LMFDB - Embedded newform 512.2.k.a.273.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [512,2,Mod(17,512)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("512.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(512, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.k (of order $32$, degree $16$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	no (minimal twist has level 128)
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			273.10
Character	$\chi$	$=$	512.273
Dual form			512.2.k.a.497.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.12781 + 0.602827i) q^{3} +(-1.29871 + 1.58248i) q^{5} +(1.93875 + 1.29543i) q^{7} +(-0.758155 - 1.13466i) q^{9} +(4.58482 + 1.39079i) q^{11} +(-1.77365 + 1.45559i) q^{13} +(-2.41866 + 1.00184i) q^{15} +(-0.698095 - 0.289160i) q^{17} +(-0.355280 + 3.60722i) q^{19} +(1.40562 + 2.62973i) q^{21} +(0.824744 + 0.164052i) q^{23} +(0.157851 + 0.793571i) q^{25} +(-0.547088 - 5.55468i) q^{27} +(2.64076 + 8.70543i) q^{29} +(-4.31573 + 4.31573i) q^{31} +(4.33241 + 4.33241i) q^{33} +(-4.56786 + 1.38565i) q^{35} +(-3.24347 + 0.319454i) q^{37} +(-2.87781 + 0.572431i) q^{39} +(2.34453 - 11.7868i) q^{41} +(7.17325 - 3.83418i) q^{43} +(2.78020 + 0.273825i) q^{45} +(1.13781 - 2.74691i) q^{47} +(-0.598174 - 1.44412i) q^{49} +(-0.613005 - 0.746949i) q^{51} +(2.85064 - 9.39731i) q^{53} +(-8.15524 + 5.44916i) q^{55} +(-2.57522 + 3.85409i) q^{57} +(3.31394 + 2.71968i) q^{59} +(0.0672870 - 0.125885i) q^{61} -3.18196i q^{63} -4.69715i q^{65} +(-3.12347 + 5.84360i) q^{67} +(0.831260 + 0.682197i) q^{69} +(6.30859 - 9.44148i) q^{71} +(-4.87067 + 3.25448i) q^{73} +(-0.300360 + 0.990154i) q^{75} +(7.08715 + 8.63572i) q^{77} +(-4.87747 - 11.7752i) q^{79} +(1.16482 - 2.81213i) q^{81} +(13.3221 + 1.31211i) q^{83} +(1.36421 - 0.729186i) q^{85} +(-2.26959 + 11.4100i) q^{87} +(-13.5456 + 2.69438i) q^{89} +(-5.32428 + 0.524395i) q^{91} +(-7.46896 + 2.26568i) q^{93} +(-5.24694 - 5.24694i) q^{95} +(4.07614 - 4.07614i) q^{97} +(-1.89793 - 6.25664i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{23}{32}\right)$	$1$

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
$3$	1.12781	+	0.602827i	0.651142	+	0.348043i	0.763671	−	0.645606i	$-0.223395\pi$
$3$	1.12781	+	0.602827i	0.651142	+	0.348043i	−0.112529	+	0.993648i	$0.535895\pi$
$4$		0			0
$5$	−1.29871	+	1.58248i	−0.580800	+	0.707706i	−0.977665	−	0.210171i	$-0.932598\pi$
$5$	−1.29871	+	1.58248i	−0.580800	+	0.707706i	0.396865	+	0.917877i	$0.370098\pi$
$6$		0			0
$7$	1.93875	+	1.29543i	0.732779	+	0.489627i	0.865112	−	0.501578i	$-0.167247\pi$
$7$	1.93875	+	1.29543i	0.732779	+	0.489627i	−0.132334	+	0.991205i	$0.542247\pi$
$8$		0			0
$9$	−0.758155	−	1.13466i	−0.252718	−	0.378220i
$10$		0			0
$11$	4.58482	+	1.39079i	1.38238	+	0.419339i	0.891946	−	0.452141i	$-0.149340\pi$
$11$	4.58482	+	1.39079i	1.38238	+	0.419339i	0.490430	+	0.871481i	$0.336840\pi$
$12$		0			0
$13$	−1.77365	+	1.45559i	−0.491921	+	0.403709i	−0.847383	−	0.530982i	$-0.821823\pi$
$13$	−1.77365	+	1.45559i	−0.491921	+	0.403709i	0.355463	+	0.934690i	$0.384323\pi$
$14$		0			0
$15$	−2.41866	+	1.00184i	−0.624495	+	0.258674i
$16$		0			0
$17$	−0.698095	−	0.289160i	−0.169313	−	0.0701317i	0.296417	−	0.955059i	$-0.404208\pi$
$17$	−0.698095	−	0.289160i	−0.169313	−	0.0701317i	−0.465730	+	0.884927i	$0.654208\pi$
$18$		0			0
$19$	−0.355280	+	3.60722i	−0.0815068	+	0.827553i	0.864333	+	0.502920i	$0.167741\pi$
$19$	−0.355280	+	3.60722i	−0.0815068	+	0.827553i	−0.945840	+	0.324633i	$0.894759\pi$
$20$		0			0
$21$	1.40562	+	2.62973i	0.306732	+	0.573855i
$22$		0			0
$23$	0.824744	+	0.164052i	0.171971	+	0.0342071i	0.280325	−	0.959905i	$-0.409558\pi$
$23$	0.824744	+	0.164052i	0.171971	+	0.0342071i	−0.108354	+	0.994112i	$0.534558\pi$
$24$		0			0
$25$	0.157851	+	0.793571i	0.0315702	+	0.158714i
$26$		0			0
$27$	−0.547088	−	5.55468i	−0.105287	−	1.06900i
$28$		0			0
$29$	2.64076	+	8.70543i	0.490378	+	1.61656i	0.757458	+	0.652884i	$0.226441\pi$
$29$	2.64076	+	8.70543i	0.490378	+	1.61656i	−0.267080	+	0.963674i	$0.586059\pi$
$30$		0			0
$31$	−4.31573	+	4.31573i	−0.775127	+	0.775127i	−0.978998	−	0.203871i	$-0.934648\pi$
$31$	−4.31573	+	4.31573i	−0.775127	+	0.775127i	0.203871	+	0.978998i	$0.434648\pi$
$32$		0			0
$33$	4.33241	+	4.33241i	0.754175	+	0.754175i
$34$		0			0
$35$	−4.56786	+	1.38565i	−0.772110	+	0.234217i
$36$		0			0
$37$	−3.24347	+	0.319454i	−0.533224	+	0.0525179i	−0.361046	−	0.932548i	$-0.617580\pi$
$37$	−3.24347	+	0.319454i	−0.533224	+	0.0525179i	−0.172178	+	0.985066i	$0.555080\pi$
$38$		0			0
$39$	−2.87781	+	0.572431i	−0.460818	+	0.0916624i
$40$		0			0
$41$	2.34453	−	11.7868i	0.366154	−	1.84078i	−0.155775	−	0.987793i	$-0.549787\pi$
$41$	2.34453	−	11.7868i	0.366154	−	1.84078i	0.521929	−	0.852989i	$-0.325213\pi$
$42$		0			0
$43$	7.17325	−	3.83418i	1.09391	−	0.584707i	0.177166	−	0.984181i	$-0.443307\pi$
$43$	7.17325	−	3.83418i	1.09391	−	0.584707i	0.916745	+	0.399474i	$0.130807\pi$
$44$		0			0
$45$	2.78020	+	0.273825i	0.414447	+	0.0408195i
$46$		0			0
$47$	1.13781	−	2.74691i	0.165966	−	0.400678i	−0.818913	−	0.573917i	$-0.805423\pi$
$47$	1.13781	−	2.74691i	0.165966	−	0.400678i	0.984880	+	0.173239i	$0.0554232\pi$
$48$		0			0
$49$	−0.598174	−	1.44412i	−0.0854535	−	0.206303i
$50$		0			0
$51$	−0.613005	−	0.746949i	−0.0858379	−	0.104594i
$52$		0			0
$53$	2.85064	−	9.39731i	0.391566	−	1.29082i	−0.510745	−	0.859732i	$-0.670630\pi$
$53$	2.85064	−	9.39731i	0.391566	−	1.29082i	0.902310	−	0.431087i	$-0.141870\pi$
$54$		0			0
$55$	−8.15524	+	5.44916i	−1.09965	+	0.734764i
$56$		0			0
$57$	−2.57522	+	3.85409i	−0.341096	+	0.510486i
$58$		0			0
$59$	3.31394	+	2.71968i	0.431439	+	0.354073i	0.824910	−	0.565264i	$-0.191226\pi$
$59$	3.31394	+	2.71968i	0.431439	+	0.354073i	−0.393471	+	0.919337i	$0.628726\pi$
$60$		0			0
$61$	0.0672870	−	0.125885i	0.00861521	−	0.0161179i	−0.877577	−	0.479436i	$-0.840841\pi$
$61$	0.0672870	−	0.125885i	0.00861521	−	0.0161179i	0.886192	+	0.463318i	$0.153341\pi$
$62$		0			0
$63$		−	3.18196i		−	0.400889i
$64$		0			0
$65$		−	4.69715i		−	0.582609i
$66$		0			0
$67$	−3.12347	+	5.84360i	−0.381593	+	0.713910i	−0.997251	−	0.0741040i	$-0.976390\pi$
$67$	−3.12347	+	5.84360i	−0.381593	+	0.713910i	0.615658	+	0.788014i	$0.288890\pi$
$68$		0			0
$69$	0.831260	+	0.682197i	0.100072	+	0.0821269i
$70$		0			0
$71$	6.30859	−	9.44148i	0.748692	−	1.12050i	−0.240034	−	0.970764i	$-0.577159\pi$
$71$	6.30859	−	9.44148i	0.748692	−	1.12050i	0.988727	−	0.149733i	$-0.0478413\pi$
$72$		0			0
$73$	−4.87067	+	3.25448i	−0.570069	+	0.380908i	−0.806940	−	0.590633i	$-0.798878\pi$
$73$	−4.87067	+	3.25448i	−0.570069	+	0.380908i	0.236871	+	0.971541i	$0.423878\pi$
$74$		0			0
$75$	−0.300360	+	0.990154i	−0.0346826	+	0.114333i
$76$		0			0
$77$	7.08715	+	8.63572i	0.807656	+	0.984132i
$78$		0			0
$79$	−4.87747	−	11.7752i	−0.548758	−	1.32482i	−0.918403	−	0.395645i	$-0.870521\pi$
$79$	−4.87747	−	11.7752i	−0.548758	−	1.32482i	0.369646	−	0.929173i	$-0.379479\pi$
$80$		0			0
$81$	1.16482	−	2.81213i	0.129425	−	0.312459i
$82$		0			0
$83$	13.3221	+	1.31211i	1.46229	+	0.144023i	0.797641	−	0.603132i	$-0.206081\pi$
$83$	13.3221	+	1.31211i	1.46229	+	0.144023i	0.664649	+	0.747155i	$0.268581\pi$
$84$		0			0
$85$	1.36421	−	0.729186i	0.147970	−	0.0790914i
$86$		0			0
$87$	−2.26959	+	11.4100i	−0.243326	+	1.22328i
$88$		0			0
$89$	−13.5456	+	2.69438i	−1.43583	+	0.285604i	−0.850834	−	0.525435i	$-0.823903\pi$
$89$	−13.5456	+	2.69438i	−1.43583	+	0.285604i	−0.584993	+	0.811038i	$0.698903\pi$
$90$		0			0
$91$	−5.32428	+	0.524395i	−0.558136	+	0.0549716i
$92$		0			0
$93$	−7.46896	+	2.26568i	−0.774495	+	0.234940i
$94$		0			0
$95$	−5.24694	−	5.24694i	−0.538325	−	0.538325i
$96$		0			0
$97$	4.07614	−	4.07614i	0.413870	−	0.413870i	−0.469214	−	0.883084i	$-0.655463\pi$
$97$	4.07614	−	4.07614i	0.413870	−	0.413870i	0.883084	+	0.469214i	$0.155463\pi$
$98$		0			0
$99$	−1.89793	−	6.25664i	−0.190749	−	0.628816i
$100$		0			0
$101$	−1.51341	−	15.3659i	−0.150590	−	1.52897i	−0.712443	−	0.701730i	$-0.752411\pi$
$101$	−1.51341	−	15.3659i	−0.150590	−	1.52897i	0.561853	−	0.827237i	$-0.310089\pi$
$102$		0			0
$103$	−0.776399	−	3.90322i	−0.0765009	−	0.384596i	−1.00000		0.000994172i	$-0.999684\pi$
$103$	−0.776399	−	3.90322i	−0.0765009	−	0.384596i	0.923499	−	0.383602i	$-0.125316\pi$
$104$		0			0
$105$	−5.98699	−	1.19089i	−0.584270	−	0.116219i
$106$		0			0
$107$	3.97584	+	7.43827i	0.384359	+	0.719084i	0.997483	−	0.0709017i	$-0.0225877\pi$
$107$	3.97584	+	7.43827i	0.384359	+	0.719084i	−0.613125	+	0.789986i	$0.710088\pi$
$108$		0			0
$109$	−0.635488	+	6.45222i	−0.0608687	+	0.618010i	0.915562	+	0.402178i	$0.131747\pi$
$109$	−0.635488	+	6.45222i	−0.0608687	+	0.618010i	−0.976430	+	0.215833i	$0.930753\pi$
$110$		0			0
$111$	−3.85060	−	1.59497i	−0.365483	−	0.151388i
$112$		0			0
$113$	12.9894	−	5.38040i	1.22194	−	0.506146i	0.323916	−	0.946086i	$-0.395000\pi$
$113$	12.9894	−	5.38040i	1.22194	−	0.506146i	0.898027	+	0.439940i	$0.145000\pi$
$114$		0			0
$115$	−1.33071	+	1.09208i	−0.124089	+	0.101837i
$116$		0			0
$117$	2.99630	+	0.908917i	0.277008	+	0.0840294i
$118$		0			0
$119$	−0.978845	−	1.46494i	−0.0897305	−	0.134291i
$120$		0			0
$121$	9.94014	+	6.64179i	0.903649	+	0.603799i
$122$		0			0
$123$	9.74956	−	11.8799i	0.879089	−	1.07117i
$124$		0			0
$125$	−10.4880	−	5.60595i	−0.938075	−	0.501412i
$126$		0			0
$127$	7.90826			0.701745			0.350872	−	0.936423i	$-0.385885\pi$
$127$	7.90826			0.701745			0.350872	+	0.936423i	$0.385885\pi$
$128$		0			0
$129$	10.4014			0.915793
$130$		0			0
$131$	−6.24968	−	3.34053i	−0.546037	−	0.291863i	0.175221	−	0.984529i	$-0.443936\pi$
$131$	−6.24968	−	3.34053i	−0.546037	−	0.291863i	−0.721258	+	0.692666i	$0.756436\pi$
$132$		0			0
$133$	−5.36170	+	6.53325i	−0.464919	+	0.566505i
$134$		0			0
$135$	9.50067	+	6.34814i	0.817687	+	0.546361i
$136$		0			0
$137$	−7.34039	−	10.9857i	−0.627132	−	0.938569i	−0.999943	−	0.0106622i	$-0.996606\pi$
$137$	−7.34039	−	10.9857i	−0.627132	−	0.938569i	0.372811	−	0.927907i	$-0.378394\pi$
$138$		0			0
$139$	−13.5247	−	4.10266i	−1.14715	−	0.347983i	−0.341212	−	0.939987i	$-0.610837\pi$
$139$	−13.5247	−	4.10266i	−1.14715	−	0.347983i	−0.805936	+	0.592003i	$0.798337\pi$
$140$		0			0
$141$	2.93915	−	2.41209i	0.247521	−	0.203135i
$142$		0			0
$143$	−10.1563	+	4.20687i	−0.849311	+	0.351796i
$144$		0			0
$145$	−17.2058	−	7.12686i	−1.42886	−	0.591853i
$146$		0			0
$147$	0.195928	−	1.98929i	0.0161599	−	0.164074i
$148$		0			0
$149$	0.0152148	+	0.0284649i	0.00124645	+	0.00233194i	0.882544	−	0.470230i	$-0.155829\pi$
$149$	0.0152148	+	0.0284649i	0.00124645	+	0.00233194i	−0.881297	+	0.472562i	$0.843329\pi$
$150$		0			0
$151$	16.3321	+	3.24865i	1.32909	+	0.264372i	0.808025	−	0.589148i	$-0.200536\pi$
$151$	16.3321	+	3.24865i	1.32909	+	0.264372i	0.521061	+	0.853519i	$0.325536\pi$
$152$		0			0
$153$	0.201166	+	1.01133i	0.0162633	+	0.0817610i
$154$		0			0
$155$	−1.22468	−	12.4344i	−0.0983689	−	0.998756i
$156$		0			0
$157$	−4.47825	−	14.7628i	−0.357404	−	1.17820i	−0.932820	−	0.360341i	$-0.882660\pi$
$157$	−4.47825	−	14.7628i	−0.357404	−	1.17820i	0.575417	−	0.817860i	$-0.304840\pi$
$158$		0			0
$159$	8.87994	−	8.87994i	0.704225	−	0.704225i
$160$		0			0
$161$	1.38645	+	1.38645i	0.109268	+	0.109268i
$162$		0			0
$163$	−17.5156	+	5.31331i	−1.37193	+	0.416171i	−0.888365	−	0.459137i	$-0.848159\pi$
$163$	−17.5156	+	5.31331i	−1.37193	+	0.416171i	−0.483566	+	0.875308i	$0.660659\pi$
$164$		0			0
$165$	−12.4825	+	1.22942i	−0.971759	+	0.0957099i
$166$		0			0
$167$	6.24830	−	1.24287i	0.483508	−	0.0961758i	0.0526833	−	0.998611i	$-0.483223\pi$
$167$	6.24830	−	1.24287i	0.483508	−	0.0961758i	0.430825	+	0.902435i	$0.358223\pi$
$168$		0			0
$169$	−1.50911	+	7.58680i	−0.116085	+	0.583600i
$170$		0			0
$171$	4.36232	−	2.33171i	0.333595	−	0.178310i
$172$		0			0
$173$	−13.6204	−	1.34149i	−1.03554	−	0.101992i	−0.434062	−	0.900883i	$-0.642920\pi$
$173$	−13.6204	−	1.34149i	−1.03554	−	0.101992i	−0.601475	+	0.798891i	$0.705420\pi$
$174$		0			0
$175$	−0.721983	+	1.74302i	−0.0545768	+	0.131760i
$176$		0			0
$177$	2.09800	+	5.06502i	0.157695	+	0.380711i
$178$		0			0
$179$	−4.99351	−	6.08461i	−0.373233	−	0.454785i	0.552192	−	0.833717i	$-0.313791\pi$
$179$	−4.99351	−	6.08461i	−0.373233	−	0.454785i	−0.925425	+	0.378932i	$0.876291\pi$
$180$		0			0
$181$	6.04367	−	19.9233i	0.449222	−	1.48089i	−0.381589	−	0.924332i	$-0.624623\pi$
$181$	6.04367	−	19.9233i	0.449222	−	1.48089i	0.830811	−	0.556555i	$-0.187877\pi$
$182$		0			0
$183$	0.151774	−	0.101412i	0.0112194	−	0.00749660i
$184$		0			0
$185$	3.70679	−	5.54761i	0.272529	−	0.407868i
$186$		0			0
$187$	−2.79848	−	2.29665i	−0.204645	−	0.167948i
$188$		0			0
$189$	6.13504	−	11.4778i	0.446258	−	0.834890i
$190$		0			0
$191$			8.56546i			0.619775i	0.950773	+	0.309887i	$0.100291\pi$
$191$			8.56546i			0.619775i	−0.950773	+	0.309887i	$0.899709\pi$
$192$		0			0
$193$			19.9244i			1.43419i	0.696974	+	0.717096i	$0.254529\pi$
$193$			19.9244i			1.43419i	−0.696974	+	0.717096i	$0.745471\pi$
$194$		0			0
$195$	2.83157	−	5.29749i	0.202773	−	0.379361i
$196$		0			0
$197$	3.61163	+	2.96399i	0.257318	+	0.211175i	0.754204	−	0.656641i	$-0.228023\pi$
$197$	3.61163	+	2.96399i	0.257318	+	0.211175i	−0.496886	+	0.867816i	$0.665523\pi$
$198$		0			0
$199$	6.68803	−	10.0094i	0.474102	−	0.709544i	−0.514932	−	0.857231i	$-0.672183\pi$
$199$	6.68803	−	10.0094i	0.474102	−	0.709544i	0.989034	+	0.147687i	$0.0471828\pi$
$200$		0			0
$201$	−7.04537	+	4.70756i	−0.496942	+	0.332046i
$202$		0			0
$203$	−6.15751	+	20.2986i	−0.432172	+	1.42468i
$204$		0			0
$205$	15.6074	+	19.0177i	1.09007	+	1.32825i
$206$		0			0
$207$	−0.439140	−	1.06018i	−0.0305224	−	0.0736875i
$208$		0			0
$209$	−6.64578	+	16.0443i	−0.459698	+	1.10981i
$210$		0			0
$211$	8.07741	+	0.795556i	0.556072	+	0.0547683i	0.372150	−	0.928173i	$-0.378621\pi$
$211$	8.07741	+	0.795556i	0.556072	+	0.0547683i	0.183922	+	0.982941i	$0.441121\pi$
$212$		0			0
$213$	12.8065	−	6.84521i	0.877486	−	0.469026i
$214$		0			0
$215$	−3.24844	+	16.3310i	−0.221542	+	1.11376i
$216$		0			0
$217$	−13.9578	+	2.77639i	−0.947520	+	0.188473i
$218$		0			0
$219$	−7.45508	+	0.734262i	−0.503768	+	0.0496168i
$220$		0			0
$221$	1.65907	−	0.503274i	0.111601	−	0.0338539i
$222$		0			0
$223$	9.25514	+	9.25514i	0.619770	+	0.619770i	0.945472	−	0.325702i	$-0.105601\pi$
$223$	9.25514	+	9.25514i	0.619770	+	0.619770i	−0.325702	+	0.945472i	$0.605601\pi$
$224$		0			0
$225$	0.780756	−	0.780756i	0.0520504	−	0.0520504i
$226$		0			0
$227$	4.93005	+	16.2522i	0.327219	+	1.07870i	0.954077	+	0.299563i	$0.0968407\pi$
$227$	4.93005	+	16.2522i	0.327219	+	1.07870i	−0.626858	+	0.779134i	$0.715659\pi$
$228$		0			0
$229$	2.34883	+	23.8481i	0.155215	+	1.57592i	0.685479	+	0.728092i	$0.259593\pi$
$229$	2.34883	+	23.8481i	0.155215	+	1.57592i	−0.530264	+	0.847832i	$0.677907\pi$
$230$		0			0
$231$	2.78712	+	14.0118i	0.183379	+	0.921908i
$232$		0			0
$233$	25.9934	+	5.17042i	1.70289	+	0.338725i	0.948276	−	0.317447i	$-0.102826\pi$
$233$	25.9934	+	5.17042i	1.70289	+	0.338725i	0.754611	+	0.656173i	$0.227826\pi$
$234$		0			0
$235$	2.86925	+	5.36799i	0.187169	+	0.350169i
$236$		0			0
$237$	1.59758	−	16.2205i	0.103774	−	1.05364i
$238$		0			0
$239$	5.29693	+	2.19406i	0.342630	+	0.141922i	0.547362	−	0.836896i	$-0.315632\pi$
$239$	5.29693	+	2.19406i	0.342630	+	0.141922i	−0.204732	+	0.978818i	$0.565632\pi$
$240$		0			0
$241$	−3.50495	+	1.45180i	−0.225774	+	0.0935186i	−0.492703	−	0.870198i	$-0.663991\pi$
$241$	−3.50495	+	1.45180i	−0.225774	+	0.0935186i	0.266929	+	0.963716i	$0.413991\pi$
$242$		0			0
$243$	−9.93487	+	8.15334i	−0.637322	+	0.523037i
$244$		0			0
$245$	3.06215	+	0.928892i	0.195633	+	0.0593447i
$246$		0			0
$247$	−4.62050	−	6.91507i	−0.293995	−	0.439995i
$248$		0			0
$249$	14.2338	+	9.51074i	0.902032	+	0.602719i
$250$		0			0
$251$	−1.54637	+	1.88426i	−0.0976063	+	0.118934i	−0.819523	−	0.573047i	$-0.805761\pi$
$251$	−1.54637	+	1.88426i	−0.0976063	+	0.118934i	0.721917	+	0.691980i	$0.243261\pi$
$252$		0			0
$253$	3.55314	+	1.89919i	0.223384	+	0.119401i
$254$		0			0
$255$	1.97815			0.123876
$256$		0			0
$257$	15.4616			0.964467			0.482234	−	0.876043i	$-0.339826\pi$
$257$	15.4616			0.964467			0.482234	+	0.876043i	$0.339826\pi$
$258$		0			0
$259$	−6.70211	−	3.58235i	−0.416449	−	0.222597i
$260$		0			0
$261$	7.87559	−	9.59643i	0.487487	−	0.594004i
$262$		0			0
$263$	−8.70225	−	5.81466i	−0.536604	−	0.358547i	0.257549	−	0.966265i	$-0.417085\pi$
$263$	−8.70225	−	5.81466i	−0.536604	−	0.358547i	−0.794153	+	0.607718i	$0.792085\pi$
$264$		0			0
$265$	11.1689	+	16.7154i	0.686100	+	1.02682i
$266$		0			0
$267$	−16.9011	−	5.12689i	−1.03433	−	0.313760i
$268$		0			0
$269$	−16.5916	+	13.6163i	−1.01161	+	0.830203i	−0.985538	−	0.169457i	$-0.945799\pi$
$269$	−16.5916	+	13.6163i	−1.01161	+	0.830203i	−0.0260680	+	0.999660i	$0.508299\pi$
$270$		0			0
$271$	−17.0828	+	7.07592i	−1.03770	+	0.429831i	−0.835488	−	0.549509i	$-0.814815\pi$
$271$	−17.0828	+	7.07592i	−1.03770	+	0.429831i	−0.202217	+	0.979341i	$0.564815\pi$
$272$		0			0
$273$	−6.32090	−	2.61820i	−0.382558	−	0.158461i
$274$		0			0
$275$	−0.379972	+	3.85792i	−0.0229132	+	0.232641i
$276$		0			0
$277$	5.81382	+	10.8769i	0.349319	+	0.653530i	0.993811	−	0.111081i	$-0.0354313\pi$
$277$	5.81382	+	10.8769i	0.349319	+	0.653530i	−0.644493	+	0.764611i	$0.722931\pi$
$278$		0			0
$279$	8.16886	+	1.62489i	0.489057	+	0.0972795i
$280$		0			0
$281$	1.80826	+	9.09076i	0.107872	+	0.542309i	0.996494	+	0.0836682i	$0.0266636\pi$
$281$	1.80826	+	9.09076i	0.107872	+	0.542309i	−0.888622	+	0.458641i	$0.848336\pi$
$282$		0			0
$283$	−0.402228	−	4.08389i	−0.0239100	−	0.242762i	−0.999710	−	0.0240957i	$-0.992329\pi$
$283$	−0.402228	−	4.08389i	−0.0239100	−	0.242762i	0.975800	−	0.218666i	$-0.0701706\pi$
$284$		0			0
$285$	−2.75456	−	9.08056i	−0.163166	−	0.537886i
$286$		0			0
$287$	19.8144	−	19.8144i	1.16961	−	1.16961i
$288$		0			0
$289$	−11.6171	−	11.6171i	−0.683358	−	0.683358i
$290$		0			0
$291$	7.05433	−	2.13991i	0.413532	−	0.125444i
$292$		0			0
$293$	−6.58898	+	0.648958i	−0.384932	+	0.0379125i	−0.288633	−	0.957440i	$-0.593201\pi$
$293$	−6.58898	+	0.648958i	−0.384932	+	0.0379125i	−0.0962995	+	0.995352i	$0.530701\pi$
$294$		0			0
$295$	−8.60769	+	1.71218i	−0.501159	+	0.0996867i
$296$		0			0
$297$	5.21709	−	26.2281i	0.302726	−	1.52191i
$298$		0			0
$299$	−1.70159	+	0.909521i	−0.0984058	+	0.0525990i
$300$		0			0
$301$	18.8741	+	1.85893i	1.08788	+	0.107147i
$302$		0			0
$303$	7.55616	−	18.2422i	0.434090	−	1.04799i
$304$		0			0
$305$	0.111824	+	0.269968i	0.00640305	+	0.0154583i
$306$		0			0
$307$	−2.90223	−	3.53637i	−0.165639	−	0.201832i	0.683576	−	0.729880i	$-0.260424\pi$
$307$	−2.90223	−	3.53637i	−0.165639	−	0.201832i	−0.849214	+	0.528048i	$0.822924\pi$
$308$		0			0
$309$	1.47734	−	4.87013i	0.0840428	−	0.277052i
$310$		0			0
$311$	−2.15935	+	1.44283i	−0.122445	+	0.0818154i	−0.615285	−	0.788305i	$-0.710959\pi$
$311$	−2.15935	+	1.44283i	−0.122445	+	0.0818154i	0.492839	+	0.870120i	$0.335959\pi$
$312$		0			0
$313$	−8.37329	+	12.5315i	−0.473287	+	0.708323i	−0.988914	−	0.148490i	$-0.952559\pi$
$313$	−8.37329	+	12.5315i	−0.473287	+	0.708323i	0.515627	+	0.856813i	$0.327559\pi$
$314$		0			0
$315$	5.03538	+	4.13243i	0.283712	+	0.232836i
$316$		0			0
$317$	4.89271	−	9.15362i	0.274802	−	0.514119i	−0.706225	−	0.707987i	$-0.749603\pi$
$317$	4.89271	−	9.15362i	0.274802	−	0.514119i	0.981028	+	0.193868i	$0.0621035\pi$
$318$		0			0
$319$			43.5856i			2.44033i
$320$		0			0
$321$			10.7857i			0.601999i
$322$		0			0
$323$	1.29108	−	2.41545i	0.0718378	−	0.134399i
$324$		0			0
$325$	−1.43509	−	1.17775i	−0.0796043	−	0.0653296i
$326$		0			0
$327$	−4.60628	+	6.89379i	−0.254728	+	0.381227i
$328$		0			0
$329$	5.76436	−	3.85162i	0.317800	−	0.212347i
$330$		0			0
$331$	0.0890693	−	0.293622i	0.00489569	−	0.0161389i	−0.954458	−	0.298344i	$-0.903566\pi$
$331$	0.0890693	−	0.293622i	0.00489569	−	0.0161389i	0.959354	+	0.282205i	$0.0910658\pi$
$332$		0			0
$333$	2.82153	+	3.43804i	0.154619	+	0.188403i
$334$		0			0
$335$	−5.19091	−	12.5320i	−0.283610	−	0.684694i
$336$		0			0
$337$	−9.80288	+	23.6662i	−0.533997	+	1.28918i	0.394859	+	0.918742i	$0.370793\pi$
$337$	−9.80288	+	23.6662i	−0.533997	+	1.28918i	−0.928856	+	0.370441i	$0.879207\pi$
$338$		0			0
$339$	17.8931	+	1.76231i	0.971819	+	0.0957158i
$340$		0			0
$341$	−25.7891	+	13.7846i	−1.39656	+	0.746476i
$342$		0			0
$343$	3.89531	−	19.5831i	0.210327	−	1.05739i
$344$		0			0
$345$	−2.15913	+	0.429477i	−0.116243	+	0.0231223i
$346$		0			0
$347$	8.64616	−	0.851573i	0.464150	−	0.0457148i	0.136760	−	0.990604i	$-0.456331\pi$
$347$	8.64616	−	0.851573i	0.464150	−	0.0457148i	0.327390	+	0.944889i	$0.393831\pi$
$348$		0			0
$349$	−15.7190	+	4.76829i	−0.841416	+	0.255241i	−0.681434	−	0.731879i	$-0.738644\pi$
$349$	−15.7190	+	4.76829i	−0.841416	+	0.255241i	−0.159982	+	0.987120i	$0.551144\pi$
$350$		0			0
$351$	9.05569	+	9.05569i	0.483357	+	0.483357i
$352$		0			0
$353$	17.4914	−	17.4914i	0.930971	−	0.930971i	−0.0667955	−	0.997767i	$-0.521278\pi$
$353$	17.4914	−	17.4914i	0.930971	−	0.930971i	0.997767	+	0.0667955i	$0.0212775\pi$
$354$		0			0
$355$	6.74793	+	22.2449i	0.358143	+	1.18064i
$356$		0			0
$357$	−0.220843	−	2.24225i	−0.0116882	−	0.118673i
$358$		0			0
$359$	−6.83412	−	34.3574i	−0.360691	−	1.81332i	−0.554392	−	0.832255i	$-0.687049\pi$
$359$	−6.83412	−	34.3574i	−0.360691	−	1.81332i	0.193701	−	0.981061i	$-0.437951\pi$
$360$		0			0
$361$	5.74912	+	1.14357i	0.302585	+	0.0601880i
$362$		0			0
$363$	7.20675	+	13.4829i	0.378256	+	0.707667i
$364$		0			0
$365$	1.17543	−	11.9344i	0.0615249	−	0.624673i
$366$		0			0
$367$	25.3978	+	10.5201i	1.32575	+	0.549146i	0.929441	−	0.368970i	$-0.120289\pi$
$367$	25.3978	+	10.5201i	1.32575	+	0.549146i	0.396313	+	0.918115i	$0.370289\pi$
$368$		0			0
$369$	−15.1515	+	6.27594i	−0.788753	+	0.326712i
$370$		0			0
$371$	17.7002	−	14.5262i	0.918951	−	0.754164i
$372$		0			0
$373$	−17.5829	−	5.33372i	−0.910409	−	0.276170i	−0.199866	−	0.979823i	$-0.564051\pi$
$373$	−17.5829	−	5.33372i	−0.910409	−	0.276170i	−0.710543	+	0.703654i	$0.751551\pi$
$374$		0			0
$375$	−8.44906	−	12.6449i	−0.436307	−	0.652980i
$376$		0			0
$377$	−17.3553	−	11.5965i	−0.893846	−	0.597249i
$378$		0			0
$379$	−19.0628	+	23.2281i	−0.979191	+	1.19315i	0.00197860	+	0.999998i	$0.499370\pi$
$379$	−19.0628	+	23.2281i	−0.979191	+	1.19315i	−0.981169	+	0.193149i	$0.938130\pi$
$380$		0			0
$381$	8.91902	+	4.76732i	0.456935	+	0.244237i
$382$		0			0
$383$	11.7228			0.599008			0.299504	−	0.954095i	$-0.403179\pi$
$383$	11.7228			0.599008			0.299504	+	0.954095i	$0.403179\pi$
$384$		0			0
$385$	−22.8700			−1.16556
$386$		0			0
$387$	−9.78892	−	5.23229i	−0.497599	−	0.265972i
$388$		0			0
$389$	2.48453	−	3.02741i	0.125971	−	0.153496i	−0.706206	−	0.708007i	$-0.749595\pi$
$389$	2.48453	−	3.02741i	0.125971	−	0.153496i	0.832176	+	0.554511i	$0.187095\pi$
$390$		0			0
$391$	−0.528312	−	0.353007i	−0.0267179	−	0.0178523i
$392$		0			0
$393$	−5.03470	−	7.53496i	−0.253967	−	0.380089i
$394$		0			0
$395$	24.9685	+	7.57411i	1.25630	+	0.381095i
$396$		0			0
$397$	15.9462	−	13.0867i	0.800316	−	0.656803i	−0.142619	−	0.989778i	$-0.545553\pi$
$397$	15.9462	−	13.0867i	0.800316	−	0.656803i	0.942936	+	0.332975i	$0.108053\pi$
$398$		0			0
$399$	−9.98541	+	4.13609i	−0.499896	+	0.207064i
$400$		0			0
$401$	−8.32912	−	3.45003i	−0.415936	−	0.172286i	0.164894	−	0.986311i	$-0.447272\pi$
$401$	−8.32912	−	3.45003i	−0.415936	−	0.172286i	−0.580830	+	0.814025i	$0.697272\pi$
$402$		0			0
$403$	1.37263	−	13.9365i	0.0683754	−	0.694227i
$404$		0			0
$405$	2.93737	+	5.49544i	0.145959	+	0.273070i
$406$		0			0
$407$	−15.3150	−	3.04635i	−0.759139	−	0.151002i
$408$		0			0
$409$	−4.53527	−	22.8003i	−0.224255	−	1.12740i	−0.914735	−	0.404053i	$-0.867601\pi$
$409$	−4.53527	−	22.8003i	−0.224255	−	1.12740i	0.690481	−	0.723351i	$-0.257399\pi$
$410$		0			0
$411$	−1.65611	−	16.8147i	−0.0816898	−	0.829410i
$412$		0			0
$413$	2.90175	+	9.56578i	0.142786	+	0.470701i
$414$		0			0
$415$	−19.3779	+	19.3779i	−0.951224	+	0.951224i
$416$		0			0
$417$	−12.7801	−	12.7801i	−0.625842	−	0.625842i
$418$		0			0
$419$	−22.3672	+	6.78501i	−1.09271	+	0.331469i	−0.784676	−	0.619906i	$-0.787171\pi$
$419$	−22.3672	+	6.78501i	−1.09271	+	0.331469i	−0.308032	+	0.951376i	$0.599671\pi$
$420$		0			0
$421$	−16.3126	+	1.60665i	−0.795029	+	0.0783035i	−0.487373	−	0.873194i	$-0.662045\pi$
$421$	−16.3126	+	1.60665i	−0.795029	+	0.0783035i	−0.307656	+	0.951498i	$0.599545\pi$
$422$		0			0
$423$	−3.97944	+	0.791560i	−0.193487	+	0.0384870i
$424$		0			0
$425$	0.119274	−	0.599632i	0.00578565	−	0.0290864i
$426$		0			0
$427$	0.293528	−	0.156894i	0.0142048	−	0.00759263i
$428$		0			0
$429$	−13.9904	−	1.37793i	−0.675461	−	0.0665272i
$430$		0			0
$431$	1.56534	−	3.77906i	0.0753997	−	0.182031i	−0.881686	−	0.471837i	$-0.843591\pi$
$431$	1.56534	−	3.77906i	0.0753997	−	0.182031i	0.957085	+	0.289806i	$0.0935909\pi$
$432$		0			0
$433$	−7.94091	−	19.1711i	−0.381616	−	0.921302i	−0.991654	−	0.128930i	$-0.958846\pi$
$433$	−7.94091	−	19.1711i	−0.381616	−	0.921302i	0.610038	−	0.792372i	$-0.291154\pi$
$434$		0			0
$435$	−15.1086	−	18.4098i	−0.724400	−	0.882684i
$436$		0			0
$437$	−0.884785	+	2.91675i	−0.0423250	+	0.139527i
$438$		0			0
$439$	−14.7929	+	9.88430i	−0.706026	+	0.471752i	−0.856025	−	0.516935i	$-0.827073\pi$
$439$	−14.7929	+	9.88430i	−0.706026	+	0.471752i	0.149999	+	0.988686i	$0.452073\pi$
$440$		0			0
$441$	−1.18508	+	1.77359i	−0.0564322	+	0.0844567i
$442$		0			0
$443$	7.99073	+	6.55782i	0.379651	+	0.311572i	0.804794	−	0.593555i	$-0.202276\pi$
$443$	7.99073	+	6.55782i	0.379651	+	0.311572i	−0.425142	+	0.905126i	$0.639776\pi$
$444$		0			0
$445$	13.3279	−	24.9348i	0.631804	−	1.18202i
$446$		0			0
$447$			0.0412749i			0.00195224i
$448$		0			0
$449$			24.7432i			1.16770i	0.811861	+	0.583851i	$0.198455\pi$
$449$			24.7432i			1.16770i	−0.811861	+	0.583851i	$0.801545\pi$
$450$		0			0
$451$	27.1422	−	50.7794i	1.27807	−	2.39111i
$452$		0			0
$453$	16.4611	+	13.5093i	0.773411	+	0.634722i
$454$		0			0
$455$	6.08483	−	9.10659i	0.285261	−	0.426924i
$456$		0			0
$457$	3.69951	−	2.47193i	0.173056	−	0.115632i	−0.466026	−	0.884771i	$-0.654315\pi$
$457$	3.69951	−	2.47193i	0.173056	−	0.115632i	0.639082	+	0.769139i	$0.279315\pi$
$458$		0			0
$459$	−1.22427	+	4.03589i	−0.0571442	+	0.188379i
$460$		0			0
$461$	−1.61495	−	1.96783i	−0.0752159	−	0.0916508i	0.734043	−	0.679103i	$-0.237631\pi$
$461$	−1.61495	−	1.96783i	−0.0752159	−	0.0916508i	−0.809259	+	0.587452i	$0.800131\pi$
$462$		0			0
$463$	4.59841	+	11.1016i	0.213706	+	0.515933i	0.993987	−	0.109497i	$-0.0349238\pi$
$463$	4.59841	+	11.1016i	0.213706	+	0.515933i	−0.780281	+	0.625429i	$0.784924\pi$
$464$		0			0
$465$	6.11459	−	14.7619i	0.283557	−	0.684568i
$466$		0			0
$467$	2.03460	+	0.200390i	0.0941499	+	0.00927296i	0.144982	−	0.989434i	$-0.453687\pi$
$467$	2.03460	+	0.200390i	0.0941499	+	0.00927296i	−0.0508325	+	0.998707i	$0.516187\pi$
$468$		0			0
$469$	−13.6256	+	7.28304i	−0.629172	+	0.336300i
$470$		0			0
$471$	3.84881	−	19.3493i	0.177344	−	0.891568i
$472$		0			0
$473$	38.2206	−	7.60255i	1.75739	−	0.349566i
$474$		0			0
$475$	−2.91866	+	0.287463i	−0.133917	+	0.0131897i
$476$		0			0
$477$	−12.8240	+	3.89011i	−0.587169	+	0.178116i
$478$		0			0
$479$	−17.7517	−	17.7517i	−0.811094	−	0.811094i	0.173704	−	0.984798i	$-0.444426\pi$
$479$	−17.7517	−	17.7517i	−0.811094	−	0.811094i	−0.984798	+	0.173704i	$0.944426\pi$
$480$		0			0
$481$	5.28778	−	5.28778i	0.241102	−	0.241102i
$482$		0			0
$483$	0.727865	+	2.39945i	0.0331190	+	0.109179i
$484$		0			0
$485$	1.15670	+	11.7441i	0.0525229	+	0.533274i
$486$		0			0
$487$	7.60982	+	38.2572i	0.344834	+	1.73360i	0.631328	+	0.775516i	$0.282510\pi$
$487$	7.60982	+	38.2572i	0.344834	+	1.73360i	−0.286494	+	0.958082i	$0.592490\pi$
$488$		0			0
$489$	−22.9573	−	4.56650i	−1.03817	−	0.206504i
$490$		0			0
$491$	−9.61608	−	17.9904i	−0.433968	−	0.811897i	0.565954	−	0.824437i	$-0.308508\pi$
$491$	−9.61608	−	17.9904i	−0.433968	−	0.811897i	−0.999921	+	0.0125405i	$0.996008\pi$
$492$		0			0
$493$	0.673763	−	6.84083i	0.0303447	−	0.308095i
$494$		0			0
$495$	12.3659	+	5.12211i	0.555805	+	0.230222i
$496$		0			0
$497$	24.4616	−	10.1323i	1.09725	−	0.454496i
$498$		0			0
$499$	6.87955	−	5.64590i	0.307971	−	0.252745i	−0.467693	−	0.883891i	$-0.654915\pi$
$499$	6.87955	−	5.64590i	0.307971	−	0.252745i	0.775665	+	0.631145i	$0.217415\pi$
$500$		0			0
$501$	7.79614	+	2.36493i	0.348306	+	0.105657i
$502$		0			0
$503$	−9.18211	−	13.7420i	−0.409410	−	0.612726i	0.568265	−	0.822845i	$-0.307615\pi$
$503$	−9.18211	−	13.7420i	−0.409410	−	0.612726i	−0.977676	+	0.210120i	$0.932615\pi$
$504$		0			0
$505$	26.2817	+	17.5609i	1.16952	+	0.781450i
$506$		0			0
$507$	−6.27552	+	7.64674i	−0.278705	+	0.339604i
$508$		0			0
$509$	19.0638	+	10.1898i	0.844986	+	0.451655i	0.836277	−	0.548308i	$-0.184728\pi$
$509$	19.0638	+	10.1898i	0.844986	+	0.451655i	0.00870943	+	0.999962i	$0.497228\pi$
$510$		0			0
$511$	−13.6590			−0.604237
$512$		0			0
$513$	20.2313			0.893234
$514$		0			0
$515$	7.18508	+	3.84051i	0.316613	+	0.169233i
$516$		0			0
$517$	9.03703	−	11.0117i	0.397448	−	0.484292i
$518$		0			0
$519$	−14.5525	−	9.72368i	−0.638784	−	0.426822i
$520$		0			0
$521$	9.36005	+	14.0083i	0.410071	+	0.613715i	0.977810	−	0.209494i	$-0.0671817\pi$
$521$	9.36005	+	14.0083i	0.410071	+	0.613715i	−0.567739	+	0.823209i	$0.692182\pi$
$522$		0			0
$523$	−21.1524	−	6.41652i	−0.924932	−	0.280575i	−0.208331	−	0.978058i	$-0.566803\pi$
$523$	−21.1524	−	6.41652i	−0.924932	−	0.280575i	−0.716601	+	0.697484i	$0.754303\pi$
$524$		0			0
$525$	−1.86500	+	1.53057i	−0.0813953	+	0.0667994i
$526$		0			0
$527$	4.26072	−	1.76485i	0.185600	−	0.0768781i
$528$		0			0
$529$	−20.5959	−	8.53112i	−0.895476	−	0.370918i
$530$		0			0
$531$	0.573430	−	5.82214i	0.0248848	−	0.252659i
$532$		0			0
$533$	12.9983	+	24.3182i	0.563021	+	1.05334i
$534$		0			0
$535$	−16.9344	−	3.36845i	−0.732136	−	0.145631i
$536$		0			0
$537$	−1.96376	−	9.87251i	−0.0847427	−	0.426030i
$538$		0			0
$539$	−0.734054	−	7.45297i	−0.0316179	−	0.321022i
$540$		0			0
$541$	−1.69409	−	5.58466i	−0.0728345	−	0.240103i	0.912963	−	0.408043i	$-0.133789\pi$
$541$	−1.69409	−	5.58466i	−0.0728345	−	0.240103i	−0.985797	+	0.167940i	$0.946289\pi$
$542$		0			0
$543$	18.8264	−	18.8264i	0.807919	−	0.807919i
$544$		0			0
$545$	−9.38519	−	9.38519i	−0.402017	−	0.402017i
$546$		0			0
$547$	35.5328	−	10.7787i	1.51927	−	0.460866i	0.583097	−	0.812402i	$-0.301841\pi$
$547$	35.5328	−	10.7787i	1.51927	−	0.460866i	0.936174	+	0.351536i	$0.114341\pi$
$548$		0			0
$549$	−0.193850	+	0.0190926i	−0.00827334	+	0.000814852i
$550$		0			0
$551$	−32.3406	+	6.43295i	−1.37776	+	0.274053i
$552$		0			0
$553$	5.79783	−	29.1477i	0.246549	−	1.23949i
$554$		0			0
$555$	7.52481	−	4.02209i	0.319410	−	0.170728i
$556$		0			0
$557$	−34.6732	−	3.41501i	−1.46915	−	0.144699i	−0.668447	−	0.743760i	$-0.733041\pi$
$557$	−34.6732	−	3.41501i	−1.46915	−	0.144699i	−0.800703	+	0.599061i	$0.795541\pi$
$558$		0			0
$559$	−7.14179	+	17.2418i	−0.302066	+	0.729251i
$560$		0			0
$561$	−1.77167	−	4.27719i	−0.0748000	−	0.180583i
$562$		0			0
$563$	8.26046	+	10.0654i	0.348137	+	0.424206i	0.917411	−	0.397942i	$-0.130276\pi$
$563$	8.26046	+	10.0654i	0.348137	+	0.424206i	−0.569274	+	0.822148i	$0.692776\pi$
$564$		0			0
$565$	−8.35510	+	27.5431i	−0.351502	+	1.15875i
$566$		0			0
$567$	5.90121	−	3.94307i	0.247828	−	0.165593i
$568$		0			0
$569$	11.7061	−	17.5195i	0.490747	−	0.734455i	−0.500606	−	0.865675i	$-0.666890\pi$
$569$	11.7061	−	17.5195i	0.490747	−	0.734455i	0.991353	+	0.131220i	$0.0418895\pi$
$570$		0			0
$571$	−2.80242	−	2.29989i	−0.117278	−	0.0962472i	0.573927	−	0.818907i	$-0.305419\pi$
$571$	−2.80242	−	2.29989i	−0.117278	−	0.0962472i	−0.691204	+	0.722660i	$0.742919\pi$
$572$		0			0
$573$	−5.16349	+	9.66021i	−0.215708	+	0.403561i
$574$		0			0
$575$			0.680388i			0.0283741i
$576$		0			0
$577$		−	22.1328i		−	0.921400i	−0.887556	−	0.460700i	$-0.847598\pi$
$577$		−	22.1328i		−	0.921400i	0.887556	−	0.460700i	$-0.152402\pi$
$578$		0			0
$579$	−12.0110	+	22.4710i	−0.499160	+	0.933863i
$580$		0			0
$581$	24.1285	+	19.8017i	1.00102	+	0.821514i
$582$		0			0
$583$	26.1394	−	39.1203i	1.08258	−	1.62020i
$584$		0			0
$585$	−5.32966	+	3.56116i	−0.220354	+	0.147236i
$586$		0			0
$587$	−4.94590	+	16.3045i	−0.204139	+	0.672957i	0.793764	+	0.608226i	$0.208119\pi$
$587$	−4.94590	+	16.3045i	−0.204139	+	0.672957i	−0.997903	+	0.0647303i	$0.979381\pi$
$588$		0			0
$589$	−14.0345	−	17.1011i	−0.578280	−	0.704637i
$590$		0			0
$591$	2.28646	+	5.52001i	0.0940525	+	0.227063i
$592$		0			0
$593$	4.37734	−	10.5678i	0.179756	−	0.433969i	−0.808160	−	0.588964i	$-0.799536\pi$
$593$	4.37734	−	10.5678i	0.179756	−	0.433969i	0.987915	+	0.154995i	$0.0495361\pi$
$594$		0			0
$595$	3.58948	+	0.353533i	0.147154	+	0.0144934i
$596$		0			0
$597$	13.5767	−	7.25692i	0.555659	−	0.297006i
$598$		0			0
$599$	−8.30753	+	41.7648i	−0.339436	+	1.70646i	0.313952	+	0.949439i	$0.398347\pi$
$599$	−8.30753	+	41.7648i	−0.339436	+	1.70646i	−0.653388	+	0.757023i	$0.726653\pi$
$600$		0			0
$601$	3.62294	−	0.720648i	0.147783	−	0.0293959i	−0.120644	−	0.992696i	$-0.538496\pi$
$601$	3.62294	−	0.720648i	0.147783	−	0.0293959i	0.268427	+	0.963300i	$0.413496\pi$
$602$		0			0
$603$	8.99857	−	0.886281i	0.366450	−	0.0360922i
$604$		0			0
$605$	−23.4198	+	7.10433i	−0.952152	+	0.288832i
$606$		0			0
$607$	−31.2373	−	31.2373i	−1.26788	−	1.26788i	−0.947180	−	0.320702i	$-0.896081\pi$
$607$	−31.2373	−	31.2373i	−1.26788	−	1.26788i	−0.320702	−	0.947180i	$-0.603919\pi$
$608$		0			0
$609$	−19.1811	+	19.1811i	−0.777255	+	0.777255i
$610$		0			0
$611$	1.98032	+	6.52823i	0.0801151	+	0.264104i
$612$		0			0
$613$	−0.697251	−	7.07931i	−0.0281617	−	0.285931i	−0.998943	−	0.0459649i	$-0.985364\pi$
$613$	−0.697251	−	7.07931i	−0.0281617	−	0.285931i	0.970781	−	0.239966i	$-0.0771362\pi$
$614$		0			0
$615$	6.13783	+	30.8570i	0.247501	+	1.24427i
$616$		0			0
$617$	3.80877	+	0.757612i	0.153335	+	0.0305003i	0.271161	−	0.962534i	$-0.412592\pi$
$617$	3.80877	+	0.757612i	0.153335	+	0.0305003i	−0.117826	+	0.993034i	$0.537592\pi$
$618$		0			0
$619$	−3.63456	−	6.79979i	−0.146085	−	0.273307i	0.798227	−	0.602357i	$-0.205771\pi$
$619$	−3.63456	−	6.79979i	−0.146085	−	0.273307i	−0.944312	+	0.329050i	$0.893271\pi$
$620$		0			0
$621$	0.460047	−	4.67093i	0.0184610	−	0.187438i
$622$		0			0
$623$	−29.7519	−	12.3236i	−1.19198	−	0.493735i
$624$		0			0
$625$	18.7545	−	7.76837i	0.750181	−	0.310735i
$626$		0			0
$627$	−17.1671	+	14.0887i	−0.685590	+	0.562649i
$628$		0			0
$629$	2.35663	+	0.714875i	0.0939648	+	0.0285039i
$630$		0			0
$631$	0.601494	+	0.900200i	0.0239451	+	0.0358364i	0.843249	−	0.537523i	$-0.180640\pi$
$631$	0.601494	+	0.900200i	0.0239451	+	0.0358364i	−0.819304	+	0.573359i	$0.805640\pi$
$632$		0			0
$633$	8.63021	+	5.76652i	0.343020	+	0.229199i
$634$		0			0
$635$	−10.2705	+	12.5147i	−0.407573	+	0.496629i
$636$		0			0
$637$	3.16300	+	1.69066i	0.125323	+	0.0669864i
$638$		0			0
$639$	−15.4957			−0.613002
$640$		0			0
$641$	−34.4270			−1.35978			−0.679892	−	0.733312i	$-0.737973\pi$
$641$	−34.4270			−1.35978			−0.679892	+	0.733312i	$0.737973\pi$
$642$		0			0
$643$	28.5064	+	15.2370i	1.12418	+	0.600888i	0.925338	−	0.379143i	$-0.123781\pi$
$643$	28.5064	+	15.2370i	1.12418	+	0.600888i	0.198845	+	0.980031i	$0.436281\pi$
$644$		0			0
$645$	−13.5084	+	16.4600i	−0.531892	+	0.648113i
$646$		0			0
$647$	−3.68625	−	2.46307i	−0.144921	−	0.0968334i	0.480996	−	0.876723i	$-0.340275\pi$
$647$	−3.68625	−	2.46307i	−0.144921	−	0.0968334i	−0.625917	+	0.779889i	$0.715275\pi$
$648$		0			0
$649$	11.4113	+	17.0783i	0.447934	+	0.670381i
$650$		0			0
$651$	−17.4155	−	5.28293i	−0.682567	−	0.207054i
$652$		0			0
$653$	−4.15254	+	3.40790i	−0.162501	+	0.133361i	−0.712130	−	0.702048i	$-0.752269\pi$
$653$	−4.15254	+	3.40790i	−0.162501	+	0.133361i	0.549628	+	0.835409i	$0.314769\pi$
$654$		0			0
$655$	13.4028	−	5.55163i	0.523692	−	0.216920i
$656$		0			0
$657$	7.38544	+	3.05915i	0.288134	+	0.119349i
$658$		0			0
$659$	−0.320700	+	3.25612i	−0.0124927	+	0.126840i	−0.999408	−	0.0343978i	$-0.989049\pi$
$659$	−0.320700	+	3.25612i	−0.0124927	+	0.126840i	0.986916	+	0.161238i	$0.0515487\pi$
$660$		0			0
$661$	−5.39046	−	10.0848i	−0.209665	−	0.392255i	0.755004	−	0.655720i	$-0.227635\pi$
$661$	−5.39046	−	10.0848i	−0.209665	−	0.392255i	−0.964669	+	0.263465i	$0.915135\pi$
$662$		0			0
$663$	2.17451	+	0.432537i	0.0844509	+	0.0167983i
$664$		0			0
$665$	−3.37546	−	16.9696i	−0.130895	−	0.658052i
$666$		0			0
$667$	0.749812	+	7.61297i	0.0290328	+	0.294775i
$668$		0			0
$669$	4.85880	+	16.0173i	0.187852	+	0.619265i
$670$		0			0
$671$	0.483579	−	0.483579i	0.0186683	−	0.0186683i
$672$		0			0
$673$	−13.5900	−	13.5900i	−0.523855	−	0.523855i	0.394879	−	0.918733i	$-0.370787\pi$
$673$	−13.5900	−	13.5900i	−0.523855	−	0.523855i	−0.918733	+	0.394879i	$0.870787\pi$
$674$		0			0
$675$	4.32167	−	1.31096i	0.166341	−	0.0504590i
$676$		0			0
$677$	−8.06571	+	0.794404i	−0.309991	+	0.0305314i	−0.251816	−	0.967775i	$-0.581028\pi$
$677$	−8.06571	+	0.794404i	−0.309991	+	0.0305314i	−0.0581742	+	0.998306i	$0.518528\pi$
$678$		0			0
$679$	13.1830	−	2.62226i	0.505917	−	0.100633i
$680$		0			0
$681$	−4.23711	+	21.3014i	−0.162366	+	0.816270i
$682$		0			0
$683$	18.1881	−	9.72176i	0.695950	−	0.371993i	−0.0851767	−	0.996366i	$-0.527145\pi$
$683$	18.1881	−	9.72176i	0.695950	−	0.371993i	0.781126	+	0.624373i	$0.214645\pi$
$684$		0			0
$685$	26.9176	+	2.65115i	1.02847	+	0.101295i
$686$		0			0
$687$	−11.7272	+	28.3120i	−0.447422	+	1.08017i
$688$		0			0
$689$	8.62263	+	20.8169i	0.328496	+	0.793059i
$690$		0			0
$691$	6.87575	+	8.37812i	0.261566	+	0.318719i	0.887189	−	0.461407i	$-0.152655\pi$
$691$	6.87575	+	8.37812i	0.261566	+	0.318719i	−0.625623	+	0.780126i	$0.715155\pi$
$692$		0			0
$693$	4.42544	−	14.5887i	0.168108	−	0.554179i
$694$		0			0
$695$	24.0570	−	16.0743i	0.912533	−	0.609735i
$696$		0			0
$697$	−5.04497	+	7.55033i	−0.191092	+	0.285989i
$698$		0			0
$699$	26.1988	+	21.5008i	0.990930	+	0.813235i
$700$		0			0
$701$	0.367114	−	0.686821i	0.0138657	−	0.0259409i	−0.874893	−	0.484316i	$-0.839068\pi$
$701$	0.367114	−	0.686821i	0.0138657	−	0.0259409i	0.888759	+	0.458375i	$0.151568\pi$
$702$		0			0
$703$		−	11.8134i		−	0.445551i
$704$		0			0
$705$			7.78374i			0.293153i
$706$		0			0
$707$	16.9714	−	31.7512i	0.638274	−	1.19413i
$708$		0			0
$709$	−11.3799	−	9.33927i	−0.427382	−	0.350744i	0.395981	−	0.918259i	$-0.370405\pi$
$709$	−11.3799	−	9.33927i	−0.427382	−	0.350744i	−0.823363	+	0.567515i	$0.807905\pi$
$710$		0			0
$711$	−9.66301	+	14.4617i	−0.362391	+	0.542357i
$712$		0			0
$713$	−4.26737	+	2.85136i	−0.159814	+	0.106784i
$714$		0			0
$715$	6.53275	−	21.5356i	0.244311	−	0.805385i
$716$		0			0
$717$	4.65130	+	5.66762i	0.173706	+	0.211661i
$718$		0			0
$719$	7.06610	+	17.0591i	0.263521	+	0.636196i	0.999151	−	0.0411873i	$-0.0131140\pi$
$719$	7.06610	+	17.0591i	0.263521	+	0.636196i	−0.735631	+	0.677383i	$0.763114\pi$
$720$		0			0
$721$	3.55111	−	8.57314i	0.132250	−	0.319281i
$722$		0			0
$723$	−4.82811	−	0.475527i	−0.179559	−	0.0176850i
$724$		0			0
$725$	−6.49153	+	3.46979i	−0.241089	+	0.128865i
$726$		0			0
$727$	0.476522	−	2.39564i	0.0176732	−	0.0888493i	−0.970942	−	0.239315i	$-0.923077\pi$
$727$	0.476522	−	2.39564i	0.0176732	−	0.0888493i	0.988615	+	0.150465i	$0.0480772\pi$
$728$		0			0
$729$	−25.0757	+	4.98787i	−0.928730	+	0.184736i
$730$		0			0
$731$	−6.11630	+	0.602403i	−0.226220	+	0.0222807i
$732$		0			0
$733$	0.187840	−	0.0569807i	0.00693804	−	0.00210463i	−0.286814	−	0.957986i	$-0.592596\pi$
$733$	0.187840	−	0.0569807i	0.00693804	−	0.00210463i	0.293752	+	0.955882i	$0.405096\pi$
$734$		0			0
$735$	2.89356	+	2.89356i	0.106731	+	0.106731i
$736$		0			0
$737$	−22.4478	+	22.4478i	−0.826875	+	0.826875i
$738$		0			0
$739$	−8.72312	−	28.7563i	−0.320885	−	1.05782i	−0.957933	−	0.286992i	$-0.907345\pi$
$739$	−8.72312	−	28.7563i	−0.320885	−	1.05782i	0.637048	−	0.770824i	$-0.280155\pi$
$740$		0			0
$741$	−1.04246	−	10.5843i	−0.0382956	−	0.388822i
$742$		0			0
$743$	−1.02215	−	5.13871i	−0.0374992	−	0.188521i	0.957496	−	0.288448i	$-0.0931392\pi$
$743$	−1.02215	−	5.13871i	−0.0374992	−	0.188521i	−0.994995	+	0.0999267i	$0.968139\pi$
$744$		0			0
$745$	−0.0648047	−	0.0128905i	−0.00237426	−	0.000472270i
$746$		0			0
$747$	−8.61141	−	16.1108i	−0.315075	−	0.589464i
$748$		0			0
$749$	−1.92761	+	19.5714i	−0.0704334	+	0.715122i
$750$		0			0
$751$	25.2258	+	10.4489i	0.920502	+	0.381284i	0.792067	−	0.610434i	$-0.209005\pi$
$751$	25.2258	+	10.4489i	0.920502	+	0.381284i	0.128434	+	0.991718i	$0.459005\pi$
$752$		0			0
$753$	−2.87990	+	1.19289i	−0.104949	+	0.0434715i
$754$		0			0
$755$	−26.3515	+	21.6261i	−0.959031	+	0.787056i
$756$		0			0
$757$	24.5864	+	7.45821i	0.893608	+	0.271073i	0.703505	−	0.710691i	$-0.251617\pi$
$757$	24.5864	+	7.45821i	0.893608	+	0.271073i	0.190104	+	0.981764i	$0.439117\pi$
$758$		0			0
$759$	2.86239	+	4.28386i	0.103898	+	0.155494i
$760$		0			0
$761$	−10.7076	−	7.15462i	−0.388152	−	0.259355i	0.346148	−	0.938180i	$-0.387489\pi$
$761$	−10.7076	−	7.15462i	−0.388152	−	0.259355i	−0.734300	+	0.678825i	$0.762489\pi$
$762$		0			0
$763$	−9.59046	+	11.6860i	−0.347198	+	0.423062i
$764$		0			0
$765$	−1.86166	−	0.995079i	−0.0673085	−	0.0359771i
$766$		0			0
$767$	−9.83651			−0.355176
$768$		0			0
$769$	−4.45912			−0.160800			−0.0804000	−	0.996763i	$-0.525620\pi$
$769$	−4.45912			−0.160800			−0.0804000	+	0.996763i	$0.525620\pi$
$770$		0			0
$771$	17.4377	+	9.32066i	0.628005	+	0.335676i
$772$		0			0
$773$	21.6653	−	26.3992i	0.779247	−	0.949515i	−0.220418	−	0.975405i	$-0.570742\pi$
$773$	21.6653	−	26.3992i	0.779247	−	0.949515i	0.999665	+	0.0258907i	$0.00824220\pi$
$774$		0			0
$775$	−4.10607	−	2.74359i	−0.147495	−	0.0985527i
$776$		0			0
$777$	−5.39917	−	8.08044i	−0.193694	−	0.289884i
$778$		0			0
$779$	41.6844	+	12.6448i	1.49350	+	0.453048i
$780$		0			0
$781$	42.0549	−	34.5136i	1.50484	−	1.23499i
$782$		0			0
$783$	46.9111	−	19.4312i	1.67647	−	0.694415i
$784$		0			0
$785$	29.1778	+	12.0858i	1.04140	+	0.431362i
$786$		0			0
$787$	−4.54779	+	46.1745i	−0.162111	+	1.64594i	0.478507	+	0.878084i	$0.341178\pi$
$787$	−4.54779	+	46.1745i	−0.162111	+	1.64594i	−0.640618	+	0.767860i	$0.721322\pi$
$788$		0			0
$789$	−6.30925	−	11.8038i	−0.224615	−	0.420226i
$790$		0			0
$791$	32.1532	+	6.39567i	1.14324	+	0.227404i
$792$		0			0
$793$	0.0638942	+	0.321218i	0.00226895	+	0.0114068i
$794$		0			0
$795$	2.51988	+	25.5848i	0.0893709	+	0.907398i
$796$		0			0
$797$	8.55456	+	28.2006i	0.303018	+	0.998917i	0.967766	+	0.251849i	$0.0810388\pi$
$797$	8.55456	+	28.2006i	0.303018	+	0.998917i	−0.664748	+	0.747067i	$0.731461\pi$
$798$		0			0
$799$	−1.58860	+	1.58860i	−0.0562005	+	0.0562005i
$800$		0			0
$801$	13.3268	+	13.3268i	0.470881	+	0.470881i
$802$		0			0
$803$	−26.8575	+	8.14712i	−0.947779	+	0.287506i
$804$		0			0
$805$	−3.99463	+	0.393437i	−0.140792	+	0.0138668i
$806$		0			0
$807$	−26.9204	+	5.35481i	−0.947645	+	0.188498i
$808$		0			0
$809$	−7.86822	+	39.5562i	−0.276632	+	1.39072i	0.553358	+	0.832944i	$0.313346\pi$
$809$	−7.86822	+	39.5562i	−0.276632	+	1.39072i	−0.829990	+	0.557779i	$0.811654\pi$
$810$		0			0
$811$	5.49315	−	2.93615i	0.192891	−	0.103102i	−0.372124	−	0.928183i	$-0.621370\pi$
$811$	5.49315	−	2.93615i	0.192891	−	0.103102i	0.565015	+	0.825081i	$0.308870\pi$
$812$		0			0
$813$	−23.5317	−	2.31767i	−0.825292	−	0.0812842i
$814$		0			0
$815$	14.3395	−	34.6186i	0.502290	−	1.21264i
$816$		0			0
$817$	11.2822	+	27.2377i	0.394715	+	0.952926i
$818$		0			0
$819$	4.63163	+	5.64366i	0.161842	+	0.197206i
$820$		0			0
$821$	−7.70916	+	25.4137i	−0.269051	+	0.886944i	0.713453	+	0.700703i	$0.247130\pi$
$821$	−7.70916	+	25.4137i	−0.269051	+	0.886944i	−0.982504	+	0.186240i	$0.940370\pi$
$822$		0			0
$823$	26.3742	−	17.6227i	0.919347	−	0.614288i	−0.00327420	−	0.999995i	$-0.501042\pi$
$823$	26.3742	−	17.6227i	0.919347	−	0.614288i	0.922622	+	0.385706i	$0.126042\pi$
$824$		0			0
$825$	−2.75420	+	4.12194i	−0.0958888	+	0.143508i
$826$		0			0
$827$	9.07202	+	7.44521i	0.315465	+	0.258895i	0.778778	−	0.627299i	$-0.215840\pi$
$827$	9.07202	+	7.44521i	0.315465	+	0.258895i	−0.463314	+	0.886194i	$0.653340\pi$
$828$		0			0
$829$	−3.05468	+	5.71490i	−0.106093	+	0.198487i	−0.929366	−	0.369159i	$-0.879646\pi$
$829$	−3.05468	+	5.71490i	−0.106093	+	0.198487i	0.823273	+	0.567646i	$0.192146\pi$
$830$		0			0
$831$			15.7718i			0.547118i
$832$		0			0
$833$			1.18110i			0.0409228i
$834$		0			0
$835$	−6.14791	+	11.5019i	−0.212757	+	0.398041i
$836$		0			0
$837$	26.3335	+	21.6114i	0.910220	+	0.746998i
$838$		0			0
$839$	−17.1370	+	25.6473i	−0.591635	+	0.885444i	−0.999621	−	0.0275443i	$-0.991231\pi$
$839$	−17.1370	+	25.6473i	−0.591635	+	0.885444i	0.407986	+	0.912988i	$0.366231\pi$
$840$		0			0
$841$	−44.6983	+	29.8665i	−1.54132	+	1.02988i
$842$		0			0
$843$	−3.44078	+	11.3427i	−0.118507	+	0.390664i
$844$		0			0
$845$	−10.0461	−	12.2412i	−0.345595	−	0.421109i
$846$		0			0
$847$	10.6675	+	25.7535i	0.366539	+	0.884902i
$848$		0			0
$849$	2.00824	−	4.84833i	0.0689227	−	0.166394i
$850$		0			0
$851$	−2.72744	−	0.268629i	−0.0934954	−	0.00920850i
$852$		0			0
$853$	−5.05371	+	2.70126i	−0.173036	+	0.0924895i	−0.555641	−	0.831423i	$-0.687527\pi$
$853$	−5.05371	+	2.70126i	−0.173036	+	0.0924895i	0.382605	+	0.923912i	$0.375027\pi$
$854$		0			0
$855$	−1.97550	+	9.93148i	−0.0675605	+	0.339650i
$856$		0			0
$857$	−15.7887	+	3.14056i	−0.539331	+	0.107280i	−0.457237	−	0.889345i	$-0.651161\pi$
$857$	−15.7887	+	3.14056i	−0.539331	+	0.107280i	−0.0820941	+	0.996625i	$0.526161\pi$
$858$		0			0
$859$	−18.3860	+	1.81087i	−0.627323	+	0.0617859i	−0.406683	−	0.913569i	$-0.633315\pi$
$859$	−18.3860	+	1.81087i	−0.627323	+	0.0617859i	−0.220640	+	0.975355i	$0.570815\pi$
$860$		0			0
$861$	34.2915	−	10.4022i	1.16865	−	0.354507i
$862$		0			0
$863$	−4.49797	−	4.49797i	−0.153113	−	0.153113i	0.626394	−	0.779507i	$-0.284530\pi$
$863$	−4.49797	−	4.49797i	−0.153113	−	0.153113i	−0.779507	+	0.626394i	$0.784530\pi$
$864$		0			0
$865$	19.8118	−	19.8118i	0.673620	−	0.673620i
$866$		0			0
$867$	−6.09878	−	20.1050i	−0.207125	−	0.682801i
$868$		0			0
$869$	−5.98542	−	60.7709i	−0.203041	−	2.06151i
$870$		0			0
$871$	−2.96598	−	14.9110i	−0.100498	−	0.505239i
$872$		0			0
$873$	−7.71538	−	1.53468i	−0.261126	−	0.0519412i
$874$		0			0
$875$	−13.0715	−	24.4550i	−0.441897	−	0.826731i
$876$		0			0
$877$	−0.495634	+	5.03225i	−0.0167364	+	0.169927i	−0.999919	−	0.0126957i	$-0.995959\pi$
$877$	−0.495634	+	5.03225i	−0.0167364	+	0.169927i	0.983183	+	0.182623i	$0.0584587\pi$
$878$		0			0
$879$	−7.82233	−	3.24011i	−0.263841	−	0.109286i
$880$		0			0
$881$	5.83767	−	2.41804i	0.196676	−	0.0814659i	−0.282171	−	0.959364i	$-0.591055\pi$
$881$	5.83767	−	2.41804i	0.196676	−	0.0814659i	0.478847	+	0.877898i	$0.341055\pi$
$882$		0			0
$883$	14.1089	−	11.5789i	0.474804	−	0.389661i	−0.366333	−	0.930484i	$-0.619387\pi$
$883$	14.1089	−	11.5789i	0.474804	−	0.389661i	0.841137	+	0.540822i	$0.181887\pi$
$884$		0			0
$885$	−10.7400	−	3.25794i	−0.361021	−	0.109514i
$886$		0			0
$887$	15.1357	+	22.6521i	0.508206	+	0.760584i	0.993508	−	0.113763i	$-0.0362904\pi$
$887$	15.1357	+	22.6521i	0.508206	+	0.760584i	−0.485302	+	0.874347i	$0.661290\pi$
$888$		0			0
$889$	15.3321	+	10.2446i	0.514224	+	0.343593i
$890$		0			0
$891$	9.25158	−	11.2731i	0.309940	−	0.377662i
$892$		0			0
$893$	9.50447	+	5.08025i	0.318055	+	0.170004i
$894$		0			0
$895$	16.1139			0.538628
$896$		0			0
$897$	−2.46736			−0.0823828
$898$		0			0
$899$	−48.9671	−	26.1734i	−1.63314	−	0.872933i
$900$		0			0
$901$	−4.70735	+	5.73592i	−0.156825	+	0.191091i
$902$		0			0
$903$	20.1657	+	13.4743i	0.671074	+	0.448397i
$904$		0			0
$905$	23.6793	+	35.4385i	0.787125	+	1.17802i
$906$		0			0
$907$	−21.3890	−	6.48830i	−0.710212	−	0.215440i	−0.0855477	−	0.996334i	$-0.527264\pi$
$907$	−21.3890	−	6.48830i	−0.710212	−	0.215440i	−0.624664	+	0.780894i	$0.714764\pi$
$908$		0			0
$909$	−16.2877	+	13.3670i	−0.540228	+	0.443354i
$910$		0			0
$911$	−48.0358	+	19.8971i	−1.59150	+	0.659220i	−0.990181	−	0.139791i	$-0.955357\pi$
$911$	−48.0358	+	19.8971i	−1.59150	+	0.659220i	−0.601316	+	0.799011i	$0.705357\pi$
$912$		0			0
$913$	59.2546	+	24.5441i	1.96104	+	0.812290i
$914$		0			0
$915$	−0.0366273	+	0.371884i	−0.00121086	+	0.0122941i
$916$		0			0
$917$	−7.78915	−	14.5725i	−0.257221	−	0.481226i
$918$		0			0
$919$	32.4140	+	6.44754i	1.06924	+	0.212685i	0.698178	−	0.715924i	$-0.253994\pi$
$919$	32.4140	+	6.44754i	1.06924	+	0.212685i	0.371060	+	0.928609i	$0.378994\pi$
$920$		0			0
$921$	−1.14134	−	5.73790i	−0.0376084	−	0.189070i
$922$		0			0
$923$	2.55374	+	25.9286i	0.0840574	+	0.853449i
$924$		0			0
$925$	−0.765495	−	2.52350i	−0.0251693	−	0.0829721i
$926$		0			0
$927$	−3.84019	+	3.84019i	−0.126129	+	0.126129i
$928$		0			0
$929$	−20.7717	−	20.7717i	−0.681498	−	0.681498i	0.278839	−	0.960338i	$-0.410050\pi$
$929$	−20.7717	−	20.7717i	−0.681498	−	0.681498i	−0.960338	+	0.278839i	$0.910050\pi$
$930$		0			0
$931$	5.42178	−	1.64468i	0.177692	−	0.0539022i
$932$		0			0
$933$	−3.30511	+	0.325525i	−0.108205	+	0.0106572i
$934$		0			0
$935$	7.26882	−	1.44586i	0.237716	−	0.0472846i
$936$		0			0
$937$	8.29179	−	41.6856i	0.270881	−	1.36181i	−0.570469	−	0.821319i	$-0.693239\pi$
$937$	8.29179	−	41.6856i	0.270881	−	1.36181i	0.841350	−	0.540491i	$-0.181761\pi$
$938$		0			0
$939$	−16.9978	+	9.08553i	−0.554703	+	0.296495i
$940$		0			0
$941$	−11.4320	−	1.12595i	−0.372671	−	0.0367049i	−0.0900520	−	0.995937i	$-0.528703\pi$
$941$	−11.4320	−	1.12595i	−0.372671	−	0.0367049i	−0.282619	+	0.959232i	$0.591203\pi$
$942$		0			0
$943$	3.86727	−	9.33642i	0.125936	−	0.304036i
$944$		0			0
$945$	10.1958	+	24.6149i	0.331671	+	0.800724i
$946$		0			0
$947$	−20.8070	−	25.3534i	−0.676136	−	0.823874i	0.316037	−	0.948747i	$-0.397648\pi$
$947$	−20.8070	−	25.3534i	−0.676136	−	0.823874i	−0.992173	+	0.124873i	$0.960148\pi$
$948$		0			0
$949$	3.90165	−	12.8620i	0.126653	−	0.417518i
$950$		0			0
$951$	11.0361	−	7.37409i	0.357870	−	0.239121i
$952$		0			0
$953$	14.4114	−	21.5682i	0.466832	−	0.698663i	−0.521110	−	0.853489i	$-0.674482\pi$
$953$	14.4114	−	21.5682i	0.466832	−	0.698663i	0.987942	+	0.154827i	$0.0494819\pi$
$954$		0			0
$955$	−13.5547	−	11.1240i	−0.438618	−	0.359965i
$956$		0			0
$957$	−26.2746	+	49.1563i	−0.849337	+	1.58900i
$958$		0			0
$959$		−	30.8075i		−	0.994825i
$960$		0			0
$961$		−	6.25097i		−	0.201644i
$962$		0			0
$963$	5.42560	−	10.1506i	0.174837	−	0.327098i
$964$		0			0
$965$	−31.5300	−	25.8760i	−1.01499	−	0.832979i
$966$		0			0
$967$	−10.3154	+	15.4380i	−0.331720	+	0.496453i	−0.959412	−	0.282008i	$-0.909000\pi$
$967$	−10.3154	+	15.4380i	−0.331720	+	0.496453i	0.627692	+	0.778461i	$0.284000\pi$
$968$		0			0
$969$	2.91220	−	1.94587i	0.0935532	−	0.0625103i
$970$		0			0
$971$	3.42337	−	11.2853i	0.109861	−	0.362164i	−0.884720	−	0.466122i	$-0.845651\pi$
$971$	3.42337	−	11.2853i	0.109861	−	0.362164i	0.994582	+	0.103958i	$0.0331508\pi$
$972$		0			0
$973$	−20.9062	−	25.4743i	−0.670223	−	0.816669i
$974$		0			0
$975$	−0.908529	−	2.19338i	−0.0290962	−	0.0702445i
$976$		0			0
$977$	0.561296	−	1.35509i	0.0179575	−	0.0433531i	−0.914646	−	0.404255i	$-0.867531\pi$
$977$	0.561296	−	1.35509i	0.0179575	−	0.0433531i	0.932604	+	0.360902i	$0.117531\pi$
$978$		0			0
$979$	−65.8513	−	6.48579i	−2.10462	−	0.207287i
$980$		0			0
$981$	7.80286	−	4.17072i	0.249126	−	0.133161i
$982$		0			0
$983$	0.896521	−	4.50711i	0.0285946	−	0.143755i	−0.963851	−	0.266443i	$-0.914152\pi$
$983$	0.896521	−	4.50711i	0.0285946	−	0.143755i	0.992445	+	0.122688i	$0.0391516\pi$
$984$		0			0
$985$	−9.38090	+	1.86598i	−0.298900	+	0.0594550i
$986$		0			0
$987$	8.82297	−	0.868987i	0.280838	−	0.0276602i
$988$		0			0
$989$	6.54509	−	1.98543i	0.208122	−	0.0631331i
$990$		0			0
$991$	10.5985	+	10.5985i	0.336672	+	0.336672i	0.855113	−	0.518441i	$-0.173488\pi$
$991$	10.5985	+	10.5985i	0.336672	+	0.336672i	−0.518441	+	0.855113i	$0.673488\pi$
$992$		0			0
$993$	0.277457	−	0.277457i	0.00880483	−	0.00880483i
$994$		0			0
$995$	7.15379	+	23.5829i	0.226791	+	0.747628i
$996$		0			0
$997$	2.15724	+	21.9028i	0.0683204	+	0.693668i	0.966951	+	0.254962i	$0.0820630\pi$
$997$	2.15724	+	21.9028i	0.0683204	+	0.693668i	−0.898631	+	0.438706i	$0.855437\pi$
$998$		0			0
$999$	3.54893	+	17.8417i	0.112283	+	0.564486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.273.10		240
4.3	odd	2		128.2.k.a.109.3	yes	240
128.27	odd	32		128.2.k.a.101.3	✓	240
128.101	even	32	inner	512.2.k.a.497.10		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.101.3	✓	240	128.27	odd	32
128.2.k.a.109.3	yes	240	4.3	odd	2
512.2.k.a.273.10		240	1.1	even	1	trivial
512.2.k.a.497.10		240	128.101	even	32	inner

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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.k (of order \(32\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.12781 + 0.602827i) q^{3} +(-1.29871 + 1.58248i) q^{5} +(1.93875 + 1.29543i) q^{7} +(-0.758155 - 1.13466i) q^{9} +(4.58482 + 1.39079i) q^{11} +(-1.77365 + 1.45559i) q^{13} +(-2.41866 + 1.00184i) q^{15} +(-0.698095 - 0.289160i) q^{17} +(-0.355280 + 3.60722i) q^{19} +(1.40562 + 2.62973i) q^{21} +(0.824744 + 0.164052i) q^{23} +(0.157851 + 0.793571i) q^{25} +(-0.547088 - 5.55468i) q^{27} +(2.64076 + 8.70543i) q^{29} +(-4.31573 + 4.31573i) q^{31} +(4.33241 + 4.33241i) q^{33} +(-4.56786 + 1.38565i) q^{35} +(-3.24347 + 0.319454i) q^{37} +(-2.87781 + 0.572431i) q^{39} +(2.34453 - 11.7868i) q^{41} +(7.17325 - 3.83418i) q^{43} +(2.78020 + 0.273825i) q^{45} +(1.13781 - 2.74691i) q^{47} +(-0.598174 - 1.44412i) q^{49} +(-0.613005 - 0.746949i) q^{51} +(2.85064 - 9.39731i) q^{53} +(-8.15524 + 5.44916i) q^{55} +(-2.57522 + 3.85409i) q^{57} +(3.31394 + 2.71968i) q^{59} +(0.0672870 - 0.125885i) q^{61} -3.18196i q^{63} -4.69715i q^{65} +(-3.12347 + 5.84360i) q^{67} +(0.831260 + 0.682197i) q^{69} +(6.30859 - 9.44148i) q^{71} +(-4.87067 + 3.25448i) q^{73} +(-0.300360 + 0.990154i) q^{75} +(7.08715 + 8.63572i) q^{77} +(-4.87747 - 11.7752i) q^{79} +(1.16482 - 2.81213i) q^{81} +(13.3221 + 1.31211i) q^{83} +(1.36421 - 0.729186i) q^{85} +(-2.26959 + 11.4100i) q^{87} +(-13.5456 + 2.69438i) q^{89} +(-5.32428 + 0.524395i) q^{91} +(-7.46896 + 2.26568i) q^{93} +(-5.24694 - 5.24694i) q^{95} +(4.07614 - 4.07614i) q^{97} +(-1.89793 - 6.25664i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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