LMFDB - Embedded newform 468.2.k.a.445.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [468,2,Mod(61,468)] 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("468.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(468, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	468.k (of order $3$, 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:	$3.73699881460$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			445.10
Character	$\chi$	$=$	468.445
Dual form			468.2.k.a.61.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.964854 - 1.43842i) q^{3} +(-0.468893 + 0.812147i) q^{5} -0.897167 q^{7} +(-1.13811 - 2.77573i) q^{9} +(1.14490 - 1.98302i) q^{11} +(2.12242 - 2.91468i) q^{13} +(0.715797 + 1.45807i) q^{15} +(2.42154 - 4.19424i) q^{17} +(3.21430 - 5.56733i) q^{19} +(-0.865635 + 1.29050i) q^{21} -2.45776 q^{23} +(2.06028 + 3.56851i) q^{25} +(-5.09079 - 1.04109i) q^{27} +(-5.24091 + 9.07753i) q^{29} +(3.53762 - 6.12734i) q^{31} +(-1.74776 - 3.56017i) q^{33} +(0.420676 - 0.728632i) q^{35} +(2.82939 + 4.90064i) q^{37} +(-2.14471 - 5.86517i) q^{39} -1.58900 q^{41} -4.11807 q^{43} +(2.78796 + 0.377207i) q^{45} +(4.34470 + 7.52524i) q^{47} -6.19509 q^{49} +(-3.69665 - 7.53003i) q^{51} -9.76841 q^{53} +(1.07367 + 1.85965i) q^{55} +(-4.90684 - 9.99518i) q^{57} +(6.06148 + 10.4988i) q^{59} +7.42626 q^{61} +(1.02108 + 2.49030i) q^{63} +(1.37196 + 3.09039i) q^{65} +10.8472 q^{67} +(-2.37137 + 3.53529i) q^{69} +(2.14956 - 3.72315i) q^{71} +6.91745 q^{73} +(7.12088 + 0.479538i) q^{75} +(-1.02716 + 1.77910i) q^{77} +(-3.32457 - 5.75832i) q^{79} +(-6.40939 + 6.31820i) q^{81} +(0.852333 + 1.47628i) q^{83} +(2.27089 + 3.93330i) q^{85} +(8.00060 + 16.2971i) q^{87} +(0.452237 + 0.783298i) q^{89} +(-1.90416 + 2.61495i) q^{91} +(-5.40042 - 11.0006i) q^{93} +(3.01433 + 5.22097i) q^{95} -4.65687 q^{97} +(-6.80735 - 0.921024i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{7} - 2 q^{9} - 4 q^{11} + q^{13} - 4 q^{15} - 8 q^{17} - q^{19} + 14 q^{21} + 8 q^{23} - 14 q^{25} - 13 q^{29} + 2 q^{31} - 25 q^{33} + 3 q^{35} - q^{37} - 3 q^{39} - 8 q^{41} - 4 q^{43}+ \cdots - 29 q^{99}+O(q^{100}) $ 28 * q - 4 * q^7 - 2 * q^9 - 4 * q^11 + q^13 - 4 * q^15 - 8 * q^17 - q^19 + 14 * q^21 + 8 * q^23 - 14 * q^25 - 13 * q^29 + 2 * q^31 - 25 * q^33 + 3 * q^35 - q^37 - 3 * q^39 - 8 * q^41 - 4 * q^43 - 38 * q^45 + 11 * q^47 + 24 * q^49 + 5 * q^51 + 52 * q^53 - q^57 - 8 * q^59 + 14 * q^61 - 21 * q^63 + 38 * q^65 + 14 * q^67 - 21 * q^69 - 12 * q^71 + 14 * q^73 - 14 * q^75 - 28 * q^77 + 5 * q^79 + 10 * q^81 + 9 * q^83 + 18 * q^85 + 18 * q^87 - 11 * q^89 - q^91 - 9 * q^93 + 28 * q^95 + 50 * q^97 - 29 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/468\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$235$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	0.964854	−	1.43842i	0.557059	−	0.830473i
$3$	0.964854	−	1.43842i	0.557059	−	0.830473i
$4$		0			0
$5$	−0.468893	+	0.812147i	−0.209696	+	0.363203i	−0.951619	−	0.307282i	$-0.900581\pi$
$5$	−0.468893	+	0.812147i	−0.209696	+	0.363203i	0.741923	+	0.670485i	$0.233914\pi$
$6$		0			0
$7$	−0.897167			−0.339097			−0.169549	−	0.985522i	$-0.554231\pi$
$7$	−0.897167			−0.339097			−0.169549	+	0.985522i	$0.554231\pi$
$8$		0			0
$9$	−1.13811	−	2.77573i	−0.379372	−	0.925244i
$10$		0			0
$11$	1.14490	−	1.98302i	0.345199	−	0.597902i	−0.640191	−	0.768216i	$-0.721145\pi$
$11$	1.14490	−	1.98302i	0.345199	−	0.597902i	0.985390	+	0.170314i	$0.0544780\pi$
$12$		0			0
$13$	2.12242	−	2.91468i	0.588653	−	0.808386i
$13$	2.12242	−	2.91468i	0.588653	−	0.808386i
$14$		0			0
$15$	0.715797	+	1.45807i	0.184818	+	0.376472i
$16$		0			0
$17$	2.42154	−	4.19424i	0.587311	−	1.01725i	−0.407273	−	0.913307i	$-0.633520\pi$
$17$	2.42154	−	4.19424i	0.587311	−	1.01725i	0.994583	−	0.103945i	$-0.0331466\pi$
$18$		0			0
$19$	3.21430	−	5.56733i	0.737411	−	1.27723i	−0.216246	−	0.976339i	$-0.569381\pi$
$19$	3.21430	−	5.56733i	0.737411	−	1.27723i	0.953657	−	0.300894i	$-0.0972852\pi$
$20$		0			0
$21$	−0.865635	+	1.29050i	−0.188897	+	0.281611i
$22$		0			0
$23$	−2.45776			−0.512477			−0.256239	−	0.966614i	$-0.582483\pi$
$23$	−2.45776			−0.512477			−0.256239	+	0.966614i	$0.582483\pi$
$24$		0			0
$25$	2.06028	+	3.56851i	0.412056	+	0.713701i
$26$		0			0
$27$	−5.09079	−	1.04109i	−0.979723	−	0.200357i
$28$		0			0
$29$	−5.24091	+	9.07753i	−0.973213	+	1.68565i	−0.287503	+	0.957780i	$0.592825\pi$
$29$	−5.24091	+	9.07753i	−0.973213	+	1.68565i	−0.685710	+	0.727874i	$0.740508\pi$
$30$		0			0
$31$	3.53762	−	6.12734i	0.635376	−	1.10050i	−0.351059	−	0.936353i	$-0.614178\pi$
$31$	3.53762	−	6.12734i	0.635376	−	1.10050i	0.986435	−	0.164150i	$-0.0524882\pi$
$32$		0			0
$33$	−1.74776	−	3.56017i	−0.304246	−	0.619745i
$34$		0			0
$35$	0.420676	−	0.728632i	0.0711072	−	0.123161i
$36$		0			0
$37$	2.82939	+	4.90064i	0.465149	+	0.805661i	0.999208	−	0.0397858i	$-0.0126676\pi$
$37$	2.82939	+	4.90064i	0.465149	+	0.805661i	−0.534060	+	0.845447i	$0.679334\pi$
$38$		0			0
$39$	−2.14471	−	5.86517i	−0.343428	−	0.939179i
$40$		0			0
$41$	−1.58900			−0.248160			−0.124080	−	0.992272i	$-0.539598\pi$
$41$	−1.58900			−0.248160			−0.124080	+	0.992272i	$0.539598\pi$
$42$		0			0
$43$	−4.11807			−0.628000			−0.314000	−	0.949423i	$-0.601669\pi$
$43$	−4.11807			−0.628000			−0.314000	+	0.949423i	$0.601669\pi$
$44$		0			0
$45$	2.78796	+	0.377207i	0.415604	+	0.0562306i
$46$		0			0
$47$	4.34470	+	7.52524i	0.633740	+	1.09767i	0.986781	+	0.162061i	$0.0518142\pi$
$47$	4.34470	+	7.52524i	0.633740	+	1.09767i	−0.353041	+	0.935608i	$0.614852\pi$
$48$		0			0
$49$	−6.19509			−0.885013
$50$		0			0
$51$	−3.69665	−	7.53003i	−0.517634	−	1.05441i
$52$		0			0
$53$	−9.76841			−1.34179			−0.670897	−	0.741550i	$-0.734091\pi$
$53$	−9.76841			−1.34179			−0.670897	+	0.741550i	$0.734091\pi$
$54$		0			0
$55$	1.07367	+	1.85965i	0.144773	+	0.250755i
$56$		0			0
$57$	−4.90684	−	9.99518i	−0.649927	−	1.32389i
$58$		0			0
$59$	6.06148	+	10.4988i	0.789137	+	1.36683i	0.926496	+	0.376304i	$0.122805\pi$
$59$	6.06148	+	10.4988i	0.789137	+	1.36683i	−0.137359	+	0.990521i	$0.543862\pi$
$60$		0			0
$61$	7.42626			0.950835			0.475417	−	0.879760i	$-0.342297\pi$
$61$	7.42626			0.950835			0.475417	+	0.879760i	$0.342297\pi$
$62$		0			0
$63$	1.02108	+	2.49030i	0.128644	+	0.313748i
$64$		0			0
$65$	1.37196	+	3.09039i	0.170170	+	0.383316i
$66$		0			0
$67$	10.8472			1.32519			0.662597	−	0.748977i	$-0.269454\pi$
$67$	10.8472			1.32519			0.662597	+	0.748977i	$0.269454\pi$
$68$		0			0
$69$	−2.37137	+	3.53529i	−0.285480	+	0.425599i
$70$		0			0
$71$	2.14956	−	3.72315i	0.255106	−	0.441856i	−0.709818	−	0.704385i	$-0.751223\pi$
$71$	2.14956	−	3.72315i	0.255106	−	0.441856i	0.964924	+	0.262528i	$0.0845563\pi$
$72$		0			0
$73$	6.91745			0.809627			0.404813	−	0.914399i	$-0.367337\pi$
$73$	6.91745			0.809627			0.404813	+	0.914399i	$0.367337\pi$
$74$		0			0
$75$	7.12088	+	0.479538i	0.822249	+	0.0553722i
$76$		0			0
$77$	−1.02716	+	1.77910i	−0.117056	+	0.202747i
$78$		0			0
$79$	−3.32457	−	5.75832i	−0.374043	−	0.647862i	0.616140	−	0.787637i	$-0.288696\pi$
$79$	−3.32457	−	5.75832i	−0.374043	−	0.647862i	−0.990183	+	0.139775i	$0.955362\pi$
$80$		0			0
$81$	−6.40939	+	6.31820i	−0.712154	+	0.702023i
$82$		0			0
$83$	0.852333	+	1.47628i	0.0935556	+	0.162043i	0.909005	−	0.416785i	$-0.136843\pi$
$83$	0.852333	+	1.47628i	0.0935556	+	0.162043i	−0.815449	+	0.578829i	$0.803510\pi$
$84$		0			0
$85$	2.27089	+	3.93330i	0.246313	+	0.426626i
$86$		0			0
$87$	8.00060	+	16.2971i	0.857754	+	1.74724i
$88$		0			0
$89$	0.452237	+	0.783298i	0.0479370	+	0.0830294i	0.888998	−	0.457910i	$-0.151402\pi$
$89$	0.452237	+	0.783298i	0.0479370	+	0.0830294i	−0.841061	+	0.540940i	$0.818069\pi$
$90$		0			0
$91$	−1.90416	+	2.61495i	−0.199611	+	0.274121i
$92$		0			0
$93$	−5.40042	−	11.0006i	−0.559997	−	1.14071i
$94$		0			0
$95$	3.01433	+	5.22097i	0.309264	+	0.535660i
$96$		0			0
$97$	−4.65687			−0.472834			−0.236417	−	0.971652i	$-0.575973\pi$
$97$	−4.65687			−0.472834			−0.236417	+	0.971652i	$0.575973\pi$
$98$		0			0
$99$	−6.80735	−	0.921024i	−0.684165	−	0.0925664i
$100$		0			0
$101$	−3.11582	+	5.39676i	−0.310036	+	0.536998i	−0.978370	−	0.206864i	$-0.933674\pi$
$101$	−3.11582	+	5.39676i	−0.310036	+	0.536998i	0.668334	+	0.743861i	$0.267008\pi$
$102$		0			0
$103$	−1.03851	+	1.79875i	−0.102327	+	0.177236i	−0.912643	−	0.408757i	$-0.865962\pi$
$103$	−1.03851	+	1.79875i	−0.102327	+	0.177236i	0.810316	+	0.585993i	$0.199296\pi$
$104$		0			0
$105$	−0.642189	−	1.30813i	−0.0626712	−	0.127661i
$106$		0			0
$107$	−2.18277	−	3.78066i	−0.211016	−	0.365490i	0.741017	−	0.671487i	$-0.234344\pi$
$107$	−2.18277	−	3.78066i	−0.211016	−	0.365490i	−0.952033	+	0.305996i	$0.901011\pi$
$108$		0			0
$109$	−0.616958			−0.0590939			−0.0295470	−	0.999563i	$-0.509406\pi$
$109$	−0.616958			−0.0590939			−0.0295470	+	0.999563i	$0.509406\pi$
$110$		0			0
$111$	9.77914	+	0.658551i	0.928195	+	0.0625069i
$112$		0			0
$113$	5.84292	+	10.1202i	0.549656	+	0.952032i	0.998298	+	0.0583204i	$0.0185745\pi$
$113$	5.84292	+	10.1202i	0.549656	+	0.952032i	−0.448642	+	0.893712i	$0.648092\pi$
$114$		0			0
$115$	1.15243	−	1.99606i	0.107464	−	0.186134i
$116$		0			0
$117$	−10.5059	−	2.57404i	−0.971273	−	0.237970i
$118$		0			0
$119$	−2.17253	+	3.76293i	−0.199155	+	0.344947i
$120$		0			0
$121$	2.87843	+	4.98558i	0.261675	+	0.453235i
$122$		0			0
$123$	−1.53315	+	2.28565i	−0.138240	+	0.206090i
$124$		0			0
$125$	−8.55314			−0.765016
$126$		0			0
$127$	6.43952	+	11.1536i	0.571415	+	0.989720i	0.996421	+	0.0845291i	$0.0269386\pi$
$127$	6.43952	+	11.1536i	0.571415	+	0.989720i	−0.425006	+	0.905190i	$0.639728\pi$
$128$		0			0
$129$	−3.97334	+	5.92353i	−0.349833	+	0.521537i
$130$		0			0
$131$	3.91937	−	6.78855i	0.342437	−	0.593119i	−0.642448	−	0.766330i	$-0.722081\pi$
$131$	3.91937	−	6.78855i	0.342437	−	0.593119i	0.984885	+	0.173211i	$0.0554143\pi$
$132$		0			0
$133$	−2.88376	+	4.99482i	−0.250054	+	0.433106i
$134$		0			0
$135$	3.23255	−	3.64631i	0.278214	−	0.313825i
$136$		0			0
$137$	−19.0085			−1.62401			−0.812003	−	0.583654i	$-0.801623\pi$
$137$	−19.0085			−1.62401			−0.812003	+	0.583654i	$0.801623\pi$
$138$		0			0
$139$	−5.96161	−	10.3258i	−0.505657	−	0.875824i	−0.999979	−	0.00654493i	$-0.997917\pi$
$139$	−5.96161	−	10.3258i	−0.505657	−	0.875824i	0.494321	−	0.869279i	$-0.335417\pi$
$140$		0			0
$141$	15.0165	+	1.01125i	1.26461	+	0.0851622i
$142$		0			0
$143$	−3.34990	−	7.54580i	−0.280133	−	0.631011i
$144$		0			0
$145$	−4.91486	−	8.51279i	−0.408157	−	0.706948i
$146$		0			0
$147$	−5.97736	+	8.91116i	−0.493004	+	0.734980i
$148$		0			0
$149$	−0.106480	−	0.184429i	−0.00872321	−	0.0151090i	0.861631	−	0.507535i	$-0.169443\pi$
$149$	−0.106480	−	0.184429i	−0.00872321	−	0.0151090i	−0.870354	+	0.492426i	$0.836110\pi$
$150$		0			0
$151$	10.3552	+	17.9357i	0.842693	+	1.45959i	0.887610	+	0.460596i	$0.152364\pi$
$151$	10.3552	+	17.9357i	0.842693	+	1.45959i	−0.0449166	+	0.998991i	$0.514302\pi$
$152$		0			0
$153$	−14.3981	−	1.94804i	−1.16402	−	0.157489i
$154$		0			0
$155$	3.31754	+	5.74614i	0.266471	+	0.461541i
$156$		0			0
$157$	−1.58686	+	2.74853i	−0.126646	+	0.219357i	−0.922375	−	0.386296i	$-0.873754\pi$
$157$	−1.58686	+	2.74853i	−0.126646	+	0.219357i	0.795729	+	0.605652i	$0.207088\pi$
$158$		0			0
$159$	−9.42509	+	14.0511i	−0.747458	+	1.11432i
$160$		0			0
$161$	2.20502			0.173780
$162$		0			0
$163$	1.17804	−	2.04043i	0.0922716	−	0.159819i	−0.816195	−	0.577776i	$-0.803921\pi$
$163$	1.17804	−	2.04043i	0.0922716	−	0.159819i	0.908467	+	0.417957i	$0.137254\pi$
$164$		0			0
$165$	3.71089	+	0.249900i	0.288893	+	0.0194547i
$166$		0			0
$167$	8.76677			0.678393			0.339196	−	0.940716i	$-0.389845\pi$
$167$	8.76677			0.678393			0.339196	+	0.940716i	$0.389845\pi$
$168$		0			0
$169$	−3.99067	−	12.3723i	−0.306974	−	0.951718i
$170$		0			0
$171$	−19.1117	−	2.58578i	−1.46151	−	0.197739i
$172$		0			0
$173$	−4.33886			−0.329877			−0.164939	−	0.986304i	$-0.552743\pi$
$173$	−4.33886			−0.329877			−0.164939	+	0.986304i	$0.552743\pi$
$174$		0			0
$175$	−1.84841	−	3.20154i	−0.139727	−	0.242014i
$176$		0			0
$177$	20.9501	+	1.41083i	1.57471	+	0.106045i
$178$		0			0
$179$	−6.38992	−	11.0677i	−0.477605	−	0.827236i	0.522066	−	0.852905i	$-0.325162\pi$
$179$	−6.38992	−	11.0677i	−0.477605	−	0.827236i	−0.999670	+	0.0256695i	$0.991828\pi$
$180$		0			0
$181$	−5.90627			−0.439009			−0.219505	−	0.975611i	$-0.570444\pi$
$181$	−5.90627			−0.439009			−0.219505	+	0.975611i	$0.570444\pi$
$182$		0			0
$183$	7.16525	−	10.6821i	0.529671	−	0.789643i
$184$		0			0
$185$	−5.30673			−0.390158
$186$		0			0
$187$	−5.54483	−	9.60393i	−0.405478	−	0.702309i
$188$		0			0
$189$	4.56729	+	0.934029i	0.332221	+	0.0679406i
$190$		0			0
$191$	23.4282			1.69521			0.847603	−	0.530631i	$-0.178045\pi$
$191$	23.4282			1.69521			0.847603	+	0.530631i	$0.178045\pi$
$192$		0			0
$193$	10.0542			0.723716			0.361858	−	0.932233i	$-0.382143\pi$
$193$	10.0542			0.723716			0.361858	+	0.932233i	$0.382143\pi$
$194$		0			0
$195$	5.76902	+	1.00832i	0.413128	+	0.0722074i
$196$		0			0
$197$	6.65982	+	11.5352i	0.474493	+	0.821845i	0.999573	−	0.0292070i	$-0.00929820\pi$
$197$	6.65982	+	11.5352i	0.474493	+	0.821845i	−0.525081	+	0.851052i	$0.675965\pi$
$198$		0			0
$199$	2.53206	−	4.38565i	0.179493	−	0.310890i	−0.762214	−	0.647325i	$-0.775888\pi$
$199$	2.53206	−	4.38565i	0.179493	−	0.310890i	0.941707	+	0.336434i	$0.109221\pi$
$200$		0			0
$201$	10.4659	−	15.6028i	0.738210	−	1.10054i
$202$		0			0
$203$	4.70197	−	8.14406i	0.330014	−	0.571601i
$204$		0			0
$205$	0.745072	−	1.29050i	0.0520381	−	0.0901326i
$206$		0			0
$207$	2.79721	+	6.82207i	0.194419	+	0.474167i
$208$		0			0
$209$	−7.36008	−	12.7480i	−0.509107	−	0.881800i
$210$		0			0
$211$	−7.41803			−0.510678			−0.255339	−	0.966852i	$-0.582187\pi$
$211$	−7.41803			−0.510678			−0.255339	+	0.966852i	$0.582187\pi$
$212$		0			0
$213$	−3.28145	−	6.68427i	−0.224841	−	0.457998i
$214$		0			0
$215$	1.93094	−	3.34448i	0.131689	−	0.228092i
$216$		0			0
$217$	−3.17384	+	5.49725i	−0.215454	+	0.373178i
$218$		0			0
$219$	6.67433	−	9.95022i	0.451009	−	0.672373i
$220$		0			0
$221$	−7.08530	−	15.9599i	−0.476609	−	1.07358i
$222$		0			0
$223$	1.48472	−	2.57161i	0.0994240	−	0.172207i	−0.812022	−	0.583626i	$-0.801633\pi$
$223$	1.48472	−	2.57161i	0.0994240	−	0.172207i	0.911446	+	0.411419i	$0.134967\pi$
$224$		0			0
$225$	7.56039	−	9.78015i	0.504026	−	0.652010i
$226$		0			0
$227$	−8.21162			−0.545024			−0.272512	−	0.962152i	$-0.587855\pi$
$227$	−8.21162			−0.545024			−0.272512	+	0.962152i	$0.587855\pi$
$228$		0			0
$229$	−13.3798	+	23.1745i	−0.884164	+	1.53142i	−0.0374944	+	0.999297i	$0.511938\pi$
$229$	−13.3798	+	23.1745i	−0.884164	+	1.53142i	−0.846669	+	0.532119i	$0.821396\pi$
$230$		0			0
$231$	1.56803	+	3.19406i	0.103169	+	0.210154i
$232$		0			0
$233$	1.48653			0.0973860			0.0486930	−	0.998814i	$-0.484494\pi$
$233$	1.48653			0.0973860			0.0486930	+	0.998814i	$0.484494\pi$
$234$		0			0
$235$	−8.14880			−0.531569
$236$		0			0
$237$	−11.4906	−	0.773806i	−0.746396	−	0.0502641i
$238$		0			0
$239$	12.7567	−	22.0952i	0.825159	−	1.42922i	−0.0766386	−	0.997059i	$-0.524419\pi$
$239$	12.7567	−	22.0952i	0.825159	−	1.42922i	0.901798	−	0.432159i	$-0.142248\pi$
$240$		0			0
$241$	21.0733			1.35745			0.678726	−	0.734391i	$-0.262532\pi$
$241$	21.0733			1.35745			0.678726	+	0.734391i	$0.262532\pi$
$242$		0			0
$243$	2.90412	+	15.3156i	0.186299	+	0.982493i
$244$		0			0
$245$	2.90484	−	5.03133i	0.185583	−	0.321440i
$246$		0			0
$247$	−9.40487	−	21.1849i	−0.598417	−	1.34796i
$248$		0			0
$249$	2.94589	+	0.198384i	0.186688	+	0.0125721i
$250$		0			0
$251$	5.87642	−	10.1783i	0.370916	−	0.642446i	−0.618791	−	0.785556i	$-0.712377\pi$
$251$	5.87642	−	10.1783i	0.370916	−	0.642446i	0.989707	+	0.143110i	$0.0457104\pi$
$252$		0			0
$253$	−2.81387	+	4.87377i	−0.176907	+	0.306412i
$254$		0			0
$255$	7.84882	+	0.528559i	0.491512	+	0.0330996i
$256$		0			0
$257$	25.9194			1.61681			0.808404	−	0.588627i	$-0.200331\pi$
$257$	25.9194			1.61681			0.808404	+	0.588627i	$0.200331\pi$
$258$		0			0
$259$	−2.53843	−	4.39670i	−0.157731	−	0.273197i
$260$		0			0
$261$	31.1616	+	4.21611i	1.92885	+	0.260971i
$262$		0			0
$263$	−11.4003	+	19.7458i	−0.702970	+	1.21758i	0.264449	+	0.964400i	$0.414810\pi$
$263$	−11.4003	+	19.7458i	−0.702970	+	1.21758i	−0.967419	+	0.253180i	$0.918523\pi$
$264$		0			0
$265$	4.58035	−	7.93339i	0.281368	−	0.487344i
$266$		0			0
$267$	1.56306	+	0.105260i	0.0956574	+	0.00644180i
$268$		0			0
$269$	13.5774	−	23.5168i	0.827831	−	1.43385i	−0.0719045	−	0.997412i	$-0.522908\pi$
$269$	13.5774	−	23.5168i	0.827831	−	1.43385i	0.899736	−	0.436435i	$-0.143759\pi$
$270$		0			0
$271$	−11.2144	−	19.4239i	−0.681224	−	1.17992i	−0.974607	−	0.223920i	$-0.928114\pi$
$271$	−11.2144	−	19.4239i	−0.681224	−	1.17992i	0.293383	−	0.955995i	$-0.405219\pi$
$272$		0			0
$273$	1.92416	+	5.26204i	0.116455	+	0.318473i
$274$		0			0
$275$	9.43522			0.568965
$276$		0			0
$277$	−1.60846			−0.0966432			−0.0483216	−	0.998832i	$-0.515387\pi$
$277$	−1.60846			−0.0966432			−0.0483216	+	0.998832i	$0.515387\pi$
$278$		0			0
$279$	−21.0341	−	2.84588i	−1.25928	−	0.170378i
$280$		0			0
$281$	−8.42019	−	14.5842i	−0.502306	−	0.870020i	−0.999996	−	0.00266532i	$-0.999152\pi$
$281$	−8.42019	−	14.5842i	−0.502306	−	0.870020i	0.497690	−	0.867355i	$-0.334182\pi$
$282$		0			0
$283$	−23.3167			−1.38603			−0.693017	−	0.720922i	$-0.743719\pi$
$283$	−23.3167			−1.38603			−0.693017	+	0.720922i	$0.743719\pi$
$284$		0			0
$285$	10.4183	+	0.701597i	0.617129	+	0.0415590i
$286$		0			0
$287$	1.42560			0.0841504
$288$		0			0
$289$	−3.22774	−	5.59062i	−0.189867	−	0.328860i
$290$		0			0
$291$	−4.49320	+	6.69854i	−0.263396	+	0.392676i
$292$		0			0
$293$	7.98254	+	13.8262i	0.466345	+	0.807733i	0.999261	−	0.0384350i	$-0.0122372\pi$
$293$	7.98254	+	13.8262i	0.466345	+	0.807733i	−0.532916	+	0.846168i	$0.678904\pi$
$294$		0			0
$295$	−11.3687			−0.661914
$296$		0			0
$297$	−7.89292	+	8.90319i	−0.457994	+	0.516615i
$298$		0			0
$299$	−5.21639	+	7.16356i	−0.301672	+	0.414279i
$300$		0			0
$301$	3.69460			0.212953
$302$		0			0
$303$	4.75651	+	9.68895i	0.273254	+	0.556616i
$304$		0			0
$305$	−3.48212	+	6.03121i	−0.199386	+	0.345346i
$306$		0			0
$307$	−31.4078			−1.79254			−0.896269	−	0.443512i	$-0.853733\pi$
$307$	−31.4078			−1.79254			−0.896269	+	0.443512i	$0.853733\pi$
$308$		0			0
$309$	1.58535	+	3.22935i	0.0901876	+	0.183711i
$310$		0			0
$311$	2.17084	−	3.76001i	0.123097	−	0.213210i	−0.797890	−	0.602803i	$-0.794051\pi$
$311$	2.17084	−	3.76001i	0.123097	−	0.213210i	0.920987	+	0.389592i	$0.127384\pi$
$312$		0			0
$313$	12.1727	+	21.0836i	0.688039	+	1.19172i	0.972471	+	0.233022i	$0.0748615\pi$
$313$	12.1727	+	21.0836i	0.688039	+	1.19172i	−0.284432	+	0.958696i	$0.591805\pi$
$314$		0			0
$315$	−2.50126	−	0.338417i	−0.140930	−	0.0190676i
$316$		0			0
$317$	−16.6834	−	28.8965i	−0.937033	−	1.62299i	−0.770968	−	0.636874i	$-0.780227\pi$
$317$	−16.6834	−	28.8965i	−0.937033	−	1.62299i	−0.166065	−	0.986115i	$-0.553106\pi$
$318$		0			0
$319$	12.0006	+	20.7856i	0.671905	+	1.16377i
$320$		0			0
$321$	−7.54424	−	0.508047i	−0.421078	−	0.0283564i
$322$		0			0
$323$	−15.5671	−	26.9631i	−0.866178	−	1.50027i
$324$		0			0
$325$	14.7738	+	1.56883i	0.819504	+	0.0870229i
$326$		0			0
$327$	−0.595275	+	0.887447i	−0.0329188	+	0.0490759i
$328$		0			0
$329$	−3.89792	−	6.75140i	−0.214899	−	0.372216i
$330$		0			0
$331$	−18.5850			−1.02152			−0.510762	−	0.859722i	$-0.670637\pi$
$331$	−18.5850			−1.02152			−0.510762	+	0.859722i	$0.670637\pi$
$332$		0			0
$333$	10.3827	−	13.4311i	0.568969	−	0.736021i
$334$		0			0
$335$	−5.08617	+	8.80950i	−0.277887	+	0.481314i
$336$		0			0
$337$	−8.74013	+	15.1384i	−0.476105	+	0.824639i	−0.999625	−	0.0273747i	$-0.991285\pi$
$337$	−8.74013	+	15.1384i	−0.476105	+	0.824639i	0.523520	+	0.852014i	$0.324619\pi$
$338$		0			0
$339$	20.1947	+	1.35996i	1.09683	+	0.0738630i
$340$		0			0
$341$	−8.10042	−	14.0303i	−0.438662	−	0.759786i
$342$		0			0
$343$	11.8382			0.639203
$344$		0			0
$345$	−1.75925	−	3.58358i	−0.0947150	−	0.192933i
$346$		0			0
$347$	2.76667	+	4.79201i	0.148522	+	0.257248i	0.930682	−	0.365830i	$-0.119215\pi$
$347$	2.76667	+	4.79201i	0.148522	+	0.257248i	−0.782159	+	0.623079i	$0.785882\pi$
$348$		0			0
$349$	−1.46906	+	2.54448i	−0.0786368	+	0.136203i	−0.902662	−	0.430350i	$-0.858390\pi$
$349$	−1.46906	+	2.54448i	−0.0786368	+	0.136203i	0.824025	+	0.566553i	$0.191723\pi$
$350$		0			0
$351$	−13.8392	+	12.6284i	−0.738683	+	0.674053i
$352$		0			0
$353$	−11.6461	+	20.1717i	−0.619860	+	1.07363i	0.369651	+	0.929171i	$0.379477\pi$
$353$	−11.6461	+	20.1717i	−0.619860	+	1.07363i	−0.989511	+	0.144459i	$0.953856\pi$
$354$		0			0
$355$	2.01583	+	3.49152i	0.106989	+	0.185311i
$356$		0			0
$357$	3.31651	+	6.75569i	0.175528	+	0.357549i
$358$		0			0
$359$	−7.00737			−0.369835			−0.184917	−	0.982754i	$-0.559202\pi$
$359$	−7.00737			−0.369835			−0.184917	+	0.982754i	$0.559202\pi$
$360$		0			0
$361$	−11.1634	−	19.3357i	−0.587550	−	1.01767i
$362$		0			0
$363$	9.94863	+	0.669965i	0.522168	+	0.0351640i
$364$		0			0
$365$	−3.24355	+	5.61799i	−0.169775	+	0.294059i
$366$		0			0
$367$	−1.19968	+	2.07791i	−0.0626230	+	0.108466i	−0.895637	−	0.444786i	$-0.853280\pi$
$367$	−1.19968	+	2.07791i	−0.0626230	+	0.108466i	0.833014	+	0.553252i	$0.186613\pi$
$368$		0			0
$369$	1.80846	+	4.41064i	0.0941449	+	0.229609i
$370$		0			0
$371$	8.76390			0.454999
$372$		0			0
$373$	2.77715	+	4.81016i	0.143795	+	0.249061i	0.928923	−	0.370273i	$-0.120736\pi$
$373$	2.77715	+	4.81016i	0.143795	+	0.249061i	−0.785128	+	0.619334i	$0.787403\pi$
$374$		0			0
$375$	−8.25253	+	12.3030i	−0.426159	+	0.635325i
$376$		0			0
$377$	15.3346	+	34.5419i	0.789773	+	1.77900i
$378$		0			0
$379$	8.99747	+	15.5841i	0.462169	+	0.800500i	0.999069	−	0.0431457i	$-0.0137380\pi$
$379$	8.99747	+	15.5841i	0.462169	+	0.800500i	−0.536900	+	0.843646i	$0.680405\pi$
$380$		0			0
$381$	22.2567	+	1.49882i	1.14025	+	0.0767870i
$382$		0			0
$383$	−5.96843	−	10.3376i	−0.304973	−	0.528228i	0.672282	−	0.740295i	$-0.265314\pi$
$383$	−5.96843	−	10.3376i	−0.304973	−	0.528228i	−0.977255	+	0.212066i	$0.931981\pi$
$384$		0			0
$385$	−0.963260	−	1.66841i	−0.0490923	−	0.0850303i
$386$		0			0
$387$	4.68684	+	11.4307i	0.238245	+	0.581054i
$388$		0			0
$389$	−6.13475	−	10.6257i	−0.311044	−	0.538745i	0.667544	−	0.744570i	$-0.267345\pi$
$389$	−6.13475	−	10.6257i	−0.311044	−	0.538745i	−0.978589	+	0.205825i	$0.934012\pi$
$390$		0			0
$391$	−5.95156	+	10.3084i	−0.300983	+	0.521319i
$392$		0			0
$393$	−5.98318	−	12.1877i	−0.301812	−	0.614787i
$394$		0			0
$395$	6.23547			0.313741
$396$		0			0
$397$	−9.46714	+	16.3976i	−0.475142	+	0.822970i	−0.999595	−	0.0284693i	$-0.990937\pi$
$397$	−9.46714	+	16.3976i	−0.475142	+	0.822970i	0.524452	+	0.851440i	$0.324270\pi$
$398$		0			0
$399$	4.40225	+	8.96734i	0.220388	+	0.448929i
$400$		0			0
$401$	33.6297			1.67939			0.839694	−	0.543060i	$-0.182734\pi$
$401$	33.6297			1.67939			0.839694	+	0.543060i	$0.182734\pi$
$402$		0			0
$403$	−10.3509	−	23.3158i	−0.515615	−	1.16144i
$404$		0			0
$405$	−2.12599	−	8.16793i	−0.105641	−	0.405868i
$406$		0			0
$407$	12.9574			0.642276
$408$		0			0
$409$	7.15085	+	12.3856i	0.353587	+	0.612431i	0.986875	−	0.161486i	$-0.0516285\pi$
$409$	7.15085	+	12.3856i	0.353587	+	0.612431i	−0.633288	+	0.773916i	$0.718295\pi$
$410$		0			0
$411$	−18.3404	+	27.3422i	−0.904666	+	1.34869i
$412$		0			0
$413$	−5.43815	−	9.41916i	−0.267594	−	0.463487i
$414$		0			0
$415$	−1.59861			−0.0784728
$416$		0			0
$417$	−20.6050	−	1.38759i	−1.00903	−	0.0679505i
$418$		0			0
$419$	11.6920			0.571190			0.285595	−	0.958350i	$-0.407809\pi$
$419$	11.6920			0.571190			0.285595	+	0.958350i	$0.407809\pi$
$420$		0			0
$421$	−15.4632	−	26.7830i	−0.753630	−	1.30532i	−0.946053	−	0.324013i	$-0.894968\pi$
$421$	−15.4632	−	26.7830i	−0.753630	−	1.30532i	0.192423	−	0.981312i	$-0.438365\pi$
$422$		0			0
$423$	15.9433	−	20.6243i	0.775190	−	1.00279i
$424$		0			0
$425$	19.9562			0.968018
$426$		0			0
$427$	−6.66259			−0.322425
$428$		0			0
$429$	−14.0862	−	2.46202i	−0.680088	−	0.118867i
$430$		0			0
$431$	14.8068	+	25.6461i	0.713218	+	1.23533i	0.963643	+	0.267194i	$0.0860965\pi$
$431$	14.8068	+	25.6461i	0.713218	+	1.23533i	−0.250424	+	0.968136i	$0.580570\pi$
$432$		0			0
$433$	−1.34968	+	2.33771i	−0.0648613	+	0.112343i	−0.896632	−	0.442776i	$-0.853994\pi$
$433$	−1.34968	+	2.33771i	−0.0648613	+	0.112343i	0.831771	+	0.555119i	$0.187327\pi$
$434$		0			0
$435$	−16.9871	−	1.14395i	−0.814469	−	0.0548483i
$436$		0			0
$437$	−7.89996	+	13.6831i	−0.377907	+	0.654553i
$438$		0			0
$439$	−15.5997	+	27.0194i	−0.744532	+	1.28957i	0.205881	+	0.978577i	$0.433994\pi$
$439$	−15.5997	+	27.0194i	−0.744532	+	1.28957i	−0.950413	+	0.310991i	$0.899339\pi$
$440$		0			0
$441$	7.05072	+	17.1959i	0.335749	+	0.818853i
$442$		0			0
$443$	−18.3073	−	31.7092i	−0.869806	−	1.50655i	−0.862195	−	0.506577i	$-0.830910\pi$
$443$	−18.3073	−	31.7092i	−0.869806	−	1.50655i	−0.00761158	−	0.999971i	$-0.502423\pi$
$444$		0			0
$445$	−0.848204			−0.0402087
$446$		0			0
$447$	−0.368025	−	0.0247837i	−0.0174070	−	0.00117223i
$448$		0			0
$449$	−16.9564	+	29.3693i	−0.800222	+	1.38602i	0.119248	+	0.992864i	$0.461952\pi$
$449$	−16.9564	+	29.3693i	−0.800222	+	1.38602i	−0.919470	+	0.393160i	$0.871382\pi$
$450$		0			0
$451$	−1.81924	+	3.15102i	−0.0856647	+	0.148376i
$452$		0			0
$453$	35.7904	+	2.41021i	1.68158	+	0.113242i
$454$		0			0
$455$	−1.23087	−	2.77260i	−0.0577043	−	0.129981i
$456$		0			0
$457$	21.1402	−	36.6159i	0.988896	−	1.71282i	0.365747	−	0.930714i	$-0.380814\pi$
$457$	21.1402	−	36.6159i	0.988896	−	1.71282i	0.623149	−	0.782103i	$-0.285853\pi$
$458$		0			0
$459$	−16.6941	+	18.8309i	−0.779215	+	0.878953i
$460$		0			0
$461$	8.35048			0.388920			0.194460	−	0.980910i	$-0.437704\pi$
$461$	8.35048			0.388920			0.194460	+	0.980910i	$0.437704\pi$
$462$		0			0
$463$	−2.81834	+	4.88150i	−0.130979	+	0.226863i	−0.924054	−	0.382261i	$-0.875145\pi$
$463$	−2.81834	+	4.88150i	−0.130979	+	0.226863i	0.793075	+	0.609124i	$0.208479\pi$
$464$		0			0
$465$	11.4663	+	0.772170i	0.531738	+	0.0358085i
$466$		0			0
$467$	−24.8169			−1.14839			−0.574195	−	0.818719i	$-0.694685\pi$
$467$	−24.8169			−1.14839			−0.574195	+	0.818719i	$0.694685\pi$
$468$		0			0
$469$	−9.73172			−0.449369
$470$		0			0
$471$	2.42245	+	4.93451i	0.111621	+	0.227370i
$472$		0			0
$473$	−4.71477	+	8.16621i	−0.216785	+	0.375483i
$474$		0			0
$475$	26.4894			1.21542
$476$		0			0
$477$	11.1176	+	27.1145i	0.509039	+	1.24149i
$478$		0			0
$479$	11.8238	−	20.4794i	0.540242	−	0.935727i	−0.458647	−	0.888618i	$-0.651666\pi$
$479$	11.8238	−	20.4794i	0.540242	−	0.935727i	0.998890	−	0.0471090i	$-0.0150008\pi$
$480$		0			0
$481$	20.2889	+	2.15448i	0.925096	+	0.0982357i
$482$		0			0
$483$	2.12752	−	3.17174i	0.0968055	−	0.144319i
$484$		0			0
$485$	2.18358	−	3.78207i	0.0991511	−	0.171735i
$486$		0			0
$487$	2.67346	−	4.63057i	0.121146	−	0.209831i	−0.799074	−	0.601233i	$-0.794676\pi$
$487$	2.67346	−	4.63057i	0.121146	−	0.209831i	0.920220	+	0.391402i	$0.128010\pi$
$488$		0			0
$489$	−1.79836	−	3.66324i	−0.0813248	−	0.165658i
$490$		0			0
$491$	−19.7581			−0.891672			−0.445836	−	0.895115i	$-0.647094\pi$
$491$	−19.7581			−0.891672			−0.445836	+	0.895115i	$0.647094\pi$
$492$		0			0
$493$	25.3822	+	43.9632i	1.14316	+	1.98001i
$494$		0			0
$495$	3.93993	−	5.09671i	0.177087	−	0.229080i
$496$		0			0
$497$	−1.92851	+	3.34028i	−0.0865057	+	0.149832i
$498$		0			0
$499$	9.13549	−	15.8231i	0.408961	−	0.708341i	−0.585813	−	0.810446i	$-0.699225\pi$
$499$	9.13549	−	15.8231i	0.408961	−	0.708341i	0.994774	+	0.102106i	$0.0325580\pi$
$500$		0			0
$501$	8.45865	−	12.6103i	0.377904	−	0.563387i
$502$		0			0
$503$	−3.12995	+	5.42124i	−0.139558	+	0.241721i	−0.927329	−	0.374246i	$-0.877901\pi$
$503$	−3.12995	+	5.42124i	−0.139558	+	0.241721i	0.787772	+	0.615968i	$0.211235\pi$
$504$		0			0
$505$	−2.92198	−	5.06101i	−0.130026	−	0.225212i
$506$		0			0
$507$	−21.6470	−	6.19723i	−0.961379	−	0.275229i
$508$		0			0
$509$	−29.4233			−1.30416			−0.652082	−	0.758148i	$-0.726104\pi$
$509$	−29.4233			−1.30416			−0.652082	+	0.758148i	$0.726104\pi$
$510$		0			0
$511$	−6.20611			−0.274542
$512$		0			0
$513$	−22.1594	+	24.9957i	−0.978362	+	1.10359i
$514$		0			0
$515$	−0.973900	−	1.68684i	−0.0429152	−	0.0743313i
$516$		0			0
$517$	19.8969			0.875065
$518$		0			0
$519$	−4.18636	+	6.24111i	−0.183761	+	0.273954i
$520$		0			0
$521$	22.1544			0.970604			0.485302	−	0.874347i	$-0.338710\pi$
$521$	22.1544			0.970604			0.485302	+	0.874347i	$0.338710\pi$
$522$		0			0
$523$	0.383884	+	0.664906i	0.0167861	+	0.0290743i	0.874296	−	0.485392i	$-0.161323\pi$
$523$	0.383884	+	0.664906i	0.0167861	+	0.0290743i	−0.857510	+	0.514467i	$0.827990\pi$
$524$		0			0
$525$	−6.38862	−	0.430225i	−0.278822	−	0.0187766i
$526$		0			0
$527$	−17.1330	−	29.6753i	−0.746326	−	1.29267i
$528$		0			0
$529$	−16.9594			−0.737367
$530$		0			0
$531$	22.2432	−	28.7739i	0.965271	−	1.24868i
$532$		0			0
$533$	−3.37253	+	4.63142i	−0.146080	+	0.200609i
$534$		0			0
$535$	4.09394			0.176996
$536$		0			0
$537$	−22.0853	−	1.48728i	−0.953051	−	0.0641808i
$538$		0			0
$539$	−7.09274	+	12.2850i	−0.305506	+	0.529151i
$540$		0			0
$541$	30.6466			1.31760			0.658799	−	0.752319i	$-0.271065\pi$
$541$	30.6466			1.31760			0.658799	+	0.752319i	$0.271065\pi$
$542$		0			0
$543$	−5.69868	+	8.49570i	−0.244554	+	0.364585i
$544$		0			0
$545$	0.289288	−	0.501061i	0.0123917	−	0.0214631i
$546$		0			0
$547$	18.0700	+	31.2982i	0.772618	+	1.33821i	0.936124	+	0.351671i	$0.114387\pi$
$547$	18.0700	+	31.2982i	0.772618	+	1.33821i	−0.163505	+	0.986542i	$0.552280\pi$
$548$		0			0
$549$	−8.45193	−	20.6133i	−0.360720	−	0.879754i
$550$		0			0
$551$	33.6917	+	58.3558i	1.43532	+	2.48604i
$552$		0			0
$553$	2.98269	+	5.16618i	0.126837	+	0.219688i
$554$		0			0
$555$	−5.12021	+	7.63331i	−0.217341	+	0.324016i
$556$		0			0
$557$	−4.10600	−	7.11180i	−0.173977	−	0.301337i	0.765830	−	0.643043i	$-0.222328\pi$
$557$	−4.10600	−	7.11180i	−0.173977	−	0.301337i	−0.939807	+	0.341707i	$0.888995\pi$
$558$		0			0
$559$	−8.74028	+	12.0028i	−0.369675	+	0.507666i
$560$		0			0
$561$	−19.1645	−	1.29058i	−0.809124	−	0.0544884i
$562$		0			0
$563$	15.9643	+	27.6510i	0.672816	+	1.16535i	0.977102	+	0.212771i	$0.0682487\pi$
$563$	15.9643	+	27.6510i	0.672816	+	1.16535i	−0.304286	+	0.952581i	$0.598418\pi$
$564$		0			0
$565$	−10.9588			−0.461042
$566$		0			0
$567$	5.75029	−	5.66848i	0.241490	−	0.238054i
$568$		0			0
$569$	14.6512	−	25.3767i	0.614211	−	1.06385i	−0.376311	−	0.926493i	$-0.622808\pi$
$569$	14.6512	−	25.3767i	0.614211	−	1.06385i	0.990522	−	0.137352i	$-0.0438591\pi$
$570$		0			0
$571$	12.4100	−	21.4948i	0.519343	−	0.899528i	−0.480405	−	0.877047i	$-0.659510\pi$
$571$	12.4100	−	21.4948i	0.519343	−	0.899528i	0.999747	−	0.0224810i	$-0.00715652\pi$
$572$		0			0
$573$	22.6048	−	33.6997i	0.944329	−	1.40782i
$574$		0			0
$575$	−5.06366	−	8.77052i	−0.211169	−	0.365756i
$576$		0			0
$577$	−32.0808			−1.33554			−0.667771	−	0.744366i	$-0.732752\pi$
$577$	−32.0808			−1.33554			−0.667771	+	0.744366i	$0.732752\pi$
$578$		0			0
$579$	9.70082	−	14.4622i	0.403152	−	0.601027i
$580$		0			0
$581$	−0.764684	−	1.32447i	−0.0317245	−	0.0549484i
$582$		0			0
$583$	−11.1838	+	19.3709i	−0.463186	+	0.802262i
$584$		0			0
$585$	7.01665	−	7.32540i	0.290103	−	0.302868i
$586$		0			0
$587$	−16.2931	+	28.2206i	−0.672490	+	1.16479i	0.304706	+	0.952447i	$0.401442\pi$
$587$	−16.2931	+	28.2206i	−0.672490	+	1.16479i	−0.977196	+	0.212341i	$0.931891\pi$
$588$		0			0
$589$	−22.7420	−	39.3902i	−0.937066	−	1.62305i
$590$		0			0
$591$	23.0182	+	1.55010i	0.946841	+	0.0637626i
$592$		0			0
$593$	−21.9727			−0.902310			−0.451155	−	0.892446i	$-0.648988\pi$
$593$	−21.9727			−0.902310			−0.451155	+	0.892446i	$0.648988\pi$
$594$		0			0
$595$	−2.03737	−	3.52883i	−0.0835240	−	0.144668i
$596$		0			0
$597$	−3.86535	−	7.87367i	−0.158198	−	0.322248i
$598$		0			0
$599$	−16.0735	+	27.8402i	−0.656746	+	1.13752i	0.324706	+	0.945815i	$0.394734\pi$
$599$	−16.0735	+	27.8402i	−0.656746	+	1.13752i	−0.981453	+	0.191703i	$0.938599\pi$
$600$		0			0
$601$	11.0940	−	19.2154i	0.452534	−	0.783812i	−0.546009	−	0.837780i	$-0.683853\pi$
$601$	11.0940	−	19.2154i	0.452534	−	0.783812i	0.998543	+	0.0539675i	$0.0171867\pi$
$602$		0			0
$603$	−12.3453	−	30.1089i	−0.502740	−	1.22613i
$604$		0			0
$605$	−5.39870			−0.219488
$606$		0			0
$607$	−12.9704	−	22.4654i	−0.526452	−	0.911842i	−0.999525	−	0.0308188i	$-0.990189\pi$
$607$	−12.9704	−	22.4654i	−0.526452	−	0.911842i	0.473073	−	0.881023i	$-0.343145\pi$
$608$		0			0
$609$	−7.17787	−	14.6212i	−0.290862	−	0.592483i
$610$		0			0
$611$	31.1549	+	3.30833i	1.26039	+	0.133841i
$612$		0			0
$613$	10.0170	+	17.3500i	0.404584	+	0.700760i	0.994273	−	0.106871i	$-0.0340831\pi$
$613$	10.0170	+	17.3500i	0.404584	+	0.700760i	−0.589689	+	0.807630i	$0.700750\pi$
$614$		0			0
$615$	−1.13740	−	2.31687i	−0.0458644	−	0.0934254i
$616$		0			0
$617$	−7.64802	−	13.2468i	−0.307898	−	0.533294i	0.670005	−	0.742357i	$-0.266292\pi$
$617$	−7.64802	−	13.2468i	−0.307898	−	0.533294i	−0.977902	+	0.209063i	$0.932959\pi$
$618$		0			0
$619$	−8.72206	−	15.1071i	−0.350569	−	0.607204i	0.635780	−	0.771870i	$-0.280679\pi$
$619$	−8.72206	−	15.1071i	−0.350569	−	0.607204i	−0.986349	+	0.164666i	$0.947345\pi$
$620$		0			0
$621$	12.5119	+	2.55874i	0.502086	+	0.102679i
$622$		0			0
$623$	−0.405732	−	0.702749i	−0.0162553	−	0.0281550i
$624$		0			0
$625$	−6.29088	+	10.8961i	−0.251635	+	0.435845i
$626$		0			0
$627$	−25.4384	−	1.71309i	−1.01591	−	0.0684141i
$628$		0			0
$629$	27.4059			1.09275
$630$		0			0
$631$	7.16539	−	12.4108i	0.285250	−	0.494067i	−0.687420	−	0.726260i	$-0.741257\pi$
$631$	7.16539	−	12.4108i	0.285250	−	0.494067i	0.972670	+	0.232193i	$0.0745901\pi$
$632$		0			0
$633$	−7.15731	+	10.6703i	−0.284478	+	0.424105i
$634$		0			0
$635$	−12.0778			−0.479293
$636$		0			0
$637$	−13.1486	+	18.0567i	−0.520966	+	0.715432i
$638$		0			0
$639$	−12.7809	−	1.72924i	−0.505605	−	0.0684076i
$640$		0			0
$641$	18.5729			0.733587			0.366794	−	0.930302i	$-0.380455\pi$
$641$	18.5729			0.733587			0.366794	+	0.930302i	$0.380455\pi$
$642$		0			0
$643$	−5.04733	−	8.74224i	−0.199047	−	0.344760i	0.749172	−	0.662375i	$-0.230451\pi$
$643$	−5.04733	−	8.74224i	−0.199047	−	0.344760i	−0.948220	+	0.317615i	$0.897118\pi$
$644$		0			0
$645$	−2.94770	−	6.00444i	−0.116066	−	0.236425i
$646$		0			0
$647$	1.75145	+	3.03361i	0.0688567	+	0.119263i	0.898398	−	0.439182i	$-0.144732\pi$
$647$	1.75145	+	3.03361i	0.0688567	+	0.119263i	−0.829542	+	0.558445i	$0.811398\pi$
$648$		0			0
$649$	27.7590			1.08964
$650$		0			0
$651$	4.84507	+	9.86936i	0.189893	+	0.386811i
$652$		0			0
$653$	−7.00545			−0.274145			−0.137072	−	0.990561i	$-0.543769\pi$
$653$	−7.00545			−0.274145			−0.137072	+	0.990561i	$0.543769\pi$
$654$		0			0
$655$	3.67554	+	6.36622i	0.143615	+	0.248749i
$656$		0			0
$657$	−7.87285	−	19.2010i	−0.307149	−	0.749103i
$658$		0			0
$659$	7.38173			0.287551			0.143776	−	0.989610i	$-0.454076\pi$
$659$	7.38173			0.287551			0.143776	+	0.989610i	$0.454076\pi$
$660$		0			0
$661$	−13.3745			−0.520208			−0.260104	−	0.965581i	$-0.583757\pi$
$661$	−13.3745			−0.520208			−0.260104	+	0.965581i	$0.583757\pi$
$662$		0			0
$663$	−29.7934	−	5.20735i	−1.15708	−	0.202237i
$664$		0			0
$665$	−2.70436	−	4.68408i	−0.104870	−	0.181641i
$666$		0			0
$667$	12.8809	−	22.3103i	0.498750	−	0.863860i
$668$		0			0
$669$	−2.26652	−	4.61687i	−0.0876287	−	0.178499i
$670$		0			0
$671$	8.50229	−	14.7264i	0.328227	−	0.568506i
$672$		0			0
$673$	3.75544	−	6.50462i	0.144762	−	0.250735i	−0.784522	−	0.620101i	$-0.787092\pi$
$673$	3.75544	−	6.50462i	0.144762	−	0.250735i	0.929284	+	0.369366i	$0.120425\pi$
$674$		0			0
$675$	−6.77331	−	20.3114i	−0.260705	−	0.781788i
$676$		0			0
$677$	−12.0939	−	20.9473i	−0.464808	−	0.805071i	0.534385	−	0.845241i	$-0.320543\pi$
$677$	−12.0939	−	20.9473i	−0.464808	−	0.805071i	−0.999193	+	0.0401706i	$0.987210\pi$
$678$		0			0
$679$	4.17799			0.160337
$680$		0			0
$681$	−7.92301	+	11.8118i	−0.303611	+	0.452628i
$682$		0			0
$683$	4.18641	−	7.25108i	0.160189	−	0.277455i	−0.774748	−	0.632271i	$-0.782123\pi$
$683$	4.18641	−	7.25108i	0.160189	−	0.277455i	0.934936	+	0.354816i	$0.115456\pi$
$684$		0			0
$685$	8.91296	−	15.4377i	0.340547	−	0.589844i
$686$		0			0
$687$	20.4252	+	41.6059i	0.779269	+	1.58736i
$688$		0			0
$689$	−20.7327	+	28.4718i	−0.789852	+	1.08469i
$690$		0			0
$691$	10.1039	−	17.5004i	0.384369	−	0.665746i	−0.607313	−	0.794463i	$-0.707753\pi$
$691$	10.1039	−	17.5004i	0.384369	−	0.665746i	0.991681	+	0.128717i	$0.0410859\pi$
$692$		0			0
$693$	6.10733	+	0.826312i	0.231998	+	0.0313890i
$694$		0			0
$695$	11.1814			0.424136
$696$		0			0
$697$	−3.84783	+	6.66464i	−0.145747	+	0.252441i
$698$		0			0
$699$	1.43429	−	2.13826i	0.0542497	−	0.0808764i
$700$		0			0
$701$	27.5279			1.03971			0.519856	−	0.854254i	$-0.325985\pi$
$701$	27.5279			1.03971			0.519856	+	0.854254i	$0.325985\pi$
$702$		0			0
$703$	36.3780			1.37202
$704$		0			0
$705$	−7.86240	+	11.7214i	−0.296115	+	0.441454i
$706$		0			0
$707$	2.79541	−	4.84180i	0.105132	−	0.182094i
$708$		0			0
$709$	1.78659			0.0670968			0.0335484	−	0.999437i	$-0.489319\pi$
$709$	1.78659			0.0670968			0.0335484	+	0.999437i	$0.489319\pi$
$710$		0			0
$711$	−12.1998	+	15.7817i	−0.457529	+	0.591862i
$712$		0			0
$713$	−8.69461	+	15.0595i	−0.325616	+	0.563983i
$714$		0			0
$715$	7.69905	+	0.817560i	0.287928	+	0.0305750i
$716$		0			0
$717$	−19.4739	−	39.6680i	−0.727265	−	1.48143i
$718$		0			0
$719$	−6.19105	+	10.7232i	−0.230887	+	0.399909i	−0.958069	−	0.286536i	$-0.907496\pi$
$719$	−6.19105	+	10.7232i	−0.230887	+	0.399909i	0.727182	+	0.686445i	$0.240830\pi$
$720$		0			0
$721$	0.931716	−	1.61378i	0.0346989	−	0.0601003i
$722$		0			0
$723$	20.3327	−	30.3123i	0.756181	−	1.12733i
$724$		0			0
$725$	−43.1909			−1.60407
$726$		0			0
$727$	−23.7662	−	41.1642i	−0.881439	−	1.52670i	−0.849742	−	0.527199i	$-0.823242\pi$
$727$	−23.7662	−	41.1642i	−0.881439	−	1.52670i	−0.0316971	−	0.999498i	$-0.510091\pi$
$728$		0			0
$729$	24.8323	+	10.5999i	0.919714	+	0.392590i
$730$		0			0
$731$	−9.97209	+	17.2722i	−0.368831	+	0.638834i
$732$		0			0
$733$	11.4300	−	19.7974i	0.422177	−	0.731232i	−0.573975	−	0.818873i	$-0.694599\pi$
$733$	11.4300	−	19.7974i	0.422177	−	0.731232i	0.996152	+	0.0876406i	$0.0279327\pi$
$734$		0			0
$735$	−4.43443	−	9.03288i	−0.163566	−	0.333183i
$736$		0			0
$737$	12.4189	−	21.5101i	0.457455	−	0.792336i
$738$		0			0
$739$	10.9525	+	18.9703i	0.402894	+	0.697833i	0.994074	−	0.108707i	$-0.0346710\pi$
$739$	10.9525	+	18.9703i	0.402894	+	0.697833i	−0.591180	+	0.806540i	$0.701338\pi$
$740$		0			0
$741$	−39.5471	−	6.91212i	−1.45280	−	0.253923i
$742$		0			0
$743$	−6.11940			−0.224499			−0.112249	−	0.993680i	$-0.535806\pi$
$743$	−6.11940			−0.224499			−0.112249	+	0.993680i	$0.535806\pi$
$744$		0			0
$745$	0.199712			0.00731687
$746$		0			0
$747$	3.12772	−	4.04603i	0.114437	−	0.148036i
$748$		0			0
$749$	1.95831	+	3.39188i	0.0715549	+	0.123937i
$750$		0			0
$751$	16.0538			0.585810			0.292905	−	0.956142i	$-0.405378\pi$
$751$	16.0538			0.585810			0.292905	+	0.956142i	$0.405378\pi$
$752$		0			0
$753$	−8.97074	−	18.2733i	−0.326912	−	0.665916i
$754$		0			0
$755$	−19.4219			−0.706836
$756$		0			0
$757$	14.6925	+	25.4481i	0.534008	+	0.924928i	0.999211	+	0.0397242i	$0.0126479\pi$
$757$	14.6925	+	25.4481i	0.534008	+	0.924928i	−0.465203	+	0.885204i	$0.654019\pi$
$758$		0			0
$759$	4.29557	+	8.75002i	0.155919	+	0.317606i
$760$		0			0
$761$	5.05541	+	8.75622i	0.183258	+	0.317413i	0.942988	−	0.332826i	$-0.108002\pi$
$761$	5.05541	+	8.75622i	0.183258	+	0.317413i	−0.759730	+	0.650239i	$0.774669\pi$
$762$		0			0
$763$	0.553515			0.0200386
$764$		0			0
$765$	8.33326	−	10.7799i	0.301290	−	0.389749i
$766$		0			0
$767$	43.4655	+	4.61559i	1.56945	+	0.166659i
$768$		0			0
$769$	48.7126			1.75662			0.878310	−	0.478092i	$-0.158671\pi$
$769$	48.7126			1.75662			0.878310	+	0.478092i	$0.158671\pi$
$770$		0			0
$771$	25.0084	−	37.2831i	0.900657	−	1.34272i
$772$		0			0
$773$	−1.21294	+	2.10087i	−0.0436264	+	0.0755631i	−0.887014	−	0.461742i	$-0.847224\pi$
$773$	−1.21294	+	2.10087i	−0.0436264	+	0.0755631i	0.843388	+	0.537306i	$0.180558\pi$
$774$		0			0
$775$	29.1539			1.04724
$776$		0			0
$777$	−8.77352	−	0.590830i	−0.314748	−	0.0211959i
$778$		0			0
$779$	−5.10752	+	8.84649i	−0.182996	+	0.316958i
$780$		0			0
$781$	−4.92205	−	8.52523i	−0.176125	−	0.305057i
$782$		0			0
$783$	36.1309	−	40.7555i	1.29121	−	1.45648i
$784$		0			0
$785$	−1.48814	−	2.57753i	−0.0531140	−	0.0919962i
$786$		0			0
$787$	9.55478	+	16.5494i	0.340591	+	0.589921i	0.984543	−	0.175145i	$-0.0560395\pi$
$787$	9.55478	+	16.5494i	0.340591	+	0.589921i	−0.643952	+	0.765066i	$0.722706\pi$
$788$		0			0
$789$	17.4033	+	35.4502i	0.619572	+	1.26206i
$790$		0			0
$791$	−5.24208	−	9.07954i	−0.186387	−	0.322831i
$792$		0			0
$793$	15.7616	−	21.6451i	0.559712	−	0.768641i
$794$		0			0
$795$	−6.99220	−	14.2430i	−0.247988	−	0.505148i
$796$		0			0
$797$	−13.5804	−	23.5220i	−0.481043	−	0.833191i	0.518720	−	0.854944i	$-0.326409\pi$
$797$	−13.5804	−	23.5220i	−0.481043	−	0.833191i	−0.999763	+	0.0217532i	$0.993075\pi$
$798$		0			0
$799$	42.0835			1.48881
$800$		0			0
$801$	1.65953	−	2.14677i	0.0586365	−	0.0758525i
$802$		0			0
$803$	7.91976	−	13.7174i	0.279482	−	0.484078i
$804$		0			0
$805$	−1.03392	+	1.79080i	−0.0364408	+	0.0631173i
$806$		0			0
$807$	−20.7269	−	42.2204i	−0.729620	−	1.48623i
$808$		0			0
$809$	24.4213	+	42.2990i	0.858609	+	1.48715i	0.873256	+	0.487261i	$0.162004\pi$
$809$	24.4213	+	42.2990i	0.858609	+	1.48715i	−0.0146479	+	0.999893i	$0.504663\pi$
$810$		0			0
$811$	39.4775			1.38624			0.693122	−	0.720821i	$-0.256235\pi$
$811$	39.4775			1.38624			0.693122	+	0.720821i	$0.256235\pi$
$812$		0			0
$813$	−38.7599	−	2.61019i	−1.35937	−	0.0915433i
$814$		0			0
$815$	1.10475	+	1.91349i	0.0386979	+	0.0670267i
$816$		0			0
$817$	−13.2367	+	22.9267i	−0.463094	+	0.802103i
$818$		0			0
$819$	9.42556	+	2.30934i	0.329356	+	0.0806949i
$820$		0			0
$821$	11.3028	−	19.5769i	0.394469	−	0.683240i	−0.598564	−	0.801075i	$-0.704262\pi$
$821$	11.3028	−	19.5769i	0.394469	−	0.683240i	0.993033	+	0.117835i	$0.0375952\pi$
$822$		0			0
$823$	5.99189	+	10.3783i	0.208864	+	0.361763i	0.951357	−	0.308091i	$-0.0996900\pi$
$823$	5.99189	+	10.3783i	0.208864	+	0.361763i	−0.742493	+	0.669854i	$0.766357\pi$
$824$		0			0
$825$	9.10360	−	13.5718i	0.316947	−	0.472510i
$826$		0			0
$827$	−46.1187			−1.60370			−0.801852	−	0.597523i	$-0.796152\pi$
$827$	−46.1187			−1.60370			−0.801852	+	0.597523i	$0.796152\pi$
$828$		0			0
$829$	−8.70889	−	15.0842i	−0.302472	−	0.523897i	0.674223	−	0.738528i	$-0.264479\pi$
$829$	−8.70889	−	15.0842i	−0.302472	−	0.523897i	−0.976695	+	0.214630i	$0.931145\pi$
$830$		0			0
$831$	−1.55193	+	2.31365i	−0.0538359	+	0.0802596i
$832$		0			0
$833$	−15.0017	+	25.9837i	−0.519778	+	0.900281i
$834$		0			0
$835$	−4.11068	+	7.11991i	−0.142256	+	0.246394i
$836$		0			0
$837$	−24.3884	+	27.5100i	−0.842986	+	0.950886i
$838$		0			0
$839$	−36.5799			−1.26288			−0.631439	−	0.775426i	$-0.717535\pi$
$839$	−36.5799			−1.26288			−0.631439	+	0.775426i	$0.717535\pi$
$840$		0			0
$841$	−40.4343	−	70.0343i	−1.39429	−	2.41498i
$842$		0			0
$843$	−29.1025	−	1.95983i	−1.00234	−	0.0675002i
$844$		0			0
$845$	11.9194	+	2.56030i	0.410038	+	0.0880769i
$846$		0			0
$847$	−2.58243	−	4.47290i	−0.0887333	−	0.153691i
$848$		0			0
$849$	−22.4972	+	33.5392i	−0.772102	+	1.15106i
$850$		0			0
$851$	−6.95395	−	12.0446i	−0.238378	−	0.412883i
$852$		0			0
$853$	17.8494	+	30.9160i	0.611150	+	1.05854i	0.991047	+	0.133514i	$0.0426262\pi$
$853$	17.8494	+	30.9160i	0.611150	+	1.05854i	−0.379897	+	0.925029i	$0.624040\pi$
$854$		0			0
$855$	11.0614	−	14.3090i	0.378291	−	0.489359i
$856$		0			0
$857$	7.40047	+	12.8180i	0.252795	+	0.437854i	0.964294	−	0.264833i	$-0.0853168\pi$
$857$	7.40047	+	12.8180i	0.252795	+	0.437854i	−0.711499	+	0.702687i	$0.751983\pi$
$858$		0			0
$859$	−12.5687	+	21.7697i	−0.428839	+	0.742771i	−0.996770	−	0.0803049i	$-0.974411\pi$
$859$	−12.5687	+	21.7697i	−0.428839	+	0.742771i	0.567931	+	0.823076i	$0.307744\pi$
$860$		0			0
$861$	1.37549	−	2.05061i	0.0468767	−	0.0698847i
$862$		0			0
$863$	−42.4676			−1.44561			−0.722807	−	0.691050i	$-0.757148\pi$
$863$	−42.4676			−1.44561			−0.722807	+	0.691050i	$0.757148\pi$
$864$		0			0
$865$	2.03446	−	3.52379i	0.0691738	−	0.119813i
$866$		0			0
$867$	−11.1560	−	0.751270i	−0.378877	−	0.0255145i
$868$		0			0
$869$	−15.2251			−0.516478
$870$		0			0
$871$	23.0223	−	31.6160i	0.780079	−	1.07127i
$872$		0			0
$873$	5.30005	+	12.9262i	0.179380	+	0.437487i
$874$		0			0
$875$	7.67359			0.259415
$876$		0			0
$877$	−17.0991	−	29.6166i	−0.577397	−	1.00008i	−0.995777	−	0.0918085i	$-0.970735\pi$
$877$	−17.0991	−	29.6166i	−0.577397	−	1.00008i	0.418380	−	0.908272i	$-0.362598\pi$
$878$		0			0
$879$	27.5898	+	1.85797i	0.930582	+	0.0626677i
$880$		0			0
$881$	11.5943	+	20.0819i	0.390621	+	0.676576i	0.992532	−	0.121988i	$-0.0389269\pi$
$881$	11.5943	+	20.0819i	0.390621	+	0.676576i	−0.601910	+	0.798564i	$0.705594\pi$
$882$		0			0
$883$	−32.2202			−1.08430			−0.542148	−	0.840283i	$-0.682389\pi$
$883$	−32.2202			−1.08430			−0.542148	+	0.840283i	$0.682389\pi$
$884$		0			0
$885$	−10.9692	+	16.3530i	−0.368725	+	0.549702i
$886$		0			0
$887$	3.13771			0.105354			0.0526769	−	0.998612i	$-0.483225\pi$
$887$	3.13771			0.105354			0.0526769	+	0.998612i	$0.483225\pi$
$888$		0			0
$889$	−5.77732	−	10.0066i	−0.193765	−	0.335611i
$890$		0			0
$891$	5.19103	+	19.9436i	0.173906	+	0.668137i
$892$		0			0
$893$	55.8607			1.86931
$894$		0			0
$895$	11.9848			0.400606
$896$		0			0
$897$	5.27117	+	14.4152i	0.175999	+	0.481308i
$898$		0			0
$899$	37.0807	+	64.2257i	1.23671	+	2.14205i
$900$		0			0
$901$	−23.6546	+	40.9710i	−0.788050	+	1.36494i
$902$		0			0
$903$	3.56475	−	5.31439i	0.118627	−	0.176852i
$904$		0			0
$905$	2.76941	−	4.79676i	0.0920583	−	0.159450i
$906$		0			0
$907$	−8.70436	+	15.0764i	−0.289023	+	0.500603i	−0.973577	−	0.228359i	$-0.926664\pi$
$907$	−8.70436	+	15.0764i	−0.289023	+	0.500603i	0.684553	+	0.728963i	$0.259997\pi$
$908$		0			0
$909$	18.5261	+	2.50656i	0.614473	+	0.0831373i
$910$		0			0
$911$	−26.1890	−	45.3606i	−0.867680	−	1.50286i	−0.864362	−	0.502870i	$-0.832277\pi$
$911$	−26.1890	−	45.3606i	−0.867680	−	1.50286i	−0.00331774	−	0.999994i	$-0.501056\pi$
$912$		0			0
$913$	3.90333			0.129181
$914$		0			0
$915$	5.31569	+	10.8280i	0.175731	+	0.357963i
$916$		0			0
$917$	−3.51633	+	6.09046i	−0.116119	+	0.201125i
$918$		0			0
$919$	−14.9366	+	25.8710i	−0.492713	+	0.853404i	−0.999965	−	0.00839378i	$-0.997328\pi$
$919$	−14.9366	+	25.8710i	−0.492713	+	0.853404i	0.507252	+	0.861798i	$0.330661\pi$
$920$		0			0
$921$	−30.3039	+	45.1777i	−0.998548	+	1.48865i
$922$		0			0
$923$	−6.28950	−	14.1674i	−0.207021	−	0.466324i
$924$		0			0
$925$	−11.6587	+	20.1934i	−0.383334	+	0.663954i
$926$		0			0
$927$	6.17479	+	0.835440i	0.202807	+	0.0274395i
$928$		0			0
$929$	42.1855			1.38406			0.692030	−	0.721869i	$-0.256717\pi$
$929$	42.1855			1.38406			0.692030	+	0.721869i	$0.256717\pi$
$930$		0			0
$931$	−19.9129	+	34.4901i	−0.652618	+	1.13037i
$932$		0			0
$933$	−3.31393	−	6.75044i	−0.108493	−	0.220999i
$934$		0			0
$935$	10.3997			0.340108
$936$		0			0
$937$	−1.90435			−0.0622125			−0.0311063	−	0.999516i	$-0.509903\pi$
$937$	−1.90435			−0.0622125			−0.0311063	+	0.999516i	$0.509903\pi$
$938$		0			0
$939$	42.0720	+	2.83323i	1.37297	+	0.0924590i
$940$		0			0
$941$	−14.7980	+	25.6309i	−0.482402	+	0.835545i	−0.999796	−	0.0202024i	$-0.993569\pi$
$941$	−14.7980	+	25.6309i	−0.482402	+	0.835545i	0.517394	+	0.855747i	$0.326902\pi$
$942$		0			0
$943$	3.90537			0.127176
$944$		0			0
$945$	−2.90014	+	3.27135i	−0.0943416	+	0.106417i
$946$		0			0
$947$	−6.05111	+	10.4808i	−0.196635	+	0.340581i	−0.947435	−	0.319948i	$-0.896335\pi$
$947$	−6.05111	+	10.4808i	−0.196635	+	0.340581i	0.750800	+	0.660529i	$0.229668\pi$
$948$		0			0
$949$	14.6817	−	20.1621i	0.476589	−	0.654490i
$950$		0			0
$951$	−57.6624	−	3.88312i	−1.86983	−	0.125919i
$952$		0			0
$953$	−1.75304	+	3.03636i	−0.0567866	+	0.0983572i	−0.893021	−	0.450015i	$-0.851419\pi$
$953$	−1.75304	+	3.03636i	−0.0567866	+	0.0983572i	0.836235	+	0.548372i	$0.184752\pi$
$954$		0			0
$955$	−10.9853	+	19.0272i	−0.355477	+	0.615704i
$956$		0			0
$957$	41.4773	+	2.79319i	1.34077	+	0.0902909i
$958$		0			0
$959$	17.0538			0.550696
$960$		0			0
$961$	−9.52956	−	16.5057i	−0.307405	−	0.532441i
$962$		0			0
$963$	−8.00987	+	10.3616i	−0.258114	+	0.333898i
$964$		0			0
$965$	−4.71434	+	8.16548i	−0.151760	+	0.262856i
$966$		0			0
$967$	−10.5692	+	18.3064i	−0.339883	+	0.588695i	−0.984410	−	0.175886i	$-0.943721\pi$
$967$	−10.5692	+	18.3064i	−0.339883	+	0.588695i	0.644527	+	0.764581i	$0.277054\pi$
$968$		0			0
$969$	−53.8043	−	3.62331i	−1.72844	−	0.116398i
$970$		0			0
$971$	18.9603	−	32.8402i	0.608464	−	1.05389i	−0.383029	−	0.923736i	$-0.625119\pi$
$971$	18.9603	−	32.8402i	0.608464	−	1.05389i	0.991494	−	0.130155i	$-0.0415475\pi$
$972$		0			0
$973$	5.34856	+	9.26398i	0.171467	+	0.296990i
$974$		0			0
$975$	16.5112	−	19.7373i	0.528782	−	0.632099i
$976$		0			0
$977$	−34.3816			−1.09997			−0.549983	−	0.835176i	$-0.685366\pi$
$977$	−34.3816			−1.09997			−0.549983	+	0.835176i	$0.685366\pi$
$978$		0			0
$979$	2.07106			0.0661913
$980$		0			0
$981$	0.702169	+	1.71251i	0.0224185	+	0.0546763i
$982$		0			0
$983$	−6.78481	−	11.7516i	−0.216402	−	0.374819i	0.737304	−	0.675562i	$-0.236099\pi$
$983$	−6.78481	−	11.7516i	−0.216402	−	0.374819i	−0.953705	+	0.300743i	$0.902765\pi$
$984$		0			0
$985$	−12.4910			−0.397996
$986$		0			0
$987$	−13.4723	−	0.907256i	−0.428827	−	0.0288783i
$988$		0			0
$989$	10.1212			0.321836
$990$		0			0
$991$	−9.73649	−	16.8641i	−0.309290	−	0.535706i	0.668917	−	0.743337i	$-0.266758\pi$
$991$	−9.73649	−	16.8641i	−0.309290	−	0.535706i	−0.978207	+	0.207631i	$0.933425\pi$
$992$		0			0
$993$	−17.9318	+	26.7331i	−0.569048	+	0.848348i
$994$		0			0
$995$	2.37453	+	4.11280i	0.0752776	+	0.130385i
$996$		0			0
$997$	−60.7212			−1.92306			−0.961530	−	0.274700i	$-0.911421\pi$
$997$	−60.7212			−1.92306			−0.961530	+	0.274700i	$0.911421\pi$
$998$		0			0
$999$	−9.30182	−	27.8938i	−0.294297	−	0.882520i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	468.2.k.a.445.10	yes	28
3.2	odd	2		1404.2.k.a.1225.9		28
9.2	odd	6		1404.2.j.a.289.9		28
9.7	even	3		468.2.j.a.133.1	✓	28
13.9	even	3		468.2.j.a.373.1	yes	28
39.35	odd	6		1404.2.j.a.685.9		28
117.61	even	3	inner	468.2.k.a.61.10	yes	28
117.74	odd	6		1404.2.k.a.1153.9		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.j.a.133.1	✓	28	9.7	even	3
468.2.j.a.373.1	yes	28	13.9	even	3
468.2.k.a.61.10	yes	28	117.61	even	3	inner
468.2.k.a.445.10	yes	28	1.1	even	1	trivial
1404.2.j.a.289.9		28	9.2	odd	6
1404.2.j.a.685.9		28	39.35	odd	6
1404.2.k.a.1153.9		28	117.74	odd	6
1404.2.k.a.1225.9		28	3.2	odd	2

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:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.964854 - 1.43842i) q^{3} +(-0.468893 + 0.812147i) q^{5} -0.897167 q^{7} +(-1.13811 - 2.77573i) q^{9} +(1.14490 - 1.98302i) q^{11} +(2.12242 - 2.91468i) q^{13} +(0.715797 + 1.45807i) q^{15} +(2.42154 - 4.19424i) q^{17} +(3.21430 - 5.56733i) q^{19} +(-0.865635 + 1.29050i) q^{21} -2.45776 q^{23} +(2.06028 + 3.56851i) q^{25} +(-5.09079 - 1.04109i) q^{27} +(-5.24091 + 9.07753i) q^{29} +(3.53762 - 6.12734i) q^{31} +(-1.74776 - 3.56017i) q^{33} +(0.420676 - 0.728632i) q^{35} +(2.82939 + 4.90064i) q^{37} +(-2.14471 - 5.86517i) q^{39} -1.58900 q^{41} -4.11807 q^{43} +(2.78796 + 0.377207i) q^{45} +(4.34470 + 7.52524i) q^{47} -6.19509 q^{49} +(-3.69665 - 7.53003i) q^{51} -9.76841 q^{53} +(1.07367 + 1.85965i) q^{55} +(-4.90684 - 9.99518i) q^{57} +(6.06148 + 10.4988i) q^{59} +7.42626 q^{61} +(1.02108 + 2.49030i) q^{63} +(1.37196 + 3.09039i) q^{65} +10.8472 q^{67} +(-2.37137 + 3.53529i) q^{69} +(2.14956 - 3.72315i) q^{71} +6.91745 q^{73} +(7.12088 + 0.479538i) q^{75} +(-1.02716 + 1.77910i) q^{77} +(-3.32457 - 5.75832i) q^{79} +(-6.40939 + 6.31820i) q^{81} +(0.852333 + 1.47628i) q^{83} +(2.27089 + 3.93330i) q^{85} +(8.00060 + 16.2971i) q^{87} +(0.452237 + 0.783298i) q^{89} +(-1.90416 + 2.61495i) q^{91} +(-5.40042 - 11.0006i) q^{93} +(3.01433 + 5.22097i) q^{95} -4.65687 q^{97} +(-6.80735 - 0.921024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{7} - 2 q^{9} - 4 q^{11} + q^{13} - 4 q^{15} - 8 q^{17} - q^{19} + 14 q^{21} + 8 q^{23} - 14 q^{25} - 13 q^{29} + 2 q^{31} - 25 q^{33} + 3 q^{35} - q^{37} - 3 q^{39} - 8 q^{41} - 4 q^{43}+ \cdots - 29 q^{99}+O(q^{100}) \) 28 * q - 4 * q^7 - 2 * q^9 - 4 * q^11 + q^13 - 4 * q^15 - 8 * q^17 - q^19 + 14 * q^21 + 8 * q^23 - 14 * q^25 - 13 * q^29 + 2 * q^31 - 25 * q^33 + 3 * q^35 - q^37 - 3 * q^39 - 8 * q^41 - 4 * q^43 - 38 * q^45 + 11 * q^47 + 24 * q^49 + 5 * q^51 + 52 * q^53 - q^57 - 8 * q^59 + 14 * q^61 - 21 * q^63 + 38 * q^65 + 14 * q^67 - 21 * q^69 - 12 * q^71 + 14 * q^73 - 14 * q^75 - 28 * q^77 + 5 * q^79 + 10 * q^81 + 9 * q^83 + 18 * q^85 + 18 * q^87 - 11 * q^89 - q^91 - 9 * q^93 + 28 * q^95 + 50 * q^97 - 29 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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