LMFDB - Embedded newform 728.2.h.a.27.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(27,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.27"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.h (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,1,0,1,0,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			27.11
Character	$\chi$	$=$	728.27
Dual form			728.2.h.a.27.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.10110 - 0.887461i) q^{2} +0.140163i q^{3} +(0.424825 + 1.95436i) q^{4} -0.986963 q^{5} +(0.124389 - 0.154333i) q^{6} +(-1.39484 + 2.24820i) q^{7} +(1.26665 - 2.52895i) q^{8} +2.98035 q^{9} +(1.08674 + 0.875891i) q^{10} -1.55783 q^{11} +(-0.273929 + 0.0595448i) q^{12} -1.00000 q^{13} +(3.53105 - 1.23762i) q^{14} -0.138336i q^{15} +(-3.63905 + 1.66052i) q^{16} +4.36043i q^{17} +(-3.28166 - 2.64495i) q^{18} -7.69522i q^{19} +(-0.419286 - 1.92888i) q^{20} +(-0.315115 - 0.195505i) q^{21} +(1.71532 + 1.38251i) q^{22} +2.65380i q^{23} +(0.354466 + 0.177537i) q^{24} -4.02591 q^{25} +(1.10110 + 0.887461i) q^{26} +0.838225i q^{27} +(-4.98636 - 1.77093i) q^{28} +5.33662i q^{29} +(-0.122768 + 0.152321i) q^{30} -9.27964 q^{31} +(5.48059 + 1.40112i) q^{32} -0.218350i q^{33} +(3.86972 - 4.80126i) q^{34} +(1.37666 - 2.21889i) q^{35} +(1.26613 + 5.82469i) q^{36} -0.0671212i q^{37} +(-6.82921 + 8.47318i) q^{38} -0.140163i q^{39} +(-1.25013 + 2.49598i) q^{40} +5.51713i q^{41} +(0.173468 + 0.494923i) q^{42} -5.43661 q^{43} +(-0.661805 - 3.04456i) q^{44} -2.94150 q^{45} +(2.35514 - 2.92208i) q^{46} -6.75979 q^{47} +(-0.232744 - 0.510060i) q^{48} +(-3.10882 - 6.27178i) q^{49} +(4.43291 + 3.57283i) q^{50} -0.611172 q^{51} +(-0.424825 - 1.95436i) q^{52} +3.62105i q^{53} +(0.743892 - 0.922966i) q^{54} +1.53752 q^{55} +(3.91883 + 6.37517i) q^{56} +1.07859 q^{57} +(4.73604 - 5.87613i) q^{58} +4.10440i q^{59} +(0.270358 - 0.0587685i) q^{60} -8.11403 q^{61} +(10.2178 + 8.23532i) q^{62} +(-4.15713 + 6.70044i) q^{63} +(-4.79122 - 6.40658i) q^{64} +0.986963 q^{65} +(-0.193777 + 0.240425i) q^{66} +5.12668 q^{67} +(-8.52186 + 1.85242i) q^{68} -0.371964 q^{69} +(-3.48501 + 1.22148i) q^{70} -1.96037i q^{71} +(3.77505 - 7.53718i) q^{72} +3.52622i q^{73} +(-0.0595674 + 0.0739068i) q^{74} -0.564283i q^{75} +(15.0392 - 3.26912i) q^{76} +(2.17293 - 3.50232i) q^{77} +(-0.124389 + 0.154333i) q^{78} +9.12508i q^{79} +(3.59160 - 1.63887i) q^{80} +8.82357 q^{81} +(4.89624 - 6.07490i) q^{82} +5.07705i q^{83} +(0.248219 - 0.698904i) q^{84} -4.30359i q^{85} +(5.98623 + 4.82478i) q^{86} -0.747996 q^{87} +(-1.97322 + 3.93968i) q^{88} +1.10613i q^{89} +(3.23887 + 2.61047i) q^{90} +(1.39484 - 2.24820i) q^{91} +(-5.18647 + 1.12740i) q^{92} -1.30066i q^{93} +(7.44317 + 5.99905i) q^{94} +7.59489i q^{95} +(-0.196385 + 0.768176i) q^{96} +10.5990i q^{97} +(-2.14285 + 9.66479i) q^{98} -4.64288 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} + q^{4} - 10 q^{6} - 5 q^{8} - 48 q^{9} - 4 q^{11} + 10 q^{12} - 48 q^{13} + 10 q^{14} + 5 q^{16} - 15 q^{18} - 22 q^{20} - 6 q^{22} + 48 q^{25} - q^{26} + 4 q^{28} - 26 q^{30} - 19 q^{32}+ \cdots + 20 q^{99}+O(q^{100}) $ 48 * q + q^2 + q^4 - 10 * q^6 - 5 * q^8 - 48 * q^9 - 4 * q^11 + 10 * q^12 - 48 * q^13 + 10 * q^14 + 5 * q^16 - 15 * q^18 - 22 * q^20 - 6 * q^22 + 48 * q^25 - q^26 + 4 * q^28 - 26 * q^30 - 19 * q^32 + 36 * q^34 + 12 * q^35 - 5 * q^36 - 10 * q^38 - 48 * q^40 + 3 * q^42 - 4 * q^43 - 30 * q^44 + 24 * q^45 + 2 * q^46 + 48 * q^48 + 11 * q^50 - 40 * q^51 - q^52 + 62 * q^54 + 10 * q^56 + 2 * q^58 + 18 * q^60 - 36 * q^62 + 20 * q^63 - 11 * q^64 + 32 * q^66 - 4 * q^67 + 62 * q^68 - 11 * q^70 + 13 * q^72 - 44 * q^74 - 48 * q^76 - 20 * q^77 + 10 * q^78 + 32 * q^80 + 64 * q^81 - 50 * q^82 + 21 * q^84 + 2 * q^86 - 40 * q^87 - 66 * q^88 + 74 * q^90 - 24 * q^92 - 26 * q^94 - 84 * q^96 - 6 * q^98 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−1.10110	−	0.887461i	−0.778592	−	0.627530i
$2$	−1.10110	−	0.887461i	−0.778592	−	0.627530i
$3$			0.140163i			0.0809232i	0.999181	+	0.0404616i	$0.0128828\pi$
$3$			0.140163i			0.0809232i	−0.999181	+	0.0404616i	$0.987117\pi$
$4$	0.424825	+	1.95436i	0.212413	+	0.977180i
$5$	−0.986963			−0.441383			−0.220692	−	0.975344i	$-0.570831\pi$
$5$	−0.986963			−0.441383			−0.220692	+	0.975344i	$0.570831\pi$
$6$	0.124389	−	0.154333i	0.0507817	−	0.0630062i
$7$	−1.39484	+	2.24820i	−0.527201	+	0.849741i
$7$	−1.39484	+	2.24820i	−0.527201	+	0.849741i
$8$	1.26665	−	2.52895i	0.447827	−	0.894120i
$9$	2.98035			0.993451
$10$	1.08674	+	0.875891i	0.343658	+	0.276981i
$11$	−1.55783			−0.469703			−0.234852	−	0.972031i	$-0.575460\pi$
$11$	−1.55783			−0.469703			−0.234852	+	0.972031i	$0.575460\pi$
$12$	−0.273929	+	0.0595448i	−0.0790765	+	0.0171891i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	3.53105	−	1.23762i	0.943712	−	0.330767i
$15$		−	0.138336i		−	0.0357181i
$16$	−3.63905	+	1.66052i	−0.909762	+	0.415131i
$17$			4.36043i			1.05756i	0.848759	+	0.528780i	$0.177350\pi$
$17$			4.36043i			1.05756i	−0.848759	+	0.528780i	$0.822650\pi$
$18$	−3.28166	−	2.64495i	−0.773494	−	0.623420i
$19$		−	7.69522i		−	1.76540i	−0.469933	−	0.882702i	$-0.655722\pi$
$19$		−	7.69522i		−	1.76540i	0.469933	−	0.882702i	$-0.344278\pi$
$20$	−0.419286	−	1.92888i	−0.0937553	−	0.431311i
$21$	−0.315115	−	0.195505i	−0.0687637	−	0.0426628i
$22$	1.71532	+	1.38251i	0.365708	+	0.294753i
$23$			2.65380i			0.553355i	0.960963	+	0.276677i	$0.0892333\pi$
$23$			2.65380i			0.553355i	−0.960963	+	0.276677i	$0.910767\pi$
$24$	0.354466	+	0.177537i	0.0723551	+	0.0362396i
$25$	−4.02591			−0.805181
$26$	1.10110	+	0.887461i	0.215943	+	0.174045i
$27$			0.838225i			0.161316i
$28$	−4.98636	−	1.77093i	−0.942334	−	0.334675i
$29$			5.33662i			0.990985i	0.868612	+	0.495492i	$0.165012\pi$
$29$			5.33662i			0.990985i	−0.868612	+	0.495492i	$0.834988\pi$
$30$	−0.122768	+	0.152321i	−0.0224142	+	0.0278099i
$31$	−9.27964			−1.66667			−0.833336	−	0.552767i	$-0.813572\pi$
$31$	−9.27964			−1.66667			−0.833336	+	0.552767i	$0.813572\pi$
$32$	5.48059	+	1.40112i	0.968841	+	0.247685i
$33$		−	0.218350i		−	0.0380099i
$34$	3.86972	−	4.80126i	0.663651	−	0.823409i
$35$	1.37666	−	2.21889i	0.232698	−	0.375061i
$36$	1.26613	+	5.82469i	0.211022	+	0.970781i
$37$		−	0.0671212i		−	0.0110347i	−0.999985	−	0.00551733i	$-0.998244\pi$
$37$		−	0.0671212i		−	0.0110347i	0.999985	−	0.00551733i	$-0.00175623\pi$
$38$	−6.82921	+	8.47318i	−1.10784	+	1.37453i
$39$		−	0.140163i		−	0.0224441i
$40$	−1.25013	+	2.49598i	−0.197663	+	0.394650i
$41$			5.51713i			0.861632i	0.902440	+	0.430816i	$0.141774\pi$
$41$			5.51713i			0.861632i	−0.902440	+	0.430816i	$0.858226\pi$
$42$	0.173468	+	0.494923i	0.0267667	+	0.0763682i
$43$	−5.43661			−0.829075			−0.414538	−	0.910032i	$-0.636057\pi$
$43$	−5.43661			−0.829075			−0.414538	+	0.910032i	$0.636057\pi$
$44$	−0.661805	−	3.04456i	−0.0997709	−	0.458985i
$45$	−2.94150			−0.438493
$46$	2.35514	−	2.92208i	0.347246	−	0.430838i
$47$	−6.75979			−0.986016			−0.493008	−	0.870025i	$-0.664103\pi$
$47$	−6.75979			−0.986016			−0.493008	+	0.870025i	$0.664103\pi$
$48$	−0.232744	−	0.510060i	−0.0335937	−	0.0736208i
$49$	−3.10882	−	6.27178i	−0.444118	−	0.895968i
$50$	4.43291	+	3.57283i	0.626908	+	0.505275i
$51$	−0.611172			−0.0855812
$52$	−0.424825	−	1.95436i	−0.0589126	−	0.271021i
$53$			3.62105i			0.497389i	0.968582	+	0.248695i	$0.0800016\pi$
$53$			3.62105i			0.497389i	−0.968582	+	0.248695i	$0.919998\pi$
$54$	0.743892	−	0.922966i	0.101231	−	0.125600i
$55$	1.53752			0.207319
$56$	3.91883	+	6.37517i	0.523675	+	0.851918i
$57$	1.07859			0.142862
$58$	4.73604	−	5.87613i	0.621872	−	0.771573i
$59$			4.10440i			0.534347i	0.963648	+	0.267173i	$0.0860897\pi$
$59$			4.10440i			0.534347i	−0.963648	+	0.267173i	$0.913910\pi$
$60$	0.270358	−	0.0587685i	0.0349030	−	0.00758698i
$61$	−8.11403			−1.03890			−0.519448	−	0.854502i	$-0.673862\pi$
$61$	−8.11403			−1.03890			−0.519448	+	0.854502i	$0.673862\pi$
$62$	10.2178	+	8.23532i	1.29766	+	1.04589i
$63$	−4.15713	+	6.70044i	−0.523749	+	0.844176i
$64$	−4.79122	−	6.40658i	−0.598902	−	0.800822i
$65$	0.986963			0.122418
$66$	−0.193777	+	0.240425i	−0.0238523	+	0.0295942i
$67$	5.12668			0.626324			0.313162	−	0.949700i	$-0.398612\pi$
$67$	5.12668			0.626324			0.313162	+	0.949700i	$0.398612\pi$
$68$	−8.52186	+	1.85242i	−1.03343	+	0.224639i
$69$	−0.371964			−0.0447792
$70$	−3.48501	+	1.22148i	−0.416539	+	0.145995i
$71$		−	1.96037i		−	0.232653i	−0.993211	−	0.116327i	$-0.962888\pi$
$71$		−	1.96037i		−	0.232653i	0.993211	−	0.116327i	$-0.0371119\pi$
$72$	3.77505	−	7.53718i	0.444894	−	0.888265i
$73$			3.52622i			0.412712i	0.978477	+	0.206356i	$0.0661605\pi$
$73$			3.52622i			0.412712i	−0.978477	+	0.206356i	$0.933839\pi$
$74$	−0.0595674	+	0.0739068i	−0.00692457	+	0.00859150i
$75$		−	0.564283i		−	0.0651578i
$76$	15.0392	−	3.26912i	1.72512	−	0.374994i
$77$	2.17293	−	3.50232i	0.247628	−	0.399126i
$78$	−0.124389	+	0.154333i	−0.0140843	+	0.0174748i
$79$			9.12508i			1.02665i	0.858194	+	0.513326i	$0.171587\pi$
$79$			9.12508i			1.02665i	−0.858194	+	0.513326i	$0.828413\pi$
$80$	3.59160	−	1.63887i	0.401553	−	0.183232i
$81$	8.82357			0.980397
$82$	4.89624	−	6.07490i	0.540700	−	0.670860i
$83$			5.07705i			0.557279i	0.960396	+	0.278640i	$0.0898835\pi$
$83$			5.07705i			0.557279i	−0.960396	+	0.278640i	$0.910117\pi$
$84$	0.248219	−	0.698904i	0.0270830	−	0.0762566i
$85$		−	4.30359i		−	0.466789i
$86$	5.98623	+	4.82478i	0.645512	+	0.520269i
$87$	−0.747996			−0.0801936
$88$	−1.97322	+	3.93968i	−0.210346	+	0.419971i
$89$			1.10613i			0.117250i	0.998280	+	0.0586248i	$0.0186715\pi$
$89$			1.10613i			0.117250i	−0.998280	+	0.0586248i	$0.981328\pi$
$90$	3.23887	+	2.61047i	0.341407	+	0.275167i
$91$	1.39484	−	2.24820i	0.146219	−	0.235676i
$92$	−5.18647	+	1.12740i	−0.540727	+	0.117539i
$93$		−	1.30066i		−	0.134872i
$94$	7.44317	+	5.99905i	0.767705	+	0.618755i
$95$			7.59489i			0.779220i
$96$	−0.196385	+	0.768176i	−0.0200435	+	0.0784017i
$97$			10.5990i			1.07616i	0.842893	+	0.538081i	$0.180850\pi$
$97$			10.5990i			1.07616i	−0.842893	+	0.538081i	$0.819150\pi$
$98$	−2.14285	+	9.66479i	−0.216460	+	0.976291i
$99$	−4.64288			−0.466627
$100$	−1.71031	−	7.86807i	−0.171031	−	0.786807i
$101$	−0.348577			−0.0346847			−0.0173424	−	0.999850i	$-0.505521\pi$
$101$	−0.348577			−0.0346847			−0.0173424	+	0.999850i	$0.505521\pi$
$102$	0.672959	+	0.542391i	0.0666329	+	0.0537047i
$103$	−10.3076			−1.01564			−0.507821	−	0.861463i	$-0.669549\pi$
$103$	−10.3076			−1.01564			−0.507821	+	0.861463i	$0.669549\pi$
$104$	−1.26665	+	2.52895i	−0.124205	+	0.247984i
$105$	0.311007	+	0.192957i	0.0303511	+	0.0188306i
$106$	3.21354	−	3.98712i	0.312127	−	0.387264i
$107$	−6.29550			−0.608609			−0.304304	−	0.952575i	$-0.598424\pi$
$107$	−6.29550			−0.608609			−0.304304	+	0.952575i	$0.598424\pi$
$108$	−1.63819	+	0.356099i	−0.157635	+	0.0342656i
$109$		−	9.07535i		−	0.869261i	−0.900609	−	0.434631i	$-0.856879\pi$
$109$		−	9.07535i		−	0.869261i	0.900609	−	0.434631i	$-0.143121\pi$
$110$	−1.69296	−	1.36449i	−0.161417	−	0.130099i
$111$	0.00940791			0.000892959
$112$	1.34271	−	10.4975i	0.126874	−	0.991919i
$113$	13.6413			1.28326			0.641632	−	0.767013i	$-0.278258\pi$
$113$	13.6413			1.28326			0.641632	+	0.767013i	$0.278258\pi$
$114$	−1.18763	−	0.957203i	−0.111231	−	0.0896503i
$115$		−	2.61920i		−	0.244241i
$116$	−10.4297	+	2.26713i	−0.968370	+	0.210498i
$117$	−2.98035			−0.275534
$118$	3.64249	−	4.51933i	0.335319	−	0.416038i
$119$	−9.80314	−	6.08212i	−0.898652	−	0.557547i
$120$	−0.349845	−	0.175222i	−0.0319363	−	0.0159955i
$121$	−8.57317			−0.779379
$122$	8.93433	+	7.20089i	0.808876	+	0.651938i
$123$	−0.773299			−0.0697260
$124$	−3.94222	−	18.1358i	−0.354022	−	1.62864i
$125$	8.90823			0.796776
$126$	10.5238	−	3.68854i	0.937532	−	0.328601i
$127$			10.7964i			0.958027i	0.877808	+	0.479013i	$0.159005\pi$
$127$			10.7964i			0.958027i	−0.877808	+	0.479013i	$0.840995\pi$
$128$	−0.409999	+	11.3063i	−0.0362392	+	0.999343i
$129$		−	0.762012i		−	0.0670914i
$130$	−1.08674	−	0.875891i	−0.0953134	−	0.0768207i
$131$		−	16.0674i		−	1.40382i	−0.712267	−	0.701908i	$-0.752332\pi$
$131$		−	16.0674i		−	1.40382i	0.712267	−	0.701908i	$-0.247668\pi$
$132$	0.426735	−	0.0927606i	0.0371425	−	0.00807378i
$133$	17.3004	+	10.7336i	1.50014	+	0.930723i
$134$	−5.64497	−	4.54973i	−0.487651	−	0.393037i
$135$		−	0.827296i		−	0.0712023i
$136$	11.0273	+	5.52313i	0.945587	+	0.473604i
$137$	2.68339			0.229257			0.114629	−	0.993408i	$-0.463432\pi$
$137$	2.68339			0.229257			0.114629	+	0.993408i	$0.463432\pi$
$138$	0.409568	+	0.330104i	0.0348648	+	0.0281003i
$139$		−	6.13776i		−	0.520598i	−0.965528	−	0.260299i	$-0.916179\pi$
$139$		−	6.13776i		−	0.520598i	0.965528	−	0.260299i	$-0.0838212\pi$
$140$	4.92135	+	1.74784i	0.415930	+	0.147720i
$141$		−	0.947472i		−	0.0797916i
$142$	−1.73975	+	2.15856i	−0.145997	+	0.181142i
$143$	1.55783			0.130272
$144$	−10.8457	+	4.94894i	−0.903804	+	0.412412i
$145$		−	5.26704i		−	0.437404i
$146$	3.12938	−	3.88270i	0.258989	−	0.321335i
$147$	0.879072	−	0.435742i	0.0725046	−	0.0359394i
$148$	0.131179	−	0.0285148i	0.0107828	−	0.00234390i
$149$		−	1.69559i		−	0.138908i	−0.997585	−	0.0694539i	$-0.977874\pi$
$149$		−	1.69559i		−	0.138908i	0.997585	−	0.0694539i	$-0.0221257\pi$
$150$	−0.500779	+	0.621330i	−0.0408885	+	0.0507314i
$151$		−	12.7033i		−	1.03378i	−0.856052	−	0.516889i	$-0.827090\pi$
$151$		−	12.7033i		−	1.03378i	0.856052	−	0.516889i	$-0.172910\pi$
$152$	−19.4609	−	9.74712i	−1.57848	−	0.790596i
$153$			12.9956i			1.05064i
$154$	−5.50077	+	1.92800i	−0.443265	+	0.155362i
$155$	9.15866			0.735641
$156$	0.273929	−	0.0595448i	0.0219319	−	0.00476740i
$157$	21.5064			1.71640			0.858201	−	0.513314i	$-0.171583\pi$
$157$	21.5064			1.71640			0.858201	+	0.513314i	$0.171583\pi$
$158$	8.09815	−	10.0476i	0.644254	−	0.799343i
$159$	−0.507537			−0.0402503
$160$	−5.40914	−	1.38285i	−0.427630	−	0.109324i
$161$	−5.96627	−	3.70163i	−0.470208	−	0.291729i
$162$	−9.71560	−	7.83058i	−0.763330	−	0.615229i
$163$	−6.62347			−0.518791			−0.259395	−	0.965771i	$-0.583523\pi$
$163$	−6.62347			−0.518791			−0.259395	+	0.965771i	$0.583523\pi$
$164$	−10.7825	+	2.34382i	−0.841969	+	0.183021i
$165$			0.215503i			0.0167769i
$166$	4.50569	−	5.59032i	0.349709	−	0.433893i
$167$	−0.155425			−0.0120271			−0.00601357	−	0.999982i	$-0.501914\pi$
$167$	−0.155425			−0.0120271			−0.00601357	+	0.999982i	$0.501914\pi$
$168$	−0.893563	+	0.549275i	−0.0689399	+	0.0423775i
$169$	1.00000			0.0769231
$170$	−3.81927	+	4.73866i	−0.292924	+	0.363439i
$171$		−	22.9345i		−	1.75384i
$172$	−2.30961	−	10.6251i	−0.176106	−	0.810156i
$173$	0.303425			0.0230690			0.0115345	−	0.999933i	$-0.496328\pi$
$173$	0.303425			0.0230690			0.0115345	+	0.999933i	$0.496328\pi$
$174$	0.823616	+	0.663818i	0.0624382	+	0.0503239i
$175$	5.61551	−	9.05105i	0.424492	−	0.684195i
$176$	5.66902	−	2.58681i	0.427318	−	0.194988i
$177$	−0.575285			−0.0432411
$178$	0.981647	−	1.21796i	0.0735776	−	0.0912896i
$179$	−17.1546			−1.28219			−0.641096	−	0.767460i	$-0.721520\pi$
$179$	−17.1546			−1.28219			−0.641096	+	0.767460i	$0.721520\pi$
$180$	−1.24962	−	5.74875i	−0.0931413	−	0.428486i
$181$	15.0801			1.12090			0.560448	−	0.828190i	$-0.310629\pi$
$181$	15.0801			1.12090			0.560448	+	0.828190i	$0.310629\pi$
$182$	−3.53105	+	1.23762i	−0.261739	+	0.0917383i
$183$		−	1.13729i		−	0.0840707i
$184$	6.71133	+	3.36142i	0.494765	+	0.247807i
$185$			0.0662461i			0.00487051i
$186$	−1.15429	+	1.43215i	−0.0846365	+	0.105011i
$187$		−	6.79282i		−	0.496740i
$188$	−2.87173	−	13.2111i	−0.209442	−	0.963515i
$189$	−1.88450	−	1.16919i	−0.137077	−	0.0850462i
$190$	6.74017	−	8.36271i	0.488984	−	0.606695i
$191$		−	16.3488i		−	1.18296i	−0.806319	−	0.591480i	$-0.798544\pi$
$191$		−	16.3488i		−	1.18296i	0.806319	−	0.591480i	$-0.201456\pi$
$192$	0.897966	−	0.671552i	0.0648051	−	0.0484651i
$193$	−2.82671			−0.203471			−0.101736	−	0.994811i	$-0.532440\pi$
$193$	−2.82671			−0.203471			−0.101736	+	0.994811i	$0.532440\pi$
$194$	9.40616	−	11.6705i	0.675323	−	0.837891i
$195$			0.138336i			0.00990642i
$196$	10.9366	−	8.74017i	0.781186	−	0.624298i
$197$		−	21.2411i		−	1.51337i	−0.653780	−	0.756684i	$-0.726818\pi$
$197$		−	21.2411i		−	1.51337i	0.653780	−	0.756684i	$-0.273182\pi$
$198$	5.11226	+	4.12038i	0.363313	+	0.292823i
$199$	21.0288			1.49070			0.745348	−	0.666676i	$-0.232284\pi$
$199$	21.0288			1.49070			0.745348	+	0.666676i	$0.232284\pi$
$200$	−5.09940	+	10.1813i	−0.360582	+	0.719929i
$201$			0.718571i			0.0506841i
$202$	0.383817	+	0.309349i	0.0270053	+	0.0217657i
$203$	−11.9978	−	7.44374i	−0.842080	−	0.522448i
$204$	−0.259641	−	1.19445i	−0.0181785	−	0.0836282i
$205$		−	5.44521i		−	0.380310i
$206$	11.3497	+	9.14763i	0.790771	+	0.637345i
$207$			7.90925i			0.549731i
$208$	3.63905	−	1.66052i	0.252323	−	0.115137i
$209$			11.9878i			0.829216i
$210$	−0.171207	−	0.488470i	−0.0118144	−	0.0337076i
$211$	−18.8736			−1.29931			−0.649656	−	0.760228i	$-0.725087\pi$
$211$	−18.8736			−1.29931			−0.649656	+	0.760228i	$0.725087\pi$
$212$	−7.07683	+	1.53831i	−0.486039	+	0.105652i
$213$	0.274772			0.0188270
$214$	6.93195	+	5.58701i	0.473858	+	0.381920i
$215$	5.36573			0.365940
$216$	2.11983	+	1.06173i	0.144236	+	0.0722418i
$217$	12.9436	−	20.8625i	0.878672	−	1.41624i
$218$	−8.05402	+	9.99284i	−0.545487	+	0.676800i
$219$	−0.494245			−0.0333980
$220$	0.653177	+	3.00487i	0.0440372	+	0.202588i
$221$		−	4.36043i		−	0.293315i
$222$	−0.0103590	−	0.00834915i	−0.000695251	−	0.000560358i
$223$	1.38884			0.0930038			0.0465019	−	0.998918i	$-0.485193\pi$
$223$	1.38884			0.0930038			0.0465019	+	0.998918i	$0.485193\pi$
$224$	−10.7946	+	10.3671i	−0.721242	+	0.692683i
$225$	−11.9986			−0.799908
$226$	−15.0204	−	12.1061i	−0.999139	−	0.805286i
$227$		−	3.80506i		−	0.252550i	−0.991995	−	0.126275i	$-0.959698\pi$
$227$		−	3.80506i		−	0.252550i	0.991995	−	0.126275i	$-0.0403022\pi$
$228$	0.458210	+	2.10794i	0.0303457	+	0.139602i
$229$	−21.9736			−1.45206			−0.726028	−	0.687666i	$-0.758636\pi$
$229$	−21.9736			−1.45206			−0.726028	+	0.687666i	$0.758636\pi$
$230$	−2.32444	+	2.88399i	−0.153269	+	0.190164i
$231$	0.490895	+	0.304564i	0.0322985	+	0.0200389i
$232$	13.4961	+	6.75960i	0.886059	+	0.443790i
$233$	28.8013			1.88684			0.943419	−	0.331603i	$-0.107589\pi$
$233$	28.8013			1.88684			0.943419	+	0.331603i	$0.107589\pi$
$234$	3.28166	+	2.64495i	0.214529	+	0.172906i
$235$	6.67166			0.435211
$236$	−8.02147	+	1.74365i	−0.522153	+	0.113502i
$237$	−1.27900			−0.0830799
$238$	5.39655	+	15.3969i	0.349806	+	0.998033i
$239$			12.5308i			0.810549i	0.914195	+	0.405274i	$0.132824\pi$
$239$			12.5308i			0.810549i	−0.914195	+	0.405274i	$0.867176\pi$
$240$	0.229709	+	0.503410i	0.0148277	+	0.0324950i
$241$		−	5.64814i		−	0.363829i	−0.983314	−	0.181914i	$-0.941771\pi$
$241$		−	5.64814i		−	0.363829i	0.983314	−	0.181914i	$-0.0582294\pi$
$242$	9.43988	+	7.60835i	0.606818	+	0.489083i
$243$			3.75141i			0.240653i
$244$	−3.44704	−	15.8577i	−0.220674	−	1.01519i
$245$	3.06829	+	6.19001i	0.196026	+	0.395465i
$246$	0.851476	+	0.686272i	0.0542881	+	0.0437551i
$247$			7.69522i			0.489635i
$248$	−11.7540	+	23.4678i	−0.746381	+	1.49021i
$249$	−0.711615			−0.0450968
$250$	−9.80882	−	7.90571i	−0.620364	−	0.500001i
$251$			21.4858i			1.35617i	0.734982	+	0.678087i	$0.237191\pi$
$251$			21.4858i			1.35617i	−0.734982	+	0.678087i	$0.762809\pi$
$252$	−14.8611	−	5.27801i	−0.936163	−	0.332483i
$253$		−	4.13416i		−	0.259912i
$254$	9.58140	−	11.8879i	0.601190	−	0.745912i
$255$	0.603204			0.0377741
$256$	10.4853	−	12.0854i	0.655333	−	0.755340i
$257$			26.5474i			1.65598i	0.560741	+	0.827991i	$0.310516\pi$
$257$			26.5474i			1.65598i	−0.560741	+	0.827991i	$0.689484\pi$
$258$	−0.676256	+	0.839048i	−0.0421019	+	0.0522369i
$259$	0.150902	+	0.0936235i	0.00937659	+	0.00581748i
$260$	0.419286	+	1.92888i	0.0260030	+	0.119624i
$261$			15.9050i			0.984495i
$262$	−14.2592	+	17.6918i	−0.880937	+	1.09300i
$263$		−	5.05439i		−	0.311667i	−0.987783	−	0.155834i	$-0.950194\pi$
$263$		−	5.05439i		−	0.311667i	0.987783	−	0.155834i	$-0.0498064\pi$
$264$	−0.552198	−	0.276572i	−0.0339854	−	0.0170219i
$265$		−	3.57384i		−	0.219539i
$266$	−9.52374	−	27.1722i	−0.583938	−	1.66603i
$267$	−0.155039			−0.00948820
$268$	2.17794	+	10.0194i	0.133039	+	0.612031i
$269$	5.06872			0.309045			0.154523	−	0.987989i	$-0.450616\pi$
$269$	5.06872			0.309045			0.154523	+	0.987989i	$0.450616\pi$
$270$	−0.734194	+	0.910933i	−0.0446816	+	0.0554376i
$271$	20.2952			1.23285			0.616424	−	0.787415i	$-0.288581\pi$
$271$	20.2952			1.23285			0.616424	+	0.787415i	$0.288581\pi$
$272$	−7.24060	−	15.8678i	−0.439026	−	0.962128i
$273$	0.315115	+	0.195505i	0.0190716	+	0.0118325i
$274$	−2.95467	−	2.38140i	−0.178498	−	0.143866i
$275$	6.27167			0.378196
$276$	−0.158020	−	0.726952i	−0.00951166	−	0.0437574i
$277$		−	2.57962i		−	0.154995i	−0.996993	−	0.0774973i	$-0.975307\pi$
$277$		−	2.57962i		−	0.154995i	0.996993	−	0.0774973i	$-0.0246929\pi$
$278$	−5.44703	+	6.75827i	−0.326691	+	0.405334i
$279$	−27.6566			−1.65576
$280$	−3.86774	−	6.29205i	−0.231141	−	0.376022i
$281$	−20.2368			−1.20723			−0.603613	−	0.797277i	$-0.706273\pi$
$281$	−20.2368			−1.20723			−0.603613	+	0.797277i	$0.706273\pi$
$282$	−0.840845	+	1.04326i	−0.0500716	+	0.0621251i
$283$			21.8971i			1.30165i	0.759228	+	0.650825i	$0.225577\pi$
$283$			21.8971i			1.30165i	−0.759228	+	0.650825i	$0.774423\pi$
$284$	3.83127	−	0.832815i	0.227344	−	0.0494185i
$285$	−1.06452			−0.0630569
$286$	−1.71532	−	1.38251i	−0.101429	−	0.0817497i
$287$	−12.4036	−	7.69554i	−0.732163	−	0.454253i
$288$	16.3341	+	4.17583i	0.962496	+	0.246063i
$289$	−2.01339			−0.118435
$290$	−4.67429	+	5.79952i	−0.274484	+	0.340559i
$291$	−1.48558			−0.0870864
$292$	−6.89149	+	1.49802i	−0.403294	+	0.0876653i
$293$	6.13771			0.358569			0.179285	−	0.983797i	$-0.442622\pi$
$293$	6.13771			0.358569			0.179285	+	0.983797i	$0.442622\pi$
$294$	−1.35465	−	0.300348i	−0.0790046	−	0.0175166i
$295$		−	4.05089i		−	0.235852i
$296$	−0.169746	−	0.0850187i	−0.00986630	−	0.00494161i
$297$		−	1.30581i		−	0.0757709i
$298$	−1.50477	+	1.86700i	−0.0871688	+	0.108153i
$299$		−	2.65380i		−	0.153473i
$300$	1.10281	−	0.239722i	0.0636709	−	0.0138403i
$301$	7.58322	−	12.2226i	0.437089	−	0.704499i
$302$	−11.2737	+	13.9875i	−0.648727	+	0.804892i
$303$		−	0.0488577i		−	0.00280680i
$304$	12.7781	+	28.0033i	0.732873	+	1.60610i
$305$	8.00825			0.458551
$306$	11.5331	−	14.3094i	0.659305	−	0.818017i
$307$			29.4120i			1.67863i	0.543644	+	0.839316i	$0.317044\pi$
$307$			29.4120i			1.67863i	−0.543644	+	0.839316i	$0.682956\pi$
$308$	7.76790	+	2.75881i	0.442617	+	0.157198i
$309$		−	1.44475i		−	0.0821889i
$310$	−10.0846	−	8.12795i	−0.572764	−	0.461637i
$311$	33.2593			1.88596			0.942982	−	0.332844i	$-0.108008\pi$
$311$	33.2593			1.88596			0.942982	+	0.332844i	$0.108008\pi$
$312$	−0.354466	−	0.177537i	−0.0200677	−	0.0100511i
$313$			12.7334i			0.719734i	0.933004	+	0.359867i	$0.117178\pi$
$313$			12.7334i			0.719734i	−0.933004	+	0.359867i	$0.882822\pi$
$314$	−23.6807	−	19.0861i	−1.33638	−	1.07709i
$315$	4.10293	−	6.61308i	0.231174	−	0.372605i
$316$	−17.8337	+	3.87656i	−1.00322	+	0.218074i
$317$			12.4765i			0.700751i	0.936609	+	0.350375i	$0.113946\pi$
$317$			12.4765i			0.700751i	−0.936609	+	0.350375i	$0.886054\pi$
$318$	0.558847	+	0.450420i	0.0313386	+	0.0252583i
$319$		−	8.31354i		−	0.465469i
$320$	4.72875	+	6.32305i	0.264345	+	0.353469i
$321$		−	0.882396i		−	0.0492505i
$322$	3.28438	+	9.37068i	0.183031	+	0.522208i
$323$	33.5545			1.86702
$324$	3.74848	+	17.2444i	0.208249	+	0.958025i
$325$	4.02591			0.223317
$326$	7.29308	+	5.87808i	0.403926	+	0.325557i
$327$	1.27203			0.0703434
$328$	13.9526	+	6.98826i	0.770402	+	0.385862i
$329$	9.42884	−	15.1974i	0.519829	−	0.837858i
$330$	0.191251	−	0.237290i	0.0105280	−	0.0130624i
$331$	30.4522			1.67380			0.836902	−	0.547353i	$-0.184364\pi$
$331$	30.4522			1.67380			0.836902	+	0.547353i	$0.184364\pi$
$332$	−9.92239	+	2.15686i	−0.544562	+	0.118373i
$333$		−	0.200045i		−	0.0109624i
$334$	0.171138	+	0.137933i	0.00936424	+	0.00754739i
$335$	−5.05984			−0.276449
$336$	1.47136	+	0.188198i	0.0802692	+	0.0102671i
$337$	9.55314			0.520393			0.260196	−	0.965556i	$-0.416213\pi$
$337$	9.55314			0.520393			0.260196	+	0.965556i	$0.416213\pi$
$338$	−1.10110	−	0.887461i	−0.0598917	−	0.0482715i
$339$			1.91200i			0.103846i
$340$	8.41076	−	1.82827i	0.456137	−	0.0991519i
$341$	14.4561			0.782842
$342$	−20.3535	+	25.2531i	−1.10059	+	1.36553i
$343$	18.4365	+	1.75888i	0.995480	+	0.0949707i
$344$	−6.88626	+	13.7489i	−0.371282	+	0.741293i
$345$	0.367115			0.0197648
$346$	−0.334100	−	0.269278i	−0.0179613	−	0.0144765i
$347$	24.0005			1.28842			0.644208	−	0.764850i	$-0.277187\pi$
$347$	24.0005			1.28842			0.644208	+	0.764850i	$0.277187\pi$
$348$	−0.317768	−	1.46185i	−0.0170341	−	0.0783636i
$349$	−21.0382			−1.12615			−0.563076	−	0.826405i	$-0.690382\pi$
$349$	−21.0382			−1.12615			−0.563076	+	0.826405i	$0.690382\pi$
$350$	−14.2157	+	4.98253i	−0.759859	+	0.266327i
$351$		−	0.838225i		−	0.0447411i
$352$	−8.53783	−	2.18270i	−0.455068	−	0.116339i
$353$			36.6708i			1.95179i	0.218247	+	0.975894i	$0.429966\pi$
$353$			36.6708i			1.95179i	−0.218247	+	0.975894i	$0.570034\pi$
$354$	0.633444	+	0.510543i	0.0336672	+	0.0271351i
$355$			1.93481i			0.102689i
$356$	−2.16178	+	0.469912i	−0.114574	+	0.0249053i
$357$	0.852489	−	1.37404i	0.0451185	−	0.0727218i
$358$	18.8888	+	15.2240i	0.998306	+	0.804614i
$359$			7.72010i			0.407451i	0.979028	+	0.203726i	$0.0653050\pi$
$359$			7.72010i			0.407451i	−0.979028	+	0.203726i	$0.934695\pi$
$360$	−3.72584	+	7.43891i	−0.196369	+	0.392065i
$361$	−40.2164			−2.11665
$362$	−16.6046	−	13.3830i	−0.872721	−	0.703395i
$363$		−	1.20164i		−	0.0630698i
$364$	4.98636	+	1.77093i	0.261356	+	0.0928221i
$365$		−	3.48024i		−	0.182164i
$366$	−1.00930	+	1.25226i	−0.0527569	+	0.0654568i
$367$	−9.67998			−0.505291			−0.252645	−	0.967559i	$-0.581301\pi$
$367$	−9.67998			−0.505291			−0.252645	+	0.967559i	$0.581301\pi$
$368$	−4.40669	−	9.65729i	−0.229714	−	0.503421i
$369$			16.4430i			0.855989i
$370$	0.0587908	−	0.0729433i	0.00305639	−	0.00379214i
$371$	−8.14085	−	5.05080i	−0.422652	−	0.262224i
$372$	2.54196	−	0.552554i	0.131795	−	0.0286486i
$373$		−	34.0083i		−	1.76088i	−0.474155	−	0.880441i	$-0.657246\pi$
$373$		−	34.0083i		−	1.76088i	0.474155	−	0.880441i	$-0.342754\pi$
$374$	−6.02836	+	7.47954i	−0.311719	+	0.386758i
$375$			1.24860i			0.0644777i
$376$	−8.56226	+	17.0952i	−0.441565	+	0.881617i
$377$		−	5.33662i		−	0.274850i
$378$	1.03740	+	2.95981i	0.0533582	+	0.152236i
$379$	−9.16549			−0.470799			−0.235400	−	0.971899i	$-0.575640\pi$
$379$	−9.16549			−0.470799			−0.235400	+	0.971899i	$0.575640\pi$
$380$	−14.8432	+	3.22650i	−0.761438	+	0.165516i
$381$	−1.51326			−0.0775266
$382$	−14.5090	+	18.0016i	−0.742343	+	0.921044i
$383$	6.02966			0.308101			0.154051	−	0.988063i	$-0.450768\pi$
$383$	6.02966			0.308101			0.154051	+	0.988063i	$0.450768\pi$
$384$	−1.58472	−	0.0574667i	−0.0808700	−	0.00293259i
$385$	−2.14460	+	3.45665i	−0.109299	+	0.176167i
$386$	3.11248	+	2.50860i	0.158421	+	0.127684i
$387$	−16.2030			−0.823646
$388$	−20.7142	+	4.50270i	−1.05160	+	0.228590i
$389$			28.5586i			1.44798i	0.689812	+	0.723988i	$0.257693\pi$
$389$			28.5586i			1.44798i	−0.689812	+	0.723988i	$0.742307\pi$
$390$	0.122768	−	0.152321i	0.00621658	−	0.00771307i
$391$	−11.5717			−0.585206
$392$	−19.7988	−	0.0820464i	−0.999991	−	0.00414397i
$393$	2.25206			0.113601
$394$	−18.8507	+	23.3885i	−0.949684	+	1.17830i
$395$		−	9.00611i		−	0.453146i
$396$	−1.97241	−	9.07387i	−0.0991175	−	0.455979i
$397$	−21.7880			−1.09351			−0.546755	−	0.837293i	$-0.684137\pi$
$397$	−21.7880			−1.09351			−0.546755	+	0.837293i	$0.684137\pi$
$398$	−23.1548	−	18.6623i	−1.16064	−	0.935456i
$399$	−1.50446	+	2.42488i	−0.0753171	+	0.121396i
$400$	14.6505	−	6.68511i	0.732523	−	0.334255i
$401$	−0.960806			−0.0479804			−0.0239902	−	0.999712i	$-0.507637\pi$
$401$	−0.960806			−0.0479804			−0.0239902	+	0.999712i	$0.507637\pi$
$402$	0.637704	−	0.791216i	0.0318058	−	0.0394623i
$403$	9.27964			0.462252
$404$	−0.148084	−	0.681246i	−0.00736747	−	0.0338932i
$405$	−8.70854			−0.432731
$406$	6.60469	+	18.8438i	0.327785	+	0.935204i
$407$			0.104563i			0.00518301i
$408$	−0.774138	+	1.54563i	−0.0383256	+	0.0765199i
$409$		−	31.0748i		−	1.53655i	−0.640120	−	0.768275i	$-0.721116\pi$
$409$		−	31.0748i		−	1.53655i	0.640120	−	0.768275i	$-0.278884\pi$
$410$	−4.83241	+	5.99569i	−0.238656	+	0.296106i
$411$			0.376112i			0.0185522i
$412$	−4.37894	−	20.1448i	−0.215735	−	0.992465i
$413$	−9.22751	−	5.72499i	−0.454056	−	0.281708i
$414$	7.01915	−	8.70884i	0.344973	−	0.428016i
$415$		−	5.01086i		−	0.245974i
$416$	−5.48059	−	1.40112i	−0.268708	−	0.0686955i
$417$	0.860288			0.0421285
$418$	10.6387	−	13.1998i	0.520358	−	0.645622i
$419$			40.3155i			1.96954i	0.173861	+	0.984770i	$0.444376\pi$
$419$			40.3155i			1.96954i	−0.173861	+	0.984770i	$0.555624\pi$
$420$	−0.244983	+	0.689792i	−0.0119540	+	0.0336584i
$421$			8.13838i			0.396641i	0.980137	+	0.198320i	$0.0635486\pi$
$421$			8.13838i			0.396641i	−0.980137	+	0.198320i	$0.936451\pi$
$422$	20.7817	+	16.7496i	1.01164	+	0.815358i
$423$	−20.1466			−0.979559
$424$	9.15747	+	4.58659i	0.444726	+	0.222744i
$425$		−	17.5547i		−	0.851528i
$426$	−0.302550	−	0.243849i	−0.0146586	−	0.0118145i
$427$	11.3178	−	18.2420i	0.547707	−	0.882792i
$428$	−2.67448	−	12.3037i	−0.129276	−	0.594720i
$429$			0.218350i			0.0105420i
$430$	−5.90818	−	4.76188i	−0.284918	−	0.229638i
$431$			15.0621i			0.725514i	0.931884	+	0.362757i	$0.118165\pi$
$431$			15.0621i			0.725514i	−0.931884	+	0.362757i	$0.881835\pi$
$432$	−1.39189	−	3.05034i	−0.0669674	−	0.146760i
$433$		−	2.94876i		−	0.141709i	−0.997487	−	0.0708543i	$-0.977427\pi$
$433$		−	2.94876i		−	0.141709i	0.997487	−	0.0708543i	$-0.0225725\pi$
$434$	−32.7669	+	11.4846i	−1.57286	+	0.551280i
$435$	0.738244			0.0353961
$436$	17.7365	−	3.85544i	0.849425	−	0.184642i
$437$	20.4215			0.976895
$438$	0.544211	+	0.438623i	0.0260034	+	0.0209582i
$439$	17.1352			0.817821			0.408910	−	0.912575i	$-0.365909\pi$
$439$	17.1352			0.817821			0.408910	+	0.912575i	$0.365909\pi$
$440$	1.94749	−	3.88832i	0.0928431	−	0.185368i
$441$	−9.26540	−	18.6921i	−0.441210	−	0.890101i
$442$	−3.86972	+	4.80126i	−0.184064	+	0.228373i
$443$	−22.7343			−1.08014			−0.540070	−	0.841620i	$-0.681602\pi$
$443$	−22.7343			−1.08014			−0.540070	+	0.841620i	$0.681602\pi$
$444$	0.00399671	+	0.0183864i	0.000189676	+	0.000872582i
$445$		−	1.09171i		−	0.0517520i
$446$	−1.52925	−	1.23254i	−0.0724120	−	0.0583626i
$447$	0.237659			0.0112409
$448$	21.0863	−	1.83545i	0.996233	−	0.0867170i
$449$	30.2983			1.42987			0.714933	−	0.699193i	$-0.246457\pi$
$449$	30.2983			1.42987			0.714933	+	0.699193i	$0.246457\pi$
$450$	13.2116	+	10.6483i	0.622803	+	0.501966i
$451$		−	8.59476i		−	0.404711i
$452$	5.79516	+	26.6600i	0.272581	+	1.25398i
$453$	1.78053			0.0836566
$454$	−3.37684	+	4.18973i	−0.158483	+	0.196634i
$455$	−1.37666	+	2.21889i	−0.0645387	+	0.104023i
$456$	1.36619	−	2.72769i	0.0639775	−	0.127736i
$457$	−18.5612			−0.868255			−0.434128	−	0.900851i	$-0.642943\pi$
$457$	−18.5612			−0.868255			−0.434128	+	0.900851i	$0.642943\pi$
$458$	24.1950	+	19.5007i	1.13056	+	0.911208i
$459$	−3.65502			−0.170602
$460$	5.11885	−	1.11270i	0.238668	−	0.0518799i
$461$	32.3108			1.50486			0.752432	−	0.658670i	$-0.228881\pi$
$461$	32.3108			1.50486			0.752432	+	0.658670i	$0.228881\pi$
$462$	−0.270234	−	0.771005i	−0.0125724	−	0.0358704i
$463$		−	11.9232i		−	0.554120i	−0.960853	−	0.277060i	$-0.910640\pi$
$463$		−	11.9232i		−	0.554120i	0.960853	−	0.277060i	$-0.0893600\pi$
$464$	−8.86157	−	19.4202i	−0.411388	−	0.901560i
$465$			1.28371i			0.0595304i
$466$	−31.7130	−	25.5601i	−1.46908	−	1.18405i
$467$		−	19.4513i		−	0.900099i	−0.893004	−	0.450049i	$-0.851406\pi$
$467$		−	19.4513i		−	0.900099i	0.893004	−	0.450049i	$-0.148594\pi$
$468$	−1.26613	−	5.82469i	−0.0585268	−	0.269246i
$469$	−7.15092	+	11.5258i	−0.330199	+	0.532213i
$470$	−7.34613	−	5.92084i	−0.338852	−	0.273108i
$471$			3.01441i			0.138897i
$472$	10.3798	+	5.19882i	0.477770	+	0.239295i
$473$	8.46931			0.389419
$474$	1.40830	+	1.13506i	0.0646854	+	0.0521351i
$475$			30.9802i			1.42147i
$476$	7.72204	−	21.7427i	0.353939	−	0.996575i
$477$			10.7920i			0.494132i
$478$	11.1206	−	13.7976i	0.508643	−	0.631087i
$479$	12.7948			0.584608			0.292304	−	0.956325i	$-0.405578\pi$
$479$	12.7948			0.584608			0.292304	+	0.956325i	$0.405578\pi$
$480$	0.193825	−	0.758161i	0.00884685	−	0.0346052i
$481$			0.0671212i			0.00306046i
$482$	−5.01251	+	6.21915i	−0.228313	+	0.283274i
$483$	0.518832	−	0.836250i	0.0236077	−	0.0380507i
$484$	−3.64210	−	16.7551i	−0.165550	−	0.761593i
$485$		−	10.4608i		−	0.474999i
$486$	3.32923	−	4.13067i	0.151017	−	0.187371i
$487$			16.6594i			0.754909i	0.926028	+	0.377454i	$0.123200\pi$
$487$			16.6594i			0.754909i	−0.926028	+	0.377454i	$0.876800\pi$
$488$	−10.2776	+	20.5200i	−0.465245	+	0.928897i
$489$		−	0.928366i		−	0.0419822i
$490$	2.11491	−	9.53879i	0.0955418	−	0.430919i
$491$	−38.6473			−1.74413			−0.872064	−	0.489392i	$-0.837219\pi$
$491$	−38.6473			−1.74413			−0.872064	+	0.489392i	$0.837219\pi$
$492$	−0.328517	−	1.51130i	−0.0148107	−	0.0681348i
$493$	−23.2700			−1.04803
$494$	6.82921	−	8.47318i	0.307261	−	0.381226i
$495$	4.58235			0.205961
$496$	33.7690	−	15.4090i	1.51627	−	0.691887i
$497$	4.40731	+	2.73441i	0.197695	+	0.122655i
$498$	0.783557	+	0.631531i	0.0351120	+	0.0282996i
$499$	13.7537			0.615702			0.307851	−	0.951435i	$-0.400390\pi$
$499$	13.7537			0.615702			0.307851	+	0.951435i	$0.400390\pi$
$500$	3.78444	+	17.4099i	0.169245	+	0.778594i
$501$		−	0.0217848i		−	0.000973274i
$502$	19.0678	−	23.6580i	0.851039	−	1.05591i
$503$	−30.4143			−1.35611			−0.678053	−	0.735013i	$-0.737176\pi$
$503$	−30.4143			−1.35611			−0.678053	+	0.735013i	$0.737176\pi$
$504$	11.6795	+	19.0003i	0.520246	+	0.846339i
$505$	0.344033			0.0153093
$506$	−3.66891	+	4.55211i	−0.163103	+	0.202366i
$507$			0.140163i			0.00622486i
$508$	−21.1001	+	4.58659i	−0.936165	+	0.203497i
$509$	−9.88923			−0.438332			−0.219166	−	0.975688i	$-0.570334\pi$
$509$	−9.88923			−0.438332			−0.219166	+	0.975688i	$0.570334\pi$
$510$	−0.664185	−	0.535320i	−0.0294106	−	0.0237044i
$511$	−7.92764	−	4.91852i	−0.350698	−	0.217582i
$512$	−22.2707	+	4.00190i	−0.984236	+	0.176861i
$513$	6.45032			0.284789
$514$	23.5598	−	29.2313i	1.03918	−	1.28934i
$515$	10.1733			0.448287
$516$	1.48925	−	0.323722i	0.0655604	−	0.0142511i
$517$	10.5306			0.463135
$518$	−0.0830703	−	0.237008i	−0.00364990	−	0.0104135i
$519$			0.0425290i			0.00186682i
$520$	1.25013	−	2.49598i	0.0548219	−	0.109456i
$521$		−	31.0780i		−	1.36155i	−0.732491	−	0.680777i	$-0.761642\pi$
$521$		−	31.0780i		−	1.36155i	0.732491	−	0.680777i	$-0.238358\pi$
$522$	14.1151	−	17.5129i	0.617800	−	0.766520i
$523$		−	4.85018i		−	0.212083i	−0.994362	−	0.106042i	$-0.966182\pi$
$523$		−	4.85018i		−	0.212083i	0.994362	−	0.106042i	$-0.0338177\pi$
$524$	31.4015	−	6.82584i	1.37178	−	0.298188i
$525$	1.26862	+	0.787087i	0.0553672	+	0.0343513i
$526$	−4.48558	+	5.56537i	−0.195580	+	0.242662i
$527$		−	40.4633i		−	1.76261i
$528$	0.362575	+	0.794587i	0.0157791	+	0.0345799i
$529$	15.9574			0.693799
$530$	−3.17164	+	3.93514i	−0.137767	+	0.170932i
$531$			12.2326i			0.530848i
$532$	−13.6277	+	38.3711i	−0.590837	+	1.66360i
$533$		−	5.51713i		−	0.238974i
$534$	0.170712	+	0.137591i	0.00738744	+	0.00595413i
$535$	6.21342			0.268630
$536$	6.49369	−	12.9651i	0.280485	−	0.560009i
$537$		−	2.40444i		−	0.103759i
$538$	−5.58115	−	4.49829i	−0.240620	−	0.193935i
$539$	4.84302	+	9.77036i	0.208604	+	0.420839i
$540$	1.61684	−	0.351456i	0.0695775	−	0.0151243i
$541$			6.42601i			0.276276i	0.990413	+	0.138138i	$0.0441117\pi$
$541$			6.42601i			0.276276i	−0.990413	+	0.138138i	$0.955888\pi$
$542$	−22.3470	−	18.0112i	−0.959886	−	0.773649i
$543$			2.11367i			0.0907064i
$544$	−6.10949	+	23.8978i	−0.261942	+	1.02461i
$545$			8.95703i			0.383677i
$546$	−0.173468	−	0.494923i	−0.00742375	−	0.0211807i
$547$	8.44150			0.360933			0.180466	−	0.983581i	$-0.442239\pi$
$547$	8.44150			0.360933			0.180466	+	0.983581i	$0.442239\pi$
$548$	1.13997	+	5.24431i	0.0486972	+	0.224026i
$549$	−24.1827			−1.03209
$550$	−6.90572	−	5.56587i	−0.294461	−	0.237329i
$551$	41.0664			1.74949
$552$	−0.471147	+	0.940680i	−0.0200533	+	0.0400380i
$553$	−20.5150	−	12.7281i	−0.872387	−	0.541252i
$554$	−2.28932	+	2.84041i	−0.0972637	+	0.120678i
$555$	−0.00928525			−0.000394137
$556$	11.9954	−	2.60748i	0.508718	−	0.110582i
$557$		−	38.6239i		−	1.63655i	−0.574829	−	0.818274i	$-0.694931\pi$
$557$		−	38.6239i		−	1.63655i	0.574829	−	0.818274i	$-0.305069\pi$
$558$	30.4526	+	24.5442i	1.28916	+	1.03904i
$559$	5.43661			0.229944
$560$	−1.32521	+	10.3606i	−0.0560001	+	0.437816i
$561$	0.952102			0.0401978
$562$	22.2827	+	17.9594i	0.939938	+	0.757571i
$563$		−	5.24596i		−	0.221091i	−0.993871	−	0.110545i	$-0.964740\pi$
$563$		−	5.24596i		−	0.221091i	0.993871	−	0.110545i	$-0.0352597\pi$
$564$	1.85170	−	0.402510i	0.0779707	−	0.0169487i
$565$	−13.4634			−0.566411
$566$	19.4329	−	24.1108i	0.816824	−	1.01345i
$567$	−12.3075	+	19.8372i	−0.516867	+	0.833083i
$568$	−4.95769	−	2.48310i	−0.208020	−	0.104188i
$569$	−45.6714			−1.91464			−0.957322	−	0.289023i	$-0.906670\pi$
$569$	−45.6714			−1.91464			−0.957322	+	0.289023i	$0.906670\pi$
$570$	1.17214	+	0.944723i	0.0490957	+	0.0395701i
$571$	−2.25685			−0.0944463			−0.0472231	−	0.998884i	$-0.515037\pi$
$571$	−2.25685			−0.0944463			−0.0472231	+	0.998884i	$0.515037\pi$
$572$	0.661805	+	3.04456i	0.0276715	+	0.127299i
$573$	2.29150			0.0957289
$574$	6.82810	+	19.4813i	0.284999	+	0.813133i
$575$		−	10.6839i		−	0.445551i
$576$	−14.2795	−	19.0939i	−0.594980	−	0.795578i
$577$			4.65138i			0.193640i	0.995302	+	0.0968198i	$0.0308670\pi$
$577$			4.65138i			0.193640i	−0.995302	+	0.0968198i	$0.969133\pi$
$578$	2.21694	+	1.78681i	0.0922124	+	0.0743214i
$579$		−	0.396201i		−	0.0164656i
$580$	10.2937	−	2.23757i	0.427422	−	0.0929100i
$581$	−11.4142	−	7.08169i	−0.473543	−	0.293798i
$582$	1.63577	+	1.31840i	0.0678048	+	0.0546493i
$583$		−	5.64098i		−	0.233625i
$584$	8.91764	+	4.46647i	0.369014	+	0.184824i
$585$	2.94150			0.121616
$586$	−6.75821	−	5.44698i	−0.279179	−	0.225013i
$587$			29.4108i			1.21391i	0.794735	+	0.606957i	$0.207610\pi$
$587$			29.4108i			1.21391i	−0.794735	+	0.606957i	$0.792390\pi$
$588$	1.22505	+	1.53291i	0.0505202	+	0.0632161i
$589$			71.4089i			2.94235i
$590$	−3.59500	+	4.46041i	−0.148004	+	0.183632i
$591$	2.97722			0.122467
$592$	0.111456	+	0.244257i	0.00458082	+	0.0100389i
$593$			12.5658i			0.516016i	0.966143	+	0.258008i	$0.0830660\pi$
$593$			12.5658i			0.516016i	−0.966143	+	0.258008i	$0.916934\pi$
$594$	−1.15886	+	1.43782i	−0.0475485	+	0.0589946i
$595$	9.67533	+	6.00283i	0.396650	+	0.246092i
$596$	3.31379	−	0.720328i	0.135738	−	0.0295058i
$597$			2.94747i			0.120632i
$598$	−2.35514	+	2.92208i	−0.0963088	+	0.119493i
$599$		−	48.7560i		−	1.99212i	−0.0887057	−	0.996058i	$-0.528273\pi$
$599$		−	48.7560i		−	1.99212i	0.0887057	−	0.996058i	$-0.471727\pi$
$600$	−1.42705	−	0.714747i	−0.0582589	−	0.0291794i
$601$		−	28.5353i		−	1.16398i	−0.813197	−	0.581989i	$-0.802275\pi$
$601$		−	28.5353i		−	1.16398i	0.813197	−	0.581989i	$-0.197725\pi$
$602$	−19.1969	+	6.72844i	−0.782409	+	0.274231i
$603$	15.2793			0.622222
$604$	24.8268	−	5.39667i	1.01019	−	0.219587i
$605$	8.46139			0.344005
$606$	−0.0433593	+	0.0537970i	−0.00176135	+	0.00218535i
$607$	33.9673			1.37869			0.689345	−	0.724433i	$-0.257898\pi$
$607$	33.9673			1.37869			0.689345	+	0.724433i	$0.257898\pi$
$608$	10.7819	−	42.1743i	0.437265	−	1.71040i
$609$	1.04334	−	1.68165i	0.0422782	−	0.0681438i
$610$	−8.81785	−	7.10701i	−0.357024	−	0.287754i
$611$	6.75979			0.273472
$612$	−25.3982	+	5.52087i	−1.02666	+	0.223168i
$613$			39.6378i			1.60096i	0.599362	+	0.800478i	$0.295421\pi$
$613$			39.6378i			1.60096i	−0.599362	+	0.800478i	$0.704579\pi$
$614$	26.1020	−	32.3854i	1.05339	−	1.30697i
$615$	0.763217			0.0307759
$616$	−6.10487	−	9.93143i	−0.245972	−	0.400149i
$617$	−28.4014			−1.14340			−0.571699	−	0.820464i	$-0.693715\pi$
$617$	−28.4014			−1.14340			−0.571699	+	0.820464i	$0.693715\pi$
$618$	−1.28216	+	1.59081i	−0.0515760	+	0.0639917i
$619$		−	4.13135i		−	0.166053i	−0.996547	−	0.0830266i	$-0.973541\pi$
$619$		−	4.13135i		−	0.166053i	0.996547	−	0.0830266i	$-0.0264586\pi$
$620$	3.89083	+	17.8993i	0.156259	+	0.718854i
$621$	−2.22448			−0.0892652
$622$	−36.6217	−	29.5164i	−1.46840	−	1.18350i
$623$	−2.48680	−	1.54288i	−0.0996317	−	0.0618141i
$624$	0.232744	+	0.510060i	0.00931721	+	0.0204187i
$625$	11.3374			0.453497
$626$	11.3004	−	14.0207i	0.451655	−	0.560380i
$627$	−1.68025			−0.0671028
$628$	9.13648	+	42.0313i	0.364585	+	1.67723i
$629$	0.292677			0.0116698
$630$	−10.3866	+	3.64045i	−0.413811	+	0.145039i
$631$		−	28.0677i		−	1.11736i	−0.829384	−	0.558678i	$-0.811309\pi$
$631$		−	28.0677i		−	1.11736i	0.829384	−	0.558678i	$-0.188691\pi$
$632$	23.0769	+	11.5582i	0.917950	+	0.459762i
$633$		−	2.64538i		−	0.105145i
$634$	11.0724	−	13.7378i	0.439742	−	0.545599i
$635$		−	10.6557i		−	0.422857i
$636$	−0.215615	−	0.991911i	−0.00854967	−	0.0393318i
$637$	3.10882	+	6.27178i	0.123176	+	0.248497i
$638$	−7.37794	+	9.15400i	−0.292096	+	0.362410i
$639$		−	5.84260i		−	0.231130i
$640$	0.404654	−	11.1589i	0.0159953	−	0.441093i
$641$	18.5418			0.732356			0.366178	−	0.930545i	$-0.380666\pi$
$641$	18.5418			0.732356			0.366178	+	0.930545i	$0.380666\pi$
$642$	−0.783092	+	0.971603i	−0.0309062	+	0.0383461i
$643$		−	25.8643i		−	1.01999i	−0.860178	−	0.509993i	$-0.829648\pi$
$643$		−	25.8643i		−	1.01999i	0.860178	−	0.509993i	$-0.170352\pi$
$644$	4.69969	−	13.2328i	0.185194	−	0.521445i
$645$			0.752077i			0.0296130i
$646$	−36.9467	−	29.7783i	−1.45365	−	1.17161i
$647$	37.0538			1.45673			0.728367	−	0.685187i	$-0.240280\pi$
$647$	37.0538			1.45673			0.728367	+	0.685187i	$0.240280\pi$
$648$	11.1763	−	22.3144i	0.439048	−	0.876593i
$649$		−	6.39395i		−	0.250985i
$650$	−4.43291	−	3.57283i	−0.173873	−	0.140138i
$651$	2.92415	+	1.81422i	0.114607	+	0.0711049i
$652$	−2.81382	−	12.9447i	−0.110198	−	0.506952i
$653$			21.6335i			0.846584i	0.905993	+	0.423292i	$0.139126\pi$
$653$			21.6335i			0.846584i	−0.905993	+	0.423292i	$0.860874\pi$
$654$	−1.40063	−	1.12888i	−0.0547688	−	0.0441426i
$655$			15.8579i			0.619621i
$656$	−9.16133	−	20.0771i	−0.357690	−	0.783880i
$657$			10.5094i			0.410010i
$658$	−23.8691	+	8.36603i	−0.930516	+	0.326142i
$659$	23.6060			0.919559			0.459780	−	0.888033i	$-0.347928\pi$
$659$	23.6060			0.919559			0.459780	+	0.888033i	$0.347928\pi$
$660$	−0.421171	+	0.0915513i	−0.0163941	+	0.00356363i
$661$	−22.7740			−0.885806			−0.442903	−	0.896570i	$-0.646051\pi$
$661$	−22.7740			−0.885806			−0.442903	+	0.896570i	$0.646051\pi$
$662$	−33.5308	−	27.0251i	−1.30321	−	1.05036i
$663$	0.611172			0.0237359
$664$	12.8396	+	6.43083i	0.498275	+	0.249565i
$665$	−17.0749	−	10.5937i	−0.662134	−	0.410805i
$666$	−0.177532	+	0.220269i	−0.00687923	+	0.00853523i
$667$	−14.1623			−0.548366
$668$	−0.0660284	−	0.303756i	−0.00255471	−	0.0117527i
$669$			0.194664i			0.00752616i
$670$	5.57137	+	4.49041i	0.215241	+	0.173480i
$671$	12.6403			0.487973
$672$	−1.45309	−	1.51300i	−0.0560541	−	0.0583652i
$673$	−17.0579			−0.657535			−0.328767	−	0.944411i	$-0.606633\pi$
$673$	−17.0579			−0.657535			−0.328767	+	0.944411i	$0.606633\pi$
$674$	−10.5189	−	8.47805i	−0.405174	−	0.326562i
$675$		−	3.37461i		−	0.129889i
$676$	0.424825	+	1.95436i	0.0163394	+	0.0751677i
$677$	−15.2323			−0.585424			−0.292712	−	0.956201i	$-0.594558\pi$
$677$	−15.2323			−0.585424			−0.292712	+	0.956201i	$0.594558\pi$
$678$	1.69683	−	2.10530i	0.0651663	−	0.0808535i
$679$	−23.8286	−	14.7839i	−0.914458	−	0.567353i
$680$	−10.8836	−	5.45112i	−0.417366	−	0.209041i
$681$	0.533328			0.0204372
$682$	−15.9176	−	12.8292i	−0.609515	−	0.491256i
$683$	−41.3628			−1.58271			−0.791353	−	0.611360i	$-0.790623\pi$
$683$	−41.3628			−1.58271			−0.791353	+	0.611360i	$0.790623\pi$
$684$	44.8222	−	9.74314i	1.71382	−	0.372538i
$685$	−2.64840			−0.101190
$686$	−18.7395	−	18.2984i	−0.715476	−	0.698637i
$687$		−	3.07988i		−	0.117505i
$688$	19.7841	−	9.02761i	0.754261	−	0.344174i
$689$		−	3.62105i		−	0.137951i
$690$	−0.404228	−	0.325800i	−0.0153887	−	0.0124030i
$691$			30.9788i			1.17849i	0.807954	+	0.589245i	$0.200575\pi$
$691$			30.9788i			1.17849i	−0.807954	+	0.589245i	$0.799425\pi$
$692$	0.128903	+	0.593002i	0.00490014	+	0.0225426i
$693$	6.47610	−	10.4381i	0.246007	−	0.396512i
$694$	−26.4269	−	21.2996i	−1.00315	−	0.808520i
$695$			6.05774i			0.229783i
$696$	−0.947446	+	1.89165i	−0.0359129	+	0.0717027i
$697$	−24.0571			−0.911228
$698$	23.1651	+	18.6706i	0.876813	+	0.706693i
$699$			4.03688i			0.152689i
$700$	20.0746	+	7.12961i	0.758749	+	0.269474i
$701$		−	14.6981i		−	0.555139i	−0.960706	−	0.277570i	$-0.910471\pi$
$701$		−	14.6981i		−	0.555139i	0.960706	−	0.277570i	$-0.0895289\pi$
$702$	−0.743892	+	0.922966i	−0.0280764	+	0.0348351i
$703$	−0.516512			−0.0194806
$704$	7.46390	+	9.98036i	0.281306	+	0.376149i
$705$			0.935120i			0.0352186i
$706$	32.5439	−	40.3780i	1.22480	−	1.51965i
$707$	0.486211	−	0.783672i	0.0182858	−	0.0294730i
$708$	−0.244395	−	1.12431i	−0.00918494	−	0.0422543i
$709$			40.4972i			1.52090i	0.649394	+	0.760452i	$0.275022\pi$
$709$			40.4972i			1.52090i	−0.649394	+	0.760452i	$0.724978\pi$
$710$	1.71707	−	2.13041i	0.0644405	−	0.0799530i
$711$			27.1960i			1.01993i
$712$	2.79735	+	1.40107i	0.104835	+	0.0525075i
$713$		−	24.6263i		−	0.922261i
$714$	−2.15808	+	0.756397i	−0.0807640	+	0.0283074i
$715$	−1.53752			−0.0575000
$716$	−7.28769	−	33.5262i	−0.272354	−	1.25293i
$717$	−1.75635			−0.0655922
$718$	6.85129	−	8.50057i	0.255688	−	0.317238i
$719$	−8.67917			−0.323678			−0.161839	−	0.986817i	$-0.551743\pi$
$719$	−8.67917			−0.323678			−0.161839	+	0.986817i	$0.551743\pi$
$720$	10.7043	−	4.88442i	0.398924	−	0.182032i
$721$	14.3775	−	23.1736i	0.535447	−	0.863032i
$722$	44.2821	+	35.6905i	1.64801	+	1.32826i
$723$	0.791661			0.0294422
$724$	6.40641	+	29.4720i	0.238092	+	1.09532i
$725$		−	21.4847i		−	0.797922i
$726$	−1.06641	+	1.32312i	−0.0395782	+	0.0491057i
$727$	−35.9939			−1.33494			−0.667469	−	0.744637i	$-0.732622\pi$
$727$	−35.9939			−1.33494			−0.667469	+	0.744637i	$0.732622\pi$
$728$	−3.91883	−	6.37517i	−0.145241	−	0.236280i
$729$	25.9449			0.960923
$730$	−3.08858	+	3.83208i	−0.114313	+	0.141832i
$731$		−	23.7060i		−	0.876797i
$732$	2.22267	−	0.483148i	0.0821522	−	0.0178577i
$733$	−26.3045			−0.971580			−0.485790	−	0.874076i	$-0.661468\pi$
$733$	−26.3045			−0.971580			−0.485790	+	0.874076i	$0.661468\pi$
$734$	10.6586	+	8.59061i	0.393416	+	0.317085i
$735$	−0.867611	+	0.430061i	−0.0320023	+	0.0158631i
$736$	−3.71828	+	14.5444i	−0.137058	+	0.536112i
$737$	−7.98650			−0.294186
$738$	14.5925	−	18.1053i	0.537159	−	0.666467i
$739$	−21.8481			−0.803696			−0.401848	−	0.915706i	$-0.631632\pi$
$739$	−21.8481			−0.803696			−0.401848	+	0.915706i	$0.631632\pi$
$740$	−0.129469	+	0.0281430i	−0.00475936	+	0.00103456i
$741$	−1.07859			−0.0396228
$742$	4.48147	+	12.7861i	0.164520	+	0.469392i
$743$			24.1041i			0.884295i	0.896942	+	0.442148i	$0.145783\pi$
$743$			24.1041i			0.884295i	−0.896942	+	0.442148i	$0.854217\pi$
$744$	−3.28932	−	1.64748i	−0.120592	−	0.0603995i
$745$			1.67348i			0.0613116i
$746$	−30.1810	+	37.4464i	−1.10501	+	1.37101i
$747$			15.1314i			0.553630i
$748$	13.2756	−	2.88576i	0.485404	−	0.105514i
$749$	8.78123	−	14.1535i	0.320859	−	0.517159i
$750$	1.10809	−	1.37483i	0.0404617	−	0.0502018i
$751$			14.4698i			0.528011i	0.964521	+	0.264005i	$0.0850437\pi$
$751$			14.4698i			0.528011i	−0.964521	+	0.264005i	$0.914956\pi$
$752$	24.5992	−	11.2248i	0.897040	−	0.409326i
$753$	−3.01152			−0.109746
$754$	−4.73604	+	5.87613i	−0.172476	+	0.213996i
$755$			12.5377i			0.456292i
$756$	1.48444	−	4.17969i	0.0539886	−	0.152014i
$757$		−	1.74116i		−	0.0632836i	−0.999499	−	0.0316418i	$-0.989926\pi$
$757$		−	1.74116i		−	0.0632836i	0.999499	−	0.0316418i	$-0.0100736\pi$
$758$	10.0921	+	8.13401i	0.366561	+	0.295441i
$759$	0.579457			0.0210329
$760$	19.2071	+	9.62004i	0.696716	+	0.348956i
$761$		−	15.9959i		−	0.579853i	−0.957049	−	0.289926i	$-0.906369\pi$
$761$		−	15.9959i		−	0.579853i	0.957049	−	0.289926i	$-0.0936308\pi$
$762$	1.66624	+	1.34296i	0.0603616	+	0.0486502i
$763$	20.4032	+	12.6587i	0.738646	+	0.458276i
$764$	31.9515	−	6.94540i	1.15597	−	0.251276i
$765$		−	12.8262i		−	0.463733i
$766$	−6.63924	−	5.35109i	−0.239885	−	0.193343i
$767$		−	4.10440i		−	0.148201i
$768$	1.69393	+	1.46966i	0.0611245	+	0.0530316i
$769$		−	37.7860i		−	1.36260i	−0.732005	−	0.681300i	$-0.761415\pi$
$769$		−	37.7860i		−	1.36260i	0.732005	−	0.681300i	$-0.238585\pi$
$770$	5.42906	−	1.90286i	0.195650	−	0.0685743i
$771$	−3.72097			−0.134007
$772$	−1.20086	−	5.52442i	−0.0432199	−	0.198828i
$773$	−36.6959			−1.31986			−0.659930	−	0.751327i	$-0.729414\pi$
$773$	−36.6959			−1.31986			−0.659930	+	0.751327i	$0.729414\pi$
$774$	17.8411	+	14.3796i	0.641285	+	0.516862i
$775$	37.3589			1.34197
$776$	26.8043	+	13.4251i	0.962217	+	0.481934i
$777$	−0.0131226	+	0.0211509i	−0.000470769	+	0.000758783i
$778$	25.3446	−	31.4457i	0.908649	−	1.12738i
$779$	42.4556			1.52113
$780$	−0.270358	+	0.0587685i	−0.00968036	+	0.00210425i
$781$			3.05392i			0.109278i
$782$	12.7416	+	10.2694i	0.455637	+	0.367234i
$783$	−4.47328			−0.159862
$784$	21.7276	+	17.6610i	0.775985	+	0.630751i
$785$	−21.2261			−0.757590
$786$	−2.47973	−	1.99861i	−0.0884491	−	0.0712882i
$787$			13.5707i			0.483743i	0.970308	+	0.241871i	$0.0777612\pi$
$787$			13.5707i			0.483743i	−0.970308	+	0.241871i	$0.922239\pi$
$788$	41.5128	−	9.02377i	1.47883	−	0.321458i
$789$	0.708439			0.0252211
$790$	−7.99257	+	9.91659i	−0.284363	+	0.352816i
$791$	−19.0274	+	30.6684i	−0.676538	+	1.09044i
$792$	−5.88089	+	11.7416i	−0.208968	+	0.417221i
$793$	8.11403			0.288138
$794$	23.9907	+	19.3360i	0.851399	+	0.686210i
$795$	0.500920			0.0177658
$796$	8.93358	+	41.0979i	0.316642	+	1.45668i
$797$	15.5920			0.552297			0.276148	−	0.961115i	$-0.410942\pi$
$797$	15.5920			0.552297			0.276148	+	0.961115i	$0.410942\pi$
$798$	3.80854	−	1.33488i	0.134821	−	0.0472541i
$799$		−	29.4756i		−	1.04277i
$800$	−22.0643	−	5.64077i	−0.780092	−	0.199431i
$801$			3.29666i			0.116482i
$802$	1.05794	+	0.852678i	0.0373572	+	0.0301091i
$803$		−	5.49324i		−	0.193852i
$804$	−1.40435	+	0.305267i	−0.0495275	+	0.0107659i
$805$	5.88848	+	3.65337i	0.207542	+	0.128764i
$806$	−10.2178	−	8.23532i	−0.359906	−	0.290077i
$807$			0.710447i			0.0250089i
$808$	−0.441524	+	0.881536i	−0.0155328	+	0.0310123i
$809$	−8.37400			−0.294414			−0.147207	−	0.989106i	$-0.547028\pi$
$809$	−8.37400			−0.294414			−0.147207	+	0.989106i	$0.547028\pi$
$810$	9.58894	+	7.72849i	0.336921	+	0.271551i
$811$			0.777328i			0.0272957i	0.999907	+	0.0136478i	$0.00434438\pi$
$811$			0.777328i			0.0272957i	−0.999907	+	0.0136478i	$0.995656\pi$
$812$	9.45079	−	26.6103i	0.331658	−	0.933838i
$813$			2.84464i			0.0997659i
$814$	0.0927959	−	0.115134i	0.00325250	−	0.00403545i
$815$	6.53712			0.228985
$816$	2.22408	−	1.01486i	0.0778585	−	0.0355274i
$817$			41.8359i			1.46365i
$818$	−27.5777	+	34.2163i	−0.964231	+	1.19635i
$819$	4.15713	−	6.70044i	0.145262	−	0.234132i
$820$	10.6419	−	2.31326i	0.371631	−	0.0807825i
$821$		−	19.9805i		−	0.697326i	−0.937248	−	0.348663i	$-0.886636\pi$
$821$		−	19.9805i		−	0.697326i	0.937248	−	0.348663i	$-0.113364\pi$
$822$	0.333785	−	0.414136i	0.0116421	−	0.0144446i
$823$		−	10.8575i		−	0.378469i	−0.981932	−	0.189234i	$-0.939399\pi$
$823$		−	10.8575i		−	0.378469i	0.981932	−	0.189234i	$-0.0606006\pi$
$824$	−13.0561	+	26.0675i	−0.454832	+	0.908106i
$825$			0.879057i			0.0306048i
$826$	5.07967	+	14.4928i	0.176744	+	0.504270i
$827$	−5.75544			−0.200136			−0.100068	−	0.994981i	$-0.531906\pi$
$827$	−5.75544			−0.200136			−0.100068	+	0.994981i	$0.531906\pi$
$828$	−15.4575	+	3.36005i	−0.537186	+	0.116770i
$829$	−46.6460			−1.62008			−0.810042	−	0.586372i	$-0.800556\pi$
$829$	−46.6460			−1.62008			−0.810042	+	0.586372i	$0.800556\pi$
$830$	−4.44695	+	5.51744i	−0.154356	+	0.191513i
$831$	0.361568			0.0125427
$832$	4.79122	+	6.40658i	0.166106	+	0.222108i
$833$	27.3477	−	13.5558i	0.947541	−	0.469682i
$834$	−0.947259	−	0.763472i	−0.0328009	−	0.0264369i
$835$	0.153398			0.00530857
$836$	−23.4286	+	5.09274i	−0.810294	+	0.176136i
$837$		−	7.77842i		−	0.268862i
$838$	35.7784	−	44.3912i	1.23595	−	1.53347i
$839$	−39.1501			−1.35161			−0.675805	−	0.737080i	$-0.736204\pi$
$839$	−39.1501			−1.35161			−0.675805	+	0.737080i	$0.736204\pi$
$840$	0.881913	−	0.542114i	0.0304289	−	0.0187047i
$841$	0.520537			0.0179496
$842$	7.22250	−	8.96114i	0.248904	−	0.308821i
$843$		−	2.83645i		−	0.0976926i
$844$	−8.01798	−	36.8858i	−0.275990	−	1.26966i
$845$	−0.986963			−0.0339525
$846$	22.1833	+	17.8793i	0.762678	+	0.614703i
$847$	11.9582	−	19.2742i	0.410889	−	0.662270i
$848$	−6.01283	−	13.1772i	−0.206482	−	0.452506i
$849$	−3.06917			−0.105334
$850$	−15.5791	+	19.3294i	−0.534359	+	0.662993i
$851$	0.178126			0.00610607
$852$	0.116730	+	0.537003i	0.00399910	+	0.0183974i
$853$	−39.1802			−1.34151			−0.670753	−	0.741681i	$-0.734029\pi$
$853$	−39.1802			−1.34151			−0.670753	+	0.741681i	$0.734029\pi$
$854$	−28.6510	+	10.0421i	−0.980419	+	0.343632i
$855$			22.6355i			0.774117i
$856$	−7.97416	+	15.9210i	−0.272551	+	0.544169i
$857$		−	36.4665i		−	1.24567i	−0.782352	−	0.622836i	$-0.785980\pi$
$857$		−	36.4665i		−	1.24567i	0.782352	−	0.622836i	$-0.214020\pi$
$858$	0.193777	−	0.240425i	0.00661545	−	0.00820796i
$859$			27.9827i			0.954757i	0.878698	+	0.477379i	$0.158413\pi$
$859$			27.9827i			0.954757i	−0.878698	+	0.477379i	$0.841587\pi$
$860$	2.27950	+	10.4866i	0.0777302	+	0.357589i
$861$	1.07863	−	1.73853i	0.0367596	−	0.0592490i
$862$	13.3670	−	16.5848i	0.455282	−	0.564880i
$863$			51.1854i			1.74237i	0.490955	+	0.871185i	$0.336648\pi$
$863$			51.1854i			1.74237i	−0.490955	+	0.871185i	$0.663352\pi$
$864$	−1.17445	+	4.59397i	−0.0399557	+	0.156290i
$865$	−0.299469			−0.0101823
$866$	−2.61691	+	3.24687i	−0.0889263	+	0.110333i
$867$		−	0.282203i		−	0.00958412i
$868$	46.2716	+	16.4336i	1.57056	+	0.557794i
$869$		−	14.2153i		−	0.482222i
$870$	−0.812878	−	0.655163i	−0.0275591	−	0.0222121i
$871$	−5.12668			−0.173711
$872$	−22.9512	−	11.4953i	−0.777224	−	0.389279i
$873$			31.5886i			1.06911i
$874$	−22.4861	−	18.1233i	−0.760603	−	0.613031i
$875$	−12.4256	+	20.0275i	−0.420061	+	0.677053i
$876$	−0.209968	−	0.965933i	−0.00709415	−	0.0326359i
$877$			4.87247i			0.164532i	0.996610	+	0.0822658i	$0.0262156\pi$
$877$			4.87247i			0.164532i	−0.996610	+	0.0822658i	$0.973784\pi$
$878$	−18.8676	−	15.2069i	−0.636749	−	0.513207i
$879$			0.860281i			0.0290166i
$880$	−5.59511	+	2.55309i	−0.188611	+	0.0860645i
$881$			52.8322i			1.77996i	0.455998	+	0.889981i	$0.349282\pi$
$881$			52.8322i			1.77996i	−0.455998	+	0.889981i	$0.650718\pi$
$882$	−6.38644	+	28.8045i	−0.215043	+	0.969898i
$883$	38.1741			1.28466			0.642330	−	0.766428i	$-0.277968\pi$
$883$	38.1741			1.28466			0.642330	+	0.766428i	$0.277968\pi$
$884$	8.52186	−	1.85242i	0.286621	−	0.0623037i
$885$	0.567785			0.0190859
$886$	25.0326	+	20.1758i	0.840988	+	0.677820i
$887$	0.0103911			0.000348898			0.000174449	−	1.00000i	$-0.499944\pi$
$887$	0.0103911			0.000348898			0.000174449		1.00000i	$0.499944\pi$
$888$	0.0119165	−	0.0237922i	0.000399891	−	0.000798413i
$889$	−24.2725	−	15.0593i	−0.814074	−	0.505073i
$890$	−0.968849	+	1.20208i	−0.0324759	+	0.0402937i
$891$	−13.7456			−0.460496
$892$	0.590015	+	2.71430i	0.0197552	+	0.0908814i
$893$			52.0180i			1.74072i
$894$	−0.261685	−	0.210913i	−0.00875205	−	0.00705398i
$895$	16.9309			0.565938
$896$	−24.8469	−	16.6922i	−0.830077	−	0.557649i
$897$	0.371964			0.0124195
$898$	−33.3614	−	26.8886i	−1.11328	−	0.897284i
$899$		−	49.5219i		−	1.65165i
$900$	−5.09732	−	23.4496i	−0.169911	−	0.781654i
$901$	−15.7893			−0.526019
$902$	−7.62751	+	9.46365i	−0.253968	+	0.315105i
$903$	1.71316	+	1.06289i	0.0570103	+	0.0353707i
$904$	17.2787	−	34.4982i	0.574680	−	1.14739i
$905$	−14.8835			−0.494744
$906$	−1.96054	−	1.58015i	−0.0651344	−	0.0524970i
$907$	42.1808			1.40059			0.700295	−	0.713854i	$-0.253052\pi$
$907$	42.1808			1.40059			0.700295	+	0.713854i	$0.253052\pi$
$908$	7.43645	−	1.61648i	0.246787	−	0.0536449i
$909$	−1.03888			−0.0344576
$910$	3.48501	−	1.22148i	0.115527	−	0.0404917i
$911$			14.7988i			0.490305i	0.969485	+	0.245153i	$0.0788381\pi$
$911$			14.7988i			0.490305i	−0.969485	+	0.245153i	$0.921162\pi$
$912$	−3.92502	+	1.79102i	−0.129971	+	0.0593064i
$913$		−	7.90919i		−	0.261756i
$914$	20.4376	+	16.4723i	0.676017	+	0.544856i
$915$			1.12246i			0.0371074i
$916$	−9.33493	−	42.9443i	−0.308435	−	1.41892i
$917$	36.1228	+	22.4115i	1.19288	+	0.740094i
$918$	4.02453	+	3.24369i	0.132829	+	0.107058i
$919$			16.6672i			0.549801i	0.961473	+	0.274901i	$0.0886449\pi$
$919$			16.6672i			0.549801i	−0.961473	+	0.274901i	$0.911355\pi$
$920$	−6.62383	−	3.31759i	−0.218381	−	0.109378i
$921$	−4.12248			−0.135840
$922$	−35.5773	−	28.6746i	−1.17168	−	0.944347i
$923$			1.96037i			0.0645264i
$924$	−0.386684	+	1.08877i	−0.0127210	+	0.0358180i
$925$			0.270223i			0.00888489i
$926$	−10.5814	+	13.1286i	−0.347727	+	0.431434i
$927$	−30.7204			−1.00899
$928$	−7.47723	+	29.2478i	−0.245452	+	0.960106i
$929$			44.7600i			1.46853i	0.678863	+	0.734265i	$0.262473\pi$
$929$			44.7600i			1.46853i	−0.678863	+	0.734265i	$0.737527\pi$
$930$	1.13924	−	1.41348i	0.0373571	−	0.0463499i
$931$	−48.2627	+	23.9231i	−1.58175	+	0.784048i
$932$	12.2355	+	56.2882i	0.400788	+	1.84378i
$933$			4.66173i			0.152618i
$934$	−17.2623	+	21.4177i	−0.564839	+	0.700810i
$935$			6.70425i			0.219253i
$936$	−3.77505	+	7.53718i	−0.123391	+	0.246360i
$937$		−	47.4249i		−	1.54930i	−0.632389	−	0.774651i	$-0.717925\pi$
$937$		−	47.4249i		−	1.54930i	0.632389	−	0.774651i	$-0.282075\pi$
$938$	18.1026	−	6.34487i	0.591069	−	0.207167i
$939$	−1.78475			−0.0582432
$940$	2.83429	+	13.0388i	0.0924442	+	0.425279i
$941$	39.1107			1.27497			0.637486	−	0.770462i	$-0.279975\pi$
$941$	39.1107			1.27497			0.637486	+	0.770462i	$0.279975\pi$
$942$	2.67517	−	3.31915i	0.0871618	−	0.108144i
$943$	−14.6413			−0.476788
$944$	−6.81544	−	14.9361i	−0.221824	−	0.486128i
$945$	1.85993	+	1.15395i	0.0605035	+	0.0375380i
$946$	−9.32553	−	7.51619i	−0.303199	−	0.244372i
$947$	18.4246			0.598719			0.299359	−	0.954140i	$-0.403227\pi$
$947$	18.4246			0.598719			0.299359	+	0.954140i	$0.403227\pi$
$948$	−0.543351	−	2.49962i	−0.0176472	−	0.0811840i
$949$		−	3.52622i		−	0.114466i
$950$	27.4937	−	34.1122i	0.892015	−	1.10675i
$951$	−1.74875			−0.0567070
$952$	−27.7985	+	17.0878i	−0.900955	+	0.553819i
$953$	−35.0327			−1.13482			−0.567410	−	0.823436i	$-0.692054\pi$
$953$	−35.0327			−1.13482			−0.567410	+	0.823436i	$0.692054\pi$
$954$	9.57749	−	11.8830i	0.310083	−	0.384728i
$955$			16.1357i			0.522139i
$956$	−24.4897	+	5.32339i	−0.792052	+	0.172171i
$957$	1.16525			0.0376672
$958$	−14.0883	−	11.3549i	−0.455171	−	0.366859i
$959$	−3.74291	+	6.03280i	−0.120865	+	0.194809i
$960$	−0.886258	+	0.662796i	−0.0286039	+	0.0213917i
$961$	55.1117			1.77780
$962$	0.0595674	−	0.0739068i	0.00192053	−	0.00238285i
$963$	−18.7628			−0.604623
$964$	11.0385	−	2.39947i	0.355526	−	0.0772818i
$965$	2.78986			0.0898088
$966$	−1.31342	+	0.460349i	−0.0422587	+	0.0148115i
$967$			24.3665i			0.783574i	0.920056	+	0.391787i	$0.128143\pi$
$967$			24.3665i			0.783574i	−0.920056	+	0.391787i	$0.871857\pi$
$968$	−10.8592	+	21.6811i	−0.349027	+	0.696858i
$969$			4.70310i			0.151085i
$970$	−9.28353	+	11.5183i	−0.298076	+	0.369831i
$971$		−	52.6513i		−	1.68966i	−0.535033	−	0.844831i	$-0.679701\pi$
$971$		−	52.6513i		−	1.68966i	0.535033	−	0.844831i	$-0.320299\pi$
$972$	−7.33161	+	1.59369i	−0.235162	+	0.0511178i
$973$	13.7989	+	8.56122i	0.442374	+	0.274460i
$974$	14.7846	−	18.3436i	0.473728	−	0.587766i
$975$			0.564283i			0.0180715i
$976$	29.5273	−	13.4735i	0.945147	−	0.431277i
$977$	−18.3841			−0.588160			−0.294080	−	0.955781i	$-0.595013\pi$
$977$	−18.3841			−0.588160			−0.294080	+	0.955781i	$0.595013\pi$
$978$	−0.823889	+	1.02222i	−0.0263451	+	0.0326870i
$979$		−	1.72316i		−	0.0550725i
$980$	−10.7940	+	8.62622i	−0.344802	+	0.275555i
$981$		−	27.0478i		−	0.863569i
$982$	42.5544	+	34.2980i	1.35796	+	1.09449i
$983$	−15.4501			−0.492782			−0.246391	−	0.969170i	$-0.579245\pi$
$983$	−15.4501			−0.492782			−0.246391	+	0.969170i	$0.579245\pi$
$984$	−0.979495	+	1.95564i	−0.0312252	+	0.0623434i
$985$			20.9642i			0.667975i
$986$	25.6225	+	20.6512i	0.815985	+	0.657668i
$987$	2.13011	+	1.32158i	0.0678021	+	0.0420662i
$988$	−15.0392	+	3.26912i	−0.478462	+	0.104005i
$989$		−	14.4276i		−	0.458773i
$990$	−5.04561	−	4.06666i	−0.160360	−	0.129247i
$991$		−	51.7005i		−	1.64232i	−0.570697	−	0.821161i	$-0.693327\pi$
$991$		−	51.7005i		−	1.64232i	0.570697	−	0.821161i	$-0.306673\pi$
$992$	−50.8579	−	13.0019i	−1.61474	−	0.412810i
$993$			4.26827i			0.135450i
$994$	−2.42619	−	6.92216i	−0.0769540	−	0.219558i
$995$	−20.7547			−0.657968
$996$	−0.302312	−	1.39075i	−0.00957912	−	0.0440677i
$997$	−6.68172			−0.211612			−0.105806	−	0.994387i	$-0.533742\pi$
$997$	−6.68172			−0.211612			−0.105806	+	0.994387i	$0.533742\pi$
$998$	−15.1442	−	12.2059i	−0.479381	−	0.386371i
$999$	0.0562626			0.00178007

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.h.a.27.11	✓	48
4.3	odd	2		2912.2.h.a.2575.24		48
7.6	odd	2		728.2.h.b.27.11	yes	48
8.3	odd	2		728.2.h.b.27.12	yes	48
8.5	even	2		2912.2.h.b.2575.24		48
28.27	even	2		2912.2.h.b.2575.25		48
56.13	odd	2		2912.2.h.a.2575.25		48
56.27	even	2	inner	728.2.h.a.27.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.h.a.27.11	✓	48	1.1	even	1	trivial
728.2.h.a.27.12	yes	48	56.27	even	2	inner
728.2.h.b.27.11	yes	48	7.6	odd	2
728.2.h.b.27.12	yes	48	8.3	odd	2
2912.2.h.a.2575.24		48	4.3	odd	2
2912.2.h.a.2575.25		48	56.13	odd	2
2912.2.h.b.2575.24		48	8.5	even	2
2912.2.h.b.2575.25		48	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.10110 - 0.887461i) q^{2} +0.140163i q^{3} +(0.424825 + 1.95436i) q^{4} -0.986963 q^{5} +(0.124389 - 0.154333i) q^{6} +(-1.39484 + 2.24820i) q^{7} +(1.26665 - 2.52895i) q^{8} +2.98035 q^{9} +(1.08674 + 0.875891i) q^{10} -1.55783 q^{11} +(-0.273929 + 0.0595448i) q^{12} -1.00000 q^{13} +(3.53105 - 1.23762i) q^{14} -0.138336i q^{15} +(-3.63905 + 1.66052i) q^{16} +4.36043i q^{17} +(-3.28166 - 2.64495i) q^{18} -7.69522i q^{19} +(-0.419286 - 1.92888i) q^{20} +(-0.315115 - 0.195505i) q^{21} +(1.71532 + 1.38251i) q^{22} +2.65380i q^{23} +(0.354466 + 0.177537i) q^{24} -4.02591 q^{25} +(1.10110 + 0.887461i) q^{26} +0.838225i q^{27} +(-4.98636 - 1.77093i) q^{28} +5.33662i q^{29} +(-0.122768 + 0.152321i) q^{30} -9.27964 q^{31} +(5.48059 + 1.40112i) q^{32} -0.218350i q^{33} +(3.86972 - 4.80126i) q^{34} +(1.37666 - 2.21889i) q^{35} +(1.26613 + 5.82469i) q^{36} -0.0671212i q^{37} +(-6.82921 + 8.47318i) q^{38} -0.140163i q^{39} +(-1.25013 + 2.49598i) q^{40} +5.51713i q^{41} +(0.173468 + 0.494923i) q^{42} -5.43661 q^{43} +(-0.661805 - 3.04456i) q^{44} -2.94150 q^{45} +(2.35514 - 2.92208i) q^{46} -6.75979 q^{47} +(-0.232744 - 0.510060i) q^{48} +(-3.10882 - 6.27178i) q^{49} +(4.43291 + 3.57283i) q^{50} -0.611172 q^{51} +(-0.424825 - 1.95436i) q^{52} +3.62105i q^{53} +(0.743892 - 0.922966i) q^{54} +1.53752 q^{55} +(3.91883 + 6.37517i) q^{56} +1.07859 q^{57} +(4.73604 - 5.87613i) q^{58} +4.10440i q^{59} +(0.270358 - 0.0587685i) q^{60} -8.11403 q^{61} +(10.2178 + 8.23532i) q^{62} +(-4.15713 + 6.70044i) q^{63} +(-4.79122 - 6.40658i) q^{64} +0.986963 q^{65} +(-0.193777 + 0.240425i) q^{66} +5.12668 q^{67} +(-8.52186 + 1.85242i) q^{68} -0.371964 q^{69} +(-3.48501 + 1.22148i) q^{70} -1.96037i q^{71} +(3.77505 - 7.53718i) q^{72} +3.52622i q^{73} +(-0.0595674 + 0.0739068i) q^{74} -0.564283i q^{75} +(15.0392 - 3.26912i) q^{76} +(2.17293 - 3.50232i) q^{77} +(-0.124389 + 0.154333i) q^{78} +9.12508i q^{79} +(3.59160 - 1.63887i) q^{80} +8.82357 q^{81} +(4.89624 - 6.07490i) q^{82} +5.07705i q^{83} +(0.248219 - 0.698904i) q^{84} -4.30359i q^{85} +(5.98623 + 4.82478i) q^{86} -0.747996 q^{87} +(-1.97322 + 3.93968i) q^{88} +1.10613i q^{89} +(3.23887 + 2.61047i) q^{90} +(1.39484 - 2.24820i) q^{91} +(-5.18647 + 1.12740i) q^{92} -1.30066i q^{93} +(7.44317 + 5.99905i) q^{94} +7.59489i q^{95} +(-0.196385 + 0.768176i) q^{96} +10.5990i q^{97} +(-2.14285 + 9.66479i) q^{98} -4.64288 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + q^{4} - 10 q^{6} - 5 q^{8} - 48 q^{9} - 4 q^{11} + 10 q^{12} - 48 q^{13} + 10 q^{14} + 5 q^{16} - 15 q^{18} - 22 q^{20} - 6 q^{22} + 48 q^{25} - q^{26} + 4 q^{28} - 26 q^{30} - 19 q^{32}+ \cdots + 20 q^{99}+O(q^{100}) \) 48 * q + q^2 + q^4 - 10 * q^6 - 5 * q^8 - 48 * q^9 - 4 * q^11 + 10 * q^12 - 48 * q^13 + 10 * q^14 + 5 * q^16 - 15 * q^18 - 22 * q^20 - 6 * q^22 + 48 * q^25 - q^26 + 4 * q^28 - 26 * q^30 - 19 * q^32 + 36 * q^34 + 12 * q^35 - 5 * q^36 - 10 * q^38 - 48 * q^40 + 3 * q^42 - 4 * q^43 - 30 * q^44 + 24 * q^45 + 2 * q^46 + 48 * q^48 + 11 * q^50 - 40 * q^51 - q^52 + 62 * q^54 + 10 * q^56 + 2 * q^58 + 18 * q^60 - 36 * q^62 + 20 * q^63 - 11 * q^64 + 32 * q^66 - 4 * q^67 + 62 * q^68 - 11 * q^70 + 13 * q^72 - 44 * q^74 - 48 * q^76 - 20 * q^77 + 10 * q^78 + 32 * q^80 + 64 * q^81 - 50 * q^82 + 21 * q^84 + 2 * q^86 - 40 * q^87 - 66 * q^88 + 74 * q^90 - 24 * q^92 - 26 * q^94 - 84 * q^96 - 6 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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