LMFDB - Embedded newform 504.2.bs.a.353.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(257,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.257"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bs (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			353.14
Character	$\chi$	$=$	504.353
Dual form			504.2.bs.a.257.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.589575 + 1.62862i) q^{3} +(1.11415 - 1.92977i) q^{5} +(-0.553477 - 2.58721i) q^{7} +(-2.30480 + 1.92039i) q^{9} +(1.83714 - 1.06068i) q^{11} +(5.10339 - 2.94644i) q^{13} +(3.79973 + 0.676785i) q^{15} +(2.34020 - 4.05335i) q^{17} +(-4.54550 + 2.62435i) q^{19} +(3.88727 - 2.42676i) q^{21} +(3.77916 + 2.18190i) q^{23} +(0.0173374 + 0.0300292i) q^{25} +(-4.48644 - 2.62143i) q^{27} +(-2.25182 - 1.30009i) q^{29} +7.61221i q^{31} +(2.81057 + 2.36666i) q^{33} +(-5.60937 - 1.81446i) q^{35} +(-1.80274 - 3.12244i) q^{37} +(7.80746 + 6.57433i) q^{39} +(-0.0395039 - 0.0684228i) q^{41} +(-1.24922 + 2.16371i) q^{43} +(1.13800 + 6.58733i) q^{45} +3.79674 q^{47} +(-6.38733 + 2.86393i) q^{49} +(7.98109 + 1.42154i) q^{51} +(4.08014 + 2.35567i) q^{53} -4.72701i q^{55} +(-6.95397 - 5.85564i) q^{57} +13.1939 q^{59} +8.15939i q^{61} +(6.24410 + 4.90012i) q^{63} -13.1311i q^{65} -4.75228 q^{67} +(-1.32538 + 7.44121i) q^{69} -10.0325i q^{71} +(-12.6610 - 7.30986i) q^{73} +(-0.0386845 + 0.0459405i) q^{75} +(-3.76101 - 4.16602i) q^{77} -14.5483 q^{79} +(1.62422 - 8.85223i) q^{81} +(-6.41294 + 11.1075i) q^{83} +(-5.21468 - 9.03209i) q^{85} +(0.789732 - 4.43386i) q^{87} +(-2.73464 - 4.73654i) q^{89} +(-10.4477 - 11.5728i) q^{91} +(-12.3974 + 4.48797i) q^{93} +11.6957i q^{95} +(12.9290 + 7.46454i) q^{97} +(-2.19734 + 5.97268i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75}+ \cdots - 64 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	0.589575	+	1.62862i	0.340392	+	0.940284i
$3$	0.589575	+	1.62862i	0.340392	+	0.940284i
$4$		0			0
$5$	1.11415	−	1.92977i	0.498263	−	0.863017i	−0.501735	−	0.865022i	$-0.667305\pi$
$5$	1.11415	−	1.92977i	0.498263	−	0.863017i	0.999998	+	0.00200427i	$0.000637980\pi$
$6$		0			0
$7$	−0.553477	−	2.58721i	−0.209195	−	0.977874i
$7$	−0.553477	−	2.58721i	−0.209195	−	0.977874i
$8$		0			0
$9$	−2.30480	+	1.92039i	−0.768267	+	0.640129i
$10$		0			0
$11$	1.83714	−	1.06068i	0.553920	−	0.319806i	−0.196782	−	0.980447i	$-0.563049\pi$
$11$	1.83714	−	1.06068i	0.553920	−	0.319806i	0.750701	+	0.660642i	$0.229716\pi$
$12$		0			0
$13$	5.10339	−	2.94644i	1.41542	−	0.817196i	0.419533	−	0.907740i	$-0.362194\pi$
$13$	5.10339	−	2.94644i	1.41542	−	0.817196i	0.995892	+	0.0905443i	$0.0288607\pi$
$14$		0			0
$15$	3.79973	+	0.676785i	0.981086	+	0.174745i
$16$		0			0
$17$	2.34020	−	4.05335i	0.567583	−	0.983082i	−0.429222	−	0.903199i	$-0.641212\pi$
$17$	2.34020	−	4.05335i	0.567583	−	0.983082i	0.996804	−	0.0798828i	$-0.0254546\pi$
$18$		0			0
$19$	−4.54550	+	2.62435i	−1.04281	+	0.602066i	−0.920628	−	0.390442i	$-0.872322\pi$
$19$	−4.54550	+	2.62435i	−1.04281	+	0.602066i	−0.122181	+	0.992508i	$0.538989\pi$
$20$		0			0
$21$	3.88727	−	2.42676i	0.848271	−	0.529563i
$22$		0			0
$23$	3.77916	+	2.18190i	0.788010	+	0.454958i	0.839261	−	0.543728i	$-0.182988\pi$
$23$	3.77916	+	2.18190i	0.788010	+	0.454958i	−0.0512518	+	0.998686i	$0.516321\pi$
$24$		0			0
$25$	0.0173374	+	0.0300292i	0.00346748	+	0.00600585i
$26$		0			0
$27$	−4.48644	−	2.62143i	−0.863415	−	0.504495i
$28$		0			0
$29$	−2.25182	−	1.30009i	−0.418152	−	0.241420i	0.276134	−	0.961119i	$-0.410947\pi$
$29$	−2.25182	−	1.30009i	−0.418152	−	0.241420i	−0.694286	+	0.719699i	$0.744280\pi$
$30$		0			0
$31$			7.61221i			1.36719i	0.729860	+	0.683597i	$0.239585\pi$
$31$			7.61221i			1.36719i	−0.729860	+	0.683597i	$0.760415\pi$
$32$		0			0
$33$	2.81057	+	2.36666i	0.489258	+	0.411983i
$34$		0			0
$35$	−5.60937	−	1.81446i	−0.948156	−	0.306700i
$36$		0			0
$37$	−1.80274	−	3.12244i	−0.296369	−	0.513326i	0.678934	−	0.734200i	$-0.262442\pi$
$37$	−1.80274	−	3.12244i	−0.296369	−	0.513326i	−0.975302	+	0.220874i	$0.929109\pi$
$38$		0			0
$39$	7.80746	+	6.57433i	1.25019	+	1.05273i
$40$		0			0
$41$	−0.0395039	−	0.0684228i	−0.00616948	−	0.0106858i	0.862924	−	0.505333i	$-0.168630\pi$
$41$	−0.0395039	−	0.0684228i	−0.00616948	−	0.0106858i	−0.869094	+	0.494648i	$0.835297\pi$
$42$		0			0
$43$	−1.24922	+	2.16371i	−0.190504	+	0.329962i	−0.945417	−	0.325862i	$-0.894345\pi$
$43$	−1.24922	+	2.16371i	−0.190504	+	0.329962i	0.754914	+	0.655824i	$0.227679\pi$
$44$		0			0
$45$	1.13800	+	6.58733i	0.169643	+	0.981981i
$46$		0			0
$47$	3.79674			0.553811			0.276905	−	0.960897i	$-0.410691\pi$
$47$	3.79674			0.553811			0.276905	+	0.960897i	$0.410691\pi$
$48$		0			0
$49$	−6.38733	+	2.86393i	−0.912475	+	0.409132i
$50$		0			0
$51$	7.98109	+	1.42154i	1.11758	+	0.199056i
$52$		0			0
$53$	4.08014	+	2.35567i	0.560451	+	0.323576i	0.753326	−	0.657647i	$-0.228448\pi$
$53$	4.08014	+	2.35567i	0.560451	+	0.323576i	−0.192876	+	0.981223i	$0.561781\pi$
$54$		0			0
$55$		−	4.72701i		−	0.637390i
$56$		0			0
$57$	−6.95397	−	5.85564i	−0.921076	−	0.775598i
$58$		0			0
$59$	13.1939			1.71770			0.858849	−	0.512229i	$-0.171180\pi$
$59$	13.1939			1.71770			0.858849	+	0.512229i	$0.171180\pi$
$60$		0			0
$61$			8.15939i			1.04470i	0.852730	+	0.522352i	$0.174945\pi$
$61$			8.15939i			1.04470i	−0.852730	+	0.522352i	$0.825055\pi$
$62$		0			0
$63$	6.24410	+	4.90012i	0.786683	+	0.617357i
$64$		0			0
$65$		−	13.1311i		−	1.62871i
$66$		0			0
$67$	−4.75228			−0.580583			−0.290292	−	0.956938i	$-0.593752\pi$
$67$	−4.75228			−0.580583			−0.290292	+	0.956938i	$0.593752\pi$
$68$		0			0
$69$	−1.32538	+	7.44121i	−0.159557	+	0.895816i
$70$		0			0
$71$		−	10.0325i		−	1.19064i	−0.803490	−	0.595318i	$-0.797026\pi$
$71$		−	10.0325i		−	1.19064i	0.803490	−	0.595318i	$-0.202974\pi$
$72$		0			0
$73$	−12.6610	−	7.30986i	−1.48186	−	0.855554i	−0.482075	−	0.876130i	$-0.660117\pi$
$73$	−12.6610	−	7.30986i	−1.48186	−	0.855554i	−0.999788	+	0.0205755i	$0.993450\pi$
$74$		0			0
$75$	−0.0386845	+	0.0459405i	−0.00446690	+	0.00530475i
$76$		0			0
$77$	−3.76101	−	4.16602i	−0.428607	−	0.474762i
$78$		0			0
$79$	−14.5483			−1.63681			−0.818405	−	0.574642i	$-0.805141\pi$
$79$	−14.5483			−1.63681			−0.818405	+	0.574642i	$0.805141\pi$
$80$		0			0
$81$	1.62422	−	8.85223i	0.180469	−	0.983581i
$82$		0			0
$83$	−6.41294	+	11.1075i	−0.703911	+	1.21921i	0.263172	+	0.964749i	$0.415231\pi$
$83$	−6.41294	+	11.1075i	−0.703911	+	1.21921i	−0.967083	+	0.254461i	$0.918102\pi$
$84$		0			0
$85$	−5.21468	−	9.03209i	−0.565611	−	0.979667i
$86$		0			0
$87$	0.789732	−	4.43386i	0.0846681	−	0.475359i
$88$		0			0
$89$	−2.73464	−	4.73654i	−0.289871	−	0.502072i	0.683907	−	0.729569i	$-0.260279\pi$
$89$	−2.73464	−	4.73654i	−0.289871	−	0.502072i	−0.973779	+	0.227497i	$0.926946\pi$
$90$		0			0
$91$	−10.4477	−	11.5728i	−1.09521	−	1.21315i
$92$		0			0
$93$	−12.3974	+	4.48797i	−1.28555	+	0.465381i
$94$		0			0
$95$			11.6957i			1.19995i
$96$		0			0
$97$	12.9290	+	7.46454i	1.31274	+	0.757909i	0.982549	−	0.186006i	$-0.0595544\pi$
$97$	12.9290	+	7.46454i	1.31274	+	0.757909i	0.330188	+	0.943915i	$0.392888\pi$
$98$		0			0
$99$	−2.19734	+	5.97268i	−0.220841	+	0.600277i
$100$		0			0
$101$	−1.63302	−	2.82847i	−0.162492	−	0.281444i	0.773270	−	0.634077i	$-0.218620\pi$
$101$	−1.63302	−	2.82847i	−0.162492	−	0.281444i	−0.935762	+	0.352633i	$0.885286\pi$
$102$		0			0
$103$	4.12945	+	2.38414i	0.406887	+	0.234916i	0.689451	−	0.724332i	$-0.257852\pi$
$103$	4.12945	+	2.38414i	0.406887	+	0.234916i	−0.282564	+	0.959248i	$0.591185\pi$
$104$		0			0
$105$	−0.352079	−	10.2053i	−0.0343594	−	0.995934i
$106$		0			0
$107$	−6.39655	+	3.69305i	−0.618378	+	0.357021i	−0.776237	−	0.630441i	$-0.782874\pi$
$107$	−6.39655	+	3.69305i	−0.618378	+	0.357021i	0.157859	+	0.987462i	$0.449541\pi$
$108$		0			0
$109$	−1.17349	+	2.03254i	−0.112400	+	0.194682i	−0.916737	−	0.399490i	$-0.869187\pi$
$109$	−1.17349	+	2.03254i	−0.112400	+	0.194682i	0.804338	+	0.594173i	$0.202520\pi$
$110$		0			0
$111$	4.02241	−	4.77689i	0.381790	−	0.453402i
$112$		0			0
$113$	11.8961	−	6.86824i	1.11909	−	0.646109i	0.177925	−	0.984044i	$-0.443062\pi$
$113$	11.8961	−	6.86824i	1.11909	−	0.646109i	0.941170	+	0.337935i	$0.109728\pi$
$114$		0			0
$115$	8.42111	−	4.86193i	0.785272	−	0.453377i
$116$		0			0
$117$	−6.10398	+	16.5914i	−0.564314	+	1.53388i
$118$		0			0
$119$	−11.7821	−	3.81116i	−1.08007	−	0.349369i
$120$		0			0
$121$	−3.24993	+	5.62905i	−0.295449	+	0.511732i
$122$		0			0
$123$	0.0881442	−	0.104677i	0.00794769	−	0.00943843i
$124$		0			0
$125$	11.2188			1.00344
$126$		0			0
$127$	−5.97913			−0.530562			−0.265281	−	0.964171i	$-0.585465\pi$
$127$	−5.97913			−0.530562			−0.265281	+	0.964171i	$0.585465\pi$
$128$		0			0
$129$	−4.26036	−	0.758830i	−0.375104	−	0.0668112i
$130$		0			0
$131$	−10.4792	+	18.1506i	−0.915576	+	1.58582i	−0.109519	+	0.993985i	$0.534931\pi$
$131$	−10.4792	+	18.1506i	−0.915576	+	1.58582i	−0.806056	+	0.591839i	$0.798402\pi$
$132$		0			0
$133$	9.30557	+	10.3077i	0.806895	+	0.893787i
$134$		0			0
$135$	−10.0573	+	5.73710i	−0.865595	+	0.493771i
$136$		0			0
$137$	−3.00063	+	1.73242i	−0.256361	+	0.148010i	−0.622674	−	0.782482i	$-0.713954\pi$
$137$	−3.00063	+	1.73242i	−0.256361	+	0.148010i	0.366312	+	0.930492i	$0.380620\pi$
$138$		0			0
$139$	0.379607	−	0.219166i	0.0321979	−	0.0185895i	−0.483815	−	0.875170i	$-0.660749\pi$
$139$	0.379607	−	0.219166i	0.0321979	−	0.0185895i	0.516013	+	0.856581i	$0.327416\pi$
$140$		0			0
$141$	2.23846	+	6.18344i	0.188512	+	0.520739i
$142$		0			0
$143$	6.25044	−	10.8261i	0.522688	−	0.905322i
$144$		0			0
$145$	−5.01773	+	2.89699i	−0.416700	+	0.240582i
$146$		0			0
$147$	−8.43006	−	8.71402i	−0.695299	−	0.718720i
$148$		0			0
$149$	−15.1560	−	8.75030i	−1.24162	−	0.716852i	−0.272200	−	0.962241i	$-0.587751\pi$
$149$	−15.1560	−	8.75030i	−1.24162	−	0.716852i	−0.969425	+	0.245388i	$0.921085\pi$
$150$		0			0
$151$	0.187420	+	0.324621i	0.0152520	+	0.0264172i	0.873551	−	0.486733i	$-0.161812\pi$
$151$	0.187420	+	0.324621i	0.0152520	+	0.0264172i	−0.858299	+	0.513150i	$0.828478\pi$
$152$		0			0
$153$	2.39030	+	13.8363i	0.193244	+	1.11860i
$154$		0			0
$155$	14.6898	+	8.48115i	1.17991	+	0.681223i
$156$		0			0
$157$			20.3549i			1.62450i	0.583311	+	0.812249i	$0.301757\pi$
$157$			20.3549i			1.62450i	−0.583311	+	0.812249i	$0.698243\pi$
$158$		0			0
$159$	−1.43094	+	8.03385i	−0.113481	+	0.637126i
$160$		0			0
$161$	3.55336	−	10.9851i	0.280044	−	0.865749i
$162$		0			0
$163$	−7.25400	−	12.5643i	−0.568177	−	0.984112i	−0.996746	−	0.0806027i	$-0.974316\pi$
$163$	−7.25400	−	12.5643i	−0.568177	−	0.984112i	0.428569	−	0.903509i	$-0.359018\pi$
$164$		0			0
$165$	7.69850	−	2.78693i	0.599327	−	0.216962i
$166$		0			0
$167$	−7.62510	−	13.2071i	−0.590048	−	1.02199i	−0.994225	−	0.107313i	$-0.965775\pi$
$167$	−7.62510	−	13.2071i	−0.590048	−	1.02199i	0.404177	−	0.914681i	$-0.367558\pi$
$168$		0			0
$169$	10.8630	−	18.8153i	0.835619	−	1.44733i
$170$		0			0
$171$	5.43671	−	14.7777i	0.415756	−	1.13008i
$172$		0			0
$173$	1.88136			0.143037			0.0715185	−	0.997439i	$-0.477215\pi$
$173$	1.88136			0.143037			0.0715185	+	0.997439i	$0.477215\pi$
$174$		0			0
$175$	0.0680961	−	0.0614760i	0.00514758	−	0.00464715i
$176$		0			0
$177$	7.77879	+	21.4878i	0.584690	+	1.61512i
$178$		0			0
$179$	8.64064	+	4.98867i	0.645831	+	0.372871i	0.786857	−	0.617135i	$-0.211707\pi$
$179$	8.64064	+	4.98867i	0.645831	+	0.372871i	−0.141026	+	0.990006i	$0.545040\pi$
$180$		0			0
$181$			11.2828i			0.838641i	0.907838	+	0.419320i	$0.137732\pi$
$181$			11.2828i			0.838641i	−0.907838	+	0.419320i	$0.862268\pi$
$182$		0			0
$183$	−13.2885	+	4.81058i	−0.982318	+	0.355608i
$184$		0			0
$185$	−8.03410			−0.590679
$186$		0			0
$187$		−	9.92879i		−	0.726065i
$188$		0			0
$189$	−4.29906	+	13.0583i	−0.312710	+	0.949849i
$190$		0			0
$191$		−	12.8654i		−	0.930907i	−0.885072	−	0.465454i	$-0.845891\pi$
$191$		−	12.8654i		−	0.930907i	0.885072	−	0.465454i	$-0.154109\pi$
$192$		0			0
$193$	−12.0372			−0.866458			−0.433229	−	0.901284i	$-0.642626\pi$
$193$	−12.0372			−0.866458			−0.433229	+	0.901284i	$0.642626\pi$
$194$		0			0
$195$	21.3856	−	7.74179i	1.53145	−	0.554401i
$196$		0			0
$197$			27.7262i			1.97541i	0.156339	+	0.987703i	$0.450031\pi$
$197$			27.7262i			1.97541i	−0.156339	+	0.987703i	$0.549969\pi$
$198$		0			0
$199$	0.382862	+	0.221045i	0.0271404	+	0.0156695i	0.513509	−	0.858084i	$-0.328345\pi$
$199$	0.382862	+	0.221045i	0.0271404	+	0.0156695i	−0.486368	+	0.873754i	$0.661679\pi$
$200$		0			0
$201$	−2.80183	−	7.73965i	−0.197626	−	0.545913i
$202$		0			0
$203$	−2.11727	+	6.54550i	−0.148603	+	0.459404i
$204$		0			0
$205$	−0.176053			−0.0122961
$206$		0			0
$207$	−12.9003	+	2.22861i	−0.896634	+	0.154899i
$208$		0			0
$209$	−5.56716	+	9.64260i	−0.385088	+	0.666993i
$210$		0			0
$211$	−0.219300	−	0.379839i	−0.0150972	−	0.0261492i	0.858378	−	0.513018i	$-0.171472\pi$
$211$	−0.219300	−	0.379839i	−0.0150972	−	0.0261492i	−0.873475	+	0.486868i	$0.838139\pi$
$212$		0			0
$213$	16.3391	−	5.91490i	1.11954	−	0.405282i
$214$		0			0
$215$	2.78363	+	4.82139i	0.189842	+	0.328816i
$216$		0			0
$217$	19.6944	−	4.21319i	1.33694	−	0.286010i
$218$		0			0
$219$	4.44034	−	24.9297i	0.300050	−	1.68460i
$220$		0			0
$221$		−	27.5811i		−	1.85531i
$222$		0			0
$223$	17.6417	+	10.1854i	1.18137	+	0.682066i	0.956332	−	0.292284i	$-0.0944151\pi$
$223$	17.6417	+	10.1854i	1.18137	+	0.682066i	0.225041	+	0.974349i	$0.427748\pi$
$224$		0			0
$225$	−0.0976270	−	0.0359169i	−0.00650847	−	0.00239446i
$226$		0			0
$227$	0.754935	+	1.30759i	0.0501068	+	0.0867875i	0.889991	−	0.455978i	$-0.150710\pi$
$227$	0.754935	+	1.30759i	0.0501068	+	0.0867875i	−0.839884	+	0.542766i	$0.817377\pi$
$228$		0			0
$229$	18.3899	+	10.6174i	1.21524	+	0.701617i	0.963895	−	0.266281i	$-0.0857950\pi$
$229$	18.3899	+	10.6174i	1.21524	+	0.701617i	0.251341	+	0.967899i	$0.419128\pi$
$230$		0			0
$231$	4.56746	−	8.58144i	0.300517	−	0.564617i
$232$		0			0
$233$	−9.85938	+	5.69231i	−0.645909	+	0.372916i	−0.786887	−	0.617097i	$-0.788309\pi$
$233$	−9.85938	+	5.69231i	−0.645909	+	0.372916i	0.140978	+	0.990013i	$0.454975\pi$
$234$		0			0
$235$	4.23013	−	7.32681i	0.275944	−	0.477948i
$236$		0			0
$237$	−8.57731	−	23.6936i	−0.557156	−	1.53907i
$238$		0			0
$239$	14.1401	−	8.16380i	0.914648	−	0.528072i	0.0327241	−	0.999464i	$-0.489582\pi$
$239$	14.1401	−	8.16380i	0.914648	−	0.528072i	0.881924	+	0.471392i	$0.156248\pi$
$240$		0			0
$241$	20.7592	−	11.9853i	1.33722	−	0.772042i	0.350822	−	0.936442i	$-0.385902\pi$
$241$	20.7592	−	11.9853i	1.33722	−	0.772042i	0.986394	+	0.164400i	$0.0525688\pi$
$242$		0			0
$243$	15.3745	−	2.57382i	0.986275	−	0.165110i
$244$		0			0
$245$	−1.58974	+	15.5169i	−0.101564	+	0.991337i
$246$		0			0
$247$	−15.4650	+	26.7861i	−0.984012	+	1.70436i
$248$		0			0
$249$	−21.8709	−	3.89551i	−1.38601	−	0.246868i
$250$		0			0
$251$	−25.9828			−1.64002			−0.820009	−	0.572351i	$-0.806031\pi$
$251$	−25.9828			−1.64002			−0.820009	+	0.572351i	$0.806031\pi$
$252$		0			0
$253$	9.25715			0.581992
$254$		0			0
$255$	11.6354	−	13.8178i	0.728636	−	0.865305i
$256$		0			0
$257$	−0.979785	+	1.69704i	−0.0611173	+	0.105858i	−0.894965	−	0.446136i	$-0.852800\pi$
$257$	−0.979785	+	1.69704i	−0.0611173	+	0.105858i	0.833848	+	0.551994i	$0.186133\pi$
$258$		0			0
$259$	−7.08063	+	6.39227i	−0.439969	+	0.397196i
$260$		0			0
$261$	7.68667	−	1.32792i	0.475793	−	0.0821962i
$262$		0			0
$263$	−3.11722	+	1.79973i	−0.192216	+	0.110976i	−0.593019	−	0.805188i	$-0.702064\pi$
$263$	−3.11722	+	1.79973i	−0.192216	+	0.110976i	0.400804	+	0.916164i	$0.368731\pi$
$264$		0			0
$265$	9.09179	−	5.24915i	0.558504	−	0.322453i
$266$		0			0
$267$	6.10174	−	7.24623i	0.373420	−	0.443462i
$268$		0			0
$269$	4.06967	−	7.04888i	0.248132	−	0.429778i	−0.714875	−	0.699252i	$-0.753517\pi$
$269$	4.06967	−	7.04888i	0.248132	−	0.429778i	0.963008	+	0.269474i	$0.0868499\pi$
$270$		0			0
$271$	16.3378	−	9.43265i	0.992452	−	0.572992i	0.0864458	−	0.996257i	$-0.472449\pi$
$271$	16.3378	−	9.43265i	0.992452	−	0.572992i	0.906006	+	0.423264i	$0.139116\pi$
$272$		0			0
$273$	12.6879	−	23.8383i	0.767907	−	1.44276i
$274$		0			0
$275$	0.0637026	+	0.0367787i	0.00384141	+	0.00221784i
$276$		0			0
$277$	−10.8340	−	18.7650i	−0.650950	−	1.12748i	−0.982893	−	0.184179i	$-0.941037\pi$
$277$	−10.8340	−	18.7650i	−0.650950	−	1.12748i	0.331943	−	0.943300i	$-0.392296\pi$
$278$		0			0
$279$	−14.6184	−	17.5446i	−0.875181	−	1.05037i
$280$		0			0
$281$	11.6851	+	6.74642i	0.697077	+	0.402457i	0.806258	−	0.591564i	$-0.201489\pi$
$281$	11.6851	+	6.74642i	0.697077	+	0.402457i	−0.109181	+	0.994022i	$0.534823\pi$
$282$		0			0
$283$		−	2.03256i		−	0.120823i	−0.998174	−	0.0604115i	$-0.980759\pi$
$283$		−	2.03256i		−	0.120823i	0.998174	−	0.0604115i	$-0.0192413\pi$
$284$		0			0
$285$	−19.0478	+	6.89548i	−1.12829	+	0.408453i
$286$		0			0
$287$	−0.155160	+	0.140075i	−0.00915879	+	0.00826839i
$288$		0			0
$289$	−2.45310	−	4.24890i	−0.144300	−	0.249935i
$290$		0			0
$291$	−4.53429	+	25.4573i	−0.265805	+	1.49233i
$292$		0			0
$293$	15.8661	+	27.4809i	0.926908	+	1.60545i	0.788463	+	0.615083i	$0.210877\pi$
$293$	15.8661	+	27.4809i	0.926908	+	1.60545i	0.138446	+	0.990370i	$0.455789\pi$
$294$		0			0
$295$	14.7000	−	25.4611i	0.855866	−	1.48240i
$296$		0			0
$297$	−11.0227	−	0.0572942i	−0.639603	−	0.00332454i
$298$		0			0
$299$	25.7154			1.48716
$300$		0			0
$301$	6.28938	+	2.03442i	0.362514	+	0.117262i
$302$		0			0
$303$	3.64372	−	4.32717i	0.209326	−	0.248589i
$304$		0			0
$305$	15.7457	+	9.09079i	0.901597	+	0.520537i
$306$		0			0
$307$		−	0.266045i		−	0.0151840i	−0.999971	−	0.00759200i	$-0.997583\pi$
$307$		−	0.266045i		−	0.0151840i	0.999971	−	0.00759200i	$-0.00241663\pi$
$308$		0			0
$309$	−1.44823	+	8.13094i	−0.0823872	+	0.462553i
$310$		0			0
$311$	4.36245			0.247372			0.123686	−	0.992321i	$-0.460528\pi$
$311$	4.36245			0.247372			0.123686	+	0.992321i	$0.460528\pi$
$312$		0			0
$313$			15.4386i			0.872640i	0.899792	+	0.436320i	$0.143718\pi$
$313$			15.4386i			0.872640i	−0.899792	+	0.436320i	$0.856282\pi$
$314$		0			0
$315$	16.4129	−	6.59019i	0.924765	−	0.371315i
$316$		0			0
$317$			21.7248i			1.22019i	0.792329	+	0.610094i	$0.208868\pi$
$317$			21.7248i			1.22019i	−0.792329	+	0.610094i	$0.791132\pi$
$318$		0			0
$319$	−5.51589			−0.308831
$320$		0			0
$321$	−9.78582	−	8.24021i	−0.546191	−	0.459924i
$322$		0			0
$323$			24.5660i			1.36689i
$324$		0			0
$325$	0.176959	+	0.102167i	0.00981591	+	0.00566722i
$326$		0			0
$327$	−4.00210	−	0.712830i	−0.221317	−	0.0394196i
$328$		0			0
$329$	−2.10141	−	9.82296i	−0.115854	−	0.541557i
$330$		0			0
$331$	−15.1462			−0.832511			−0.416255	−	0.909248i	$-0.636658\pi$
$331$	−15.1462			−0.832511			−0.416255	+	0.909248i	$0.636658\pi$
$332$		0			0
$333$	10.1513	+	3.73464i	0.556285	+	0.204657i
$334$		0			0
$335$	−5.29475	+	9.17078i	−0.289283	+	0.501053i
$336$		0			0
$337$	3.75166	+	6.49807i	0.204366	+	0.353973i	0.949931	−	0.312461i	$-0.101153\pi$
$337$	3.75166	+	6.49807i	0.204366	+	0.353973i	−0.745564	+	0.666434i	$0.767820\pi$
$338$		0			0
$339$	18.1994	+	15.3249i	0.988456	+	0.832336i
$340$		0			0
$341$	8.07409	+	13.9847i	0.437237	+	0.757316i
$342$		0			0
$343$	10.9448	+	14.9402i	0.590965	+	0.806697i
$344$		0			0
$345$	12.8831	+	10.8483i	0.693603	+	0.584053i
$346$		0			0
$347$		−	4.89571i		−	0.262816i	−0.991328	−	0.131408i	$-0.958050\pi$
$347$		−	4.89571i		−	0.262816i	0.991328	−	0.131408i	$-0.0419497\pi$
$348$		0			0
$349$	2.64213	+	1.52543i	0.141430	+	0.0816546i	0.569045	−	0.822306i	$-0.307313\pi$
$349$	2.64213	+	1.52543i	0.141430	+	0.0816546i	−0.427615	+	0.903961i	$0.640646\pi$
$350$		0			0
$351$	−30.6199	−	0.159157i	−1.63437	−	0.00849517i
$352$		0			0
$353$	−8.51890	−	14.7552i	−0.453415	−	0.785338i	0.545180	−	0.838319i	$-0.316461\pi$
$353$	−8.51890	−	14.7552i	−0.453415	−	0.785338i	−0.998596	+	0.0529806i	$0.983128\pi$
$354$		0			0
$355$	−19.3603	−	11.1777i	−1.02754	−	0.593250i
$356$		0			0
$357$	−0.739520	−	21.4356i	−0.0391395	−	1.13449i
$358$		0			0
$359$	2.27682	−	1.31452i	0.120166	−	0.0693778i	−0.438712	−	0.898628i	$-0.644565\pi$
$359$	2.27682	−	1.31452i	0.120166	−	0.0693778i	0.558878	+	0.829250i	$0.311232\pi$
$360$		0			0
$361$	4.27438	−	7.40344i	0.224967	−	0.389655i
$362$		0			0
$363$	−11.0837	−	1.97416i	−0.581741	−	0.103616i
$364$		0			0
$365$	−28.2126	+	16.2886i	−1.47672	+	0.852583i
$366$		0			0
$367$	16.2436	−	9.37824i	0.847908	−	0.489540i	−0.0120362	−	0.999928i	$-0.503831\pi$
$367$	16.2436	−	9.37824i	0.847908	−	0.489540i	0.859945	+	0.510387i	$0.170498\pi$
$368$		0			0
$369$	0.222447	+	0.0818381i	0.0115801	+	0.00426032i
$370$		0			0
$371$	3.83635	−	11.8600i	0.199174	−	0.615741i
$372$		0			0
$373$	−2.42980	+	4.20853i	−0.125810	+	0.217910i	−0.922049	−	0.387072i	$-0.873486\pi$
$373$	−2.42980	+	4.20853i	−0.125810	+	0.217910i	0.796239	+	0.604982i	$0.206820\pi$
$374$		0			0
$375$	6.61431	+	18.2711i	0.341562	+	0.943516i
$376$		0			0
$377$	−15.3225			−0.789151
$378$		0			0
$379$	−3.46902			−0.178192			−0.0890959	−	0.996023i	$-0.528398\pi$
$379$	−3.46902			−0.178192			−0.0890959	+	0.996023i	$0.528398\pi$
$380$		0			0
$381$	−3.52515	−	9.73773i	−0.180599	−	0.498879i
$382$		0			0
$383$	−9.30298	+	16.1132i	−0.475360	+	0.823348i	−0.999602	−	0.0282216i	$-0.991016\pi$
$383$	−9.30298	+	16.1132i	−0.475360	+	0.823348i	0.524241	+	0.851570i	$0.324349\pi$
$384$		0			0
$385$	−12.2298	+	2.61629i	−0.623287	+	0.133339i
$386$		0			0
$387$	−1.27596	−	7.38589i	−0.0648606	−	0.375446i
$388$		0			0
$389$	13.4613	−	7.77186i	0.682513	−	0.394049i	−0.118288	−	0.992979i	$-0.537741\pi$
$389$	13.4613	−	7.77186i	0.682513	−	0.394049i	0.800801	+	0.598930i	$0.204407\pi$
$390$		0			0
$391$	17.6880	−	10.2122i	0.894521	−	0.516452i
$392$		0			0
$393$	−35.7387	−	6.36556i	−1.80278	−	0.321100i
$394$		0			0
$395$	−16.2090	+	28.0748i	−0.815562	+	1.41260i
$396$		0			0
$397$	−13.0507	+	7.53483i	−0.654996	+	0.378162i	−0.790368	−	0.612633i	$-0.790111\pi$
$397$	−13.0507	+	7.53483i	−0.654996	+	0.378162i	0.135371	+	0.990795i	$0.456777\pi$
$398$		0			0
$399$	−11.3009	+	21.2324i	−0.565753	+	1.06295i
$400$		0			0
$401$	−6.74463	−	3.89401i	−0.336811	−	0.194458i	0.322050	−	0.946723i	$-0.395628\pi$
$401$	−6.74463	−	3.89401i	−0.336811	−	0.194458i	−0.658861	+	0.752265i	$0.728961\pi$
$402$		0			0
$403$	22.4289	+	38.8481i	1.11727	+	1.93516i
$404$		0			0
$405$	−15.2731	−	12.9971i	−0.758926	−	0.645830i
$406$		0			0
$407$	−6.62379	−	3.82425i	−0.328329	−	0.189561i
$408$		0			0
$409$		−	8.99874i		−	0.444959i	−0.974937	−	0.222480i	$-0.928585\pi$
$409$		−	8.99874i		−	0.444959i	0.974937	−	0.222480i	$-0.0714151\pi$
$410$		0			0
$411$	−4.59055	−	3.86550i	−0.226435	−	0.190671i
$412$		0			0
$413$	−7.30252	−	34.1354i	−0.359334	−	1.67969i
$414$		0			0
$415$	14.2900	+	24.7509i	0.701466	+	1.21498i
$416$		0			0
$417$	0.580746	+	0.489021i	0.0284392	+	0.0239474i
$418$		0			0
$419$	6.70022	+	11.6051i	0.327327	+	0.566947i	0.981981	−	0.188982i	$-0.0605187\pi$
$419$	6.70022	+	11.6051i	0.327327	+	0.566947i	−0.654653	+	0.755929i	$0.727185\pi$
$420$		0			0
$421$	9.44700	−	16.3627i	0.460419	−	0.797469i	−0.538563	−	0.842585i	$-0.681033\pi$
$421$	9.44700	−	16.3627i	0.460419	−	0.797469i	0.998982	+	0.0451166i	$0.0143659\pi$
$422$		0			0
$423$	−8.75072	+	7.29120i	−0.425475	+	0.354510i
$424$		0			0
$425$	0.162292			0.00787232
$426$		0			0
$427$	21.1101	−	4.51604i	1.02159	−	0.218547i
$428$		0			0
$429$	21.3167	+	3.79680i	1.02918	+	0.183311i
$430$		0			0
$431$	−25.4056	−	14.6679i	−1.22375	−	0.706530i	−0.258031	−	0.966137i	$-0.583074\pi$
$431$	−25.4056	−	14.6679i	−1.22375	−	0.706530i	−0.965714	+	0.259607i	$0.916407\pi$
$432$		0			0
$433$			9.41744i			0.452573i	0.974061	+	0.226287i	$0.0726586\pi$
$433$			9.41744i			0.452573i	−0.974061	+	0.226287i	$0.927341\pi$
$434$		0			0
$435$	−7.67642	−	6.46398i	−0.368056	−	0.309924i
$436$		0			0
$437$	−22.9042			−1.09566
$438$		0			0
$439$		−	31.7980i		−	1.51764i	−0.651302	−	0.758819i	$-0.725777\pi$
$439$		−	31.7980i		−	1.51764i	0.651302	−	0.758819i	$-0.274223\pi$
$440$		0			0
$441$	9.22167	−	18.8669i	0.439127	−	0.898425i
$442$		0			0
$443$		−	37.0295i		−	1.75932i	−0.475600	−	0.879662i	$-0.657769\pi$
$443$		−	37.0295i		−	1.75932i	0.475600	−	0.879662i	$-0.342231\pi$
$444$		0			0
$445$	−12.1872			−0.577729
$446$		0			0
$447$	5.31532	−	29.8423i	0.251406	−	1.41149i
$448$		0			0
$449$			19.3840i			0.914789i	0.889264	+	0.457394i	$0.151217\pi$
$449$			19.3840i			0.914789i	−0.889264	+	0.457394i	$0.848783\pi$
$450$		0			0
$451$	−0.145149	−	0.0838017i	−0.00683479	−	0.00394607i
$452$		0			0
$453$	−0.418185	+	0.496624i	−0.0196481	+	0.0233334i
$454$		0			0
$455$	−33.9730	+	7.26778i	−1.59268	+	0.340719i
$456$		0			0
$457$	10.5349			0.492803			0.246401	−	0.969168i	$-0.420752\pi$
$457$	10.5349			0.492803			0.246401	+	0.969168i	$0.420752\pi$
$458$		0			0
$459$	−21.1247	+	12.0504i	−0.986019	+	0.562465i
$460$		0			0
$461$	−7.09138	+	12.2826i	−0.330278	+	0.572059i	−0.982566	−	0.185912i	$-0.940476\pi$
$461$	−7.09138	+	12.2826i	−0.330278	+	0.572059i	0.652288	+	0.757971i	$0.273809\pi$
$462$		0			0
$463$	5.05071	+	8.74808i	0.234726	+	0.406558i	0.959193	−	0.282752i	$-0.0912473\pi$
$463$	5.05071	+	8.74808i	0.234726	+	0.406558i	−0.724467	+	0.689310i	$0.757914\pi$
$464$		0			0
$465$	−5.15183	+	28.9243i	−0.238910	+	1.34133i
$466$		0			0
$467$	−11.1047	−	19.2340i	−0.513866	−	0.890042i	−0.999871	−	0.0160858i	$-0.994880\pi$
$467$	−11.1047	−	19.2340i	−0.513866	−	0.890042i	0.486005	−	0.873956i	$-0.338454\pi$
$468$		0			0
$469$	2.63028	+	12.2951i	0.121455	+	0.567737i
$470$		0			0
$471$	−33.1504	+	12.0008i	−1.52749	+	0.552965i
$472$		0			0
$473$			5.30005i			0.243697i
$474$		0			0
$475$	−0.157614	−	0.0909986i	−0.00723184	−	0.00417530i
$476$		0			0
$477$	−13.9277	+	2.40610i	−0.637707	+	0.110168i
$478$		0			0
$479$	−4.71275	−	8.16272i	−0.215331	−	0.372964i	0.738044	−	0.674753i	$-0.235750\pi$
$479$	−4.71275	−	8.16272i	−0.215331	−	0.372964i	−0.953375	+	0.301788i	$0.902416\pi$
$480$		0			0
$481$	−18.4002	−	10.6233i	−0.838975	−	0.484383i
$482$		0			0
$483$	19.9856	−	0.689495i	0.909374	−	0.0313731i
$484$		0			0
$485$	28.8096	−	16.6332i	1.30818	−	0.755276i
$486$		0			0
$487$	14.6113	−	25.3076i	0.662103	−	1.14680i	−0.317959	−	0.948104i	$-0.602997\pi$
$487$	14.6113	−	25.3076i	0.662103	−	1.14680i	0.980062	−	0.198692i	$-0.0636692\pi$
$488$		0			0
$489$	16.1857	−	19.2216i	0.731942	−	0.869231i
$490$		0			0
$491$	6.31308	−	3.64486i	0.284905	−	0.164490i	−0.350737	−	0.936474i	$-0.614069\pi$
$491$	6.31308	−	3.64486i	0.284905	−	0.164490i	0.635642	+	0.771984i	$0.280735\pi$
$492$		0			0
$493$	−10.5394	+	6.08494i	−0.474672	+	0.274052i
$494$		0			0
$495$	9.07769	+	10.8948i	0.408012	+	0.489686i
$496$		0			0
$497$	−25.9561	+	5.55275i	−1.16429	+	0.249075i
$498$		0			0
$499$	−7.80996	+	13.5272i	−0.349622	+	0.605563i	−0.986182	−	0.165664i	$-0.947023\pi$
$499$	−7.80996	+	13.5272i	−0.349622	+	0.605563i	0.636561	+	0.771227i	$0.280357\pi$
$500$		0			0
$501$	17.0137	−	20.2049i	0.760116	−	0.902690i
$502$		0			0
$503$	6.09425			0.271729			0.135865	−	0.990727i	$-0.456619\pi$
$503$	6.09425			0.271729			0.135865	+	0.990727i	$0.456619\pi$
$504$		0			0
$505$	−7.27772			−0.323854
$506$		0			0
$507$	37.0476	+	6.59870i	1.64534	+	0.293058i
$508$		0			0
$509$	14.1799	−	24.5604i	0.628515	−	1.08862i	−0.359335	−	0.933208i	$-0.616997\pi$
$509$	14.1799	−	24.5604i	0.628515	−	1.08862i	0.987850	−	0.155411i	$-0.0496701\pi$
$510$		0			0
$511$	−11.9045	+	36.8026i	−0.526626	+	1.62805i
$512$		0			0
$513$	27.2726	+	0.141758i	1.20412	+	0.00625879i
$514$		0			0
$515$	9.20167	−	5.31258i	0.405474	−	0.234100i
$516$		0			0
$517$	6.97515	−	4.02710i	0.306767	−	0.177112i
$518$		0			0
$519$	1.10920	+	3.06402i	0.0486886	+	0.134495i
$520$		0			0
$521$	−19.2896	+	33.4105i	−0.845091	+	1.46374i	0.0404517	+	0.999181i	$0.487120\pi$
$521$	−19.2896	+	33.4105i	−0.845091	+	1.46374i	−0.885542	+	0.464559i	$0.846213\pi$
$522$		0			0
$523$	−24.1399	+	13.9372i	−1.05556	+	0.609429i	−0.924201	−	0.381905i	$-0.875268\pi$
$523$	−24.1399	+	13.9372i	−1.05556	+	0.609429i	−0.131361	+	0.991335i	$0.541935\pi$
$524$		0			0
$525$	0.140269	+	0.0746579i	0.00612183	+	0.00325834i
$526$		0			0
$527$	30.8550	+	17.8141i	1.34406	+	0.775996i
$528$		0			0
$529$	−1.97863	−	3.42708i	−0.0860273	−	0.149004i
$530$		0			0
$531$	−30.4093	+	25.3374i	−1.31965	+	1.09955i
$532$		0			0
$533$	−0.403208	−	0.232792i	−0.0174649	−	0.0100833i
$534$		0			0
$535$			16.4585i			0.711561i
$536$		0			0
$537$	−3.03034	+	17.0135i	−0.130769	+	0.734187i
$538$		0			0
$539$	−8.69674	+	12.0363i	−0.374595	+	0.518441i
$540$		0			0
$541$	−10.9182	−	18.9109i	−0.469410	−	0.813041i	0.529979	−	0.848011i	$-0.322200\pi$
$541$	−10.9182	−	18.9109i	−0.469410	−	0.813041i	−0.999388	+	0.0349697i	$0.988867\pi$
$542$		0			0
$543$	−18.3753	+	6.65204i	−0.788560	+	0.285466i
$544$		0			0
$545$	2.61489	+	4.52912i	0.112009	+	0.194006i
$546$		0			0
$547$	12.5173	−	21.6806i	0.535201	−	0.926995i	−0.463953	−	0.885860i	$-0.653569\pi$
$547$	12.5173	−	21.6806i	0.535201	−	0.926995i	0.999154	−	0.0411350i	$-0.0130974\pi$
$548$		0			0
$549$	−15.6692	−	18.8058i	−0.668745	−	0.802611i
$550$		0			0
$551$	13.6475			0.581404
$552$		0			0
$553$	8.05215	+	37.6395i	0.342412	+	1.60059i
$554$		0			0
$555$	−4.73671	−	13.0845i	−0.201062	−	0.555406i
$556$		0			0
$557$	11.1937	+	6.46267i	0.474291	+	0.273832i	0.718034	−	0.696008i	$-0.245042\pi$
$557$	11.1937	+	6.46267i	0.474291	+	0.273832i	−0.243743	+	0.969840i	$0.578375\pi$
$558$		0			0
$559$			14.7230i			0.622715i
$560$		0			0
$561$	16.1702	−	5.85377i	0.682707	−	0.247146i
$562$		0			0
$563$	−15.6211			−0.658352			−0.329176	−	0.944269i	$-0.606771\pi$
$563$	−15.6211			−0.658352			−0.329176	+	0.944269i	$0.606771\pi$
$564$		0			0
$565$		−	30.6090i		−	1.28773i
$566$		0			0
$567$	−23.8015	+	0.697304i	−0.999571	+	0.0292840i
$568$		0			0
$569$		−	42.6069i		−	1.78617i	−0.449884	−	0.893087i	$-0.648535\pi$
$569$		−	42.6069i		−	1.78617i	0.449884	−	0.893087i	$-0.351465\pi$
$570$		0			0
$571$	−19.7970			−0.828477			−0.414239	−	0.910168i	$-0.635952\pi$
$571$	−19.7970			−0.828477			−0.414239	+	0.910168i	$0.635952\pi$
$572$		0			0
$573$	20.9528	−	7.58512i	0.875317	−	0.316873i
$574$		0			0
$575$			0.151314i			0.00631022i
$576$		0			0
$577$	−40.6443	−	23.4660i	−1.69204	−	0.976902i	−0.952866	−	0.303391i	$-0.901881\pi$
$577$	−40.6443	−	23.4660i	−1.69204	−	0.976902i	−0.739178	−	0.673511i	$-0.764786\pi$
$578$		0			0
$579$	−7.09685	−	19.6040i	−0.294935	−	0.814716i
$580$		0			0
$581$	32.2870	+	10.4439i	1.33949	+	0.433284i
$582$		0			0
$583$	9.99442			0.413927
$584$		0			0
$585$	25.2168	+	30.2646i	1.04259	+	1.25129i
$586$		0			0
$587$	−2.18063	+	3.77696i	−0.0900041	+	0.155892i	−0.907513	−	0.420025i	$-0.862021\pi$
$587$	−2.18063	+	3.77696i	−0.0900041	+	0.155892i	0.817509	+	0.575917i	$0.195355\pi$
$588$		0			0
$589$	−19.9771	−	34.6013i	−0.823141	−	1.42572i
$590$		0			0
$591$	−45.1554	+	16.3467i	−1.85744	+	0.672412i
$592$		0			0
$593$	2.31077	+	4.00236i	0.0948918	+	0.164357i	0.909563	−	0.415565i	$-0.136416\pi$
$593$	2.31077	+	4.00236i	0.0948918	+	0.164357i	−0.814672	+	0.579922i	$0.803083\pi$
$594$		0			0
$595$	−20.4817	+	18.4905i	−0.839668	+	0.758038i
$596$		0			0
$597$	−0.134273	+	0.753859i	−0.00549542	+	0.0308534i
$598$		0			0
$599$		−	25.5173i		−	1.04261i	−0.853371	−	0.521304i	$-0.825446\pi$
$599$		−	25.5173i		−	1.04261i	0.853371	−	0.521304i	$-0.174554\pi$
$600$		0			0
$601$	−22.6824	−	13.0957i	−0.925235	−	0.534185i	−0.0399336	−	0.999202i	$-0.512715\pi$
$601$	−22.6824	−	13.0957i	−0.925235	−	0.534185i	−0.885301	+	0.465018i	$0.846048\pi$
$602$		0			0
$603$	10.9531	−	9.12622i	0.446043	−	0.371648i
$604$		0			0
$605$	7.24183	+	12.5432i	0.294422	+	0.509954i
$606$		0			0
$607$	−5.08757	−	2.93731i	−0.206498	−	0.119222i	0.393185	−	0.919459i	$-0.371373\pi$
$607$	−5.08757	−	2.93731i	−0.206498	−	0.119222i	−0.599683	+	0.800238i	$0.704707\pi$
$608$		0			0
$609$	−11.9084	+	0.410836i	−0.482554	+	0.0166479i
$610$		0			0
$611$	19.3762	−	11.1869i	0.783878	−	0.452572i
$612$		0			0
$613$	12.4511	−	21.5660i	0.502896	−	0.871041i	−0.497099	−	0.867694i	$-0.665601\pi$
$613$	12.4511	−	21.5660i	0.502896	−	0.871041i	0.999994	−	0.00334675i	$-0.00106531\pi$
$614$		0			0
$615$	−0.103797	−	0.286724i	−0.00418549	−	0.0115618i
$616$		0			0
$617$	26.1105	−	15.0749i	1.05117	−	0.606894i	0.128194	−	0.991749i	$-0.459082\pi$
$617$	26.1105	−	15.0749i	1.05117	−	0.606894i	0.922977	+	0.384855i	$0.125749\pi$
$618$		0			0
$619$	−29.5953	+	17.0869i	−1.18954	+	0.686779i	−0.958201	−	0.286096i	$-0.907642\pi$
$619$	−29.5953	+	17.0869i	−1.18954	+	0.686779i	−0.231334	+	0.972874i	$0.574309\pi$
$620$		0			0
$621$	−11.2353	−	19.6958i	−0.450855	−	0.790364i
$622$		0			0
$623$	−10.7409	+	9.69666i	−0.430323	+	0.388489i
$624$		0			0
$625$	12.4127	−	21.4994i	0.496508	−	0.859978i
$626$		0			0
$627$	−18.9864	−	3.38174i	−0.758243	−	0.135054i
$628$		0			0
$629$	−16.8751			−0.672855
$630$		0			0
$631$	8.55990			0.340764			0.170382	−	0.985378i	$-0.445500\pi$
$631$	8.55990			0.340764			0.170382	+	0.985378i	$0.445500\pi$
$632$		0			0
$633$	0.489319	−	0.581100i	0.0194487	−	0.0230967i
$634$		0			0
$635$	−6.66165	+	11.5383i	−0.264360	+	0.457884i
$636$		0			0
$637$	−24.1586	+	33.4356i	−0.957199	+	1.32477i
$638$		0			0
$639$	19.2662	+	23.1229i	0.762161	+	0.914726i
$640$		0			0
$641$	−35.0737	+	20.2498i	−1.38533	+	0.799818i	−0.992784	−	0.119916i	$-0.961738\pi$
$641$	−35.0737	+	20.2498i	−1.38533	+	0.799818i	−0.392542	+	0.919734i	$0.628404\pi$
$642$		0			0
$643$	31.8435	−	18.3849i	1.25579	−	0.725028i	0.283533	−	0.958963i	$-0.408493\pi$
$643$	31.8435	−	18.3849i	1.25579	−	0.725028i	0.972252	+	0.233935i	$0.0751602\pi$
$644$		0			0
$645$	−6.21105	+	7.37604i	−0.244560	+	0.290431i
$646$		0			0
$647$	23.5492	−	40.7884i	0.925815	−	1.60356i	0.135569	−	0.990768i	$-0.456714\pi$
$647$	23.5492	−	40.7884i	0.925815	−	1.60356i	0.790246	−	0.612790i	$-0.209953\pi$
$648$		0			0
$649$	24.2391	−	13.9944i	0.951467	−	0.549330i
$650$		0			0
$651$	18.4730	+	29.5907i	0.724015	+	1.15975i
$652$		0			0
$653$	−2.16748	−	1.25139i	−0.0848199	−	0.0489708i	0.456990	−	0.889472i	$-0.348927\pi$
$653$	−2.16748	−	1.25139i	−0.0848199	−	0.0489708i	−0.541810	+	0.840501i	$0.682261\pi$
$654$		0			0
$655$	23.3509	+	40.4450i	0.912395	+	1.58032i
$656$		0			0
$657$	43.2190	−	7.46635i	1.68613	−	0.291290i
$658$		0			0
$659$	36.2490	+	20.9284i	1.41206	+	0.815254i	0.995582	−	0.0938917i	$-0.0299307\pi$
$659$	36.2490	+	20.9284i	1.41206	+	0.815254i	0.416479	+	0.909146i	$0.363264\pi$
$660$		0			0
$661$			8.49304i			0.330341i	0.986265	+	0.165170i	$0.0528174\pi$
$661$			8.49304i			0.330341i	−0.986265	+	0.165170i	$0.947183\pi$
$662$		0			0
$663$	44.9191	−	16.2611i	1.74451	−	0.631530i
$664$		0			0
$665$	30.2592	−	6.47329i	1.17340	−	0.251023i
$666$		0			0
$667$	−5.67333	−	9.82649i	−0.219672	−	0.380483i
$668$		0			0
$669$	−6.18708	+	34.7366i	−0.239206	+	1.34299i
$670$		0			0
$671$	8.65447	+	14.9900i	0.334102	+	0.578682i
$672$		0			0
$673$	−16.9974	+	29.4403i	−0.655201	+	1.13484i	0.326642	+	0.945148i	$0.394083\pi$
$673$	−16.9974	+	29.4403i	−0.655201	+	1.13484i	−0.981843	+	0.189694i	$0.939251\pi$
$674$		0			0
$675$	0.000936508	−	0.180173i	3.60462e−5	−	0.00693486i
$676$		0			0
$677$	−39.0351			−1.50024			−0.750121	−	0.661301i	$-0.770005\pi$
$677$	−39.0351			−1.50024			−0.750121	+	0.661301i	$0.770005\pi$
$678$		0			0
$679$	12.1564	−	37.5814i	0.466522	−	1.44224i
$680$		0			0
$681$	−1.68447	+	2.00042i	−0.0645490	+	0.0766564i
$682$		0			0
$683$	−1.91400	−	1.10505i	−0.0732373	−	0.0422836i	0.462934	−	0.886393i	$-0.346797\pi$
$683$	−1.91400	−	1.10505i	−0.0732373	−	0.0422836i	−0.536171	+	0.844109i	$0.680130\pi$
$684$		0			0
$685$			7.72069i			0.294992i
$686$		0			0
$687$	−6.44948	+	36.2099i	−0.246063	+	1.38149i
$688$		0			0
$689$	27.7634			1.05770
$690$		0			0
$691$		−	3.41836i		−	0.130041i	−0.997884	−	0.0650203i	$-0.979289\pi$
$691$		−	3.41836i		−	0.130041i	0.997884	−	0.0650203i	$-0.0207112\pi$
$692$		0			0
$693$	16.6688	+	2.37925i	0.633194	+	0.0903803i
$694$		0			0
$695$		−	0.976737i		−	0.0370498i
$696$		0			0
$697$	−0.369789			−0.0140068
$698$		0			0
$699$	−15.0835	−	12.7011i	−0.570509	−	0.480401i
$700$		0			0
$701$		−	37.5732i		−	1.41912i	−0.704645	−	0.709560i	$-0.748894\pi$
$701$		−	37.5732i		−	1.41912i	0.704645	−	0.709560i	$-0.251106\pi$
$702$		0			0
$703$	16.3887	+	9.46203i	0.618112	+	0.356867i
$704$		0			0
$705$	14.4266	+	2.56957i	0.543336	+	0.0967757i
$706$		0			0
$707$	−6.41402	+	5.79046i	−0.241224	+	0.217773i
$708$		0			0
$709$	−26.8780			−1.00942			−0.504712	−	0.863288i	$-0.668401\pi$
$709$	−26.8780			−1.00942			−0.504712	+	0.863288i	$0.668401\pi$
$710$		0			0
$711$	33.5309	−	27.9384i	1.25751	−	1.04777i
$712$		0			0
$713$	−16.6091	+	28.7678i	−0.622015	+	1.07736i
$714$		0			0
$715$	−13.9279	−	24.1238i	−0.520872	−	0.902177i
$716$		0			0
$717$	21.6324	+	18.2157i	0.807876	+	0.680277i
$718$		0			0
$719$	1.41278	+	2.44701i	0.0526879	+	0.0912580i	0.891166	−	0.453676i	$-0.149888\pi$
$719$	1.41278	+	2.44701i	0.0526879	+	0.0912580i	−0.838479	+	0.544935i	$0.816554\pi$
$720$		0			0
$721$	3.88272	−	12.0033i	0.144600	−	0.447028i
$722$		0			0
$723$	31.7586	+	26.7425i	1.18112	+	0.994566i
$724$		0			0
$725$		−	0.0901606i		−	0.00334848i
$726$		0			0
$727$	−0.622076	−	0.359156i	−0.0230715	−	0.0133203i	0.488420	−	0.872609i	$-0.337573\pi$
$727$	−0.622076	−	0.359156i	−0.0230715	−	0.0133203i	−0.511491	+	0.859288i	$0.670907\pi$
$728$		0			0
$729$	13.2562	+	23.5218i	0.490970	+	0.871176i
$730$		0			0
$731$	5.84684	+	10.1270i	0.216253	+	0.374561i
$732$		0			0
$733$	33.4490	+	19.3118i	1.23547	+	0.713297i	0.968164	−	0.250315i	$-0.0805343\pi$
$733$	33.4490	+	19.3118i	1.23547	+	0.713297i	0.267303	+	0.963613i	$0.413868\pi$
$734$		0			0
$735$	−26.2084	+	6.55930i	−0.966710	+	0.241943i
$736$		0			0
$737$	−8.73062	+	5.04063i	−0.321596	+	0.185674i
$738$		0			0
$739$	11.9491	−	20.6965i	0.439556	−	0.761334i	−0.558099	−	0.829775i	$-0.688469\pi$
$739$	11.9491	−	20.6965i	0.439556	−	0.761334i	0.997655	+	0.0684405i	$0.0218023\pi$
$740$		0			0
$741$	−52.7421	−	9.39411i	−1.93753	−	0.345101i
$742$		0			0
$743$	20.5325	−	11.8544i	0.753264	−	0.434897i	−0.0736078	−	0.997287i	$-0.523451\pi$
$743$	20.5325	−	11.8544i	0.753264	−	0.434897i	0.826872	+	0.562390i	$0.190118\pi$
$744$		0			0
$745$	−33.7720	+	19.4983i	−1.23731	+	0.714362i
$746$		0			0
$747$	−6.55022	−	37.9160i	−0.239660	−	1.38727i
$748$		0			0
$749$	13.0950	+	14.5052i	0.478483	+	0.530009i
$750$		0			0
$751$	−6.89344	+	11.9398i	−0.251545	+	0.435689i	−0.963951	−	0.266078i	$-0.914272\pi$
$751$	−6.89344	+	11.9398i	−0.251545	+	0.435689i	0.712406	+	0.701767i	$0.247605\pi$
$752$		0			0
$753$	−15.3188	−	42.3160i	−0.558248	−	1.54208i
$754$		0			0
$755$	0.835255			0.0303981
$756$		0			0
$757$	−19.6447			−0.714000			−0.357000	−	0.934104i	$-0.616200\pi$
$757$	−19.6447			−0.714000			−0.357000	+	0.934104i	$0.616200\pi$
$758$		0			0
$759$	5.45779	+	15.0764i	0.198105	+	0.547238i
$760$		0			0
$761$	26.4732	−	45.8529i	0.959653	−	1.66217i	0.236312	−	0.971677i	$-0.424061\pi$
$761$	26.4732	−	45.8529i	0.959653	−	1.66217i	0.723341	−	0.690491i	$-0.242605\pi$
$762$		0			0
$763$	5.90812	+	1.91110i	0.213888	+	0.0691864i
$764$		0			0
$765$	29.3639	+	10.8030i	1.06165	+	0.390582i
$766$		0			0
$767$	67.3335	−	38.8750i	2.43127	−	1.40370i
$768$		0			0
$769$	−17.6774	+	10.2060i	−0.637462	+	0.368039i	−0.783636	−	0.621220i	$-0.786637\pi$
$769$	−17.6774	+	10.2060i	−0.637462	+	0.368039i	0.146174	+	0.989259i	$0.453304\pi$
$770$		0			0
$771$	−3.34149	−	0.595165i	−0.120341	−	0.0214344i
$772$		0			0
$773$	−1.07789	+	1.86697i	−0.0387692	+	0.0671501i	−0.884759	−	0.466049i	$-0.845677\pi$
$773$	−1.07789	+	1.86697i	−0.0387692	+	0.0671501i	0.845990	+	0.533199i	$0.179010\pi$
$774$		0			0
$775$	−0.228589	+	0.131976i	−0.00821116	+	0.00474072i
$776$		0			0
$777$	−14.5851	−	7.76293i	−0.523239	−	0.278494i
$778$		0			0
$779$	0.359130	+	0.207344i	0.0128672	+	0.00742887i
$780$		0			0
$781$	−10.6412	−	18.4311i	−0.380772	−	0.659517i
$782$		0			0
$783$	6.69455	+	11.7358i	0.239244	+	0.419402i
$784$		0			0
$785$	39.2802	+	22.6784i	1.40197	+	0.809428i
$786$		0			0
$787$			20.8939i			0.744786i	0.928075	+	0.372393i	$0.121463\pi$
$787$			20.8939i			0.744786i	−0.928075	+	0.372393i	$0.878537\pi$
$788$		0			0
$789$	−4.76890	−	4.01569i	−0.169777	−	0.142962i
$790$		0			0
$791$	−24.3538	−	26.9764i	−0.865922	−	0.959170i
$792$		0			0
$793$	24.0412	+	41.6405i	0.853727	+	1.47870i
$794$		0			0
$795$	13.9092	+	11.7123i	0.493307	+	0.415392i
$796$		0			0
$797$	−13.9964	−	24.2424i	−0.495777	−	0.858710i	0.504211	−	0.863580i	$-0.331783\pi$
$797$	−13.9964	−	24.2424i	−0.495777	−	0.858710i	−0.999988	+	0.00486976i	$0.998450\pi$
$798$		0			0
$799$	8.88513	−	15.3895i	0.314333	−	0.544441i
$800$		0			0
$801$	15.3988	+	5.66521i	0.544090	+	0.200170i
$802$		0			0
$803$	−31.0136			−1.09444
$804$		0			0
$805$	−17.2397	−	19.0962i	−0.607621	−	0.673053i
$806$		0			0
$807$	13.8793	+	2.47210i	0.488575	+	0.0870221i
$808$		0			0
$809$	37.1345	+	21.4396i	1.30558	+	0.753777i	0.981355	−	0.192203i	$-0.0615633\pi$
$809$	37.1345	+	21.4396i	1.30558	+	0.753777i	0.324225	+	0.945980i	$0.394897\pi$
$810$		0			0
$811$			23.7421i			0.833699i	0.908976	+	0.416849i	$0.136866\pi$
$811$			23.7421i			0.833699i	−0.908976	+	0.416849i	$0.863134\pi$
$812$		0			0
$813$	24.9946	+	21.0468i	0.876598	+	0.738145i
$814$		0			0
$815$	−32.3282			−1.13241
$816$		0			0
$817$		−	13.1135i		−	0.458783i
$818$		0			0
$819$	46.3040	+	6.60930i	1.61799	+	0.230948i
$820$		0			0
$821$			1.58699i			0.0553863i	0.999616	+	0.0276932i	$0.00881614\pi$
$821$			1.58699i			0.0553863i	−0.999616	+	0.0276932i	$0.991184\pi$
$822$		0			0
$823$	3.08203			0.107433			0.0537164	−	0.998556i	$-0.482893\pi$
$823$	3.08203			0.107433			0.0537164	+	0.998556i	$0.482893\pi$
$824$		0			0
$825$	−0.0223410	+	0.125431i	−0.000777815	+	0.00436695i
$826$		0			0
$827$		−	20.7448i		−	0.721369i	−0.932688	−	0.360685i	$-0.882543\pi$
$827$		−	20.7448i		−	0.721369i	0.932688	−	0.360685i	$-0.117457\pi$
$828$		0			0
$829$	−0.917576	−	0.529763i	−0.0318687	−	0.0183994i	0.483981	−	0.875079i	$-0.339190\pi$
$829$	−0.917576	−	0.529763i	−0.0318687	−	0.0183994i	−0.515850	+	0.856679i	$0.672524\pi$
$830$		0			0
$831$	24.1736	−	28.7078i	0.838572	−	0.995862i
$832$		0			0
$833$	−3.33914	+	32.5922i	−0.115694	+	1.12925i
$834$		0			0
$835$	−33.9820			−1.17600
$836$		0			0
$837$	19.9549	−	34.1517i	0.689742	−	1.18046i
$838$		0			0
$839$	19.2137	−	33.2792i	0.663332	−	1.14892i	−0.316403	−	0.948625i	$-0.602475\pi$
$839$	19.2137	−	33.2792i	0.663332	−	1.14892i	0.979735	−	0.200299i	$-0.0641914\pi$
$840$		0			0
$841$	−11.1195	−	19.2596i	−0.383432	−	0.664124i
$842$		0			0
$843$	−4.09807	+	23.0082i	−0.141145	+	0.792443i
$844$		0			0
$845$	−24.2061	−	41.9262i	−0.832716	−	1.44231i
$846$		0			0
$847$	16.3623	+	5.29271i	0.562216	+	0.181860i
$848$		0			0
$849$	3.31026	−	1.19835i	0.113608	−	0.0411271i
$850$		0			0
$851$		−	15.7336i		−	0.539341i
$852$		0			0
$853$	12.0659	+	6.96626i	0.413129	+	0.238520i	0.692133	−	0.721770i	$-0.256671\pi$
$853$	12.0659	+	6.96626i	0.413129	+	0.238520i	−0.279004	+	0.960290i	$0.590004\pi$
$854$		0			0
$855$	−22.4602	−	26.9562i	−0.768123	−	0.921882i
$856$		0			0
$857$	−13.4632	−	23.3189i	−0.459894	−	0.796560i	0.539061	−	0.842267i	$-0.318779\pi$
$857$	−13.4632	−	23.3189i	−0.459894	−	0.796560i	−0.998955	+	0.0457070i	$0.985446\pi$
$858$		0			0
$859$	−17.4938	−	10.1000i	−0.596880	−	0.344609i	0.170933	−	0.985283i	$-0.445322\pi$
$859$	−17.4938	−	10.1000i	−0.596880	−	0.344609i	−0.767813	+	0.640674i	$0.778655\pi$
$860$		0			0
$861$	−0.319608	−	0.170111i	−0.0108922	−	0.00579737i
$862$		0			0
$863$	38.1427	−	22.0217i	1.29839	−	0.749627i	0.318266	−	0.948001i	$-0.396899\pi$
$863$	38.1427	−	22.0217i	1.29839	−	0.749627i	0.980126	+	0.198374i	$0.0635662\pi$
$864$		0			0
$865$	2.09612	−	3.63058i	0.0712701	−	0.123443i
$866$		0			0
$867$	5.47355	−	6.50022i	0.185891	−	0.220759i
$868$		0			0
$869$	−26.7273	+	15.4310i	−0.906662	+	0.523461i
$870$		0			0
$871$	−24.2527	+	14.0023i	−0.821772	+	0.474450i
$872$		0			0
$873$	−44.1335	+	7.62434i	−1.49369	+	0.258045i
$874$		0			0
$875$	−6.20934	−	29.0253i	−0.209914	−	0.981235i
$876$		0			0
$877$	27.0436	−	46.8409i	0.913198	−	1.58170i	0.103678	−	0.994611i	$-0.466939\pi$
$877$	27.0436	−	46.8409i	0.913198	−	1.58170i	0.809519	−	0.587094i	$-0.199728\pi$
$878$		0			0
$879$	−35.4017	+	42.0419i	−1.19407	+	1.41804i
$880$		0			0
$881$	−6.82593			−0.229972			−0.114986	−	0.993367i	$-0.536682\pi$
$881$	−6.82593			−0.229972			−0.114986	+	0.993367i	$0.536682\pi$
$882$		0			0
$883$	−9.87685			−0.332382			−0.166191	−	0.986094i	$-0.553147\pi$
$883$	−9.87685			−0.332382			−0.166191	+	0.986094i	$0.553147\pi$
$884$		0			0
$885$	50.1332	+	8.92943i	1.68521	+	0.300159i
$886$		0			0
$887$	17.5412	−	30.3823i	0.588977	−	1.02014i	−0.405390	−	0.914144i	$-0.632864\pi$
$887$	17.5412	−	30.3823i	0.588977	−	1.02014i	0.994367	−	0.105994i	$-0.0338024\pi$
$888$		0			0
$889$	3.30931	+	15.4693i	0.110991	+	0.518823i
$890$		0			0
$891$	−6.40541	−	17.9856i	−0.214589	−	0.602540i
$892$		0			0
$893$	−17.2581	+	9.96395i	−0.577519	+	0.333431i
$894$		0			0
$895$	19.2539	−	11.1163i	0.643588	−	0.371576i
$896$		0			0
$897$	15.1611	+	41.8805i	0.506216	+	1.39835i
$898$		0			0
$899$	9.89655	−	17.1413i	0.330069	−	0.571695i
$900$		0			0
$901$	19.0967	−	11.0255i	0.636204	−	0.367313i
$902$		0			0
$903$	0.394760	+	11.4424i	0.0131368	+	0.380781i
$904$		0			0
$905$	21.7731	+	12.5707i	0.723761	+	0.417864i
$906$		0			0
$907$	−17.2231	−	29.8313i	−0.571885	−	0.990533i	−0.996372	−	0.0850994i	$-0.972879\pi$
$907$	−17.2231	−	29.8313i	−0.571885	−	0.990533i	0.424488	−	0.905434i	$-0.360454\pi$
$908$		0			0
$909$	9.19555	+	3.38304i	0.304997	+	0.112208i
$910$		0			0
$911$	−45.9046	−	26.5030i	−1.52089	−	0.878084i	−0.999696	−	0.0246430i	$-0.992155\pi$
$911$	−45.9046	−	26.5030i	−1.52089	−	0.878084i	−0.521190	−	0.853441i	$-0.674512\pi$
$912$		0			0
$913$			27.2082i			0.900460i
$914$		0			0
$915$	−5.52215	+	31.0035i	−0.182557	+	1.02494i
$916$		0			0
$917$	52.7594	+	17.0661i	1.74227	+	0.563571i
$918$		0			0
$919$	5.73193	+	9.92799i	0.189079	+	0.327494i	0.944943	−	0.327234i	$-0.106116\pi$
$919$	5.73193	+	9.92799i	0.189079	+	0.327494i	−0.755865	+	0.654728i	$0.772783\pi$
$920$		0			0
$921$	0.433286	−	0.156854i	0.0142773	−	0.00516850i
$922$		0			0
$923$	−29.5601	−	51.1996i	−0.972983	−	1.68526i
$924$		0			0
$925$	0.0625096	−	0.108270i	0.00205530	−	0.00355989i
$926$		0			0
$927$	−14.0960	+	2.43518i	−0.462975	+	0.0799818i
$928$		0			0
$929$	34.7866			1.14131			0.570656	−	0.821189i	$-0.306689\pi$
$929$	34.7866			1.14131			0.570656	+	0.821189i	$0.306689\pi$
$930$		0			0
$931$	21.5177	−	29.7805i	0.705213	−	0.976017i
$932$		0			0
$933$	2.57199	+	7.10477i	0.0842033	+	0.232600i
$934$		0			0
$935$	−19.1602	−	11.0622i	−0.626606	−	0.361771i
$936$		0			0
$937$			18.5180i			0.604956i	0.953156	+	0.302478i	$0.0978139\pi$
$937$			18.5180i			0.604956i	−0.953156	+	0.302478i	$0.902186\pi$
$938$		0			0
$939$	−25.1436	+	9.10221i	−0.820529	+	0.297039i
$940$		0			0
$941$	−9.78447			−0.318965			−0.159482	−	0.987201i	$-0.550983\pi$
$941$	−9.78447			−0.318965			−0.159482	+	0.987201i	$0.550983\pi$
$942$		0			0
$943$		−	0.344774i		−	0.0112274i
$944$		0			0
$945$	20.4096	+	22.8450i	0.663924	+	0.743149i
$946$		0			0
$947$			33.5503i			1.09024i	0.838359	+	0.545119i	$0.183516\pi$
$947$			33.5503i			1.09024i	−0.838359	+	0.545119i	$0.816484\pi$
$948$		0			0
$949$	−86.1523			−2.79662
$950$		0			0
$951$	−35.3815	+	12.8084i	−1.14732	+	0.415342i
$952$		0			0
$953$		−	10.8871i		−	0.352668i	−0.984330	−	0.176334i	$-0.943576\pi$
$953$		−	10.8871i		−	0.352668i	0.984330	−	0.176334i	$-0.0564239\pi$
$954$		0			0
$955$	−24.8272	−	14.3340i	−0.803389	−	0.463837i
$956$		0			0
$957$	−3.25203	−	8.98328i	−0.105123	−	0.290388i
$958$		0			0
$959$	6.14291	+	6.80442i	0.198365	+	0.219726i
$960$		0			0
$961$	−26.9458			−0.869220
$962$		0			0
$963$	7.65069	−	20.7956i	0.246540	−	0.670129i
$964$		0			0
$965$	−13.4113	+	23.2290i	−0.431724	+	0.747768i
$966$		0			0
$967$	26.3931	+	45.7142i	0.848746	+	1.47007i	0.882328	+	0.470635i	$0.155975\pi$
$967$	26.3931	+	45.7142i	0.848746	+	1.47007i	−0.0335826	+	0.999436i	$0.510692\pi$
$968$		0			0
$969$	−40.0087	+	14.4835i	−1.28526	+	0.465278i
$970$		0			0
$971$	15.7931	+	27.3544i	0.506824	+	0.877844i	0.999969	+	0.00789735i	$0.00251383\pi$
$971$	15.7931	+	27.3544i	0.506824	+	0.877844i	−0.493145	+	0.869947i	$0.664153\pi$
$972$		0			0
$973$	−0.777134	−	0.860821i	−0.0249138	−	0.0275966i
$974$		0			0
$975$	−0.0620609	+	0.348434i	−0.00198754	+	0.0111588i
$976$		0			0
$977$			39.2654i			1.25621i	0.778128	+	0.628106i	$0.216169\pi$
$977$			39.2654i			1.25621i	−0.778128	+	0.628106i	$0.783831\pi$
$978$		0			0
$979$	−10.0479	−	5.80113i	−0.321131	−	0.185405i
$980$		0			0
$981$	−1.19861	−	6.93816i	−0.0382687	−	0.221519i
$982$		0			0
$983$	−19.9170	−	34.4973i	−0.635255	−	1.10029i	−0.986461	−	0.163996i	$-0.947562\pi$
$983$	−19.9170	−	34.4973i	−0.635255	−	1.10029i	0.351206	−	0.936298i	$-0.385772\pi$
$984$		0			0
$985$	53.5050	+	30.8911i	1.70481	+	0.984273i
$986$		0			0
$987$	14.7589	−	9.21377i	0.469782	−	0.293277i
$988$		0			0
$989$	−9.44198	+	5.45133i	−0.300237	+	0.173342i
$990$		0			0
$991$	−19.9472	+	34.5496i	−0.633645	+	1.09750i	0.353156	+	0.935565i	$0.385109\pi$
$991$	−19.9472	+	34.5496i	−0.633645	+	1.09750i	−0.986801	+	0.161940i	$0.948225\pi$
$992$		0			0
$993$	−8.92983	−	24.6674i	−0.283380	−	0.782796i
$994$		0			0
$995$	0.853132	−	0.492556i	0.0270461	−	0.0156151i
$996$		0			0
$997$	25.6084	−	14.7850i	0.811026	−	0.468246i	−0.0362863	−	0.999341i	$-0.511553\pi$
$997$	25.6084	−	14.7850i	0.811026	−	0.468246i	0.847312	+	0.531096i	$0.178219\pi$
$998$		0			0
$999$	−0.0973781	+	18.7344i	−0.00308091	+	0.592729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bs.a.353.14	yes	48
3.2	odd	2		1512.2.bs.a.521.6		48
4.3	odd	2		1008.2.ca.e.353.11		48
7.5	odd	6		504.2.cx.a.425.22	yes	48
9.4	even	3		1512.2.cx.a.17.6		48
9.5	odd	6		504.2.cx.a.185.22	yes	48
12.11	even	2		3024.2.ca.e.2033.6		48
21.5	even	6		1512.2.cx.a.89.6		48
28.19	even	6		1008.2.df.e.929.3		48
36.23	even	6		1008.2.df.e.689.3		48
36.31	odd	6		3024.2.df.e.17.6		48
63.5	even	6	inner	504.2.bs.a.257.14	✓	48
63.40	odd	6		1512.2.bs.a.1097.6		48
84.47	odd	6		3024.2.df.e.1601.6		48
252.103	even	6		3024.2.ca.e.2609.6		48
252.131	odd	6		1008.2.ca.e.257.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.14	✓	48	63.5	even	6	inner
504.2.bs.a.353.14	yes	48	1.1	even	1	trivial
504.2.cx.a.185.22	yes	48	9.5	odd	6
504.2.cx.a.425.22	yes	48	7.5	odd	6
1008.2.ca.e.257.11		48	252.131	odd	6
1008.2.ca.e.353.11		48	4.3	odd	2
1008.2.df.e.689.3		48	36.23	even	6
1008.2.df.e.929.3		48	28.19	even	6
1512.2.bs.a.521.6		48	3.2	odd	2
1512.2.bs.a.1097.6		48	63.40	odd	6
1512.2.cx.a.17.6		48	9.4	even	3
1512.2.cx.a.89.6		48	21.5	even	6
3024.2.ca.e.2033.6		48	12.11	even	2
3024.2.ca.e.2609.6		48	252.103	even	6
3024.2.df.e.17.6		48	36.31	odd	6
3024.2.df.e.1601.6		48	84.47	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.589575 + 1.62862i) q^{3} +(1.11415 - 1.92977i) q^{5} +(-0.553477 - 2.58721i) q^{7} +(-2.30480 + 1.92039i) q^{9} +(1.83714 - 1.06068i) q^{11} +(5.10339 - 2.94644i) q^{13} +(3.79973 + 0.676785i) q^{15} +(2.34020 - 4.05335i) q^{17} +(-4.54550 + 2.62435i) q^{19} +(3.88727 - 2.42676i) q^{21} +(3.77916 + 2.18190i) q^{23} +(0.0173374 + 0.0300292i) q^{25} +(-4.48644 - 2.62143i) q^{27} +(-2.25182 - 1.30009i) q^{29} +7.61221i q^{31} +(2.81057 + 2.36666i) q^{33} +(-5.60937 - 1.81446i) q^{35} +(-1.80274 - 3.12244i) q^{37} +(7.80746 + 6.57433i) q^{39} +(-0.0395039 - 0.0684228i) q^{41} +(-1.24922 + 2.16371i) q^{43} +(1.13800 + 6.58733i) q^{45} +3.79674 q^{47} +(-6.38733 + 2.86393i) q^{49} +(7.98109 + 1.42154i) q^{51} +(4.08014 + 2.35567i) q^{53} -4.72701i q^{55} +(-6.95397 - 5.85564i) q^{57} +13.1939 q^{59} +8.15939i q^{61} +(6.24410 + 4.90012i) q^{63} -13.1311i q^{65} -4.75228 q^{67} +(-1.32538 + 7.44121i) q^{69} -10.0325i q^{71} +(-12.6610 - 7.30986i) q^{73} +(-0.0386845 + 0.0459405i) q^{75} +(-3.76101 - 4.16602i) q^{77} -14.5483 q^{79} +(1.62422 - 8.85223i) q^{81} +(-6.41294 + 11.1075i) q^{83} +(-5.21468 - 9.03209i) q^{85} +(0.789732 - 4.43386i) q^{87} +(-2.73464 - 4.73654i) q^{89} +(-10.4477 - 11.5728i) q^{91} +(-12.3974 + 4.48797i) q^{93} +11.6957i q^{95} +(12.9290 + 7.46454i) q^{97} +(-2.19734 + 5.97268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75}+ \cdots - 64 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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