LMFDB - Embedded newform 350.2.r.a.13.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(13,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([19, 10]))

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

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

chi := DirichletCharacter("350.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.r (of order $20$, degree $8$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.6
Character	$\chi$	$=$	350.13
Dual form			350.2.r.a.27.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987688 + 0.156434i) q^{2} +(0.353713 + 0.180226i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.95928 - 1.07760i) q^{5} +(-0.377552 - 0.122674i) q^{6} +(1.23406 - 2.34032i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-1.67072 - 2.29955i) q^{9} +O(q^{10})$	\(q+(-0.987688 + 0.156434i) q^{2} +(0.353713 + 0.180226i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.95928 - 1.07760i) q^{5} +(-0.377552 - 0.122674i) q^{6} +(1.23406 - 2.34032i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-1.67072 - 2.29955i) q^{9} +(-1.76658 + 1.37083i) q^{10} +(-1.94915 - 1.41614i) q^{11} +(0.392094 + 0.0621016i) q^{12} +(0.351128 - 2.21694i) q^{13} +(-0.852764 + 2.50455i) q^{14} +(0.887235 - 0.0280490i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-0.883433 + 0.450132i) q^{17} +(2.00988 + 2.00988i) q^{18} +(-2.37903 + 7.32189i) q^{19} +(1.53039 - 1.63031i) q^{20} +(0.858291 - 0.605391i) q^{21} +(2.14669 + 1.09379i) q^{22} +(-0.877254 - 5.53876i) q^{23} -0.396982 q^{24} +(2.67755 - 4.22264i) q^{25} +2.24457i q^{26} +(-0.362823 - 2.29077i) q^{27} +(0.450467 - 2.60712i) q^{28} +(-0.0626281 + 0.0203491i) q^{29} +(-0.871923 + 0.166498i) q^{30} +(7.76645 + 2.52347i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.434215 - 0.852195i) q^{33} +(0.802141 - 0.582789i) q^{34} +(-0.104053 - 5.91516i) q^{35} +(-2.29955 - 1.67072i) q^{36} +(1.11862 - 7.06267i) q^{37} +(1.20434 - 7.60391i) q^{38} +(0.523748 - 0.720878i) q^{39} +(-1.25651 + 1.84964i) q^{40} +(7.07833 + 9.74248i) q^{41} +(-0.753020 + 0.732204i) q^{42} +(7.68725 + 7.68725i) q^{43} +(-2.29136 - 0.744509i) q^{44} +(-5.75142 - 2.70510i) q^{45} +(1.73291 + 5.33334i) q^{46} +(1.87075 - 3.67155i) q^{47} +(0.392094 - 0.0621016i) q^{48} +(-3.95417 - 5.77620i) q^{49} +(-1.98402 + 4.58952i) q^{50} -0.393607 q^{51} +(-0.351128 - 2.21694i) q^{52} +(-1.21329 + 2.38122i) q^{53} +(0.716712 + 2.20581i) q^{54} +(-5.34497 - 0.674208i) q^{55} +(-0.0370771 + 2.64549i) q^{56} +(-2.16109 + 2.16109i) q^{57} +(0.0586737 - 0.0298957i) q^{58} +(-11.8366 + 8.59978i) q^{59} +(0.835143 - 0.300847i) q^{60} +(4.72449 - 6.50270i) q^{61} +(-8.06559 - 1.27746i) q^{62} +(-7.44347 + 1.07223i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-1.70102 - 4.72198i) q^{65} +(0.562182 + 0.773777i) q^{66} +(4.32520 + 8.48868i) q^{67} +(-0.701097 + 0.701097i) q^{68} +(0.687932 - 2.11724i) q^{69} +(1.02811 + 5.82606i) q^{70} +(3.41448 + 10.5087i) q^{71} +(2.53260 + 1.29043i) q^{72} +(13.1634 - 2.08488i) q^{73} +7.15071i q^{74} +(1.70811 - 1.01104i) q^{75} +7.69869i q^{76} +(-5.71960 + 2.81402i) q^{77} +(-0.404530 + 0.793935i) q^{78} +(-5.28143 + 1.71604i) q^{79} +(0.951692 - 2.02343i) q^{80} +(-2.35053 + 7.23420i) q^{81} +(-8.51524 - 8.51524i) q^{82} +(-3.36957 - 6.61316i) q^{83} +(0.629207 - 0.840987i) q^{84} +(-1.24583 + 1.83392i) q^{85} +(-8.79516 - 6.39006i) q^{86} +(-0.0258198 - 0.00408945i) q^{87} +(2.37962 + 0.376895i) q^{88} +(-6.20646 - 4.50926i) q^{89} +(6.10378 + 1.77207i) q^{90} +(-4.75502 - 3.55759i) q^{91} +(-2.54589 - 4.99659i) q^{92} +(2.29230 + 2.29230i) q^{93} +(-1.27336 + 3.91899i) q^{94} +(3.22890 + 16.9093i) q^{95} +(-0.377552 + 0.122674i) q^{96} +(-6.20713 + 12.1822i) q^{97} +(4.80909 + 5.08652i) q^{98} +6.84816i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{7}+O(q^{10}) $ 160 * q + 8 * q^7	$ 160 q + 8 q^{7} + 16 q^{15} + 40 q^{16} - 8 q^{18} - 24 q^{22} - 32 q^{23} + 12 q^{28} - 40 q^{29} - 56 q^{30} + 28 q^{35} + 40 q^{36} - 32 q^{37} + 40 q^{39} - 112 q^{43} - 32 q^{50} + 112 q^{53} - 152 q^{57} + 16 q^{58} + 8 q^{60} - 100 q^{63} - 8 q^{65} - 16 q^{67} - 56 q^{70} - 8 q^{72} - 144 q^{77} + 40 q^{78} + 40 q^{81} - 60 q^{84} + 48 q^{85} - 16 q^{88} + 8 q^{92} + 56 q^{93} - 104 q^{95} - 32 q^{98}+O(q^{100}) $ 160 * q + 8 * q^7 + 16 * q^15 + 40 * q^16 - 8 * q^18 - 24 * q^22 - 32 * q^23 + 12 * q^28 - 40 * q^29 - 56 * q^30 + 28 * q^35 + 40 * q^36 - 32 * q^37 + 40 * q^39 - 112 * q^43 - 32 * q^50 + 112 * q^53 - 152 * q^57 + 16 * q^58 + 8 * q^60 - 100 * q^63 - 8 * q^65 - 16 * q^67 - 56 * q^70 - 8 * q^72 - 144 * q^77 + 40 * q^78 + 40 * q^81 - 60 * q^84 + 48 * q^85 - 16 * q^88 + 8 * q^92 + 56 * q^93 - 104 * q^95 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$3$	0.353713	+	0.180226i	0.204216	+	0.104053i	0.553108	−	0.833110i	$-0.313442\pi$
$3$	0.353713	+	0.180226i	0.204216	+	0.104053i	−0.348891	+	0.937163i	$0.613442\pi$
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	1.95928	−	1.07760i	0.876216	−	0.481918i
$5$	1.95928	−	1.07760i	0.876216	−	0.481918i
$6$	−0.377552	−	0.122674i	−0.154135	−	0.0500815i
$7$	1.23406	−	2.34032i	0.466432	−	0.884557i
$7$	1.23406	−	2.34032i	0.466432	−	0.884557i
$8$	−0.891007	+	0.453990i	−0.315018	+	0.160510i
$9$	−1.67072	−	2.29955i	−0.556908	−	0.766518i
$10$	−1.76658	+	1.37083i	−0.558643	+	0.433495i
$11$	−1.94915	−	1.41614i	−0.587691	−	0.426983i	0.253798	−	0.967257i	$-0.418320\pi$
$11$	−1.94915	−	1.41614i	−0.587691	−	0.426983i	−0.841489	+	0.540275i	$0.818320\pi$
$12$	0.392094	+	0.0621016i	0.113188	+	0.0179272i
$13$	0.351128	−	2.21694i	0.0973855	−	0.614868i	−0.889930	−	0.456097i	$-0.849247\pi$
$13$	0.351128	−	2.21694i	0.0973855	−	0.614868i	0.987315	−	0.158771i	$-0.0507530\pi$
$14$	−0.852764	+	2.50455i	−0.227911	+	0.669370i
$15$	0.887235	−	0.0280490i	0.229083	−	0.00724221i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−0.883433	+	0.450132i	−0.214264	+	0.109173i	−0.557829	−	0.829956i	$-0.688365\pi$
$17$	−0.883433	+	0.450132i	−0.214264	+	0.109173i	0.343565	+	0.939129i	$0.388365\pi$
$18$	2.00988	+	2.00988i	0.473734	+	0.473734i
$19$	−2.37903	+	7.32189i	−0.545786	+	1.67976i	0.173328	+	0.984864i	$0.444548\pi$
$19$	−2.37903	+	7.32189i	−0.545786	+	1.67976i	−0.719114	+	0.694892i	$0.755452\pi$
$20$	1.53039	−	1.63031i	0.342205	−	0.364548i
$21$	0.858291	−	0.605391i	0.187294	−	0.132107i
$22$	2.14669	+	1.09379i	0.457675	+	0.233197i
$23$	−0.877254	−	5.53876i	−0.182920	−	1.15491i	−0.892755	−	0.450543i	$-0.851230\pi$
$23$	−0.877254	−	5.53876i	−0.182920	−	1.15491i	0.709835	−	0.704368i	$-0.248770\pi$
$24$	−0.396982			−0.0810335
$25$	2.67755	−	4.22264i	0.535510	−	0.844529i
$26$			2.24457i			0.440197i
$27$	−0.362823	−	2.29077i	−0.0698253	−	0.440859i
$28$	0.450467	−	2.60712i	0.0851302	−	0.492700i
$29$	−0.0626281	+	0.0203491i	−0.0116297	+	0.00377873i	−0.314826	−	0.949149i	$-0.601946\pi$
$29$	−0.0626281	+	0.0203491i	−0.0116297	+	0.00377873i	0.303196	+	0.952928i	$0.401946\pi$
$30$	−0.871923	+	0.166498i	−0.159191	+	0.0303982i
$31$	7.76645	+	2.52347i	1.39490	+	0.453229i	0.907537	−	0.419973i	$-0.137960\pi$
$31$	7.76645	+	2.52347i	1.39490	+	0.453229i	0.487359	+	0.873202i	$0.337960\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−0.434215	−	0.852195i	−0.0755872	−	0.148348i
$34$	0.802141	−	0.582789i	0.137566	−	0.0999475i
$35$	−0.104053	−	5.91516i	−0.0175882	−	0.999845i
$36$	−2.29955	−	1.67072i	−0.383259	−	0.278454i
$37$	1.11862	−	7.06267i	0.183899	−	1.16110i	−0.707108	−	0.707106i	$-0.750000\pi$
$37$	1.11862	−	7.06267i	0.183899	−	1.16110i	0.891007	−	0.453990i	$-0.150000\pi$
$38$	1.20434	−	7.60391i	0.195370	−	1.23352i
$39$	0.523748	−	0.720878i	0.0838668	−	0.115433i
$40$	−1.25651	+	1.84964i	−0.198672	+	0.292454i
$41$	7.07833	+	9.74248i	1.10545	+	1.52152i	0.827956	+	0.560792i	$0.189503\pi$
$41$	7.07833	+	9.74248i	1.10545	+	1.52152i	0.277493	+	0.960728i	$0.410497\pi$
$42$	−0.753020	+	0.732204i	−0.116193	+	0.112982i
$43$	7.68725	+	7.68725i	1.17229	+	1.17229i	0.981661	+	0.190633i	$0.0610541\pi$
$43$	7.68725	+	7.68725i	1.17229	+	1.17229i	0.190633	+	0.981661i	$0.438946\pi$
$44$	−2.29136	−	0.744509i	−0.345436	−	0.112239i
$45$	−5.75142	−	2.70510i	−0.857371	−	0.403252i
$46$	1.73291	+	5.33334i	0.255503	+	0.786358i
$47$	1.87075	−	3.67155i	0.272877	−	0.535550i	−0.713379	−	0.700779i	$-0.752836\pi$
$47$	1.87075	−	3.67155i	0.272877	−	0.535550i	0.986255	+	0.165228i	$0.0528361\pi$
$48$	0.392094	−	0.0621016i	0.0565939	−	0.00896360i
$49$	−3.95417	−	5.77620i	−0.564882	−	0.825172i
$50$	−1.98402	+	4.58952i	−0.280583	+	0.649056i
$51$	−0.393607			−0.0551161
$52$	−0.351128	−	2.21694i	−0.0486927	−	0.307434i
$53$	−1.21329	+	2.38122i	−0.166658	+	0.327086i	−0.959198	−	0.282735i	$-0.908758\pi$
$53$	−1.21329	+	2.38122i	−0.166658	+	0.327086i	0.792540	+	0.609820i	$0.208758\pi$
$54$	0.716712	+	2.20581i	0.0975321	+	0.300173i
$55$	−5.34497	−	0.674208i	−0.720715	−	0.0909102i
$56$	−0.0370771	+	2.64549i	−0.00495463	+	0.353519i
$57$	−2.16109	+	2.16109i	−0.286243	+	0.286243i
$58$	0.0586737	−	0.0298957i	0.00770423	−	0.00392550i
$59$	−11.8366	+	8.59978i	−1.54099	+	1.11960i	−0.591282	+	0.806465i	$0.701378\pi$
$59$	−11.8366	+	8.59978i	−1.54099	+	1.11960i	−0.949710	+	0.313131i	$0.898622\pi$
$60$	0.835143	−	0.300847i	0.107816	−	0.0388391i
$61$	4.72449	−	6.50270i	0.604909	−	0.832586i	−0.391238	−	0.920290i	$-0.627953\pi$
$61$	4.72449	−	6.50270i	0.604909	−	0.832586i	0.996147	+	0.0877040i	$0.0279530\pi$
$62$	−8.06559	−	1.27746i	−1.02433	−	0.162238i
$63$	−7.44347	+	1.07223i	−0.937789	+	0.135088i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	−1.70102	−	4.72198i	−0.210985	−	0.585689i
$66$	0.562182	+	0.773777i	0.0691998	+	0.0952454i
$67$	4.32520	+	8.48868i	0.528407	+	1.03706i	0.988787	+	0.149335i	$0.0477133\pi$
$67$	4.32520	+	8.48868i	0.528407	+	1.03706i	−0.460380	+	0.887722i	$0.652287\pi$
$68$	−0.701097	+	0.701097i	−0.0850205	+	0.0850205i
$69$	0.687932	−	2.11724i	0.0828173	−	0.254885i
$70$	1.02811	+	5.82606i	0.122882	+	0.696348i
$71$	3.41448	+	10.5087i	0.405224	+	1.24715i	0.920708	+	0.390252i	$0.127612\pi$
$71$	3.41448	+	10.5087i	0.405224	+	1.24715i	−0.515484	+	0.856899i	$0.672388\pi$
$72$	2.53260	+	1.29043i	0.298470	+	0.152078i
$73$	13.1634	−	2.08488i	1.54066	−	0.244017i	0.672424	−	0.740166i	$-0.265253\pi$
$73$	13.1634	−	2.08488i	1.54066	−	0.244017i	0.868237	+	0.496149i	$0.165253\pi$
$74$			7.15071i			0.831253i
$75$	1.70811	−	1.01104i	0.197236	−	0.116745i
$76$			7.69869i			0.883100i
$77$	−5.71960	+	2.81402i	−0.651809	+	0.320688i
$78$	−0.404530	+	0.793935i	−0.0458040	+	0.0898954i
$79$	−5.28143	+	1.71604i	−0.594207	+	0.193070i	−0.590655	−	0.806924i	$-0.701131\pi$
$79$	−5.28143	+	1.71604i	−0.594207	+	0.193070i	−0.00355215	+	0.999994i	$0.501131\pi$
$80$	0.951692	−	2.02343i	0.106402	−	0.226227i
$81$	−2.35053	+	7.23420i	−0.261170	+	0.803800i
$82$	−8.51524	−	8.51524i	−0.940351	−	0.940351i
$83$	−3.36957	−	6.61316i	−0.369859	−	0.725889i	0.628805	−	0.777563i	$-0.283544\pi$
$83$	−3.36957	−	6.61316i	−0.369859	−	0.725889i	−0.998664	+	0.0516741i	$0.983544\pi$
$84$	0.629207	−	0.840987i	0.0686521	−	0.0917592i
$85$	−1.24583	+	1.83392i	−0.135129	+	0.198917i
$86$	−8.79516	−	6.39006i	−0.948406	−	0.689057i
$87$	−0.0258198	−	0.00408945i	−0.00276817	−	0.000438436i
$88$	2.37962	+	0.376895i	0.253668	+	0.0401771i
$89$	−6.20646	−	4.50926i	−0.657884	−	0.477980i	0.208064	−	0.978115i	$-0.433284\pi$
$89$	−6.20646	−	4.50926i	−0.657884	−	0.477980i	−0.865948	+	0.500135i	$0.833284\pi$
$90$	6.10378	+	1.77207i	0.643395	+	0.186793i
$91$	−4.75502	−	3.55759i	−0.498462	−	0.372937i
$92$	−2.54589	−	4.99659i	−0.265427	−	0.520931i
$93$	2.29230	+	2.29230i	0.237700	+	0.237700i
$94$	−1.27336	+	3.91899i	−0.131337	+	0.404213i
$95$	3.22890	+	16.9093i	0.331278	+	1.73485i
$96$	−0.377552	+	0.122674i	−0.0385337	+	0.0125204i
$97$	−6.20713	+	12.1822i	−0.630239	+	1.23691i	0.326288	+	0.945270i	$0.394202\pi$
$97$	−6.20713	+	12.1822i	−0.630239	+	1.23691i	−0.956527	+	0.291643i	$0.905798\pi$
$98$	4.80909	+	5.08652i	0.485791	+	0.513816i
$99$			6.84816i			0.688266i
$100$	1.24163	−	4.84338i	0.124163	−	0.484338i
$101$		−	0.432114i		−	0.0429969i	−0.999769	−	0.0214985i	$-0.993156\pi$
$101$		−	0.432114i		−	0.0429969i	0.999769	−	0.0214985i	$-0.00684370\pi$
$102$	0.388761	−	0.0615738i	0.0384931	−	0.00609671i
$103$	1.43427	+	0.730795i	0.141322	+	0.0720074i	0.523222	−	0.852197i	$-0.324730\pi$
$103$	1.43427	+	0.730795i	0.141322	+	0.0720074i	−0.381899	+	0.924204i	$0.624730\pi$
$104$	0.693611	+	2.13471i	0.0680141	+	0.209326i
$105$	1.02926	−	2.11103i	0.100446	−	0.206015i
$106$	0.825849	−	2.54170i	0.0802136	−	0.246872i
$107$	−5.18600	+	5.18600i	−0.501350	+	0.501350i	−0.911857	−	0.410508i	$-0.865352\pi$
$107$	−5.18600	+	5.18600i	−0.501350	+	0.501350i	0.410508	+	0.911857i	$0.365352\pi$
$108$	−1.05295	−	2.06654i	−0.101320	−	0.198853i
$109$	2.33281	+	3.21084i	0.223443	+	0.307542i	0.905990	−	0.423299i	$-0.139128\pi$
$109$	2.33281	+	3.21084i	0.223443	+	0.307542i	−0.682548	+	0.730841i	$0.739128\pi$
$110$	5.38463	−	0.170229i	0.513404	−	0.0162307i
$111$	1.66855	−	2.29656i	0.158371	−	0.217979i
$112$	−0.377225	−	2.61872i	−0.0356445	−	0.247446i
$113$	−6.10423	−	0.966815i	−0.574238	−	0.0909503i	−0.137440	−	0.990510i	$-0.543887\pi$
$113$	−6.10423	−	0.966815i	−0.574238	−	0.0909503i	−0.436798	+	0.899560i	$0.643887\pi$
$114$	1.79641	−	2.47255i	0.168249	−	0.231575i
$115$	−7.68736	−	9.90665i	−0.716850	−	0.923800i
$116$	−0.0532746	+	0.0387063i	−0.00494642	+	0.00359379i
$117$	−5.68461	+	2.89645i	−0.525542	+	0.267777i
$118$	10.3456	−	10.3456i	0.952385	−	0.952385i
$119$	−0.0367619	+	2.62301i	−0.00336996	+	0.240451i
$120$	−0.777798	+	0.427788i	−0.0710029	+	0.0390515i
$121$	−1.60545	−	4.94108i	−0.145950	−	0.449189i
$122$	−3.64908	+	7.16172i	−0.330372	+	0.648391i
$123$	0.747851	+	4.72174i	0.0674314	+	0.425745i
$124$	8.16613			0.733340
$125$	0.695744	−	11.1587i	0.0622292	−	0.998062i
$126$	7.18409	−	2.22344i	0.640010	−	0.198080i
$127$	1.53366	−	0.242908i	0.136090	−	0.0215546i	−0.0880175	−	0.996119i	$-0.528053\pi$
$127$	1.53366	−	0.242908i	0.136090	−	0.0215546i	0.224108	+	0.974564i	$0.428053\pi$
$128$	−0.453990	+	0.891007i	−0.0401275	+	0.0787546i
$129$	1.33364	+	4.10452i	0.117420	+	0.361383i
$130$	2.41875	+	4.39774i	0.212139	+	0.385708i
$131$	−0.368900	−	0.119863i	−0.0322310	−	0.0104725i	0.292857	−	0.956156i	$-0.405394\pi$
$131$	−0.368900	−	0.119863i	−0.0322310	−	0.0104725i	−0.325088	+	0.945684i	$0.605394\pi$
$132$	−0.676306	−	0.676306i	−0.0588649	−	0.0588649i
$133$	14.1997	+	14.6034i	1.23127	+	1.26627i
$134$	−5.59987	−	7.70756i	−0.483755	−	0.665832i
$135$	−3.17941	−	4.09729i	−0.273640	−	0.352638i
$136$	0.582789	−	0.802141i	0.0499738	−	0.0687830i
$137$	2.60794	−	16.4659i	0.222811	−	1.40677i	−0.581973	−	0.813208i	$-0.697719\pi$
$137$	2.60794	−	16.4659i	0.222811	−	1.40677i	0.804785	−	0.593567i	$-0.202281\pi$
$138$	−0.348254	+	2.19879i	−0.0296453	+	0.187173i
$139$	8.73738	+	6.34808i	0.741095	+	0.538437i	0.893054	−	0.449950i	$-0.148558\pi$
$139$	8.73738	+	6.34808i	0.741095	+	0.538437i	−0.151959	+	0.988387i	$0.548558\pi$
$140$	−1.92685	−	5.59350i	−0.162848	−	0.472737i
$141$	1.32342	−	0.961518i	0.111452	−	0.0809744i
$142$	−5.01636	−	9.84516i	−0.420964	−	0.826187i
$143$	−3.82390	+	3.82390i	−0.319770	+	0.319770i
$144$	−2.70329	−	0.878352i	−0.225274	−	0.0731960i
$145$	−0.100778	+	0.107358i	−0.00836913	+	0.00891556i
$146$	−12.6752	+	4.11843i	−1.04901	+	0.340843i
$147$	−0.357622	−	2.75576i	−0.0294961	−	0.227292i
$148$	−1.11862	−	7.06267i	−0.0919497	−	0.580548i
$149$		−	10.9845i		−	0.899886i	−0.893057	−	0.449943i	$-0.851444\pi$
$149$		−	10.9845i		−	0.899886i	0.893057	−	0.449943i	$-0.148556\pi$
$150$	−1.52892	+	1.26580i	−0.124836	+	0.103352i
$151$	16.5509			1.34689			0.673445	−	0.739237i	$-0.264814\pi$
$151$	16.5509			1.34689			0.673445	+	0.739237i	$0.264814\pi$
$152$	−1.20434	−	7.60391i	−0.0976849	−	0.616758i
$153$	2.51108	+	1.27946i	0.203008	+	0.103438i
$154$	5.20897	−	3.67412i	0.419751	−	0.296069i
$155$	17.9359	−	3.42495i	1.44065	−	0.275098i
$156$	0.275351	−	0.847442i	0.0220457	−	0.0678497i
$157$	2.43980	+	2.43980i	0.194717	+	0.194717i	0.797731	−	0.603014i	$-0.206034\pi$
$157$	2.43980	+	2.43980i	0.194717	+	0.194717i	−0.603014	+	0.797731i	$0.706034\pi$
$158$	4.94796	−	2.52111i	0.393639	−	0.200569i
$159$	−0.858314	+	0.623602i	−0.0680688	+	0.0494548i
$160$	−0.623441	+	2.14740i	−0.0492873	+	0.169767i
$161$	−14.0451	−	4.78213i	−1.10691	−	0.376885i
$162$	1.18992	−	7.51284i	0.0934887	−	0.590264i
$163$	−7.36751	−	1.16690i	−0.577068	−	0.0913985i	−0.138923	−	0.990303i	$-0.544364\pi$
$163$	−7.36751	−	1.16690i	−0.577068	−	0.0913985i	−0.438144	+	0.898905i	$0.644364\pi$
$164$	9.74248	+	7.07833i	0.760760	+	0.552725i
$165$	−1.76908	−	1.20178i	−0.137722	−	0.0935583i
$166$	4.36262	+	6.00462i	0.338605	+	0.466049i
$167$	−7.80993	+	3.97936i	−0.604350	+	0.307932i	−0.729260	−	0.684236i	$-0.760136\pi$
$167$	−7.80993	+	3.97936i	−0.604350	+	0.307932i	0.124910	+	0.992168i	$0.460136\pi$
$168$	−0.489901	+	0.929063i	−0.0377967	+	0.0716788i
$169$	7.57221	+	2.46036i	0.582478	+	0.189259i
$170$	0.943603	−	2.00623i	0.0723711	−	0.153871i
$171$	20.8118	−	6.76216i	1.59152	−	0.517115i
$172$	9.68650	+	4.93552i	0.738589	+	0.376330i
$173$	−4.35910	+	0.690413i	−0.331416	+	0.0524912i	−0.319925	−	0.947443i	$-0.603658\pi$
$173$	−4.35910	+	0.690413i	−0.331416	+	0.0524912i	−0.0114910	+	0.999934i	$0.503658\pi$
$174$	0.0261416			0.00198179
$175$	−6.57806	−	11.4773i	−0.497254	−	0.867605i
$176$	−2.40928			−0.181607
$177$	−5.73666	+	0.908597i	−0.431194	+	0.0682944i
$178$	6.83545	+	3.48284i	0.512339	+	0.261050i
$179$	−6.19537	+	2.01300i	−0.463064	+	0.150458i	−0.531252	−	0.847214i	$-0.678278\pi$
$179$	−6.19537	+	2.01300i	−0.463064	+	0.150458i	0.0681882	+	0.997672i	$0.478278\pi$
$180$	−6.30584	−	0.795412i	−0.470010	−	0.0592865i
$181$	−7.47631	−	2.42920i	−0.555709	−	0.180561i	0.0176803	−	0.999844i	$-0.494372\pi$
$181$	−7.47631	−	2.42920i	−0.555709	−	0.180561i	−0.573390	+	0.819283i	$0.694372\pi$
$182$	5.25301	+	2.76995i	0.389379	+	0.205322i
$183$	2.84307	−	1.44862i	0.210166	−	0.107085i
$184$	3.29618	+	4.53681i	0.242998	+	0.334458i
$185$	−5.41906	−	15.0432i	−0.398417	−	1.10600i
$186$	−2.62267	−	1.90548i	−0.192304	−	0.139717i
$187$	2.35939	+	0.373691i	0.172536	+	0.0273270i
$188$	0.644616	−	4.06994i	0.0470134	−	0.296831i
$189$	−5.80888	−	1.97784i	−0.422534	−	0.143867i
$190$	−5.83434	−	16.1960i	−0.423267	−	1.17498i
$191$	−5.20039	+	3.77831i	−0.376287	+	0.273389i	−0.759813	−	0.650141i	$-0.774710\pi$
$191$	−5.20039	+	3.77831i	−0.376287	+	0.273389i	0.383526	+	0.923530i	$0.374710\pi$
$192$	0.353713	−	0.180226i	0.0255271	−	0.0130067i
$193$	−7.21057	−	7.21057i	−0.519028	−	0.519028i	0.398249	−	0.917277i	$-0.369618\pi$
$193$	−7.21057	−	7.21057i	−0.519028	−	0.519028i	−0.917277	+	0.398249i	$0.869618\pi$
$194$	4.22500	−	13.0032i	0.303337	−	0.933576i
$195$	0.249350	−	1.97679i	0.0178564	−	0.141561i
$196$	−5.54559	−	4.27159i	−0.396113	−	0.305113i
$197$	11.9558	+	6.09176i	0.851812	+	0.434020i	0.824672	−	0.565612i	$-0.191360\pi$
$197$	11.9558	+	6.09176i	0.851812	+	0.434020i	0.0271404	+	0.999632i	$0.491360\pi$
$198$	−1.07129	−	6.76385i	−0.0761331	−	0.480686i
$199$	−2.71337			−0.192346			−0.0961729	−	0.995365i	$-0.530660\pi$
$199$	−2.71337			−0.192346			−0.0961729	+	0.995365i	$0.530660\pi$
$200$	−0.468675	+	4.97799i	−0.0331403	+	0.351997i
$201$			3.78207i			0.266767i
$202$	0.0675975	+	0.426794i	0.00475614	+	0.0300291i
$203$	−0.0296637	+	0.171682i	−0.00208198	+	0.0120497i
$204$	−0.374343	+	0.121631i	−0.0262092	+	0.00851590i
$205$	24.3669	+	11.4606i	1.70186	+	0.800445i
$206$	−1.53093	−	0.497429i	−0.106665	−	0.0346575i
$207$	−11.2710	+	11.2710i	−0.783391	+	0.783391i
$208$	−1.01901	−	1.99993i	−0.0706559	−	0.138670i
$209$	15.0059	−	10.9024i	1.03798	−	0.754137i
$210$	−0.686352	+	2.24605i	−0.0473628	+	0.154992i
$211$	−0.860715	−	0.625346i	−0.0592541	−	0.0430506i	0.557764	−	0.830000i	$-0.311659\pi$
$211$	−0.860715	−	0.625346i	−0.0592541	−	0.0430506i	−0.617018	+	0.786949i	$0.711659\pi$
$212$	−0.418072	+	2.63960i	−0.0287133	+	0.181289i
$213$	−0.686191	+	4.33244i	−0.0470170	+	0.296854i
$214$	4.31088	−	5.93342i	0.294686	−	0.405600i
$215$	23.3453	+	6.77768i	1.59213	+	0.462234i
$216$	1.36327	+	1.87638i	0.0927585	+	0.127671i
$217$	15.4900	−	15.0618i	1.05153	−	1.02246i
$218$	−2.80637	−	2.80637i	−0.190072	−	0.190072i
$219$	5.03183	+	1.63494i	0.340019	+	0.110479i
$220$	−5.29171	+	1.01048i	−0.356767	+	0.0681262i
$221$	0.687715	+	2.11657i	0.0462607	+	0.142376i
$222$	−1.28874	+	2.52930i	−0.0864947	+	0.169755i
$223$	−12.3752	+	1.96004i	−0.828703	+	0.131254i	−0.556355	−	0.830945i	$-0.687800\pi$
$223$	−12.3752	+	1.96004i	−0.828703	+	0.131254i	−0.272349	+	0.962199i	$0.587800\pi$
$224$	0.782239	+	2.52747i	0.0522656	+	0.168874i
$225$	−14.1836	+	0.897698i	−0.945577	+	0.0598466i
$226$	6.18032			0.411109
$227$	0.169290	+	1.06885i	0.0112362	+	0.0709423i	0.992669	−	0.120862i	$-0.0385660\pi$
$227$	0.169290	+	1.06885i	0.0112362	+	0.0709423i	−0.981433	+	0.191805i	$0.938566\pi$
$228$	−1.38750	+	2.72313i	−0.0918896	+	0.180344i
$229$	−1.77172	−	5.45280i	−0.117079	−	0.360331i	0.875296	−	0.483587i	$-0.160666\pi$
$229$	−1.77172	−	5.45280i	−0.117079	−	0.360331i	−0.992375	+	0.123256i	$0.960666\pi$
$230$	9.14246	+	8.58212i	0.602836	+	0.565888i
$231$	−2.53026	−	0.0354620i	−0.166479	−	0.00233323i
$232$	0.0465637	−	0.0465637i	0.00305706	−	0.00305706i
$233$	5.66500	−	2.88646i	0.371126	−	0.189098i	−0.258473	−	0.966019i	$-0.583219\pi$
$233$	5.66500	−	2.88646i	0.371126	−	0.189098i	0.629599	+	0.776920i	$0.283219\pi$
$234$	5.16151	−	3.75006i	0.337419	−	0.245149i
$235$	−0.291149	−	9.20951i	−0.0189924	−	0.600762i
$236$	−8.59978	+	11.8366i	−0.559798	+	0.770496i
$237$	−2.17739	−	0.344864i	−0.141436	−	0.0224013i
$238$	−0.374019	−	2.59646i	−0.0242441	−	0.168304i
$239$	3.24492	−	4.46625i	0.209897	−	0.288898i	−0.691069	−	0.722789i	$-0.742860\pi$
$239$	3.24492	−	4.46625i	0.209897	−	0.288898i	0.900965	+	0.433891i	$0.142860\pi$
$240$	0.701301	−	0.544196i	0.0452688	−	0.0351277i
$241$	−10.9283	−	15.0415i	−0.703953	−	0.968908i	−0.999906	−	0.0137059i	$-0.995637\pi$
$241$	−10.9283	−	15.0415i	−0.703953	−	0.968908i	0.295953	−	0.955203i	$-0.404363\pi$
$242$	2.35864	+	4.62910i	0.151619	+	0.297570i
$243$	−7.05524	+	7.05524i	−0.452594	+	0.452594i
$244$	2.48381	−	7.64438i	0.159010	−	0.489382i
$245$	−13.9718	−	7.05617i	−0.892624	−	0.450802i
$246$	−1.47729	−	4.54662i	−0.0941884	−	0.289882i
$247$	15.3968	+	7.84507i	0.979677	+	0.499170i
$248$	−8.06559	+	1.27746i	−0.512165	+	0.0811190i
$249$		−	2.94645i		−	0.186723i
$250$	1.05842	+	11.1301i	0.0669405	+	0.703931i
$251$			14.1268i			0.891673i	0.895114	+	0.445837i	$0.147094\pi$
$251$			14.1268i			0.891673i	−0.895114	+	0.445837i	$0.852906\pi$
$252$	−6.74782	+	3.31991i	−0.425073	+	0.209135i
$253$	−6.13377	+	12.0382i	−0.385627	+	0.756835i
$254$	−1.47678	+	0.479835i	−0.0926615	+	0.0301075i
$255$	−0.771187	+	0.424152i	−0.0482936	+	0.0265614i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	15.5859	+	15.5859i	0.972220	+	0.972220i	0.999624	−	0.0274044i	$-0.00872419\pi$
$257$	15.5859	+	15.5859i	0.972220	+	0.972220i	−0.0274044	+	0.999624i	$0.508724\pi$
$258$	−1.95931	−	3.84536i	−0.121981	−	0.239402i
$259$	−15.1484	−	11.3337i	−0.941278	−	0.704242i
$260$	−3.07693	−	3.96522i	−0.190823	−	0.245913i
$261$	0.151428	+	0.110019i	0.00937316	+	0.00681000i
$262$	0.383109	+	0.0606786i	0.0236686	+	0.00374873i
$263$	15.2246	+	2.41133i	0.938787	+	0.148689i	0.607033	−	0.794677i	$-0.292360\pi$
$263$	15.2246	+	2.41133i	0.938787	+	0.148689i	0.331754	+	0.943366i	$0.392360\pi$
$264$	0.773777	+	0.562182i	0.0476227	+	0.0345999i
$265$	0.188827	+	5.97292i	0.0115996	+	0.366913i
$266$	−16.3093	−	12.2022i	−0.999989	−	0.748168i
$267$	−1.38262	−	2.71355i	−0.0846151	−	0.166067i
$268$	6.73665	+	6.73665i	0.411507	+	0.411507i
$269$	−7.76375	+	23.8944i	−0.473364	+	1.45686i	0.374788	+	0.927111i	$0.377716\pi$
$269$	−7.76375	+	23.8944i	−0.473364	+	1.45686i	−0.848152	+	0.529754i	$0.822284\pi$
$270$	3.78122	+	3.54947i	0.230118	+	0.216014i
$271$	−19.2659	+	6.25988i	−1.17032	+	0.380261i	−0.828763	−	0.559600i	$-0.810955\pi$
$271$	−19.2659	+	6.25988i	−1.17032	+	0.380261i	−0.341559	+	0.939860i	$0.610955\pi$
$272$	−0.450132	+	0.883433i	−0.0272932	+	0.0535660i
$273$	−1.04074	−	2.11535i	−0.0629887	−	0.128027i
$274$			16.6711i			1.00714i
$275$	−11.1988	+	4.43878i	−0.675314	+	0.267669i
$276$		−	2.22620i		−	0.134001i
$277$	−17.1387	+	2.71450i	−1.02976	+	0.163098i	−0.648378	−	0.761319i	$-0.724552\pi$
$277$	−17.1387	+	2.71450i	−1.02976	+	0.163098i	−0.381384	+	0.924417i	$0.624552\pi$
$278$	−9.62287	−	4.90310i	−0.577141	−	0.294068i
$279$	−7.17273	−	22.0754i	−0.429420	−	1.32162i
$280$	2.77814	+	5.22321i	0.166026	+	0.312147i
$281$	3.19493	−	9.83300i	0.190594	−	0.586587i	−0.809406	−	0.587249i	$-0.800211\pi$
$281$	3.19493	−	9.83300i	0.190594	−	0.586587i	1.00000		0.000662124i	$0.000210761\pi$
$282$	−1.15671	+	1.15671i	−0.0688810	+	0.0688810i
$283$	6.42765	+	12.6150i	0.382084	+	0.749882i	0.999319	−	0.0368966i	$-0.0117472\pi$
$283$	6.42765	+	12.6150i	0.382084	+	0.749882i	−0.617235	+	0.786779i	$0.711747\pi$
$284$	6.49472	+	8.93922i	0.385391	+	0.530445i
$285$	−1.90538	+	6.56296i	−0.112865	+	0.388756i
$286$	3.17863	−	4.37501i	0.187956	−	0.258700i
$287$	31.5356	−	4.54269i	1.86149	−	0.268146i
$288$	2.80741	+	0.444650i	0.165428	+	0.0262013i
$289$	−9.41451	+	12.9580i	−0.553795	+	0.762233i
$290$	0.0827425	−	0.121801i	0.00485881	−	0.00715240i
$291$	−4.39109	+	3.19031i	−0.257410	+	0.187019i
$292$	11.8749	−	6.05056i	0.694926	−	0.354082i
$293$	3.04182	−	3.04182i	0.177705	−	0.177705i	−0.612650	−	0.790355i	$-0.709896\pi$
$293$	3.04182	−	3.04182i	0.177705	−	0.177705i	0.790355	+	0.612650i	$0.209896\pi$
$294$	0.784315	+	2.66589i	0.0457422	+	0.155478i
$295$	−13.9240	+	29.6045i	−0.810689	+	1.72364i
$296$	2.20969	+	6.80073i	0.128436	+	0.395284i
$297$	−2.53686	+	4.97887i	−0.147204	+	0.288903i
$298$	1.71836	+	10.8493i	0.0995416	+	0.628481i
$299$	−12.5871			−0.727932
$300$	1.31208	−	1.48939i	0.0757533	−	0.0859902i
$301$	27.4772	−	8.50405i	1.58376	−	0.490165i
$302$	−16.3471	+	2.58913i	−0.940670	+	0.148988i
$303$	0.0778781	−	0.152844i	0.00447398	−	0.00878068i
$304$	2.37903	+	7.32189i	0.136446	+	0.419939i
$305$	2.24927	−	17.8317i	0.128793	−	1.02104i
$306$	−2.68031	−	0.870886i	−0.153223	−	0.0497852i
$307$	−14.8674	−	14.8674i	−0.848529	−	0.848529i	0.141420	−	0.989950i	$-0.454833\pi$
$307$	−14.8674	−	14.8674i	−0.848529	−	0.848529i	−0.989950	+	0.141420i	$0.954833\pi$
$308$	−4.57008	+	4.44375i	−0.260404	+	0.253206i
$309$	0.375611	+	0.516984i	0.0213677	+	0.0294102i
$310$	−17.1793	+	6.18858i	−0.975721	+	0.351488i
$311$	12.4845	−	17.1835i	0.707932	−	0.974384i	−0.291908	−	0.956447i	$-0.594290\pi$
$311$	12.4845	−	17.1835i	0.707932	−	0.974384i	0.999839	−	0.0179376i	$-0.00571002\pi$
$312$	−0.139392	+	0.880083i	−0.00789149	+	0.0498249i
$313$	0.156436	−	0.987697i	0.00884228	−	0.0558280i	−0.982873	−	0.184286i	$-0.941003\pi$
$313$	0.156436	−	0.987697i	0.00884228	−	0.0558280i	0.991715	+	0.128458i	$0.0410027\pi$
$314$	−2.79143	−	2.02809i	−0.157529	−	0.114452i
$315$	−13.4284	+	10.1219i	−0.756605	+	0.570304i
$316$	−4.49265	+	3.26410i	−0.252732	+	0.183620i
$317$	11.8740	+	23.3040i	0.666909	+	1.30888i	0.938103	+	0.346357i	$0.112581\pi$
$317$	11.8740	+	23.3040i	0.666909	+	1.30888i	−0.271194	+	0.962525i	$0.587419\pi$
$318$	0.750194	−	0.750194i	0.0420688	−	0.0420688i
$319$	0.150889	+	0.0490267i	0.00844815	+	0.00274497i
$320$	0.279838	−	2.21849i	0.0156434	−	0.124017i
$321$	−2.76901	+	0.899706i	−0.154551	+	0.0502167i
$322$	14.6202	+	2.52613i	0.814753	+	0.140776i
$323$	−1.19410	−	7.53928i	−0.0664417	−	0.419497i
$324$			7.60649i			0.422583i
$325$	−8.42117	−	7.41865i	−0.467123	−	0.411513i
$326$	7.45934			0.413135
$327$	0.246470	+	1.55615i	0.0136298	+	0.0860552i
$328$	−10.7298	−	5.46712i	−0.592456	−	0.301871i
$329$	−6.28397	−	8.90907i	−0.346446	−	0.491173i
$330$	1.93529	+	0.910237i	0.106534	+	0.0501069i
$331$	−1.54339	+	4.75005i	−0.0848321	+	0.261086i	−0.984471	−	0.175549i	$-0.943830\pi$
$331$	−1.54339	+	4.75005i	−0.0848321	+	0.261086i	0.899639	+	0.436635i	$0.143830\pi$
$332$	−5.24823	−	5.24823i	−0.288034	−	0.288034i
$333$	−18.1099	+	9.22745i	−0.992416	+	0.505661i
$334$	7.09126	−	5.15211i	0.388017	−	0.281911i
$335$	17.6217	+	11.9709i	0.962775	+	0.654038i
$336$	0.338532	−	0.994262i	0.0184684	−	0.0542414i
$337$	0.263546	−	1.66396i	0.0143563	−	0.0906419i	−0.979470	−	0.201591i	$-0.935389\pi$
$337$	0.263546	−	1.66396i	0.0143563	−	0.0906419i	0.993826	+	0.110949i	$0.0353889\pi$
$338$	−7.86387	−	1.24552i	−0.427738	−	0.0677471i
$339$	−1.98490	−	1.44212i	−0.107805	−	0.0783250i
$340$	−0.618142	+	2.12915i	−0.0335234	+	0.115469i
$341$	−11.5644	−	15.9170i	−0.626247	−	0.861955i
$342$	−19.4977	+	9.93458i	−1.05432	+	0.537201i
$343$	−18.3979	+	2.12582i	−0.993391	+	0.114783i
$344$	−10.3393	−	3.35945i	−0.557459	−	0.181129i
$345$	−0.933686	−	4.88958i	−0.0502680	−	0.263246i
$346$	4.19743	−	1.36383i	0.225655	−	0.0733198i
$347$	4.11095	+	2.09463i	0.220687	+	0.112446i	0.560839	−	0.827925i	$-0.310479\pi$
$347$	4.11095	+	2.09463i	0.220687	+	0.112446i	−0.340152	+	0.940370i	$0.610479\pi$
$348$	−0.0258198	+	0.00408945i	−0.00138409	+	0.000219218i
$349$	31.1145			1.66552			0.832761	−	0.553633i	$-0.186759\pi$
$349$	31.1145			1.66552			0.832761	+	0.553633i	$0.186759\pi$
$350$	8.29252	+	10.3070i	0.443254	+	0.550932i
$351$	−5.20590			−0.277870
$352$	2.37962	−	0.376895i	0.126834	−	0.0200886i
$353$	−3.54297	−	1.80523i	−0.188573	−	0.0960828i	0.357155	−	0.934045i	$-0.383747\pi$
$353$	−3.54297	−	1.80523i	−0.188573	−	0.0960828i	−0.545728	+	0.837962i	$0.683747\pi$
$354$	5.52389	−	1.79482i	0.293592	−	0.0953937i
$355$	18.0141	+	16.9100i	0.956088	+	0.897489i
$356$	−7.29613	−	2.37066i	−0.386694	−	0.125645i
$357$	−0.485737	+	0.921166i	−0.0257079	+	0.0487533i
$358$	5.80419	−	2.95738i	0.306761	−	0.156303i
$359$	12.9206	+	17.7836i	0.681921	+	0.938584i	0.999955	−	0.00949539i	$-0.00302252\pi$
$359$	12.9206	+	17.7836i	0.681921	+	0.938584i	−0.318034	+	0.948079i	$0.603023\pi$
$360$	6.35264	−	0.200832i	0.334813	−	0.0105848i
$361$	−32.5790	−	23.6700i	−1.71468	−	1.24579i
$362$	7.76427	+	1.22974i	0.408081	+	0.0646337i
$363$	0.322640	−	2.03707i	0.0169342	−	0.106918i
$364$	−5.62165	−	1.91409i	−0.294655	−	0.100326i
$365$	23.5441	−	18.2698i	1.23236	−	0.956284i
$366$	−2.58145	+	1.87554i	−0.134935	+	0.0980358i
$367$	−0.445755	+	0.227123i	−0.0232682	+	0.0118557i	−0.465586	−	0.885003i	$-0.654156\pi$
$367$	−0.445755	+	0.227123i	−0.0232682	+	0.0118557i	0.442318	+	0.896858i	$0.354156\pi$
$368$	−3.96532	−	3.96532i	−0.206706	−	0.206706i
$369$	10.5774	−	32.5540i	0.550639	−	1.69469i
$370$	7.70561	+	14.0102i	0.400596	+	0.728357i
$371$	4.07553	+	5.77806i	0.211591	+	0.299982i
$372$	2.88847	+	1.47175i	0.149760	+	0.0763065i
$373$	0.918889	+	5.80164i	0.0475783	+	0.300397i	0.999990	−	0.00441638i	$-0.00140578\pi$
$373$	0.918889	+	5.80164i	0.0475783	+	0.300397i	−0.952412	+	0.304814i	$0.901406\pi$
$374$	−2.38881			−0.123522
$375$	2.25718	−	3.82158i	0.116560	−	0.197345i
$376$			4.12067i			0.212508i
$377$	0.0231222	+	0.145988i	0.00119085	+	0.00751874i
$378$	6.04677	+	1.04478i	0.311012	+	0.0537377i
$379$	9.86690	−	3.20595i	0.506829	−	0.164679i	−0.0444308	−	0.999012i	$-0.514147\pi$
$379$	9.86690	−	3.20595i	0.506829	−	0.164679i	0.551260	+	0.834334i	$0.314147\pi$
$380$	8.29612	+	15.0839i	0.425582	+	0.773787i
$381$	0.586255	+	0.190486i	0.0300347	+	0.00975888i
$382$	4.54531	−	4.54531i	0.232558	−	0.232558i
$383$	−9.50667	−	18.6579i	−0.485768	−	0.953373i	−0.995654	−	0.0931313i	$-0.970312\pi$
$383$	−9.50667	−	18.6579i	−0.485768	−	0.953373i	0.509886	−	0.860242i	$-0.329688\pi$
$384$	−0.321165	+	0.233340i	−0.0163894	+	0.0119076i
$385$	−8.17389	+	11.6769i	−0.416580	+	0.595110i
$386$	8.24978	+	5.99382i	0.419903	+	0.305077i
$387$	4.83398	−	30.5205i	0.245725	−	1.55145i
$388$	−2.13883	+	13.5041i	−0.108583	+	0.685565i
$389$	3.52746	−	4.85514i	0.178849	−	0.246165i	−0.710175	−	0.704026i	$-0.751384\pi$
$389$	3.52746	−	4.85514i	0.178849	−	0.246165i	0.889024	+	0.457860i	$0.151384\pi$
$390$	0.0629579	+	1.99146i	0.00318800	+	0.100842i
$391$	3.26817	+	4.49825i	0.165278	+	0.227486i
$392$	6.14553	+	3.35148i	0.310396	+	0.169275i
$393$	−0.108883	−	0.108883i	−0.00549240	−	0.00549240i
$394$	−12.7615	−	4.14647i	−0.642916	−	0.208896i
$395$	−8.49859	+	9.05348i	−0.427611	+	0.455530i
$396$	2.11620	+	6.51299i	0.106343	+	0.327290i
$397$	−1.35849	+	2.66619i	−0.0681807	+	0.133812i	−0.922581	−	0.385803i	$-0.873925\pi$
$397$	−1.35849	+	2.66619i	−0.0681807	+	0.133812i	0.854401	+	0.519615i	$0.173925\pi$
$398$	2.67997	−	0.424465i	0.134335	−	0.0212765i
$399$	2.39071	+	7.72455i	0.119685	+	0.386711i
$400$	−0.315824	−	4.99002i	−0.0157912	−	0.249501i
$401$	26.5131			1.32400			0.661999	−	0.749504i	$-0.269708\pi$
$401$	26.5131			1.32400			0.661999	+	0.749504i	$0.269708\pi$
$402$	−0.591646	−	3.73551i	−0.0295086	−	0.186310i
$403$	8.32140	−	16.3317i	0.414518	−	0.813538i
$404$	−0.133530	−	0.410964i	−0.00664339	−	0.0204462i
$405$	3.19023	+	16.7068i	0.158524	+	0.830165i
$406$	0.00244156	−	0.174208i	0.000121173	−	0.00864581i
$407$	−12.1821	+	12.1821i	−0.603844	+	0.603844i
$408$	0.350707	−	0.178694i	0.0173626	−	0.00884667i
$409$	5.96962	−	4.33718i	0.295179	−	0.214460i	−0.430332	−	0.902671i	$-0.641604\pi$
$409$	5.96962	−	4.33718i	0.295179	−	0.214460i	0.725511	+	0.688211i	$0.241604\pi$
$410$	−25.8598	−	7.50770i	−1.27712	−	0.370779i
$411$	3.89004	−	5.35418i	0.191882	−	0.264102i
$412$	1.58990	+	0.251815i	0.0783285	+	0.0124060i
$413$	5.51912	+	38.3140i	0.271578	+	1.88531i
$414$	9.36909	−	12.8955i	0.460466	−	0.633777i
$415$	−13.7283	−	9.32597i	−0.673895	−	0.457794i
$416$	1.31933	+	1.81590i	0.0646853	+	0.0890317i
$417$	1.94644	+	3.82010i	0.0953175	+	0.187071i
$418$	−13.1156	+	13.1156i	−0.641507	+	0.641507i
$419$	2.36930	−	7.29194i	0.115748	−	0.356235i	−0.876355	−	0.481667i	$-0.840032\pi$
$419$	2.36930	−	7.29194i	0.115748	−	0.356235i	0.992102	+	0.125432i	$0.0400317\pi$
$420$	0.326543	−	2.32576i	0.0159336	−	0.113486i
$421$	4.70838	+	14.4909i	0.229473	+	0.706244i	0.997807	+	0.0661949i	$0.0210859\pi$
$421$	4.70838	+	14.4909i	0.229473	+	0.706244i	−0.768334	+	0.640049i	$0.778914\pi$
$422$	0.947944	+	0.483002i	0.0461452	+	0.0235121i
$423$	−11.5684	+	1.83226i	−0.562476	+	0.0890875i
$424$		−	2.67250i		−	0.129788i
$425$	−0.464692	+	4.93567i	−0.0225409	+	0.239415i
$426$		−	4.38644i		−	0.212524i
$427$	−9.38807	−	19.0816i	−0.454320	−	0.923421i
$428$	−3.32962	+	6.53474i	−0.160943	+	0.315869i
$429$	−2.04173	+	0.663398i	−0.0985756	+	0.0320292i
$430$	−24.1181	−	3.04223i	−1.16308	−	0.146709i
$431$	10.0313	−	30.8732i	0.483191	−	1.48711i	−0.351394	−	0.936228i	$-0.614292\pi$
$431$	10.0313	−	30.8732i	0.483191	−	1.48711i	0.834584	−	0.550880i	$-0.185708\pi$
$432$	−1.64001	−	1.64001i	−0.0789051	−	0.0789051i
$433$	−8.43418	−	16.5530i	−0.405321	−	0.795486i	0.594643	−	0.803990i	$-0.297293\pi$
$433$	−8.43418	−	16.5530i	−0.405321	−	0.795486i	−0.999964	+	0.00850320i	$0.997293\pi$
$434$	−12.9431	+	17.2996i	−0.621290	+	0.830406i
$435$	−0.0549950	+	0.0198111i	−0.00263681	+	0.000949868i
$436$	3.21084	+	2.33281i	0.153771	+	0.111721i
$437$	42.6412	+	6.75370i	2.03981	+	0.323074i
$438$	−5.22564	−	0.827659i	−0.249691	−	0.0395471i
$439$	−14.1815	−	10.3035i	−0.676848	−	0.491759i	0.195462	−	0.980711i	$-0.437379\pi$
$439$	−14.1815	−	10.3035i	−0.676848	−	0.491759i	−0.872311	+	0.488952i	$0.837379\pi$
$440$	5.06848	−	1.82584i	0.241631	−	0.0870435i
$441$	−6.67636	+	18.7433i	−0.317922	+	0.892537i
$442$	−1.01035	−	1.98293i	−0.0480576	−	0.0943183i
$443$	0.570312	+	0.570312i	0.0270963	+	0.0270963i	0.720525	−	0.693429i	$-0.243901\pi$
$443$	0.570312	+	0.570312i	0.0270963	+	0.0270963i	−0.693429	+	0.720525i	$0.743901\pi$
$444$	0.877206	−	2.69976i	0.0416304	−	0.128125i
$445$	−17.0194	−	2.14681i	−0.806796	−	0.101768i
$446$	11.9162	−	3.87181i	0.564249	−	0.183335i
$447$	1.97969	−	3.88536i	0.0936362	−	0.183771i
$448$	−1.16799	−	2.37398i	−0.0551824	−	0.112160i
$449$		−	24.8305i		−	1.17182i	−0.810375	−	0.585912i	$-0.800736\pi$
$449$		−	24.8305i		−	1.17182i	0.810375	−	0.585912i	$-0.199264\pi$
$450$	13.8686	−	3.10546i	0.653772	−	0.146393i
$451$		−	29.0135i		−	1.36619i
$452$	−6.10423	+	0.966815i	−0.287119	+	0.0454752i
$453$	5.85426	+	2.98290i	0.275057	+	0.140149i
$454$	−0.334411	−	1.02921i	−0.0156947	−	0.0483033i
$455$	−13.1501	−	1.84630i	−0.616486	−	0.0865560i
$456$	0.944430	−	2.90666i	0.0442270	−	0.136117i
$457$	−19.8760	+	19.8760i	−0.929762	+	0.929762i	−0.997690	−	0.0679283i	$-0.978361\pi$
$457$	−19.8760	+	19.8760i	−0.929762	+	0.929762i	0.0679283	+	0.997690i	$0.478361\pi$
$458$	2.60291	+	5.10851i	0.121626	+	0.238705i
$459$	1.35168	+	1.86043i	0.0630910	+	0.0868373i
$460$	−10.3724	−	7.04626i	−0.483618	−	0.328534i
$461$	−22.2256	+	30.5909i	−1.03515	+	1.42476i	−0.134137	+	0.990963i	$0.542826\pi$
$461$	−22.2256	+	30.5909i	−1.03515	+	1.42476i	−0.901011	+	0.433796i	$0.857174\pi$
$462$	2.50465	−	0.360794i	0.116527	−	0.0167857i
$463$	−18.9307	−	2.99833i	−0.879785	−	0.139344i	−0.299830	−	0.953993i	$-0.596930\pi$
$463$	−18.9307	−	2.99833i	−0.879785	−	0.139344i	−0.579955	+	0.814648i	$0.696930\pi$
$464$	−0.0387063	+	0.0532746i	−0.00179689	+	0.00247321i
$465$	6.96144	+	2.02107i	0.322829	+	0.0937249i
$466$	−5.14371	+	3.73712i	−0.238278	+	0.173119i
$467$	13.8247	−	7.04402i	0.639729	−	0.325958i	−0.103863	−	0.994592i	$-0.533120\pi$
$467$	13.8247	−	7.04402i	0.639729	−	0.325958i	0.743592	+	0.668633i	$0.233120\pi$
$468$	−4.51133	+	4.51133i	−0.208536	+	0.208536i
$469$	25.2038	+	0.353236i	1.16380	+	0.0163109i
$470$	1.72825	+	9.05058i	0.0797182	+	0.417472i
$471$	0.423274	+	1.30270i	0.0195034	+	0.0600253i
$472$	6.64225	−	13.0362i	0.305734	−	0.600038i
$473$	−4.09738	−	25.8698i	−0.188398	−	1.18950i
$474$	2.20453			0.101257
$475$	24.5478	+	29.6505i	1.12633	+	1.36046i
$476$	0.775591	+	2.50599i	0.0355491	+	0.114862i
$477$	7.50282	−	1.18833i	0.343530	−	0.0544099i
$478$	−2.50630	+	4.91889i	−0.114635	+	0.224985i
$479$	6.77396	+	20.8481i	0.309510	+	0.952574i	0.977956	+	0.208813i	$0.0669600\pi$
$479$	6.77396	+	20.8481i	0.309510	+	0.952574i	−0.668446	+	0.743761i	$0.733040\pi$
$480$	−0.607536	+	0.647203i	−0.0277301	+	0.0295407i
$481$	−15.2647	−	4.95981i	−0.696011	−	0.226148i
$482$	13.1468	+	13.1468i	0.598818	+	0.598818i
$483$	−4.10606	−	4.22279i	−0.186832	−	0.192143i
$484$	−3.05375	−	4.20313i	−0.138807	−	0.191051i
$485$	0.966030	+	30.5571i	0.0438652	+	1.38753i
$486$	5.86470	−	8.07206i	0.266028	−	0.366156i
$487$	6.45693	−	40.7674i	0.292591	−	1.84735i	−0.203496	−	0.979076i	$-0.565230\pi$
$487$	6.45693	−	40.7674i	0.292591	−	1.84735i	0.496087	−	0.868273i	$-0.334770\pi$
$488$	−1.25739	+	7.93882i	−0.0569192	+	0.359374i
$489$	−2.39568	−	1.74056i	−0.108336	−	0.0787110i
$490$	14.9036	+	4.78363i	0.673275	+	0.216103i
$491$	11.8962	−	8.64312i	0.536870	−	0.390059i	−0.286051	−	0.958214i	$-0.592343\pi$
$491$	11.8962	−	8.64312i	0.536870	−	0.390059i	0.822921	+	0.568156i	$0.192343\pi$
$492$	2.17035	+	4.25955i	0.0978468	+	0.192035i
$493$	0.0461679	−	0.0461679i	0.00207930	−	0.00207930i
$494$	−16.4345	−	5.33989i	−0.739423	−	0.240253i
$495$	7.37959	+	13.4175i	0.331688	+	0.603070i
$496$	7.76645	−	2.52347i	0.348724	−	0.113307i
$497$	28.8073	+	4.97742i	1.29219	+	0.223268i
$498$	0.460926	+	2.91017i	0.0206546	+	0.130408i
$499$		−	32.3838i		−	1.44970i	−0.688907	−	0.724849i	$-0.741909\pi$
$499$		−	32.3838i		−	1.44970i	0.688907	−	0.724849i	$-0.258091\pi$
$500$	−2.78653	−	10.8275i	−0.124617	−	0.484222i
$501$	−3.47966			−0.155460
$502$	−2.20991	−	13.9528i	−0.0986332	−	0.622746i
$503$	−39.0332	−	19.8884i	−1.74040	−	0.886779i	−0.967736	−	0.251968i	$-0.918922\pi$
$503$	−39.0332	−	19.8884i	−1.74040	−	0.886779i	−0.772667	−	0.634812i	$-0.781078\pi$
$504$	6.14540	−	4.33463i	0.273738	−	0.193080i
$505$	−0.465646	−	0.846631i	−0.0207210	−	0.0376746i
$506$	4.17506	−	12.8495i	0.185604	−	0.571231i
$507$	2.23497	+	2.23497i	0.0992586	+	0.0992586i
$508$	1.38354	−	0.704947i	0.0613845	−	0.0312770i
$509$	−6.07618	+	4.41461i	−0.269322	+	0.195674i	−0.714247	−	0.699894i	$-0.753231\pi$
$509$	−6.07618	+	4.41461i	−0.269322	+	0.195674i	0.444925	+	0.895568i	$0.353231\pi$
$510$	0.695340	−	0.539570i	0.0307902	−	0.0238926i
$511$	11.3652	−	33.3795i	0.502768	−	1.47662i
$512$	−0.156434	+	0.987688i	−0.00691349	+	0.0436501i
$513$	17.6359	+	2.79326i	0.778646	+	0.123325i
$514$	−17.8322	−	12.9558i	−0.786543	−	0.571457i
$515$	3.59763	−	0.113735i	0.158531	−	0.00501177i
$516$	2.53673	+	3.49152i	0.111674	+	0.153705i
$517$	−8.84580	+	4.50716i	−0.389038	+	0.198225i
$518$	16.7349	+	8.82443i	0.735290	+	0.387723i
$519$	−1.66630	−	0.541414i	−0.0731425	−	0.0237654i
$520$	3.65935	+	3.43507i	0.160473	+	0.150638i
$521$	−28.4160	+	9.23290i	−1.24493	+	0.404501i	−0.856100	−	0.516810i	$-0.827119\pi$
$521$	−28.4160	+	9.23290i	−1.24493	+	0.404501i	−0.388826	+	0.921311i	$0.627119\pi$
$522$	−0.166774	−	0.0849758i	−0.00729952	−	0.00371929i
$523$	13.6662	−	2.16451i	0.597581	−	0.0946476i	0.149686	−	0.988734i	$-0.452174\pi$
$523$	13.6662	−	2.16451i	0.597581	−	0.0946476i	0.447895	+	0.894086i	$0.352174\pi$
$524$	−0.387885			−0.0169448
$525$	−0.258234	−	5.24522i	−0.0112702	−	0.228920i
$526$	−15.4143			−0.672097
$527$	−7.99703	+	1.26661i	−0.348356	+	0.0551742i
$528$	−0.852195	−	0.434215i	−0.0370870	−	0.0188968i
$529$	−8.03402	+	2.61041i	−0.349305	+	0.113496i
$530$	−1.12087	−	5.86984i	−0.0486876	−	0.254970i
$531$	39.5513	+	12.8510i	1.71638	+	0.557686i
$532$	18.0174	+	9.50068i	0.781152	+	0.411907i
$533$	24.0839	−	12.2713i	1.04319	−	0.531531i
$534$	1.79009	+	2.46385i	0.0774649	+	0.106621i
$535$	−4.57238	+	15.7493i	−0.197681	+	0.680900i
$536$	−7.70756	−	5.59987i	−0.332916	−	0.241878i
$537$	−2.55418	−	0.404542i	−0.110221	−	0.0174573i
$538$	3.93026	−	24.8147i	0.169446	−	1.06984i
$539$	−0.472639	+	16.8584i	−0.0203580	+	0.726141i
$540$	−4.28993	−	2.91426i	−0.184609	−	0.125410i
$541$	−11.9525	+	8.68402i	−0.513879	+	0.373355i	−0.814293	−	0.580454i	$-0.802875\pi$
$541$	−11.9525	+	8.68402i	−0.513879	+	0.373355i	0.300414	+	0.953809i	$0.402875\pi$
$542$	18.0495	−	9.19667i	0.775291	−	0.395031i
$543$	−2.20666	−	2.20666i	−0.0946970	−	0.0946970i
$544$	0.306390	−	0.942973i	0.0131364	−	0.0404296i
$545$	8.03063	+	3.77709i	0.343994	+	0.161793i
$546$	1.35884	+	1.92649i	0.0581531	+	0.0824464i
$547$	9.98167	+	5.08592i	0.426785	+	0.217458i	0.654171	−	0.756347i	$-0.273018\pi$
$547$	9.98167	+	5.08592i	0.426785	+	0.217458i	−0.227385	+	0.973805i	$0.573018\pi$
$548$	−2.60794	−	16.4659i	−0.111406	−	0.703387i
$549$	−22.8466			−0.975071
$550$	10.3666	−	6.13601i	0.442031	−	0.261640i
$551$		−	0.506967i		−	0.0215975i
$552$	0.348254	+	2.19879i	0.0148227	+	0.0935866i
$553$	−2.50154	+	14.4779i	−0.106376	+	0.615664i
$554$	16.5030	−	5.36215i	0.701145	−	0.227816i
$555$	0.794375	−	6.29762i	0.0337193	−	0.267319i
$556$	10.2714	+	3.33738i	0.435605	+	0.141537i
$557$	−1.78257	+	1.78257i	−0.0755300	+	0.0755300i	−0.743863	−	0.668333i	$-0.767008\pi$
$557$	−1.78257	+	1.78257i	−0.0755300	+	0.0755300i	0.668333	+	0.743863i	$0.267008\pi$
$558$	10.5378	+	20.6815i	0.446100	+	0.875520i
$559$	19.7414	−	14.3429i	0.834971	−	0.606642i
$560$	−3.56103	−	4.72431i	−0.150481	−	0.199638i
$561$	0.767200	+	0.557404i	0.0323912	+	0.0235336i
$562$	−1.61738	+	10.2117i	−0.0682250	+	0.430756i
$563$	4.04056	−	25.5111i	0.170289	−	1.07517i	−0.743428	−	0.668816i	$-0.766802\pi$
$563$	4.04056	−	25.5111i	0.170289	−	1.07517i	0.913718	−	0.406349i	$-0.133198\pi$
$564$	0.961518	−	1.32342i	0.0404872	−	0.0557259i
$565$	−13.0017	+	4.68367i	−0.546987	+	0.197043i
$566$	−8.32193	−	11.4542i	−0.349797	−	0.481454i
$567$	14.0296	+	14.4285i	0.589188	+	0.605938i
$568$	−7.81316	−	7.81316i	−0.327833	−	0.327833i
$569$	21.0319	+	6.83368i	0.881703	+	0.286483i	0.714664	−	0.699468i	$-0.246579\pi$
$569$	21.0319	+	6.83368i	0.881703	+	0.286483i	0.167039	+	0.985950i	$0.446579\pi$
$570$	0.855251	−	6.78023i	0.0358225	−	0.283993i
$571$	9.88348	+	30.4182i	0.413611	+	1.27296i	0.913488	+	0.406866i	$0.133379\pi$
$571$	9.88348	+	30.4182i	0.413611	+	1.27296i	−0.499877	+	0.866096i	$0.666621\pi$
$572$	−2.45509	+	4.81839i	−0.102653	+	0.201467i
$573$	−2.52040	+	0.399191i	−0.105291	+	0.0166765i
$574$	−30.4367	+	9.42002i	−1.27040	+	0.393184i
$575$	−25.7371	−	11.1260i	−1.07331	−	0.463986i
$576$	−2.84241			−0.118434
$577$	3.41258	+	21.5462i	0.142068	+	0.896980i	0.951025	+	0.309113i	$0.100032\pi$
$577$	3.41258	+	21.5462i	0.142068	+	0.896980i	−0.808958	+	0.587867i	$0.799968\pi$
$578$	7.27153	−	14.2712i	0.302456	−	0.593603i
$579$	−1.25094	−	3.85001i	−0.0519874	−	0.160001i
$580$	−0.0626699	+	0.133245i	−0.00260223	+	0.00553270i
$581$	−19.6352	−	0.275191i	−0.814604	−	0.0114168i
$582$	3.83795	−	3.83795i	0.159088	−	0.159088i
$583$	5.73703	−	2.92316i	0.237603	−	0.121065i
$584$	−10.7822	+	7.83371i	−0.446170	+	0.324161i
$585$	−8.01651	+	11.8007i	−0.331442	+	0.487899i
$586$	−2.52852	+	3.48021i	−0.104452	+	0.143766i
$587$	−20.5966	−	3.26218i	−0.850114	−	0.134645i	−0.283850	−	0.958869i	$-0.591612\pi$
$587$	−20.5966	−	3.26218i	−0.850114	−	0.134645i	−0.566264	+	0.824224i	$0.691612\pi$
$588$	−1.19170	−	2.51038i	−0.0491447	−	0.103526i
$589$	−36.9532	+	50.8617i	−1.52263	+	2.09572i
$590$	9.12145	−	31.4182i	0.375524	−	1.29347i
$591$	3.13101	+	4.30947i	0.128793	+	0.177268i
$592$	−3.24635	−	6.37133i	−0.133424	−	0.261860i
$593$	22.7984	−	22.7984i	0.936219	−	0.936219i	−0.0618658	−	0.998084i	$-0.519705\pi$
$593$	22.7984	−	22.7984i	0.936219	−	0.936219i	0.998084	+	0.0618658i	$0.0197051\pi$
$594$	1.72676	−	5.31442i	0.0708499	−	0.218053i
$595$	2.75453	+	5.17882i	0.112925	+	0.212311i
$596$	−3.39440	−	10.4469i	−0.139040	−	0.427921i
$597$	−0.959756	−	0.489020i	−0.0392802	−	0.0200143i
$598$	12.4322	−	1.96906i	0.508388	−	0.0805208i
$599$		−	21.1030i		−	0.862247i	−0.902293	−	0.431123i	$-0.858117\pi$
$599$		−	21.1030i		−	0.862247i	0.902293	−	0.431123i	$-0.141883\pi$
$600$	−1.06294	+	1.67631i	−0.0433943	+	0.0684352i
$601$			39.8950i			1.62735i	0.581319	+	0.813675i	$0.302537\pi$
$601$			39.8950i			1.62735i	−0.581319	+	0.813675i	$0.697463\pi$
$602$	−25.8085	+	12.6977i	−1.05188	+	0.517521i
$603$	12.2940	−	24.1283i	0.500649	−	0.982579i
$604$	15.7408	−	5.11450i	0.640485	−	0.208106i
$605$	−8.47004	−	7.95091i	−0.344356	−	0.323250i
$606$	−0.0530091	+	0.163145i	−0.00215335	+	0.00662733i
$607$	−23.2635	−	23.2635i	−0.944238	−	0.944238i	0.0542876	−	0.998525i	$-0.482711\pi$
$607$	−23.2635	−	23.2635i	−0.944238	−	0.944238i	−0.998525	+	0.0542876i	$0.982711\pi$
$608$	−3.49513	−	6.85958i	−0.141746	−	0.278193i
$609$	−0.0414339	+	0.0553799i	−0.00167899	+	0.00224411i
$610$	0.567914	+	17.9641i	0.0229942	+	0.727343i
$611$	−7.48272	−	5.43651i	−0.302718	−	0.219938i
$612$	2.78355	+	0.440871i	0.112518	+	0.0178211i
$613$	−9.77839	−	1.54874i	−0.394945	−	0.0625532i	−0.0441968	−	0.999023i	$-0.514073\pi$
$613$	−9.77839	−	1.54874i	−0.394945	−	0.0625532i	−0.350749	+	0.936470i	$0.614073\pi$
$614$	17.0102	+	12.3586i	0.686474	+	0.498753i
$615$	6.55340	+	8.44533i	0.264259	+	0.340549i
$616$	3.81866	−	5.10396i	0.153858	−	0.205644i
$617$	−18.5057	−	36.3195i	−0.745012	−	1.46217i	−0.881828	−	0.471571i	$-0.843687\pi$
$617$	−18.5057	−	36.3195i	−0.745012	−	1.46217i	0.136816	−	0.990596i	$-0.456313\pi$
$618$	−0.451860	−	0.451860i	−0.0181765	−	0.0181765i
$619$	−5.65827	+	17.4144i	−0.227425	+	0.699942i	0.770611	+	0.637305i	$0.219951\pi$
$619$	−5.65827	+	17.4144i	−0.227425	+	0.699942i	−0.998036	+	0.0626369i	$0.980049\pi$
$620$	15.9997	−	8.79983i	0.642564	−	0.353410i
$621$	−12.3698	+	4.01918i	−0.496381	+	0.161284i
$622$	−9.64272	+	18.9249i	−0.386638	+	0.758819i
$623$	−18.2123	+	8.96038i	−0.729659	+	0.358990i
$624$		−	0.891054i		−	0.0356707i
$625$	−10.6614	−	22.6127i	−0.426458	−	0.904508i
$626$			1.00001i			0.0399684i
$627$	7.27269	−	1.15188i	0.290443	−	0.0460017i
$628$	3.07432	+	1.56645i	0.122679	+	0.0625080i
$629$	2.19091	+	6.74292i	0.0873572	+	0.268858i
$630$	11.6797	−	12.0979i	0.465329	−	0.481993i
$631$	2.43811	−	7.50374i	0.0970598	−	0.298719i	−0.890725	−	0.454542i	$-0.849803\pi$
$631$	2.43811	−	7.50374i	0.0970598	−	0.298719i	0.987785	+	0.155823i	$0.0498029\pi$
$632$	3.92672	−	3.92672i	0.156197	−	0.156197i
$633$	−0.191743	−	0.376316i	−0.00762109	−	0.0149572i
$634$	−15.3733	−	21.1596i	−0.610553	−	0.840354i
$635$	2.74311	−	2.12860i	0.108857	−	0.0844709i
$636$	−0.623602	+	0.858314i	−0.0247274	+	0.0340344i
$637$	−14.1939	+	6.73796i	−0.562383	+	0.266968i
$638$	−0.156700	−	0.0248189i	−0.00620383	−	0.000982590i
$639$	18.4606	−	25.4089i	0.730291	−	1.00516i
$640$	0.0706556	+	2.23495i	0.00279291	+	0.0883442i
$641$	0.0698290	−	0.0507337i	0.00275808	−	0.00200386i	−0.586405	−	0.810018i	$-0.699457\pi$
$641$	0.0698290	−	0.0507337i	0.00275808	−	0.00200386i	0.589163	+	0.808014i	$0.299457\pi$
$642$	2.59417	−	1.32180i	0.102384	−	0.0521672i
$643$	−7.38582	+	7.38582i	−0.291268	+	0.291268i	−0.837581	−	0.546313i	$-0.816031\pi$
$643$	−7.38582	+	7.38582i	−0.291268	+	0.291268i	0.546313	+	0.837581i	$0.316031\pi$
$644$	−14.8354	−	0.207921i	−0.584597	−	0.00819323i
$645$	7.03601	+	6.60477i	0.277043	+	0.260063i
$646$	2.35881	+	7.25966i	0.0928059	+	0.285627i
$647$	5.48309	−	10.7612i	0.215562	−	0.423065i	−0.757751	−	0.652543i	$-0.773702\pi$
$647$	5.48309	−	10.7612i	0.215562	−	0.423065i	0.973314	+	0.229478i	$0.0737020\pi$
$648$	−1.18992	−	7.51284i	−0.0467443	−	0.295132i
$649$	35.2498			1.38368
$650$	9.47803	+	6.00996i	0.371759	+	0.235730i
$651$	8.19356	−	2.53587i	0.321131	−	0.0993884i
$652$	−7.36751	+	1.16690i	−0.288534	+	0.0456993i
$653$	−15.1401	+	29.7140i	−0.592476	+	1.16280i	0.378941	+	0.925421i	$0.376288\pi$
$653$	−15.1401	+	29.7140i	−0.592476	+	1.16280i	−0.971417	+	0.237379i	$0.923712\pi$
$654$	−0.486870	−	1.49843i	−0.0190381	−	0.0585934i
$655$	−0.851943	+	0.162682i	−0.0332882	+	0.00635653i
$656$	11.4530	+	3.72130i	0.447164	+	0.145292i
$657$	−26.7867	−	26.7867i	−1.04505	−	1.04505i
$658$	7.60029	+	7.81635i	0.296290	+	0.304713i
$659$	−4.74497	−	6.53090i	−0.184838	−	0.254408i	0.706535	−	0.707678i	$-0.250257\pi$
$659$	−4.74497	−	6.53090i	−0.184838	−	0.254408i	−0.891373	+	0.453270i	$0.850257\pi$
$660$	−2.05386	−	0.596284i	−0.0799464	−	0.0232103i
$661$	9.55969	−	13.1578i	0.371829	−	0.511779i	−0.581568	−	0.813498i	$-0.697561\pi$
$661$	9.55969	−	13.1578i	0.371829	−	0.511779i	0.953397	+	0.301719i	$0.0975605\pi$
$662$	0.781312	−	4.93301i	0.0303666	−	0.191727i
$663$	−0.138207	+	0.872603i	−0.00536751	+	0.0338891i
$664$	6.00462	+	4.36262i	0.233025	+	0.169302i
$665$	43.5577	+	13.3105i	1.68910	+	0.516158i
$666$	16.4434	−	11.9469i	0.637170	−	0.462931i
$667$	0.167649	+	0.329031i	0.00649141	+	0.0127401i
$668$	−6.19799	+	6.19799i	−0.239808	+	0.239808i
$669$	−4.73051	−	1.53704i	−0.182892	−	0.0594253i
$670$	−19.2774	−	9.06684i	−0.744750	−	0.350282i
$671$	−18.4175	+	5.98420i	−0.710999	+	0.231018i
$672$	−0.178827	+	1.03498i	−0.00689840	+	0.0399252i
$673$	5.83791	+	36.8591i	0.225035	+	1.42082i	0.798702	+	0.601727i	$0.205520\pi$
$673$	5.83791	+	36.8591i	0.225035	+	1.42082i	−0.573667	+	0.819089i	$0.694480\pi$
$674$			1.68471i			0.0648925i
$675$	−10.6446	−	4.60159i	−0.409711	−	0.177115i
$676$	7.96190			0.306227
$677$	4.72961	+	29.8616i	0.181774	+	1.14767i	0.894777	+	0.446513i	$0.147334\pi$
$677$	4.72961	+	29.8616i	0.181774	+	1.14767i	−0.713004	+	0.701160i	$0.752666\pi$
$678$	2.18606	+	1.11385i	0.0839552	+	0.0427773i
$679$	20.8502	+	29.5603i	0.800157	+	1.13442i
$680$	0.277459	−	2.19963i	0.0106401	−	0.0843520i
$681$	−0.132755	+	0.408578i	−0.00508718	+	0.0156567i
$682$	13.9120	+	13.9120i	0.532717	+	0.532717i
$683$	−20.4431	+	10.4163i	−0.782235	+	0.398569i	−0.799031	−	0.601290i	$-0.794654\pi$
$683$	−20.4431	+	10.4163i	−0.782235	+	0.398569i	0.0167956	+	0.999859i	$0.494654\pi$
$684$	17.7036	−	12.8624i	0.676912	−	0.491806i
$685$	−12.6340	−	35.0716i	−0.482719	−	1.34002i
$686$	17.8388	−	4.97770i	0.681088	−	0.190050i
$687$	0.356054	−	2.24804i	0.0135843	−	0.0857679i
$688$	10.7376	+	1.70066i	0.409366	+	0.0648372i
$689$	4.85299	+	3.52590i	0.184884	+	0.134326i
$690$	1.68709	+	4.68332i	0.0642264	+	0.178291i
$691$	−3.67568	−	5.05914i	−0.139829	−	0.192459i	0.733359	−	0.679842i	$-0.237952\pi$
$691$	−3.67568	−	5.05914i	−0.139829	−	0.192459i	−0.873188	+	0.487383i	$0.837952\pi$
$692$	−3.93240	+	2.00366i	−0.149487	+	0.0761676i
$693$	16.0269	+	8.45107i	0.608810	+	0.321029i
$694$	−4.38801	−	1.42575i	−0.166567	−	0.0541208i
$695$	23.9597	+	3.02225i	0.908842	+	0.114640i
$696$	0.0248622	−	0.00807821i	0.000942399	−	0.000306204i
$697$	−10.6386	−	5.42065i	−0.402967	−	0.205322i
$698$	−30.7314	+	4.86738i	−1.16320	+	0.184233i
$699$	2.52400			0.0954664
$700$	−9.80280	−	8.88286i	−0.370511	−	0.335741i
$701$	−18.0922			−0.683333			−0.341666	−	0.939821i	$-0.610991\pi$
$701$	−18.0922			−0.683333			−0.341666	+	0.939821i	$0.610991\pi$
$702$	5.14180	−	0.814382i	0.194065	−	0.0307369i
$703$	49.0509	+	24.9927i	1.84999	+	0.942616i
$704$	−2.29136	+	0.744509i	−0.0863590	+	0.0280598i
$705$	1.55681	−	3.31000i	0.0586328	−	0.124662i
$706$	3.78175	+	1.22876i	0.142328	+	0.0462452i
$707$	−1.01128	−	0.533256i	−0.0380332	−	0.0200551i
$708$	−5.17511	+	2.63685i	−0.194493	+	0.0990990i
$709$	23.2830	+	32.0463i	0.874410	+	1.20352i	0.977938	+	0.208896i	$0.0669869\pi$
$709$	23.2830	+	32.0463i	0.874410	+	1.20352i	−0.103528	+	0.994627i	$0.533013\pi$
$710$	−20.4376	−	13.8838i	−0.767010	−	0.521049i
$711$	12.7699	+	9.27791i	0.478910	+	0.347949i
$712$	7.57716	+	1.20010i	0.283966	+	0.0449758i
$713$	7.16377	−	45.2302i	0.268285	−	1.69389i
$714$	0.335654	−	0.985811i	0.0125615	−	0.0368931i
$715$	−3.37145	+	11.6127i	−0.126085	+	0.434291i
$716$	−5.27010	+	3.82895i	−0.196953	+	0.143095i
$717$	1.95271	−	0.994954i	0.0729252	−	0.0371572i
$718$	−15.5435	−	15.5435i	−0.580077	−	0.580077i
$719$	−12.1071	+	37.2618i	−0.451518	+	1.38963i	0.423657	+	0.905823i	$0.360746\pi$
$719$	−12.1071	+	37.2618i	−0.451518	+	1.38963i	−0.875175	+	0.483807i	$0.839254\pi$
$720$	−6.24301	+	1.19213i	−0.232663	+	0.0444281i
$721$	3.48027	−	2.45479i	0.129612	−	0.0914212i
$722$	35.8807	+	18.2821i	1.33534	+	0.680390i
$723$	−1.15461	−	7.28994i	−0.0429405	−	0.271116i
$724$	−7.86105			−0.292154
$725$	−0.0817629	+	0.318942i	−0.00303660	+	0.0118452i
$726$			2.06246i			0.0765451i
$727$	−6.71524	−	42.3984i	−0.249054	−	1.57247i	−0.722327	−	0.691552i	$-0.756927\pi$
$727$	−6.71524	−	42.3984i	−0.249054	−	1.57247i	0.473272	−	0.880916i	$-0.343073\pi$
$728$	5.85187	+	1.01110i	0.216885	+	0.0374740i
$729$	17.9355	−	5.82761i	0.664279	−	0.215837i
$730$	−20.3963	+	21.7280i	−0.754899	+	0.804188i
$731$	−10.2514	−	3.33090i	−0.379163	−	0.123198i
$732$	2.25627	−	2.25627i	0.0833942	−	0.0833942i
$733$	11.6744	+	22.9123i	0.431204	+	0.846285i	0.999721	+	0.0236137i	$0.00751716\pi$
$733$	11.6744	+	22.9123i	0.431204	+	0.846285i	−0.568518	+	0.822671i	$0.692483\pi$
$734$	0.404737	−	0.294058i	0.0149391	−	0.0108539i
$735$	−3.67030	−	5.01394i	−0.135381	−	0.184942i
$736$	4.53681	+	3.29618i	0.167229	+	0.121499i
$737$	3.59070	−	22.6708i	0.132265	−	0.835090i
$738$	−5.35464	+	33.8079i	−0.197107	+	1.24449i
$739$	−8.48151	+	11.6738i	−0.311997	+	0.429428i	−0.936003	−	0.351992i	$-0.885504\pi$
$739$	−8.48151	+	11.6738i	−0.311997	+	0.429428i	0.624005	+	0.781420i	$0.285504\pi$
$740$	−9.80242	−	12.6323i	−0.360344	−	0.464373i
$741$	4.03218	+	5.54981i	0.148126	+	0.203877i
$742$	−4.92924	−	5.06937i	−0.180958	−	0.186103i
$743$	0.0323033	+	0.0323033i	0.00118509	+	0.00118509i	0.707699	−	0.706514i	$-0.249733\pi$
$743$	0.0323033	+	0.0323033i	0.00118509	+	0.00118509i	−0.706514	+	0.707699i	$0.749733\pi$
$744$	−3.08314	−	1.00177i	−0.113033	−	0.0367267i
$745$	−11.8369	−	21.5217i	−0.433671	−	0.788495i
$746$	−1.81515	−	5.58646i	−0.0664574	−	0.204535i
$747$	−9.57770	+	18.7973i	−0.350430	+	0.687757i
$748$	2.35939	−	0.373691i	0.0862680	−	0.0136635i
$749$	5.73703	+	18.5367i	0.209627	+	0.677318i
$750$	−1.63156	+	4.12763i	−0.0595761	+	0.150720i
$751$	−19.5678			−0.714040			−0.357020	−	0.934097i	$-0.616207\pi$
$751$	−19.5678			−0.714040			−0.357020	+	0.934097i	$0.616207\pi$
$752$	−0.644616	−	4.06994i	−0.0235067	−	0.148416i
$753$	−2.54601	+	4.99682i	−0.0927817	+	0.182094i
$754$	−0.0456750	−	0.140573i	−0.00166338	−	0.00511937i
$755$	32.4278	−	17.8352i	1.18017	−	0.649091i
$756$	−6.13576	−	0.0859939i	−0.223155	−	0.00312757i
$757$	−28.7110	+	28.7110i	−1.04352	+	1.04352i	−0.0445103	+	0.999009i	$0.514173\pi$
$757$	−28.7110	+	28.7110i	−1.04352	+	1.04352i	−0.999009	+	0.0445103i	$0.985827\pi$
$758$	−9.24390	+	4.71000i	−0.335754	+	0.171075i
$759$	−4.33919	+	3.15261i	−0.157503	+	0.114432i
$760$	−10.5536	−	13.6004i	−0.382820	−	0.493338i
$761$	−17.1480	+	23.6023i	−0.621616	+	0.855581i	−0.997469	−	0.0710981i	$-0.977350\pi$
$761$	−17.1480	+	23.6023i	−0.621616	+	0.855581i	0.375853	+	0.926679i	$0.377350\pi$
$762$	−0.608836	−	0.0964301i	−0.0220558	−	0.00349329i
$763$	10.3932	−	1.49714i	0.376259	−	0.0542000i
$764$	−3.77831	+	5.20039i	−0.136694	+	0.188144i
$765$	6.29864	−	0.199125i	0.227728	−	0.00719937i
$766$	12.3084	+	16.9410i	0.444719	+	0.612103i
$767$	14.9090	+	29.2606i	0.538333	+	1.05654i
$768$	0.280708	−	0.280708i	0.0101292	−	0.0101292i
$769$	12.8297	−	39.4857i	0.462650	−	1.42389i	−0.399263	−	0.916836i	$-0.630734\pi$
$769$	12.8297	−	39.4857i	0.462650	−	1.42389i	0.861914	−	0.507055i	$-0.169266\pi$
$770$	6.24659	−	12.8118i	0.225111	−	0.461706i
$771$	2.70395	+	8.32191i	0.0973804	+	0.299706i
$772$	−9.08585	−	4.62947i	−0.327007	−	0.166618i
$773$	27.4980	−	4.35526i	0.989034	−	0.156648i	0.359103	−	0.933298i	$-0.383083\pi$
$773$	27.4980	−	4.35526i	0.989034	−	0.156648i	0.629932	+	0.776650i	$0.283083\pi$
$774$			30.9010i			1.11071i
$775$	31.4508	−	26.0382i	1.12975	−	0.935320i
$776$		−	13.6724i		−	0.490810i
$777$	−3.31558	−	6.73902i	−0.118946	−	0.241761i
$778$	−2.72452	+	5.34718i	−0.0976789	+	0.191706i
$779$	−88.1729	+	28.6491i	−3.15912	+	1.02646i
$780$	−0.373716	−	1.95709i	−0.0133812	−	0.0700752i
$781$	8.22644	−	25.3184i	0.294365	−	0.905963i
$782$	−3.93161	−	3.93161i	−0.140594	−	0.140594i
$783$	0.0693380	+	0.136084i	0.00247794	+	0.00486323i
$784$	−6.59416	−	2.34884i	−0.235506	−	0.0838872i
$785$	7.40937	+	2.15111i	0.264452	+	0.0767766i
$786$	0.124575	+	0.0905090i	0.00444344	+	0.00322835i
$787$	−29.0185	−	4.59609i	−1.03440	−	0.163833i	−0.383928	−	0.923363i	$-0.625429\pi$
$787$	−29.0185	−	4.59609i	−1.03440	−	0.163833i	−0.650472	+	0.759530i	$0.725429\pi$
$788$	13.2531	+	2.09908i	0.472120	+	0.0747765i
$789$	4.95055	+	3.59678i	0.176244	+	0.128049i
$790$	6.97768	−	10.2715i	0.248255	−	0.365443i
$791$	−9.79567	+	13.0927i	−0.348294	+	0.465524i
$792$	−3.10900	−	6.10175i	−0.110473	−	0.216816i
$793$	−12.7572	−	12.7572i	−0.453021	−	0.453021i
$794$	0.924682	−	2.84588i	0.0328157	−	0.100996i
$795$	−1.00968	+	2.14673i	−0.0358098	+	0.0761367i
$796$	−2.58057	+	0.838478i	−0.0914659	+	0.0297191i
$797$	−9.70731	+	19.0517i	−0.343851	+	0.674845i	−0.996570	−	0.0827550i	$-0.973628\pi$
$797$	−9.70731	+	19.0517i	−0.343851	+	0.674845i	0.652719	+	0.757600i	$0.273628\pi$
$798$	−3.56966	−	7.25546i	−0.126365	−	0.256840i
$799$			4.08565i			0.144540i
$800$	1.09255	+	4.87917i	0.0386273	+	0.172505i
$801$			21.8058i			0.770471i
$802$	−26.1866	+	4.14756i	−0.924682	+	0.146455i
$803$	−28.6100	−	14.5775i	−1.00962	−	0.514429i
$804$	1.16872	+	3.59696i	0.0412177	+	0.126855i
$805$	−32.6714	+	5.76543i	−1.15152	+	0.203205i
$806$	−5.66411	+	17.4323i	−0.199510	+	0.614028i
$807$	−7.05252	+	7.05252i	−0.248260	+	0.248260i
$808$	0.196175	+	0.385016i	0.00690143	+	0.0135448i
$809$	5.04489	+	6.94369i	0.177369	+	0.244127i	0.888440	−	0.458993i	$-0.151790\pi$
$809$	5.04489	+	6.94369i	0.177369	+	0.244127i	−0.711071	+	0.703120i	$0.751790\pi$
$810$	−5.76446	−	16.0020i	−0.202543	−	0.562253i
$811$	−32.2570	+	44.3980i	−1.13270	+	1.55902i	−0.349853	+	0.936805i	$0.613768\pi$
$811$	−32.2570	+	44.3980i	−1.13270	+	1.55902i	−0.782844	+	0.622219i	$0.786232\pi$
$812$	0.0248407	+	0.172445i	0.000871737	+	0.00605165i
$813$	−7.94281	−	1.25802i	−0.278566	−	0.0441206i
$814$	10.1264	−	13.9378i	0.354930	−	0.488520i
$815$	−15.6925	+	5.65296i	−0.549683	+	0.198014i
$816$	−0.318435	+	0.231357i	−0.0111475	+	0.00809910i
$817$	−74.5734	+	37.9970i	−2.60899	+	1.32935i
$818$	−5.21764	+	5.21764i	−0.182431	+	0.182431i
$819$	−0.236551	+	16.8782i	−0.00826576	+	0.589772i
$820$	26.7159	+	3.36991i	0.932958	+	0.117682i
$821$	0.920620	+	2.83338i	0.0321299	+	0.0988855i	0.965835	−	0.259156i	$-0.0834445\pi$
$821$	0.920620	+	2.83338i	0.0321299	+	0.0988855i	−0.933706	+	0.358042i	$0.883444\pi$
$822$	−3.00457	+	5.89680i	−0.104796	+	0.205674i
$823$	5.51998	+	34.8518i	0.192414	+	1.21486i	0.875026	+	0.484076i	$0.160844\pi$
$823$	5.51998	+	34.8518i	0.192414	+	1.21486i	−0.682612	+	0.730781i	$0.739156\pi$
$824$	−1.60971			−0.0560771
$825$	−4.76115	−	0.448260i	−0.165762	−	0.0156064i
$826$	−11.4448	−	36.9789i	−0.398216	−	1.28666i
$827$	30.0847	−	4.76495i	1.04615	−	0.165694i	0.390378	−	0.920655i	$-0.372344\pi$
$827$	30.0847	−	4.76495i	1.04615	−	0.165694i	0.655770	+	0.754961i	$0.272344\pi$
$828$	−7.23645	+	14.2023i	−0.251484	+	0.493565i
$829$	−13.0085	−	40.0360i	−0.451803	−	1.39051i	−0.874847	−	0.484399i	$-0.839038\pi$
$829$	−13.0085	−	40.0360i	−0.451803	−	1.39051i	0.423044	−	0.906109i	$-0.360962\pi$
$830$	15.0182	+	7.06358i	0.521288	+	0.245180i
$831$	−6.55139	−	2.12868i	−0.227265	−	0.0738429i
$832$	−1.58715	−	1.58715i	−0.0550246	−	0.0550246i
$833$	6.09330	+	3.32299i	0.211120	+	0.115135i
$834$	−2.52007	−	3.46858i	−0.0872629	−	0.120107i
$835$	−11.0137	+	16.2127i	−0.381144	+	0.561062i
$836$	10.9024	−	15.0059i	0.377068	−	0.518990i
$837$	2.96286	−	18.7067i	0.102411	−	0.646600i
$838$	−1.19941	+	7.57280i	−0.0414331	+	0.261598i
$839$	19.4823	+	14.1547i	0.672604	+	0.488675i	0.870896	−	0.491468i	$-0.163539\pi$
$839$	19.4823	+	14.1547i	0.672604	+	0.488675i	−0.198292	+	0.980143i	$0.563539\pi$
$840$	0.0413072	+	2.34821i	0.00142523	+	0.0810210i
$841$	−23.4580	+	17.0432i	−0.808896	+	0.587697i
$842$	−6.91729	−	13.5759i	−0.238386	−	0.467858i
$843$	2.90225	−	2.90225i	0.0999588	−	0.0999588i
$844$	−1.01183	−	0.328764i	−0.0348287	−	0.0113165i
$845$	17.4874	−	3.33929i	0.601584	−	0.114875i
$846$	11.1394	−	3.61940i	0.382979	−	0.124438i
$847$	−13.5449	−	2.34033i	−0.465409	−	0.0804148i
$848$	0.418072	+	2.63960i	0.0143566	+	0.0906443i
$849$			5.62051i			0.192895i
$850$	−0.313139	−	4.94760i	−0.0107406	−	0.169701i
$851$	−40.0998			−1.37460
$852$	0.686191	+	4.33244i	0.0235085	+	0.148427i
$853$	−1.20011	−	0.611488i	−0.0410911	−	0.0209369i	0.433324	−	0.901238i	$-0.357340\pi$
$853$	−1.20011	−	0.611488i	−0.0410911	−	0.0209369i	−0.474415	+	0.880301i	$0.657340\pi$
$854$	12.2575	+	17.3780i	0.419443	+	0.594663i
$855$	33.4892	−	35.6758i	1.14531	−	1.22008i
$856$	2.26637	−	6.97516i	0.0774628	−	0.238406i
$857$	5.97285	+	5.97285i	0.204029	+	0.204029i	0.801724	−	0.597695i	$-0.203917\pi$
$857$	5.97285	+	5.97285i	0.204029	+	0.204029i	−0.597695	+	0.801724i	$0.703917\pi$
$858$	1.91281	−	0.974627i	0.0653024	−	0.0332732i
$859$	−1.07502	+	0.781047i	−0.0366792	+	0.0266490i	−0.605974	−	0.795485i	$-0.707216\pi$
$859$	−1.07502	+	0.781047i	−0.0366792	+	0.0266490i	0.569295	+	0.822134i	$0.307216\pi$
$860$	24.2971	−	0.768126i	0.828523	−	0.0261929i
$861$	11.9733	+	4.07672i	0.408048	+	0.138934i
$862$	−5.07817	+	32.0623i	−0.172963	+	1.09205i
$863$	10.5177	+	1.66584i	0.358028	+	0.0567060i	0.332857	−	0.942977i	$-0.391987\pi$
$863$	10.5177	+	1.66584i	0.358028	+	0.0567060i	0.0251702	+	0.999683i	$0.491987\pi$
$864$	1.87638	+	1.36327i	0.0638356	+	0.0463793i
$865$	−7.79670	+	6.05008i	−0.265096	+	0.205709i
$866$	10.9198	+	15.0298i	0.371070	+	0.510734i
$867$	−5.66540	+	2.88666i	−0.192407	+	0.0980363i
$868$	10.0775	−	19.1113i	0.342053	−	0.648681i
$869$	12.7245	+	4.13443i	0.431648	+	0.140251i
$870$	0.0512188	−	0.0281703i	0.00173648	−	0.000955062i
$871$	20.3376	−	6.60808i	0.689112	−	0.223906i
$872$	−3.53624	−	1.80180i	−0.119752	−	0.0610167i
$873$	38.3840	−	6.07943i	1.29910	−	0.205757i
$874$	−43.1727			−1.46034
$875$	−25.2562	−	15.3988i	−0.853817	−	0.520574i
$876$	5.29077			0.178759
$877$	54.4094	−	8.61760i	1.83727	−	0.290996i	0.861173	−	0.508313i	$-0.169731\pi$
$877$	54.4094	−	8.61760i	1.83727	−	0.290996i	0.976101	+	0.217317i	$0.0697306\pi$
$878$	15.6188	+	7.95816i	0.527108	+	0.268575i
$879$	1.62414	−	0.527717i	0.0547810	−	0.0177994i
$880$	−4.72046	+	2.59625i	−0.159127	+	0.0875194i
$881$	17.6061	+	5.72058i	0.593165	+	0.192731i	0.590190	−	0.807264i	$-0.299053\pi$
$881$	17.6061	+	5.72058i	0.593165	+	0.192731i	0.00297554	+	0.999996i	$0.499053\pi$
$882$	3.66207	−	19.5569i	0.123308	−	0.658516i
$883$	−25.8572	+	13.1749i	−0.870163	+	0.443370i	−0.831267	−	0.555873i	$-0.812384\pi$
$883$	−25.8572	+	13.1749i	−0.870163	+	0.443370i	−0.0388956	+	0.999243i	$0.512384\pi$
$884$	1.30811	+	1.80046i	0.0439966	+	0.0605561i
$885$	−10.2606	+	7.96203i	−0.344907	+	0.267641i
$886$	−0.652507	−	0.474074i	−0.0219214	−	0.0159268i
$887$	0.100264	+	0.0158803i	0.00336655	+	0.000533209i	0.158118	−	0.987420i	$-0.449458\pi$
$887$	0.100264	+	0.0158803i	0.00336655	+	0.000533209i	−0.154751	+	0.987954i	$0.549458\pi$
$888$	−0.444070	+	2.80375i	−0.0149020	+	0.0940877i
$889$	1.32415	−	3.88902i	0.0444107	−	0.130434i
$890$	17.1457	−	0.542042i	0.574724	−	0.0181693i
$891$	14.8262	−	10.7719i	0.496696	−	0.360871i
$892$	−11.1638	+	5.68824i	−0.373792	+	0.190457i
$893$	22.4321	+	22.4321i	0.750662	+	0.750662i
$894$	−1.34751	+	4.14722i	−0.0450676	+	0.138704i
$895$	−9.96925	+	10.6202i	−0.333235	+	0.354993i
$896$	1.52498	+	2.16204i	0.0509462	+	0.0722287i
$897$	−4.45223	−	2.26852i	−0.148656	−	0.0757438i
$898$	3.88435	+	24.5248i	0.129622	+	0.818403i
$899$	−0.537748			−0.0179349
$900$	−13.2120	+	5.23675i	−0.440402	+	0.174558i
$901$		−	2.64979i		−	0.0882773i
$902$	4.53871	+	28.6563i	0.151122	+	0.954150i
$903$	11.2517	+	1.94410i	0.374433	+	0.0646957i
$904$	5.87784	−	1.90982i	0.195494	−	0.0635198i
$905$	−17.2659	+	3.29700i	−0.573937	+	0.109596i
$906$	−6.24881	−	2.03036i	−0.207603	−	0.0674543i
$907$	17.7803	−	17.7803i	0.590385	−	0.590385i	−0.347350	−	0.937735i	$-0.612919\pi$
$907$	17.7803	−	17.7803i	0.590385	−	0.590385i	0.937735	+	0.347350i	$0.112919\pi$
$908$	0.491298	+	0.964227i	0.0163043	+	0.0319990i
$909$	−0.993669	+	0.721943i	−0.0329579	+	0.0239453i
$910$	13.2770	−	0.233555i	0.440129	−	0.00774227i
$911$	0.379161	+	0.275477i	0.0125622	+	0.00912696i	0.594049	−	0.804429i	$-0.297529\pi$
$911$	0.379161	+	0.275477i	0.0125622	+	0.00912696i	−0.581486	+	0.813556i	$0.697529\pi$
$912$	−0.478101	+	3.01861i	−0.0158315	+	0.0999562i
$913$	−2.79736	+	17.6618i	−0.0925791	+	0.584522i
$914$	16.5220	−	22.7406i	0.546500	−	0.752193i
$915$	4.00934	−	5.90194i	0.132545	−	0.195112i
$916$	−3.37001	−	4.63843i	−0.111348	−	0.153258i
$917$	−0.735764	+	0.715425i	−0.0242971	+	0.0236254i
$918$	−1.62607	−	1.62607i	−0.0536684	−	0.0536684i
$919$	−9.81429	−	3.18886i	−0.323743	−	0.105191i	0.142636	−	0.989775i	$-0.454442\pi$
$919$	−9.81429	−	3.18886i	−0.323743	−	0.105191i	−0.466380	+	0.884585i	$0.654442\pi$
$920$	11.3470	+	5.33690i	0.374100	+	0.175952i
$921$	−2.57931	−	7.93830i	−0.0849912	−	0.261576i
$922$	17.1665	−	33.6911i	0.565347	−	1.10956i
$923$	24.4960	−	3.87979i	0.806296	−	0.127705i
$924$	−2.41738	+	0.748166i	−0.0795258	+	0.0246129i
$925$	−26.8280	−	23.6342i	−0.882099	−	0.777087i
$926$	19.1667			0.629856
$927$	−0.715760	−	4.51913i	−0.0235086	−	0.148428i
$928$	0.0298957	−	0.0586737i	0.000981376	−	0.00192606i
$929$	2.19517	+	6.75605i	0.0720213	+	0.221659i	0.980587	−	0.196082i	$-0.0628219\pi$
$929$	2.19517	+	6.75605i	0.0720213	+	0.221659i	−0.908566	+	0.417741i	$0.862822\pi$
$930$	−7.19190	−	0.907179i	−0.235832	−	0.0297476i
$931$	51.6998	−	15.2103i	1.69439	−	0.498497i
$932$	4.49577	−	4.49577i	0.147264	−	0.147264i
$933$	7.51284	−	3.82798i	0.245959	−	0.125323i
$934$	−12.5525	+	9.11995i	−0.410731	+	0.298414i
$935$	5.02540	−	1.81032i	0.164348	−	0.0592038i
$936$	3.75006	−	5.16151i	0.122575	−	0.168709i
$937$	−33.8364	−	5.35915i	−1.10539	−	0.175076i	−0.423044	−	0.906109i	$-0.639038\pi$
$937$	−33.8364	−	5.35915i	−1.10539	−	0.175076i	−0.682342	+	0.731033i	$0.739038\pi$
$938$	−24.9487	+	3.59385i	−0.814605	+	0.117343i
$939$	0.233342	−	0.321168i	0.00761483	−	0.0104809i
$940$	−3.12279	−	8.66879i	−0.101854	−	0.282745i
$941$	−6.50345	−	8.95124i	−0.212007	−	0.291802i	0.689749	−	0.724049i	$-0.257721\pi$
$941$	−6.50345	−	8.95124i	−0.212007	−	0.291802i	−0.901755	+	0.432247i	$0.857721\pi$
$942$	−0.621850	−	1.22045i	−0.0202610	−	0.0397644i
$943$	47.7518	−	47.7518i	1.55501	−	1.55501i
$944$	−4.52117	+	13.9147i	−0.147152	+	0.452886i
$945$	−13.5125	+	2.38452i	−0.439563	+	0.0775684i
$946$	8.09387	+	24.9104i	0.263154	+	0.809906i
$947$	−31.6867	−	16.1452i	−1.02968	−	0.524647i	−0.144307	−	0.989533i	$-0.546095\pi$
$947$	−31.6867	−	16.1452i	−1.02968	−	0.524647i	−0.885371	+	0.464886i	$0.846095\pi$
$948$	−2.17739	+	0.344864i	−0.0707182	+	0.0112007i
$949$		−	29.9145i		−	0.971067i
$950$	−28.8839	−	25.4453i	−0.937118	−	0.825556i
$951$			10.3829i			0.336689i
$952$	−1.15806	−	2.35380i	−0.0375331	−	0.0762873i
$953$	11.8874	−	23.3303i	0.385070	−	0.755742i	−0.614377	−	0.789013i	$-0.710593\pi$
$953$	11.8874	−	23.3303i	0.385070	−	0.755742i	0.999446	+	0.0332712i	$0.0105925\pi$
$954$	−7.22455	+	2.34740i	−0.233903	+	0.0759998i
$955$	−6.11751	+	13.0067i	−0.197958	+	0.420887i
$956$	1.70596	−	5.25040i	0.0551746	−	0.169810i
$957$	0.0445354	+	0.0445354i	0.00143963	+	0.00143963i
$958$	−9.95192	−	19.5317i	−0.321532	−	0.631042i
$959$	−35.3170	−	26.4234i	−1.14045	−	0.853255i
$960$	0.498811	−	0.734275i	0.0160991	−	0.0236986i
$961$	28.8703	+	20.9755i	0.931299	+	0.676629i
$962$	15.8527	+	2.51082i	0.511110	+	0.0809519i
$963$	20.5899	+	3.26112i	0.663499	+	0.105088i
$964$	−15.0415	−	10.9283i	−0.484454	−	0.351977i
$965$	−21.8976	−	6.35740i	−0.704910	−	0.204652i
$966$	4.71609	+	3.52847i	0.151738	+	0.113527i
$967$	−15.2906	−	30.0095i	−0.491713	−	0.965042i	−0.994900	−	0.100864i	$-0.967839\pi$
$967$	−15.2906	−	30.0095i	−0.491713	−	0.965042i	0.503187	−	0.864178i	$-0.332161\pi$
$968$	3.67367	+	3.67367i	0.118076	+	0.118076i
$969$	0.936402	−	2.88195i	0.0300816	−	0.0925816i
$970$	−5.73432	−	30.0298i	−0.184118	−	0.964198i
$971$	13.8228	−	4.49129i	0.443594	−	0.144132i	−0.0786992	−	0.996898i	$-0.525077\pi$
$971$	13.8228	−	4.49129i	0.443594	−	0.144132i	0.522293	+	0.852766i	$0.325077\pi$
$972$	−4.52974	+	8.89012i	−0.145292	+	0.285151i
$973$	25.6390	−	12.6143i	0.821949	−	0.404396i
$974$			41.2756i			1.32256i
$975$	−1.64165	−	4.14179i	−0.0525748	−	0.132643i
$976$		−	8.03778i		−	0.257283i
$977$	−51.3090	+	8.12654i	−1.64152	+	0.259991i	−0.907782	−	0.419442i	$-0.862226\pi$
$977$	−51.3090	+	8.12654i	−1.64152	+	0.259991i	−0.733737	+	0.679433i	$0.762226\pi$
$978$	2.63847	+	1.34437i	0.0843689	+	0.0429881i
$979$	5.71158	+	17.5784i	0.182543	+	0.561810i
$980$	−15.4684	−	2.39330i	−0.494121	−	0.0764513i
$981$	3.48601	−	10.7288i	0.111300	−	0.342546i
$982$	−10.3977	+	10.3977i	−0.331804	+	0.331804i
$983$	−16.8826	−	33.1340i	−0.538472	−	1.05681i	−0.986648	−	0.162865i	$-0.947926\pi$
$983$	−16.8826	−	33.1340i	−0.538472	−	1.05681i	0.448177	−	0.893945i	$-0.352074\pi$
$984$	−2.80997	−	3.86759i	−0.0895784	−	0.123294i
$985$	29.9891	−	0.948074i	0.955534	−	0.0302082i
$986$	−0.0383773	+	0.0528218i	−0.00122218	+	0.00168219i
$987$	−0.617078	−	4.28379i	−0.0196418	−	0.136354i
$988$	17.0675	+	2.70323i	0.542990	+	0.0860012i
$989$	35.8342	−	49.3215i	1.13946	−	1.56833i
$990$	−9.38768	−	12.0978i	−0.298360	−	0.384495i
$991$	−0.244732	+	0.177808i	−0.00777417	+	0.00564826i	−0.591666	−	0.806184i	$-0.701529\pi$
$991$	−0.244732	+	0.177808i	−0.00777417	+	0.00564826i	0.583891	+	0.811832i	$0.301529\pi$
$992$	−7.27607	+	3.70734i	−0.231016	+	0.117708i
$993$	−1.40200	+	1.40200i	−0.0444911	+	0.0444911i
$994$	−29.2313	−	0.409682i	−0.927161	−	0.0129943i
$995$	−5.31625	+	2.92393i	−0.168537	+	0.0926949i
$996$	−0.910502	−	2.80224i	−0.0288504	−	0.0887923i
$997$	−1.80476	+	3.54203i	−0.0571572	+	0.112177i	−0.917818	−	0.397001i	$-0.870051\pi$
$997$	−1.80476	+	3.54203i	−0.0571572	+	0.112177i	0.860661	+	0.509179i	$0.170051\pi$
$998$	5.06595	+	31.9851i	0.160360	+	1.01247i
$999$	−16.5848			−0.524721

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.r.a.13.6	yes	160
7.6	odd	2	inner	350.2.r.a.13.5	✓	160
25.2	odd	20	inner	350.2.r.a.27.5	yes	160
175.27	even	20	inner	350.2.r.a.27.6	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.r.a.13.5	✓	160	7.6	odd	2	inner
350.2.r.a.13.6	yes	160	1.1	even	1	trivial
350.2.r.a.27.5	yes	160	25.2	odd	20	inner
350.2.r.a.27.6	yes	160	175.27	even	20	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.r (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 + 0.156434i) q^{2} +(0.353713 + 0.180226i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.95928 - 1.07760i) q^{5} +(-0.377552 - 0.122674i) q^{6} +(1.23406 - 2.34032i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-1.67072 - 2.29955i) q^{9} +O(q^{10})\)	\(q+(-0.987688 + 0.156434i) q^{2} +(0.353713 + 0.180226i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.95928 - 1.07760i) q^{5} +(-0.377552 - 0.122674i) q^{6} +(1.23406 - 2.34032i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-1.67072 - 2.29955i) q^{9} +(-1.76658 + 1.37083i) q^{10} +(-1.94915 - 1.41614i) q^{11} +(0.392094 + 0.0621016i) q^{12} +(0.351128 - 2.21694i) q^{13} +(-0.852764 + 2.50455i) q^{14} +(0.887235 - 0.0280490i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-0.883433 + 0.450132i) q^{17} +(2.00988 + 2.00988i) q^{18} +(-2.37903 + 7.32189i) q^{19} +(1.53039 - 1.63031i) q^{20} +(0.858291 - 0.605391i) q^{21} +(2.14669 + 1.09379i) q^{22} +(-0.877254 - 5.53876i) q^{23} -0.396982 q^{24} +(2.67755 - 4.22264i) q^{25} +2.24457i q^{26} +(-0.362823 - 2.29077i) q^{27} +(0.450467 - 2.60712i) q^{28} +(-0.0626281 + 0.0203491i) q^{29} +(-0.871923 + 0.166498i) q^{30} +(7.76645 + 2.52347i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.434215 - 0.852195i) q^{33} +(0.802141 - 0.582789i) q^{34} +(-0.104053 - 5.91516i) q^{35} +(-2.29955 - 1.67072i) q^{36} +(1.11862 - 7.06267i) q^{37} +(1.20434 - 7.60391i) q^{38} +(0.523748 - 0.720878i) q^{39} +(-1.25651 + 1.84964i) q^{40} +(7.07833 + 9.74248i) q^{41} +(-0.753020 + 0.732204i) q^{42} +(7.68725 + 7.68725i) q^{43} +(-2.29136 - 0.744509i) q^{44} +(-5.75142 - 2.70510i) q^{45} +(1.73291 + 5.33334i) q^{46} +(1.87075 - 3.67155i) q^{47} +(0.392094 - 0.0621016i) q^{48} +(-3.95417 - 5.77620i) q^{49} +(-1.98402 + 4.58952i) q^{50} -0.393607 q^{51} +(-0.351128 - 2.21694i) q^{52} +(-1.21329 + 2.38122i) q^{53} +(0.716712 + 2.20581i) q^{54} +(-5.34497 - 0.674208i) q^{55} +(-0.0370771 + 2.64549i) q^{56} +(-2.16109 + 2.16109i) q^{57} +(0.0586737 - 0.0298957i) q^{58} +(-11.8366 + 8.59978i) q^{59} +(0.835143 - 0.300847i) q^{60} +(4.72449 - 6.50270i) q^{61} +(-8.06559 - 1.27746i) q^{62} +(-7.44347 + 1.07223i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-1.70102 - 4.72198i) q^{65} +(0.562182 + 0.773777i) q^{66} +(4.32520 + 8.48868i) q^{67} +(-0.701097 + 0.701097i) q^{68} +(0.687932 - 2.11724i) q^{69} +(1.02811 + 5.82606i) q^{70} +(3.41448 + 10.5087i) q^{71} +(2.53260 + 1.29043i) q^{72} +(13.1634 - 2.08488i) q^{73} +7.15071i q^{74} +(1.70811 - 1.01104i) q^{75} +7.69869i q^{76} +(-5.71960 + 2.81402i) q^{77} +(-0.404530 + 0.793935i) q^{78} +(-5.28143 + 1.71604i) q^{79} +(0.951692 - 2.02343i) q^{80} +(-2.35053 + 7.23420i) q^{81} +(-8.51524 - 8.51524i) q^{82} +(-3.36957 - 6.61316i) q^{83} +(0.629207 - 0.840987i) q^{84} +(-1.24583 + 1.83392i) q^{85} +(-8.79516 - 6.39006i) q^{86} +(-0.0258198 - 0.00408945i) q^{87} +(2.37962 + 0.376895i) q^{88} +(-6.20646 - 4.50926i) q^{89} +(6.10378 + 1.77207i) q^{90} +(-4.75502 - 3.55759i) q^{91} +(-2.54589 - 4.99659i) q^{92} +(2.29230 + 2.29230i) q^{93} +(-1.27336 + 3.91899i) q^{94} +(3.22890 + 16.9093i) q^{95} +(-0.377552 + 0.122674i) q^{96} +(-6.20713 + 12.1822i) q^{97} +(4.80909 + 5.08652i) q^{98} +6.84816i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{7}+O(q^{10}) \) 160 * q + 8 * q^7	\( 160 q + 8 q^{7} + 16 q^{15} + 40 q^{16} - 8 q^{18} - 24 q^{22} - 32 q^{23} + 12 q^{28} - 40 q^{29} - 56 q^{30} + 28 q^{35} + 40 q^{36} - 32 q^{37} + 40 q^{39} - 112 q^{43} - 32 q^{50} + 112 q^{53} - 152 q^{57} + 16 q^{58} + 8 q^{60} - 100 q^{63} - 8 q^{65} - 16 q^{67} - 56 q^{70} - 8 q^{72} - 144 q^{77} + 40 q^{78} + 40 q^{81} - 60 q^{84} + 48 q^{85} - 16 q^{88} + 8 q^{92} + 56 q^{93} - 104 q^{95} - 32 q^{98}+O(q^{100}) \) 160 * q + 8 * q^7 + 16 * q^15 + 40 * q^16 - 8 * q^18 - 24 * q^22 - 32 * q^23 + 12 * q^28 - 40 * q^29 - 56 * q^30 + 28 * q^35 + 40 * q^36 - 32 * q^37 + 40 * q^39 - 112 * q^43 - 32 * q^50 + 112 * q^53 - 152 * q^57 + 16 * q^58 + 8 * q^60 - 100 * q^63 - 8 * q^65 - 16 * q^67 - 56 * q^70 - 8 * q^72 - 144 * q^77 + 40 * q^78 + 40 * q^81 - 60 * q^84 + 48 * q^85 - 16 * q^88 + 8 * q^92 + 56 * q^93 - 104 * q^95 - 32 * q^98

Introduction

L-functions

Modular forms

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Database

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