LMFDB - Embedded newform 546.2.g.d.209.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(209,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("546.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 4x^{10} - 8x^{8} + 26x^{7} - 50x^{6} + 78x^{5} - 72x^{4} + 324x^{2} - 486x + 729 $ x^12 - 2x^11 + 4x^10 - 8x^8 + 26x^7 - 50x^6 + 78x^5 - 72x^4 + 324x^2 - 486*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			209.10
Root			$1.64187 - 0.551597i$ of defining polynomial
Character	$\chi$	$=$	546.209
Dual form			546.2.g.d.209.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.551597 - 1.64187i) q^{3} -1.00000 q^{4} -0.124244 q^{5} +(1.64187 + 0.551597i) q^{6} +(1.46370 - 2.20399i) q^{7} -1.00000i q^{8} +(-2.39148 - 1.81130i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.551597 - 1.64187i) q^{3} -1.00000 q^{4} -0.124244 q^{5} +(1.64187 + 0.551597i) q^{6} +(1.46370 - 2.20399i) q^{7} -1.00000i q^{8} +(-2.39148 - 1.81130i) q^{9} -0.124244i q^{10} +3.15950i q^{11} +(-0.551597 + 1.64187i) q^{12} -1.00000i q^{13} +(2.20399 + 1.46370i) q^{14} +(-0.0685329 + 0.203993i) q^{15} +1.00000 q^{16} +5.18986 q^{17} +(1.81130 - 2.39148i) q^{18} -7.80424i q^{19} +0.124244 q^{20} +(-2.81130 - 3.61892i) q^{21} -3.15950 q^{22} -8.49945i q^{23} +(-1.64187 - 0.551597i) q^{24} -4.98456 q^{25} +1.00000 q^{26} +(-4.29306 + 2.92740i) q^{27} +(-1.46370 + 2.20399i) q^{28} -0.988265i q^{29} +(-0.203993 - 0.0685329i) q^{30} +2.03612i q^{31} +1.00000i q^{32} +(5.18749 + 1.74277i) q^{33} +5.18986i q^{34} +(-0.181856 + 0.273834i) q^{35} +(2.39148 + 1.81130i) q^{36} +4.99544 q^{37} +7.80424 q^{38} +(-1.64187 - 0.551597i) q^{39} +0.124244i q^{40} -0.374977 q^{41} +(3.61892 - 2.81130i) q^{42} +0.643654 q^{43} -3.15950i q^{44} +(0.297128 + 0.225044i) q^{45} +8.49945 q^{46} +0.322562 q^{47} +(0.551597 - 1.64187i) q^{48} +(-2.71517 - 6.45196i) q^{49} -4.98456i q^{50} +(2.86271 - 8.52109i) q^{51} +1.00000i q^{52} +11.3835i q^{53} +(-2.92740 - 4.29306i) q^{54} -0.392550i q^{55} +(-2.20399 - 1.46370i) q^{56} +(-12.8136 - 4.30479i) q^{57} +0.988265 q^{58} +6.22502 q^{59} +(0.0685329 - 0.203993i) q^{60} +9.38452i q^{61} -2.03612 q^{62} +(-7.49251 + 2.61961i) q^{63} -1.00000 q^{64} +0.124244i q^{65} +(-1.74277 + 5.18749i) q^{66} +11.0585 q^{67} -5.18986 q^{68} +(-13.9550 - 4.68827i) q^{69} +(-0.273834 - 0.181856i) q^{70} +10.1781i q^{71} +(-1.81130 + 2.39148i) q^{72} -10.3117i q^{73} +4.99544i q^{74} +(-2.74947 + 8.18401i) q^{75} +7.80424i q^{76} +(6.96351 + 4.62455i) q^{77} +(0.551597 - 1.64187i) q^{78} +0.149958 q^{79} -0.124244 q^{80} +(2.43837 + 8.66339i) q^{81} -0.374977i q^{82} +7.17707 q^{83} +(2.81130 + 3.61892i) q^{84} -0.644812 q^{85} +0.643654i q^{86} +(-1.62260 - 0.545124i) q^{87} +3.15950 q^{88} -6.93771 q^{89} +(-0.225044 + 0.297128i) q^{90} +(-2.20399 - 1.46370i) q^{91} +8.49945i q^{92} +(3.34304 + 1.12311i) q^{93} +0.322562i q^{94} +0.969633i q^{95} +(1.64187 + 0.551597i) q^{96} +4.53137i q^{97} +(6.45196 - 2.71517i) q^{98} +(5.72280 - 7.55588i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} - 12 q^{4} - 4 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9}+O(q^{10}) $ 12 * q + 2 * q^3 - 12 * q^4 - 4 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9	$ 12 q + 2 q^{3} - 12 q^{4} - 4 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9} - 2 q^{12} + 10 q^{14} + 4 q^{15} + 12 q^{16} + 12 q^{17} + 8 q^{18} + 4 q^{20} - 20 q^{21} - 2 q^{24} + 20 q^{25} + 12 q^{26} + 8 q^{27} + 8 q^{28} + 14 q^{30} + 46 q^{33} - 22 q^{35} - 4 q^{36} + 16 q^{37} - 8 q^{38} - 2 q^{39} + 28 q^{41} + 4 q^{42} - 8 q^{43} + 24 q^{46} - 68 q^{47} + 2 q^{48} + 26 q^{49} - 50 q^{51} + 16 q^{54} - 10 q^{56} - 28 q^{57} - 24 q^{58} + 8 q^{59} - 4 q^{60} + 16 q^{62} - 2 q^{63} - 12 q^{64} - 12 q^{66} + 8 q^{67} - 12 q^{68} - 24 q^{69} - 28 q^{70} - 8 q^{72} + 92 q^{75} - 8 q^{77} + 2 q^{78} + 36 q^{79} - 4 q^{80} + 16 q^{81} - 32 q^{83} + 20 q^{84} + 8 q^{87} - 48 q^{89} + 2 q^{90} - 10 q^{91} + 8 q^{93} + 2 q^{96} + 16 q^{98}+O(q^{100}) $ 12 * q + 2 * q^3 - 12 * q^4 - 4 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9 - 2 * q^12 + 10 * q^14 + 4 * q^15 + 12 * q^16 + 12 * q^17 + 8 * q^18 + 4 * q^20 - 20 * q^21 - 2 * q^24 + 20 * q^25 + 12 * q^26 + 8 * q^27 + 8 * q^28 + 14 * q^30 + 46 * q^33 - 22 * q^35 - 4 * q^36 + 16 * q^37 - 8 * q^38 - 2 * q^39 + 28 * q^41 + 4 * q^42 - 8 * q^43 + 24 * q^46 - 68 * q^47 + 2 * q^48 + 26 * q^49 - 50 * q^51 + 16 * q^54 - 10 * q^56 - 28 * q^57 - 24 * q^58 + 8 * q^59 - 4 * q^60 + 16 * q^62 - 2 * q^63 - 12 * q^64 - 12 * q^66 + 8 * q^67 - 12 * q^68 - 24 * q^69 - 28 * q^70 - 8 * q^72 + 92 * q^75 - 8 * q^77 + 2 * q^78 + 36 * q^79 - 4 * q^80 + 16 * q^81 - 32 * q^83 + 20 * q^84 + 8 * q^87 - 48 * q^89 + 2 * q^90 - 10 * q^91 + 8 * q^93 + 2 * q^96 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.551597	−	1.64187i	0.318465	−	0.947935i
$3$	0.551597	−	1.64187i	0.318465	−	0.947935i
$4$	−1.00000			−0.500000
$5$	−0.124244			−0.0555638			−0.0277819	−	0.999614i	$-0.508844\pi$
$5$	−0.124244			−0.0555638			−0.0277819	+	0.999614i	$0.508844\pi$
$6$	1.64187	+	0.551597i	0.670291	+	0.225188i
$7$	1.46370	−	2.20399i	0.553226	−	0.833031i
$7$	1.46370	−	2.20399i	0.553226	−	0.833031i
$8$		−	1.00000i		−	0.353553i
$9$	−2.39148	−	1.81130i	−0.797161	−	0.603767i
$10$		−	0.124244i		−	0.0392895i
$11$			3.15950i			0.952624i	0.879276	+	0.476312i	$0.158027\pi$
$11$			3.15950i			0.952624i	−0.879276	+	0.476312i	$0.841973\pi$
$12$	−0.551597	+	1.64187i	−0.159232	+	0.473967i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	2.20399	+	1.46370i	0.589042	+	0.391190i
$15$	−0.0685329	+	0.203993i	−0.0176951	+	0.0526709i
$16$	1.00000			0.250000
$17$	5.18986			1.25873			0.629364	−	0.777111i	$-0.283316\pi$
$17$	5.18986			1.25873			0.629364	+	0.777111i	$0.283316\pi$
$18$	1.81130	−	2.39148i	0.426928	−	0.563678i
$19$		−	7.80424i		−	1.79042i	−0.445649	−	0.895208i	$-0.647027\pi$
$19$		−	7.80424i		−	1.79042i	0.445649	−	0.895208i	$-0.352973\pi$
$20$	0.124244			0.0277819
$21$	−2.81130	−	3.61892i	−0.613476	−	0.789713i
$22$	−3.15950			−0.673607
$23$		−	8.49945i		−	1.77226i	−0.463440	−	0.886128i	$-0.653385\pi$
$23$		−	8.49945i		−	1.77226i	0.463440	−	0.886128i	$-0.346615\pi$
$24$	−1.64187	−	0.551597i	−0.335146	−	0.112594i
$25$	−4.98456			−0.996913
$26$	1.00000			0.196116
$27$	−4.29306	+	2.92740i	−0.826199	+	0.563378i
$28$	−1.46370	+	2.20399i	−0.276613	+	0.416516i
$29$		−	0.988265i		−	0.183516i	−0.995781	−	0.0917581i	$-0.970751\pi$
$29$		−	0.988265i		−	0.183516i	0.995781	−	0.0917581i	$-0.0292487\pi$
$30$	−0.203993	−	0.0685329i	−0.0372439	−	0.0125123i
$31$			2.03612i			0.365697i	0.983141	+	0.182849i	$0.0585318\pi$
$31$			2.03612i			0.365697i	−0.983141	+	0.182849i	$0.941468\pi$
$32$			1.00000i			0.176777i
$33$	5.18749	+	1.74277i	0.903026	+	0.303377i
$34$			5.18986i			0.890054i
$35$	−0.181856	+	0.273834i	−0.0307393	+	0.0462864i
$36$	2.39148	+	1.81130i	0.398580	+	0.301884i
$37$	4.99544			0.821245			0.410622	−	0.911806i	$-0.365311\pi$
$37$	4.99544			0.821245			0.410622	+	0.911806i	$0.365311\pi$
$38$	7.80424			1.26601
$39$	−1.64187	−	0.551597i	−0.262910	−	0.0883262i
$40$			0.124244i			0.0196448i
$41$	−0.374977			−0.0585616			−0.0292808	−	0.999571i	$-0.509322\pi$
$41$	−0.374977			−0.0585616			−0.0292808	+	0.999571i	$0.509322\pi$
$42$	3.61892	−	2.81130i	0.558411	−	0.433793i
$43$	0.643654			0.0981564			0.0490782	−	0.998795i	$-0.484372\pi$
$43$	0.643654			0.0981564			0.0490782	+	0.998795i	$0.484372\pi$
$44$		−	3.15950i		−	0.476312i
$45$	0.297128	+	0.225044i	0.0442933	+	0.0335476i
$46$	8.49945			1.25317
$47$	0.322562			0.0470506			0.0235253	−	0.999723i	$-0.492511\pi$
$47$	0.322562			0.0470506			0.0235253	+	0.999723i	$0.492511\pi$
$48$	0.551597	−	1.64187i	0.0796161	−	0.236984i
$49$	−2.71517	−	6.45196i	−0.387882	−	0.921709i
$50$		−	4.98456i		−	0.704924i
$51$	2.86271	−	8.52109i	0.400860	−	1.19319i
$52$			1.00000i			0.138675i
$53$			11.3835i			1.56364i	0.623505	+	0.781819i	$0.285708\pi$
$53$			11.3835i			1.56364i	−0.623505	+	0.781819i	$0.714292\pi$
$54$	−2.92740	−	4.29306i	−0.398368	−	0.584211i
$55$		−	0.392550i		−	0.0529314i
$56$	−2.20399	−	1.46370i	−0.294521	−	0.195595i
$57$	−12.8136	−	4.30479i	−1.69720	−	0.570184i
$58$	0.988265			0.129766
$59$	6.22502			0.810428			0.405214	−	0.914222i	$-0.367197\pi$
$59$	6.22502			0.810428			0.405214	+	0.914222i	$0.367197\pi$
$60$	0.0685329	−	0.203993i	0.00884755	−	0.0263354i
$61$			9.38452i			1.20156i	0.799413	+	0.600782i	$0.205144\pi$
$61$			9.38452i			1.20156i	−0.799413	+	0.600782i	$0.794856\pi$
$62$	−2.03612			−0.258587
$63$	−7.49251	+	2.61961i	−0.943967	+	0.330040i
$64$	−1.00000			−0.125000
$65$			0.124244i			0.0154106i
$66$	−1.74277	+	5.18749i	−0.214520	+	0.638536i
$67$	11.0585			1.35101			0.675504	−	0.737356i	$-0.263926\pi$
$67$	11.0585			1.35101			0.675504	+	0.737356i	$0.263926\pi$
$68$	−5.18986			−0.629364
$69$	−13.9550	−	4.68827i	−1.67998	−	0.564401i
$70$	−0.273834	−	0.181856i	−0.0327294	−	0.0217360i
$71$			10.1781i			1.20792i	0.797014	+	0.603961i	$0.206412\pi$
$71$			10.1781i			1.20792i	−0.797014	+	0.603961i	$0.793588\pi$
$72$	−1.81130	+	2.39148i	−0.213464	+	0.281839i
$73$		−	10.3117i		−	1.20689i	−0.797404	−	0.603446i	$-0.793794\pi$
$73$		−	10.3117i		−	1.20689i	0.797404	−	0.603446i	$-0.206206\pi$
$74$			4.99544i			0.580708i
$75$	−2.74947	+	8.18401i	−0.317481	+	0.945008i
$76$			7.80424i			0.895208i
$77$	6.96351	+	4.62455i	0.793566	+	0.527017i
$78$	0.551597	−	1.64187i	0.0624560	−	0.185905i
$79$	0.149958			0.0168716			0.00843581	−	0.999964i	$-0.497315\pi$
$79$	0.149958			0.0168716			0.00843581	+	0.999964i	$0.497315\pi$
$80$	−0.124244			−0.0138910
$81$	2.43837	+	8.66339i	0.270930	+	0.962599i
$82$		−	0.374977i		−	0.0414093i
$83$	7.17707			0.787786			0.393893	−	0.919156i	$-0.371128\pi$
$83$	7.17707			0.787786			0.393893	+	0.919156i	$0.371128\pi$
$84$	2.81130	+	3.61892i	0.306738	+	0.394857i
$85$	−0.644812			−0.0699397
$86$			0.643654i			0.0694070i
$87$	−1.62260	−	0.545124i	−0.173961	−	0.0584434i
$88$	3.15950			0.336804
$89$	−6.93771			−0.735396			−0.367698	−	0.929945i	$-0.619854\pi$
$89$	−6.93771			−0.735396			−0.367698	+	0.929945i	$0.619854\pi$
$90$	−0.225044	+	0.297128i	−0.0237217	+	0.0313201i
$91$	−2.20399	−	1.46370i	−0.231041	−	0.153437i
$92$			8.49945i			0.886128i
$93$	3.34304	+	1.12311i	0.346657	+	0.116462i
$94$			0.322562i			0.0332698i
$95$			0.969633i			0.0994823i
$96$	1.64187	+	0.551597i	0.167573	+	0.0562971i
$97$			4.53137i			0.460091i	0.973180	+	0.230045i	$0.0738875\pi$
$97$			4.53137i			0.460091i	−0.973180	+	0.230045i	$0.926113\pi$
$98$	6.45196	−	2.71517i	0.651747	−	0.274274i
$99$	5.72280	−	7.55588i	0.575163	−	0.759395i
$100$	4.98456			0.498456
$101$	−14.8286			−1.47550			−0.737751	−	0.675073i	$-0.764112\pi$
$101$	−14.8286			−1.47550			−0.737751	+	0.675073i	$0.764112\pi$
$102$	8.52109	+	2.86271i	0.843714	+	0.283451i
$103$		−	0.578134i		−	0.0569652i	−0.999594	−	0.0284826i	$-0.990932\pi$
$103$		−	0.578134i		−	0.0569652i	0.999594	−	0.0284826i	$-0.00906752\pi$
$104$	−1.00000			−0.0980581
$105$	0.349289	+	0.449631i	0.0340871	+	0.0438795i
$106$	−11.3835			−1.10566
$107$			18.6047i			1.79859i	0.437344	+	0.899294i	$0.355919\pi$
$107$			18.6047i			1.79859i	−0.437344	+	0.899294i	$0.644081\pi$
$108$	4.29306	−	2.92740i	0.413100	−	0.281689i
$109$	−4.91894			−0.471149			−0.235575	−	0.971856i	$-0.575697\pi$
$109$	−4.91894			−0.471149			−0.235575	+	0.971856i	$0.575697\pi$
$110$	0.392550			0.0374282
$111$	2.75547	−	8.20186i	0.261537	−	0.778486i
$112$	1.46370	−	2.20399i	0.138307	−	0.208258i
$113$			13.6446i			1.28358i	0.766882	+	0.641788i	$0.221807\pi$
$113$			13.6446i			1.28358i	−0.766882	+	0.641788i	$0.778193\pi$
$114$	4.30479	−	12.8136i	0.403181	−	1.20010i
$115$			1.05601i			0.0984734i
$116$			0.988265i			0.0917581i
$117$	−1.81130	+	2.39148i	−0.167455	+	0.221093i
$118$			6.22502i			0.573059i
$119$	7.59640	−	11.4384i	0.696361	−	1.04856i
$120$	0.203993	+	0.0685329i	0.0186220	+	0.00625616i
$121$	1.01757			0.0925066
$122$	−9.38452			−0.849634
$123$	−0.206836	+	0.615664i	−0.0186498	+	0.0555125i
$124$		−	2.03612i		−	0.182849i
$125$	1.24053			0.110956
$126$	−2.61961	−	7.49251i	−0.233373	−	0.667485i
$127$	6.96593			0.618126			0.309063	−	0.951041i	$-0.399985\pi$
$127$	6.96593			0.618126			0.309063	+	0.951041i	$0.399985\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	0.355038	−	1.05680i	0.0312593	−	0.0930459i
$130$	−0.124244			−0.0108970
$131$	−10.5712			−0.923606			−0.461803	−	0.886983i	$-0.652797\pi$
$131$	−10.5712			−0.923606			−0.461803	+	0.886983i	$0.652797\pi$
$132$	−5.18749	−	1.74277i	−0.451513	−	0.151689i
$133$	−17.2005	−	11.4231i	−1.49147	−	0.990504i
$134$			11.0585i			0.955307i
$135$	0.533389	−	0.363713i	0.0459068	−	0.0313034i
$136$		−	5.18986i		−	0.445027i
$137$			22.1462i			1.89208i	0.324049	+	0.946040i	$0.394956\pi$
$137$			22.1462i			1.89208i	−0.324049	+	0.946040i	$0.605044\pi$
$138$	4.68827	−	13.9550i	0.399092	−	1.18793i
$139$			11.7008i			0.992451i	0.868194	+	0.496225i	$0.165281\pi$
$139$			11.7008i			0.992451i	−0.868194	+	0.496225i	$0.834719\pi$
$140$	0.181856	−	0.273834i	0.0153697	−	0.0231432i
$141$	0.177924	−	0.529606i	0.0149839	−	0.0446009i
$142$	−10.1781			−0.854130
$143$	3.15950			0.264210
$144$	−2.39148	−	1.81130i	−0.199290	−	0.150942i
$145$			0.122786i			0.0101969i
$146$	10.3117			0.853402
$147$	−12.0910	+	0.899083i	−0.997247	+	0.0741551i
$148$	−4.99544			−0.410622
$149$		−	24.2302i		−	1.98502i	−0.122176	−	0.992508i	$-0.538987\pi$
$149$		−	24.2302i		−	1.98502i	0.122176	−	0.992508i	$-0.461013\pi$
$150$	−8.18401	−	2.74947i	−0.668222	−	0.224493i
$151$	15.4209			1.25493			0.627466	−	0.778644i	$-0.284092\pi$
$151$	15.4209			1.25493			0.627466	+	0.778644i	$0.284092\pi$
$152$	−7.80424			−0.633007
$153$	−12.4115	−	9.40041i	−1.00341	−	0.759978i
$154$	−4.62455	+	6.96351i	−0.372657	+	0.561136i
$155$		−	0.252976i		−	0.0203195i
$156$	1.64187	+	0.551597i	0.131455	+	0.0441631i
$157$		−	15.5649i		−	1.24221i	−0.783727	−	0.621106i	$-0.786684\pi$
$157$		−	15.5649i		−	1.24221i	0.783727	−	0.621106i	$-0.213316\pi$
$158$			0.149958i			0.0119300i
$159$	18.6902	+	6.27908i	1.48223	+	0.497963i
$160$		−	0.124244i		−	0.00982239i
$161$	−18.7327	−	12.4406i	−1.47635	−	0.980459i
$162$	−8.66339	+	2.43837i	−0.680660	+	0.191577i
$163$	6.45488			0.505585			0.252792	−	0.967521i	$-0.418651\pi$
$163$	6.45488			0.505585			0.252792	+	0.967521i	$0.418651\pi$
$164$	0.374977			0.0292808
$165$	−0.644517	−	0.216529i	−0.0501756	−	0.0168568i
$166$			7.17707i			0.557049i
$167$	−22.4303			−1.73571			−0.867853	−	0.496821i	$-0.834500\pi$
$167$	−22.4303			−1.73571			−0.867853	+	0.496821i	$0.834500\pi$
$168$	−3.61892	+	2.81130i	−0.279206	+	0.216897i
$169$	−1.00000			−0.0769231
$170$		−	0.644812i		−	0.0494548i
$171$	−14.1358	+	18.6637i	−1.08099	+	1.42725i
$172$	−0.643654			−0.0490782
$173$	11.0835			0.842666			0.421333	−	0.906906i	$-0.361562\pi$
$173$	11.0835			0.842666			0.421333	+	0.906906i	$0.361562\pi$
$174$	0.545124	−	1.62260i	0.0413257	−	0.123009i
$175$	−7.29590	+	10.9859i	−0.551518	+	0.830459i
$176$			3.15950i			0.238156i
$177$	3.43370	−	10.2207i	0.258093	−	0.768233i
$178$		−	6.93771i		−	0.520003i
$179$		−	0.910490i		−	0.0680532i	−0.999421	−	0.0340266i	$-0.989167\pi$
$179$		−	0.910490i		−	0.0680532i	0.999421	−	0.0340266i	$-0.0108331\pi$
$180$	−0.297128	−	0.225044i	−0.0221466	−	0.0167738i
$181$			3.83313i			0.284915i	0.989801	+	0.142457i	$0.0455004\pi$
$181$			3.83313i			0.284915i	−0.989801	+	0.142457i	$0.954500\pi$
$182$	1.46370	−	2.20399i	0.108497	−	0.163371i
$183$	15.4082	+	5.17647i	1.13900	+	0.382656i
$184$	−8.49945			−0.626587
$185$	−0.620655			−0.0456315
$186$	−1.12311	+	3.34304i	−0.0823508	+	0.245124i
$187$			16.3974i			1.19909i
$188$	−0.322562			−0.0235253
$189$	0.168221	+	13.7467i	0.0122363	+	0.999925i
$190$	−0.969633			−0.0703446
$191$		−	4.10415i		−	0.296966i	−0.988915	−	0.148483i	$-0.952561\pi$
$191$		−	4.10415i		−	0.296966i	0.988915	−	0.148483i	$-0.0474391\pi$
$192$	−0.551597	+	1.64187i	−0.0398081	+	0.118492i
$193$	−8.09615			−0.582774			−0.291387	−	0.956605i	$-0.594117\pi$
$193$	−8.09615			−0.582774			−0.291387	+	0.956605i	$0.594117\pi$
$194$	−4.53137			−0.325333
$195$	0.203993	+	0.0685329i	0.0146083	+	0.00490774i
$196$	2.71517	+	6.45196i	0.193941	+	0.460855i
$197$		−	15.0484i		−	1.07215i	−0.844170	−	0.536076i	$-0.819906\pi$
$197$		−	15.0484i		−	1.07215i	0.844170	−	0.536076i	$-0.180094\pi$
$198$	7.55588	+	5.72280i	0.536973	+	0.406702i
$199$			16.5733i			1.17485i	0.809279	+	0.587425i	$0.199858\pi$
$199$			16.5733i			1.17485i	−0.809279	+	0.587425i	$0.800142\pi$
$200$			4.98456i			0.352462i
$201$	6.09982	−	18.1566i	0.430248	−	1.28067i
$202$		−	14.8286i		−	1.04334i
$203$	−2.17813	−	1.44652i	−0.152875	−	0.101526i
$204$	−2.86271	+	8.52109i	−0.200430	+	0.596596i
$205$	0.0465888			0.00325390
$206$	0.578134			0.0402805
$207$	−15.3951	+	20.3263i	−1.07003	+	1.41277i
$208$		−	1.00000i		−	0.0693375i
$209$	24.6575			1.70559
$210$	−0.449631	+	0.349289i	−0.0310275	+	0.0241032i
$211$	23.6447			1.62777			0.813885	−	0.581026i	$-0.197349\pi$
$211$	23.6447			1.62777			0.813885	+	0.581026i	$0.197349\pi$
$212$		−	11.3835i		−	0.781819i
$213$	16.7112	+	5.61422i	1.14503	+	0.384680i
$214$	−18.6047			−1.27179
$215$	−0.0799705			−0.00545394
$216$	2.92740	+	4.29306i	0.199184	+	0.292106i
$217$	4.48759	+	2.98026i	0.304637	+	0.202313i
$218$		−	4.91894i		−	0.333153i
$219$	−16.9305	−	5.68790i	−1.14405	−	0.384352i
$220$			0.392550i			0.0264657i
$221$		−	5.18986i		−	0.349108i
$222$	8.20186	+	2.75547i	0.550473	+	0.184935i
$223$		−	20.4113i		−	1.36684i	−0.730024	−	0.683421i	$-0.760491\pi$
$223$		−	20.4113i		−	1.36684i	0.730024	−	0.683421i	$-0.239509\pi$
$224$	2.20399	+	1.46370i	0.147261	+	0.0977975i
$225$	11.9205	+	9.02855i	0.794700	+	0.601903i
$226$	−13.6446			−0.907625
$227$	8.72027			0.578785			0.289392	−	0.957211i	$-0.406547\pi$
$227$	8.72027			0.578785			0.289392	+	0.957211i	$0.406547\pi$
$228$	12.8136	+	4.30479i	0.848598	+	0.285092i
$229$		−	12.6352i		−	0.834956i	−0.908687	−	0.417478i	$-0.862914\pi$
$229$		−	12.6352i		−	0.834956i	0.908687	−	0.417478i	$-0.137086\pi$
$230$	−1.05601			−0.0696312
$231$	11.4340	−	8.88230i	0.752300	−	0.584413i
$232$	−0.988265			−0.0648828
$233$		−	10.1218i		−	0.663098i	−0.943438	−	0.331549i	$-0.892429\pi$
$233$		−	10.1218i		−	0.663098i	0.943438	−	0.331549i	$-0.107571\pi$
$234$	−2.39148	−	1.81130i	−0.156336	−	0.118409i
$235$	−0.0400766			−0.00261431
$236$	−6.22502			−0.405214
$237$	0.0827165	−	0.246212i	0.00537301	−	0.0159932i
$238$	11.4384	+	7.59640i	0.741443	+	0.492401i
$239$		−	11.3900i		−	0.736756i	−0.929676	−	0.368378i	$-0.879913\pi$
$239$		−	11.3900i		−	0.736756i	0.929676	−	0.368378i	$-0.120087\pi$
$240$	−0.0685329	+	0.203993i	−0.00442378	+	0.0131677i
$241$			10.1714i			0.655199i	0.944817	+	0.327599i	$0.106240\pi$
$241$			10.1714i			0.655199i	−0.944817	+	0.327599i	$0.893760\pi$
$242$			1.01757i			0.0654121i
$243$	15.5692	+	0.775207i	0.998763	+	0.0497296i
$244$		−	9.38452i		−	0.600782i
$245$	0.337345	+	0.801621i	0.0215522	+	0.0512137i
$246$	−0.615664	−	0.206836i	−0.0392533	−	0.0131874i
$247$	−7.80424			−0.496572
$248$	2.03612			0.129293
$249$	3.95885	−	11.7838i	0.250882	−	0.746770i
$250$			1.24053i			0.0784578i
$251$	22.8458			1.44201			0.721007	−	0.692927i	$-0.243679\pi$
$251$	22.8458			1.44201			0.721007	+	0.692927i	$0.243679\pi$
$252$	7.49251	−	2.61961i	0.471983	−	0.165020i
$253$	26.8540			1.68830
$254$			6.96593i			0.437081i
$255$	−0.355676	+	1.05870i	−0.0222733	+	0.0662982i
$256$	1.00000			0.0625000
$257$	−3.37630			−0.210608			−0.105304	−	0.994440i	$-0.533582\pi$
$257$	−3.37630			−0.210608			−0.105304	+	0.994440i	$0.533582\pi$
$258$	1.05680	+	0.355038i	0.0657934	+	0.0221037i
$259$	7.31181	−	11.0099i	0.454334	−	0.684122i
$260$		−	0.124244i		−	0.00770531i
$261$	−1.79005	+	2.36342i	−0.110801	+	0.146292i
$262$		−	10.5712i		−	0.653088i
$263$			4.54885i			0.280494i	0.990117	+	0.140247i	$0.0447897\pi$
$263$			4.54885i			0.280494i	−0.990117	+	0.140247i	$0.955210\pi$
$264$	1.74277	−	5.18749i	0.107260	−	0.319268i
$265$		−	1.41433i		−	0.0868817i
$266$	11.4231	−	17.2005i	0.700392	−	1.05463i
$267$	−3.82682	+	11.3908i	−0.234197	+	0.697107i
$268$	−11.0585			−0.675504
$269$	−7.73403			−0.471552			−0.235776	−	0.971807i	$-0.575763\pi$
$269$	−7.73403			−0.471552			−0.235776	+	0.971807i	$0.575763\pi$
$270$	0.363713	+	0.533389i	0.0221349	+	0.0324610i
$271$		−	6.93234i		−	0.421110i	−0.977582	−	0.210555i	$-0.932473\pi$
$271$		−	6.93234i		−	0.421110i	0.977582	−	0.210555i	$-0.0675271\pi$
$272$	5.18986			0.314682
$273$	−3.61892	+	2.81130i	−0.219027	+	0.170148i
$274$	−22.1462			−1.33790
$275$		−	15.7487i		−	0.949683i
$276$	13.9550	+	4.68827i	0.839992	+	0.282201i
$277$	5.97653			0.359095			0.179547	−	0.983749i	$-0.442537\pi$
$277$	5.97653			0.359095			0.179547	+	0.983749i	$0.442537\pi$
$278$	−11.7008			−0.701769
$279$	3.68802	−	4.86933i	0.220796	−	0.291519i
$280$	0.273834	+	0.181856i	0.0163647	+	0.0108680i
$281$			12.7998i			0.763574i	0.924250	+	0.381787i	$0.124691\pi$
$281$			12.7998i			0.763574i	−0.924250	+	0.381787i	$0.875309\pi$
$282$	0.529606	+	0.177924i	0.0315376	+	0.0105952i
$283$			12.2413i			0.727668i	0.931464	+	0.363834i	$0.118532\pi$
$283$			12.2413i			0.727668i	−0.931464	+	0.363834i	$0.881468\pi$
$284$		−	10.1781i		−	0.603961i
$285$	1.59201	+	0.534847i	0.0943027	+	0.0316816i
$286$			3.15950i			0.186825i
$287$	−0.548853	+	0.826447i	−0.0323978	+	0.0487836i
$288$	1.81130	−	2.39148i	0.106732	−	0.140919i
$289$	9.93469			0.584394
$290$	−0.122786			−0.00721027
$291$	7.43992	+	2.49949i	0.436136	+	0.146523i
$292$			10.3117i			0.603446i
$293$	24.6407			1.43953			0.719763	−	0.694220i	$-0.244251\pi$
$293$	24.6407			1.43953			0.719763	+	0.694220i	$0.244251\pi$
$294$	−0.899083	−	12.0910i	−0.0524356	−	0.705160i
$295$	−0.773424			−0.0450305
$296$		−	4.99544i		−	0.290354i
$297$	−9.24910	−	13.5639i	−0.536687	−	0.787058i
$298$	24.2302			1.40362
$299$	−8.49945			−0.491536
$300$	2.74947	−	8.18401i	0.158741	−	0.472504i
$301$	0.942116	−	1.41861i	0.0543027	−	0.0817673i
$302$			15.4209i			0.887371i
$303$	−8.17942	+	24.3467i	−0.469895	+	1.39868i
$304$		−	7.80424i		−	0.447604i
$305$		−	1.16597i		−	0.0667635i
$306$	9.40041	−	12.4115i	0.537386	−	0.709516i
$307$			19.5052i			1.11322i	0.830774	+	0.556610i	$0.187898\pi$
$307$			19.5052i			1.11322i	−0.830774	+	0.556610i	$0.812102\pi$
$308$	−6.96351	−	4.62455i	−0.396783	−	0.263508i
$309$	−0.949221	−	0.318897i	−0.0539993	−	0.0181414i
$310$	0.252976			0.0143681
$311$	6.05188			0.343170			0.171585	−	0.985169i	$-0.445111\pi$
$311$	6.05188			0.343170			0.171585	+	0.985169i	$0.445111\pi$
$312$	−0.551597	+	1.64187i	−0.0312280	+	0.0929527i
$313$			23.2819i			1.31597i	0.753030	+	0.657986i	$0.228592\pi$
$313$			23.2819i			1.31597i	−0.753030	+	0.657986i	$0.771408\pi$
$314$	15.5649			0.878376
$315$	0.930902	−	0.325472i	0.0524504	−	0.0183383i
$316$	−0.149958			−0.00843581
$317$		−	2.14295i		−	0.120360i	−0.998188	−	0.0601800i	$-0.980833\pi$
$317$		−	2.14295i		−	0.120360i	0.998188	−	0.0601800i	$-0.0191675\pi$
$318$	−6.27908	+	18.6902i	−0.352113	+	1.04809i
$319$	3.12242			0.174822
$320$	0.124244			0.00694548
$321$	30.5466	+	10.2623i	1.70494	+	0.572787i
$322$	12.4406	−	18.7327i	0.693289	−	1.04393i
$323$		−	40.5029i		−	2.25364i
$324$	−2.43837	−	8.66339i	−0.135465	−	0.481300i
$325$			4.98456i			0.276494i
$326$			6.45488i			0.357503i
$327$	−2.71327	+	8.07627i	−0.150044	+	0.446619i
$328$			0.374977i			0.0207046i
$329$	0.472134	−	0.710925i	0.0260296	−	0.0391946i
$330$	0.216529	−	0.644517i	0.0119196	−	0.0354795i
$331$	13.3421			0.733346			0.366673	−	0.930350i	$-0.380497\pi$
$331$	13.3421			0.733346			0.366673	+	0.930350i	$0.380497\pi$
$332$	−7.17707			−0.393893
$333$	−11.9465	−	9.04824i	−0.654664	−	0.495841i
$334$		−	22.4303i		−	1.22733i
$335$	−1.37395			−0.0750672
$336$	−2.81130	−	3.61892i	−0.153369	−	0.197428i
$337$	−33.1596			−1.80632			−0.903160	−	0.429304i	$-0.858759\pi$
$337$	−33.1596			−1.80632			−0.903160	+	0.429304i	$0.858759\pi$
$338$		−	1.00000i		−	0.0543928i
$339$	22.4027	+	7.52631i	1.21675	+	0.408773i
$340$	0.644812			0.0349698
$341$	−6.43310			−0.348372
$342$	−18.6637	−	14.1358i	−1.00922	−	0.764378i
$343$	−18.1943	−	3.45950i	−0.982399	−	0.186796i
$344$		−	0.643654i		−	0.0347035i
$345$	1.73383	+	0.582491i	0.0933463	+	0.0313603i
$346$			11.0835i			0.595855i
$347$		−	3.53681i		−	0.189866i	−0.995484	−	0.0949328i	$-0.969736\pi$
$347$		−	3.53681i		−	0.189866i	0.995484	−	0.0949328i	$-0.0302636\pi$
$348$	1.62260	+	0.545124i	0.0869807	+	0.0292217i
$349$			17.8637i			0.956221i	0.878300	+	0.478110i	$0.158678\pi$
$349$			17.8637i			0.956221i	−0.878300	+	0.478110i	$0.841322\pi$
$350$	−10.9859	−	7.29590i	−0.587223	−	0.389982i
$351$	2.92740	+	4.29306i	0.156253	+	0.229146i
$352$	−3.15950			−0.168402
$353$	−3.37871			−0.179830			−0.0899152	−	0.995949i	$-0.528660\pi$
$353$	−3.37871			−0.179830			−0.0899152	+	0.995949i	$0.528660\pi$
$354$	10.2207	+	3.43370i	0.543223	+	0.182499i
$355$		−	1.26458i		−	0.0671167i
$356$	6.93771			0.367698
$357$	−14.5903	−	18.7817i	−0.772199	−	0.994033i
$358$	0.910490			0.0481209
$359$		−	0.644499i		−	0.0340154i	−0.999855	−	0.0170077i	$-0.994586\pi$
$359$		−	0.644499i		−	0.0340154i	0.999855	−	0.0170077i	$-0.00541397\pi$
$360$	0.225044	−	0.297128i	0.0118609	−	0.0156600i
$361$	−41.9061			−2.20559
$362$	−3.83313			−0.201465
$363$	0.561290	−	1.67072i	0.0294601	−	0.0876903i
$364$	2.20399	+	1.46370i	0.115521	+	0.0767186i
$365$			1.28117i			0.0670595i
$366$	−5.17647	+	15.4082i	−0.270578	+	0.805398i
$367$		−	14.7009i		−	0.767381i	−0.923462	−	0.383690i	$-0.874653\pi$
$367$		−	14.7009i		−	0.767381i	0.923462	−	0.383690i	$-0.125347\pi$
$368$		−	8.49945i		−	0.443064i
$369$	0.896751	+	0.679196i	0.0466830	+	0.0353576i
$370$		−	0.620655i		−	0.0322663i
$371$	25.0891	+	16.6619i	1.30256	+	0.865045i
$372$	−3.34304	−	1.12311i	−0.173329	−	0.0582308i
$373$	−20.6490			−1.06917			−0.534583	−	0.845116i	$-0.679531\pi$
$373$	−20.6490			−1.06917			−0.534583	+	0.845116i	$0.679531\pi$
$374$	−16.3974			−0.847888
$375$	0.684271	−	2.03679i	0.0353356	−	0.105179i
$376$		−	0.322562i		−	0.0166349i
$377$	−0.988265			−0.0508982
$378$	−13.7467	+	0.168221i	−0.707054	+	0.00865235i
$379$	8.57681			0.440561			0.220281	−	0.975437i	$-0.429303\pi$
$379$	8.57681			0.440561			0.220281	+	0.975437i	$0.429303\pi$
$380$		−	0.969633i		−	0.0497411i
$381$	3.84239	−	11.4372i	0.196851	−	0.585944i
$382$	4.10415			0.209987
$383$	−15.0175			−0.767356			−0.383678	−	0.923467i	$-0.625343\pi$
$383$	−15.0175			−0.767356			−0.383678	+	0.923467i	$0.625343\pi$
$384$	−1.64187	−	0.551597i	−0.0837864	−	0.0281486i
$385$	−0.865178	−	0.574575i	−0.0440935	−	0.0292831i
$386$		−	8.09615i		−	0.412083i
$387$	−1.53929	−	1.16585i	−0.0782464	−	0.0592636i
$388$		−	4.53137i		−	0.230045i
$389$			29.5429i			1.49788i	0.662635	+	0.748942i	$0.269438\pi$
$389$			29.5429i			1.49788i	−0.662635	+	0.748942i	$0.730562\pi$
$390$	−0.0685329	+	0.203993i	−0.00347030	+	0.0103296i
$391$		−	44.1110i		−	2.23079i
$392$	−6.45196	+	2.71517i	−0.325873	+	0.137137i
$393$	−5.83101	+	17.3565i	−0.294136	+	0.875518i
$394$	15.0484			0.758125
$395$	−0.0186315			−0.000937451
$396$	−5.72280	+	7.55588i	−0.287582	+	0.379697i
$397$		−	36.8561i		−	1.84975i	−0.380268	−	0.924876i	$-0.624168\pi$
$397$		−	36.8561i		−	1.84975i	0.380268	−	0.924876i	$-0.375832\pi$
$398$	−16.5733			−0.830744
$399$	−28.2429	+	21.9401i	−1.41391	+	1.09838i
$400$	−4.98456			−0.249228
$401$		−	13.7772i		−	0.687998i	−0.938970	−	0.343999i	$-0.888218\pi$
$401$		−	13.7772i		−	0.687998i	0.938970	−	0.343999i	$-0.111782\pi$
$402$	18.1566	+	6.09982i	0.905569	+	0.304231i
$403$	2.03612			0.101426
$404$	14.8286			0.737751
$405$	−0.302954	−	1.07638i	−0.0150539	−	0.0534857i
$406$	1.44652	−	2.17813i	0.0717897	−	0.108099i
$407$			15.7831i			0.782338i
$408$	−8.52109	−	2.86271i	−0.421857	−	0.141725i
$409$		−	2.27730i		−	0.112605i	−0.998414	−	0.0563026i	$-0.982069\pi$
$409$		−	2.27730i		−	0.112605i	0.998414	−	0.0563026i	$-0.0179311\pi$
$410$			0.0465888i			0.00230086i
$411$	36.3613	+	12.2158i	1.79357	+	0.602561i
$412$			0.578134i			0.0284826i
$413$	9.11155	−	13.7199i	0.448350	−	0.675112i
$414$	−20.3263	−	15.3951i	−0.998982	−	0.756626i
$415$	−0.891711			−0.0437724
$416$	1.00000			0.0490290
$417$	19.2112	+	6.45414i	0.940779	+	0.316060i
$418$			24.6575i			1.20604i
$419$	−13.1561			−0.642718			−0.321359	−	0.946957i	$-0.604140\pi$
$419$	−13.1561			−0.642718			−0.321359	+	0.946957i	$0.604140\pi$
$420$	−0.349289	−	0.449631i	−0.0170435	−	0.0219397i
$421$	30.2957			1.47652			0.738262	−	0.674514i	$-0.235647\pi$
$421$	30.2957			1.47652			0.738262	+	0.674514i	$0.235647\pi$
$422$			23.6447i			1.15101i
$423$	−0.771402	−	0.584258i	−0.0375069	−	0.0284076i
$424$	11.3835			0.552830
$425$	−25.8692			−1.25484
$426$	−5.61422	+	16.7112i	−0.272010	+	0.809659i
$427$	20.6834	+	13.7361i	1.00094	+	0.664737i
$428$		−	18.6047i		−	0.899294i
$429$	1.74277	−	5.18749i	0.0841417	−	0.250454i
$430$		−	0.0799705i		−	0.00385652i
$431$		−	3.82945i		−	0.184458i	−0.995738	−	0.0922291i	$-0.970601\pi$
$431$		−	3.82945i		−	0.184458i	0.995738	−	0.0922291i	$-0.0293992\pi$
$432$	−4.29306	+	2.92740i	−0.206550	+	0.140844i
$433$			8.62531i			0.414506i	0.978287	+	0.207253i	$0.0664523\pi$
$433$			8.62531i			0.414506i	−0.978287	+	0.207253i	$0.933548\pi$
$434$	−2.98026	+	4.48759i	−0.143057	+	0.215411i
$435$	0.201600	+	0.0677286i	0.00966596	+	0.00324734i
$436$	4.91894			0.235575
$437$	−66.3317			−3.17308
$438$	5.68790	−	16.9305i	0.271778	−	0.808969i
$439$		−	8.37200i		−	0.399574i	−0.979839	−	0.199787i	$-0.935975\pi$
$439$		−	8.37200i		−	0.399574i	0.979839	−	0.199787i	$-0.0640250\pi$
$440$	−0.392550			−0.0187141
$441$	−5.19316	+	20.3478i	−0.247294	+	0.968941i
$442$	5.18986			0.246857
$443$			16.3126i			0.775034i	0.921863	+	0.387517i	$0.126667\pi$
$443$			16.3126i			0.775034i	−0.921863	+	0.387517i	$0.873333\pi$
$444$	−2.75547	+	8.20186i	−0.130769	+	0.389243i
$445$	0.861972			0.0408614
$446$	20.4113			0.966503
$447$	−39.7829	−	13.3653i	−1.88167	−	0.632158i
$448$	−1.46370	+	2.20399i	−0.0691533	+	0.104129i
$449$		−	20.3899i		−	0.962258i	−0.876650	−	0.481129i	$-0.840227\pi$
$449$		−	20.3899i		−	0.962258i	0.876650	−	0.481129i	$-0.159773\pi$
$450$	−9.02855	+	11.9205i	−0.425610	+	0.561937i
$451$		−	1.18474i		−	0.0557872i
$452$		−	13.6446i		−	0.641788i
$453$	8.50610	−	25.3191i	0.399651	−	1.18959i
$454$			8.72027i			0.409263i
$455$	0.273834	+	0.181856i	0.0128375	+	0.00852556i
$456$	−4.30479	+	12.8136i	−0.201590	+	0.600050i
$457$	−18.5156			−0.866124			−0.433062	−	0.901364i	$-0.642567\pi$
$457$	−18.5156			−0.866124			−0.433062	+	0.901364i	$0.642567\pi$
$458$	12.6352			0.590403
$459$	−22.2804	+	15.1928i	−1.03996	+	0.709139i
$460$		−	1.05601i		−	0.0492367i
$461$	−23.9362			−1.11482			−0.557410	−	0.830237i	$-0.688205\pi$
$461$	−23.9362			−1.11482			−0.557410	+	0.830237i	$0.688205\pi$
$462$	8.88230	+	11.4340i	0.413242	+	0.531956i
$463$	7.52582			0.349754			0.174877	−	0.984590i	$-0.444047\pi$
$463$	7.52582			0.349754			0.174877	+	0.984590i	$0.444047\pi$
$464$		−	0.988265i		−	0.0458790i
$465$	−0.415354	−	0.139541i	−0.0192616	−	0.00647105i
$466$	10.1218			0.468881
$467$	−38.4422			−1.77889			−0.889447	−	0.457038i	$-0.848910\pi$
$467$	−38.4422			−1.77889			−0.889447	+	0.457038i	$0.848910\pi$
$468$	1.81130	−	2.39148i	0.0837275	−	0.110546i
$469$	16.1863	−	24.3728i	0.747413	−	1.12543i
$470$		−	0.0400766i		−	0.00184860i
$471$	−25.5555	−	8.58553i	−1.17754	−	0.395600i
$472$		−	6.22502i		−	0.286530i
$473$			2.03363i			0.0935062i
$474$	0.246212	+	0.0827165i	0.0113089	+	0.00379929i
$475$			38.9007i			1.78489i
$476$	−7.59640	+	11.4384i	−0.348180	+	0.524279i
$477$	20.6189	−	27.2233i	0.944074	−	1.24647i
$478$	11.3900			0.520965
$479$	14.2485			0.651032			0.325516	−	0.945537i	$-0.394462\pi$
$479$	14.2485			0.651032			0.325516	+	0.945537i	$0.394462\pi$
$480$	−0.203993	−	0.0685329i	−0.00931098	−	0.00312808i
$481$		−	4.99544i		−	0.227772i
$482$	−10.1714			−0.463295
$483$	−30.7588	+	23.8945i	−1.39957	+	1.08724i
$484$	−1.01757			−0.0462533
$485$		−	0.562998i		−	0.0255644i
$486$	−0.775207	+	15.5692i	−0.0351641	+	0.706232i
$487$	2.29079			0.103806			0.0519028	−	0.998652i	$-0.483471\pi$
$487$	2.29079			0.103806			0.0519028	+	0.998652i	$0.483471\pi$
$488$	9.38452			0.424817
$489$	3.56049	−	10.5981i	0.161011	−	0.479262i
$490$	−0.801621	+	0.337345i	−0.0362135	+	0.0152397i
$491$		−	28.2076i		−	1.27299i	−0.771281	−	0.636495i	$-0.780384\pi$
$491$		−	28.2076i		−	1.27299i	0.771281	−	0.636495i	$-0.219616\pi$
$492$	0.206836	−	0.615664i	0.00932489	−	0.0277563i
$493$		−	5.12896i		−	0.230997i
$494$		−	7.80424i		−	0.351129i
$495$	−0.711027	+	0.938777i	−0.0319583	+	0.0421949i
$496$			2.03612i			0.0914243i
$497$	22.4325	+	14.8977i	1.00624	+	0.668254i
$498$	11.7838	+	3.95885i	0.528046	+	0.177400i
$499$	7.25740			0.324886			0.162443	−	0.986718i	$-0.448063\pi$
$499$	7.25740			0.324886			0.162443	+	0.986718i	$0.448063\pi$
$500$	−1.24053			−0.0554780
$501$	−12.3725	+	36.8276i	−0.552761	+	1.64534i
$502$			22.8458i			1.01966i
$503$	4.44557			0.198218			0.0991091	−	0.995077i	$-0.468401\pi$
$503$	4.44557			0.198218			0.0991091	+	0.995077i	$0.468401\pi$
$504$	2.61961	+	7.49251i	0.116687	+	0.333743i
$505$	1.84237			0.0819846
$506$			26.8540i			1.19381i
$507$	−0.551597	+	1.64187i	−0.0244973	+	0.0729181i
$508$	−6.96593			−0.309063
$509$	−5.00425			−0.221810			−0.110905	−	0.993831i	$-0.535375\pi$
$509$	−5.00425			−0.221810			−0.110905	+	0.993831i	$0.535375\pi$
$510$	−1.05870	−	0.355676i	−0.0468799	−	0.0157496i
$511$	−22.7269	−	15.0932i	−1.00538	−	0.667684i
$512$			1.00000i			0.0441942i
$513$	22.8461	+	33.5040i	1.00868	+	1.47924i
$514$		−	3.37630i		−	0.148922i
$515$			0.0718299i			0.00316520i
$516$	−0.355038	+	1.05680i	−0.0156297	+	0.0465229i
$517$			1.01914i			0.0448215i
$518$	11.0099	+	7.31181i	0.483748	+	0.321263i
$519$	6.11365	−	18.1977i	0.268359	−	0.798792i
$520$	0.124244			0.00544848
$521$	8.60868			0.377153			0.188577	−	0.982058i	$-0.439613\pi$
$521$	8.60868			0.377153			0.188577	+	0.982058i	$0.439613\pi$
$522$	−2.36342	−	1.79005i	−0.103444	−	0.0783482i
$523$		−	2.31380i		−	0.101175i	−0.998720	−	0.0505876i	$-0.983891\pi$
$523$		−	2.31380i		−	0.101175i	0.998720	−	0.0505876i	$-0.0161094\pi$
$524$	10.5712			0.461803
$525$	14.0131	+	18.0387i	0.611582	+	0.787275i
$526$	−4.54885			−0.198339
$527$			10.5672i			0.460313i
$528$	5.18749	+	1.74277i	0.225756	+	0.0758443i
$529$	−49.2406			−2.14089
$530$	1.41433			0.0614346
$531$	−14.8870	−	11.2754i	−0.646042	−	0.489310i
$532$	17.2005	+	11.4231i	0.745736	+	0.495252i
$533$			0.374977i			0.0162421i
$534$	−11.3908	−	3.82682i	−0.492929	−	0.165603i
$535$		−	2.31154i		−	0.0999365i
$536$		−	11.0585i		−	0.477653i
$537$	−1.49491	−	0.502223i	−0.0645100	−	0.0216725i
$538$		−	7.73403i		−	0.333438i
$539$	20.3850	−	8.57859i	0.878043	−	0.369506i
$540$	−0.533389	+	0.363713i	−0.0229534	+	0.0156517i
$541$	3.59839			0.154707			0.0773534	−	0.997004i	$-0.475353\pi$
$541$	3.59839			0.154707			0.0773534	+	0.997004i	$0.475353\pi$
$542$	6.93234			0.297770
$543$	6.29351	+	2.11434i	0.270081	+	0.0907352i
$544$			5.18986i			0.222514i
$545$	0.611151			0.0261789
$546$	−2.81130	−	3.61892i	−0.120313	−	0.154875i
$547$	27.3170			1.16799			0.583995	−	0.811757i	$-0.301489\pi$
$547$	27.3170			1.16799			0.583995	+	0.811757i	$0.301489\pi$
$548$		−	22.1462i		−	0.946040i
$549$	16.9982	−	22.4429i	0.725465	−	0.957840i
$550$	15.7487			0.671528
$551$	−7.71266			−0.328570
$552$	−4.68827	+	13.9550i	−0.199546	+	0.593964i
$553$	0.219494	−	0.330507i	0.00933382	−	0.0140546i
$554$			5.97653i			0.253918i
$555$	−0.342351	+	1.01904i	−0.0145320	+	0.0432557i
$556$		−	11.7008i		−	0.496225i
$557$		−	19.0462i		−	0.807015i	−0.914976	−	0.403508i	$-0.867791\pi$
$557$		−	19.0462i		−	0.807015i	0.914976	−	0.403508i	$-0.132209\pi$
$558$	4.86933	+	3.68802i	0.206135	+	0.156126i
$559$		−	0.643654i		−	0.0272237i
$560$	−0.181856	+	0.273834i	−0.00768484	+	0.0115716i
$561$	26.9224	+	9.04473i	1.13666	+	0.381869i
$562$	−12.7998			−0.539928
$563$	7.29866			0.307602			0.153801	−	0.988102i	$-0.450849\pi$
$563$	7.29866			0.307602			0.153801	+	0.988102i	$0.450849\pi$
$564$	−0.177924	+	0.529606i	−0.00749197	+	0.0223004i
$565$		−	1.69527i		−	0.0713203i
$566$	−12.2413			−0.514539
$567$	22.6631	+	7.30644i	0.951761	+	0.306842i
$568$	10.1781			0.427065
$569$			21.4605i			0.899671i	0.893112	+	0.449835i	$0.148517\pi$
$569$			21.4605i			0.899671i	−0.893112	+	0.449835i	$0.851483\pi$
$570$	−0.534847	+	1.59201i	−0.0224023	+	0.0666821i
$571$	36.6944			1.53561			0.767806	−	0.640682i	$-0.221348\pi$
$571$	36.6944			1.53561			0.767806	+	0.640682i	$0.221348\pi$
$572$	−3.15950			−0.132105
$573$	−6.73849	−	2.26384i	−0.281505	−	0.0945732i
$574$	−0.826447	−	0.548853i	−0.0344952	−	0.0229087i
$575$			42.3660i			1.76679i
$576$	2.39148	+	1.81130i	0.0996451	+	0.0754709i
$577$			25.7075i			1.07022i	0.844784	+	0.535108i	$0.179729\pi$
$577$			25.7075i			1.07022i	−0.844784	+	0.535108i	$0.820271\pi$
$578$			9.93469i			0.413229i
$579$	−4.46581	+	13.2928i	−0.185593	+	0.552431i
$580$		−	0.122786i		−	0.00509843i
$581$	10.5051	−	15.8182i	0.435824	−	0.656250i
$582$	−2.49949	+	7.43992i	−0.103607	+	0.308395i
$583$	−35.9660			−1.48956
$584$	−10.3117			−0.426701
$585$	0.225044	−	0.297128i	0.00930443	−	0.0122847i
$586$			24.6407i			1.01790i
$587$	19.4004			0.800739			0.400369	−	0.916354i	$-0.368882\pi$
$587$	19.4004			0.800739			0.400369	+	0.916354i	$0.368882\pi$
$588$	12.0910	−	0.899083i	0.498623	−	0.0370776i
$589$	15.8903			0.654750
$590$		−	0.773424i		−	0.0318414i
$591$	−24.7075	−	8.30063i	−1.01633	−	0.341442i
$592$	4.99544			0.205311
$593$	−24.0394			−0.987181			−0.493591	−	0.869694i	$-0.664316\pi$
$593$	−24.0394			−0.987181			−0.493591	+	0.869694i	$0.664316\pi$
$594$	13.5639	−	9.24910i	0.556534	−	0.379495i
$595$	−0.943810	+	1.42116i	−0.0386924	+	0.0582619i
$596$			24.2302i			0.992508i
$597$	27.2112	+	9.14178i	1.11368	+	0.374148i
$598$		−	8.49945i		−	0.347568i
$599$		−	8.88663i		−	0.363098i	−0.983382	−	0.181549i	$-0.941889\pi$
$599$		−	8.88663i		−	0.363098i	0.983382	−	0.181549i	$-0.0581111\pi$
$600$	8.18401	+	2.74947i	0.334111	+	0.112247i
$601$			23.8259i			0.971881i	0.873992	+	0.485940i	$0.161523\pi$
$601$			23.8259i			0.971881i	−0.873992	+	0.485940i	$0.838477\pi$
$602$	1.41861	+	0.942116i	0.0578182	+	0.0383978i
$603$	−26.4461	−	20.0302i	−1.07697	−	0.815694i
$604$	−15.4209			−0.627466
$605$	−0.126428			−0.00514002
$606$	−24.3467	−	8.17942i	−0.989016	−	0.332266i
$607$		−	38.5757i		−	1.56574i	−0.622187	−	0.782869i	$-0.713755\pi$
$607$		−	38.5757i		−	1.56574i	0.622187	−	0.782869i	$-0.286245\pi$
$608$	7.80424			0.316504
$609$	−3.57645	+	2.77831i	−0.144925	+	0.112583i
$610$	1.16597			0.0472089
$611$		−	0.322562i		−	0.0130495i
$612$	12.4115	+	9.40041i	0.501704	+	0.379989i
$613$	−18.0124			−0.727515			−0.363757	−	0.931494i	$-0.618506\pi$
$613$	−18.0124			−0.727515			−0.363757	+	0.931494i	$0.618506\pi$
$614$	−19.5052			−0.787166
$615$	0.0256982	−	0.0764928i	0.00103625	−	0.00308449i
$616$	4.62455	−	6.96351i	0.186329	−	0.280568i
$617$			15.7284i			0.633203i	0.948559	+	0.316602i	$0.102542\pi$
$617$			15.7284i			0.633203i	−0.948559	+	0.316602i	$0.897458\pi$
$618$	0.318897	−	0.949221i	0.0128279	−	0.0381833i
$619$			28.2469i			1.13534i	0.823256	+	0.567670i	$0.192155\pi$
$619$			28.2469i			1.13534i	−0.823256	+	0.567670i	$0.807845\pi$
$620$			0.252976i			0.0101598i
$621$	24.8812	+	36.4886i	0.998450	+	1.46424i
$622$			6.05188i			0.242658i
$623$	−10.1547	+	15.2907i	−0.406840	+	0.612608i
$624$	−1.64187	−	0.551597i	−0.0657274	−	0.0220815i
$625$	24.7687			0.990748
$626$	−23.2819			−0.930533
$627$	13.6010	−	40.4844i	0.543171	−	1.61679i
$628$			15.5649i			0.621106i
$629$	25.9256			1.03372
$630$	0.325472	+	0.930902i	0.0129671	+	0.0370880i
$631$	−18.7479			−0.746342			−0.373171	−	0.927763i	$-0.621730\pi$
$631$	−18.7479			−0.746342			−0.373171	+	0.927763i	$0.621730\pi$
$632$		−	0.149958i		−	0.00596502i
$633$	13.0424	−	38.8216i	0.518387	−	1.54302i
$634$	2.14295			0.0851073
$635$	−0.865478			−0.0343455
$636$	−18.6902	−	6.27908i	−0.741114	−	0.248982i
$637$	−6.45196	+	2.71517i	−0.255636	+	0.107579i
$638$			3.12242i			0.123618i
$639$	18.4357	−	24.3408i	0.729304	−	0.962908i
$640$			0.124244i			0.00491119i
$641$		−	43.5297i		−	1.71932i	−0.510867	−	0.859660i	$-0.670676\pi$
$641$		−	43.5297i		−	1.71932i	0.510867	−	0.859660i	$-0.329324\pi$
$642$	−10.2623	+	30.5466i	−0.405021	+	1.20558i
$643$			24.9955i			0.985724i	0.870107	+	0.492862i	$0.164049\pi$
$643$			24.9955i			0.985724i	−0.870107	+	0.492862i	$0.835951\pi$
$644$	18.7327	+	12.4406i	0.738173	+	0.490229i
$645$	−0.0441115	+	0.131301i	−0.00173689	+	0.00516998i
$646$	40.5029			1.59357
$647$	−28.3710			−1.11538			−0.557691	−	0.830049i	$-0.688312\pi$
$647$	−28.3710			−1.11538			−0.557691	+	0.830049i	$0.688312\pi$
$648$	8.66339	−	2.43837i	0.340330	−	0.0957883i
$649$			19.6679i			0.772034i
$650$	−4.98456			−0.195511
$651$	7.36854	−	5.72414i	0.288796	−	0.224347i
$652$	−6.45488			−0.252792
$653$			23.4531i			0.917790i	0.888490	+	0.458895i	$0.151755\pi$
$653$			23.4531i			0.917790i	−0.888490	+	0.458895i	$0.848245\pi$
$654$	−8.07627	−	2.71327i	−0.315807	−	0.106097i
$655$	1.31341			0.0513191
$656$	−0.374977			−0.0146404
$657$	−18.6776	+	24.6602i	−0.728682	+	0.962087i
$658$	0.710925	+	0.472134i	0.0277148	+	0.0184057i
$659$			28.4739i			1.10919i	0.832122	+	0.554593i	$0.187126\pi$
$659$			28.4739i			1.10919i	−0.832122	+	0.554593i	$0.812874\pi$
$660$	0.644517	+	0.216529i	0.0250878	+	0.00842840i
$661$			2.92424i			0.113740i	0.998382	+	0.0568698i	$0.0181120\pi$
$661$			2.92424i			0.113740i	−0.998382	+	0.0568698i	$0.981888\pi$
$662$			13.3421i			0.518554i
$663$	−8.52109	−	2.86271i	−0.330932	−	0.111179i
$664$		−	7.17707i		−	0.278524i
$665$	2.13707	+	1.41925i	0.0828719	+	0.0550362i
$666$	9.04824	−	11.9465i	0.350612	−	0.462917i
$667$	−8.39970			−0.325238
$668$	22.4303			0.867853
$669$	−33.5127	−	11.2588i	−1.29568	−	0.435291i
$670$		−	1.37395i		−	0.0530805i
$671$	−29.6504			−1.14464
$672$	3.61892	−	2.81130i	0.139603	−	0.108448i
$673$	−49.0052			−1.88901			−0.944505	−	0.328496i	$-0.893458\pi$
$673$	−49.0052			−1.88901			−0.944505	+	0.328496i	$0.893458\pi$
$674$		−	33.1596i		−	1.27726i
$675$	21.3990	−	14.5918i	0.823649	−	0.561638i
$676$	1.00000			0.0384615
$677$	−7.79695			−0.299661			−0.149831	−	0.988712i	$-0.547873\pi$
$677$	−7.79695			−0.299661			−0.149831	+	0.988712i	$0.547873\pi$
$678$	−7.52631	+	22.4027i	−0.289046	+	0.860369i
$679$	9.98711	+	6.63256i	0.383270	+	0.254534i
$680$			0.644812i			0.0247274i
$681$	4.81007	−	14.3176i	0.184322	−	0.548650i
$682$		−	6.43310i		−	0.246336i
$683$		−	16.8062i		−	0.643071i	−0.946898	−	0.321535i	$-0.895801\pi$
$683$		−	16.8062i		−	0.643071i	0.946898	−	0.321535i	$-0.104199\pi$
$684$	14.1358	−	18.6637i	0.540497	−	0.713624i
$685$		−	2.75155i		−	0.105131i
$686$	3.45950	−	18.1943i	0.132084	−	0.694661i
$687$	−20.7453	−	6.96952i	−0.791484	−	0.265904i
$688$	0.643654			0.0245391
$689$	11.3835			0.433675
$690$	−0.582491	+	1.73383i	−0.0221751	+	0.0660058i
$691$		−	34.9724i		−	1.33041i	−0.746660	−	0.665206i	$-0.768344\pi$
$691$		−	34.9724i		−	1.33041i	0.746660	−	0.665206i	$-0.231656\pi$
$692$	−11.0835			−0.421333
$693$	−8.27665	−	23.6726i	−0.314404	−	0.899246i
$694$	3.53681			0.134255
$695$		−	1.45376i		−	0.0551443i
$696$	−0.545124	+	1.62260i	−0.0206629	+	0.0615046i
$697$	−1.94608			−0.0737130
$698$	−17.8637			−0.676150
$699$	−16.6186	−	5.58313i	−0.628574	−	0.211173i
$700$	7.29590	−	10.9859i	0.275759	−	0.415230i
$701$		−	35.5652i		−	1.34328i	−0.740878	−	0.671639i	$-0.765591\pi$
$701$		−	35.5652i		−	1.34328i	0.740878	−	0.671639i	$-0.234409\pi$
$702$	−4.29306	+	2.92740i	−0.162031	+	0.110487i
$703$		−	38.9856i		−	1.47037i
$704$		−	3.15950i		−	0.119078i
$705$	−0.0221061	+	0.0658006i	−0.000832565	+	0.00247819i
$706$		−	3.37871i		−	0.127159i
$707$	−21.7046	+	32.6822i	−0.816286	+	1.22914i
$708$	−3.43370	+	10.2207i	−0.129046	+	0.384117i
$709$	−27.3777			−1.02819			−0.514095	−	0.857733i	$-0.671872\pi$
$709$	−27.3777			−1.02819			−0.514095	+	0.857733i	$0.671872\pi$
$710$	1.26458			0.0474587
$711$	−0.358622	−	0.271620i	−0.0134494	−	0.0101865i
$712$			6.93771i			0.260002i
$713$	17.3059			0.648109
$714$	18.7817	−	14.5903i	0.702888	−	0.546027i
$715$	−0.392550			−0.0146805
$716$			0.910490i			0.0340266i
$717$	−18.7009	−	6.28267i	−0.698397	−	0.234631i
$718$	0.644499			0.0240525
$719$	−16.6195			−0.619802			−0.309901	−	0.950769i	$-0.600296\pi$
$719$	−16.6195			−0.619802			−0.309901	+	0.950769i	$0.600296\pi$
$720$	0.297128	+	0.225044i	0.0110733	+	0.00838690i
$721$	−1.27420	−	0.846213i	−0.0474538	−	0.0315146i
$722$		−	41.9061i		−	1.55959i
$723$	16.7002	+	5.61052i	0.621086	+	0.208658i
$724$		−	3.83313i		−	0.142457i
$725$			4.92607i			0.182950i
$726$	1.67072	+	0.561290i	0.0620064	+	0.0208314i
$727$		−	1.30212i		−	0.0482931i	−0.999708	−	0.0241466i	$-0.992313\pi$
$727$		−	1.30212i		−	0.0482931i	0.999708	−	0.0241466i	$-0.00768684\pi$
$728$	−1.46370	+	2.20399i	−0.0542483	+	0.0816854i
$729$	9.86070	−	25.1350i	0.365211	−	0.930925i
$730$	−1.28117			−0.0474182
$731$	3.34048			0.123552
$732$	−15.4082	−	5.17647i	−0.569502	−	0.191328i
$733$			33.3250i			1.23089i	0.788180	+	0.615444i	$0.211023\pi$
$733$			33.3250i			1.23089i	−0.788180	+	0.615444i	$0.788977\pi$
$734$	14.7009			0.542620
$735$	1.50224	−	0.111706i	0.0554108	−	0.00412034i
$736$	8.49945			0.313294
$737$			34.9392i			1.28700i
$738$	−0.679196	+	0.896751i	−0.0250016	+	0.0330098i
$739$	14.3308			0.527167			0.263583	−	0.964637i	$-0.415096\pi$
$739$	14.3308			0.527167			0.263583	+	0.964637i	$0.415096\pi$
$740$	0.620655			0.0228157
$741$	−4.30479	+	12.8136i	−0.158141	+	0.470718i
$742$	−16.6619	+	25.0891i	−0.611679	+	0.921049i
$743$		−	16.8346i		−	0.617600i	−0.951127	−	0.308800i	$-0.900073\pi$
$743$		−	16.8346i		−	0.617600i	0.951127	−	0.308800i	$-0.0999274\pi$
$744$	1.12311	−	3.34304i	0.0411754	−	0.122562i
$745$			3.01047i			0.110295i
$746$		−	20.6490i		−	0.756014i
$747$	−17.1638	−	12.9998i	−0.627992	−	0.475639i
$748$		−	16.3974i		−	0.599547i
$749$	41.0047	+	27.2317i	1.49828	+	0.995026i
$750$	2.03679	+	0.684271i	0.0743729	+	0.0249860i
$751$	−20.0038			−0.729949			−0.364975	−	0.931017i	$-0.618922\pi$
$751$	−20.0038			−0.729949			−0.364975	+	0.931017i	$0.618922\pi$
$752$	0.322562			0.0117626
$753$	12.6017	−	37.5099i	0.459231	−	1.36694i
$754$		−	0.988265i		−	0.0359905i
$755$	−1.91596			−0.0697288
$756$	−0.168221	−	13.7467i	−0.00611814	−	0.499963i
$757$	−22.8314			−0.829820			−0.414910	−	0.909862i	$-0.636187\pi$
$757$	−22.8314			−0.829820			−0.414910	+	0.909862i	$0.636187\pi$
$758$			8.57681i			0.311524i
$759$	14.8126	−	44.0908i	0.537662	−	1.60039i
$760$	0.969633			0.0351723
$761$	49.2050			1.78368			0.891840	−	0.452351i	$-0.149415\pi$
$761$	49.2050			1.78368			0.891840	+	0.452351i	$0.149415\pi$
$762$	11.4372	+	3.84239i	0.414325	+	0.139195i
$763$	−7.19985	+	10.8413i	−0.260652	+	0.392482i
$764$			4.10415i			0.148483i
$765$	1.54206	+	1.16795i	0.0557532	+	0.0422273i
$766$		−	15.0175i		−	0.542603i
$767$		−	6.22502i		−	0.224772i
$768$	0.551597	−	1.64187i	0.0199040	−	0.0592459i
$769$			22.1710i			0.799506i	0.916623	+	0.399753i	$0.130904\pi$
$769$			22.1710i			0.799506i	−0.916623	+	0.399753i	$0.869096\pi$
$770$	0.574575	−	0.865178i	0.0207062	−	0.0311788i
$771$	−1.86236	+	5.54345i	−0.0670711	+	0.199642i
$772$	8.09615			0.291387
$773$	18.8854			0.679262			0.339631	−	0.940559i	$-0.389698\pi$
$773$	18.8854			0.679262			0.339631	+	0.940559i	$0.389698\pi$
$774$	1.16585	−	1.53929i	0.0419057	−	0.0553286i
$775$		−	10.1491i		−	0.364568i
$776$	4.53137			0.162667
$777$	−14.0437	−	18.0781i	−0.503814	−	0.648548i
$778$	−29.5429			−1.05916
$779$			2.92641i			0.104850i
$780$	−0.203993	−	0.0685329i	−0.00730414	−	0.00245387i
$781$	−32.1578			−1.15070
$782$	44.1110			1.57741
$783$	2.89304	+	4.24268i	0.103389	+	0.151621i
$784$	−2.71517	−	6.45196i	−0.0969705	−	0.230427i
$785$			1.93385i			0.0690220i
$786$	−17.3565	−	5.83101i	−0.619085	−	0.207985i
$787$			12.4746i			0.444673i	0.974970	+	0.222336i	$0.0713683\pi$
$787$			12.4746i			0.444673i	−0.974970	+	0.222336i	$0.928632\pi$
$788$			15.0484i			0.536076i
$789$	7.46863	+	2.50913i	0.265890	+	0.0893275i
$790$		−	0.0186315i		−	0.000662878i
$791$	30.0726	+	19.9716i	1.06926	+	0.710107i
$792$	−7.55588	−	5.72280i	−0.268487	−	0.203351i
$793$	9.38452			0.333254
$794$	36.8561			1.30797
$795$	−2.32215	−	0.780141i	−0.0823582	−	0.0276687i
$796$		−	16.5733i		−	0.587425i
$797$	2.69149			0.0953374			0.0476687	−	0.998863i	$-0.484821\pi$
$797$	2.69149			0.0953374			0.0476687	+	0.998863i	$0.484821\pi$
$798$	−21.9401	−	28.2429i	−0.776670	−	0.999788i
$799$	1.67406			0.0592238
$800$		−	4.98456i		−	0.176231i
$801$	16.5914	+	12.5663i	0.586229	+	0.444008i
$802$	13.7772			0.486488
$803$	32.5798			1.14971
$804$	−6.09982	+	18.1566i	−0.215124	+	0.640334i
$805$	2.32744	+	1.54568i	0.0820314	+	0.0544780i
$806$			2.03612i			0.0717191i
$807$	−4.26606	+	12.6983i	−0.150173	+	0.447000i
$808$			14.8286i			0.521669i
$809$		−	3.83361i		−	0.134782i	−0.997727	−	0.0673912i	$-0.978532\pi$
$809$		−	3.83361i		−	0.134782i	0.997727	−	0.0673912i	$-0.0214676\pi$
$810$	1.07638	−	0.302954i	0.0378201	−	0.0106447i
$811$		−	43.1125i		−	1.51388i	−0.653482	−	0.756942i	$-0.726692\pi$
$811$		−	43.1125i		−	1.51388i	0.653482	−	0.756942i	$-0.273308\pi$
$812$	2.17813	+	1.44652i	0.0764374	+	0.0507630i
$813$	−11.3820	−	3.82386i	−0.399185	−	0.134109i
$814$	−15.7831			−0.553196
$815$	−0.801983			−0.0280922
$816$	2.86271	−	8.52109i	0.100215	−	0.298298i
$817$		−	5.02323i		−	0.175741i
$818$	2.27730			0.0796239
$819$	2.61961	+	7.49251i	0.0915366	+	0.261809i
$820$	−0.0465888			−0.00162695
$821$			42.3073i			1.47653i	0.674509	+	0.738267i	$0.264355\pi$
$821$			42.3073i			1.47653i	−0.674509	+	0.738267i	$0.735645\pi$
$822$	−12.2158	+	36.3613i	−0.426075	+	1.26824i
$823$	−31.3358			−1.09230			−0.546149	−	0.837688i	$-0.683907\pi$
$823$	−31.3358			−1.09230			−0.546149	+	0.837688i	$0.683907\pi$
$824$	−0.578134			−0.0201402
$825$	−25.8574	−	8.68694i	−0.900238	−	0.302441i
$826$	13.7199	+	9.11155i	0.477376	+	0.317031i
$827$			8.39803i			0.292028i	0.989283	+	0.146014i	$0.0466445\pi$
$827$			8.39803i			0.292028i	−0.989283	+	0.146014i	$0.953356\pi$
$828$	15.3951	−	20.3263i	0.535015	−	0.706387i
$829$			39.8138i			1.38279i	0.722477	+	0.691395i	$0.243004\pi$
$829$			39.8138i			1.38279i	−0.722477	+	0.691395i	$0.756996\pi$
$830$		−	0.891711i		−	0.0309518i
$831$	3.29663	−	9.81269i	0.114359	−	0.340399i
$832$			1.00000i			0.0346688i
$833$	−14.0914	−	33.4848i	−0.488238	−	1.16018i
$834$	−6.45414	+	19.2112i	−0.223488	+	0.665231i
$835$	2.78684			0.0964424
$836$	−24.6575			−0.852797
$837$	−5.96052	−	8.74116i	−0.206026	−	0.302139i
$838$		−	13.1561i		−	0.454471i
$839$	22.7370			0.784967			0.392484	−	0.919759i	$-0.371616\pi$
$839$	22.7370			0.784967			0.392484	+	0.919759i	$0.371616\pi$
$840$	0.449631	−	0.349289i	0.0155137	−	0.0120516i
$841$	28.0233			0.966322
$842$			30.2957i			1.04406i
$843$	21.0157	+	7.06035i	0.723818	+	0.243171i
$844$	−23.6447			−0.813885
$845$	0.124244			0.00427414
$846$	0.584258	−	0.771402i	0.0200872	−	0.0265214i
$847$	1.48942	−	2.24272i	0.0511771	−	0.0770609i
$848$			11.3835i			0.390910i
$849$	20.0986	+	6.75224i	0.689782	+	0.231736i
$850$		−	25.8692i		−	0.887307i
$851$		−	42.4584i		−	1.45546i
$852$	−16.7112	−	5.61422i	−0.572515	−	0.192340i
$853$		−	39.4064i		−	1.34925i	−0.738160	−	0.674625i	$-0.764305\pi$
$853$		−	39.4064i		−	1.34925i	0.738160	−	0.674625i	$-0.235695\pi$
$854$	−13.7361	+	20.6834i	−0.470040	+	0.707772i
$855$	1.75630	−	2.31886i	0.0600642	−	0.0793034i
$856$	18.6047			0.635897
$857$	41.6581			1.42301			0.711506	−	0.702680i	$-0.248013\pi$
$857$	41.6581			1.42301			0.711506	+	0.702680i	$0.248013\pi$
$858$	5.18749	+	1.74277i	0.177098	+	0.0594972i
$859$		−	36.9939i		−	1.26221i	−0.775696	−	0.631107i	$-0.782601\pi$
$859$		−	36.9939i		−	1.26221i	0.775696	−	0.631107i	$-0.217399\pi$
$860$	0.0799705			0.00272697
$861$	1.05417	+	1.35701i	0.0359261	+	0.0462468i
$862$	3.82945			0.130432
$863$		−	10.0590i		−	0.342411i	−0.985235	−	0.171205i	$-0.945234\pi$
$863$		−	10.0590i		−	0.342411i	0.985235	−	0.171205i	$-0.0547662\pi$
$864$	−2.92740	−	4.29306i	−0.0995921	−	0.146053i
$865$	−1.37707			−0.0468217
$866$	−8.62531			−0.293100
$867$	5.47995	−	16.3115i	0.186109	−	0.553967i
$868$	−4.48759	−	2.98026i	−0.152319	−	0.101157i
$869$			0.473793i			0.0160723i
$870$	−0.0677286	+	0.201600i	−0.00229622	+	0.00683486i
$871$		−	11.0585i		−	0.374702i
$872$			4.91894i			0.166576i
$873$	8.20768	−	10.8367i	0.277788	−	0.366766i
$874$		−	66.3317i		−	2.24370i
$875$	1.81576	−	2.73411i	0.0613838	−	0.0924299i
$876$	16.9305	+	5.68790i	0.572027	+	0.192176i
$877$	45.1345			1.52408			0.762042	−	0.647528i	$-0.224197\pi$
$877$	45.1345			1.52408			0.762042	+	0.647528i	$0.224197\pi$
$878$	8.37200			0.282541
$879$	13.5917	−	40.4569i	0.458438	−	1.36458i
$880$		−	0.392550i		−	0.0132329i
$881$	−27.1323			−0.914111			−0.457056	−	0.889438i	$-0.651096\pi$
$881$	−27.1323			−0.914111			−0.457056	+	0.889438i	$0.651096\pi$
$882$	−20.3478	−	5.19316i	−0.685144	−	0.174863i
$883$	−39.6851			−1.33551			−0.667755	−	0.744381i	$-0.732745\pi$
$883$	−39.6851			−1.33551			−0.667755	+	0.744381i	$0.732745\pi$
$884$			5.18986i			0.174554i
$885$	−0.426618	+	1.26986i	−0.0143406	+	0.0426860i
$886$	−16.3126			−0.548032
$887$	18.9220			0.635339			0.317670	−	0.948201i	$-0.397100\pi$
$887$	18.9220			0.635339			0.317670	+	0.948201i	$0.397100\pi$
$888$	−8.20186	−	2.75547i	−0.275236	−	0.0924674i
$889$	10.1960	−	15.3529i	0.341964	−	0.514919i
$890$			0.861972i			0.0288934i
$891$	−27.3720	+	7.70403i	−0.916995	+	0.258095i
$892$			20.4113i			0.683421i
$893$		−	2.51735i		−	0.0842400i
$894$	13.3653	−	39.7829i	0.447003	−	1.33054i
$895$			0.113123i			0.00378130i
$896$	−2.20399	−	1.46370i	−0.0736303	−	0.0488987i
$897$	−4.68827	+	13.9550i	−0.156537	+	0.465944i
$898$	20.3899			0.680419
$899$	2.01222			0.0671113
$900$	−11.9205	−	9.02855i	−0.397350	−	0.300952i
$901$			59.0786i			1.96819i
$902$	1.18474			0.0394475
$903$	−1.80951	−	2.32933i	−0.0602166	−	0.0775154i
$904$	13.6446			0.453812
$905$		−	0.476246i		−	0.0158309i
$906$	25.3191	+	8.50610i	0.841169	+	0.282596i
$907$	4.14265			0.137554			0.0687772	−	0.997632i	$-0.478090\pi$
$907$	4.14265			0.137554			0.0687772	+	0.997632i	$0.478090\pi$
$908$	−8.72027			−0.289392
$909$	35.4624	+	26.8591i	1.17621	+	0.890860i
$910$	−0.181856	+	0.273834i	−0.00602848	+	0.00907751i
$911$		−	29.2725i		−	0.969843i	−0.874558	−	0.484921i	$-0.838848\pi$
$911$		−	29.2725i		−	0.969843i	0.874558	−	0.484921i	$-0.161152\pi$
$912$	−12.8136	−	4.30479i	−0.424299	−	0.142546i
$913$			22.6759i			0.750464i
$914$		−	18.5156i		−	0.612442i
$915$	−1.91438	−	0.643148i	−0.0632874	−	0.0212618i
$916$			12.6352i			0.417478i
$917$	−15.4730	+	23.2987i	−0.510963	+	0.769392i
$918$	−15.1928	−	22.2804i	−0.501437	−	0.735362i
$919$	24.4878			0.807779			0.403890	−	0.914808i	$-0.367658\pi$
$919$	24.4878			0.807779			0.403890	+	0.914808i	$0.367658\pi$
$920$	1.05601			0.0348156
$921$	32.0250	+	10.7590i	1.05526	+	0.354521i
$922$		−	23.9362i		−	0.788297i
$923$	10.1781			0.335017
$924$	−11.4340	+	8.88230i	−0.376150	+	0.292206i
$925$	−24.9001			−0.818709
$926$			7.52582i			0.247314i
$927$	−1.04717	+	1.38260i	−0.0343937	+	0.0454104i
$928$	0.988265			0.0324414
$929$	30.0493			0.985886			0.492943	−	0.870062i	$-0.335921\pi$
$929$	30.0493			0.985886			0.492943	+	0.870062i	$0.335921\pi$
$930$	0.139541	−	0.415354i	0.00457572	−	0.0136200i
$931$	−50.3527	+	21.1899i	−1.65024	+	0.694470i
$932$			10.1218i			0.331549i
$933$	3.33820	−	9.93640i	0.109288	−	0.325303i
$934$		−	38.4422i		−	1.25787i
$935$		−	2.03728i		−	0.0666262i
$936$	2.39148	+	1.81130i	0.0781680	+	0.0592043i
$937$			46.8815i			1.53155i	0.643107	+	0.765776i	$0.277645\pi$
$937$			46.8815i			1.53155i	−0.643107	+	0.765776i	$0.722355\pi$
$938$	24.3728	+	16.1863i	0.795800	+	0.528501i
$939$	38.2259	+	12.8422i	1.24746	+	0.419091i
$940$	0.0400766			0.00130715
$941$	12.7550			0.415800			0.207900	−	0.978150i	$-0.433337\pi$
$941$	12.7550			0.415800			0.207900	+	0.978150i	$0.433337\pi$
$942$	8.58553	−	25.5555i	0.279732	−	0.832644i
$943$			3.18710i			0.103786i
$944$	6.22502			0.202607
$945$	−0.0209005	−	1.70795i	−0.000679894	−	0.0555597i
$946$	−2.03363			−0.0661189
$947$			21.8570i			0.710257i	0.934817	+	0.355129i	$0.115563\pi$
$947$			21.8570i			0.710257i	−0.934817	+	0.355129i	$0.884437\pi$
$948$	−0.0827165	+	0.246212i	−0.00268651	+	0.00799660i
$949$	−10.3117			−0.334732
$950$	−38.9007			−1.26211
$951$	−3.51844	−	1.18204i	−0.114093	−	0.0383304i
$952$	−11.4384	−	7.59640i	−0.370722	−	0.246201i
$953$			21.2742i			0.689137i	0.938761	+	0.344569i	$0.111975\pi$
$953$			21.2742i			0.689137i	−0.938761	+	0.344569i	$0.888025\pi$
$954$	27.2233	+	20.6189i	0.881388	+	0.667561i
$955$			0.509919i			0.0165006i
$956$			11.3900i			0.368378i
$957$	1.72232	−	5.12661i	0.0556746	−	0.165720i
$958$			14.2485i			0.460349i
$959$	48.8102	+	32.4154i	1.57616	+	1.04675i
$960$	0.0685329	−	0.203993i	0.00221189	−	0.00658386i
$961$	26.8542			0.866266
$962$	4.99544			0.161059
$963$	33.6988	−	44.4929i	1.08593	−	1.43376i
$964$		−	10.1714i		−	0.327599i
$965$	1.00590			0.0323811
$966$	−23.8945	−	30.7588i	−0.768793	−	0.989649i
$967$	−4.17220			−0.134169			−0.0670845	−	0.997747i	$-0.521370\pi$
$967$	−4.17220			−0.134169			−0.0670845	+	0.997747i	$0.521370\pi$
$968$		−	1.01757i		−	0.0327060i
$969$	−66.5006	−	22.3413i	−2.13631	−	0.717706i
$970$	0.562998			0.0180768
$971$	−47.3425			−1.51929			−0.759647	−	0.650336i	$-0.774628\pi$
$971$	−47.3425			−1.51929			−0.759647	+	0.650336i	$0.774628\pi$
$972$	−15.5692	−	0.775207i	−0.499381	−	0.0248648i
$973$	25.7885	+	17.1265i	0.826742	+	0.549050i
$974$			2.29079i			0.0734016i
$975$	8.18401	+	2.74947i	0.262098	+	0.0880535i
$976$			9.38452i			0.300391i
$977$		−	23.6190i		−	0.755640i	−0.925879	−	0.377820i	$-0.876674\pi$
$977$		−	23.6190i		−	0.755640i	0.925879	−	0.377820i	$-0.123326\pi$
$978$	10.5981	+	3.56049i	0.338889	+	0.113852i
$979$		−	21.9197i		−	0.700556i
$980$	−0.337345	−	0.801621i	−0.0107761	−	0.0256068i
$981$	11.7636	+	8.90969i	0.375582	+	0.284465i
$982$	28.2076			0.900140
$983$	−36.2816			−1.15720			−0.578602	−	0.815610i	$-0.696402\pi$
$983$	−36.2816			−1.15720			−0.578602	+	0.815610i	$0.696402\pi$
$984$	0.615664	+	0.206836i	0.0196266	+	0.00659369i
$985$			1.86968i			0.0595728i
$986$	5.12896			0.163339
$987$	−0.906820	−	1.16733i	−0.0288644	−	0.0371564i
$988$	7.80424			0.248286
$989$		−	5.47071i		−	0.173958i
$990$	−0.938777	−	0.711027i	−0.0298363	−	0.0225979i
$991$	−6.84537			−0.217450			−0.108725	−	0.994072i	$-0.534677\pi$
$991$	−6.84537			−0.217450			−0.108725	+	0.994072i	$0.534677\pi$
$992$	−2.03612			−0.0646467
$993$	7.35944	−	21.9059i	0.233545	−	0.695164i
$994$	−14.8977	+	22.4325i	−0.472527	+	0.711517i
$995$		−	2.05914i		−	0.0652791i
$996$	−3.95885	+	11.7838i	−0.125441	+	0.373385i
$997$			49.2377i			1.55937i	0.626169	+	0.779687i	$0.284622\pi$
$997$			49.2377i			1.55937i	−0.626169	+	0.779687i	$0.715378\pi$
$998$			7.25740i			0.229729i
$999$	−21.4457	+	14.6236i	−0.678512	+	0.462671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.g.d.209.10	yes	12
3.2	odd	2		546.2.g.c.209.3	✓	12
7.6	odd	2		546.2.g.c.209.9	yes	12
21.20	even	2	inner	546.2.g.d.209.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.g.c.209.3	✓	12	3.2	odd	2
546.2.g.c.209.9	yes	12	7.6	odd	2
546.2.g.d.209.4	yes	12	21.20	even	2	inner
546.2.g.d.209.10	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.551597 - 1.64187i) q^{3} -1.00000 q^{4} -0.124244 q^{5} +(1.64187 + 0.551597i) q^{6} +(1.46370 - 2.20399i) q^{7} -1.00000i q^{8} +(-2.39148 - 1.81130i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.551597 - 1.64187i) q^{3} -1.00000 q^{4} -0.124244 q^{5} +(1.64187 + 0.551597i) q^{6} +(1.46370 - 2.20399i) q^{7} -1.00000i q^{8} +(-2.39148 - 1.81130i) q^{9} -0.124244i q^{10} +3.15950i q^{11} +(-0.551597 + 1.64187i) q^{12} -1.00000i q^{13} +(2.20399 + 1.46370i) q^{14} +(-0.0685329 + 0.203993i) q^{15} +1.00000 q^{16} +5.18986 q^{17} +(1.81130 - 2.39148i) q^{18} -7.80424i q^{19} +0.124244 q^{20} +(-2.81130 - 3.61892i) q^{21} -3.15950 q^{22} -8.49945i q^{23} +(-1.64187 - 0.551597i) q^{24} -4.98456 q^{25} +1.00000 q^{26} +(-4.29306 + 2.92740i) q^{27} +(-1.46370 + 2.20399i) q^{28} -0.988265i q^{29} +(-0.203993 - 0.0685329i) q^{30} +2.03612i q^{31} +1.00000i q^{32} +(5.18749 + 1.74277i) q^{33} +5.18986i q^{34} +(-0.181856 + 0.273834i) q^{35} +(2.39148 + 1.81130i) q^{36} +4.99544 q^{37} +7.80424 q^{38} +(-1.64187 - 0.551597i) q^{39} +0.124244i q^{40} -0.374977 q^{41} +(3.61892 - 2.81130i) q^{42} +0.643654 q^{43} -3.15950i q^{44} +(0.297128 + 0.225044i) q^{45} +8.49945 q^{46} +0.322562 q^{47} +(0.551597 - 1.64187i) q^{48} +(-2.71517 - 6.45196i) q^{49} -4.98456i q^{50} +(2.86271 - 8.52109i) q^{51} +1.00000i q^{52} +11.3835i q^{53} +(-2.92740 - 4.29306i) q^{54} -0.392550i q^{55} +(-2.20399 - 1.46370i) q^{56} +(-12.8136 - 4.30479i) q^{57} +0.988265 q^{58} +6.22502 q^{59} +(0.0685329 - 0.203993i) q^{60} +9.38452i q^{61} -2.03612 q^{62} +(-7.49251 + 2.61961i) q^{63} -1.00000 q^{64} +0.124244i q^{65} +(-1.74277 + 5.18749i) q^{66} +11.0585 q^{67} -5.18986 q^{68} +(-13.9550 - 4.68827i) q^{69} +(-0.273834 - 0.181856i) q^{70} +10.1781i q^{71} +(-1.81130 + 2.39148i) q^{72} -10.3117i q^{73} +4.99544i q^{74} +(-2.74947 + 8.18401i) q^{75} +7.80424i q^{76} +(6.96351 + 4.62455i) q^{77} +(0.551597 - 1.64187i) q^{78} +0.149958 q^{79} -0.124244 q^{80} +(2.43837 + 8.66339i) q^{81} -0.374977i q^{82} +7.17707 q^{83} +(2.81130 + 3.61892i) q^{84} -0.644812 q^{85} +0.643654i q^{86} +(-1.62260 - 0.545124i) q^{87} +3.15950 q^{88} -6.93771 q^{89} +(-0.225044 + 0.297128i) q^{90} +(-2.20399 - 1.46370i) q^{91} +8.49945i q^{92} +(3.34304 + 1.12311i) q^{93} +0.322562i q^{94} +0.969633i q^{95} +(1.64187 + 0.551597i) q^{96} +4.53137i q^{97} +(6.45196 - 2.71517i) q^{98} +(5.72280 - 7.55588i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} - 12 q^{4} - 4 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9}+O(q^{10}) \) 12 * q + 2 * q^3 - 12 * q^4 - 4 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9	\( 12 q + 2 q^{3} - 12 q^{4} - 4 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9} - 2 q^{12} + 10 q^{14} + 4 q^{15} + 12 q^{16} + 12 q^{17} + 8 q^{18} + 4 q^{20} - 20 q^{21} - 2 q^{24} + 20 q^{25} + 12 q^{26} + 8 q^{27} + 8 q^{28} + 14 q^{30} + 46 q^{33} - 22 q^{35} - 4 q^{36} + 16 q^{37} - 8 q^{38} - 2 q^{39} + 28 q^{41} + 4 q^{42} - 8 q^{43} + 24 q^{46} - 68 q^{47} + 2 q^{48} + 26 q^{49} - 50 q^{51} + 16 q^{54} - 10 q^{56} - 28 q^{57} - 24 q^{58} + 8 q^{59} - 4 q^{60} + 16 q^{62} - 2 q^{63} - 12 q^{64} - 12 q^{66} + 8 q^{67} - 12 q^{68} - 24 q^{69} - 28 q^{70} - 8 q^{72} + 92 q^{75} - 8 q^{77} + 2 q^{78} + 36 q^{79} - 4 q^{80} + 16 q^{81} - 32 q^{83} + 20 q^{84} + 8 q^{87} - 48 q^{89} + 2 q^{90} - 10 q^{91} + 8 q^{93} + 2 q^{96} + 16 q^{98}+O(q^{100}) \) 12 * q + 2 * q^3 - 12 * q^4 - 4 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9 - 2 * q^12 + 10 * q^14 + 4 * q^15 + 12 * q^16 + 12 * q^17 + 8 * q^18 + 4 * q^20 - 20 * q^21 - 2 * q^24 + 20 * q^25 + 12 * q^26 + 8 * q^27 + 8 * q^28 + 14 * q^30 + 46 * q^33 - 22 * q^35 - 4 * q^36 + 16 * q^37 - 8 * q^38 - 2 * q^39 + 28 * q^41 + 4 * q^42 - 8 * q^43 + 24 * q^46 - 68 * q^47 + 2 * q^48 + 26 * q^49 - 50 * q^51 + 16 * q^54 - 10 * q^56 - 28 * q^57 - 24 * q^58 + 8 * q^59 - 4 * q^60 + 16 * q^62 - 2 * q^63 - 12 * q^64 - 12 * q^66 + 8 * q^67 - 12 * q^68 - 24 * q^69 - 28 * q^70 - 8 * q^72 + 92 * q^75 - 8 * q^77 + 2 * q^78 + 36 * q^79 - 4 * q^80 + 16 * q^81 - 32 * q^83 + 20 * q^84 + 8 * q^87 - 48 * q^89 + 2 * q^90 - 10 * q^91 + 8 * q^93 + 2 * q^96 + 16 * q^98

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