LMFDB - Embedded newform 225.2.h.a.46.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,2,Mod(46,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("225.46"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(225, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			46.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	225.46
Dual form			225.2.h.a.181.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{4} +(-1.80902 + 1.31433i) q^{5} -4.47214 q^{7} +(-2.42705 + 1.76336i) q^{8} +(-0.690983 - 2.12663i) q^{10} +(0.381966 - 1.17557i) q^{11} +(1.73607 + 5.34307i) q^{13} +(1.38197 - 4.25325i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(3.11803 - 2.26538i) q^{17} +(-1.00000 + 0.726543i) q^{19} -2.23607 q^{20} +(1.00000 + 0.726543i) q^{22} +(-1.38197 + 4.25325i) q^{23} +(1.54508 - 4.75528i) q^{25} -5.61803 q^{26} +(-3.61803 - 2.62866i) q^{28} +(5.35410 + 3.88998i) q^{29} +(-2.23607 + 1.62460i) q^{31} -5.00000 q^{32} +(1.19098 + 3.66547i) q^{34} +(8.09017 - 5.87785i) q^{35} +(-0.954915 - 2.93893i) q^{37} +(-0.381966 - 1.17557i) q^{38} +(2.07295 - 6.37988i) q^{40} +(1.11803 + 3.44095i) q^{41} +7.70820 q^{43} +(1.00000 - 0.726543i) q^{44} +(-3.61803 - 2.62866i) q^{46} +(-0.618034 - 0.449028i) q^{47} +13.0000 q^{49} +(4.04508 + 2.93893i) q^{50} +(-1.73607 + 5.34307i) q^{52} +(2.92705 + 2.12663i) q^{53} +(0.854102 + 2.62866i) q^{55} +(10.8541 - 7.88597i) q^{56} +(-5.35410 + 3.88998i) q^{58} +(1.23607 + 3.80423i) q^{59} +(0.500000 - 1.53884i) q^{61} +(-0.854102 - 2.62866i) q^{62} +(2.16312 - 6.65740i) q^{64} +(-10.1631 - 7.38394i) q^{65} +(-0.618034 + 0.449028i) q^{67} +3.85410 q^{68} +(3.09017 + 9.51057i) q^{70} +(-4.23607 - 3.07768i) q^{71} +(-2.50000 + 7.69421i) q^{73} +3.09017 q^{74} -1.23607 q^{76} +(-1.70820 + 5.25731i) q^{77} +(1.80902 + 1.31433i) q^{80} -3.61803 q^{82} +(10.0902 - 7.33094i) q^{83} +(-2.66312 + 8.19624i) q^{85} +(-2.38197 + 7.33094i) q^{86} +(1.14590 + 3.52671i) q^{88} +(-1.66312 + 5.11855i) q^{89} +(-7.76393 - 23.8949i) q^{91} +(-3.61803 + 2.62866i) q^{92} +(0.618034 - 0.449028i) q^{94} +(0.854102 - 2.62866i) q^{95} +(-1.73607 - 1.26133i) q^{97} +(-4.01722 + 12.3637i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{4} - 5 q^{5} - 3 q^{8} - 5 q^{10} + 6 q^{11} - 2 q^{13} + 10 q^{14} + q^{16} + 8 q^{17} - 4 q^{19} + 4 q^{22} - 10 q^{23} - 5 q^{25} - 18 q^{26} - 10 q^{28} + 8 q^{29} - 20 q^{32} + 7 q^{34}+ \cdots + 13 q^{98}+O(q^{100}) $ 4 * q + q^2 + q^4 - 5 * q^5 - 3 * q^8 - 5 * q^10 + 6 * q^11 - 2 * q^13 + 10 * q^14 + q^16 + 8 * q^17 - 4 * q^19 + 4 * q^22 - 10 * q^23 - 5 * q^25 - 18 * q^26 - 10 * q^28 + 8 * q^29 - 20 * q^32 + 7 * q^34 + 10 * q^35 - 15 * q^37 - 6 * q^38 + 15 * q^40 + 4 * q^43 + 4 * q^44 - 10 * q^46 + 2 * q^47 + 52 * q^49 + 5 * q^50 + 2 * q^52 + 5 * q^53 - 10 * q^55 + 30 * q^56 - 8 * q^58 - 4 * q^59 + 2 * q^61 + 10 * q^62 - 7 * q^64 - 25 * q^65 + 2 * q^67 + 2 * q^68 - 10 * q^70 - 8 * q^71 - 10 * q^73 - 10 * q^74 + 4 * q^76 + 20 * q^77 + 5 * q^80 - 10 * q^82 + 18 * q^83 + 5 * q^85 - 14 * q^86 + 18 * q^88 + 9 * q^89 - 40 * q^91 - 10 * q^92 - 2 * q^94 - 10 * q^95 + 2 * q^97 + 13 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i	0.780378	+	0.625308i	$0.215027\pi$
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i	−0.998886	+	0.0471903i	$0.984973\pi$
$3$		0			0
$3$		0			0
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−1.80902	+	1.31433i	−0.809017	+	0.587785i
$5$	−1.80902	+	1.31433i	−0.809017	+	0.587785i
$6$		0			0
$7$	−4.47214			−1.69031			−0.845154	−	0.534522i	$-0.820491\pi$
$7$	−4.47214			−1.69031			−0.845154	+	0.534522i	$0.820491\pi$
$8$	−2.42705	+	1.76336i	−0.858092	+	0.623440i
$9$		0			0
$10$	−0.690983	−	2.12663i	−0.218508	−	0.672499i
$11$	0.381966	−	1.17557i	0.115167	−	0.354448i	−0.876815	−	0.480828i	$-0.840336\pi$
$11$	0.381966	−	1.17557i	0.115167	−	0.354448i	0.991982	+	0.126380i	$0.0403360\pi$
$12$		0			0
$13$	1.73607	+	5.34307i	0.481499	+	1.48190i	0.836989	+	0.547220i	$0.184314\pi$
$13$	1.73607	+	5.34307i	0.481499	+	1.48190i	−0.355490	+	0.934680i	$0.615686\pi$
$14$	1.38197	−	4.25325i	0.369346	−	1.13673i
$15$		0			0
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	3.11803	−	2.26538i	0.756234	−	0.549436i	−0.141519	−	0.989936i	$-0.545199\pi$
$17$	3.11803	−	2.26538i	0.756234	−	0.549436i	0.897753	+	0.440499i	$0.145199\pi$
$18$		0			0
$19$	−1.00000	+	0.726543i	−0.229416	+	0.166680i	−0.696555	−	0.717504i	$-0.745285\pi$
$19$	−1.00000	+	0.726543i	−0.229416	+	0.166680i	0.467139	+	0.884184i	$0.345285\pi$
$20$	−2.23607			−0.500000
$21$		0			0
$22$	1.00000	+	0.726543i	0.213201	+	0.154899i
$23$	−1.38197	+	4.25325i	−0.288160	+	0.886865i	0.697274	+	0.716805i	$0.254396\pi$
$23$	−1.38197	+	4.25325i	−0.288160	+	0.886865i	−0.985434	+	0.170060i	$0.945604\pi$
$24$		0			0
$25$	1.54508	−	4.75528i	0.309017	−	0.951057i
$26$	−5.61803			−1.10179
$27$		0			0
$28$	−3.61803	−	2.62866i	−0.683744	−	0.496769i
$29$	5.35410	+	3.88998i	0.994232	+	0.722352i	0.960844	−	0.277091i	$-0.0893703\pi$
$29$	5.35410	+	3.88998i	0.994232	+	0.722352i	0.0333880	+	0.999442i	$0.489370\pi$
$30$		0			0
$31$	−2.23607	+	1.62460i	−0.401610	+	0.291787i	−0.770196	−	0.637807i	$-0.779842\pi$
$31$	−2.23607	+	1.62460i	−0.401610	+	0.291787i	0.368587	+	0.929593i	$0.379842\pi$
$32$	−5.00000			−0.883883
$33$		0			0
$34$	1.19098	+	3.66547i	0.204252	+	0.628623i
$35$	8.09017	−	5.87785i	1.36749	−	0.993538i
$36$		0			0
$37$	−0.954915	−	2.93893i	−0.156987	−	0.483157i	0.841370	−	0.540460i	$-0.181750\pi$
$37$	−0.954915	−	2.93893i	−0.156987	−	0.483157i	−0.998357	+	0.0573034i	$0.981750\pi$
$38$	−0.381966	−	1.17557i	−0.0619631	−	0.190703i
$39$		0			0
$40$	2.07295	−	6.37988i	0.327762	−	1.00875i
$41$	1.11803	+	3.44095i	0.174608	+	0.537387i	0.999615	−	0.0277346i	$-0.00882932\pi$
$41$	1.11803	+	3.44095i	0.174608	+	0.537387i	−0.825008	+	0.565121i	$0.808829\pi$
$42$		0			0
$43$	7.70820			1.17549			0.587745	−	0.809046i	$-0.300016\pi$
$43$	7.70820			1.17549			0.587745	+	0.809046i	$0.300016\pi$
$44$	1.00000	−	0.726543i	0.150756	−	0.109530i
$45$		0			0
$46$	−3.61803	−	2.62866i	−0.533450	−	0.387574i
$47$	−0.618034	−	0.449028i	−0.0901495	−	0.0654975i	0.541797	−	0.840509i	$-0.317744\pi$
$47$	−0.618034	−	0.449028i	−0.0901495	−	0.0654975i	−0.631947	+	0.775012i	$0.717744\pi$
$48$		0			0
$49$	13.0000			1.85714
$50$	4.04508	+	2.93893i	0.572061	+	0.415627i
$51$		0			0
$52$	−1.73607	+	5.34307i	−0.240749	+	0.740950i
$53$	2.92705	+	2.12663i	0.402061	+	0.292115i	0.770380	−	0.637585i	$-0.220066\pi$
$53$	2.92705	+	2.12663i	0.402061	+	0.292115i	−0.368319	+	0.929700i	$0.620066\pi$
$54$		0			0
$55$	0.854102	+	2.62866i	0.115167	+	0.354448i
$56$	10.8541	−	7.88597i	1.45044	−	1.05381i
$57$		0			0
$58$	−5.35410	+	3.88998i	−0.703028	+	0.510780i
$59$	1.23607	+	3.80423i	0.160922	+	0.495268i	0.998713	−	0.0507240i	$-0.0161529\pi$
$59$	1.23607	+	3.80423i	0.160922	+	0.495268i	−0.837790	+	0.545992i	$0.816153\pi$
$60$		0			0
$61$	0.500000	−	1.53884i	0.0640184	−	0.197028i	−0.913931	−	0.405869i	$-0.866969\pi$
$61$	0.500000	−	1.53884i	0.0640184	−	0.197028i	0.977950	+	0.208840i	$0.0669689\pi$
$62$	−0.854102	−	2.62866i	−0.108471	−	0.333840i
$63$		0			0
$64$	2.16312	−	6.65740i	0.270390	−	0.832174i
$65$	−10.1631	−	7.38394i	−1.26058	−	0.915865i
$66$		0			0
$67$	−0.618034	+	0.449028i	−0.0755049	+	0.0548575i	−0.624897	−	0.780707i	$-0.714859\pi$
$67$	−0.618034	+	0.449028i	−0.0755049	+	0.0548575i	0.549392	+	0.835564i	$0.314859\pi$
$68$	3.85410			0.467379
$69$		0			0
$70$	3.09017	+	9.51057i	0.369346	+	1.13673i
$71$	−4.23607	−	3.07768i	−0.502729	−	0.365254i	0.307330	−	0.951603i	$-0.400565\pi$
$71$	−4.23607	−	3.07768i	−0.502729	−	0.365254i	−0.810058	+	0.586349i	$0.800565\pi$
$72$		0			0
$73$	−2.50000	+	7.69421i	−0.292603	+	0.900539i	0.691413	+	0.722460i	$0.256988\pi$
$73$	−2.50000	+	7.69421i	−0.292603	+	0.900539i	−0.984016	+	0.178080i	$0.943012\pi$
$74$	3.09017			0.359225
$75$		0			0
$76$	−1.23607			−0.141787
$77$	−1.70820	+	5.25731i	−0.194668	+	0.599126i
$78$		0			0
$79$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$79$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$80$	1.80902	+	1.31433i	0.202254	+	0.146946i
$81$		0			0
$82$	−3.61803			−0.399545
$83$	10.0902	−	7.33094i	1.10754	−	0.804675i	0.125266	−	0.992123i	$-0.460022\pi$
$83$	10.0902	−	7.33094i	1.10754	−	0.804675i	0.982274	+	0.187448i	$0.0600217\pi$
$84$		0			0
$85$	−2.66312	+	8.19624i	−0.288856	+	0.889007i
$86$	−2.38197	+	7.33094i	−0.256854	+	0.790515i
$87$		0			0
$88$	1.14590	+	3.52671i	0.122153	+	0.375949i
$89$	−1.66312	+	5.11855i	−0.176290	+	0.542566i	−0.999690	−	0.0248961i	$-0.992075\pi$
$89$	−1.66312	+	5.11855i	−0.176290	+	0.542566i	0.823400	+	0.567462i	$0.192075\pi$
$90$		0			0
$91$	−7.76393	−	23.8949i	−0.813881	−	2.50487i
$92$	−3.61803	+	2.62866i	−0.377206	+	0.274056i
$93$		0			0
$94$	0.618034	−	0.449028i	0.0637453	−	0.0463137i
$95$	0.854102	−	2.62866i	0.0876290	−	0.269694i
$96$		0			0
$97$	−1.73607	−	1.26133i	−0.176271	−	0.128068i	0.496151	−	0.868236i	$-0.334746\pi$
$97$	−1.73607	−	1.26133i	−0.176271	−	0.128068i	−0.672422	+	0.740168i	$0.734746\pi$
$98$	−4.01722	+	12.3637i	−0.405801	+	1.24893i
$99$		0			0
$100$	4.04508	−	2.93893i	0.404508	−	0.293893i
$101$	−3.56231			−0.354463			−0.177231	−	0.984169i	$-0.556714\pi$
$101$	−3.56231			−0.354463			−0.177231	+	0.984169i	$0.556714\pi$
$102$		0			0
$103$	−2.61803	−	1.90211i	−0.257963	−	0.187421i	0.451286	−	0.892379i	$-0.350966\pi$
$103$	−2.61803	−	1.90211i	−0.257963	−	0.187421i	−0.709248	+	0.704959i	$0.750966\pi$
$104$	−13.6353	−	9.90659i	−1.33705	−	0.971421i
$105$		0			0
$106$	−2.92705	+	2.12663i	−0.284300	+	0.206556i
$107$	−7.52786			−0.727746			−0.363873	−	0.931449i	$-0.618546\pi$
$107$	−7.52786			−0.727746			−0.363873	+	0.931449i	$0.618546\pi$
$108$		0			0
$109$	−2.44427	−	7.52270i	−0.234119	−	0.720544i	−0.997237	−	0.0742847i	$-0.976333\pi$
$109$	−2.44427	−	7.52270i	−0.234119	−	0.720544i	0.763118	−	0.646259i	$-0.223667\pi$
$110$	−2.76393			−0.263531
$111$		0			0
$112$	1.38197	+	4.25325i	0.130584	+	0.401895i
$113$	−5.66312	−	17.4293i	−0.532741	−	1.63961i	−0.748479	−	0.663158i	$-0.769216\pi$
$113$	−5.66312	−	17.4293i	−0.532741	−	1.63961i	0.215738	−	0.976451i	$-0.430784\pi$
$114$		0			0
$115$	−3.09017	−	9.51057i	−0.288160	−	0.886865i
$116$	2.04508	+	6.29412i	0.189881	+	0.584395i
$117$		0			0
$118$	−4.00000			−0.368230
$119$	−13.9443	+	10.1311i	−1.27827	+	0.928717i
$120$		0			0
$121$	7.66312	+	5.56758i	0.696647	+	0.506144i
$122$	1.30902	+	0.951057i	0.118513	+	0.0861046i
$123$		0			0
$124$	−2.76393			−0.248208
$125$	3.45492	+	10.6331i	0.309017	+	0.951057i
$126$		0			0
$127$	−1.14590	+	3.52671i	−0.101682	+	0.312945i	−0.988937	−	0.148333i	$-0.952609\pi$
$127$	−1.14590	+	3.52671i	−0.101682	+	0.312945i	0.887255	+	0.461279i	$0.152609\pi$
$128$	−2.42705	−	1.76336i	−0.214523	−	0.155860i
$129$		0			0
$130$	10.1631	−	7.38394i	0.891364	−	0.647614i
$131$	−6.61803	+	4.80828i	−0.578220	+	0.420102i	−0.838082	−	0.545544i	$-0.816323\pi$
$131$	−6.61803	+	4.80828i	−0.578220	+	0.420102i	0.259862	+	0.965646i	$0.416323\pi$
$132$		0			0
$133$	4.47214	−	3.24920i	0.387783	−	0.281741i
$134$	−0.236068	−	0.726543i	−0.0203932	−	0.0627637i
$135$		0			0
$136$	−3.57295	+	10.9964i	−0.306378	+	0.942934i
$137$	2.35410	+	7.24518i	0.201125	+	0.618998i	0.999850	+	0.0173024i	$0.00550780\pi$
$137$	2.35410	+	7.24518i	0.201125	+	0.618998i	−0.798726	+	0.601695i	$0.794492\pi$
$138$		0			0
$139$	−7.09017	+	21.8213i	−0.601380	+	1.85086i	−0.0813976	+	0.996682i	$0.525938\pi$
$139$	−7.09017	+	21.8213i	−0.601380	+	1.85086i	−0.519983	+	0.854177i	$0.674062\pi$
$140$	10.0000			0.845154
$141$		0			0
$142$	4.23607	−	3.07768i	0.355483	−	0.258273i
$143$	6.94427			0.580709
$144$		0			0
$145$	−14.7984			−1.22894
$146$	−6.54508	−	4.75528i	−0.541675	−	0.393550i
$147$		0			0
$148$	0.954915	−	2.93893i	0.0784935	−	0.241578i
$149$	18.8541			1.54459			0.772294	−	0.635265i	$-0.219109\pi$
$149$	18.8541			1.54459			0.772294	+	0.635265i	$0.219109\pi$
$150$		0			0
$151$	7.52786			0.612609			0.306304	−	0.951934i	$-0.400907\pi$
$151$	7.52786			0.612609			0.306304	+	0.951934i	$0.400907\pi$
$152$	1.14590	−	3.52671i	0.0929446	−	0.286054i
$153$		0			0
$154$	−4.47214	−	3.24920i	−0.360375	−	0.261828i
$155$	1.90983	−	5.87785i	0.153401	−	0.472120i
$156$		0			0
$157$	10.7984			0.861804			0.430902	−	0.902399i	$-0.358195\pi$
$157$	10.7984			0.861804			0.430902	+	0.902399i	$0.358195\pi$
$158$		0			0
$159$		0			0
$160$	9.04508	−	6.57164i	0.715077	−	0.519534i
$161$	6.18034	−	19.0211i	0.487079	−	1.49908i
$162$		0			0
$163$	−4.61803	−	14.2128i	−0.361712	−	1.11324i	−0.952014	−	0.306054i	$-0.900991\pi$
$163$	−4.61803	−	14.2128i	−0.361712	−	1.11324i	0.590302	−	0.807183i	$-0.299009\pi$
$164$	−1.11803	+	3.44095i	−0.0873038	+	0.268693i
$165$		0			0
$166$	3.85410	+	11.8617i	0.299136	+	0.920647i
$167$	2.76393	−	2.00811i	0.213879	−	0.155393i	−0.475688	−	0.879614i	$-0.657801\pi$
$167$	2.76393	−	2.00811i	0.213879	−	0.155393i	0.689567	+	0.724222i	$0.257801\pi$
$168$		0			0
$169$	−15.0172	+	10.9106i	−1.15517	+	0.839281i
$170$	−6.97214	−	5.06555i	−0.534738	−	0.388510i
$171$		0			0
$172$	6.23607	+	4.53077i	0.475496	+	0.345468i
$173$	−6.51722	+	20.0579i	−0.495495	+	1.52498i	0.320689	+	0.947185i	$0.396086\pi$
$173$	−6.51722	+	20.0579i	−0.495495	+	1.52498i	−0.816184	+	0.577793i	$0.803914\pi$
$174$		0			0
$175$	−6.90983	+	21.2663i	−0.522334	+	1.60758i
$176$	−1.23607			−0.0931721
$177$		0			0
$178$	−4.35410	−	3.16344i	−0.326354	−	0.237110i
$179$	−13.0902	−	9.51057i	−0.978405	−	0.710853i	−0.0210536	−	0.999778i	$-0.506702\pi$
$179$	−13.0902	−	9.51057i	−0.978405	−	0.710853i	−0.957352	+	0.288925i	$0.906702\pi$
$180$		0			0
$181$	−11.9721	+	8.69827i	−0.889882	+	0.646537i	−0.935847	−	0.352406i	$-0.885364\pi$
$181$	−11.9721	+	8.69827i	−0.889882	+	0.646537i	0.0459654	+	0.998943i	$0.485364\pi$
$182$	25.1246			1.86236
$183$		0			0
$184$	−4.14590	−	12.7598i	−0.305640	−	0.940662i
$185$	5.59017	+	4.06150i	0.410997	+	0.298607i
$186$		0			0
$187$	−1.47214	−	4.53077i	−0.107653	−	0.331323i
$188$	−0.236068	−	0.726543i	−0.0172170	−	0.0529886i
$189$		0			0
$190$	2.23607	+	1.62460i	0.162221	+	0.117861i
$191$	−2.05573	−	6.32688i	−0.148747	−	0.457797i	0.848727	−	0.528832i	$-0.177370\pi$
$191$	−2.05573	−	6.32688i	−0.148747	−	0.457797i	−0.997474	+	0.0710349i	$0.977370\pi$
$192$		0			0
$193$	23.3262			1.67906			0.839530	−	0.543314i	$-0.182831\pi$
$193$	23.3262			1.67906			0.839530	+	0.543314i	$0.182831\pi$
$194$	1.73607	−	1.26133i	0.124642	−	0.0905580i
$195$		0			0
$196$	10.5172	+	7.64121i	0.751230	+	0.545801i
$197$	6.16312	+	4.47777i	0.439104	+	0.319028i	0.785279	−	0.619142i	$-0.212520\pi$
$197$	6.16312	+	4.47777i	0.439104	+	0.319028i	−0.346175	+	0.938170i	$0.612520\pi$
$198$		0			0
$199$	12.6525			0.896910			0.448455	−	0.893805i	$-0.351974\pi$
$199$	12.6525			0.896910			0.448455	+	0.893805i	$0.351974\pi$
$200$	4.63525	+	14.2658i	0.327762	+	1.00875i
$201$		0			0
$202$	1.10081	−	3.38795i	0.0774529	−	0.238376i
$203$	−23.9443	−	17.3965i	−1.68056	−	1.22100i
$204$		0			0
$205$	−6.54508	−	4.75528i	−0.457129	−	0.332123i
$206$	2.61803	−	1.90211i	0.182407	−	0.132526i
$207$		0			0
$208$	4.54508	−	3.30220i	0.315145	−	0.228966i
$209$	0.472136	+	1.45309i	0.0326583	+	0.100512i
$210$		0			0
$211$	5.52786	−	17.0130i	0.380554	−	1.17122i	−0.559101	−	0.829100i	$-0.688854\pi$
$211$	5.52786	−	17.0130i	0.380554	−	1.17122i	0.939655	−	0.342125i	$-0.111146\pi$
$212$	1.11803	+	3.44095i	0.0767869	+	0.236326i
$213$		0			0
$214$	2.32624	−	7.15942i	0.159018	−	0.489408i
$215$	−13.9443	+	10.1311i	−0.950991	+	0.690936i
$216$		0			0
$217$	10.0000	−	7.26543i	0.678844	−	0.493209i
$218$	7.90983			0.535721
$219$		0			0
$220$	−0.854102	+	2.62866i	−0.0575835	+	0.177224i
$221$	17.5172	+	12.7270i	1.17834	+	0.856111i
$222$		0			0
$223$	2.52786	−	7.77997i	0.169278	−	0.520985i	−0.830048	−	0.557692i	$-0.811687\pi$
$223$	2.52786	−	7.77997i	0.169278	−	0.520985i	0.999326	+	0.0367073i	$0.0116869\pi$
$224$	22.3607			1.49404
$225$		0			0
$226$	18.3262			1.21904
$227$	6.18034	−	19.0211i	0.410204	−	1.26248i	−0.506268	−	0.862376i	$-0.668975\pi$
$227$	6.18034	−	19.0211i	0.410204	−	1.26248i	0.916471	−	0.400100i	$-0.131025\pi$
$228$		0			0
$229$	−17.7812	−	12.9188i	−1.17501	−	0.853696i	−0.183411	−	0.983036i	$-0.558714\pi$
$229$	−17.7812	−	12.9188i	−1.17501	−	0.853696i	−0.991600	+	0.129340i	$0.958714\pi$
$230$	10.0000			0.659380
$231$		0			0
$232$	−19.8541			−1.30349
$233$	10.0172	−	7.27794i	0.656250	−	0.476794i	−0.209144	−	0.977885i	$-0.567068\pi$
$233$	10.0172	−	7.27794i	0.656250	−	0.476794i	0.865394	+	0.501091i	$0.167068\pi$
$234$		0			0
$235$	1.70820			0.111431
$236$	−1.23607	+	3.80423i	−0.0804612	+	0.247634i
$237$		0			0
$238$	−5.32624	−	16.3925i	−0.345249	−	1.06257i
$239$	7.70820	−	23.7234i	0.498602	−	1.53454i	−0.312664	−	0.949864i	$-0.601222\pi$
$239$	7.70820	−	23.7234i	0.498602	−	1.53454i	0.811267	−	0.584676i	$-0.198778\pi$
$240$		0			0
$241$	8.66312	+	26.6623i	0.558041	+	1.71747i	0.687775	+	0.725923i	$0.258587\pi$
$241$	8.66312	+	26.6623i	0.558041	+	1.71747i	−0.129735	+	0.991549i	$0.541413\pi$
$242$	−7.66312	+	5.56758i	−0.492604	+	0.357898i
$243$		0			0
$244$	1.30902	−	0.951057i	0.0838012	−	0.0608852i
$245$	−23.5172	+	17.0863i	−1.50246	+	1.09160i
$246$		0			0
$247$	−5.61803	−	4.08174i	−0.357467	−	0.259715i
$248$	2.56231	−	7.88597i	0.162707	−	0.500759i
$249$		0			0
$250$	−11.1803			−0.707107
$251$	9.05573			0.571592			0.285796	−	0.958290i	$-0.407742\pi$
$251$	9.05573			0.571592			0.285796	+	0.958290i	$0.407742\pi$
$252$		0			0
$253$	4.47214	+	3.24920i	0.281161	+	0.204275i
$254$	−3.00000	−	2.17963i	−0.188237	−	0.136762i
$255$		0			0
$256$	13.7533	−	9.99235i	0.859581	−	0.624522i
$257$	−11.7984			−0.735962			−0.367981	−	0.929833i	$-0.619951\pi$
$257$	−11.7984			−0.735962			−0.367981	+	0.929833i	$0.619951\pi$
$258$		0			0
$259$	4.27051	+	13.1433i	0.265357	+	0.816684i
$260$	−3.88197	−	11.9475i	−0.240749	−	0.740950i
$261$		0			0
$262$	−2.52786	−	7.77997i	−0.156172	−	0.480648i
$263$	7.38197	+	22.7194i	0.455192	+	1.40094i	0.870910	+	0.491442i	$0.163530\pi$
$263$	7.38197	+	22.7194i	0.455192	+	1.40094i	−0.415719	+	0.909493i	$0.636470\pi$
$264$		0			0
$265$	−8.09017			−0.496975
$266$	1.70820	+	5.25731i	0.104737	+	0.322346i
$267$		0			0
$268$	−0.763932			−0.0466646
$269$	−5.54508	+	4.02874i	−0.338090	+	0.245637i	−0.743855	−	0.668341i	$-0.767005\pi$
$269$	−5.54508	+	4.02874i	−0.338090	+	0.245637i	0.405766	+	0.913977i	$0.367005\pi$
$270$		0			0
$271$	0.145898	+	0.106001i	0.00886267	+	0.00643911i	0.592208	−	0.805785i	$-0.298256\pi$
$271$	0.145898	+	0.106001i	0.00886267	+	0.00643911i	−0.583345	+	0.812224i	$0.698256\pi$
$272$	−3.11803	−	2.26538i	−0.189059	−	0.137359i
$273$		0			0
$274$	−7.61803			−0.460222
$275$	−5.00000	−	3.63271i	−0.301511	−	0.219061i
$276$		0			0
$277$	5.80902	−	17.8783i	0.349030	−	1.07420i	−0.610361	−	0.792124i	$-0.708976\pi$
$277$	5.80902	−	17.8783i	0.349030	−	1.07420i	0.959391	−	0.282080i	$-0.0910245\pi$
$278$	−18.5623	−	13.4863i	−1.11329	−	0.808855i
$279$		0			0
$280$	−9.27051	+	28.5317i	−0.554019	+	1.70509i
$281$	−15.8713	+	11.5312i	−0.946804	+	0.687893i	−0.950049	−	0.312102i	$-0.898967\pi$
$281$	−15.8713	+	11.5312i	−0.946804	+	0.687893i	0.00324500	+	0.999995i	$0.498967\pi$
$282$		0			0
$283$	−11.0902	+	8.05748i	−0.659242	+	0.478967i	−0.866407	−	0.499339i	$-0.833576\pi$
$283$	−11.0902	+	8.05748i	−0.659242	+	0.478967i	0.207165	+	0.978306i	$0.433576\pi$
$284$	−1.61803	−	4.97980i	−0.0960127	−	0.295497i
$285$		0			0
$286$	−2.14590	+	6.60440i	−0.126890	+	0.390526i
$287$	−5.00000	−	15.3884i	−0.295141	−	0.908350i
$288$		0			0
$289$	−0.663119	+	2.04087i	−0.0390070	+	0.120051i
$290$	4.57295	−	14.0741i	0.268533	−	0.826459i
$291$		0			0
$292$	−6.54508	+	4.75528i	−0.383022	+	0.278282i
$293$	20.7984			1.21505			0.607527	−	0.794299i	$-0.292162\pi$
$293$	20.7984			1.21505			0.607527	+	0.794299i	$0.292162\pi$
$294$		0			0
$295$	−7.23607	−	5.25731i	−0.421300	−	0.306092i
$296$	7.50000	+	5.44907i	0.435929	+	0.316721i
$297$		0			0
$298$	−5.82624	+	17.9313i	−0.337505	+	1.03873i
$299$	−25.1246			−1.45299
$300$		0			0
$301$	−34.4721			−1.98694
$302$	−2.32624	+	7.15942i	−0.133860	+	0.411979i
$303$		0			0
$304$	1.00000	+	0.726543i	0.0573539	+	0.0416701i
$305$	1.11803	+	3.44095i	0.0640184	+	0.197028i
$306$		0			0
$307$	32.6525			1.86358			0.931788	−	0.363004i	$-0.118249\pi$
$307$	32.6525			1.86358			0.931788	+	0.363004i	$0.118249\pi$
$308$	−4.47214	+	3.24920i	−0.254824	+	0.185140i
$309$		0			0
$310$	5.00000	+	3.63271i	0.283981	+	0.206324i
$311$	−5.47214	+	16.8415i	−0.310296	+	0.954994i	0.667351	+	0.744743i	$0.267428\pi$
$311$	−5.47214	+	16.8415i	−0.310296	+	0.954994i	−0.977647	+	0.210251i	$0.932572\pi$
$312$		0			0
$313$	−0.145898	−	0.449028i	−0.00824664	−	0.0253806i	0.946849	−	0.321680i	$-0.104247\pi$
$313$	−0.145898	−	0.449028i	−0.00824664	−	0.0253806i	−0.955095	+	0.296299i	$0.904247\pi$
$314$	−3.33688	+	10.2699i	−0.188311	+	0.579562i
$315$		0			0
$316$		0			0
$317$	23.3262	−	16.9475i	1.31013	−	0.951867i	0.310133	−	0.950693i	$-0.399627\pi$
$317$	23.3262	−	16.9475i	1.31013	−	0.951867i	0.999999	−	0.00117338i	$-0.000373499\pi$
$318$		0			0
$319$	6.61803	−	4.80828i	0.370539	−	0.269212i
$320$	4.83688	+	14.8864i	0.270390	+	0.832174i
$321$		0			0
$322$	16.1803	+	11.7557i	0.901695	+	0.655120i
$323$	−1.47214	+	4.53077i	−0.0819118	+	0.252099i
$324$		0			0
$325$	28.0902			1.55816
$326$	14.9443			0.827687
$327$		0			0
$328$	−8.78115	−	6.37988i	−0.484858	−	0.352270i
$329$	2.76393	+	2.00811i	0.152381	+	0.110711i
$330$		0			0
$331$	5.61803	−	4.08174i	0.308795	−	0.224353i	−0.422584	−	0.906324i	$-0.638877\pi$
$331$	5.61803	−	4.08174i	0.308795	−	0.224353i	0.731379	+	0.681971i	$0.238877\pi$
$332$	12.4721			0.684497
$333$		0			0
$334$	1.05573	+	3.24920i	0.0577669	+	0.177788i
$335$	0.527864	−	1.62460i	0.0288403	−	0.0887613i
$336$		0			0
$337$	0.909830	+	2.80017i	0.0495616	+	0.152535i	0.972774	−	0.231754i	$-0.0744465\pi$
$337$	0.909830	+	2.80017i	0.0495616	+	0.152535i	−0.923213	+	0.384289i	$0.874447\pi$
$338$	−5.73607	−	17.6538i	−0.312001	−	0.960240i
$339$		0			0
$340$	−6.97214	+	5.06555i	−0.378117	+	0.274718i
$341$	1.05573	+	3.24920i	0.0571709	+	0.175954i
$342$		0			0
$343$	−26.8328			−1.44884
$344$	−18.7082	+	13.5923i	−1.00868	+	0.732848i
$345$		0			0
$346$	−17.0623	−	12.3965i	−0.917275	−	0.666439i
$347$	−16.4164	−	11.9272i	−0.881279	−	0.640287i	0.0523106	−	0.998631i	$-0.483341\pi$
$347$	−16.4164	−	11.9272i	−0.881279	−	0.640287i	−0.933590	+	0.358344i	$0.883341\pi$
$348$		0			0
$349$	−4.03444			−0.215959			−0.107979	−	0.994153i	$-0.534438\pi$
$349$	−4.03444			−0.215959			−0.107979	+	0.994153i	$0.534438\pi$
$350$	−18.0902	−	13.1433i	−0.966960	−	0.702538i
$351$		0			0
$352$	−1.90983	+	5.87785i	−0.101794	+	0.313291i
$353$	11.6180	+	8.44100i	0.618366	+	0.449269i	0.852350	−	0.522971i	$-0.175177\pi$
$353$	11.6180	+	8.44100i	0.618366	+	0.449269i	−0.233985	+	0.972240i	$0.575177\pi$
$354$		0			0
$355$	11.7082			0.621407
$356$	−4.35410	+	3.16344i	−0.230767	+	0.167662i
$357$		0			0
$358$	13.0902	−	9.51057i	0.691837	−	0.502649i
$359$	11.5623	+	35.5851i	0.610235	+	1.87811i	0.455728	+	0.890119i	$0.349379\pi$
$359$	11.5623	+	35.5851i	0.610235	+	1.87811i	0.154507	+	0.987992i	$0.450621\pi$
$360$		0			0
$361$	−5.39919	+	16.6170i	−0.284168	+	0.874578i
$362$	−4.57295	−	14.0741i	−0.240349	−	0.739718i
$363$		0			0
$364$	7.76393	−	23.8949i	0.406941	−	1.25243i
$365$	−5.59017	−	17.2048i	−0.292603	−	0.900539i
$366$		0			0
$367$	4.85410	−	3.52671i	0.253382	−	0.184093i	−0.453842	−	0.891082i	$-0.649947\pi$
$367$	4.85410	−	3.52671i	0.253382	−	0.184093i	0.707224	+	0.706989i	$0.249947\pi$
$368$	4.47214			0.233126
$369$		0			0
$370$	−5.59017	+	4.06150i	−0.290619	+	0.211147i
$371$	−13.0902	−	9.51057i	−0.679608	−	0.493764i
$372$		0			0
$373$	0.798374	−	2.45714i	0.0413382	−	0.127226i	−0.928258	−	0.371938i	$-0.878693\pi$
$373$	0.798374	−	2.45714i	0.0413382	−	0.127226i	0.969596	+	0.244712i	$0.0786934\pi$
$374$	4.76393			0.246337
$375$		0			0
$376$	2.29180			0.118190
$377$	−11.4894	+	35.3606i	−0.591732	+	1.82116i
$378$		0			0
$379$	2.76393	+	2.00811i	0.141974	+	0.103150i	0.656505	−	0.754322i	$-0.272034\pi$
$379$	2.76393	+	2.00811i	0.141974	+	0.103150i	−0.514531	+	0.857472i	$0.672034\pi$
$380$	2.23607	−	1.62460i	0.114708	−	0.0833401i
$381$		0			0
$382$	6.65248			0.340370
$383$	−26.5623	+	19.2986i	−1.35727	+	0.986115i	−0.358657	+	0.933469i	$0.616765\pi$
$383$	−26.5623	+	19.2986i	−1.35727	+	0.986115i	−0.998613	+	0.0526453i	$0.983235\pi$
$384$		0			0
$385$	−3.81966	−	11.7557i	−0.194668	−	0.599126i
$386$	−7.20820	+	22.1846i	−0.366888	+	1.12916i
$387$		0			0
$388$	−0.663119	−	2.04087i	−0.0336648	−	0.103609i
$389$	8.00658	−	24.6417i	0.405950	−	1.24938i	−0.514150	−	0.857700i	$-0.671893\pi$
$389$	8.00658	−	24.6417i	0.405950	−	1.24938i	0.920100	−	0.391684i	$-0.128107\pi$
$390$		0			0
$391$	5.32624	+	16.3925i	0.269359	+	0.829003i
$392$	−31.5517	+	22.9236i	−1.59360	+	1.15782i
$393$		0			0
$394$	−6.16312	+	4.47777i	−0.310493	+	0.225587i
$395$		0			0
$396$		0			0
$397$	5.61803	+	4.08174i	0.281961	+	0.204857i	0.719772	−	0.694210i	$-0.244246\pi$
$397$	5.61803	+	4.08174i	0.281961	+	0.204857i	−0.437811	+	0.899067i	$0.644246\pi$
$398$	−3.90983	+	12.0332i	−0.195982	+	0.603171i
$399$		0			0
$400$	−5.00000			−0.250000
$401$	22.4508			1.12114			0.560571	−	0.828106i	$-0.310582\pi$
$401$	22.4508			1.12114			0.560571	+	0.828106i	$0.310582\pi$
$402$		0			0
$403$	−12.5623	−	9.12705i	−0.625773	−	0.454651i
$404$	−2.88197	−	2.09387i	−0.143383	−	0.104174i
$405$		0			0
$406$	23.9443	−	17.3965i	1.18833	−	0.863375i
$407$	−3.81966			−0.189334
$408$		0			0
$409$	0.371323	+	1.14281i	0.0183607	+	0.0565085i	0.959817	−	0.280626i	$-0.0905422\pi$
$409$	0.371323	+	1.14281i	0.0183607	+	0.0565085i	−0.941456	+	0.337135i	$0.890542\pi$
$410$	6.54508	−	4.75528i	0.323239	−	0.234847i
$411$		0			0
$412$	−1.00000	−	3.07768i	−0.0492665	−	0.151627i
$413$	−5.52786	−	17.0130i	−0.272008	−	0.837156i
$414$		0			0
$415$	−8.61803	+	26.5236i	−0.423043	+	1.30199i
$416$	−8.68034	−	26.7153i	−0.425589	−	1.30983i
$417$		0			0
$418$	−1.52786			−0.0747303
$419$	12.1803	−	8.84953i	0.595049	−	0.432328i	−0.249069	−	0.968486i	$-0.580125\pi$
$419$	12.1803	−	8.84953i	0.595049	−	0.432328i	0.844118	+	0.536158i	$0.180125\pi$
$420$		0			0
$421$	−24.1525	−	17.5478i	−1.17712	−	0.855227i	−0.185276	−	0.982687i	$-0.559318\pi$
$421$	−24.1525	−	17.5478i	−1.17712	−	0.855227i	−0.991844	+	0.127459i	$0.959318\pi$
$422$	14.4721	+	10.5146i	0.704493	+	0.511844i
$423$		0			0
$424$	−10.8541			−0.527122
$425$	−5.95492	−	18.3273i	−0.288856	−	0.889007i
$426$		0			0
$427$	−2.23607	+	6.88191i	−0.108211	+	0.333039i
$428$	−6.09017	−	4.42477i	−0.294379	−	0.213879i
$429$		0			0
$430$	−5.32624	−	16.3925i	−0.256854	−	0.790515i
$431$	16.7082	−	12.1392i	0.804806	−	0.584726i	−0.107514	−	0.994204i	$-0.534289\pi$
$431$	16.7082	−	12.1392i	0.804806	−	0.584726i	0.912320	+	0.409478i	$0.134289\pi$
$432$		0			0
$433$	17.7812	−	12.9188i	0.854508	−	0.620836i	−0.0718775	−	0.997413i	$-0.522899\pi$
$433$	17.7812	−	12.9188i	0.854508	−	0.620836i	0.926385	+	0.376577i	$0.122899\pi$
$434$	3.81966	+	11.7557i	0.183350	+	0.564292i
$435$		0			0
$436$	2.44427	−	7.52270i	0.117059	−	0.360272i
$437$	−1.70820	−	5.25731i	−0.0817145	−	0.251491i
$438$		0			0
$439$	5.00000	−	15.3884i	0.238637	−	0.734449i	−0.757981	−	0.652276i	$-0.773814\pi$
$439$	5.00000	−	15.3884i	0.238637	−	0.734449i	0.996618	−	0.0821726i	$-0.0261859\pi$
$440$	−6.70820	−	4.87380i	−0.319801	−	0.232349i
$441$		0			0
$442$	−17.5172	+	12.7270i	−0.833209	+	0.605362i
$443$	35.2361			1.67412			0.837058	−	0.547114i	$-0.184274\pi$
$443$	35.2361			1.67412			0.837058	+	0.547114i	$0.184274\pi$
$444$		0			0
$445$	−3.71885	−	11.4454i	−0.176290	−	0.542566i
$446$	6.61803	+	4.80828i	0.313373	+	0.227679i
$447$		0			0
$448$	−9.67376	+	29.7728i	−0.457042	+	1.40663i
$449$	−16.7984			−0.792764			−0.396382	−	0.918086i	$-0.629734\pi$
$449$	−16.7984			−0.792764			−0.396382	+	0.918086i	$0.629734\pi$
$450$		0			0
$451$	4.47214			0.210585
$452$	5.66312	−	17.4293i	0.266371	−	0.819805i
$453$		0			0
$454$	16.1803	+	11.7557i	0.759381	+	0.551723i
$455$	45.4508	+	33.0220i	2.13077	+	1.54809i
$456$		0			0
$457$	−22.3607			−1.04599			−0.522994	−	0.852336i	$-0.675185\pi$
$457$	−22.3607			−1.04599			−0.522994	+	0.852336i	$0.675185\pi$
$458$	17.7812	−	12.9188i	0.830859	−	0.603654i
$459$		0			0
$460$	3.09017	−	9.51057i	0.144080	−	0.443432i
$461$	10.1353	−	31.1931i	0.472046	−	1.45281i	−0.377855	−	0.925865i	$-0.623338\pi$
$461$	10.1353	−	31.1931i	0.472046	−	1.45281i	0.849901	−	0.526943i	$-0.176662\pi$
$462$		0			0
$463$	5.79837	+	17.8456i	0.269473	+	0.829353i	0.990629	+	0.136580i	$0.0436112\pi$
$463$	5.79837	+	17.8456i	0.269473	+	0.829353i	−0.721156	+	0.692773i	$0.756389\pi$
$464$	2.04508	−	6.29412i	0.0949407	−	0.292197i
$465$		0			0
$466$	3.82624	+	11.7759i	0.177247	+	0.545510i
$467$	22.7984	−	16.5640i	1.05498	−	0.766490i	0.0818293	−	0.996646i	$-0.473924\pi$
$467$	22.7984	−	16.5640i	1.05498	−	0.766490i	0.973154	+	0.230156i	$0.0739238\pi$
$468$		0			0
$469$	2.76393	−	2.00811i	0.127627	−	0.0927261i
$470$	−0.527864	+	1.62460i	−0.0243486	+	0.0749371i
$471$		0			0
$472$	−9.70820	−	7.05342i	−0.446856	−	0.324660i
$473$	2.94427	−	9.06154i	0.135378	−	0.416650i
$474$		0			0
$475$	1.90983	+	5.87785i	0.0876290	+	0.269694i
$476$	−17.2361			−0.790014
$477$		0			0
$478$	20.1803	+	14.6619i	0.923027	+	0.670619i
$479$	15.3262	+	11.1352i	0.700274	+	0.508779i	0.880021	−	0.474934i	$-0.157528\pi$
$479$	15.3262	+	11.1352i	0.700274	+	0.508779i	−0.179748	+	0.983713i	$0.557528\pi$
$480$		0			0
$481$	14.0451	−	10.2044i	0.640401	−	0.465278i
$482$	−28.0344			−1.27693
$483$		0			0
$484$	2.92705	+	9.00854i	0.133048	+	0.409479i
$485$	4.79837			0.217883
$486$		0			0
$487$	3.00000	+	9.23305i	0.135943	+	0.418389i	0.995736	−	0.0922541i	$-0.0294072\pi$
$487$	3.00000	+	9.23305i	0.135943	+	0.418389i	−0.859793	+	0.510644i	$0.829407\pi$
$488$	1.50000	+	4.61653i	0.0679018	+	0.208980i
$489$		0			0
$490$	−8.98278	−	27.6462i	−0.405801	−	1.24893i
$491$	−1.81966	−	5.60034i	−0.0821201	−	0.252740i	0.901563	−	0.432647i	$-0.142420\pi$
$491$	−1.81966	−	5.60034i	−0.0821201	−	0.252740i	−0.983684	+	0.179907i	$0.942420\pi$
$492$		0			0
$493$	25.5066			1.14876
$494$	5.61803	−	4.08174i	0.252767	−	0.183646i
$495$		0			0
$496$	2.23607	+	1.62460i	0.100402	+	0.0729466i
$497$	18.9443	+	13.7638i	0.849767	+	0.617392i
$498$		0			0
$499$	−6.00000			−0.268597			−0.134298	−	0.990941i	$-0.542878\pi$
$499$	−6.00000			−0.268597			−0.134298	+	0.990941i	$0.542878\pi$
$500$	−3.45492	+	10.6331i	−0.154508	+	0.475528i
$501$		0			0
$502$	−2.79837	+	8.61251i	−0.124898	+	0.384395i
$503$	6.94427	+	5.04531i	0.309630	+	0.224959i	0.731738	−	0.681586i	$-0.238710\pi$
$503$	6.94427	+	5.04531i	0.309630	+	0.224959i	−0.422108	+	0.906546i	$0.638710\pi$
$504$		0			0
$505$	6.44427	−	4.68204i	0.286766	−	0.208348i
$506$	−4.47214	+	3.24920i	−0.198811	+	0.144444i
$507$		0			0
$508$	−3.00000	+	2.17963i	−0.133103	+	0.0967053i
$509$	−6.22542	−	19.1599i	−0.275937	−	0.849247i	−0.988970	−	0.148116i	$-0.952679\pi$
$509$	−6.22542	−	19.1599i	−0.275937	−	0.849247i	0.713033	−	0.701131i	$-0.247321\pi$
$510$		0			0
$511$	11.1803	−	34.4095i	0.494589	−	1.52219i
$512$	3.39919	+	10.4616i	0.150224	+	0.462343i
$513$		0			0
$514$	3.64590	−	11.2209i	0.160814	−	0.494934i
$515$	7.23607			0.318859
$516$		0			0
$517$	−0.763932	+	0.555029i	−0.0335977	+	0.0244102i
$518$	−13.8197			−0.607201
$519$		0			0
$520$	37.6869			1.65268
$521$	−21.8713	−	15.8904i	−0.958200	−	0.696173i	−0.00546804	−	0.999985i	$-0.501741\pi$
$521$	−21.8713	−	15.8904i	−0.958200	−	0.696173i	−0.952732	+	0.303812i	$0.901741\pi$
$522$		0			0
$523$	−7.94427	+	24.4500i	−0.347379	+	1.06912i	0.612919	+	0.790146i	$0.289995\pi$
$523$	−7.94427	+	24.4500i	−0.347379	+	1.06912i	−0.960298	+	0.278976i	$0.910005\pi$
$524$	−8.18034			−0.357360
$525$		0			0
$526$	−23.8885			−1.04159
$527$	−3.29180	+	10.1311i	−0.143393	+	0.441318i
$528$		0			0
$529$	2.42705	+	1.76336i	0.105524	+	0.0766676i
$530$	2.50000	−	7.69421i	0.108593	−	0.334215i
$531$		0			0
$532$	5.52786			0.239663
$533$	−16.4443	+	11.9475i	−0.712280	+	0.517502i
$534$		0			0
$535$	13.6180	−	9.89408i	0.588759	−	0.427758i
$536$	0.708204	−	2.17963i	0.0305898	−	0.0941456i
$537$		0			0
$538$	−2.11803	−	6.51864i	−0.0913149	−	0.281038i
$539$	4.96556	−	15.2824i	0.213882	−	0.658260i
$540$		0			0
$541$	−6.07953	−	18.7109i	−0.261379	−	0.804443i	−0.992505	−	0.122200i	$-0.961005\pi$
$541$	−6.07953	−	18.7109i	−0.261379	−	0.804443i	0.731126	−	0.682242i	$-0.238995\pi$
$542$	−0.145898	+	0.106001i	−0.00626686	+	0.00455314i
$543$		0			0
$544$	−15.5902	+	11.3269i	−0.668423	+	0.485638i
$545$	14.3090	+	10.3961i	0.612931	+	0.445320i
$546$		0			0
$547$	−34.2705	−	24.8990i	−1.46530	−	1.06460i	−0.981942	−	0.189181i	$-0.939417\pi$
$547$	−34.2705	−	24.8990i	−1.46530	−	1.06460i	−0.483359	−	0.875422i	$-0.660583\pi$
$548$	−2.35410	+	7.24518i	−0.100562	+	0.309499i
$549$		0			0
$550$	5.00000	−	3.63271i	0.213201	−	0.154899i
$551$	−8.18034			−0.348494
$552$		0			0
$553$		0			0
$554$	15.2082	+	11.0494i	0.646135	+	0.469444i
$555$		0			0
$556$	−18.5623	+	13.4863i	−0.787217	+	0.571947i
$557$	11.2705			0.477547			0.238773	−	0.971075i	$-0.423255\pi$
$557$	11.2705			0.477547			0.238773	+	0.971075i	$0.423255\pi$
$558$		0			0
$559$	13.3820	+	41.1855i	0.565997	+	1.74196i
$560$	−8.09017	−	5.87785i	−0.341872	−	0.248385i
$561$		0			0
$562$	−6.06231	−	18.6579i	−0.255723	−	0.787034i
$563$	8.18034	+	25.1765i	0.344760	+	1.06106i	0.961712	+	0.274062i	$0.0883673\pi$
$563$	8.18034	+	25.1765i	0.344760	+	1.06106i	−0.616952	+	0.787001i	$0.711633\pi$
$564$		0			0
$565$	33.1525	+	24.0867i	1.39474	+	1.01333i
$566$	−4.23607	−	13.0373i	−0.178055	−	0.547998i
$567$		0			0
$568$	15.7082			0.659102
$569$	2.64590	−	1.92236i	0.110922	−	0.0805894i	−0.530942	−	0.847408i	$-0.678162\pi$
$569$	2.64590	−	1.92236i	0.110922	−	0.0805894i	0.641863	+	0.766819i	$0.278162\pi$
$570$		0			0
$571$	13.5623	+	9.85359i	0.567565	+	0.412360i	0.834220	−	0.551432i	$-0.185918\pi$
$571$	13.5623	+	9.85359i	0.567565	+	0.412360i	−0.266655	+	0.963792i	$0.585918\pi$
$572$	5.61803	+	4.08174i	0.234902	+	0.170666i
$573$		0			0
$574$	16.1803			0.675354
$575$	18.0902	+	13.1433i	0.754412	+	0.548113i
$576$		0			0
$577$	−4.03444	+	12.4167i	−0.167956	+	0.516915i	−0.999242	−	0.0389296i	$-0.987605\pi$
$577$	−4.03444	+	12.4167i	−0.167956	+	0.516915i	0.831286	+	0.555845i	$0.187605\pi$
$578$	−1.73607	−	1.26133i	−0.0722109	−	0.0524643i
$579$		0			0
$580$	−11.9721	−	8.69827i	−0.497116	−	0.361176i
$581$	−45.1246	+	32.7849i	−1.87208	+	1.36015i
$582$		0			0
$583$	3.61803	−	2.62866i	0.149844	−	0.108868i
$584$	−7.50000	−	23.0826i	−0.310352	−	0.955166i
$585$		0			0
$586$	−6.42705	+	19.7804i	−0.265499	+	0.817122i
$587$	12.7984	+	39.3893i	0.528245	+	1.62577i	0.757807	+	0.652478i	$0.226271\pi$
$587$	12.7984	+	39.3893i	0.528245	+	1.62577i	−0.229562	+	0.973294i	$0.573729\pi$
$588$		0			0
$589$	1.05573	−	3.24920i	0.0435005	−	0.133881i
$590$	7.23607	−	5.25731i	0.297904	−	0.216440i
$591$		0			0
$592$	−2.50000	+	1.81636i	−0.102749	+	0.0746518i
$593$	−9.74265			−0.400083			−0.200041	−	0.979787i	$-0.564108\pi$
$593$	−9.74265			−0.400083			−0.200041	+	0.979787i	$0.564108\pi$
$594$		0			0
$595$	11.9098	−	36.6547i	0.488255	−	1.50270i
$596$	15.2533	+	11.0822i	0.624799	+	0.453943i
$597$		0			0
$598$	7.76393	−	23.8949i	0.317491	−	0.977136i
$599$	3.52786			0.144145			0.0720723	−	0.997399i	$-0.477039\pi$
$599$	3.52786			0.144145			0.0720723	+	0.997399i	$0.477039\pi$
$600$		0			0
$601$	−8.67376			−0.353810			−0.176905	−	0.984228i	$-0.556609\pi$
$601$	−8.67376			−0.353810			−0.176905	+	0.984228i	$0.556609\pi$
$602$	10.6525	−	32.7849i	0.434163	−	1.33621i
$603$		0			0
$604$	6.09017	+	4.42477i	0.247806	+	0.180041i
$605$	−21.1803			−0.861103
$606$		0			0
$607$	−34.7639			−1.41102			−0.705512	−	0.708698i	$-0.749283\pi$
$607$	−34.7639			−1.41102			−0.705512	+	0.708698i	$0.749283\pi$
$608$	5.00000	−	3.63271i	0.202777	−	0.147326i
$609$		0			0
$610$	−3.61803			−0.146490
$611$	1.32624	−	4.08174i	0.0536538	−	0.165130i
$612$		0			0
$613$	0.461493	+	1.42033i	0.0186395	+	0.0573665i	0.959944	−	0.280193i	$-0.0903985\pi$
$613$	0.461493	+	1.42033i	0.0186395	+	0.0573665i	−0.941304	+	0.337560i	$0.890399\pi$
$614$	−10.0902	+	31.0543i	−0.407206	+	1.25325i
$615$		0			0
$616$	−5.12461	−	15.7719i	−0.206476	−	0.635469i
$617$	−16.1631	+	11.7432i	−0.650703	+	0.472763i	−0.863510	−	0.504331i	$-0.831739\pi$
$617$	−16.1631	+	11.7432i	−0.650703	+	0.472763i	0.212808	+	0.977094i	$0.431739\pi$
$618$		0			0
$619$	13.2361	−	9.61657i	0.532002	−	0.386522i	−0.289104	−	0.957298i	$-0.593357\pi$
$619$	13.2361	−	9.61657i	0.532002	−	0.386522i	0.821106	+	0.570775i	$0.193357\pi$
$620$	5.00000	−	3.63271i	0.200805	−	0.145893i
$621$		0			0
$622$	−14.3262	−	10.4086i	−0.574430	−	0.417348i
$623$	7.43769	−	22.8909i	0.297985	−	0.917103i
$624$		0			0
$625$	−20.2254	−	14.6946i	−0.809017	−	0.587785i
$626$	0.472136			0.0188703
$627$		0			0
$628$	8.73607	+	6.34712i	0.348607	+	0.253278i
$629$	−9.63525	−	7.00042i	−0.384183	−	0.279125i
$630$		0			0
$631$	−19.1803	+	13.9353i	−0.763557	+	0.554757i	−0.899999	−	0.435891i	$-0.856433\pi$
$631$	−19.1803	+	13.9353i	−0.763557	+	0.554757i	0.136442	+	0.990648i	$0.456433\pi$
$632$		0			0
$633$		0			0
$634$	8.90983	+	27.4216i	0.353855	+	1.08905i
$635$	−2.56231	−	7.88597i	−0.101682	−	0.312945i
$636$		0			0
$637$	22.5689	+	69.4599i	0.894212	+	2.75210i
$638$	2.52786	+	7.77997i	0.100079	+	0.308012i
$639$		0			0
$640$	6.70820			0.265165
$641$	−6.50658	−	20.0252i	−0.256994	−	0.790947i	−0.993430	−	0.114440i	$-0.963493\pi$
$641$	−6.50658	−	20.0252i	−0.256994	−	0.790947i	0.736436	−	0.676507i	$-0.236507\pi$
$642$		0			0
$643$	−21.8885			−0.863200			−0.431600	−	0.902065i	$-0.642051\pi$
$643$	−21.8885			−0.863200			−0.431600	+	0.902065i	$0.642051\pi$
$644$	16.1803	−	11.7557i	0.637595	−	0.463240i
$645$		0			0
$646$	−3.85410	−	2.80017i	−0.151638	−	0.110171i
$647$	−27.7984	−	20.1967i	−1.09287	−	0.794014i	−0.112986	−	0.993597i	$-0.536041\pi$
$647$	−27.7984	−	20.1967i	−1.09287	−	0.794014i	−0.979881	+	0.199582i	$0.936041\pi$
$648$		0			0
$649$	4.94427			0.194080
$650$	−8.68034	+	26.7153i	−0.340471	+	1.04786i
$651$		0			0
$652$	4.61803	−	14.2128i	0.180856	−	0.556618i
$653$	−34.0623	−	24.7477i	−1.33296	−	0.968453i	−0.999672	−	0.0256283i	$-0.991841\pi$
$653$	−34.0623	−	24.7477i	−1.33296	−	0.968453i	−0.333289	−	0.942825i	$-0.608159\pi$
$654$		0			0
$655$	5.65248	−	17.3965i	0.220861	−	0.679739i
$656$	2.92705	−	2.12663i	0.114282	−	0.0830308i
$657$		0			0
$658$	−2.76393	+	2.00811i	−0.107749	+	0.0782844i
$659$	10.3262	+	31.7809i	0.402253	+	1.23801i	0.923167	+	0.384399i	$0.125591\pi$
$659$	10.3262	+	31.7809i	0.402253	+	1.23801i	−0.520914	+	0.853609i	$0.674409\pi$
$660$		0			0
$661$	−0.437694	+	1.34708i	−0.0170243	+	0.0523955i	−0.959208	−	0.282702i	$-0.908769\pi$
$661$	−0.437694	+	1.34708i	−0.0170243	+	0.0523955i	0.942183	+	0.335097i	$0.108769\pi$
$662$	2.14590	+	6.60440i	0.0834027	+	0.256687i
$663$		0			0
$664$	−11.5623	+	35.5851i	−0.448704	+	1.38097i
$665$	−3.81966	+	11.7557i	−0.148120	+	0.455867i
$666$		0			0
$667$	−23.9443	+	17.3965i	−0.927126	+	0.673596i
$668$	3.41641			0.132185
$669$		0			0
$670$	1.38197	+	1.00406i	0.0533900	+	0.0387901i
$671$	−1.61803	−	1.17557i	−0.0624635	−	0.0453824i
$672$		0			0
$673$	1.60739	−	4.94704i	0.0619604	−	0.190694i	−0.915285	−	0.402807i	$-0.868034\pi$
$673$	1.60739	−	4.94704i	0.0619604	−	0.190694i	0.977245	+	0.212113i	$0.0680345\pi$
$674$	−2.94427			−0.113409
$675$		0			0
$676$	−18.5623			−0.713935
$677$	−3.27051	+	10.0656i	−0.125696	+	0.386852i	−0.994027	−	0.109132i	$-0.965193\pi$
$677$	−3.27051	+	10.0656i	−0.125696	+	0.386852i	0.868331	+	0.495985i	$0.165193\pi$
$678$		0			0
$679$	7.76393	+	5.64083i	0.297952	+	0.216475i
$680$	−7.98936	−	24.5887i	−0.306378	−	0.942934i
$681$		0			0
$682$	−3.41641			−0.130821
$683$	−15.7082	+	11.4127i	−0.601058	+	0.436694i	−0.846254	−	0.532779i	$-0.821148\pi$
$683$	−15.7082	+	11.4127i	−0.601058	+	0.436694i	0.245196	+	0.969473i	$0.421148\pi$
$684$		0			0
$685$	−13.7812	−	10.0126i	−0.526551	−	0.382562i
$686$	8.29180	−	25.5195i	0.316582	−	0.974340i
$687$		0			0
$688$	−2.38197	−	7.33094i	−0.0908116	−	0.279489i
$689$	−6.28115	+	19.3314i	−0.239293	+	0.736468i
$690$		0			0
$691$	−5.18034	−	15.9434i	−0.197069	−	0.606517i	−0.999946	−	0.0103723i	$-0.996698\pi$
$691$	−5.18034	−	15.9434i	−0.197069	−	0.606517i	0.802877	−	0.596145i	$-0.203302\pi$
$692$	−17.0623	+	12.3965i	−0.648612	+	0.471244i
$693$		0			0
$694$	16.4164	−	11.9272i	0.623158	−	0.452751i
$695$	−15.8541	−	48.7939i	−0.601380	−	1.85086i
$696$		0			0
$697$	11.2812	+	8.19624i	0.427304	+	0.310455i
$698$	1.24671	−	3.83698i	0.0471887	−	0.145232i
$699$		0			0
$700$	−18.0902	+	13.1433i	−0.683744	+	0.496769i
$701$	−20.5623			−0.776628			−0.388314	−	0.921527i	$-0.626942\pi$
$701$	−20.5623			−0.776628			−0.388314	+	0.921527i	$0.626942\pi$
$702$		0			0
$703$	3.09017	+	2.24514i	0.116548	+	0.0846771i
$704$	−7.00000	−	5.08580i	−0.263822	−	0.191678i
$705$		0			0
$706$	−11.6180	+	8.44100i	−0.437250	+	0.317681i
$707$	15.9311			0.599151
$708$		0			0
$709$	−12.4443	−	38.2995i	−0.467354	−	1.43837i	−0.855997	−	0.516981i	$-0.827056\pi$
$709$	−12.4443	−	38.2995i	−0.467354	−	1.43837i	0.388643	−	0.921389i	$-0.372944\pi$
$710$	−3.61803	+	11.1352i	−0.135782	+	0.417895i
$711$		0			0
$712$	−4.98936	−	15.3557i	−0.186984	−	0.575478i
$713$	−3.81966	−	11.7557i	−0.143047	−	0.440255i
$714$		0			0
$715$	−12.5623	+	9.12705i	−0.469804	+	0.341332i
$716$	−5.00000	−	15.3884i	−0.186859	−	0.575092i
$717$		0			0
$718$	−37.4164			−1.39637
$719$	−0.0901699	+	0.0655123i	−0.00336277	+	0.00244320i	−0.589465	−	0.807794i	$-0.700662\pi$
$719$	−0.0901699	+	0.0655123i	−0.00336277	+	0.00244320i	0.586103	+	0.810237i	$0.300662\pi$
$720$		0			0
$721$	11.7082	+	8.50651i	0.436036	+	0.316799i
$722$	−14.1353	−	10.2699i	−0.526060	−	0.382205i
$723$		0			0
$724$	−14.7984			−0.549977
$725$	26.7705	−	19.4499i	0.994232	−	0.722352i
$726$		0			0
$727$	14.4164	−	44.3691i	0.534675	−	1.64556i	−0.209675	−	0.977771i	$-0.567241\pi$
$727$	14.4164	−	44.3691i	0.534675	−	1.64556i	0.744350	−	0.667789i	$-0.232759\pi$
$728$	60.9787	+	44.3036i	2.26002	+	1.64200i
$729$		0			0
$730$	18.0902			0.669547
$731$	24.0344	−	17.4620i	0.888946	−	0.645857i
$732$		0			0
$733$	−23.7984	+	17.2905i	−0.879013	+	0.638640i	−0.932990	−	0.359902i	$-0.882810\pi$
$733$	−23.7984	+	17.2905i	−0.879013	+	0.638640i	0.0539772	+	0.998542i	$0.482810\pi$
$734$	1.85410	+	5.70634i	0.0684362	+	0.210625i
$735$		0			0
$736$	6.90983	−	21.2663i	0.254700	−	0.783885i
$737$	0.291796	+	0.898056i	0.0107484	+	0.0330803i
$738$		0			0
$739$	1.32624	−	4.08174i	0.0487865	−	0.150149i	−0.923696	−	0.383127i	$-0.874847\pi$
$739$	1.32624	−	4.08174i	0.0487865	−	0.150149i	0.972482	+	0.232978i	$0.0748470\pi$
$740$	2.13525	+	6.57164i	0.0784935	+	0.241578i
$741$		0			0
$742$	13.0902	−	9.51057i	0.480555	−	0.349144i
$743$	−41.1246			−1.50872			−0.754358	−	0.656463i	$-0.772052\pi$
$743$	−41.1246			−1.50872			−0.754358	+	0.656463i	$0.772052\pi$
$744$		0			0
$745$	−34.1074	+	24.7805i	−1.24960	+	0.907886i
$746$	2.09017	+	1.51860i	0.0765266	+	0.0555998i
$747$		0			0
$748$	1.47214	−	4.53077i	0.0538266	−	0.165661i
$749$	33.6656			1.23012
$750$		0			0
$751$	36.6525			1.33747			0.668734	−	0.743502i	$-0.266837\pi$
$751$	36.6525			1.33747			0.668734	+	0.743502i	$0.266837\pi$
$752$	−0.236068	+	0.726543i	−0.00860851	+	0.0264943i
$753$		0			0
$754$	−30.0795	−	21.8541i	−1.09543	−	0.795878i
$755$	−13.6180	+	9.89408i	−0.495611	+	0.360082i
$756$		0			0
$757$	29.6180			1.07649			0.538243	−	0.842790i	$-0.319088\pi$
$757$	29.6180			1.07649			0.538243	+	0.842790i	$0.319088\pi$
$758$	−2.76393	+	2.00811i	−0.100391	+	0.0729380i
$759$		0			0
$760$	2.56231	+	7.88597i	0.0929446	+	0.286054i
$761$	−10.1180	+	31.1401i	−0.366778	+	1.12883i	0.582081	+	0.813130i	$0.302238\pi$
$761$	−10.1180	+	31.1401i	−0.366778	+	1.12883i	−0.948860	+	0.315697i	$0.897762\pi$
$762$		0			0
$763$	10.9311	+	33.6425i	0.395733	+	1.21794i
$764$	2.05573	−	6.32688i	0.0743736	−	0.228899i
$765$		0			0
$766$	−10.1459	−	31.2259i	−0.366586	−	1.12824i
$767$	−18.1803	+	13.2088i	−0.656454	+	0.476942i
$768$		0			0
$769$	40.7426	−	29.6013i	1.46922	−	1.06745i	0.488378	−	0.872632i	$-0.337589\pi$
$769$	40.7426	−	29.6013i	1.46922	−	1.06745i	0.980840	−	0.194817i	$-0.0624112\pi$
$770$	12.3607			0.445448
$771$		0			0
$772$	18.8713	+	13.7108i	0.679194	+	0.493463i
$773$	−8.93769	+	27.5074i	−0.321467	+	0.989372i	0.651544	+	0.758611i	$0.274122\pi$
$773$	−8.93769	+	27.5074i	−0.321467	+	0.989372i	−0.973010	+	0.230761i	$0.925878\pi$
$774$		0			0
$775$	4.27051	+	13.1433i	0.153401	+	0.472120i
$776$	6.43769			0.231100
$777$		0			0
$778$	20.9615	+	15.2294i	0.751506	+	0.546001i
$779$	−3.61803	−	2.62866i	−0.129630	−	0.0941814i
$780$		0			0
$781$	−5.23607	+	3.80423i	−0.187361	+	0.136126i
$782$	−17.2361			−0.616361
$783$		0			0
$784$	−4.01722	−	12.3637i	−0.143472	−	0.441562i
$785$	−19.5344	+	14.1926i	−0.697214	+	0.506556i
$786$		0			0
$787$	−4.38197	−	13.4863i	−0.156200	−	0.480735i	0.842080	−	0.539352i	$-0.181331\pi$
$787$	−4.38197	−	13.4863i	−0.156200	−	0.480735i	−0.998281	+	0.0586173i	$0.981331\pi$
$788$	2.35410	+	7.24518i	0.0838614	+	0.258099i
$789$		0			0
$790$		0			0
$791$	25.3262	+	77.9461i	0.900497	+	2.77145i
$792$		0			0
$793$	9.09017			0.322801
$794$	−5.61803	+	4.08174i	−0.199377	+	0.144856i
$795$		0			0
$796$	10.2361	+	7.43694i	0.362808	+	0.263595i
$797$	−39.7254	−	28.8622i	−1.40715	−	1.02235i	−0.993730	−	0.111810i	$-0.964335\pi$
$797$	−39.7254	−	28.8622i	−1.40715	−	1.02235i	−0.413417	−	0.910542i	$-0.635665\pi$
$798$		0			0
$799$	−2.94427			−0.104161
$800$	−7.72542	+	23.7764i	−0.273135	+	0.840623i
$801$		0			0
$802$	−6.93769	+	21.3520i	−0.244978	+	0.753966i
$803$	8.09017	+	5.87785i	0.285496	+	0.207425i
$804$		0			0
$805$	13.8197	+	42.5325i	0.487079	+	1.49908i
$806$	12.5623	−	9.12705i	0.442488	−	0.321487i
$807$		0			0
$808$	8.64590	−	6.28161i	0.304162	−	0.220986i
$809$	−8.71885	−	26.8339i	−0.306538	−	0.943428i	−0.979099	−	0.203386i	$-0.934805\pi$
$809$	−8.71885	−	26.8339i	−0.306538	−	0.943428i	0.672560	−	0.740042i	$-0.265195\pi$
$810$		0			0
$811$	1.47214	−	4.53077i	0.0516937	−	0.159097i	−0.921877	−	0.387483i	$-0.873345\pi$
$811$	1.47214	−	4.53077i	0.0516937	−	0.159097i	0.973571	+	0.228386i	$0.0733447\pi$
$812$	−9.14590	−	28.1482i	−0.320958	−	0.987807i
$813$		0			0
$814$	1.18034	−	3.63271i	0.0413709	−	0.127327i
$815$	27.0344	+	19.6417i	0.946975	+	0.688018i
$816$		0			0
$817$	−7.70820	+	5.60034i	−0.269676	+	0.195931i
$818$	−1.20163			−0.0420139
$819$		0			0
$820$	−2.50000	−	7.69421i	−0.0873038	−	0.268693i
$821$	18.5623	+	13.4863i	0.647829	+	0.470675i	0.862531	−	0.506004i	$-0.168878\pi$
$821$	18.5623	+	13.4863i	0.647829	+	0.470675i	−0.214702	+	0.976680i	$0.568878\pi$
$822$		0			0
$823$	−5.94427	+	18.2946i	−0.207204	+	0.637709i	0.792411	+	0.609987i	$0.208825\pi$
$823$	−5.94427	+	18.2946i	−0.207204	+	0.637709i	−0.999616	+	0.0277222i	$0.991175\pi$
$824$	9.70820			0.338201
$825$		0			0
$826$	17.8885			0.622422
$827$	11.1459	−	34.3035i	0.387581	−	1.19285i	−0.547010	−	0.837126i	$-0.684234\pi$
$827$	11.1459	−	34.3035i	0.387581	−	1.19285i	0.934591	−	0.355725i	$-0.115766\pi$
$828$		0			0
$829$	−9.30902	−	6.76340i	−0.323316	−	0.234902i	0.414273	−	0.910152i	$-0.364036\pi$
$829$	−9.30902	−	6.76340i	−0.323316	−	0.234902i	−0.737589	+	0.675250i	$0.764036\pi$
$830$	−22.5623	−	16.3925i	−0.783149	−	0.568991i
$831$		0			0
$832$	39.3262			1.36339
$833$	40.5344	−	29.4500i	1.40444	−	1.02038i
$834$		0			0
$835$	−2.36068	+	7.26543i	−0.0816947	+	0.251430i
$836$	−0.472136	+	1.45309i	−0.0163292	+	0.0502560i
$837$		0			0
$838$	4.65248	+	14.3188i	0.160717	+	0.494636i
$839$	−4.34752	+	13.3803i	−0.150093	+	0.461939i	−0.997631	−	0.0687961i	$-0.978084\pi$
$839$	−4.34752	+	13.3803i	−0.150093	+	0.461939i	0.847538	+	0.530735i	$0.178084\pi$
$840$		0			0
$841$	4.57295	+	14.0741i	0.157688	+	0.485313i
$842$	24.1525	−	17.5478i	0.832349	−	0.604737i
$843$		0			0
$844$	14.4721	−	10.5146i	0.498151	−	0.361928i
$845$	12.8262	−	39.4751i	0.441236	−	1.35798i
$846$		0			0
$847$	−34.2705	−	24.8990i	−1.17755	−	0.855539i
$848$	1.11803	−	3.44095i	0.0383934	−	0.118163i
$849$		0			0
$850$	19.2705			0.660973
$851$	13.8197			0.473732
$852$		0			0
$853$	−18.7254	−	13.6048i	−0.641146	−	0.465820i	0.219097	−	0.975703i	$-0.429689\pi$
$853$	−18.7254	−	13.6048i	−0.641146	−	0.465820i	−0.860244	+	0.509883i	$0.829689\pi$
$854$	−5.85410	−	4.25325i	−0.200323	−	0.145543i
$855$		0			0
$856$	18.2705	−	13.2743i	0.624473	−	0.453706i
$857$	12.4721			0.426040			0.213020	−	0.977048i	$-0.431670\pi$
$857$	12.4721			0.426040			0.213020	+	0.977048i	$0.431670\pi$
$858$		0			0
$859$	−7.23607	−	22.2703i	−0.246891	−	0.759854i	−0.995320	−	0.0966379i	$-0.969191\pi$
$859$	−7.23607	−	22.2703i	−0.246891	−	0.759854i	0.748428	−	0.663216i	$-0.230809\pi$
$860$	−17.2361			−0.587745
$861$		0			0
$862$	6.38197	+	19.6417i	0.217371	+	0.668998i
$863$	−3.36068	−	10.3431i	−0.114399	−	0.352084i	0.877422	−	0.479719i	$-0.159261\pi$
$863$	−3.36068	−	10.3431i	−0.114399	−	0.352084i	−0.991821	+	0.127635i	$0.959261\pi$
$864$		0			0
$865$	−14.5729	−	44.8509i	−0.495495	−	1.52498i
$866$	6.79180	+	20.9030i	0.230795	+	0.710313i
$867$		0			0
$868$	12.3607			0.419549
$869$		0			0
$870$		0			0
$871$	−3.47214	−	2.52265i	−0.117649	−	0.0854769i
$872$	19.1976	+	13.9478i	0.650111	+	0.472334i
$873$		0			0
$874$	5.52786			0.186983
$875$	−15.4508	−	47.5528i	−0.522334	−	1.60758i
$876$		0			0
$877$	−10.2639	+	31.5891i	−0.346588	+	1.06669i	0.614140	+	0.789197i	$0.289503\pi$
$877$	−10.2639	+	31.5891i	−0.346588	+	1.06669i	−0.960728	+	0.277492i	$0.910497\pi$
$878$	13.0902	+	9.51057i	0.441772	+	0.320966i
$879$		0			0
$880$	2.23607	−	1.62460i	0.0753778	−	0.0547652i
$881$	34.7426	−	25.2420i	1.17051	−	0.850425i	0.179440	−	0.983769i	$-0.442572\pi$
$881$	34.7426	−	25.2420i	1.17051	−	0.850425i	0.991070	+	0.133344i	$0.0425715\pi$
$882$		0			0
$883$	−17.9443	+	13.0373i	−0.603873	+	0.438739i	−0.847251	−	0.531192i	$-0.821744\pi$
$883$	−17.9443	+	13.0373i	−0.603873	+	0.438739i	0.243379	+	0.969931i	$0.421744\pi$
$884$	6.69098	+	20.5927i	0.225042	+	0.692608i
$885$		0			0
$886$	−10.8885	+	33.5115i	−0.365808	+	1.12584i
$887$	7.14590	+	21.9928i	0.239936	+	0.738446i	0.996428	+	0.0844440i	$0.0269114\pi$
$887$	7.14590	+	21.9928i	0.239936	+	0.738446i	−0.756492	+	0.654002i	$0.773089\pi$
$888$		0			0
$889$	5.12461	−	15.7719i	0.171874	−	0.528974i
$890$	12.0344			0.403395
$891$		0			0
$892$	6.61803	−	4.80828i	0.221588	−	0.160993i
$893$	0.944272			0.0315989
$894$		0			0
$895$	36.1803			1.20938
$896$	10.8541	+	7.88597i	0.362610	+	0.263452i
$897$		0			0
$898$	5.19098	−	15.9762i	0.173225	−	0.533133i
$899$	−18.2918			−0.610066
$900$		0			0
$901$	13.9443			0.464551
$902$	−1.38197	+	4.25325i	−0.0460144	+	0.141618i
$903$		0			0
$904$	44.4787	+	32.3157i	1.47934	+	1.07480i
$905$	10.2254	−	31.4706i	0.339905	−	1.04612i
$906$		0			0
$907$	7.12461			0.236569			0.118284	−	0.992980i	$-0.462261\pi$
$907$	7.12461			0.236569			0.118284	+	0.992980i	$0.462261\pi$
$908$	16.1803	−	11.7557i	0.536963	−	0.390127i
$909$		0			0
$910$	−45.4508	+	33.0220i	−1.50668	+	1.09467i
$911$	−5.61803	+	17.2905i	−0.186134	+	0.572861i	−0.999966	−	0.00823898i	$-0.997377\pi$
$911$	−5.61803	+	17.2905i	−0.186134	+	0.572861i	0.813832	+	0.581100i	$0.197377\pi$
$912$		0			0
$913$	−4.76393	−	14.6619i	−0.157663	−	0.485237i
$914$	6.90983	−	21.2663i	0.228557	−	0.703426i
$915$		0			0
$916$	−6.79180	−	20.9030i	−0.224407	−	0.690655i
$917$	29.5967	−	21.5033i	0.977371	−	0.710101i
$918$		0			0
$919$	−39.7984	+	28.9152i	−1.31283	+	0.953825i	−0.312835	+	0.949807i	$0.601279\pi$
$919$	−39.7984	+	28.9152i	−1.31283	+	0.953825i	−0.999992	+	0.00401741i	$0.998721\pi$
$920$	24.2705	+	17.6336i	0.800175	+	0.581361i
$921$		0			0
$922$	26.5344	+	19.2784i	0.873865	+	0.634900i
$923$	9.09017	−	27.9767i	0.299207	−	0.920863i
$924$		0			0
$925$	−15.4508			−0.508021
$926$	−18.7639			−0.616621
$927$		0			0
$928$	−26.7705	−	19.4499i	−0.878785	−	0.638475i
$929$	−7.35410	−	5.34307i	−0.241280	−	0.175300i	0.460573	−	0.887622i	$-0.347644\pi$
$929$	−7.35410	−	5.34307i	−0.241280	−	0.175300i	−0.701853	+	0.712321i	$0.747644\pi$
$930$		0			0
$931$	−13.0000	+	9.44505i	−0.426058	+	0.309549i
$932$	12.3820			0.405585
$933$		0			0
$934$	8.70820	+	26.8011i	0.284941	+	0.876959i
$935$	8.61803	+	6.26137i	0.281840	+	0.204769i
$936$		0			0
$937$	−15.0451	−	46.3040i	−0.491502	−	1.51269i	−0.822339	−	0.568998i	$-0.807331\pi$
$937$	−15.0451	−	46.3040i	−0.491502	−	1.51269i	0.330837	−	0.943688i	$-0.392669\pi$
$938$	1.05573	+	3.24920i	0.0344707	+	0.106090i
$939$		0			0
$940$	1.38197	+	1.00406i	0.0450748	+	0.0327487i
$941$	3.19098	+	9.82084i	0.104023	+	0.320150i	0.989500	−	0.144533i	$-0.0461681\pi$
$941$	3.19098	+	9.82084i	0.104023	+	0.320150i	−0.885477	+	0.464683i	$0.846168\pi$
$942$		0			0
$943$	−16.1803			−0.526904
$944$	3.23607	−	2.35114i	0.105325	−	0.0765231i
$945$		0			0
$946$	7.70820	+	5.60034i	0.250615	+	0.182083i
$947$	2.09017	+	1.51860i	0.0679214	+	0.0493478i	0.621228	−	0.783630i	$-0.286634\pi$
$947$	2.09017	+	1.51860i	0.0679214	+	0.0493478i	−0.553306	+	0.832978i	$0.686634\pi$
$948$		0			0
$949$	−45.4508			−1.47540
$950$	−6.18034			−0.200517
$951$		0			0
$952$	15.9787	−	49.1774i	0.517873	−	1.59385i
$953$	−0.881966	−	0.640786i	−0.0285697	−	0.0207571i	0.573409	−	0.819269i	$-0.305621\pi$
$953$	−0.881966	−	0.640786i	−0.0285697	−	0.0207571i	−0.601978	+	0.798512i	$0.705621\pi$
$954$		0			0
$955$	12.0344	+	8.74353i	0.389425	+	0.282934i
$956$	20.1803	−	14.6619i	0.652679	−	0.474199i
$957$		0			0
$958$	−15.3262	+	11.1352i	−0.495168	+	0.359761i
$959$	−10.5279	−	32.4014i	−0.339962	−	1.04630i
$960$		0			0
$961$	−7.21885	+	22.2173i	−0.232866	+	0.716688i
$962$	5.36475	+	16.5110i	0.172966	+	0.532336i
$963$		0			0
$964$	−8.66312	+	26.6623i	−0.279020	+	0.858736i
$965$	−42.1976	+	30.6583i	−1.35839	+	0.986926i
$966$		0			0
$967$	15.2361	−	11.0697i	0.489959	−	0.355976i	−0.315210	−	0.949022i	$-0.602075\pi$
$967$	15.2361	−	11.0697i	0.489959	−	0.355976i	0.805169	+	0.593046i	$0.202075\pi$
$968$	−28.4164			−0.913338
$969$		0			0
$970$	−1.48278	+	4.56352i	−0.0476092	+	0.146526i
$971$	−27.0344	−	19.6417i	−0.867577	−	0.630331i	0.0623590	−	0.998054i	$-0.480138\pi$
$971$	−27.0344	−	19.6417i	−0.867577	−	0.630331i	−0.929936	+	0.367723i	$0.880138\pi$
$972$		0			0
$973$	31.7082	−	97.5878i	1.01652	−	3.12852i
$974$	−9.70820			−0.311071
$975$		0			0
$976$	−1.61803			−0.0517920
$977$	1.00658	−	3.09793i	0.0322033	−	0.0991115i	−0.933663	−	0.358153i	$-0.883407\pi$
$977$	1.00658	−	3.09793i	0.0322033	−	0.0991115i	0.965866	+	0.259041i	$0.0834066\pi$
$978$		0			0
$979$	5.38197	+	3.91023i	0.172008	+	0.124971i
$980$	−29.0689			−0.928571
$981$		0			0
$982$	5.88854			0.187911
$983$	6.70820	−	4.87380i	0.213958	−	0.155450i	−0.475644	−	0.879638i	$-0.657785\pi$
$983$	6.70820	−	4.87380i	0.213958	−	0.155450i	0.689603	+	0.724188i	$0.257785\pi$
$984$		0			0
$985$	−17.0344			−0.542762
$986$	−7.88197	+	24.2582i	−0.251013	+	0.772538i
$987$		0			0
$988$	−2.14590	−	6.60440i	−0.0682701	−	0.210114i
$989$	−10.6525	+	32.7849i	−0.338729	+	1.04250i
$990$		0			0
$991$	11.4721	+	35.3076i	0.364424	+	1.12158i	0.950341	+	0.311211i	$0.100735\pi$
$991$	11.4721	+	35.3076i	0.364424	+	1.12158i	−0.585916	+	0.810372i	$0.699265\pi$
$992$	11.1803	−	8.12299i	0.354976	−	0.257905i
$993$		0			0
$994$	−18.9443	+	13.7638i	−0.600876	+	0.436562i
$995$	−22.8885	+	16.6295i	−0.725616	+	0.527191i
$996$		0			0
$997$	14.0902	+	10.2371i	0.446240	+	0.324212i	0.788110	−	0.615535i	$-0.211060\pi$
$997$	14.0902	+	10.2371i	0.446240	+	0.324212i	−0.341869	+	0.939747i	$0.611060\pi$
$998$	1.85410	−	5.70634i	0.0586906	−	0.180631i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.h.a.46.1		4
3.2	odd	2		75.2.g.a.46.1	yes	4
15.2	even	4		375.2.i.a.274.2		8
15.8	even	4		375.2.i.a.274.1		8
15.14	odd	2		375.2.g.a.226.1		4
25.6	even	5	inner	225.2.h.a.181.1		4
25.9	even	10		5625.2.a.h.1.2		2
25.16	even	5		5625.2.a.a.1.1		2
75.8	even	20		375.2.i.a.349.2		8
75.17	even	20		375.2.i.a.349.1		8
75.38	even	20		1875.2.b.b.1249.2		4
75.41	odd	10		1875.2.a.d.1.1		2
75.44	odd	10		375.2.g.a.151.1		4
75.56	odd	10		75.2.g.a.31.1	✓	4
75.59	odd	10		1875.2.a.a.1.2		2
75.62	even	20		1875.2.b.b.1249.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.a.31.1	✓	4	75.56	odd	10
75.2.g.a.46.1	yes	4	3.2	odd	2
225.2.h.a.46.1		4	1.1	even	1	trivial
225.2.h.a.181.1		4	25.6	even	5	inner
375.2.g.a.151.1		4	75.44	odd	10
375.2.g.a.226.1		4	15.14	odd	2
375.2.i.a.274.1		8	15.8	even	4
375.2.i.a.274.2		8	15.2	even	4
375.2.i.a.349.1		8	75.17	even	20
375.2.i.a.349.2		8	75.8	even	20
1875.2.a.a.1.2		2	75.59	odd	10
1875.2.a.d.1.1		2	75.41	odd	10
1875.2.b.b.1249.2		4	75.38	even	20
1875.2.b.b.1249.3		4	75.62	even	20
5625.2.a.a.1.1		2	25.16	even	5
5625.2.a.h.1.2		2	25.9	even	10

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{4} +(-1.80902 + 1.31433i) q^{5} -4.47214 q^{7} +(-2.42705 + 1.76336i) q^{8} +(-0.690983 - 2.12663i) q^{10} +(0.381966 - 1.17557i) q^{11} +(1.73607 + 5.34307i) q^{13} +(1.38197 - 4.25325i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(3.11803 - 2.26538i) q^{17} +(-1.00000 + 0.726543i) q^{19} -2.23607 q^{20} +(1.00000 + 0.726543i) q^{22} +(-1.38197 + 4.25325i) q^{23} +(1.54508 - 4.75528i) q^{25} -5.61803 q^{26} +(-3.61803 - 2.62866i) q^{28} +(5.35410 + 3.88998i) q^{29} +(-2.23607 + 1.62460i) q^{31} -5.00000 q^{32} +(1.19098 + 3.66547i) q^{34} +(8.09017 - 5.87785i) q^{35} +(-0.954915 - 2.93893i) q^{37} +(-0.381966 - 1.17557i) q^{38} +(2.07295 - 6.37988i) q^{40} +(1.11803 + 3.44095i) q^{41} +7.70820 q^{43} +(1.00000 - 0.726543i) q^{44} +(-3.61803 - 2.62866i) q^{46} +(-0.618034 - 0.449028i) q^{47} +13.0000 q^{49} +(4.04508 + 2.93893i) q^{50} +(-1.73607 + 5.34307i) q^{52} +(2.92705 + 2.12663i) q^{53} +(0.854102 + 2.62866i) q^{55} +(10.8541 - 7.88597i) q^{56} +(-5.35410 + 3.88998i) q^{58} +(1.23607 + 3.80423i) q^{59} +(0.500000 - 1.53884i) q^{61} +(-0.854102 - 2.62866i) q^{62} +(2.16312 - 6.65740i) q^{64} +(-10.1631 - 7.38394i) q^{65} +(-0.618034 + 0.449028i) q^{67} +3.85410 q^{68} +(3.09017 + 9.51057i) q^{70} +(-4.23607 - 3.07768i) q^{71} +(-2.50000 + 7.69421i) q^{73} +3.09017 q^{74} -1.23607 q^{76} +(-1.70820 + 5.25731i) q^{77} +(1.80902 + 1.31433i) q^{80} -3.61803 q^{82} +(10.0902 - 7.33094i) q^{83} +(-2.66312 + 8.19624i) q^{85} +(-2.38197 + 7.33094i) q^{86} +(1.14590 + 3.52671i) q^{88} +(-1.66312 + 5.11855i) q^{89} +(-7.76393 - 23.8949i) q^{91} +(-3.61803 + 2.62866i) q^{92} +(0.618034 - 0.449028i) q^{94} +(0.854102 - 2.62866i) q^{95} +(-1.73607 - 1.26133i) q^{97} +(-4.01722 + 12.3637i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{4} - 5 q^{5} - 3 q^{8} - 5 q^{10} + 6 q^{11} - 2 q^{13} + 10 q^{14} + q^{16} + 8 q^{17} - 4 q^{19} + 4 q^{22} - 10 q^{23} - 5 q^{25} - 18 q^{26} - 10 q^{28} + 8 q^{29} - 20 q^{32} + 7 q^{34}+ \cdots + 13 q^{98}+O(q^{100}) \) 4 * q + q^2 + q^4 - 5 * q^5 - 3 * q^8 - 5 * q^10 + 6 * q^11 - 2 * q^13 + 10 * q^14 + q^16 + 8 * q^17 - 4 * q^19 + 4 * q^22 - 10 * q^23 - 5 * q^25 - 18 * q^26 - 10 * q^28 + 8 * q^29 - 20 * q^32 + 7 * q^34 + 10 * q^35 - 15 * q^37 - 6 * q^38 + 15 * q^40 + 4 * q^43 + 4 * q^44 - 10 * q^46 + 2 * q^47 + 52 * q^49 + 5 * q^50 + 2 * q^52 + 5 * q^53 - 10 * q^55 + 30 * q^56 - 8 * q^58 - 4 * q^59 + 2 * q^61 + 10 * q^62 - 7 * q^64 - 25 * q^65 + 2 * q^67 + 2 * q^68 - 10 * q^70 - 8 * q^71 - 10 * q^73 - 10 * q^74 + 4 * q^76 + 20 * q^77 + 5 * q^80 - 10 * q^82 + 18 * q^83 + 5 * q^85 - 14 * q^86 + 18 * q^88 + 9 * q^89 - 40 * q^91 - 10 * q^92 - 2 * q^94 - 10 * q^95 + 2 * q^97 + 13 * q^98

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