LMFDB - Embedded newform 264.3.e.a.109.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [264,3,Mod(109,264)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(264, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("264.109");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 264 = 2^{3} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	264.e (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:	$7.19347897911$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.38
Character	$\chi$	$=$	264.109
Dual form			264.3.e.a.109.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37848 + 1.44906i) q^{2} -1.73205i q^{3} +(-0.199564 + 3.99502i) q^{4} +0.815967i q^{5} +(2.50985 - 2.38760i) q^{6} +6.88302i q^{7} +(-6.06413 + 5.21789i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(1.37848 + 1.44906i) q^{2} -1.73205i q^{3} +(-0.199564 + 3.99502i) q^{4} +0.815967i q^{5} +(2.50985 - 2.38760i) q^{6} +6.88302i q^{7} +(-6.06413 + 5.21789i) q^{8} -3.00000 q^{9} +(-1.18239 + 1.12480i) q^{10} +(10.1983 + 4.12254i) q^{11} +(6.91958 + 0.345656i) q^{12} -6.65647 q^{13} +(-9.97393 + 9.48813i) q^{14} +1.41330 q^{15} +(-15.9203 - 1.59453i) q^{16} +23.6786i q^{17} +(-4.13545 - 4.34719i) q^{18} +16.3364 q^{19} +(-3.25980 - 0.162838i) q^{20} +11.9217 q^{21} +(8.08432 + 20.4608i) q^{22} -41.3431 q^{23} +(9.03765 + 10.5034i) q^{24} +24.3342 q^{25} +(-9.17583 - 9.64564i) q^{26} +5.19615i q^{27} +(-27.4978 - 1.37361i) q^{28} +47.8312 q^{29} +(1.94821 + 2.04795i) q^{30} -4.84015 q^{31} +(-19.6354 - 25.2676i) q^{32} +(7.14045 - 17.6639i) q^{33} +(-34.3118 + 32.6406i) q^{34} -5.61632 q^{35} +(0.598693 - 11.9851i) q^{36} +40.4958i q^{37} +(22.5194 + 23.6724i) q^{38} +11.5293i q^{39} +(-4.25762 - 4.94813i) q^{40} -63.6191i q^{41} +(16.4339 + 17.2753i) q^{42} -8.57307 q^{43} +(-18.5048 + 39.9196i) q^{44} -2.44790i q^{45} +(-56.9908 - 59.9088i) q^{46} -14.2113 q^{47} +(-2.76180 + 27.5749i) q^{48} +1.62403 q^{49} +(33.5443 + 35.2618i) q^{50} +41.0125 q^{51} +(1.32839 - 26.5927i) q^{52} -94.3971i q^{53} +(-7.52955 + 7.16281i) q^{54} +(-3.36386 + 8.32145i) q^{55} +(-35.9148 - 41.7395i) q^{56} -28.2954i q^{57} +(65.9345 + 69.3104i) q^{58} -93.5546i q^{59} +(-0.282044 + 5.64614i) q^{60} +79.9870 q^{61} +(-6.67207 - 7.01368i) q^{62} -20.6491i q^{63} +(9.54730 - 63.2839i) q^{64} -5.43146i q^{65} +(35.4391 - 14.0025i) q^{66} -44.1127i q^{67} +(-94.5964 - 4.72540i) q^{68} +71.6084i q^{69} +(-7.74200 - 8.13839i) q^{70} -52.2676 q^{71} +(18.1924 - 15.6537i) q^{72} +37.1462i q^{73} +(-58.6809 + 55.8228i) q^{74} -42.1481i q^{75} +(-3.26016 + 65.2641i) q^{76} +(-28.3755 + 70.1949i) q^{77} +(-16.7067 + 15.8930i) q^{78} +82.2793i q^{79} +(1.30108 - 12.9905i) q^{80} +9.00000 q^{81} +(92.1880 - 87.6979i) q^{82} -25.6841 q^{83} +(-2.37915 + 47.6276i) q^{84} -19.3210 q^{85} +(-11.8178 - 12.4229i) q^{86} -82.8460i q^{87} +(-83.3546 + 28.2138i) q^{88} +170.778 q^{89} +(3.54716 - 3.37439i) q^{90} -45.8166i q^{91} +(8.25061 - 165.167i) q^{92} +8.38338i q^{93} +(-19.5901 - 20.5931i) q^{94} +13.3299i q^{95} +(-43.7648 + 34.0095i) q^{96} +74.2138 q^{97} +(2.23870 + 2.35332i) q^{98} +(-30.5948 - 12.3676i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{4} - 144 q^{9}+O(q^{10}) $ 48 * q - 12 * q^4 - 144 * q^9	$ 48 q - 12 q^{4} - 144 q^{9} + 24 q^{12} - 36 q^{14} + 68 q^{16} - 20 q^{20} - 44 q^{22} - 128 q^{23} - 240 q^{25} + 44 q^{26} + 48 q^{34} + 36 q^{36} + 128 q^{38} - 108 q^{42} + 100 q^{44} + 48 q^{48} - 336 q^{49} - 128 q^{55} + 92 q^{56} + 368 q^{58} - 36 q^{60} + 444 q^{64} - 96 q^{66} - 24 q^{70} + 512 q^{71} - 348 q^{78} - 692 q^{80} + 432 q^{81} - 320 q^{82} + 568 q^{86} + 244 q^{88} + 436 q^{92} - 32 q^{97}+O(q^{100}) $ 48 * q - 12 * q^4 - 144 * q^9 + 24 * q^12 - 36 * q^14 + 68 * q^16 - 20 * q^20 - 44 * q^22 - 128 * q^23 - 240 * q^25 + 44 * q^26 + 48 * q^34 + 36 * q^36 + 128 * q^38 - 108 * q^42 + 100 * q^44 + 48 * q^48 - 336 * q^49 - 128 * q^55 + 92 * q^56 + 368 * q^58 - 36 * q^60 + 444 * q^64 - 96 * q^66 - 24 * q^70 + 512 * q^71 - 348 * q^78 - 692 * q^80 + 432 * q^81 - 320 * q^82 + 568 * q^86 + 244 * q^88 + 436 * q^92 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/264\mathbb{Z}\right)^\times$.

$n$	$89$	$133$	$145$	$199$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	1.37848	+	1.44906i	0.689242	+	0.724531i
$2$	1.37848	+	1.44906i	0.689242	+	0.724531i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−0.199564	+	3.99502i	−0.0498911	+	0.998755i
$5$			0.815967i			0.163193i	0.996665	+	0.0815967i	$0.0260019\pi$
$5$			0.815967i			0.163193i	−0.996665	+	0.0815967i	$0.973998\pi$
$6$	2.50985	−	2.38760i	0.418308	−	0.397934i
$7$			6.88302i			0.983289i	0.870796	+	0.491644i	$0.163604\pi$
$7$			6.88302i			0.983289i	−0.870796	+	0.491644i	$0.836396\pi$
$8$	−6.06413	+	5.21789i	−0.758016	+	0.652236i
$9$	−3.00000			−0.333333
$10$	−1.18239	+	1.12480i	−0.118239	+	0.112480i
$11$	10.1983	+	4.12254i	0.927115	+	0.374777i
$11$	10.1983	+	4.12254i	0.927115	+	0.374777i
$12$	6.91958	+	0.345656i	0.576631	+	0.0288046i
$13$	−6.65647			−0.512036			−0.256018	−	0.966672i	$-0.582411\pi$
$13$	−6.65647			−0.512036			−0.256018	+	0.966672i	$0.582411\pi$
$14$	−9.97393	+	9.48813i	−0.712423	+	0.677724i
$15$	1.41330			0.0942197
$16$	−15.9203	−	1.59453i	−0.995022	−	0.0996579i
$17$			23.6786i			1.39286i	0.717625	+	0.696429i	$0.245229\pi$
$17$			23.6786i			1.39286i	−0.717625	+	0.696429i	$0.754771\pi$
$18$	−4.13545	−	4.34719i	−0.229747	−	0.241510i
$19$	16.3364			0.859809			0.429905	−	0.902874i	$-0.358547\pi$
$19$	16.3364			0.859809			0.429905	+	0.902874i	$0.358547\pi$
$20$	−3.25980	−	0.162838i	−0.162990	−	0.00814189i
$21$	11.9217			0.567702
$22$	8.08432	+	20.4608i	0.367469	+	0.930036i
$23$	−41.3431			−1.79753			−0.898764	−	0.438433i	$-0.855534\pi$
$23$	−41.3431			−1.79753			−0.898764	+	0.438433i	$0.855534\pi$
$24$	9.03765	+	10.5034i	0.376569	+	0.437641i
$25$	24.3342			0.973368
$26$	−9.17583	−	9.64564i	−0.352917	−	0.370986i
$27$			5.19615i			0.192450i
$28$	−27.4978	−	1.37361i	−0.982064	−	0.0490573i
$29$	47.8312			1.64935			0.824676	−	0.565606i	$-0.191358\pi$
$29$	47.8312			1.64935			0.824676	+	0.565606i	$0.191358\pi$
$30$	1.94821	+	2.04795i	0.0649402	+	0.0682652i
$31$	−4.84015			−0.156134			−0.0780669	−	0.996948i	$-0.524875\pi$
$31$	−4.84015			−0.156134			−0.0780669	+	0.996948i	$0.524875\pi$
$32$	−19.6354	−	25.2676i	−0.613605	−	0.789613i
$33$	7.14045	−	17.6639i	0.216377	−	0.535270i
$34$	−34.3118	+	32.6406i	−1.00917	+	0.960017i
$35$	−5.61632			−0.160466
$36$	0.598693	−	11.9851i	0.0166304	−	0.332918i
$37$			40.4958i			1.09448i	0.836975	+	0.547240i	$0.184322\pi$
$37$			40.4958i			1.09448i	−0.836975	+	0.547240i	$0.815678\pi$
$38$	22.5194	+	23.6724i	0.592617	+	0.622959i
$39$			11.5293i			0.295624i
$40$	−4.25762	−	4.94813i	−0.106441	−	0.123703i
$41$		−	63.6191i		−	1.55169i	−0.630927	−	0.775843i	$-0.717325\pi$
$41$		−	63.6191i		−	1.55169i	0.630927	−	0.775843i	$-0.282675\pi$
$42$	16.4339	+	17.2753i	0.391284	+	0.411318i
$43$	−8.57307			−0.199374			−0.0996869	−	0.995019i	$-0.531784\pi$
$43$	−8.57307			−0.199374			−0.0996869	+	0.995019i	$0.531784\pi$
$44$	−18.5048	+	39.9196i	−0.420565	+	0.907263i
$45$		−	2.44790i		−	0.0543978i
$46$	−56.9908	−	59.9088i	−1.23893	−	1.30236i
$47$	−14.2113			−0.302369			−0.151185	−	0.988506i	$-0.548309\pi$
$47$	−14.2113			−0.302369			−0.151185	+	0.988506i	$0.548309\pi$
$48$	−2.76180	+	27.5749i	−0.0575375	+	0.574476i
$49$	1.62403			0.0331435
$50$	33.5443	+	35.2618i	0.670886	+	0.705235i
$51$	41.0125			0.804167
$52$	1.32839	−	26.5927i	0.0255460	−	0.511398i
$53$		−	94.3971i		−	1.78108i	−0.454907	−	0.890539i	$-0.650328\pi$
$53$		−	94.3971i		−	1.78108i	0.454907	−	0.890539i	$-0.349672\pi$
$54$	−7.52955	+	7.16281i	−0.139436	+	0.132645i
$55$	−3.36386	+	8.32145i	−0.0611611	+	0.151299i
$56$	−35.9148	−	41.7395i	−0.641336	−	0.745349i
$57$		−	28.2954i		−	0.496411i
$58$	65.9345	+	69.3104i	1.13680	+	1.19501i
$59$		−	93.5546i		−	1.58567i	−0.609435	−	0.792836i	$-0.708604\pi$
$59$		−	93.5546i		−	1.58567i	0.609435	−	0.792836i	$-0.291396\pi$
$60$	−0.282044	+	5.64614i	−0.00470073	+	0.0941024i
$61$	79.9870			1.31126			0.655631	−	0.755081i	$-0.272403\pi$
$61$	79.9870			1.31126			0.655631	+	0.755081i	$0.272403\pi$
$62$	−6.67207	−	7.01368i	−0.107614	−	0.113124i
$63$		−	20.6491i		−	0.327763i
$64$	9.54730	−	63.2839i	0.149177	−	0.988811i
$65$		−	5.43146i		−	0.0835609i
$66$	35.4391	−	14.0025i	0.536956	−	0.212158i
$67$		−	44.1127i		−	0.658398i	−0.944261	−	0.329199i	$-0.893221\pi$
$67$		−	44.1127i		−	0.658398i	0.944261	−	0.329199i	$-0.106779\pi$
$68$	−94.5964	−	4.72540i	−1.39112	−	0.0694912i
$69$			71.6084i			1.03780i
$70$	−7.74200	−	8.13839i	−0.110600	−	0.116263i
$71$	−52.2676			−0.736164			−0.368082	−	0.929793i	$-0.619985\pi$
$71$	−52.2676			−0.736164			−0.368082	+	0.929793i	$0.619985\pi$
$72$	18.1924	−	15.6537i	0.252672	−	0.217412i
$73$			37.1462i			0.508852i	0.967092	+	0.254426i	$0.0818865\pi$
$73$			37.1462i			0.508852i	−0.967092	+	0.254426i	$0.918113\pi$
$74$	−58.6809	+	55.8228i	−0.792986	+	0.754362i
$75$		−	42.1481i		−	0.561974i
$76$	−3.26016	+	65.2641i	−0.0428968	+	0.858738i
$77$	−28.3755	+	70.1949i	−0.368514	+	0.911622i
$78$	−16.7067	+	15.8930i	−0.214189	+	0.203757i
$79$			82.2793i			1.04151i	0.853706	+	0.520755i	$0.174349\pi$
$79$			82.2793i			1.04151i	−0.853706	+	0.520755i	$0.825651\pi$
$80$	1.30108	−	12.9905i	0.0162635	−	0.162381i
$81$	9.00000			0.111111
$82$	92.1880	−	87.6979i	1.12424	−	1.06949i
$83$	−25.6841			−0.309447			−0.154724	−	0.987958i	$-0.549449\pi$
$83$	−25.6841			−0.309447			−0.154724	+	0.987958i	$0.549449\pi$
$84$	−2.37915	+	47.6276i	−0.0283233	+	0.566995i
$85$	−19.3210			−0.227305
$86$	−11.8178	−	12.4229i	−0.137417	−	0.144453i
$87$		−	82.8460i		−	0.952253i
$88$	−83.3546	+	28.2138i	−0.947211	+	0.320611i
$89$	170.778			1.91886			0.959428	−	0.281953i	$-0.0909822\pi$
$89$	170.778			1.91886			0.959428	+	0.281953i	$0.0909822\pi$
$90$	3.54716	−	3.37439i	0.0394129	−	0.0374932i
$91$		−	45.8166i		−	0.503479i
$92$	8.25061	−	165.167i	0.0896806	−	1.79529i
$93$			8.38338i			0.0901439i
$94$	−19.5901	−	20.5931i	−0.208405	−	0.219076i
$95$			13.3299i			0.140315i
$96$	−43.7648	+	34.0095i	−0.455883	+	0.354265i
$97$	74.2138			0.765091			0.382546	−	0.923937i	$-0.375048\pi$
$97$	74.2138			0.765091			0.382546	+	0.923937i	$0.375048\pi$
$98$	2.23870	+	2.35332i	0.0228439	+	0.0240135i
$99$	−30.5948	−	12.3676i	−0.309038	−	0.124926i
$100$	−4.85624	+	97.2156i	−0.0485624	+	0.972156i
$101$	−2.97413			−0.0294468			−0.0147234	−	0.999892i	$-0.504687\pi$
$101$	−2.97413			−0.0294468			−0.0147234	+	0.999892i	$0.504687\pi$
$102$	56.5351	+	59.4297i	0.554266	+	0.582644i
$103$	89.2633			0.866634			0.433317	−	0.901242i	$-0.357343\pi$
$103$	89.2633			0.866634			0.433317	+	0.901242i	$0.357343\pi$
$104$	40.3657	−	34.7327i	0.388131	−	0.333968i
$105$			9.72775i			0.0926452i
$106$	136.787	−	130.125i	1.29045	−	1.22759i
$107$	34.5405			0.322809			0.161404	−	0.986888i	$-0.448398\pi$
$107$	34.5405			0.322809			0.161404	+	0.986888i	$0.448398\pi$
$108$	−20.7587	−	1.03697i	−0.192210	−	0.00960154i
$109$	49.6019			0.455064			0.227532	−	0.973771i	$-0.426934\pi$
$109$	49.6019			0.455064			0.227532	+	0.973771i	$0.426934\pi$
$110$	−16.6953	+	6.59654i	−0.151776	+	0.0599685i
$111$	70.1408			0.631899
$112$	10.9752	−	109.580i	0.0979925	−	0.978394i
$113$	−146.793			−1.29905			−0.649526	−	0.760339i	$-0.725033\pi$
$113$	−146.793			−1.29905			−0.649526	+	0.760339i	$0.725033\pi$
$114$	41.0018	−	39.0048i	0.359665	−	0.342147i
$115$		−	33.7346i		−	0.293345i
$116$	−9.54540	+	191.086i	−0.0822879	+	1.64730i
$117$	19.9694			0.170679
$118$	135.567	−	128.964i	1.14887	−	1.09291i
$119$	−162.980			−1.36958
$120$	−8.57041	+	7.37442i	−0.0714201	+	0.0614535i
$121$	87.0093	+	84.0856i	0.719085	+	0.694922i
$122$	110.261	+	115.906i	0.903777	+	0.950051i
$123$	−110.191			−0.895866
$124$	0.965921	−	19.3365i	0.00778969	−	0.155939i
$125$			40.2551i			0.322041i
$126$	29.9218	−	28.4644i	0.237474	−	0.225908i
$127$			120.147i			0.946037i	0.881052	+	0.473019i	$0.156836\pi$
$127$			120.147i			0.946037i	−0.881052	+	0.473019i	$0.843164\pi$
$128$	104.863	−	73.4012i	0.819243	−	0.573447i
$129$			14.8490i			0.115109i
$130$	7.87052	−	7.48718i	0.0605425	−	0.0575937i
$131$	−67.0812			−0.512070			−0.256035	−	0.966668i	$-0.582416\pi$
$131$	−67.0812			−0.512070			−0.256035	+	0.966668i	$0.582416\pi$
$132$	69.1427	+	32.0513i	0.523808	+	0.242813i
$133$			112.444i			0.845441i
$134$	63.9220	−	60.8086i	0.477030	−	0.453796i
$135$	−4.23989			−0.0314066
$136$	−123.552	−	143.590i	−0.908472	−	1.05581i
$137$	85.4577			0.623779			0.311890	−	0.950118i	$-0.399038\pi$
$137$	85.4577			0.623779			0.311890	+	0.950118i	$0.399038\pi$
$138$	−103.765	+	98.7110i	−0.751921	+	0.715297i
$139$	−60.9977			−0.438833			−0.219416	−	0.975631i	$-0.570415\pi$
$139$	−60.9977			−0.438833			−0.219416	+	0.975631i	$0.570415\pi$
$140$	1.12082	−	22.4373i	0.00800583	−	0.160266i
$141$			24.6148i			0.174573i
$142$	−72.0501	−	75.7390i	−0.507395	−	0.533374i
$143$	−67.8844	−	27.4416i	−0.474716	−	0.191899i
$144$	47.7610	+	4.78358i	0.331674	+	0.0332193i
$145$			39.0287i			0.269163i
$146$	−53.8272	+	51.2054i	−0.368679	+	0.350722i
$147$		−	2.81290i		−	0.0191354i
$148$	−161.781	−	8.08152i	−1.09312	−	0.0546048i
$149$	−258.670			−1.73604			−0.868021	−	0.496527i	$-0.834608\pi$
$149$	−258.670			−1.73604			−0.868021	+	0.496527i	$0.834608\pi$
$150$	61.0752	−	58.1004i	0.407168	−	0.387336i
$151$		−	121.991i		−	0.807885i	−0.914784	−	0.403943i	$-0.867640\pi$
$151$		−	121.991i		−	0.807885i	0.914784	−	0.403943i	$-0.132360\pi$
$152$	−99.0659	+	85.2414i	−0.651749	+	0.560798i
$153$		−	71.0358i		−	0.464286i
$154$	−140.832	+	55.6446i	−0.914494	+	0.361328i
$155$		−	3.94940i		−	0.0254800i
$156$	−46.0599	−	2.30084i	−0.295256	−	0.0147490i
$157$			117.164i			0.746265i	0.927778	+	0.373133i	$0.121716\pi$
$157$			117.164i			0.746265i	−0.927778	+	0.373133i	$0.878284\pi$
$158$	−119.228	+	113.421i	−0.754607	+	0.717852i
$159$	−163.501			−1.02831
$160$	20.6175	−	16.0218i	0.128860	−	0.100136i
$161$		−	284.566i		−	1.76749i
$162$	12.4064	+	13.0416i	0.0765824	+	0.0805035i
$163$		−	230.915i		−	1.41666i	−0.705884	−	0.708328i	$-0.749450\pi$
$163$		−	230.915i		−	1.41666i	0.705884	−	0.708328i	$-0.250550\pi$
$164$	254.159	+	12.6961i	1.54975	+	0.0774152i
$165$	14.4132	+	5.82638i	0.0873526	+	0.0353114i
$166$	−35.4051	−	37.2179i	−0.213284	−	0.224204i
$167$			114.603i			0.686244i	0.939291	+	0.343122i	$0.111484\pi$
$167$			114.603i			0.686244i	−0.939291	+	0.343122i	$0.888516\pi$
$168$	−72.2950	+	62.2063i	−0.430327	+	0.370276i
$169$	−124.691			−0.737819
$170$	−26.6336	−	27.9973i	−0.156668	−	0.164690i
$171$	−49.0091			−0.286603
$172$	1.71088	−	34.2496i	0.00994698	−	0.199126i
$173$	33.9685			0.196349			0.0981747	−	0.995169i	$-0.468700\pi$
$173$	33.9685			0.196349			0.0981747	+	0.995169i	$0.468700\pi$
$174$	120.049	−	114.202i	0.689937	−	0.656333i
$175$			167.493i			0.957102i
$176$	−155.786	−	81.8937i	−0.885150	−	0.465305i
$177$	−162.041			−0.915488
$178$	235.415	+	247.468i	1.32256	+	1.39027i
$179$			220.715i			1.23304i	0.787338	+	0.616521i	$0.211459\pi$
$179$			220.715i			1.23304i	−0.787338	+	0.616521i	$0.788541\pi$
$180$	9.77941	+	0.488514i	0.0543301	+	0.00271396i
$181$			53.9295i			0.297953i	0.988841	+	0.148977i	$0.0475979\pi$
$181$			53.9295i			0.297953i	−0.988841	+	0.148977i	$0.952402\pi$
$182$	66.3911	−	63.1574i	0.364786	−	0.347019i
$183$		−	138.542i		−	0.757058i
$184$	250.710	−	215.724i	1.36255	−	1.17241i
$185$	−33.0432			−0.178612
$186$	−12.1480	+	11.5564i	−0.0653121	+	0.0621310i
$187$	−97.6160	+	241.481i	−0.522011	+	1.29134i
$188$	2.83608	−	56.7746i	0.0150855	−	0.301992i
$189$	−35.7652			−0.189234
$190$	−19.3159	+	18.3751i	−0.101663	+	0.0967111i
$191$	−53.0046			−0.277511			−0.138756	−	0.990327i	$-0.544310\pi$
$191$	−53.0046			−0.277511			−0.138756	+	0.990327i	$0.544310\pi$
$192$	−109.611	−	16.5364i	−0.570890	−	0.0861271i
$193$			109.979i			0.569838i	0.958552	+	0.284919i	$0.0919667\pi$
$193$			109.979i			0.569838i	−0.958552	+	0.284919i	$0.908033\pi$
$194$	102.303	+	107.540i	0.527333	+	0.554332i
$195$	−9.40756			−0.0482439
$196$	−0.324099	+	6.48804i	−0.00165356	+	0.0331022i
$197$	−30.6209			−0.155436			−0.0777179	−	0.996975i	$-0.524763\pi$
$197$	−30.6209			−0.155436			−0.0777179	+	0.996975i	$0.524763\pi$
$198$	−24.2530	−	61.3824i	−0.122490	−	0.310012i
$199$	140.453			0.705796			0.352898	−	0.935662i	$-0.385196\pi$
$199$	140.453			0.705796			0.352898	+	0.935662i	$0.385196\pi$
$200$	−147.566	+	126.973i	−0.737828	+	0.634866i
$201$	−76.4054			−0.380126
$202$	−4.09979	−	4.30970i	−0.0202960	−	0.0213351i
$203$			329.223i			1.62179i
$204$	−8.18464	+	163.846i	−0.0401208	+	0.803166i
$205$	51.9111			0.253225
$206$	123.048	+	129.348i	0.597321	+	0.627903i
$207$	124.029			0.599176
$208$	105.973	+	10.6139i	0.509487	+	0.0510284i
$209$	166.603	+	67.3474i	0.797142	+	0.322236i
$210$	−14.0961	+	13.4095i	−0.0671243	+	0.0638550i
$211$	−67.3995			−0.319429			−0.159715	−	0.987163i	$-0.551057\pi$
$211$	−67.3995			−0.319429			−0.159715	+	0.987163i	$0.551057\pi$
$212$	377.118	+	18.8383i	1.77886	+	0.0888599i
$213$			90.5302i			0.425024i
$214$	47.6135	+	50.0514i	0.222493	+	0.233885i
$215$		−	6.99535i		−	0.0325365i
$216$	−27.1129	−	31.5101i	−0.125523	−	0.145880i
$217$		−	33.3148i		−	0.153525i
$218$	68.3755	+	71.8763i	0.313649	+	0.329708i
$219$	64.3391			0.293786
$220$	−32.5730	−	15.0993i	−0.148059	−	0.0686334i
$221$		−	157.616i		−	0.713194i
$222$	96.6879	+	101.638i	0.435531	+	0.457830i
$223$	−155.040			−0.695246			−0.347623	−	0.937634i	$-0.613011\pi$
$223$	−155.040			−0.695246			−0.347623	+	0.937634i	$0.613011\pi$
$224$	173.917	−	135.151i	0.776417	−	0.603351i
$225$	−73.0026			−0.324456
$226$	−202.352	−	212.712i	−0.895361	−	0.941204i
$227$	87.3145			0.384645			0.192323	−	0.981332i	$-0.438398\pi$
$227$	87.3145			0.384645			0.192323	+	0.981332i	$0.438398\pi$
$228$	113.041	+	5.64676i	0.495793	+	0.0247665i
$229$		−	21.9545i		−	0.0958711i	−0.998850	−	0.0479356i	$-0.984736\pi$
$229$		−	21.9545i		−	0.0958711i	0.998850	−	0.0479356i	$-0.0152642\pi$
$230$	48.8836	−	46.5026i	0.212537	−	0.202185i
$231$	121.581	+	49.1479i	0.526325	+	0.212761i
$232$	−290.054	+	249.578i	−1.25023	+	1.07577i
$233$		−	254.680i		−	1.09305i	−0.837444	−	0.546523i	$-0.815951\pi$
$233$		−	254.680i		−	1.09305i	0.837444	−	0.546523i	$-0.184049\pi$
$234$	27.5275	+	28.9369i	0.117639	+	0.123662i
$235$		−	11.5960i		−	0.0493446i
$236$	373.752	+	18.6702i	1.58370	+	0.0791109i
$237$	142.512			0.601316
$238$	−224.666	−	236.169i	−0.943973	−	0.992305i
$239$			60.4289i			0.252840i	0.991977	+	0.126420i	$0.0403488\pi$
$239$			60.4289i			0.252840i	−0.991977	+	0.126420i	$0.959651\pi$
$240$	−22.5002	−	2.25354i	−0.0937507	−	0.00938974i
$241$			392.139i			1.62713i	0.581472	+	0.813566i	$0.302477\pi$
$241$			392.139i			1.62713i	−0.581472	+	0.813566i	$0.697523\pi$
$242$	−1.90440	+	241.993i	−0.00786941	+	0.999969i
$243$		−	15.5885i		−	0.0641500i
$244$	−15.9626	+	319.550i	−0.0654203	+	1.30963i
$245$			1.32516i			0.00540880i
$246$	−151.897	−	159.674i	−0.617468	−	0.649083i
$247$	−108.743			−0.440253
$248$	29.3513	−	25.2554i	0.118352	−	0.101836i
$249$			44.4862i			0.178659i
$250$	−58.3321	+	55.4910i	−0.233328	+	0.221964i
$251$			50.8359i			0.202533i	0.994859	+	0.101267i	$0.0322896\pi$
$251$			50.8359i			0.202533i	−0.994859	+	0.101267i	$0.967710\pi$
$252$	82.4934	+	4.12082i	0.327355	+	0.0163524i
$253$	−421.628	−	170.439i	−1.66651	−	0.673671i
$254$	−174.100	+	165.620i	−0.685434	+	0.652049i
$255$			33.4649i			0.131235i
$256$	250.915	+	50.7708i	0.980137	+	0.198324i
$257$	391.075			1.52169			0.760846	−	0.648933i	$-0.224784\pi$
$257$	391.075			1.52169			0.760846	+	0.648933i	$0.224784\pi$
$258$	−21.5171	+	20.4691i	−0.0833997	+	0.0793376i
$259$	−278.733			−1.07619
$260$	21.6988	+	1.08393i	0.0834568	+	0.00416894i
$261$	−143.494			−0.549784
$262$	−92.4703	−	97.2048i	−0.352940	−	0.371011i
$263$		−	271.906i		−	1.03386i	−0.856027	−	0.516931i	$-0.827074\pi$
$263$		−	271.906i		−	1.03386i	0.856027	−	0.516931i	$-0.172926\pi$
$264$	48.8677	+	144.374i	0.185105	+	0.546872i
$265$	77.0249			0.290660
$266$	−162.938	+	155.002i	−0.612548	+	0.582713i
$267$		−	295.797i		−	1.10785i
$268$	176.231	+	8.80332i	0.657578	+	0.0328482i
$269$		−	386.896i		−	1.43827i	−0.694868	−	0.719137i	$-0.744537\pi$
$269$		−	386.896i		−	1.43827i	0.694868	−	0.719137i	$-0.255463\pi$
$270$	−5.84462	−	6.14386i	−0.0216467	−	0.0227551i
$271$		−	208.204i		−	0.768280i	−0.923275	−	0.384140i	$-0.874498\pi$
$271$		−	208.204i		−	0.768280i	0.923275	−	0.384140i	$-0.125502\pi$
$272$	37.7561	−	376.971i	0.138809	−	1.38592i
$273$	−79.3567			−0.290684
$274$	117.802	+	123.834i	0.429935	+	0.451947i
$275$	248.167	+	100.319i	0.902424	+	0.364796i
$276$	−286.077	−	14.2905i	−1.03651	−	0.0517771i
$277$	19.3202			0.0697479			0.0348740	−	0.999392i	$-0.488897\pi$
$277$	19.3202			0.0697479			0.0348740	+	0.999392i	$0.488897\pi$
$278$	−84.0844	−	88.3895i	−0.302462	−	0.317948i
$279$	14.5204			0.0520446
$280$	34.0581	−	29.3053i	0.121636	−	0.104662i
$281$			268.488i			0.955474i	0.878503	+	0.477737i	$0.158543\pi$
$281$			268.488i			0.955474i	−0.878503	+	0.477737i	$0.841457\pi$
$282$	−35.6683	+	33.9311i	−0.126483	+	0.120323i
$283$	409.223			1.44602			0.723010	−	0.690838i	$-0.242758\pi$
$283$	409.223			1.44602			0.723010	+	0.690838i	$0.242758\pi$
$284$	10.4308	−	208.810i	0.0367280	−	0.735247i
$285$	23.0881			0.0810110
$286$	−53.8130	−	136.197i	−0.188157	−	0.476212i
$287$	437.891			1.52575
$288$	58.9061	+	75.8028i	0.204535	+	0.263204i
$289$	−271.676			−0.940055
$290$	−56.5550	+	53.8004i	−0.195017	+	0.185519i
$291$		−	128.542i		−	0.441726i
$292$	−148.400	−	7.41306i	−0.508218	−	0.0253872i
$293$	204.196			0.696913			0.348457	−	0.937325i	$-0.386706\pi$
$293$	204.196			0.696913			0.348457	+	0.937325i	$0.386706\pi$
$294$	4.07607	−	3.87754i	0.0138642	−	0.0131889i
$295$	76.3375			0.258771
$296$	−211.302	−	245.572i	−0.713860	−	0.829634i
$297$	−21.4214	+	52.9917i	−0.0721258	+	0.178423i
$298$	−356.573	−	374.830i	−1.19655	−	1.25782i
$299$	275.199			0.920399
$300$	168.382	+	8.41125i	0.561274	+	0.0280375i
$301$		−	59.0086i		−	0.196042i
$302$	176.772	−	168.162i	0.585338	−	0.556828i
$303$			5.15134i			0.0170011i
$304$	−260.081	−	26.0488i	−0.855529	−	0.0856868i
$305$			65.2668i			0.213989i
$306$	102.935	−	97.9217i	0.336390	−	0.320006i
$307$	82.8238			0.269784			0.134892	−	0.990860i	$-0.456931\pi$
$307$	82.8238			0.269784			0.134892	+	0.990860i	$0.456931\pi$
$308$	−274.767	−	127.369i	−0.892101	−	0.413537i
$309$		−	154.609i		−	0.500351i
$310$	5.72293	−	5.44419i	0.0184611	−	0.0175619i
$311$	−321.523			−1.03383			−0.516917	−	0.856035i	$-0.672921\pi$
$311$	−321.523			−1.03383			−0.516917	+	0.856035i	$0.672921\pi$
$312$	−60.1588	−	69.9154i	−0.192817	−	0.224088i
$313$	−491.764			−1.57113			−0.785565	−	0.618779i	$-0.787628\pi$
$313$	−491.764			−1.57113			−0.785565	+	0.618779i	$0.787628\pi$
$314$	−169.777	+	161.508i	−0.540692	+	0.514357i
$315$	16.8490			0.0534887
$316$	−328.707	−	16.4200i	−1.04021	−	0.0519621i
$317$		−	287.750i		−	0.907729i	−0.891071	−	0.453864i	$-0.850045\pi$
$317$		−	287.750i		−	0.907729i	0.891071	−	0.453864i	$-0.149955\pi$
$318$	−225.383	−	236.923i	−0.708751	−	0.745040i
$319$	487.795	+	197.186i	1.52914	+	0.618138i
$320$	51.6376	+	7.79028i	0.161367	+	0.0243446i
$321$		−	59.8259i		−	0.186374i
$322$	412.353	−	392.269i	1.28060	−	1.21823i
$323$			386.822i			1.19759i
$324$	−1.79608	+	35.9552i	−0.00554345	+	0.110973i
$325$	−161.980			−0.498399
$326$	334.610	−	318.312i	1.02641	−	0.976419i
$327$		−	85.9131i		−	0.262731i
$328$	331.957	+	385.794i	1.01206	+	1.17620i
$329$		−	97.8170i		−	0.297316i
$330$	11.4255	+	28.9172i	0.0346229	+	0.0876277i
$331$		−	296.386i		−	0.895427i	−0.894177	−	0.447714i	$-0.852238\pi$
$331$		−	296.386i		−	0.895427i	0.894177	−	0.447714i	$-0.147762\pi$
$332$	5.12563	−	102.609i	0.0154387	−	0.309062i
$333$		−	121.487i		−	0.364827i
$334$	−166.066	+	157.978i	−0.497205	+	0.472988i
$335$	35.9945			0.107446
$336$	−189.798	−	19.0095i	−0.564876	−	0.0565760i
$337$		−	590.932i		−	1.75351i	−0.480941	−	0.876753i	$-0.659705\pi$
$337$		−	590.932i		−	1.75351i	0.480941	−	0.876753i	$-0.340295\pi$
$338$	−171.885	−	180.686i	−0.508536	−	0.534573i
$339$			254.253i			0.750008i
$340$	3.85577	−	77.1876i	0.0113405	−	0.227022i
$341$	−49.3611	−	19.9537i	−0.144754	−	0.0585153i
$342$	−67.5583	−	71.0173i	−0.197539	−	0.207653i
$343$			348.446i			1.01588i
$344$	51.9882	−	44.7333i	0.151129	−	0.130039i
$345$	−58.4301			−0.169363
$346$	46.8250	+	49.2224i	0.135332	+	0.142261i
$347$	−553.202			−1.59424			−0.797121	−	0.603819i	$-0.793645\pi$
$347$	−553.202			−1.59424			−0.797121	+	0.603819i	$0.793645\pi$
$348$	330.971	+	16.5331i	0.951068	+	0.0475090i
$349$	292.817			0.839018			0.419509	−	0.907751i	$-0.362202\pi$
$349$	292.817			0.839018			0.419509	+	0.907751i	$0.362202\pi$
$350$	−242.708	+	230.886i	−0.693450	+	0.659675i
$351$		−	34.5880i		−	0.0985414i
$352$	−96.0800	−	338.633i	−0.272954	−	0.962027i
$353$	291.329			0.825294			0.412647	−	0.910891i	$-0.364604\pi$
$353$	291.329			0.825294			0.412647	+	0.910891i	$0.364604\pi$
$354$	−223.371	−	234.808i	−0.630993	−	0.663300i
$355$		−	42.6486i		−	0.120137i
$356$	−34.0812	+	682.262i	−0.0957338	+	1.91647i
$357$			282.290i			0.790729i
$358$	−319.829	+	304.252i	−0.893378	+	0.849865i
$359$		−	352.989i		−	0.983256i	−0.870805	−	0.491628i	$-0.836402\pi$
$359$		−	352.989i		−	0.983256i	0.870805	−	0.491628i	$-0.163598\pi$
$360$	12.7729	+	14.8444i	0.0354802	+	0.0412344i
$361$	−94.1229			−0.260728
$362$	−78.1472	+	74.3409i	−0.215876	+	0.205362i
$363$	145.641	−	150.704i	0.401214	−	0.415164i
$364$	183.038	+	9.14336i	0.502852	+	0.0251191i
$365$	−30.3101			−0.0830413
$366$	200.755	−	190.977i	0.548512	−	0.521796i
$367$	616.097			1.67874			0.839369	−	0.543562i	$-0.182925\pi$
$367$	616.097			1.67874			0.839369	+	0.543562i	$0.182925\pi$
$368$	658.197	+	65.9227i	1.78858	+	0.179138i
$369$			190.857i			0.517228i
$370$	−45.5496	−	47.8817i	−0.123107	−	0.129410i
$371$	649.737			1.75131
$372$	−33.4918	−	1.67302i	−0.0900316	−	0.00449738i
$373$	478.196			1.28203			0.641014	−	0.767530i	$-0.278514\pi$
$373$	478.196			1.28203			0.641014	+	0.767530i	$0.278514\pi$
$374$	−484.483	+	191.425i	−1.29541	+	0.511833i
$375$	69.7238			0.185930
$376$	86.1794	−	74.1532i	0.229201	−	0.197216i
$377$	−318.387			−0.844527
$378$	−49.3018	−	51.8260i	−0.130428	−	0.137106i
$379$			103.118i			0.272080i	0.990703	+	0.136040i	$0.0434376\pi$
$379$			103.118i			0.272080i	−0.990703	+	0.136040i	$0.956562\pi$
$380$	−53.2534	−	2.66018i	−0.140140	−	0.00700048i
$381$	208.100			0.546195
$382$	−73.0660	−	76.8070i	−0.191272	−	0.201065i
$383$	−94.0194			−0.245482			−0.122741	−	0.992439i	$-0.539168\pi$
$383$	−94.0194			−0.245482			−0.122741	+	0.992439i	$0.539168\pi$
$384$	−127.135	−	181.628i	−0.331080	−	0.472990i
$385$	−57.2767	−	23.1535i	−0.148771	−	0.0601390i
$386$	−159.366	+	151.604i	−0.412865	+	0.392756i
$387$	25.7192			0.0664579
$388$	−14.8104	+	296.486i	−0.0381712	+	0.764138i
$389$		−	393.780i		−	1.01229i	−0.862449	−	0.506143i	$-0.831071\pi$
$389$		−	393.780i		−	1.01229i	0.862449	−	0.506143i	$-0.168929\pi$
$390$	−12.9682	−	13.6321i	−0.0332517	−	0.0349542i
$391$		−	978.947i		−	2.50370i
$392$	−9.84833	+	8.47401i	−0.0251233	+	0.0216174i
$393$			116.188i			0.295644i
$394$	−42.2104	−	44.3715i	−0.107133	−	0.112618i
$395$	−67.1372			−0.169968
$396$	55.5145	−	119.759i	0.140188	−	0.302421i
$397$		−	255.238i		−	0.642916i	−0.946924	−	0.321458i	$-0.895827\pi$
$397$		−	255.238i		−	0.642916i	0.946924	−	0.321458i	$-0.104173\pi$
$398$	193.613	+	203.526i	0.486464	+	0.511371i
$399$	194.758			0.488115
$400$	−387.409	−	38.8015i	−0.968522	−	0.0970038i
$401$	96.5850			0.240860			0.120430	−	0.992722i	$-0.461573\pi$
$401$	96.5850			0.240860			0.120430	+	0.992722i	$0.461573\pi$
$402$	−105.324	−	110.716i	−0.261999	−	0.275413i
$403$	32.2183			0.0799461
$404$	0.593530	−	11.8817i	0.00146913	−	0.0294101i
$405$			7.34370i			0.0181326i
$406$	−477.065	+	453.829i	−1.17504	+	1.11780i
$407$	−166.946	+	412.987i	−0.410186	+	1.01471i
$408$	−248.705	+	213.999i	−0.609572	+	0.524507i
$409$		−	124.861i		−	0.305284i	−0.988282	−	0.152642i	$-0.951222\pi$
$409$		−	124.861i		−	0.305284i	0.988282	−	0.152642i	$-0.0487782\pi$
$410$	71.5586	+	75.2224i	0.174533	+	0.183469i
$411$		−	148.017i		−	0.360139i
$412$	−17.8138	+	356.609i	−0.0432373	+	0.865555i
$413$	643.938			1.55917
$414$	170.973	+	179.726i	0.412977	+	0.434122i
$415$		−	20.9574i		−	0.0504997i
$416$	130.702	+	168.193i	0.314188	+	0.404310i
$417$			105.651i			0.253360i
$418$	132.069	+	334.255i	0.315953	+	0.799653i
$419$			456.625i			1.08980i	0.838502	+	0.544898i	$0.183432\pi$
$419$			456.625i			1.08980i	−0.838502	+	0.544898i	$0.816568\pi$
$420$	−38.8625	−	1.94131i	−0.0925298	−	0.00462217i
$421$		−	421.405i		−	1.00096i	−0.865747	−	0.500481i	$-0.833156\pi$
$421$		−	421.405i		−	1.00096i	0.865747	−	0.500481i	$-0.166844\pi$
$422$	−92.9092	−	97.6661i	−0.220164	−	0.231436i
$423$	42.6340			0.100790
$424$	492.554	+	572.436i	1.16168	+	1.35009i
$425$			576.200i			1.35576i
$426$	−131.184	+	124.794i	−0.307943	+	0.292945i
$427$			550.552i			1.28935i
$428$	−6.89306	+	137.990i	−0.0161053	+	0.322407i
$429$	−47.5302	+	117.579i	−0.110793	+	0.274078i
$430$	10.1367	−	9.64297i	0.0235737	−	0.0224255i
$431$			527.823i			1.22465i	0.790608	+	0.612323i	$0.209765\pi$
$431$			527.823i			1.22465i	−0.790608	+	0.612323i	$0.790235\pi$
$432$	8.28540	−	82.7246i	0.0191792	−	0.191492i
$433$	−384.044			−0.886938			−0.443469	−	0.896290i	$-0.646252\pi$
$433$	−384.044			−0.886938			−0.443469	+	0.896290i	$0.646252\pi$
$434$	48.2753	−	45.9240i	0.111233	−	0.105816i
$435$	67.5996			0.155401
$436$	−9.89878	+	198.161i	−0.0227036	+	0.454497i
$437$	−675.397			−1.54553
$438$	88.6904	+	93.2314i	0.202490	+	0.212857i
$439$		−	582.820i		−	1.32761i	−0.747907	−	0.663804i	$-0.768941\pi$
$439$		−	582.820i		−	1.32761i	0.747907	−	0.663804i	$-0.231059\pi$
$440$	−23.0215	−	68.0146i	−0.0523216	−	0.154579i
$441$	−4.87209			−0.0110478
$442$	228.395	−	217.271i	0.516731	−	0.491563i
$443$			237.992i			0.537228i	0.963248	+	0.268614i	$0.0865656\pi$
$443$			237.992i			0.537228i	−0.963248	+	0.268614i	$0.913434\pi$
$444$	−13.9976	+	280.214i	−0.0315261	+	0.631112i
$445$			139.349i			0.313145i
$446$	−213.720	−	224.663i	−0.479193	−	0.503728i
$447$			448.030i			1.00230i
$448$	435.584	+	65.7142i	0.972286	+	0.146684i
$449$	−606.631			−1.35107			−0.675536	−	0.737327i	$-0.736088\pi$
$449$	−606.631			−1.35107			−0.675536	+	0.737327i	$0.736088\pi$
$450$	−100.633	−	105.785i	−0.223629	−	0.235078i
$451$	262.272	−	648.804i	0.581535	−	1.43859i
$452$	29.2946	−	586.440i	0.0648111	−	1.29743i
$453$	−211.294			−0.466433
$454$	120.362	+	126.524i	0.265114	+	0.278688i
$455$	37.3848			0.0821645
$456$	147.642	+	171.587i	0.323777	+	0.376288i
$457$			424.013i			0.927819i	0.885883	+	0.463910i	$0.153554\pi$
$457$			424.013i			0.927819i	−0.885883	+	0.463910i	$0.846446\pi$
$458$	31.8134	−	30.2639i	0.0694616	−	0.0660784i
$459$	−123.038			−0.268056
$460$	134.770	+	6.73223i	0.292979	+	0.0146353i
$461$	−331.015			−0.718037			−0.359018	−	0.933330i	$-0.616888\pi$
$461$	−331.015			−0.718037			−0.359018	+	0.933330i	$0.616888\pi$
$462$	96.3792	+	243.928i	0.208613	+	0.527983i
$463$	−182.362			−0.393870			−0.196935	−	0.980417i	$-0.563099\pi$
$463$	−182.362			−0.393870			−0.196935	+	0.980417i	$0.563099\pi$
$464$	−761.489	−	76.2681i	−1.64114	−	0.164371i
$465$	−6.84056			−0.0147109
$466$	369.047	−	351.072i	0.791946	−	0.753373i
$467$		−	759.886i		−	1.62717i	−0.581449	−	0.813583i	$-0.697514\pi$
$467$		−	759.886i		−	1.62717i	0.581449	−	0.813583i	$-0.302486\pi$
$468$	−3.98518	+	79.7781i	−0.00851534	+	0.170466i
$469$	303.628			0.647395
$470$	16.8033	−	15.9849i	0.0357517	−	0.0340104i
$471$	202.933			0.430856
$472$	488.158	+	567.327i	1.03423	+	1.20196i
$473$	−87.4305	−	35.3429i	−0.184842	−	0.0747207i
$474$	196.450	+	206.509i	0.414452	+	0.435672i
$475$	397.533			0.836911
$476$	32.5250	−	651.109i	0.0683299	−	1.36788i
$477$			283.191i			0.593693i
$478$	−87.5652	+	83.3002i	−0.183191	+	0.174268i
$479$			616.933i			1.28796i	0.765043	+	0.643980i	$0.222718\pi$
$479$			616.933i			1.28796i	−0.765043	+	0.643980i	$0.777282\pi$
$480$	−27.7506	−	35.7106i	−0.0578138	−	0.0743971i
$481$		−	269.559i		−	0.560413i
$482$	−568.234	+	540.557i	−1.17891	+	1.12149i
$483$	−492.882			−1.02046
$484$	−353.287	+	330.823i	−0.729933	+	0.683519i
$485$			60.5560i			0.124858i
$486$	22.5886	−	21.4884i	0.0464787	−	0.0442149i
$487$	−697.177			−1.43158			−0.715788	−	0.698318i	$-0.753932\pi$
$487$	−697.177			−1.43158			−0.715788	+	0.698318i	$0.753932\pi$
$488$	−485.051	+	417.363i	−0.993958	+	0.855253i
$489$	−399.956			−0.817907
$490$	−1.92023	+	1.82671i	−0.00391884	+	0.00372797i
$491$	345.736			0.704146			0.352073	−	0.935972i	$-0.385477\pi$
$491$	345.736			0.704146			0.352073	+	0.935972i	$0.385477\pi$
$492$	21.9903	−	440.217i	0.0446957	−	0.894750i
$493$			1132.58i			2.29731i
$494$	−149.900	−	157.575i	−0.303441	−	0.318977i
$495$	10.0916	−	24.9643i	0.0203870	−	0.0504330i
$496$	77.0569	+	7.71774i	0.155357	+	0.0155600i
$497$		−	359.759i		−	0.723861i
$498$	−64.4633	+	61.3235i	−0.129444	+	0.123140i
$499$			549.719i			1.10164i	0.834624	+	0.550821i	$0.185685\pi$
$499$			549.719i			1.10164i	−0.834624	+	0.550821i	$0.814315\pi$
$500$	−160.820	−	8.03348i	−0.321640	−	0.0160670i
$501$	198.498			0.396203
$502$	−73.6644	+	70.0765i	−0.146742	+	0.139595i
$503$		−	493.699i		−	0.981508i	−0.871298	−	0.490754i	$-0.836721\pi$
$503$		−	493.699i		−	0.981508i	0.871298	−	0.490754i	$-0.163279\pi$
$504$	107.744	+	125.219i	0.213779	+	0.248450i
$505$		−	2.42679i		−	0.00480552i
$506$	−334.231	−	845.913i	−0.660536	−	1.67176i
$507$			215.972i			0.425980i
$508$	−479.988	−	23.9770i	−0.944859	−	0.0471988i
$509$		−	132.789i		−	0.260883i	−0.991456	−	0.130442i	$-0.958361\pi$
$509$		−	132.789i		−	0.260883i	0.991456	−	0.130442i	$-0.0416395\pi$
$510$	−48.4927	+	46.1308i	−0.0950837	+	0.0904525i
$511$	−255.678			−0.500348
$512$	272.312	+	433.578i	0.531860	+	0.846833i
$513$			84.8863i			0.165470i
$514$	539.090	+	566.692i	1.04881	+	1.10251i
$515$			72.8359i			0.141429i
$516$	−59.3220	−	2.96333i	−0.114965	−	0.00574289i
$517$	−144.931	−	58.5869i	−0.280331	−	0.113321i
$518$	−384.229	−	403.902i	−0.741756	−	0.779734i
$519$		−	58.8351i		−	0.113362i
$520$	28.3407	+	32.9370i	0.0545014	+	0.0633405i
$521$	375.234			0.720219			0.360109	−	0.932910i	$-0.382739\pi$
$521$	375.234			0.720219			0.360109	+	0.932910i	$0.382739\pi$
$522$	−197.804	−	207.931i	−0.378934	−	0.398336i
$523$	−104.225			−0.199284			−0.0996419	−	0.995023i	$-0.531770\pi$
$523$	−104.225			−0.199284			−0.0996419	+	0.995023i	$0.531770\pi$
$524$	13.3870	−	267.991i	0.0255477	−	0.511432i
$525$	290.106			0.552583
$526$	394.008	−	374.817i	0.749065	−	0.712581i
$527$		−	114.608i		−	0.217472i
$528$	−141.844	+	269.830i	−0.268644	+	0.511042i
$529$	1180.25			2.23111
$530$	106.178	+	111.614i	0.200335	+	0.210592i
$531$			280.664i			0.528557i
$532$	−449.214	−	22.4397i	−0.844388	−	0.0421799i
$533$			423.478i			0.794518i
$534$	428.628	−	407.751i	0.802674	−	0.763578i
$535$			28.1839i			0.0526802i
$536$	230.175	+	267.505i	0.429431	+	0.499076i
$537$	382.289			0.711898
$538$	560.636	−	533.329i	1.04207	−	0.991319i
$539$	16.5623	+	6.69514i	0.0307278	+	0.0124214i
$540$	0.846131	−	16.9384i	0.00156691	−	0.0313675i
$541$	−158.210			−0.292440			−0.146220	−	0.989252i	$-0.546711\pi$
$541$	−158.210			−0.292440			−0.146220	+	0.989252i	$0.546711\pi$
$542$	301.701	−	287.006i	0.556643	−	0.529531i
$543$	93.4086			0.172023
$544$	598.301	−	464.938i	1.09982	−	0.854666i
$545$			40.4735i			0.0742634i
$546$	−109.392	−	114.993i	−0.200351	−	0.210609i
$547$	−796.609			−1.45632			−0.728161	−	0.685406i	$-0.759625\pi$
$547$	−796.609			−1.45632			−0.728161	+	0.685406i	$0.759625\pi$
$548$	−17.0543	+	341.405i	−0.0311210	+	0.623002i
$549$	−239.961			−0.437087
$550$	196.726	+	497.897i	0.357683	+	0.905267i
$551$	781.388			1.41813
$552$	−373.645	−	434.243i	−0.676892	−	0.786671i
$553$	−566.330			−1.02410
$554$	26.6326	+	27.9961i	0.0480732	+	0.0505346i
$555$			57.2325i			0.103122i
$556$	12.1730	−	243.687i	0.0218938	−	0.438286i
$557$	−288.040			−0.517127			−0.258563	−	0.965994i	$-0.583249\pi$
$557$	−288.040			−0.517127			−0.258563	+	0.965994i	$0.583249\pi$
$558$	20.0162	+	21.0410i	0.0358713	+	0.0377079i
$559$	57.0664			0.102087
$560$	89.4137	+	8.95537i	0.159667	+	0.0159917i
$561$	418.257	+	169.076i	0.745556	+	0.301383i
$562$	−389.056	+	370.107i	−0.692271	+	0.658553i
$563$	−694.692			−1.23391			−0.616956	−	0.786998i	$-0.711634\pi$
$563$	−694.692			−1.23391			−0.616956	+	0.786998i	$0.711634\pi$
$564$	−98.3365	−	4.91223i	−0.174355	−	0.00870963i
$565$		−	119.778i		−	0.211997i
$566$	564.108	+	592.990i	0.996657	+	1.04769i
$567$			61.9472i			0.109254i
$568$	316.958	−	272.727i	0.558024	−	0.480152i
$569$		−	192.576i		−	0.338447i	−0.985578	−	0.169224i	$-0.945874\pi$
$569$		−	192.576i		−	0.338447i	0.985578	−	0.169224i	$-0.0541260\pi$
$570$	31.8266	+	33.4562i	0.0558362	+	0.0586950i
$571$	338.089			0.592100			0.296050	−	0.955172i	$-0.404330\pi$
$571$	338.089			0.592100			0.296050	+	0.955172i	$0.404330\pi$
$572$	123.177	−	265.723i	0.215344	−	0.464551i
$573$			91.8067i			0.160221i
$574$	603.626	+	634.532i	1.05161	+	1.10546i
$575$	−1006.05			−1.74966
$576$	−28.6419	+	189.852i	−0.0497255	+	0.329604i
$577$	−998.324			−1.73020			−0.865099	−	0.501601i	$-0.832745\pi$
$577$	−998.324			−1.73020			−0.865099	+	0.501601i	$0.832745\pi$
$578$	−374.501	−	393.675i	−0.647925	−	0.681099i
$579$	190.489			0.328996
$580$	−155.920	−	7.78873i	−0.268828	−	0.0134288i
$581$		−	176.784i		−	0.304276i
$582$	186.266	−	177.193i	0.320044	−	0.304456i
$583$	389.156	−	962.687i	0.667506	−	1.65126i
$584$	−193.825	−	225.259i	−0.331892	−	0.385718i
$585$			16.2944i			0.0278536i
$586$	281.480	+	295.892i	0.480342	+	0.504935i
$587$		−	685.580i		−	1.16794i	−0.811776	−	0.583969i	$-0.801499\pi$
$587$		−	685.580i		−	1.16794i	0.811776	−	0.583969i	$-0.198501\pi$
$588$	11.2376	+	0.561355i	0.0191116	+	0.000954686i
$589$	−79.0705			−0.134245
$590$	105.230	+	110.618i	0.178356	+	0.187488i
$591$			53.0369i			0.0897409i
$592$	64.5716	−	644.707i	0.109074	−	1.08903i
$593$			384.408i			0.648243i	0.946016	+	0.324121i	$0.105069\pi$
$593$			384.408i			0.648243i	−0.946016	+	0.324121i	$0.894931\pi$
$594$	−106.317	+	42.0074i	−0.178985	+	0.0707195i
$595$		−	132.986i		−	0.223507i
$596$	51.6214	−	1033.39i	0.0866131	−	1.73388i
$597$		−	243.273i		−	0.407492i
$598$	379.358	+	398.781i	0.634377	+	0.666858i
$599$	−418.694			−0.698989			−0.349495	−	0.936938i	$-0.613647\pi$
$599$	−418.694			−0.698989			−0.349495	+	0.936938i	$0.613647\pi$
$600$	219.924	+	255.591i	0.366540	+	0.425985i
$601$		−	516.268i		−	0.859015i	−0.903063	−	0.429508i	$-0.858687\pi$
$601$		−	516.268i		−	0.859015i	0.903063	−	0.429508i	$-0.141313\pi$
$602$	85.5072	−	81.3425i	0.142039	−	0.135120i
$603$			132.338i			0.219466i
$604$	487.355	+	24.3450i	0.806879	+	0.0403063i
$605$	−68.6111	+	70.9967i	−0.113407	+	0.117350i
$606$	−7.46461	+	7.10104i	−0.0123178	+	0.0117179i
$607$			400.034i			0.659034i	0.944150	+	0.329517i	$0.106886\pi$
$607$			400.034i			0.659034i	−0.944150	+	0.329517i	$0.893114\pi$
$608$	−320.771	−	412.781i	−0.527584	−	0.678916i
$609$	570.231			0.936340
$610$	−94.5756	+	89.9692i	−0.155042	+	0.147490i
$611$	94.5973			0.154824
$612$	283.789	+	14.1762i	0.463708	+	0.0231637i
$613$	−489.692			−0.798844			−0.399422	−	0.916767i	$-0.630789\pi$
$613$	−489.692			−0.798844			−0.399422	+	0.916767i	$0.630789\pi$
$614$	114.171	+	120.017i	0.185947	+	0.195467i
$615$		−	89.9126i		−	0.146199i
$616$	−194.196	−	573.731i	−0.315253	−	0.931382i
$617$	460.694			0.746669			0.373334	−	0.927697i	$-0.378214\pi$
$617$	460.694			0.746669			0.373334	+	0.927697i	$0.378214\pi$
$618$	224.038	−	213.125i	0.362520	−	0.344863i
$619$		−	332.665i		−	0.537424i	−0.963221	−	0.268712i	$-0.913402\pi$
$619$		−	332.665i		−	0.537424i	0.963221	−	0.268712i	$-0.0865979\pi$
$620$	15.7779	+	0.788160i	0.0254483	+	0.00127123i
$621$		−	214.825i		−	0.345934i
$622$	−443.214	−	465.906i	−0.712562	−	0.749046i
$623$			1175.47i			1.88679i
$624$	18.3838	−	183.551i	0.0294613	−	0.294152i
$625$	575.508			0.920813
$626$	−677.888	−	712.596i	−1.08289	−	1.13833i
$627$	116.649	−	288.564i	0.186043	−	0.460230i
$628$	−468.071	−	23.3817i	−0.745336	−	0.0372320i
$629$	−958.883			−1.52446
$630$	23.2260	+	24.4152i	0.0368667	+	0.0387543i
$631$	−625.527			−0.991327			−0.495663	−	0.868515i	$-0.665075\pi$
$631$	−625.527			−0.991327			−0.495663	+	0.868515i	$0.665075\pi$
$632$	−429.324	−	498.952i	−0.679310	−	0.789481i
$633$			116.739i			0.184422i
$634$	416.968	−	396.659i	0.657678	−	0.625645i
$635$	−98.0358			−0.154387
$636$	32.6289	−	653.188i	0.0513033	−	1.02703i
$637$	−10.8103			−0.0169707
$638$	386.683	+	978.664i	0.606086	+	1.53396i
$639$	156.803			0.245388
$640$	59.8929	+	85.5648i	0.0935827	+	0.133695i
$641$	−70.3254			−0.109712			−0.0548560	−	0.998494i	$-0.517470\pi$
$641$	−70.3254			−0.109712			−0.0548560	+	0.998494i	$0.517470\pi$
$642$	86.6915	−	82.4691i	0.135034	−	0.128457i
$643$			465.761i			0.724356i	0.932109	+	0.362178i	$0.117967\pi$
$643$			465.761i			0.724356i	−0.932109	+	0.362178i	$0.882033\pi$
$644$	1136.84	+	56.7891i	1.76529	+	0.0881819i
$645$	−12.1163			−0.0187850
$646$	−560.530	+	533.228i	−0.867693	+	0.825431i
$647$	−536.154			−0.828677			−0.414339	−	0.910123i	$-0.635987\pi$
$647$	−536.154			−0.828677			−0.414339	+	0.910123i	$0.635987\pi$
$648$	−54.5772	+	46.9610i	−0.0842240	+	0.0724707i
$649$	385.683	−	954.095i	0.594273	−	1.47010i
$650$	−223.287	−	234.719i	−0.343518	−	0.361106i
$651$	−57.7030			−0.0886375
$652$	922.509	+	46.0824i	1.41489	+	0.0706785i
$653$		−	239.213i		−	0.366329i	−0.983082	−	0.183164i	$-0.941366\pi$
$653$		−	239.213i		−	0.366329i	0.983082	−	0.183164i	$-0.0586340\pi$
$654$	124.493	−	118.430i	0.190357	−	0.181085i
$655$		−	54.7360i		−	0.0835664i
$656$	−101.442	+	1012.84i	−0.154638	+	1.54396i
$657$		−	111.439i		−	0.169617i
$658$	141.743	−	134.839i	0.215415	−	0.204923i
$659$	−1002.62			−1.52142			−0.760712	−	0.649089i	$-0.775150\pi$
$659$	−1002.62			−1.52142			−0.760712	+	0.649089i	$0.775150\pi$
$660$	−26.1528	+	56.4182i	−0.0396255	+	0.0854820i
$661$			604.607i			0.914686i	0.889290	+	0.457343i	$0.151199\pi$
$661$			604.607i			0.914686i	−0.889290	+	0.457343i	$0.848801\pi$
$662$	429.482	−	408.564i	0.648765	−	0.617166i
$663$	−272.999			−0.411762
$664$	155.752	−	134.017i	0.234566	−	0.201833i
$665$	−91.7503			−0.137970
$666$	176.043	−	167.468i	0.264329	−	0.251454i
$667$	−1977.49			−2.96475
$668$	−457.840	−	22.8706i	−0.685389	−	0.0342374i
$669$			268.537i			0.401401i
$670$	49.6178	+	52.1583i	0.0740564	+	0.0778481i
$671$	815.729	+	329.750i	1.21569	+	0.491431i
$672$	−234.088	−	301.234i	−0.348345	−	0.448265i
$673$		−	550.857i		−	0.818509i	−0.912420	−	0.409255i	$-0.865789\pi$
$673$		−	550.857i		−	0.818509i	0.912420	−	0.409255i	$-0.134211\pi$
$674$	856.297	−	814.590i	1.27047	−	1.20859i
$675$			126.444i			0.187325i
$676$	24.8840	−	498.145i	0.0368106	−	0.736900i
$677$	867.027			1.28069			0.640345	−	0.768087i	$-0.278791\pi$
$677$	867.027			1.28069			0.640345	+	0.768087i	$0.278791\pi$
$678$	−368.428	+	350.483i	−0.543404	+	0.516937i
$679$			510.815i			0.752305i
$680$	117.165	−	100.815i	0.172301	−	0.148257i
$681$		−	151.233i		−	0.222075i
$682$	−39.1293	−	99.0332i	−0.0573744	−	0.145210i
$683$			62.0673i			0.0908745i	0.998967	+	0.0454372i	$0.0144681\pi$
$683$			62.0673i			0.0908745i	−0.998967	+	0.0454372i	$0.985532\pi$
$684$	9.78047	−	195.792i	0.0142989	−	0.286246i
$685$			69.7307i			0.101797i
$686$	−504.920	+	480.328i	−0.736036	+	0.700186i
$687$	−38.0263			−0.0553512
$688$	136.486	+	13.6700i	0.198381	+	0.0198692i
$689$			628.351i			0.911976i
$690$	−80.5449	−	84.6689i	−0.116732	−	0.122708i
$691$		−	524.861i		−	0.759567i	−0.925075	−	0.379784i	$-0.875998\pi$
$691$		−	524.861i		−	0.759567i	0.925075	−	0.379784i	$-0.124002\pi$
$692$	−6.77889	+	135.705i	−0.00979609	+	0.196105i
$693$	85.1266	−	210.585i	0.122838	−	0.303874i
$694$	−762.580	−	801.624i	−1.09882	−	1.15508i
$695$		−	49.7721i		−	0.0716146i
$696$	432.281	+	502.389i	0.621094	+	0.721823i
$697$	1506.41			2.16128
$698$	403.644	+	424.310i	0.578286	+	0.607894i
$699$	−441.118			−0.631070
$700$	−669.137	−	33.4256i	−0.955910	−	0.0477508i
$701$	−37.0671			−0.0528774			−0.0264387	−	0.999650i	$-0.508417\pi$
$701$	−37.0671			−0.0528774			−0.0264387	+	0.999650i	$0.508417\pi$
$702$	50.1202	−	47.6790i	0.0713963	−	0.0679188i
$703$			661.554i			0.941045i
$704$	358.256	−	606.027i	0.508887	−	0.860833i
$705$	−20.0848			−0.0284891
$706$	401.592	+	422.154i	0.568827	+	0.597951i
$707$		−	20.4710i		−	0.0289547i
$708$	32.3377	−	647.358i	0.0456747	−	0.914348i
$709$		−	567.981i		−	0.801102i	−0.916275	−	0.400551i	$-0.868819\pi$
$709$		−	567.981i		−	0.801102i	0.916275	−	0.400551i	$-0.131181\pi$
$710$	61.8006	−	58.7905i	0.0870430	−	0.0828035i
$711$		−	246.838i		−	0.347170i
$712$	−1035.62	+	891.102i	−1.45452	+	1.25155i
$713$	200.107			0.280655
$714$	−409.056	+	389.132i	−0.572908	+	0.545003i
$715$	22.3914	−	55.3914i	0.0313167	−	0.0774705i
$716$	−881.759	−	44.0468i	−1.23151	−	0.0615178i
$717$	104.666			0.145978
$718$	511.503	−	486.590i	0.712400	−	0.677701i
$719$	−132.231			−0.183909			−0.0919547	−	0.995763i	$-0.529311\pi$
$719$	−132.231			−0.183909			−0.0919547	+	0.995763i	$0.529311\pi$
$720$	−3.90324	+	38.9714i	−0.00542117	+	0.0541270i
$721$			614.401i			0.852151i
$722$	−129.747	−	136.390i	−0.179705	−	0.188906i
$723$	679.205			0.939426
$724$	−215.449	−	10.7624i	−0.297582	−	0.0148652i
$725$	1163.93			1.60543
$726$	419.143	+	3.29851i	0.577332	+	0.00454341i
$727$	−330.501			−0.454610			−0.227305	−	0.973824i	$-0.572991\pi$
$727$	−330.501			−0.454610			−0.227305	+	0.973824i	$0.572991\pi$
$728$	239.066	+	277.838i	0.328387	+	0.381645i
$729$	−27.0000			−0.0370370
$730$	−41.7819	−	43.9212i	−0.0572355	−	0.0601660i
$731$		−	202.998i		−	0.277700i
$732$	553.476	+	27.6480i	0.756115	+	0.0377704i
$733$	−644.778			−0.879643			−0.439822	−	0.898085i	$-0.644958\pi$
$733$	−644.778			−0.879643			−0.439822	+	0.898085i	$0.644958\pi$
$734$	849.280	+	892.763i	1.15706	+	1.21630i
$735$	2.29524			0.00312277
$736$	811.788	+	1044.64i	1.10297	+	1.41935i
$737$	181.856	−	449.873i	0.246752	−	0.610411i
$738$	−276.564	+	263.094i	−0.374748	+	0.356495i
$739$	1250.88			1.69267			0.846335	−	0.532651i	$-0.178804\pi$
$739$	1250.88			1.69267			0.846335	+	0.532651i	$0.178804\pi$
$740$	6.59425	−	132.008i	0.00891115	−	0.178390i
$741$			188.348i			0.254180i
$742$	895.652	+	941.510i	1.20708	+	1.26888i
$743$		−	1357.80i		−	1.82745i	−0.406330	−	0.913726i	$-0.633192\pi$
$743$		−	1357.80i		−	1.82745i	0.406330	−	0.913726i	$-0.366808\pi$
$744$	−43.7436	−	50.8379i	−0.0587951	−	0.0683305i
$745$		−	211.066i		−	0.283311i
$746$	659.186	+	692.936i	0.883627	+	0.928869i
$747$	77.0523			0.103149
$748$	−945.239	−	438.169i	−1.26369	−	0.585787i
$749$			237.743i			0.317414i
$750$	96.1132	+	101.034i	0.128151	+	0.134712i
$751$	376.583			0.501442			0.250721	−	0.968059i	$-0.419332\pi$
$751$	376.583			0.501442			0.250721	+	0.968059i	$0.419332\pi$
$752$	226.250	+	22.6604i	0.300864	+	0.0301335i
$753$	88.0504			0.116933
$754$	−438.891	−	461.362i	−0.582083	−	0.611886i
$755$	99.5404			0.131842
$756$	7.13746	−	142.883i	0.00944109	−	0.188998i
$757$			134.176i			0.177247i	0.996065	+	0.0886237i	$0.0282468\pi$
$757$			134.176i			0.177247i	−0.996065	+	0.0886237i	$0.971753\pi$
$758$	−149.425	+	142.147i	−0.197130	+	0.187529i
$759$	−295.209	+	730.282i	−0.388944	+	0.962163i
$760$	−69.5541	−	80.8345i	−0.0915186	−	0.106361i
$761$		−	467.483i		−	0.614301i	−0.951661	−	0.307151i	$-0.900624\pi$
$761$		−	467.483i		−	0.614301i	0.951661	−	0.307151i	$-0.0993755\pi$
$762$	286.863	+	301.550i	0.376460	+	0.395735i
$763$			341.411i			0.447459i
$764$	10.5778	−	211.754i	0.0138453	−	0.277166i
$765$	57.9629			0.0757684
$766$	−129.604	−	136.240i	−0.169196	−	0.177859i
$767$			622.743i			0.811921i
$768$	87.9377	−	434.597i	0.114502	−	0.565882i
$769$			358.934i			0.466754i	0.972386	+	0.233377i	$0.0749776\pi$
$769$			358.934i			0.466754i	−0.972386	+	0.233377i	$0.925022\pi$
$770$	−45.4041	−	114.914i	−0.0589664	−	0.149239i
$771$		−	677.361i		−	0.878549i
$772$	−439.367	−	21.9478i	−0.569128	−	0.0284298i
$773$			1478.19i			1.91228i	0.292909	+	0.956140i	$0.405377\pi$
$773$			1478.19i			1.91228i	−0.292909	+	0.956140i	$0.594623\pi$
$774$	35.4535	+	37.2688i	0.0458056	+	0.0481509i
$775$	−117.781			−0.151976
$776$	−450.042	+	387.239i	−0.579951	+	0.499020i
$777$			482.780i			0.621339i
$778$	570.611	−	542.819i	0.733434	−	0.697711i
$779$		−	1039.31i		−	1.33415i
$780$	1.87741	−	37.5834i	0.00240694	−	0.0481838i
$781$	−533.039	−	215.476i	−0.682508	−	0.275897i
$782$	1418.56	−	1349.46i	1.81401	−	1.72566i
$783$			248.538i			0.317418i
$784$	−25.8551	−	2.58956i	−0.0329785	−	0.00330301i
$785$	−95.6016			−0.121786
$786$	−168.364	+	160.163i	−0.214203	+	0.203770i
$787$	−808.210			−1.02695			−0.513476	−	0.858104i	$-0.671642\pi$
$787$	−808.210			−1.02695			−0.513476	+	0.858104i	$0.671642\pi$
$788$	6.11083	−	122.331i	0.00775486	−	0.155242i
$789$	−470.954			−0.596900
$790$	−92.5475	−	97.2860i	−0.117149	−	0.123147i
$791$		−	1010.38i		−	1.27734i
$792$	250.064	−	84.6413i	0.315737	−	0.106870i
$793$	−532.431			−0.671413
$794$	369.855	−	351.841i	0.465813	−	0.443125i
$795$		−	133.411i		−	0.167813i
$796$	−28.0295	+	561.114i	−0.0352129	+	0.704917i
$797$			968.488i			1.21517i	0.794256	+	0.607584i	$0.207861\pi$
$797$			968.488i			1.21517i	−0.794256	+	0.607584i	$0.792139\pi$
$798$	268.471	+	282.217i	0.336430	+	0.353655i
$799$		−	336.505i		−	0.421157i
$800$	−477.811	−	614.867i	−0.597264	−	0.768584i
$801$	−512.335			−0.639619
$802$	133.141	+	139.958i	0.166011	+	0.174511i
$803$	−153.137	+	378.827i	−0.190706	+	0.471764i
$804$	15.2478	−	305.241i	0.0189649	−	0.379653i
$805$	232.196			0.288442
$806$	44.4124	+	46.6863i	0.0551022	+	0.0579235i
$807$	−670.123			−0.830388
$808$	18.0355	−	15.5187i	0.0223211	−	0.0192063i
$809$		−	335.049i		−	0.414151i	−0.978325	−	0.207076i	$-0.933605\pi$
$809$		−	335.049i		−	0.414151i	0.978325	−	0.207076i	$-0.0663947\pi$
$810$	−10.6415	+	10.1232i	−0.0131376	+	0.0124977i
$811$	676.279			0.833883			0.416942	−	0.908933i	$-0.363102\pi$
$811$	676.279			0.833883			0.416942	+	0.908933i	$0.363102\pi$
$812$	−1315.25	−	65.7012i	−1.61977	−	0.0809128i
$813$	−360.620			−0.443567
$814$	−828.576	+	327.381i	−1.01791	+	0.402188i
$815$	188.419			0.231189
$816$	−652.934	−	65.3956i	−0.800164	−	0.0801416i
$817$	−140.053			−0.171423
$818$	180.932	−	172.119i	0.221188	−	0.210415i
$819$			137.450i			0.167826i
$820$	−10.3596	+	207.386i	−0.0126337	+	0.252909i
$821$	550.109			0.670048			0.335024	−	0.942210i	$-0.391256\pi$
$821$	550.109			0.670048			0.335024	+	0.942210i	$0.391256\pi$
$822$	214.486	−	204.039i	0.260932	−	0.248223i
$823$	−849.036			−1.03164			−0.515818	−	0.856698i	$-0.672512\pi$
$823$	−849.036			−1.03164			−0.515818	+	0.856698i	$0.672512\pi$
$824$	−541.304	+	465.766i	−0.656923	+	0.565250i
$825$	173.757	−	429.837i	0.210615	−	0.521015i
$826$	887.659	+	933.107i	1.07465	+	1.12967i
$827$	833.306			1.00762			0.503812	−	0.863813i	$-0.331930\pi$
$827$	833.306			1.00762			0.503812	+	0.863813i	$0.331930\pi$
$828$	−24.7518	+	495.500i	−0.0298935	+	0.598430i
$829$			155.036i			0.187016i	0.995619	+	0.0935081i	$0.0298081\pi$
$829$			155.036i			0.187016i	−0.995619	+	0.0935081i	$0.970192\pi$
$830$	30.3686	−	28.8894i	0.0365886	−	0.0348065i
$831$		−	33.4635i		−	0.0402690i
$832$	−63.5513	+	421.247i	−0.0763837	+	0.506307i
$833$			38.4548i			0.0461642i
$834$	−153.095	+	145.638i	−0.183567	+	0.174626i
$835$	−93.5120			−0.111990
$836$	−302.302	+	652.141i	−0.361605	+	0.780073i
$837$		−	25.1502i		−	0.0300480i
$838$	−661.677	+	629.450i	−0.789591	+	0.751133i
$839$	−218.554			−0.260494			−0.130247	−	0.991482i	$-0.541577\pi$
$839$	−218.554			−0.260494			−0.130247	+	0.991482i	$0.541577\pi$
$840$	−50.7583	−	58.9903i	−0.0604265	−	0.0702265i
$841$	1446.82			1.72036
$842$	610.643	−	580.900i	0.725229	−	0.689906i
$843$	465.035			0.551643
$844$	13.4505	−	269.262i	0.0159367	−	0.319031i
$845$		−	101.744i		−	0.120407i
$846$	58.7703	+	61.7794i	0.0694685	+	0.0730253i
$847$	−578.763	+	598.887i	−0.683309	+	0.707068i
$848$	−150.519	+	1502.84i	−0.177498	+	1.77221i
$849$		−	708.796i		−	0.834860i
$850$	−834.949	+	794.282i	−0.982293	+	0.934449i
$851$		−	1674.22i		−	1.96736i
$852$	−361.670	−	18.0666i	−0.424495	−	0.0212049i
$853$	1258.77			1.47569			0.737846	−	0.674969i	$-0.235843\pi$
$853$	1258.77			1.47569			0.737846	+	0.674969i	$0.235843\pi$
$854$	−797.785	+	758.927i	−0.934174	+	0.888674i
$855$		−	39.9898i		−	0.0467717i
$856$	−209.458	+	180.229i	−0.244694	+	0.210547i
$857$			1404.25i			1.63856i	0.573394	+	0.819280i	$0.305626\pi$
$857$			1404.25i			1.63856i	−0.573394	+	0.819280i	$0.694374\pi$
$858$	−235.899	+	93.2069i	−0.274941	+	0.108633i
$859$		−	90.5807i		−	0.105449i	−0.998609	−	0.0527245i	$-0.983209\pi$
$859$		−	90.5807i		−	0.105449i	0.998609	−	0.0527245i	$-0.0167905\pi$
$860$	27.9465	+	1.39602i	0.0324960	+	0.00162328i
$861$		−	758.450i		−	0.880895i
$862$	−764.848	+	727.595i	−0.887295	+	0.844078i
$863$	192.945			0.223575			0.111787	−	0.993732i	$-0.464342\pi$
$863$	192.945			0.223575			0.111787	+	0.993732i	$0.464342\pi$
$864$	131.294	−	102.028i	0.151961	−	0.118088i
$865$			27.7171i			0.0320429i
$866$	−529.399	−	556.504i	−0.611315	−	0.642614i
$867$			470.556i			0.542741i
$868$	133.093	+	6.64845i	0.153333	+	0.00765951i
$869$	−339.200	+	839.106i	−0.390334	+	0.965600i
$870$	93.1850	+	97.9561i	0.107109	+	0.112593i
$871$			293.635i			0.337123i
$872$	−300.793	+	258.817i	−0.344946	+	0.296809i
$873$	−222.641			−0.255030
$874$	−931.024	−	978.692i	−1.06524	−	1.11979i
$875$	−277.077			−0.316659
$876$	−12.8398	+	257.036i	−0.0146573	+	0.293420i
$877$	−670.426			−0.764454			−0.382227	−	0.924068i	$-0.624843\pi$
$877$	−670.426			−0.764454			−0.382227	+	0.924068i	$0.624843\pi$
$878$	844.542	−	803.408i	0.961893	−	0.915043i
$879$		−	353.677i		−	0.402363i
$880$	66.8226	−	127.117i	0.0759347	−	0.144451i
$881$	−552.563			−0.627199			−0.313600	−	0.949555i	$-0.601535\pi$
$881$	−552.563			−0.627199			−0.313600	+	0.949555i	$0.601535\pi$
$882$	−6.71610	−	7.05997i	−0.00761463	−	0.00800450i
$883$		−	74.8171i		−	0.0847306i	−0.999102	−	0.0423653i	$-0.986511\pi$
$883$		−	74.8171i		−	0.0847306i	0.999102	−	0.0423653i	$-0.0134893\pi$
$884$	629.678	+	31.4545i	0.712305	+	0.0355820i
$885$		−	132.220i		−	0.149402i
$886$	−344.865	+	328.068i	−0.389239	+	0.370280i
$887$		−	1238.50i		−	1.39628i	−0.715963	−	0.698138i	$-0.754012\pi$
$887$		−	1238.50i		−	1.39628i	0.715963	−	0.698138i	$-0.245988\pi$
$888$	−425.343	+	365.987i	−0.478989	+	0.412147i
$889$	−826.972			−0.930228
$890$	−201.926	+	192.091i	−0.226883	+	0.215832i
$891$	91.7844	+	37.1029i	0.103013	+	0.0416419i
$892$	30.9404	−	619.387i	0.0346866	−	0.694381i
$893$	−232.162			−0.259980
$894$	−649.224	+	617.602i	−0.726201	+	0.690831i
$895$	−180.096			−0.201224
$896$	505.222	+	721.775i	0.563864	+	0.805552i
$897$		−	476.659i		−	0.531392i
$898$	−836.231	−	879.046i	−0.931215	−	0.978893i
$899$	−231.510			−0.257520
$900$	14.5687	−	291.647i	0.0161875	−	0.324052i
$901$	2235.19			2.48079
$902$	1301.70	−	514.317i	1.44312	−	0.570197i
$903$	−102.206			−0.113185
$904$	890.171	−	765.949i	0.984702	−	0.847289i
$905$	−44.0047			−0.0486240
$906$	−291.265	−	306.178i	−0.321485	−	0.337945i
$907$		−	794.339i		−	0.875787i	−0.899027	−	0.437894i	$-0.855725\pi$
$907$		−	794.339i		−	0.875787i	0.899027	−	0.437894i	$-0.144275\pi$
$908$	−17.4249	+	348.823i	−0.0191904	+	0.384166i
$909$	8.92238			0.00981560
$910$	51.5344	+	54.1730i	0.0566312	+	0.0595307i
$911$	1105.49			1.21350			0.606748	−	0.794895i	$-0.292474\pi$
$911$	1105.49			1.21350			0.606748	+	0.794895i	$0.292474\pi$
$912$	−45.1178	+	450.473i	−0.0494713	+	0.493940i
$913$	−261.933	−	105.884i	−0.286893	−	0.115974i
$914$	−614.422	+	584.496i	−0.672234	+	0.639492i
$915$	113.045			0.123547
$916$	87.7086	+	4.38133i	0.0957517	+	0.00478311i
$917$		−	461.721i		−	0.503513i
$918$	−169.605	−	178.289i	−0.184755	−	0.194215i
$919$		−	1507.12i		−	1.63996i	−0.572393	−	0.819979i	$-0.693985\pi$
$919$		−	1507.12i		−	1.63996i	0.572393	−	0.819979i	$-0.306015\pi$
$920$	176.024	+	204.571i	0.191330	+	0.222360i
$921$		−	143.455i		−	0.155760i
$922$	−456.299	−	479.661i	−0.494901	−	0.520240i
$923$	347.918			0.376942
$924$	−220.610	+	475.911i	−0.238755	+	0.515055i
$925$			985.433i			1.06533i
$926$	−251.383	−	264.254i	−0.271472	−	0.285371i
$927$	−267.790			−0.288878
$928$	−939.183	−	1208.58i	−1.01205	−	1.30235i
$929$	−498.268			−0.536349			−0.268174	−	0.963370i	$-0.586420\pi$
$929$	−498.268			−0.536349			−0.268174	+	0.963370i	$0.586420\pi$
$930$	−9.42961	−	9.91240i	−0.0101394	−	0.0106585i
$931$	26.5308			0.0284971
$932$	1017.45	+	50.8250i	1.09168	+	0.0545332i
$933$			556.894i			0.596885i
$934$	1101.12	−	1047.49i	1.17893	−	1.12151i
$935$	−197.040	−	79.6515i	−0.210738	−	0.0851887i
$936$	−121.097	+	104.198i	−0.129377	+	0.111323i
$937$			672.565i			0.717786i	0.933379	+	0.358893i	$0.116846\pi$
$937$			672.565i			0.717786i	−0.933379	+	0.358893i	$0.883154\pi$
$938$	418.547	+	439.977i	0.446212	+	0.469058i
$939$			851.760i			0.907092i
$940$	46.3262	+	2.31415i	0.0492832	+	0.00246186i
$941$	1810.66			1.92419			0.962093	−	0.272720i	$-0.0879232\pi$
$941$	1810.66			1.92419			0.962093	+	0.272720i	$0.0879232\pi$
$942$	279.740	+	294.063i	0.296964	+	0.312169i
$943$			2630.21i			2.78920i
$944$	−149.175	+	1489.42i	−0.158025	+	1.57778i
$945$		−	29.1832i		−	0.0308817i
$946$	−69.3075	−	175.412i	−0.0732637	−	0.185425i
$947$			653.407i			0.689976i	0.938607	+	0.344988i	$0.112117\pi$
$947$			653.407i			0.689976i	−0.938607	+	0.344988i	$0.887883\pi$
$948$	−28.4403	+	569.338i	−0.0300003	+	0.600567i
$949$		−	247.262i		−	0.260551i
$950$	547.992	+	576.050i	0.576834	+	0.606368i
$951$	−498.398			−0.524078
$952$	988.333	−	850.413i	1.03817	−	0.893291i
$953$		−	4.99815i		−	0.00524465i	−0.999997	−	0.00262232i	$-0.999165\pi$
$953$		−	4.99815i		−	0.00524465i	0.999997	−	0.00262232i	$-0.000834713\pi$
$954$	−410.362	+	390.375i	−0.430149	+	0.409198i
$955$		−	43.2500i		−	0.0452880i
$956$	−241.414	−	12.0594i	−0.252526	−	0.0126145i
$957$	341.536	−	844.886i	0.356882	−	0.882849i
$958$	−893.974	+	850.432i	−0.933167	+	0.887716i
$959$			588.207i			0.613355i
$960$	13.4932	−	89.4389i	0.0140554	−	0.0931655i
$961$	−937.573			−0.975622
$962$	390.608	−	371.583i	0.406037	−	0.386260i
$963$	−103.622			−0.107603
$964$	−1566.60	−	78.2570i	−1.62511	−	0.0811794i
$965$	−89.7390			−0.0929938
$966$	−679.430	−	714.217i	−0.703344	−	0.739355i
$967$		−	91.3832i		−	0.0945017i	−0.998883	−	0.0472509i	$-0.984954\pi$
$967$		−	91.3832i		−	0.0945017i	0.998883	−	0.0472509i	$-0.0150460\pi$
$968$	−966.385	−	55.9012i	−0.998331	−	0.0577491i
$969$	669.996			0.691430
$970$	−87.7495	+	83.4755i	−0.0904634	+	0.0860572i
$971$			1134.90i			1.16879i	0.811469	+	0.584396i	$0.198668\pi$
$971$			1134.90i			1.16879i	−0.811469	+	0.584396i	$0.801332\pi$
$972$	62.2762	+	3.11090i	0.0640701	+	0.00320051i
$973$		−	419.849i		−	0.431499i
$974$	−961.048	−	1010.25i	−0.986702	−	1.03722i
$975$			280.557i			0.287751i
$976$	−1273.42	−	127.541i	−1.30473	−	0.130678i
$977$	371.469			0.380213			0.190107	−	0.981763i	$-0.439117\pi$
$977$	371.469			0.380213			0.190107	+	0.981763i	$0.439117\pi$
$978$	−551.333	−	579.562i	−0.563736	−	0.592599i
$979$	1741.64	+	704.041i	1.77900	+	0.719143i
$980$	−5.29402	−	0.264454i	−0.00540206	−	0.000269851i
$981$	−148.806			−0.151688
$982$	476.591	+	500.993i	0.485327	+	0.510176i
$983$	1715.54			1.74521			0.872603	−	0.488430i	$-0.162430\pi$
$983$	1715.54			1.74521			0.872603	+	0.488430i	$0.162430\pi$
$984$	668.215	−	574.967i	0.679081	−	0.584316i
$985$		−	24.9856i		−	0.0253661i
$986$	−1641.17	+	1561.24i	−1.66448	+	1.58340i
$987$	−169.424			−0.171655
$988$	21.7011	−	434.428i	0.0219647	−	0.439705i
$989$	354.438			0.358380
$990$	50.0860	−	19.7896i	0.0505919	−	0.0199895i
$991$	1198.59			1.20948			0.604738	−	0.796424i	$-0.293278\pi$
$991$	1198.59			1.20948			0.604738	+	0.796424i	$0.293278\pi$
$992$	95.0381	+	122.299i	0.0958046	+	0.123285i
$993$	−513.356			−0.516975
$994$	521.313	−	495.922i	0.524460	−	0.498916i
$995$			114.605i			0.115181i
$996$	−177.723	−	8.87786i	−0.178437	−	0.00891351i
$997$	−166.678			−0.167179			−0.0835897	−	0.996500i	$-0.526638\pi$
$997$	−166.678			−0.167179			−0.0835897	+	0.996500i	$0.526638\pi$
$998$	−796.577	+	757.779i	−0.798174	+	0.759298i
$999$	−210.422			−0.210633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	264.3.e.a.109.38	yes	48
4.3	odd	2		1056.3.e.a.241.37		48
8.3	odd	2		1056.3.e.a.241.11		48
8.5	even	2	inner	264.3.e.a.109.12	yes	48
11.10	odd	2	inner	264.3.e.a.109.11	✓	48
44.43	even	2		1056.3.e.a.241.38		48
88.21	odd	2	inner	264.3.e.a.109.37	yes	48
88.43	even	2		1056.3.e.a.241.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.3.e.a.109.11	✓	48	11.10	odd	2	inner
264.3.e.a.109.12	yes	48	8.5	even	2	inner
264.3.e.a.109.37	yes	48	88.21	odd	2	inner
264.3.e.a.109.38	yes	48	1.1	even	1	trivial
1056.3.e.a.241.11		48	8.3	odd	2
1056.3.e.a.241.12		48	88.43	even	2
1056.3.e.a.241.37		48	4.3	odd	2
1056.3.e.a.241.38		48	44.43	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	264.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37848 + 1.44906i) q^{2} -1.73205i q^{3} +(-0.199564 + 3.99502i) q^{4} +0.815967i q^{5} +(2.50985 - 2.38760i) q^{6} +6.88302i q^{7} +(-6.06413 + 5.21789i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(1.37848 + 1.44906i) q^{2} -1.73205i q^{3} +(-0.199564 + 3.99502i) q^{4} +0.815967i q^{5} +(2.50985 - 2.38760i) q^{6} +6.88302i q^{7} +(-6.06413 + 5.21789i) q^{8} -3.00000 q^{9} +(-1.18239 + 1.12480i) q^{10} +(10.1983 + 4.12254i) q^{11} +(6.91958 + 0.345656i) q^{12} -6.65647 q^{13} +(-9.97393 + 9.48813i) q^{14} +1.41330 q^{15} +(-15.9203 - 1.59453i) q^{16} +23.6786i q^{17} +(-4.13545 - 4.34719i) q^{18} +16.3364 q^{19} +(-3.25980 - 0.162838i) q^{20} +11.9217 q^{21} +(8.08432 + 20.4608i) q^{22} -41.3431 q^{23} +(9.03765 + 10.5034i) q^{24} +24.3342 q^{25} +(-9.17583 - 9.64564i) q^{26} +5.19615i q^{27} +(-27.4978 - 1.37361i) q^{28} +47.8312 q^{29} +(1.94821 + 2.04795i) q^{30} -4.84015 q^{31} +(-19.6354 - 25.2676i) q^{32} +(7.14045 - 17.6639i) q^{33} +(-34.3118 + 32.6406i) q^{34} -5.61632 q^{35} +(0.598693 - 11.9851i) q^{36} +40.4958i q^{37} +(22.5194 + 23.6724i) q^{38} +11.5293i q^{39} +(-4.25762 - 4.94813i) q^{40} -63.6191i q^{41} +(16.4339 + 17.2753i) q^{42} -8.57307 q^{43} +(-18.5048 + 39.9196i) q^{44} -2.44790i q^{45} +(-56.9908 - 59.9088i) q^{46} -14.2113 q^{47} +(-2.76180 + 27.5749i) q^{48} +1.62403 q^{49} +(33.5443 + 35.2618i) q^{50} +41.0125 q^{51} +(1.32839 - 26.5927i) q^{52} -94.3971i q^{53} +(-7.52955 + 7.16281i) q^{54} +(-3.36386 + 8.32145i) q^{55} +(-35.9148 - 41.7395i) q^{56} -28.2954i q^{57} +(65.9345 + 69.3104i) q^{58} -93.5546i q^{59} +(-0.282044 + 5.64614i) q^{60} +79.9870 q^{61} +(-6.67207 - 7.01368i) q^{62} -20.6491i q^{63} +(9.54730 - 63.2839i) q^{64} -5.43146i q^{65} +(35.4391 - 14.0025i) q^{66} -44.1127i q^{67} +(-94.5964 - 4.72540i) q^{68} +71.6084i q^{69} +(-7.74200 - 8.13839i) q^{70} -52.2676 q^{71} +(18.1924 - 15.6537i) q^{72} +37.1462i q^{73} +(-58.6809 + 55.8228i) q^{74} -42.1481i q^{75} +(-3.26016 + 65.2641i) q^{76} +(-28.3755 + 70.1949i) q^{77} +(-16.7067 + 15.8930i) q^{78} +82.2793i q^{79} +(1.30108 - 12.9905i) q^{80} +9.00000 q^{81} +(92.1880 - 87.6979i) q^{82} -25.6841 q^{83} +(-2.37915 + 47.6276i) q^{84} -19.3210 q^{85} +(-11.8178 - 12.4229i) q^{86} -82.8460i q^{87} +(-83.3546 + 28.2138i) q^{88} +170.778 q^{89} +(3.54716 - 3.37439i) q^{90} -45.8166i q^{91} +(8.25061 - 165.167i) q^{92} +8.38338i q^{93} +(-19.5901 - 20.5931i) q^{94} +13.3299i q^{95} +(-43.7648 + 34.0095i) q^{96} +74.2138 q^{97} +(2.23870 + 2.35332i) q^{98} +(-30.5948 - 12.3676i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{4} - 144 q^{9}+O(q^{10}) \) 48 * q - 12 * q^4 - 144 * q^9	\( 48 q - 12 q^{4} - 144 q^{9} + 24 q^{12} - 36 q^{14} + 68 q^{16} - 20 q^{20} - 44 q^{22} - 128 q^{23} - 240 q^{25} + 44 q^{26} + 48 q^{34} + 36 q^{36} + 128 q^{38} - 108 q^{42} + 100 q^{44} + 48 q^{48} - 336 q^{49} - 128 q^{55} + 92 q^{56} + 368 q^{58} - 36 q^{60} + 444 q^{64} - 96 q^{66} - 24 q^{70} + 512 q^{71} - 348 q^{78} - 692 q^{80} + 432 q^{81} - 320 q^{82} + 568 q^{86} + 244 q^{88} + 436 q^{92} - 32 q^{97}+O(q^{100}) \) 48 * q - 12 * q^4 - 144 * q^9 + 24 * q^12 - 36 * q^14 + 68 * q^16 - 20 * q^20 - 44 * q^22 - 128 * q^23 - 240 * q^25 + 44 * q^26 + 48 * q^34 + 36 * q^36 + 128 * q^38 - 108 * q^42 + 100 * q^44 + 48 * q^48 - 336 * q^49 - 128 * q^55 + 92 * q^56 + 368 * q^58 - 36 * q^60 + 444 * q^64 - 96 * q^66 - 24 * q^70 + 512 * q^71 - 348 * q^78 - 692 * q^80 + 432 * q^81 - 320 * q^82 + 568 * q^86 + 244 * q^88 + 436 * q^92 - 32 * q^97

Introduction

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