LMFDB - Embedded newform 728.2.h.b.27.4

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			27.4
Character	$\chi$	$=$	728.27
Dual form			728.2.h.b.27.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39580 + 0.227483i) q^{2} +1.35635i q^{3} +(1.89650 - 0.635042i) q^{4} -2.01767 q^{5} +(-0.308546 - 1.89318i) q^{6} +(2.18534 + 1.49140i) q^{7} +(-2.50267 + 1.31781i) q^{8} +1.16033 q^{9} +(2.81626 - 0.458986i) q^{10} -4.92824 q^{11} +(0.861336 + 2.57231i) q^{12} +1.00000 q^{13} +(-3.38957 - 1.58456i) q^{14} -2.73666i q^{15} +(3.19344 - 2.40872i) q^{16} +4.50218i q^{17} +(-1.61958 + 0.263955i) q^{18} +4.26085i q^{19} +(-3.82651 + 1.28130i) q^{20} +(-2.02285 + 2.96408i) q^{21} +(6.87883 - 1.12109i) q^{22} -9.28723i q^{23} +(-1.78741 - 3.39449i) q^{24} -0.929012 q^{25} +(-1.39580 + 0.227483i) q^{26} +5.64284i q^{27} +(5.09161 + 1.44066i) q^{28} +6.03717i q^{29} +(0.622544 + 3.81982i) q^{30} -2.67926 q^{31} +(-3.90946 + 4.08854i) q^{32} -6.68440i q^{33} +(-1.02417 - 6.28413i) q^{34} +(-4.40930 - 3.00915i) q^{35} +(2.20056 - 0.736856i) q^{36} -1.91540i q^{37} +(-0.969273 - 5.94728i) q^{38} +1.35635i q^{39} +(5.04956 - 2.65891i) q^{40} +9.84828i q^{41} +(2.14922 - 4.59742i) q^{42} -1.98858 q^{43} +(-9.34643 + 3.12964i) q^{44} -2.34116 q^{45} +(2.11269 + 12.9631i) q^{46} -6.61191 q^{47} +(3.26705 + 4.33141i) q^{48} +(2.55145 + 6.51844i) q^{49} +(1.29671 - 0.211335i) q^{50} -6.10651 q^{51} +(1.89650 - 0.635042i) q^{52} -7.90627i q^{53} +(-1.28365 - 7.87626i) q^{54} +9.94356 q^{55} +(-7.43458 - 0.852612i) q^{56} -5.77918 q^{57} +(-1.37336 - 8.42666i) q^{58} -9.77831i q^{59} +(-1.73789 - 5.19007i) q^{60} -10.0807 q^{61} +(3.73971 - 0.609487i) q^{62} +(2.53571 + 1.73051i) q^{63} +(4.52674 - 6.59611i) q^{64} -2.01767 q^{65} +(1.52059 + 9.33007i) q^{66} -15.8803 q^{67} +(2.85907 + 8.53839i) q^{68} +12.5967 q^{69} +(6.83902 + 3.19712i) q^{70} -2.17824i q^{71} +(-2.90392 + 1.52909i) q^{72} -7.87181i q^{73} +(0.435723 + 2.67351i) q^{74} -1.26006i q^{75} +(2.70582 + 8.08071i) q^{76} +(-10.7699 - 7.34998i) q^{77} +(-0.308546 - 1.89318i) q^{78} +6.79571i q^{79} +(-6.44331 + 4.85999i) q^{80} -4.17266 q^{81} +(-2.24032 - 13.7462i) q^{82} +15.5710i q^{83} +(-1.95403 + 6.90598i) q^{84} -9.08390i q^{85} +(2.77565 - 0.452369i) q^{86} -8.18848 q^{87} +(12.3338 - 6.49450i) q^{88} +5.33818i q^{89} +(3.26778 - 0.532574i) q^{90} +(2.18534 + 1.49140i) q^{91} +(-5.89778 - 17.6132i) q^{92} -3.63400i q^{93} +(9.22889 - 1.50410i) q^{94} -8.59698i q^{95} +(-5.54547 - 5.30258i) q^{96} -5.40946i q^{97} +(-5.04415 - 8.51801i) q^{98} -5.71838 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} - 6 q^{14} + 5 q^{16} - 15 q^{18} + 22 q^{20} - 6 q^{22} + 48 q^{25} + q^{26} - 26 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 - 6 * q^14 + 5 * q^16 - 15 * q^18 + 22 * q^20 - 6 * q^22 + 48 * q^25 + q^26 - 26 * q^28 - 26 * q^30 - 19 * q^32 - 36 * q^34 + 12 * q^35 - 5 * q^36 + 10 * q^38 + 48 * q^40 + 39 * 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 - 14 * 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 - 37 * 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 - 45 * q^84 + 2 * q^86 + 40 * q^87 - 66 * q^88 - 74 * q^90 - 24 * q^92 + 26 * q^94 + 84 * q^96 - 20 * 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 $

$2$	−1.39580	+	0.227483i	−0.986978	+	0.160855i
$2$	−1.39580	+	0.227483i	−0.986978	+	0.160855i
$3$			1.35635i			0.783086i	0.920160	+	0.391543i	$0.128059\pi$
$3$			1.35635i			0.783086i	−0.920160	+	0.391543i	$0.871941\pi$
$4$	1.89650	−	0.635042i	0.948251	−	0.317521i
$5$	−2.01767			−0.902329			−0.451164	−	0.892441i	$-0.648991\pi$
$5$	−2.01767			−0.902329			−0.451164	+	0.892441i	$0.648991\pi$
$6$	−0.308546	−	1.89318i	−0.125963	−	0.772889i
$7$	2.18534	+	1.49140i	0.825982	+	0.563696i
$7$	2.18534	+	1.49140i	0.825982	+	0.563696i
$8$	−2.50267	+	1.31781i	−0.884828	+	0.465917i
$9$	1.16033			0.386776
$10$	2.81626	−	0.458986i	0.890579	−	0.145144i
$11$	−4.92824			−1.48592			−0.742961	−	0.669335i	$-0.766579\pi$
$11$	−4.92824			−1.48592			−0.742961	+	0.669335i	$0.766579\pi$
$12$	0.861336	+	2.57231i	0.248646	+	0.742563i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−3.38957	−	1.58456i	−0.905900	−	0.423492i
$15$		−	2.73666i		−	0.706601i
$16$	3.19344	−	2.40872i	0.798361	−	0.602179i
$17$			4.50218i			1.09194i	0.837805	+	0.545969i	$0.183838\pi$
$17$			4.50218i			1.09194i	−0.837805	+	0.545969i	$0.816162\pi$
$18$	−1.61958	+	0.263955i	−0.381739	+	0.0622149i
$19$			4.26085i			0.977506i	0.872422	+	0.488753i	$0.162548\pi$
$19$			4.26085i			0.977506i	−0.872422	+	0.488753i	$0.837452\pi$
$20$	−3.82651	+	1.28130i	−0.855635	+	0.286508i
$21$	−2.02285	+	2.96408i	−0.441423	+	0.646815i
$22$	6.87883	−	1.12109i	1.46657	−	0.239018i
$23$		−	9.28723i		−	1.93652i	−0.249944	−	0.968260i	$-0.580412\pi$
$23$		−	9.28723i		−	1.93652i	0.249944	−	0.968260i	$-0.419588\pi$
$24$	−1.78741	−	3.39449i	−0.364853	−	0.692897i
$25$	−0.929012			−0.185802
$26$	−1.39580	+	0.227483i	−0.273738	+	0.0446132i
$27$			5.64284i			1.08597i
$28$	5.09161	+	1.44066i	0.962224	+	0.272259i
$29$			6.03717i			1.12107i	0.828130	+	0.560537i	$0.189405\pi$
$29$			6.03717i			1.12107i	−0.828130	+	0.560537i	$0.810595\pi$
$30$	0.622544	+	3.81982i	0.113660	+	0.697400i
$31$	−2.67926			−0.481209			−0.240605	−	0.970623i	$-0.577346\pi$
$31$	−2.67926			−0.481209			−0.240605	+	0.970623i	$0.577346\pi$
$32$	−3.90946	+	4.08854i	−0.691101	+	0.722758i
$33$		−	6.68440i		−	1.16360i
$34$	−1.02417	−	6.28413i	−0.175644	−	1.07772i
$35$	−4.40930	−	3.00915i	−0.745308	−	0.508639i
$36$	2.20056	−	0.736856i	0.366761	−	0.122809i
$37$		−	1.91540i		−	0.314890i	−0.987528	−	0.157445i	$-0.949674\pi$
$37$		−	1.91540i		−	0.314890i	0.987528	−	0.157445i	$-0.0503257\pi$
$38$	−0.969273	−	5.94728i	−0.157237	−	0.964777i
$39$			1.35635i			0.217189i
$40$	5.04956	−	2.65891i	0.798406	−	0.420411i
$41$			9.84828i			1.53804i	0.639223	+	0.769022i	$0.279256\pi$
$41$			9.84828i			1.53804i	−0.639223	+	0.769022i	$0.720744\pi$
$42$	2.14922	−	4.59742i	0.331631	−	0.709398i
$43$	−1.98858			−0.303255			−0.151628	−	0.988438i	$-0.548451\pi$
$43$	−1.98858			−0.303255			−0.151628	+	0.988438i	$0.548451\pi$
$44$	−9.34643	+	3.12964i	−1.40903	+	0.471811i
$45$	−2.34116			−0.348999
$46$	2.11269	+	12.9631i	0.311499	+	1.91130i
$47$	−6.61191			−0.964446			−0.482223	−	0.876048i	$-0.660171\pi$
$47$	−6.61191			−0.964446			−0.482223	+	0.876048i	$0.660171\pi$
$48$	3.26705	+	4.33141i	0.471558	+	0.625186i
$49$	2.55145	+	6.51844i	0.364493	+	0.931206i
$50$	1.29671	−	0.211335i	0.183383	−	0.0298873i
$51$	−6.10651			−0.855082
$52$	1.89650	−	0.635042i	0.262998	−	0.0880645i
$53$		−	7.90627i		−	1.08601i	−0.839730	−	0.543005i	$-0.817287\pi$
$53$		−	7.90627i		−	1.08601i	0.839730	−	0.543005i	$-0.182713\pi$
$54$	−1.28365	−	7.87626i	−0.174683	−	1.07182i
$55$	9.94356			1.34079
$56$	−7.43458	−	0.852612i	−0.993488	−	0.113935i
$57$	−5.77918			−0.765471
$58$	−1.37336	−	8.42666i	−0.180330	−	1.10647i
$59$		−	9.77831i		−	1.27303i	−0.771265	−	0.636514i	$-0.780376\pi$
$59$		−	9.77831i		−	1.27303i	0.771265	−	0.636514i	$-0.219624\pi$
$60$	−1.73789	−	5.19007i	−0.224361	−	0.670036i
$61$	−10.0807			−1.29070			−0.645352	−	0.763885i	$-0.723289\pi$
$61$	−10.0807			−1.29070			−0.645352	+	0.763885i	$0.723289\pi$
$62$	3.73971	−	0.609487i	0.474943	−	0.0774050i
$63$	2.53571	+	1.73051i	0.319470	+	0.218024i
$64$	4.52674	−	6.59611i	0.565842	−	0.824514i
$65$	−2.01767			−0.250261
$66$	1.52059	+	9.33007i	0.187172	+	1.14845i
$67$	−15.8803			−1.94008			−0.970041	−	0.242942i	$-0.921888\pi$
$67$	−15.8803			−1.94008			−0.970041	+	0.242942i	$0.921888\pi$
$68$	2.85907	+	8.53839i	0.346713	+	1.03543i
$69$	12.5967			1.51646
$70$	6.83902	+	3.19712i	0.817419	+	0.382129i
$71$		−	2.17824i		−	0.258510i	−0.991611	−	0.129255i	$-0.958741\pi$
$71$		−	2.17824i		−	0.258510i	0.991611	−	0.129255i	$-0.0412586\pi$
$72$	−2.90392	+	1.52909i	−0.342230	+	0.180205i
$73$		−	7.87181i		−	0.921326i	−0.887575	−	0.460663i	$-0.847612\pi$
$73$		−	7.87181i		−	0.921326i	0.887575	−	0.460663i	$-0.152388\pi$
$74$	0.435723	+	2.67351i	0.0506517	+	0.310790i
$75$		−	1.26006i		−	0.145499i
$76$	2.70582	+	8.08071i	0.310379	+	0.926921i
$77$	−10.7699	−	7.34998i	−1.22734	−	0.837608i
$78$	−0.308546	−	1.89318i	−0.0349360	−	0.214361i
$79$			6.79571i			0.764577i	0.924043	+	0.382289i	$0.124864\pi$
$79$			6.79571i			0.764577i	−0.924043	+	0.382289i	$0.875136\pi$
$80$	−6.44331	+	4.85999i	−0.720384	+	0.543364i
$81$	−4.17266			−0.463629
$82$	−2.24032	−	13.7462i	−0.247402	−	1.51801i
$83$			15.5710i			1.70913i	0.519340	+	0.854567i	$0.326178\pi$
$83$			15.5710i			1.70913i	−0.519340	+	0.854567i	$0.673822\pi$
$84$	−1.95403	+	6.90598i	−0.213202	+	0.753504i
$85$		−	9.08390i		−	0.985288i
$86$	2.77565	−	0.452369i	0.299306	−	0.0487802i
$87$	−8.18848			−0.877897
$88$	12.3338	−	6.49450i	1.31479	−	0.692316i
$89$			5.33818i			0.565846i	0.959143	+	0.282923i	$0.0913041\pi$
$89$			5.33818i			0.565846i	−0.959143	+	0.282923i	$0.908696\pi$
$90$	3.26778	−	0.532574i	0.344454	−	0.0561383i
$91$	2.18534	+	1.49140i	0.229086	+	0.156341i
$92$	−5.89778	−	17.6132i	−0.614886	−	1.83631i
$93$		−	3.63400i		−	0.376828i
$94$	9.22889	−	1.50410i	0.951887	−	0.155136i
$95$		−	8.59698i		−	0.882032i
$96$	−5.54547	−	5.30258i	−0.565982	−	0.541192i
$97$		−	5.40946i		−	0.549248i	−0.961552	−	0.274624i	$-0.911447\pi$
$97$		−	5.40946i		−	0.549248i	0.961552	−	0.274624i	$-0.0885533\pi$
$98$	−5.04415	−	8.51801i	−0.509536	−	0.860449i
$99$	−5.71838			−0.574718
$100$	−1.76187	+	0.589962i	−0.176187	+	0.0589962i
$101$	14.7053			1.46323			0.731617	−	0.681716i	$-0.238766\pi$
$101$	14.7053			1.46323			0.731617	+	0.681716i	$0.238766\pi$
$102$	8.52345	−	1.38913i	0.843947	−	0.137544i
$103$	−15.8101			−1.55782			−0.778909	−	0.627136i	$-0.784227\pi$
$103$	−15.8101			−1.55782			−0.778909	+	0.627136i	$0.784227\pi$
$104$	−2.50267	+	1.31781i	−0.245407	+	0.129222i
$105$	4.08145	−	5.98053i	0.398309	−	0.583640i
$106$	1.79855	+	11.0356i	0.174690	+	1.07187i
$107$	−5.79170			−0.559904			−0.279952	−	0.960014i	$-0.590319\pi$
$107$	−5.79170			−0.559904			−0.279952	+	0.960014i	$0.590319\pi$
$108$	3.58344	+	10.7017i	0.344817	+	1.02977i
$109$			14.0192i			1.34279i	0.741099	+	0.671396i	$0.234305\pi$
$109$			14.0192i			1.34279i	−0.741099	+	0.671396i	$0.765695\pi$
$110$	−13.8792	+	2.26200i	−1.32333	+	0.215673i
$111$	2.59795			0.246586
$112$	10.5711	−	0.501172i	0.998878	−	0.0473563i
$113$	−2.00196			−0.188328			−0.0941641	−	0.995557i	$-0.530018\pi$
$113$	−2.00196			−0.188328			−0.0941641	+	0.995557i	$0.530018\pi$
$114$	8.06657	−	1.31467i	0.755503	−	0.123130i
$115$			18.7385i			1.74738i
$116$	3.83385	+	11.4495i	0.355964	+	1.06306i
$117$	1.16033			0.107272
$118$	2.22440	+	13.6485i	0.204773	+	1.25645i
$119$	−6.71455	+	9.83880i	−0.615522	+	0.901922i
$120$	3.60640	+	6.84895i	0.329218	+	0.625221i
$121$	13.2876			1.20796
$122$	14.0706	−	2.29320i	1.27390	−	0.207616i
$123$	−13.3577			−1.20442
$124$	−5.08122	+	1.70144i	−0.456307	+	0.152794i
$125$	11.9628			1.06998
$126$	−3.93301	−	1.83861i	−0.350380	−	0.163797i
$127$			13.9958i			1.24193i	0.783839	+	0.620964i	$0.213259\pi$
$127$			13.9958i			1.24193i	−0.783839	+	0.620964i	$0.786741\pi$
$128$	−4.81790	+	10.2366i	−0.425847	+	0.904795i
$129$		−	2.69720i		−	0.237475i
$130$	2.81626	−	0.458986i	0.247002	−	0.0402558i
$131$			0.946942i			0.0827347i	0.999144	+	0.0413674i	$0.0131714\pi$
$131$			0.946942i			0.0827347i	−0.999144	+	0.0413674i	$0.986829\pi$
$132$	−4.24487	−	12.6770i	−0.369469	−	1.10339i
$133$	−6.35463	+	9.31142i	−0.551016	+	0.807402i
$134$	22.1656	−	3.61250i	1.91482	−	0.312072i
$135$		−	11.3854i		−	0.979898i
$136$	−5.93303	−	11.2675i	−0.508753	−	0.966178i
$137$	13.4840			1.15201			0.576007	−	0.817445i	$-0.304610\pi$
$137$	13.4840			1.15201			0.576007	+	0.817445i	$0.304610\pi$
$138$	−17.5824	+	2.86554i	−1.49672	+	0.243931i
$139$		−	10.4050i		−	0.882544i	−0.897373	−	0.441272i	$-0.854527\pi$
$139$		−	10.4050i		−	0.882544i	0.897373	−	0.441272i	$-0.145473\pi$
$140$	−10.2732	−	2.90677i	−0.868243	−	0.245667i
$141$		−	8.96803i		−	0.755245i
$142$	0.495514	+	3.04039i	0.0415826	+	0.255144i
$143$	−4.92824			−0.412120
$144$	3.70544	−	2.79490i	0.308787	−	0.232908i
$145$		−	12.1810i		−	1.01158i
$146$	1.79071	+	10.9875i	0.148200	+	0.909328i
$147$	−8.84126	+	3.46065i	−0.729215	+	0.285430i
$148$	−1.21636	−	3.63257i	−0.0999843	−	0.298595i
$149$		−	4.85942i		−	0.398100i	−0.979989	−	0.199050i	$-0.936214\pi$
$149$		−	4.85942i		−	0.398100i	0.979989	−	0.199050i	$-0.0637855\pi$
$150$	0.286643	+	1.75879i	0.0234043	+	0.143605i
$151$			1.05783i			0.0860854i	0.999073	+	0.0430427i	$0.0137051\pi$
$151$			1.05783i			0.0860854i	−0.999073	+	0.0430427i	$0.986295\pi$
$152$	−5.61500	−	10.6635i	−0.455437	−	0.864925i
$153$			5.22400i			0.422335i
$154$	16.7046	+	7.80911i	1.34610	+	0.629276i
$155$	5.40586			0.434209
$156$	0.861336	+	2.57231i	0.0689621	+	0.205950i
$157$	8.12606			0.648531			0.324265	−	0.945966i	$-0.394883\pi$
$157$	8.12606			0.648531			0.324265	+	0.945966i	$0.394883\pi$
$158$	−1.54591	−	9.48544i	−0.122986	−	0.754621i
$159$	10.7236			0.850439
$160$	7.88799	−	8.24931i	0.623600	−	0.652166i
$161$	13.8510	−	20.2958i	1.09161	−	1.59953i
$162$	5.82419	−	0.949211i	0.457591	−	0.0745771i
$163$	9.36955			0.733880			0.366940	−	0.930245i	$-0.380405\pi$
$163$	9.36955			0.733880			0.366940	+	0.930245i	$0.380405\pi$
$164$	6.25407	+	18.6773i	0.488361	+	1.45845i
$165$			13.4869i			1.04995i
$166$	−3.54214	−	21.7339i	−0.274923	−	1.68688i
$167$	15.0871			1.16747			0.583737	−	0.811942i	$-0.301590\pi$
$167$	15.0871			1.16747			0.583737	+	0.811942i	$0.301590\pi$
$168$	1.15644	−	10.0839i	0.0892210	−	0.777987i
$169$	1.00000			0.0769231
$170$	2.06644	+	12.6793i	0.158489	+	0.972457i
$171$			4.94398i			0.378075i
$172$	−3.77134	+	1.26283i	−0.287562	+	0.0962900i
$173$	9.07705			0.690116			0.345058	−	0.938581i	$-0.387859\pi$
$173$	9.07705			0.690116			0.345058	+	0.938581i	$0.387859\pi$
$174$	11.4295	−	1.86274i	0.866465	−	0.141214i
$175$	−2.03021	−	1.38553i	−0.153470	−	0.104736i
$176$	−15.7381	+	11.8707i	−1.18630	+	0.894791i
$177$	13.2628			0.996891
$178$	−1.21435	−	7.45102i	−0.0910192	−	0.558478i
$179$	16.7901			1.25495			0.627476	−	0.778636i	$-0.284088\pi$
$179$	16.7901			1.25495			0.627476	+	0.778636i	$0.284088\pi$
$180$	−4.44001	+	1.48673i	−0.330939	+	0.110814i
$181$	3.66980			0.272774			0.136387	−	0.990656i	$-0.456451\pi$
$181$	3.66980			0.272774			0.136387	+	0.990656i	$0.456451\pi$
$182$	−3.38957	−	1.58456i	−0.251251	−	0.117456i
$183$		−	13.6729i		−	1.01073i
$184$	12.2388	+	23.2429i	0.902258	+	1.71349i
$185$			3.86465i			0.284135i
$186$	0.826676	+	5.07233i	0.0606148	+	0.371921i
$187$		−	22.1878i		−	1.62253i
$188$	−12.5395	+	4.19884i	−0.914537	+	0.306232i
$189$	−8.41573	+	12.3315i	−0.612155	+	0.896988i
$190$	1.95567	+	11.9996i	0.141879	+	0.870546i
$191$			25.9830i			1.88007i	0.341082	+	0.940033i	$0.389206\pi$
$191$			25.9830i			1.88007i	−0.341082	+	0.940033i	$0.610794\pi$
$192$	8.94660	+	6.13982i	0.645665	+	0.443103i
$193$	18.2177			1.31134			0.655669	−	0.755049i	$-0.272387\pi$
$193$	18.2177			1.31134			0.655669	+	0.755049i	$0.272387\pi$
$194$	1.23056	+	7.55052i	0.0883493	+	0.542095i
$195$		−	2.73666i		−	0.195976i
$196$	8.97832	+	10.7420i	0.641308	+	0.767283i
$197$			6.35885i			0.453049i	0.974005	+	0.226525i	$0.0727363\pi$
$197$			6.35885i			0.453049i	−0.974005	+	0.226525i	$0.927264\pi$
$198$	7.98170	−	1.30084i	0.567234	−	0.0924464i
$199$	7.66867			0.543617			0.271809	−	0.962351i	$-0.412378\pi$
$199$	7.66867			0.543617			0.271809	+	0.962351i	$0.412378\pi$
$200$	2.32501	−	1.22426i	0.164403	−	0.0865686i
$201$		−	21.5391i		−	1.51925i
$202$	−20.5257	+	3.34522i	−1.44418	+	0.235369i
$203$	−9.00383	+	13.1933i	−0.631945	+	0.925987i
$204$	−11.5810	+	3.87789i	−0.810833	+	0.271507i
$205$		−	19.8706i		−	1.38782i
$206$	22.0677	−	3.59654i	1.53753	−	0.250583i
$207$		−	10.7762i		−	0.748999i
$208$	3.19344	−	2.40872i	0.221425	−	0.167014i
$209$		−	20.9985i		−	1.45250i
$210$	−4.33640	+	9.27608i	−0.299240	+	0.640110i
$211$	18.9359			1.30360			0.651801	−	0.758390i	$-0.274014\pi$
$211$	18.9359			1.30360			0.651801	+	0.758390i	$0.274014\pi$
$212$	−5.02081	−	14.9943i	−0.344831	−	1.02981i
$213$	2.95445			0.202436
$214$	8.08404	−	1.31752i	0.552613	−	0.0900635i
$215$	4.01229			0.273636
$216$	−7.43621	−	14.1222i	−0.505970	−	0.960893i
$217$	−5.85510	−	3.99585i	−0.397470	−	0.271256i
$218$	−3.18913	−	19.5679i	−0.215995	−	1.32531i
$219$	10.6769			0.721478
$220$	18.8580	−	6.31458i	1.27141	−	0.425729i
$221$			4.50218i			0.302849i
$222$	−3.62621	+	0.590990i	−0.243375	+	0.0396647i
$223$	0.523181			0.0350348			0.0175174	−	0.999847i	$-0.494424\pi$
$223$	0.523181			0.0350348			0.0175174	+	0.999847i	$0.494424\pi$
$224$	−14.6412	+	3.10429i	−0.978253	+	0.207414i
$225$	−1.07796			−0.0718639
$226$	2.79433	−	0.455412i	0.185876	−	0.0302936i
$227$			6.25764i			0.415334i	0.978200	+	0.207667i	$0.0665870\pi$
$227$			6.25764i			0.415334i	−0.978200	+	0.207667i	$0.933413\pi$
$228$	−10.9602	+	3.67002i	−0.725859	+	0.243053i
$229$	9.29723			0.614379			0.307189	−	0.951648i	$-0.400612\pi$
$229$	9.29723			0.614379			0.307189	+	0.951648i	$0.400612\pi$
$230$	−4.26271	−	26.1552i	−0.281075	−	1.72462i
$231$	9.96912	−	14.6077i	0.655920	−	0.961117i
$232$	−7.95586	−	15.1090i	−0.522328	−	0.991958i
$233$	−0.709761			−0.0464980			−0.0232490	−	0.999730i	$-0.507401\pi$
$233$	−0.709761			−0.0464980			−0.0232490	+	0.999730i	$0.507401\pi$
$234$	−1.61958	+	0.263955i	−0.105875	+	0.0172553i
$235$	13.3406			0.870248
$236$	−6.20964	−	18.5446i	−0.404213	−	1.20715i
$237$	−9.21733			−0.598730
$238$	7.13399	−	15.2604i	0.462428	−	0.989187i
$239$		−	3.28084i		−	0.212220i	−0.994354	−	0.106110i	$-0.966160\pi$
$239$		−	3.28084i		−	0.212220i	0.994354	−	0.106110i	$-0.0338395\pi$
$240$	−6.59183	−	8.73936i	−0.425501	−	0.564123i
$241$			10.9276i			0.703907i	0.936017	+	0.351954i	$0.114483\pi$
$241$			10.9276i			0.703907i	−0.936017	+	0.351954i	$0.885517\pi$
$242$	−18.5468	+	3.02271i	−1.19223	+	0.194307i
$243$			11.2690i			0.722904i
$244$	−19.1181	+	6.40168i	−1.22391	+	0.409826i
$245$	−5.14798	−	13.1521i	−0.328893	−	0.840254i
$246$	18.6446	−	3.03865i	1.18874	−	0.193737i
$247$			4.26085i			0.271111i
$248$	6.70531	−	3.53076i	0.425788	−	0.224204i
$249$	−21.1196			−1.33840
$250$	−16.6976	+	2.72134i	−1.05605	+	0.172112i
$251$			11.2022i			0.707078i	0.935420	+	0.353539i	$0.115022\pi$
$251$			11.2022i			0.707078i	−0.935420	+	0.353539i	$0.884978\pi$
$252$	5.90793	+	1.67164i	0.372165	+	0.105303i
$253$			45.7697i			2.87752i
$254$	−3.18382	−	19.5353i	−0.199770	−	1.22576i
$255$	12.3209			0.771565
$256$	4.39616	−	15.3842i	0.274760	−	0.961513i
$257$			19.9074i			1.24179i	0.783894	+	0.620894i	$0.213230\pi$
$257$			19.9074i			1.24179i	−0.783894	+	0.620894i	$0.786770\pi$
$258$	0.613568	+	3.76475i	0.0381991	+	0.234383i
$259$	2.85663	−	4.18581i	0.177502	−	0.260094i
$260$	−3.82651	+	1.28130i	−0.237310	+	0.0794631i
$261$			7.00509i			0.433604i
$262$	−0.215414	−	1.32174i	−0.0133083	−	0.0816574i
$263$		−	25.7281i		−	1.58646i	−0.608919	−	0.793232i	$-0.708397\pi$
$263$		−	25.7281i		−	1.58646i	0.608919	−	0.793232i	$-0.291603\pi$
$264$	8.80879	+	16.7289i	0.542144	+	1.02959i
$265$			15.9522i			0.979938i
$266$	6.75158	−	14.4424i	0.413966	−	0.885522i
$267$	−7.24042			−0.443106
$268$	−30.1169	+	10.0846i	−1.83968	+	0.616017i
$269$	−22.5092			−1.37241			−0.686206	−	0.727407i	$-0.740725\pi$
$269$	−22.5092			−1.37241			−0.686206	+	0.727407i	$0.740725\pi$
$270$	2.58999	+	15.8917i	0.157622	+	0.967138i
$271$	−26.5569			−1.61322			−0.806608	−	0.591086i	$-0.798699\pi$
$271$	−26.5569			−1.61322			−0.806608	+	0.591086i	$0.798699\pi$
$272$	10.8445	+	14.3775i	0.657543	+	0.871761i
$273$	−2.02285	+	2.96408i	−0.122429	+	0.179394i
$274$	−18.8209	+	3.06738i	−1.13701	+	0.185307i
$275$	4.57840			0.276088
$276$	23.8896	−	7.99942i	1.43799	−	0.481509i
$277$			0.199021i			0.0119580i	0.999982	+	0.00597902i	$0.00190319\pi$
$277$			0.199021i			0.0119580i	−0.999982	+	0.00597902i	$0.998097\pi$
$278$	2.36697	+	14.5233i	0.141962	+	0.871052i
$279$	−3.10882			−0.186120
$280$	15.0005	+	1.72029i	0.896453	+	0.102807i
$281$	−2.06373			−0.123112			−0.0615558	−	0.998104i	$-0.519606\pi$
$281$	−2.06373			−0.123112			−0.0615558	+	0.998104i	$0.519606\pi$
$282$	2.04008	+	12.5176i	0.121485	+	0.745410i
$283$			4.87971i			0.290069i	0.989427	+	0.145034i	$0.0463293\pi$
$283$			4.87971i			0.290069i	−0.989427	+	0.145034i	$0.953671\pi$
$284$	−1.38328	−	4.13104i	−0.0820823	−	0.245132i
$285$	11.6605			0.690707
$286$	6.87883	−	1.12109i	0.406754	−	0.0662917i
$287$	−14.6877	+	21.5219i	−0.866989	+	1.27040i
$288$	−4.53625	+	4.74404i	−0.267301	+	0.279545i
$289$	−3.26961			−0.192330
$290$	2.77098	+	17.0022i	0.162717	+	0.998404i
$291$	7.33710			0.430108
$292$	−4.99893	−	14.9289i	−0.292540	−	0.873648i
$293$	−24.0764			−1.40656			−0.703280	−	0.710913i	$-0.748282\pi$
$293$	−24.0764			−1.40656			−0.703280	+	0.710913i	$0.748282\pi$
$294$	11.5534	−	6.84161i	0.673806	−	0.399011i
$295$			19.7294i			1.14869i
$296$	2.52414	+	4.79363i	0.146713	+	0.278624i
$297$		−	27.8093i		−	1.61366i
$298$	1.10544	+	6.78277i	0.0640363	+	0.392915i
$299$		−	9.28723i		−	0.537094i
$300$	−0.800192	−	2.38971i	−0.0461991	−	0.137970i
$301$	−4.34573	−	2.96577i	−0.250484	−	0.170944i
$302$	−0.240640	−	1.47652i	−0.0138473	−	0.0849644i
$303$			19.9455i			1.14584i
$304$	10.2632	+	13.6068i	0.588634	+	0.780402i
$305$	20.3396			1.16464
$306$	−1.18837	−	7.29165i	−0.0679348	−	0.416836i
$307$		−	13.1626i		−	0.751229i	−0.926776	−	0.375615i	$-0.877432\pi$
$307$		−	13.1626i		−	0.751229i	0.926776	−	0.375615i	$-0.122568\pi$
$308$	−25.0927	−	7.09992i	−1.42979	−	0.404556i
$309$		−	21.4440i		−	1.21991i
$310$	−7.54549	+	1.22974i	−0.428555	+	0.0698448i
$311$	−11.0951			−0.629146			−0.314573	−	0.949233i	$-0.601861\pi$
$311$	−11.0951			−0.629146			−0.314573	+	0.949233i	$0.601861\pi$
$312$	−1.78741	−	3.39449i	−0.101192	−	0.192175i
$313$			11.4566i			0.647563i	0.946132	+	0.323782i	$0.104954\pi$
$313$			11.4566i			0.647563i	−0.946132	+	0.323782i	$0.895046\pi$
$314$	−11.3423	+	1.84855i	−0.640085	+	0.104319i
$315$	−5.11623	−	3.49160i	−0.288267	−	0.196729i
$316$	4.31556	+	12.8881i	0.242769	+	0.725011i
$317$		−	4.30825i		−	0.241975i	−0.992654	−	0.120988i	$-0.961394\pi$
$317$		−	4.30825i		−	0.241975i	0.992654	−	0.120988i	$-0.0386061\pi$
$318$	−14.9680	+	2.43945i	−0.839365	+	0.136798i
$319$		−	29.7526i		−	1.66583i
$320$	−9.13346	+	13.3088i	−0.510576	+	0.743982i
$321$		−	7.85554i		−	0.438453i
$322$	−14.7162	+	31.4797i	−0.820102	+	1.75429i
$323$	−19.1831			−1.06738
$324$	−7.91346	+	2.64981i	−0.439637	+	0.147212i
$325$	−0.929012			−0.0515323
$326$	−13.0780	+	2.13142i	−0.724323	+	0.118048i
$327$	−19.0148			−1.05152
$328$	−12.9782	−	24.6470i	−0.716601	−	1.36090i
$329$	−14.4493	−	9.86100i	−0.796615	−	0.543655i
$330$	−3.06805	−	18.8250i	−0.168891	−	1.03628i
$331$	−1.04258			−0.0573055			−0.0286527	−	0.999589i	$-0.509122\pi$
$331$	−1.04258			−0.0573055			−0.0286527	+	0.999589i	$0.509122\pi$
$332$	9.88821	+	29.5304i	0.542686	+	1.62069i
$333$		−	2.22249i		−	0.121792i
$334$	−21.0585	+	3.43207i	−1.15227	+	0.187794i
$335$	32.0411			1.75059
$336$	0.679762	+	14.3381i	0.0370840	+	0.782208i
$337$	−3.99839			−0.217806			−0.108903	−	0.994052i	$-0.534734\pi$
$337$	−3.99839			−0.217806			−0.108903	+	0.994052i	$0.534734\pi$
$338$	−1.39580	+	0.227483i	−0.0759214	+	0.0123735i
$339$		−	2.71534i		−	0.147477i
$340$	−5.76866	−	17.2276i	−0.312850	−	0.934300i
$341$	13.2040			0.715039
$342$	−1.12467	−	6.90079i	−0.0608154	−	0.373152i
$343$	−4.14581	+	18.0503i	−0.223853	+	0.974623i
$344$	4.97676	−	2.62058i	0.268329	−	0.141292i
$345$	−25.4159			−1.36835
$346$	−12.6697	+	2.06488i	−0.681129	+	0.111009i
$347$	−3.26373			−0.175206			−0.0876030	−	0.996155i	$-0.527921\pi$
$347$	−3.26373			−0.175206			−0.0876030	+	0.996155i	$0.527921\pi$
$348$	−15.5295	+	5.20003i	−0.832467	+	0.278751i
$349$	−3.99174			−0.213673			−0.106837	−	0.994277i	$-0.534072\pi$
$349$	−3.99174			−0.213673			−0.106837	+	0.994277i	$0.534072\pi$
$350$	3.14895	+	1.47208i	0.168318	+	0.0786859i
$351$			5.64284i			0.301193i
$352$	19.2668	−	20.1493i	1.02692	−	1.07396i
$353$		−	4.75882i		−	0.253286i	−0.991948	−	0.126643i	$-0.959580\pi$
$353$		−	4.75882i		−	0.253286i	0.991948	−	0.126643i	$-0.0404203\pi$
$354$	−18.5121	+	3.01706i	−0.983909	+	0.160355i
$355$			4.39497i			0.233261i
$356$	3.38997	+	10.1239i	0.179668	+	0.536564i
$357$	−13.3448	−	9.10725i	−0.706283	−	0.482007i
$358$	−23.4356	+	3.81948i	−1.23861	+	0.201866i
$359$		−	15.2984i		−	0.807418i	−0.914887	−	0.403709i	$-0.867721\pi$
$359$		−	15.2984i		−	0.807418i	0.914887	−	0.403709i	$-0.132279\pi$
$360$	5.85915	−	3.08521i	0.308804	−	0.162605i
$361$	0.845169			0.0444826
$362$	−5.12229	+	0.834818i	−0.269222	+	0.0438771i
$363$			18.0226i			0.945939i
$364$	5.09161	+	1.44066i	0.266873	+	0.0755111i
$365$			15.8827i			0.831339i
$366$	3.11037	+	19.0847i	0.162582	+	0.997571i
$367$	24.0456			1.25517			0.627585	−	0.778548i	$-0.284044\pi$
$367$	24.0456			1.25517			0.627585	+	0.778548i	$0.284044\pi$
$368$	−22.3703	−	29.6582i	−1.16613	−	1.54604i
$369$			11.4272i			0.594878i
$370$	−0.879144	−	5.39427i	−0.0457045	−	0.280435i
$371$	11.7914	−	17.2779i	0.612180	−	0.897025i
$372$	−2.30774	−	6.89189i	−0.119651	−	0.357328i
$373$		−	7.07711i		−	0.366439i	−0.983072	−	0.183219i	$-0.941348\pi$
$373$		−	7.07711i		−	0.366439i	0.983072	−	0.183219i	$-0.0586519\pi$
$374$	5.04737	+	30.9697i	0.260993	+	1.60141i
$375$			16.2257i			0.837890i
$376$	16.5474	−	8.71326i	0.853369	−	0.449352i
$377$			6.03717i			0.310930i
$378$	8.94144	−	19.1268i	0.459898	−	0.983775i
$379$	19.0848			0.980322			0.490161	−	0.871632i	$-0.336938\pi$
$379$	19.0848			0.980322			0.490161	+	0.871632i	$0.336938\pi$
$380$	−5.45944	−	16.3042i	−0.280064	−	0.836388i
$381$	−18.9832			−0.972536
$382$	−5.91071	−	36.2671i	−0.302418	−	1.85558i
$383$	−16.0328			−0.819236			−0.409618	−	0.912257i	$-0.634338\pi$
$383$	−16.0328			−0.819236			−0.409618	+	0.912257i	$0.634338\pi$
$384$	−13.8844	−	6.53474i	−0.708533	−	0.333475i
$385$	21.7301	+	14.8298i	1.10747	+	0.755798i
$386$	−25.4282	+	4.14422i	−1.29426	+	0.210935i
$387$	−2.30740			−0.117292
$388$	−3.43524	−	10.2591i	−0.174398	−	0.520825i
$389$			23.9199i			1.21279i	0.795164	+	0.606395i	$0.207385\pi$
$389$			23.9199i			1.21279i	−0.795164	+	0.606395i	$0.792615\pi$
$390$	0.622544	+	3.81982i	0.0315237	+	0.193424i
$391$	41.8128			2.11456
$392$	−14.9755	−	12.9512i	−0.756379	−	0.654134i
$393$	−1.28438			−0.0647884
$394$	−1.44653	−	8.87566i	−0.0728753	−	0.447149i
$395$		−	13.7115i		−	0.689900i
$396$	−10.8449	+	3.63141i	−0.544977	+	0.182485i
$397$	20.5439			1.03107			0.515535	−	0.856869i	$-0.327593\pi$
$397$	20.5439			1.03107			0.515535	+	0.856869i	$0.327593\pi$
$398$	−10.7039	+	1.74450i	−0.536538	+	0.0874436i
$399$	−12.6295	−	8.61907i	−0.632266	−	0.431493i
$400$	−2.96675	+	2.23773i	−0.148337	+	0.111886i
$401$	31.3007			1.56308			0.781542	−	0.623852i	$-0.214433\pi$
$401$	31.3007			1.56308			0.781542	+	0.623852i	$0.214433\pi$
$402$	4.89979	+	30.0642i	0.244379	+	1.49947i
$403$	−2.67926			−0.133463
$404$	27.8887	−	9.33849i	1.38751	−	0.464607i
$405$	8.41904			0.418346
$406$	9.56627	−	20.4634i	0.474766	−	1.01558i
$407$			9.43957i			0.467902i
$408$	15.2826	−	8.04724i	0.756601	−	0.398398i
$409$			15.6476i			0.773722i	0.922138	+	0.386861i	$0.126441\pi$
$409$			15.6476i			0.773722i	−0.922138	+	0.386861i	$0.873559\pi$
$410$	4.52023	+	27.7353i	0.223238	+	1.36975i
$411$			18.2889i			0.902126i
$412$	−29.9840	+	10.0401i	−1.47720	+	0.494640i
$413$	14.5834	−	21.3690i	0.717601	−	1.05150i
$414$	2.45141	+	15.0414i	0.120480	+	0.739246i
$415$		−	31.4170i		−	1.54220i
$416$	−3.90946	+	4.08854i	−0.191677	+	0.200457i
$417$	14.1128			0.691108
$418$	4.77681	+	29.3097i	0.233642	+	1.43358i
$419$			20.5740i			1.00511i	0.864546	+	0.502553i	$0.167606\pi$
$419$			20.5740i			1.00511i	−0.864546	+	0.502553i	$0.832394\pi$
$420$	3.94259	−	13.9340i	0.192379	−	0.679909i
$421$		−	21.4079i		−	1.04336i	−0.853141	−	0.521680i	$-0.825306\pi$
$421$		−	21.4079i		−	1.04336i	0.853141	−	0.521680i	$-0.174694\pi$
$422$	−26.4307	+	4.30761i	−1.28663	+	0.209691i
$423$	−7.67198			−0.373024
$424$	10.4190	+	19.7868i	0.505991	+	0.960932i
$425$		−	4.18258i		−	0.202885i
$426$	−4.12381	+	0.672089i	−0.199799	+	0.0325628i
$427$	−22.0298	−	15.0344i	−1.06610	−	0.727565i
$428$	−10.9840	+	3.67797i	−0.530930	+	0.177781i
$429$		−	6.68440i		−	0.322726i
$430$	−5.60035	+	0.912731i	−0.270073	+	0.0440158i
$431$			10.3475i			0.498422i	0.968449	+	0.249211i	$0.0801712\pi$
$431$			10.3475i			0.498422i	−0.968449	+	0.249211i	$0.919829\pi$
$432$	13.5920	+	18.0201i	0.653946	+	0.866992i
$433$		−	9.33066i		−	0.448403i	−0.974543	−	0.224201i	$-0.928023\pi$
$433$		−	9.33066i		−	0.448403i	0.974543	−	0.224201i	$-0.0719773\pi$
$434$	9.08153	+	4.24546i	0.435927	+	0.203788i
$435$	16.5216			0.792152
$436$	8.90275	+	26.5874i	0.426364	+	1.27330i
$437$	39.5715			1.89296
$438$	−14.9028	+	2.42882i	−0.712083	+	0.116053i
$439$	1.46740			0.0700351			0.0350176	−	0.999387i	$-0.488851\pi$
$439$	1.46740			0.0700351			0.0350176	+	0.999387i	$0.488851\pi$
$440$	−24.8855	+	13.1038i	−1.18637	+	0.624697i
$441$	2.96052	+	7.56353i	0.140977	+	0.360168i
$442$	−1.02417	−	6.28413i	−0.0487149	−	0.298906i
$443$	−15.1974			−0.722049			−0.361024	−	0.932556i	$-0.617573\pi$
$443$	−15.1974			−0.722049			−0.361024	+	0.932556i	$0.617573\pi$
$444$	4.92701	−	1.64981i	0.233826	−	0.0782963i
$445$		−	10.7707i		−	0.510579i
$446$	−0.730255	+	0.119015i	−0.0345786	+	0.00563552i
$447$	6.59106			0.311746
$448$	19.7299	−	7.66358i	0.932151	−	0.362070i
$449$	2.85625			0.134795			0.0673974	−	0.997726i	$-0.478530\pi$
$449$	2.85625			0.134795			0.0673974	+	0.997726i	$0.478530\pi$
$450$	1.50461	−	0.245218i	0.0709281	−	0.0115597i
$451$		−	48.5347i		−	2.28541i
$452$	−3.79672	+	1.27133i	−0.178583	+	0.0597982i
$453$	−1.43479			−0.0674123
$454$	−1.42351	−	8.73440i	−0.0668086	−	0.409926i
$455$	−4.40930	−	3.00915i	−0.206711	−	0.141071i
$456$	14.4634	−	7.61588i	0.677311	−	0.356646i
$457$	−18.5765			−0.868972			−0.434486	−	0.900679i	$-0.643070\pi$
$457$	−18.5765			−0.868972			−0.434486	+	0.900679i	$0.643070\pi$
$458$	−12.9771	+	2.11497i	−0.606378	+	0.0988259i
$459$	−25.4051			−1.18581
$460$	11.8998	+	35.5377i	0.554829	+	1.65695i
$461$	15.7972			0.735751			0.367875	−	0.929875i	$-0.380085\pi$
$461$	15.7972			0.735751			0.367875	+	0.929875i	$0.380085\pi$
$462$	−10.5919	+	22.6572i	−0.492778	+	1.05411i
$463$		−	29.8412i		−	1.38684i	−0.720534	−	0.693420i	$-0.756103\pi$
$463$		−	29.8412i		−	1.38684i	0.720534	−	0.693420i	$-0.243897\pi$
$464$	14.5418	+	19.2793i	0.675087	+	0.895021i
$465$			7.33221i			0.340023i
$466$	0.990683	−	0.161459i	0.0458925	−	0.00747944i
$467$		−	28.2989i		−	1.30952i	−0.755838	−	0.654759i	$-0.772770\pi$
$467$		−	28.2989i		−	1.30952i	0.755838	−	0.654759i	$-0.227230\pi$
$468$	2.20056	−	0.736856i	0.101721	−	0.0340612i
$469$	−34.7038	−	23.6838i	−1.60247	−	1.09362i
$470$	−18.6208	+	3.03478i	−0.858915	+	0.139984i
$471$			11.0218i			0.507855i
$472$	12.8860	+	24.4719i	0.593126	+	1.12641i
$473$	9.80020			0.450614
$474$	12.8655	−	2.09679i	0.590933	−	0.0963088i
$475$		−	3.95838i		−	0.181623i
$476$	−6.48611	+	22.9233i	−0.297290	+	1.05069i
$477$		−	9.17386i		−	0.420042i
$478$	0.746336	+	4.57938i	0.0341366	+	0.209456i
$479$	−34.1779			−1.56163			−0.780814	−	0.624763i	$-0.785196\pi$
$479$	−34.1779			−1.56163			−0.780814	+	0.624763i	$0.785196\pi$
$480$	11.1889	+	10.6988i	0.510702	+	0.488333i
$481$		−	1.91540i		−	0.0873349i
$482$	−2.48584	−	15.2527i	−0.113227	−	0.694741i
$483$	27.5281	+	18.7867i	1.25257	+	0.854825i
$484$	25.1999	−	8.43817i	1.14545	−	0.383553i
$485$			10.9145i			0.495602i
$486$	−2.56350	−	15.7292i	−0.116283	−	0.713490i
$487$			19.3724i			0.877846i	0.898525	+	0.438923i	$0.144640\pi$
$487$			19.3724i			0.877846i	−0.898525	+	0.438923i	$0.855360\pi$
$488$	25.2287	−	13.2845i	1.14205	−	0.601361i
$489$			12.7083i			0.574691i
$490$	10.1774	+	17.1865i	0.459769	+	0.776408i
$491$	7.16183			0.323209			0.161604	−	0.986856i	$-0.448333\pi$
$491$	7.16183			0.323209			0.161604	+	0.986856i	$0.448333\pi$
$492$	−25.3329	+	8.48268i	−1.14209	+	0.382429i
$493$	−27.1804			−1.22414
$494$	−0.969273	−	5.94728i	−0.0436096	−	0.267581i
$495$	11.5378			0.518585
$496$	−8.55607	+	6.45358i	−0.384179	+	0.289774i
$497$	3.24863	−	4.76021i	0.145721	−	0.213525i
$498$	29.4787	−	4.80436i	1.32097	−	0.215289i
$499$	−3.75215			−0.167969			−0.0839846	−	0.996467i	$-0.526765\pi$
$499$	−3.75215			−0.167969			−0.0839846	+	0.996467i	$0.526765\pi$
$500$	22.6874	−	7.59687i	1.01461	−	0.339742i
$501$			20.4633i			0.914234i
$502$	−2.54832	−	15.6360i	−0.113737	−	0.697871i
$503$	16.8477			0.751200			0.375600	−	0.926782i	$-0.377437\pi$
$503$	16.8477			0.751200			0.375600	+	0.926782i	$0.377437\pi$
$504$	−8.62655	−	0.989309i	−0.384257	−	0.0440673i
$505$	−29.6705			−1.32032
$506$	−10.4119	−	63.8853i	−0.462863	−	2.84005i
$507$			1.35635i			0.0602374i
$508$	8.88793	+	26.5431i	0.394338	+	1.17766i
$509$	27.6736			1.22661			0.613305	−	0.789846i	$-0.289840\pi$
$509$	27.6736			1.22661			0.613305	+	0.789846i	$0.289840\pi$
$510$	−17.1975	+	2.80280i	−0.761518	+	0.124110i
$511$	11.7400	−	17.2026i	0.519348	−	0.760999i
$512$	−2.63650	+	22.4733i	−0.116518	+	0.993189i
$513$	−24.0433			−1.06154
$514$	−4.52860	−	27.7867i	−0.199748	−	1.22562i
$515$	31.8996			1.40567
$516$	−1.71283	−	5.11525i	−0.0754034	−	0.225186i
$517$	32.5851			1.43309
$518$	−3.03508	+	6.49238i	−0.133354	+	0.285259i
$519$			12.3116i			0.540420i
$520$	5.04956	−	2.65891i	0.221438	−	0.116601i
$521$			17.6143i			0.771696i	0.922562	+	0.385848i	$0.126091\pi$
$521$			17.6143i			0.771696i	−0.922562	+	0.385848i	$0.873909\pi$
$522$	−1.59354	−	9.77769i	−0.0697474	−	0.427958i
$523$		−	11.0393i		−	0.482714i	−0.970436	−	0.241357i	$-0.922407\pi$
$523$		−	11.0393i		−	0.482714i	0.970436	−	0.241357i	$-0.0775926\pi$
$524$	0.601348	+	1.79588i	0.0262700	+	0.0784533i
$525$	1.87926	−	2.75367i	0.0820175	−	0.120180i
$526$	5.85273	+	35.9113i	0.255191	+	1.56581i
$527$		−	12.0625i		−	0.525451i
$528$	−16.1008	−	21.3463i	−0.700699	−	0.928977i
$529$	−63.2526			−2.75011
$530$	−3.62887	−	22.2661i	−0.157628	−	0.967177i
$531$		−	11.3460i		−	0.492376i
$532$	−6.13843	+	21.6946i	−0.266135	+	0.940579i
$533$			9.84828i			0.426576i
$534$	10.1062	−	1.64708i	0.437336	−	0.0712759i
$535$	11.6857			0.505218
$536$	39.7431	−	20.9272i	1.71664	−	0.903918i
$537$			22.7732i			0.982736i
$538$	31.4183	−	5.12048i	1.35454	−	0.220759i
$539$	−12.5742	−	32.1245i	−0.541608	−	1.38370i
$540$	−7.23020	−	21.5924i	−0.311138	−	0.929189i
$541$			2.04925i			0.0881043i	0.999029	+	0.0440522i	$0.0140268\pi$
$541$			2.04925i			0.0881043i	−0.999029	+	0.0440522i	$0.985973\pi$
$542$	37.0681	−	6.04126i	1.59221	−	0.259494i
$543$			4.97751i			0.213606i
$544$	−18.4073	−	17.6011i	−0.789207	−	0.754640i
$545$		−	28.2860i		−	1.21164i
$546$	2.14922	−	4.59742i	0.0919779	−	0.196752i
$547$	−4.74971			−0.203083			−0.101542	−	0.994831i	$-0.532377\pi$
$547$	−4.74971			−0.203083			−0.101542	+	0.994831i	$0.532377\pi$
$548$	25.5724	−	8.56289i	1.09240	−	0.365788i
$549$	−11.6969			−0.499213
$550$	−6.39052	+	1.04151i	−0.272493	+	0.0444101i
$551$	−25.7234			−1.09586
$552$	−31.5254	+	16.6001i	−1.34181	+	0.706546i
$553$	−10.1351	+	14.8510i	−0.430989	+	0.631527i
$554$	−0.0452741	−	0.277794i	−0.00192351	−	0.0118023i
$555$	−5.24180			−0.222502
$556$	−6.60764	−	19.7332i	−0.280226	−	0.836873i
$557$			3.12828i			0.132550i	0.997801	+	0.0662748i	$0.0211114\pi$
$557$			3.12828i			0.132550i	−0.997801	+	0.0662748i	$0.978889\pi$
$558$	4.33928	−	0.707205i	0.183696	−	0.0299384i
$559$	−1.98858			−0.0841079
$560$	−21.3290	+	1.01120i	−0.901317	+	0.0427309i
$561$	30.0944			1.27058
$562$	2.88054	−	0.469464i	0.121508	−	0.0198031i
$563$			3.85763i			0.162580i	0.996691	+	0.0812898i	$0.0259039\pi$
$563$			3.85763i			0.162580i	−0.996691	+	0.0812898i	$0.974096\pi$
$564$	−5.69508	−	17.0079i	−0.239806	−	0.716162i
$565$	4.03929			0.169934
$566$	−1.11005	−	6.81109i	−0.0466590	−	0.286291i
$567$	−9.11869	−	6.22310i	−0.382949	−	0.261346i
$568$	2.87052	+	5.45143i	0.120444	+	0.228737i
$569$	−31.1969			−1.30784			−0.653922	−	0.756562i	$-0.726877\pi$
$569$	−31.1969			−1.30784			−0.653922	+	0.756562i	$0.726877\pi$
$570$	−16.2757	+	2.65257i	−0.681713	+	0.111104i
$571$	26.0516			1.09023			0.545113	−	0.838363i	$-0.316487\pi$
$571$	26.0516			1.09023			0.545113	+	0.838363i	$0.316487\pi$
$572$	−9.34643	+	3.12964i	−0.390794	+	0.130857i
$573$	−35.2420			−1.47225
$574$	15.6052	−	33.3814i	0.651350	−	1.39331i
$575$			8.62795i			0.359810i
$576$	5.25250	−	7.65364i	0.218854	−	0.318902i
$577$			3.98708i			0.165984i	0.996550	+	0.0829921i	$0.0264476\pi$
$577$			3.98708i			0.165984i	−0.996550	+	0.0829921i	$0.973552\pi$
$578$	4.56371	−	0.743782i	0.189825	−	0.0309372i
$579$			24.7095i			1.02689i
$580$	−7.73545	−	23.1013i	−0.321197	−	0.959229i
$581$	−23.2225	+	34.0279i	−0.963433	+	1.41171i
$582$	−10.2411	+	1.66907i	−0.424508	+	0.0691851i
$583$			38.9640i			1.61373i
$584$	10.3736	+	19.7006i	0.429262	+	0.815215i
$585$	−2.34116			−0.0967949
$586$	33.6058	−	5.47699i	1.38824	−	0.226252i
$587$		−	27.6198i		−	1.13999i	−0.821648	−	0.569996i	$-0.806945\pi$
$587$		−	27.6198i		−	1.13999i	0.821648	−	0.569996i	$-0.193055\pi$
$588$	−14.5698	+	12.1777i	−0.600849	+	0.502200i
$589$		−	11.4159i		−	0.470385i
$590$	−4.48811	−	27.5382i	−0.184773	−	1.13373i
$591$	−8.62479			−0.354777
$592$	−4.61366	−	6.11673i	−0.189620	−	0.251396i
$593$		−	28.0907i		−	1.15355i	−0.816904	−	0.576774i	$-0.804311\pi$
$593$		−	28.0907i		−	1.15355i	0.816904	−	0.576774i	$-0.195689\pi$
$594$	6.32616	+	38.8161i	0.259565	+	1.59265i
$595$	13.5477	−	19.8515i	0.555403	−	0.813830i
$596$	−3.08594	−	9.21591i	−0.126405	−	0.377498i
$597$			10.4014i			0.425699i
$598$	2.11269	+	12.9631i	0.0863944	+	0.530100i
$599$			26.7663i			1.09364i	0.837250	+	0.546821i	$0.184162\pi$
$599$			26.7663i			1.09364i	−0.837250	+	0.546821i	$0.815838\pi$
$600$	1.66053	+	3.15352i	0.0677907	+	0.128742i
$601$			35.5607i			1.45055i	0.688458	+	0.725276i	$0.258288\pi$
$601$			35.5607i			1.45055i	−0.688458	+	0.725276i	$0.741712\pi$
$602$	6.74042	+	3.15103i	0.274719	+	0.128426i
$603$	−18.4263			−0.750377
$604$	0.671769	+	2.00619i	0.0273339	+	0.0816306i
$605$	−26.8099			−1.08998
$606$	−4.53727	−	27.8399i	−0.184314	−	1.13092i
$607$	−33.7272			−1.36895			−0.684473	−	0.729038i	$-0.739968\pi$
$607$	−33.7272			−1.36895			−0.684473	+	0.729038i	$0.739968\pi$
$608$	−17.4206	−	16.6576i	−0.706500	−	0.675555i
$609$	−17.8946	−	12.2123i	−0.725128	−	0.494868i
$610$	−28.3899	+	4.62691i	−1.14947	+	0.187338i
$611$	−6.61191			−0.267489
$612$	3.31746	+	9.90733i	0.134100	+	0.400480i
$613$		−	40.6244i		−	1.64080i	−0.571788	−	0.820401i	$-0.693750\pi$
$613$		−	40.6244i		−	1.64080i	0.571788	−	0.820401i	$-0.306250\pi$
$614$	2.99427	+	18.3723i	0.120839	+	0.741447i
$615$	26.9514			1.08678
$616$	36.6394	+	4.20188i	1.47625	+	0.169299i
$617$	16.6113			0.668745			0.334372	−	0.942441i	$-0.391476\pi$
$617$	16.6113			0.668745			0.334372	+	0.942441i	$0.391476\pi$
$618$	4.87816	+	29.9315i	0.196228	+	1.20402i
$619$			7.83199i			0.314794i	0.987535	+	0.157397i	$0.0503103\pi$
$619$			7.83199i			0.314794i	−0.987535	+	0.157397i	$0.949690\pi$
$620$	10.2522	−	3.43295i	0.411739	−	0.137870i
$621$	52.4063			2.10299
$622$	15.4865	−	2.52396i	0.620954	−	0.101201i
$623$	−7.96136	+	11.6658i	−0.318965	+	0.467379i
$624$	3.26705	+	4.33141i	0.130787	+	0.173395i
$625$	−19.4919			−0.779675
$626$	−2.60618	−	15.9910i	−0.104164	−	0.639131i
$627$	28.4812			1.13743
$628$	15.4111	−	5.16039i	0.614970	−	0.205922i
$629$	8.62348			0.343841
$630$	7.93550	+	3.70971i	0.316158	+	0.147798i
$631$		−	23.8991i		−	0.951407i	−0.879606	−	0.475703i	$-0.842194\pi$
$631$		−	23.8991i		−	0.951407i	0.879606	−	0.475703i	$-0.157806\pi$
$632$	−8.95547	−	17.0074i	−0.356230	−	0.676519i
$633$			25.6836i			1.02083i
$634$	0.980055	+	6.01344i	0.0389230	+	0.238824i
$635$		−	28.2389i		−	1.12063i
$636$	20.3374	−	6.80996i	0.806430	−	0.270032i
$637$	2.55145	+	6.51844i	0.101092	+	0.258270i
$638$	6.76823	+	41.5286i	0.267957	+	1.64413i
$639$		−	2.52747i		−	0.0999854i
$640$	9.72094	−	20.6541i	0.384254	−	0.816423i
$641$	43.1306			1.70356			0.851778	−	0.523902i	$-0.175524\pi$
$641$	43.1306			1.70356			0.851778	+	0.523902i	$0.175524\pi$
$642$	1.78701	+	10.9647i	0.0705275	+	0.432744i
$643$			27.6333i			1.08975i	0.838517	+	0.544876i	$0.183423\pi$
$643$			27.6333i			1.08975i	−0.838517	+	0.544876i	$0.816577\pi$
$644$	13.3797	−	47.2869i	0.527235	−	1.86337i
$645$			5.44206i			0.214281i
$646$	26.7757	−	4.36384i	1.05348	−	0.171693i
$647$	−1.50328			−0.0591000			−0.0295500	−	0.999563i	$-0.509407\pi$
$647$	−1.50328			−0.0591000			−0.0295500	+	0.999563i	$0.509407\pi$
$648$	10.4428	−	5.49878i	0.410232	−	0.216013i
$649$			48.1899i			1.89162i
$650$	1.29671	−	0.211335i	0.0508613	−	0.00828924i
$651$	5.41975	−	7.94154i	0.212417	−	0.311254i
$652$	17.7694	−	5.95006i	0.695903	−	0.233022i
$653$			13.8056i			0.540254i	0.962825	+	0.270127i	$0.0870658\pi$
$653$			13.8056i			0.540254i	−0.962825	+	0.270127i	$0.912934\pi$
$654$	26.5408	−	4.32556i	1.03783	−	0.169143i
$655$		−	1.91062i		−	0.0746539i
$656$	23.7217	+	31.4499i	0.926178	+	1.22791i
$657$		−	9.13388i		−	0.356346i
$658$	22.4115	+	10.4770i	0.873692	+	0.408436i
$659$	7.47530			0.291197			0.145598	−	0.989344i	$-0.453489\pi$
$659$	7.47530			0.291197			0.145598	+	0.989344i	$0.453489\pi$
$660$	8.56475	+	25.5780i	0.333382	+	0.995620i
$661$	3.90310			0.151813			0.0759065	−	0.997115i	$-0.475815\pi$
$661$	3.90310			0.151813			0.0759065	+	0.997115i	$0.475815\pi$
$662$	1.45523	−	0.237170i	0.0565593	−	0.00921788i
$663$	−6.10651			−0.237157
$664$	−20.5196	−	38.9690i	−0.796315	−	1.51229i
$665$	12.8215	−	18.7874i	0.497198	−	0.728542i
$666$	0.505581	+	3.10215i	0.0195909	+	0.120206i
$667$	56.0685			2.17098
$668$	28.6127	−	9.58094i	1.10706	−	0.370698i
$669$			0.709614i			0.0274353i
$670$	−44.7229	+	7.28882i	−1.72780	+	0.281592i
$671$	49.6803			1.91789
$672$	−4.21049	−	19.8585i	−0.162423	−	0.766057i
$673$	23.7338			0.914871			0.457436	−	0.889243i	$-0.348768\pi$
$673$	23.7338			0.914871			0.457436	+	0.889243i	$0.348768\pi$
$674$	5.58094	−	0.909567i	0.214970	−	0.0350352i
$675$		−	5.24227i		−	0.201775i
$676$	1.89650	−	0.635042i	0.0729424	−	0.0244247i
$677$	−36.7018			−1.41056			−0.705282	−	0.708927i	$-0.749179\pi$
$677$	−36.7018			−1.41056			−0.705282	+	0.708927i	$0.749179\pi$
$678$	0.617696	+	3.79007i	0.0237225	+	0.145557i
$679$	8.06767	−	11.8215i	0.309609	−	0.453669i
$680$	11.9709	+	22.7340i	0.459063	+	0.871810i
$681$	−8.48752			−0.325242
$682$	−18.4302	+	3.00370i	−0.705728	+	0.115018i
$683$	−6.55245			−0.250722			−0.125361	−	0.992111i	$-0.540009\pi$
$683$	−6.55245			−0.250722			−0.125361	+	0.992111i	$0.540009\pi$
$684$	3.13963	+	9.37627i	0.120047	+	0.358511i
$685$	−27.2062			−1.03950
$686$	1.68057	−	26.1376i	0.0641646	−	0.997939i
$687$			12.6103i			0.481111i
$688$	−6.35041	+	4.78992i	−0.242107	+	0.182614i
$689$		−	7.90627i		−	0.301205i
$690$	35.4755	−	5.78171i	1.35053	−	0.220106i
$691$		−	30.3755i		−	1.15554i	−0.816200	−	0.577770i	$-0.803923\pi$
$691$		−	30.3755i		−	1.15554i	0.816200	−	0.577770i	$-0.196077\pi$
$692$	17.2147	−	5.76431i	0.654403	−	0.219126i
$693$	−12.4966	−	8.52839i	−0.474707	−	0.323967i
$694$	4.55550	−	0.742444i	0.172924	−	0.0281828i
$695$			20.9939i			0.796345i
$696$	20.4931	−	10.7909i	0.776788	−	0.409028i
$697$	−44.3387			−1.67945
$698$	5.57167	−	0.908056i	0.210891	−	0.0343704i
$699$		−	0.962681i		−	0.0364119i
$700$	−4.73017	−	1.33839i	−0.178784	−	0.0505864i
$701$			14.6155i			0.552021i	0.961155	+	0.276010i	$0.0890124\pi$
$701$			14.6155i			0.552021i	−0.961155	+	0.276010i	$0.910988\pi$
$702$	−1.28365	−	7.87626i	−0.0484484	−	0.297270i
$703$	8.16124			0.307807
$704$	−22.3089	+	32.5072i	−0.840797	+	1.22516i
$705$			18.0945i			0.681479i
$706$	1.08255	+	6.64235i	0.0407424	+	0.249988i
$707$	32.1362	+	21.9315i	1.20861	+	0.824820i
$708$	25.1529	−	8.42241i	0.945303	−	0.316534i
$709$			11.8485i			0.444981i	0.974935	+	0.222490i	$0.0714186\pi$
$709$			11.8485i			0.444981i	−0.974935	+	0.222490i	$0.928581\pi$
$710$	−0.999784	−	6.13449i	−0.0375212	−	0.230223i
$711$			7.88525i			0.295720i
$712$	−7.03472	−	13.3597i	−0.263637	−	0.500677i
$713$			24.8829i			0.931872i
$714$	20.6984	+	9.67615i	0.774619	+	0.362121i
$715$	9.94356			0.371868
$716$	31.8425	−	10.6624i	1.19001	−	0.398474i
$717$	4.44995			0.166186
$718$	3.48013	+	21.3534i	0.129877	+	0.796904i
$719$	28.6394			1.06807			0.534035	−	0.845463i	$-0.320675\pi$
$719$	28.6394			1.06807			0.534035	+	0.845463i	$0.320675\pi$
$720$	−7.47635	+	5.63918i	−0.278627	+	0.210160i
$721$	−34.5506	−	23.5792i	−1.28673	−	0.878137i
$722$	−1.17969	+	0.192262i	−0.0439033	+	0.00715525i
$723$	−14.8216			−0.551220
$724$	6.95978	−	2.33048i	0.258658	−	0.0866114i
$725$		−	5.60860i		−	0.208298i
$726$	−4.09983	−	25.1558i	−0.152159	−	0.933621i
$727$	−23.6706			−0.877896			−0.438948	−	0.898513i	$-0.644649\pi$
$727$	−23.6706			−0.877896			−0.438948	+	0.898513i	$0.644649\pi$
$728$	−7.43458	−	0.852612i	−0.275544	−	0.0315999i
$729$	−27.8026			−1.02972
$730$	−3.61305	−	22.1690i	−0.133725	−	0.820513i
$731$		−	8.95294i		−	0.331136i
$732$	−8.68289	−	25.9308i	−0.320929	−	0.958429i
$733$	33.9964			1.25569			0.627844	−	0.778340i	$-0.283938\pi$
$733$	33.9964			1.25569			0.627844	+	0.778340i	$0.283938\pi$
$734$	−33.5628	+	5.46997i	−1.23882	+	0.201900i
$735$	17.8387	−	6.98244i	0.657992	−	0.257551i
$736$	37.9712	+	36.3080i	1.39964	+	1.33833i
$737$	78.2618			2.88281
$738$	−2.59951	−	15.9501i	−0.0956891	−	0.587131i
$739$	17.0248			0.626267			0.313134	−	0.949709i	$-0.398621\pi$
$739$	17.0248			0.626267			0.313134	+	0.949709i	$0.398621\pi$
$740$	2.45421	+	7.32932i	0.0902187	+	0.269431i
$741$	−5.77918			−0.212304
$742$	−12.5280	+	26.7988i	−0.459917	+	0.983816i
$743$		−	34.0743i		−	1.25006i	−0.780599	−	0.625032i	$-0.785086\pi$
$743$		−	34.0743i		−	1.25006i	0.780599	−	0.625032i	$-0.214914\pi$
$744$	4.78894	+	9.09472i	0.175571	+	0.333429i
$745$			9.80471i			0.359217i
$746$	1.60993	+	9.87821i	0.0589436	+	0.361667i
$747$			18.0674i			0.661052i
$748$	−14.0902	−	42.0793i	−0.515189	−	1.53857i
$749$	−12.6568	−	8.63774i	−0.462471	−	0.315616i
$750$	−3.69107	−	22.6477i	−0.134779	−	0.826979i
$751$			21.2437i			0.775193i	0.921829	+	0.387596i	$0.126695\pi$
$751$			21.2437i			0.775193i	−0.921829	+	0.387596i	$0.873305\pi$
$752$	−21.1148	+	15.9262i	−0.769976	+	0.580770i
$753$	−15.1941			−0.553703
$754$	−1.37336	−	8.42666i	−0.0500147	−	0.306881i
$755$		−	2.13436i		−	0.0776773i
$756$	−8.12941	+	28.7311i	−0.295664	+	1.04494i
$757$			12.9931i			0.472243i	0.971724	+	0.236122i	$0.0758764\pi$
$757$			12.9931i			0.472243i	−0.971724	+	0.236122i	$0.924124\pi$
$758$	−26.6386	+	4.34149i	−0.967556	+	0.157690i
$759$	−62.0795			−2.25334
$760$	11.3292	+	21.5154i	0.410954	+	0.780447i
$761$			7.45111i			0.270103i	0.990839	+	0.135051i	$0.0431199\pi$
$761$			7.45111i			0.270103i	−0.990839	+	0.135051i	$0.956880\pi$
$762$	26.4966	−	4.31835i	0.959872	−	0.156437i
$763$	−20.9082	+	30.6367i	−0.756926	+	1.10912i
$764$	16.5003	+	49.2769i	0.596961	+	1.78278i
$765$		−	10.5403i		−	0.381085i
$766$	22.3785	−	3.64719i	0.808568	−	0.131778i
$767$		−	9.77831i		−	0.353074i
$768$	20.8663	+	5.96272i	0.752948	+	0.215161i
$769$			41.8737i			1.51000i	0.655723	+	0.755001i	$0.272364\pi$
$769$			41.8737i			1.51000i	−0.655723	+	0.755001i	$0.727636\pi$
$770$	−33.7044	−	15.7562i	−1.21462	−	0.567814i
$771$	−27.0013			−0.972427
$772$	34.5499	−	11.5690i	1.24348	−	0.416377i
$773$	40.7234			1.46472			0.732360	−	0.680918i	$-0.238419\pi$
$773$	40.7234			1.46472			0.732360	+	0.680918i	$0.238419\pi$
$774$	3.22067	−	0.524896i	0.115764	−	0.0188670i
$775$	2.48907			0.0894099
$776$	7.12866	+	13.5381i	0.255904	+	0.485990i
$777$	5.67741	+	3.87458i	0.203676	+	0.139000i
$778$	−5.44139	−	33.3874i	−0.195083	−	1.19700i
$779$	−41.9620			−1.50345
$780$	−1.73789	−	5.19007i	−0.0622265	−	0.185834i
$781$			10.7349i			0.384125i
$782$	−58.3621	+	9.51171i	−2.08703	+	0.340138i
$783$	−34.0668			−1.21745
$784$	23.8490	+	14.6706i	0.851750	+	0.523948i
$785$	−16.3957			−0.585188
$786$	1.79274	−	0.292175i	0.0639448	−	0.0104216i
$787$			53.4793i			1.90633i	0.302447	+	0.953166i	$0.402196\pi$
$787$			53.4793i			1.90633i	−0.302447	+	0.953166i	$0.597804\pi$
$788$	4.03813	+	12.0596i	0.143853	+	0.429604i
$789$	34.8962			1.24234
$790$	3.11914	+	19.1385i	0.110974	+	0.680916i
$791$	−4.37496	−	2.98572i	−0.155556	−	0.106160i
$792$	14.3112	−	7.53575i	0.508527	−	0.267771i
$793$	−10.0807			−0.357977
$794$	−28.6751	+	4.67340i	−1.01764	+	0.165853i
$795$	−21.6367			−0.767376
$796$	14.5436	−	4.86992i	0.515486	−	0.172610i
$797$	−31.1556			−1.10359			−0.551793	−	0.833981i	$-0.686056\pi$
$797$	−31.1556			−1.10359			−0.551793	+	0.833981i	$0.686056\pi$
$798$	19.5889	+	9.15748i	0.693440	+	0.324171i
$799$		−	29.7680i		−	1.05312i
$800$	3.63193	−	3.79830i	0.128408	−	0.134290i
$801$			6.19404i			0.218856i
$802$	−43.6895	+	7.12040i	−1.54273	+	0.251430i
$803$			38.7942i			1.36902i
$804$	−13.6782	−	40.8490i	−0.482394	−	1.44063i
$805$	−27.9467	+	40.9502i	−0.984991	+	1.44330i
$806$	3.73971	−	0.609487i	0.131726	−	0.0214683i
$807$		−	30.5303i		−	1.07472i
$808$	−36.8026	+	19.3789i	−1.29471	+	0.681746i
$809$	−36.8766			−1.29651			−0.648256	−	0.761423i	$-0.724501\pi$
$809$	−36.8766			−1.29651			−0.648256	+	0.761423i	$0.724501\pi$
$810$	−11.7513	+	1.91519i	−0.412898	+	0.0672930i
$811$		−	2.50108i		−	0.0878247i	−0.999035	−	0.0439123i	$-0.986018\pi$
$811$		−	2.50108i		−	0.0878247i	0.999035	−	0.0439123i	$-0.0139822\pi$
$812$	−8.69750	+	30.7389i	−0.305222	+	1.07872i
$813$		−	36.0203i		−	1.26329i
$814$	−2.14735	−	13.1757i	−0.0752645	−	0.461809i
$815$	−18.9047			−0.662201
$816$	−19.5008	+	14.7089i	−0.682664	+	0.514913i
$817$		−	8.47303i		−	0.296434i
$818$	−3.55956	−	21.8408i	−0.124457	−	0.763647i
$819$	2.53571	+	1.73051i	0.0886050	+	0.0604690i
$820$	−12.6186	−	37.6846i	−0.440662	−	1.31600i
$821$			0.865705i			0.0302133i	0.999886	+	0.0151067i	$0.00480878\pi$
$821$			0.865705i			0.0302133i	−0.999886	+	0.0151067i	$0.995191\pi$
$822$	−4.16043	−	25.5276i	−0.145112	−	0.890379i
$823$		−	32.1222i		−	1.11971i	−0.828590	−	0.559856i	$-0.810857\pi$
$823$		−	32.1222i		−	1.11971i	0.828590	−	0.559856i	$-0.189143\pi$
$824$	39.5676	−	20.8348i	1.37840	−	0.725815i
$825$			6.20989i			0.216201i
$826$	−15.4944	+	33.1442i	−0.539118	+	1.15324i
$827$	34.3275			1.19369			0.596843	−	0.802358i	$-0.296422\pi$
$827$	34.3275			1.19369			0.596843	+	0.802358i	$0.296422\pi$
$828$	−6.84335	−	20.4371i	−0.237823	−	0.710239i
$829$	−2.07242			−0.0719781			−0.0359891	−	0.999352i	$-0.511458\pi$
$829$	−2.07242			−0.0719781			−0.0359891	+	0.999352i	$0.511458\pi$
$830$	7.14686	+	43.8518i	0.248071	+	1.52212i
$831$	−0.269942			−0.00936417
$832$	4.52674	−	6.59611i	0.156936	−	0.228679i
$833$	−29.3472	+	11.4871i	−1.01682	+	0.398004i
$834$	−19.6987	+	3.21044i	−0.682109	+	0.111168i
$835$	−30.4408			−1.05345
$836$	−13.3349	−	39.8237i	−0.461198	−	1.37733i
$837$		−	15.1186i		−	0.522577i
$838$	−4.68025	−	28.7172i	−0.161677	−	0.992018i
$839$	56.4106			1.94751			0.973754	−	0.227602i	$-0.0730884\pi$
$839$	56.4106			1.94751			0.973754	+	0.227602i	$0.0730884\pi$
$840$	−2.33331	+	20.3459i	−0.0805067	+	0.702000i
$841$	−7.44737			−0.256806
$842$	4.86995	+	29.8812i	0.167830	+	1.02977i
$843$		−	2.79913i		−	0.0964070i
$844$	35.9120	−	12.0251i	1.23614	−	0.413921i
$845$	−2.01767			−0.0694099
$846$	10.7085	−	1.74525i	0.368167	−	0.0600029i
$847$	29.0379	+	19.8171i	0.997755	+	0.680924i
$848$	−19.0440	−	25.2482i	−0.653973	−	0.867028i
$849$	−6.61857			−0.227149
$850$	0.951468	+	5.83803i	0.0326351	+	0.200243i
$851$	−17.7888			−0.609792
$852$	5.60312	−	1.87620i	0.191960	−	0.0642775i
$853$	−13.1684			−0.450877			−0.225439	−	0.974257i	$-0.572381\pi$
$853$	−13.1684			−0.450877			−0.225439	+	0.974257i	$0.572381\pi$
$854$	34.1693	+	15.9735i	1.16925	+	0.546603i
$855$		−	9.97531i		−	0.341148i
$856$	14.4947	−	7.63237i	0.495419	−	0.260869i
$857$		−	40.7607i		−	1.39236i	−0.717867	−	0.696180i	$-0.754882\pi$
$857$		−	40.7607i		−	1.39236i	0.717867	−	0.696180i	$-0.245118\pi$
$858$	1.52059	+	9.33007i	0.0519121	+	0.318523i
$859$			13.0322i			0.444653i	0.974972	+	0.222327i	$0.0713651\pi$
$859$			13.0322i			0.444653i	−0.974972	+	0.222327i	$0.928635\pi$
$860$	7.60933	−	2.54797i	0.259476	−	0.0868852i
$861$	−29.1911	−	19.9216i	−0.994830	−	0.678927i
$862$	−2.35389	−	14.4430i	−0.0801737	−	0.491931i
$863$			1.78583i			0.0607905i	0.999538	+	0.0303952i	$0.00967659\pi$
$863$			1.78583i			0.0607905i	−0.999538	+	0.0303952i	$0.990323\pi$
$864$	−23.0710	−	22.0604i	−0.784890	−	0.750512i
$865$	−18.3145			−0.622711
$866$	2.12257	+	13.0237i	0.0721279	+	0.442564i
$867$		−	4.43472i		−	0.150611i
$868$	−13.6418	−	3.85990i	−0.463031	−	0.131014i
$869$		−	33.4909i		−	1.13610i
$870$	−23.0609	+	3.75840i	−0.781837	+	0.127422i
$871$	−15.8803			−0.538082
$872$	−18.4746	−	35.0853i	−0.625630	−	1.18814i
$873$		−	6.27675i		−	0.212436i
$874$	−55.2338	+	9.00186i	−1.86831	+	0.304492i
$875$	26.1428	+	17.8413i	0.883788	+	0.603146i
$876$	20.2488	−	6.78027i	0.684142	−	0.229084i
$877$		−	14.4070i		−	0.486488i	−0.969965	−	0.243244i	$-0.921788\pi$
$877$		−	14.4070i		−	0.486488i	0.969965	−	0.243244i	$-0.0782116\pi$
$878$	−2.04819	+	0.333809i	−0.0691231	+	0.0112655i
$879$		−	32.6559i		−	1.10146i
$880$	31.7542	−	23.9512i	1.07043	−	0.807396i
$881$		−	10.1248i		−	0.341112i	−0.985348	−	0.170556i	$-0.945444\pi$
$881$		−	10.1248i		−	0.341112i	0.985348	−	0.170556i	$-0.0545564\pi$
$882$	−5.85286	−	9.88368i	−0.197076	−	0.332801i
$883$	−0.613830			−0.0206570			−0.0103285	−	0.999947i	$-0.503288\pi$
$883$	−0.613830			−0.0206570			−0.0103285	+	0.999947i	$0.503288\pi$
$884$	2.85907	+	8.53839i	0.0961610	+	0.287177i
$885$	−26.7599			−0.899523
$886$	21.2125	−	3.45715i	0.712646	−	0.116145i
$887$	−4.17783			−0.140278			−0.0701389	−	0.997537i	$-0.522344\pi$
$887$	−4.17783			−0.140278			−0.0701389	+	0.997537i	$0.522344\pi$
$888$	−6.50181	+	3.42361i	−0.218187	+	0.114889i
$889$	−20.8734	+	30.5857i	−0.700070	+	1.02581i
$890$	2.45015	+	15.0337i	0.0821293	+	0.503931i
$891$	20.5639			0.688916
$892$	0.992214	−	0.332242i	0.0332218	−	0.0111243i
$893$		−	28.1724i		−	0.942752i
$894$	−9.19978	+	1.49936i	−0.307687	+	0.0501460i
$895$	−33.8769			−1.13238
$896$	−25.7956	+	15.1850i	−0.861771	+	0.507297i
$897$	12.5967			0.420591
$898$	−3.98675	+	0.649750i	−0.133039	+	0.0216824i
$899$		−	16.1751i		−	0.539471i
$900$	−2.04435	+	0.684549i	−0.0681450	+	0.0228183i
$901$	35.5954			1.18586
$902$	11.0409	+	67.7447i	0.367620	+	2.25565i
$903$	4.02260	−	5.89431i	0.133864	−	0.196150i
$904$	5.01024	−	2.63820i	0.166638	−	0.0877454i
$905$	−7.40444			−0.246132
$906$	2.00268	−	0.326391i	0.0665345	−	0.0108436i
$907$	17.4110			0.578123			0.289061	−	0.957311i	$-0.406657\pi$
$907$	17.4110			0.578123			0.289061	+	0.957311i	$0.406657\pi$
$908$	3.97386	+	11.8676i	0.131877	+	0.393841i
$909$	17.0630			0.565943
$910$	6.83902	+	3.19712i	0.226711	+	0.105984i
$911$		−	15.7090i		−	0.520462i	−0.965546	−	0.260231i	$-0.916201\pi$
$911$		−	15.7090i		−	0.520462i	0.965546	−	0.260231i	$-0.0837987\pi$
$912$	−18.4555	+	13.9204i	−0.611122	+	0.460951i
$913$		−	76.7375i		−	2.53964i
$914$	25.9290	−	4.22585i	0.857656	−	0.139779i
$915$			27.5875i			0.912014i
$916$	17.6322	−	5.90413i	0.582585	−	0.195078i
$917$	−1.41227	+	2.06939i	−0.0466373	+	0.0683374i
$918$	35.4603	−	5.77923i	1.17037	−	0.190743i
$919$			42.1694i			1.39104i	0.718507	+	0.695520i	$0.244826\pi$
$919$			42.1694i			1.39104i	−0.718507	+	0.695520i	$0.755174\pi$
$920$	−24.6939	−	46.8964i	−0.814134	−	1.54613i
$921$	17.8530			0.588278
$922$	−22.0498	+	3.59361i	−0.726170	+	0.118349i
$923$		−	2.17824i		−	0.0716977i
$924$	9.62995	−	34.0344i	0.316802	−	1.11965i
$925$			1.77943i			0.0585074i
$926$	6.78839	+	41.6523i	0.223080	+	1.36878i
$927$	−18.3449			−0.602527
$928$	−24.6832	−	23.6020i	−0.810265	−	0.774775i
$929$			52.3499i			1.71754i	0.512359	+	0.858772i	$0.328772\pi$
$929$			52.3499i			1.71754i	−0.512359	+	0.858772i	$0.671228\pi$
$930$	−1.66796	−	10.2343i	−0.0546945	−	0.335595i
$931$	−27.7741	+	10.8713i	−0.910259	+	0.356294i
$932$	−1.34606	+	0.450728i	−0.0440918	+	0.0147641i
$933$		−	15.0488i		−	0.492676i
$934$	6.43753	+	39.4995i	0.210643	+	1.29246i
$935$			44.7677i			1.46406i
$936$	−2.90392	+	1.52909i	−0.0949176	+	0.0499800i
$937$		−	8.53783i		−	0.278919i	−0.990228	−	0.139459i	$-0.955464\pi$
$937$		−	8.53783i		−	0.278919i	0.990228	−	0.139459i	$-0.0445365\pi$
$938$	53.8272	+	25.1633i	1.75752	+	0.821610i
$939$	−15.5391			−0.507098
$940$	25.3006	−	8.47187i	0.825214	−	0.276322i
$941$	35.4337			1.15511			0.577553	−	0.816353i	$-0.304008\pi$
$941$	35.4337			1.15511			0.577553	+	0.816353i	$0.304008\pi$
$942$	−2.50727	−	15.3841i	−0.0816911	−	0.501242i
$943$	91.4632			2.97845
$944$	−23.5532	−	31.2265i	−0.766591	−	1.01634i
$945$	16.9802	−	24.8810i	0.552365	−	0.809378i
$946$	−13.6791	+	2.22938i	−0.444746	+	0.0724835i
$947$	12.5985			0.409397			0.204698	−	0.978825i	$-0.434379\pi$
$947$	12.5985			0.409397			0.204698	+	0.978825i	$0.434379\pi$
$948$	−17.4807	+	5.85339i	−0.567746	+	0.190109i
$949$		−	7.87181i		−	0.255530i
$950$	0.900466	+	5.52510i	0.0292150	+	0.179258i
$951$	5.84347			0.189488
$952$	3.83861	−	33.4718i	0.124410	−	1.08483i
$953$	−21.7924			−0.705927			−0.352963	−	0.935637i	$-0.614826\pi$
$953$	−21.7924			−0.705927			−0.352963	+	0.935637i	$0.614826\pi$
$954$	2.08690	+	12.8049i	0.0675659	+	0.414572i
$955$		−	52.4252i		−	1.69644i
$956$	−2.08347	−	6.22212i	−0.0673842	−	0.201238i
$957$	40.3548			1.30449
$958$	47.7055	−	7.77491i	1.54129	−	0.251196i
$959$	29.4671	+	20.1100i	0.951543	+	0.649386i
$960$	−18.0513	−	12.3881i	−0.582603	−	0.399825i
$961$	−23.8216			−0.768438
$962$	0.435723	+	2.67351i	0.0140483	+	0.0861976i
$963$	−6.72026			−0.216557
$964$	6.93947	+	20.7242i	0.223505	+	0.667481i
$965$	−36.7572			−1.18326
$966$	−42.6973	−	19.9603i	−1.37376	−	0.642211i
$967$			30.2075i			0.971408i	0.874123	+	0.485704i	$0.161437\pi$
$967$			30.2075i			0.971408i	−0.874123	+	0.485704i	$0.838563\pi$
$968$	−33.2545	+	17.5106i	−1.06884	+	0.562811i
$969$		−	26.0189i		−	0.835848i
$970$	−2.48287	−	15.2344i	−0.0797201	−	0.489148i
$971$			26.3321i			0.845037i	0.906354	+	0.422518i	$0.138854\pi$
$971$			26.3321i			0.845037i	−0.906354	+	0.422518i	$0.861146\pi$
$972$	7.15626	+	21.3716i	0.229537	+	0.685494i
$973$	15.5181	−	22.7386i	0.497487	−	0.728966i
$974$	−4.40690	−	27.0399i	−0.141206	−	0.866415i
$975$		−	1.26006i		−	0.0403543i
$976$	−32.1922	+	24.2816i	−1.03045	+	0.777235i
$977$	24.2718			0.776523			0.388261	−	0.921549i	$-0.373076\pi$
$977$	24.2718			0.776523			0.388261	+	0.921549i	$0.373076\pi$
$978$	−2.89094	−	17.7383i	−0.0924421	−	0.567208i
$979$		−	26.3079i		−	0.840803i
$980$	−18.1153	−	21.6737i	−0.578671	−	0.692342i
$981$			16.2668i			0.519359i
$982$	−9.99646	+	1.62920i	−0.319000	+	0.0519898i
$983$	−50.3405			−1.60561			−0.802806	−	0.596240i	$-0.796661\pi$
$983$	−50.3405			−1.60561			−0.802806	+	0.596240i	$0.796661\pi$
$984$	33.4299	−	17.6029i	1.06571	−	0.561160i
$985$		−	12.8300i		−	0.408799i
$986$	37.9383	−	6.18309i	1.20820	−	0.196910i
$987$	13.3749	−	19.5982i	0.425729	−	0.623819i
$988$	2.70582	+	8.08071i	0.0860835	+	0.257082i
$989$			18.4684i			0.587260i
$990$	−16.1044	+	2.62466i	−0.511832	+	0.0834171i
$991$			32.0033i			1.01662i	0.861175	+	0.508309i	$0.169729\pi$
$991$			32.0033i			1.01662i	−0.861175	+	0.508309i	$0.830271\pi$
$992$	10.4745	−	10.9543i	0.332564	−	0.347798i
$993$		−	1.41410i		−	0.0448752i
$994$	−3.45156	+	7.38330i	−0.109477	+	0.234184i
$995$	−15.4728			−0.490522
$996$	−40.0534	+	13.4118i	−1.26914	+	0.424970i
$997$	−15.9693			−0.505752			−0.252876	−	0.967499i	$-0.581376\pi$
$997$	−15.9693			−0.505752			−0.252876	+	0.967499i	$0.581376\pi$
$998$	5.23724	−	0.853552i	0.165782	−	0.0270187i
$999$	10.8083			0.341960

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.h.b.27.4	yes	48
4.3	odd	2		2912.2.h.b.2575.16		48
7.6	odd	2		728.2.h.a.27.4	yes	48
8.3	odd	2		728.2.h.a.27.3	✓	48
8.5	even	2		2912.2.h.a.2575.16		48
28.27	even	2		2912.2.h.a.2575.33		48
56.13	odd	2		2912.2.h.b.2575.33		48
56.27	even	2	inner	728.2.h.b.27.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.h.a.27.3	✓	48	8.3	odd	2
728.2.h.a.27.4	yes	48	7.6	odd	2
728.2.h.b.27.3	yes	48	56.27	even	2	inner
728.2.h.b.27.4	yes	48	1.1	even	1	trivial
2912.2.h.a.2575.16		48	8.5	even	2
2912.2.h.a.2575.33		48	28.27	even	2
2912.2.h.b.2575.16		48	4.3	odd	2
2912.2.h.b.2575.33		48	56.13	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.39580 + 0.227483i) q^{2} +1.35635i q^{3} +(1.89650 - 0.635042i) q^{4} -2.01767 q^{5} +(-0.308546 - 1.89318i) q^{6} +(2.18534 + 1.49140i) q^{7} +(-2.50267 + 1.31781i) q^{8} +1.16033 q^{9} +(2.81626 - 0.458986i) q^{10} -4.92824 q^{11} +(0.861336 + 2.57231i) q^{12} +1.00000 q^{13} +(-3.38957 - 1.58456i) q^{14} -2.73666i q^{15} +(3.19344 - 2.40872i) q^{16} +4.50218i q^{17} +(-1.61958 + 0.263955i) q^{18} +4.26085i q^{19} +(-3.82651 + 1.28130i) q^{20} +(-2.02285 + 2.96408i) q^{21} +(6.87883 - 1.12109i) q^{22} -9.28723i q^{23} +(-1.78741 - 3.39449i) q^{24} -0.929012 q^{25} +(-1.39580 + 0.227483i) q^{26} +5.64284i q^{27} +(5.09161 + 1.44066i) q^{28} +6.03717i q^{29} +(0.622544 + 3.81982i) q^{30} -2.67926 q^{31} +(-3.90946 + 4.08854i) q^{32} -6.68440i q^{33} +(-1.02417 - 6.28413i) q^{34} +(-4.40930 - 3.00915i) q^{35} +(2.20056 - 0.736856i) q^{36} -1.91540i q^{37} +(-0.969273 - 5.94728i) q^{38} +1.35635i q^{39} +(5.04956 - 2.65891i) q^{40} +9.84828i q^{41} +(2.14922 - 4.59742i) q^{42} -1.98858 q^{43} +(-9.34643 + 3.12964i) q^{44} -2.34116 q^{45} +(2.11269 + 12.9631i) q^{46} -6.61191 q^{47} +(3.26705 + 4.33141i) q^{48} +(2.55145 + 6.51844i) q^{49} +(1.29671 - 0.211335i) q^{50} -6.10651 q^{51} +(1.89650 - 0.635042i) q^{52} -7.90627i q^{53} +(-1.28365 - 7.87626i) q^{54} +9.94356 q^{55} +(-7.43458 - 0.852612i) q^{56} -5.77918 q^{57} +(-1.37336 - 8.42666i) q^{58} -9.77831i q^{59} +(-1.73789 - 5.19007i) q^{60} -10.0807 q^{61} +(3.73971 - 0.609487i) q^{62} +(2.53571 + 1.73051i) q^{63} +(4.52674 - 6.59611i) q^{64} -2.01767 q^{65} +(1.52059 + 9.33007i) q^{66} -15.8803 q^{67} +(2.85907 + 8.53839i) q^{68} +12.5967 q^{69} +(6.83902 + 3.19712i) q^{70} -2.17824i q^{71} +(-2.90392 + 1.52909i) q^{72} -7.87181i q^{73} +(0.435723 + 2.67351i) q^{74} -1.26006i q^{75} +(2.70582 + 8.08071i) q^{76} +(-10.7699 - 7.34998i) q^{77} +(-0.308546 - 1.89318i) q^{78} +6.79571i q^{79} +(-6.44331 + 4.85999i) q^{80} -4.17266 q^{81} +(-2.24032 - 13.7462i) q^{82} +15.5710i q^{83} +(-1.95403 + 6.90598i) q^{84} -9.08390i q^{85} +(2.77565 - 0.452369i) q^{86} -8.18848 q^{87} +(12.3338 - 6.49450i) q^{88} +5.33818i q^{89} +(3.26778 - 0.532574i) q^{90} +(2.18534 + 1.49140i) q^{91} +(-5.89778 - 17.6132i) q^{92} -3.63400i q^{93} +(9.22889 - 1.50410i) q^{94} -8.59698i q^{95} +(-5.54547 - 5.30258i) q^{96} -5.40946i q^{97} +(-5.04415 - 8.51801i) q^{98} -5.71838 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + q^{4} + 10 q^{6} - 5 q^{8} - 48 q^{9} - 4 q^{11} - 10 q^{12} + 48 q^{13} - 6 q^{14} + 5 q^{16} - 15 q^{18} + 22 q^{20} - 6 q^{22} + 48 q^{25} + q^{26} - 26 q^{28} - 26 q^{30} - 19 q^{32}+ \cdots + 20 q^{99}+O(q^{100}) \) 48 * q + q^2 + q^4 + 10 * q^6 - 5 * q^8 - 48 * q^9 - 4 * q^11 - 10 * q^12 + 48 * q^13 - 6 * q^14 + 5 * q^16 - 15 * q^18 + 22 * q^20 - 6 * q^22 + 48 * q^25 + q^26 - 26 * q^28 - 26 * q^30 - 19 * q^32 - 36 * q^34 + 12 * q^35 - 5 * q^36 + 10 * q^38 + 48 * q^40 + 39 * 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 - 14 * 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 - 37 * 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 - 45 * q^84 + 2 * q^86 + 40 * q^87 - 66 * q^88 - 74 * q^90 - 24 * q^92 + 26 * q^94 + 84 * q^96 - 20 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more