LMFDB - Embedded newform 624.2.bv.f.433.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [624,2,Mod(49,624)] 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("624.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(624, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.bv (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,2,0,0,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-43})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 10x^{2} - 11x + 121 $ x^4 - x^3 - 10x^2 - 11x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 156)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			433.1
Root			$-2.58945 - 2.07237i$ of defining polynomial
Character	$\chi$	$=$	624.433
Dual form			624.2.bv.f.49.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{3} -4.14474i q^{5} +(-2.08945 + 1.20635i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-3.00000 - 1.73205i) q^{11} +(1.50000 + 3.27872i) q^{13} +(-3.58945 - 2.07237i) q^{15} +(-2.58945 - 4.48507i) q^{17} +(3.00000 - 1.73205i) q^{19} +2.41269i q^{21} +(-1.00000 + 1.73205i) q^{23} -12.1789 q^{25} -1.00000 q^{27} +(-1.58945 + 2.75302i) q^{29} +1.05141i q^{31} +(-3.00000 + 1.73205i) q^{33} +(5.00000 + 8.66025i) q^{35} +(6.58945 + 3.80442i) q^{37} +(3.58945 + 0.340322i) q^{39} +(-0.589454 - 0.340322i) q^{41} +(-6.08945 - 10.5472i) q^{43} +(-3.58945 + 2.07237i) q^{45} -10.3923i q^{47} +(-0.589454 + 1.02096i) q^{49} -5.17891 q^{51} +1.17891 q^{53} +(-7.17891 + 12.4342i) q^{55} -3.46410i q^{57} +(10.1789 - 5.87680i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(2.08945 + 1.20635i) q^{63} +(13.5895 - 6.21712i) q^{65} +(2.08945 + 1.20635i) q^{67} +(1.00000 + 1.73205i) q^{69} +(3.00000 - 1.73205i) q^{71} -14.8469i q^{73} +(-6.08945 + 10.5472i) q^{75} +8.35782 q^{77} -1.82109 q^{79} +(-0.500000 + 0.866025i) q^{81} -1.36129i q^{83} +(-18.5895 + 10.7326i) q^{85} +(1.58945 + 2.75302i) q^{87} +(6.00000 + 3.46410i) q^{89} +(-7.08945 - 5.04121i) q^{91} +(0.910546 + 0.525704i) q^{93} +(-7.17891 - 12.4342i) q^{95} +(15.2684 - 8.81519i) q^{97} +3.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 3 q^{7} - 2 q^{9} - 12 q^{11} + 6 q^{13} - 3 q^{15} + q^{17} + 12 q^{19} - 4 q^{23} - 26 q^{25} - 4 q^{27} + 5 q^{29} - 12 q^{33} + 20 q^{35} + 15 q^{37} + 3 q^{39} + 9 q^{41} - 13 q^{43}+ \cdots + 27 q^{97}+O(q^{100}) $ 4 * q + 2 * q^3 + 3 * q^7 - 2 * q^9 - 12 * q^11 + 6 * q^13 - 3 * q^15 + q^17 + 12 * q^19 - 4 * q^23 - 26 * q^25 - 4 * q^27 + 5 * q^29 - 12 * q^33 + 20 * q^35 + 15 * q^37 + 3 * q^39 + 9 * q^41 - 13 * q^43 - 3 * q^45 + 9 * q^49 + 2 * q^51 - 18 * q^53 - 6 * q^55 + 18 * q^59 - 10 * q^61 - 3 * q^63 + 43 * q^65 - 3 * q^67 + 4 * q^69 + 12 * q^71 - 13 * q^75 - 12 * q^77 - 30 * q^79 - 2 * q^81 - 63 * q^85 - 5 * q^87 + 24 * q^89 - 17 * q^91 + 15 * q^93 - 6 * q^95 + 27 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$		−	4.14474i		−	1.85359i	−0.375572	−	0.926793i	$-0.622554\pi$
$5$		−	4.14474i		−	1.85359i	0.375572	−	0.926793i	$-0.377446\pi$
$6$		0			0
$7$	−2.08945	+	1.20635i	−0.789739	+	0.455956i	−0.839871	−	0.542786i	$-0.817369\pi$
$7$	−2.08945	+	1.20635i	−0.789739	+	0.455956i	0.0501314	+	0.998743i	$0.484036\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−3.00000	−	1.73205i	−0.904534	−	0.522233i	−0.0258656	−	0.999665i	$-0.508234\pi$
$11$	−3.00000	−	1.73205i	−0.904534	−	0.522233i	−0.878668	+	0.477432i	$0.841568\pi$
$12$		0			0
$13$	1.50000	+	3.27872i	0.416025	+	0.909353i
$13$	1.50000	+	3.27872i	0.416025	+	0.909353i
$14$		0			0
$15$	−3.58945	−	2.07237i	−0.926793	−	0.535084i
$16$		0			0
$17$	−2.58945	−	4.48507i	−0.628035	−	1.08779i	−0.987946	−	0.154802i	$-0.950526\pi$
$17$	−2.58945	−	4.48507i	−0.628035	−	1.08779i	0.359911	−	0.932987i	$-0.382807\pi$
$18$		0			0
$19$	3.00000	−	1.73205i	0.688247	−	0.397360i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.00000	−	1.73205i	0.688247	−	0.397360i	0.802955	+	0.596040i	$0.203260\pi$
$20$		0			0
$21$			2.41269i			0.526493i
$22$		0			0
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	−0.951247	−	0.308431i	$-0.900196\pi$
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	0.742732	+	0.669588i	$0.233529\pi$
$24$		0			0
$25$	−12.1789			−2.43578
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−1.58945	+	2.75302i	−0.295154	+	0.511222i	−0.975021	−	0.222114i	$-0.928704\pi$
$29$	−1.58945	+	2.75302i	−0.295154	+	0.511222i	0.679867	+	0.733336i	$0.262038\pi$
$30$		0			0
$31$			1.05141i			0.188838i	0.995533	+	0.0944192i	$0.0300994\pi$
$31$			1.05141i			0.188838i	−0.995533	+	0.0944192i	$0.969901\pi$
$32$		0			0
$33$	−3.00000	+	1.73205i	−0.522233	+	0.301511i
$34$		0			0
$35$	5.00000	+	8.66025i	0.845154	+	1.46385i
$36$		0			0
$37$	6.58945	+	3.80442i	1.08330	+	0.625443i	0.931785	−	0.363012i	$-0.118251\pi$
$37$	6.58945	+	3.80442i	1.08330	+	0.625443i	0.151515	+	0.988455i	$0.451585\pi$
$38$		0			0
$39$	3.58945	+	0.340322i	0.574773	+	0.0544951i
$40$		0			0
$41$	−0.589454	−	0.340322i	−0.0920573	−	0.0531493i	0.453265	−	0.891376i	$-0.350259\pi$
$41$	−0.589454	−	0.340322i	−0.0920573	−	0.0531493i	−0.545322	+	0.838227i	$0.683593\pi$
$42$		0			0
$43$	−6.08945	−	10.5472i	−0.928633	−	1.60844i	−0.785612	−	0.618720i	$-0.787652\pi$
$43$	−6.08945	−	10.5472i	−0.928633	−	1.60844i	−0.143022	−	0.989720i	$-0.545682\pi$
$44$		0			0
$45$	−3.58945	+	2.07237i	−0.535084	+	0.308931i
$46$		0			0
$47$		−	10.3923i		−	1.51587i	−0.652328	−	0.757937i	$-0.726208\pi$
$47$		−	10.3923i		−	1.51587i	0.652328	−	0.757937i	$-0.273792\pi$
$48$		0			0
$49$	−0.589454	+	1.02096i	−0.0842077	+	0.145852i
$50$		0			0
$51$	−5.17891			−0.725192
$52$		0			0
$53$	1.17891			0.161936			0.0809678	−	0.996717i	$-0.474199\pi$
$53$	1.17891			0.161936			0.0809678	+	0.996717i	$0.474199\pi$
$54$		0			0
$55$	−7.17891	+	12.4342i	−0.968004	+	1.67663i
$56$		0			0
$57$		−	3.46410i		−	0.458831i
$58$		0			0
$59$	10.1789	−	5.87680i	1.32518	−	0.765094i	0.340631	−	0.940197i	$-0.389359\pi$
$59$	10.1789	−	5.87680i	1.32518	−	0.765094i	0.984550	+	0.175103i	$0.0560260\pi$
$60$		0			0
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	0.660415	−	0.750901i	$-0.270381\pi$
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	−0.980507	+	0.196485i	$0.937047\pi$
$62$		0			0
$63$	2.08945	+	1.20635i	0.263246	+	0.151985i
$64$		0			0
$65$	13.5895	−	6.21712i	1.68556	−	0.771138i
$66$		0			0
$67$	2.08945	+	1.20635i	0.255267	+	0.147379i	0.622174	−	0.782879i	$-0.286250\pi$
$67$	2.08945	+	1.20635i	0.255267	+	0.147379i	−0.366906	+	0.930258i	$0.619583\pi$
$68$		0			0
$69$	1.00000	+	1.73205i	0.120386	+	0.208514i
$70$		0			0
$71$	3.00000	−	1.73205i	0.356034	−	0.205557i	−0.311305	−	0.950310i	$-0.600766\pi$
$71$	3.00000	−	1.73205i	0.356034	−	0.205557i	0.667340	+	0.744753i	$0.267433\pi$
$72$		0			0
$73$		−	14.8469i		−	1.73770i	−0.495074	−	0.868851i	$-0.664859\pi$
$73$		−	14.8469i		−	1.73770i	0.495074	−	0.868851i	$-0.335141\pi$
$74$		0			0
$75$	−6.08945	+	10.5472i	−0.703150	+	1.21789i
$76$		0			0
$77$	8.35782			0.952462
$78$		0			0
$79$	−1.82109			−0.204889			−0.102444	−	0.994739i	$-0.532666\pi$
$79$	−1.82109			−0.204889			−0.102444	+	0.994739i	$0.532666\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	1.36129i		−	0.149421i	−0.997205	−	0.0747103i	$-0.976197\pi$
$83$		−	1.36129i		−	0.149421i	0.997205	−	0.0747103i	$-0.0238032\pi$
$84$		0			0
$85$	−18.5895	+	10.7326i	−2.01631	+	1.16412i
$86$		0			0
$87$	1.58945	+	2.75302i	0.170407	+	0.295154i
$88$		0			0
$89$	6.00000	+	3.46410i	0.635999	+	0.367194i	0.783072	−	0.621932i	$-0.213652\pi$
$89$	6.00000	+	3.46410i	0.635999	+	0.367194i	−0.147073	+	0.989126i	$0.546985\pi$
$90$		0			0
$91$	−7.08945	−	5.04121i	−0.743177	−	0.528463i
$92$		0			0
$93$	0.910546	+	0.525704i	0.0944192	+	0.0545130i
$94$		0			0
$95$	−7.17891	−	12.4342i	−0.736540	−	1.27573i
$96$		0			0
$97$	15.2684	−	8.81519i	1.55027	−	0.895047i	0.552148	−	0.833746i	$-0.313808\pi$
$97$	15.2684	−	8.81519i	1.55027	−	0.895047i	0.998119	−	0.0613012i	$-0.0195250\pi$
$98$		0			0
$99$			3.46410i			0.348155i
$100$		0			0
$101$	−0.410546	+	0.711086i	−0.0408508	+	0.0707557i	−0.885728	−	0.464205i	$-0.846340\pi$
$101$	−0.410546	+	0.711086i	−0.0408508	+	0.0707557i	0.844877	+	0.534960i	$0.179674\pi$
$102$		0			0
$103$	8.17891			0.805892			0.402946	−	0.915224i	$-0.367986\pi$
$103$	8.17891			0.805892			0.402946	+	0.915224i	$0.367986\pi$
$104$		0			0
$105$	10.0000			0.975900
$106$		0			0
$107$	−5.00000	+	8.66025i	−0.483368	+	0.837218i	−0.999818	−	0.0190994i	$-0.993920\pi$
$107$	−5.00000	+	8.66025i	−0.483368	+	0.837218i	0.516449	+	0.856318i	$0.327253\pi$
$108$		0			0
$109$		−	1.05141i		−	0.100707i	−0.998731	−	0.0503533i	$-0.983965\pi$
$109$		−	1.05141i		−	0.100707i	0.998731	−	0.0503533i	$-0.0160347\pi$
$110$		0			0
$111$	6.58945	−	3.80442i	0.625443	−	0.361100i
$112$		0			0
$113$	−0.410546	−	0.711086i	−0.0386209	−	0.0668934i	0.846069	−	0.533074i	$-0.178963\pi$
$113$	−0.410546	−	0.711086i	−0.0386209	−	0.0668934i	−0.884690	+	0.466180i	$0.845630\pi$
$114$		0			0
$115$	7.17891	+	4.14474i	0.669437	+	0.386499i
$116$		0			0
$117$	2.08945	−	2.93840i	0.193170	−	0.271655i
$118$		0			0
$119$	10.8211	+	6.24756i	0.991968	+	0.572713i
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$		0			0
$123$	−0.589454	+	0.340322i	−0.0531493	+	0.0306858i
$124$		0			0
$125$			29.7547i			2.66135i
$126$		0			0
$127$	−7.08945	+	12.2793i	−0.629087	+	1.08961i	0.358648	+	0.933473i	$0.383238\pi$
$127$	−7.08945	+	12.2793i	−0.629087	+	1.08961i	−0.987735	+	0.156138i	$0.950095\pi$
$128$		0			0
$129$	−12.1789			−1.07229
$130$		0			0
$131$	16.3578			1.42919			0.714595	−	0.699539i	$-0.246611\pi$
$131$	16.3578			1.42919			0.714595	+	0.699539i	$0.246611\pi$
$132$		0			0
$133$	−4.17891	+	7.23808i	−0.362357	+	0.627621i
$134$		0			0
$135$			4.14474i			0.356723i
$136$		0			0
$137$	−5.41055	+	3.12378i	−0.462254	+	0.266883i	−0.712992	−	0.701173i	$-0.752660\pi$
$137$	−5.41055	+	3.12378i	−0.462254	+	0.266883i	0.250737	+	0.968055i	$0.419327\pi$
$138$		0			0
$139$	2.91055	+	5.04121i	0.246869	+	0.427590i	0.962656	−	0.270729i	$-0.0872648\pi$
$139$	2.91055	+	5.04121i	0.246869	+	0.427590i	−0.715786	+	0.698319i	$0.753932\pi$
$140$		0			0
$141$	−9.00000	−	5.19615i	−0.757937	−	0.437595i
$142$		0			0
$143$	1.17891	−	12.4342i	0.0985853	−	1.03980i
$144$		0			0
$145$	11.4105	+	6.58788i	0.947594	+	0.547094i
$146$		0			0
$147$	0.589454	+	1.02096i	0.0486174	+	0.0842077i
$148$		0			0
$149$	−0.589454	+	0.340322i	−0.0482900	+	0.0278802i	−0.523951	−	0.851749i	$-0.675542\pi$
$149$	−0.589454	+	0.340322i	−0.0482900	+	0.0278802i	0.475661	+	0.879629i	$0.342209\pi$
$150$		0			0
$151$		−	6.18667i		−	0.503464i	−0.967797	−	0.251732i	$-0.919000\pi$
$151$		−	6.18667i		−	0.503464i	0.967797	−	0.251732i	$-0.0810002\pi$
$152$		0			0
$153$	−2.58945	+	4.48507i	−0.209345	+	0.362596i
$154$		0			0
$155$	4.35782			0.350028
$156$		0			0
$157$	7.00000			0.558661			0.279330	−	0.960195i	$-0.409888\pi$
$157$	7.00000			0.558661			0.279330	+	0.960195i	$0.409888\pi$
$158$		0			0
$159$	0.589454	−	1.02096i	0.0467468	−	0.0809678i
$160$		0			0
$161$		−	4.82539i		−	0.380294i
$162$		0			0
$163$	0.910546	−	0.525704i	0.0713195	−	0.0411763i	−0.463916	−	0.885879i	$-0.653556\pi$
$163$	0.910546	−	0.525704i	0.0713195	−	0.0411763i	0.535236	+	0.844703i	$0.320223\pi$
$164$		0			0
$165$	7.17891	+	12.4342i	0.558877	+	0.968004i
$166$		0			0
$167$	−6.00000	−	3.46410i	−0.464294	−	0.268060i	0.249554	−	0.968361i	$-0.419716\pi$
$167$	−6.00000	−	3.46410i	−0.464294	−	0.268060i	−0.713848	+	0.700301i	$0.753049\pi$
$168$		0			0
$169$	−8.50000	+	9.83616i	−0.653846	+	0.756628i
$170$		0			0
$171$	−3.00000	−	1.73205i	−0.229416	−	0.132453i
$172$		0			0
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	−0.973670	−	0.227964i	$-0.926793\pi$
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	0.289412	−	0.957205i	$-0.406540\pi$
$174$		0			0
$175$	25.4473	−	14.6920i	1.92363	−	1.11061i
$176$		0			0
$177$		−	11.7536i		−	0.883454i
$178$		0			0
$179$	7.17891	−	12.4342i	0.536577	−	0.929378i	−0.462508	−	0.886615i	$-0.653051\pi$
$179$	7.17891	−	12.4342i	0.536577	−	0.929378i	0.999085	−	0.0427634i	$-0.0136162\pi$
$180$		0			0
$181$	13.5367			1.00618			0.503088	−	0.864235i	$-0.332197\pi$
$181$	13.5367			1.00618			0.503088	+	0.864235i	$0.332197\pi$
$182$		0			0
$183$	−5.00000			−0.369611
$184$		0			0
$185$	15.7684	−	27.3116i	1.15931	−	2.00799i
$186$		0			0
$187$			17.9403i			1.31192i
$188$		0			0
$189$	2.08945	−	1.20635i	0.151985	−	0.0877488i
$190$		0			0
$191$	10.1789	+	17.6304i	0.736520	+	1.27569i	0.954053	+	0.299637i	$0.0968656\pi$
$191$	10.1789	+	17.6304i	0.736520	+	1.27569i	−0.217533	+	0.976053i	$0.569801\pi$
$192$		0			0
$193$	−0.321092	−	0.185382i	−0.0231127	−	0.0133441i	0.488399	−	0.872620i	$-0.337581\pi$
$193$	−0.321092	−	0.185382i	−0.0231127	−	0.0133441i	−0.511512	+	0.859276i	$0.670914\pi$
$194$		0			0
$195$	1.41055	−	14.8774i	0.101011	−	1.06539i
$196$		0			0
$197$	14.3578	+	8.28949i	1.02295	+	0.590602i	0.914958	−	0.403550i	$-0.132224\pi$
$197$	14.3578	+	8.28949i	1.02295	+	0.590602i	0.107994	+	0.994152i	$0.465557\pi$
$198$		0			0
$199$	6.26836	+	10.8571i	0.444352	+	0.769641i	0.998007	−	0.0631055i	$-0.0201005\pi$
$199$	6.26836	+	10.8571i	0.444352	+	0.769641i	−0.553654	+	0.832747i	$0.686767\pi$
$200$		0			0
$201$	2.08945	−	1.20635i	0.147379	−	0.0850892i
$202$		0			0
$203$		−	7.66973i		−	0.538310i
$204$		0			0
$205$	−1.41055	+	2.44314i	−0.0985168	+	0.170636i
$206$		0			0
$207$	2.00000			0.139010
$208$		0			0
$209$	−12.0000			−0.830057
$210$		0			0
$211$	9.26836	−	16.0533i	0.638060	−	1.10515i	−0.347798	−	0.937570i	$-0.613070\pi$
$211$	9.26836	−	16.0533i	0.638060	−	1.10515i	0.985858	−	0.167583i	$-0.0535963\pi$
$212$		0			0
$213$		−	3.46410i		−	0.237356i
$214$		0			0
$215$	−43.7156	+	25.2392i	−2.98138	+	1.72130i
$216$		0			0
$217$	−1.26836	−	2.19687i	−0.0861021	−	0.149133i
$218$		0			0
$219$	−12.8578	−	7.42346i	−0.868851	−	0.501631i
$220$		0			0
$221$	10.8211	−	15.2177i	0.727905	−	1.02365i
$222$		0			0
$223$	1.82109	+	1.05141i	0.121949	+	0.0704075i	0.559734	−	0.828672i	$-0.310903\pi$
$223$	1.82109	+	1.05141i	0.121949	+	0.0704075i	−0.437784	+	0.899080i	$0.644237\pi$
$224$		0			0
$225$	6.08945	+	10.5472i	0.405964	+	0.703150i
$226$		0			0
$227$	−19.1789	+	11.0729i	−1.27295	+	0.734937i	−0.975542	−	0.219813i	$-0.929455\pi$
$227$	−19.1789	+	11.0729i	−1.27295	+	0.734937i	−0.297407	+	0.954751i	$0.596122\pi$
$228$		0			0
$229$			16.5790i			1.09557i	0.836619	+	0.547785i	$0.184529\pi$
$229$			16.5790i			1.09557i	−0.836619	+	0.547785i	$0.815471\pi$
$230$		0			0
$231$	4.17891	−	7.23808i	0.274952	−	0.476231i
$232$		0			0
$233$	−22.7156			−1.48815			−0.744075	−	0.668096i	$-0.767110\pi$
$233$	−22.7156			−1.48815			−0.744075	+	0.668096i	$0.767110\pi$
$234$		0			0
$235$	−43.0735			−2.80980
$236$		0			0
$237$	−0.910546	+	1.57711i	−0.0591463	+	0.102444i
$238$		0			0
$239$		−	15.2177i		−	0.984351i	−0.870496	−	0.492175i	$-0.836202\pi$
$239$		−	15.2177i		−	0.984351i	0.870496	−	0.492175i	$-0.163798\pi$
$240$		0			0
$241$	−0.589454	+	0.340322i	−0.0379701	+	0.0219220i	−0.518865	−	0.854856i	$-0.673645\pi$
$241$	−0.589454	+	0.340322i	−0.0379701	+	0.0219220i	0.480895	+	0.876778i	$0.340312\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	4.23164	+	2.44314i	0.270349	+	0.156086i
$246$		0			0
$247$	10.1789	+	7.23808i	0.647668	+	0.460548i
$248$		0			0
$249$	−1.17891	−	0.680643i	−0.0747103	−	0.0431340i
$250$		0			0
$251$	12.3578	+	21.4044i	0.780018	+	1.35103i	0.931930	+	0.362638i	$0.118124\pi$
$251$	12.3578	+	21.4044i	0.780018	+	1.35103i	−0.151912	+	0.988394i	$0.548543\pi$
$252$		0			0
$253$	6.00000	−	3.46410i	0.377217	−	0.217786i
$254$		0			0
$255$			21.4653i			1.34421i
$256$		0			0
$257$	−5.41055	+	9.37134i	−0.337501	+	0.584568i	−0.983962	−	0.178379i	$-0.942915\pi$
$257$	−5.41055	+	9.37134i	−0.337501	+	0.584568i	0.646461	+	0.762947i	$0.276248\pi$
$258$		0			0
$259$	−18.3578			−1.14070
$260$		0			0
$261$	3.17891			0.196769
$262$		0			0
$263$	4.82109	−	8.35038i	0.297281	−	0.514906i	−0.678232	−	0.734848i	$-0.737253\pi$
$263$	4.82109	−	8.35038i	0.297281	−	0.514906i	0.975513	+	0.219942i	$0.0705868\pi$
$264$		0			0
$265$		−	4.88627i		−	0.300161i
$266$		0			0
$267$	6.00000	−	3.46410i	0.367194	−	0.212000i
$268$		0			0
$269$	−5.17891	−	8.97013i	−0.315764	−	0.546919i	0.663836	−	0.747878i	$-0.268927\pi$
$269$	−5.17891	−	8.97013i	−0.315764	−	0.546919i	−0.979600	+	0.200960i	$0.935594\pi$
$270$		0			0
$271$	6.91055	+	3.98981i	0.419786	+	0.242363i	0.694986	−	0.719024i	$-0.255411\pi$
$271$	6.91055	+	3.98981i	0.419786	+	0.242363i	−0.275200	+	0.961387i	$0.588744\pi$
$272$		0			0
$273$	−7.91055	+	3.61904i	−0.478768	+	0.219034i
$274$		0			0
$275$	36.5367	+	21.0945i	2.20325	+	1.27205i
$276$		0			0
$277$	−5.58945	−	9.68122i	−0.335838	−	0.581688i	0.647808	−	0.761804i	$-0.275686\pi$
$277$	−5.58945	−	9.68122i	−0.335838	−	0.581688i	−0.983645	+	0.180116i	$0.942353\pi$
$278$		0			0
$279$	0.910546	−	0.525704i	0.0545130	−	0.0314731i
$280$		0			0
$281$		−	18.0012i		−	1.07386i	−0.843627	−	0.536929i	$-0.819584\pi$
$281$		−	18.0012i		−	1.07386i	0.843627	−	0.536929i	$-0.180416\pi$
$282$		0			0
$283$	−7.91055	+	13.7015i	−0.470233	+	0.814468i	−0.999421	−	0.0340373i	$-0.989164\pi$
$283$	−7.91055	+	13.7015i	−0.470233	+	0.814468i	0.529187	+	0.848505i	$0.322497\pi$
$284$		0			0
$285$	−14.3578			−0.850484
$286$		0			0
$287$	1.64218			0.0969350
$288$		0			0
$289$	−4.91055	+	8.50531i	−0.288856	+	0.500313i
$290$		0			0
$291$		−	17.6304i		−	1.03351i
$292$		0			0
$293$	0.0527291	−	0.0304432i	0.00308047	−	0.00177851i	−0.498459	−	0.866913i	$-0.666101\pi$
$293$	0.0527291	−	0.0304432i	0.00308047	−	0.00177851i	0.501539	+	0.865135i	$0.332767\pi$
$294$		0			0
$295$	−24.3578	−	42.1890i	−1.41817	−	2.45634i
$296$		0			0
$297$	3.00000	+	1.73205i	0.174078	+	0.100504i
$298$		0			0
$299$	−7.17891	−	0.680643i	−0.415167	−	0.0393626i
$300$		0			0
$301$	25.4473	+	14.6920i	1.46676	+	0.846832i
$302$		0			0
$303$	0.410546	+	0.711086i	0.0235852	+	0.0408508i
$304$		0			0
$305$	−17.9473	+	10.3619i	−1.02766	+	0.593318i
$306$		0			0
$307$			4.51551i			0.257714i	0.991663	+	0.128857i	$0.0411308\pi$
$307$			4.51551i			0.257714i	−0.991663	+	0.128857i	$0.958869\pi$
$308$		0			0
$309$	4.08945	−	7.08314i	0.232641	−	0.402946i
$310$		0			0
$311$	−34.3578			−1.94825			−0.974127	−	0.226003i	$-0.927434\pi$
$311$	−34.3578			−1.94825			−0.974127	+	0.226003i	$0.927434\pi$
$312$		0			0
$313$	−28.8945			−1.63322			−0.816608	−	0.577193i	$-0.804148\pi$
$313$	−28.8945			−1.63322			−0.816608	+	0.577193i	$0.804148\pi$
$314$		0			0
$315$	5.00000	−	8.66025i	0.281718	−	0.487950i
$316$		0			0
$317$			15.8983i			0.892939i	0.894799	+	0.446470i	$0.147319\pi$
$317$			15.8983i			0.892939i	−0.894799	+	0.446470i	$0.852681\pi$
$318$		0			0
$319$	9.53673	−	5.50603i	0.533954	−	0.308279i
$320$		0			0
$321$	5.00000	+	8.66025i	0.279073	+	0.483368i
$322$		0			0
$323$	−15.5367	−	8.97013i	−0.864487	−	0.499112i
$324$		0			0
$325$	−18.2684	−	39.9312i	−1.01335	−	2.21499i
$326$		0			0
$327$	−0.910546	−	0.525704i	−0.0503533	−	0.0290715i
$328$		0			0
$329$	12.5367	+	21.7142i	0.691172	+	1.19715i
$330$		0			0
$331$	23.0895	−	13.3307i	1.26911	−	0.732722i	0.294291	−	0.955716i	$-0.404916\pi$
$331$	23.0895	−	13.3307i	1.26911	−	0.732722i	0.974820	+	0.222994i	$0.0715831\pi$
$332$		0			0
$333$		−	7.60885i		−	0.416962i
$334$		0			0
$335$	5.00000	−	8.66025i	0.273179	−	0.473160i
$336$		0			0
$337$	−2.64218			−0.143929			−0.0719644	−	0.997407i	$-0.522927\pi$
$337$	−2.64218			−0.143929			−0.0719644	+	0.997407i	$0.522927\pi$
$338$		0			0
$339$	−0.821092			−0.0445956
$340$		0			0
$341$	1.82109	−	3.15422i	0.0986176	−	0.170811i
$342$		0			0
$343$		−	19.7332i		−	1.06549i
$344$		0			0
$345$	7.17891	−	4.14474i	0.386499	−	0.223146i
$346$		0			0
$347$	−1.17891	−	2.04193i	−0.0632871	−	0.109617i	0.832646	−	0.553806i	$-0.186825\pi$
$347$	−1.17891	−	2.04193i	−0.0632871	−	0.109617i	−0.895933	+	0.444189i	$0.853492\pi$
$348$		0			0
$349$	−19.4473	−	11.2279i	−1.04099	−	0.601015i	−0.120875	−	0.992668i	$-0.538570\pi$
$349$	−19.4473	−	11.2279i	−1.04099	−	0.601015i	−0.920113	+	0.391653i	$0.871903\pi$
$350$		0			0
$351$	−1.50000	−	3.27872i	−0.0800641	−	0.175005i
$352$		0			0
$353$	−11.9473	−	6.89776i	−0.635889	−	0.367131i	0.147140	−	0.989116i	$-0.452993\pi$
$353$	−11.9473	−	6.89776i	−0.635889	−	0.367131i	−0.783029	+	0.621985i	$0.786327\pi$
$354$		0			0
$355$	−7.17891	−	12.4342i	−0.381017	−	0.659941i
$356$		0			0
$357$	10.8211	−	6.24756i	0.572713	−	0.330656i
$358$		0			0
$359$		−	5.56692i		−	0.293811i	−0.989151	−	0.146905i	$-0.953069\pi$
$359$		−	5.56692i		−	0.293811i	0.989151	−	0.146905i	$-0.0469313\pi$
$360$		0			0
$361$	−3.50000	+	6.06218i	−0.184211	+	0.319062i
$362$		0			0
$363$	1.00000			0.0524864
$364$		0			0
$365$	−61.5367			−3.22098
$366$		0			0
$367$	12.0895	−	20.9395i	0.631064	−	1.09304i	−0.356270	−	0.934383i	$-0.615952\pi$
$367$	12.0895	−	20.9395i	0.631064	−	1.09304i	0.987334	−	0.158653i	$-0.0507150\pi$
$368$		0			0
$369$			0.680643i			0.0354329i
$370$		0			0
$371$	−2.46327	+	1.42217i	−0.127887	+	0.0738355i
$372$		0			0
$373$	−5.67891	−	9.83616i	−0.294043	−	0.509297i	0.680719	−	0.732545i	$-0.261667\pi$
$373$	−5.67891	−	9.83616i	−0.294043	−	0.509297i	−0.974762	+	0.223248i	$0.928334\pi$
$374$		0			0
$375$	25.7684	+	14.8774i	1.33067	+	0.768264i
$376$		0			0
$377$	−11.4105	−	1.08185i	−0.587673	−	0.0557182i
$378$		0			0
$379$	11.0895	+	6.40250i	0.569627	+	0.328874i	0.757000	−	0.653414i	$-0.226664\pi$
$379$	11.0895	+	6.40250i	0.569627	+	0.328874i	−0.187373	+	0.982289i	$0.559997\pi$
$380$		0			0
$381$	7.08945	+	12.2793i	0.363204	+	0.629087i
$382$		0			0
$383$	−28.7156	+	16.5790i	−1.46730	+	0.847146i	−0.999330	−	0.0365980i	$-0.988348\pi$
$383$	−28.7156	+	16.5790i	−1.46730	+	0.847146i	−0.467970	+	0.883744i	$0.655015\pi$
$384$		0			0
$385$		−	34.6410i		−	1.76547i
$386$		0			0
$387$	−6.08945	+	10.5472i	−0.309544	+	0.536147i
$388$		0			0
$389$	27.5367			1.39617			0.698084	−	0.716016i	$-0.254036\pi$
$389$	27.5367			1.39617			0.698084	+	0.716016i	$0.254036\pi$
$390$		0			0
$391$	10.3578			0.523817
$392$		0			0
$393$	8.17891	−	14.1663i	0.412571	−	0.714595i
$394$		0			0
$395$			7.54796i			0.379779i
$396$		0			0
$397$	12.9105	−	7.45391i	0.647962	−	0.374101i	−0.139713	−	0.990192i	$-0.544618\pi$
$397$	12.9105	−	7.45391i	0.647962	−	0.374101i	0.787675	+	0.616091i	$0.211285\pi$
$398$		0			0
$399$	4.17891	+	7.23808i	0.209207	+	0.362357i
$400$		0			0
$401$	−7.76836	−	4.48507i	−0.387934	−	0.223974i	0.293331	−	0.956011i	$-0.405236\pi$
$401$	−7.76836	−	4.48507i	−0.387934	−	0.223974i	−0.681264	+	0.732037i	$0.738570\pi$
$402$		0			0
$403$	−3.44727	+	1.57711i	−0.171721	+	0.0785615i
$404$		0			0
$405$	3.58945	+	2.07237i	0.178361	+	0.102977i
$406$		0			0
$407$	−13.1789	−	22.8265i	−0.653254	−	1.13147i
$408$		0			0
$409$	21.8578	−	12.6196i	1.08080	−	0.624000i	0.149688	−	0.988733i	$-0.452173\pi$
$409$	21.8578	−	12.6196i	1.08080	−	0.624000i	0.931112	+	0.364733i	$0.118840\pi$
$410$		0			0
$411$			6.24756i			0.308169i
$412$		0			0
$413$	−14.1789	+	24.5586i	−0.697698	+	1.20845i
$414$		0			0
$415$	−5.64218			−0.276964
$416$		0			0
$417$	5.82109			0.285060
$418$		0			0
$419$	16.3578	−	28.3326i	0.799132	−	1.38414i	−0.121051	−	0.992646i	$-0.538626\pi$
$419$	16.3578	−	28.3326i	0.799132	−	1.38414i	0.920182	−	0.391490i	$-0.128040\pi$
$420$		0			0
$421$			5.93768i			0.289385i	0.989477	+	0.144692i	$0.0462193\pi$
$421$			5.93768i			0.289385i	−0.989477	+	0.144692i	$0.953781\pi$
$422$		0			0
$423$	−9.00000	+	5.19615i	−0.437595	+	0.252646i
$424$		0			0
$425$	31.5367	+	54.6232i	1.52976	+	2.64961i
$426$		0			0
$427$	10.4473	+	6.03173i	0.505579	+	0.291896i
$428$		0			0
$429$	−10.1789	−	7.23808i	−0.491442	−	0.349458i
$430$		0			0
$431$	4.82109	+	2.78346i	0.232224	+	0.134074i	0.611598	−	0.791169i	$-0.290527\pi$
$431$	4.82109	+	2.78346i	0.232224	+	0.134074i	−0.379374	+	0.925244i	$0.623861\pi$
$432$		0			0
$433$	12.6789	+	21.9605i	0.609309	+	1.05535i	0.991354	+	0.131211i	$0.0418866\pi$
$433$	12.6789	+	21.9605i	0.609309	+	1.05535i	−0.382045	+	0.924144i	$0.624780\pi$
$434$		0			0
$435$	11.4105	−	6.58788i	0.547094	−	0.315865i
$436$		0			0
$437$			6.92820i			0.331421i
$438$		0			0
$439$	−16.4473	+	28.4875i	−0.784985	+	1.35963i	0.144022	+	0.989574i	$0.453996\pi$
$439$	−16.4473	+	28.4875i	−0.784985	+	1.35963i	−0.929008	+	0.370060i	$0.879337\pi$
$440$		0			0
$441$	1.17891			0.0561385
$442$		0			0
$443$	−8.00000			−0.380091			−0.190046	−	0.981775i	$-0.560864\pi$
$443$	−8.00000			−0.380091			−0.190046	+	0.981775i	$0.560864\pi$
$444$		0			0
$445$	14.3578	−	24.8685i	0.680626	−	1.17888i
$446$		0			0
$447$			0.680643i			0.0321933i
$448$		0			0
$449$	24.5367	−	14.1663i	1.15796	−	0.668548i	0.207145	−	0.978310i	$-0.433583\pi$
$449$	24.5367	−	14.1663i	1.15796	−	0.668548i	0.950814	+	0.309762i	$0.100249\pi$
$450$		0			0
$451$	1.17891	+	2.04193i	0.0555126	+	0.0961507i
$452$		0			0
$453$	−5.35782	−	3.09334i	−0.251732	−	0.145338i
$454$		0			0
$455$	−20.8945	+	29.3840i	−0.979551	+	1.37754i
$456$		0			0
$457$	17.6789	+	10.2069i	0.826984	+	0.477460i	0.852819	−	0.522207i	$-0.174891\pi$
$457$	17.6789	+	10.2069i	0.826984	+	0.477460i	−0.0258346	+	0.999666i	$0.508224\pi$
$458$		0			0
$459$	2.58945	+	4.48507i	0.120865	+	0.209345i
$460$		0			0
$461$	−4.23164	+	2.44314i	−0.197087	+	0.113788i	−0.595296	−	0.803506i	$-0.702965\pi$
$461$	−4.23164	+	2.44314i	−0.197087	+	0.113788i	0.398209	+	0.917295i	$0.369632\pi$
$462$		0			0
$463$			21.0945i			0.980344i	0.871626	+	0.490172i	$0.163066\pi$
$463$			21.0945i			0.980344i	−0.871626	+	0.490172i	$0.836934\pi$
$464$		0			0
$465$	2.17891	−	3.77398i	0.101044	−	0.175014i
$466$		0			0
$467$	6.00000			0.277647			0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000			0.277647			0.138823	+	0.990317i	$0.455668\pi$
$468$		0			0
$469$	−5.82109			−0.268793
$470$		0			0
$471$	3.50000	−	6.06218i	0.161271	−	0.279330i
$472$		0			0
$473$			42.1890i			1.93985i
$474$		0			0
$475$	−36.5367	+	21.0945i	−1.67642	+	0.967881i
$476$		0			0
$477$	−0.589454	−	1.02096i	−0.0269893	−	0.0467468i
$478$		0			0
$479$	6.00000	+	3.46410i	0.274147	+	0.158279i	0.630771	−	0.775969i	$-0.282739\pi$
$479$	6.00000	+	3.46410i	0.274147	+	0.158279i	−0.356624	+	0.934248i	$0.616072\pi$
$480$		0			0
$481$	−2.58945	+	27.3116i	−0.118069	+	1.24530i
$482$		0			0
$483$	−4.17891	−	2.41269i	−0.190147	−	0.109781i
$484$		0			0
$485$	−36.5367	−	63.2835i	−1.65905	−	2.87355i
$486$		0			0
$487$	−21.0000	+	12.1244i	−0.951601	+	0.549407i	−0.893578	−	0.448908i	$-0.851813\pi$
$487$	−21.0000	+	12.1244i	−0.951601	+	0.549407i	−0.0580230	+	0.998315i	$0.518480\pi$
$488$		0			0
$489$		−	1.05141i		−	0.0475463i
$490$		0			0
$491$	−13.3578	+	23.1364i	−0.602830	+	1.04413i	0.389561	+	0.921001i	$0.372627\pi$
$491$	−13.3578	+	23.1364i	−0.602830	+	1.04413i	−0.992390	+	0.123131i	$0.960706\pi$
$492$		0			0
$493$	16.4633			0.741469
$494$		0			0
$495$	14.3578			0.645336
$496$		0			0
$497$	−4.17891	+	7.23808i	−0.187450	+	0.324672i
$498$		0			0
$499$		−	11.7536i		−	0.526163i	−0.964774	−	0.263081i	$-0.915261\pi$
$499$		−	11.7536i		−	0.526163i	0.964774	−	0.263081i	$-0.0847388\pi$
$500$		0			0
$501$	−6.00000	+	3.46410i	−0.268060	+	0.154765i
$502$		0			0
$503$	3.00000	+	5.19615i	0.133763	+	0.231685i	0.925124	−	0.379664i	$-0.123960\pi$
$503$	3.00000	+	5.19615i	0.133763	+	0.231685i	−0.791361	+	0.611349i	$0.790627\pi$
$504$		0			0
$505$	2.94727	+	1.70161i	0.131152	+	0.0757205i
$506$		0			0
$507$	4.26836	+	12.2793i	0.189565	+	0.545343i
$508$		0			0
$509$	4.76836	+	2.75302i	0.211354	+	0.122025i	0.601940	−	0.798541i	$-0.294394\pi$
$509$	4.76836	+	2.75302i	0.211354	+	0.122025i	−0.390587	+	0.920566i	$0.627728\pi$
$510$		0			0
$511$	17.9105	+	31.0220i	0.792316	+	1.37233i
$512$		0			0
$513$	−3.00000	+	1.73205i	−0.132453	+	0.0764719i
$514$		0			0
$515$		−	33.8995i		−	1.49379i
$516$		0			0
$517$	−18.0000	+	31.1769i	−0.791639	+	1.37116i
$518$		0			0
$519$	−18.0000			−0.790112
$520$		0			0
$521$	17.8945			0.783974			0.391987	−	0.919971i	$-0.371788\pi$
$521$	17.8945			0.783974			0.391987	+	0.919971i	$0.371788\pi$
$522$		0			0
$523$	0.821092	−	1.42217i	0.0359038	−	0.0621873i	−0.847515	−	0.530771i	$-0.821902\pi$
$523$	0.821092	−	1.42217i	0.0359038	−	0.0621873i	0.883419	+	0.468584i	$0.155236\pi$
$524$		0			0
$525$		−	29.3840i		−	1.28242i
$526$		0			0
$527$	4.71563	−	2.72257i	0.205416	−	0.118597i
$528$		0			0
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$		0			0
$531$	−10.1789	−	5.87680i	−0.441727	−	0.255031i
$532$		0			0
$533$	0.231637	−	2.44314i	0.0100333	−	0.105824i
$534$		0			0
$535$	35.8945	+	20.7237i	1.55186	+	0.895965i
$536$		0			0
$537$	−7.17891	−	12.4342i	−0.309793	−	0.536577i
$538$		0			0
$539$	3.53673	−	2.04193i	0.152338	−	0.0879521i
$540$		0			0
$541$		−	10.0215i		−	0.430860i	−0.976519	−	0.215430i	$-0.930885\pi$
$541$		−	10.0215i		−	0.430860i	0.976519	−	0.215430i	$-0.0691153\pi$
$542$		0			0
$543$	6.76836	−	11.7231i	0.290458	−	0.503088i
$544$		0			0
$545$	−4.35782			−0.186668
$546$		0			0
$547$	20.5367			0.878087			0.439043	−	0.898466i	$-0.355317\pi$
$547$	20.5367			0.878087			0.439043	+	0.898466i	$0.355317\pi$
$548$		0			0
$549$	−2.50000	+	4.33013i	−0.106697	+	0.184805i
$550$		0			0
$551$			11.0121i			0.469130i
$552$		0			0
$553$	3.80509	−	2.19687i	0.161809	−	0.0934203i
$554$		0			0
$555$	−15.7684	−	27.3116i	−0.669330	−	1.15931i
$556$		0			0
$557$	23.3051	+	13.4552i	0.987468	+	0.570115i	0.904517	−	0.426439i	$-0.140232\pi$
$557$	23.3051	+	13.4552i	0.987468	+	0.570115i	0.0829517	+	0.996554i	$0.473565\pi$
$558$		0			0
$559$	25.4473	−	35.7865i	1.07630	−	1.51361i
$560$		0			0
$561$	15.5367	+	8.97013i	0.655961	+	0.378719i
$562$		0			0
$563$	2.17891	+	3.77398i	0.0918300	+	0.159054i	0.908281	−	0.418360i	$-0.137395\pi$
$563$	2.17891	+	3.77398i	0.0918300	+	0.159054i	−0.816451	+	0.577414i	$0.804062\pi$
$564$		0			0
$565$	−2.94727	+	1.70161i	−0.123993	+	0.0715872i
$566$		0			0
$567$		−	2.41269i		−	0.101324i
$568$		0			0
$569$	−7.35782	+	12.7441i	−0.308456	+	0.534261i	−0.978025	−	0.208489i	$-0.933145\pi$
$569$	−7.35782	+	12.7441i	−0.308456	+	0.534261i	0.669569	+	0.742750i	$0.266479\pi$
$570$		0			0
$571$	30.3578			1.27044			0.635218	−	0.772333i	$-0.280910\pi$
$571$	30.3578			1.27044			0.635218	+	0.772333i	$0.280910\pi$
$572$		0			0
$573$	20.3578			0.850460
$574$		0			0
$575$	12.1789	−	21.0945i	0.507896	−	0.879701i
$576$		0			0
$577$		−	10.4532i		−	0.435172i	−0.976041	−	0.217586i	$-0.930182\pi$
$577$		−	10.4532i		−	0.435172i	0.976041	−	0.217586i	$-0.0698183\pi$
$578$		0			0
$579$	−0.321092	+	0.185382i	−0.0133441	+	0.00770423i
$580$		0			0
$581$	1.64218	+	2.84434i	0.0681292	+	0.118003i
$582$		0			0
$583$	−3.53673	−	2.04193i	−0.146476	−	0.0845681i
$584$		0			0
$585$	−12.1789	−	8.66025i	−0.503536	−	0.358057i
$586$		0			0
$587$	7.82109	+	4.51551i	0.322811	+	0.186375i	0.652645	−	0.757664i	$-0.273659\pi$
$587$	7.82109	+	4.51551i	0.322811	+	0.186375i	−0.329834	+	0.944039i	$0.606993\pi$
$588$		0			0
$589$	1.82109	+	3.15422i	0.0750368	+	0.129968i
$590$		0			0
$591$	14.3578	−	8.28949i	0.590602	−	0.340984i
$592$		0			0
$593$		−	0.0608864i		−	0.00250030i	−0.999999	−	0.00125015i	$-0.999602\pi$
$593$		−	0.0608864i		−	0.00250030i	0.999999	−	0.00125015i	$-0.000397936\pi$
$594$		0			0
$595$	25.8945	−	44.8507i	1.06157	−	1.83870i
$596$		0			0
$597$	12.5367			0.513094
$598$		0			0
$599$	−32.3578			−1.32210			−0.661052	−	0.750340i	$-0.729890\pi$
$599$	−32.3578			−1.32210			−0.661052	+	0.750340i	$0.729890\pi$
$600$		0			0
$601$	−5.58945	+	9.68122i	−0.227999	+	0.394905i	−0.957215	−	0.289378i	$-0.906551\pi$
$601$	−5.58945	+	9.68122i	−0.227999	+	0.394905i	0.729216	+	0.684283i	$0.239885\pi$
$602$		0			0
$603$		−	2.41269i		−	0.0982525i
$604$		0			0
$605$	3.58945	−	2.07237i	0.145932	−	0.0842539i
$606$		0			0
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	0.981454	−	0.191700i	$-0.0614000\pi$
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	−0.656744	+	0.754114i	$0.728067\pi$
$608$		0			0
$609$	−6.64218	−	3.83487i	−0.269155	−	0.155397i
$610$		0			0
$611$	34.0735	−	15.5885i	1.37846	−	0.630641i
$612$		0			0
$613$	−24.8578	−	14.3517i	−1.00400	−	0.579658i	−0.0945691	−	0.995518i	$-0.530147\pi$
$613$	−24.8578	−	14.3517i	−1.00400	−	0.579658i	−0.909429	+	0.415860i	$0.863481\pi$
$614$		0			0
$615$	1.41055	+	2.44314i	0.0568787	+	0.0985168i
$616$		0			0
$617$	−3.58945	+	2.07237i	−0.144506	+	0.0834306i	−0.570510	−	0.821291i	$-0.693254\pi$
$617$	−3.58945	+	2.07237i	−0.144506	+	0.0834306i	0.426004	+	0.904721i	$0.359921\pi$
$618$		0			0
$619$			22.4558i			0.902574i	0.892379	+	0.451287i	$0.149035\pi$
$619$			22.4558i			0.902574i	−0.892379	+	0.451287i	$0.850965\pi$
$620$		0			0
$621$	1.00000	−	1.73205i	0.0401286	−	0.0695048i
$622$		0			0
$623$	−16.7156			−0.669698
$624$		0			0
$625$	62.4313			2.49725
$626$		0			0
$627$	−6.00000	+	10.3923i	−0.239617	+	0.415029i
$628$		0			0
$629$		−	39.4055i		−	1.57120i
$630$		0			0
$631$	−11.0895	+	6.40250i	−0.441464	+	0.254879i	−0.704219	−	0.709983i	$-0.748702\pi$
$631$	−11.0895	+	6.40250i	−0.441464	+	0.254879i	0.262754	+	0.964863i	$0.415369\pi$
$632$		0			0
$633$	−9.26836	−	16.0533i	−0.368384	−	0.638060i
$634$		0			0
$635$	50.8945	+	29.3840i	2.01969	+	1.16607i
$636$		0			0
$637$	−4.23164	−	0.401208i	−0.167664	−	0.0158964i
$638$		0			0
$639$	−3.00000	−	1.73205i	−0.118678	−	0.0685189i
$640$		0			0
$641$	−16.7684	−	29.0437i	−0.662310	−	1.14716i	−0.980007	−	0.198963i	$-0.936243\pi$
$641$	−16.7684	−	29.0437i	−0.662310	−	1.14716i	0.317697	−	0.948192i	$-0.397091\pi$
$642$		0			0
$643$	−3.26836	+	1.88699i	−0.128892	+	0.0744156i	−0.563059	−	0.826416i	$-0.690376\pi$
$643$	−3.26836	+	1.88699i	−0.128892	+	0.0744156i	0.434168	+	0.900832i	$0.357042\pi$
$644$		0			0
$645$			50.4785i			1.98759i
$646$		0			0
$647$	18.1789	−	31.4868i	0.714687	−	1.23787i	−0.248394	−	0.968659i	$-0.579903\pi$
$647$	18.1789	−	31.4868i	0.714687	−	1.23787i	0.963080	−	0.269214i	$-0.0867640\pi$
$648$		0			0
$649$	−40.7156			−1.59823
$650$		0			0
$651$	−2.53673			−0.0994221
$652$		0			0
$653$	11.1789	−	19.3624i	0.437464	−	0.757711i	−0.560029	−	0.828473i	$-0.689210\pi$
$653$	11.1789	−	19.3624i	0.437464	−	0.757711i	0.997493	+	0.0707625i	$0.0225432\pi$
$654$		0			0
$655$		−	67.7990i		−	2.64913i
$656$		0			0
$657$	−12.8578	+	7.42346i	−0.501631	+	0.289617i
$658$		0			0
$659$	18.3578	+	31.7967i	0.715119	+	1.23862i	0.962914	+	0.269810i	$0.0869609\pi$
$659$	18.3578	+	31.7967i	0.715119	+	1.23862i	−0.247795	+	0.968813i	$0.579706\pi$
$660$		0			0
$661$	33.8578	+	19.5478i	1.31692	+	0.760322i	0.983231	−	0.182363i	$-0.0583745\pi$
$661$	33.8578	+	19.5478i	1.31692	+	0.760322i	0.333685	+	0.942685i	$0.391708\pi$
$662$		0			0
$663$	−7.76836	−	16.9802i	−0.301698	−	0.659456i
$664$		0			0
$665$	30.0000	+	17.3205i	1.16335	+	0.671660i
$666$		0			0
$667$	−3.17891	−	5.50603i	−0.123088	−	0.213194i
$668$		0			0
$669$	1.82109	−	1.05141i	0.0704075	−	0.0406498i
$670$		0			0
$671$			17.3205i			0.668651i
$672$		0			0
$673$	−8.67891	+	15.0323i	−0.334547	+	0.579453i	−0.983398	−	0.181463i	$-0.941917\pi$
$673$	−8.67891	+	15.0323i	−0.334547	+	0.579453i	0.648850	+	0.760916i	$0.275250\pi$
$674$		0			0
$675$	12.1789			0.468766
$676$		0			0
$677$	−26.3578			−1.01301			−0.506507	−	0.862236i	$-0.669063\pi$
$677$	−26.3578			−1.01301			−0.506507	+	0.862236i	$0.669063\pi$
$678$		0			0
$679$	−21.2684	+	36.8379i	−0.816205	+	1.41371i
$680$		0			0
$681$			22.1459i			0.848633i
$682$		0			0
$683$	−18.5367	+	10.7022i	−0.709288	+	0.409508i	−0.810797	−	0.585327i	$-0.800966\pi$
$683$	−18.5367	+	10.7022i	−0.709288	+	0.409508i	0.101509	+	0.994835i	$0.467633\pi$
$684$		0			0
$685$	12.9473	+	22.4253i	0.494690	+	0.856828i
$686$		0			0
$687$	14.3578	+	8.28949i	0.547785	+	0.316264i
$688$		0			0
$689$	1.76836	+	3.86531i	0.0673692	+	0.147257i
$690$		0			0
$691$	−32.6262	−	18.8367i	−1.24116	−	0.716583i	−0.271828	−	0.962346i	$-0.587628\pi$
$691$	−32.6262	−	18.8367i	−1.24116	−	0.716583i	−0.969330	+	0.245763i	$0.920962\pi$
$692$		0			0
$693$	−4.17891	−	7.23808i	−0.158744	−	0.274952i
$694$		0			0
$695$	20.8945	−	12.0635i	0.792575	−	0.457593i
$696$		0			0
$697$			3.52499i			0.133518i
$698$		0			0
$699$	−11.3578	+	19.6723i	−0.429592	+	0.744075i
$700$		0			0
$701$	25.6422			0.968492			0.484246	−	0.874932i	$-0.339094\pi$
$701$	25.6422			0.968492			0.484246	+	0.874932i	$0.339094\pi$
$702$		0			0
$703$	26.3578			0.994104
$704$		0			0
$705$	−21.5367	+	37.3027i	−0.811120	+	1.40490i
$706$		0			0
$707$		−	1.98104i		−	0.0745048i
$708$		0			0
$709$	25.5000	−	14.7224i	0.957673	−	0.552913i	0.0622167	−	0.998063i	$-0.480183\pi$
$709$	25.5000	−	14.7224i	0.957673	−	0.552913i	0.895456	+	0.445150i	$0.146850\pi$
$710$		0			0
$711$	0.910546	+	1.57711i	0.0341481	+	0.0591463i
$712$		0			0
$713$	−1.82109	−	1.05141i	−0.0682004	−	0.0393755i
$714$		0			0
$715$	−51.5367	−	4.88627i	−1.92736	−	0.182736i
$716$		0			0
$717$	−13.1789	−	7.60885i	−0.492175	−	0.284158i
$718$		0			0
$719$	−3.82109	−	6.61832i	−0.142503	−	0.246822i	0.785936	−	0.618308i	$-0.212182\pi$
$719$	−3.82109	−	6.61832i	−0.142503	−	0.246822i	−0.928438	+	0.371486i	$0.878848\pi$
$720$		0			0
$721$	−17.0895	+	9.86660i	−0.636445	+	0.367451i
$722$		0			0
$723$			0.680643i			0.0253134i
$724$		0			0
$725$	19.3578	−	33.5287i	0.718931	−	1.24523i
$726$		0			0
$727$	16.5367			0.613313			0.306657	−	0.951820i	$-0.400790\pi$
$727$	16.5367			0.613313			0.306657	+	0.951820i	$0.400790\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−31.5367	+	54.6232i	−1.16643	+	2.02031i
$732$		0			0
$733$		−	41.8182i		−	1.54459i	−0.635264	−	0.772295i	$-0.719109\pi$
$733$		−	41.8182i		−	1.54459i	0.635264	−	0.772295i	$-0.280891\pi$
$734$		0			0
$735$	4.23164	−	2.44314i	0.156086	−	0.0901165i
$736$		0			0
$737$	−4.17891	−	7.23808i	−0.153932	−	0.266618i
$738$		0			0
$739$	1.82109	+	1.05141i	0.0669899	+	0.0386767i	0.533121	−	0.846039i	$-0.321019\pi$
$739$	1.82109	+	1.05141i	0.0669899	+	0.0386767i	−0.466131	+	0.884716i	$0.654352\pi$
$740$		0			0
$741$	11.3578	−	5.19615i	0.417240	−	0.190885i
$742$		0			0
$743$	−10.1789	−	5.87680i	−0.373428	−	0.215599i	0.301527	−	0.953458i	$-0.402504\pi$
$743$	−10.1789	−	5.87680i	−0.373428	−	0.215599i	−0.674955	+	0.737859i	$0.735837\pi$
$744$		0			0
$745$	1.41055	+	2.44314i	0.0516784	+	0.0895096i
$746$		0			0
$747$	−1.17891	+	0.680643i	−0.0431340	+	0.0249034i
$748$		0			0
$749$		−	24.1269i		−	0.881579i
$750$		0			0
$751$	−21.1789	+	36.6829i	−0.772829	+	1.33858i	0.163177	+	0.986597i	$0.447826\pi$
$751$	−21.1789	+	36.6829i	−0.772829	+	1.33858i	−0.936006	+	0.351983i	$0.885508\pi$
$752$		0			0
$753$	24.7156			0.900688
$754$		0			0
$755$	−25.6422			−0.933215
$756$		0			0
$757$	−3.35782	+	5.81591i	−0.122042	+	0.211383i	−0.920573	−	0.390571i	$-0.872278\pi$
$757$	−3.35782	+	5.81591i	−0.122042	+	0.211383i	0.798531	+	0.601954i	$0.205611\pi$
$758$		0			0
$759$		−	6.92820i		−	0.251478i
$760$		0			0
$761$	−42.0000	+	24.2487i	−1.52250	+	0.879015i	−0.522852	+	0.852423i	$0.675132\pi$
$761$	−42.0000	+	24.2487i	−1.52250	+	0.879015i	−0.999646	+	0.0265919i	$0.991535\pi$
$762$		0			0
$763$	1.26836	+	2.19687i	0.0459178	+	0.0795320i
$764$		0			0
$765$	18.5895	+	10.7326i	0.672103	+	0.388039i
$766$		0			0
$767$	34.5367	+	24.5586i	1.24705	+	0.886759i
$768$		0			0
$769$	−6.00000	−	3.46410i	−0.216366	−	0.124919i	0.387901	−	0.921701i	$-0.373200\pi$
$769$	−6.00000	−	3.46410i	−0.216366	−	0.124919i	−0.604266	+	0.796782i	$0.706534\pi$
$770$		0			0
$771$	5.41055	+	9.37134i	0.194856	+	0.337501i
$772$		0			0
$773$	6.53673	−	3.77398i	0.235110	−	0.135741i	−0.377817	−	0.925880i	$-0.623325\pi$
$773$	6.53673	−	3.77398i	0.235110	−	0.135741i	0.612927	+	0.790140i	$0.289992\pi$
$774$		0			0
$775$		−	12.8050i		−	0.459969i
$776$		0			0
$777$	−9.17891	+	15.8983i	−0.329292	+	0.570350i
$778$		0			0
$779$	−2.35782			−0.0844775
$780$		0			0
$781$	−12.0000			−0.429394
$782$		0			0
$783$	1.58945	−	2.75302i	0.0568025	−	0.0983847i
$784$		0			0
$785$		−	29.0132i		−	1.03553i
$786$		0			0
$787$	35.0895	−	20.2589i	1.25080	−	0.722152i	0.279535	−	0.960136i	$-0.409820\pi$
$787$	35.0895	−	20.2589i	1.25080	−	0.722152i	0.971269	+	0.237984i	$0.0764864\pi$
$788$		0			0
$789$	−4.82109	−	8.35038i	−0.171635	−	0.297281i
$790$		0			0
$791$	1.71563	+	0.990521i	0.0610009	+	0.0352189i
$792$		0			0
$793$	10.4473	−	14.6920i	0.370993	−	0.521728i
$794$		0			0
$795$	−4.23164	−	2.44314i	−0.150081	−	0.0866491i
$796$		0			0
$797$	25.5367	+	44.2309i	0.904557	+	1.56674i	0.821510	+	0.570193i	$0.193132\pi$
$797$	25.5367	+	44.2309i	0.904557	+	1.56674i	0.0830467	+	0.996546i	$0.473535\pi$
$798$		0			0
$799$	−46.6102	+	26.9104i	−1.64895	+	0.952021i
$800$		0			0
$801$		−	6.92820i		−	0.244796i
$802$		0			0
$803$	−25.7156	+	44.5408i	−0.907485	+	1.57181i
$804$		0			0
$805$	−20.0000			−0.704907
$806$		0			0
$807$	−10.3578			−0.364612
$808$		0			0
$809$	−6.23164	+	10.7935i	−0.219093	+	0.379480i	−0.954531	−	0.298112i	$-0.903643\pi$
$809$	−6.23164	+	10.7935i	−0.219093	+	0.379480i	0.735438	+	0.677592i	$0.236976\pi$
$810$		0			0
$811$		−	5.87680i		−	0.206362i	−0.994663	−	0.103181i	$-0.967098\pi$
$811$		−	5.87680i		−	0.206362i	0.994663	−	0.103181i	$-0.0329021\pi$
$812$		0			0
$813$	6.91055	−	3.98981i	0.242363	−	0.139929i
$814$		0			0
$815$	−2.17891	−	3.77398i	−0.0763238	−	0.132197i
$816$		0			0
$817$	−36.5367	−	21.0945i	−1.27826	−	0.738003i
$818$		0			0
$819$	−0.821092	+	8.66025i	−0.0286913	+	0.302614i
$820$		0			0
$821$	−6.53673	−	3.77398i	−0.228133	−	0.131713i	0.381577	−	0.924337i	$-0.375381\pi$
$821$	−6.53673	−	3.77398i	−0.228133	−	0.131713i	−0.609711	+	0.792624i	$0.708714\pi$
$822$		0			0
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	0.577474	−	0.816409i	$-0.304038\pi$
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	−0.995768	+	0.0919029i	$0.970705\pi$
$824$		0			0
$825$	36.5367	−	21.0945i	1.27205	−	0.734416i
$826$		0			0
$827$		−	42.8087i		−	1.48861i	−0.667842	−	0.744303i	$-0.732782\pi$
$827$		−	42.8087i		−	1.48861i	0.667842	−	0.744303i	$-0.267218\pi$
$828$		0			0
$829$	−0.321092	+	0.556147i	−0.0111520	+	0.0193158i	−0.871548	−	0.490311i	$-0.836883\pi$
$829$	−0.321092	+	0.556147i	−0.0111520	+	0.0193158i	0.860396	+	0.509627i	$0.170217\pi$
$830$		0			0
$831$	−11.1789			−0.387792
$832$		0			0
$833$	6.10546			0.211542
$834$		0			0
$835$	−14.3578	+	24.8685i	−0.496873	+	0.860609i
$836$		0			0
$837$		−	1.05141i		−	0.0363420i
$838$		0			0
$839$	1.82109	−	1.05141i	0.0628711	−	0.0362986i	−0.468235	−	0.883604i	$-0.655110\pi$
$839$	1.82109	−	1.05141i	0.0628711	−	0.0362986i	0.531106	+	0.847305i	$0.321777\pi$
$840$		0			0
$841$	9.44727	+	16.3632i	0.325768	+	0.564247i
$842$		0			0
$843$	−15.5895	−	9.00058i	−0.536929	−	0.309996i
$844$		0			0
$845$	40.7684	+	35.2303i	1.40247	+	1.21196i
$846$		0			0
$847$	−2.08945	−	1.20635i	−0.0717945	−	0.0414506i
$848$		0			0
$849$	7.91055	+	13.7015i	0.271489	+	0.470233i
$850$		0			0
$851$	−13.1789	+	7.60885i	−0.451767	+	0.260828i
$852$		0			0
$853$			37.7344i			1.29200i	0.763338	+	0.646000i	$0.223559\pi$
$853$			37.7344i			1.29200i	−0.763338	+	0.646000i	$0.776441\pi$
$854$		0			0
$855$	−7.17891	+	12.4342i	−0.245513	+	0.425242i
$856$		0			0
$857$	−8.82109			−0.301323			−0.150661	−	0.988585i	$-0.548140\pi$
$857$	−8.82109			−0.301323			−0.150661	+	0.988585i	$0.548140\pi$
$858$		0			0
$859$	25.2524			0.861599			0.430800	−	0.902448i	$-0.358232\pi$
$859$	25.2524			0.861599			0.430800	+	0.902448i	$0.358232\pi$
$860$		0			0
$861$	0.821092	−	1.42217i	0.0279827	−	0.0484675i
$862$		0			0
$863$		−	6.18667i		−	0.210597i	−0.994441	−	0.105298i	$-0.966420\pi$
$863$		−	6.18667i		−	0.210597i	0.994441	−	0.105298i	$-0.0335798\pi$
$864$		0			0
$865$	−64.6102	+	37.3027i	−2.19681	+	1.26833i
$866$		0			0
$867$	4.91055	+	8.50531i	0.166771	+	0.288856i
$868$		0			0
$869$	5.46327	+	3.15422i	0.185329	+	0.107000i
$870$		0			0
$871$	−0.821092	+	8.66025i	−0.0278216	+	0.293442i
$872$		0			0
$873$	−15.2684	−	8.81519i	−0.516756	−	0.298349i
$874$		0			0
$875$	−35.8945	−	62.1712i	−1.21346	−	2.10177i
$876$		0			0
$877$	5.41055	−	3.12378i	0.182701	−	0.105483i	−0.405860	−	0.913935i	$-0.633028\pi$
$877$	5.41055	−	3.12378i	0.182701	−	0.105483i	0.588561	+	0.808453i	$0.299695\pi$
$878$		0			0
$879$		−	0.0608864i		−	0.00205365i
$880$		0			0
$881$	24.5895	−	42.5902i	0.828440	−	1.43490i	−0.0708220	−	0.997489i	$-0.522562\pi$
$881$	24.5895	−	42.5902i	0.828440	−	1.43490i	0.899262	−	0.437411i	$-0.144104\pi$
$882$		0			0
$883$	−38.8945			−1.30891			−0.654453	−	0.756103i	$-0.727101\pi$
$883$	−38.8945			−1.30891			−0.654453	+	0.756103i	$0.727101\pi$
$884$		0			0
$885$	−48.7156			−1.63756
$886$		0			0
$887$	22.1789	−	38.4150i	0.744695	−	1.28985i	−0.205642	−	0.978627i	$-0.565928\pi$
$887$	22.1789	−	38.4150i	0.744695	−	1.28985i	0.950337	−	0.311222i	$-0.100738\pi$
$888$		0			0
$889$		−	34.2094i		−	1.14735i
$890$		0			0
$891$	3.00000	−	1.73205i	0.100504	−	0.0580259i
$892$		0			0
$893$	−18.0000	−	31.1769i	−0.602347	−	1.04330i
$894$		0			0
$895$	−51.5367	−	29.7547i	−1.72268	−	0.994591i
$896$		0			0
$897$	−4.17891	+	5.87680i	−0.139530	+	0.196220i
$898$		0			0
$899$	−2.89454	−	1.67116i	−0.0965384	−	0.0557365i
$900$		0			0
$901$	−3.05273	−	5.28748i	−0.101701	−	0.176152i
$902$		0			0
$903$	25.4473	−	14.6920i	0.846832	−	0.488919i
$904$		0			0
$905$		−	56.1063i		−	1.86504i
$906$		0			0
$907$	14.0000	−	24.2487i	0.464862	−	0.805165i	−0.534333	−	0.845274i	$-0.679437\pi$
$907$	14.0000	−	24.2487i	0.464862	−	0.805165i	0.999195	+	0.0401089i	$0.0127705\pi$
$908$		0			0
$909$	0.821092			0.0272339
$910$		0			0
$911$	40.7156			1.34897			0.674485	−	0.738289i	$-0.264366\pi$
$911$	40.7156			1.34897			0.674485	+	0.738289i	$0.264366\pi$
$912$		0			0
$913$	−2.35782	+	4.08386i	−0.0780323	+	0.135156i
$914$		0			0
$915$			20.7237i			0.685105i
$916$		0			0
$917$	−34.1789	+	19.7332i	−1.12869	+	0.651648i
$918$		0			0
$919$	12.0000	+	20.7846i	0.395843	+	0.685621i	0.993208	−	0.116348i	$-0.0371189\pi$
$919$	12.0000	+	20.7846i	0.395843	+	0.685621i	−0.597365	+	0.801970i	$0.703786\pi$
$920$		0			0
$921$	3.91055	+	2.25775i	0.128857	+	0.0743955i
$922$		0			0
$923$	10.1789	+	7.23808i	0.335043	+	0.238244i
$924$		0			0
$925$	−80.2524	−	46.3337i	−2.63868	−	1.52344i
$926$		0			0
$927$	−4.08945	−	7.08314i	−0.134315	−	0.232641i
$928$		0			0
$929$	−10.2316	+	5.90724i	−0.335689	+	0.193810i	−0.658364	−	0.752700i	$-0.728751\pi$
$929$	−10.2316	+	5.90724i	−0.335689	+	0.193810i	0.322675	+	0.946510i	$0.395418\pi$
$930$		0			0
$931$			4.08386i			0.133843i
$932$		0			0
$933$	−17.1789	+	29.7547i	−0.562412	+	0.974127i
$934$		0			0
$935$	74.3578			2.43176
$936$		0			0
$937$	−7.89454			−0.257903			−0.128952	−	0.991651i	$-0.541161\pi$
$937$	−7.89454			−0.257903			−0.128952	+	0.991651i	$0.541161\pi$
$938$		0			0
$939$	−14.4473	+	25.0234i	−0.471469	+	0.816608i
$940$		0			0
$941$			54.5623i			1.77868i	0.457246	+	0.889340i	$0.348836\pi$
$941$			54.5623i			1.77868i	−0.457246	+	0.889340i	$0.651164\pi$
$942$		0			0
$943$	1.17891	−	0.680643i	0.0383905	−	0.0221648i
$944$		0			0
$945$	−5.00000	−	8.66025i	−0.162650	−	0.281718i
$946$		0			0
$947$	3.64218	+	2.10282i	0.118355	+	0.0683323i	0.558009	−	0.829835i	$-0.311566\pi$
$947$	3.64218	+	2.10282i	0.118355	+	0.0683323i	−0.439654	+	0.898167i	$0.644899\pi$
$948$		0			0
$949$	48.6789	−	22.2704i	1.58018	−	0.722928i
$950$		0			0
$951$	13.7684	+	7.94917i	0.446470	+	0.257769i
$952$		0			0
$953$	−3.00000	−	5.19615i	−0.0971795	−	0.168320i	0.813337	−	0.581793i	$-0.197649\pi$
$953$	−3.00000	−	5.19615i	−0.0971795	−	0.168320i	−0.910516	+	0.413473i	$0.864315\pi$
$954$		0			0
$955$	73.0735	−	42.1890i	2.36460	−	1.36520i
$956$		0			0
$957$		−	11.0121i		−	0.355969i
$958$		0			0
$959$	7.53673	−	13.0540i	0.243374	−	0.421535i
$960$		0			0
$961$	29.8945			0.964340
$962$		0			0
$963$	10.0000			0.322245
$964$		0			0
$965$	−0.768363	+	1.33084i	−0.0247345	+	0.0428413i
$966$		0			0
$967$			61.6123i			1.98132i	0.136363	+	0.990659i	$0.456459\pi$
$967$			61.6123i			1.98132i	−0.136363	+	0.990659i	$0.543541\pi$
$968$		0			0
$969$	−15.5367	+	8.97013i	−0.499112	+	0.288162i
$970$		0			0
$971$	−20.3578	−	35.2608i	−0.653313	−	1.13157i	−0.982314	−	0.187242i	$-0.940045\pi$
$971$	−20.3578	−	35.2608i	−0.653313	−	1.13157i	0.329000	−	0.944330i	$-0.393288\pi$
$972$		0			0
$973$	−12.1629	−	7.02226i	−0.389925	−	0.225123i
$974$		0			0
$975$	−43.7156	−	4.14474i	−1.40002	−	0.132738i
$976$		0			0
$977$	31.7684	+	18.3415i	1.01636	+	0.586796i	0.913047	−	0.407853i	$-0.133723\pi$
$977$	31.7684	+	18.3415i	1.01636	+	0.586796i	0.103312	+	0.994649i	$0.467056\pi$
$978$		0			0
$979$	−12.0000	−	20.7846i	−0.383522	−	0.664279i
$980$		0			0
$981$	−0.910546	+	0.525704i	−0.0290715	+	0.0167844i
$982$		0			0
$983$		−	14.4762i		−	0.461718i	−0.972987	−	0.230859i	$-0.925846\pi$
$983$		−	14.4762i		−	0.461718i	0.972987	−	0.230859i	$-0.0741536\pi$
$984$		0			0
$985$	34.3578	−	59.5095i	1.09473	−	1.89613i
$986$		0			0
$987$	25.0735			0.798097
$988$		0			0
$989$	24.3578			0.774534
$990$		0			0
$991$	11.5367	−	19.9822i	0.366476	−	0.634755i	−0.622536	−	0.782591i	$-0.713897\pi$
$991$	11.5367	−	19.9822i	0.366476	−	0.634755i	0.989012	+	0.147836i	$0.0472308\pi$
$992$		0			0
$993$		−	26.6614i		−	0.846074i
$994$		0			0
$995$	45.0000	−	25.9808i	1.42660	−	0.823646i
$996$		0			0
$997$	−6.32109	−	10.9485i	−0.200191	−	0.346741i	0.748399	−	0.663249i	$-0.230823\pi$
$997$	−6.32109	−	10.9485i	−0.200191	−	0.346741i	−0.948590	+	0.316508i	$0.897490\pi$
$998$		0			0
$999$	−6.58945	−	3.80442i	−0.208481	−	0.120367i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.bv.f.433.1		4
3.2	odd	2		1872.2.by.j.433.2		4
4.3	odd	2		156.2.q.b.121.1	yes	4
12.11	even	2		468.2.t.d.433.2		4
13.6	odd	12		8112.2.a.cr.1.1		4
13.7	odd	12		8112.2.a.cr.1.4		4
13.10	even	6	inner	624.2.bv.f.49.2		4
20.3	even	4		3900.2.bw.j.2149.1		8
20.7	even	4		3900.2.bw.j.2149.4		8
20.19	odd	2		3900.2.cd.i.901.1		4
39.23	odd	6		1872.2.by.j.1297.1		4
52.3	odd	6		2028.2.q.f.361.1		4
52.7	even	12		2028.2.a.m.1.4		4
52.11	even	12		2028.2.i.n.2005.4		8
52.15	even	12		2028.2.i.n.2005.1		8
52.19	even	12		2028.2.a.m.1.1		4
52.23	odd	6		156.2.q.b.49.2	✓	4
52.31	even	4		2028.2.i.n.529.1		8
52.35	odd	6		2028.2.b.e.337.1		4
52.43	odd	6		2028.2.b.e.337.4		4
52.47	even	4		2028.2.i.n.529.4		8
52.51	odd	2		2028.2.q.f.1837.2		4
156.23	even	6		468.2.t.d.361.1		4
156.35	even	6		6084.2.b.o.4393.4		4
156.59	odd	12		6084.2.a.bd.1.1		4
156.71	odd	12		6084.2.a.bd.1.4		4
156.95	even	6		6084.2.b.o.4393.1		4
260.23	even	12		3900.2.bw.j.49.4		8
260.127	even	12		3900.2.bw.j.49.1		8
260.179	odd	6		3900.2.cd.i.2701.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.q.b.49.2	✓	4	52.23	odd	6
156.2.q.b.121.1	yes	4	4.3	odd	2
468.2.t.d.361.1		4	156.23	even	6
468.2.t.d.433.2		4	12.11	even	2
624.2.bv.f.49.2		4	13.10	even	6	inner
624.2.bv.f.433.1		4	1.1	even	1	trivial
1872.2.by.j.433.2		4	3.2	odd	2
1872.2.by.j.1297.1		4	39.23	odd	6
2028.2.a.m.1.1		4	52.19	even	12
2028.2.a.m.1.4		4	52.7	even	12
2028.2.b.e.337.1		4	52.35	odd	6
2028.2.b.e.337.4		4	52.43	odd	6
2028.2.i.n.529.1		8	52.31	even	4
2028.2.i.n.529.4		8	52.47	even	4
2028.2.i.n.2005.1		8	52.15	even	12
2028.2.i.n.2005.4		8	52.11	even	12
2028.2.q.f.361.1		4	52.3	odd	6
2028.2.q.f.1837.2		4	52.51	odd	2
3900.2.bw.j.49.1		8	260.127	even	12
3900.2.bw.j.49.4		8	260.23	even	12
3900.2.bw.j.2149.1		8	20.3	even	4
3900.2.bw.j.2149.4		8	20.7	even	4
3900.2.cd.i.901.1		4	20.19	odd	2
3900.2.cd.i.2701.1		4	260.179	odd	6
6084.2.a.bd.1.1		4	156.59	odd	12
6084.2.a.bd.1.4		4	156.71	odd	12
6084.2.b.o.4393.1		4	156.95	even	6
6084.2.b.o.4393.4		4	156.35	even	6
8112.2.a.cr.1.1		4	13.6	odd	12
8112.2.a.cr.1.4		4	13.7	odd	12

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.bv (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} -4.14474i q^{5} +(-2.08945 + 1.20635i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-3.00000 - 1.73205i) q^{11} +(1.50000 + 3.27872i) q^{13} +(-3.58945 - 2.07237i) q^{15} +(-2.58945 - 4.48507i) q^{17} +(3.00000 - 1.73205i) q^{19} +2.41269i q^{21} +(-1.00000 + 1.73205i) q^{23} -12.1789 q^{25} -1.00000 q^{27} +(-1.58945 + 2.75302i) q^{29} +1.05141i q^{31} +(-3.00000 + 1.73205i) q^{33} +(5.00000 + 8.66025i) q^{35} +(6.58945 + 3.80442i) q^{37} +(3.58945 + 0.340322i) q^{39} +(-0.589454 - 0.340322i) q^{41} +(-6.08945 - 10.5472i) q^{43} +(-3.58945 + 2.07237i) q^{45} -10.3923i q^{47} +(-0.589454 + 1.02096i) q^{49} -5.17891 q^{51} +1.17891 q^{53} +(-7.17891 + 12.4342i) q^{55} -3.46410i q^{57} +(10.1789 - 5.87680i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(2.08945 + 1.20635i) q^{63} +(13.5895 - 6.21712i) q^{65} +(2.08945 + 1.20635i) q^{67} +(1.00000 + 1.73205i) q^{69} +(3.00000 - 1.73205i) q^{71} -14.8469i q^{73} +(-6.08945 + 10.5472i) q^{75} +8.35782 q^{77} -1.82109 q^{79} +(-0.500000 + 0.866025i) q^{81} -1.36129i q^{83} +(-18.5895 + 10.7326i) q^{85} +(1.58945 + 2.75302i) q^{87} +(6.00000 + 3.46410i) q^{89} +(-7.08945 - 5.04121i) q^{91} +(0.910546 + 0.525704i) q^{93} +(-7.17891 - 12.4342i) q^{95} +(15.2684 - 8.81519i) q^{97} +3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 3 q^{7} - 2 q^{9} - 12 q^{11} + 6 q^{13} - 3 q^{15} + q^{17} + 12 q^{19} - 4 q^{23} - 26 q^{25} - 4 q^{27} + 5 q^{29} - 12 q^{33} + 20 q^{35} + 15 q^{37} + 3 q^{39} + 9 q^{41} - 13 q^{43}+ \cdots + 27 q^{97}+O(q^{100}) \) 4 * q + 2 * q^3 + 3 * q^7 - 2 * q^9 - 12 * q^11 + 6 * q^13 - 3 * q^15 + q^17 + 12 * q^19 - 4 * q^23 - 26 * q^25 - 4 * q^27 + 5 * q^29 - 12 * q^33 + 20 * q^35 + 15 * q^37 + 3 * q^39 + 9 * q^41 - 13 * q^43 - 3 * q^45 + 9 * q^49 + 2 * q^51 - 18 * q^53 - 6 * q^55 + 18 * q^59 - 10 * q^61 - 3 * q^63 + 43 * q^65 - 3 * q^67 + 4 * q^69 + 12 * q^71 - 13 * q^75 - 12 * q^77 - 30 * q^79 - 2 * q^81 - 63 * q^85 - 5 * q^87 + 24 * q^89 - 17 * q^91 + 15 * q^93 - 6 * q^95 + 27 * q^97

Introduction

L-functions

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