LMFDB - Embedded newform 243.2.i.a.106.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(4,243)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(162))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("243.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.i (of order $81$, degree $54$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			106.9
Character	$\chi$	$=$	243.106
Dual form			243.2.i.a.94.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.393620 + 1.01950i) q^{2} +(-1.23216 - 1.21729i) q^{3} +(0.596640 + 0.541422i) q^{4} +(-1.58909 - 1.13581i) q^{5} +(1.72603 - 0.777038i) q^{6} +(-1.04545 - 0.810284i) q^{7} +(-2.74004 + 1.37610i) q^{8} +(0.0364234 + 2.99978i) q^{9} +(1.78346 - 1.17300i) q^{10} +(-2.98804 + 4.35667i) q^{11} +(-0.0760884 - 1.39340i) q^{12} +(-3.16922 + 0.622415i) q^{13} +(1.23760 - 0.746893i) q^{14} +(0.575397 + 3.33387i) q^{15} +(-0.168405 - 1.73135i) q^{16} +(-1.42997 - 3.31504i) q^{17} +(-3.07262 - 1.14364i) q^{18} +(0.642100 + 0.862491i) q^{19} +(-0.333160 - 1.53804i) q^{20} +(0.301809 + 2.27101i) q^{21} +(-3.26548 - 4.76119i) q^{22} +(-1.77146 - 0.723721i) q^{23} +(5.05128 + 1.63985i) q^{24} +(-0.383540 - 1.12094i) q^{25} +(0.612917 - 3.47602i) q^{26} +(3.60671 - 3.74054i) q^{27} +(-0.185051 - 1.04948i) q^{28} +(-5.83486 + 3.21954i) q^{29} +(-3.62538 - 0.725662i) q^{30} +(1.78860 + 3.39558i) q^{31} +(-4.07634 - 1.13473i) q^{32} +(8.98506 - 1.73080i) q^{33} +(3.94256 - 0.152989i) q^{34} +(0.740979 + 2.47504i) q^{35} +(-1.60242 + 1.80951i) q^{36} +(0.174788 + 0.185265i) q^{37} +(-1.13205 + 0.315129i) q^{38} +(4.66264 + 3.09094i) q^{39} +(5.91716 + 0.925427i) q^{40} +(4.05007 - 5.02129i) q^{41} +(-2.43410 - 0.586220i) q^{42} +(5.39199 + 5.28842i) q^{43} +(-4.14159 + 0.981574i) q^{44} +(3.34930 - 4.80828i) q^{45} +(1.43512 - 1.52114i) q^{46} +(-0.388126 + 0.736840i) q^{47} +(-1.90005 + 2.33830i) q^{48} +(-1.30969 - 5.08451i) q^{49} +(1.29377 + 0.0502041i) q^{50} +(-2.27341 + 5.82533i) q^{51} +(-2.22787 - 1.34453i) q^{52} +(7.49472 + 2.72786i) q^{53} +(2.39381 + 5.14940i) q^{54} +(9.69662 - 3.52928i) q^{55} +(3.97961 + 0.781570i) q^{56} +(0.258730 - 1.84434i) q^{57} +(-0.985607 - 7.21592i) q^{58} +(3.47251 - 0.269904i) q^{59} +(-1.46173 + 2.30066i) q^{60} +(-7.83383 + 7.10883i) q^{61} +(-4.16583 + 0.486916i) q^{62} +(2.39259 - 3.16563i) q^{63} +(4.83893 - 6.49981i) q^{64} +(5.74311 + 2.61056i) q^{65} +(-1.77215 + 9.84157i) q^{66} +(0.871831 + 0.481056i) q^{67} +(0.941660 - 2.75210i) q^{68} +(1.30174 + 3.04811i) q^{69} +(-2.81498 - 0.218797i) q^{70} +(0.332732 + 5.71279i) q^{71} +(-4.22780 - 8.16940i) q^{72} +(-6.58751 - 4.33267i) q^{73} +(-0.257678 + 0.105273i) q^{74} +(-0.891921 + 1.84805i) q^{75} +(-0.0838686 + 0.862244i) q^{76} +(6.65399 - 2.13352i) q^{77} +(-4.98653 + 3.53691i) q^{78} +(-8.62793 + 1.34938i) q^{79} +(-1.69888 + 2.94255i) q^{80} +(-8.99735 + 0.218524i) q^{81} +(3.52503 + 6.10553i) q^{82} +(10.2439 + 12.7004i) q^{83} +(-1.04950 + 1.51838i) q^{84} +(-1.49291 + 6.89206i) q^{85} +(-7.51395 + 3.41551i) q^{86} +(11.1086 + 3.13572i) q^{87} +(2.19214 - 16.0493i) q^{88} +(0.638494 - 10.9625i) q^{89} +(3.58370 + 5.30726i) q^{90} +(3.81759 + 1.91727i) q^{91} +(-0.665086 - 1.39091i) q^{92} +(1.92956 - 6.36113i) q^{93} +(-0.598435 - 0.685731i) q^{94} +(-0.0407271 - 2.09988i) q^{95} +(3.64141 + 6.36024i) q^{96} +(-15.4551 + 11.0467i) q^{97} +(5.69919 + 0.666139i) q^{98} +(-13.1779 - 8.80478i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) $ 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{50}{81}\right)$

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 $

$2$	−0.393620	+	1.01950i	−0.278332	+	0.720897i	0.721270	+	0.692654i	$0.243559\pi$
$2$	−0.393620	+	1.01950i	−0.278332	+	0.720897i	−0.999601	+	0.0282423i	$0.991009\pi$
$3$	−1.23216	−	1.21729i	−0.711386	−	0.702801i
$3$	−1.23216	−	1.21729i	−0.711386	−	0.702801i
$4$	0.596640	+	0.541422i	0.298320	+	0.270711i
$5$	−1.58909	−	1.13581i	−0.710661	−	0.507950i	0.167766	−	0.985827i	$-0.446345\pi$
$5$	−1.58909	−	1.13581i	−0.710661	−	0.507950i	−0.878427	+	0.477877i	$0.841407\pi$
$6$	1.72603	−	0.777038i	0.704648	−	0.317224i
$7$	−1.04545	−	0.810284i	−0.395142	−	0.306259i	0.395582	−	0.918431i	$-0.370543\pi$
$7$	−1.04545	−	0.810284i	−0.395142	−	0.306259i	−0.790725	+	0.612172i	$0.790296\pi$
$8$	−2.74004	+	1.37610i	−0.968752	+	0.486525i
$9$	0.0364234	+	2.99978i	0.0121411	+	0.999926i
$10$	1.78346	−	1.17300i	0.563979	−	0.370935i
$11$	−2.98804	+	4.35667i	−0.900929	+	1.31359i	0.0482453	+	0.998836i	$0.484637\pi$
$11$	−2.98804	+	4.35667i	−0.900929	+	1.31359i	−0.949174	+	0.314751i	$0.898079\pi$
$12$	−0.0760884	−	1.39340i	−0.0219648	−	0.402240i
$13$	−3.16922	+	0.622415i	−0.878984	+	0.172627i	−0.611794	−	0.791017i	$-0.709552\pi$
$13$	−3.16922	+	0.622415i	−0.878984	+	0.172627i	−0.267190	+	0.963644i	$0.586095\pi$
$14$	1.23760	−	0.746893i	0.330761	−	0.199616i
$15$	0.575397	+	3.33387i	0.148567	+	0.860802i
$16$	−0.168405	−	1.73135i	−0.0421012	−	0.432838i
$17$	−1.42997	−	3.31504i	−0.346818	−	0.804015i	−0.998946	−	0.0459060i	$-0.985383\pi$
$17$	−1.42997	−	3.31504i	−0.346818	−	0.804015i	0.652127	−	0.758109i	$-0.273877\pi$
$18$	−3.07262	−	1.14364i	−0.724223	−	0.269559i
$19$	0.642100	+	0.862491i	0.147308	+	0.197869i	0.869652	−	0.493664i	$-0.164343\pi$
$19$	0.642100	+	0.862491i	0.147308	+	0.197869i	−0.722345	+	0.691533i	$0.756935\pi$
$20$	−0.333160	−	1.53804i	−0.0744968	−	0.343916i
$21$	0.301809	+	2.27101i	0.0658601	+	0.495575i
$22$	−3.26548	−	4.76119i	−0.696203	−	1.01509i
$23$	−1.77146	−	0.723721i	−0.369375	−	0.150906i	0.185909	−	0.982567i	$-0.440477\pi$
$23$	−1.77146	−	0.723721i	−0.369375	−	0.150906i	−0.555284	+	0.831661i	$0.687390\pi$
$24$	5.05128	+	1.63985i	1.03109	+	0.334732i
$25$	−0.383540	−	1.12094i	−0.0767080	−	0.224187i
$26$	0.612917	−	3.47602i	0.120203	−	0.681704i
$27$	3.60671	−	3.74054i	0.694112	−	0.719867i
$28$	−0.185051	−	1.04948i	−0.0349714	−	0.198333i
$29$	−5.83486	+	3.21954i	−1.08351	+	0.597853i	−0.921280	−	0.388901i	$-0.872855\pi$
$29$	−5.83486	+	3.21954i	−1.08351	+	0.597853i	−0.162226	+	0.986754i	$0.551867\pi$
$30$	−3.62538	−	0.725662i	−0.661900	−	0.132487i
$31$	1.78860	+	3.39558i	0.321243	+	0.609864i	0.991175	−	0.132558i	$-0.0423190\pi$
$31$	1.78860	+	3.39558i	0.321243	+	0.609864i	−0.669933	+	0.742422i	$0.733677\pi$
$32$	−4.07634	−	1.13473i	−0.720602	−	0.200593i
$33$	8.98506	−	1.73080i	1.56410	−	0.301294i
$34$	3.94256	−	0.152989i	0.676143	−	0.0262374i
$35$	0.740979	+	2.47504i	0.125248	+	0.418359i
$36$	−1.60242	+	1.80951i	−0.267069	+	0.301585i
$37$	0.174788	+	0.185265i	0.0287350	+	0.0304573i	0.741582	−	0.670863i	$-0.234076\pi$
$37$	0.174788	+	0.185265i	0.0287350	+	0.0304573i	−0.712847	+	0.701320i	$0.752594\pi$
$38$	−1.13205	+	0.315129i	−0.183644	+	0.0511207i
$39$	4.66264	+	3.09094i	0.746619	+	0.494946i
$40$	5.91716	+	0.925427i	0.935585	+	0.146323i
$41$	4.05007	−	5.02129i	0.632514	−	0.784194i	−0.356136	−	0.934434i	$-0.615906\pi$
$41$	4.05007	−	5.02129i	0.632514	−	0.784194i	0.988650	+	0.150240i	$0.0480047\pi$
$42$	−2.43410	−	0.586220i	−0.375589	−	0.0904557i
$43$	5.39199	+	5.28842i	0.822270	+	0.806477i	0.983589	−	0.180426i	$-0.0577475\pi$
$43$	5.39199	+	5.28842i	0.822270	+	0.806477i	−0.161319	+	0.986902i	$0.551575\pi$
$44$	−4.14159	+	0.981574i	−0.624368	+	0.147978i
$45$	3.34930	−	4.80828i	0.499284	−	0.716776i
$46$	1.43512	−	1.52114i	0.211596	−	0.224279i
$47$	−0.388126	+	0.736840i	−0.0566140	+	0.107479i	−0.911435	−	0.411444i	$-0.865025\pi$
$47$	−0.388126	+	0.736840i	−0.0566140	+	0.107479i	0.854821	+	0.518923i	$0.173667\pi$
$48$	−1.90005	+	2.33830i	−0.274249	+	0.337504i
$49$	−1.30969	−	5.08451i	−0.187098	−	0.726358i
$50$	1.29377	+	0.0502041i	0.182966	+	0.00709993i
$51$	−2.27341	+	5.82533i	−0.318341	+	0.815710i
$52$	−2.22787	−	1.34453i	−0.308951	−	0.186453i
$53$	7.49472	+	2.72786i	1.02948	+	0.374700i	0.800883	−	0.598821i	$-0.204364\pi$
$53$	7.49472	+	2.72786i	1.02948	+	0.374700i	0.228597	+	0.973521i	$0.426586\pi$
$54$	2.39381	+	5.14940i	0.325756	+	0.700745i
$55$	9.69662	−	3.52928i	1.30749	−	0.475888i
$56$	3.97961	+	0.781570i	0.531798	+	0.104442i
$57$	0.258730	−	1.84434i	0.0342696	−	0.244289i
$58$	−0.985607	−	7.21592i	−0.129417	−	0.947497i
$59$	3.47251	−	0.269904i	0.452082	−	0.0351386i	0.150566	−	0.988600i	$-0.451890\pi$
$59$	3.47251	−	0.269904i	0.452082	−	0.0351386i	0.301515	+	0.953461i	$0.402508\pi$
$60$	−1.46173	+	2.30066i	−0.188708	+	0.297013i
$61$	−7.83383	+	7.10883i	−1.00302	+	0.910192i	−0.995961	−	0.0897833i	$-0.971383\pi$
$61$	−7.83383	+	7.10883i	−1.00302	+	0.910192i	−0.00705836	+	0.999975i	$0.502247\pi$
$62$	−4.16583	+	0.486916i	−0.529061	+	0.0618384i
$63$	2.39259	−	3.16563i	0.301438	−	0.398832i
$64$	4.83893	−	6.49981i	0.604867	−	0.812477i
$65$	5.74311	+	2.61056i	0.712345	+	0.323801i
$66$	−1.77215	+	9.84157i	−0.218136	+	1.21141i
$67$	0.871831	+	0.481056i	0.106511	+	0.0587704i	0.535474	−	0.844552i	$-0.320133\pi$
$67$	0.871831	+	0.481056i	0.106511	+	0.0587704i	−0.428963	+	0.903322i	$0.641121\pi$
$68$	0.941660	−	2.75210i	0.114193	−	0.333742i
$69$	1.30174	+	3.04811i	0.156711	+	0.366950i
$70$	−2.81498	−	0.218797i	−0.336454	−	0.0261513i
$71$	0.332732	+	5.71279i	0.0394881	+	0.677984i	0.958735	+	0.284302i	$0.0917618\pi$
$71$	0.332732	+	5.71279i	0.0394881	+	0.677984i	−0.919247	+	0.393682i	$0.871201\pi$
$72$	−4.22780	−	8.16940i	−0.498251	−	0.962774i
$73$	−6.58751	−	4.33267i	−0.771009	−	0.507101i	0.102012	−	0.994783i	$-0.467472\pi$
$73$	−6.58751	−	4.33267i	−0.771009	−	0.507101i	−0.873021	+	0.487682i	$0.837842\pi$
$74$	−0.257678	+	0.105273i	−0.0299545	+	0.0122377i
$75$	−0.891921	+	1.84805i	−0.102990	+	0.213394i
$76$	−0.0838686	+	0.862244i	−0.00962038	+	0.0989062i
$77$	6.65399	−	2.13352i	0.758292	−	0.243137i
$78$	−4.98653	+	3.53691i	−0.564613	+	0.400476i
$79$	−8.62793	+	1.34938i	−0.970718	+	0.151818i	−0.619947	−	0.784644i	$-0.712846\pi$
$79$	−8.62793	+	1.34938i	−0.970718	+	0.151818i	−0.350771	+	0.936461i	$0.614080\pi$
$80$	−1.69888	+	2.94255i	−0.189941	+	0.328987i
$81$	−8.99735	+	0.218524i	−0.999705	+	0.0242804i
$82$	3.52503	+	6.10553i	0.389275	+	0.674243i
$83$	10.2439	+	12.7004i	1.12441	+	1.39405i	0.908626	+	0.417610i	$0.137132\pi$
$83$	10.2439	+	12.7004i	1.12441	+	1.39405i	0.215785	+	0.976441i	$0.430769\pi$
$84$	−1.04950	+	1.51838i	−0.114510	+	0.165669i
$85$	−1.49291	+	6.89206i	−0.161929	+	0.747549i
$86$	−7.51395	+	3.41551i	−0.810250	+	0.368304i
$87$	11.1086	+	3.13572i	1.19096	+	0.336184i
$88$	2.19214	−	16.0493i	0.233683	−	1.71086i
$89$	0.638494	−	10.9625i	0.0676802	−	1.16202i	−0.777975	−	0.628295i	$-0.783753\pi$
$89$	0.638494	−	10.9625i	0.0676802	−	1.16202i	0.845655	−	0.533729i	$-0.179210\pi$
$90$	3.58370	+	5.30726i	0.377755	+	0.559434i
$91$	3.81759	+	1.91727i	0.400192	+	0.200984i
$92$	−0.665086	−	1.39091i	−0.0693400	−	0.145012i
$93$	1.92956	−	6.36113i	0.200086	−	0.659619i
$94$	−0.598435	−	0.685731i	−0.0617239	−	0.0707277i
$95$	−0.0407271	−	2.09988i	−0.00417851	−	0.215443i
$96$	3.64141	+	6.36024i	0.371649	+	0.649140i
$97$	−15.4551	+	11.0467i	−1.56923	+	1.12162i	−0.630910	+	0.775856i	$0.717318\pi$
$97$	−15.4551	+	11.0467i	−1.56923	+	1.12162i	−0.938322	+	0.345763i	$0.887620\pi$
$98$	5.69919	+	0.666139i	0.575705	+	0.0672902i
$99$	−13.1779	−	8.80478i	−1.32443	−	0.884914i
$100$	0.378065	−	0.876454i	0.0378065	−	0.0876454i
$101$	−7.67454	−	2.46074i	−0.763645	−	0.244853i	−0.102116	−	0.994772i	$-0.532561\pi$
$101$	−7.67454	−	2.46074i	−0.763645	−	0.244853i	−0.661529	+	0.749919i	$0.730092\pi$
$102$	−5.04408	−	4.61072i	−0.499438	−	0.456529i
$103$	2.69178	−	5.62938i	0.265229	−	0.554680i	−0.725866	−	0.687836i	$-0.758561\pi$
$103$	2.69178	−	5.62938i	0.265229	−	0.554680i	0.991095	+	0.133157i	$0.0425113\pi$
$104$	7.82730	−	6.06661i	0.767530	−	0.594880i
$105$	2.09984	−	3.95163i	0.204923	−	0.385639i
$106$	−5.73113	+	6.56715i	−0.556657	+	0.637858i
$107$	−13.5791	−	11.3942i	−1.31274	−	1.10152i	−0.987790	−	0.155794i	$-0.950206\pi$
$107$	−13.5791	−	11.3942i	−1.31274	−	1.10152i	−0.324955	−	0.945729i	$-0.605349\pi$
$108$	4.17712	−	0.279001i	0.401944	−	0.0268468i
$109$	13.1104	−	11.0010i	1.25575	−	1.05370i	0.259631	−	0.965708i	$-0.416399\pi$
$109$	13.1104	−	11.0010i	1.25575	−	1.05370i	0.996121	−	0.0879933i	$-0.0280454\pi$
$110$	−0.218677	+	11.2749i	−0.0208500	+	1.07502i
$111$	0.0101538	−	0.441043i	0.000963753	−	0.0418620i
$112$	−1.22683	+	1.94650i	−0.115924	+	0.183927i
$113$	−2.18217	+	2.14026i	−0.205281	+	0.201338i	−0.795584	−	0.605844i	$-0.792836\pi$
$113$	−2.18217	+	2.14026i	−0.205281	+	0.201338i	0.590302	+	0.807182i	$0.299008\pi$
$114$	1.77847	+	0.989747i	0.166569	+	0.0926983i
$115$	1.99299	+	3.16210i	0.185847	+	0.294867i
$116$	−5.22444	−	1.23822i	−0.485077	−	0.114965i
$117$	−1.98254	−	9.48429i	−0.183286	−	0.876823i
$118$	−1.09168	+	3.64647i	−0.100497	+	0.335684i
$119$	−1.19116	+	4.62439i	−0.109194	+	0.423917i
$120$	−6.16436	−	8.34315i	−0.562727	−	0.761622i
$121$	−6.09025	−	15.7741i	−0.553659	−	1.43401i
$122$	−4.16391	−	10.7848i	−0.376982	−	0.976409i
$123$	−11.1027	+	1.25693i	−1.00109	+	0.113334i
$124$	−0.771290	+	2.99433i	−0.0692639	+	0.268899i
$125$	−3.46472	+	11.5730i	−0.309894	+	1.03512i
$126$	2.28559	+	3.68531i	0.203617	+	0.328313i
$127$	−13.3954	−	3.17477i	−1.18865	−	0.281715i	−0.411725	−	0.911308i	$-0.635073\pi$
$127$	−13.3954	−	3.17477i	−1.18865	−	0.281715i	−0.776925	+	0.629593i	$0.783222\pi$
$128$	0.209542	+	0.332461i	0.0185210	+	0.0293856i
$129$	−0.206245	−	13.0798i	−0.0181589	−	1.15161i
$130$	−4.92208	+	4.82754i	−0.431695	+	0.423404i
$131$	3.39952	−	5.39371i	0.297018	−	0.471251i	−0.664002	−	0.747731i	$-0.731143\pi$
$131$	3.39952	−	5.39371i	0.297018	−	0.471251i	0.961020	+	0.276480i	$0.0891680\pi$
$132$	6.29795	+	3.83205i	0.548166	+	0.333537i
$133$	0.0275791	−	1.42197i	0.00239141	−	0.123301i
$134$	−0.833608	+	0.699480i	−0.0720128	+	0.0604259i
$135$	−9.97992	+	1.84749i	−0.858935	+	0.159007i
$136$	8.48001	+	7.11557i	0.727155	+	0.610155i
$137$	12.2793	−	14.0705i	1.04909	−	1.20212i	0.0702414	−	0.997530i	$-0.477623\pi$
$137$	12.2793	−	14.0705i	1.04909	−	1.20212i	0.978847	−	0.204592i	$-0.0655868\pi$
$138$	−3.61995	+	0.127328i	−0.308151	+	0.0108389i
$139$	−7.62625	+	5.91079i	−0.646850	+	0.501347i	−0.882391	−	0.470518i	$-0.844067\pi$
$139$	−7.62625	+	5.91079i	−0.646850	+	0.501347i	0.235540	+	0.971865i	$0.424314\pi$
$140$	−0.897945	+	1.87789i	−0.0758902	+	0.158711i
$141$	1.37518	−	0.435441i	0.115811	−	0.0366708i
$142$	−5.95517	−	1.90945i	−0.499747	−	0.160237i
$143$	6.75811	−	15.6671i	0.565142	−	1.31015i
$144$	5.18754	−	0.568239i	0.432295	−	0.0473533i
$145$	12.9289	+	1.51117i	1.07368	+	0.125496i
$146$	7.01014	−	5.01055i	0.580163	−	0.414676i
$147$	−4.57557	+	7.85918i	−0.377387	+	0.648214i
$148$	0.00397928	+	0.205171i	0.000327095	+	0.0168649i
$149$	15.1598	+	17.3712i	1.24194	+	1.42310i	0.868681	+	0.495372i	$0.164968\pi$
$149$	15.1598	+	17.3712i	1.24194	+	1.42310i	0.373255	+	0.927729i	$0.378242\pi$
$150$	−1.53301	−	1.63675i	−0.125170	−	0.133640i
$151$	9.66379	+	20.2101i	0.786428	+	1.64468i	0.764249	+	0.644921i	$0.223110\pi$
$151$	9.66379	+	20.2101i	0.786428	+	1.64468i	0.0221792	+	0.999754i	$0.492940\pi$
$152$	−2.94626	−	1.47967i	−0.238973	−	0.120017i
$153$	9.89230	−	4.41034i	0.799745	−	0.356555i
$154$	−0.444021	+	7.62355i	−0.0357802	+	0.614323i
$155$	1.01449	−	7.42739i	0.0814859	−	0.596582i
$156$	1.10841	+	4.36864i	0.0887441	+	0.349771i
$157$	−1.91970	+	0.872611i	−0.153209	+	0.0696419i	−0.488947	−	0.872313i	$-0.662619\pi$
$157$	−1.91970	+	0.872611i	−0.153209	+	0.0696419i	0.335739	+	0.941955i	$0.391014\pi$
$158$	2.02043	−	9.32734i	0.160737	−	0.742043i
$159$	−5.91409	−	12.4844i	−0.469018	−	0.990076i
$160$	5.18883	+	6.43313i	0.410213	+	0.508584i
$161$	1.26555	+	2.19200i	0.0997394	+	0.172754i
$162$	3.31875	−	9.25883i	0.260746	−	0.727442i
$163$	−9.57637	+	16.5868i	−0.750079	+	1.29917i	0.197705	+	0.980262i	$0.436651\pi$
$163$	−9.57637	+	16.5868i	−0.750079	+	1.29917i	−0.947784	+	0.318913i	$0.896682\pi$
$164$	5.13507	−	0.803111i	0.400982	−	0.0627124i
$165$	−16.2439	−	7.45494i	−1.26459	−	0.580366i
$166$	−16.9803	+	5.44451i	−1.31793	+	0.422576i
$167$	−1.63226	+	16.7811i	−0.126308	+	1.29856i	0.691207	+	0.722657i	$0.257079\pi$
$167$	−1.63226	+	16.7811i	−0.126308	+	1.29856i	−0.817515	+	0.575907i	$0.804649\pi$
$168$	−3.95211	−	5.80734i	−0.304912	−	0.448046i
$169$	−2.37785	+	0.971459i	−0.182912	+	0.0747276i
$170$	−6.43883	−	4.23488i	−0.493836	−	0.324801i
$171$	−2.56389	+	1.95757i	−0.196066	+	0.149699i
$172$	0.353807	+	6.07463i	0.0269775	+	0.463186i
$173$	0.104143	+	0.00809461i	0.00791783	+	0.000615422i	0.0814507	−	0.996677i	$-0.474045\pi$
$173$	0.104143	+	0.00809461i	0.00791783	+	0.000615422i	−0.0735329	+	0.997293i	$0.523427\pi$
$174$	−7.56943	+	10.0909i	−0.573837	+	0.764991i
$175$	−0.507306	+	1.48266i	−0.0383488	+	0.112078i
$176$	8.04615	+	4.43968i	0.606501	+	0.334653i
$177$	−4.60722	−	3.89447i	−0.346300	−	0.292726i
$178$	10.9250	+	4.96601i	0.818862	+	0.372218i
$179$	−11.5458	+	15.5087i	−0.862975	+	1.15918i	0.123020	+	0.992404i	$0.460742\pi$
$179$	−11.5458	+	15.5087i	−0.862975	+	1.15918i	−0.985995	+	0.166773i	$0.946665\pi$
$180$	4.60164	−	1.05543i	0.342986	−	0.0786669i
$181$	−14.0034	+	1.63676i	−1.04086	+	0.121660i	−0.619312	−	0.785145i	$-0.712589\pi$
$181$	−14.0034	+	1.63676i	−1.04086	+	0.121660i	−0.421552	+	0.906804i	$0.638514\pi$
$182$	−3.45734	+	3.13737i	−0.256275	+	0.232557i
$183$	18.3060	+	0.776835i	1.35322	+	0.0574253i
$184$	5.84979	−	0.454682i	0.431252	−	0.0335196i
$185$	−0.0673280	−	0.492928i	−0.00495005	−	0.0362408i
$186$	5.72568	+	4.47106i	0.419827	+	0.327834i
$187$	18.7154	+	3.67558i	1.36860	+	0.268785i
$188$	−0.630513	+	0.229488i	−0.0459849	+	0.0167371i
$189$	−6.80153	+	0.988078i	−0.494739	+	0.0718721i
$190$	2.15686	+	0.785033i	0.156475	+	0.0569523i
$191$	−3.88522	−	2.34474i	−0.281125	−	0.169660i	0.369126	−	0.929379i	$-0.379657\pi$
$191$	−3.88522	−	2.34474i	−0.281125	−	0.169660i	−0.650251	+	0.759720i	$0.725336\pi$
$192$	−13.8745	+	2.11842i	−1.00130	+	0.152884i
$193$	−15.3105	−	0.594117i	−1.10207	−	0.0427655i	−0.518690	−	0.854962i	$-0.673580\pi$
$193$	−15.3105	−	0.594117i	−1.10207	−	0.0427655i	−0.583384	+	0.812197i	$0.698272\pi$
$194$	−5.17865	−	20.1047i	−0.371805	−	1.44344i
$195$	−3.89861	−	10.2076i	−0.279185	−	0.730985i
$196$	1.97146	−	3.74272i	0.140818	−	0.267337i
$197$	−5.14438	+	5.45272i	−0.366522	+	0.388490i	−0.884218	−	0.467074i	$-0.845308\pi$
$197$	−5.14438	+	5.45272i	−0.366522	+	0.388490i	0.517697	+	0.855564i	$0.326790\pi$
$198$	14.1636	−	9.96915i	1.00656	−	0.708476i
$199$	−6.50834	+	1.54250i	−0.461364	+	0.109345i	−0.454723	−	0.890633i	$-0.650262\pi$
$199$	−6.50834	+	1.54250i	−0.461364	+	0.109345i	−0.00664048	+	0.999978i	$0.502114\pi$
$200$	2.59344	+	2.54363i	0.183384	+	0.179862i
$201$	−0.488650	−	1.65401i	−0.0344667	−	0.116665i
$202$	5.52959	−	6.85561i	0.389060	−	0.482359i
$203$	8.70878	+	1.36203i	0.611237	+	0.0955957i
$204$	−4.51037	+	2.24476i	−0.315789	+	0.157164i
$205$	−12.1391	+	3.37916i	−0.847835	+	0.236011i
$206$	4.67963	+	4.96012i	0.326045	+	0.345588i
$207$	2.10648	−	5.34035i	0.146410	−	0.371180i
$208$	1.61133	+	5.38223i	0.111726	+	0.373190i
$209$	−5.67621	+	0.220263i	−0.392632	+	0.0152359i
$210$	3.20215	+	3.69623i	0.220970	+	0.255064i
$211$	17.6861	+	4.92326i	1.21756	+	0.338931i	0.816622	−	0.577173i	$-0.195844\pi$
$211$	17.6861	+	4.92326i	1.21756	+	0.338931i	0.400939	+	0.916105i	$0.368684\pi$
$212$	2.99473	+	5.68536i	0.205679	+	0.390472i
$213$	6.54413	−	7.44409i	0.448396	−	0.510061i
$214$	16.9615	−	9.35895i	1.15946	−	0.639765i
$215$	−2.56168	−	14.5280i	−0.174705	−	0.990804i
$216$	−4.73519	+	15.2124i	−0.322189	+	1.03508i
$217$	0.881491	−	4.99918i	0.0598395	−	0.339367i
$218$	6.05497	+	17.6963i	0.410094	+	1.19855i
$219$	2.84274	+	13.3574i	0.192094	+	0.902611i
$220$	7.69622	+	3.14425i	0.518879	+	0.211986i
$221$	6.59522	+	9.61606i	0.443642	+	0.646846i
$222$	0.445648	+	0.183955i	0.0299099	+	0.0123463i
$223$	3.30688	+	15.2663i	0.221445	+	1.02230i	0.943732	+	0.330711i	$0.107288\pi$
$223$	3.30688	+	15.2663i	0.221445	+	1.02230i	−0.722287	+	0.691593i	$0.756909\pi$
$224$	3.34216	+	4.48929i	0.223307	+	0.299954i
$225$	3.34859	−	1.19136i	0.223240	−	0.0794242i
$226$	−1.32305	−	3.06717i	−0.0880080	−	0.204025i
$227$	−1.31065	−	13.4747i	−0.0869911	−	0.894347i	−0.932688	−	0.360684i	$-0.882543\pi$
$227$	−1.31065	−	13.4747i	−0.0869911	−	0.894347i	0.845697	−	0.533663i	$-0.179185\pi$
$228$	1.15294	−	0.960328i	0.0763552	−	0.0635993i
$229$	16.2271	−	9.79310i	1.07232	−	0.647147i	0.133320	−	0.991073i	$-0.457436\pi$
$229$	16.2271	−	9.79310i	1.07232	−	0.647147i	0.938997	+	0.343926i	$0.111757\pi$
$230$	−4.00825	+	0.787194i	−0.264296	+	0.0519060i
$231$	−10.7959	−	5.47099i	−0.710316	−	0.359965i
$232$	11.5574	−	16.8510i	0.758777	−	1.10632i
$233$	4.40925	−	2.90001i	0.288859	−	0.189986i	−0.396806	−	0.917902i	$-0.629882\pi$
$233$	4.40925	−	2.90001i	0.288859	−	0.189986i	0.685666	+	0.727917i	$0.259511\pi$
$234$	10.4496	+	1.71201i	0.683113	+	0.111917i
$235$	1.45368	−	0.730064i	0.0948274	−	0.0476241i
$236$	2.21797	+	1.71906i	0.144378	+	0.111901i
$237$	12.2736	+	8.84002i	0.797253	+	0.574221i
$238$	−4.24570	−	3.03465i	−0.275208	−	0.196707i
$239$	−5.53195	−	5.01998i	−0.357832	−	0.324716i	0.473184	−	0.880964i	$-0.343105\pi$
$239$	−5.53195	−	5.01998i	−0.357832	−	0.324716i	−0.831016	+	0.556248i	$0.812240\pi$
$240$	5.67521	−	1.55766i	0.366333	−	0.100546i
$241$	3.77317	−	9.77274i	0.243051	−	0.629518i	−0.756654	−	0.653816i	$-0.773167\pi$
$241$	3.77317	−	9.77274i	0.243051	−	0.629518i	0.999705	+	0.0242979i	$0.00773504\pi$
$242$	18.4790			1.18788
$243$	11.3522	+	10.6831i	0.728241	+	0.685321i
$244$	−8.52286			−0.545620
$245$	−3.69384	+	9.56728i	−0.235991	+	0.611231i
$246$	3.08879	−	11.8140i	0.196934	−	0.753230i
$247$	−2.57178	−	2.33377i	−0.163639	−	0.148494i
$248$	−9.57352	−	6.84274i	−0.607919	−	0.434514i
$249$	2.83798	−	28.1186i	0.179850	−	1.78195i
$250$	−10.4349	−	8.08763i	−0.659959	−	0.511507i
$251$	9.41917	−	4.73048i	0.594532	−	0.298585i	−0.125974	−	0.992034i	$-0.540206\pi$
$251$	9.41917	−	4.73048i	0.594532	−	0.298585i	0.720507	+	0.693448i	$0.243909\pi$
$252$	3.14146	−	0.593338i	0.197893	−	0.0373768i
$253$	8.44621	−	5.55516i	0.531009	−	0.349250i
$254$	8.50939	−	12.4070i	0.533926	−	0.778484i
$255$	10.2291	−	6.67480i	0.640573	−	0.417992i
$256$	15.4813	−	3.04043i	0.967582	−	0.190027i
$257$	12.5727	−	7.58768i	0.784265	−	0.473307i	−0.0671857	−	0.997740i	$-0.521402\pi$
$257$	12.5727	−	7.58768i	0.784265	−	0.473307i	0.851451	+	0.524434i	$0.175723\pi$
$258$	13.4160	+	4.93819i	0.835245	+	0.307438i
$259$	−0.0326151	−	0.335313i	−0.00202661	−	0.0208353i
$260$	2.01315	+	4.66702i	0.124851	+	0.289436i
$261$	−9.87042	−	17.3860i	−0.610964	−	1.07617i
$262$	4.16078	+	5.58890i	0.257054	+	0.345283i
$263$	−2.39228	−	11.0440i	−0.147514	−	0.681001i	−0.989858	−	0.142060i	$-0.954627\pi$
$263$	−2.39228	−	11.0440i	−0.147514	−	0.681001i	0.842344	−	0.538940i	$-0.181175\pi$
$264$	−22.2377	+	17.1068i	−1.36864	+	1.05285i
$265$	−8.81144	−	12.8474i	−0.541282	−	0.789209i
$266$	1.43885	+	0.587834i	0.0882215	+	0.0360424i
$267$	−14.1313	+	12.7303i	−0.864819	+	0.779082i
$268$	0.259715	+	0.759047i	0.0158646	+	0.0463662i
$269$	−2.64710	+	15.0124i	−0.161396	+	0.915325i	0.791306	+	0.611420i	$0.209401\pi$
$269$	−2.64710	+	15.0124i	−0.161396	+	0.915325i	−0.952702	+	0.303905i	$0.901710\pi$
$270$	2.04478	−	10.9018i	0.124441	−	0.663460i
$271$	0.285155	+	1.61719i	0.0173219	+	0.0982376i	0.992243	−	0.124313i	$-0.0396728\pi$
$271$	0.285155	+	1.61719i	0.0173219	+	0.0982376i	−0.974921	+	0.222551i	$0.928562\pi$
$272$	−5.49869	+	3.03405i	−0.333407	+	0.183966i
$273$	−2.37001	−	7.00948i	−0.143439	−	0.424233i
$274$	9.51151	+	18.0572i	0.574612	+	1.09087i
$275$	6.02959	+	1.67845i	0.363598	+	0.101214i
$276$	−0.873645	+	2.52342i	−0.0525873	+	0.151892i
$277$	−26.8195	+	1.04072i	−1.61143	+	0.0625307i	−0.828648	−	0.559770i	$-0.810890\pi$
$277$	−26.8195	+	1.04072i	−1.61143	+	0.0625307i	−0.782778	+	0.622301i	$0.786198\pi$
$278$	−3.02422	−	10.1016i	−0.181381	−	0.605853i
$279$	−10.1208	+	5.48909i	−0.605919	+	0.328624i
$280$	−5.43623	−	5.76206i	−0.324877	−	0.344349i
$281$	−10.4853	+	2.91879i	−0.625502	+	0.174120i	−0.566399	−	0.824131i	$-0.691664\pi$
$281$	−10.4853	+	2.91879i	−0.625502	+	0.174120i	−0.0591036	+	0.998252i	$0.518824\pi$
$282$	−0.0973649	+	1.57340i	−0.00579799	+	0.0936943i
$283$	−26.1664	−	4.09236i	−1.55543	−	0.243265i	−0.682419	−	0.730961i	$-0.739072\pi$
$283$	−26.1664	−	4.09236i	−1.55543	−	0.243265i	−0.873014	+	0.487696i	$0.837838\pi$
$284$	−2.89451	+	3.58863i	−0.171758	+	0.212946i
$285$	−2.50597	+	2.63695i	−0.148441	+	0.156200i
$286$	13.3125	+	13.0568i	0.787183	+	0.772064i
$287$	−8.30281	+	1.96780i	−0.490099	+	0.116156i
$288$	3.25546	−	12.2695i	0.191830	−	0.722985i
$289$	2.72142	−	2.88454i	0.160084	−	0.169679i
$290$	−6.62971	+	12.5862i	−0.389310	+	0.739086i
$291$	32.4901	+	5.20211i	1.90461	+	0.304953i
$292$	−1.58457	−	6.15167i	−0.0927298	−	0.359999i
$293$	−15.2585	−	0.592098i	−0.891410	−	0.0345908i	−0.411000	−	0.911635i	$-0.634821\pi$
$293$	−15.2585	−	0.592098i	−0.891410	−	0.0345908i	−0.480409	+	0.877044i	$0.659512\pi$
$294$	−6.21141	−	7.75834i	−0.362257	−	0.452475i
$295$	−5.82467	−	3.51521i	−0.339126	−	0.204663i
$296$	−0.733871	−	0.267107i	−0.0426554	−	0.0155253i
$297$	5.51928	+	26.8902i	0.320261	+	1.56033i
$298$	−23.6771	+	8.61777i	−1.37158	+	0.499214i
$299$	6.06460	+	1.19105i	0.350725	+	0.0688801i
$300$	−1.53273	+	0.619715i	−0.0884923	+	0.0357793i
$301$	−1.35192	−	9.89781i	−0.0779234	−	0.570500i
$302$	−24.4081	+	1.89715i	−1.40453	+	0.109169i
$303$	6.46081	+	12.3741i	0.371164	+	0.710876i
$304$	1.38514	−	1.25695i	0.0794434	−	0.0720911i
$305$	20.5229	−	2.39879i	1.17514	−	0.137354i
$306$	0.602535	+	11.8212i	0.0344446	+	0.675774i
$307$	−1.71639	+	2.30551i	−0.0979596	+	0.131583i	−0.848400	−	0.529355i	$-0.822434\pi$
$307$	−1.71639	+	2.30551i	−0.0979596	+	0.131583i	0.750441	+	0.660938i	$0.229841\pi$
$308$	5.12517	+	2.32968i	0.292034	+	0.132746i
$309$	−10.1693	+	3.65961i	−0.578510	+	0.208188i
$310$	7.17291	+	3.95785i	0.407394	+	0.224791i
$311$	−5.36802	+	15.6886i	−0.304393	+	0.889621i	0.682872	+	0.730538i	$0.260730\pi$
$311$	−5.36802	+	15.6886i	−0.304393	+	0.889621i	−0.987265	+	0.159083i	$0.949146\pi$
$312$	−17.0293	−	2.05305i	−0.964093	−	0.116231i
$313$	12.0090	+	0.933412i	0.678788	+	0.0527596i	0.412258	−	0.911067i	$-0.364740\pi$
$313$	12.0090	+	0.933412i	0.678788	+	0.0527596i	0.266530	+	0.963827i	$0.414123\pi$
$314$	−0.133996	−	2.30062i	−0.00756181	−	0.129831i
$315$	−7.39759	+	2.31292i	−0.416807	+	0.130318i
$316$	−5.87836	−	3.86626i	−0.330684	−	0.217494i
$317$	3.01212	−	1.23058i	0.169177	−	0.0691165i	−0.292029	−	0.956409i	$-0.594330\pi$
$317$	3.01212	−	1.23058i	0.169177	−	0.0691165i	0.461206	+	0.887293i	$0.347417\pi$
$318$	15.0558	−	1.11533i	0.844285	−	0.0625444i
$319$	3.40833	−	35.0407i	0.190830	−	1.96190i
$320$	−15.0720	+	4.83266i	−0.842553	+	0.270154i
$321$	2.86156	+	30.5692i	0.159717	+	1.70621i
$322$	−2.73289	+	0.427417i	−0.152298	+	0.0238190i
$323$	1.94101	−	3.36192i	0.108001	−	0.187062i
$324$	−5.48649	−	4.74098i	−0.304805	−	0.263388i
$325$	1.91321	+	3.31378i	0.106126	+	0.183815i
$326$	−13.1408	−	16.2920i	−0.727800	−	0.902331i
$327$	−29.5455	−	2.40425i	−1.63387	−	0.132955i
$328$	−4.18755	+	19.3319i	−0.231219	+	1.06742i
$329$	1.00282	−	0.455835i	0.0552870	−	0.0251310i
$330$	13.9943	−	13.6263i	0.770359	−	0.750102i
$331$	0.981224	−	7.18383i	0.0539330	−	0.394859i	−0.943965	−	0.330047i	$-0.892935\pi$
$331$	0.981224	−	7.18383i	0.0539330	−	0.394859i	0.997897	−	0.0648122i	$-0.0206448\pi$
$332$	−0.764377	+	13.1238i	−0.0419506	+	0.720264i
$333$	−0.549387	+	0.531074i	−0.0301062	+	0.0291027i
$334$	−16.4659	−	8.26950i	−0.900975	−	0.452487i
$335$	−0.839027	−	1.75468i	−0.0458409	−	0.0958682i
$336$	3.88109	−	0.904987i	0.211731	−	0.0493711i
$337$	21.6724	+	24.8338i	1.18057	+	1.35278i	0.922188	+	0.386741i	$0.126399\pi$
$337$	21.6724	+	24.8338i	1.18057	+	1.35278i	0.258382	+	0.966043i	$0.416811\pi$
$338$	−0.0544341	−	2.80661i	−0.00296083	−	0.152659i
$339$	5.29408	+	0.0191941i	0.287535	+	0.00104248i
$340$	−4.62225	+	3.30379i	−0.250677	+	0.179173i
$341$	−20.1379	−	2.35378i	−1.09053	−	0.127464i
$342$	−0.986550	−	3.38444i	−0.0533465	−	0.183009i
$343$	−6.41794	+	14.8785i	−0.346536	+	0.803361i
$344$	−22.0517	−	7.07059i	−1.18895	−	0.381221i
$345$	1.39350	−	6.32225i	0.0750236	−	0.340378i
$346$	−0.0492452	+	0.102988i	−0.00264744	+	0.00553664i
$347$	22.4891	−	17.4304i	1.20728	−	0.935713i	0.208179	−	0.978091i	$-0.433246\pi$
$347$	22.4891	−	17.4304i	1.20728	−	0.935713i	0.999102	+	0.0423780i	$0.0134934\pi$
$348$	4.93007	+	7.88532i	0.264279	+	0.422698i
$349$	5.92051	−	6.78415i	0.316917	−	0.363147i	−0.572771	−	0.819716i	$-0.694132\pi$
$349$	5.92051	−	6.78415i	0.316917	−	0.363147i	0.889688	+	0.456568i	$0.150922\pi$
$350$	−1.31189	−	1.10080i	−0.0701233	−	0.0588405i
$351$	−9.10231	+	14.0995i	−0.485845	+	0.752574i
$352$	17.1239	−	14.3687i	0.912708	−	0.765853i
$353$	−0.0215288	+	1.11002i	−0.00114586	+	0.0590803i	0.998803	+	0.0489230i	$0.0155789\pi$
$353$	−0.0215288	+	1.11002i	−0.00114586	+	0.0590803i	−0.999948	+	0.0101573i	$0.996767\pi$
$354$	5.78392	−	3.16413i	0.307412	−	0.168172i
$355$	5.95991	−	9.45604i	0.316319	−	0.501875i
$356$	6.31630	−	6.19498i	0.334763	−	0.328333i
$357$	7.09691	−	4.24798i	0.375608	−	0.224827i
$358$	−11.2665	−	17.8755i	−0.595454	−	0.944752i
$359$	−19.9042	−	4.71738i	−1.05050	−	0.248974i	−0.331121	−	0.943588i	$-0.607427\pi$
$359$	−19.9042	−	4.71738i	−1.05050	−	0.248974i	−0.719382	+	0.694614i	$0.755575\pi$
$360$	−2.56055	+	17.7839i	−0.134953	+	0.937292i
$361$	5.11766	−	17.0942i	0.269351	−	0.899694i
$362$	3.84334	−	14.9208i	0.202001	−	0.784218i
$363$	−11.6975	+	26.8498i	−0.613960	+	1.40925i
$364$	1.23968	+	3.21085i	0.0649768	+	0.168294i
$365$	5.54702	+	14.3671i	0.290344	+	0.752011i
$366$	−7.99760	+	18.3572i	−0.418041	+	0.959548i
$367$	5.95263	−	23.1095i	0.310725	−	1.20631i	−0.602255	−	0.798304i	$-0.705731\pi$
$367$	5.95263	−	23.1095i	0.310725	−	1.20631i	0.912980	−	0.408004i	$-0.133775\pi$
$368$	−0.954694	+	3.18890i	−0.0497669	+	0.166233i
$369$	15.2103	+	11.9664i	0.791816	+	0.622946i
$370$	0.529043	+	0.125386i	0.0275036	+	0.00651848i
$371$	−5.62501	−	8.92469i	−0.292036	−	0.463347i
$372$	4.59531	−	2.75061i	0.238256	−	0.142612i
$373$	−21.6550	+	21.2391i	−1.12125	+	1.09972i	−0.127082	+	0.991892i	$0.540561\pi$
$373$	−21.6550	+	21.2391i	−1.12125	+	1.09972i	−0.994170	+	0.107824i	$0.965612\pi$
$374$	−11.1140	+	17.6336i	−0.574691	+	0.911810i
$375$	18.3567	−	10.0421i	0.947935	−	0.518574i
$376$	0.0495168	−	2.55307i	0.00255364	−	0.131665i
$377$	16.4881	−	13.8351i	0.849178	−	0.712545i
$378$	1.66987	−	7.32310i	0.0858890	−	0.376660i
$379$	4.65432	+	3.90544i	0.239076	+	0.200609i	0.754451	−	0.656356i	$-0.227903\pi$
$379$	4.65432	+	3.90544i	0.239076	+	0.200609i	−0.515375	+	0.856965i	$0.672347\pi$
$380$	1.11262	−	1.27492i	0.0570762	−	0.0654021i
$381$	12.6406	+	20.2179i	0.647599	+	1.03579i
$382$	3.91978	−	3.03806i	0.200553	−	0.155440i
$383$	−10.6426	+	22.2570i	−0.543809	+	1.13728i	0.428491	+	0.903546i	$0.359045\pi$
$383$	−10.6426	+	22.2570i	−0.543809	+	1.13728i	−0.972300	+	0.233735i	$0.924905\pi$
$384$	0.146512	−	0.664716i	0.00747664	−	0.0339212i
$385$	−12.9970	−	4.16733i	−0.662390	−	0.212387i
$386$	6.63223	−	15.3752i	0.337571	−	0.782579i
$387$	−15.6677	+	16.3674i	−0.796434	+	0.832001i
$388$	−15.2021	−	1.77687i	−0.771768	−	0.0902068i
$389$	8.57017	−	6.12559i	0.434525	−	0.310580i	−0.343111	−	0.939295i	$-0.611481\pi$
$389$	8.57017	−	6.12559i	0.434525	−	0.310580i	0.777636	+	0.628715i	$0.216419\pi$
$390$	11.9413	+	0.0432941i	0.604670	+	0.00219228i
$391$	0.133968	+	6.90736i	0.00677506	+	0.349320i
$392$	10.5854	+	12.1295i	0.534643	+	0.612633i
$393$	−10.7544	+	2.50771i	−0.542490	+	0.126497i
$394$	−3.53413	−	7.39100i	−0.178047	−	0.372353i
$395$	15.2432	+	7.65541i	0.766967	+	0.385185i
$396$	−3.09536	−	12.3881i	−0.155548	−	0.622525i
$397$	2.06196	−	35.4024i	0.103487	−	1.77680i	−0.403632	−	0.914921i	$-0.632252\pi$
$397$	2.06196	−	35.4024i	0.103487	−	1.77680i	0.507119	−	0.861876i	$-0.330710\pi$
$398$	0.989227	−	7.24243i	0.0495855	−	0.363030i
$399$	−1.76493	+	1.71852i	−0.0883571	+	0.0860338i
$400$	−1.87615	+	0.852815i	−0.0938075	+	0.0426407i
$401$	−7.42665	+	34.2852i	−0.370869	+	1.71212i	0.286095	+	0.958201i	$0.407643\pi$
$401$	−7.42665	+	34.2852i	−0.370869	+	1.71212i	−0.656964	+	0.753922i	$0.728160\pi$
$402$	1.87861	+	0.152871i	0.0936963	+	0.00762451i
$403$	−7.78194	−	9.64809i	−0.387646	−	0.480606i
$404$	−3.24664	−	5.62335i	−0.161526	−	0.279772i
$405$	14.5458	+	9.87203i	0.722785	+	0.490545i
$406$	−4.81654	+	8.34250i	−0.239041	+	0.414031i
$407$	−1.32941	+	0.207916i	−0.0658966	+	0.0103060i
$408$	−1.78701	−	19.0901i	−0.0884702	−	0.945102i
$409$	−4.20054	+	1.34685i	−0.207703	+	0.0665973i	−0.407356	−	0.913269i	$-0.633549\pi$
$409$	−4.20054	+	1.34685i	−0.207703	+	0.0665973i	0.199653	+	0.979867i	$0.436018\pi$
$410$	1.33315	−	13.7060i	0.0658396	−	0.676891i
$411$	−32.2578	+	2.38965i	−1.59116	+	0.117873i
$412$	4.65390	−	1.90133i	0.229281	−	0.0936717i
$413$	−3.84903	−	2.53154i	−0.189398	−	0.124569i
$414$	4.61534	+	4.24963i	0.226832	+	0.208858i
$415$	−1.85314	−	31.8172i	−0.0909670	−	1.56184i
$416$	13.6251	+	1.05903i	0.668026	+	0.0519231i
$417$	16.5919	+	2.00032i	0.812508	+	0.0979559i
$418$	2.00971	−	5.87361i	0.0982983	−	0.287288i
$419$	9.25418	+	5.10624i	0.452096	+	0.249456i	0.692782	−	0.721147i	$-0.256385\pi$
$419$	9.25418	+	5.10624i	0.452096	+	0.249456i	−0.240686	+	0.970603i	$0.577372\pi$
$420$	3.39235	−	1.22080i	0.165530	−	0.0595691i
$421$	14.8761	+	6.76202i	0.725017	+	0.329561i	0.742096	−	0.670293i	$-0.233832\pi$
$421$	14.8761	+	6.76202i	0.725017	+	0.329561i	−0.0170791	+	0.999854i	$0.505437\pi$
$422$	−11.9809	+	16.0931i	−0.583220	+	0.783401i
$423$	−2.22449	−	1.13745i	−0.108159	−	0.0553049i
$424$	−24.2897	+	2.83906i	−1.17961	+	0.137877i
$425$	−3.16750	+	2.87436i	−0.153646	+	0.139427i
$426$	5.01336	+	9.60190i	0.242898	+	0.465214i
$427$	13.9500	−	1.08428i	0.675090	−	0.0524721i
$428$	−1.93276	−	14.1503i	−0.0934236	−	0.683981i
$429$	−27.3984	+	11.0777i	−1.32281	+	0.534838i
$430$	15.8197	+	3.10689i	0.762893	+	0.149827i
$431$	−4.80056	+	1.74726i	−0.231235	+	0.0841626i	−0.455039	−	0.890472i	$-0.650375\pi$
$431$	−4.80056	+	1.74726i	−0.231235	+	0.0841626i	0.223804	+	0.974634i	$0.428152\pi$
$432$	−7.08358	−	5.61457i	−0.340809	−	0.270131i
$433$	11.4849	+	4.18016i	0.551929	+	0.200886i	0.602903	−	0.797814i	$-0.294010\pi$
$433$	11.4849	+	4.18016i	0.551929	+	0.200886i	−0.0509742	+	0.998700i	$0.516233\pi$
$434$	4.74970	+	2.86646i	0.227993	+	0.137595i
$435$	−14.0909	−	17.6002i	−0.675606	−	0.843863i
$436$	13.7784	+	0.534664i	0.659865	+	0.0256058i
$437$	−0.513252	−	1.99257i	−0.0245522	−	0.0953175i
$438$	−14.7369	−	2.35957i	−0.704155	−	0.112745i
$439$	18.0736	−	34.3119i	0.862606	−	1.63762i	0.0961061	−	0.995371i	$-0.469361\pi$
$439$	18.0736	−	34.3119i	0.862606	−	1.63762i	0.766499	−	0.642245i	$-0.221997\pi$
$440$	−21.7125	+	23.0139i	−1.03510	+	1.09715i
$441$	15.2047	−	4.11396i	0.724033	−	0.195903i
$442$	−12.3996	+	2.93876i	−0.589789	+	0.139783i
$443$	−9.23757	−	9.06015i	−0.438890	−	0.430460i	0.446873	−	0.894597i	$-0.352537\pi$
$443$	−9.23757	−	9.06015i	−0.438890	−	0.430460i	−0.885764	+	0.464137i	$0.846365\pi$
$444$	0.244849	−	0.257647i	0.0116200	−	0.0122274i
$445$	−13.4660	+	16.6952i	−0.638348	+	0.791427i
$446$	−16.8656	−	2.63774i	−0.798611	−	0.124900i
$447$	2.46648	−	39.8578i	0.116661	−	1.88521i
$448$	−10.3255	+	2.87431i	−0.487836	+	0.135799i
$449$	0.745068	+	0.789726i	0.0351620	+	0.0372695i	0.744716	−	0.667382i	$-0.232585\pi$
$449$	0.745068	+	0.789726i	0.0351620	+	0.0372695i	−0.709554	+	0.704651i	$0.751104\pi$
$450$	−0.103478	+	3.88284i	−0.00487799	+	0.183039i
$451$	9.77437	+	32.6487i	0.460257	+	1.53737i
$452$	−2.46075	+	0.0954884i	−0.115744	+	0.00449140i
$453$	12.6942	−	36.6656i	0.596425	−	1.72270i
$454$	14.2534	+	3.96770i	0.668944	+	0.186213i
$455$	−3.88883	−	7.38276i	−0.182311	−	0.346109i
$456$	1.82907	+	5.40962i	0.0856543	+	0.253329i
$457$	2.13802	−	1.17971i	0.100012	−	0.0551844i	−0.432318	−	0.901721i	$-0.642304\pi$
$457$	2.13802	−	1.17971i	0.100012	−	0.0551844i	0.532330	+	0.846537i	$0.321317\pi$
$458$	3.59678	+	20.3983i	0.168066	+	0.953151i
$459$	−17.5575	−	6.60755i	−0.819515	−	0.308414i
$460$	−0.522930	+	2.96569i	−0.0243818	+	0.138276i
$461$	−2.19319	−	6.40984i	−0.102147	−	0.298536i	0.883226	−	0.468948i	$-0.155367\pi$
$461$	−2.19319	−	6.40984i	−0.102147	−	0.298536i	−0.985373	+	0.170412i	$0.945490\pi$
$462$	9.82715	−	8.85291i	0.457201	−	0.411875i
$463$	5.53507	+	2.26133i	0.257237	+	0.105093i	0.503150	−	0.864199i	$-0.332174\pi$
$463$	5.53507	+	2.26133i	0.257237	+	0.105093i	−0.245913	+	0.969292i	$0.579088\pi$
$464$	6.55678	+	9.56001i	0.304391	+	0.443813i
$465$	−10.2913	+	7.91678i	−0.477247	+	0.367132i
$466$	1.22099	+	5.63674i	0.0565615	+	0.261117i
$467$	−8.47868	−	11.3888i	−0.392346	−	0.527013i	0.561432	−	0.827523i	$-0.310251\pi$
$467$	−8.47868	−	11.3888i	−0.392346	−	0.527013i	−0.953779	+	0.300510i	$0.902843\pi$
$468$	3.95214	−	6.73210i	0.182688	−	0.311192i
$469$	−0.521663	−	1.20935i	−0.0240882	−	0.0558426i
$470$	0.172105	+	1.76939i	0.00793861	+	0.0816161i
$471$	3.42759	+	1.26163i	0.157935	+	0.0581330i
$472$	−9.14340	+	5.51807i	−0.420859	+	0.253990i
$473$	−39.1514	+	7.68909i	−1.80018	+	0.353545i
$474$	−13.8435	+	9.03331i	−0.635855	+	0.414913i
$475$	0.720527	−	1.05055i	0.0330600	−	0.0482027i
$476$	−3.21444	+	2.11417i	−0.147334	+	0.0969029i
$477$	−7.90998	+	22.5819i	−0.362173	+	1.03395i
$478$	7.29537	−	3.66387i	0.333682	−	0.167582i
$479$	−0.282368	−	0.218852i	−0.0129017	−	0.00999960i	0.606129	−	0.795366i	$-0.292721\pi$
$479$	−0.282368	−	0.218852i	−0.0129017	−	0.00999960i	−0.619031	+	0.785367i	$0.712474\pi$
$480$	1.43752	−	14.2429i	0.0656137	−	0.650098i
$481$	−0.669254	−	0.478354i	−0.0305154	−	0.0218111i
$482$	8.47814	+	7.69350i	0.386169	+	0.350429i
$483$	1.10893	−	4.24142i	0.0504582	−	0.192992i
$484$	4.90678	−	12.7089i	0.223036	−	0.577677i
$485$	37.1065			1.68492
$486$	−15.3599	+	7.36846i	−0.696738	+	0.334240i
$487$	23.9736			1.08635			0.543174	−	0.839620i	$-0.317222\pi$
$487$	23.9736			1.08635			0.543174	+	0.839620i	$0.317222\pi$
$488$	11.6826	−	30.2586i	0.528846	−	1.36974i
$489$	31.9904	−	8.78030i	1.44666	−	0.397059i
$490$	−8.29989	−	7.53175i	−0.374951	−	0.340250i
$491$	−1.99602	−	1.42667i	−0.0900791	−	0.0643847i	0.535561	−	0.844497i	$-0.320100\pi$
$491$	−1.99602	−	1.42667i	−0.0900791	−	0.0643847i	−0.625640	+	0.780112i	$0.715162\pi$
$492$	−7.30483	−	5.26130i	−0.329327	−	0.237198i
$493$	19.0166	+	14.7389i	0.856463	+	0.663809i
$494$	3.39159	−	1.70332i	0.152595	−	0.0766360i
$495$	10.9402	+	28.9592i	0.491727	+	1.30162i
$496$	5.57774	−	3.66854i	0.250448	−	0.164722i
$497$	4.28113	−	6.24204i	0.192035	−	0.279994i
$498$	27.5499	+	13.9614i	1.23454	+	0.625625i
$499$	24.1278	−	4.73854i	1.08011	−	0.212126i	0.379155	−	0.925333i	$-0.376215\pi$
$499$	24.1278	−	4.73854i	1.08011	−	0.212126i	0.700954	+	0.713207i	$0.252758\pi$
$500$	−8.33305	+	5.02902i	−0.372665	+	0.224905i
$501$	22.4387	−	18.6901i	1.00249	−	0.835011i
$502$	1.11516	+	11.4649i	0.0497721	+	0.511702i
$503$	−2.50583	−	5.80916i	−0.111729	−	0.259018i	0.853172	−	0.521629i	$-0.174676\pi$
$503$	−2.50583	−	5.80916i	−0.111729	−	0.259018i	−0.964902	+	0.262611i	$0.915416\pi$
$504$	−2.19959	+	11.9664i	−0.0979773	+	0.533026i
$505$	9.40057	+	12.6272i	0.418320	+	0.561901i
$506$	2.33890	+	10.7976i	0.103977	+	0.480010i
$507$	4.11243	+	1.69754i	0.182639	+	0.0753903i
$508$	−6.27335	−	9.14677i	−0.278335	−	0.405822i
$509$	−27.2536	−	11.1343i	−1.20800	−	0.493521i	−0.317390	−	0.948295i	$-0.602806\pi$
$509$	−27.2536	−	11.1343i	−1.20800	−	0.493521i	−0.890607	+	0.454774i	$0.849720\pi$
$510$	2.77858	+	13.0559i	0.123038	+	0.578127i
$511$	3.37621	+	9.86733i	0.149355	+	0.436505i
$512$	−3.13052	+	17.7540i	−0.138351	+	0.784625i
$513$	5.54205	+	0.708956i	0.244687	+	0.0313012i
$514$	2.78678	+	15.8046i	0.122919	+	0.697111i
$515$	−10.6714	+	5.88822i	−0.470238	+	0.259466i
$516$	6.95862	−	7.91558i	0.306336	−	0.348464i
$517$	−2.05043	−	3.89265i	−0.0901779	−	0.171198i
$518$	0.354690	+	0.0987348i	0.0155842	+	0.00433816i
$519$	−0.118467	−	0.136745i	−0.00520011	−	0.00600246i
$520$	−19.3288	+	0.750045i	−0.847623	+	0.0328916i
$521$	−1.43729	−	4.80089i	−0.0629689	−	0.210331i	0.920715	−	0.390235i	$-0.127606\pi$
$521$	−1.43729	−	4.80089i	−0.0629689	−	0.210331i	−0.983684	+	0.179904i	$0.942421\pi$
$522$	21.6103	−	3.21943i	0.945856	−	0.140911i
$523$	−10.5058	−	11.1355i	−0.459386	−	0.486921i	0.455726	−	0.890120i	$-0.349380\pi$
$523$	−10.5058	−	11.1355i	−0.459386	−	0.486921i	−0.915112	+	0.403199i	$0.867898\pi$
$524$	4.94857	−	1.37753i	0.216179	−	0.0601776i
$525$	2.42990	−	1.20933i	0.106050	−	0.0527795i
$526$	12.2010	+	1.90820i	0.531989	+	0.0832016i
$527$	8.69884	−	10.7849i	0.378927	−	0.469796i
$528$	−4.50976	−	15.2648i	−0.196262	−	0.664317i
$529$	−13.8061	−	13.5409i	−0.600265	−	0.588735i
$530$	16.5663	−	3.92629i	0.719594	−	0.170547i
$531$	0.936134	+	10.4069i	0.0406248	+	0.451622i
$532$	0.786343	−	0.833475i	0.0340923	−	0.0361357i
$533$	−9.71023	+	18.4344i	−0.420597	+	0.798483i
$534$	−7.41623	−	19.4177i	−0.320932	−	0.840288i
$535$	8.63671	+	33.5298i	0.373398	+	1.44962i
$536$	−3.05084	−	0.118386i	−0.131776	−	0.00511352i
$537$	33.1049	−	5.05461i	1.42858	−	0.218123i
$538$	−14.2633	−	8.60792i	−0.614933	−	0.371114i
$539$	26.0649	+	9.48686i	1.12270	+	0.408628i
$540$	−6.95470	−	4.30106i	−0.299283	−	0.185088i
$541$	−14.9519	+	5.44205i	−0.642833	+	0.233972i	−0.642807	−	0.766028i	$-0.722230\pi$
$541$	−14.9519	+	5.44205i	−0.642833	+	0.233972i	−2.54225e−5		1.00000i	$0.500008\pi$
$542$	−1.76098	−	0.345844i	−0.0756404	−	0.0148553i
$543$	19.2468	+	15.0294i	0.825959	+	0.644974i
$544$	2.06738	+	15.1359i	0.0886380	+	0.648945i
$545$	−33.3286	+	2.59051i	−1.42764	+	0.110965i
$546$	8.07906	+	0.342844i	0.345752	+	0.0146724i
$547$	3.80649	−	3.45420i	0.162754	−	0.147691i	−0.586561	−	0.809905i	$-0.699519\pi$
$547$	3.80649	−	3.45420i	0.162754	−	0.147691i	0.749315	+	0.662214i	$0.230383\pi$
$548$	14.9444	−	1.74675i	0.638392	−	0.0746174i
$549$	−21.6102	−	23.2408i	−0.922303	−	0.991895i
$550$	−4.08455	+	5.48651i	−0.174166	+	0.233946i
$551$	−6.52338	−	2.96524i	−0.277905	−	0.126324i
$552$	−7.76134	−	6.56064i	−0.330345	−	0.279239i
$553$	10.1134	+	5.58036i	0.430067	+	0.237301i
$554$	9.49568	−	27.7522i	0.403433	−	1.17908i
$555$	−0.517077	+	0.689323i	−0.0219487	+	0.0292601i
$556$	−7.75037	−	0.602406i	−0.328689	−	0.0255477i
$557$	−1.13486	−	19.4848i	−0.0480855	−	0.825596i	−0.933008	−	0.359857i	$-0.882826\pi$
$557$	−1.13486	−	19.4848i	−0.0480855	−	0.825596i	0.884922	−	0.465739i	$-0.154211\pi$
$558$	−1.61237	−	12.4788i	−0.0682572	−	0.528271i
$559$	−20.3800	−	13.4041i	−0.861981	−	0.566934i
$560$	4.16039	−	1.69971i	0.175809	−	0.0718257i
$561$	−18.5860	−	27.3109i	−0.784703	−	1.15307i
$562$	1.15152	−	11.8387i	0.0485741	−	0.499386i
$563$	5.41695	−	1.73688i	0.228297	−	0.0732006i	−0.188976	−	0.981982i	$-0.560517\pi$
$563$	5.41695	−	1.73688i	0.228297	−	0.0732006i	0.417273	+	0.908781i	$0.362986\pi$
$564$	1.05624	+	0.484750i	0.0444759	+	0.0204117i
$565$	5.89858	−	0.922521i	0.248155	−	0.0388108i
$566$	14.4718	−	25.0659i	0.608295	−	1.05360i
$567$	9.58333	+	7.06195i	0.402462	+	0.296574i
$568$	−8.77308	−	15.1954i	−0.368110	−	0.637586i
$569$	8.02333	+	9.94736i	0.336355	+	0.417015i	0.918095	−	0.396360i	$-0.129727\pi$
$569$	8.02333	+	9.94736i	0.336355	+	0.417015i	−0.581740	+	0.813375i	$0.697628\pi$
$570$	−1.70198	−	3.59280i	−0.0712881	−	0.150486i
$571$	−5.50808	+	25.4281i	−0.230506	+	1.06413i	0.704555	+	0.709649i	$0.251147\pi$
$571$	−5.50808	+	25.4281i	−0.230506	+	1.06413i	−0.935061	+	0.354486i	$0.884656\pi$
$572$	12.5147	−	5.68861i	0.523264	−	0.237853i
$573$	1.93298	+	7.61853i	0.0807514	+	0.318269i
$574$	1.26198	−	9.23930i	0.0526738	−	0.385641i
$575$	−0.131821	+	2.26327i	−0.00549730	+	0.0943849i
$576$	19.6743	+	14.2790i	0.819761	+	0.594958i
$577$	24.3521	+	12.2301i	1.01379	+	0.509144i	0.876508	−	0.481388i	$-0.159867\pi$
$577$	24.3521	+	12.2301i	1.01379	+	0.509144i	0.137282	+	0.990532i	$0.456163\pi$
$578$	1.86959	+	3.90991i	0.0777646	+	0.162631i
$579$	18.1417	+	19.3693i	0.753945	+	0.804962i
$580$	6.89571	+	7.90161i	0.286329	+	0.328096i
$581$	−0.418506	−	21.5781i	−0.0173626	−	0.895209i
$582$	−18.0923	+	31.0761i	−0.749952	+	1.28815i
$583$	−34.2789	+	24.5011i	−1.41969	+	1.01473i
$584$	24.0123	+	2.80663i	0.993634	+	0.116139i
$585$	−7.62193	+	17.3232i	−0.315128	+	0.716224i
$586$	6.60969	−	15.3230i	0.273044	−	0.632987i
$587$	−32.4040	−	10.3899i	−1.33746	−	0.428839i	−0.451362	−	0.892341i	$-0.649062\pi$
$587$	−32.4040	−	10.3899i	−1.33746	−	0.428839i	−0.886096	+	0.463502i	$0.846593\pi$
$588$	−6.98511	+	2.21179i	−0.288061	+	0.0912126i
$589$	−1.78019	+	3.72296i	−0.0733516	+	0.153402i
$590$	5.87647	−	4.55461i	0.241930	−	0.187510i
$591$	12.9762	−	0.456425i	0.533770	−	0.0187748i
$592$	0.291324	−	0.333820i	0.0119733	−	0.0137199i
$593$	30.1412	+	25.2915i	1.23775	+	1.03860i	0.997696	+	0.0678372i	$0.0216098\pi$
$593$	30.1412	+	25.2915i	1.23775	+	1.03860i	0.240055	+	0.970759i	$0.422835\pi$
$594$	−29.5871	−	4.95759i	−1.21397	−	0.203412i
$595$	7.14529	−	5.99561i	0.292928	−	0.245796i
$596$	−0.360207	+	18.5722i	−0.0147546	+	0.760746i
$597$	9.89697	+	6.02191i	0.405056	+	0.246460i
$598$	−3.60143	+	5.71405i	−0.147273	+	0.233665i
$599$	3.55900	−	3.49064i	0.145417	−	0.142624i	−0.623868	−	0.781530i	$-0.714440\pi$
$599$	3.55900	−	3.49064i	0.145417	−	0.142624i	0.769285	+	0.638906i	$0.220613\pi$
$600$	−0.0992001	−	6.29111i	−0.00404983	−	0.256834i
$601$	17.5104	+	27.7822i	0.714264	+	1.13326i	0.985324	+	0.170695i	$0.0546013\pi$
$601$	17.5104	+	27.7822i	0.714264	+	1.13326i	−0.271059	+	0.962563i	$0.587374\pi$
$602$	10.6230	+	2.51769i	0.432960	+	0.102614i
$603$	−1.41131	+	2.63282i	−0.0574729	+	0.107217i
$604$	−5.17639	+	17.2904i	−0.210624	+	0.703535i
$605$	−8.23851	+	31.9838i	−0.334943	+	1.30033i
$606$	−15.1586	+	1.71610i	−0.615775	+	0.0697117i
$607$	7.69277	+	19.9248i	0.312240	+	0.808721i	0.996813	+	0.0797769i	$0.0254208\pi$
$607$	7.69277	+	19.9248i	0.312240	+	0.808721i	−0.684573	+	0.728944i	$0.740011\pi$
$608$	−1.63873	−	4.24442i	−0.0664593	−	0.172134i
$609$	−9.07261	−	12.2793i	−0.367641	−	0.497583i
$610$	−5.63267	+	21.8674i	−0.228060	+	0.885384i
$611$	0.771438	−	2.57678i	0.0312090	−	0.104245i
$612$	8.29000	+	2.72453i	0.335104	+	0.110133i
$613$	−30.5194	−	7.23323i	−1.23267	−	0.292147i	−0.437879	−	0.899034i	$-0.644270\pi$
$613$	−30.5194	−	7.23323i	−1.23267	−	0.292147i	−0.794788	+	0.606887i	$0.792418\pi$
$614$	−1.67487	−	2.65736i	−0.0675922	−	0.107242i
$615$	19.0707	+	10.6132i	0.769007	+	0.427964i
$616$	−15.2963	+	15.0025i	−0.616305	+	0.604468i
$617$	13.9499	−	22.1330i	0.561600	−	0.891040i	−0.438370	−	0.898795i	$-0.644444\pi$
$617$	13.9499	−	22.1330i	0.561600	−	0.891040i	0.999970	+	0.00775514i	$0.00246856\pi$
$618$	0.271848	−	11.8081i	0.0109353	−	0.474991i
$619$	0.683360	−	35.2339i	0.0274666	−	1.41617i	−0.692128	−	0.721775i	$-0.743327\pi$
$619$	0.683360	−	35.2339i	0.0274666	−	1.41617i	0.719595	−	0.694394i	$-0.244328\pi$
$620$	4.62664	−	3.88221i	0.185810	−	0.155913i
$621$	−9.09625	+	4.01596i	−0.365020	+	0.161155i
$622$	−13.8816	−	11.6481i	−0.556603	−	0.467045i
$623$	−9.55026	+	10.9434i	−0.382623	+	0.438437i
$624$	4.56630	−	8.59320i	0.182798	−	0.344003i
$625$	13.9684	−	10.8263i	0.558735	−	0.433052i
$626$	−5.67859	+	11.8758i	−0.226962	+	0.474651i
$627$	7.26211	+	6.63818i	0.290021	+	0.265104i
$628$	−1.61782	−	0.518734i	−0.0645581	−	0.0206997i
$629$	0.364218	−	0.844353i	0.0145223	−	0.0336666i
$630$	0.553812	−	8.45227i	0.0220644	−	0.336747i
$631$	45.0634	+	5.26716i	1.79395	+	0.209682i	0.946832	−	0.321729i	$-0.104264\pi$
$631$	45.0634	+	5.26716i	1.79395	+	0.209682i	0.847114	+	0.531412i	$0.178338\pi$
$632$	21.7840	−	15.5703i	0.866522	−	0.619353i
$633$	−15.7990	−	27.5953i	−0.627955	−	1.09681i
$634$	0.0689538	+	3.55524i	0.00273851	+	0.141197i
$635$	17.6805	+	20.2596i	0.701630	+	0.803979i
$636$	3.23074	−	10.6507i	0.128107	−	0.422328i
$637$	7.31535	+	15.2988i	0.289845	+	0.606159i
$638$	34.3825	+	17.2675i	1.36121	+	0.683628i
$639$	−17.1250	+	1.20620i	−0.677454	+	0.0477166i
$640$	0.0446324	−	0.766308i	0.00176425	−	0.0302910i
$641$	2.50841	−	18.3648i	0.0990762	−	0.725366i	−0.872496	−	0.488622i	$-0.837500\pi$
$641$	2.50841	−	18.3648i	0.0990762	−	0.725366i	0.971572	−	0.236744i	$-0.0760804\pi$
$642$	−32.2917	−	9.11530i	−1.27445	−	0.359752i
$643$	6.30555	−	2.86623i	0.248667	−	0.113033i	−0.285600	−	0.958349i	$-0.592193\pi$
$643$	6.30555	−	2.86623i	0.248667	−	0.113033i	0.534267	+	0.845316i	$0.320588\pi$
$644$	−0.431718	+	1.99303i	−0.0170121	+	0.0785365i
$645$	−14.5284	+	21.0191i	−0.572055	+	0.827627i
$646$	2.66347	+	3.30218i	0.104793	+	0.129923i
$647$	1.14109	+	1.97642i	0.0448607	+	0.0777010i	0.887584	−	0.460646i	$-0.152382\pi$
$647$	1.14109	+	1.97642i	0.0448607	+	0.0777010i	−0.842723	+	0.538347i	$0.819049\pi$
$648$	24.3524	−	12.9800i	0.956653	−	0.509904i
$649$	−9.20011	+	15.9351i	−0.361136	+	0.625506i
$650$	−4.13148	+	0.646152i	−0.162050	+	0.0253442i
$651$	−7.17158	+	5.08675i	−0.281076	+	0.199366i
$652$	−14.6941	+	4.71147i	−0.575465	+	0.184515i
$653$	−3.90651	+	40.1625i	−0.152874	+	1.57168i	0.534369	+	0.845251i	$0.320549\pi$
$653$	−3.90651	+	40.1625i	−0.152874	+	1.57168i	−0.687243	+	0.726428i	$0.741179\pi$
$654$	14.0808	−	29.1753i	0.550604	−	1.14084i
$655$	−11.5284	+	4.70986i	−0.450451	+	0.184029i
$656$	−9.37569	−	6.16649i	−0.366059	−	0.240761i
$657$	12.7571	−	19.9189i	0.497702	−	0.777109i
$658$	0.0699968	+	1.20180i	0.00272876	+	0.0468510i
$659$	−11.7249	−	0.911329i	−0.456736	−	0.0355004i	−0.152936	−	0.988236i	$-0.548873\pi$
$659$	−11.7249	−	0.911329i	−0.456736	−	0.0355004i	−0.303800	+	0.952736i	$0.598256\pi$
$660$	−5.65550	−	13.2427i	−0.220140	−	0.515473i
$661$	−1.11830	+	3.26836i	−0.0434969	+	0.127124i	−0.965759	−	0.259440i	$-0.916462\pi$
$661$	−1.11830	+	3.26836i	−0.0434969	+	0.127124i	0.922262	+	0.386565i	$0.126338\pi$
$662$	6.93770	+	3.82806i	0.269641	+	0.148782i
$663$	3.57916	−	19.8768i	0.139003	−	0.771950i
$664$	−45.5457	−	20.7031i	−1.76752	−	0.803435i
$665$	−1.65892	+	2.22831i	−0.0643301	+	0.0864103i
$666$	−0.325181	−	0.769143i	−0.0126005	−	0.0298037i
$667$	12.6663	−	1.48047i	0.490439	−	0.0573241i
$668$	−10.0596	+	9.12857i	−0.389216	+	0.353195i
$669$	14.5088	−	22.8359i	0.560944	−	0.882885i
$670$	2.11915	−	0.164714i	0.0818700	−	0.00636344i
$671$	−7.56300	−	55.3709i	−0.291966	−	2.13757i
$672$	1.34670	−	9.59988i	0.0519500	−	0.370323i
$673$	4.84682	+	0.951885i	0.186831	+	0.0366925i	0.285253	−	0.958452i	$-0.407922\pi$
$673$	4.84682	+	0.951885i	0.186831	+	0.0366925i	−0.0984214	+	0.995145i	$0.531379\pi$
$674$	−33.8488	+	12.3200i	−1.30381	+	0.474547i
$675$	−5.57623	−	2.60825i	−0.214629	−	0.100392i
$676$	−1.94469	−	0.707810i	−0.0747958	−	0.0272235i
$677$	−35.6784	−	21.5320i	−1.37123	−	0.827544i	−0.376148	−	0.926560i	$-0.622752\pi$
$677$	−35.6784	−	21.5320i	−1.37123	−	0.827544i	−0.995086	+	0.0990158i	$0.968431\pi$
$678$	−2.10343	+	5.38977i	−0.0807816	+	0.206993i
$679$	25.1085	+	0.974324i	0.963576	+	0.0373911i
$680$	−5.39353	−	20.9390i	−0.206832	−	0.802972i
$681$	−14.7876	+	18.1984i	−0.566664	+	0.697364i
$682$	10.3264	−	19.6041i	0.395417	−	0.750680i
$683$	−6.95595	+	7.37288i	−0.266162	+	0.282115i	−0.846646	−	0.532156i	$-0.821382\pi$
$683$	−6.95595	+	7.37288i	−0.266162	+	0.282115i	0.580484	+	0.814272i	$0.302863\pi$
$684$	−2.58960	−	0.220181i	−0.0990157	−	0.00841884i
$685$	−35.4942	+	8.41229i	−1.35616	+	0.321417i
$686$	−12.6424	−	12.3996i	−0.482688	−	0.473417i
$687$	−31.9154	−	7.68640i	−1.21765	−	0.293254i
$688$	8.24809	−	10.2260i	0.314456	−	0.389864i
$689$	−25.4503	−	3.98035i	−0.969579	−	0.151639i
$690$	5.89703	+	3.90924i	0.224496	+	0.148822i
$691$	44.2683	−	12.3229i	1.68405	−	0.468786i	0.711729	−	0.702454i	$-0.247913\pi$
$691$	44.2683	−	12.3229i	1.68405	−	0.468786i	0.972316	+	0.233668i	$0.0750730\pi$
$692$	0.0577532	+	0.0612148i	0.00219545	+	0.00232704i
$693$	6.64244	+	19.8828i	0.252325	+	0.755284i
$694$	8.91815	+	29.7887i	0.338528	+	1.13076i
$695$	18.8323	−	0.730780i	0.714351	−	0.0277201i
$696$	−34.7530	+	6.69450i	−1.31731	+	0.253754i
$697$	−22.4373	−	6.24584i	−0.849872	−	0.236578i
$698$	4.58602	+	8.70635i	0.173583	+	0.329540i
$699$	−8.96303	−	1.79406i	−0.339013	−	0.0678574i
$700$	−1.10542	+	0.609947i	−0.0417811	+	0.0230538i
$701$	5.30514	+	30.0869i	0.200372	+	1.13637i	0.904557	+	0.426352i	$0.140201\pi$
$701$	5.30514	+	30.0869i	0.200372	+	1.13637i	−0.704185	+	0.710016i	$0.748688\pi$
$702$	−10.7916	−	14.8297i	−0.407302	−	0.559709i
$703$	−0.0475575	+	0.269712i	−0.00179366	+	0.0101724i
$704$	13.8586	+	40.5034i	0.522317	+	1.52653i
$705$	−2.67986	−	0.869989i	−0.100929	−	0.0327657i
$706$	−1.12319	−	0.458874i	−0.0422719	−	0.0172700i
$707$	6.02944	+	8.79114i	0.226760	+	0.330625i
$708$	−0.640302	−	4.81805i	−0.0240640	−	0.181074i
$709$	8.71914	+	40.2520i	0.327454	+	1.51170i	0.783303	+	0.621640i	$0.213533\pi$
$709$	8.71914	+	40.2520i	0.327454	+	1.51170i	−0.455849	+	0.890057i	$0.650664\pi$
$710$	7.29451	+	9.79823i	0.273758	+	0.367721i
$711$	−4.36211	−	25.8327i	−0.163592	−	0.968803i
$712$	13.3360	+	30.9164i	0.499789	+	1.15864i
$713$	−0.710987	−	7.30958i	−0.0266267	−	0.273746i
$714$	1.53734	+	8.90740i	0.0575334	+	0.333351i
$715$	−28.5340	+	17.2204i	−1.06711	+	0.644006i
$716$	−15.2855	+	3.00197i	−0.571245	+	0.112189i
$717$	0.705479	+	12.9194i	0.0263466	+	0.482483i
$718$	12.6441	−	18.4355i	0.471873	−	0.688007i
$719$	38.2558	−	25.1612i	1.42670	−	0.938355i	0.427285	−	0.904117i	$-0.359470\pi$
$719$	38.2558	−	25.1612i	1.42670	−	0.938355i	0.999414	−	0.0342379i	$-0.0109004\pi$
$720$	−8.88887	−	4.98909i	−0.331269	−	0.185932i
$721$	−7.37552	+	3.70412i	−0.274679	+	0.137949i
$722$	15.4131	+	11.9461i	0.573618	+	0.444587i
$723$	−16.5454	+	7.44853i	−0.615329	+	0.277014i
$724$	−9.24117	−	6.60519i	−0.343446	−	0.245480i
$725$	5.84680	+	5.30569i	0.217145	+	0.197048i
$726$	−22.7691	−	22.4943i	−0.845039	−	0.834841i
$727$	−5.89569	+	15.2702i	−0.218659	+	0.566342i	−0.998198	−	0.0600129i	$-0.980886\pi$
$727$	−5.89569	+	15.2702i	−0.218659	+	0.566342i	0.779538	+	0.626354i	$0.215454\pi$
$728$	−13.0987			−0.485471
$729$	−0.983237	−	26.9821i	−0.0364162	−	0.999337i
$730$	−16.8308			−0.622934
$731$	9.82096	−	25.4369i	0.363241	−	0.940819i
$732$	10.5015	+	10.3748i	0.388147	+	0.383462i
$733$	−27.4548	−	24.9139i	−1.01407	−	0.920217i	−0.0172435	−	0.999851i	$-0.505489\pi$
$733$	−27.4548	−	24.9139i	−1.01407	−	0.920217i	−0.996824	+	0.0796340i	$0.974625\pi$
$734$	21.2171	+	15.1651i	0.783139	+	0.559754i
$735$	16.1975	−	7.29193i	0.597454	−	0.268967i
$736$	6.39985	+	4.96026i	0.235902	+	0.182838i
$737$	−4.70088	+	2.36087i	−0.173159	+	0.0869637i
$738$	−18.1869	+	10.7967i	−0.669467	+	0.397432i
$739$	0.594987	−	0.391329i	0.0218869	−	0.0143953i	−0.538518	−	0.842614i	$-0.681016\pi$
$739$	0.594987	−	0.391329i	0.0218869	−	0.0143953i	0.560405	+	0.828219i	$0.310645\pi$
$740$	0.226712	−	0.330554i	0.00833409	−	0.0121514i
$741$	0.327975	+	6.00617i	0.0120484	+	0.220642i
$742$	11.3129	−	2.22177i	0.415308	−	0.0815638i
$743$	−5.85373	+	3.53275i	−0.214753	+	0.129604i	−0.619996	−	0.784605i	$-0.712866\pi$
$743$	−5.85373	+	3.53275i	−0.214753	+	0.129604i	0.405243	+	0.914209i	$0.367187\pi$
$744$	3.46650	+	20.0851i	0.127088	+	0.736354i
$745$	−4.35982	−	44.8229i	−0.159732	−	1.64218i
$746$	−13.1294	−	30.4374i	−0.480702	−	1.11439i
$747$	−37.7253	+	31.1919i	−1.38030	+	1.14125i
$748$	9.17630	+	12.3259i	0.335519	+	0.450680i
$749$	4.96371	+	22.9151i	0.181370	+	0.837298i
$750$	3.01243	+	22.6675i	0.109998	+	0.827699i
$751$	−8.90633	−	12.9857i	−0.324997	−	0.473857i	0.627409	−	0.778690i	$-0.284115\pi$
$751$	−8.90633	−	12.9857i	−0.324997	−	0.473857i	−0.952406	+	0.304833i	$0.901399\pi$
$752$	1.34109	+	0.547897i	0.0489046	+	0.0199797i
$753$	−17.3642	−	5.63713i	−0.632788	−	0.205428i
$754$	7.61490	+	22.2554i	0.277318	+	0.810494i
$755$	7.59826	−	43.0918i	0.276529	−	1.56827i
$756$	−4.59304	−	3.09297i	−0.167047	−	0.112490i
$757$	0.606573	+	3.44005i	0.0220463	+	0.125031i	0.993845	−	0.110783i	$-0.0353357\pi$
$757$	0.606573	+	3.44005i	0.0220463	+	0.125031i	−0.971798	+	0.235813i	$0.924225\pi$
$758$	−5.81363	+	3.20783i	−0.211161	+	0.116514i
$759$	−17.1693	−	3.43663i	−0.623206	−	0.124742i
$760$	3.00124	+	5.69771i	0.108866	+	0.206678i
$761$	25.7634	+	7.17173i	0.933922	+	0.259975i	0.701524	−	0.712646i	$-0.252503\pi$
$761$	25.7634	+	7.17173i	0.933922	+	0.259975i	0.232398	+	0.972621i	$0.425343\pi$
$762$	−25.5878	+	4.92899i	−0.926947	+	0.178559i
$763$	−22.6202	+	0.877766i	−0.818906	+	0.0317773i
$764$	−1.04858	−	3.50252i	−0.0379365	−	0.126717i
$765$	−20.7290	−	4.22738i	−0.749460	−	0.152841i
$766$	−18.5020	−	19.6109i	−0.668503	−	0.708572i
$767$	−10.8371	+	3.01673i	−0.391307	+	0.108928i
$768$	−22.7765	−	15.0989i	−0.821876	−	0.544835i
$769$	−23.3587	−	3.65323i	−0.842335	−	0.131739i	−0.281392	−	0.959593i	$-0.590796\pi$
$769$	−23.3587	−	3.65323i	−0.842335	−	0.131739i	−0.560943	+	0.827854i	$0.689562\pi$
$770$	9.36450	−	11.6102i	0.337473	−	0.418401i
$771$	−24.7280	−	5.95541i	−0.890556	−	0.214479i
$772$	−8.81320	−	8.64392i	−0.317194	−	0.311102i
$773$	−8.36437	+	1.98239i	−0.300846	+	0.0713017i	−0.378266	−	0.925697i	$-0.623480\pi$
$773$	−8.36437	+	1.98239i	−0.300846	+	0.0713017i	0.0774208	+	0.996999i	$0.475332\pi$
$774$	−10.5195	−	22.4158i	−0.378114	−	0.805719i
$775$	3.12023	−	3.30725i	0.112082	−	0.118800i
$776$	27.1464	−	51.5362i	0.974500	−	1.85004i
$777$	−0.367985	+	0.452860i	−0.0132014	+	0.0162463i
$778$	2.87166	+	11.1485i	0.102954	+	0.399692i
$779$	6.93137	+	0.268969i	0.248342	+	0.00963680i
$780$	3.20058	−	8.20109i	0.114599	−	0.293646i
$781$	−25.8830	−	15.6205i	−0.926166	−	0.558944i
$782$	−7.09480	−	2.58230i	−0.253709	−	0.0923427i
$783$	−9.00185	+	33.4374i	−0.321700	+	1.19496i
$784$	−8.58253	+	3.12378i	−0.306519	+	0.111564i
$785$	4.04169	+	0.793762i	0.144254	+	0.0283306i
$786$	1.67656	−	11.9513i	0.0598009	−	0.426288i
$787$	−3.16350	−	23.1609i	−0.112767	−	0.825598i	−0.957095	−	0.289773i	$-0.906420\pi$
$787$	−3.16350	−	23.1609i	−0.112767	−	0.825598i	0.844329	−	0.535825i	$-0.179999\pi$
$788$	−6.02157	+	0.468033i	−0.214509	+	0.0166730i
$789$	−10.4960	+	16.5200i	−0.373669	+	0.588128i
$790$	−13.8047	+	12.5271i	−0.491150	+	0.445695i
$791$	4.01556	−	0.469352i	0.142777	−	0.0166882i
$792$	48.2243	+	5.99138i	1.71358	+	0.212894i
$793$	20.4025	−	27.4053i	0.724515	−	0.973192i
$794$	35.2812	+	16.0373i	1.25208	+	0.569142i
$795$	−4.78189	+	26.5561i	−0.169596	+	0.941846i
$796$	−4.71828	−	2.60344i	−0.167235	−	0.0922765i
$797$	−8.98350	+	26.2553i	−0.318212	+	0.930009i	0.664889	+	0.746943i	$0.268479\pi$
$797$	−8.98350	+	26.2553i	−0.318212	+	0.930009i	−0.983100	+	0.183067i	$0.941398\pi$
$798$	−1.05732	−	2.47580i	−0.0374289	−	0.0876423i
$799$	2.99766	+	0.232997i	0.106050	+	0.00824283i
$800$	0.291481	+	5.00454i	0.0103054	+	0.176937i
$801$	32.9084	+	1.51605i	1.16276	+	0.0535669i
$802$	−32.0306	−	21.0669i	−1.13104	−	0.743896i
$803$	38.5598	−	15.7534i	1.36075	−	0.555926i
$804$	0.603968	−	1.25141i	0.0213003	−	0.0441339i
$805$	0.478625	−	4.92070i	0.0168693	−	0.173432i
$806$	12.8994	−	4.13602i	0.454361	−	0.145685i
$807$	21.5361	−	15.2754i	0.758107	−	0.537720i
$808$	24.4148	−	3.81841i	0.858910	−	0.134331i
$809$	11.0590	−	19.1547i	0.388812	−	0.673443i	−0.603478	−	0.797380i	$-0.706219\pi$
$809$	11.0590	−	19.1547i	0.388812	−	0.673443i	0.992290	+	0.123937i	$0.0395521\pi$
$810$	−15.7901	+	10.9436i	−0.554806	+	0.384519i
$811$	5.31835	+	9.21165i	0.186752	+	0.323465i	0.944166	−	0.329471i	$-0.106870\pi$
$811$	5.31835	+	9.21165i	0.186752	+	0.323465i	−0.757413	+	0.652936i	$0.773537\pi$
$812$	4.45858	+	5.52777i	0.156465	+	0.193987i
$813$	1.61723	−	2.33975i	0.0567189	−	0.0820587i
$814$	0.311313	−	1.43718i	0.0109115	−	0.0503731i
$815$	34.0571	−	15.4808i	1.19297	−	0.542270i
$816$	10.4686	+	2.95506i	0.366473	+	0.103448i
$817$	−1.09902	+	8.04623i	−0.0384498	+	0.281502i
$818$	0.280302	−	4.81260i	0.00980053	−	0.168269i
$819$	−5.61232	+	11.5218i	−0.196110	+	0.402603i
$820$	−9.07226	−	4.55626i	−0.316817	−	0.159111i
$821$	−19.7333	−	41.2686i	−0.688696	−	1.44029i	−0.887764	−	0.460299i	$-0.847742\pi$
$821$	−19.7333	−	41.2686i	−0.688696	−	1.44029i	0.199068	−	0.979986i	$-0.436209\pi$
$822$	10.2611	−	33.8275i	0.357896	−	1.17987i
$823$	−0.0418960	−	0.0480075i	−0.00146040	−	0.00167344i	0.752705	−	0.658358i	$-0.228749\pi$
$823$	−0.0418960	−	0.0480075i	−0.00146040	−	0.00167344i	−0.754166	+	0.656684i	$0.771958\pi$
$824$	0.371005	+	19.1289i	0.0129246	+	0.666388i
$825$	−5.38625	−	9.40786i	−0.187525	−	0.327540i
$826$	4.09597	−	2.92762i	0.142517	−	0.101865i
$827$	−31.6376	−	3.69791i	−1.10015	−	0.128589i	−0.453411	−	0.891302i	$-0.649793\pi$
$827$	−31.6376	−	3.69791i	−1.10015	−	0.128589i	−0.646738	+	0.762713i	$0.723867\pi$
$828$	4.14819	−	2.04577i	0.144160	−	0.0710955i
$829$	0.965750	−	2.23886i	0.0335419	−	0.0777588i	−0.900622	−	0.434604i	$-0.856888\pi$
$829$	0.965750	−	2.23886i	0.0335419	−	0.0777588i	0.934164	+	0.356845i	$0.116148\pi$
$830$	33.1671	+	10.6346i	1.15125	+	0.369132i
$831$	34.3127	+	31.3647i	1.19029	+	1.08803i
$832$	−11.2901	+	23.6112i	−0.391413	+	0.818570i
$833$	−14.9825	+	11.6124i	−0.519114	+	0.402344i
$834$	−8.57023	+	16.1281i	−0.296763	+	0.558470i
$835$	21.6540	−	24.8128i	0.749368	−	0.858681i
$836$	−3.50591	−	2.94181i	−0.121255	−	0.101745i
$837$	19.1523	+	5.55655i	0.662000	+	0.192062i
$838$	−8.84845	+	7.42473i	−0.305665	+	0.256483i
$839$	−0.0192785	+	0.993994i	−0.000665568	+	0.0343165i	−0.999998	−	0.00223023i	$-0.999290\pi$
$839$	−0.0192785	+	0.993994i	−0.000665568	+	0.0343165i	0.999332	+	0.0365467i	$0.0116358\pi$
$840$	−0.315800	+	13.7172i	−0.0108961	+	0.473289i
$841$	8.21719	−	13.0375i	0.283351	−	0.449568i
$842$	−12.7494	+	12.5046i	−0.439374	+	0.430935i
$843$	16.4726	+	9.16725i	0.567346	+	0.315737i
$844$	7.88668	+	12.5131i	0.271471	+	0.430718i
$845$	4.88200	+	1.15706i	0.167946	+	0.0398039i
$846$	2.03524	−	1.82015i	0.0699731	−	0.0625780i
$847$	−6.41449	+	21.4259i	−0.220404	+	0.736202i
$848$	3.46074	−	13.4354i	0.118842	−	0.461374i
$849$	27.2596	+	36.8945i	0.935547	+	1.26622i
$850$	−1.68362	−	4.36068i	−0.0577476	−	0.149570i
$851$	−0.175550	−	0.454687i	−0.00601779	−	0.0155865i
$852$	7.93489	−	0.898306i	0.271845	−	0.0307755i
$853$	−11.8350	+	45.9461i	−0.405221	+	1.57316i	0.362250	+	0.932081i	$0.382009\pi$
$853$	−11.8350	+	45.9461i	−0.405221	+	1.57316i	−0.767471	+	0.641084i	$0.778485\pi$
$854$	−4.38559	+	14.6489i	−0.150072	+	0.501275i
$855$	6.29768	−	0.198657i	0.215376	−	0.00679392i
$856$	52.8871	+	12.5345i	1.80764	+	0.428419i
$857$	14.7714	+	23.4365i	0.504583	+	0.800575i	0.997585	−	0.0694526i	$-0.0221253\pi$
$857$	14.7714	+	23.4365i	0.504583	+	0.800575i	−0.493002	+	0.870028i	$0.664101\pi$
$858$	−0.509207	−	32.2931i	−0.0173840	−	1.10247i
$859$	10.4663	−	10.2653i	0.357107	−	0.350248i	−0.499411	−	0.866365i	$-0.666450\pi$
$859$	10.4663	−	10.2653i	0.357107	−	0.350248i	0.856518	+	0.516117i	$0.172623\pi$
$860$	6.33740	−	10.0550i	0.216103	−	0.342872i
$861$	12.6257	+	7.68226i	0.430284	+	0.261811i
$862$	0.108262	−	5.58194i	0.00368741	−	0.190122i
$863$	−12.8467	+	10.7796i	−0.437305	+	0.366943i	−0.834700	−	0.550705i	$-0.814359\pi$
$863$	−12.8467	+	10.7796i	−0.437305	+	0.366943i	0.397394	+	0.917648i	$0.369914\pi$
$864$	−18.9467	+	11.1551i	−0.644579	+	0.379503i
$865$	−0.156298	−	0.131150i	−0.00531429	−	0.00445922i
$866$	−8.78238	+	10.0635i	−0.298437	+	0.341971i
$867$	−6.86454	+	0.241453i	−0.233132	+	0.00820019i
$868$	3.23260	−	2.50546i	0.109722	−	0.0850407i
$869$	19.9018	−	41.6211i	0.675123	−	1.41190i
$870$	23.4898	−	7.43791i	0.796380	−	0.252169i
$871$	−3.06244	−	0.981933i	−0.103767	−	0.0332715i
$872$	−20.7847	+	48.1844i	−0.703860	+	1.63173i
$873$	−33.7005	−	45.9596i	−1.14059	−	1.55550i
$874$	2.23345	+	0.261053i	0.0755477	+	0.00883026i
$875$	12.9996	−	9.29153i	0.439465	−	0.314111i
$876$	−5.53591	+	9.50870i	−0.187041	+	0.321269i
$877$	0.287083	+	14.8019i	0.00969410	+	0.499825i	0.972921	+	0.231137i	$0.0742446\pi$
$877$	0.287083	+	14.8019i	0.00969410	+	0.499825i	−0.963227	+	0.268689i	$0.913410\pi$
$878$	27.8669	+	31.9319i	0.940462	+	1.07765i
$879$	18.0801	+	19.3035i	0.609826	+	0.651091i
$880$	−7.74339	−	16.1939i	−0.261030	−	0.545897i
$881$	−17.1002	−	8.58806i	−0.576121	−	0.289339i	0.136782	−	0.990601i	$-0.456324\pi$
$881$	−17.1002	−	8.58806i	−0.576121	−	0.289339i	−0.712904	+	0.701262i	$0.752620\pi$
$882$	−1.79069	+	17.1206i	−0.0602956	+	0.576479i
$883$	−0.488507	+	8.38734i	−0.0164396	+	0.282256i	0.980063	+	0.198689i	$0.0636684\pi$
$883$	−0.488507	+	8.38734i	−0.0164396	+	0.282256i	−0.996502	+	0.0835673i	$0.973369\pi$
$884$	−1.27138	+	9.30813i	−0.0427611	+	0.313066i
$885$	2.89789	+	11.4216i	0.0974117	+	0.383932i
$886$	12.8729	−	5.85147i	0.432475	−	0.196584i
$887$	−2.42241	+	11.1831i	−0.0813366	+	0.375492i	−0.999800	−	0.0200151i	$-0.993629\pi$
$887$	−2.42241	+	11.1831i	−0.0813366	+	0.375492i	0.918463	+	0.395507i	$0.129431\pi$
$888$	0.579098	+	1.22245i	0.0194333	+	0.0410227i
$889$	11.4317	+	14.1731i	0.383408	+	0.475352i
$890$	−11.7203	−	20.3001i	−0.392865	−	0.680462i
$891$	25.9324	−	39.8515i	0.868769	−	1.33507i
$892$	−6.29247	+	10.8989i	−0.210688	+	0.364922i
$893$	−0.884733	+	0.138370i	−0.0296065	+	0.00463037i
$894$	39.6642	+	18.2034i	1.32657	+	0.608813i
$895$	35.9623	−	11.5308i	1.20209	−	0.385434i
$896$	0.0503223	−	0.517359i	0.00168115	−	0.0172837i
$897$	−6.02269	−	8.84992i	−0.201092	−	0.295490i
$898$	−1.09840	+	0.448747i	−0.0366541	+	0.0149749i
$899$	−21.3684	−	14.0542i	−0.712677	−	0.468735i
$900$	2.64294	+	1.10219i	0.0880979	+	0.0367396i
$901$	−1.67427	−	28.7461i	−0.0557779	−	0.957670i
$902$	−37.1328	−	2.88619i	−1.23639	−	0.0960995i
$903$	−10.3827	+	13.8413i	−0.345515	+	0.460611i
$904$	3.03403	−	8.86728i	0.100910	−	0.294921i
$905$	24.1117	+	13.3043i	0.801499	+	0.442248i
$906$	32.3840	+	27.3741i	1.07589	+	0.909443i
$907$	−26.3912	−	11.9963i	−0.876304	−	0.398329i	−0.0754222	−	0.997152i	$-0.524030\pi$
$907$	−26.3912	−	11.9963i	−0.876304	−	0.398329i	−0.800882	+	0.598823i	$0.795635\pi$
$908$	6.51351	−	8.74916i	0.216158	−	0.290351i
$909$	7.10215	−	23.1116i	0.235563	−	0.766562i
$910$	9.05746	−	1.05867i	0.300252	−	0.0350944i
$911$	−26.6255	+	24.1614i	−0.882144	+	0.800503i	−0.980881	−	0.194611i	$-0.937656\pi$
$911$	−26.6255	+	24.1614i	−0.882144	+	0.800503i	0.0987369	+	0.995114i	$0.468520\pi$
$912$	−3.23678	−	0.137357i	−0.107181	−	0.00454833i
$913$	−85.9407	+	6.67984i	−2.84422	+	0.221070i
$914$	0.361148	+	2.64407i	0.0119457	+	0.0874581i
$915$	−28.2075	−	22.0266i	−0.932510	−	0.728177i
$916$	14.9840	+	2.94275i	0.495084	+	0.0972313i
$917$	−7.92447	+	2.88427i	−0.261689	+	0.0952470i
$918$	13.6474	−	15.2991i	0.450432	−	0.504944i
$919$	−27.7619	−	10.1045i	−0.915781	−	0.333317i	−0.159222	−	0.987243i	$-0.550899\pi$
$919$	−27.7619	−	10.1045i	−0.915781	−	0.333317i	−0.756559	+	0.653926i	$0.773121\pi$
$920$	−9.81226	−	5.92173i	−0.323500	−	0.195234i
$921$	4.92134	−	0.751414i	0.162164	−	0.0247599i
$922$	7.39813	+	0.287081i	0.243645	+	0.00945452i
$923$	−4.61023	−	17.8980i	−0.151747	−	0.589120i
$924$	−3.47913	−	9.10933i	−0.114455	−	0.299675i
$925$	0.140632	−	0.266983i	0.00462395	−	0.00877835i
$926$	−4.48414	+	4.75292i	−0.147358	+	0.156190i
$927$	16.9849	+	7.86971i	0.557859	+	0.258475i
$928$	27.4382	−	6.50297i	0.900702	−	0.213470i
$929$	23.2697	+	22.8227i	0.763453	+	0.748789i	0.973447	−	0.228914i	$-0.0735173\pi$
$929$	23.2697	+	22.8227i	0.763453	+	0.748789i	−0.209994	+	0.977703i	$0.567344\pi$
$930$	−4.02032	−	13.6082i	−0.131832	−	0.446230i
$931$	3.54439	−	4.39436i	0.116163	−	0.144019i
$932$	4.20086	+	0.657003i	0.137604	+	0.0215209i
$933$	25.7118	−	12.7964i	0.841767	−	0.418937i
$934$	14.9483	−	4.16115i	0.489124	−	0.136157i
$935$	−25.5656	−	27.0979i	−0.836083	−	0.886197i
$936$	18.4836	+	23.2592i	0.604155	+	0.760251i
$937$	5.64620	+	18.8596i	0.184453	+	0.616117i	0.999334	+	0.0364882i	$0.0116171\pi$
$937$	5.64620	+	18.8596i	0.184453	+	0.616117i	−0.814881	+	0.579628i	$0.803198\pi$
$938$	1.43827	−	0.0558115i	0.0469613	−	0.00182231i
$939$	−13.6607	−	15.7685i	−0.445801	−	0.514585i
$940$	1.26260	+	0.351467i	0.0411813	+	0.0114636i
$941$	−19.9720	−	37.9159i	−0.651069	−	1.23602i	−0.958673	−	0.284510i	$-0.908169\pi$
$941$	−19.9720	−	37.9159i	−0.651069	−	1.23602i	0.307604	−	0.951514i	$-0.400473\pi$
$942$	−2.63541	+	2.99783i	−0.0858662	+	0.0976746i
$943$	−10.8085	+	5.96390i	−0.351974	+	0.194211i
$944$	−1.05209	−	5.96668i	−0.0342425	−	0.194199i
$945$	11.9305	+	6.15511i	0.388099	+	0.200226i
$946$	7.57175	−	42.9415i	0.246179	−	1.39615i
$947$	−11.0925	−	32.4191i	−0.360458	−	1.05348i	−0.966195	−	0.257813i	$-0.916998\pi$
$947$	−11.0925	−	32.4191i	−0.360458	−	1.05348i	0.605737	−	0.795665i	$-0.292878\pi$
$948$	2.53672	+	11.9195i	0.0823887	+	0.387127i
$949$	23.5740	+	9.63103i	0.765244	+	0.312636i
$950$	0.787428	+	1.14810i	0.0255475	+	0.0372492i
$951$	−5.20938	−	2.15034i	−0.168926	−	0.0697294i
$952$	−3.09978	−	14.3102i	−0.100464	−	0.463796i
$953$	31.0716	+	41.7364i	1.00651	+	1.35198i	0.935044	+	0.354532i	$0.115360\pi$
$953$	31.0716	+	41.7364i	1.00651	+	1.35198i	0.0714648	+	0.997443i	$0.477233\pi$
$954$	−19.9087	−	16.9529i	−0.644569	−	0.548871i
$955$	3.51077	+	8.13888i	0.113606	+	0.263368i
$956$	−0.582658	−	5.99025i	−0.0188445	−	0.193738i
$957$	−46.8542	+	39.0267i	−1.51458	+	1.26155i
$958$	0.334266	−	0.201730i	0.0107996	−	0.00651761i
$959$	−24.2384	+	4.76027i	−0.782700	+	0.153717i
$960$	24.4539	+	12.3924i	0.789245	+	0.399963i
$961$	9.20295	−	13.4182i	0.296869	−	0.432846i
$962$	0.751115	−	0.494016i	0.0242169	−	0.0159277i
$963$	33.6856	−	41.1494i	1.08550	−	1.32602i
$964$	7.54241	−	3.78794i	0.242925	−	0.122001i
$965$	23.6549	+	18.3339i	0.761478	+	0.590190i
$966$	3.88764	+	2.80007i	0.125083	+	0.0900908i
$967$	31.5657	+	22.5618i	1.01508	+	0.725538i	0.961999	−	0.273052i	$-0.0880330\pi$
$967$	31.5657	+	22.5618i	1.01508	+	0.725538i	0.0530844	+	0.998590i	$0.483095\pi$
$968$	38.3944	+	34.8410i	1.23404	+	1.11983i
$969$	−6.48405	+	1.77966i	−0.208298	+	0.0571708i
$970$	−14.6059	+	37.8301i	−0.468966	+	1.21465i
$971$	−48.9782			−1.57179			−0.785893	−	0.618363i	$-0.787796\pi$
$971$	−48.9782			−1.57179			−0.785893	+	0.618363i	$0.787796\pi$
$972$	0.989085	+	12.5203i	0.0317249	+	0.401588i
$973$	12.7623			0.409140
$974$	−9.43650	+	24.4411i	−0.302365	+	0.783145i
$975$	1.67644	−	6.41202i	0.0536891	−	0.205349i
$976$	13.6271	+	12.3660i	0.436194	+	0.395825i
$977$	−11.5644	−	8.26575i	−0.369978	−	0.264445i	0.381271	−	0.924463i	$-0.375487\pi$
$977$	−11.5644	−	8.26575i	−0.369978	−	0.264445i	−0.751249	+	0.660019i	$0.770548\pi$
$978$	−3.64055	+	36.0704i	−0.116412	+	1.15340i
$979$	45.8522	+	35.5382i	1.46544	+	1.13580i
$980$	−7.38383	+	3.70830i	−0.235868	+	0.118457i
$981$	33.4780	+	38.9277i	1.06887	+	1.24287i
$982$	2.24017	−	1.47338i	0.0714865	−	0.0470174i
$983$	−26.4120	+	38.5097i	−0.842413	+	1.22827i	0.129183	+	0.991621i	$0.458765\pi$
$983$	−26.4120	+	38.5097i	−0.842413	+	1.22827i	−0.971596	+	0.236647i	$0.923951\pi$
$984$	28.6922	−	18.7225i	0.914672	−	0.596850i
$985$	14.3681	−	2.82181i	0.457806	−	0.0899102i
$986$	−22.5117	+	13.5859i	−0.716918	+	0.432662i
$987$	−1.79051	−	0.659053i	−0.0569925	−	0.0209779i
$988$	−0.270875	−	2.78484i	−0.00861770	−	0.0885977i
$989$	−5.72434	−	13.2705i	−0.182023	−	0.421978i
$990$	−33.8302	−	0.245312i	−1.07520	−	0.00779652i
$991$	−9.04003	−	12.1429i	−0.287166	−	0.385731i	0.635008	−	0.772505i	$-0.280997\pi$
$991$	−9.04003	−	12.1429i	−0.287166	−	0.385731i	−0.922174	+	0.386774i	$0.873589\pi$
$992$	−3.43790	−	15.8711i	−0.109154	−	0.503909i
$993$	−9.95381	+	7.65718i	−0.315875	+	0.242993i
$994$	4.67863	+	6.82161i	0.148397	+	0.216368i
$995$	12.0943	+	4.94107i	0.383415	+	0.156642i
$996$	16.9173	−	15.2402i	0.536046	−	0.482903i
$997$	9.90916	+	28.9606i	0.313826	+	0.917191i	0.984492	+	0.175432i	$0.0561321\pi$
$997$	9.90916	+	28.9606i	0.313826	+	0.917191i	−0.670666	+	0.741760i	$0.733991\pi$
$998$	−4.66623	+	26.4635i	−0.147707	+	0.837688i
$999$	1.32340	+	0.0143948i	0.0418706	+	0.000455431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.i.a.106.9	yes	1404
3.2	odd	2		729.2.i.a.559.18		1404
243.94	even	81	inner	243.2.i.a.94.9	✓	1404
243.149	odd	162		729.2.i.a.253.18		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.94.9	✓	1404	243.94	even	81	inner
243.2.i.a.106.9	yes	1404	1.1	even	1	trivial
729.2.i.a.253.18		1404	243.149	odd	162
729.2.i.a.559.18		1404	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.i (of order \(81\), degree \(54\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.393620 + 1.01950i) q^{2} +(-1.23216 - 1.21729i) q^{3} +(0.596640 + 0.541422i) q^{4} +(-1.58909 - 1.13581i) q^{5} +(1.72603 - 0.777038i) q^{6} +(-1.04545 - 0.810284i) q^{7} +(-2.74004 + 1.37610i) q^{8} +(0.0364234 + 2.99978i) q^{9} +(1.78346 - 1.17300i) q^{10} +(-2.98804 + 4.35667i) q^{11} +(-0.0760884 - 1.39340i) q^{12} +(-3.16922 + 0.622415i) q^{13} +(1.23760 - 0.746893i) q^{14} +(0.575397 + 3.33387i) q^{15} +(-0.168405 - 1.73135i) q^{16} +(-1.42997 - 3.31504i) q^{17} +(-3.07262 - 1.14364i) q^{18} +(0.642100 + 0.862491i) q^{19} +(-0.333160 - 1.53804i) q^{20} +(0.301809 + 2.27101i) q^{21} +(-3.26548 - 4.76119i) q^{22} +(-1.77146 - 0.723721i) q^{23} +(5.05128 + 1.63985i) q^{24} +(-0.383540 - 1.12094i) q^{25} +(0.612917 - 3.47602i) q^{26} +(3.60671 - 3.74054i) q^{27} +(-0.185051 - 1.04948i) q^{28} +(-5.83486 + 3.21954i) q^{29} +(-3.62538 - 0.725662i) q^{30} +(1.78860 + 3.39558i) q^{31} +(-4.07634 - 1.13473i) q^{32} +(8.98506 - 1.73080i) q^{33} +(3.94256 - 0.152989i) q^{34} +(0.740979 + 2.47504i) q^{35} +(-1.60242 + 1.80951i) q^{36} +(0.174788 + 0.185265i) q^{37} +(-1.13205 + 0.315129i) q^{38} +(4.66264 + 3.09094i) q^{39} +(5.91716 + 0.925427i) q^{40} +(4.05007 - 5.02129i) q^{41} +(-2.43410 - 0.586220i) q^{42} +(5.39199 + 5.28842i) q^{43} +(-4.14159 + 0.981574i) q^{44} +(3.34930 - 4.80828i) q^{45} +(1.43512 - 1.52114i) q^{46} +(-0.388126 + 0.736840i) q^{47} +(-1.90005 + 2.33830i) q^{48} +(-1.30969 - 5.08451i) q^{49} +(1.29377 + 0.0502041i) q^{50} +(-2.27341 + 5.82533i) q^{51} +(-2.22787 - 1.34453i) q^{52} +(7.49472 + 2.72786i) q^{53} +(2.39381 + 5.14940i) q^{54} +(9.69662 - 3.52928i) q^{55} +(3.97961 + 0.781570i) q^{56} +(0.258730 - 1.84434i) q^{57} +(-0.985607 - 7.21592i) q^{58} +(3.47251 - 0.269904i) q^{59} +(-1.46173 + 2.30066i) q^{60} +(-7.83383 + 7.10883i) q^{61} +(-4.16583 + 0.486916i) q^{62} +(2.39259 - 3.16563i) q^{63} +(4.83893 - 6.49981i) q^{64} +(5.74311 + 2.61056i) q^{65} +(-1.77215 + 9.84157i) q^{66} +(0.871831 + 0.481056i) q^{67} +(0.941660 - 2.75210i) q^{68} +(1.30174 + 3.04811i) q^{69} +(-2.81498 - 0.218797i) q^{70} +(0.332732 + 5.71279i) q^{71} +(-4.22780 - 8.16940i) q^{72} +(-6.58751 - 4.33267i) q^{73} +(-0.257678 + 0.105273i) q^{74} +(-0.891921 + 1.84805i) q^{75} +(-0.0838686 + 0.862244i) q^{76} +(6.65399 - 2.13352i) q^{77} +(-4.98653 + 3.53691i) q^{78} +(-8.62793 + 1.34938i) q^{79} +(-1.69888 + 2.94255i) q^{80} +(-8.99735 + 0.218524i) q^{81} +(3.52503 + 6.10553i) q^{82} +(10.2439 + 12.7004i) q^{83} +(-1.04950 + 1.51838i) q^{84} +(-1.49291 + 6.89206i) q^{85} +(-7.51395 + 3.41551i) q^{86} +(11.1086 + 3.13572i) q^{87} +(2.19214 - 16.0493i) q^{88} +(0.638494 - 10.9625i) q^{89} +(3.58370 + 5.30726i) q^{90} +(3.81759 + 1.91727i) q^{91} +(-0.665086 - 1.39091i) q^{92} +(1.92956 - 6.36113i) q^{93} +(-0.598435 - 0.685731i) q^{94} +(-0.0407271 - 2.09988i) q^{95} +(3.64141 + 6.36024i) q^{96} +(-15.4551 + 11.0467i) q^{97} +(5.69919 + 0.666139i) q^{98} +(-13.1779 - 8.80478i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) \) 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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