LMFDB - Embedded newform 1323.2.s.d.656.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(656,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("1323.656");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.s (of order $6$, degree $2$, 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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			656.2
Character	$\chi$	$=$	1323.656
Dual form			1323.2.s.d.962.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.34591 + 1.35441i) q^{2} +(2.66888 - 4.62263i) q^{4} -1.20293 q^{5} +9.04141i q^{8} +O(q^{10})$	\(q+(-2.34591 + 1.35441i) q^{2} +(2.66888 - 4.62263i) q^{4} -1.20293 q^{5} +9.04141i q^{8} +(2.82197 - 1.62926i) q^{10} -2.48666i q^{11} +(-1.63211 + 0.942300i) q^{13} +(-6.90806 - 11.9651i) q^{16} +(0.601863 + 1.04246i) q^{17} +(6.46933 + 3.73507i) q^{19} +(-3.21047 + 5.56070i) q^{20} +(3.36797 + 5.83350i) q^{22} -3.04101i q^{23} -3.55296 q^{25} +(2.55253 - 4.42111i) q^{26} +(0.173847 + 0.100371i) q^{29} +(-3.03381 - 1.75157i) q^{31} +(16.7513 + 9.67135i) q^{32} +(-2.82384 - 1.63034i) q^{34} +(-0.865458 + 1.49902i) q^{37} -20.2353 q^{38} -10.8762i q^{40} +(3.36029 + 5.82020i) q^{41} +(0.00656005 - 0.0113623i) q^{43} +(-11.4949 - 6.63660i) q^{44} +(4.11878 + 7.13394i) q^{46} +(-0.717403 - 1.24258i) q^{47} +(8.33495 - 4.81219i) q^{50} +10.0595i q^{52} +(-8.58085 + 4.95416i) q^{53} +2.99128i q^{55} -0.543775 q^{58} +(6.10954 - 10.5820i) q^{59} +(9.73903 - 5.62283i) q^{61} +9.48942 q^{62} -24.7638 q^{64} +(1.96331 - 1.13352i) q^{65} +(2.57932 - 4.46752i) q^{67} +6.42520 q^{68} -12.0452i q^{71} +(7.51020 - 4.33602i) q^{73} -4.68875i q^{74} +(34.5317 - 19.9369i) q^{76} +(-2.74801 - 4.75969i) q^{79} +(8.30991 + 14.3932i) q^{80} +(-15.7659 - 9.10246i) q^{82} +(1.60854 - 2.78607i) q^{83} +(-0.723998 - 1.25400i) q^{85} +0.0355401i q^{86} +22.4829 q^{88} +(3.98364 - 6.89986i) q^{89} +(-14.0574 - 8.11607i) q^{92} +(3.36593 + 1.94332i) q^{94} +(-7.78214 - 4.49302i) q^{95} +(-2.06260 - 1.19084i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 120 q^{32} - 96 q^{44} - 48 q^{50} - 48 q^{53} - 48 q^{64} + 120 q^{65} - 24 q^{79} - 24 q^{85} + 144 q^{92} + 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 120 * q^32 - 96 * q^44 - 48 * q^50 - 48 * q^53 - 48 * q^64 + 120 * q^65 - 24 * q^79 - 24 * q^85 + 144 * q^92 + 96 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−2.34591	+	1.35441i	−1.65881	+	0.957716i	−0.685548	+	0.728027i	$0.740437\pi$
$2$	−2.34591	+	1.35441i	−1.65881	+	0.957716i	−0.973264	+	0.229689i	$0.926229\pi$
$3$		0			0
$3$		0			0
$4$	2.66888	−	4.62263i	1.33444	−	2.31132i
$5$	−1.20293			−0.537966			−0.268983	−	0.963145i	$-0.586688\pi$
$5$	−1.20293			−0.537966			−0.268983	+	0.963145i	$0.586688\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			9.04141i			3.19662i
$9$		0			0
$10$	2.82197	−	1.62926i	0.892385	−	0.515219i
$11$		−	2.48666i		−	0.749757i	−0.927074	−	0.374879i	$-0.877684\pi$
$11$		−	2.48666i		−	0.749757i	0.927074	−	0.374879i	$-0.122316\pi$
$12$		0			0
$13$	−1.63211	+	0.942300i	−0.452666	+	0.261347i	−0.708956	−	0.705253i	$-0.750833\pi$
$13$	−1.63211	+	0.942300i	−0.452666	+	0.261347i	0.256289	+	0.966600i	$0.417500\pi$
$14$		0			0
$15$		0			0
$16$	−6.90806	−	11.9651i	−1.72702	−	2.99128i
$17$	0.601863	+	1.04246i	0.145973	+	0.252833i	0.929736	−	0.368228i	$-0.120035\pi$
$17$	0.601863	+	1.04246i	0.145973	+	0.252833i	−0.783762	+	0.621061i	$0.786702\pi$
$18$		0			0
$19$	6.46933	+	3.73507i	1.48417	+	0.856883i	0.999838	−	0.0180038i	$-0.00573111\pi$
$19$	6.46933	+	3.73507i	1.48417	+	0.856883i	0.484327	+	0.874887i	$0.339064\pi$
$20$	−3.21047	+	5.56070i	−0.717883	+	1.24341i
$21$		0			0
$22$	3.36797	+	5.83350i	0.718054	+	1.24371i
$23$		−	3.04101i		−	0.634093i	−0.948410	−	0.317047i	$-0.897309\pi$
$23$		−	3.04101i		−	0.634093i	0.948410	−	0.317047i	$-0.102691\pi$
$24$		0			0
$25$	−3.55296			−0.710593
$26$	2.55253	−	4.42111i	0.500592	−	0.867052i
$27$		0			0
$28$		0			0
$29$	0.173847	+	0.100371i	0.0322826	+	0.0186384i	0.516054	−	0.856556i	$-0.327400\pi$
$29$	0.173847	+	0.100371i	0.0322826	+	0.0186384i	−0.483772	+	0.875194i	$0.660734\pi$
$30$		0			0
$31$	−3.03381	−	1.75157i	−0.544889	−	0.314592i	0.202169	−	0.979351i	$-0.435201\pi$
$31$	−3.03381	−	1.75157i	−0.544889	−	0.314592i	−0.747058	+	0.664759i	$0.768534\pi$
$32$	16.7513	+	9.67135i	2.96124	+	1.70967i
$33$		0			0
$34$	−2.82384	−	1.63034i	−0.484285	−	0.279602i
$35$		0			0
$36$		0			0
$37$	−0.865458	+	1.49902i	−0.142280	+	0.246437i	−0.928355	−	0.371695i	$-0.878777\pi$
$37$	−0.865458	+	1.49902i	−0.142280	+	0.246437i	0.786075	+	0.618132i	$0.212110\pi$
$38$	−20.2353			−3.28260
$39$		0			0
$40$		−	10.8762i		−	1.71967i
$41$	3.36029	+	5.82020i	0.524790	+	0.908963i	0.999583	+	0.0288655i	$0.00918944\pi$
$41$	3.36029	+	5.82020i	0.524790	+	0.908963i	−0.474793	+	0.880097i	$0.657477\pi$
$42$		0			0
$43$	0.00656005	−	0.0113623i	0.00100040	−	0.00173274i	−0.865525	−	0.500866i	$-0.833015\pi$
$43$	0.00656005	−	0.0113623i	0.00100040	−	0.00173274i	0.866525	+	0.499133i	$0.166348\pi$
$44$	−11.4949	−	6.63660i	−1.73293	−	1.00051i
$45$		0			0
$46$	4.11878	+	7.13394i	0.607281	+	1.05184i
$47$	−0.717403	−	1.24258i	−0.104644	−	0.181249i	0.808949	−	0.587879i	$-0.200037\pi$
$47$	−0.717403	−	1.24258i	−0.104644	−	0.181249i	−0.913593	+	0.406631i	$0.866704\pi$
$48$		0			0
$49$		0			0
$50$	8.33495	−	4.81219i	1.17874	−	0.680546i
$51$		0			0
$52$			10.0595i			1.39501i
$53$	−8.58085	+	4.95416i	−1.17867	+	0.680506i	−0.955707	−	0.294321i	$-0.904906\pi$
$53$	−8.58085	+	4.95416i	−1.17867	+	0.680506i	−0.222964	+	0.974827i	$0.571573\pi$
$54$		0			0
$55$			2.99128i			0.403344i
$56$		0			0
$57$		0			0
$58$	−0.543775			−0.0714011
$59$	6.10954	−	10.5820i	0.795394	−	1.37766i	−0.127194	−	0.991878i	$-0.540597\pi$
$59$	6.10954	−	10.5820i	0.795394	−	1.37766i	0.922588	−	0.385786i	$-0.126070\pi$
$60$		0			0
$61$	9.73903	−	5.62283i	1.24696	−	0.719930i	0.276454	−	0.961027i	$-0.410841\pi$
$61$	9.73903	−	5.62283i	1.24696	−	0.719930i	0.970501	+	0.241097i	$0.0775073\pi$
$62$	9.48942			1.20516
$63$		0			0
$64$	−24.7638			−3.09548
$65$	1.96331	−	1.13352i	0.243519	−	0.140596i
$66$		0			0
$67$	2.57932	−	4.46752i	0.315115	−	0.545794i	−0.664347	−	0.747424i	$-0.731290\pi$
$67$	2.57932	−	4.46752i	0.315115	−	0.545794i	0.979462	+	0.201630i	$0.0646237\pi$
$68$	6.42520			0.779170
$69$		0			0
$70$		0			0
$71$		−	12.0452i		−	1.42950i	−0.699379	−	0.714751i	$-0.746540\pi$
$71$		−	12.0452i		−	1.42950i	0.699379	−	0.714751i	$-0.253460\pi$
$72$		0			0
$73$	7.51020	−	4.33602i	0.879003	−	0.507493i	0.00867336	−	0.999962i	$-0.497239\pi$
$73$	7.51020	−	4.33602i	0.879003	−	0.507493i	0.870330	+	0.492470i	$0.163906\pi$
$74$		−	4.68875i		−	0.545057i
$75$		0			0
$76$	34.5317	−	19.9369i	3.96106	−	2.28692i
$77$		0			0
$78$		0			0
$79$	−2.74801	−	4.75969i	−0.309175	−	0.535507i	0.669007	−	0.743256i	$-0.266719\pi$
$79$	−2.74801	−	4.75969i	−0.309175	−	0.535507i	−0.978182	+	0.207749i	$0.933386\pi$
$80$	8.30991	+	14.3932i	0.929076	+	1.60921i
$81$		0			0
$82$	−15.7659	−	9.10246i	−1.74106	−	1.00520i
$83$	1.60854	−	2.78607i	0.176560	−	0.305811i	−0.764140	−	0.645051i	$-0.776836\pi$
$83$	1.60854	−	2.78607i	0.176560	−	0.305811i	0.940700	+	0.339239i	$0.110170\pi$
$84$		0			0
$85$	−0.723998	−	1.25400i	−0.0785286	−	0.136016i
$86$			0.0355401i			0.00383239i
$87$		0			0
$88$	22.4829			2.39669
$89$	3.98364	−	6.89986i	0.422265	−	0.731384i	−0.573896	−	0.818928i	$-0.694569\pi$
$89$	3.98364	−	6.89986i	0.422265	−	0.731384i	0.996161	+	0.0875442i	$0.0279019\pi$
$90$		0			0
$91$		0			0
$92$	−14.0574	−	8.11607i	−1.46559	−	0.846159i
$93$		0			0
$94$	3.36593	+	1.94332i	0.347170	+	0.200438i
$95$	−7.78214	−	4.49302i	−0.798430	−	0.460974i
$96$		0			0
$97$	−2.06260	−	1.19084i	−0.209425	−	0.120912i	0.391619	−	0.920128i	$-0.371915\pi$
$97$	−2.06260	−	1.19084i	−0.209425	−	0.120912i	−0.601044	+	0.799216i	$0.705249\pi$
$98$		0			0
$99$		0			0
$100$	−9.48242	+	16.4240i	−0.948242	+	1.64240i
$101$	9.46543			0.941846			0.470923	−	0.882174i	$-0.343921\pi$
$101$	9.46543			0.941846			0.470923	+	0.882174i	$0.343921\pi$
$102$		0			0
$103$			17.2582i			1.70050i	0.526381	+	0.850249i	$0.323549\pi$
$103$			17.2582i			1.70050i	−0.526381	+	0.850249i	$0.676451\pi$
$104$	−8.51973	−	14.7566i	−0.835428	−	1.44700i
$105$		0			0
$106$	13.4200	−	23.2441i	1.30346	−	2.25766i
$107$	8.55935	+	4.94175i	0.827464	+	0.477737i	0.852984	−	0.521938i	$-0.174791\pi$
$107$	8.55935	+	4.94175i	0.827464	+	0.477737i	−0.0255196	+	0.999674i	$0.508124\pi$
$108$		0			0
$109$	−5.20678	−	9.01841i	−0.498719	−	0.863807i	0.501280	−	0.865285i	$-0.332863\pi$
$109$	−5.20678	−	9.01841i	−0.498719	−	0.863807i	−0.999999	+	0.00147852i	$0.999529\pi$
$110$	−4.05143	−	7.01729i	−0.386289	−	0.669072i
$111$		0			0
$112$		0			0
$113$	9.56137	−	5.52026i	0.899458	−	0.519303i	0.0224339	−	0.999748i	$-0.492858\pi$
$113$	9.56137	−	5.52026i	0.899458	−	0.519303i	0.877024	+	0.480446i	$0.159525\pi$
$114$		0			0
$115$			3.65811i			0.341121i
$116$	0.927954	−	0.535755i	0.0861584	−	0.0497436i
$117$		0			0
$118$			33.0994i			3.04705i
$119$		0			0
$120$		0			0
$121$	4.81650			0.437864
$122$	−15.2313	+	26.3814i	−1.37898	+	2.38846i
$123$		0			0
$124$	−16.1937	+	9.34946i	−1.45424	+	0.839607i
$125$	10.2886			0.920241
$126$		0			0
$127$	13.8634			1.23018			0.615090	−	0.788457i	$-0.289119\pi$
$127$	13.8634			1.23018			0.615090	+	0.788457i	$0.289119\pi$
$128$	24.5913	−	14.1978i	2.17359	−	1.25492i
$129$		0			0
$130$	−3.07051	+	5.31828i	−0.269302	+	0.466444i
$131$	12.3595			1.07985			0.539927	−	0.841712i	$-0.318452\pi$
$131$	12.3595			1.07985			0.539927	+	0.841712i	$0.318452\pi$
$132$		0			0
$133$		0			0
$134$			13.9739i			1.20716i
$135$		0			0
$136$	−9.42529	+	5.44169i	−0.808212	+	0.466621i
$137$			11.6614i			0.996301i	0.867091	+	0.498150i	$0.165987\pi$
$137$			11.6614i			0.996301i	−0.867091	+	0.498150i	$0.834013\pi$
$138$		0			0
$139$	−8.73893	+	5.04543i	−0.741227	+	0.427947i	−0.822515	−	0.568743i	$-0.807430\pi$
$139$	−8.73893	+	5.04543i	−0.741227	+	0.427947i	0.0812884	+	0.996691i	$0.474097\pi$
$140$		0			0
$141$		0			0
$142$	16.3142	+	28.2570i	1.36906	+	2.37128i
$143$	2.34318	+	4.05851i	0.195947	+	0.339390i
$144$		0			0
$145$	−0.209126	−	0.120739i	−0.0173670	−	0.0100268i
$146$	−11.7455	+	20.3439i	−0.972067	+	1.68367i
$147$		0			0
$148$	4.61960	+	8.00138i	0.379729	+	0.657710i
$149$		−	4.79212i		−	0.392586i	−0.980545	−	0.196293i	$-0.937110\pi$
$149$		−	4.79212i		−	0.392586i	0.980545	−	0.196293i	$-0.0628904\pi$
$150$		0			0
$151$	−11.3185			−0.921085			−0.460542	−	0.887638i	$-0.652345\pi$
$151$	−11.3185			−0.921085			−0.460542	+	0.887638i	$0.652345\pi$
$152$	−33.7703	+	58.4918i	−2.73913	+	4.74431i
$153$		0			0
$154$		0			0
$155$	3.64946	+	2.10702i	0.293132	+	0.169240i
$156$		0			0
$157$	−12.7580	−	7.36581i	−1.01820	−	0.587856i	−0.104615	−	0.994513i	$-0.533361\pi$
$157$	−12.7580	−	7.36581i	−1.01820	−	0.587856i	−0.913581	+	0.406657i	$0.866694\pi$
$158$	12.8932	+	7.44388i	1.02573	+	0.592203i
$159$		0			0
$160$	−20.1506	−	11.6339i	−1.59304	−	0.919744i
$161$		0			0
$162$		0			0
$163$	9.07900	−	15.7253i	0.711122	−	1.23170i	−0.253314	−	0.967384i	$-0.581521\pi$
$163$	9.07900	−	15.7253i	0.711122	−	1.23170i	0.964436	−	0.264316i	$-0.0851460\pi$
$164$	35.8729			2.80120
$165$		0			0
$166$			8.71452i			0.676378i
$167$	0.599436	+	1.03825i	0.0463857	+	0.0803425i	0.888286	−	0.459291i	$-0.151896\pi$
$167$	0.599436	+	1.03825i	0.0463857	+	0.0803425i	−0.841900	+	0.539633i	$0.818563\pi$
$168$		0			0
$169$	−4.72414	+	8.18245i	−0.363395	+	0.629419i
$170$	3.39688	+	1.96119i	0.260529	+	0.150416i
$171$		0			0
$172$	−0.0350159	−	0.0606494i	−0.00266994	−	0.00462447i
$173$	9.00403	+	15.5954i	0.684564	+	1.18570i	0.973574	+	0.228373i	$0.0733405\pi$
$173$	9.00403	+	15.5954i	0.684564	+	1.18570i	−0.289010	+	0.957326i	$0.593326\pi$
$174$		0			0
$175$		0			0
$176$	−29.7532	+	17.1780i	−2.24273	+	1.29484i
$177$		0			0
$178$			21.5820i			1.61764i
$179$	13.1137	−	7.57118i	0.980162	−	0.565897i	0.0778428	−	0.996966i	$-0.475197\pi$
$179$	13.1137	−	7.57118i	0.980162	−	0.565897i	0.902319	+	0.431069i	$0.141863\pi$
$180$		0			0
$181$			7.98716i			0.593681i	0.954927	+	0.296840i	$0.0959329\pi$
$181$			7.98716i			0.593681i	−0.954927	+	0.296840i	$0.904067\pi$
$182$		0			0
$183$		0			0
$184$	27.4950			2.02696
$185$	1.04108	−	1.80321i	0.0765420	−	0.132575i
$186$		0			0
$187$	2.59224	−	1.49663i	0.189563	−	0.109445i
$188$	−7.65865			−0.558564
$189$		0			0
$190$	24.3416			1.76593
$191$	13.8711	−	8.00848i	1.00368	−	0.579473i	0.0943426	−	0.995540i	$-0.469925\pi$
$191$	13.8711	−	8.00848i	1.00368	−	0.579473i	0.909334	+	0.416067i	$0.136592\pi$
$192$		0			0
$193$	6.85468	−	11.8726i	0.493410	−	0.854612i	−0.506561	−	0.862204i	$-0.669083\pi$
$193$	6.85468	−	11.8726i	0.493410	−	0.854612i	0.999971	+	0.00759239i	$0.00241676\pi$
$194$	6.45158			0.463197
$195$		0			0
$196$		0			0
$197$		−	18.9248i		−	1.34834i	−0.738577	−	0.674170i	$-0.764502\pi$
$197$		−	18.9248i		−	1.34834i	0.738577	−	0.674170i	$-0.235498\pi$
$198$		0			0
$199$	21.5055	−	12.4162i	1.52449	−	0.880163i	0.524908	−	0.851159i	$-0.324100\pi$
$199$	21.5055	−	12.4162i	1.52449	−	0.880163i	0.999579	−	0.0290036i	$-0.00923344\pi$
$200$		−	32.1238i		−	2.27150i
$201$		0			0
$202$	−22.2051	+	12.8201i	−1.56235	+	0.902020i
$203$		0			0
$204$		0			0
$205$	−4.04219	−	7.00129i	−0.282319	−	0.488991i
$206$	−23.3747	−	40.4862i	−1.62859	−	2.82081i
$207$		0			0
$208$	22.5495	+	13.0189i	1.56352	+	0.902701i
$209$	9.28786	−	16.0870i	0.642454	−	1.11276i
$210$		0			0
$211$	3.60761	+	6.24857i	0.248358	+	0.430169i	0.963070	−	0.269250i	$-0.0867757\pi$
$211$	3.60761	+	6.24857i	0.248358	+	0.430169i	−0.714712	+	0.699419i	$0.753442\pi$
$212$			52.8881i			3.63237i
$213$		0			0
$214$	−26.7727			−1.83014
$215$	−0.00789127	+	0.0136681i	−0.000538180	+	0.000932155i
$216$		0			0
$217$		0			0
$218$	24.4293	+	14.1043i	1.65456	+	0.955262i
$219$		0			0
$220$	13.8276	+	7.98336i	0.932255	+	0.538238i
$221$	−1.96462	−	1.13427i	−0.132154	−	0.0762994i
$222$		0			0
$223$	21.0706	+	12.1651i	1.41099	+	0.814635i	0.995482	−	0.0949545i	$-0.0302705\pi$
$223$	21.0706	+	12.1651i	1.41099	+	0.814635i	0.415508	+	0.909590i	$0.363604\pi$
$224$		0			0
$225$		0			0
$226$	−14.9534	+	25.9001i	−0.994688	+	1.72285i
$227$	0.480577			0.0318970			0.0159485	−	0.999873i	$-0.494923\pi$
$227$	0.480577			0.0318970			0.0159485	+	0.999873i	$0.494923\pi$
$228$		0			0
$229$		−	9.01176i		−	0.595514i	−0.954642	−	0.297757i	$-0.903761\pi$
$229$		−	9.01176i		−	0.595514i	0.954642	−	0.297757i	$-0.0962385\pi$
$230$	−4.95460	−	8.58162i	−0.326697	−	0.565855i
$231$		0			0
$232$	−0.907493	+	1.57182i	−0.0595799	+	0.103195i
$233$	−9.62742	−	5.55840i	−0.630713	−	0.364143i	0.150315	−	0.988638i	$-0.451971\pi$
$233$	−9.62742	−	5.55840i	−0.630713	−	0.364143i	−0.781028	+	0.624496i	$0.785305\pi$
$234$		0			0
$235$	0.862985	+	1.49473i	0.0562949	+	0.0975057i
$236$	−32.6112	−	56.4843i	−2.12281	−	3.67682i
$237$		0			0
$238$		0			0
$239$	−12.0446	+	6.95395i	−0.779100	+	0.449813i	−0.836111	−	0.548560i	$-0.815176\pi$
$239$	−12.0446	+	6.95395i	−0.779100	+	0.449813i	0.0570114	+	0.998374i	$0.481843\pi$
$240$		0			0
$241$			12.3761i			0.797217i	0.917121	+	0.398609i	$0.130507\pi$
$241$			12.3761i			0.797217i	−0.917121	+	0.398609i	$0.869493\pi$
$242$	−11.2991	+	6.52354i	−0.726334	+	0.419349i
$243$		0			0
$244$		−	60.0266i		−	3.84281i
$245$		0			0
$246$		0			0
$247$	−14.0782			−0.895776
$248$	15.8367	−	27.4299i	1.00563	−	1.74180i
$249$		0			0
$250$	−24.1362	+	13.9350i	−1.52651	+	0.881329i
$251$	−19.7147			−1.24438			−0.622191	−	0.782866i	$-0.713757\pi$
$251$	−19.7147			−1.24438			−0.622191	+	0.782866i	$0.713757\pi$
$252$		0			0
$253$	−7.56196			−0.475416
$254$	−32.5224	+	18.7768i	−2.04064	+	1.17816i
$255$		0			0
$256$	−13.6956	+	23.7214i	−0.855973	+	1.48259i
$257$	11.2405			0.701163			0.350581	−	0.936532i	$-0.385984\pi$
$257$	11.2405			0.701163			0.350581	+	0.936532i	$0.385984\pi$
$258$		0			0
$259$		0			0
$260$		−	12.1009i		−	0.750466i
$261$		0			0
$262$	−28.9943	+	16.7399i	−1.79127	+	1.03419i
$263$		−	3.25794i		−	0.200893i	−0.994942	−	0.100447i	$-0.967973\pi$
$263$		−	3.25794i		−	0.200893i	0.994942	−	0.100447i	$-0.0320272\pi$
$264$		0			0
$265$	10.3221	−	5.95949i	0.634084	−	0.366089i
$266$		0			0
$267$		0			0
$268$	−13.7678	−	23.8465i	−0.841002	−	1.45666i
$269$	−0.121147	−	0.209832i	−0.00738644	−	0.0127937i	0.862309	−	0.506383i	$-0.169018\pi$
$269$	−0.121147	−	0.209832i	−0.00738644	−	0.0127937i	−0.869695	+	0.493590i	$0.835685\pi$
$270$		0			0
$271$	0.929287	+	0.536524i	0.0564502	+	0.0325915i	0.527959	−	0.849270i	$-0.322957\pi$
$271$	0.929287	+	0.536524i	0.0564502	+	0.0325915i	−0.471509	+	0.881861i	$0.656291\pi$
$272$	8.31542	−	14.4027i	0.504196	−	0.873294i
$273$		0			0
$274$	−15.7944	−	27.3567i	−0.954173	−	1.65268i
$275$			8.83502i			0.532772i
$276$		0			0
$277$	−4.90153			−0.294504			−0.147252	−	0.989099i	$-0.547043\pi$
$277$	−4.90153			−0.294504			−0.147252	+	0.989099i	$0.547043\pi$
$278$	13.6672	−	23.6723i	0.819704	−	1.41977i
$279$		0			0
$280$		0			0
$281$	−11.5613	−	6.67494i	−0.689691	−	0.398194i	0.113805	−	0.993503i	$-0.463696\pi$
$281$	−11.5613	−	6.67494i	−0.689691	−	0.398194i	−0.803496	+	0.595310i	$0.797029\pi$
$282$		0			0
$283$	−3.25329	−	1.87829i	−0.193388	−	0.111653i	0.400180	−	0.916437i	$-0.368948\pi$
$283$	−3.25329	−	1.87829i	−0.193388	−	0.111653i	−0.593568	+	0.804784i	$0.702281\pi$
$284$	−55.6805	−	32.1472i	−3.30403	−	1.90758i
$285$		0			0
$286$	−10.9938	−	6.34729i	−0.650078	−	0.375323i
$287$		0			0
$288$		0			0
$289$	7.77552	−	13.4676i	0.457384	−	0.792212i
$290$	0.654122			0.0384114
$291$		0			0
$292$		−	46.2892i		−	2.70887i
$293$	6.38430	+	11.0579i	0.372975	+	0.646011i	0.990022	−	0.140915i	$-0.0450045\pi$
$293$	6.38430	+	11.0579i	0.372975	+	0.646011i	−0.617047	+	0.786926i	$0.711671\pi$
$294$		0			0
$295$	−7.34934	+	12.7294i	−0.427895	+	0.741136i
$296$	−13.5532	−	7.82496i	−0.787765	−	0.454816i
$297$		0			0
$298$	6.49052	+	11.2419i	0.375986	+	0.651227i
$299$	2.86554	+	4.96326i	0.165718	+	0.287033i
$300$		0			0
$301$		0			0
$302$	26.5522	−	15.3299i	1.52791	−	0.882137i
$303$		0			0
$304$		−	103.208i		−	5.91940i
$305$	−11.7154	+	6.76387i	−0.670819	+	0.387298i
$306$		0			0
$307$		−	10.7257i		−	0.612148i	−0.952008	−	0.306074i	$-0.900984\pi$
$307$		−	10.7257i		−	0.612148i	0.952008	−	0.306074i	$-0.0990155\pi$
$308$		0			0
$309$		0			0
$310$	−11.4151			−0.648334
$311$	−9.41743	+	16.3115i	−0.534013	+	0.924938i	0.465197	+	0.885207i	$0.345983\pi$
$311$	−9.41743	+	16.3115i	−0.534013	+	0.924938i	−0.999210	+	0.0397310i	$0.987350\pi$
$312$		0			0
$313$	22.5774	−	13.0351i	1.27615	−	0.736787i	0.300013	−	0.953935i	$-0.403009\pi$
$313$	22.5774	−	13.0351i	1.27615	−	0.736787i	0.976139	+	0.217148i	$0.0696756\pi$
$314$	39.9054			2.25199
$315$		0			0
$316$	−29.3364			−1.65030
$317$	12.0290	−	6.94495i	0.675616	−	0.390067i	−0.122585	−	0.992458i	$-0.539118\pi$
$317$	12.0290	−	6.94495i	0.675616	−	0.390067i	0.798201	+	0.602391i	$0.205785\pi$
$318$		0			0
$319$	0.249588	−	0.432300i	0.0139743	−	0.0242041i
$320$	29.7891			1.66526
$321$		0			0
$322$		0			0
$323$			8.99200i			0.500328i
$324$		0			0
$325$	5.79883	−	3.34796i	0.321661	−	0.185711i
$326$			49.1869i			2.72421i
$327$		0			0
$328$	−52.6228	+	30.3818i	−2.90561	+	1.67755i
$329$		0			0
$330$		0			0
$331$	−2.24230	−	3.88378i	−0.123248	−	0.213472i	0.797799	−	0.602924i	$-0.205998\pi$
$331$	−2.24230	−	3.88378i	−0.123248	−	0.213472i	−0.921047	+	0.389452i	$0.872664\pi$
$332$	−8.58600	−	14.8714i	−0.471218	−	0.816173i
$333$		0			0
$334$	−2.81245	−	1.62377i	−0.153891	−	0.0888487i
$335$	−3.10274	+	5.37411i	−0.169521	+	0.293619i
$336$		0			0
$337$	−16.4010	−	28.4074i	−0.893420	−	1.54745i	−0.835748	−	0.549113i	$-0.814965\pi$
$337$	−16.4010	−	28.4074i	−0.893420	−	1.54745i	−0.0576723	−	0.998336i	$-0.518368\pi$
$338$		−	25.5938i		−	1.39212i
$339$		0			0
$340$	−7.72905			−0.419167
$341$	−4.35557	+	7.54407i	−0.235867	+	0.408534i
$342$		0			0
$343$		0			0
$344$	0.102732	+	0.0593121i	0.00553891	+	0.00319789i
$345$		0			0
$346$	−42.2454	−	24.3904i	−2.27112	−	1.31123i
$347$	11.6112	+	6.70374i	0.623323	+	0.359876i	0.778162	−	0.628064i	$-0.216152\pi$
$347$	11.6112	+	6.70374i	0.623323	+	0.359876i	−0.154839	+	0.987940i	$0.549486\pi$
$348$		0			0
$349$	−19.3276	−	11.1588i	−1.03458	−	0.597316i	−0.116288	−	0.993215i	$-0.537100\pi$
$349$	−19.3276	−	11.1588i	−1.03458	−	0.597316i	−0.918294	+	0.395899i	$0.870433\pi$
$350$		0			0
$351$		0			0
$352$	24.0494	−	41.6548i	1.28184	−	2.22021i
$353$	−17.2168			−0.916360			−0.458180	−	0.888859i	$-0.651499\pi$
$353$	−17.2168			−0.916360			−0.458180	+	0.888859i	$0.651499\pi$
$354$		0			0
$355$			14.4895i			0.769024i
$356$	−21.2637	−	36.8298i	−1.12697	−	1.95198i
$357$		0			0
$358$	−20.5090	+	35.5227i	−1.08394	+	1.87743i
$359$	−5.62867	−	3.24971i	−0.297070	−	0.171513i	0.344056	−	0.938949i	$-0.388199\pi$
$359$	−5.62867	−	3.24971i	−0.297070	−	0.171513i	−0.641126	+	0.767436i	$0.721532\pi$
$360$		0			0
$361$	18.4015	+	31.8722i	0.968497	+	1.67749i
$362$	−10.8179	−	18.7372i	−0.568577	−	0.984805i
$363$		0			0
$364$		0			0
$365$	−9.03424	+	5.21592i	−0.472874	+	0.273014i
$366$		0			0
$367$		−	9.00360i		−	0.469984i	−0.971997	−	0.234992i	$-0.924494\pi$
$367$		−	9.00360i		−	0.469984i	0.971997	−	0.234992i	$-0.0755064\pi$
$368$	−36.3860	+	21.0075i	−1.89675	+	1.09509i
$369$		0			0
$370$			5.64024i			0.293222i
$371$		0			0
$372$		0			0
$373$	11.5062			0.595771			0.297885	−	0.954602i	$-0.403719\pi$
$373$	11.5062			0.595771			0.297885	+	0.954602i	$0.403719\pi$
$374$	−4.05412	+	7.02194i	−0.209633	+	0.363096i
$375$		0			0
$376$	11.2347	−	6.48634i	0.579384	−	0.334507i
$377$	−0.378318			−0.0194844
$378$		0			0
$379$	17.0982			0.878275			0.439138	−	0.898420i	$-0.355284\pi$
$379$	17.0982			0.878275			0.439138	+	0.898420i	$0.355284\pi$
$380$	−41.5391	+	23.9826i	−2.13091	+	1.23028i
$381$		0			0
$382$	−21.6936	+	37.5744i	−1.10994	+	1.92247i
$383$	−16.2156			−0.828577			−0.414288	−	0.910146i	$-0.635970\pi$
$383$	−16.2156			−0.828577			−0.414288	+	0.910146i	$0.635970\pi$
$384$		0			0
$385$		0			0
$386$			37.1363i			1.89019i
$387$		0			0
$388$	−11.0097	+	6.35643i	−0.558931	+	0.322699i
$389$		−	18.7475i		−	0.950537i	−0.879841	−	0.475269i	$-0.842351\pi$
$389$		−	18.7475i		−	0.950537i	0.879841	−	0.475269i	$-0.157649\pi$
$390$		0			0
$391$	3.17012	−	1.83027i	0.160320	−	0.0925607i
$392$		0			0
$393$		0			0
$394$	25.6321	+	44.3961i	1.29133	+	2.23664i
$395$	3.30565	+	5.72556i	0.166326	+	0.288084i
$396$		0			0
$397$	−26.8216	−	15.4854i	−1.34614	−	0.777192i	−0.358436	−	0.933554i	$-0.616690\pi$
$397$	−26.8216	−	15.4854i	−1.34614	−	0.777192i	−0.987700	+	0.156362i	$0.950023\pi$
$398$	−33.6334	+	58.2548i	−1.68589	+	2.92005i
$399$		0			0
$400$	24.5441	+	42.5116i	1.22720	+	2.12558i
$401$			0.924990i			0.0461918i	0.999733	+	0.0230959i	$0.00735231\pi$
$401$			0.924990i			0.0461918i	−0.999733	+	0.0230959i	$0.992648\pi$
$402$		0			0
$403$	6.60203			0.328870
$404$	25.2621	−	43.7552i	1.25684	−	2.17690i
$405$		0			0
$406$		0			0
$407$	3.72755	+	2.15210i	0.184768	+	0.106676i
$408$		0			0
$409$	6.56585	+	3.79079i	0.324660	+	0.187443i	0.653468	−	0.756954i	$-0.273313\pi$
$409$	6.56585	+	3.79079i	0.324660	+	0.187443i	−0.328808	+	0.944397i	$0.606647\pi$
$410$	18.9653	+	10.9496i	0.936629	+	0.540763i
$411$		0			0
$412$	79.7782	+	46.0599i	3.93039	+	2.26921i
$413$		0			0
$414$		0			0
$415$	−1.93496	+	3.35145i	−0.0949834	+	0.164516i
$416$	−36.4533			−1.78727
$417$		0			0
$418$			50.3184i			2.46115i
$419$	2.85061	+	4.93740i	0.139262	+	0.241208i	0.927217	−	0.374524i	$-0.122194\pi$
$419$	2.85061	+	4.93740i	0.139262	+	0.241208i	−0.787956	+	0.615732i	$0.788860\pi$
$420$		0			0
$421$	−5.86189	+	10.1531i	−0.285691	+	0.494832i	−0.972777	−	0.231745i	$-0.925557\pi$
$421$	−5.86189	+	10.1531i	−0.285691	+	0.494832i	0.687085	+	0.726577i	$0.258890\pi$
$422$	−16.9263	−	9.77240i	−0.823959	−	0.475713i
$423$		0			0
$424$	−44.7926	−	77.5830i	−2.17532	−	3.76776i
$425$	−2.13840	−	3.70381i	−0.103728	−	0.179661i
$426$		0			0
$427$		0			0
$428$	45.6877	−	26.3778i	2.20840	−	1.27502i
$429$		0			0
$430$		−	0.0427522i		−	0.00206169i
$431$	23.2973	−	13.4507i	1.12219	−	0.647897i	0.180231	−	0.983624i	$-0.442315\pi$
$431$	23.2973	−	13.4507i	1.12219	−	0.647897i	0.941959	+	0.335728i	$0.108982\pi$
$432$		0			0
$433$		−	28.1028i		−	1.35053i	−0.737574	−	0.675266i	$-0.764029\pi$
$433$		−	28.1028i		−	1.35053i	0.737574	−	0.675266i	$-0.235971\pi$
$434$		0			0
$435$		0			0
$436$	−55.5850			−2.66204
$437$	11.3584	−	19.6733i	0.543344	−	0.941099i
$438$		0			0
$439$	8.07680	−	4.66314i	0.385485	−	0.222560i	−0.294717	−	0.955585i	$-0.595225\pi$
$439$	8.07680	−	4.66314i	0.385485	−	0.222560i	0.680202	+	0.733025i	$0.261892\pi$
$440$	−27.0454			−1.28934
$441$		0			0
$442$	6.14510			0.292292
$443$	9.82131	−	5.67034i	0.466624	−	0.269406i	−0.248201	−	0.968709i	$-0.579839\pi$
$443$	9.82131	−	5.67034i	0.466624	−	0.269406i	0.714826	+	0.699303i	$0.246506\pi$
$444$		0			0
$445$	−4.79203	+	8.30004i	−0.227164	+	0.393460i
$446$	−65.9063			−3.12076
$447$		0			0
$448$		0			0
$449$			15.3295i			0.723444i	0.932286	+	0.361722i	$0.117811\pi$
$449$			15.3295i			0.723444i	−0.932286	+	0.361722i	$0.882189\pi$
$450$		0			0
$451$	14.4729	−	8.35592i	0.681501	−	0.393465i
$452$		−	58.9316i		−	2.77191i
$453$		0			0
$454$	−1.12739	+	0.650900i	−0.0529111	+	0.0305483i
$455$		0			0
$456$		0			0
$457$	4.58649	+	7.94404i	0.214547	+	0.371606i	0.953132	−	0.302554i	$-0.0978391\pi$
$457$	4.58649	+	7.94404i	0.214547	+	0.371606i	−0.738585	+	0.674160i	$0.764506\pi$
$458$	12.2057	+	21.1408i	0.570333	+	0.987846i
$459$		0			0
$460$	16.9101	+	9.76305i	0.788438	+	0.455205i
$461$	16.5365	−	28.6420i	0.770181	−	1.33399i	−0.167283	−	0.985909i	$-0.553499\pi$
$461$	16.5365	−	28.6420i	0.770181	−	1.33399i	0.937464	−	0.348083i	$-0.113167\pi$
$462$		0			0
$463$	3.91594	+	6.78260i	0.181989	+	0.315214i	0.942558	−	0.334043i	$-0.108413\pi$
$463$	3.91594	+	6.78260i	0.181989	+	0.315214i	−0.760569	+	0.649257i	$0.775080\pi$
$464$		−	2.77347i		−	0.128755i
$465$		0			0
$466$	30.1135			1.39498
$467$	−10.3385	+	17.9068i	−0.478408	+	0.828627i	−0.999694	−	0.0247555i	$-0.992119\pi$
$467$	−10.3385	+	17.9068i	−0.478408	+	0.828627i	0.521286	+	0.853382i	$0.325453\pi$
$468$		0			0
$469$		0			0
$470$	−4.04898	−	2.33768i	−0.186765	−	0.107829i
$471$		0			0
$472$	95.6765	+	55.2389i	4.40387	+	2.54257i
$473$	−0.0282543	−	0.0163126i	−0.00129913	−	0.000750056i
$474$		0			0
$475$	−22.9853	−	13.2706i	−1.05464	−	0.608895i
$476$		0			0
$477$		0			0
$478$	18.8371	−	32.6267i	0.861587	−	1.49231i
$479$	2.65998			0.121538			0.0607688	−	0.998152i	$-0.480645\pi$
$479$	2.65998			0.121538			0.0607688	+	0.998152i	$0.480645\pi$
$480$		0			0
$481$		−	3.26208i		−	0.148738i
$482$	−16.7624	−	29.0334i	−0.763508	−	1.32243i
$483$		0			0
$484$	12.8547	−	22.2649i	0.584303	−	1.01204i
$485$	2.48116	+	1.43250i	0.112664	+	0.0650465i
$486$		0			0
$487$	0.521900	+	0.903957i	0.0236495	+	0.0409622i	0.877608	−	0.479379i	$-0.159138\pi$
$487$	0.521900	+	0.903957i	0.0236495	+	0.0409622i	−0.853958	+	0.520341i	$0.825805\pi$
$488$	50.8383	+	88.0546i	2.30134	+	3.98604i
$489$		0			0
$490$		0			0
$491$	−36.0415	+	20.8085i	−1.62653	+	0.939076i	−0.641410	+	0.767198i	$0.721650\pi$
$491$	−36.0415	+	20.8085i	−1.62653	+	0.939076i	−0.985118	+	0.171878i	$0.945016\pi$
$492$		0			0
$493$			0.241638i			0.0108828i
$494$	33.0263	−	19.0677i	1.48592	−	0.857898i
$495$		0			0
$496$			48.3999i			2.17322i
$497$		0			0
$498$		0			0
$499$	−32.2895			−1.44548			−0.722738	−	0.691122i	$-0.757117\pi$
$499$	−32.2895			−1.44548			−0.722738	+	0.691122i	$0.757117\pi$
$500$	27.4590	−	47.5604i	1.22800	−	2.12697i
$501$		0			0
$502$	46.2490	−	26.7019i	2.06420	−	1.19176i
$503$	−39.9702			−1.78218			−0.891091	−	0.453825i	$-0.850059\pi$
$503$	−39.9702			−1.78218			−0.891091	+	0.453825i	$0.850059\pi$
$504$		0			0
$505$	−11.3862			−0.506681
$506$	17.7397	−	10.2420i	0.788626	−	0.455314i
$507$		0			0
$508$	36.9998	−	64.0856i	1.64160	−	2.84334i
$509$	−22.7262			−1.00732			−0.503661	−	0.863901i	$-0.668014\pi$
$509$	−22.7262			−1.00732			−0.503661	+	0.863901i	$0.668014\pi$
$510$		0			0
$511$		0			0
$512$		−	17.4067i		−	0.769277i
$513$		0			0
$514$	−26.3692	+	15.2243i	−1.16310	+	0.671515i
$515$		−	20.7603i		−	0.914810i
$516$		0			0
$517$	−3.08988	+	1.78394i	−0.135893	+	0.0784576i
$518$		0			0
$519$		0			0
$520$	10.2486	+	17.7511i	0.449432	+	0.778439i
$521$	15.0179	+	26.0118i	0.657948	+	1.13960i	0.981146	+	0.193268i	$0.0619087\pi$
$521$	15.0179	+	26.0118i	0.657948	+	1.13960i	−0.323198	+	0.946331i	$0.604758\pi$
$522$		0			0
$523$	0.675300	+	0.389885i	0.0295288	+	0.0170485i	0.514692	−	0.857375i	$-0.327906\pi$
$523$	0.675300	+	0.389885i	0.0295288	+	0.0170485i	−0.485163	+	0.874424i	$0.661240\pi$
$524$	32.9860	−	57.1334i	1.44100	−	2.49588i
$525$		0			0
$526$	4.41260	+	7.64285i	0.192399	+	0.333244i
$527$		−	4.21683i		−	0.183688i
$528$		0			0
$529$	13.7523			0.597926
$530$	−16.1433	+	27.9609i	−0.701218	+	1.21455i
$531$		0			0
$532$		0			0
$533$	−10.9688	−	6.33281i	−0.475110	−	0.274305i
$534$		0			0
$535$	−10.2963	−	5.94457i	−0.445147	−	0.257006i
$536$	40.3927	+	23.3207i	1.74470	+	1.00730i
$537$		0			0
$538$	0.568399	+	0.328165i	0.0245054	+	0.0141482i
$539$		0			0
$540$		0			0
$541$	−1.02015	+	1.76696i	−0.0438598	+	0.0759674i	−0.887122	−	0.461535i	$-0.847299\pi$
$541$	−1.02015	+	1.76696i	−0.0438598	+	0.0759674i	0.843262	+	0.537503i	$0.180632\pi$
$542$	−2.90670			−0.124854
$543$		0			0
$544$			23.2833i			0.998264i
$545$	6.26338	+	10.8485i	0.268294	+	0.464699i
$546$		0			0
$547$	−8.93590	+	15.4774i	−0.382071	+	0.661767i	−0.991358	−	0.131183i	$-0.958123\pi$
$547$	−8.93590	+	15.4774i	−0.382071	+	0.661767i	0.609287	+	0.792950i	$0.291456\pi$
$548$	53.9064	+	31.1229i	2.30277	+	1.32950i
$549$		0			0
$550$	−11.9663	−	20.7262i	−0.510244	−	0.883769i
$551$	0.749783	+	1.29866i	0.0319418	+	0.0553249i
$552$		0			0
$553$		0			0
$554$	11.4986	−	6.63870i	0.488527	−	0.282051i
$555$		0			0
$556$			53.8625i			2.28428i
$557$	−37.2049	+	21.4802i	−1.57642	+	0.910147i	−0.581068	+	0.813855i	$0.697365\pi$
$557$	−37.2049	+	21.4802i	−1.57642	+	0.910147i	−0.995353	+	0.0962924i	$0.969302\pi$
$558$		0			0
$559$			0.0247261i			0.00104580i
$560$		0			0
$561$		0			0
$562$	36.1625			1.52543
$563$	−0.773739	+	1.34016i	−0.0326092	+	0.0564808i	−0.881869	−	0.471494i	$-0.843715\pi$
$563$	−0.773739	+	1.34016i	−0.0326092	+	0.0564808i	0.849260	+	0.527975i	$0.177048\pi$
$564$		0			0
$565$	−11.5016	+	6.64048i	−0.483878	+	0.279367i
$566$	10.1759			0.427726
$567$		0			0
$568$	108.906			4.56958
$569$	−8.65905	+	4.99931i	−0.363006	+	0.209582i	−0.670399	−	0.742001i	$-0.733877\pi$
$569$	−8.65905	+	4.99931i	−0.363006	+	0.209582i	0.307392	+	0.951583i	$0.400544\pi$
$570$		0			0
$571$	1.39715	−	2.41994i	0.0584689	−	0.101271i	−0.835309	−	0.549780i	$-0.814711\pi$
$571$	1.39715	−	2.41994i	0.0584689	−	0.101271i	0.893778	+	0.448509i	$0.148045\pi$
$572$	25.0147			1.04592
$573$		0			0
$574$		0			0
$575$			10.8046i			0.450582i
$576$		0			0
$577$	3.23689	−	1.86882i	0.134754	−	0.0778000i	−0.431108	−	0.902300i	$-0.641877\pi$
$577$	3.23689	−	1.86882i	0.134754	−	0.0778000i	0.565861	+	0.824500i	$0.308544\pi$
$578$			42.1251i			1.75217i
$579$		0			0
$580$	−1.11626	+	0.644475i	−0.0463503	+	0.0267604i
$581$		0			0
$582$		0			0
$583$	12.3193	+	21.3377i	0.510214	+	0.883717i
$584$	39.2037	+	67.9028i	1.62226	+	2.80984i
$585$		0			0
$586$	−29.9540	−	17.2940i	−1.23739	−	0.714407i
$587$	−13.1249	+	22.7331i	−0.541725	+	0.938295i	0.457081	+	0.889425i	$0.348895\pi$
$587$	−13.1249	+	22.7331i	−0.541725	+	0.938295i	−0.998805	+	0.0488692i	$0.984438\pi$
$588$		0			0
$589$	−13.0845	−	22.6630i	−0.539136	−	0.933812i
$590$		−	39.8162i		−	1.63921i
$591$		0			0
$592$	23.9145			0.982882
$593$	1.79833	−	3.11481i	0.0738488	−	0.127910i	−0.826736	−	0.562590i	$-0.809805\pi$
$593$	1.79833	−	3.11481i	0.0738488	−	0.127910i	0.900585	+	0.434680i	$0.143138\pi$
$594$		0			0
$595$		0			0
$596$	−22.1522	−	12.7896i	−0.907391	−	0.523882i
$597$		0			0
$598$	−13.4446	−	7.76226i	−0.549792	−	0.317422i
$599$	20.6400	+	11.9165i	0.843326	+	0.486895i	0.858394	−	0.512992i	$-0.171463\pi$
$599$	20.6400	+	11.9165i	0.843326	+	0.486895i	−0.0150672	+	0.999886i	$0.504796\pi$
$600$		0			0
$601$	14.6034	+	8.43126i	0.595684	+	0.343918i	0.767342	−	0.641238i	$-0.221579\pi$
$601$	14.6034	+	8.43126i	0.595684	+	0.343918i	−0.171658	+	0.985157i	$0.554912\pi$
$602$		0			0
$603$		0			0
$604$	−30.2076	+	52.3212i	−1.22913	+	2.12892i
$605$	−5.79391			−0.235556
$606$		0			0
$607$			10.4816i			0.425437i	0.977114	+	0.212718i	$0.0682317\pi$
$607$			10.4816i			0.425437i	−0.977114	+	0.212718i	$0.931768\pi$
$608$	72.2463	+	125.134i	2.92997	+	5.07487i
$609$		0			0
$610$	18.3222	−	31.7349i	0.741842	−	1.28491i
$611$	2.34176	+	1.35202i	0.0947377	+	0.0546968i
$612$		0			0
$613$	23.9500	+	41.4827i	0.967333	+	1.67547i	0.703213	+	0.710979i	$0.251748\pi$
$613$	23.9500	+	41.4827i	0.967333	+	1.67547i	0.264120	+	0.964490i	$0.414919\pi$
$614$	14.5270	+	25.1616i	0.586264	+	1.01544i
$615$		0			0
$616$		0			0
$617$	−4.69477	+	2.71053i	−0.189004	+	0.109122i	−0.591516	−	0.806293i	$-0.701470\pi$
$617$	−4.69477	+	2.71053i	−0.189004	+	0.109122i	0.402512	+	0.915415i	$0.368137\pi$
$618$		0			0
$619$			32.3003i			1.29826i	0.760678	+	0.649129i	$0.224866\pi$
$619$			32.3003i			1.29826i	−0.760678	+	0.649129i	$0.775134\pi$
$620$	19.4799	−	11.2467i	0.782332	−	0.451680i
$621$		0			0
$622$		−	51.0204i		−	2.04573i
$623$		0			0
$624$		0			0
$625$	5.38836			0.215534
$626$	−35.3098	+	61.1584i	−1.41126	+	2.44438i
$627$		0			0
$628$	−68.0989	+	39.3169i	−2.71744	+	1.56892i
$629$	−2.08355			−0.0830765
$630$		0			0
$631$	−18.3539			−0.730656			−0.365328	−	0.930879i	$-0.619043\pi$
$631$	−18.3539			−0.730656			−0.365328	+	0.930879i	$0.619043\pi$
$632$	43.0343	−	24.8459i	1.71181	−	0.988315i
$633$		0			0
$634$	−18.8127	+	32.5845i	−0.747147	+	1.29410i
$635$	−16.6767			−0.661795
$636$		0			0
$637$		0			0
$638$			1.35218i			0.0535335i
$639$		0			0
$640$	−29.5816	+	17.0789i	−1.16931	+	0.675104i
$641$			10.4732i			0.413665i	0.978376	+	0.206833i	$0.0663155\pi$
$641$			10.4732i			0.413665i	−0.978376	+	0.206833i	$0.933684\pi$
$642$		0			0
$643$	−3.37572	+	1.94897i	−0.133125	+	0.0768600i	−0.565084	−	0.825034i	$-0.691156\pi$
$643$	−3.37572	+	1.94897i	−0.133125	+	0.0768600i	0.431958	+	0.901894i	$0.357823\pi$
$644$		0			0
$645$		0			0
$646$	−12.1789	−	21.0945i	−0.479172	−	0.829950i
$647$	−6.20269	−	10.7434i	−0.243853	−	0.422366i	0.717955	−	0.696089i	$-0.245078\pi$
$647$	−6.20269	−	10.7434i	−0.243853	−	0.422366i	−0.961809	+	0.273723i	$0.911745\pi$
$648$		0			0
$649$	−26.3140	−	15.1924i	−1.03291	−	0.596353i
$650$	−9.06905	+	15.7081i	−0.355717	+	0.616120i
$651$		0			0
$652$	−48.4615	−	83.9377i	−1.89790	−	3.28726i
$653$			14.1738i			0.554664i	0.960774	+	0.277332i	$0.0894502\pi$
$653$			14.1738i			0.554664i	−0.960774	+	0.277332i	$0.910550\pi$
$654$		0			0
$655$	−14.8676			−0.580925
$656$	46.4263	−	80.4126i	1.81264	−	3.13959i
$657$		0			0
$658$		0			0
$659$	17.2962	+	9.98594i	0.673763	+	0.388997i	0.797501	−	0.603318i	$-0.206155\pi$
$659$	17.2962	+	9.98594i	0.673763	+	0.388997i	−0.123738	+	0.992315i	$0.539488\pi$
$660$		0			0
$661$	−21.0493	−	12.1528i	−0.818721	−	0.472689i	0.0312540	−	0.999511i	$-0.490050\pi$
$661$	−21.0493	−	12.1528i	−0.818721	−	0.472689i	−0.849975	+	0.526823i	$0.823383\pi$
$662$	10.5205	+	6.07401i	0.408891	+	0.236073i
$663$		0			0
$664$	25.1900	+	14.5435i	0.977563	+	0.564396i
$665$		0			0
$666$		0			0
$667$	0.305228	−	0.528670i	0.0118185	−	0.0204702i
$668$	6.39929			0.247596
$669$		0			0
$670$		−	16.8096i		−	0.649411i
$671$	−13.9821	−	24.2177i	−0.539773	−	0.934914i
$672$		0			0
$673$	−1.82521	+	3.16135i	−0.0703566	+	0.121861i	−0.899058	−	0.437830i	$-0.855747\pi$
$673$	−1.82521	+	3.16135i	−0.0703566	+	0.121861i	0.828701	+	0.559692i	$0.189080\pi$
$674$	76.9508	+	44.4275i	2.96403	+	1.71129i
$675$		0			0
$676$	25.2163	+	43.6759i	0.969858	+	1.67984i
$677$	−0.968676	−	1.67780i	−0.0372292	−	0.0644829i	0.846810	−	0.531895i	$-0.178520\pi$
$677$	−0.968676	−	1.67780i	−0.0372292	−	0.0644829i	−0.884040	+	0.467412i	$0.845187\pi$
$678$		0			0
$679$		0			0
$680$	11.3379	−	6.54597i	0.434790	−	0.251026i
$681$		0			0
$682$		−	23.5970i		−	0.903575i
$683$	16.8815	−	9.74656i	0.645954	−	0.372942i	−0.140950	−	0.990017i	$-0.545016\pi$
$683$	16.8815	−	9.74656i	0.645954	−	0.372942i	0.786905	+	0.617075i	$0.211682\pi$
$684$		0			0
$685$		−	14.0278i		−	0.535976i
$686$		0			0
$687$		0			0
$688$	−0.181269			−0.00691081
$689$	9.33660	−	16.1715i	0.355696	−	0.616084i
$690$		0			0
$691$	−35.7855	+	20.6608i	−1.36134	+	0.785972i	−0.989803	−	0.142444i	$-0.954504\pi$
$691$	−35.7855	+	20.6608i	−1.36134	+	0.785972i	−0.371541	+	0.928416i	$0.621171\pi$
$692$	96.1226			3.65403
$693$		0			0
$694$	−36.3186			−1.37863
$695$	10.5123	−	6.06929i	0.398755	−	0.230221i
$696$		0			0
$697$	−4.04488	+	7.00593i	−0.153211	+	0.265369i
$698$	60.4545			2.28824
$699$		0			0
$700$		0			0
$701$		−	27.3333i		−	1.03236i	−0.856479	−	0.516182i	$-0.827353\pi$
$701$		−	27.3333i		−	1.03236i	0.856479	−	0.516182i	$-0.172647\pi$
$702$		0			0
$703$	−11.1979	+	6.46508i	−0.422335	+	0.243835i
$704$			61.5793i			2.32086i
$705$		0			0
$706$	40.3893	−	23.3187i	1.52007	−	0.877613i
$707$		0			0
$708$		0			0
$709$	−1.35635	−	2.34926i	−0.0509387	−	0.0882283i	0.839432	−	0.543465i	$-0.182888\pi$
$709$	−1.35635	−	2.34926i	−0.0509387	−	0.0882283i	−0.890370	+	0.455237i	$0.849555\pi$
$710$	−19.6248	−	33.9912i	−0.736506	−	1.27567i
$711$		0			0
$712$	62.3845	+	36.0177i	2.33796	+	1.34982i
$713$	−5.32654	+	9.22584i	−0.199480	+	0.345510i
$714$		0			0
$715$	−2.81868	−	4.88210i	−0.105413	−	0.182580i
$716$		−	80.8262i		−	3.02062i
$717$		0			0
$718$	17.6058			0.657044
$719$	−8.13931	+	14.0977i	−0.303545	+	0.525756i	−0.976936	−	0.213531i	$-0.931504\pi$
$719$	−8.13931	+	14.0977i	−0.303545	+	0.525756i	0.673391	+	0.739286i	$0.264837\pi$
$720$		0			0
$721$		0			0
$722$	−86.3365	−	49.8464i	−3.21311	−	1.85509i
$723$		0			0
$724$	36.9217	+	21.3167i	1.37218	+	0.792231i
$725$	−0.617673	−	0.356614i	−0.0229398	−	0.0132443i
$726$		0			0
$727$	0.980123	+	0.565874i	0.0363508	+	0.0209871i	0.518065	−	0.855341i	$-0.326652\pi$
$727$	0.980123	+	0.565874i	0.0363508	+	0.0209871i	−0.481714	+	0.876328i	$0.659986\pi$
$728$		0			0
$729$		0			0
$730$	14.1290	−	24.4722i	0.522939	−	0.905757i
$731$	0.0157930			0.000584125
$732$		0			0
$733$		−	38.3459i		−	1.41634i	−0.706043	−	0.708169i	$-0.749522\pi$
$733$		−	38.3459i		−	1.41634i	0.706043	−	0.708169i	$-0.250478\pi$
$734$	12.1946	+	21.1217i	0.450111	+	0.779615i
$735$		0			0
$736$	29.4106	−	50.9407i	1.08409	−	1.87770i
$737$	−11.1092	−	6.41391i	−0.409213	−	0.236259i
$738$		0			0
$739$	−5.36489	−	9.29226i	−0.197351	−	0.341821i	0.750318	−	0.661077i	$-0.229900\pi$
$739$	−5.36489	−	9.29226i	−0.197351	−	0.341821i	−0.947669	+	0.319256i	$0.896567\pi$
$740$	−5.55705	−	9.62509i	−0.204281	−	0.353825i
$741$		0			0
$742$		0			0
$743$	11.3308	−	6.54185i	0.415687	−	0.239997i	−0.277543	−	0.960713i	$-0.589520\pi$
$743$	11.3308	−	6.54185i	0.415687	−	0.239997i	0.693230	+	0.720716i	$0.256187\pi$
$744$		0			0
$745$			5.76458i			0.211198i
$746$	−26.9927	+	15.5842i	−0.988272	+	0.570579i
$747$		0			0
$748$		−	15.9773i		−	0.584188i
$749$		0			0
$750$		0			0
$751$	26.3354			0.960991			0.480495	−	0.876997i	$-0.340457\pi$
$751$	26.3354			0.960991			0.480495	+	0.876997i	$0.340457\pi$
$752$	−9.91173	+	17.1676i	−0.361444	+	0.626039i
$753$		0			0
$754$	0.887501	−	0.512399i	0.0323209	−	0.0186605i
$755$	13.6153			0.495512
$756$		0			0
$757$	−32.6280			−1.18588			−0.592942	−	0.805245i	$-0.702034\pi$
$757$	−32.6280			−1.18588			−0.592942	+	0.805245i	$0.702034\pi$
$758$	−40.1109	+	23.1580i	−1.45689	+	0.841138i
$759$		0			0
$760$	40.6232	−	70.3615i	1.47356	−	2.55228i
$761$	25.3454			0.918770			0.459385	−	0.888237i	$-0.348070\pi$
$761$	25.3454			0.918770			0.459385	+	0.888237i	$0.348070\pi$
$762$		0			0
$763$		0			0
$764$		−	85.4946i		−	3.09309i
$765$		0			0
$766$	38.0403	−	21.9626i	1.37445	−	0.793541i
$767$			23.0281i			0.831496i
$768$		0			0
$769$	11.4964	−	6.63744i	0.414570	−	0.239352i	−0.278181	−	0.960529i	$-0.589732\pi$
$769$	11.4964	−	6.63744i	0.414570	−	0.239352i	0.692752	+	0.721176i	$0.256398\pi$
$770$		0			0
$771$		0			0
$772$	−36.5886	−	63.3733i	−1.31685	−	2.28085i
$773$	8.00680	+	13.8682i	0.287985	+	0.498804i	0.973329	−	0.229416i	$-0.0736815\pi$
$773$	8.00680	+	13.8682i	0.287985	+	0.498804i	−0.685344	+	0.728219i	$0.740348\pi$
$774$		0			0
$775$	10.7790	+	6.22327i	0.387194	+	0.223546i
$776$	10.7669	−	18.6488i	0.386509	−	0.669454i
$777$		0			0
$778$	25.3919	+	43.9801i	0.910344	+	1.57676i
$779$			50.2037i			1.79873i
$780$		0			0
$781$	−29.9524			−1.07178
$782$	−4.95789	+	8.58731i	−0.177294	+	0.307082i
$783$		0			0
$784$		0			0
$785$	15.3469	+	8.86054i	0.547755	+	0.316246i
$786$		0			0
$787$	4.24659	+	2.45177i	0.151375	+	0.0873961i	0.573774	−	0.819014i	$-0.305479\pi$
$787$	4.24659	+	2.45177i	0.151375	+	0.0873961i	−0.422400	+	0.906410i	$0.638812\pi$
$788$	−87.4826	−	50.5081i	−3.11644	−	1.79928i
$789$		0			0
$790$	−15.5096	−	8.95445i	−0.551806	−	0.318585i
$791$		0			0
$792$		0			0
$793$	−10.5968	+	18.3542i	−0.376303	+	0.651776i
$794$	83.8948			2.97732
$795$		0			0
$796$		−	132.550i		−	4.69809i
$797$	−21.3994	−	37.0649i	−0.758006	−	1.31290i	−0.943866	−	0.330328i	$-0.892841\pi$
$797$	−21.3994	−	37.0649i	−0.758006	−	1.31290i	0.185860	−	0.982576i	$-0.440493\pi$
$798$		0			0
$799$	0.863557	−	1.49572i	0.0305505	−	0.0529149i
$800$	−59.5167	−	34.3620i	−2.10423	−	1.21488i
$801$		0			0
$802$	−1.25282	−	2.16995i	−0.0442386	−	0.0766235i
$803$	−10.7822	−	18.6754i	−0.380496	−	0.659039i
$804$		0			0
$805$		0			0
$806$	−15.4878	+	8.94188i	−0.545534	+	0.314964i
$807$		0			0
$808$			85.5809i			3.01072i
$809$	30.5649	−	17.6467i	1.07461	−	0.620424i	0.145169	−	0.989407i	$-0.453627\pi$
$809$	30.5649	−	17.6467i	1.07461	−	0.620424i	0.929436	+	0.368983i	$0.120294\pi$
$810$		0			0
$811$			21.0223i			0.738193i	0.929391	+	0.369096i	$0.120333\pi$
$811$			21.0223i			0.738193i	−0.929391	+	0.369096i	$0.879667\pi$
$812$		0			0
$813$		0			0
$814$	−11.6594			−0.408660
$815$	−10.9214	+	18.9164i	−0.382559	+	0.662612i
$816$		0			0
$817$	0.0848782	−	0.0490044i	0.00296951	−	0.00171445i
$818$	−20.5372			−0.718067
$819$		0			0
$820$	−43.1525			−1.50695
$821$	−29.8623	+	17.2410i	−1.04220	+	0.601716i	−0.920456	−	0.390845i	$-0.872183\pi$
$821$	−29.8623	+	17.2410i	−1.04220	+	0.601716i	−0.121746	+	0.992561i	$0.538849\pi$
$822$		0			0
$823$	19.4950	−	33.7663i	0.679552	−	1.17702i	−0.295564	−	0.955323i	$-0.595508\pi$
$823$	19.4950	−	33.7663i	0.679552	−	1.17702i	0.975116	−	0.221695i	$-0.0711590\pi$
$824$	−156.038			−5.43585
$825$		0			0
$826$		0			0
$827$			47.2537i			1.64317i	0.570086	+	0.821585i	$0.306910\pi$
$827$			47.2537i			1.64317i	−0.570086	+	0.821585i	$0.693090\pi$
$828$		0			0
$829$	−42.5588	+	24.5713i	−1.47813	+	0.853397i	−0.999694	−	0.0247275i	$-0.992128\pi$
$829$	−42.5588	+	24.5713i	−1.47813	+	0.853397i	−0.478432	+	0.878124i	$0.658795\pi$
$830$		−	10.4829i		−	0.363868i
$831$		0			0
$832$	40.4174	−	23.3350i	1.40122	−	0.808995i
$833$		0			0
$834$		0			0
$835$	−0.721079	−	1.24894i	−0.0249540	−	0.0432215i
$836$	−49.5763	−	85.8687i	−1.71463	−	2.96983i
$837$		0			0
$838$	−13.3746	−	7.72182i	−0.462017	−	0.266746i
$839$	26.0780	−	45.1684i	0.900312	−	1.55939i	0.0732219	−	0.997316i	$-0.476672\pi$
$839$	26.0780	−	45.1684i	0.900312	−	1.55939i	0.827090	−	0.562070i	$-0.189995\pi$
$840$		0			0
$841$	−14.4799	−	25.0798i	−0.499305	−	0.864822i
$842$		−	31.7577i		−	1.09444i
$843$		0			0
$844$	38.5131			1.32568
$845$	5.68280	−	9.84290i	0.195494	−	0.338606i
$846$		0			0
$847$		0			0
$848$	118.554	+	68.4472i	4.07116	+	2.35049i
$849$		0			0
$850$	10.0330	+	5.79255i	0.344129	+	0.198683i
$851$	4.55852	+	2.63186i	0.156264	+	0.0902190i
$852$		0			0
$853$	13.4028	+	7.73808i	0.458902	+	0.264947i	0.711582	−	0.702603i	$-0.247979\pi$
$853$	13.4028	+	7.73808i	0.458902	+	0.264947i	−0.252681	+	0.967550i	$0.581312\pi$
$854$		0			0
$855$		0			0
$856$	−44.6804	+	77.3886i	−1.52714	+	2.64509i
$857$	−48.8713			−1.66941			−0.834706	−	0.550696i	$-0.814362\pi$
$857$	−48.8713			−1.66941			−0.834706	+	0.550696i	$0.814362\pi$
$858$		0			0
$859$			9.75722i			0.332912i	0.986049	+	0.166456i	$0.0532324\pi$
$859$			9.75722i			0.332912i	−0.986049	+	0.166456i	$0.946768\pi$
$860$	0.0421217	+	0.0729569i	0.00143634	+	0.00248781i
$861$		0			0
$862$	−36.4356	+	63.1083i	−1.24100	+	2.14948i
$863$	−23.9462	−	13.8253i	−0.815138	−	0.470620i	0.0335987	−	0.999435i	$-0.489303\pi$
$863$	−23.9462	−	13.8253i	−0.815138	−	0.470620i	−0.848737	+	0.528815i	$0.822637\pi$
$864$		0			0
$865$	−10.8312	−	18.7602i	−0.368272	−	0.637866i
$866$	38.0628	+	65.9267i	1.29343	+	2.24028i
$867$		0			0
$868$		0			0
$869$	−11.8357	+	6.83337i	−0.401500	+	0.231806i
$870$		0			0
$871$			9.72199i			0.329417i
$872$	81.5391	−	47.0766i	2.76126	−	1.59422i
$873$		0			0
$874$			61.5357i			2.08148i
$875$		0			0
$876$		0			0
$877$	−1.86524			−0.0629848			−0.0314924	−	0.999504i	$-0.510026\pi$
$877$	−1.86524			−0.0629848			−0.0314924	+	0.999504i	$0.510026\pi$
$878$	−12.6317	+	21.8787i	−0.426298	+	0.738370i
$879$		0			0
$880$	35.7910	−	20.6639i	1.20651	−	0.696581i
$881$	0.0273875			0.000922707			0.000461353	−	1.00000i	$-0.499853\pi$
$881$	0.0273875			0.000922707			0.000461353		1.00000i	$0.499853\pi$
$882$		0			0
$883$	36.2074			1.21848			0.609239	−	0.792987i	$-0.291475\pi$
$883$	36.2074			1.21848			0.609239	+	0.792987i	$0.291475\pi$
$884$	−10.4866	+	6.05447i	−0.352704	+	0.203634i
$885$		0			0
$886$	−15.3600	+	26.6043i	−0.516028	+	0.893787i
$887$	25.3253			0.850339			0.425170	−	0.905114i	$-0.360214\pi$
$887$	25.3253			0.850339			0.425170	+	0.905114i	$0.360214\pi$
$888$		0			0
$889$		0			0
$890$		−	25.9616i		−	0.870235i
$891$		0			0
$892$	112.470	−	64.9343i	3.76576	−	2.17416i
$893$		−	10.7182i		−	0.358671i
$894$		0			0
$895$	−15.7748	+	9.10759i	−0.527294	+	0.304433i
$896$		0			0
$897$		0			0
$898$	−20.7625	−	35.9617i	−0.692854	−	1.20006i
$899$	−0.351613	−	0.609012i	−0.0117270	−	0.0203117i
$900$		0			0
$901$	−10.3290	−	5.96345i	−0.344109	−	0.198671i
$902$	−22.6348	+	39.2046i	−0.753655	+	1.30537i
$903$		0			0
$904$	49.9110	+	86.4483i	1.66001	+	2.87523i
$905$		−	9.60798i		−	0.319380i
$906$		0			0
$907$	−38.8120			−1.28873			−0.644366	−	0.764717i	$-0.722879\pi$
$907$	−38.8120			−1.28873			−0.644366	+	0.764717i	$0.722879\pi$
$908$	1.28260	−	2.22153i	0.0425646	−	0.0737240i
$909$		0			0
$910$		0			0
$911$	43.6110	+	25.1788i	1.44490	+	0.834211i	0.998171	−	0.0604602i	$-0.0192568\pi$
$911$	43.6110	+	25.1788i	1.44490	+	0.834211i	0.446725	+	0.894671i	$0.352590\pi$
$912$		0			0
$913$	−6.92803	−	3.99990i	−0.229284	−	0.132377i
$914$	−21.5190	−	12.4240i	−0.711787	−	0.410950i
$915$		0			0
$916$	−41.6581	−	24.0513i	−1.37642	−	0.794677i
$917$		0			0
$918$		0			0
$919$	1.49845	−	2.59539i	0.0494293	−	0.0856140i	−0.840252	−	0.542196i	$-0.817593\pi$
$919$	1.49845	−	2.59539i	0.0494293	−	0.0856140i	0.889681	+	0.456582i	$0.150926\pi$
$920$	−33.0745			−1.09043
$921$		0			0
$922$			89.5890i			2.95046i
$923$	11.3502	+	19.6591i	0.373596	+	0.647088i
$924$		0			0
$925$	3.07494	−	5.32595i	0.101103	−	0.175116i
$926$	−18.3729	−	10.6076i	−0.603771	−	0.348588i
$927$		0			0
$928$	1.94144	+	3.36268i	0.0637310	+	0.110385i
$929$	−16.1108	−	27.9047i	−0.528577	−	0.915522i	−0.999445	−	0.0333184i	$-0.989392\pi$
$929$	−16.1108	−	27.9047i	−0.528577	−	0.915522i	0.470868	−	0.882204i	$-0.343941\pi$
$930$		0			0
$931$		0			0
$932$	−51.3888	+	29.6694i	−1.68330	+	0.971852i
$933$		0			0
$934$		−	56.0104i		−	1.83272i
$935$	−3.11828	+	1.80034i	−0.101979	+	0.0588774i
$936$		0			0
$937$			3.07038i			0.100305i	0.998742	+	0.0501525i	$0.0159708\pi$
$937$			3.07038i			0.100305i	−0.998742	+	0.0501525i	$0.984029\pi$
$938$		0			0
$939$		0			0
$940$	9.21280			0.300489
$941$	19.4136	−	33.6253i	0.632865	−	1.09615i	−0.354099	−	0.935208i	$-0.615212\pi$
$941$	19.4136	−	33.6253i	0.632865	−	1.09615i	0.986963	−	0.160946i	$-0.0514543\pi$
$942$		0			0
$943$	17.6993	−	10.2187i	0.576367	−	0.332766i
$944$	−168.820			−5.49464
$945$		0			0
$946$	0.0883763			0.00287336
$947$	16.2391	−	9.37567i	0.527701	−	0.304668i	−0.212379	−	0.977187i	$-0.568121\pi$
$947$	16.2391	−	9.37567i	0.527701	−	0.304668i	0.740080	+	0.672519i	$0.234788\pi$
$948$		0			0
$949$	−8.17166	+	14.1537i	−0.265263	+	0.459450i
$950$	71.8953			2.33259
$951$		0			0
$952$		0			0
$953$		−	47.6453i		−	1.54338i	−0.635997	−	0.771692i	$-0.719411\pi$
$953$		−	47.6453i		−	1.54338i	0.635997	−	0.771692i	$-0.280589\pi$
$954$		0			0
$955$	−16.6859	+	9.63362i	−0.539944	+	0.311737i
$956$			74.2370i			2.40099i
$957$		0			0
$958$	−6.24009	+	3.60272i	−0.201608	+	0.116398i
$959$		0			0
$960$		0			0
$961$	−9.36399	−	16.2189i	−0.302064	−	0.523191i
$962$	4.41821	+	7.65257i	0.142449	+	0.246729i
$963$		0			0
$964$	57.2104	+	33.0304i	1.84262	+	1.06384i
$965$	−8.24569	+	14.2819i	−0.265438	+	0.459752i
$966$		0			0
$967$	25.8005	+	44.6878i	0.829689	+	1.43706i	0.898282	+	0.439419i	$0.144815\pi$
$967$	25.8005	+	44.6878i	0.829689	+	1.43706i	−0.0685936	+	0.997645i	$0.521851\pi$
$968$			43.5480i			1.39969i
$969$		0			0
$970$	−7.76079			−0.249184
$971$	−14.1933	+	24.5836i	−0.455485	+	0.788924i	−0.998716	−	0.0506597i	$-0.983868\pi$
$971$	−14.1933	+	24.5836i	−0.455485	+	0.788924i	0.543231	+	0.839584i	$0.317201\pi$
$972$		0			0
$973$		0			0
$974$	−2.44867	−	1.41374i	−0.0784603	−	0.0452991i
$975$		0			0
$976$	−134.556	−	77.6858i	−4.30702	−	2.48666i
$977$	35.6722	+	20.5954i	1.14126	+	0.658904i	0.946741	−	0.321995i	$-0.104353\pi$
$977$	35.6722	+	20.5954i	1.14126	+	0.658904i	0.194515	+	0.980900i	$0.437687\pi$
$978$		0			0
$979$	−17.1576	−	9.90597i	−0.548361	−	0.316596i
$980$		0			0
$981$		0			0
$982$	56.3668	−	97.6302i	1.79874	−	3.11550i
$983$	52.8035			1.68417			0.842085	−	0.539346i	$-0.181328\pi$
$983$	52.8035			1.68417			0.842085	+	0.539346i	$0.181328\pi$
$984$		0			0
$985$			22.7652i			0.725361i
$986$	−0.327278	−	0.566862i	−0.0104227	−	0.0180526i
$987$		0			0
$988$	−37.5731	+	65.0784i	−1.19536	+	2.07042i
$989$	−0.0345529	−	0.0199491i	−0.00109872	−	0.000634346i
$990$		0			0
$991$	−8.24486	−	14.2805i	−0.261907	−	0.453636i	0.704842	−	0.709364i	$-0.251018\pi$
$991$	−8.24486	−	14.2805i	−0.261907	−	0.453636i	−0.966749	+	0.255729i	$0.917685\pi$
$992$	−33.8801	−	58.6821i	−1.07570	−	1.86316i
$993$		0			0
$994$		0			0
$995$	−25.8696	+	14.9358i	−0.820122	+	0.473498i
$996$		0			0
$997$		−	49.0582i		−	1.55369i	−0.629692	−	0.776845i	$-0.716819\pi$
$997$		−	49.0582i		−	1.55369i	0.629692	−	0.776845i	$-0.283181\pi$
$998$	75.7484	−	43.7333i	2.39777	−	1.38435i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.s.d.656.2		48
3.2	odd	2		441.2.s.d.362.23		48
7.2	even	3		1323.2.o.e.440.24		48
7.3	odd	6		1323.2.i.d.521.6		48
7.4	even	3		1323.2.i.d.521.21		48
7.5	odd	6		1323.2.o.e.440.23		48
7.6	odd	2	inner	1323.2.s.d.656.1		48
9.4	even	3		441.2.i.d.68.2		48
9.5	odd	6		1323.2.i.d.1097.6		48
21.2	odd	6		441.2.o.e.146.2	yes	48
21.5	even	6		441.2.o.e.146.1	✓	48
21.11	odd	6		441.2.i.d.227.23		48
21.17	even	6		441.2.i.d.227.24		48
21.20	even	2		441.2.s.d.362.24		48
63.4	even	3		441.2.s.d.374.24		48
63.5	even	6		1323.2.o.e.881.24		48
63.13	odd	6		441.2.i.d.68.1		48
63.23	odd	6		1323.2.o.e.881.23		48
63.31	odd	6		441.2.s.d.374.23		48
63.32	odd	6	inner	1323.2.s.d.962.1		48
63.40	odd	6		441.2.o.e.293.2	yes	48
63.41	even	6		1323.2.i.d.1097.21		48
63.58	even	3		441.2.o.e.293.1	yes	48
63.59	even	6	inner	1323.2.s.d.962.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.1		48	63.13	odd	6
441.2.i.d.68.2		48	9.4	even	3
441.2.i.d.227.23		48	21.11	odd	6
441.2.i.d.227.24		48	21.17	even	6
441.2.o.e.146.1	✓	48	21.5	even	6
441.2.o.e.146.2	yes	48	21.2	odd	6
441.2.o.e.293.1	yes	48	63.58	even	3
441.2.o.e.293.2	yes	48	63.40	odd	6
441.2.s.d.362.23		48	3.2	odd	2
441.2.s.d.362.24		48	21.20	even	2
441.2.s.d.374.23		48	63.31	odd	6
441.2.s.d.374.24		48	63.4	even	3
1323.2.i.d.521.6		48	7.3	odd	6
1323.2.i.d.521.21		48	7.4	even	3
1323.2.i.d.1097.6		48	9.5	odd	6
1323.2.i.d.1097.21		48	63.41	even	6
1323.2.o.e.440.23		48	7.5	odd	6
1323.2.o.e.440.24		48	7.2	even	3
1323.2.o.e.881.23		48	63.23	odd	6
1323.2.o.e.881.24		48	63.5	even	6
1323.2.s.d.656.1		48	7.6	odd	2	inner
1323.2.s.d.656.2		48	1.1	even	1	trivial
1323.2.s.d.962.1		48	63.32	odd	6	inner
1323.2.s.d.962.2		48	63.59	even	6	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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.34591 + 1.35441i) q^{2} +(2.66888 - 4.62263i) q^{4} -1.20293 q^{5} +9.04141i q^{8} +O(q^{10})\)	\(q+(-2.34591 + 1.35441i) q^{2} +(2.66888 - 4.62263i) q^{4} -1.20293 q^{5} +9.04141i q^{8} +(2.82197 - 1.62926i) q^{10} -2.48666i q^{11} +(-1.63211 + 0.942300i) q^{13} +(-6.90806 - 11.9651i) q^{16} +(0.601863 + 1.04246i) q^{17} +(6.46933 + 3.73507i) q^{19} +(-3.21047 + 5.56070i) q^{20} +(3.36797 + 5.83350i) q^{22} -3.04101i q^{23} -3.55296 q^{25} +(2.55253 - 4.42111i) q^{26} +(0.173847 + 0.100371i) q^{29} +(-3.03381 - 1.75157i) q^{31} +(16.7513 + 9.67135i) q^{32} +(-2.82384 - 1.63034i) q^{34} +(-0.865458 + 1.49902i) q^{37} -20.2353 q^{38} -10.8762i q^{40} +(3.36029 + 5.82020i) q^{41} +(0.00656005 - 0.0113623i) q^{43} +(-11.4949 - 6.63660i) q^{44} +(4.11878 + 7.13394i) q^{46} +(-0.717403 - 1.24258i) q^{47} +(8.33495 - 4.81219i) q^{50} +10.0595i q^{52} +(-8.58085 + 4.95416i) q^{53} +2.99128i q^{55} -0.543775 q^{58} +(6.10954 - 10.5820i) q^{59} +(9.73903 - 5.62283i) q^{61} +9.48942 q^{62} -24.7638 q^{64} +(1.96331 - 1.13352i) q^{65} +(2.57932 - 4.46752i) q^{67} +6.42520 q^{68} -12.0452i q^{71} +(7.51020 - 4.33602i) q^{73} -4.68875i q^{74} +(34.5317 - 19.9369i) q^{76} +(-2.74801 - 4.75969i) q^{79} +(8.30991 + 14.3932i) q^{80} +(-15.7659 - 9.10246i) q^{82} +(1.60854 - 2.78607i) q^{83} +(-0.723998 - 1.25400i) q^{85} +0.0355401i q^{86} +22.4829 q^{88} +(3.98364 - 6.89986i) q^{89} +(-14.0574 - 8.11607i) q^{92} +(3.36593 + 1.94332i) q^{94} +(-7.78214 - 4.49302i) q^{95} +(-2.06260 - 1.19084i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 120 q^{32} - 96 q^{44} - 48 q^{50} - 48 q^{53} - 48 q^{64} + 120 q^{65} - 24 q^{79} - 24 q^{85} + 144 q^{92} + 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 120 * q^32 - 96 * q^44 - 48 * q^50 - 48 * q^53 - 48 * q^64 + 120 * q^65 - 24 * q^79 - 24 * q^85 + 144 * q^92 + 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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