LMFDB - Embedded newform 504.2.cx.a.425.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(185,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.185"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cx (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			425.3
Character	$\chi$	$=$	504.425
Dual form			504.2.cx.a.185.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.67230 - 0.451026i) q^{3} -0.203178 q^{5} +(-1.27132 + 2.32029i) q^{7} +(2.59315 + 1.50850i) q^{9} -4.46863i q^{11} +(1.25586 - 0.725070i) q^{13} +(0.339774 + 0.0916388i) q^{15} +(-1.60586 - 2.78143i) q^{17} +(-6.20156 - 3.58047i) q^{19} +(3.17254 - 3.30681i) q^{21} +1.26655i q^{23} -4.95872 q^{25} +(-3.65614 - 3.69224i) q^{27} +(-0.944433 - 0.545269i) q^{29} +(-5.60021 - 3.23328i) q^{31} +(-2.01547 + 7.47288i) q^{33} +(0.258305 - 0.471432i) q^{35} +(3.02855 - 5.24561i) q^{37} +(-2.42719 + 0.646106i) q^{39} +(-0.370687 - 0.642048i) q^{41} +(-4.69802 + 8.13721i) q^{43} +(-0.526872 - 0.306494i) q^{45} +(-0.0465845 - 0.0806866i) q^{47} +(-3.76748 - 5.89967i) q^{49} +(1.43098 + 5.37566i) q^{51} +(9.35260 - 5.39973i) q^{53} +0.907929i q^{55} +(8.75596 + 8.78468i) q^{57} +(5.16447 - 8.94512i) q^{59} +(-7.34727 + 4.24195i) q^{61} +(-6.79689 + 4.09907i) q^{63} +(-0.255163 + 0.147318i) q^{65} +(4.02663 - 6.97432i) q^{67} +(0.571249 - 2.11805i) q^{69} -15.6777i q^{71} +(0.984428 - 0.568360i) q^{73} +(8.29245 + 2.23651i) q^{75} +(10.3685 + 5.68108i) q^{77} +(5.86893 + 10.1653i) q^{79} +(4.44886 + 7.82353i) q^{81} +(-2.29931 + 3.98252i) q^{83} +(0.326276 + 0.565127i) q^{85} +(1.33344 + 1.33782i) q^{87} +(-3.52692 + 6.10881i) q^{89} +(0.0857700 + 3.83575i) q^{91} +(7.90692 + 7.93285i) q^{93} +(1.26002 + 0.727474i) q^{95} +(-3.17914 - 1.83548i) q^{97} +(6.74093 - 11.5878i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{9} + 8 q^{15} - 10 q^{21} + 48 q^{25} + 18 q^{27} + 18 q^{29} + 18 q^{31} + 12 q^{33} - 4 q^{39} - 6 q^{41} - 6 q^{43} - 18 q^{45} + 18 q^{47} - 12 q^{49} + 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61}+ \cdots - 64 q^{99}+O(q^{100}) $ 48 * q + 2 * q^9 + 8 * q^15 - 10 * q^21 + 48 * q^25 + 18 * q^27 + 18 * q^29 + 18 * q^31 + 12 * q^33 - 4 * q^39 - 6 * q^41 - 6 * q^43 - 18 * q^45 + 18 * q^47 - 12 * q^49 + 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 - 32 * q^63 - 36 * q^65 - 12 * q^77 + 6 * q^79 + 6 * q^81 - 54 * q^87 - 18 * q^89 + 6 * q^91 + 4 * q^93 - 54 * q^95 - 64 * q^99

Character values

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

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

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
$3$	−1.67230	−	0.451026i	−0.965501	−	0.260400i
$3$	−1.67230	−	0.451026i	−0.965501	−	0.260400i
$4$		0			0
$5$	−0.203178			−0.0908641			−0.0454320	−	0.998967i	$-0.514466\pi$
$5$	−0.203178			−0.0908641			−0.0454320	+	0.998967i	$0.514466\pi$
$6$		0			0
$7$	−1.27132	+	2.32029i	−0.480515	+	0.876987i
$7$	−1.27132	+	2.32029i	−0.480515	+	0.876987i
$8$		0			0
$9$	2.59315	+	1.50850i	0.864383	+	0.502833i
$10$		0			0
$11$		−	4.46863i		−	1.34734i	−0.739031	−	0.673672i	$-0.764716\pi$
$11$		−	4.46863i		−	1.34734i	0.739031	−	0.673672i	$-0.235284\pi$
$12$		0			0
$13$	1.25586	−	0.725070i	0.348312	−	0.201098i	−0.315629	−	0.948883i	$-0.602216\pi$
$13$	1.25586	−	0.725070i	0.348312	−	0.201098i	0.663942	+	0.747784i	$0.268882\pi$
$14$		0			0
$15$	0.339774	+	0.0916388i	0.0877293	+	0.0236610i
$16$		0			0
$17$	−1.60586	−	2.78143i	−0.389478	−	0.674596i	0.602901	−	0.797816i	$-0.294011\pi$
$17$	−1.60586	−	2.78143i	−0.389478	−	0.674596i	−0.992379	+	0.123220i	$0.960678\pi$
$18$		0			0
$19$	−6.20156	−	3.58047i	−1.42274	−	0.821417i	−0.426203	−	0.904627i	$-0.640149\pi$
$19$	−6.20156	−	3.58047i	−1.42274	−	0.821417i	−0.996532	+	0.0832106i	$0.973483\pi$
$20$		0			0
$21$	3.17254	−	3.30681i	0.692305	−	0.721605i
$22$		0			0
$23$			1.26655i			0.264095i	0.991243	+	0.132047i	$0.0421551\pi$
$23$			1.26655i			0.264095i	−0.991243	+	0.132047i	$0.957845\pi$
$24$		0			0
$25$	−4.95872			−0.991744
$26$		0			0
$27$	−3.65614	−	3.69224i	−0.703625	−	0.710572i
$28$		0			0
$29$	−0.944433	−	0.545269i	−0.175377	−	0.101254i	0.409742	−	0.912202i	$-0.365619\pi$
$29$	−0.944433	−	0.545269i	−0.175377	−	0.101254i	−0.585119	+	0.810948i	$0.698952\pi$
$30$		0			0
$31$	−5.60021	−	3.23328i	−1.00583	−	0.580715i	−0.0958603	−	0.995395i	$-0.530560\pi$
$31$	−5.60021	−	3.23328i	−1.00583	−	0.580715i	−0.909967	+	0.414680i	$0.863894\pi$
$32$		0			0
$33$	−2.01547	+	7.47288i	−0.350849	+	1.30086i
$34$		0			0
$35$	0.258305	−	0.471432i	0.0436616	−	0.0796866i
$36$		0			0
$37$	3.02855	−	5.24561i	0.497891	−	0.862373i	−0.502106	−	0.864806i	$-0.667441\pi$
$37$	3.02855	−	5.24561i	0.497891	−	0.862373i	0.999997	+	0.00243316i	$0.000774500\pi$
$38$		0			0
$39$	−2.42719	+	0.646106i	−0.388662	+	0.103460i
$40$		0			0
$41$	−0.370687	−	0.642048i	−0.0578915	−	0.100271i	0.835627	−	0.549297i	$-0.185104\pi$
$41$	−0.370687	−	0.642048i	−0.0578915	−	0.100271i	−0.893519	+	0.449026i	$0.851771\pi$
$42$		0			0
$43$	−4.69802	+	8.13721i	−0.716442	+	1.24091i	0.245959	+	0.969280i	$0.420897\pi$
$43$	−4.69802	+	8.13721i	−0.716442	+	1.24091i	−0.962401	+	0.271633i	$0.912436\pi$
$44$		0			0
$45$	−0.526872	−	0.306494i	−0.0785414	−	0.0456895i
$46$		0			0
$47$	−0.0465845	−	0.0806866i	−0.00679504	−	0.0117694i	0.862608	−	0.505873i	$-0.168830\pi$
$47$	−0.0465845	−	0.0806866i	−0.00679504	−	0.0117694i	−0.869403	+	0.494104i	$0.835496\pi$
$48$		0			0
$49$	−3.76748	−	5.89967i	−0.538211	−	0.842810i
$50$		0			0
$51$	1.43098	+	5.37566i	0.200377	+	0.752744i
$52$		0			0
$53$	9.35260	−	5.39973i	1.28468	−	0.741710i	0.306979	−	0.951716i	$-0.400682\pi$
$53$	9.35260	−	5.39973i	1.28468	−	0.741710i	0.977700	+	0.210007i	$0.0673486\pi$
$54$		0			0
$55$			0.907929i			0.122425i
$56$		0			0
$57$	8.75596	+	8.78468i	1.15976	+	1.16356i
$58$		0			0
$59$	5.16447	−	8.94512i	0.672356	−	1.16456i	−0.304878	−	0.952392i	$-0.598616\pi$
$59$	5.16447	−	8.94512i	0.672356	−	1.16456i	0.977234	−	0.212164i	$-0.0680511\pi$
$60$		0			0
$61$	−7.34727	+	4.24195i	−0.940722	+	0.543126i	−0.890186	−	0.455596i	$-0.849426\pi$
$61$	−7.34727	+	4.24195i	−0.940722	+	0.543126i	−0.0505352	+	0.998722i	$0.516093\pi$
$62$		0			0
$63$	−6.79689	+	4.09907i	−0.856327	+	0.516434i
$64$		0			0
$65$	−0.255163	+	0.147318i	−0.0316491	+	0.0182726i
$66$		0			0
$67$	4.02663	−	6.97432i	0.491931	−	0.852049i	−0.508026	−	0.861342i	$-0.669625\pi$
$67$	4.02663	−	6.97432i	0.491931	−	0.852049i	0.999957	+	0.00929244i	$0.00295792\pi$
$68$		0			0
$69$	0.571249	−	2.11805i	0.0687703	−	0.254983i
$70$		0			0
$71$		−	15.6777i		−	1.86060i	−0.366802	−	0.930299i	$-0.619547\pi$
$71$		−	15.6777i		−	1.86060i	0.366802	−	0.930299i	$-0.380453\pi$
$72$		0			0
$73$	0.984428	−	0.568360i	0.115219	−	0.0665215i	−0.441283	−	0.897368i	$-0.645477\pi$
$73$	0.984428	−	0.568360i	0.115219	−	0.0665215i	0.556502	+	0.830846i	$0.312143\pi$
$74$		0			0
$75$	8.29245	+	2.23651i	0.957529	+	0.258250i
$76$		0			0
$77$	10.3685	+	5.68108i	1.18160	+	0.647419i
$78$		0			0
$79$	5.86893	+	10.1653i	0.660306	+	1.14368i	0.980535	+	0.196344i	$0.0629068\pi$
$79$	5.86893	+	10.1653i	0.660306	+	1.14368i	−0.320229	+	0.947340i	$0.603760\pi$
$80$		0			0
$81$	4.44886	+	7.82353i	0.494317	+	0.869281i
$82$		0			0
$83$	−2.29931	+	3.98252i	−0.252382	+	0.437139i	−0.964181	−	0.265245i	$-0.914547\pi$
$83$	−2.29931	+	3.98252i	−0.252382	+	0.437139i	0.711799	+	0.702383i	$0.247881\pi$
$84$		0			0
$85$	0.326276	+	0.565127i	0.0353896	+	0.0612966i
$86$		0			0
$87$	1.33344	+	1.33782i	0.142960	+	0.143429i
$88$		0			0
$89$	−3.52692	+	6.10881i	−0.373853	+	0.647532i	−0.990155	−	0.139978i	$-0.955297\pi$
$89$	−3.52692	+	6.10881i	−0.373853	+	0.647532i	0.616302	+	0.787510i	$0.288630\pi$
$90$		0			0
$91$	0.0857700	+	3.83575i	0.00899114	+	0.402096i
$92$		0			0
$93$	7.90692	+	7.93285i	0.819909	+	0.822598i
$94$		0			0
$95$	1.26002	+	0.727474i	0.129276	+	0.0746373i
$96$		0			0
$97$	−3.17914	−	1.83548i	−0.322793	−	0.186365i	0.329844	−	0.944036i	$-0.393004\pi$
$97$	−3.17914	−	1.83548i	−0.322793	−	0.186365i	−0.652637	+	0.757671i	$0.726337\pi$
$98$		0			0
$99$	6.74093	−	11.5878i	0.677489	−	1.16462i
$100$		0			0
$101$	−13.1682			−1.31029			−0.655143	−	0.755505i	$-0.727391\pi$
$101$	−13.1682			−1.31029			−0.655143	+	0.755505i	$0.727391\pi$
$102$		0			0
$103$			13.5351i			1.33365i	0.745214	+	0.666826i	$0.232347\pi$
$103$			13.5351i			1.33365i	−0.745214	+	0.666826i	$0.767653\pi$
$104$		0			0
$105$	−0.644591	+	0.671872i	−0.0629057	+	0.0655680i
$106$		0			0
$107$	13.0095	+	7.51105i	1.25768	+	0.726121i	0.972623	−	0.232390i	$-0.0746545\pi$
$107$	13.0095	+	7.51105i	1.25768	+	0.726121i	0.285056	+	0.958511i	$0.407988\pi$
$108$		0			0
$109$	2.72560	+	4.72088i	0.261065	+	0.452178i	0.966525	−	0.256571i	$-0.0825928\pi$
$109$	2.72560	+	4.72088i	0.261065	+	0.452178i	−0.705460	+	0.708750i	$0.749260\pi$
$110$		0			0
$111$	−7.43055	+	7.40626i	−0.705277	+	0.702971i
$112$		0			0
$113$	−6.03027	+	3.48158i	−0.567280	+	0.327519i	−0.756062	−	0.654500i	$-0.772879\pi$
$113$	−6.03027	+	3.48158i	−0.567280	+	0.327519i	0.188782	+	0.982019i	$0.439546\pi$
$114$		0			0
$115$		−	0.257336i		−	0.0239967i
$116$		0			0
$117$	4.35039	+	0.0142461i	0.402194	+	0.00131705i
$118$		0			0
$119$	8.49529	−	0.189961i	0.778762	−	0.0174137i
$120$		0			0
$121$	−8.96868			−0.815335
$122$		0			0
$123$	0.330317	+	1.24088i	0.0297837	+	0.111887i
$124$		0			0
$125$	2.02340			0.180978
$126$		0			0
$127$	2.68718			0.238448			0.119224	−	0.992867i	$-0.461959\pi$
$127$	2.68718			0.238448			0.119224	+	0.992867i	$0.461959\pi$
$128$		0			0
$129$	11.5266	−	11.4889i	1.01486	−	1.01154i
$130$		0			0
$131$	6.13987			0.536443			0.268222	−	0.963357i	$-0.413564\pi$
$131$	6.13987			0.536443			0.268222	+	0.963357i	$0.413564\pi$
$132$		0			0
$133$	16.1919	−	9.83747i	1.40402	−	0.853017i
$134$		0			0
$135$	0.742849	+	0.750183i	0.0639342	+	0.0645654i
$136$		0			0
$137$			4.28221i			0.365854i	0.983127	+	0.182927i	$0.0585571\pi$
$137$			4.28221i			0.365854i	−0.983127	+	0.182927i	$0.941443\pi$
$138$		0			0
$139$	3.43981	−	1.98597i	0.291761	−	0.168448i	−0.346975	−	0.937874i	$-0.612791\pi$
$139$	3.43981	−	1.98597i	0.291761	−	0.168448i	0.638736	+	0.769426i	$0.279458\pi$
$140$		0			0
$141$	0.0415112	+	0.155943i	0.00349587	+	0.0131328i
$142$		0			0
$143$	−3.24007	−	5.61197i	−0.270948	−	0.469296i
$144$		0			0
$145$	0.191888	+	0.110787i	0.0159355	+	0.00920034i
$146$		0			0
$147$	3.63943	+	11.5652i	0.300175	+	0.953884i
$148$		0			0
$149$		−	4.63300i		−	0.379550i	−0.981828	−	0.189775i	$-0.939224\pi$
$149$		−	4.63300i		−	0.379550i	0.981828	−	0.189775i	$-0.0607759\pi$
$150$		0			0
$151$	−15.6948			−1.27722			−0.638612	−	0.769529i	$-0.720491\pi$
$151$	−15.6948			−1.27722			−0.638612	+	0.769529i	$0.720491\pi$
$152$		0			0
$153$	0.0315517	−	9.63511i	0.00255081	−	0.778953i
$154$		0			0
$155$	1.13784	+	0.656933i	0.0913936	+	0.0527661i
$156$		0			0
$157$	−6.55598	−	3.78510i	−0.523224	−	0.302084i	0.215029	−	0.976608i	$-0.431016\pi$
$157$	−6.55598	−	3.78510i	−0.523224	−	0.302084i	−0.738253	+	0.674524i	$0.764349\pi$
$158$		0			0
$159$	−18.0757	+	4.81167i	−1.43350	+	0.381591i
$160$		0			0
$161$	−2.93877	−	1.61020i	−0.231607	−	0.126901i
$162$		0			0
$163$	−3.97454	+	6.88410i	−0.311310	+	0.539204i	−0.978646	−	0.205552i	$-0.934101\pi$
$163$	−3.97454	+	6.88410i	−0.311310	+	0.539204i	0.667337	+	0.744756i	$0.267434\pi$
$164$		0			0
$165$	0.409500	−	1.51833i	0.0318795	−	0.118202i
$166$		0			0
$167$	1.72342	+	2.98506i	0.133363	+	0.230991i	0.924971	−	0.380038i	$-0.124089\pi$
$167$	1.72342	+	2.98506i	0.133363	+	0.230991i	−0.791608	+	0.611029i	$0.790756\pi$
$168$		0			0
$169$	−5.44855	+	9.43716i	−0.419119	+	0.725936i
$170$		0			0
$171$	−10.6804	−	18.6398i	−0.816753	−	1.42542i
$172$		0			0
$173$	−7.21800	−	12.5019i	−0.548775	−	0.950505i	−0.998359	−	0.0572675i	$-0.981761\pi$
$173$	−7.21800	−	12.5019i	−0.548775	−	0.950505i	0.449584	−	0.893238i	$-0.351572\pi$
$174$		0			0
$175$	6.30413	−	11.5057i	0.476548	−	0.869746i
$176$		0			0
$177$	−12.6710	+	12.6296i	−0.952411	+	0.949297i
$178$		0			0
$179$	−19.7102	+	11.3797i	−1.47321	+	0.850558i	−0.999545	−	0.0301471i	$-0.990402\pi$
$179$	−19.7102	+	11.3797i	−1.47321	+	0.850558i	−0.473665	+	0.880705i	$0.657069\pi$
$180$		0			0
$181$		−	8.95105i		−	0.665326i	−0.943046	−	0.332663i	$-0.892053\pi$
$181$		−	8.95105i		−	0.665326i	0.943046	−	0.332663i	$-0.107947\pi$
$182$		0			0
$183$	14.2000	−	3.77998i	1.04970	−	0.279424i
$184$		0			0
$185$	−0.615337	+	1.06579i	−0.0452404	+	0.0783587i
$186$		0			0
$187$	−12.4292	+	7.17600i	−0.908913	+	0.524761i
$188$		0			0
$189$	13.2152	−	3.78928i	0.961264	−	0.275629i
$190$		0			0
$191$	21.2572	−	12.2729i	1.53812	−	0.888033i	0.539170	−	0.842197i	$-0.318738\pi$
$191$	21.2572	−	12.2729i	1.53812	−	0.888033i	0.998949	−	0.0458359i	$-0.0145951\pi$
$192$		0			0
$193$	−2.28259	+	3.95356i	−0.164305	+	0.284584i	−0.936408	−	0.350913i	$-0.885871\pi$
$193$	−2.28259	+	3.95356i	−0.164305	+	0.284584i	0.772104	+	0.635497i	$0.219205\pi$
$194$		0			0
$195$	0.493153	−	0.131275i	0.0353154	−	0.00940078i
$196$		0			0
$197$		−	12.1315i		−	0.864333i	−0.901794	−	0.432166i	$-0.857749\pi$
$197$		−	12.1315i		−	0.864333i	0.901794	−	0.432166i	$-0.142251\pi$
$198$		0			0
$199$	12.8273	−	7.40587i	0.909306	−	0.524988i	0.0290981	−	0.999577i	$-0.490736\pi$
$199$	12.8273	−	7.40587i	0.909306	−	0.524988i	0.880208	+	0.474589i	$0.157403\pi$
$200$		0			0
$201$	−9.87932	+	9.84702i	−0.696834	+	0.694555i
$202$		0			0
$203$	2.46586	−	1.49814i	0.173070	−	0.105149i
$204$		0			0
$205$	0.0753154	+	0.130450i	0.00526026	+	0.00911104i
$206$		0			0
$207$	−1.91059	+	3.28436i	−0.132796	+	0.228279i
$208$		0			0
$209$	−15.9998	+	27.7125i	−1.10673	+	1.91691i
$210$		0			0
$211$	−3.77116	−	6.53184i	−0.259617	−	0.449670i	0.706522	−	0.707691i	$-0.250263\pi$
$211$	−3.77116	−	6.53184i	−0.259617	−	0.449670i	−0.966139	+	0.258021i	$0.916930\pi$
$212$		0			0
$213$	−7.07105	+	26.2177i	−0.484500	+	1.79641i
$214$		0			0
$215$	0.954536	−	1.65331i	0.0650988	−	0.112754i
$216$		0			0
$217$	14.6218	−	8.88356i	0.992594	−	0.603055i
$218$		0			0
$219$	−1.90260	+	0.506463i	−0.128566	+	0.0342236i
$220$		0			0
$221$	−4.03346	−	2.32872i	−0.271320	−	0.156647i
$222$		0			0
$223$	25.2846	+	14.5980i	1.69318	+	0.977557i	0.951924	+	0.306334i	$0.0991024\pi$
$223$	25.2846	+	14.5980i	1.69318	+	0.977557i	0.741255	+	0.671224i	$0.234231\pi$
$224$		0			0
$225$	−12.8587	−	7.48023i	−0.857247	−	0.498682i
$226$		0			0
$227$	29.1575			1.93525			0.967625	−	0.252391i	$-0.0812169\pi$
$227$	29.1575			1.93525			0.967625	+	0.252391i	$0.0812169\pi$
$228$		0			0
$229$		−	17.4121i		−	1.15062i	−0.817934	−	0.575312i	$-0.804881\pi$
$229$		−	17.4121i		−	1.15062i	0.817934	−	0.575312i	$-0.195119\pi$
$230$		0			0
$231$	−14.7769	−	14.1769i	−0.972250	−	0.932773i
$232$		0			0
$233$	14.3517	+	8.28596i	0.940212	+	0.542831i	0.890027	−	0.455908i	$-0.150686\pi$
$233$	14.3517	+	8.28596i	0.940212	+	0.542831i	0.0501850	+	0.998740i	$0.484019\pi$
$234$		0			0
$235$	0.00946495	+	0.0163938i	0.000617425	+	0.00106941i
$236$		0			0
$237$	−5.22978	−	19.6464i	−0.339711	−	1.27617i
$238$		0			0
$239$	−8.45527	+	4.88165i	−0.546926	+	0.315768i	−0.747881	−	0.663833i	$-0.768929\pi$
$239$	−8.45527	+	4.88165i	−0.546926	+	0.315768i	0.200955	+	0.979600i	$0.435595\pi$
$240$		0			0
$241$		−	10.8582i		−	0.699437i	−0.936855	−	0.349719i	$-0.886277\pi$
$241$		−	10.8582i		−	0.699437i	0.936855	−	0.349719i	$-0.113723\pi$
$242$		0			0
$243$	−3.91119	−	15.0898i	−0.250903	−	0.968012i
$244$		0			0
$245$	0.765469	+	1.19869i	0.0489040	+	0.0765812i
$246$		0			0
$247$	−10.3844			−0.660741
$248$		0			0
$249$	5.64135	−	5.62291i	0.357506	−	0.356337i
$250$		0			0
$251$	−27.4155			−1.73045			−0.865224	−	0.501385i	$-0.832824\pi$
$251$	−27.4155			−1.73045			−0.865224	+	0.501385i	$0.832824\pi$
$252$		0			0
$253$	5.65976			0.355826
$254$		0			0
$255$	−0.290743	−	1.09222i	−0.0182070	−	0.0683974i
$256$		0			0
$257$	−27.3169			−1.70398			−0.851989	−	0.523559i	$-0.824604\pi$
$257$	−27.3169			−1.70398			−0.851989	+	0.523559i	$0.824604\pi$
$258$		0			0
$259$	8.32106	+	13.6960i	0.517045	+	0.851027i
$260$		0			0
$261$	−1.62652	−	2.83864i	−0.100679	−	0.175708i
$262$		0			0
$263$		−	13.8160i		−	0.851928i	−0.904740	−	0.425964i	$-0.859935\pi$
$263$		−	13.8160i		−	0.851928i	0.904740	−	0.425964i	$-0.140065\pi$
$264$		0			0
$265$	−1.90025	+	1.09711i	−0.116731	+	0.0673948i
$266$		0			0
$267$	8.65329	−	8.62500i	0.529573	−	0.527841i
$268$		0			0
$269$	10.7471	+	18.6145i	0.655260	+	1.13494i	0.981828	+	0.189770i	$0.0607744\pi$
$269$	10.7471	+	18.6145i	0.655260	+	1.13494i	−0.326568	+	0.945174i	$0.605892\pi$
$270$		0			0
$271$	27.2614	+	15.7394i	1.65601	+	0.956101i	0.974527	+	0.224271i	$0.0720002\pi$
$271$	27.2614	+	15.7394i	1.65601	+	0.956101i	0.681488	+	0.731829i	$0.261333\pi$
$272$		0			0
$273$	1.58659	−	6.45319i	0.0960249	−	0.390565i
$274$		0			0
$275$			22.1587i			1.33622i
$276$		0			0
$277$	−11.8408			−0.711445			−0.355722	−	0.934592i	$-0.615765\pi$
$277$	−11.8408			−0.711445			−0.355722	+	0.934592i	$0.615765\pi$
$278$		0			0
$279$	−9.64478	−	16.8323i	−0.577418	−	1.00772i
$280$		0			0
$281$	−19.4588	−	11.2346i	−1.16082	−	0.670198i	−0.209317	−	0.977848i	$-0.567124\pi$
$281$	−19.4588	−	11.2346i	−1.16082	−	0.670198i	−0.951500	+	0.307650i	$0.900457\pi$
$282$		0			0
$283$	−1.17672	−	0.679378i	−0.0699486	−	0.0403848i	0.464618	−	0.885511i	$-0.346192\pi$
$283$	−1.17672	−	0.679378i	−0.0699486	−	0.0403848i	−0.534566	+	0.845126i	$0.679525\pi$
$284$		0			0
$285$	−1.77902	−	1.78486i	−0.105380	−	0.105726i
$286$		0			0
$287$	1.96100	−	0.0438493i	0.115754	−	0.00258834i
$288$		0			0
$289$	3.34242	−	5.78925i	0.196613	−	0.340544i
$290$		0			0
$291$	4.48862	+	4.50334i	0.263128	+	0.263991i
$292$		0			0
$293$	−8.10060	−	14.0307i	−0.473242	−	0.819680i	0.526289	−	0.850306i	$-0.323583\pi$
$293$	−8.10060	−	14.0307i	−0.473242	−	0.819680i	−0.999531	+	0.0306263i	$0.990250\pi$
$294$		0			0
$295$	−1.04931	+	1.81745i	−0.0610931	+	0.105816i
$296$		0			0
$297$	−16.4993	+	16.3380i	−0.957384	+	0.948025i
$298$		0			0
$299$	0.918339	+	1.59061i	0.0531089	+	0.0919873i
$300$		0			0
$301$	−12.9080	−	21.2458i	−0.744003	−	1.22459i
$302$		0			0
$303$	22.0211	+	5.93921i	1.26508	+	0.341199i
$304$		0			0
$305$	1.49281	−	0.861872i	0.0854778	−	0.0493506i
$306$		0			0
$307$		−	9.22930i		−	0.526744i	−0.964694	−	0.263372i	$-0.915165\pi$
$307$		−	9.22930i		−	0.526744i	0.964694	−	0.263372i	$-0.0848346\pi$
$308$		0			0
$309$	6.10468	−	22.6347i	0.347283	−	1.28764i
$310$		0			0
$311$	−0.313334	+	0.542711i	−0.0177676	+	0.0307743i	−0.874772	−	0.484534i	$-0.838989\pi$
$311$	−0.313334	+	0.542711i	−0.0177676	+	0.0307743i	0.857005	+	0.515308i	$0.172323\pi$
$312$		0			0
$313$	−4.43528	+	2.56071i	−0.250697	+	0.144740i	−0.620083	−	0.784536i	$-0.712901\pi$
$313$	−4.43528	+	2.56071i	−0.250697	+	0.144740i	0.369387	+	0.929276i	$0.379568\pi$
$314$		0			0
$315$	1.38098	−	0.832841i	0.0778094	−	0.0469253i
$316$		0			0
$317$	−3.62803	+	2.09464i	−0.203770	+	0.117647i	−0.598413	−	0.801188i	$-0.704202\pi$
$317$	−3.62803	+	2.09464i	−0.203770	+	0.117647i	0.394643	+	0.918835i	$0.370868\pi$
$318$		0			0
$319$	−2.43661	+	4.22033i	−0.136424	+	0.236293i
$320$		0			0
$321$	−18.3681	−	18.4283i	−1.02521	−	1.02857i
$322$		0			0
$323$			22.9990i			1.27970i
$324$		0			0
$325$	−6.22744	+	3.59542i	−0.345436	+	0.199438i
$326$		0			0
$327$	−2.42877	−	9.12403i	−0.134311	−	0.504560i
$328$		0			0
$329$	0.246440	−	0.00551057i	0.0135867	−	0.000303808i
$330$		0			0
$331$	−12.9710	−	22.4664i	−0.712949	−	1.23486i	−0.963745	−	0.266824i	$-0.914026\pi$
$331$	−12.9710	−	22.4664i	−0.712949	−	1.23486i	0.250797	−	0.968040i	$-0.419307\pi$
$332$		0			0
$333$	15.7665	−	9.03408i	0.863999	−	0.495065i
$334$		0			0
$335$	−0.818123	+	1.41703i	−0.0446989	+	0.0774207i
$336$		0			0
$337$	8.40130	+	14.5515i	0.457648	+	0.792669i	0.998836	−	0.0482321i	$-0.0153587\pi$
$337$	8.40130	+	14.5515i	0.457648	+	0.792669i	−0.541188	+	0.840901i	$0.682025\pi$
$338$		0			0
$339$	11.6547	−	3.10242i	0.632996	−	0.168500i
$340$		0			0
$341$	−14.4484	+	25.0253i	−0.782423	+	1.35520i
$342$		0			0
$343$	18.4786	−	1.24124i	0.997752	−	0.0670206i
$344$		0			0
$345$	−0.116065	+	0.430342i	−0.00624875	+	0.0231688i
$346$		0			0
$347$	−25.0574	−	14.4669i	−1.34515	−	0.776624i	−0.357594	−	0.933877i	$-0.616403\pi$
$347$	−25.0574	−	14.4669i	−1.34515	−	0.776624i	−0.987558	+	0.157253i	$0.949736\pi$
$348$		0			0
$349$	20.7481	+	11.9789i	1.11062	+	0.641217i	0.938990	−	0.343944i	$-0.111763\pi$
$349$	20.7481	+	11.9789i	1.11062	+	0.641217i	0.171630	+	0.985161i	$0.445097\pi$
$350$		0			0
$351$	−7.26872	−	1.98597i	−0.387976	−	0.106003i
$352$		0			0
$353$	15.5894			0.829743			0.414871	−	0.909880i	$-0.363827\pi$
$353$	15.5894			0.829743			0.414871	+	0.909880i	$0.363827\pi$
$354$		0			0
$355$			3.18536i			0.169062i
$356$		0			0
$357$	−14.2923	−	3.51393i	−0.756430	−	0.185977i
$358$		0			0
$359$	−11.7053	−	6.75809i	−0.617785	−	0.356678i	0.158221	−	0.987404i	$-0.449424\pi$
$359$	−11.7053	−	6.75809i	−0.617785	−	0.356678i	−0.776006	+	0.630726i	$0.782757\pi$
$360$		0			0
$361$	16.1396	+	27.9545i	0.849451	+	1.47129i
$362$		0			0
$363$	14.9983	+	4.04511i	0.787207	+	0.212313i
$364$		0			0
$365$	−0.200014	+	0.115478i	−0.0104692	+	0.00604442i
$366$		0			0
$367$		−	19.1785i		−	1.00111i	−0.865705	−	0.500554i	$-0.833130\pi$
$367$		−	19.1785i		−	1.00111i	0.865705	−	0.500554i	$-0.166870\pi$
$368$		0			0
$369$	0.00728320	−	2.22411i	0.000379148	−	0.115782i
$370$		0			0
$371$	0.638745	+	28.5655i	0.0331620	+	1.48305i
$372$		0			0
$373$	2.53539			0.131278			0.0656388	−	0.997843i	$-0.479091\pi$
$373$	2.53539			0.131278			0.0656388	+	0.997843i	$0.479091\pi$
$374$		0			0
$375$	−3.38372	−	0.912605i	−0.174734	−	0.0471267i
$376$		0			0
$377$	−1.58143			−0.0814479
$378$		0			0
$379$	6.11511			0.314112			0.157056	−	0.987590i	$-0.449800\pi$
$379$	6.11511			0.314112			0.157056	+	0.987590i	$0.449800\pi$
$380$		0			0
$381$	−4.49375	−	1.21199i	−0.230222	−	0.0620920i
$382$		0			0
$383$	5.67449			0.289953			0.144976	−	0.989435i	$-0.453689\pi$
$383$	5.67449			0.289953			0.144976	+	0.989435i	$0.453689\pi$
$384$		0			0
$385$	−2.10666	−	1.15427i	−0.107365	−	0.0588271i
$386$		0			0
$387$	−24.4577	+	14.0141i	−1.24325	+	0.712374i
$388$		0			0
$389$			7.88653i			0.399863i	0.979810	+	0.199932i	$0.0640720\pi$
$389$			7.88653i			0.399863i	−0.979810	+	0.199932i	$0.935928\pi$
$390$		0			0
$391$	3.52283	−	2.03391i	0.178157	−	0.102859i
$392$		0			0
$393$	−10.2677	−	2.76925i	−0.517936	−	0.139690i
$394$		0			0
$395$	−1.19244	−	2.06536i	−0.0599981	−	0.103920i
$396$		0			0
$397$	10.2548	+	5.92061i	0.514674	+	0.297147i	0.734753	−	0.678335i	$-0.237298\pi$
$397$	10.2548	+	5.92061i	0.514674	+	0.297147i	−0.220079	+	0.975482i	$0.570632\pi$
$398$		0			0
$399$	−31.5146	+	9.14818i	−1.57771	+	0.457982i
$400$		0			0
$401$		−	38.1732i		−	1.90628i	−0.302534	−	0.953139i	$-0.597832\pi$
$401$		−	38.1732i		−	1.90628i	0.302534	−	0.953139i	$-0.402168\pi$
$402$		0			0
$403$	−9.37742			−0.467123
$404$		0			0
$405$	−0.903911	−	1.58957i	−0.0449157	−	0.0789865i
$406$		0			0
$407$	−23.4407	−	13.5335i	−1.16191	−	0.670831i
$408$		0			0
$409$	11.2828	+	6.51411i	0.557897	+	0.322102i	0.752301	−	0.658820i	$-0.228944\pi$
$409$	11.2828	+	6.51411i	0.557897	+	0.322102i	−0.194404	+	0.980922i	$0.562277\pi$
$410$		0			0
$411$	1.93139	−	7.16112i	0.0952684	−	0.353232i
$412$		0			0
$413$	14.1896	+	23.3552i	0.698222	+	1.14923i
$414$		0			0
$415$	0.467170	−	0.809162i	0.0229325	−	0.0397202i
$416$		0			0
$417$	−6.64811	+	1.76969i	−0.325559	+	0.0866622i
$418$		0			0
$419$	15.1454	+	26.2325i	0.739899	+	1.28154i	0.952540	+	0.304412i	$0.0984601\pi$
$419$	15.1454	+	26.2325i	0.739899	+	1.28154i	−0.212641	+	0.977130i	$0.568207\pi$
$420$		0			0
$421$	−3.20295	+	5.54767i	−0.156102	+	0.270377i	−0.933460	−	0.358682i	$-0.883226\pi$
$421$	−3.20295	+	5.54767i	−0.156102	+	0.270377i	0.777358	+	0.629059i	$0.216560\pi$
$422$		0			0
$423$	0.000915285	−	0.279505i	4.45027e−5	−	0.0135900i
$424$		0			0
$425$	7.96301	+	13.7923i	0.386263	+	0.669027i
$426$		0			0
$427$	−0.501789	−	22.4407i	−0.0242833	−	1.08598i
$428$		0			0
$429$	2.88721	+	10.8462i	0.139396	+	0.523661i
$430$		0			0
$431$	10.0071	−	5.77758i	0.482023	−	0.278296i	−0.239236	−	0.970961i	$-0.576897\pi$
$431$	10.0071	−	5.77758i	0.482023	−	0.278296i	0.721259	+	0.692665i	$0.243564\pi$
$432$		0			0
$433$		−	0.696999i		−	0.0334956i	−0.999860	−	0.0167478i	$-0.994669\pi$
$433$		−	0.696999i		−	0.0334956i	0.999860	−	0.0167478i	$-0.00533125\pi$
$434$		0			0
$435$	−0.270926	−	0.271815i	−0.0129899	−	0.0130325i
$436$		0			0
$437$	4.53486	−	7.85460i	0.216932	−	0.375737i
$438$		0			0
$439$	20.4771	−	11.8224i	0.977316	−	0.564254i	0.0758575	−	0.997119i	$-0.475831\pi$
$439$	20.4771	−	11.8224i	0.977316	−	0.564254i	0.901459	+	0.432865i	$0.142497\pi$
$440$		0			0
$441$	−0.869976	−	20.9820i	−0.0414274	−	0.999142i
$442$		0			0
$443$	11.3308	−	6.54184i	0.538343	−	0.310812i	−0.206064	−	0.978538i	$-0.566066\pi$
$443$	11.3308	−	6.54184i	0.538343	−	0.310812i	0.744407	+	0.667726i	$0.232732\pi$
$444$		0			0
$445$	0.716594	−	1.24118i	0.0339698	−	0.0588374i
$446$		0			0
$447$	−2.08961	+	7.74775i	−0.0988349	+	0.366456i
$448$		0			0
$449$		−	11.5463i		−	0.544906i	−0.962169	−	0.272453i	$-0.912165\pi$
$449$		−	11.5463i		−	0.544906i	0.962169	−	0.272453i	$-0.0878348\pi$
$450$		0			0
$451$	−2.86908	+	1.65646i	−0.135100	+	0.0779998i
$452$		0			0
$453$	26.2463	+	7.07876i	1.23316	+	0.332589i
$454$		0			0
$455$	−0.0174266	−	0.779341i	−0.000816971	−	0.0365361i
$456$		0			0
$457$	5.51833	+	9.55803i	0.258137	+	0.447106i	0.965743	−	0.259501i	$-0.0835582\pi$
$457$	5.51833	+	9.55803i	0.258137	+	0.447106i	−0.707606	+	0.706607i	$0.750225\pi$
$458$		0			0
$459$	−4.39845	+	16.0985i	−0.205302	+	0.751415i
$460$		0			0
$461$	−6.69369	+	11.5938i	−0.311756	+	0.539978i	−0.978743	−	0.205092i	$-0.934251\pi$
$461$	−6.69369	+	11.5938i	−0.311756	+	0.539978i	0.666986	+	0.745070i	$0.267584\pi$
$462$		0			0
$463$	10.6622	+	18.4675i	0.495515	+	0.858258i	0.999987	−	0.00517079i	$-0.00164592\pi$
$463$	10.6622	+	18.4675i	0.495515	+	0.858258i	−0.504471	+	0.863428i	$0.668313\pi$
$464$		0			0
$465$	−1.60651	−	1.61178i	−0.0745003	−	0.0747447i
$466$		0			0
$467$	7.97308	−	13.8098i	0.368950	−	0.639041i	−0.620451	−	0.784245i	$-0.713051\pi$
$467$	7.97308	−	13.8098i	0.368950	−	0.639041i	0.989402	+	0.145204i	$0.0463839\pi$
$468$		0			0
$469$	11.0633	+	18.2096i	0.510856	+	0.840839i
$470$		0			0
$471$	9.25636	+	9.28673i	0.426511	+	0.427910i
$472$		0			0
$473$	36.3622	+	20.9937i	1.67194	+	0.965293i
$474$		0			0
$475$	30.7518	+	17.7546i	1.41099	+	0.814635i
$476$		0			0
$477$	32.3982	+	0.106093i	1.48341	+	0.00485767i
$478$		0			0
$479$	−30.7187			−1.40357			−0.701787	−	0.712387i	$-0.747614\pi$
$479$	−30.7187			−1.40357			−0.701787	+	0.712387i	$0.747614\pi$
$480$		0			0
$481$		−	8.78365i		−	0.400500i
$482$		0			0
$483$	4.18825	+	4.01819i	0.190572	+	0.182834i
$484$		0			0
$485$	0.645933	+	0.372930i	0.0293303	+	0.0169339i
$486$		0			0
$487$	0.423250	+	0.733091i	0.0191793	+	0.0332195i	0.875456	−	0.483298i	$-0.160561\pi$
$487$	0.423250	+	0.733091i	0.0191793	+	0.0332195i	−0.856276	+	0.516518i	$0.827228\pi$
$488$		0			0
$489$	9.75151	−	9.71963i	0.440979	−	0.439537i
$490$		0			0
$491$	1.78204	−	1.02886i	0.0804225	−	0.0464319i	−0.459249	−	0.888307i	$-0.651882\pi$
$491$	1.78204	−	1.02886i	0.0804225	−	0.0464319i	0.539672	+	0.841875i	$0.318548\pi$
$492$		0			0
$493$			3.50250i			0.157745i
$494$		0			0
$495$	−1.36961	+	2.35440i	−0.0615594	+	0.105822i
$496$		0			0
$497$	36.3767	+	19.9314i	1.63172	+	0.894045i
$498$		0			0
$499$	−41.1863			−1.84375			−0.921877	−	0.387483i	$-0.873345\pi$
$499$	−41.1863			−1.84375			−0.921877	+	0.387483i	$0.873345\pi$
$500$		0			0
$501$	−1.53574	−	5.76921i	−0.0686116	−	0.257749i
$502$		0			0
$503$	1.48781			0.0663383			0.0331692	−	0.999450i	$-0.489440\pi$
$503$	1.48781			0.0663383			0.0331692	+	0.999450i	$0.489440\pi$
$504$		0			0
$505$	2.67549			0.119058
$506$		0			0
$507$	13.3680	−	13.3243i	0.593694	−	0.591753i
$508$		0			0
$509$	16.7882			0.744123			0.372062	−	0.928208i	$-0.378651\pi$
$509$	16.7882			0.744123			0.372062	+	0.928208i	$0.378651\pi$
$510$		0			0
$511$	0.0672325	+	3.00673i	0.00297419	+	0.133010i
$512$		0			0
$513$	9.45383	+	35.9884i	0.417397	+	1.58892i
$514$		0			0
$515$		−	2.75004i		−	0.121181i
$516$		0			0
$517$	−0.360559	+	0.208169i	−0.0158574	+	0.00915526i
$518$		0			0
$519$	6.43193	+	24.1625i	0.282330	+	1.06061i
$520$		0			0
$521$	1.00777	+	1.74551i	0.0441512	+	0.0764722i	0.887257	−	0.461276i	$-0.152608\pi$
$521$	1.00777	+	1.74551i	0.0441512	+	0.0764722i	−0.843105	+	0.537749i	$0.819275\pi$
$522$		0			0
$523$	−37.4865	−	21.6429i	−1.63917	−	0.946376i	−0.981119	−	0.193403i	$-0.938047\pi$
$523$	−37.4865	−	21.6429i	−1.63917	−	0.946376i	−0.658052	−	0.752973i	$-0.728619\pi$
$524$		0			0
$525$	−15.7317	+	16.3975i	−0.686589	+	0.715647i
$526$		0			0
$527$			20.7688i			0.904704i
$528$		0			0
$529$	21.3958			0.930254
$530$		0			0
$531$	26.8860	−	15.4054i	1.16675	−	0.668539i
$532$		0			0
$533$	−0.931059	−	0.537547i	−0.0403286	−	0.0232837i
$534$		0			0
$535$	−2.64325	−	1.52608i	−0.114278	−	0.0659783i
$536$		0			0
$537$	38.0939	−	10.1404i	1.64387	−	0.437590i
$538$		0			0
$539$	−26.3635	+	16.8355i	−1.13556	+	0.725155i
$540$		0			0
$541$	12.3502	−	21.3912i	0.530977	−	0.919679i	−0.468370	−	0.883533i	$-0.655158\pi$
$541$	12.3502	−	21.3912i	0.530977	−	0.919679i	0.999347	−	0.0361463i	$-0.0115082\pi$
$542$		0			0
$543$	−4.03716	+	14.9688i	−0.173251	+	0.642373i
$544$		0			0
$545$	−0.553783	−	0.959181i	−0.0237215	−	0.0410868i
$546$		0			0
$547$	−5.52320	+	9.56646i	−0.236155	+	0.409032i	−0.959608	−	0.281342i	$-0.909221\pi$
$547$	−5.52320	+	9.56646i	−0.236155	+	0.409032i	0.723453	+	0.690374i	$0.242554\pi$
$548$		0			0
$549$	−25.4516	−	0.0833452i	−1.08625	−	0.00355709i
$550$		0			0
$551$	3.90464	+	6.76304i	0.166343	+	0.288115i
$552$		0			0
$553$	−31.0477	+	0.694248i	−1.32028	+	0.0295224i
$554$		0			0
$555$	1.50973	−	1.50479i	0.0640843	−	0.0638748i
$556$		0			0
$557$	22.3351	−	12.8952i	0.946369	−	0.546386i	0.0544176	−	0.998518i	$-0.482670\pi$
$557$	22.3351	−	12.8952i	0.946369	−	0.546386i	0.891951	+	0.452132i	$0.149336\pi$
$558$		0			0
$559$			13.6256i			0.576300i
$560$		0			0
$561$	24.0219	−	6.39450i	1.01420	−	0.269976i
$562$		0			0
$563$	−18.9859	+	32.8846i	−0.800161	+	1.38592i	0.119349	+	0.992852i	$0.461919\pi$
$563$	−18.9859	+	32.8846i	−0.800161	+	1.38592i	−0.919510	+	0.393067i	$0.871414\pi$
$564$		0			0
$565$	1.22522	−	0.707381i	0.0515454	−	0.0297597i
$566$		0			0
$567$	−23.8088	+	0.376393i	−0.999875	+	0.0158070i
$568$		0			0
$569$	19.8834	−	11.4797i	0.833555	−	0.481253i	−0.0215131	−	0.999769i	$-0.506848\pi$
$569$	19.8834	−	11.4797i	0.833555	−	0.481253i	0.855068	+	0.518515i	$0.173515\pi$
$570$		0			0
$571$	5.91228	−	10.2404i	0.247421	−	0.428546i	−0.715388	−	0.698727i	$-0.753750\pi$
$571$	5.91228	−	10.2404i	0.247421	−	0.428546i	0.962810	+	0.270181i	$0.0870836\pi$
$572$		0			0
$573$	−41.0838	+	10.9363i	−1.71630	+	0.456870i
$574$		0			0
$575$		−	6.28048i		−	0.261914i
$576$		0			0
$577$	−22.4185	+	12.9433i	−0.933293	+	0.538837i	−0.887852	−	0.460130i	$-0.847803\pi$
$577$	−22.4185	+	12.9433i	−0.933293	+	0.538837i	−0.0454415	+	0.998967i	$0.514469\pi$
$578$		0			0
$579$	5.60033	−	5.58202i	0.232742	−	0.231981i
$580$		0			0
$581$	−6.31743	−	10.3981i	−0.262091	−	0.431387i
$582$		0			0
$583$	−24.1294	−	41.7933i	−0.999338	−	1.73090i
$584$		0			0
$585$	−0.883906	−	0.00289449i	−0.0365450	−	0.000119672i
$586$		0			0
$587$	−1.28769	+	2.23034i	−0.0531487	+	0.0920562i	−0.891376	−	0.453265i	$-0.850259\pi$
$587$	−1.28769	+	2.23034i	−0.0531487	+	0.0920562i	0.838227	+	0.545321i	$0.183592\pi$
$588$		0			0
$589$	23.1534	+	40.1028i	0.954018	+	1.65241i
$590$		0			0
$591$	−5.47162	+	20.2874i	−0.225072	+	0.834514i
$592$		0			0
$593$	11.0904	−	19.2092i	0.455430	−	0.788828i	−0.543283	−	0.839550i	$-0.682819\pi$
$593$	11.0904	−	19.2092i	0.455430	−	0.788828i	0.998713	+	0.0507220i	$0.0161523\pi$
$594$		0			0
$595$	−1.72606	+	0.0385959i	−0.0707615	+	0.00158228i
$596$		0			0
$597$	−24.7914	+	6.59934i	−1.01464	+	0.270093i
$598$		0			0
$599$	−22.0096	−	12.7072i	−0.899287	−	0.519204i	−0.0223184	−	0.999751i	$-0.507105\pi$
$599$	−22.0096	−	12.7072i	−0.899287	−	0.519204i	−0.876969	+	0.480547i	$0.840438\pi$
$600$		0			0
$601$	−3.04486	−	1.75795i	−0.124203	−	0.0717084i	0.436612	−	0.899650i	$-0.356178\pi$
$601$	−3.04486	−	1.75795i	−0.124203	−	0.0717084i	−0.560814	+	0.827942i	$0.689512\pi$
$602$		0			0
$603$	20.9624	−	12.0113i	0.853656	−	0.489138i
$604$		0			0
$605$	1.82224			0.0740847
$606$		0			0
$607$			32.7626i			1.32979i	0.746936	+	0.664896i	$0.231524\pi$
$607$			32.7626i			1.32979i	−0.746936	+	0.664896i	$0.768476\pi$
$608$		0			0
$609$	−4.79935	+	1.39317i	−0.194480	+	0.0564543i
$610$		0			0
$611$	−0.117007	−	0.0675539i	−0.00473359	−	0.00273294i
$612$		0			0
$613$	−0.757167	−	1.31145i	−0.0305817	−	0.0529691i	0.850329	−	0.526251i	$-0.176403\pi$
$613$	−0.757167	−	1.31145i	−0.0305817	−	0.0529691i	−0.880911	+	0.473282i	$0.843069\pi$
$614$		0			0
$615$	−0.0671133	−	0.252121i	−0.00270627	−	0.0101665i
$616$		0			0
$617$	−6.52621	+	3.76791i	−0.262735	+	0.151690i	−0.625582	−	0.780159i	$-0.715138\pi$
$617$	−6.52621	+	3.76791i	−0.262735	+	0.151690i	0.362846	+	0.931849i	$0.381805\pi$
$618$		0			0
$619$		−	32.6456i		−	1.31214i	−0.754702	−	0.656068i	$-0.772218\pi$
$619$		−	32.6456i		−	1.31214i	0.754702	−	0.656068i	$-0.227782\pi$
$620$		0			0
$621$	4.67641	−	4.63070i	0.187658	−	0.185823i
$622$		0			0
$623$	−9.69033	−	15.9497i	−0.388235	−	0.639013i
$624$		0			0
$625$	24.3825			0.975299
$626$		0			0
$627$	39.2555	−	39.1272i	1.56771	−	1.56259i
$628$		0			0
$629$	−19.4537			−0.775672
$630$		0			0
$631$	−6.79887			−0.270659			−0.135329	−	0.990801i	$-0.543209\pi$
$631$	−6.79887			−0.270659			−0.135329	+	0.990801i	$0.543209\pi$
$632$		0			0
$633$	3.36046	+	12.6241i	0.133566	+	0.501761i
$634$		0			0
$635$	−0.545976			−0.0216664
$636$		0			0
$637$	−9.00908	−	4.67746i	−0.356953	−	0.185328i
$638$		0			0
$639$	23.6498	−	40.6546i	0.935570	−	1.60827i
$640$		0			0
$641$		−	32.4927i		−	1.28338i	−0.766962	−	0.641692i	$-0.778233\pi$
$641$		−	32.4927i		−	1.28338i	0.766962	−	0.641692i	$-0.221767\pi$
$642$		0			0
$643$	20.5970	−	11.8917i	0.812267	−	0.468963i	−0.0354756	−	0.999371i	$-0.511295\pi$
$643$	20.5970	−	11.8917i	0.812267	−	0.468963i	0.847742	+	0.530408i	$0.177961\pi$
$644$		0			0
$645$	−2.34195	+	2.33430i	−0.0922143	+	0.0919128i
$646$		0			0
$647$	−11.1964	−	19.3928i	−0.440177	−	0.762410i	0.557525	−	0.830160i	$-0.311751\pi$
$647$	−11.1964	−	19.3928i	−0.440177	−	0.762410i	−0.997702	+	0.0677505i	$0.978418\pi$
$648$		0			0
$649$	−39.9725	−	23.0781i	−1.56906	−	0.905895i
$650$		0			0
$651$	−28.4587	+	8.26111i	−1.11539	+	0.323778i
$652$		0			0
$653$		−	40.7245i		−	1.59367i	−0.604196	−	0.796836i	$-0.706506\pi$
$653$		−	40.7245i		−	1.59367i	0.604196	−	0.796836i	$-0.293494\pi$
$654$		0			0
$655$	−1.24749			−0.0487434
$656$		0			0
$657$	3.41014	+	0.0111671i	0.133042	+	0.000435668i
$658$		0			0
$659$	−24.8786	−	14.3637i	−0.969134	−	0.559530i	−0.0701619	−	0.997536i	$-0.522352\pi$
$659$	−24.8786	−	14.3637i	−0.969134	−	0.559530i	−0.898972	+	0.438006i	$0.855685\pi$
$660$		0			0
$661$	32.3398	+	18.6714i	1.25787	+	0.726234i	0.972661	−	0.232230i	$-0.0746023\pi$
$661$	32.3398	+	18.6714i	1.25787	+	0.726234i	0.285213	+	0.958464i	$0.407936\pi$
$662$		0			0
$663$	5.69483	+	5.71351i	0.221169	+	0.221894i
$664$		0			0
$665$	−3.28985	+	1.99876i	−0.127575	+	0.0775086i
$666$		0			0
$667$	0.690612	−	1.19617i	0.0267406	−	0.0463161i
$668$		0			0
$669$	−35.6992	−	35.8163i	−1.38021	−	1.38474i
$670$		0			0
$671$	18.9557	+	32.8323i	0.731777	+	1.26748i
$672$		0			0
$673$	−16.5131	+	28.6015i	−0.636532	+	1.10251i	0.349656	+	0.936878i	$0.386298\pi$
$673$	−16.5131	+	28.6015i	−0.636532	+	1.10251i	−0.986188	+	0.165628i	$0.947035\pi$
$674$		0			0
$675$	18.1298	+	18.3088i	0.697816	+	0.704705i
$676$		0			0
$677$	−10.4381	−	18.0793i	−0.401169	−	0.694845i	0.592698	−	0.805424i	$-0.298063\pi$
$677$	−10.4381	−	18.0793i	−0.401169	−	0.694845i	−0.993867	+	0.110580i	$0.964729\pi$
$678$		0			0
$679$	8.30056	−	5.04304i	0.318546	−	0.193534i
$680$		0			0
$681$	−48.7600	−	13.1508i	−1.86849	−	0.503940i
$682$		0			0
$683$	−1.17377	+	0.677674i	−0.0449129	+	0.0259305i	−0.522288	−	0.852769i	$-0.674922\pi$
$683$	−1.17377	+	0.677674i	−0.0449129	+	0.0259305i	0.477375	+	0.878699i	$0.341588\pi$
$684$		0			0
$685$		−	0.870051i		−	0.0332430i
$686$		0			0
$687$	−7.85331	+	29.1182i	−0.299623	+	1.11093i
$688$		0			0
$689$	7.83036	−	13.5626i	0.298313	−	0.516693i
$690$		0			0
$691$	−9.62041	+	5.55435i	−0.365978	+	0.211297i	−0.671700	−	0.740823i	$-0.734436\pi$
$691$	−9.62041	+	5.55435i	−0.365978	+	0.211297i	0.305722	+	0.952121i	$0.401102\pi$
$692$		0			0
$693$	18.3172	+	30.3728i	0.695814	+	1.15377i
$694$		0			0
$695$	−0.698894	+	0.403507i	−0.0265106	+	0.0153059i
$696$		0			0
$697$	−1.19054	+	2.06208i	−0.0450950	+	0.0781068i
$698$		0			0
$699$	−20.2631	−	20.3296i	−0.766422	−	0.768936i
$700$		0			0
$701$		−	0.375966i		−	0.0142000i	−0.999975	−	0.00710002i	$-0.997740\pi$
$701$		−	0.375966i		−	0.0142000i	0.999975	−	0.00710002i	$-0.00226003\pi$
$702$		0			0
$703$	−37.5635	+	21.6873i	−1.41674	+	0.817953i
$704$		0			0
$705$	−0.00843417	−	0.0316842i	−0.000317649	−	0.00119330i
$706$		0			0
$707$	16.7410	−	30.5540i	0.629612	−	1.14910i
$708$		0			0
$709$	−1.94936	−	3.37639i	−0.0732098	−	0.126803i	0.827097	−	0.562060i	$-0.189991\pi$
$709$	−1.94936	−	3.37639i	−0.0732098	−	0.126803i	−0.900306	+	0.435257i	$0.856658\pi$
$710$		0			0
$711$	−0.115312	+	35.2134i	−0.00432453	+	1.32061i
$712$		0			0
$713$	4.09512	−	7.09296i	0.153364	−	0.265634i
$714$		0			0
$715$	0.658312	+	1.14023i	0.0246195	+	0.0426422i
$716$		0			0
$717$	16.3415	−	4.35002i	0.610284	−	0.162454i
$718$		0			0
$719$	24.4338	−	42.3205i	0.911225	−	1.57829i	0.0988894	−	0.995098i	$-0.468471\pi$
$719$	24.4338	−	42.3205i	0.911225	−	1.57829i	0.812336	−	0.583190i	$-0.198196\pi$
$720$		0			0
$721$	−31.4053	−	17.2075i	−1.16959	−	0.640840i
$722$		0			0
$723$	−4.89733	+	18.1581i	−0.182134	+	0.675307i
$724$		0			0
$725$	4.68318	+	2.70384i	0.173929	+	0.100418i
$726$		0			0
$727$	−11.8420	−	6.83700i	−0.439196	−	0.253570i	0.264060	−	0.964506i	$-0.414938\pi$
$727$	−11.8420	−	6.83700i	−0.439196	−	0.253570i	−0.703257	+	0.710936i	$0.748272\pi$
$728$		0			0
$729$	−0.265242	+	26.9987i	−0.00982379	+	0.999952i
$730$		0			0
$731$	30.1775			1.11615
$732$		0			0
$733$			16.1607i			0.596910i	0.954424	+	0.298455i	$0.0964713\pi$
$733$			16.1607i			0.596910i	−0.954424	+	0.298455i	$0.903529\pi$
$734$		0			0
$735$	−0.739452	−	2.34980i	−0.0272751	−	0.0866738i
$736$		0			0
$737$	−31.1657	−	17.9935i	−1.14800	−	0.662800i
$738$		0			0
$739$	−15.7914	−	27.3515i	−0.580895	−	1.00614i	−0.995374	−	0.0960807i	$-0.969369\pi$
$739$	−15.7914	−	27.3515i	−0.580895	−	1.00614i	0.414478	−	0.910059i	$-0.363964\pi$
$740$		0			0
$741$	17.3657	+	4.68362i	0.637946	+	0.172057i
$742$		0			0
$743$	−8.63924	+	4.98787i	−0.316943	+	0.182987i	−0.650029	−	0.759909i	$-0.725243\pi$
$743$	−8.63924	+	4.98787i	−0.316943	+	0.182987i	0.333086	+	0.942896i	$0.391910\pi$
$744$		0			0
$745$			0.941325i			0.0344875i
$746$		0			0
$747$	−11.9701	+	6.85877i	−0.437963	+	0.250949i
$748$		0			0
$749$	−33.9671	+	20.6369i	−1.24113	+	0.754055i
$750$		0			0
$751$	−20.9066			−0.762892			−0.381446	−	0.924391i	$-0.624574\pi$
$751$	−20.9066			−0.762892			−0.381446	+	0.924391i	$0.624574\pi$
$752$		0			0
$753$	45.8468	+	12.3651i	1.67075	+	0.450609i
$754$		0			0
$755$	3.18884			0.116054
$756$		0			0
$757$	−50.5460			−1.83713			−0.918563	−	0.395274i	$-0.870650\pi$
$757$	−50.5460			−1.83713			−0.918563	+	0.395274i	$0.870650\pi$
$758$		0			0
$759$	−9.46480	−	2.55270i	−0.343550	−	0.0926572i
$760$		0			0
$761$	−20.8424			−0.755535			−0.377768	−	0.925900i	$-0.623308\pi$
$761$	−20.8424			−0.755535			−0.377768	+	0.925900i	$0.623308\pi$
$762$		0			0
$763$	−14.4189	+	0.322417i	−0.522000	+	0.0116723i
$764$		0			0
$765$	−0.00641062	+	1.95765i	−0.000231777	+	0.0707788i
$766$		0			0
$767$		−	14.9784i		−	0.540838i
$768$		0			0
$769$	25.3167	−	14.6166i	0.912944	−	0.527088i	0.0315668	−	0.999502i	$-0.489950\pi$
$769$	25.3167	−	14.6166i	0.912944	−	0.527088i	0.881377	+	0.472413i	$0.156617\pi$
$770$		0			0
$771$	45.6819	+	12.3206i	1.64519	+	0.443716i
$772$		0			0
$773$	10.9472	+	18.9612i	0.393745	+	0.681986i	0.992940	−	0.118617i	$-0.0378459\pi$
$773$	10.9472	+	18.9612i	0.393745	+	0.681986i	−0.599195	+	0.800603i	$0.704513\pi$
$774$		0			0
$775$	27.7699	+	16.0329i	0.997523	+	0.575920i
$776$		0			0
$777$	−7.73802	−	26.6568i	−0.277600	−	0.956306i
$778$		0			0
$779$			5.30893i			0.190212i
$780$		0			0
$781$	−70.0578			−2.50686
$782$		0			0
$783$	1.43972	+	5.48065i	0.0514514	+	0.195863i
$784$		0			0
$785$	1.33203	+	0.769050i	0.0475423	+	0.0274486i
$786$		0			0
$787$	7.08328	+	4.08953i	0.252492	+	0.145776i	0.620905	−	0.783886i	$-0.286765\pi$
$787$	7.08328	+	4.08953i	0.252492	+	0.145776i	−0.368413	+	0.929662i	$0.620099\pi$
$788$		0			0
$789$	−6.23136	+	23.1044i	−0.221842	+	0.822538i
$790$		0			0
$791$	−0.411843	−	18.4182i	−0.0146435	−	0.654875i
$792$		0			0
$793$	−6.15142	+	10.6546i	−0.218443	+	0.378355i
$794$		0			0
$795$	3.67260	−	0.977627i	0.130254	−	0.0346729i
$796$		0			0
$797$	4.86546	+	8.42722i	0.172343	+	0.298508i	0.939239	−	0.343265i	$-0.111533\pi$
$797$	4.86546	+	8.42722i	0.172343	+	0.298508i	−0.766895	+	0.641772i	$0.778199\pi$
$798$		0			0
$799$	−0.149616	+	0.259143i	−0.00529304	+	0.00916782i
$800$		0			0
$801$	−18.3610	+	10.5207i	−0.648753	+	0.371730i
$802$		0			0
$803$	−2.53979	−	4.39905i	−0.0896273	−	0.155239i
$804$		0			0
$805$	0.597094	+	0.327157i	0.0210448	+	0.0115308i
$806$		0			0
$807$	−9.57667	−	35.9761i	−0.337115	−	1.26642i
$808$		0			0
$809$	36.2263	−	20.9153i	1.27365	−	0.735341i	0.297976	−	0.954574i	$-0.403689\pi$
$809$	36.2263	−	20.9153i	1.27365	−	0.735341i	0.975673	+	0.219232i	$0.0703553\pi$
$810$		0			0
$811$		−	40.7323i		−	1.43031i	−0.698968	−	0.715153i	$-0.746357\pi$
$811$		−	40.7323i		−	1.43031i	0.698968	−	0.715153i	$-0.253643\pi$
$812$		0			0
$813$	−38.4903	−	38.6166i	−1.34991	−	1.35434i
$814$		0			0
$815$	0.807539	−	1.39870i	0.0282869	−	0.0489943i
$816$		0			0
$817$	58.2701	−	33.6423i	2.03861	−	1.17699i
$818$		0			0
$819$	−5.56381	+	10.0761i	−0.194415	+	0.352086i
$820$		0			0
$821$	19.3422	−	11.1672i	0.675049	−	0.389740i	−0.122938	−	0.992414i	$-0.539232\pi$
$821$	19.3422	−	11.1672i	0.675049	−	0.389740i	0.797987	+	0.602675i	$0.205898\pi$
$822$		0			0
$823$	13.5308	−	23.4360i	0.471654	−	0.816929i	−0.527820	−	0.849356i	$-0.676991\pi$
$823$	13.5308	−	23.4360i	0.471654	−	0.816929i	0.999474	+	0.0324276i	$0.0103238\pi$
$824$		0			0
$825$	9.99416	−	37.0559i	0.347952	−	1.29012i
$826$		0			0
$827$			22.1709i			0.770957i	0.922717	+	0.385479i	$0.125964\pi$
$827$			22.1709i			0.770957i	−0.922717	+	0.385479i	$0.874036\pi$
$828$		0			0
$829$	−32.2166	+	18.6003i	−1.11893	+	0.646013i	−0.941127	−	0.338053i	$-0.890232\pi$
$829$	−32.2166	+	18.6003i	−1.11893	+	0.646013i	−0.177801	+	0.984066i	$0.556898\pi$
$830$		0			0
$831$	19.8013	+	5.34052i	0.686901	+	0.185260i
$832$		0			0
$833$	−10.3595	+	19.9530i	−0.358935	+	0.691331i
$834$		0			0
$835$	−0.350162	−	0.606499i	−0.0121179	−	0.0209888i
$836$		0			0
$837$	8.53712	+	32.4987i	0.295086	+	1.12332i
$838$		0			0
$839$	−7.96294	+	13.7922i	−0.274911	+	0.476160i	−0.970113	−	0.242655i	$-0.921982\pi$
$839$	−7.96294	+	13.7922i	−0.274911	+	0.476160i	0.695202	+	0.718815i	$0.255315\pi$
$840$		0			0
$841$	−13.9054	−	24.0848i	−0.479495	−	0.830510i
$842$		0			0
$843$	27.4739	+	27.5640i	0.946250	+	0.949354i
$844$		0			0
$845$	1.10703	−	1.91743i	0.0380829	−	0.0659615i
$846$		0			0
$847$	11.4021	−	20.8099i	0.391781	−	0.715038i
$848$		0			0
$849$	1.66140	+	1.66685i	0.0570192	+	0.0572062i
$850$		0			0
$851$	6.64384	+	3.83582i	0.227748	+	0.131490i
$852$		0			0
$853$	40.4364	+	23.3459i	1.38451	+	0.799350i	0.992690	−	0.120690i	$-0.0385107\pi$
$853$	40.4364	+	23.3459i	1.38451	+	0.799350i	0.391824	+	0.920040i	$0.371844\pi$
$854$		0			0
$855$	2.17003	+	3.78719i	0.0742135	+	0.129519i
$856$		0			0
$857$	−5.33848			−0.182359			−0.0911795	−	0.995834i	$-0.529064\pi$
$857$	−5.33848			−0.182359			−0.0911795	+	0.995834i	$0.529064\pi$
$858$		0			0
$859$		−	10.0559i		−	0.343102i	−0.985175	−	0.171551i	$-0.945122\pi$
$859$		−	10.0559i		−	0.343102i	0.985175	−	0.171551i	$-0.0548779\pi$
$860$		0			0
$861$	−3.29915	−	0.811133i	−0.112435	−	0.0276433i
$862$		0			0
$863$	32.7144	+	18.8877i	1.11361	+	0.642943i	0.939762	−	0.341829i	$-0.111046\pi$
$863$	32.7144	+	18.8877i	1.11361	+	0.642943i	0.173849	+	0.984772i	$0.444380\pi$
$864$		0			0
$865$	1.46654	+	2.54012i	0.0498639	+	0.0863668i
$866$		0			0
$867$	−8.20063	+	8.17382i	−0.278508	+	0.277597i
$868$		0			0
$869$	45.4249	−	26.2261i	1.54094	−	0.889659i
$870$		0			0
$871$		−	11.6783i		−	0.395706i
$872$		0			0
$873$	−5.47518	−	9.55541i	−0.185307	−	0.323402i
$874$		0			0
$875$	−2.57239	+	4.69486i	−0.0869626	+	0.158715i
$876$		0			0
$877$	−46.5264			−1.57109			−0.785543	−	0.618807i	$-0.787616\pi$
$877$	−46.5264			−1.57109			−0.785543	+	0.618807i	$0.787616\pi$
$878$		0			0
$879$	7.21841	+	27.1170i	0.243471	+	0.914634i
$880$		0			0
$881$	31.9474			1.07633			0.538167	−	0.842838i	$-0.319117\pi$
$881$	31.9474			1.07633			0.538167	+	0.842838i	$0.319117\pi$
$882$		0			0
$883$	−38.2919			−1.28862			−0.644312	−	0.764763i	$-0.722856\pi$
$883$	−38.2919			−1.28862			−0.644312	+	0.764763i	$0.722856\pi$
$884$		0			0
$885$	2.57447	−	2.56606i	0.0865400	−	0.0862570i
$886$		0			0
$887$	40.6168			1.36378			0.681889	−	0.731455i	$-0.261159\pi$
$887$	40.6168			1.36378			0.681889	+	0.731455i	$0.261159\pi$
$888$		0			0
$889$	−3.41627	+	6.23502i	−0.114578	+	0.209116i
$890$		0			0
$891$	34.9605	−	19.8803i	1.17122	−	0.666016i
$892$		0			0
$893$			0.667177i			0.0223262i
$894$		0			0
$895$	4.00469	−	2.31211i	0.133862	−	0.0772852i
$896$		0			0
$897$	−0.818328	−	3.07417i	−0.0273232	−	0.102643i
$898$		0			0
$899$	3.52602	+	6.10724i	0.117599	+	0.203688i
$900$		0			0
$901$	−30.0379	−	17.3424i	−1.00071	−	0.577760i
$902$		0			0
$903$	12.0035	+	41.3511i	0.399453	+	1.37608i
$904$		0			0
$905$			1.81866i			0.0604543i
$906$		0			0
$907$	−29.9969			−0.996030			−0.498015	−	0.867168i	$-0.665938\pi$
$907$	−29.9969			−0.996030			−0.498015	+	0.867168i	$0.665938\pi$
$908$		0			0
$909$	−34.1471	−	19.8642i	−1.13259	−	0.658855i
$910$		0			0
$911$	−34.2362	−	19.7663i	−1.13430	−	0.654886i	−0.189284	−	0.981922i	$-0.560617\pi$
$911$	−34.2362	−	19.7663i	−1.13430	−	0.654886i	−0.945012	+	0.327036i	$0.893950\pi$
$912$		0			0
$913$	17.7964	+	10.2748i	0.588976	+	0.340045i
$914$		0			0
$915$	−2.88514	+	0.768010i	−0.0953798	+	0.0253896i
$916$		0			0
$917$	−7.80576	+	14.2463i	−0.257769	+	0.470453i
$918$		0			0
$919$	9.74272	−	16.8749i	0.321383	−	0.556651i	−0.659391	−	0.751800i	$-0.729186\pi$
$919$	9.74272	−	16.8749i	0.321383	−	0.556651i	0.980774	+	0.195149i	$0.0625191\pi$
$920$		0			0
$921$	−4.16266	+	15.4341i	−0.137164	+	0.508571i
$922$		0			0
$923$	−11.3674	−	19.6889i	−0.374163	−	0.648069i
$924$		0			0
$925$	−15.0178	+	26.0115i	−0.493781	+	0.855253i
$926$		0			0
$927$	−20.4177	+	35.0985i	−0.670604	+	1.15279i
$928$		0			0
$929$	−6.93060	−	12.0041i	−0.227386	−	0.393843i	0.729647	−	0.683824i	$-0.239684\pi$
$929$	−6.93060	−	12.0041i	−0.227386	−	0.393843i	−0.957032	+	0.289981i	$0.906351\pi$
$930$		0			0
$931$	2.24061	+	50.0765i	0.0734330	+	1.64119i
$932$		0			0
$933$	0.768765	−	0.766251i	0.0251682	−	0.0250859i
$934$		0			0
$935$	2.52534	−	1.45801i	0.0825876	−	0.0476819i
$936$		0			0
$937$		−	5.38328i		−	0.175864i	−0.996126	−	0.0879320i	$-0.971974\pi$
$937$		−	5.38328i		−	0.175864i	0.996126	−	0.0879320i	$-0.0280258\pi$
$938$		0			0
$939$	8.57204	−	2.28184i	0.279738	−	0.0744649i
$940$		0			0
$941$	3.28619	−	5.69185i	0.107127	−	0.185549i	−0.807478	−	0.589897i	$-0.799168\pi$
$941$	3.28619	−	5.69185i	0.107127	−	0.185549i	0.914605	+	0.404348i	$0.132502\pi$
$942$		0			0
$943$	0.813188	−	0.469494i	0.0264810	−	0.0152888i
$944$		0			0
$945$	−2.68504	+	0.769899i	−0.0873444	+	0.0250448i
$946$		0			0
$947$	−27.7081	+	15.9973i	−0.900392	+	0.519841i	−0.877327	−	0.479893i	$-0.840676\pi$
$947$	−27.7081	+	15.9973i	−0.900392	+	0.519841i	−0.0230644	+	0.999734i	$0.507342\pi$
$948$		0			0
$949$	0.824201	−	1.42756i	0.0267547	−	0.0463405i
$950$		0			0
$951$	7.01187	−	1.86653i	0.227376	−	0.0605263i
$952$		0			0
$953$		−	51.5312i		−	1.66926i	−0.550812	−	0.834629i	$-0.685682\pi$
$953$		−	51.5312i		−	1.66926i	0.550812	−	0.834629i	$-0.314318\pi$
$954$		0			0
$955$	−4.31901	+	2.49358i	−0.139760	+	0.0806903i
$956$		0			0
$957$	5.97821	−	5.95866i	0.193248	−	0.192616i
$958$		0			0
$959$	−9.93595	−	5.44407i	−0.320849	−	0.175798i
$960$		0			0
$961$	5.40825	+	9.36736i	0.174460	+	0.302173i
$962$		0			0
$963$	22.4052	+	39.1022i	0.721999	+	1.26005i
$964$		0			0
$965$	0.463773	−	0.803278i	0.0149294	−	0.0258584i
$966$		0			0
$967$	6.01867	+	10.4246i	0.193547	+	0.335234i	0.946423	−	0.322929i	$-0.104667\pi$
$967$	6.01867	+	10.4246i	0.193547	+	0.335234i	−0.752876	+	0.658162i	$0.771334\pi$
$968$		0			0
$969$	10.3731	−	38.4611i	0.333233	−	1.23555i
$970$		0			0
$971$	23.4783	−	40.6656i	0.753454	−	1.30502i	−0.192685	−	0.981261i	$-0.561719\pi$
$971$	23.4783	−	40.6656i	0.753454	−	1.30502i	0.946139	−	0.323761i	$-0.104947\pi$
$972$		0			0
$973$	0.234925	+	10.5062i	0.00753135	+	0.336812i
$974$		0			0
$975$	12.0358	−	3.20386i	0.385453	−	0.102606i
$976$		0			0
$977$	−28.4083	−	16.4015i	−0.908863	−	0.524732i	−0.0287976	−	0.999585i	$-0.509168\pi$
$977$	−28.4083	−	16.4015i	−0.908863	−	0.524732i	−0.880065	+	0.474853i	$0.842501\pi$
$978$		0			0
$979$	27.2980	+	15.7605i	0.872448	+	0.503708i
$980$		0			0
$981$	−0.0535523	+	16.3535i	−0.00170979	+	0.522128i
$982$		0			0
$983$	30.0145			0.957314			0.478657	−	0.878002i	$-0.341124\pi$
$983$	30.0145			0.957314			0.478657	+	0.878002i	$0.341124\pi$
$984$		0			0
$985$			2.46485i			0.0785368i
$986$		0			0
$987$	−0.414606	−	0.101936i	−0.0131971	−	0.00324465i
$988$		0			0
$989$	−10.3062	−	5.95029i	−0.327718	−	0.189208i
$990$		0			0
$991$	24.9364	+	43.1911i	0.792131	+	1.37201i	0.924645	+	0.380831i	$0.124362\pi$
$991$	24.9364	+	43.1911i	0.792131	+	1.37201i	−0.132514	+	0.991181i	$0.542305\pi$
$992$		0			0
$993$	11.5584	+	43.4207i	0.366794	+	1.37791i
$994$		0			0
$995$	−2.60624	+	1.50471i	−0.0826232	+	0.0477026i
$996$		0			0
$997$		−	1.48520i		−	0.0470368i	−0.999723	−	0.0235184i	$-0.992513\pi$
$997$		−	1.48520i		−	0.0470368i	0.999723	−	0.0235184i	$-0.00748683\pi$
$998$		0			0
$999$	−30.4409	+	7.99656i	−0.963107	+	0.253000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cx.a.425.3	yes	48
3.2	odd	2		1512.2.cx.a.89.11		48
4.3	odd	2		1008.2.df.e.929.22		48
7.3	odd	6		504.2.bs.a.353.10	yes	48
9.4	even	3		1512.2.bs.a.1097.11		48
9.5	odd	6		504.2.bs.a.257.10	✓	48
12.11	even	2		3024.2.df.e.1601.11		48
21.17	even	6		1512.2.bs.a.521.11		48
28.3	even	6		1008.2.ca.e.353.15		48
36.23	even	6		1008.2.ca.e.257.15		48
36.31	odd	6		3024.2.ca.e.2609.11		48
63.31	odd	6		1512.2.cx.a.17.11		48
63.59	even	6	inner	504.2.cx.a.185.3	yes	48
84.59	odd	6		3024.2.ca.e.2033.11		48
252.31	even	6		3024.2.df.e.17.11		48
252.59	odd	6		1008.2.df.e.689.22		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.10	✓	48	9.5	odd	6
504.2.bs.a.353.10	yes	48	7.3	odd	6
504.2.cx.a.185.3	yes	48	63.59	even	6	inner
504.2.cx.a.425.3	yes	48	1.1	even	1	trivial
1008.2.ca.e.257.15		48	36.23	even	6
1008.2.ca.e.353.15		48	28.3	even	6
1008.2.df.e.689.22		48	252.59	odd	6
1008.2.df.e.929.22		48	4.3	odd	2
1512.2.bs.a.521.11		48	21.17	even	6
1512.2.bs.a.1097.11		48	9.4	even	3
1512.2.cx.a.17.11		48	63.31	odd	6
1512.2.cx.a.89.11		48	3.2	odd	2
3024.2.ca.e.2033.11		48	84.59	odd	6
3024.2.ca.e.2609.11		48	36.31	odd	6
3024.2.df.e.17.11		48	252.31	even	6
3024.2.df.e.1601.11		48	12.11	even	2

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.cx (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.67230 - 0.451026i) q^{3} -0.203178 q^{5} +(-1.27132 + 2.32029i) q^{7} +(2.59315 + 1.50850i) q^{9} -4.46863i q^{11} +(1.25586 - 0.725070i) q^{13} +(0.339774 + 0.0916388i) q^{15} +(-1.60586 - 2.78143i) q^{17} +(-6.20156 - 3.58047i) q^{19} +(3.17254 - 3.30681i) q^{21} +1.26655i q^{23} -4.95872 q^{25} +(-3.65614 - 3.69224i) q^{27} +(-0.944433 - 0.545269i) q^{29} +(-5.60021 - 3.23328i) q^{31} +(-2.01547 + 7.47288i) q^{33} +(0.258305 - 0.471432i) q^{35} +(3.02855 - 5.24561i) q^{37} +(-2.42719 + 0.646106i) q^{39} +(-0.370687 - 0.642048i) q^{41} +(-4.69802 + 8.13721i) q^{43} +(-0.526872 - 0.306494i) q^{45} +(-0.0465845 - 0.0806866i) q^{47} +(-3.76748 - 5.89967i) q^{49} +(1.43098 + 5.37566i) q^{51} +(9.35260 - 5.39973i) q^{53} +0.907929i q^{55} +(8.75596 + 8.78468i) q^{57} +(5.16447 - 8.94512i) q^{59} +(-7.34727 + 4.24195i) q^{61} +(-6.79689 + 4.09907i) q^{63} +(-0.255163 + 0.147318i) q^{65} +(4.02663 - 6.97432i) q^{67} +(0.571249 - 2.11805i) q^{69} -15.6777i q^{71} +(0.984428 - 0.568360i) q^{73} +(8.29245 + 2.23651i) q^{75} +(10.3685 + 5.68108i) q^{77} +(5.86893 + 10.1653i) q^{79} +(4.44886 + 7.82353i) q^{81} +(-2.29931 + 3.98252i) q^{83} +(0.326276 + 0.565127i) q^{85} +(1.33344 + 1.33782i) q^{87} +(-3.52692 + 6.10881i) q^{89} +(0.0857700 + 3.83575i) q^{91} +(7.90692 + 7.93285i) q^{93} +(1.26002 + 0.727474i) q^{95} +(-3.17914 - 1.83548i) q^{97} +(6.74093 - 11.5878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{9} + 8 q^{15} - 10 q^{21} + 48 q^{25} + 18 q^{27} + 18 q^{29} + 18 q^{31} + 12 q^{33} - 4 q^{39} - 6 q^{41} - 6 q^{43} - 18 q^{45} + 18 q^{47} - 12 q^{49} + 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61}+ \cdots - 64 q^{99}+O(q^{100}) \) 48 * q + 2 * q^9 + 8 * q^15 - 10 * q^21 + 48 * q^25 + 18 * q^27 + 18 * q^29 + 18 * q^31 + 12 * q^33 - 4 * q^39 - 6 * q^41 - 6 * q^43 - 18 * q^45 + 18 * q^47 - 12 * q^49 + 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 - 32 * q^63 - 36 * q^65 - 12 * q^77 + 6 * q^79 + 6 * q^81 - 54 * q^87 - 18 * q^89 + 6 * q^91 + 4 * q^93 - 54 * q^95 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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