LMFDB - Embedded newform 1008.2.ca.e.353.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(257,1008)] 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, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.257"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.ca (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			353.15
Character	$\chi$	$=$	1008.353
Dual form			1008.2.ca.e.257.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.445548 + 1.67376i) q^{3} +(-0.101589 + 0.175958i) q^{5} +(1.37377 - 2.26114i) q^{7} +(-2.60297 + 1.49148i) q^{9} +(3.86995 - 2.23432i) q^{11} +(-1.25586 + 0.725070i) q^{13} +(-0.339774 - 0.0916388i) q^{15} +(1.60586 - 2.78143i) q^{17} +(6.20156 - 3.58047i) q^{19} +(4.39670 + 1.29192i) q^{21} +(1.09687 + 0.633276i) q^{23} +(2.47936 + 4.29438i) q^{25} +(-3.65614 - 3.69224i) q^{27} +(-0.944433 - 0.545269i) q^{29} +6.46657i q^{31} +(5.46397 + 5.48189i) q^{33} +(0.258305 + 0.471432i) q^{35} +(3.02855 + 5.24561i) q^{37} +(-1.77314 - 1.77896i) q^{39} +(0.370687 + 0.642048i) q^{41} +(4.69802 - 8.13721i) q^{43} +(0.00199601 - 0.609532i) q^{45} +0.0931689 q^{47} +(-3.22553 - 6.21257i) q^{49} +(5.37095 + 1.44857i) q^{51} +(-9.35260 - 5.39973i) q^{53} +0.907929i q^{55} +(8.75596 + 8.78468i) q^{57} -10.3289 q^{59} +8.48390i q^{61} +(-0.203422 + 7.93465i) q^{63} -0.294637i q^{65} +8.05326 q^{67} +(-0.571249 + 2.11805i) q^{69} +15.6777i q^{71} +(0.984428 + 0.568360i) q^{73} +(-6.08310 + 6.06321i) q^{75} +(0.264302 - 11.8199i) q^{77} +11.7379 q^{79} +(4.55095 - 7.76459i) q^{81} +(-2.29931 + 3.98252i) q^{83} +(0.326276 + 0.565127i) q^{85} +(0.491861 - 1.82370i) q^{87} +(3.52692 + 6.10881i) q^{89} +(-0.0857700 + 3.83575i) q^{91} +(-10.8235 + 2.88117i) q^{93} +1.45495i q^{95} +(3.17914 + 1.83548i) q^{97} +(-6.74093 + 11.5878i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9} - 8 q^{15} + 8 q^{21} + 12 q^{23} - 24 q^{25} + 18 q^{27} + 18 q^{29} + 10 q^{39} + 6 q^{41} + 6 q^{43} + 6 q^{45} - 36 q^{47} + 6 q^{49} + 12 q^{51} + 12 q^{53} + 4 q^{57} - 46 q^{63} + 54 q^{75}+ \cdots + 64 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 - 8 * q^15 + 8 * q^21 + 12 * q^23 - 24 * q^25 + 18 * q^27 + 18 * q^29 + 10 * q^39 + 6 * q^41 + 6 * q^43 + 6 * q^45 - 36 * q^47 + 6 * q^49 + 12 * q^51 + 12 * q^53 + 4 * q^57 - 46 * q^63 + 54 * q^75 - 36 * q^77 + 12 * q^79 + 24 * q^87 + 18 * q^89 - 6 * q^91 + 16 * q^93 + 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

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

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
$3$	0.445548	+	1.67376i	0.257237	+	0.966348i
$3$	0.445548	+	1.67376i	0.257237	+	0.966348i
$4$		0			0
$5$	−0.101589	+	0.175958i	−0.0454320	+	0.0786906i	−0.887847	−	0.460138i	$-0.847800\pi$
$5$	−0.101589	+	0.175958i	−0.0454320	+	0.0786906i	0.842415	+	0.538829i	$0.181133\pi$
$6$		0			0
$7$	1.37377	−	2.26114i	0.519235	−	0.854631i
$7$	1.37377	−	2.26114i	0.519235	−	0.854631i
$8$		0			0
$9$	−2.60297	+	1.49148i	−0.867658	+	0.497161i
$10$		0			0
$11$	3.86995	−	2.23432i	1.16683	−	0.673672i	0.213902	−	0.976855i	$-0.431383\pi$
$11$	3.86995	−	2.23432i	1.16683	−	0.673672i	0.952932	+	0.303183i	$0.0980495\pi$
$12$		0			0
$13$	−1.25586	+	0.725070i	−0.348312	+	0.201098i	−0.663942	−	0.747784i	$-0.731118\pi$
$13$	−1.25586	+	0.725070i	−0.348312	+	0.201098i	0.315629	+	0.948883i	$0.397784\pi$
$14$		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	$-0.705989\pi$
$17$	1.60586	−	2.78143i	0.389478	−	0.674596i	0.992379	+	0.123220i	$0.0393220\pi$
$18$		0			0
$19$	6.20156	−	3.58047i	1.42274	−	0.821417i	0.426203	−	0.904627i	$-0.359851\pi$
$19$	6.20156	−	3.58047i	1.42274	−	0.821417i	0.996532	+	0.0832106i	$0.0265174\pi$
$20$		0			0
$21$	4.39670	+	1.29192i	0.959438	+	0.281919i
$22$		0			0
$23$	1.09687	+	0.633276i	0.228713	+	0.132047i	0.609978	−	0.792418i	$-0.291178\pi$
$23$	1.09687	+	0.633276i	0.228713	+	0.132047i	−0.381265	+	0.924466i	$0.624512\pi$
$24$		0			0
$25$	2.47936	+	4.29438i	0.495872	+	0.858875i
$26$		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
$31$			6.46657i			1.16143i	0.814107	+	0.580715i	$0.197227\pi$
$31$			6.46657i			1.16143i	−0.814107	+	0.580715i	$0.802773\pi$
$32$		0			0
$33$	5.46397	+	5.48189i	0.951155	+	0.954274i
$34$		0			0
$35$	0.258305	+	0.471432i	0.0436616	+	0.0796866i
$36$		0			0
$37$	3.02855	+	5.24561i	0.497891	+	0.862373i	0.999997	−	0.00243316i	$-0.000774500\pi$
$37$	3.02855	+	5.24561i	0.497891	+	0.862373i	−0.502106	+	0.864806i	$0.667441\pi$
$38$		0			0
$39$	−1.77314	−	1.77896i	−0.283930	−	0.284861i
$40$		0			0
$41$	0.370687	+	0.642048i	0.0578915	+	0.100271i	0.893519	−	0.449026i	$-0.148229\pi$
$41$	0.370687	+	0.642048i	0.0578915	+	0.100271i	−0.835627	+	0.549297i	$0.814896\pi$
$42$		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
$45$	0.00199601	−	0.609532i	0.000297547	−	0.0908636i
$46$		0			0
$47$	0.0931689			0.0135901			0.00679504	−	0.999977i	$-0.497837\pi$
$47$	0.0931689			0.0135901			0.00679504	+	0.999977i	$0.497837\pi$
$48$		0			0
$49$	−3.22553	−	6.21257i	−0.460790	−	0.887509i
$50$		0			0
$51$	5.37095	+	1.44857i	0.752083	+	0.202841i
$52$		0			0
$53$	−9.35260	−	5.39973i	−1.28468	−	0.741710i	−0.306979	−	0.951716i	$-0.599318\pi$
$53$	−9.35260	−	5.39973i	−1.28468	−	0.741710i	−0.977700	+	0.210007i	$0.932651\pi$
$54$		0			0
$55$			0.907929i			0.122425i
$56$		0			0
$57$	8.75596	+	8.78468i	1.15976	+	1.16356i
$58$		0			0
$59$	−10.3289			−1.34471			−0.672356	−	0.740228i	$-0.734718\pi$
$59$	−10.3289			−1.34471			−0.672356	+	0.740228i	$0.734718\pi$
$60$		0			0
$61$			8.48390i			1.08625i	0.839651	+	0.543126i	$0.182759\pi$
$61$			8.48390i			1.08625i	−0.839651	+	0.543126i	$0.817241\pi$
$62$		0			0
$63$	−0.203422	+	7.93465i	−0.0256288	+	0.999672i
$64$		0			0
$65$		−	0.294637i		−	0.0365452i
$66$		0			0
$67$	8.05326			0.983862			0.491931	−	0.870634i	$-0.336291\pi$
$67$	8.05326			0.983862			0.491931	+	0.870634i	$0.336291\pi$
$68$		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	0.556502	−	0.830846i	$-0.312143\pi$
$73$	0.984428	+	0.568360i	0.115219	+	0.0665215i	−0.441283	+	0.897368i	$0.645477\pi$
$74$		0			0
$75$	−6.08310	+	6.06321i	−0.702416	+	0.700120i
$76$		0			0
$77$	0.264302	−	11.8199i	0.0301200	−	1.34701i
$78$		0			0
$79$	11.7379			1.32061			0.660306	−	0.750996i	$-0.270427\pi$
$79$	11.7379			1.32061			0.660306	+	0.750996i	$0.270427\pi$
$80$		0			0
$81$	4.55095	−	7.76459i	0.505661	−	0.862732i
$82$		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
$87$	0.491861	−	1.82370i	0.0527331	−	0.195521i
$88$		0			0
$89$	3.52692	+	6.10881i	0.373853	+	0.647532i	0.990155	−	0.139978i	$-0.0447032\pi$
$89$	3.52692	+	6.10881i	0.373853	+	0.647532i	−0.616302	+	0.787510i	$0.711370\pi$
$90$		0			0
$91$	−0.0857700	+	3.83575i	−0.00899114	+	0.402096i
$92$		0			0
$93$	−10.8235	+	2.88117i	−1.12235	+	0.298763i
$94$		0			0
$95$			1.45495i			0.149275i
$96$		0			0
$97$	3.17914	+	1.83548i	0.322793	+	0.186365i	0.652637	−	0.757671i	$-0.273663\pi$
$97$	3.17914	+	1.83548i	0.322793	+	0.186365i	−0.329844	+	0.944036i	$0.606996\pi$
$98$		0			0
$99$	−6.74093	+	11.5878i	−0.677489	+	1.16462i
$100$		0			0
$101$	−6.58410	−	11.4040i	−0.655143	−	1.13474i	−0.981858	−	0.189618i	$-0.939275\pi$
$101$	−6.58410	−	11.4040i	−0.655143	−	1.13474i	0.326715	−	0.945123i	$-0.394058\pi$
$102$		0			0
$103$	−11.7217	−	6.76754i	−1.15498	−	0.666826i	−0.204881	−	0.978787i	$-0.565681\pi$
$103$	−11.7217	−	6.76754i	−1.15498	−	0.666826i	−0.950095	+	0.311961i	$0.899014\pi$
$104$		0			0
$105$	−0.673979	+	0.642388i	−0.0657736	+	0.0626906i
$106$		0			0
$107$	13.0095	−	7.51105i	1.25768	−	0.726121i	0.285056	−	0.958511i	$-0.407988\pi$
$107$	13.0095	−	7.51105i	1.25768	−	0.726121i	0.972623	+	0.232390i	$0.0746545\pi$
$108$		0			0
$109$	2.72560	−	4.72088i	0.261065	−	0.452178i	−0.705460	−	0.708750i	$-0.749260\pi$
$109$	2.72560	−	4.72088i	0.261065	−	0.452178i	0.966525	+	0.256571i	$0.0825928\pi$
$110$		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
$115$	−0.222860	+	0.128668i	−0.0207818	+	0.0119984i
$116$		0			0
$117$	2.18753	−	3.76043i	0.202238	−	0.347652i
$118$		0			0
$119$	−4.08313	−	7.45212i	−0.374300	−	0.683135i
$120$		0			0
$121$	4.48434	−	7.76711i	0.407667	−	0.706101i
$122$		0			0
$123$	−0.909478	+	0.906505i	−0.0820049	+	0.0817368i
$124$		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
$129$	15.7130	+	4.23787i	1.38345	+	0.373123i
$130$		0			0
$131$	−3.06994	+	5.31729i	−0.268222	+	0.464573i	−0.968403	−	0.249392i	$-0.919769\pi$
$131$	−3.06994	+	5.31729i	−0.268222	+	0.464573i	0.700181	+	0.713965i	$0.253103\pi$
$132$		0			0
$133$	0.423541	−	18.9413i	0.0367257	−	1.64242i
$134$		0			0
$135$	1.02110	−	0.268235i	0.0878824	−	0.0230860i
$136$		0			0
$137$	3.70850	−	2.14110i	0.316839	−	0.182927i	−0.333144	−	0.942876i	$-0.608110\pi$
$137$	3.70850	−	2.14110i	0.316839	−	0.182927i	0.649983	+	0.759949i	$0.274776\pi$
$138$		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
$147$	8.96124	−	8.16677i	0.739111	−	0.673584i
$148$		0			0
$149$	4.01230	+	2.31650i	0.328700	+	0.189775i	0.655264	−	0.755400i	$-0.272557\pi$
$149$	4.01230	+	2.31650i	0.328700	+	0.189775i	−0.326564	+	0.945175i	$0.605891\pi$
$150$		0			0
$151$	−7.84739	−	13.5921i	−0.638612	−	1.10611i	−0.985738	−	0.168290i	$-0.946176\pi$
$151$	−7.84739	−	13.5921i	−0.638612	−	1.10611i	0.347126	−	0.937819i	$-0.387158\pi$
$152$		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
$157$		−	7.57020i		−	0.604167i	−0.953281	−	0.302084i	$-0.902318\pi$
$157$		−	7.57020i		−	0.604167i	0.953281	−	0.302084i	$-0.0976822\pi$
$158$		0			0
$159$	4.87084	−	18.0599i	0.386283	−	1.43224i
$160$		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	$-0.0658990\pi$
$163$	3.97454	+	6.88410i	0.311310	+	0.539204i	−0.667337	+	0.744756i	$0.732566\pi$
$164$		0			0
$165$	−1.51966	+	0.404526i	−0.118305	+	0.0314923i
$166$		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
$171$	−10.8023	+	18.5694i	−0.826071	+	1.42004i
$172$		0			0
$173$	−14.4360			−1.09755			−0.548775	−	0.835970i	$-0.684905\pi$
$173$	−14.4360			−1.09755			−0.548775	+	0.835970i	$0.684905\pi$
$174$		0			0
$175$	13.1163	+	0.293289i	0.991496	+	0.0221705i
$176$		0			0
$177$	−4.60204	−	17.2882i	−0.345910	−	1.29946i
$178$		0			0
$179$	−19.7102	−	11.3797i	−1.47321	−	0.850558i	−0.473665	−	0.880705i	$-0.657069\pi$
$179$	−19.7102	−	11.3797i	−1.47321	−	0.850558i	−0.999545	+	0.0301471i	$0.990402\pi$
$180$		0			0
$181$			8.95105i			0.665326i	0.943046	+	0.332663i	$0.107947\pi$
$181$			8.95105i			0.665326i	−0.943046	+	0.332663i	$0.892053\pi$
$182$		0			0
$183$	−14.2000	+	3.77998i	−1.04970	+	0.279424i
$184$		0			0
$185$	−1.23067			−0.0904809
$186$		0			0
$187$		−	14.3520i		−	1.04952i
$188$		0			0
$189$	−13.3714	+	3.19478i	−0.972624	+	0.232386i
$190$		0			0
$191$		−	24.5457i		−	1.77607i	−0.459779	−	0.888033i	$-0.652072\pi$
$191$		−	24.5457i		−	1.77607i	0.459779	−	0.888033i	$-0.347928\pi$
$192$		0			0
$193$	4.56518			0.328609			0.164305	−	0.986410i	$-0.447462\pi$
$193$	4.56518			0.328609			0.164305	+	0.986410i	$0.447462\pi$
$194$		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	$-0.509264\pi$
$199$	−12.8273	−	7.40587i	−0.909306	−	0.524988i	−0.880208	+	0.474589i	$0.842597\pi$
$200$		0			0
$201$	3.58811	+	13.4793i	0.253086	+	0.950753i
$202$		0			0
$203$	−2.53036	+	1.38643i	−0.177597	+	0.0973080i
$204$		0			0
$205$	−0.150631			−0.0105205
$206$		0			0
$207$	−3.79964	−	0.0124425i	−0.264093	−	0.000864815i
$208$		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
$213$	−26.2407	+	6.98515i	−1.79799	+	0.478615i
$214$		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
$219$	−0.512691	+	1.90093i	−0.0346444	+	0.128453i
$220$		0			0
$221$			4.65744i			0.313293i
$222$		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
$227$	−14.5787	−	25.2511i	−0.967625	−	1.67598i	−0.702390	−	0.711793i	$-0.747884\pi$
$227$	−14.5787	−	25.2511i	−0.967625	−	1.67598i	−0.265236	−	0.964184i	$-0.585450\pi$
$228$		0			0
$229$	−15.0793	−	8.70604i	−0.996469	−	0.575312i	−0.0892672	−	0.996008i	$-0.528453\pi$
$229$	−15.0793	−	8.70604i	−0.996469	−	0.575312i	−0.907202	+	0.420696i	$0.861786\pi$
$230$		0			0
$231$	19.9016	−	4.82397i	1.30943	−	0.317394i
$232$		0			0
$233$	−14.3517	+	8.28596i	−0.940212	+	0.542831i	−0.890027	−	0.455908i	$-0.849314\pi$
$233$	−14.3517	+	8.28596i	−0.940212	+	0.542831i	−0.0501850	+	0.998740i	$0.515981\pi$
$234$		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
$241$	9.40347	−	5.42909i	0.605731	−	0.349719i	−0.165562	−	0.986199i	$-0.552944\pi$
$241$	9.40347	−	5.42909i	0.605731	−	0.349719i	0.771293	+	0.636481i	$0.219610\pi$
$242$		0			0
$243$	15.0238	+	4.15772i	0.963775	+	0.266718i
$244$		0			0
$245$	1.42083	+	0.0635731i	0.0907733	+	0.00406154i
$246$		0			0
$247$	−5.19218	+	8.99313i	−0.330371	+	0.572219i
$248$		0			0
$249$	−7.69026	−	2.07410i	−0.487350	−	0.131441i
$250$		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
$255$	−0.800517	+	0.797900i	−0.0501303	+	0.0499664i
$256$		0			0
$257$	−13.6584	+	23.6571i	−0.851989	+	1.47569i	0.0274208	+	0.999624i	$0.491271\pi$
$257$	−13.6584	+	23.6571i	−0.851989	+	1.47569i	−0.879410	+	0.476065i	$0.842063\pi$
$258$		0			0
$259$	16.0216	+	0.358254i	0.995534	+	0.0222608i
$260$		0			0
$261$	3.27160	+	0.0107134i	0.202507	+	0.000663141i
$262$		0			0
$263$	11.9650	−	6.90798i	0.737792	−	0.425964i	−0.0834742	−	0.996510i	$-0.526602\pi$
$263$	11.9650	−	6.90798i	0.737792	−	0.425964i	0.821266	+	0.570546i	$0.193268\pi$
$264$		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	0.326568	+	0.945174i	$0.394108\pi$
$269$	−10.7471	+	18.6145i	−0.655260	+	1.13494i	−0.981828	+	0.189770i	$0.939226\pi$
$270$		0			0
$271$	−27.2614	+	15.7394i	−1.65601	+	0.956101i	−0.681488	+	0.731829i	$0.738667\pi$
$271$	−27.2614	+	15.7394i	−1.65601	+	0.956101i	−0.974527	+	0.224271i	$0.928000\pi$
$272$		0			0
$273$	−6.45835	+	1.56545i	−0.390877	+	0.0947454i
$274$		0			0
$275$	19.1900	+	11.0793i	1.15720	+	0.668110i
$276$		0			0
$277$	5.92040	+	10.2544i	0.355722	+	0.616129i	0.987241	−	0.159231i	$-0.0509015\pi$
$277$	5.92040	+	10.2544i	0.355722	+	0.616129i	−0.631519	+	0.775361i	$0.717568\pi$
$278$		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
$283$			1.35876i			0.0807697i	0.999184	+	0.0403848i	$0.0128584\pi$
$283$			1.35876i			0.0807697i	−0.999184	+	0.0403848i	$0.987142\pi$
$284$		0			0
$285$	−2.43524	+	0.648249i	−0.144251	+	0.0383990i
$286$		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
$291$	−1.65570	+	6.13893i	−0.0970588	+	0.359871i
$292$		0			0
$293$	8.10060	+	14.0307i	0.473242	+	0.819680i	0.999531	−	0.0306263i	$-0.00975018\pi$
$293$	8.10060	+	14.0307i	0.473242	+	0.819680i	−0.526289	+	0.850306i	$0.676417\pi$
$294$		0			0
$295$	1.04931	−	1.81745i	0.0610931	−	0.105816i
$296$		0			0
$297$	−22.3987	−	6.11980i	−1.29971	−	0.355107i
$298$		0			0
$299$	−1.83668			−0.106218
$300$		0			0
$301$	−11.9454	−	21.8015i	−0.688522	−	1.25662i
$302$		0			0
$303$	16.1541	−	16.1013i	0.928027	−	0.924993i
$304$		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
$311$	0.626668			0.0355351			0.0177676	−	0.999842i	$-0.494344\pi$
$311$	0.626668			0.0355351			0.0177676	+	0.999842i	$0.494344\pi$
$312$		0			0
$313$			5.12142i			0.289480i	0.989470	+	0.144740i	$0.0462345\pi$
$313$			5.12142i			0.289480i	−0.989470	+	0.144740i	$0.953765\pi$
$314$		0			0
$315$	−1.37550	−	0.841868i	−0.0775004	−	0.0474339i
$316$		0			0
$317$		−	4.18928i		−	0.235294i	−0.993055	−	0.117647i	$-0.962465\pi$
$317$		−	4.18928i		−	0.235294i	0.993055	−	0.117647i	$-0.0375351\pi$
$318$		0			0
$319$	−4.87321			−0.272848
$320$		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
$327$	9.11603	+	2.45864i	0.504118	+	0.135963i
$328$		0			0
$329$	0.127992	−	0.210668i	0.00705645	−	0.0116145i
$330$		0			0
$331$	−25.9419			−1.42590			−0.712949	−	0.701216i	$-0.752641\pi$
$331$	−25.9419			−1.42590			−0.712949	+	0.701216i	$0.752641\pi$
$332$		0			0
$333$	−15.7070	−	9.13715i	−0.860738	−	0.500713i
$334$		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
$339$	−8.51412	−	8.54204i	−0.462423	−	0.463940i
$340$		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
$345$	−0.314655	−	0.315687i	−0.0169404	−	0.0169960i
$346$		0			0
$347$		−	28.9338i		−	1.55325i	−0.629965	−	0.776624i	$-0.716931\pi$
$347$		−	28.9338i		−	1.55325i	0.629965	−	0.776624i	$-0.283069\pi$
$348$		0			0
$349$	−20.7481	−	11.9789i	−1.11062	−	0.641217i	−0.171630	−	0.985161i	$-0.554903\pi$
$349$	−20.7481	−	11.9789i	−1.11062	−	0.641217i	−0.938990	+	0.343944i	$0.888237\pi$
$350$		0			0
$351$	7.26872	+	1.98597i	0.387976	+	0.106003i
$352$		0			0
$353$	7.79472	+	13.5009i	0.414871	+	0.718578i	0.995415	−	0.0956510i	$-0.0304933\pi$
$353$	7.79472	+	13.5009i	0.414871	+	0.718578i	−0.580544	+	0.814229i	$0.697160\pi$
$354$		0			0
$355$	−2.75861	−	1.59268i	−0.146412	−	0.0845308i
$356$		0			0
$357$	10.6539	−	10.1545i	0.563862	−	0.537432i
$358$		0			0
$359$	−11.7053	+	6.75809i	−0.617785	+	0.356678i	−0.776006	−	0.630726i	$-0.782757\pi$
$359$	−11.7053	+	6.75809i	−0.617785	+	0.356678i	0.158221	+	0.987404i	$0.449424\pi$
$360$		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
$367$	−16.6091	+	9.58924i	−0.866986	+	0.500554i	−0.866345	−	0.499445i	$-0.833537\pi$
$367$	−16.6091	+	9.58924i	−0.866986	+	0.500554i	−0.000640244		1.00000i	$0.500204\pi$
$368$		0			0
$369$	−1.92249	−	1.11836i	−0.100081	−	0.0582195i
$370$		0			0
$371$	−25.0578	+	13.7296i	−1.30094	+	0.712805i
$372$		0			0
$373$	−1.26770	+	2.19571i	−0.0656388	+	0.113690i	−0.896977	−	0.442077i	$-0.854242\pi$
$373$	−1.26770	+	2.19571i	−0.0656388	+	0.113690i	0.831338	+	0.555767i	$0.187575\pi$
$374$		0			0
$375$	−0.901519	−	3.38669i	−0.0465543	−	0.174888i
$376$		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
$381$	−1.19727	−	4.49770i	−0.0613378	−	0.230424i
$382$		0			0
$383$	−2.83725	+	4.91425i	−0.144976	+	0.251107i	−0.929364	−	0.369164i	$-0.879644\pi$
$383$	−2.83725	+	4.91425i	−0.144976	+	0.251107i	0.784388	+	0.620271i	$0.212977\pi$
$384$		0			0
$385$	2.05296	+	1.24728i	0.104628	+	0.0635674i
$386$		0			0
$387$	−0.0923061	+	28.1880i	−0.00469218	+	1.43288i
$388$		0			0
$389$	6.82994	−	3.94327i	0.346292	−	0.199932i	−0.316759	−	0.948506i	$-0.602595\pi$
$389$	6.82994	−	3.94327i	0.346292	−	0.199932i	0.663051	+	0.748574i	$0.269261\pi$
$390$		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	−0.220079	−	0.975482i	$-0.570632\pi$
$397$	10.2548	−	5.92061i	0.514674	−	0.297147i	0.734753	+	0.678335i	$0.237298\pi$
$398$		0			0
$399$	31.8921	−	7.73037i	1.59660	−	0.387002i
$400$		0			0
$401$	33.0589	+	19.0866i	1.65088	+	0.953139i	0.976709	+	0.214567i	$0.0688342\pi$
$401$	33.0589	+	19.0866i	1.65088	+	0.953139i	0.674175	+	0.738571i	$0.264499\pi$
$402$		0			0
$403$	−4.68871	−	8.12109i	−0.233561	−	0.404540i
$404$		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
$409$			13.0282i			0.644204i	0.946705	+	0.322102i	$0.104389\pi$
$409$			13.0282i			0.644204i	−0.946705	+	0.322102i	$0.895611\pi$
$410$		0			0
$411$	5.23602	+	5.25319i	0.258274	+	0.259121i
$412$		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
$417$	4.85665	+	4.87258i	0.237831	+	0.238611i
$418$		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
$423$	−0.242516	+	0.138960i	−0.0117915	+	0.00675646i
$424$		0			0
$425$	15.9260			0.772525
$426$		0			0
$427$	19.1833	+	11.6549i	0.928345	+	0.564020i
$428$		0			0
$429$	−10.8367	−	2.92271i	−0.523202	−	0.141110i
$430$		0			0
$431$	10.0071	+	5.77758i	0.482023	+	0.278296i	0.721259	−	0.692665i	$-0.243564\pi$
$431$	10.0071	+	5.77758i	0.482023	+	0.278296i	−0.239236	+	0.970961i	$0.576897\pi$
$432$		0			0
$433$			0.696999i			0.0334956i	0.999860	+	0.0167478i	$0.00533125\pi$
$433$			0.696999i			0.0334956i	−0.999860	+	0.0167478i	$0.994669\pi$
$434$		0			0
$435$	0.270926	+	0.271815i	0.0129899	+	0.0130325i
$436$		0			0
$437$	9.06971			0.433863
$438$		0			0
$439$			23.6449i			1.12851i	0.825601	+	0.564254i	$0.190836\pi$
$439$			23.6449i			1.12851i	−0.825601	+	0.564254i	$0.809164\pi$
$440$		0			0
$441$	17.6619	+	11.3603i	0.841043	+	0.540968i
$442$		0			0
$443$		−	13.0837i		−	0.621625i	−0.950471	−	0.310812i	$-0.899399\pi$
$443$		−	13.0837i		−	0.621625i	0.950471	−	0.310812i	$-0.100601\pi$
$444$		0			0
$445$	−1.43319			−0.0679396
$446$		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
$453$	19.2536	−	19.1906i	0.904611	−	0.901654i
$454$		0			0
$455$	−0.666216	−	0.404762i	−0.0312327	−	0.0189755i
$456$		0			0
$457$	−11.0367			−0.516273			−0.258137	−	0.966108i	$-0.583108\pi$
$457$	−11.0367			−0.516273			−0.258137	+	0.966108i	$0.583108\pi$
$458$		0			0
$459$	−16.1410	+	4.24009i	−0.753396	+	0.197911i
$460$		0			0
$461$	6.69369	−	11.5938i	0.311756	−	0.539978i	−0.666986	−	0.745070i	$-0.732416\pi$
$461$	6.69369	−	11.5938i	0.311756	−	0.539978i	0.978743	+	0.205092i	$0.0657494\pi$
$462$		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
$465$	0.592588	−	2.19717i	0.0274806	−	0.101891i
$466$		0			0
$467$	7.97308	+	13.8098i	0.368950	+	0.639041i	0.989402	−	0.145204i	$-0.0463839\pi$
$467$	7.97308	+	13.8098i	0.368950	+	0.639041i	−0.620451	+	0.784245i	$0.713051\pi$
$468$		0			0
$469$	11.0633	−	18.2096i	0.510856	−	0.840839i
$470$		0			0
$471$	12.6707	−	3.37288i	0.583836	−	0.155414i
$472$		0			0
$473$		−	41.9875i		−	1.93059i
$474$		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
$479$	15.3594	+	26.6032i	0.701787	+	1.21553i	0.967839	+	0.251572i	$0.0809476\pi$
$479$	15.3594	+	26.6032i	0.701787	+	1.21553i	−0.266051	+	0.963959i	$0.585719\pi$
$480$		0			0
$481$	−7.60687	−	4.39183i	−0.346843	−	0.200250i
$482$		0			0
$483$	4.00445	+	4.20138i	0.182209	+	0.191170i
$484$		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	$-0.839439\pi$
$487$	−0.423250	+	0.733091i	−0.0191793	+	0.0332195i	0.856276	+	0.516518i	$0.172772\pi$
$488$		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
$493$	−3.03326	+	1.75125i	−0.136611	+	0.0788724i
$494$		0			0
$495$	−1.35416	−	2.36332i	−0.0608651	−	0.106223i
$496$		0			0
$497$	35.4495	+	21.5375i	1.59013	+	0.966088i
$498$		0			0
$499$	−20.5932	+	35.6684i	−0.921877	+	1.59674i	−0.125368	+	0.992110i	$0.540011\pi$
$499$	−20.5932	+	35.6684i	−0.921877	+	1.59674i	−0.796509	+	0.604627i	$0.793322\pi$
$500$		0			0
$501$	−4.22842	+	4.21459i	−0.188912	+	0.188294i
$502$		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
$507$	−18.2232	−	4.91488i	−0.809320	−	0.218277i
$508$		0			0
$509$	8.39409	−	14.5390i	0.372062	−	0.644430i	−0.617821	−	0.786319i	$-0.711984\pi$
$509$	8.39409	−	14.5390i	0.372062	−	0.644430i	0.989883	+	0.141889i	$0.0453176\pi$
$510$		0			0
$511$	2.63752	−	1.44514i	0.116677	−	0.0639292i
$512$		0			0
$513$	−35.8937	−	9.80692i	−1.58475	−	0.432986i
$514$		0			0
$515$	2.38160	−	1.37502i	0.104946	−	0.0605905i
$516$		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	$-0.847392\pi$
$521$	−1.00777	+	1.74551i	−0.0441512	+	0.0764722i	0.843105	+	0.537749i	$0.180725\pi$
$522$		0			0
$523$	37.4865	−	21.6429i	1.63917	−	0.946376i	0.658052	−	0.752973i	$-0.271381\pi$
$523$	37.4865	−	21.6429i	1.63917	−	0.946376i	0.981119	−	0.193403i	$-0.0619526\pi$
$524$		0			0
$525$	5.35302	+	22.0842i	0.233625	+	0.963833i
$526$		0			0
$527$	17.9863	+	10.3844i	0.783496	+	0.452352i
$528$		0			0
$529$	−10.6979	−	18.5293i	−0.465127	−	0.805624i
$530$		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
$535$			3.05217i			0.131957i
$536$		0			0
$537$	10.2651	−	38.0604i	0.442971	−	1.64243i
$538$		0			0
$539$	−26.3635	−	16.8355i	−1.13556	−	0.725155i
$540$		0			0
$541$	12.3502	+	21.3912i	0.530977	+	0.919679i	0.999347	+	0.0361463i	$0.0115082\pi$
$541$	12.3502	+	21.3912i	0.530977	+	0.919679i	−0.468370	+	0.883533i	$0.655158\pi$
$542$		0			0
$543$	−14.9819	+	3.98812i	−0.642937	+	0.171147i
$544$		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
$549$	−12.6536	−	22.0834i	−0.540042	−	0.942495i
$550$		0			0
$551$	−7.80928			−0.332687
$552$		0			0
$553$	16.1251	−	26.5410i	0.685708	−	1.12864i
$554$		0			0
$555$	−0.548324	−	2.05986i	−0.0232750	−	0.0874360i
$556$		0			0
$557$	−22.3351	−	12.8952i	−0.946369	−	0.546386i	−0.0544176	−	0.998518i	$-0.517330\pi$
$557$	−22.3351	−	12.8952i	−0.946369	−	0.546386i	−0.891951	+	0.452132i	$0.850664\pi$
$558$		0			0
$559$			13.6256i			0.576300i
$560$		0			0
$561$	24.0219	−	6.39450i	1.01420	−	0.269976i
$562$		0			0
$563$	37.9718			1.60032			0.800161	−	0.599786i	$-0.204747\pi$
$563$	37.9718			1.60032			0.800161	+	0.599786i	$0.204747\pi$
$564$		0			0
$565$		−	1.41476i		−	0.0595195i
$566$		0			0
$567$	−11.3049	−	20.9571i	−0.474761	−	0.880115i
$568$		0			0
$569$			22.9594i			0.962507i	0.876582	+	0.481253i	$0.159818\pi$
$569$			22.9594i			0.962507i	−0.876582	+	0.481253i	$0.840182\pi$
$570$		0			0
$571$	11.8246			0.494842			0.247421	−	0.968908i	$-0.420417\pi$
$571$	11.8246			0.494842			0.247421	+	0.968908i	$0.420417\pi$
$572$		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	−0.0454415	−	0.998967i	$-0.514469\pi$
$577$	−22.4185	−	12.9433i	−0.933293	−	0.538837i	−0.887852	+	0.460130i	$0.847803\pi$
$578$		0			0
$579$	2.03401	+	7.64104i	0.0845305	+	0.317551i
$580$		0			0
$581$	5.84633	+	10.6701i	0.242547	+	0.442671i
$582$		0			0
$583$	−48.2588			−1.99868
$584$		0			0
$585$	0.439446	+	0.766932i	0.0181689	+	0.0317087i
$586$		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
$591$	20.3053	−	5.40516i	0.835247	−	0.222339i
$592$		0			0
$593$	−11.0904	−	19.2092i	−0.455430	−	0.788828i	0.543283	−	0.839550i	$-0.317181\pi$
$593$	−11.0904	−	19.2092i	−0.455430	−	0.788828i	−0.998713	+	0.0507220i	$0.983848\pi$
$594$		0			0
$595$	1.72606	+	0.0385959i	0.0707615	+	0.00158228i
$596$		0			0
$597$	6.68048	−	24.7696i	0.273414	−	1.01375i
$598$		0			0
$599$		−	25.4145i		−	1.03841i	−0.854650	−	0.519204i	$-0.826229\pi$
$599$		−	25.4145i		−	1.03841i	0.854650	−	0.519204i	$-0.173771\pi$
$600$		0			0
$601$	3.04486	+	1.75795i	0.124203	+	0.0717084i	0.560814	−	0.827942i	$-0.310488\pi$
$601$	3.04486	+	1.75795i	0.124203	+	0.0717084i	−0.436612	+	0.899650i	$0.643822\pi$
$602$		0			0
$603$	−20.9624	+	12.0113i	−0.853656	+	0.489138i
$604$		0			0
$605$	0.911121	+	1.57811i	0.0370423	+	0.0641592i
$606$		0			0
$607$	−28.3732	−	16.3813i	−1.15163	−	0.664896i	−0.202349	−	0.979314i	$-0.564857\pi$
$607$	−28.3732	−	16.3813i	−1.15163	−	0.664896i	−0.949285	+	0.314418i	$0.898191\pi$
$608$		0			0
$609$	−3.44795	−	3.61751i	−0.139718	−	0.146589i
$610$		0			0
$611$	−0.117007	+	0.0675539i	−0.00473359	+	0.00273294i
$612$		0			0
$613$	−0.757167	+	1.31145i	−0.0305817	+	0.0529691i	−0.880911	−	0.473282i	$-0.843069\pi$
$613$	−0.757167	+	1.31145i	−0.0305817	+	0.0529691i	0.850329	+	0.526251i	$0.176403\pi$
$614$		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
$619$	−28.2719	+	16.3228i	−1.13634	+	0.656068i	−0.945522	−	0.325557i	$-0.894448\pi$
$619$	−28.2719	+	16.3228i	−1.13634	+	0.656068i	−0.190821	+	0.981625i	$0.561115\pi$
$620$		0			0
$621$	−1.67209	−	6.36524i	−0.0670988	−	0.255428i
$622$		0			0
$623$	18.6580	+	0.417207i	0.747519	+	0.0167150i
$624$		0			0
$625$	−12.1912	+	21.1158i	−0.487650	+	0.844634i
$626$		0			0
$627$	53.5129	+	14.4327i	2.13710	+	0.576386i
$628$		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
$633$	−9.25252	+	9.22228i	−0.367755	+	0.366553i
$634$		0			0
$635$	0.272988	−	0.472829i	0.0108332	−	0.0187636i
$636$		0			0
$637$	8.55535	+	5.46336i	0.338975	+	0.216466i
$638$		0			0
$639$	−23.3830	−	40.8086i	−0.925017	−	1.61436i
$640$		0			0
$641$	−28.1395	+	16.2464i	−1.11144	+	0.641692i	−0.939203	−	0.343362i	$-0.888434\pi$
$641$	−28.1395	+	16.2464i	−1.11144	+	0.641692i	−0.172241	+	0.985055i	$0.555101\pi$
$642$		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	−0.997702	−	0.0677505i	$-0.978418\pi$
$647$	−11.1964	+	19.3928i	−0.440177	+	0.762410i	0.557525	+	0.830160i	$0.311751\pi$
$648$		0			0
$649$	−39.9725	+	23.0781i	−1.56906	+	0.905895i
$650$		0			0
$651$	−8.35426	+	28.4315i	−0.327429	+	1.11432i
$652$		0			0
$653$	35.2684	+	20.3622i	1.38016	+	0.796836i	0.992178	−	0.124831i	$-0.0398390\pi$
$653$	35.2684	+	20.3622i	1.38016	+	0.796836i	0.387982	+	0.921667i	$0.373172\pi$
$654$		0			0
$655$	−0.623744	−	1.08036i	−0.0243717	−	0.0422130i
$656$		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
$661$			37.3428i			1.45247i	0.687448	+	0.726234i	$0.258731\pi$
$661$			37.3428i			1.45247i	−0.687448	+	0.726234i	$0.741269\pi$
$662$		0			0
$663$	−7.79546	+	2.07511i	−0.302751	+	0.0805907i
$664$		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
$669$	−13.1682	+	48.8245i	−0.509112	+	1.88766i
$670$		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
$675$	6.79097	−	24.8552i	0.261384	−	0.956679i
$676$		0			0
$677$	−20.8762			−0.802338			−0.401169	−	0.916004i	$-0.631396\pi$
$677$	−20.8762			−0.802338			−0.401169	+	0.916004i	$0.631396\pi$
$678$		0			0
$679$	8.51768	−	4.66698i	0.326879	−	0.179102i
$680$		0			0
$681$	35.7689	−	35.6520i	1.37067	−	1.36619i
$682$		0			0
$683$	−1.17377	−	0.677674i	−0.0449129	−	0.0259305i	0.477375	−	0.878699i	$-0.341588\pi$
$683$	−1.17377	−	0.677674i	−0.0449129	−	0.0259305i	−0.522288	+	0.852769i	$0.674922\pi$
$684$		0			0
$685$			0.870051i			0.0332430i
$686$		0			0
$687$	7.85331	−	29.1182i	0.299623	−	1.11093i
$688$		0			0
$689$	15.6607			0.596626
$690$		0			0
$691$		−	11.1087i		−	0.422595i	−0.977422	−	0.211297i	$-0.932231\pi$
$691$		−	11.1087i		−	0.422595i	0.977422	−	0.211297i	$-0.0677688\pi$
$692$		0			0
$693$	16.9413	+	31.1612i	0.643546	+	1.18372i
$694$		0			0
$695$			0.807014i			0.0306118i
$696$		0			0
$697$	2.38108			0.0901900
$698$		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
$705$	−0.0316564	−	0.00853788i	−0.00119225	−	0.000321555i
$706$		0			0
$707$	−34.8311	−	0.778847i	−1.30996	−	0.0292916i
$708$		0			0
$709$	3.89872			0.146420			0.0732098	−	0.997317i	$-0.476676\pi$
$709$	3.89872			0.146420			0.0732098	+	0.997317i	$0.476676\pi$
$710$		0			0
$711$	−30.5533	+	17.5068i	−1.14584	+	0.656557i
$712$		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
$717$	11.9380	+	11.9771i	0.445831	+	0.447294i
$718$		0			0
$719$	24.4338	+	42.3205i	0.911225	+	1.57829i	0.812336	+	0.583190i	$0.198196\pi$
$719$	24.4338	+	42.3205i	0.911225	+	1.57829i	0.0988894	+	0.995098i	$0.468471\pi$
$720$		0			0
$721$	−31.4053	+	17.2075i	−1.16959	+	0.640840i
$722$		0			0
$723$	13.2767	+	13.3203i	0.493767	+	0.495386i
$724$		0			0
$725$		−	5.40767i		−	0.200836i
$726$		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
$731$	−15.0887	−	26.1345i	−0.558077	−	0.966618i
$732$		0			0
$733$	13.9956	+	8.08036i	0.516939	+	0.298455i	0.735681	−	0.677328i	$-0.236862\pi$
$733$	13.9956	+	8.08036i	0.516939	+	0.298455i	−0.218742	+	0.975783i	$0.570195\pi$
$734$		0			0
$735$	0.526640	+	2.40645i	0.0194254	+	0.0887634i
$736$		0			0
$737$	31.1657	−	17.9935i	1.14800	−	0.662800i
$738$		0			0
$739$	15.7914	−	27.3515i	0.580895	−	1.00614i	−0.414478	−	0.910059i	$-0.636036\pi$
$739$	15.7914	−	27.3515i	0.580895	−	1.00614i	0.995374	−	0.0960807i	$-0.0306307\pi$
$740$		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
$745$	−0.815211	+	0.470662i	−0.0298670	+	0.0172437i
$746$		0			0
$747$	0.0451765	−	13.7958i	0.00165292	−	0.504761i
$748$		0			0
$749$	0.888498	−	39.7348i	0.0324650	−	1.45188i
$750$		0			0
$751$	−10.4533	+	18.1056i	−0.381446	+	0.660684i	−0.991269	−	0.131854i	$-0.957907\pi$
$751$	−10.4533	+	18.1056i	−0.381446	+	0.660684i	0.609823	+	0.792537i	$0.291240\pi$
$752$		0			0
$753$	−12.2149	−	45.8870i	−0.445136	−	1.67222i
$754$		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
$759$	2.52169	+	9.47310i	0.0915317	+	0.343852i
$760$		0			0
$761$	−10.4212	+	18.0500i	−0.377768	+	0.654313i	−0.990737	−	0.135794i	$-0.956642\pi$
$761$	−10.4212	+	18.0500i	−0.377768	+	0.654313i	0.612969	+	0.790107i	$0.289975\pi$
$762$		0			0
$763$	−6.93024	−	12.6484i	−0.250892	−	0.457902i
$764$		0			0
$765$	−1.69217	−	0.984374i	−0.0611804	−	0.0355901i
$766$		0			0
$767$	12.9717	−	7.48920i	0.468380	−	0.270419i
$768$		0			0
$769$	−25.3167	+	14.6166i	−0.912944	+	0.527088i	−0.881377	−	0.472413i	$-0.843383\pi$
$769$	−25.3167	+	14.6166i	−0.912944	+	0.527088i	−0.0315668	+	0.999502i	$0.510050\pi$
$770$		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	$-0.962154\pi$
$773$	−10.9472	+	18.9612i	−0.393745	+	0.681986i	0.599195	+	0.800603i	$0.295487\pi$
$774$		0			0
$775$	−27.7699	+	16.0329i	−0.997523	+	0.575920i
$776$		0			0
$777$	6.53876	+	26.9760i	0.234577	+	0.967759i
$778$		0			0
$779$	4.59767	+	2.65447i	0.164729	+	0.0951061i
$780$		0			0
$781$	35.0289	+	60.6718i	1.25343	+	2.17101i
$782$		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
$787$		−	8.17907i		−	0.291552i	−0.989318	−	0.145776i	$-0.953432\pi$
$787$		−	8.17907i		−	0.291552i	0.989318	−	0.145776i	$-0.0465679\pi$
$788$		0			0
$789$	16.8933	+	16.9487i	0.601417	+	0.603390i
$790$		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
$795$	2.68295	+	2.69175i	0.0951544	+	0.0954665i
$796$		0			0
$797$	−4.86546	−	8.42722i	−0.172343	−	0.298508i	0.766895	−	0.641772i	$-0.221801\pi$
$797$	−4.86546	−	8.42722i	−0.172343	−	0.298508i	−0.939239	+	0.343265i	$0.888467\pi$
$798$		0			0
$799$	0.149616	−	0.259143i	0.00529304	−	0.00916782i
$800$		0			0
$801$	−18.2917	−	10.6407i	−0.646304	−	0.375971i
$802$		0			0
$803$	5.07959			0.179255
$804$		0			0
$805$	−0.0152204	+	0.680677i	−0.000536449	+	0.0239907i
$806$		0			0
$807$	−35.9446	−	9.69442i	−1.26531	−	0.341260i
$808$		0			0
$809$	−36.2263	−	20.9153i	−1.27365	−	0.735341i	−0.297976	−	0.954574i	$-0.596311\pi$
$809$	−36.2263	−	20.9153i	−1.27365	−	0.735341i	−0.975673	+	0.219232i	$0.929645\pi$
$810$		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
$815$	−1.61508			−0.0565737
$816$		0			0
$817$		−	67.2846i		−	2.35399i
$818$		0			0
$819$	−5.49770	−	10.1123i	−0.192105	−	0.353352i
$820$		0			0
$821$			22.3345i			0.779479i	0.920925	+	0.389740i	$0.127435\pi$
$821$			22.3345i			0.779479i	−0.920925	+	0.389740i	$0.872565\pi$
$822$		0			0
$823$	27.0616			0.943308			0.471654	−	0.881784i	$-0.343657\pi$
$823$	27.0616			0.943308			0.471654	+	0.881784i	$0.343657\pi$
$824$		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	−0.177801	−	0.984066i	$-0.556898\pi$
$829$	−32.2166	−	18.6003i	−1.11893	−	0.646013i	−0.941127	+	0.338053i	$0.890232\pi$
$830$		0			0
$831$	−14.5257	+	14.4782i	−0.503891	+	0.502243i
$832$		0			0
$833$	−22.4596	−	1.00493i	−0.778178	−	0.0348186i
$834$		0			0
$835$	−0.700325			−0.0242357
$836$		0			0
$837$	23.8761	−	23.6427i	0.825279	−	0.817211i
$838$		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
$843$	10.1342	−	37.5750i	0.349039	−	1.29415i
$844$		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
$849$	−2.27424	+	0.605391i	−0.0780516	+	0.0207770i
$850$		0			0
$851$			7.67165i			0.262981i
$852$		0			0
$853$	−40.4364	−	23.3459i	−1.38451	−	0.799350i	−0.391824	−	0.920040i	$-0.628156\pi$
$853$	−40.4364	−	23.3459i	−1.38451	−	0.799350i	−0.992690	+	0.120690i	$0.961489\pi$
$854$		0			0
$855$	−2.17003	−	3.78719i	−0.0742135	−	0.129519i
$856$		0			0
$857$	−2.66924	−	4.62326i	−0.0911795	−	0.157928i	0.816828	−	0.576881i	$-0.195730\pi$
$857$	−2.66924	−	4.62326i	−0.0911795	−	0.157928i	−0.908008	+	0.418953i	$0.862397\pi$
$858$		0			0
$859$	8.70865	+	5.02794i	0.297135	+	0.171551i	0.641155	−	0.767411i	$-0.278455\pi$
$859$	8.70865	+	5.02794i	0.297135	+	0.171551i	−0.344020	+	0.938962i	$0.611789\pi$
$860$		0			0
$861$	0.800325	+	3.30179i	0.0272750	+	0.112525i
$862$		0			0
$863$	32.7144	−	18.8877i	1.11361	−	0.642943i	0.173849	−	0.984772i	$-0.444380\pi$
$863$	32.7144	−	18.8877i	1.11361	−	0.642943i	0.939762	+	0.341829i	$0.111046\pi$
$864$		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
$871$	−10.1137	+	5.83917i	−0.342691	+	0.197853i
$872$		0			0
$873$	−11.0128	−	0.0360633i	−0.372727	−	0.00122056i
$874$		0			0
$875$	−2.77967	+	4.57518i	−0.0939701	+	0.154669i
$876$		0			0
$877$	23.2632	−	40.2931i	0.785543	−	1.36060i	−0.143131	−	0.989704i	$-0.545717\pi$
$877$	23.2632	−	40.2931i	0.785543	−	1.36060i	0.928674	−	0.370897i	$-0.120950\pi$
$878$		0			0
$879$	−19.8748	+	19.8098i	−0.670361	+	0.668169i
$880$		0			0
$881$	−31.9474			−1.07633			−0.538167	−	0.842838i	$-0.680883\pi$
$881$	−31.9474			−1.07633			−0.538167	+	0.842838i	$0.680883\pi$
$882$		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
$885$	3.50951	+	0.946531i	0.117971	+	0.0318173i
$886$		0			0
$887$	−20.3084	+	35.1752i	−0.681889	+	1.18107i	0.292514	+	0.956261i	$0.405508\pi$
$887$	−20.3084	+	35.1752i	−0.681889	+	1.18107i	−0.974404	+	0.224806i	$0.927825\pi$
$888$		0			0
$889$	−3.69155	+	6.07609i	−0.123811	+	0.203785i
$890$		0			0
$891$	0.263396	−	40.2168i	0.00882409	−	1.34731i
$892$		0			0
$893$	0.577793	−	0.333589i	0.0193351	−	0.0111631i
$894$		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
$903$	31.1684	−	29.7074i	1.03722	−	0.988601i
$904$		0			0
$905$	−1.57500	−	0.909330i	−0.0523549	−	0.0302271i
$906$		0			0
$907$	−14.9984	−	25.9781i	−0.498015	−	0.862588i	0.501982	−	0.864878i	$-0.332604\pi$
$907$	−14.9984	−	25.9781i	−0.498015	−	0.862588i	−0.999997	+	0.00229028i	$0.999271\pi$
$908$		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
$913$			20.5495i			0.680091i
$914$		0			0
$915$	0.777454	−	2.88261i	0.0257018	−	0.0952962i
$916$		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	$-0.270814\pi$
$919$	−9.74272	−	16.8749i	−0.321383	−	0.556651i	−0.980774	+	0.195149i	$0.937481\pi$
$920$		0			0
$921$	15.4477	−	4.11209i	0.509018	−	0.135498i
$922$		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
$927$	40.6050	+	0.132968i	1.33364	+	0.00436723i
$928$		0			0
$929$	−13.8612			−0.454771			−0.227386	−	0.973805i	$-0.573018\pi$
$929$	−13.8612			−0.454771			−0.227386	+	0.973805i	$0.573018\pi$
$930$		0			0
$931$	−42.2472	−	26.9787i	−1.38460	−	0.884191i
$932$		0			0
$933$	0.279211	+	1.04890i	0.00914095	+	0.0343393i
$934$		0			0
$935$	2.52534	+	1.45801i	0.0825876	+	0.0476819i
$936$		0			0
$937$			5.38328i			0.175864i	0.996126	+	0.0879320i	$0.0280258\pi$
$937$			5.38328i			0.175864i	−0.996126	+	0.0879320i	$0.971974\pi$
$938$		0			0
$939$	−8.57204	+	2.28184i	−0.279738	+	0.0744649i
$940$		0			0
$941$	6.57238			0.214253			0.107127	−	0.994245i	$-0.465835\pi$
$941$	6.57238			0.214253			0.107127	+	0.994245i	$0.465835\pi$
$942$		0			0
$943$			0.938988i			0.0305777i
$944$		0			0
$945$	0.796239	−	2.67735i	0.0259017	−	0.0870941i
$946$		0			0
$947$			31.9945i			1.03968i	0.854263	+	0.519841i	$0.174009\pi$
$947$			31.9945i			1.03968i	−0.854263	+	0.519841i	$0.825991\pi$
$948$		0			0
$949$	−1.64840			−0.0535094
$950$		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
$957$	−2.17125	−	8.15661i	−0.0701865	−	0.263666i
$958$		0			0
$959$	0.253276	−	11.3268i	0.00817869	−	0.365762i
$960$		0			0
$961$	−10.8165			−0.348919
$962$		0			0
$963$	−22.6608	+	38.9546i	−0.730236	+	1.25529i
$964$		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
$969$	38.4948	−	10.2471i	1.23663	−	0.329185i
$970$		0			0
$971$	23.4783	+	40.6656i	0.753454	+	1.30502i	0.946139	+	0.323761i	$0.104947\pi$
$971$	23.4783	+	40.6656i	0.753454	+	1.30502i	−0.192685	+	0.981261i	$0.561719\pi$
$972$		0			0
$973$	0.234925	−	10.5062i	0.00753135	−	0.336812i
$974$		0			0
$975$	3.24326	−	12.0252i	0.103867	−	0.385115i
$976$		0			0
$977$			32.8031i			1.04946i	0.851267	+	0.524732i	$0.175834\pi$
$977$			32.8031i			1.04946i	−0.851267	+	0.524732i	$0.824166\pi$
$978$		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
$983$	−15.0073	−	25.9933i	−0.478657	−	0.829059i	0.521043	−	0.853530i	$-0.325543\pi$
$983$	−15.0073	−	25.9933i	−0.478657	−	0.829059i	−0.999701	+	0.0244717i	$0.992210\pi$
$984$		0			0
$985$	2.13463	+	1.23243i	0.0680149	+	0.0392684i
$986$		0			0
$987$	0.409636	+	0.120366i	0.0130388	+	0.00383130i
$988$		0			0
$989$	10.3062	−	5.95029i	0.327718	−	0.189208i
$990$		0			0
$991$	−24.9364	+	43.1911i	−0.792131	+	1.37201i	0.132514	+	0.991181i	$0.457695\pi$
$991$	−24.9364	+	43.1911i	−0.792131	+	1.37201i	−0.924645	+	0.380831i	$0.875638\pi$
$992$		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
$997$	1.28622	−	0.742601i	0.0407351	−	0.0235184i	−0.479494	−	0.877545i	$-0.659180\pi$
$997$	1.28622	−	0.742601i	0.0407351	−	0.0235184i	0.520229	+	0.854027i	$0.325847\pi$
$998$		0			0
$999$	8.29521	−	30.3608i	0.262449	−	0.960575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.ca.e.353.15		48
3.2	odd	2		3024.2.ca.e.2033.11		48
4.3	odd	2		504.2.bs.a.353.10	yes	48
7.5	odd	6		1008.2.df.e.929.22		48
9.4	even	3		3024.2.df.e.17.11		48
9.5	odd	6		1008.2.df.e.689.22		48
12.11	even	2		1512.2.bs.a.521.11		48
21.5	even	6		3024.2.df.e.1601.11		48
28.19	even	6		504.2.cx.a.425.3	yes	48
36.23	even	6		504.2.cx.a.185.3	yes	48
36.31	odd	6		1512.2.cx.a.17.11		48
63.5	even	6	inner	1008.2.ca.e.257.15		48
63.40	odd	6		3024.2.ca.e.2609.11		48
84.47	odd	6		1512.2.cx.a.89.11		48
252.103	even	6		1512.2.bs.a.1097.11		48
252.131	odd	6		504.2.bs.a.257.10	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.10	✓	48	252.131	odd	6
504.2.bs.a.353.10	yes	48	4.3	odd	2
504.2.cx.a.185.3	yes	48	36.23	even	6
504.2.cx.a.425.3	yes	48	28.19	even	6
1008.2.ca.e.257.15		48	63.5	even	6	inner
1008.2.ca.e.353.15		48	1.1	even	1	trivial
1008.2.df.e.689.22		48	9.5	odd	6
1008.2.df.e.929.22		48	7.5	odd	6
1512.2.bs.a.521.11		48	12.11	even	2
1512.2.bs.a.1097.11		48	252.103	even	6
1512.2.cx.a.17.11		48	36.31	odd	6
1512.2.cx.a.89.11		48	84.47	odd	6
3024.2.ca.e.2033.11		48	3.2	odd	2
3024.2.ca.e.2609.11		48	63.40	odd	6
3024.2.df.e.17.11		48	9.4	even	3
3024.2.df.e.1601.11		48	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.445548 + 1.67376i) q^{3} +(-0.101589 + 0.175958i) q^{5} +(1.37377 - 2.26114i) q^{7} +(-2.60297 + 1.49148i) q^{9} +(3.86995 - 2.23432i) q^{11} +(-1.25586 + 0.725070i) q^{13} +(-0.339774 - 0.0916388i) q^{15} +(1.60586 - 2.78143i) q^{17} +(6.20156 - 3.58047i) q^{19} +(4.39670 + 1.29192i) q^{21} +(1.09687 + 0.633276i) q^{23} +(2.47936 + 4.29438i) q^{25} +(-3.65614 - 3.69224i) q^{27} +(-0.944433 - 0.545269i) q^{29} +6.46657i q^{31} +(5.46397 + 5.48189i) q^{33} +(0.258305 + 0.471432i) q^{35} +(3.02855 + 5.24561i) q^{37} +(-1.77314 - 1.77896i) q^{39} +(0.370687 + 0.642048i) q^{41} +(4.69802 - 8.13721i) q^{43} +(0.00199601 - 0.609532i) q^{45} +0.0931689 q^{47} +(-3.22553 - 6.21257i) q^{49} +(5.37095 + 1.44857i) q^{51} +(-9.35260 - 5.39973i) q^{53} +0.907929i q^{55} +(8.75596 + 8.78468i) q^{57} -10.3289 q^{59} +8.48390i q^{61} +(-0.203422 + 7.93465i) q^{63} -0.294637i q^{65} +8.05326 q^{67} +(-0.571249 + 2.11805i) q^{69} +15.6777i q^{71} +(0.984428 + 0.568360i) q^{73} +(-6.08310 + 6.06321i) q^{75} +(0.264302 - 11.8199i) q^{77} +11.7379 q^{79} +(4.55095 - 7.76459i) q^{81} +(-2.29931 + 3.98252i) q^{83} +(0.326276 + 0.565127i) q^{85} +(0.491861 - 1.82370i) q^{87} +(3.52692 + 6.10881i) q^{89} +(-0.0857700 + 3.83575i) q^{91} +(-10.8235 + 2.88117i) q^{93} +1.45495i q^{95} +(3.17914 + 1.83548i) q^{97} +(-6.74093 + 11.5878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9} - 8 q^{15} + 8 q^{21} + 12 q^{23} - 24 q^{25} + 18 q^{27} + 18 q^{29} + 10 q^{39} + 6 q^{41} + 6 q^{43} + 6 q^{45} - 36 q^{47} + 6 q^{49} + 12 q^{51} + 12 q^{53} + 4 q^{57} - 46 q^{63} + 54 q^{75}+ \cdots + 64 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 - 8 * q^15 + 8 * q^21 + 12 * q^23 - 24 * q^25 + 18 * q^27 + 18 * q^29 + 10 * q^39 + 6 * q^41 + 6 * q^43 + 6 * q^45 - 36 * q^47 + 6 * q^49 + 12 * q^51 + 12 * q^53 + 4 * q^57 - 46 * q^63 + 54 * q^75 - 36 * q^77 + 12 * q^79 + 24 * q^87 + 18 * q^89 - 6 * q^91 + 16 * q^93 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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