LMFDB - Embedded newform 184.2.h.c.91.6

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			91.6
Root			$0.408906 + 1.35381i$ of defining polynomial
Character	$\chi$	$=$	184.91
Dual form			184.2.h.c.91.8

$q$-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} +(-0.103426 + 6.78154i) 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} +(9.33736 - 2.19401i) 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	$-0.289797\pi$
$5$	2.74325			1.22682			0.613410	+	0.789765i	$0.289797\pi$
$6$	−0.107160	−	0.426723i	−0.0437478	−	0.174209i
$7$	3.33118			1.25907			0.629535	−	0.776972i	$-0.283246\pi$
$7$	3.33118			1.25907			0.629535	+	0.776972i	$0.283246\pi$
$8$	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	$-0.813781\pi$
$13$		−	3.98212i		−	1.10444i	0.833698	−	0.552221i	$-0.186219\pi$
$14$	−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	$0.183544\pi$
$29$			5.87192i			1.09039i	−0.838310	+	0.545194i	$0.816456\pi$
$30$	−0.293966	−	1.17061i	−0.0536707	−	0.213723i
$31$			3.53370i			0.634670i	0.948313	+	0.317335i	$0.102788\pi$
$31$			3.53370i			0.634670i	−0.948313	+	0.317335i	$0.897212\pi$
$32$	−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	$-0.307149\pi$
$37$	6.92788			1.13894			0.569468	+	0.822013i	$0.307149\pi$
$38$	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
$46$	−0.103426	+	6.78154i	−0.0152493	+	0.999884i
$47$		−	9.02020i		−	1.31573i	−0.753135	−	0.657866i	$-0.771460\pi$
$47$		−	9.02020i		−	1.31573i	0.753135	−	0.657866i	$-0.228540\pi$
$48$	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	$-0.471501\pi$
$53$	1.30187			0.178826			0.0894129	+	0.995995i	$0.471501\pi$
$54$	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	$-0.614239\pi$
$61$	−5.48650			−0.702475			−0.351237	+	0.936286i	$0.614239\pi$
$62$	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	$0.104296\pi$
$71$			5.42350i			0.643651i	−0.946799	+	0.321826i	$0.895704\pi$
$72$	−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	$-0.507253\pi$
$79$	−0.405022			−0.0455686			−0.0227843	+	0.999740i	$0.507253\pi$
$80$	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
$92$	9.33736	−	2.19401i	0.973487	−	0.228742i
$93$			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	$-0.895522\pi$
$101$		−	6.47946i		−	0.644730i	0.946615	−	0.322365i	$-0.104478\pi$
$102$	−2.44928	+	0.615071i	−0.242515	+	0.0609011i
$103$	6.74497			0.664602			0.332301	−	0.943173i	$-0.392175\pi$
$103$	6.74497			0.664602			0.332301	+	0.943173i	$0.392175\pi$
$104$	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	$-0.557937\pi$
$109$	−3.77961			−0.362021			−0.181010	+	0.983481i	$0.557937\pi$
$110$	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	$-0.925305\pi$
$127$		−	5.24059i		−	0.465027i	0.972593	−	0.232514i	$-0.0746950\pi$
$128$	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	$0.777714\pi$
$138$	−0.0321767	+	2.10979i	−0.00273906	+	0.179597i
$139$	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	$-0.399792\pi$
$149$	7.55922			0.619275			0.309638	+	0.950855i	$0.399792\pi$
$150$	−0.270624	−	1.07766i	−0.0220964	−	0.0879905i
$151$			0.0630028i			0.00512710i	0.999997	+	0.00256355i	$0.000816004\pi$
$151$			0.0630028i			0.00512710i	−0.999997	+	0.00256355i	$0.999184\pi$
$152$	−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	$-0.408996\pi$
$157$	7.06739			0.564039			0.282020	+	0.959409i	$0.408996\pi$
$158$	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	$-0.849860\pi$
$167$		−	11.7438i		−	0.908766i	0.890806	−	0.454383i	$-0.150140\pi$
$168$	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	$-0.987982\pi$
$173$		−	0.992955i		−	0.0754930i	0.999287	−	0.0377465i	$-0.0120179\pi$
$174$	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	$-0.313307\pi$
$181$	14.8921			1.10692			0.553461	+	0.832875i	$0.313307\pi$
$182$	−18.1949	+	4.56914i	−1.34869	+	0.338687i
$183$	−1.70689			−0.126177
$184$	−6.22558	−	12.0516i	−0.458956	−	0.888459i
$185$	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	$-0.612766\pi$
$191$	−9.58853			−0.693802			−0.346901	+	0.937902i	$0.612766\pi$
$192$	−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	$-0.739413\pi$
$197$		−	20.4985i		−	1.46046i	0.683201	−	0.730230i	$-0.260587\pi$
$198$	−7.11079	+	1.78568i	−0.505342	+	0.126903i
$199$	6.70577			0.475359			0.237680	−	0.971344i	$-0.423613\pi$
$199$	6.70577			0.475359			0.237680	+	0.971344i	$0.423613\pi$
$200$	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	$-0.818632\pi$
$223$		−	16.1114i		−	1.07890i	0.842018	−	0.539449i	$-0.181368\pi$
$224$	−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	$-0.231770\pi$
$229$	22.5908			1.49285			0.746423	+	0.665472i	$0.231770\pi$
$230$	−0.283724	+	18.6035i	−0.0187082	+	1.22668i
$231$			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	$0.377875\pi$
$239$			28.6714i			1.85460i	−0.374322	+	0.927299i	$0.622125\pi$
$240$	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	$-0.479259\pi$
$263$	2.11192			0.130226			0.0651132	+	0.997878i	$0.479259\pi$
$264$	−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	$-0.901395\pi$
$269$		−	9.99965i		−	0.609689i	0.952402	−	0.304845i	$-0.0986046\pi$
$270$	1.73535	+	6.91036i	0.105610	+	0.420551i
$271$		−	27.0275i		−	1.64180i	−0.571070	−	0.820902i	$-0.693471\pi$
$271$		−	27.0275i		−	1.64180i	0.571070	−	0.820902i	$-0.306529\pi$
$272$	−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
$276$	2.90493	−	0.682575i	0.174856	−	0.0410862i
$277$			12.6603i			0.760684i	0.924846	+	0.380342i	$0.124194\pi$
$277$			12.6603i			0.760684i	−0.924846	+	0.380342i	$0.875806\pi$
$278$	−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	$-0.350195\pi$
$293$	15.5235			0.906890			0.453445	+	0.891284i	$0.350195\pi$
$294$	−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	$-0.948829\pi$
$311$		−	5.64561i		−	0.320133i	0.987106	−	0.160067i	$-0.0511709\pi$
$312$	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	$0.151109\pi$
$317$			16.2766i			0.914185i	−0.889419	+	0.457092i	$0.848891\pi$
$318$	−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
$322$	−0.344531	+	22.5906i	−0.0192000	+	1.25892i
$323$	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	$0.0966884\pi$
$349$			11.1755i			0.598212i	−0.954220	+	0.299106i	$0.903312\pi$
$350$	−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	$-0.687064\pi$
$359$	−21.0100			−1.10886			−0.554432	+	0.832229i	$0.687064\pi$
$360$	−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	$-0.297128\pi$
$367$	22.7995			1.19012			0.595061	+	0.803681i	$0.297128\pi$
$368$	−14.3860	+	12.6903i	−0.749920	+	0.661528i
$369$	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	$-0.648827\pi$
$373$	−17.4091			−0.901407			−0.450703	+	0.892674i	$0.648827\pi$
$374$	−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	$-0.681575\pi$
$383$	−21.1360			−1.08000			−0.539999	+	0.841666i	$0.681575\pi$
$384$	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	$-0.107512\pi$
$389$	37.2175			1.88700			0.943500	+	0.331373i	$0.107512\pi$
$390$	−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	$-0.910567\pi$
$397$		−	11.0495i		−	0.554559i	0.960789	−	0.277280i	$-0.0894328\pi$
$398$	−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
$414$	0.300268	−	19.6883i	0.0147574	−	0.967625i
$415$			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	$-0.649265\pi$
$421$	−18.5457			−0.903863			−0.451932	+	0.892053i	$0.649265\pi$
$422$	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	$-0.471954\pi$
$431$	3.65360			0.175988			0.0879939	+	0.996121i	$0.471954\pi$
$432$	−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	$-0.878368\pi$
$439$		−	15.6257i		−	0.745772i	0.927877	−	0.372886i	$-0.121632\pi$
$440$	−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
$460$	25.6147	−	6.01873i	1.19429	−	0.280625i
$461$			14.4241i			0.671797i	0.941898	+	0.335899i	$0.109040\pi$
$461$			14.4241i			0.671797i	−0.941898	+	0.335899i	$0.890960\pi$
$462$	2.53833	−	0.637433i	0.118094	−	0.0296561i
$463$			35.7057i			1.65938i	0.558222	+	0.829692i	$0.311484\pi$
$463$			35.7057i			1.65938i	−0.558222	+	0.829692i	$0.688516\pi$
$464$	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	$-0.334252\pi$
$479$	21.7766			0.994998			0.497499	+	0.867464i	$0.334252\pi$
$480$	−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	$-0.806065\pi$
$487$		−	25.2576i		−	1.14453i	0.820068	−	0.572265i	$-0.193935\pi$
$488$	−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	$-0.196547\pi$
$503$	36.5726			1.63069			0.815346	+	0.578974i	$0.196547\pi$
$504$	−18.4062	−	20.2351i	−0.819878	−	0.901341i
$505$		−	17.7748i		−	0.790967i
$506$	−12.1097	−	0.184686i	−0.538340	−	0.00821029i
$507$	−0.888922			−0.0394784
$508$	4.95184	+	9.23766i	0.219703	+	0.409855i
$509$			5.46690i			0.242316i	0.992633	+	0.121158i	$0.0386608\pi$
$509$			5.46690i			0.242316i	−0.992633	+	0.121158i	$0.961339\pi$
$510$	−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	$0.0291982\pi$
$541$			4.26114i			0.183201i	−0.995796	+	0.0916003i	$0.970802\pi$
$542$	−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
$552$	−1.93683	−	3.74936i	−0.0824368	−	0.159583i
$553$	−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	$-0.308005\pi$
$557$	26.7755			1.13451			0.567257	+	0.823541i	$0.308005\pi$
$558$	−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
$598$	27.0049	+	0.411855i	1.10431	+	0.0168420i
$599$			19.2163i			0.785155i	0.919719	+	0.392578i	$0.128417\pi$
$599$			19.2163i			0.785155i	−0.919719	+	0.392578i	$0.871583\pi$
$600$	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	$0.220361\pi$
$607$			31.4519i			1.27659i	−0.769790	+	0.638297i	$0.779639\pi$
$608$	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	$-0.632159\pi$
$613$	−19.9736			−0.806726			−0.403363	+	0.915040i	$0.632159\pi$
$614$	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	$-0.486065\pi$
$631$	2.19872			0.0875297			0.0437648	+	0.999042i	$0.486065\pi$
$632$	−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	$0.766099\pi$
$644$	31.1045	−	7.30866i	1.22569	−	0.288002i
$645$			9.79714i			0.385762i
$646$	−10.2494	−	40.8142i	−0.403255	−	1.60581i
$647$			13.6398i			0.536234i	0.963386	+	0.268117i	$0.0864014\pi$
$647$			13.6398i			0.536234i	−0.963386	+	0.268117i	$0.913599\pi$
$648$	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	$-0.797727\pi$
$653$		−	30.3349i		−	1.18710i	0.804799	−	0.593548i	$-0.202273\pi$
$654$	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	$-0.636734\pi$
$661$	−21.4150			−0.832946			−0.416473	+	0.909148i	$0.636734\pi$
$662$	−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	$-0.676118\pi$
$677$	−27.3457			−1.05098			−0.525490	+	0.850799i	$0.676118\pi$
$678$	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
$690$	−0.0882687	+	5.78769i	−0.00336033	+	0.220333i
$691$	−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	$-0.503795\pi$
$701$	−0.631335			−0.0238452			−0.0119226	+	0.999929i	$0.503795\pi$
$702$	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	$-0.831190\pi$
$709$	−45.9390			−1.72528			−0.862638	+	0.505821i	$0.831190\pi$
$710$	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	$-0.892549\pi$
$719$		−	17.7614i		−	0.662388i	0.943563	−	0.331194i	$-0.107451\pi$
$720$	−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	$-0.538259\pi$
$727$	−6.46596			−0.239809			−0.119905	+	0.992785i	$0.538259\pi$
$728$	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	$-0.487892\pi$
$733$	2.05921			0.0760587			0.0380294	+	0.999277i	$0.487892\pi$
$734$	−7.85318	−	31.2723i	−0.289866	−	1.15428i
$735$	3.49639			0.128966
$736$	22.3615	+	15.3610i	0.824257	+	0.566215i
$737$	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	$-0.946911\pi$
$743$	−53.7596			−1.97225			−0.986124	+	0.166013i	$0.946911\pi$
$744$	−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	$-0.731864\pi$
$751$	−36.4858			−1.33139			−0.665693	+	0.746226i	$0.731864\pi$
$752$	−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	$-0.637950\pi$
$757$	−23.1084			−0.839888			−0.419944	+	0.907550i	$0.637950\pi$
$758$	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	$-0.355804\pi$
$773$	24.3369			0.875339			0.437670	+	0.899136i	$0.355804\pi$
$774$	−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
$782$	38.9243	+	0.593640i	1.39193	+	0.0212285i
$783$		−	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	$-0.486027\pi$
$797$	2.47774			0.0877660			0.0438830	+	0.999037i	$0.486027\pi$
$798$	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	$0.191839\pi$
$821$			32.4841i			1.13370i	−0.823820	+	0.566851i	$0.808161\pi$
$822$	6.42255	−	1.61285i	0.224012	−	0.0562545i
$823$		−	30.3391i		−	1.05755i	−0.848761	−	0.528777i	$-0.822651\pi$
$823$		−	30.3391i		−	1.05755i	0.848761	−	0.528777i	$-0.177349\pi$
$824$	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	$-0.202526\pi$
$828$	−27.1083	+	6.36969i	−0.942080	+	0.221362i
$829$			51.0163i			1.77187i	0.463810	+	0.885935i	$0.346482\pi$
$829$			51.0163i			1.77187i	−0.463810	+	0.885935i	$0.653518\pi$
$830$	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	$-0.293862\pi$
$839$	34.9483			1.20655			0.603275	+	0.797533i	$0.293862\pi$
$840$	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	$-0.904858\pi$
$853$		−	17.2005i		−	0.588932i	0.955662	−	0.294466i	$-0.0951418\pi$
$854$	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	$-0.932656\pi$
$863$		−	12.3379i		−	0.419986i	0.977703	−	0.209993i	$-0.0673442\pi$
$864$	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
$874$	−35.1569	−	0.536182i	−1.18920	−	0.0181366i
$875$	−22.6133			−0.764470
$876$	6.50246	−	3.48564i	0.219698	−	0.117769i
$877$		−	50.2063i		−	1.69535i	−0.530520	−	0.847673i	$-0.678003\pi$
$877$		−	50.2063i		−	1.69535i	0.530520	−	0.847673i	$-0.321997\pi$
$878$	−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	$0.0439188\pi$
$887$			8.19245i			0.275076i	−0.990497	+	0.137538i	$0.956081\pi$
$888$	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	$-0.0940845\pi$
$911$	57.7478			1.91327			0.956635	+	0.291290i	$0.0940845\pi$
$912$	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	$-0.697907\pi$
$919$	−35.3141			−1.16491			−0.582453	+	0.812864i	$0.697907\pi$
$920$	−17.0783	−	33.0607i	−0.563056	−	1.08998i
$921$	−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	$-0.728573\pi$
$941$	−40.3657			−1.31589			−0.657943	+	0.753068i	$0.728573\pi$
$942$	−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
$966$	−0.107186	+	7.02810i	−0.00344867	+	0.226125i
$967$		−	44.6176i		−	1.43480i	−0.696659	−	0.717402i	$-0.745331\pi$
$967$		−	44.6176i		−	1.43480i	0.696659	−	0.717402i	$-0.254669\pi$
$968$	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	$-0.345010\pi$
$983$	29.3400			0.935801			0.467901	+	0.883781i	$0.345010\pi$
$984$	−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	$-0.833040\pi$
$991$		−	31.5303i		−	1.00159i	0.865565	−	0.500797i	$-0.166960\pi$
$992$	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	$0.0835725\pi$
$997$			16.3904i			0.519089i	−0.965731	+	0.259545i	$0.916428\pi$
$998$	−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.91.6	yes	12
4.3	odd	2		736.2.h.c.367.7		12
8.3	odd	2	inner	184.2.h.c.91.7	yes	12
8.5	even	2		736.2.h.c.367.5		12
23.22	odd	2	inner	184.2.h.c.91.5	✓	12
92.91	even	2		736.2.h.c.367.6		12
184.45	odd	2		736.2.h.c.367.8		12
184.91	even	2	inner	184.2.h.c.91.8	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.h.c.91.5	✓	12	23.22	odd	2	inner
184.2.h.c.91.6	yes	12	1.1	even	1	trivial
184.2.h.c.91.7	yes	12	8.3	odd	2	inner
184.2.h.c.91.8	yes	12	184.91	even	2	inner
736.2.h.c.367.5		12	8.5	even	2
736.2.h.c.367.6		12	92.91	even	2
736.2.h.c.367.7		12	4.3	odd	2
736.2.h.c.367.8		12	184.45	odd	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} +(-0.103426 + 6.78154i) 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} +(9.33736 - 2.19401i) 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

Introduction

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