LMFDB - Embedded newform 864.2.bf.a.49.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(49,864)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 14]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("864.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bf (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.14
Character	$\chi$	$=$	864.49
Dual form			864.2.bf.a.529.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.375176 + 1.69093i) q^{3} +(0.429535 + 1.18014i) q^{5} +(0.899466 + 5.10113i) q^{7} +(-2.71849 - 1.26879i) q^{9} +O(q^{10})$	\(q+(-0.375176 + 1.69093i) q^{3} +(0.429535 + 1.18014i) q^{5} +(0.899466 + 5.10113i) q^{7} +(-2.71849 - 1.26879i) q^{9} +(-0.393815 + 1.08200i) q^{11} +(-1.99720 + 2.38017i) q^{13} +(-2.15668 + 0.283553i) q^{15} +(2.72750 - 4.72417i) q^{17} +(-3.50074 + 2.02115i) q^{19} +(-8.96310 - 0.392889i) q^{21} +(0.316107 - 1.79273i) q^{23} +(2.62200 - 2.20012i) q^{25} +(3.16535 - 4.12075i) q^{27} +(4.80401 + 5.72520i) q^{29} +(0.634441 - 3.59809i) q^{31} +(-1.68183 - 1.07185i) q^{33} +(-5.63367 + 3.25260i) q^{35} +(-7.09501 - 4.09630i) q^{37} +(-3.27539 - 4.27010i) q^{39} +(2.51525 + 2.11055i) q^{41} +(1.13402 - 3.11569i) q^{43} +(0.329667 - 3.75317i) q^{45} +(0.324072 + 1.83790i) q^{47} +(-18.6346 + 6.78244i) q^{49} +(6.96495 + 6.38441i) q^{51} +6.66321i q^{53} -1.44606 q^{55} +(-2.10423 - 6.67779i) q^{57} +(-0.492801 - 1.35396i) q^{59} +(8.70846 - 1.53554i) q^{61} +(4.02709 - 15.0086i) q^{63} +(-3.66678 - 1.33460i) q^{65} +(-6.80127 + 8.10544i) q^{67} +(2.91279 + 1.20711i) q^{69} +(0.0275657 - 0.0477451i) q^{71} +(-1.41872 - 2.45729i) q^{73} +(2.73653 + 5.25905i) q^{75} +(-5.87364 - 1.03568i) q^{77} +(-6.31005 + 5.29476i) q^{79} +(5.78032 + 6.89840i) q^{81} +(-4.61797 - 5.50348i) q^{83} +(6.74672 + 1.18963i) q^{85} +(-11.4833 + 5.97528i) q^{87} +(6.63574 + 11.4934i) q^{89} +(-13.9379 - 8.04707i) q^{91} +(5.84609 + 2.42271i) q^{93} +(-3.88892 - 3.26319i) q^{95} +(3.34396 + 1.21710i) q^{97} +(2.44342 - 2.44173i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 12 q^{7} - 12 q^{9}+O(q^{10}) $ 204 * q + 12 * q^7 - 12 * q^9	$ 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73} + 12 q^{79} - 12 q^{81} + 48 q^{87} - 6 q^{89} + 42 q^{95} - 12 q^{97}+O(q^{100}) $ 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$	$1$

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
$3$	−0.375176	+	1.69093i	−0.216608	+	0.976259i
$3$	−0.375176	+	1.69093i	−0.216608	+	0.976259i
$4$		0			0
$5$	0.429535	+	1.18014i	0.192094	+	0.527773i	0.997926	−	0.0643707i	$-0.0205040\pi$
$5$	0.429535	+	1.18014i	0.192094	+	0.527773i	−0.805832	+	0.592144i	$0.798282\pi$
$6$		0			0
$7$	0.899466	+	5.10113i	0.339966	+	1.92804i	0.371248	+	0.928534i	$0.378930\pi$
$7$	0.899466	+	5.10113i	0.339966	+	1.92804i	−0.0312816	+	0.999511i	$0.509959\pi$
$8$		0			0
$9$	−2.71849	−	1.26879i	−0.906162	−	0.422931i
$10$		0			0
$11$	−0.393815	+	1.08200i	−0.118740	+	0.326235i	−0.984797	−	0.173710i	$-0.944424\pi$
$11$	−0.393815	+	1.08200i	−0.118740	+	0.326235i	0.866057	+	0.499945i	$0.166647\pi$
$12$		0			0
$13$	−1.99720	+	2.38017i	−0.553922	+	0.660139i	−0.968249	−	0.249989i	$-0.919573\pi$
$13$	−1.99720	+	2.38017i	−0.553922	+	0.660139i	0.414326	+	0.910129i	$0.364017\pi$
$14$		0			0
$15$	−2.15668	+	0.283553i	−0.556852	+	0.0732131i
$16$		0			0
$17$	2.72750	−	4.72417i	0.661517	−	1.14578i	−0.318701	−	0.947855i	$-0.603246\pi$
$17$	2.72750	−	4.72417i	0.661517	−	1.14578i	0.980217	−	0.197925i	$-0.0634202\pi$
$18$		0			0
$19$	−3.50074	+	2.02115i	−0.803124	+	0.463684i	−0.844562	−	0.535457i	$-0.820139\pi$
$19$	−3.50074	+	2.02115i	−0.803124	+	0.463684i	0.0414383	+	0.999141i	$0.486806\pi$
$20$		0			0
$21$	−8.96310	−	0.392889i	−1.95591	−	0.0857353i
$22$		0			0
$23$	0.316107	−	1.79273i	0.0659129	−	0.373811i	−0.933952	−	0.357397i	$-0.883664\pi$
$23$	0.316107	−	1.79273i	0.0659129	−	0.373811i	0.999865	−	0.0164132i	$-0.00522472\pi$
$24$		0			0
$25$	2.62200	−	2.20012i	0.524400	−	0.440024i
$26$		0			0
$27$	3.16535	−	4.12075i	0.609172	−	0.793038i
$28$		0			0
$29$	4.80401	+	5.72520i	0.892082	+	1.06314i	0.997635	+	0.0687286i	$0.0218943\pi$
$29$	4.80401	+	5.72520i	0.892082	+	1.06314i	−0.105553	+	0.994414i	$0.533661\pi$
$30$		0			0
$31$	0.634441	−	3.59809i	0.113949	−	0.646236i	−0.873316	−	0.487154i	$-0.838035\pi$
$31$	0.634441	−	3.59809i	0.113949	−	0.646236i	0.987265	−	0.159083i	$-0.0508537\pi$
$32$		0			0
$33$	−1.68183	−	1.07185i	−0.292770	−	0.186586i
$34$		0			0
$35$	−5.63367	+	3.25260i	−0.952264	+	0.549790i
$36$		0			0
$37$	−7.09501	−	4.09630i	−1.16641	−	0.673428i	−0.213579	−	0.976926i	$-0.568512\pi$
$37$	−7.09501	−	4.09630i	−1.16641	−	0.673428i	−0.952832	+	0.303498i	$0.901846\pi$
$38$		0			0
$39$	−3.27539	−	4.27010i	−0.524482	−	0.683763i
$40$		0			0
$41$	2.51525	+	2.11055i	0.392816	+	0.329612i	0.817709	−	0.575632i	$-0.195244\pi$
$41$	2.51525	+	2.11055i	0.392816	+	0.329612i	−0.424893	+	0.905244i	$0.639688\pi$
$42$		0			0
$43$	1.13402	−	3.11569i	0.172936	−	0.475139i	−0.822698	−	0.568479i	$-0.807532\pi$
$43$	1.13402	−	3.11569i	0.172936	−	0.475139i	0.995634	+	0.0933400i	$0.0297543\pi$
$44$		0			0
$45$	0.329667	−	3.75317i	0.0491438	−	0.559490i
$46$		0			0
$47$	0.324072	+	1.83790i	0.0472707	+	0.268086i	0.999278	−	0.0379894i	$-0.0120953\pi$
$47$	0.324072	+	1.83790i	0.0472707	+	0.268086i	−0.952007	+	0.306075i	$0.900984\pi$
$48$		0			0
$49$	−18.6346	+	6.78244i	−2.66209	+	0.968920i
$50$		0			0
$51$	6.96495	+	6.38441i	0.975288	+	0.893997i
$52$		0			0
$53$			6.66321i			0.915262i	0.889142	+	0.457631i	$0.151302\pi$
$53$			6.66321i			0.915262i	−0.889142	+	0.457631i	$0.848698\pi$
$54$		0			0
$55$	−1.44606			−0.194987
$56$		0			0
$57$	−2.10423	−	6.67779i	−0.278712	−	0.884495i
$58$		0			0
$59$	−0.492801	−	1.35396i	−0.0641572	−	0.176270i	0.903472	−	0.428648i	$-0.141010\pi$
$59$	−0.492801	−	1.35396i	−0.0641572	−	0.176270i	−0.967629	+	0.252377i	$0.918788\pi$
$60$		0			0
$61$	8.70846	−	1.53554i	1.11500	−	0.196605i	0.414357	−	0.910114i	$-0.364006\pi$
$61$	8.70846	−	1.53554i	1.11500	−	0.196605i	0.700646	+	0.713509i	$0.252895\pi$
$62$		0			0
$63$	4.02709	−	15.0086i	0.507366	−	1.89090i
$64$		0			0
$65$	−3.66678	−	1.33460i	−0.454809	−	0.165537i
$66$		0			0
$67$	−6.80127	+	8.10544i	−0.830907	+	0.990237i	0.169082	+	0.985602i	$0.445920\pi$
$67$	−6.80127	+	8.10544i	−0.830907	+	0.990237i	−0.999989	+	0.00463493i	$0.998525\pi$
$68$		0			0
$69$	2.91279	+	1.20711i	0.350659	+	0.145318i
$70$		0			0
$71$	0.0275657	−	0.0477451i	0.00327144	−	0.00566631i	−0.864385	−	0.502830i	$-0.832292\pi$
$71$	0.0275657	−	0.0477451i	0.00327144	−	0.00566631i	0.867656	+	0.497164i	$0.165625\pi$
$72$		0			0
$73$	−1.41872	−	2.45729i	−0.166048	−	0.287604i	0.770979	−	0.636861i	$-0.219767\pi$
$73$	−1.41872	−	2.45729i	−0.166048	−	0.287604i	−0.937027	+	0.349257i	$0.886434\pi$
$74$		0			0
$75$	2.73653	+	5.25905i	0.315988	+	0.607263i
$76$		0			0
$77$	−5.87364	−	1.03568i	−0.669363	−	0.118027i
$78$		0			0
$79$	−6.31005	+	5.29476i	−0.709937	+	0.595707i	−0.924581	−	0.380985i	$-0.875585\pi$
$79$	−6.31005	+	5.29476i	−0.709937	+	0.595707i	0.214645	+	0.976692i	$0.431141\pi$
$80$		0			0
$81$	5.78032	+	6.89840i	0.642258	+	0.766488i
$82$		0			0
$83$	−4.61797	−	5.50348i	−0.506888	−	0.604085i	0.450541	−	0.892756i	$-0.351231\pi$
$83$	−4.61797	−	5.50348i	−0.506888	−	0.604085i	−0.957428	+	0.288671i	$0.906787\pi$
$84$		0			0
$85$	6.74672	+	1.18963i	0.731785	+	0.129033i
$86$		0			0
$87$	−11.4833	+	5.97528i	−1.23113	+	0.640618i
$88$		0			0
$89$	6.63574	+	11.4934i	0.703387	+	1.21830i	0.967271	+	0.253747i	$0.0816631\pi$
$89$	6.63574	+	11.4934i	0.703387	+	1.21830i	−0.263884	+	0.964554i	$0.585004\pi$
$90$		0			0
$91$	−13.9379	−	8.04707i	−1.46109	−	0.843562i
$92$		0			0
$93$	5.84609	+	2.42271i	0.606212	+	0.251224i
$94$		0			0
$95$	−3.88892	−	3.26319i	−0.398995	−	0.334796i
$96$		0			0
$97$	3.34396	+	1.21710i	0.339528	+	0.123578i	0.506156	−	0.862442i	$-0.331066\pi$
$97$	3.34396	+	1.21710i	0.339528	+	0.123578i	−0.166629	+	0.986020i	$0.553288\pi$
$98$		0			0
$99$	2.44342	−	2.44173i	0.245572	−	0.245403i
$100$		0			0
$101$	−11.3385	+	1.99929i	−1.12823	+	0.198937i	−0.706450	−	0.707762i	$-0.749705\pi$
$101$	−11.3385	+	1.99929i	−1.12823	+	0.198937i	−0.421777	+	0.906699i	$0.638594\pi$
$102$		0			0
$103$	−7.62136	+	2.77395i	−0.750955	+	0.273325i	−0.689008	−	0.724754i	$-0.741953\pi$
$103$	−7.62136	+	2.77395i	−0.750955	+	0.273325i	−0.0619475	+	0.998079i	$0.519731\pi$
$104$		0			0
$105$	−3.38630	−	10.7464i	−0.330469	−	1.04875i
$106$		0			0
$107$		−	1.34799i		−	0.130315i	−0.997875	−	0.0651575i	$-0.979245\pi$
$107$		−	1.34799i		−	0.130315i	0.997875	−	0.0651575i	$-0.0207550\pi$
$108$		0			0
$109$		−	4.50754i		−	0.431744i	−0.976422	−	0.215872i	$-0.930741\pi$
$109$		−	4.50754i		−	0.431744i	0.976422	−	0.215872i	$-0.0692594\pi$
$110$		0			0
$111$	9.58844	−	10.4603i	0.910094	−	0.992849i
$112$		0			0
$113$	14.9764	−	5.45097i	1.40886	−	0.512784i	0.478067	−	0.878323i	$-0.341337\pi$
$113$	14.9764	−	5.45097i	1.40886	−	0.512784i	0.930796	+	0.365539i	$0.119115\pi$
$114$		0			0
$115$	2.25145	−	0.396991i	0.209949	−	0.0370196i
$116$		0			0
$117$	8.44929	−	3.93641i	0.781137	−	0.363922i
$118$		0			0
$119$	26.5519	+	9.66410i	2.43401	+	0.885907i
$120$		0			0
$121$	7.41086	+	6.21845i	0.673714	+	0.565313i
$122$		0			0
$123$	−4.51245	+	3.46129i	−0.406874	+	0.312094i
$124$		0			0
$125$	9.16078	+	5.28898i	0.819365	+	0.473061i
$126$		0			0
$127$	−0.0774993	−	0.134233i	−0.00687695	−	0.0119112i	0.862566	−	0.505944i	$-0.168856\pi$
$127$	−0.0774993	−	0.134233i	−0.00687695	−	0.0119112i	−0.869443	+	0.494033i	$0.835522\pi$
$128$		0			0
$129$	4.84296	+	3.08648i	0.426399	+	0.271750i
$130$		0			0
$131$	10.6508	+	1.87802i	0.930562	+	0.164083i	0.618326	−	0.785922i	$-0.287811\pi$
$131$	10.6508	+	1.87802i	0.930562	+	0.164083i	0.312236	+	0.950005i	$0.398922\pi$
$132$		0			0
$133$	−13.4589	−	16.0397i	−1.16704	−	1.39082i
$134$		0			0
$135$	6.22267	+	1.96555i	0.535562	+	0.169167i
$136$		0			0
$137$	0.120739	−	0.101312i	0.0103155	−	0.00865569i	−0.637615	−	0.770355i	$-0.720079\pi$
$137$	0.120739	−	0.101312i	0.0103155	−	0.00865569i	0.647931	+	0.761699i	$0.275635\pi$
$138$		0			0
$139$	9.51228	+	1.67727i	0.806821	+	0.142264i	0.561821	−	0.827259i	$-0.310101\pi$
$139$	9.51228	+	1.67727i	0.806821	+	0.142264i	0.245000	+	0.969523i	$0.421212\pi$
$140$		0			0
$141$	−3.22935	−	0.141555i	−0.271960	−	0.0119211i
$142$		0			0
$143$	−1.78881	−	3.09831i	−0.149588	−	0.259094i
$144$		0			0
$145$	−4.69302	+	8.12856i	−0.389734	+	0.675040i
$146$		0			0
$147$	−4.47736	−	34.0544i	−0.369287	−	2.80876i
$148$		0			0
$149$	−3.75096	+	4.47021i	−0.307290	+	0.366214i	−0.897484	−	0.441048i	$-0.854607\pi$
$149$	−3.75096	+	4.47021i	−0.307290	+	0.366214i	0.590193	+	0.807262i	$0.299051\pi$
$150$		0			0
$151$	3.45565	+	1.25775i	0.281217	+	0.102354i	0.478778	−	0.877936i	$-0.341080\pi$
$151$	3.45565	+	1.25775i	0.281217	+	0.102354i	−0.197561	+	0.980291i	$0.563302\pi$
$152$		0			0
$153$	−13.4087	+	9.38196i	−1.08403	+	0.758486i
$154$		0			0
$155$	4.51875	−	0.796778i	0.362955	−	0.0639988i
$156$		0			0
$157$	0.360618	+	0.990790i	0.0287804	+	0.0790736i	0.953251	−	0.302180i	$-0.0977145\pi$
$157$	0.360618	+	0.990790i	0.0287804	+	0.0790736i	−0.924470	+	0.381254i	$0.875492\pi$
$158$		0			0
$159$	−11.2670	−	2.49988i	−0.893532	−	0.198253i
$160$		0			0
$161$	9.42928			0.743132
$162$		0			0
$163$			14.1215i			1.10608i	0.833154	+	0.553041i	$0.186533\pi$
$163$			14.1215i			1.10608i	−0.833154	+	0.553041i	$0.813467\pi$
$164$		0			0
$165$	0.542529	−	2.44519i	0.0422358	−	0.190358i
$166$		0			0
$167$	−7.55405	+	2.74945i	−0.584550	+	0.212759i	−0.617331	−	0.786704i	$-0.711786\pi$
$167$	−7.55405	+	2.74945i	−0.584550	+	0.212759i	0.0327807	+	0.999463i	$0.489564\pi$
$168$		0			0
$169$	0.581030	+	3.29519i	0.0446946	+	0.253476i
$170$		0			0
$171$	12.0811	−	1.05276i	0.923867	−	0.0805063i
$172$		0			0
$173$	4.47832	−	12.3041i	0.340480	−	0.935462i	−0.644775	−	0.764372i	$-0.723049\pi$
$173$	4.47832	−	12.3041i	0.340480	−	0.935462i	0.985255	−	0.171090i	$-0.0547289\pi$
$174$		0			0
$175$	13.5815	+	11.3962i	1.02666	+	0.861473i
$176$		0			0
$177$	2.47434	−	0.325318i	0.185982	−	0.0244524i
$178$		0			0
$179$	19.5431	+	11.2832i	1.46072	+	0.843345i	0.999044	−	0.0437059i	$-0.0139165\pi$
$179$	19.5431	+	11.2832i	1.46072	+	0.843345i	0.461672	+	0.887051i	$0.347250\pi$
$180$		0			0
$181$	−3.30401	+	1.90757i	−0.245585	+	0.141789i	−0.617741	−	0.786382i	$-0.711952\pi$
$181$	−3.30401	+	1.90757i	−0.245585	+	0.141789i	0.372156	+	0.928170i	$0.378619\pi$
$182$		0			0
$183$	−0.670725	+	15.3015i	−0.0495814	+	1.13112i
$184$		0			0
$185$	1.78665	−	10.1326i	0.131357	−	0.744962i
$186$		0			0
$187$	4.03742	+	4.81161i	0.295245	+	0.351860i
$188$		0			0
$189$	23.8676	+	12.4404i	1.73611	+	0.904905i
$190$		0			0
$191$	14.0367	−	11.7782i	1.01566	−	0.852243i	0.0265869	−	0.999647i	$-0.491536\pi$
$191$	14.0367	−	11.7782i	1.01566	−	0.852243i	0.989076	+	0.147404i	$0.0470917\pi$
$192$		0			0
$193$	−1.62021	+	9.18865i	−0.116625	+	0.661413i	0.869308	+	0.494271i	$0.164565\pi$
$193$	−1.62021	+	9.18865i	−0.116625	+	0.661413i	−0.985933	+	0.167142i	$0.946546\pi$
$194$		0			0
$195$	3.63241	−	5.69956i	0.260122	−	0.408154i
$196$		0			0
$197$	18.6029	−	10.7404i	1.32540	−	0.765219i	0.340815	−	0.940131i	$-0.389297\pi$
$197$	18.6029	−	10.7404i	1.32540	−	0.765219i	0.984584	+	0.174911i	$0.0559638\pi$
$198$		0			0
$199$	−5.96591	+	10.3333i	−0.422912	+	0.732506i	−0.996223	−	0.0868324i	$-0.972326\pi$
$199$	−5.96591	+	10.3333i	−0.422912	+	0.732506i	0.573311	+	0.819338i	$0.305659\pi$
$200$		0			0
$201$	−11.1540	−	14.5414i	−0.786746	−	1.02567i
$202$		0			0
$203$	−24.8839	+	29.6555i	−1.74651	+	2.08141i
$204$		0			0
$205$	−1.41035	+	3.87489i	−0.0985028	+	0.270634i
$206$		0			0
$207$	−3.13394	+	4.47244i	−0.217824	+	0.310856i
$208$		0			0
$209$	−0.808239	−	4.58375i	−0.0559071	−	0.317065i
$210$		0			0
$211$	−4.67879	−	12.8549i	−0.322101	−	0.884966i	−0.990045	−	0.140754i	$-0.955047\pi$
$211$	−4.67879	−	12.8549i	−0.322101	−	0.884966i	0.667943	−	0.744212i	$-0.267175\pi$
$212$		0			0
$213$	0.0703917	+	0.0645245i	0.00482316	+	0.00442114i
$214$		0			0
$215$	4.16404			0.283985
$216$		0			0
$217$	18.9250			1.28471
$218$		0			0
$219$	4.68737	−	1.47703i	0.316743	−	0.0998086i
$220$		0			0
$221$	5.79696	+	15.9270i	0.389945	+	1.07137i
$222$		0			0
$223$	2.32829	+	13.2044i	0.155914	+	0.884230i	0.957946	+	0.286949i	$0.0926411\pi$
$223$	2.32829	+	13.2044i	0.155914	+	0.884230i	−0.802032	+	0.597281i	$0.796248\pi$
$224$		0			0
$225$	−9.91937	+	2.65421i	−0.661291	+	0.176948i
$226$		0			0
$227$	9.87640	−	27.1352i	0.655519	−	1.80102i	0.0592462	−	0.998243i	$-0.481130\pi$
$227$	9.87640	−	27.1352i	0.655519	−	1.80102i	0.596273	−	0.802782i	$-0.296647\pi$
$228$		0			0
$229$	−6.65085	+	7.92617i	−0.439501	+	0.523776i	−0.939638	−	0.342170i	$-0.888838\pi$
$229$	−6.65085	+	7.92617i	−0.439501	+	0.523776i	0.500138	+	0.865946i	$0.333283\pi$
$230$		0			0
$231$	3.95491	−	9.54334i	0.260214	−	0.627906i
$232$		0			0
$233$	−11.9218	+	20.6491i	−0.781022	+	1.35277i	0.150325	+	0.988637i	$0.451968\pi$
$233$	−11.9218	+	20.6491i	−0.781022	+	1.35277i	−0.931347	+	0.364133i	$0.881365\pi$
$234$		0			0
$235$	−2.02977	+	1.17189i	−0.132408	+	0.0764457i
$236$		0			0
$237$	−6.58569	−	12.6563i	−0.427786	−	0.822117i
$238$		0			0
$239$	0.0755846	−	0.428662i	0.00488916	−	0.0277278i	−0.982266	−	0.187495i	$-0.939963\pi$
$239$	0.0755846	−	0.428662i	0.00488916	−	0.0277278i	0.987155	+	0.159767i	$0.0510743\pi$
$240$		0			0
$241$	5.15245	−	4.32342i	0.331899	−	0.278496i	−0.461574	−	0.887102i	$-0.652715\pi$
$241$	5.15245	−	4.32342i	0.331899	−	0.278496i	0.793473	+	0.608606i	$0.208271\pi$
$242$		0			0
$243$	−13.8333	+	7.18600i	−0.887409	+	0.460982i
$244$		0			0
$245$	−16.0084	−	19.0781i	−1.02274	−	1.21885i
$246$		0			0
$247$	2.18098	−	12.3690i	0.138773	−	0.787019i
$248$		0			0
$249$	11.0385	−	5.74388i	0.699539	−	0.364004i
$250$		0			0
$251$	16.9187	−	9.76804i	1.06790	−	0.616553i	0.140294	−	0.990110i	$-0.455195\pi$
$251$	16.9187	−	9.76804i	1.06790	−	0.616553i	0.927607	+	0.373557i	$0.121862\pi$
$252$		0			0
$253$	1.81525	+	1.04803i	0.114124	+	0.0658893i
$254$		0			0
$255$	−4.54279	+	10.9619i	−0.284481	+	0.686462i
$256$		0			0
$257$	−23.6373	−	19.8341i	−1.47446	−	1.23722i	−0.911871	−	0.410476i	$-0.865362\pi$
$257$	−23.6373	−	19.8341i	−1.47446	−	1.23722i	−0.562585	−	0.826739i	$-0.690193\pi$
$258$		0			0
$259$	14.5140	−	39.8770i	0.901859	−	2.47784i
$260$		0			0
$261$	−5.79554	−	21.6592i	−0.358735	−	1.34067i
$262$		0			0
$263$	−0.890573	−	5.05069i	−0.0549151	−	0.311439i	0.944961	−	0.327183i	$-0.106099\pi$
$263$	−0.890573	−	5.05069i	−0.0549151	−	0.311439i	−0.999876	+	0.0157442i	$0.994988\pi$
$264$		0			0
$265$	−7.86349	+	2.86208i	−0.483050	+	0.175816i
$266$		0			0
$267$	−21.9242	+	6.90850i	−1.34174	+	0.422793i
$268$		0			0
$269$			0.181715i			0.0110793i	0.999985	+	0.00553967i	$0.00176334\pi$
$269$			0.181715i			0.0110793i	−0.999985	+	0.00553967i	$0.998237\pi$
$270$		0			0
$271$	−2.49169			−0.151359			−0.0756797	−	0.997132i	$-0.524113\pi$
$271$	−2.49169			−0.151359			−0.0756797	+	0.997132i	$0.524113\pi$
$272$		0			0
$273$	18.8362	−	20.5490i	1.14002	−	1.24368i
$274$		0			0
$275$	1.34794	+	3.70344i	0.0812840	+	0.223326i
$276$		0			0
$277$	−6.23597	+	1.09957i	−0.374683	+	0.0660668i	−0.357819	−	0.933791i	$-0.616479\pi$
$277$	−6.23597	+	1.09957i	−0.374683	+	0.0660668i	−0.0168644	+	0.999858i	$0.505368\pi$
$278$		0			0
$279$	−6.28996	+	8.97639i	−0.376570	+	0.537402i
$280$		0			0
$281$	18.5512	+	6.75208i	1.10667	+	0.402795i	0.829771	−	0.558103i	$-0.188471\pi$
$281$	18.5512	+	6.75208i	1.10667	+	0.402795i	0.276900	+	0.960899i	$0.410693\pi$
$282$		0			0
$283$	13.0163	−	15.5122i	0.773737	−	0.922104i	−0.224895	−	0.974383i	$-0.572204\pi$
$283$	13.0163	−	15.5122i	0.773737	−	0.922104i	0.998633	+	0.0522790i	$0.0166485\pi$
$284$		0			0
$285$	6.97686	−	5.35162i	0.413274	−	0.317003i
$286$		0			0
$287$	−8.50378	+	14.7290i	−0.501962	+	0.869424i
$288$		0			0
$289$	−6.37854	−	11.0480i	−0.375208	−	0.649880i
$290$		0			0
$291$	−3.31261	+	5.19778i	−0.194189	+	0.304699i
$292$		0			0
$293$	−31.4774	−	5.55032i	−1.83893	−	0.324253i	−0.857268	−	0.514871i	$-0.827840\pi$
$293$	−31.4774	−	5.55032i	−1.83893	−	0.324253i	−0.981664	+	0.190618i	$0.938951\pi$
$294$		0			0
$295$	1.38618	−	1.16314i	0.0807066	−	0.0677209i
$296$		0			0
$297$	3.21208	+	5.04772i	0.186384	+	0.292899i
$298$		0			0
$299$	3.63567	+	4.33283i	0.210256	+	0.250574i
$300$		0			0
$301$	16.9136	+	2.98232i	0.974881	+	0.171898i
$302$		0			0
$303$	0.873295	−	19.9228i	0.0501695	−	1.14453i
$304$		0			0
$305$	5.55272	+	9.61760i	0.317948	+	0.550702i
$306$		0			0
$307$	5.52956	+	3.19249i	0.315589	+	0.182205i	0.649425	−	0.760426i	$-0.275010\pi$
$307$	5.52956	+	3.19249i	0.315589	+	0.182205i	−0.333836	+	0.942631i	$0.608343\pi$
$308$		0			0
$309$	−1.83120	−	13.9279i	−0.104173	−	0.792331i
$310$		0			0
$311$	13.6918	+	11.4888i	0.776389	+	0.651468i	0.942337	−	0.334667i	$-0.108624\pi$
$311$	13.6918	+	11.4888i	0.776389	+	0.651468i	−0.165947	+	0.986135i	$0.553068\pi$
$312$		0			0
$313$	−3.95049	−	1.43786i	−0.223295	−	0.0812726i	0.227950	−	0.973673i	$-0.426798\pi$
$313$	−3.95049	−	1.43786i	−0.223295	−	0.0812726i	−0.451245	+	0.892400i	$0.649020\pi$
$314$		0			0
$315$	19.4419	−	1.69418i	1.09543	−	0.0954563i
$316$		0			0
$317$	19.2133	−	3.38782i	1.07913	−	0.190279i	0.394298	−	0.918983i	$-0.370988\pi$
$317$	19.2133	−	3.38782i	1.07913	−	0.190279i	0.684829	+	0.728704i	$0.259877\pi$
$318$		0			0
$319$	−8.08655	+	2.94326i	−0.452760	+	0.164791i
$320$		0			0
$321$	2.27935	+	0.505733i	0.127221	+	0.0282273i
$322$		0			0
$323$			22.0508i			1.22694i
$324$		0			0
$325$			10.6349i			0.589916i
$326$		0			0
$327$	7.62193	+	1.69112i	0.421494	+	0.0935193i
$328$		0			0
$329$	−9.08388	+	3.30626i	−0.500810	+	0.182280i
$330$		0			0
$331$	−12.2441	+	2.15896i	−0.672994	+	0.118667i	−0.499694	−	0.866202i	$-0.666554\pi$
$331$	−12.2441	+	2.15896i	−0.672994	+	0.118667i	−0.173300	+	0.984869i	$0.555443\pi$
$332$		0			0
$333$	14.0903	+	20.1378i	0.772144	+	1.10355i
$334$		0			0
$335$	−12.4869	−	4.54486i	−0.682232	−	0.248312i
$336$		0			0
$337$	−2.65326	−	2.22635i	−0.144532	−	0.121277i	0.567655	−	0.823267i	$-0.307851\pi$
$337$	−2.65326	−	2.22635i	−0.144532	−	0.121277i	−0.712187	+	0.701990i	$0.752295\pi$
$338$		0			0
$339$	3.59841	+	27.3692i	0.195439	+	1.48649i
$340$		0			0
$341$	3.64328	+	2.10345i	0.197295	+	0.113908i
$342$		0			0
$343$	−33.2299	−	57.5559i	−1.79425	−	3.10773i
$344$		0			0
$345$	−0.173406	+	3.95598i	−0.00933589	+	0.212983i
$346$		0			0
$347$	−13.6416	−	2.40538i	−0.732318	−	0.129127i	−0.204959	−	0.978770i	$-0.565706\pi$
$347$	−13.6416	−	2.40538i	−0.732318	−	0.129127i	−0.527358	+	0.849643i	$0.676817\pi$
$348$		0			0
$349$	−3.12849	−	3.72839i	−0.167464	−	0.199576i	0.675785	−	0.737099i	$-0.263805\pi$
$349$	−3.12849	−	3.72839i	−0.167464	−	0.199576i	−0.843249	+	0.537523i	$0.819360\pi$
$350$		0			0
$351$	3.48623	+	15.7640i	0.186081	+	0.841420i
$352$		0			0
$353$	0.191445	−	0.160642i	0.0101896	−	0.00855010i	−0.637679	−	0.770303i	$-0.720105\pi$
$353$	0.191445	−	0.160642i	0.0101896	−	0.00855010i	0.647868	+	0.761752i	$0.275661\pi$
$354$		0			0
$355$	0.0681862	+	0.0120231i	0.00361895	+	0.000638118i
$356$		0			0
$357$	−26.3030	+	41.2716i	−1.39210	+	2.18433i
$358$		0			0
$359$	−1.02024	−	1.76711i	−0.0538462	−	0.0932644i	0.837846	−	0.545907i	$-0.183815\pi$
$359$	−1.02024	−	1.76711i	−0.0538462	−	0.0932644i	−0.891692	+	0.452642i	$0.850481\pi$
$360$		0			0
$361$	−1.32990	+	2.30345i	−0.0699945	+	0.121234i
$362$		0			0
$363$	−13.2953	+	10.1982i	−0.697824	+	0.535268i
$364$		0			0
$365$	2.29055	−	2.72977i	0.119893	−	0.142883i
$366$		0			0
$367$	23.8292	+	8.67311i	1.24387	+	0.452733i	0.878327	−	0.478061i	$-0.158660\pi$
$367$	23.8292	+	8.67311i	1.24387	+	0.452733i	0.365546	+	0.930793i	$0.380882\pi$
$368$		0			0
$369$	−4.15982	−	8.92882i	−0.216552	−	0.464816i
$370$		0			0
$371$	−33.9898	+	5.99333i	−1.76467	+	0.311158i
$372$		0			0
$373$	8.36056	+	22.9705i	0.432893	+	1.18936i	0.944028	+	0.329864i	$0.107003\pi$
$373$	8.36056	+	22.9705i	0.432893	+	1.18936i	−0.511135	+	0.859501i	$0.670775\pi$
$374$		0			0
$375$	−12.3802	+	13.5059i	−0.639311	+	0.697443i
$376$		0			0
$377$	−23.2215			−1.19597
$378$		0			0
$379$		−	17.1052i		−	0.878636i	−0.898332	−	0.439318i	$-0.855220\pi$
$379$		−	17.1052i		−	0.878636i	0.898332	−	0.439318i	$-0.144780\pi$
$380$		0			0
$381$	0.256054	−	0.0806849i	0.0131180	−	0.00413361i
$382$		0			0
$383$	−25.7920	+	9.38754i	−1.31791	+	0.479681i	−0.902789	−	0.430084i	$-0.858484\pi$
$383$	−25.7920	+	9.38754i	−1.31791	+	0.479681i	−0.415123	+	0.909765i	$0.636262\pi$
$384$		0			0
$385$	−1.30069	−	7.37655i	−0.0662891	−	0.375944i
$386$		0			0
$387$	−7.03599	+	7.03113i	−0.357659	+	0.357412i
$388$		0			0
$389$	1.46875	−	4.03536i	0.0744687	−	0.204601i	−0.896873	−	0.442288i	$-0.854167\pi$
$389$	1.46875	−	4.03536i	0.0744687	−	0.204601i	0.971342	+	0.237687i	$0.0763892\pi$
$390$		0			0
$391$	−7.60700	−	6.38303i	−0.384702	−	0.322804i
$392$		0			0
$393$	−7.17151	+	17.3051i	−0.361755	+	0.872927i
$394$		0			0
$395$	−8.95893	−	5.17244i	−0.450773	−	0.260254i
$396$		0			0
$397$	−2.23509	+	1.29043i	−0.112176	+	0.0647647i	−0.555038	−	0.831825i	$-0.687296\pi$
$397$	−2.23509	+	1.29043i	−0.112176	+	0.0647647i	0.442862	+	0.896590i	$0.353963\pi$
$398$		0			0
$399$	32.1715	−	16.7404i	1.61059	−	0.838068i
$400$		0			0
$401$	−2.88825	+	16.3801i	−0.144232	+	0.817983i	0.823748	+	0.566956i	$0.191879\pi$
$401$	−2.88825	+	16.3801i	−0.144232	+	0.817983i	−0.967980	+	0.251026i	$0.919232\pi$
$402$		0			0
$403$	7.29695	+	8.69617i	0.363487	+	0.433187i
$404$		0			0
$405$	−5.65820	+	9.78467i	−0.281158	+	0.486204i
$406$		0			0
$407$	7.22632	−	6.06360i	0.358195	−	0.300562i
$408$		0			0
$409$	1.70985	−	9.69705i	0.0845467	−	0.479488i	−0.912907	−	0.408168i	$-0.866168\pi$
$409$	1.70985	−	9.69705i	0.0845467	−	0.479488i	0.997453	−	0.0713200i	$-0.0227212\pi$
$410$		0			0
$411$	0.126013	+	0.242172i	0.00621578	+	0.0119454i
$412$		0			0
$413$	6.46346	−	3.73168i	0.318046	−	0.183624i
$414$		0			0
$415$	4.51128	−	7.81376i	0.221450	−	0.383563i
$416$		0			0
$417$	−6.40493	+	15.4553i	−0.313651	+	0.756850i
$418$		0			0
$419$	−3.09972	+	3.69411i	−0.151431	+	0.180469i	−0.836427	−	0.548078i	$-0.815360\pi$
$419$	−3.09972	+	3.69411i	−0.151431	+	0.180469i	0.684996	+	0.728547i	$0.259804\pi$
$420$		0			0
$421$	−0.305504	+	0.839366i	−0.0148894	+	0.0409082i	−0.946915	−	0.321485i	$-0.895818\pi$
$421$	−0.305504	+	0.839366i	−0.0148894	+	0.0409082i	0.932025	+	0.362393i	$0.118040\pi$
$422$		0			0
$423$	1.45093	−	5.40749i	0.0705468	−	0.262921i
$424$		0			0
$425$	−3.24223	−	18.3876i	−0.157271	−	0.891930i
$426$		0			0
$427$	15.6659	+	43.0418i	0.758127	+	2.08294i
$428$		0			0
$429$	5.91014	−	1.86234i	0.285344	−	0.0899146i
$430$		0			0
$431$	−12.0811			−0.581925			−0.290963	−	0.956734i	$-0.593976\pi$
$431$	−12.0811			−0.581925			−0.290963	+	0.956734i	$0.593976\pi$
$432$		0			0
$433$	15.6536			0.752263			0.376131	−	0.926566i	$-0.377254\pi$
$433$	15.6536			0.752263			0.376131	+	0.926566i	$0.377254\pi$
$434$		0			0
$435$	−11.9841	−	10.9852i	−0.574594	−	0.526701i
$436$		0			0
$437$	2.51678	+	6.91479i	0.120394	+	0.330779i
$438$		0			0
$439$	−3.25553	−	18.4630i	−0.155378	−	0.881193i	−0.958439	−	0.285296i	$-0.907908\pi$
$439$	−3.25553	−	18.4630i	−0.155378	−	0.881193i	0.803061	−	0.595897i	$-0.203203\pi$
$440$		0			0
$441$	59.2634	+	5.20550i	2.82207	+	0.247881i
$442$		0			0
$443$	2.21970	−	6.09859i	0.105461	−	0.289753i	−0.875727	−	0.482807i	$-0.839617\pi$
$443$	2.21970	−	6.09859i	0.105461	−	0.289753i	0.981188	+	0.193054i	$0.0618394\pi$
$444$		0			0
$445$	−10.7135	+	12.7679i	−0.507870	+	0.605256i
$446$		0			0
$447$	−6.15155	−	8.01972i	−0.290958	−	0.379320i
$448$		0			0
$449$	−10.9120	+	18.9001i	−0.514968	+	0.891951i	0.484881	+	0.874580i	$0.338863\pi$
$449$	−10.9120	+	18.9001i	−0.514968	+	0.891951i	−0.999849	+	0.0173706i	$0.994470\pi$
$450$		0			0
$451$	−3.27415	+	1.89033i	−0.154174	+	0.0890123i
$452$		0			0
$453$	−3.42325	+	5.37138i	−0.160838	+	0.252369i
$454$		0			0
$455$	3.50982	−	19.9052i	0.164543	−	0.933168i
$456$		0			0
$457$	−10.6989	+	8.97747i	−0.500475	+	0.419948i	−0.857763	−	0.514046i	$-0.828146\pi$
$457$	−10.6989	+	8.97747i	−0.500475	+	0.419948i	0.357288	+	0.933994i	$0.383702\pi$
$458$		0			0
$459$	−10.8336	−	26.1930i	−0.505669	−	1.22259i
$460$		0			0
$461$	−3.60109	−	4.29162i	−0.167720	−	0.199881i	0.675637	−	0.737234i	$-0.263869\pi$
$461$	−3.60109	−	4.29162i	−0.167720	−	0.199881i	−0.843357	+	0.537354i	$0.819424\pi$
$462$		0			0
$463$	−4.63858	+	26.3067i	−0.215573	+	1.22258i	0.664336	+	0.747434i	$0.268714\pi$
$463$	−4.63858	+	26.3067i	−0.215573	+	1.22258i	−0.879909	+	0.475142i	$0.842397\pi$
$464$		0			0
$465$	−0.348034	+	7.93983i	−0.0161397	+	0.368201i
$466$		0			0
$467$	−5.21358	+	3.01006i	−0.241256	+	0.139289i	−0.615754	−	0.787939i	$-0.711148\pi$
$467$	−5.21358	+	3.01006i	−0.241256	+	0.139289i	0.374498	+	0.927228i	$0.377815\pi$
$468$		0			0
$469$	−47.4644	−	27.4036i	−2.19170	−	1.26538i
$470$		0			0
$471$	−1.81065	+	0.238059i	−0.0834304	+	0.0109692i
$472$		0			0
$473$	2.92458	+	2.45402i	0.134472	+	0.112836i
$474$		0			0
$475$	−4.73216	+	13.0015i	−0.217126	+	0.596550i
$476$		0			0
$477$	8.45423	−	18.1138i	0.387093	−	0.829375i
$478$		0			0
$479$	0.446183	+	2.53043i	0.0203866	+	0.115618i	0.993303	−	0.115540i	$-0.0368597\pi$
$479$	0.446183	+	2.53043i	0.0203866	+	0.115618i	−0.972916	+	0.231158i	$0.925749\pi$
$480$		0			0
$481$	23.9200	−	8.70617i	1.09066	−	0.396967i
$482$		0			0
$483$	−3.53765	+	15.9443i	−0.160968	+	0.725489i
$484$		0			0
$485$			4.46912i			0.202932i
$486$		0			0
$487$	36.7691			1.66617			0.833084	−	0.553147i	$-0.186573\pi$
$487$	36.7691			1.66617			0.833084	+	0.553147i	$0.186573\pi$
$488$		0			0
$489$	−23.8785	−	5.29806i	−1.07982	−	0.239586i
$490$		0			0
$491$	−5.32079	−	14.6188i	−0.240124	−	0.659735i	−0.999954	−	0.00961329i	$-0.996940\pi$
$491$	−5.32079	−	14.6188i	−0.240124	−	0.659735i	0.759830	−	0.650122i	$-0.225282\pi$
$492$		0			0
$493$	40.1498	−	7.07949i	1.80825	−	0.318844i
$494$		0			0
$495$	3.93110	+	1.83476i	0.176690	+	0.0824662i
$496$		0			0
$497$	0.268348	+	0.0976708i	0.0120371	+	0.00438113i
$498$		0			0
$499$	−24.8520	+	29.6175i	−1.11253	+	1.32586i	−0.172406	+	0.985026i	$0.555154\pi$
$499$	−24.8520	+	29.6175i	−1.11253	+	1.32586i	−0.940123	+	0.340834i	$0.889291\pi$
$500$		0			0
$501$	−1.81502	−	13.8049i	−0.0810893	−	0.616757i
$502$		0			0
$503$	11.2376	−	19.4640i	0.501058	−	0.867858i	−0.498941	−	0.866636i	$-0.666278\pi$
$503$	11.2376	−	19.4640i	0.501058	−	0.867858i	0.999999	−	0.00122205i	$-0.000388991\pi$
$504$		0			0
$505$	−7.22974	−	12.5223i	−0.321719	−	0.557234i
$506$		0			0
$507$	−5.78992	−	0.253795i	−0.257139	−	0.0112714i
$508$		0			0
$509$	−27.9666	−	4.93126i	−1.23960	−	0.218574i	−0.484854	−	0.874595i	$-0.661127\pi$
$509$	−27.9666	−	4.93126i	−1.23960	−	0.218574i	−0.754743	+	0.656021i	$0.772238\pi$
$510$		0			0
$511$	11.2588	−	9.44730i	0.498062	−	0.417924i
$512$		0			0
$513$	−2.75242	+	20.8233i	−0.121522	+	0.919371i
$514$		0			0
$515$	−6.54728	−	7.80274i	−0.288507	−	0.343830i
$516$		0			0
$517$	−2.11623	−	0.373149i	−0.0930718	−	0.0164111i
$518$		0			0
$519$	19.1252	+	12.1887i	0.839502	+	0.535026i
$520$		0			0
$521$	−15.3545	−	26.5947i	−0.672691	−	1.16513i	−0.977138	−	0.212605i	$-0.931805\pi$
$521$	−15.3545	−	26.5947i	−0.672691	−	1.16513i	0.304447	−	0.952529i	$-0.401528\pi$
$522$		0			0
$523$	−30.5786	−	17.6545i	−1.33711	−	0.771979i	−0.350729	−	0.936477i	$-0.614066\pi$
$523$	−30.5786	−	17.6545i	−1.33711	−	0.771979i	−0.986377	+	0.164498i	$0.947400\pi$
$524$		0			0
$525$	−24.3657	+	18.6897i	−1.06340	+	0.815687i
$526$		0			0
$527$	−15.2676	−	12.8110i	−0.665066	−	0.558056i
$528$		0			0
$529$	18.4990	+	6.73307i	0.804303	+	0.292742i
$530$		0			0
$531$	−0.378223	+	4.30598i	−0.0164135	+	0.186864i
$532$		0			0
$533$	−10.0469	+	1.77154i	−0.435180	+	0.0767339i
$534$		0			0
$535$	1.59081	−	0.579007i	0.0687767	−	0.0250327i
$536$		0			0
$537$	−26.4112	+	28.8127i	−1.13973	+	1.24336i
$538$		0			0
$539$		−	22.8336i		−	0.983515i
$540$		0			0
$541$			41.6495i			1.79065i	0.445411	+	0.895326i	$0.353058\pi$
$541$			41.6495i			1.79065i	−0.445411	+	0.895326i	$0.646942\pi$
$542$		0			0
$543$	−1.98598	−	6.30253i	−0.0852267	−	0.270467i
$544$		0			0
$545$	5.31951	−	1.93614i	0.227863	−	0.0829353i
$546$		0			0
$547$	12.9019	−	2.27495i	0.551644	−	0.0972697i	0.109124	−	0.994028i	$-0.465196\pi$
$547$	12.9019	−	2.27495i	0.551644	−	0.0972697i	0.442520	+	0.896758i	$0.354084\pi$
$548$		0			0
$549$	−25.6221	−	6.87490i	−1.09352	−	0.293414i
$550$		0			0
$551$	−28.3891	−	10.3328i	−1.20941	−	0.440191i
$552$		0			0
$553$	−32.6849	−	27.4259i	−1.38990	−	1.16627i
$554$		0			0
$555$	16.4632	+	6.82260i	0.698822	+	0.289603i
$556$		0			0
$557$	8.60943	+	4.97066i	0.364793	+	0.210613i	0.671181	−	0.741293i	$-0.265787\pi$
$557$	8.60943	+	4.97066i	0.364793	+	0.210613i	−0.306388	+	0.951907i	$0.599121\pi$
$558$		0			0
$559$	5.15101	+	8.92181i	0.217864	+	0.377352i
$560$		0			0
$561$	−9.65083	+	5.02179i	−0.407458	+	0.212020i
$562$		0			0
$563$	32.6087	+	5.74979i	1.37429	+	0.242325i	0.811538	−	0.584300i	$-0.198631\pi$
$563$	32.6087	+	5.74979i	1.37429	+	0.242325i	0.562754	+	0.826624i	$0.309742\pi$
$564$		0			0
$565$	12.8658	+	15.3328i	0.541268	+	0.645057i
$566$		0			0
$567$	−29.9904	+	35.6910i	−1.25948	+	1.49888i
$568$		0			0
$569$	9.48978	−	7.96287i	0.397832	−	0.333821i	−0.421823	−	0.906678i	$-0.638610\pi$
$569$	9.48978	−	7.96287i	0.397832	−	0.333821i	0.819655	+	0.572857i	$0.194165\pi$
$570$		0			0
$571$	17.8145	+	3.14117i	0.745513	+	0.131454i	0.533485	−	0.845810i	$-0.320882\pi$
$571$	17.8145	+	3.14117i	0.745513	+	0.131454i	0.212028	+	0.977264i	$0.431993\pi$
$572$		0			0
$573$	14.6499	+	28.1541i	0.612008	+	1.17615i
$574$		0			0
$575$	−3.11539	−	5.39602i	−0.129921	−	0.225030i
$576$		0			0
$577$	8.80849	−	15.2568i	0.366702	−	0.635147i	−0.622346	−	0.782743i	$-0.713820\pi$
$577$	8.80849	−	15.2568i	0.366702	−	0.635147i	0.989048	+	0.147596i	$0.0471535\pi$
$578$		0			0
$579$	−14.9295	−	6.18702i	−0.620449	−	0.257124i
$580$		0			0
$581$	23.9202	−	28.5070i	0.992378	−	1.18267i
$582$		0			0
$583$	−7.20958	−	2.62407i	−0.298590	−	0.108678i
$584$		0			0
$585$	8.27477	+	8.28048i	0.342119	+	0.342356i
$586$		0			0
$587$	39.7826	−	7.01474i	1.64200	−	0.289529i	0.725101	−	0.688643i	$-0.241793\pi$
$587$	39.7826	−	7.01474i	1.64200	−	0.289529i	0.916902	+	0.399113i	$0.130682\pi$
$588$		0			0
$589$	5.05128	+	13.8783i	0.208134	+	0.571844i
$590$		0			0
$591$	11.1818	+	35.4857i	0.459960	+	1.45968i
$592$		0			0
$593$	−17.9514			−0.737175			−0.368588	−	0.929593i	$-0.620159\pi$
$593$	−17.9514			−0.737175			−0.368588	+	0.929593i	$0.620159\pi$
$594$		0			0
$595$			35.4859i			1.45478i
$596$		0			0
$597$	−15.2346	−	13.9647i	−0.623509	−	0.571539i
$598$		0			0
$599$	20.1742	−	7.34283i	0.824297	−	0.300020i	0.104781	−	0.994495i	$-0.466586\pi$
$599$	20.1742	−	7.34283i	0.824297	−	0.300020i	0.719516	+	0.694476i	$0.244364\pi$
$600$		0			0
$601$	2.03547	+	11.5437i	0.0830286	+	0.470879i	0.997765	+	0.0668266i	$0.0212874\pi$
$601$	2.03547	+	11.5437i	0.0830286	+	0.470879i	−0.914736	+	0.404052i	$0.867601\pi$
$602$		0			0
$603$	28.7733	−	13.4051i	1.17174	−	0.545898i
$604$		0			0
$605$	−4.15540	+	11.4169i	−0.168941	+	0.464161i
$606$		0			0
$607$	−17.9889	−	15.0945i	−0.730146	−	0.612665i	0.200026	−	0.979791i	$-0.435897\pi$
$607$	−17.9889	−	15.0945i	−0.730146	−	0.612665i	−0.930171	+	0.367126i	$0.880342\pi$
$608$		0			0
$609$	−40.8095	−	53.2030i	−1.65368	−	2.15589i
$610$		0			0
$611$	−5.02174	−	2.89931i	−0.203158	−	0.117293i
$612$		0			0
$613$	17.2818	−	9.97766i	0.698006	−	0.402994i	−0.108599	−	0.994086i	$-0.534636\pi$
$613$	17.2818	−	9.97766i	0.698006	−	0.402994i	0.806604	+	0.591092i	$0.201303\pi$
$614$		0			0
$615$	−6.02304	−	3.83856i	−0.242872	−	0.154786i
$616$		0			0
$617$	6.90201	−	39.1433i	0.277865	−	1.57585i	−0.451849	−	0.892095i	$-0.649235\pi$
$617$	6.90201	−	39.1433i	0.277865	−	1.57585i	0.729713	−	0.683753i	$-0.239654\pi$
$618$		0			0
$619$	−1.11829	−	1.33273i	−0.0449478	−	0.0535667i	0.743102	−	0.669178i	$-0.233354\pi$
$619$	−1.11829	−	1.33273i	−0.0449478	−	0.0535667i	−0.788050	+	0.615611i	$0.788909\pi$
$620$		0			0
$621$	−6.38680	−	6.97723i	−0.256294	−	0.279987i
$622$		0			0
$623$	−52.6608	+	44.1877i	−2.10981	+	1.77034i
$624$		0			0
$625$	0.664952	−	3.77113i	0.0265981	−	0.150845i
$626$		0			0
$627$	8.05404	+	0.353041i	0.321647	+	0.0140991i
$628$		0			0
$629$	−38.7033	+	22.3454i	−1.54320	+	0.890968i
$630$		0			0
$631$	0.745909	−	1.29195i	0.0296942	−	0.0514318i	−0.850796	−	0.525495i	$-0.823880\pi$
$631$	0.745909	−	1.29195i	0.0296942	−	0.0514318i	0.880491	+	0.474064i	$0.157213\pi$
$632$		0			0
$633$	23.4921	−	3.08866i	0.933726	−	0.122763i
$634$		0			0
$635$	0.125124	−	0.149117i	0.00496540	−	0.00591754i
$636$		0			0
$637$	21.0736	−	57.8993i	0.834967	−	2.29405i
$638$		0			0
$639$	−0.135516	+	0.0948193i	−0.00536091	+	0.00375099i
$640$		0			0
$641$	5.54166	+	31.4283i	0.218883	+	1.24134i	0.874041	+	0.485853i	$0.161491\pi$
$641$	5.54166	+	31.4283i	0.218883	+	1.24134i	−0.655158	+	0.755492i	$0.727398\pi$
$642$		0			0
$643$	10.5303	+	28.9318i	0.415275	+	1.14096i	0.954347	+	0.298700i	$0.0965529\pi$
$643$	10.5303	+	28.9318i	0.415275	+	1.14096i	−0.539072	+	0.842260i	$0.681225\pi$
$644$		0			0
$645$	−1.56225	+	7.04110i	−0.0615136	+	0.277243i
$646$		0			0
$647$	−9.37700			−0.368648			−0.184324	−	0.982866i	$-0.559010\pi$
$647$	−9.37700			−0.368648			−0.184324	+	0.982866i	$0.559010\pi$
$648$		0			0
$649$	1.65905			0.0651236
$650$		0			0
$651$	−7.10021	+	32.0008i	−0.278279	+	1.25421i
$652$		0			0
$653$	9.82157	+	26.9845i	0.384348	+	1.05599i	0.969506	+	0.245068i	$0.0788102\pi$
$653$	9.82157	+	26.9845i	0.384348	+	1.05599i	−0.585158	+	0.810919i	$0.698968\pi$
$654$		0			0
$655$	2.35856	+	13.3760i	0.0921564	+	0.522645i
$656$		0			0
$657$	0.738966	+	8.48016i	0.0288298	+	0.330843i
$658$		0			0
$659$	3.29739	−	9.05950i	0.128448	−	0.352908i	−0.858753	−	0.512390i	$-0.828760\pi$
$659$	3.29739	−	9.05950i	0.128448	−	0.352908i	0.987201	+	0.159482i	$0.0509824\pi$
$660$		0			0
$661$	30.8776	−	36.7985i	1.20100	−	1.43130i	0.327237	−	0.944942i	$-0.393882\pi$
$661$	30.8776	−	36.7985i	1.20100	−	1.43130i	0.873762	−	0.486353i	$-0.161673\pi$
$662$		0			0
$663$	−29.1063	+	3.82681i	−1.13040	+	0.148621i
$664$		0			0
$665$	13.1480	−	22.7730i	0.509858	−	0.883099i
$666$		0			0
$667$	11.7823	−	6.80253i	0.456214	−	0.263395i
$668$		0			0
$669$	−23.2012	−	1.01700i	−0.897009	−	0.0393195i
$670$		0			0
$671$	−1.76808	+	10.0273i	−0.0682558	+	0.387098i
$672$		0			0
$673$	13.0122	−	10.9185i	0.501583	−	0.420878i	−0.356573	−	0.934268i	$-0.616055\pi$
$673$	13.0122	−	10.9185i	0.501583	−	0.420878i	0.858156	+	0.513389i	$0.171610\pi$
$674$		0			0
$675$	−0.766576	−	17.7687i	−0.0295055	−	0.683920i
$676$		0			0
$677$	8.79131	+	10.4771i	0.337878	+	0.402667i	0.908052	−	0.418857i	$-0.137569\pi$
$677$	8.79131	+	10.4771i	0.337878	+	0.402667i	−0.570175	+	0.821523i	$0.693125\pi$
$678$		0			0
$679$	−3.20081	+	18.1527i	−0.122836	+	0.696637i
$680$		0			0
$681$	42.1783	+	26.8808i	1.61628	+	1.03007i
$682$		0			0
$683$	13.7936	−	7.96374i	0.527798	−	0.304724i	−0.212322	−	0.977200i	$-0.568102\pi$
$683$	13.7936	−	7.96374i	0.527798	−	0.304724i	0.740119	+	0.672476i	$0.234769\pi$
$684$		0			0
$685$	0.171424	+	0.0989717i	0.00654978	+	0.00378151i
$686$		0			0
$687$	−10.9074	−	14.2198i	−0.416142	−	0.542520i
$688$		0			0
$689$	−15.8595	−	13.3077i	−0.604200	−	0.506984i
$690$		0			0
$691$	7.15256	−	19.6515i	0.272096	−	0.747579i	−0.726102	−	0.687587i	$-0.758670\pi$
$691$	7.15256	−	19.6515i	0.272096	−	0.747579i	0.998199	−	0.0599922i	$-0.0191076\pi$
$692$		0			0
$693$	14.6533	+	10.2679i	0.556634	+	0.390046i
$694$		0			0
$695$	2.10644	+	11.9462i	0.0799019	+	0.453146i
$696$		0			0
$697$	16.8309	−	6.12596i	0.637517	−	0.232037i
$698$		0			0
$699$	−30.4435	−	27.9060i	−1.15148	−	1.05550i
$700$		0			0
$701$		−	47.5635i		−	1.79645i	−0.439539	−	0.898224i	$-0.644858\pi$
$701$		−	47.5635i		−	1.79645i	0.439539	−	0.898224i	$-0.355142\pi$
$702$		0			0
$703$	33.1170			1.24903
$704$		0			0
$705$	−1.22006	−	3.87187i	−0.0459502	−	0.145823i
$706$		0			0
$707$	−20.3973	−	56.0411i	−0.767119	−	2.10764i
$708$		0			0
$709$	16.3062	−	2.87523i	0.612393	−	0.107981i	0.141155	−	0.989987i	$-0.454918\pi$
$709$	16.3062	−	2.87523i	0.612393	−	0.107981i	0.471238	+	0.882006i	$0.343807\pi$
$710$		0			0
$711$	23.8718	−	6.38758i	0.895261	−	0.239553i
$712$		0			0
$713$	−6.24987	−	2.27477i	−0.234059	−	0.0851906i
$714$		0			0
$715$	2.88807	−	3.44187i	0.108008	−	0.128719i
$716$		0			0
$717$	0.696479	+	0.288632i	0.0260105	+	0.0107792i
$718$		0			0
$719$	−10.3014	+	17.8425i	−0.384176	+	0.665413i	−0.991655	−	0.128923i	$-0.958848\pi$
$719$	−10.3014	+	17.8425i	−0.384176	+	0.665413i	0.607478	+	0.794336i	$0.292181\pi$
$720$		0			0
$721$	−21.0054	−	36.3825i	−0.782283	−	1.35495i
$722$		0			0
$723$	5.37752	+	10.3345i	0.199992	+	0.384343i
$724$		0			0
$725$	25.1922	+	4.44207i	0.935616	+	0.164974i
$726$		0			0
$727$	17.7569	−	14.8998i	0.658569	−	0.552605i	−0.251089	−	0.967964i	$-0.580789\pi$
$727$	17.7569	−	14.8998i	0.658569	−	0.552605i	0.909657	+	0.415359i	$0.136344\pi$
$728$		0			0
$729$	−6.96108	−	26.0872i	−0.257818	−	0.966194i
$730$		0			0
$731$	−11.6260	−	13.8554i	−0.430004	−	0.512459i
$732$		0			0
$733$	−27.9660	−	4.93115i	−1.03295	−	0.182136i	−0.368621	−	0.929580i	$-0.620170\pi$
$733$	−27.9660	−	4.93115i	−1.03295	−	0.182136i	−0.664325	+	0.747444i	$0.731281\pi$
$734$		0			0
$735$	38.2657	−	19.9114i	1.41145	−	0.734445i
$736$		0			0
$737$	−6.09163	−	10.5510i	−0.224388	−	0.388652i
$738$		0			0
$739$	−23.5486	−	13.5958i	−0.866248	−	0.500129i	−0.000148621	−	1.00000i	$-0.500047\pi$
$739$	−23.5486	−	13.5958i	−0.866248	−	0.500129i	−0.866100	+	0.499871i	$0.833381\pi$
$740$		0			0
$741$	20.0968	+	8.32843i	0.738274	+	0.305953i
$742$		0			0
$743$	3.72327	+	3.12419i	0.136593	+	0.114615i	0.708525	−	0.705686i	$-0.249361\pi$
$743$	3.72327	+	3.12419i	0.136593	+	0.114615i	−0.571931	+	0.820302i	$0.693806\pi$
$744$		0			0
$745$	−6.88663	−	2.50653i	−0.252307	−	0.0918321i
$746$		0			0
$747$	5.57109	+	20.8204i	0.203836	+	0.761778i
$748$		0			0
$749$	6.87626	−	1.21247i	0.251253	−	0.0443027i
$750$		0			0
$751$	27.5280	−	10.0194i	1.00451	−	0.365612i	0.213189	−	0.977011i	$-0.431615\pi$
$751$	27.5280	−	10.0194i	1.00451	−	0.365612i	0.791323	+	0.611399i	$0.209393\pi$
$752$		0			0
$753$	10.1696	+	32.2731i	0.370599	+	1.17610i
$754$		0			0
$755$			4.61838i			0.168080i
$756$		0			0
$757$		−	41.1950i		−	1.49726i	−0.662989	−	0.748629i	$-0.730712\pi$
$757$		−	41.1950i		−	1.49726i	0.662989	−	0.748629i	$-0.269288\pi$
$758$		0			0
$759$	−2.45319	+	2.67626i	−0.0890451	+	0.0971420i
$760$		0			0
$761$	−35.3515	+	12.8669i	−1.28149	+	0.466424i	−0.890925	−	0.454151i	$-0.849943\pi$
$761$	−35.3515	+	12.8669i	−1.28149	+	0.466424i	−0.390565	+	0.920575i	$0.627720\pi$
$762$		0			0
$763$	22.9935	−	4.05438i	0.832421	−	0.146778i
$764$		0			0
$765$	−16.8315	−	11.7942i	−0.608543	−	0.426420i
$766$		0			0
$767$	4.20686	+	1.53117i	0.151901	+	0.0552875i
$768$		0			0
$769$	2.79352	+	2.34404i	0.100737	+	0.0845284i	0.691765	−	0.722123i	$-0.256833\pi$
$769$	2.79352	+	2.34404i	0.100737	+	0.0845284i	−0.591028	+	0.806651i	$0.701278\pi$
$770$		0			0
$771$	42.4062	−	32.5278i	1.52722	−	1.17146i
$772$		0			0
$773$	9.39576	+	5.42465i	0.337942	+	0.195111i	0.659362	−	0.751826i	$-0.270827\pi$
$773$	9.39576	+	5.42465i	0.337942	+	0.195111i	−0.321420	+	0.946937i	$0.604160\pi$
$774$		0			0
$775$	−6.25273	−	10.8300i	−0.224605	−	0.389027i
$776$		0			0
$777$	61.9839	+	39.5031i	2.22366	+	1.41717i
$778$		0			0
$779$	−13.0710	−	2.30476i	−0.468316	−	0.0825767i
$780$		0			0
$781$	0.0408044	+	0.0486288i	0.00146010	+	0.00174008i
$782$		0			0
$783$	38.7985	−	1.67384i	1.38654	−	0.0598180i
$784$		0			0
$785$	−1.01437	+	0.851157i	−0.0362044	+	0.0303791i
$786$		0			0
$787$	−26.6398	−	4.69732i	−0.949607	−	0.167441i	−0.322670	−	0.946512i	$-0.604580\pi$
$787$	−26.6398	−	4.69732i	−0.949607	−	0.167441i	−0.626937	+	0.779070i	$0.715692\pi$
$788$		0			0
$789$	8.87448	+	0.389004i	0.315940	+	0.0138489i
$790$		0			0
$791$	41.2769	+	71.4937i	1.46764	+	2.54202i
$792$		0			0
$793$	−13.7377	+	23.7943i	−0.487839	+	0.844961i
$794$		0			0
$795$	−1.88937	−	14.3704i	−0.0670092	−	0.509665i
$796$		0			0
$797$	−16.2301	+	19.3423i	−0.574899	+	0.685138i	−0.972629	−	0.232364i	$-0.925354\pi$
$797$	−16.2301	+	19.3423i	−0.574899	+	0.685138i	0.397730	+	0.917503i	$0.369798\pi$
$798$		0			0
$799$	9.56647	+	3.48191i	0.338437	+	0.123181i
$800$		0			0
$801$	−3.45635	−	39.6641i	−0.122124	−	1.40146i
$802$		0			0
$803$	3.21750	−	0.567331i	0.113543	−	0.0200207i
$804$		0			0
$805$	4.05020	+	11.1278i	0.142751	+	0.392205i
$806$		0			0
$807$	−0.307267	−	0.0681751i	−0.0108163	−	0.00239988i
$808$		0			0
$809$	36.8194			1.29450			0.647251	−	0.762277i	$-0.275919\pi$
$809$	36.8194			1.29450			0.647251	+	0.762277i	$0.275919\pi$
$810$		0			0
$811$			20.4061i			0.716556i	0.933615	+	0.358278i	$0.116636\pi$
$811$			20.4061i			0.716556i	−0.933615	+	0.358278i	$0.883364\pi$
$812$		0			0
$813$	0.934823	−	4.21327i	0.0327857	−	0.147766i
$814$		0			0
$815$	−16.6653	+	6.06568i	−0.583760	+	0.212471i
$816$		0			0
$817$	2.32738	+	13.1992i	0.0814248	+	0.461783i
$818$		0			0
$819$	27.6800	+	39.5602i	0.967217	+	1.38235i
$820$		0			0
$821$	12.1265	−	33.3173i	0.423217	−	1.16278i	−0.526638	−	0.850090i	$-0.676548\pi$
$821$	12.1265	−	33.3173i	0.423217	−	1.16278i	0.949855	−	0.312691i	$-0.101230\pi$
$822$		0			0
$823$	−39.8654	−	33.4510i	−1.38962	−	1.16603i	−0.965494	−	0.260426i	$-0.916137\pi$
$823$	−39.8654	−	33.4510i	−1.38962	−	1.16603i	−0.424126	−	0.905603i	$-0.639419\pi$
$824$		0			0
$825$	−6.76798	+	0.889832i	−0.235631	+	0.0309800i
$826$		0			0
$827$	19.9562	+	11.5217i	0.693944	+	0.400649i	0.805088	−	0.593156i	$-0.202118\pi$
$827$	19.9562	+	11.5217i	0.693944	+	0.400649i	−0.111144	+	0.993804i	$0.535451\pi$
$828$		0			0
$829$	7.80591	−	4.50674i	0.271110	−	0.156526i	−0.358282	−	0.933613i	$-0.616637\pi$
$829$	7.80591	−	4.50674i	0.271110	−	0.156526i	0.629392	+	0.777088i	$0.283304\pi$
$830$		0			0
$831$	0.480294	−	10.9571i	0.0166612	−	0.380098i
$832$		0			0
$833$	−18.7845	+	106.532i	−0.650844	+	3.69112i
$834$		0			0
$835$	−6.48945	−	7.73383i	−0.224577	−	0.267640i
$836$		0			0
$837$	−12.8186	−	14.0036i	−0.443075	−	0.484035i
$838$		0			0
$839$	29.4168	−	24.6836i	1.01558	−	0.852173i	0.0265148	−	0.999648i	$-0.491559\pi$
$839$	29.4168	−	24.6836i	1.01558	−	0.852173i	0.989066	+	0.147475i	$0.0471147\pi$
$840$		0			0
$841$	−4.66356	+	26.4484i	−0.160813	+	0.912013i
$842$		0			0
$843$	−18.3773	+	28.8355i	−0.632947	+	0.993149i
$844$		0			0
$845$	−3.63920	+	2.10109i	−0.125192	+	0.0722798i
$846$		0			0
$847$	−25.0553	+	43.3970i	−0.860909	+	1.49114i
$848$		0			0
$849$	21.3466	+	27.8294i	0.732614	+	0.955103i
$850$		0			0
$851$	−9.58636	+	11.4246i	−0.328616	+	0.391629i
$852$		0			0
$853$	−15.6988	+	43.1320i	−0.537515	+	1.47681i	0.312430	+	0.949941i	$0.398857\pi$
$853$	−15.6988	+	43.1320i	−0.537515	+	1.47681i	−0.849945	+	0.526871i	$0.823365\pi$
$854$		0			0
$855$	6.43166	+	13.8052i	0.219958	+	0.472127i
$856$		0			0
$857$	7.08838	+	40.2002i	0.242134	+	1.37321i	0.827054	+	0.562122i	$0.190015\pi$
$857$	7.08838	+	40.2002i	0.242134	+	1.37321i	−0.584920	+	0.811091i	$0.698874\pi$
$858$		0			0
$859$	−7.94399	−	21.8259i	−0.271045	−	0.744691i	−0.998298	−	0.0583209i	$-0.981425\pi$
$859$	−7.94399	−	21.8259i	−0.271045	−	0.744691i	0.727253	−	0.686370i	$-0.240797\pi$
$860$		0			0
$861$	−21.7152	−	19.9053i	−0.740054	−	0.678369i
$862$		0			0
$863$	−21.7914			−0.741790			−0.370895	−	0.928675i	$-0.620949\pi$
$863$	−21.7914			−0.741790			−0.370895	+	0.928675i	$0.620949\pi$
$864$		0			0
$865$	16.4441			0.559116
$866$		0			0
$867$	21.0744	−	6.64073i	0.715724	−	0.225531i
$868$		0			0
$869$	−3.24393	−	8.91263i	−0.110043	−	0.302340i
$870$		0			0
$871$	−5.70882	−	32.3763i	−0.193436	−	1.09703i
$872$		0			0
$873$	−7.54626	−	7.55147i	−0.255402	−	0.255579i
$874$		0			0
$875$	−18.7399	+	51.4875i	−0.633525	+	1.74060i
$876$		0			0
$877$	19.4903	−	23.2276i	0.658139	−	0.784340i	−0.328978	−	0.944338i	$-0.606704\pi$
$877$	19.4903	−	23.2276i	0.658139	−	0.784340i	0.987117	+	0.159998i	$0.0511486\pi$
$878$		0			0
$879$	21.1948	−	51.1438i	0.714883	−	1.72504i
$880$		0			0
$881$	11.2487	−	19.4834i	0.378980	−	0.656412i	−0.611934	−	0.790909i	$-0.709608\pi$
$881$	11.2487	−	19.4834i	0.378980	−	0.656412i	0.990914	+	0.134496i	$0.0429416\pi$
$882$		0			0
$883$	41.2040	−	23.7891i	1.38662	−	0.800568i	0.393691	−	0.919243i	$-0.371198\pi$
$883$	41.2040	−	23.7891i	1.38662	−	0.800568i	0.992933	+	0.118675i	$0.0378647\pi$
$884$		0			0
$885$	1.44673	+	2.78032i	0.0486314	+	0.0934594i
$886$		0			0
$887$	6.08263	−	34.4963i	0.204235	−	1.15827i	−0.694405	−	0.719584i	$-0.744332\pi$
$887$	6.08263	−	34.4963i	0.204235	−	1.15827i	0.898640	−	0.438688i	$-0.144557\pi$
$888$		0			0
$889$	0.615030	−	0.516071i	0.0206274	−	0.0173085i
$890$		0			0
$891$	−9.74044	+	3.53761i	−0.326317	+	0.118514i
$892$		0			0
$893$	−4.84917	−	5.77901i	−0.162271	−	0.193387i
$894$		0			0
$895$	−4.92128	+	27.9100i	−0.164500	+	0.932928i
$896$		0			0
$897$	−8.69052	+	4.52209i	−0.290168	+	0.150988i
$898$		0			0
$899$	23.6476	−	13.6530i	0.788693	−	0.455352i
$900$		0			0
$901$	31.4781	+	18.1739i	1.04869	+	0.605461i
$902$		0			0
$903$	−11.3885	+	27.4807i	−0.378984	+	0.914502i
$904$		0			0
$905$	−3.67038	−	3.07982i	−0.122008	−	0.102377i
$906$		0			0
$907$	−17.2401	+	47.3669i	−0.572450	+	1.57279i	0.228171	+	0.973621i	$0.426725\pi$
$907$	−17.2401	+	47.3669i	−0.572450	+	1.57279i	−0.800621	+	0.599171i	$0.795497\pi$
$908$		0			0
$909$	33.3604	+	8.95124i	1.10649	+	0.296894i
$910$		0			0
$911$	−8.27878	−	46.9513i	−0.274288	−	1.55557i	−0.741214	−	0.671269i	$-0.765749\pi$
$911$	−8.27878	−	46.9513i	−0.274288	−	1.55557i	0.466926	−	0.884297i	$-0.345362\pi$
$912$		0			0
$913$	7.77338	−	2.82928i	0.257261	−	0.0936355i
$914$		0			0
$915$	−18.3459	+	5.78097i	−0.606498	+	0.191113i
$916$		0			0
$917$			56.0201i			1.84995i
$918$		0			0
$919$	29.5451			0.974602			0.487301	−	0.873234i	$-0.337981\pi$
$919$	29.5451			0.974602			0.487301	+	0.873234i	$0.337981\pi$
$920$		0			0
$921$	−7.47284	+	8.15235i	−0.246239	+	0.268629i
$922$		0			0
$923$	0.0585873	+	0.160967i	0.00192842	+	0.00529830i
$924$		0			0
$925$	−27.6155	+	4.86935i	−0.907991	+	0.160103i
$926$		0			0
$927$	24.2381	+	2.12900i	0.796085	+	0.0699255i
$928$		0			0
$929$	3.79645	+	1.38179i	0.124557	+	0.0453352i	0.403547	−	0.914959i	$-0.367777\pi$
$929$	3.79645	+	1.38179i	0.124557	+	0.0453352i	−0.278989	+	0.960294i	$0.589999\pi$
$930$		0			0
$931$	51.5265	−	61.4069i	1.68871	−	2.01253i
$932$		0			0
$933$	−24.5635	+	18.8415i	−0.804173	+	0.616843i
$934$		0			0
$935$	−3.94414	+	6.83145i	−0.128987	+	0.223412i
$936$		0			0
$937$	−17.2708	−	29.9139i	−0.564213	−	0.977245i	−0.997122	−	0.0758079i	$-0.975846\pi$
$937$	−17.2708	−	29.9139i	−0.564213	−	0.977245i	0.432910	−	0.901437i	$-0.357487\pi$
$938$		0			0
$939$	3.91345	−	6.14054i	0.127711	−	0.200389i
$940$		0			0
$941$	25.6078	+	4.51534i	0.834789	+	0.147196i	0.574675	−	0.818382i	$-0.305129\pi$
$941$	25.6078	+	4.51534i	0.834789	+	0.147196i	0.260115	+	0.965578i	$0.416240\pi$
$942$		0			0
$943$	4.57873	−	3.84201i	0.149104	−	0.125113i
$944$		0			0
$945$	−4.42942	+	33.5106i	−0.144089	+	1.09010i
$946$		0			0
$947$	−17.1834	−	20.4783i	−0.558384	−	0.665456i	0.410819	−	0.911717i	$-0.365243\pi$
$947$	−17.1834	−	20.4783i	−0.558384	−	0.665456i	−0.969204	+	0.246260i	$0.920798\pi$
$948$		0			0
$949$	8.68221	+	1.53091i	0.281836	+	0.0496954i
$950$		0			0
$951$	−1.47981	+	33.7594i	−0.0479861	+	1.09472i
$952$		0			0
$953$	12.9817	+	22.4849i	0.420517	+	0.728357i	0.995990	−	0.0894637i	$-0.0285153\pi$
$953$	12.9817	+	22.4849i	0.420517	+	0.728357i	−0.575473	+	0.817821i	$0.695182\pi$
$954$		0			0
$955$	19.9292	+	11.5061i	0.644893	+	0.372329i
$956$		0			0
$957$	−1.94297	−	14.7780i	−0.0628072	−	0.477706i
$958$		0			0
$959$	0.625408	+	0.524779i	0.0201955	+	0.0169460i
$960$		0			0
$961$	16.5867	+	6.03707i	0.535055	+	0.194744i
$962$		0			0
$963$	−1.71032	+	3.66449i	−0.0551143	+	0.118086i
$964$		0			0
$965$	−11.5398	+	2.03478i	−0.371479	+	0.0655018i
$966$		0			0
$967$	6.10279	−	2.22123i	0.196253	−	0.0714301i	−0.242024	−	0.970270i	$-0.577811\pi$
$967$	6.10279	−	2.22123i	0.196253	−	0.0714301i	0.438277	+	0.898840i	$0.355589\pi$
$968$		0			0
$969$	−37.2863	−	8.27293i	−1.19781	−	0.265765i
$970$		0			0
$971$			11.8917i			0.381623i	0.981627	+	0.190811i	$0.0611119\pi$
$971$			11.8917i			0.381623i	−0.981627	+	0.190811i	$0.938888\pi$
$972$		0			0
$973$			50.0320i			1.60395i
$974$		0			0
$975$	−17.9828	−	3.98995i	−0.575911	−	0.127781i
$976$		0			0
$977$	43.6565	−	15.8896i	1.39669	−	0.508355i	0.469498	−	0.882933i	$-0.344435\pi$
$977$	43.6565	−	15.8896i	1.39669	−	0.508355i	0.927195	+	0.374578i	$0.122213\pi$
$978$		0			0
$979$	−15.0491	+	2.65357i	−0.480973	+	0.0848084i
$980$		0			0
$981$	−5.71914	+	12.2537i	−0.182598	+	0.391230i
$982$		0			0
$983$	10.5691	+	3.84682i	0.337101	+	0.122695i	0.505024	−	0.863106i	$-0.331484\pi$
$983$	10.5691	+	3.84682i	0.337101	+	0.122695i	−0.167923	+	0.985800i	$0.553706\pi$
$984$		0			0
$985$	20.6657	+	17.3406i	0.658463	+	0.552516i
$986$		0			0
$987$	−2.18260	−	16.6006i	−0.0694728	−	0.528404i
$988$		0			0
$989$	−5.22713	−	3.01789i	−0.166213	−	0.0959632i
$990$		0			0
$991$	20.2286	+	35.0369i	0.642582	+	1.11298i	0.984854	+	0.173384i	$0.0554702\pi$
$991$	20.2286	+	35.0369i	0.642582	+	1.11298i	−0.342272	+	0.939601i	$0.611196\pi$
$992$		0			0
$993$	0.943037	−	21.5138i	0.0299264	−	0.682721i
$994$		0			0
$995$	−14.7572	−	2.60210i	−0.467836	−	0.0824920i
$996$		0			0
$997$	1.29636	+	1.54495i	0.0410562	+	0.0489289i	0.786182	−	0.617995i	$-0.212055\pi$
$997$	1.29636	+	1.54495i	0.0410562	+	0.0489289i	−0.745126	+	0.666924i	$0.767610\pi$
$998$		0			0
$999$	−39.3380	+	16.2705i	−1.24460	+	0.514775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bf.a.49.14		204
4.3	odd	2		216.2.t.a.157.15	yes	204
8.3	odd	2		216.2.t.a.157.2	✓	204
8.5	even	2	inner	864.2.bf.a.49.21		204
12.11	even	2		648.2.t.a.37.20		204
24.11	even	2		648.2.t.a.37.33		204
27.16	even	9	inner	864.2.bf.a.529.21		204
108.11	even	18		648.2.t.a.613.33		204
108.43	odd	18		216.2.t.a.205.2	yes	204
216.11	even	18		648.2.t.a.613.20		204
216.43	odd	18		216.2.t.a.205.15	yes	204
216.205	even	18	inner	864.2.bf.a.529.14		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.2	✓	204	8.3	odd	2
216.2.t.a.157.15	yes	204	4.3	odd	2
216.2.t.a.205.2	yes	204	108.43	odd	18
216.2.t.a.205.15	yes	204	216.43	odd	18
648.2.t.a.37.20		204	12.11	even	2
648.2.t.a.37.33		204	24.11	even	2
648.2.t.a.613.20		204	216.11	even	18
648.2.t.a.613.33		204	108.11	even	18
864.2.bf.a.49.14		204	1.1	even	1	trivial
864.2.bf.a.49.21		204	8.5	even	2	inner
864.2.bf.a.529.14		204	216.205	even	18	inner
864.2.bf.a.529.21		204	27.16	even	9	inner

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bf (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.375176 + 1.69093i) q^{3} +(0.429535 + 1.18014i) q^{5} +(0.899466 + 5.10113i) q^{7} +(-2.71849 - 1.26879i) q^{9} +O(q^{10})\)	\(q+(-0.375176 + 1.69093i) q^{3} +(0.429535 + 1.18014i) q^{5} +(0.899466 + 5.10113i) q^{7} +(-2.71849 - 1.26879i) q^{9} +(-0.393815 + 1.08200i) q^{11} +(-1.99720 + 2.38017i) q^{13} +(-2.15668 + 0.283553i) q^{15} +(2.72750 - 4.72417i) q^{17} +(-3.50074 + 2.02115i) q^{19} +(-8.96310 - 0.392889i) q^{21} +(0.316107 - 1.79273i) q^{23} +(2.62200 - 2.20012i) q^{25} +(3.16535 - 4.12075i) q^{27} +(4.80401 + 5.72520i) q^{29} +(0.634441 - 3.59809i) q^{31} +(-1.68183 - 1.07185i) q^{33} +(-5.63367 + 3.25260i) q^{35} +(-7.09501 - 4.09630i) q^{37} +(-3.27539 - 4.27010i) q^{39} +(2.51525 + 2.11055i) q^{41} +(1.13402 - 3.11569i) q^{43} +(0.329667 - 3.75317i) q^{45} +(0.324072 + 1.83790i) q^{47} +(-18.6346 + 6.78244i) q^{49} +(6.96495 + 6.38441i) q^{51} +6.66321i q^{53} -1.44606 q^{55} +(-2.10423 - 6.67779i) q^{57} +(-0.492801 - 1.35396i) q^{59} +(8.70846 - 1.53554i) q^{61} +(4.02709 - 15.0086i) q^{63} +(-3.66678 - 1.33460i) q^{65} +(-6.80127 + 8.10544i) q^{67} +(2.91279 + 1.20711i) q^{69} +(0.0275657 - 0.0477451i) q^{71} +(-1.41872 - 2.45729i) q^{73} +(2.73653 + 5.25905i) q^{75} +(-5.87364 - 1.03568i) q^{77} +(-6.31005 + 5.29476i) q^{79} +(5.78032 + 6.89840i) q^{81} +(-4.61797 - 5.50348i) q^{83} +(6.74672 + 1.18963i) q^{85} +(-11.4833 + 5.97528i) q^{87} +(6.63574 + 11.4934i) q^{89} +(-13.9379 - 8.04707i) q^{91} +(5.84609 + 2.42271i) q^{93} +(-3.88892 - 3.26319i) q^{95} +(3.34396 + 1.21710i) q^{97} +(2.44342 - 2.44173i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 12 q^{7} - 12 q^{9}+O(q^{10}) \) 204 * q + 12 * q^7 - 12 * q^9	\( 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73} + 12 q^{79} - 12 q^{81} + 48 q^{87} - 6 q^{89} + 42 q^{95} - 12 q^{97}+O(q^{100}) \) 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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