LMFDB - Embedded newform 156.3.f.a.79.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,3,Mod(79,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("156.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	156.f (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:	$4.25069212402$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			79.19
Character	$\chi$	$=$	156.79
Dual form			156.3.f.a.79.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.69411 - 1.06301i) q^{2} +1.73205i q^{3} +(1.74001 - 3.60171i) q^{4} +5.51671 q^{5} +(1.84119 + 2.93428i) q^{6} +1.01261i q^{7} +(-0.880886 - 7.95135i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(1.69411 - 1.06301i) q^{2} +1.73205i q^{3} +(1.74001 - 3.60171i) q^{4} +5.51671 q^{5} +(1.84119 + 2.93428i) q^{6} +1.01261i q^{7} +(-0.880886 - 7.95135i) q^{8} -3.00000 q^{9} +(9.34592 - 5.86433i) q^{10} +5.63101i q^{11} +(6.23835 + 3.01379i) q^{12} +3.60555 q^{13} +(1.07642 + 1.71548i) q^{14} +9.55523i q^{15} +(-9.94470 - 12.5341i) q^{16} +8.22149 q^{17} +(-5.08233 + 3.18903i) q^{18} -11.5444i q^{19} +(9.59916 - 19.8696i) q^{20} -1.75390 q^{21} +(5.98583 + 9.53955i) q^{22} -5.25666i q^{23} +(13.7722 - 1.52574i) q^{24} +5.43413 q^{25} +(6.10820 - 3.83274i) q^{26} -5.19615i q^{27} +(3.64714 + 1.76196i) q^{28} -48.7699 q^{29} +(10.1573 + 16.1876i) q^{30} +59.3391i q^{31} +(-30.1713 - 10.6628i) q^{32} -9.75320 q^{33} +(13.9281 - 8.73953i) q^{34} +5.58630i q^{35} +(-5.22004 + 10.8051i) q^{36} -19.4001 q^{37} +(-12.2718 - 19.5575i) q^{38} +6.24500i q^{39} +(-4.85960 - 43.8653i) q^{40} -65.6042 q^{41} +(-2.97129 + 1.86441i) q^{42} +14.0189i q^{43} +(20.2813 + 9.79804i) q^{44} -16.5501 q^{45} +(-5.58788 - 8.90535i) q^{46} -9.34635i q^{47} +(21.7097 - 17.2247i) q^{48} +47.9746 q^{49} +(9.20601 - 5.77654i) q^{50} +14.2400i q^{51} +(6.27371 - 12.9862i) q^{52} -25.9791 q^{53} +(-5.52357 - 8.80285i) q^{54} +31.0647i q^{55} +(8.05165 - 0.891997i) q^{56} +19.9955 q^{57} +(-82.6216 + 51.8429i) q^{58} -38.4414i q^{59} +(34.4152 + 16.6262i) q^{60} +72.1566 q^{61} +(63.0781 + 100.527i) q^{62} -3.03784i q^{63} +(-62.4481 + 14.0085i) q^{64} +19.8908 q^{65} +(-16.5230 + 10.3678i) q^{66} +101.440i q^{67} +(14.3055 - 29.6115i) q^{68} +9.10480 q^{69} +(5.93829 + 9.46380i) q^{70} -80.3131i q^{71} +(2.64266 + 23.8541i) q^{72} +5.60676 q^{73} +(-32.8659 + 20.6225i) q^{74} +9.41219i q^{75} +(-41.5797 - 20.0875i) q^{76} -5.70204 q^{77} +(6.63850 + 10.5797i) q^{78} -28.5754i q^{79} +(-54.8620 - 69.1469i) q^{80} +9.00000 q^{81} +(-111.141 + 69.7380i) q^{82} -103.937i q^{83} +(-3.05181 + 6.31704i) q^{84} +45.3556 q^{85} +(14.9022 + 23.7495i) q^{86} -84.4720i q^{87} +(44.7742 - 4.96028i) q^{88} +69.8749 q^{89} +(-28.0378 + 17.5930i) q^{90} +3.65103i q^{91} +(-18.9330 - 9.14666i) q^{92} -102.778 q^{93} +(-9.93528 - 15.8337i) q^{94} -63.6872i q^{95} +(18.4685 - 52.2582i) q^{96} -27.6984 q^{97} +(81.2743 - 50.9975i) q^{98} -16.8930i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9	$ 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9} - 12 q^{10} + 12 q^{12} + 32 q^{14} + 4 q^{16} - 12 q^{18} + 84 q^{20} + 28 q^{22} - 36 q^{24} + 104 q^{25} - 96 q^{28} + 64 q^{29} - 12 q^{30} + 44 q^{32} + 48 q^{33} + 40 q^{34} - 24 q^{36} - 192 q^{37} - 104 q^{38} + 220 q^{40} - 220 q^{44} - 104 q^{46} - 144 q^{48} - 248 q^{49} + 100 q^{50} - 52 q^{52} + 336 q^{53} + 36 q^{54} + 168 q^{56} - 16 q^{58} + 60 q^{60} + 16 q^{61} + 152 q^{62} - 16 q^{64} - 132 q^{66} + 400 q^{68} - 192 q^{69} + 208 q^{70} + 96 q^{72} + 112 q^{73} - 104 q^{74} - 264 q^{76} - 272 q^{77} - 300 q^{80} + 216 q^{81} - 4 q^{82} + 96 q^{84} + 64 q^{85} + 288 q^{86} - 492 q^{88} + 36 q^{90} + 328 q^{92} - 96 q^{93} - 884 q^{94} + 72 q^{96} - 80 q^{97} - 572 q^{98}+O(q^{100}) $ 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9 - 12 * q^10 + 12 * q^12 + 32 * q^14 + 4 * q^16 - 12 * q^18 + 84 * q^20 + 28 * q^22 - 36 * q^24 + 104 * q^25 - 96 * q^28 + 64 * q^29 - 12 * q^30 + 44 * q^32 + 48 * q^33 + 40 * q^34 - 24 * q^36 - 192 * q^37 - 104 * q^38 + 220 * q^40 - 220 * q^44 - 104 * q^46 - 144 * q^48 - 248 * q^49 + 100 * q^50 - 52 * q^52 + 336 * q^53 + 36 * q^54 + 168 * q^56 - 16 * q^58 + 60 * q^60 + 16 * q^61 + 152 * q^62 - 16 * q^64 - 132 * q^66 + 400 * q^68 - 192 * q^69 + 208 * q^70 + 96 * q^72 + 112 * q^73 - 104 * q^74 - 264 * q^76 - 272 * q^77 - 300 * q^80 + 216 * q^81 - 4 * q^82 + 96 * q^84 + 64 * q^85 + 288 * q^86 - 492 * q^88 + 36 * q^90 + 328 * q^92 - 96 * q^93 - 884 * q^94 + 72 * q^96 - 80 * q^97 - 572 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	1.69411	−	1.06301i	0.847055	−	0.531506i
$2$	1.69411	−	1.06301i	0.847055	−	0.531506i
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	1.74001	−	3.60171i	0.435004	−	0.900429i
$5$	5.51671			1.10334			0.551671	−	0.834062i	$-0.313990\pi$
$5$	5.51671			1.10334			0.551671	+	0.834062i	$0.313990\pi$
$6$	1.84119	+	2.93428i	0.306865	+	0.489047i
$7$			1.01261i			0.144659i	0.997381	+	0.0723295i	$0.0230433\pi$
$7$			1.01261i			0.144659i	−0.997381	+	0.0723295i	$0.976957\pi$
$8$	−0.880886	−	7.95135i	−0.110111	−	0.993919i
$9$	−3.00000			−0.333333
$10$	9.34592	−	5.86433i	0.934592	−	0.586433i
$11$			5.63101i			0.511910i	0.966689	+	0.255955i	$0.0823899\pi$
$11$			5.63101i			0.511910i	−0.966689	+	0.255955i	$0.917610\pi$
$12$	6.23835	+	3.01379i	0.519863	+	0.251150i
$13$	3.60555			0.277350
$13$	3.60555			0.277350
$14$	1.07642	+	1.71548i	0.0768871	+	0.122534i
$15$			9.55523i			0.637015i
$16$	−9.94470	−	12.5341i	−0.621543	−	0.783380i
$17$	8.22149			0.483617			0.241808	−	0.970324i	$-0.422259\pi$
$17$	8.22149			0.483617			0.241808	+	0.970324i	$0.422259\pi$
$18$	−5.08233	+	3.18903i	−0.282352	+	0.177169i
$19$		−	11.5444i		−	0.607601i	−0.952736	−	0.303800i	$-0.901744\pi$
$19$		−	11.5444i		−	0.607601i	0.952736	−	0.303800i	$-0.0982556\pi$
$20$	9.59916	−	19.8696i	0.479958	−	0.993481i
$21$	−1.75390			−0.0835189
$22$	5.98583	+	9.53955i	0.272083	+	0.433616i
$23$		−	5.25666i		−	0.228550i	−0.993449	−	0.114275i	$-0.963545\pi$
$23$		−	5.25666i		−	0.228550i	0.993449	−	0.114275i	$-0.0364545\pi$
$24$	13.7722	−	1.52574i	0.573840	−	0.0635725i
$25$	5.43413			0.217365
$26$	6.10820	−	3.83274i	0.234931	−	0.147413i
$27$		−	5.19615i		−	0.192450i
$28$	3.64714	+	1.76196i	0.130255	+	0.0629272i
$29$	−48.7699			−1.68172			−0.840860	−	0.541252i	$-0.817951\pi$
$29$	−48.7699			−1.68172			−0.840860	+	0.541252i	$0.817951\pi$
$30$	10.1573	+	16.1876i	0.338577	+	0.539587i
$31$			59.3391i			1.91417i	0.289815	+	0.957083i	$0.406406\pi$
$31$			59.3391i			1.91417i	−0.289815	+	0.957083i	$0.593594\pi$
$32$	−30.1713	−	10.6628i	−0.942852	−	0.333212i
$33$	−9.75320			−0.295551
$34$	13.9281	−	8.73953i	0.409650	−	0.257045i
$35$			5.58630i			0.159608i
$36$	−5.22004	+	10.8051i	−0.145001	+	0.300143i
$37$	−19.4001			−0.524327			−0.262164	−	0.965023i	$-0.584436\pi$
$37$	−19.4001			−0.524327			−0.262164	+	0.965023i	$0.584436\pi$
$38$	−12.2718	−	19.5575i	−0.322943	−	0.514671i
$39$			6.24500i			0.160128i
$40$	−4.85960	−	43.8653i	−0.121490	−	1.09663i
$41$	−65.6042			−1.60010			−0.800052	−	0.599931i	$-0.795195\pi$
$41$	−65.6042			−1.60010			−0.800052	+	0.599931i	$0.795195\pi$
$42$	−2.97129	+	1.86441i	−0.0707451	+	0.0443908i
$43$			14.0189i			0.326021i	0.986624	+	0.163010i	$0.0521204\pi$
$43$			14.0189i			0.326021i	−0.986624	+	0.163010i	$0.947880\pi$
$44$	20.2813	+	9.79804i	0.460939	+	0.222683i
$45$	−16.5501			−0.367781
$46$	−5.58788	−	8.90535i	−0.121476	−	0.193595i
$47$		−	9.34635i		−	0.198859i	−0.995045	−	0.0994293i	$-0.968298\pi$
$47$		−	9.34635i		−	0.198859i	0.995045	−	0.0994293i	$-0.0317017\pi$
$48$	21.7097	−	17.2247i	0.452284	−	0.358848i
$49$	47.9746			0.979074
$50$	9.20601	−	5.77654i	0.184120	−	0.115531i
$51$			14.2400i			0.279216i
$52$	6.27371	−	12.9862i	0.120648	−	0.249734i
$53$	−25.9791			−0.490172			−0.245086	−	0.969501i	$-0.578816\pi$
$53$	−25.9791			−0.490172			−0.245086	+	0.969501i	$0.578816\pi$
$54$	−5.52357	−	8.80285i	−0.102288	−	0.163016i
$55$			31.0647i			0.564812i
$56$	8.05165	−	0.891997i	0.143779	−	0.0159285i
$57$	19.9955			0.350798
$58$	−82.6216	+	51.8429i	−1.42451	+	0.893844i
$59$		−	38.4414i		−	0.651548i	−0.945448	−	0.325774i	$-0.894375\pi$
$59$		−	38.4414i		−	0.651548i	0.945448	−	0.325774i	$-0.105625\pi$
$60$	34.4152	+	16.6262i	0.573587	+	0.277104i
$61$	72.1566			1.18289			0.591447	−	0.806344i	$-0.298557\pi$
$61$	72.1566			1.18289			0.591447	+	0.806344i	$0.298557\pi$
$62$	63.0781	+	100.527i	1.01739	+	1.62140i
$63$		−	3.03784i		−	0.0482197i
$64$	−62.4481	+	14.0085i	−0.975751	+	0.218882i
$65$	19.8908			0.306012
$66$	−16.5230	+	10.3678i	−0.250348	+	0.157087i
$67$			101.440i			1.51403i	0.653399	+	0.757013i	$0.273342\pi$
$67$			101.440i			1.51403i	−0.653399	+	0.757013i	$0.726658\pi$
$68$	14.3055	−	29.6115i	0.210375	−	0.435463i
$69$	9.10480			0.131954
$70$	5.93829	+	9.46380i	0.0848328	+	0.135197i
$71$		−	80.3131i		−	1.13117i	−0.824690	−	0.565585i	$-0.808650\pi$
$71$		−	80.3131i		−	1.13117i	0.824690	−	0.565585i	$-0.191350\pi$
$72$	2.64266	+	23.8541i	0.0367036	+	0.331306i
$73$	5.60676			0.0768049			0.0384025	−	0.999262i	$-0.487773\pi$
$73$	5.60676			0.0768049			0.0384025	+	0.999262i	$0.487773\pi$
$74$	−32.8659	+	20.6225i	−0.444134	+	0.278683i
$75$			9.41219i			0.125496i
$76$	−41.5797	−	20.0875i	−0.547101	−	0.264309i
$77$	−5.70204			−0.0740524
$78$	6.63850	+	10.5797i	0.0851090	+	0.135637i
$79$		−	28.5754i		−	0.361715i	−0.983509	−	0.180857i	$-0.942113\pi$
$79$		−	28.5754i		−	0.361715i	0.983509	−	0.180857i	$-0.0578872\pi$
$80$	−54.8620	−	69.1469i	−0.685775	−	0.864336i
$81$	9.00000			0.111111
$82$	−111.141	+	69.7380i	−1.35538	+	0.850464i
$83$		−	103.937i		−	1.25226i	−0.779720	−	0.626128i	$-0.784639\pi$
$83$		−	103.937i		−	1.25226i	0.779720	−	0.626128i	$-0.215361\pi$
$84$	−3.05181	+	6.31704i	−0.0363310	+	0.0752028i
$85$	45.3556			0.533595
$86$	14.9022	+	23.7495i	0.173282	+	0.276157i
$87$		−	84.4720i		−	0.970942i
$88$	44.7742	−	4.96028i	0.508797	−	0.0563668i
$89$	69.8749			0.785111			0.392555	−	0.919728i	$-0.371591\pi$
$89$	69.8749			0.785111			0.392555	+	0.919728i	$0.371591\pi$
$90$	−28.0378	+	17.5930i	−0.311531	+	0.195478i
$91$			3.65103i			0.0401212i
$92$	−18.9330	−	9.14666i	−0.205793	−	0.0994202i
$93$	−102.778			−1.10514
$94$	−9.93528	−	15.8337i	−0.105694	−	0.168444i
$95$		−	63.6872i		−	0.670392i
$96$	18.4685	−	52.2582i	0.192380	−	0.544356i
$97$	−27.6984			−0.285550			−0.142775	−	0.989755i	$-0.545603\pi$
$97$	−27.6984			−0.285550			−0.142775	+	0.989755i	$0.545603\pi$
$98$	81.2743	−	50.9975i	0.829329	−	0.520383i
$99$		−	16.8930i		−	0.170637i
$100$	9.45547	−	19.5722i	0.0945547	−	0.195722i
$101$	−39.6436			−0.392511			−0.196255	−	0.980553i	$-0.562878\pi$
$101$	−39.6436			−0.392511			−0.196255	+	0.980553i	$0.562878\pi$
$102$	15.1373	+	24.1242i	0.148405	+	0.236512i
$103$		−	80.8239i		−	0.784698i	−0.919816	−	0.392349i	$-0.871662\pi$
$103$		−	80.8239i		−	0.784698i	0.919816	−	0.392349i	$-0.128338\pi$
$104$	−3.17608	−	28.6690i	−0.0305392	−	0.275664i
$105$	−9.67575			−0.0921500
$106$	−44.0114	+	27.6161i	−0.415202	+	0.260529i
$107$			97.0127i			0.906661i	0.891342	+	0.453331i	$0.149764\pi$
$107$			97.0127i			0.906661i	−0.891342	+	0.453331i	$0.850236\pi$
$108$	−18.7151	−	9.04138i	−0.173288	−	0.0837165i
$109$	211.083			1.93654			0.968271	−	0.249904i	$-0.0803992\pi$
$109$	211.083			1.93654			0.968271	+	0.249904i	$0.0803992\pi$
$110$	33.0221	+	52.6270i	0.300201	+	0.478427i
$111$		−	33.6020i		−	0.302721i
$112$	12.6922	−	10.0701i	0.113323	−	0.0899119i
$113$	68.4234			0.605517			0.302759	−	0.953067i	$-0.402092\pi$
$113$	68.4234			0.605517			0.302759	+	0.953067i	$0.402092\pi$
$114$	33.8746	−	21.2555i	0.297146	−	0.186451i
$115$		−	28.9995i		−	0.252169i
$116$	−84.8604	+	175.655i	−0.731555	+	1.51427i
$117$	−10.8167			−0.0924500
$118$	−40.8636	−	65.1239i	−0.346302	−	0.551897i
$119$			8.32519i			0.0699596i
$120$	75.9770	−	8.41707i	0.633142	−	0.0701422i
$121$	89.2917			0.737948
$122$	122.241	−	76.7032i	1.00198	−	0.628715i
$123$		−	113.630i		−	0.923820i
$124$	213.723	+	103.251i	1.72357	+	0.832669i
$125$	−107.939			−0.863514
$126$	−3.22926	−	5.14643i	−0.0256290	−	0.0408447i
$127$		−	47.0102i		−	0.370159i	−0.982724	−	0.185080i	$-0.940746\pi$
$127$		−	47.0102i		−	0.370159i	0.982724	−	0.185080i	$-0.0592543\pi$
$128$	−90.9027	+	90.1149i	−0.710178	+	0.704023i
$129$	−24.2814			−0.188228
$130$	33.6972	−	21.1441i	0.259209	−	0.162647i
$131$			85.1555i			0.650042i	0.945707	+	0.325021i	$0.105371\pi$
$131$			85.1555i			0.650042i	−0.945707	+	0.325021i	$0.894629\pi$
$132$	−16.9707	+	35.1282i	−0.128566	+	0.266123i
$133$	11.6900			0.0878949
$134$	107.832	+	171.850i	0.804714	+	1.28246i
$135$		−	28.6657i		−	0.212338i
$136$	−7.24220	−	65.3720i	−0.0532514	−	0.480676i
$137$	199.295			1.45471			0.727354	−	0.686263i	$-0.240750\pi$
$137$	199.295			1.45471			0.727354	+	0.686263i	$0.240750\pi$
$138$	15.4245	−	9.67850i	0.111772	−	0.0701341i
$139$			68.3395i			0.491651i	0.969314	+	0.245825i	$0.0790590\pi$
$139$			68.3395i			0.491651i	−0.969314	+	0.245825i	$0.920941\pi$
$140$	20.1202	+	9.72024i	0.143716	+	0.0694303i
$141$	16.1884			0.114811
$142$	−85.3737	−	136.059i	−0.601223	−	0.958163i
$143$			20.3029i			0.141978i
$144$	29.8341	+	37.6022i	0.207181	+	0.261127i
$145$	−269.050			−1.85551
$146$	9.49847	−	5.96005i	0.0650580	−	0.0408223i
$147$			83.0945i			0.565269i
$148$	−33.7565	+	69.8737i	−0.228084	+	0.472119i
$149$	158.760			1.06550			0.532751	−	0.846272i	$-0.321158\pi$
$149$	158.760			1.06550			0.532751	+	0.846272i	$0.321158\pi$
$150$	10.0053	+	15.9453i	0.0667017	+	0.106302i
$151$		−	262.554i		−	1.73877i	−0.494135	−	0.869385i	$-0.664515\pi$
$151$		−	262.554i		−	1.73877i	0.494135	−	0.869385i	$-0.335485\pi$
$152$	−91.7937	+	10.1693i	−0.603906	+	0.0669034i
$153$	−24.6645			−0.161206
$154$	−9.65987	+	6.06133i	−0.0627265	+	0.0393593i
$155$			327.357i			2.11198i
$156$	22.4927	+	10.8664i	0.144184	+	0.0696563i
$157$	112.088			0.713935			0.356967	−	0.934117i	$-0.383811\pi$
$157$	112.088			0.713935			0.356967	+	0.934117i	$0.383811\pi$
$158$	−30.3760	−	48.4099i	−0.192253	−	0.306392i
$159$		−	44.9971i		−	0.283001i
$160$	−166.446	−	58.8235i	−1.04029	−	0.367647i
$161$	5.32296			0.0330619
$162$	15.2470	−	9.56710i	0.0941172	−	0.0590562i
$163$		−	7.91246i		−	0.0485427i	−0.999705	−	0.0242714i	$-0.992273\pi$
$163$		−	7.91246i		−	0.0485427i	0.999705	−	0.0242714i	$-0.00772657\pi$
$164$	−114.152	+	236.288i	−0.696051	+	1.44078i
$165$	−53.8056			−0.326095
$166$	−110.486	−	176.081i	−0.665581	−	1.06073i
$167$		−	244.909i		−	1.46652i	−0.679949	−	0.733260i	$-0.737998\pi$
$167$		−	244.909i		−	1.46652i	0.679949	−	0.733260i	$-0.262002\pi$
$168$	1.54498	+	13.9459i	0.00919633	+	0.0830111i
$169$	13.0000			0.0769231
$170$	76.8374	−	48.2135i	0.451984	−	0.283609i
$171$			34.6332i			0.202534i
$172$	50.4920	+	24.3931i	0.293558	+	0.141820i
$173$	−168.979			−0.976759			−0.488379	−	0.872631i	$-0.662412\pi$
$173$	−168.979			−0.976759			−0.488379	+	0.872631i	$0.662412\pi$
$174$	−89.7946	−	143.105i	−0.516061	−	0.822441i
$175$			5.50267i			0.0314438i
$176$	70.5795	−	55.9987i	0.401020	−	0.318174i
$177$	66.5824			0.376172
$178$	118.376	−	74.2778i	0.665032	−	0.417291i
$179$			124.469i			0.695355i	0.937614	+	0.347678i	$0.113030\pi$
$179$			124.469i			0.695355i	−0.937614	+	0.347678i	$0.886970\pi$
$180$	−28.7975	+	59.6089i	−0.159986	+	0.331160i
$181$	−232.729			−1.28579			−0.642897	−	0.765952i	$-0.722268\pi$
$181$	−232.729			−1.28579			−0.642897	+	0.765952i	$0.722268\pi$
$182$	3.88108	+	6.18524i	0.0213246	+	0.0339848i
$183$			124.979i			0.682944i
$184$	−41.7975	+	4.63052i	−0.227161	+	0.0251659i
$185$	−107.025			−0.578513
$186$	−174.118	+	109.255i	−0.936117	+	0.587390i
$187$			46.2953i			0.247568i
$188$	−33.6629	−	16.2628i	−0.179058	−	0.0865042i
$189$	5.26169			0.0278396
$190$	−67.7002	−	107.893i	−0.356317	−	0.567859i
$191$			278.249i			1.45680i	0.685150	+	0.728402i	$0.259736\pi$
$191$			278.249i			1.45680i	−0.685150	+	0.728402i	$0.740264\pi$
$192$	−24.2634	−	108.163i	−0.126372	−	0.563350i
$193$	−6.91306			−0.0358190			−0.0179095	−	0.999840i	$-0.505701\pi$
$193$	−6.91306			−0.0358190			−0.0179095	+	0.999840i	$0.505701\pi$
$194$	−46.9241	+	29.4437i	−0.241877	+	0.151772i
$195$			34.4519i			0.176676i
$196$	83.4765	−	172.791i	0.425901	−	0.881586i
$197$	−278.468			−1.41354			−0.706771	−	0.707443i	$-0.749849\pi$
$197$	−278.468			−1.41354			−0.706771	+	0.707443i	$0.749849\pi$
$198$	−17.9575	−	28.6187i	−0.0906944	−	0.144539i
$199$		−	148.075i		−	0.744097i	−0.928213	−	0.372049i	$-0.878655\pi$
$199$		−	148.075i		−	0.744097i	0.928213	−	0.372049i	$-0.121345\pi$
$200$	−4.78685	−	43.2087i	−0.0239343	−	0.216043i
$201$	−175.699			−0.874124
$202$	−67.1606	+	42.1416i	−0.332478	+	0.208622i
$203$		−	49.3850i		−	0.243276i
$204$	51.2885	+	24.7779i	0.251414	+	0.121460i
$205$	−361.920			−1.76546
$206$	−85.9167	−	136.925i	−0.417072	−	0.664683i
$207$			15.7700i			0.0761834i
$208$	−35.8561	−	45.1922i	−0.172385	−	0.217270i
$209$	65.0067			0.311037
$210$	−16.3918	+	10.2854i	−0.0780561	+	0.0489782i
$211$			390.419i			1.85033i	0.379568	+	0.925164i	$0.376073\pi$
$211$			390.419i			1.85033i	−0.379568	+	0.925164i	$0.623927\pi$
$212$	−45.2040	+	93.5693i	−0.213227	+	0.441365i
$213$	139.106			0.653081
$214$	103.126	+	164.350i	0.481895	+	0.767992i
$215$			77.3382i			0.359712i
$216$	−41.3165	+	4.57722i	−0.191280	+	0.0211908i
$217$	−60.0876			−0.276901
$218$	357.598	−	224.384i	1.64036	−	1.02928i
$219$			9.71120i			0.0443434i
$220$	111.886	+	54.0530i	0.508573	+	0.245695i
$221$	29.6430			0.134131
$222$	−35.7193	−	56.9254i	−0.160898	−	0.256421i
$223$			317.454i			1.42356i	0.702403	+	0.711779i	$0.252110\pi$
$223$			317.454i			1.42356i	−0.702403	+	0.711779i	$0.747890\pi$
$224$	10.7973	−	30.5518i	0.0482021	−	0.136392i
$225$	−16.3024			−0.0724551
$226$	115.917	−	72.7349i	0.512906	−	0.321836i
$227$			428.142i			1.88609i	0.332668	+	0.943044i	$0.392051\pi$
$227$			428.142i			1.88609i	−0.332668	+	0.943044i	$0.607949\pi$
$228$	34.7925	−	72.0181i	0.152599	−	0.315869i
$229$	409.617			1.78872			0.894361	−	0.447345i	$-0.147631\pi$
$229$	409.617			1.78872			0.894361	+	0.447345i	$0.147631\pi$
$230$	−30.8268	−	49.1283i	−0.134029	−	0.213601i
$231$		−	9.87622i		−	0.0427542i
$232$	42.9607	+	387.787i	0.185176	+	1.67149i
$233$	−84.1548			−0.361180			−0.180590	−	0.983559i	$-0.557801\pi$
$233$	−84.1548			−0.361180			−0.180590	+	0.983559i	$0.557801\pi$
$234$	−18.3246	+	11.4982i	−0.0783102	+	0.0491377i
$235$		−	51.5611i		−	0.219409i
$236$	−138.455	−	66.8885i	−0.586673	−	0.283426i
$237$	49.4941			0.208836
$238$	8.84977	+	14.1038i	0.0371839	+	0.0592596i
$239$		−	243.858i		−	1.02033i	−0.860078	−	0.510163i	$-0.829585\pi$
$239$		−	243.858i		−	1.02033i	0.860078	−	0.510163i	$-0.170415\pi$
$240$	119.766	−	95.0238i	0.499025	−	0.395933i
$241$	−222.925			−0.925002			−0.462501	−	0.886619i	$-0.653048\pi$
$241$	−222.925			−0.925002			−0.462501	+	0.886619i	$0.653048\pi$
$242$	151.270	−	94.9181i	0.625082	−	0.392223i
$243$			15.5885i			0.0641500i
$244$	125.553	−	259.887i	0.514563	−	1.06511i
$245$	264.662			1.08025
$246$	−120.790	−	192.501i	−0.491015	−	0.782526i
$247$		−	41.6240i		−	0.168518i
$248$	471.826	−	52.2710i	1.90253	−	0.210770i
$249$	180.025			0.722990
$250$	−182.861	+	114.741i	−0.731444	+	0.458963i
$251$		−	441.458i		−	1.75880i	−0.476085	−	0.879399i	$-0.657945\pi$
$251$		−	441.458i		−	1.75880i	0.476085	−	0.879399i	$-0.342055\pi$
$252$	−10.9414	−	5.28589i	−0.0434184	−	0.0209757i
$253$	29.6003			0.116997
$254$	−49.9724	−	79.6405i	−0.196742	−	0.313545i
$255$			78.5582i			0.308071i
$256$	−58.2061	+	249.295i	−0.227367	+	0.973809i
$257$	−289.124			−1.12500			−0.562498	−	0.826799i	$-0.690160\pi$
$257$	−289.124			−1.12500			−0.562498	+	0.826799i	$0.690160\pi$
$258$	−41.1354	+	25.8114i	−0.159439	+	0.100044i
$259$		−	19.6448i		−	0.0758487i
$260$	34.6103	−	71.6410i	0.133116	−	0.275542i
$261$	146.310			0.560574
$262$	90.5213	+	144.263i	0.345501	+	0.550621i
$263$		−	411.852i		−	1.56598i	−0.622037	−	0.782988i	$-0.713695\pi$
$263$		−	411.852i		−	1.56598i	0.622037	−	0.782988i	$-0.286305\pi$
$264$	8.59146	+	77.5511i	0.0325434	+	0.293754i
$265$	−143.319			−0.540827
$266$	19.8042	−	12.4266i	0.0744518	−	0.0467166i
$267$			121.027i			0.453284i
$268$	365.357	+	176.507i	1.36327	+	0.658607i
$269$	−17.9467			−0.0667165			−0.0333583	−	0.999443i	$-0.510620\pi$
$269$	−17.9467			−0.0667165			−0.0333583	+	0.999443i	$0.510620\pi$
$270$	−30.4719	−	48.5628i	−0.112859	−	0.179862i
$271$		−	323.464i		−	1.19359i	−0.802392	−	0.596797i	$-0.796440\pi$
$271$		−	323.464i		−	1.19359i	0.802392	−	0.596797i	$-0.203560\pi$
$272$	−81.7602	−	103.049i	−0.300589	−	0.378856i
$273$	−6.32377			−0.0231640
$274$	337.627	−	211.853i	1.23222	−	0.773185i
$275$			30.5997i			0.111271i
$276$	15.8425	−	32.7929i	0.0574003	−	0.118815i
$277$	179.377			0.647571			0.323786	−	0.946130i	$-0.395044\pi$
$277$	179.377			0.647571			0.323786	+	0.946130i	$0.395044\pi$
$278$	72.6456	+	115.775i	0.261315	+	0.416455i
$279$		−	178.017i		−	0.638055i
$280$	44.4186	−	4.92089i	0.158638	−	0.0175746i
$281$	437.349			1.55640			0.778201	−	0.628016i	$-0.216133\pi$
$281$	437.349			1.55640			0.778201	+	0.628016i	$0.216133\pi$
$282$	27.4249	−	17.2084i	0.0972512	−	0.0610227i
$283$			492.934i			1.74182i	0.491447	+	0.870908i	$0.336468\pi$
$283$			492.934i			1.74182i	−0.491447	+	0.870908i	$0.663532\pi$
$284$	−289.265	−	139.746i	−1.01854	−	0.492063i
$285$	110.310			0.387051
$286$	21.5822	+	34.3953i	0.0754623	+	0.120263i
$287$		−	66.4317i		−	0.231469i
$288$	90.5138	+	31.9883i	0.314284	+	0.111071i
$289$	−221.407			−0.766115
$290$	−455.800	+	286.003i	−1.57172	+	0.986216i
$291$		−	47.9750i		−	0.164863i
$292$	9.75585	−	20.1940i	0.0334104	−	0.0691574i
$293$	61.8712			0.211164			0.105582	−	0.994411i	$-0.466329\pi$
$293$	61.8712			0.211164			0.105582	+	0.994411i	$0.466329\pi$
$294$	88.3303	+	140.771i	0.300443	+	0.478813i
$295$		−	212.070i		−	0.718881i
$296$	17.0893	+	154.257i	0.0577341	+	0.521139i
$297$	29.2596			0.0985171
$298$	268.956	−	168.763i	0.902538	−	0.566320i
$299$		−	18.9531i		−	0.0633885i
$300$	33.9000	+	16.3774i	0.113000	+	0.0545912i
$301$	−14.1957			−0.0471618
$302$	−279.098	−	444.796i	−0.924166	−	1.47283i
$303$		−	68.6647i		−	0.226616i
$304$	−144.699	+	114.806i	−0.475982	+	0.377650i
$305$	398.067			1.30514
$306$	−41.7843	+	26.2186i	−0.136550	+	0.0856817i
$307$		−	446.721i		−	1.45512i	−0.686045	−	0.727559i	$-0.740655\pi$
$307$		−	446.721i		−	1.45512i	0.686045	−	0.727559i	$-0.259345\pi$
$308$	−9.92163	+	20.5371i	−0.0322131	+	0.0666789i
$309$	139.991			0.453046
$310$	347.984	+	554.579i	1.12253	+	1.78896i
$311$			248.932i			0.800423i	0.916423	+	0.400211i	$0.131063\pi$
$311$			248.932i			0.800423i	−0.916423	+	0.400211i	$0.868937\pi$
$312$	49.6562	−	5.50113i	0.159154	−	0.0176318i
$313$	−56.7003			−0.181151			−0.0905756	−	0.995890i	$-0.528871\pi$
$313$	−56.7003			−0.181151			−0.0905756	+	0.995890i	$0.528871\pi$
$314$	189.889	−	119.151i	0.604742	−	0.379460i
$315$		−	16.7589i		−	0.0532028i
$316$	−102.921	−	49.7217i	−0.325698	−	0.157347i
$317$	−57.8199			−0.182397			−0.0911986	−	0.995833i	$-0.529070\pi$
$317$	−57.8199			−0.182397			−0.0911986	+	0.995833i	$0.529070\pi$
$318$	−47.8324	−	76.2301i	−0.150416	−	0.239717i
$319$		−	274.624i		−	0.860890i
$320$	−344.508	+	77.2808i	−1.07659	+	0.241502i
$321$	−168.031			−0.523461
$322$	9.01768	−	5.65836i	0.0280052	−	0.0175726i
$323$		−	94.9123i		−	0.293846i
$324$	15.6601	−	32.4154i	0.0483337	−	0.100048i
$325$	19.5930			0.0602863
$326$	−8.41103	−	13.4046i	−0.0258007	−	0.0411183i
$327$			365.606i			1.11806i
$328$	57.7899	+	521.642i	0.176189	+	1.59037i
$329$	9.46424			0.0287667
$330$	−91.1526	+	57.1959i	−0.276220	+	0.173321i
$331$			49.0850i			0.148293i	0.997247	+	0.0741465i	$0.0236232\pi$
$331$			49.0850i			0.148293i	−0.997247	+	0.0741465i	$0.976377\pi$
$332$	−374.352	−	180.852i	−1.12757	−	0.544736i
$333$	58.2003			0.174776
$334$	−260.341	−	414.902i	−0.779463	−	1.24222i
$335$			559.614i			1.67049i
$336$	17.4420	+	21.9835i	0.0519106	+	0.0654270i
$337$	−402.253			−1.19363			−0.596815	−	0.802379i	$-0.703567\pi$
$337$	−402.253			−1.19363			−0.596815	+	0.802379i	$0.703567\pi$
$338$	22.0234	−	13.8191i	0.0651581	−	0.0408850i
$339$			118.513i			0.349596i
$340$	78.9194	−	163.358i	0.232116	−	0.480464i
$341$	−334.139			−0.979881
$342$	36.8155	+	58.6725i	0.107648	+	0.171557i
$343$			98.1978i			0.286291i
$344$	111.469	−	12.3490i	0.324038	−	0.0358984i
$345$	50.2286			0.145590
$346$	−286.269	+	179.627i	−0.827368	+	0.519153i
$347$		−	81.1956i		−	0.233993i	−0.993132	−	0.116997i	$-0.962673\pi$
$347$		−	81.1956i		−	0.233993i	0.993132	−	0.116997i	$-0.0373266\pi$
$348$	−304.244	−	146.982i	−0.874264	−	0.422363i
$349$	230.981			0.661835			0.330918	−	0.943660i	$-0.392642\pi$
$349$	230.981			0.661835			0.330918	+	0.943660i	$0.392642\pi$
$350$	5.84940	+	9.32213i	0.0167126	+	0.0266347i
$351$		−	18.7350i		−	0.0533761i
$352$	60.0422	−	169.895i	0.170574	−	0.482655i
$353$	274.410			0.777366			0.388683	−	0.921372i	$-0.372930\pi$
$353$	274.410			0.777366			0.388683	+	0.921372i	$0.372930\pi$
$354$	112.798	−	70.7778i	0.318638	−	0.199937i
$355$		−	443.064i		−	1.24807i
$356$	121.583	−	251.669i	0.341526	−	0.706936i
$357$	−14.4196			−0.0403912
$358$	132.311	+	210.863i	0.369585	+	0.589004i
$359$		−	537.223i		−	1.49644i	−0.663450	−	0.748221i	$-0.730908\pi$
$359$		−	537.223i		−	1.49644i	0.663450	−	0.748221i	$-0.269092\pi$
$360$	14.5788	+	131.596i	0.0404966	+	0.365545i
$361$	227.726			0.630821
$362$	−394.268	+	247.393i	−1.08914	+	0.683407i
$363$			154.658i			0.426054i
$364$	13.1500	+	6.35284i	0.0361263	+	0.0174529i
$365$	30.9309			0.0847422
$366$	132.854	+	211.728i	0.362989	+	0.578491i
$367$			567.303i			1.54578i	0.634537	+	0.772892i	$0.281191\pi$
$367$			567.303i			1.54578i	−0.634537	+	0.772892i	$0.718809\pi$
$368$	−65.8873	+	52.2759i	−0.179042	+	0.142054i
$369$	196.813			0.533368
$370$	−181.312	+	113.769i	−0.490032	+	0.307483i
$371$		−	26.3068i		−	0.0709077i
$372$	−178.836	+	370.178i	−0.480742	+	0.995103i
$373$	−511.015			−1.37001			−0.685007	−	0.728537i	$-0.740201\pi$
$373$	−511.015			−1.37001			−0.685007	+	0.728537i	$0.740201\pi$
$374$	49.2124	+	78.4293i	0.131584	+	0.209704i
$375$		−	186.956i		−	0.498550i
$376$	−74.3162	+	8.23307i	−0.197649	+	0.0218965i
$377$	−175.842			−0.466425
$378$	8.91388	−	5.59324i	0.0235817	−	0.0147969i
$379$		−	245.900i		−	0.648813i	−0.945918	−	0.324406i	$-0.894836\pi$
$379$		−	245.900i		−	0.648813i	0.945918	−	0.324406i	$-0.105164\pi$
$380$	−229.383	−	110.817i	−0.603640	−	0.291623i
$381$	81.4241			0.213712
$382$	295.782	+	471.385i	0.774299	+	1.23399i
$383$		−	277.986i		−	0.725812i	−0.931826	−	0.362906i	$-0.881785\pi$
$383$		−	277.986i		−	0.725812i	0.931826	−	0.362906i	$-0.118215\pi$
$384$	−156.084	−	157.448i	−0.406468	−	0.410021i
$385$	−31.4565			−0.0817052
$386$	−11.7115	+	7.34866i	−0.0303406	+	0.0190380i
$387$		−	42.0566i		−	0.108674i
$388$	−48.1956	+	99.7617i	−0.124215	+	0.257118i
$389$	132.554			0.340756			0.170378	−	0.985379i	$-0.445501\pi$
$389$	132.554			0.340756			0.170378	+	0.985379i	$0.445501\pi$
$390$	36.6227	+	58.3652i	0.0939044	+	0.149654i
$391$		−	43.2175i		−	0.110531i
$392$	−42.2602	−	381.463i	−0.107807	−	0.973120i
$393$	−147.494			−0.375302
$394$	−471.755	+	296.014i	−1.19735	+	0.751305i
$395$		−	157.643i		−	0.399095i
$396$	−60.8439	−	29.3941i	−0.153646	−	0.0742276i
$397$	−469.545			−1.18273			−0.591366	−	0.806403i	$-0.701411\pi$
$397$	−469.545			−1.18273			−0.591366	+	0.806403i	$0.701411\pi$
$398$	−157.406	−	250.856i	−0.395492	−	0.630291i
$399$			20.2477i			0.0507462i
$400$	−54.0408	−	68.1118i	−0.135102	−	0.170279i
$401$	169.002			0.421451			0.210726	−	0.977545i	$-0.432417\pi$
$401$	169.002			0.421451			0.210726	+	0.977545i	$0.432417\pi$
$402$	−297.653	+	186.770i	−0.740431	+	0.464602i
$403$			213.950i			0.530894i
$404$	−68.9804	+	142.785i	−0.170744	+	0.353428i
$405$	49.6504			0.122594
$406$	−52.4968	−	83.6637i	−0.129303	−	0.206068i
$407$		−	109.242i		−	0.268409i
$408$	113.228	−	12.5439i	0.277519	−	0.0307447i
$409$	330.022			0.806900			0.403450	−	0.915002i	$-0.367811\pi$
$409$	330.022			0.806900			0.403450	+	0.915002i	$0.367811\pi$
$410$	−613.132	+	384.725i	−1.49544	+	0.938353i
$411$			345.189i			0.839876i
$412$	−291.105	−	140.635i	−0.706565	−	0.341347i
$413$	38.9262			0.0942523
$414$	16.7637	+	26.7161i	0.0404919	+	0.0645315i
$415$		−	573.392i		−	1.38167i
$416$	−108.784	−	38.4452i	−0.261500	−	0.0924163i
$417$	−118.367			−0.283855
$418$	110.129	−	69.1029i	0.263465	−	0.165318i
$419$		−	459.934i		−	1.09769i	−0.835923	−	0.548847i	$-0.815067\pi$
$419$		−	459.934i		−	1.09769i	0.835923	−	0.548847i	$-0.184933\pi$
$420$	−16.8359	+	34.8493i	−0.0400856	+	0.0829745i
$421$	−62.9112			−0.149433			−0.0747163	−	0.997205i	$-0.523805\pi$
$421$	−62.9112			−0.149433			−0.0747163	+	0.997205i	$0.523805\pi$
$422$	415.020	+	661.413i	0.983460	+	1.56733i
$423$			28.0391i			0.0662862i
$424$	22.8846	+	206.569i	0.0539732	+	0.487191i
$425$	44.6766			0.105122
$426$	235.661	−	147.872i	0.553196	−	0.347116i
$427$			73.0667i			0.171116i
$428$	349.412	+	168.804i	0.816384	+	0.394401i
$429$	−35.1657			−0.0819712
$430$	82.2113	+	131.019i	0.191189	+	0.304696i
$431$			383.771i			0.890421i	0.895426	+	0.445210i	$0.146871\pi$
$431$			383.771i			0.890421i	−0.895426	+	0.445210i	$0.853129\pi$
$432$	−65.1290	+	51.6742i	−0.150761	+	0.119616i
$433$	536.435			1.23888			0.619439	−	0.785044i	$-0.287360\pi$
$433$	536.435			1.23888			0.619439	+	0.785044i	$0.287360\pi$
$434$	−101.795	+	63.8738i	−0.234551	+	0.147175i
$435$		−	466.008i		−	1.07128i
$436$	367.288	−	760.261i	0.842403	−	1.74372i
$437$	−60.6850			−0.138867
$438$	10.3231	+	16.4518i	0.0235687	+	0.0375613i
$439$		−	263.036i		−	0.599170i	−0.954070	−	0.299585i	$-0.903152\pi$
$439$		−	263.036i		−	0.599170i	0.954070	−	0.299585i	$-0.0968482\pi$
$440$	247.006	−	27.3644i	0.561378	−	0.0621919i
$441$	−143.924			−0.326358
$442$	50.2185	−	31.5108i	0.113616	−	0.0712915i
$443$			696.607i			1.57248i	0.617924	+	0.786238i	$0.287974\pi$
$443$			696.607i			1.57248i	−0.617924	+	0.786238i	$0.712026\pi$
$444$	−121.025	−	58.4680i	−0.272578	−	0.131685i
$445$	385.480			0.866246
$446$	337.457	+	537.801i	0.756629	+	1.20583i
$447$			274.980i			0.615167i
$448$	−14.1852	−	63.2357i	−0.0316633	−	0.141151i
$449$	−189.583			−0.422233			−0.211117	−	0.977461i	$-0.567710\pi$
$449$	−189.583			−0.422233			−0.211117	+	0.977461i	$0.567710\pi$
$450$	−27.6180	+	17.3296i	−0.0613734	+	0.0385103i
$451$		−	369.418i		−	0.819109i
$452$	119.058	−	246.442i	0.263402	−	0.545225i
$453$	454.758			1.00388
$454$	455.120	+	725.319i	1.00247	+	1.59762i
$455$			20.1417i			0.0442674i
$456$	−17.6138	−	158.991i	−0.0386267	−	0.348665i
$457$	149.051			0.326150			0.163075	−	0.986614i	$-0.447859\pi$
$457$	149.051			0.326150			0.163075	+	0.986614i	$0.447859\pi$
$458$	693.937	−	435.428i	1.51515	−	0.950716i
$459$		−	42.7201i		−	0.0930721i
$460$	−104.448	−	50.4595i	−0.227060	−	0.109695i
$461$	−34.1785			−0.0741400			−0.0370700	−	0.999313i	$-0.511802\pi$
$461$	−34.1785			−0.0741400			−0.0370700	+	0.999313i	$0.511802\pi$
$462$	−10.4985	−	16.7314i	−0.0227241	−	0.0362151i
$463$			553.129i			1.19466i	0.801994	+	0.597332i	$0.203772\pi$
$463$			553.129i			1.19466i	−0.801994	+	0.597332i	$0.796228\pi$
$464$	485.002	+	611.286i	1.04526	+	1.31743i
$465$	−566.999			−1.21935
$466$	−142.568	+	89.4575i	−0.305939	+	0.191969i
$467$			8.93243i			0.0191273i	0.999954	+	0.00956363i	$0.00304424\pi$
$467$			8.93243i			0.0191273i	−0.999954	+	0.00956363i	$0.996956\pi$
$468$	−18.8211	+	38.9585i	−0.0402161	+	0.0832447i
$469$	−102.719			−0.219018
$470$	−54.8101	−	87.3502i	−0.116617	−	0.185852i
$471$			194.142i			0.412190i
$472$	−305.661	+	33.8625i	−0.647587	+	0.0717425i
$473$	−78.9405			−0.166893
$474$	83.8485	−	52.6128i	0.176896	−	0.110997i
$475$		−	62.7339i		−	0.132071i
$476$	29.9849	+	14.4859i	0.0629936	+	0.0304327i
$477$	77.9373			0.163391
$478$	−259.224	−	413.122i	−0.542309	−	0.864272i
$479$		−	569.142i		−	1.18819i	−0.804396	−	0.594094i	$-0.797511\pi$
$479$		−	569.142i		−	1.18819i	0.804396	−	0.594094i	$-0.202489\pi$
$480$	101.885	−	288.293i	0.212261	−	0.600611i
$481$	−69.9481			−0.145422
$482$	−377.660	+	236.972i	−0.783527	+	0.491644i
$483$			9.21964i			0.0190883i
$484$	155.369	−	321.603i	0.321010	−	0.664470i
$485$	−152.804			−0.315060
$486$	16.5707	+	26.4086i	0.0340961	+	0.0543386i
$487$		−	225.936i		−	0.463935i	−0.972724	−	0.231968i	$-0.925484\pi$
$487$		−	225.936i		−	0.463935i	0.972724	−	0.231968i	$-0.0745163\pi$
$488$	−63.5617	−	573.742i	−0.130249	−	1.17570i
$489$	13.7048			0.0280261
$490$	448.367	−	281.339i	0.915034	−	0.574161i
$491$			876.858i			1.78586i	0.450194	+	0.892931i	$0.351355\pi$
$491$			876.858i			1.78586i	−0.450194	+	0.892931i	$0.648645\pi$
$492$	−409.262	−	197.718i	−0.831834	−	0.401865i
$493$	−400.961			−0.813309
$494$	−44.2468	−	70.5156i	−0.0895683	−	0.142744i
$495$		−	93.1940i		−	0.188271i
$496$	743.761	−	590.110i	1.49952	−	1.18974i
$497$	81.3261			0.163634
$498$	304.981	−	191.368i	0.612412	−	0.384273i
$499$		−	259.904i		−	0.520851i	−0.965494	−	0.260425i	$-0.916137\pi$
$499$		−	259.904i		−	0.520851i	0.965494	−	0.260425i	$-0.0838628\pi$
$500$	−187.816	+	388.767i	−0.375632	+	0.777533i
$501$	424.194			0.846695
$502$	−469.275	−	747.879i	−0.934811	−	1.48980i
$503$			172.379i			0.342702i	0.985210	+	0.171351i	$0.0548132\pi$
$503$			172.379i			0.342702i	−0.985210	+	0.171351i	$0.945187\pi$
$504$	−24.1549	+	2.67599i	−0.0479265	+	0.00530951i
$505$	−218.702			−0.433074
$506$	50.1461	−	31.4654i	0.0991031	−	0.0621847i
$507$			22.5167i			0.0444116i
$508$	−169.317	−	81.7985i	−0.333302	−	0.161021i
$509$	−713.109			−1.40100			−0.700500	−	0.713653i	$-0.747039\pi$
$509$	−713.109			−1.40100			−0.700500	+	0.713653i	$0.747039\pi$
$510$	83.5082	+	133.086i	0.163742	+	0.260953i
$511$			5.67748i			0.0111105i
$512$	166.396	+	484.207i	0.324992	+	0.945717i
$513$	−59.9865			−0.116933
$514$	−489.808	+	307.342i	−0.952933	+	0.597942i
$515$		−	445.882i		−	0.865791i
$516$	−42.2500	+	87.4547i	−0.0818799	+	0.169486i
$517$	52.6294			0.101798
$518$	−20.8827	−	33.2805i	−0.0403140	−	0.0642480i
$519$		−	292.681i		−	0.563932i
$520$	−17.5215	−	158.159i	−0.0336952	−	0.304151i
$521$	−475.193			−0.912078			−0.456039	−	0.889960i	$-0.650732\pi$
$521$	−475.193			−0.912078			−0.456039	+	0.889960i	$0.650732\pi$
$522$	247.865	−	155.529i	0.474837	−	0.297948i
$523$			807.769i			1.54449i	0.635324	+	0.772246i	$0.280867\pi$
$523$			807.769i			1.54449i	−0.635324	+	0.772246i	$0.719133\pi$
$524$	306.706	+	148.172i	0.585317	+	0.282771i
$525$	−9.53091			−0.0181541
$526$	−437.803	−	697.722i	−0.832325	−	1.32647i
$527$			487.856i			0.925723i
$528$	96.9926	+	122.247i	0.183698	+	0.231529i
$529$	501.368			0.947765
$530$	−242.799	+	152.350i	−0.458110	+	0.287453i
$531$			115.324i			0.217183i
$532$	20.3408	−	42.1041i	0.0382346	−	0.0791431i
$533$	−236.539			−0.443789
$534$	128.653	+	205.033i	0.240923	+	0.383956i
$535$			535.191i			1.00036i
$536$	806.584	−	89.3569i	1.50482	−	0.166711i
$537$	−215.586			−0.401464
$538$	−30.4038	+	19.0776i	−0.0565126	+	0.0354602i
$539$			270.146i			0.501198i
$540$	−103.246	−	49.8787i	−0.191196	−	0.0923680i
$541$	−38.9119			−0.0719258			−0.0359629	−	0.999353i	$-0.511450\pi$
$541$	−38.9119			−0.0719258			−0.0359629	+	0.999353i	$0.511450\pi$
$542$	−343.846	−	547.984i	−0.634402	−	1.01104i
$543$		−	403.098i		−	0.742354i
$544$	−248.053	−	87.6639i	−0.455979	−	0.161147i
$545$	1164.48			2.13667
$546$	−10.7132	+	6.72223i	−0.0196212	+	0.0123118i
$547$			329.904i			0.603116i	0.953448	+	0.301558i	$0.0975066\pi$
$547$			329.904i			0.603116i	−0.953448	+	0.301558i	$0.902493\pi$
$548$	346.776	−	717.803i	0.632803	−	1.30986i
$549$	−216.470			−0.394298
$550$	32.5278	+	51.8392i	0.0591414	+	0.0942530i
$551$			563.020i			1.02181i
$552$	−8.02029	−	72.3955i	−0.0145295	−	0.131151i
$553$	28.9359			0.0523253
$554$	303.885	−	190.680i	0.548529	−	0.344188i
$555$		−	185.373i		−	0.334005i
$556$	246.139	+	118.912i	0.442696	+	0.213870i
$557$	−499.645			−0.897028			−0.448514	−	0.893776i	$-0.648047\pi$
$557$	−499.645			−0.897028			−0.448514	+	0.893776i	$0.648047\pi$
$558$	−189.234	−	301.581i	−0.339130	−	0.540468i
$559$			50.5458i			0.0904218i
$560$	70.0191	−	55.5540i	0.125034	−	0.0992036i
$561$	−80.1858			−0.142934
$562$	740.917	−	464.907i	1.31836	−	0.827236i
$563$			79.9277i			0.141967i	0.997477	+	0.0709837i	$0.0226138\pi$
$563$			79.9277i			0.141967i	−0.997477	+	0.0709837i	$0.977386\pi$
$564$	28.1680	−	58.3058i	0.0499432	−	0.103379i
$565$	377.473			0.668093
$566$	523.994	+	835.084i	0.925784	+	1.47541i
$567$			9.11352i			0.0160732i
$568$	−638.598	+	70.7467i	−1.12429	+	0.124554i
$569$	822.992			1.44638			0.723192	−	0.690647i	$-0.242674\pi$
$569$	822.992			1.44638			0.723192	+	0.690647i	$0.242674\pi$
$570$	186.876	−	117.260i	0.327853	−	0.205720i
$571$		−	237.913i		−	0.416660i	−0.978059	−	0.208330i	$-0.933197\pi$
$571$		−	237.913i		−	0.416660i	0.978059	−	0.208330i	$-0.0668028\pi$
$572$	73.1253	+	35.3274i	0.127841	+	0.0617611i
$573$	−481.942			−0.841086
$574$	−70.6176	−	112.543i	−0.123027	−	0.196067i
$575$		−	28.5654i		−	0.0496789i
$576$	187.344	−	42.0254i	0.325250	−	0.0729608i
$577$	−764.467			−1.32490			−0.662450	−	0.749106i	$-0.730483\pi$
$577$	−764.467			−1.32490			−0.662450	+	0.749106i	$0.730483\pi$
$578$	−375.088	+	235.358i	−0.648941	+	0.407194i
$579$		−	11.9738i		−	0.0206801i
$580$	−468.150	+	969.040i	−0.807156	+	1.67076i
$581$	105.248			0.181150
$582$	−50.9980	−	81.2749i	−0.0876254	−	0.139648i
$583$		−	146.289i		−	0.250924i
$584$	−4.93892	−	44.5813i	−0.00845705	−	0.0763379i
$585$	−59.6724			−0.102004
$586$	104.817	−	65.7697i	0.178868	−	0.112235i
$587$		−	349.212i		−	0.594910i	−0.954736	−	0.297455i	$-0.903862\pi$
$587$		−	349.212i		−	0.594910i	0.954736	−	0.297455i	$-0.0961379\pi$
$588$	299.283	+	144.586i	0.508984	+	0.245894i
$589$	685.036			1.16305
$590$	−225.433	−	359.270i	−0.382089	−	0.608932i
$591$		−	482.320i		−	0.816109i
$592$	192.928	+	243.162i	0.325892	+	0.410747i
$593$	−240.972			−0.406360			−0.203180	−	0.979141i	$-0.565128\pi$
$593$	−240.972			−0.406360			−0.203180	+	0.979141i	$0.565128\pi$
$594$	49.5690	−	31.1033i	0.0834494	−	0.0523624i
$595$			45.9277i			0.0771894i
$596$	276.244	−	571.807i	0.463497	−	0.959408i
$597$	256.474			0.429605
$598$	−20.1474	−	32.1087i	−0.0336913	−	0.0536935i
$599$			429.935i			0.717755i	0.933385	+	0.358878i	$0.116840\pi$
$599$			429.935i			0.717755i	−0.933385	+	0.358878i	$0.883160\pi$
$600$	74.8397	−	8.29107i	0.124733	−	0.0138184i
$601$	812.327			1.35163			0.675813	−	0.737073i	$-0.263793\pi$
$601$	812.327			1.35163			0.675813	+	0.737073i	$0.263793\pi$
$602$	−24.0491	+	15.0902i	−0.0399486	+	0.0250668i
$603$		−	304.319i		−	0.504676i
$604$	−945.646	−	456.849i	−1.56564	−	0.756372i
$605$	492.597			0.814210
$606$	−72.9914	−	116.326i	−0.120448	−	0.191956i
$607$			772.664i			1.27292i	0.771308	+	0.636462i	$0.219603\pi$
$607$			772.664i			1.27292i	−0.771308	+	0.636462i	$0.780397\pi$
$608$	−123.096	+	348.310i	−0.202460	+	0.572878i
$609$	85.5374			0.140456
$610$	674.369	−	423.150i	1.10552	−	0.693688i
$611$		−	33.6988i		−	0.0551534i
$612$	−42.9165	+	88.8344i	−0.0701251	+	0.145154i
$613$	323.297			0.527402			0.263701	−	0.964605i	$-0.415057\pi$
$613$	323.297			0.527402			0.263701	+	0.964605i	$0.415057\pi$
$614$	−474.869	−	756.794i	−0.773403	−	1.23256i
$615$		−	626.863i		−	1.01929i
$616$	5.02284	+	45.3389i	0.00815397	+	0.0736021i
$617$	−440.441			−0.713842			−0.356921	−	0.934135i	$-0.616173\pi$
$617$	−440.441			−0.713842			−0.356921	+	0.934135i	$0.616173\pi$
$618$	237.160	−	148.812i	0.383755	−	0.240796i
$619$			444.566i			0.718200i	0.933299	+	0.359100i	$0.116916\pi$
$619$			444.566i			0.718200i	−0.933299	+	0.359100i	$0.883084\pi$
$620$	1179.05	+	569.606i	1.90169	+	0.918719i
$621$	−27.3144			−0.0439845
$622$	264.617	+	421.717i	0.425429	+	0.678002i
$623$			70.7562i			0.113573i
$624$	78.2753	−	62.1046i	0.125441	−	0.0995266i
$625$	−731.323			−1.17012
$626$	−96.0566	+	60.2731i	−0.153445	+	0.0962829i
$627$			112.595i			0.179577i
$628$	195.034	−	403.708i	0.310564	−	0.642847i
$629$	−159.498			−0.253574
$630$	−17.8149	−	28.3914i	−0.0282776	−	0.0450657i
$631$			394.541i			0.625263i	0.949874	+	0.312632i	$0.101211\pi$
$631$			394.541i			0.625263i	−0.949874	+	0.312632i	$0.898789\pi$
$632$	−227.214	+	25.1717i	−0.359515	+	0.0398287i
$633$	−676.226			−1.06829
$634$	−97.9533	+	61.4632i	−0.154500	+	0.0969452i
$635$		−	259.342i		−	0.408413i
$636$	−162.067	−	78.2957i	−0.254822	−	0.123106i
$637$	172.975			0.271546
$638$	−291.928	−	465.243i	−0.457568	−	0.729221i
$639$			240.939i			0.377057i
$640$	−501.484	+	497.138i	−0.783569	+	0.776778i
$641$	941.707			1.46912			0.734561	−	0.678543i	$-0.237388\pi$
$641$	941.707			1.46912			0.734561	+	0.678543i	$0.237388\pi$
$642$	−284.663	+	178.619i	−0.443400	+	0.278222i
$643$		−	187.307i		−	0.291301i	−0.989336	−	0.145651i	$-0.953472\pi$
$643$		−	187.307i		−	0.291301i	0.989336	−	0.145651i	$-0.0465275\pi$
$644$	9.26203	−	19.1718i	0.0143820	−	0.0297698i
$645$	−133.954			−0.207680
$646$	−100.893	−	160.792i	−0.156181	−	0.248904i
$647$		−	324.114i		−	0.500949i	−0.968123	−	0.250474i	$-0.919413\pi$
$647$		−	324.114i		−	0.500949i	0.968123	−	0.250474i	$-0.0805866\pi$
$648$	−7.92798	−	71.5622i	−0.0122345	−	0.110435i
$649$	216.464			0.333534
$650$	33.1928	−	20.8276i	0.0510658	−	0.0320425i
$651$		−	104.075i		−	0.159869i
$652$	−28.4984	−	13.7678i	−0.0437092	−	0.0211163i
$653$	−746.434			−1.14308			−0.571542	−	0.820573i	$-0.693654\pi$
$653$	−746.434			−1.14308			−0.571542	+	0.820573i	$0.693654\pi$
$654$	388.644	+	619.377i	0.594256	+	0.947060i
$655$			469.779i			0.717219i
$656$	652.414	+	822.288i	0.994534	+	1.25349i
$657$	−16.8203			−0.0256016
$658$	16.0335	−	10.0606i	0.0243670	−	0.0152896i
$659$		−	797.604i		−	1.21032i	−0.796102	−	0.605162i	$-0.793108\pi$
$659$		−	797.604i		−	1.21032i	0.796102	−	0.605162i	$-0.206892\pi$
$660$	−93.6226	+	193.792i	−0.141852	+	0.293625i
$661$	−606.767			−0.917952			−0.458976	−	0.888449i	$-0.651784\pi$
$661$	−606.767			−0.917952			−0.458976	+	0.888449i	$0.651784\pi$
$662$	52.1779	+	83.1553i	0.0788185	+	0.125612i
$663$			51.3432i			0.0774407i
$664$	−826.442	+	91.5569i	−1.24464	+	0.137887i
$665$	64.4905			0.0969782
$666$	98.5978	−	61.8676i	0.148045	−	0.0928943i
$667$			256.367i			0.384358i
$668$	−882.091	−	426.145i	−1.32050	−	0.637942i
$669$	−549.846			−0.821892
$670$	594.876	+	948.048i	0.887875	+	1.41500i
$671$			406.314i			0.605536i
$672$	52.9173	+	18.7014i	0.0787460	+	0.0278295i
$673$	−402.160			−0.597563			−0.298782	−	0.954322i	$-0.596580\pi$
$673$	−402.160			−0.597563			−0.298782	+	0.954322i	$0.596580\pi$
$674$	−681.461	+	427.600i	−1.01107	+	0.634421i
$675$		−	28.2366i		−	0.0418320i
$676$	22.6202	−	46.8223i	0.0334618	−	0.0692637i
$677$	−673.548			−0.994901			−0.497450	−	0.867492i	$-0.665730\pi$
$677$	−673.548			−0.994901			−0.497450	+	0.867492i	$0.665730\pi$
$678$	125.980	+	200.774i	0.185812	+	0.296127i
$679$		−	28.0477i		−	0.0413074i
$680$	−39.9531	−	360.638i	−0.0587546	−	0.530351i
$681$	−741.564			−1.08893
$682$	−566.069	+	355.194i	−0.830013	+	0.520812i
$683$			562.406i			0.823435i	0.911312	+	0.411717i	$0.135071\pi$
$683$			562.406i			0.823435i	−0.911312	+	0.411717i	$0.864929\pi$
$684$	124.739	+	60.2624i	0.182367	+	0.0881029i
$685$	1099.45			1.60504
$686$	104.385	+	166.358i	0.152165	+	0.242504i
$687$			709.478i			1.03272i
$688$	175.714	−	139.414i	0.255398	−	0.202636i
$689$	−93.6690			−0.135949
$690$	85.0927	−	53.3935i	0.123323	−	0.0773819i
$691$			206.103i			0.298268i	0.988817	+	0.149134i	$0.0476486\pi$
$691$			206.103i			0.298268i	−0.988817	+	0.149134i	$0.952351\pi$
$692$	−294.026	+	608.615i	−0.424894	+	0.879502i
$693$	17.1061			0.0246841
$694$	−86.3118	−	137.554i	−0.124369	−	0.198205i
$695$			377.009i			0.542459i
$696$	−671.666	+	74.4102i	−0.965038	+	0.106911i
$697$	−539.364			−0.773837
$698$	391.306	−	245.535i	0.560611	−	0.351769i
$699$		−	145.760i		−	0.208527i
$700$	19.8191	+	9.57473i	0.0283129	+	0.0136782i
$701$	42.7330			0.0609601			0.0304801	−	0.999535i	$-0.490296\pi$
$701$	42.7330			0.0609601			0.0304801	+	0.999535i	$0.490296\pi$
$702$	−19.9155	−	31.7391i	−0.0283697	−	0.0452124i
$703$			223.963i			0.318582i
$704$	−78.8819	−	351.646i	−0.112048	−	0.499497i
$705$	89.3065			0.126676
$706$	464.881	−	291.701i	0.658472	−	0.413174i
$707$		−	40.1436i		−	0.0567802i
$708$	115.854	−	239.811i	0.163636	−	0.338716i
$709$	−89.9432			−0.126859			−0.0634296	−	0.997986i	$-0.520204\pi$
$709$	−89.9432			−0.126859			−0.0634296	+	0.997986i	$0.520204\pi$
$710$	−470.982	−	750.599i	−0.663355	−	1.05718i
$711$			85.7263i			0.120572i
$712$	−61.5518	−	555.600i	−0.0864492	−	0.780337i
$713$	311.925			0.437483
$714$	−24.4285	+	15.3282i	−0.0342135	+	0.0214681i
$715$			112.005i			0.156651i
$716$	448.300	+	216.577i	0.626118	+	0.302482i
$717$	422.374			0.589085
$718$	−571.074	−	910.114i	−0.795367	−	1.26757i
$719$		−	699.403i		−	0.972744i	−0.873752	−	0.486372i	$-0.838320\pi$
$719$		−	699.403i		−	0.972744i	0.873752	−	0.486372i	$-0.161680\pi$
$720$	164.586	+	207.441i	0.228592	+	0.288112i
$721$	81.8434			0.113514
$722$	385.794	−	242.076i	0.534340	−	0.335285i
$723$		−	386.118i		−	0.534050i
$724$	−404.952	+	838.223i	−0.559325	+	1.15777i
$725$	−265.022			−0.365548
$726$	164.403	+	262.007i	0.226450	+	0.360892i
$727$		−	1083.55i		−	1.49044i	−0.666817	−	0.745221i	$-0.732344\pi$
$727$		−	1083.55i		−	1.49044i	0.666817	−	0.745221i	$-0.267656\pi$
$728$	29.0306	−	3.21614i	0.0398772	−	0.00441778i
$729$	−27.0000			−0.0370370
$730$	52.4003	−	32.8799i	0.0717813	−	0.0450409i
$731$			115.256i			0.157669i
$732$	450.138	+	217.465i	0.614943	+	0.297083i
$733$	−459.669			−0.627107			−0.313553	−	0.949571i	$-0.601519\pi$
$733$	−459.669			−0.627107			−0.313553	+	0.949571i	$0.601519\pi$
$734$	603.049	+	961.073i	0.821593	+	1.30936i
$735$			458.408i			0.623685i
$736$	−56.0506	+	158.600i	−0.0761556	+	0.215489i
$737$	−571.209			−0.775046
$738$	333.422	−	209.214i	0.451792	−	0.283488i
$739$		−	779.296i		−	1.05453i	−0.849702	−	0.527264i	$-0.823218\pi$
$739$		−	779.296i		−	1.05453i	0.849702	−	0.527264i	$-0.176782\pi$
$740$	−186.225	+	385.473i	−0.251655	+	0.520910i
$741$	72.0948			0.0972940
$742$	−27.9644	−	44.5666i	−0.0376879	−	0.0600628i
$743$		−	696.785i		−	0.937799i	−0.883251	−	0.468900i	$-0.844651\pi$
$743$		−	696.785i		−	0.937799i	0.883251	−	0.468900i	$-0.155349\pi$
$744$	90.5361	+	817.227i	0.121688	+	1.09842i
$745$	875.832			1.17561
$746$	−865.716	+	543.215i	−1.16048	+	0.728170i
$747$			311.812i			0.417419i
$748$	166.742	+	80.5545i	0.222918	+	0.107693i
$749$	−98.2364			−0.131157
$750$	−198.737	−	316.725i	−0.264982	−	0.422299i
$751$		−	237.983i		−	0.316889i	−0.987368	−	0.158444i	$-0.949352\pi$
$751$		−	237.983i		−	0.316889i	0.987368	−	0.158444i	$-0.0506478\pi$
$752$	−117.148	+	92.9466i	−0.155782	+	0.123599i
$753$	764.628			1.01544
$754$	−297.896	+	186.922i	−0.395088	+	0.247908i
$755$		−	1448.44i		−	1.91846i
$756$	9.15542	−	18.9511i	0.0121103	−	0.0250676i
$757$	−62.2735			−0.0822635			−0.0411318	−	0.999154i	$-0.513096\pi$
$757$	−62.2735			−0.0822635			−0.0411318	+	0.999154i	$0.513096\pi$
$758$	−261.394	−	416.581i	−0.344847	−	0.549580i
$759$			51.2692i			0.0675484i
$760$	−506.400	+	56.1012i	−0.666315	+	0.0738174i
$761$	−734.114			−0.964670			−0.482335	−	0.875987i	$-0.660211\pi$
$761$	−734.114			−0.964670			−0.482335	+	0.875987i	$0.660211\pi$
$762$	137.941	−	86.5547i	0.181025	−	0.113589i
$763$			213.745i			0.280138i
$764$	1002.18	+	484.158i	1.31175	+	0.633715i
$765$	−136.067			−0.177865
$766$	−295.502	−	470.939i	−0.385773	−	0.614803i
$767$		−	138.602i		−	0.180707i
$768$	−431.792	−	100.816i	−0.562229	−	0.131271i
$769$	378.181			0.491783			0.245891	−	0.969297i	$-0.420919\pi$
$769$	378.181			0.491783			0.245891	+	0.969297i	$0.420919\pi$
$770$	−53.2908	+	33.4386i	−0.0692088	+	0.0434268i
$771$		−	500.777i		−	0.649517i
$772$	−12.0288	+	24.8989i	−0.0155814	+	0.0322524i
$773$	−1276.10			−1.65084			−0.825421	−	0.564517i	$-0.809062\pi$
$773$	−1276.10			−1.65084			−0.825421	+	0.564517i	$0.809062\pi$
$774$	−44.7067	−	71.2486i	−0.0577606	−	0.0920524i
$775$			322.457i			0.416073i
$776$	24.3991	+	220.240i	0.0314422	+	0.283814i
$777$	34.0258			0.0437913
$778$	224.561	−	140.907i	0.288639	−	0.181114i
$779$			757.362i			0.972224i
$780$	124.086	+	59.9468i	0.159084	+	0.0768548i
$781$	452.244			0.579057
$782$	−45.9407	−	73.2153i	−0.0587477	−	0.0936257i
$783$			253.416i			0.323647i
$784$	−477.093	−	601.317i	−0.608537	−	0.766986i
$785$	618.356			0.787715
$786$	−249.871	+	156.787i	−0.317901	+	0.199475i
$787$		−	1247.47i		−	1.58509i	−0.609811	−	0.792547i	$-0.708755\pi$
$787$		−	1247.47i		−	1.58509i	0.609811	−	0.792547i	$-0.291245\pi$
$788$	−484.538	+	1002.96i	−0.614896	+	1.27279i
$789$	713.348			0.904117
$790$	−167.576	−	267.064i	−0.212121	−	0.338055i
$791$			69.2865i			0.0875935i
$792$	−134.323	+	14.8808i	−0.169599	+	0.0187889i
$793$	260.164			0.328076
$794$	−795.460	+	499.131i	−1.00184	+	0.628629i
$795$		−	248.236i		−	0.312247i
$796$	−533.325	−	257.653i	−0.670007	−	0.323685i
$797$	252.682			0.317042			0.158521	−	0.987356i	$-0.449328\pi$
$797$	252.682			0.317042			0.158521	+	0.987356i	$0.449328\pi$
$798$	21.5235	+	34.3019i	0.0269719	+	0.0429848i
$799$		−	76.8409i		−	0.0961714i
$800$	−163.955	−	57.9429i	−0.204943	−	0.0724286i
$801$	−209.625			−0.261704
$802$	286.308	−	179.651i	0.356992	−	0.224004i
$803$			31.5717i			0.0393172i
$804$	−305.719	+	632.817i	−0.380247	+	0.787086i
$805$	29.3652			0.0364786
$806$	227.431	+	362.455i	0.282173	+	0.449696i
$807$		−	31.0847i		−	0.0385188i
$808$	34.9215	+	315.220i	0.0432197	+	0.390124i
$809$	412.690			0.510124			0.255062	−	0.966925i	$-0.417904\pi$
$809$	412.690			0.510124			0.255062	+	0.966925i	$0.417904\pi$
$810$	84.1133	−	52.7789i	0.103844	−	0.0651592i
$811$		−	1013.28i		−	1.24942i	−0.780857	−	0.624710i	$-0.785217\pi$
$811$		−	1013.28i		−	1.24942i	0.780857	−	0.624710i	$-0.214783\pi$
$812$	−177.871	−	85.9307i	−0.219053	−	0.105826i
$813$	560.256			0.689122
$814$	−116.126	−	185.068i	−0.142661	−	0.227357i
$815$		−	43.6508i		−	0.0535592i
$816$	178.486	−	141.613i	0.218732	−	0.173545i
$817$	161.840			0.198090
$818$	559.093	−	350.817i	0.683488	−	0.428872i
$819$		−	10.9531i		−	0.0133737i
$820$	−629.746	+	1303.53i	−0.767983	+	1.58967i
$821$	13.0550			0.0159014			0.00795070	−	0.999968i	$-0.497469\pi$
$821$	13.0550			0.0159014			0.00795070	+	0.999968i	$0.497469\pi$
$822$	366.940	+	584.788i	0.446399	+	0.711421i
$823$			724.939i			0.880850i	0.897789	+	0.440425i	$0.145172\pi$
$823$			724.939i			0.880850i	−0.897789	+	0.440425i	$0.854828\pi$
$824$	−642.660	+	71.1967i	−0.779927	+	0.0864037i
$825$	−53.0002			−0.0642426
$826$	65.9453	−	41.3790i	0.0798369	−	0.0500956i
$827$		−	1270.08i		−	1.53576i	−0.640592	−	0.767882i	$-0.721311\pi$
$827$		−	1270.08i		−	1.53576i	0.640592	−	0.767882i	$-0.278689\pi$
$828$	56.7989	+	27.4400i	0.0685977	+	0.0331401i
$829$	524.786			0.633035			0.316517	−	0.948587i	$-0.397486\pi$
$829$	524.786			0.633035			0.316517	+	0.948587i	$0.397486\pi$
$830$	−609.522	−	971.389i	−0.734364	−	1.17035i
$831$			310.691i			0.373876i
$832$	−225.160	+	50.5083i	−0.270625	+	0.0607071i
$833$	394.423			0.473497
$834$	−200.527	+	125.826i	−0.240441	+	0.150870i
$835$		−	1351.09i		−	1.61807i
$836$	113.113	−	234.136i	0.135302	−	0.280067i
$837$	308.335			0.368381
$838$	−488.915	−	779.179i	−0.583431	−	0.929808i
$839$		−	566.375i		−	0.675060i	−0.941315	−	0.337530i	$-0.890409\pi$
$839$		−	566.375i		−	0.675060i	0.941315	−	0.337530i	$-0.109591\pi$
$840$	8.52323	+	76.9353i	0.0101467	+	0.0915897i
$841$	1537.50			1.82819
$842$	−106.578	+	66.8753i	−0.126578	+	0.0794243i
$843$			757.510i			0.898589i
$844$	1406.18	+	679.335i	1.66609	+	0.804900i
$845$	71.7173			0.0848725
$846$	29.8058	+	47.5012i	0.0352315	+	0.0561480i
$847$			90.4180i			0.106751i
$848$	258.354	+	325.624i	0.304663	+	0.383991i
$849$	−853.786			−1.00564
$850$	75.6871	−	47.4918i	0.0890437	−	0.0558727i
$851$			101.980i			0.119835i
$852$	242.047	−	501.021i	0.284093	−	0.588053i
$853$	918.949			1.07731			0.538657	−	0.842525i	$-0.318932\pi$
$853$	918.949			1.07731			0.538657	+	0.842525i	$0.318932\pi$
$854$	77.6707	+	123.783i	0.0909493	+	0.144945i
$855$			191.062i			0.223464i
$856$	771.383	−	85.4572i	0.901148	−	0.0998332i
$857$	1131.98			1.32086			0.660429	−	0.750888i	$-0.270374\pi$
$857$	1131.98			1.32086			0.660429	+	0.750888i	$0.270374\pi$
$858$	−59.5745	+	37.3815i	−0.0694341	+	0.0435682i
$859$			275.908i			0.321197i	0.987020	+	0.160598i	$0.0513424\pi$
$859$			275.908i			0.321197i	−0.987020	+	0.160598i	$0.948658\pi$
$860$	278.550	+	134.570i	0.323895	+	0.156476i
$861$	115.063			0.133639
$862$	407.953	+	650.151i	0.473263	+	0.754235i
$863$			976.882i			1.13196i	0.824419	+	0.565980i	$0.191502\pi$
$863$			976.882i			1.13196i	−0.824419	+	0.565980i	$0.808498\pi$
$864$	−55.4054	+	156.774i	−0.0641266	+	0.181452i
$865$	−932.210			−1.07770
$866$	908.779	−	570.236i	1.04940	−	0.658471i
$867$		−	383.488i		−	0.442316i
$868$	−104.553	+	216.418i	−0.120453	+	0.249330i
$869$	160.909			0.185165
$870$	−495.371	−	789.468i	−0.569392	−	0.907434i
$871$			365.746i			0.419916i
$872$	−185.940	−	1678.40i	−0.213234	−	1.92477i
$873$	83.0951			0.0951834
$874$	−102.807	+	64.5089i	−0.117628	+	0.0738088i
$875$		−	109.301i		−	0.124915i
$876$	34.9770	+	16.8976i	0.0399280	+	0.0192895i
$877$	1188.18			1.35482			0.677410	−	0.735606i	$-0.263102\pi$
$877$	1188.18			1.35482			0.677410	+	0.735606i	$0.263102\pi$
$878$	−279.610	−	445.611i	−0.318462	−	0.507530i
$879$			107.164i			0.121916i
$880$	389.367	−	308.929i	0.442462	−	0.351055i
$881$	450.708			0.511587			0.255793	−	0.966731i	$-0.417663\pi$
$881$	450.708			0.511587			0.255793	+	0.966731i	$0.417663\pi$
$882$	−243.823	+	152.993i	−0.276443	+	0.173461i
$883$			607.667i			0.688184i	0.938936	+	0.344092i	$0.111813\pi$
$883$			607.667i			0.688184i	−0.938936	+	0.344092i	$0.888187\pi$
$884$	51.5793	−	106.766i	0.0583476	−	0.120776i
$885$	367.316			0.415046
$886$	740.501	+	1180.13i	0.835780	+	1.33197i
$887$		−	653.859i		−	0.737158i	−0.929596	−	0.368579i	$-0.879844\pi$
$887$		−	653.859i		−	0.737158i	0.929596	−	0.368579i	$-0.120156\pi$
$888$	−267.181	+	29.5995i	−0.300880	+	0.0333328i
$889$	47.6032			0.0535469
$890$	653.045	−	409.769i	0.733758	−	0.460415i
$891$			50.6791i			0.0568789i
$892$	1143.38	+	552.374i	1.28181	+	0.619253i
$893$	−107.898			−0.120827
$894$	292.307	+	465.846i	0.326965	+	0.521081i
$895$			686.658i			0.767215i
$896$	−91.2515	−	92.0493i	−0.101843	−	0.102734i
$897$	32.8278			0.0365973
$898$	−321.174	+	201.529i	−0.357655	+	0.224419i
$899$		−	2893.96i		−	3.21909i
$900$	−28.3664	+	58.7166i	−0.0315182	+	0.0652406i
$901$	−213.587			−0.237055
$902$	−392.696	−	625.835i	−0.435361	−	0.693830i
$903$		−	24.5877i		−	0.0272289i
$904$	−60.2733	−	544.059i	−0.0666740	−	0.601835i
$905$	−1283.90			−1.41867
$906$	770.409	−	483.412i	0.850341	−	0.533568i
$907$		−	183.685i		−	0.202519i	−0.994860	−	0.101260i	$-0.967713\pi$
$907$		−	183.685i		−	0.202519i	0.994860	−	0.101260i	$-0.0322873\pi$
$908$	1542.04	+	744.973i	1.69829	+	0.820455i
$909$	118.931			0.130837
$910$	21.4108	+	34.1222i	0.0235284	+	0.0374969i
$911$			1057.82i			1.16116i	0.814203	+	0.580581i	$0.197174\pi$
$911$			1057.82i			1.16116i	−0.814203	+	0.580581i	$0.802826\pi$
$912$	−198.849	−	250.625i	−0.218037	−	0.274808i
$913$	585.272			0.641043
$914$	252.508	−	158.442i	0.276267	−	0.173351i
$915$			689.472i			0.753522i
$916$	712.741	−	1475.33i	0.778101	−	1.61062i
$917$	−86.2296			−0.0940345
$918$	−45.4119	−	72.3725i	−0.0494684	−	0.0788372i
$919$			1464.17i			1.59322i	0.604494	+	0.796609i	$0.293375\pi$
$919$			1464.17i			1.59322i	−0.604494	+	0.796609i	$0.706625\pi$
$920$	−230.585	+	25.5452i	−0.250636	+	0.0277666i
$921$	773.744			0.840112
$922$	−57.9022	+	36.3321i	−0.0628006	+	0.0394058i
$923$		−	289.573i		−	0.313730i
$924$	−35.5713	−	17.1848i	−0.0384971	−	0.0185982i
$925$	−105.423			−0.113971
$926$	587.982	+	937.061i	0.634970	+	1.01195i
$927$			242.472i			0.261566i
$928$	1471.45	+	520.023i	1.58561	+	0.560369i
$929$	431.688			0.464680			0.232340	−	0.972635i	$-0.425362\pi$
$929$	431.688			0.464680			0.232340	+	0.972635i	$0.425362\pi$
$930$	−960.558	+	602.726i	−1.03286	+	0.648093i
$931$		−	553.839i		−	0.594886i
$932$	−146.431	+	303.102i	−0.157114	+	0.325216i
$933$	−431.162			−0.462124
$934$	9.49527	+	15.1325i	0.0101662	+	0.0162018i
$935$			255.398i			0.273153i
$936$	9.52824	+	86.0070i	0.0101797	+	0.0918879i
$937$	−1476.62			−1.57590			−0.787952	−	0.615736i	$-0.788859\pi$
$937$	−1476.62			−1.57590			−0.787952	+	0.615736i	$0.788859\pi$
$938$	−174.018	+	109.192i	−0.185520	+	0.116409i
$939$		−	98.2079i		−	0.104588i
$940$	−185.709	−	89.7172i	−0.197562	−	0.0954438i
$941$	540.724			0.574627			0.287314	−	0.957837i	$-0.407238\pi$
$941$	540.724			0.574627			0.287314	+	0.957837i	$0.407238\pi$
$942$	206.375	+	328.897i	0.219081	+	0.349148i
$943$			344.859i			0.365704i
$944$	−481.827	+	382.288i	−0.510410	+	0.404966i
$945$	29.0272			0.0307167
$946$	−133.734	+	83.9146i	−0.141368	+	0.0887047i
$947$			857.512i			0.905504i	0.891636	+	0.452752i	$0.149558\pi$
$947$			857.512i			0.905504i	−0.891636	+	0.452752i	$0.850442\pi$
$948$	86.1205	−	178.264i	0.0908444	−	0.188042i
$949$	20.2155			0.0213019
$950$	−66.6868	−	106.278i	−0.0701966	−	0.111872i
$951$		−	100.147i		−	0.105307i
$952$	66.1965	−	7.33354i	0.0695341	−	0.00770330i
$953$	−1044.61			−1.09613			−0.548064	−	0.836436i	$-0.684635\pi$
$953$	−1044.61			−1.09613			−0.548064	+	0.836436i	$0.684635\pi$
$954$	132.034	−	82.8482i	0.138401	−	0.0868430i
$955$			1535.02i			1.60735i
$956$	−878.306	−	424.316i	−0.918731	−	0.443846i
$957$	475.663			0.497035
$958$	−605.004	−	964.188i	−0.631528	−	1.00646i
$959$			201.809i			0.210437i
$960$	−133.854	−	596.706i	−0.139431	−	0.621568i
$961$	−2560.13			−2.66403
$962$	−118.500	+	74.3556i	−0.123181	+	0.0772927i
$963$		−	291.038i		−	0.302220i
$964$	−387.894	+	802.914i	−0.402379	+	0.832898i
$965$	−38.1374			−0.0395206
$966$	9.80058	+	15.6191i	0.0101455	+	0.0161688i
$967$		−	523.468i		−	0.541332i	−0.962673	−	0.270666i	$-0.912756\pi$
$967$		−	523.468i		−	0.541332i	0.962673	−	0.270666i	$-0.0872440\pi$
$968$	−78.6558	−	709.990i	−0.0812560	−	0.733461i
$969$	164.393			0.169652
$970$	−258.867	+	162.432i	−0.266873	+	0.167456i
$971$			533.084i			0.549005i	0.961586	+	0.274503i	$0.0885132\pi$
$971$			533.084i			0.549005i	−0.961586	+	0.274503i	$0.911487\pi$
$972$	56.1452	+	27.1241i	0.0577625	+	0.0279055i
$973$	−69.2014			−0.0711217
$974$	−240.173	−	382.761i	−0.246584	−	0.392979i
$975$			33.9361i			0.0348063i
$976$	−717.575	−	904.416i	−0.735220	−	0.926655i
$977$	1316.34			1.34733			0.673667	−	0.739035i	$-0.264718\pi$
$977$	1316.34			1.34733			0.673667	+	0.739035i	$0.264718\pi$
$978$	23.2174	−	14.5683i	0.0237397	−	0.0148960i
$979$			393.466i			0.401906i
$980$	460.516	−	953.238i	0.469915	−	0.972692i
$981$	−633.249			−0.645514
$982$	932.110	+	1485.49i	0.949195	+	1.51272i
$983$			761.922i			0.775098i	0.921849	+	0.387549i	$0.126678\pi$
$983$			761.922i			0.775098i	−0.921849	+	0.387549i	$0.873322\pi$
$984$	−903.511	+	100.095i	−0.918203	+	0.101723i
$985$	−1536.23			−1.55962
$986$	−679.272	+	426.226i	−0.688917	+	0.432278i
$987$			16.3925i			0.0166085i
$988$	−149.918	−	72.4263i	−0.151739	−	0.0733060i
$989$	73.6925			0.0745121
$990$	−99.0663	−	157.881i	−0.100067	−	0.159476i
$991$		−	1048.30i		−	1.05782i	−0.848679	−	0.528908i	$-0.822602\pi$
$991$		−	1048.30i		−	1.05782i	0.848679	−	0.528908i	$-0.177398\pi$
$992$	632.720	−	1790.34i	0.637822	−	1.80477i
$993$	−85.0177			−0.0856170
$994$	137.775	−	86.4505i	0.138607	−	0.0869723i
$995$		−	816.890i		−	0.820994i
$996$	313.245	−	648.397i	0.314504	−	0.651001i
$997$	−1347.16			−1.35121			−0.675607	−	0.737262i	$-0.736118\pi$
$997$	−1347.16			−1.35121			−0.675607	+	0.737262i	$0.736118\pi$
$998$	−276.281	−	440.307i	−0.276835	−	0.441189i
$999$			100.806i			0.100907i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.3.f.a.79.19	✓	24
3.2	odd	2		468.3.f.b.235.6		24
4.3	odd	2	inner	156.3.f.a.79.20	yes	24
8.3	odd	2		2496.3.k.e.703.18		24
8.5	even	2		2496.3.k.e.703.17		24
12.11	even	2		468.3.f.b.235.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.f.a.79.19	✓	24	1.1	even	1	trivial
156.3.f.a.79.20	yes	24	4.3	odd	2	inner
468.3.f.b.235.5		24	12.11	even	2
468.3.f.b.235.6		24	3.2	odd	2
2496.3.k.e.703.17		24	8.5	even	2
2496.3.k.e.703.18		24	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	156.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.69411 - 1.06301i) q^{2} +1.73205i q^{3} +(1.74001 - 3.60171i) q^{4} +5.51671 q^{5} +(1.84119 + 2.93428i) q^{6} +1.01261i q^{7} +(-0.880886 - 7.95135i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(1.69411 - 1.06301i) q^{2} +1.73205i q^{3} +(1.74001 - 3.60171i) q^{4} +5.51671 q^{5} +(1.84119 + 2.93428i) q^{6} +1.01261i q^{7} +(-0.880886 - 7.95135i) q^{8} -3.00000 q^{9} +(9.34592 - 5.86433i) q^{10} +5.63101i q^{11} +(6.23835 + 3.01379i) q^{12} +3.60555 q^{13} +(1.07642 + 1.71548i) q^{14} +9.55523i q^{15} +(-9.94470 - 12.5341i) q^{16} +8.22149 q^{17} +(-5.08233 + 3.18903i) q^{18} -11.5444i q^{19} +(9.59916 - 19.8696i) q^{20} -1.75390 q^{21} +(5.98583 + 9.53955i) q^{22} -5.25666i q^{23} +(13.7722 - 1.52574i) q^{24} +5.43413 q^{25} +(6.10820 - 3.83274i) q^{26} -5.19615i q^{27} +(3.64714 + 1.76196i) q^{28} -48.7699 q^{29} +(10.1573 + 16.1876i) q^{30} +59.3391i q^{31} +(-30.1713 - 10.6628i) q^{32} -9.75320 q^{33} +(13.9281 - 8.73953i) q^{34} +5.58630i q^{35} +(-5.22004 + 10.8051i) q^{36} -19.4001 q^{37} +(-12.2718 - 19.5575i) q^{38} +6.24500i q^{39} +(-4.85960 - 43.8653i) q^{40} -65.6042 q^{41} +(-2.97129 + 1.86441i) q^{42} +14.0189i q^{43} +(20.2813 + 9.79804i) q^{44} -16.5501 q^{45} +(-5.58788 - 8.90535i) q^{46} -9.34635i q^{47} +(21.7097 - 17.2247i) q^{48} +47.9746 q^{49} +(9.20601 - 5.77654i) q^{50} +14.2400i q^{51} +(6.27371 - 12.9862i) q^{52} -25.9791 q^{53} +(-5.52357 - 8.80285i) q^{54} +31.0647i q^{55} +(8.05165 - 0.891997i) q^{56} +19.9955 q^{57} +(-82.6216 + 51.8429i) q^{58} -38.4414i q^{59} +(34.4152 + 16.6262i) q^{60} +72.1566 q^{61} +(63.0781 + 100.527i) q^{62} -3.03784i q^{63} +(-62.4481 + 14.0085i) q^{64} +19.8908 q^{65} +(-16.5230 + 10.3678i) q^{66} +101.440i q^{67} +(14.3055 - 29.6115i) q^{68} +9.10480 q^{69} +(5.93829 + 9.46380i) q^{70} -80.3131i q^{71} +(2.64266 + 23.8541i) q^{72} +5.60676 q^{73} +(-32.8659 + 20.6225i) q^{74} +9.41219i q^{75} +(-41.5797 - 20.0875i) q^{76} -5.70204 q^{77} +(6.63850 + 10.5797i) q^{78} -28.5754i q^{79} +(-54.8620 - 69.1469i) q^{80} +9.00000 q^{81} +(-111.141 + 69.7380i) q^{82} -103.937i q^{83} +(-3.05181 + 6.31704i) q^{84} +45.3556 q^{85} +(14.9022 + 23.7495i) q^{86} -84.4720i q^{87} +(44.7742 - 4.96028i) q^{88} +69.8749 q^{89} +(-28.0378 + 17.5930i) q^{90} +3.65103i q^{91} +(-18.9330 - 9.14666i) q^{92} -102.778 q^{93} +(-9.93528 - 15.8337i) q^{94} -63.6872i q^{95} +(18.4685 - 52.2582i) q^{96} -27.6984 q^{97} +(81.2743 - 50.9975i) q^{98} -16.8930i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9	\( 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9} - 12 q^{10} + 12 q^{12} + 32 q^{14} + 4 q^{16} - 12 q^{18} + 84 q^{20} + 28 q^{22} - 36 q^{24} + 104 q^{25} - 96 q^{28} + 64 q^{29} - 12 q^{30} + 44 q^{32} + 48 q^{33} + 40 q^{34} - 24 q^{36} - 192 q^{37} - 104 q^{38} + 220 q^{40} - 220 q^{44} - 104 q^{46} - 144 q^{48} - 248 q^{49} + 100 q^{50} - 52 q^{52} + 336 q^{53} + 36 q^{54} + 168 q^{56} - 16 q^{58} + 60 q^{60} + 16 q^{61} + 152 q^{62} - 16 q^{64} - 132 q^{66} + 400 q^{68} - 192 q^{69} + 208 q^{70} + 96 q^{72} + 112 q^{73} - 104 q^{74} - 264 q^{76} - 272 q^{77} - 300 q^{80} + 216 q^{81} - 4 q^{82} + 96 q^{84} + 64 q^{85} + 288 q^{86} - 492 q^{88} + 36 q^{90} + 328 q^{92} - 96 q^{93} - 884 q^{94} + 72 q^{96} - 80 q^{97} - 572 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9 - 12 * q^10 + 12 * q^12 + 32 * q^14 + 4 * q^16 - 12 * q^18 + 84 * q^20 + 28 * q^22 - 36 * q^24 + 104 * q^25 - 96 * q^28 + 64 * q^29 - 12 * q^30 + 44 * q^32 + 48 * q^33 + 40 * q^34 - 24 * q^36 - 192 * q^37 - 104 * q^38 + 220 * q^40 - 220 * q^44 - 104 * q^46 - 144 * q^48 - 248 * q^49 + 100 * q^50 - 52 * q^52 + 336 * q^53 + 36 * q^54 + 168 * q^56 - 16 * q^58 + 60 * q^60 + 16 * q^61 + 152 * q^62 - 16 * q^64 - 132 * q^66 + 400 * q^68 - 192 * q^69 + 208 * q^70 + 96 * q^72 + 112 * q^73 - 104 * q^74 - 264 * q^76 - 272 * q^77 - 300 * q^80 + 216 * q^81 - 4 * q^82 + 96 * q^84 + 64 * q^85 + 288 * q^86 - 492 * q^88 + 36 * q^90 + 328 * q^92 - 96 * q^93 - 884 * q^94 + 72 * q^96 - 80 * q^97 - 572 * q^98

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