LMFDB - Embedded newform 1323.2.o.e.440.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(440,1323)]

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, 3]))

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

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

chi := DirichletCharacter("1323.440");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.o (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			440.23
Character	$\chi$	$=$	1323.440
Dual form			1323.2.o.e.881.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.34591 + 1.35441i) q^{2} +(2.66888 + 4.62263i) q^{4} +(-0.601464 - 1.04177i) q^{5} +9.04141i q^{8} +O(q^{10})$	\(q+(2.34591 + 1.35441i) q^{2} +(2.66888 + 4.62263i) q^{4} +(-0.601464 - 1.04177i) q^{5} +9.04141i q^{8} -3.25853i q^{10} +(2.15351 + 1.24333i) q^{11} +(1.63211 - 0.942300i) q^{13} +(-6.90806 + 11.9651i) q^{16} +1.20373 q^{17} +7.47013i q^{19} +(3.21047 - 5.56070i) q^{20} +(3.36797 + 5.83350i) q^{22} +(-2.63359 + 1.52050i) q^{23} +(1.77648 - 3.07696i) q^{25} +5.10506 q^{26} +(0.173847 + 0.100371i) q^{29} +(-3.03381 + 1.75157i) q^{31} +(-16.7513 + 9.67135i) q^{32} +(2.82384 + 1.63034i) q^{34} +1.73092 q^{37} +(-10.1177 + 17.5243i) q^{38} +(9.41904 - 5.43809i) q^{40} +(-3.36029 - 5.82020i) q^{41} +(0.00656005 - 0.0113623i) q^{43} +13.2732i q^{44} -8.23756 q^{46} +(0.717403 - 1.24258i) q^{47} +(8.33495 - 4.81219i) q^{50} +(8.71182 + 5.02977i) q^{52} -9.90831i q^{53} -2.99128i q^{55} +(0.271887 + 0.470923i) q^{58} +(-6.10954 - 10.5820i) q^{59} +(9.73903 + 5.62283i) q^{61} -9.48942 q^{62} -24.7638 q^{64} +(-1.96331 - 1.13352i) q^{65} +(2.57932 + 4.46752i) q^{67} +(3.21260 + 5.56438i) q^{68} -12.0452i q^{71} -8.67204i q^{73} +(4.06058 + 2.34438i) q^{74} +(-34.5317 + 19.9369i) q^{76} +(-2.74801 + 4.75969i) q^{79} +16.6198 q^{80} -18.2049i q^{82} +(-1.60854 + 2.78607i) q^{83} +(-0.723998 - 1.25400i) q^{85} +(0.0307786 - 0.0177700i) q^{86} +(-11.2415 + 19.4708i) q^{88} +7.96728 q^{89} +(-14.0574 - 8.11607i) q^{92} +(3.36593 - 1.94332i) q^{94} +(7.78214 - 4.49302i) q^{95} +(2.06260 + 1.19084i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	2.34591	+	1.35441i	1.65881	+	0.957716i	0.973264	+	0.229689i	$0.0737707\pi$
$2$	2.34591	+	1.35441i	1.65881	+	0.957716i	0.685548	+	0.728027i	$0.259563\pi$
$3$		0			0
$3$		0			0
$4$	2.66888	+	4.62263i	1.33444	+	2.31132i
$5$	−0.601464	−	1.04177i	−0.268983	−	0.465892i	0.699616	−	0.714519i	$-0.253354\pi$
$5$	−0.601464	−	1.04177i	−0.268983	−	0.465892i	−0.968599	+	0.248626i	$0.920021\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			9.04141i			3.19662i
$9$		0			0
$10$		−	3.25853i		−	1.03044i
$11$	2.15351	+	1.24333i	0.649309	+	0.374879i	0.788191	−	0.615430i	$-0.211018\pi$
$11$	2.15351	+	1.24333i	0.649309	+	0.374879i	−0.138882	+	0.990309i	$0.544351\pi$
$12$		0			0
$13$	1.63211	−	0.942300i	0.452666	−	0.261347i	−0.256289	−	0.966600i	$-0.582500\pi$
$13$	1.63211	−	0.942300i	0.452666	−	0.261347i	0.708956	+	0.705253i	$0.249167\pi$
$14$		0			0
$15$		0			0
$16$	−6.90806	+	11.9651i	−1.72702	+	2.99128i
$17$	1.20373			0.291947			0.145973	−	0.989289i	$-0.453369\pi$
$17$	1.20373			0.291947			0.145973	+	0.989289i	$0.453369\pi$
$18$		0			0
$19$			7.47013i			1.71377i	0.515511	+	0.856883i	$0.327602\pi$
$19$			7.47013i			1.71377i	−0.515511	+	0.856883i	$0.672398\pi$
$20$	3.21047	−	5.56070i	0.717883	−	1.24341i
$21$		0			0
$22$	3.36797	+	5.83350i	0.718054	+	1.24371i
$23$	−2.63359	+	1.52050i	−0.549141	+	0.317047i	−0.748775	−	0.662824i	$-0.769358\pi$
$23$	−2.63359	+	1.52050i	−0.549141	+	0.317047i	0.199634	+	0.979870i	$0.436025\pi$
$24$		0			0
$25$	1.77648	−	3.07696i	0.355296	−	0.615391i
$26$	5.10506			1.00118
$27$		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	−0.747058	−	0.664759i	$-0.768534\pi$
$31$	−3.03381	+	1.75157i	−0.544889	+	0.314592i	0.202169	+	0.979351i	$0.435201\pi$
$32$	−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
$37$	1.73092			0.284561			0.142280	−	0.989826i	$-0.454557\pi$
$37$	1.73092			0.284561			0.142280	+	0.989826i	$0.454557\pi$
$38$	−10.1177	+	17.5243i	−1.64130	+	2.84282i
$39$		0			0
$40$	9.41904	−	5.43809i	1.48928	−	0.859837i
$41$	−3.36029	−	5.82020i	−0.524790	−	0.908963i	−0.999583	−	0.0288655i	$-0.990811\pi$
$41$	−3.36029	−	5.82020i	−0.524790	−	0.908963i	0.474793	−	0.880097i	$-0.342523\pi$
$42$		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	$0.166348\pi$
$44$			13.2732i			2.00101i
$45$		0			0
$46$	−8.23756			−1.21456
$47$	0.717403	−	1.24258i	0.104644	−	0.181249i	−0.808949	−	0.587879i	$-0.799963\pi$
$47$	0.717403	−	1.24258i	0.104644	−	0.181249i	0.913593	+	0.406631i	$0.133296\pi$
$48$		0			0
$49$		0			0
$50$	8.33495	−	4.81219i	1.17874	−	0.680546i
$51$		0			0
$52$	8.71182	+	5.02977i	1.20811	+	0.697504i
$53$		−	9.90831i		−	1.36101i	−0.732743	−	0.680506i	$-0.761760\pi$
$53$		−	9.90831i		−	1.36101i	0.732743	−	0.680506i	$-0.238240\pi$
$54$		0			0
$55$		−	2.99128i		−	0.403344i
$56$		0			0
$57$		0			0
$58$	0.271887	+	0.470923i	0.0357005	+	0.0618352i
$59$	−6.10954	−	10.5820i	−0.795394	−	1.37766i	−0.922588	−	0.385786i	$-0.873930\pi$
$59$	−6.10954	−	10.5820i	−0.795394	−	1.37766i	0.127194	−	0.991878i	$-0.459403\pi$
$60$		0			0
$61$	9.73903	+	5.62283i	1.24696	+	0.719930i	0.970501	−	0.241097i	$-0.0775073\pi$
$61$	9.73903	+	5.62283i	1.24696	+	0.719930i	0.276454	+	0.961027i	$0.410841\pi$
$62$	−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	0.979462	−	0.201630i	$-0.0646237\pi$
$67$	2.57932	+	4.46752i	0.315115	+	0.545794i	−0.664347	+	0.747424i	$0.731290\pi$
$68$	3.21260	+	5.56438i	0.389585	+	0.674781i
$69$		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
$73$		−	8.67204i		−	1.01499i	−0.861656	−	0.507493i	$-0.830572\pi$
$73$		−	8.67204i		−	1.01499i	0.861656	−	0.507493i	$-0.169428\pi$
$74$	4.06058	+	2.34438i	0.472033	+	0.272528i
$75$		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	−0.978182	−	0.207749i	$-0.933386\pi$
$79$	−2.74801	+	4.75969i	−0.309175	+	0.535507i	0.669007	+	0.743256i	$0.266719\pi$
$80$	16.6198			1.85815
$81$		0			0
$82$		−	18.2049i		−	2.01040i
$83$	−1.60854	+	2.78607i	−0.176560	+	0.305811i	−0.940700	−	0.339239i	$-0.889830\pi$
$83$	−1.60854	+	2.78607i	−0.176560	+	0.305811i	0.764140	+	0.645051i	$0.223164\pi$
$84$		0			0
$85$	−0.723998	−	1.25400i	−0.0785286	−	0.136016i
$86$	0.0307786	−	0.0177700i	0.00331894	−	0.00191619i
$87$		0			0
$88$	−11.2415	+	19.4708i	−1.19835	+	2.07559i
$89$	7.96728			0.844530			0.422265	−	0.906473i	$-0.361235\pi$
$89$	7.96728			0.844530			0.422265	+	0.906473i	$0.361235\pi$
$90$		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	0.601044	−	0.799216i	$-0.294751\pi$
$97$	2.06260	+	1.19084i	0.209425	+	0.120912i	−0.391619	+	0.920128i	$0.628085\pi$
$98$		0			0
$99$		0			0
$100$	18.9648			1.89648
$101$	4.73272	−	8.19730i	0.470923	−	0.815662i	−0.528524	−	0.848918i	$-0.677254\pi$
$101$	4.73272	−	8.19730i	0.470923	−	0.815662i	0.999447	+	0.0332561i	$0.0105877\pi$
$102$		0			0
$103$	−14.9460	+	8.62908i	−1.47267	+	0.850249i	−0.999528	−	0.0307347i	$-0.990215\pi$
$103$	−14.9460	+	8.62908i	−1.47267	+	0.850249i	−0.473147	+	0.880984i	$0.656882\pi$
$104$	8.51973	+	14.7566i	0.835428	+	1.44700i
$105$		0			0
$106$	13.4200	−	23.2441i	1.30346	−	2.25766i
$107$		−	9.88349i		−	0.955473i	−0.878503	−	0.477737i	$-0.841457\pi$
$107$		−	9.88349i		−	0.955473i	0.878503	−	0.477737i	$-0.158543\pi$
$108$		0			0
$109$	10.4136			0.997438			0.498719	−	0.866764i	$-0.333804\pi$
$109$	10.4136			0.997438			0.498719	+	0.866764i	$0.333804\pi$
$110$	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
$115$	3.16802	+	1.82906i	0.295419	+	0.170560i
$116$			1.07151i			0.0994871i
$117$		0			0
$118$		−	33.0994i		−	3.04705i
$119$		0			0
$120$		0			0
$121$	−2.40825	−	4.17121i	−0.218932	−	0.379201i
$122$	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
$131$	6.17975	+	10.7036i	0.539927	+	0.935181i	0.998907	+	0.0467344i	$0.0148814\pi$
$131$	6.17975	+	10.7036i	0.539927	+	0.935181i	−0.458981	+	0.888446i	$0.651785\pi$
$132$		0			0
$133$		0			0
$134$			13.9739i			1.20716i
$135$		0			0
$136$			10.8834i			0.933243i
$137$	−10.0991	−	5.83070i	−0.862822	−	0.498150i	0.00213432	−	0.999998i	$-0.499321\pi$
$137$	−10.0991	−	5.83070i	−0.862822	−	0.498150i	−0.864956	+	0.501847i	$0.832654\pi$
$138$		0			0
$139$	8.73893	−	5.04543i	0.741227	−	0.427947i	−0.0812884	−	0.996691i	$-0.525903\pi$
$139$	8.73893	−	5.04543i	0.741227	−	0.427947i	0.822515	+	0.568743i	$0.192570\pi$
$140$		0			0
$141$		0			0
$142$	16.3142	−	28.2570i	1.36906	−	2.37128i
$143$	4.68637			0.391894
$144$		0			0
$145$		−	0.241478i		−	0.0200536i
$146$	11.7455	−	20.3439i	0.972067	−	1.68367i
$147$		0			0
$148$	4.61960	+	8.00138i	0.379729	+	0.657710i
$149$	−4.15010	+	2.39606i	−0.339990	+	0.196293i	−0.660267	−	0.751031i	$-0.729557\pi$
$149$	−4.15010	+	2.39606i	−0.339990	+	0.196293i	0.320278	+	0.947324i	$0.396224\pi$
$150$		0			0
$151$	5.65924	−	9.80209i	0.460542	−	0.797683i	−0.538446	−	0.842660i	$-0.680988\pi$
$151$	5.65924	−	9.80209i	0.460542	−	0.797683i	0.998988	+	0.0449774i	$0.0143216\pi$
$152$	−67.5406			−5.47826
$153$		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	−0.913581	−	0.406657i	$-0.866694\pi$
$157$	−12.7580	+	7.36581i	−1.01820	+	0.587856i	−0.104615	+	0.994513i	$0.533361\pi$
$158$	−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
$163$	−18.1580			−1.42224			−0.711122	−	0.703069i	$-0.751813\pi$
$163$	−18.1580			−1.42224			−0.711122	+	0.703069i	$0.751813\pi$
$164$	17.9364	−	31.0668i	1.40060	−	2.42591i
$165$		0			0
$166$	−7.54700	+	4.35726i	−0.585761	+	0.338189i
$167$	−0.599436	−	1.03825i	−0.0463857	−	0.0803425i	0.841900	−	0.539633i	$-0.181437\pi$
$167$	−0.599436	−	1.03825i	−0.0463857	−	0.0803425i	−0.888286	+	0.459291i	$0.848104\pi$
$168$		0			0
$169$	−4.72414	+	8.18245i	−0.363395	+	0.629419i
$170$		−	3.92238i		−	0.300833i
$171$		0			0
$172$	0.0700319			0.00533988
$173$	−9.00403	+	15.5954i	−0.684564	+	1.18570i	0.289010	+	0.957326i	$0.406674\pi$
$173$	−9.00403	+	15.5954i	−0.684564	+	1.18570i	−0.973574	+	0.228373i	$0.926660\pi$
$174$		0			0
$175$		0			0
$176$	−29.7532	+	17.1780i	−2.24273	+	1.29484i
$177$		0			0
$178$	18.6906	+	10.7910i	1.40092	+	0.808819i
$179$			15.1424i			1.13179i	0.824476	+	0.565897i	$0.191470\pi$
$179$			15.1424i			1.13179i	−0.824476	+	0.565897i	$0.808530\pi$
$180$		0			0
$181$		−	7.98716i		−	0.593681i	−0.954927	−	0.296840i	$-0.904067\pi$
$181$		−	7.98716i		−	0.593681i	0.954927	−	0.296840i	$-0.0959329\pi$
$182$		0			0
$183$		0			0
$184$	−13.7475	−	23.8114i	−1.01348	−	1.75540i
$185$	−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	$-0.530075\pi$
$191$	−13.8711	−	8.00848i	−1.00368	−	0.579473i	−0.909334	+	0.416067i	$0.863408\pi$
$192$		0			0
$193$	6.85468	+	11.8726i	0.493410	+	0.854612i	0.999971	−	0.00759239i	$-0.00241676\pi$
$193$	6.85468	+	11.8726i	0.493410	+	0.854612i	−0.506561	+	0.862204i	$0.669083\pi$
$194$	3.22579	+	5.58724i	0.231598	+	0.401140i
$195$		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
$199$		−	24.8325i		−	1.76033i	−0.474672	−	0.880163i	$-0.657433\pi$
$199$		−	24.8325i		−	1.76033i	0.474672	−	0.880163i	$-0.342567\pi$
$200$	27.8200	+	16.0619i	1.96717	+	1.13575i
$201$		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
$206$	−46.7494			−3.25719
$207$		0			0
$208$			26.0379i			1.80540i
$209$	−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	$0.753442\pi$
$212$	45.8025	−	26.4441i	3.14573	−	1.81619i
$213$		0			0
$214$	13.3863	−	23.1858i	0.915072	−	1.58495i
$215$	−0.0157825			−0.00107636
$216$		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	−0.415508	−	0.909590i	$-0.636396\pi$
$223$	−21.0706	−	12.1651i	−1.41099	−	0.814635i	−0.995482	+	0.0949545i	$0.969729\pi$
$224$		0			0
$225$		0			0
$226$	29.9069			1.98938
$227$	0.240288	−	0.416192i	0.0159485	−	0.0276236i	−0.857941	−	0.513748i	$-0.828257\pi$
$227$	0.240288	−	0.416192i	0.0159485	−	0.0276236i	0.873890	+	0.486125i	$0.161590\pi$
$228$		0			0
$229$	7.80442	−	4.50588i	0.515730	−	0.297757i	−0.219456	−	0.975622i	$-0.570428\pi$
$229$	7.80442	−	4.50588i	0.515730	−	0.297757i	0.735186	+	0.677865i	$0.237095\pi$
$230$	4.95460	+	8.58162i	0.326697	+	0.565855i
$231$		0			0
$232$	−0.907493	+	1.57182i	−0.0595799	+	0.103195i
$233$			11.1168i			0.728285i	0.931343	+	0.364143i	$0.118638\pi$
$233$			11.1168i			0.728285i	−0.931343	+	0.364143i	$0.881362\pi$
$234$		0			0
$235$	−1.72597			−0.112590
$236$	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
$241$	10.7181	+	6.18807i	0.690411	+	0.398609i	0.803766	−	0.594946i	$-0.202827\pi$
$241$	10.7181	+	6.18807i	0.690411	+	0.398609i	−0.113355	+	0.993555i	$0.536160\pi$
$242$		−	13.0471i		−	0.838698i
$243$		0			0
$244$			60.0266i			3.84281i
$245$		0			0
$246$		0			0
$247$	7.03911	+	12.1921i	0.447888	+	0.775764i
$248$	−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	$-0.286243\pi$
$251$	19.7147			1.24438			0.622191	+	0.782866i	$0.286243\pi$
$252$		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
$257$	5.62025	+	9.73456i	0.350581	+	0.607225i	0.986351	−	0.164654i	$-0.0526506\pi$
$257$	5.62025	+	9.73456i	0.350581	+	0.607225i	−0.635770	+	0.771879i	$0.719317\pi$
$258$		0			0
$259$		0			0
$260$		−	12.1009i		−	0.750466i
$261$		0			0
$262$			33.4797i			2.06839i
$263$	2.82146	+	1.62897i	0.173979	+	0.100447i	0.584461	−	0.811422i	$-0.301306\pi$
$263$	2.82146	+	1.62897i	0.173979	+	0.100447i	−0.410482	+	0.911869i	$0.634640\pi$
$264$		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
$269$	−0.242293			−0.0147729			−0.00738644	−	0.999973i	$-0.502351\pi$
$269$	−0.242293			−0.0147729			−0.00738644	+	0.999973i	$0.502351\pi$
$270$		0			0
$271$			1.07305i			0.0651830i	0.999469	+	0.0325915i	$0.0103760\pi$
$271$			1.07305i			0.0651830i	−0.999469	+	0.0325915i	$0.989624\pi$
$272$	−8.31542	+	14.4027i	−0.504196	+	0.873294i
$273$		0			0
$274$	−15.7944	−	27.3567i	−0.954173	−	1.65268i
$275$	7.65136	−	4.41751i	0.461394	−	0.266386i
$276$		0			0
$277$	2.45076	−	4.24485i	0.147252	−	0.255048i	−0.782959	−	0.622074i	$-0.786290\pi$
$277$	2.45076	−	4.24485i	0.147252	−	0.255048i	0.930211	+	0.367025i	$0.119624\pi$
$278$	27.3344			1.63941
$279$		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	−0.593568	−	0.804784i	$-0.702281\pi$
$283$	−3.25329	+	1.87829i	−0.193388	+	0.111653i	0.400180	+	0.916437i	$0.368948\pi$
$284$	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
$289$	−15.5510			−0.914767
$290$	0.327061	−	0.566486i	0.0192057	−	0.0332652i
$291$		0			0
$292$	40.0876	−	23.1446i	2.34595	−	1.35444i
$293$	−6.38430	−	11.0579i	−0.372975	−	0.646011i	0.617047	−	0.786926i	$-0.288329\pi$
$293$	−6.38430	−	11.0579i	−0.372975	−	0.646011i	−0.990022	+	0.140915i	$0.954995\pi$
$294$		0			0
$295$	−7.34934	+	12.7294i	−0.427895	+	0.741136i
$296$			15.6499i			0.909633i
$297$		0			0
$298$	−12.9810			−0.751972
$299$	−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
$304$	−89.3810	−	51.6042i	−5.12635	−	2.95970i
$305$		−	13.5277i		−	0.774596i
$306$		0			0
$307$			10.7257i			0.612148i	0.952008	+	0.306074i	$0.0990155\pi$
$307$			10.7257i			0.612148i	−0.952008	+	0.306074i	$0.900984\pi$
$308$		0			0
$309$		0			0
$310$	5.70755	+	9.88576i	0.324167	+	0.561473i
$311$	9.41743	+	16.3115i	0.534013	+	0.924938i	0.999210	+	0.0397310i	$0.0126501\pi$
$311$	9.41743	+	16.3115i	0.534013	+	0.924938i	−0.465197	+	0.885207i	$0.654017\pi$
$312$		0			0
$313$	22.5774	+	13.0351i	1.27615	+	0.736787i	0.976139	−	0.217148i	$-0.0696756\pi$
$313$	22.5774	+	13.0351i	1.27615	+	0.736787i	0.300013	+	0.953935i	$0.403009\pi$
$314$	−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	$-0.460882\pi$
$317$	−12.0290	−	6.94495i	−0.675616	−	0.390067i	−0.798201	+	0.602391i	$0.794215\pi$
$318$		0			0
$319$	0.249588	+	0.432300i	0.0139743	+	0.0242041i
$320$	14.8946	+	25.7981i	0.832631	+	1.44216i
$321$		0			0
$322$		0			0
$323$			8.99200i			0.500328i
$324$		0			0
$325$		−	6.69592i		−	0.371423i
$326$	−42.5971	−	24.5935i	−2.35924	−	1.36211i
$327$		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	−0.921047	−	0.389452i	$-0.872664\pi$
$331$	−2.24230	+	3.88378i	−0.123248	+	0.213472i	0.797799	+	0.602924i	$0.205998\pi$
$332$	−17.1720			−0.942435
$333$		0			0
$334$		−	3.24754i		−	0.177697i
$335$	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	$-0.518368\pi$
$338$	−22.1649	+	12.7969i	−1.20561	+	0.696059i
$339$		0			0
$340$	3.86453	−	6.69356i	0.209583	−	0.363009i
$341$	−8.71114			−0.471735
$342$		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	$-0.783848\pi$
$347$	−11.6112	+	6.70374i	−0.623323	+	0.359876i	0.154839	+	0.987940i	$0.450514\pi$
$348$		0			0
$349$	19.3276	+	11.1588i	1.03458	+	0.597316i	0.918294	−	0.395899i	$-0.129567\pi$
$349$	19.3276	+	11.1588i	1.03458	+	0.597316i	0.116288	+	0.993215i	$0.462900\pi$
$350$		0			0
$351$		0			0
$352$	−48.0988			−2.56368
$353$	−8.60842	+	14.9102i	−0.458180	+	0.793591i	−0.998865	−	0.0476341i	$-0.984832\pi$
$353$	−8.60842	+	14.9102i	−0.458180	+	0.793591i	0.540685	+	0.841225i	$0.318165\pi$
$354$		0			0
$355$	−12.5483	+	7.24476i	−0.665994	+	0.384512i
$356$	21.2637	+	36.8298i	1.12697	+	1.95198i
$357$		0			0
$358$	−20.5090	+	35.5227i	−1.08394	+	1.87743i
$359$			6.49943i			0.343027i	0.985182	+	0.171513i	$0.0548656\pi$
$359$			6.49943i			0.343027i	−0.985182	+	0.171513i	$0.945134\pi$
$360$		0			0
$361$	−36.8029			−1.93699
$362$	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
$367$	−7.79734	−	4.50180i	−0.407018	−	0.234992i	0.282490	−	0.959270i	$-0.408840\pi$
$367$	−7.79734	−	4.50180i	−0.407018	−	0.234992i	−0.689508	+	0.724278i	$0.742173\pi$
$368$		−	42.0149i		−	2.19018i
$369$		0			0
$370$		−	5.64024i		−	0.293222i
$371$		0			0
$372$		0			0
$373$	−5.75312	−	9.96470i	−0.297885	−	0.515953i	0.677767	−	0.735277i	$-0.262948\pi$
$373$	−5.75312	−	9.96470i	−0.297885	−	0.515953i	−0.975652	+	0.219324i	$0.929615\pi$
$374$	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
$383$	−8.10778	−	14.0431i	−0.414288	−	0.717569i	0.581065	−	0.813857i	$-0.302636\pi$
$383$	−8.10778	−	14.0431i	−0.414288	−	0.717569i	−0.995353	+	0.0962885i	$0.969303\pi$
$384$		0			0
$385$		0			0
$386$			37.1363i			1.89019i
$387$		0			0
$388$			12.7129i			0.645398i
$389$	16.2358	+	9.37376i	0.823189	+	0.475269i	0.851515	−	0.524330i	$-0.175684\pi$
$389$	16.2358	+	9.37376i	0.823189	+	0.475269i	−0.0283257	+	0.999599i	$0.509018\pi$
$390$		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
$395$	6.61131			0.332651
$396$		0			0
$397$		−	30.9709i		−	1.55438i	−0.629264	−	0.777192i	$-0.716643\pi$
$397$		−	30.9709i		−	1.55438i	0.629264	−	0.777192i	$-0.283357\pi$
$398$	33.6334	−	58.2548i	1.68589	−	2.92005i
$399$		0			0
$400$	24.5441	+	42.5116i	1.22720	+	2.12558i
$401$	0.801065	−	0.462495i	0.0400033	−	0.0230959i	−0.479865	−	0.877342i	$-0.659314\pi$
$401$	0.801065	−	0.462495i	0.0400033	−	0.0230959i	0.519868	+	0.854246i	$0.325981\pi$
$402$		0			0
$403$	−3.30101	+	5.71752i	−0.164435	+	0.284810i
$404$	50.5242			2.51367
$405$		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	−0.328808	−	0.944397i	$-0.606647\pi$
$409$	6.56585	−	3.79079i	0.324660	−	0.187443i	0.653468	+	0.756954i	$0.273313\pi$
$410$	−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
$415$	3.86992			0.189967
$416$	−18.2266	+	31.5695i	−0.893635	+	1.54782i
$417$		0			0
$418$	−43.5770	+	25.1592i	−2.13142	+	1.23058i
$419$	−2.85061	−	4.93740i	−0.139262	−	0.241208i	0.787956	−	0.615732i	$-0.211140\pi$
$419$	−2.85061	−	4.93740i	−0.139262	−	0.241208i	−0.927217	+	0.374524i	$0.877806\pi$
$420$		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	$0.258890\pi$
$422$			19.5448i			0.951426i
$423$		0			0
$424$	89.5851			4.35064
$425$	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
$430$	−0.0370245	−	0.0213761i	−0.00178548	−	0.00103085i
$431$			26.9014i			1.29579i	0.761728	+	0.647897i	$0.224351\pi$
$431$			26.9014i			1.29579i	−0.761728	+	0.647897i	$0.775649\pi$
$432$		0			0
$433$			28.1028i			1.35053i	0.737574	+	0.675266i	$0.235971\pi$
$433$			28.1028i			1.35053i	−0.737574	+	0.675266i	$0.764029\pi$
$434$		0			0
$435$		0			0
$436$	27.7925	+	48.1381i	1.33102	+	2.30539i
$437$	−11.3584	−	19.6733i	−0.543344	−	0.941099i
$438$		0			0
$439$	8.07680	+	4.66314i	0.385485	+	0.222560i	0.680202	−	0.733025i	$-0.261892\pi$
$439$	8.07680	+	4.66314i	0.385485	+	0.222560i	−0.294717	+	0.955585i	$0.595225\pi$
$440$	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	$-0.420161\pi$
$443$	−9.82131	−	5.67034i	−0.466624	−	0.269406i	−0.714826	+	0.699303i	$0.753494\pi$
$444$		0			0
$445$	−4.79203	−	8.30004i	−0.227164	−	0.393460i
$446$	−32.9532	−	57.0766i	−1.56038	−	2.70265i
$447$		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
$451$		−	16.7118i		−	0.786930i
$452$	51.0363	+	29.4658i	2.40054	+	1.38596i
$453$		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	−0.738585	−	0.674160i	$-0.764506\pi$
$457$	4.58649	−	7.94404i	0.214547	−	0.371606i	0.953132	+	0.302554i	$0.0978391\pi$
$458$	24.4113			1.14067
$459$		0			0
$460$			19.5261i			0.910410i
$461$	−16.5365	+	28.6420i	−0.770181	+	1.33399i	0.167283	+	0.985909i	$0.446501\pi$
$461$	−16.5365	+	28.6420i	−0.770181	+	1.33399i	−0.937464	+	0.348083i	$0.886833\pi$
$462$		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	$0.775080\pi$
$464$	−2.40190	+	1.38674i	−0.111505	+	0.0643776i
$465$		0			0
$466$	−15.0567	+	26.0790i	−0.697490	+	1.20809i
$467$	−20.6770			−0.956816			−0.478408	−	0.878138i	$-0.658786\pi$
$467$	−20.6770			−0.956816			−0.478408	+	0.878138i	$0.658786\pi$
$468$		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
$478$	−37.6741			−1.72317
$479$	1.32999	−	2.30361i	0.0607688	−	0.105255i	−0.834040	−	0.551703i	$-0.813978\pi$
$479$	1.32999	−	2.30361i	0.0607688	−	0.105255i	0.894809	+	0.446449i	$0.147311\pi$
$480$		0			0
$481$	2.82505	−	1.63104i	0.128811	−	0.0743691i
$482$	16.7624	+	29.0334i	0.763508	+	1.32243i
$483$		0			0
$484$	12.8547	−	22.2649i	0.584303	−	1.01204i
$485$		−	2.86500i		−	0.130093i
$486$		0			0
$487$	−1.04380			−0.0472991			−0.0236495	−	0.999720i	$-0.507529\pi$
$487$	−1.04380			−0.0472991			−0.0236495	+	0.999720i	$0.507529\pi$
$488$	−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
$493$	0.209265	+	0.120819i	0.00942480	+	0.00544141i
$494$			38.1355i			1.71580i
$495$		0			0
$496$		−	48.3999i		−	2.17322i
$497$		0			0
$498$		0			0
$499$	16.1447	+	27.9635i	0.722738	+	1.25182i	0.959898	+	0.280348i	$0.0904499\pi$
$499$	16.1447	+	27.9635i	0.722738	+	1.25182i	−0.237161	+	0.971470i	$0.576217\pi$
$500$	−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	$-0.149941\pi$
$503$	39.9702			1.78218			0.891091	+	0.453825i	$0.149941\pi$
$504$		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
$509$	−11.3631	−	19.6815i	−0.503661	−	0.872367i	−0.999991	−	0.00423260i	$-0.998653\pi$
$509$	−11.3631	−	19.6815i	−0.503661	−	0.872367i	0.496330	−	0.868134i	$-0.334681\pi$
$510$		0			0
$511$		0			0
$512$		−	17.4067i		−	0.769277i
$513$		0			0
$514$			30.4486i			1.34303i
$515$	17.9790	+	10.3802i	0.792249	+	0.457405i
$516$		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
$521$	30.0359			1.31590			0.657948	−	0.753063i	$-0.271425\pi$
$521$	30.0359			1.31590			0.657948	+	0.753063i	$0.271425\pi$
$522$		0			0
$523$			0.779769i			0.0340969i	0.999855	+	0.0170485i	$0.00542696\pi$
$523$			0.779769i			0.0340969i	−0.999855	+	0.0170485i	$0.994573\pi$
$524$	−32.9860	+	57.1334i	−1.44100	+	2.49588i
$525$		0			0
$526$	4.41260	+	7.64285i	0.192399	+	0.333244i
$527$	−3.65188	+	2.10841i	−0.159078	+	0.0918439i
$528$		0			0
$529$	−6.87614	+	11.9098i	−0.298963	+	0.517819i
$530$	−32.2865			−1.40244
$531$		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
$541$	2.04030			0.0877196			0.0438598	−	0.999038i	$-0.486035\pi$
$541$	2.04030			0.0877196			0.0438598	+	0.999038i	$0.486035\pi$
$542$	−1.45335	+	2.51728i	−0.0624268	+	0.108126i
$543$		0			0
$544$	−20.1640	+	11.6417i	−0.864522	+	0.499132i
$545$	−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	$0.291456\pi$
$548$		−	62.2457i		−	2.65901i
$549$		0			0
$550$	23.9326			1.02049
$551$	−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
$556$	46.6463	+	26.9313i	1.97824	+	1.14214i
$557$		−	42.9605i		−	1.82029i	−0.414285	−	0.910147i	$-0.635968\pi$
$557$		−	42.9605i		−	1.82029i	0.414285	−	0.910147i	$-0.364032\pi$
$558$		0			0
$559$		−	0.0247261i		−	0.00104580i
$560$		0			0
$561$		0			0
$562$	−18.0813	−	31.3177i	−0.762713	−	1.32106i
$563$	0.773739	+	1.34016i	0.0326092	+	0.0564808i	0.881869	−	0.471494i	$-0.156285\pi$
$563$	0.773739	+	1.34016i	0.0326092	+	0.0564808i	−0.849260	+	0.527975i	$0.822952\pi$
$564$		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	$-0.266123\pi$
$569$	8.65905	+	4.99931i	0.363006	+	0.209582i	−0.307392	+	0.951583i	$0.599456\pi$
$570$		0			0
$571$	1.39715	+	2.41994i	0.0584689	+	0.101271i	0.893778	−	0.448509i	$-0.148045\pi$
$571$	1.39715	+	2.41994i	0.0584689	+	0.101271i	−0.835309	+	0.549780i	$0.814711\pi$
$572$	12.5073	+	21.6634i	0.522958	+	0.905790i
$573$		0			0
$574$		0			0
$575$			10.8046i			0.450582i
$576$		0			0
$577$		−	3.73764i		−	0.155600i	−0.996969	−	0.0778000i	$-0.975210\pi$
$577$		−	3.73764i		−	0.155600i	0.996969	−	0.0778000i	$-0.0247896\pi$
$578$	−36.4814	−	21.0626i	−1.51743	−	0.876087i
$579$		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
$584$	78.4074			3.24452
$585$		0			0
$586$		−	34.5879i		−	1.42881i
$587$	13.1249	−	22.7331i	0.541725	−	0.938295i	−0.457081	−	0.889425i	$-0.651105\pi$
$587$	13.1249	−	22.7331i	0.541725	−	0.938295i	0.998805	−	0.0488692i	$-0.0155618\pi$
$588$		0			0
$589$	−13.0845	−	22.6630i	−0.539136	−	0.933812i
$590$	−34.4819	+	19.9081i	−1.41960	+	0.819604i
$591$		0			0
$592$	−11.9573	+	20.7106i	−0.491441	+	0.851201i
$593$	3.59667			0.147698			0.0738488	−	0.997269i	$-0.476472\pi$
$593$	3.59667			0.147698			0.0738488	+	0.997269i	$0.476472\pi$
$594$		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	$-0.828537\pi$
$599$	−20.6400	+	11.9165i	−0.843326	+	0.486895i	0.0150672	+	0.999886i	$0.495204\pi$
$600$		0			0
$601$	−14.6034	−	8.43126i	−0.595684	−	0.343918i	0.171658	−	0.985157i	$-0.445088\pi$
$601$	−14.6034	−	8.43126i	−0.595684	−	0.343918i	−0.767342	+	0.641238i	$0.778421\pi$
$602$		0			0
$603$		0			0
$604$	60.4153			2.45826
$605$	−2.89695	+	5.01767i	−0.117778	+	0.203997i
$606$		0			0
$607$	−9.07737	+	5.24082i	−0.368439	+	0.212718i	−0.672776	−	0.739846i	$-0.734898\pi$
$607$	−9.07737	+	5.24082i	−0.368439	+	0.212718i	0.304337	+	0.952564i	$0.401565\pi$
$608$	−72.2463	−	125.134i	−2.92997	−	5.07487i
$609$		0			0
$610$	18.3222	−	31.7349i	0.741842	−	1.28491i
$611$		−	2.70404i		−	0.109394i
$612$		0			0
$613$	−47.9001			−1.93467			−0.967333	−	0.253510i	$-0.918415\pi$
$613$	−47.9001			−1.93467			−0.967333	+	0.253510i	$0.918415\pi$
$614$	−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
$619$	27.9729	+	16.1501i	1.12432	+	0.649129i	0.942501	−	0.334202i	$-0.108467\pi$
$619$	27.9729	+	16.1501i	1.12432	+	0.649129i	0.181823	+	0.983331i	$0.441800\pi$
$620$			22.4935i			0.903359i
$621$		0			0
$622$			51.0204i			2.04573i
$623$		0			0
$624$		0			0
$625$	−2.69418	−	4.66646i	−0.107767	−	0.186658i
$626$	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
$635$	−8.33836	−	14.4425i	−0.330898	−	0.573132i
$636$		0			0
$637$		0			0
$638$			1.35218i			0.0535335i
$639$		0			0
$640$			34.1579i			1.35021i
$641$	−9.07003	−	5.23658i	−0.358245	−	0.206833i	0.310066	−	0.950715i	$-0.399649\pi$
$641$	−9.07003	−	5.23658i	−0.358245	−	0.206833i	−0.668310	+	0.743882i	$0.732982\pi$
$642$		0			0
$643$	3.37572	−	1.94897i	0.133125	−	0.0768600i	−0.431958	−	0.901894i	$-0.642177\pi$
$643$	3.37572	−	1.94897i	0.133125	−	0.0768600i	0.565084	+	0.825034i	$0.308844\pi$
$644$		0			0
$645$		0			0
$646$	−12.1789	+	21.0945i	−0.479172	+	0.829950i
$647$	−12.4054			−0.487706			−0.243853	−	0.969812i	$-0.578411\pi$
$647$	−12.4054			−0.487706			−0.243853	+	0.969812i	$0.578411\pi$
$648$		0			0
$649$		−	30.3847i		−	1.19271i
$650$	9.06905	−	15.7081i	0.355717	−	0.616120i
$651$		0			0
$652$	−48.4615	−	83.9377i	−1.89790	−	3.28726i
$653$	12.2749	−	7.08690i	0.480353	−	0.277332i	−0.240211	−	0.970721i	$-0.577216\pi$
$653$	12.2749	−	7.08690i	0.480353	−	0.277332i	0.720564	+	0.693389i	$0.243883\pi$
$654$		0			0
$655$	7.43379	−	12.8757i	0.290462	−	0.503095i
$656$	92.8525			3.62528
$657$		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	−0.849975	−	0.526823i	$-0.823383\pi$
$661$	−21.0493	+	12.1528i	−0.818721	+	0.472689i	0.0312540	+	0.999511i	$0.490050\pi$
$662$	−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
$667$	−0.610456			−0.0236370
$668$	3.19964	−	5.54194i	0.123798	−	0.214424i
$669$		0			0
$670$	14.5575	−	8.40480i	0.562407	−	0.324706i
$671$	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	$0.189080\pi$
$674$		−	88.8551i		−	3.42257i
$675$		0			0
$676$	−50.4326			−1.93972
$677$	0.968676	−	1.67780i	0.0372292	−	0.0644829i	−0.846810	−	0.531895i	$-0.821480\pi$
$677$	0.968676	−	1.67780i	0.0372292	−	0.0644829i	0.884040	+	0.467412i	$0.154813\pi$
$678$		0			0
$679$		0			0
$680$	11.3379	−	6.54597i	0.434790	−	0.251026i
$681$		0			0
$682$	−20.4356	−	11.7985i	−0.782519	−	0.451788i
$683$			19.4931i			0.745884i	0.927855	+	0.372942i	$0.121651\pi$
$683$			19.4931i			0.745884i	−0.927855	+	0.372942i	$0.878349\pi$
$684$		0			0
$685$			14.0278i			0.535976i
$686$		0			0
$687$		0			0
$688$	0.0906345	+	0.156983i	0.00345541	+	0.00598494i
$689$	−9.33660	−	16.1715i	−0.355696	−	0.616084i
$690$		0			0
$691$	−35.7855	−	20.6608i	−1.36134	−	0.785972i	−0.371541	−	0.928416i	$-0.621171\pi$
$691$	−35.7855	−	20.6608i	−1.36134	−	0.785972i	−0.989803	+	0.142444i	$0.954504\pi$
$692$	−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
$698$	30.2273	+	52.3552i	1.14412	+	1.98167i
$699$		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
$703$			12.9302i			0.487671i
$704$	−53.3293	−	30.7897i	−2.00992	−	1.16043i
$705$		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	−0.890370	−	0.455237i	$-0.849555\pi$
$709$	−1.35635	+	2.34926i	−0.0509387	+	0.0882283i	0.839432	+	0.543465i	$0.182888\pi$
$710$	−39.2496			−1.47301
$711$		0			0
$712$			72.0354i			2.69964i
$713$	5.32654	−	9.22584i	0.199480	−	0.345510i
$714$		0			0
$715$	−2.81868	−	4.88210i	−0.105413	−	0.182580i
$716$	−69.9976	+	40.4131i	−2.61593	+	1.51031i
$717$		0			0
$718$	−8.80292	+	15.2471i	−0.328522	+	0.569017i
$719$	−16.2786			−0.607090			−0.303545	−	0.952817i	$-0.598170\pi$
$719$	−16.2786			−0.607090			−0.303545	+	0.952817i	$0.598170\pi$
$720$		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	0.481714	−	0.876328i	$-0.340014\pi$
$727$	−0.980123	−	0.565874i	−0.0363508	−	0.0209871i	−0.518065	+	0.855341i	$0.673348\pi$
$728$		0			0
$729$		0			0
$730$	−28.2581			−1.04588
$731$	0.00789650	−	0.0136771i	0.000292063	−	0.000505867i
$732$		0			0
$733$	33.2085	−	19.1729i	1.22658	−	0.708169i	0.260270	−	0.965536i	$-0.416188\pi$
$733$	33.2085	−	19.1729i	1.22658	−	0.708169i	0.966314	+	0.257367i	$0.0828549\pi$
$734$	−12.1946	−	21.1217i	−0.450111	−	0.779615i
$735$		0			0
$736$	29.4106	−	50.9407i	1.08409	−	1.87770i
$737$			12.8278i			0.472519i
$738$		0			0
$739$	10.7298			0.394701			0.197351	−	0.980333i	$-0.436766\pi$
$739$	10.7298			0.394701			0.197351	+	0.980333i	$0.436766\pi$
$740$	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
$745$	4.99228	+	2.88229i	0.182903	+	0.105599i
$746$		−	31.1685i		−	1.14116i
$747$		0			0
$748$			15.9773i			0.584188i
$749$		0			0
$750$		0			0
$751$	−13.1677	−	22.8071i	−0.480495	−	0.832242i	0.519254	−	0.854620i	$-0.326210\pi$
$751$	−13.1677	−	22.8071i	−0.480495	−	0.832242i	−0.999750	+	0.0223774i	$0.992876\pi$
$752$	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
$761$	12.6727	+	21.9498i	0.459385	+	0.795679i	0.998929	−	0.0462793i	$-0.0147364\pi$
$761$	12.6727	+	21.9498i	0.459385	+	0.795679i	−0.539543	+	0.841958i	$0.681403\pi$
$762$		0			0
$763$		0			0
$764$		−	85.4946i		−	3.09309i
$765$		0			0
$766$		−	43.9252i		−	1.58708i
$767$	−19.9429	−	11.5140i	−0.720097	−	0.415748i
$768$		0			0
$769$	−11.4964	+	6.63744i	−0.414570	+	0.239352i	−0.692752	−	0.721176i	$-0.743602\pi$
$769$	−11.4964	+	6.63744i	−0.414570	+	0.239352i	0.278181	+	0.960529i	$0.410268\pi$
$770$		0			0
$771$		0			0
$772$	−36.5886	+	63.3733i	−1.31685	+	2.28085i
$773$	16.0136			0.575969			0.287985	−	0.957635i	$-0.407015\pi$
$773$	16.0136			0.575969			0.287985	+	0.957635i	$0.407015\pi$
$774$		0			0
$775$			12.4465i			0.447093i
$776$	−10.7669	+	18.6488i	−0.386509	+	0.669454i
$777$		0			0
$778$	25.3919	+	43.9801i	0.910344	+	1.57676i
$779$	43.4777	−	25.1019i	1.55775	−	0.899367i
$780$		0			0
$781$	14.9762	−	25.9395i	0.535890	−	0.928189i
$782$	−9.91577			−0.354587
$783$		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	−0.422400	−	0.906410i	$-0.638812\pi$
$787$	4.24659	−	2.45177i	0.151375	−	0.0873961i	0.573774	+	0.819014i	$0.305479\pi$
$788$	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
$793$	21.1936			0.752606
$794$	41.9474	−	72.6551i	1.48866	−	2.57843i
$795$		0			0
$796$	114.791	−	66.2748i	4.06867	−	2.34905i
$797$	21.3994	+	37.0649i	0.758006	+	1.31290i	0.943866	+	0.330328i	$0.107159\pi$
$797$	21.3994	+	37.0649i	0.758006	+	1.31290i	−0.185860	+	0.982576i	$0.559507\pi$
$798$		0			0
$799$	0.863557	−	1.49572i	0.0305505	−	0.0529149i
$800$			68.7239i			2.42976i
$801$		0			0
$802$	2.50564			0.0884772
$803$	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
$808$	74.1152	+	42.7904i	2.60736	+	1.50536i
$809$			35.2933i			1.24085i	0.784267	+	0.620424i	$0.213039\pi$
$809$			35.2933i			1.24085i	−0.784267	+	0.620424i	$0.786961\pi$
$810$		0			0
$811$		−	21.0223i		−	0.738193i	−0.929391	−	0.369096i	$-0.879667\pi$
$811$		−	21.0223i		−	0.738193i	0.929391	−	0.369096i	$-0.120333\pi$
$812$		0			0
$813$		0			0
$814$	5.82968	+	10.0973i	0.204330	+	0.353910i
$815$	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	$-0.127817\pi$
$821$	29.8623	+	17.2410i	1.04220	+	0.601716i	0.121746	+	0.992561i	$0.461151\pi$
$822$		0			0
$823$	19.4950	+	33.7663i	0.679552	+	1.17702i	0.975116	+	0.221695i	$0.0711590\pi$
$823$	19.4950	+	33.7663i	0.679552	+	1.17702i	−0.295564	+	0.955323i	$0.595508\pi$
$824$	−78.0191	−	135.133i	−2.71792	−	4.70758i
$825$		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
$829$			49.1426i			1.70679i	0.521262	+	0.853397i	$0.325462\pi$
$829$			49.1426i			1.70679i	−0.521262	+	0.853397i	$0.674538\pi$
$830$	9.07850	+	5.24147i	0.315119	+	0.181934i
$831$		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
$836$	−99.1526			−3.42926
$837$		0			0
$838$		−	15.4436i		−	0.533492i
$839$	−26.0780	+	45.1684i	−0.900312	+	1.55939i	−0.0732219	+	0.997316i	$0.523328\pi$
$839$	−26.0780	+	45.1684i	−0.900312	+	1.55939i	−0.827090	+	0.562070i	$0.810005\pi$
$840$		0			0
$841$	−14.4799	−	25.0798i	−0.499305	−	0.864822i
$842$	−27.5030	+	15.8789i	−0.947816	+	0.547222i
$843$		0			0
$844$	−19.2565	+	33.3533i	−0.662838	+	1.14807i
$845$	11.3656			0.390989
$846$		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	0.252681	−	0.967550i	$-0.418688\pi$
$853$	−13.4028	−	7.73808i	−0.458902	−	0.264947i	−0.711582	+	0.702603i	$0.752021\pi$
$854$		0			0
$855$		0			0
$856$	89.3607			3.05429
$857$	−24.4356	+	42.3238i	−0.834706	+	1.44575i	0.0595642	+	0.998224i	$0.481029\pi$
$857$	−24.4356	+	42.3238i	−0.834706	+	1.44575i	−0.894270	+	0.447528i	$0.852304\pi$
$858$		0			0
$859$	−8.45000	+	4.87861i	−0.288310	+	0.166456i	−0.637180	−	0.770715i	$-0.719899\pi$
$859$	−8.45000	+	4.87861i	−0.288310	+	0.166456i	0.348869	+	0.937171i	$0.386566\pi$
$860$	−0.0421217	−	0.0729569i	−0.00143634	−	0.00248781i
$861$		0			0
$862$	−36.4356	+	63.1083i	−1.24100	+	2.14948i
$863$			27.6507i			0.941241i	0.882336	+	0.470620i	$0.155970\pi$
$863$			27.6507i			0.941241i	−0.882336	+	0.470620i	$0.844030\pi$
$864$		0			0
$865$	21.6624			0.736544
$866$	−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
$871$	8.41949	+	4.86100i	0.285284	+	0.164709i
$872$			94.1533i			3.18843i
$873$		0			0
$874$		−	61.5357i		−	2.08148i
$875$		0			0
$876$		0			0
$877$	0.932622	+	1.61535i	0.0314924	+	0.0545465i	0.881342	−	0.472479i	$-0.156641\pi$
$877$	0.932622	+	1.61535i	0.0314924	+	0.0545465i	−0.849850	+	0.527025i	$0.823307\pi$
$878$	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	$-0.500147\pi$
$881$	−0.0273875			−0.000922707			−0.000461353		1.00000i	$0.500147\pi$
$882$		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
$887$	12.6626	+	21.9323i	0.425170	+	0.736415i	0.996436	−	0.0843491i	$-0.0268811\pi$
$887$	12.6626	+	21.9323i	0.425170	+	0.736415i	−0.571267	+	0.820765i	$0.693548\pi$
$888$		0			0
$889$		0			0
$890$		−	25.9616i		−	0.870235i
$891$		0			0
$892$		−	129.869i		−	4.34832i
$893$	9.28223	+	5.35910i	0.310618	+	0.179335i
$894$		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
$899$	−0.703226			−0.0234539
$900$		0			0
$901$		−	11.9269i		−	0.397342i
$902$	22.6348	−	39.2046i	0.753655	−	1.30537i
$903$		0			0
$904$	49.9110	+	86.4483i	1.66001	+	2.87523i
$905$	−8.32075	+	4.80399i	−0.276591	+	0.159690i
$906$		0			0
$907$	19.4060	−	33.6122i	0.644366	−	1.11608i	−0.340081	−	0.940396i	$-0.610455\pi$
$907$	19.4060	−	33.6122i	0.644366	−	1.11608i	0.984447	−	0.175679i	$-0.0562121\pi$
$908$	2.56520			0.0851292
$909$		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
$919$	−2.99690			−0.0988585			−0.0494293	−	0.998778i	$-0.515740\pi$
$919$	−2.99690			−0.0988585			−0.0494293	+	0.998778i	$0.515740\pi$
$920$	−16.5372	+	28.6434i	−0.545217	+	0.944343i
$921$		0			0
$922$	−77.5863	+	44.7945i	−2.55517	+	1.47523i
$923$	−11.3502	−	19.6591i	−0.373596	−	0.647088i
$924$		0			0
$925$	3.07494	−	5.32595i	0.101103	−	0.175116i
$926$			21.2152i			0.697175i
$927$		0			0
$928$	−3.88289			−0.127462
$929$	16.1108	−	27.9047i	0.528577	−	0.915522i	−0.470868	−	0.882204i	$-0.656059\pi$
$929$	16.1108	−	27.9047i	0.528577	−	0.915522i	0.999445	−	0.0333184i	$-0.0106075\pi$
$930$		0			0
$931$		0			0
$932$	−51.3888	+	29.6694i	−1.68330	+	0.971852i
$933$		0			0
$934$	−48.5064	−	28.0052i	−1.58718	−	0.916358i
$935$		−	3.60068i		−	0.117755i
$936$		0			0
$937$		−	3.07038i		−	0.100305i	−0.998742	−	0.0501525i	$-0.984029\pi$
$937$		−	3.07038i		−	0.100305i	0.998742	−	0.0501525i	$-0.0159708\pi$
$938$		0			0
$939$		0			0
$940$	−4.60640	−	7.97852i	−0.150244	−	0.260231i
$941$	−19.4136	−	33.6253i	−0.632865	−	1.09615i	−0.986963	−	0.160946i	$-0.948546\pi$
$941$	−19.4136	−	33.6253i	−0.632865	−	1.09615i	0.354099	−	0.935208i	$-0.384788\pi$
$942$		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	$-0.431879\pi$
$947$	−16.2391	−	9.37567i	−0.527701	−	0.304668i	−0.740080	+	0.672519i	$0.765212\pi$
$948$		0			0
$949$	−8.17166	−	14.1537i	−0.265263	−	0.459450i
$950$	35.9477	+	62.2632i	1.16630	+	2.02008i
$951$		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
$955$			19.2672i			0.623474i
$956$	−64.2911	−	37.1185i	−2.07932	−	1.20050i
$957$		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
$962$	8.83643			0.284898
$963$		0			0
$964$			66.0608i			2.12768i
$965$	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	$0.521851\pi$
$968$	37.7137	−	21.7740i	1.21216	−	0.699843i
$969$		0			0
$970$	3.88040	−	6.72104i	0.124592	−	0.215800i
$971$	−28.3866			−0.910971			−0.455485	−	0.890243i	$-0.650534\pi$
$971$	−28.3866			−0.910971			−0.455485	+	0.890243i	$0.650534\pi$
$972$		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	$-0.895647\pi$
$977$	−35.6722	+	20.5954i	−1.14126	+	0.658904i	−0.194515	+	0.980900i	$0.562313\pi$
$978$		0			0
$979$	17.1576	+	9.90597i	0.548361	+	0.316596i
$980$		0			0
$981$		0			0
$982$	−112.734			−3.59747
$983$	26.4017	−	45.7291i	0.842085	−	1.45853i	−0.0460447	−	0.998939i	$-0.514662\pi$
$983$	26.4017	−	45.7291i	0.842085	−	1.45853i	0.888129	−	0.459594i	$-0.152005\pi$
$984$		0			0
$985$	−19.7153	+	11.3826i	−0.628181	+	0.362680i
$986$	0.327278	+	0.566862i	0.0104227	+	0.0180526i
$987$		0			0
$988$	−37.5731	+	65.0784i	−1.19536	+	2.07042i
$989$			0.0398983i			0.00126869i
$990$		0			0
$991$	16.4897			0.523813			0.261907	−	0.965093i	$-0.415649\pi$
$991$	16.4897			0.523813			0.261907	+	0.965093i	$0.415649\pi$
$992$	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
$997$	−42.4857	−	24.5291i	−1.34553	−	0.776845i	−0.357921	−	0.933752i	$-0.616514\pi$
$997$	−42.4857	−	24.5291i	−1.34553	−	0.776845i	−0.987613	+	0.156907i	$0.949848\pi$
$998$			87.4667i			2.76871i
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.34591 + 1.35441i) q^{2} +(2.66888 + 4.62263i) q^{4} +(-0.601464 - 1.04177i) q^{5} +9.04141i q^{8} +O(q^{10})\)	\(q+(2.34591 + 1.35441i) q^{2} +(2.66888 + 4.62263i) q^{4} +(-0.601464 - 1.04177i) q^{5} +9.04141i q^{8} -3.25853i q^{10} +(2.15351 + 1.24333i) q^{11} +(1.63211 - 0.942300i) q^{13} +(-6.90806 + 11.9651i) q^{16} +1.20373 q^{17} +7.47013i q^{19} +(3.21047 - 5.56070i) q^{20} +(3.36797 + 5.83350i) q^{22} +(-2.63359 + 1.52050i) q^{23} +(1.77648 - 3.07696i) q^{25} +5.10506 q^{26} +(0.173847 + 0.100371i) q^{29} +(-3.03381 + 1.75157i) q^{31} +(-16.7513 + 9.67135i) q^{32} +(2.82384 + 1.63034i) q^{34} +1.73092 q^{37} +(-10.1177 + 17.5243i) q^{38} +(9.41904 - 5.43809i) q^{40} +(-3.36029 - 5.82020i) q^{41} +(0.00656005 - 0.0113623i) q^{43} +13.2732i q^{44} -8.23756 q^{46} +(0.717403 - 1.24258i) q^{47} +(8.33495 - 4.81219i) q^{50} +(8.71182 + 5.02977i) q^{52} -9.90831i q^{53} -2.99128i q^{55} +(0.271887 + 0.470923i) q^{58} +(-6.10954 - 10.5820i) q^{59} +(9.73903 + 5.62283i) q^{61} -9.48942 q^{62} -24.7638 q^{64} +(-1.96331 - 1.13352i) q^{65} +(2.57932 + 4.46752i) q^{67} +(3.21260 + 5.56438i) q^{68} -12.0452i q^{71} -8.67204i q^{73} +(4.06058 + 2.34438i) q^{74} +(-34.5317 + 19.9369i) q^{76} +(-2.74801 + 4.75969i) q^{79} +16.6198 q^{80} -18.2049i q^{82} +(-1.60854 + 2.78607i) q^{83} +(-0.723998 - 1.25400i) q^{85} +(0.0307786 - 0.0177700i) q^{86} +(-11.2415 + 19.4708i) q^{88} +7.96728 q^{89} +(-14.0574 - 8.11607i) q^{92} +(3.36593 - 1.94332i) q^{94} +(7.78214 - 4.49302i) q^{95} +(2.06260 + 1.19084i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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