LMFDB - Embedded newform 420.2.bn.a.269.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [420,2,Mod(89,420)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("420.89"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(420, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 3, 5])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.10
Character	$\chi$	$=$	420.269
Dual form			420.2.bn.a.89.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.528155 - 1.64956i) q^{3} +(-0.225553 - 2.22466i) q^{5} +(-2.08204 + 1.63251i) q^{7} +(-2.44211 - 1.74245i) q^{9} +(-5.09034 - 2.93891i) q^{11} +3.54004 q^{13} +(-3.78885 - 0.802902i) q^{15} +(-2.69171 - 1.55406i) q^{17} +(3.58419 - 2.06933i) q^{19} +(1.59329 + 4.29667i) q^{21} +(3.57587 + 6.19358i) q^{23} +(-4.89825 + 1.00356i) q^{25} +(-4.16408 + 3.10812i) q^{27} -6.84761i q^{29} +(-3.90384 - 2.25388i) q^{31} +(-7.53639 + 6.84463i) q^{33} +(4.10141 + 4.26362i) q^{35} +(1.70926 - 0.986843i) q^{37} +(1.86969 - 5.83952i) q^{39} +6.33142 q^{41} -3.88979i q^{43} +(-3.32553 + 5.82588i) q^{45} +(1.58829 - 0.916997i) q^{47} +(1.66979 - 6.79793i) q^{49} +(-3.98516 + 3.61936i) q^{51} +(6.90391 - 11.9579i) q^{53} +(-5.38994 + 11.9872i) q^{55} +(-1.52048 - 7.00526i) q^{57} +(-2.32584 + 4.02848i) q^{59} +(0.702144 - 0.405383i) q^{61} +(7.92913 - 0.358927i) q^{63} +(-0.798468 - 7.87540i) q^{65} +(8.84158 + 5.10469i) q^{67} +(12.1053 - 2.62744i) q^{69} -1.18684i q^{71} +(-1.08522 + 1.87966i) q^{73} +(-0.931602 + 8.61000i) q^{75} +(15.3961 - 2.19112i) q^{77} +(-5.05228 - 8.75081i) q^{79} +(2.92776 + 8.51048i) q^{81} +5.31243i q^{83} +(-2.85014 + 6.33868i) q^{85} +(-11.2956 - 3.61660i) q^{87} +(6.28986 + 10.8944i) q^{89} +(-7.37052 + 5.77917i) q^{91} +(-5.77975 + 5.24922i) q^{93} +(-5.41199 - 7.50686i) q^{95} +4.50686 q^{97} +(7.31025 + 16.0468i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{15} + 12 q^{19} - 8 q^{21} + 6 q^{25} - 12 q^{31} + 24 q^{39} + 33 q^{45} - 44 q^{49} - 10 q^{51} - 24 q^{61} + 21 q^{75} - 28 q^{79} - 20 q^{81} - 4 q^{85} + 16 q^{91} - 28 q^{99}+O(q^{100}) $ 32 * q + 2 * q^15 + 12 * q^19 - 8 * q^21 + 6 * q^25 - 12 * q^31 + 24 * q^39 + 33 * q^45 - 44 * q^49 - 10 * q^51 - 24 * q^61 + 21 * q^75 - 28 * q^79 - 20 * q^81 - 4 * q^85 + 16 * q^91 - 28 * q^99

Character values

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

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.528155	−	1.64956i	0.304930	−	0.952375i
$3$	0.528155	−	1.64956i	0.304930	−	0.952375i
$4$		0			0
$5$	−0.225553	−	2.22466i	−0.100870	−	0.994900i
$5$	−0.225553	−	2.22466i	−0.100870	−	0.994900i
$6$		0			0
$7$	−2.08204	+	1.63251i	−0.786938	+	0.617033i
$7$	−2.08204	+	1.63251i	−0.786938	+	0.617033i
$8$		0			0
$9$	−2.44211	−	1.74245i	−0.814035	−	0.580816i
$10$		0			0
$11$	−5.09034	−	2.93891i	−1.53479	−	0.886114i	−0.999131	−	0.0416823i	$-0.986728\pi$
$11$	−5.09034	−	2.93891i	−1.53479	−	0.886114i	−0.535663	−	0.844432i	$-0.679938\pi$
$12$		0			0
$13$	3.54004			0.981831			0.490916	−	0.871207i	$-0.336662\pi$
$13$	3.54004			0.981831			0.490916	+	0.871207i	$0.336662\pi$
$14$		0			0
$15$	−3.78885	−	0.802902i	−0.978276	−	0.207309i
$16$		0			0
$17$	−2.69171	−	1.55406i	−0.652836	−	0.376915i	0.136706	−	0.990612i	$-0.456348\pi$
$17$	−2.69171	−	1.55406i	−0.652836	−	0.376915i	−0.789542	+	0.613697i	$0.789682\pi$
$18$		0			0
$19$	3.58419	−	2.06933i	0.822269	−	0.474737i	−0.0289296	−	0.999581i	$-0.509210\pi$
$19$	3.58419	−	2.06933i	0.822269	−	0.474737i	0.851198	+	0.524844i	$0.175877\pi$
$20$		0			0
$21$	1.59329	+	4.29667i	0.347685	+	0.937611i
$22$		0			0
$23$	3.57587	+	6.19358i	0.745620	+	1.29145i	0.949905	+	0.312539i	$0.101180\pi$
$23$	3.57587	+	6.19358i	0.745620	+	1.29145i	−0.204285	+	0.978911i	$0.565487\pi$
$24$		0			0
$25$	−4.89825	+	1.00356i	−0.979650	+	0.200712i
$26$		0			0
$27$	−4.16408	+	3.10812i	−0.801378	+	0.598158i
$28$		0			0
$29$		−	6.84761i		−	1.27157i	−0.771867	−	0.635785i	$-0.780677\pi$
$29$		−	6.84761i		−	1.27157i	0.771867	−	0.635785i	$-0.219323\pi$
$30$		0			0
$31$	−3.90384	−	2.25388i	−0.701150	−	0.404809i	0.106626	−	0.994299i	$-0.465995\pi$
$31$	−3.90384	−	2.25388i	−0.701150	−	0.404809i	−0.807776	+	0.589490i	$0.799329\pi$
$32$		0			0
$33$	−7.53639	+	6.84463i	−1.31192	+	1.19150i
$34$		0			0
$35$	4.10141	+	4.26362i	0.693264	+	0.720684i
$36$		0			0
$37$	1.70926	−	0.986843i	0.281001	−	0.162236i	−0.352875	−	0.935670i	$-0.614796\pi$
$37$	1.70926	−	0.986843i	0.281001	−	0.162236i	0.633876	+	0.773434i	$0.281463\pi$
$38$		0			0
$39$	1.86969	−	5.83952i	0.299390	−	0.935071i
$40$		0			0
$41$	6.33142			0.988801			0.494401	−	0.869234i	$-0.335388\pi$
$41$	6.33142			0.988801			0.494401	+	0.869234i	$0.335388\pi$
$42$		0			0
$43$		−	3.88979i		−	0.593187i	−0.955004	−	0.296594i	$-0.904149\pi$
$43$		−	3.88979i		−	0.593187i	0.955004	−	0.296594i	$-0.0958507\pi$
$44$		0			0
$45$	−3.32553	+	5.82588i	−0.495741	+	0.868470i
$46$		0			0
$47$	1.58829	−	0.916997i	0.231675	−	0.133758i	−0.379669	−	0.925122i	$-0.623962\pi$
$47$	1.58829	−	0.916997i	0.231675	−	0.133758i	0.611345	+	0.791364i	$0.290629\pi$
$48$		0			0
$49$	1.66979	−	6.79793i	0.238541	−	0.971132i
$50$		0			0
$51$	−3.98516	+	3.61936i	−0.558034	+	0.506812i
$52$		0			0
$53$	6.90391	−	11.9579i	0.948325	−	1.64255i	0.199371	−	0.979924i	$-0.436110\pi$
$53$	6.90391	−	11.9579i	0.948325	−	1.64255i	0.748954	−	0.662622i	$-0.230557\pi$
$54$		0			0
$55$	−5.38994	+	11.9872i	−0.726779	+	1.61635i
$56$		0			0
$57$	−1.52048	−	7.00526i	−0.201393	−	0.927869i
$58$		0			0
$59$	−2.32584	+	4.02848i	−0.302799	+	0.524463i	−0.976769	−	0.214296i	$-0.931254\pi$
$59$	−2.32584	+	4.02848i	−0.302799	+	0.524463i	0.673970	+	0.738759i	$0.264588\pi$
$60$		0			0
$61$	0.702144	−	0.405383i	0.0899003	−	0.0519040i	−0.454376	−	0.890810i	$-0.650138\pi$
$61$	0.702144	−	0.405383i	0.0899003	−	0.0519040i	0.544276	+	0.838906i	$0.316804\pi$
$62$		0			0
$63$	7.92913	−	0.358927i	0.998977	−	0.0452206i
$64$		0			0
$65$	−0.798468	−	7.87540i	−0.0990377	−	0.976824i
$66$		0			0
$67$	8.84158	+	5.10469i	1.08017	+	0.623637i	0.930942	−	0.365166i	$-0.118988\pi$
$67$	8.84158	+	5.10469i	1.08017	+	0.623637i	0.149228	+	0.988803i	$0.452321\pi$
$68$		0			0
$69$	12.1053	−	2.62744i	1.45731	−	0.316307i
$70$		0			0
$71$		−	1.18684i		−	0.140852i	−0.997517	−	0.0704262i	$-0.977564\pi$
$71$		−	1.18684i		−	0.140852i	0.997517	−	0.0704262i	$-0.0224359\pi$
$72$		0			0
$73$	−1.08522	+	1.87966i	−0.127016	+	0.219998i	−0.922519	−	0.385951i	$-0.873873\pi$
$73$	−1.08522	+	1.87966i	−0.127016	+	0.219998i	0.795503	+	0.605949i	$0.207207\pi$
$74$		0			0
$75$	−0.931602	+	8.61000i	−0.107572	+	0.994197i
$76$		0			0
$77$	15.3961	−	2.19112i	1.75455	−	0.249702i
$78$		0			0
$79$	−5.05228	−	8.75081i	−0.568426	−	0.984543i	−0.996722	−	0.0809043i	$-0.974219\pi$
$79$	−5.05228	−	8.75081i	−0.568426	−	0.984543i	0.428296	−	0.903639i	$-0.359114\pi$
$80$		0			0
$81$	2.92776	+	8.51048i	0.325306	+	0.945609i
$82$		0			0
$83$			5.31243i			0.583115i	0.956553	+	0.291558i	$0.0941735\pi$
$83$			5.31243i			0.583115i	−0.956553	+	0.291558i	$0.905826\pi$
$84$		0			0
$85$	−2.85014	+	6.33868i	−0.309141	+	0.687526i
$86$		0			0
$87$	−11.2956	−	3.61660i	−1.21101	−	0.387740i
$88$		0			0
$89$	6.28986	+	10.8944i	0.666724	+	1.15480i	0.978815	+	0.204747i	$0.0656373\pi$
$89$	6.28986	+	10.8944i	0.666724	+	1.15480i	−0.312091	+	0.950052i	$0.601029\pi$
$90$		0			0
$91$	−7.37052	+	5.77917i	−0.772640	+	0.605822i
$92$		0			0
$93$	−5.77975	+	5.24922i	−0.599332	+	0.544319i
$94$		0			0
$95$	−5.41199	−	7.50686i	−0.555258	−	0.770188i
$96$		0			0
$97$	4.50686			0.457602			0.228801	−	0.973473i	$-0.426519\pi$
$97$	4.50686			0.457602			0.228801	+	0.973473i	$0.426519\pi$
$98$		0			0
$99$	7.31025	+	16.0468i	0.734708	+	1.61276i
$100$		0			0
$101$	−0.896791	+	1.55329i	−0.0892340	+	0.154558i	−0.907188	−	0.420726i	$-0.861775\pi$
$101$	−0.896791	+	1.55329i	−0.0892340	+	0.154558i	0.817954	+	0.575284i	$0.195109\pi$
$102$		0			0
$103$	−6.30688	−	10.9238i	−0.621436	−	1.07636i	−0.989219	−	0.146446i	$-0.953216\pi$
$103$	−6.30688	−	10.9238i	−0.621436	−	1.07636i	0.367783	−	0.929912i	$-0.380117\pi$
$104$		0			0
$105$	9.19928	−	4.51367i	0.897758	−	0.440489i
$106$		0			0
$107$	1.73976	+	3.01335i	0.168189	+	0.291311i	0.937783	−	0.347222i	$-0.112875\pi$
$107$	1.73976	+	3.01335i	0.168189	+	0.291311i	−0.769594	+	0.638533i	$0.779542\pi$
$108$		0			0
$109$	4.98802	−	8.63951i	0.477766	−	0.827515i	−0.521909	−	0.853001i	$-0.674780\pi$
$109$	4.98802	−	8.63951i	0.477766	−	0.827515i	0.999675	+	0.0254860i	$0.00811333\pi$
$110$		0			0
$111$	−0.725103	−	3.34074i	−0.0688238	−	0.317089i
$112$		0			0
$113$	2.54532			0.239444			0.119722	−	0.992807i	$-0.461800\pi$
$113$	2.54532			0.239444			0.119722	+	0.992807i	$0.461800\pi$
$114$		0			0
$115$	12.9721	−	9.35208i	1.20965	−	0.872086i
$116$		0			0
$117$	−8.64516	−	6.16834i	−0.799245	−	0.570263i
$118$		0			0
$119$	8.14128	−	1.15864i	0.746310	−	0.106213i
$120$		0			0
$121$	11.7744	+	20.3938i	1.07040	+	1.85398i
$122$		0			0
$123$	3.34397	−	10.4441i	0.301515	−	0.941709i
$124$		0			0
$125$	3.33740	+	10.6706i	0.298506	+	0.954408i
$126$		0			0
$127$			12.6616i			1.12353i	0.827295	+	0.561767i	$0.189878\pi$
$127$			12.6616i			1.12353i	−0.827295	+	0.561767i	$0.810122\pi$
$128$		0			0
$129$	−6.41644	−	2.05441i	−0.564936	−	0.180881i
$130$		0			0
$131$	6.34770	+	10.9945i	0.554601	+	0.960597i	0.997934	+	0.0642406i	$0.0204625\pi$
$131$	6.34770	+	10.9945i	0.554601	+	0.960597i	−0.443333	+	0.896357i	$0.646204\pi$
$132$		0			0
$133$	−4.08421	+	10.1597i	−0.354146	+	0.880955i
$134$		0			0
$135$	7.85374	+	8.56263i	0.675943	+	0.736954i
$136$		0			0
$137$	2.62391	−	4.54475i	0.224176	−	0.388284i	−0.731896	−	0.681416i	$-0.761364\pi$
$137$	2.62391	−	4.54475i	0.224176	−	0.388284i	0.956072	+	0.293132i	$0.0946977\pi$
$138$		0			0
$139$		−	14.2842i		−	1.21157i	−0.795627	−	0.605787i	$-0.792858\pi$
$139$		−	14.2842i		−	1.21157i	0.795627	−	0.605787i	$-0.207142\pi$
$140$		0			0
$141$	−0.673782	−	3.10429i	−0.0567427	−	0.261428i
$142$		0			0
$143$	−18.0200	−	10.4039i	−1.50691	−	0.870014i
$144$		0			0
$145$	−15.2336	+	1.54450i	−1.26508	+	0.128264i
$146$		0			0
$147$	−10.3317	−	6.34478i	−0.852143	−	0.523308i
$148$		0			0
$149$	13.0762	−	7.54956i	1.07125	−	0.618484i	0.142724	−	0.989763i	$-0.454414\pi$
$149$	13.0762	−	7.54956i	1.07125	−	0.618484i	0.928521	+	0.371279i	$0.121081\pi$
$150$		0			0
$151$	4.16979	−	7.22229i	0.339333	−	0.587742i	−0.644975	−	0.764204i	$-0.723132\pi$
$151$	4.16979	−	7.22229i	0.339333	−	0.587742i	0.984307	+	0.176462i	$0.0564654\pi$
$152$		0			0
$153$	3.86558	+	8.48535i	0.312513	+	0.686000i
$154$		0			0
$155$	−4.13361	+	9.19310i	−0.332019	+	0.738407i
$156$		0			0
$157$	0.480298	−	0.831900i	0.0383319	−	0.0663929i	−0.846223	−	0.532829i	$-0.821129\pi$
$157$	0.480298	−	0.831900i	0.0383319	−	0.0663929i	0.884555	+	0.466436i	$0.154462\pi$
$158$		0			0
$159$	−16.0790	−	17.7040i	−1.27515	−	1.40402i
$160$		0			0
$161$	−17.5562	−	7.05764i	−1.38362	−	0.556220i
$162$		0			0
$163$	−16.1698	+	9.33565i	−1.26652	+	0.731224i	−0.974327	−	0.225136i	$-0.927717\pi$
$163$	−16.1698	+	9.33565i	−1.26652	+	0.731224i	−0.292190	+	0.956360i	$0.594384\pi$
$164$		0			0
$165$	16.9268	+	15.2221i	1.31775	+	1.18504i
$166$		0			0
$167$			14.2212i			1.10047i	0.835011	+	0.550233i	$0.185461\pi$
$167$			14.2212i			1.10047i	−0.835011	+	0.550233i	$0.814539\pi$
$168$		0			0
$169$	−0.468096			−0.0360074
$170$		0			0
$171$	−12.3587	−	1.19173i	−0.945090	−	0.0911338i
$172$		0			0
$173$	−0.618569	+	0.357131i	−0.0470289	+	0.0271522i	−0.523330	−	0.852130i	$-0.675311\pi$
$173$	−0.618569	+	0.357131i	−0.0470289	+	0.0271522i	0.476301	+	0.879282i	$0.341977\pi$
$174$		0			0
$175$	8.56004	−	10.0859i	0.647078	−	0.762424i
$176$		0			0
$177$	5.41682	+	5.96428i	0.407153	+	0.448303i
$178$		0			0
$179$	−9.68510	−	5.59169i	−0.723898	−	0.417943i	0.0922876	−	0.995732i	$-0.470582\pi$
$179$	−9.68510	−	5.59169i	−0.723898	−	0.417943i	−0.816186	+	0.577790i	$0.803915\pi$
$180$		0			0
$181$			3.69700i			0.274796i	0.990516	+	0.137398i	$0.0438739\pi$
$181$			3.69700i			0.274796i	−0.990516	+	0.137398i	$0.956126\pi$
$182$		0			0
$183$	−0.297864	−	1.37233i	−0.0220187	−	0.101446i
$184$		0			0
$185$	−2.58092	−	3.57995i	−0.189753	−	0.263203i
$186$		0			0
$187$	9.13448	+	15.8214i	0.667979	+	1.15697i
$188$		0			0
$189$	3.59574	−	13.2692i	0.261551	−	0.965190i
$190$		0			0
$191$	8.99652	−	5.19414i	0.650965	−	0.375835i	−0.137861	−	0.990452i	$-0.544023\pi$
$191$	8.99652	−	5.19414i	0.650965	−	0.375835i	0.788826	+	0.614617i	$0.210689\pi$
$192$		0			0
$193$	−5.12779	−	2.96053i	−0.369106	−	0.213104i	0.303962	−	0.952684i	$-0.401691\pi$
$193$	−5.12779	−	2.96053i	−0.369106	−	0.213104i	−0.673068	+	0.739581i	$0.735024\pi$
$194$		0			0
$195$	−13.4127	−	2.84231i	−0.960502	−	0.203542i
$196$		0			0
$197$	−11.1053			−0.791221			−0.395610	−	0.918418i	$-0.629467\pi$
$197$	−11.1053			−0.791221			−0.395610	+	0.918418i	$0.629467\pi$
$198$		0			0
$199$	11.4667	+	6.62029i	0.812851	+	0.469300i	0.847945	−	0.530084i	$-0.177840\pi$
$199$	11.4667	+	6.62029i	0.812851	+	0.469300i	−0.0350939	+	0.999384i	$0.511173\pi$
$200$		0			0
$201$	13.0902	−	11.8887i	0.923312	−	0.838561i
$202$		0			0
$203$	11.1788	+	14.2570i	0.784600	+	1.00065i
$204$		0			0
$205$	−1.42807	−	14.0853i	−0.0997408	−	0.983758i
$206$		0			0
$207$	2.05934	−	21.3561i	0.143134	−	1.48435i
$208$		0			0
$209$	−24.3263			−1.68268
$210$		0			0
$211$	−19.9122			−1.37082			−0.685408	−	0.728160i	$-0.740376\pi$
$211$	−19.9122			−1.37082			−0.685408	+	0.728160i	$0.740376\pi$
$212$		0			0
$213$	−1.95777	−	0.626837i	−0.134144	−	0.0429502i
$214$		0			0
$215$	−8.65347	+	0.877354i	−0.590162	+	0.0598350i
$216$		0			0
$217$	11.8074	−	1.68040i	0.801542	−	0.114073i
$218$		0			0
$219$	2.52745	+	2.78289i	0.170789	+	0.188051i
$220$		0			0
$221$	−9.52878	−	5.50144i	−0.640975	−	0.370067i
$222$		0			0
$223$	10.4924			0.702623			0.351311	−	0.936259i	$-0.385736\pi$
$223$	10.4924			0.702623			0.351311	+	0.936259i	$0.385736\pi$
$224$		0			0
$225$	13.7107	+	6.08415i	0.914046	+	0.405610i
$226$		0			0
$227$	−14.2249	−	8.21273i	−0.944138	−	0.545098i	−0.0528829	−	0.998601i	$-0.516841\pi$
$227$	−14.2249	−	8.21273i	−0.944138	−	0.545098i	−0.891255	+	0.453502i	$0.850174\pi$
$228$		0			0
$229$	−0.903838	+	0.521831i	−0.0597273	+	0.0344836i	−0.529566	−	0.848269i	$-0.677645\pi$
$229$	−0.903838	+	0.521831i	−0.0597273	+	0.0344836i	0.469839	+	0.882752i	$0.344312\pi$
$230$		0			0
$231$	4.51713	−	26.5541i	0.297205	−	1.74713i
$232$		0			0
$233$	−14.4619	−	25.0488i	−0.947431	−	1.64100i	−0.750809	−	0.660519i	$-0.770336\pi$
$233$	−14.4619	−	25.0488i	−0.947431	−	1.64100i	−0.196622	−	0.980479i	$-0.562997\pi$
$234$		0			0
$235$	−2.39825	−	3.32657i	−0.156445	−	0.217001i
$236$		0			0
$237$	−17.1034	+	3.71227i	−1.11098	+	0.241138i
$238$		0			0
$239$		−	5.69731i		−	0.368528i	−0.982877	−	0.184264i	$-0.941010\pi$
$239$		−	5.69731i		−	0.368528i	0.982877	−	0.184264i	$-0.0589902\pi$
$240$		0			0
$241$	−6.10598	−	3.52529i	−0.393321	−	0.227084i	0.290277	−	0.956943i	$-0.406253\pi$
$241$	−6.10598	−	3.52529i	−0.393321	−	0.227084i	−0.683598	+	0.729859i	$0.739586\pi$
$242$		0			0
$243$	15.5849	−	0.334668i	0.999770	−	0.0214690i
$244$		0			0
$245$	−15.4997	−	2.18143i	−0.990241	−	0.139366i
$246$		0			0
$247$	12.6882	−	7.32552i	0.807329	−	0.466112i
$248$		0			0
$249$	8.76319	+	2.80579i	0.555344	+	0.177809i
$250$		0			0
$251$	−3.93237			−0.248209			−0.124105	−	0.992269i	$-0.539606\pi$
$251$	−3.93237			−0.248209			−0.124105	+	0.992269i	$0.539606\pi$
$252$		0			0
$253$		−	42.0366i		−	2.64282i
$254$		0			0
$255$	8.95072	+	8.04928i	0.560516	+	0.504065i
$256$		0			0
$257$	−13.2552	+	7.65287i	−0.826834	+	0.477373i	−0.852767	−	0.522291i	$-0.825078\pi$
$257$	−13.2552	+	7.65287i	−0.826834	+	0.477373i	0.0259335	+	0.999664i	$0.491744\pi$
$258$		0			0
$259$	−1.94772	+	4.84504i	−0.121025	+	0.301056i
$260$		0			0
$261$	−11.9316	+	16.7226i	−0.738547	+	1.03510i
$262$		0			0
$263$	−9.75977	+	16.9044i	−0.601813	+	1.04237i	0.390733	+	0.920504i	$0.372222\pi$
$263$	−9.75977	+	16.9044i	−0.601813	+	1.04237i	−0.992546	+	0.121867i	$0.961112\pi$
$264$		0			0
$265$	−28.1595	−	12.6617i	−1.72983	−	0.777803i
$266$		0			0
$267$	21.2929	−	4.62161i	1.30311	−	0.282838i
$268$		0			0
$269$	−4.91865	+	8.51935i	−0.299895	+	0.519434i	−0.976112	−	0.217269i	$-0.930285\pi$
$269$	−4.91865	+	8.51935i	−0.299895	+	0.519434i	0.676216	+	0.736703i	$0.263618\pi$
$270$		0			0
$271$	18.0820	−	10.4397i	1.09841	−	0.634164i	0.162603	−	0.986691i	$-0.448011\pi$
$271$	18.0820	−	10.4397i	1.09841	−	0.634164i	0.935802	+	0.352527i	$0.114678\pi$
$272$		0			0
$273$	5.64033	+	15.2104i	0.341368	+	0.920576i
$274$		0			0
$275$	27.8831	+	9.28705i	1.68142	+	0.560030i
$276$		0			0
$277$	7.36446	+	4.25187i	0.442487	+	0.255470i	0.704652	−	0.709553i	$-0.251103\pi$
$277$	7.36446	+	4.25187i	0.442487	+	0.255470i	−0.262165	+	0.965023i	$0.584436\pi$
$278$		0			0
$279$	5.60632	+	12.3064i	0.335641	+	0.736768i
$280$		0			0
$281$			7.63690i			0.455579i	0.973710	+	0.227790i	$0.0731499\pi$
$281$			7.63690i			0.455579i	−0.973710	+	0.227790i	$0.926850\pi$
$282$		0			0
$283$	−4.50375	+	7.80072i	−0.267720	+	0.463705i	−0.968273	−	0.249896i	$-0.919604\pi$
$283$	−4.50375	+	7.80072i	−0.267720	+	0.463705i	0.700553	+	0.713601i	$0.252937\pi$
$284$		0			0
$285$	−15.2414	+	4.96262i	−0.902822	+	0.293960i
$286$		0			0
$287$	−13.1823	+	10.3361i	−0.778125	+	0.610123i
$288$		0			0
$289$	−3.66979	−	6.35626i	−0.215870	−	0.373898i
$290$		0			0
$291$	2.38032	−	7.43434i	0.139537	−	0.435809i
$292$		0			0
$293$			27.6102i			1.61301i	0.591231	+	0.806503i	$0.298642\pi$
$293$			27.6102i			1.61301i	−0.591231	+	0.806503i	$0.701358\pi$
$294$		0			0
$295$	9.48660	+	4.26558i	0.552331	+	0.248352i
$296$		0			0
$297$	30.3311	−	3.58353i	1.75999	−	0.207938i
$298$		0			0
$299$	12.6587	+	21.9255i	0.732073	+	1.26799i
$300$		0			0
$301$	6.35014	+	8.09870i	0.366016	+	0.466801i
$302$		0			0
$303$	2.08860	+	2.29969i	0.119987	+	0.132114i
$304$		0			0
$305$	−1.06021	−	1.47060i	−0.0607075	−	0.0842062i
$306$		0			0
$307$	−9.99609			−0.570507			−0.285253	−	0.958452i	$-0.592078\pi$
$307$	−9.99609			−0.570507			−0.285253	+	0.958452i	$0.592078\pi$
$308$		0			0
$309$	−21.3506	+	4.63411i	−1.21459	+	0.263625i
$310$		0			0
$311$	11.9336	−	20.6696i	0.676693	−	1.17207i	−0.299278	−	0.954166i	$-0.596746\pi$
$311$	11.9336	−	20.6696i	0.676693	−	1.17207i	0.975971	−	0.217901i	$-0.0699210\pi$
$312$		0			0
$313$	2.79759	+	4.84558i	0.158129	+	0.273888i	0.934194	−	0.356765i	$-0.116120\pi$
$313$	2.79759	+	4.84558i	0.158129	+	0.273888i	−0.776065	+	0.630653i	$0.782787\pi$
$314$		0			0
$315$	−2.58693	−	17.5587i	−0.145757	−	0.989320i
$316$		0			0
$317$	−5.86828	−	10.1642i	−0.329596	−	0.570876i	0.652836	−	0.757499i	$-0.273579\pi$
$317$	−5.86828	−	10.1642i	−0.329596	−	0.570876i	−0.982432	+	0.186623i	$0.940246\pi$
$318$		0			0
$319$	−20.1245	+	34.8566i	−1.12676	+	1.95160i
$320$		0			0
$321$	5.88956	−	1.27832i	0.328723	−	0.0713490i
$322$		0			0
$323$	−12.8635			−0.715742
$324$		0			0
$325$	−17.3400	+	3.55264i	−0.961851	+	0.197065i
$326$		0			0
$327$	−11.6170	−	12.7910i	−0.642419	−	0.707347i
$328$		0			0
$329$	−1.80986	+	4.50212i	−0.0997810	+	0.248210i
$330$		0			0
$331$	−1.26453	−	2.19023i	−0.0695050	−	0.120386i	0.829179	−	0.558984i	$-0.188809\pi$
$331$	−1.26453	−	2.19023i	−0.0695050	−	0.120386i	−0.898684	+	0.438598i	$0.855475\pi$
$332$		0			0
$333$	−5.89372	−	0.568324i	−0.322974	−	0.0311440i
$334$		0			0
$335$	9.36196	−	20.8209i	0.511499	−	1.13757i
$336$		0			0
$337$			34.3299i			1.87007i	0.354560	+	0.935033i	$0.384631\pi$
$337$			34.3299i			1.87007i	−0.354560	+	0.935033i	$0.615369\pi$
$338$		0			0
$339$	1.34432	−	4.19866i	0.0730136	−	0.228040i
$340$		0			0
$341$	13.2479	+	22.9460i	0.717414	+	1.24260i
$342$		0			0
$343$	7.62114	+	16.8795i	0.411503	+	0.911408i
$344$		0			0
$345$	−8.57556	−	26.3376i	−0.461693	−	1.41797i
$346$		0			0
$347$	0.297864	−	0.515915i	0.0159902	−	0.0276958i	−0.857920	−	0.513784i	$-0.828243\pi$
$347$	0.297864	−	0.515915i	0.0159902	−	0.0276958i	0.873910	+	0.486088i	$0.161577\pi$
$348$		0			0
$349$			23.0392i			1.23326i	0.787253	+	0.616630i	$0.211503\pi$
$349$			23.0392i			1.23326i	−0.787253	+	0.616630i	$0.788497\pi$
$350$		0			0
$351$	−14.7410	+	11.0029i	−0.786818	+	0.587290i
$352$		0			0
$353$	9.43718	+	5.44856i	0.502290	+	0.289997i	0.729659	−	0.683811i	$-0.239679\pi$
$353$	9.43718	+	5.44856i	0.502290	+	0.289997i	−0.227369	+	0.973809i	$0.573012\pi$
$354$		0			0
$355$	−2.64033	+	0.267696i	−0.140134	+	0.0142078i
$356$		0			0
$357$	2.38861	−	14.0415i	0.126418	−	0.743154i
$358$		0			0
$359$	9.03320	−	5.21532i	0.476754	−	0.275254i	−0.242309	−	0.970199i	$-0.577905\pi$
$359$	9.03320	−	5.21532i	0.476754	−	0.275254i	0.719063	+	0.694945i	$0.244571\pi$
$360$		0			0
$361$	−0.935743	+	1.62075i	−0.0492496	+	0.0853028i
$362$		0			0
$363$	39.8595	−	8.65145i	2.09208	−	0.454083i
$364$		0			0
$365$	4.42639	+	1.99029i	0.231688	+	0.104177i
$366$		0			0
$367$	4.27471	−	7.40402i	0.223138	−	0.386486i	−0.732621	−	0.680637i	$-0.761703\pi$
$367$	4.27471	−	7.40402i	0.223138	−	0.386486i	0.955759	+	0.294150i	$0.0950366\pi$
$368$		0			0
$369$	−15.4620	−	11.0322i	−0.804919	−	0.574311i
$370$		0			0
$371$	5.14726	+	36.1676i	0.267232	+	1.87773i
$372$		0			0
$373$	5.74129	−	3.31473i	0.297273	−	0.171630i	−0.343944	−	0.938990i	$-0.611763\pi$
$373$	5.74129	−	3.31473i	0.297273	−	0.171630i	0.641217	+	0.767360i	$0.278430\pi$
$374$		0			0
$375$	19.3645	+	0.130488i	0.999977	+	0.00673837i
$376$		0			0
$377$		−	24.2408i		−	1.24847i
$378$		0			0
$379$	22.3165			1.14632			0.573162	−	0.819442i	$-0.305717\pi$
$379$	22.3165			1.14632			0.573162	+	0.819442i	$0.305717\pi$
$380$		0			0
$381$	20.8861	+	6.68728i	1.07003	+	0.342600i
$382$		0			0
$383$	24.4124	−	14.0945i	1.24742	−	0.720196i	0.276822	−	0.960921i	$-0.410719\pi$
$383$	24.4124	−	14.0945i	1.24742	−	0.720196i	0.970593	+	0.240725i	$0.0773853\pi$
$384$		0			0
$385$	−8.34715	−	33.7569i	−0.425410	−	1.72041i
$386$		0			0
$387$	−6.77775	+	9.49927i	−0.344532	+	0.482875i
$388$		0			0
$389$	−3.57909	−	2.06639i	−0.181467	−	0.104770i	0.406515	−	0.913644i	$-0.366744\pi$
$389$	−3.57909	−	2.06639i	−0.181467	−	0.104770i	−0.587982	+	0.808874i	$0.700077\pi$
$390$		0			0
$391$		−	22.2284i		−	1.12414i
$392$		0			0
$393$	21.4887	−	4.66411i	1.08396	−	0.235273i
$394$		0			0
$395$	−18.3280	+	13.2134i	−0.922184	+	0.664838i
$396$		0			0
$397$	6.61890	+	11.4643i	0.332193	+	0.575375i	0.982942	−	0.183918i	$-0.0588781\pi$
$397$	6.61890	+	11.4643i	0.332193	+	0.575375i	−0.650748	+	0.759293i	$0.725545\pi$
$398$		0			0
$399$	14.6019	+	12.1030i	0.731009	+	0.605909i
$400$		0			0
$401$	−0.671383	+	0.387623i	−0.0335273	+	0.0193570i	−0.516670	−	0.856185i	$-0.672829\pi$
$401$	−0.671383	+	0.387623i	−0.0335273	+	0.0193570i	0.483143	+	0.875542i	$0.339495\pi$
$402$		0			0
$403$	−13.8198	−	7.97884i	−0.688411	−	0.397454i
$404$		0			0
$405$	18.2726	−	8.43284i	0.907972	−	0.419031i
$406$		0			0
$407$	−11.6010			−0.575038
$408$		0			0
$409$	3.97093	+	2.29262i	0.196350	+	0.113363i	0.594952	−	0.803761i	$-0.297171\pi$
$409$	3.97093	+	2.29262i	0.196350	+	0.113363i	−0.398602	+	0.917124i	$0.630504\pi$
$410$		0			0
$411$	−6.11101	−	6.72863i	−0.301434	−	0.331899i
$412$		0			0
$413$	−1.73405	−	12.1844i	−0.0853270	−	0.599556i
$414$		0			0
$415$	11.8184	−	1.19824i	0.580141	−	0.0588191i
$416$		0			0
$417$	−23.5627	−	7.54429i	−1.15387	−	0.369445i
$418$		0			0
$419$	11.9761			0.585070			0.292535	−	0.956255i	$-0.405501\pi$
$419$	11.9761			0.585070			0.292535	+	0.956255i	$0.405501\pi$
$420$		0			0
$421$	25.5487			1.24517			0.622584	−	0.782553i	$-0.286083\pi$
$421$	25.5487			1.24517			0.622584	+	0.782553i	$0.286083\pi$
$422$		0			0
$423$	−5.47658	−	0.528099i	−0.266280	−	0.0256771i
$424$		0			0
$425$	14.7443	+	4.91089i	0.715202	+	0.238213i
$426$		0			0
$427$	−0.800099	+	1.99028i	−0.0387195	+	0.0963166i
$428$		0			0
$429$	−26.6792	+	24.2303i	−1.28808	+	1.16985i
$430$		0			0
$431$	12.5634	+	7.25351i	0.605160	+	0.349389i	0.771069	−	0.636752i	$-0.219722\pi$
$431$	12.5634	+	7.25351i	0.605160	+	0.349389i	−0.165909	+	0.986141i	$0.553056\pi$
$432$		0			0
$433$	40.0655			1.92543			0.962713	−	0.270524i	$-0.0871969\pi$
$433$	40.0655			1.92543			0.962713	+	0.270524i	$0.0871969\pi$
$434$		0			0
$435$	−5.49796	+	25.9445i	−0.263607	+	1.24395i
$436$		0			0
$437$	25.6331	+	14.7993i	1.22620	+	0.707946i
$438$		0			0
$439$	−27.1838	+	15.6945i	−1.29741	+	0.749060i	−0.979956	−	0.199214i	$-0.936161\pi$
$439$	−27.1838	+	15.6945i	−1.29741	+	0.749060i	−0.317454	+	0.948274i	$0.602828\pi$
$440$		0			0
$441$	−15.9228	+	13.6917i	−0.758230	+	0.651987i
$442$		0			0
$443$	−5.01776	−	8.69101i	−0.238401	−	0.412923i	0.721855	−	0.692045i	$-0.243290\pi$
$443$	−5.01776	−	8.69101i	−0.238401	−	0.412923i	−0.960256	+	0.279122i	$0.909957\pi$
$444$		0			0
$445$	22.8176	−	16.4501i	1.08166	−	0.779808i
$446$		0			0
$447$	−5.54719	−	25.5574i	−0.262373	−	1.20882i
$448$		0			0
$449$		−	16.7060i		−	0.788405i	−0.919024	−	0.394203i	$-0.871021\pi$
$449$		−	16.7060i		−	0.788405i	0.919024	−	0.394203i	$-0.128979\pi$
$450$		0			0
$451$	−32.2291	−	18.6075i	−1.51761	−	0.876191i
$452$		0			0
$453$	−9.71131	−	10.6928i	−0.456277	−	0.502392i
$454$		0			0
$455$	14.5192	+	15.0934i	0.680668	+	0.707590i
$456$		0			0
$457$	−12.2526	+	7.07406i	−0.573154	+	0.330910i	−0.758408	−	0.651780i	$-0.774022\pi$
$457$	−12.2526	+	7.07406i	−0.573154	+	0.330910i	0.185254	+	0.982691i	$0.440689\pi$
$458$		0			0
$459$	16.0387	−	1.89493i	0.748623	−	0.0884478i
$460$		0			0
$461$	−4.22519			−0.196787			−0.0983935	−	0.995148i	$-0.531370\pi$
$461$	−4.22519			−0.196787			−0.0983935	+	0.995148i	$0.531370\pi$
$462$		0			0
$463$		−	33.2490i		−	1.54521i	−0.634886	−	0.772606i	$-0.718953\pi$
$463$		−	33.2490i		−	1.54521i	0.634886	−	0.772606i	$-0.281047\pi$
$464$		0			0
$465$	12.9814	+	11.6740i	0.601998	+	0.541369i
$466$		0			0
$467$	31.9242	−	18.4314i	1.47727	−	0.852905i	0.477604	−	0.878575i	$-0.341505\pi$
$467$	31.9242	−	18.4314i	1.47727	−	0.852905i	0.999670	+	0.0256700i	$0.00817193\pi$
$468$		0			0
$469$	−26.7420	+	3.80584i	−1.23483	+	0.175737i
$470$		0			0
$471$	−1.11860	−	1.23165i	−0.0515423	−	0.0567516i
$472$		0			0
$473$	−11.4317	+	19.8003i	−0.525631	+	0.910420i
$474$		0			0
$475$	−15.4795	+	13.7330i	−0.710250	+	0.630115i
$476$		0			0
$477$	−37.6961	+	17.1728i	−1.72599	+	0.786289i
$478$		0			0
$479$	4.66797	−	8.08516i	0.213285	−	0.369420i	−0.739456	−	0.673205i	$-0.764917\pi$
$479$	4.66797	−	8.08516i	0.213285	−	0.369420i	0.952741	+	0.303785i	$0.0982504\pi$
$480$		0			0
$481$	6.05086	−	3.49347i	0.275896	−	0.159288i
$482$		0			0
$483$	−20.9144	+	25.2325i	−0.951638	+	1.14812i
$484$		0			0
$485$	−1.01654	−	10.0262i	−0.0461585	−	0.455268i
$486$		0			0
$487$	21.9442	+	12.6695i	0.994385	+	0.574109i	0.906582	−	0.422029i	$-0.138682\pi$
$487$	21.9442	+	12.6695i	0.994385	+	0.574109i	0.0878031	+	0.996138i	$0.472015\pi$
$488$		0			0
$489$	6.85956	+	31.6038i	0.310200	+	1.42917i
$490$		0			0
$491$		−	35.4614i		−	1.60035i	−0.599765	−	0.800176i	$-0.704739\pi$
$491$		−	35.4614i		−	1.60035i	0.599765	−	0.800176i	$-0.295261\pi$
$492$		0			0
$493$	−10.6416	+	18.4318i	−0.479274	+	0.830126i
$494$		0			0
$495$	34.0498	−	19.8822i	1.53042	−	0.893640i
$496$		0			0
$497$	1.93754	+	2.47106i	0.0869106	+	0.110842i
$498$		0			0
$499$	14.7087	+	25.4762i	0.658451	+	1.14047i	0.981017	+	0.193923i	$0.0621213\pi$
$499$	14.7087	+	25.4762i	0.658451	+	1.14047i	−0.322566	+	0.946547i	$0.604545\pi$
$500$		0			0
$501$	23.4587	+	7.51097i	1.04806	+	0.335565i
$502$		0			0
$503$		−	20.9709i		−	0.935046i	−0.883981	−	0.467523i	$-0.845147\pi$
$503$		−	20.9709i		−	0.935046i	0.883981	−	0.467523i	$-0.154853\pi$
$504$		0			0
$505$	3.65781	+	1.64471i	0.162771	+	0.0731886i
$506$		0			0
$507$	−0.247227	+	0.772153i	−0.0109797	+	0.0342925i
$508$		0			0
$509$	−3.71821	−	6.44013i	−0.164807	−	0.285454i	0.771780	−	0.635890i	$-0.219367\pi$
$509$	−3.71821	−	6.44013i	−0.164807	−	0.285454i	−0.936587	+	0.350436i	$0.886033\pi$
$510$		0			0
$511$	−0.809096	−	5.68518i	−0.0357923	−	0.251497i
$512$		0			0
$513$	−8.49311	+	19.7569i	−0.374980	+	0.872290i
$514$		0			0
$515$	−22.8793	+	16.4946i	−1.00818	+	0.726839i
$516$		0			0
$517$	−10.7799			−0.474098
$518$		0			0
$519$	0.262409	+	1.20899i	0.0115185	+	0.0530687i
$520$		0			0
$521$	−2.55125	+	4.41889i	−0.111772	+	0.193595i	−0.916485	−	0.400069i	$-0.868986\pi$
$521$	−2.55125	+	4.41889i	−0.111772	+	0.193595i	0.804713	+	0.593665i	$0.202319\pi$
$522$		0			0
$523$	−8.24829	−	14.2865i	−0.360673	−	0.624703i	0.627399	−	0.778698i	$-0.284119\pi$
$523$	−8.24829	−	14.2865i	−0.360673	−	0.624703i	−0.988072	+	0.153995i	$0.950786\pi$
$524$		0			0
$525$	−12.1163	−	19.4472i	−0.528800	−	0.848747i
$526$		0			0
$527$	7.00534	+	12.1336i	0.305157	+	0.528548i
$528$		0			0
$529$	−14.0736	+	24.3762i	−0.611897	+	1.05984i
$530$		0			0
$531$	12.6994	−	5.78531i	0.551105	−	0.251061i
$532$		0			0
$533$	22.4135			0.970836
$534$		0			0
$535$	6.31128	−	4.55004i	0.272860	−	0.196716i
$536$		0			0
$537$	−14.3391	+	13.0229i	−0.618777	+	0.561979i
$538$		0			0
$539$	−28.4783	+	29.6964i	−1.22665	+	1.27911i
$540$		0			0
$541$	−10.3077	−	17.8534i	−0.443162	−	0.767578i	0.554760	−	0.832010i	$-0.312810\pi$
$541$	−10.3077	−	17.8534i	−0.443162	−	0.767578i	−0.997922	+	0.0644316i	$0.979477\pi$
$542$		0			0
$543$	6.09843	+	1.95259i	0.261709	+	0.0837935i
$544$		0			0
$545$	−20.3451	−	9.14800i	−0.871487	−	0.391857i
$546$		0			0
$547$		−	25.6070i		−	1.09488i	−0.836846	−	0.547438i	$-0.815603\pi$
$547$		−	25.6070i		−	1.09488i	0.836846	−	0.547438i	$-0.184397\pi$
$548$		0			0
$549$	−2.42107	−	0.233460i	−0.103329	−	0.00996385i
$550$		0			0
$551$	−14.1700	−	24.5431i	−0.603661	−	1.04557i
$552$		0			0
$553$	24.8049	+	9.97162i	1.05481	+	0.424036i
$554$		0			0
$555$	−7.26847	+	2.36662i	−0.308529	+	0.100458i
$556$		0			0
$557$	−18.0986	+	31.3477i	−0.766862	+	1.32824i	0.172394	+	0.985028i	$0.444850\pi$
$557$	−18.0986	+	31.3477i	−0.766862	+	1.32824i	−0.939256	+	0.343216i	$0.888484\pi$
$558$		0			0
$559$		−	13.7700i		−	0.582410i
$560$		0			0
$561$	30.9228	−	6.71175i	1.30556	−	0.283370i
$562$		0			0
$563$	26.5408	+	15.3233i	1.11856	+	0.645801i	0.941033	−	0.338315i	$-0.109857\pi$
$563$	26.5408	+	15.3233i	1.11856	+	0.645801i	0.177527	+	0.984116i	$0.443190\pi$
$564$		0			0
$565$	−0.574105	−	5.66248i	−0.0241528	−	0.238222i
$566$		0			0
$567$	−19.9892	−	12.9396i	−0.839467	−	0.543410i
$568$		0			0
$569$	−13.2153	+	7.62988i	−0.554016	+	0.319861i	−0.750740	−	0.660598i	$-0.770303\pi$
$569$	−13.2153	+	7.62988i	−0.554016	+	0.319861i	0.196724	+	0.980459i	$0.436970\pi$
$570$		0			0
$571$	9.05228	−	15.6790i	0.378826	−	0.656146i	−0.612066	−	0.790807i	$-0.709661\pi$
$571$	9.05228	−	15.6790i	0.378826	−	0.656146i	0.990892	+	0.134661i	$0.0429945\pi$
$572$		0			0
$573$	−3.81650	−	17.5836i	−0.159437	−	0.734566i
$574$		0			0
$575$	−23.7311	−	26.7491i	−0.989656	−	1.11552i
$576$		0			0
$577$	−3.28336	+	5.68695i	−0.136688	+	0.236751i	−0.926241	−	0.376932i	$-0.876979\pi$
$577$	−3.28336	+	5.68695i	−0.136688	+	0.236751i	0.789553	+	0.613682i	$0.210312\pi$
$578$		0			0
$579$	−7.59184	+	6.89498i	−0.315506	+	0.286546i
$580$		0			0
$581$	−8.67263	−	11.0607i	−0.359801	−	0.458875i
$582$		0			0
$583$	−70.2864	+	40.5799i	−2.91097	+	1.68065i
$584$		0			0
$585$	−11.7725	+	20.6239i	−0.486734	+	0.852691i
$586$		0			0
$587$		−	9.35074i		−	0.385946i	−0.981204	−	0.192973i	$-0.938187\pi$
$587$		−	9.35074i		−	0.385946i	0.981204	−	0.192973i	$-0.0618130\pi$
$588$		0			0
$589$	−18.6561			−0.768712
$590$		0			0
$591$	−5.86532	+	18.3189i	−0.241267	+	0.753539i
$592$		0			0
$593$	−23.3806	+	13.4988i	−0.960126	+	0.554329i	−0.896212	−	0.443626i	$-0.853692\pi$
$593$	−23.3806	+	13.4988i	−0.960126	+	0.554329i	−0.0639141	+	0.997955i	$0.520358\pi$
$594$		0			0
$595$	−4.41388	−	17.8503i	−0.180951	−	0.731790i
$596$		0			0
$597$	16.9768	−	15.4185i	0.694812	−	0.631035i
$598$		0			0
$599$	−19.7216	−	11.3863i	−0.805803	−	0.465231i	0.0396931	−	0.999212i	$-0.487362\pi$
$599$	−19.7216	−	11.3863i	−0.805803	−	0.465231i	−0.845496	+	0.533981i	$0.820695\pi$
$600$		0			0
$601$			5.26871i			0.214915i	0.994210	+	0.107458i	$0.0342710\pi$
$601$			5.26871i			0.214915i	−0.994210	+	0.107458i	$0.965729\pi$
$602$		0			0
$603$	−12.6974	−	27.8722i	−0.517079	−	1.13504i
$604$		0			0
$605$	42.7135	−	30.7938i	1.73655	−	1.25195i
$606$		0			0
$607$	4.67749	+	8.10166i	0.189854	+	0.328836i	0.945201	−	0.326488i	$-0.105865\pi$
$607$	4.67749	+	8.10166i	0.189854	+	0.328836i	−0.755348	+	0.655324i	$0.772532\pi$
$608$		0			0
$609$	29.4220	−	10.9103i	1.19224	−	0.442106i
$610$		0			0
$611$	5.62260	−	3.24621i	0.227466	−	0.131328i
$612$		0			0
$613$	−27.3310	−	15.7796i	−1.10389	−	0.637330i	−0.166649	−	0.986016i	$-0.553295\pi$
$613$	−27.3310	−	15.7796i	−1.10389	−	0.637330i	−0.937240	+	0.348686i	$0.886628\pi$
$614$		0			0
$615$	−23.9888	−	5.08351i	−0.967320	−	0.204987i
$616$		0			0
$617$	39.6450			1.59605			0.798023	−	0.602626i	$-0.205879\pi$
$617$	39.6450			1.59605			0.798023	+	0.602626i	$0.205879\pi$
$618$		0			0
$619$	33.2406	+	19.1915i	1.33605	+	0.771370i	0.986219	−	0.165443i	$-0.0529052\pi$
$619$	33.2406	+	19.1915i	1.33605	+	0.771370i	0.349832	+	0.936812i	$0.386239\pi$
$620$		0			0
$621$	−34.1406	−	14.6764i	−1.37002	−	0.588942i
$622$		0			0
$623$	−30.8810	−	12.4142i	−1.23722	−	0.497365i
$624$		0			0
$625$	22.9857	−	9.83137i	0.919430	−	0.393255i
$626$		0			0
$627$	−12.8480	+	40.1277i	−0.513101	+	1.60255i
$628$		0			0
$629$	−6.13446			−0.244597
$630$		0			0
$631$	1.06381			0.0423495			0.0211748	−	0.999776i	$-0.493259\pi$
$631$	1.06381			0.0423495			0.0211748	+	0.999776i	$0.493259\pi$
$632$		0			0
$633$	−10.5167	+	32.8465i	−0.418003	+	1.30553i
$634$		0			0
$635$	28.1678	−	2.85586i	1.11780	−	0.113331i
$636$		0			0
$637$	5.91113	−	24.0650i	0.234207	−	0.953488i
$638$		0			0
$639$	−2.06801	+	2.89840i	−0.0818093	+	0.114659i
$640$		0			0
$641$	−25.9645	−	14.9906i	−1.02553	−	0.592093i	−0.109832	−	0.993950i	$-0.535031\pi$
$641$	−25.9645	−	14.9906i	−1.02553	−	0.592093i	−0.915702	+	0.401858i	$0.868365\pi$
$642$		0			0
$643$	16.0861			0.634373			0.317187	−	0.948363i	$-0.397262\pi$
$643$	16.0861			0.634373			0.317187	+	0.948363i	$0.397262\pi$
$644$		0			0
$645$	−3.12312	+	14.7378i	−0.122973	+	0.580301i
$646$		0			0
$647$	21.6193	+	12.4819i	0.849944	+	0.490716i	0.860632	−	0.509227i	$-0.170069\pi$
$647$	21.6193	+	12.4819i	0.849944	+	0.490716i	−0.0106878	+	0.999943i	$0.503402\pi$
$648$		0			0
$649$	23.6786	−	13.6709i	0.929468	−	0.536629i
$650$		0			0
$651$	3.46424	−	20.3646i	0.135774	−	0.798152i
$652$		0			0
$653$	−2.19607	−	3.80370i	−0.0859387	−	0.148850i	0.819852	−	0.572575i	$-0.194056\pi$
$653$	−2.19607	−	3.80370i	−0.0859387	−	0.148850i	−0.905791	+	0.423725i	$0.860722\pi$
$654$		0			0
$655$	23.0274	−	16.6013i	0.899755	−	0.648668i
$656$		0			0
$657$	5.92544	−	2.69939i	0.231173	−	0.105313i
$658$		0			0
$659$		−	1.93959i		−	0.0755557i	−0.999286	−	0.0377778i	$-0.987972\pi$
$659$		−	1.93959i		−	0.0755557i	0.999286	−	0.0377778i	$-0.0120279\pi$
$660$		0			0
$661$	21.6034	+	12.4727i	0.840274	+	0.485132i	0.857357	−	0.514722i	$-0.172105\pi$
$661$	21.6034	+	12.4727i	0.840274	+	0.485132i	−0.0170833	+	0.999854i	$0.505438\pi$
$662$		0			0
$663$	−14.1076	+	12.8127i	−0.547895	+	0.497604i
$664$		0			0
$665$	23.5230	+	6.79444i	0.912184	+	0.263477i
$666$		0			0
$667$	42.4112	−	24.4861i	1.64217	−	0.948107i
$668$		0			0
$669$	5.54161	−	17.3078i	0.214251	−	0.669160i
$670$		0			0
$671$	−4.76553			−0.183971
$672$		0			0
$673$			6.21519i			0.239578i	0.992799	+	0.119789i	$0.0382218\pi$
$673$			6.21519i			0.239578i	−0.992799	+	0.119789i	$0.961778\pi$
$674$		0			0
$675$	17.2775	−	19.4033i	0.665013	−	0.746832i
$676$		0			0
$677$	14.4283	−	8.33017i	0.554524	−	0.320154i	−0.196421	−	0.980520i	$-0.562932\pi$
$677$	14.4283	−	8.33017i	0.554524	−	0.320154i	0.750945	+	0.660365i	$0.229599\pi$
$678$		0			0
$679$	−9.38346	+	7.35751i	−0.360104	+	0.282355i
$680$		0			0
$681$	−21.0603	+	19.1272i	−0.807034	+	0.732956i
$682$		0			0
$683$	11.1339	−	19.2844i	0.426025	−	0.737898i	−0.570490	−	0.821304i	$-0.693247\pi$
$683$	11.1339	−	19.2844i	0.426025	−	0.737898i	0.996516	+	0.0834067i	$0.0265800\pi$
$684$		0			0
$685$	−10.7024	−	4.81224i	−0.408916	−	0.183866i
$686$		0			0
$687$	0.383426	+	1.76654i	0.0146286	+	0.0673979i
$688$		0			0
$689$	24.4401	−	42.3315i	0.931095	−	1.61270i
$690$		0			0
$691$	−24.0492	+	13.8848i	−0.914873	+	0.528202i	−0.881996	−	0.471257i	$-0.843800\pi$
$691$	−24.0492	+	13.8848i	−0.914873	+	0.528202i	−0.0328772	+	0.999459i	$0.510467\pi$
$692$		0			0
$693$	−41.4168	−	21.4759i	−1.57329	−	0.815803i
$694$		0			0
$695$	−31.7776	+	3.22185i	−1.20539	+	0.122212i
$696$		0			0
$697$	−17.0424	−	9.83941i	−0.645525	−	0.372694i
$698$		0			0
$699$	−48.9576	+	10.6262i	−1.85175	+	0.401919i
$700$		0			0
$701$		−	0.789291i		−	0.0298111i	−0.999889	−	0.0149056i	$-0.995255\pi$
$701$		−	0.789291i		−	0.0298111i	0.999889	−	0.0149056i	$-0.00474476\pi$
$702$		0			0
$703$	4.08421	−	7.07406i	0.154039	−	0.266803i
$704$		0			0
$705$	−6.75403	+	2.19912i	−0.254371	+	0.0828237i
$706$		0			0
$707$	−0.668609	−	4.69803i	−0.0251456	−	0.176688i
$708$		0			0
$709$	−7.93432	−	13.7427i	−0.297980	−	0.516116i	0.677694	−	0.735344i	$-0.262979\pi$
$709$	−7.93432	−	13.7427i	−0.297980	−	0.516116i	−0.975674	+	0.219228i	$0.929646\pi$
$710$		0			0
$711$	−2.90961	+	30.1737i	−0.109119	+	1.13160i
$712$		0			0
$713$		−	32.2383i		−	1.20733i
$714$		0			0
$715$	−19.0806	+	42.4351i	−0.713574	+	1.58698i
$716$		0			0
$717$	−9.39806	−	3.00906i	−0.350977	−	0.112375i
$718$		0			0
$719$	−22.6303	−	39.1968i	−0.843967	−	1.46179i	−0.886516	−	0.462699i	$-0.846881\pi$
$719$	−22.6303	−	39.1968i	−0.843967	−	1.46179i	0.0425492	−	0.999094i	$-0.486452\pi$
$720$		0			0
$721$	30.9645	+	12.4478i	1.15318	+	0.463581i
$722$		0			0
$723$	−9.04009	+	8.21029i	−0.336204	+	0.305344i
$724$		0			0
$725$	6.87198	+	33.5413i	0.255219	+	1.24569i
$726$		0			0
$727$	21.4724			0.796369			0.398185	−	0.917305i	$-0.369640\pi$
$727$	21.4724			0.796369			0.398185	+	0.917305i	$0.369640\pi$
$728$		0			0
$729$	7.67916	−	25.8849i	0.284413	−	0.958702i
$730$		0			0
$731$	−6.04497	+	10.4702i	−0.223581	+	0.387254i
$732$		0			0
$733$	−7.38122	−	12.7846i	−0.272631	−	0.472211i	0.696903	−	0.717165i	$-0.254561\pi$
$733$	−7.38122	−	12.7846i	−0.272631	−	0.472211i	−0.969535	+	0.244954i	$0.921227\pi$
$734$		0			0
$735$	−11.7846	+	24.4156i	−0.434683	+	0.900583i
$736$		0			0
$737$	−30.0044	−	51.9691i	−1.10523	−	1.91431i
$738$		0			0
$739$	1.22065	−	2.11423i	0.0449024	−	0.0777733i	−0.842701	−	0.538382i	$-0.819036\pi$
$739$	1.22065	−	2.11423i	0.0449024	−	0.0777733i	0.887603	+	0.460609i	$0.152369\pi$
$740$		0			0
$741$	−5.38258	−	24.7989i	−0.197734	−	0.911011i
$742$		0			0
$743$	32.2677			1.18379			0.591894	−	0.806016i	$-0.298380\pi$
$743$	32.2677			1.18379			0.591894	+	0.806016i	$0.298380\pi$
$744$		0			0
$745$	−19.7446	−	27.3873i	−0.723386	−	1.00339i
$746$		0			0
$747$	9.25663	−	12.9735i	0.338683	−	0.474676i
$748$		0			0
$749$	−8.54158	−	3.43373i	−0.312103	−	0.125466i
$750$		0			0
$751$	−7.00840	−	12.1389i	−0.255740	−	0.442955i	0.709356	−	0.704850i	$-0.248986\pi$
$751$	−7.00840	−	12.1389i	−0.255740	−	0.442955i	−0.965096	+	0.261895i	$0.915652\pi$
$752$		0			0
$753$	−2.07690	+	6.48669i	−0.0756864	+	0.236388i
$754$		0			0
$755$	−17.0077	−	7.64737i	−0.618972	−	0.278316i
$756$		0			0
$757$			41.4500i			1.50653i	0.657720	+	0.753263i	$0.271521\pi$
$757$			41.4500i			1.50653i	−0.657720	+	0.753263i	$0.728479\pi$
$758$		0			0
$759$	−69.3419	−	22.2018i	−2.51695	−	0.805874i
$760$		0			0
$761$	20.0586	+	34.7425i	0.727124	+	1.25942i	0.958094	+	0.286455i	$0.0924769\pi$
$761$	20.0586	+	34.7425i	0.727124	+	1.25942i	−0.230969	+	0.972961i	$0.574190\pi$
$762$		0			0
$763$	3.71886	+	26.1308i	0.134632	+	0.946000i
$764$		0			0
$765$	18.0051	−	10.5135i	0.650977	−	0.380116i
$766$		0			0
$767$	−8.23358	+	14.2610i	−0.297297	+	0.514934i
$768$		0			0
$769$		−	22.4441i		−	0.809355i	−0.914459	−	0.404677i	$-0.867384\pi$
$769$		−	22.4441i		−	0.809355i	0.914459	−	0.404677i	$-0.132616\pi$
$770$		0			0
$771$	5.62310	+	25.9071i	0.202511	+	0.933021i
$772$		0			0
$773$	25.1951	+	14.5464i	0.906206	+	0.523198i	0.879208	−	0.476437i	$-0.158072\pi$
$773$	25.1951	+	14.5464i	0.906206	+	0.523198i	0.0269973	+	0.999636i	$0.491405\pi$
$774$		0			0
$775$	21.3839	+	7.12235i	0.768132	+	0.255842i
$776$		0			0
$777$	6.96350	+	5.77181i	0.249814	+	0.207063i
$778$		0			0
$779$	22.6930	−	13.1018i	0.813060	−	0.469421i
$780$		0			0
$781$	−3.48802	+	6.04143i	−0.124811	+	0.216180i
$782$		0			0
$783$	21.2832	+	28.5140i	0.760600	+	1.01901i
$784$		0			0
$785$	−1.95903	−	0.880863i	−0.0699208	−	0.0314394i
$786$		0			0
$787$	−16.9461	+	29.3516i	−0.604064	+	1.04627i	0.388134	+	0.921603i	$0.373120\pi$
$787$	−16.9461	+	29.3516i	−0.604064	+	1.04627i	−0.992199	+	0.124667i	$0.960214\pi$
$788$		0			0
$789$	22.7302	+	25.0275i	0.809217	+	0.891002i
$790$		0			0
$791$	−5.29946	+	4.15527i	−0.188427	+	0.147745i
$792$		0			0
$793$	2.48562	−	1.43507i	0.0882669	−	0.0509609i
$794$		0			0
$795$	−35.7589	+	39.7635i	−1.26824	+	1.41027i
$796$		0			0
$797$			30.8362i			1.09227i	0.837696	+	0.546137i	$0.183902\pi$
$797$			30.8362i			1.09227i	−0.837696	+	0.546137i	$0.816098\pi$
$798$		0			0
$799$	−5.70028			−0.201661
$800$		0			0
$801$	3.62234	−	37.5649i	0.127989	−	1.32729i
$802$		0			0
$803$	11.0483	−	6.37874i	0.389886	−	0.225101i
$804$		0			0
$805$	−11.7410	+	40.6485i	−0.413816	+	1.43267i
$806$		0			0
$807$	11.4554	+	12.6131i	0.403249	+	0.444004i
$808$		0			0
$809$	32.1338	+	18.5524i	1.12976	+	0.652269i	0.943875	−	0.330302i	$-0.107151\pi$
$809$	32.1338	+	18.5524i	1.12976	+	0.652269i	0.185888	+	0.982571i	$0.440484\pi$
$810$		0			0
$811$			33.9956i			1.19375i	0.802336	+	0.596873i	$0.203590\pi$
$811$			33.9956i			1.19375i	−0.802336	+	0.596873i	$0.796410\pi$
$812$		0			0
$813$	−7.67076	−	35.3412i	−0.269025	−	1.23947i
$814$		0			0
$815$	24.4158	+	33.8667i	0.855249	+	1.18630i
$816$		0			0
$817$	−8.04926	−	13.9417i	−0.281608	−	0.487759i
$818$		0			0
$819$	28.0695	−	1.27062i	0.980827	−	0.0443990i
$820$		0			0
$821$	40.0563	−	23.1265i	1.39798	−	0.807122i	0.403796	−	0.914849i	$-0.367691\pi$
$821$	40.0563	−	23.1265i	1.39798	−	0.807122i	0.994180	+	0.107727i	$0.0343573\pi$
$822$		0			0
$823$	−40.7593	−	23.5324i	−1.42078	−	0.820288i	−0.424414	−	0.905468i	$-0.639520\pi$
$823$	−40.7593	−	23.5324i	−1.42078	−	0.820288i	−0.996366	+	0.0851803i	$0.972853\pi$
$824$		0			0
$825$	30.0462	−	41.0899i	1.04607	−	1.43057i
$826$		0			0
$827$	−14.6102			−0.508046			−0.254023	−	0.967198i	$-0.581754\pi$
$827$	−14.6102			−0.508046			−0.254023	+	0.967198i	$0.581754\pi$
$828$		0			0
$829$	27.9876	+	16.1586i	0.972049	+	0.561213i	0.899860	−	0.436178i	$-0.143668\pi$
$829$	27.9876	+	16.1586i	0.972049	+	0.561213i	0.0721885	+	0.997391i	$0.477002\pi$
$830$		0			0
$831$	10.9033	−	9.90248i	0.378231	−	0.343513i
$832$		0			0
$833$	−15.0590	+	15.7031i	−0.521763	+	0.544080i
$834$		0			0
$835$	31.6373	−	3.20763i	1.09485	−	0.111004i
$836$		0			0
$837$	23.2612	−	2.74825i	0.804026	−	0.0949935i
$838$		0			0
$839$	15.0113			0.518249			0.259124	−	0.965844i	$-0.416566\pi$
$839$	15.0113			0.518249			0.259124	+	0.965844i	$0.416566\pi$
$840$		0			0
$841$	−17.8898			−0.616888
$842$		0			0
$843$	12.5975	+	4.03346i	0.433882	+	0.138920i
$844$		0			0
$845$	0.105580	+	1.04136i	0.00363208	+	0.0358237i
$846$		0			0
$847$	−57.8078	−	23.2389i	−1.98630	−	0.798497i
$848$		0			0
$849$	10.4891	+	11.5492i	0.359985	+	0.396367i
$850$		0			0
$851$	12.2242	+	7.05764i	0.419040	+	0.241933i
$852$		0			0
$853$	43.2807			1.48190			0.740952	−	0.671558i	$-0.234374\pi$
$853$	43.2807			1.48190			0.740952	+	0.671558i	$0.234374\pi$
$854$		0			0
$855$	0.136336	+	27.7626i	0.00466260	+	0.949463i
$856$		0			0
$857$	−18.3255	−	10.5802i	−0.625986	−	0.361413i	0.153210	−	0.988194i	$-0.451039\pi$
$857$	−18.3255	−	10.5802i	−0.625986	−	0.361413i	−0.779196	+	0.626780i	$0.784372\pi$
$858$		0			0
$859$	36.5871	−	21.1236i	1.24834	−	0.720728i	0.277560	−	0.960708i	$-0.410474\pi$
$859$	36.5871	−	21.1236i	1.24834	−	0.720728i	0.970778	+	0.239981i	$0.0771411\pi$
$860$		0			0
$861$	10.0878	+	27.2040i	0.343792	+	0.927111i
$862$		0			0
$863$	17.8457	+	30.9097i	0.607475	+	1.05218i	0.991655	+	0.128919i	$0.0411507\pi$
$863$	17.8457	+	30.9097i	0.607475	+	1.05218i	−0.384181	+	0.923258i	$0.625516\pi$
$864$		0			0
$865$	0.934016	+	1.29556i	0.0317575	+	0.0440502i
$866$		0			0
$867$	−12.4233	+	2.69645i	−0.421916	+	0.0915764i
$868$		0			0
$869$			59.3927i			2.01476i
$870$		0			0
$871$	31.2996	+	18.0708i	1.06055	+	0.612306i
$872$		0			0
$873$	−11.0062	−	7.85296i	−0.372504	−	0.265782i
$874$		0			0
$875$	−24.3685	−	16.7683i	−0.823806	−	0.566872i
$876$		0			0
$877$	−1.90519	+	1.09996i	−0.0643336	+	0.0371430i	−0.531822	−	0.846856i	$-0.678492\pi$
$877$	−1.90519	+	1.09996i	−0.0643336	+	0.0371430i	0.467488	+	0.883999i	$0.345159\pi$
$878$		0			0
$879$	45.5447	+	14.5825i	1.53619	+	0.491854i
$880$		0			0
$881$	−29.2075			−0.984025			−0.492013	−	0.870588i	$-0.663739\pi$
$881$	−29.2075			−0.984025			−0.492013	+	0.870588i	$0.663739\pi$
$882$		0			0
$883$			2.21069i			0.0743956i	0.999308	+	0.0371978i	$0.0118432\pi$
$883$			2.21069i			0.0743956i	−0.999308	+	0.0371978i	$0.988157\pi$
$884$		0			0
$885$	12.0467	−	13.3959i	0.404946	−	0.450297i
$886$		0			0
$887$	11.5724	−	6.68134i	0.388564	−	0.224337i	−0.292974	−	0.956120i	$-0.594645\pi$
$887$	11.5724	−	6.68134i	0.388564	−	0.224337i	0.681538	+	0.731783i	$0.261312\pi$
$888$		0			0
$889$	−20.6702	−	26.3620i	−0.693258	−	0.884152i
$890$		0			0
$891$	10.1082	−	51.9256i	0.338639	−	1.73957i
$892$		0			0
$893$	3.79514	−	6.57337i	0.126999	−	0.219970i
$894$		0			0
$895$	−10.2551	+	22.8073i	−0.342791	+	0.762364i
$896$		0			0
$897$	42.8533	−	9.30126i	1.43083	−	0.310560i
$898$		0			0
$899$	−15.4337	+	26.7320i	−0.514743	+	0.891561i
$900$		0			0
$901$	−37.1667	+	21.4582i	−1.23820	+	0.714876i
$902$		0			0
$903$	16.7132	−	6.19758i	0.556179	−	0.206242i
$904$		0			0
$905$	8.22458	−	0.833869i	0.273394	−	0.0277188i
$906$		0			0
$907$	3.62770	+	2.09445i	0.120456	+	0.0695451i	0.559017	−	0.829156i	$-0.311179\pi$
$907$	3.62770	+	2.09445i	0.120456	+	0.0695451i	−0.438562	+	0.898701i	$0.644512\pi$
$908$		0			0
$909$	4.89658	−	2.23068i	0.162409	−	0.0739870i
$910$		0			0
$911$			22.5190i			0.746087i	0.927814	+	0.373043i	$0.121686\pi$
$911$			22.5190i			0.746087i	−0.927814	+	0.373043i	$0.878314\pi$
$912$		0			0
$913$	15.6128	−	27.0421i	0.516707	−	0.894962i
$914$		0			0
$915$	−2.98580	+	0.972180i	−0.0987074	+	0.0321393i
$916$		0			0
$917$	−31.1649	−	12.5284i	−1.02916	−	0.413723i
$918$		0			0
$919$	−7.26453	−	12.5825i	−0.239635	−	0.415060i	0.720975	−	0.692961i	$-0.243694\pi$
$919$	−7.26453	−	12.5825i	−0.239635	−	0.415060i	−0.960610	+	0.277902i	$0.910361\pi$
$920$		0			0
$921$	−5.27948	+	16.4892i	−0.173965	+	0.543336i
$922$		0			0
$923$		−	4.20148i		−	0.138293i
$924$		0			0
$925$	−7.38204	+	6.54915i	−0.242720	+	0.215335i
$926$		0			0
$927$	−3.63214	+	37.6666i	−0.119295	+	1.23713i
$928$		0			0
$929$	20.7788	+	35.9900i	0.681732	+	1.18079i	0.974452	+	0.224596i	$0.0721062\pi$
$929$	20.7788	+	35.9900i	0.681732	+	1.18079i	−0.292720	+	0.956198i	$0.594560\pi$
$930$		0			0
$931$	−8.08232	−	27.8204i	−0.264887	−	0.911776i
$932$		0			0
$933$	−27.7930	−	30.6020i	−0.909903	−	1.00186i
$934$		0			0
$935$	33.1369	−	23.8897i	1.08369	−	0.781277i
$936$		0			0
$937$	−45.5010			−1.48645			−0.743226	−	0.669040i	$-0.766705\pi$
$937$	−45.5010			−1.48645			−0.743226	+	0.669040i	$0.766705\pi$
$938$		0			0
$939$	9.47064	−	2.05559i	0.309063	−	0.0670817i
$940$		0			0
$941$	10.0244	−	17.3627i	0.326785	−	0.566007i	−0.655087	−	0.755553i	$-0.727368\pi$
$941$	10.0244	−	17.3627i	0.326785	−	0.566007i	0.981872	+	0.189546i	$0.0607015\pi$
$942$		0			0
$943$	22.6403	+	39.2142i	0.737270	+	1.27699i
$944$		0			0
$945$	−30.3304	−	5.00640i	−0.986649	−	0.162858i
$946$		0			0
$947$	14.7490	+	25.5460i	0.479278	+	0.830133i	0.999718	−	0.0237652i	$-0.00756541\pi$
$947$	14.7490	+	25.5460i	0.479278	+	0.830133i	−0.520440	+	0.853898i	$0.674232\pi$
$948$		0			0
$949$	−3.84174	+	6.65408i	−0.124708	+	0.216001i
$950$		0			0
$951$	−19.8658	+	4.31184i	−0.644192	+	0.139821i
$952$		0			0
$953$	−1.26250			−0.0408964			−0.0204482	−	0.999791i	$-0.506509\pi$
$953$	−1.26250			−0.0408964			−0.0204482	+	0.999791i	$0.506509\pi$
$954$		0			0
$955$	−13.5844	−	18.8427i	−0.439581	−	0.609734i
$956$		0			0
$957$	46.8693	+	51.6063i	1.51507	+	1.66819i
$958$		0			0
$959$	1.95628	+	13.7459i	0.0631715	+	0.443879i
$960$		0			0
$961$	−5.34003	−	9.24920i	−0.172259	−	0.298361i
$962$		0			0
$963$	1.00193	−	10.3903i	0.0322867	−	0.334824i
$964$		0			0
$965$	−5.42959	+	12.0754i	−0.174785	+	0.388719i
$966$		0			0
$967$		−	26.0942i		−	0.839132i	−0.907725	−	0.419566i	$-0.862182\pi$
$967$		−	26.0942i		−	0.839132i	0.907725	−	0.419566i	$-0.137818\pi$
$968$		0			0
$969$	−6.79390	+	21.2191i	−0.218251	+	0.681655i
$970$		0			0
$971$	−6.95317	−	12.0432i	−0.223138	−	0.386486i	0.732621	−	0.680636i	$-0.238297\pi$
$971$	−6.95317	−	12.0432i	−0.223138	−	0.386486i	−0.955759	+	0.294150i	$0.904963\pi$
$972$		0			0
$973$	23.3192	+	29.7404i	0.747580	+	0.953433i
$974$		0			0
$975$	−3.29791	+	30.4798i	−0.105618	+	0.976134i
$976$		0			0
$977$	−1.41905	+	2.45787i	−0.0453995	+	0.0786342i	−0.887832	−	0.460167i	$-0.847789\pi$
$977$	−1.41905	+	2.45787i	−0.0453995	+	0.0786342i	0.842433	+	0.538802i	$0.181123\pi$
$978$		0			0
$979$		−	73.9413i		−	2.36317i
$980$		0			0
$981$	−27.2352	+	12.4072i	−0.869552	+	0.396132i
$982$		0			0
$983$	−42.5573	−	24.5705i	−1.35737	−	0.783677i	−0.368099	−	0.929787i	$-0.619991\pi$
$983$	−42.5573	−	24.5705i	−1.35737	−	0.783677i	−0.989268	+	0.146110i	$0.953325\pi$
$984$		0			0
$985$	2.50484	+	24.7056i	0.0798108	+	0.787185i
$986$		0			0
$987$	6.47064	+	5.36330i	0.205963	+	0.170716i
$988$		0			0
$989$	24.0917	−	13.9094i	0.766072	−	0.442292i
$990$		0			0
$991$	−10.3281	+	17.8887i	−0.328081	+	0.568254i	−0.982131	−	0.188198i	$-0.939735\pi$
$991$	−10.3281	+	17.8887i	−0.328081	+	0.568254i	0.654050	+	0.756452i	$0.273069\pi$
$992$		0			0
$993$	−4.28080	+	0.929142i	−0.135847	+	0.0294854i
$994$		0			0
$995$	12.1416	−	27.0027i	0.384914	−	0.856044i
$996$		0			0
$997$	20.8453	−	36.1051i	0.660177	−	1.14346i	−0.320392	−	0.947285i	$-0.603814\pi$
$997$	20.8453	−	36.1051i	0.660177	−	1.14346i	0.980569	−	0.196175i	$-0.0628522\pi$
$998$		0			0
$999$	−4.05028	+	9.42189i	−0.128145	+	0.298095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bn.a.269.10	yes	32
3.2	odd	2	inner	420.2.bn.a.269.12	yes	32
5.2	odd	4		2100.2.bi.n.101.2		32
5.3	odd	4		2100.2.bi.n.101.15		32
5.4	even	2	inner	420.2.bn.a.269.7	yes	32
7.3	odd	6		2940.2.f.a.1469.29		32
7.4	even	3		2940.2.f.a.1469.4		32
7.5	odd	6	inner	420.2.bn.a.89.5	✓	32
15.2	even	4		2100.2.bi.n.101.4		32
15.8	even	4		2100.2.bi.n.101.13		32
15.14	odd	2	inner	420.2.bn.a.269.5	yes	32
21.5	even	6	inner	420.2.bn.a.89.7	yes	32
21.11	odd	6		2940.2.f.a.1469.1		32
21.17	even	6		2940.2.f.a.1469.32		32
35.4	even	6		2940.2.f.a.1469.30		32
35.12	even	12		2100.2.bi.n.1601.4		32
35.19	odd	6	inner	420.2.bn.a.89.12	yes	32
35.24	odd	6		2940.2.f.a.1469.3		32
35.33	even	12		2100.2.bi.n.1601.13		32
105.47	odd	12		2100.2.bi.n.1601.2		32
105.59	even	6		2940.2.f.a.1469.2		32
105.68	odd	12		2100.2.bi.n.1601.15		32
105.74	odd	6		2940.2.f.a.1469.31		32
105.89	even	6	inner	420.2.bn.a.89.10	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bn.a.89.5	✓	32	7.5	odd	6	inner
420.2.bn.a.89.7	yes	32	21.5	even	6	inner
420.2.bn.a.89.10	yes	32	105.89	even	6	inner
420.2.bn.a.89.12	yes	32	35.19	odd	6	inner
420.2.bn.a.269.5	yes	32	15.14	odd	2	inner
420.2.bn.a.269.7	yes	32	5.4	even	2	inner
420.2.bn.a.269.10	yes	32	1.1	even	1	trivial
420.2.bn.a.269.12	yes	32	3.2	odd	2	inner
2100.2.bi.n.101.2		32	5.2	odd	4
2100.2.bi.n.101.4		32	15.2	even	4
2100.2.bi.n.101.13		32	15.8	even	4
2100.2.bi.n.101.15		32	5.3	odd	4
2100.2.bi.n.1601.2		32	105.47	odd	12
2100.2.bi.n.1601.4		32	35.12	even	12
2100.2.bi.n.1601.13		32	35.33	even	12
2100.2.bi.n.1601.15		32	105.68	odd	12
2940.2.f.a.1469.1		32	21.11	odd	6
2940.2.f.a.1469.2		32	105.59	even	6
2940.2.f.a.1469.3		32	35.24	odd	6
2940.2.f.a.1469.4		32	7.4	even	3
2940.2.f.a.1469.29		32	7.3	odd	6
2940.2.f.a.1469.30		32	35.4	even	6
2940.2.f.a.1469.31		32	105.74	odd	6
2940.2.f.a.1469.32		32	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.528155 - 1.64956i) q^{3} +(-0.225553 - 2.22466i) q^{5} +(-2.08204 + 1.63251i) q^{7} +(-2.44211 - 1.74245i) q^{9} +(-5.09034 - 2.93891i) q^{11} +3.54004 q^{13} +(-3.78885 - 0.802902i) q^{15} +(-2.69171 - 1.55406i) q^{17} +(3.58419 - 2.06933i) q^{19} +(1.59329 + 4.29667i) q^{21} +(3.57587 + 6.19358i) q^{23} +(-4.89825 + 1.00356i) q^{25} +(-4.16408 + 3.10812i) q^{27} -6.84761i q^{29} +(-3.90384 - 2.25388i) q^{31} +(-7.53639 + 6.84463i) q^{33} +(4.10141 + 4.26362i) q^{35} +(1.70926 - 0.986843i) q^{37} +(1.86969 - 5.83952i) q^{39} +6.33142 q^{41} -3.88979i q^{43} +(-3.32553 + 5.82588i) q^{45} +(1.58829 - 0.916997i) q^{47} +(1.66979 - 6.79793i) q^{49} +(-3.98516 + 3.61936i) q^{51} +(6.90391 - 11.9579i) q^{53} +(-5.38994 + 11.9872i) q^{55} +(-1.52048 - 7.00526i) q^{57} +(-2.32584 + 4.02848i) q^{59} +(0.702144 - 0.405383i) q^{61} +(7.92913 - 0.358927i) q^{63} +(-0.798468 - 7.87540i) q^{65} +(8.84158 + 5.10469i) q^{67} +(12.1053 - 2.62744i) q^{69} -1.18684i q^{71} +(-1.08522 + 1.87966i) q^{73} +(-0.931602 + 8.61000i) q^{75} +(15.3961 - 2.19112i) q^{77} +(-5.05228 - 8.75081i) q^{79} +(2.92776 + 8.51048i) q^{81} +5.31243i q^{83} +(-2.85014 + 6.33868i) q^{85} +(-11.2956 - 3.61660i) q^{87} +(6.28986 + 10.8944i) q^{89} +(-7.37052 + 5.77917i) q^{91} +(-5.77975 + 5.24922i) q^{93} +(-5.41199 - 7.50686i) q^{95} +4.50686 q^{97} +(7.31025 + 16.0468i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{15} + 12 q^{19} - 8 q^{21} + 6 q^{25} - 12 q^{31} + 24 q^{39} + 33 q^{45} - 44 q^{49} - 10 q^{51} - 24 q^{61} + 21 q^{75} - 28 q^{79} - 20 q^{81} - 4 q^{85} + 16 q^{91} - 28 q^{99}+O(q^{100}) \) 32 * q + 2 * q^15 + 12 * q^19 - 8 * q^21 + 6 * q^25 - 12 * q^31 + 24 * q^39 + 33 * q^45 - 44 * q^49 - 10 * q^51 - 24 * q^61 + 21 * q^75 - 28 * q^79 - 20 * q^81 - 4 * q^85 + 16 * q^91 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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