LMFDB - Embedded newform 625.2.g.a.26.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(26,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([14]))

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

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

chi := DirichletCharacter("625.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.g (of order $25$, degree $20$, not 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:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$11$ over $\Q(\zeta_{25})$
Twist minimal:	no (minimal twist has level 125)
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			26.4
Character	$\chi$	$=$	625.26
Dual form			625.2.g.a.601.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.792152 - 0.957548i) q^{2} +(-2.36710 + 0.299035i) q^{3} +(0.0853705 - 0.447528i) q^{4} +(2.16144 + 2.02973i) q^{6} +(2.62061 - 1.90398i) q^{7} +(-2.67420 + 1.47015i) q^{8} +(2.60800 - 0.669621i) q^{9} +O(q^{10})$	\(q+(-0.792152 - 0.957548i) q^{2} +(-2.36710 + 0.299035i) q^{3} +(0.0853705 - 0.447528i) q^{4} +(2.16144 + 2.02973i) q^{6} +(2.62061 - 1.90398i) q^{7} +(-2.67420 + 1.47015i) q^{8} +(2.60800 - 0.669621i) q^{9} +(-0.631715 - 0.763612i) q^{11} +(-0.0682544 + 1.08487i) q^{12} +(4.52083 - 1.16075i) q^{13} +(-3.89908 - 1.00111i) q^{14} +(2.67891 + 1.06065i) q^{16} +(-0.256883 - 1.34663i) q^{17} +(-2.70713 - 1.96684i) q^{18} +(5.47517 + 0.691675i) q^{19} +(-5.63389 + 5.29058i) q^{21} +(-0.230780 + 1.20979i) q^{22} +(0.119645 - 0.188530i) q^{23} +(5.89047 - 4.27968i) q^{24} +(-4.69266 - 3.40942i) q^{26} +(0.681940 - 0.269999i) q^{27} +(-0.628363 - 1.33534i) q^{28} +(-3.69654 - 7.85554i) q^{29} +(0.289633 + 1.51831i) q^{31} +(0.779561 + 2.39924i) q^{32} +(1.72368 + 1.61864i) q^{33} +(-1.08597 + 1.31271i) q^{34} +(-0.0770276 - 1.22432i) q^{36} +(-9.11089 - 3.60725i) q^{37} +(-3.67486 - 5.79065i) q^{38} +(-10.3542 + 4.09950i) q^{39} +(-3.84937 - 6.06563i) q^{41} +(9.52888 + 1.20378i) q^{42} +(-2.28152 + 7.02180i) q^{43} +(-0.395667 + 0.217520i) q^{44} +(-0.275303 + 0.0347789i) q^{46} +(-7.12232 - 3.91553i) q^{47} +(-6.65841 - 1.70959i) q^{48} +(1.07932 - 3.32180i) q^{49} +(1.01076 + 3.11078i) q^{51} +(-0.133523 - 2.12229i) q^{52} +(-0.393632 + 0.369645i) q^{53} +(-0.798737 - 0.439110i) q^{54} +(-4.20888 + 8.94432i) q^{56} -13.1671 q^{57} +(-4.59383 + 9.76239i) q^{58} +(0.282815 - 4.49522i) q^{59} +(-3.79996 + 5.98778i) q^{61} +(1.22442 - 1.48007i) q^{62} +(5.55960 - 6.72041i) q^{63} +(4.76754 - 7.51245i) q^{64} +(0.184511 - 2.93272i) q^{66} +(6.38100 - 13.5603i) q^{67} -0.624583 q^{68} +(-0.226835 + 0.482048i) q^{69} +(-2.50197 - 1.37547i) q^{71} +(-5.98987 + 5.62486i) q^{72} +(-0.439573 - 6.98681i) q^{73} +(3.76309 + 11.5816i) q^{74} +(0.776961 - 2.39124i) q^{76} +(-3.10938 - 0.798353i) q^{77} +(12.1275 + 6.66717i) q^{78} +(-4.20085 + 0.530691i) q^{79} +(-8.61210 + 4.73454i) q^{81} +(-2.75884 + 8.49085i) q^{82} +(9.16976 + 1.15841i) q^{83} +(1.88671 + 2.97298i) q^{84} +(8.53101 - 3.37767i) q^{86} +(11.0992 + 17.4895i) q^{87} +(2.81196 + 1.11333i) q^{88} +(0.717756 + 11.4084i) q^{89} +(9.63727 - 11.6495i) q^{91} +(-0.0741583 - 0.0696393i) q^{92} +(-1.13962 - 3.50738i) q^{93} +(1.89266 + 9.92165i) q^{94} +(-2.56276 - 5.44613i) q^{96} +(-6.65706 - 14.1470i) q^{97} +(-4.03576 + 1.59787i) q^{98} +(-2.15884 - 1.56849i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 15 q^{7} + 5 q^{8} - 20 q^{9}+O(q^{10}) $ 220 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 15 * q^7 + 5 * q^8 - 20 * q^9	$ 220 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 15 q^{7} + 5 q^{8} - 20 q^{9} - 15 q^{11} + 100 q^{12} + 20 q^{13} - 10 q^{14} + 15 q^{17} - 10 q^{18} - 10 q^{19} - 5 q^{21} - 25 q^{22} + 90 q^{23} + 15 q^{24} + 15 q^{26} - 10 q^{27} - 30 q^{28} - 10 q^{29} - 10 q^{31} - 20 q^{32} - 15 q^{33} + 5 q^{34} - 210 q^{36} - 20 q^{37} - 30 q^{38} - 5 q^{41} - 70 q^{42} - 25 q^{43} + 15 q^{44} + 100 q^{47} - 105 q^{48} - 20 q^{49} + 25 q^{51} - 85 q^{52} - 20 q^{53} + 60 q^{54} - 105 q^{56} - 40 q^{57} + 225 q^{58} + 5 q^{59} - 65 q^{62} - 85 q^{63} + 45 q^{64} + 55 q^{66} + 105 q^{67} - 80 q^{68} + 40 q^{69} - 85 q^{71} - 160 q^{72} - 40 q^{73} + 35 q^{74} + 35 q^{76} - 75 q^{77} + 10 q^{78} + 55 q^{81} + 95 q^{82} - 50 q^{83} + 115 q^{84} + 40 q^{86} - 95 q^{87} - 165 q^{88} + 55 q^{89} - 105 q^{91} - 155 q^{92} + 185 q^{93} + 60 q^{94} + 135 q^{96} - 65 q^{97} - 135 q^{98} + 45 q^{99}+O(q^{100}) $ 220 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 15 * q^7 + 5 * q^8 - 20 * q^9 - 15 * q^11 + 100 * q^12 + 20 * q^13 - 10 * q^14 + 15 * q^17 - 10 * q^18 - 10 * q^19 - 5 * q^21 - 25 * q^22 + 90 * q^23 + 15 * q^24 + 15 * q^26 - 10 * q^27 - 30 * q^28 - 10 * q^29 - 10 * q^31 - 20 * q^32 - 15 * q^33 + 5 * q^34 - 210 * q^36 - 20 * q^37 - 30 * q^38 - 5 * q^41 - 70 * q^42 - 25 * q^43 + 15 * q^44 + 100 * q^47 - 105 * q^48 - 20 * q^49 + 25 * q^51 - 85 * q^52 - 20 * q^53 + 60 * q^54 - 105 * q^56 - 40 * q^57 + 225 * q^58 + 5 * q^59 - 65 * q^62 - 85 * q^63 + 45 * q^64 + 55 * q^66 + 105 * q^67 - 80 * q^68 + 40 * q^69 - 85 * q^71 - 160 * q^72 - 40 * q^73 + 35 * q^74 + 35 * q^76 - 75 * q^77 + 10 * q^78 + 55 * q^81 + 95 * q^82 - 50 * q^83 + 115 * q^84 + 40 * q^86 - 95 * q^87 - 165 * q^88 + 55 * q^89 - 105 * q^91 - 155 * q^92 + 185 * q^93 + 60 * q^94 + 135 * q^96 - 65 * q^97 - 135 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{25}\right)$

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 $

$2$	−0.792152	−	0.957548i	−0.560136	−	0.677088i	0.412087	−	0.911145i	$-0.364800\pi$
$2$	−0.792152	−	0.957548i	−0.560136	−	0.677088i	−0.972223	+	0.234056i	$0.924800\pi$
$3$	−2.36710	+	0.299035i	−1.36665	+	0.172648i	−0.774189	−	0.632954i	$-0.781842\pi$
$3$	−2.36710	+	0.299035i	−1.36665	+	0.172648i	−0.592458	+	0.805602i	$0.701842\pi$
$4$	0.0853705	−	0.447528i	0.0426852	−	0.223764i
$5$		0			0
$5$		0			0
$6$	2.16144	+	2.02973i	0.882406	+	0.828635i
$7$	2.62061	−	1.90398i	0.990497	−	0.719638i	0.0304671	−	0.999536i	$-0.490301\pi$
$7$	2.62061	−	1.90398i	0.990497	−	0.719638i	0.960030	+	0.279898i	$0.0903005\pi$
$8$	−2.67420	+	1.47015i	−0.945472	+	0.519778i
$9$	2.60800	−	0.669621i	0.869334	−	0.223207i
$10$		0			0
$11$	−0.631715	−	0.763612i	−0.190469	−	0.230238i	0.666630	−	0.745388i	$-0.267736\pi$
$11$	−0.631715	−	0.763612i	−0.190469	−	0.230238i	−0.857100	+	0.515151i	$0.827736\pi$
$12$	−0.0682544	+	1.08487i	−0.0197033	+	0.313176i
$13$	4.52083	−	1.16075i	1.25385	−	0.321935i	0.437358	−	0.899288i	$-0.355914\pi$
$13$	4.52083	−	1.16075i	1.25385	−	0.321935i	0.816495	+	0.577353i	$0.195914\pi$
$14$	−3.89908	−	1.00111i	−1.04207	−	0.267559i
$15$		0			0
$16$	2.67891	+	1.06065i	0.669726	+	0.265163i
$17$	−0.256883	−	1.34663i	−0.0623032	−	0.326605i	0.937466	−	0.348076i	$-0.113165\pi$
$17$	−0.256883	−	1.34663i	−0.0623032	−	0.326605i	−0.999769	+	0.0214713i	$0.993165\pi$
$18$	−2.70713	−	1.96684i	−0.638076	−	0.463589i
$19$	5.47517	+	0.691675i	1.25609	+	0.158681i	0.725068	−	0.688677i	$-0.241808\pi$
$19$	5.47517	+	0.691675i	1.25609	+	0.158681i	0.531022	+	0.847358i	$0.321808\pi$
$20$		0			0
$21$	−5.63389	+	5.29058i	−1.22942	+	1.15450i
$22$	−0.230780	+	1.20979i	−0.0492026	+	0.257929i
$23$	0.119645	−	0.188530i	0.0249477	−	0.0393112i	−0.831625	−	0.555337i	$-0.812589\pi$
$23$	0.119645	−	0.188530i	0.0249477	−	0.0393112i	0.856573	+	0.516026i	$0.172589\pi$
$24$	5.89047	−	4.27968i	1.20239	−	0.873586i
$25$		0			0
$26$	−4.69266	−	3.40942i	−0.920306	−	0.668642i
$27$	0.681940	−	0.269999i	0.131239	−	0.0519614i
$28$	−0.628363	−	1.33534i	−0.118749	−	0.252355i
$29$	−3.69654	−	7.85554i	−0.686429	−	1.45874i	−0.878690	−	0.477393i	$-0.841582\pi$
$29$	−3.69654	−	7.85554i	−0.686429	−	1.45874i	0.192261	−	0.981344i	$-0.438418\pi$
$30$		0			0
$31$	0.289633	+	1.51831i	0.0520196	+	0.272696i	0.998788	−	0.0492193i	$-0.0156733\pi$
$31$	0.289633	+	1.51831i	0.0520196	+	0.272696i	−0.946768	+	0.321915i	$0.895673\pi$
$32$	0.779561	+	2.39924i	0.137808	+	0.424130i
$33$	1.72368	+	1.61864i	0.300054	+	0.281769i
$34$	−1.08597	+	1.31271i	−0.186242	+	0.225128i
$35$		0			0
$36$	−0.0770276	−	1.22432i	−0.0128379	−	0.204053i
$37$	−9.11089	−	3.60725i	−1.49782	−	0.593029i	−0.530748	−	0.847530i	$-0.678089\pi$
$37$	−9.11089	−	3.60725i	−1.49782	−	0.593029i	−0.967073	+	0.254501i	$0.918089\pi$
$38$	−3.67486	−	5.79065i	−0.596140	−	0.939367i
$39$	−10.3542	+	4.09950i	−1.65799	+	0.656446i
$40$		0			0
$41$	−3.84937	−	6.06563i	−0.601170	−	0.947292i	−0.999548	−	0.0300707i	$-0.990427\pi$
$41$	−3.84937	−	6.06563i	−0.601170	−	0.947292i	0.398378	−	0.917221i	$-0.369573\pi$
$42$	9.52888	+	1.20378i	1.47034	+	0.185747i
$43$	−2.28152	+	7.02180i	−0.347929	+	1.07081i	0.612069	+	0.790805i	$0.290338\pi$
$43$	−2.28152	+	7.02180i	−0.347929	+	1.07081i	−0.959997	+	0.280009i	$0.909662\pi$
$44$	−0.395667	+	0.217520i	−0.0596491	+	0.0327924i
$45$		0			0
$46$	−0.275303	+	0.0347789i	−0.0405913	+	0.00512787i
$47$	−7.12232	−	3.91553i	−1.03890	−	0.571138i	−0.131458	−	0.991322i	$-0.541966\pi$
$47$	−7.12232	−	3.91553i	−1.03890	−	0.571138i	−0.907439	+	0.420183i	$0.861966\pi$
$48$	−6.65841	−	1.70959i	−0.961059	−	0.246758i
$49$	1.07932	−	3.32180i	0.154188	−	0.474542i
$50$		0			0
$51$	1.01076	+	3.11078i	0.141534	+	0.435597i
$52$	−0.133523	−	2.12229i	−0.0185163	−	0.294309i
$53$	−0.393632	+	0.369645i	−0.0540695	+	0.0507747i	−0.711111	−	0.703080i	$-0.751808\pi$
$53$	−0.393632	+	0.369645i	−0.0540695	+	0.0507747i	0.657041	+	0.753854i	$0.271808\pi$
$54$	−0.798737	−	0.439110i	−0.108694	−	0.0597553i
$55$		0			0
$56$	−4.20888	+	8.94432i	−0.562435	+	1.19524i
$57$	−13.1671			−1.74403
$58$	−4.59383	+	9.76239i	−0.603200	+	1.28186i
$59$	0.282815	−	4.49522i	0.0368194	−	0.585228i	−0.935757	−	0.352645i	$-0.885282\pi$
$59$	0.282815	−	4.49522i	0.0368194	−	0.585228i	0.972577	−	0.232583i	$-0.0747177\pi$
$60$		0			0
$61$	−3.79996	+	5.98778i	−0.486535	+	0.766657i	−0.995563	−	0.0940928i	$-0.970005\pi$
$61$	−3.79996	+	5.98778i	−0.486535	+	0.766657i	0.509028	+	0.860750i	$0.330005\pi$
$62$	1.22442	−	1.48007i	0.155501	−	0.187969i
$63$	5.55960	−	6.72041i	0.700444	−	0.846691i
$64$	4.76754	−	7.51245i	0.595943	−	0.939056i
$65$		0			0
$66$	0.184511	−	2.93272i	0.0227117	−	0.360992i
$67$	6.38100	−	13.5603i	0.779563	−	1.65666i	0.0256600	−	0.999671i	$-0.491831\pi$
$67$	6.38100	−	13.5603i	0.779563	−	1.65666i	0.753903	−	0.656986i	$-0.228169\pi$
$68$	−0.624583			−0.0757418
$69$	−0.226835	+	0.482048i	−0.0273077	+	0.0580317i
$70$		0			0
$71$	−2.50197	−	1.37547i	−0.296930	−	0.163238i	0.326325	−	0.945258i	$-0.394190\pi$
$71$	−2.50197	−	1.37547i	−0.296930	−	0.163238i	−0.623254	+	0.782019i	$0.714190\pi$
$72$	−5.98987	+	5.62486i	−0.705912	+	0.662896i
$73$	−0.439573	−	6.98681i	−0.0514481	−	0.817744i	−0.936153	−	0.351593i	$-0.885640\pi$
$73$	−0.439573	−	6.98681i	−0.0514481	−	0.817744i	0.884705	−	0.466152i	$-0.154360\pi$
$74$	3.76309	+	11.5816i	0.437450	+	1.34633i
$75$		0			0
$76$	0.776961	−	2.39124i	0.0891236	−	0.274294i
$77$	−3.10938	−	0.798353i	−0.354347	−	0.0909808i
$78$	12.1275	+	6.66717i	1.37317	+	0.754909i
$79$	−4.20085	+	0.530691i	−0.472633	+	0.0597074i	−0.358042	−	0.933705i	$-0.616556\pi$
$79$	−4.20085	+	0.530691i	−0.472633	+	0.0597074i	−0.114591	+	0.993413i	$0.536556\pi$
$80$		0			0
$81$	−8.61210	+	4.73454i	−0.956900	+	0.526060i
$82$	−2.75884	+	8.49085i	−0.304663	+	0.937658i
$83$	9.16976	+	1.15841i	1.00651	+	0.127152i	0.611267	−	0.791424i	$-0.290660\pi$
$83$	9.16976	+	1.15841i	1.00651	+	0.127152i	0.395244	+	0.918576i	$0.370660\pi$
$84$	1.88671	+	2.97298i	0.205857	+	0.324379i
$85$		0			0
$86$	8.53101	−	3.37767i	0.919923	−	0.364223i
$87$	11.0992	+	17.4895i	1.18995	+	1.87507i
$88$	2.81196	+	1.11333i	0.299755	+	0.118682i
$89$	0.717756	+	11.4084i	0.0760820	+	1.20929i	0.832058	+	0.554689i	$0.187163\pi$
$89$	0.717756	+	11.4084i	0.0760820	+	1.20929i	−0.755976	+	0.654599i	$0.772837\pi$
$90$		0			0
$91$	9.63727	−	11.6495i	1.01026	−	1.22120i
$92$	−0.0741583	−	0.0696393i	−0.00773154	−	0.00726040i
$93$	−1.13962	−	3.50738i	−0.118173	−	0.363698i
$94$	1.89266	+	9.92165i	0.195213	+	1.02334i
$95$		0			0
$96$	−2.56276	−	5.44613i	−0.261560	−	0.555844i
$97$	−6.65706	−	14.1470i	−0.675922	−	1.43641i	−0.888320	−	0.459224i	$-0.848127\pi$
$97$	−6.65706	−	14.1470i	−0.675922	−	1.43641i	0.212398	−	0.977183i	$-0.431873\pi$
$98$	−4.03576	+	1.59787i	−0.407673	+	0.161409i
$99$	−2.15884	−	1.56849i	−0.216972	−	0.157639i
$100$		0			0
$101$	11.1631	−	8.11046i	1.11077	−	0.807021i	0.127984	−	0.991776i	$-0.459149\pi$
$101$	11.1631	−	8.11046i	1.11077	−	0.807021i	0.982785	+	0.184755i	$0.0591492\pi$
$102$	2.17805	−	3.43206i	0.215659	−	0.339825i
$103$	−2.83256	+	14.8488i	−0.279100	+	1.46310i	0.515985	+	0.856598i	$0.327426\pi$
$103$	−2.83256	+	14.8488i	−0.279100	+	1.46310i	−0.795085	+	0.606498i	$0.792574\pi$
$104$	−10.3831	+	9.75039i	−1.01815	+	0.956105i
$105$		0			0
$106$	0.665769	+	0.0841062i	0.0646652	+	0.00816912i
$107$	12.7584	+	9.26955i	1.23341	+	0.896121i	0.997141	−	0.0755674i	$-0.0240768\pi$
$107$	12.7584	+	9.26955i	1.23341	+	0.896121i	0.236265	+	0.971689i	$0.424077\pi$
$108$	−0.0626146	−	0.328237i	−0.00602509	−	0.0315846i
$109$	4.92206	+	1.94878i	0.471448	+	0.186660i	0.591821	−	0.806069i	$-0.298409\pi$
$109$	4.92206	+	1.94878i	0.471448	+	0.186660i	−0.120373	+	0.992729i	$0.538409\pi$
$110$		0			0
$111$	22.6451	+	5.81427i	2.14938	+	0.551866i
$112$	9.03983	−	2.32103i	0.854184	−	0.219317i
$113$	0.913801	−	14.5244i	0.0859631	−	1.36635i	−0.684571	−	0.728946i	$-0.740010\pi$
$113$	0.913801	−	14.5244i	0.0859631	−	1.36635i	0.770534	−	0.637399i	$-0.219990\pi$
$114$	10.4304	+	12.6081i	0.976893	+	1.18086i
$115$		0			0
$116$	−3.83115	+	0.983671i	−0.355713	+	0.0913316i
$117$	11.0131	−	6.05448i	1.01816	−	0.559737i
$118$	−4.52842	+	3.29009i	−0.416875	+	0.302877i
$119$	−3.23714	−	3.03988i	−0.296748	−	0.278665i
$120$		0			0
$121$	1.87715	−	9.84039i	0.170650	−	0.894581i
$122$	8.74374	−	1.10459i	0.791621	−	0.100005i
$123$	10.9257	+	13.2069i	0.985135	+	1.19082i
$124$	0.704211			0.0632400
$125$		0			0
$126$	−10.8392			−0.965629
$127$	4.72608	+	5.71284i	0.419371	+	0.506933i	0.937316	−	0.348481i	$-0.113303\pi$
$127$	4.72608	+	5.71284i	0.419371	+	0.506933i	−0.517944	+	0.855414i	$0.673303\pi$
$128$	−5.96451	+	0.753492i	−0.527193	+	0.0665999i
$129$	3.30083	−	17.3036i	0.290622	−	1.52349i
$130$		0			0
$131$	−1.97957	−	1.85894i	−0.172956	−	0.162416i	0.593235	−	0.805029i	$-0.297850\pi$
$131$	−1.97957	−	1.85894i	−0.172956	−	0.162416i	−0.766191	+	0.642613i	$0.777850\pi$
$132$	0.871539	−	0.633210i	0.0758577	−	0.0551138i
$133$	15.6652	−	8.61202i	1.35835	−	0.746757i
$134$	−18.0394	+	4.63172i	−1.55836	+	0.400120i
$135$		0			0
$136$	2.66670	+	3.22349i	0.228668	+	0.276412i
$137$	−0.717230	+	11.4001i	−0.0612771	+	0.973972i	0.840511	+	0.541794i	$0.182255\pi$
$137$	−0.717230	+	11.4001i	−0.0612771	+	0.973972i	−0.901788	+	0.432178i	$0.857745\pi$
$138$	0.641271	−	0.164650i	0.0545886	−	0.0140160i
$139$	−11.3326	−	2.90972i	−0.961220	−	0.246799i	−0.264695	−	0.964332i	$-0.585271\pi$
$139$	−11.3326	−	2.90972i	−0.961220	−	0.246799i	−0.696525	+	0.717533i	$0.745271\pi$
$140$		0			0
$141$	18.0301	+	7.13863i	1.51841	+	0.601181i
$142$	0.664864	+	3.48534i	0.0557942	+	0.292483i
$143$	−3.74224	−	2.71890i	−0.312942	−	0.227365i
$144$	7.69682	+	0.972335i	0.641402	+	0.0810279i
$145$		0			0
$146$	−6.34200	+	5.95553i	−0.524867	+	0.492883i
$147$	−1.56152	+	8.18578i	−0.128792	+	0.675152i
$148$	−2.39215	+	3.76942i	−0.196633	+	0.309844i
$149$	2.32856	−	1.69180i	0.190763	−	0.138598i	−0.488304	−	0.872673i	$-0.662384\pi$
$149$	2.32856	−	1.69180i	0.190763	−	0.138598i	0.679067	+	0.734076i	$0.262384\pi$
$150$		0			0
$151$	−7.37815	−	5.36054i	−0.600426	−	0.436235i	0.245604	−	0.969370i	$-0.421014\pi$
$151$	−7.37815	−	5.36054i	−0.600426	−	0.436235i	−0.846030	+	0.533135i	$0.821014\pi$
$152$	−15.6586	+	6.19966i	−1.27008	+	0.502859i
$153$	−1.57168	−	3.33999i	−0.127063	−	0.270022i
$154$	1.69864	+	3.60980i	0.136880	+	0.290886i
$155$		0			0
$156$	0.950701	+	4.98375i	0.0761170	+	0.399019i
$157$	−2.16061	−	6.64966i	−0.172435	−	0.530701i	0.827072	−	0.562096i	$-0.190005\pi$
$157$	−2.16061	−	6.64966i	−0.172435	−	0.530701i	−0.999507	+	0.0313955i	$0.990005\pi$
$158$	3.83588	+	3.60213i	0.305166	+	0.286570i
$159$	0.821231	−	0.992698i	0.0651278	−	0.0787260i
$160$		0			0
$161$	−0.0454159	−	0.721865i	−0.00357928	−	0.0568910i
$162$	11.3556	+	4.49602i	0.892183	+	0.353240i
$163$	5.81060	+	9.15605i	0.455122	+	0.717157i	0.991963	−	0.126526i	$-0.0403827\pi$
$163$	5.81060	+	9.15605i	0.455122	+	0.717157i	−0.536842	+	0.843683i	$0.680383\pi$
$164$	−3.04316	+	1.20487i	−0.237631	+	0.0940847i
$165$		0			0
$166$	−6.15461	−	9.69812i	−0.477691	−	0.752720i
$167$	−5.63547	−	0.711926i	−0.436086	−	0.0550905i	−0.0957740	−	0.995403i	$-0.530533\pi$
$167$	−5.63547	−	0.711926i	−0.436086	−	0.0550905i	−0.340312	+	0.940313i	$0.610533\pi$
$168$	7.28819	−	22.4307i	0.562296	−	1.73057i
$169$	7.69857	−	4.23233i	0.592198	−	0.325564i
$170$		0			0
$171$	14.7424	−	1.86240i	1.12738	−	0.142421i
$172$	2.94767	+	1.62050i	0.224758	+	0.123562i
$173$	−13.2509	−	3.40226i	−1.00745	−	0.258669i	−0.291311	−	0.956628i	$-0.594092\pi$
$173$	−13.2509	−	3.40226i	−1.00745	−	0.258669i	−0.716137	+	0.697959i	$0.754092\pi$
$174$	7.95478	−	24.4823i	0.603050	−	1.85600i
$175$		0			0
$176$	−0.882376	−	2.71567i	−0.0665116	−	0.204702i
$177$	0.674773	+	10.7252i	0.0507191	+	0.806157i
$178$	10.3555	−	9.72448i	0.776179	−	0.728880i
$179$	11.6804	+	6.42136i	0.873036	+	0.479955i	0.854247	−	0.519868i	$-0.174019\pi$
$179$	11.6804	+	6.42136i	0.873036	+	0.479955i	0.0187890	+	0.999823i	$0.494019\pi$
$180$		0			0
$181$	1.24441	−	2.64450i	0.0924960	−	0.196564i	−0.853226	−	0.521542i	$-0.825357\pi$
$181$	1.24441	−	2.64450i	0.0924960	−	0.196564i	0.945722	+	0.324978i	$0.105357\pi$
$182$	−18.7891			−1.39274
$183$	7.20435	−	15.3100i	0.532561	−	1.13175i
$184$	−0.0427859	+	0.680063i	−0.00315422	+	0.0501349i
$185$		0			0
$186$	−2.45573	+	3.86961i	−0.180063	+	0.283734i
$187$	−0.866023	+	1.04684i	−0.0633299	+	0.0765527i
$188$	−2.36034	+	2.85316i	−0.172146	+	0.208088i
$189$	1.27302	−	2.00596i	0.0925989	−	0.145912i
$190$		0			0
$191$	0.364982	−	5.80123i	0.0264092	−	0.419762i	−0.962504	−	0.271267i	$-0.912557\pi$
$191$	0.364982	−	5.80123i	0.0264092	−	0.419762i	0.988913	−	0.148495i	$-0.0474428\pi$
$192$	−9.03878	+	19.2084i	−0.652318	+	1.38625i
$193$	−10.0838			−0.725850			−0.362925	−	0.931818i	$-0.618222\pi$
$193$	−10.0838			−0.725850			−0.362925	+	0.931818i	$0.618222\pi$
$194$	−8.27299	+	17.5810i	−0.593966	+	1.26224i
$195$		0			0
$196$	−1.39445	−	0.766607i	−0.0996038	−	0.0547577i
$197$	8.23150	−	7.72989i	0.586470	−	0.550732i	−0.333485	−	0.942755i	$-0.608225\pi$
$197$	8.23150	−	7.72989i	0.586470	−	0.550732i	0.919955	+	0.392023i	$0.128225\pi$
$198$	0.208227	+	3.30968i	0.0147981	+	0.235209i
$199$	−0.332337	−	1.02283i	−0.0235588	−	0.0725064i	0.938586	−	0.345046i	$-0.112137\pi$
$199$	−0.332337	−	1.02283i	−0.0235588	−	0.0725064i	−0.962145	+	0.272539i	$0.912137\pi$
$200$		0			0
$201$	−11.0495	+	34.0068i	−0.779370	+	2.39865i
$202$	−16.6090	−	4.26447i	−1.16861	−	0.300047i
$203$	−24.6440	−	13.5481i	−1.72967	−	0.950894i
$204$	1.47845	−	0.186772i	0.103512	−	0.0130766i
$205$		0			0
$206$	16.4622	−	9.05020i	1.14698	−	0.630557i
$207$	0.185790	−	0.571803i	0.0129133	−	0.0397431i
$208$	13.3420	+	1.68549i	0.925103	+	0.116868i
$209$	−2.93057	−	4.61784i	−0.202712	−	0.319423i
$210$		0			0
$211$	10.6629	−	4.22172i	0.734061	−	0.290635i	0.0288023	−	0.999585i	$-0.490831\pi$
$211$	10.6629	−	4.22172i	0.734061	−	0.290635i	0.705259	+	0.708950i	$0.250831\pi$
$212$	0.131822	+	0.207718i	0.00905357	+	0.0142661i
$213$	6.33374	+	2.50770i	0.433981	+	0.171825i
$214$	−1.23059	−	19.5597i	−0.0841216	−	1.33707i
$215$		0			0
$216$	−1.42670	+	1.72459i	−0.0970748	+	0.117343i
$217$	3.64985	+	3.42743i	0.247768	+	0.232669i
$218$	−2.03297	−	6.25684i	−0.137690	−	0.423767i
$219$	3.12981	+	16.4070i	0.211493	+	1.10869i
$220$		0			0
$221$	−2.72442	−	5.78969i	−0.183264	−	0.389457i
$222$	−12.3709	−	26.2895i	−0.830282	−	1.76444i
$223$	16.4582	−	6.51625i	1.10212	−	0.436360i	0.254559	−	0.967057i	$-0.418070\pi$
$223$	16.4582	−	6.51625i	1.10212	−	0.436360i	0.847562	+	0.530697i	$0.178070\pi$
$224$	6.61104	+	4.80320i	0.441719	+	0.320927i
$225$		0			0
$226$	−14.6317	+	10.6306i	−0.973287	+	0.707135i
$227$	−2.29233	+	3.61214i	−0.152147	+	0.239746i	−0.911849	−	0.410526i	$-0.865345\pi$
$227$	−2.29233	+	3.61214i	−0.152147	+	0.239746i	0.759701	+	0.650272i	$0.225345\pi$
$228$	−1.12408	+	5.89265i	−0.0744442	+	0.390250i
$229$	7.99173	−	7.50473i	0.528108	−	0.495927i	−0.374004	−	0.927427i	$-0.622016\pi$
$229$	7.99173	−	7.50473i	0.528108	−	0.495927i	0.902113	+	0.431500i	$0.142016\pi$
$230$		0			0
$231$	7.59896	+	0.959971i	0.499975	+	0.0631615i
$232$	21.4341	+	15.5728i	1.40722	+	1.02240i
$233$	2.34393	+	12.2873i	0.153556	+	0.804969i	0.972822	+	0.231555i	$0.0743814\pi$
$233$	2.34393	+	12.2873i	0.153556	+	0.804969i	−0.819266	+	0.573414i	$0.805619\pi$
$234$	−14.5215	−	5.74946i	−0.949299	−	0.375854i
$235$		0			0
$236$	−1.98759	−	0.510327i	−0.129381	−	0.0332194i
$237$	9.78516	−	2.51240i	0.635614	−	0.163198i
$238$	−0.346519	+	5.50777i	−0.0224615	+	0.357015i
$239$	9.00679	+	10.8873i	0.582601	+	0.704243i	0.976648	−	0.214847i	$-0.0689253\pi$
$239$	9.00679	+	10.8873i	0.582601	+	0.704243i	−0.394047	+	0.919090i	$0.628925\pi$
$240$		0			0
$241$	−13.9061	+	3.57047i	−0.895769	+	0.229994i	−0.668389	−	0.743812i	$-0.733016\pi$
$241$	−13.9061	+	3.57047i	−0.895769	+	0.229994i	−0.227380	+	0.973806i	$0.573016\pi$
$242$	−10.9096	+	5.99762i	−0.701298	+	0.385542i
$243$	17.1898	−	12.4891i	1.10273	−	0.801178i
$244$	2.35529	+	2.21177i	0.150782	+	0.141594i
$245$		0			0
$246$	3.99141	−	20.9237i	0.254483	−	1.33405i
$247$	25.5552	−	3.22837i	1.62604	−	0.205416i
$248$	−3.00668	−	3.63445i	−0.190924	−	0.230788i
$249$	−22.0522			−1.39750
$250$		0			0
$251$	−4.00206			−0.252608			−0.126304	−	0.991992i	$-0.540311\pi$
$251$	−4.00206			−0.252608			−0.126304	+	0.991992i	$0.540311\pi$
$252$	−2.53294	−	3.06180i	−0.159560	−	0.192875i
$253$	−0.219545	+	0.0277350i	−0.0138027	+	0.00174368i
$254$	1.72655	−	9.05088i	0.108333	−	0.567903i
$255$		0			0
$256$	−7.52576	−	7.06716i	−0.470360	−	0.441698i
$257$	7.82522	−	5.68535i	0.488124	−	0.354643i	−0.316339	−	0.948646i	$-0.602454\pi$
$257$	7.82522	−	5.68535i	0.488124	−	0.354643i	0.804462	+	0.594004i	$0.202454\pi$
$258$	−19.1837	+	10.5464i	−1.19433	+	0.656587i
$259$	−30.7442	+	7.89377i	−1.91035	+	0.490495i
$260$		0			0
$261$	−14.9008	−	18.0120i	−0.922336	−	1.11491i
$262$	−0.211902	+	3.36809i	−0.0130914	+	0.208081i
$263$	−7.83802	+	2.01246i	−0.483313	+	0.124094i	−0.482482	−	0.875906i	$-0.660265\pi$
$263$	−7.83802	+	2.01246i	−0.483313	+	0.124094i	−0.000831154		1.00000i	$0.500265\pi$
$264$	−6.98911	−	1.79450i	−0.430150	−	0.110444i
$265$		0			0
$266$	−20.6557	−	8.17815i	−1.26648	−	0.501435i
$267$	−5.11051	−	26.7902i	−0.312758	−	1.63953i
$268$	−5.52387	−	4.01333i	−0.337424	−	0.245153i
$269$	−3.30959	−	0.418099i	−0.201789	−	0.0254919i	0.0237888	−	0.999717i	$-0.492427\pi$
$269$	−3.30959	−	0.418099i	−0.201789	−	0.0254919i	−0.225578	+	0.974225i	$0.572427\pi$
$270$		0			0
$271$	−12.6232	+	11.8540i	−0.766806	+	0.720079i	−0.965620	−	0.259959i	$-0.916291\pi$
$271$	−12.6232	+	11.8540i	−0.766806	+	0.720079i	0.198814	+	0.980037i	$0.436291\pi$
$272$	0.740140	−	3.87995i	0.0448776	−	0.235256i
$273$	−19.3288	+	30.4573i	−1.16983	+	1.84336i
$274$	11.4842	−	8.34379i	0.693789	−	0.504067i
$275$		0			0
$276$	0.196365	+	0.142667i	0.0118198	+	0.00858757i
$277$	14.1761	−	5.61270i	0.851757	−	0.337234i	0.0986414	−	0.995123i	$-0.468550\pi$
$277$	14.1761	−	5.61270i	0.851757	−	0.337234i	0.753115	+	0.657889i	$0.228550\pi$
$278$	6.19096	+	13.1565i	0.371309	+	0.789072i
$279$	1.77205	+	3.76580i	0.106090	+	0.225453i
$280$		0			0
$281$	−0.0932931	−	0.489060i	−0.00556540	−	0.0291748i	0.979396	−	0.201948i	$-0.0647272\pi$
$281$	−0.0932931	−	0.489060i	−0.00556540	−	0.0291748i	−0.984962	+	0.172773i	$0.944727\pi$
$282$	−7.44703	−	22.9196i	−0.443464	−	1.36484i
$283$	1.60122	+	1.50365i	0.0951828	+	0.0893826i	0.730678	−	0.682722i	$-0.239204\pi$
$283$	1.60122	+	1.50365i	0.0951828	+	0.0893826i	−0.635495	+	0.772105i	$0.719204\pi$
$284$	−0.829156	+	1.00228i	−0.0492014	+	0.0594742i
$285$		0			0
$286$	0.360951	+	5.73715i	0.0213435	+	0.339245i
$287$	−21.6365	−	8.56651i	−1.27716	−	0.505665i
$288$	3.63968	+	5.73521i	0.214470	+	0.337951i
$289$	14.0588	−	5.56627i	0.826987	−	0.327428i
$290$		0			0
$291$	19.9884	+	31.4966i	1.17174	+	1.84637i
$292$	−3.16432	−	0.399746i	−0.185178	−	0.0233934i
$293$	−0.847815	+	2.60931i	−0.0495299	+	0.152437i	−0.972762	−	0.231804i	$-0.925537\pi$
$293$	−0.847815	+	2.60931i	−0.0495299	+	0.152437i	0.923233	+	0.384242i	$0.125537\pi$
$294$	9.07524	−	4.98915i	0.529279	−	0.290973i
$295$		0			0
$296$	29.6675	−	3.74788i	1.72439	−	0.217841i
$297$	−0.636966	−	0.350175i	−0.0369605	−	0.0203192i
$298$	−3.46455	−	0.889546i	−0.200696	−	0.0515300i
$299$	0.322057	−	0.991190i	0.0186251	−	0.0573220i
$300$		0			0
$301$	7.39041	+	22.7454i	0.425976	+	1.31102i
$302$	0.711647	+	11.3113i	0.0409507	+	0.650892i
$303$	−23.9989	+	22.5364i	−1.37870	+	1.29468i
$304$	13.9338	+	7.66019i	0.799160	+	0.439342i
$305$		0			0
$306$	−1.95319	+	4.15074i	−0.111656	+	0.237282i
$307$	−20.5783			−1.17447			−0.587233	−	0.809418i	$-0.699783\pi$
$307$	−20.5783			−1.17447			−0.587233	+	0.809418i	$0.699783\pi$
$308$	−0.622735	+	1.32338i	−0.0354836	+	0.0754065i
$309$	2.26465	−	35.9957i	0.128832	−	2.04772i
$310$		0			0
$311$	−6.15309	+	9.69571i	−0.348909	+	0.549793i	−0.972779	−	0.231735i	$-0.925560\pi$
$311$	−6.15309	+	9.69571i	−0.348909	+	0.549793i	0.623869	+	0.781529i	$0.285560\pi$
$312$	21.6622	−	26.1851i	1.22638	−	1.48244i
$313$	−8.59922	+	10.3947i	−0.486057	+	0.587542i	−0.955341	−	0.295505i	$-0.904512\pi$
$313$	−8.59922	+	10.3947i	−0.486057	+	0.587542i	0.469284	+	0.883047i	$0.344512\pi$
$314$	−4.65584	+	7.33642i	−0.262744	+	0.414018i
$315$		0			0
$316$	−0.121130	+	1.92530i	−0.00681409	+	0.108307i
$317$	−9.25429	+	19.6664i	−0.519773	+	1.10457i	0.456836	+	0.889551i	$0.348983\pi$
$317$	−9.25429	+	19.6664i	−0.519773	+	1.10457i	−0.976609	+	0.215023i	$0.931017\pi$
$318$	−1.60109			−0.0897849
$319$	−3.66343	+	7.78518i	−0.205112	+	0.435886i
$320$		0			0
$321$	−32.9725	−	18.1268i	−1.84034	−	1.01174i
$322$	−0.655244	+	0.615315i	−0.0365153	+	0.0342902i
$323$	−0.475049	−	7.55068i	−0.0264324	−	0.420131i
$324$	1.38362	+	4.25834i	0.0768677	+	0.236575i
$325$		0			0
$326$	4.16447	−	12.8169i	0.230649	−	0.709863i
$327$	−12.2338	−	3.14110i	−0.676530	−	0.173703i
$328$	19.2114	+	10.5615i	1.06077	+	0.583163i
$329$	−26.1199	+	3.29971i	−1.44004	+	0.181919i
$330$		0			0
$331$	−0.622828	+	0.342403i	−0.0342337	+	0.0188202i	−0.498779	−	0.866729i	$-0.666218\pi$
$331$	−0.622828	+	0.342403i	−0.0342337	+	0.0188202i	0.464545	+	0.885550i	$0.346218\pi$
$332$	1.30125	−	4.00483i	0.0714152	−	0.219793i
$333$	−26.1767	−	3.30689i	−1.43447	−	0.181216i
$334$	3.78245	+	5.96019i	0.206966	+	0.326127i
$335$		0			0
$336$	−20.7041	+	8.19734i	−1.12950	+	0.447202i
$337$	−16.5968	−	26.1524i	−0.904085	−	1.42461i	−0.905376	−	0.424611i	$-0.860411\pi$
$337$	−16.5968	−	26.1524i	−0.904085	−	1.42461i	0.00129090	−	0.999999i	$-0.499589\pi$
$338$	−10.1511	−	4.01910i	−0.552147	−	0.218610i
$339$	2.18025	+	34.6541i	0.118415	+	1.88215i
$340$		0			0
$341$	0.976432	−	1.18030i	0.0528768	−	0.0639170i
$342$	−13.4616	−	12.6413i	−0.727918	−	0.683561i
$343$	3.51071	+	10.8048i	0.189560	+	0.583407i
$344$	−4.22188	−	22.1319i	−0.227628	−	1.19327i
$345$		0			0
$346$	7.23892	+	15.3835i	0.389167	+	0.827021i
$347$	10.7935	+	22.9374i	0.579426	+	1.23134i	0.952782	+	0.303656i	$0.0982072\pi$
$347$	10.7935	+	22.9374i	0.579426	+	1.23134i	−0.373355	+	0.927688i	$0.621793\pi$
$348$	8.77456	−	3.47409i	0.470366	−	0.186231i
$349$	17.0863	+	12.4139i	0.914608	+	0.664501i	0.942176	−	0.335119i	$-0.108776\pi$
$349$	17.0863	+	12.4139i	0.914608	+	0.664501i	−0.0275683	+	0.999620i	$0.508776\pi$
$350$		0			0
$351$	2.76953	−	2.01218i	0.147827	−	0.107402i
$352$	1.33963	−	2.11092i	0.0714025	−	0.112512i
$353$	4.78586	−	25.0884i	0.254726	−	1.33532i	−0.593137	−	0.805102i	$-0.702111\pi$
$353$	4.78586	−	25.0884i	0.254726	−	1.33532i	0.847862	−	0.530217i	$-0.177889\pi$
$354$	9.73538	−	9.14213i	0.517430	−	0.485899i
$355$		0			0
$356$	5.16685	+	0.652725i	0.273843	+	0.0345944i
$357$	8.57168	+	6.22769i	0.453661	+	0.329604i
$358$	−3.10391	−	16.2713i	−0.164047	−	0.859963i
$359$	20.5454	+	8.13450i	1.08434	+	0.429322i	0.841231	−	0.540675i	$-0.181831\pi$
$359$	20.5454	+	8.13450i	1.08434	+	0.429322i	0.243113	+	0.969998i	$0.421831\pi$
$360$		0			0
$361$	11.0960	+	2.84896i	0.583999	+	0.149945i
$362$	−3.51799	+	0.903267i	−0.184902	+	0.0474747i
$363$	−1.50080	+	23.8545i	−0.0787716	+	1.25204i
$364$	−4.39072	−	5.30747i	−0.230136	−	0.278187i
$365$		0			0
$366$	−20.3670	+	5.22936i	−1.06460	+	0.273343i
$367$	9.00585	−	4.95101i	0.470102	−	0.258441i	−0.229049	−	0.973415i	$-0.573562\pi$
$367$	9.00585	−	4.95101i	0.470102	−	0.258441i	0.699151	+	0.714974i	$0.253562\pi$
$368$	0.520482	−	0.378152i	0.0271320	−	0.0197126i
$369$	−14.1008	−	13.2416i	−0.734059	−	0.689328i
$370$		0			0
$371$	−0.327757	+	1.71816i	−0.0170163	+	0.0892027i
$372$	−1.66694	+	0.210583i	−0.0864267	+	0.0109182i
$373$	−10.1273	−	12.2417i	−0.524369	−	0.633854i	0.440132	−	0.897933i	$-0.354932\pi$
$373$	−10.1273	−	12.2417i	−0.524369	−	0.633854i	−0.964501	+	0.264080i	$0.914932\pi$
$374$	1.68842			0.0873063
$375$		0			0
$376$	24.8029			1.27911
$377$	−25.8297	−	31.2228i	−1.33030	−	1.60806i
$378$	−2.92924	+	0.370049i	−0.150664	+	0.0190332i
$379$	4.27525	−	22.4116i	0.219605	−	1.15121i	−0.686167	−	0.727444i	$-0.740708\pi$
$379$	4.27525	−	22.4116i	0.219605	−	1.15121i	0.905772	−	0.423765i	$-0.139292\pi$
$380$		0			0
$381$	−12.8954	−	12.1096i	−0.660653	−	0.620395i
$382$	−5.84407	+	4.24597i	−0.299009	+	0.217243i
$383$	16.5384	−	9.09204i	0.845071	−	0.464582i	0.000483752	−	1.00000i	$-0.499846\pi$
$383$	16.5384	−	9.09204i	0.845071	−	0.464582i	0.844587	+	0.535418i	$0.179846\pi$
$384$	13.8933	−	3.56719i	0.708988	−	0.182037i
$385$		0			0
$386$	7.98793	+	9.65575i	0.406575	+	0.491465i
$387$	−1.24827	+	19.8406i	−0.0634529	+	1.00855i
$388$	−6.89948	+	1.77148i	−0.350268	+	0.0899335i
$389$	27.4626	+	7.05118i	1.39241	+	0.357509i	0.869101	−	0.494636i	$-0.164698\pi$
$389$	27.4626	+	7.05118i	1.39241	+	0.357509i	0.523306	+	0.852145i	$0.324698\pi$
$390$		0			0
$391$	−0.284614	−	0.112687i	−0.0143936	−	0.00569881i
$392$	1.99724	+	10.4699i	0.100876	+	0.528810i
$393$	5.24172	+	3.80834i	0.264410	+	0.192105i
$394$	−13.9223	−	1.75880i	−0.701397	−	0.0886071i
$395$		0			0
$396$	−0.886245	+	0.832239i	−0.0445355	+	0.0418216i
$397$	−0.492007	+	2.57919i	−0.0246931	+	0.129446i	−0.992499	−	0.122251i	$-0.960989\pi$
$397$	−0.492007	+	2.57919i	−0.0246931	+	0.129446i	0.967806	+	0.251697i	$0.0809886\pi$
$398$	−0.716145	+	1.12846i	−0.0358971	+	0.0565648i
$399$	−34.5059	+	25.0700i	−1.72745	+	1.25507i
$400$		0			0
$401$	−16.0038	−	11.6275i	−0.799193	−	0.580648i	0.111484	−	0.993766i	$-0.464440\pi$
$401$	−16.0038	−	11.6275i	−0.799193	−	0.580648i	−0.910677	+	0.413118i	$0.864440\pi$
$402$	41.3160	−	16.3582i	2.06065	−	0.815871i
$403$	3.07176	+	6.52782i	0.153015	+	0.325174i
$404$	−2.67666	−	5.68819i	−0.133169	−	0.282998i
$405$		0			0
$406$	6.54879	+	34.3300i	0.325011	+	1.70377i
$407$	3.00094	+	9.23593i	0.148751	+	0.457808i
$408$	−7.27629	−	6.83289i	−0.360230	−	0.338278i
$409$	−7.81004	+	9.44072i	−0.386182	+	0.466814i	−0.927401	−	0.374068i	$-0.877963\pi$
$409$	−7.81004	+	9.44072i	−0.386182	+	0.466814i	0.541220	+	0.840881i	$0.317963\pi$
$410$		0			0
$411$	−1.71125	−	27.1996i	−0.0844098	−	1.34166i
$412$	6.40343	+	2.53530i	0.315474	+	0.124905i
$413$	−7.81768	−	12.3187i	−0.384683	−	0.606163i
$414$	−0.694703	+	0.275052i	−0.0341428	+	0.0135181i
$415$		0			0
$416$	6.30919	+	9.94169i	0.309333	+	0.487431i
$417$	27.6956	+	3.49876i	1.35626	+	0.171335i
$418$	−2.10035	+	6.46420i	−0.102731	+	0.316174i
$419$	15.0160	−	8.25514i	0.733582	−	0.403290i	−0.0707316	−	0.997495i	$-0.522533\pi$
$419$	15.0160	−	8.25514i	0.733582	−	0.403290i	0.804313	+	0.594205i	$0.202533\pi$
$420$		0			0
$421$	7.19455	−	0.908882i	0.350641	−	0.0442962i	0.0519596	−	0.998649i	$-0.483453\pi$
$421$	7.19455	−	0.908882i	0.350641	−	0.0442962i	0.298681	+	0.954353i	$0.403453\pi$
$422$	−12.4891	−	6.86595i	−0.607960	−	0.334229i
$423$	−21.1969	−	5.44245i	−1.03063	−	0.264621i
$424$	0.509215	−	1.56720i	0.0247297	−	0.0761102i
$425$		0			0
$426$	−2.61604	−	8.05134i	−0.126747	−	0.390089i
$427$	1.44243	+	22.9267i	0.0698039	+	1.10950i
$428$	5.23758	−	4.91841i	0.253168	−	0.237740i
$429$	9.67130	+	5.31684i	0.466935	+	0.256700i
$430$		0			0
$431$	−3.57865	+	7.60502i	−0.172378	+	0.366321i	−0.972284	−	0.233804i	$-0.924883\pi$
$431$	−3.57865	+	7.60502i	−0.172378	+	0.366321i	0.799906	+	0.600125i	$0.204883\pi$
$432$	2.11323			0.101673
$433$	1.51709	−	3.22399i	0.0729068	−	0.154935i	−0.865051	−	0.501683i	$-0.832714\pi$
$433$	1.51709	−	3.22399i	0.0729068	−	0.154935i	0.937958	+	0.346748i	$0.112714\pi$
$434$	0.390697	−	6.20995i	0.0187541	−	0.298087i
$435$		0			0
$436$	1.29233	−	2.03639i	0.0618915	−	0.0975255i
$437$	0.785477	−	0.949479i	0.0375745	−	0.0454197i
$438$	13.2312	−	15.9938i	0.632213	−	0.764214i
$439$	5.93040	−	9.34481i	0.283043	−	0.446004i	−0.672825	−	0.739802i	$-0.734919\pi$
$439$	5.93040	−	9.34481i	0.283043	−	0.446004i	0.955868	+	0.293798i	$0.0949193\pi$
$440$		0			0
$441$	0.590516	−	9.38598i	0.0281198	−	0.446951i
$442$	−3.38575	+	7.19508i	−0.161044	+	0.342235i
$443$	16.4449			0.781322			0.390661	−	0.920535i	$-0.372247\pi$
$443$	16.4449			0.781322			0.390661	+	0.920535i	$0.372247\pi$
$444$	4.53527	−	9.63794i	0.215234	−	0.457396i
$445$		0			0
$446$	−19.2770	−	10.5976i	−0.912792	−	0.501812i
$447$	−5.00604	+	4.70098i	−0.236777	+	0.222349i
$448$	−1.80971	−	28.7645i	−0.0855007	−	1.35900i
$449$	0.472326	+	1.45367i	0.0222904	+	0.0686029i	0.961583	−	0.274514i	$-0.0885171\pi$
$449$	0.472326	+	1.45367i	0.0222904	+	0.0686029i	−0.939293	+	0.343117i	$0.888517\pi$
$450$		0			0
$451$	−2.20009	+	6.77117i	−0.103598	+	0.318842i
$452$	−6.42208	−	1.64891i	−0.302069	−	0.0775582i
$453$	19.0678	+	10.4826i	0.895885	+	0.492517i
$454$	5.27467	−	0.666346i	0.247553	−	0.0312732i
$455$		0			0
$456$	35.2115	−	19.3577i	1.64893	−	0.906506i
$457$	−7.18741	+	22.1206i	−0.336213	+	1.03476i	0.629909	+	0.776669i	$0.283092\pi$
$457$	−7.18741	+	22.1206i	−0.336213	+	1.03476i	−0.966122	+	0.258088i	$0.916908\pi$
$458$	−13.5168	−	1.70757i	−0.631599	−	0.0797895i
$459$	−0.538767	−	0.848960i	−0.0251475	−	0.0396261i
$460$		0			0
$461$	0.759478	−	0.300699i	0.0353724	−	0.0140049i	−0.350372	−	0.936611i	$-0.613945\pi$
$461$	0.759478	−	0.300699i	0.0353724	−	0.0140049i	0.385744	+	0.922606i	$0.373945\pi$
$462$	−5.10031	−	8.03681i	−0.237288	−	0.373906i
$463$	−7.65736	−	3.03176i	−0.355867	−	0.140898i	0.183387	−	0.983041i	$-0.441294\pi$
$463$	−7.65736	−	3.03176i	−0.355867	−	0.140898i	−0.539254	+	0.842143i	$0.681294\pi$
$464$	−1.57066	−	24.9650i	−0.0729162	−	1.15897i
$465$		0			0
$466$	9.90895	−	11.9779i	0.459023	−	0.554864i
$467$	−18.8521	−	17.7033i	−0.872370	−	0.819210i	0.112293	−	0.993675i	$-0.464180\pi$
$467$	−18.8521	−	17.7033i	−0.872370	−	0.819210i	−0.984663	+	0.174465i	$0.944180\pi$
$468$	−1.76936	−	5.44553i	−0.0817886	−	0.251720i
$469$	−9.09651	−	47.6856i	−0.420038	−	2.20192i
$470$		0			0
$471$	7.10285	+	15.0943i	0.327282	+	0.695510i
$472$	5.85236	+	12.4369i	0.269377	+	0.572454i
$473$	6.80320	−	2.69358i	0.312811	−	0.123851i
$474$	−10.1571	−	7.37955i	−0.466530	−	0.338954i
$475$		0			0
$476$	−1.63679	+	1.18920i	−0.0750220	+	0.0545067i
$477$	−0.779071	+	1.22762i	−0.0356712	+	0.0562088i
$478$	3.29039	−	17.2489i	0.150499	−	0.788944i
$479$	−13.0957	+	12.2977i	−0.598357	+	0.561895i	−0.923417	−	0.383799i	$-0.874616\pi$
$479$	−13.0957	+	12.2977i	−0.598357	+	0.561895i	0.325060	+	0.945694i	$0.394616\pi$
$480$		0			0
$481$	−45.3759	−	5.73231i	−2.06896	−	0.261371i
$482$	14.4346	+	10.4874i	0.657479	+	0.477687i
$483$	0.323367	+	1.69515i	0.0147137	+	0.0771319i
$484$	−4.24359	−	1.68016i	−0.192891	−	0.0763708i
$485$		0			0
$486$	−25.5759	−	6.56677i	−1.16015	−	0.297875i
$487$	7.72499	−	1.98344i	0.350053	−	0.0898783i	−0.0695694	−	0.997577i	$-0.522163\pi$
$487$	7.72499	−	1.98344i	0.350053	−	0.0898783i	0.419622	+	0.907699i	$0.362163\pi$
$488$	1.35890	−	21.5990i	0.0615144	−	0.977743i
$489$	−16.4923	−	19.9357i	−0.745806	−	0.901525i
$490$		0			0
$491$	35.7104	−	9.16886i	1.61159	−	0.413785i	0.667800	−	0.744341i	$-0.267236\pi$
$491$	35.7104	−	9.16886i	1.61159	−	0.413785i	0.943786	+	0.330556i	$0.107236\pi$
$492$	6.84317	−	3.76206i	0.308514	−	0.169607i
$493$	−9.62890	+	6.99580i	−0.433664	+	0.315075i
$494$	−23.3349	−	21.9129i	−1.04989	−	0.985909i
$495$		0			0
$496$	−0.834500	+	4.37460i	−0.0374702	+	0.196425i
$497$	−9.17556	+	1.15914i	−0.411580	+	0.0519947i
$498$	17.4687	+	21.1160i	0.782790	+	0.946230i
$499$	3.97365			0.177885			0.0889426	−	0.996037i	$-0.471651\pi$
$499$	3.97365			0.177885			0.0889426	+	0.996037i	$0.471651\pi$
$500$		0			0
$501$	13.5526			0.605487
$502$	3.17024	+	3.83216i	0.141495	+	0.171038i
$503$	34.7386	−	4.38851i	1.54892	−	0.195674i	0.696124	−	0.717922i	$-0.254906\pi$
$503$	34.7386	−	4.38851i	1.54892	−	0.195674i	0.852794	+	0.522248i	$0.174906\pi$
$504$	−4.98746	+	26.1452i	−0.222159	+	1.16460i
$505$		0			0
$506$	0.200471	+	0.188255i	0.00891201	+	0.00836894i
$507$	−16.9577	+	12.3205i	−0.753118	+	0.547172i
$508$	2.96012	−	1.62734i	0.131334	−	0.0722016i
$509$	21.9314	−	5.63104i	0.972094	−	0.249591i	0.270936	−	0.962597i	$-0.412667\pi$
$509$	21.9314	−	5.63104i	0.972094	−	0.249591i	0.701158	+	0.713006i	$0.252667\pi$
$510$		0			0
$511$	−14.4547	−	17.4728i	−0.639439	−	0.772949i
$512$	−1.56058	+	24.8046i	−0.0689683	+	1.09622i
$513$	3.92049	−	1.00661i	0.173094	−	0.0444429i
$514$	−11.6428	−	2.98935i	−0.513540	−	0.131855i
$515$		0			0
$516$	−7.46203	−	2.95443i	−0.328498	−	0.130061i
$517$	1.50933	+	7.91218i	0.0663802	+	0.347977i
$518$	31.9128	+	23.1860i	1.40217	+	1.01873i
$519$	32.3837	+	4.09101i	1.42149	+	0.179575i
$520$		0			0
$521$	−24.6868	+	23.1824i	−1.08155	+	1.01564i	−0.0817286	+	0.996655i	$0.526044\pi$
$521$	−24.6868	+	23.1824i	−1.08155	+	1.01564i	−0.999820	+	0.0189869i	$0.993956\pi$
$522$	−5.44362	+	28.5365i	−0.238261	+	1.24901i
$523$	4.25187	−	6.69988i	0.185921	−	0.292965i	−0.738564	−	0.674184i	$-0.764496\pi$
$523$	4.25187	−	6.69988i	0.185921	−	0.292965i	0.924485	+	0.381219i	$0.124496\pi$
$524$	−1.00092	+	0.727213i	−0.0437255	+	0.0317684i
$525$		0			0
$526$	8.13593	+	5.91110i	0.354744	+	0.257736i
$527$	1.97019	−	0.780054i	0.0858229	−	0.0339797i
$528$	2.90075	+	6.16442i	0.126239	+	0.268272i
$529$	9.77169	+	20.7659i	0.424856	+	0.902866i
$530$		0			0
$531$	−2.27251	−	11.9129i	−0.0986186	−	0.516977i
$532$	−2.51677	−	7.74583i	−0.109116	−	0.335824i
$533$	−24.4430	−	22.9535i	−1.05874	−	0.994227i
$534$	−21.6046	+	26.1155i	−0.934923	+	1.13013i
$535$		0			0
$536$	2.87168	+	45.6440i	0.124038	+	1.97152i
$537$	−29.5690	−	11.7072i	−1.27599	−	0.505202i
$538$	2.22135	+	3.50029i	0.0957692	+	0.150908i
$539$	−3.21838	+	1.27425i	−0.138626	+	0.0548857i
$540$		0			0
$541$	18.5551	+	29.2381i	0.797744	+	1.25704i	0.962654	+	0.270735i	$0.0872668\pi$
$541$	18.5551	+	29.2381i	0.797744	+	1.25704i	−0.164909	+	0.986309i	$0.552733\pi$
$542$	21.3503	+	2.69717i	0.917073	+	0.115853i
$543$	−2.15484	+	6.63192i	−0.0924731	+	0.284603i
$544$	3.03063	−	1.66610i	0.129937	−	0.0714335i
$545$		0			0
$546$	44.4757	−	5.61859i	1.90339	−	0.240453i
$547$	9.26322	+	5.09250i	0.396067	+	0.217740i	0.667324	−	0.744767i	$-0.267440\pi$
$547$	9.26322	+	5.09250i	0.396067	+	0.217740i	−0.271258	+	0.962507i	$0.587440\pi$
$548$	5.04061	+	1.29421i	0.215324	+	0.0552858i
$549$	−5.90076	+	18.1607i	−0.251838	+	0.775079i
$550$		0			0
$551$	−14.8057	−	45.5672i	−0.630743	−	1.94123i
$552$	−0.102084	−	1.62257i	−0.00434497	−	0.0690613i
$553$	−9.99837	+	9.38909i	−0.425174	+	0.399265i
$554$	−16.6040	−	9.12814i	−0.705437	−	0.387817i
$555$		0			0
$556$	−2.26965	+	4.82326i	−0.0962547	+	0.204552i
$557$	30.2508			1.28177			0.640884	−	0.767638i	$-0.278568\pi$
$557$	30.2508			1.28177			0.640884	+	0.767638i	$0.278568\pi$
$558$	2.20220	−	4.67991i	0.0932266	−	0.198117i
$559$	−2.16380	+	34.3926i	−0.0915190	+	1.45465i
$560$		0			0
$561$	1.73692	−	2.73695i	0.0733329	−	0.115554i
$562$	−0.394395	+	0.476742i	−0.0166366	+	0.0201102i
$563$	−2.05949	+	2.48949i	−0.0867971	+	0.104920i	−0.812124	−	0.583485i	$-0.801689\pi$
$563$	−2.05949	+	2.48949i	−0.0867971	+	0.104920i	0.725327	+	0.688405i	$0.241689\pi$
$564$	4.73398	−	7.45955i	0.199336	−	0.314104i
$565$		0			0
$566$	0.171403	−	2.72437i	0.00720459	−	0.114514i
$567$	−13.5544	+	28.8047i	−0.569233	+	1.20968i
$568$	8.71292			0.365586
$569$	−16.5328	+	35.1341i	−0.693092	+	1.47290i	0.179150	+	0.983822i	$0.442665\pi$
$569$	−16.5328	+	35.1341i	−0.693092	+	1.47290i	−0.872242	+	0.489075i	$0.837335\pi$
$570$		0			0
$571$	32.4698	+	17.8504i	1.35882	+	0.747017i	0.983676	−	0.179950i	$-0.0575935\pi$
$571$	32.4698	+	17.8504i	1.35882	+	0.747017i	0.375143	+	0.926967i	$0.377594\pi$
$572$	−1.53626	+	1.44264i	−0.0642342	+	0.0603199i
$573$	0.870817	+	13.8412i	0.0363789	+	0.578226i
$574$	8.93659	+	27.5040i	0.373006	+	1.14799i
$575$		0			0
$576$	7.40327	−	22.7849i	0.308469	−	0.949371i
$577$	11.3783	+	2.92145i	0.473685	+	0.121622i	0.477983	−	0.878369i	$-0.341368\pi$
$577$	11.3783	+	2.92145i	0.473685	+	0.121622i	−0.00429816	+	0.999991i	$0.501368\pi$
$578$	−16.4667	−	9.05263i	−0.684923	−	0.376540i
$579$	23.8695	−	3.01541i	0.991981	−	0.125316i
$580$		0			0
$581$	26.2359	−	14.4233i	1.08845	−	0.598381i
$582$	14.3257	−	44.0899i	0.593819	−	1.82759i
$583$	0.530929	+	0.0670719i	0.0219888	+	0.00277783i
$584$	11.4472	+	18.0379i	0.473688	+	0.746413i
$585$		0			0
$586$	3.17013	−	1.25515i	0.130957	−	0.0518496i
$587$	−4.01909	−	6.33308i	−0.165886	−	0.261394i	0.751208	−	0.660065i	$-0.229471\pi$
$587$	−4.01909	−	6.33308i	−0.165886	−	0.261394i	−0.917094	+	0.398671i	$0.869471\pi$
$588$	3.53006	+	1.39765i	0.145577	+	0.0576380i
$589$	0.535613	+	8.51332i	0.0220695	+	0.350785i
$590$		0			0
$591$	−17.1733	+	20.7589i	−0.706415	+	0.853909i
$592$	−20.5811	−	19.3270i	−0.845880	−	0.794334i
$593$	9.55357	+	29.4029i	0.392318	+	1.20743i	0.931031	+	0.364941i	$0.118911\pi$
$593$	9.55357	+	29.4029i	0.392318	+	1.20743i	−0.538713	+	0.842490i	$0.681089\pi$
$594$	0.169265	+	0.887317i	0.00694502	+	0.0364071i
$595$		0			0
$596$	−0.558336	−	1.18653i	−0.0228703	−	0.0486020i
$597$	1.09254	+	2.32176i	0.0447146	+	0.0950233i
$598$	−1.20423	+	0.476789i	−0.0492446	+	0.0194973i
$599$	−11.5916	−	8.42180i	−0.473621	−	0.344105i	0.325230	−	0.945635i	$-0.394558\pi$
$599$	−11.5916	−	8.42180i	−0.473621	−	0.344105i	−0.798851	+	0.601529i	$0.794558\pi$
$600$		0			0
$601$	25.1810	−	18.2951i	1.02715	−	0.746271i	0.0594166	−	0.998233i	$-0.481076\pi$
$601$	25.1810	−	18.2951i	1.02715	−	0.746271i	0.967737	+	0.251962i	$0.0810760\pi$
$602$	15.9254	−	25.0945i	0.649072	−	1.02277i
$603$	7.56138	−	39.6382i	0.307923	−	1.61419i
$604$	−3.02887	+	2.84430i	−0.123243	+	0.115733i
$605$		0			0
$606$	40.5905	+	5.12777i	1.64887	+	0.208301i
$607$	23.1572	+	16.8247i	0.939922	+	0.682894i	0.948402	−	0.317071i	$-0.102699\pi$
$607$	23.1572	+	16.8247i	0.939922	+	0.682894i	−0.00847967	+	0.999964i	$0.502699\pi$
$608$	2.60873	+	13.6755i	0.105798	+	0.554613i
$609$	62.3862	+	24.7004i	2.52802	+	1.00091i
$610$		0			0
$611$	−36.7437	−	9.43419i	−1.48649	−	0.381666i
$612$	−1.62891	+	0.418234i	−0.0658449	+	0.0169061i
$613$	−0.724799	+	11.5204i	−0.0292744	+	0.465303i	0.955894	+	0.293712i	$0.0948906\pi$
$613$	−0.724799	+	11.5204i	−0.0292744	+	0.465303i	−0.985168	+	0.171591i	$0.945109\pi$
$614$	16.3011	+	19.7047i	0.657860	+	0.795217i
$615$		0			0
$616$	9.48880	−	2.43631i	0.382315	−	0.0981617i
$617$	23.5591	−	12.9517i	0.948455	−	0.521417i	0.0691129	−	0.997609i	$-0.477983\pi$
$617$	23.5591	−	12.9517i	0.948455	−	0.521417i	0.879342	+	0.476192i	$0.157983\pi$
$618$	−36.2615	+	26.3455i	−1.45865	+	1.05977i
$619$	15.9757	+	15.0022i	0.642118	+	0.602989i	0.935637	−	0.352964i	$-0.114826\pi$
$619$	15.9757	+	15.0022i	0.642118	+	0.602989i	−0.293519	+	0.955953i	$0.594826\pi$
$620$		0			0
$621$	0.0306876	−	0.160870i	0.00123145	−	0.00645550i
$622$	14.1583	−	1.78861i	0.567695	−	0.0717166i
$623$	23.6024	+	28.5304i	0.945609	+	1.14304i
$624$	−32.0860			−1.28447
$625$		0			0
$626$	16.7653			0.670076
$627$	8.31786	+	10.0546i	0.332183	+	0.401541i
$628$	−3.16036	+	0.399246i	−0.126112	+	0.0159317i
$629$	−2.51719	+	13.1956i	−0.100367	+	0.526143i
$630$		0			0
$631$	−4.04166	−	3.79537i	−0.160896	−	0.151091i	0.599918	−	0.800062i	$-0.295200\pi$
$631$	−4.04166	−	3.79537i	−0.160896	−	0.151091i	−0.760814	+	0.648970i	$0.775200\pi$
$632$	10.4537	−	7.59507i	0.415827	−	0.302116i
$633$	−23.9776	+	13.1818i	−0.953025	+	0.523930i
$634$	26.1623	−	6.71734i	1.03904	−	0.266779i
$635$		0			0
$636$	−0.374151	−	0.452271i	−0.0148360	−	0.0179337i
$637$	1.02363	−	16.2701i	0.0405576	−	0.644644i
$638$	10.3567	−	2.65914i	0.410024	−	0.105276i
$639$	−7.44619	−	1.91186i	−0.294567	−	0.0756319i
$640$		0			0
$641$	−4.56524	−	1.80751i	−0.180316	−	0.0713922i	0.276232	−	0.961091i	$-0.410914\pi$
$641$	−4.56524	−	1.80751i	−0.180316	−	0.0713922i	−0.456548	+	0.889699i	$0.650914\pi$
$642$	8.76197	+	45.9318i	0.345807	+	1.81279i
$643$	−9.99429	−	7.26128i	−0.394136	−	0.286357i	0.373012	−	0.927826i	$-0.378325\pi$
$643$	−9.99429	−	7.26128i	−0.394136	−	0.286357i	−0.767148	+	0.641470i	$0.778325\pi$
$644$	−0.326932	−	0.0413011i	−0.0128829	−	0.00162749i
$645$		0			0
$646$	−6.85383	+	6.43617i	−0.269660	+	0.253228i
$647$	−5.32666	+	27.9234i	−0.209413	+	1.09778i	0.709915	+	0.704287i	$0.248733\pi$
$647$	−5.32666	+	27.9234i	−0.209413	+	1.09778i	−0.919328	+	0.393493i	$0.871267\pi$
$648$	16.0700	−	25.3222i	0.631287	−	0.994750i
$649$	−3.61126	+	2.62374i	−0.141754	+	0.102991i
$650$		0			0
$651$	−9.66448	−	7.02166i	−0.378781	−	0.275200i
$652$	4.59364	−	1.81875i	0.179901	−	0.0712278i
$653$	3.28613	+	6.98337i	0.128596	+	0.273280i	0.958748	−	0.284256i	$-0.0917466\pi$
$653$	3.28613	+	6.98337i	0.128596	+	0.273280i	−0.830152	+	0.557537i	$0.811747\pi$
$654$	6.68326	+	14.2027i	0.261336	+	0.555368i
$655$		0			0
$656$	−3.87855	−	20.3321i	−0.151432	−	0.793835i
$657$	−5.82492	−	17.9273i	−0.227252	−	0.699409i
$658$	23.8506	+	22.3972i	0.929792	+	0.873133i
$659$	31.0368	−	37.5171i	1.20902	−	1.46146i	0.360121	−	0.932906i	$-0.382735\pi$
$659$	31.0368	−	37.5171i	1.20902	−	1.46146i	0.848901	−	0.528551i	$-0.177265\pi$
$660$		0			0
$661$	−2.75591	−	43.8039i	−0.107192	−	1.70378i	−0.573543	−	0.819176i	$-0.694431\pi$
$661$	−2.75591	−	43.8039i	−0.107192	−	1.70378i	0.466350	−	0.884600i	$-0.345569\pi$
$662$	0.821242	+	0.325153i	0.0319185	+	0.0126374i
$663$	8.18030	+	12.8901i	0.317697	+	0.500610i
$664$	−26.2248	+	10.3831i	−1.01772	+	0.402944i
$665$		0			0
$666$	17.5694	+	27.6850i	0.680801	+	1.07277i
$667$	−1.92328	−	0.242966i	−0.0744696	−	0.00940769i
$668$	−0.799709	+	2.46125i	−0.0309417	+	0.0952287i
$669$	−37.0096	+	20.3462i	−1.43087	+	0.786629i
$670$		0			0
$671$	6.97283	−	0.880874i	0.269183	−	0.0340058i
$672$	−17.0853	−	9.39274i	−0.659081	−	0.362333i
$673$	8.90445	+	2.28627i	0.343241	+	0.0881294i	0.416376	−	0.909193i	$-0.363300\pi$
$673$	8.90445	+	2.28627i	0.343241	+	0.0881294i	−0.0731342	+	0.997322i	$0.523300\pi$
$674$	−11.8949	+	36.6089i	−0.458176	+	1.41012i
$675$		0			0
$676$	−1.23685	−	3.80664i	−0.0475712	−	0.146409i
$677$	0.909582	+	14.4574i	0.0349581	+	0.555642i	0.976058	+	0.217513i	$0.0697943\pi$
$677$	0.909582	+	14.4574i	0.0349581	+	0.555642i	−0.941099	+	0.338130i	$0.890206\pi$
$678$	31.4559	−	29.5390i	1.20806	−	1.13444i
$679$	−44.3811	−	24.3987i	−1.70319	−	0.936338i
$680$		0			0
$681$	4.34603	−	9.23579i	0.166540	−	0.353916i
$682$	−1.90368			−0.0728957
$683$	−7.57258	+	16.0925i	−0.289757	+	0.615764i	−0.995714	−	0.0924907i	$-0.970517\pi$
$683$	−7.57258	+	16.0925i	−0.289757	+	0.615764i	0.705957	+	0.708255i	$0.250517\pi$
$684$	0.425091	−	6.75663i	0.0162538	−	0.258346i
$685$		0			0
$686$	7.56514	−	11.9207i	0.288838	−	0.455136i
$687$	−16.6731	+	20.1543i	−0.636117	+	0.768934i
$688$	−13.5597	+	16.3908i	−0.516958	+	0.624894i
$689$	−1.35048	+	2.12801i	−0.0514491	+	0.0810708i
$690$		0			0
$691$	2.07219	−	32.9366i	0.0788299	−	1.25297i	−0.737487	−	0.675361i	$-0.763988\pi$
$691$	2.07219	−	32.9366i	0.0788299	−	1.25297i	0.816317	−	0.577604i	$-0.196012\pi$
$692$	−2.65384	+	5.63970i	−0.100884	+	0.214389i
$693$	−8.64386			−0.328353
$694$	13.4135	−	28.5052i	0.509171	−	1.08204i
$695$		0			0
$696$	−55.3935	−	30.4528i	−2.09969	−	1.15431i
$697$	−7.17930	+	6.74181i	−0.271935	+	0.255364i
$698$	−1.64803	−	26.1946i	−0.0623787	−	0.991481i
$699$	−9.22266	−	28.3844i	−0.348833	−	1.07360i
$700$		0			0
$701$	−6.37034	+	19.6059i	−0.240604	+	0.740504i	0.755724	+	0.654890i	$0.227285\pi$
$701$	−6.37034	+	19.6059i	−0.240604	+	0.740504i	−0.996328	+	0.0856138i	$0.972715\pi$
$702$	−4.12065	−	1.05800i	−0.155524	−	0.0399318i
$703$	−47.3886	−	26.0521i	−1.78729	−	0.982573i
$704$	−8.74832	+	1.10517i	−0.329715	+	0.0416526i
$705$		0			0
$706$	−27.8144	+	15.2911i	−1.04681	+	0.575489i
$707$	13.8119	−	42.5087i	0.519450	−	1.59870i
$708$	4.85744	+	0.613637i	0.182554	+	0.0230619i
$709$	−6.91590	−	10.8977i	−0.259732	−	0.409272i	0.689288	−	0.724487i	$-0.257923\pi$
$709$	−6.91590	−	10.8977i	−0.259732	−	0.409272i	−0.949020	+	0.315215i	$0.897923\pi$
$710$		0			0
$711$	−10.6005	+	4.19702i	−0.397549	+	0.157401i
$712$	−18.6915	−	29.4531i	−0.700494	−	1.10380i
$713$	0.320900	+	0.127053i	0.0120178	+	0.00475818i
$714$	−0.826766	−	13.1411i	−0.0309409	−	0.491792i
$715$		0			0
$716$	3.87090	−	4.67912i	0.144662	−	0.174867i
$717$	−24.5757	−	23.0781i	−0.917795	−	0.861867i
$718$	−8.48591	−	26.1170i	−0.316691	−	0.974676i
$719$	9.33718	+	48.9472i	0.348218	+	1.82542i	0.537214	+	0.843446i	$0.319477\pi$
$719$	9.33718	+	48.9472i	0.348218	+	1.82542i	−0.188996	+	0.981978i	$0.560523\pi$
$720$		0			0
$721$	20.8488	+	44.3060i	0.776451	+	1.65004i
$722$	−6.06169	−	12.8817i	−0.225593	−	0.479409i
$723$	31.8494	−	12.6101i	1.18449	−	0.468974i
$724$	−1.07725	−	0.782669i	−0.0400357	−	0.0290877i
$725$		0			0
$726$	24.0307	−	17.4593i	0.891864	−	0.647977i
$727$	−17.9612	+	28.3023i	−0.666142	+	1.04967i	0.328319	+	0.944567i	$0.393518\pi$
$727$	−17.9612	+	28.3023i	−0.666142	+	1.04967i	−0.994461	+	0.105105i	$0.966482\pi$
$728$	−8.64549	+	45.3212i	−0.320423	+	1.67972i
$729$	−15.4631	+	14.5208i	−0.572706	+	0.537807i
$730$		0			0
$731$	10.0418	+	1.26858i	0.371410	+	0.0469200i
$732$	−6.23662	−	4.53117i	−0.230512	−	0.167477i
$733$	−4.50188	−	23.5997i	−0.166281	−	0.871673i	−0.963444	−	0.267910i	$-0.913667\pi$
$733$	−4.50188	−	23.5997i	−0.166281	−	0.871673i	0.797163	−	0.603764i	$-0.206333\pi$
$734$	−11.8748	−	4.70158i	−0.438308	−	0.173538i
$735$		0			0
$736$	0.545600	+	0.140086i	0.0201111	+	0.00516364i
$737$	−14.3858	+	3.69364i	−0.529907	+	0.136057i
$738$	−1.50942	+	23.9915i	−0.0555625	+	0.883140i
$739$	−25.5021	−	30.8267i	−0.938110	−	1.13398i	−0.990795	−	0.135369i	$-0.956778\pi$
$739$	−25.5021	−	30.8267i	−0.938110	−	1.13398i	0.0526852	−	0.998611i	$-0.483222\pi$
$740$		0			0
$741$	−59.5263	+	15.2838i	−2.18675	+	0.561463i
$742$	1.90486	−	1.04720i	0.0699295	−	0.0384441i
$743$	22.4501	−	16.3109i	0.823613	−	0.598390i	−0.0941319	−	0.995560i	$-0.530008\pi$
$743$	22.4501	−	16.3109i	0.823613	−	0.598390i	0.917745	+	0.397170i	$0.130008\pi$
$744$	8.20394	+	7.70401i	0.300771	+	0.282443i
$745$		0			0
$746$	−3.69973	+	19.3947i	−0.135457	+	0.710089i
$747$	24.6904	−	3.11913i	0.903376	−	0.114123i
$748$	0.394558	+	0.476939i	0.0144265	+	0.0174386i
$749$	51.0840			1.86657
$750$		0			0
$751$	−8.81046			−0.321498			−0.160749	−	0.986995i	$-0.551391\pi$
$751$	−8.81046			−0.321498			−0.160749	+	0.986995i	$0.551391\pi$
$752$	−14.9270	−	18.0436i	−0.544331	−	0.657984i
$753$	9.47329	−	1.19675i	0.345226	−	0.0436122i
$754$	−9.43622	+	49.4664i	−0.343647	+	1.80146i
$755$		0			0
$756$	−0.789046	−	0.740964i	−0.0286973	−	0.0269486i
$757$	−42.4292	+	30.8266i	−1.54212	+	1.12041i	−0.593124	+	0.805111i	$0.702106\pi$
$757$	−42.4292	+	30.8266i	−1.54212	+	1.12041i	−0.948992	+	0.315301i	$0.897894\pi$
$758$	−24.8469	+	13.6597i	−0.902479	+	0.496142i
$759$	0.511392	−	0.131303i	0.0185624	−	0.00476600i
$760$		0			0
$761$	1.05209	+	1.27175i	0.0381381	+	0.0461010i	0.789237	−	0.614088i	$-0.210476\pi$
$761$	1.05209	+	1.27175i	0.0381381	+	0.0461010i	−0.751099	+	0.660189i	$0.770476\pi$
$762$	−1.38039	+	21.9407i	−0.0500062	+	0.794826i
$763$	16.6093	−	4.26453i	0.601295	−	0.154386i
$764$	−2.56505	−	0.658593i	−0.0928003	−	0.0238271i
$765$		0			0
$766$	−21.8070	−	8.63399i	−0.787918	−	0.311959i
$767$	−3.93928	−	20.6504i	−0.142239	−	0.745643i
$768$	19.9276	+	14.4782i	0.719074	+	0.522438i
$769$	−36.0811	−	4.55811i	−1.30112	−	0.164370i	−0.555933	−	0.831227i	$-0.687639\pi$
$769$	−36.0811	−	4.55811i	−1.30112	−	0.164370i	−0.745185	+	0.666857i	$0.767639\pi$
$770$		0			0
$771$	−16.8230	+	15.7978i	−0.605865	+	0.568945i
$772$	−0.860862	+	4.51280i	−0.0309831	+	0.162419i
$773$	−7.20819	+	11.3583i	−0.259261	+	0.408529i	−0.948877	−	0.315645i	$-0.897779\pi$
$773$	−7.20819	+	11.3583i	−0.259261	+	0.408529i	0.689617	+	0.724175i	$0.257779\pi$
$774$	19.9871	−	14.5215i	0.718423	−	0.521965i
$775$		0			0
$776$	38.6005	+	28.0449i	1.38568	+	1.00675i
$777$	70.4142	−	27.8789i	2.52609	−	1.00015i
$778$	−15.0027	−	31.8823i	−0.537872	−	1.14304i
$779$	−16.8805	−	35.8728i	−0.604806	−	1.28528i
$780$		0			0
$781$	0.530207	+	2.77944i	0.0189723	+	0.0994562i
$782$	0.117555	+	0.361797i	0.00420375	+	0.0129378i
$783$	−4.64180	−	4.35894i	−0.165885	−	0.155776i
$784$	6.41466	−	7.75399i	0.229095	−	0.276928i
$785$		0			0
$786$	−0.505581	−	8.03598i	−0.0180335	−	0.286634i
$787$	−14.9433	−	5.91648i	−0.532672	−	0.210900i	0.0863624	−	0.996264i	$-0.472476\pi$
$787$	−14.9433	−	5.91648i	−0.532672	−	0.210900i	−0.619034	+	0.785364i	$0.712476\pi$
$788$	−2.75661	−	4.34373i	−0.0982003	−	0.154739i
$789$	17.9516	−	7.10754i	0.639094	−	0.253035i
$790$		0			0
$791$	−25.2596	−	39.8028i	−0.898128	−	1.41522i
$792$	8.07909	+	1.02063i	0.287078	+	0.0362664i
$793$	−10.2287	+	31.4806i	−0.363230	+	1.11791i
$794$	2.85944	−	1.57199i	0.101478	−	0.0557879i
$795$		0			0
$796$	−0.486116	+	0.0614107i	−0.0172299	+	0.00217665i
$797$	35.7753	+	19.6676i	1.26723	+	0.696663i	0.966407	−	0.257018i	$-0.0827400\pi$
$797$	35.7753	+	19.6676i	1.26723	+	0.696663i	0.300819	+	0.953681i	$0.402740\pi$
$798$	51.3396	+	13.1818i	1.81740	+	0.466629i
$799$	−3.44315	+	10.5969i	−0.121810	+	0.374892i
$800$		0			0
$801$	9.51121	+	29.2725i	0.336062	+	1.03429i
$802$	1.54362	+	24.5351i	0.0545071	+	0.866366i
$803$	−5.05753	+	4.74933i	−0.178476	+	0.167600i
$804$	14.2757	+	7.84812i	0.503465	+	0.276782i
$805$		0			0
$806$	3.81740	−	8.11238i	0.134462	−	0.285746i
$807$	7.95917			0.280176
$808$	−17.9287	+	38.1004i	−0.630729	+	1.34037i
$809$	−0.309936	+	4.92629i	−0.0108968	+	0.173199i	0.988814	+	0.149153i	$0.0476548\pi$
$809$	−0.309936	+	4.92629i	−0.0108968	+	0.173199i	−0.999711	+	0.0240459i	$0.992345\pi$
$810$		0			0
$811$	−5.59369	+	8.81424i	−0.196421	+	0.309510i	−0.928235	−	0.371995i	$-0.878674\pi$
$811$	−5.59369	+	8.81424i	−0.196421	+	0.309510i	0.731814	+	0.681504i	$0.238674\pi$
$812$	−8.16704	+	9.87226i	−0.286607	+	0.346448i
$813$	26.3357	−	31.8344i	0.923633	−	1.11648i
$814$	6.46665	−	10.1898i	0.226656	−	0.357152i
$815$		0			0
$816$	−0.591748	+	9.40556i	−0.0207153	+	0.329260i
$817$	−17.3485	+	36.8674i	−0.606947	+	1.28983i
$818$	15.2267			0.532388
$819$	17.3333	−	36.8351i	0.605674	−	1.28712i
$820$		0			0
$821$	24.2012	+	13.3047i	0.844628	+	0.464338i	0.844433	−	0.535662i	$-0.179938\pi$
$821$	24.2012	+	13.3047i	0.844628	+	0.464338i	0.000195198		1.00000i	$0.499938\pi$
$822$	−24.6893	+	23.1848i	−0.861138	+	0.808663i
$823$	−0.602048	−	9.56928i	−0.0209861	−	0.333564i	−0.994485	−	0.104875i	$-0.966556\pi$
$823$	−0.602048	−	9.56928i	−0.0209861	−	0.333564i	0.973499	−	0.228690i	$-0.0734441\pi$
$824$	−14.2552	−	43.8729i	−0.496603	−	1.52839i
$825$		0			0
$826$	−5.60294	+	17.2441i	−0.194951	+	0.599998i
$827$	16.1990	+	4.15919i	0.563293	+	0.144629i	0.519590	−	0.854416i	$-0.326085\pi$
$827$	16.1990	+	4.15919i	0.563293	+	0.144629i	0.0437026	+	0.999045i	$0.486085\pi$
$828$	−0.240037	−	0.131961i	−0.00834186	−	0.00458597i
$829$	1.67867	−	0.212066i	0.0583028	−	0.00736535i	−0.0961277	−	0.995369i	$-0.530646\pi$
$829$	1.67867	−	0.212066i	0.0583028	−	0.00736535i	0.154431	+	0.988004i	$0.450646\pi$
$830$		0			0
$831$	−31.8778	+	17.5250i	−1.10583	+	0.607934i
$832$	12.8332	−	39.4964i	0.444910	−	1.36929i
$833$	−4.75047	−	0.600124i	−0.164594	−	0.0207931i
$834$	−18.5889	−	29.2914i	−0.643680	−	1.01428i
$835$		0			0
$836$	−2.31680	+	0.917285i	−0.0801281	+	0.0317250i
$837$	0.607454	+	0.957194i	0.0209967	+	0.0330855i
$838$	−19.7997	−	7.83925i	−0.683969	−	0.270802i
$839$	−1.62676	−	25.8566i	−0.0561620	−	0.892669i	−0.920742	−	0.390173i	$-0.872415\pi$
$839$	−1.62676	−	25.8566i	−0.0561620	−	0.892669i	0.864580	−	0.502496i	$-0.167585\pi$
$840$		0			0
$841$	−29.5598	+	35.7317i	−1.01930	+	1.23213i
$842$	−6.56947	−	6.16915i	−0.226399	−	0.212603i
$843$	0.367080	+	1.12976i	0.0126429	+	0.0389109i
$844$	−0.979045	−	5.13234i	−0.0337001	−	0.176662i
$845$		0			0
$846$	11.5798	+	24.6083i	0.398121	+	0.846051i
$847$	−13.8167	−	29.3619i	−0.474746	−	1.00889i
$848$	−1.44657	+	0.572737i	−0.0496754	+	0.0196679i
$849$	−4.23990	−	3.08047i	−0.145513	−	0.105721i
$850$		0			0
$851$	−1.77015	+	1.28609i	−0.0606798	+	0.0440865i
$852$	1.66298	−	2.62044i	0.0569728	−	0.0897748i
$853$	2.04532	−	10.7219i	0.0700303	−	0.367112i	−0.929970	−	0.367637i	$-0.880167\pi$
$853$	2.04532	−	10.7219i	0.0700303	−	0.367112i	1.00000		0.000524838i	$0.000167061\pi$
$854$	20.8108	−	19.5426i	0.712130	−	0.668735i
$855$		0			0
$856$	−47.7463	−	6.03176i	−1.63193	−	0.206161i
$857$	−22.5065	−	16.3519i	−0.768807	−	0.558571i	0.132792	−	0.991144i	$-0.457606\pi$
$857$	−22.5065	−	16.3519i	−0.768807	−	0.558571i	−0.901599	+	0.432573i	$0.857606\pi$
$858$	−2.57001	−	13.4725i	−0.0877388	−	0.459943i
$859$	−31.4422	−	12.4488i	−1.07279	−	0.424749i	−0.235710	−	0.971823i	$-0.575742\pi$
$859$	−31.4422	−	12.4488i	−1.07279	−	0.424749i	−0.837084	+	0.547074i	$0.815742\pi$
$860$		0			0
$861$	53.7776	+	13.8077i	1.83273	+	0.470566i
$862$	10.1170	−	2.59761i	0.344587	−	0.0884748i
$863$	0.836287	−	13.2924i	0.0284675	−	0.452479i	−0.957812	−	0.287395i	$-0.907211\pi$
$863$	0.836287	−	13.2924i	0.0284675	−	0.452479i	0.986280	−	0.165083i	$-0.0527893\pi$
$864$	1.17941	+	1.42566i	0.0401242	+	0.0485019i
$865$		0			0
$866$	−4.28889	+	1.10120i	−0.145742	+	0.0374203i
$867$	−31.6141	+	17.3800i	−1.07367	+	0.590255i
$868$	1.84546	−	1.34081i	0.0626390	−	0.0455099i
$869$	3.05898	+	2.87258i	0.103769	+	0.0974455i
$870$		0			0
$871$	13.1073	−	68.7106i	0.444122	−	2.32817i
$872$	−16.0276	+	2.02475i	−0.542762	+	0.0685668i
$873$	−26.8347	−	32.4376i	−0.908218	−	1.09785i
$874$	−1.53139			−0.0518000
$875$		0			0
$876$	7.60980			0.257111
$877$	20.7065	+	25.0299i	0.699209	+	0.845199i	0.993887	−	0.110398i	$-0.0352125\pi$
$877$	20.7065	+	25.0299i	0.699209	+	0.845199i	−0.294678	+	0.955597i	$0.595212\pi$
$878$	−13.6459	+	1.72388i	−0.460526	+	0.0581780i
$879$	1.22659	−	6.43002i	0.0413719	−	0.216879i
$880$		0			0
$881$	−22.3861	−	21.0220i	−0.754208	−	0.708248i	0.208730	−	0.977973i	$-0.433067\pi$
$881$	−22.3861	−	21.0220i	−0.754208	−	0.708248i	−0.962937	+	0.269725i	$0.913067\pi$
$882$	−9.45530	+	6.86968i	−0.318376	+	0.231314i
$883$	7.00543	−	3.85127i	0.235752	−	0.129605i	−0.359500	−	0.933145i	$-0.617053\pi$
$883$	7.00543	−	3.85127i	0.235752	−	0.129605i	0.595251	+	0.803540i	$0.297053\pi$
$884$	−2.82363	+	0.724986i	−0.0949690	+	0.0243839i
$885$		0			0
$886$	−13.0269	−	15.7468i	−0.437647	−	0.529024i
$887$	1.19853	−	19.0501i	0.0402428	−	0.639641i	−0.925274	−	0.379299i	$-0.876165\pi$
$887$	1.19853	−	19.0501i	0.0402428	−	0.639641i	0.965517	−	0.260341i	$-0.0838350\pi$
$888$	−69.1053	+	17.7432i	−2.31902	+	0.595424i
$889$	23.2624	+	5.97276i	0.780194	+	0.200320i
$890$		0			0
$891$	9.05574	+	3.58542i	0.303379	+	0.120116i
$892$	−1.51116	−	7.92178i	−0.0505974	−	0.265241i
$893$	−36.2876	−	26.3645i	−1.21432	−	0.882254i
$894$	8.46695	+	1.06962i	0.283177	+	0.0357736i
$895$		0			0
$896$	−14.1960	+	13.3309i	−0.474255	+	0.445355i
$897$	−0.465942	+	2.44256i	−0.0155574	+	0.0815545i
$898$	1.01780	−	1.60380i	0.0339646	−	0.0535196i
$899$	10.8565	−	7.88770i	0.362084	−	0.263069i
$900$		0			0
$901$	0.598891	+	0.435120i	0.0199520	+	0.0144959i
$902$	8.22652	−	3.25711i	0.273913	−	0.108450i
$903$	−24.2955	−	51.6306i	−0.808504	−	1.71816i
$904$	18.9095	+	40.1847i	0.628920	+	1.33652i
$905$		0			0
$906$	−5.06701	−	26.5622i	−0.168340	−	0.882470i
$907$	−9.94487	−	30.6072i	−0.330214	−	1.01629i	−0.969032	−	0.246936i	$-0.920576\pi$
$907$	−9.94487	−	30.6072i	−0.330214	−	1.01629i	0.638818	−	0.769358i	$-0.279424\pi$
$908$	1.42083	+	1.33425i	0.0471521	+	0.0442787i
$909$	23.6824	−	28.6271i	0.785496	−	0.949502i
$910$		0			0
$911$	0.944825	+	15.0176i	0.0313034	+	0.497554i	0.982175	+	0.187969i	$0.0601903\pi$
$911$	0.944825	+	15.0176i	0.0313034	+	0.497554i	−0.950872	+	0.309586i	$0.899810\pi$
$912$	−35.2735	−	13.9658i	−1.16802	−	0.462452i
$913$	−4.90809	−	7.73392i	−0.162434	−	0.255955i
$914$	26.8750	−	10.6406i	0.888947	−	0.351959i
$915$		0			0
$916$	−2.67632	−	4.21720i	−0.0884281	−	0.139340i
$917$	−8.72706	−	1.10248i	−0.288193	−	0.0364072i
$918$	−0.386135	+	1.18840i	−0.0127443	+	0.0392231i
$919$	−37.5133	+	20.6231i	−1.23745	+	0.680293i	−0.959879	−	0.280413i	$-0.909529\pi$
$919$	−37.5133	+	20.6231i	−1.23745	+	0.680293i	−0.277569	+	0.960706i	$0.589529\pi$
$920$		0			0
$921$	48.7109	−	6.15362i	1.60508	−	0.202769i
$922$	−0.889556	−	0.489037i	−0.0292960	−	0.0161056i
$923$	−12.9076	−	3.31410i	−0.424858	−	0.109085i
$924$	1.07834	−	3.31879i	0.0354748	−	0.109180i
$925$		0			0
$926$	3.16274	+	9.73390i	0.103934	+	0.319876i
$927$	2.55575	+	40.6224i	0.0839417	+	1.33422i
$928$	15.9657	−	14.9928i	0.524098	−	0.492161i
$929$	27.2326	+	14.9713i	0.893474	+	0.491191i	0.861188	−	0.508287i	$-0.169721\pi$
$929$	27.2326	+	14.9713i	0.893474	+	0.491191i	0.0322863	+	0.999479i	$0.489721\pi$
$930$		0			0
$931$	8.20704	−	17.4409i	0.268975	−	0.571601i
$932$	5.69902			0.186678
$933$	11.6656	−	24.7907i	0.381916	−	0.811612i
$934$	−2.01802	+	32.0755i	−0.0660315	+	1.04954i
$935$		0			0
$936$	−20.5501	+	32.3818i	−0.671701	+	1.05843i
$937$	19.4945	−	23.5648i	0.636857	−	0.769828i	−0.349053	−	0.937103i	$-0.613497\pi$
$937$	19.4945	−	23.5648i	0.636857	−	0.769828i	0.985910	+	0.167275i	$0.0534966\pi$
$938$	−38.4554	+	46.4846i	−1.25561	+	1.51778i
$939$	17.2469	−	27.1767i	0.562830	−	0.886879i
$940$		0			0
$941$	−1.38273	+	21.9779i	−0.0450759	+	0.716460i	0.908982	+	0.416836i	$0.136861\pi$
$941$	−1.38273	+	21.9779i	−0.0450759	+	0.716460i	−0.954057	+	0.299624i	$0.903139\pi$
$942$	8.82700	−	18.7583i	0.287599	−	0.611179i
$943$	−1.60411			−0.0522370
$944$	5.52551	−	11.7423i	0.179840	−	0.382179i
$945$		0			0
$946$	−7.96839	−	4.38066i	−0.259075	−	0.142428i
$947$	−11.0775	+	10.4025i	−0.359970	+	0.338034i	−0.843339	−	0.537383i	$-0.819413\pi$
$947$	−11.0775	+	10.4025i	−0.359970	+	0.338034i	0.483368	+	0.875417i	$0.339413\pi$
$948$	−0.289006	−	4.59361i	−0.00938647	−	0.149194i
$949$	−10.0972	−	31.0760i	−0.327769	−	1.00877i
$950$		0			0
$951$	16.0249	−	49.3197i	0.519644	−	1.59930i
$952$	13.1258	+	3.37015i	0.425411	+	0.109227i
$953$	−3.54558	−	1.94920i	−0.114853	−	0.0631407i	0.423292	−	0.905993i	$-0.360874\pi$
$953$	−3.54558	−	1.94920i	−0.114853	−	0.0631407i	−0.538144	+	0.842853i	$0.680874\pi$
$954$	1.79265	−	0.226464i	0.0580391	−	0.00733204i
$955$		0			0
$956$	5.64130	−	3.10133i	0.182453	−	0.100304i
$957$	6.34367	−	19.5238i	0.205062	−	0.631115i
$958$	22.1494	+	2.79812i	0.715614	+	0.0904031i
$959$	19.8259	+	31.2407i	0.640213	+	1.00881i
$960$		0			0
$961$	26.6017	−	10.5324i	0.858119	−	0.339753i
$962$	30.4557	+	47.9904i	0.981930	+	1.54727i
$963$	39.4811	+	15.6317i	1.27226	+	0.503724i
$964$	0.410718	+	6.52817i	0.0132283	+	0.210258i
$965$		0			0
$966$	1.36703	−	1.65245i	0.0439834	−	0.0531668i
$967$	2.34127	+	2.19859i	0.0752900	+	0.0707020i	0.721279	−	0.692645i	$-0.243555\pi$
$967$	2.34127	+	2.19859i	0.0752900	+	0.0707020i	−0.645989	+	0.763347i	$0.723555\pi$
$968$	9.44699	+	29.0749i	0.303638	+	0.934501i
$969$	3.38240	+	17.7312i	0.108658	+	0.569608i
$970$		0			0
$971$	22.1357	+	47.0407i	0.710367	+	1.50961i	0.854166	+	0.520000i	$0.174068\pi$
$971$	22.1357	+	47.0407i	0.710367	+	1.50961i	−0.143799	+	0.989607i	$0.545932\pi$
$972$	−4.12173	−	8.75912i	−0.132205	−	0.280949i
$973$	−35.2384	+	13.9519i	−1.12969	+	0.447277i
$974$	−8.01861	−	5.82586i	−0.256933	−	0.186673i
$975$		0			0
$976$	−16.5307	+	12.0103i	−0.529135	+	0.384439i
$977$	31.2780	−	49.2863i	1.00067	−	1.57681i	0.198162	−	0.980169i	$-0.436503\pi$
$977$	31.2780	−	49.2863i	1.00067	−	1.57681i	0.802510	−	0.596638i	$-0.203497\pi$
$978$	−6.02502	+	31.5843i	−0.192659	+	1.00995i
$979$	8.25817	−	7.75494i	0.263932	−	0.247849i
$980$		0			0
$981$	14.1417	+	1.78651i	0.451510	+	0.0570389i
$982$	−37.0677	−	26.9312i	−1.18288	−	0.859410i
$983$	0.856033	+	4.48748i	0.0273032	+	0.143128i	0.993328	−	0.115319i	$-0.0367891\pi$
$983$	0.856033	+	4.48748i	0.0273032	+	0.143128i	−0.966025	+	0.258448i	$0.916789\pi$
$984$	−48.6335	−	19.2554i	−1.55038	−	0.613839i
$985$		0			0
$986$	14.3264	+	3.67839i	0.456244	+	0.117144i
$987$	60.8418	−	15.6215i	1.93661	−	0.497238i
$988$	0.736873	−	11.7123i	0.0234430	−	0.372616i
$989$	1.05085	+	1.27026i	0.0334150	+	0.0403918i
$990$		0			0
$991$	38.7549	−	9.95058i	1.23109	−	0.316091i	0.423534	−	0.905880i	$-0.360789\pi$
$991$	38.7549	−	9.95058i	1.23109	−	0.316091i	0.807557	+	0.589790i	$0.200789\pi$
$992$	−3.41700	+	1.87851i	−0.108490	+	0.0596428i
$993$	1.37191	−	0.996750i	0.0435362	−	0.0316309i
$994$	8.37838	+	7.86782i	0.265746	+	0.249552i
$995$		0			0
$996$	−1.88260	+	9.86895i	−0.0596526	+	0.312710i
$997$	36.7288	−	4.63992i	1.16321	−	0.146948i	0.480068	−	0.877231i	$-0.340612\pi$
$997$	36.7288	−	4.63992i	1.16321	−	0.146948i	0.683144	+	0.730283i	$0.260612\pi$
$998$	−3.14774	−	3.80496i	−0.0996399	−	0.120444i
$999$	−7.18703			−0.227388

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.g.a.26.4		220
5.2	odd	4		625.2.h.b.599.16		440
5.3	odd	4		625.2.h.b.599.7		440
5.4	even	2		125.2.g.a.81.8	yes	220
125.47	odd	100		625.2.h.b.24.7		440
125.54	even	50		125.2.g.a.71.8	✓	220
125.71	even	25	inner	625.2.g.a.601.4		220
125.78	odd	100		625.2.h.b.24.16		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.g.a.71.8	✓	220	125.54	even	50
125.2.g.a.81.8	yes	220	5.4	even	2
625.2.g.a.26.4		220	1.1	even	1	trivial
625.2.g.a.601.4		220	125.71	even	25	inner
625.2.h.b.24.7		440	125.47	odd	100
625.2.h.b.24.16		440	125.78	odd	100
625.2.h.b.599.7		440	5.3	odd	4
625.2.h.b.599.16		440	5.2	odd	4

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.g (of order \(25\), degree \(20\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.792152 - 0.957548i) q^{2} +(-2.36710 + 0.299035i) q^{3} +(0.0853705 - 0.447528i) q^{4} +(2.16144 + 2.02973i) q^{6} +(2.62061 - 1.90398i) q^{7} +(-2.67420 + 1.47015i) q^{8} +(2.60800 - 0.669621i) q^{9} +O(q^{10})\)	\(q+(-0.792152 - 0.957548i) q^{2} +(-2.36710 + 0.299035i) q^{3} +(0.0853705 - 0.447528i) q^{4} +(2.16144 + 2.02973i) q^{6} +(2.62061 - 1.90398i) q^{7} +(-2.67420 + 1.47015i) q^{8} +(2.60800 - 0.669621i) q^{9} +(-0.631715 - 0.763612i) q^{11} +(-0.0682544 + 1.08487i) q^{12} +(4.52083 - 1.16075i) q^{13} +(-3.89908 - 1.00111i) q^{14} +(2.67891 + 1.06065i) q^{16} +(-0.256883 - 1.34663i) q^{17} +(-2.70713 - 1.96684i) q^{18} +(5.47517 + 0.691675i) q^{19} +(-5.63389 + 5.29058i) q^{21} +(-0.230780 + 1.20979i) q^{22} +(0.119645 - 0.188530i) q^{23} +(5.89047 - 4.27968i) q^{24} +(-4.69266 - 3.40942i) q^{26} +(0.681940 - 0.269999i) q^{27} +(-0.628363 - 1.33534i) q^{28} +(-3.69654 - 7.85554i) q^{29} +(0.289633 + 1.51831i) q^{31} +(0.779561 + 2.39924i) q^{32} +(1.72368 + 1.61864i) q^{33} +(-1.08597 + 1.31271i) q^{34} +(-0.0770276 - 1.22432i) q^{36} +(-9.11089 - 3.60725i) q^{37} +(-3.67486 - 5.79065i) q^{38} +(-10.3542 + 4.09950i) q^{39} +(-3.84937 - 6.06563i) q^{41} +(9.52888 + 1.20378i) q^{42} +(-2.28152 + 7.02180i) q^{43} +(-0.395667 + 0.217520i) q^{44} +(-0.275303 + 0.0347789i) q^{46} +(-7.12232 - 3.91553i) q^{47} +(-6.65841 - 1.70959i) q^{48} +(1.07932 - 3.32180i) q^{49} +(1.01076 + 3.11078i) q^{51} +(-0.133523 - 2.12229i) q^{52} +(-0.393632 + 0.369645i) q^{53} +(-0.798737 - 0.439110i) q^{54} +(-4.20888 + 8.94432i) q^{56} -13.1671 q^{57} +(-4.59383 + 9.76239i) q^{58} +(0.282815 - 4.49522i) q^{59} +(-3.79996 + 5.98778i) q^{61} +(1.22442 - 1.48007i) q^{62} +(5.55960 - 6.72041i) q^{63} +(4.76754 - 7.51245i) q^{64} +(0.184511 - 2.93272i) q^{66} +(6.38100 - 13.5603i) q^{67} -0.624583 q^{68} +(-0.226835 + 0.482048i) q^{69} +(-2.50197 - 1.37547i) q^{71} +(-5.98987 + 5.62486i) q^{72} +(-0.439573 - 6.98681i) q^{73} +(3.76309 + 11.5816i) q^{74} +(0.776961 - 2.39124i) q^{76} +(-3.10938 - 0.798353i) q^{77} +(12.1275 + 6.66717i) q^{78} +(-4.20085 + 0.530691i) q^{79} +(-8.61210 + 4.73454i) q^{81} +(-2.75884 + 8.49085i) q^{82} +(9.16976 + 1.15841i) q^{83} +(1.88671 + 2.97298i) q^{84} +(8.53101 - 3.37767i) q^{86} +(11.0992 + 17.4895i) q^{87} +(2.81196 + 1.11333i) q^{88} +(0.717756 + 11.4084i) q^{89} +(9.63727 - 11.6495i) q^{91} +(-0.0741583 - 0.0696393i) q^{92} +(-1.13962 - 3.50738i) q^{93} +(1.89266 + 9.92165i) q^{94} +(-2.56276 - 5.44613i) q^{96} +(-6.65706 - 14.1470i) q^{97} +(-4.03576 + 1.59787i) q^{98} +(-2.15884 - 1.56849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 15 q^{7} + 5 q^{8} - 20 q^{9}+O(q^{10}) \) 220 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 15 * q^7 + 5 * q^8 - 20 * q^9	\( 220 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 15 q^{7} + 5 q^{8} - 20 q^{9} - 15 q^{11} + 100 q^{12} + 20 q^{13} - 10 q^{14} + 15 q^{17} - 10 q^{18} - 10 q^{19} - 5 q^{21} - 25 q^{22} + 90 q^{23} + 15 q^{24} + 15 q^{26} - 10 q^{27} - 30 q^{28} - 10 q^{29} - 10 q^{31} - 20 q^{32} - 15 q^{33} + 5 q^{34} - 210 q^{36} - 20 q^{37} - 30 q^{38} - 5 q^{41} - 70 q^{42} - 25 q^{43} + 15 q^{44} + 100 q^{47} - 105 q^{48} - 20 q^{49} + 25 q^{51} - 85 q^{52} - 20 q^{53} + 60 q^{54} - 105 q^{56} - 40 q^{57} + 225 q^{58} + 5 q^{59} - 65 q^{62} - 85 q^{63} + 45 q^{64} + 55 q^{66} + 105 q^{67} - 80 q^{68} + 40 q^{69} - 85 q^{71} - 160 q^{72} - 40 q^{73} + 35 q^{74} + 35 q^{76} - 75 q^{77} + 10 q^{78} + 55 q^{81} + 95 q^{82} - 50 q^{83} + 115 q^{84} + 40 q^{86} - 95 q^{87} - 165 q^{88} + 55 q^{89} - 105 q^{91} - 155 q^{92} + 185 q^{93} + 60 q^{94} + 135 q^{96} - 65 q^{97} - 135 q^{98} + 45 q^{99}+O(q^{100}) \) 220 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 15 * q^7 + 5 * q^8 - 20 * q^9 - 15 * q^11 + 100 * q^12 + 20 * q^13 - 10 * q^14 + 15 * q^17 - 10 * q^18 - 10 * q^19 - 5 * q^21 - 25 * q^22 + 90 * q^23 + 15 * q^24 + 15 * q^26 - 10 * q^27 - 30 * q^28 - 10 * q^29 - 10 * q^31 - 20 * q^32 - 15 * q^33 + 5 * q^34 - 210 * q^36 - 20 * q^37 - 30 * q^38 - 5 * q^41 - 70 * q^42 - 25 * q^43 + 15 * q^44 + 100 * q^47 - 105 * q^48 - 20 * q^49 + 25 * q^51 - 85 * q^52 - 20 * q^53 + 60 * q^54 - 105 * q^56 - 40 * q^57 + 225 * q^58 + 5 * q^59 - 65 * q^62 - 85 * q^63 + 45 * q^64 + 55 * q^66 + 105 * q^67 - 80 * q^68 + 40 * q^69 - 85 * q^71 - 160 * q^72 - 40 * q^73 + 35 * q^74 + 35 * q^76 - 75 * q^77 + 10 * q^78 + 55 * q^81 + 95 * q^82 - 50 * q^83 + 115 * q^84 + 40 * q^86 - 95 * q^87 - 165 * q^88 + 55 * q^89 - 105 * q^91 - 155 * q^92 + 185 * q^93 + 60 * q^94 + 135 * q^96 - 65 * q^97 - 135 * q^98 + 45 * q^99

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