413	+	0.920435i	−0.467914	+	0.883774i	$0.654994\pi$
$140$	0.0260214	−	0.857606i	0.00219921	−	0.0724809i
$141$		0			0
$142$	2.62352			0.220161
$143$	−0.166313	+	0.288063i	−0.0139078	+	0.0240890i
$144$		0			0
$145$	0.360872	+	0.625048i	0.0299688	+	0.0519074i
$146$	1.59897	−	2.76950i	0.132332	−	0.229206i
$147$		0			0
$148$	−7.76161	−	13.4435i	−0.638000	−	1.10505i
$149$	8.88364	−	15.3869i	0.727776	−	1.26054i	−0.230045	−	0.973180i	$-0.573887\pi$
$149$	8.88364	−	15.3869i	0.727776	−	1.26054i	0.957821	−	0.287365i	$-0.0927792\pi$
$150$		0			0
$151$	−4.23300	−	7.33177i	−0.344476	−	0.596651i	0.640782	−	0.767723i	$-0.278610\pi$
$151$	−4.23300	−	7.33177i	−0.344476	−	0.596651i	−0.985259	+	0.171072i	$0.945277\pi$
$152$	−1.54463	−	2.67538i	−0.125286	−	0.217002i
$153$		0			0
$154$	7.68942	+	4.75612i	0.619631	+	0.383259i
$155$	0.184108	−	0.318885i	0.0147879	−	0.0256135i
$156$		0			0
$157$	5.69935			0.454858			0.227429	−	0.973795i	$-0.426968\pi$
$157$	5.69935			0.454858			0.227429	+	0.973795i	$0.426968\pi$
$158$	−26.2779			−2.09056
$159$		0			0
$160$	−0.593572	+	1.02810i	−0.0469260	+	0.0812782i
$161$	0.496032	−	16.3481i	0.0390928	−	1.28841i
$162$		0			0
$163$	−1.06267	−	1.84060i	−0.0832349	−	0.144167i	0.821403	−	0.570349i	$-0.193192\pi$
$163$	−1.06267	−	1.84060i	−0.0832349	−	0.144167i	−0.904638	+	0.426181i	$0.859859\pi$
$164$	−2.56993	−	4.45125i	−0.200678	−	0.347584i
$165$		0			0
$166$	7.71528	−	13.3632i	0.598821	−	1.03719i
$167$	5.78723	+	10.0238i	0.447829	+	0.775663i	0.998244	−	0.0592278i	$-0.0188638\pi$
$167$	5.78723	+	10.0238i	0.447829	+	0.775663i	−0.550415	+	0.834891i	$0.685530\pi$
$168$		0			0
$169$	6.48002	−	11.2237i	0.498463	−	0.863364i
$170$	0.941721	+	1.63111i	0.0722267	+	0.125100i
$171$		0			0
$172$	−2.08661	+	3.61412i	−0.159103	+	0.275574i
$173$	15.9109			1.20968			0.604842	−	0.796345i	$-0.293236\pi$
$173$	15.9109			1.20968			0.604842	+	0.796345i	$0.293236\pi$
$174$		0			0
$175$	−11.2024	−	6.92902i	−0.846825	−	0.523785i
$176$	−2.92688	−	5.06950i	−0.220622	−	0.382128i
$177$		0			0
$178$	9.31110	+	16.1273i	0.697897	+	1.20879i
$179$	−3.87665	+	6.71456i	−0.289755	+	0.501870i	−0.973751	−	0.227615i	$-0.926907\pi$
$179$	−3.87665	+	6.71456i	−0.289755	+	0.501870i	0.683996	+	0.729485i	$0.260240\pi$
$180$		0			0
$181$	−12.1618			−0.903982			−0.451991	−	0.892022i	$-0.649286\pi$
$181$	−12.1618			−0.903982			−0.451991	+	0.892022i	$0.649286\pi$
$182$	0.923682	+	0.571323i	0.0684679	+	0.0423493i
$183$		0			0
$184$	1.38035	−	2.39084i	0.101761	−	0.176255i
$185$	1.02379			0.0752703
$186$		0			0
$187$	−10.4354			−0.763110
$188$	4.01754			0.293009
$189$		0			0
$190$	2.07760			0.150725
$191$	4.96765			0.359447			0.179723	−	0.983717i	$-0.442480\pi$
$191$	4.96765			0.359447			0.179723	+	0.983717i	$0.442480\pi$
$192$		0			0
$193$	−14.9044			−1.07284			−0.536422	−	0.843950i	$-0.680224\pi$
$193$	−14.9044			−1.07284			−0.536422	+	0.843950i	$0.680224\pi$
$194$	8.18406	−	14.1752i	0.587581	−	1.01772i
$195$		0			0
$196$	8.56183	−	12.9474i	0.611559	−	0.924811i
$197$	21.2608			1.51477			0.757386	−	0.652968i	$-0.226476\pi$
$197$	21.2608			1.51477			0.757386	+	0.652968i	$0.226476\pi$
$198$		0			0
$199$	−9.97208	+	17.2722i	−0.706902	+	1.22439i	0.259098	+	0.965851i	$0.416575\pi$
$199$	−9.97208	+	17.2722i	−0.706902	+	1.22439i	−0.966001	+	0.258540i	$0.916759\pi$
$200$	−1.11168	−	1.92549i	−0.0786077	−	0.136152i
$201$		0			0
$202$	−15.2411	−	26.3984i	−1.07236	−	1.85739i
$203$	−0.395997	+	13.0512i	−0.0277935	+	0.916012i
$204$		0			0
$205$	0.338983			0.0236756
$206$	−0.209419	+	0.362724i	−0.0145909	+	0.0252722i
$207$		0			0
$208$	−0.351587	−	0.608967i	−0.0243782	−	0.0422243i
$209$	−5.75556	+	9.96893i	−0.398121	+	0.689565i
$210$		0			0
$211$	11.7569	+	20.3636i	0.809381	+	1.40189i	0.913293	+	0.407303i	$0.133531\pi$
$211$	11.7569	+	20.3636i	0.809381	+	1.40189i	−0.103912	+	0.994587i	$0.533136\pi$
$212$	5.92742	−	10.2666i	0.407097	−	0.705112i
$213$		0			0
$214$	7.15581	+	12.3942i	0.489161	+	0.847252i
$215$	−0.137616	−	0.238358i	−0.00938535	−	0.0162559i
$216$		0			0
$217$	5.86735	−	3.15424i	0.398302	−	0.214123i
$218$	−6.83983	+	11.8469i	−0.463252	+	0.802376i
$219$		0			0
$220$	−0.539638			−0.0363824
$221$	−1.25354			−0.0843220
$222$		0			0
$223$	2.03052	−	3.51696i	0.135974	−	0.235513i	−0.789995	−	0.613113i	$-0.789917\pi$
$223$	2.03052	−	3.51696i	0.135974	−	0.235513i	0.925969	+	0.377600i	$0.123250\pi$
$224$	−18.9166	+	10.1694i	−1.26392	+	0.679470i
$225$		0			0
$226$	−0.0396834	−	0.0687336i	−0.00263970	−	0.00457209i
$227$	−1.92643	−	3.33667i	−0.127861	−	0.221462i	0.794986	−	0.606627i	$-0.207478\pi$
$227$	−1.92643	−	3.33667i	−0.127861	−	0.221462i	−0.922848	+	0.385165i	$0.874145\pi$
$228$		0			0
$229$	−6.55812	+	11.3590i	−0.433373	+	0.750624i	−0.997161	−	0.0752952i	$-0.976010\pi$
$229$	−6.55812	+	11.3590i	−0.433373	+	0.750624i	0.563788	+	0.825919i	$0.309343\pi$
$230$	0.928316	+	1.60789i	0.0612113	+	0.106021i
$231$		0			0
$232$	−1.10197	+	1.90868i	−0.0723481	+	0.125311i
$233$	8.75115	+	15.1574i	0.573307	+	0.992997i	0.996223	+	0.0868284i	$0.0276732\pi$
$233$	8.75115	+	15.1574i	0.573307	+	0.992997i	−0.422916	+	0.906169i	$0.638993\pi$
$234$		0			0
$235$	−0.132482	+	0.229466i	−0.00864218	+	0.0149687i
$236$	10.1360			0.659795
$237$		0			0
$238$	−1.03338	+	34.0580i	−0.0669843	+	2.20765i
$239$	−3.65857	−	6.33683i	−0.236653	−	0.409895i	0.723099	−	0.690745i	$-0.242717\pi$
$239$	−3.65857	−	6.33683i	−0.236653	−	0.409895i	−0.959752	+	0.280849i	$0.909384\pi$
$240$		0			0
$241$	−3.11553	−	5.39626i	−0.200689	−	0.347604i	0.748062	−	0.663629i	$-0.230985\pi$
$241$	−3.11553	−	5.39626i	−0.200689	−	0.347604i	−0.948751	+	0.316026i	$0.897651\pi$
$242$	−8.45174	+	14.6389i	−0.543299	+	0.941021i
$243$		0			0
$244$	−1.50405			−0.0962868
$245$	0.457167	+	0.915969i	0.0292074	+	0.0585191i
$246$		0			0
$247$	−0.691380	+	1.19751i	−0.0439915	+	0.0761954i
$248$	1.12440			0.0713997
$249$		0			0
$250$	2.99694			0.189543
$251$	−5.65283			−0.356803			−0.178402	−	0.983958i	$-0.557093\pi$
$251$	−5.65283			−0.356803			−0.178402	+	0.983958i	$0.557093\pi$
$252$		0			0
$253$	−10.2868			−0.646727
$254$	−27.6808			−1.73684
$255$		0			0
$256$	11.9760			0.748501
$257$	5.90082	−	10.2205i	0.368083	−	0.637539i	−0.621183	−	0.783666i	$-0.713347\pi$
$257$	5.90082	−	10.2205i	0.368083	−	0.637539i	0.989266	+	0.146127i	$0.0466808\pi$
$258$		0			0
$259$	15.7518	+	9.74293i	0.978770	+	0.605396i
$260$	−0.0648233			−0.00402017
$261$		0			0
$262$	20.3653	−	35.2737i	1.25817	−	2.17922i
$263$	−11.1200	−	19.2605i	−0.685691	−	1.18765i	−0.973219	−	0.229879i	$-0.926167\pi$
$263$	−11.1200	−	19.2605i	−0.685691	−	1.18765i	0.287528	−	0.957772i	$-0.407166\pi$
$264$		0			0
$265$	0.390925	+	0.677101i	0.0240143	+	0.0415940i
$266$	31.9657	+	19.7716i	1.95994	+	1.21228i
$267$		0			0
$268$	−13.7191			−0.838024
$269$	1.19442	−	2.06880i	0.0728251	−	0.126137i	−0.827313	−	0.561741i	$-0.810132\pi$
$269$	1.19442	−	2.06880i	0.0728251	−	0.126137i	0.900138	+	0.435604i	$0.143465\pi$
$270$		0			0
$271$	−11.6129	−	20.1142i	−0.705435	−	1.22185i	−0.966534	−	0.256537i	$-0.917419\pi$
$271$	−11.6129	−	20.1142i	−0.705435	−	1.22185i	0.261100	−	0.965312i	$-0.415915\pi$
$272$	11.0302	−	19.1049i	0.668806	−	1.15841i
$273$		0			0
$274$	6.61797	+	11.4627i	0.399806	+	0.692484i
$275$	−4.14231	+	7.17469i	−0.249790	+	0.432650i
$276$		0			0
$277$	2.30900	+	3.99931i	0.138734	+	0.240295i	0.927018	−	0.375017i	$-0.122363\pi$
$277$	2.30900	+	3.99931i	0.138734	+	0.240295i	−0.788283	+	0.615312i	$0.789030\pi$
$278$	−12.8666	−	22.2857i	−0.771690	−	1.33661i
$279$		0			0
$280$	−0.00524055	+	0.172716i	−0.000313183	+	0.0103218i
$281$	−5.90841	+	10.2337i	−0.352466	+	0.610489i	−0.986681	−	0.162668i	$-0.947990\pi$
$281$	−5.90841	+	10.2337i	−0.352466	+	0.610489i	0.634215	+	0.773157i	$0.281324\pi$
$282$		0			0
$283$	15.8497			0.942165			0.471082	−	0.882089i	$-0.343863\pi$
$283$	15.8497			0.942165			0.471082	+	0.882089i	$0.343863\pi$
$284$	−2.83279			−0.168095
$285$		0			0
$286$	0.341548	−	0.591579i	0.0201962	−	0.0349808i
$287$	5.21555	+	3.22596i	0.307864	+	0.190422i
$288$		0			0
$289$	−11.1634	−	19.3355i	−0.656669	−	1.13738i
$290$	−0.741102	−	1.28363i	−0.0435190	−	0.0753772i
$291$		0			0
$292$	−1.72652	+	2.99042i	−0.101037	+	0.175001i
$293$	−7.04804	−	12.2076i	−0.411751	−	0.713173i	0.583330	−	0.812235i	$-0.301749\pi$
$293$	−7.04804	−	12.2076i	−0.411751	−	0.713173i	−0.995081	+	0.0990615i	$0.968416\pi$
$294$		0			0
$295$	−0.334243	+	0.578927i	−0.0194604	+	0.0337064i
$296$	1.56314	+	2.70744i	0.0908557	+	0.157367i
$297$		0			0
$298$	−18.2438	+	31.5993i	−1.05684	+	1.83050i
$299$	−1.23569			−0.0714619
$300$		0			0
$301$	0.151011	−	4.97698i	0.00870413	−	0.286868i
$302$	8.69307	+	15.0568i	0.500230	+	0.866424i
$303$		0			0
$304$	−12.1673	−	21.0744i	−0.697843	−	1.20870i
$305$	0.0495974	−	0.0859053i	0.00283994	−	0.00491892i
$306$		0			0
$307$	27.3916			1.56332			0.781660	−	0.623704i	$-0.214373\pi$
$307$	27.3916			1.56332			0.781660	+	0.623704i	$0.214373\pi$
$308$	−8.30279	−	5.13550i	−0.473095	−	0.292622i
$309$		0			0
$310$	−0.378093	+	0.654877i	−0.0214742	+	0.0371945i
$311$	14.0557			0.797026			0.398513	−	0.917163i	$-0.369526\pi$
$311$	14.0557			0.797026			0.398513	+	0.917163i	$0.369526\pi$
$312$		0			0
$313$	21.7446			1.22908			0.614540	−	0.788886i	$-0.289342\pi$
$313$	21.7446			1.22908			0.614540	+	0.788886i	$0.289342\pi$
$314$	−11.7045			−0.660520
$315$		0			0
$316$	28.3740			1.59616
$317$	−8.56297			−0.480944			−0.240472	−	0.970656i	$-0.577302\pi$
$317$	−8.56297			−0.480944			−0.240472	+	0.970656i	$0.577302\pi$
$318$		0			0
$319$	8.21228			0.459799
$320$	0.704524	−	1.22027i	0.0393841	−	0.0682153i
$321$		0			0
$322$	−1.01867	+	33.5731i	−0.0567684	+	1.87096i
$323$	−43.3808			−2.41377
$324$		0			0
$325$	−0.497589	+	0.861850i	−0.0276013	+	0.0478068i
$326$	2.18235	+	3.77995i	0.120869	+	0.209352i
$327$		0			0
$328$	0.517568	+	0.896453i	0.0285779	+	0.0494984i
$329$	−4.22208	+	2.26975i	−0.232771	+	0.125135i
$330$		0			0
$331$	10.8472			0.596216			0.298108	−	0.954532i	$-0.403644\pi$
$331$	10.8472			0.596216			0.298108	+	0.954532i	$0.403644\pi$
$332$	−8.33070	+	14.4292i	−0.457207	+	0.791905i
$333$		0			0
$334$	−11.8849	−	20.5853i	−0.650314	−	1.12638i
$335$	0.452399	−	0.783578i	0.0247172	−	0.0428114i
$336$		0			0
$337$	1.67411	+	2.89964i	0.0911945	+	0.157954i	0.908014	−	0.418940i	$-0.137598\pi$
$337$	1.67411	+	2.89964i	0.0911945	+	0.157954i	−0.816819	+	0.576893i	$0.804265\pi$
$338$	−13.3077	+	23.0496i	−0.723842	+	1.25373i
$339$		0			0
$340$	−1.01684	−	1.76122i	−0.0551459	−	0.0955154i
$341$	−2.09486	−	3.62840i	−0.113443	−	0.196489i
$342$		0			0
$343$	−1.68298	+	18.4436i	−0.0908723	+	0.995863i
$344$	0.420231	−	0.727861i	0.0226573	−	0.0392437i
$345$		0			0
$346$	−32.6754			−1.75664
$347$	11.5330			0.619126			0.309563	−	0.950879i	$-0.399817\pi$
$347$	11.5330			0.619126			0.309563	+	0.950879i	$0.399817\pi$
$348$		0			0
$349$	−4.44917	+	7.70619i	−0.238159	+	0.412503i	−0.960186	−	0.279362i	$-0.909877\pi$
$349$	−4.44917	+	7.70619i	−0.238159	+	0.412503i	0.722027	+	0.691865i	$0.243211\pi$
$350$	23.0058	+	14.2297i	1.22971	+	0.760612i
$351$		0			0
$352$	6.75390	+	11.6981i	0.359984	+	0.623511i
$353$	−1.32349	−	2.29236i	−0.0704424	−	0.122010i	0.828653	−	0.559763i	$-0.189108\pi$
$353$	−1.32349	−	2.29236i	−0.0704424	−	0.122010i	−0.899095	+	0.437753i	$0.855774\pi$
$354$		0			0
$355$	0.0934139	−	0.161798i	0.00495790	−	0.00858733i
$356$	−10.0538	−	17.4137i	−0.532852	−	0.922926i
$357$		0			0
$358$	7.96127	−	13.7893i	0.420766	−	0.728789i
$359$	12.9835	+	22.4882i	0.685245	+	1.18688i	0.973360	+	0.229284i	$0.0736384\pi$
$359$	12.9835	+	22.4882i	0.685245	+	1.18688i	−0.288114	+	0.957596i	$0.593028\pi$
$360$		0			0
$361$	−14.4264	+	24.9873i	−0.759286	+	1.31512i
$362$	24.9761			1.31271
$363$		0			0
$364$	−0.997362	−	0.616896i	−0.0522760	−	0.0323341i
$365$	−0.113867	−	0.197224i	−0.00596009	−	0.0103232i
$366$		0			0
$367$	−8.79371	−	15.2312i	−0.459028	−	0.795060i	0.539882	−	0.841741i	$-0.318469\pi$
$367$	−8.79371	−	15.2312i	−0.459028	−	0.795060i	−0.998910	+	0.0466808i	$0.985136\pi$
$368$	10.8732	−	18.8330i	0.566806	−	0.981736i
$369$		0			0
$370$	−2.10249			−0.109303
$371$	−0.428975	+	14.1380i	−0.0222713	+	0.734011i
$372$		0			0
$373$	−0.407538	+	0.705876i	−0.0211015	+	0.0365489i	−0.876383	−	0.481614i	$-0.840051\pi$
$373$	−0.407538	+	0.705876i	−0.0211015	+	0.0365489i	0.855282	+	0.518163i	$0.173384\pi$
$374$	21.4306			1.10815
$375$		0			0
$376$	−0.809107			−0.0417265
$377$	0.986490			0.0508068
$378$		0			0
$379$	−20.4312			−1.04948			−0.524741	−	0.851262i	$-0.675838\pi$
$379$	−20.4312			−1.04948			−0.524741	+	0.851262i	$0.675838\pi$
$380$	−2.24333			−0.115080
$381$		0			0
$382$	−10.2018			−0.521969
$383$	8.94638	−	15.4956i	0.457139	−	0.791788i	−0.541670	−	0.840591i	$-0.682208\pi$
$383$	8.94638	−	15.4956i	0.457139	−	0.791788i	0.998808	+	0.0488039i	$0.0155409\pi$
$384$		0			0
$385$	0.567112	−	0.304874i	0.0289027	−	0.0155378i
$386$	30.6084			1.55793
$387$		0			0
$388$	−8.83688	+	15.3059i	−0.448625	+	0.777041i
$389$	7.81392	+	13.5341i	0.396181	+	0.686206i	0.993251	−	0.115983i	$-0.0370018\pi$
$389$	7.81392	+	13.5341i	0.396181	+	0.686206i	−0.597070	+	0.802189i	$0.703669\pi$
$390$		0			0
$391$	−19.3835	−	33.5731i	−0.980264	−	1.69787i
$392$	−1.72430	+	2.60752i	−0.0870902	+	0.131700i
$393$		0			0
$394$	−43.6622			−2.19967
$395$	−0.935661	+	1.62061i	−0.0470782	+	0.0815419i
$396$		0			0
$397$	9.63064	+	16.6808i	0.483348	+	0.837183i	0.999817	−	0.0191225i	$-0.00608724\pi$
$397$	9.63064	+	16.6808i	0.483348	+	0.837183i	−0.516469	+	0.856306i	$0.672754\pi$
$398$	20.4791	−	35.4709i	1.02653	−	1.77799i
$399$		0			0
$400$	−8.75687	−	15.1673i	−0.437843	−	0.758367i
$401$	7.15064	−	12.3853i	0.357086	−	0.618491i	−0.630387	−	0.776281i	$-0.717104\pi$
$401$	7.15064	−	12.3853i	0.357086	−	0.618491i	0.987473	+	0.157790i	$0.0504370\pi$
$402$		0			0
$403$	−0.251642	−	0.435857i	−0.0125352	−	0.0217116i
$404$	16.4569	+	28.5041i	0.818760	+	1.41813i
$405$		0			0
$406$	0.813237	−	26.8024i	0.0403603	−	1.33018i
$407$	5.82452	−	10.0884i	0.288711	−	0.500062i
$408$		0			0
$409$	31.8610			1.57542			0.787712	−	0.616044i	$-0.211266\pi$
$409$	31.8610			1.57542			0.787712	+	0.616044i	$0.211266\pi$
$410$	−0.696152			−0.0343805
$411$		0			0
$412$	0.226124	−	0.391657i	0.0111403	−	0.0192956i
$413$	−10.6520	+	5.72643i	−0.524151	+	0.281779i
$414$		0			0
$415$	−0.549426	−	0.951633i	−0.0269702	−	0.0467138i
$416$	0.811304	+	1.40522i	0.0397774	+	0.0688965i
$417$		0			0
$418$	11.8199	−	20.4726i	0.578130	−	1.00135i
$419$	−11.9480	−	20.6945i	−0.583697	−	1.01099i	−0.995036	−	0.0995110i	$-0.968272\pi$
$419$	−11.9480	−	20.6945i	−0.583697	−	1.01099i	0.411339	−	0.911482i	$-0.365061\pi$
$420$		0			0
$421$	−1.22251	+	2.11744i	−0.0595813	+	0.103198i	−0.894278	−	0.447513i	$-0.852310\pi$
$421$	−1.22251	+	2.11744i	−0.0595813	+	0.103198i	0.834696	+	0.550711i	$0.185643\pi$
$422$	−24.1446	−	41.8197i	−1.17534	−	2.03575i
$423$		0			0
$424$	−1.19375	+	2.06763i	−0.0579734	+	0.100413i
$425$	−31.2214			−1.51446
$426$		0			0
$427$	1.58062	−	0.849728i	0.0764917	−	0.0411212i
$428$	−7.72661	−	13.3829i	−0.373480	−	0.646886i
$429$		0			0
$430$	0.282615	+	0.489503i	0.0136289	+	0.0236059i
$431$	−2.46382	+	4.26746i	−0.118678	+	0.205556i	−0.919244	−	0.393688i	$-0.871199\pi$
$431$	−2.46382	+	4.26746i	−0.118678	+	0.205556i	0.800566	+	0.599244i	$0.204532\pi$
$432$		0			0
$433$	30.8539			1.48274			0.741371	−	0.671095i	$-0.234176\pi$
$433$	30.8539			1.48274			0.741371	+	0.671095i	$0.234176\pi$
$434$	−12.0495	+	6.47768i	−0.578393	+	0.310939i
$435$		0			0
$436$	7.38543	−	12.7919i	0.353698	−	0.612622i
$437$	−42.7633			−2.04565
$438$		0			0
$439$	2.44822			0.116847			0.0584235	−	0.998292i	$-0.481393\pi$
$439$	2.44822			0.116847			0.0584235	+	0.998292i	$0.481393\pi$
$440$	0.108680			0.00518110
$441$		0			0
$442$	2.57432			0.122448
$443$	26.2950			1.24931			0.624657	−	0.780899i	$-0.285239\pi$
$443$	26.2950			1.24931			0.624657	+	0.780899i	$0.285239\pi$
$444$		0			0
$445$	1.32614			0.0628650
$446$	−4.16996	+	7.22259i	−0.197453	+	0.341999i
$447$		0			0
$448$	22.4525	−	12.0703i	1.06078	−	0.570266i
$449$	38.7077			1.82673			0.913365	−	0.407141i	$-0.133474\pi$
$449$	38.7077			1.82673			0.913365	+	0.407141i	$0.133474\pi$
$450$		0			0
$451$	1.92854	−	3.34034i	0.0908116	−	0.157290i
$452$	0.0428488	+	0.0742163i	0.00201544	+	0.00349084i
$453$		0			0
$454$	3.95620	+	6.85233i	0.185673	+	0.321596i
$455$	0.0681236	−	0.0366226i	0.00319368	−	0.00171690i
$456$		0			0
$457$	−9.15511			−0.428258			−0.214129	−	0.976805i	$-0.568691\pi$
$457$	−9.15511			−0.428258			−0.214129	+	0.976805i	$0.568691\pi$
$458$	13.4681	−	23.3274i	0.629321	−	1.09002i
$459$		0			0
$460$	−1.00237	−	1.73615i	−0.0467355	−	0.0809483i
$461$	−14.6152	+	25.3143i	−0.680698	+	1.17900i	0.294070	+	0.955784i	$0.404990\pi$
$461$	−14.6152	+	25.3143i	−0.680698	+	1.17900i	−0.974768	+	0.223220i	$0.928343\pi$
$462$		0			0
$463$	−8.21031	−	14.2207i	−0.381565	−	0.660891i	0.609721	−	0.792616i	$-0.291282\pi$
$463$	−8.21031	−	14.2207i	−0.381565	−	0.660891i	−0.991286	+	0.131726i	$0.957948\pi$
$464$	−8.68041	+	15.0349i	−0.402978	+	0.697978i
$465$		0			0
$466$	−17.9718	−	31.1280i	−0.832526	−	1.44198i
$467$	−7.68632	−	13.3131i	−0.355680	−	0.616057i	0.631554	−	0.775332i	$-0.282418\pi$
$467$	−7.68632	−	13.3131i	−0.355680	−	0.616057i	−0.987234	+	0.159276i	$0.949084\pi$
$468$		0			0
$469$	14.4175	−	7.75073i	0.665739	−	0.357895i
$470$	0.272071	−	0.471241i	0.0125497	−	0.0217367i
$471$		0			0
$472$	−2.04132			−0.0939594
$473$	−3.13170			−0.143996
$474$		0			0
$475$	−17.2200	+	29.8259i	−0.790106	+	1.36850i
$476$	1.11581	−	36.7747i	0.0511432	−	1.68556i
$477$		0			0
$478$	7.51341	+	13.0136i	0.343655	+	0.595228i
$479$	−18.9646	−	32.8476i	−0.866513	−	1.50084i	−0.865537	−	0.500844i	$-0.833023\pi$
$479$	−18.9646	−	32.8476i	−0.866513	−	1.50084i	−0.000975329	−	1.00000i	$-0.500310\pi$
$480$		0			0
$481$	0.699663	−	1.21185i	0.0319019	−	0.0552557i
$482$	6.39820	+	11.0820i	0.291430	+	0.504772i
$483$		0			0
$484$	9.12591	−	15.8065i	0.414814	−	0.718479i
$485$	−0.582809	−	1.00946i	−0.0264640	−	0.0458370i
$486$		0			0
$487$	2.30247	−	3.98800i	0.104335	−	0.180714i	−0.809131	−	0.587628i	$-0.800062\pi$
$487$	2.30247	−	3.98800i	0.104335	−	0.180714i	0.913466	+	0.406914i	$0.133395\pi$
$488$	0.302906			0.0137119
$489$		0			0
$490$	−0.938860	−	1.88108i	−0.0424134	−	0.0849784i
$491$	15.1876	+	26.3056i	0.685405	+	1.18716i	0.973309	+	0.229497i	$0.0737082\pi$
$491$	15.1876	+	26.3056i	0.685405	+	1.18716i	−0.287904	+	0.957659i	$0.592958\pi$
$492$		0			0
$493$	15.4744	+	26.8024i	0.696932	+	1.20712i
$494$	1.41985	−	2.45925i	0.0638820	−	0.110647i
$495$		0			0
$496$	8.85709			0.397695
$497$	2.97701	−	1.60041i	0.133537	−	0.0717884i
$498$		0			0
$499$	−4.63436	+	8.02694i	−0.207462	+	0.359335i	−0.950914	−	0.309454i	$-0.899854\pi$
$499$	−4.63436	+	8.02694i	−0.207462	+	0.359335i	0.743452	+	0.668789i	$0.233187\pi$
$500$	−3.23600			−0.144718
$501$		0			0
$502$	11.6089			0.518131
$503$	22.4230			0.999791			0.499896	−	0.866086i	$-0.333372\pi$
$503$	22.4230			0.999791			0.499896	+	0.866086i	$0.333372\pi$
$504$		0			0
$505$	−2.17072			−0.0965960
$506$	21.1255			0.939143
$507$		0			0
$508$	29.8888			1.32610
$509$	−18.8207	+	32.5984i	−0.834213	+	1.44490i	0.0604572	+	0.998171i	$0.480744\pi$
$509$	−18.8207	+	32.5984i	−0.834213	+	1.44490i	−0.894670	+	0.446728i	$0.852589\pi$
$510$		0			0
$511$	0.124951	−	4.11808i	0.00552748	−	0.182173i
$512$	−31.6976			−1.40085
$513$		0			0
$514$	−12.1182	+	20.9893i	−0.534511	+	0.925800i
$515$	0.0149133	+	0.0258306i	0.000657158	+	0.00113823i
$516$		0			0
$517$	1.50743	+	2.61095i	0.0662969	+	0.114830i
$518$	−32.3486	−	20.0085i	−1.42132	−	0.879124i
$519$		0			0
$520$	0.0130550			0.000572500
$521$	−17.4641	+	30.2488i	−0.765117	+	1.32522i	0.175067	+	0.984556i	$0.443986\pi$
$521$	−17.4641	+	30.2488i	−0.765117	+	1.32522i	−0.940185	+	0.340666i	$0.889348\pi$
$522$		0			0
$523$	−11.8735	−	20.5656i	−0.519194	−	0.899270i	−0.999751	−	0.0223069i	$-0.992899\pi$
$523$	−11.8735	−	20.5656i	−0.519194	−	0.899270i	0.480557	−	0.876963i	$-0.340434\pi$
$524$	−21.9898	+	38.0874i	−0.960628	+	1.66386i
$525$		0			0
$526$	22.8366	+	39.5542i	0.995723	+	1.72464i
$527$	7.89468	−	13.6740i	0.343898	−	0.595648i
$528$		0			0
$529$	−7.60755	−	13.1767i	−0.330763	−	0.572898i
$530$	−0.802820	−	1.39053i	−0.0348723	−	0.0604006i
$531$		0			0
$532$	−34.5155	−	21.3488i	−1.49644	−	0.925587i
$533$	0.231664	−	0.401254i	0.0100345	−	0.0173802i
$534$		0			0
$535$	1.01917			0.0440626
$536$	2.76293			0.119340
$537$		0			0
$538$	−2.45292	+	4.24857i	−0.105753	+	0.183169i
$539$	11.6269	+	0.706212i	0.500804	+	0.0304187i
$540$		0			0
$541$	8.58542	+	14.8704i	0.369116	+	0.639328i	0.989428	−	0.145028i	$-0.0463271\pi$
$541$	8.58542	+	14.8704i	0.369116	+	0.639328i	−0.620311	+	0.784356i	$0.712994\pi$
$542$	23.8488	+	41.3074i	1.02439	+	1.77430i
$543$		0			0
$544$	−25.4527	+	44.0854i	−1.09128	+	1.89015i
$545$	0.487083	+	0.843653i	0.0208643	+	0.0361381i
$546$		0			0
$547$	−10.0046	+	17.3284i	−0.427765	+	0.740910i	−0.996674	−	0.0814901i	$-0.974032\pi$
$547$	−10.0046	+	17.3284i	−0.427765	+	0.740910i	0.568910	+	0.822400i	$0.307365\pi$
$548$	−7.14586	−	12.3770i	−0.305256	−	0.528719i
$549$		0			0
$550$	8.50683	−	14.7343i	0.362732	−	0.628271i
$551$	34.1392			1.45438
$552$		0			0
$553$	−29.8186	+	16.0302i	−1.26802	+	0.681674i
$554$	−4.74187	−	8.21316i	−0.201463	−	0.348944i
$555$		0			0
$556$	13.8930	+	24.0633i	0.589193	+	1.02051i
$557$	0.122740	−	0.212593i	0.00520068	−	0.00900784i	−0.863413	−	0.504497i	$-0.831678\pi$
$557$	0.122740	−	0.212593i	0.00520068	−	0.00900784i	0.868614	+	0.495489i	$0.165011\pi$
$558$		0			0
$559$	−0.376192			−0.0159112
$560$	−0.0412806	+	1.36051i	−0.00174442	+	0.0574922i
$561$		0			0
$562$	12.1338	−	21.0163i	0.511833	−	0.886520i
$563$	44.2509			1.86495			0.932477	−	0.361230i	$-0.117643\pi$
$563$	44.2509			1.86495			0.932477	+	0.361230i	$0.117643\pi$
$564$		0			0
$565$	−0.00565192			−0.000237778
$566$	−32.5496			−1.36816
$567$		0			0
$568$	0.570506			0.0239379
$569$	5.53533			0.232053			0.116027	−	0.993246i	$-0.462984\pi$
$569$	5.53533			0.232053			0.116027	+	0.993246i	$0.462984\pi$
$570$		0			0
$571$	−4.10381			−0.171739			−0.0858696	−	0.996306i	$-0.527367\pi$
$571$	−4.10381			−0.171739			−0.0858696	+	0.996306i	$0.527367\pi$
$572$	−0.368793	+	0.638768i	−0.0154200	+	0.0267082i
$573$		0			0
$574$	−10.7109	−	6.62498i	−0.447064	−	0.276521i
$575$	−30.7770			−1.28349
$576$		0			0
$577$	−2.82275	+	4.88915i	−0.117513	+	0.203538i	−0.918781	−	0.394767i	$-0.870825\pi$
$577$	−2.82275	+	4.88915i	−0.117513	+	0.203538i	0.801269	+	0.598305i	$0.204159\pi$
$578$	22.9256	+	39.7083i	0.953579	+	1.65165i
$579$		0			0
$580$	0.800218	+	1.38602i	0.0332272	+	0.0575513i
$581$	0.602904	−	19.8703i	0.0250127	−	0.824360i
$582$		0			0
$583$	8.89619			0.368442
$584$	0.347710	−	0.602252i	0.0143884	−	0.0249214i
$585$		0			0
$586$	14.4742	+	25.0700i	0.597923	+	1.03563i
$587$	−9.36644	+	16.2232i	−0.386595	+	0.669601i	−0.991989	−	0.126324i	$-0.959682\pi$
$587$	−9.36644	+	16.2232i	−0.386595	+	0.669601i	0.605394	+	0.795926i	$0.293015\pi$
$588$		0			0
$589$	−8.70852	−	15.0836i	−0.358828	−	0.621509i
$590$	0.686417	−	1.18891i	0.0282594	−	0.0489466i
$591$		0			0
$592$	12.3131	+	21.3269i	0.506065	+	0.876530i
$593$	9.43516	+	16.3422i	0.387456	+	0.671093i	0.992107	−	0.125398i	$-0.0400207\pi$
$593$	9.43516	+	16.3422i	0.387456	+	0.671093i	−0.604651	+	0.796491i	$0.706687\pi$
$594$		0			0
$595$	2.06363	+	1.27641i	0.0846005	+	0.0523277i
$596$	19.6991	−	34.1198i	0.806906	−	1.39760i
$597$		0			0
$598$	2.53767			0.103773
$599$	−2.67451			−0.109278			−0.0546388	−	0.998506i	$-0.517401\pi$
$599$	−2.67451			−0.109278			−0.0546388	+	0.998506i	$0.517401\pi$
$600$		0			0
$601$	−6.60716	+	11.4439i	−0.269511	+	0.466808i	−0.968736	−	0.248095i	$-0.920196\pi$
$601$	−6.60716	+	11.4439i	−0.269511	+	0.466808i	0.699224	+	0.714902i	$0.253529\pi$
$602$	−0.310123	+	10.2209i	−0.0126397	+	0.416575i
$603$		0			0
$604$	−9.38650	−	16.2579i	−0.381931	−	0.661524i
$605$	0.601872	+	1.04247i	0.0244696	+	0.0423825i
$606$		0			0
$607$	−12.9026	+	22.3480i	−0.523701	+	0.907076i	0.475919	+	0.879489i	$0.342116\pi$
$607$	−12.9026	+	22.3480i	−0.523701	+	0.907076i	−0.999619	+	0.0275869i	$0.991218\pi$
$608$	28.0766	+	48.6301i	1.13866	+	1.97221i
$609$		0			0
$610$	−0.101856	+	0.176419i	−0.00412401	+	0.00714299i
$611$	0.181079	+	0.313637i	0.00732565	+	0.0126884i
$612$		0			0
$613$	13.4766	−	23.3422i	0.544316	−	0.942784i	−0.454333	−	0.890832i	$-0.650122\pi$
$613$	13.4766	−	23.3422i	0.544316	−	0.942784i	0.998650	−	0.0519519i	$-0.0165443\pi$
$614$	−56.2526			−2.27017
$615$		0			0
$616$	1.67213	+	1.03426i	0.0673720	+	0.0416715i
$617$	4.76588	+	8.25474i	0.191867	+	0.332323i	0.945869	−	0.324549i	$-0.105212\pi$
$617$	4.76588	+	8.25474i	0.191867	+	0.332323i	−0.754002	+	0.656872i	$0.771879\pi$
$618$		0			0
$619$	−17.3536	−	30.0573i	−0.697499	−	1.20810i	−0.969331	−	0.245759i	$-0.920963\pi$
$619$	−17.3536	−	30.0573i	−0.697499	−	1.20810i	0.271832	−	0.962345i	$-0.412370\pi$
$620$	0.408253	−	0.707114i	0.0163958	−	0.0283984i
$621$		0			0
$622$	−28.8654			−1.15740
$623$	20.4038	+	12.6203i	0.817459	+	0.505621i
$624$		0			0
$625$	−12.3398	+	21.3732i	−0.493593	+	0.854928i
$626$	−44.6558			−1.78480
$627$		0			0
$628$	12.6381			0.504314
$629$	43.9006			1.75043
$630$		0			0
$631$	−36.7963			−1.46484			−0.732419	−	0.680854i	$-0.761609\pi$
$631$	−36.7963			−1.46484			−0.732419	+	0.680854i	$0.761609\pi$
$632$	−5.71435			−0.227305
$633$		0			0
$634$	17.5853			0.698401
$635$	−0.985611	+	1.70713i	−0.0391128	+	0.0677453i
$636$		0			0
$637$	1.39666	+	0.0848329i	0.0553378	+	0.00336120i
$638$	−16.8651			−0.667696
$639$		0			0
$640$	−0.259699	+	0.449811i	−0.0102655	+	0.0177804i
$641$	−22.0922	−	38.2648i	−0.872590	−	1.51137i	−0.859308	−	0.511458i	$-0.829106\pi$
$641$	−22.0922	−	38.2648i	−0.872590	−	1.51137i	−0.0132813	−	0.999912i	$-0.504228\pi$
$642$		0			0
$643$	7.24065	+	12.5412i	0.285543	+	0.494575i	0.972741	−	0.231895i	$-0.0744926\pi$
$643$	7.24065	+	12.5412i	0.285543	+	0.494575i	−0.687197	+	0.726471i	$0.741159\pi$
$644$	1.09993	−	36.2512i	0.0433433	−	1.42850i
$645$		0			0
$646$	89.0889			3.50515
$647$	16.6536	−	28.8448i	0.654719	−	1.13401i	−0.327245	−	0.944940i	$-0.606120\pi$
$647$	16.6536	−	28.8448i	0.654719	−	1.13401i	0.981964	−	0.189068i	$-0.0605465\pi$
$648$		0			0
$649$	3.80315	+	6.58725i	0.149287	+	0.258572i
$650$	1.02187	−	1.76993i	0.0400811	−	0.0694225i
$651$		0			0
$652$	−2.35643	−	4.08146i	−0.0922850	−	0.159842i
$653$	−4.53322	+	7.85176i	−0.177398	+	0.307263i	−0.940989	−	0.338438i	$-0.890101\pi$
$653$	−4.53322	+	7.85176i	−0.177398	+	0.307263i	0.763590	+	0.645701i	$0.223435\pi$
$654$		0			0
$655$	−1.45027	−	2.51194i	−0.0566666	−	0.0981495i
$656$	4.07696	+	7.06150i	0.159178	+	0.275705i
$657$		0			0
$658$	8.67065	−	4.66126i	0.338017	−	0.181715i
$659$	−16.1806	+	28.0256i	−0.630305	+	1.09172i	0.357184	+	0.934034i	$0.383737\pi$
$659$	−16.1806	+	28.0256i	−0.630305	+	1.09172i	−0.987489	+	0.157686i	$0.949596\pi$
$660$		0			0
$661$	−8.65915			−0.336802			−0.168401	−	0.985719i	$-0.553860\pi$
$661$	−8.65915			−0.336802			−0.168401	+	0.985719i	$0.553860\pi$
$662$	−22.2763			−0.865794
$663$		0			0
$664$	1.67775	−	2.90595i	0.0651094	−	0.112773i
$665$	2.35754	−	1.26739i	0.0914214	−	0.0491473i
$666$		0			0
$667$	15.2541	+	26.4209i	0.590642	+	1.02302i
$668$	12.8329	+	22.2273i	0.496522	+	0.860001i
$669$		0			0
$670$	−0.929067	+	1.60919i	−0.0358930	+	0.0621685i
$671$	−0.564339	−	0.977464i	−0.0217861	−	0.0377346i
$672$		0			0
$673$	7.24842	−	12.5546i	0.279406	−	0.483946i	−0.691831	−	0.722059i	$-0.743196\pi$
$673$	7.24842	−	12.5546i	0.279406	−	0.483946i	0.971237	+	0.238114i	$0.0765291\pi$
$674$	−3.43803	−	5.95484i	−0.132428	−	0.229372i
$675$		0			0
$676$	14.3692	−	24.8881i	0.552661	−	0.957236i
$677$	−38.3315			−1.47320			−0.736600	−	0.676329i	$-0.763570\pi$
$677$	−38.3315			−1.47320			−0.736600	+	0.676329i	$0.763570\pi$
$678$		0			0
$679$	0.639537	−	21.0777i	0.0245432	−	0.808887i
$680$	0.204785	+	0.354698i	0.00785315	+	0.0136021i
$681$		0			0
$682$	4.30209	+	7.45144i	0.164736	+	0.285330i
$683$	3.31659	−	5.74450i	0.126906	−	0.219807i	−0.795570	−	0.605861i	$-0.792829\pi$
$683$	3.31659	−	5.74450i	0.126906	−	0.219807i	0.922476	+	0.386054i	$0.126162\pi$
$684$		0			0
$685$	0.942567			0.0360136
$686$	3.45624	−	37.8767i	0.131960	−	1.44614i
$687$		0			0
$688$	3.31022	−	5.73347i	0.126201	−	0.218587i
$689$	1.06864			0.0407121
$690$		0			0
$691$	−23.3875			−0.889704			−0.444852	−	0.895604i	$-0.646744\pi$
$691$	−23.3875			−0.889704			−0.444852	+	0.895604i	$0.646744\pi$
$692$	35.2818			1.34121
$693$		0			0
$694$	−23.6848			−0.899061
$695$	−1.83254			−0.0695121
$696$		0			0
$697$	14.5358			0.550583
$698$	9.13702	−	15.8258i	0.345841	−	0.599015i
$699$		0			0
$700$	−24.8410	−	15.3648i	−0.938900	−	0.580735i
$701$	−9.26736			−0.350023			−0.175012	−	0.984566i	$-0.555996\pi$
$701$	−9.26736			−0.350023			−0.175012	+	0.984566i	$0.555996\pi$
$702$		0			0
$703$	24.2131	−	41.9383i	0.913214	−	1.58173i
$704$	−8.01636	−	13.8847i	−0.302128	−	0.523301i
$705$		0			0
$706$	2.71799	+	4.70769i	0.102293	+	0.177176i
$707$	−33.3984	−	20.6579i	−1.25608	−	0.776918i
$708$		0			0
$709$	14.2355			0.534626			0.267313	−	0.963610i	$-0.413864\pi$
$709$	14.2355			0.534626			0.267313	+	0.963610i	$0.413864\pi$
$710$	−0.191839	+	0.332275i	−0.00719959	+	0.0124701i
$711$		0			0
$712$	2.02478	+	3.50702i	0.0758817	+	0.131431i
$713$	7.78230	−	13.4793i	0.291449	−	0.504805i
$714$		0			0
$715$	−0.0243226	−	0.0421280i	−0.000909613	−	0.00157550i
$716$	−8.59632	+	14.8893i	−0.321260	+	0.556438i
$717$		0			0
$718$	−26.6636	−	46.1827i	−0.995077	−	1.72352i
$719$	−6.92848	−	12.0005i	−0.258389	−	0.447542i	0.707422	−	0.706792i	$-0.249858\pi$
$719$	−6.92848	−	12.0005i	−0.258389	−	0.447542i	−0.965810	+	0.259249i	$0.916525\pi$
$720$		0			0
$721$	−0.0163649	+	0.539348i	−0.000609459	+	0.0200864i
$722$	29.6268	−	51.3151i	1.10259	−	1.90975i
$723$		0			0
$724$	−26.9684			−1.00227
$725$	24.5702			0.912513
$726$		0			0
$727$	15.7000	−	27.1932i	0.582280	−	1.00854i	−0.412928	−	0.910764i	$-0.635494\pi$
$727$	15.7000	−	27.1932i	0.582280	−	1.00854i	0.995208	−	0.0977755i	$-0.0311727\pi$
$728$	0.200862	+	0.124239i	0.00744446	+	0.00460460i
$729$		0			0
$730$	0.233843	+	0.405028i	0.00865492	+	0.0149908i
$731$	−5.90107	−	10.2209i	−0.218259	−	0.378035i
$732$		0			0
$733$	13.3003	−	23.0368i	0.491257	−	0.850883i	−0.508692	−	0.860949i	$-0.669871\pi$
$733$	13.3003	−	23.0368i	0.491257	−	0.850883i	0.999949	+	0.0100658i	$0.00320409\pi$
$734$	18.0592	+	31.2794i	0.666576	+	1.15454i
$735$		0			0
$736$	−25.0904	+	43.4579i	−0.924845	+	1.60188i
$737$	−5.14757	−	8.91586i	−0.189613	−	0.328420i
$738$		0			0
$739$	16.5019	−	28.5822i	0.607034	−	1.05141i	−0.384693	−	0.923045i	$-0.625693\pi$
$739$	16.5019	−	28.5822i	0.607034	−	1.05141i	0.991727	−	0.128368i	$-0.0409740\pi$
$740$	2.27020			0.0834543
$741$		0			0
$742$	0.880963	−	29.0345i	0.0323412	−	1.06589i
$743$	−19.3008	−	33.4299i	−0.708076	−	1.22642i	−0.965570	−	0.260144i	$-0.916230\pi$
$743$	−19.3008	−	33.4299i	−0.708076	−	1.22642i	0.257493	−	0.966280i	$-0.417103\pi$
$744$		0			0
$745$	1.29919	+	2.25027i	0.0475988	+	0.0824435i
$746$	0.836938	−	1.44962i	0.0306425	−	0.0530743i
$747$		0			0
$748$	−23.1400			−0.846082
$749$	15.6808	+	9.69900i	0.572964	+	0.354394i
$750$		0			0
$751$	18.9498	−	32.8220i	0.691487	−	1.19769i	−0.279863	−	0.960040i	$-0.590289\pi$
$751$	18.9498	−	32.8220i	0.691487	−	1.19769i	0.971351	−	0.237651i	$-0.0763776\pi$
$752$	−6.37345			−0.232416
$753$		0			0
$754$	−2.02590			−0.0737789
$755$	1.23811			0.0450596
$756$		0			0
$757$	22.5927			0.821147			0.410573	−	0.911828i	$-0.365329\pi$
$757$	22.5927			0.821147			0.410573	+	0.911828i	$0.365329\pi$
$758$	41.9585			1.52400
$759$		0			0
$760$	0.451792			0.0163882
$761$	13.8735	−	24.0296i	0.502913	−	0.871072i	−0.497081	−	0.867704i	$-0.665595\pi$
$761$	13.8735	−	24.0296i	0.502913	−	0.871072i	0.999994	−	0.00336738i	$-0.00107187\pi$
$762$		0			0
$763$	−0.534493	+	17.6157i	−0.0193500	+	0.637730i
$764$	11.0156			0.398529
$765$		0			0
$766$	−18.3727	+	31.8224i	−0.663832	+	1.14979i
$767$	0.456849	+	0.791286i	0.0164959	+	0.0285717i
$768$		0			0
$769$	−6.07668	−	10.5251i	−0.219131	−	0.379546i	0.735412	−	0.677621i	$-0.236989\pi$
$769$	−6.07668	−	10.5251i	−0.219131	−	0.379546i	−0.954542	+	0.298075i	$0.903655\pi$
$770$	−1.16465	+	0.626104i	−0.0419710	+	0.0225632i
$771$		0			0
$772$	−33.0499			−1.18949
$773$	20.7795	−	35.9912i	0.747388	−	1.29451i	−0.201682	−	0.979451i	$-0.564641\pi$
$773$	20.7795	−	35.9912i	0.747388	−	1.29451i	0.949071	−	0.315063i	$-0.102026\pi$
$774$		0			0
$775$	−6.26756	−	10.8557i	−0.225137	−	0.389950i
$776$	1.77969	−	3.08252i	0.0638873	−	0.110656i
$777$		0			0
$778$	−16.0470	−	27.7942i	−0.575313	−	0.996472i
$779$	8.01714	−	13.8861i	0.287244	−	0.497521i
$780$		0			0
$781$	−1.06290	−	1.84100i	−0.0380336	−	0.0658761i
$782$	39.8068	+	68.9473i	1.42349	+	2.46555i
$783$		0			0
$784$	−13.5826	+	20.5398i	−0.485091	+	0.733564i
$785$	−0.416753	+	0.721837i	−0.0148746	+	0.0257635i
$786$		0			0
$787$	−20.8969			−0.744893			−0.372446	−	0.928054i	$-0.621481\pi$
$787$	−20.8969			−0.744893			−0.372446	+	0.928054i	$0.621481\pi$
$788$	47.1450			1.67947
$789$		0			0
$790$	1.92152	−	3.32816i	0.0683645	−	0.118411i
$791$	−0.0869596	−	0.0537869i	−0.00309193	−	0.00191244i
$792$		0			0
$793$	−0.0677905	−	0.117417i	−0.00240731	−	0.00416959i
$794$	−19.7779	−	34.2564i	−0.701892	−	1.21571i
$795$		0			0
$796$	−22.1127	+	38.3003i	−0.783763	+	1.35752i
$797$	0.319383	+	0.553188i	0.0113131	+	0.0195949i	0.871627	−	0.490171i	$-0.163066\pi$
$797$	0.319383	+	0.553188i	0.0113131	+	0.0195949i	−0.860313	+	0.509765i	$0.829732\pi$
$798$		0			0
$799$	−5.68091	+	9.83963i	−0.200976	+	0.348101i
$800$	20.2069	+	34.9993i	0.714420	+	1.23741i
$801$		0			0
$802$	−14.6849	+	25.4350i	−0.518541	+	0.898139i
$803$	−2.59125			−0.0914433
$804$		0			0
$805$	2.03425	+	1.25824i	0.0716980	+	0.0443472i
$806$	0.516783	+	0.895095i	0.0182029	+	0.0315284i
$807$		0			0
$808$	−3.31431	−	5.74055i	−0.116597	−	0.201952i
$809$	−25.2796	+	43.7856i	−0.888783	+	1.53942i	−0.0474686	+	0.998873i	$0.515115\pi$
$809$	−25.2796	+	43.7856i	−0.888783	+	1.53942i	−0.841315	+	0.540545i	$0.818218\pi$
$810$		0			0
$811$	−0.784071			−0.0275325			−0.0137662	−	0.999905i	$-0.504382\pi$
$811$	−0.784071			−0.0275325			−0.0137662	+	0.999905i	$0.504382\pi$
$812$	−0.878107	+	28.9404i	−0.0308155	+	1.01561i
$813$		0			0
$814$	−11.9615	+	20.7179i	−0.419250	+	0.726163i
$815$	0.310823			0.0108876
$816$		0			0
$817$	−13.0188			−0.455470
$818$	−65.4311			−2.28775
$819$		0			0
$820$	0.751682			0.0262499
$821$	−43.4413			−1.51611			−0.758056	−	0.652189i	$-0.773851\pi$
$821$	−43.4413			−1.51611			−0.758056	+	0.652189i	$0.773851\pi$
$822$		0			0
$823$	3.96546			0.138227			0.0691136	−	0.997609i	$-0.477983\pi$
$823$	3.96546			0.138227			0.0691136	+	0.997609i	$0.477983\pi$
$824$	−0.0455399	+	0.0788774i	−0.00158646	+	0.00274782i
$825$		0			0
$826$	21.8755	−	11.7600i	0.761144	−	0.409184i
$827$	−29.3159			−1.01941			−0.509707	−	0.860348i	$-0.670246\pi$
$827$	−29.3159			−1.01941			−0.509707	+	0.860348i	$0.670246\pi$
$828$		0			0
$829$	−17.5213	+	30.3478i	−0.608541	+	1.05402i	0.382940	+	0.923773i	$0.374912\pi$
$829$	−17.5213	+	30.3478i	−0.608541	+	1.05402i	−0.991481	+	0.130251i	$0.958422\pi$
$830$	1.12833	+	1.95432i	0.0391648	+	0.0678353i
$831$		0			0
$832$	−0.962955	−	1.66789i	−0.0333844	−	0.0578236i
$833$	19.6036	+	39.2773i	0.679225	+	1.36088i
$834$		0			0
$835$	−1.69272			−0.0585788
$836$	−12.7627	+	22.1057i	−0.441408	+	0.764541i
$837$		0			0
$838$	24.5369	+	42.4992i	0.847614	+	1.46811i
$839$	18.7921	−	32.5489i	0.648777	−	1.12371i	−0.334639	−	0.942347i	$-0.608614\pi$
$839$	18.7921	−	32.5489i	0.648777	−	1.12371i	0.983415	−	0.181368i	$-0.0580524\pi$
$840$		0			0
$841$	2.32218	+	4.02213i	0.0800750	+	0.138694i
$842$	2.51060	−	4.34848i	0.0865208	−	0.149858i
$843$		0			0
$844$	26.0705	+	45.1555i	0.897385	+	1.55432i
$845$	0.947675	+	1.64142i	0.0326010	+	0.0564666i
$846$		0			0
$847$	−0.660455	+	21.7671i	−0.0226935	+	0.747926i
$848$	−9.40331	+	16.2870i	−0.322911	+	0.559298i
$849$		0			0
$850$	64.1177			2.19922
$851$	43.2757			1.48347
$852$		0			0
$853$	16.3849	−	28.3795i	0.561009	−	0.971696i	−0.436400	−	0.899753i	$-0.643747\pi$
$853$	16.3849	−	28.3795i	0.561009	−	0.971696i	0.997409	−	0.0719434i	$-0.0229201\pi$
$854$	−3.24604	+	1.74504i	−0.111077	+	0.0597140i
$855$		0			0
$856$	1.55609	+	2.69523i	0.0531861	+	0.0921211i
$857$	13.7673	+	23.8457i	0.470283	+	0.814554i	0.999422	−	0.0339808i	$-0.0108185\pi$
$857$	13.7673	+	23.8457i	0.470283	+	0.814554i	−0.529139	+	0.848535i	$0.677485\pi$
$858$		0			0
$859$	23.2550	−	40.2789i	0.793451	−	1.37430i	−0.130366	−	0.991466i	$-0.541615\pi$
$859$	23.2550	−	40.2789i	0.793451	−	1.37430i	0.923818	−	0.382832i	$-0.125051\pi$
$860$	−0.305158	−	0.528549i	−0.0104058	−	0.0180234i
$861$		0			0
$862$	5.05981	−	8.76384i	0.172338	−	0.298498i
$863$	−2.44007	−	4.22633i	−0.0830610	−	0.143866i	0.821502	−	0.570205i	$-0.193136\pi$
$863$	−2.44007	−	4.22633i	−0.0830610	−	0.143866i	−0.904563	+	0.426339i	$0.859803\pi$
$864$		0			0
$865$	−1.16345	+	2.01516i	−0.0395585	+	0.0685174i
$866$	−63.3629			−2.15316
$867$		0			0
$868$	13.0106	−	6.99439i	0.441609	−	0.237405i
$869$	10.6463	+	18.4400i	0.361152	+	0.625533i
$870$		0			0
$871$	−0.618346	−	1.07101i	−0.0209518	−	0.0362897i
$872$	−1.48738	+	2.57622i	−0.0503690	+	0.0872417i
$873$		0			0
$874$	87.8207			2.97058
$875$	3.40075	−	1.82821i	0.114966	−	0.0618049i
$876$		0			0
$877$	−19.6446	+	34.0255i	−0.663352	+	1.14896i	0.316378	+	0.948633i	$0.397533\pi$
$877$	−19.6446	+	34.0255i	−0.663352	+	1.14896i	−0.979729	+	0.200326i	$0.935800\pi$
$878$	−5.02777			−0.169679
$879$		0			0
$880$	0.856086			0.0288587
$881$	−47.3713			−1.59598			−0.797990	−	0.602670i	$-0.794103\pi$
$881$	−47.3713			−1.59598			−0.797990	+	0.602670i	$0.794103\pi$
$882$		0			0
$883$	−2.67206			−0.0899221			−0.0449610	−	0.998989i	$-0.514316\pi$
$883$	−2.67206			−0.0899221			−0.0449610	+	0.998989i	$0.514316\pi$
$884$	−2.77966			−0.0934902
$885$		0			0
$886$	−54.0007			−1.81419
$887$	−11.4800	+	19.8840i	−0.385461	+	0.667638i	−0.991833	−	0.127543i	$-0.959291\pi$
$887$	−11.4800	+	19.8840i	−0.385461	+	0.667638i	0.606372	+	0.795181i	$0.292624\pi$
$888$		0			0
$889$	−31.4105	+	16.8860i	−1.05347	+	0.566338i
$890$	−2.72342			−0.0912891
$891$		0			0
$892$	4.50259	−	7.79871i	0.150758	−	0.261120i
$893$	6.26655	+	10.8540i	0.209702	+	0.363214i
$894$		0			0
$895$	−0.566944	−	0.981976i	−0.0189508	−	0.0328238i
$896$	−8.27635	+	4.44929i	−0.276493	+	0.148640i
$897$		0			0
$898$	−79.4920			−2.65268
$899$	−6.21284	+	10.7610i	−0.207210	+	0.358898i
$900$		0			0
$901$	16.7631	+	29.0345i	0.558459	+	0.967280i
$902$	−3.96054	+	6.85986i	−0.131872	+	0.228408i
$903$		0			0
$904$	−0.00862948	−	0.0149467i	−0.000287012	−	0.000497120i
$905$	0.889308	−	1.54033i	0.0295616	−	0.0512022i
$906$		0			0
$907$	13.9491	+	24.1606i	0.463173	+	0.802238i	0.999117	−	0.0420148i	$-0.0133777\pi$
$907$	13.9491	+	24.1606i	0.463173	+	0.802238i	−0.535944	+	0.844253i	$0.680044\pi$
$908$	−4.27177	−	7.39892i	−0.141764	−	0.245542i
$909$		0			0
$910$	−0.139902	+	0.0752099i	−0.00463770	+	0.00249318i
$911$	18.7381	−	32.4553i	0.620820	−	1.07529i	−0.368513	−	0.929623i	$-0.620133\pi$
$911$	18.7381	−	32.4553i	0.620820	−	1.07529i	0.989333	−	0.145670i	$-0.0465337\pi$
$912$		0			0
$913$	−12.5032			−0.413794
$914$	18.8014			0.621894
$915$		0			0
$916$	−14.5424	+	25.1881i	−0.480493	+	0.832239i
$917$	1.59143	−	52.4499i	0.0525536	−	1.73205i
$918$		0			0
$919$	−15.1073	−	26.1667i	−0.498345	−	0.863160i	0.501653	−	0.865069i	$-0.332726\pi$
$919$	−15.1073	−	26.1667i	−0.498345	−	0.863160i	−0.999998	+	0.00190951i	$0.999392\pi$
$920$	0.201870	+	0.349649i	0.00665546	+	0.0115276i
$921$		0			0
$922$	30.0145	−	51.9866i	0.988474	−	1.71209i
$923$	−0.127680	−	0.221147i	−0.00420262	−	0.00727916i
$924$		0			0
$925$	17.4263	−	30.1832i	0.572972	−	0.992417i
$926$	16.8611	+	29.2042i	0.554089	+	0.959710i
$927$		0			0
$928$	20.0304	−	34.6937i	0.657531	−	1.13888i
$929$	45.9351			1.50708			0.753540	−	0.657402i	$-0.228344\pi$
$929$	45.9351			1.50708			0.753540	+	0.657402i	$0.228344\pi$
$930$		0			0
$931$	48.3340	+	2.93579i	1.58408	+	0.0962167i
$932$	19.4053	+	33.6110i	0.635642	+	1.10096i
$933$		0			0
$934$	15.7850	+	27.3404i	0.516500	+	0.894604i
$935$	0.763064	−	1.32167i	0.0249549	−	0.0432231i
$936$		0			0
$937$	−45.3797			−1.48249			−0.741245	−	0.671235i	$-0.765764\pi$
$937$	−45.3797			−1.48249			−0.741245	+	0.671235i	$0.765764\pi$
$938$	−29.6085	+	15.9172i	−0.966751	+	0.519716i
$939$		0			0
$940$	−0.293774	+	0.508831i	−0.00958184	+	0.0165962i
$941$	−49.4003			−1.61040			−0.805202	−	0.593000i	$-0.797943\pi$
$941$	−49.4003			−1.61040			−0.805202	+	0.593000i	$0.797943\pi$
$942$		0			0
$943$	14.3289			0.466613
$944$	−16.0798			−0.523353
$945$		0			0
$946$	6.43141			0.209103
$947$	−31.6505			−1.02850			−0.514252	−	0.857639i	$-0.671930\pi$
$947$	−31.6505			−1.02850			−0.514252	+	0.857639i	$0.671930\pi$
$948$		0			0
$949$	−0.311271			−0.0101043
$950$	35.3637	−	61.2517i	1.14735	−	1.98727i
$951$		0			0
$952$	−0.224718	+	7.40619i	−0.00728315	+	0.240036i
$953$	19.1237			0.619477			0.309739	−	0.950822i	$-0.399758\pi$
$953$	19.1237			0.619477			0.309739	+	0.950822i	$0.399758\pi$
$954$		0			0
$955$	−0.363249	+	0.629165i	−0.0117545	+	0.0203593i
$956$	−8.11273	−	14.0517i	−0.262384	−	0.454463i
$957$		0			0
$958$	38.9465	+	67.4573i	1.25830	+	2.17945i
$959$	14.5022	+	8.97001i	0.468300	+	0.289657i
$960$		0			0
$961$	−24.6607			−0.795507
$962$	−1.43686	+	2.48871i	−0.0463262	+	0.0802394i
$963$		0			0
$964$	−6.90857	−	11.9660i	−0.222510	−	0.385399i
$965$	1.08985	−	1.88768i	0.0350836	−	0.0607666i
$966$		0			0
$967$	4.98525	+	8.63470i	0.160315	+	0.277673i	0.934982	−	0.354696i	$-0.115416\pi$
$967$	4.98525	+	8.63470i	0.160315	+	0.277673i	−0.774667	+	0.632370i	$0.782082\pi$
$968$	−1.83790	+	3.18334i	−0.0590724	+	0.102316i
$969$		0			0
$970$	1.19688	+	2.07306i	0.0384296	+	0.0665621i
$971$	−0.522554	−	0.905090i	−0.0167695	−	0.0290457i	0.857519	−	0.514453i	$-0.172005\pi$
$971$	−0.522554	−	0.905090i	−0.0167695	−	0.0290457i	−0.874288	+	0.485407i	$0.838671\pi$
$972$		0			0
$973$	−28.1951	−	17.4395i	−0.903895	−	0.559084i
$974$	−4.72847	+	8.18994i	−0.151510	+	0.262423i
$975$		0			0
$976$	2.38603			0.0763751
$977$	18.8862			0.604222			0.302111	−	0.953273i	$-0.402309\pi$
$977$	18.8862			0.604222			0.302111	+	0.953273i	$0.402309\pi$
$978$		0			0
$979$	7.54466	−	13.0677i	0.241128	−	0.417647i
$980$	1.01375	+	2.03112i	0.0323830	+	0.0648819i
$981$		0			0
$982$	−31.1899	−	54.0224i	−0.995309	−	1.72393i
$983$	1.14446	+	1.98226i	0.0365025	+	0.0632242i	0.883700	−	0.468055i	$-0.155045\pi$
$983$	1.14446	+	1.98226i	0.0365025	+	0.0632242i	−0.847197	+	0.531279i	$0.821712\pi$
$984$		0			0
$985$	−1.55465	+	2.69274i	−0.0495353	+	0.0857977i
$986$	−31.7789	−	55.0427i	−1.01205	−	1.75292i
$987$		0			0
$988$	−1.53311	+	2.65542i	−0.0487746	+	0.0844801i
$989$	−5.81707	−	10.0755i	−0.184972	−	0.320381i
$990$		0			0
$991$	−9.53491	+	16.5150i	−0.302886	+	0.524615i	−0.976789	−	0.214206i	$-0.931284\pi$
$991$	−9.53491	+	16.5150i	−0.302886	+	0.524615i	0.673902	+	0.738821i	$0.264617\pi$
$992$	−20.4381			−0.648911
$993$		0			0
$994$	−6.11372	+	3.28668i	−0.193916	+	0.104247i
$995$	−1.45837	−	2.52598i	−0.0462336	−	0.0800789i
$996$		0			0
$997$	−18.5075	−	32.0560i	−0.586139	−	1.01522i	−0.994732	−	0.102507i	$-0.967314\pi$
$997$	−18.5075	−	32.0560i	−0.586139	−	1.01522i	0.408593	−	0.912717i	$-0.366020\pi$
$998$	9.51732	−	16.4845i	0.301266	−	0.521807i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.h.b.46.1		10
3.2	odd	2		63.2.h.b.25.5	yes	10
4.3	odd	2		3024.2.q.i.2881.3		10
7.2	even	3		189.2.g.b.100.5		10
7.3	odd	6		1323.2.f.f.883.5		10
7.4	even	3		1323.2.f.e.883.5		10
7.5	odd	6		1323.2.g.f.667.5		10
7.6	odd	2		1323.2.h.f.802.1		10
9.2	odd	6		567.2.e.f.487.1		10
9.4	even	3		189.2.g.b.172.5		10
9.5	odd	6		63.2.g.b.4.1	✓	10
9.7	even	3		567.2.e.e.487.5		10
12.11	even	2		1008.2.q.i.529.5		10
21.2	odd	6		63.2.g.b.16.1	yes	10
21.5	even	6		441.2.g.f.79.1		10
21.11	odd	6		441.2.f.e.295.1		10
21.17	even	6		441.2.f.f.295.1		10
21.20	even	2		441.2.h.f.214.5		10
28.23	odd	6		3024.2.t.i.289.3		10
36.23	even	6		1008.2.t.i.193.2		10
36.31	odd	6		3024.2.t.i.1873.3		10
63.2	odd	6		567.2.e.f.163.1		10
63.4	even	3		1323.2.f.e.442.5		10
63.5	even	6		441.2.h.f.373.5		10
63.11	odd	6		3969.2.a.z.1.5		5
63.13	odd	6		1323.2.g.f.361.5		10
63.16	even	3		567.2.e.e.163.5		10
63.23	odd	6		63.2.h.b.58.5	yes	10
63.25	even	3		3969.2.a.bc.1.1		5
63.31	odd	6		1323.2.f.f.442.5		10
63.32	odd	6		441.2.f.e.148.1		10
63.38	even	6		3969.2.a.ba.1.5		5
63.40	odd	6		1323.2.h.f.226.1		10
63.41	even	6		441.2.g.f.67.1		10
63.52	odd	6		3969.2.a.bb.1.1		5
63.58	even	3	inner	189.2.h.b.37.1		10
63.59	even	6		441.2.f.f.148.1		10
84.23	even	6		1008.2.t.i.961.2		10
252.23	even	6		1008.2.q.i.625.5		10
252.247	odd	6		3024.2.q.i.2305.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.1	✓	10	9.5	odd	6
63.2.g.b.16.1	yes	10	21.2	odd	6
63.2.h.b.25.5	yes	10	3.2	odd	2
63.2.h.b.58.5	yes	10	63.23	odd	6
189.2.g.b.100.5		10	7.2	even	3
189.2.g.b.172.5		10	9.4	even	3
189.2.h.b.37.1		10	63.58	even	3	inner
189.2.h.b.46.1		10	1.1	even	1	trivial
441.2.f.e.148.1		10	63.32	odd	6
441.2.f.e.295.1		10	21.11	odd	6
441.2.f.f.148.1		10	63.59	even	6
441.2.f.f.295.1		10	21.17	even	6
441.2.g.f.67.1		10	63.41	even	6
441.2.g.f.79.1		10	21.5	even	6
441.2.h.f.214.5		10	21.20	even	2
441.2.h.f.373.5		10	63.5	even	6
567.2.e.e.163.5		10	63.16	even	3
567.2.e.e.487.5		10	9.7	even	3
567.2.e.f.163.1		10	63.2	odd	6
567.2.e.f.487.1		10	9.2	odd	6
1008.2.q.i.529.5		10	12.11	even	2
1008.2.q.i.625.5		10	252.23	even	6
1008.2.t.i.193.2		10	36.23	even	6
1008.2.t.i.961.2		10	84.23	even	6
1323.2.f.e.442.5		10	63.4	even	3
1323.2.f.e.883.5		10	7.4	even	3
1323.2.f.f.442.5		10	63.31	odd	6
1323.2.f.f.883.5		10	7.3	odd	6
1323.2.g.f.361.5		10	63.13	odd	6
1323.2.g.f.667.5		10	7.5	odd	6
1323.2.h.f.226.1		10	63.40	odd	6
1323.2.h.f.802.1		10	7.6	odd	2
3024.2.q.i.2305.3		10	252.247	odd	6
3024.2.q.i.2881.3		10	4.3	odd	2
3024.2.t.i.289.3		10	28.23	odd	6
3024.2.t.i.1873.3		10	36.31	odd	6
3969.2.a.z.1.5		5	63.11	odd	6
3969.2.a.ba.1.5		5	63.38	even	6
3969.2.a.bb.1.1		5	63.52	odd	6
3969.2.a.bc.1.1		5	63.25	even	3

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.05365 q^{2} +2.21746 q^{4} +(-0.0731228 + 0.126652i) q^{5} +(-2.33035 + 1.25278i) q^{7} -0.446582 q^{8} +O(q^{10})\)	\(q-2.05365 q^{2} +2.21746 q^{4} +(-0.0731228 + 0.126652i) q^{5} +(-2.33035 + 1.25278i) q^{7} -0.446582 q^{8} +(0.150168 - 0.260099i) q^{10} +(0.832020 + 1.44110i) q^{11} +(0.0999454 + 0.173111i) q^{13} +(4.78572 - 2.57276i) q^{14} -3.51780 q^{16} +(-3.13555 + 5.43093i) q^{17} +(3.45879 + 5.99080i) q^{19} +(-0.162147 + 0.280847i) q^{20} +(-1.70867 - 2.95951i) q^{22} +(-3.09092 + 5.35363i) q^{23} +(2.48931 + 4.31160i) q^{25} +(-0.205252 - 0.355508i) q^{26} +(-5.16746 + 2.77798i) q^{28} +(2.46757 - 4.27396i) q^{29} -2.51780 q^{31} +8.11747 q^{32} +(6.43931 - 11.1532i) q^{34} +(0.0117348 - 0.386752i) q^{35} +(-3.50023 - 6.06257i) q^{37} +(-7.10312 - 12.3030i) q^{38} +(0.0326554 - 0.0565608i) q^{40} +(-1.15895 - 2.00736i) q^{41} +(-0.940993 + 1.62985i) q^{43} +(1.84497 + 3.19558i) q^{44} +(6.34765 - 10.9944i) q^{46} +1.81177 q^{47} +(3.86110 - 5.83883i) q^{49} +(-5.11215 - 8.85451i) q^{50} +(0.221625 + 0.383865i) q^{52} +(2.67307 - 4.62989i) q^{53} -0.243359 q^{55} +(1.04069 - 0.559468i) q^{56} +(-5.06752 + 8.77720i) q^{58} +4.57099 q^{59} -0.678276 q^{61} +5.17066 q^{62} -9.63481 q^{64} -0.0292332 q^{65} -6.18684 q^{67} +(-6.95296 + 12.0429i) q^{68} +(-0.0240991 + 0.794251i) q^{70} -1.27749 q^{71} +(-0.778603 + 1.34858i) q^{73} +(7.18823 + 12.4504i) q^{74} +(7.66972 + 13.2843i) q^{76} +(-3.74428 - 2.31594i) q^{77} +12.7957 q^{79} +(0.257231 - 0.445537i) q^{80} +(2.38008 + 4.12241i) q^{82} +(-3.75687 + 6.50709i) q^{83} +(-0.458561 - 0.794251i) q^{85} +(1.93247 - 3.34713i) q^{86} +(-0.371566 - 0.643571i) q^{88} +(-4.53394 - 7.85301i) q^{89} +(-0.449777 - 0.278199i) q^{91} +(-6.85398 + 11.8714i) q^{92} -3.72074 q^{94} -1.01167 q^{95} +(-3.98514 + 6.90246i) q^{97} +(-7.92933 + 11.9909i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) \) 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8	\( 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8} - 7 q^{10} - 4 q^{11} - 8 q^{13} + 20 q^{14} - 4 q^{16} - 12 q^{17} + q^{19} - 5 q^{20} - q^{22} - 3 q^{23} - q^{25} - 11 q^{26} - 2 q^{28} - 7 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{34} - 5 q^{35} - 20 q^{38} - 3 q^{40} - 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} + 54 q^{47} - 8 q^{49} - 19 q^{50} - 10 q^{52} + 21 q^{53} + 4 q^{55} - 18 q^{56} - 10 q^{58} + 60 q^{59} + 28 q^{61} + 12 q^{62} - 50 q^{64} - 22 q^{65} + 4 q^{67} - 27 q^{68} + 40 q^{70} + 6 q^{71} + 15 q^{73} + 36 q^{74} + 5 q^{76} - 11 q^{77} + 8 q^{79} - 20 q^{80} - 5 q^{82} - 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} - 28 q^{89} - 4 q^{91} - 27 q^{92} + 6 q^{94} - 28 q^{95} - 12 q^{97} - 59 q^{98}+O(q^{100}) \) 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8 - 7 * q^10 - 4 * q^11 - 8 * q^13 + 20 * q^14 - 4 * q^16 - 12 * q^17 + q^19 - 5 * q^20 - q^22 - 3 * q^23 - q^25 - 11 * q^26 - 2 * q^28 - 7 * q^29 + 6 * q^31 - 4 * q^32 + 3 * q^34 - 5 * q^35 - 20 * q^38 - 3 * q^40 - 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 + 54 * q^47 - 8 * q^49 - 19 * q^50 - 10 * q^52 + 21 * q^53 + 4 * q^55 - 18 * q^56 - 10 * q^58 + 60 * q^59 + 28 * q^61 + 12 * q^62 - 50 * q^64 - 22 * q^65 + 4 * q^67 - 27 * q^68 + 40 * q^70 + 6 * q^71 + 15 * q^73 + 36 * q^74 + 5 * q^76 - 11 * q^77 + 8 * q^79 - 20 * q^80 - 5 * q^82 - 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 - 28 * q^89 - 4 * q^91 - 27 * q^92 + 6 * q^94 - 28 * q^95 - 12 * q^97 - 59 * q^98

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