LMFDB - Embedded newform 1008.2.df.e.929.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(689,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, 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("1008.689"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.df (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			929.22
Character	$\chi$	$=$	1008.929
Dual form			1008.2.df.e.689.22

$q$-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 $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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	$0.235284\pi$
$11$			4.46863i			1.34734i	−0.739031	+	0.673672i	$0.764716\pi$
$12$		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	0.996532	−	0.0832106i	$-0.0265174\pi$
$19$	6.20156	+	3.58047i	1.42274	+	0.821417i	0.426203	+	0.904627i	$0.359851\pi$
$20$		0			0
$21$	3.17254	−	3.30681i	0.692305	−	0.721605i
$22$		0			0
$23$		−	1.26655i		−	0.264095i	−0.991243	−	0.132047i	$-0.957845\pi$
$23$		−	1.26655i		−	0.264095i	0.991243	−	0.132047i	$-0.0421551\pi$
$24$		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	0.909967	−	0.414680i	$-0.136106\pi$
$31$	5.60021	+	3.23328i	1.00583	+	0.580715i	0.0958603	+	0.995395i	$0.469440\pi$
$32$		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	$-0.579103\pi$
$43$	4.69802	−	8.13721i	0.716442	−	1.24091i	0.962401	−	0.271633i	$-0.0875638\pi$
$44$		0			0
$45$	−0.526872	−	0.306494i	−0.0785414	−	0.0456895i
$46$		0			0
$47$	0.0465845	+	0.0806866i	0.00679504	+	0.0117694i	0.869403	−	0.494104i	$-0.164504\pi$
$47$	0.0465845	+	0.0806866i	0.00679504	+	0.0117694i	−0.862608	+	0.505873i	$0.831170\pi$
$48$		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	$0.401384\pi$
$59$	−5.16447	+	8.94512i	−0.672356	+	1.16456i	−0.977234	+	0.212164i	$0.931949\pi$
$60$		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	−0.999957	−	0.00929244i	$-0.997042\pi$
$67$	−4.02663	+	6.97432i	−0.491931	+	0.852049i	0.508026	+	0.861342i	$0.330375\pi$
$68$		0			0
$69$	0.571249	−	2.11805i	0.0687703	−	0.254983i
$70$		0			0
$71$			15.6777i			1.86060i	0.366802	+	0.930299i	$0.380453\pi$
$71$			15.6777i			1.86060i	−0.366802	+	0.930299i	$0.619547\pi$
$72$		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	$-0.937093\pi$
$79$	−5.86893	−	10.1653i	−0.660306	−	1.14368i	0.320229	−	0.947340i	$-0.396240\pi$
$80$		0			0
$81$	4.44886	+	7.82353i	0.494317	+	0.869281i
$82$		0			0
$83$	2.29931	−	3.98252i	0.252382	−	0.437139i	−0.711799	−	0.702383i	$-0.752119\pi$
$83$	2.29931	−	3.98252i	0.252382	−	0.437139i	0.964181	+	0.265245i	$0.0854527\pi$
$84$		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	$-0.767653\pi$
$103$		−	13.5351i		−	1.33365i	0.745214	−	0.666826i	$-0.232347\pi$
$104$		0			0
$105$	−0.644591	+	0.671872i	−0.0629057	+	0.0655680i
$106$		0			0
$107$	−13.0095	−	7.51105i	−1.25768	−	0.726121i	−0.285056	−	0.958511i	$-0.592012\pi$
$107$	−13.0095	−	7.51105i	−1.25768	−	0.726121i	−0.972623	+	0.232390i	$0.925345\pi$
$108$		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	$-0.538041\pi$
$127$	−2.68718			−0.238448			−0.119224	+	0.992867i	$0.538041\pi$
$128$		0			0
$129$	11.5266	−	11.4889i	1.01486	−	1.01154i
$130$		0			0
$131$	−6.13987			−0.536443			−0.268222	−	0.963357i	$-0.586436\pi$
$131$	−6.13987			−0.536443			−0.268222	+	0.963357i	$0.586436\pi$
$132$		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	−0.638736	−	0.769426i	$-0.720542\pi$
$139$	−3.43981	+	1.98597i	−0.291761	+	0.168448i	0.346975	+	0.937874i	$0.387209\pi$
$140$		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	$-0.279509\pi$
$151$	15.6948			1.27722			0.638612	+	0.769529i	$0.279509\pi$
$152$		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	−0.667337	−	0.744756i	$-0.732566\pi$
$163$	3.97454	−	6.88410i	0.311310	−	0.539204i	0.978646	+	0.205552i	$0.0658990\pi$
$164$		0			0
$165$	0.409500	−	1.51833i	0.0318795	−	0.118202i
$166$		0			0
$167$	−1.72342	−	2.98506i	−0.133363	−	0.230991i	0.791608	−	0.611029i	$-0.209244\pi$
$167$	−1.72342	−	2.98506i	−0.133363	−	0.230991i	−0.924971	+	0.380038i	$0.875911\pi$
$168$		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	0.473665	−	0.880705i	$-0.342931\pi$
$179$	19.7102	−	11.3797i	1.47321	−	0.850558i	0.999545	+	0.0301471i	$0.00959757\pi$
$180$		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	$0.681262\pi$
$191$	−21.2572	+	12.2729i	−1.53812	+	0.888033i	−0.998949	+	0.0458359i	$0.985405\pi$
$192$		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	−0.880208	−	0.474589i	$-0.842597\pi$
$199$	−12.8273	+	7.40587i	−0.909306	+	0.524988i	−0.0290981	+	0.999577i	$0.509264\pi$
$200$		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	0.966139	−	0.258021i	$-0.0830703\pi$
$211$	3.77116	+	6.53184i	0.259617	+	0.449670i	−0.706522	+	0.707691i	$0.749737\pi$
$212$		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	$-0.900898\pi$
$223$	−25.2846	−	14.5980i	−1.69318	−	0.977557i	−0.741255	−	0.671224i	$-0.765769\pi$
$224$		0			0
$225$	−12.8587	−	7.48023i	−0.857247	−	0.498682i
$226$		0			0
$227$	−29.1575			−1.93525			−0.967625	−	0.252391i	$-0.918783\pi$
$227$	−29.1575			−1.93525			−0.967625	+	0.252391i	$0.918783\pi$
$228$		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	−0.200955	−	0.979600i	$-0.564405\pi$
$239$	8.45527	−	4.88165i	0.546926	−	0.315768i	0.747881	+	0.663833i	$0.231071\pi$
$240$		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	$-0.167176\pi$
$251$	27.4155			1.73045			0.865224	+	0.501385i	$0.167176\pi$
$252$		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	$0.140065\pi$
$263$			13.8160i			0.851928i	−0.904740	+	0.425964i	$0.859935\pi$
$264$		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	$-0.928000\pi$
$271$	−27.2614	−	15.7394i	−1.65601	−	0.956101i	−0.681488	−	0.731829i	$-0.738667\pi$
$272$		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	0.534566	−	0.845126i	$-0.320475\pi$
$283$	1.17672	+	0.679378i	0.0699486	+	0.0403848i	−0.464618	+	0.885511i	$0.653808\pi$
$284$		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	$0.0848346\pi$
$307$			9.22930i			0.526744i	−0.964694	+	0.263372i	$0.915165\pi$
$308$		0			0
$309$	6.10468	−	22.6347i	0.347283	−	1.28764i
$310$		0			0
$311$	0.313334	−	0.542711i	0.0177676	−	0.0307743i	−0.857005	−	0.515308i	$-0.827677\pi$
$311$	0.313334	−	0.542711i	0.0177676	−	0.0307743i	0.874772	+	0.484534i	$0.161011\pi$
$312$		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	$0.0859741\pi$
$331$	12.9710	+	22.4664i	0.712949	+	1.23486i	−0.250797	+	0.968040i	$0.580693\pi$
$332$		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	0.987558	−	0.157253i	$-0.0502639\pi$
$347$	25.0574	+	14.4669i	1.34515	+	0.776624i	0.357594	+	0.933877i	$0.383597\pi$
$348$		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	0.776006	−	0.630726i	$-0.217243\pi$
$359$	11.7053	+	6.75809i	0.617785	+	0.356678i	−0.158221	+	0.987404i	$0.550576\pi$
$360$		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	$0.166870\pi$
$367$			19.1785i			1.00111i	−0.865705	+	0.500554i	$0.833130\pi$
$368$		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	$-0.550200\pi$
$379$	−6.11511			−0.314112			−0.157056	+	0.987590i	$0.550200\pi$
$380$		0			0
$381$	−4.49375	−	1.21199i	−0.230222	−	0.0620920i
$382$		0			0
$383$	−5.67449			−0.289953			−0.144976	−	0.989435i	$-0.546311\pi$
$383$	−5.67449			−0.289953			−0.144976	+	0.989435i	$0.546311\pi$
$384$		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	$-0.901540\pi$
$419$	−15.1454	−	26.2325i	−0.739899	−	1.28154i	0.212641	−	0.977130i	$-0.431793\pi$
$420$		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	−0.721259	−	0.692665i	$-0.756436\pi$
$431$	−10.0071	+	5.77758i	−0.482023	+	0.278296i	0.239236	+	0.970961i	$0.423103\pi$
$432$		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	−0.901459	−	0.432865i	$-0.857503\pi$
$439$	−20.4771	+	11.8224i	−0.977316	+	0.564254i	−0.0758575	+	0.997119i	$0.524169\pi$
$440$		0			0
$441$	−0.869976	−	20.9820i	−0.0414274	−	0.999142i
$442$		0			0
$443$	−11.3308	+	6.54184i	−0.538343	+	0.310812i	−0.744407	−	0.667726i	$-0.767268\pi$
$443$	−11.3308	+	6.54184i	−0.538343	+	0.310812i	0.206064	+	0.978538i	$0.433934\pi$
$444$		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	0.504471	−	0.863428i	$-0.331687\pi$
$463$	−10.6622	−	18.4675i	−0.495515	−	0.858258i	−0.999987	+	0.00517079i	$0.998354\pi$
$464$		0			0
$465$	−1.60651	−	1.61178i	−0.0745003	−	0.0747447i
$466$		0			0
$467$	−7.97308	+	13.8098i	−0.368950	+	0.639041i	−0.989402	−	0.145204i	$-0.953616\pi$
$467$	−7.97308	+	13.8098i	−0.368950	+	0.639041i	0.620451	+	0.784245i	$0.286949\pi$
$468$		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	$-0.252386\pi$
$479$	30.7187			1.40357			0.701787	+	0.712387i	$0.252386\pi$
$480$		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	0.856276	−	0.516518i	$-0.172772\pi$
$487$	−0.423250	−	0.733091i	−0.0191793	−	0.0332195i	−0.875456	+	0.483298i	$0.839439\pi$
$488$		0			0
$489$	9.75151	−	9.71963i	0.440979	−	0.439537i
$490$		0			0
$491$	−1.78204	+	1.02886i	−0.0804225	+	0.0464319i	−0.539672	−	0.841875i	$-0.681452\pi$
$491$	−1.78204	+	1.02886i	−0.0804225	+	0.0464319i	0.459249	+	0.888307i	$0.348118\pi$
$492$		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	$-0.126655\pi$
$499$	41.1863			1.84375			0.921877	+	0.387483i	$0.126655\pi$
$500$		0			0
$501$	−1.53574	−	5.76921i	−0.0686116	−	0.257749i
$502$		0			0
$503$	−1.48781			−0.0663383			−0.0331692	−	0.999450i	$-0.510560\pi$
$503$	−1.48781			−0.0663383			−0.0331692	+	0.999450i	$0.510560\pi$
$504$		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	$0.0619526\pi$
$523$	37.4865	+	21.6429i	1.63917	+	0.946376i	0.658052	+	0.752973i	$0.271381\pi$
$524$		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	−0.723453	−	0.690374i	$-0.757446\pi$
$547$	5.52320	−	9.56646i	0.236155	−	0.409032i	0.959608	+	0.281342i	$0.0907794\pi$
$548$		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	$-0.538081\pi$
$563$	18.9859	−	32.8846i	0.800161	−	1.38592i	0.919510	−	0.393067i	$-0.128586\pi$
$564$		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	−0.962810	−	0.270181i	$-0.912916\pi$
$571$	−5.91228	+	10.2404i	−0.247421	+	0.428546i	0.715388	+	0.698727i	$0.246250\pi$
$572$		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	−0.838227	−	0.545321i	$-0.816408\pi$
$587$	1.28769	−	2.23034i	0.0531487	−	0.0920562i	0.891376	+	0.453265i	$0.149741\pi$
$588$		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	0.876969	−	0.480547i	$-0.159562\pi$
$599$	22.0096	+	12.7072i	0.899287	+	0.519204i	0.0223184	+	0.999751i	$0.492895\pi$
$600$		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	$-0.768476\pi$
$607$		−	32.7626i		−	1.32979i	0.746936	−	0.664896i	$-0.231524\pi$
$608$		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	$0.227782\pi$
$619$			32.6456i			1.31214i	−0.754702	+	0.656068i	$0.772218\pi$
$620$		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	$-0.456791\pi$
$631$	6.79887			0.270659			0.135329	+	0.990801i	$0.456791\pi$
$632$		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	−0.847742	−	0.530408i	$-0.822039\pi$
$643$	−20.5970	+	11.8917i	−0.812267	+	0.468963i	0.0354756	+	0.999371i	$0.488705\pi$
$644$		0			0
$645$	−2.34195	+	2.33430i	−0.0922143	+	0.0919128i
$646$		0			0
$647$	11.1964	+	19.3928i	0.440177	+	0.762410i	0.997702	−	0.0677505i	$-0.0215822\pi$
$647$	11.1964	+	19.3928i	0.440177	+	0.762410i	−0.557525	+	0.830160i	$0.688249\pi$
$648$		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	0.898972	−	0.438006i	$-0.144315\pi$
$659$	24.8786	+	14.3637i	0.969134	+	0.559530i	0.0701619	+	0.997536i	$0.477648\pi$
$660$		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	−0.477375	−	0.878699i	$-0.658412\pi$
$683$	1.17377	−	0.677674i	0.0449129	−	0.0259305i	0.522288	+	0.852769i	$0.325078\pi$
$684$		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	−0.305722	−	0.952121i	$-0.598898\pi$
$691$	9.62041	−	5.55435i	0.365978	−	0.211297i	0.671700	+	0.740823i	$0.265564\pi$
$692$		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	$0.531529\pi$
$719$	−24.4338	+	42.3205i	−0.911225	+	1.57829i	−0.812336	+	0.583190i	$0.801804\pi$
$720$		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	0.703257	−	0.710936i	$-0.251728\pi$
$727$	11.8420	+	6.83700i	0.439196	+	0.253570i	−0.264060	+	0.964506i	$0.585062\pi$
$728$		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	$0.0306307\pi$
$739$	15.7914	+	27.3515i	0.580895	+	1.00614i	−0.414478	+	0.910059i	$0.636036\pi$
$740$		0			0
$741$	17.3657	+	4.68362i	0.637946	+	0.172057i
$742$		0			0
$743$	8.63924	−	4.98787i	0.316943	−	0.182987i	−0.333086	−	0.942896i	$-0.608090\pi$
$743$	8.63924	−	4.98787i	0.316943	−	0.182987i	0.650029	+	0.759909i	$0.274757\pi$
$744$		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	$-0.375426\pi$
$751$	20.9066			0.762892			0.381446	+	0.924391i	$0.375426\pi$
$752$		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	0.368413	−	0.929662i	$-0.379901\pi$
$787$	−7.08328	−	4.08953i	−0.252492	−	0.145776i	−0.620905	+	0.783886i	$0.713235\pi$
$788$		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	$0.253643\pi$
$811$			40.7323i			1.43031i	−0.698968	+	0.715153i	$0.746357\pi$
$812$		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	−0.999474	−	0.0324276i	$-0.989676\pi$
$823$	−13.5308	+	23.4360i	−0.471654	+	0.816929i	0.527820	+	0.849356i	$0.323009\pi$
$824$		0			0
$825$	9.99416	−	37.0559i	0.347952	−	1.29012i
$826$		0			0
$827$		−	22.1709i		−	0.770957i	−0.922717	−	0.385479i	$-0.874036\pi$
$827$		−	22.1709i		−	0.770957i	0.922717	−	0.385479i	$-0.125964\pi$
$828$		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	−0.695202	−	0.718815i	$-0.744685\pi$
$839$	7.96294	−	13.7922i	0.274911	−	0.476160i	0.970113	+	0.242655i	$0.0780182\pi$
$840$		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	$0.0548779\pi$
$859$			10.0559i			0.343102i	−0.985175	+	0.171551i	$0.945122\pi$
$860$		0			0
$861$	−3.29915	−	0.811133i	−0.112435	−	0.0276433i
$862$		0			0
$863$	−32.7144	−	18.8877i	−1.11361	−	0.642943i	−0.173849	−	0.984772i	$-0.555620\pi$
$863$	−32.7144	−	18.8877i	−1.11361	−	0.642943i	−0.939762	+	0.341829i	$0.888954\pi$
$864$		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	$-0.277144\pi$
$883$	38.2919			1.28862			0.644312	+	0.764763i	$0.277144\pi$
$884$		0			0
$885$	2.57447	−	2.56606i	0.0865400	−	0.0862570i
$886$		0			0
$887$	−40.6168			−1.36378			−0.681889	−	0.731455i	$-0.738841\pi$
$887$	−40.6168			−1.36378			−0.681889	+	0.731455i	$0.738841\pi$
$888$		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	$-0.334062\pi$
$907$	29.9969			0.996030			0.498015	+	0.867168i	$0.334062\pi$
$908$		0			0
$909$	−34.1471	−	19.8642i	−1.13259	−	0.658855i
$910$		0			0
$911$	34.2362	+	19.7663i	1.13430	+	0.654886i	0.945012	−	0.327036i	$-0.106050\pi$
$911$	34.2362	+	19.7663i	1.13430	+	0.654886i	0.189284	+	0.981922i	$0.439383\pi$
$912$		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	−0.980774	−	0.195149i	$-0.937481\pi$
$919$	−9.74272	+	16.8749i	−0.321383	+	0.556651i	0.659391	+	0.751800i	$0.270814\pi$
$920$		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	0.0230644	−	0.999734i	$-0.492658\pi$
$947$	27.7081	−	15.9973i	0.900392	−	0.519841i	0.877327	+	0.479893i	$0.159324\pi$
$948$		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	0.752876	−	0.658162i	$-0.228666\pi$
$967$	−6.01867	−	10.4246i	−0.193547	−	0.335234i	−0.946423	+	0.322929i	$0.895333\pi$
$968$		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	$0.438281\pi$
$971$	−23.4783	+	40.6656i	−0.753454	+	1.30502i	−0.946139	+	0.323761i	$0.895053\pi$
$972$		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	$-0.658876\pi$
$983$	−30.0145			−0.957314			−0.478657	+	0.878002i	$0.658876\pi$
$984$		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	$-0.875638\pi$
$991$	−24.9364	−	43.1911i	−0.792131	−	1.37201i	0.132514	−	0.991181i	$-0.457695\pi$
$992$		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	1008.2.df.e.929.22		48
3.2	odd	2		3024.2.df.e.1601.11		48
4.3	odd	2		504.2.cx.a.425.3	yes	48
7.3	odd	6		1008.2.ca.e.353.15		48
9.4	even	3		3024.2.ca.e.2609.11		48
9.5	odd	6		1008.2.ca.e.257.15		48
12.11	even	2		1512.2.cx.a.89.11		48
21.17	even	6		3024.2.ca.e.2033.11		48
28.3	even	6		504.2.bs.a.353.10	yes	48
36.23	even	6		504.2.bs.a.257.10	✓	48
36.31	odd	6		1512.2.bs.a.1097.11		48
63.31	odd	6		3024.2.df.e.17.11		48
63.59	even	6	inner	1008.2.df.e.689.22		48
84.59	odd	6		1512.2.bs.a.521.11		48
252.31	even	6		1512.2.cx.a.17.11		48
252.59	odd	6		504.2.cx.a.185.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.10	✓	48	36.23	even	6
504.2.bs.a.353.10	yes	48	28.3	even	6
504.2.cx.a.185.3	yes	48	252.59	odd	6
504.2.cx.a.425.3	yes	48	4.3	odd	2
1008.2.ca.e.257.15		48	9.5	odd	6
1008.2.ca.e.353.15		48	7.3	odd	6
1008.2.df.e.689.22		48	63.59	even	6	inner
1008.2.df.e.929.22		48	1.1	even	1	trivial
1512.2.bs.a.521.11		48	84.59	odd	6
1512.2.bs.a.1097.11		48	36.31	odd	6
1512.2.cx.a.17.11		48	252.31	even	6
1512.2.cx.a.89.11		48	12.11	even	2
3024.2.ca.e.2033.11		48	21.17	even	6
3024.2.ca.e.2609.11		48	9.4	even	3
3024.2.df.e.17.11		48	63.31	odd	6
3024.2.df.e.1601.11		48	3.2	odd	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.df (of order \(6\), degree \(2\), not 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

Fields

Representations

Groups

Database

Properties

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