LMFDB - Embedded newform 420.2.bb.a.109.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [420,2,Mod(109,420)] 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("420.109"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(420, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.81284711803392324796416.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 20 x^{13} - 12 x^{12} + 124 x^{11} - 24 x^{10} + 328 x^{9} + 1132 x^{8} + \cdots + 16 $ x^16 - 2x^15 + 2x^14 - 20x^13 - 12x^12 + 124x^11 - 24x^10 + 328x^9 + 1132x^8 - 760x^7 + 96x^6 - 640x^5 + 96x^4 + 224x^3 + 32x^2 + 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.4
Root			$-0.389934 - 0.104482i$ of defining polynomial
Character	$\chi$	$=$	420.109
Dual form			420.2.bb.a.289.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{3} +(1.77792 - 1.35609i) q^{5} +(2.57243 + 0.618546i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-1.46616 + 2.53947i) q^{11} -5.76936i q^{13} +(-2.21777 + 0.285451i) q^{15} +(0.205328 + 0.118546i) q^{17} +(2.37016 + 4.10523i) q^{19} +(-1.91852 - 1.82189i) q^{21} +(5.86244 - 3.38468i) q^{23} +(1.32201 - 4.82206i) q^{25} -1.00000i q^{27} -6.03549 q^{29} +(5.26936 - 9.12679i) q^{31} +(2.53947 - 1.46616i) q^{33} +(5.41239 - 2.38873i) q^{35} +(2.66227 - 1.53706i) q^{37} +(-2.88468 + 4.99641i) q^{39} +1.06768 q^{41} +9.79697i q^{43} +(2.06337 + 0.861678i) q^{45} +(-3.21530 + 1.85635i) q^{47} +(6.23480 + 3.18233i) q^{49} +(-0.118546 - 0.205328i) q^{51} +(-9.53186 - 5.50322i) q^{53} +(0.837035 + 6.50322i) q^{55} -4.74032i q^{57} +(-4.65633 + 8.06499i) q^{59} +(4.06861 + 7.04704i) q^{61} +(0.750539 + 2.53706i) q^{63} +(-7.82379 - 10.2575i) q^{65} +(-1.94296 - 1.12177i) q^{67} -6.76936 q^{69} -11.8421 q^{71} +(-3.28827 - 1.89848i) q^{73} +(-3.55593 + 3.51502i) q^{75} +(-5.34237 + 5.62571i) q^{77} +(0.00873900 + 0.0151364i) q^{79} +(-0.500000 + 0.866025i) q^{81} +7.30162i q^{83} +(0.525816 - 0.0676782i) q^{85} +(5.22689 + 3.01774i) q^{87} +(8.97583 + 15.5466i) q^{89} +(3.56861 - 14.8413i) q^{91} +(-9.12679 + 5.26936i) q^{93} +(9.78104 + 4.08463i) q^{95} -2.31122i q^{97} -2.93232 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{5} + 8 q^{9} - 8 q^{11} + 4 q^{15} + 8 q^{19} - 4 q^{21} + 12 q^{25} + 24 q^{29} + 10 q^{35} - 4 q^{39} + 48 q^{41} - 2 q^{45} + 8 q^{49} + 4 q^{51} - 40 q^{55} - 28 q^{59} - 32 q^{61} - 26 q^{65}+ \cdots - 16 q^{99}+O(q^{100}) $ 16 * q + 2 * q^5 + 8 * q^9 - 8 * q^11 + 4 * q^15 + 8 * q^19 - 4 * q^21 + 12 * q^25 + 24 * q^29 + 10 * q^35 - 4 * q^39 + 48 * q^41 - 2 * q^45 + 8 * q^49 + 4 * q^51 - 40 * q^55 - 28 * q^59 - 32 * q^61 - 26 * q^65 - 24 * q^69 - 56 * q^71 - 8 * q^75 - 16 * q^79 - 8 * q^81 + 32 * q^85 - 16 * q^89 - 40 * q^91 + 22 * q^95 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$		0			0
$5$	1.77792	−	1.35609i	0.795111	−	0.606464i
$5$	1.77792	−	1.35609i	0.795111	−	0.606464i
$6$		0			0
$7$	2.57243	+	0.618546i	0.972288	+	0.233788i
$7$	2.57243	+	0.618546i	0.972288	+	0.233788i
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−1.46616	+	2.53947i	−0.442064	+	0.765678i	−0.997843	−	0.0656529i	$-0.979087\pi$
$11$	−1.46616	+	2.53947i	−0.442064	+	0.765678i	0.555778	+	0.831330i	$0.312420\pi$
$12$		0			0
$13$		−	5.76936i		−	1.60013i	−0.599912	−	0.800066i	$-0.704798\pi$
$13$		−	5.76936i		−	1.60013i	0.599912	−	0.800066i	$-0.295202\pi$
$14$		0			0
$15$	−2.21777	+	0.285451i	−0.572627	+	0.0737032i
$16$		0			0
$17$	0.205328	+	0.118546i	0.0497993	+	0.0287516i	0.524693	−	0.851292i	$-0.324180\pi$
$17$	0.205328	+	0.118546i	0.0497993	+	0.0287516i	−0.474894	+	0.880043i	$0.657513\pi$
$18$		0			0
$19$	2.37016	+	4.10523i	0.543752	+	0.941805i	0.998684	+	0.0512796i	$0.0163300\pi$
$19$	2.37016	+	4.10523i	0.543752	+	0.941805i	−0.454933	+	0.890526i	$0.650337\pi$
$20$		0			0
$21$	−1.91852	−	1.82189i	−0.418655	−	0.397569i
$22$		0			0
$23$	5.86244	−	3.38468i	1.22240	−	0.705754i	0.256973	−	0.966419i	$-0.417275\pi$
$23$	5.86244	−	3.38468i	1.22240	−	0.705754i	0.965429	+	0.260664i	$0.0839416\pi$
$24$		0			0
$25$	1.32201	−	4.82206i	0.264403	−	0.964412i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−6.03549			−1.12076			−0.560381	−	0.828235i	$-0.689345\pi$
$29$	−6.03549			−1.12076			−0.560381	+	0.828235i	$0.689345\pi$
$30$		0			0
$31$	5.26936	−	9.12679i	0.946404	−	1.63922i	0.193490	−	0.981102i	$-0.438019\pi$
$31$	5.26936	−	9.12679i	0.946404	−	1.63922i	0.752915	−	0.658118i	$-0.228647\pi$
$32$		0			0
$33$	2.53947	−	1.46616i	0.442064	−	0.255226i
$34$		0			0
$35$	5.41239	−	2.38873i	0.914861	−	0.403770i
$36$		0			0
$37$	2.66227	−	1.53706i	0.437675	−	0.252692i	−0.264936	−	0.964266i	$-0.585351\pi$
$37$	2.66227	−	1.53706i	0.437675	−	0.252692i	0.702611	+	0.711574i	$0.252018\pi$
$38$		0			0
$39$	−2.88468	+	4.99641i	−0.461918	+	0.800066i
$40$		0			0
$41$	1.06768			0.166743			0.0833717	−	0.996519i	$-0.473431\pi$
$41$	1.06768			0.166743			0.0833717	+	0.996519i	$0.473431\pi$
$42$		0			0
$43$			9.79697i			1.49402i	0.664811	+	0.747012i	$0.268512\pi$
$43$			9.79697i			1.49402i	−0.664811	+	0.747012i	$0.731488\pi$
$44$		0			0
$45$	2.06337	+	0.861678i	0.307590	+	0.128451i
$46$		0			0
$47$	−3.21530	+	1.85635i	−0.469000	+	0.270777i	−0.715821	−	0.698284i	$-0.753947\pi$
$47$	−3.21530	+	1.85635i	−0.469000	+	0.270777i	0.246821	+	0.969061i	$0.420614\pi$
$48$		0			0
$49$	6.23480	+	3.18233i	0.890686	+	0.454619i
$50$		0			0
$51$	−0.118546	−	0.205328i	−0.0165998	−	0.0287516i
$52$		0			0
$53$	−9.53186	−	5.50322i	−1.30930	−	0.755926i	−0.327323	−	0.944913i	$-0.606146\pi$
$53$	−9.53186	−	5.50322i	−1.30930	−	0.755926i	−0.981980	+	0.188987i	$0.939480\pi$
$54$		0			0
$55$	0.837035	+	6.50322i	0.112866	+	0.876895i
$56$		0			0
$57$		−	4.74032i		−	0.627870i
$58$		0			0
$59$	−4.65633	+	8.06499i	−0.606202	+	1.04997i	0.385658	+	0.922642i	$0.373974\pi$
$59$	−4.65633	+	8.06499i	−0.606202	+	1.04997i	−0.991860	+	0.127331i	$0.959359\pi$
$60$		0			0
$61$	4.06861	+	7.04704i	0.520932	+	0.902281i	0.999704	+	0.0243418i	$0.00774899\pi$
$61$	4.06861	+	7.04704i	0.520932	+	0.902281i	−0.478771	+	0.877940i	$0.658918\pi$
$62$		0			0
$63$	0.750539	+	2.53706i	0.0945590	+	0.319640i
$64$		0			0
$65$	−7.82379	−	10.2575i	−0.970422	−	1.27228i
$66$		0			0
$67$	−1.94296	−	1.12177i	−0.237371	−	0.137046i	0.376597	−	0.926377i	$-0.377094\pi$
$67$	−1.94296	−	1.12177i	−0.237371	−	0.137046i	−0.613968	+	0.789331i	$0.710428\pi$
$68$		0			0
$69$	−6.76936			−0.814935
$70$		0			0
$71$	−11.8421			−1.40539			−0.702696	−	0.711490i	$-0.748021\pi$
$71$	−11.8421			−1.40539			−0.702696	+	0.711490i	$0.748021\pi$
$72$		0			0
$73$	−3.28827	−	1.89848i	−0.384863	−	0.222201i	0.295069	−	0.955476i	$-0.404657\pi$
$73$	−3.28827	−	1.89848i	−0.384863	−	0.222201i	−0.679932	+	0.733275i	$0.737991\pi$
$74$		0			0
$75$	−3.55593	+	3.51502i	−0.410603	+	0.405880i
$76$		0			0
$77$	−5.34237	+	5.62571i	−0.608820	+	0.641109i
$78$		0			0
$79$	0.00873900	+	0.0151364i	0.000983215	+	0.00170298i	0.866517	−	0.499148i	$-0.166354\pi$
$79$	0.00873900	+	0.0151364i	0.000983215	+	0.00170298i	−0.865533	+	0.500851i	$0.833020\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			7.30162i			0.801457i	0.916197	+	0.400729i	$0.131243\pi$
$83$			7.30162i			0.801457i	−0.916197	+	0.400729i	$0.868757\pi$
$84$		0			0
$85$	0.525816	−	0.0676782i	0.0570328	−	0.00734073i
$86$		0			0
$87$	5.22689	+	3.01774i	0.560381	+	0.323536i
$88$		0			0
$89$	8.97583	+	15.5466i	0.951437	+	1.64794i	0.742320	+	0.670046i	$0.233726\pi$
$89$	8.97583	+	15.5466i	0.951437	+	1.64794i	0.209117	+	0.977891i	$0.432941\pi$
$90$		0			0
$91$	3.56861	−	14.8413i	0.374092	−	1.55579i
$92$		0			0
$93$	−9.12679	+	5.26936i	−0.946404	+	0.546407i
$94$		0			0
$95$	9.78104	+	4.08463i	1.00351	+	0.419074i
$96$		0			0
$97$		−	2.31122i		−	0.234669i	−0.993092	−	0.117334i	$-0.962565\pi$
$97$		−	2.31122i		−	0.234669i	0.993092	−	0.117334i	$-0.0374349\pi$
$98$		0			0
$99$	−2.93232			−0.294709
$100$		0			0
$101$	3.92103	−	6.79142i	0.390157	−	0.675771i	−0.602313	−	0.798260i	$-0.705754\pi$
$101$	3.92103	−	6.79142i	0.390157	−	0.675771i	0.992470	+	0.122489i	$0.0390875\pi$
$102$		0			0
$103$	−3.53388	+	2.04029i	−0.348204	+	0.201036i	−0.663894	−	0.747827i	$-0.731097\pi$
$103$	−3.53388	+	2.04029i	−0.348204	+	0.201036i	0.315690	+	0.948862i	$0.397764\pi$
$104$		0			0
$105$	−5.88163	−	0.637491i	−0.573989	−	0.0622127i
$106$		0			0
$107$	−15.8887	+	9.17335i	−1.53602	+	0.886822i	−0.536954	+	0.843611i	$0.680425\pi$
$107$	−15.8887	+	9.17335i	−1.53602	+	0.886822i	−0.999066	+	0.0432102i	$0.986241\pi$
$108$		0			0
$109$	−5.20719	+	9.01912i	−0.498759	+	0.863875i	−0.999999	−	0.00143278i	$-0.999544\pi$
$109$	−5.20719	+	9.01912i	−0.498759	+	0.863875i	0.501240	+	0.865308i	$0.332877\pi$
$110$		0			0
$111$	−3.07413			−0.291783
$112$		0			0
$113$		−	2.14825i		−	0.202091i	−0.994882	−	0.101045i	$-0.967781\pi$
$113$		−	2.14825i		−	0.202091i	0.994882	−	0.101045i	$-0.0322187\pi$
$114$		0			0
$115$	5.83301	−	13.9677i	0.543931	−	1.30250i
$116$		0			0
$117$	4.99641	−	2.88468i	0.461918	−	0.266689i
$118$		0			0
$119$	0.454865	+	0.431956i	0.0416974	+	0.0395973i
$120$		0			0
$121$	1.20074	+	2.07975i	0.109159	+	0.189068i
$122$		0			0
$123$	−0.924636	−	0.533839i	−0.0833717	−	0.0481347i
$124$		0			0
$125$	−4.18873	−	10.3660i	−0.374652	−	0.927166i
$126$		0			0
$127$			1.82457i			0.161905i	0.996718	+	0.0809524i	$0.0257962\pi$
$127$			1.82457i			0.161905i	−0.996718	+	0.0809524i	$0.974204\pi$
$128$		0			0
$129$	4.89848	−	8.48442i	0.431287	−	0.747012i
$130$		0			0
$131$	−1.35313	−	2.34369i	−0.118223	−	0.204769i	0.800840	−	0.598878i	$-0.204387\pi$
$131$	−1.35313	−	2.34369i	−0.118223	−	0.204769i	−0.919064	+	0.394109i	$0.871053\pi$
$132$		0			0
$133$	3.55779	+	12.0265i	0.308500	+	1.04283i
$134$		0			0
$135$	−1.35609	−	1.77792i	−0.116714	−	0.153019i
$136$		0			0
$137$	8.66460	+	5.00251i	0.740267	+	0.427393i	0.822166	−	0.569247i	$-0.192765\pi$
$137$	8.66460	+	5.00251i	0.740267	+	0.427393i	−0.0818996	+	0.996641i	$0.526099\pi$
$138$		0			0
$139$	2.07269			0.175804			0.0879018	−	0.996129i	$-0.471984\pi$
$139$	2.07269			0.175804			0.0879018	+	0.996129i	$0.471984\pi$
$140$		0			0
$141$	3.71271			0.312666
$142$		0			0
$143$	14.6511	+	8.45881i	1.22518	+	0.707361i
$144$		0			0
$145$	−10.7306	+	8.18469i	−0.891130	+	0.679702i
$146$		0			0
$147$	−3.80833	−	5.87338i	−0.314106	−	0.484428i
$148$		0			0
$149$	−0.551584	−	0.955371i	−0.0451875	−	0.0782671i	0.842547	−	0.538623i	$-0.181055\pi$
$149$	−0.551584	−	0.955371i	−0.0451875	−	0.0782671i	−0.887735	+	0.460356i	$0.847722\pi$
$150$		0			0
$151$	−5.23158	+	9.06136i	−0.425740	+	0.737403i	−0.996489	−	0.0837214i	$-0.973319\pi$
$151$	−5.23158	+	9.06136i	−0.425740	+	0.737403i	0.570749	+	0.821124i	$0.306653\pi$
$152$		0			0
$153$			0.237092i			0.0191677i
$154$		0			0
$155$	−3.00829	−	23.3725i	−0.241632	−	1.87732i
$156$		0			0
$157$	−7.84763	−	4.53083i	−0.626309	−	0.361600i	0.153012	−	0.988224i	$-0.451103\pi$
$157$	−7.84763	−	4.53083i	−0.626309	−	0.361600i	−0.779321	+	0.626624i	$0.784436\pi$
$158$		0			0
$159$	5.50322	+	9.53186i	0.436434	+	0.755926i
$160$		0			0
$161$	17.1743	−	5.08067i	1.35352	−	0.400413i
$162$		0			0
$163$	7.22164	−	4.16941i	0.565642	−	0.326574i	−0.189765	−	0.981830i	$-0.560773\pi$
$163$	7.22164	−	4.16941i	0.565642	−	0.326574i	0.755407	+	0.655256i	$0.227439\pi$
$164$		0			0
$165$	2.52672	−	6.05048i	0.196705	−	0.471029i
$166$		0			0
$167$			10.2886i			0.796158i	0.917351	+	0.398079i	$0.130323\pi$
$167$			10.2886i			0.796158i	−0.917351	+	0.398079i	$0.869677\pi$
$168$		0			0
$169$	−20.2855			−1.56042
$170$		0			0
$171$	−2.37016	+	4.10523i	−0.181251	+	0.313935i
$172$		0			0
$173$	14.9768	−	8.64687i	1.13867	−	0.657409i	0.192566	−	0.981284i	$-0.438319\pi$
$173$	14.9768	−	8.64687i	1.13867	−	0.657409i	0.946100	+	0.323875i	$0.104986\pi$
$174$		0			0
$175$	6.38346	−	11.5867i	0.482544	−	0.875872i
$176$		0			0
$177$	8.06499	−	4.65633i	0.606202	−	0.349991i
$178$		0			0
$179$	−5.50967	+	9.54303i	−0.411812	+	0.713280i	−0.995088	−	0.0989944i	$-0.968437\pi$
$179$	−5.50967	+	9.54303i	−0.411812	+	0.713280i	0.583276	+	0.812274i	$0.301771\pi$
$180$		0			0
$181$	4.53685			0.337221			0.168611	−	0.985683i	$-0.446072\pi$
$181$	4.53685			0.337221			0.168611	+	0.985683i	$0.446072\pi$
$182$		0			0
$183$		−	8.13722i		−	0.601521i
$184$		0			0
$185$	2.64891	−	6.34307i	0.194752	−	0.466352i
$186$		0			0
$187$	−0.602087	+	0.347615i	−0.0440289	+	0.0254201i
$188$		0			0
$189$	0.618546	−	2.57243i	0.0449926	−	0.187117i
$190$		0			0
$191$	−4.34026	−	7.51755i	−0.314050	−	0.543951i	0.665185	−	0.746679i	$-0.268353\pi$
$191$	−4.34026	−	7.51755i	−0.314050	−	0.543951i	−0.979235	+	0.202728i	$0.935019\pi$
$192$		0			0
$193$	−6.11520	−	3.53061i	−0.440182	−	0.254139i	0.263493	−	0.964661i	$-0.415125\pi$
$193$	−6.11520	−	3.53061i	−0.440182	−	0.254139i	−0.703675	+	0.710522i	$0.748459\pi$
$194$		0			0
$195$	1.64687	+	12.7951i	0.117935	+	0.916278i
$196$		0			0
$197$		−	3.58891i		−	0.255700i	−0.991794	−	0.127850i	$-0.959192\pi$
$197$		−	3.58891i		−	0.255700i	0.991794	−	0.127850i	$-0.0408075\pi$
$198$		0			0
$199$	−1.49126	+	2.58294i	−0.105713	+	0.183100i	−0.914029	−	0.405648i	$-0.867046\pi$
$199$	−1.49126	+	2.58294i	−0.105713	+	0.183100i	0.808316	+	0.588748i	$0.200379\pi$
$200$		0			0
$201$	1.12177	+	1.94296i	0.0791236	+	0.137046i
$202$		0			0
$203$	−15.5259	−	3.73323i	−1.08970	−	0.262021i
$204$		0			0
$205$	1.89825	−	1.44787i	0.132579	−	0.101124i
$206$		0			0
$207$	5.86244	+	3.38468i	0.407467	+	0.235251i
$208$		0			0
$209$	−13.9001			−0.961492
$210$		0			0
$211$	−21.4273			−1.47512			−0.737558	−	0.675284i	$-0.764021\pi$
$211$	−21.4273			−1.47512			−0.737558	+	0.675284i	$0.764021\pi$
$212$		0			0
$213$	10.2555	+	5.92103i	0.702696	+	0.405702i
$214$		0			0
$215$	13.2856	+	17.4182i	0.906071	+	1.18791i
$216$		0			0
$217$	19.2004	−	20.2187i	1.30341	−	1.37254i
$218$		0			0
$219$	1.89848	+	3.28827i	0.128288	+	0.222201i
$220$		0			0
$221$	0.683934	−	1.18461i	0.0460064	−	0.0796854i
$222$		0			0
$223$		−	16.3969i		−	1.09802i	−0.835816	−	0.549009i	$-0.815005\pi$
$223$		−	16.3969i		−	1.09802i	0.835816	−	0.549009i	$-0.184995\pi$
$224$		0			0
$225$	4.83704	−	1.26613i	0.322469	−	0.0844088i
$226$		0			0
$227$	−8.25642	−	4.76685i	−0.547998	−	0.316387i	0.200316	−	0.979731i	$-0.435803\pi$
$227$	−8.25642	−	4.76685i	−0.547998	−	0.316387i	−0.748314	+	0.663344i	$0.769136\pi$
$228$		0			0
$229$	9.05987	+	15.6922i	0.598693	+	1.03697i	0.993014	+	0.117994i	$0.0376465\pi$
$229$	9.05987	+	15.6922i	0.598693	+	1.03697i	−0.394321	+	0.918973i	$0.629020\pi$
$230$		0			0
$231$	7.43949	−	2.20082i	0.489482	−	0.144803i
$232$		0			0
$233$	10.4394	−	6.02720i	0.683909	−	0.394855i	−0.117417	−	0.993083i	$-0.537462\pi$
$233$	10.4394	−	6.02720i	0.683909	−	0.394855i	0.801326	+	0.598228i	$0.204128\pi$
$234$		0			0
$235$	−3.19916	+	7.66070i	−0.208690	+	0.499729i
$236$		0			0
$237$		−	0.0174780i		−	0.00113532i
$238$		0			0
$239$	21.3868			1.38340			0.691698	−	0.722187i	$-0.256863\pi$
$239$	21.3868			1.38340			0.691698	+	0.722187i	$0.256863\pi$
$240$		0			0
$241$	−8.59443	+	14.8860i	−0.553616	+	0.958891i	0.444394	+	0.895831i	$0.353419\pi$
$241$	−8.59443	+	14.8860i	−0.553616	+	0.958891i	−0.998010	+	0.0630593i	$0.979914\pi$
$242$		0			0
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$		0			0
$245$	15.4005	−	2.79704i	0.983904	−	0.178696i
$246$		0			0
$247$	23.6846	−	13.6743i	1.50701	−	0.870074i
$248$		0			0
$249$	3.65081	−	6.32339i	0.231361	−	0.400729i
$250$		0			0
$251$	23.1939			1.46398			0.731992	−	0.681313i	$-0.238591\pi$
$251$	23.1939			1.46398			0.731992	+	0.681313i	$0.238591\pi$
$252$		0			0
$253$			19.8499i			1.24795i
$254$		0			0
$255$	−0.489209	−	0.204297i	−0.0306355	−	0.0127936i
$256$		0			0
$257$	−22.6519	+	13.0781i	−1.41299	+	0.815787i	−0.995669	−	0.0929737i	$-0.970363\pi$
$257$	−22.6519	+	13.0781i	−1.41299	+	0.815787i	−0.417317	+	0.908761i	$0.637029\pi$
$258$		0			0
$259$	7.79926	−	2.30725i	0.484622	−	0.143366i
$260$		0			0
$261$	−3.01774	−	5.22689i	−0.186794	−	0.323536i
$262$		0			0
$263$	−6.66823	−	3.84991i	−0.411181	−	0.237395i	0.280116	−	0.959966i	$-0.409627\pi$
$263$	−6.66823	−	3.84991i	−0.411181	−	0.237395i	−0.691297	+	0.722571i	$0.742960\pi$
$264$		0			0
$265$	−24.4098	+	3.14181i	−1.49948	+	0.193000i
$266$		0			0
$267$		−	17.9517i		−	1.09862i
$268$		0			0
$269$	12.5194	−	21.6842i	0.763321	−	1.32211i	−0.177809	−	0.984065i	$-0.556901\pi$
$269$	12.5194	−	21.6842i	0.763321	−	1.32211i	0.941130	−	0.338046i	$-0.109766\pi$
$270$		0			0
$271$	−9.54423	−	16.5311i	−0.579771	−	1.00419i	−0.995505	−	0.0947062i	$-0.969809\pi$
$271$	−9.54423	−	16.5311i	−0.579771	−	1.00419i	0.415735	−	0.909486i	$-0.363524\pi$
$272$		0			0
$273$	−10.5111	+	11.0686i	−0.636163	+	0.669903i
$274$		0			0
$275$	10.3072	+	10.4271i	0.621546	+	0.628779i
$276$		0			0
$277$	10.5124	+	6.06933i	0.631628	+	0.364671i	0.781382	−	0.624053i	$-0.214515\pi$
$277$	10.5124	+	6.06933i	0.631628	+	0.364671i	−0.149754	+	0.988723i	$0.547848\pi$
$278$		0			0
$279$	10.5387			0.630936
$280$		0			0
$281$	−6.34537			−0.378533			−0.189267	−	0.981926i	$-0.560611\pi$
$281$	−6.34537			−0.378533			−0.189267	+	0.981926i	$0.560611\pi$
$282$		0			0
$283$	−11.7947	−	6.80964i	−0.701119	−	0.404791i	0.106645	−	0.994297i	$-0.465989\pi$
$283$	−11.7947	−	6.80964i	−0.701119	−	0.404791i	−0.807764	+	0.589506i	$0.799323\pi$
$284$		0			0
$285$	−6.42832	−	8.42791i	−0.380781	−	0.499227i
$286$		0			0
$287$	2.74653	+	0.660408i	0.162122	+	0.0389827i
$288$		0			0
$289$	−8.47189	−	14.6738i	−0.498347	−	0.863162i
$290$		0			0
$291$	−1.15561	+	2.00157i	−0.0677430	+	0.117334i
$292$		0			0
$293$		−	15.5221i		−	0.906813i	−0.891304	−	0.453406i	$-0.850209\pi$
$293$		−	15.5221i		−	0.906813i	0.891304	−	0.453406i	$-0.149791\pi$
$294$		0			0
$295$	2.65831	+	20.6533i	0.154773	+	1.20248i
$296$		0			0
$297$	2.53947	+	1.46616i	0.147355	+	0.0850753i
$298$		0			0
$299$	−19.5274	−	33.8225i	−1.12930	−	1.95600i
$300$		0			0
$301$	−6.05987	+	25.2020i	−0.349285	+	1.45262i
$302$		0			0
$303$	−6.79142	+	3.92103i	−0.390157	+	0.225257i
$304$		0			0
$305$	16.7901	+	7.01167i	0.961400	+	0.401487i
$306$		0			0
$307$		−	13.4406i		−	0.767093i	−0.923521	−	0.383547i	$-0.874703\pi$
$307$		−	13.4406i		−	0.767093i	0.923521	−	0.383547i	$-0.125297\pi$
$308$		0			0
$309$	4.08058			0.232136
$310$		0			0
$311$	−1.22580	+	2.12314i	−0.0695085	+	0.120392i	−0.898685	−	0.438595i	$-0.855476\pi$
$311$	−1.22580	+	2.12314i	−0.0695085	+	0.120392i	0.829177	+	0.558987i	$0.188810\pi$
$312$		0			0
$313$	8.59047	−	4.95971i	0.485562	−	0.280340i	−0.237169	−	0.971468i	$-0.576220\pi$
$313$	8.59047	−	4.95971i	0.485562	−	0.280340i	0.722732	+	0.691129i	$0.242886\pi$
$314$		0			0
$315$	4.77490	+	3.49290i	0.269035	+	0.196803i
$316$		0			0
$317$	−22.5124	+	12.9975i	−1.26442	+	0.730013i	−0.973927	−	0.226863i	$-0.927153\pi$
$317$	−22.5124	+	12.9975i	−1.26442	+	0.730013i	−0.290494	+	0.956877i	$0.593820\pi$
$318$		0			0
$319$	8.84900	−	15.3269i	0.495449	−	0.858142i
$320$		0			0
$321$	18.3467			1.02401
$322$		0			0
$323$			1.12389i			0.0625350i
$324$		0			0
$325$	−27.8202	−	7.62717i	−1.54319	−	0.423080i
$326$		0			0
$327$	9.01912	−	5.20719i	0.498759	−	0.287958i
$328$		0			0
$329$	−9.41938	+	2.78653i	−0.519307	+	0.153626i
$330$		0			0
$331$	−3.76613	−	6.52313i	−0.207005	−	0.358544i	0.743764	−	0.668442i	$-0.233038\pi$
$331$	−3.76613	−	6.52313i	−0.207005	−	0.358544i	−0.950770	+	0.309898i	$0.899705\pi$
$332$		0			0
$333$	2.66227	+	1.53706i	0.145892	+	0.0842306i
$334$		0			0
$335$	−4.97566	+	0.640422i	−0.271850	+	0.0349900i
$336$		0			0
$337$			15.7050i			0.855505i	0.903896	+	0.427752i	$0.140694\pi$
$337$			15.7050i			0.855505i	−0.903896	+	0.427752i	$0.859306\pi$
$338$		0			0
$339$	−1.07413	+	1.86044i	−0.0583386	+	0.101045i
$340$		0			0
$341$	15.4515	+	26.7627i	0.836743	+	1.44928i
$342$		0			0
$343$	14.0702	+	12.0428i	0.759718	+	0.650252i
$344$		0			0
$345$	−12.0354	+	9.17989i	−0.647964	+	0.494229i
$346$		0			0
$347$	−7.97850	−	4.60639i	−0.428309	−	0.247284i	0.270317	−	0.962771i	$-0.412871\pi$
$347$	−7.97850	−	4.60639i	−0.428309	−	0.247284i	−0.698626	+	0.715487i	$0.746205\pi$
$348$		0			0
$349$	−21.1518			−1.13223			−0.566116	−	0.824326i	$-0.691555\pi$
$349$	−21.1518			−1.13223			−0.566116	+	0.824326i	$0.691555\pi$
$350$		0			0
$351$	−5.76936			−0.307945
$352$		0			0
$353$	12.9725	+	7.48969i	0.690457	+	0.398636i	0.803783	−	0.594922i	$-0.202817\pi$
$353$	12.9725	+	7.48969i	0.690457	+	0.398636i	−0.113326	+	0.993558i	$0.536150\pi$
$354$		0			0
$355$	−21.0542	+	16.0589i	−1.11744	+	0.852320i
$356$		0			0
$357$	−0.177947	−	0.601517i	−0.00941794	−	0.0318357i
$358$		0			0
$359$	10.4823	+	18.1559i	0.553236	+	0.958233i	0.998038	+	0.0626045i	$0.0199407\pi$
$359$	10.4823	+	18.1559i	0.553236	+	0.958233i	−0.444802	+	0.895629i	$0.646726\pi$
$360$		0			0
$361$	−1.73530	+	3.00563i	−0.0913316	+	0.158191i
$362$		0			0
$363$		−	2.40149i		−	0.126045i
$364$		0			0
$365$	−8.42081	+	1.08385i	−0.440765	+	0.0567312i
$366$		0			0
$367$	−16.5538	−	9.55732i	−0.864099	−	0.498888i	0.00128371	−	0.999999i	$-0.499591\pi$
$367$	−16.5538	−	9.55732i	−0.864099	−	0.498888i	−0.865383	+	0.501111i	$0.832925\pi$
$368$		0			0
$369$	0.533839	+	0.924636i	0.0277906	+	0.0481347i
$370$		0			0
$371$	−21.1161	−	20.0526i	−1.09629	−	1.04108i
$372$		0			0
$373$	−5.64151	+	3.25713i	−0.292106	+	0.168648i	−0.638891	−	0.769297i	$-0.720607\pi$
$373$	−5.64151	+	3.25713i	−0.292106	+	0.168648i	0.346785	+	0.937945i	$0.387273\pi$
$374$		0			0
$375$	−1.55546	+	11.0716i	−0.0803239	+	0.571735i
$376$		0			0
$377$			34.8209i			1.79337i
$378$		0			0
$379$	−14.4254			−0.740984			−0.370492	−	0.928836i	$-0.620811\pi$
$379$	−14.4254			−0.740984			−0.370492	+	0.928836i	$0.620811\pi$
$380$		0			0
$381$	0.912287	−	1.58013i	0.0467379	−	0.0809524i
$382$		0			0
$383$	21.9018	−	12.6450i	1.11913	−	0.646131i	0.177952	−	0.984039i	$-0.443053\pi$
$383$	21.9018	−	12.6450i	1.11913	−	0.646131i	0.941179	+	0.337908i	$0.109719\pi$
$384$		0			0
$385$	−1.86933	+	17.2468i	−0.0952698	+	0.878980i
$386$		0			0
$387$	−8.48442	+	4.89848i	−0.431287	+	0.249004i
$388$		0			0
$389$	13.4984	−	23.3799i	0.684395	−	1.18541i	−0.289232	−	0.957259i	$-0.593400\pi$
$389$	13.4984	−	23.3799i	0.684395	−	1.18541i	0.973627	−	0.228148i	$-0.0732669\pi$
$390$		0			0
$391$	1.60496			0.0811663
$392$		0			0
$393$			2.70626i			0.136513i
$394$		0			0
$395$	0.0360637	+	0.0150604i	0.00181456	+	0.000757772i
$396$		0			0
$397$	−27.3806	+	15.8082i	−1.37419	+	0.793391i	−0.991453	−	0.130464i	$-0.958353\pi$
$397$	−27.3806	+	15.8082i	−1.37419	+	0.793391i	−0.382741	+	0.923856i	$0.625020\pi$
$398$		0			0
$399$	2.93210	−	12.1941i	0.146789	−	0.610470i
$400$		0			0
$401$	6.24497	+	10.8166i	0.311859	+	0.540156i	0.978765	−	0.204986i	$-0.0657150\pi$
$401$	6.24497	+	10.8166i	0.311859	+	0.540156i	−0.666906	+	0.745142i	$0.732382\pi$
$402$		0			0
$403$	−52.6557	−	30.4008i	−2.62297	−	1.51437i
$404$		0			0
$405$	0.285451	+	2.21777i	0.0141842	+	0.110202i
$406$		0			0
$407$			9.01433i			0.446824i
$408$		0			0
$409$	6.28039	−	10.8779i	0.310545	−	0.537880i	−0.667935	−	0.744219i	$-0.732822\pi$
$409$	6.28039	−	10.8779i	0.310545	−	0.537880i	0.978480	+	0.206339i	$0.0661551\pi$
$410$		0			0
$411$	−5.00251	−	8.66460i	−0.246756	−	0.427393i
$412$		0			0
$413$	−16.9666	+	17.8665i	−0.834874	+	0.879152i
$414$		0			0
$415$	9.90169	+	12.9817i	0.486055	+	0.637247i
$416$		0			0
$417$	−1.79501	−	1.03635i	−0.0879018	−	0.0507502i
$418$		0			0
$419$	17.6520			0.862357			0.431179	−	0.902267i	$-0.358098\pi$
$419$	17.6520			0.862357			0.431179	+	0.902267i	$0.358098\pi$
$420$		0			0
$421$	29.2634			1.42621			0.713106	−	0.701056i	$-0.247288\pi$
$421$	29.2634			1.42621			0.713106	+	0.701056i	$0.247288\pi$
$422$		0			0
$423$	−3.21530	−	1.85635i	−0.156333	−	0.0902590i
$424$		0			0
$425$	0.843082	−	0.833383i	0.0408955	−	0.0404250i
$426$		0			0
$427$	6.10730	+	20.6447i	0.295553	+	0.999065i
$428$		0			0
$429$	−8.45881	−	14.6511i	−0.408395	−	0.707361i
$430$		0			0
$431$	−14.4613	+	25.0477i	−0.696577	+	1.20651i	0.273069	+	0.961994i	$0.411961\pi$
$431$	−14.4613	+	25.0477i	−0.696577	+	1.20651i	−0.969646	+	0.244512i	$0.921372\pi$
$432$		0			0
$433$			10.0338i			0.482192i	0.970501	+	0.241096i	$0.0775069\pi$
$433$			10.0338i			0.482192i	−0.970501	+	0.241096i	$0.922493\pi$
$434$		0			0
$435$	13.3853	−	1.72284i	0.641778	−	0.0826038i
$436$		0			0
$437$	27.7898	+	16.0444i	1.32937	+	0.767510i
$438$		0			0
$439$	−8.40744	−	14.5621i	−0.401265	−	0.695012i	0.592614	−	0.805487i	$-0.298096\pi$
$439$	−8.40744	−	14.5621i	−0.401265	−	0.695012i	−0.993879	+	0.110475i	$0.964763\pi$
$440$		0			0
$441$	0.361419	+	6.99066i	0.0172104	+	0.332889i
$442$		0			0
$443$	−8.81665	+	5.09030i	−0.418892	+	0.241847i	−0.694603	−	0.719393i	$-0.744420\pi$
$443$	−8.81665	+	5.09030i	−0.418892	+	0.241847i	0.275711	+	0.961241i	$0.411087\pi$
$444$		0			0
$445$	37.0410	+	15.4686i	1.75591	+	0.733280i
$446$		0			0
$447$			1.10317i			0.0521780i
$448$		0			0
$449$	33.9937			1.60426			0.802131	−	0.597148i	$-0.203700\pi$
$449$	33.9937			1.60426			0.802131	+	0.597148i	$0.203700\pi$
$450$		0			0
$451$	−1.56539	+	2.71133i	−0.0737112	+	0.127672i
$452$		0			0
$453$	9.06136	−	5.23158i	0.425740	−	0.245801i
$454$		0			0
$455$	−13.7815	−	31.2260i	−0.646085	−	1.46390i
$456$		0			0
$457$	20.5960	−	11.8911i	0.963442	−	0.556243i	0.0662113	−	0.997806i	$-0.478909\pi$
$457$	20.5960	−	11.8911i	0.963442	−	0.556243i	0.897231	+	0.441562i	$0.145576\pi$
$458$		0			0
$459$	0.118546	−	0.205328i	0.00553325	−	0.00958387i
$460$		0			0
$461$	−35.2649			−1.64245			−0.821224	−	0.570606i	$-0.806708\pi$
$461$	−35.2649			−1.64245			−0.821224	+	0.570606i	$0.806708\pi$
$462$		0			0
$463$			38.6505i			1.79624i	0.439750	+	0.898120i	$0.355067\pi$
$463$			38.6505i			1.79624i	−0.439750	+	0.898120i	$0.644933\pi$
$464$		0			0
$465$	−9.08098	+	21.7453i	−0.421120	+	1.00841i
$466$		0			0
$467$	−7.67142	+	4.42910i	−0.354991	+	0.204954i	−0.666881	−	0.745164i	$-0.732371\pi$
$467$	−7.67142	+	4.42910i	−0.354991	+	0.204954i	0.311890	+	0.950118i	$0.399038\pi$
$468$		0			0
$469$	−4.30427	−	4.08749i	−0.198753	−	0.188743i
$470$		0			0
$471$	4.53083	+	7.84763i	0.208770	+	0.361600i
$472$		0			0
$473$	−24.8791	−	14.3639i	−1.14394	−	0.660454i
$474$		0			0
$475$	22.9291	−	6.00187i	1.05206	−	0.275385i
$476$		0			0
$477$		−	11.0064i		−	0.503951i
$478$		0			0
$479$	−4.26797	+	7.39235i	−0.195009	+	0.337765i	−0.946903	−	0.321518i	$-0.895807\pi$
$479$	−4.26797	+	7.39235i	−0.195009	+	0.337765i	0.751895	+	0.659283i	$0.229140\pi$
$480$		0			0
$481$	−8.86787	−	15.3596i	−0.404340	−	0.700337i
$482$		0			0
$483$	−17.4137	−	4.18716i	−0.792351	−	0.190522i
$484$		0			0
$485$	−3.13423	−	4.10917i	−0.142318	−	0.186588i
$486$		0			0
$487$	1.70528	+	0.984545i	0.0772737	+	0.0446140i	0.538139	−	0.842856i	$-0.319128\pi$
$487$	1.70528	+	0.984545i	0.0772737	+	0.0446140i	−0.460865	+	0.887470i	$0.652461\pi$
$488$		0			0
$489$	−8.33883			−0.377095
$490$		0			0
$491$	21.4549			0.968246			0.484123	−	0.875000i	$-0.339139\pi$
$491$	21.4549			0.968246			0.484123	+	0.875000i	$0.339139\pi$
$492$		0			0
$493$	−1.23925	−	0.715483i	−0.0558131	−	0.0322237i
$494$		0			0
$495$	−5.21344	+	3.97651i	−0.234327	+	0.178731i
$496$		0			0
$497$	−30.4629	−	7.32485i	−1.36645	−	0.328565i
$498$		0			0
$499$	−7.47239	−	12.9426i	−0.334510	−	0.579389i	0.648880	−	0.760890i	$-0.275238\pi$
$499$	−7.47239	−	12.9426i	−0.334510	−	0.579389i	−0.983391	+	0.181502i	$0.941904\pi$
$500$		0			0
$501$	5.14431	−	8.91021i	0.229831	−	0.398079i
$502$		0			0
$503$		−	10.9715i		−	0.489195i	−0.969625	−	0.244597i	$-0.921344\pi$
$503$		−	10.9715i		−	0.489195i	0.969625	−	0.244597i	$-0.0786558\pi$
$504$		0			0
$505$	−2.23852	−	17.3919i	−0.0996130	−	0.773929i
$506$		0			0
$507$	17.5677	+	10.1427i	0.780211	+	0.450455i
$508$		0			0
$509$	−18.6050	−	32.2247i	−0.824650	−	1.42834i	−0.902186	−	0.431347i	$-0.858039\pi$
$509$	−18.6050	−	32.2247i	−0.824650	−	1.42834i	0.0775359	−	0.996990i	$-0.475295\pi$
$510$		0			0
$511$	−7.28454	−	6.91766i	−0.322249	−	0.306019i
$512$		0			0
$513$	4.10523	−	2.37016i	0.181251	−	0.104645i
$514$		0			0
$515$	−3.51614	+	8.41975i	−0.154940	+	0.371019i
$516$		0			0
$517$		−	10.8869i		−	0.478803i
$518$		0			0
$519$	−17.2937			−0.759111
$520$		0			0
$521$	−8.24999	+	14.2894i	−0.361439	+	0.626030i	−0.988198	−	0.153183i	$-0.951048\pi$
$521$	−8.24999	+	14.2894i	−0.361439	+	0.626030i	0.626759	+	0.779213i	$0.284381\pi$
$522$		0			0
$523$	36.6757	−	21.1747i	1.60372	−	0.925907i	0.612982	−	0.790097i	$-0.289970\pi$
$523$	36.6757	−	21.1747i	1.60372	−	0.925907i	0.990735	−	0.135810i	$-0.0433637\pi$
$524$		0			0
$525$	−11.3216	+	6.84264i	−0.494114	+	0.298637i
$526$		0			0
$527$	2.16389	−	1.24932i	0.0942605	−	0.0544213i
$528$		0			0
$529$	11.4121	−	19.7663i	0.496178	−	0.859406i
$530$		0			0
$531$	−9.31265			−0.404135
$532$		0			0
$533$		−	6.15982i		−	0.266811i
$534$		0			0
$535$	−15.8090	+	37.8561i	−0.683481	+	1.63666i
$536$		0			0
$537$	9.54303	−	5.50967i	0.411812	−	0.237760i
$538$		0			0
$539$	−17.2226	+	11.1672i	−0.741832	+	0.481007i
$540$		0			0
$541$	21.1579	+	36.6466i	0.909650	+	1.57556i	0.814550	+	0.580093i	$0.196984\pi$
$541$	21.1579	+	36.6466i	0.909650	+	1.57556i	0.0951000	+	0.995468i	$0.469683\pi$
$542$		0			0
$543$	−3.92902	−	2.26842i	−0.168611	−	0.0973473i
$544$		0			0
$545$	2.97280	+	23.0967i	0.127341	+	0.989356i
$546$		0			0
$547$			1.34528i			0.0575199i	0.999586	+	0.0287599i	$0.00915583\pi$
$547$			1.34528i			0.0575199i	−0.999586	+	0.0287599i	$0.990844\pi$
$548$		0			0
$549$	−4.06861	+	7.04704i	−0.173644	+	0.300760i
$550$		0			0
$551$	−14.3051	−	24.7771i	−0.609416	−	1.05554i
$552$		0			0
$553$	0.0131179	+	0.0443428i	0.000557831	+	0.00188565i
$554$		0			0
$555$	−5.46556	+	4.16881i	−0.232000	+	0.176956i
$556$		0			0
$557$	2.58930	+	1.49493i	0.109712	+	0.0633424i	0.553852	−	0.832615i	$-0.313157\pi$
$557$	2.58930	+	1.49493i	0.109712	+	0.0633424i	−0.444140	+	0.895958i	$0.646491\pi$
$558$		0			0
$559$	56.5222			2.39063
$560$		0			0
$561$	0.695230			0.0293526
$562$		0			0
$563$	15.7647	+	9.10174i	0.664402	+	0.383592i	0.793952	−	0.607980i	$-0.208020\pi$
$563$	15.7647	+	9.10174i	0.664402	+	0.383592i	−0.129550	+	0.991573i	$0.541353\pi$
$564$		0			0
$565$	−2.91324	−	3.81943i	−0.122561	−	0.160685i
$566$		0			0
$567$	−1.82189	+	1.91852i	−0.0765123	+	0.0805702i
$568$		0			0
$569$	−9.88700	−	17.1248i	−0.414484	−	0.717908i	0.580890	−	0.813982i	$-0.302705\pi$
$569$	−9.88700	−	17.1248i	−0.414484	−	0.717908i	−0.995374	+	0.0960741i	$0.969371\pi$
$570$		0			0
$571$	9.87481	−	17.1037i	0.413248	−	0.715767i	−0.581995	−	0.813193i	$-0.697728\pi$
$571$	9.87481	−	17.1037i	0.413248	−	0.715767i	0.995243	+	0.0974259i	$0.0310609\pi$
$572$		0			0
$573$			8.68052i			0.362634i
$574$		0			0
$575$	−8.57090	−	32.7436i	−0.357431	−	1.36550i
$576$		0			0
$577$	−14.7851	−	8.53616i	−0.615510	−	0.355365i	0.159609	−	0.987180i	$-0.448977\pi$
$577$	−14.7851	−	8.53616i	−0.615510	−	0.355365i	−0.775119	+	0.631815i	$0.782310\pi$
$578$		0			0
$579$	3.53061	+	6.11520i	0.146727	+	0.254139i
$580$		0			0
$581$	−4.51639	+	18.7829i	−0.187371	+	0.779247i
$582$		0			0
$583$	27.9505	−	16.1372i	1.15759	−	0.668336i
$584$		0			0
$585$	4.97133	−	11.9043i	0.205539	−	0.492184i
$586$		0			0
$587$		−	17.5308i		−	0.723575i	−0.932261	−	0.361787i	$-0.882167\pi$
$587$		−	17.5308i		−	0.723575i	0.932261	−	0.361787i	$-0.117833\pi$
$588$		0			0
$589$	49.9568			2.05844
$590$		0			0
$591$	−1.79446	+	3.10809i	−0.0738141	+	0.127850i
$592$		0			0
$593$	22.6519	−	13.0781i	0.930201	−	0.537052i	0.0433259	−	0.999061i	$-0.486205\pi$
$593$	22.6519	−	13.0781i	0.930201	−	0.537052i	0.886875	+	0.462009i	$0.152871\pi$
$594$		0			0
$595$	1.39449	+	0.151144i	0.0571684	+	0.00619630i
$596$		0			0
$597$	2.58294	−	1.49126i	0.105713	−	0.0610332i
$598$		0			0
$599$	14.9595	−	25.9107i	0.611229	−	1.05868i	−0.379804	−	0.925067i	$-0.624009\pi$
$599$	14.9595	−	25.9107i	0.611229	−	1.05868i	0.991034	−	0.133614i	$-0.0426581\pi$
$600$		0			0
$601$	15.6887			0.639955			0.319977	−	0.947425i	$-0.396325\pi$
$601$	15.6887			0.639955			0.319977	+	0.947425i	$0.396325\pi$
$602$		0			0
$603$		−	2.24354i		−	0.0913640i
$604$		0			0
$605$	4.95517	+	2.06931i	0.201456	+	0.0841295i
$606$		0			0
$607$	30.0913	−	17.3732i	1.22137	−	0.705156i	0.256157	−	0.966635i	$-0.417544\pi$
$607$	30.0913	−	17.3732i	1.22137	−	0.705156i	0.965209	+	0.261479i	$0.0842102\pi$
$608$		0			0
$609$	11.5792	+	10.9960i	0.469213	+	0.445581i
$610$		0			0
$611$	10.7100	+	18.5502i	0.433279	+	0.750461i
$612$		0			0
$613$	5.50712	+	3.17954i	0.222430	+	0.128420i	0.607075	−	0.794644i	$-0.292343\pi$
$613$	5.50712	+	3.17954i	0.222430	+	0.128420i	−0.384645	+	0.923065i	$0.625676\pi$
$614$		0			0
$615$	−2.36787	+	0.304770i	−0.0954817	+	0.0122895i
$616$		0			0
$617$		−	25.1778i		−	1.01362i	−0.862057	−	0.506811i	$-0.830824\pi$
$617$		−	25.1778i		−	1.01362i	0.862057	−	0.506811i	$-0.169176\pi$
$618$		0			0
$619$	3.35963	−	5.81904i	0.135035	−	0.233887i	−0.790576	−	0.612364i	$-0.790219\pi$
$619$	3.35963	−	5.81904i	0.135035	−	0.233887i	0.925611	+	0.378477i	$0.123552\pi$
$620$		0			0
$621$	−3.38468	−	5.86244i	−0.135822	−	0.235251i
$622$		0			0
$623$	13.4734	+	45.5445i	0.539801	+	1.82470i
$624$		0			0
$625$	−21.5046	−	12.7497i	−0.860182	−	0.509987i
$626$		0			0
$627$	12.0379	+	6.95007i	0.480746	+	0.277559i
$628$		0			0
$629$	0.728851			0.0290612
$630$		0			0
$631$	0.439228			0.0174854			0.00874269	−	0.999962i	$-0.497217\pi$
$631$	0.439228			0.0174854			0.00874269	+	0.999962i	$0.497217\pi$
$632$		0			0
$633$	18.5566	+	10.7136i	0.737558	+	0.425829i
$634$		0			0
$635$	2.47429	+	3.24395i	0.0981894	+	0.128732i
$636$		0			0
$637$	18.3600	−	35.9708i	0.727450	−	1.42521i
$638$		0			0
$639$	−5.92103	−	10.2555i	−0.234232	−	0.405702i
$640$		0			0
$641$	5.53886	−	9.59358i	0.218772	−	0.378924i	−0.735661	−	0.677350i	$-0.763128\pi$
$641$	5.53886	−	9.59358i	0.218772	−	0.378924i	0.954433	+	0.298426i	$0.0964617\pi$
$642$		0			0
$643$		−	16.2243i		−	0.639826i	−0.947447	−	0.319913i	$-0.896346\pi$
$643$		−	16.2243i		−	0.639826i	0.947447	−	0.319913i	$-0.103654\pi$
$644$		0			0
$645$	−2.79656	−	21.7274i	−0.110114	−	0.855517i
$646$		0			0
$647$	−22.4844	−	12.9813i	−0.883951	−	0.510349i	−0.0119921	−	0.999928i	$-0.503817\pi$
$647$	−22.4844	−	12.9813i	−0.883951	−	0.510349i	−0.871959	+	0.489579i	$0.837151\pi$
$648$		0			0
$649$	−13.6538	−	23.6492i	−0.535960	−	0.928310i
$650$		0			0
$651$	−26.7374	+	7.90972i	−1.04792	+	0.310006i
$652$		0			0
$653$	−6.34249	+	3.66184i	−0.248201	+	0.143299i	−0.618940	−	0.785438i	$-0.712438\pi$
$653$	−6.34249	+	3.66184i	−0.248201	+	0.143299i	0.370739	+	0.928737i	$0.379104\pi$
$654$		0			0
$655$	−5.58402	−	2.33193i	−0.218186	−	0.0911159i
$656$		0			0
$657$		−	3.79697i		−	0.148134i
$658$		0			0
$659$	−2.45499			−0.0956328			−0.0478164	−	0.998856i	$-0.515226\pi$
$659$	−2.45499			−0.0956328			−0.0478164	+	0.998856i	$0.515226\pi$
$660$		0			0
$661$	7.64417	−	13.2401i	0.297324	−	0.514980i	−0.678199	−	0.734878i	$-0.737239\pi$
$661$	7.64417	−	13.2401i	0.297324	−	0.514980i	0.975523	+	0.219898i	$0.0705726\pi$
$662$		0			0
$663$	−1.18461	+	0.683934i	−0.0460064	+	0.0265618i
$664$		0			0
$665$	22.6345	+	16.5574i	0.877729	+	0.642070i
$666$		0			0
$667$	−35.3827	+	20.4282i	−1.37002	+	0.790983i
$668$		0			0
$669$	−8.19845	+	14.2001i	−0.316971	+	0.549009i
$670$		0			0
$671$	−23.8610			−0.921142
$672$		0			0
$673$			39.7823i			1.53349i	0.641950	+	0.766747i	$0.278126\pi$
$673$			39.7823i			1.53349i	−0.641950	+	0.766747i	$0.721874\pi$
$674$		0			0
$675$	−4.82206	−	1.32201i	−0.185601	−	0.0508844i
$676$		0			0
$677$	28.1167	−	16.2332i	1.08061	−	0.623892i	0.149551	−	0.988754i	$-0.452217\pi$
$677$	28.1167	−	16.2332i	1.08061	−	0.623892i	0.931061	+	0.364862i	$0.118884\pi$
$678$		0			0
$679$	1.42960	−	5.94545i	0.0548628	−	0.228165i
$680$		0			0
$681$	4.76685	+	8.25642i	0.182666	+	0.316387i
$682$		0			0
$683$	8.98285	+	5.18625i	0.343719	+	0.198446i	0.661916	−	0.749578i	$-0.269744\pi$
$683$	8.98285	+	5.18625i	0.343719	+	0.198446i	−0.318196	+	0.948025i	$0.603077\pi$
$684$		0			0
$685$	22.1889	−	2.85595i	0.847793	−	0.109120i
$686$		0			0
$687$		−	18.1197i		−	0.691311i
$688$		0			0
$689$	−31.7501	+	54.9927i	−1.20958	+	2.09506i
$690$		0			0
$691$	2.73852	+	4.74326i	0.104178	+	0.180442i	0.913402	−	0.407058i	$-0.133445\pi$
$691$	2.73852	+	4.74326i	0.104178	+	0.180442i	−0.809224	+	0.587500i	$0.800112\pi$
$692$		0			0
$693$	−7.54320	−	1.81378i	−0.286542	−	0.0688996i
$694$		0			0
$695$	3.68509	−	2.81077i	0.139783	−	0.106619i
$696$		0			0
$697$	0.219224	+	0.126569i	0.00830370	+	0.00479414i
$698$		0			0
$699$	−12.0544			−0.455939
$700$		0			0
$701$	29.8292			1.12663			0.563317	−	0.826241i	$-0.309525\pi$
$701$	29.8292			1.12663			0.563317	+	0.826241i	$0.309525\pi$
$702$		0			0
$703$	12.6200	+	7.28617i	0.475973	+	0.274803i
$704$		0			0
$705$	6.60091	−	5.03478i	0.248604	−	0.189621i
$706$		0			0
$707$	14.2874	−	15.0451i	0.537332	−	0.565830i
$708$		0			0
$709$	20.0525	+	34.7319i	0.753086	+	1.30438i	0.946320	+	0.323231i	$0.104769\pi$
$709$	20.0525	+	34.7319i	0.753086	+	1.30438i	−0.193234	+	0.981153i	$0.561898\pi$
$710$		0			0
$711$	−0.00873900	+	0.0151364i	−0.000327738	+	0.000567659i
$712$		0			0
$713$		−	71.3403i		−	2.67172i
$714$		0			0
$715$	37.5194	−	4.82915i	1.40315	−	0.180600i
$716$		0			0
$717$	−18.5215	−	10.6934i	−0.691698	−	0.399352i
$718$		0			0
$719$	−10.5888	−	18.3403i	−0.394895	−	0.683979i	0.598193	−	0.801352i	$-0.295886\pi$
$719$	−10.5888	−	18.3403i	−0.394895	−	0.683979i	−0.993088	+	0.117374i	$0.962552\pi$
$720$		0			0
$721$	−10.3527	+	3.06263i	−0.385554	+	0.114058i
$722$		0			0
$723$	14.8860	−	8.59443i	0.553616	−	0.319630i
$724$		0			0
$725$	−7.97901	+	29.1035i	−0.296333	+	1.08088i
$726$		0			0
$727$			12.3642i			0.458562i	0.973360	+	0.229281i	$0.0736375\pi$
$727$			12.3642i			0.458562i	−0.973360	+	0.229281i	$0.926362\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−1.16139	+	2.01159i	−0.0429556	+	0.0744013i
$732$		0			0
$733$	−31.5698	+	18.2268i	−1.16606	+	0.673222i	−0.952748	−	0.303763i	$-0.901757\pi$
$733$	−31.5698	+	18.2268i	−1.16606	+	0.673222i	−0.213308	+	0.976985i	$0.568424\pi$
$734$		0			0
$735$	−14.7358	−	5.27796i	−0.543537	−	0.194681i
$736$		0			0
$737$	5.69739	−	3.28939i	0.209866	−	0.121166i
$738$		0			0
$739$	−19.2136	+	33.2790i	−0.706785	+	1.22419i	0.259258	+	0.965808i	$0.416522\pi$
$739$	−19.2136	+	33.2790i	−0.706785	+	1.22419i	−0.966043	+	0.258380i	$0.916811\pi$
$740$		0			0
$741$	−27.3486			−1.00468
$742$		0			0
$743$			38.1561i			1.39981i	0.714235	+	0.699906i	$0.246775\pi$
$743$			38.1561i			1.39981i	−0.714235	+	0.699906i	$0.753225\pi$
$744$		0			0
$745$	−2.27625	−	0.950576i	−0.0833952	−	0.0348264i
$746$		0			0
$747$	−6.32339	+	3.65081i	−0.231361	+	0.133576i
$748$		0			0
$749$	−46.5468	+	13.7699i	−1.70078	+	0.503142i
$750$		0			0
$751$	6.58058	+	11.3979i	0.240129	+	0.415915i	0.960751	−	0.277413i	$-0.0894770\pi$
$751$	6.58058	+	11.3979i	0.240129	+	0.415915i	−0.720622	+	0.693328i	$0.756144\pi$
$752$		0			0
$753$	−20.0865	−	11.5969i	−0.731992	−	0.422616i
$754$		0			0
$755$	2.98672	+	23.2049i	0.108698	+	0.844513i
$756$		0			0
$757$		−	1.92272i		−	0.0698826i	−0.999389	−	0.0349413i	$-0.988876\pi$
$757$		−	1.92272i		−	0.0698826i	0.999389	−	0.0349413i	$-0.0111244\pi$
$758$		0			0
$759$	9.92497	−	17.1905i	0.360253	−	0.623977i
$760$		0			0
$761$	9.10658	+	15.7731i	0.330113	+	0.571773i	0.982534	−	0.186084i	$-0.0595797\pi$
$761$	9.10658	+	15.7731i	0.330113	+	0.571773i	−0.652420	+	0.757857i	$0.726246\pi$
$762$		0			0
$763$	−18.9739	+	19.9802i	−0.686901	+	0.723331i
$764$		0			0
$765$	0.321519	+	0.421531i	0.0116245	+	0.0152405i
$766$		0			0
$767$	46.5298	+	26.8640i	1.68009	+	0.970003i
$768$		0			0
$769$	−32.1465			−1.15923			−0.579617	−	0.814889i	$-0.696798\pi$
$769$	−32.1465			−1.15923			−0.579617	+	0.814889i	$0.696798\pi$
$770$		0			0
$771$	26.1561			0.941990
$772$		0			0
$773$	−25.3202	−	14.6186i	−0.910704	−	0.525795i	−0.0300465	−	0.999549i	$-0.509566\pi$
$773$	−25.3202	−	14.6186i	−0.910704	−	0.525795i	−0.880658	+	0.473753i	$0.842899\pi$
$774$		0			0
$775$	−37.0438	−	37.4749i	−1.33065	−	1.34614i
$776$		0			0
$777$	−7.90798	−	1.90149i	−0.283697	−	0.0682155i
$778$		0			0
$779$	2.53057	+	4.38307i	0.0906669	+	0.157040i
$780$		0			0
$781$	17.3624	−	30.0725i	0.621274	−	1.07608i
$782$		0			0
$783$			6.03549i			0.215691i
$784$		0			0
$785$	−20.0967	+	2.58666i	−0.717283	+	0.0923220i
$786$		0			0
$787$	6.24645	+	3.60639i	0.222662	+	0.128554i	0.607182	−	0.794563i	$-0.292300\pi$
$787$	6.24645	+	3.60639i	0.222662	+	0.128554i	−0.384520	+	0.923117i	$0.625633\pi$
$788$		0			0
$789$	3.84991	+	6.66823i	0.137060	+	0.237395i
$790$		0			0
$791$	1.32879	−	5.52624i	0.0472465	−	0.196490i
$792$		0			0
$793$	40.6569	−	23.4733i	1.44377	−	0.833561i
$794$		0			0
$795$	22.7104	+	9.48402i	0.805455	+	0.336364i
$796$		0			0
$797$			32.3827i			1.14706i	0.819186	+	0.573528i	$0.194425\pi$
$797$			32.3827i			1.14706i	−0.819186	+	0.573528i	$0.805575\pi$
$798$		0			0
$799$	−0.880253			−0.0311411
$800$		0			0
$801$	−8.97583	+	15.5466i	−0.317146	+	0.549312i
$802$		0			0
$803$	9.64226	−	5.56696i	0.340268	−	0.196454i
$804$		0			0
$805$	23.6447	−	32.3230i	0.833366	−	1.13924i
$806$		0			0
$807$	−21.6842	+	12.5194i	−0.763321	+	0.440704i
$808$		0			0
$809$	16.2132	−	28.0821i	0.570026	−	0.987313i	−0.426537	−	0.904470i	$-0.640267\pi$
$809$	16.2132	−	28.0821i	0.570026	−	0.987313i	0.996563	−	0.0828431i	$-0.0264000\pi$
$810$		0			0
$811$	5.01118			0.175966			0.0879832	−	0.996122i	$-0.471958\pi$
$811$	5.01118			0.175966			0.0879832	+	0.996122i	$0.471958\pi$
$812$		0			0
$813$			19.0885i			0.669461i
$814$		0			0
$815$	7.18539	−	17.2061i	0.251693	−	0.602704i
$816$		0			0
$817$	−40.2188	+	23.2204i	−1.40708	+	0.812377i
$818$		0			0
$819$	14.6372	−	4.33013i	0.511466	−	0.151307i
$820$		0			0
$821$	−25.5256	−	44.2116i	−0.890849	−	1.54300i	−0.838860	−	0.544348i	$-0.816777\pi$
$821$	−25.5256	−	44.2116i	−0.890849	−	1.54300i	−0.0519891	−	0.998648i	$-0.516556\pi$
$822$		0			0
$823$	−44.5317	−	25.7104i	−1.55228	−	0.896207i	−0.997956	−	0.0639036i	$-0.979645\pi$
$823$	−44.5317	−	25.7104i	−1.55228	−	0.896207i	−0.554320	−	0.832303i	$-0.687022\pi$
$824$		0			0
$825$	−3.71271	−	14.1837i	−0.129260	−	0.493815i
$826$		0			0
$827$		−	11.7679i		−	0.409211i	−0.978845	−	0.204605i	$-0.934409\pi$
$827$		−	11.7679i		−	0.409211i	0.978845	−	0.204605i	$-0.0655911\pi$
$828$		0			0
$829$	21.0994	−	36.5453i	0.732814	−	1.26927i	−0.222862	−	0.974850i	$-0.571540\pi$
$829$	21.0994	−	36.5453i	0.732814	−	1.26927i	0.955676	−	0.294421i	$-0.0951268\pi$
$830$		0			0
$831$	−6.06933	−	10.5124i	−0.210543	−	0.364671i
$832$		0			0
$833$	0.902924	+	1.39253i	0.0312845	+	0.0482484i
$834$		0			0
$835$	13.9524	+	18.2924i	0.482841	+	0.633034i
$836$		0			0
$837$	−9.12679	−	5.26936i	−0.315468	−	0.182136i
$838$		0			0
$839$	34.6127			1.19496			0.597482	−	0.801882i	$-0.296168\pi$
$839$	34.6127			1.19496			0.597482	+	0.801882i	$0.296168\pi$
$840$		0			0
$841$	7.42713			0.256108
$842$		0			0
$843$	5.49525	+	3.17269i	0.189267	+	0.109273i
$844$		0			0
$845$	−36.0660	+	27.5090i	−1.24071	+	0.946339i
$846$		0			0
$847$	1.80241	+	6.09273i	0.0619316	+	0.209349i
$848$		0			0
$849$	6.80964	+	11.7947i	0.233706	+	0.404791i
$850$		0			0
$851$	10.4049	−	18.0219i	0.356676	−	0.617782i
$852$		0			0
$853$		−	7.87710i		−	0.269707i	−0.990866	−	0.134853i	$-0.956944\pi$
$853$		−	7.87710i		−	0.269707i	0.990866	−	0.134853i	$-0.0430564\pi$
$854$		0			0
$855$	1.35313	+	10.5129i	0.0462761	+	0.359535i
$856$		0			0
$857$	−3.88158	−	2.24103i	−0.132592	−	0.0765522i	0.432237	−	0.901760i	$-0.357725\pi$
$857$	−3.88158	−	2.24103i	−0.132592	−	0.0765522i	−0.564829	+	0.825208i	$0.691058\pi$
$858$		0			0
$859$	13.2214	+	22.9002i	0.451110	+	0.781345i	0.998455	−	0.0555615i	$-0.0176949\pi$
$859$	13.2214	+	22.9002i	0.451110	+	0.781345i	−0.547345	+	0.836907i	$0.684362\pi$
$860$		0			0
$861$	−2.04836	−	1.94519i	−0.0698079	−	0.0662920i
$862$		0			0
$863$	−32.9090	+	19.0000i	−1.12024	+	0.646768i	−0.941461	−	0.337122i	$-0.890547\pi$
$863$	−32.9090	+	19.0000i	−1.12024	+	0.646768i	−0.178775	+	0.983890i	$0.557213\pi$
$864$		0			0
$865$	14.9016	−	35.6834i	0.506671	−	1.21327i
$866$		0			0
$867$			16.9438i			0.575441i
$868$		0			0
$869$	−0.0512511			−0.00173858
$870$		0			0
$871$	−6.47189	+	11.2096i	−0.219292	+	0.379824i
$872$		0			0
$873$	2.00157	−	1.15561i	0.0677430	−	0.0391115i
$874$		0			0
$875$	−4.36336	−	29.2568i	−0.147509	−	0.989061i
$876$		0			0
$877$	11.1355	−	6.42910i	0.376020	−	0.217095i	−0.300065	−	0.953919i	$-0.597008\pi$
$877$	11.1355	−	6.42910i	0.376020	−	0.217095i	0.676085	+	0.736823i	$0.263675\pi$
$878$		0			0
$879$	−7.76107	+	13.4426i	−0.261774	+	0.453406i
$880$		0			0
$881$	32.9744			1.11094			0.555468	−	0.831538i	$-0.312539\pi$
$881$	32.9744			1.11094			0.555468	+	0.831538i	$0.312539\pi$
$882$		0			0
$883$			20.3321i			0.684229i	0.939658	+	0.342115i	$0.111143\pi$
$883$			20.3321i			0.684229i	−0.939658	+	0.342115i	$0.888857\pi$
$884$		0			0
$885$	8.02451	−	19.2155i	0.269741	−	0.645921i
$886$		0			0
$887$	−34.8639	+	20.1287i	−1.17062	+	0.675856i	−0.953825	−	0.300362i	$-0.902892\pi$
$887$	−34.8639	+	20.1287i	−1.17062	+	0.675856i	−0.216791	+	0.976218i	$0.569559\pi$
$888$		0			0
$889$	−1.12858	+	4.69359i	−0.0378515	+	0.157418i
$890$		0			0
$891$	−1.46616	−	2.53947i	−0.0491182	−	0.0850753i
$892$		0			0
$893$	−15.2415	−	8.79970i	−0.510039	−	0.294471i
$894$		0			0
$895$	3.14549	+	24.4384i	0.105142	+	0.816886i
$896$		0			0
$897$			39.0548i			1.30400i
$898$		0			0
$899$	−31.8031	+	55.0847i	−1.06069	+	1.83718i
$900$		0			0
$901$	−1.30477	−	2.25993i	−0.0434682	−	0.0752891i
$902$		0			0
$903$	17.8490	−	18.7957i	0.593978	−	0.625480i
$904$		0			0
$905$	8.06616	−	6.15239i	0.268128	−	0.204512i
$906$		0			0
$907$	41.7005	+	24.0758i	1.38464	+	0.799423i	0.992705	−	0.120569i	$-0.0384720\pi$
$907$	41.7005	+	24.0758i	1.38464	+	0.799423i	0.391936	+	0.919992i	$0.371805\pi$
$908$		0			0
$909$	7.84205			0.260104
$910$		0			0
$911$	−30.2224			−1.00131			−0.500656	−	0.865646i	$-0.666908\pi$
$911$	−30.2224			−1.00131			−0.500656	+	0.865646i	$0.666908\pi$
$912$		0			0
$913$	−18.5422	−	10.7054i	−0.613658	−	0.354295i
$914$		0			0
$915$	−11.0348	−	14.4674i	−0.364801	−	0.478276i
$916$		0			0
$917$	−2.03115	−	6.86595i	−0.0670746	−	0.226734i
$918$		0			0
$919$	12.6387	+	21.8908i	0.416911	+	0.722111i	0.995627	−	0.0934183i	$-0.0297794\pi$
$919$	12.6387	+	21.8908i	0.416911	+	0.722111i	−0.578716	+	0.815529i	$0.696446\pi$
$920$		0			0
$921$	−6.72028	+	11.6399i	−0.221441	+	0.383547i
$922$		0			0
$923$			68.3210i			2.24881i
$924$		0			0
$925$	−3.89225	−	14.8697i	−0.127976	−	0.488911i
$926$		0			0
$927$	−3.53388	−	2.04029i	−0.116068	−	0.0670118i
$928$		0			0
$929$	−13.8502	−	23.9892i	−0.454409	−	0.787060i	0.544245	−	0.838927i	$-0.316816\pi$
$929$	−13.8502	−	23.9892i	−0.454409	−	0.787060i	−0.998654	+	0.0518664i	$0.983483\pi$
$930$		0			0
$931$	1.71324	+	33.1380i	0.0561492	+	1.08605i
$932$		0			0
$933$	2.12314	−	1.22580i	0.0695085	−	0.0401308i
$934$		0			0
$935$	−0.599065	+	1.43452i	−0.0195915	+	0.0469138i
$936$		0			0
$937$			30.8163i			1.00673i	0.864075	+	0.503363i	$0.167904\pi$
$937$			30.8163i			1.00673i	−0.864075	+	0.503363i	$0.832096\pi$
$938$		0			0
$939$	−9.91942			−0.323708
$940$		0			0
$941$	14.1180	−	24.4532i	0.460235	−	0.797151i	−0.538737	−	0.842474i	$-0.681098\pi$
$941$	14.1180	−	24.4532i	0.460235	−	0.797151i	0.998972	+	0.0453231i	$0.0144317\pi$
$942$		0			0
$943$	6.25919	−	3.61375i	0.203827	−	0.117680i
$944$		0			0
$945$	−2.38873	−	5.41239i	−0.0777055	−	0.176065i
$946$		0			0
$947$	−2.59436	+	1.49785i	−0.0843052	+	0.0486736i	−0.541560	−	0.840662i	$-0.682166\pi$
$947$	−2.59436	+	1.49785i	−0.0843052	+	0.0486736i	0.457255	+	0.889336i	$0.348833\pi$
$948$		0			0
$949$	−10.9530	+	18.9712i	−0.355550	+	0.615831i
$950$		0			0
$951$	25.9950			0.842947
$952$		0			0
$953$			10.0423i			0.325303i	0.986684	+	0.162651i	$0.0520046\pi$
$953$			10.0423i			0.325303i	−0.986684	+	0.162651i	$0.947995\pi$
$954$		0			0
$955$	−17.9112	−	7.47982i	−0.579591	−	0.242041i
$956$		0			0
$957$	−15.3269	+	8.84900i	−0.495449	+	0.286047i
$958$		0			0
$959$	19.1948	+	18.2281i	0.619832	+	0.588615i
$960$		0			0
$961$	−40.0322	−	69.3379i	−1.29136	−	2.23671i
$962$		0			0
$963$	−15.8887	−	9.17335i	−0.512007	−	0.295607i
$964$		0			0
$965$	−15.6602	+	2.01564i	−0.504120	+	0.0648857i
$966$		0			0
$967$			21.3514i			0.686616i	0.939223	+	0.343308i	$0.111547\pi$
$967$			21.3514i			0.686616i	−0.939223	+	0.343308i	$0.888453\pi$
$968$		0			0
$969$	0.561945	−	0.973318i	0.0180523	−	0.0312675i
$970$		0			0
$971$	−19.0000	−	32.9090i	−0.609740	−	1.05610i	−0.991283	−	0.131749i	$-0.957941\pi$
$971$	−19.0000	−	32.9090i	−0.609740	−	1.05610i	0.381543	−	0.924351i	$-0.375393\pi$
$972$		0			0
$973$	5.33186	+	1.28206i	0.170932	+	0.0411009i
$974$		0			0
$975$	20.2794	+	20.5154i	0.649461	+	0.657019i
$976$		0			0
$977$	−37.0401	−	21.3851i	−1.18502	−	0.684170i	−0.227848	−	0.973697i	$-0.573169\pi$
$977$	−37.0401	−	21.3851i	−1.18502	−	0.684170i	−0.957170	+	0.289526i	$0.906502\pi$
$978$		0			0
$979$	−52.6401			−1.68238
$980$		0			0
$981$	−10.4144			−0.332506
$982$		0			0
$983$	−11.6735	−	6.73968i	−0.372326	−	0.214962i	0.302148	−	0.953261i	$-0.402296\pi$
$983$	−11.6735	−	6.73968i	−0.372326	−	0.214962i	−0.674474	+	0.738299i	$0.735630\pi$
$984$		0			0
$985$	−4.86691	−	6.38081i	−0.155073	−	0.203310i
$986$		0			0
$987$	9.55068	+	2.29648i	0.304002	+	0.0730978i
$988$		0			0
$989$	33.1596	+	57.4341i	1.05441	+	1.82630i
$990$		0			0
$991$	−13.2993	+	23.0351i	−0.422467	+	0.731735i	−0.996180	−	0.0873218i	$-0.972169\pi$
$991$	−13.2993	+	23.0351i	−0.422467	+	0.731735i	0.573713	+	0.819056i	$0.305503\pi$
$992$		0			0
$993$			7.53226i			0.239029i
$994$		0			0
$995$	0.851365	+	6.61456i	0.0269901	+	0.209696i
$996$		0			0
$997$	−12.4598	−	7.19366i	−0.394605	−	0.227825i	0.289548	−	0.957163i	$-0.406495\pi$
$997$	−12.4598	−	7.19366i	−0.394605	−	0.227825i	−0.684154	+	0.729338i	$0.739828\pi$
$998$		0			0
$999$	−1.53706	−	2.66227i	−0.0486305	−	0.0842306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bb.a.109.4	✓	16
3.2	odd	2		1260.2.bm.c.109.2		16
4.3	odd	2		1680.2.di.e.529.8		16
5.2	odd	4		2100.2.q.l.1201.3		8
5.3	odd	4		2100.2.q.m.1201.2		8
5.4	even	2	inner	420.2.bb.a.109.5	yes	16
7.2	even	3	inner	420.2.bb.a.289.5	yes	16
7.3	odd	6		2940.2.k.g.589.2		8
7.4	even	3		2940.2.k.f.589.7		8
7.5	odd	6		2940.2.bb.i.1549.4		16
7.6	odd	2		2940.2.bb.i.949.5		16
15.14	odd	2		1260.2.bm.c.109.7		16
20.19	odd	2		1680.2.di.e.529.1		16
21.2	odd	6		1260.2.bm.c.289.7		16
28.23	odd	6		1680.2.di.e.289.1		16
35.2	odd	12		2100.2.q.l.1801.3		8
35.4	even	6		2940.2.k.f.589.3		8
35.9	even	6	inner	420.2.bb.a.289.4	yes	16
35.19	odd	6		2940.2.bb.i.1549.5		16
35.23	odd	12		2100.2.q.m.1801.2		8
35.24	odd	6		2940.2.k.g.589.6		8
35.34	odd	2		2940.2.bb.i.949.4		16
105.44	odd	6		1260.2.bm.c.289.2		16
140.79	odd	6		1680.2.di.e.289.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bb.a.109.4	✓	16	1.1	even	1	trivial
420.2.bb.a.109.5	yes	16	5.4	even	2	inner
420.2.bb.a.289.4	yes	16	35.9	even	6	inner
420.2.bb.a.289.5	yes	16	7.2	even	3	inner
1260.2.bm.c.109.2		16	3.2	odd	2
1260.2.bm.c.109.7		16	15.14	odd	2
1260.2.bm.c.289.2		16	105.44	odd	6
1260.2.bm.c.289.7		16	21.2	odd	6
1680.2.di.e.289.1		16	28.23	odd	6
1680.2.di.e.289.8		16	140.79	odd	6
1680.2.di.e.529.1		16	20.19	odd	2
1680.2.di.e.529.8		16	4.3	odd	2
2100.2.q.l.1201.3		8	5.2	odd	4
2100.2.q.l.1801.3		8	35.2	odd	12
2100.2.q.m.1201.2		8	5.3	odd	4
2100.2.q.m.1801.2		8	35.23	odd	12
2940.2.k.f.589.3		8	35.4	even	6
2940.2.k.f.589.7		8	7.4	even	3
2940.2.k.g.589.2		8	7.3	odd	6
2940.2.k.g.589.6		8	35.24	odd	6
2940.2.bb.i.949.4		16	35.34	odd	2
2940.2.bb.i.949.5		16	7.6	odd	2
2940.2.bb.i.1549.4		16	7.5	odd	6
2940.2.bb.i.1549.5		16	35.19	odd	6

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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{3} +(1.77792 - 1.35609i) q^{5} +(2.57243 + 0.618546i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-1.46616 + 2.53947i) q^{11} -5.76936i q^{13} +(-2.21777 + 0.285451i) q^{15} +(0.205328 + 0.118546i) q^{17} +(2.37016 + 4.10523i) q^{19} +(-1.91852 - 1.82189i) q^{21} +(5.86244 - 3.38468i) q^{23} +(1.32201 - 4.82206i) q^{25} -1.00000i q^{27} -6.03549 q^{29} +(5.26936 - 9.12679i) q^{31} +(2.53947 - 1.46616i) q^{33} +(5.41239 - 2.38873i) q^{35} +(2.66227 - 1.53706i) q^{37} +(-2.88468 + 4.99641i) q^{39} +1.06768 q^{41} +9.79697i q^{43} +(2.06337 + 0.861678i) q^{45} +(-3.21530 + 1.85635i) q^{47} +(6.23480 + 3.18233i) q^{49} +(-0.118546 - 0.205328i) q^{51} +(-9.53186 - 5.50322i) q^{53} +(0.837035 + 6.50322i) q^{55} -4.74032i q^{57} +(-4.65633 + 8.06499i) q^{59} +(4.06861 + 7.04704i) q^{61} +(0.750539 + 2.53706i) q^{63} +(-7.82379 - 10.2575i) q^{65} +(-1.94296 - 1.12177i) q^{67} -6.76936 q^{69} -11.8421 q^{71} +(-3.28827 - 1.89848i) q^{73} +(-3.55593 + 3.51502i) q^{75} +(-5.34237 + 5.62571i) q^{77} +(0.00873900 + 0.0151364i) q^{79} +(-0.500000 + 0.866025i) q^{81} +7.30162i q^{83} +(0.525816 - 0.0676782i) q^{85} +(5.22689 + 3.01774i) q^{87} +(8.97583 + 15.5466i) q^{89} +(3.56861 - 14.8413i) q^{91} +(-9.12679 + 5.26936i) q^{93} +(9.78104 + 4.08463i) q^{95} -2.31122i q^{97} -2.93232 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{5} + 8 q^{9} - 8 q^{11} + 4 q^{15} + 8 q^{19} - 4 q^{21} + 12 q^{25} + 24 q^{29} + 10 q^{35} - 4 q^{39} + 48 q^{41} - 2 q^{45} + 8 q^{49} + 4 q^{51} - 40 q^{55} - 28 q^{59} - 32 q^{61} - 26 q^{65}+ \cdots - 16 q^{99}+O(q^{100}) \) 16 * q + 2 * q^5 + 8 * q^9 - 8 * q^11 + 4 * q^15 + 8 * q^19 - 4 * q^21 + 12 * q^25 + 24 * q^29 + 10 * q^35 - 4 * q^39 + 48 * q^41 - 2 * q^45 + 8 * q^49 + 4 * q^51 - 40 * q^55 - 28 * q^59 - 32 * q^61 - 26 * q^65 - 24 * q^69 - 56 * q^71 - 8 * q^75 - 16 * q^79 - 8 * q^81 + 32 * q^85 - 16 * q^89 - 40 * q^91 + 22 * q^95 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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