LMFDB - Embedded newform 184.2.h.c.91.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [184,2,Mod(91,184)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("184.91"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(184, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 184 = 2^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	184.h (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.46924739719$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.64974433091584.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{11} + 8x^{10} - 10x^{9} + 24x^{7} - 46x^{6} + 48x^{5} - 80x^{3} + 128x^{2} - 128x + 64 $ x^12 - 4x^11 + 8x^10 - 10x^9 + 24x^7 - 46x^6 + 48x^5 - 80x^3 + 128x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 23 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.7
Root			$1.35381 + 0.408906i$ of defining polynomial
Character	$\chi$	$=$	184.91
Dual form			184.2.h.c.91.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.344446 + 1.37163i) q^{2} +0.311108 q^{3} +(-1.76271 - 0.944902i) q^{4} -2.74325 q^{5} +(-0.107160 + 0.426723i) q^{6} -3.33118 q^{7} +(1.90321 - 2.09232i) q^{8} -2.90321 q^{9} +(0.944902 - 3.76271i) q^{10} +1.78568i q^{11} +(-0.548394 - 0.293966i) q^{12} +3.98212i q^{13} +(1.14741 - 4.56914i) q^{14} -0.853447 q^{15} +(2.21432 + 3.33118i) q^{16} -5.73975i q^{17} +(1.00000 - 3.98212i) q^{18} +5.18421i q^{19} +(4.83557 + 2.59210i) q^{20} -1.03636 q^{21} +(-2.44928 - 0.615071i) q^{22} +(4.63306 + 1.23887i) q^{23} +(0.592104 - 0.650936i) q^{24} +2.52543 q^{25} +(-5.46198 - 1.37163i) q^{26} -1.83654 q^{27} +(5.87192 + 3.14764i) q^{28} -5.87192i q^{29} +(0.293966 - 1.17061i) q^{30} -3.53370i q^{31} +(-5.33185 + 1.88980i) q^{32} +0.555539i q^{33} +(7.87278 + 1.97703i) q^{34} +9.13828 q^{35} +(5.11753 + 2.74325i) q^{36} -6.92788 q^{37} +(-7.11079 - 1.78568i) q^{38} +1.23887i q^{39} +(-5.22099 + 5.73975i) q^{40} -5.70964 q^{41} +(0.356969 - 1.42149i) q^{42} +11.4795i q^{43} +(1.68729 - 3.14764i) q^{44} +7.96424 q^{45} +(-3.29510 + 5.92809i) q^{46} +9.02020i q^{47} +(0.688892 + 1.03636i) q^{48} +4.09679 q^{49} +(-0.869874 + 3.46394i) q^{50} -1.78568i q^{51} +(3.76271 - 7.01934i) q^{52} -1.30187 q^{53} +(0.632587 - 2.51904i) q^{54} -4.89857i q^{55} +(-6.33995 + 6.96989i) q^{56} +1.61285i q^{57} +(8.05408 + 2.02256i) q^{58} -6.62222 q^{59} +(1.50438 + 0.806424i) q^{60} +5.48650 q^{61} +(4.84691 + 1.21717i) q^{62} +9.67113 q^{63} +(-0.755569 - 7.96424i) q^{64} -10.9240i q^{65} +(-0.761992 - 0.191353i) q^{66} -3.39853i q^{67} +(-5.42350 + 10.1175i) q^{68} +(1.44138 + 0.385422i) q^{69} +(-3.14764 + 12.5343i) q^{70} -5.42350i q^{71} +(-5.52543 + 6.07444i) q^{72} -11.8573 q^{73} +(2.38628 - 9.50246i) q^{74} +0.785680 q^{75} +(4.89857 - 9.13828i) q^{76} -5.94843i q^{77} +(-1.69926 - 0.426723i) q^{78} +0.405022 q^{79} +(-6.07444 - 9.13828i) q^{80} +8.13828 q^{81} +(1.96666 - 7.83148i) q^{82} +3.39853i q^{83} +(1.82680 + 0.979256i) q^{84} +15.7456i q^{85} +(-15.7456 - 3.95407i) q^{86} -1.82680i q^{87} +(3.73621 + 3.39853i) q^{88} -16.6637i q^{89} +(-2.74325 + 10.9240i) q^{90} -13.2652i q^{91} +(-6.99614 - 6.56156i) q^{92} -1.09936i q^{93} +(-12.3723 - 3.10697i) q^{94} -14.2216i q^{95} +(-1.65878 + 0.587933i) q^{96} +14.4953i q^{97} +(-1.41112 + 5.61926i) q^{98} -5.18421i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + 4 q^{3} - 8 q^{4} + 12 q^{6} - 4 q^{8} - 8 q^{9} - 20 q^{12} + 12 q^{18} - 20 q^{24} + 4 q^{25} - 12 q^{26} + 4 q^{27} + 16 q^{32} - 24 q^{35} + 8 q^{36} + 12 q^{41} + 20 q^{46} + 8 q^{48}+ \cdots - 16 q^{98}+O(q^{100}) $ 12 * q - 4 * q^2 + 4 * q^3 - 8 * q^4 + 12 * q^6 - 4 * q^8 - 8 * q^9 - 20 * q^12 + 12 * q^18 - 20 * q^24 + 4 * q^25 - 12 * q^26 + 4 * q^27 + 16 * q^32 - 24 * q^35 + 8 * q^36 + 12 * q^41 + 20 * q^46 + 8 * q^48 + 76 * q^49 + 16 * q^50 + 32 * q^52 - 32 * q^54 + 16 * q^58 - 80 * q^59 - 8 * q^62 - 8 * q^64 - 12 * q^70 - 40 * q^72 - 36 * q^73 + 36 * q^75 + 20 * q^78 - 36 * q^81 + 24 * q^82 + 28 * q^92 - 56 * q^94 + 8 * q^96 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/184\mathbb{Z}\right)^\times$.

$n$	$47$	$93$	$97$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−0.344446	+	1.37163i	−0.243560	+	0.969886i
$2$	−0.344446	+	1.37163i	−0.243560	+	0.969886i
$3$	0.311108			0.179618			0.0898091	−	0.995959i	$-0.471374\pi$
$3$	0.311108			0.179618			0.0898091	+	0.995959i	$0.471374\pi$
$4$	−1.76271	−	0.944902i	−0.881357	−	0.472451i
$5$	−2.74325			−1.22682			−0.613410	−	0.789765i	$-0.710203\pi$
$5$	−2.74325			−1.22682			−0.613410	+	0.789765i	$0.710203\pi$
$6$	−0.107160	+	0.426723i	−0.0437478	+	0.174209i
$7$	−3.33118			−1.25907			−0.629535	−	0.776972i	$-0.716754\pi$
$7$	−3.33118			−1.25907			−0.629535	+	0.776972i	$0.716754\pi$
$8$	1.90321	−	2.09232i	0.672887	−	0.739745i
$9$	−2.90321			−0.967737
$10$	0.944902	−	3.76271i	0.298804	−	1.18987i
$11$			1.78568i			0.538403i	0.963084	+	0.269201i	$0.0867597\pi$
$11$			1.78568i			0.538403i	−0.963084	+	0.269201i	$0.913240\pi$
$12$	−0.548394	−	0.293966i	−0.158308	−	0.0848608i
$13$			3.98212i			1.10444i	0.833698	+	0.552221i	$0.186219\pi$
$13$			3.98212i			1.10444i	−0.833698	+	0.552221i	$0.813781\pi$
$14$	1.14741	−	4.56914i	0.306659	−	1.22115i
$15$	−0.853447			−0.220359
$16$	2.21432	+	3.33118i	0.553580	+	0.832796i
$17$		−	5.73975i		−	1.39209i	−0.717997	−	0.696047i	$-0.754941\pi$
$17$		−	5.73975i		−	1.39209i	0.717997	−	0.696047i	$-0.245059\pi$
$18$	1.00000	−	3.98212i	0.235702	−	0.938595i
$19$			5.18421i			1.18934i	0.803970	+	0.594669i	$0.202717\pi$
$19$			5.18421i			1.18934i	−0.803970	+	0.594669i	$0.797283\pi$
$20$	4.83557	+	2.59210i	1.08127	+	0.579612i
$21$	−1.03636			−0.226152
$22$	−2.44928	−	0.615071i	−0.522189	−	0.131133i
$23$	4.63306	+	1.23887i	0.966059	+	0.258322i
$23$	4.63306	+	1.23887i	0.966059	+	0.258322i
$24$	0.592104	−	0.650936i	0.120863	−	0.132872i
$25$	2.52543			0.505086
$26$	−5.46198	−	1.37163i	−1.07118	−	0.268998i
$27$	−1.83654			−0.353441
$28$	5.87192	+	3.14764i	1.10969	+	0.594849i
$29$		−	5.87192i		−	1.09039i	−0.838310	−	0.545194i	$-0.816456\pi$
$29$		−	5.87192i		−	1.09039i	0.838310	−	0.545194i	$-0.183544\pi$
$30$	0.293966	−	1.17061i	0.0536707	−	0.213723i
$31$		−	3.53370i		−	0.634670i	−0.948313	−	0.317335i	$-0.897212\pi$
$31$		−	3.53370i		−	0.634670i	0.948313	−	0.317335i	$-0.102788\pi$
$32$	−5.33185	+	1.88980i	−0.942547	+	0.334073i
$33$			0.555539i			0.0967069i
$34$	7.87278	+	1.97703i	1.35017	+	0.339058i
$35$	9.13828			1.54465
$36$	5.11753	+	2.74325i	0.852922	+	0.457209i
$37$	−6.92788			−1.13894			−0.569468	−	0.822013i	$-0.692851\pi$
$37$	−6.92788			−1.13894			−0.569468	+	0.822013i	$0.692851\pi$
$38$	−7.11079	−	1.78568i	−1.15352	−	0.289676i
$39$			1.23887i			0.198378i
$40$	−5.22099	+	5.73975i	−0.825511	+	0.907534i
$41$	−5.70964			−0.891695			−0.445848	−	0.895109i	$-0.647098\pi$
$41$	−5.70964			−0.891695			−0.445848	+	0.895109i	$0.647098\pi$
$42$	0.356969	−	1.42149i	0.0550816	−	0.219341i
$43$			11.4795i			1.75061i	0.483574	+	0.875303i	$0.339338\pi$
$43$			11.4795i			1.75061i	−0.483574	+	0.875303i	$0.660662\pi$
$44$	1.68729	−	3.14764i	0.254369	−	0.474525i
$45$	7.96424			1.18724
$46$	−3.29510	+	5.92809i	−0.485836	+	0.874050i
$47$			9.02020i			1.31573i	0.753135	+	0.657866i	$0.228540\pi$
$47$			9.02020i			1.31573i	−0.753135	+	0.657866i	$0.771460\pi$
$48$	0.688892	+	1.03636i	0.0994330	+	0.149585i
$49$	4.09679			0.585255
$50$	−0.869874	+	3.46394i	−0.123019	+	0.489875i
$51$		−	1.78568i		−	0.250045i
$52$	3.76271	−	7.01934i	0.521795	−	0.973407i
$53$	−1.30187			−0.178826			−0.0894129	−	0.995995i	$-0.528499\pi$
$53$	−1.30187			−0.178826			−0.0894129	+	0.995995i	$0.528499\pi$
$54$	0.632587	−	2.51904i	0.0860842	−	0.342798i
$55$		−	4.89857i		−	0.660523i
$56$	−6.33995	+	6.96989i	−0.847211	+	0.931391i
$57$			1.61285i			0.213627i
$58$	8.05408	+	2.02256i	1.05755	+	0.265575i
$59$	−6.62222			−0.862139			−0.431070	−	0.902319i	$-0.641864\pi$
$59$	−6.62222			−0.862139			−0.431070	+	0.902319i	$0.641864\pi$
$60$	1.50438	+	0.806424i	0.194215	+	0.104109i
$61$	5.48650			0.702475			0.351237	−	0.936286i	$-0.385761\pi$
$61$	5.48650			0.702475			0.351237	+	0.936286i	$0.385761\pi$
$62$	4.84691	+	1.21717i	0.615558	+	0.154580i
$63$	9.67113			1.21845
$64$	−0.755569	−	7.96424i	−0.0944461	−	0.995530i
$65$		−	10.9240i		−	1.35495i
$66$	−0.761992	−	0.191353i	−0.0937947	−	0.0235540i
$67$		−	3.39853i		−	0.415196i	−0.978214	−	0.207598i	$-0.933435\pi$
$67$		−	3.39853i		−	0.415196i	0.978214	−	0.207598i	$-0.0665646\pi$
$68$	−5.42350	+	10.1175i	−0.657696	+	1.22693i
$69$	1.44138	+	0.385422i	0.173522	+	0.0463993i
$70$	−3.14764	+	12.5343i	−0.376215	+	1.49813i
$71$		−	5.42350i		−	0.643651i	−0.946799	−	0.321826i	$-0.895704\pi$
$71$		−	5.42350i		−	0.643651i	0.946799	−	0.321826i	$-0.104296\pi$
$72$	−5.52543	+	6.07444i	−0.651178	+	0.715879i
$73$	−11.8573			−1.38779			−0.693895	−	0.720076i	$-0.744107\pi$
$73$	−11.8573			−1.38779			−0.693895	+	0.720076i	$0.744107\pi$
$74$	2.38628	−	9.50246i	0.277400	−	1.10464i
$75$	0.785680			0.0907225
$76$	4.89857	−	9.13828i	0.561904	−	1.04823i
$77$		−	5.94843i		−	0.677886i
$78$	−1.69926	−	0.426723i	−0.192404	−	0.0483169i
$79$	0.405022			0.0455686			0.0227843	−	0.999740i	$-0.492747\pi$
$79$	0.405022			0.0455686			0.0227843	+	0.999740i	$0.492747\pi$
$80$	−6.07444	−	9.13828i	−0.679143	−	1.02169i
$81$	8.13828			0.904253
$82$	1.96666	−	7.83148i	0.217181	−	0.864843i
$83$			3.39853i			0.373037i	0.982451	+	0.186518i	$0.0597204\pi$
$83$			3.39853i			0.373037i	−0.982451	+	0.186518i	$0.940280\pi$
$84$	1.82680	+	0.979256i	0.199320	+	0.106846i
$85$			15.7456i			1.70785i
$86$	−15.7456	−	3.95407i	−1.69789	−	0.426378i
$87$		−	1.82680i		−	0.195854i
$88$	3.73621	+	3.39853i	0.398281	+	0.362284i
$89$		−	16.6637i		−	1.76635i	−0.469045	−	0.883174i	$-0.655402\pi$
$89$		−	16.6637i		−	1.76635i	0.469045	−	0.883174i	$-0.344598\pi$
$90$	−2.74325	+	10.9240i	−0.289164	+	1.15149i
$91$		−	13.2652i		−	1.39057i
$92$	−6.99614	−	6.56156i	−0.729398	−	0.684089i
$93$		−	1.09936i		−	0.113998i
$94$	−12.3723	−	3.10697i	−1.27611	−	0.320460i
$95$		−	14.2216i		−	1.45910i
$96$	−1.65878	+	0.587933i	−0.169299	+	0.0600057i
$97$			14.4953i			1.47178i	0.677103	+	0.735888i	$0.263235\pi$
$97$			14.4953i			1.47178i	−0.677103	+	0.735888i	$0.736765\pi$
$98$	−1.41112	+	5.61926i	−0.142545	+	0.567631i
$99$		−	5.18421i		−	0.521033i
$100$	−4.45161	−	2.38628i	−0.445161	−	0.238628i
$101$			6.47946i			0.644730i	0.946615	+	0.322365i	$0.104478\pi$
$101$			6.47946i			0.644730i	−0.946615	+	0.322365i	$0.895522\pi$
$102$	2.44928	+	0.615071i	0.242515	+	0.0609011i
$103$	−6.74497			−0.664602			−0.332301	−	0.943173i	$-0.607825\pi$
$103$	−6.74497			−0.664602			−0.332301	+	0.943173i	$0.607825\pi$
$104$	8.33185	+	7.57882i	0.817005	+	0.743164i
$105$	2.84299			0.277447
$106$	0.448425	−	1.78568i	0.0435548	−	0.173441i
$107$		−	11.4795i		−	1.10976i	−0.831929	−	0.554882i	$-0.812763\pi$
$107$		−	11.4795i		−	1.10976i	0.831929	−	0.554882i	$-0.187237\pi$
$108$	3.23729	+	1.73535i	0.311508	+	0.166984i
$109$	3.77961			0.362021			0.181010	−	0.983481i	$-0.442063\pi$
$109$	3.77961			0.362021			0.181010	+	0.983481i	$0.442063\pi$
$110$	6.71900	+	1.68729i	0.640632	+	0.160877i
$111$	−2.15532			−0.204574
$112$	−7.37631	−	11.0968i	−0.696995	−	1.04855i
$113$			2.16839i			0.203985i	0.994785	+	0.101992i	$0.0325217\pi$
$113$			2.16839i			0.203985i	−0.994785	+	0.101992i	$0.967478\pi$
$114$	−2.21222	−	0.555539i	−0.207194	−	0.0520310i
$115$	−12.7096	−	3.39853i	−1.18518	−	0.316914i
$116$	−5.54839	+	10.3505i	−0.515155	+	0.961022i
$117$		−	11.5609i		−	1.06881i
$118$	2.28100	−	9.08320i	0.209983	−	0.836176i
$119$			19.1202i			1.75274i
$120$	−1.62429	+	1.78568i	−0.148277	+	0.163010i
$121$	7.81135			0.710122
$122$	−1.88980	+	7.52543i	−0.171095	+	0.681320i
$123$	−1.77631			−0.160165
$124$	−3.33900	+	6.22889i	−0.299851	+	0.559371i
$125$	6.78837			0.607171
$126$	−3.33118	+	13.2652i	−0.296765	+	1.18176i
$127$			5.24059i			0.465027i	0.972593	+	0.232514i	$0.0746950\pi$
$127$			5.24059i			0.465027i	−0.972593	+	0.232514i	$0.925305\pi$
$128$	11.1842	+	1.70689i	0.988554	+	0.150870i
$129$			3.57136i			0.314441i
$130$	14.9836	+	3.76271i	1.31415	+	0.330012i
$131$	−0.887390			−0.0775317			−0.0387658	−	0.999248i	$-0.512343\pi$
$131$	−0.887390			−0.0775317			−0.0387658	+	0.999248i	$0.512343\pi$
$132$	0.524930	−	0.979256i	0.0456893	−	0.0852333i
$133$		−	17.2696i		−	1.49746i
$134$	4.66151	+	1.17061i	0.402693	+	0.101125i
$135$	5.03808			0.433609
$136$	−12.0094	−	10.9240i	−1.02979	−	0.936721i
$137$			15.0509i			1.28588i	0.765916	+	0.642941i	$0.222286\pi$
$137$			15.0509i			1.28588i	−0.765916	+	0.642941i	$0.777714\pi$
$138$	−1.02513	+	1.84428i	−0.0872650	+	0.156995i
$139$	16.0716			1.36318			0.681588	−	0.731737i	$-0.261290\pi$
$139$	16.0716			1.36318			0.681588	+	0.731737i	$0.261290\pi$
$140$	−16.1082	−	8.63478i	−1.36139	−	0.729772i
$141$			2.80625i			0.236329i
$142$	7.43901	+	1.86810i	0.624268	+	0.156768i
$143$	−7.11079			−0.594634
$144$	−6.42864	−	9.67113i	−0.535720	−	0.805928i
$145$			16.1082i			1.33771i
$146$	4.08419	−	16.2637i	0.338010	−	1.34600i
$147$	1.27454			0.105123
$148$	12.2119	+	6.54617i	1.00381	+	0.538092i
$149$	−7.55922			−0.619275			−0.309638	−	0.950855i	$-0.600208\pi$
$149$	−7.55922			−0.619275			−0.309638	+	0.950855i	$0.600208\pi$
$150$	−0.270624	+	1.07766i	−0.0220964	+	0.0879905i
$151$		−	0.0630028i		−	0.00512710i	−0.999997	−	0.00256355i	$-0.999184\pi$
$151$		−	0.0630028i		−	0.00512710i	0.999997	−	0.00256355i	$-0.000816004\pi$
$152$	10.8470	+	9.86665i	0.879808	+	0.800291i
$153$			16.6637i			1.34718i
$154$	8.15902	+	2.04891i	0.657472	+	0.165106i
$155$			9.69381i			0.778626i
$156$	1.17061	−	2.18377i	0.0937238	−	0.174842i
$157$	−7.06739			−0.564039			−0.282020	−	0.959409i	$-0.591004\pi$
$157$	−7.06739			−0.564039			−0.282020	+	0.959409i	$0.591004\pi$
$158$	−0.139508	+	0.555539i	−0.0110987	+	0.0441963i
$159$	−0.405022			−0.0321204
$160$	14.6266	−	5.18421i	1.15633	−	0.409848i
$161$	−15.4336	−	4.12690i	−1.21634	−	0.325245i
$162$	−2.80320	+	11.1627i	−0.220240	+	0.877022i
$163$	−1.73038			−0.135534			−0.0677669	−	0.997701i	$-0.521587\pi$
$163$	−1.73038			−0.135534			−0.0677669	+	0.997701i	$0.521587\pi$
$164$	10.0645	+	5.39505i	0.785902	+	0.421282i
$165$		−	1.52398i		−	0.118642i
$166$	−4.66151	−	1.17061i	−0.361803	−	0.0908569i
$167$			11.7438i			0.908766i	0.890806	+	0.454383i	$0.150140\pi$
$167$			11.7438i			0.908766i	−0.890806	+	0.454383i	$0.849860\pi$
$168$	−1.97241	+	2.16839i	−0.152175	+	0.167295i
$169$	−2.85728			−0.219791
$170$	−21.5970	−	5.42350i	−1.65642	−	0.415963i
$171$		−	15.0509i		−	1.15097i
$172$	10.8470	−	20.2351i	0.827076	−	1.54291i
$173$			0.992955i			0.0754930i	0.999287	+	0.0377465i	$0.0120179\pi$
$173$			0.992955i			0.0754930i	−0.999287	+	0.0377465i	$0.987982\pi$
$174$	2.50569	+	0.629235i	0.189956	+	0.0477022i
$175$	−8.41266			−0.635938
$176$	−5.94843	+	3.95407i	−0.448380	+	0.298049i
$177$	−2.06022			−0.154856
$178$	22.8564	+	5.73975i	1.71316	+	0.430212i
$179$	−9.83654			−0.735217			−0.367609	−	0.929981i	$-0.619823\pi$
$179$	−9.83654			−0.735217			−0.367609	+	0.929981i	$0.619823\pi$
$180$	−14.0387	−	7.52543i	−1.04638	−	0.560912i
$181$	−14.8921			−1.10692			−0.553461	−	0.832875i	$-0.686693\pi$
$181$	−14.8921			−1.10692			−0.553461	+	0.832875i	$0.686693\pi$
$182$	18.1949	+	4.56914i	1.34869	+	0.338687i
$183$	1.70689			0.126177
$184$	11.4098	−	7.33598i	0.841141	−	0.540816i
$185$	19.0049			1.39727
$186$	1.50791	+	0.378670i	0.110565	+	0.0277655i
$187$	10.2494			0.749507
$188$	8.52320	−	15.9000i	0.621619	−	1.15963i
$189$	6.11784			0.445007
$190$	19.5067	+	4.89857i	1.41516	+	0.355380i
$191$	9.58853			0.693802			0.346901	−	0.937902i	$-0.387234\pi$
$191$	9.58853			0.693802			0.346901	+	0.937902i	$0.387234\pi$
$192$	−0.235063	−	2.47774i	−0.0169642	−	0.178815i
$193$	18.9956			1.36733			0.683665	−	0.729796i	$-0.260385\pi$
$193$	18.9956			1.36733			0.683665	+	0.729796i	$0.260385\pi$
$194$	−19.8821	−	4.99285i	−1.42745	−	0.358466i
$195$		−	3.39853i		−	0.243374i
$196$	−7.22146	−	3.87106i	−0.515819	−	0.276505i
$197$			20.4985i			1.46046i	0.683201	+	0.730230i	$0.260587\pi$
$197$			20.4985i			1.46046i	−0.683201	+	0.730230i	$0.739413\pi$
$198$	7.11079	+	1.78568i	0.505342	+	0.126903i
$199$	−6.70577			−0.475359			−0.237680	−	0.971344i	$-0.576387\pi$
$199$	−6.70577			−0.475359			−0.237680	+	0.971344i	$0.576387\pi$
$200$	4.80642	−	5.28399i	0.339865	−	0.373635i
$201$		−	1.05731i		−	0.0745768i
$202$	−8.88739	−	2.23182i	−0.625315	−	0.157031i
$203$			19.5605i			1.37288i
$204$	−1.68729	+	3.14764i	−0.118134	+	0.220379i
$205$	15.6630			1.09395
$206$	2.32328	−	9.25158i	0.161871	−	0.644588i
$207$	−13.4507	−	3.59670i	−0.934891	−	0.249988i
$208$	−13.2652	+	8.81769i	−0.919774	+	0.611397i
$209$	−9.25734			−0.640343
$210$	−0.979256	+	3.89952i	−0.0675751	+	0.269092i
$211$	−18.9590			−1.30519			−0.652595	−	0.757707i	$-0.726320\pi$
$211$	−18.9590			−1.30519			−0.652595	+	0.757707i	$0.726320\pi$
$212$	2.29483	+	1.23014i	0.157609	+	0.0844864i
$213$		−	1.68729i		−	0.115611i
$214$	15.7456	+	3.95407i	1.07634	+	0.270294i
$215$		−	31.4911i		−	2.14768i
$216$	−3.49532	+	3.84261i	−0.237826	+	0.261457i
$217$			11.7714i			0.799094i
$218$	−1.30187	+	5.18421i	−0.0881739	+	0.351119i
$219$	−3.68889			−0.249272
$220$	−4.62867	+	8.63478i	−0.312065	+	0.582156i
$221$	22.8564			1.53749
$222$	0.742391	−	2.95629i	0.0498260	−	0.198413i
$223$			16.1114i			1.07890i	0.842018	+	0.539449i	$0.181368\pi$
$223$			16.1114i			1.07890i	−0.842018	+	0.539449i	$0.818632\pi$
$224$	17.7614	−	6.29529i	1.18673	−	0.420622i
$225$	−7.33185			−0.488790
$226$	−2.97421	−	0.746892i	−0.197842	−	0.0496825i
$227$			0.674602i			0.0447749i	0.999749	+	0.0223875i	$0.00712674\pi$
$227$			0.674602i			0.0447749i	−0.999749	+	0.0223875i	$0.992873\pi$
$228$	1.52398	−	2.84299i	0.100928	−	0.188282i
$229$	−22.5908			−1.49285			−0.746423	−	0.665472i	$-0.768230\pi$
$229$	−22.5908			−1.49285			−0.746423	+	0.665472i	$0.768230\pi$
$230$	9.03929	−	16.2623i	0.596033	−	1.07230i
$231$		−	1.85060i		−	0.121761i
$232$	−12.2859	−	11.1755i	−0.806610	−	0.733709i
$233$	14.1842			0.929238			0.464619	−	0.885511i	$-0.346191\pi$
$233$	14.1842			0.929238			0.464619	+	0.885511i	$0.346191\pi$
$234$	15.8573	+	3.98212i	1.03662	+	0.260319i
$235$		−	24.7447i		−	1.61416i
$236$	11.6731	+	6.25735i	0.759852	+	0.407319i
$237$	0.126006			0.00818495
$238$	−26.2257	−	6.58586i	−1.69996	−	0.426898i
$239$		−	28.6714i		−	1.85460i	−0.374322	−	0.927299i	$-0.622125\pi$
$239$		−	28.6714i		−	1.85460i	0.374322	−	0.927299i	$-0.377875\pi$
$240$	−1.88980	−	2.84299i	−0.121986	−	0.183514i
$241$		−	7.35260i		−	0.473622i	−0.971556	−	0.236811i	$-0.923898\pi$
$241$		−	7.35260i		−	0.473622i	0.971556	−	0.236811i	$-0.0761023\pi$
$242$	−2.69059	+	10.7142i	−0.172958	+	0.688738i
$243$	8.04149			0.515862
$244$	−9.67113	−	5.18421i	−0.619131	−	0.331885i
$245$	−11.2385			−0.718003
$246$	0.611844	−	2.43644i	0.0390097	−	0.155341i
$247$	−20.6441			−1.31356
$248$	−7.39361	−	6.72537i	−0.469494	−	0.427061i
$249$			1.05731i			0.0670042i
$250$	−2.33823	+	9.31111i	−0.147883	+	0.588886i
$251$			6.96989i			0.439935i	0.975507	+	0.219968i	$0.0705952\pi$
$251$			6.96989i			0.439935i	−0.975507	+	0.219968i	$0.929405\pi$
$252$	−17.0474	−	9.13828i	−1.07389	−	0.575657i
$253$	−2.21222	+	8.27316i	−0.139081	+	0.520129i
$254$	−7.18813	−	1.80510i	−0.451023	−	0.113262i
$255$			4.89857i			0.306760i
$256$	−6.19358	+	14.7526i	−0.387099	+	0.922038i
$257$	−8.37778			−0.522592			−0.261296	−	0.965259i	$-0.584150\pi$
$257$	−8.37778			−0.522592			−0.261296	+	0.965259i	$0.584150\pi$
$258$	−4.89857	−	1.23014i	−0.304972	−	0.0765852i
$259$	23.0781			1.43400
$260$	−10.3221	+	19.2558i	−0.640148	+	1.19419i
$261$			17.0474i			1.05521i
$262$	0.305658	−	1.21717i	0.0188836	−	0.0751969i
$263$	−2.11192			−0.130226			−0.0651132	−	0.997878i	$-0.520741\pi$
$263$	−2.11192			−0.130226			−0.0651132	+	0.997878i	$0.520741\pi$
$264$	1.16236	+	1.05731i	0.0715385	+	0.0650728i
$265$	3.57136			0.219387
$266$	23.6874	+	5.94843i	1.45237	+	0.364722i
$267$		−	5.18421i		−	0.317268i
$268$	−3.21128	+	5.99063i	−0.196160	+	0.365936i
$269$			9.99965i			0.609689i	0.952402	+	0.304845i	$0.0986046\pi$
$269$			9.99965i			0.609689i	−0.952402	+	0.304845i	$0.901395\pi$
$270$	−1.73535	+	6.91036i	−0.105610	+	0.420551i
$271$			27.0275i			1.64180i	0.571070	+	0.820902i	$0.306529\pi$
$271$			27.0275i			1.64180i	−0.571070	+	0.820902i	$0.693471\pi$
$272$	19.1202	−	12.7096i	1.15933	−	0.770635i
$273$		−	4.12690i		−	0.249771i
$274$	−20.6441	−	5.18421i	−1.24716	−	0.313189i
$275$			4.50961i			0.271939i
$276$	−2.17655	−	2.04135i	−0.131013	−	0.122875i
$277$		−	12.6603i		−	0.760684i	−0.924846	−	0.380342i	$-0.875806\pi$
$277$		−	12.6603i		−	0.760684i	0.924846	−	0.380342i	$-0.124194\pi$
$278$	−5.53580	+	22.0442i	−0.332015	+	1.32212i
$279$			10.2591i			0.614194i
$280$	17.3921	−	19.1202i	1.03938	−	1.14265i
$281$		−	13.3842i		−	0.798437i	−0.916856	−	0.399218i	$-0.869282\pi$
$281$		−	13.3842i		−	0.798437i	0.916856	−	0.399218i	$-0.130718\pi$
$282$	−3.84913	−	0.966603i	−0.229212	−	0.0575604i
$283$		−	4.50961i		−	0.268068i	−0.990977	−	0.134034i	$-0.957207\pi$
$283$		−	4.50961i		−	0.268068i	0.990977	−	0.134034i	$-0.0427932\pi$
$284$	−5.12468	+	9.56008i	−0.304094	+	0.567286i
$285$		−	4.42445i		−	0.262082i
$286$	2.44928	−	9.75335i	0.144829	−	0.576727i
$287$	19.0198			1.12271
$288$	15.4795	−	5.48650i	0.912138	−	0.323295i
$289$	−15.9447			−0.937923
$290$	−22.0944	−	5.54839i	−1.29743	−	0.325813i
$291$			4.50961i			0.264358i
$292$	20.9010	+	11.2040i	1.22314	+	0.655663i
$293$	−15.5235			−0.906890			−0.453445	−	0.891284i	$-0.649805\pi$
$293$	−15.5235			−0.906890			−0.453445	+	0.891284i	$0.649805\pi$
$294$	−0.439011	+	1.74820i	−0.0256037	+	0.101957i
$295$	18.1664			1.05769
$296$	−13.1852	+	14.4953i	−0.766376	+	0.842523i
$297$		−	3.27946i		−	0.190294i
$298$	2.60374	−	10.3684i	0.150831	−	0.600626i
$299$	−4.93332	+	18.4494i	−0.285301	+	1.06696i
$300$	−1.38493	−	0.742391i	−0.0799589	−	0.0428620i
$301$		−	38.2403i		−	2.20413i
$302$	0.0864163	+	0.0217011i	0.00497270	+	0.00124876i
$303$			2.01581i			0.115805i
$304$	−17.2696	+	11.4795i	−0.990477	+	0.658394i
$305$	−15.0509			−0.861809
$306$	−22.8564	−	5.73975i	−1.30661	−	0.328120i
$307$	−30.8385			−1.76005			−0.880024	−	0.474929i	$-0.842474\pi$
$307$	−30.8385			−1.76005			−0.880024	+	0.474929i	$0.842474\pi$
$308$	−5.62068	+	10.4854i	−0.320268	+	0.597460i
$309$	−2.09841			−0.119375
$310$	−13.2963	−	3.33900i	−0.755178	−	0.189642i
$311$			5.64561i			0.320133i	0.987106	+	0.160067i	$0.0511709\pi$
$311$			5.64561i			0.320133i	−0.987106	+	0.160067i	$0.948829\pi$
$312$	2.59210	+	2.35783i	0.146749	+	0.133486i
$313$		−	12.3269i		−	0.696759i	−0.937354	−	0.348380i	$-0.886732\pi$
$313$		−	12.3269i		−	0.696759i	0.937354	−	0.348380i	$-0.113268\pi$
$314$	2.43434	−	9.69381i	0.137377	−	0.547054i
$315$	−26.5303			−1.49482
$316$	−0.713939	−	0.382707i	−0.0401622	−	0.0215289i
$317$		−	16.2766i		−	0.914185i	−0.889419	−	0.457092i	$-0.848891\pi$
$317$		−	16.2766i		−	0.914185i	0.889419	−	0.457092i	$-0.151109\pi$
$318$	0.139508	−	0.555539i	0.00782324	−	0.0311531i
$319$	10.4854			0.587069
$320$	2.07271	+	21.8479i	0.115868	+	1.22134i
$321$		−	3.57136i		−	0.199334i
$322$	10.9766	−	19.7476i	0.611702	−	1.10049i
$323$	29.7560			1.65567
$324$	−14.3454	−	7.68987i	−0.796969	−	0.427215i
$325$			10.0566i			0.557837i
$326$	0.596022	−	2.37343i	0.0330106	−	0.131452i
$327$	1.17587			0.0650255
$328$	−10.8666	+	11.9464i	−0.600010	+	0.659627i
$329$		−	30.0479i		−	1.65660i
$330$	2.09033	+	0.524930i	0.115069	+	0.0288965i
$331$	6.13182			0.337035			0.168518	−	0.985699i	$-0.446102\pi$
$331$	6.13182			0.337035			0.168518	+	0.985699i	$0.446102\pi$
$332$	3.21128	−	5.99063i	0.176242	−	0.328779i
$333$	20.1131			1.10219
$334$	−16.1082	−	4.04512i	−0.881400	−	0.221339i
$335$			9.32302i			0.509371i
$336$	−2.29483	−	3.45230i	−0.125193	−	0.188338i
$337$		−	11.9813i		−	0.652661i	−0.945256	−	0.326331i	$-0.894188\pi$
$337$		−	11.9813i		−	0.652661i	0.945256	−	0.326331i	$-0.105812\pi$
$338$	0.984179	−	3.91912i	0.0535323	−	0.213172i
$339$			0.674602i			0.0366394i
$340$	14.8780	−	27.7549i	0.806874	−	1.50522i
$341$	6.31005			0.341708
$342$	20.6441	+	5.18421i	1.11631	+	0.280330i
$343$	9.67113			0.522192
$344$	24.0187	+	21.8479i	1.29500	+	1.17796i
$345$	−3.95407	−	1.05731i	−0.212880	−	0.0569236i
$346$	−1.36196	−	0.342020i	−0.0732196	−	0.0183871i
$347$	27.8938			1.49742			0.748710	−	0.662898i	$-0.230674\pi$
$347$	27.8938			1.49742			0.748710	+	0.662898i	$0.230674\pi$
$348$	−1.72615	+	3.22013i	−0.0925313	+	0.172617i
$349$		−	11.1755i		−	0.598212i	−0.954220	−	0.299106i	$-0.903312\pi$
$349$		−	11.1755i		−	0.598212i	0.954220	−	0.299106i	$-0.0966884\pi$
$350$	2.89771	−	11.5390i	0.154889	−	0.616787i
$351$		−	7.31330i		−	0.390355i
$352$	−3.37459	−	9.52098i	−0.179866	−	0.507470i
$353$	−5.72393			−0.304654			−0.152327	−	0.988330i	$-0.548677\pi$
$353$	−5.72393			−0.304654			−0.152327	+	0.988330i	$0.548677\pi$
$354$	0.709636	−	2.82585i	0.0377167	−	0.150192i
$355$			14.8780i			0.789643i
$356$	−15.7456	+	29.3733i	−0.834513	+	1.55678i
$357$			5.94843i			0.314824i
$358$	3.38816	−	13.4920i	0.179070	−	0.713077i
$359$	21.0100			1.10886			0.554432	−	0.832229i	$-0.312936\pi$
$359$	21.0100			1.10886			0.554432	+	0.832229i	$0.312936\pi$
$360$	15.1576	−	16.6637i	0.798878	−	0.878254i
$361$	−7.87601			−0.414527
$362$	5.12953	−	20.4264i	0.269602	−	1.07359i
$363$	2.43017			0.127551
$364$	−12.5343	+	23.3827i	−0.656975	+	1.22559i
$365$	32.5275			1.70257
$366$	−0.587933	+	2.34122i	−0.0307317	+	0.122377i
$367$	−22.7995			−1.19012			−0.595061	−	0.803681i	$-0.702872\pi$
$367$	−22.7995			−1.19012			−0.595061	+	0.803681i	$0.702872\pi$
$368$	6.13217	+	18.1768i	0.319661	+	0.947532i
$369$	16.5763			0.862927
$370$	−6.54617	+	26.0676i	−0.340319	+	1.35519i
$371$	4.33677			0.225154
$372$	−1.03879	+	1.93786i	−0.0538586	+	0.100473i
$373$	17.4091			0.901407			0.450703	−	0.892674i	$-0.351173\pi$
$373$	17.4091			0.901407			0.450703	+	0.892674i	$0.351173\pi$
$374$	−3.53035	+	14.0583i	−0.182550	+	0.726936i
$375$	2.11192			0.109059
$376$	18.8731	+	17.1673i	0.973306	+	0.885338i
$377$	23.3827			1.20427
$378$	−2.10727	+	8.39138i	−0.108386	+	0.431606i
$379$			24.5718i			1.26217i	0.775713	+	0.631085i	$0.217390\pi$
$379$			24.5718i			1.26217i	−0.775713	+	0.631085i	$0.782610\pi$
$380$	−13.4380	+	25.0686i	−0.689355	+	1.28599i
$381$			1.63039i			0.0835273i
$382$	−3.30273	+	13.1519i	−0.168982	+	0.672908i
$383$	21.1360			1.08000			0.539999	−	0.841666i	$-0.318425\pi$
$383$	21.1360			1.08000			0.539999	+	0.841666i	$0.318425\pi$
$384$	3.47949	+	0.531028i	0.177562	+	0.0270989i
$385$			16.3180i			0.831644i
$386$	−6.54294	+	26.0548i	−0.333027	+	1.32615i
$387$		−	33.3274i		−	1.69413i
$388$	13.6967	−	25.5511i	0.695342	−	1.29716i
$389$	−37.2175			−1.88700			−0.943500	−	0.331373i	$-0.892488\pi$
$389$	−37.2175			−1.88700			−0.943500	+	0.331373i	$0.892488\pi$
$390$	4.66151	+	1.17061i	0.236045	+	0.0592761i
$391$	7.11079	−	26.5926i	0.359608	−	1.34484i
$392$	7.79706	−	8.57177i	0.393811	−	0.432940i
$393$	−0.276074			−0.0139261
$394$	−28.1163	−	7.06064i	−1.41648	−	0.355710i
$395$	−1.11108			−0.0559044
$396$	−4.89857	+	9.13828i	−0.246162	+	0.459216i
$397$			11.0495i			0.554559i	0.960789	+	0.277280i	$0.0894328\pi$
$397$			11.0495i			0.554559i	−0.960789	+	0.277280i	$0.910567\pi$
$398$	2.30978	−	9.19781i	0.115779	−	0.461044i
$399$		−	5.37269i		−	0.268971i
$400$	5.59210	+	8.41266i	0.279605	+	0.420633i
$401$		−	16.4538i		−	0.821665i	−0.911711	−	0.410833i	$-0.865238\pi$
$401$		−	16.4538i		−	0.821665i	0.911711	−	0.410833i	$-0.134762\pi$
$402$	1.45023	+	0.364186i	0.0723310	+	0.0181639i
$403$	14.0716			0.700956
$404$	6.12245	−	11.4214i	0.304603	−	0.568237i
$405$	−22.3253			−1.10935
$406$	−26.8296	−	6.73752i	−1.33153	−	0.334378i
$407$		−	12.3710i		−	0.613207i
$408$	−3.73621	−	3.39853i	−0.184970	−	0.168252i
$409$	−18.4193			−0.910774			−0.455387	−	0.890293i	$-0.650499\pi$
$409$	−18.4193			−0.910774			−0.455387	+	0.890293i	$0.650499\pi$
$410$	−5.39505	+	21.4837i	−0.266442	+	1.06101i
$411$			4.68244i			0.230968i
$412$	11.8895	+	6.37334i	0.585751	+	0.313992i
$413$	22.0598			1.08549
$414$	9.56638	−	17.2105i	0.470162	−	0.845851i
$415$		−	9.32302i		−	0.457649i
$416$	−7.52543	−	21.2321i	−0.368964	−	1.04099i
$417$	5.00000			0.244851
$418$	3.18865	−	12.6976i	0.155962	−	0.621060i
$419$			31.7146i			1.54936i	0.632355	+	0.774679i	$0.282088\pi$
$419$			31.7146i			1.54936i	−0.632355	+	0.774679i	$0.717912\pi$
$420$	−5.01138	−	2.68635i	−0.244530	−	0.131080i
$421$	18.5457			0.903863			0.451932	−	0.892053i	$-0.350735\pi$
$421$	18.5457			0.903863			0.451932	+	0.892053i	$0.350735\pi$
$422$	6.53035	−	26.0046i	0.317892	−	1.26589i
$423$		−	26.1875i		−	1.27328i
$424$	−2.47774	+	2.72393i	−0.120330	+	0.132286i
$425$		−	14.4953i		−	0.703126i
$426$	2.31433	+	0.581182i	0.112130	+	0.0281583i
$427$	−18.2766			−0.884464
$428$	−10.8470	+	20.2351i	−0.524310	+	0.978099i
$429$	−2.21222			−0.106807
$430$	43.1941	+	10.8470i	2.08300	+	0.523089i
$431$	−3.65360			−0.175988			−0.0879939	−	0.996121i	$-0.528046\pi$
$431$	−3.65360			−0.175988			−0.0879939	+	0.996121i	$0.528046\pi$
$432$	−4.06668	−	6.11784i	−0.195658	−	0.294345i
$433$			2.51405i			0.120818i	0.998174	+	0.0604088i	$0.0192404\pi$
$433$			2.51405i			0.120818i	−0.998174	+	0.0604088i	$0.980760\pi$
$434$	−16.1459	−	4.05461i	−0.775030	−	0.194627i
$435$			5.01138i			0.240277i
$436$	−6.66237	−	3.57136i	−0.319070	−	0.171037i
$437$	−6.42255	+	24.0187i	−0.307232	+	1.14897i
$438$	1.27062	−	5.05978i	0.0607128	−	0.241766i
$439$			15.6257i			0.745772i	0.927877	+	0.372886i	$0.121632\pi$
$439$			15.6257i			0.745772i	−0.927877	+	0.372886i	$0.878368\pi$
$440$	−10.2494	−	9.32302i	−0.488619	−	0.444457i
$441$	−11.8938			−0.566374
$442$	−7.87278	+	31.3504i	−0.374470	+	1.49119i
$443$	−29.6987			−1.41103			−0.705515	−	0.708695i	$-0.749284\pi$
$443$	−29.6987			−1.41103			−0.705515	+	0.708695i	$0.749284\pi$
$444$	3.79921	+	2.03657i	0.180302	+	0.0966511i
$445$			45.7127i			2.16699i
$446$	−22.0988	−	5.54951i	−1.04641	−	0.262777i
$447$	−2.35173			−0.111233
$448$	2.51694	+	26.5303i	0.118914	+	1.25344i
$449$	15.6731			0.739658			0.369829	−	0.929100i	$-0.379416\pi$
$449$	15.6731			0.739658			0.369829	+	0.929100i	$0.379416\pi$
$450$	2.52543	−	10.0566i	0.119050	−	0.474071i
$451$		−	10.1956i		−	0.480091i
$452$	2.04891	−	3.82225i	0.0963728	−	0.179783i
$453$		−	0.0196007i		−	0.000920920i
$454$	−0.925302	−	0.232364i	−0.0434266	−	0.0109054i
$455$			36.3897i			1.70598i
$456$	3.37459	+	3.06959i	0.158029	+	0.143747i
$457$			33.8829i			1.58498i	0.609887	+	0.792489i	$0.291215\pi$
$457$			33.8829i			1.58498i	−0.609887	+	0.792489i	$0.708785\pi$
$458$	7.78133	−	30.9862i	0.363598	−	1.44789i
$459$			10.5412i			0.492023i
$460$	19.1922	+	18.0000i	0.894840	+	0.839254i
$461$		−	14.4241i		−	0.671797i	−0.941898	−	0.335899i	$-0.890960\pi$
$461$		−	14.4241i		−	0.671797i	0.941898	−	0.335899i	$-0.109040\pi$
$462$	2.53833	+	0.637433i	0.118094	+	0.0296561i
$463$		−	35.7057i		−	1.65938i	−0.558222	−	0.829692i	$-0.688516\pi$
$463$		−	35.7057i		−	1.65938i	0.558222	−	0.829692i	$-0.311484\pi$
$464$	19.5605	−	13.0023i	0.908072	−	0.603617i
$465$			3.01582i			0.139855i
$466$	−4.88570	+	19.4554i	−0.226325	+	0.901255i
$467$			27.0321i			1.25090i	0.780265	+	0.625449i	$0.215084\pi$
$467$			27.0321i			1.25090i	−0.780265	+	0.625449i	$0.784916\pi$
$468$	−10.9240	+	20.3786i	−0.504960	+	0.942002i
$469$			11.3211i			0.522761i
$470$	33.9404	+	8.52320i	1.56555	+	0.393146i
$471$	−2.19872			−0.101312
$472$	−12.6035	+	13.8558i	−0.580122	+	0.637763i
$473$	−20.4987			−0.942532
$474$	−0.0434021	+	0.172833i	−0.00199353	+	0.00793846i
$475$			13.0923i			0.600718i
$476$	18.0667	−	33.7034i	0.828085	−	1.54479i
$477$	3.77961			0.173056
$478$	39.3264	+	9.87575i	1.79875	+	0.451706i
$479$	−21.7766			−0.994998			−0.497499	−	0.867464i	$-0.665748\pi$
$479$	−21.7766			−0.994998			−0.497499	+	0.867464i	$0.665748\pi$
$480$	4.55045	−	1.61285i	0.207699	−	0.0736161i
$481$		−	27.5877i		−	1.25789i
$482$	10.0850	+	2.53257i	0.459360	+	0.115356i
$483$	−4.80150	−	1.28391i	−0.218476	−	0.0584200i
$484$	−13.7692	−	7.38096i	−0.625871	−	0.335498i
$485$		−	39.7643i		−	1.80560i
$486$	−2.76986	+	11.0299i	−0.125643	+	0.500327i
$487$			25.2576i			1.14453i	0.820068	+	0.572265i	$0.193935\pi$
$487$			25.2576i			1.14453i	−0.820068	+	0.572265i	$0.806065\pi$
$488$	10.4420	−	11.4795i	0.472686	−	0.519652i
$489$	−0.538335			−0.0243443
$490$	3.87106	−	15.4150i	0.174877	−	0.696381i
$491$	4.73530			0.213701			0.106851	−	0.994275i	$-0.465923\pi$
$491$	4.73530			0.213701			0.106851	+	0.994275i	$0.465923\pi$
$492$	3.13113	+	1.67844i	0.141162	+	0.0756700i
$493$	−33.7034			−1.51792
$494$	7.11079	−	28.3160i	0.319930	−	1.27400i
$495$			14.2216i			0.639213i
$496$	11.7714	−	7.82473i	0.528551	−	0.351341i
$497$			18.0667i			0.810401i
$498$	−1.45023	−	0.364186i	−0.0649864	−	0.0163196i
$499$	25.1956			1.12791			0.563955	−	0.825806i	$-0.309279\pi$
$499$	25.1956			1.12791			0.563955	+	0.825806i	$0.309279\pi$
$500$	−11.9660	−	6.41435i	−0.535134	−	0.286858i
$501$			3.65360i			0.163231i
$502$	−9.56008	−	2.40075i	−0.426687	−	0.107151i
$503$	−36.5726			−1.63069			−0.815346	−	0.578974i	$-0.803453\pi$
$503$	−36.5726			−1.63069			−0.815346	+	0.578974i	$0.803453\pi$
$504$	18.4062	−	20.2351i	0.819878	−	0.901341i
$505$		−	17.7748i		−	0.790967i
$506$	−10.5857	−	5.88400i	−0.470591	−	0.261576i
$507$	−0.888922			−0.0394784
$508$	4.95184	−	9.23766i	0.219703	−	0.409855i
$509$		−	5.46690i		−	0.242316i	−0.992633	−	0.121158i	$-0.961339\pi$
$509$		−	5.46690i		−	0.242316i	0.992633	−	0.121158i	$-0.0386608\pi$
$510$	−6.71900	−	1.68729i	−0.297522	−	0.0747146i
$511$	39.4988			1.74732
$512$	−18.1017	−	13.5767i	−0.799990	−	0.600013i
$513$		−	9.52098i		−	0.420362i
$514$	2.88570	−	11.4912i	0.127283	−	0.506854i
$515$	18.5032			0.815346
$516$	3.37459	−	6.29529i	0.148558	−	0.277135i
$517$	−16.1072			−0.708393
$518$	−7.94914	+	31.6544i	−0.349265	+	1.39082i
$519$			0.308916i			0.0135599i
$520$	−22.8564	−	20.7906i	−1.00232	−	0.911728i
$521$		−	18.8859i		−	0.827405i	−0.910412	−	0.413702i	$-0.864235\pi$
$521$		−	18.8859i		−	0.827405i	0.910412	−	0.413702i	$-0.135765\pi$
$522$	−23.3827	−	5.87192i	−1.02343	−	0.257007i
$523$		−	24.3990i		−	1.06689i	−0.845834	−	0.533447i	$-0.820896\pi$
$523$		−	24.3990i		−	1.06689i	0.845834	−	0.533447i	$-0.179104\pi$
$524$	1.56422	+	0.838497i	0.0683331	+	0.0366299i
$525$	−2.61725			−0.114226
$526$	0.727441	−	2.89676i	0.0317179	−	0.126305i
$527$	−20.2825			−0.883520
$528$	−1.85060	+	1.23014i	−0.0805372	+	0.0535350i
$529$	19.9304	+	11.4795i	0.866540	+	0.499108i
$530$	−1.23014	+	4.89857i	−0.0534339	+	0.212780i
$531$	19.2257			0.834324
$532$	−16.3180	+	30.4413i	−0.707477	+	1.31980i
$533$		−	22.7365i		−	0.984825i
$534$	7.11079	+	1.78568i	0.307714	+	0.0772739i
$535$			31.4911i			1.36148i
$536$	−7.11079	−	6.46812i	−0.307139	−	0.279380i
$537$	−3.06022			−0.132058
$538$	−13.7158	−	3.44434i	−0.591329	−	0.148496i
$539$			7.31555i			0.315103i
$540$	−8.88069	−	4.76049i	−0.382164	−	0.204859i
$541$		−	4.26114i		−	0.183201i	−0.995796	−	0.0916003i	$-0.970802\pi$
$541$		−	4.26114i		−	0.183201i	0.995796	−	0.0916003i	$-0.0291982\pi$
$542$	−37.0716	−	9.30951i	−1.59236	−	0.399878i
$543$	−4.63306			−0.198823
$544$	10.8470	+	30.6035i	0.465061	+	1.31211i
$545$	−10.3684			−0.444134
$546$	5.66056	+	1.42149i	0.242250	+	0.0608343i
$547$	−28.1733			−1.20460			−0.602302	−	0.798268i	$-0.705750\pi$
$547$	−28.1733			−1.20460			−0.602302	+	0.798268i	$0.705750\pi$
$548$	14.2216	−	26.5303i	0.607516	−	1.13332i
$549$	−15.9285			−0.679811
$550$	−6.18549	−	1.55332i	−0.263750	−	0.0662336i
$551$	30.4413			1.29684
$552$	3.54968	−	2.28228i	0.151084	−	0.0971404i
$553$	−1.34920			−0.0573740
$554$	17.3652	+	4.36079i	0.737776	+	0.185272i
$555$	5.91258			0.250975
$556$	−28.3296	−	15.1861i	−1.20144	−	0.644034i
$557$	−26.7755			−1.13451			−0.567257	−	0.823541i	$-0.691995\pi$
$557$	−26.7755			−1.13451			−0.567257	+	0.823541i	$0.691995\pi$
$558$	−14.0716	−	3.53370i	−0.595698	−	0.149593i
$559$	−45.7127			−1.93344
$560$	20.2351	+	30.4413i	0.855087	+	1.28638i
$561$	3.18865			0.134625
$562$	18.3582	+	4.61015i	0.774392	+	0.194467i
$563$		−	26.5303i		−	1.11812i	−0.829127	−	0.559060i	$-0.811162\pi$
$563$		−	26.5303i		−	1.11812i	0.829127	−	0.559060i	$-0.188838\pi$
$564$	2.65164	−	4.94662i	0.111654	−	0.208290i
$565$		−	5.94843i		−	0.250252i
$566$	6.18549	+	1.55332i	0.259996	+	0.0652908i
$567$	−27.1101			−1.13852
$568$	−11.3477	−	10.3221i	−0.476138	−	0.433104i
$569$			0.291896i			0.0122369i	0.999981	+	0.00611845i	$0.00194757\pi$
$569$			0.291896i			0.0122369i	−0.999981	+	0.00611845i	$0.998052\pi$
$570$	6.06868	+	1.52398i	0.254189	+	0.0638326i
$571$		−	23.1318i		−	0.968037i	−0.875058	−	0.484018i	$-0.839177\pi$
$571$		−	23.1318i		−	0.968037i	0.875058	−	0.484018i	$-0.160823\pi$
$572$	12.5343	+	6.71900i	0.524085	+	0.280936i
$573$	2.98307			0.124619
$574$	−6.55131	+	26.0881i	−0.273446	+	1.08890i
$575$	11.7004	+	3.12867i	0.487942	+	0.130475i
$576$	2.19358	+	23.1219i	0.0913990	+	0.963412i
$577$	44.2498			1.84214			0.921072	−	0.389392i	$-0.127315\pi$
$577$	44.2498			1.84214			0.921072	+	0.389392i	$0.127315\pi$
$578$	5.49209	−	21.8702i	0.228441	−	0.909679i
$579$	5.90967			0.245597
$580$	15.2206	−	28.3941i	0.632003	−	1.17900i
$581$		−	11.3211i		−	0.469679i
$582$	−6.18549	−	1.55332i	−0.256397	−	0.0643870i
$583$		−	2.32473i		−	0.0962803i
$584$	−22.5669	+	24.8092i	−0.933826	+	1.02661i
$585$			31.7146i			1.31124i
$586$	5.34699	−	21.2924i	0.220882	−	0.879580i
$587$	2.69826			0.111369			0.0556846	−	0.998448i	$-0.482266\pi$
$587$	2.69826			0.111369			0.0556846	+	0.998448i	$0.482266\pi$
$588$	−2.24665	−	1.20432i	−0.0926505	−	0.0496652i
$589$	18.3194			0.754838
$590$	−6.25735	+	24.9175i	−0.257611	+	1.02584i
$591$			6.37725i			0.262325i
$592$	−15.3405	−	23.0781i	−0.630493	−	0.948502i
$593$	−20.4558			−0.840021			−0.420010	−	0.907519i	$-0.637974\pi$
$593$	−20.4558			−0.840021			−0.420010	+	0.907519i	$0.637974\pi$
$594$	4.49820	+	1.12960i	0.184563	+	0.0463480i
$595$		−	52.4514i		−	2.15030i
$596$	13.3247	+	7.14272i	0.545802	+	0.292577i
$597$	−2.08622			−0.0853832
$598$	−23.6064	−	13.1215i	−0.965337	−	0.536578i
$599$		−	19.2163i		−	0.785155i	−0.919719	−	0.392578i	$-0.871583\pi$
$599$		−	19.2163i		−	0.785155i	0.919719	−	0.392578i	$-0.128417\pi$
$600$	1.49532	−	1.64389i	0.0610460	−	0.0671116i
$601$	−7.16193			−0.292141			−0.146071	−	0.989274i	$-0.546663\pi$
$601$	−7.16193			−0.292141			−0.146071	+	0.989274i	$0.546663\pi$
$602$	52.4514	+	13.1717i	2.13776	+	0.536839i
$603$			9.86665i			0.401801i
$604$	−0.0595315	+	0.111056i	−0.00242230	+	0.00451880i
$605$	−21.4285			−0.871192
$606$	−2.76494	−	0.694338i	−0.112318	−	0.0282055i
$607$		−	31.4519i		−	1.27659i	−0.769790	−	0.638297i	$-0.779639\pi$
$607$		−	31.4519i		−	1.27659i	0.769790	−	0.638297i	$-0.220361\pi$
$608$	−9.79714	−	27.6414i	−0.397326	−	1.12101i
$609$			6.08541i			0.246593i
$610$	5.18421	−	20.6441i	0.209902	−	0.835857i
$611$	−35.9195			−1.45315
$612$	15.7456	−	29.3733i	0.636477	−	1.18735i
$613$	19.9736			0.806726			0.403363	−	0.915040i	$-0.367841\pi$
$613$	19.9736			0.806726			0.403363	+	0.915040i	$0.367841\pi$
$614$	10.6222	−	42.2989i	0.428678	−	1.70705i
$615$	4.87287			0.196493
$616$	−12.4460	−	11.3211i	−0.501463	−	0.456141i
$617$			31.3689i			1.26286i	0.775431	+	0.631432i	$0.217533\pi$
$617$			31.3689i			1.26286i	−0.775431	+	0.631432i	$0.782467\pi$
$618$	0.722790	−	2.87824i	0.0290749	−	0.115780i
$619$			10.6321i			0.427339i	0.976906	+	0.213669i	$0.0685415\pi$
$619$			10.6321i			0.427339i	−0.976906	+	0.213669i	$0.931459\pi$
$620$	9.15971	−	17.0874i	0.367863	−	0.686247i
$621$	−8.50877	−	2.27523i	−0.341445	−	0.0913017i
$622$	−7.74367	−	1.94461i	−0.310493	−	0.0779717i
$623$			55.5099i			2.22396i
$624$	−4.12690	+	2.74325i	−0.165208	+	0.109818i
$625$	−31.2494			−1.24997
$626$	16.9079	+	4.24596i	0.675777	+	0.169703i
$627$	−2.88003			−0.115017
$628$	12.4578	+	6.67799i	0.497120	+	0.266481i
$629$			39.7643i			1.58551i
$630$	9.13828	−	36.3897i	0.364078	−	1.44980i
$631$	−2.19872			−0.0875297			−0.0437648	−	0.999042i	$-0.513935\pi$
$631$	−2.19872			−0.0875297			−0.0437648	+	0.999042i	$0.513935\pi$
$632$	0.770843	−	0.847435i	0.0306625	−	0.0337091i
$633$	−5.89829			−0.234436
$634$	22.3254	+	5.60641i	0.886655	+	0.222659i
$635$		−	14.3763i		−	0.570504i
$636$	0.713939	+	0.382707i	0.0283095	+	0.0151753i
$637$			16.3139i			0.646380i
$638$	−3.61165	+	14.3820i	−0.142987	+	0.569389i
$639$			15.7456i			0.622885i
$640$	−30.6811	−	4.68244i	−1.21278	−	0.185090i
$641$			31.7146i			1.25265i	0.779562	+	0.626325i	$0.215442\pi$
$641$			31.7146i			1.25265i	−0.779562	+	0.626325i	$0.784558\pi$
$642$	4.89857	+	1.23014i	0.193331	+	0.0485498i
$643$			34.0020i			1.34091i	0.741951	+	0.670454i	$0.233901\pi$
$643$			34.0020i			1.34091i	−0.741951	+	0.670454i	$0.766099\pi$
$644$	23.3054	+	21.8577i	0.918363	+	0.861316i
$645$		−	9.79714i		−	0.385762i
$646$	−10.2494	+	40.8142i	−0.403255	+	1.60581i
$647$		−	13.6398i		−	0.536234i	−0.963386	−	0.268117i	$-0.913599\pi$
$647$		−	13.6398i		−	0.536234i	0.963386	−	0.268117i	$-0.0864014\pi$
$648$	15.4889	−	17.0278i	0.608460	−	0.668917i
$649$		−	11.8252i		−	0.464178i
$650$	−13.7938	−	3.46394i	−0.541038	−	0.135867i
$651$			3.66217i			0.143532i
$652$	3.05016	+	1.63504i	0.119454	+	0.0640331i
$653$			30.3349i			1.18710i	0.804799	+	0.593548i	$0.202273\pi$
$653$			30.3349i			1.18710i	−0.804799	+	0.593548i	$0.797727\pi$
$654$	−0.405022	+	1.61285i	−0.0158376	+	0.0630673i
$655$	2.43434			0.0951173
$656$	−12.6430	−	19.0198i	−0.493625	−	0.742600i
$657$	34.4242			1.34302
$658$	41.2145	+	10.3499i	1.60671	+	0.403481i
$659$			15.7255i			0.612577i	0.951939	+	0.306288i	$0.0990872\pi$
$659$			15.7255i			0.612577i	−0.951939	+	0.306288i	$0.900913\pi$
$660$	−1.44002	+	2.68635i	−0.0560525	+	0.104566i
$661$	21.4150			0.832946			0.416473	−	0.909148i	$-0.363266\pi$
$661$	21.4150			0.832946			0.416473	+	0.909148i	$0.363266\pi$
$662$	−2.11208	+	8.41056i	−0.0820884	+	0.326886i
$663$	7.11079			0.276160
$664$	7.11079	+	6.46812i	0.275952	+	0.251012i
$665$			47.3747i			1.83711i
$666$	−6.92788	+	27.5877i	−0.268450	+	1.06900i
$667$	7.27454	−	27.2050i	0.281671	−	1.05338i
$668$	11.0968	−	20.7010i	0.429348	−	0.800947i
$669$			5.01238i			0.193790i
$670$	−12.7877	−	3.21128i	−0.494031	−	0.124062i
$671$			9.79714i			0.378214i
$672$	5.52570	−	1.95851i	0.213159	−	0.0755513i
$673$	14.5526			0.560962			0.280481	−	0.959860i	$-0.409506\pi$
$673$	14.5526			0.560962			0.280481	+	0.959860i	$0.409506\pi$
$674$	16.4338	+	4.12690i	0.633007	+	0.158962i
$675$	−4.63804			−0.178518
$676$	5.03657	+	2.69985i	0.193714	+	0.103840i
$677$	27.3457			1.05098			0.525490	−	0.850799i	$-0.323882\pi$
$677$	27.3457			1.05098			0.525490	+	0.850799i	$0.323882\pi$
$678$	−0.925302	−	0.232364i	−0.0355360	−	0.00892389i
$679$		−	48.2866i		−	1.85307i
$680$	32.9447	+	29.9672i	1.26337	+	1.14919i
$681$			0.209874i			0.00804239i
$682$	−2.17347	+	8.65503i	−0.0832265	+	0.331418i
$683$	−44.3196			−1.69584			−0.847921	−	0.530123i	$-0.822146\pi$
$683$	−44.3196			−1.69584			−0.847921	+	0.530123i	$0.822146\pi$
$684$	−14.2216	+	26.5303i	−0.543776	+	1.01441i
$685$		−	41.2883i		−	1.57754i
$686$	−3.33118	+	13.2652i	−0.127185	+	0.506467i
$687$	−7.02819			−0.268142
$688$	−38.2403	+	25.4193i	−1.45790	+	0.969101i
$689$		−	5.18421i		−	0.197503i
$690$	2.81219	−	5.05931i	0.107058	−	0.192605i
$691$	−0.723926			−0.0275394			−0.0137697	−	0.999905i	$-0.504383\pi$
$691$	−0.723926			−0.0275394			−0.0137697	+	0.999905i	$0.504383\pi$
$692$	0.938246	−	1.75030i	0.0356667	−	0.0665363i
$693$			17.2696i			0.656016i
$694$	−9.60793	+	38.2599i	−0.364712	+	1.45233i
$695$	−44.0884			−1.67237
$696$	−3.82225	−	3.47679i	−0.144882	−	0.131787i
$697$			32.7719i			1.24132i
$698$	15.3286	+	3.84936i	0.580197	+	0.145701i
$699$	4.41282			0.166908
$700$	14.8291	+	7.94914i	0.560488	+	0.300449i
$701$	0.631335			0.0238452			0.0119226	−	0.999929i	$-0.496205\pi$
$701$	0.631335			0.0238452			0.0119226	+	0.999929i	$0.496205\pi$
$702$	10.0311	+	2.51904i	0.378600	+	0.0950750i
$703$		−	35.9156i		−	1.35458i
$704$	14.2216	−	1.34920i	0.535996	−	0.0508500i
$705$		−	7.69826i		−	0.289933i
$706$	1.97158	−	7.85108i	0.0742015	−	0.295479i
$707$		−	21.5843i		−	0.811760i
$708$	3.63158	+	1.94671i	0.136483	+	0.0731618i
$709$	45.9390			1.72528			0.862638	−	0.505821i	$-0.168810\pi$
$709$	45.9390			1.72528			0.862638	+	0.505821i	$0.168810\pi$
$710$	−20.4071	−	5.12468i	−0.765864	−	0.192326i
$711$	−1.17587			−0.0440984
$712$	−34.8657	−	31.7146i	−1.30665	−	1.18855i
$713$	4.37778	−	16.3718i	0.163949	−	0.613129i
$714$	−8.15902	−	2.04891i	−0.305344	−	0.0766787i
$715$	19.5067			0.729509
$716$	17.3390	+	9.29456i	0.647989	+	0.347354i
$717$		−	8.91989i		−	0.333119i
$718$	−7.23680	+	28.8178i	−0.270075	+	1.07547i
$719$			17.7614i			0.662388i	0.943563	+	0.331194i	$0.107451\pi$
$719$			17.7614i			0.662388i	−0.943563	+	0.331194i	$0.892549\pi$
$720$	17.6354	+	26.5303i	0.657232	+	0.988728i
$721$	22.4687			0.836780
$722$	2.71286	−	10.8029i	0.100962	−	0.402044i
$723$		−	2.28745i		−	0.0850712i
$724$	26.2505	+	14.0716i	0.975594	+	0.522967i
$725$		−	14.8291i		−	0.550740i
$726$	−0.837063	+	3.33328i	−0.0310663	+	0.123710i
$727$	6.46596			0.239809			0.119905	−	0.992785i	$-0.461741\pi$
$727$	6.46596			0.239809			0.119905	+	0.992785i	$0.461741\pi$
$728$	−27.7549	−	25.2464i	−1.02867	−	0.935695i
$729$	−21.9131			−0.811595
$730$	−11.2040	+	44.6155i	−0.414677	+	1.65130i
$731$	65.8894			2.43701
$732$	−3.00877	−	1.61285i	−0.111207	−	0.0596126i
$733$	−2.05921			−0.0760587			−0.0380294	−	0.999277i	$-0.512108\pi$
$733$	−2.05921			−0.0760587			−0.0380294	+	0.999277i	$0.512108\pi$
$734$	7.85318	−	31.2723i	0.289866	−	1.15428i
$735$	−3.49639			−0.128966
$736$	−27.0440	+	2.15011i	−0.996854	+	0.0792539i
$737$	6.06868			0.223543
$738$	−5.70964	+	22.7365i	−0.210175	+	0.836940i
$739$	−44.2321			−1.62711			−0.813553	−	0.581491i	$-0.802470\pi$
$739$	−44.2321			−1.62711			−0.813553	+	0.581491i	$0.802470\pi$
$740$	−33.5002	−	17.9578i	−1.23149	−	0.660142i
$741$	−6.42255			−0.235938
$742$	−1.49378	+	5.94843i	−0.0548386	+	0.218374i
$743$	53.7596			1.97225			0.986124	−	0.166013i	$-0.0530893\pi$
$743$	53.7596			1.97225			0.986124	+	0.166013i	$0.0530893\pi$
$744$	−2.30021	−	2.09232i	−0.0843297	−	0.0767080i
$745$	20.7368			0.759739
$746$	−5.99648	+	23.8787i	−0.219547	+	0.874262i
$747$		−	9.86665i		−	0.361002i
$748$	−18.0667	−	9.68464i	−0.660583	−	0.354105i
$749$			38.2403i			1.39727i
$750$	−0.727441	+	2.89676i	−0.0265624	+	0.105775i
$751$	36.4858			1.33139			0.665693	−	0.746226i	$-0.268136\pi$
$751$	36.4858			1.33139			0.665693	+	0.746226i	$0.268136\pi$
$752$	−30.0479	+	19.9736i	−1.09574	+	0.728362i
$753$			2.16839i			0.0790204i
$754$	−8.05408	+	32.0723i	−0.293312	+	1.16800i
$755$			0.172833i			0.00629002i
$756$	−10.7840	−	5.78076i	−0.392210	−	0.210244i
$757$	23.1084			0.839888			0.419944	−	0.907550i	$-0.362050\pi$
$757$	23.1084			0.839888			0.419944	+	0.907550i	$0.362050\pi$
$758$	−33.7034	−	8.46367i	−1.22416	−	0.307414i
$759$	−0.688240	+	2.57384i	−0.0249815	+	0.0934246i
$760$	−29.7560	−	27.0667i	−1.07937	−	0.981812i
$761$	−6.58565			−0.238730			−0.119365	−	0.992850i	$-0.538086\pi$
$761$	−6.58565			−0.238730			−0.119365	+	0.992850i	$0.538086\pi$
$762$	−2.23628	−	0.561581i	−0.0810120	−	0.0203439i
$763$	−12.5906			−0.455809
$764$	−16.9018	−	9.06022i	−0.611487	−	0.327787i
$765$		−	45.7127i		−	1.65275i
$766$	−7.28020	+	28.9906i	−0.263044	+	1.04747i
$767$		−	26.3705i		−	0.952182i
$768$	−1.92687	+	4.58965i	−0.0695299	+	0.165615i
$769$		−	39.9146i		−	1.43936i	−0.694308	−	0.719678i	$-0.744289\pi$
$769$		−	39.9146i		−	1.43936i	0.694308	−	0.719678i	$-0.255711\pi$
$770$	−22.3822	−	5.62068i	−0.806600	−	0.202555i
$771$	−2.60639			−0.0938670
$772$	−33.4837	−	17.9489i	−1.20511	−	0.645997i
$773$	−24.3369			−0.875339			−0.437670	−	0.899136i	$-0.644196\pi$
$773$	−24.3369			−0.875339			−0.437670	+	0.899136i	$0.644196\pi$
$774$	45.7127	+	11.4795i	1.64311	+	0.412622i
$775$		−	8.92409i		−	0.320563i
$776$	30.3288	+	27.5877i	1.08874	+	0.990339i
$777$	7.17976			0.257573
$778$	12.8194	−	51.0484i	0.459598	−	1.83017i
$779$		−	29.5999i		−	1.06053i
$780$	−3.21128	+	5.99063i	−0.114982	+	0.214499i
$781$	9.68464			0.346544
$782$	34.0258	+	18.9131i	1.21676	+	0.676329i
$783$			10.7840i			0.385389i
$784$	9.07160	+	13.6472i	0.323986	+	0.487398i
$785$	19.3876			0.691974
$786$	0.0950927	−	0.378670i	0.00339184	−	0.0135067i
$787$		−	10.8702i		−	0.387480i	−0.981053	−	0.193740i	$-0.937938\pi$
$787$		−	10.8702i		−	0.387480i	0.981053	−	0.193740i	$-0.0620619\pi$
$788$	19.3691	−	36.1330i	0.689996	−	1.28719i
$789$	−0.657034			−0.0233910
$790$	0.382707	−	1.52398i	0.0136161	−	0.0542209i
$791$		−	7.22330i		−	0.256831i
$792$	−10.8470	−	9.86665i	−0.385431	−	0.350596i
$793$			21.8479i			0.775842i
$794$	−15.1558	−	3.80596i	−0.537859	−	0.135068i
$795$	1.11108			0.0394059
$796$	11.8204	+	6.33630i	0.418961	+	0.224584i
$797$	−2.47774			−0.0877660			−0.0438830	−	0.999037i	$-0.513973\pi$
$797$	−2.47774			−0.0877660			−0.0438830	+	0.999037i	$0.513973\pi$
$798$	7.36932	+	1.85060i	0.260871	+	0.0655106i
$799$	51.7737			1.83162
$800$	−13.4652	+	4.77256i	−0.476067	+	0.168736i
$801$			48.3783i			1.70936i
$802$	22.5685	+	5.66746i	0.796921	+	0.200125i
$803$		−	21.1733i		−	0.747190i
$804$	−0.999053	+	1.86373i	−0.0352339	+	0.0657288i
$805$	42.3381	+	11.3211i	1.49222	+	0.399017i
$806$	−4.84691	+	19.3010i	−0.170725	+	0.679848i
$807$			3.11097i			0.109511i
$808$	13.5571	+	12.3318i	0.476936	+	0.433831i
$809$	10.5861			0.372188			0.186094	−	0.982532i	$-0.440417\pi$
$809$	10.5861			0.372188			0.186094	+	0.982532i	$0.440417\pi$
$810$	7.68987	−	30.6220i	0.270195	−	1.07595i
$811$	14.3022			0.502219			0.251109	−	0.967959i	$-0.419205\pi$
$811$	14.3022			0.502219			0.251109	+	0.967959i	$0.419205\pi$
$812$	18.4827	−	34.4795i	0.648616	−	1.20999i
$813$			8.40846i			0.294898i
$814$	16.9684	+	4.26114i	0.594741	+	0.149353i
$815$	4.74687			0.166275
$816$	5.94843	−	3.95407i	0.208237	−	0.138420i
$817$	−59.5121			−2.08206
$818$	6.34445	−	25.2643i	0.221828	−	0.883347i
$819$			38.5116i			1.34570i
$820$	−27.6093	−	14.8000i	−0.964159	−	0.516837i
$821$		−	32.4841i		−	1.13370i	−0.823820	−	0.566851i	$-0.808161\pi$
$821$		−	32.4841i		−	1.13370i	0.823820	−	0.566851i	$-0.191839\pi$
$822$	−6.42255	−	1.61285i	−0.224012	−	0.0562545i
$823$			30.3391i			1.05755i	0.848761	+	0.528777i	$0.177349\pi$
$823$			30.3391i			1.05755i	−0.848761	+	0.528777i	$0.822651\pi$
$824$	−12.8371	+	14.1126i	−0.447202	+	0.491636i
$825$			1.40297i			0.0488453i
$826$	−7.59842	+	30.2578i	−0.264383	+	1.05280i
$827$		−	34.1748i		−	1.18838i	−0.804326	−	0.594188i	$-0.797474\pi$
$827$		−	34.1748i		−	1.18838i	0.804326	−	0.594188i	$-0.202526\pi$
$828$	20.3113	+	19.0496i	0.705866	+	0.662019i
$829$		−	51.0163i		−	1.77187i	−0.463810	−	0.885935i	$-0.653518\pi$
$829$		−	51.0163i		−	1.77187i	0.463810	−	0.885935i	$-0.346482\pi$
$830$	12.7877	+	3.21128i	0.443867	+	0.111465i
$831$		−	3.93872i		−	0.136633i
$832$	31.7146	−	3.00877i	1.09950	−	0.104310i
$833$		−	23.5145i		−	0.814730i
$834$	−1.72223	+	6.85813i	−0.0596360	+	0.237478i
$835$		−	32.2163i		−	1.11489i
$836$	16.3180	+	8.74728i	0.564371	+	0.302531i
$837$			6.48976i			0.224319i
$838$	−43.5005	−	10.9240i	−1.50270	−	0.377362i
$839$	−34.9483			−1.20655			−0.603275	−	0.797533i	$-0.706138\pi$
$839$	−34.9483			−1.20655			−0.603275	+	0.797533i	$0.706138\pi$
$840$	5.41081	−	5.94843i	0.186691	−	0.205240i
$841$	−5.47949			−0.188948
$842$	−6.38800	+	25.4378i	−0.220145	+	0.876644i
$843$		−	4.16394i		−	0.143414i
$844$	33.4193	+	17.9144i	1.15034	+	0.616639i
$845$	7.83823			0.269643
$846$	35.9195	+	9.02020i	1.23494	+	0.310121i
$847$	−26.0210			−0.894093
$848$	−2.88276	−	4.33677i	−0.0989944	−	0.148925i
$849$		−	1.40297i		−	0.0481499i
$850$	19.8821	+	4.99285i	0.681952	+	0.171254i
$851$	−32.0973	−	8.58274i	−1.10028	−	0.294212i
$852$	−1.59433	+	2.97421i	−0.0546207	+	0.101895i
$853$			17.2005i			0.588932i	0.955662	+	0.294466i	$0.0951418\pi$
$853$			17.2005i			0.588932i	−0.955662	+	0.294466i	$0.904858\pi$
$854$	6.29529	−	25.0686i	0.215420	−	0.857829i
$855$			41.2883i			1.41203i
$856$	−24.0187	−	21.8479i	−0.820943	−	0.746746i
$857$	−32.8292			−1.12142			−0.560712	−	0.828011i	$-0.689472\pi$
$857$	−32.8292			−1.12142			−0.560712	+	0.828011i	$0.689472\pi$
$858$	0.761992	−	3.03434i	0.0260140	−	0.103591i
$859$	11.1497			0.380421			0.190211	−	0.981743i	$-0.439083\pi$
$859$	11.1497			0.380421			0.190211	+	0.981743i	$0.439083\pi$
$860$	−29.7560	+	55.5099i	−1.01467	+	1.89287i
$861$	5.91722			0.201658
$862$	1.25847	−	5.01138i	0.0428636	−	0.170688i
$863$			12.3379i			0.419986i	0.977703	+	0.209993i	$0.0673442\pi$
$863$			12.3379i			0.419986i	−0.977703	+	0.209993i	$0.932656\pi$
$864$	9.79213	−	3.47069i	0.333135	−	0.118075i
$865$		−	2.72393i		−	0.0926163i
$866$	−3.44834	−	0.865955i	−0.117179	−	0.0294264i
$867$	−4.96052			−0.168468
$868$	11.1228	−	20.7496i	0.377533	−	0.704287i
$869$			0.723240i			0.0245343i
$870$	−6.87373	−	1.72615i	−0.233041	−	0.0585219i
$871$	13.5333			0.458560
$872$	7.19340	−	7.90813i	0.243599	−	0.267803i
$873$		−	42.0830i		−	1.42429i
$874$	−30.7325	−	17.0825i	−1.03954	−	0.577824i
$875$	−22.6133			−0.764470
$876$	6.50246	+	3.48564i	0.219698	+	0.117769i
$877$			50.2063i			1.69535i	0.530520	+	0.847673i	$0.321997\pi$
$877$			50.2063i			1.69535i	−0.530520	+	0.847673i	$0.678003\pi$
$878$	−21.4326	−	5.38220i	−0.723314	−	0.181640i
$879$	−4.82947			−0.162894
$880$	16.3180	−	10.8470i	0.550081	−	0.365652i
$881$		−	12.0350i		−	0.405471i	−0.979234	−	0.202735i	$-0.935017\pi$
$881$		−	12.0350i		−	0.405471i	0.979234	−	0.202735i	$-0.0649831\pi$
$882$	4.09679	−	16.3139i	0.137946	−	0.549318i
$883$	14.4099			0.484932			0.242466	−	0.970160i	$-0.422044\pi$
$883$	14.4099			0.484932			0.242466	+	0.970160i	$0.422044\pi$
$884$	−40.2892	−	21.5970i	−1.35507	−	0.726387i
$885$	5.65171			0.189980
$886$	10.2296	−	40.7355i	0.343671	−	1.36854i
$887$		−	8.19245i		−	0.275076i	−0.990497	−	0.137538i	$-0.956081\pi$
$887$		−	8.19245i		−	0.275076i	0.990497	−	0.137538i	$-0.0439188\pi$
$888$	−4.10203	+	4.50961i	−0.137655	+	0.151332i
$889$		−	17.4574i		−	0.585501i
$890$	−62.7007	−	15.7456i	−2.10173	−	0.527793i
$891$			14.5324i			0.486852i
$892$	15.2237	−	28.3998i	0.509727	−	0.950895i
$893$	−46.7626			−1.56485
$894$	0.810045	−	3.22570i	0.0270919	−	0.107883i
$895$	26.9841			0.901979
$896$	−37.2567	−	5.68598i	−1.24466	−	0.189955i
$897$	−1.53480	+	5.73975i	−0.0512453	+	0.191645i
$898$	−5.39853	+	21.4976i	−0.180151	+	0.717384i
$899$	−20.7496			−0.692038
$900$	12.9240	+	6.92788i	0.430799	+	0.230929i
$901$			7.47241i			0.248942i
$902$	13.9845	+	3.51183i	0.465634	+	0.116931i
$903$		−	11.8969i		−	0.395903i
$904$	4.53695	+	4.12690i	0.150897	+	0.137259i
$905$	40.8528			1.35799
$906$	0.0268848	+	0.00675137i	0.000893187	+	0.000224299i
$907$			11.1338i			0.369693i	0.982767	+	0.184846i	$0.0591788\pi$
$907$			11.1338i			0.369693i	−0.982767	+	0.184846i	$0.940821\pi$
$908$	0.637433	−	1.18913i	0.0211540	−	0.0394627i
$909$		−	18.8112i		−	0.623929i
$910$	−49.9131	−	12.5343i	−1.65460	−	0.415508i
$911$	−57.7478			−1.91327			−0.956635	−	0.291290i	$-0.905915\pi$
$911$	−57.7478			−1.91327			−0.956635	+	0.291290i	$0.905915\pi$
$912$	−5.37269	+	3.57136i	−0.177908	+	0.118260i
$913$	−6.06868			−0.200844
$914$	−46.4747	−	11.6708i	−1.53725	−	0.386037i
$915$	−4.68244			−0.154797
$916$	39.8212	+	21.3461i	1.31573	+	0.705296i
$917$	2.95606			0.0976177
$918$	−14.4586	−	3.63089i	−0.477206	−	0.119837i
$919$	35.3141			1.16491			0.582453	−	0.812864i	$-0.302093\pi$
$919$	35.3141			1.16491			0.582453	+	0.812864i	$0.302093\pi$
$920$	−31.2999	+	20.1244i	−1.03193	+	0.663483i
$921$	−9.59411			−0.316137
$922$	19.7845	+	4.96832i	0.651567	+	0.163623i
$923$	21.5970			0.710875
$924$	−1.74864	+	3.26208i	−0.0575260	+	0.107315i
$925$	−17.4959			−0.575261
$926$	48.9748	+	12.2987i	1.60941	+	0.404160i
$927$	19.5821			0.643160
$928$	11.0968	+	31.3082i	0.364270	+	1.02774i
$929$	−12.3733			−0.405956			−0.202978	−	0.979183i	$-0.565062\pi$
$929$	−12.3733			−0.405956			−0.202978	+	0.979183i	$0.565062\pi$
$930$	−4.13658	−	1.03879i	−0.135644	−	0.0340632i
$931$			21.2386i			0.696067i
$932$	−25.0027	−	13.4027i	−0.818991	−	0.439020i
$933$			1.75639i			0.0575018i
$934$	−37.0779	−	9.31111i	−1.21323	−	0.304669i
$935$	−28.1166			−0.919510
$936$	−24.1891	−	22.0029i	−0.790646	−	0.719188i
$937$			19.1778i			0.626510i	0.949669	+	0.313255i	$0.101419\pi$
$937$			19.1778i			0.626510i	−0.949669	+	0.313255i	$0.898581\pi$
$938$	−15.5283	−	3.89952i	−0.507018	−	0.127324i
$939$		−	3.83500i		−	0.125151i
$940$	−23.3813	+	43.6178i	−0.762614	+	1.42265i
$941$	40.3657			1.31589			0.657943	−	0.753068i	$-0.271427\pi$
$941$	40.3657			1.31589			0.657943	+	0.753068i	$0.271427\pi$
$942$	0.757341	−	3.01582i	0.0246755	−	0.0982608i
$943$	−26.4531	−	7.07349i	−0.861430	−	0.230344i
$944$	−14.6637	−	22.0598i	−0.477263	−	0.717986i
$945$	−16.7828			−0.545943
$946$	7.06070	−	28.1166i	0.229563	−	0.914148i
$947$	29.1956			0.948729			0.474364	−	0.880329i	$-0.342678\pi$
$947$	29.1956			0.948729			0.474364	+	0.880329i	$0.342678\pi$
$948$	−0.222112	−	0.119063i	−0.00721386	−	0.00386699i
$949$		−	47.2171i		−	1.53273i
$950$	−17.9578	−	4.50961i	−0.582628	−	0.146311i
$951$		−	5.06378i		−	0.164204i
$952$	40.0054	+	36.3897i	1.29658	+	1.17940i
$953$		−	42.0830i		−	1.36320i	−0.731724	−	0.681601i	$-0.761284\pi$
$953$		−	42.0830i		−	1.36320i	0.731724	−	0.681601i	$-0.238716\pi$
$954$	−1.30187	+	5.18421i	−0.0421496	+	0.167845i
$955$	−26.3037			−0.851169
$956$	−27.0917	+	50.5394i	−0.876207	+	1.63456i
$957$	3.26208			0.105448
$958$	7.50087	−	29.8693i	0.242342	−	0.965035i
$959$		−	50.1372i		−	1.61901i
$960$	0.644838	+	6.79706i	0.0208121	+	0.219374i
$961$	18.5130			0.597193
$962$	37.8399	+	9.50246i	1.22001	+	0.306372i
$963$			33.3274i			1.07396i
$964$	−6.94748	+	12.9605i	−0.223763	+	0.417430i
$965$	−52.1096			−1.67747
$966$	3.41490	−	6.14362i	0.109873	−	0.197668i
$967$			44.6176i			1.43480i	0.696659	+	0.717402i	$0.254669\pi$
$967$			44.6176i			1.43480i	−0.696659	+	0.717402i	$0.745331\pi$
$968$	14.8666	−	16.3438i	0.477832	−	0.525310i
$969$	9.25734			0.297389
$970$	54.5417	+	13.6967i	1.75123	+	0.439773i
$971$			43.6958i			1.40227i	0.713031	+	0.701133i	$0.247322\pi$
$971$			43.6958i			1.40227i	−0.713031	+	0.701133i	$0.752678\pi$
$972$	−14.1748	−	7.59842i	−0.454658	−	0.243719i
$973$	−53.5375			−1.71633
$974$	−34.6440	−	8.69988i	−1.11006	−	0.278762i
$975$			3.12867i			0.100198i
$976$	12.1489	+	18.2766i	0.388876	+	0.585018i
$977$			51.3941i			1.64424i	0.569313	+	0.822121i	$0.307209\pi$
$977$			51.3941i			1.64424i	−0.569313	+	0.822121i	$0.692791\pi$
$978$	0.185427	−	0.738393i	0.00592931	−	0.0236112i
$979$	29.7560			0.951007
$980$	19.8103	+	10.6193i	0.632817	+	0.339221i
$981$	−10.9730			−0.350341
$982$	−1.63106	+	6.49506i	−0.0520491	+	0.207266i
$983$	−29.3400			−0.935801			−0.467901	−	0.883781i	$-0.654990\pi$
$983$	−29.3400			−0.935801			−0.467901	+	0.883781i	$0.654990\pi$
$984$	−3.38070	+	3.71661i	−0.107773	+	0.118481i
$985$		−	56.2326i		−	1.79172i
$986$	11.6090	−	46.2284i	0.369706	−	1.47221i
$987$		−	9.34815i		−	0.297555i
$988$	36.3897	+	19.5067i	1.15771	+	0.620591i
$989$	−14.2216	+	53.1851i	−0.452220	+	1.69119i
$990$	−19.5067	−	4.89857i	−0.619963	−	0.155687i
$991$			31.5303i			1.00159i	0.865565	+	0.500797i	$0.166960\pi$
$991$			31.5303i			1.00159i	−0.865565	+	0.500797i	$0.833040\pi$
$992$	6.67799	+	18.8411i	0.212026	+	0.598207i
$993$	1.90766			0.0605377
$994$	−24.7807	−	6.22300i	−0.785997	−	0.197381i
$995$	18.3956			0.583180
$996$	0.999053	−	1.86373i	0.0316562	−	0.0590546i
$997$		−	16.3904i		−	0.519089i	−0.965731	−	0.259545i	$-0.916428\pi$
$997$		−	16.3904i		−	0.519089i	0.965731	−	0.259545i	$-0.0835725\pi$
$998$	−8.67852	+	34.5589i	−0.274714	+	1.09394i
$999$	12.7233			0.402547

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	184.2.h.c.91.7	yes	12
4.3	odd	2		736.2.h.c.367.5		12
8.3	odd	2	inner	184.2.h.c.91.6	yes	12
8.5	even	2		736.2.h.c.367.7		12
23.22	odd	2	inner	184.2.h.c.91.8	yes	12
92.91	even	2		736.2.h.c.367.8		12
184.45	odd	2		736.2.h.c.367.6		12
184.91	even	2	inner	184.2.h.c.91.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.h.c.91.5	✓	12	184.91	even	2	inner
184.2.h.c.91.6	yes	12	8.3	odd	2	inner
184.2.h.c.91.7	yes	12	1.1	even	1	trivial
184.2.h.c.91.8	yes	12	23.22	odd	2	inner
736.2.h.c.367.5		12	4.3	odd	2
736.2.h.c.367.6		12	184.45	odd	2
736.2.h.c.367.7		12	8.5	even	2
736.2.h.c.367.8		12	92.91	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:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	184.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.344446 + 1.37163i) q^{2} +0.311108 q^{3} +(-1.76271 - 0.944902i) q^{4} -2.74325 q^{5} +(-0.107160 + 0.426723i) q^{6} -3.33118 q^{7} +(1.90321 - 2.09232i) q^{8} -2.90321 q^{9} +(0.944902 - 3.76271i) q^{10} +1.78568i q^{11} +(-0.548394 - 0.293966i) q^{12} +3.98212i q^{13} +(1.14741 - 4.56914i) q^{14} -0.853447 q^{15} +(2.21432 + 3.33118i) q^{16} -5.73975i q^{17} +(1.00000 - 3.98212i) q^{18} +5.18421i q^{19} +(4.83557 + 2.59210i) q^{20} -1.03636 q^{21} +(-2.44928 - 0.615071i) q^{22} +(4.63306 + 1.23887i) q^{23} +(0.592104 - 0.650936i) q^{24} +2.52543 q^{25} +(-5.46198 - 1.37163i) q^{26} -1.83654 q^{27} +(5.87192 + 3.14764i) q^{28} -5.87192i q^{29} +(0.293966 - 1.17061i) q^{30} -3.53370i q^{31} +(-5.33185 + 1.88980i) q^{32} +0.555539i q^{33} +(7.87278 + 1.97703i) q^{34} +9.13828 q^{35} +(5.11753 + 2.74325i) q^{36} -6.92788 q^{37} +(-7.11079 - 1.78568i) q^{38} +1.23887i q^{39} +(-5.22099 + 5.73975i) q^{40} -5.70964 q^{41} +(0.356969 - 1.42149i) q^{42} +11.4795i q^{43} +(1.68729 - 3.14764i) q^{44} +7.96424 q^{45} +(-3.29510 + 5.92809i) q^{46} +9.02020i q^{47} +(0.688892 + 1.03636i) q^{48} +4.09679 q^{49} +(-0.869874 + 3.46394i) q^{50} -1.78568i q^{51} +(3.76271 - 7.01934i) q^{52} -1.30187 q^{53} +(0.632587 - 2.51904i) q^{54} -4.89857i q^{55} +(-6.33995 + 6.96989i) q^{56} +1.61285i q^{57} +(8.05408 + 2.02256i) q^{58} -6.62222 q^{59} +(1.50438 + 0.806424i) q^{60} +5.48650 q^{61} +(4.84691 + 1.21717i) q^{62} +9.67113 q^{63} +(-0.755569 - 7.96424i) q^{64} -10.9240i q^{65} +(-0.761992 - 0.191353i) q^{66} -3.39853i q^{67} +(-5.42350 + 10.1175i) q^{68} +(1.44138 + 0.385422i) q^{69} +(-3.14764 + 12.5343i) q^{70} -5.42350i q^{71} +(-5.52543 + 6.07444i) q^{72} -11.8573 q^{73} +(2.38628 - 9.50246i) q^{74} +0.785680 q^{75} +(4.89857 - 9.13828i) q^{76} -5.94843i q^{77} +(-1.69926 - 0.426723i) q^{78} +0.405022 q^{79} +(-6.07444 - 9.13828i) q^{80} +8.13828 q^{81} +(1.96666 - 7.83148i) q^{82} +3.39853i q^{83} +(1.82680 + 0.979256i) q^{84} +15.7456i q^{85} +(-15.7456 - 3.95407i) q^{86} -1.82680i q^{87} +(3.73621 + 3.39853i) q^{88} -16.6637i q^{89} +(-2.74325 + 10.9240i) q^{90} -13.2652i q^{91} +(-6.99614 - 6.56156i) q^{92} -1.09936i q^{93} +(-12.3723 - 3.10697i) q^{94} -14.2216i q^{95} +(-1.65878 + 0.587933i) q^{96} +14.4953i q^{97} +(-1.41112 + 5.61926i) q^{98} -5.18421i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 4 q^{3} - 8 q^{4} + 12 q^{6} - 4 q^{8} - 8 q^{9} - 20 q^{12} + 12 q^{18} - 20 q^{24} + 4 q^{25} - 12 q^{26} + 4 q^{27} + 16 q^{32} - 24 q^{35} + 8 q^{36} + 12 q^{41} + 20 q^{46} + 8 q^{48}+ \cdots - 16 q^{98}+O(q^{100}) \) 12 * q - 4 * q^2 + 4 * q^3 - 8 * q^4 + 12 * q^6 - 4 * q^8 - 8 * q^9 - 20 * q^12 + 12 * q^18 - 20 * q^24 + 4 * q^25 - 12 * q^26 + 4 * q^27 + 16 * q^32 - 24 * q^35 + 8 * q^36 + 12 * q^41 + 20 * q^46 + 8 * q^48 + 76 * q^49 + 16 * q^50 + 32 * q^52 - 32 * q^54 + 16 * q^58 - 80 * q^59 - 8 * q^62 - 8 * q^64 - 12 * q^70 - 40 * q^72 - 36 * q^73 + 36 * q^75 + 20 * q^78 - 36 * q^81 + 24 * q^82 + 28 * q^92 - 56 * q^94 + 8 * q^96 - 16 * q^98

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