LMFDB - Embedded newform 504.2.bu.a.41.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(41,504)] 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("504.41"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bu (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
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			41.5
Character	$\chi$	$=$	504.41
Dual form			504.2.bu.a.209.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.31185 - 1.13095i) q^{3} +(0.965651 - 1.67256i) q^{5} +(2.53170 - 0.768427i) q^{7} +(0.441899 + 2.96728i) q^{9} +(1.10681 - 0.639015i) q^{11} +(2.52802 + 1.45955i) q^{13} +(-3.15837 + 1.10204i) q^{15} -0.475237 q^{17} -6.10647i q^{19} +(-4.19027 - 1.85517i) q^{21} +(-6.51132 - 3.75931i) q^{23} +(0.635036 + 1.09991i) q^{25} +(2.77614 - 4.39239i) q^{27} +(3.76797 - 2.17544i) q^{29} +(-4.21872 - 2.43568i) q^{31} +(-2.17466 - 0.413453i) q^{33} +(1.15950 - 4.97645i) q^{35} +1.76145 q^{37} +(-1.66570 - 4.77378i) q^{39} +(-1.16103 + 2.01097i) q^{41} +(4.63638 + 8.03045i) q^{43} +(5.38966 + 2.12625i) q^{45} +(-4.00447 - 6.93595i) q^{47} +(5.81904 - 3.89086i) q^{49} +(0.623440 + 0.537470i) q^{51} -10.3345i q^{53} -2.46826i q^{55} +(-6.90612 + 8.01077i) q^{57} +(-1.74272 + 3.01848i) q^{59} +(-4.26195 + 2.46064i) q^{61} +(3.39889 + 7.17269i) q^{63} +(4.88237 - 2.81883i) q^{65} +(0.602527 - 1.04361i) q^{67} +(4.29027 + 12.2956i) q^{69} +11.2114i q^{71} -1.84336i q^{73} +(0.410878 - 2.16112i) q^{75} +(2.31107 - 2.46830i) q^{77} +(8.54654 + 14.8030i) q^{79} +(-8.60945 + 2.62247i) q^{81} +(-0.225217 - 0.390088i) q^{83} +(-0.458913 + 0.794861i) q^{85} +(-7.40333 - 1.40754i) q^{87} -11.2580 q^{89} +(7.52175 + 1.75255i) q^{91} +(2.77969 + 7.96642i) q^{93} +(-10.2134 - 5.89672i) q^{95} +(-9.22775 + 5.32764i) q^{97} +(2.38523 + 3.00182i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9} + 8 q^{15} - 4 q^{21} + 12 q^{23} - 24 q^{25} - 36 q^{29} + 32 q^{39} + 12 q^{43} + 6 q^{49} + 24 q^{51} + 28 q^{57} - 14 q^{63} + 36 q^{65} - 60 q^{77} - 12 q^{79} - 36 q^{81} - 12 q^{91}+ \cdots + 44 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 + 8 * q^15 - 4 * q^21 + 12 * q^23 - 24 * q^25 - 36 * q^29 + 32 * q^39 + 12 * q^43 + 6 * q^49 + 24 * q^51 + 28 * q^57 - 14 * q^63 + 36 * q^65 - 60 * q^77 - 12 * q^79 - 36 * q^81 - 12 * q^91 + 16 * q^93 - 108 * q^95 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−1.31185	−	1.13095i	−0.757397	−	0.652955i
$3$	−1.31185	−	1.13095i	−0.757397	−	0.652955i
$4$		0			0
$5$	0.965651	−	1.67256i	0.431852	−	0.747990i	−0.565181	−	0.824967i	$-0.691194\pi$
$5$	0.965651	−	1.67256i	0.431852	−	0.747990i	0.997033	+	0.0769771i	$0.0245268\pi$
$6$		0			0
$7$	2.53170	−	0.768427i	0.956894	−	0.290438i
$7$	2.53170	−	0.768427i	0.956894	−	0.290438i
$8$		0			0
$9$	0.441899	+	2.96728i	0.147300	+	0.989092i
$10$		0			0
$11$	1.10681	−	0.639015i	0.333715	−	0.192670i	−0.323774	−	0.946134i	$-0.604952\pi$
$11$	1.10681	−	0.639015i	0.333715	−	0.192670i	0.657489	+	0.753464i	$0.271619\pi$
$12$		0			0
$13$	2.52802	+	1.45955i	0.701146	+	0.404807i	0.807774	−	0.589492i	$-0.200672\pi$
$13$	2.52802	+	1.45955i	0.701146	+	0.404807i	−0.106628	+	0.994299i	$0.534005\pi$
$14$		0			0
$15$	−3.15837	+	1.10204i	−0.815487	+	0.284545i
$16$		0			0
$17$	−0.475237			−0.115262			−0.0576310	−	0.998338i	$-0.518355\pi$
$17$	−0.475237			−0.115262			−0.0576310	+	0.998338i	$0.518355\pi$
$18$		0			0
$19$		−	6.10647i		−	1.40092i	−0.713691	−	0.700460i	$-0.752978\pi$
$19$		−	6.10647i		−	1.40092i	0.713691	−	0.700460i	$-0.247022\pi$
$20$		0			0
$21$	−4.19027	−	1.85517i	−0.914391	−	0.404832i
$22$		0			0
$23$	−6.51132	−	3.75931i	−1.35770	−	0.783871i	−0.368390	−	0.929671i	$-0.620091\pi$
$23$	−6.51132	−	3.75931i	−1.35770	−	0.783871i	−0.989314	+	0.145801i	$0.953424\pi$
$24$		0			0
$25$	0.635036	+	1.09991i	0.127007	+	0.219983i
$26$		0			0
$27$	2.77614	−	4.39239i	0.534268	−	0.845315i
$28$		0			0
$29$	3.76797	−	2.17544i	0.699695	−	0.403969i	−0.107539	−	0.994201i	$-0.534297\pi$
$29$	3.76797	−	2.17544i	0.699695	−	0.403969i	0.807234	+	0.590232i	$0.200964\pi$
$30$		0			0
$31$	−4.21872	−	2.43568i	−0.757705	−	0.437461i	0.0707660	−	0.997493i	$-0.477456\pi$
$31$	−4.21872	−	2.43568i	−0.757705	−	0.437461i	−0.828471	+	0.560032i	$0.810789\pi$
$32$		0			0
$33$	−2.17466	−	0.413453i	−0.378559	−	0.0719728i
$34$		0			0
$35$	1.15950	−	4.97645i	0.195992	−	0.841173i
$36$		0			0
$37$	1.76145			0.289580			0.144790	−	0.989462i	$-0.453749\pi$
$37$	1.76145			0.289580			0.144790	+	0.989462i	$0.453749\pi$
$38$		0			0
$39$	−1.66570	−	4.77378i	−0.266725	−	0.764416i
$40$		0			0
$41$	−1.16103	+	2.01097i	−0.181323	+	0.314060i	−0.942331	−	0.334682i	$-0.891371\pi$
$41$	−1.16103	+	2.01097i	−0.181323	+	0.314060i	0.761009	+	0.648742i	$0.224704\pi$
$42$		0			0
$43$	4.63638	+	8.03045i	0.707042	+	1.22463i	0.965950	+	0.258730i	$0.0833041\pi$
$43$	4.63638	+	8.03045i	0.707042	+	1.22463i	−0.258908	+	0.965902i	$0.583363\pi$
$44$		0			0
$45$	5.38966	+	2.12625i	0.803443	+	0.316963i
$46$		0			0
$47$	−4.00447	−	6.93595i	−0.584112	−	1.01171i	−0.994985	−	0.100020i	$-0.968109\pi$
$47$	−4.00447	−	6.93595i	−0.584112	−	1.01171i	0.410873	−	0.911693i	$-0.365224\pi$
$48$		0			0
$49$	5.81904	−	3.89086i	0.831291	−	0.555837i
$50$		0			0
$51$	0.623440	+	0.537470i	0.0872990	+	0.0752609i
$52$		0			0
$53$		−	10.3345i		−	1.41955i	−0.704428	−	0.709775i	$-0.748796\pi$
$53$		−	10.3345i		−	1.41955i	0.704428	−	0.709775i	$-0.251204\pi$
$54$		0			0
$55$		−	2.46826i		−	0.332820i
$56$		0			0
$57$	−6.90612	+	8.01077i	−0.914738	+	1.06105i
$58$		0			0
$59$	−1.74272	+	3.01848i	−0.226883	+	0.392973i	−0.956883	−	0.290475i	$-0.906187\pi$
$59$	−1.74272	+	3.01848i	−0.226883	+	0.392973i	0.730000	+	0.683447i	$0.239520\pi$
$60$		0			0
$61$	−4.26195	+	2.46064i	−0.545686	+	0.315052i	−0.747380	−	0.664396i	$-0.768689\pi$
$61$	−4.26195	+	2.46064i	−0.545686	+	0.315052i	0.201694	+	0.979449i	$0.435355\pi$
$62$		0			0
$63$	3.39889	+	7.17269i	0.428220	+	0.903674i
$64$		0			0
$65$	4.88237	−	2.81883i	0.605583	−	0.349633i
$66$		0			0
$67$	0.602527	−	1.04361i	0.0736104	−	0.127497i	−0.826871	−	0.562392i	$-0.809881\pi$
$67$	0.602527	−	1.04361i	0.0736104	−	0.127497i	0.900481	+	0.434895i	$0.143215\pi$
$68$		0			0
$69$	4.29027	+	12.2956i	0.516488	+	1.48022i
$70$		0			0
$71$			11.2114i			1.33055i	0.746598	+	0.665275i	$0.231686\pi$
$71$			11.2114i			1.33055i	−0.746598	+	0.665275i	$0.768314\pi$
$72$		0			0
$73$		−	1.84336i		−	0.215749i	−0.994164	−	0.107875i	$-0.965595\pi$
$73$		−	1.84336i		−	0.215749i	0.994164	−	0.107875i	$-0.0344045\pi$
$74$		0			0
$75$	0.410878	−	2.16112i	0.0474441	−	0.249544i
$76$		0			0
$77$	2.31107	−	2.46830i	0.263371	−	0.281288i
$78$		0			0
$79$	8.54654	+	14.8030i	0.961561	+	1.66547i	0.718584	+	0.695440i	$0.244791\pi$
$79$	8.54654	+	14.8030i	0.961561	+	1.66547i	0.242977	+	0.970032i	$0.421876\pi$
$80$		0			0
$81$	−8.60945	+	2.62247i	−0.956606	+	0.291386i
$82$		0			0
$83$	−0.225217	−	0.390088i	−0.0247208	−	0.0428177i	0.853400	−	0.521256i	$-0.174536\pi$
$83$	−0.225217	−	0.390088i	−0.0247208	−	0.0428177i	−0.878121	+	0.478438i	$0.841203\pi$
$84$		0			0
$85$	−0.458913	+	0.794861i	−0.0497761	+	0.0862148i
$86$		0			0
$87$	−7.40333	−	1.40754i	−0.793720	−	0.150904i
$88$		0			0
$89$	−11.2580			−1.19335			−0.596675	−	0.802483i	$-0.703512\pi$
$89$	−11.2580			−1.19335			−0.596675	+	0.802483i	$0.703512\pi$
$90$		0			0
$91$	7.52175	+	1.75255i	0.788493	+	0.183718i
$92$		0			0
$93$	2.77969	+	7.96642i	0.288241	+	0.826079i
$94$		0			0
$95$	−10.2134	−	5.89672i	−1.04787	−	0.604991i
$96$		0			0
$97$	−9.22775	+	5.32764i	−0.936936	+	0.540940i	−0.888998	−	0.457910i	$-0.848598\pi$
$97$	−9.22775	+	5.32764i	−0.936936	+	0.540940i	−0.0479373	+	0.998850i	$0.515265\pi$
$98$		0			0
$99$	2.38523	+	3.00182i	0.239725	+	0.301694i
$100$		0			0
$101$	6.65330	+	11.5239i	0.662028	+	1.14667i	0.980082	+	0.198594i	$0.0636375\pi$
$101$	6.65330	+	11.5239i	0.662028	+	1.14667i	−0.318054	+	0.948073i	$0.603029\pi$
$102$		0			0
$103$	16.4947	+	9.52323i	1.62527	+	0.938352i	0.985478	+	0.169806i	$0.0543141\pi$
$103$	16.4947	+	9.52323i	1.62527	+	0.938352i	0.639795	+	0.768546i	$0.279019\pi$
$104$		0			0
$105$	−7.14922	+	5.21701i	−0.697692	+	0.509128i
$106$		0			0
$107$		−	16.1392i		−	1.56024i	−0.625630	−	0.780120i	$-0.715158\pi$
$107$		−	16.1392i		−	1.56024i	0.625630	−	0.780120i	$-0.284842\pi$
$108$		0			0
$109$	3.40434			0.326077			0.163038	−	0.986620i	$-0.447871\pi$
$109$	3.40434			0.326077			0.163038	+	0.986620i	$0.447871\pi$
$110$		0			0
$111$	−2.31075	−	1.99211i	−0.219327	−	0.189083i
$112$		0			0
$113$	3.64150	+	2.10242i	0.342563	+	0.197779i	0.661405	−	0.750029i	$-0.269960\pi$
$113$	3.64150	+	2.10242i	0.342563	+	0.197779i	−0.318842	+	0.947808i	$0.603294\pi$
$114$		0			0
$115$	−12.5753	+	7.26037i	−1.17265	+	0.677033i
$116$		0			0
$117$	−3.21376	+	8.14630i	−0.297113	+	0.753126i
$118$		0			0
$119$	−1.20316	+	0.365185i	−0.110293	+	0.0334765i
$120$		0			0
$121$	−4.68332	+	8.11175i	−0.425756	+	0.737432i
$122$		0			0
$123$	3.79740	−	1.32501i	0.342400	−	0.119473i
$124$		0			0
$125$	12.1094			1.08310
$126$		0			0
$127$	17.1828			1.52473			0.762363	−	0.647150i	$-0.224039\pi$
$127$	17.1828			1.52473			0.762363	+	0.647150i	$0.224039\pi$
$128$		0			0
$129$	2.99981	−	15.7783i	0.264119	−	1.38920i
$130$		0			0
$131$	−4.00420	+	6.93548i	−0.349848	+	0.605955i	−0.986222	−	0.165425i	$-0.947100\pi$
$131$	−4.00420	+	6.93548i	−0.349848	+	0.605955i	0.636374	+	0.771381i	$0.280434\pi$
$132$		0			0
$133$	−4.69238	−	15.4598i	−0.406881	−	1.34053i
$134$		0			0
$135$	−4.66573	−	8.88476i	−0.401562	−	0.764679i
$136$		0			0
$137$	8.44241	−	4.87423i	0.721284	−	0.416433i	−0.0939411	−	0.995578i	$-0.529947\pi$
$137$	8.44241	−	4.87423i	0.721284	−	0.416433i	0.815225	+	0.579144i	$0.196613\pi$
$138$		0			0
$139$	6.76047	+	3.90316i	0.573416	+	0.331062i	0.758513	−	0.651658i	$-0.225926\pi$
$139$	6.76047	+	3.90316i	0.573416	+	0.331062i	−0.185097	+	0.982720i	$0.559260\pi$
$140$		0			0
$141$	−2.59096	+	13.6278i	−0.218198	+	1.14767i
$142$		0			0
$143$	3.73070			0.311977
$144$		0			0
$145$		−	8.40286i		−	0.697820i
$146$		0			0
$147$	−12.0341	−	1.47683i	−0.992554	−	0.121807i
$148$		0			0
$149$	9.62284	+	5.55575i	0.788333	+	0.455145i	0.839376	−	0.543552i	$-0.182921\pi$
$149$	9.62284	+	5.55575i	0.788333	+	0.455145i	−0.0510420	+	0.998697i	$0.516254\pi$
$150$		0			0
$151$	−1.88730	−	3.26890i	−0.153586	−	0.266020i	0.778957	−	0.627077i	$-0.215749\pi$
$151$	−1.88730	−	3.26890i	−0.153586	−	0.266020i	−0.932543	+	0.361058i	$0.882416\pi$
$152$		0			0
$153$	−0.210007	−	1.41016i	−0.0169780	−	0.114005i
$154$		0			0
$155$	−8.14763	+	4.70404i	−0.654433	+	0.377837i
$156$		0			0
$157$	3.55162	+	2.05053i	0.283450	+	0.163650i	0.634984	−	0.772525i	$-0.281007\pi$
$157$	3.55162	+	2.05053i	0.283450	+	0.163650i	−0.351534	+	0.936175i	$0.614340\pi$
$158$		0			0
$159$	−11.6878	+	13.5573i	−0.926903	+	1.07516i
$160$		0			0
$161$	−19.3735	−	4.51399i	−1.52684	−	0.355752i
$162$		0			0
$163$	−14.3871			−1.12689			−0.563443	−	0.826155i	$-0.690523\pi$
$163$	−14.3871			−1.12689			−0.563443	+	0.826155i	$0.690523\pi$
$164$		0			0
$165$	−2.79148	+	3.23799i	−0.217317	+	0.252077i
$166$		0			0
$167$	−8.06975	+	13.9772i	−0.624456	+	1.08159i	0.364190	+	0.931325i	$0.381346\pi$
$167$	−8.06975	+	13.9772i	−0.624456	+	1.08159i	−0.988646	+	0.150265i	$0.951987\pi$
$168$		0			0
$169$	−2.23942	−	3.87879i	−0.172263	−	0.298368i
$170$		0			0
$171$	18.1196	−	2.69844i	1.38564	−	0.206355i
$172$		0			0
$173$	−0.695376	−	1.20443i	−0.0528685	−	0.0915709i	0.838380	−	0.545086i	$-0.183503\pi$
$173$	−0.695376	−	1.20443i	−0.0528685	−	0.0915709i	−0.891248	+	0.453515i	$0.850170\pi$
$174$		0			0
$175$	2.45293	+	2.29668i	0.185424	+	0.173613i
$176$		0			0
$177$	5.69994	−	1.98886i	0.428434	−	0.149492i
$178$		0			0
$179$		−	4.60605i		−	0.344273i	−0.985073	−	0.172136i	$-0.944933\pi$
$179$		−	4.60605i		−	0.344273i	0.985073	−	0.172136i	$-0.0550669\pi$
$180$		0			0
$181$		−	16.3732i		−	1.21701i	−0.793550	−	0.608505i	$-0.791769\pi$
$181$		−	16.3732i		−	1.21701i	0.793550	−	0.608505i	$-0.208231\pi$
$182$		0			0
$183$	8.37389	+	1.59207i	0.619016	+	0.117689i
$184$		0			0
$185$	1.70094	−	2.94612i	0.125056	−	0.216603i
$186$		0			0
$187$	−0.525996	+	0.303684i	−0.0384646	+	0.0222075i
$188$		0			0
$189$	3.65313	−	13.2535i	0.265726	−	0.964049i
$190$		0			0
$191$	−12.7953	+	7.38735i	−0.925833	+	0.534530i	−0.885491	−	0.464656i	$-0.846178\pi$
$191$	−12.7953	+	7.38735i	−0.925833	+	0.534530i	−0.0403419	+	0.999186i	$0.512845\pi$
$192$		0			0
$193$	8.91923	−	15.4486i	0.642020	−	1.11201i	−0.342961	−	0.939350i	$-0.611430\pi$
$193$	8.91923	−	15.4486i	0.642020	−	1.11201i	0.984981	−	0.172662i	$-0.0552369\pi$
$194$		0			0
$195$	−9.59289	−	1.82383i	−0.686961	−	0.130607i
$196$		0			0
$197$			8.00352i			0.570227i	0.958494	+	0.285113i	$0.0920313\pi$
$197$			8.00352i			0.570227i	−0.958494	+	0.285113i	$0.907969\pi$
$198$		0			0
$199$		−	16.3034i		−	1.15572i	−0.816137	−	0.577858i	$-0.803889\pi$
$199$		−	16.3034i		−	1.15572i	0.816137	−	0.577858i	$-0.196111\pi$
$200$		0			0
$201$	−1.97070	+	0.687628i	−0.139002	+	0.0485015i
$202$		0			0
$203$	7.86772	−	8.40298i	0.552205	−	0.589773i
$204$		0			0
$205$	2.24230	+	3.88378i	0.156609	+	0.271255i
$206$		0			0
$207$	8.27757	−	20.9821i	0.575331	−	1.45836i
$208$		0			0
$209$	−3.90213	−	6.75868i	−0.269916	−	0.467508i
$210$		0			0
$211$	−10.1930	+	17.6548i	−0.701717	+	1.21541i	0.266147	+	0.963933i	$0.414249\pi$
$211$	−10.1930	+	17.6548i	−0.701717	+	1.21541i	−0.967863	+	0.251476i	$0.919084\pi$
$212$		0			0
$213$	12.6796	−	14.7077i	0.868790	−	1.00775i
$214$		0			0
$215$	17.9085			1.22135
$216$		0			0
$217$	−12.5522	−	2.92464i	−0.852099	−	0.198537i
$218$		0			0
$219$	−2.08475	+	2.41822i	−0.140875	+	0.163408i
$220$		0			0
$221$	−1.20141	−	0.693633i	−0.0808154	−	0.0466588i
$222$		0			0
$223$	−1.95301	+	1.12757i	−0.130783	+	0.0755078i	−0.563964	−	0.825799i	$-0.690724\pi$
$223$	−1.95301	+	1.12757i	−0.130783	+	0.0755078i	0.433181	+	0.901307i	$0.357391\pi$
$224$		0			0
$225$	−2.98313	+	2.37038i	−0.198875	+	0.158025i
$226$		0			0
$227$	10.8916	+	18.8648i	0.722899	+	1.25210i	0.959833	+	0.280572i	$0.0905243\pi$
$227$	10.8916	+	18.8648i	0.722899	+	1.25210i	−0.236934	+	0.971526i	$0.576142\pi$
$228$		0			0
$229$	10.4832	+	6.05247i	0.692748	+	0.399958i	0.804641	−	0.593762i	$-0.202358\pi$
$229$	10.4832	+	6.05247i	0.692748	+	0.399958i	−0.111893	+	0.993720i	$0.535691\pi$
$230$		0			0
$231$	−5.82330	+	0.624328i	−0.383145	+	0.0410777i
$232$		0			0
$233$			21.9876i			1.44046i	0.693736	+	0.720229i	$0.255963\pi$
$233$			21.9876i			1.44046i	−0.693736	+	0.720229i	$0.744037\pi$
$234$		0			0
$235$	−15.4677			−1.00900
$236$		0			0
$237$	5.52974	−	29.0851i	0.359195	−	1.88928i
$238$		0			0
$239$	18.7861	+	10.8462i	1.21517	+	0.701581i	0.963882	−	0.266330i	$-0.0858111\pi$
$239$	18.7861	+	10.8462i	1.21517	+	0.701581i	0.251292	+	0.967911i	$0.419144\pi$
$240$		0			0
$241$	−23.1674	+	13.3757i	−1.49234	+	0.861604i	−0.999961	−	0.00877651i	$-0.997206\pi$
$241$	−23.1674	+	13.3757i	−1.49234	+	0.861604i	−0.492380	+	0.870380i	$0.663873\pi$
$242$		0			0
$243$	14.2602	+	6.29658i	0.914792	+	0.403926i
$244$		0			0
$245$	−0.888520	−	13.4899i	−0.0567655	−	0.861837i
$246$		0			0
$247$	8.91271	−	15.4373i	0.567102	−	0.982250i
$248$		0			0
$249$	−0.145719	+	0.766446i	−0.00923456	+	0.0485715i
$250$		0			0
$251$	−1.75601			−0.110839			−0.0554193	−	0.998463i	$-0.517650\pi$
$251$	−1.75601			−0.110839			−0.0554193	+	0.998463i	$0.517650\pi$
$252$		0			0
$253$	−9.60903			−0.604114
$254$		0			0
$255$	1.50097	−	0.523730i	0.0939947	−	0.0327972i
$256$		0			0
$257$	14.9860	−	25.9565i	0.934800	−	1.61912i	0.159809	−	0.987148i	$-0.448912\pi$
$257$	14.9860	−	25.9565i	0.934800	−	1.61912i	0.774991	−	0.631972i	$-0.217754\pi$
$258$		0			0
$259$	4.45946	−	1.35354i	0.277097	−	0.0841050i
$260$		0			0
$261$	8.12019	+	10.2193i	0.502627	+	0.632558i
$262$		0			0
$263$	−13.4273	+	7.75223i	−0.827960	+	0.478023i	−0.853154	−	0.521659i	$-0.825313\pi$
$263$	−13.4273	+	7.75223i	−0.827960	+	0.478023i	0.0251934	+	0.999683i	$0.491980\pi$
$264$		0			0
$265$	−17.2850	−	9.97951i	−1.06181	−	0.613036i
$266$		0			0
$267$	14.7689	+	12.7323i	0.903839	+	0.779204i
$268$		0			0
$269$	0.412404			0.0251447			0.0125724	−	0.999921i	$-0.495998\pi$
$269$	0.412404			0.0251447			0.0125724	+	0.999921i	$0.495998\pi$
$270$		0			0
$271$		−	0.360056i		−	0.0218718i	−0.999940	−	0.0109359i	$-0.996519\pi$
$271$		−	0.360056i		−	0.0218718i	0.999940	−	0.0109359i	$-0.00348108\pi$
$272$		0			0
$273$	−7.88535	−	10.8058i	−0.477243	−	0.653998i
$274$		0			0
$275$	1.40572	+	0.811595i	0.0847683	+	0.0489410i
$276$		0			0
$277$	−3.03617	−	5.25881i	−0.182426	−	0.315971i	0.760280	−	0.649595i	$-0.225062\pi$
$277$	−3.03617	−	5.25881i	−0.182426	−	0.315971i	−0.942706	+	0.333624i	$0.891728\pi$
$278$		0			0
$279$	5.36309	−	13.5944i	0.321080	−	0.813878i
$280$		0			0
$281$	−8.22494	+	4.74867i	−0.490659	+	0.283282i	−0.724848	−	0.688909i	$-0.758090\pi$
$281$	−8.22494	+	4.74867i	−0.490659	+	0.283282i	0.234189	+	0.972191i	$0.424757\pi$
$282$		0			0
$283$	−9.81761	−	5.66820i	−0.583596	−	0.336939i	0.178965	−	0.983855i	$-0.442725\pi$
$283$	−9.81761	−	5.66820i	−0.583596	−	0.336939i	−0.762561	+	0.646916i	$0.776058\pi$
$284$		0			0
$285$	6.72957	+	19.2865i	0.398625	+	1.14243i
$286$		0			0
$287$	−1.39411	+	5.98333i	−0.0822915	+	0.353185i
$288$		0			0
$289$	−16.7741			−0.986715
$290$		0			0
$291$	18.1307	+	3.44707i	1.06284	+	0.202071i
$292$		0			0
$293$	9.22450	−	15.9773i	0.538901	−	0.933404i	−0.460062	−	0.887887i	$-0.652173\pi$
$293$	9.22450	−	15.9773i	0.538901	−	0.933404i	0.998964	−	0.0455177i	$-0.0144937\pi$
$294$		0			0
$295$	3.36572	+	5.82960i	0.195960	+	0.339412i
$296$		0			0
$297$	0.265849	−	6.63552i	0.0154261	−	0.385032i
$298$		0			0
$299$	−10.9738	−	19.0072i	−0.634632	−	1.09922i
$300$		0			0
$301$	17.9088	+	16.7680i	1.03224	+	0.966491i
$302$		0			0
$303$	4.30479	−	22.6421i	0.247304	−	1.30076i
$304$		0			0
$305$			9.50447i			0.544224i
$306$		0			0
$307$			11.0961i			0.633285i	0.948545	+	0.316643i	$0.102556\pi$
$307$			11.0961i			0.633285i	−0.948545	+	0.316643i	$0.897444\pi$
$308$		0			0
$309$	−10.8683	−	31.1478i	−0.618275	−	1.77193i
$310$		0			0
$311$	1.06866	−	1.85097i	0.0605979	−	0.104959i	−0.834135	−	0.551560i	$-0.814033\pi$
$311$	1.06866	−	1.85097i	0.0605979	−	0.104959i	0.894733	+	0.446602i	$0.147366\pi$
$312$		0			0
$313$	22.3161	−	12.8842i	1.26138	−	0.728259i	0.288039	−	0.957619i	$-0.406997\pi$
$313$	22.3161	−	12.8842i	1.26138	−	0.728259i	0.973342	+	0.229360i	$0.0736634\pi$
$314$		0			0
$315$	15.2789	+	1.24148i	0.860867	+	0.0699495i
$316$		0			0
$317$	−5.82524	+	3.36320i	−0.327178	+	0.188896i	−0.654588	−	0.755986i	$-0.727158\pi$
$317$	−5.82524	+	3.36320i	−0.327178	+	0.188896i	0.327409	+	0.944883i	$0.393824\pi$
$318$		0			0
$319$	2.78028	−	4.81558i	0.155666	−	0.269621i
$320$		0			0
$321$	−18.2527	+	21.1723i	−1.01877	+	1.18172i
$322$		0			0
$323$			2.90202i			0.161473i
$324$		0			0
$325$			3.70747i			0.205653i
$326$		0			0
$327$	−4.46599	−	3.85015i	−0.246970	−	0.212914i
$328$		0			0
$329$	−15.4679	−	14.4826i	−0.852773	−	0.798453i
$330$		0			0
$331$	−12.0006	−	20.7857i	−0.659615	−	1.14249i	−0.980715	−	0.195441i	$-0.937386\pi$
$331$	−12.0006	−	20.7857i	−0.659615	−	1.14249i	0.321101	−	0.947045i	$-0.395947\pi$
$332$		0			0
$333$	0.778381	+	5.22669i	0.0426550	+	0.286421i
$334$		0			0
$335$	−1.16366	−	2.01552i	−0.0635777	−	0.110120i
$336$		0			0
$337$	−1.07839	+	1.86783i	−0.0587438	+	0.101747i	−0.893902	−	0.448263i	$-0.852043\pi$
$337$	−1.07839	+	1.86783i	−0.0587438	+	0.101747i	0.835158	+	0.550010i	$0.185376\pi$
$338$		0			0
$339$	−2.39936	−	6.87641i	−0.130316	−	0.373476i
$340$		0			0
$341$	−6.22575			−0.337143
$342$		0			0
$343$	11.7422	−	14.3220i	0.634021	−	0.773316i
$344$		0			0
$345$	24.7081	+	4.69757i	1.33024	+	0.252909i
$346$		0			0
$347$	7.31897	+	4.22561i	0.392903	+	0.226843i	0.683417	−	0.730028i	$-0.260493\pi$
$347$	7.31897	+	4.22561i	0.392903	+	0.226843i	−0.290514	+	0.956871i	$0.593826\pi$
$348$		0			0
$349$	−11.6656	+	6.73516i	−0.624447	+	0.360525i	−0.778598	−	0.627523i	$-0.784069\pi$
$349$	−11.6656	+	6.73516i	−0.624447	+	0.360525i	0.154151	+	0.988047i	$0.450736\pi$
$350$		0			0
$351$	13.4290	−	7.05211i	0.716789	−	0.376414i
$352$		0			0
$353$	14.8956	+	25.7999i	0.792813	+	1.37319i	0.924219	+	0.381863i	$0.124718\pi$
$353$	14.8956	+	25.7999i	0.792813	+	1.37319i	−0.131406	+	0.991329i	$0.541949\pi$
$354$		0			0
$355$	18.7517	+	10.8263i	0.995239	+	0.574601i
$356$		0			0
$357$	1.99137	+	0.881646i	0.105395	+	0.0466617i
$358$		0			0
$359$			8.88758i			0.469068i	0.972108	+	0.234534i	$0.0753565\pi$
$359$			8.88758i			0.469068i	−0.972108	+	0.234534i	$0.924644\pi$
$360$		0			0
$361$	−18.2890			−0.962579
$362$		0			0
$363$	15.3178	−	5.34479i	0.803976	−	0.280529i
$364$		0			0
$365$	−3.08313	−	1.78005i	−0.161378	−	0.0931719i
$366$		0			0
$367$	−32.0068	+	18.4792i	−1.67074	+	0.964604i	−0.703520	+	0.710675i	$0.748390\pi$
$367$	−32.0068	+	18.4792i	−1.67074	+	0.964604i	−0.967223	+	0.253929i	$0.918277\pi$
$368$		0			0
$369$	−6.48015	−	2.55646i	−0.337343	−	0.133084i
$370$		0			0
$371$	−7.94130	−	26.1638i	−0.412292	−	1.35836i
$372$		0			0
$373$	16.8546	−	29.1931i	0.872700	−	1.51156i	0.0135064	−	0.999909i	$-0.495701\pi$
$373$	16.8546	−	29.1931i	0.872700	−	1.51156i	0.859193	−	0.511651i	$-0.170966\pi$
$374$		0			0
$375$	−15.8857	−	13.6951i	−0.820335	−	0.707214i
$376$		0			0
$377$	12.7007			0.654117
$378$		0			0
$379$	−29.7512			−1.52821			−0.764107	−	0.645089i	$-0.776820\pi$
$379$	−29.7512			−1.52821			−0.764107	+	0.645089i	$0.776820\pi$
$380$		0			0
$381$	−22.5412	−	19.4329i	−1.15482	−	0.995577i
$382$		0			0
$383$	−7.62871	+	13.2133i	−0.389809	+	0.675169i	−0.992424	−	0.122863i	$-0.960792\pi$
$383$	−7.62871	+	13.2133i	−0.389809	+	0.675169i	0.602615	+	0.798032i	$0.294126\pi$
$384$		0			0
$385$	−1.89668	−	6.24891i	−0.0966637	−	0.318474i
$386$		0			0
$387$	−21.7798	+	17.3061i	−1.10713	+	0.879717i
$388$		0			0
$389$	−0.947612	+	0.547104i	−0.0480458	+	0.0277393i	−0.523831	−	0.851823i	$-0.675497\pi$
$389$	−0.947612	+	0.547104i	−0.0480458	+	0.0277393i	0.475785	+	0.879562i	$0.342164\pi$
$390$		0			0
$391$	3.09442	+	1.78656i	0.156492	+	0.0903504i
$392$		0			0
$393$	13.0966	−	4.56975i	0.660636	−	0.230513i
$394$		0			0
$395$	33.0119			1.66101
$396$		0			0
$397$			18.2381i			0.915345i	0.889121	+	0.457672i	$0.151317\pi$
$397$			18.2381i			0.915345i	−0.889121	+	0.457672i	$0.848683\pi$
$398$		0			0
$399$	−11.3286	+	25.5877i	−0.567137	+	1.28099i
$400$		0			0
$401$	14.3050	+	8.25900i	0.714358	+	0.412435i	0.812673	−	0.582721i	$-0.198012\pi$
$401$	14.3050	+	8.25900i	0.714358	+	0.412435i	−0.0983146	+	0.995155i	$0.531345\pi$
$402$		0			0
$403$	−7.11001	−	12.3149i	−0.354175	−	0.613448i
$404$		0			0
$405$	−3.92749	+	16.9322i	−0.195159	+	0.841367i
$406$		0			0
$407$	1.94958	−	1.12559i	0.0966371	−	0.0557934i
$408$		0			0
$409$	−12.3657	−	7.13935i	−0.611445	−	0.353018i	0.162086	−	0.986777i	$-0.448178\pi$
$409$	−12.3657	−	7.13935i	−0.611445	−	0.353018i	−0.773531	+	0.633759i	$0.781511\pi$
$410$		0			0
$411$	−16.5877	−	3.15370i	−0.818210	−	0.155561i
$412$		0			0
$413$	−2.09257	+	8.98105i	−0.102969	+	0.441928i
$414$		0			0
$415$	−0.869925			−0.0427029
$416$		0			0
$417$	−4.45444	−	12.7661i	−0.218135	−	0.625160i
$418$		0			0
$419$	−19.2168	+	33.2845i	−0.938804	+	1.62606i	−0.171098	+	0.985254i	$0.554732\pi$
$419$	−19.2168	+	33.2845i	−0.938804	+	1.62606i	−0.767706	+	0.640802i	$0.778602\pi$
$420$		0			0
$421$	−5.90196	−	10.2225i	−0.287644	−	0.498214i	0.685603	−	0.727976i	$-0.259539\pi$
$421$	−5.90196	−	10.2225i	−0.287644	−	0.498214i	−0.973247	+	0.229762i	$0.926205\pi$
$422$		0			0
$423$	18.8113	−	14.9474i	0.914637	−	0.726766i
$424$		0			0
$425$	−0.301793	−	0.522720i	−0.0146391	−	0.0253557i
$426$		0			0
$427$	−8.89917	+	9.50460i	−0.430661	+	0.459960i
$428$		0			0
$429$	−4.89412	−	4.21924i	−0.236290	−	0.203707i
$430$		0			0
$431$			33.9984i			1.63765i	0.574047	+	0.818823i	$0.305373\pi$
$431$			33.9984i			1.63765i	−0.574047	+	0.818823i	$0.694627\pi$
$432$		0			0
$433$		−	1.24413i		−	0.0597893i	−0.999553	−	0.0298946i	$-0.990483\pi$
$433$		−	1.24413i		−	0.0597893i	0.999553	−	0.0298946i	$-0.00951718\pi$
$434$		0			0
$435$	−9.50323	+	11.0233i	−0.455645	+	0.528526i
$436$		0			0
$437$	−22.9561	+	39.7612i	−1.09814	+	1.90204i
$438$		0			0
$439$	10.3661	−	5.98485i	0.494745	−	0.285641i	−0.231796	−	0.972765i	$-0.574460\pi$
$439$	10.3661	−	5.98485i	0.494745	−	0.285641i	0.726541	+	0.687123i	$0.241127\pi$
$440$		0			0
$441$	14.1167	+	15.5473i	0.672223	+	0.740349i
$442$		0			0
$443$	5.07711	−	2.93127i	0.241221	−	0.139269i	−0.374517	−	0.927220i	$-0.622191\pi$
$443$	5.07711	−	2.93127i	0.241221	−	0.139269i	0.615738	+	0.787951i	$0.288858\pi$
$444$		0			0
$445$	−10.8713	+	18.8297i	−0.515351	+	0.892614i
$446$		0			0
$447$	−6.34044	−	18.1713i	−0.299892	−	0.859471i
$448$		0			0
$449$		−	13.7990i		−	0.651215i	−0.945505	−	0.325607i	$-0.894431\pi$
$449$		−	13.7990i		−	0.651215i	0.945505	−	0.325607i	$-0.105569\pi$
$450$		0			0
$451$			2.96767i			0.139742i
$452$		0			0
$453$	−1.22111	+	6.42276i	−0.0573729	+	0.301767i
$454$		0			0
$455$	10.1946	−	10.8882i	0.477932	−	0.510446i
$456$		0			0
$457$	17.6082	+	30.4983i	0.823676	+	1.42665i	0.902927	+	0.429794i	$0.141414\pi$
$457$	17.6082	+	30.4983i	0.823676	+	1.42665i	−0.0792505	+	0.996855i	$0.525253\pi$
$458$		0			0
$459$	−1.31932	+	2.08742i	−0.0615808	+	0.0974326i
$460$		0			0
$461$	11.6988	+	20.2629i	0.544867	+	0.943736i	0.998615	+	0.0526068i	$0.0167530\pi$
$461$	11.6988	+	20.2629i	0.544867	+	0.943736i	−0.453749	+	0.891130i	$0.649914\pi$
$462$		0			0
$463$	2.67980	−	4.64155i	0.124541	−	0.215711i	−0.797013	−	0.603963i	$-0.793588\pi$
$463$	2.67980	−	4.64155i	0.124541	−	0.215711i	0.921553	+	0.388252i	$0.126921\pi$
$464$		0			0
$465$	16.0085	+	3.04358i	0.742377	+	0.141143i
$466$		0			0
$467$	−31.3997			−1.45300			−0.726502	−	0.687164i	$-0.758855\pi$
$467$	−31.3997			−1.45300			−0.726502	+	0.687164i	$0.758855\pi$
$468$		0			0
$469$	0.723484	−	3.10510i	0.0334074	−	0.143380i
$470$		0			0
$471$	−2.34014	−	6.70670i	−0.107828	−	0.309028i
$472$		0			0
$473$	10.2632	+	5.92544i	0.471901	+	0.272452i
$474$		0			0
$475$	6.71660	−	3.87783i	0.308179	−	0.177927i
$476$		0			0
$477$	30.6653	−	4.56680i	1.40407	−	0.209099i
$478$		0			0
$479$	10.7485	+	18.6169i	0.491109	+	0.850626i	0.999948	−	0.0102359i	$-0.00325824\pi$
$479$	10.7485	+	18.6169i	0.491109	+	0.850626i	−0.508838	+	0.860862i	$0.669925\pi$
$480$		0			0
$481$	4.45296	+	2.57092i	0.203038	+	0.117224i
$482$		0			0
$483$	20.3100	+	27.8321i	0.924137	+	1.26641i
$484$		0			0
$485$			20.5786i			0.934425i
$486$		0			0
$487$	2.61173			0.118349			0.0591744	−	0.998248i	$-0.481153\pi$
$487$	2.61173			0.118349			0.0591744	+	0.998248i	$0.481153\pi$
$488$		0			0
$489$	18.8737	+	16.2711i	0.853499	+	0.735805i
$490$		0			0
$491$	−11.1818	−	6.45580i	−0.504626	−	0.291346i	0.225996	−	0.974128i	$-0.427437\pi$
$491$	−11.1818	−	6.45580i	−0.504626	−	0.291346i	−0.730622	+	0.682782i	$0.760770\pi$
$492$		0			0
$493$	−1.79068	+	1.03385i	−0.0806482	+	0.0465622i
$494$		0			0
$495$	7.32401	−	1.09072i	0.329190	−	0.0490243i
$496$		0			0
$497$	8.61516	+	28.3840i	0.386443	+	1.27320i
$498$		0			0
$499$	0.117182	−	0.202964i	0.00524577	−	0.00908593i	−0.863391	−	0.504536i	$-0.831664\pi$
$499$	0.117182	−	0.202964i	0.00524577	−	0.00908593i	0.868636	+	0.495450i	$0.164997\pi$
$500$		0			0
$501$	26.3938	−	9.20951i	1.17919	−	0.411451i
$502$		0			0
$503$	13.6460			0.608445			0.304223	−	0.952601i	$-0.401603\pi$
$503$	13.6460			0.608445			0.304223	+	0.952601i	$0.401603\pi$
$504$		0			0
$505$	25.6991			1.14359
$506$		0			0
$507$	−1.44894	+	7.62106i	−0.0643496	+	0.338463i
$508$		0			0
$509$	−1.71269	+	2.96647i	−0.0759136	+	0.131486i	−0.901483	−	0.432814i	$-0.857521\pi$
$509$	−1.71269	+	2.96647i	−0.0759136	+	0.131486i	0.825570	+	0.564300i	$0.190854\pi$
$510$		0			0
$511$	−1.41649	−	4.66685i	−0.0626619	−	0.206449i
$512$		0			0
$513$	−26.8220	−	16.9524i	−1.18422	−	0.748468i
$514$		0			0
$515$	31.8563	−	18.3922i	1.40376	−	0.810459i
$516$		0			0
$517$	−8.86435	−	5.11784i	−0.389854	−	0.225082i
$518$		0			0
$519$	−0.449919	+	2.36646i	−0.0197493	+	0.103876i
$520$		0			0
$521$	−37.3500			−1.63633			−0.818167	−	0.574981i	$-0.805009\pi$
$521$	−37.3500			−1.63633			−0.818167	+	0.574981i	$0.805009\pi$
$522$		0			0
$523$		−	8.99132i		−	0.393163i	−0.980487	−	0.196581i	$-0.937016\pi$
$523$		−	8.99132i		−	0.393163i	0.980487	−	0.196581i	$-0.0629840\pi$
$524$		0			0
$525$	−0.620440	−	5.78704i	−0.0270782	−	0.252567i
$526$		0			0
$527$	2.00489	+	1.15753i	0.0873346	+	0.0504226i
$528$		0			0
$529$	16.7648	+	29.0376i	0.728906	+	1.26250i
$530$		0			0
$531$	−9.72677	−	3.83727i	−0.422106	−	0.166523i
$532$		0			0
$533$	−5.87021	+	3.38917i	−0.254267	+	0.146801i
$534$		0			0
$535$	−26.9938	−	15.5849i	−1.16704	−	0.673793i
$536$		0			0
$537$	−5.20922	+	6.04245i	−0.224794	+	0.260751i
$538$		0			0
$539$	3.95423	−	8.02488i	0.170321	−	0.345656i
$540$		0			0
$541$	7.90934			0.340049			0.170025	−	0.985440i	$-0.445615\pi$
$541$	7.90934			0.340049			0.170025	+	0.985440i	$0.445615\pi$
$542$		0			0
$543$	−18.5173	+	21.4792i	−0.794653	+	0.921760i
$544$		0			0
$545$	3.28741	−	5.69396i	0.140817	−	0.243902i
$546$		0			0
$547$	−17.2958	−	29.9573i	−0.739516	−	1.28088i	−0.952713	−	0.303871i	$-0.901721\pi$
$547$	−17.2958	−	29.9573i	−0.739516	−	1.28088i	0.213197	−	0.977009i	$-0.431612\pi$
$548$		0			0
$549$	−9.18474	−	11.5590i	−0.391995	−	0.493327i
$550$		0			0
$551$	−13.2843	−	23.0090i	−0.565928	−	0.980217i
$552$		0			0
$553$	33.0124	+	30.9095i	1.40383	+	1.31441i
$554$		0			0
$555$	−5.56329	+	1.94118i	−0.236149	+	0.0823985i
$556$		0			0
$557$		−	2.42861i		−	0.102903i	−0.998675	−	0.0514517i	$-0.983615\pi$
$557$		−	2.42861i		−	0.102903i	0.998675	−	0.0514517i	$-0.0163848\pi$
$558$		0			0
$559$			27.0682i			1.14486i
$560$		0			0
$561$	1.03348	+	0.196488i	0.0436335	+	0.00829573i
$562$		0			0
$563$	8.53869	−	14.7894i	0.359863	−	0.623301i	−0.628075	−	0.778153i	$-0.716157\pi$
$563$	8.53869	−	14.7894i	0.359863	−	0.623301i	0.987938	+	0.154852i	$0.0494901\pi$
$564$		0			0
$565$	7.03283	−	4.06041i	0.295873	−	0.170823i
$566$		0			0
$567$	−19.7814	+	13.2551i	−0.830740	+	0.556660i
$568$		0			0
$569$	19.9471	−	11.5165i	0.836228	−	0.482796i	−0.0197523	−	0.999805i	$-0.506288\pi$
$569$	19.9471	−	11.5165i	0.836228	−	0.482796i	0.855980	+	0.517008i	$0.172954\pi$
$570$		0			0
$571$	4.11356	−	7.12490i	0.172147	−	0.298168i	−0.767023	−	0.641619i	$-0.778263\pi$
$571$	4.11356	−	7.12490i	0.172147	−	0.298168i	0.939170	+	0.343452i	$0.111596\pi$
$572$		0			0
$573$	25.1402	+	4.77973i	1.05025	+	0.199676i
$574$		0			0
$575$		−	9.54919i		−	0.398229i
$576$		0			0
$577$			11.3064i			0.470691i	0.971912	+	0.235346i	$0.0756222\pi$
$577$			11.3064i			0.470691i	−0.971912	+	0.235346i	$0.924378\pi$
$578$		0			0
$579$	−29.1723	+	10.1790i	−1.21236	+	0.423024i
$580$		0			0
$581$	−0.869937	−	0.814523i	−0.0360911	−	0.0337921i
$582$		0			0
$583$	−6.60389	−	11.4383i	−0.273505	−	0.473725i
$584$		0			0
$585$	10.5218	+	13.2417i	0.435022	+	0.547476i
$586$		0			0
$587$	−17.2862	−	29.9407i	−0.713480	−	1.23578i	−0.963543	−	0.267553i	$-0.913785\pi$
$587$	−17.2862	−	29.9407i	−0.713480	−	1.23578i	0.250063	−	0.968229i	$-0.419549\pi$
$588$		0			0
$589$	−14.8734	+	25.7615i	−0.612849	+	1.06149i
$590$		0			0
$591$	9.05159	−	10.4994i	0.372333	−	0.431888i
$592$		0			0
$593$	9.64649			0.396134			0.198067	−	0.980188i	$-0.436534\pi$
$593$	9.64649			0.396134			0.198067	+	0.980188i	$0.436534\pi$
$594$		0			0
$595$	−0.551039	+	2.36499i	−0.0225904	+	0.0969553i
$596$		0			0
$597$	−18.4383	+	21.3876i	−0.754631	+	0.875336i
$598$		0			0
$599$	5.22049	+	3.01405i	0.213303	+	0.123151i	0.602846	−	0.797858i	$-0.294033\pi$
$599$	5.22049	+	3.01405i	0.213303	+	0.123151i	−0.389542	+	0.921009i	$0.627367\pi$
$600$		0			0
$601$	−23.4624	+	13.5460i	−0.957052	+	0.552555i	−0.895265	−	0.445535i	$-0.853014\pi$
$601$	−23.4624	+	13.5460i	−0.957052	+	0.552555i	−0.0617879	+	0.998089i	$0.519680\pi$
$602$		0			0
$603$	3.36293	+	1.32670i	0.136949	+	0.0540272i
$604$		0			0
$605$	9.04491	+	15.6662i	0.367728	+	0.636923i
$606$		0			0
$607$	−16.1410	−	9.31904i	−0.655145	−	0.378248i	0.135280	−	0.990807i	$-0.456807\pi$
$607$	−16.1410	−	9.31904i	−0.655145	−	0.378248i	−0.790425	+	0.612559i	$0.790140\pi$
$608$		0			0
$609$	−19.8246	+	2.12544i	−0.803334	+	0.0861271i
$610$		0			0
$611$		−	23.3789i		−	0.945811i
$612$		0			0
$613$	24.7398			0.999232			0.499616	−	0.866247i	$-0.333474\pi$
$613$	24.7398			0.999232			0.499616	+	0.866247i	$0.333474\pi$
$614$		0			0
$615$	1.45080	−	7.63087i	0.0585021	−	0.307706i
$616$		0			0
$617$	−42.5759	−	24.5812i	−1.71404	−	0.989603i	−0.928934	−	0.370245i	$-0.879274\pi$
$617$	−42.5759	−	24.5812i	−1.71404	−	0.989603i	−0.785109	−	0.619358i	$-0.787393\pi$
$618$		0			0
$619$	0.334357	−	0.193041i	0.0134389	−	0.00775898i	−0.493265	−	0.869879i	$-0.664197\pi$
$619$	0.334357	−	0.193041i	0.0134389	−	0.00775898i	0.506704	+	0.862120i	$0.330864\pi$
$620$		0			0
$621$	−34.5887	+	18.1638i	−1.38800	+	0.728890i
$622$		0			0
$623$	−28.5020	+	8.65098i	−1.14191	+	0.346594i
$624$		0			0
$625$	8.51828	−	14.7541i	0.340731	−	0.590164i
$626$		0			0
$627$	−2.52474	+	13.2795i	−0.100828	+	0.530332i
$628$		0			0
$629$	−0.837104			−0.0333775
$630$		0			0
$631$	45.6531			1.81742			0.908710	−	0.417429i	$-0.137069\pi$
$631$	45.6531			1.81742			0.908710	+	0.417429i	$0.137069\pi$
$632$		0			0
$633$	33.3385	−	11.6327i	1.32509	−	0.462357i
$634$		0			0
$635$	16.5926	−	28.7392i	0.658456	−	1.14048i
$636$		0			0
$637$	20.3895	−	1.34297i	0.807863	−	0.0532104i
$638$		0			0
$639$	−33.2674	+	4.95431i	−1.31604	+	0.195990i
$640$		0			0
$641$	−34.2119	+	19.7523i	−1.35129	+	0.780167i	−0.988430	−	0.151677i	$-0.951533\pi$
$641$	−34.2119	+	19.7523i	−1.35129	+	0.780167i	−0.362859	+	0.931844i	$0.618199\pi$
$642$		0			0
$643$	23.1404	+	13.3601i	0.912570	+	0.526873i	0.881257	−	0.472637i	$-0.156698\pi$
$643$	23.1404	+	13.3601i	0.912570	+	0.526873i	0.0313129	+	0.999510i	$0.490031\pi$
$644$		0			0
$645$	−23.4933	−	20.2537i	−0.925047	−	0.797487i
$646$		0			0
$647$	40.2634			1.58292			0.791459	−	0.611222i	$-0.209322\pi$
$647$	40.2634			1.58292			0.791459	+	0.611222i	$0.209322\pi$
$648$		0			0
$649$			4.45450i			0.174854i
$650$		0			0
$651$	13.1590	+	18.0326i	0.515741	+	0.706754i
$652$		0			0
$653$	−36.6920	−	21.1841i	−1.43587	−	0.828998i	−0.438308	−	0.898825i	$-0.644422\pi$
$653$	−36.6920	−	21.1841i	−1.43587	−	0.828998i	−0.997559	+	0.0698266i	$0.977755\pi$
$654$		0			0
$655$	7.73332	+	13.3945i	0.302166	+	0.523366i
$656$		0			0
$657$	5.46977	−	0.814580i	0.213396	−	0.0317798i
$658$		0			0
$659$	33.3031	−	19.2276i	1.29731	−	0.749000i	0.317368	−	0.948302i	$-0.397201\pi$
$659$	33.3031	−	19.2276i	1.29731	−	0.749000i	0.979938	+	0.199302i	$0.0638676\pi$
$660$		0			0
$661$	−14.2400	−	8.22149i	−0.553874	−	0.319779i	0.196809	−	0.980442i	$-0.436942\pi$
$661$	−14.2400	−	8.22149i	−0.553874	−	0.319779i	−0.750683	+	0.660663i	$0.770275\pi$
$662$		0			0
$663$	0.791601	+	2.26868i	0.0307432	+	0.0881081i
$664$		0			0
$665$	−30.3885	−	7.08048i	−1.17842	−	0.274569i
$666$		0			0
$667$	−32.7126			−1.26664
$668$		0			0
$669$	3.83729	+	0.729557i	0.148358	+	0.0282063i
$670$		0			0
$671$	−3.14477	+	5.44690i	−0.121402	+	0.210275i
$672$		0			0
$673$	−16.8254	−	29.1424i	−0.648570	−	1.12336i	−0.983465	−	0.181100i	$-0.942034\pi$
$673$	−16.8254	−	29.1424i	−0.648570	−	1.12336i	0.334895	−	0.942255i	$-0.391299\pi$
$674$		0			0
$675$	6.59420	+	0.264193i	0.253811	+	0.0101688i
$676$		0			0
$677$	−21.0119	−	36.3938i	−0.807555	−	1.39873i	−0.914553	−	0.404466i	$-0.867457\pi$
$677$	−21.0119	−	36.3938i	−0.807555	−	1.39873i	0.106998	−	0.994259i	$-0.465876\pi$
$678$		0			0
$679$	−19.2680	+	20.5789i	−0.739438	+	0.789744i
$680$		0			0
$681$	7.04702	−	37.0656i	0.270042	−	1.42036i
$682$		0			0
$683$		−	28.0238i		−	1.07230i	−0.844122	−	0.536151i	$-0.819878\pi$
$683$		−	28.0238i		−	1.07230i	0.844122	−	0.536151i	$-0.180122\pi$
$684$		0			0
$685$		−	18.8272i		−	0.719351i
$686$		0			0
$687$	−6.90731	−	19.7959i	−0.263530	−	0.755260i
$688$		0			0
$689$	15.0837	−	26.1258i	0.574644	−	0.995312i
$690$		0			0
$691$	−4.58578	+	2.64760i	−0.174451	+	0.100720i	−0.584683	−	0.811262i	$-0.698781\pi$
$691$	−4.58578	+	2.64760i	−0.174451	+	0.100720i	0.410232	+	0.911981i	$0.365448\pi$
$692$		0			0
$693$	8.34537	+	5.76684i	0.317015	+	0.219064i
$694$		0			0
$695$	13.0565	−	7.53818i	0.495262	−	0.285940i
$696$		0			0
$697$	0.551765	−	0.955685i	0.0208996	−	0.0361992i
$698$		0			0
$699$	24.8670	−	28.8445i	0.940555	−	1.09100i
$700$		0			0
$701$		−	38.6055i		−	1.45811i	−0.684455	−	0.729055i	$-0.739960\pi$
$701$		−	38.6055i		−	1.45811i	0.684455	−	0.729055i	$-0.260040\pi$
$702$		0			0
$703$		−	10.7562i		−	0.405678i
$704$		0			0
$705$	20.2913	+	17.4932i	0.764214	+	0.658832i
$706$		0			0
$707$	25.6994	+	24.0624i	0.966526	+	0.904960i
$708$		0			0
$709$	21.9037	+	37.9383i	0.822610	+	1.42480i	0.903732	+	0.428098i	$0.140816\pi$
$709$	21.9037	+	37.9383i	0.822610	+	1.42480i	−0.0811228	+	0.996704i	$0.525851\pi$
$710$		0			0
$711$	−40.1480	+	31.9014i	−1.50567	+	1.19640i
$712$		0			0
$713$	18.3130	+	31.7190i	0.685826	+	1.18789i
$714$		0			0
$715$	3.60256	−	6.23981i	0.134728	−	0.233356i
$716$		0			0
$717$	−12.3781	−	35.4748i	−0.462268	−	1.32483i
$718$		0			0
$719$	−21.2855			−0.793813			−0.396907	−	0.917859i	$-0.629916\pi$
$719$	−21.2855			−0.793813			−0.396907	+	0.917859i	$0.629916\pi$
$720$		0			0
$721$	49.0776	+	11.4350i	1.82775	+	0.425862i
$722$		0			0
$723$	45.5194	+	8.65428i	1.69288	+	0.321856i
$724$		0			0
$725$	4.78559	+	2.76296i	0.177733	+	0.102614i
$726$		0			0
$727$	36.2267	−	20.9155i	1.34358	−	0.775713i	0.356245	−	0.934393i	$-0.384057\pi$
$727$	36.2267	−	20.9155i	1.34358	−	0.775713i	0.987330	+	0.158679i	$0.0507236\pi$
$728$		0			0
$729$	−11.5861	−	24.3877i	−0.429115	−	0.903250i
$730$		0			0
$731$	−2.20338	−	3.81637i	−0.0814950	−	0.141154i
$732$		0			0
$733$	−36.6457	−	21.1574i	−1.35354	−	0.781466i	−0.364795	−	0.931088i	$-0.618861\pi$
$733$	−36.6457	−	21.1574i	−1.35354	−	0.781466i	−0.988743	+	0.149622i	$0.952194\pi$
$734$		0			0
$735$	−14.0908	+	18.7016i	−0.519747	+	0.689818i
$736$		0			0
$737$		−	1.54010i		−	0.0567302i
$738$		0			0
$739$	20.4280			0.751456			0.375728	−	0.926730i	$-0.377393\pi$
$739$	20.4280			0.751456			0.375728	+	0.926730i	$0.377393\pi$
$740$		0			0
$741$	−29.1509	+	10.1715i	−1.07089	+	0.373661i
$742$		0			0
$743$	−7.44740	−	4.29976i	−0.273219	−	0.157743i	0.357131	−	0.934054i	$-0.383755\pi$
$743$	−7.44740	−	4.29976i	−0.273219	−	0.157743i	−0.630349	+	0.776312i	$0.717088\pi$
$744$		0			0
$745$	18.5846	−	10.7298i	0.680887	−	0.393110i
$746$		0			0
$747$	1.05797	−	0.840661i	0.0387093	−	0.0307582i
$748$		0			0
$749$	−12.4018	−	40.8598i	−0.453153	−	1.49298i
$750$		0			0
$751$	20.0359	−	34.7032i	0.731120	−	1.26634i	−0.225285	−	0.974293i	$-0.572331\pi$
$751$	20.0359	−	34.7032i	0.731120	−	1.26634i	0.956405	−	0.292043i	$-0.0943352\pi$
$752$		0			0
$753$	2.30362	+	1.98596i	0.0839487	+	0.0723726i
$754$		0			0
$755$	−7.28990			−0.265307
$756$		0			0
$757$	10.6186			0.385941			0.192970	−	0.981205i	$-0.438188\pi$
$757$	10.6186			0.385941			0.192970	+	0.981205i	$0.438188\pi$
$758$		0			0
$759$	12.6056	+	10.8673i	0.457554	+	0.394459i
$760$		0			0
$761$	−1.36550	+	2.36512i	−0.0494993	+	0.0857354i	−0.889713	−	0.456519i	$-0.849096\pi$
$761$	−1.36550	+	2.36512i	−0.0494993	+	0.0857354i	0.840214	+	0.542255i	$0.182429\pi$
$762$		0			0
$763$	8.61878	−	2.61599i	0.312021	−	0.0947052i
$764$		0			0
$765$	−2.56137	−	1.01047i	−0.0926064	−	0.0365338i
$766$		0			0
$767$	−8.81125	+	5.08718i	−0.318156	+	0.183687i
$768$		0			0
$769$	−5.44566	−	3.14405i	−0.196376	−	0.113377i	0.398588	−	0.917130i	$-0.369500\pi$
$769$	−5.44566	−	3.14405i	−0.196376	−	0.113377i	−0.594964	+	0.803753i	$0.702834\pi$
$770$		0			0
$771$	−49.0149	+	17.1026i	−1.76523	+	0.615934i
$772$		0			0
$773$	15.6236			0.561942			0.280971	−	0.959716i	$-0.409344\pi$
$773$	15.6236			0.561942			0.280971	+	0.959716i	$0.409344\pi$
$774$		0			0
$775$		−	6.18698i		−	0.222243i
$776$		0			0
$777$	−7.38093	−	3.26778i	−0.264789	−	0.117231i
$778$		0			0
$779$	12.2799	+	7.08981i	0.439973	+	0.254019i
$780$		0			0
$781$	7.16426	+	12.4089i	0.256358	+	0.444024i
$782$		0			0
$783$	0.905046	−	22.5897i	0.0323437	−	0.807290i
$784$		0			0
$785$	6.85925	−	3.96019i	0.244817	−	0.141345i
$786$		0			0
$787$	−39.7379	−	22.9427i	−1.41650	−	0.817819i	−0.420514	−	0.907286i	$-0.638150\pi$
$787$	−39.7379	−	22.9427i	−1.41650	−	0.817819i	−0.995990	+	0.0894671i	$0.971484\pi$
$788$		0			0
$789$	26.3819	+	5.01581i	0.939222	+	0.178568i
$790$		0			0
$791$	10.8347	+	2.52448i	0.385239	+	0.0897600i
$792$		0			0
$793$	−14.3657			−0.510141
$794$		0			0
$795$	11.3890	+	32.6401i	0.403926	+	1.15763i
$796$		0			0
$797$	14.8057	−	25.6442i	0.524444	−	0.908364i	−0.475151	−	0.879904i	$-0.657606\pi$
$797$	14.8057	−	25.6442i	0.524444	−	0.908364i	0.999595	−	0.0284597i	$-0.00906022\pi$
$798$		0			0
$799$	1.90307	+	3.29622i	0.0673259	+	0.116612i
$800$		0			0
$801$	−4.97491	−	33.4057i	−0.175780	−	1.18033i
$802$		0			0
$803$	−1.17794	−	2.04025i	−0.0415685	−	0.0719987i
$804$		0			0
$805$	−26.2579	+	28.0443i	−0.925470	+	0.988432i
$806$		0			0
$807$	−0.541012	−	0.466409i	−0.0190445	−	0.0164184i
$808$		0			0
$809$		−	27.7761i		−	0.976556i	−0.872688	−	0.488278i	$-0.837625\pi$
$809$		−	27.7761i		−	0.976556i	0.872688	−	0.488278i	$-0.162375\pi$
$810$		0			0
$811$		−	17.8221i		−	0.625820i	−0.949783	−	0.312910i	$-0.898696\pi$
$811$		−	17.8221i		−	0.625820i	0.949783	−	0.312910i	$-0.101304\pi$
$812$		0			0
$813$	−0.407206	+	0.472339i	−0.0142813	+	0.0165657i
$814$		0			0
$815$	−13.8929	+	24.0633i	−0.486648	+	0.842899i
$816$		0			0
$817$	49.0377	−	28.3119i	1.71561	−	0.990510i
$818$		0			0
$819$	−1.87646	+	23.0936i	−0.0655688	+	0.806954i
$820$		0			0
$821$	0.242236	−	0.139855i	0.00845409	−	0.00488097i	−0.495767	−	0.868456i	$-0.665113\pi$
$821$	0.242236	−	0.139855i	0.00845409	−	0.00488097i	0.504221	+	0.863575i	$0.331780\pi$
$822$		0			0
$823$	−5.56224	+	9.63408i	−0.193887	+	0.335823i	−0.946535	−	0.322600i	$-0.895443\pi$
$823$	−5.56224	+	9.63408i	−0.193887	+	0.335823i	0.752648	+	0.658423i	$0.228776\pi$
$824$		0			0
$825$	−0.926224	−	2.65450i	−0.0322470	−	0.0924177i
$826$		0			0
$827$		−	22.9832i		−	0.799205i	−0.916688	−	0.399603i	$-0.869148\pi$
$827$		−	22.9832i		−	0.799205i	0.916688	−	0.399603i	$-0.130852\pi$
$828$		0			0
$829$			6.30082i			0.218837i	0.993996	+	0.109418i	$0.0348988\pi$
$829$			6.30082i			0.218837i	−0.993996	+	0.109418i	$0.965101\pi$
$830$		0			0
$831$	−1.96445	+	10.3325i	−0.0681461	+	0.358432i
$832$		0			0
$833$	−2.76542	+	1.84908i	−0.0958163	+	0.0640668i
$834$		0			0
$835$	15.5851	+	26.9942i	0.539345	+	0.934174i
$836$		0			0
$837$	−22.4102	+	11.7685i	−0.774610	+	0.406778i
$838$		0			0
$839$	11.7701	+	20.3864i	0.406349	+	0.703816i	0.994477	−	0.104951i	$-0.0334685\pi$
$839$	11.7701	+	20.3864i	0.406349	+	0.703816i	−0.588129	+	0.808767i	$0.700135\pi$
$840$		0			0
$841$	−5.03493	+	8.72075i	−0.173618	+	0.300716i
$842$		0			0
$843$	16.1604	+	3.07246i	0.556593	+	0.105821i
$844$		0			0
$845$	−8.64999			−0.297569
$846$		0			0
$847$	−5.62349	+	24.1353i	−0.193225	+	0.829300i
$848$		0			0
$849$	6.46877	+	18.5391i	0.222008	+	0.636259i
$850$		0			0
$851$	−11.4693	−	6.62182i	−0.393164	−	0.226993i
$852$		0			0
$853$	−1.56621	+	0.904252i	−0.0536260	+	0.0309610i	−0.526573	−	0.850130i	$-0.676523\pi$
$853$	−1.56621	+	0.904252i	−0.0536260	+	0.0309610i	0.472947	+	0.881091i	$0.343190\pi$
$854$		0			0
$855$	12.9839	−	32.9118i	0.444040	−	1.12556i
$856$		0			0
$857$	0.704571	+	1.22035i	0.0240677	+	0.0416865i	0.877808	−	0.479012i	$-0.159005\pi$
$857$	0.704571	+	1.22035i	0.0240677	+	0.0416865i	−0.853741	+	0.520698i	$0.825672\pi$
$858$		0			0
$859$	35.4862	+	20.4879i	1.21077	+	0.699040i	0.962928	−	0.269760i	$-0.0869444\pi$
$859$	35.4862	+	20.4879i	1.21077	+	0.699040i	0.247845	+	0.968800i	$0.420278\pi$
$860$		0			0
$861$	8.59572	−	6.27257i	0.292941	−	0.213769i
$862$		0			0
$863$		−	7.34316i		−	0.249964i	−0.992159	−	0.124982i	$-0.960113\pi$
$863$		−	7.34316i		−	0.249964i	0.992159	−	0.124982i	$-0.0398873\pi$
$864$		0			0
$865$	−2.68596			−0.0913255
$866$		0			0
$867$	22.0052	+	18.9707i	0.747334	+	0.644280i
$868$		0			0
$869$	18.9187	+	10.9227i	0.641774	+	0.370528i
$870$		0			0
$871$	3.04640	−	1.75884i	0.103223	−	0.0595960i
$872$		0			0
$873$	−19.8863	−	25.0270i	−0.673050	−	0.847035i
$874$		0			0
$875$	30.6574	−	9.30519i	1.03641	−	0.314573i
$876$		0			0
$877$	1.80443	−	3.12536i	0.0609312	−	0.105536i	−0.833951	−	0.551839i	$-0.813926\pi$
$877$	1.80443	−	3.12536i	0.0609312	−	0.105536i	0.894882	+	0.446303i	$0.147260\pi$
$878$		0			0
$879$	−30.1707	+	10.5274i	−1.01763	+	0.355079i
$880$		0			0
$881$	12.6937			0.427660			0.213830	−	0.976871i	$-0.431406\pi$
$881$	12.6937			0.427660			0.213830	+	0.976871i	$0.431406\pi$
$882$		0			0
$883$	−8.55621			−0.287939			−0.143970	−	0.989582i	$-0.545987\pi$
$883$	−8.55621			−0.287939			−0.143970	+	0.989582i	$0.545987\pi$
$884$		0			0
$885$	2.17767	−	11.4540i	0.0732016	−	0.385023i
$886$		0			0
$887$	−7.45990	+	12.9209i	−0.250479	+	0.433842i	−0.963658	−	0.267140i	$-0.913921\pi$
$887$	−7.45990	+	12.9209i	−0.250479	+	0.433842i	0.713179	+	0.700982i	$0.247255\pi$
$888$		0			0
$889$	43.5017	−	13.2037i	1.45900	−	0.442839i
$890$		0			0
$891$	−7.85320	+	8.40414i	−0.263092	+	0.281549i
$892$		0			0
$893$	−42.3542	+	24.4532i	−1.41733	+	0.818295i
$894$		0			0
$895$	−7.70388	−	4.44784i	−0.257512	−	0.148675i
$896$		0			0
$897$	−7.10023	+	37.3455i	−0.237070	+	1.24693i
$898$		0			0
$899$	−21.1947			−0.706883
$900$		0			0
$901$			4.91133i			0.163620i
$902$		0			0
$903$	−4.52982	−	42.2510i	−0.150743	−	1.40603i
$904$		0			0
$905$	−27.3851	−	15.8108i	−0.910312	−	0.525569i
$906$		0			0
$907$	16.1506	+	27.9737i	0.536273	+	0.928852i	0.999101	+	0.0424034i	$0.0135015\pi$
$907$	16.1506	+	27.9737i	0.536273	+	0.928852i	−0.462828	+	0.886448i	$0.653165\pi$
$908$		0			0
$909$	−31.2544	+	24.8346i	−1.03664	+	0.823710i
$910$		0			0
$911$	13.3778	−	7.72366i	0.443225	−	0.255896i	−0.261740	−	0.965139i	$-0.584296\pi$
$911$	13.3778	−	7.72366i	0.443225	−	0.255896i	0.704965	+	0.709242i	$0.250963\pi$
$912$		0			0
$913$	−0.498544	−	0.287834i	−0.0164994	−	0.00952593i
$914$		0			0
$915$	10.7491	−	12.4684i	0.355354	−	0.412194i
$916$		0			0
$917$	−4.80803	+	20.6355i	−0.158775	+	0.681444i
$918$		0			0
$919$	−1.01879			−0.0336069			−0.0168034	−	0.999859i	$-0.505349\pi$
$919$	−1.01879			−0.0336069			−0.0168034	+	0.999859i	$0.505349\pi$
$920$		0			0
$921$	12.5491	−	14.5564i	0.413507	−	0.479648i
$922$		0			0
$923$	−16.3636	+	28.3427i	−0.538616	+	0.932910i
$924$		0			0
$925$	1.11858	+	1.93744i	0.0367787	+	0.0637026i
$926$		0			0
$927$	−20.9690	+	53.1527i	−0.688714	+	1.74576i
$928$		0			0
$929$	17.5872	+	30.4619i	0.577016	+	0.999421i	0.995819	+	0.0913443i	$0.0291164\pi$
$929$	17.5872	+	30.4619i	0.577016	+	0.999421i	−0.418803	+	0.908077i	$0.637550\pi$
$930$		0			0
$931$	−23.7594	−	35.5338i	−0.778684	−	1.16457i
$932$		0			0
$933$	−3.49527	+	1.21959i	−0.114430	+	0.0399276i
$934$		0			0
$935$			1.17301i			0.0383615i
$936$		0			0
$937$		−	19.5780i		−	0.639586i	−0.947487	−	0.319793i	$-0.896387\pi$
$937$		−	19.5780i		−	0.639586i	0.947487	−	0.319793i	$-0.103613\pi$
$938$		0			0
$939$	−43.8468	−	8.33628i	−1.43089	−	0.272044i
$940$		0			0
$941$	−23.2160	+	40.2113i	−0.756820	+	1.31085i	0.187645	+	0.982237i	$0.439915\pi$
$941$	−23.2160	+	40.2113i	−0.756820	+	1.31085i	−0.944464	+	0.328614i	$0.893419\pi$
$942$		0			0
$943$	15.1197	−	8.72936i	0.492365	−	0.284267i
$944$		0			0
$945$	−18.6395	−	18.9083i	−0.606344	−	0.615087i
$946$		0			0
$947$	−32.1063	+	18.5366i	−1.04331	+	0.602358i	−0.920770	−	0.390105i	$-0.872439\pi$
$947$	−32.1063	+	18.5366i	−1.04331	+	0.602358i	−0.122544	+	0.992463i	$0.539105\pi$
$948$		0			0
$949$	2.69048	−	4.66006i	0.0873368	−	0.151272i
$950$		0			0
$951$	11.4455	+	2.17604i	0.371144	+	0.0705631i
$952$		0			0
$953$		−	2.73116i		−	0.0884709i	−0.999021	−	0.0442354i	$-0.985915\pi$
$953$		−	2.73116i		−	0.0884709i	0.999021	−	0.0442354i	$-0.0140852\pi$
$954$		0			0
$955$			28.5344i			0.923352i
$956$		0			0
$957$	−9.09349	+	3.17296i	−0.293951	+	0.102567i
$958$		0			0
$959$	17.6282	−	18.8275i	0.569244	−	0.607971i
$960$		0			0
$961$	−3.63491	−	6.29585i	−0.117255	−	0.203092i
$962$		0			0
$963$	47.8896	−	7.13191i	1.54322	−	0.229823i
$964$		0			0
$965$	−17.2257	−	29.8358i	−0.554516	−	0.960450i
$966$		0			0
$967$	14.6811	−	25.4285i	0.472113	−	0.817724i	−0.527378	−	0.849631i	$-0.676825\pi$
$967$	14.6811	−	25.4285i	0.472113	−	0.817724i	0.999491	+	0.0319070i	$0.0101580\pi$
$968$		0			0
$969$	3.28205	−	3.80702i	0.105435	−	0.122299i
$970$		0			0
$971$	17.1103			0.549094			0.274547	−	0.961574i	$-0.411472\pi$
$971$	17.1103			0.549094			0.274547	+	0.961574i	$0.411472\pi$
$972$		0			0
$973$	20.1148	+	4.68671i	0.644851	+	0.150249i
$974$		0			0
$975$	4.19297	−	4.86364i	0.134282	−	0.155761i
$976$		0			0
$977$	36.4251	+	21.0301i	1.16534	+	0.672812i	0.952579	−	0.304292i	$-0.0984198\pi$
$977$	36.4251	+	21.0301i	1.16534	+	0.672812i	0.212765	+	0.977103i	$0.431753\pi$
$978$		0			0
$979$	−12.4605	+	7.19406i	−0.398238	+	0.229923i
$980$		0			0
$981$	1.50437	+	10.1016i	0.0480310	+	0.322520i
$982$		0			0
$983$	−3.87731	−	6.71569i	−0.123667	−	0.214197i	0.797544	−	0.603261i	$-0.206132\pi$
$983$	−3.87731	−	6.71569i	−0.123667	−	0.214197i	−0.921211	+	0.389063i	$0.872799\pi$
$984$		0			0
$985$	13.3863	+	7.72860i	0.426524	+	0.246254i
$986$		0			0
$987$	3.91243	+	36.4925i	0.124534	+	1.16157i
$988$		0			0
$989$		−	69.7184i		−	2.21692i
$990$		0			0
$991$	−11.5135			−0.365738			−0.182869	−	0.983137i	$-0.558538\pi$
$991$	−11.5135			−0.365738			−0.182869	+	0.983137i	$0.558538\pi$
$992$		0			0
$993$	−7.76460	+	40.8399i	−0.246402	+	1.29601i
$994$		0			0
$995$	−27.2683	−	15.7434i	−0.864464	−	0.499099i
$996$		0			0
$997$	15.0836	−	8.70850i	0.477701	−	0.275801i	−0.241757	−	0.970337i	$-0.577724\pi$
$997$	15.0836	−	8.70850i	0.477701	−	0.275801i	0.719458	+	0.694536i	$0.244390\pi$
$998$		0			0
$999$	4.89002	−	7.73695i	0.154713	−	0.244786i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bu.a.41.5	✓	48
3.2	odd	2		1512.2.bu.a.881.8		48
4.3	odd	2		1008.2.cc.d.545.20		48
7.6	odd	2	inner	504.2.bu.a.41.20	yes	48
9.2	odd	6	inner	504.2.bu.a.209.20	yes	48
9.4	even	3		4536.2.k.a.3401.16		48
9.5	odd	6		4536.2.k.a.3401.33		48
9.7	even	3		1512.2.bu.a.1385.17		48
12.11	even	2		3024.2.cc.d.881.8		48
21.20	even	2		1512.2.bu.a.881.17		48
28.27	even	2		1008.2.cc.d.545.5		48
36.7	odd	6		3024.2.cc.d.2897.17		48
36.11	even	6		1008.2.cc.d.209.5		48
63.13	odd	6		4536.2.k.a.3401.34		48
63.20	even	6	inner	504.2.bu.a.209.5	yes	48
63.34	odd	6		1512.2.bu.a.1385.8		48
63.41	even	6		4536.2.k.a.3401.15		48
84.83	odd	2		3024.2.cc.d.881.17		48
252.83	odd	6		1008.2.cc.d.209.20		48
252.223	even	6		3024.2.cc.d.2897.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bu.a.41.5	✓	48	1.1	even	1	trivial
504.2.bu.a.41.20	yes	48	7.6	odd	2	inner
504.2.bu.a.209.5	yes	48	63.20	even	6	inner
504.2.bu.a.209.20	yes	48	9.2	odd	6	inner
1008.2.cc.d.209.5		48	36.11	even	6
1008.2.cc.d.209.20		48	252.83	odd	6
1008.2.cc.d.545.5		48	28.27	even	2
1008.2.cc.d.545.20		48	4.3	odd	2
1512.2.bu.a.881.8		48	3.2	odd	2
1512.2.bu.a.881.17		48	21.20	even	2
1512.2.bu.a.1385.8		48	63.34	odd	6
1512.2.bu.a.1385.17		48	9.7	even	3
3024.2.cc.d.881.8		48	12.11	even	2
3024.2.cc.d.881.17		48	84.83	odd	2
3024.2.cc.d.2897.8		48	252.223	even	6
3024.2.cc.d.2897.17		48	36.7	odd	6
4536.2.k.a.3401.15		48	63.41	even	6
4536.2.k.a.3401.16		48	9.4	even	3
4536.2.k.a.3401.33		48	9.5	odd	6
4536.2.k.a.3401.34		48	63.13	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bu (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31185 - 1.13095i) q^{3} +(0.965651 - 1.67256i) q^{5} +(2.53170 - 0.768427i) q^{7} +(0.441899 + 2.96728i) q^{9} +(1.10681 - 0.639015i) q^{11} +(2.52802 + 1.45955i) q^{13} +(-3.15837 + 1.10204i) q^{15} -0.475237 q^{17} -6.10647i q^{19} +(-4.19027 - 1.85517i) q^{21} +(-6.51132 - 3.75931i) q^{23} +(0.635036 + 1.09991i) q^{25} +(2.77614 - 4.39239i) q^{27} +(3.76797 - 2.17544i) q^{29} +(-4.21872 - 2.43568i) q^{31} +(-2.17466 - 0.413453i) q^{33} +(1.15950 - 4.97645i) q^{35} +1.76145 q^{37} +(-1.66570 - 4.77378i) q^{39} +(-1.16103 + 2.01097i) q^{41} +(4.63638 + 8.03045i) q^{43} +(5.38966 + 2.12625i) q^{45} +(-4.00447 - 6.93595i) q^{47} +(5.81904 - 3.89086i) q^{49} +(0.623440 + 0.537470i) q^{51} -10.3345i q^{53} -2.46826i q^{55} +(-6.90612 + 8.01077i) q^{57} +(-1.74272 + 3.01848i) q^{59} +(-4.26195 + 2.46064i) q^{61} +(3.39889 + 7.17269i) q^{63} +(4.88237 - 2.81883i) q^{65} +(0.602527 - 1.04361i) q^{67} +(4.29027 + 12.2956i) q^{69} +11.2114i q^{71} -1.84336i q^{73} +(0.410878 - 2.16112i) q^{75} +(2.31107 - 2.46830i) q^{77} +(8.54654 + 14.8030i) q^{79} +(-8.60945 + 2.62247i) q^{81} +(-0.225217 - 0.390088i) q^{83} +(-0.458913 + 0.794861i) q^{85} +(-7.40333 - 1.40754i) q^{87} -11.2580 q^{89} +(7.52175 + 1.75255i) q^{91} +(2.77969 + 7.96642i) q^{93} +(-10.2134 - 5.89672i) q^{95} +(-9.22775 + 5.32764i) q^{97} +(2.38523 + 3.00182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9} + 8 q^{15} - 4 q^{21} + 12 q^{23} - 24 q^{25} - 36 q^{29} + 32 q^{39} + 12 q^{43} + 6 q^{49} + 24 q^{51} + 28 q^{57} - 14 q^{63} + 36 q^{65} - 60 q^{77} - 12 q^{79} - 36 q^{81} - 12 q^{91}+ \cdots + 44 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 + 8 * q^15 - 4 * q^21 + 12 * q^23 - 24 * q^25 - 36 * q^29 + 32 * q^39 + 12 * q^43 + 6 * q^49 + 24 * q^51 + 28 * q^57 - 14 * q^63 + 36 * q^65 - 60 * q^77 - 12 * q^79 - 36 * q^81 - 12 * q^91 + 16 * q^93 - 108 * q^95 + 44 * q^99

Introduction

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