LMFDB - Embedded newform 135.3.l.a.37.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,3,Mod(37,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("135.37"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.l (of order $12$, degree $4$, 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:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.9
Character	$\chi$	$=$	135.37
Dual form			135.3.l.a.73.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.644680 - 2.40598i) q^{2} +(-1.90902 - 1.10217i) q^{4} +(4.49898 - 2.18155i) q^{5} +(0.0176356 - 0.0658171i) q^{7} +(3.16269 - 3.16269i) q^{8} +(-2.34837 - 12.2309i) q^{10} +(-4.62292 - 8.00713i) q^{11} +(3.38696 + 12.6403i) q^{13} +(-0.146985 - 0.0848619i) q^{14} +(-9.97912 - 17.2843i) q^{16} +(-13.6029 - 13.6029i) q^{17} +5.80704i q^{19} +(-10.9931 - 0.794023i) q^{20} +(-22.2453 + 5.96060i) q^{22} +(11.7365 + 43.8013i) q^{23} +(15.4816 - 19.6295i) q^{25} +32.5958 q^{26} +(-0.106208 + 0.106208i) q^{28} +(-6.37222 + 3.67900i) q^{29} +(-8.35363 + 14.4689i) q^{31} +(-30.7378 + 8.23618i) q^{32} +(-41.4978 + 23.9587i) q^{34} +(-0.0642412 - 0.334583i) q^{35} +(36.0680 + 36.0680i) q^{37} +(13.9716 + 3.74368i) q^{38} +(7.32929 - 21.1284i) q^{40} +(31.1567 - 53.9649i) q^{41} +(9.70259 + 2.59980i) q^{43} +20.3810i q^{44} +112.951 q^{46} +(-11.9633 + 44.6476i) q^{47} +(42.4312 + 24.4977i) q^{49} +(-37.2475 - 49.9033i) q^{50} +(7.46602 - 27.8636i) q^{52} +(-28.0258 + 28.0258i) q^{53} +(-38.2664 - 25.9388i) q^{55} +(-0.152383 - 0.263935i) q^{56} +(4.74356 + 17.7032i) q^{58} +(-16.3509 - 9.44022i) q^{59} +(2.69547 + 4.66870i) q^{61} +(29.4265 + 29.4265i) q^{62} -0.568692i q^{64} +(42.8134 + 49.4796i) q^{65} +(-47.9117 + 12.8379i) q^{67} +(10.9754 + 40.9609i) q^{68} +(-0.846414 - 0.0611359i) q^{70} -56.4200 q^{71} +(-54.7135 + 54.7135i) q^{73} +(110.031 - 63.5264i) q^{74} +(6.40036 - 11.0857i) q^{76} +(-0.608534 + 0.163056i) q^{77} +(-40.9692 + 23.6536i) q^{79} +(-82.6026 - 55.9919i) q^{80} +(-109.752 - 109.752i) q^{82} +(-60.0267 - 16.0841i) q^{83} +(-90.8746 - 31.5237i) q^{85} +(12.5101 - 21.6682i) q^{86} +(-39.9449 - 10.7032i) q^{88} +59.1599i q^{89} +0.891679 q^{91} +(25.8713 - 96.5530i) q^{92} +(99.7085 + 57.5668i) q^{94} +(12.6684 + 26.1258i) q^{95} +(40.2595 - 150.251i) q^{97} +(86.2954 - 86.2954i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 2 q^{2} + 2 q^{5} - 2 q^{7} + 24 q^{8} - 8 q^{10} - 8 q^{11} - 2 q^{13} + 28 q^{16} - 28 q^{17} + 114 q^{20} + 14 q^{22} - 82 q^{23} - 8 q^{25} + 112 q^{26} - 88 q^{28} - 4 q^{31} + 14 q^{32} - 352 q^{35}+ \cdots + 1876 q^{98}+O(q^{100}) $ 40 * q + 2 * q^2 + 2 * q^5 - 2 * q^7 + 24 * q^8 - 8 * q^10 - 8 * q^11 - 2 * q^13 + 28 * q^16 - 28 * q^17 + 114 * q^20 + 14 * q^22 - 82 * q^23 - 8 * q^25 + 112 * q^26 - 88 * q^28 - 4 * q^31 + 14 * q^32 - 352 * q^35 - 92 * q^37 - 330 * q^38 + 30 * q^40 + 28 * q^41 - 2 * q^43 - 136 * q^46 - 64 * q^47 + 458 * q^50 - 74 * q^52 + 608 * q^53 + 224 * q^55 + 192 * q^56 + 30 * q^58 + 92 * q^61 + 100 * q^62 + 326 * q^65 - 80 * q^67 - 626 * q^68 - 102 * q^70 - 248 * q^71 - 8 * q^73 - 96 * q^76 - 338 * q^77 - 1444 * q^80 + 104 * q^82 - 370 * q^83 - 98 * q^85 + 328 * q^86 - 210 * q^88 + 152 * q^91 - 388 * q^92 + 360 * q^95 + 292 * q^97 + 1876 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.644680	−	2.40598i	0.322340	−	1.20299i	−0.594619	−	0.804008i	$-0.702697\pi$
$2$	0.644680	−	2.40598i	0.322340	−	1.20299i	0.916959	−	0.398981i	$-0.130636\pi$
$3$		0			0
$3$		0			0
$4$	−1.90902	−	1.10217i	−0.477254	−	0.275543i
$5$	4.49898	−	2.18155i	0.899796	−	0.436311i
$5$	4.49898	−	2.18155i	0.899796	−	0.436311i
$6$		0			0
$7$	0.0176356	−	0.0658171i	0.00251938	−	0.00940244i	−0.964655	−	0.263517i	$-0.915117\pi$
$7$	0.0176356	−	0.0658171i	0.00251938	−	0.00940244i	0.967174	+	0.254115i	$0.0817841\pi$
$8$	3.16269	−	3.16269i	0.395336	−	0.395336i
$9$		0			0
$10$	−2.34837	−	12.2309i	−0.234837	−	1.22309i
$11$	−4.62292	−	8.00713i	−0.420265	−	0.727921i	0.575700	−	0.817661i	$-0.304730\pi$
$11$	−4.62292	−	8.00713i	−0.420265	−	0.727921i	−0.995965	+	0.0897404i	$0.971396\pi$
$12$		0			0
$13$	3.38696	+	12.6403i	0.260535	+	0.972331i	0.964927	+	0.262519i	$0.0845534\pi$
$13$	3.38696	+	12.6403i	0.260535	+	0.972331i	−0.704391	+	0.709812i	$0.748780\pi$
$14$	−0.146985	−	0.0848619i	−0.0104989	−	0.00606156i
$15$		0			0
$16$	−9.97912	−	17.2843i	−0.623695	−	1.08027i
$17$	−13.6029	−	13.6029i	−0.800170	−	0.800170i	0.182952	−	0.983122i	$-0.441435\pi$
$17$	−13.6029	−	13.6029i	−0.800170	−	0.800170i	−0.983122	+	0.182952i	$0.941435\pi$
$18$		0			0
$19$			5.80704i			0.305634i	0.988255	+	0.152817i	$0.0488345\pi$
$19$			5.80704i			0.305634i	−0.988255	+	0.152817i	$0.951166\pi$
$20$	−10.9931	−	0.794023i	−0.549654	−	0.0397011i
$21$		0			0
$22$	−22.2453	+	5.96060i	−1.01115	+	0.270936i
$23$	11.7365	+	43.8013i	0.510283	+	1.90440i	0.417390	+	0.908728i	$0.362945\pi$
$23$	11.7365	+	43.8013i	0.510283	+	1.90440i	0.0928936	+	0.995676i	$0.470388\pi$
$24$		0			0
$25$	15.4816	−	19.6295i	0.619266	−	0.785182i
$26$	32.5958			1.25368
$27$		0			0
$28$	−0.106208	+	0.106208i	−0.00379316	+	0.00379316i
$29$	−6.37222	+	3.67900i	−0.219732	+	0.126862i	−0.605826	−	0.795597i	$-0.707157\pi$
$29$	−6.37222	+	3.67900i	−0.219732	+	0.126862i	0.386094	+	0.922459i	$0.373824\pi$
$30$		0			0
$31$	−8.35363	+	14.4689i	−0.269472	+	0.466739i	−0.968726	−	0.248135i	$-0.920183\pi$
$31$	−8.35363	+	14.4689i	−0.269472	+	0.466739i	0.699254	+	0.714874i	$0.253516\pi$
$32$	−30.7378	+	8.23618i	−0.960558	+	0.257381i
$33$		0			0
$34$	−41.4978	+	23.9587i	−1.22052	+	0.704669i
$35$	−0.0642412	−	0.334583i	−0.00183546	−	0.00955951i
$36$		0			0
$37$	36.0680	+	36.0680i	0.974810	+	0.974810i	0.999690	−	0.0248806i	$-0.00792055\pi$
$37$	36.0680	+	36.0680i	0.974810	+	0.974810i	−0.0248806	+	0.999690i	$0.507921\pi$
$38$	13.9716	+	3.74368i	0.367674	+	0.0985180i
$39$		0			0
$40$	7.32929	−	21.1284i	0.183232	−	0.528211i
$41$	31.1567	−	53.9649i	0.759919	−	1.31622i	−0.182973	−	0.983118i	$-0.558572\pi$
$41$	31.1567	−	53.9649i	0.759919	−	1.31622i	0.942892	−	0.333100i	$-0.108095\pi$
$42$		0			0
$43$	9.70259	+	2.59980i	0.225642	+	0.0604605i	0.369868	−	0.929084i	$-0.379403\pi$
$43$	9.70259	+	2.59980i	0.225642	+	0.0604605i	−0.144227	+	0.989545i	$0.546069\pi$
$44$			20.3810i			0.463204i
$45$		0			0
$46$	112.951			2.45546
$47$	−11.9633	+	44.6476i	−0.254538	+	0.949948i	0.713809	+	0.700340i	$0.246968\pi$
$47$	−11.9633	+	44.6476i	−0.254538	+	0.949948i	−0.968347	+	0.249608i	$0.919698\pi$
$48$		0			0
$49$	42.4312	+	24.4977i	0.865943	+	0.499953i
$50$	−37.2475	−	49.9033i	−0.744951	−	0.998065i
$51$		0			0
$52$	7.46602	−	27.8636i	0.143577	−	0.535838i
$53$	−28.0258	+	28.0258i	−0.528789	+	0.528789i	−0.920211	−	0.391423i	$-0.871983\pi$
$53$	−28.0258	+	28.0258i	−0.528789	+	0.528789i	0.391423	+	0.920211i	$0.371983\pi$
$54$		0			0
$55$	−38.2664	−	25.9388i	−0.695753	−	0.471614i
$56$	−0.152383	−	0.263935i	−0.00272112	−	0.00471312i
$57$		0			0
$58$	4.74356	+	17.7032i	0.0817855	+	0.305228i
$59$	−16.3509	−	9.44022i	−0.277135	−	0.160004i	0.354991	−	0.934870i	$-0.384484\pi$
$59$	−16.3509	−	9.44022i	−0.277135	−	0.160004i	−0.632126	+	0.774866i	$0.717817\pi$
$60$		0			0
$61$	2.69547	+	4.66870i	0.0441881	+	0.0765360i	0.887274	−	0.461244i	$-0.152597\pi$
$61$	2.69547	+	4.66870i	0.0441881	+	0.0765360i	−0.843085	+	0.537780i	$0.819263\pi$
$62$	29.4265	+	29.4265i	0.474621	+	0.474621i
$63$		0			0
$64$		−	0.568692i		−	0.00888582i
$65$	42.8134	+	49.4796i	0.658667	+	0.761225i
$66$		0			0
$67$	−47.9117	+	12.8379i	−0.715100	+	0.191610i	−0.597984	−	0.801508i	$-0.704031\pi$
$67$	−47.9117	+	12.8379i	−0.715100	+	0.191610i	−0.117116	+	0.993118i	$0.537365\pi$
$68$	10.9754	+	40.9609i	0.161403	+	0.602366i
$69$		0			0
$70$	−0.846414	−	0.0611359i	−0.0120916	−	0.000873370i
$71$	−56.4200			−0.794648			−0.397324	−	0.917678i	$-0.630061\pi$
$71$	−56.4200			−0.794648			−0.397324	+	0.917678i	$0.630061\pi$
$72$		0			0
$73$	−54.7135	+	54.7135i	−0.749500	+	0.749500i	−0.974385	−	0.224885i	$-0.927799\pi$
$73$	−54.7135	+	54.7135i	−0.749500	+	0.749500i	0.224885	+	0.974385i	$0.427799\pi$
$74$	110.031	−	63.5264i	1.48691	−	0.858465i
$75$		0			0
$76$	6.40036	−	11.0857i	0.0842152	−	0.145865i
$77$	−0.608534	+	0.163056i	−0.00790303	+	0.00211761i
$78$		0			0
$79$	−40.9692	+	23.6536i	−0.518597	+	0.299412i	−0.736361	−	0.676589i	$-0.763457\pi$
$79$	−40.9692	+	23.6536i	−0.518597	+	0.299412i	0.217763	+	0.976002i	$0.430124\pi$
$80$	−82.6026	−	55.9919i	−1.03253	−	0.699899i
$81$		0			0
$82$	−109.752	−	109.752i	−1.33844	−	1.33844i
$83$	−60.0267	−	16.0841i	−0.723213	−	0.193784i	−0.121608	−	0.992578i	$-0.538805\pi$
$83$	−60.0267	−	16.0841i	−0.723213	−	0.193784i	−0.601605	+	0.798794i	$0.705472\pi$
$84$		0			0
$85$	−90.8746	−	31.5237i	−1.06911	−	0.370867i
$86$	12.5101	−	21.6682i	0.145467	−	0.251956i
$87$		0			0
$88$	−39.9449	−	10.7032i	−0.453919	−	0.121627i
$89$			59.1599i			0.664718i	0.943153	+	0.332359i	$0.107844\pi$
$89$			59.1599i			0.664718i	−0.943153	+	0.332359i	$0.892156\pi$
$90$		0			0
$91$	0.891679			0.00979867
$92$	25.8713	−	96.5530i	0.281210	−	1.04949i
$93$		0			0
$94$	99.7085	+	57.5668i	1.06073	+	0.612412i
$95$	12.6684	+	26.1258i	0.133351	+	0.275008i
$96$		0			0
$97$	40.2595	−	150.251i	0.415047	−	1.54898i	−0.369695	−	0.929153i	$-0.620538\pi$
$97$	40.2595	−	150.251i	0.415047	−	1.54898i	0.784742	−	0.619823i	$-0.212796\pi$
$98$	86.2954	−	86.2954i	0.880566	−	0.880566i
$99$		0			0
$100$	−51.1898	+	20.4097i	−0.511898	+	0.204097i
$101$	−27.6053	−	47.8137i	−0.273319	−	0.473403i	0.696390	−	0.717663i	$-0.254788\pi$
$101$	−27.6053	−	47.8137i	−0.273319	−	0.473403i	−0.969710	+	0.244260i	$0.921455\pi$
$102$		0			0
$103$	−23.6658	−	88.3218i	−0.229765	−	0.857493i	−0.980439	−	0.196821i	$-0.936938\pi$
$103$	−23.6658	−	88.3218i	−0.229765	−	0.857493i	0.750675	−	0.660672i	$-0.229729\pi$
$104$	50.6892	+	29.2654i	0.487397	+	0.281399i
$105$		0			0
$106$	49.3618	+	85.4971i	0.465677	+	0.806576i
$107$	14.6336	+	14.6336i	0.136762	+	0.136762i	0.772174	−	0.635411i	$-0.219169\pi$
$107$	14.6336	+	14.6336i	0.136762	+	0.136762i	−0.635411	+	0.772174i	$0.719169\pi$
$108$		0			0
$109$		−	112.055i		−	1.02803i	−0.857781	−	0.514015i	$-0.828157\pi$
$109$		−	112.055i		−	1.02803i	0.857781	−	0.514015i	$-0.171843\pi$
$110$	−87.0777	+	75.3459i	−0.791615	+	0.684963i
$111$		0			0
$112$	−1.31359	+	0.351976i	−0.0117285	+	0.00314264i
$113$	−9.59771	−	35.8191i	−0.0849355	−	0.316984i	0.910366	−	0.413803i	$-0.135800\pi$
$113$	−9.59771	−	35.8191i	−0.0849355	−	0.316984i	−0.995302	+	0.0968194i	$0.969133\pi$
$114$		0			0
$115$	148.357	+	171.457i	1.29006	+	1.49093i
$116$	16.2196			0.139824
$117$		0			0
$118$	−33.2541	+	33.2541i	−0.281814	+	0.281814i
$119$	−1.13520	+	0.655407i	−0.00953948	+	0.00550762i
$120$		0			0
$121$	17.7573	−	30.7565i	0.146754	−	0.254186i
$122$	12.9705	−	3.47543i	0.106316	−	0.0284872i
$123$		0			0
$124$	31.8944	−	18.4143i	0.257213	−	0.148502i
$125$	26.8287	−	122.087i	0.214629	−	0.976696i
$126$		0			0
$127$	151.793	+	151.793i	1.19522	+	1.19522i	0.975580	+	0.219643i	$0.0704892\pi$
$127$	151.793	+	151.793i	1.19522	+	1.19522i	0.219643	+	0.975580i	$0.429511\pi$
$128$	−124.320	−	33.3113i	−0.971247	−	0.260245i
$129$		0			0
$130$	146.648	−	71.1095i	1.12806	−	0.546996i
$131$	0.751448	−	1.30155i	0.00573624	−	0.00993547i	−0.863143	−	0.504960i	$-0.831507\pi$
$131$	0.751448	−	1.30155i	0.00573624	−	0.00993547i	0.868879	+	0.495024i	$0.164841\pi$
$132$		0			0
$133$	0.382203	+	0.102411i	0.00287370	+	0.000770006i
$134$			123.551i			0.922021i
$135$		0			0
$136$	−86.0434			−0.632672
$137$	18.0785	−	67.4699i	0.131960	−	0.492481i	−0.868032	−	0.496508i	$-0.834615\pi$
$137$	18.0785	−	67.4699i	0.131960	−	0.492481i	0.999992	+	0.00402717i	$0.00128189\pi$
$138$		0			0
$139$	−106.332	−	61.3909i	−0.764980	−	0.441661i	0.0661012	−	0.997813i	$-0.478944\pi$
$139$	−106.332	−	61.3909i	−0.764980	−	0.441661i	−0.831081	+	0.556152i	$0.812277\pi$
$140$	−0.246130	+	0.709529i	−0.00175807	+	0.00506806i
$141$		0			0
$142$	−36.3728	+	135.745i	−0.256147	+	0.955953i
$143$	85.5549	−	85.5549i	0.598286	−	0.598286i
$144$		0			0
$145$	−20.6426	+	30.4531i	−0.142362	+	0.210021i
$146$	96.3668	+	166.912i	0.660047	+	1.14323i
$147$		0			0
$148$	−29.1013	−	108.607i	−0.196630	−	0.733834i
$149$	23.0090	+	13.2842i	0.154423	+	0.0891560i	0.575220	−	0.817999i	$-0.304916\pi$
$149$	23.0090	+	13.2842i	0.154423	+	0.0891560i	−0.420797	+	0.907155i	$0.638250\pi$
$150$		0			0
$151$	−49.2414	−	85.2887i	−0.326102	−	0.564826i	0.655633	−	0.755080i	$-0.272402\pi$
$151$	−49.2414	−	85.2887i	−0.326102	−	0.564826i	−0.981735	+	0.190254i	$0.939069\pi$
$152$	18.3659	+	18.3659i	0.120828	+	0.120828i
$153$		0			0
$154$			1.56924i			0.0101899i
$155$	−6.01810	+	83.3193i	−0.0388264	+	0.537544i
$156$		0			0
$157$	166.811	−	44.6968i	1.06249	−	0.284693i	0.315086	−	0.949063i	$-0.397967\pi$
$157$	166.811	−	44.6968i	1.06249	−	0.284693i	0.747404	+	0.664370i	$0.231300\pi$
$158$	30.4980	+	113.820i	0.193025	+	0.720379i
$159$		0			0
$160$	−120.321	+	104.111i	−0.752008	+	0.650692i
$161$	3.08985			0.0191916
$162$		0			0
$163$	−65.0824	+	65.0824i	−0.399278	+	0.399278i	−0.877978	−	0.478700i	$-0.841108\pi$
$163$	−65.0824	+	65.0824i	−0.399278	+	0.399278i	0.478700	+	0.877978i	$0.341108\pi$
$164$	−118.957	+	68.6800i	−0.725349	+	0.418780i
$165$		0			0
$166$	−77.3960	+	134.054i	−0.466241	+	0.807553i
$167$	−192.960	+	51.7034i	−1.15545	+	0.309601i	−0.785146	−	0.619311i	$-0.787412\pi$
$167$	−192.960	+	51.7034i	−1.15545	+	0.309601i	−0.370301	+	0.928912i	$0.620745\pi$
$168$		0			0
$169$	−1.94752	+	1.12440i	−0.0115238	+	0.00665325i
$170$	−134.430	+	198.320i	−0.790767	+	1.16659i
$171$		0			0
$172$	−15.6570	−	15.6570i	−0.0910290	−	0.0910290i
$173$	33.4003	+	8.94958i	0.193065	+	0.0517317i	0.354056	−	0.935224i	$-0.384802\pi$
$173$	33.4003	+	8.94958i	0.193065	+	0.0517317i	−0.160991	+	0.986956i	$0.551469\pi$
$174$		0			0
$175$	−1.01893	−	1.36514i	−0.00582246	−	0.00780077i
$176$	−92.2653	+	159.808i	−0.524235	+	0.908001i
$177$		0			0
$178$	142.337	+	38.1392i	0.799648	+	0.214265i
$179$		−	185.962i		−	1.03890i	−0.854502	−	0.519448i	$-0.826138\pi$
$179$		−	185.962i		−	1.03890i	0.854502	−	0.519448i	$-0.173862\pi$
$180$		0			0
$181$	−97.7851			−0.540249			−0.270125	−	0.962825i	$-0.587065\pi$
$181$	−97.7851			−0.540249			−0.270125	+	0.962825i	$0.587065\pi$
$182$	0.574847	−	2.14536i	0.00315850	−	0.0117877i
$183$		0			0
$184$	175.649	+	101.411i	0.954613	+	0.551146i
$185$	240.953	+	83.5848i	1.30245	+	0.451810i
$186$		0			0
$187$	−46.0350	+	171.805i	−0.246177	+	0.918744i
$188$	72.0473	−	72.0473i	0.383231	−	0.383231i
$189$		0			0
$190$	71.0251	−	13.6371i	0.373816	−	0.0717741i
$191$	68.2090	+	118.141i	0.357115	+	0.618542i	0.987478	−	0.157759i	$-0.0504270\pi$
$191$	68.2090	+	118.141i	0.357115	+	0.618542i	−0.630362	+	0.776301i	$0.717094\pi$
$192$		0			0
$193$	23.9050	+	89.2148i	0.123860	+	0.462253i	0.999796	−	0.0201740i	$-0.00642202\pi$
$193$	23.9050	+	89.2148i	0.123860	+	0.462253i	−0.875936	+	0.482427i	$0.839755\pi$
$194$	−335.545	−	193.727i	−1.72961	−	0.998594i
$195$		0			0
$196$	−54.0013	−	93.5329i	−0.275517	−	0.477209i
$197$	170.623	+	170.623i	0.866107	+	0.866107i	0.992039	−	0.125932i	$-0.0401920\pi$
$197$	170.623	+	170.623i	0.866107	+	0.866107i	−0.125932	+	0.992039i	$0.540192\pi$
$198$		0			0
$199$		−	36.4196i		−	0.183013i	−0.995804	−	0.0915066i	$-0.970832\pi$
$199$		−	36.4196i		−	0.183013i	0.995804	−	0.0915066i	$-0.0291683\pi$
$200$	−13.1185	−	111.046i	−0.0655925	−	0.555229i
$201$		0			0
$202$	−132.835	+	35.5931i	−0.657601	+	0.176204i
$203$	0.129763	+	0.484283i	0.000639227	+	0.00238563i
$204$		0			0
$205$	22.4458	−	310.757i	0.109492	−	1.51589i
$206$	−227.757			−1.10562
$207$		0			0
$208$	184.681	−	184.681i	0.887887	−	0.887887i
$209$	46.4977	−	26.8455i	0.222477	−	0.128447i
$210$		0			0
$211$	96.8033	−	167.668i	0.458784	−	0.794636i	−0.540113	−	0.841592i	$-0.681619\pi$
$211$	96.8033	−	167.668i	0.458784	−	0.794636i	0.998897	+	0.0469559i	$0.0149520\pi$
$212$	84.3909	−	22.6125i	0.398070	−	0.106663i
$213$		0			0
$214$	44.6420	−	25.7741i	0.208607	−	0.120440i
$215$	49.3234	−	9.47028i	0.229411	−	0.0440478i
$216$		0			0
$217$	0.804980	+	0.804980i	0.00370959	+	0.00370959i
$218$	−269.603	−	72.2398i	−1.23671	−	0.331375i
$219$		0			0
$220$	44.4622	+	91.6936i	0.202101	+	0.416789i
$221$	125.872	−	218.017i	0.569558	−	0.986503i
$222$		0			0
$223$	92.4808	+	24.7802i	0.414712	+	0.111122i	0.460141	−	0.887846i	$-0.347799\pi$
$223$	92.4808	+	24.7802i	0.414712	+	0.111122i	−0.0454290	+	0.998968i	$0.514465\pi$
$224$			2.16833i			0.00968002i
$225$		0			0
$226$	−92.3675			−0.408706
$227$	85.2664	−	318.219i	0.375623	−	1.40184i	−0.476810	−	0.879007i	$-0.658207\pi$
$227$	85.2664	−	318.219i	0.375623	−	1.40184i	0.852433	−	0.522837i	$-0.175126\pi$
$228$		0			0
$229$	−360.256	−	207.994i	−1.57317	−	0.908269i	−0.995777	−	0.0918017i	$-0.970737\pi$
$229$	−360.256	−	207.994i	−1.57317	−	0.908269i	−0.577391	−	0.816468i	$-0.695929\pi$
$230$	508.165	−	246.409i	2.20941	−	1.07134i
$231$		0			0
$232$	−8.51781	+	31.7889i	−0.0367147	+	0.137021i
$233$	22.0213	−	22.0213i	0.0945121	−	0.0945121i	−0.658270	−	0.752782i	$-0.728711\pi$
$233$	22.0213	−	22.0213i	0.0945121	−	0.0945121i	0.752782	+	0.658270i	$0.228711\pi$
$234$		0			0
$235$	43.5785	+	226.967i	0.185441	+	0.965817i
$236$	20.8095	+	36.0431i	0.0881758	+	0.152725i
$237$		0			0
$238$	0.845055	+	3.15379i	0.00355065	+	0.0132512i
$239$	−267.552	−	154.471i	−1.11946	−	0.646323i	−0.178200	−	0.983994i	$-0.557027\pi$
$239$	−267.552	−	154.471i	−1.11946	−	0.646323i	−0.941264	+	0.337672i	$0.890361\pi$
$240$		0			0
$241$	−12.8569	−	22.2688i	−0.0533481	−	0.0924016i	0.838118	−	0.545489i	$-0.183656\pi$
$241$	−12.8569	−	22.2688i	−0.0533481	−	0.0924016i	−0.891466	+	0.453087i	$0.850323\pi$
$242$	−62.5517	−	62.5517i	−0.258478	−	0.258478i
$243$		0			0
$244$		−	11.8835i		−	0.0487028i
$245$	244.340	+	17.6485i	0.997307	+	0.0720349i
$246$		0			0
$247$	−73.4028	+	19.6682i	−0.297177	+	0.0796284i
$248$	19.3407	+	72.1806i	0.0779868	+	0.291051i
$249$		0			0
$250$	−276.443	−	143.256i	−1.10577	−	0.573025i
$251$	−275.877			−1.09911			−0.549556	−	0.835457i	$-0.685203\pi$
$251$	−275.877			−1.09911			−0.549556	+	0.835457i	$0.685203\pi$
$252$		0			0
$253$	296.465	−	296.465i	1.17180	−	1.17180i
$254$	463.070	−	267.353i	1.82311	−	1.05257i
$255$		0			0
$256$	−159.155	+	275.665i	−0.621701	+	1.07682i
$257$	6.18001	−	1.65593i	0.0240467	−	0.00644330i	−0.246776	−	0.969073i	$-0.579371\pi$
$257$	6.18001	−	1.65593i	0.0240467	−	0.00644330i	0.270822	+	0.962629i	$0.412704\pi$
$258$		0			0
$259$	3.00997	−	1.73781i	0.0116215	−	0.00670968i
$260$	−27.1964	−	141.645i	−0.104602	−	0.544789i
$261$		0			0
$262$	−2.64705	−	2.64705i	−0.0101032	−	0.0101032i
$263$	205.249	+	54.9964i	0.780416	+	0.209112i	0.626968	−	0.779045i	$-0.284296\pi$
$263$	205.249	+	54.9964i	0.780416	+	0.209112i	0.153448	+	0.988157i	$0.450962\pi$
$264$		0			0
$265$	−64.9477	+	187.227i	−0.245086	+	0.706518i
$266$	0.492797	−	0.853549i	0.00185262	−	0.00320883i
$267$		0			0
$268$	105.614	+	28.2991i	0.394081	+	0.105594i
$269$			349.046i			1.29757i	0.760973	+	0.648784i	$0.224722\pi$
$269$			349.046i			1.29757i	−0.760973	+	0.648784i	$0.775278\pi$
$270$		0			0
$271$	−202.277			−0.746409			−0.373205	−	0.927749i	$-0.621741\pi$
$271$	−202.277			−0.746409			−0.373205	+	0.927749i	$0.621741\pi$
$272$	−99.3722	+	370.862i	−0.365339	+	1.36346i
$273$		0			0
$274$	−150.676	−	86.9930i	−0.549913	−	0.317493i
$275$	−228.747	−	33.2177i	−0.831806	−	0.120792i
$276$		0			0
$277$	62.8000	−	234.373i	0.226715	−	0.846112i	−0.754995	−	0.655730i	$-0.772361\pi$
$277$	62.8000	−	234.373i	0.226715	−	0.846112i	0.981710	−	0.190381i	$-0.0609725\pi$
$278$	−216.255	+	216.255i	−0.777897	+	0.777897i
$279$		0			0
$280$	−1.26136	−	0.855006i	−0.00450484	−	0.00305359i
$281$	−140.160	−	242.764i	−0.498789	−	0.863929i	0.501210	−	0.865326i	$-0.332889\pi$
$281$	−140.160	−	242.764i	−0.498789	−	0.863929i	−0.999999	+	0.00139729i	$0.999555\pi$
$282$		0			0
$283$	99.8610	+	372.686i	0.352866	+	1.31691i	0.883149	+	0.469092i	$0.155419\pi$
$283$	99.8610	+	372.686i	0.352866	+	1.31691i	−0.530283	+	0.847820i	$0.677914\pi$
$284$	107.707	+	62.1845i	0.379249	+	0.218959i
$285$		0			0
$286$	−150.688	−	260.999i	−0.526880	−	0.912583i
$287$	−3.00235	−	3.00235i	−0.0104611	−	0.0104611i
$288$		0			0
$289$			81.0774i			0.280545i
$290$	59.9617	+	69.2980i	0.206764	+	0.238959i
$291$		0			0
$292$	164.753	−	44.1453i	0.564222	−	0.151183i
$293$	10.9337	+	40.8052i	0.0373164	+	0.139267i	0.982071	−	0.188512i	$-0.0603665\pi$
$293$	10.9337	+	40.8052i	0.0373164	+	0.139267i	−0.944754	+	0.327779i	$0.893700\pi$
$294$		0			0
$295$	−94.1569	−	6.80090i	−0.319176	−	0.0230539i
$296$	228.143			0.770755
$297$		0			0
$298$	46.7950	−	46.7950i	0.157030	−	0.157030i
$299$	−513.910	+	296.706i	−1.71876	+	0.992329i
$300$		0			0
$301$	0.342223	−	0.592747i	0.00113695	−	0.00196926i
$302$	−236.948	+	63.4899i	−0.784595	+	0.210232i
$303$		0			0
$304$	100.371	−	57.9492i	0.330168	−	0.190622i
$305$	22.3119	+	15.1240i	0.0731537	+	0.0495870i
$306$		0			0
$307$	−85.1111	−	85.1111i	−0.277235	−	0.277235i	0.554769	−	0.832004i	$-0.312806\pi$
$307$	−85.1111	−	85.1111i	−0.277235	−	0.277235i	−0.832004	+	0.554769i	$0.812806\pi$
$308$	1.34142	+	0.359431i	0.00435525	+	0.00116699i
$309$		0			0
$310$	196.585	+	68.1937i	0.634144	+	0.219980i
$311$	−227.093	+	393.336i	−0.730202	+	1.26475i	0.226595	+	0.973989i	$0.427241\pi$
$311$	−227.093	+	393.336i	−0.730202	+	1.26475i	−0.956797	+	0.290758i	$0.906093\pi$
$312$		0			0
$313$	−287.001	−	76.9018i	−0.916937	−	0.245693i	−0.230661	−	0.973034i	$-0.574089\pi$
$313$	−287.001	−	76.9018i	−0.916937	−	0.245693i	−0.686276	+	0.727342i	$0.740756\pi$
$314$		−	430.158i		−	1.36993i
$315$		0			0
$316$	104.281			0.330004
$317$	22.8819	−	85.3965i	0.0721827	−	0.269389i	−0.920397	−	0.390985i	$-0.872134\pi$
$317$	22.8819	−	85.3965i	0.0721827	−	0.269389i	0.992580	+	0.121596i	$0.0388011\pi$
$318$		0			0
$319$	58.9165	+	34.0155i	0.184691	+	0.106632i
$320$	−1.24063	−	2.55854i	−0.00387698	−	0.00799542i
$321$		0			0
$322$	1.99197	−	7.43412i	0.00618623	−	0.0230873i
$323$	78.9926	−	78.9926i	0.244559	−	0.244559i
$324$		0			0
$325$	300.559	+	129.208i	0.924797	+	0.397564i
$326$	114.629	+	198.544i	0.351624	+	0.609031i
$327$		0			0
$328$	−72.1354	−	269.213i	−0.219925	−	0.820771i
$329$	2.72759	+	1.57478i	0.00829055	+	0.00478655i
$330$		0			0
$331$	223.152	+	386.510i	0.674175	+	1.16770i	0.976709	+	0.214566i	$0.0688338\pi$
$331$	223.152	+	386.510i	0.674175	+	1.16770i	−0.302535	+	0.953138i	$0.597833\pi$
$332$	96.8645	+	96.8645i	0.291761	+	0.291761i
$333$		0			0
$334$			497.589i			1.48979i
$335$	−187.547	+	162.279i	−0.559842	+	0.484416i
$336$		0			0
$337$	−28.2958	+	7.58184i	−0.0839638	+	0.0224980i	−0.300556	−	0.953764i	$-0.597172\pi$
$337$	−28.2958	+	7.58184i	−0.0839638	+	0.0224980i	0.216593	+	0.976262i	$0.430506\pi$
$338$	1.44975	+	5.41056i	0.00428921	+	0.0160076i
$339$		0			0
$340$	138.737	+	160.339i	0.408049	+	0.471584i
$341$	154.473			0.452999
$342$		0			0
$343$	4.72156	−	4.72156i	0.0137655	−	0.0137655i
$344$	38.9086	−	22.4639i	0.113107	−	0.0653021i
$345$		0			0
$346$	43.0650	−	74.5907i	0.124465	−	0.215580i
$347$	326.160	−	87.3943i	0.939942	−	0.251857i	0.243853	−	0.969812i	$-0.421589\pi$
$347$	326.160	−	87.3943i	0.939942	−	0.251857i	0.696089	+	0.717956i	$0.254922\pi$
$348$		0			0
$349$	−51.4915	+	29.7286i	−0.147540	+	0.0851823i	−0.571953	−	0.820287i	$-0.693814\pi$
$349$	−51.4915	+	29.7286i	−0.147540	+	0.0851823i	0.424413	+	0.905469i	$0.360481\pi$
$350$	−3.94137	+	1.57145i	−0.0112611	+	0.00448985i
$351$		0			0
$352$	208.047	+	208.047i	0.591042	+	0.591042i
$353$	−514.426	−	137.840i	−1.45730	−	0.390482i	−0.558742	−	0.829342i	$-0.688716\pi$
$353$	−514.426	−	137.840i	−1.45730	−	0.390482i	−0.898555	+	0.438860i	$0.855382\pi$
$354$		0			0
$355$	−253.832	+	123.083i	−0.715021	+	0.346713i
$356$	65.2043	−	112.937i	0.183158	−	0.317239i
$357$		0			0
$358$	−447.421	−	119.886i	−1.24978	−	0.334878i
$359$			342.196i			0.953192i	0.879122	+	0.476596i	$0.158130\pi$
$359$			342.196i			0.953192i	−0.879122	+	0.476596i	$0.841870\pi$
$360$		0			0
$361$	327.278			0.906588
$362$	−63.0401	+	235.269i	−0.174144	+	0.649914i
$363$		0			0
$364$	−1.70223	−	0.982783i	−0.00467646	−	0.00269995i
$365$	−126.795	+	365.516i	−0.347382	+	1.00141i
$366$		0			0
$367$	−95.2584	+	355.509i	−0.259560	+	0.968690i	0.705937	+	0.708275i	$0.250526\pi$
$367$	−95.2584	+	355.509i	−0.259560	+	0.968690i	−0.965497	+	0.260416i	$0.916140\pi$
$368$	639.956	−	639.956i	1.73901	−	1.73901i
$369$		0			0
$370$	356.441	−	525.843i	0.963354	−	1.42120i
$371$	1.35032	+	2.33883i	0.00363968	+	0.00630412i
$372$		0			0
$373$	86.1459	+	321.501i	0.230954	+	0.861933i	0.979931	+	0.199337i	$0.0638787\pi$
$373$	86.1459	+	321.501i	0.230954	+	0.861933i	−0.748977	+	0.662596i	$0.769455\pi$
$374$	383.681	+	221.519i	1.02589	+	0.592296i
$375$		0			0
$376$	103.370	+	179.042i	0.274921	+	0.476177i
$377$	−68.0862	−	68.0862i	−0.180600	−	0.180600i
$378$		0			0
$379$		−	203.700i		−	0.537466i	−0.963215	−	0.268733i	$-0.913395\pi$
$379$		−	203.700i		−	0.537466i	0.963215	−	0.268733i	$-0.0866049\pi$
$380$	4.61092	−	63.8373i	0.0121340	−	0.167993i
$381$		0			0
$382$	328.219	−	87.9460i	0.859212	−	0.230225i
$383$	5.35538	+	19.9865i	0.0139827	+	0.0521842i	0.972565	−	0.232633i	$-0.0747339\pi$
$383$	5.35538	+	19.9865i	0.0139827	+	0.0521842i	−0.958582	+	0.284817i	$0.908067\pi$
$384$		0			0
$385$	−2.38206	+	2.06114i	−0.00618718	+	0.00535360i
$386$	230.060			0.596010
$387$		0			0
$388$	−242.458	+	242.458i	−0.624892	+	0.624892i
$389$	160.439	−	92.6297i	0.412440	−	0.238123i	−0.279397	−	0.960176i	$-0.590135\pi$
$389$	160.439	−	92.6297i	0.412440	−	0.238123i	0.691838	+	0.722053i	$0.256801\pi$
$390$		0			0
$391$	436.174	−	755.475i	1.11553	−	1.93216i
$392$	211.675	−	56.7182i	0.539988	−	0.144689i
$393$		0			0
$394$	520.513	−	300.518i	1.32110	−	0.762737i
$395$	−132.718	+	195.793i	−0.335995	+	0.495680i
$396$		0			0
$397$	−236.474	−	236.474i	−0.595652	−	0.595652i	0.343501	−	0.939152i	$-0.388387\pi$
$397$	−236.474	−	236.474i	−0.595652	−	0.595652i	−0.939152	+	0.343501i	$0.888387\pi$
$398$	−87.6248	−	23.4790i	−0.220163	−	0.0589925i
$399$		0			0
$400$	−493.777	−	71.7045i	−1.23444	−	0.179261i
$401$	34.0375	−	58.9547i	0.0848816	−	0.147019i	−0.820459	−	0.571705i	$-0.806282\pi$
$401$	34.0375	−	58.9547i	0.0848816	−	0.147019i	0.905341	+	0.424686i	$0.139615\pi$
$402$		0			0
$403$	−211.185	−	56.5868i	−0.524032	−	0.140414i
$404$			121.703i			0.301245i
$405$		0			0
$406$	1.24883			0.00307593
$407$	122.062	−	455.540i	0.299906	−	1.11926i
$408$		0			0
$409$	326.511	+	188.511i	0.798315	+	0.460907i	0.842882	−	0.538099i	$-0.180857\pi$
$409$	326.511	+	188.511i	0.798315	+	0.460907i	−0.0445668	+	0.999006i	$0.514191\pi$
$410$	−733.204	−	254.343i	−1.78830	−	0.620348i
$411$		0			0
$412$	−52.1674	+	194.691i	−0.126620	+	0.472552i
$413$	−0.909687	+	0.909687i	−0.00220263	+	0.00220263i
$414$		0			0
$415$	−305.147	+	58.5894i	−0.735295	+	0.141179i
$416$	−208.216	−	360.640i	−0.500518	−	0.866923i
$417$		0			0
$418$	−34.6135	−	129.179i	−0.0828074	−	0.309041i
$419$	198.025	+	114.330i	0.472613	+	0.272863i	0.717333	−	0.696731i	$-0.245363\pi$
$419$	198.025	+	114.330i	0.472613	+	0.272863i	−0.244720	+	0.969594i	$0.578696\pi$
$420$		0			0
$421$	204.894	+	354.887i	0.486684	+	0.842961i	0.999883	−	0.0153086i	$-0.00487306\pi$
$421$	204.894	+	354.887i	0.486684	+	0.842961i	−0.513199	+	0.858270i	$0.671540\pi$
$422$	−340.999	−	340.999i	−0.808055	−	0.808055i
$423$		0			0
$424$			177.274i			0.418098i
$425$	−477.614	+	56.4234i	−1.12380	+	0.132761i
$426$		0			0
$427$	0.354816	−	0.0950727i	0.000830951	−	0.000222653i
$428$	−11.8070	−	44.0644i	−0.0275865	−	0.102954i
$429$		0			0
$430$	9.01251	−	124.776i	0.0209593	−	0.290177i
$431$	−46.4787			−0.107839			−0.0539196	−	0.998545i	$-0.517171\pi$
$431$	−46.4787			−0.107839			−0.0539196	+	0.998545i	$0.517171\pi$
$432$		0			0
$433$	−430.638	+	430.638i	−0.994544	+	0.994544i	−0.999985	−	0.00544093i	$-0.998268\pi$
$433$	−430.638	+	430.638i	−0.994544	+	0.994544i	0.00544093	+	0.999985i	$0.498268\pi$
$434$	2.45572	−	1.41781i	0.00565834	−	0.00326684i
$435$		0			0
$436$	−123.504	+	213.916i	−0.283266	+	0.490632i
$437$	−254.356	+	68.1545i	−0.582050	+	0.155960i
$438$		0			0
$439$	335.332	−	193.604i	0.763855	−	0.441012i	−0.0668232	−	0.997765i	$-0.521286\pi$
$439$	335.332	−	193.604i	0.763855	−	0.441012i	0.830678	+	0.556753i	$0.187953\pi$
$440$	−203.061	+	38.9885i	−0.461502	+	0.0886101i
$441$		0			0
$442$	−443.397	−	443.397i	−1.00316	−	1.00316i
$443$	708.648	+	189.882i	1.59966	+	0.428627i	0.944939	−	0.327247i	$-0.106121\pi$
$443$	708.648	+	189.882i	1.59966	+	0.428627i	0.654717	+	0.755874i	$0.272788\pi$
$444$		0			0
$445$	129.060	+	266.159i	0.290024	+	0.598110i
$446$	119.241	−	206.531i	0.267357	−	0.463075i
$447$		0			0
$448$	−0.0374297	−	0.0100292i	−8.35483e−5	−	2.23867e-5i
$449$		−	141.098i		−	0.314250i	−0.987579	−	0.157125i	$-0.949777\pi$
$449$		−	141.098i		−	0.314250i	0.987579	−	0.157125i	$-0.0502226\pi$
$450$		0			0
$451$	−576.139			−1.27747
$452$	−21.1566	+	78.9577i	−0.0468067	+	0.174685i
$453$		0			0
$454$	−710.657	−	410.298i	−1.56532	−	0.903740i
$455$	4.01165	−	1.94525i	0.00881680	−	0.00427527i
$456$		0			0
$457$	190.044	−	709.254i	0.415851	−	1.55198i	−0.367273	−	0.930113i	$-0.619709\pi$
$457$	190.044	−	709.254i	0.415851	−	1.55198i	0.783124	−	0.621865i	$-0.213625\pi$
$458$	−732.678	+	732.678i	−1.59973	+	1.59973i
$459$		0			0
$460$	−94.2412	−	490.830i	−0.204872	−	1.06702i
$461$	321.041	+	556.060i	0.696402	+	1.20620i	0.969706	+	0.244275i	$0.0785501\pi$
$461$	321.041	+	556.060i	0.696402	+	1.20620i	−0.273304	+	0.961928i	$0.588117\pi$
$462$		0			0
$463$	−71.8346	−	268.091i	−0.155150	−	0.579029i	−0.999092	−	0.0425948i	$-0.986438\pi$
$463$	−71.8346	−	268.091i	−0.155150	−	0.579029i	0.843942	−	0.536434i	$-0.180229\pi$
$464$	127.178	+	73.4265i	0.274091	+	0.158247i
$465$		0			0
$466$	−38.7861	−	67.1795i	−0.0832320	−	0.144162i
$467$	57.4439	+	57.4439i	0.123006	+	0.123006i	0.765930	−	0.642924i	$-0.222279\pi$
$467$	57.4439	+	57.4439i	0.123006	+	0.123006i	−0.642924	+	0.765930i	$0.722279\pi$
$468$		0			0
$469$			3.37981i			0.00720642i
$470$	574.172	+	41.4721i	1.22164	+	0.0882384i
$471$		0			0
$472$	−81.5694	+	21.8565i	−0.172817	+	0.0463061i
$473$	−24.0373	−	89.7086i	−0.0508189	−	0.189659i
$474$		0			0
$475$	113.990	+	89.9026i	0.239978	+	0.189269i
$476$	2.88948			0.00607034
$477$		0			0
$478$	−544.139	+	544.139i	−1.13837	+	1.13837i
$479$	419.328	−	242.099i	0.875423	−	0.505426i	0.00627671	−	0.999980i	$-0.498002\pi$
$479$	419.328	−	242.099i	0.875423	−	0.505426i	0.869147	+	0.494554i	$0.164669\pi$
$480$		0			0
$481$	−333.749	+	578.071i	−0.693866	+	1.20181i
$482$	−61.8668	+	16.5771i	−0.128354	+	0.0343924i
$483$		0			0
$484$	−67.7979	+	39.1431i	−0.140078	+	0.0808742i
$485$	−146.653	−	763.803i	−0.302378	−	1.57485i
$486$		0			0
$487$	−162.179	−	162.179i	−0.333017	−	0.333017i	0.520714	−	0.853731i	$-0.325666\pi$
$487$	−162.179	−	162.179i	−0.333017	−	0.333017i	−0.853731	+	0.520714i	$0.825666\pi$
$488$	23.2906	+	6.24069i	0.0477266	+	0.0127883i
$489$		0			0
$490$	199.983	−	576.500i	0.408129	−	1.17653i
$491$	395.023	−	684.199i	0.804527	−	1.39348i	−0.112083	−	0.993699i	$-0.535752\pi$
$491$	395.023	−	684.199i	0.804527	−	1.39348i	0.916610	−	0.399783i	$-0.130914\pi$
$492$		0			0
$493$	136.726	+	36.6356i	0.277334	+	0.0743115i
$494$			189.285i			0.383168i
$495$		0			0
$496$	333.448			0.672274
$497$	−0.995002	+	3.71340i	−0.00200202	+	0.00747163i
$498$		0			0
$499$	422.362	+	243.851i	0.846418	+	0.488680i	0.859441	−	0.511236i	$-0.170812\pi$
$499$	422.362	+	243.851i	0.846418	+	0.488680i	−0.0130228	+	0.999915i	$0.504145\pi$
$500$	−185.777	+	203.496i	−0.371554	+	0.406992i
$501$		0			0
$502$	−177.852	+	663.754i	−0.354288	+	1.32222i
$503$	−346.274	+	346.274i	−0.688418	+	0.688418i	−0.961882	−	0.273465i	$-0.911830\pi$
$503$	−346.274	+	346.274i	−0.688418	+	0.688418i	0.273465	+	0.961882i	$0.411830\pi$
$504$		0			0
$505$	−228.504	−	154.891i	−0.452483	−	0.306714i
$506$	−522.164	−	904.415i	−1.03194	−	1.78738i
$507$		0			0
$508$	−122.474	−	457.078i	−0.241090	−	0.899760i
$509$	362.182	+	209.106i	0.711557	+	0.410818i	0.811637	−	0.584162i	$-0.198577\pi$
$509$	362.182	+	209.106i	0.711557	+	0.410818i	−0.100080	+	0.994979i	$0.531910\pi$
$510$		0			0
$511$	2.63618	+	4.56599i	0.00515886	+	0.00893540i
$512$	196.607	+	196.607i	0.383998	+	0.383998i
$513$		0			0
$514$		−	15.9365i		−	0.0310049i
$515$	−299.151	−	345.730i	−0.580875	−	0.671320i
$516$		0			0
$517$	412.804	−	110.610i	0.798460	−	0.213947i
$518$	−2.24066	−	8.36225i	−0.00432559	−	0.0161433i
$519$		0			0
$520$	291.894	+	21.0833i	0.561335	+	0.0405449i
$521$	17.3149			0.0332341			0.0166170	−	0.999862i	$-0.494710\pi$
$521$	17.3149			0.0332341			0.0166170	+	0.999862i	$0.494710\pi$
$522$		0			0
$523$	577.571	−	577.571i	1.10434	−	1.10434i	0.110462	−	0.993880i	$-0.464767\pi$
$523$	577.571	−	577.571i	1.10434	−	1.10434i	0.993880	−	0.110462i	$-0.0352329\pi$
$524$	−2.86905	+	1.65645i	−0.00547529	+	0.00316116i
$525$		0			0
$526$	264.640	−	458.370i	0.503118	−	0.871427i
$527$	310.453	−	83.1855i	0.589094	−	0.157847i
$528$		0			0
$529$	−1322.68	+	763.649i	−2.50034	+	1.44357i
$530$	408.594	+	276.964i	0.770932	+	0.522574i
$531$		0			0
$532$	−0.616757	−	0.616757i	−0.00115932	−	0.00115932i
$533$	787.659	+	211.053i	1.47778	+	0.395971i
$534$		0			0
$535$	97.7600	+	33.9122i	0.182729	+	0.0633873i
$536$	−110.927	+	192.132i	−0.206954	+	0.358455i
$537$		0			0
$538$	839.797	+	225.023i	1.56096	+	0.418258i
$539$		−	453.003i		−	0.840451i
$540$		0			0
$541$	846.162			1.56407			0.782035	−	0.623234i	$-0.214182\pi$
$541$	846.162			1.56407			0.782035	+	0.623234i	$0.214182\pi$
$542$	−130.404	+	486.674i	−0.240598	+	0.897922i
$543$		0			0
$544$	530.160	+	306.088i	0.974558	+	0.562661i
$545$	−244.455	−	504.135i	−0.448541	−	0.925018i
$546$		0			0
$547$	−17.6950	+	66.0385i	−0.0323491	+	0.120728i	−0.980212	−	0.197949i	$-0.936572\pi$
$547$	−17.6950	+	66.0385i	−0.0323491	+	0.120728i	0.947863	+	0.318677i	$0.103239\pi$
$548$	−108.876	+	108.876i	−0.198678	+	0.198678i
$549$		0			0
$550$	−227.389	+	528.944i	−0.413435	+	0.961717i
$551$	−21.3641	−	37.0038i	−0.0387734	−	0.0671575i
$552$		0			0
$553$	0.834291	+	3.11362i	0.00150866	+	0.00563041i
$554$	−523.410	−	302.191i	−0.944784	−	0.545471i
$555$		0			0
$556$	135.327	+	234.392i	0.243393	+	0.421569i
$557$	−367.003	−	367.003i	−0.658893	−	0.658893i	0.296225	−	0.955118i	$-0.404272\pi$
$557$	−367.003	−	367.003i	−0.658893	−	0.658893i	−0.955118	+	0.296225i	$0.904272\pi$
$558$		0			0
$559$			131.449i			0.235151i
$560$	−5.14197	+	4.44921i	−0.00918210	+	0.00794502i
$561$		0			0
$562$	−674.443	+	180.716i	−1.20008	+	0.321560i
$563$	−81.4441	−	303.953i	−0.144661	−	0.539882i	−0.999770	−	0.0214341i	$-0.993177\pi$
$563$	−81.4441	−	303.953i	−0.144661	−	0.539882i	0.855109	−	0.518448i	$-0.173490\pi$
$564$		0			0
$565$	−121.321	−	140.212i	−0.214728	−	0.248162i
$566$	961.053			1.69797
$567$		0			0
$568$	−178.439	+	178.439i	−0.314153	+	0.314153i
$569$	−882.789	+	509.679i	−1.55148	+	0.895745i	−0.553453	+	0.832880i	$0.686690\pi$
$569$	−882.789	+	509.679i	−1.55148	+	0.895745i	−0.998022	+	0.0628645i	$0.979976\pi$
$570$		0			0
$571$	443.096	−	767.465i	0.776000	−	1.34407i	−0.158231	−	0.987402i	$-0.550579\pi$
$571$	443.096	−	767.465i	0.776000	−	1.34407i	0.934231	−	0.356669i	$-0.116088\pi$
$572$	−257.622	+	69.0296i	−0.450388	+	0.120681i
$573$		0			0
$574$	−9.15913	+	5.28803i	−0.0159567	+	0.00921259i
$575$	1041.50	+	447.733i	1.81130	+	0.778667i
$576$		0			0
$577$	194.509	+	194.509i	0.337105	+	0.337105i	0.855277	−	0.518172i	$-0.173387\pi$
$577$	194.509	+	194.509i	0.337105	+	0.337105i	−0.518172	+	0.855277i	$0.673387\pi$
$578$	195.070	+	52.2689i	0.337492	+	0.0904307i
$579$		0			0
$580$	72.9715	−	35.3839i	0.125813	−	0.0610067i
$581$	−2.11722	+	3.66713i	−0.00364409	+	0.00631175i
$582$		0			0
$583$	353.967	+	94.8452i	0.607147	+	0.162685i
$584$			346.084i			0.592609i
$585$		0			0
$586$	105.225			0.179565
$587$	−207.853	+	775.720i	−0.354095	+	1.32150i	0.527526	+	0.849539i	$0.323120\pi$
$587$	−207.853	+	775.720i	−0.354095	+	1.32150i	−0.881620	+	0.471960i	$0.843547\pi$
$588$		0			0
$589$	−84.0216	−	48.5099i	−0.142651	−	0.0823598i
$590$	−77.0639	+	222.155i	−0.130617	+	0.376534i
$591$		0			0
$592$	263.485	−	983.338i	0.445075	−	1.66104i
$593$	−572.308	+	572.308i	−0.965106	+	0.965106i	−0.999411	−	0.0343049i	$-0.989078\pi$
$593$	−572.308	+	572.308i	−0.965106	+	0.965106i	0.0343049	+	0.999411i	$0.489078\pi$
$594$		0			0
$595$	−3.67743	+	5.42516i	−0.00618055	+	0.00911791i
$596$	−29.2830	−	50.7197i	−0.0491326	−	0.0851001i
$597$		0			0
$598$	382.561	+	1427.74i	0.639734	+	2.38752i
$599$	263.198	+	151.957i	0.439396	+	0.253685i	0.703341	−	0.710852i	$-0.251691\pi$
$599$	263.198	+	151.957i	0.439396	+	0.253685i	−0.263945	+	0.964538i	$0.585024\pi$
$600$		0			0
$601$	−52.0948	−	90.2308i	−0.0866801	−	0.150134i	0.819426	−	0.573185i	$-0.194292\pi$
$601$	−52.0948	−	90.2308i	−0.0866801	−	0.150134i	−0.906106	+	0.423051i	$0.860959\pi$
$602$	−1.20551	−	1.20551i	−0.00200251	−	0.00200251i
$603$		0			0
$604$			217.090i			0.359420i
$605$	12.7926	−	177.111i	0.0211449	−	0.292746i
$606$		0			0
$607$	−283.439	+	75.9472i	−0.466950	+	0.125119i	−0.484620	−	0.874725i	$-0.661042\pi$
$607$	−283.439	+	75.9472i	−0.466950	+	0.125119i	0.0176696	+	0.999844i	$0.494375\pi$
$608$	−47.8279	−	178.496i	−0.0786642	−	0.293579i
$609$		0			0
$610$	50.7721	−	43.9317i	0.0832330	−	0.0720193i
$611$	−604.878			−0.989980
$612$		0			0
$613$	610.767	−	610.767i	0.996357	−	0.996357i	−0.00363596	−	0.999993i	$-0.501157\pi$
$613$	610.767	−	610.767i	0.996357	−	0.996357i	0.999993	+	0.00363596i	$0.00115736\pi$
$614$	−259.645	+	149.906i	−0.422874	+	0.244147i
$615$		0			0
$616$	−1.40891	+	2.44030i	−0.00228719	+	0.00396152i
$617$	−972.818	+	260.666i	−1.57669	+	0.422473i	−0.937899	−	0.346908i	$-0.887232\pi$
$617$	−972.818	+	260.666i	−1.57669	+	0.422473i	−0.638791	+	0.769381i	$0.720565\pi$
$618$		0			0
$619$	−189.444	+	109.376i	−0.306049	+	0.176697i	−0.645157	−	0.764050i	$-0.723208\pi$
$619$	−189.444	+	109.376i	−0.306049	+	0.176697i	0.339108	+	0.940747i	$0.389875\pi$
$620$	103.321	−	152.425i	0.166646	−	0.245847i
$621$		0			0
$622$	799.956	+	799.956i	1.28610	+	1.28610i
$623$	3.89373	+	1.04332i	0.00624997	+	0.00167467i
$624$		0			0
$625$	−145.638	−	607.795i	−0.233020	−	0.972472i
$626$	−370.048	+	640.942i	−0.591131	+	1.02387i
$627$		0			0
$628$	−367.708	−	98.5271i	−0.585523	−	0.156890i
$629$		−	981.257i		−	1.56003i
$630$		0			0
$631$	−427.714			−0.677835			−0.338917	−	0.940816i	$-0.610061\pi$
$631$	−427.714			−0.677835			−0.338917	+	0.940816i	$0.610061\pi$
$632$	−54.7639	+	204.382i	−0.0866517	+	0.323389i
$633$		0			0
$634$	−190.711	−	110.107i	−0.300805	−	0.173670i
$635$	1014.06	+	351.770i	1.59695	+	0.553968i
$636$		0			0
$637$	−165.945	+	619.316i	−0.260511	+	0.972239i
$638$	119.823	−	119.823i	0.187810	−	0.187810i
$639$		0			0
$640$	−631.982	+	121.343i	−0.987472	+	0.189598i
$641$	256.912	+	444.984i	0.400798	+	0.694203i	0.993822	−	0.110982i	$-0.0353995\pi$
$641$	256.912	+	444.984i	0.400798	+	0.694203i	−0.593024	+	0.805185i	$0.702066\pi$
$642$		0			0
$643$	−50.3713	−	187.988i	−0.0783379	−	0.292361i	0.915632	−	0.402019i	$-0.131691\pi$
$643$	−50.3713	−	187.988i	−0.0783379	−	0.292361i	−0.993969	+	0.109657i	$0.965025\pi$
$644$	−5.89858	−	3.40555i	−0.00915929	−	0.00528812i
$645$		0			0
$646$	−139.129	−	240.979i	−0.215371	−	0.373033i
$647$	139.726	+	139.726i	0.215960	+	0.215960i	0.806794	−	0.590833i	$-0.201201\pi$
$647$	139.726	+	139.726i	0.215960	+	0.215960i	−0.590833	+	0.806794i	$0.701201\pi$
$648$		0			0
$649$			174.565i			0.268976i
$650$	504.636	−	639.841i	0.776364	−	0.984370i
$651$		0			0
$652$	195.975	−	52.5114i	0.300576	−	0.0805390i
$653$	166.789	+	622.466i	0.255420	+	0.953240i	0.967856	+	0.251503i	$0.0809250\pi$
$653$	166.789	+	622.466i	0.255420	+	0.953240i	−0.712437	+	0.701737i	$0.752408\pi$
$654$		0			0
$655$	0.541356	−	7.49495i	0.000826498	−	0.0114427i
$656$	−1243.66			−1.89583
$657$		0			0
$658$	5.54730	−	5.54730i	0.00843054	−	0.00843054i
$659$	−210.200	+	121.359i	−0.318968	+	0.184156i	−0.650932	−	0.759136i	$-0.725622\pi$
$659$	−210.200	+	121.359i	−0.318968	+	0.184156i	0.331965	+	0.943292i	$0.392289\pi$
$660$		0			0
$661$	−331.364	+	573.939i	−0.501307	+	0.868288i	0.498692	+	0.866779i	$0.333814\pi$
$661$	−331.364	+	573.939i	−0.501307	+	0.868288i	−0.999999	+	0.00150927i	$0.999520\pi$
$662$	1073.80	−	287.723i	1.62205	−	0.434627i
$663$		0			0
$664$	−240.715	+	138.977i	−0.362522	+	0.209302i
$665$	1.94294	−	0.373051i	0.00292171	−	0.000560979i
$666$		0			0
$667$	−235.933	−	235.933i	−0.353722	−	0.353722i
$668$	425.349	+	113.972i	0.636750	+	0.170617i
$669$		0			0
$670$	269.533	+	555.853i	0.402288	+	0.829631i
$671$	24.9219	−	43.1660i	0.0371414	−	0.0643308i
$672$		0			0
$673$	−467.643	−	125.305i	−0.694864	−	0.186188i	−0.105935	−	0.994373i	$-0.533784\pi$
$673$	−467.643	−	125.305i	−0.694864	−	0.186188i	−0.588929	+	0.808185i	$0.700450\pi$
$674$			72.9670i			0.108260i
$675$		0			0
$676$	4.95712			0.00733302
$677$	113.880	−	425.004i	0.168212	−	0.627776i	−0.829397	−	0.558660i	$-0.811316\pi$
$677$	113.880	−	425.004i	0.168212	−	0.627776i	0.997609	−	0.0691156i	$-0.0220177\pi$
$678$		0			0
$679$	−9.17906	−	5.29953i	−0.0135185	−	0.00780490i
$680$	−387.108	+	187.708i	−0.569276	+	0.276042i
$681$		0			0
$682$	99.5854	−	371.658i	0.146020	−	0.544953i
$683$	336.034	−	336.034i	0.491998	−	0.491998i	−0.416938	−	0.908935i	$-0.636897\pi$
$683$	336.034	−	336.034i	0.491998	−	0.491998i	0.908935	+	0.416938i	$0.136897\pi$
$684$		0			0
$685$	−65.8544	−	342.985i	−0.0961379	−	0.500708i
$686$	−8.31607	−	14.4039i	−0.0121226	−	0.0209969i
$687$		0			0
$688$	−51.8875	−	193.647i	−0.0754179	−	0.281463i
$689$	−449.177	−	259.332i	−0.651926	−	0.376389i
$690$		0			0
$691$	−465.054	−	805.496i	−0.673015	−	1.16570i	−0.977045	−	0.213034i	$-0.931665\pi$
$691$	−465.054	−	805.496i	−0.673015	−	1.16570i	0.304029	−	0.952663i	$-0.401668\pi$
$692$	−53.8977	−	53.8977i	−0.0778869	−	0.0778869i
$693$		0			0
$694$		−	841.075i		−	1.21192i
$695$	−612.314	−	44.2270i	−0.881027	−	0.0636360i
$696$		0			0
$697$	−1157.90	+	310.258i	−1.66126	+	0.445134i
$698$	38.3309	+	143.053i	0.0549153	+	0.204947i
$699$		0			0
$700$	0.440541	+	3.72910i	0.000629345	+	0.00532729i
$701$	1057.58			1.50868			0.754338	−	0.656486i	$-0.227958\pi$
$701$	1057.58			1.50868			0.754338	+	0.656486i	$0.227958\pi$
$702$		0			0
$703$	−209.448	+	209.448i	−0.297935	+	0.297935i
$704$	−4.55359	+	2.62902i	−0.00646817	+	0.00373440i
$705$		0			0
$706$	−663.280	+	1148.83i	−0.939490	+	1.62724i
$707$	−3.63379	+	0.973672i	−0.00513974	+	0.00137719i
$708$		0			0
$709$	450.749	−	260.240i	0.635754	−	0.367053i	−0.147223	−	0.989103i	$-0.547034\pi$
$709$	450.749	−	260.240i	0.635754	−	0.367053i	0.782977	+	0.622051i	$0.213700\pi$
$710$	132.495	+	690.065i	0.186613	+	0.971922i
$711$		0			0
$712$	187.104	+	187.104i	0.262787	+	0.262787i
$713$	−731.800	−	196.085i	−1.02637	−	0.275014i
$714$		0			0
$715$	198.267	−	571.552i	0.277297	−	0.799374i
$716$	−204.962	+	355.005i	−0.286260	+	0.495817i
$717$		0			0
$718$	823.316	+	220.607i	1.14668	+	0.307252i
$719$		−	1211.89i		−	1.68553i	−0.538285	−	0.842763i	$-0.680928\pi$
$719$		−	1211.89i		−	1.68553i	0.538285	−	0.842763i	$-0.319072\pi$
$720$		0			0
$721$	−6.23044			−0.00864139
$722$	210.990	−	787.424i	0.292230	−	1.09062i
$723$		0			0
$724$	186.673	+	107.776i	0.257836	+	0.148862i
$725$	−26.4353	+	182.041i	−0.0364625	+	0.251091i
$726$		0			0
$727$	53.9360	−	201.292i	0.0741899	−	0.276880i	−0.918859	−	0.394587i	$-0.870888\pi$
$727$	53.9360	−	201.292i	0.0741899	−	0.276880i	0.993048	+	0.117707i	$0.0375543\pi$
$728$	2.82010	−	2.82010i	0.00387377	−	0.00387377i
$729$		0			0
$730$	797.680	+	540.705i	1.09271	+	0.740692i
$731$	−96.6185	−	167.348i	−0.132173	−	0.228930i
$732$		0			0
$733$	−189.606	−	707.621i	−0.258672	−	0.965376i	−0.966011	−	0.258502i	$-0.916771\pi$
$733$	−189.606	−	707.621i	−0.258672	−	0.965376i	0.707339	−	0.706874i	$-0.249895\pi$
$734$	793.936	+	458.379i	1.08166	+	0.624495i
$735$		0			0
$736$	−721.511	−	1249.69i	−0.980313	−	1.69795i
$737$	324.286	+	324.286i	0.440009	+	0.440009i
$738$		0			0
$739$		−	1243.93i		−	1.68326i	−0.540056	−	0.841629i	$-0.681597\pi$
$739$		−	1243.93i		−	1.68326i	0.540056	−	0.841629i	$-0.318403\pi$
$740$	−367.859	−	425.137i	−0.497107	−	0.574509i
$741$		0			0
$742$	6.49769	−	1.74105i	0.00875700	−	0.00234643i
$743$	−332.161	−	1239.64i	−0.447054	−	1.66843i	−0.710455	−	0.703743i	$-0.751511\pi$
$743$	−332.161	−	1239.64i	−0.447054	−	1.66843i	0.263400	−	0.964687i	$-0.415156\pi$
$744$		0			0
$745$	132.497	+	9.57019i	0.177849	+	0.0128459i
$746$	829.060			1.11134
$747$		0			0
$748$	277.240	−	277.240i	0.370642	−	0.370642i
$749$	1.22121	−	0.705066i	0.00163045	−	0.000941343i
$750$		0			0
$751$	−470.274	+	814.539i	−0.626198	+	1.08461i	0.362110	+	0.932135i	$0.382056\pi$
$751$	−470.274	+	814.539i	−0.626198	+	1.08461i	−0.988308	+	0.152471i	$0.951277\pi$
$752$	891.087	−	238.766i	1.18496	−	0.317508i
$753$		0			0
$754$	−207.708	+	119.920i	−0.275474	+	0.159045i
$755$	−407.598	−	276.289i	−0.539865	−	0.365946i
$756$		0			0
$757$	872.169	+	872.169i	1.15214	+	1.15214i	0.986123	+	0.166015i	$0.0530901\pi$
$757$	872.169	+	872.169i	1.15214	+	1.15214i	0.166015	+	0.986123i	$0.446910\pi$
$758$	−490.097	−	131.321i	−0.646566	−	0.173247i
$759$		0			0
$760$	122.694	+	42.5615i	0.161439	+	0.0560020i
$761$	229.806	−	398.036i	0.301979	−	0.523043i	−0.674605	−	0.738179i	$-0.735686\pi$
$761$	229.806	−	398.036i	0.301979	−	0.523043i	0.976584	+	0.215136i	$0.0690194\pi$
$762$		0			0
$763$	−7.37515	−	1.97617i	−0.00966599	−	0.00259000i
$764$		−	300.712i		−	0.393602i
$765$		0			0
$766$	51.5397			0.0672842
$767$	63.9473	−	238.655i	0.0833733	−	0.311153i
$768$		0			0
$769$	775.372	+	447.661i	1.00829	+	0.582134i	0.910689	−	0.413092i	$-0.135551\pi$
$769$	775.372	+	447.661i	1.00829	+	0.582134i	0.0975969	+	0.995226i	$0.468884\pi$
$770$	3.42338	+	7.05997i	0.00444594	+	0.00916879i
$771$		0			0
$772$	52.6949	−	196.660i	0.0682576	−	0.254741i
$773$	−94.0446	+	94.0446i	−0.121662	+	0.121662i	−0.765316	−	0.643654i	$-0.777417\pi$
$773$	−94.0446	+	94.0446i	−0.121662	+	0.121662i	0.643654	+	0.765316i	$0.277417\pi$
$774$		0			0
$775$	154.690	+	387.981i	0.199600	+	0.500620i
$776$	−347.868	−	602.524i	−0.448283	−	0.776449i
$777$		0			0
$778$	−119.433	−	445.730i	−0.153513	−	0.572918i
$779$	313.377	+	180.928i	0.402281	+	0.232257i
$780$		0			0
$781$	260.825	+	451.762i	0.333963	+	0.578441i
$782$	−1536.46	−	1536.46i	−1.96479	−	1.96479i
$783$		0			0
$784$		−	977.861i		−	1.24727i
$785$	652.970	−	564.997i	0.831809	−	0.719742i
$786$		0			0
$787$	899.963	−	241.144i	1.14354	−	0.306410i	0.363164	−	0.931725i	$-0.381696\pi$
$787$	899.963	−	241.144i	1.14354	−	0.306410i	0.780372	+	0.625315i	$0.215030\pi$
$788$	−137.666	−	513.778i	−0.174704	−	0.652003i
$789$		0			0
$790$	385.514	+	445.541i	0.487993	+	0.563976i
$791$	−2.52677			−0.00319440
$792$		0			0
$793$	−49.8843	+	49.8843i	−0.0629058	+	0.0629058i
$794$	−721.400	+	416.501i	−0.908565	+	0.524560i
$795$		0			0
$796$	−40.1407	+	69.5257i	−0.0504280	+	0.0873438i
$797$	−163.649	+	43.8496i	−0.205331	+	0.0550183i	−0.360019	−	0.932945i	$-0.617230\pi$
$797$	−163.649	+	43.8496i	−0.205331	+	0.0550183i	0.154687	+	0.987963i	$0.450563\pi$
$798$		0			0
$799$	770.071	−	444.601i	0.963793	−	0.556446i
$800$	−314.200	+	730.879i	−0.392750	+	0.913599i
$801$		0			0
$802$	−119.900	−	119.900i	−0.149502	−	0.149502i
$803$	691.034	+	185.162i	0.860565	+	0.230588i
$804$		0			0
$805$	13.9012	−	6.74068i	0.0172686	−	0.00837352i
$806$	−272.293	+	471.626i	−0.337833	+	0.585144i
$807$		0			0
$808$	−238.527	−	63.9130i	−0.295206	−	0.0791003i
$809$			1540.82i			1.90459i	0.305175	+	0.952296i	$0.401285\pi$
$809$			1540.82i			1.90459i	−0.305175	+	0.952296i	$0.598715\pi$
$810$		0			0
$811$	−895.419			−1.10409			−0.552046	−	0.833813i	$-0.686153\pi$
$811$	−895.419			−1.10409			−0.552046	+	0.833813i	$0.686153\pi$
$812$	0.286042	−	1.06752i	0.000352269	−	0.00131469i
$813$		0			0
$814$	−1017.33	−	587.355i	−1.24979	−	0.721566i
$815$	−150.824	+	434.785i	−0.185060	+	0.533479i
$816$		0			0
$817$	−15.0972	+	56.3434i	−0.0184788	+	0.0689637i
$818$	664.048	−	664.048i	0.811795	−	0.811795i
$819$		0			0
$820$	−385.357	+	568.501i	−0.469947	+	0.693294i
$821$	322.268	+	558.185i	0.392531	+	0.679884i	0.992783	−	0.119927i	$-0.0382661\pi$
$821$	322.268	+	558.185i	0.392531	+	0.679884i	−0.600251	+	0.799811i	$0.704933\pi$
$822$		0			0
$823$	−56.6061	−	211.257i	−0.0687802	−	0.256691i	0.922971	−	0.384870i	$-0.125754\pi$
$823$	−56.6061	−	211.257i	−0.0687802	−	0.256691i	−0.991751	+	0.128179i	$0.959087\pi$
$824$	−354.182	−	204.487i	−0.429832	−	0.248164i
$825$		0			0
$826$	1.60223	+	2.77514i	0.00193975	+	0.00335974i
$827$	982.768	+	982.768i	1.18835	+	1.18835i	0.977522	+	0.210831i	$0.0676170\pi$
$827$	982.768	+	982.768i	1.18835	+	1.18835i	0.210831	+	0.977522i	$0.432383\pi$
$828$		0			0
$829$		−	763.031i		−	0.920424i	−0.887809	−	0.460212i	$-0.847773\pi$
$829$		−	763.031i		−	0.920424i	0.887809	−	0.460212i	$-0.152227\pi$
$830$	−55.7574	+	771.949i	−0.0671776	+	0.930059i
$831$		0			0
$832$	7.18844	−	1.92614i	0.00863996	−	0.00231507i
$833$	−243.948	−	910.427i	−0.292855	−	1.09295i
$834$		0			0
$835$	−755.327	+	653.564i	−0.904584	+	0.782711i
$836$	−118.353			−0.141571
$837$		0			0
$838$	402.737	−	402.737i	0.480593	−	0.480593i
$839$	946.477	−	546.449i	1.12810	−	0.651309i	0.184644	−	0.982805i	$-0.440887\pi$
$839$	946.477	−	546.449i	1.12810	−	0.651309i	0.943457	+	0.331496i	$0.107553\pi$
$840$		0			0
$841$	−393.430	+	681.440i	−0.467812	+	0.810274i
$842$	985.940	−	264.182i	1.17095	−	0.313755i
$843$		0			0
$844$	−369.598	+	213.388i	−0.437913	+	0.252829i
$845$	−6.30890	+	9.30726i	−0.00746615	+	0.0110145i
$846$		0			0
$847$	−1.71114	−	1.71114i	−0.00202024	−	0.00202024i
$848$	764.080	+	204.735i	0.901038	+	0.241432i
$849$		0			0
$850$	−172.154	+	1185.50i	−0.202535	+	1.39471i
$851$	−1156.51	+	2003.14i	−1.35900	+	2.35386i
$852$		0			0
$853$	−1588.02	−	425.510i	−1.86169	−	0.498839i	−0.861729	−	0.507369i	$-0.830618\pi$
$853$	−1588.02	−	425.510i	−1.86169	−	0.498839i	−0.999964	+	0.00853057i	$0.997285\pi$
$854$		−	0.914971i		−	0.00107140i
$855$		0			0
$856$	92.5628			0.108134
$857$	−85.2695	+	318.230i	−0.0994977	+	0.371330i	−0.997663	−	0.0683276i	$-0.978234\pi$
$857$	−85.2695	+	318.230i	−0.0994977	+	0.371330i	0.898165	+	0.439658i	$0.144900\pi$
$858$		0			0
$859$	1361.73	+	786.197i	1.58525	+	0.915247i	0.994074	+	0.108707i	$0.0346710\pi$
$859$	1361.73	+	786.197i	1.58525	+	0.915247i	0.591180	+	0.806540i	$0.298662\pi$
$860$	−104.597	−	36.2839i	−0.121624	−	0.0421906i
$861$		0			0
$862$	−29.9639	+	111.827i	−0.0347609	+	0.129729i
$863$	−458.505	+	458.505i	−0.531292	+	0.531292i	−0.920957	−	0.389665i	$-0.872591\pi$
$863$	−458.505	+	458.505i	−0.531292	+	0.531292i	0.389665	+	0.920957i	$0.372591\pi$
$864$		0			0
$865$	169.791	−	32.6006i	0.196290	−	0.0376885i
$866$	758.481	+	1313.73i	0.875844	+	1.51701i
$867$		0			0
$868$	−0.649494	−	2.42395i	−0.000748265	−	0.00279256i
$869$	378.794	+	218.697i	0.435897	+	0.251665i
$870$		0			0
$871$	−324.550	−	562.137i	−0.372618	−	0.645393i
$872$	−354.396	−	354.396i	−0.406418	−	0.406418i
$873$		0			0
$874$			655.913i			0.750472i
$875$	−7.56226	−	3.91887i	−0.00864259	−	0.00447870i
$876$		0			0
$877$	−1041.72	+	279.129i	−1.18783	+	0.318277i	−0.798026	−	0.602623i	$-0.794122\pi$
$877$	−1041.72	+	279.129i	−1.18783	+	0.318277i	−0.389800	+	0.920900i	$0.627456\pi$
$878$	−249.625	−	931.615i	−0.284311	−	1.06106i
$879$		0			0
$880$	−66.4695	+	920.256i	−0.0755335	+	1.04574i
$881$	−1585.15			−1.79927			−0.899633	−	0.436647i	$-0.856166\pi$
$881$	−1585.15			−1.79927			−0.899633	+	0.436647i	$0.856166\pi$
$882$		0			0
$883$	−1004.45	+	1004.45i	−1.13755	+	1.13755i	−0.148657	+	0.988889i	$0.547495\pi$
$883$	−1004.45	+	1004.45i	−1.13755	+	1.13755i	−0.988889	+	0.148657i	$0.952505\pi$
$884$	−480.584	+	277.466i	−0.543648	+	0.313875i
$885$		0			0
$886$	913.702	−	1582.58i	1.03127	−	1.78621i
$887$	302.408	−	81.0299i	0.340933	−	0.0913528i	−0.0842901	−	0.996441i	$-0.526862\pi$
$887$	302.408	−	81.0299i	0.340933	−	0.0913528i	0.425223	+	0.905088i	$0.360196\pi$
$888$		0			0
$889$	12.6676	−	7.31362i	0.0142492	−	0.00822680i
$890$	723.576	−	138.929i	0.813006	−	0.156100i
$891$		0			0
$892$	−149.235	−	149.235i	−0.167304	−	0.167304i
$893$	−259.270	−	69.4713i	−0.290336	−	0.0777954i
$894$		0			0
$895$	−405.687	−	836.641i	−0.453281	−	0.934794i
$896$	−4.38491	+	7.59489i	−0.00489387	+	0.00847644i
$897$		0			0
$898$	−339.479	−	90.9632i	−0.378039	−	0.101295i
$899$		−	122.932i		−	0.136743i
$900$		0			0
$901$	762.464			0.846242
$902$	−371.425	+	1386.18i	−0.411779	+	1.53678i
$903$		0			0
$904$	−143.639	−	82.9302i	−0.158893	−	0.0917370i
$905$	−439.933	+	213.324i	−0.486114	+	0.235717i
$906$		0			0
$907$	95.9237	−	357.992i	0.105759	−	0.394699i	−0.892671	−	0.450709i	$-0.851171\pi$
$907$	95.9237	−	357.992i	0.105759	−	0.394699i	0.998430	+	0.0560100i	$0.0178379\pi$
$908$	−513.506	+	513.506i	−0.565536	+	0.565536i
$909$		0			0
$910$	−2.09399	−	10.9060i	−0.00230109	−	0.0119846i
$911$	−490.084	−	848.851i	−0.537963	−	0.931779i	−0.999014	−	0.0444052i	$-0.985861\pi$
$911$	−490.084	−	848.851i	−0.537963	−	0.931779i	0.461051	−	0.887374i	$-0.347473\pi$
$912$		0			0
$913$	148.711	+	554.997i	0.162882	+	0.607883i
$914$	−1583.93	−	914.484i	−1.73297	−	1.00053i
$915$		0			0
$916$	458.489	+	794.127i	0.500534	+	0.866951i
$917$	−0.0724117	−	0.0724117i	−7.89659e−5	−	7.89659e-5i
$918$		0			0
$919$			1321.17i			1.43762i	0.695205	+	0.718811i	$0.255313\pi$
$919$			1321.17i			1.43762i	−0.695205	+	0.718811i	$0.744687\pi$
$920$	1011.47	+	73.0581i	1.09943	+	0.0794110i
$921$		0			0
$922$	1544.84	−	413.938i	1.67553	−	0.448956i
$923$	−191.092	−	713.166i	−0.207034	−	0.772661i
$924$		0			0
$925$	1266.39	−	149.606i	1.36907	−	0.161736i
$926$	−691.330			−0.746577
$927$		0			0
$928$	165.567	−	165.567i	0.178413	−	0.178413i
$929$	672.297	−	388.151i	0.723678	−	0.417816i	−0.0924267	−	0.995719i	$-0.529462\pi$
$929$	672.297	−	388.151i	0.723678	−	0.417816i	0.816105	+	0.577904i	$0.196129\pi$
$930$		0			0
$931$	−142.259	+	246.400i	−0.152802	+	0.264662i
$932$	−66.3103	+	17.7678i	−0.0711484	+	0.0190642i
$933$		0			0
$934$	175.242	−	101.176i	0.187625	−	0.108325i
$935$	167.691	+	873.376i	0.179349	+	0.934092i
$936$		0			0
$937$	295.586	+	295.586i	0.315459	+	0.315459i	0.847020	−	0.531561i	$-0.178394\pi$
$937$	295.586	+	295.586i	0.315459	+	0.315459i	−0.531561	+	0.847020i	$0.678394\pi$
$938$	8.13175	+	2.17890i	0.00866925	+	0.00232292i
$939$		0			0
$940$	166.964	−	481.315i	0.177622	−	0.512037i
$941$	48.8020	−	84.5275i	0.0518618	−	0.0898273i	−0.838929	−	0.544241i	$-0.816818\pi$
$941$	48.8020	−	84.5275i	0.0518618	−	0.0898273i	0.890791	+	0.454413i	$0.150151\pi$
$942$		0			0
$943$	2729.40	+	731.341i	2.89438	+	0.775548i
$944$			376.820i			0.399174i
$945$		0			0
$946$	−231.333			−0.244538
$947$	−47.4532	+	177.098i	−0.0501090	+	0.187009i	−0.986444	−	0.164099i	$-0.947528\pi$
$947$	−47.4532	+	177.098i	−0.0501090	+	0.187009i	0.936335	+	0.351108i	$0.114195\pi$
$948$		0			0
$949$	−876.908	−	506.283i	−0.924034	−	0.533491i
$950$	289.790	−	216.298i	0.305042	−	0.227682i
$951$		0			0
$952$	−1.51743	+	5.66313i	−0.00159394	+	0.00594866i
$953$	16.8810	−	16.8810i	0.0177135	−	0.0177135i	−0.698195	−	0.715908i	$-0.746013\pi$
$953$	16.8810	−	16.8810i	0.0177135	−	0.0177135i	0.715908	+	0.698195i	$0.246013\pi$
$954$		0			0
$955$	564.603	+	382.714i	0.591207	+	0.400748i
$956$	340.507	+	589.776i	0.356179	+	0.616920i
$957$		0			0
$958$	−312.153	−	1164.97i	−0.325838	−	1.21604i
$959$	−4.12185	−	2.37975i	−0.00429807	−	0.00248149i
$960$		0			0
$961$	340.934	+	590.514i	0.354770	+	0.614479i
$962$	1175.66	+	1175.66i	1.22210	+	1.22210i
$963$		0			0
$964$			56.6819i			0.0587987i
$965$	302.175	+	349.226i	0.313135	+	0.361892i
$966$		0			0
$967$	1161.19	−	311.140i	1.20082	−	0.321758i	0.397665	−	0.917531i	$-0.369821\pi$
$967$	1161.19	−	311.140i	1.20082	−	0.321758i	0.803153	+	0.595772i	$0.203154\pi$
$968$	−41.1125	−	153.434i	−0.0424716	−	0.158506i
$969$		0			0
$970$	−1932.24	−	139.564i	−1.99200	−	0.143881i
$971$	608.975			0.627163			0.313582	−	0.949561i	$-0.398471\pi$
$971$	608.975			0.627163			0.313582	+	0.949561i	$0.398471\pi$
$972$		0			0
$973$	−5.91580	+	5.91580i	−0.00607996	+	0.00607996i
$974$	−494.753	+	285.646i	−0.507960	+	0.293271i
$975$		0			0
$976$	53.7969	−	93.1790i	0.0551198	−	0.0954702i
$977$	−85.2493	+	22.8425i	−0.0872562	+	0.0233802i	−0.302183	−	0.953250i	$-0.597715\pi$
$977$	−85.2493	+	22.8425i	−0.0872562	+	0.0233802i	0.214927	+	0.976630i	$0.431049\pi$
$978$		0			0
$979$	473.701	−	273.491i	0.483862	−	0.279358i
$980$	−446.998	−	302.996i	−0.456120	−	0.309180i
$981$		0			0
$982$	−1391.51	−	1391.51i	−1.41701	−	1.41701i
$983$	−1378.97	−	369.494i	−1.40282	−	0.375884i	−0.523461	−	0.852049i	$-0.675360\pi$
$983$	−1378.97	−	369.494i	−1.40282	−	0.375884i	−0.879356	+	0.476166i	$0.842026\pi$
$984$		0			0
$985$	1139.85	+	395.406i	1.15721	+	0.401428i
$986$	176.289	−	305.341i	0.178792	−	0.309676i
$987$		0			0
$988$	161.805	+	43.3555i	0.163770	+	0.0438821i
$989$			455.499i			0.460565i
$990$		0			0
$991$	14.7275			0.0148613			0.00743063	−	0.999972i	$-0.497635\pi$
$991$	14.7275			0.0148613			0.00743063	+	0.999972i	$0.497635\pi$
$992$	137.604	−	513.545i	0.138714	−	0.517687i
$993$		0			0
$994$	8.29290	+	4.78791i	0.00834296	+	0.00481681i
$995$	−79.4514	−	163.851i	−0.0798506	−	0.164675i
$996$		0			0
$997$	−59.6878	+	222.758i	−0.0598674	+	0.223428i	−0.989378	−	0.145368i	$-0.953563\pi$
$997$	−59.6878	+	222.758i	−0.0598674	+	0.223428i	0.929510	+	0.368796i	$0.120230\pi$
$998$	858.989	−	858.989i	0.860710	−	0.860710i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.l.a.37.9		40
3.2	odd	2		45.3.k.a.22.2	yes	40
5.3	odd	4	inner	135.3.l.a.118.2		40
9.2	odd	6		45.3.k.a.7.9	✓	40
9.4	even	3		405.3.g.g.82.9		20
9.5	odd	6		405.3.g.h.82.2		20
9.7	even	3	inner	135.3.l.a.127.2		40
15.2	even	4		225.3.o.b.193.2		40
15.8	even	4		45.3.k.a.13.9	yes	40
15.14	odd	2		225.3.o.b.157.9		40
45.2	even	12		225.3.o.b.43.9		40
45.13	odd	12		405.3.g.g.163.9		20
45.23	even	12		405.3.g.h.163.2		20
45.29	odd	6		225.3.o.b.7.2		40
45.38	even	12		45.3.k.a.43.2	yes	40
45.43	odd	12	inner	135.3.l.a.73.9		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.9	✓	40	9.2	odd	6
45.3.k.a.13.9	yes	40	15.8	even	4
45.3.k.a.22.2	yes	40	3.2	odd	2
45.3.k.a.43.2	yes	40	45.38	even	12
135.3.l.a.37.9		40	1.1	even	1	trivial
135.3.l.a.73.9		40	45.43	odd	12	inner
135.3.l.a.118.2		40	5.3	odd	4	inner
135.3.l.a.127.2		40	9.7	even	3	inner
225.3.o.b.7.2		40	45.29	odd	6
225.3.o.b.43.9		40	45.2	even	12
225.3.o.b.157.9		40	15.14	odd	2
225.3.o.b.193.2		40	15.2	even	4
405.3.g.g.82.9		20	9.4	even	3
405.3.g.g.163.9		20	45.13	odd	12
405.3.g.h.82.2		20	9.5	odd	6
405.3.g.h.163.2		20	45.23	even	12

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.644680 - 2.40598i) q^{2} +(-1.90902 - 1.10217i) q^{4} +(4.49898 - 2.18155i) q^{5} +(0.0176356 - 0.0658171i) q^{7} +(3.16269 - 3.16269i) q^{8} +(-2.34837 - 12.2309i) q^{10} +(-4.62292 - 8.00713i) q^{11} +(3.38696 + 12.6403i) q^{13} +(-0.146985 - 0.0848619i) q^{14} +(-9.97912 - 17.2843i) q^{16} +(-13.6029 - 13.6029i) q^{17} +5.80704i q^{19} +(-10.9931 - 0.794023i) q^{20} +(-22.2453 + 5.96060i) q^{22} +(11.7365 + 43.8013i) q^{23} +(15.4816 - 19.6295i) q^{25} +32.5958 q^{26} +(-0.106208 + 0.106208i) q^{28} +(-6.37222 + 3.67900i) q^{29} +(-8.35363 + 14.4689i) q^{31} +(-30.7378 + 8.23618i) q^{32} +(-41.4978 + 23.9587i) q^{34} +(-0.0642412 - 0.334583i) q^{35} +(36.0680 + 36.0680i) q^{37} +(13.9716 + 3.74368i) q^{38} +(7.32929 - 21.1284i) q^{40} +(31.1567 - 53.9649i) q^{41} +(9.70259 + 2.59980i) q^{43} +20.3810i q^{44} +112.951 q^{46} +(-11.9633 + 44.6476i) q^{47} +(42.4312 + 24.4977i) q^{49} +(-37.2475 - 49.9033i) q^{50} +(7.46602 - 27.8636i) q^{52} +(-28.0258 + 28.0258i) q^{53} +(-38.2664 - 25.9388i) q^{55} +(-0.152383 - 0.263935i) q^{56} +(4.74356 + 17.7032i) q^{58} +(-16.3509 - 9.44022i) q^{59} +(2.69547 + 4.66870i) q^{61} +(29.4265 + 29.4265i) q^{62} -0.568692i q^{64} +(42.8134 + 49.4796i) q^{65} +(-47.9117 + 12.8379i) q^{67} +(10.9754 + 40.9609i) q^{68} +(-0.846414 - 0.0611359i) q^{70} -56.4200 q^{71} +(-54.7135 + 54.7135i) q^{73} +(110.031 - 63.5264i) q^{74} +(6.40036 - 11.0857i) q^{76} +(-0.608534 + 0.163056i) q^{77} +(-40.9692 + 23.6536i) q^{79} +(-82.6026 - 55.9919i) q^{80} +(-109.752 - 109.752i) q^{82} +(-60.0267 - 16.0841i) q^{83} +(-90.8746 - 31.5237i) q^{85} +(12.5101 - 21.6682i) q^{86} +(-39.9449 - 10.7032i) q^{88} +59.1599i q^{89} +0.891679 q^{91} +(25.8713 - 96.5530i) q^{92} +(99.7085 + 57.5668i) q^{94} +(12.6684 + 26.1258i) q^{95} +(40.2595 - 150.251i) q^{97} +(86.2954 - 86.2954i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 2 q^{5} - 2 q^{7} + 24 q^{8} - 8 q^{10} - 8 q^{11} - 2 q^{13} + 28 q^{16} - 28 q^{17} + 114 q^{20} + 14 q^{22} - 82 q^{23} - 8 q^{25} + 112 q^{26} - 88 q^{28} - 4 q^{31} + 14 q^{32} - 352 q^{35}+ \cdots + 1876 q^{98}+O(q^{100}) \) 40 * q + 2 * q^2 + 2 * q^5 - 2 * q^7 + 24 * q^8 - 8 * q^10 - 8 * q^11 - 2 * q^13 + 28 * q^16 - 28 * q^17 + 114 * q^20 + 14 * q^22 - 82 * q^23 - 8 * q^25 + 112 * q^26 - 88 * q^28 - 4 * q^31 + 14 * q^32 - 352 * q^35 - 92 * q^37 - 330 * q^38 + 30 * q^40 + 28 * q^41 - 2 * q^43 - 136 * q^46 - 64 * q^47 + 458 * q^50 - 74 * q^52 + 608 * q^53 + 224 * q^55 + 192 * q^56 + 30 * q^58 + 92 * q^61 + 100 * q^62 + 326 * q^65 - 80 * q^67 - 626 * q^68 - 102 * q^70 - 248 * q^71 - 8 * q^73 - 96 * q^76 - 338 * q^77 - 1444 * q^80 + 104 * q^82 - 370 * q^83 - 98 * q^85 + 328 * q^86 - 210 * q^88 + 152 * q^91 - 388 * q^92 + 360 * q^95 + 292 * q^97 + 1876 * q^98

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