LMFDB - Embedded newform 625.2.h.a.274.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(24,625)]

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([11]))

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

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

chi := DirichletCharacter("625.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.h (of order $50$, 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:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	no (minimal twist has level 125)
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			274.2
Character	$\chi$	$=$	625.274
Dual form			625.2.h.a.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.625230 - 2.43511i) q^{2} +(-0.668288 + 0.127483i) q^{3} +(-3.78623 + 2.08150i) q^{4} +(0.728267 + 1.54765i) q^{6} +(-2.37830 + 3.27344i) q^{7} +(3.99390 + 4.25307i) q^{8} +(-2.35897 + 0.933983i) q^{9} +O(q^{10})$	\(q+(-0.625230 - 2.43511i) q^{2} +(-0.668288 + 0.127483i) q^{3} +(-3.78623 + 2.08150i) q^{4} +(0.728267 + 1.54765i) q^{6} +(-2.37830 + 3.27344i) q^{7} +(3.99390 + 4.25307i) q^{8} +(-2.35897 + 0.933983i) q^{9} +(4.48501 - 1.15156i) q^{11} +(2.26493 - 1.87372i) q^{12} +(-0.747710 - 1.88850i) q^{13} +(9.45817 + 3.74475i) q^{14} +(3.22933 - 5.08861i) q^{16} +(0.916541 - 1.66718i) q^{17} +(3.74925 + 5.16040i) q^{18} +(1.17961 - 6.18373i) q^{19} +(1.17208 - 2.49079i) q^{21} +(-5.60833 - 10.2015i) q^{22} +(1.75873 + 0.110650i) q^{23} +(-3.21127 - 2.33312i) q^{24} +(-4.13121 + 3.00150i) q^{26} +(3.18069 - 2.01853i) q^{27} +(2.19111 - 17.3444i) q^{28} +(7.17322 + 0.906188i) q^{29} +(0.812167 + 0.446493i) q^{31} +(-3.31276 - 1.07638i) q^{32} +(-2.85048 + 1.34133i) q^{33} +(-4.63282 - 1.18951i) q^{34} +(6.98753 - 8.44647i) q^{36} +(7.63067 + 4.84257i) q^{37} +(-15.7956 + 0.993774i) q^{38} +(0.740437 + 1.16674i) q^{39} +(0.0493658 + 0.784647i) q^{41} +(-6.79817 - 1.29682i) q^{42} +(4.68827 - 1.52331i) q^{43} +(-14.5843 + 13.6956i) q^{44} +(-0.830165 - 4.35188i) q^{46} +(-0.0705648 + 0.0751439i) q^{47} +(-1.50941 + 3.81234i) q^{48} +(-2.89602 - 8.91304i) q^{49} +(-0.399976 + 1.23100i) q^{51} +(6.76191 + 5.59394i) q^{52} +(2.94761 + 1.38704i) q^{53} +(-6.90400 - 6.48329i) q^{54} +(-23.4209 + 2.95874i) q^{56} +4.28289i q^{57} +(-2.27824 - 18.0341i) q^{58} +(-1.14190 - 1.38031i) q^{59} +(-0.456975 + 7.26340i) q^{61} +(0.579467 - 2.25688i) q^{62} +(2.55299 - 9.94325i) q^{63} +(0.206985 - 3.28993i) q^{64} +(5.04849 + 6.10258i) q^{66} +(1.23491 + 9.77534i) q^{67} +8.22011i q^{68} +(-1.18944 + 0.150262i) q^{69} +(-5.78426 - 5.43179i) q^{71} +(-13.3938 - 6.30264i) q^{72} +(-0.531334 - 0.439558i) q^{73} +(7.02126 - 21.6092i) q^{74} +(8.40514 + 25.8684i) q^{76} +(-6.89714 + 17.4202i) q^{77} +(2.37820 - 2.53253i) q^{78} +(1.78188 + 9.34094i) q^{79} +(3.68020 - 3.45593i) q^{81} +(1.87984 - 0.610795i) q^{82} +(6.63224 + 1.26517i) q^{83} +(0.746821 + 11.8704i) q^{84} +(-6.64067 - 10.4640i) q^{86} +(-4.90930 + 0.308867i) q^{87} +(22.8103 + 14.4759i) q^{88} +(-5.44616 + 6.58328i) q^{89} +(7.96018 + 2.04383i) q^{91} +(-6.88927 + 3.24184i) q^{92} +(-0.599682 - 0.194848i) q^{93} +(0.227103 + 0.124851i) q^{94} +(2.35110 + 0.297013i) q^{96} +(1.49092 - 11.8018i) q^{97} +(-19.8935 + 12.6248i) q^{98} +(-9.50449 + 6.90542i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 25 q^{7} + 35 q^{8} - 20 q^{9}+O(q^{10}) $ 240 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 25 * q^7 + 35 * q^8 - 20 * q^9	$ 240 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 25 q^{7} + 35 q^{8} - 20 q^{9} - 25 q^{11} - 60 q^{12} + 20 q^{13} - 30 q^{14} - 40 q^{16} + 15 q^{17} + 25 q^{18} - 10 q^{19} - 35 q^{21} + 25 q^{22} - 70 q^{23} + 15 q^{24} - 45 q^{26} + 20 q^{27} + 10 q^{28} - 10 q^{29} - 30 q^{31} + 25 q^{32} + 35 q^{33} - 20 q^{34} + 170 q^{36} + 55 q^{37} + 40 q^{38} - 35 q^{41} + 10 q^{42} + 25 q^{43} + 15 q^{44} - 40 q^{46} - 100 q^{47} - 5 q^{48} + 35 q^{49} - 55 q^{51} + 15 q^{52} + 15 q^{53} + 30 q^{54} + 65 q^{56} - 255 q^{58} + 5 q^{59} - 40 q^{61} - 5 q^{62} + 35 q^{63} + 25 q^{64} - 95 q^{66} - 105 q^{67} - 10 q^{69} + 45 q^{71} + 30 q^{72} + 40 q^{73} + 35 q^{74} - 65 q^{76} + 35 q^{77} - 100 q^{78} - 95 q^{81} - 175 q^{82} - 20 q^{83} + 45 q^{84} - 80 q^{86} + 5 q^{87} + 5 q^{88} + 30 q^{89} + 65 q^{91} + 55 q^{92} - 275 q^{93} + 60 q^{94} - 135 q^{96} - 35 q^{97} + 15 q^{98} + 45 q^{99}+O(q^{100}) $ 240 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 25 * q^7 + 35 * q^8 - 20 * q^9 - 25 * q^11 - 60 * q^12 + 20 * q^13 - 30 * q^14 - 40 * q^16 + 15 * q^17 + 25 * q^18 - 10 * q^19 - 35 * q^21 + 25 * q^22 - 70 * q^23 + 15 * q^24 - 45 * q^26 + 20 * q^27 + 10 * q^28 - 10 * q^29 - 30 * q^31 + 25 * q^32 + 35 * q^33 - 20 * q^34 + 170 * q^36 + 55 * q^37 + 40 * q^38 - 35 * q^41 + 10 * q^42 + 25 * q^43 + 15 * q^44 - 40 * q^46 - 100 * q^47 - 5 * q^48 + 35 * q^49 - 55 * q^51 + 15 * q^52 + 15 * q^53 + 30 * q^54 + 65 * q^56 - 255 * q^58 + 5 * q^59 - 40 * q^61 - 5 * q^62 + 35 * q^63 + 25 * q^64 - 95 * q^66 - 105 * q^67 - 10 * q^69 + 45 * q^71 + 30 * q^72 + 40 * q^73 + 35 * q^74 - 65 * q^76 + 35 * q^77 - 100 * q^78 - 95 * q^81 - 175 * q^82 - 20 * q^83 + 45 * q^84 - 80 * q^86 + 5 * q^87 + 5 * q^88 + 30 * q^89 + 65 * q^91 + 55 * q^92 - 275 * q^93 + 60 * q^94 - 135 * q^96 - 35 * q^97 + 15 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{21}{50}\right)$

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 $

$2$	−0.625230	−	2.43511i	−0.442104	−	1.72188i	−0.664825	−	0.746999i	$-0.731494\pi$
$2$	−0.625230	−	2.43511i	−0.442104	−	1.72188i	0.222721	−	0.974882i	$-0.428506\pi$
$3$	−0.668288	+	0.127483i	−0.385836	+	0.0736022i	−0.376650	−	0.926356i	$-0.622924\pi$
$3$	−0.668288	+	0.127483i	−0.385836	+	0.0736022i	−0.00918605	+	0.999958i	$0.502924\pi$
$4$	−3.78623	+	2.08150i	−1.89311	+	1.04075i
$5$		0			0
$5$		0			0
$6$	0.728267	+	1.54765i	0.297314	+	0.631824i
$7$	−2.37830	+	3.27344i	−0.898911	+	1.23725i	0.0719027	+	0.997412i	$0.477093\pi$
$7$	−2.37830	+	3.27344i	−0.898911	+	1.23725i	−0.970814	+	0.239834i	$0.922907\pi$
$8$	3.99390	+	4.25307i	1.41206	+	1.50369i
$9$	−2.35897	+	0.933983i	−0.786324	+	0.311328i
$10$		0			0
$11$	4.48501	−	1.15156i	1.35228	−	0.347207i	0.498073	−	0.867135i	$-0.334041\pi$
$11$	4.48501	−	1.15156i	1.35228	−	0.347207i	0.854210	+	0.519928i	$0.174041\pi$
$12$	2.26493	−	1.87372i	0.653830	−	0.540895i
$13$	−0.747710	−	1.88850i	−0.207378	−	0.523776i	0.788443	−	0.615108i	$-0.210888\pi$
$13$	−0.747710	−	1.88850i	−0.207378	−	0.523776i	−0.995820	+	0.0913320i	$0.970888\pi$
$14$	9.45817	+	3.74475i	2.52780	+	1.00083i
$15$		0			0
$16$	3.22933	−	5.08861i	0.807333	−	1.27215i
$17$	0.916541	−	1.66718i	0.222294	−	0.404351i	−0.741519	−	0.670932i	$-0.765894\pi$
$17$	0.916541	−	1.66718i	0.222294	−	0.404351i	0.963812	+	0.266581i	$0.0858941\pi$
$18$	3.74925	+	5.16040i	0.883707	+	1.21632i
$19$	1.17961	−	6.18373i	0.270621	−	1.41865i	−0.544211	−	0.838948i	$-0.683171\pi$
$19$	1.17961	−	6.18373i	0.270621	−	1.41865i	0.814832	−	0.579697i	$-0.196829\pi$
$20$		0			0
$21$	1.17208	−	2.49079i	0.255768	−	0.543536i
$22$	−5.60833	−	10.2015i	−1.19570	−	2.17497i
$23$	1.75873	+	0.110650i	0.366720	+	0.0230721i	0.245082	−	0.969502i	$-0.421185\pi$
$23$	1.75873	+	0.110650i	0.366720	+	0.0230721i	0.121639	+	0.992574i	$0.461185\pi$
$24$	−3.21127	−	2.33312i	−0.655497	−	0.476247i
$25$		0			0
$26$	−4.13121	+	3.00150i	−0.810198	+	0.588643i
$27$	3.18069	−	2.01853i	0.612124	−	0.388466i
$28$	2.19111	−	17.3444i	0.414081	−	3.27779i
$29$	7.17322	+	0.906188i	1.33203	+	0.168275i	0.758911	−	0.651195i	$-0.225732\pi$
$29$	7.17322	+	0.906188i	1.33203	+	0.168275i	0.573123	+	0.819470i	$0.305732\pi$
$30$		0			0
$31$	0.812167	+	0.446493i	0.145870	+	0.0801925i	0.553017	−	0.833170i	$-0.313476\pi$
$31$	0.812167	+	0.446493i	0.145870	+	0.0801925i	−0.407147	+	0.913362i	$0.633476\pi$
$32$	−3.31276	−	1.07638i	−0.585619	−	0.190279i
$33$	−2.85048	+	1.34133i	−0.496204	+	0.233496i
$34$	−4.63282	−	1.18951i	−0.794522	−	0.203999i
$35$		0			0
$36$	6.98753	−	8.44647i	1.16459	−	1.40774i
$37$	7.63067	+	4.84257i	1.25447	+	0.796114i	0.985931	−	0.167154i	$-0.0534576\pi$
$37$	7.63067	+	4.84257i	1.25447	+	0.796114i	0.268544	+	0.963268i	$0.413458\pi$
$38$	−15.7956	+	0.993774i	−2.56238	+	0.161211i
$39$	0.740437	+	1.16674i	0.118565	+	0.186828i
$40$		0			0
$41$	0.0493658	+	0.784647i	0.00770964	+	0.122541i	0.999999	−	0.00140146i	$-0.000446099\pi$
$41$	0.0493658	+	0.784647i	0.00770964	+	0.122541i	−0.992289	+	0.123943i	$0.960446\pi$
$42$	−6.79817	−	1.29682i	−1.04898	−	0.200104i
$43$	4.68827	−	1.52331i	0.714954	−	0.232303i	0.0711198	−	0.997468i	$-0.477343\pi$
$43$	4.68827	−	1.52331i	0.714954	−	0.232303i	0.643834	+	0.765165i	$0.277343\pi$
$44$	−14.5843	+	13.6956i	−2.19867	+	2.06469i
$45$		0			0
$46$	−0.830165	−	4.35188i	−0.122401	−	0.641650i
$47$	−0.0705648	+	0.0751439i	−0.0102929	+	0.0109609i	−0.734094	−	0.679047i	$-0.762393\pi$
$47$	−0.0705648	+	0.0751439i	−0.0102929	+	0.0109609i	0.723802	+	0.690008i	$0.242393\pi$
$48$	−1.50941	+	3.81234i	−0.217865	+	0.550264i
$49$	−2.89602	−	8.91304i	−0.413717	−	1.27329i
$50$		0			0
$51$	−0.399976	+	1.23100i	−0.0560079	+	0.172375i
$52$	6.76191	+	5.59394i	0.937708	+	0.775740i
$53$	2.94761	+	1.38704i	0.404886	+	0.190525i	0.617428	−	0.786627i	$-0.288175\pi$
$53$	2.94761	+	1.38704i	0.404886	+	0.190525i	−0.212543	+	0.977152i	$0.568175\pi$
$54$	−6.90400	−	6.48329i	−0.939515	−	0.882263i
$55$		0			0
$56$	−23.4209	+	2.95874i	−3.12974	+	0.395379i
$57$			4.28289i			0.567283i
$58$	−2.27824	−	18.0341i	−0.299148	−	2.36800i
$59$	−1.14190	−	1.38031i	−0.148662	−	0.179702i	0.690925	−	0.722926i	$-0.257203\pi$
$59$	−1.14190	−	1.38031i	−0.148662	−	0.179702i	−0.839588	+	0.543224i	$0.817203\pi$
$60$		0			0
$61$	−0.456975	+	7.26340i	−0.0585096	+	0.929984i	0.853831	+	0.520551i	$0.174273\pi$
$61$	−0.456975	+	7.26340i	−0.0585096	+	0.929984i	−0.912340	+	0.409433i	$0.865727\pi$
$62$	0.579467	−	2.25688i	0.0735924	−	0.286624i
$63$	2.55299	−	9.94325i	0.321647	−	1.25273i
$64$	0.206985	−	3.28993i	0.0258731	−	0.411241i
$65$		0			0
$66$	5.04849	+	6.10258i	0.621426	+	0.751175i
$67$	1.23491	+	9.77534i	0.150869	+	1.19425i	0.867731	+	0.497034i	$0.165577\pi$
$67$	1.23491	+	9.77534i	0.150869	+	1.19425i	−0.716863	+	0.697214i	$0.754423\pi$
$68$			8.22011i			0.996835i
$69$	−1.18944	+	0.150262i	−0.143192	+	0.0180894i
$70$		0			0
$71$	−5.78426	−	5.43179i	−0.686466	−	0.644634i	0.260685	−	0.965424i	$-0.416052\pi$
$71$	−5.78426	−	5.43179i	−0.686466	−	0.644634i	−0.947150	+	0.320790i	$0.896052\pi$
$72$	−13.3938	−	6.30264i	−1.57847	−	0.742774i
$73$	−0.531334	−	0.439558i	−0.0621879	−	0.0514463i	0.605811	−	0.795609i	$-0.292849\pi$
$73$	−0.531334	−	0.439558i	−0.0621879	−	0.0514463i	−0.667999	+	0.744162i	$0.732849\pi$
$74$	7.02126	−	21.6092i	0.816205	−	2.51202i
$75$		0			0
$76$	8.40514	+	25.8684i	0.964136	+	2.96731i
$77$	−6.89714	+	17.4202i	−0.786002	+	1.98521i
$78$	2.37820	−	2.53253i	0.269278	−	0.286752i
$79$	1.78188	+	9.34094i	0.200477	+	1.05094i	0.930161	+	0.367153i	$0.119667\pi$
$79$	1.78188	+	9.34094i	0.200477	+	1.05094i	−0.729684	+	0.683785i	$0.760333\pi$
$80$		0			0
$81$	3.68020	−	3.45593i	0.408911	−	0.383993i
$82$	1.87984	−	0.610795i	0.207593	−	0.0674511i
$83$	6.63224	+	1.26517i	0.727982	+	0.138870i	0.538033	−	0.842924i	$-0.319168\pi$
$83$	6.63224	+	1.26517i	0.727982	+	0.138870i	0.189949	+	0.981794i	$0.439168\pi$
$84$	0.746821	+	11.8704i	0.0814849	+	1.29517i
$85$		0			0
$86$	−6.64067	−	10.4640i	−0.716082	−	1.12836i
$87$	−4.90930	+	0.308867i	−0.526332	+	0.0331140i
$88$	22.8103	+	14.4759i	2.43159	+	1.54313i
$89$	−5.44616	+	6.58328i	−0.577292	+	0.697826i	−0.975632	−	0.219412i	$-0.929586\pi$
$89$	−5.44616	+	6.58328i	−0.577292	+	0.697826i	0.398341	+	0.917238i	$0.369586\pi$
$90$		0			0
$91$	7.96018	+	2.04383i	0.834453	+	0.214251i
$92$	−6.88927	+	3.24184i	−0.718256	+	0.337986i
$93$	−0.599682	−	0.194848i	−0.0621841	−	0.0202048i
$94$	0.227103	+	0.124851i	0.0234238	+	0.0128774i
$95$		0			0
$96$	2.35110	+	0.297013i	0.239958	+	0.0303137i
$97$	1.49092	−	11.8018i	0.151380	−	1.19829i	−0.715078	−	0.699044i	$-0.753609\pi$
$97$	1.49092	−	11.8018i	0.151380	−	1.19829i	0.866458	−	0.499250i	$-0.166391\pi$
$98$	−19.8935	+	12.6248i	−2.00955	+	1.27530i
$99$	−9.50449	+	6.90542i	−0.955237	+	0.694021i
$100$		0			0
$101$	12.6247	+	9.17238i	1.25620	+	0.912686i	0.998565	−	0.0535553i	$-0.0170554\pi$
$101$	12.6247	+	9.17238i	1.25620	+	0.912686i	0.257639	+	0.966241i	$0.417055\pi$
$102$	3.24770	+	0.204328i	0.321570	+	0.0202315i
$103$	−5.19585	−	9.45121i	−0.511962	−	0.931255i	−0.998345	−	0.0575097i	$-0.981684\pi$
$103$	−5.19585	−	9.45121i	−0.511962	−	0.931255i	0.486383	−	0.873746i	$-0.338316\pi$
$104$	5.04565	−	10.7225i	0.494767	−	1.05143i
$105$		0			0
$106$	1.53466	−	8.04497i	0.149059	−	0.781397i
$107$	−2.10182	−	2.89291i	−0.203191	−	0.279668i	0.695245	−	0.718773i	$-0.255296\pi$
$107$	−2.10182	−	2.89291i	−0.203191	−	0.279668i	−0.898436	+	0.439105i	$0.855296\pi$
$108$	−7.84126	+	14.2632i	−0.754526	+	1.37248i
$109$	3.34023	−	5.26336i	0.319936	−	0.504139i	−0.645855	−	0.763460i	$-0.723499\pi$
$109$	3.34023	−	5.26336i	0.319936	−	0.504139i	0.965791	+	0.259321i	$0.0834989\pi$
$110$		0			0
$111$	−5.71683	−	2.26345i	−0.542617	−	0.214837i
$112$	8.97697	+	22.6732i	0.848244	+	2.14242i
$113$	1.22149	−	1.01050i	0.114908	−	0.0950602i	−0.578195	−	0.815898i	$-0.696243\pi$
$113$	1.22149	−	1.01050i	0.114908	−	0.0950602i	0.693103	+	0.720838i	$0.256243\pi$
$114$	10.4293	−	2.67779i	0.976794	−	0.250798i
$115$		0			0
$116$	−29.0457	+	11.5000i	−2.69682	+	1.06775i
$117$	3.52766	+	3.75657i	0.326132	+	0.347295i
$118$	−2.64727	+	3.64365i	−0.243701	+	0.335426i
$119$	3.27762	+	6.96530i	0.300459	+	0.638508i
$120$		0			0
$121$	9.14989	−	5.03020i	0.831808	−	0.457290i
$122$	17.9729	−	3.42851i	1.62719	−	0.310403i
$123$	−0.133019	−	0.518076i	−0.0119940	−	0.0467134i
$124$	−4.00442			−0.359608
$125$		0			0
$126$	−25.8091			−2.29926
$127$	−3.33724	−	12.9977i	−0.296132	−	1.15336i	−0.926266	−	0.376871i	$-0.877000\pi$
$127$	−3.33724	−	12.9977i	−0.296132	−	1.15336i	0.630134	−	0.776487i	$-0.283000\pi$
$128$	−14.9838	+	2.85832i	−1.32440	+	0.252642i
$129$	−2.93891	+	1.61568i	−0.258757	+	0.142253i
$130$		0			0
$131$	−4.37634	−	9.30021i	−0.382363	−	0.812563i	−0.999666	−	0.0258373i	$-0.991775\pi$
$131$	−4.37634	−	9.30021i	−0.382363	−	0.812563i	0.617303	−	0.786725i	$-0.288225\pi$
$132$	8.00057	−	11.0118i	0.696360	−	0.958458i
$133$	17.4366	+	18.5681i	1.51195	+	1.61006i
$134$	23.0319	−	9.11898i	1.98965	−	0.787760i
$135$		0			0
$136$	10.7512	−	2.76044i	0.921910	−	0.236706i
$137$	7.41139	−	6.13123i	0.633198	−	0.523827i	−0.264530	−	0.964377i	$-0.585217\pi$
$137$	7.41139	−	6.13123i	0.633198	−	0.523827i	0.897728	+	0.440551i	$0.145217\pi$
$138$	1.10958	+	2.80248i	0.0944536	+	0.238563i
$139$	2.94202	+	1.16483i	0.249539	+	0.0987995i	0.489564	−	0.871967i	$-0.337156\pi$
$139$	2.94202	+	1.16483i	0.249539	+	0.0987995i	−0.240025	+	0.970767i	$0.577156\pi$
$140$		0			0
$141$	0.0375780	−	0.0592135i	0.00316464	−	0.00498668i
$142$	−9.61049	+	17.4814i	−0.806495	+	1.46701i
$143$	−5.52821	−	7.60892i	−0.462292	−	0.636290i
$144$	−2.86522	+	15.0200i	−0.238769	+	1.25167i
$145$		0			0
$146$	−0.738165	+	1.56868i	−0.0610910	+	0.129825i
$147$	3.07163	+	5.58728i	0.253344	+	0.460831i
$148$	−38.9712	−	2.45186i	−3.20342	−	0.201542i
$149$	8.19412	+	5.95338i	0.671289	+	0.487720i	0.870456	−	0.492246i	$-0.163824\pi$
$149$	8.19412	+	5.95338i	0.671289	+	0.487720i	−0.199168	+	0.979965i	$0.563824\pi$
$150$		0			0
$151$	14.1488	−	10.2797i	1.15141	−	0.836551i	0.162745	−	0.986668i	$-0.447965\pi$
$151$	14.1488	−	10.2797i	1.15141	−	0.836551i	0.988668	+	0.150117i	$0.0479652\pi$
$152$	31.0111	−	19.6802i	2.51533	−	1.59628i
$153$	−0.604975	+	4.78887i	−0.0489094	+	0.387157i
$154$	46.7323	+	5.90366i	3.76580	+	0.475731i
$155$		0			0
$156$	−5.23203	−	2.87633i	−0.418898	−	0.230291i
$157$	10.4356	+	3.39073i	0.832851	+	0.270610i	0.694246	−	0.719738i	$-0.255738\pi$
$157$	10.4356	+	3.39073i	0.832851	+	0.270610i	0.138605	+	0.990348i	$0.455738\pi$
$158$	21.6321	−	10.1793i	1.72096	−	0.809821i
$159$	−2.14668	−	0.551173i	−0.170242	−	0.0437108i
$160$		0			0
$161$	−4.54499	+	5.49394i	−0.358195	+	0.432983i
$162$	−10.7165	−	6.80093i	−0.841971	−	0.534331i
$163$	−3.94178	+	0.247996i	−0.308744	+	0.0194245i	−0.216407	−	0.976303i	$-0.569434\pi$
$163$	−3.94178	+	0.247996i	−0.308744	+	0.0194245i	−0.0923370	+	0.995728i	$0.529434\pi$
$164$	−1.82015	−	2.86810i	−0.142130	−	0.223961i
$165$		0			0
$166$	−1.06585	−	16.9412i	−0.0827262	−	1.31489i
$167$	−6.69737	−	1.27759i	−0.518258	−	0.0988629i	−0.0783851	−	0.996923i	$-0.524976\pi$
$167$	−6.69737	−	1.27759i	−0.518258	−	0.0988629i	−0.439873	+	0.898060i	$0.644976\pi$
$168$	15.2747	−	4.96305i	1.17847	−	0.382907i
$169$	6.46923	−	6.07501i	0.497633	−	0.467308i
$170$		0			0
$171$	2.99283	+	15.6890i	0.228868	+	1.19977i
$172$	−14.5801	+	15.5262i	−1.11172	+	1.18386i
$173$	8.48424	−	21.4287i	0.645045	−	1.62920i	−0.125711	−	0.992067i	$-0.540121\pi$
$173$	8.48424	−	21.4287i	0.645045	−	1.62920i	0.770756	−	0.637131i	$-0.219879\pi$
$174$	3.82156	+	11.7616i	0.289712	+	0.891641i
$175$		0			0
$176$	8.62377	−	26.5412i	0.650041	−	2.00062i
$177$	0.939081	+	0.776875i	0.0705857	+	0.0583935i
$178$	19.4361	+	9.14593i	1.45680	+	0.685516i
$179$	−6.12304	−	5.74992i	−0.457658	−	0.429769i	0.421117	−	0.907006i	$-0.361638\pi$
$179$	−6.12304	−	5.74992i	−0.457658	−	0.429769i	−0.878774	+	0.477237i	$0.841638\pi$
$180$		0			0
$181$	−3.61539	+	0.456730i	−0.268730	+	0.0339485i	−0.258543	−	0.966000i	$-0.583243\pi$
$181$	−3.61539	+	0.456730i	−0.268730	+	0.0339485i	−0.0101865	+	0.999948i	$0.503243\pi$
$182$		−	20.6618i		−	1.53155i
$183$	−0.620568	−	4.91230i	−0.0458737	−	0.363128i
$184$	6.55359	+	7.92193i	0.483137	+	0.584012i
$185$		0			0
$186$	−0.0995382	+	1.58211i	−0.00729850	+	0.116006i
$187$	2.19085	−	8.53278i	0.160211	−	0.623979i
$188$	0.110763	−	0.431392i	0.00807820	−	0.0314625i
$189$	−0.957088	+	15.2125i	−0.0696179	+	1.10654i
$190$		0			0
$191$	12.8934	+	15.5854i	0.932933	+	1.12772i	0.991587	+	0.129443i	$0.0413191\pi$
$191$	12.8934	+	15.5854i	0.932933	+	1.12772i	−0.0586542	+	0.998278i	$0.518681\pi$
$192$	0.281084	+	2.22501i	0.0202855	+	0.160576i
$193$			24.4110i			1.75714i	0.477612	+	0.878571i	$0.341502\pi$
$193$			24.4110i			1.75714i	−0.477612	+	0.878571i	$0.658498\pi$
$194$	−29.6709	+	3.74831i	−2.13025	+	0.269113i
$195$		0			0
$196$	29.5174	+	27.7187i	2.10839	+	1.97991i
$197$	11.3535	+	5.34256i	0.808904	+	0.380641i	0.785327	−	0.619081i	$-0.212495\pi$
$197$	11.3535	+	5.34256i	0.808904	+	0.380641i	0.0235767	+	0.999722i	$0.492495\pi$
$198$	22.7579	+	18.8270i	1.61734	+	1.33798i
$199$	−6.09362	+	18.7542i	−0.431966	+	1.32945i	0.464199	+	0.885731i	$0.346342\pi$
$199$	−6.09362	+	18.7542i	−0.431966	+	1.32945i	−0.896164	+	0.443722i	$0.853658\pi$
$200$		0			0
$201$	−2.07146	−	6.37531i	−0.146110	−	0.449680i
$202$	14.4424	−	36.4773i	1.01616	−	2.56654i
$203$	−20.0264	+	21.3259i	−1.40558	+	1.49679i
$204$	−1.04792	−	5.49340i	−0.0733692	−	0.384615i
$205$		0			0
$206$	−19.7661	+	18.5616i	−1.37717	+	1.29325i
$207$	−4.25214	+	1.38160i	−0.295544	+	0.0960281i
$208$	−12.0244	−	2.29379i	−0.833745	−	0.159045i
$209$	−1.83035	−	29.0925i	−0.126608	−	2.01237i
$210$		0			0
$211$	−14.8100	−	23.3368i	−1.01956	−	1.60657i	−0.769820	−	0.638260i	$-0.779654\pi$
$211$	−14.8100	−	23.3368i	−1.01956	−	1.60657i	−0.249742	−	0.968312i	$-0.580346\pi$
$212$	−14.0474	+	0.883790i	−0.964783	+	0.0606990i
$213$	4.55801	+	2.89260i	0.312310	+	0.198198i
$214$	−5.73043	+	6.92689i	−0.391724	+	0.473513i
$215$		0			0
$216$	21.2883	+	5.46591i	1.44849	+	0.371908i
$217$	−3.39314	+	1.59669i	−0.230342	+	0.108391i
$218$	−14.9053	−	4.84302i	−1.00951	−	0.328010i
$219$	0.411120	+	0.226015i	0.0277809	+	0.0152727i
$220$		0			0
$221$	−3.83378	−	0.484319i	−0.257888	−	0.0325788i
$222$	−1.93742	+	15.3363i	−0.130031	+	1.02930i
$223$	0.299025	−	0.189767i	0.0200242	−	0.0127078i	−0.525777	−	0.850622i	$-0.676225\pi$
$223$	0.299025	−	0.189767i	0.0200242	−	0.0127078i	0.545801	+	0.837915i	$0.316225\pi$
$224$	11.4022	−	8.28418i	0.761841	−	0.553510i
$225$		0			0
$226$	−3.22440	−	2.34266i	−0.214484	−	0.155832i
$227$	−15.0139	−	0.944593i	−0.996506	−	0.0626948i	−0.443847	−	0.896103i	$-0.646387\pi$
$227$	−15.0139	−	0.944593i	−0.996506	−	0.0626948i	−0.552659	+	0.833408i	$0.686387\pi$
$228$	−8.91482	−	16.2160i	−0.590398	−	1.07393i
$229$	7.66111	−	16.2807i	0.506260	−	1.07586i	−0.474430	−	0.880293i	$-0.657346\pi$
$229$	7.66111	−	16.2807i	0.506260	−	1.07586i	0.980691	−	0.195565i	$-0.0626541\pi$
$230$		0			0
$231$	2.38850	−	12.5210i	0.157152	−	0.823818i
$232$	24.7950	+	34.1274i	1.62787	+	2.24058i
$233$	−6.37540	+	11.5968i	−0.417666	+	0.759732i	−0.998526	−	0.0542713i	$-0.982716\pi$
$233$	−6.37540	+	11.5968i	−0.417666	+	0.759732i	0.580860	+	0.814004i	$0.302716\pi$
$234$	6.94207	−	10.9389i	0.453817	−	0.715101i
$235$		0			0
$236$	7.19660	+	2.84933i	0.468459	+	0.185476i
$237$	−2.38162	−	6.01527i	−0.154703	−	0.390734i
$238$	14.9120	−	12.3363i	0.966601	−	0.799642i
$239$	−12.2827	+	3.15367i	−0.794503	+	0.203994i	−0.624063	−	0.781374i	$-0.714519\pi$
$239$	−12.2827	+	3.15367i	−0.794503	+	0.203994i	−0.170440	+	0.985368i	$0.554519\pi$
$240$		0			0
$241$	−11.2845	+	4.46785i	−0.726899	+	0.287800i	−0.702284	−	0.711897i	$-0.747836\pi$
$241$	−11.2845	+	4.46785i	−0.726899	+	0.287800i	−0.0246154	+	0.999697i	$0.507836\pi$
$242$	−17.9699	−	19.1360i	−1.15515	−	1.23011i
$243$	−8.66165	+	11.9217i	−0.555645	+	0.764779i
$244$	−13.3885	−	28.4521i	−0.857113	−	1.82146i
$245$		0			0
$246$	−1.17840	+	0.647833i	−0.0751323	+	0.0413044i
$247$	−12.5600	+	2.39595i	−0.799173	+	0.152450i
$248$	1.34475	+	5.23745i	0.0853917	+	0.332579i
$249$	−4.59353			−0.291103
$250$		0			0
$251$	−22.9649			−1.44953			−0.724767	−	0.688994i	$-0.758053\pi$
$251$	−22.9649			−1.44953			−0.724767	+	0.688994i	$0.758053\pi$
$252$	11.0306	+	42.9615i	0.694864	+	2.70632i
$253$	8.01535	−	1.52901i	0.503920	−	0.0961280i
$254$	−29.5642	+	16.2531i	−1.85502	+	1.01981i
$255$		0			0
$256$	13.5216	+	28.7348i	0.845097	+	1.79592i
$257$	−1.92193	+	2.64530i	−0.119886	+	0.165009i	−0.864742	−	0.502216i	$-0.832518\pi$
$257$	−1.92193	+	2.64530i	−0.119886	+	0.165009i	0.744856	+	0.667225i	$0.232518\pi$
$258$	5.77186	+	6.14640i	0.359340	+	0.382658i
$259$	−33.9999	+	13.4615i	−2.11265	+	0.836457i
$260$		0			0
$261$	−17.7678	+	4.56199i	−1.09980	+	0.282380i
$262$	−19.9108	+	16.4716i	−1.23009	+	1.01762i
$263$	4.13196	+	10.4361i	0.254788	+	0.643520i	0.999721	−	0.0236186i	$-0.00751873\pi$
$263$	4.13196	+	10.4361i	0.254788	+	0.643520i	−0.744933	+	0.667139i	$0.767519\pi$
$264$	−17.0893	−	6.76613i	−1.05177	−	0.416427i
$265$		0			0
$266$	34.3135	−	54.0694i	2.10390	−	3.31521i
$267$	2.80035	−	5.09381i	0.171378	−	0.311736i
$268$	−25.0230	−	34.4412i	−1.52852	−	2.10383i
$269$	−2.46334	+	12.9133i	−0.150192	+	0.787335i	0.824856	+	0.565343i	$0.191256\pi$
$269$	−2.46334	+	12.9133i	−0.150192	+	0.787335i	−0.975048	+	0.221992i	$0.928744\pi$
$270$		0			0
$271$	7.60495	−	16.1613i	0.461968	−	0.981732i	−0.529123	−	0.848545i	$-0.677479\pi$
$271$	7.60495	−	16.1613i	0.461968	−	0.981732i	0.991091	−	0.133187i	$-0.0425210\pi$
$272$	−5.52383	−	10.0478i	−0.334931	−	0.609238i
$273$	−5.58024	−	0.351079i	−0.337731	−	0.0212483i
$274$	−19.5640	−	14.2141i	−1.18191	−	0.858706i
$275$		0			0
$276$	4.19073	−	3.04475i	0.252253	−	0.183272i
$277$	−15.0004	+	9.51952i	−0.901285	+	0.571973i	−0.903767	−	0.428024i	$-0.859210\pi$
$277$	−15.0004	+	9.51952i	−0.901285	+	0.571973i	0.00248258	+	0.999997i	$0.499210\pi$
$278$	0.997045	−	7.89243i	0.0597988	−	0.473356i
$279$	−2.33290	−	0.294714i	−0.139667	−	0.0176440i
$280$		0			0
$281$	6.55318	+	3.60264i	0.390930	+	0.214915i	0.665081	−	0.746771i	$-0.268397\pi$
$281$	6.55318	+	3.60264i	0.390930	+	0.214915i	−0.274151	+	0.961687i	$0.588397\pi$
$282$	−0.167686	−	0.0544845i	−0.00998557	−	0.00324451i
$283$	17.3902	−	8.18319i	1.03374	−	0.486440i	0.167395	−	0.985890i	$-0.446464\pi$
$283$	17.3902	−	8.18319i	1.03374	−	0.486440i	0.866343	+	0.499449i	$0.166464\pi$
$284$	33.2068	+	8.52605i	1.97046	+	0.505928i
$285$		0			0
$286$	−15.0722	+	18.2191i	−0.891235	+	1.07732i
$287$	−2.68590	−	1.70453i	−0.158544	−	0.100615i
$288$	8.82004	−	0.554910i	0.519726	−	0.0326984i
$289$	7.16961	+	11.2975i	0.421742	+	0.664558i
$290$		0			0
$291$	0.508167	+	8.07708i	0.0297893	+	0.473487i
$292$	2.92669	+	0.558296i	0.171272	+	0.0326718i
$293$	24.3387	−	7.90812i	1.42188	−	0.461997i	0.505682	−	0.862720i	$-0.331241\pi$
$293$	24.3387	−	7.90812i	1.42188	−	0.461997i	0.916199	+	0.400723i	$0.131241\pi$
$294$	11.6852	−	10.9731i	0.681492	−	0.639964i
$295$		0			0
$296$	9.88034	+	51.7945i	0.574283	+	3.01050i
$297$	11.9410	−	12.7159i	0.692887	−	0.737850i
$298$	9.37392	−	23.6758i	0.543016	−	1.37150i
$299$	−1.10606	−	3.40410i	−0.0639650	−	0.196864i
$300$		0			0
$301$	−6.16361	+	18.9697i	−0.355265	+	1.09339i
$302$	−33.8785	−	28.0267i	−1.94949	−	1.61275i
$303$	−9.60625	−	4.52036i	−0.551865	−	0.259688i
$304$	−27.6572	−	25.9719i	−1.58625	−	1.48959i
$305$		0			0
$306$	12.0397	−	1.52096i	0.688262	−	0.0869477i
$307$			20.8747i			1.19138i	0.803214	+	0.595691i	$0.203122\pi$
$307$			20.8747i			1.19138i	−0.803214	+	0.595691i	$0.796878\pi$
$308$	−10.1459	−	80.3131i	−0.578117	−	4.57626i
$309$	4.67719	+	5.65375i	0.266076	+	0.321630i
$310$		0			0
$311$	−0.0674150	+	1.07153i	−0.00382275	+	0.0607609i	−0.999476	−	0.0323810i	$-0.989691\pi$
$311$	−0.0674150	+	1.07153i	−0.00382275	+	0.0607609i	0.995653	+	0.0931419i	$0.0296910\pi$
$312$	−2.00501	+	7.80898i	−0.113511	+	0.442096i
$313$	−0.548302	+	2.13549i	−0.0309918	+	0.120705i	−0.982197	−	0.187854i	$-0.939847\pi$
$313$	−0.548302	+	2.13549i	−0.0309918	+	0.120705i	0.951205	+	0.308559i	$0.0998468\pi$
$314$	1.73215	−	27.5318i	0.0977510	−	1.55371i
$315$		0			0
$316$	−26.1897	−	31.6579i	−1.47329	−	1.78090i
$317$	−1.10986	−	8.78545i	−0.0623360	−	0.493440i	−0.992116	−	0.125324i	$-0.960003\pi$
$317$	−1.10986	−	8.78545i	−0.0623360	−	0.493440i	0.929780	−	0.368116i	$-0.119997\pi$
$318$			5.57200i			0.312462i
$319$	33.2155	−	4.19609i	1.85971	−	0.234936i
$320$		0			0
$321$	1.77342	+	1.66535i	0.0989825	+	0.0929507i
$322$	16.2200	+	7.63256i	0.903906	+	0.425346i
$323$	−9.22825	−	7.63427i	−0.513473	−	0.424782i
$324$	−6.74055	+	20.7453i	−0.374475	+	1.15252i
$325$		0			0
$326$	3.06841	+	9.44360i	0.169944	+	0.523033i
$327$	−1.56125	+	3.94326i	−0.0863372	+	0.218063i
$328$	−3.14000	+	3.34376i	−0.173377	+	0.184628i
$329$	−0.0781552	−	0.409704i	−0.00430884	−	0.0225877i
$330$		0			0
$331$	10.7484	−	10.0934i	0.590784	−	0.554783i	−0.330434	−	0.943829i	$-0.607195\pi$
$331$	10.7484	−	10.0934i	0.590784	−	0.554783i	0.921218	+	0.389046i	$0.127195\pi$
$332$	−27.7446	+	9.01477i	−1.52268	+	0.494750i
$333$	−22.5234	−	4.29657i	−1.23428	−	0.235451i
$334$	1.07632	+	17.1076i	0.0588935	+	0.936086i
$335$		0			0
$336$	−8.88965	−	14.0078i	−0.484970	−	0.764190i
$337$	−7.94953	+	0.500142i	−0.433038	+	0.0272445i	−0.277814	−	0.960635i	$-0.589610\pi$
$337$	−7.94953	+	0.500142i	−0.433038	+	0.0272445i	−0.155224	+	0.987879i	$0.549610\pi$
$338$	−18.8381	−	11.9550i	−1.02466	−	0.650266i
$339$	−0.687485	+	0.831026i	−0.0373390	+	0.0451351i
$340$		0			0
$341$	4.15674	+	1.06727i	0.225100	+	0.0577959i
$342$	36.3332	−	17.0971i	1.96467	−	0.924505i
$343$	9.12677	+	2.96547i	0.492799	+	0.160120i
$344$	25.2032	+	13.8556i	1.35887	+	0.747043i
$345$		0			0
$346$	−57.4859	−	7.26216i	−3.09046	−	0.390416i
$347$	1.70397	−	13.4883i	0.0914737	−	0.724089i	−0.877960	−	0.478734i	$-0.841096\pi$
$347$	1.70397	−	13.4883i	0.0914737	−	0.724089i	0.969433	−	0.245354i	$-0.0789043\pi$
$348$	17.9448	−	11.3881i	0.961943	−	0.610467i
$349$	19.8463	−	14.4192i	1.06235	−	0.771841i	0.0878265	−	0.996136i	$-0.472008\pi$
$349$	19.8463	−	14.4192i	1.06235	−	0.771841i	0.974521	+	0.224295i	$0.0720079\pi$
$350$		0			0
$351$	−6.19023	−	4.49746i	−0.330410	−	0.240057i
$352$	−16.0973	−	1.01276i	−0.857988	−	0.0539801i
$353$	7.31526	+	13.3064i	0.389352	+	0.708229i	0.996247	−	0.0865531i	$-0.0275852\pi$
$353$	7.31526	+	13.3064i	0.389352	+	0.708229i	−0.606895	+	0.794782i	$0.707585\pi$
$354$	1.30463	−	2.77249i	0.0693406	−	0.147356i
$355$		0			0
$356$	6.91734	−	36.2619i	0.366618	−	1.92188i
$357$	−3.07835	−	4.23698i	−0.162923	−	0.224245i
$358$	−10.1734	+	18.5053i	−0.537679	+	0.978035i
$359$	−11.5646	+	18.2230i	−0.610358	+	0.961771i	0.388823	+	0.921313i	$0.372882\pi$
$359$	−11.5646	+	18.2230i	−0.610358	+	0.961771i	−0.999181	+	0.0404585i	$0.987118\pi$
$360$		0			0
$361$	−19.1813	−	7.59441i	−1.00954	−	0.399706i
$362$	3.37264	+	8.51831i	0.177262	+	0.447712i
$363$	−5.47350	+	4.52807i	−0.287284	+	0.237662i
$364$	−34.3933	+	8.83069i	−1.80270	+	0.462854i
$365$		0			0
$366$	−11.5740	+	4.58246i	−0.604982	+	0.239529i
$367$	6.76402	+	7.20295i	0.353079	+	0.375991i	0.880850	−	0.473396i	$-0.156972\pi$
$367$	6.76402	+	7.20295i	0.353079	+	0.375991i	−0.527771	+	0.849387i	$0.676972\pi$
$368$	6.24257	−	8.59216i	0.325417	−	0.447898i
$369$	−0.849300	−	1.80485i	−0.0442128	−	0.0939569i
$370$		0			0
$371$	−11.5507	+	6.35005i	−0.599682	+	0.329678i
$372$	2.67611	−	0.510495i	0.138750	−	0.0264679i
$373$	−0.960970	−	3.74273i	−0.0497571	−	0.193791i	0.938846	−	0.344338i	$-0.111897\pi$
$373$	−0.960970	−	3.74273i	−0.0497571	−	0.193791i	−0.988603	+	0.150547i	$0.951897\pi$
$374$	−22.1480			−1.14525
$375$		0			0
$376$	−0.601421			−0.0310159
$377$	−3.65215	−	14.2242i	−0.188095	−	0.732583i
$378$	37.6424	−	7.18067i	1.93612	−	0.369334i
$379$	0.486034	−	0.267199i	0.0249659	−	0.0137251i	−0.469222	−	0.883080i	$-0.655466\pi$
$379$	0.486034	−	0.267199i	0.0249659	−	0.0137251i	0.494188	+	0.869355i	$0.335466\pi$
$380$		0			0
$381$	3.88721	+	8.26075i	0.199148	+	0.423211i
$382$	29.8909	−	41.1413i	1.52935	−	2.10497i
$383$	−10.4254	−	11.1019i	−0.532711	−	0.567279i	0.405168	−	0.914242i	$-0.367213\pi$
$383$	−10.4254	−	11.1019i	−0.532711	−	0.567279i	−0.937879	+	0.346963i	$0.887213\pi$
$384$	9.64913	−	3.82036i	0.492405	−	0.194957i
$385$		0			0
$386$	59.4434	−	15.2625i	3.02559	−	0.776839i
$387$	−9.63675	+	7.97221i	−0.489863	+	0.405250i
$388$	18.9205	+	47.7877i	0.960543	+	2.42605i
$389$	−2.51568	−	0.996028i	−0.127550	−	0.0505006i	0.303483	−	0.952837i	$-0.401851\pi$
$389$	−2.51568	−	0.996028i	−0.127550	−	0.0505006i	−0.431033	+	0.902336i	$0.641851\pi$
$390$		0			0
$391$	1.79642	−	2.83071i	0.0908490	−	0.143155i
$392$	26.3414	−	47.9148i	1.33044	−	2.42006i
$393$	4.11027	+	5.65730i	0.207336	+	0.285373i
$394$	5.91115	−	30.9874i	0.297800	−	1.56112i
$395$		0			0
$396$	21.6126	−	45.9290i	1.08607	−	2.30802i
$397$	−13.6122	−	24.7606i	−0.683179	−	1.24270i	−0.959521	−	0.281639i	$-0.909122\pi$
$397$	−13.6122	−	24.7606i	−0.683179	−	1.24270i	0.276342	−	0.961059i	$-0.410878\pi$
$398$	49.4785	+	3.11293i	2.48013	+	0.156037i
$399$	−14.0198	−	10.1860i	−0.701868	−	0.509937i
$400$		0			0
$401$	−16.7945	+	12.2019i	−0.838679	+	0.609336i	−0.922001	−	0.387187i	$-0.873447\pi$
$401$	−16.7945	+	12.2019i	−0.838679	+	0.609336i	0.0833222	+	0.996523i	$0.473447\pi$
$402$	−14.2294	+	9.03027i	−0.709699	+	0.450389i
$403$	0.235936	−	1.86763i	0.0117528	−	0.0930331i
$404$	−66.8922	−	8.45046i	−3.32801	−	0.420426i
$405$		0			0
$406$	64.4521	+	35.4328i	3.19870	+	1.75850i
$407$	39.8001	+	12.9319i	1.97282	+	0.641008i
$408$	−6.83300	+	3.21537i	−0.338284	+	0.159184i
$409$	19.3158	+	4.95945i	0.955105	+	0.245229i	0.693914	−	0.720058i	$-0.255885\pi$
$409$	19.3158	+	4.95945i	0.955105	+	0.245229i	0.261191	+	0.965287i	$0.415885\pi$
$410$		0			0
$411$	−4.17131	+	5.04225i	−0.205756	+	0.248716i
$412$	39.3453	+	24.9693i	1.93840	+	1.23015i
$413$	7.23415	−	0.455134i	0.355969	−	0.0223957i
$414$	6.02292	+	9.49060i	0.296010	+	0.466438i
$415$		0			0
$416$	0.444239	+	7.06097i	0.0217806	+	0.346193i
$417$	−2.11461	−	0.403384i	−0.103553	−	0.0197538i
$418$	−69.6990	+	22.6466i	−3.40909	+	1.10768i
$419$	13.5265	−	12.7022i	0.660812	−	0.620544i	−0.279788	−	0.960062i	$-0.590264\pi$
$419$	13.5265	−	12.7022i	0.660812	−	0.620544i	0.940599	+	0.339518i	$0.110264\pi$
$420$		0			0
$421$	−5.53498	−	29.0154i	−0.269758	−	1.41412i	−0.816754	−	0.576987i	$-0.804228\pi$
$421$	−5.53498	−	29.0154i	−0.269758	−	1.41412i	0.546995	−	0.837136i	$-0.315772\pi$
$422$	−47.5680	+	50.6548i	−2.31558	+	2.46584i
$423$	0.0962773	−	0.243169i	0.00468116	−	0.0118233i
$424$	5.87328	+	18.0761i	0.285232	+	0.877853i
$425$		0			0
$426$	4.19400	−	12.9078i	0.203200	−	0.625384i
$427$	−22.6895	−	18.7704i	−1.09802	−	0.908363i
$428$	13.9796	+	6.57828i	0.675727	+	0.317973i
$429$	4.66444	+	4.38020i	0.225201	+	0.211478i
$430$		0			0
$431$	−6.38032	+	0.806022i	−0.307329	+	0.0388247i	−0.277485	−	0.960730i	$-0.589501\pi$
$431$	−6.38032	+	0.806022i	−0.307329	+	0.0388247i	−0.0298439	+	0.999555i	$0.509501\pi$
$432$		−	22.7038i		−	1.09234i
$433$	−0.506888	−	4.01243i	−0.0243595	−	0.192825i	0.975239	−	0.221153i	$-0.0709819\pi$
$433$	−0.506888	−	4.01243i	−0.0243595	−	0.192825i	−0.999599	+	0.0283274i	$0.990982\pi$
$434$	6.00961	+	7.26437i	0.288471	+	0.348701i
$435$		0			0
$436$	−1.69121	+	26.8810i	−0.0809941	+	1.28737i
$437$	2.75884	−	10.7450i	0.131973	−	0.514002i
$438$	0.293327	−	1.14243i	0.0140157	−	0.0545876i
$439$	−1.86027	+	29.5682i	−0.0887861	+	1.41121i	0.661423	+	0.750013i	$0.269953\pi$
$439$	−1.86027	+	29.5682i	−0.0887861	+	1.41121i	−0.750209	+	0.661201i	$0.770047\pi$
$440$		0			0
$441$	15.1563	+	18.3208i	0.721727	+	0.872418i
$442$	1.21762	+	9.63849i	0.0579165	+	0.458456i
$443$			8.31037i			0.394837i	0.980319	+	0.197419i	$0.0632558\pi$
$443$			8.31037i			0.394837i	−0.980319	+	0.197419i	$0.936744\pi$
$444$	26.3566	−	3.32961i	1.25083	−	0.158016i
$445$		0			0
$446$	−0.649063	−	0.609511i	−0.0307340	−	0.0288612i
$447$	−6.23498	−	2.93396i	−0.294905	−	0.138772i
$448$	10.2771	+	8.50198i	0.485549	+	0.401681i
$449$	−3.02883	+	9.32178i	−0.142939	+	0.439922i	−0.996740	−	0.0806776i	$-0.974292\pi$
$449$	−3.02883	+	9.32178i	−0.142939	+	0.439922i	0.853801	+	0.520600i	$0.174292\pi$
$450$		0			0
$451$	1.12497	+	3.46230i	0.0529728	+	0.163034i
$452$	−2.52148	+	6.36853i	−0.118600	+	0.299550i
$453$	−8.14499	+	8.67353i	−0.382685	+	0.407518i
$454$	7.08693	+	37.1510i	0.332606	+	1.74358i
$455$		0			0
$456$	−18.2154	+	17.1054i	−0.853016	+	0.801036i
$457$	8.78434	−	2.85420i	0.410914	−	0.133514i	−0.0962631	−	0.995356i	$-0.530689\pi$
$457$	8.78434	−	2.85420i	0.410914	−	0.133514i	0.507177	+	0.861842i	$0.330689\pi$
$458$	−44.4352	−	8.47647i	−2.07632	−	0.396079i
$459$	−0.450020	−	7.15286i	−0.0210051	−	0.333867i
$460$		0			0
$461$	21.0552	+	33.1777i	0.980638	+	1.54524i	0.830832	+	0.556523i	$0.187865\pi$
$461$	21.0552	+	33.1777i	0.980638	+	1.54524i	0.149806	+	0.988715i	$0.452135\pi$
$462$	−31.9832	+	2.01222i	−1.48800	+	0.0936167i
$463$	−6.14228	−	3.89801i	−0.285456	−	0.181156i	0.385387	−	0.922755i	$-0.374068\pi$
$463$	−6.14228	−	3.89801i	−0.285456	−	0.181156i	−0.670844	+	0.741599i	$0.734068\pi$
$464$	27.7759	−	33.5753i	1.28947	−	1.55870i
$465$		0			0
$466$	32.2256	+	8.27412i	1.49282	+	0.383291i
$467$	−2.87290	+	1.35188i	−0.132942	+	0.0625577i	−0.491100	−	0.871103i	$-0.663405\pi$
$467$	−2.87290	+	1.35188i	−0.132942	+	0.0625577i	0.358158	+	0.933661i	$0.383405\pi$
$468$	−21.1758	−	6.88044i	−0.978852	−	0.318048i
$469$	−34.9360	−	19.2062i	−1.61320	−	0.886862i
$470$		0			0
$471$	−7.40623	−	0.935625i	−0.341261	−	0.0431113i
$472$	1.30996	−	10.3694i	0.0602958	−	0.477291i
$473$	19.2728	−	12.2309i	0.886162	−	0.562376i
$474$	−13.1588	+	9.56042i	−0.604403	+	0.439125i
$475$		0			0
$476$	−26.9081	−	19.5499i	−1.23333	−	0.896066i
$477$	−8.24881	−	0.518971i	−0.377687	−	0.0237621i
$478$	15.3590	+	27.9380i	0.702506	+	1.27785i
$479$	11.8409	−	25.1631i	0.541023	−	1.14973i	−0.428231	−	0.903669i	$-0.640863\pi$
$479$	11.8409	−	25.1631i	0.541023	−	1.14973i	0.969254	−	0.246063i	$-0.0791369\pi$
$480$		0			0
$481$	3.43967	−	18.0314i	0.156835	−	0.822160i
$482$	17.9351	+	24.6856i	0.816922	+	1.12440i
$483$	2.33697	−	4.25094i	0.106336	−	0.193425i
$484$	−24.1732	+	38.0909i	−1.09878	+	1.73141i
$485$		0			0
$486$	34.4462	+	13.6382i	1.56251	+	0.618642i
$487$	−2.77035	−	6.99711i	−0.125537	−	0.317069i	0.853393	−	0.521268i	$-0.174541\pi$
$487$	−2.77035	−	6.99711i	−0.125537	−	0.317069i	−0.978929	+	0.204199i	$0.934541\pi$
$488$	−32.7169	+	27.0658i	−1.48102	+	1.22521i
$489$	2.60263	−	0.668241i	0.117695	−	0.0302189i
$490$		0			0
$491$	3.83743	−	1.51935i	0.173181	−	0.0685672i	−0.279934	−	0.960019i	$-0.590313\pi$
$491$	3.83743	−	1.51935i	0.173181	−	0.0685672i	0.453115	+	0.891452i	$0.350313\pi$
$492$	1.58202	+	1.68468i	0.0713228	+	0.0759511i
$493$	8.08533	−	11.1285i	0.364145	−	0.501203i
$494$	13.6873	+	29.0869i	0.615819	+	1.30868i
$495$		0			0
$496$	4.89478	−	2.69093i	0.219782	−	0.120826i
$497$	31.5373	−	6.01607i	1.41464	−	0.269858i
$498$	2.87201	+	11.1857i	0.128698	+	0.501245i
$499$	35.0385			1.56854			0.784269	−	0.620422i	$-0.213038\pi$
$499$	35.0385			1.56854			0.784269	+	0.620422i	$0.213038\pi$
$500$		0			0
$501$	4.63864			0.207239
$502$	14.3584	+	55.9221i	0.640845	+	2.49593i
$503$	−29.5896	+	5.64452i	−1.31934	+	0.251677i	−0.798507	−	0.601985i	$-0.794377\pi$
$503$	−29.5896	+	5.64452i	−1.31934	+	0.251677i	−0.520828	+	0.853662i	$0.674377\pi$
$504$	52.4858	−	28.8543i	2.33790	−	1.28527i
$505$		0			0
$506$	−8.73473	−	18.5623i	−0.388306	−	0.825193i
$507$	−3.54885	+	4.88457i	−0.157610	+	0.216931i
$508$	39.6902	+	42.2657i	1.76097	+	1.87524i
$509$	0.706530	−	0.279735i	0.0313164	−	0.0123990i	−0.352414	−	0.935844i	$-0.614639\pi$
$509$	0.706530	−	0.279735i	0.0313164	−	0.0123990i	0.383731	+	0.923445i	$0.374639\pi$
$510$		0			0
$511$	2.70254	−	0.693893i	0.119553	−	0.0306960i
$512$	38.0113	−	31.4457i	1.67988	−	1.38972i
$513$	−8.73006	−	22.0496i	−0.385442	−	0.973514i
$514$	7.64324	+	3.02617i	0.337129	+	0.133479i
$515$		0			0
$516$	7.76436	−	12.2347i	0.341807	−	0.538602i
$517$	−0.229952	+	0.418281i	−0.0101133	+	0.0183960i
$518$	54.0379	+	74.3768i	2.37429	+	3.26793i
$519$	−2.93812	+	15.4022i	−0.128969	+	0.676080i
$520$		0			0
$521$	1.46977	−	3.12342i	0.0643918	−	0.136840i	−0.870041	−	0.492980i	$-0.835908\pi$
$521$	1.46977	−	3.12342i	0.0643918	−	0.136840i	0.934432	+	0.356140i	$0.115908\pi$
$522$	22.2179	+	40.4142i	0.972451	+	1.76888i
$523$	7.18758	+	0.452204i	0.314291	+	0.0197735i	0.219153	−	0.975691i	$-0.429671\pi$
$523$	7.18758	+	0.452204i	0.314291	+	0.0197735i	0.0951381	+	0.995464i	$0.469671\pi$
$524$	35.9282	+	26.1034i	1.56953	+	1.14033i
$525$		0			0
$526$	22.8297	−	16.5868i	0.995423	−	0.723217i
$527$	1.48877	−	0.944802i	0.0648518	−	0.0411562i
$528$	−2.37961	+	18.8366i	−0.103559	+	0.819756i
$529$	−19.7378	−	2.49346i	−0.858163	−	0.108411i
$530$		0			0
$531$	3.98289	+	2.18961i	0.172843	+	0.0950211i
$532$	−104.669	−	34.0089i	−4.53796	−	1.47447i
$533$	1.44489	−	0.679916i	0.0625853	−	0.0294504i
$534$	−14.1548	−	3.63435i	−0.612540	−	0.157274i
$535$		0			0
$536$	−36.6431	+	44.2939i	−1.58274	+	1.91321i
$537$	4.82497	+	3.06202i	0.208213	+	0.132136i
$538$	32.9853	−	2.07526i	1.42210	−	0.0894709i
$539$	−23.2526	−	36.6402i	−1.00156	−	1.57820i
$540$		0			0
$541$	−1.02363	−	16.2702i	−0.0440094	−	0.699510i	−0.956739	−	0.290946i	$-0.906030\pi$
$541$	−1.02363	−	16.2702i	−0.0440094	−	0.699510i	0.912730	−	0.408563i	$-0.133970\pi$
$542$	−44.1095	−	8.41433i	−1.89466	−	0.361426i
$543$	2.35790	−	0.766127i	0.101187	−	0.0328776i
$544$	−4.83081	+	4.53643i	−0.207119	+	0.194498i
$545$		0			0
$546$	2.63402	+	13.8080i	0.112725	+	0.590928i
$547$	3.03854	−	3.23572i	0.129919	−	0.138349i	−0.660720	−	0.750633i	$-0.729749\pi$
$547$	3.03854	−	3.23572i	0.129919	−	0.138349i	0.790638	+	0.612283i	$0.209749\pi$
$548$	−15.2991	+	38.6410i	−0.653544	+	1.65066i
$549$	−5.70591	−	17.5610i	−0.243522	−	0.749484i
$550$		0			0
$551$	14.0652	−	43.2883i	0.599199	−	1.84414i
$552$	−5.38959	−	4.45866i	−0.229396	−	0.189773i
$553$	−34.8149	−	16.3826i	−1.48048	−	0.696660i
$554$	32.5597	+	30.5756i	1.38333	+	1.29903i
$555$		0			0
$556$	−13.5638	+	1.71350i	−0.575231	+	0.0726686i
$557$			24.8887i			1.05457i	0.849689	+	0.527284i	$0.176790\pi$
$557$			24.8887i			1.05457i	−0.849689	+	0.527284i	$0.823210\pi$
$558$	0.740937	+	5.86512i	0.0313664	+	0.248290i
$559$	−6.38224	−	7.71480i	−0.269940	−	0.326301i
$560$		0			0
$561$	−0.376333	+	5.98165i	−0.0158888	+	0.252545i
$562$	4.67558	−	18.2102i	0.197227	−	0.768150i
$563$	2.76002	−	10.7496i	0.116321	−	0.453040i	−0.883562	−	0.468314i	$-0.844862\pi$
$563$	2.76002	−	10.7496i	0.116321	−	0.453040i	0.999883	+	0.0152732i	$0.00486179\pi$
$564$	−0.0190263	+	0.302414i	−0.000801152	+	0.0127339i
$565$		0			0
$566$	−30.7998	−	37.2306i	−1.29461	−	1.56492i
$567$	2.56021	+	20.2661i	0.107519	+	0.851098i
$568$		−	46.2949i		−	1.94249i
$569$	34.2945	−	4.33240i	1.43770	−	0.181624i	0.632468	−	0.774586i	$-0.282042\pi$
$569$	34.2945	−	4.33240i	1.43770	−	0.181624i	0.805230	+	0.592963i	$0.202042\pi$
$570$		0			0
$571$	−0.698633	−	0.656060i	−0.0292369	−	0.0274553i	0.669791	−	0.742550i	$-0.266384\pi$
$571$	−0.698633	−	0.656060i	−0.0292369	−	0.0274553i	−0.699028	+	0.715094i	$0.746384\pi$
$572$	36.7690	+	17.3022i	1.53739	+	0.723440i
$573$	−10.6034	−	8.77186i	−0.442962	−	0.366450i
$574$	−2.47140	+	7.60619i	−0.103154	+	0.317476i
$575$		0			0
$576$	2.58447	+	7.95418i	0.107686	+	0.331424i
$577$	10.8582	−	27.4247i	0.452034	−	1.14171i	−0.507884	−	0.861425i	$-0.669572\pi$
$577$	10.8582	−	27.4247i	0.452034	−	1.14171i	0.959918	−	0.280282i	$-0.0904278\pi$
$578$	23.0280	−	24.5223i	0.957837	−	1.01999i
$579$	−3.11198	−	16.3136i	−0.129329	−	0.677969i
$580$		0			0
$581$	−19.9149	+	18.7013i	−0.826208	+	0.775861i
$582$	19.3508	−	6.28747i	0.802118	−	0.260624i
$583$	14.8173	+	2.82656i	0.613671	+	0.117064i
$584$	−0.252624	−	4.01535i	−0.0104537	−	0.166156i
$585$		0			0
$586$	−34.4744	−	54.3229i	−1.42412	−	2.24406i
$587$	43.0897	−	2.71097i	1.77850	−	0.111894i	0.860745	−	0.509036i	$-0.169998\pi$
$587$	43.0897	−	2.71097i	1.77850	−	0.111894i	0.917757	+	0.397142i	$0.129998\pi$
$588$	−23.2598	−	14.7611i	−0.959218	−	0.608738i
$589$	3.71903	−	4.49554i	0.153240	−	0.185235i
$590$		0			0
$591$	−8.26849	−	2.12299i	−0.340120	−	0.0873281i
$592$	49.2839	−	23.1912i	2.02556	−	0.953154i
$593$	−9.18806	−	2.98538i	−0.377308	−	0.122595i	0.114222	−	0.993455i	$-0.463562\pi$
$593$	−9.18806	−	2.98538i	−0.377308	−	0.122595i	−0.491531	+	0.870860i	$0.663562\pi$
$594$	−38.4304	−	21.1273i	−1.57682	−	0.866863i
$595$		0			0
$596$	−43.4168	−	5.48481i	−1.77842	−	0.224667i
$597$	1.68145	−	13.3101i	0.0688172	−	0.544745i
$598$	−7.59780	+	4.82171i	−0.310697	+	0.197175i
$599$	3.86284	−	2.80652i	0.157832	−	0.114671i	−0.506066	−	0.862495i	$-0.668901\pi$
$599$	3.86284	−	2.80652i	0.157832	−	0.114671i	0.663898	+	0.747823i	$0.268901\pi$
$600$		0			0
$601$	−0.352353	−	0.255999i	−0.0143728	−	0.0104424i	0.580576	−	0.814206i	$-0.302828\pi$
$601$	−0.352353	−	0.255999i	−0.0143728	−	0.0104424i	−0.594948	+	0.803764i	$0.702828\pi$
$602$	50.0468	+	3.14868i	2.03976	+	0.128331i
$603$	−12.0431	−	21.9064i	−0.490434	−	0.892097i
$604$	−32.1734	+	68.3720i	−1.30912	+	2.78202i
$605$		0			0
$606$	−5.00145	+	26.2185i	−0.203170	+	1.06505i
$607$	−18.1510	−	24.9827i	−0.736727	−	1.01402i	−0.998800	−	0.0489700i	$-0.984406\pi$
$607$	−18.1510	−	24.9827i	−0.736727	−	1.01402i	0.262073	−	0.965048i	$-0.415594\pi$
$608$	−10.5638	+	19.2155i	−0.428419	+	0.779292i
$609$	10.6647	−	16.8049i	0.432156	−	0.680968i
$610$		0			0
$611$	0.194671	+	0.0770758i	0.00787556	+	0.00311815i
$612$	−7.67745	−	19.3910i	−0.310342	−	0.783835i
$613$	−8.83805	+	7.31147i	−0.356965	+	0.295307i	−0.798570	−	0.601903i	$-0.794410\pi$
$613$	−8.83805	+	7.31147i	−0.356965	+	0.295307i	0.441604	+	0.897210i	$0.354410\pi$
$614$	50.8321	−	13.0515i	2.05142	−	0.526715i
$615$		0			0
$616$	−101.636	+	40.2404i	−4.09502	+	1.62133i
$617$	−0.123921	−	0.131963i	−0.00498887	−	0.00531261i	0.726469	−	0.687199i	$-0.241160\pi$
$617$	−0.123921	−	0.131963i	−0.00498887	−	0.00531261i	−0.731458	+	0.681886i	$0.761160\pi$
$618$	10.8432	−	14.9243i	0.436176	−	0.600345i
$619$	2.08860	+	4.43851i	0.0839480	+	0.178399i	0.942394	−	0.334506i	$-0.108569\pi$
$619$	2.08860	+	4.43851i	0.0839480	+	0.178399i	−0.858446	+	0.512905i	$0.828569\pi$
$620$		0			0
$621$	5.81733	−	3.19810i	0.233441	−	0.128335i
$622$	2.65144	−	0.505790i	0.106313	−	0.0202803i
$623$	−8.59740	−	33.4847i	−0.344448	−	1.34154i
$624$	8.32821			0.333395
$625$		0			0
$626$	5.54297			0.221542
$627$	4.93199	+	19.2088i	0.196965	+	0.767126i
$628$	−46.5693	+	8.88357i	−1.85832	+	0.354493i
$629$	15.0673	−	8.28330i	0.600772	−	0.330277i
$630$		0			0
$631$	4.02011	+	8.54318i	0.160038	+	0.340098i	0.968723	−	0.248143i	$-0.0798204\pi$
$631$	4.02011	+	8.54318i	0.160038	+	0.340098i	−0.808685	+	0.588242i	$0.799820\pi$
$632$	−32.6110	+	44.8852i	−1.29720	+	1.78544i
$633$	12.8724	+	13.7077i	0.511631	+	0.544832i
$634$	−20.6996	+	8.19555i	−0.822086	+	0.325487i
$635$		0			0
$636$	9.27507	−	2.38143i	0.367780	−	0.0944299i
$637$	−14.6669	+	12.1335i	−0.581123	+	0.480747i
$638$	−30.9853	−	78.2598i	−1.22672	−	3.09834i
$639$	18.7181	+	7.41103i	0.740477	+	0.293176i
$640$		0			0
$641$	−20.8927	+	32.9216i	−0.825212	+	1.30033i	0.126075	+	0.992021i	$0.459762\pi$
$641$	−20.8927	+	32.9216i	−0.825212	+	1.30033i	−0.951287	+	0.308306i	$0.900238\pi$
$642$	2.94651	−	5.35969i	0.116290	−	0.211530i
$643$	−18.1743	−	25.0147i	−0.716723	−	0.986484i	−0.999626	−	0.0273358i	$-0.991298\pi$
$643$	−18.1743	−	25.0147i	−0.716723	−	0.986484i	0.282904	−	0.959148i	$-0.408702\pi$
$644$	5.77273	−	30.2617i	0.227477	−	1.19248i
$645$		0			0
$646$	−12.8205	+	27.2450i	−0.504416	+	1.07194i
$647$	7.83671	+	14.2549i	0.308093	+	0.560419i	0.984345	−	0.176251i	$-0.0563971\pi$
$647$	7.83671	+	14.2549i	0.308093	+	0.560419i	−0.676252	+	0.736670i	$0.736397\pi$
$648$	29.3967	+	1.84948i	1.15481	+	0.0726545i
$649$	−6.71093	−	4.87577i	−0.263427	−	0.191391i
$650$		0			0
$651$	2.06404	−	1.49962i	0.0808963	−	0.0587746i
$652$	14.4083	−	9.14376i	0.564271	−	0.358097i
$653$	−5.86105	+	46.3950i	−0.229361	+	1.81558i	0.285584	+	0.958354i	$0.407813\pi$
$653$	−5.86105	+	46.3950i	−0.229361	+	1.81558i	−0.514945	+	0.857223i	$0.672187\pi$
$654$	10.5784	+	1.33636i	0.413649	+	0.0522560i
$655$		0			0
$656$	4.15218	+	2.28268i	0.162115	+	0.0891237i
$657$	1.66394	+	0.540648i	0.0649166	+	0.0210927i
$658$	−0.948809	+	0.446476i	−0.0369884	+	0.0174054i
$659$	−23.3899	−	6.00549i	−0.911139	−	0.233941i	−0.236105	−	0.971727i	$-0.575871\pi$
$659$	−23.3899	−	6.00549i	−0.911139	−	0.233941i	−0.675034	+	0.737787i	$0.735871\pi$
$660$		0			0
$661$	−11.9501	+	14.4452i	−0.464804	+	0.561852i	−0.949878	−	0.312622i	$-0.898793\pi$
$661$	−11.9501	+	14.4452i	−0.464804	+	0.561852i	0.485074	+	0.874473i	$0.338793\pi$
$662$	−31.2987	−	19.8628i	−1.21646	−	0.771988i
$663$	2.62381	−	0.165076i	0.101900	−	0.00641103i
$664$	21.1076	+	33.2603i	0.819135	+	1.29075i
$665$		0			0
$666$	3.61969	+	57.5333i	0.140260	+	2.22937i
$667$	12.5155	+	2.38746i	0.484601	+	0.0924427i
$668$	28.0171	−	9.10329i	1.08401	−	0.352217i
$669$	−0.175643	+	0.164940i	−0.00679075	+	0.00637693i
$670$		0			0
$671$	6.31468	+	33.1027i	0.243775	+	1.27792i
$672$	−6.56386	+	6.98980i	−0.253206	+	0.269637i
$673$	−10.2958	+	26.0043i	−0.396875	+	1.00239i	0.584689	+	0.811258i	$0.301217\pi$
$673$	−10.2958	+	26.0043i	−0.396875	+	1.00239i	−0.981564	+	0.191134i	$0.938783\pi$
$674$	6.18818	+	19.0453i	0.238360	+	0.733596i
$675$		0			0
$676$	−11.8489	+	36.4670i	−0.455725	+	1.40258i
$677$	31.2051	+	25.8151i	1.19931	+	0.992156i	0.999925	+	0.0122346i	$0.00389448\pi$
$677$	31.2051	+	25.8151i	1.19931	+	0.992156i	0.199385	+	0.979921i	$0.436106\pi$
$678$	2.45347	+	1.15452i	0.0942251	+	0.0443390i
$679$	35.0868	+	32.9487i	1.34651	+	1.26445i
$680$		0			0
$681$	10.1540	−	1.28275i	0.389102	−	0.0491551i
$682$		−	10.7894i		−	0.413148i
$683$	5.72423	+	45.3120i	0.219032	+	1.73381i	0.591972	+	0.805959i	$0.298350\pi$
$683$	5.72423	+	45.3120i	0.219032	+	1.73381i	−0.372940	+	0.927855i	$0.621650\pi$
$684$	−43.9881	−	53.1725i	−1.68193	−	2.03310i
$685$		0			0
$686$	1.51491	−	24.0788i	0.0578395	−	0.919332i
$687$	−3.04432	+	11.8568i	−0.116148	+	0.452367i
$688$	7.38843	−	28.7760i	0.281681	−	1.09708i
$689$	0.415468	−	6.60367i	0.0158281	−	0.251580i
$690$		0			0
$691$	2.16131	+	2.61257i	0.0822200	+	0.0993869i	0.810019	−	0.586403i	$-0.199457\pi$
$691$	2.16131	+	2.61257i	0.0822200	+	0.0993869i	−0.727799	+	0.685790i	$0.759457\pi$
$692$	12.4806	+	98.7940i	0.474441	+	3.75559i
$693$		−	47.5355i		−	1.80573i
$694$	−33.9108	+	4.28393i	−1.28724	+	0.162616i
$695$		0			0
$696$	−20.9209	−	19.6460i	−0.793004	−	0.744680i
$697$	1.35340	+	0.636859i	0.0512635	+	0.0241228i
$698$	−47.5208	−	39.3126i	−1.79869	−	1.48800i
$699$	2.78221	−	8.56276i	0.105233	−	0.323873i
$700$		0			0
$701$	8.94805	+	27.5393i	0.337963	+	1.04014i	0.965244	+	0.261351i	$0.0841679\pi$
$701$	8.94805	+	27.5393i	0.337963	+	1.04014i	−0.627281	+	0.778793i	$0.715832\pi$
$702$	−7.08150	+	17.8858i	−0.267274	+	0.675057i
$703$	38.9464	−	41.4737i	1.46889	−	1.56421i
$704$	−2.86021	−	14.9937i	−0.107798	−	0.565098i
$705$		0			0
$706$	27.8288	−	26.1330i	1.04735	−	0.983529i
$707$	−60.0505	+	19.5116i	−2.25843	+	0.733809i
$708$	−5.17264	−	0.986734i	−0.194400	−	0.0370837i
$709$	−2.17009	−	34.4926i	−0.0814993	−	1.29539i	−0.800055	−	0.599926i	$-0.795197\pi$
$709$	−2.17009	−	34.4926i	−0.0814993	−	1.29539i	0.718556	−	0.695469i	$-0.244803\pi$
$710$		0			0
$711$	−12.9277	−	20.3708i	−0.484826	−	0.763964i
$712$	−49.7506	+	3.13004i	−1.86448	+	0.117303i
$713$	1.37898	+	0.875126i	0.0516431	+	0.0327737i
$714$	−8.39284	+	10.1452i	−0.314094	+	0.379675i
$715$		0			0
$716$	35.1517	+	9.02541i	1.31368	+	0.337296i
$717$	7.80635	−	3.67339i	0.291533	−	0.137185i
$718$	51.6054	+	16.7676i	1.92590	+	0.625762i
$719$	−13.7870	−	7.57947i	−0.514169	−	0.282667i	0.203471	−	0.979081i	$-0.434778\pi$
$719$	−13.7870	−	7.57947i	−0.514169	−	0.282667i	−0.717640	+	0.696414i	$0.754778\pi$
$720$		0			0
$721$	43.2953	+	5.46946i	1.61240	+	0.203693i
$722$	−6.50050	+	51.4568i	−0.241924	+	1.91502i
$723$	6.97172	−	4.42439i	0.259281	−	0.164545i
$724$	12.7380	−	9.25471i	0.473404	−	0.343948i
$725$		0			0
$726$	14.4485	+	10.4975i	0.536235	+	0.389598i
$727$	−45.8667	−	2.88569i	−1.70110	−	0.107024i	−0.817702	−	0.575642i	$-0.804752\pi$
$727$	−45.8667	−	2.88569i	−1.70110	−	0.107024i	−0.883401	+	0.468618i	$0.844752\pi$
$728$	23.0996	+	42.0180i	0.856129	+	1.55729i
$729$	−2.17998	+	4.63270i	−0.0807401	+	0.171581i
$730$		0			0
$731$	1.75735	−	9.21237i	0.0649981	−	0.340732i
$732$	12.5745	+	17.3074i	0.464768	+	0.639699i
$733$	−20.5002	+	37.2896i	−0.757190	+	1.37732i	0.163307	+	0.986575i	$0.447784\pi$
$733$	−20.5002	+	37.2896i	−0.757190	+	1.37732i	−0.920497	+	0.390749i	$0.872216\pi$
$734$	13.3109	−	20.9746i	0.491314	−	0.774188i
$735$		0			0
$736$	−5.70715	−	2.25962i	−0.210368	−	0.0832907i
$737$	16.7955	+	42.4205i	0.618668	+	1.56258i
$738$	−3.86401	+	3.19658i	−0.142236	+	0.117668i
$739$	−6.34931	+	1.63023i	−0.233563	+	0.0599688i	−0.363657	−	0.931533i	$-0.618472\pi$
$739$	−6.34931	+	1.63023i	−0.233563	+	0.0599688i	0.130094	+	0.991502i	$0.458472\pi$
$740$		0			0
$741$	8.08824	−	3.20236i	0.297129	−	0.117642i
$742$	22.6849	+	24.1569i	0.832788	+	0.886829i
$743$	−1.45377	+	2.00095i	−0.0533338	+	0.0734077i	−0.834851	−	0.550476i	$-0.814446\pi$
$743$	−1.45377	+	2.00095i	−0.0533338	+	0.0734077i	0.781517	+	0.623884i	$0.214446\pi$
$744$	−1.56636	−	3.32869i	−0.0574257	−	0.122036i
$745$		0			0
$746$	−8.51313	+	4.68013i	−0.311688	+	0.171352i
$747$	−16.8269	+	3.20990i	−0.615664	+	0.117444i
$748$	9.46591	+	36.8673i	0.346108	+	1.34800i
$749$	14.4685			0.528668
$750$		0			0
$751$	2.31139			0.0843439			0.0421720	−	0.999110i	$-0.486572\pi$
$751$	2.31139			0.0843439			0.0421720	+	0.999110i	$0.486572\pi$
$752$	0.154501	+	0.601741i	0.00563407	+	0.0219432i
$753$	15.3472	−	2.92763i	0.559282	−	0.106689i
$754$	−32.3540	+	17.7868i	−1.17826	+	0.647756i
$755$		0			0
$756$	−28.0409	−	59.5901i	−1.01984	−	2.16727i
$757$	32.0574	−	44.1233i	1.16515	−	1.60369i	0.475082	−	0.879942i	$-0.342419\pi$
$757$	32.0574	−	44.1233i	1.16515	−	1.60369i	0.690066	−	0.723746i	$-0.257581\pi$
$758$	−0.954542	−	1.01648i	−0.0346705	−	0.0369204i
$759$	−5.16163	+	2.04364i	−0.187355	+	0.0741793i
$760$		0			0
$761$	−6.41543	+	1.64720i	−0.232559	+	0.0597110i	−0.363171	−	0.931723i	$-0.618306\pi$
$761$	−6.41543	+	1.64720i	−0.232559	+	0.0597110i	0.130612	+	0.991434i	$0.458306\pi$
$762$	17.6854	−	14.6307i	0.640675	−	0.530013i
$763$	9.28526	+	23.4519i	0.336149	+	0.849016i
$764$	−81.2583	−	32.1724i	−2.93982	−	1.16396i
$765$		0			0
$766$	−20.5160	+	32.3281i	−0.741274	+	1.16806i
$767$	−1.75292	+	3.18855i	−0.0632942	+	0.115132i
$768$	−12.6995	−	17.4793i	−0.458253	−	0.630731i
$769$	−4.96375	+	26.0209i	−0.178997	+	0.938337i	0.773501	+	0.633795i	$0.218504\pi$
$769$	−4.96375	+	26.0209i	−0.178997	+	0.938337i	−0.952499	+	0.304543i	$0.901496\pi$
$770$		0			0
$771$	0.947168	−	2.01284i	0.0341114	−	0.0724905i
$772$	−50.8114	−	92.4256i	−1.82874	−	3.32647i
$773$	−36.3847	−	2.28913i	−1.30867	−	0.0823343i	−0.606921	−	0.794762i	$-0.707596\pi$
$773$	−36.3847	−	2.28913i	−1.30867	−	0.0823343i	−0.701745	+	0.712428i	$0.747596\pi$
$774$	25.4384	+	18.4821i	0.914363	+	0.664324i
$775$		0			0
$776$	56.1486	−	40.7943i	2.01562	−	1.46443i
$777$	21.0056	−	13.3305i	0.753571	−	0.478231i
$778$	−0.852559	+	6.74870i	−0.0305657	+	0.241953i
$779$	4.91028	+	0.620312i	0.175929	+	0.0222250i
$780$		0			0
$781$	−32.1975	−	17.7007i	−1.15212	−	0.633382i
$782$	−8.01626	−	2.60464i	−0.286661	−	0.0931417i
$783$	24.6450	−	11.5970i	0.880739	−	0.414444i
$784$	−54.7072	−	14.0464i	−1.95383	−	0.501658i
$785$		0			0
$786$	11.2063	−	13.5461i	0.399715	−	0.483172i
$787$	−36.7893	−	23.3472i	−1.31140	−	0.832239i	−0.318127	−	0.948048i	$-0.603054\pi$
$787$	−36.7893	−	23.3472i	−1.31140	−	0.832239i	−0.993271	+	0.115809i	$0.963054\pi$
$788$	−54.1075	+	3.40415i	−1.92750	+	0.121268i
$789$	−4.09177	−	6.44759i	−0.145671	−	0.229540i
$790$		0			0
$791$	0.402764	+	6.40175i	0.0143206	+	0.227620i
$792$	−67.3292	−	12.8437i	−2.39244	−	0.456382i
$793$	14.0586	−	4.56793i	0.499237	−	0.162212i
$794$	−51.7839	+	48.6283i	−1.83774	+	1.72576i
$795$		0			0
$796$	−15.9650	−	83.6917i	−0.565866	−	2.96637i
$797$	−1.26868	+	1.35101i	−0.0449391	+	0.0478552i	−0.751045	−	0.660251i	$-0.770450\pi$
$797$	−1.26868	+	1.35101i	−0.0449391	+	0.0478552i	0.706106	+	0.708106i	$0.250450\pi$
$798$	−16.0384	+	40.5083i	−0.567752	+	1.43398i
$799$	0.0606030	+	0.186517i	0.00214398	+	0.00659849i
$800$		0			0
$801$	6.69867	−	20.6164i	0.236686	−	0.728444i
$802$	40.2135	+	33.2675i	1.41999	+	1.17472i
$803$	−2.88922	−	1.35956i	−0.101958	−	0.0479779i
$804$	21.1132	+	19.8266i	0.744606	+	0.699231i
$805$		0			0
$806$	−4.69539	+	0.593165i	−0.165388	+	0.0208934i
$807$		−	8.94380i		−	0.314837i
$808$	11.4110	+	90.3273i	0.401437	+	3.17770i
$809$	22.0152	+	26.6118i	0.774014	+	0.935622i	0.999252	−	0.0386819i	$-0.0123159\pi$
$809$	22.0152	+	26.6118i	0.774014	+	0.935622i	−0.225238	+	0.974304i	$0.572316\pi$
$810$		0			0
$811$	0.387896	−	6.16543i	0.0136209	−	0.216498i	−0.985328	−	0.170669i	$-0.945407\pi$
$811$	0.387896	−	6.16543i	0.0136209	−	0.216498i	0.998949	−	0.0458287i	$-0.0145928\pi$
$812$	31.4346	−	122.430i	1.10314	−	4.29644i
$813$	−3.02200	+	11.7699i	−0.105986	+	0.412789i
$814$	6.60623	−	105.003i	0.231548	−	3.68036i
$815$		0			0
$816$	4.97243	+	6.01063i	0.174070	+	0.210414i
$817$	−3.88941	−	30.7879i	−0.136073	−	1.07713i
$818$		−	50.1369i		−	1.75299i
$819$	−20.6867	+	2.61334i	−0.722853	+	0.0913176i
$820$		0			0
$821$	20.2589	+	19.0244i	0.707041	+	0.663956i	0.952182	−	0.305532i	$-0.0988342\pi$
$821$	20.2589	+	19.0244i	0.707041	+	0.663956i	−0.245141	+	0.969488i	$0.578834\pi$
$822$	14.8865	+	7.00503i	0.519225	+	0.244329i
$823$	−20.5292	−	16.9832i	−0.715602	−	0.591997i	0.206729	−	0.978398i	$-0.433718\pi$
$823$	−20.5292	−	16.9832i	−0.715602	−	0.591997i	−0.922331	+	0.386401i	$0.873718\pi$
$824$	19.4450	−	59.8455i	0.677398	−	2.08482i
$825$		0			0
$826$	−5.63130	−	17.3314i	−0.195938	−	0.603036i
$827$	−6.66968	+	16.8457i	−0.231928	+	0.585782i	−0.998403	−	0.0564914i	$-0.982009\pi$
$827$	−6.66968	+	16.8457i	−0.231928	+	0.585782i	0.766476	+	0.642273i	$0.222009\pi$
$828$	13.2238	−	14.0819i	0.459558	−	0.489379i
$829$	−10.1798	−	53.3646i	−0.353561	−	1.85343i	−0.502492	−	0.864582i	$-0.667583\pi$
$829$	−10.1798	−	53.3646i	−0.353561	−	1.85343i	0.148931	−	0.988848i	$-0.452417\pi$
$830$		0			0
$831$	8.81098	−	8.27407i	0.305650	−	0.287024i
$832$	−6.36780	+	2.06902i	−0.220764	+	0.0717305i
$833$	−17.5140	−	3.34097i	−0.606823	−	0.115758i
$834$	0.339835	+	5.40152i	0.0117675	+	0.187039i
$835$		0			0
$836$	67.4860	+	106.341i	2.33405	+	3.67788i
$837$	3.48451	−	0.219227i	0.120442	−	0.00757759i
$838$	−39.3884	−	24.9967i	−1.36065	−	0.863495i
$839$	−12.6007	+	15.2317i	−0.435026	+	0.525856i	−0.941778	−	0.336236i	$-0.890846\pi$
$839$	−12.6007	+	15.2317i	−0.435026	+	0.525856i	0.506752	+	0.862092i	$0.330846\pi$
$840$		0			0
$841$	22.5450	+	5.78857i	0.777413	+	0.199606i
$842$	−67.1949	+	31.6195i	−2.31569	+	1.08968i
$843$	−4.83868	−	1.57218i	−0.166653	−	0.0541488i
$844$	104.650	+	57.5316i	3.60219	+	1.98032i
$845$		0			0
$846$	−0.652338	−	0.0824094i	−0.0224278	−	0.00283329i
$847$	−5.29509	+	41.9149i	−0.181941	+	1.44021i
$848$	16.5769	−	10.5200i	0.569254	−	0.361259i
$849$	−10.5784	+	7.68567i	−0.363050	+	0.263772i
$850$		0			0
$851$	12.8845	+	9.36111i	0.441673	+	0.320895i
$852$	−23.2786	−	1.46457i	−0.797512	−	0.0501752i
$853$	4.29926	+	7.82032i	0.147204	+	0.267763i	0.939621	−	0.342217i	$-0.111178\pi$
$853$	4.29926	+	7.82032i	0.147204	+	0.267763i	−0.792417	+	0.609979i	$0.791178\pi$
$854$	−31.5218	+	66.9872i	−1.07865	+	2.29226i
$855$		0			0
$856$	3.90928	−	20.4932i	0.133617	−	0.700443i
$857$	−2.07323	−	2.85356i	−0.0708202	−	0.0974757i	0.772137	−	0.635456i	$-0.219188\pi$
$857$	−2.07323	−	2.85356i	−0.0708202	−	0.0974757i	−0.842958	+	0.537980i	$0.819188\pi$
$858$	7.74991	−	14.0970i	0.264578	−	0.481265i
$859$	24.1425	−	38.0424i	0.823730	−	1.29799i	−0.128222	−	0.991745i	$-0.540927\pi$
$859$	24.1425	−	38.0424i	0.823730	−	1.29799i	0.951952	−	0.306246i	$-0.0990730\pi$
$860$		0			0
$861$	2.01225	+	0.796707i	0.0685774	+	0.0271517i
$862$	5.95192	+	15.0328i	0.202723	+	0.512020i
$863$	12.8206	−	10.6061i	0.436417	−	0.361036i	−0.393120	−	0.919487i	$-0.628604\pi$
$863$	12.8206	−	10.6061i	0.436417	−	0.361036i	0.829537	+	0.558451i	$0.188604\pi$
$864$	−12.7096	+	3.26326i	−0.432389	+	0.111019i
$865$		0			0
$866$	−9.45379	+	3.74302i	−0.321253	+	0.127193i
$867$	−6.23159	−	6.63597i	−0.211636	−	0.225369i
$868$	9.52370	−	13.1083i	0.323256	−	0.444923i
$869$	18.7484	+	39.8423i	0.635995	+	1.35156i
$870$		0			0
$871$	17.5374	−	9.64126i	0.594232	−	0.326682i
$872$	35.7260	−	6.81510i	1.20984	−	0.230788i
$873$	7.50568	+	29.2327i	0.254029	+	0.989376i
$874$	−27.8901			−0.943397
$875$		0			0
$876$	−2.02704			−0.0684874
$877$	1.76183	+	6.86188i	0.0594928	+	0.231709i	0.991376	−	0.131050i	$-0.0418348\pi$
$877$	1.76183	+	6.86188i	0.0594928	+	0.231709i	−0.931883	+	0.362759i	$0.881835\pi$
$878$	73.1649	−	13.9570i	2.46920	−	0.471024i
$879$	−15.2571	+	8.38766i	−0.514609	+	0.282909i
$880$		0			0
$881$	−2.74917	−	5.84228i	−0.0926218	−	0.196831i	0.853148	−	0.521669i	$-0.174690\pi$
$881$	−2.74917	−	5.84228i	−0.0926218	−	0.196831i	−0.945770	+	0.324838i	$0.894690\pi$
$882$	35.1369	−	48.3618i	1.18312	−	1.62843i
$883$	−22.3800	−	23.8322i	−0.753146	−	0.802019i	0.232185	−	0.972672i	$-0.425412\pi$
$883$	−22.3800	−	23.8322i	−0.753146	−	0.802019i	−0.985331	+	0.170653i	$0.945412\pi$
$884$	15.5237	−	6.14626i	0.522118	−	0.206721i
$885$		0			0
$886$	20.2366	−	5.19589i	0.679863	−	0.174559i
$887$	44.4453	−	36.7684i	1.49233	−	1.23456i	0.587186	−	0.809452i	$-0.300236\pi$
$887$	44.4453	−	36.7684i	1.49233	−	1.23456i	0.905142	−	0.425109i	$-0.139764\pi$
$888$	−13.2058	−	33.3541i	−0.443158	−	1.11929i
$889$	50.4841	+	19.9881i	1.69318	+	0.670379i
$890$		0			0
$891$	12.5260	−	19.7379i	0.419638	−	0.661243i
$892$	−0.737178	+	1.34092i	−0.0246825	+	0.0448974i
$893$	0.381431	+	0.524994i	0.0127641	+	0.0175683i
$894$	−3.24622	+	17.0173i	−0.108570	+	0.569142i
$895$		0			0
$896$	26.2795	−	55.8467i	0.877935	−	1.86571i
$897$	1.17313	+	2.13391i	0.0391696	+	0.0712493i
$898$	24.5933	+	1.54728i	0.820688	+	0.0516333i
$899$	5.42125	+	3.93877i	0.180809	+	0.131365i
$900$		0			0
$901$	5.01406	−	3.64293i	0.167042	−	0.121363i
$902$	7.72772	−	4.90416i	0.257305	−	0.163291i
$903$	1.70076	−	13.4629i	0.0565979	−	0.448019i
$904$	9.17625	+	1.15923i	0.305198	+	0.0385554i
$905$		0			0
$906$	26.2135	+	14.4110i	0.870884	+	0.478773i
$907$	−24.8668	−	8.07971i	−0.825688	−	0.268282i	−0.134460	−	0.990919i	$-0.542930\pi$
$907$	−24.8668	−	8.07971i	−0.825688	−	0.268282i	−0.691228	+	0.722637i	$0.742930\pi$
$908$	58.8121	−	27.6749i	1.95175	−	0.918423i
$909$	−38.3482	−	9.84614i	−1.27193	−	0.326576i
$910$		0			0
$911$	3.91437	−	4.73166i	0.129689	−	0.156767i	−0.701672	−	0.712501i	$-0.747563\pi$
$911$	3.91437	−	4.73166i	0.129689	−	0.156767i	0.831360	+	0.555734i	$0.187563\pi$
$912$	21.7940	+	13.8309i	0.721670	+	0.457986i
$913$	31.2026	−	1.96310i	1.03265	−	0.0649691i
$914$	−12.4425	−	19.6063i	−0.411562	−	0.648518i
$915$		0			0
$916$	4.88148	+	77.5890i	0.161289	+	2.56361i
$917$	40.8519	+	7.79292i	1.34905	+	0.257345i
$918$	−17.1366	+	5.56802i	−0.565593	+	0.183772i
$919$	3.20908	−	3.01353i	0.105858	−	0.0994070i	−0.629811	−	0.776748i	$-0.716868\pi$
$919$	3.20908	−	3.01353i	0.105858	−	0.0994070i	0.735669	+	0.677341i	$0.236868\pi$
$920$		0			0
$921$	−2.66116	−	13.9503i	−0.0876883	−	0.459678i
$922$	67.6269	−	72.0153i	2.22717	−	2.37170i
$923$	−5.93298	+	14.9850i	−0.195286	+	0.493237i
$924$	17.0189	+	52.3788i	0.559881	+	1.72314i
$925$		0			0
$926$	−5.65174	+	17.3943i	−0.185728	+	0.571611i
$927$	21.0841	+	17.4423i	0.692494	+	0.572881i
$928$	−22.7878	−	10.7231i	−0.748045	−	0.352003i
$929$	7.97026	+	7.48457i	0.261496	+	0.245561i	0.804194	−	0.594367i	$-0.202597\pi$
$929$	7.97026	+	7.48457i	0.261496	+	0.245561i	−0.542698	+	0.839928i	$0.682597\pi$
$930$		0			0
$931$	−58.5320	+	7.39431i	−1.91831	+	0.242339i
$932$		−	57.1785i		−	1.87295i
$933$	−0.0915490	−	0.724685i	−0.00299718	−	0.0237251i
$934$	5.08820	+	6.15058i	0.166491	+	0.201253i
$935$		0			0
$936$	−1.88787	+	30.0068i	−0.0617068	+	0.980802i
$937$	−5.13122	+	19.9848i	−0.167630	+	0.652874i	0.828102	+	0.560578i	$0.189421\pi$
$937$	−5.13122	+	19.9848i	−0.167630	+	0.652874i	−0.995732	+	0.0922968i	$0.970579\pi$
$938$	−24.9262	+	97.0813i	−0.813871	+	3.16982i
$939$	0.0941847	−	1.49702i	0.00307360	−	0.0488535i
$940$		0			0
$941$	−32.7961	−	39.6437i	−1.06912	−	1.29235i	−0.954264	−	0.298967i	$-0.903358\pi$
$941$	−32.7961	−	39.6437i	−1.06912	−	1.29235i	−0.114860	−	0.993382i	$-0.536642\pi$
$942$	2.35225	+	18.6200i	0.0766404	+	0.606671i
$943$			1.38544i			0.0451163i
$944$	−10.7114	+	1.35317i	−0.348628	+	0.0440419i
$945$		0			0
$946$	−41.8334	−	39.2842i	−1.36012	−	1.27724i
$947$	−35.3076	−	16.6145i	−1.14734	−	0.539898i	−0.244406	−	0.969673i	$-0.578593\pi$
$947$	−35.3076	−	16.6145i	−1.14734	−	0.539898i	−0.902936	+	0.429775i	$0.858593\pi$
$948$	21.5381	+	17.8179i	0.699525	+	0.578698i
$949$	−0.432821	+	1.33209i	−0.0140500	+	0.0432414i
$950$		0			0
$951$	1.86170	+	5.72972i	0.0603697	+	0.185799i
$952$	−16.5334	+	41.7587i	−0.535851	+	1.35341i
$953$	17.9049	−	19.0668i	0.579998	−	0.617635i	−0.370324	−	0.928902i	$-0.620753\pi$
$953$	17.9049	−	19.0668i	0.579998	−	0.617635i	0.950322	+	0.311267i	$0.100753\pi$
$954$	3.89365	+	20.4112i	0.126062	+	0.660838i
$955$		0			0
$956$	39.9408	−	37.5069i	1.29178	−	1.21306i
$957$	−21.6626	+	7.03860i	−0.700252	+	0.227526i
$958$	−68.6782	−	13.1011i	−2.21889	−	0.423276i
$959$	2.44377	+	38.8426i	0.0789135	+	1.25429i
$960$		0			0
$961$	−16.1504	−	25.4489i	−0.520980	−	0.820933i
$962$	−46.0589	+	2.89778i	−1.48500	+	0.0934282i
$963$	7.66007	+	4.86123i	0.246842	+	0.156651i
$964$	33.4259	−	40.4050i	1.07658	−	1.30136i
$965$		0			0
$966$	−11.8126	−	3.03297i	−0.380066	−	0.0975843i
$967$	49.2070	−	23.1551i	1.58239	−	0.744617i	0.584618	−	0.811309i	$-0.301244\pi$
$967$	49.2070	−	23.1551i	1.58239	−	0.744617i	0.997774	+	0.0666916i	$0.0212444\pi$
$968$	57.9375	+	18.8250i	1.86218	+	0.605060i
$969$	7.14036	+	3.92545i	0.229381	+	0.126103i
$970$		0			0
$971$	−1.22217	−	0.154395i	−0.0392212	−	0.00495479i	0.105698	−	0.994398i	$-0.466292\pi$
$971$	−1.22217	−	0.154395i	−0.0392212	−	0.00495479i	−0.144919	+	0.989443i	$0.546292\pi$
$972$	7.97992	−	63.1676i	0.255956	−	2.02610i
$973$	−10.8100	+	6.86023i	−0.346553	+	0.219929i
$974$	−15.3066	+	11.1209i	−0.490455	+	0.356337i
$975$		0			0
$976$	35.4849	+	25.7813i	1.13584	+	0.825239i
$977$	7.69832	+	0.484337i	0.246291	+	0.0154953i	0.185456	−	0.982653i	$-0.440624\pi$
$977$	7.69832	+	0.484337i	0.246291	+	0.0154953i	0.0608349	+	0.998148i	$0.480624\pi$
$978$	−3.25448	−	5.91987i	−0.104067	−	0.189297i
$979$	−16.8451	+	35.7976i	−0.538371	+	1.14410i
$980$		0			0
$981$	−2.96362	+	15.5359i	−0.0946212	+	0.496022i
$982$	−6.09905	−	8.39462i	−0.194629	−	0.267883i
$983$	3.10530	−	5.64852i	0.0990437	−	0.180160i	−0.822143	−	0.569282i	$-0.807221\pi$
$983$	3.10530	−	5.64852i	0.0990437	−	0.180160i	0.921186	+	0.389122i	$0.127221\pi$
$984$	1.67215	−	2.63489i	0.0533062	−	0.0839971i
$985$		0			0
$986$	−32.1543	−	12.7308i	−1.02400	−	0.405431i
$987$	0.104460	+	0.263837i	0.00332501	+	0.00839802i
$988$	42.5678	−	35.2152i	1.35426	−	1.12034i
$989$	8.41395	−	2.16033i	0.267548	−	0.0686946i
$990$		0			0
$991$	−26.7825	+	10.6039i	−0.850773	+	0.336845i	−0.752724	−	0.658337i	$-0.771260\pi$
$991$	−26.7825	+	10.6039i	−0.850773	+	0.336845i	−0.0980493	+	0.995182i	$0.531260\pi$
$992$	−2.20992	−	2.35333i	−0.0701650	−	0.0747182i
$993$	−5.89627	+	8.11552i	−0.187113	+	0.257538i
$994$	−34.3678	−	73.0354i	−1.09008	−	2.31654i
$995$		0			0
$996$	17.3921	−	9.56141i	0.551091	−	0.302965i
$997$	−23.0148	+	4.39031i	−0.728886	+	0.139042i	−0.538450	−	0.842657i	$-0.680990\pi$
$997$	−23.0148	+	4.39031i	−0.728886	+	0.139042i	−0.190436	+	0.981700i	$0.560990\pi$
$998$	−21.9071	−	85.3225i	−0.693457	−	2.70084i
$999$	34.0457			1.07716

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.h.a.274.2		240
5.2	odd	4		625.2.g.b.351.22		480
5.3	odd	4		625.2.g.b.351.3		480
5.4	even	2		125.2.h.a.104.11	✓	240
125.6	even	25		125.2.h.a.119.11	yes	240
125.33	odd	100		625.2.g.b.276.3		480
125.92	odd	100		625.2.g.b.276.22		480
125.119	even	50	inner	625.2.h.a.349.2		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.h.a.104.11	✓	240	5.4	even	2
125.2.h.a.119.11	yes	240	125.6	even	25
625.2.g.b.276.3		480	125.33	odd	100
625.2.g.b.276.22		480	125.92	odd	100
625.2.g.b.351.3		480	5.3	odd	4
625.2.g.b.351.22		480	5.2	odd	4
625.2.h.a.274.2		240	1.1	even	1	trivial
625.2.h.a.349.2		240	125.119	even	50	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.h (of order \(50\), degree \(20\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.625230 - 2.43511i) q^{2} +(-0.668288 + 0.127483i) q^{3} +(-3.78623 + 2.08150i) q^{4} +(0.728267 + 1.54765i) q^{6} +(-2.37830 + 3.27344i) q^{7} +(3.99390 + 4.25307i) q^{8} +(-2.35897 + 0.933983i) q^{9} +O(q^{10})\)	\(q+(-0.625230 - 2.43511i) q^{2} +(-0.668288 + 0.127483i) q^{3} +(-3.78623 + 2.08150i) q^{4} +(0.728267 + 1.54765i) q^{6} +(-2.37830 + 3.27344i) q^{7} +(3.99390 + 4.25307i) q^{8} +(-2.35897 + 0.933983i) q^{9} +(4.48501 - 1.15156i) q^{11} +(2.26493 - 1.87372i) q^{12} +(-0.747710 - 1.88850i) q^{13} +(9.45817 + 3.74475i) q^{14} +(3.22933 - 5.08861i) q^{16} +(0.916541 - 1.66718i) q^{17} +(3.74925 + 5.16040i) q^{18} +(1.17961 - 6.18373i) q^{19} +(1.17208 - 2.49079i) q^{21} +(-5.60833 - 10.2015i) q^{22} +(1.75873 + 0.110650i) q^{23} +(-3.21127 - 2.33312i) q^{24} +(-4.13121 + 3.00150i) q^{26} +(3.18069 - 2.01853i) q^{27} +(2.19111 - 17.3444i) q^{28} +(7.17322 + 0.906188i) q^{29} +(0.812167 + 0.446493i) q^{31} +(-3.31276 - 1.07638i) q^{32} +(-2.85048 + 1.34133i) q^{33} +(-4.63282 - 1.18951i) q^{34} +(6.98753 - 8.44647i) q^{36} +(7.63067 + 4.84257i) q^{37} +(-15.7956 + 0.993774i) q^{38} +(0.740437 + 1.16674i) q^{39} +(0.0493658 + 0.784647i) q^{41} +(-6.79817 - 1.29682i) q^{42} +(4.68827 - 1.52331i) q^{43} +(-14.5843 + 13.6956i) q^{44} +(-0.830165 - 4.35188i) q^{46} +(-0.0705648 + 0.0751439i) q^{47} +(-1.50941 + 3.81234i) q^{48} +(-2.89602 - 8.91304i) q^{49} +(-0.399976 + 1.23100i) q^{51} +(6.76191 + 5.59394i) q^{52} +(2.94761 + 1.38704i) q^{53} +(-6.90400 - 6.48329i) q^{54} +(-23.4209 + 2.95874i) q^{56} +4.28289i q^{57} +(-2.27824 - 18.0341i) q^{58} +(-1.14190 - 1.38031i) q^{59} +(-0.456975 + 7.26340i) q^{61} +(0.579467 - 2.25688i) q^{62} +(2.55299 - 9.94325i) q^{63} +(0.206985 - 3.28993i) q^{64} +(5.04849 + 6.10258i) q^{66} +(1.23491 + 9.77534i) q^{67} +8.22011i q^{68} +(-1.18944 + 0.150262i) q^{69} +(-5.78426 - 5.43179i) q^{71} +(-13.3938 - 6.30264i) q^{72} +(-0.531334 - 0.439558i) q^{73} +(7.02126 - 21.6092i) q^{74} +(8.40514 + 25.8684i) q^{76} +(-6.89714 + 17.4202i) q^{77} +(2.37820 - 2.53253i) q^{78} +(1.78188 + 9.34094i) q^{79} +(3.68020 - 3.45593i) q^{81} +(1.87984 - 0.610795i) q^{82} +(6.63224 + 1.26517i) q^{83} +(0.746821 + 11.8704i) q^{84} +(-6.64067 - 10.4640i) q^{86} +(-4.90930 + 0.308867i) q^{87} +(22.8103 + 14.4759i) q^{88} +(-5.44616 + 6.58328i) q^{89} +(7.96018 + 2.04383i) q^{91} +(-6.88927 + 3.24184i) q^{92} +(-0.599682 - 0.194848i) q^{93} +(0.227103 + 0.124851i) q^{94} +(2.35110 + 0.297013i) q^{96} +(1.49092 - 11.8018i) q^{97} +(-19.8935 + 12.6248i) q^{98} +(-9.50449 + 6.90542i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 25 q^{7} + 35 q^{8} - 20 q^{9}+O(q^{10}) \) 240 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 25 * q^7 + 35 * q^8 - 20 * q^9	\( 240 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 25 q^{7} + 35 q^{8} - 20 q^{9} - 25 q^{11} - 60 q^{12} + 20 q^{13} - 30 q^{14} - 40 q^{16} + 15 q^{17} + 25 q^{18} - 10 q^{19} - 35 q^{21} + 25 q^{22} - 70 q^{23} + 15 q^{24} - 45 q^{26} + 20 q^{27} + 10 q^{28} - 10 q^{29} - 30 q^{31} + 25 q^{32} + 35 q^{33} - 20 q^{34} + 170 q^{36} + 55 q^{37} + 40 q^{38} - 35 q^{41} + 10 q^{42} + 25 q^{43} + 15 q^{44} - 40 q^{46} - 100 q^{47} - 5 q^{48} + 35 q^{49} - 55 q^{51} + 15 q^{52} + 15 q^{53} + 30 q^{54} + 65 q^{56} - 255 q^{58} + 5 q^{59} - 40 q^{61} - 5 q^{62} + 35 q^{63} + 25 q^{64} - 95 q^{66} - 105 q^{67} - 10 q^{69} + 45 q^{71} + 30 q^{72} + 40 q^{73} + 35 q^{74} - 65 q^{76} + 35 q^{77} - 100 q^{78} - 95 q^{81} - 175 q^{82} - 20 q^{83} + 45 q^{84} - 80 q^{86} + 5 q^{87} + 5 q^{88} + 30 q^{89} + 65 q^{91} + 55 q^{92} - 275 q^{93} + 60 q^{94} - 135 q^{96} - 35 q^{97} + 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 25 * q^7 + 35 * q^8 - 20 * q^9 - 25 * q^11 - 60 * q^12 + 20 * q^13 - 30 * q^14 - 40 * q^16 + 15 * q^17 + 25 * q^18 - 10 * q^19 - 35 * q^21 + 25 * q^22 - 70 * q^23 + 15 * q^24 - 45 * q^26 + 20 * q^27 + 10 * q^28 - 10 * q^29 - 30 * q^31 + 25 * q^32 + 35 * q^33 - 20 * q^34 + 170 * q^36 + 55 * q^37 + 40 * q^38 - 35 * q^41 + 10 * q^42 + 25 * q^43 + 15 * q^44 - 40 * q^46 - 100 * q^47 - 5 * q^48 + 35 * q^49 - 55 * q^51 + 15 * q^52 + 15 * q^53 + 30 * q^54 + 65 * q^56 - 255 * q^58 + 5 * q^59 - 40 * q^61 - 5 * q^62 + 35 * q^63 + 25 * q^64 - 95 * q^66 - 105 * q^67 - 10 * q^69 + 45 * q^71 + 30 * q^72 + 40 * q^73 + 35 * q^74 - 65 * q^76 + 35 * q^77 - 100 * q^78 - 95 * q^81 - 175 * q^82 - 20 * q^83 + 45 * q^84 - 80 * q^86 + 5 * q^87 + 5 * q^88 + 30 * q^89 + 65 * q^91 + 55 * q^92 - 275 * q^93 + 60 * q^94 - 135 * q^96 - 35 * q^97 + 15 * q^98 + 45 * q^99

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