LMFDB - Embedded newform 220.2.g.b.219.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(219,220)] 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("220.219"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			219.17
Character	$\chi$	$=$	220.219
Dual form			220.2.g.b.219.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.896270 - 1.09394i) q^{2} -2.84322 q^{3} +(-0.393401 - 1.96093i) q^{4} +(-1.64854 + 1.51074i) q^{5} +(-2.54829 + 3.11030i) q^{6} +3.37357i q^{7} +(-2.49773 - 1.32716i) q^{8} +5.08387 q^{9} +(0.175122 + 3.15742i) q^{10} +(1.92430 + 2.70131i) q^{11} +(1.11852 + 5.57534i) q^{12} -2.23147 q^{13} +(3.69047 + 3.02362i) q^{14} +(4.68714 - 4.29536i) q^{15} +(-3.69047 + 1.54286i) q^{16} -2.76398 q^{17} +(4.55652 - 5.56144i) q^{18} -7.85859 q^{19} +(3.61098 + 2.63833i) q^{20} -9.59177i q^{21} +(4.67976 + 0.316037i) q^{22} -0.606168 q^{23} +(7.10157 + 3.77341i) q^{24} +(0.435337 - 4.98101i) q^{25} +(-2.00000 + 2.44109i) q^{26} -5.92490 q^{27} +(6.61532 - 1.32716i) q^{28} +7.54682i q^{29} +(-0.497910 - 8.97724i) q^{30} -2.02302i q^{31} +(-1.61986 + 5.41997i) q^{32} +(-5.47120 - 7.68040i) q^{33} +(-2.47727 + 3.02362i) q^{34} +(-5.09658 - 5.56144i) q^{35} +(-2.00000 - 9.96910i) q^{36} +1.18865i q^{37} +(-7.04342 + 8.59682i) q^{38} +6.34455 q^{39} +(6.12259 - 1.58554i) q^{40} +2.04495i q^{41} +(-10.4928 - 8.59682i) q^{42} -3.09062i q^{43} +(4.54005 - 4.83611i) q^{44} +(-8.38094 + 7.68040i) q^{45} +(-0.543290 + 0.663111i) q^{46} +8.76811 q^{47} +(10.4928 - 4.38669i) q^{48} -4.38094 q^{49} +(-5.05874 - 4.94056i) q^{50} +7.85859 q^{51} +(0.877863 + 4.37575i) q^{52} -4.21013i q^{53} +(-5.31031 + 6.48147i) q^{54} +(-7.25325 - 1.54609i) q^{55} +(4.47727 - 8.42624i) q^{56} +22.3437 q^{57} +(8.25576 + 6.76399i) q^{58} -4.33992i q^{59} +(-10.2668 - 7.50134i) q^{60} -2.84943i q^{61} +(-2.21306 - 1.81318i) q^{62} +17.1508i q^{63} +(4.47727 + 6.62978i) q^{64} +(3.67866 - 3.37117i) q^{65} +(-13.3056 - 0.898561i) q^{66} +0.606168 q^{67} +(1.08735 + 5.41997i) q^{68} +1.72347 q^{69} +(-10.6518 + 0.590786i) q^{70} +9.55104i q^{71} +(-12.6981 - 6.74713i) q^{72} -6.00371 q^{73} +(1.30031 + 1.06535i) q^{74} +(-1.23776 + 14.1621i) q^{75} +(3.09158 + 15.4101i) q^{76} +(-9.11304 + 6.49175i) q^{77} +(5.68643 - 6.94055i) q^{78} -3.84860 q^{79} +(3.75301 - 8.11880i) q^{80} +1.59414 q^{81} +(2.23705 + 1.83283i) q^{82} +8.39927i q^{83} +(-18.8088 + 3.77341i) q^{84} +(4.55652 - 4.17565i) q^{85} +(-3.38094 - 2.77003i) q^{86} -21.4572i q^{87} +(-1.22129 - 9.30099i) q^{88} +8.67801 q^{89} +(0.890299 + 16.0519i) q^{90} -7.52801i q^{91} +(0.238467 + 1.18865i) q^{92} +5.75189i q^{93} +(7.85859 - 9.59177i) q^{94} +(12.9552 - 11.8723i) q^{95} +(4.60562 - 15.4101i) q^{96} +3.02148i q^{97} +(-3.92651 + 4.79248i) q^{98} +(9.78289 + 13.7331i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{4} - 4 q^{5} + 40 q^{9} + 12 q^{14} - 12 q^{16} - 20 q^{20} - 36 q^{25} - 48 q^{26} + 28 q^{34} - 48 q^{36} + 56 q^{44} - 48 q^{45} + 48 q^{49} + 20 q^{56} - 8 q^{60} + 20 q^{64} - 52 q^{66}+ \cdots - 16 q^{89}+O(q^{100}) $ 24 * q - 4 * q^4 - 4 * q^5 + 40 * q^9 + 12 * q^14 - 12 * q^16 - 20 * q^20 - 36 * q^25 - 48 * q^26 + 28 * q^34 - 48 * q^36 + 56 * q^44 - 48 * q^45 + 48 * q^49 + 20 * q^56 - 8 * q^60 + 20 * q^64 - 52 * q^66 - 8 * q^69 - 64 * q^70 + 64 * q^80 - 104 * q^81 + 72 * q^86 - 16 * q^89

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.896270	−	1.09394i	0.633758	−	0.773531i
$2$	0.896270	−	1.09394i	0.633758	−	0.773531i
$3$	−2.84322			−1.64153			−0.820766	−	0.571265i	$-0.806453\pi$
$3$	−2.84322			−1.64153			−0.820766	+	0.571265i	$0.806453\pi$
$4$	−0.393401	−	1.96093i	−0.196700	−	0.980464i
$5$	−1.64854	+	1.51074i	−0.737247	+	0.675623i
$5$	−1.64854	+	1.51074i	−0.737247	+	0.675623i
$6$	−2.54829	+	3.11030i	−1.04033	+	1.26978i
$7$			3.37357i			1.27509i	0.770414	+	0.637544i	$0.220050\pi$
$7$			3.37357i			1.27509i	−0.770414	+	0.637544i	$0.779950\pi$
$8$	−2.49773	−	1.32716i	−0.883080	−	0.469223i
$9$	5.08387			1.69462
$10$	0.175122	+	3.15742i	0.0553785	+	0.998465i
$11$	1.92430	+	2.70131i	0.580198	+	0.814475i
$11$	1.92430	+	2.70131i	0.580198	+	0.814475i
$12$	1.11852	+	5.57534i	0.322890	+	1.60946i
$13$	−2.23147			−0.618899			−0.309449	−	0.950916i	$-0.600145\pi$
$13$	−2.23147			−0.618899			−0.309449	+	0.950916i	$0.600145\pi$
$14$	3.69047	+	3.02362i	0.986320	+	0.808098i
$15$	4.68714	−	4.29536i	1.21021	−	1.10906i
$16$	−3.69047	+	1.54286i	−0.922618	+	0.385715i
$17$	−2.76398			−0.670364			−0.335182	−	0.942153i	$-0.608798\pi$
$17$	−2.76398			−0.670364			−0.335182	+	0.942153i	$0.608798\pi$
$18$	4.55652	−	5.56144i	1.07398	−	1.31084i
$19$	−7.85859			−1.80289			−0.901443	−	0.432899i	$-0.857491\pi$
$19$	−7.85859			−1.80289			−0.901443	+	0.432899i	$0.857491\pi$
$20$	3.61098	+	2.63833i	0.807441	+	0.589949i
$21$		−	9.59177i		−	2.09310i
$22$	4.67976	+	0.316037i	0.997727	+	0.0673793i
$23$	−0.606168			−0.126395			−0.0631974	−	0.998001i	$-0.520130\pi$
$23$	−0.606168			−0.126395			−0.0631974	+	0.998001i	$0.520130\pi$
$24$	7.10157	+	3.77341i	1.44960	+	0.770244i
$25$	0.435337	−	4.98101i	0.0870674	−	0.996202i
$26$	−2.00000	+	2.44109i	−0.392232	+	0.478737i
$27$	−5.92490			−1.14025
$28$	6.61532	−	1.32716i	1.25018	−	0.250810i
$29$			7.54682i			1.40141i	0.713451	+	0.700705i	$0.247131\pi$
$29$			7.54682i			1.40141i	−0.713451	+	0.700705i	$0.752869\pi$
$30$	−0.497910	−	8.97724i	−0.0909055	−	1.63901i
$31$		−	2.02302i		−	0.363346i	−0.983359	−	0.181673i	$-0.941849\pi$
$31$		−	2.02302i		−	0.363346i	0.983359	−	0.181673i	$-0.0581512\pi$
$32$	−1.61986	+	5.41997i	−0.286354	+	0.958124i
$33$	−5.47120	−	7.68040i	−0.952413	−	1.33699i
$34$	−2.47727	+	3.02362i	−0.424849	+	0.518547i
$35$	−5.09658	−	5.56144i	−0.861479	−	0.940055i
$36$	−2.00000	−	9.96910i	−0.333333	−	1.66152i
$37$			1.18865i			0.195413i	0.995215	+	0.0977066i	$0.0311507\pi$
$37$			1.18865i			0.195413i	−0.995215	+	0.0977066i	$0.968849\pi$
$38$	−7.04342	+	8.59682i	−1.14259	+	1.39459i
$39$	6.34455			1.01594
$40$	6.12259	−	1.58554i	0.968066	−	0.250695i
$41$			2.04495i			0.319367i	0.987168	+	0.159684i	$0.0510474\pi$
$41$			2.04495i			0.319367i	−0.987168	+	0.159684i	$0.948953\pi$
$42$	−10.4928	−	8.59682i	−1.61907	−	1.32652i
$43$		−	3.09062i		−	0.471315i	−0.971836	−	0.235657i	$-0.924276\pi$
$43$		−	3.09062i		−	0.471315i	0.971836	−	0.235657i	$-0.0757243\pi$
$44$	4.54005	−	4.83611i	0.684438	−	0.729071i
$45$	−8.38094	+	7.68040i	−1.24936	+	1.14493i
$46$	−0.543290	+	0.663111i	−0.0801038	+	0.0977703i
$47$	8.76811			1.27896			0.639480	−	0.768807i	$-0.279150\pi$
$47$	8.76811			1.27896			0.639480	+	0.768807i	$0.279150\pi$
$48$	10.4928	−	4.38669i	1.51451	−	0.633164i
$49$	−4.38094			−0.625849
$50$	−5.05874	−	4.94056i	−0.715414	−	0.698701i
$51$	7.85859			1.10042
$52$	0.877863	+	4.37575i	0.121738	+	0.606808i
$53$		−	4.21013i		−	0.578306i	−0.957283	−	0.289153i	$-0.906626\pi$
$53$		−	4.21013i		−	0.578306i	0.957283	−	0.289153i	$-0.0933736\pi$
$54$	−5.31031	+	6.48147i	−0.722641	+	0.882016i
$55$	−7.25325	−	1.54609i	−0.978028	−	0.208475i
$56$	4.47727	−	8.42624i	0.598301	−	1.12600i
$57$	22.3437			2.95949
$58$	8.25576	+	6.76399i	1.08403	+	0.888155i
$59$		−	4.33992i		−	0.565010i	−0.959266	−	0.282505i	$-0.908835\pi$
$59$		−	4.33992i		−	0.565010i	0.959266	−	0.282505i	$-0.0911653\pi$
$60$	−10.2668	−	7.50134i	−1.32544	−	0.968419i
$61$		−	2.84943i		−	0.364833i	−0.983221	−	0.182416i	$-0.941608\pi$
$61$		−	2.84943i		−	0.364833i	0.983221	−	0.182416i	$-0.0583918\pi$
$62$	−2.21306	−	1.81318i	−0.281059	−	0.230274i
$63$			17.1508i			2.16079i
$64$	4.47727	+	6.62978i	0.559659	+	0.828723i
$65$	3.67866	−	3.37117i	0.456281	−	0.418142i
$66$	−13.3056	−	0.898561i	−1.63780	−	0.110605i
$67$	0.606168			0.0740552			0.0370276	−	0.999314i	$-0.488211\pi$
$67$	0.606168			0.0740552			0.0370276	+	0.999314i	$0.488211\pi$
$68$	1.08735	+	5.41997i	0.131861	+	0.657268i
$69$	1.72347			0.207481
$70$	−10.6518	+	0.590786i	−1.27313	+	0.0706124i
$71$			9.55104i			1.13350i	0.823890	+	0.566750i	$0.191799\pi$
$71$			9.55104i			1.13350i	−0.823890	+	0.566750i	$0.808201\pi$
$72$	−12.6981	−	6.74713i	−1.49649	−	0.795157i
$73$	−6.00371			−0.702681			−0.351340	−	0.936248i	$-0.614274\pi$
$73$	−6.00371			−0.702681			−0.351340	+	0.936248i	$0.614274\pi$
$74$	1.30031	+	1.06535i	0.151158	+	0.123845i
$75$	−1.23776	+	14.1621i	−0.142924	+	1.63530i
$76$	3.09158	+	15.4101i	0.354628	+	1.76766i
$77$	−9.11304	+	6.49175i	−1.03853	+	0.739804i
$78$	5.68643	−	6.94055i	0.643861	−	0.785862i
$79$	−3.84860			−0.433001			−0.216501	−	0.976282i	$-0.569464\pi$
$79$	−3.84860			−0.433001			−0.216501	+	0.976282i	$0.569464\pi$
$80$	3.75301	−	8.11880i	0.419600	−	0.907709i
$81$	1.59414			0.177127
$82$	2.23705	+	1.83283i	0.247040	+	0.202402i
$83$			8.39927i			0.921940i	0.887416	+	0.460970i	$0.152498\pi$
$83$			8.39927i			0.921940i	−0.887416	+	0.460970i	$0.847502\pi$
$84$	−18.8088	+	3.77341i	−2.05220	+	0.411713i
$85$	4.55652	−	4.17565i	0.494224	−	0.452913i
$86$	−3.38094	−	2.77003i	−0.364576	−	0.298700i
$87$		−	21.4572i		−	2.30046i
$88$	−1.22129	−	9.30099i	−0.130190	−	0.991489i
$89$	8.67801			0.919868			0.459934	−	0.887953i	$-0.347873\pi$
$89$	8.67801			0.919868			0.459934	+	0.887953i	$0.347873\pi$
$90$	0.890299	+	16.0519i	0.0938457	+	1.69202i
$91$		−	7.52801i		−	0.789150i
$92$	0.238467	+	1.18865i	0.0248619	+	0.123926i
$93$			5.75189i			0.596444i
$94$	7.85859	−	9.59177i	0.810552	−	0.989316i
$95$	12.9552	−	11.8723i	1.32917	−	1.21807i
$96$	4.60562	−	15.4101i	0.470059	−	1.57279i
$97$			3.02148i			0.306785i	0.988165	+	0.153392i	$0.0490198\pi$
$97$			3.02148i			0.306785i	−0.988165	+	0.153392i	$0.950980\pi$
$98$	−3.92651	+	4.79248i	−0.396637	+	0.484114i
$99$	9.78289	+	13.7331i	0.983218	+	1.38023i
$100$	−9.93866	+	1.10587i	−0.993866	+	0.110587i
$101$			12.4412i			1.23795i	0.785412	+	0.618973i	$0.212451\pi$
$101$			12.4412i			1.23795i	−0.785412	+	0.618973i	$0.787549\pi$
$102$	7.04342	−	8.59682i	0.697403	−	0.851212i
$103$	1.86935			0.184192			0.0920961	−	0.995750i	$-0.470643\pi$
$103$	1.86935			0.184192			0.0920961	+	0.995750i	$0.470643\pi$
$104$	5.57360	+	2.96153i	0.546537	+	0.290402i
$105$	14.4907	+	15.8124i	1.41414	+	1.54313i
$106$	−4.60562	−	3.77341i	−0.447337	−	0.366506i
$107$		−	9.47074i		−	0.915571i	−0.889063	−	0.457786i	$-0.848643\pi$
$107$		−	9.47074i		−	0.915571i	0.889063	−	0.457786i	$-0.151357\pi$
$108$	2.33086	+	11.6183i	0.224287	+	1.11797i
$109$		−	8.78729i		−	0.841669i	−0.907137	−	0.420835i	$-0.861737\pi$
$109$		−	8.78729i		−	0.841669i	0.907137	−	0.420835i	$-0.138263\pi$
$110$	−8.19219	+	6.54889i	−0.781095	+	0.624412i
$111$		−	3.37959i		−	0.320777i
$112$	−5.20494	−	12.4500i	−0.491821	−	1.17642i
$113$			19.2799i			1.81370i	0.421456	+	0.906849i	$0.361519\pi$
$113$			19.2799i			1.81370i	−0.421456	+	0.906849i	$0.638481\pi$
$114$	20.0260	−	24.4426i	1.87560	−	2.28926i
$115$	0.999290	−	0.915762i	0.0931843	−	0.0853952i
$116$	14.7988	−	2.96893i	1.37403	−	0.275658i
$117$	−11.3445			−1.04880
$118$	−4.74760	−	3.88974i	−0.437052	−	0.358080i
$119$		−	9.32447i		−	0.854773i
$120$	−17.4078	+	4.50802i	−1.58911	+	0.411524i
$121$	−3.59414	+	10.3963i	−0.326740	+	0.945114i
$122$	−3.11710	−	2.55386i	−0.282209	−	0.231216i
$123$		−	5.81423i		−	0.524251i
$124$	−3.96700	+	0.795860i	−0.356248	+	0.0714703i
$125$	6.80734	+	8.86905i	0.608867	+	0.793272i
$126$	18.7619	+	15.3717i	1.67144	+	1.36942i
$127$			12.7750i			1.13360i	0.823855	+	0.566800i	$0.191819\pi$
$127$			12.7750i			1.13360i	−0.823855	+	0.566800i	$0.808181\pi$
$128$	11.2654	+	1.04421i	0.995732	+	0.0922964i
$129$			8.78729i			0.773678i
$130$	−0.390780	−	7.04570i	−0.0342737	−	0.617949i
$131$	−8.67911			−0.758297			−0.379149	−	0.925336i	$-0.623783\pi$
$131$	−8.67911			−0.758297			−0.379149	+	0.925336i	$0.623783\pi$
$132$	−12.9083	+	13.7501i	−1.12353	+	1.19679i
$133$		−	26.5115i		−	2.29884i
$134$	0.543290	−	0.663111i	0.0469331	−	0.0572840i
$135$	9.76740	−	8.95097i	0.840644	−	0.770377i
$136$	6.90367	+	3.66826i	0.591985	+	0.314550i
$137$		−	12.3393i		−	1.05422i	−0.849797	−	0.527110i	$-0.823276\pi$
$137$		−	12.3393i		−	1.05422i	0.849797	−	0.527110i	$-0.176724\pi$
$138$	1.54469	−	1.88537i	0.131493	−	0.160493i
$139$	−2.49595			−0.211704			−0.105852	−	0.994382i	$-0.533757\pi$
$139$	−2.49595			−0.211704			−0.105852	+	0.994382i	$0.533757\pi$
$140$	−8.90058	+	12.1819i	−0.752237	+	1.02956i
$141$	−24.9296			−2.09945
$142$	10.4482	+	8.56031i	0.876797	+	0.718365i
$143$	−4.29402	−	6.02789i	−0.359084	−	0.504078i
$144$	−18.7619	+	7.84371i	−1.56349	+	0.653642i
$145$	−11.4013	−	12.4412i	−0.946825	−	1.03319i
$146$	−5.38094	+	6.56769i	−0.445330	+	0.543546i
$147$	12.4560			1.02735
$148$	2.33086	−	0.467617i	0.191596	−	0.0384379i
$149$			13.6817i			1.12085i	0.828207	+	0.560423i	$0.189361\pi$
$149$			13.6817i			1.12085i	−0.828207	+	0.560423i	$0.810639\pi$
$150$	14.3831	+	14.0471i	1.17437	+	1.14694i
$151$	−3.02809			−0.246422			−0.123211	−	0.992380i	$-0.539319\pi$
$151$	−3.02809			−0.246422			−0.123211	+	0.992380i	$0.539319\pi$
$152$	19.6286	+	10.4296i	1.59209	+	0.845956i
$153$	−14.0517			−1.13602
$154$	−1.06617	+	15.7875i	−0.0859145	+	1.27219i
$155$	3.05626	+	3.33503i	0.245485	+	0.267876i
$156$	−2.49595	−	12.4412i	−0.199836	−	0.996094i
$157$		−	5.75189i		−	0.459051i	−0.973303	−	0.229526i	$-0.926283\pi$
$157$		−	5.75189i		−	0.459051i	0.973303	−	0.229526i	$-0.0737175\pi$
$158$	−3.44938	+	4.21013i	−0.274418	+	0.334940i
$159$			11.9703i			0.949307i
$160$	−5.51775	−	11.3822i	−0.436217	−	0.899842i
$161$		−	2.04495i		−	0.161165i
$162$	1.42878	−	1.74389i	0.112256	−	0.137013i
$163$	−12.2175			−0.956948			−0.478474	−	0.878102i	$-0.658810\pi$
$163$	−12.2175			−0.956948			−0.478474	+	0.878102i	$0.658810\pi$
$164$	4.01000	−	0.804485i	0.313128	−	0.0628197i
$165$	20.6225	+	4.39586i	1.60546	+	0.342218i
$166$	9.18828	+	7.52801i	0.713149	+	0.584287i
$167$			13.5635i			1.04958i	0.851232	+	0.524789i	$0.175856\pi$
$167$			13.5635i			1.04958i	−0.851232	+	0.524789i	$0.824144\pi$
$168$	−12.7299	+	23.9576i	−0.982129	+	1.84837i
$169$	−8.02054			−0.616964
$170$	−0.484035	−	8.72706i	−0.0371238	−	0.669335i
$171$	−39.9521			−3.05521
$172$	−6.06047	+	1.21585i	−0.462107	+	0.0927078i
$173$	16.7589			1.27416			0.637080	−	0.770798i	$-0.280142\pi$
$173$	16.7589			1.27416			0.637080	+	0.770798i	$0.280142\pi$
$174$	−23.4729	−	19.2315i	−1.77948	−	1.45793i
$175$	16.8038	+	1.46864i	1.27025	+	0.111019i
$176$	−11.2693	−	7.00018i	−0.849457	−	0.527658i
$177$			12.3393i			0.927481i
$178$	7.77784	−	9.49321i	0.582974	−	0.711546i
$179$			1.69409i			0.126622i	0.997994	+	0.0633111i	$0.0201660\pi$
$179$			1.69409i			0.126622i	−0.997994	+	0.0633111i	$0.979834\pi$
$180$	18.3578	+	13.4129i	1.36831	+	0.999742i
$181$	21.6326			1.60794			0.803968	−	0.594673i	$-0.202718\pi$
$181$	21.6326			1.60794			0.803968	+	0.594673i	$0.202718\pi$
$182$	−8.23518	−	6.74713i	−0.610432	−	0.500131i
$183$			8.10155i			0.598884i
$184$	1.51404	+	0.804485i	0.111617	+	0.0593074i
$185$	−1.79574	−	1.95953i	−0.132026	−	0.144068i
$186$	6.29222	+	5.15525i	0.461368	+	0.378001i
$187$	−5.31873	−	7.46637i	−0.388944	−	0.545995i
$188$	−3.44938	−	17.1936i	−0.251572	−	1.25397i
$189$		−	19.9880i		−	1.45392i
$190$	−1.37621	−	24.8129i	−0.0998411	−	1.80012i
$191$		−	13.9933i		−	1.01252i	−0.862380	−	0.506261i	$-0.831027\pi$
$191$		−	13.9933i		−	1.01252i	0.862380	−	0.506261i	$-0.168973\pi$
$192$	−12.7299	−	18.8499i	−0.918698	−	1.36037i
$193$	−7.99126			−0.575223			−0.287612	−	0.957747i	$-0.592861\pi$
$193$	−7.99126			−0.575223			−0.287612	+	0.957747i	$0.592861\pi$
$194$	3.30531	+	2.70806i	0.237307	+	0.194427i
$195$	−10.4592	+	9.58496i	−0.749000	+	0.686393i
$196$	1.72347	+	8.59071i	0.123105	+	0.613622i
$197$	5.93008			0.422501			0.211250	−	0.977432i	$-0.432246\pi$
$197$	5.93008			0.422501			0.211250	+	0.977432i	$0.432246\pi$
$198$	23.7913	+	1.60669i	1.69077	+	0.114183i
$199$		−	9.46191i		−	0.670737i	−0.942087	−	0.335368i	$-0.891139\pi$
$199$		−	9.46191i		−	0.670737i	0.942087	−	0.335368i	$-0.108861\pi$
$200$	−7.69797	+	11.8634i	−0.544329	+	0.838872i
$201$	−1.72347			−0.121564
$202$	13.6099	+	11.1507i	0.957590	+	0.784559i
$203$	−25.4597			−1.78692
$204$	−3.09158	−	15.4101i	−0.216454	−	1.07893i
$205$	−3.08938	−	3.37117i	−0.215772	−	0.235453i
$206$	1.67544	−	2.04495i	0.116733	−	0.142478i
$207$	−3.08168			−0.214192
$208$	8.23518	−	3.44285i	0.571007	−	0.238719i
$209$	−15.1223	−	21.2285i	−1.04603	−	1.46841i
$210$	30.2853	−	1.67973i	2.08988	−	0.115913i
$211$	18.8723			1.29922			0.649610	−	0.760268i	$-0.274932\pi$
$211$	18.8723			1.29922			0.649610	+	0.760268i	$0.274932\pi$
$212$	−8.25576	+	1.65627i	−0.567008	+	0.113753i
$213$		−	27.1557i		−	1.86067i
$214$	−10.3604	−	8.48834i	−0.708223	−	0.580251i
$215$	4.66911	+	5.09499i	0.318431	+	0.347475i
$216$	14.7988	+	7.86331i	1.00693	+	0.535030i
$217$	6.82481			0.463298
$218$	−9.61275	−	7.87578i	−0.651057	−	0.533415i
$219$	17.0698			1.15347
$220$	−0.178334	+	14.8313i	−0.0120233	+	0.999928i
$221$	6.16774			0.414887
$222$	−3.69707	−	3.02903i	−0.248131	−	0.203295i
$223$	7.98187			0.534506			0.267253	−	0.963626i	$-0.413884\pi$
$223$	7.98187			0.534506			0.267253	+	0.963626i	$0.413884\pi$
$224$	−18.2846	−	5.46472i	−1.22169	−	0.365127i
$225$	2.21320	−	25.3228i	0.147547	−	1.68819i
$226$	21.0910	+	17.2800i	1.40295	+	1.14945i
$227$			4.58942i			0.304610i	0.988334	+	0.152305i	$0.0486696\pi$
$227$			4.58942i			0.304610i	−0.988334	+	0.152305i	$0.951330\pi$
$228$	−8.79002	−	43.8143i	−0.582133	−	2.90167i
$229$	9.59149			0.633823			0.316912	−	0.948455i	$-0.397354\pi$
$229$	9.59149			0.633823			0.316912	+	0.948455i	$0.397354\pi$
$230$	−0.106154	−	1.91393i	−0.00699956	−	0.126201i
$231$	25.9103	−	18.4574i	1.70478	−	1.21441i
$232$	10.0159	−	18.8499i	0.657574	−	1.23756i
$233$	−22.8194			−1.49495			−0.747475	−	0.664290i	$-0.768734\pi$
$233$	−22.8194			−1.49495			−0.747475	+	0.664290i	$0.768734\pi$
$234$	−10.1677	+	12.4102i	−0.664686	+	0.811280i
$235$	−14.4545	+	13.2463i	−0.942910	+	0.864095i
$236$	−8.51027	+	1.70733i	−0.553971	+	0.111138i
$237$	10.9424			0.710785
$238$	−10.2004	−	8.35724i	−0.661193	−	0.541720i
$239$	−11.5458			−0.746836			−0.373418	−	0.927663i	$-0.621814\pi$
$239$	−11.5458			−0.746836			−0.373418	+	0.927663i	$0.621814\pi$
$240$	−10.6706	+	23.0835i	−0.688786	+	1.49003i
$241$		−	18.5761i		−	1.19659i	−0.801276	−	0.598294i	$-0.795845\pi$
$241$		−	18.5761i		−	1.19659i	0.801276	−	0.598294i	$-0.204155\pi$
$242$	8.15154	+	13.2496i	0.524001	+	0.851718i
$243$	13.2422			0.849488
$244$	−5.58753	+	1.12097i	−0.357705	+	0.0717627i
$245$	7.22214	−	6.61846i	0.461406	−	0.422838i
$246$	−6.36041	−	5.21112i	−0.405525	−	0.332249i
$247$	17.5362			1.11580
$248$	−2.68489	+	5.05296i	−0.170490	+	0.320863i
$249$		−	23.8809i		−	1.51339i
$250$	15.8034	+	0.502258i	0.999495	+	0.0317656i
$251$			22.1527i			1.39827i	0.714991	+	0.699134i	$0.246431\pi$
$251$			22.1527i			1.39827i	−0.714991	+	0.699134i	$0.753569\pi$
$252$	33.6314	−	6.74713i	2.11858	−	0.425029i
$253$	−1.16645	−	1.63745i	−0.0733341	−	0.102945i
$254$	13.9751	+	11.4499i	0.876875	+	0.718429i
$255$	−12.9552	+	11.8723i	−0.811284	+	0.743471i
$256$	11.2392	−	11.3878i	0.702447	−	0.711736i
$257$			12.9835i			0.809889i	0.914341	+	0.404944i	$0.132709\pi$
$257$			12.9835i			0.809889i	−0.914341	+	0.404944i	$0.867291\pi$
$258$	9.61275	+	7.87578i	0.598464	+	0.490325i
$259$	−4.01000			−0.249169
$260$	−8.05781	−	5.88736i	−0.499724	−	0.365119i
$261$			38.3671i			2.37486i
$262$	−7.77882	+	9.49441i	−0.480577	+	0.586566i
$263$			4.81204i			0.296723i	0.988933	+	0.148362i	$0.0473999\pi$
$263$			4.81204i			0.296723i	−0.988933	+	0.148362i	$0.952600\pi$
$264$	3.47240	+	26.4447i	0.213712	+	1.62756i
$265$	6.36041	+	6.94055i	0.390717	+	0.426354i
$266$	−29.0019	−	23.7614i	−1.77822	−	1.45691i
$267$	−24.6735			−1.50999
$268$	−0.238467	−	1.18865i	−0.0145667	−	0.0726085i
$269$	−13.0205			−0.793876			−0.396938	−	0.917845i	$-0.629927\pi$
$269$	−13.0205			−0.793876			−0.396938	+	0.917845i	$0.629927\pi$
$270$	−1.03758	−	18.7074i	−0.0631452	−	1.13850i
$271$	−18.2131			−1.10637			−0.553185	−	0.833059i	$-0.686588\pi$
$271$	−18.2131			−1.10637			−0.553185	+	0.833059i	$0.686588\pi$
$272$	10.2004	−	4.26444i	0.618490	−	0.258570i
$273$			21.4038i			1.29541i
$274$	−13.4985	−	11.0594i	−0.815472	−	0.668121i
$275$	14.2930	−	8.40898i	0.861899	−	0.507081i
$276$	−0.678013	−	3.37959i	−0.0408116	−	0.203428i
$277$	−6.19087			−0.371973			−0.185987	−	0.982552i	$-0.559548\pi$
$277$	−6.19087			−0.371973			−0.185987	+	0.982552i	$0.559548\pi$
$278$	−2.23705	+	2.73042i	−0.134169	+	0.163760i
$279$		−	10.2848i		−	0.615735i
$280$	5.34891	+	20.6549i	0.319658	+	1.23437i
$281$		−	31.1888i		−	1.86057i	−0.366843	−	0.930283i	$-0.619561\pi$
$281$		−	31.1888i		−	1.86057i	0.366843	−	0.930283i	$-0.380439\pi$
$282$	−22.3437	+	27.2715i	−1.33055	+	1.62399i
$283$			15.7123i			0.933999i	0.884258	+	0.467000i	$0.154665\pi$
$283$			15.7123i			0.933999i	−0.884258	+	0.467000i	$0.845335\pi$
$284$	18.7289	−	3.75739i	1.11136	−	0.222960i
$285$	−36.8343	+	33.7555i	−2.18188	+	1.99950i
$286$	−10.4427	−	0.705227i	−0.617492	−	0.0417010i
$287$	−6.89877			−0.407221
$288$	−8.23518	+	27.5544i	−0.485263	+	1.62366i
$289$	−9.36041			−0.550612
$290$	−23.8285	+	1.32162i	−1.39926	+	0.0776080i
$291$		−	8.59071i		−	0.503596i
$292$	2.36186	+	11.7728i	0.138218	+	0.688953i
$293$	33.0421			1.93034			0.965171	−	0.261618i	$-0.0842561\pi$
$293$	33.0421			1.93034			0.965171	+	0.261618i	$0.0842561\pi$
$294$	11.1639	−	13.6261i	0.651092	−	0.794687i
$295$	6.55649	+	7.15451i	0.381733	+	0.416552i
$296$	1.57754	−	2.96893i	0.0916924	−	0.172565i
$297$	−11.4013	−	16.0050i	−0.661569	−	0.928703i
$298$	14.9669	+	12.2625i	0.867009	+	0.710346i
$299$	1.35265			0.0782256
$300$	28.2578	−	3.14423i	1.63146	−	0.181532i
$301$	10.4264			0.600967
$302$	−2.71398	+	3.31254i	−0.156172	+	0.190615i
$303$		−	35.3730i		−	2.03213i
$304$	29.0019	−	12.1247i	1.66337	−	0.695400i
$305$	4.30475	+	4.69739i	0.246489	+	0.268972i
$306$	−12.5941	+	15.3717i	−0.719959	+	0.878743i
$307$		−	3.15094i		−	0.179834i	−0.995949	−	0.0899168i	$-0.971340\pi$
$307$		−	3.15094i		−	0.179834i	0.995949	−	0.0899168i	$-0.0286601\pi$
$308$	16.3149	+	15.3162i	0.929629	+	0.872719i
$309$	−5.31495			−0.302357
$310$	6.38755	−	0.354277i	0.362788	−	0.0201216i
$311$		−	1.59172i		−	0.0902581i	−0.998981	−	0.0451291i	$-0.985630\pi$
$311$		−	1.59172i		−	0.0902581i	0.998981	−	0.0451291i	$-0.0143699\pi$
$312$	−15.8470	−	8.42026i	−0.897157	−	0.476703i
$313$			20.7596i			1.17340i	0.809804	+	0.586701i	$0.199573\pi$
$313$			20.7596i			1.17340i	−0.809804	+	0.586701i	$0.800427\pi$
$314$	−6.29222	−	5.15525i	−0.355090	−	0.290928i
$315$	−25.9103	−	28.2737i	−1.45988	−	1.59304i
$316$	1.51404	+	7.54682i	0.0851715	+	0.424542i
$317$		−	13.2746i		−	0.745574i	−0.927917	−	0.372787i	$-0.878402\pi$
$317$		−	13.2746i		−	0.745574i	0.927917	−	0.372787i	$-0.121598\pi$
$318$	13.0948	+	10.7286i	0.734318	+	0.601631i
$319$	−20.3863	+	14.5224i	−1.14141	+	0.813096i
$320$	−17.3968	−	4.16544i	−0.972511	−	0.232855i
$321$			26.9274i			1.50294i
$322$	−2.23705	−	1.83283i	−0.124666	−	0.102139i
$323$	21.7210			1.20859
$324$	−0.627137	−	3.12599i	−0.0348409	−	0.173666i
$325$	−0.971442	+	11.1150i	−0.0538859	+	0.616548i
$326$	−10.9502	+	13.3652i	−0.606474	+	0.740229i
$327$			24.9841i			1.38163i
$328$	2.71398	−	5.10772i	0.149855	−	0.282027i
$329$			29.5798i			1.63079i
$330$	23.2922	−	18.6199i	1.28219	−	1.02499i
$331$			31.1747i			1.71352i	0.515716	+	0.856760i	$0.327526\pi$
$331$			31.1747i			1.71352i	−0.515716	+	0.856760i	$0.672474\pi$
$332$	16.4704	−	3.30428i	0.903928	−	0.181346i
$333$			6.04295i			0.331152i
$334$	14.8377	+	12.1566i	0.811882	+	0.665179i
$335$	−0.999290	+	0.915762i	−0.0545970	+	0.0500334i
$336$	14.7988	+	35.3982i	0.807339	+	1.93113i
$337$	−18.8600			−1.02737			−0.513685	−	0.857979i	$-0.671720\pi$
$337$	−18.8600			−1.02737			−0.513685	+	0.857979i	$0.671720\pi$
$338$	−7.18857	+	8.77397i	−0.391006	+	0.477241i
$339$		−	54.8168i		−	2.97724i
$340$	−9.98069	−	7.29230i	−0.541279	−	0.395481i
$341$	5.46482	−	3.89291i	0.295936	−	0.210813i
$342$	−35.8079	+	43.7051i	−1.93627	+	2.36330i
$343$			8.83556i			0.477075i
$344$	−4.10175	+	7.71951i	−0.221152	+	0.416208i
$345$	−2.84120	+	2.60371i	−0.152965	+	0.140179i
$346$	15.0205	−	18.3332i	0.807509	−	0.985602i
$347$			18.6496i			1.00116i	0.865690	+	0.500581i	$0.166880\pi$
$347$			18.6496i			1.00116i	−0.865690	+	0.500581i	$0.833120\pi$
$348$	−42.0761	+	8.44130i	−2.25552	+	0.452501i
$349$		−	8.35131i		−	0.447035i	−0.974700	−	0.223518i	$-0.928246\pi$
$349$		−	8.35131i		−	0.447035i	0.974700	−	0.223518i	$-0.0717540\pi$
$350$	16.6673	−	17.0660i	0.890905	−	0.912215i
$351$	13.2212			0.705697
$352$	−17.7581	+	6.05389i	−0.946510	+	0.322673i
$353$			5.39878i			0.287348i	0.989625	+	0.143674i	$0.0458917\pi$
$353$			5.39878i			0.287348i	−0.989625	+	0.143674i	$0.954108\pi$
$354$	13.4985	+	11.0594i	0.717435	+	0.587799i
$355$	−14.4291	−	15.7452i	−0.765818	−	0.835670i
$356$	−3.41394	−	17.0170i	−0.180938	−	0.901897i
$357$			26.5115i			1.40314i
$358$	1.85323	+	1.51836i	0.0979462	+	0.0802479i
$359$	14.3645			0.758132			0.379066	−	0.925370i	$-0.376245\pi$
$359$	14.3645			0.758132			0.379066	+	0.925370i	$0.376245\pi$
$360$	31.1265	−	8.06066i	1.64051	−	0.424834i
$361$	42.7575			2.25040
$362$	19.3886	−	23.6647i	1.01904	−	1.24379i
$363$	10.2189	−	29.5588i	0.536354	−	1.55143i
$364$	−14.7619	+	2.96153i	−0.773733	+	0.155226i
$365$	9.89733	−	9.07004i	0.518050	−	0.474747i
$366$	8.86259	+	7.26118i	0.463255	+	0.379548i
$367$	−24.3058			−1.26875			−0.634375	−	0.773025i	$-0.718743\pi$
$367$	−24.3058			−1.26875			−0.634375	+	0.773025i	$0.718743\pi$
$368$	2.23705	−	0.935234i	0.116614	−	0.0487524i
$369$			10.3963i			0.541207i
$370$	−3.75308	+	0.208159i	−0.195113	+	0.0108217i
$371$	14.2031			0.737391
$372$	11.2790	−	2.26280i	0.584791	−	0.117321i
$373$	−6.11724			−0.316739			−0.158369	−	0.987380i	$-0.550624\pi$
$373$	−6.11724			−0.316739			−0.158369	+	0.987380i	$0.550624\pi$
$374$	−12.9348	−	0.873520i	−0.668841	−	0.0451687i
$375$	−19.3547	−	25.2166i	−0.999474	−	1.30218i
$376$	−21.9003	−	11.6367i	−1.12942	−	0.600118i
$377$		−	16.8405i		−	0.867331i
$378$	−21.8657	−	17.9147i	−1.12465	−	0.921431i
$379$		−	28.2805i		−	1.45267i	−0.687339	−	0.726337i	$-0.741221\pi$
$379$		−	28.2805i		−	1.45267i	0.687339	−	0.726337i	$-0.258779\pi$
$380$	−28.3773	−	20.7336i	−1.45572	−	1.06361i
$381$		−	36.3221i		−	1.86084i
$382$	−15.3078	−	12.5418i	−0.783217	−	0.641694i
$383$	25.0412			1.27954			0.639772	−	0.768565i	$-0.279029\pi$
$383$	25.0412			1.27954			0.639772	+	0.768565i	$0.279029\pi$
$384$	−32.0300	−	2.96893i	−1.63452	−	0.151507i
$385$	5.21583	−	24.4693i	0.265823	−	1.24707i
$386$	−7.16232	+	8.74194i	−0.364553	+	0.444953i
$387$		−	15.7123i		−	0.798701i
$388$	5.92490	−	1.18865i	0.300791	−	0.0603447i
$389$	−12.9117			−0.654652			−0.327326	−	0.944912i	$-0.606147\pi$
$389$	−12.9117			−0.654652			−0.327326	+	0.944912i	$0.606147\pi$
$390$	1.11107	+	20.0324i	0.0562613	+	1.01438i
$391$	1.67544			0.0847305
$392$	10.9424	+	5.81423i	0.552674	+	0.293663i
$393$	24.6766			1.24477
$394$	5.31495	−	6.48714i	0.267763	−	0.326817i
$395$	6.34455	−	5.81423i	0.319229	−	0.292546i
$396$	23.0810	−	24.5862i	1.15987	−	1.23550i
$397$			3.66565i			0.183974i	0.995760	+	0.0919869i	$0.0293218\pi$
$397$			3.66565i			0.183974i	−0.995760	+	0.0919869i	$0.970678\pi$
$398$	−10.3507	−	8.48042i	−0.518836	−	0.425085i
$399$			75.3778i			3.77361i
$400$	6.07841	+	19.0539i	0.303921	+	0.952697i
$401$	−35.0314			−1.74938			−0.874692	−	0.484679i	$-0.838936\pi$
$401$	−35.0314			−1.74938			−0.874692	+	0.484679i	$0.838936\pi$
$402$	−1.54469	+	1.88537i	−0.0770422	+	0.0940335i
$403$			4.51432i			0.224874i
$404$	24.3963	−	4.89438i	1.21376	−	0.243505i
$405$	−2.62800	+	2.40833i	−0.130586	+	0.119671i
$406$	−22.8188	+	27.8513i	−1.13248	+	1.38224i
$407$	−3.21092	+	2.28732i	−0.159159	+	0.113378i
$408$	−19.6286	−	10.4296i	−0.971761	−	0.516344i
$409$			23.8809i			1.18084i	0.807098	+	0.590418i	$0.201037\pi$
$409$			23.8809i			1.18084i	−0.807098	+	0.590418i	$0.798963\pi$
$410$	−6.45677	+	0.358116i	−0.318877	+	0.0176861i
$411$			35.0834i			1.73053i
$412$	−0.735402	−	3.66565i	−0.0362307	−	0.180594i
$413$	14.6410			0.720437
$414$	−2.76202	+	3.37117i	−0.135746	+	0.165684i
$415$	−12.6891	−	13.8465i	−0.622884	−	0.679698i
$416$	3.61468	−	12.0945i	0.177224	−	0.592982i
$417$	7.09653			0.347519
$418$	−36.7763	−	2.48361i	−1.79879	−	0.121477i
$419$			20.7070i			1.01160i	0.862649	+	0.505802i	$0.168804\pi$
$419$			20.7070i			1.01160i	−0.862649	+	0.505802i	$0.831196\pi$
$420$	25.3063	−	34.6357i	1.23482	−	1.69005i
$421$	−3.57360			−0.174167			−0.0870834	−	0.996201i	$-0.527755\pi$
$421$	−3.57360			−0.174167			−0.0870834	+	0.996201i	$0.527755\pi$
$422$	16.9146	−	20.6451i	0.823392	−	1.00499i
$423$	44.5760			2.16736
$424$	−5.58753	+	10.5158i	−0.271354	+	0.510690i
$425$	−1.20326	+	13.7674i	−0.0583669	+	0.667818i
$426$	−29.7066	−	24.3388i	−1.43929	−	1.17922i
$427$	9.61275			0.465193
$428$	−18.5714	+	3.72580i	−0.897684	+	0.180093i
$429$	12.2088	+	17.1386i	0.589447	+	0.827459i
$430$	9.75839	−	0.541236i	0.470591	−	0.0261007i
$431$	37.4561			1.80420			0.902099	−	0.431528i	$-0.142026\pi$
$431$	37.4561			1.80420			0.902099	+	0.431528i	$0.142026\pi$
$432$	21.8657	−	9.14129i	1.05201	−	0.439811i
$433$			35.0314i			1.68350i	0.539865	+	0.841752i	$0.318475\pi$
$433$			35.0314i			1.68350i	−0.539865	+	0.841752i	$0.681525\pi$
$434$	6.11687	−	7.46592i	0.293619	−	0.358375i
$435$	32.4163	+	35.3730i	1.55424	+	1.69601i
$436$	−17.2312	+	3.45693i	−0.825226	+	0.165557i
$437$	4.76363			0.227875
$438$	15.2992	−	18.6733i	0.731023	−	0.892247i
$439$	28.4063			1.35576			0.677879	−	0.735173i	$-0.262899\pi$
$439$	28.4063			1.35576			0.677879	+	0.735173i	$0.262899\pi$
$440$	16.0647	+	13.4880i	0.765855	+	0.643013i
$441$	−22.2722			−1.06058
$442$	5.52796	−	6.74713i	0.262938	−	0.320928i
$443$	−12.9329			−0.614461			−0.307230	−	0.951635i	$-0.599402\pi$
$443$	−12.9329			−0.614461			−0.307230	+	0.951635i	$0.599402\pi$
$444$	−6.62714	+	1.32954i	−0.314510	+	0.0630969i
$445$	−14.3060	+	13.1102i	−0.678170	+	0.621484i
$446$	7.15391	−	8.73167i	0.338747	−	0.413457i
$447$		−	38.8999i		−	1.83990i
$448$	−22.3660	+	15.1044i	−1.05669	+	0.713615i
$449$	6.61202			0.312041			0.156020	−	0.987754i	$-0.450133\pi$
$449$	6.61202			0.312041			0.156020	+	0.987754i	$0.450133\pi$
$450$	−25.7180	−	25.1172i	−1.21236	−	1.18404i
$451$	−5.52404	+	3.93509i	−0.260117	+	0.185296i
$452$	37.8064	−	7.58472i	1.77826	−	0.356755i
$453$	8.60950			0.404509
$454$	5.02054	+	4.11336i	0.235625	+	0.193049i
$455$	11.3729	+	12.4102i	0.533168	+	0.581799i
$456$	−55.8084	−	29.6537i	−2.61347	−	1.38866i
$457$	24.4616			1.14427			0.572133	−	0.820161i	$-0.306116\pi$
$457$	24.4616			1.14427			0.572133	+	0.820161i	$0.306116\pi$
$458$	8.59656	−	10.4925i	0.401691	−	0.490282i
$459$	16.3763			0.764381
$460$	−2.18886	−	1.59927i	−0.102056	−	0.0745665i
$461$		−	13.2457i		−	0.616913i	−0.951238	−	0.308457i	$-0.900188\pi$
$461$		−	13.2457i		−	0.616913i	0.951238	−	0.308457i	$-0.0998125\pi$
$462$	3.03135	−	44.8872i	0.141031	−	2.08834i
$463$	−27.5675			−1.28117			−0.640586	−	0.767887i	$-0.721308\pi$
$463$	−27.5675			−1.28117			−0.640586	+	0.767887i	$0.721308\pi$
$464$	−11.6437	−	27.8513i	−0.540545	−	1.29297i
$465$	−8.68961	−	9.48220i	−0.402971	−	0.439727i
$466$	−20.4524	+	24.9630i	−0.947437	+	1.15639i
$467$	−5.26789			−0.243769			−0.121884	−	0.992544i	$-0.538894\pi$
$467$	−5.26789			−0.243769			−0.121884	+	0.992544i	$0.538894\pi$
$468$	4.46294	+	22.2458i	0.206300	+	1.02831i
$469$			2.04495i			0.0944269i
$470$	1.53549	+	27.6847i	0.0708269	+	1.27700i
$471$			16.3539i			0.753547i
$472$	−5.75978	+	10.8399i	−0.265116	+	0.498948i
$473$	8.34871	−	5.94727i	0.383874	−	0.273456i
$474$	9.80734	−	11.9703i	0.450466	−	0.549814i
$475$	−3.42114	+	39.1438i	−0.156973	+	1.79604i
$476$	−18.2846	+	3.66826i	−0.838074	+	0.168134i
$477$		−	21.4038i		−	0.980011i
$478$	−10.3482	+	12.6304i	−0.473313	+	0.577701i
$479$	−32.7870			−1.49808			−0.749039	−	0.662526i	$-0.769484\pi$
$479$	−32.7870			−1.49808			−0.749039	+	0.662526i	$0.769484\pi$
$480$	15.6882	+	32.3620i	0.716063	+	1.47712i
$481$		−	2.65244i		−	0.120941i
$482$	−20.3210	−	16.6492i	−0.925598	−	0.758348i
$483$			5.81423i			0.264557i
$484$	21.8002	+	2.95795i	0.990920	+	0.134452i
$485$	−4.56466	−	4.98101i	−0.207271	−	0.226176i
$486$	11.8686	−	14.4862i	0.538370	−	0.657105i
$487$	36.8910			1.67169			0.835844	−	0.548966i	$-0.184979\pi$
$487$	36.8910			1.67169			0.835844	+	0.548966i	$0.184979\pi$
$488$	−3.78166	+	7.11710i	−0.171188	+	0.322176i
$489$	34.7370			1.57086
$490$	−0.767200	−	13.8325i	−0.0346586	−	0.624889i
$491$	5.68543			0.256580			0.128290	−	0.991737i	$-0.459051\pi$
$491$	5.68543			0.256580			0.128290	+	0.991737i	$0.459051\pi$
$492$	−11.4013	+	2.28732i	−0.514009	+	0.103120i
$493$		−	20.8593i		−	0.939455i
$494$	15.7172	−	19.1835i	0.707150	−	0.863108i
$495$	−36.8746	−	7.86012i	−1.65739	−	0.353286i
$496$	3.12125	+	7.46592i	0.140148	+	0.335229i
$497$	−32.2210			−1.44531
$498$	−26.1243	−	21.4038i	−1.17066	−	0.959125i
$499$		−	14.1934i		−	0.635385i	−0.948194	−	0.317692i	$-0.897092\pi$
$499$		−	14.1934i		−	0.635385i	0.948194	−	0.317692i	$-0.102908\pi$
$500$	14.7136	−	16.8378i	0.658010	−	0.753009i
$501$		−	38.5641i		−	1.72292i
$502$	24.2337	+	19.8548i	1.08160	+	0.886164i
$503$		−	18.4507i		−	0.822675i	−0.911483	−	0.411338i	$-0.865062\pi$
$503$		−	18.4507i		−	0.822675i	0.911483	−	0.411338i	$-0.134938\pi$
$504$	22.7619	−	42.8379i	1.01389	−	1.90815i
$505$	−18.7954	−	20.5098i	−0.836385	−	0.912673i
$506$	−2.83672	−	0.191572i	−0.126108	−	0.00851640i
$507$	22.8041			1.01277
$508$	25.0509	−	5.02571i	1.11145	−	0.222980i
$509$	13.0027			0.576333			0.288166	−	0.957580i	$-0.406954\pi$
$509$	13.0027			0.576333			0.288166	+	0.957580i	$0.406954\pi$
$510$	1.37621	+	24.8129i	0.0609398	+	1.09873i
$511$		−	20.2539i		−	0.895980i
$512$	−2.38420	−	22.5015i	−0.105368	−	0.994433i
$513$	46.5614			2.05573
$514$	14.2031	+	11.6367i	0.626474	+	0.513274i
$515$	−3.08168	+	2.82409i	−0.135795	+	0.124444i
$516$	17.2312	−	3.45693i	0.758563	−	0.152183i
$517$	16.8725	+	23.6854i	0.742051	+	1.04168i
$518$	−3.59404	+	4.38669i	−0.157913	+	0.192740i
$519$	−47.6493			−2.09157
$520$	−13.6624	+	3.53808i	−0.599135	+	0.155155i
$521$	−11.8912			−0.520963			−0.260482	−	0.965479i	$-0.583881\pi$
$521$	−11.8912			−0.520963			−0.260482	+	0.965479i	$0.583881\pi$
$522$	41.9712	+	34.3873i	1.83703	+	1.50509i
$523$		−	30.8439i		−	1.34871i	−0.738407	−	0.674355i	$-0.764422\pi$
$523$		−	30.8439i		−	1.34871i	0.738407	−	0.674355i	$-0.235578\pi$
$524$	3.41437	+	17.0191i	0.149157	+	0.743483i
$525$	−47.7767	−	4.17565i	−2.08515	−	0.182240i
$526$	5.26408	+	4.31289i	0.229525	+	0.188051i
$527$			5.59160i			0.243574i
$528$	32.0411	+	19.9030i	1.39441	+	0.866167i
$529$	−22.6326			−0.984024
$530$	13.2932	−	0.737287i	0.577418	−	0.0320257i
$531$		−	22.0636i		−	0.957479i
$532$	−51.9871	+	10.4296i	−2.25393	+	0.452182i
$533$		−	4.56324i		−	0.197656i
$534$	−22.1141	+	26.9912i	−0.956970	+	1.16803i
$535$	14.3078	+	15.6129i	0.618581	+	0.675002i
$536$	−1.51404	−	0.804485i	−0.0653967	−	0.0347484i
$537$		−	4.81666i		−	0.207854i
$538$	−11.6699	+	14.2437i	−0.503126	+	0.614088i
$539$	−8.43025	−	11.8343i	−0.363116	−	0.509739i
$540$	−21.3947	−	15.6318i	−0.920682	−	0.672688i
$541$			39.1716i			1.68412i	0.539386	+	0.842059i	$0.318656\pi$
$541$			39.1716i			1.68412i	−0.539386	+	0.842059i	$0.681344\pi$
$542$	−16.3239	+	19.9240i	−0.701171	+	0.855811i
$543$	−61.5060			−2.63948
$544$	4.47727	−	14.9807i	0.191962	−	0.642292i
$545$	13.2753	+	14.4862i	0.568651	+	0.620519i
$546$	23.4144	+	19.1835i	1.00204	+	0.820980i
$547$		−	6.39490i		−	0.273426i	−0.990611	−	0.136713i	$-0.956346\pi$
$547$		−	6.39490i		−	0.273426i	0.990611	−	0.136713i	$-0.0436538\pi$
$548$	−24.1965	+	4.85430i	−1.03362	+	0.207366i
$549$		−	14.4862i		−	0.618254i
$550$	3.61146	−	23.1723i	0.153993	−	0.988072i
$551$		−	59.3074i		−	2.52658i
$552$	−4.30475	−	2.28732i	−0.183222	−	0.0973549i
$553$		−	12.9835i		−	0.552115i
$554$	−5.54869	+	6.77243i	−0.235741	+	0.287733i
$555$	5.10568	+	5.57138i	0.216724	+	0.236492i
$556$	0.981910	+	4.89438i	0.0416423	+	0.207568i
$557$	−33.1557			−1.40485			−0.702426	−	0.711757i	$-0.747900\pi$
$557$	−33.1557			−1.40485			−0.702426	+	0.711757i	$0.747900\pi$
$558$	−11.2509	−	9.21796i	−0.476290	−	0.390227i
$559$			6.89662i			0.291696i
$560$	27.3893	+	12.6610i	1.15741	+	0.535026i
$561$	15.1223	+	21.2285i	0.638464	+	0.896268i
$562$	−34.1186	−	27.9536i	−1.43921	−	1.17915i
$563$		−	17.7167i		−	0.746669i	−0.927697	−	0.373334i	$-0.878214\pi$
$563$		−	17.7167i		−	0.746669i	0.927697	−	0.373334i	$-0.121786\pi$
$564$	9.80734	+	48.8852i	0.412963	+	2.05844i
$565$	−29.1269	−	31.7836i	−1.22538	−	1.33714i
$566$	17.1883	+	14.0825i	0.722477	+	0.591930i
$567$			5.37794i			0.225852i
$568$	12.6758	−	23.8559i	0.531864	−	1.00097i
$569$		−	8.78729i		−	0.368382i	−0.982890	−	0.184191i	$-0.941033\pi$
$569$		−	8.78729i		−	0.368382i	0.982890	−	0.184191i	$-0.0589665\pi$
$570$	3.91287	+	70.5485i	0.163892	+	2.95495i
$571$	−25.7489			−1.07756			−0.538780	−	0.842447i	$-0.681115\pi$
$571$	−25.7489			−1.07756			−0.538780	+	0.842447i	$0.681115\pi$
$572$	−10.1310	+	10.7916i	−0.423598	+	0.451221i
$573$			39.7860i			1.66209i
$574$	−6.18316	+	7.54682i	−0.258080	+	0.314998i
$575$	−0.263888	+	3.01933i	−0.0110049	+	0.125915i
$576$	22.7619	+	33.7050i	0.948412	+	1.40437i
$577$		−	20.5682i		−	0.856266i	−0.903716	−	0.428133i	$-0.859171\pi$
$577$		−	20.5682i		−	0.856266i	0.903716	−	0.428133i	$-0.140829\pi$
$578$	−8.38945	+	10.2397i	−0.348955	+	0.425916i
$579$	22.7209			0.944247
$580$	−19.9110	+	27.2515i	−0.826760	+	1.13156i
$581$	−28.3355			−1.17555
$582$	−9.39770	−	7.69959i	−0.389547	−	0.319158i
$583$	11.3729	−	8.10155i	0.471016	−	0.335532i
$584$	14.9956	+	7.96790i	0.620523	+	0.329714i
$585$	18.7018	−	17.1386i	0.773226	−	0.708594i
$586$	29.6147	−	36.1461i	1.22337	−	1.49318i
$587$	−19.1163			−0.789013			−0.394506	−	0.918893i	$-0.629084\pi$
$587$	−19.1163			−0.789013			−0.394506	+	0.918893i	$0.629084\pi$
$588$	−4.90019	−	24.4252i	−0.202080	−	1.00728i
$589$			15.8981i			0.655071i
$590$	13.7030	−	0.760016i	0.564142	−	0.0312894i
$591$	−16.8605			−0.693548
$592$	−1.83392	−	4.38669i	−0.0753738	−	0.180292i
$593$	−0.402117			−0.0165130			−0.00825649	−	0.999966i	$-0.502628\pi$
$593$	−0.402117			−0.0165130			−0.00825649	+	0.999966i	$0.502628\pi$
$594$	−27.7271	−	1.87249i	−1.13766	−	0.0768291i
$595$	14.0868	+	15.3717i	0.577504	+	0.630179i
$596$	26.8288	−	5.38238i	1.09895	−	0.220471i
$597$			26.9022i			1.10104i
$598$	1.21234	−	1.47971i	0.0495761	−	0.0605099i
$599$			1.68550i			0.0688678i	0.999407	+	0.0344339i	$0.0109628\pi$
$599$			1.68550i			0.0688678i	−0.999407	+	0.0344339i	$0.989037\pi$
$600$	21.8870	−	33.7303i	0.893533	−	1.37703i
$601$			36.3221i			1.48161i	0.671720	+	0.740805i	$0.265556\pi$
$601$			36.3221i			1.48161i	−0.671720	+	0.740805i	$0.734444\pi$
$602$	9.34486	−	11.4058i	0.380868	−	0.464867i
$603$	3.08168			0.125496
$604$	1.19125	+	5.93785i	0.0484713	+	0.241608i
$605$	−9.78096	−	22.5684i	−0.397653	−	0.917536i
$606$	−38.6959	−	31.7038i	−1.57191	−	1.28788i
$607$		−	24.6864i		−	1.00199i	−0.865450	−	0.500996i	$-0.832967\pi$
$607$		−	24.6864i		−	1.00199i	0.865450	−	0.500996i	$-0.167033\pi$
$608$	12.7299	−	42.5933i	0.516264	−	1.72739i
$609$	72.3874			2.93329
$610$	8.99687	−	0.498999i	0.364273	−	0.0202039i
$611$	−19.5658			−0.791547
$612$	5.52796	+	27.5544i	0.223455	+	1.11382i
$613$	−8.75083			−0.353443			−0.176721	−	0.984261i	$-0.556549\pi$
$613$	−8.75083			−0.353443			−0.176721	+	0.984261i	$0.556549\pi$
$614$	−3.44693	−	2.82409i	−0.139107	−	0.113971i
$615$	8.78378	+	9.58496i	0.354196	+	0.386503i
$616$	31.3775	−	4.12012i	1.26424	−	0.166004i
$617$		−	42.8075i		−	1.72337i	−0.507447	−	0.861683i	$-0.669411\pi$
$617$		−	42.8075i		−	1.72337i	0.507447	−	0.861683i	$-0.330589\pi$
$618$	−4.76363	+	5.81423i	−0.191621	+	0.233883i
$619$		−	30.3386i		−	1.21941i	−0.792628	−	0.609706i	$-0.791288\pi$
$619$		−	30.3386i		−	1.21941i	0.792628	−	0.609706i	$-0.208712\pi$
$620$	5.33741	−	7.30511i	0.214356	−	0.293380i
$621$	3.59149			0.144121
$622$	−1.74124	−	1.42661i	−0.0698175	−	0.0572019i
$623$			29.2758i			1.17291i
$624$	−23.4144	+	9.78876i	−0.937326	+	0.391864i
$625$	−24.6210	−	4.33684i	−0.984839	−	0.173474i
$626$	22.7097	+	18.6062i	0.907662	+	0.743653i
$627$	42.9959	+	60.3572i	1.71709	+	2.41043i
$628$	−11.2790	+	2.26280i	−0.450083	+	0.0902956i
$629$		−	3.28541i		−	0.130998i
$630$	−54.1523	+	3.00348i	−2.15748	+	0.119662i
$631$			36.0437i			1.43488i	0.696622	+	0.717438i	$0.254685\pi$
$631$			36.0437i			1.43488i	−0.696622	+	0.717438i	$0.745315\pi$
$632$	9.61275	+	5.10772i	0.382375	+	0.203174i
$633$	−53.6579			−2.13271
$634$	−14.5215	−	11.8976i	−0.576724	−	0.472514i
$635$	−19.2997	−	21.0601i	−0.765886	−	0.835744i
$636$	23.4729	−	4.70913i	0.930761	−	0.186729i
$637$	9.77595			0.387337
$638$	−2.38508	+	35.3173i	−0.0944260	+	1.39823i
$639$			48.5563i			1.92086i
$640$	−20.1490	+	15.2977i	−0.796458	+	0.604694i
$641$	13.5255			0.534225			0.267112	−	0.963665i	$-0.413930\pi$
$641$	13.5255			0.534225			0.267112	+	0.963665i	$0.413930\pi$
$642$	29.4569	+	24.1342i	1.16257	+	0.952500i
$643$	8.27118			0.326183			0.163092	−	0.986611i	$-0.447853\pi$
$643$	8.27118			0.326183			0.163092	+	0.986611i	$0.447853\pi$
$644$	−4.01000	+	0.804485i	−0.158016	+	0.0317011i
$645$	−13.2753	−	14.4862i	−0.522714	−	0.570392i
$646$	19.4679	−	23.7614i	0.765954	−	0.934881i
$647$	−18.8778			−0.742163			−0.371081	−	0.928600i	$-0.621013\pi$
$647$	−18.8778			−0.742163			−0.371081	+	0.928600i	$0.621013\pi$
$648$	−3.98173	−	2.11569i	−0.156417	−	0.0831120i
$649$	11.7235	−	8.35131i	0.460186	−	0.327818i
$650$	11.2884	+	11.0247i	0.442769	+	0.432425i
$651$	−19.4044			−0.760518
$652$	4.80637	+	23.9576i	0.188232	+	0.938253i
$653$			8.12920i			0.318120i	0.987269	+	0.159060i	$0.0508464\pi$
$653$			8.12920i			0.318120i	−0.987269	+	0.159060i	$0.949154\pi$
$654$	27.3311	+	22.3925i	1.06873	+	0.875618i
$655$	14.3078	−	13.1119i	0.559053	−	0.512323i
$656$	−3.15507	−	7.54682i	−0.123185	−	0.294654i
$657$	−30.5221			−1.19078
$658$	32.3585	+	26.5115i	1.26146	+	1.03353i
$659$	−12.5621			−0.489351			−0.244675	−	0.969605i	$-0.578681\pi$
$659$	−12.5621			−0.489351			−0.244675	+	0.969605i	$0.578681\pi$
$660$	0.507042	−	42.1686i	0.0197366	−	1.64141i
$661$	23.0384			0.896091			0.448045	−	0.894011i	$-0.352120\pi$
$661$	23.0384			0.896091			0.448045	+	0.894011i	$0.352120\pi$
$662$	34.1032	+	27.9410i	1.32546	+	1.08596i
$663$	−17.5362			−0.681051
$664$	11.1472	−	20.9791i	0.432596	−	0.814146i
$665$	40.0519	+	43.7051i	1.55315	+	1.69481i
$666$	6.61062	+	5.41612i	0.256156	+	0.209870i
$667$		−	4.57465i		−	0.177131i
$668$	26.5971	−	5.33591i	1.02907	−	0.206453i
$669$	−22.6942			−0.877407
$670$	0.106154	+	1.91393i	0.00410107	+	0.0739416i
$671$	7.69720	−	5.48316i	0.297147	−	0.211675i
$672$	51.9871	+	15.5374i	2.00545	+	0.599367i
$673$	44.5570			1.71754			0.858772	−	0.512358i	$-0.171228\pi$
$673$	44.5570			1.71754			0.858772	+	0.512358i	$0.171228\pi$
$674$	−16.9037	+	20.6317i	−0.651105	+	0.794703i
$675$	−2.57933	+	29.5120i	−0.0992784	+	1.13592i
$676$	3.15529	+	15.7277i	0.121357	+	0.604911i
$677$	−40.7002			−1.56423			−0.782117	−	0.623132i	$-0.785860\pi$
$677$	−40.7002			−1.56423			−0.782117	+	0.623132i	$0.785860\pi$
$678$	−59.9662	−	49.1307i	−2.30299	−	1.88685i
$679$	−10.1932			−0.391177
$680$	−16.9227	+	4.38239i	−0.648957	+	0.168057i
$681$		−	13.0487i		−	0.500027i
$682$	0.639351	−	9.46726i	0.0244820	−	0.362520i
$683$	38.3418			1.46711			0.733553	−	0.679632i	$-0.237860\pi$
$683$	38.3418			1.46711			0.733553	+	0.679632i	$0.237860\pi$
$684$	15.7172	+	78.3431i	0.600962	+	2.99553i
$685$	18.6415	+	20.3418i	0.712255	+	0.777221i
$686$	9.66556	+	7.91905i	0.369033	+	0.302351i
$687$	−27.2707			−1.04044
$688$	4.76839	+	11.4058i	0.181793	+	0.434843i
$689$			9.39478i			0.357913i
$690$	0.301817	+	5.44172i	0.0114900	+	0.207163i
$691$		−	37.4135i		−	1.42328i	−0.702546	−	0.711638i	$-0.747954\pi$
$691$		−	37.4135i		−	1.42328i	0.702546	−	0.711638i	$-0.252046\pi$
$692$	−6.59298	−	32.8631i	−0.250628	−	1.24927i
$693$	−46.3295	+	33.0032i	−1.75991	+	1.25369i
$694$	20.4015	+	16.7151i	0.774430	+	0.634495i
$695$	4.11467	−	3.77073i	0.156078	−	0.143032i
$696$	−28.4773	+	53.5943i	−1.07943	+	2.03149i
$697$		−	5.65220i		−	0.214092i
$698$	−9.13581	−	7.48503i	−0.345796	−	0.283312i
$699$	64.8805			2.45401
$700$	−3.73073	−	33.5287i	−0.141008	−	1.26727i
$701$		−	27.1663i		−	1.02606i	−0.858371	−	0.513029i	$-0.828523\pi$
$701$		−	27.1663i		−	1.02606i	0.858371	−	0.513029i	$-0.171477\pi$
$702$	11.8498	−	14.4632i	0.447242	−	0.545879i
$703$		−	9.34113i		−	0.352308i
$704$	−9.29348	+	24.8522i	−0.350261	+	0.936652i
$705$	41.0974	−	37.6622i	1.54782	−	1.41844i
$706$	5.90593	+	4.83876i	0.222273	+	0.182109i
$707$	−41.9712			−1.57849
$708$	24.1965	−	4.85430i	0.909361	−	0.182436i
$709$	8.91175			0.334688			0.167344	−	0.985899i	$-0.446481\pi$
$709$	8.91175			0.334688			0.167344	+	0.985899i	$0.446481\pi$
$710$	−30.1567	+	1.67260i	−1.13176	+	0.0627715i
$711$	−19.5658			−0.733774
$712$	−21.6753	−	11.5171i	−0.812316	−	0.431623i
$713$			1.22629i			0.0459251i
$714$	29.0019	+	23.7614i	1.08537	+	0.889250i
$715$	16.1854	+	3.45005i	0.605300	+	0.129025i
$716$	3.32199	−	0.666456i	0.124148	−	0.0249066i
$717$	32.8272			1.22595
$718$	12.8745	−	15.7139i	0.480472	−	0.586438i
$719$		−	19.6576i		−	0.733104i	−0.930398	−	0.366552i	$-0.880538\pi$
$719$		−	19.6576i		−	0.733104i	0.930398	−	0.366552i	$-0.119462\pi$
$720$	19.0798	−	41.2749i	0.711063	−	1.53823i
$721$			6.30636i			0.234861i
$722$	38.3223	−	46.7741i	1.42621	−	1.74075i
$723$			52.8157i			1.96424i
$724$	−8.51027	−	42.4199i	−0.316282	−	1.57652i
$725$	37.5908	+	3.28541i	1.39609	+	0.122017i
$726$	−23.1766	−	37.6715i	−0.860164	−	1.39812i
$727$	−38.5802			−1.43086			−0.715431	−	0.698684i	$-0.753769\pi$
$727$	−38.5802			−1.43086			−0.715431	+	0.698684i	$0.753769\pi$
$728$	−9.99091	+	18.8029i	−0.370288	+	0.696882i
$729$	−42.4329			−1.57159
$730$	−1.05138	−	18.9563i	−0.0389134	−	0.701603i
$731$			8.54241i			0.315952i
$732$	15.8866	−	3.18716i	0.587184	−	0.117801i
$733$	12.6124			0.465849			0.232925	−	0.972495i	$-0.425170\pi$
$733$	12.6124			0.465849			0.232925	+	0.972495i	$0.425170\pi$
$734$	−21.7845	+	26.5890i	−0.804081	+	0.981418i
$735$	−20.5341	+	18.8177i	−0.757411	+	0.694102i
$736$	0.981910	−	3.28541i	0.0361937	−	0.121102i
$737$	1.16645	+	1.63745i	0.0429667	+	0.0603162i
$738$	11.3729	+	9.31785i	0.418641	+	0.342995i
$739$	36.1035			1.32809			0.664044	−	0.747693i	$-0.268839\pi$
$739$	36.1035			1.32809			0.664044	+	0.747693i	$0.268839\pi$
$740$	−3.13606	+	4.29220i	−0.115284	+	0.157785i
$741$	−49.8593			−1.83163
$742$	12.7299	−	15.5374i	0.467328	−	0.570395i
$743$			1.73620i			0.0636949i	0.999493	+	0.0318474i	$0.0101391\pi$
$743$			1.73620i			0.0636949i	−0.999493	+	0.0318474i	$0.989861\pi$
$744$	7.63371	−	14.3667i	0.279865	−	0.526707i
$745$	−20.6694	−	22.5547i	−0.757269	−	0.826341i
$746$	−5.48270	+	6.69188i	−0.200736	+	0.245007i
$747$			42.7008i			1.56234i
$748$	−12.5486	+	13.3669i	−0.458823	+	0.488743i
$749$	31.9502			1.16743
$750$	−44.9325	−	1.42803i	−1.64070	−	0.0521442i
$751$			29.1062i			1.06210i	0.847340	+	0.531051i	$0.178203\pi$
$751$			29.1062i			1.06210i	−0.847340	+	0.531051i	$0.821797\pi$
$752$	−32.3585	+	13.5280i	−1.17999	+	0.493315i
$753$		−	62.9850i		−	2.29530i
$754$	−18.4225	−	15.0936i	−0.670907	−	0.549678i
$755$	4.99190	−	4.57465i	0.181674	−	0.166488i
$756$	−39.1951	+	7.86331i	−1.42551	+	0.285986i
$757$			40.9371i			1.48788i	0.668245	+	0.743941i	$0.267046\pi$
$757$			40.9371i			1.48788i	−0.668245	+	0.743941i	$0.732954\pi$
$758$	−30.9371	−	25.3470i	−1.12369	−	0.920644i
$759$	3.31647	+	4.65562i	0.120380	+	0.168988i
$760$	−48.1149	+	12.4601i	−1.74531	+	0.451975i
$761$		−	30.0158i		−	1.08807i	−0.839062	−	0.544036i	$-0.816896\pi$
$761$		−	30.0158i		−	1.08807i	0.839062	−	0.544036i	$-0.183104\pi$
$762$	−39.7342	−	32.5544i	−1.43942	−	1.17932i
$763$	29.6445			1.07320
$764$	−27.4399	+	5.50499i	−0.992741	+	0.199163i
$765$	23.1648	−	21.2285i	0.837524	−	0.767518i
$766$	22.4436	−	27.3935i	0.810922	−	0.989767i
$767$			9.68441i			0.349684i
$768$	−31.9553	+	32.3779i	−1.15309	+	1.16834i
$769$			1.43745i			0.0518359i	0.999664	+	0.0259180i	$0.00825087\pi$
$769$			1.43745i			0.0518359i	−0.999664	+	0.0259180i	$0.991749\pi$
$770$	−22.0931	−	27.6369i	−0.796180	−	0.995965i
$771$		−	36.9149i		−	1.32946i
$772$	3.14377	+	15.6703i	0.113147	+	0.563985i
$773$		−	24.6410i		−	0.886276i	−0.896453	−	0.443138i	$-0.853865\pi$
$773$		−	24.6410i		−	0.886276i	0.896453	−	0.443138i	$-0.146135\pi$
$774$	−17.1883	−	14.0825i	−0.617820	−	0.506184i
$775$	−10.0767	−	0.880698i	−0.361966	−	0.0316356i
$776$	4.01000	−	7.54682i	0.143950	−	0.270915i
$777$	11.4013			0.409019
$778$	−11.5724	+	14.1247i	−0.414891	+	0.506393i
$779$		−	16.0704i		−	0.575783i
$780$	22.9101	+	16.7390i	0.820312	+	0.599354i
$781$	−25.8003	+	18.3791i	−0.923207	+	0.657654i
$782$	1.50164	−	1.83283i	0.0536987	−	0.0655417i
$783$		−	44.7142i		−	1.59795i
$784$	16.1677	−	6.75919i	0.577419	−	0.241400i
$785$	8.68961	+	9.48220i	0.310145	+	0.338434i
$786$	22.1169	−	26.9946i	0.788883	−	0.962867i
$787$		−	27.6295i		−	0.984886i	−0.870345	−	0.492443i	$-0.836104\pi$
$787$		−	27.6295i		−	0.984886i	0.870345	−	0.492443i	$-0.163896\pi$
$788$	−2.33290	−	11.6285i	−0.0831061	−	0.414247i
$789$		−	13.6817i		−	0.487080i
$790$	−0.673975	−	12.1517i	−0.0239790	−	0.432337i
$791$	−65.0419			−2.31262
$792$	−6.20891	−	47.2851i	−0.220624	−	1.68020i
$793$			6.35843i			0.225794i
$794$	4.01000	+	3.28541i	0.142309	+	0.116595i
$795$	−18.0840	−	19.7335i	−0.641373	−	0.699874i
$796$	−18.5541	+	3.72232i	−0.657633	+	0.131934i
$797$		−	35.2228i		−	1.24766i	−0.781562	−	0.623828i	$-0.785577\pi$
$797$		−	35.2228i		−	1.24766i	0.781562	−	0.623828i	$-0.214423\pi$
$798$	82.4587	+	67.5589i	2.91901	+	2.39156i
$799$	−24.2349			−0.857369
$800$	26.2917	+	10.4281i	0.929553	+	0.368688i
$801$	44.1179			1.55883
$802$	−31.3976	+	38.3222i	−1.10869	+	1.35320i
$803$	−11.5529	−	16.2179i	−0.407694	−	0.572316i
$804$	0.678013	+	3.37959i	0.0239117	+	0.119189i
$805$	3.08938	+	3.37117i	0.108886	+	0.118818i
$806$	4.93839	+	4.04605i	0.173947	+	0.142516i
$807$	37.0202			1.30317
$808$	16.5115	−	31.0747i	0.580873	−	1.09320i
$809$		−	8.35131i		−	0.293616i	−0.989165	−	0.146808i	$-0.953100\pi$
$809$		−	8.35131i		−	0.293616i	0.989165	−	0.146808i	$-0.0469000\pi$
$810$	0.279169	+	5.03338i	0.00980902	+	0.176855i
$811$	26.0717			0.915502			0.457751	−	0.889080i	$-0.348655\pi$
$811$	26.0717			0.915502			0.457751	+	0.889080i	$0.348655\pi$
$812$	10.0159	+	49.9246i	0.351488	+	1.75201i
$813$	51.7839			1.81614
$814$	−0.375658	+	5.56260i	−0.0131668	+	0.194969i
$815$	20.1410	−	18.4574i	0.705508	−	0.646536i
$816$	−29.0019	+	12.1247i	−1.01527	+	0.424450i
$817$			24.2879i			0.849726i
$818$	26.1243	+	21.4038i	0.913413	+	0.748365i
$819$		−	38.2715i		−	1.33731i
$820$	−5.39525	+	7.38428i	−0.188410	+	0.257870i
$821$			43.0645i			1.50296i	0.659755	+	0.751480i	$0.270660\pi$
$821$			43.0645i			1.50296i	−0.659755	+	0.751480i	$0.729340\pi$
$822$	38.3790	+	31.4442i	1.33862	+	1.09674i
$823$	−1.08310			−0.0377546			−0.0188773	−	0.999822i	$-0.506009\pi$
$823$	−1.08310			−0.0377546			−0.0188773	+	0.999822i	$0.506009\pi$
$824$	−4.66911	−	2.48093i	−0.162656	−	0.0864272i
$825$	−40.6380	+	23.9085i	−1.41483	+	0.832389i
$826$	13.1223	−	16.0164i	0.456583	−	0.557280i
$827$			1.85103i			0.0643667i	0.999482	+	0.0321834i	$0.0102461\pi$
$827$			1.85103i			0.0643667i	−0.999482	+	0.0321834i	$0.989754\pi$
$828$	1.21234	+	6.04295i	0.0421316	+	0.210007i
$829$	−18.5763			−0.645180			−0.322590	−	0.946539i	$-0.604554\pi$
$829$	−18.5763			−0.645180			−0.322590	+	0.946539i	$0.604554\pi$
$830$	−26.5201	+	1.47090i	−0.920525	+	0.0510556i
$831$	17.6020			0.610606
$832$	−9.99091	−	14.7942i	−0.346372	−	0.512896i
$833$	12.1088			0.419547
$834$	6.36041	−	7.76316i	0.220243	−	0.268816i
$835$	−20.4910	−	22.3600i	−0.709119	−	0.773799i
$836$	−35.6784	+	38.0050i	−1.23396	+	1.31443i
$837$			11.9862i			0.414304i
$838$	22.6522	+	18.5591i	0.782508	+	0.641113i
$839$			48.0140i			1.65763i	0.559525	+	0.828814i	$0.310984\pi$
$839$			48.0140i			1.65763i	−0.559525	+	0.828814i	$0.689016\pi$
$840$	−15.2081	−	58.7265i	−0.524729	−	2.02626i
$841$	−27.9545			−0.963950
$842$	−3.20291	+	3.90930i	−0.110380	+	0.134723i
$843$			88.6764i			3.05418i
$844$	−7.42436	−	37.0071i	−0.255557	−	1.27384i
$845$	13.2221	−	12.1169i	0.454855	−	0.416835i
$846$	39.9521	−	48.7633i	1.37358	−	1.67652i
$847$	−35.0725	−	12.1251i	−1.20510	−	0.416622i
$848$	6.49564	+	15.5374i	0.223061	+	0.533555i
$849$		−	44.6734i		−	1.53319i
$850$	13.9823	+	13.6556i	0.479588	+	0.468384i
$851$		−	0.720523i		−	0.0246992i
$852$	−53.2503	+	10.6831i	−1.82432	+	0.365996i
$853$	−26.5228			−0.908123			−0.454062	−	0.890970i	$-0.650025\pi$
$853$	−26.5228			−0.908123			−0.454062	+	0.890970i	$0.650025\pi$
$854$	8.61562	−	10.5158i	0.294820	−	0.359842i
$855$	65.8624	−	60.3572i	2.25245	−	2.06417i
$856$	−12.5692	+	23.6553i	−0.429607	+	0.808522i
$857$	13.7800			0.470716			0.235358	−	0.971909i	$-0.424374\pi$
$857$	13.7800			0.470716			0.235358	+	0.971909i	$0.424374\pi$
$858$	29.6910	+	2.00511i	1.01363	+	0.0684534i
$859$			38.3871i			1.30975i	0.755737	+	0.654875i	$0.227279\pi$
$859$			38.3871i			1.30975i	−0.755737	+	0.654875i	$0.772721\pi$
$860$	8.15407	−	11.1602i	0.278052	−	0.380559i
$861$	19.6147			0.668466
$862$	33.5708	−	40.9747i	1.14343	−	1.39560i
$863$	29.8246			1.01524			0.507620	−	0.861581i	$-0.330525\pi$
$863$	29.8246			1.01524			0.507620	+	0.861581i	$0.330525\pi$
$864$	9.59753	−	32.1127i	0.326514	−	1.09250i
$865$	−27.6277	+	25.3184i	−0.939370	+	0.860851i
$866$	38.3222	+	31.3976i	1.30224	+	1.06693i
$867$	26.6136			0.903847
$868$	−2.68489	−	13.3829i	−0.0911309	−	0.454247i
$869$	−7.40586	−	10.3963i	−0.251227	−	0.352669i
$870$	67.7496	−	3.75764i	2.29693	−	0.127396i
$871$	−1.35265			−0.0458327
$872$	−11.6622	+	21.9482i	−0.394931	+	0.743261i
$873$			15.3608i			0.519885i
$874$	4.26950	−	5.21112i	0.144418	−	0.176269i
$875$	−29.9203	+	22.9650i	−1.01149	+	0.776359i
$876$	−6.71529	−	33.4727i	−0.226889	−	1.13094i
$877$	38.6836			1.30625			0.653127	−	0.757249i	$-0.273457\pi$
$877$	38.6836			1.30625			0.653127	+	0.757249i	$0.273457\pi$
$878$	25.4597	−	31.0747i	0.859223	−	1.04872i
$879$	−93.9459			−3.16872
$880$	29.1533	−	5.48496i	0.982758	−	0.184898i
$881$	−29.9680			−1.00965			−0.504825	−	0.863222i	$-0.668443\pi$
$881$	−29.9680			−1.00965			−0.504825	+	0.863222i	$0.668443\pi$
$882$	−19.9619	+	24.3644i	−0.672151	+	0.820391i
$883$	40.7513			1.37139			0.685696	−	0.727888i	$-0.259498\pi$
$883$	40.7513			1.37139			0.685696	+	0.727888i	$0.259498\pi$
$884$	−2.42640	−	12.0945i	−0.0816085	−	0.406782i
$885$	−18.6415	−	20.3418i	−0.626627	−	0.683783i
$886$	−11.5914	+	14.1478i	−0.389420	+	0.475304i
$887$			9.27185i			0.311318i	0.987811	+	0.155659i	$0.0497501\pi$
$887$			9.27185i			0.311318i	−0.987811	+	0.155659i	$0.950250\pi$
$888$	−4.48527	+	8.44130i	−0.150516	+	0.283271i
$889$	−43.0974			−1.44544
$890$	1.51971	+	27.4002i	0.0509409	+	0.918456i
$891$	3.06761	+	4.30627i	0.102769	+	0.144265i
$892$	−3.14007	−	15.6519i	−0.105137	−	0.524063i
$893$	−68.9050			−2.30582
$894$	−42.5541	−	34.8648i	−1.42322	−	1.16605i
$895$	−2.55933	−	2.79277i	−0.0855489	−	0.0933519i
$896$	−3.52273	+	38.0046i	−0.117686	+	1.26965i
$897$	−3.84587			−0.128410
$898$	5.92616	−	7.23314i	0.197758	−	0.241373i
$899$	15.2674			0.509197
$900$	−50.5269	+	5.62210i	−1.68423	+	0.187403i
$901$			11.6367i			0.387675i
$902$	−0.646279	+	9.56986i	−0.0215187	+	0.318641i
$903$	−29.6445			−0.986507
$904$	25.5875	−	48.1559i	0.851029	−	1.60164i
$905$	−35.6620	+	32.6811i	−1.18545	+	1.08636i
$906$	7.71643	−	9.41826i	0.256361	−	0.312901i
$907$	34.9632			1.16093			0.580467	−	0.814284i	$-0.302870\pi$
$907$	34.9632			1.16093			0.580467	+	0.814284i	$0.302870\pi$
$908$	8.99951	−	1.80548i	0.298659	−	0.0599170i
$909$			63.2495i			2.09785i
$910$	23.7691	−	1.31832i	0.787939	−	0.0437020i
$911$			13.7800i			0.456552i	0.973596	+	0.228276i	$0.0733088\pi$
$911$			13.7800i			0.456552i	−0.973596	+	0.228276i	$0.926691\pi$
$912$	−82.4587	+	34.4732i	−2.73048	+	1.14152i
$913$	−22.6890	+	16.1627i	−0.750897	+	0.534908i
$914$	21.9242	−	26.7595i	0.725188	−	0.885125i
$915$	−12.2393	−	13.3557i	−0.404620	−	0.441526i
$916$	−3.77330	−	18.8082i	−0.124673	−	0.621441i
$917$		−	29.2795i		−	0.966896i
$918$	14.6776	−	17.9147i	0.484433	−	0.591272i
$919$	14.0762			0.464330			0.232165	−	0.972676i	$-0.425419\pi$
$919$	14.0762			0.464330			0.232165	+	0.972676i	$0.425419\pi$
$920$	−3.71132	+	0.961101i	−0.122359	+	0.0316866i
$921$			8.95880i			0.295203i
$922$	−14.4900	−	11.8717i	−0.477202	−	0.390974i
$923$		−	21.3129i		−	0.701521i
$924$	−46.3869	−	43.5471i	−1.52602	−	1.43259i
$925$	5.92069	+	0.517464i	0.194671	+	0.0170141i
$926$	−24.7079	+	30.1572i	−0.811953	+	0.991026i
$927$	9.50351			0.312136
$928$	−40.9035	−	12.2248i	−1.34272	−	0.401300i
$929$	15.9340			0.522778			0.261389	−	0.965234i	$-0.415819\pi$
$929$	15.9340			0.522778			0.261389	+	0.965234i	$0.415819\pi$
$930$	−18.1612	+	1.00728i	−0.595528	+	0.0330302i
$931$	34.4281			1.12833
$932$	8.97718	+	44.7472i	0.294057	+	1.46574i
$933$			4.52560i			0.148162i
$934$	−4.72145	+	5.76274i	−0.154491	+	0.188563i
$935$	20.0478	+	4.27336i	0.655635	+	0.139754i
$936$	28.3355	+	15.0560i	0.926174	+	0.492122i
$937$	18.5883			0.607253			0.303627	−	0.952791i	$-0.401802\pi$
$937$	18.5883			0.607253			0.303627	+	0.952791i	$0.401802\pi$
$938$	2.23705	+	1.83283i	0.0730422	+	0.0598439i
$939$		−	59.0240i		−	1.92617i
$940$	31.6615	+	23.1332i	1.03268	+	0.754521i
$941$			40.6090i			1.32382i	0.749585	+	0.661908i	$0.230253\pi$
$941$			40.6090i			1.32382i	−0.749585	+	0.661908i	$0.769747\pi$
$942$	17.8901	+	14.6575i	0.582892	+	0.477567i
$943$		−	1.23958i		−	0.0403664i
$944$	6.69589	+	16.0164i	0.217933	+	0.521288i
$945$	30.1967	+	32.9510i	0.982298	+	1.07190i
$946$	0.976749	−	14.4633i	0.0317569	−	0.470243i
$947$	0.895476			0.0290991			0.0145495	−	0.999894i	$-0.495369\pi$
$947$	0.895476			0.0290991			0.0145495	+	0.999894i	$0.495369\pi$
$948$	−4.30475	−	21.4572i	−0.139812	−	0.696899i
$949$	13.3971			0.434888
$950$	39.7546	+	38.8259i	1.28981	+	1.25968i
$951$			37.7424i			1.22388i
$952$	−12.3751	+	23.2900i	−0.401079	+	0.754833i
$953$	−6.76328			−0.219084			−0.109542	−	0.993982i	$-0.534938\pi$
$953$	−6.76328			−0.219084			−0.109542	+	0.993982i	$0.534938\pi$
$954$	−23.4144	−	19.1835i	−0.758069	−	0.621090i
$955$	21.1403	+	23.0685i	0.684083	+	0.746479i
$956$	4.54213	+	22.6405i	0.146903	+	0.732245i
$957$	57.9626	−	41.2902i	1.87367	−	1.33472i
$958$	−29.3860	+	35.8670i	−0.949419	+	1.15881i
$959$	41.6275			1.34422
$960$	49.4629	+	11.8432i	1.59641	+	0.382239i
$961$	26.9074			0.867980
$962$	−2.90161	−	2.37730i	−0.0935516	−	0.0766474i
$963$		−	48.1480i		−	1.55155i
$964$	−36.4263	+	7.30783i	−1.17321	+	0.235370i
$965$	13.1739	−	12.0727i	0.424082	−	0.388634i
$966$	6.36041	+	5.21112i	0.204643	+	0.167665i
$967$		−	40.1851i		−	1.29226i	−0.763225	−	0.646132i	$-0.776385\pi$
$967$		−	40.1851i		−	1.29226i	0.763225	−	0.646132i	$-0.223615\pi$
$968$	22.7747	−	21.1970i	0.732007	−	0.681297i
$969$	−61.7575			−1.98394
$970$	−9.54009	+	0.529128i	−0.306314	+	0.0169893i
$971$		−	10.4004i		−	0.333765i	−0.985977	−	0.166883i	$-0.946630\pi$
$971$		−	10.4004i		−	0.333765i	0.985977	−	0.166883i	$-0.0533701\pi$
$972$	−5.20950	−	25.9670i	−0.167095	−	0.832892i
$973$		−	8.42026i		−	0.269941i
$974$	33.0642	−	40.3564i	1.05945	−	1.29310i
$975$	2.76202	−	31.6023i	0.0884554	−	1.01208i
$976$	4.39628	+	10.5158i	0.140721	+	0.336601i
$977$			39.5947i			1.26675i	0.773847	+	0.633373i	$0.218330\pi$
$977$			39.5947i			1.26675i	−0.773847	+	0.633373i	$0.781670\pi$
$978$	31.1337	−	38.0001i	0.995546	−	1.21511i
$979$	16.6991	+	23.4420i	0.533706	+	0.749209i
$980$	−15.8195	−	11.5584i	−0.505336	−	0.369219i
$981$		−	44.6734i		−	1.42631i
$982$	5.09568	−	6.21951i	0.162610	−	0.198473i
$983$	−21.1857			−0.675718			−0.337859	−	0.941197i	$-0.609703\pi$
$983$	−21.1857			−0.675718			−0.337859	+	0.941197i	$0.609703\pi$
$984$	−7.71643	+	14.5224i	−0.245991	+	0.462956i
$985$	−9.77595	+	8.95880i	−0.311488	+	0.285451i
$986$	−22.8188	−	18.6955i	−0.726697	−	0.595387i
$987$		−	84.1017i		−	2.67699i
$988$	−6.89877	−	34.3873i	−0.219479	−	1.09400i
$989$			1.87343i			0.0595717i
$990$	−41.6481	+	33.2937i	−1.32366	+	1.05814i
$991$			31.5123i			1.00102i	0.865731	+	0.500510i	$0.166854\pi$
$991$			31.5123i			1.00102i	−0.865731	+	0.500510i	$0.833146\pi$
$992$	10.9647	+	3.27702i	0.348130	+	0.104046i
$993$		−	88.6365i		−	2.81279i
$994$	−28.8788	+	35.2478i	−0.915978	+	1.11799i
$995$	14.2945	+	15.5983i	0.453165	+	0.494499i
$996$	−46.8288	+	9.39478i	−1.48383	+	0.297685i
$997$	4.10073			0.129871			0.0649357	−	0.997889i	$-0.479316\pi$
$997$	4.10073			0.129871			0.0649357	+	0.997889i	$0.479316\pi$
$998$	−15.5267	−	12.7211i	−0.491490	−	0.402680i
$999$		−	7.04264i		−	0.222819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.g.b.219.17	yes	24
4.3	odd	2	inner	220.2.g.b.219.20	yes	24
5.4	even	2	inner	220.2.g.b.219.8	yes	24
11.10	odd	2	inner	220.2.g.b.219.7	yes	24
20.19	odd	2	inner	220.2.g.b.219.5	✓	24
44.43	even	2	inner	220.2.g.b.219.6	yes	24
55.54	odd	2	inner	220.2.g.b.219.18	yes	24
220.219	even	2	inner	220.2.g.b.219.19	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.g.b.219.5	✓	24	20.19	odd	2	inner
220.2.g.b.219.6	yes	24	44.43	even	2	inner
220.2.g.b.219.7	yes	24	11.10	odd	2	inner
220.2.g.b.219.8	yes	24	5.4	even	2	inner
220.2.g.b.219.17	yes	24	1.1	even	1	trivial
220.2.g.b.219.18	yes	24	55.54	odd	2	inner
220.2.g.b.219.19	yes	24	220.219	even	2	inner
220.2.g.b.219.20	yes	24	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.896270 - 1.09394i) q^{2} -2.84322 q^{3} +(-0.393401 - 1.96093i) q^{4} +(-1.64854 + 1.51074i) q^{5} +(-2.54829 + 3.11030i) q^{6} +3.37357i q^{7} +(-2.49773 - 1.32716i) q^{8} +5.08387 q^{9} +(0.175122 + 3.15742i) q^{10} +(1.92430 + 2.70131i) q^{11} +(1.11852 + 5.57534i) q^{12} -2.23147 q^{13} +(3.69047 + 3.02362i) q^{14} +(4.68714 - 4.29536i) q^{15} +(-3.69047 + 1.54286i) q^{16} -2.76398 q^{17} +(4.55652 - 5.56144i) q^{18} -7.85859 q^{19} +(3.61098 + 2.63833i) q^{20} -9.59177i q^{21} +(4.67976 + 0.316037i) q^{22} -0.606168 q^{23} +(7.10157 + 3.77341i) q^{24} +(0.435337 - 4.98101i) q^{25} +(-2.00000 + 2.44109i) q^{26} -5.92490 q^{27} +(6.61532 - 1.32716i) q^{28} +7.54682i q^{29} +(-0.497910 - 8.97724i) q^{30} -2.02302i q^{31} +(-1.61986 + 5.41997i) q^{32} +(-5.47120 - 7.68040i) q^{33} +(-2.47727 + 3.02362i) q^{34} +(-5.09658 - 5.56144i) q^{35} +(-2.00000 - 9.96910i) q^{36} +1.18865i q^{37} +(-7.04342 + 8.59682i) q^{38} +6.34455 q^{39} +(6.12259 - 1.58554i) q^{40} +2.04495i q^{41} +(-10.4928 - 8.59682i) q^{42} -3.09062i q^{43} +(4.54005 - 4.83611i) q^{44} +(-8.38094 + 7.68040i) q^{45} +(-0.543290 + 0.663111i) q^{46} +8.76811 q^{47} +(10.4928 - 4.38669i) q^{48} -4.38094 q^{49} +(-5.05874 - 4.94056i) q^{50} +7.85859 q^{51} +(0.877863 + 4.37575i) q^{52} -4.21013i q^{53} +(-5.31031 + 6.48147i) q^{54} +(-7.25325 - 1.54609i) q^{55} +(4.47727 - 8.42624i) q^{56} +22.3437 q^{57} +(8.25576 + 6.76399i) q^{58} -4.33992i q^{59} +(-10.2668 - 7.50134i) q^{60} -2.84943i q^{61} +(-2.21306 - 1.81318i) q^{62} +17.1508i q^{63} +(4.47727 + 6.62978i) q^{64} +(3.67866 - 3.37117i) q^{65} +(-13.3056 - 0.898561i) q^{66} +0.606168 q^{67} +(1.08735 + 5.41997i) q^{68} +1.72347 q^{69} +(-10.6518 + 0.590786i) q^{70} +9.55104i q^{71} +(-12.6981 - 6.74713i) q^{72} -6.00371 q^{73} +(1.30031 + 1.06535i) q^{74} +(-1.23776 + 14.1621i) q^{75} +(3.09158 + 15.4101i) q^{76} +(-9.11304 + 6.49175i) q^{77} +(5.68643 - 6.94055i) q^{78} -3.84860 q^{79} +(3.75301 - 8.11880i) q^{80} +1.59414 q^{81} +(2.23705 + 1.83283i) q^{82} +8.39927i q^{83} +(-18.8088 + 3.77341i) q^{84} +(4.55652 - 4.17565i) q^{85} +(-3.38094 - 2.77003i) q^{86} -21.4572i q^{87} +(-1.22129 - 9.30099i) q^{88} +8.67801 q^{89} +(0.890299 + 16.0519i) q^{90} -7.52801i q^{91} +(0.238467 + 1.18865i) q^{92} +5.75189i q^{93} +(7.85859 - 9.59177i) q^{94} +(12.9552 - 11.8723i) q^{95} +(4.60562 - 15.4101i) q^{96} +3.02148i q^{97} +(-3.92651 + 4.79248i) q^{98} +(9.78289 + 13.7331i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{4} - 4 q^{5} + 40 q^{9} + 12 q^{14} - 12 q^{16} - 20 q^{20} - 36 q^{25} - 48 q^{26} + 28 q^{34} - 48 q^{36} + 56 q^{44} - 48 q^{45} + 48 q^{49} + 20 q^{56} - 8 q^{60} + 20 q^{64} - 52 q^{66}+ \cdots - 16 q^{89}+O(q^{100}) \) 24 * q - 4 * q^4 - 4 * q^5 + 40 * q^9 + 12 * q^14 - 12 * q^16 - 20 * q^20 - 36 * q^25 - 48 * q^26 + 28 * q^34 - 48 * q^36 + 56 * q^44 - 48 * q^45 + 48 * q^49 + 20 * q^56 - 8 * q^60 + 20 * q^64 - 52 * q^66 - 8 * q^69 - 64 * q^70 + 64 * q^80 - 104 * q^81 + 72 * q^86 - 16 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more