LMFDB - Embedded newform 441.2.o.e.293.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(146,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.146"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.24
Character	$\chi$	$=$	441.293
Dual form			441.2.o.e.146.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.23278 - 1.28910i) q^{2} +(1.71146 - 0.266270i) q^{3} +(2.32354 - 4.02449i) q^{4} +(-1.16595 + 2.01948i) q^{5} +(3.47807 - 2.80076i) q^{6} -6.82470i q^{8} +(2.85820 - 0.911422i) q^{9} +6.01207i q^{10} +(-3.78114 + 2.18304i) q^{11} +(2.90505 - 7.50646i) q^{12} +(1.14392 + 0.660445i) q^{13} +(-1.45774 + 3.76671i) q^{15} +(-4.15061 - 7.18908i) q^{16} -5.78655 q^{17} +(5.20683 - 5.71950i) q^{18} +0.675357i q^{19} +(5.41825 + 9.38468i) q^{20} +(-5.62830 + 9.74851i) q^{22} +(-4.81799 - 2.78167i) q^{23} +(-1.81721 - 11.6802i) q^{24} +(-0.218858 - 0.379074i) q^{25} +3.40551 q^{26} +(4.64902 - 2.32092i) q^{27} +(3.86926 - 2.23392i) q^{29} +(1.60083 + 10.2894i) q^{30} +(-3.47965 - 2.00898i) q^{31} +(-6.71411 - 3.87639i) q^{32} +(-5.88999 + 4.74299i) q^{33} +(-12.9201 + 7.45942i) q^{34} +(2.97314 - 13.6205i) q^{36} +3.01658 q^{37} +(0.870601 + 1.50792i) q^{38} +(2.13364 + 0.825733i) q^{39} +(13.7823 + 7.95723i) q^{40} +(3.29501 - 5.70713i) q^{41} +(3.89217 + 6.74143i) q^{43} +20.2896i q^{44} +(-1.49191 + 6.83474i) q^{45} -14.3434 q^{46} +(-0.246705 - 0.427306i) q^{47} +(-9.01785 - 11.1986i) q^{48} +(-0.977326 - 0.564259i) q^{50} +(-9.90345 + 1.54078i) q^{51} +(5.31591 - 3.06914i) q^{52} +4.14566i q^{53} +(7.38835 - 11.1751i) q^{54} -10.1812i q^{55} +(0.179827 + 1.15585i) q^{57} +(5.75947 - 9.97570i) q^{58} +(-2.15699 + 3.73602i) q^{59} +(11.7720 + 14.6188i) q^{60} +(-1.77661 + 1.02572i) q^{61} -10.3591 q^{62} -3.38572 q^{64} +(-2.66751 + 1.54009i) q^{65} +(-7.03689 + 18.1828i) q^{66} +(2.41218 - 4.17802i) q^{67} +(-13.4453 + 23.2879i) q^{68} +(-8.98648 - 3.47783i) q^{69} +1.17135i q^{71} +(-6.22018 - 19.5064i) q^{72} -15.1153i q^{73} +(6.73536 - 3.88866i) q^{74} +(-0.475504 - 0.590495i) q^{75} +(2.71797 + 1.56922i) q^{76} +(5.82840 - 0.906785i) q^{78} +(5.30428 + 9.18728i) q^{79} +19.3576 q^{80} +(7.33862 - 5.21005i) q^{81} -16.9904i q^{82} +(5.32432 + 9.22199i) q^{83} +(6.74680 - 11.6858i) q^{85} +(17.3807 + 10.0348i) q^{86} +(6.02726 - 4.85353i) q^{87} +(14.8986 + 25.8051i) q^{88} -3.32535 q^{89} +(5.47953 + 17.1837i) q^{90} +(-22.3896 + 12.9266i) q^{92} +(-6.49022 - 2.51176i) q^{93} +(-1.10168 - 0.636053i) q^{94} +(-1.36387 - 0.787429i) q^{95} +(-12.5231 - 4.84653i) q^{96} +(12.7531 - 7.36299i) q^{97} +(-8.81758 + 9.68578i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} + 16 q^{9} - 24 q^{11} - 40 q^{15} - 24 q^{16} - 16 q^{18} - 48 q^{23} - 24 q^{25} - 24 q^{30} + 120 q^{32} - 8 q^{36} + 88 q^{39} + 48 q^{50} + 24 q^{51} + 80 q^{57} - 96 q^{60} - 48 q^{64}+ \cdots - 72 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 + 16 * q^9 - 24 * q^11 - 40 * q^15 - 24 * q^16 - 16 * q^18 - 48 * q^23 - 24 * q^25 - 24 * q^30 + 120 * q^32 - 8 * q^36 + 88 * q^39 + 48 * q^50 + 24 * q^51 + 80 * q^57 - 96 * q^60 - 48 * q^64 + 120 * q^65 + 56 * q^72 - 168 * q^74 - 88 * q^78 - 24 * q^79 - 96 * q^81 - 24 * q^85 + 24 * q^86 - 144 * q^92 - 32 * q^93 + 96 * q^95 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.23278	−	1.28910i	1.57882	−	0.911529i	0.583790	−	0.811905i	$-0.301569\pi$
$2$	2.23278	−	1.28910i	1.57882	−	0.911529i	0.995025	−	0.0996245i	$-0.0317642\pi$
$3$	1.71146	−	0.266270i	0.988113	−	0.153731i
$3$	1.71146	−	0.266270i	0.988113	−	0.153731i
$4$	2.32354	−	4.02449i	1.16177	−	2.01225i
$5$	−1.16595	+	2.01948i	−0.521427	+	0.903138i	0.478263	+	0.878217i	$0.341267\pi$
$5$	−1.16595	+	2.01948i	−0.521427	+	0.903138i	−0.999689	+	0.0249208i	$0.992067\pi$
$6$	3.47807	−	2.80076i	1.41992	−	1.14341i
$7$		0			0
$7$		0			0
$8$		−	6.82470i		−	2.41290i
$9$	2.85820	−	0.911422i	0.952734	−	0.303807i
$10$			6.01207i			1.90118i
$11$	−3.78114	+	2.18304i	−1.14006	+	0.658212i	−0.946444	−	0.322867i	$-0.895353\pi$
$11$	−3.78114	+	2.18304i	−1.14006	+	0.658212i	−0.193612	+	0.981078i	$0.562020\pi$
$12$	2.90505	−	7.50646i	0.838616	−	2.16693i
$13$	1.14392	+	0.660445i	0.317267	+	0.183174i	0.650174	−	0.759785i	$-0.274696\pi$
$13$	1.14392	+	0.660445i	0.317267	+	0.183174i	−0.332906	+	0.942960i	$0.608029\pi$
$14$		0			0
$15$	−1.45774	+	3.76671i	−0.376388	+	0.972561i
$16$	−4.15061	−	7.18908i	−1.03765	−	1.79727i
$17$	−5.78655			−1.40344			−0.701722	−	0.712451i	$-0.747585\pi$
$17$	−5.78655			−1.40344			−0.701722	+	0.712451i	$0.747585\pi$
$18$	5.20683	−	5.71950i	1.22726	−	1.34810i
$19$			0.675357i			0.154937i	0.996995	+	0.0774687i	$0.0246838\pi$
$19$			0.675357i			0.154937i	−0.996995	+	0.0774687i	$0.975316\pi$
$20$	5.41825	+	9.38468i	1.21156	+	2.09848i
$21$		0			0
$22$	−5.62830	+	9.74851i	−1.19996	+	2.07839i
$23$	−4.81799	−	2.78167i	−1.00462	−	0.580018i	−0.0950080	−	0.995477i	$-0.530288\pi$
$23$	−4.81799	−	2.78167i	−1.00462	−	0.580018i	−0.909612	+	0.415459i	$0.863621\pi$
$24$	−1.81721	−	11.6802i	−0.370937	−	2.38421i
$25$	−0.218858	−	0.379074i	−0.0437717	−	0.0758147i
$26$	3.40551			0.667875
$27$	4.64902	−	2.32092i	0.894704	−	0.446661i
$28$		0			0
$29$	3.86926	−	2.23392i	0.718503	−	0.414828i	−0.0956983	−	0.995410i	$-0.530508\pi$
$29$	3.86926	−	2.23392i	0.718503	−	0.414828i	0.814202	+	0.580582i	$0.197175\pi$
$30$	1.60083	+	10.2894i	0.292271	+	1.87858i
$31$	−3.47965	−	2.00898i	−0.624964	−	0.360823i	0.153835	−	0.988097i	$-0.450838\pi$
$31$	−3.47965	−	2.00898i	−0.624964	−	0.360823i	−0.778799	+	0.627273i	$0.784171\pi$
$32$	−6.71411	−	3.87639i	−1.18690	−	0.685256i
$33$	−5.88999	+	4.74299i	−1.02532	+	0.825649i
$34$	−12.9201	+	7.45942i	−2.21578	+	1.27928i
$35$		0			0
$36$	2.97314	−	13.6205i	0.495523	−	2.27009i
$37$	3.01658			0.495923			0.247961	−	0.968770i	$-0.420239\pi$
$37$	3.01658			0.495923			0.247961	+	0.968770i	$0.420239\pi$
$38$	0.870601	+	1.50792i	0.141230	+	0.244618i
$39$	2.13364	+	0.825733i	0.341656	+	0.132223i
$40$	13.7823	+	7.95723i	2.17918	+	1.25815i
$41$	3.29501	−	5.70713i	0.514594	−	0.891303i	−0.485262	−	0.874369i	$-0.661276\pi$
$41$	3.29501	−	5.70713i	0.514594	−	0.891303i	0.999857	−	0.0169348i	$-0.00539076\pi$
$42$		0			0
$43$	3.89217	+	6.74143i	0.593550	+	1.02806i	0.993750	+	0.111631i	$0.0356074\pi$
$43$	3.89217	+	6.74143i	0.593550	+	1.02806i	−0.400200	+	0.916428i	$0.631059\pi$
$44$			20.2896i			3.05877i
$45$	−1.49191	+	6.83474i	−0.222401	+	1.01886i
$46$	−14.3434			−2.11481
$47$	−0.246705	−	0.427306i	−0.0359856	−	0.0623289i	0.847472	−	0.530841i	$-0.178124\pi$
$47$	−0.246705	−	0.427306i	−0.0359856	−	0.0623289i	−0.883457	+	0.468512i	$0.844790\pi$
$48$	−9.01785	−	11.1986i	−1.30161	−	1.61638i
$49$		0			0
$50$	−0.977326	−	0.564259i	−0.138215	−	0.0797983i
$51$	−9.90345	+	1.54078i	−1.38676	+	0.215753i
$52$	5.31591	−	3.06914i	0.737184	−	0.425614i
$53$			4.14566i			0.569451i	0.958609	+	0.284725i	$0.0919024\pi$
$53$			4.14566i			0.569451i	−0.958609	+	0.284725i	$0.908098\pi$
$54$	7.38835	−	11.1751i	1.00543	−	1.52074i
$55$		−	10.1812i		−	1.37284i
$56$		0			0
$57$	0.179827	+	1.15585i	0.0238187	+	0.153096i
$58$	5.75947	−	9.97570i	0.756256	−	1.30987i
$59$	−2.15699	+	3.73602i	−0.280816	+	0.486388i	−0.971586	−	0.236687i	$-0.923939\pi$
$59$	−2.15699	+	3.73602i	−0.280816	+	0.486388i	0.690770	+	0.723075i	$0.257272\pi$
$60$	11.7720	+	14.6188i	1.51976	+	1.88728i
$61$	−1.77661	+	1.02572i	−0.227471	+	0.131330i	−0.609405	−	0.792859i	$-0.708592\pi$
$61$	−1.77661	+	1.02572i	−0.227471	+	0.131330i	0.381934	+	0.924190i	$0.375258\pi$
$62$	−10.3591			−1.31560
$63$		0			0
$64$	−3.38572			−0.423215
$65$	−2.66751	+	1.54009i	−0.330863	+	0.191024i
$66$	−7.03689	+	18.1828i	−0.866181	+	2.23815i
$67$	2.41218	−	4.17802i	0.294695	−	0.510427i	−0.680219	−	0.733009i	$-0.738115\pi$
$67$	2.41218	−	4.17802i	0.294695	−	0.510427i	0.974914	+	0.222582i	$0.0714486\pi$
$68$	−13.4453	+	23.2879i	−1.63048	+	2.82408i
$69$	−8.98648	−	3.47783i	−1.08184	−	0.418681i
$70$		0			0
$71$			1.17135i			0.139014i	0.997581	+	0.0695068i	$0.0221426\pi$
$71$			1.17135i			0.139014i	−0.997581	+	0.0695068i	$0.977857\pi$
$72$	−6.22018	−	19.5064i	−0.733055	−	2.29885i
$73$		−	15.1153i		−	1.76911i	−0.466432	−	0.884557i	$-0.654461\pi$
$73$		−	15.1153i		−	1.76911i	0.466432	−	0.884557i	$-0.345539\pi$
$74$	6.73536	−	3.88866i	0.782970	−	0.452048i
$75$	−0.475504	−	0.590495i	−0.0549064	−	0.0681844i
$76$	2.71797	+	1.56922i	0.311772	+	0.180002i
$77$		0			0
$78$	5.82840	−	0.906785i	0.659936	−	0.102673i
$79$	5.30428	+	9.18728i	0.596778	+	1.03365i	0.993293	+	0.115622i	$0.0368861\pi$
$79$	5.30428	+	9.18728i	0.596778	+	1.03365i	−0.396515	+	0.918028i	$0.629781\pi$
$80$	19.3576			2.16424
$81$	7.33862	−	5.21005i	0.815402	−	0.578895i
$82$		−	16.9904i		−	1.87627i
$83$	5.32432	+	9.22199i	0.584420	+	1.01225i	0.994947	+	0.100397i	$0.0320113\pi$
$83$	5.32432	+	9.22199i	0.584420	+	1.01225i	−0.410527	+	0.911848i	$0.634655\pi$
$84$		0			0
$85$	6.74680	−	11.6858i	0.731793	−	1.26750i
$86$	17.3807	+	10.0348i	1.87421	+	1.08208i
$87$	6.02726	−	4.85353i	0.646190	−	0.520353i
$88$	14.8986	+	25.8051i	1.58820	+	2.75084i
$89$	−3.32535			−0.352486			−0.176243	−	0.984347i	$-0.556395\pi$
$89$	−3.32535			−0.352486			−0.176243	+	0.984347i	$0.556395\pi$
$90$	5.47953	+	17.1837i	0.577593	+	1.81132i
$91$		0			0
$92$	−22.3896	+	12.9266i	−2.33428	+	1.34770i
$93$	−6.49022	−	2.51176i	−0.673005	−	0.260458i
$94$	−1.10168	−	0.636053i	−0.113629	−	0.0656039i
$95$	−1.36387	−	0.787429i	−0.139930	−	0.0807886i
$96$	−12.5231	−	4.84653i	−1.27813	−	0.494647i
$97$	12.7531	−	7.36299i	1.29488	−	0.747598i	0.315363	−	0.948971i	$-0.397874\pi$
$97$	12.7531	−	7.36299i	1.29488	−	0.747598i	0.979515	+	0.201373i	$0.0645403\pi$
$98$		0			0
$99$	−8.81758	+	9.68578i	−0.886200	+	0.973458i
$100$	−2.03411			−0.203411
$101$	0.832092	+	1.44123i	0.0827963	+	0.143407i	0.904450	−	0.426580i	$-0.140282\pi$
$101$	0.832092	+	1.44123i	0.0827963	+	0.143407i	−0.821654	+	0.569987i	$0.806948\pi$
$102$	−20.1260	+	16.2067i	−1.99277	+	1.60471i
$103$	−1.40783	−	0.812812i	−0.138718	−	0.0800887i	0.429035	−	0.903288i	$-0.358854\pi$
$103$	−1.40783	−	0.812812i	−0.138718	−	0.0800887i	−0.567753	+	0.823199i	$0.692187\pi$
$104$	4.50734	−	7.80694i	0.441981	−	0.765533i
$105$		0			0
$106$	5.34416	+	9.25636i	0.519071	+	0.899057i
$107$		−	18.3130i		−	1.77039i	−0.465221	−	0.885194i	$-0.654025\pi$
$107$		−	18.3130i		−	1.77039i	0.465221	−	0.885194i	$-0.345975\pi$
$108$	1.46167	−	24.1027i	0.140650	−	2.31928i
$109$	−15.9736			−1.52999			−0.764995	−	0.644036i	$-0.777259\pi$
$109$	−15.9736			−1.52999			−0.764995	+	0.644036i	$0.777259\pi$
$110$	−13.1246	−	22.7325i	−1.25138	−	2.16746i
$111$	5.16276	−	0.803225i	0.490027	−	0.0762387i
$112$		0			0
$113$	−5.07612	−	2.93070i	−0.477521	−	0.275697i	0.241862	−	0.970311i	$-0.422242\pi$
$113$	−5.07612	−	2.93070i	−0.477521	−	0.275697i	−0.719383	+	0.694614i	$0.755575\pi$
$114$	1.89151	+	2.34894i	0.177157	+	0.219998i
$115$	11.2350	−	6.48654i	1.04767	−	0.604873i
$116$		−	20.7624i		−	1.92774i
$117$	3.87151	+	0.845087i	0.357921	+	0.0781283i
$118$			11.1223i			1.02389i
$119$		0			0
$120$	25.7067	+	9.94867i	2.34669	+	0.908185i
$121$	4.03134	−	6.98248i	0.366485	−	0.634771i
$122$	−2.64451	+	4.58043i	−0.239423	+	0.414693i
$123$	4.11965	−	10.6449i	0.371456	−	0.959817i
$124$	−16.1702	+	9.33589i	−1.45213	+	0.838388i
$125$	−10.6387			−0.951559
$126$		0			0
$127$	−16.5710			−1.47044			−0.735218	−	0.677831i	$-0.762920\pi$
$127$	−16.5710			−1.47044			−0.735218	+	0.677831i	$0.762920\pi$
$128$	5.86864	−	3.38826i	0.518719	−	0.299483i
$129$	8.45633	+	10.5013i	0.744539	+	0.924591i
$130$	−3.97064	+	6.87735i	−0.348248	+	0.603183i
$131$	3.55989	−	6.16591i	0.311029	−	0.538718i	−0.667556	−	0.744559i	$-0.732660\pi$
$131$	3.55989	−	6.16591i	0.311029	−	0.538718i	0.978585	+	0.205841i	$0.0659930\pi$
$132$	5.40250	+	34.7248i	0.470227	+	3.02241i
$133$		0			0
$134$		−	12.4382i		−	1.07449i
$135$	−0.733463	+	12.0946i	−0.0631264	+	1.04094i
$136$			39.4914i			3.38636i
$137$	−0.716584	+	0.413720i	−0.0612219	+	0.0353465i	−0.530298	−	0.847811i	$-0.677920\pi$
$137$	−0.716584	+	0.413720i	−0.0612219	+	0.0353465i	0.469077	+	0.883157i	$0.344587\pi$
$138$	−24.5481	+	3.81920i	−2.08967	+	0.325112i
$139$	12.0735	+	6.97062i	1.02406	+	0.591241i	0.915277	−	0.402825i	$-0.131972\pi$
$139$	12.0735	+	6.97062i	1.02406	+	0.591241i	0.108782	+	0.994066i	$0.465305\pi$
$140$		0			0
$141$	−0.536005	−	0.665627i	−0.0451397	−	0.0560559i
$142$	1.50998	+	2.61537i	0.126715	+	0.219477i
$143$	−5.76711			−0.482270
$144$	−18.4156	−	16.7649i	−1.53463	−	1.39707i
$145$			10.4185i			0.865210i
$146$	−19.4851	−	33.7492i	−1.61260	−	2.79310i
$147$		0			0
$148$	7.00915	−	12.1402i	0.576149	−	0.997919i
$149$	−9.46916	−	5.46702i	−0.775744	−	0.447876i	0.0591761	−	0.998248i	$-0.481153\pi$
$149$	−9.46916	−	5.46702i	−0.775744	−	0.447876i	−0.834920	+	0.550372i	$0.814486\pi$
$150$	−1.82290	−	0.705475i	−0.148839	−	0.0576018i
$151$	6.97277	+	12.0772i	0.567436	+	0.982828i	0.996818	+	0.0797050i	$0.0253978\pi$
$151$	6.97277	+	12.0772i	0.567436	+	0.982828i	−0.429383	+	0.903123i	$0.641269\pi$
$152$	4.60911			0.373848
$153$	−16.5391	+	5.27399i	−1.33711	+	0.426376i
$154$		0			0
$155$	8.11417	−	4.68472i	0.651746	−	0.376286i
$156$	8.28076	−	6.66819i	0.662991	−	0.533882i
$157$	13.6641	+	7.88894i	1.09051	+	0.629606i	0.933712	−	0.358024i	$-0.116550\pi$
$157$	13.6641	+	7.88894i	1.09051	+	0.629606i	0.156798	+	0.987631i	$0.449883\pi$
$158$	23.6866	+	13.6755i	1.88440	+	1.08796i
$159$	1.10387	+	7.09514i	0.0875423	+	0.562681i
$160$	15.6566	−	9.03932i	1.23776	−	0.714621i
$161$		0			0
$162$	9.66928	−	21.0931i	0.759690	−	1.65723i
$163$	−6.76552			−0.529916			−0.264958	−	0.964260i	$-0.585358\pi$
$163$	−6.76552			−0.529916			−0.264958	+	0.964260i	$0.585358\pi$
$164$	−15.3122	−	26.5215i	−1.19568	−	2.07098i
$165$	−2.71096	−	17.4248i	−0.211048	−	1.35652i
$166$	23.7761	+	13.7271i	1.84538	+	1.06543i
$167$	−9.54631	+	16.5347i	−0.738716	+	1.27949i	0.214358	+	0.976755i	$0.431234\pi$
$167$	−9.54631	+	16.5347i	−0.738716	+	1.27949i	−0.953074	+	0.302738i	$0.902099\pi$
$168$		0			0
$169$	−5.62763	−	9.74733i	−0.432894	−	0.749795i
$170$		−	34.7891i		−	2.66820i
$171$	0.615535	+	1.93031i	0.0470711	+	0.147614i
$172$	36.1745			2.75828
$173$	10.9246	+	18.9219i	0.830579	+	1.43860i	0.897580	+	0.440851i	$0.145323\pi$
$173$	10.9246	+	18.9219i	0.830579	+	1.43860i	−0.0670016	+	0.997753i	$0.521343\pi$
$174$	7.20089	−	18.6066i	0.545898	−	1.41056i
$175$		0			0
$176$	31.3881	+	18.1219i	2.36597	+	1.36599i
$177$	−2.69682	+	6.96840i	−0.202705	+	0.523777i
$178$	−7.42478	+	4.28670i	−0.556511	+	0.321302i
$179$			17.1896i			1.28481i	0.766364	+	0.642406i	$0.222064\pi$
$179$			17.1896i			1.28481i	−0.766364	+	0.642406i	$0.777936\pi$
$180$	24.0398	+	21.8850i	1.79182	+	1.63121i
$181$		−	16.6462i		−	1.23730i	−0.785666	−	0.618650i	$-0.787680\pi$
$181$		−	16.6462i		−	1.23730i	0.785666	−	0.618650i	$-0.212320\pi$
$182$		0			0
$183$	−2.76747	+	2.22854i	−0.204577	+	0.164739i
$184$	−18.9840	+	32.8813i	−1.39952	+	2.42404i
$185$	−3.51717	+	6.09191i	−0.258587	+	0.447886i
$186$	−17.7292	+	2.75831i	−1.29996	+	0.202249i
$187$	21.8797	−	12.6323i	1.60000	−	0.923763i
$188$	−2.29292			−0.167228
$189$		0			0
$190$	−4.06029			−0.294565
$191$	0.826254	−	0.477038i	0.0597857	−	0.0345173i	−0.469809	−	0.882768i	$-0.655677\pi$
$191$	0.826254	−	0.477038i	0.0597857	−	0.0345173i	0.529595	+	0.848251i	$0.322344\pi$
$192$	−5.79453	+	0.901516i	−0.418184	+	0.0650613i
$193$	0.847203	−	1.46740i	0.0609830	−	0.105626i	−0.833922	−	0.551882i	$-0.813910\pi$
$193$	0.847203	−	1.46740i	0.0609830	−	0.105626i	0.894905	+	0.446257i	$0.147243\pi$
$194$	18.9832	−	32.8799i	1.36292	−	2.36064i
$195$	−4.15526	+	3.34607i	−0.297564	+	0.239617i
$196$		0			0
$197$		−	12.7486i		−	0.908301i	−0.890925	−	0.454150i	$-0.849943\pi$
$197$		−	12.7486i		−	0.908301i	0.890925	−	0.454150i	$-0.150057\pi$
$198$	−7.20182	+	32.9929i	−0.511811	+	2.34471i
$199$		−	4.35807i		−	0.308935i	−0.987998	−	0.154468i	$-0.950634\pi$
$199$		−	4.35807i		−	0.308935i	0.987998	−	0.154468i	$-0.0493662\pi$
$200$	−2.58706	+	1.49364i	−0.182933	+	0.105616i
$201$	3.01588	−	7.79282i	0.212724	−	0.549663i
$202$	3.71576	+	2.14530i	0.261440	+	0.150942i
$203$		0			0
$204$	−16.8102	+	43.4365i	−1.17695	+	3.04116i
$205$	7.68361	+	13.3084i	0.536646	+	0.929499i
$206$	−4.19117			−0.292013
$207$	−16.3060	−	3.55934i	−1.13335	−	0.247391i
$208$		−	10.9650i		−	0.760287i
$209$	−1.47433	−	2.55362i	−0.101982	−	0.176637i
$210$		0			0
$211$	−2.24368	+	3.88617i	−0.154461	+	0.267535i	−0.932863	−	0.360232i	$-0.882698\pi$
$211$	−2.24368	+	3.88617i	−0.154461	+	0.267535i	0.778401	+	0.627767i	$0.216031\pi$
$212$	16.6842	+	9.63263i	1.14588	+	0.661571i
$213$	0.311895	+	2.00472i	0.0213707	+	0.137361i
$214$	−23.6073	−	40.8890i	−1.61376	−	2.79512i
$215$	−18.1522			−1.23797
$216$	−15.8396	−	31.7281i	−1.07775	−	2.15883i
$217$		0			0
$218$	−35.6655	+	20.5915i	−2.41557	+	1.39463i
$219$	−4.02476	−	25.8693i	−0.271968	−	1.74808i
$220$	−40.9743	−	23.6565i	−2.76249	−	1.59492i
$221$	−6.61937	−	3.82170i	−0.445267	−	0.257075i
$222$	10.4919	−	8.44872i	0.704169	−	0.567041i
$223$	−18.0005	+	10.3926i	−1.20540	+	0.695939i	−0.961751	−	0.273924i	$-0.911678\pi$
$223$	−18.0005	+	10.3926i	−1.20540	+	0.695939i	−0.243650	+	0.969863i	$0.578345\pi$
$224$		0			0
$225$	−0.971037	−	0.883997i	−0.0647358	−	0.0589331i
$226$	−15.1118			−1.00522
$227$	−14.1579	−	24.5223i	−0.939696	−	1.62760i	−0.766039	−	0.642795i	$-0.777775\pi$
$227$	−14.1579	−	24.5223i	−0.939696	−	1.62760i	−0.173657	−	0.984806i	$-0.555558\pi$
$228$	5.06954	+	1.96195i	0.335738	+	0.129933i
$229$	−18.8670	−	10.8929i	−1.24677	−	0.719821i	−0.276303	−	0.961071i	$-0.589109\pi$
$229$	−18.8670	−	10.8929i	−1.24677	−	0.719821i	−0.970463	+	0.241250i	$0.922443\pi$
$230$	16.7236	−	28.9661i	1.10272	−	1.90997i
$231$		0			0
$232$	−15.2458	−	26.4065i	−1.00094	−	1.73367i
$233$			15.2335i			0.997978i	0.866608	+	0.498989i	$0.166295\pi$
$233$			15.2335i			0.997978i	−0.866608	+	0.498989i	$0.833705\pi$
$234$	9.73363	−	3.10386i	0.636307	−	0.202905i
$235$	1.15058			0.0750554
$236$	10.0237	+	17.3616i	0.652489	+	1.13014i
$237$	11.5244	+	14.3113i	0.748588	+	0.929619i
$238$		0			0
$239$	−4.95125	−	2.85861i	−0.320270	−	0.184908i	0.331243	−	0.943545i	$-0.392532\pi$
$239$	−4.95125	−	2.85861i	−0.320270	−	0.184908i	−0.651513	+	0.758638i	$0.725865\pi$
$240$	33.1297	−	5.15434i	2.13851	−	0.332711i
$241$	3.87212	−	2.23557i	0.249425	−	0.144006i	−0.370076	−	0.929002i	$-0.620668\pi$
$241$	3.87212	−	2.23557i	0.249425	−	0.144006i	0.619501	+	0.784996i	$0.287335\pi$
$242$		−	20.7871i		−	1.33625i
$243$	11.1725	−	10.8709i	0.716715	−	0.697366i
$244$			9.53325i			0.610304i
$245$		0			0
$246$	−4.52402	−	29.0783i	−0.288441	−	1.85397i
$247$	−0.446036	+	0.772557i	−0.0283806	+	0.0491566i
$248$	−13.7107	+	23.7476i	−0.870629	+	1.50797i
$249$	11.5679	+	14.3654i	0.733086	+	0.910369i
$250$	−23.7540	+	13.7144i	−1.50234	+	0.867374i
$251$	11.6265			0.733861			0.366931	−	0.930248i	$-0.380409\pi$
$251$	11.6265			0.733861			0.366931	+	0.930248i	$0.380409\pi$
$252$		0			0
$253$	24.2900			1.52710
$254$	−36.9993	+	21.3616i	−2.32155	+	1.34034i
$255$	8.43531	−	21.7963i	0.528240	−	1.36494i
$256$	12.1213	−	20.9947i	0.757582	−	1.31217i
$257$	−1.05140	+	1.82108i	−0.0655846	+	0.113596i	−0.896953	−	0.442126i	$-0.854225\pi$
$257$	−1.05140	+	1.82108i	−0.0655846	+	0.113596i	0.831369	+	0.555721i	$0.187558\pi$
$258$	32.4184	+	12.5461i	2.01828	+	0.781089i
$259$		0			0
$260$			14.3138i			0.887705i
$261$	9.02308	−	9.91151i	0.558514	−	0.613507i
$262$		−	18.3562i		−	1.13405i
$263$	−1.90773	+	1.10143i	−0.117636	+	0.0679170i	−0.557663	−	0.830067i	$-0.688302\pi$
$263$	−1.90773	+	1.10143i	−0.117636	+	0.0679170i	0.440028	+	0.897984i	$0.354969\pi$
$264$	32.3695	+	40.1974i	1.99221	+	2.47398i
$265$	−8.37207	−	4.83362i	−0.514292	−	0.296927i
$266$		0			0
$267$	−5.69121	+	0.885441i	−0.348296	+	0.0541881i
$268$	−11.2096	−	19.4156i	−0.684737	−	1.18600i
$269$	27.8623			1.69880			0.849398	−	0.527753i	$-0.176965\pi$
$269$	27.8623			1.69880			0.849398	+	0.527753i	$0.176965\pi$
$270$	13.9535	+	27.9502i	0.849183	+	1.70100i
$271$		−	11.4804i		−	0.697382i	−0.937238	−	0.348691i	$-0.886626\pi$
$271$		−	11.4804i		−	0.697382i	0.937238	−	0.348691i	$-0.113374\pi$
$272$	24.0177	+	41.5999i	1.45629	+	2.52237i
$273$		0			0
$274$	−1.06665	+	1.84749i	−0.0644387	+	0.111611i
$275$	1.65507	+	0.955553i	0.0998043	+	0.0576220i
$276$	−34.8770	+	28.0851i	−2.09935	+	1.69053i
$277$	5.10000	+	8.83346i	0.306429	+	0.530751i	0.977579	−	0.210571i	$-0.0675323\pi$
$277$	5.10000	+	8.83346i	0.306429	+	0.530751i	−0.671149	+	0.741322i	$0.734199\pi$
$278$	35.9432			2.15573
$279$	−11.7766	−	2.57063i	−0.705045	−	0.153900i
$280$		0			0
$281$	9.45116	−	5.45663i	0.563809	−	0.325515i	−0.190864	−	0.981617i	$-0.561129\pi$
$281$	9.45116	−	5.45663i	0.563809	−	0.325515i	0.754673	+	0.656101i	$0.227796\pi$
$282$	−2.05484	−	0.795237i	−0.122364	−	0.0473557i
$283$	−10.2766	−	5.93322i	−0.610882	−	0.352693i	0.162428	−	0.986720i	$-0.448067\pi$
$283$	−10.2766	−	5.93322i	−0.610882	−	0.352693i	−0.773311	+	0.634027i	$0.781401\pi$
$284$	4.71409	+	2.72168i	0.279730	+	0.161502i
$285$	−2.54388	−	0.984498i	−0.150686	−	0.0583166i
$286$	−12.8767	+	7.43437i	−0.761415	+	0.439603i
$287$		0			0
$288$	−22.7233	−	4.96012i	−1.33898	−	0.292278i
$289$	16.4841			0.969655
$290$	13.4305	+	23.2622i	0.788664	+	1.36601i
$291$	19.8658	−	15.9972i	1.16456	−	0.937774i
$292$	−60.8315	−	35.1211i	−3.55989	−	2.05531i
$293$	−9.55012	+	16.5413i	−0.557924	+	0.966353i	0.439746	+	0.898122i	$0.355069\pi$
$293$	−9.55012	+	16.5413i	−0.557924	+	0.966353i	−0.997670	+	0.0682302i	$0.978265\pi$
$294$		0			0
$295$	−5.02987	−	8.71199i	−0.292850	−	0.507232i
$296$		−	20.5872i		−	1.19661i
$297$	−12.5119	+	18.9247i	−0.726015	+	1.09812i
$298$	−28.1901			−1.63301
$299$	−3.67427	−	6.36403i	−0.212489	−	0.368041i
$300$	−3.48129	+	0.541622i	−0.200993	+	0.0312705i
$301$		0			0
$302$	31.1373	+	17.9772i	1.79175	+	1.03447i
$303$	1.80785	+	2.24504i	0.103858	+	0.128974i
$304$	4.85519	−	2.80315i	0.278464	−	0.160771i
$305$		−	4.78375i		−	0.273917i
$306$	−30.1296	+	33.0962i	−1.72239	+	1.89198i
$307$		−	2.35488i		−	0.134400i	−0.997740	−	0.0672001i	$-0.978593\pi$
$307$		−	2.35488i		−	0.134400i	0.997740	−	0.0672001i	$-0.0214066\pi$
$308$		0			0
$309$	−2.62588	−	1.01623i	−0.149381	−	0.0578114i
$310$	12.0781	−	20.9199i	0.685991	−	1.18817i
$311$	−3.92483	+	6.79801i	−0.222557	+	0.385480i	−0.955584	−	0.294720i	$-0.904774\pi$
$311$	−3.92483	+	6.79801i	−0.222557	+	0.385480i	0.733027	+	0.680200i	$0.238107\pi$
$312$	5.63538	−	14.5614i	0.319041	−	0.824379i
$313$	26.0268	−	15.0266i	1.47112	−	0.849352i	0.471647	−	0.881787i	$-0.343660\pi$
$313$	26.0268	−	15.0266i	1.47112	−	0.849352i	0.999474	+	0.0324349i	$0.0103262\pi$
$314$	40.6785			2.29562
$315$		0			0
$316$	49.2989			2.77328
$317$	−9.61906	+	5.55356i	−0.540260	+	0.311919i	−0.745184	−	0.666859i	$-0.767639\pi$
$317$	−9.61906	+	5.55356i	−0.540260	+	0.311919i	0.204924	+	0.978778i	$0.434305\pi$
$318$	11.6110	+	14.4189i	0.651114	+	0.808573i
$319$	−9.75347	+	16.8935i	−0.546089	+	0.945854i
$320$	3.94757	−	6.83739i	0.220676	−	0.382222i
$321$	−4.87621	−	31.3421i	−0.272164	−	1.74934i
$322$		0			0
$323$		−	3.90798i		−	0.217446i
$324$	−3.91622	−	41.6400i	−0.217568	−	2.31333i
$325$		−	0.578175i		−	0.0320714i
$326$	−15.1059	+	8.72141i	−0.836640	+	0.483034i
$327$	−27.3381	+	4.25328i	−1.51180	+	0.235207i
$328$	−38.9494	−	22.4875i	−2.15062	−	1.24166i
$329$		0			0
$330$	−28.5152	−	35.4110i	−1.56971	−	1.94931i
$331$	8.63362	+	14.9539i	0.474547	+	0.821939i	0.999575	−	0.0291457i	$-0.00927866\pi$
$331$	8.63362	+	14.9539i	0.474547	+	0.821939i	−0.525028	+	0.851085i	$0.675945\pi$
$332$	49.4851			2.71585
$333$	8.62199	−	2.74938i	0.472482	−	0.150665i
$334$			49.2245i			2.69345i
$335$	5.62495	+	9.74270i	0.307324	+	0.532300i
$336$		0			0
$337$	−3.82962	+	6.63309i	−0.208612	+	0.361327i	−0.951278	−	0.308336i	$-0.900228\pi$
$337$	−3.82962	+	6.63309i	−0.208612	+	0.361327i	0.742665	+	0.669663i	$0.233561\pi$
$338$	−25.1305	−	14.5091i	−1.36692	−	0.789192i
$339$	−9.46794	−	3.66416i	−0.514228	−	0.199010i
$340$	−31.3530	−	54.3049i	−1.70035	−	2.94510i
$341$	17.5427			0.949992
$342$	3.86271	+	3.51647i	0.208871	+	0.190149i
$343$		0			0
$344$	46.0082	−	26.5629i	2.48060	−	1.43217i
$345$	17.5011	−	14.0930i	0.942230	−	0.758743i
$346$	48.7843	+	28.1656i	2.62266	+	1.51419i
$347$	−11.4014	−	6.58262i	−0.612061	−	0.353374i	0.161711	−	0.986838i	$-0.448299\pi$
$347$	−11.4014	−	6.58262i	−0.612061	−	0.353374i	−0.773772	+	0.633465i	$0.781632\pi$
$348$	−5.52841	−	35.5341i	−0.296354	−	1.90483i
$349$	1.05185	−	0.607283i	0.0563040	−	0.0325071i	−0.471584	−	0.881821i	$-0.656318\pi$
$349$	1.05185	−	0.607283i	0.0563040	−	0.0325071i	0.527888	+	0.849314i	$0.322984\pi$
$350$		0			0
$351$	6.85096	+	0.415467i	0.365677	+	0.0221760i
$352$	33.8493			1.80417
$353$	13.4114	+	23.2292i	0.713816	+	1.23637i	0.963414	+	0.268016i	$0.0863681\pi$
$353$	13.4114	+	23.2292i	0.713816	+	1.23637i	−0.249598	+	0.968349i	$0.580299\pi$
$354$	2.96153	+	19.0354i	0.157404	+	1.01172i
$355$	−2.36551	−	1.36573i	−0.125548	−	0.0724854i
$356$	−7.72659	+	13.3829i	−0.409509	+	0.709290i
$357$		0			0
$358$	22.1591	+	38.3807i	1.17114	+	2.02848i
$359$			7.45024i			0.393208i	0.980483	+	0.196604i	$0.0629914\pi$
$359$			7.45024i			0.393208i	−0.980483	+	0.196604i	$0.937009\pi$
$360$	46.6450	+	10.1818i	2.45841	+	0.536630i
$361$	18.5439			0.975994
$362$	−21.4585	−	37.1673i	−1.12784	−	1.95347i
$363$	5.04025	−	13.0237i	0.264545	−	0.683565i
$364$		0			0
$365$	30.5250	+	17.6236i	1.59775	+	0.922463i
$366$	−3.30635	+	8.54339i	−0.172826	+	0.446570i
$367$	−30.3000	+	17.4937i	−1.58165	+	0.913166i	−0.587031	+	0.809565i	$0.699703\pi$
$367$	−30.3000	+	17.4937i	−1.58165	+	0.913166i	−0.994619	+	0.103601i	$0.966963\pi$
$368$			46.1825i			2.40743i
$369$	4.21620	−	19.3153i	0.219487	−	1.00551i
$370$			18.1359i			0.942840i
$371$		0			0
$372$	−25.1889	+	20.2837i	−1.30598	+	1.05166i
$373$	15.0495	−	26.0665i	0.779233	−	1.34967i	−0.153151	−	0.988203i	$-0.548942\pi$
$373$	15.0495	−	26.0665i	0.779233	−	1.34967i	0.932384	−	0.361469i	$-0.117725\pi$
$374$	32.5684	−	56.4102i	1.68407	−	2.91690i
$375$	−18.2078	+	2.83278i	−0.940247	+	0.146284i
$376$	−2.91623	+	1.68369i	−0.150393	+	0.0868295i
$377$	5.90152			0.303944
$378$		0			0
$379$	−27.0996			−1.39201			−0.696006	−	0.718036i	$-0.745041\pi$
$379$	−27.0996			−1.39201			−0.696006	+	0.718036i	$0.745041\pi$
$380$	−6.33801	+	3.65925i	−0.325133	+	0.187716i
$381$	−28.3606	+	4.41235i	−1.45296	+	0.226052i
$382$	1.22990	−	2.13024i	0.0629270	−	0.108993i
$383$	−1.83015	+	3.16992i	−0.0935164	+	0.161975i	−0.908988	−	0.416821i	$-0.863144\pi$
$383$	−1.83015	+	3.16992i	−0.0935164	+	0.161975i	0.815472	+	0.578796i	$0.196477\pi$
$384$	9.14176	−	7.36152i	0.466513	−	0.375666i
$385$		0			0
$386$		−	4.36851i		−	0.222351i
$387$	17.2689	+	15.7210i	0.877827	+	0.799141i
$388$		−	68.4329i		−	3.47415i
$389$	10.5387	−	6.08449i	0.534331	−	0.308496i	−0.208447	−	0.978034i	$-0.566841\pi$
$389$	10.5387	−	6.08449i	0.534331	−	0.308496i	0.742778	+	0.669537i	$0.233508\pi$
$390$	−4.96436	+	12.8276i	−0.251380	+	0.649550i
$391$	27.8795	+	16.0962i	1.40993	+	0.814022i
$392$		0			0
$393$	4.45082	−	11.5006i	0.224514	−	0.580129i
$394$	−16.4342	−	28.4649i	−0.827943	−	1.43404i
$395$	−24.7380			−1.24470
$396$	18.4923	+	57.9916i	0.929275	+	2.91419i
$397$			26.7741i			1.34375i	0.740663	+	0.671876i	$0.234511\pi$
$397$			26.7741i			1.34375i	−0.740663	+	0.671876i	$0.765489\pi$
$398$	−5.61797	−	9.73061i	−0.281603	−	0.487752i
$399$		0			0
$400$	−1.81679	+	3.14678i	−0.0908397	+	0.157339i
$401$	6.69428	+	3.86494i	0.334296	+	0.193006i	0.657747	−	0.753239i	$-0.271510\pi$
$401$	6.69428	+	3.86494i	0.334296	+	0.193006i	−0.323451	+	0.946245i	$0.604843\pi$
$402$	−3.31191	−	21.2874i	−0.165183	−	1.06172i
$403$	−2.65364	−	4.59624i	−0.132187	−	0.228955i
$404$	7.73361			0.384761
$405$	1.96515	+	20.8948i	0.0976490	+	1.03827i
$406$		0			0
$407$	−11.4061	+	6.58532i	−0.565380	+	0.326422i
$408$	10.5154	+	67.5881i	0.520589	+	3.34611i
$409$	7.84660	+	4.53024i	0.387989	+	0.224006i	0.681289	−	0.732015i	$-0.261420\pi$
$409$	7.84660	+	4.53024i	0.387989	+	0.224006i	−0.293299	+	0.956021i	$0.594753\pi$
$410$	34.3116	+	19.8098i	1.69453	+	0.978338i
$411$	−1.11624	+	0.898870i	−0.0550603	+	0.0443380i
$412$	−6.54231	+	3.77720i	−0.322316	+	0.186090i
$413$		0			0
$414$	−40.9962	+	13.0728i	−2.01485	+	0.642495i
$415$	−24.8315			−1.21893
$416$	−5.12029	−	8.86860i	−0.251043	−	0.434819i
$417$	22.5194	+	8.71515i	1.10278	+	0.426783i
$418$	−6.58372	−	3.80111i	−0.322020	−	0.185919i
$419$	3.30466	−	5.72384i	0.161443	−	0.279628i	−0.773943	−	0.633255i	$-0.781718\pi$
$419$	3.30466	−	5.72384i	0.161443	−	0.279628i	0.935386	+	0.353627i	$0.115052\pi$
$420$		0			0
$421$	6.39209	+	11.0714i	0.311531	+	0.539588i	0.978694	−	0.205324i	$-0.0658248\pi$
$421$	6.39209	+	11.0714i	0.311531	+	0.539588i	−0.667163	+	0.744912i	$0.732491\pi$
$422$			11.5693i			0.563184i
$423$	−1.09459	−	0.996473i	−0.0532207	−	0.0484502i
$424$	28.2929			1.37403
$425$	1.26643	+	2.19353i	0.0614311	+	0.106402i
$426$	3.28067	+	4.07404i	0.158949	+	0.197388i
$427$		0			0
$428$	−73.7007	−	42.5511i	−3.56246	−	2.05679i
$429$	−9.87019	+	1.53561i	−0.476537	+	0.0741399i
$430$	−40.5299	+	23.4000i	−1.95453	+	1.12845i
$431$			21.9112i			1.05542i	0.849424	+	0.527712i	$0.176950\pi$
$431$			21.9112i			1.05542i	−0.849424	+	0.527712i	$0.823050\pi$
$432$	−35.9815	−	23.7889i	−1.73116	−	1.14454i
$433$		−	8.21181i		−	0.394635i	−0.980340	−	0.197317i	$-0.936777\pi$
$433$		−	8.21181i		−	0.394635i	0.980340	−	0.197317i	$-0.0632229\pi$
$434$		0			0
$435$	2.77414	+	17.8309i	0.133010	+	0.854925i
$436$	−37.1153	+	64.2855i	−1.77750	+	3.07872i
$437$	1.87862	−	3.25386i	0.0898665	−	0.155653i
$438$	−42.3344	−	52.5722i	−2.02282	−	2.51199i
$439$	−32.7996	+	18.9368i	−1.56544	+	0.903806i	−0.568749	+	0.822511i	$0.692572\pi$
$439$	−32.7996	+	18.9368i	−1.56544	+	0.903806i	−0.996690	+	0.0812949i	$0.974094\pi$
$440$	−69.4838			−3.31251
$441$		0			0
$442$	−19.7061			−0.937326
$443$	17.7210	−	10.2312i	0.841950	−	0.486100i	−0.0159769	−	0.999872i	$-0.505086\pi$
$443$	17.7210	−	10.2312i	0.841950	−	0.486100i	0.857926	+	0.513773i	$0.171752\pi$
$444$	8.76332	−	22.6438i	0.415889	−	1.07463i
$445$	3.87718	−	6.71547i	0.183796	−	0.318344i
$446$	−26.7941	+	46.4087i	−1.26874	+	2.19752i
$447$	−17.6618	−	6.83524i	−0.835375	−	0.323296i
$448$		0			0
$449$			35.7054i			1.68504i	0.538665	+	0.842520i	$0.318929\pi$
$449$			35.7054i			1.68504i	−0.538665	+	0.842520i	$0.681071\pi$
$450$	−3.30767	−	0.722010i	−0.155925	−	0.0340359i
$451$			28.7726i			1.35485i
$452$	−23.5892	+	13.6192i	−1.10954	+	0.640594i
$453$	15.1494	+	18.8130i	0.711782	+	0.883912i
$454$	−63.2232	−	36.5019i	−2.96721	−	1.71312i
$455$		0			0
$456$	7.88831	−	1.22727i	0.369404	−	0.0574720i
$457$	0.127090	+	0.220126i	0.00594501	+	0.0102971i	0.868983	−	0.494843i	$-0.164774\pi$
$457$	0.127090	+	0.220126i	0.00594501	+	0.0102971i	−0.863038	+	0.505140i	$0.831441\pi$
$458$	−56.1678			−2.62455
$459$	−26.9018	+	13.4301i	−1.25567	+	0.626863i
$460$		−	60.2870i		−	2.81090i
$461$	12.2175	+	21.1613i	0.569025	+	0.985581i	0.996663	+	0.0816304i	$0.0260127\pi$
$461$	12.2175	+	21.1613i	0.569025	+	0.985581i	−0.427637	+	0.903950i	$0.640654\pi$
$462$		0			0
$463$	0.409986	−	0.710116i	0.0190536	−	0.0330019i	−0.856341	−	0.516410i	$-0.827268\pi$
$463$	0.409986	−	0.710116i	0.0190536	−	0.0330019i	0.875395	+	0.483408i	$0.160601\pi$
$464$	−32.1196	−	18.5443i	−1.49112	−	0.860896i
$465$	12.6397	−	10.1783i	0.586152	−	0.472006i
$466$	19.6374	+	34.0130i	0.909686	+	1.57562i
$467$	1.81925			0.0841848			0.0420924	−	0.999114i	$-0.486598\pi$
$467$	1.81925			0.0841848			0.0420924	+	0.999114i	$0.486598\pi$
$468$	12.3967	−	13.6173i	0.573036	−	0.629458i
$469$		0			0
$470$	2.56899	−	1.48321i	0.118499	−	0.0684152i
$471$	25.4861	+	9.86330i	1.17434	+	0.454477i
$472$	25.4972	+	14.7208i	1.17360	+	0.677581i
$473$	−29.4336	−	16.9935i	−1.35336	−	0.781363i
$474$	44.1801	+	17.0980i	2.02926	+	0.785337i
$475$	0.256010	−	0.147807i	0.0117465	−	0.00678187i
$476$		0			0
$477$	3.77845	+	11.8491i	0.173003	+	0.542535i
$478$	−14.7401			−0.674196
$479$	0.681074	+	1.17965i	0.0311191	+	0.0538998i	0.881166	−	0.472808i	$-0.156760\pi$
$479$	0.681074	+	1.17965i	0.0311191	+	0.0538998i	−0.850046	+	0.526708i	$0.823426\pi$
$480$	24.3887	−	19.6393i	1.11319	−	0.896409i
$481$	3.45074	+	1.99228i	0.157340	+	0.0908403i
$482$	5.76373	−	9.98308i	0.262531	−	0.454717i
$483$		0			0
$484$	−18.7340	−	32.4482i	−0.851544	−	1.47492i
$485$			34.3394i			1.55927i
$486$	10.9321	−	38.6747i	0.495892	−	1.75432i
$487$	31.6121			1.43248			0.716241	−	0.697853i	$-0.245861\pi$
$487$	31.6121			1.43248			0.716241	+	0.697853i	$0.245861\pi$
$488$	7.00026	+	12.1248i	0.316887	+	0.548864i
$489$	−11.5789	+	1.80145i	−0.523617	+	0.0814646i
$490$		0			0
$491$	−1.97415	−	1.13977i	−0.0890919	−	0.0514373i	0.454792	−	0.890598i	$-0.349714\pi$
$491$	−1.97415	−	1.13977i	−0.0890919	−	0.0514373i	−0.543884	+	0.839160i	$0.683047\pi$
$492$	−33.2681	−	41.3133i	−1.49984	−	1.86255i
$493$	−22.3897	+	12.9267i	−1.00838	+	0.582188i
$494$			2.29993i			0.103479i
$495$	−9.27939	−	29.1000i	−0.417078	−	1.30795i
$496$			33.3540i			1.49764i
$497$		0			0
$498$	44.3470	+	17.1626i	1.98724	+	0.769074i
$499$	−13.5195	+	23.4164i	−0.605215	+	1.04826i	0.386802	+	0.922163i	$0.373580\pi$
$499$	−13.5195	+	23.4164i	−0.605215	+	1.04826i	−0.992017	+	0.126101i	$0.959754\pi$
$500$	−24.7196	+	42.8156i	−1.10549	+	1.91477i
$501$	−11.9355	+	30.8404i	−0.533237	+	1.37785i
$502$	25.9595	−	14.9877i	1.15863	−	0.668936i
$503$	0.276948			0.0123485			0.00617426	−	0.999981i	$-0.498035\pi$
$503$	0.276948			0.0123485			0.00617426	+	0.999981i	$0.498035\pi$
$504$		0			0
$505$	−3.88070			−0.172689
$506$	54.2342	−	31.3121i	2.41100	−	1.39199i
$507$	−12.2269	−	15.1837i	−0.543015	−	0.674333i
$508$	−38.5033	+	66.6897i	−1.70831	+	2.95888i
$509$	9.21476	−	15.9604i	0.408437	−	0.707434i	−0.586278	−	0.810110i	$-0.699407\pi$
$509$	9.21476	−	15.9604i	0.408437	−	0.707434i	0.994715	+	0.102676i	$0.0327406\pi$
$510$	−9.26330	−	59.5402i	−0.410186	−	2.63649i
$511$		0			0
$512$		−	48.9492i		−	2.16327i
$513$	1.56745	+	3.13974i	0.0692045	+	0.138623i
$514$			5.42143i			0.239129i
$515$	3.28291	−	1.89539i	0.144662	−	0.0835208i
$516$	61.9112	−	9.63217i	2.72549	−	0.424033i
$517$	1.86565	+	1.07713i	0.0820512	+	0.0473723i
$518$		0			0
$519$	23.7353	+	29.4752i	1.04186	+	1.29382i
$520$	10.5106	+	18.2049i	0.460921	+	0.798339i
$521$	23.2527			1.01872			0.509360	−	0.860554i	$-0.329882\pi$
$521$	23.2527			1.01872			0.509360	+	0.860554i	$0.329882\pi$
$522$	7.36966	−	33.7619i	0.322561	−	1.47772i
$523$			13.3052i			0.581798i	0.956754	+	0.290899i	$0.0939543\pi$
$523$			13.3052i			0.581798i	−0.956754	+	0.290899i	$0.906046\pi$
$524$	−16.5431	−	28.6535i	−0.722689	−	1.25173i
$525$		0			0
$526$	−2.83970	+	4.91850i	−0.123817	+	0.214457i
$527$	20.1352	+	11.6251i	0.877102	+	0.506395i
$528$	58.5448	+	22.6573i	2.54784	+	0.986031i
$529$	3.97534	+	6.88549i	0.172841	+	0.299369i
$530$	−24.9240			−1.08263
$531$	−2.76003	+	12.6442i	−0.119775	+	0.548712i
$532$		0			0
$533$	7.53848	−	4.35235i	0.326528	−	0.188521i
$534$	−11.5658	+	9.31352i	−0.500501	+	0.403035i
$535$	36.9828	+	21.3520i	1.59890	+	0.923128i
$536$	−28.5138	−	16.4624i	−1.23161	−	0.711069i
$537$	4.57708	+	29.4194i	0.197516	+	1.26954i
$538$	62.2105	−	35.9172i	2.68208	−	1.54850i
$539$		0			0
$540$	46.9706	+	31.0542i	2.02129	+	1.33636i
$541$	−30.1692			−1.29707			−0.648537	−	0.761183i	$-0.724619\pi$
$541$	−30.1692			−1.29707			−0.648537	+	0.761183i	$0.724619\pi$
$542$	−14.7993	−	25.6331i	−0.635684	−	1.10104i
$543$	−4.43238	−	28.4893i	−0.190212	−	1.22259i
$544$	38.8515	+	22.4309i	1.66574	+	0.961718i
$545$	18.6243	−	32.2582i	0.797778	−	1.38179i
$546$		0			0
$547$	−0.572061	−	0.990840i	−0.0244596	−	0.0423652i	0.853537	−	0.521033i	$-0.174453\pi$
$547$	−0.572061	−	0.990840i	−0.0244596	−	0.0423652i	−0.877996	+	0.478668i	$0.841120\pi$
$548$			3.84518i			0.164258i
$549$	−4.14303	+	4.55096i	−0.176820	+	0.194230i
$550$	4.92720			0.210097
$551$	1.50869	+	2.61313i	0.0642724	+	0.111323i
$552$	−23.7351	+	61.3300i	−1.01023	+	2.61038i
$553$		0			0
$554$	22.7744	+	13.1488i	0.967591	+	0.558639i
$555$	−4.39740	+	11.3626i	−0.186659	+	0.482315i
$556$	56.1065	−	32.3931i	2.37944	−	1.37377i
$557$		−	9.64623i		−	0.408724i	−0.978895	−	0.204362i	$-0.934488\pi$
$557$		−	9.64623i		−	0.408724i	0.978895	−	0.204362i	$-0.0655120\pi$
$558$	−29.6083	+	9.44148i	−1.25342	+	0.399690i
$559$			10.2822i			0.434893i
$560$		0			0
$561$	34.0827	−	27.4456i	1.43897	−	1.15875i
$562$	14.0683	−	24.3669i	0.593434	−	1.02786i
$563$	−1.54395	+	2.67420i	−0.0650698	+	0.112704i	−0.896725	−	0.442588i	$-0.854060\pi$
$563$	−1.54395	+	2.67420i	−0.0650698	+	0.112704i	0.831655	+	0.555292i	$0.187394\pi$
$564$	−3.92424	+	0.610535i	−0.165240	+	0.0257082i
$565$	11.8370	−	6.83407i	0.497985	−	0.287512i
$566$	−30.5940			−1.28596
$567$		0			0
$568$	7.99411			0.335425
$569$	7.30588	−	4.21805i	0.306278	−	0.176830i	−0.338982	−	0.940793i	$-0.610082\pi$
$569$	7.30588	−	4.21805i	0.306278	−	0.176830i	0.645260	+	0.763963i	$0.276749\pi$
$570$	−6.94903	+	1.08113i	−0.291063	+	0.0452837i
$571$	17.0208	−	29.4808i	0.712297	−	1.23373i	−0.251696	−	0.967806i	$-0.580988\pi$
$571$	17.0208	−	29.4808i	0.712297	−	1.23373i	0.963993	−	0.265928i	$-0.0856782\pi$
$572$	−13.4001	+	23.2097i	−0.560288	+	0.970447i
$573$	1.28708	−	1.03644i	0.0537686	−	0.0432979i
$574$		0			0
$575$			2.43516i			0.101553i
$576$	−9.67707	+	3.08582i	−0.403211	+	0.128576i
$577$		−	18.1052i		−	0.753730i	−0.926268	−	0.376865i	$-0.877002\pi$
$577$		−	18.1052i		−	0.753730i	0.926268	−	0.376865i	$-0.122998\pi$
$578$	36.8055	−	21.2497i	1.53091	−	0.883869i
$579$	1.05923	−	2.73698i	0.0440201	−	0.113745i
$580$	41.9292	+	24.2078i	1.74102	+	1.00518i
$581$		0			0
$582$	23.7341	−	61.3273i	0.983810	−	2.54210i
$583$	−9.05015	−	15.6753i	−0.374819	−	0.649206i
$584$	−103.157			−4.26869
$585$	−6.22060	+	6.83310i	−0.257190	+	0.282514i
$586$			49.2441i			2.03426i
$587$	−4.04900	−	7.01308i	−0.167120	−	0.289461i	0.770286	−	0.637699i	$-0.220113\pi$
$587$	−4.04900	−	7.01308i	−0.167120	−	0.289461i	−0.937406	+	0.348238i	$0.886780\pi$
$588$		0			0
$589$	1.35678	−	2.35001i	0.0559050	−	0.0968304i
$590$	−22.4612	−	12.9680i	−0.924713	−	0.533883i
$591$	−3.39457	−	21.8188i	−0.139634	−	0.897504i
$592$	−12.5207	−	21.6864i	−0.514596	−	0.891306i
$593$	−6.66433			−0.273671			−0.136836	−	0.990594i	$-0.543693\pi$
$593$	−6.66433			−0.273671			−0.136836	+	0.990594i	$0.543693\pi$
$594$	−3.54060	+	58.3838i	−0.145273	+	2.39552i
$595$		0			0
$596$	−44.0040	+	25.4057i	−1.80247	+	1.04066i
$597$	−1.16042	−	7.45866i	−0.0474929	−	0.305263i
$598$	−16.4077	−	9.47299i	−0.670961	−	0.387380i
$599$	−3.10562	−	1.79303i	−0.126892	−	0.0732614i	0.435210	−	0.900329i	$-0.356674\pi$
$599$	−3.10562	−	1.79303i	−0.126892	−	0.0732614i	−0.562103	+	0.827068i	$0.690007\pi$
$600$	−4.02995	+	3.24517i	−0.164522	+	0.132483i
$601$	−4.86949	+	2.81140i	−0.198631	+	0.114679i	−0.596017	−	0.802972i	$-0.703251\pi$
$601$	−4.86949	+	2.81140i	−0.198631	+	0.114679i	0.397386	+	0.917652i	$0.369917\pi$
$602$		0			0
$603$	3.08656	−	14.1401i	0.125695	−	0.575831i
$604$	64.8061			2.63692
$605$	9.40064	+	16.2824i	0.382190	+	0.661973i
$606$	6.93061	+	2.68220i	0.281537	+	0.108957i
$607$	1.93239	+	1.11566i	0.0784332	+	0.0452834i	0.538704	−	0.842495i	$-0.318914\pi$
$607$	1.93239	+	1.11566i	0.0784332	+	0.0452834i	−0.460270	+	0.887779i	$0.652248\pi$
$608$	2.61795	−	4.53442i	0.106172	−	0.183895i
$609$		0			0
$610$	−6.16672	−	10.6811i	−0.249683	−	0.432464i
$611$		−	0.651740i		−	0.0263666i
$612$	−17.2042	+	78.8159i	−0.695439	+	3.18594i
$613$	−6.82038			−0.275473			−0.137736	−	0.990469i	$-0.543983\pi$
$613$	−6.82038			−0.275473			−0.137736	+	0.990469i	$0.543983\pi$
$614$	−3.03567	−	5.25793i	−0.122510	−	0.212193i
$615$	16.6938	+	20.7309i	0.673160	+	0.835950i
$616$		0			0
$617$	−2.35139	−	1.35757i	−0.0946632	−	0.0546538i	0.451921	−	0.892058i	$-0.350739\pi$
$617$	−2.35139	−	1.35757i	−0.0946632	−	0.0546538i	−0.546584	+	0.837404i	$0.684072\pi$
$618$	−7.17303	+	1.11598i	−0.288542	+	0.0448914i
$619$	−23.1886	+	13.3880i	−0.932029	+	0.538107i	−0.887453	−	0.460899i	$-0.847527\pi$
$619$	−23.1886	+	13.3880i	−0.932029	+	0.538107i	−0.0445762	+	0.999006i	$0.514194\pi$
$620$		−	43.5406i		−	1.74863i
$621$	−28.8549	−	1.74987i	−1.15791	−	0.0702197i
$622$			20.2380i			0.811469i
$623$		0			0
$624$	−2.91965	−	18.7662i	−0.116880	−	0.751249i
$625$	13.4985	−	23.3801i	0.539940	−	0.935203i
$626$	38.7414	−	67.1021i	1.54842	−	2.68194i
$627$	−3.20321	−	3.97785i	−0.127924	−	0.158860i
$628$	63.4980	−	36.6606i	2.53385	−	1.46292i
$629$	−17.4556			−0.696000
$630$		0			0
$631$	−11.1620			−0.444354			−0.222177	−	0.975006i	$-0.571316\pi$
$631$	−11.1620			−0.444354			−0.222177	+	0.975006i	$0.571316\pi$
$632$	62.7004	−	36.2001i	2.49409	−	1.43996i
$633$	−2.80520	+	7.24845i	−0.111497	+	0.288100i
$634$	−14.3182	+	24.7998i	−0.568647	+	0.984926i
$635$	19.3208	−	33.4647i	0.766724	−	1.32801i
$636$	31.1192	+	12.0434i	1.23396	+	0.477551i
$637$		0			0
$638$			50.2927i			1.99111i
$639$	1.06759	+	3.34795i	0.0422334	+	0.132443i
$640$			15.8021i			0.624633i
$641$	38.6251	−	22.3002i	1.52560	−	0.880805i	0.526059	−	0.850448i	$-0.323669\pi$
$641$	38.6251	−	22.3002i	1.52560	−	0.880805i	0.999539	−	0.0303565i	$-0.00966427\pi$
$642$	−51.2905	−	63.6941i	−2.02427	−	2.51380i
$643$	23.6268	+	13.6410i	0.931751	+	0.537947i	0.887365	−	0.461068i	$-0.152534\pi$
$643$	23.6268	+	13.6410i	0.931751	+	0.537947i	0.0443860	+	0.999014i	$0.485867\pi$
$644$		0			0
$645$	−31.0668	+	4.83339i	−1.22326	+	0.190315i
$646$	−5.03777	−	8.72568i	−0.198208	−	0.343307i
$647$	44.9350			1.76658			0.883288	−	0.468831i	$-0.155325\pi$
$647$	44.9350			1.76658			0.883288	+	0.468831i	$0.155325\pi$
$648$	−35.5570	−	50.0839i	−1.39681	−	1.96748i
$649$		−	18.8352i		−	0.739347i
$650$	−0.745324	−	1.29094i	−0.0292340	−	0.0506348i
$651$		0			0
$652$	−15.7200	+	27.2278i	−0.615642	+	1.06632i
$653$	−24.0549	−	13.8881i	−0.941343	−	0.543484i	−0.0509617	−	0.998701i	$-0.516229\pi$
$653$	−24.0549	−	13.8881i	−0.941343	−	0.543484i	−0.890381	+	0.455216i	$0.849562\pi$
$654$	−55.5572	+	44.7382i	−2.17246	+	1.74940i
$655$	8.30128	+	14.3782i	0.324358	+	0.561804i
$656$	−54.7053			−2.13588
$657$	−13.7764	−	43.2026i	−0.537470	−	1.68549i
$658$		0			0
$659$	0.801975	−	0.463021i	0.0312405	−	0.0180367i	−0.484298	−	0.874903i	$-0.660925\pi$
$659$	0.801975	−	0.463021i	0.0312405	−	0.0180367i	0.515539	+	0.856866i	$0.327592\pi$
$660$	−76.4249	−	29.5770i	−2.97484	−	1.15128i
$661$	−28.3028	−	16.3406i	−1.10085	−	0.635577i	−0.164408	−	0.986392i	$-0.552571\pi$
$661$	−28.3028	−	16.3406i	−1.10085	−	0.635577i	−0.936445	+	0.350815i	$0.885905\pi$
$662$	38.5540	+	22.2592i	1.49844	+	0.865126i
$663$	−12.3464	−	4.77814i	−0.479495	−	0.185568i
$664$	62.9373	−	36.3369i	2.44244	−	1.41014i
$665$		0			0
$666$	15.7068	−	17.2533i	0.608626	−	0.668553i
$667$	−24.8561			−0.962430
$668$	44.3625	+	76.8382i	1.71644	+	2.97296i
$669$	−28.0399	+	22.5795i	−1.08409	+	0.872974i
$670$	25.1186	+	14.5022i	0.970415	+	0.560269i
$671$	4.47839	−	7.75681i	0.172886	−	0.299448i
$672$		0			0
$673$	−15.6947	−	27.1840i	−0.604987	−	1.04787i	−0.992054	−	0.125816i	$-0.959845\pi$
$673$	−15.6947	−	27.1840i	−0.604987	−	1.04787i	0.387067	−	0.922052i	$-0.373488\pi$
$674$			19.7470i			0.760625i
$675$	−1.89727	−	1.25437i	−0.0730261	−	0.0482806i
$676$	−52.3041			−2.01170
$677$	−10.7882	−	18.6858i	−0.414626	−	0.718153i	0.580763	−	0.814072i	$-0.302754\pi$
$677$	−10.7882	−	18.6858i	−0.414626	−	0.718153i	−0.995389	+	0.0959196i	$0.969421\pi$
$678$	−25.8633	+	4.02383i	−0.993274	+	0.154534i
$679$		0			0
$680$	−79.7521	−	46.0449i	−3.05835	−	1.76574i
$681$	−30.7603	−	38.1991i	−1.17874	−	1.46379i
$682$	39.1691	−	22.6143i	1.49986	−	0.865946i
$683$		−	36.2593i		−	1.38742i	−0.720253	−	0.693711i	$-0.755974\pi$
$683$		−	36.2593i		−	1.38742i	0.720253	−	0.693711i	$-0.244026\pi$
$684$	9.19872	+	2.00793i	0.351722	+	0.0767751i
$685$		−	1.92950i		−	0.0737224i
$686$		0			0
$687$	−35.1906	−	13.6190i	−1.34260	−	0.519597i
$688$	32.3098	−	55.9622i	1.23180	−	2.13354i
$689$	−2.73798	+	4.74232i	−0.104309	+	0.180668i
$690$	20.9089	−	54.0273i	0.795990	−	2.05678i
$691$	6.16389	−	3.55872i	0.234485	−	0.135380i	−0.378154	−	0.925743i	$-0.623441\pi$
$691$	6.16389	−	3.55872i	0.234485	−	0.135380i	0.612640	+	0.790362i	$0.290108\pi$
$692$	101.535			3.85977
$693$		0			0
$694$	−33.9426			−1.28844
$695$	−28.1540	+	16.2547i	−1.06794	+	0.616577i
$696$	−33.1239	−	41.1342i	−1.25556	−	1.55919i
$697$	−19.0667	+	33.0246i	−0.722204	+	1.25089i
$698$	1.56569	−	2.71186i	0.0592624	−	0.102645i
$699$	4.05622	+	26.0715i	0.153420	+	0.986115i
$700$		0			0
$701$			29.4609i			1.11272i	0.830940	+	0.556362i	$0.187803\pi$
$701$			29.4609i			1.11272i	−0.830940	+	0.556362i	$0.812197\pi$
$702$	15.8323	−	7.90390i	0.597551	−	0.298314i
$703$			2.03727i			0.0768370i
$704$	12.8019	−	7.39117i	0.482489	−	0.278565i
$705$	1.96917	−	0.306364i	0.0741632	−	0.0115384i
$706$	59.8894	+	34.5772i	2.25397	+	1.30133i
$707$		0			0
$708$	21.7781	+	27.0447i	0.818471	+	1.01640i
$709$	19.0361	+	32.9715i	0.714916	+	1.23827i	0.962992	+	0.269530i	$0.0868683\pi$
$709$	19.0361	+	32.9715i	0.714916	+	1.23827i	−0.248076	+	0.968740i	$0.579798\pi$
$710$	−7.04224			−0.264290
$711$	23.5342	+	21.4247i	0.882601	+	0.803488i
$712$			22.6945i			0.850513i
$713$	11.1766	+	19.3585i	0.418568	+	0.724980i
$714$		0			0
$715$	6.72414	−	11.6466i	0.251469	−	0.435556i
$716$	69.1795	+	39.9408i	2.58536	+	1.49266i
$717$	−9.23504	−	3.57403i	−0.344889	−	0.133474i
$718$	9.60408	+	16.6348i	0.358421	+	0.620803i
$719$	−38.2114			−1.42505			−0.712523	−	0.701649i	$-0.752447\pi$
$719$	−38.2114			−1.42505			−0.712523	+	0.701649i	$0.752447\pi$
$720$	55.3278	−	17.6429i	2.06195	−	0.657512i
$721$		0			0
$722$	41.4045	−	23.9049i	1.54091	−	0.889647i
$723$	6.03172	−	4.85712i	0.224322	−	0.180638i
$724$	−66.9924	−	38.6781i	−2.48975	−	1.43746i
$725$	−1.69364	−	0.977823i	−0.0629002	−	0.0363154i
$726$	−5.53499	−	35.5764i	−0.205423	−	1.32036i
$727$	−17.7563	+	10.2516i	−0.658546	+	0.380212i	−0.791723	−	0.610881i	$-0.790816\pi$
$727$	−17.7563	+	10.2516i	−0.658546	+	0.380212i	0.133177	+	0.991092i	$0.457482\pi$
$728$		0			0
$729$	16.2267	−	21.5800i	0.600989	−	0.799257i
$730$	90.8743			3.36341
$731$	−22.5222	−	39.0096i	−0.833014	−	1.44282i
$732$	2.53842	+	16.3158i	0.0938227	+	0.603049i
$733$	−0.900627	−	0.519977i	−0.0332654	−	0.0192058i	0.483275	−	0.875469i	$-0.339447\pi$
$733$	−0.900627	−	0.519977i	−0.0332654	−	0.0192058i	−0.516540	+	0.856263i	$0.672780\pi$
$734$	−45.1023	+	78.1194i	−1.66475	+	2.88344i
$735$		0			0
$736$	21.5657	+	37.3528i	0.794921	+	1.37684i
$737$			21.0636i			0.775887i
$738$	−15.4854	−	48.5618i	−0.570025	−	1.78759i
$739$	24.1609			0.888774			0.444387	−	0.895835i	$-0.353422\pi$
$739$	24.1609			0.888774			0.444387	+	0.895835i	$0.353422\pi$
$740$	16.3446	+	28.3096i	0.600839	+	1.04068i
$741$	−0.557665	+	1.44097i	−0.0204863	+	0.0529353i
$742$		0			0
$743$	−13.1637	−	7.60008i	−0.482930	−	0.278820i	0.238707	−	0.971092i	$-0.423277\pi$
$743$	−13.1637	−	7.60008i	−0.482930	−	0.278820i	−0.721637	+	0.692272i	$0.756610\pi$
$744$	−17.1420	+	44.2938i	−0.628457	+	1.62389i
$745$	22.0810	−	12.7485i	0.808987	−	0.467069i
$746$		−	77.6010i		−	2.84118i
$747$	23.6231	+	21.5056i	0.864324	+	0.786849i
$748$		−	117.406i		−	4.29281i
$749$		0			0
$750$	−37.0023	+	29.7966i	−1.35113	+	1.08802i
$751$	−1.52037	+	2.63336i	−0.0554791	+	0.0960926i	−0.892431	−	0.451184i	$-0.851002\pi$
$751$	−1.52037	+	2.63336i	−0.0554791	+	0.0960926i	0.836952	+	0.547276i	$0.184335\pi$
$752$	−2.04795	+	3.54716i	−0.0746812	+	0.129352i
$753$	19.8984	−	3.09580i	0.725138	−	0.112817i
$754$	13.1768	−	7.60763i	0.479871	−	0.277053i
$755$	−32.5195			−1.18350
$756$		0			0
$757$	43.3700			1.57631			0.788155	−	0.615477i	$-0.211036\pi$
$757$	43.3700			1.57631			0.788155	+	0.615477i	$0.211036\pi$
$758$	−60.5075	+	34.9340i	−2.19773	+	1.26886i
$759$	41.5713	−	6.46769i	1.50894	−	0.234762i
$760$	−5.37397	+	9.30799i	−0.194934	+	0.337636i
$761$	−14.6319	+	25.3432i	−0.530406	+	0.918690i	0.468965	+	0.883217i	$0.344627\pi$
$761$	−14.6319	+	25.3432i	−0.530406	+	0.918690i	−0.999371	+	0.0354731i	$0.988706\pi$
$762$	−57.6350	+	46.4113i	−2.08790	+	1.68131i
$763$		0			0
$764$		−	4.43367i		−	0.160405i
$765$	8.63302	−	39.5495i	0.312127	−	1.42992i
$766$			9.43698i			0.340972i
$767$	−4.93487	+	2.84915i	−0.178188	+	0.102877i
$768$	15.1549	−	39.1592i	0.546855	−	1.41304i
$769$	−29.6496	−	17.1182i	−1.06919	−	0.617299i	−0.141232	−	0.989977i	$-0.545106\pi$
$769$	−29.6496	−	17.1182i	−1.06919	−	0.617299i	−0.927961	+	0.372678i	$0.878440\pi$
$770$		0			0
$771$	−1.31453	+	3.39666i	−0.0473418	+	0.122328i
$772$	−3.93702	−	6.81912i	−0.141697	−	0.245426i
$773$	33.9854			1.22237			0.611185	−	0.791488i	$-0.290693\pi$
$773$	33.9854			1.22237			0.611185	+	0.791488i	$0.290693\pi$
$774$	58.8235	+	12.8402i	2.11437	+	0.461531i
$775$			1.75873i			0.0631753i
$776$	−50.2502	−	87.0359i	−1.80388	−	3.12441i
$777$		0			0
$778$	15.6870	−	27.1707i	0.562406	−	0.974117i
$779$	3.85435	+	2.22531i	0.138096	+	0.0797299i
$780$	3.81134	+	24.4975i	0.136468	+	0.877153i
$781$	−2.55710	−	4.42904i	−0.0915004	−	0.158483i
$782$	82.9985			2.96802
$783$	12.8035	−	19.3657i	0.457560	−	0.692075i
$784$		0			0
$785$	−31.8631	+	18.3962i	−1.13724	+	0.656587i
$786$	−4.88770	−	31.4159i	−0.174338	−	1.12057i
$787$	23.8225	+	13.7539i	0.849180	+	0.490274i	0.860374	−	0.509663i	$-0.170230\pi$
$787$	23.8225	+	13.7539i	0.849180	+	0.490274i	−0.0111939	+	0.999937i	$0.503563\pi$
$788$	−51.3067	−	29.6219i	−1.82773	−	1.05524i
$789$	−2.97173	+	2.39303i	−0.105796	+	0.0851940i
$790$	−55.2346	+	31.8897i	−1.96516	+	1.13458i
$791$		0			0
$792$	66.1025	+	60.1773i	2.34885	+	2.13831i
$793$	−2.70974			−0.0962255
$794$	34.5144	+	59.7807i	1.22487	+	2.12154i
$795$	−15.6155	−	6.04332i	−0.553826	−	0.214334i
$796$	−17.5390	−	10.1262i	−0.621654	−	0.358912i
$797$	21.0873	−	36.5243i	0.746952	−	1.29376i	−0.202326	−	0.979318i	$-0.564850\pi$
$797$	21.0873	−	36.5243i	0.746952	−	1.29376i	0.949277	−	0.314440i	$-0.101817\pi$
$798$		0			0
$799$	1.42757	+	2.47262i	0.0505038	+	0.0874751i
$800$			3.39352i			0.119979i
$801$	−9.50452	+	3.03080i	−0.335826	+	0.107088i
$802$	19.9292			0.703723
$803$	32.9974	+	57.1531i	1.16445	+	2.01689i
$804$	−24.3546	−	30.2443i	−0.858922	−	1.06664i
$805$		0			0
$806$	−11.8500	−	6.84160i	−0.417398	−	0.240985i
$807$	47.6853	−	7.41890i	1.67860	−	0.261158i
$808$	9.83594	−	5.67878i	0.346027	−	0.199779i
$809$			4.83100i			0.169849i	0.996387	+	0.0849245i	$0.0270649\pi$
$809$			4.83100i			0.169849i	−0.996387	+	0.0849245i	$0.972935\pi$
$810$	31.3232	+	44.1203i	1.10058	+	1.55023i
$811$		−	6.46035i		−	0.226853i	−0.993546	−	0.113427i	$-0.963817\pi$
$811$		−	6.46035i		−	0.226853i	0.993546	−	0.113427i	$-0.0361827\pi$
$812$		0			0
$813$	−3.05687	−	19.6482i	−0.107209	−	0.689092i
$814$	−16.9782	+	29.4071i	−0.595086	+	1.03072i
$815$	7.88823	−	13.6628i	0.276313	−	0.478587i
$816$	52.1822	+	64.8015i	1.82674	+	2.26851i
$817$	−4.55287	+	2.62860i	−0.159285	+	0.0919631i
$818$	23.3597			0.816751
$819$		0			0
$820$	71.4128			2.49384
$821$	14.5455	−	8.39783i	0.507640	−	0.293086i	−0.224223	−	0.974538i	$-0.571984\pi$
$821$	14.5455	−	8.39783i	0.507640	−	0.293086i	0.731863	+	0.681452i	$0.238651\pi$
$822$	−1.33360	+	3.44593i	−0.0465146	+	0.120191i
$823$	7.51749	−	13.0207i	0.262043	−	0.453872i	−0.704741	−	0.709464i	$-0.748937\pi$
$823$	7.51749	−	13.0207i	0.262043	−	0.453872i	0.966785	+	0.255592i	$0.0822703\pi$
$824$	−5.54719	+	9.60802i	−0.193246	+	0.334711i
$825$	3.08702	+	1.19470i	0.107476	+	0.0415940i
$826$		0			0
$827$		−	29.2462i		−	1.01699i	−0.861065	−	0.508495i	$-0.830202\pi$
$827$		−	29.2462i		−	1.01699i	0.861065	−	0.508495i	$-0.169798\pi$
$828$	−52.2123	+	57.3533i	−1.81450	+	1.99317i
$829$			1.50423i			0.0522440i	0.999659	+	0.0261220i	$0.00831584\pi$
$829$			1.50423i			0.0522440i	−0.999659	+	0.0261220i	$0.991684\pi$
$830$	−55.4433	+	32.0102i	−1.92446	+	1.11109i
$831$	11.0805	+	13.7602i	0.384380	+	0.477334i
$832$	−3.87301	−	2.23608i	−0.134272	−	0.0775222i
$833$		0			0
$834$	61.5155	−	9.57061i	2.13011	−	0.331403i
$835$	−22.2610	−	38.5571i	−0.770373	−	1.33432i
$836$	−13.7027			−0.473917
$837$	−20.8396	−	1.26379i	−0.720323	−	0.0436830i
$838$		−	17.0401i		−	0.588641i
$839$	−22.9477	−	39.7466i	−0.792243	−	1.37221i	−0.924575	−	0.381000i	$-0.875580\pi$
$839$	−22.9477	−	39.7466i	−0.792243	−	1.37221i	0.132331	−	0.991206i	$-0.457754\pi$
$840$		0			0
$841$	−4.51923	+	7.82753i	−0.155835	+	0.269915i
$842$	28.5443	+	16.4800i	0.983701	+	0.567940i
$843$	14.7224	−	11.8554i	0.507065	−	0.408321i
$844$	10.4266	+	18.0593i	0.358897	+	0.621628i
$845$	26.2460			0.902891
$846$	−3.72853	−	0.813876i	−0.128189	−	0.0279816i
$847$		0			0
$848$	29.8035	−	17.2071i	1.02346	−	0.590893i
$849$	−19.1679	−	7.41811i	−0.657840	−	0.254589i
$850$	5.65534	+	3.26511i	0.193977	+	0.111992i
$851$	−14.5338	−	8.39112i	−0.498214	−	0.287644i
$852$	8.79269	+	3.40283i	0.301232	+	0.116579i
$853$	−24.3086	+	14.0346i	−0.832310	+	0.480534i	−0.854643	−	0.519216i	$-0.826224\pi$
$853$	−24.3086	+	14.0346i	−0.832310	+	0.480534i	0.0223330	+	0.999751i	$0.492891\pi$
$854$		0			0
$855$	−4.61589	−	1.00757i	−0.157860	−	0.0344583i
$856$	−124.981			−4.27176
$857$	−8.55426	−	14.8164i	−0.292208	−	0.506119i	0.682123	−	0.731237i	$-0.261057\pi$
$857$	−8.55426	−	14.8164i	−0.292208	−	0.506119i	−0.974332	+	0.225118i	$0.927723\pi$
$858$	−20.0584	+	16.1523i	−0.684784	+	0.551431i
$859$	4.50996	+	2.60383i	0.153878	+	0.0888414i	0.574962	−	0.818180i	$-0.305017\pi$
$859$	4.50996	+	2.60383i	0.153878	+	0.0888414i	−0.421084	+	0.907022i	$0.638350\pi$
$860$	−42.1775	+	73.0535i	−1.43824	+	2.49110i
$861$		0			0
$862$	28.2456	+	48.9228i	0.962049	+	1.66632i
$863$		−	44.7024i		−	1.52169i	−0.648935	−	0.760844i	$-0.724785\pi$
$863$		−	44.7024i		−	1.52169i	0.648935	−	0.760844i	$-0.275215\pi$
$864$	−40.2108	−	2.43853i	−1.36800	−	0.0829603i
$865$	−50.9497			−1.73234
$866$	−10.5858	−	18.3352i	−0.359721	−	0.623055i
$867$	28.2120	−	4.38923i	0.958129	−	0.149066i
$868$		0			0
$869$	−40.1124	−	23.1589i	−1.36072	−	0.785613i
$870$	29.1798	+	36.2363i	0.989287	+	1.22853i
$871$	5.51871	−	3.18623i	0.186994	−	0.107961i
$872$			109.015i			3.69171i
$873$	29.7400	−	32.6683i	1.00655	−	1.10566i
$874$		−	9.68688i		−	0.327664i
$875$		0			0
$876$	−113.462	−	43.9108i	−3.83354	−	1.48361i
$877$	2.87432	−	4.97846i	0.0970587	−	0.168111i	−0.813407	−	0.581695i	$-0.802390\pi$
$877$	2.87432	−	4.97846i	0.0970587	−	0.168111i	0.910466	+	0.413584i	$0.135723\pi$
$878$	−48.8229	+	84.5637i	−1.64769	+	2.85389i
$879$	−11.9402	+	30.8527i	−0.402733	+	1.04064i
$880$	−73.1936	+	42.2584i	−2.46736	+	1.42453i
$881$	9.98120			0.336275			0.168138	−	0.985764i	$-0.446225\pi$
$881$	9.98120			0.336275			0.168138	+	0.985764i	$0.446225\pi$
$882$		0			0
$883$	−32.0942			−1.08006			−0.540028	−	0.841647i	$-0.681586\pi$
$883$	−32.0942			−1.08006			−0.540028	+	0.841647i	$0.681586\pi$
$884$	−30.7608	+	17.7597i	−1.03460	+	0.597325i
$885$	−10.9282	−	13.5709i	−0.367346	−	0.456182i
$886$	26.3781	−	45.6881i	0.886188	−	1.53492i
$887$	4.26812	−	7.39260i	0.143309	−	0.248219i	−0.785432	−	0.618949i	$-0.787559\pi$
$887$	4.26812	−	7.39260i	0.143309	−	0.248219i	0.928741	+	0.370729i	$0.120892\pi$
$888$	−5.48177	−	35.2343i	−0.183956	−	1.18239i
$889$		0			0
$890$		−	19.9922i		−	0.670141i
$891$	−16.3746	+	35.7204i	−0.548569	+	1.19668i
$892$			96.5904i			3.23409i
$893$	0.288584	−	0.166614i	0.00965709	−	0.00557552i
$894$	−48.2462	+	7.50617i	−1.61360	+	0.251044i
$895$	−34.7140	−	20.0422i	−1.16036	−	0.669935i
$896$		0			0
$897$	−7.98293	−	9.91344i	−0.266542	−	0.331000i
$898$	46.0277	+	79.7223i	1.53596	+	2.66037i
$899$	−17.9516			−0.598718
$900$	−5.81388	+	1.85393i	−0.193796	+	0.0617976i
$901$		−	23.9891i		−	0.799192i
$902$	37.0906	+	64.2429i	1.23498	+	2.13905i
$903$		0			0
$904$	−20.0011	+	34.6430i	−0.665228	+	1.15221i
$905$	33.6166	+	19.4085i	1.11745	+	0.645162i
$906$	58.0771	+	22.4763i	1.92948	+	0.746724i
$907$	−16.0272	−	27.7599i	−0.532175	−	0.921754i	−0.999294	−	0.0375597i	$-0.988042\pi$
$907$	−16.0272	−	27.7599i	−0.532175	−	0.921754i	0.467120	−	0.884194i	$-0.345292\pi$
$908$	−131.586			−4.36685
$909$	3.69185	+	3.36093i	0.122451	+	0.111475i
$910$		0			0
$911$	26.3261	−	15.1994i	0.872221	−	0.503577i	0.00413539	−	0.999991i	$-0.498684\pi$
$911$	26.3261	−	15.1994i	0.872221	−	0.503577i	0.868086	+	0.496414i	$0.165350\pi$
$912$	7.56308	−	6.09027i	0.250439	−	0.201669i
$913$	−40.2640	−	23.2464i	−1.33254	−	0.769344i
$914$	0.567527	+	0.327662i	0.0187721	+	0.0108381i
$915$	−1.27377	−	8.18721i	−0.0421095	−	0.270661i
$916$	−87.6765	+	50.6201i	−2.89691	+	1.67253i
$917$		0			0
$918$	−42.7530	+	64.6654i	−1.41106	+	2.13428i
$919$	−17.4431			−0.575393			−0.287697	−	0.957722i	$-0.592889\pi$
$919$	−17.4431			−0.575393			−0.287697	+	0.957722i	$0.592889\pi$
$920$	−44.2687	−	76.6757i	−1.45950	−	2.52792i
$921$	−0.627034	−	4.03029i	−0.0206615	−	0.132802i
$922$	54.5580	+	31.4991i	1.79677	+	1.03737i
$923$	−0.773612	+	1.33994i	−0.0254637	+	0.0441045i
$924$		0			0
$925$	−0.660203	−	1.14351i	−0.0217074	−	0.0375982i
$926$		−	2.11405i		−	0.0694718i
$927$	−4.76468	−	1.04005i	−0.156493	−	0.0341598i
$928$	−34.6382			−1.13705
$929$	5.21392	+	9.03077i	0.171063	+	0.296290i	0.938792	−	0.344485i	$-0.111946\pi$
$929$	5.21392	+	9.03077i	0.171063	+	0.296290i	−0.767729	+	0.640775i	$0.778613\pi$
$930$	15.1009	−	39.0197i	0.495178	−	1.27951i
$931$		0			0
$932$	61.3070	+	35.3956i	2.00818	+	1.15942i
$933$	−4.90710	+	12.6796i	−0.160651	+	0.415111i
$934$	4.06199	−	2.34519i	0.132912	−	0.0767369i
$935$			58.9142i			1.92670i
$936$	5.76746	−	26.4219i	0.188515	−	0.863626i
$937$			51.3201i			1.67655i	0.545245	+	0.838277i	$0.316437\pi$
$937$			51.3201i			1.67655i	−0.545245	+	0.838277i	$0.683563\pi$
$938$		0			0
$939$	40.5427	−	32.6476i	1.32306	−	1.06541i
$940$	2.67342	−	4.63049i	0.0871973	−	0.151030i
$941$	24.6673	−	42.7251i	0.804133	−	1.39280i	−0.112742	−	0.993624i	$-0.535963\pi$
$941$	24.6673	−	42.7251i	0.804133	−	1.39280i	0.916875	−	0.399174i	$-0.130703\pi$
$942$	69.6196	−	10.8315i	2.26833	−	0.352908i
$943$	−31.7506	+	18.3312i	−1.03394	+	0.596947i
$944$	35.8114			1.16556
$945$		0			0
$946$	−87.6252			−2.84894
$947$	−38.0468	+	21.9663i	−1.23636	+	0.713810i	−0.968347	−	0.249607i	$-0.919699\pi$
$947$	−38.0468	+	21.9663i	−1.23636	+	0.713810i	−0.268008	+	0.963417i	$0.586365\pi$
$948$	84.3731	−	13.1268i	2.74031	−	0.426339i
$949$	9.98283	−	17.2908i	0.324056	−	0.561282i
$950$	0.381076	−	0.660044i	0.0123637	−	0.0214146i
$951$	−14.9839	+	12.0660i	−0.485886	+	0.391266i
$952$		0			0
$953$		−	21.0833i		−	0.682956i	−0.939890	−	0.341478i	$-0.889072\pi$
$953$		−	21.0833i		−	0.682956i	0.939890	−	0.341478i	$-0.110928\pi$
$954$	23.7111	+	21.5858i	0.767676	+	0.698865i
$955$			2.22480i			0.0719929i
$956$	−23.0089	+	13.2842i	−0.744161	+	0.429641i
$957$	−12.1945	+	31.5096i	−0.394191	+	1.01856i
$958$	3.04138	+	1.75594i	0.0982625	+	0.0567319i
$959$		0			0
$960$	4.93552	−	12.7530i	0.159293	−	0.411603i
$961$	−7.42801	−	12.8657i	−0.239613	−	0.415022i
$962$	10.2730			0.331215
$963$	−16.6909	−	52.3423i	−0.537857	−	1.68671i
$964$		−	20.7778i		−	0.669207i
$965$	1.97558	+	3.42181i	0.0635963	+	0.110152i
$966$		0			0
$967$	−27.6671	+	47.9209i	−0.889716	+	1.54103i	−0.0495039	+	0.998774i	$0.515764\pi$
$967$	−27.6671	+	47.9209i	−0.889716	+	1.54103i	−0.840212	+	0.542259i	$0.817569\pi$
$968$	−47.6533	−	27.5127i	−1.53164	−	0.884290i
$969$	−1.04058	−	6.68837i	−0.0334282	−	0.214861i
$970$	44.2668	+	76.6723i	1.42132	+	2.46180i
$971$	−6.83465			−0.219334			−0.109667	−	0.993968i	$-0.534979\pi$
$971$	−6.83465			−0.219334			−0.109667	+	0.993968i	$0.534979\pi$
$972$	−17.7900	−	70.2225i	−0.570613	−	2.25239i
$973$		0			0
$974$	70.5830	−	40.7511i	2.26162	−	1.30575i
$975$	−0.153951	−	0.989525i	−0.00493037	−	0.0316902i
$976$	14.7480	+	8.51477i	0.472072	+	0.272551i
$977$	31.1982	+	18.0123i	0.998118	+	0.576264i	0.907691	−	0.419639i	$-0.137843\pi$
$977$	31.1982	+	18.0123i	0.998118	+	0.576264i	0.0904272	+	0.995903i	$0.471177\pi$
$978$	−23.5310	+	18.9486i	−0.752437	+	0.605910i
$979$	12.5736	−	7.25938i	0.401854	−	0.232011i
$980$		0			0
$981$	−45.6557	+	14.5587i	−1.45767	+	0.464822i
$982$	−5.87711			−0.187546
$983$	−20.6863	−	35.8298i	−0.659791	−	1.14279i	−0.980670	−	0.195671i	$-0.937311\pi$
$983$	−20.6863	−	35.8298i	−0.659791	−	1.14279i	0.320878	−	0.947120i	$-0.396022\pi$
$984$	−72.6482	−	28.1154i	−2.31594	−	0.896285i
$985$	25.7455	+	14.8642i	0.820321	+	0.473612i
$986$	−33.3275	+	57.7249i	−1.06136	+	1.83833i
$987$		0			0
$988$	2.07277	+	3.59014i	0.0659435	+	0.114218i
$989$		−	43.3068i		−	1.37708i
$990$	−58.2316	−	53.0119i	−1.85072	−	1.68483i
$991$	−21.6734			−0.688478			−0.344239	−	0.938882i	$-0.611863\pi$
$991$	−21.6734			−0.688478			−0.344239	+	0.938882i	$0.611863\pi$
$992$	15.5752	+	26.9770i	0.494512	+	0.856520i
$993$	18.7579	+	23.2941i	0.595263	+	0.739216i
$994$		0			0
$995$	8.80102	+	5.08127i	0.279011	+	0.161087i
$996$	84.6919	−	13.1764i	2.68357	−	0.417510i
$997$	11.8699	−	6.85308i	0.375923	−	0.217039i	−0.300120	−	0.953901i	$-0.597027\pi$
$997$	11.8699	−	6.85308i	0.375923	−	0.217039i	0.676043	+	0.736862i	$0.263693\pi$
$998$			69.7117i			2.20669i
$999$	14.0241	−	7.00123i	0.443704	−	0.221509i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.o.e.293.24	yes	48
3.2	odd	2		1323.2.o.e.881.1		48
7.2	even	3		441.2.s.d.374.1		48
7.3	odd	6		441.2.i.d.68.24		48
7.4	even	3		441.2.i.d.68.23		48
7.5	odd	6		441.2.s.d.374.2		48
7.6	odd	2	inner	441.2.o.e.293.23	yes	48
9.2	odd	6	inner	441.2.o.e.146.23	✓	48
9.7	even	3		1323.2.o.e.440.2		48
21.2	odd	6		1323.2.s.d.962.24		48
21.5	even	6		1323.2.s.d.962.23		48
21.11	odd	6		1323.2.i.d.1097.14		48
21.17	even	6		1323.2.i.d.1097.2		48
21.20	even	2		1323.2.o.e.881.2		48
63.2	odd	6		441.2.i.d.227.2		48
63.11	odd	6		441.2.s.d.362.2		48
63.16	even	3		1323.2.i.d.521.2		48
63.20	even	6	inner	441.2.o.e.146.24	yes	48
63.25	even	3		1323.2.s.d.656.23		48
63.34	odd	6		1323.2.o.e.440.1		48
63.38	even	6		441.2.s.d.362.1		48
63.47	even	6		441.2.i.d.227.1		48
63.52	odd	6		1323.2.s.d.656.24		48
63.61	odd	6		1323.2.i.d.521.14		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.23		48	7.4	even	3
441.2.i.d.68.24		48	7.3	odd	6
441.2.i.d.227.1		48	63.47	even	6
441.2.i.d.227.2		48	63.2	odd	6
441.2.o.e.146.23	✓	48	9.2	odd	6	inner
441.2.o.e.146.24	yes	48	63.20	even	6	inner
441.2.o.e.293.23	yes	48	7.6	odd	2	inner
441.2.o.e.293.24	yes	48	1.1	even	1	trivial
441.2.s.d.362.1		48	63.38	even	6
441.2.s.d.362.2		48	63.11	odd	6
441.2.s.d.374.1		48	7.2	even	3
441.2.s.d.374.2		48	7.5	odd	6
1323.2.i.d.521.2		48	63.16	even	3
1323.2.i.d.521.14		48	63.61	odd	6
1323.2.i.d.1097.2		48	21.17	even	6
1323.2.i.d.1097.14		48	21.11	odd	6
1323.2.o.e.440.1		48	63.34	odd	6
1323.2.o.e.440.2		48	9.7	even	3
1323.2.o.e.881.1		48	3.2	odd	2
1323.2.o.e.881.2		48	21.20	even	2
1323.2.s.d.656.23		48	63.25	even	3
1323.2.s.d.656.24		48	63.52	odd	6
1323.2.s.d.962.23		48	21.5	even	6
1323.2.s.d.962.24		48	21.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.23278 - 1.28910i) q^{2} +(1.71146 - 0.266270i) q^{3} +(2.32354 - 4.02449i) q^{4} +(-1.16595 + 2.01948i) q^{5} +(3.47807 - 2.80076i) q^{6} -6.82470i q^{8} +(2.85820 - 0.911422i) q^{9} +6.01207i q^{10} +(-3.78114 + 2.18304i) q^{11} +(2.90505 - 7.50646i) q^{12} +(1.14392 + 0.660445i) q^{13} +(-1.45774 + 3.76671i) q^{15} +(-4.15061 - 7.18908i) q^{16} -5.78655 q^{17} +(5.20683 - 5.71950i) q^{18} +0.675357i q^{19} +(5.41825 + 9.38468i) q^{20} +(-5.62830 + 9.74851i) q^{22} +(-4.81799 - 2.78167i) q^{23} +(-1.81721 - 11.6802i) q^{24} +(-0.218858 - 0.379074i) q^{25} +3.40551 q^{26} +(4.64902 - 2.32092i) q^{27} +(3.86926 - 2.23392i) q^{29} +(1.60083 + 10.2894i) q^{30} +(-3.47965 - 2.00898i) q^{31} +(-6.71411 - 3.87639i) q^{32} +(-5.88999 + 4.74299i) q^{33} +(-12.9201 + 7.45942i) q^{34} +(2.97314 - 13.6205i) q^{36} +3.01658 q^{37} +(0.870601 + 1.50792i) q^{38} +(2.13364 + 0.825733i) q^{39} +(13.7823 + 7.95723i) q^{40} +(3.29501 - 5.70713i) q^{41} +(3.89217 + 6.74143i) q^{43} +20.2896i q^{44} +(-1.49191 + 6.83474i) q^{45} -14.3434 q^{46} +(-0.246705 - 0.427306i) q^{47} +(-9.01785 - 11.1986i) q^{48} +(-0.977326 - 0.564259i) q^{50} +(-9.90345 + 1.54078i) q^{51} +(5.31591 - 3.06914i) q^{52} +4.14566i q^{53} +(7.38835 - 11.1751i) q^{54} -10.1812i q^{55} +(0.179827 + 1.15585i) q^{57} +(5.75947 - 9.97570i) q^{58} +(-2.15699 + 3.73602i) q^{59} +(11.7720 + 14.6188i) q^{60} +(-1.77661 + 1.02572i) q^{61} -10.3591 q^{62} -3.38572 q^{64} +(-2.66751 + 1.54009i) q^{65} +(-7.03689 + 18.1828i) q^{66} +(2.41218 - 4.17802i) q^{67} +(-13.4453 + 23.2879i) q^{68} +(-8.98648 - 3.47783i) q^{69} +1.17135i q^{71} +(-6.22018 - 19.5064i) q^{72} -15.1153i q^{73} +(6.73536 - 3.88866i) q^{74} +(-0.475504 - 0.590495i) q^{75} +(2.71797 + 1.56922i) q^{76} +(5.82840 - 0.906785i) q^{78} +(5.30428 + 9.18728i) q^{79} +19.3576 q^{80} +(7.33862 - 5.21005i) q^{81} -16.9904i q^{82} +(5.32432 + 9.22199i) q^{83} +(6.74680 - 11.6858i) q^{85} +(17.3807 + 10.0348i) q^{86} +(6.02726 - 4.85353i) q^{87} +(14.8986 + 25.8051i) q^{88} -3.32535 q^{89} +(5.47953 + 17.1837i) q^{90} +(-22.3896 + 12.9266i) q^{92} +(-6.49022 - 2.51176i) q^{93} +(-1.10168 - 0.636053i) q^{94} +(-1.36387 - 0.787429i) q^{95} +(-12.5231 - 4.84653i) q^{96} +(12.7531 - 7.36299i) q^{97} +(-8.81758 + 9.68578i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} + 16 q^{9} - 24 q^{11} - 40 q^{15} - 24 q^{16} - 16 q^{18} - 48 q^{23} - 24 q^{25} - 24 q^{30} + 120 q^{32} - 8 q^{36} + 88 q^{39} + 48 q^{50} + 24 q^{51} + 80 q^{57} - 96 q^{60} - 48 q^{64}+ \cdots - 72 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 + 16 * q^9 - 24 * q^11 - 40 * q^15 - 24 * q^16 - 16 * q^18 - 48 * q^23 - 24 * q^25 - 24 * q^30 + 120 * q^32 - 8 * q^36 + 88 * q^39 + 48 * q^50 + 24 * q^51 + 80 * q^57 - 96 * q^60 - 48 * q^64 + 120 * q^65 + 56 * q^72 - 168 * q^74 - 88 * q^78 - 24 * q^79 - 96 * q^81 - 24 * q^85 + 24 * q^86 - 144 * q^92 - 32 * q^93 + 96 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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