LMFDB - Embedded newform 840.2.g.b.421.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(421,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.421"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.3058043990573056.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + x^{10} - 8x^{7} - 16x^{5} + 16x^{2} + 64 $ x^12 + x^10 - 8x^7 - 16x^5 + 16*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			421.5
Root			$-1.23149 - 0.695292i$ of defining polynomial
Character	$\chi$	$=$	840.421
Dual form			840.2.g.b.421.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.695292 - 1.23149i) q^{2} -1.00000i q^{3} +(-1.03314 + 1.71249i) q^{4} -1.00000i q^{5} +(-1.23149 + 0.695292i) q^{6} -1.00000 q^{7} +(2.82725 + 0.0816198i) q^{8} -1.00000 q^{9} +(-1.23149 + 0.695292i) q^{10} +3.45686i q^{11} +(1.71249 + 1.03314i) q^{12} +3.45686i q^{13} +(0.695292 + 1.23149i) q^{14} -1.00000 q^{15} +(-1.86525 - 3.53848i) q^{16} +1.15712 q^{17} +(0.695292 + 1.23149i) q^{18} +5.88796i q^{19} +(1.71249 + 1.03314i) q^{20} +1.00000i q^{21} +(4.25709 - 2.40353i) q^{22} +2.37595 q^{23} +(0.0816198 - 2.82725i) q^{24} -1.00000 q^{25} +(4.25709 - 2.40353i) q^{26} +1.00000i q^{27} +(1.03314 - 1.71249i) q^{28} +3.63769i q^{29} +(0.695292 + 1.23149i) q^{30} -5.40739 q^{31} +(-3.06071 + 4.75731i) q^{32} +3.45686 q^{33} +(-0.804535 - 1.42498i) q^{34} +1.00000i q^{35} +(1.03314 - 1.71249i) q^{36} -4.15908i q^{37} +(7.25097 - 4.09385i) q^{38} +3.45686 q^{39} +(0.0816198 - 2.82725i) q^{40} +3.26174 q^{41} +(1.23149 - 0.695292i) q^{42} +4.97544i q^{43} +(-5.91984 - 3.57142i) q^{44} +1.00000i q^{45} +(-1.65198 - 2.92596i) q^{46} +13.0778 q^{47} +(-3.53848 + 1.86525i) q^{48} +1.00000 q^{49} +(0.695292 + 1.23149i) q^{50} -1.15712i q^{51} +(-5.91984 - 3.57142i) q^{52} +5.92814i q^{53} +(1.23149 - 0.695292i) q^{54} +3.45686 q^{55} +(-2.82725 - 0.0816198i) q^{56} +5.88796 q^{57} +(4.47979 - 2.52926i) q^{58} +12.5571i q^{59} +(1.03314 - 1.71249i) q^{60} -13.8161i q^{61} +(3.75971 + 6.65915i) q^{62} +1.00000 q^{63} +(7.98668 + 0.461519i) q^{64} +3.45686 q^{65} +(-2.40353 - 4.25709i) q^{66} +3.21227i q^{67} +(-1.19546 + 1.98156i) q^{68} -2.37595i q^{69} +(1.23149 - 0.695292i) q^{70} +2.33991 q^{71} +(-2.82725 - 0.0816198i) q^{72} +5.95172 q^{73} +(-5.12187 + 2.89178i) q^{74} +1.00000i q^{75} +(-10.0831 - 6.08308i) q^{76} -3.45686i q^{77} +(-2.40353 - 4.25709i) q^{78} -14.2934 q^{79} +(-3.53848 + 1.86525i) q^{80} +1.00000 q^{81} +(-2.26786 - 4.01680i) q^{82} -8.18770i q^{83} +(-1.71249 - 1.03314i) q^{84} -1.15712i q^{85} +(6.12720 - 3.45938i) q^{86} +3.63769 q^{87} +(-0.282148 + 9.77341i) q^{88} -2.61172 q^{89} +(1.23149 - 0.695292i) q^{90} -3.45686i q^{91} +(-2.45469 + 4.06880i) q^{92} +5.40739i q^{93} +(-9.09292 - 16.1052i) q^{94} +5.88796 q^{95} +(4.75731 + 3.06071i) q^{96} +0.962000 q^{97} +(-0.695292 - 1.23149i) q^{98} -3.45686i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 2 q^{4} - 12 q^{7} - 2 q^{8} - 12 q^{9} + 2 q^{14} - 12 q^{15} + 2 q^{16} + 2 q^{18} + 40 q^{23} - 12 q^{25} - 2 q^{28} + 2 q^{30} - 8 q^{31} - 2 q^{32} - 20 q^{34} - 2 q^{36} + 24 q^{38}+ \cdots - 2 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 + 2 * q^4 - 12 * q^7 - 2 * q^8 - 12 * q^9 + 2 * q^14 - 12 * q^15 + 2 * q^16 + 2 * q^18 + 40 * q^23 - 12 * q^25 - 2 * q^28 + 2 * q^30 - 8 * q^31 - 2 * q^32 - 20 * q^34 - 2 * q^36 + 24 * q^38 + 24 * q^46 - 32 * q^47 + 12 * q^49 + 2 * q^50 + 2 * q^56 - 20 * q^58 - 2 * q^60 + 52 * q^62 + 12 * q^63 + 2 * q^64 - 20 * q^66 - 4 * q^68 - 8 * q^71 + 2 * q^72 - 60 * q^74 - 48 * q^76 - 20 * q^78 - 80 * q^79 + 12 * q^81 + 24 * q^86 + 16 * q^87 + 40 * q^88 - 8 * q^92 + 36 * q^94 + 40 * q^96 - 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$1$	$1$	$1$	$-1$	$1$

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 $

$2$	−0.695292	−	1.23149i	−0.491646	−	0.870795i
$2$	−0.695292	−	1.23149i	−0.491646	−	0.870795i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.03314	+	1.71249i	−0.516569	+	0.856245i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−1.23149	+	0.695292i	−0.502754	+	0.283852i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	2.82725	+	0.0816198i	0.999584	+	0.0288570i
$9$	−1.00000			−0.333333
$10$	−1.23149	+	0.695292i	−0.389432	+	0.219871i
$11$			3.45686i			1.04228i	0.853470	+	0.521141i	$0.174494\pi$
$11$			3.45686i			1.04228i	−0.853470	+	0.521141i	$0.825506\pi$
$12$	1.71249	+	1.03314i	0.494353	+	0.298241i
$13$			3.45686i			0.958761i	0.877607	+	0.479380i	$0.159139\pi$
$13$			3.45686i			0.958761i	−0.877607	+	0.479380i	$0.840861\pi$
$14$	0.695292	+	1.23149i	0.185825	+	0.329130i
$15$	−1.00000			−0.258199
$16$	−1.86525	−	3.53848i	−0.466312	−	0.884620i
$17$	1.15712			0.280643			0.140321	−	0.990106i	$-0.455186\pi$
$17$	1.15712			0.280643			0.140321	+	0.990106i	$0.455186\pi$
$18$	0.695292	+	1.23149i	0.163882	+	0.290265i
$19$			5.88796i			1.35079i	0.737456	+	0.675396i	$0.236027\pi$
$19$			5.88796i			1.35079i	−0.737456	+	0.675396i	$0.763973\pi$
$20$	1.71249	+	1.03314i	0.382925	+	0.231017i
$21$			1.00000i			0.218218i
$22$	4.25709	−	2.40353i	0.907615	−	0.512434i
$23$	2.37595			0.495420			0.247710	−	0.968834i	$-0.420322\pi$
$23$	2.37595			0.495420			0.247710	+	0.968834i	$0.420322\pi$
$24$	0.0816198	−	2.82725i	0.0166606	−	0.577110i
$25$	−1.00000			−0.200000
$26$	4.25709	−	2.40353i	0.834884	−	0.471370i
$27$			1.00000i			0.192450i
$28$	1.03314	−	1.71249i	0.195245	−	0.323630i
$29$			3.63769i			0.675503i	0.941235	+	0.337751i	$0.109666\pi$
$29$			3.63769i			0.675503i	−0.941235	+	0.337751i	$0.890334\pi$
$30$	0.695292	+	1.23149i	0.126942	+	0.224838i
$31$	−5.40739			−0.971196			−0.485598	−	0.874182i	$-0.661398\pi$
$31$	−5.40739			−0.971196			−0.485598	+	0.874182i	$0.661398\pi$
$32$	−3.06071	+	4.75731i	−0.541063	+	0.840982i
$33$	3.45686			0.601762
$34$	−0.804535	−	1.42498i	−0.137977	−	0.244382i
$35$			1.00000i			0.169031i
$36$	1.03314	−	1.71249i	0.172190	−	0.285415i
$37$		−	4.15908i		−	0.683749i	−0.939746	−	0.341874i	$-0.888938\pi$
$37$		−	4.15908i		−	0.683749i	0.939746	−	0.341874i	$-0.111062\pi$
$38$	7.25097	−	4.09385i	1.17626	−	0.664111i
$39$	3.45686			0.553541
$40$	0.0816198	−	2.82725i	0.0129052	−	0.447027i
$41$	3.26174			0.509398			0.254699	−	0.967020i	$-0.418024\pi$
$41$	3.26174			0.509398			0.254699	+	0.967020i	$0.418024\pi$
$42$	1.23149	−	0.695292i	0.190023	−	0.107286i
$43$			4.97544i			0.758747i	0.925244	+	0.379373i	$0.123860\pi$
$43$			4.97544i			0.758747i	−0.925244	+	0.379373i	$0.876140\pi$
$44$	−5.91984	−	3.57142i	−0.892450	−	0.538411i
$45$			1.00000i			0.149071i
$46$	−1.65198	−	2.92596i	−0.243571	−	0.431410i
$47$	13.0778			1.90760			0.953800	−	0.300444i	$-0.0971348\pi$
$47$	13.0778			1.90760			0.953800	+	0.300444i	$0.0971348\pi$
$48$	−3.53848	+	1.86525i	−0.510736	+	0.269226i
$49$	1.00000			0.142857
$50$	0.695292	+	1.23149i	0.0983291	+	0.174159i
$51$		−	1.15712i		−	0.162029i
$52$	−5.91984	−	3.57142i	−0.820934	−	0.495266i
$53$			5.92814i			0.814292i	0.913363	+	0.407146i	$0.133476\pi$
$53$			5.92814i			0.814292i	−0.913363	+	0.407146i	$0.866524\pi$
$54$	1.23149	−	0.695292i	0.167585	−	0.0946172i
$55$	3.45686			0.466123
$56$	−2.82725	−	0.0816198i	−0.377807	−	0.0109069i
$57$	5.88796			0.779880
$58$	4.47979	−	2.52926i	0.588225	−	0.332108i
$59$			12.5571i			1.63479i	0.576075	+	0.817397i	$0.304584\pi$
$59$			12.5571i			1.63479i	−0.576075	+	0.817397i	$0.695416\pi$
$60$	1.03314	−	1.71249i	0.133378	−	0.221082i
$61$		−	13.8161i		−	1.76897i	−0.466568	−	0.884485i	$-0.654510\pi$
$61$		−	13.8161i		−	1.76897i	0.466568	−	0.884485i	$-0.345490\pi$
$62$	3.75971	+	6.65915i	0.477484	+	0.845713i
$63$	1.00000			0.125988
$64$	7.98668	+	0.461519i	0.998335	+	0.0576899i
$65$	3.45686			0.428771
$66$	−2.40353	−	4.25709i	−0.295854	−	0.524012i
$67$			3.21227i			0.392441i	0.980560	+	0.196221i	$0.0628669\pi$
$67$			3.21227i			0.392441i	−0.980560	+	0.196221i	$0.937133\pi$
$68$	−1.19546	+	1.98156i	−0.144971	+	0.240299i
$69$		−	2.37595i		−	0.286031i
$70$	1.23149	−	0.695292i	0.147191	−	0.0831033i
$71$	2.33991			0.277697			0.138848	−	0.990314i	$-0.455660\pi$
$71$	2.33991			0.277697			0.138848	+	0.990314i	$0.455660\pi$
$72$	−2.82725	−	0.0816198i	−0.333195	−	0.00961899i
$73$	5.95172			0.696596			0.348298	−	0.937384i	$-0.386760\pi$
$73$	5.95172			0.696596			0.348298	+	0.937384i	$0.386760\pi$
$74$	−5.12187	+	2.89178i	−0.595405	+	0.336162i
$75$			1.00000i			0.115470i
$76$	−10.0831	−	6.08308i	−1.15661	−	0.697777i
$77$		−	3.45686i		−	0.393946i
$78$	−2.40353	−	4.25709i	−0.272146	−	0.482021i
$79$	−14.2934			−1.60813			−0.804066	−	0.594540i	$-0.797334\pi$
$79$	−14.2934			−1.60813			−0.804066	+	0.594540i	$0.797334\pi$
$80$	−3.53848	+	1.86525i	−0.395614	+	0.208541i
$81$	1.00000			0.111111
$82$	−2.26786	−	4.01680i	−0.250443	−	0.443582i
$83$		−	8.18770i		−	0.898717i	−0.893351	−	0.449359i	$-0.851653\pi$
$83$		−	8.18770i		−	0.898717i	0.893351	−	0.449359i	$-0.148347\pi$
$84$	−1.71249	−	1.03314i	−0.186848	−	0.112725i
$85$		−	1.15712i		−	0.125507i
$86$	6.12720	−	3.45938i	0.660713	−	0.373034i
$87$	3.63769			0.390002
$88$	−0.282148	+	9.77341i	−0.0300771	+	1.04185i
$89$	−2.61172			−0.276842			−0.138421	−	0.990373i	$-0.544203\pi$
$89$	−2.61172			−0.276842			−0.138421	+	0.990373i	$0.544203\pi$
$90$	1.23149	−	0.695292i	0.129811	−	0.0732902i
$91$		−	3.45686i		−	0.362377i
$92$	−2.45469	+	4.06880i	−0.255919	+	0.424201i
$93$			5.40739i			0.560720i
$94$	−9.09292	−	16.1052i	−0.937863	−	1.66113i
$95$	5.88796			0.604092
$96$	4.75731	+	3.06071i	0.485541	+	0.312383i
$97$	0.962000			0.0976763			0.0488382	−	0.998807i	$-0.484448\pi$
$97$	0.962000			0.0976763			0.0488382	+	0.998807i	$0.484448\pi$
$98$	−0.695292	−	1.23149i	−0.0702351	−	0.124399i
$99$		−	3.45686i		−	0.347428i
$100$	1.03314	−	1.71249i	0.103314	−	0.171249i
$101$		−	8.65394i		−	0.861099i	−0.902567	−	0.430550i	$-0.858320\pi$
$101$		−	8.65394i		−	0.861099i	0.902567	−	0.430550i	$-0.141680\pi$
$102$	−1.42498	+	0.804535i	−0.141094	+	0.0796609i
$103$	12.5278			1.23440			0.617202	−	0.786805i	$-0.288266\pi$
$103$	12.5278			1.23440			0.617202	+	0.786805i	$0.288266\pi$
$104$	−0.282148	+	9.77341i	−0.0276669	+	0.958361i
$105$	1.00000			0.0975900
$106$	7.30044	−	4.12178i	0.709082	−	0.400343i
$107$			13.7265i			1.32699i	0.748182	+	0.663493i	$0.230927\pi$
$107$			13.7265i			1.32699i	−0.748182	+	0.663493i	$0.769073\pi$
$108$	−1.71249	−	1.03314i	−0.164784	−	0.0994138i
$109$		−	0.912317i		−	0.0873841i	−0.999045	−	0.0436921i	$-0.986088\pi$
$109$		−	0.912317i		−	0.0873841i	0.999045	−	0.0436921i	$-0.0139120\pi$
$110$	−2.40353	−	4.25709i	−0.229167	−	0.405898i
$111$	−4.15908			−0.394763
$112$	1.86525	+	3.53848i	0.176249	+	0.334355i
$113$	−1.85435			−0.174443			−0.0872215	−	0.996189i	$-0.527799\pi$
$113$	−1.85435			−0.174443			−0.0872215	+	0.996189i	$0.527799\pi$
$114$	−4.09385	−	7.25097i	−0.383424	−	0.679116i
$115$		−	2.37595i		−	0.221559i
$116$	−6.22952	−	3.75824i	−0.578396	−	0.348944i
$117$		−	3.45686i		−	0.319587i
$118$	15.4639	−	8.73084i	1.42357	−	0.803739i
$119$	−1.15712			−0.106073
$120$	−2.82725	−	0.0816198i	−0.258091	−	0.00745084i
$121$	−0.949887			−0.0863534
$122$	−17.0144	+	9.60622i	−1.54041	+	0.869706i
$123$		−	3.26174i		−	0.294101i
$124$	5.58658	−	9.26010i	0.501690	−	0.831582i
$125$			1.00000i			0.0894427i
$126$	−0.695292	−	1.23149i	−0.0619415	−	0.109710i
$127$	−9.75004			−0.865176			−0.432588	−	0.901592i	$-0.642400\pi$
$127$	−9.75004			−0.865176			−0.432588	+	0.901592i	$0.642400\pi$
$128$	−4.98471	−	10.1564i	−0.440591	−	0.897708i
$129$	4.97544			0.438063
$130$	−2.40353	−	4.25709i	−0.210803	−	0.373372i
$131$			7.32913i			0.640349i	0.947359	+	0.320175i	$0.103742\pi$
$131$			7.32913i			0.640349i	−0.947359	+	0.320175i	$0.896258\pi$
$132$	−3.57142	+	5.91984i	−0.310852	+	0.515256i
$133$		−	5.88796i		−	0.510551i
$134$	3.95588	−	2.23346i	0.341736	−	0.192942i
$135$	1.00000			0.0860663
$136$	3.27146	+	0.0944439i	0.280526	+	0.00809850i
$137$	−4.09652			−0.349989			−0.174995	−	0.984569i	$-0.555991\pi$
$137$	−4.09652			−0.349989			−0.174995	+	0.984569i	$0.555991\pi$
$138$	−2.92596	+	1.65198i	−0.249074	+	0.140626i
$139$			18.1531i			1.53972i	0.638211	+	0.769862i	$0.279675\pi$
$139$			18.1531i			1.53972i	−0.638211	+	0.769862i	$0.720325\pi$
$140$	−1.71249	−	1.03314i	−0.144732	−	0.0873162i
$141$		−	13.0778i		−	1.10135i
$142$	−1.62692	−	2.88158i	−0.136528	−	0.241817i
$143$	−11.9499			−0.999300
$144$	1.86525	+	3.53848i	0.155437	+	0.294873i
$145$	3.63769			0.302094
$146$	−4.13818	−	7.32949i	−0.342478	−	0.606593i
$147$		−	1.00000i		−	0.0824786i
$148$	7.12239	+	4.29691i	0.585457	+	0.353204i
$149$		−	4.96179i		−	0.406486i	−0.979128	−	0.203243i	$-0.934852\pi$
$149$		−	4.96179i		−	0.406486i	0.979128	−	0.203243i	$-0.0651481\pi$
$150$	1.23149	−	0.695292i	0.100551	−	0.0567703i
$151$	−19.8109			−1.61219			−0.806096	−	0.591785i	$-0.798423\pi$
$151$	−19.8109			−1.61219			−0.806096	+	0.591785i	$0.798423\pi$
$152$	−0.480575	+	16.6467i	−0.0389797	+	1.35023i
$153$	−1.15712			−0.0935475
$154$	−4.25709	+	2.40353i	−0.343046	+	0.193682i
$155$			5.40739i			0.434332i
$156$	−3.57142	+	5.91984i	−0.285942	+	0.473967i
$157$			22.7995i			1.81960i	0.415052	+	0.909798i	$0.363763\pi$
$157$			22.7995i			1.81960i	−0.415052	+	0.909798i	$0.636237\pi$
$158$	9.93808	+	17.6022i	0.790631	+	1.40035i
$159$	5.92814			0.470132
$160$	4.75731	+	3.06071i	0.376099	+	0.241971i
$161$	−2.37595			−0.187251
$162$	−0.695292	−	1.23149i	−0.0546273	−	0.0967550i
$163$			7.57926i			0.593654i	0.954931	+	0.296827i	$0.0959284\pi$
$163$			7.57926i			0.593654i	−0.954931	+	0.296827i	$0.904072\pi$
$164$	−3.36983	+	5.58570i	−0.263140	+	0.436170i
$165$		−	3.45686i		−	0.269116i
$166$	−10.0831	+	5.69284i	−0.782599	+	0.441850i
$167$	7.14851			0.553168			0.276584	−	0.960990i	$-0.410798\pi$
$167$	7.14851			0.553168			0.276584	+	0.960990i	$0.410798\pi$
$168$	−0.0816198	+	2.82725i	−0.00629711	+	0.218127i
$169$	1.05011			0.0807779
$170$	−1.42498	+	0.804535i	−0.109291	+	0.0617051i
$171$		−	5.88796i		−	0.450264i
$172$	−8.52039	−	5.14031i	−0.649673	−	0.391945i
$173$			1.60976i			0.122388i	0.998126	+	0.0611940i	$0.0194908\pi$
$173$			1.60976i			0.122388i	−0.998126	+	0.0611940i	$0.980509\pi$
$174$	−2.52926	−	4.47979i	−0.191743	−	0.339612i
$175$	1.00000			0.0755929
$176$	12.2320	−	6.44791i	0.922024	−	0.486029i
$177$	12.5571			0.943849
$178$	1.81591	+	3.21631i	0.136108	+	0.241073i
$179$			17.9373i			1.34069i	0.742048	+	0.670347i	$0.233855\pi$
$179$			17.9373i			1.34069i	−0.742048	+	0.670347i	$0.766145\pi$
$180$	−1.71249	−	1.03314i	−0.127642	−	0.0770056i
$181$			12.5922i			0.935973i	0.883736	+	0.467986i	$0.155020\pi$
$181$			12.5922i			0.935973i	−0.883736	+	0.467986i	$0.844980\pi$
$182$	−4.25709	+	2.40353i	−0.315557	+	0.178161i
$183$	−13.8161			−1.02132
$184$	6.71741	+	0.193925i	0.495214	+	0.0142963i
$185$	−4.15908			−0.305782
$186$	6.65915	−	3.75971i	0.488272	−	0.275676i
$187$			4.00000i			0.292509i
$188$	−13.5112	+	22.3957i	−0.985407	+	1.63337i
$189$		−	1.00000i		−	0.0727393i
$190$	−4.09385	−	7.25097i	−0.296999	−	0.526041i
$191$	0.362860			0.0262556			0.0131278	−	0.999914i	$-0.495821\pi$
$191$	0.362860			0.0262556			0.0131278	+	0.999914i	$0.495821\pi$
$192$	0.461519	−	7.98668i	0.0333073	−	0.576389i
$193$	−21.4416			−1.54340			−0.771698	−	0.635989i	$-0.780592\pi$
$193$	−21.4416			−1.54340			−0.771698	+	0.635989i	$0.780592\pi$
$194$	−0.668871	−	1.18469i	−0.0480221	−	0.0850561i
$195$		−	3.45686i		−	0.247551i
$196$	−1.03314	+	1.71249i	−0.0737956	+	0.122321i
$197$		−	19.6997i		−	1.40355i	−0.712400	−	0.701773i	$-0.752392\pi$
$197$		−	19.6997i		−	1.40355i	0.712400	−	0.701773i	$-0.247608\pi$
$198$	−4.25709	+	2.40353i	−0.302538	+	0.170811i
$199$	8.33424			0.590798			0.295399	−	0.955374i	$-0.404547\pi$
$199$	8.33424			0.590798			0.295399	+	0.955374i	$0.404547\pi$
$200$	−2.82725	−	0.0816198i	−0.199917	−	0.00577139i
$201$	3.21227			0.226576
$202$	−10.6572	+	6.01702i	−0.749841	+	0.423356i
$203$		−	3.63769i		−	0.255316i
$204$	1.98156	+	1.19546i	0.138737	+	0.0836993i
$205$		−	3.26174i		−	0.227810i
$206$	−8.71050	−	15.4279i	−0.606889	−	1.07491i
$207$	−2.37595			−0.165140
$208$	12.2320	−	6.44791i	0.848139	−	0.447082i
$209$	−20.3539			−1.40791
$210$	−0.695292	−	1.23149i	−0.0479797	−	0.0849809i
$211$		−	15.0108i		−	1.03339i	−0.856171	−	0.516693i	$-0.827163\pi$
$211$		−	15.0108i		−	1.03339i	0.856171	−	0.516693i	$-0.172837\pi$
$212$	−10.1519	−	6.12459i	−0.697234	−	0.420638i
$213$		−	2.33991i		−	0.160328i
$214$	16.9040	−	9.54389i	1.15553	−	0.652407i
$215$	4.97544			0.339322
$216$	−0.0816198	+	2.82725i	−0.00555353	+	0.192370i
$217$	5.40739			0.367077
$218$	−1.12351	+	0.634327i	−0.0760937	+	0.0429620i
$219$		−	5.95172i		−	0.402180i
$220$	−3.57142	+	5.91984i	−0.240785	+	0.399116i
$221$			4.00000i			0.269069i
$222$	2.89178	+	5.12187i	0.194083	+	0.343757i
$223$	−20.0655			−1.34369			−0.671843	−	0.740693i	$-0.734497\pi$
$223$	−20.0655			−1.34369			−0.671843	+	0.740693i	$0.734497\pi$
$224$	3.06071	−	4.75731i	0.204503	−	0.317861i
$225$	1.00000			0.0666667
$226$	1.28932	+	2.28362i	0.0857641	+	0.151904i
$227$			21.6784i			1.43884i	0.694573	+	0.719422i	$0.255593\pi$
$227$			21.6784i			1.43884i	−0.694573	+	0.719422i	$0.744407\pi$
$228$	−6.08308	+	10.0831i	−0.402862	+	0.667768i
$229$			7.83904i			0.518019i	0.965875	+	0.259009i	$0.0833960\pi$
$229$			7.83904i			0.518019i	−0.965875	+	0.259009i	$0.916604\pi$
$230$	−2.92596	+	1.65198i	−0.192932	+	0.108928i
$231$	−3.45686			−0.227445
$232$	−0.296908	+	10.2847i	−0.0194930	+	0.675221i
$233$	24.9587			1.63510			0.817550	−	0.575857i	$-0.195332\pi$
$233$	24.9587			1.63510			0.817550	+	0.575857i	$0.195332\pi$
$234$	−4.25709	+	2.40353i	−0.278295	+	0.157123i
$235$		−	13.0778i		−	0.853104i
$236$	−21.5039	−	12.9732i	−1.39979	−	0.844485i
$237$			14.2934i			0.928455i
$238$	0.804535	+	1.42498i	0.0521503	+	0.0923678i
$239$	−2.64981			−0.171402			−0.0857009	−	0.996321i	$-0.527313\pi$
$239$	−2.64981			−0.171402			−0.0857009	+	0.996321i	$0.527313\pi$
$240$	1.86525	+	3.53848i	0.120401	+	0.228408i
$241$	−5.92835			−0.381878			−0.190939	−	0.981602i	$-0.561153\pi$
$241$	−5.92835			−0.381878			−0.190939	+	0.981602i	$0.561153\pi$
$242$	0.660449	+	1.16978i	0.0424552	+	0.0751961i
$243$		−	1.00000i		−	0.0641500i
$244$	23.6599	+	14.2739i	1.51467	+	0.913796i
$245$		−	1.00000i		−	0.0638877i
$246$	−4.01680	+	2.26786i	−0.256102	+	0.144594i
$247$	−20.3539			−1.29509
$248$	−15.2880	−	0.441350i	−0.970791	−	0.0280258i
$249$	−8.18770			−0.518875
$250$	1.23149	−	0.695292i	0.0778863	−	0.0439741i
$251$		−	13.3090i		−	0.840056i	−0.907511	−	0.420028i	$-0.862020\pi$
$251$		−	13.3090i		−	0.840056i	0.907511	−	0.420028i	$-0.137980\pi$
$252$	−1.03314	+	1.71249i	−0.0650816	+	0.107877i
$253$			8.21334i			0.516368i
$254$	6.77912	+	12.0071i	0.425360	+	0.753391i
$255$	−1.15712			−0.0724616
$256$	−9.04169	+	13.2003i	−0.565106	+	0.825019i
$257$	21.0189			1.31112			0.655560	−	0.755143i	$-0.272432\pi$
$257$	21.0189			1.31112			0.655560	+	0.755143i	$0.272432\pi$
$258$	−3.45938	−	6.12720i	−0.215372	−	0.381463i
$259$			4.15908i			0.258433i
$260$	−3.57142	+	5.91984i	−0.221490	+	0.367133i
$261$		−	3.63769i		−	0.225168i
$262$	9.02576	−	5.09589i	0.557613	−	0.314825i
$263$	−21.3307			−1.31531			−0.657654	−	0.753320i	$-0.728451\pi$
$263$	−21.3307			−1.31531			−0.657654	+	0.753320i	$0.728451\pi$
$264$	9.77341	+	0.282148i	0.601512	+	0.0173650i
$265$	5.92814			0.364162
$266$	−7.25097	+	4.09385i	−0.444586	+	0.251010i
$267$			2.61172i			0.159835i
$268$	−5.50098	−	3.31872i	−0.336026	−	0.202723i
$269$			10.3670i			0.632087i	0.948745	+	0.316043i	$0.102355\pi$
$269$			10.3670i			0.632087i	−0.948745	+	0.316043i	$0.897645\pi$
$270$	−0.695292	−	1.23149i	−0.0423141	−	0.0749461i
$271$	−18.7588			−1.13951			−0.569757	−	0.821813i	$-0.692963\pi$
$271$	−18.7588			−1.13951			−0.569757	+	0.821813i	$0.692963\pi$
$272$	−2.15832	−	4.09444i	−0.130867	−	0.248262i
$273$	−3.45686			−0.209219
$274$	2.84827	+	5.04482i	0.172071	+	0.304769i
$275$		−	3.45686i		−	0.208457i
$276$	4.06880	+	2.45469i	0.244913	+	0.147755i
$277$		−	25.1344i		−	1.51018i	−0.655621	−	0.755090i	$-0.727593\pi$
$277$		−	25.1344i		−	1.51018i	0.655621	−	0.755090i	$-0.272407\pi$
$278$	22.3553	−	12.6217i	1.34078	−	0.756998i
$279$	5.40739			0.323732
$280$	−0.0816198	+	2.82725i	−0.00487772	+	0.168960i
$281$	8.31424			0.495986			0.247993	−	0.968762i	$-0.420229\pi$
$281$	8.31424			0.495986			0.247993	+	0.968762i	$0.420229\pi$
$282$	−16.1052	+	9.09292i	−0.959053	+	0.541475i
$283$			10.9655i			0.651831i	0.945399	+	0.325916i	$0.105673\pi$
$283$			10.9655i			0.651831i	−0.945399	+	0.325916i	$0.894327\pi$
$284$	−2.41746	+	4.00708i	−0.143450	+	0.237777i
$285$		−	5.88796i		−	0.348773i
$286$	8.30866	+	14.7162i	0.491301	+	0.870186i
$287$	−3.26174			−0.192535
$288$	3.06071	−	4.75731i	0.180354	−	0.280327i
$289$	−15.6611			−0.921240
$290$	−2.52926	−	4.47979i	−0.148523	−	0.263062i
$291$		−	0.962000i		−	0.0563934i
$292$	−6.14895	+	10.1923i	−0.359840	+	0.596457i
$293$		−	17.0513i		−	0.996148i	−0.867134	−	0.498074i	$-0.834041\pi$
$293$		−	17.0513i		−	0.996148i	0.867134	−	0.498074i	$-0.165959\pi$
$294$	−1.23149	+	0.695292i	−0.0718220	+	0.0405502i
$295$	12.5571			0.731102
$296$	0.339464	−	11.7588i	0.0197309	−	0.683464i
$297$	−3.45686			−0.200587
$298$	−6.11040	+	3.44989i	−0.353966	+	0.199847i
$299$			8.21334i			0.474989i
$300$	−1.71249	−	1.03314i	−0.0988707	−	0.0596483i
$301$		−	4.97544i		−	0.286779i
$302$	13.7744	+	24.3970i	0.792627	+	1.40389i
$303$	−8.65394			−0.497156
$304$	20.8344	−	10.9825i	1.19494	−	0.629891i
$305$	−13.8161			−0.791108
$306$	0.804535	+	1.42498i	0.0459922	+	0.0814608i
$307$		−	22.1618i		−	1.26484i	−0.774625	−	0.632421i	$-0.782061\pi$
$307$		−	22.1618i		−	1.26484i	0.774625	−	0.632421i	$-0.217939\pi$
$308$	5.91984	+	3.57142i	0.337314	+	0.203500i
$309$		−	12.5278i		−	0.712683i
$310$	6.65915	−	3.75971i	0.378214	−	0.213537i
$311$	15.5650			0.882609			0.441304	−	0.897357i	$-0.354516\pi$
$311$	15.5650			0.882609			0.441304	+	0.897357i	$0.354516\pi$
$312$	9.77341	+	0.282148i	0.553310	+	0.0159735i
$313$	25.6560			1.45016			0.725081	−	0.688663i	$-0.241802\pi$
$313$	25.6560			1.45016			0.725081	+	0.688663i	$0.241802\pi$
$314$	28.0773	−	15.8523i	1.58450	−	0.894596i
$315$		−	1.00000i		−	0.0563436i
$316$	14.7671	−	24.4773i	0.830712	−	1.37696i
$317$		−	21.9692i		−	1.23391i	−0.786998	−	0.616956i	$-0.788366\pi$
$317$		−	21.9692i		−	1.23391i	0.786998	−	0.616956i	$-0.211634\pi$
$318$	−4.12178	−	7.30044i	−0.231138	−	0.409389i
$319$	−12.5750			−0.704065
$320$	0.461519	−	7.98668i	0.0257997	−	0.446469i
$321$	13.7265			0.766136
$322$	1.65198	+	2.92596i	0.0920612	+	0.163058i
$323$			6.81307i			0.379090i
$324$	−1.03314	+	1.71249i	−0.0573966	+	0.0951384i
$325$		−	3.45686i		−	0.191752i
$326$	9.33379	−	5.26980i	0.516951	−	0.291867i
$327$	−0.912317			−0.0504512
$328$	9.22176	+	0.266223i	0.509186	+	0.0146997i
$329$	−13.0778			−0.721005
$330$	−4.25709	+	2.40353i	−0.234345	+	0.132310i
$331$			17.1940i			0.945068i	0.881312	+	0.472534i	$0.156661\pi$
$331$			17.1940i			0.945068i	−0.881312	+	0.472534i	$0.843339\pi$
$332$	14.0214	+	8.45903i	0.769523	+	0.464250i
$333$			4.15908i			0.227916i
$334$	−4.97030	−	8.80332i	−0.271963	−	0.481696i
$335$	3.21227			0.175505
$336$	3.53848	−	1.86525i	0.193040	−	0.101758i
$337$	2.89078			0.157471			0.0787353	−	0.996896i	$-0.474912\pi$
$337$	2.89078			0.157471			0.0787353	+	0.996896i	$0.474912\pi$
$338$	−0.730135	−	1.29320i	−0.0397141	−	0.0703410i
$339$			1.85435i			0.100715i
$340$	1.98156	+	1.19546i	0.107465	+	0.0648332i
$341$		−	18.6926i		−	1.01226i
$342$	−7.25097	+	4.09385i	−0.392088	+	0.221370i
$343$	−1.00000			−0.0539949
$344$	−0.406094	+	14.0668i	−0.0218951	+	0.758431i
$345$	−2.37595			−0.127917
$346$	1.98241	−	1.11925i	0.106575	−	0.0601715i
$347$		−	35.6670i		−	1.91471i	−0.288922	−	0.957353i	$-0.593297\pi$
$347$		−	35.6670i		−	1.91471i	0.288922	−	0.957353i	$-0.406703\pi$
$348$	−3.75824	+	6.22952i	−0.201463	+	0.333937i
$349$		−	4.17512i		−	0.223489i	−0.993737	−	0.111745i	$-0.964356\pi$
$349$		−	4.17512i		−	0.223489i	0.993737	−	0.111745i	$-0.0356438\pi$
$350$	−0.695292	−	1.23149i	−0.0371649	−	0.0658259i
$351$	−3.45686			−0.184514
$352$	−16.4454	−	10.5805i	−0.876541	−	0.563940i
$353$	−25.4091			−1.35239			−0.676195	−	0.736723i	$-0.736372\pi$
$353$	−25.4091			−1.35239			−0.676195	+	0.736723i	$0.736372\pi$
$354$	−8.73084	−	15.4639i	−0.464039	−	0.821899i
$355$		−	2.33991i		−	0.124190i
$356$	2.69827	−	4.47255i	0.143008	−	0.237045i
$357$			1.15712i			0.0612412i
$358$	22.0896	−	12.4716i	1.16747	−	0.659146i
$359$	7.66401			0.404491			0.202245	−	0.979335i	$-0.435176\pi$
$359$	7.66401			0.404491			0.202245	+	0.979335i	$0.435176\pi$
$360$	−0.0816198	+	2.82725i	−0.00430174	+	0.149009i
$361$	−15.6681			−0.824637
$362$	15.5072	−	8.75527i	0.815041	−	0.460167i
$363$			0.949887i			0.0498561i
$364$	5.91984	+	3.57142i	0.310284	+	0.187193i
$365$		−	5.95172i		−	0.311527i
$366$	9.60622	+	17.0144i	0.502125	+	0.889357i
$367$	18.5662			0.969149			0.484574	−	0.874750i	$-0.338974\pi$
$367$	18.5662			0.969149			0.484574	+	0.874750i	$0.338974\pi$
$368$	−4.43174	−	8.40726i	−0.231021	−	0.438259i
$369$	−3.26174			−0.169799
$370$	2.89178	+	5.12187i	0.150336	+	0.266273i
$371$		−	5.92814i		−	0.307773i
$372$	−9.26010	−	5.58658i	−0.480114	−	0.289651i
$373$			26.1444i			1.35371i	0.736118	+	0.676853i	$0.236657\pi$
$373$			26.1444i			1.35371i	−0.736118	+	0.676853i	$0.763343\pi$
$374$	4.92596	−	2.78117i	0.254715	−	0.143811i
$375$	1.00000			0.0516398
$376$	36.9743	+	1.06741i	1.90680	+	0.0550475i
$377$	−12.5750			−0.647646
$378$	−1.23149	+	0.695292i	−0.0633410	+	0.0357620i
$379$		−	12.3622i		−	0.635003i	−0.948258	−	0.317501i	$-0.897156\pi$
$379$		−	12.3622i		−	0.635003i	0.948258	−	0.317501i	$-0.102844\pi$
$380$	−6.08308	+	10.0831i	−0.312056	+	0.517251i
$381$			9.75004i			0.499510i
$382$	−0.252294	−	0.446859i	−0.0129085	−	0.0228633i
$383$	17.1552			0.876592			0.438296	−	0.898831i	$-0.355582\pi$
$383$	17.1552			0.876592			0.438296	+	0.898831i	$0.355582\pi$
$384$	−10.1564	+	4.98471i	−0.518292	+	0.254375i
$385$	−3.45686			−0.176178
$386$	14.9081	+	26.4051i	0.758804	+	1.34398i
$387$		−	4.97544i		−	0.252916i
$388$	−0.993879	+	1.64742i	−0.0504566	+	0.0836349i
$389$		−	10.3584i		−	0.525191i	−0.964906	−	0.262595i	$-0.915422\pi$
$389$		−	10.3584i		−	0.525191i	0.964906	−	0.262595i	$-0.0845784\pi$
$390$	−4.25709	+	2.40353i	−0.215566	+	0.121707i
$391$	2.74926			0.139036
$392$	2.82725	+	0.0816198i	0.142798	+	0.00412242i
$393$	7.32913			0.369706
$394$	−24.2600	+	13.6971i	−1.22220	+	0.690047i
$395$			14.2934i			0.719178i
$396$	5.91984	+	3.57142i	0.297483	+	0.179470i
$397$			2.12996i			0.106899i	0.998571	+	0.0534497i	$0.0170217\pi$
$397$			2.12996i			0.106899i	−0.998571	+	0.0534497i	$0.982978\pi$
$398$	−5.79473	−	10.2635i	−0.290463	−	0.514465i
$399$	−5.88796			−0.294767
$400$	1.86525	+	3.53848i	0.0932625	+	0.176924i
$401$	30.7553			1.53585			0.767924	−	0.640541i	$-0.221290\pi$
$401$	30.7553			1.53585			0.767924	+	0.640541i	$0.221290\pi$
$402$	−2.23346	−	3.95588i	−0.111395	−	0.197301i
$403$		−	18.6926i		−	0.931144i
$404$	14.8198	+	8.94072i	0.737312	+	0.444818i
$405$		−	1.00000i		−	0.0496904i
$406$	−4.47979	+	2.52926i	−0.222328	+	0.125525i
$407$	14.3774			0.712660
$408$	0.0944439	−	3.27146i	0.00467567	−	0.161962i
$409$	2.50335			0.123783			0.0618913	−	0.998083i	$-0.480287\pi$
$409$	2.50335			0.123783			0.0618913	+	0.998083i	$0.480287\pi$
$410$	−4.01680	+	2.26786i	−0.198376	+	0.112002i
$411$			4.09652i			0.202066i
$412$	−12.9430	+	21.4538i	−0.637655	+	1.05695i
$413$		−	12.5571i		−	0.617894i
$414$	1.65198	+	2.92596i	0.0811904	+	0.143803i
$415$	−8.18770			−0.401919
$416$	−16.4454	−	10.5805i	−0.806301	−	0.518750i
$417$	18.1531			0.888960
$418$	14.1519	+	25.0656i	0.692191	+	1.22600i
$419$		−	36.8405i		−	1.79978i	−0.436118	−	0.899889i	$-0.643647\pi$
$419$		−	36.8405i		−	1.79978i	0.436118	−	0.899889i	$-0.356353\pi$
$420$	−1.03314	+	1.71249i	−0.0504120	+	0.0835610i
$421$		−	15.2623i		−	0.743837i	−0.928265	−	0.371919i	$-0.878700\pi$
$421$		−	15.2623i		−	0.743837i	0.928265	−	0.371919i	$-0.121300\pi$
$422$	−18.4857	+	10.4369i	−0.899868	+	0.508060i
$423$	−13.0778			−0.635866
$424$	−0.483854	+	16.7603i	−0.0234980	+	0.813953i
$425$	−1.15712			−0.0561285
$426$	−2.88158	+	1.62692i	−0.139613	+	0.0788247i
$427$			13.8161i			0.668608i
$428$	−23.5064	−	14.1813i	−1.13623	−	0.685480i
$429$			11.9499i			0.576946i
$430$	−3.45938	−	6.12720i	−0.166826	−	0.295480i
$431$	13.1302			0.632460			0.316230	−	0.948683i	$-0.397583\pi$
$431$	13.1302			0.632460			0.316230	+	0.948683i	$0.397583\pi$
$432$	3.53848	−	1.86525i	0.170245	−	0.0897418i
$433$	29.3975			1.41275			0.706376	−	0.707837i	$-0.250329\pi$
$433$	29.3975			1.41275			0.706376	+	0.707837i	$0.250329\pi$
$434$	−3.75971	−	6.65915i	−0.180472	−	0.319649i
$435$		−	3.63769i		−	0.174414i
$436$	1.56233	+	0.942550i	0.0748222	+	0.0451400i
$437$			13.9895i			0.669209i
$438$	−7.32949	+	4.13818i	−0.350217	+	0.197730i
$439$	22.6867			1.08278			0.541389	−	0.840773i	$-0.317899\pi$
$439$	22.6867			1.08278			0.541389	+	0.840773i	$0.317899\pi$
$440$	9.77341	+	0.282148i	0.465929	+	0.0134509i
$441$	−1.00000			−0.0476190
$442$	4.92596	−	2.78117i	0.234304	−	0.132287i
$443$		−	35.7201i		−	1.69711i	−0.529106	−	0.848556i	$-0.677473\pi$
$443$		−	35.7201i		−	1.69711i	0.529106	−	0.848556i	$-0.322527\pi$
$444$	4.29691	−	7.12239i	0.203922	−	0.338014i
$445$			2.61172i			0.123808i
$446$	13.9514	+	24.7105i	0.660617	+	1.17008i
$447$	−4.96179			−0.234685
$448$	−7.98668	−	0.461519i	−0.377335	−	0.0218047i
$449$	−23.1828			−1.09406			−0.547031	−	0.837112i	$-0.684242\pi$
$449$	−23.1828			−1.09406			−0.547031	+	0.837112i	$0.684242\pi$
$450$	−0.695292	−	1.23149i	−0.0327764	−	0.0580530i
$451$			11.2754i			0.530937i
$452$	1.91580	−	3.17556i	0.0901119	−	0.149366i
$453$			19.8109i			0.930799i
$454$	26.6967	−	15.0728i	1.25294	−	0.707402i
$455$	−3.45686			−0.162060
$456$	16.6467	+	0.480575i	0.779555	+	0.0225050i
$457$	−2.26681			−0.106037			−0.0530185	−	0.998594i	$-0.516884\pi$
$457$	−2.26681			−0.106037			−0.0530185	+	0.998594i	$0.516884\pi$
$458$	9.65371	−	5.45042i	0.451088	−	0.254682i
$459$			1.15712i			0.0540097i
$460$	4.06880	+	2.45469i	0.189709	+	0.114450i
$461$			1.56217i			0.0727575i	0.999338	+	0.0363787i	$0.0115823\pi$
$461$			1.56217i			0.0727575i	−0.999338	+	0.0363787i	$0.988418\pi$
$462$	2.40353	+	4.25709i	0.111822	+	0.198058i
$463$	−32.5631			−1.51334			−0.756668	−	0.653799i	$-0.773174\pi$
$463$	−32.5631			−1.51334			−0.756668	+	0.653799i	$0.773174\pi$
$464$	12.8719	−	6.78521i	0.597563	−	0.314995i
$465$	5.40739			0.250762
$466$	−17.3536	−	30.7364i	−0.803890	−	1.42384i
$467$		−	23.9641i		−	1.10892i	−0.832209	−	0.554462i	$-0.812924\pi$
$467$		−	23.9641i		−	1.10892i	0.832209	−	0.554462i	$-0.187076\pi$
$468$	5.91984	+	3.57142i	0.273645	+	0.165089i
$469$		−	3.21227i		−	0.148329i
$470$	−16.1052	+	9.09292i	−0.742879	+	0.419425i
$471$	22.7995			1.05054
$472$	−1.02491	+	35.5020i	−0.0471752	+	1.63411i
$473$	−17.1994			−0.790829
$474$	17.6022	−	9.93808i	0.808495	−	0.456471i
$475$		−	5.88796i		−	0.270158i
$476$	1.19546	−	1.98156i	0.0547940	−	0.0908245i
$477$		−	5.92814i		−	0.271431i
$478$	1.84239	+	3.26321i	0.0842689	+	0.149256i
$479$	20.5143			0.937321			0.468661	−	0.883378i	$-0.344737\pi$
$479$	20.5143			0.937321			0.468661	+	0.883378i	$0.344737\pi$
$480$	3.06071	−	4.75731i	0.139702	−	0.217141i
$481$	14.3774			0.655551
$482$	4.12193	+	7.30070i	0.187749	+	0.332538i
$483$			2.37595i			0.108110i
$484$	0.981365	−	1.62667i	0.0446075	−	0.0739397i
$485$		−	0.962000i		−	0.0436822i
$486$	−1.23149	+	0.695292i	−0.0558616	+	0.0315391i
$487$	35.7867			1.62165			0.810826	−	0.585288i	$-0.199018\pi$
$487$	35.7867			1.62165			0.810826	+	0.585288i	$0.199018\pi$
$488$	1.12767	−	39.0616i	0.0510471	−	1.76823i
$489$	7.57926			0.342746
$490$	−1.23149	+	0.695292i	−0.0556331	+	0.0314101i
$491$			23.8613i			1.07684i	0.842675	+	0.538422i	$0.180979\pi$
$491$			23.8613i			1.07684i	−0.842675	+	0.538422i	$0.819021\pi$
$492$	5.58570	+	3.36983i	0.251823	+	0.151924i
$493$			4.20925i			0.189575i
$494$	14.1519	+	25.0656i	0.636723	+	1.12775i
$495$	−3.45686			−0.155374
$496$	10.0861	+	19.1339i	0.452880	+	0.859139i
$497$	−2.33991			−0.104960
$498$	5.69284	+	10.0831i	0.255102	+	0.451834i
$499$			34.5650i			1.54734i	0.633587	+	0.773672i	$0.281582\pi$
$499$			34.5650i			1.54734i	−0.633587	+	0.773672i	$0.718418\pi$
$500$	−1.71249	−	1.03314i	−0.0765849	−	0.0462034i
$501$		−	7.14851i		−	0.319372i
$502$	−16.3899	+	9.25364i	−0.731517	+	0.413010i
$503$	15.1957			0.677542			0.338771	−	0.940869i	$-0.389989\pi$
$503$	15.1957			0.677542			0.338771	+	0.940869i	$0.389989\pi$
$504$	2.82725	+	0.0816198i	0.125936	+	0.00363564i
$505$	−8.65394			−0.385095
$506$	10.1146	−	5.71066i	0.449651	−	0.253870i
$507$		−	1.05011i		−	0.0466372i
$508$	10.0731	−	16.6969i	0.446923	−	0.740803i
$509$			6.28118i			0.278408i	0.990264	+	0.139204i	$0.0444544\pi$
$509$			6.28118i			0.278408i	−0.990264	+	0.139204i	$0.955546\pi$
$510$	0.804535	+	1.42498i	0.0356254	+	0.0630992i
$511$	−5.95172			−0.263289
$512$	22.5427	+	1.95670i	0.996254	+	0.0864748i
$513$	−5.88796			−0.259960
$514$	−14.6142	−	25.8845i	−0.644607	−	1.14172i
$515$		−	12.5278i		−	0.552042i
$516$	−5.14031	+	8.52039i	−0.226290	+	0.375089i
$517$			45.2083i			1.98826i
$518$	5.12187	−	2.89178i	0.225042	−	0.127057i
$519$	1.60976			0.0706607
$520$	9.77341	+	0.282148i	0.428592	+	0.0123730i
$521$	5.88279			0.257730			0.128865	−	0.991662i	$-0.458867\pi$
$521$	5.88279			0.257730			0.128865	+	0.991662i	$0.458867\pi$
$522$	−4.47979	+	2.52926i	−0.196075	+	0.110703i
$523$		−	1.16662i		−	0.0510129i	−0.999675	−	0.0255065i	$-0.991880\pi$
$523$		−	1.16662i		−	0.0510129i	0.999675	−	0.0255065i	$-0.00811984\pi$
$524$	−12.5511	−	7.57201i	−0.548296	−	0.330785i
$525$		−	1.00000i		−	0.0436436i
$526$	14.8311	+	26.2686i	0.646665	+	1.14536i
$527$	−6.25699			−0.272559
$528$	−6.44791	−	12.2320i	−0.280609	−	0.532331i
$529$	−17.3549			−0.754559
$530$	−4.12178	−	7.30044i	−0.179039	−	0.317111i
$531$		−	12.5571i		−	0.544931i
$532$	10.0831	+	6.08308i	0.437157	+	0.263735i
$533$			11.2754i			0.488391i
$534$	3.21631	−	1.81591i	0.139184	−	0.0785821i
$535$	13.7265			0.593446
$536$	−0.262185	+	9.08189i	−0.0113247	+	0.392278i
$537$	17.9373			0.774050
$538$	12.7669	−	7.20809i	0.550418	−	0.310763i
$539$			3.45686i			0.148898i
$540$	−1.03314	+	1.71249i	−0.0444592	+	0.0736939i
$541$			13.7558i			0.591408i	0.955280	+	0.295704i	$0.0955541\pi$
$541$			13.7558i			0.591408i	−0.955280	+	0.295704i	$0.904446\pi$
$542$	13.0428	+	23.1013i	0.560237	+	0.992284i
$543$	12.5922			0.540384
$544$	−3.54161	+	5.50478i	−0.151845	+	0.236015i
$545$	−0.912317			−0.0390794
$546$	2.40353	+	4.25709i	0.102861	+	0.182187i
$547$		−	15.0151i		−	0.641998i	−0.947080	−	0.320999i	$-0.895981\pi$
$547$		−	15.0151i		−	0.641998i	0.947080	−	0.320999i	$-0.104019\pi$
$548$	4.23227	−	7.01525i	0.180794	−	0.299677i
$549$			13.8161i			0.589657i
$550$	−4.25709	+	2.40353i	−0.181523	+	0.102487i
$551$	−21.4186			−0.912463
$552$	0.193925	−	6.71741i	0.00825399	−	0.285912i
$553$	14.2934			0.607817
$554$	−30.9528	+	17.4757i	−1.31506	+	0.742473i
$555$			4.15908i			0.176543i
$556$	−31.0870	−	18.7546i	−1.31838	−	0.795374i
$557$		−	16.4658i		−	0.697678i	−0.937183	−	0.348839i	$-0.886576\pi$
$557$		−	16.4658i		−	0.697678i	0.937183	−	0.348839i	$-0.113424\pi$
$558$	−3.75971	−	6.65915i	−0.159161	−	0.281904i
$559$	−17.1994			−0.727457
$560$	3.53848	−	1.86525i	0.149528	−	0.0788212i
$561$	4.00000			0.168880
$562$	−5.78082	−	10.2389i	−0.243849	−	0.431902i
$563$			5.43891i			0.229223i	0.993410	+	0.114611i	$0.0365623\pi$
$563$			5.43891i			0.229223i	−0.993410	+	0.114611i	$0.963438\pi$
$564$	22.3957	+	13.5112i	0.943028	+	0.568925i
$565$			1.85435i			0.0780132i
$566$	13.5039	−	7.62422i	0.567611	−	0.320470i
$567$	−1.00000			−0.0419961
$568$	6.61552	+	0.190983i	0.277581	+	0.00801349i
$569$	−46.1886			−1.93633			−0.968163	−	0.250319i	$-0.919464\pi$
$569$	−46.1886			−1.93633			−0.968163	+	0.250319i	$0.919464\pi$
$570$	−7.25097	+	4.09385i	−0.303710	+	0.171473i
$571$		−	30.7029i		−	1.28488i	−0.766338	−	0.642438i	$-0.777923\pi$
$571$		−	30.7029i		−	1.28488i	0.766338	−	0.642438i	$-0.222077\pi$
$572$	12.3459	−	20.4641i	0.516208	−	0.855646i
$573$		−	0.362860i		−	0.0151587i
$574$	2.26786	+	4.01680i	0.0946587	+	0.167658i
$575$	−2.37595			−0.0990840
$576$	−7.98668	−	0.461519i	−0.332778	−	0.0192300i
$577$	42.3096			1.76137			0.880687	−	0.473699i	$-0.157082\pi$
$577$	42.3096			1.76137			0.880687	+	0.473699i	$0.157082\pi$
$578$	10.8890	+	19.2865i	0.452923	+	0.802211i
$579$			21.4416i			0.891080i
$580$	−3.75824	+	6.22952i	−0.156053	+	0.258667i
$581$			8.18770i			0.339683i
$582$	−1.18469	+	0.668871i	−0.0491072	+	0.0277256i
$583$	−20.4927			−0.848723
$584$	16.8270	+	0.485779i	0.696306	+	0.0201017i
$585$	−3.45686			−0.142924
$586$	−20.9985	+	11.8556i	−0.867441	+	0.489752i
$587$		−	33.7492i		−	1.39298i	−0.717567	−	0.696490i	$-0.754744\pi$
$587$		−	33.7492i		−	1.39298i	0.717567	−	0.696490i	$-0.245256\pi$
$588$	1.71249	+	1.03314i	0.0706219	+	0.0426059i
$589$		−	31.8385i		−	1.31188i
$590$	−8.73084	−	15.4639i	−0.359443	−	0.636640i
$591$	−19.6997			−0.810338
$592$	−14.7168	+	7.75772i	−0.604858	+	0.318840i
$593$	−18.7826			−0.771308			−0.385654	−	0.922643i	$-0.626024\pi$
$593$	−18.7826			−0.771308			−0.385654	+	0.922643i	$0.626024\pi$
$594$	2.40353	+	4.25709i	0.0986179	+	0.174671i
$595$			1.15712i			0.0474373i
$596$	8.49702	+	5.12622i	0.348051	+	0.209978i
$597$		−	8.33424i		−	0.341098i
$598$	10.1146	−	5.71066i	0.413619	−	0.233526i
$599$	36.0553			1.47318			0.736590	−	0.676340i	$-0.236435\pi$
$599$	36.0553			1.47318			0.736590	+	0.676340i	$0.236435\pi$
$600$	−0.0816198	+	2.82725i	−0.00333212	+	0.115422i
$601$	−40.1760			−1.63881			−0.819406	−	0.573213i	$-0.805697\pi$
$601$	−40.1760			−1.63881			−0.819406	+	0.573213i	$0.805697\pi$
$602$	−6.12720	+	3.45938i	−0.249726	+	0.140994i
$603$		−	3.21227i		−	0.130814i
$604$	20.4674	−	33.9261i	0.832809	−	1.38043i
$605$			0.949887i			0.0386184i
$606$	6.01702	+	10.6572i	0.244425	+	0.432921i
$607$	−1.19349			−0.0484425			−0.0242212	−	0.999707i	$-0.507711\pi$
$607$	−1.19349			−0.0484425			−0.0242212	+	0.999707i	$0.507711\pi$
$608$	−28.0109	−	18.0214i	−1.13599	−	0.730863i
$609$	−3.63769			−0.147407
$610$	9.60622	+	17.0144i	0.388944	+	0.688893i
$611$			45.2083i			1.82893i
$612$	1.19546	−	1.98156i	0.0483238	−	0.0800996i
$613$		−	5.58254i		−	0.225477i	−0.993625	−	0.112738i	$-0.964038\pi$
$613$		−	5.58254i		−	0.225477i	0.993625	−	0.112738i	$-0.0359622\pi$
$614$	−27.2921	+	15.4089i	−1.10142	+	0.621854i
$615$	−3.26174			−0.131526
$616$	0.282148	−	9.77341i	0.0113681	−	0.393782i
$617$	1.04871			0.0422194			0.0211097	−	0.999777i	$-0.493280\pi$
$617$	1.04871			0.0422194			0.0211097	+	0.999777i	$0.493280\pi$
$618$	−15.4279	+	8.71050i	−0.620601	+	0.350388i
$619$		−	20.7700i		−	0.834818i	−0.908719	−	0.417409i	$-0.862938\pi$
$619$		−	20.7700i		−	0.834818i	0.908719	−	0.417409i	$-0.137062\pi$
$620$	−9.26010	−	5.58658i	−0.371895	−	0.224363i
$621$			2.37595i			0.0953437i
$622$	−10.8222	−	19.1681i	−0.433931	−	0.768572i
$623$	2.61172			0.104637
$624$	−6.44791	−	12.2320i	−0.258123	−	0.489673i
$625$	1.00000			0.0400000
$626$	−17.8384	−	31.5951i	−0.712966	−	1.26279i
$627$			20.3539i			0.812855i
$628$	−39.0439	−	23.5550i	−1.55802	−	0.939947i
$629$		−	4.81255i		−	0.191889i
$630$	−1.23149	+	0.695292i	−0.0490638	+	0.0277011i
$631$	−13.4246			−0.534426			−0.267213	−	0.963637i	$-0.586103\pi$
$631$	−13.4246			−0.534426			−0.267213	+	0.963637i	$0.586103\pi$
$632$	−40.4110	−	1.16662i	−1.60746	−	0.0464058i
$633$	−15.0108			−0.596626
$634$	−27.0548	+	15.2750i	−1.07448	+	0.606647i
$635$			9.75004i			0.386918i
$636$	−6.12459	+	10.1519i	−0.242856	+	0.402548i
$637$			3.45686i			0.136966i
$638$	8.74330	+	15.4860i	0.346150	+	0.613096i
$639$	−2.33991			−0.0925656
$640$	−10.1564	+	4.98471i	−0.401467	+	0.197038i
$641$	−5.50664			−0.217499			−0.108750	−	0.994069i	$-0.534685\pi$
$641$	−5.50664			−0.217499			−0.108750	+	0.994069i	$0.534685\pi$
$642$	−9.54389	−	16.9040i	−0.376667	−	0.667148i
$643$		−	44.9187i		−	1.77142i	−0.464239	−	0.885710i	$-0.653672\pi$
$643$		−	44.9187i		−	1.77142i	0.464239	−	0.885710i	$-0.346328\pi$
$644$	2.45469	−	4.06880i	0.0967283	−	0.160333i
$645$		−	4.97544i		−	0.195908i
$646$	8.39024	−	4.73707i	0.330110	−	0.186378i
$647$	33.1838			1.30459			0.652295	−	0.757965i	$-0.273806\pi$
$647$	33.1838			1.30459			0.652295	+	0.757965i	$0.273806\pi$
$648$	2.82725	+	0.0816198i	0.111065	+	0.00320633i
$649$	−43.4081			−1.70392
$650$	−4.25709	+	2.40353i	−0.166977	+	0.0942741i
$651$		−	5.40739i		−	0.211932i
$652$	−12.9794	−	7.83043i	−0.508313	−	0.306663i
$653$		−	13.1201i		−	0.513429i	−0.966487	−	0.256714i	$-0.917360\pi$
$653$		−	13.1201i		−	0.513429i	0.966487	−	0.256714i	$-0.0826400\pi$
$654$	0.634327	+	1.12351i	0.0248041	+	0.0439327i
$655$	7.32913			0.286373
$656$	−6.08396	−	11.5416i	−0.237539	−	0.450624i
$657$	−5.95172			−0.232199
$658$	9.09292	+	16.1052i	0.354479	+	0.627848i
$659$			13.6449i			0.531528i	0.964038	+	0.265764i	$0.0856243\pi$
$659$			13.6449i			0.531528i	−0.964038	+	0.265764i	$0.914376\pi$
$660$	5.91984	+	3.57142i	0.230430	+	0.139017i
$661$			35.1275i			1.36630i	0.730278	+	0.683150i	$0.239391\pi$
$661$			35.1275i			1.36630i	−0.730278	+	0.683150i	$0.760609\pi$
$662$	21.1743	−	11.9549i	0.822961	−	0.464639i
$663$	4.00000			0.155347
$664$	0.668279	−	23.1487i	0.0259343	−	0.898343i
$665$	−5.88796			−0.228325
$666$	5.12187	−	2.89178i	0.198468	−	0.112054i
$667$			8.64299i			0.334658i
$668$	−7.38540	+	12.2418i	−0.285750	+	0.473648i
$669$			20.0655i			0.775778i
$670$	−2.23346	−	3.95588i	−0.0862863	−	0.152829i
$671$	47.7603			1.84377
$672$	−4.75731	−	3.06071i	−0.183517	−	0.118070i
$673$	−7.01462			−0.270394			−0.135197	−	0.990819i	$-0.543167\pi$
$673$	−7.01462			−0.270394			−0.135197	+	0.990819i	$0.543167\pi$
$674$	−2.00993	−	3.55996i	−0.0774197	−	0.137125i
$675$		−	1.00000i		−	0.0384900i
$676$	−1.08491	+	1.79831i	−0.0417274	+	0.0691657i
$677$		−	24.1419i		−	0.927850i	−0.885874	−	0.463925i	$-0.846441\pi$
$677$		−	24.1419i		−	0.927850i	0.885874	−	0.463925i	$-0.153559\pi$
$678$	2.28362	−	1.28932i	0.0877019	−	0.0495159i
$679$	−0.962000			−0.0369182
$680$	0.0944439	−	3.27146i	0.00362176	−	0.125455i
$681$	21.6784			0.830718
$682$	−23.0197	+	12.9968i	−0.881472	+	0.497673i
$683$		−	13.3089i		−	0.509252i	−0.967040	−	0.254626i	$-0.918048\pi$
$683$		−	13.3089i		−	0.509252i	0.967040	−	0.254626i	$-0.0819523\pi$
$684$	10.0831	+	6.08308i	0.385536	+	0.232592i
$685$			4.09652i			0.156520i
$686$	0.695292	+	1.23149i	0.0265464	+	0.0470185i
$687$	7.83904			0.299078
$688$	17.6055	−	9.28043i	0.671203	−	0.353813i
$689$	−20.4927			−0.780711
$690$	1.65198	+	2.92596i	0.0628898	+	0.111389i
$691$		−	1.62524i		−	0.0618271i	−0.999522	−	0.0309136i	$-0.990158\pi$
$691$		−	1.62524i		−	0.0618271i	0.999522	−	0.0309136i	$-0.00984166\pi$
$692$	−2.75670	−	1.66311i	−0.104794	−	0.0632218i
$693$			3.45686i			0.131315i
$694$	−43.9236	+	24.7990i	−1.66732	+	0.941356i
$695$	18.1531			0.688585
$696$	10.2847	+	0.296908i	0.389839	+	0.0112543i
$697$	3.77422			0.142959
$698$	−5.14162	+	2.90293i	−0.194613	+	0.109877i
$699$		−	24.9587i		−	0.944026i
$700$	−1.03314	+	1.71249i	−0.0390490	+	0.0647261i
$701$			35.1489i			1.32755i	0.747931	+	0.663777i	$0.231048\pi$
$701$			35.1489i			1.32755i	−0.747931	+	0.663777i	$0.768952\pi$
$702$	2.40353	+	4.25709i	0.0907153	+	0.160674i
$703$	24.4885			0.923602
$704$	−1.59541	+	27.6088i	−0.0601292	+	1.04055i
$705$	−13.0778			−0.492540
$706$	17.6667	+	31.2911i	0.664897	+	1.17766i
$707$			8.65394i			0.325465i
$708$	−12.9732	+	21.5039i	−0.487563	+	0.808166i
$709$		−	20.0114i		−	0.751542i	−0.926713	−	0.375771i	$-0.877378\pi$
$709$		−	20.0114i		−	0.751542i	0.926713	−	0.375771i	$-0.122622\pi$
$710$	−2.88158	+	1.62692i	−0.108144	+	0.0610573i
$711$	14.2934			0.536044
$712$	−7.38400	−	0.213169i	−0.276727	−	0.00798883i
$713$	−12.8477			−0.481150
$714$	1.42498	−	0.804535i	0.0533286	−	0.0301090i
$715$			11.9499i			0.446900i
$716$	−30.7174	−	18.5317i	−1.14796	−	0.692561i
$717$			2.64981i			0.0989589i
$718$	−5.32872	−	9.43816i	−0.198866	−	0.352229i
$719$	−31.7901			−1.18557			−0.592785	−	0.805361i	$-0.701972\pi$
$719$	−31.7901			−1.18557			−0.592785	+	0.805361i	$0.701972\pi$
$720$	3.53848	−	1.86525i	0.131871	−	0.0695137i
$721$	−12.5278			−0.466561
$722$	10.8939	+	19.2951i	0.405429	+	0.718090i
$723$			5.92835i			0.220478i
$724$	−21.5641	−	13.0095i	−0.801423	−	0.483495i
$725$		−	3.63769i		−	0.135101i
$726$	1.16978	−	0.660449i	0.0434145	−	0.0245115i
$727$	25.9394			0.962041			0.481020	−	0.876709i	$-0.340266\pi$
$727$	25.9394			0.962041			0.481020	+	0.876709i	$0.340266\pi$
$728$	0.282148	−	9.77341i	0.0104571	−	0.362227i
$729$	−1.00000			−0.0370370
$730$	−7.32949	+	4.13818i	−0.271277	+	0.153161i
$731$			5.75717i			0.212937i
$732$	14.2739	−	23.6599i	0.527580	−	0.874497i
$733$			16.8200i			0.621262i	0.950531	+	0.310631i	$0.100540\pi$
$733$			16.8200i			0.621262i	−0.950531	+	0.310631i	$0.899460\pi$
$734$	−12.9089	−	22.8641i	−0.476478	−	0.843930i
$735$	−1.00000			−0.0368856
$736$	−7.27211	+	11.3031i	−0.268053	+	0.416640i
$737$	−11.1044			−0.409035
$738$	2.26786	+	4.01680i	0.0834812	+	0.147861i
$739$			43.9284i			1.61593i	0.589228	+	0.807967i	$0.299432\pi$
$739$			43.9284i			1.61593i	−0.589228	+	0.807967i	$0.700568\pi$
$740$	4.29691	−	7.12239i	0.157957	−	0.261824i
$741$			20.3539i			0.747718i
$742$	−7.30044	+	4.12178i	−0.268008	+	0.151315i
$743$	−24.5519			−0.900723			−0.450362	−	0.892846i	$-0.648705\pi$
$743$	−24.5519			−0.900723			−0.450362	+	0.892846i	$0.648705\pi$
$744$	−0.441350	+	15.2880i	−0.0161807	+	0.560487i
$745$	−4.96179			−0.181786
$746$	32.1966	−	18.1780i	1.17880	−	0.665544i
$747$			8.18770i			0.299572i
$748$	−6.84996	−	4.13255i	−0.250459	−	0.151101i
$749$		−	13.7265i		−	0.501554i
$750$	−0.695292	−	1.23149i	−0.0253885	−	0.0449677i
$751$	−10.0855			−0.368026			−0.184013	−	0.982924i	$-0.558909\pi$
$751$	−10.0855			−0.368026			−0.184013	+	0.982924i	$0.558909\pi$
$752$	−24.3934	−	46.2757i	−0.889537	−	1.68750i
$753$	−13.3090			−0.485007
$754$	8.74330	+	15.4860i	0.318412	+	0.563967i
$755$			19.8109i			0.720994i
$756$	1.71249	+	1.03314i	0.0622827	+	0.0375749i
$757$			20.2698i			0.736719i	0.929684	+	0.368359i	$0.120080\pi$
$757$			20.2698i			0.736719i	−0.929684	+	0.368359i	$0.879920\pi$
$758$	−15.2239	+	8.59533i	−0.552957	+	0.312196i
$759$	8.21334			0.298125
$760$	16.6467	+	0.480575i	0.603841	+	0.0174323i
$761$	19.4494			0.705042			0.352521	−	0.935804i	$-0.385325\pi$
$761$	19.4494			0.705042			0.352521	+	0.935804i	$0.385325\pi$
$762$	12.0071	−	6.77912i	0.434971	−	0.245582i
$763$			0.912317i			0.0330281i
$764$	−0.374885	+	0.621395i	−0.0135629	+	0.0224813i
$765$			1.15712i			0.0418357i
$766$	−11.9279	−	21.1265i	−0.430973	−	0.763332i
$767$	−43.4081			−1.56738
$768$	13.2003	+	9.04169i	0.476325	+	0.326264i
$769$	−22.6523			−0.816863			−0.408431	−	0.912789i	$-0.633924\pi$
$769$	−22.6523			−0.816863			−0.408431	+	0.912789i	$0.633924\pi$
$770$	2.40353	+	4.25709i	0.0866171	+	0.153415i
$771$		−	21.0189i		−	0.756976i
$772$	22.1521	−	36.7185i	0.797271	−	1.32153i
$773$			32.3487i			1.16350i	0.813367	+	0.581751i	$0.197632\pi$
$773$			32.3487i			1.16350i	−0.813367	+	0.581751i	$0.802368\pi$
$774$	−6.12720	+	3.45938i	−0.220238	+	0.124345i
$775$	5.40739			0.194239
$776$	2.71981	+	0.0785183i	0.0976356	+	0.00281864i
$777$	4.15908			0.149206
$778$	−12.7562	+	7.20210i	−0.457334	+	0.258208i
$779$			19.2050i			0.688091i
$780$	5.91984	+	3.57142i	0.211964	+	0.127877i
$781$			8.08876i			0.289439i
$782$	−1.91154	−	3.38569i	−0.0683564	−	0.121072i
$783$	−3.63769			−0.130001
$784$	−1.86525	−	3.53848i	−0.0666160	−	0.126374i
$785$	22.7995			0.813748
$786$	−5.09589	−	9.02576i	−0.181764	−	0.321938i
$787$		−	31.4411i		−	1.12076i	−0.828237	−	0.560378i	$-0.810656\pi$
$787$		−	31.4411i		−	1.12076i	0.828237	−	0.560378i	$-0.189344\pi$
$788$	33.7356	+	20.3525i	1.20178	+	0.725029i
$789$			21.3307i			0.759393i
$790$	17.6022	−	9.93808i	0.626257	−	0.353581i
$791$	1.85435			0.0659332
$792$	0.282148	−	9.77341i	0.0100257	−	0.347283i
$793$	47.7603			1.69602
$794$	2.62302	−	1.48094i	0.0930875	−	0.0525566i
$795$		−	5.92814i		−	0.210249i
$796$	−8.61042	+	14.2723i	−0.305188	+	0.505868i
$797$		−	28.1515i		−	0.997177i	−0.866839	−	0.498589i	$-0.833852\pi$
$797$		−	28.1515i		−	0.997177i	0.866839	−	0.498589i	$-0.166148\pi$
$798$	4.09385	+	7.25097i	0.144921	+	0.256682i
$799$	15.1326			0.535354
$800$	3.06071	−	4.75731i	0.108213	−	0.168196i
$801$	2.61172			0.0922807
$802$	−21.3839	−	37.8749i	−0.755093	−	1.33741i
$803$			20.5743i			0.726050i
$804$	−3.31872	+	5.50098i	−0.117042	+	0.194005i
$805$			2.37595i			0.0837413i
$806$	−23.0197	+	12.9968i	−0.810836	+	0.457793i
$807$	10.3670			0.364936
$808$	0.706333	−	24.4669i	0.0248487	−	0.860741i
$809$	14.9984			0.527316			0.263658	−	0.964616i	$-0.415071\pi$
$809$	14.9984			0.527316			0.263658	+	0.964616i	$0.415071\pi$
$810$	−1.23149	+	0.695292i	−0.0432702	+	0.0244301i
$811$		−	18.8356i		−	0.661406i	−0.943735	−	0.330703i	$-0.892714\pi$
$811$		−	18.8356i		−	0.661406i	0.943735	−	0.330703i	$-0.107286\pi$
$812$	6.22952	+	3.75824i	0.218613	+	0.131888i
$813$			18.7588i			0.657899i
$814$	−9.99647	−	17.7056i	−0.350376	−	0.620581i
$815$	7.57926			0.265490
$816$	−4.09444	+	2.15832i	−0.143334	+	0.0755562i
$817$	−29.2952			−1.02491
$818$	−1.74056	−	3.08285i	−0.0608572	−	0.107789i
$819$			3.45686i			0.120792i
$820$	5.58570	+	3.36983i	0.195061	+	0.117680i
$821$			35.1179i			1.22562i	0.790229	+	0.612811i	$0.209961\pi$
$821$			35.1179i			1.22562i	−0.790229	+	0.612811i	$0.790039\pi$
$822$	5.04482	−	2.84827i	0.175958	−	0.0993450i
$823$	10.8181			0.377097			0.188548	−	0.982064i	$-0.439622\pi$
$823$	10.8181			0.377097			0.188548	+	0.982064i	$0.439622\pi$
$824$	35.4193	+	1.02252i	1.23389	+	0.0356212i
$825$	−3.45686			−0.120352
$826$	−15.4639	+	8.73084i	−0.538059	+	0.303785i
$827$			38.7858i			1.34871i	0.738406	+	0.674357i	$0.235579\pi$
$827$			38.7858i			1.34871i	−0.738406	+	0.674357i	$0.764421\pi$
$828$	2.45469	−	4.06880i	0.0853063	−	0.141400i
$829$		−	38.0268i		−	1.32072i	−0.750947	−	0.660362i	$-0.770403\pi$
$829$		−	38.0268i		−	1.32072i	0.750947	−	0.660362i	$-0.229597\pi$
$830$	5.69284	+	10.0831i	0.197601	+	0.349989i
$831$	−25.1344			−0.871903
$832$	−1.59541	+	27.6088i	−0.0553108	+	0.957164i
$833$	1.15712			0.0400918
$834$	−12.6217	−	22.3553i	−0.437053	−	0.774102i
$835$		−	7.14851i		−	0.247384i
$836$	21.0284	−	34.8558i	0.727281	−	1.20551i
$837$		−	5.40739i		−	0.186907i
$838$	−45.3688	+	25.6149i	−1.56724	+	0.884853i
$839$	33.7281			1.16442			0.582211	−	0.813038i	$-0.302188\pi$
$839$	33.7281			1.16442			0.582211	+	0.813038i	$0.302188\pi$
$840$	2.82725	+	0.0816198i	0.0975494	+	0.00281615i
$841$	15.7672			0.543696
$842$	−18.7953	+	10.6117i	−0.647730	+	0.365704i
$843$		−	8.31424i		−	0.286358i
$844$	25.7059	+	15.5082i	0.884832	+	0.533815i
$845$		−	1.05011i		−	0.0361250i
$846$	9.09292	+	16.1052i	0.312621	+	0.553710i
$847$	0.949887			0.0326385
$848$	20.9766	−	11.0575i	0.720339	−	0.379714i
$849$	10.9655			0.376335
$850$	0.804535	+	1.42498i	0.0275953	+	0.0488765i
$851$		−	9.88178i		−	0.338743i
$852$	4.00708	+	2.41746i	0.137280	+	0.0828207i
$853$			43.8436i			1.50118i	0.660770	+	0.750589i	$0.270230\pi$
$853$			43.8436i			1.50118i	−0.660770	+	0.750589i	$0.729770\pi$
$854$	17.0144	−	9.60622i	0.582221	−	0.328718i
$855$	−5.88796			−0.201364
$856$	−1.12035	+	38.8081i	−0.0382928	+	1.32643i
$857$	−20.7396			−0.708451			−0.354225	−	0.935160i	$-0.615255\pi$
$857$	−20.7396			−0.708451			−0.354225	+	0.935160i	$0.615255\pi$
$858$	14.7162	−	8.30866i	0.502402	−	0.283653i
$859$			24.7972i			0.846071i	0.906113	+	0.423036i	$0.139035\pi$
$859$			24.7972i			0.846071i	−0.906113	+	0.423036i	$0.860965\pi$
$860$	−5.14031	+	8.52039i	−0.175283	+	0.290543i
$861$			3.26174i			0.111160i
$862$	−9.12933	−	16.1697i	−0.310946	−	0.550743i
$863$	−31.3753			−1.06803			−0.534014	−	0.845475i	$-0.679317\pi$
$863$	−31.3753			−1.06803			−0.534014	+	0.845475i	$0.679317\pi$
$864$	−4.75731	−	3.06071i	−0.161847	−	0.104128i
$865$	1.60976			0.0547335
$866$	−20.4398	−	36.2027i	−0.694573	−	1.23022i
$867$			15.6611i			0.531878i
$868$	−5.58658	+	9.26010i	−0.189621	+	0.314308i
$869$		−	49.4103i		−	1.67613i
$870$	−4.47979	+	2.52926i	−0.151879	+	0.0857499i
$871$	−11.1044			−0.376257
$872$	0.0744632	−	2.57935i	0.00252164	−	0.0873477i
$873$	−0.962000			−0.0325588
$874$	17.2280	−	9.72680i	0.582744	−	0.329014i
$875$		−	1.00000i		−	0.0338062i
$876$	10.1923	+	6.14895i	0.344365	+	0.207754i
$877$			22.7957i			0.769755i	0.922968	+	0.384878i	$0.125756\pi$
$877$			22.7957i			0.769755i	−0.922968	+	0.384878i	$0.874244\pi$
$878$	−15.7739	−	27.9385i	−0.532343	−	0.942877i
$879$	−17.0513			−0.575127
$880$	−6.44791	−	12.2320i	−0.217359	−	0.412342i
$881$	−14.2101			−0.478749			−0.239375	−	0.970927i	$-0.576942\pi$
$881$	−14.2101			−0.478749			−0.239375	+	0.970927i	$0.576942\pi$
$882$	0.695292	+	1.23149i	0.0234117	+	0.0414664i
$883$		−	11.3850i		−	0.383135i	−0.981479	−	0.191568i	$-0.938643\pi$
$883$		−	11.3850i		−	0.383135i	0.981479	−	0.191568i	$-0.0613572\pi$
$884$	−6.84996	−	4.13255i	−0.230389	−	0.138993i
$885$		−	12.5571i		−	0.422102i
$886$	−43.9889	+	24.8359i	−1.47784	+	0.834377i
$887$	−11.5024			−0.386212			−0.193106	−	0.981178i	$-0.561856\pi$
$887$	−11.5024			−0.386212			−0.193106	+	0.981178i	$0.561856\pi$
$888$	−11.7588	−	0.339464i	−0.394598	−	0.0113917i
$889$	9.75004			0.327006
$890$	3.21631	−	1.81591i	0.107811	−	0.0608695i
$891$			3.45686i			0.115809i
$892$	20.7305	−	34.3620i	0.694107	−	1.15053i
$893$			77.0018i			2.57677i
$894$	3.44989	+	6.11040i	0.115382	+	0.204362i
$895$	17.9373			0.599577
$896$	4.98471	+	10.1564i	0.166528	+	0.339302i
$897$	8.21334			0.274235
$898$	16.1188	+	28.5493i	0.537891	+	0.952704i
$899$		−	19.6704i		−	0.656045i
$900$	−1.03314	+	1.71249i	−0.0344380	+	0.0570830i
$901$			6.85956i			0.228525i
$902$	13.8855	−	7.83968i	0.462338	−	0.261033i
$903$	−4.97544			−0.165572
$904$	−5.24272	−	0.151352i	−0.174370	−	0.00503389i
$905$	12.5922			0.418580
$906$	24.3970	−	13.7744i	0.810536	−	0.457623i
$907$		−	34.8718i		−	1.15790i	−0.815364	−	0.578949i	$-0.803463\pi$
$907$		−	34.8718i		−	1.15790i	0.815364	−	0.578949i	$-0.196537\pi$
$908$	−37.1240	−	22.3968i	−1.23200	−	0.743263i
$909$			8.65394i			0.287033i
$910$	2.40353	+	4.25709i	0.0796761	+	0.141121i
$911$	8.14049			0.269706			0.134853	−	0.990866i	$-0.456944\pi$
$911$	8.14049			0.269706			0.134853	+	0.990866i	$0.456944\pi$
$912$	−10.9825	−	20.8344i	−0.363667	−	0.689897i
$913$	28.3038			0.936718
$914$	1.57609	+	2.79156i	0.0521326	+	0.0923365i
$915$			13.8161i			0.456746i
$916$	−13.4243	−	8.09882i	−0.443551	−	0.267593i
$917$		−	7.32913i		−	0.242029i
$918$	1.42498	−	0.804535i	0.0470314	−	0.0265536i
$919$	−16.9557			−0.559318			−0.279659	−	0.960099i	$-0.590221\pi$
$919$	−16.9557			−0.559318			−0.279659	+	0.960099i	$0.590221\pi$
$920$	0.193925	−	6.71741i	0.00639351	−	0.221466i
$921$	−22.1618			−0.730257
$922$	1.92380	−	1.08616i	0.0633569	−	0.0357709i
$923$			8.08876i			0.266245i
$924$	3.57142	−	5.91984i	0.117491	−	0.194749i
$925$			4.15908i			0.136750i
$926$	22.6409	+	40.1012i	0.744025	+	1.31781i
$927$	−12.5278			−0.411468
$928$	−17.3056	−	11.1339i	−0.568086	−	0.365489i
$929$	−11.1454			−0.365670			−0.182835	−	0.983144i	$-0.558527\pi$
$929$	−11.1454			−0.365670			−0.182835	+	0.983144i	$0.558527\pi$
$930$	−3.75971	−	6.65915i	−0.123286	−	0.218362i
$931$			5.88796i			0.192970i
$932$	−25.7858	+	42.7416i	−0.844643	+	1.40005i
$933$		−	15.5650i		−	0.509575i
$934$	−29.5115	+	16.6620i	−0.965646	+	0.545198i
$935$	4.00000			0.130814
$936$	0.282148	−	9.77341i	0.00922231	−	0.319454i
$937$	−18.5833			−0.607089			−0.303545	−	0.952817i	$-0.598170\pi$
$937$	−18.5833			−0.607089			−0.303545	+	0.952817i	$0.598170\pi$
$938$	−3.95588	+	2.23346i	−0.129164	+	0.0729252i
$939$		−	25.6560i		−	0.837252i
$940$	22.3957	+	13.5112i	0.730467	+	0.440687i
$941$			41.3754i			1.34880i	0.738367	+	0.674399i	$0.235597\pi$
$941$			41.3754i			1.34880i	−0.738367	+	0.674399i	$0.764403\pi$
$942$	−15.8523	−	28.0773i	−0.516495	−	0.914809i
$943$	7.74974			0.252366
$944$	44.4330	−	23.4221i	1.44617	−	0.762325i
$945$	−1.00000			−0.0325300
$946$	11.9586	+	21.1809i	0.388807	+	0.688650i
$947$		−	48.0763i		−	1.56227i	−0.624363	−	0.781134i	$-0.714641\pi$
$947$		−	48.0763i		−	1.56227i	0.624363	−	0.781134i	$-0.285359\pi$
$948$	−24.4773	−	14.7671i	−0.794986	−	0.479612i
$949$			20.5743i			0.667869i
$950$	−7.25097	+	4.09385i	−0.235253	+	0.132822i
$951$	−21.9692			−0.712399
$952$	−3.27146	−	0.0944439i	−0.106029	−	0.00306094i
$953$	17.6285			0.571042			0.285521	−	0.958372i	$-0.407833\pi$
$953$	17.6285			0.571042			0.285521	+	0.958372i	$0.407833\pi$
$954$	−7.30044	+	4.12178i	−0.236361	+	0.133448i
$955$		−	0.362860i		−	0.0117419i
$956$	2.73762	−	4.53777i	0.0885409	−	0.146762i
$957$			12.5750i			0.406492i
$958$	−14.2634	−	25.2631i	−0.460830	−	0.816215i
$959$	4.09652			0.132283
$960$	−7.98668	−	0.461519i	−0.257769	−	0.0148955i
$961$	−1.76015			−0.0567791
$962$	−9.99647	−	17.7056i	−0.322299	−	0.570851i
$963$		−	13.7265i		−	0.442329i
$964$	6.12480	−	10.1522i	0.197267	−	0.326982i
$965$			21.4416i			0.690228i
$966$	2.92596	−	1.65198i	0.0941413	−	0.0531516i
$967$	−16.9567			−0.545291			−0.272646	−	0.962115i	$-0.587899\pi$
$967$	−16.9567			−0.545291			−0.272646	+	0.962115i	$0.587899\pi$
$968$	−2.68557	−	0.0775296i	−0.0863174	−	0.00249190i
$969$	6.81307			0.218867
$970$	−1.18469	+	0.668871i	−0.0380382	+	0.0214761i
$971$			15.0779i			0.483873i	0.970292	+	0.241937i	$0.0777826\pi$
$971$			15.0779i			0.483873i	−0.970292	+	0.241937i	$0.922217\pi$
$972$	1.71249	+	1.03314i	0.0549282	+	0.0331379i
$973$		−	18.1531i		−	0.581961i
$974$	−24.8822	−	44.0710i	−0.797278	−	1.41213i
$975$	−3.45686			−0.110708
$976$	−48.8880	+	25.7705i	−1.56487	+	0.824893i
$977$	39.9107			1.27686			0.638428	−	0.769682i	$-0.279585\pi$
$977$	39.9107			1.27686			0.638428	+	0.769682i	$0.279585\pi$
$978$	−5.26980	−	9.33379i	−0.168510	−	0.298462i
$979$		−	9.02837i		−	0.288548i
$980$	1.71249	+	1.03314i	0.0547035	+	0.0330024i
$981$			0.912317i			0.0291280i
$982$	29.3849	−	16.5905i	0.937711	−	0.529425i
$983$	24.0536			0.767190			0.383595	−	0.923502i	$-0.374686\pi$
$983$	24.0536			0.767190			0.383595	+	0.923502i	$0.374686\pi$
$984$	0.266223	−	9.22176i	0.00848687	−	0.293979i
$985$	−19.6997			−0.627685
$986$	5.18365	−	2.92665i	0.165081	−	0.0932036i
$987$			13.0778i			0.416272i
$988$	21.0284	−	34.8558i	0.669002	−	1.10891i
$989$			11.8214i			0.375899i
$990$	2.40353	+	4.25709i	0.0763891	+	0.135299i
$991$	−47.3455			−1.50398			−0.751990	−	0.659174i	$-0.770906\pi$
$991$	−47.3455			−1.50398			−0.751990	+	0.659174i	$0.770906\pi$
$992$	16.5505	−	25.7246i	0.525478	−	0.816758i
$993$	17.1940			0.545636
$994$	1.62692	+	2.88158i	0.0516029	+	0.0913983i
$995$		−	8.33424i		−	0.264213i
$996$	8.45903	−	14.0214i	0.268035	−	0.444284i
$997$			25.2053i			0.798261i	0.916894	+	0.399130i	$0.130688\pi$
$997$			25.2053i			0.798261i	−0.916894	+	0.399130i	$0.869312\pi$
$998$	42.5665	−	24.0328i	1.34742	−	0.760745i
$999$	4.15908			0.131588

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.g.b.421.5	✓	12
4.3	odd	2		3360.2.g.c.1681.8		12
8.3	odd	2		3360.2.g.c.1681.5		12
8.5	even	2	inner	840.2.g.b.421.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.g.b.421.5	✓	12	1.1	even	1	trivial
840.2.g.b.421.6	yes	12	8.5	even	2	inner
3360.2.g.c.1681.5		12	8.3	odd	2
3360.2.g.c.1681.8		12	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.695292 - 1.23149i) q^{2} -1.00000i q^{3} +(-1.03314 + 1.71249i) q^{4} -1.00000i q^{5} +(-1.23149 + 0.695292i) q^{6} -1.00000 q^{7} +(2.82725 + 0.0816198i) q^{8} -1.00000 q^{9} +(-1.23149 + 0.695292i) q^{10} +3.45686i q^{11} +(1.71249 + 1.03314i) q^{12} +3.45686i q^{13} +(0.695292 + 1.23149i) q^{14} -1.00000 q^{15} +(-1.86525 - 3.53848i) q^{16} +1.15712 q^{17} +(0.695292 + 1.23149i) q^{18} +5.88796i q^{19} +(1.71249 + 1.03314i) q^{20} +1.00000i q^{21} +(4.25709 - 2.40353i) q^{22} +2.37595 q^{23} +(0.0816198 - 2.82725i) q^{24} -1.00000 q^{25} +(4.25709 - 2.40353i) q^{26} +1.00000i q^{27} +(1.03314 - 1.71249i) q^{28} +3.63769i q^{29} +(0.695292 + 1.23149i) q^{30} -5.40739 q^{31} +(-3.06071 + 4.75731i) q^{32} +3.45686 q^{33} +(-0.804535 - 1.42498i) q^{34} +1.00000i q^{35} +(1.03314 - 1.71249i) q^{36} -4.15908i q^{37} +(7.25097 - 4.09385i) q^{38} +3.45686 q^{39} +(0.0816198 - 2.82725i) q^{40} +3.26174 q^{41} +(1.23149 - 0.695292i) q^{42} +4.97544i q^{43} +(-5.91984 - 3.57142i) q^{44} +1.00000i q^{45} +(-1.65198 - 2.92596i) q^{46} +13.0778 q^{47} +(-3.53848 + 1.86525i) q^{48} +1.00000 q^{49} +(0.695292 + 1.23149i) q^{50} -1.15712i q^{51} +(-5.91984 - 3.57142i) q^{52} +5.92814i q^{53} +(1.23149 - 0.695292i) q^{54} +3.45686 q^{55} +(-2.82725 - 0.0816198i) q^{56} +5.88796 q^{57} +(4.47979 - 2.52926i) q^{58} +12.5571i q^{59} +(1.03314 - 1.71249i) q^{60} -13.8161i q^{61} +(3.75971 + 6.65915i) q^{62} +1.00000 q^{63} +(7.98668 + 0.461519i) q^{64} +3.45686 q^{65} +(-2.40353 - 4.25709i) q^{66} +3.21227i q^{67} +(-1.19546 + 1.98156i) q^{68} -2.37595i q^{69} +(1.23149 - 0.695292i) q^{70} +2.33991 q^{71} +(-2.82725 - 0.0816198i) q^{72} +5.95172 q^{73} +(-5.12187 + 2.89178i) q^{74} +1.00000i q^{75} +(-10.0831 - 6.08308i) q^{76} -3.45686i q^{77} +(-2.40353 - 4.25709i) q^{78} -14.2934 q^{79} +(-3.53848 + 1.86525i) q^{80} +1.00000 q^{81} +(-2.26786 - 4.01680i) q^{82} -8.18770i q^{83} +(-1.71249 - 1.03314i) q^{84} -1.15712i q^{85} +(6.12720 - 3.45938i) q^{86} +3.63769 q^{87} +(-0.282148 + 9.77341i) q^{88} -2.61172 q^{89} +(1.23149 - 0.695292i) q^{90} -3.45686i q^{91} +(-2.45469 + 4.06880i) q^{92} +5.40739i q^{93} +(-9.09292 - 16.1052i) q^{94} +5.88796 q^{95} +(4.75731 + 3.06071i) q^{96} +0.962000 q^{97} +(-0.695292 - 1.23149i) q^{98} -3.45686i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 2 q^{4} - 12 q^{7} - 2 q^{8} - 12 q^{9} + 2 q^{14} - 12 q^{15} + 2 q^{16} + 2 q^{18} + 40 q^{23} - 12 q^{25} - 2 q^{28} + 2 q^{30} - 8 q^{31} - 2 q^{32} - 20 q^{34} - 2 q^{36} + 24 q^{38}+ \cdots - 2 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 + 2 * q^4 - 12 * q^7 - 2 * q^8 - 12 * q^9 + 2 * q^14 - 12 * q^15 + 2 * q^16 + 2 * q^18 + 40 * q^23 - 12 * q^25 - 2 * q^28 + 2 * q^30 - 8 * q^31 - 2 * q^32 - 20 * q^34 - 2 * q^36 + 24 * q^38 + 24 * q^46 - 32 * q^47 + 12 * q^49 + 2 * q^50 + 2 * q^56 - 20 * q^58 - 2 * q^60 + 52 * q^62 + 12 * q^63 + 2 * q^64 - 20 * q^66 - 4 * q^68 - 8 * q^71 + 2 * q^72 - 60 * q^74 - 48 * q^76 - 20 * q^78 - 80 * q^79 + 12 * q^81 + 24 * q^86 + 16 * q^87 + 40 * q^88 - 8 * q^92 + 36 * q^94 + 40 * q^96 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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