LMFDB - Embedded newform 504.2.bs.a.353.8

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			353.8
Character	$\chi$	$=$	504.353
Dual form			504.2.bs.a.257.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.09564 - 1.34148i) q^{3} +(-0.271038 + 0.469451i) q^{5} +(1.60655 + 2.10214i) q^{7} +(-0.599164 + 2.93956i) q^{9} +(-0.666300 + 0.384688i) q^{11} +(-2.96386 + 1.71119i) q^{13} +(0.926720 - 0.150754i) q^{15} +(-3.23477 + 5.60278i) q^{17} +(5.60413 - 3.23554i) q^{19} +(1.05981 - 4.45834i) q^{21} +(0.100353 + 0.0579388i) q^{23} +(2.35308 + 4.07565i) q^{25} +(4.59984 - 2.41692i) q^{27} +(4.40174 + 2.54135i) q^{29} +4.63530i q^{31} +(1.24608 + 0.472353i) q^{33} +(-1.42229 + 0.184434i) q^{35} +(5.47518 + 9.48329i) q^{37} +(5.54284 + 2.10114i) q^{39} +(-4.04575 - 7.00745i) q^{41} +(3.32569 - 5.76026i) q^{43} +(-1.21758 - 1.07801i) q^{45} +1.54617 q^{47} +(-1.83802 + 6.75438i) q^{49} +(11.0602 - 1.79922i) q^{51} +(-0.221011 - 0.127601i) q^{53} -0.417060i q^{55} +(-10.4805 - 3.97287i) q^{57} -10.2411 q^{59} -5.57913i q^{61} +(-7.14196 + 3.46301i) q^{63} -1.85518i q^{65} -3.28349 q^{67} +(-0.0322262 - 0.198102i) q^{69} +5.67917i q^{71} +(-5.35354 - 3.09087i) q^{73} +(2.88931 - 7.62205i) q^{75} +(-1.87911 - 0.782639i) q^{77} +4.02459 q^{79} +(-8.28201 - 3.52255i) q^{81} +(-5.80057 + 10.0469i) q^{83} +(-1.75349 - 3.03713i) q^{85} +(-1.41353 - 8.68926i) q^{87} +(-2.00832 - 3.47851i) q^{89} +(-8.35874 - 3.48136i) q^{91} +(6.21818 - 5.07860i) q^{93} +3.50781i q^{95} +(15.0653 + 8.69795i) q^{97} +(-0.731591 - 2.18912i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.09564	−	1.34148i	−0.632566	−	0.774507i
$3$	−1.09564	−	1.34148i	−0.632566	−	0.774507i
$4$		0			0
$5$	−0.271038	+	0.469451i	−0.121212	+	0.209945i	−0.920246	−	0.391341i	$-0.872011\pi$
$5$	−0.271038	+	0.469451i	−0.121212	+	0.209945i	0.799034	+	0.601286i	$0.205345\pi$
$6$		0			0
$7$	1.60655	+	2.10214i	0.607217	+	0.794536i
$7$	1.60655	+	2.10214i	0.607217	+	0.794536i
$8$		0			0
$9$	−0.599164	+	2.93956i	−0.199721	+	0.979853i
$10$		0			0
$11$	−0.666300	+	0.384688i	−0.200897	+	0.115988i	−0.597074	−	0.802186i	$-0.703670\pi$
$11$	−0.666300	+	0.384688i	−0.200897	+	0.115988i	0.396177	+	0.918174i	$0.370337\pi$
$12$		0			0
$13$	−2.96386	+	1.71119i	−0.822027	+	0.474598i	−0.851115	−	0.524979i	$-0.824073\pi$
$13$	−2.96386	+	1.71119i	−0.822027	+	0.474598i	0.0290877	+	0.999577i	$0.490740\pi$
$14$		0			0
$15$	0.926720	−	0.150754i	0.239278	−	0.0389246i
$16$		0			0
$17$	−3.23477	+	5.60278i	−0.784547	+	1.35887i	0.144723	+	0.989472i	$0.453771\pi$
$17$	−3.23477	+	5.60278i	−0.784547	+	1.35887i	−0.929269	+	0.369403i	$0.879562\pi$
$18$		0			0
$19$	5.60413	−	3.23554i	1.28567	−	0.742285i	0.307795	−	0.951453i	$-0.400409\pi$
$19$	5.60413	−	3.23554i	1.28567	−	0.742285i	0.977880	+	0.209168i	$0.0670756\pi$
$20$		0			0
$21$	1.05981	−	4.45834i	0.231268	−	0.972890i
$22$		0			0
$23$	0.100353	+	0.0579388i	0.0209250	+	0.0120811i	0.510426	−	0.859922i	$-0.329488\pi$
$23$	0.100353	+	0.0579388i	0.0209250	+	0.0120811i	−0.489501	+	0.872003i	$0.662821\pi$
$24$		0			0
$25$	2.35308	+	4.07565i	0.470615	+	0.815130i
$26$		0			0
$27$	4.59984	−	2.41692i	0.885239	−	0.465136i
$28$		0			0
$29$	4.40174	+	2.54135i	0.817383	+	0.471916i	0.849513	−	0.527568i	$-0.176896\pi$
$29$	4.40174	+	2.54135i	0.817383	+	0.471916i	−0.0321304	+	0.999484i	$0.510229\pi$
$30$		0			0
$31$			4.63530i			0.832524i	0.909245	+	0.416262i	$0.136660\pi$
$31$			4.63530i			0.832524i	−0.909245	+	0.416262i	$0.863340\pi$
$32$		0			0
$33$	1.24608	+	0.472353i	0.216914	+	0.0822261i
$34$		0			0
$35$	−1.42229	+	0.184434i	−0.240410	+	0.0311751i
$36$		0			0
$37$	5.47518	+	9.48329i	0.900114	+	1.55904i	0.827345	+	0.561694i	$0.189850\pi$
$37$	5.47518	+	9.48329i	0.900114	+	1.55904i	0.0727692	+	0.997349i	$0.476816\pi$
$38$		0			0
$39$	5.54284	+	2.10114i	0.887565	+	0.336451i
$40$		0			0
$41$	−4.04575	−	7.00745i	−0.631841	−	1.09438i	−0.987175	−	0.159641i	$-0.948966\pi$
$41$	−4.04575	−	7.00745i	−0.631841	−	1.09438i	0.355334	−	0.934739i	$-0.384367\pi$
$42$		0			0
$43$	3.32569	−	5.76026i	0.507162	−	0.878431i	−0.492803	−	0.870141i	$-0.664028\pi$
$43$	3.32569	−	5.76026i	0.507162	−	0.878431i	0.999966	−	0.00829006i	$-0.00263884\pi$
$44$		0			0
$45$	−1.21758	−	1.07801i	−0.181506	−	0.160700i
$46$		0			0
$47$	1.54617			0.225532			0.112766	−	0.993622i	$-0.464029\pi$
$47$	1.54617			0.225532			0.112766	+	0.993622i	$0.464029\pi$
$48$		0			0
$49$	−1.83802	+	6.75438i	−0.262574	+	0.964912i
$50$		0			0
$51$	11.0602	−	1.79922i	1.54873	−	0.251941i
$52$		0			0
$53$	−0.221011	−	0.127601i	−0.0303582	−	0.0175273i	0.484744	−	0.874656i	$-0.338913\pi$
$53$	−0.221011	−	0.127601i	−0.0303582	−	0.0175273i	−0.515102	+	0.857129i	$0.672246\pi$
$54$		0			0
$55$		−	0.417060i		−	0.0562364i
$56$		0			0
$57$	−10.4805	−	3.97287i	−1.38818	−	0.526220i
$58$		0			0
$59$	−10.2411			−1.33328			−0.666640	−	0.745380i	$-0.732268\pi$
$59$	−10.2411			−1.33328			−0.666640	+	0.745380i	$0.732268\pi$
$60$		0			0
$61$		−	5.57913i		−	0.714335i	−0.934040	−	0.357167i	$-0.883743\pi$
$61$		−	5.57913i		−	0.714335i	0.934040	−	0.357167i	$-0.116257\pi$
$62$		0			0
$63$	−7.14196	+	3.46301i	−0.899802	+	0.436298i
$64$		0			0
$65$		−	1.85518i		−	0.230107i
$66$		0			0
$67$	−3.28349			−0.401143			−0.200571	−	0.979679i	$-0.564280\pi$
$67$	−3.28349			−0.401143			−0.200571	+	0.979679i	$0.564280\pi$
$68$		0			0
$69$	−0.0322262	−	0.198102i	−0.00387958	−	0.0238486i
$70$		0			0
$71$			5.67917i			0.673994i	0.941506	+	0.336997i	$0.109411\pi$
$71$			5.67917i			0.673994i	−0.941506	+	0.336997i	$0.890589\pi$
$72$		0			0
$73$	−5.35354	−	3.09087i	−0.626585	−	0.361759i	0.152844	−	0.988250i	$-0.451157\pi$
$73$	−5.35354	−	3.09087i	−0.626585	−	0.361759i	−0.779428	+	0.626492i	$0.784490\pi$
$74$		0			0
$75$	2.88931	−	7.62205i	0.333628	−	0.880118i
$76$		0			0
$77$	−1.87911	−	0.782639i	−0.214145	−	0.0891900i
$78$		0			0
$79$	4.02459			0.452802			0.226401	−	0.974034i	$-0.427304\pi$
$79$	4.02459			0.452802			0.226401	+	0.974034i	$0.427304\pi$
$80$		0			0
$81$	−8.28201	−	3.52255i	−0.920223	−	0.391395i
$82$		0			0
$83$	−5.80057	+	10.0469i	−0.636695	+	1.10279i	0.349458	+	0.936952i	$0.386366\pi$
$83$	−5.80057	+	10.0469i	−0.636695	+	1.10279i	−0.986153	+	0.165836i	$0.946968\pi$
$84$		0			0
$85$	−1.75349	−	3.03713i	−0.190192	−	0.329423i
$86$		0			0
$87$	−1.41353	−	8.68926i	−0.151546	−	0.931586i
$88$		0			0
$89$	−2.00832	−	3.47851i	−0.212881	−	0.368721i	0.739734	−	0.672900i	$-0.234951\pi$
$89$	−2.00832	−	3.47851i	−0.212881	−	0.368721i	−0.952615	+	0.304178i	$0.901618\pi$
$90$		0			0
$91$	−8.35874	−	3.48136i	−0.876234	−	0.364946i
$92$		0			0
$93$	6.21818	−	5.07860i	0.644795	−	0.526626i
$94$		0			0
$95$			3.50781i			0.359894i
$96$		0			0
$97$	15.0653	+	8.69795i	1.52965	+	0.883143i	0.999376	+	0.0353150i	$0.0112435\pi$
$97$	15.0653	+	8.69795i	1.52965	+	0.883143i	0.530272	+	0.847828i	$0.322090\pi$
$98$		0			0
$99$	−0.731591	−	2.18912i	−0.0735277	−	0.220015i
$100$		0			0
$101$	−8.25113	−	14.2914i	−0.821019	−	1.42205i	−0.904925	−	0.425572i	$-0.860073\pi$
$101$	−8.25113	−	14.2914i	−0.821019	−	1.42205i	0.0839060	−	0.996474i	$-0.473260\pi$
$102$		0			0
$103$	0.254604	+	0.146996i	0.0250869	+	0.0144839i	0.512491	−	0.858693i	$-0.328723\pi$
$103$	0.254604	+	0.146996i	0.0250869	+	0.0144839i	−0.487404	+	0.873177i	$0.662056\pi$
$104$		0			0
$105$	1.80572	+	1.70590i	0.176221	+	0.166479i
$106$		0			0
$107$	−3.17327	+	1.83209i	−0.306772	+	0.177115i	−0.645481	−	0.763776i	$-0.723343\pi$
$107$	−3.17327	+	1.83209i	−0.306772	+	0.177115i	0.338709	+	0.940891i	$0.390010\pi$
$108$		0			0
$109$	1.26497	−	2.19099i	0.121162	−	0.209858i	−0.799064	−	0.601246i	$-0.794671\pi$
$109$	1.26497	−	2.19099i	0.121162	−	0.209858i	0.920226	+	0.391387i	$0.128005\pi$
$110$		0			0
$111$	6.72289	−	17.7351i	0.638108	−	1.68334i
$112$		0			0
$113$	−11.9275	+	6.88637i	−1.12205	+	0.647815i	−0.941923	−	0.335828i	$-0.890984\pi$
$113$	−11.9275	+	6.88637i	−1.12205	+	0.647815i	−0.180126	+	0.983644i	$0.557650\pi$
$114$		0			0
$115$	−0.0543988	+	0.0314072i	−0.00507271	+	0.00292873i
$116$		0			0
$117$	−3.25429	−	9.73773i	−0.300860	−	0.900253i
$118$		0			0
$119$	−16.9747	+	2.20118i	−1.55607	+	0.201782i
$120$		0			0
$121$	−5.20403	+	9.01364i	−0.473094	+	0.819422i
$122$		0			0
$123$	−4.96772	+	13.1049i	−0.447924	+	1.18163i
$124$		0			0
$125$	−5.26146			−0.470600
$126$		0			0
$127$	9.44974			0.838529			0.419265	−	0.907864i	$-0.362288\pi$
$127$	9.44974			0.838529			0.419265	+	0.907864i	$0.362288\pi$
$128$		0			0
$129$	−11.3710	+	1.84979i	−1.00116	+	0.162865i
$130$		0			0
$131$	6.25067	−	10.8265i	0.546123	−	0.945913i	−0.452412	−	0.891809i	$-0.649436\pi$
$131$	6.25067	−	10.8265i	0.546123	−	0.945913i	0.998535	−	0.0541043i	$-0.0172303\pi$
$132$		0			0
$133$	15.8049	+	6.58263i	1.37046	+	0.570786i
$134$		0			0
$135$	−0.112106	+	2.81447i	−0.00964852	+	0.242231i
$136$		0			0
$137$	16.7171	−	9.65163i	1.42824	−	0.824594i	0.431257	−	0.902229i	$-0.358070\pi$
$137$	16.7171	−	9.65163i	1.42824	−	0.824594i	0.996982	+	0.0776349i	$0.0247368\pi$
$138$		0			0
$139$	−0.863952	+	0.498803i	−0.0732794	+	0.0423079i	−0.536192	−	0.844096i	$-0.680138\pi$
$139$	−0.863952	+	0.498803i	−0.0732794	+	0.0423079i	0.462913	+	0.886404i	$0.346804\pi$
$140$		0			0
$141$	−1.69404	−	2.07417i	−0.142664	−	0.174676i
$142$		0			0
$143$	1.31655	−	2.28033i	0.110095	−	0.190690i
$144$		0			0
$145$	−2.38607	+	1.37760i	−0.198153	+	0.114403i
$146$		0			0
$147$	11.0747	−	4.93467i	0.913426	−	0.407005i
$148$		0			0
$149$	17.0179	+	9.82530i	1.39416	+	0.804920i	0.993773	−	0.111425i	$-0.0355415\pi$
$149$	17.0179	+	9.82530i	1.39416	+	0.804920i	0.400390	+	0.916345i	$0.368875\pi$
$150$		0			0
$151$	−8.51708	−	14.7520i	−0.693111	−	1.20050i	−0.970813	−	0.239836i	$-0.922906\pi$
$151$	−8.51708	−	14.7520i	−0.693111	−	1.20050i	0.277703	−	0.960667i	$-0.410427\pi$
$152$		0			0
$153$	−14.5316	−	12.8658i	−1.17481	−	1.04014i
$154$		0			0
$155$	−2.17604	−	1.25634i	−0.174784	−	0.100912i
$156$		0			0
$157$		−	1.12908i		−	0.0901107i	−0.998984	−	0.0450553i	$-0.985654\pi$
$157$		−	1.12908i		−	0.0901107i	0.998984	−	0.0450553i	$-0.0143464\pi$
$158$		0			0
$159$	0.0709731	+	0.436287i	0.00562854	+	0.0345998i
$160$		0			0
$161$	0.0394259	+	0.304037i	0.00310720	+	0.0239615i
$162$		0			0
$163$	−8.60142	−	14.8981i	−0.673715	−	1.16691i	−0.976843	−	0.213959i	$-0.931364\pi$
$163$	−8.60142	−	14.8981i	−0.673715	−	1.16691i	0.303127	−	0.952950i	$-0.401969\pi$
$164$		0			0
$165$	−0.559480	+	0.456946i	−0.0435554	+	0.0355732i
$166$		0			0
$167$	−2.22256	−	3.84959i	−0.171987	−	0.297890i	0.767128	−	0.641495i	$-0.221685\pi$
$167$	−2.22256	−	3.84959i	−0.171987	−	0.297890i	−0.939114	+	0.343605i	$0.888352\pi$
$168$		0			0
$169$	−0.643682	+	1.11489i	−0.0495140	+	0.0857607i
$170$		0			0
$171$	6.15328	+	18.4123i	0.470553	+	1.40802i
$172$		0			0
$173$	19.8858			1.51189			0.755946	−	0.654634i	$-0.227177\pi$
$173$	19.8858			1.51189			0.755946	+	0.654634i	$0.227177\pi$
$174$		0			0
$175$	−4.78728	+	11.4942i	−0.361884	+	0.868882i
$176$		0			0
$177$	11.2205	+	13.7383i	0.843387	+	1.03263i
$178$		0			0
$179$	1.71472	+	0.989994i	0.128164	+	0.0739956i	0.562711	−	0.826653i	$-0.309758\pi$
$179$	1.71472	+	0.989994i	0.128164	+	0.0739956i	−0.434547	+	0.900649i	$0.643092\pi$
$180$		0			0
$181$		−	5.68137i		−	0.422293i	−0.977454	−	0.211146i	$-0.932280\pi$
$181$		−	5.68137i		−	0.422293i	0.977454	−	0.211146i	$-0.0677197\pi$
$182$		0			0
$183$	−7.48432	+	6.11270i	−0.553257	+	0.451864i
$184$		0			0
$185$	−5.93592			−0.436417
$186$		0			0
$187$		−	4.97751i		−	0.363992i
$188$		0			0
$189$	12.4706	+	5.78664i	0.907100	+	0.420916i
$190$		0			0
$191$		−	4.15021i		−	0.300299i	−0.988663	−	0.150149i	$-0.952025\pi$
$191$		−	4.15021i		−	0.300299i	0.988663	−	0.150149i	$-0.0479755\pi$
$192$		0			0
$193$	5.87065			0.422579			0.211289	−	0.977424i	$-0.432234\pi$
$193$	5.87065			0.422579			0.211289	+	0.977424i	$0.432234\pi$
$194$		0			0
$195$	−2.48870	+	2.03260i	−0.178219	+	0.145558i
$196$		0			0
$197$			3.37912i			0.240753i	0.992728	+	0.120376i	$0.0384101\pi$
$197$			3.37912i			0.240753i	−0.992728	+	0.120376i	$0.961590\pi$
$198$		0			0
$199$	−4.03812	−	2.33141i	−0.286255	−	0.165269i	0.349997	−	0.936751i	$-0.386183\pi$
$199$	−4.03812	−	2.33141i	−0.286255	−	0.165269i	−0.636252	+	0.771482i	$0.719516\pi$
$200$		0			0
$201$	3.59751	+	4.40476i	0.253749	+	0.310688i
$202$		0			0
$203$	1.72932	+	13.3359i	0.121375	+	0.935995i
$204$		0			0
$205$	4.38620			0.306346
$206$		0			0
$207$	−0.230442	+	0.260278i	−0.0160168	+	0.0180906i
$208$		0			0
$209$	−2.48935	+	4.31168i	−0.172192	+	0.298245i
$210$		0			0
$211$	−3.09622	−	5.36281i	−0.213153	−	0.369191i	0.739547	−	0.673105i	$-0.235040\pi$
$211$	−3.09622	−	5.36281i	−0.213153	−	0.369191i	−0.952699	+	0.303914i	$0.901706\pi$
$212$		0			0
$213$	7.61852	−	6.22230i	0.522013	−	0.426345i
$214$		0			0
$215$	1.80277	+	3.12249i	0.122948	+	0.212952i
$216$		0			0
$217$	−9.74406	+	7.44682i	−0.661470	+	0.505523i
$218$		0			0
$219$	1.71918	+	10.5682i	0.116171	+	0.714130i
$220$		0			0
$221$		−	22.1412i		−	1.48938i
$222$		0			0
$223$	8.84510	+	5.10672i	0.592312	+	0.341971i	0.766011	−	0.642827i	$-0.222239\pi$
$223$	8.84510	+	5.10672i	0.592312	+	0.341971i	−0.173699	+	0.984799i	$0.555572\pi$
$224$		0			0
$225$	−13.3905	+	4.47503i	−0.892699	+	0.298335i
$226$		0			0
$227$	8.12394	+	14.0711i	0.539205	+	0.933930i	0.998947	+	0.0458777i	$0.0146084\pi$
$227$	8.12394	+	14.0711i	0.539205	+	0.933930i	−0.459742	+	0.888052i	$0.652058\pi$
$228$		0			0
$229$	−7.51527	−	4.33894i	−0.496623	−	0.286726i	0.230695	−	0.973026i	$-0.425900\pi$
$229$	−7.51527	−	4.33894i	−0.496623	−	0.286726i	−0.727318	+	0.686301i	$0.759233\pi$
$230$		0			0
$231$	1.00892	+	3.37829i	0.0663824	+	0.222275i
$232$		0			0
$233$	19.0308	−	10.9874i	1.24675	−	0.719811i	0.276290	−	0.961074i	$-0.410895\pi$
$233$	19.0308	−	10.9874i	1.24675	−	0.719811i	0.970460	+	0.241263i	$0.0775617\pi$
$234$		0			0
$235$	−0.419070	+	0.725851i	−0.0273371	+	0.0473493i
$236$		0			0
$237$	−4.40948	−	5.39893i	−0.286427	−	0.350698i
$238$		0			0
$239$	14.3752	−	8.29955i	0.929857	−	0.536853i	0.0430908	−	0.999071i	$-0.486280\pi$
$239$	14.3752	−	8.29955i	0.929857	−	0.536853i	0.886766	+	0.462218i	$0.152946\pi$
$240$		0			0
$241$	−9.52821	+	5.50112i	−0.613766	+	0.354358i	−0.774438	−	0.632650i	$-0.781967\pi$
$241$	−9.52821	+	5.50112i	−0.613766	+	0.354358i	0.160672	+	0.987008i	$0.448634\pi$
$242$		0			0
$243$	4.34861	+	14.9696i	0.278963	+	0.960302i
$244$		0			0
$245$	−2.67268	−	2.69355i	−0.170751	−	0.172085i
$246$		0			0
$247$	−11.0732	+	19.1794i	−0.704573	+	1.22036i
$248$		0			0
$249$	19.8330	−	3.22635i	1.25687	−	0.204461i
$250$		0			0
$251$	−18.0406			−1.13871			−0.569356	−	0.822091i	$-0.692808\pi$
$251$	−18.0406			−1.13871			−0.569356	+	0.822091i	$0.692808\pi$
$252$		0			0
$253$	−0.0891535			−0.00560503
$254$		0			0
$255$	−2.15308	+	5.67986i	−0.134831	+	0.355687i
$256$		0			0
$257$	−7.20321	+	12.4763i	−0.449324	+	0.778252i	−0.998342	−	0.0575585i	$-0.981668\pi$
$257$	−7.20321	+	12.4763i	−0.449324	+	0.778252i	0.549018	+	0.835810i	$0.315002\pi$
$258$		0			0
$259$	−11.1391	+	26.7450i	−0.692151	+	1.66185i
$260$		0			0
$261$	−10.1078	+	11.4165i	−0.625657	+	0.706663i
$262$		0			0
$263$	−21.6064	+	12.4745i	−1.33231	+	0.769209i	−0.985653	−	0.168783i	$-0.946016\pi$
$263$	−21.6064	+	12.4745i	−1.33231	+	0.769209i	−0.346656	+	0.937992i	$0.612683\pi$
$264$		0			0
$265$	0.119805	−	0.0691692i	0.00735954	−	0.00424903i
$266$		0			0
$267$	−2.46598	+	6.50531i	−0.150916	+	0.398118i
$268$		0			0
$269$	11.0059	−	19.0627i	0.671040	−	1.16228i	−0.306569	−	0.951848i	$-0.599181\pi$
$269$	11.0059	−	19.0627i	0.671040	−	1.16228i	0.977609	−	0.210428i	$-0.0674856\pi$
$270$		0			0
$271$	22.7444	−	13.1315i	1.38162	−	0.797680i	0.389271	−	0.921123i	$-0.372727\pi$
$271$	22.7444	−	13.1315i	1.38162	−	0.797680i	0.992352	+	0.123443i	$0.0393935\pi$
$272$		0			0
$273$	4.48794	+	15.0274i	0.271622	+	0.909502i
$274$		0			0
$275$	−3.13571	−	1.81040i	−0.189090	−	0.109171i
$276$		0			0
$277$	−2.38206	−	4.12584i	−0.143124	−	0.247898i	0.785548	−	0.618801i	$-0.212381\pi$
$277$	−2.38206	−	4.12584i	−0.143124	−	0.247898i	−0.928671	+	0.370903i	$0.879048\pi$
$278$		0			0
$279$	−13.6257	−	2.77730i	−0.815751	−	0.166273i
$280$		0			0
$281$	19.1963	+	11.0830i	1.14515	+	0.661155i	0.947702	−	0.319158i	$-0.103400\pi$
$281$	19.1963	+	11.0830i	1.14515	+	0.661155i	0.197452	+	0.980312i	$0.436733\pi$
$282$		0			0
$283$		−	2.90557i		−	0.172718i	−0.996264	−	0.0863590i	$-0.972477\pi$
$283$		−	2.90557i		−	0.172718i	0.996264	−	0.0863590i	$-0.0275232\pi$
$284$		0			0
$285$	4.70568	−	3.84329i	0.278740	−	0.227657i
$286$		0			0
$287$	8.23098	−	19.7626i	0.485860	−	1.16655i
$288$		0			0
$289$	−12.4275	−	21.5250i	−0.731027	−	1.26618i
$290$		0			0
$291$	−4.83790	−	29.7396i	−0.283603	−	1.74337i
$292$		0			0
$293$	13.9866	+	24.2255i	0.817104	+	1.41527i	0.907807	+	0.419388i	$0.137755\pi$
$293$	13.9866	+	24.2255i	0.817104	+	1.41527i	−0.0907025	+	0.995878i	$0.528911\pi$
$294$		0			0
$295$	2.77573	−	4.80770i	0.161609	−	0.279915i
$296$		0			0
$297$	−2.13511	+	3.37990i	−0.123892	+	0.196121i
$298$		0			0
$299$	−0.396576			−0.0229346
$300$		0			0
$301$	17.4518	−	2.26305i	1.00590	−	0.130440i
$302$		0			0
$303$	−10.1314	+	26.7269i	−0.582036	+	1.53542i
$304$		0			0
$305$	2.61913	+	1.51215i	0.149971	+	0.0865857i
$306$		0			0
$307$		−	30.3968i		−	1.73484i	−0.497579	−	0.867419i	$-0.665777\pi$
$307$		−	30.3968i		−	1.73484i	0.497579	−	0.867419i	$-0.334223\pi$
$308$		0			0
$309$	−0.0817608	−	0.502601i	−0.00465121	−	0.0285920i
$310$		0			0
$311$	27.8260			1.57787			0.788934	−	0.614477i	$-0.210633\pi$
$311$	27.8260			1.57787			0.788934	+	0.614477i	$0.210633\pi$
$312$		0			0
$313$		−	0.0465719i		−	0.00263240i	−0.999999	−	0.00131620i	$-0.999581\pi$
$313$		−	0.0465719i		−	0.00263240i	0.999999	−	0.00131620i	$-0.000418959\pi$
$314$		0			0
$315$	0.310028	−	4.29140i	0.0174681	−	0.241793i
$316$		0			0
$317$		−	8.49402i		−	0.477072i	−0.971134	−	0.238536i	$-0.923333\pi$
$317$		−	8.49402i		−	0.477072i	0.971134	−	0.238536i	$-0.0766675\pi$
$318$		0			0
$319$	−3.91051			−0.218946
$320$		0			0
$321$	5.93448	+	2.24960i	0.331230	+	0.125560i
$322$		0			0
$323$			41.8649i			2.32943i
$324$		0			0
$325$	−13.9484	−	8.05311i	−0.773718	−	0.446706i
$326$		0			0
$327$	−4.32512	+	0.703590i	−0.239180	+	0.0389086i
$328$		0			0
$329$	2.48399	+	3.25027i	0.136947	+	0.179193i
$330$		0			0
$331$	7.25461			0.398749			0.199375	−	0.979923i	$-0.436109\pi$
$331$	7.25461			0.398749			0.199375	+	0.979923i	$0.436109\pi$
$332$		0			0
$333$	−31.1572	+	10.4126i	−1.70740	+	0.570605i
$334$		0			0
$335$	0.889950	−	1.54144i	0.0486232	−	0.0842178i
$336$		0			0
$337$	−4.82349	−	8.35454i	−0.262752	−	0.455101i	0.704220	−	0.709982i	$-0.251297\pi$
$337$	−4.82349	−	8.35454i	−0.262752	−	0.455101i	−0.966972	+	0.254881i	$0.917964\pi$
$338$		0			0
$339$	22.3062	+	8.45567i	1.21151	+	0.459249i
$340$		0			0
$341$	−1.78315	−	3.08850i	−0.0965627	−	0.167252i
$342$		0			0
$343$	−17.1515	+	6.98745i	−0.926097	+	0.377287i
$344$		0			0
$345$	0.101733	+	0.0385643i	0.00547715	+	0.00207623i
$346$		0			0
$347$			13.0603i			0.701113i	0.936542	+	0.350556i	$0.114008\pi$
$347$			13.0603i			0.701113i	−0.936542	+	0.350556i	$0.885992\pi$
$348$		0			0
$349$	17.4929	+	10.0995i	0.936372	+	0.540614i	0.888821	−	0.458254i	$-0.151525\pi$
$349$	17.4929	+	10.0995i	0.936372	+	0.540614i	0.0475506	+	0.998869i	$0.484858\pi$
$350$		0			0
$351$	−9.49749	+	15.0346i	−0.506939	+	0.802487i
$352$		0			0
$353$	2.05422	+	3.55801i	0.109335	+	0.189374i	0.915501	−	0.402316i	$-0.131795\pi$
$353$	2.05422	+	3.55801i	0.109335	+	0.189374i	−0.806166	+	0.591689i	$0.798461\pi$
$354$		0			0
$355$	−2.66609	−	1.53927i	−0.141501	−	0.0816959i
$356$		0			0
$357$	21.5509	+	20.3596i	1.14059	+	1.07754i
$358$		0			0
$359$	28.7322	−	16.5885i	1.51643	−	0.875510i	0.516613	−	0.856219i	$-0.327192\pi$
$359$	28.7322	−	16.5885i	1.51643	−	0.875510i	0.999814	−	0.0192910i	$-0.00614090\pi$
$360$		0			0
$361$	11.4375	−	19.8103i	0.601973	−	1.04265i
$362$		0			0
$363$	17.7934	−	2.89454i	0.933911	−	0.151924i
$364$		0			0
$365$	2.90202	−	1.67548i	0.151899	−	0.0876988i
$366$		0			0
$367$	−2.75059	+	1.58806i	−0.143580	+	0.0828958i	−0.570069	−	0.821597i	$-0.693084\pi$
$367$	−2.75059	+	1.58806i	−0.143580	+	0.0828958i	0.426489	+	0.904493i	$0.359750\pi$
$368$		0			0
$369$	23.0229	−	7.69412i	1.19852	−	0.400540i
$370$		0			0
$371$	−0.0868292	−	0.669594i	−0.00450795	−	0.0347636i
$372$		0			0
$373$	−10.4803	+	18.1524i	−0.542649	+	0.939895i	0.456102	+	0.889927i	$0.349245\pi$
$373$	−10.4803	+	18.1524i	−0.542649	+	0.939895i	−0.998751	+	0.0499677i	$0.984088\pi$
$374$		0			0
$375$	5.76465	+	7.05817i	0.297685	+	0.364483i
$376$		0			0
$377$	−17.3949			−0.895881
$378$		0			0
$379$	−20.1198			−1.03348			−0.516742	−	0.856141i	$-0.672855\pi$
$379$	−20.1198			−1.03348			−0.516742	+	0.856141i	$0.672855\pi$
$380$		0			0
$381$	−10.3535	−	12.6767i	−0.530425	−	0.649447i
$382$		0			0
$383$	12.5838	−	21.7958i	0.643003	−	1.11371i	−0.341756	−	0.939789i	$-0.611022\pi$
$383$	12.5838	−	21.7958i	0.643003	−	1.11371i	0.984759	−	0.173925i	$-0.0556451\pi$
$384$		0			0
$385$	0.876720	−	0.670026i	0.0446818	−	0.0341477i
$386$		0			0
$387$	14.9400	+	13.2274i	0.759442	+	0.672386i
$388$		0			0
$389$	17.4054	−	10.0490i	0.882488	−	0.509505i	0.0110101	−	0.999939i	$-0.496495\pi$
$389$	17.4054	−	10.0490i	0.882488	−	0.509505i	0.871478	+	0.490435i	$0.163162\pi$
$390$		0			0
$391$	−0.649237	+	0.374837i	−0.0328333	+	0.0189563i
$392$		0			0
$393$	−21.3720	+	3.47670i	−1.07808	+	0.175376i
$394$		0			0
$395$	−1.09081	+	1.88935i	−0.0548848	+	0.0950633i
$396$		0			0
$397$	6.64273	−	3.83518i	0.333389	−	0.192482i	−0.323956	−	0.946072i	$-0.605013\pi$
$397$	6.64273	−	3.83518i	0.333389	−	0.192482i	0.657345	+	0.753590i	$0.271680\pi$
$398$		0			0
$399$	−8.48588	−	28.4142i	−0.424825	−	1.42249i
$400$		0			0
$401$	3.07360	+	1.77454i	0.153488	+	0.0886165i	0.574777	−	0.818310i	$-0.305089\pi$
$401$	3.07360	+	1.77454i	0.153488	+	0.0886165i	−0.421289	+	0.906927i	$0.638422\pi$
$402$		0			0
$403$	−7.93186	−	13.7384i	−0.395114	−	0.684357i
$404$		0			0
$405$	3.89840	−	2.93325i	0.193713	−	0.145754i
$406$		0			0
$407$	−7.29622	−	4.21248i	−0.361660	−	0.208805i
$408$		0			0
$409$		−	3.45157i		−	0.170669i	−0.996352	−	0.0853345i	$-0.972804\pi$
$409$		−	3.45157i		−	0.170669i	0.996352	−	0.0853345i	$-0.0271959\pi$
$410$		0			0
$411$	−31.2634	−	11.8511i	−1.54211	−	0.584571i
$412$		0			0
$413$	−16.4528	−	21.5283i	−0.809590	−	1.05934i
$414$		0			0
$415$	−3.14434	−	5.44616i	−0.154350	−	0.267342i
$416$		0			0
$417$	1.61571	+	0.612472i	0.0791218	+	0.0299929i
$418$		0			0
$419$	−8.49112	−	14.7071i	−0.414818	−	0.718487i	0.580591	−	0.814195i	$-0.302822\pi$
$419$	−8.49112	−	14.7071i	−0.414818	−	0.718487i	−0.995409	+	0.0957088i	$0.969488\pi$
$420$		0			0
$421$	10.3437	−	17.9158i	0.504120	−	0.873162i	−0.495869	−	0.868398i	$-0.665150\pi$
$421$	10.3437	−	17.9158i	0.504120	−	0.873162i	0.999989	−	0.00476397i	$-0.00151642\pi$
$422$		0			0
$423$	−0.926410	+	4.54506i	−0.0450436	+	0.220988i
$424$		0			0
$425$	−30.4466			−1.47688
$426$		0			0
$427$	11.7281	−	8.96313i	0.567564	−	0.433756i
$428$		0			0
$429$	−4.50148	+	0.732279i	−0.217334	+	0.0353548i
$430$		0			0
$431$	32.0588	+	18.5091i	1.54422	+	0.891554i	0.998566	+	0.0535418i	$0.0170511\pi$
$431$	32.0588	+	18.5091i	1.54422	+	0.891554i	0.545651	+	0.838012i	$0.316282\pi$
$432$		0			0
$433$			15.2206i			0.731453i	0.930722	+	0.365727i	$0.119179\pi$
$433$			15.2206i			0.731453i	−0.930722	+	0.365727i	$0.880821\pi$
$434$		0			0
$435$	4.46230	+	1.69153i	0.213951	+	0.0811028i
$436$		0			0
$437$	0.749853			0.0358704
$438$		0			0
$439$			32.8075i			1.56582i	0.622136	+	0.782909i	$0.286265\pi$
$439$			32.8075i			1.56582i	−0.622136	+	0.782909i	$0.713735\pi$
$440$		0			0
$441$	−18.7536	−	9.44995i	−0.893030	−	0.449997i
$442$		0			0
$443$		−	23.7626i		−	1.12900i	−0.825434	−	0.564499i	$-0.809070\pi$
$443$		−	23.7626i		−	1.12900i	0.825434	−	0.564499i	$-0.190930\pi$
$444$		0			0
$445$	2.17732			0.103215
$446$		0			0
$447$	−5.46495	−	33.5942i	−0.258483	−	1.58895i
$448$		0			0
$449$		−	21.8105i		−	1.02930i	−0.857400	−	0.514651i	$-0.827921\pi$
$449$		−	21.8105i		−	1.02930i	0.857400	−	0.514651i	$-0.172079\pi$
$450$		0			0
$451$	5.39137	+	3.11271i	0.253870	+	0.146572i
$452$		0			0
$453$	−10.4580	+	27.5884i	−0.491359	+	1.29622i
$454$		0			0
$455$	3.89986	−	2.98044i	0.182828	−	0.139725i
$456$		0			0
$457$	−39.7064			−1.85739			−0.928693	−	0.370849i	$-0.879067\pi$
$457$	−39.7064			−1.85739			−0.928693	+	0.370849i	$0.879067\pi$
$458$		0			0
$459$	−1.33795	+	33.5901i	−0.0624504	+	1.56785i
$460$		0			0
$461$	−7.37073	+	12.7665i	−0.343289	+	0.594594i	−0.985041	−	0.172318i	$-0.944874\pi$
$461$	−7.37073	+	12.7665i	−0.343289	+	0.594594i	0.641752	+	0.766912i	$0.278208\pi$
$462$		0			0
$463$	−12.4381	−	21.5434i	−0.578046	−	1.00120i	−0.995703	−	0.0926000i	$-0.970482\pi$
$463$	−12.4381	−	21.5434i	−0.578046	−	1.00120i	0.417658	−	0.908604i	$-0.362851\pi$
$464$		0			0
$465$	0.698791	+	4.29562i	0.0324057	+	0.199205i
$466$		0			0
$467$	−6.70092	−	11.6063i	−0.310081	−	0.537077i	0.668298	−	0.743893i	$-0.267023\pi$
$467$	−6.70092	−	11.6063i	−0.310081	−	0.537077i	−0.978380	+	0.206817i	$0.933690\pi$
$468$		0			0
$469$	−5.27509	−	6.90238i	−0.243581	−	0.318722i
$470$		0			0
$471$	−1.51465	+	1.23706i	−0.0697913	+	0.0570009i
$472$		0			0
$473$			5.11741i			0.235299i
$474$		0			0
$475$	26.3739	+	15.2270i	1.21012	+	0.698661i
$476$		0			0
$477$	0.507512	−	0.573221i	0.0232374	−	0.0262460i
$478$		0			0
$479$	−20.5731	−	35.6336i	−0.940007	−	1.62814i	−0.765452	−	0.643493i	$-0.777485\pi$
$479$	−20.5731	−	35.6336i	−0.940007	−	1.62814i	−0.174555	−	0.984647i	$-0.555849\pi$
$480$		0			0
$481$	−32.4554	−	18.7381i	−1.47984	−	0.854384i
$482$		0			0
$483$	0.364665	−	0.386004i	0.0165928	−	0.0175638i
$484$		0			0
$485$	−8.16651	+	4.71494i	−0.370822	+	0.214094i
$486$		0			0
$487$	−14.7695	+	25.5814i	−0.669268	+	1.15921i	0.308841	+	0.951114i	$0.400059\pi$
$487$	−14.7695	+	25.5814i	−0.669268	+	1.15921i	−0.978109	+	0.208092i	$0.933275\pi$
$488$		0			0
$489$	−10.5615	+	27.8616i	−0.477610	+	1.25994i
$490$		0			0
$491$	8.53341	−	4.92676i	0.385107	−	0.222342i	−0.294931	−	0.955519i	$-0.595297\pi$
$491$	8.53341	−	4.92676i	0.385107	−	0.222342i	0.680038	+	0.733177i	$0.261963\pi$
$492$		0			0
$493$	−28.4772	+	16.4413i	−1.28255	+	0.740480i
$494$		0			0
$495$	1.22597	+	0.249887i	0.0551033	+	0.0112316i
$496$		0			0
$497$	−11.9384	+	9.12385i	−0.535512	+	0.409261i
$498$		0			0
$499$	20.3875	−	35.3122i	0.912671	−	1.58079i	0.102396	−	0.994744i	$-0.467349\pi$
$499$	20.3875	−	35.3122i	0.912671	−	1.58079i	0.810275	−	0.586050i	$-0.199318\pi$
$500$		0			0
$501$	−2.72905	+	7.19928i	−0.121925	+	0.321640i
$502$		0			0
$503$	23.6750			1.05561			0.527807	−	0.849364i	$-0.323014\pi$
$503$	23.6750			1.05561			0.527807	+	0.849364i	$0.323014\pi$
$504$		0			0
$505$	8.94547			0.398068
$506$		0			0
$507$	2.20085	−	0.358024i	0.0977431	−	0.0159004i
$508$		0			0
$509$	−14.3838	+	24.9135i	−0.637551	+	1.10427i	0.348418	+	0.937339i	$0.386719\pi$
$509$	−14.3838	+	24.9135i	−0.637551	+	1.10427i	−0.985969	+	0.166931i	$0.946614\pi$
$510$		0			0
$511$	−2.10326	−	16.2195i	−0.0930427	−	0.717510i
$512$		0			0
$513$	17.9580	−	28.4277i	0.792867	−	1.25511i
$514$		0			0
$515$	−0.138015	+	0.0796827i	−0.00608165	+	0.00351124i
$516$		0			0
$517$	−1.03021	+	0.594794i	−0.0453087	+	0.0261590i
$518$		0			0
$519$	−21.7876	−	26.6765i	−0.956371	−	1.17097i
$520$		0			0
$521$	3.64967	−	6.32142i	0.159895	−	0.276947i	−0.774936	−	0.632040i	$-0.782218\pi$
$521$	3.64967	−	6.32142i	0.159895	−	0.276947i	0.934831	+	0.355094i	$0.115551\pi$
$522$		0			0
$523$	−21.2167	+	12.2495i	−0.927742	+	0.535632i	−0.886097	−	0.463501i	$-0.846593\pi$
$523$	−21.2167	+	12.2495i	−0.927742	+	0.535632i	−0.0416450	+	0.999132i	$0.513260\pi$
$524$		0			0
$525$	20.6644	−	6.17143i	0.901870	−	0.269343i
$526$		0			0
$527$	−25.9706	−	14.9941i	−1.13130	−	0.653154i
$528$		0			0
$529$	−11.4933	−	19.9070i	−0.499708	−	0.865520i
$530$		0			0
$531$	6.13610	−	30.1043i	0.266284	−	1.30642i
$532$		0			0
$533$	23.9821	+	13.8461i	1.03878	+	0.599740i
$534$		0			0
$535$		−	1.98626i		−	0.0858736i
$536$		0			0
$537$	−0.550647	−	3.38494i	−0.0237622	−	0.146071i
$538$		0			0
$539$	−1.37366	−	5.20751i	−0.0591678	−	0.224303i
$540$		0			0
$541$	−12.1854	−	21.1057i	−0.523891	−	0.907406i	−0.999613	−	0.0278106i	$-0.991146\pi$
$541$	−12.1854	−	21.1057i	−0.523891	−	0.907406i	0.475722	−	0.879596i	$-0.342187\pi$
$542$		0			0
$543$	−7.62147	+	6.22471i	−0.327069	+	0.267128i
$544$		0			0
$545$	0.685707	+	1.18768i	0.0293724	+	0.0508746i
$546$		0			0
$547$	19.3409	−	33.4994i	0.826957	−	1.43233i	−0.0734566	−	0.997298i	$-0.523403\pi$
$547$	19.3409	−	33.4994i	0.826957	−	1.43233i	0.900414	−	0.435034i	$-0.143264\pi$
$548$		0			0
$549$	16.4002	+	3.34281i	0.699943	+	0.142668i
$550$		0			0
$551$	32.8905			1.40118
$552$		0			0
$553$	6.46569	+	8.46027i	0.274949	+	0.359767i
$554$		0			0
$555$	6.50360	+	7.96294i	0.276063	+	0.338008i
$556$		0			0
$557$	−5.55184	−	3.20536i	−0.235239	−	0.135815i	0.377748	−	0.925909i	$-0.376699\pi$
$557$	−5.55184	−	3.20536i	−0.235239	−	0.135815i	−0.612987	+	0.790093i	$0.710032\pi$
$558$		0			0
$559$			22.7635i			0.962792i
$560$		0			0
$561$	−6.67726	+	5.45354i	−0.281914	+	0.230249i
$562$		0			0
$563$	−16.9507			−0.714388			−0.357194	−	0.934030i	$-0.616267\pi$
$563$	−16.9507			−0.714388			−0.357194	+	0.934030i	$0.616267\pi$
$564$		0			0
$565$		−	7.46586i		−	0.314091i
$566$		0			0
$567$	−5.90051	−	23.0691i	−0.247798	−	0.968812i
$568$		0			0
$569$			12.5694i			0.526938i	0.964668	+	0.263469i	$0.0848666\pi$
$569$			12.5694i			0.526938i	−0.964668	+	0.263469i	$0.915133\pi$
$570$		0			0
$571$	−9.64161			−0.403489			−0.201744	−	0.979438i	$-0.564661\pi$
$571$	−9.64161			−0.403489			−0.201744	+	0.979438i	$0.564661\pi$
$572$		0			0
$573$	−5.56745	+	4.54712i	−0.232584	+	0.189959i
$574$		0			0
$575$			0.545337i			0.0227421i
$576$		0			0
$577$	20.9563	+	12.0991i	0.872421	+	0.503692i	0.868152	−	0.496299i	$-0.165308\pi$
$577$	20.9563	+	12.0991i	0.872421	+	0.503692i	0.00426870	+	0.999991i	$0.498641\pi$
$578$		0			0
$579$	−6.43210	−	7.87539i	−0.267309	−	0.327290i
$580$		0			0
$581$	−30.4389	+	3.94714i	−1.26282	+	0.163755i
$582$		0			0
$583$	0.196346			0.00813183
$584$		0			0
$585$	5.45342	+	1.11156i	0.225471	+	0.0459573i
$586$		0			0
$587$	−12.5498	+	21.7368i	−0.517984	+	0.897175i	0.481798	+	0.876283i	$0.339984\pi$
$587$	−12.5498	+	21.7368i	−0.517984	+	0.897175i	−0.999782	+	0.0208923i	$0.993349\pi$
$588$		0			0
$589$	14.9977	+	25.9768i	0.617970	+	1.07035i
$590$		0			0
$591$	4.53304	−	3.70229i	0.186464	−	0.152292i
$592$		0			0
$593$	19.1605	+	33.1869i	0.786826	+	1.36282i	0.927902	+	0.372824i	$0.121610\pi$
$593$	19.1605	+	33.1869i	0.786826	+	1.36282i	−0.141076	+	0.989999i	$0.545056\pi$
$594$		0			0
$595$	3.56743	−	8.56537i	0.146250	−	0.351146i
$596$		0			0
$597$	1.29676	+	7.97145i	0.0530728	+	0.326250i
$598$		0			0
$599$		−	1.27897i		−	0.0522572i	−0.999659	−	0.0261286i	$-0.991682\pi$
$599$		−	1.27897i		−	0.0522572i	0.999659	−	0.0261286i	$-0.00831794\pi$
$600$		0			0
$601$	31.2150	+	18.0220i	1.27329	+	0.735133i	0.975605	−	0.219532i	$-0.0704531\pi$
$601$	31.2150	+	18.0220i	1.27329	+	0.735133i	0.297682	+	0.954665i	$0.403786\pi$
$602$		0			0
$603$	1.96735	−	9.65202i	0.0801167	−	0.393061i
$604$		0			0
$605$	−2.82097	−	4.88607i	−0.114689	−	0.198647i
$606$		0			0
$607$	39.1131	+	22.5820i	1.58755	+	0.916573i	0.993709	+	0.111992i	$0.0357231\pi$
$607$	39.1131	+	22.5820i	1.58755	+	0.916573i	0.593843	+	0.804581i	$0.297610\pi$
$608$		0			0
$609$	15.9952	−	16.9311i	0.648157	−	0.686084i
$610$		0			0
$611$	−4.58264	+	2.64579i	−0.185394	+	0.107037i
$612$		0			0
$613$	−9.50638	+	16.4655i	−0.383959	+	0.665037i	−0.991624	−	0.129157i	$-0.958773\pi$
$613$	−9.50638	+	16.4655i	−0.383959	+	0.665037i	0.607665	+	0.794193i	$0.292106\pi$
$614$		0			0
$615$	−4.80568	−	5.88403i	−0.193784	−	0.237267i
$616$		0			0
$617$	17.2379	−	9.95232i	0.693973	−	0.400665i	−0.111126	−	0.993806i	$-0.535446\pi$
$617$	17.2379	−	9.95232i	0.693973	−	0.400665i	0.805099	+	0.593141i	$0.202112\pi$
$618$		0			0
$619$	−22.0428	+	12.7264i	−0.885977	+	0.511519i	−0.872624	−	0.488392i	$-0.837584\pi$
$619$	−22.0428	+	12.7264i	−0.885977	+	0.511519i	−0.0133522	+	0.999911i	$0.504250\pi$
$620$		0			0
$621$	0.601640	+	0.0239644i	0.0241430	+	0.000961660i
$622$		0			0
$623$	4.08587	−	9.81016i	0.163697	−	0.393036i
$624$		0			0
$625$	−10.3393	+	17.9082i	−0.413573	+	0.716330i
$626$		0			0
$627$	8.51148	−	1.38461i	0.339916	−	0.0552959i
$628$		0			0
$629$	−70.8438			−2.82473
$630$		0			0
$631$	40.8171			1.62490			0.812452	−	0.583028i	$-0.198132\pi$
$631$	40.8171			1.62490			0.812452	+	0.583028i	$0.198132\pi$
$632$		0			0
$633$	−3.80180	+	10.0292i	−0.151108	+	0.398626i
$634$		0			0
$635$	−2.56124	+	4.43619i	−0.101640	+	0.176045i
$636$		0			0
$637$	−6.11037	−	23.1643i	−0.242102	−	0.917801i
$638$		0			0
$639$	−16.6943	−	3.40275i	−0.660415	−	0.134611i
$640$		0			0
$641$	−8.64806	+	4.99296i	−0.341578	+	0.197210i	−0.660970	−	0.750413i	$-0.729855\pi$
$641$	−8.64806	+	4.99296i	−0.341578	+	0.197210i	0.319392	+	0.947623i	$0.396521\pi$
$642$		0			0
$643$	4.32793	−	2.49873i	0.170677	−	0.0985403i	−0.412228	−	0.911081i	$-0.635249\pi$
$643$	4.32793	−	2.49873i	0.170677	−	0.0985403i	0.582905	+	0.812540i	$0.301916\pi$
$644$		0			0
$645$	2.21359	−	5.83950i	0.0871602	−	0.229930i
$646$		0			0
$647$	5.04602	−	8.73996i	0.198379	−	0.343603i	−0.749624	−	0.661864i	$-0.769766\pi$
$647$	5.04602	−	8.73996i	0.198379	−	0.343603i	0.948003	+	0.318261i	$0.103099\pi$
$648$		0			0
$649$	6.82365	−	3.93964i	0.267852	−	0.154644i
$650$		0			0
$651$	20.6657	+	4.91251i	0.809954	+	0.192537i
$652$		0			0
$653$	14.8236	+	8.55844i	0.580094	+	0.334918i	0.761171	−	0.648551i	$-0.224625\pi$
$653$	14.8236	+	8.55844i	0.580094	+	0.334918i	−0.181077	+	0.983469i	$0.557958\pi$
$654$		0			0
$655$	3.38833	+	5.86876i	0.132393	+	0.229311i
$656$		0			0
$657$	12.2934	−	13.8851i	0.479613	−	0.541710i
$658$		0			0
$659$	12.7790	+	7.37798i	0.497800	+	0.287405i	0.727805	−	0.685784i	$-0.240541\pi$
$659$	12.7790	+	7.37798i	0.497800	+	0.287405i	−0.230004	+	0.973190i	$0.573874\pi$
$660$		0			0
$661$		−	30.0316i		−	1.16810i	−0.811719	−	0.584048i	$-0.801468\pi$
$661$		−	30.0316i		−	1.16810i	0.811719	−	0.584048i	$-0.198532\pi$
$662$		0			0
$663$	−29.7020	+	24.2587i	−1.15353	+	0.942128i
$664$		0			0
$665$	−7.37393	+	5.63547i	−0.285949	+	0.218534i
$666$		0			0
$667$	0.294485	+	0.510063i	0.0114025	+	0.0197497i
$668$		0			0
$669$	−2.84042	−	17.4607i	−0.109817	−	0.675069i
$670$		0			0
$671$	2.14623	+	3.71737i	0.0828542	+	0.143508i
$672$		0			0
$673$	18.1953	−	31.5152i	0.701378	−	1.21482i	−0.266605	−	0.963806i	$-0.585902\pi$
$673$	18.1953	−	31.5152i	0.701378	−	1.21482i	0.967983	−	0.251016i	$-0.0807648\pi$
$674$		0			0
$675$	20.6743	+	13.0601i	0.795753	+	0.502685i
$676$		0			0
$677$	−18.3219			−0.704168			−0.352084	−	0.935968i	$-0.614527\pi$
$677$	−18.3219			−0.704168			−0.352084	+	0.935968i	$0.614527\pi$
$678$		0			0
$679$	5.91874	+	45.6431i	0.227140	+	1.75162i
$680$		0			0
$681$	9.97526	−	26.3149i	0.382253	−	1.00839i
$682$		0			0
$683$	6.46067	+	3.73007i	0.247210	+	0.142727i	0.618486	−	0.785796i	$-0.287746\pi$
$683$	6.46067	+	3.73007i	0.247210	+	0.142727i	−0.371276	+	0.928523i	$0.621080\pi$
$684$		0			0
$685$			10.4638i			0.399802i
$686$		0			0
$687$	2.41337	+	14.8355i	0.0920759	+	0.566011i
$688$		0			0
$689$	0.873395			0.0332737
$690$		0			0
$691$			17.5167i			0.666365i	0.942862	+	0.333182i	$0.108122\pi$
$691$			17.5167i			0.666365i	−0.942862	+	0.333182i	$0.891878\pi$
$692$		0			0
$693$	3.42651	−	5.05483i	0.130162	−	0.192017i
$694$		0			0
$695$		−	0.540777i		−	0.0205128i
$696$		0			0
$697$	52.3483			1.98283
$698$		0			0
$699$	−35.5903	−	13.4913i	−1.34615	−	0.510288i
$700$		0			0
$701$			37.8622i			1.43004i	0.699106	+	0.715018i	$0.253582\pi$
$701$			37.8622i			1.43004i	−0.699106	+	0.715018i	$0.746418\pi$
$702$		0			0
$703$	61.3672	+	35.4304i	2.31451	+	1.33628i
$704$		0			0
$705$	1.43287	−	0.233092i	0.0539649	−	0.00877875i
$706$		0			0
$707$	16.7867	−	40.3048i	0.631330	−	1.51582i
$708$		0			0
$709$	−37.1014			−1.39337			−0.696686	−	0.717376i	$-0.745343\pi$
$709$	−37.1014			−1.39337			−0.696686	+	0.717376i	$0.745343\pi$
$710$		0			0
$711$	−2.41139	+	11.8305i	−0.0904341	+	0.443679i
$712$		0			0
$713$	−0.268563	+	0.465165i	−0.0100578	+	0.0174206i
$714$		0			0
$715$	0.713667	+	1.23611i	0.0266896	+	0.0462278i
$716$		0			0
$717$	−26.8838	−	10.1909i	−1.00399	−	0.380586i
$718$		0			0
$719$	5.73941	+	9.94096i	0.214044	+	0.370735i	0.952976	−	0.303044i	$-0.0980031\pi$
$719$	5.73941	+	9.94096i	0.214044	+	0.370735i	−0.738932	+	0.673780i	$0.764670\pi$
$720$		0			0
$721$	0.100027	+	0.771370i	0.00372520	+	0.0287273i
$722$		0			0
$723$	17.8191	+	6.75473i	0.662700	+	0.251211i
$724$		0			0
$725$			23.9199i			0.888364i
$726$		0			0
$727$	13.1105	+	7.56936i	0.486242	+	0.280732i	0.723014	−	0.690833i	$-0.242756\pi$
$727$	13.1105	+	7.56936i	0.486242	+	0.280732i	−0.236772	+	0.971565i	$0.576089\pi$
$728$		0			0
$729$	15.3170	−	22.2349i	0.567297	−	0.823513i
$730$		0			0
$731$	21.5156	+	37.2662i	0.795785	+	1.37834i
$732$		0			0
$733$	−7.96753	−	4.60005i	−0.294287	−	0.169907i	0.345586	−	0.938387i	$-0.387680\pi$
$733$	−7.96753	−	4.60005i	−0.294287	−	0.169907i	−0.639874	+	0.768480i	$0.721013\pi$
$734$		0			0
$735$	−0.685076	+	6.53651i	−0.0252694	+	0.241103i
$736$		0			0
$737$	2.18779	−	1.26312i	0.0805884	−	0.0465277i
$738$		0			0
$739$	−14.6669	+	25.4038i	−0.539529	+	0.934492i	0.459400	+	0.888230i	$0.348065\pi$
$739$	−14.6669	+	25.4038i	−0.539529	+	0.934492i	−0.998929	+	0.0462628i	$0.985269\pi$
$740$		0			0
$741$	37.8611	−	6.15907i	1.39086	−	0.226259i
$742$		0			0
$743$	−33.9829	+	19.6200i	−1.24671	+	0.719789i	−0.970452	−	0.241294i	$-0.922428\pi$
$743$	−33.9829	+	19.6200i	−1.24671	+	0.719789i	−0.276259	+	0.961083i	$0.589095\pi$
$744$		0			0
$745$	−9.22499	+	5.32605i	−0.337977	+	0.195131i
$746$		0			0
$747$	−26.0579	−	23.0708i	−0.953409	−	0.844118i
$748$		0			0
$749$	−8.94933	−	3.72734i	−0.327001	−	0.136194i
$750$		0			0
$751$	−10.5034	+	18.1924i	−0.383274	+	0.663851i	−0.991528	−	0.129892i	$-0.958537\pi$
$751$	−10.5034	+	18.1924i	−0.383274	+	0.663851i	0.608254	+	0.793743i	$0.291870\pi$
$752$		0			0
$753$	19.7659	+	24.2012i	0.720311	+	0.881941i
$754$		0			0
$755$	9.23380			0.336052
$756$		0			0
$757$	12.1528			0.441703			0.220851	−	0.975307i	$-0.429116\pi$
$757$	12.1528			0.441703			0.220851	+	0.975307i	$0.429116\pi$
$758$		0			0
$759$	0.0976797	+	0.119598i	0.00354555	+	0.00434113i
$760$		0			0
$761$	7.24026	−	12.5405i	0.262459	−	0.454593i	−0.704436	−	0.709768i	$-0.748800\pi$
$761$	7.24026	−	12.5405i	0.262459	−	0.454593i	0.966895	+	0.255175i	$0.0821331\pi$
$762$		0			0
$763$	6.63799	−	0.860778i	0.240312	−	0.0311623i
$764$		0			0
$765$	9.97844	−	3.33474i	0.360771	−	0.120568i
$766$		0			0
$767$	30.3532	−	17.5245i	1.09599	−	0.632771i
$768$		0			0
$769$	6.13371	−	3.54130i	0.221187	−	0.127702i	−0.385313	−	0.922786i	$-0.625906\pi$
$769$	6.13371	−	3.54130i	0.221187	−	0.127702i	0.606500	+	0.795084i	$0.292573\pi$
$770$		0			0
$771$	24.6289	−	4.00651i	0.886988	−	0.144291i
$772$		0			0
$773$	−19.1640	+	33.1930i	−0.689280	+	1.19387i	0.282791	+	0.959182i	$0.408740\pi$
$773$	−19.1640	+	33.1930i	−0.689280	+	1.19387i	−0.972071	+	0.234687i	$0.924593\pi$
$774$		0			0
$775$	−18.8918	+	10.9072i	−0.678615	+	0.391799i
$776$		0			0
$777$	48.0824	−	14.3598i	1.72495	−	0.515154i
$778$		0			0
$779$	−45.3458	−	26.1804i	−1.62468	−	0.938011i
$780$		0			0
$781$	−2.18471	−	3.78403i	−0.0781751	−	0.135403i
$782$		0			0
$783$	26.3895	+	1.05114i	0.943084	+	0.0375648i
$784$		0			0
$785$	0.530049	+	0.306024i	0.0189183	+	0.0109225i
$786$		0			0
$787$		−	15.6191i		−	0.556760i	−0.960471	−	0.278380i	$-0.910203\pi$
$787$		−	15.6191i		−	0.556760i	0.960471	−	0.278380i	$-0.0897974\pi$
$788$		0			0
$789$	40.4071	+	15.3172i	1.43853	+	0.545307i
$790$		0			0
$791$	−33.6383	−	14.0101i	−1.19604	−	0.498143i
$792$		0			0
$793$	9.54693	+	16.5358i	0.339022	+	0.587203i
$794$		0			0
$795$	−0.224052	−	0.0849318i	−0.00794630	−	0.00301222i
$796$		0			0
$797$	12.0230	+	20.8244i	0.425875	+	0.737637i	0.996502	−	0.0835726i	$-0.0266330\pi$
$797$	12.0230	+	20.8244i	0.425875	+	0.737637i	−0.570627	+	0.821210i	$0.693300\pi$
$798$		0			0
$799$	−5.00151	+	8.66286i	−0.176941	+	0.306470i
$800$		0			0
$801$	11.4286	−	3.81937i	0.403809	−	0.134951i
$802$		0			0
$803$	4.75608			0.167839
$804$		0			0
$805$	−0.153417	−	0.0638970i	−0.00540722	−	0.00225207i
$806$		0			0
$807$	−37.6308	+	6.12160i	−1.32467	+	0.215491i
$808$		0			0
$809$	−25.2846	−	14.5980i	−0.888958	−	0.513240i	−0.0153562	−	0.999882i	$-0.504888\pi$
$809$	−25.2846	−	14.5980i	−0.888958	−	0.513240i	−0.873601	+	0.486642i	$0.838222\pi$
$810$		0			0
$811$			26.0991i			0.916464i	0.888833	+	0.458232i	$0.151517\pi$
$811$			26.0991i			0.916464i	−0.888833	+	0.458232i	$0.848483\pi$
$812$		0			0
$813$	−42.5352	−	16.1239i	−1.49178	−	0.565491i
$814$		0			0
$815$	9.32523			0.326649
$816$		0			0
$817$		−	43.0416i		−	1.50583i
$818$		0			0
$819$	15.2419	−	22.4851i	0.532596	−	0.785693i
$820$		0			0
$821$		−	54.9905i		−	1.91918i	−0.281402	−	0.959590i	$-0.590799\pi$
$821$		−	54.9905i		−	1.91918i	0.281402	−	0.959590i	$-0.409201\pi$
$822$		0			0
$823$	−18.1157			−0.631474			−0.315737	−	0.948847i	$-0.602252\pi$
$823$	−18.1157			−0.631474			−0.315737	+	0.948847i	$0.602252\pi$
$824$		0			0
$825$	1.00697	+	6.19005i	0.0350581	+	0.215510i
$826$		0			0
$827$			38.1934i			1.32812i	0.747681	+	0.664058i	$0.231167\pi$
$827$			38.1934i			1.32812i	−0.747681	+	0.664058i	$0.768833\pi$
$828$		0			0
$829$	47.0722	+	27.1771i	1.63488	+	0.943901i	0.982557	+	0.185963i	$0.0595404\pi$
$829$	47.0722	+	27.1771i	1.63488	+	0.943901i	0.652327	+	0.757938i	$0.273793\pi$
$830$		0			0
$831$	−2.92489	+	7.71592i	−0.101463	+	0.267662i
$832$		0			0
$833$	−31.8978	−	32.1469i	−1.10519	−	1.11382i
$834$		0			0
$835$	2.40959			0.0833873
$836$		0			0
$837$	11.2031	+	21.3216i	0.387237	+	0.736983i
$838$		0			0
$839$	−13.3919	+	23.1955i	−0.462341	+	0.800798i	−0.999077	−	0.0429523i	$-0.986324\pi$
$839$	−13.3919	+	23.1955i	−0.462341	+	0.800798i	0.536736	+	0.843750i	$0.319657\pi$
$840$		0			0
$841$	−1.58312	−	2.74205i	−0.0545904	−	0.0945534i
$842$		0			0
$843$	−6.16449	−	37.8944i	−0.212316	−	1.30515i
$844$		0			0
$845$	−0.348924	−	0.604354i	−0.0120033	−	0.0207904i
$846$		0			0
$847$	−27.3085	+	3.54121i	−0.938331	+	0.121678i
$848$		0			0
$849$	−3.89777	+	3.18344i	−0.133771	+	0.109255i
$850$		0			0
$851$			1.26890i			0.0434973i
$852$		0			0
$853$	−15.6735	−	9.04908i	−0.536649	−	0.309835i	0.207071	−	0.978326i	$-0.433607\pi$
$853$	−15.6735	−	9.04908i	−0.536649	−	0.309835i	−0.743720	+	0.668491i	$0.766940\pi$
$854$		0			0
$855$	−10.3114	−	2.10176i	−0.352643	−	0.0718785i
$856$		0			0
$857$	17.6561	+	30.5812i	0.603120	+	1.04464i	0.992346	+	0.123492i	$0.0394095\pi$
$857$	17.6561	+	30.5812i	0.603120	+	1.04464i	−0.389225	+	0.921143i	$0.627257\pi$
$858$		0			0
$859$	−20.1598	−	11.6393i	−0.687844	−	0.397127i	0.114960	−	0.993370i	$-0.463326\pi$
$859$	−20.1598	−	11.6393i	−0.687844	−	0.397127i	−0.802804	+	0.596243i	$0.796659\pi$
$860$		0			0
$861$	−35.5293	+	10.6108i	−1.21084	+	0.361616i
$862$		0			0
$863$	−28.3933	+	16.3929i	−0.966520	+	0.558020i	−0.898173	−	0.439641i	$-0.855106\pi$
$863$	−28.3933	+	16.3929i	−0.966520	+	0.558020i	−0.0683462	+	0.997662i	$0.521772\pi$
$864$		0			0
$865$	−5.38980	+	9.33541i	−0.183259	+	0.317414i
$866$		0			0
$867$	−15.2595	+	40.2548i	−0.518239	+	1.36712i
$868$		0			0
$869$	−2.68158	+	1.54821i	−0.0909665	+	0.0525195i
$870$		0			0
$871$	9.73182	−	5.61867i	0.329750	−	0.190381i
$872$		0			0
$873$	−34.5947	+	39.0738i	−1.17085	+	1.32245i
$874$		0			0
$875$	−8.45278	−	11.0604i	−0.285756	−	0.373908i
$876$		0			0
$877$	−10.7688	+	18.6521i	−0.363636	+	0.629837i	−0.988556	−	0.150852i	$-0.951798\pi$
$877$	−10.7688	+	18.6521i	−0.363636	+	0.629837i	0.624920	+	0.780689i	$0.285132\pi$
$878$		0			0
$879$	17.1739	−	45.3051i	0.579261	−	1.52810i
$880$		0			0
$881$	22.9322			0.772606			0.386303	−	0.922372i	$-0.373752\pi$
$881$	22.9322			0.772606			0.386303	+	0.922372i	$0.373752\pi$
$882$		0			0
$883$	31.8225			1.07091			0.535455	−	0.844564i	$-0.320140\pi$
$883$	31.8225			1.07091			0.535455	+	0.844564i	$0.320140\pi$
$884$		0			0
$885$	−9.49064	+	1.54389i	−0.319024	+	0.0518974i
$886$		0			0
$887$	−11.1135	+	19.2492i	−0.373156	+	0.646325i	−0.990049	−	0.140722i	$-0.955058\pi$
$887$	−11.1135	+	19.2492i	−0.373156	+	0.646325i	0.616893	+	0.787047i	$0.288391\pi$
$888$		0			0
$889$	15.1814	+	19.8647i	0.509169	+	0.666241i
$890$		0			0
$891$	6.87338	−	0.838914i	0.230267	−	0.0281047i
$892$		0			0
$893$	8.66494	−	5.00270i	0.289961	−	0.167409i
$894$		0			0
$895$	−0.929507	+	0.536651i	−0.0310700	+	0.0179383i
$896$		0			0
$897$	0.434503	+	0.532001i	0.0145076	+	0.0177630i
$898$		0			0
$899$	−11.7799	+	20.4034i	−0.392881	+	0.680491i
$900$		0			0
$901$	1.42984	−	0.825518i	0.0476349	−	0.0275020i
$902$		0			0
$903$	−22.1566	−	20.9318i	−0.737326	−	0.696566i
$904$		0			0
$905$	2.66712	+	1.53986i	0.0886581	+	0.0511868i
$906$		0			0
$907$	−19.9099	−	34.4849i	−0.661097	−	1.14505i	−0.980328	−	0.197376i	$-0.936758\pi$
$907$	−19.9099	−	34.4849i	−0.661097	−	1.14505i	0.319231	−	0.947677i	$-0.396575\pi$
$908$		0			0
$909$	46.9541	−	15.6918i	1.55737	−	0.520464i
$910$		0			0
$911$	5.87819	+	3.39378i	0.194753	+	0.112441i	0.594206	−	0.804313i	$-0.297466\pi$
$911$	5.87819	+	3.39378i	0.194753	+	0.112441i	−0.399453	+	0.916754i	$0.630800\pi$
$912$		0			0
$913$		−	8.92565i		−	0.295396i
$914$		0			0
$915$	−0.841078	−	5.17029i	−0.0278052	−	0.170925i
$916$		0			0
$917$	32.8008	−	4.25342i	1.08318	−	0.140460i
$918$		0			0
$919$	14.0173	+	24.2787i	0.462389	+	0.800882i	0.999079	−	0.0428977i	$-0.0136590\pi$
$919$	14.0173	+	24.2787i	0.462389	+	0.800882i	−0.536690	+	0.843779i	$0.680326\pi$
$920$		0			0
$921$	−40.7769	+	33.3038i	−1.34364	+	1.09740i
$922$		0			0
$923$	−9.71812	−	16.8323i	−0.319876	−	0.554041i
$924$		0			0
$925$	−25.7670	+	44.6298i	−0.847215	+	1.46742i
$926$		0			0
$927$	−0.584652	+	0.660349i	−0.0192025	+	0.0216887i
$928$		0			0
$929$	−17.7408			−0.582057			−0.291028	−	0.956714i	$-0.593997\pi$
$929$	−17.7408			−0.582057			−0.291028	+	0.956714i	$0.593997\pi$
$930$		0			0
$931$	11.5536	+	43.7994i	0.378654	+	1.43547i
$932$		0			0
$933$	−30.4872	−	37.3282i	−0.998106	−	1.22207i
$934$		0			0
$935$	2.33670	+	1.34909i	0.0764182	+	0.0441200i
$936$		0			0
$937$		−	10.2459i		−	0.334719i	−0.985896	−	0.167360i	$-0.946476\pi$
$937$		−	10.2459i		−	0.334719i	0.985896	−	0.167360i	$-0.0535241\pi$
$938$		0			0
$939$	−0.0624755	+	0.0510258i	−0.00203881	+	0.00166517i
$940$		0			0
$941$	9.99655			0.325878			0.162939	−	0.986636i	$-0.447903\pi$
$941$	9.99655			0.325878			0.162939	+	0.986636i	$0.447903\pi$
$942$		0			0
$943$		−	0.937624i		−	0.0305332i
$944$		0			0
$945$	−6.09653	+	4.28592i	−0.198320	+	0.139421i
$946$		0			0
$947$		−	48.2494i		−	1.56790i	−0.620827	−	0.783948i	$-0.713203\pi$
$947$		−	48.2494i		−	1.56790i	0.620827	−	0.783948i	$-0.286797\pi$
$948$		0			0
$949$	21.1562			0.686760
$950$		0			0
$951$	−11.3946	+	9.30636i	−0.369495	+	0.301779i
$952$		0			0
$953$		−	40.4708i		−	1.31098i	−0.755205	−	0.655489i	$-0.772463\pi$
$953$		−	40.4708i		−	1.31098i	0.755205	−	0.655489i	$-0.227537\pi$
$954$		0			0
$955$	1.94832	+	1.12486i	0.0630462	+	0.0363997i
$956$		0			0
$957$	4.28449	+	5.24588i	0.138498	+	0.169575i
$958$		0			0
$959$	47.1459	+	19.6360i	1.52242	+	0.634079i
$960$		0			0
$961$	9.51402			0.306904
$962$		0			0
$963$	−3.48423	−	10.4257i	−0.112278	−	0.335965i
$964$		0			0
$965$	−1.59117	+	2.75598i	−0.0512215	+	0.0887182i
$966$		0			0
$967$	−14.6566	−	25.3860i	−0.471325	−	0.816359i	0.528137	−	0.849159i	$-0.322891\pi$
$967$	−14.6566	−	25.3860i	−0.471325	−	0.816359i	−0.999462	+	0.0328000i	$0.989558\pi$
$968$		0			0
$969$	56.1612	−	45.8687i	1.80416	−	1.47352i
$970$		0			0
$971$	−9.02830	−	15.6375i	−0.289732	−	0.501831i	0.684014	−	0.729469i	$-0.260233\pi$
$971$	−9.02830	−	15.6375i	−0.289732	−	0.501831i	−0.973746	+	0.227639i	$0.926900\pi$
$972$		0			0
$973$	−2.43653	−	1.01480i	−0.0781117	−	0.0325330i
$974$		0			0
$975$	4.47924	+	27.5348i	0.143450	+	0.881820i
$976$		0			0
$977$		−	39.2466i		−	1.25561i	−0.778371	−	0.627805i	$-0.783953\pi$
$977$		−	39.2466i		−	1.25561i	0.778371	−	0.627805i	$-0.216047\pi$
$978$		0			0
$979$	2.67628	+	1.54515i	0.0855344	+	0.0493833i
$980$		0			0
$981$	5.68261	+	5.03120i	0.181432	+	0.160634i
$982$		0			0
$983$	−13.2334	−	22.9209i	−0.422079	−	0.731063i	0.574063	−	0.818811i	$-0.305366\pi$
$983$	−13.2334	−	22.9209i	−0.422079	−	0.731063i	−0.996143	+	0.0877479i	$0.972033\pi$
$984$		0			0
$985$	−1.58633	−	0.915869i	−0.0505447	−	0.0291820i
$986$		0			0
$987$	1.63864	−	6.89336i	0.0521585	−	0.219418i
$988$		0			0
$989$	0.667484	−	0.385372i	0.0212248	−	0.0122541i
$990$		0			0
$991$	7.32864	−	12.6936i	0.232802	−	0.403225i	−0.725830	−	0.687875i	$-0.758544\pi$
$991$	7.32864	−	12.6936i	0.232802	−	0.403225i	0.958632	+	0.284650i	$0.0918773\pi$
$992$		0			0
$993$	−7.94841	−	9.73195i	−0.252235	−	0.308834i
$994$		0			0
$995$	2.18896	−	1.26380i	0.0693948	−	0.0400651i
$996$		0			0
$997$	3.41103	−	1.96936i	0.108028	−	0.0623703i	−0.445012	−	0.895524i	$-0.646801\pi$
$997$	3.41103	−	1.96936i	0.108028	−	0.0623703i	0.553041	+	0.833154i	$0.313467\pi$
$998$		0			0
$999$	48.1053	+	30.3886i	1.52198	+	0.961451i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bs.a.353.8	yes	48
3.2	odd	2		1512.2.bs.a.521.13		48
4.3	odd	2		1008.2.ca.e.353.17		48
7.5	odd	6		504.2.cx.a.425.1	yes	48
9.4	even	3		1512.2.cx.a.17.13		48
9.5	odd	6		504.2.cx.a.185.1	yes	48
12.11	even	2		3024.2.ca.e.2033.13		48
21.5	even	6		1512.2.cx.a.89.13		48
28.19	even	6		1008.2.df.e.929.24		48
36.23	even	6		1008.2.df.e.689.24		48
36.31	odd	6		3024.2.df.e.17.13		48
63.5	even	6	inner	504.2.bs.a.257.8	✓	48
63.40	odd	6		1512.2.bs.a.1097.13		48
84.47	odd	6		3024.2.df.e.1601.13		48
252.103	even	6		3024.2.ca.e.2609.13		48
252.131	odd	6		1008.2.ca.e.257.17		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.8	✓	48	63.5	even	6	inner
504.2.bs.a.353.8	yes	48	1.1	even	1	trivial
504.2.cx.a.185.1	yes	48	9.5	odd	6
504.2.cx.a.425.1	yes	48	7.5	odd	6
1008.2.ca.e.257.17		48	252.131	odd	6
1008.2.ca.e.353.17		48	4.3	odd	2
1008.2.df.e.689.24		48	36.23	even	6
1008.2.df.e.929.24		48	28.19	even	6
1512.2.bs.a.521.13		48	3.2	odd	2
1512.2.bs.a.1097.13		48	63.40	odd	6
1512.2.cx.a.17.13		48	9.4	even	3
1512.2.cx.a.89.13		48	21.5	even	6
3024.2.ca.e.2033.13		48	12.11	even	2
3024.2.ca.e.2609.13		48	252.103	even	6
3024.2.df.e.17.13		48	36.31	odd	6
3024.2.df.e.1601.13		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)

\(f(q)\)	\(=\)	\(q+(-1.09564 - 1.34148i) q^{3} +(-0.271038 + 0.469451i) q^{5} +(1.60655 + 2.10214i) q^{7} +(-0.599164 + 2.93956i) q^{9} +(-0.666300 + 0.384688i) q^{11} +(-2.96386 + 1.71119i) q^{13} +(0.926720 - 0.150754i) q^{15} +(-3.23477 + 5.60278i) q^{17} +(5.60413 - 3.23554i) q^{19} +(1.05981 - 4.45834i) q^{21} +(0.100353 + 0.0579388i) q^{23} +(2.35308 + 4.07565i) q^{25} +(4.59984 - 2.41692i) q^{27} +(4.40174 + 2.54135i) q^{29} +4.63530i q^{31} +(1.24608 + 0.472353i) q^{33} +(-1.42229 + 0.184434i) q^{35} +(5.47518 + 9.48329i) q^{37} +(5.54284 + 2.10114i) q^{39} +(-4.04575 - 7.00745i) q^{41} +(3.32569 - 5.76026i) q^{43} +(-1.21758 - 1.07801i) q^{45} +1.54617 q^{47} +(-1.83802 + 6.75438i) q^{49} +(11.0602 - 1.79922i) q^{51} +(-0.221011 - 0.127601i) q^{53} -0.417060i q^{55} +(-10.4805 - 3.97287i) q^{57} -10.2411 q^{59} -5.57913i q^{61} +(-7.14196 + 3.46301i) q^{63} -1.85518i q^{65} -3.28349 q^{67} +(-0.0322262 - 0.198102i) q^{69} +5.67917i q^{71} +(-5.35354 - 3.09087i) q^{73} +(2.88931 - 7.62205i) q^{75} +(-1.87911 - 0.782639i) q^{77} +4.02459 q^{79} +(-8.28201 - 3.52255i) q^{81} +(-5.80057 + 10.0469i) q^{83} +(-1.75349 - 3.03713i) q^{85} +(-1.41353 - 8.68926i) q^{87} +(-2.00832 - 3.47851i) q^{89} +(-8.35874 - 3.48136i) q^{91} +(6.21818 - 5.07860i) q^{93} +3.50781i q^{95} +(15.0653 + 8.69795i) q^{97} +(-0.731591 - 2.18912i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75}+ \cdots - 64 q^{99}+O(q^{100}) \) 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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Database

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