LMFDB - Embedded newform 150.2.g.b.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(31,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("150.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.g (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			121.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	150.121
Dual form			150.2.g.b.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.80902 - 1.31433i) q^{5} +(-0.809017 + 0.587785i) q^{6} +2.00000 q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.690983 + 2.12663i) q^{10} +(-1.61803 + 4.97980i) q^{11} +(-0.309017 - 0.951057i) q^{12} +(-1.50000 - 4.61653i) q^{13} +(-0.618034 + 1.90211i) q^{14} +2.23607 q^{15} +(0.309017 + 0.951057i) q^{16} +(-6.35410 + 4.61653i) q^{17} -1.00000 q^{18} +(2.23607 - 1.62460i) q^{19} -2.23607 q^{20} +(1.61803 + 1.17557i) q^{21} +(-4.23607 - 3.07768i) q^{22} +(1.85410 - 5.70634i) q^{23} +1.00000 q^{24} +(1.54508 - 4.75528i) q^{25} +4.85410 q^{26} +(-0.309017 + 0.951057i) q^{27} +(-1.61803 - 1.17557i) q^{28} +(1.11803 + 0.812299i) q^{29} +(-0.690983 + 2.12663i) q^{30} +(-3.00000 + 2.17963i) q^{31} -1.00000 q^{32} +(-4.23607 + 3.07768i) q^{33} +(-2.42705 - 7.46969i) q^{34} +(3.61803 - 2.62866i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-0.663119 - 2.04087i) q^{37} +(0.854102 + 2.62866i) q^{38} +(1.50000 - 4.61653i) q^{39} +(0.690983 - 2.12663i) q^{40} +(-1.88197 - 5.79210i) q^{41} +(-1.61803 + 1.17557i) q^{42} -1.23607 q^{43} +(4.23607 - 3.07768i) q^{44} +(1.80902 + 1.31433i) q^{45} +(4.85410 + 3.52671i) q^{46} +(-3.85410 - 2.80017i) q^{47} +(-0.309017 + 0.951057i) q^{48} -3.00000 q^{49} +(4.04508 + 2.93893i) q^{50} -7.85410 q^{51} +(-1.50000 + 4.61653i) q^{52} +(-6.92705 - 5.03280i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(3.61803 + 11.1352i) q^{55} +(1.61803 - 1.17557i) q^{56} +2.76393 q^{57} +(-1.11803 + 0.812299i) q^{58} +(2.76393 + 8.50651i) q^{59} +(-1.80902 - 1.31433i) q^{60} +(-2.73607 + 8.42075i) q^{61} +(-1.14590 - 3.52671i) q^{62} +(0.618034 + 1.90211i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-8.78115 - 6.37988i) q^{65} +(-1.61803 - 4.97980i) q^{66} +(7.85410 - 5.70634i) q^{67} +7.85410 q^{68} +(4.85410 - 3.52671i) q^{69} +(1.38197 + 4.25325i) q^{70} +(11.4721 + 8.33499i) q^{71} +(0.809017 + 0.587785i) q^{72} +(-0.972136 + 2.99193i) q^{73} +2.14590 q^{74} +(4.04508 - 2.93893i) q^{75} -2.76393 q^{76} +(-3.23607 + 9.95959i) q^{77} +(3.92705 + 2.85317i) q^{78} +(1.80902 + 1.31433i) q^{80} +(-0.809017 + 0.587785i) q^{81} +6.09017 q^{82} +(-4.85410 + 3.52671i) q^{83} +(-0.618034 - 1.90211i) q^{84} +(-5.42705 + 16.7027i) q^{85} +(0.381966 - 1.17557i) q^{86} +(0.427051 + 1.31433i) q^{87} +(1.61803 + 4.97980i) q^{88} +(0.427051 - 1.31433i) q^{89} +(-1.80902 + 1.31433i) q^{90} +(-3.00000 - 9.23305i) q^{91} +(-4.85410 + 3.52671i) q^{92} -3.70820 q^{93} +(3.85410 - 2.80017i) q^{94} +(1.90983 - 5.87785i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(11.2082 + 8.14324i) q^{97} +(0.927051 - 2.85317i) q^{98} -5.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{3} - q^{4} + 5 q^{5} - q^{6} + 8 q^{7} + q^{8} - q^{9} + 5 q^{10} - 2 q^{11} + q^{12} - 6 q^{13} + 2 q^{14} - q^{16} - 12 q^{17} - 4 q^{18} + 2 q^{21} - 8 q^{22} - 6 q^{23} + 4 q^{24}+ \cdots - 12 q^{99}+O(q^{100}) $ 4 * q + q^2 + q^3 - q^4 + 5 * q^5 - q^6 + 8 * q^7 + q^8 - q^9 + 5 * q^10 - 2 * q^11 + q^12 - 6 * q^13 + 2 * q^14 - q^16 - 12 * q^17 - 4 * q^18 + 2 * q^21 - 8 * q^22 - 6 * q^23 + 4 * q^24 - 5 * q^25 + 6 * q^26 + q^27 - 2 * q^28 - 5 * q^30 - 12 * q^31 - 4 * q^32 - 8 * q^33 - 3 * q^34 + 10 * q^35 - q^36 + 13 * q^37 - 10 * q^38 + 6 * q^39 + 5 * q^40 - 12 * q^41 - 2 * q^42 + 4 * q^43 + 8 * q^44 + 5 * q^45 + 6 * q^46 - 2 * q^47 + q^48 - 12 * q^49 + 5 * q^50 - 18 * q^51 - 6 * q^52 - 21 * q^53 - q^54 + 10 * q^55 + 2 * q^56 + 20 * q^57 + 20 * q^59 - 5 * q^60 - 2 * q^61 - 18 * q^62 - 2 * q^63 - q^64 - 15 * q^65 - 2 * q^66 + 18 * q^67 + 18 * q^68 + 6 * q^69 + 10 * q^70 + 28 * q^71 + q^72 + 14 * q^73 + 22 * q^74 + 5 * q^75 - 20 * q^76 - 4 * q^77 + 9 * q^78 + 5 * q^80 - q^81 + 2 * q^82 - 6 * q^83 + 2 * q^84 - 15 * q^85 + 6 * q^86 - 5 * q^87 + 2 * q^88 - 5 * q^89 - 5 * q^90 - 12 * q^91 - 6 * q^92 + 12 * q^93 + 2 * q^94 + 30 * q^95 - q^96 + 18 * q^97 - 3 * q^98 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	1.80902	−	1.31433i	0.809017	−	0.587785i
$5$	1.80902	−	1.31433i	0.809017	−	0.587785i
$6$	−0.809017	+	0.587785i	−0.330280	+	0.239962i
$7$	2.00000			0.755929			0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000			0.755929			0.377964	+	0.925820i	$0.376624\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	0.690983	+	2.12663i	0.218508	+	0.672499i
$11$	−1.61803	+	4.97980i	−0.487856	+	1.50147i	0.339946	+	0.940445i	$0.389591\pi$
$11$	−1.61803	+	4.97980i	−0.487856	+	1.50147i	−0.827802	+	0.561020i	$0.810409\pi$
$12$	−0.309017	−	0.951057i	−0.0892055	−	0.274546i
$13$	−1.50000	−	4.61653i	−0.416025	−	1.28039i	−0.911331	−	0.411675i	$-0.864944\pi$
$13$	−1.50000	−	4.61653i	−0.416025	−	1.28039i	0.495306	−	0.868719i	$-0.335056\pi$
$14$	−0.618034	+	1.90211i	−0.165177	+	0.508361i
$15$	2.23607			0.577350
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−6.35410	+	4.61653i	−1.54110	+	1.11967i	−0.591452	+	0.806340i	$0.701445\pi$
$17$	−6.35410	+	4.61653i	−1.54110	+	1.11967i	−0.949644	+	0.313332i	$0.898555\pi$
$18$	−1.00000			−0.235702
$19$	2.23607	−	1.62460i	0.512989	−	0.372708i	−0.300967	−	0.953635i	$-0.597309\pi$
$19$	2.23607	−	1.62460i	0.512989	−	0.372708i	0.813956	+	0.580926i	$0.197309\pi$
$20$	−2.23607			−0.500000
$21$	1.61803	+	1.17557i	0.353084	+	0.256531i
$22$	−4.23607	−	3.07768i	−0.903133	−	0.656164i
$23$	1.85410	−	5.70634i	0.386607	−	1.18985i	−0.548701	−	0.836019i	$-0.684877\pi$
$23$	1.85410	−	5.70634i	0.386607	−	1.18985i	0.935308	−	0.353835i	$-0.115123\pi$
$24$	1.00000			0.204124
$25$	1.54508	−	4.75528i	0.309017	−	0.951057i
$26$	4.85410			0.951968
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−1.61803	−	1.17557i	−0.305780	−	0.222162i
$29$	1.11803	+	0.812299i	0.207614	+	0.150840i	0.686733	−	0.726909i	$-0.259044\pi$
$29$	1.11803	+	0.812299i	0.207614	+	0.150840i	−0.479120	+	0.877750i	$0.659044\pi$
$30$	−0.690983	+	2.12663i	−0.126156	+	0.388267i
$31$	−3.00000	+	2.17963i	−0.538816	+	0.391473i	−0.823645	−	0.567106i	$-0.808063\pi$
$31$	−3.00000	+	2.17963i	−0.538816	+	0.391473i	0.284829	+	0.958578i	$0.408063\pi$
$32$	−1.00000			−0.176777
$33$	−4.23607	+	3.07768i	−0.737405	+	0.535756i
$34$	−2.42705	−	7.46969i	−0.416236	−	1.28104i
$35$	3.61803	−	2.62866i	0.611559	−	0.444324i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	−0.663119	−	2.04087i	−0.109016	−	0.335517i	0.881636	−	0.471930i	$-0.156443\pi$
$37$	−0.663119	−	2.04087i	−0.109016	−	0.335517i	−0.990652	+	0.136413i	$0.956443\pi$
$38$	0.854102	+	2.62866i	0.138554	+	0.426424i
$39$	1.50000	−	4.61653i	0.240192	−	0.739236i
$40$	0.690983	−	2.12663i	0.109254	−	0.336249i
$41$	−1.88197	−	5.79210i	−0.293914	−	0.904573i	−0.983584	−	0.180450i	$-0.942245\pi$
$41$	−1.88197	−	5.79210i	−0.293914	−	0.904573i	0.689670	−	0.724123i	$-0.257755\pi$
$42$	−1.61803	+	1.17557i	−0.249668	+	0.181394i
$43$	−1.23607			−0.188499			−0.0942493	−	0.995549i	$-0.530045\pi$
$43$	−1.23607			−0.188499			−0.0942493	+	0.995549i	$0.530045\pi$
$44$	4.23607	−	3.07768i	0.638611	−	0.463978i
$45$	1.80902	+	1.31433i	0.269672	+	0.195928i
$46$	4.85410	+	3.52671i	0.715698	+	0.519985i
$47$	−3.85410	−	2.80017i	−0.562179	−	0.408447i	0.270077	−	0.962839i	$-0.412951\pi$
$47$	−3.85410	−	2.80017i	−0.562179	−	0.408447i	−0.832256	+	0.554392i	$0.812951\pi$
$48$	−0.309017	+	0.951057i	−0.0446028	+	0.137273i
$49$	−3.00000			−0.428571
$50$	4.04508	+	2.93893i	0.572061	+	0.415627i
$51$	−7.85410			−1.09979
$52$	−1.50000	+	4.61653i	−0.208013	+	0.640197i
$53$	−6.92705	−	5.03280i	−0.951504	−	0.691308i	−0.000341607	−	1.00000i	$-0.500109\pi$
$53$	−6.92705	−	5.03280i	−0.951504	−	0.691308i	−0.951162	+	0.308692i	$0.900109\pi$
$54$	−0.809017	−	0.587785i	−0.110093	−	0.0799874i
$55$	3.61803	+	11.1352i	0.487856	+	1.50147i
$56$	1.61803	−	1.17557i	0.216219	−	0.157092i
$57$	2.76393			0.366092
$58$	−1.11803	+	0.812299i	−0.146805	+	0.106660i
$59$	2.76393	+	8.50651i	0.359833	+	1.10745i	0.953154	+	0.302487i	$0.0978167\pi$
$59$	2.76393	+	8.50651i	0.359833	+	1.10745i	−0.593320	+	0.804966i	$0.702183\pi$
$60$	−1.80902	−	1.31433i	−0.233543	−	0.169679i
$61$	−2.73607	+	8.42075i	−0.350318	+	1.07817i	0.608357	+	0.793663i	$0.291829\pi$
$61$	−2.73607	+	8.42075i	−0.350318	+	1.07817i	−0.958675	+	0.284504i	$0.908171\pi$
$62$	−1.14590	−	3.52671i	−0.145529	−	0.447893i
$63$	0.618034	+	1.90211i	0.0778650	+	0.239644i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−8.78115	−	6.37988i	−1.08917	−	0.791327i
$66$	−1.61803	−	4.97980i	−0.199166	−	0.612971i
$67$	7.85410	−	5.70634i	0.959531	−	0.697140i	0.00648944	−	0.999979i	$-0.497934\pi$
$67$	7.85410	−	5.70634i	0.959531	−	0.697140i	0.953042	+	0.302839i	$0.0979343\pi$
$68$	7.85410			0.952450
$69$	4.85410	−	3.52671i	0.584365	−	0.424566i
$70$	1.38197	+	4.25325i	0.165177	+	0.508361i
$71$	11.4721	+	8.33499i	1.36149	+	0.989182i	0.998348	+	0.0574487i	$0.0182966\pi$
$71$	11.4721	+	8.33499i	1.36149	+	0.989182i	0.363144	+	0.931733i	$0.381703\pi$
$72$	0.809017	+	0.587785i	0.0953436	+	0.0692712i
$73$	−0.972136	+	2.99193i	−0.113780	+	0.350179i	−0.991691	−	0.128646i	$-0.958937\pi$
$73$	−0.972136	+	2.99193i	−0.113780	+	0.350179i	0.877911	+	0.478824i	$0.158937\pi$
$74$	2.14590			0.249456
$75$	4.04508	−	2.93893i	0.467086	−	0.339358i
$76$	−2.76393			−0.317045
$77$	−3.23607	+	9.95959i	−0.368784	+	1.13500i
$78$	3.92705	+	2.85317i	0.444651	+	0.323058i
$79$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$79$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$80$	1.80902	+	1.31433i	0.202254	+	0.146946i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	6.09017			0.672547
$83$	−4.85410	+	3.52671i	−0.532807	+	0.387107i	−0.821407	−	0.570343i	$-0.806810\pi$
$83$	−4.85410	+	3.52671i	−0.532807	+	0.387107i	0.288600	+	0.957450i	$0.406810\pi$
$84$	−0.618034	−	1.90211i	−0.0674330	−	0.207538i
$85$	−5.42705	+	16.7027i	−0.588646	+	1.81167i
$86$	0.381966	−	1.17557i	0.0411885	−	0.126765i
$87$	0.427051	+	1.31433i	0.0457847	+	0.140911i
$88$	1.61803	+	4.97980i	0.172483	+	0.530848i
$89$	0.427051	−	1.31433i	0.0452673	−	0.139318i	−0.925868	−	0.377846i	$-0.876665\pi$
$89$	0.427051	−	1.31433i	0.0452673	−	0.139318i	0.971136	+	0.238528i	$0.0766648\pi$
$90$	−1.80902	+	1.31433i	−0.190687	+	0.138542i
$91$	−3.00000	−	9.23305i	−0.314485	−	0.967887i
$92$	−4.85410	+	3.52671i	−0.506075	+	0.367685i
$93$	−3.70820			−0.384523
$94$	3.85410	−	2.80017i	0.397520	−	0.288815i
$95$	1.90983	−	5.87785i	0.195944	−	0.603055i
$96$	−0.809017	−	0.587785i	−0.0825700	−	0.0599906i
$97$	11.2082	+	8.14324i	1.13802	+	0.826820i	0.986842	−	0.161686i	$-0.0516932\pi$
$97$	11.2082	+	8.14324i	1.13802	+	0.826820i	0.151178	+	0.988506i	$0.451693\pi$
$98$	0.927051	−	2.85317i	0.0936463	−	0.288214i
$99$	−5.23607			−0.526245
$100$	−4.04508	+	2.93893i	−0.404508	+	0.293893i
$101$	1.67376			0.166546			0.0832728	−	0.996527i	$-0.473463\pi$
$101$	1.67376			0.166546			0.0832728	+	0.996527i	$0.473463\pi$
$102$	2.42705	−	7.46969i	0.240314	−	0.739610i
$103$	1.85410	+	1.34708i	0.182690	+	0.132732i	0.675372	−	0.737478i	$-0.263983\pi$
$103$	1.85410	+	1.34708i	0.182690	+	0.132732i	−0.492682	+	0.870210i	$0.663983\pi$
$104$	−3.92705	−	2.85317i	−0.385079	−	0.279776i
$105$	4.47214			0.436436
$106$	6.92705	−	5.03280i	0.672815	−	0.488828i
$107$	10.9443			1.05802			0.529011	−	0.848615i	$-0.322563\pi$
$107$	10.9443			1.05802			0.529011	+	0.848615i	$0.322563\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	0.791796	+	2.43690i	0.0758403	+	0.233412i	0.981789	−	0.189975i	$-0.0608408\pi$
$109$	0.791796	+	2.43690i	0.0758403	+	0.233412i	−0.905949	+	0.423388i	$0.860841\pi$
$110$	−11.7082			−1.11633
$111$	0.663119	−	2.04087i	0.0629405	−	0.193711i
$112$	0.618034	+	1.90211i	0.0583987	+	0.179733i
$113$	−3.57295	−	10.9964i	−0.336115	−	1.03445i	−0.966170	−	0.257905i	$-0.916968\pi$
$113$	−3.57295	−	10.9964i	−0.336115	−	1.03445i	0.630056	−	0.776550i	$-0.283032\pi$
$114$	−0.854102	+	2.62866i	−0.0799940	+	0.246196i
$115$	−4.14590	−	12.7598i	−0.386607	−	1.18985i
$116$	−0.427051	−	1.31433i	−0.0396507	−	0.122032i
$117$	3.92705	−	2.85317i	0.363056	−	0.263776i
$118$	−8.94427			−0.823387
$119$	−12.7082	+	9.23305i	−1.16496	+	0.846392i
$120$	1.80902	−	1.31433i	0.165140	−	0.119981i
$121$	−13.2812	−	9.64932i	−1.20738	−	0.877211i
$122$	−7.16312	−	5.20431i	−0.648518	−	0.471176i
$123$	1.88197	−	5.79210i	0.169691	−	0.522256i
$124$	3.70820			0.333007
$125$	−3.45492	−	10.6331i	−0.309017	−	0.951057i
$126$	−2.00000			−0.178174
$127$	0.0901699	−	0.277515i	0.00800129	−	0.0246254i	−0.946976	−	0.321304i	$-0.895879\pi$
$127$	0.0901699	−	0.277515i	0.00800129	−	0.0246254i	0.954977	+	0.296678i	$0.0958789\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−1.00000	−	0.726543i	−0.0880451	−	0.0639685i
$130$	8.78115	−	6.37988i	0.770158	−	0.559553i
$131$	0.618034	−	0.449028i	0.0539979	−	0.0392318i	−0.560459	−	0.828182i	$-0.689375\pi$
$131$	0.618034	−	0.449028i	0.0539979	−	0.0392318i	0.614457	+	0.788950i	$0.289375\pi$
$132$	5.23607			0.455741
$133$	4.47214	−	3.24920i	0.387783	−	0.281741i
$134$	3.00000	+	9.23305i	0.259161	+	0.797614i
$135$	0.690983	+	2.12663i	0.0594703	+	0.183031i
$136$	−2.42705	+	7.46969i	−0.208118	+	0.640521i
$137$	−4.64590	−	14.2986i	−0.396926	−	1.22161i	−0.927452	−	0.373943i	$-0.878005\pi$
$137$	−4.64590	−	14.2986i	−0.396926	−	1.22161i	0.530526	−	0.847669i	$-0.321995\pi$
$138$	1.85410	+	5.70634i	0.157832	+	0.485756i
$139$	−4.14590	+	12.7598i	−0.351650	+	1.08227i	0.606276	+	0.795254i	$0.292663\pi$
$139$	−4.14590	+	12.7598i	−0.351650	+	1.08227i	−0.957926	+	0.287014i	$0.907337\pi$
$140$	−4.47214			−0.377964
$141$	−1.47214	−	4.53077i	−0.123976	−	0.381560i
$142$	−11.4721	+	8.33499i	−0.962720	+	0.699457i
$143$	25.4164			2.12543
$144$	−0.809017	+	0.587785i	−0.0674181	+	0.0489821i
$145$	3.09017			0.256625
$146$	−2.54508	−	1.84911i	−0.210633	−	0.153034i
$147$	−2.42705	−	1.76336i	−0.200180	−	0.145439i
$148$	−0.663119	+	2.04087i	−0.0545080	+	0.167759i
$149$	7.03444			0.576284			0.288142	−	0.957588i	$-0.406962\pi$
$149$	7.03444			0.576284			0.288142	+	0.957588i	$0.406962\pi$
$150$	1.54508	+	4.75528i	0.126156	+	0.388267i
$151$	−6.94427			−0.565117			−0.282558	−	0.959250i	$-0.591183\pi$
$151$	−6.94427			−0.565117			−0.282558	+	0.959250i	$0.591183\pi$
$152$	0.854102	−	2.62866i	0.0692768	−	0.213212i
$153$	−6.35410	−	4.61653i	−0.513699	−	0.373224i
$154$	−8.47214	−	6.15537i	−0.682704	−	0.496014i
$155$	−2.56231	+	7.88597i	−0.205809	+	0.633416i
$156$	−3.92705	+	2.85317i	−0.314416	+	0.228436i
$157$	17.8541			1.42491			0.712456	−	0.701717i	$-0.247583\pi$
$157$	17.8541			1.42491			0.712456	+	0.701717i	$0.247583\pi$
$158$		0			0
$159$	−2.64590	−	8.14324i	−0.209833	−	0.645801i
$160$	−1.80902	+	1.31433i	−0.143015	+	0.103907i
$161$	3.70820	−	11.4127i	0.292247	−	0.899445i
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	6.32624	+	19.4702i	0.495509	+	1.52502i	0.816162	+	0.577824i	$0.196098\pi$
$163$	6.32624	+	19.4702i	0.495509	+	1.52502i	−0.320652	+	0.947197i	$0.603902\pi$
$164$	−1.88197	+	5.79210i	−0.146957	+	0.452287i
$165$	−3.61803	+	11.1352i	−0.281664	+	0.866871i
$166$	−1.85410	−	5.70634i	−0.143906	−	0.442898i
$167$	−5.23607	+	3.80423i	−0.405179	+	0.294380i	−0.771647	−	0.636051i	$-0.780567\pi$
$167$	−5.23607	+	3.80423i	−0.405179	+	0.294380i	0.366468	+	0.930431i	$0.380567\pi$
$168$	2.00000			0.154303
$169$	−8.54508	+	6.20837i	−0.657314	+	0.477567i
$170$	−14.2082	−	10.3229i	−1.08972	−	0.791728i
$171$	2.23607	+	1.62460i	0.170996	+	0.124236i
$172$	1.00000	+	0.726543i	0.0762493	+	0.0553983i
$173$	−3.37132	+	10.3759i	−0.256317	+	0.788862i	0.737250	+	0.675620i	$0.236124\pi$
$173$	−3.37132	+	10.3759i	−0.256317	+	0.788862i	−0.993567	+	0.113243i	$0.963876\pi$
$174$	−1.38197			−0.104767
$175$	3.09017	−	9.51057i	0.233595	−	0.718931i
$176$	−5.23607			−0.394683
$177$	−2.76393	+	8.50651i	−0.207750	+	0.639388i
$178$	1.11803	+	0.812299i	0.0838002	+	0.0608844i
$179$	3.09017	+	2.24514i	0.230970	+	0.167810i	0.697251	−	0.716827i	$-0.254406\pi$
$179$	3.09017	+	2.24514i	0.230970	+	0.167810i	−0.466281	+	0.884637i	$0.654406\pi$
$180$	−0.690983	−	2.12663i	−0.0515028	−	0.158509i
$181$	16.2082	−	11.7759i	1.20475	−	0.875299i	0.210003	−	0.977701i	$-0.432653\pi$
$181$	16.2082	−	11.7759i	1.20475	−	0.875299i	0.994743	+	0.102401i	$0.0326526\pi$
$182$	9.70820			0.719620
$183$	−7.16312	+	5.20431i	−0.529513	+	0.384714i
$184$	−1.85410	−	5.70634i	−0.136686	−	0.420677i
$185$	−3.88197	−	2.82041i	−0.285408	−	0.207361i
$186$	1.14590	−	3.52671i	0.0840213	−	0.258591i
$187$	−12.7082	−	39.1118i	−0.929316	−	2.86014i
$188$	1.47214	+	4.53077i	0.107367	+	0.330440i
$189$	−0.618034	+	1.90211i	−0.0449554	+	0.138358i
$190$	5.00000	+	3.63271i	0.362738	+	0.263545i
$191$	−0.236068	−	0.726543i	−0.0170813	−	0.0525708i	0.942153	−	0.335184i	$-0.108799\pi$
$191$	−0.236068	−	0.726543i	−0.0170813	−	0.0525708i	−0.959234	+	0.282614i	$0.908799\pi$
$192$	0.809017	−	0.587785i	0.0583858	−	0.0424197i
$193$	2.38197			0.171458			0.0857288	−	0.996319i	$-0.472678\pi$
$193$	2.38197			0.171458			0.0857288	+	0.996319i	$0.472678\pi$
$194$	−11.2082	+	8.14324i	−0.804702	+	0.584650i
$195$	−3.35410	−	10.3229i	−0.240192	−	0.739236i
$196$	2.42705	+	1.76336i	0.173361	+	0.125954i
$197$	10.7812	+	7.83297i	0.768125	+	0.558076i	0.901392	−	0.433005i	$-0.142547\pi$
$197$	10.7812	+	7.83297i	0.768125	+	0.558076i	−0.133266	+	0.991080i	$0.542547\pi$
$198$	1.61803	−	4.97980i	0.114989	−	0.353899i
$199$	−6.18034			−0.438113			−0.219056	−	0.975712i	$-0.570298\pi$
$199$	−6.18034			−0.438113			−0.219056	+	0.975712i	$0.570298\pi$
$200$	−1.54508	−	4.75528i	−0.109254	−	0.336249i
$201$	9.70820			0.684764
$202$	−0.517221	+	1.59184i	−0.0363915	+	0.112002i
$203$	2.23607	+	1.62460i	0.156941	+	0.114024i
$204$	6.35410	+	4.61653i	0.444876	+	0.323221i
$205$	−11.0172	−	8.00448i	−0.769476	−	0.559057i
$206$	−1.85410	+	1.34708i	−0.129181	+	0.0938558i
$207$	6.00000			0.417029
$208$	3.92705	−	2.85317i	0.272292	−	0.197832i
$209$	4.47214	+	13.7638i	0.309344	+	0.952063i
$210$	−1.38197	+	4.25325i	−0.0953647	+	0.293502i
$211$	−2.47214	+	7.60845i	−0.170189	+	0.523787i	−0.999381	−	0.0351760i	$-0.988801\pi$
$211$	−2.47214	+	7.60845i	−0.170189	+	0.523787i	0.829192	+	0.558963i	$0.188801\pi$
$212$	2.64590	+	8.14324i	0.181721	+	0.559280i
$213$	4.38197	+	13.4863i	0.300247	+	0.924066i
$214$	−3.38197	+	10.4086i	−0.231186	+	0.711519i
$215$	−2.23607	+	1.62460i	−0.152499	+	0.110797i
$216$	0.309017	+	0.951057i	0.0210259	+	0.0647112i
$217$	−6.00000	+	4.35926i	−0.407307	+	0.295926i
$218$	−2.56231			−0.173541
$219$	−2.54508	+	1.84911i	−0.171981	+	0.124951i
$220$	3.61803	−	11.1352i	0.243928	−	0.750733i
$221$	30.8435	+	22.4091i	2.07476	+	1.50740i
$222$	1.73607	+	1.26133i	0.116517	+	0.0846547i
$223$	−0.708204	+	2.17963i	−0.0474248	+	0.145959i	−0.971965	−	0.235127i	$-0.924450\pi$
$223$	−0.708204	+	2.17963i	−0.0474248	+	0.145959i	0.924540	+	0.381085i	$0.124450\pi$
$224$	−2.00000			−0.133631
$225$	5.00000			0.333333
$226$	11.5623			0.769113
$227$	−5.23607	+	16.1150i	−0.347530	+	1.06959i	0.612685	+	0.790327i	$0.290089\pi$
$227$	−5.23607	+	16.1150i	−0.347530	+	1.06959i	−0.960215	+	0.279261i	$0.909911\pi$
$228$	−2.23607	−	1.62460i	−0.148087	−	0.107592i
$229$	19.6353	+	14.2658i	1.29753	+	0.942714i	0.999928	−	0.0119751i	$-0.00381187\pi$
$229$	19.6353	+	14.2658i	1.29753	+	0.942714i	0.297606	+	0.954689i	$0.403812\pi$
$230$	13.4164			0.884652
$231$	−8.47214	+	6.15537i	−0.557426	+	0.404993i
$232$	1.38197			0.0907305
$233$	17.8713	−	12.9843i	1.17079	−	0.850628i	0.179686	−	0.983724i	$-0.442492\pi$
$233$	17.8713	−	12.9843i	1.17079	−	0.850628i	0.991103	+	0.133096i	$0.0424918\pi$
$234$	1.50000	+	4.61653i	0.0980581	+	0.301792i
$235$	−10.6525			−0.694891
$236$	2.76393	−	8.50651i	0.179917	−	0.553727i
$237$		0			0
$238$	−4.85410	−	14.9394i	−0.314645	−	0.968377i
$239$	8.29180	−	25.5195i	0.536352	−	1.65072i	−0.204358	−	0.978896i	$-0.565511\pi$
$239$	8.29180	−	25.5195i	0.536352	−	1.65072i	0.740710	−	0.671825i	$-0.234489\pi$
$240$	0.690983	+	2.12663i	0.0446028	+	0.137273i
$241$	−4.28115	−	13.1760i	−0.275773	−	0.848743i	−0.989014	−	0.147824i	$-0.952773\pi$
$241$	−4.28115	−	13.1760i	−0.275773	−	0.848743i	0.713240	−	0.700919i	$-0.247227\pi$
$242$	13.2812	−	9.64932i	0.853745	−	0.620282i
$243$	−1.00000			−0.0641500
$244$	7.16312	−	5.20431i	0.458572	−	0.333172i
$245$	−5.42705	+	3.94298i	−0.346722	+	0.251908i
$246$	4.92705	+	3.57971i	0.314137	+	0.228234i
$247$	−10.8541	−	7.88597i	−0.690630	−	0.501772i
$248$	−1.14590	+	3.52671i	−0.0727646	+	0.223946i
$249$	−6.00000			−0.380235
$250$	11.1803			0.707107
$251$	−12.4721			−0.787234			−0.393617	−	0.919274i	$-0.628776\pi$
$251$	−12.4721			−0.787234			−0.393617	+	0.919274i	$0.628776\pi$
$252$	0.618034	−	1.90211i	0.0389325	−	0.119822i
$253$	25.4164	+	18.4661i	1.59792	+	1.16095i
$254$	0.236068	+	0.171513i	0.0148122	+	0.0107617i
$255$	−14.2082	+	10.3229i	−0.889752	+	0.646443i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−11.6180			−0.724713			−0.362357	−	0.932040i	$-0.618028\pi$
$257$	−11.6180			−0.724713			−0.362357	+	0.932040i	$0.618028\pi$
$258$	1.00000	−	0.726543i	0.0622573	−	0.0452326i
$259$	−1.32624	−	4.08174i	−0.0824084	−	0.253627i
$260$	3.35410	+	10.3229i	0.208013	+	0.640197i
$261$	−0.427051	+	1.31433i	−0.0264338	+	0.0813548i
$262$	0.236068	+	0.726543i	0.0145843	+	0.0448859i
$263$	0.145898	+	0.449028i	0.00899646	+	0.0276883i	0.955454	−	0.295140i	$-0.0953663\pi$
$263$	0.145898	+	0.449028i	0.00899646	+	0.0276883i	−0.946458	+	0.322828i	$0.895366\pi$
$264$	−1.61803	+	4.97980i	−0.0995831	+	0.306485i
$265$	−19.1459			−1.17612
$266$	1.70820	+	5.25731i	0.104737	+	0.322346i
$267$	1.11803	−	0.812299i	0.0684226	−	0.0497119i
$268$	−9.70820			−0.593023
$269$	1.54508	−	1.12257i	0.0942055	−	0.0684443i	−0.539685	−	0.841867i	$-0.681457\pi$
$269$	1.54508	−	1.12257i	0.0942055	−	0.0684443i	0.633891	+	0.773422i	$0.281457\pi$
$270$	−2.23607			−0.136083
$271$	−22.7984	−	16.5640i	−1.38490	−	1.00619i	−0.996403	−	0.0847417i	$-0.972993\pi$
$271$	−22.7984	−	16.5640i	−1.38490	−	1.00619i	−0.388500	−	0.921449i	$-0.627007\pi$
$272$	−6.35410	−	4.61653i	−0.385274	−	0.279918i
$273$	3.00000	−	9.23305i	0.181568	−	0.558810i
$274$	15.0344			0.908264
$275$	21.1803	+	15.3884i	1.27722	+	0.927957i
$276$	−6.00000			−0.361158
$277$	−6.84346	+	21.0620i	−0.411184	+	1.26549i	0.504437	+	0.863449i	$0.331700\pi$
$277$	−6.84346	+	21.0620i	−0.411184	+	1.26549i	−0.915620	+	0.402044i	$0.868300\pi$
$278$	−10.8541	−	7.88597i	−0.650986	−	0.472969i
$279$	−3.00000	−	2.17963i	−0.179605	−	0.130491i
$280$	1.38197	−	4.25325i	0.0825883	−	0.254181i
$281$	4.92705	−	3.57971i	0.293923	−	0.213548i	−0.431044	−	0.902331i	$-0.641855\pi$
$281$	4.92705	−	3.57971i	0.293923	−	0.213548i	0.724968	+	0.688783i	$0.241855\pi$
$282$	4.76393			0.283688
$283$	−2.61803	+	1.90211i	−0.155626	+	0.113069i	−0.662873	−	0.748732i	$-0.730663\pi$
$283$	−2.61803	+	1.90211i	−0.155626	+	0.113069i	0.507247	+	0.861801i	$0.330663\pi$
$284$	−4.38197	−	13.4863i	−0.260022	−	0.800265i
$285$	5.00000	−	3.63271i	0.296174	−	0.215183i
$286$	−7.85410	+	24.1724i	−0.464423	+	1.42935i
$287$	−3.76393	−	11.5842i	−0.222178	−	0.683793i
$288$	−0.309017	−	0.951057i	−0.0182090	−	0.0560415i
$289$	13.8090	−	42.4998i	0.812295	−	2.49999i
$290$	−0.954915	+	2.93893i	−0.0560745	+	0.172580i
$291$	4.28115	+	13.1760i	0.250966	+	0.772393i
$292$	2.54508	−	1.84911i	0.148940	−	0.108211i
$293$	−28.7984			−1.68242			−0.841209	−	0.540709i	$-0.818156\pi$
$293$	−28.7984			−1.68242			−0.841209	+	0.540709i	$0.818156\pi$
$294$	2.42705	−	1.76336i	0.141548	−	0.102841i
$295$	16.1803	+	11.7557i	0.942056	+	0.684444i
$296$	−1.73607	−	1.26133i	−0.100907	−	0.0733132i
$297$	−4.23607	−	3.07768i	−0.245802	−	0.178585i
$298$	−2.17376	+	6.69015i	−0.125923	+	0.387550i
$299$	−29.1246			−1.68432
$300$	−5.00000			−0.288675
$301$	−2.47214			−0.142492
$302$	2.14590	−	6.60440i	0.123483	−	0.380040i
$303$	1.35410	+	0.983813i	0.0777911	+	0.0565186i
$304$	2.23607	+	1.62460i	0.128247	+	0.0931771i
$305$	6.11803	+	18.8294i	0.350318	+	1.07817i
$306$	6.35410	−	4.61653i	0.363240	−	0.263909i
$307$	−16.2918			−0.929822			−0.464911	−	0.885357i	$-0.653914\pi$
$307$	−16.2918			−0.929822			−0.464911	+	0.885357i	$0.653914\pi$
$308$	8.47214	−	6.15537i	0.482745	−	0.350735i
$309$	0.708204	+	2.17963i	0.0402883	+	0.123995i
$310$	−6.70820	−	4.87380i	−0.381000	−	0.276813i
$311$	−5.76393	+	17.7396i	−0.326843	+	1.00592i	0.643759	+	0.765228i	$0.277374\pi$
$311$	−5.76393	+	17.7396i	−0.326843	+	1.00592i	−0.970602	+	0.240690i	$0.922626\pi$
$312$	−1.50000	−	4.61653i	−0.0849208	−	0.261359i
$313$	−8.14590	−	25.0705i	−0.460433	−	1.41707i	−0.864636	−	0.502399i	$-0.832451\pi$
$313$	−8.14590	−	25.0705i	−0.460433	−	1.41707i	0.404203	−	0.914669i	$-0.367549\pi$
$314$	−5.51722	+	16.9803i	−0.311355	+	0.958252i
$315$	3.61803	+	2.62866i	0.203853	+	0.148108i
$316$		0			0
$317$	5.61803	−	4.08174i	0.315540	−	0.229253i	−0.418730	−	0.908111i	$-0.637525\pi$
$317$	5.61803	−	4.08174i	0.315540	−	0.229253i	0.734270	+	0.678857i	$0.237525\pi$
$318$	8.56231			0.480150
$319$	−5.85410	+	4.25325i	−0.327767	+	0.238137i
$320$	−0.690983	−	2.12663i	−0.0386271	−	0.118882i
$321$	8.85410	+	6.43288i	0.494188	+	0.359048i
$322$	9.70820	+	7.05342i	0.541017	+	0.393072i
$323$	−6.70820	+	20.6457i	−0.373254	+	1.14876i
$324$	1.00000			0.0555556
$325$	−24.2705			−1.34629
$326$	−20.4721			−1.13385
$327$	−0.791796	+	2.43690i	−0.0437864	+	0.134761i
$328$	−4.92705	−	3.57971i	−0.272051	−	0.197657i
$329$	−7.70820	−	5.60034i	−0.424967	−	0.308757i
$330$	−9.47214	−	6.88191i	−0.521424	−	0.378837i
$331$	26.2705	−	19.0866i	1.44396	−	1.04910i	0.456761	−	0.889589i	$-0.349009\pi$
$331$	26.2705	−	19.0866i	1.44396	−	1.04910i	0.987197	−	0.159507i	$-0.0509906\pi$
$332$	6.00000			0.329293
$333$	1.73607	−	1.26133i	0.0951359	−	0.0691203i
$334$	−2.00000	−	6.15537i	−0.109435	−	0.336807i
$335$	6.70820	−	20.6457i	0.366508	−	1.12800i
$336$	−0.618034	+	1.90211i	−0.0337165	+	0.103769i
$337$	8.90983	+	27.4216i	0.485349	+	1.49375i	0.831474	+	0.555563i	$0.187497\pi$
$337$	8.90983	+	27.4216i	0.485349	+	1.49375i	−0.346125	+	0.938188i	$0.612503\pi$
$338$	−3.26393	−	10.0453i	−0.177534	−	0.546395i
$339$	3.57295	−	10.9964i	0.194056	−	0.597243i
$340$	14.2082	−	10.3229i	0.770548	−	0.559836i
$341$	−6.00000	−	18.4661i	−0.324918	−	0.999995i
$342$	−2.23607	+	1.62460i	−0.120913	+	0.0878482i
$343$	−20.0000			−1.07990
$344$	−1.00000	+	0.726543i	−0.0539164	+	0.0391725i
$345$	4.14590	−	12.7598i	0.223208	−	0.686963i
$346$	−8.82624	−	6.41264i	−0.474501	−	0.344746i
$347$	4.23607	+	3.07768i	0.227404	+	0.165219i	0.695653	−	0.718378i	$-0.255115\pi$
$347$	4.23607	+	3.07768i	0.227404	+	0.165219i	−0.468249	+	0.883596i	$0.655115\pi$
$348$	0.427051	−	1.31433i	0.0228923	−	0.0704554i
$349$	14.7984			0.792139			0.396069	−	0.918221i	$-0.370374\pi$
$349$	14.7984			0.792139			0.396069	+	0.918221i	$0.370374\pi$
$350$	8.09017	+	5.87785i	0.432438	+	0.314184i
$351$	4.85410			0.259093
$352$	1.61803	−	4.97980i	0.0862415	−	0.265424i
$353$	−16.5623	−	12.0332i	−0.881523	−	0.640464i	0.0521313	−	0.998640i	$-0.483399\pi$
$353$	−16.5623	−	12.0332i	−0.881523	−	0.640464i	−0.933654	+	0.358177i	$0.883399\pi$
$354$	−7.23607	−	5.25731i	−0.384593	−	0.279423i
$355$	31.7082			1.68290
$356$	−1.11803	+	0.812299i	−0.0592557	+	0.0430518i
$357$	−15.7082			−0.831366
$358$	−3.09017	+	2.24514i	−0.163321	+	0.118659i
$359$	−8.61803	−	26.5236i	−0.454842	−	1.39986i	−0.871320	−	0.490715i	$-0.836736\pi$
$359$	−8.61803	−	26.5236i	−0.454842	−	1.39986i	0.416478	−	0.909146i	$-0.363264\pi$
$360$	2.23607			0.117851
$361$	−3.51064	+	10.8046i	−0.184771	+	0.568666i
$362$	6.19098	+	19.0539i	0.325391	+	1.00145i
$363$	−5.07295	−	15.6129i	−0.266261	−	0.819466i
$364$	−3.00000	+	9.23305i	−0.157243	+	0.483943i
$365$	2.17376	+	6.69015i	0.113780	+	0.350179i
$366$	−2.73607	−	8.42075i	−0.143017	−	0.440160i
$367$	10.0902	−	7.33094i	0.526703	−	0.382672i	−0.292420	−	0.956290i	$-0.594461\pi$
$367$	10.0902	−	7.33094i	0.526703	−	0.382672i	0.819123	+	0.573618i	$0.194461\pi$
$368$	6.00000			0.312772
$369$	4.92705	−	3.57971i	0.256492	−	0.186352i
$370$	3.88197	−	2.82041i	0.201814	−	0.146626i
$371$	−13.8541	−	10.0656i	−0.719269	−	0.522580i
$372$	3.00000	+	2.17963i	0.155543	+	0.113008i
$373$	0.798374	−	2.45714i	0.0413382	−	0.127226i	−0.928258	−	0.371938i	$-0.878693\pi$
$373$	0.798374	−	2.45714i	0.0413382	−	0.127226i	0.969596	+	0.244712i	$0.0786934\pi$
$374$	41.1246			2.12650
$375$	3.45492	−	10.6331i	0.178411	−	0.549093i
$376$	−4.76393			−0.245681
$377$	2.07295	−	6.37988i	0.106762	−	0.328581i
$378$	−1.61803	−	1.17557i	−0.0832227	−	0.0604648i
$379$	2.76393	+	2.00811i	0.141974	+	0.103150i	0.656505	−	0.754322i	$-0.272034\pi$
$379$	2.76393	+	2.00811i	0.141974	+	0.103150i	−0.514531	+	0.857472i	$0.672034\pi$
$380$	−5.00000	+	3.63271i	−0.256495	+	0.186354i
$381$	0.236068	−	0.171513i	0.0120941	−	0.00878690i
$382$	0.763932			0.0390862
$383$	−16.5623	+	12.0332i	−0.846294	+	0.614869i	−0.924122	−	0.382098i	$-0.875202\pi$
$383$	−16.5623	+	12.0332i	−0.846294	+	0.614869i	0.0778275	+	0.996967i	$0.475202\pi$
$384$	0.309017	+	0.951057i	0.0157695	+	0.0485334i
$385$	7.23607	+	22.2703i	0.368784	+	1.13500i
$386$	−0.736068	+	2.26538i	−0.0374649	+	0.115305i
$387$	−0.381966	−	1.17557i	−0.0194164	−	0.0597576i
$388$	−4.28115	−	13.1760i	−0.217343	−	0.668912i
$389$	4.93769	−	15.1967i	0.250351	−	0.770501i	−0.744359	−	0.667780i	$-0.767245\pi$
$389$	4.93769	−	15.1967i	0.250351	−	0.770501i	0.994710	−	0.102722i	$-0.0327551\pi$
$390$	10.8541			0.549619
$391$	14.5623	+	44.8182i	0.736447	+	2.26655i
$392$	−2.42705	+	1.76336i	−0.122585	+	0.0890629i
$393$	0.763932			0.0385353
$394$	−10.7812	+	7.83297i	−0.543147	+	0.394619i
$395$		0			0
$396$	4.23607	+	3.07768i	0.212870	+	0.154659i
$397$	−23.3262	−	16.9475i	−1.17071	−	0.850571i	−0.179617	−	0.983737i	$-0.557486\pi$
$397$	−23.3262	−	16.9475i	−1.17071	−	0.850571i	−0.991094	+	0.133166i	$0.957486\pi$
$398$	1.90983	−	5.87785i	0.0957311	−	0.294630i
$399$	5.52786			0.276739
$400$	5.00000			0.250000
$401$	−26.0902			−1.30288			−0.651440	−	0.758700i	$-0.725835\pi$
$401$	−26.0902			−1.30288			−0.651440	+	0.758700i	$0.725835\pi$
$402$	−3.00000	+	9.23305i	−0.149626	+	0.460503i
$403$	14.5623	+	10.5801i	0.725400	+	0.527034i
$404$	−1.35410	−	0.983813i	−0.0673691	−	0.0489465i
$405$	−0.690983	+	2.12663i	−0.0343352	+	0.105673i
$406$	−2.23607	+	1.62460i	−0.110974	+	0.0806275i
$407$	11.2361			0.556951
$408$	−6.35410	+	4.61653i	−0.314575	+	0.228552i
$409$	6.48278	+	19.9519i	0.320553	+	0.986560i	0.973408	+	0.229077i	$0.0735709\pi$
$409$	6.48278	+	19.9519i	0.320553	+	0.986560i	−0.652855	+	0.757483i	$0.726429\pi$
$410$	11.0172	−	8.00448i	0.544102	−	0.395313i
$411$	4.64590	−	14.2986i	0.229165	−	0.705298i
$412$	−0.708204	−	2.17963i	−0.0348907	−	0.107383i
$413$	5.52786	+	17.0130i	0.272008	+	0.837156i
$414$	−1.85410	+	5.70634i	−0.0911241	+	0.280451i
$415$	−4.14590	+	12.7598i	−0.203514	+	0.626352i
$416$	1.50000	+	4.61653i	0.0735436	+	0.226344i
$417$	−10.8541	+	7.88597i	−0.531528	+	0.386177i
$418$	−14.4721			−0.707855
$419$	30.6525	−	22.2703i	1.49747	−	1.08798i	0.526097	−	0.850425i	$-0.323655\pi$
$419$	30.6525	−	22.2703i	1.49747	−	1.08798i	0.971375	−	0.237552i	$-0.0763450\pi$
$420$	−3.61803	−	2.62866i	−0.176542	−	0.128265i
$421$	8.97214	+	6.51864i	0.437275	+	0.317699i	0.784551	−	0.620064i	$-0.212893\pi$
$421$	8.97214	+	6.51864i	0.437275	+	0.317699i	−0.347276	+	0.937763i	$0.612893\pi$
$422$	−6.47214	−	4.70228i	−0.315059	−	0.228904i
$423$	1.47214	−	4.53077i	0.0715777	−	0.220294i
$424$	−8.56231			−0.415822
$425$	12.1353	+	37.3485i	0.588646	+	1.81167i
$426$	−14.1803			−0.687040
$427$	−5.47214	+	16.8415i	−0.264815	+	0.815017i
$428$	−8.85410	−	6.43288i	−0.427979	−	0.310945i
$429$	20.5623	+	14.9394i	0.992757	+	0.721281i
$430$	−0.854102	−	2.62866i	−0.0411885	−	0.126765i
$431$	−3.00000	+	2.17963i	−0.144505	+	0.104989i	−0.657689	−	0.753290i	$-0.728466\pi$
$431$	−3.00000	+	2.17963i	−0.144505	+	0.104989i	0.513184	+	0.858279i	$0.328466\pi$
$432$	−1.00000			−0.0481125
$433$	18.7254	−	13.6048i	0.899886	−	0.653806i	−0.0385504	−	0.999257i	$-0.512274\pi$
$433$	18.7254	−	13.6048i	0.899886	−	0.653806i	0.938437	+	0.345451i	$0.112274\pi$
$434$	−2.29180	−	7.05342i	−0.110010	−	0.338575i
$435$	2.50000	+	1.81636i	0.119866	+	0.0870876i
$436$	0.791796	−	2.43690i	0.0379202	−	0.116706i
$437$	−5.12461	−	15.7719i	−0.245143	−	0.754474i
$438$	−0.972136	−	2.99193i	−0.0464505	−	0.142960i
$439$	−7.76393	+	23.8949i	−0.370552	+	1.14044i	0.575878	+	0.817535i	$0.304660\pi$
$439$	−7.76393	+	23.8949i	−0.370552	+	1.14044i	−0.946431	+	0.322907i	$0.895340\pi$
$440$	9.47214	+	6.88191i	0.451566	+	0.328082i
$441$	−0.927051	−	2.85317i	−0.0441453	−	0.135865i
$442$	−30.8435	+	22.4091i	−1.46707	+	1.06589i
$443$	30.0689			1.42862			0.714308	−	0.699832i	$-0.246742\pi$
$443$	30.0689			1.42862			0.714308	+	0.699832i	$0.246742\pi$
$444$	−1.73607	+	1.26133i	−0.0823901	+	0.0598599i
$445$	−0.954915	−	2.93893i	−0.0452673	−	0.139318i
$446$	−1.85410	−	1.34708i	−0.0877943	−	0.0637863i
$447$	5.69098	+	4.13474i	0.269174	+	0.195567i
$448$	0.618034	−	1.90211i	0.0291994	−	0.0898664i
$449$	4.79837			0.226449			0.113225	−	0.993569i	$-0.463882\pi$
$449$	4.79837			0.226449			0.113225	+	0.993569i	$0.463882\pi$
$450$	−1.54508	+	4.75528i	−0.0728360	+	0.224166i
$451$	31.8885			1.50157
$452$	−3.57295	+	10.9964i	−0.168057	+	0.517227i
$453$	−5.61803	−	4.08174i	−0.263958	−	0.191777i
$454$	−13.7082	−	9.95959i	−0.643358	−	0.467427i
$455$	−17.5623	−	12.7598i	−0.823334	−	0.598187i
$456$	2.23607	−	1.62460i	0.104713	−	0.0760788i
$457$	−12.4721			−0.583422			−0.291711	−	0.956507i	$-0.594225\pi$
$457$	−12.4721			−0.583422			−0.291711	+	0.956507i	$0.594225\pi$
$458$	−19.6353	+	14.2658i	−0.917495	+	0.666599i
$459$	−2.42705	−	7.46969i	−0.113285	−	0.348655i
$460$	−4.14590	+	12.7598i	−0.193303	+	0.594927i
$461$	7.75329	−	23.8622i	0.361107	−	1.11137i	−0.591277	−	0.806469i	$-0.701376\pi$
$461$	7.75329	−	23.8622i	0.361107	−	1.11137i	0.952383	−	0.304903i	$-0.0986241\pi$
$462$	−3.23607	−	9.95959i	−0.150556	−	0.463362i
$463$	−3.79837	−	11.6902i	−0.176525	−	0.543289i	0.823174	−	0.567789i	$-0.192201\pi$
$463$	−3.79837	−	11.6902i	−0.176525	−	0.543289i	−0.999700	+	0.0244992i	$0.992201\pi$
$464$	−0.427051	+	1.31433i	−0.0198253	+	0.0610161i
$465$	−6.70820	+	4.87380i	−0.311086	+	0.226017i
$466$	6.82624	+	21.0090i	0.316219	+	0.973223i
$467$	−12.7984	+	9.29856i	−0.592238	+	0.430286i	−0.843115	−	0.537733i	$-0.819281\pi$
$467$	−12.7984	+	9.29856i	−0.592238	+	0.430286i	0.250877	+	0.968019i	$0.419281\pi$
$468$	−4.85410			−0.224381
$469$	15.7082	−	11.4127i	0.725337	−	0.526989i
$470$	3.29180	−	10.1311i	0.151839	−	0.467313i
$471$	14.4443	+	10.4944i	0.665557	+	0.483555i
$472$	7.23607	+	5.25731i	0.333067	+	0.241987i
$473$	2.00000	−	6.15537i	0.0919601	−	0.283024i
$474$		0			0
$475$	−4.27051	−	13.1433i	−0.195944	−	0.603055i
$476$	15.7082			0.719984
$477$	2.64590	−	8.14324i	0.121147	−	0.372853i
$478$	21.7082	+	15.7719i	0.992910	+	0.721391i
$479$	−3.61803	−	2.62866i	−0.165312	−	0.120106i	0.502053	−	0.864837i	$-0.332578\pi$
$479$	−3.61803	−	2.62866i	−0.165312	−	0.120106i	−0.667366	+	0.744730i	$0.732578\pi$
$480$	−2.23607			−0.102062
$481$	−8.42705	+	6.12261i	−0.384240	+	0.279167i
$482$	13.8541			0.631037
$483$	9.70820	−	7.05342i	0.441739	−	0.320942i
$484$	5.07295	+	15.6129i	0.230589	+	0.709679i
$485$	30.9787			1.40667
$486$	0.309017	−	0.951057i	0.0140173	−	0.0431408i
$487$	3.18034	+	9.78808i	0.144115	+	0.443540i	0.996896	−	0.0787282i	$-0.0250859\pi$
$487$	3.18034	+	9.78808i	0.144115	+	0.443540i	−0.852781	+	0.522268i	$0.825086\pi$
$488$	2.73607	+	8.42075i	0.123856	+	0.381190i
$489$	−6.32624	+	19.4702i	−0.286082	+	0.880471i
$490$	−2.07295	−	6.37988i	−0.0936463	−	0.288214i
$491$	9.23607	+	28.4257i	0.416818	+	1.28283i	0.910615	+	0.413256i	$0.135609\pi$
$491$	9.23607	+	28.4257i	0.416818	+	1.28283i	−0.493797	+	0.869577i	$0.664391\pi$
$492$	−4.92705	+	3.57971i	−0.222129	+	0.161386i
$493$	−10.8541			−0.488844
$494$	10.8541	−	7.88597i	0.488349	−	0.354806i
$495$	−9.47214	+	6.88191i	−0.425741	+	0.309319i
$496$	−3.00000	−	2.17963i	−0.134704	−	0.0978682i
$497$	22.9443	+	16.6700i	1.02919	+	0.747751i
$498$	1.85410	−	5.70634i	0.0830843	−	0.255707i
$499$	−33.4164			−1.49592			−0.747962	−	0.663742i	$-0.768967\pi$
$499$	−33.4164			−1.49592			−0.747962	+	0.663742i	$0.768967\pi$
$500$	−3.45492	+	10.6331i	−0.154508	+	0.475528i
$501$	−6.47214			−0.289154
$502$	3.85410	−	11.8617i	0.172017	−	0.529414i
$503$	−17.4164	−	12.6538i	−0.776559	−	0.564203i	0.127385	−	0.991853i	$-0.459342\pi$
$503$	−17.4164	−	12.6538i	−0.776559	−	0.564203i	−0.903944	+	0.427650i	$0.859342\pi$
$504$	1.61803	+	1.17557i	0.0720730	+	0.0523641i
$505$	3.02786	−	2.19987i	0.134738	−	0.0978930i
$506$	−25.4164	+	18.4661i	−1.12990	+	0.820918i
$507$	−10.5623			−0.469088
$508$	−0.236068	+	0.171513i	−0.0104738	+	0.00760968i
$509$	−4.24671	−	13.0700i	−0.188232	−	0.579319i	0.811757	−	0.583995i	$-0.198511\pi$
$509$	−4.24671	−	13.0700i	−0.188232	−	0.579319i	−0.999989	+	0.00467647i	$0.998511\pi$
$510$	−5.42705	−	16.7027i	−0.240314	−	0.739610i
$511$	−1.94427	+	5.98385i	−0.0860095	+	0.264710i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	0.854102	+	2.62866i	0.0377095	+	0.116058i
$514$	3.59017	−	11.0494i	0.158356	−	0.487368i
$515$	5.12461			0.225817
$516$	0.381966	+	1.17557i	0.0168151	+	0.0517516i
$517$	20.1803	−	14.6619i	0.887530	−	0.644829i
$518$	4.29180			0.188571
$519$	−8.82624	+	6.41264i	−0.387429	+	0.281484i
$520$	−10.8541			−0.475984
$521$	−5.07295	−	3.68571i	−0.222250	−	0.161474i	0.471089	−	0.882086i	$-0.343861\pi$
$521$	−5.07295	−	3.68571i	−0.222250	−	0.161474i	−0.693339	+	0.720612i	$0.743861\pi$
$522$	−1.11803	−	0.812299i	−0.0489350	−	0.0355534i
$523$	−0.708204	+	2.17963i	−0.0309676	+	0.0953085i	−0.965346	−	0.260975i	$-0.915956\pi$
$523$	−0.708204	+	2.17963i	−0.0309676	+	0.0953085i	0.934378	+	0.356283i	$0.115956\pi$
$524$	−0.763932			−0.0333725
$525$	8.09017	−	5.87785i	0.353084	−	0.256531i
$526$	−0.472136			−0.0205861
$527$	9.00000	−	27.6992i	0.392046	−	1.20659i
$528$	−4.23607	−	3.07768i	−0.184351	−	0.133939i
$529$	−10.5172	−	7.64121i	−0.457270	−	0.332226i
$530$	5.91641	−	18.2088i	0.256992	−	0.790941i
$531$	−7.23607	+	5.25731i	−0.314019	+	0.228148i
$532$	−5.52786			−0.239663
$533$	−23.9164	+	17.3763i	−1.03593	+	0.752651i
$534$	0.427051	+	1.31433i	0.0184803	+	0.0568765i
$535$	19.7984	−	14.3844i	0.855958	−	0.621890i
$536$	3.00000	−	9.23305i	0.129580	−	0.398807i
$537$	1.18034	+	3.63271i	0.0509354	+	0.156763i
$538$	0.590170	+	1.81636i	0.0254440	+	0.0783087i
$539$	4.85410	−	14.9394i	0.209081	−	0.643485i
$540$	0.690983	−	2.12663i	0.0297352	−	0.0915155i
$541$	6.57295	+	20.2295i	0.282593	+	0.869732i	0.987110	+	0.160045i	$0.0511639\pi$
$541$	6.57295	+	20.2295i	0.282593	+	0.869732i	−0.704517	+	0.709688i	$0.748836\pi$
$542$	22.7984	−	16.5640i	0.979274	−	0.711484i
$543$	20.0344			0.859760
$544$	6.35410	−	4.61653i	0.272430	−	0.197932i
$545$	4.63525	+	3.36771i	0.198553	+	0.144257i
$546$	7.85410	+	5.70634i	0.336125	+	0.244209i
$547$	−1.61803	−	1.17557i	−0.0691821	−	0.0502638i	0.552657	−	0.833409i	$-0.313614\pi$
$547$	−1.61803	−	1.17557i	−0.0691821	−	0.0502638i	−0.621839	+	0.783145i	$0.713614\pi$
$548$	−4.64590	+	14.2986i	−0.198463	+	0.610806i
$549$	−8.85410			−0.377884
$550$	−21.1803	+	15.3884i	−0.903133	+	0.656164i
$551$	3.81966			0.162723
$552$	1.85410	−	5.70634i	0.0789158	−	0.242878i
$553$		0			0
$554$	−17.9164	−	13.0170i	−0.761195	−	0.553041i
$555$	−1.48278	−	4.56352i	−0.0629405	−	0.193711i
$556$	10.8541	−	7.88597i	0.460316	−	0.334439i
$557$	−27.2705			−1.15549			−0.577744	−	0.816218i	$-0.696067\pi$
$557$	−27.2705			−1.15549			−0.577744	+	0.816218i	$0.696067\pi$
$558$	3.00000	−	2.17963i	0.127000	−	0.0922710i
$559$	1.85410	+	5.70634i	0.0784202	+	0.241352i
$560$	3.61803	+	2.62866i	0.152890	+	0.111081i
$561$	12.7082	−	39.1118i	0.536541	−	1.65130i
$562$	1.88197	+	5.79210i	0.0793859	+	0.244325i
$563$	3.23607	+	9.95959i	0.136384	+	0.419747i	0.995803	−	0.0915256i	$-0.0291743\pi$
$563$	3.23607	+	9.95959i	0.136384	+	0.419747i	−0.859419	+	0.511272i	$0.829174\pi$
$564$	−1.47214	+	4.53077i	−0.0619881	+	0.190780i
$565$	−20.9164	−	15.1967i	−0.879960	−	0.639328i
$566$	−1.00000	−	3.07768i	−0.0420331	−	0.129365i
$567$	−1.61803	+	1.17557i	−0.0679510	+	0.0493693i
$568$	14.1803			0.594994
$569$	−17.2984	+	12.5680i	−0.725186	+	0.526878i	−0.888037	−	0.459772i	$-0.847931\pi$
$569$	−17.2984	+	12.5680i	−0.725186	+	0.526878i	0.162851	+	0.986651i	$0.447931\pi$
$570$	1.90983	+	5.87785i	0.0799940	+	0.246196i
$571$	−27.2705	−	19.8132i	−1.14124	−	0.829156i	−0.153944	−	0.988080i	$-0.549198\pi$
$571$	−27.2705	−	19.8132i	−1.14124	−	0.829156i	−0.987291	+	0.158924i	$0.949198\pi$
$572$	−20.5623	−	14.9394i	−0.859753	−	0.624647i
$573$	0.236068	−	0.726543i	0.00986188	−	0.0303517i
$574$	12.1803			0.508398
$575$	−24.2705	−	17.6336i	−1.01215	−	0.735370i
$576$	1.00000			0.0416667
$577$	8.90983	−	27.4216i	0.370921	−	1.14158i	−0.575268	−	0.817965i	$-0.695102\pi$
$577$	8.90983	−	27.4216i	0.370921	−	1.14158i	0.946190	−	0.323613i	$-0.104898\pi$
$578$	36.1525	+	26.2663i	1.50374	+	1.09253i
$579$	1.92705	+	1.40008i	0.0800855	+	0.0581855i
$580$	−2.50000	−	1.81636i	−0.103807	−	0.0754201i
$581$	−9.70820	+	7.05342i	−0.402764	+	0.292625i
$582$	−13.8541			−0.574271
$583$	36.2705	−	26.3521i	1.50217	−	1.09139i
$584$	0.972136	+	2.99193i	0.0402273	+	0.123807i
$585$	3.35410	−	10.3229i	0.138675	−	0.426798i
$586$	8.89919	−	27.3889i	0.367622	−	1.13142i
$587$	−4.90983	−	15.1109i	−0.202650	−	0.623694i	−0.999802	−	0.0199141i	$-0.993661\pi$
$587$	−4.90983	−	15.1109i	−0.202650	−	0.623694i	0.797151	−	0.603780i	$-0.206339\pi$
$588$	0.927051	+	2.85317i	0.0382309	+	0.117663i
$589$	−3.16718	+	9.74759i	−0.130502	+	0.401642i
$590$	−16.1803	+	11.7557i	−0.666134	+	0.483975i
$591$	4.11803	+	12.6740i	0.169393	+	0.521339i
$592$	1.73607	−	1.26133i	0.0713520	−	0.0518402i
$593$	−6.03444			−0.247805			−0.123902	−	0.992294i	$-0.539541\pi$
$593$	−6.03444			−0.247805			−0.123902	+	0.992294i	$0.539541\pi$
$594$	4.23607	−	3.07768i	0.173808	−	0.126279i
$595$	−10.8541	+	33.4055i	−0.444975	+	1.36949i
$596$	−5.69098	−	4.13474i	−0.233112	−	0.169366i
$597$	−5.00000	−	3.63271i	−0.204636	−	0.148677i
$598$	9.00000	−	27.6992i	0.368037	−	1.13270i
$599$	1.05573			0.0431359			0.0215679	−	0.999767i	$-0.493134\pi$
$599$	1.05573			0.0431359			0.0215679	+	0.999767i	$0.493134\pi$
$600$	1.54508	−	4.75528i	0.0630778	−	0.194134i
$601$	7.32624			0.298843			0.149422	−	0.988774i	$-0.452259\pi$
$601$	7.32624			0.298843			0.149422	+	0.988774i	$0.452259\pi$
$602$	0.763932	−	2.35114i	0.0311355	−	0.0958254i
$603$	7.85410	+	5.70634i	0.319844	+	0.232380i
$604$	5.61803	+	4.08174i	0.228595	+	0.166084i
$605$	−36.7082			−1.49240
$606$	−1.35410	+	0.983813i	−0.0550066	+	0.0399647i
$607$	−1.81966			−0.0738577			−0.0369289	−	0.999318i	$-0.511757\pi$
$607$	−1.81966			−0.0738577			−0.0369289	+	0.999318i	$0.511757\pi$
$608$	−2.23607	+	1.62460i	−0.0906845	+	0.0658862i
$609$	0.854102	+	2.62866i	0.0346100	+	0.106518i
$610$	−19.7984			−0.801613
$611$	−7.14590	+	21.9928i	−0.289092	+	0.889734i
$612$	2.42705	+	7.46969i	0.0981077	+	0.301945i
$613$	−6.66312	−	20.5070i	−0.269121	−	0.828269i	−0.990715	−	0.135953i	$-0.956590\pi$
$613$	−6.66312	−	20.5070i	−0.269121	−	0.828269i	0.721594	−	0.692316i	$-0.243410\pi$
$614$	5.03444	−	15.4944i	0.203174	−	0.625304i
$615$	−4.20820	−	12.9515i	−0.169691	−	0.522256i
$616$	3.23607	+	9.95959i	0.130385	+	0.401283i
$617$	−6.78115	+	4.92680i	−0.272999	+	0.198345i	−0.715858	−	0.698246i	$-0.753964\pi$
$617$	−6.78115	+	4.92680i	−0.272999	+	0.198345i	0.442859	+	0.896591i	$0.353964\pi$
$618$	−2.29180			−0.0921896
$619$	−2.76393	+	2.00811i	−0.111092	+	0.0807129i	−0.641944	−	0.766751i	$-0.721872\pi$
$619$	−2.76393	+	2.00811i	−0.111092	+	0.0807129i	0.530852	+	0.847464i	$0.321872\pi$
$620$	6.70820	−	4.87380i	0.269408	−	0.195736i
$621$	4.85410	+	3.52671i	0.194788	+	0.141522i
$622$	−15.0902	−	10.9637i	−0.605061	−	0.439602i
$623$	0.854102	−	2.62866i	0.0342189	−	0.105315i
$624$	4.85410			0.194320
$625$	−20.2254	−	14.6946i	−0.809017	−	0.587785i
$626$	26.3607			1.05358
$627$	−4.47214	+	13.7638i	−0.178600	+	0.549674i
$628$	−14.4443	−	10.4944i	−0.576389	−	0.418771i
$629$	13.6353	+	9.90659i	0.543673	+	0.395002i
$630$	−3.61803	+	2.62866i	−0.144146	+	0.104728i
$631$	34.8885	−	25.3480i	1.38889	−	1.00909i	0.392905	−	0.919579i	$-0.371470\pi$
$631$	34.8885	−	25.3480i	1.38889	−	1.00909i	0.995986	−	0.0895093i	$-0.0285299\pi$
$632$		0			0
$633$	−6.47214	+	4.70228i	−0.257244	+	0.186899i
$634$	2.14590	+	6.60440i	0.0852245	+	0.262294i
$635$	−0.201626	−	0.620541i	−0.00800129	−	0.0246254i
$636$	−2.64590	+	8.14324i	−0.104917	+	0.322900i
$637$	4.50000	+	13.8496i	0.178296	+	0.548740i
$638$	−2.23607	−	6.88191i	−0.0885268	−	0.272457i
$639$	−4.38197	+	13.4863i	−0.173348	+	0.533510i
$640$	2.23607			0.0883883
$641$	−8.32624	−	25.6255i	−0.328867	−	1.01215i	−0.969665	−	0.244438i	$-0.921397\pi$
$641$	−8.32624	−	25.6255i	−0.328867	−	1.01215i	0.640798	−	0.767709i	$-0.278603\pi$
$642$	−8.85410	+	6.43288i	−0.349444	+	0.253886i
$643$	−39.7771			−1.56866			−0.784328	−	0.620347i	$-0.786992\pi$
$643$	−39.7771			−1.56866			−0.784328	+	0.620347i	$0.786992\pi$
$644$	−9.70820	+	7.05342i	−0.382557	+	0.277944i
$645$	−2.76393			−0.108830
$646$	−17.5623	−	12.7598i	−0.690980	−	0.502026i
$647$	29.0344	+	21.0948i	1.14146	+	0.829320i	0.987322	−	0.158729i	$-0.0507395\pi$
$647$	29.0344	+	21.0948i	1.14146	+	0.829320i	0.154139	+	0.988049i	$0.450739\pi$
$648$	−0.309017	+	0.951057i	−0.0121393	+	0.0373610i
$649$	−46.8328			−1.83835
$650$	7.50000	−	23.0826i	0.294174	−	0.905375i
$651$	−7.41641			−0.290672
$652$	6.32624	−	19.4702i	0.247755	−	0.762510i
$653$	26.0623	+	18.9354i	1.01990	+	0.740998i	0.966262	−	0.257562i	$-0.0829192\pi$
$653$	26.0623	+	18.9354i	1.01990	+	0.740998i	0.0536351	+	0.998561i	$0.482919\pi$
$654$	−2.07295	−	1.50609i	−0.0810587	−	0.0588926i
$655$	0.527864	−	1.62460i	0.0206254	−	0.0634783i
$656$	4.92705	−	3.57971i	0.192369	−	0.139764i
$657$	−3.14590			−0.122733
$658$	7.70820	−	5.60034i	0.300497	−	0.218324i
$659$	12.0344	+	37.0382i	0.468795	+	1.44280i	0.854146	+	0.520033i	$0.174080\pi$
$659$	12.0344	+	37.0382i	0.468795	+	1.44280i	−0.385351	+	0.922770i	$0.625920\pi$
$660$	9.47214	−	6.88191i	0.368702	−	0.267878i
$661$	−7.27051	+	22.3763i	−0.282790	+	0.870338i	0.704262	+	0.709940i	$0.251278\pi$
$661$	−7.27051	+	22.3763i	−0.282790	+	0.870338i	−0.987052	+	0.160398i	$0.948722\pi$
$662$	10.0344	+	30.8828i	0.390000	+	1.20030i
$663$	11.7812	+	36.2587i	0.457542	+	1.40817i
$664$	−1.85410	+	5.70634i	−0.0719531	+	0.221449i
$665$	3.81966	−	11.7557i	0.148120	−	0.455867i
$666$	0.663119	+	2.04087i	0.0256953	+	0.0790821i
$667$	6.70820	−	4.87380i	0.259743	−	0.188714i
$668$	6.47214			0.250414
$669$	−1.85410	+	1.34708i	−0.0716837	+	0.0520813i
$670$	17.5623	+	12.7598i	0.678491	+	0.492953i
$671$	−37.5066	−	27.2501i	−1.44793	−	1.05198i
$672$	−1.61803	−	1.17557i	−0.0624170	−	0.0453486i
$673$	−5.80902	+	17.8783i	−0.223921	+	0.689158i	0.774478	+	0.632601i	$0.218013\pi$
$673$	−5.80902	+	17.8783i	−0.223921	+	0.689158i	−0.998399	+	0.0565578i	$0.981987\pi$
$674$	−28.8328			−1.11060
$675$	4.04508	+	2.93893i	0.155695	+	0.113119i
$676$	10.5623			0.406243
$677$	11.2705	−	34.6871i	0.433161	−	1.33313i	−0.461799	−	0.886985i	$-0.652796\pi$
$677$	11.2705	−	34.6871i	0.433161	−	1.33313i	0.894960	−	0.446147i	$-0.147204\pi$
$678$	9.35410	+	6.79615i	0.359242	+	0.261005i
$679$	22.4164	+	16.2865i	0.860263	+	0.625017i
$680$	5.42705	+	16.7027i	0.208118	+	0.640521i
$681$	−13.7082	+	9.95959i	−0.525300	+	0.381652i
$682$	19.4164			0.743493
$683$	−15.7082	+	11.4127i	−0.601058	+	0.436694i	−0.846254	−	0.532779i	$-0.821148\pi$
$683$	−15.7082	+	11.4127i	−0.601058	+	0.436694i	0.245196	+	0.969473i	$0.421148\pi$
$684$	−0.854102	−	2.62866i	−0.0326574	−	0.100509i
$685$	−27.1976	−	19.7602i	−1.03917	−	0.754998i
$686$	6.18034	−	19.0211i	0.235966	−	0.726230i
$687$	7.50000	+	23.0826i	0.286143	+	0.880657i
$688$	−0.381966	−	1.17557i	−0.0145623	−	0.0448182i
$689$	−12.8435	+	39.5281i	−0.489297	+	1.50590i
$690$	10.8541	+	7.88597i	0.413209	+	0.300214i
$691$	−7.47214	−	22.9969i	−0.284253	−	0.874842i	−0.986621	−	0.163028i	$-0.947874\pi$
$691$	−7.47214	−	22.9969i	−0.284253	−	0.874842i	0.702368	−	0.711814i	$-0.252126\pi$
$692$	8.82624	−	6.41264i	0.335523	−	0.243772i
$693$	−10.4721			−0.397804
$694$	−4.23607	+	3.07768i	−0.160799	+	0.116827i
$695$	9.27051	+	28.5317i	0.351650	+	1.08227i
$696$	1.11803	+	0.812299i	0.0423790	+	0.0307901i
$697$	38.6976	+	28.1154i	1.46577	+	1.06495i
$698$	−4.57295	+	14.0741i	−0.173089	+	0.532712i
$699$	22.0902			0.835527
$700$	−8.09017	+	5.87785i	−0.305780	+	0.222162i
$701$	−20.1591			−0.761397			−0.380698	−	0.924699i	$-0.624316\pi$
$701$	−20.1591			−0.761397			−0.380698	+	0.924699i	$0.624316\pi$
$702$	−1.50000	+	4.61653i	−0.0566139	+	0.174240i
$703$	−4.79837	−	3.48622i	−0.180974	−	0.131485i
$704$	4.23607	+	3.07768i	0.159653	+	0.115995i
$705$	−8.61803	−	6.26137i	−0.324574	−	0.235817i
$706$	16.5623	−	12.0332i	0.623331	−	0.452876i
$707$	3.34752			0.125897
$708$	7.23607	−	5.25731i	0.271948	−	0.197582i
$709$	−9.20820	−	28.3399i	−0.345821	−	1.06433i	−0.961143	−	0.276052i	$-0.910974\pi$
$709$	−9.20820	−	28.3399i	−0.345821	−	1.06433i	0.615321	−	0.788276i	$-0.289026\pi$
$710$	−9.79837	+	30.1563i	−0.367726	+	1.13175i
$711$		0			0
$712$	−0.427051	−	1.31433i	−0.0160044	−	0.0492565i
$713$	6.87539	+	21.1603i	0.257485	+	0.792458i
$714$	4.85410	−	14.9394i	0.181660	−	0.559093i
$715$	45.9787	−	33.4055i	1.71951	−	1.24929i
$716$	−1.18034	−	3.63271i	−0.0441114	−	0.135761i
$717$	21.7082	−	15.7719i	0.810708	−	0.589014i
$718$	27.8885			1.04079
$719$	−18.0902	+	13.1433i	−0.674649	+	0.490162i	−0.871578	−	0.490256i	$-0.836903\pi$
$719$	−18.0902	+	13.1433i	−0.674649	+	0.490162i	0.196929	+	0.980418i	$0.436903\pi$
$720$	−0.690983	+	2.12663i	−0.0257514	+	0.0792547i
$721$	3.70820	+	2.69417i	0.138101	+	0.100336i
$722$	−9.19098	−	6.67764i	−0.342053	−	0.248516i
$723$	4.28115	−	13.1760i	0.159218	−	0.490022i
$724$	−20.0344			−0.744574
$725$	5.59017	−	4.06150i	0.207614	−	0.150840i
$726$	16.4164			0.609270
$727$	3.18034	−	9.78808i	0.117952	−	0.363020i	−0.874599	−	0.484847i	$-0.838875\pi$
$727$	3.18034	−	9.78808i	0.117952	−	0.363020i	0.992551	+	0.121827i	$0.0388753\pi$
$728$	−7.85410	−	5.70634i	−0.291092	−	0.211491i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−7.03444			−0.260356
$731$	7.85410	−	5.70634i	0.290494	−	0.211057i
$732$	8.85410			0.327257
$733$	5.14590	−	3.73871i	0.190068	−	0.138093i	−0.488682	−	0.872462i	$-0.662522\pi$
$733$	5.14590	−	3.73871i	0.190068	−	0.138093i	0.678750	+	0.734370i	$0.262522\pi$
$734$	3.85410	+	11.8617i	0.142257	+	0.437824i
$735$	−6.70820			−0.247436
$736$	−1.85410	+	5.70634i	−0.0683431	+	0.210338i
$737$	15.7082	+	48.3449i	0.578619	+	1.78081i
$738$	1.88197	+	5.79210i	0.0692761	+	0.213210i
$739$	2.56231	−	7.88597i	0.0942559	−	0.290090i	−0.892803	−	0.450447i	$-0.851265\pi$
$739$	2.56231	−	7.88597i	0.0942559	−	0.290090i	0.987059	+	0.160357i	$0.0512646\pi$
$740$	1.48278	+	4.56352i	0.0545080	+	0.167759i
$741$	−4.14590	−	12.7598i	−0.152303	−	0.468742i
$742$	13.8541	−	10.0656i	0.508600	−	0.369520i
$743$	6.65248			0.244056			0.122028	−	0.992527i	$-0.461060\pi$
$743$	6.65248			0.244056			0.122028	+	0.992527i	$0.461060\pi$
$744$	−3.00000	+	2.17963i	−0.109985	+	0.0799090i
$745$	12.7254	−	9.24556i	0.466223	−	0.338731i
$746$	2.09017	+	1.51860i	0.0765266	+	0.0555998i
$747$	−4.85410	−	3.52671i	−0.177602	−	0.129036i
$748$	−12.7082	+	39.1118i	−0.464658	+	1.43007i
$749$	21.8885			0.799790
$750$	9.04508	+	6.57164i	0.330280	+	0.239962i
$751$	14.7639			0.538744			0.269372	−	0.963036i	$-0.413184\pi$
$751$	14.7639			0.538744			0.269372	+	0.963036i	$0.413184\pi$
$752$	1.47214	−	4.53077i	0.0536833	−	0.165220i
$753$	−10.0902	−	7.33094i	−0.367706	−	0.267154i
$754$	5.42705	+	3.94298i	0.197642	+	0.143595i
$755$	−12.5623	+	9.12705i	−0.457189	+	0.332167i
$756$	1.61803	−	1.17557i	0.0588473	−	0.0427551i
$757$	−28.8541			−1.04872			−0.524360	−	0.851497i	$-0.675695\pi$
$757$	−28.8541			−1.04872			−0.524360	+	0.851497i	$0.675695\pi$
$758$	−2.76393	+	2.00811i	−0.100391	+	0.0729380i
$759$	9.70820	+	29.8788i	0.352385	+	1.08453i
$760$	−1.90983	−	5.87785i	−0.0692768	−	0.213212i
$761$	7.46556	−	22.9766i	0.270626	−	0.832902i	−0.719717	−	0.694267i	$-0.755729\pi$
$761$	7.46556	−	22.9766i	0.270626	−	0.832902i	0.990344	−	0.138635i	$-0.0442714\pi$
$762$	0.0901699	+	0.277515i	0.00326651	+	0.0100533i
$763$	1.58359	+	4.87380i	0.0573299	+	0.176443i
$764$	−0.236068	+	0.726543i	−0.00854064	+	0.0262854i
$765$	−17.5623			−0.634967
$766$	−6.32624	−	19.4702i	−0.228576	−	0.703485i
$767$	35.1246	−	25.5195i	1.26828	−	0.921457i
$768$	−1.00000			−0.0360844
$769$	1.90983	−	1.38757i	0.0688702	−	0.0500372i	−0.552817	−	0.833302i	$-0.686447\pi$
$769$	1.90983	−	1.38757i	0.0688702	−	0.0500372i	0.621688	+	0.783265i	$0.286447\pi$
$770$	−23.4164			−0.843869
$771$	−9.39919	−	6.82891i	−0.338503	−	0.245937i
$772$	−1.92705	−	1.40008i	−0.0693561	−	0.0503901i
$773$	4.35410	−	13.4005i	0.156606	−	0.481984i	−0.841714	−	0.539924i	$-0.818453\pi$
$773$	4.35410	−	13.4005i	0.156606	−	0.481984i	0.998320	+	0.0579395i	$0.0184531\pi$
$774$	1.23607			0.0444295
$775$	5.72949	+	17.6336i	0.205809	+	0.633416i
$776$	13.8541			0.497333
$777$	1.32624	−	4.08174i	0.0475785	−	0.146432i
$778$	12.9271	+	9.39205i	0.463457	+	0.336721i
$779$	−13.6180	−	9.89408i	−0.487917	−	0.354492i
$780$	−3.35410	+	10.3229i	−0.120096	+	0.369618i
$781$	−60.0689	+	43.6426i	−2.14943	+	1.56165i
$782$	−47.1246			−1.68517
$783$	−1.11803	+	0.812299i	−0.0399553	+	0.0290292i
$784$	−0.927051	−	2.85317i	−0.0331090	−	0.101899i
$785$	32.2984	−	23.4661i	1.15278	−	0.837543i
$786$	−0.236068	+	0.726543i	−0.00842027	+	0.0259149i
$787$	9.43769	+	29.0462i	0.336417	+	1.03539i	0.966020	+	0.258469i	$0.0832179\pi$
$787$	9.43769	+	29.0462i	0.336417	+	1.03539i	−0.629602	+	0.776918i	$0.716782\pi$
$788$	−4.11803	−	12.6740i	−0.146699	−	0.451493i
$789$	−0.145898	+	0.449028i	−0.00519411	+	0.0159858i
$790$		0			0
$791$	−7.14590	−	21.9928i	−0.254079	−	0.781974i
$792$	−4.23607	+	3.07768i	−0.150522	+	0.109361i
$793$	42.9787			1.52622
$794$	23.3262	−	16.9475i	0.827817	−	0.601444i
$795$	−15.4894	−	11.2537i	−0.549351	−	0.399127i
$796$	5.00000	+	3.63271i	0.177220	+	0.128758i
$797$	10.7812	+	7.83297i	0.381888	+	0.277458i	0.762123	−	0.647432i	$-0.224157\pi$
$797$	10.7812	+	7.83297i	0.381888	+	0.277458i	−0.380235	+	0.924890i	$0.624157\pi$
$798$	−1.70820	+	5.25731i	−0.0604698	+	0.186107i
$799$	37.4164			1.32370
$800$	−1.54508	+	4.75528i	−0.0546270	+	0.168125i
$801$	1.38197			0.0488294
$802$	8.06231	−	24.8132i	0.284690	−	0.876185i
$803$	−13.3262	−	9.68208i	−0.470273	−	0.341673i
$804$	−7.85410	−	5.70634i	−0.276993	−	0.201247i
$805$	−8.29180	−	25.5195i	−0.292247	−	0.899445i
$806$	−14.5623	+	10.5801i	−0.512935	+	0.372669i
$807$	1.90983			0.0672292
$808$	1.35410	−	0.983813i	0.0476371	−	0.0346104i
$809$	2.53851	+	7.81272i	0.0892492	+	0.274681i	0.985712	−	0.168438i	$-0.0538722\pi$
$809$	2.53851	+	7.81272i	0.0892492	+	0.274681i	−0.896463	+	0.443118i	$0.853872\pi$
$810$	−1.80902	−	1.31433i	−0.0635624	−	0.0461808i
$811$	3.18034	−	9.78808i	0.111677	−	0.343706i	−0.879563	−	0.475783i	$-0.842165\pi$
$811$	3.18034	−	9.78808i	0.111677	−	0.343706i	0.991239	+	0.132077i	$0.0421647\pi$
$812$	−0.854102	−	2.62866i	−0.0299731	−	0.0922477i
$813$	−8.70820	−	26.8011i	−0.305410	−	0.939955i
$814$	−3.47214	+	10.6861i	−0.121698	+	0.374549i
$815$	37.0344	+	26.9071i	1.29726	+	0.942514i
$816$	−2.42705	−	7.46969i	−0.0849638	−	0.261492i
$817$	−2.76393	+	2.00811i	−0.0966977	+	0.0702550i
$818$	−20.9787			−0.733504
$819$	7.85410	−	5.70634i	0.274445	−	0.199396i
$820$	4.20820	+	12.9515i	0.146957	+	0.452287i
$821$	36.2705	+	26.3521i	1.26585	+	0.919694i	0.999029	−	0.0440528i	$-0.0140270\pi$
$821$	36.2705	+	26.3521i	1.26585	+	0.919694i	0.266820	+	0.963746i	$0.414027\pi$
$822$	12.1631	+	8.83702i	0.424237	+	0.308227i
$823$	−7.29180	+	22.4418i	−0.254176	+	0.782273i	0.739815	+	0.672811i	$0.234913\pi$
$823$	−7.29180	+	22.4418i	−0.254176	+	0.782273i	−0.993991	+	0.109463i	$0.965087\pi$
$824$	2.29180			0.0798385
$825$	8.09017	+	24.8990i	0.281664	+	0.866871i
$826$	−17.8885			−0.622422
$827$	4.56231	−	14.0413i	0.158647	−	0.488265i	−0.839865	−	0.542795i	$-0.817366\pi$
$827$	4.56231	−	14.0413i	0.158647	−	0.488265i	0.998512	+	0.0545300i	$0.0173661\pi$
$828$	−4.85410	−	3.52671i	−0.168692	−	0.122562i
$829$	−31.6697	−	23.0094i	−1.09993	−	0.799149i	−0.118885	−	0.992908i	$-0.537932\pi$
$829$	−31.6697	−	23.0094i	−1.09993	−	0.799149i	−0.981049	+	0.193759i	$0.937932\pi$
$830$	−10.8541	−	7.88597i	−0.376751	−	0.273726i
$831$	−17.9164	+	13.0170i	−0.621513	+	0.451556i
$832$	−4.85410			−0.168286
$833$	19.0623	−	13.8496i	0.660470	−	0.479859i
$834$	−4.14590	−	12.7598i	−0.143561	−	0.441834i
$835$	−4.47214	+	13.7638i	−0.154765	+	0.476317i
$836$	4.47214	−	13.7638i	0.154672	−	0.476032i
$837$	−1.14590	−	3.52671i	−0.0396080	−	0.121901i
$838$	11.7082	+	36.0341i	0.404453	+	1.24478i
$839$	−1.58359	+	4.87380i	−0.0546717	+	0.168262i	−0.974664	−	0.223674i	$-0.928195\pi$
$839$	−1.58359	+	4.87380i	−0.0546717	+	0.168262i	0.919992	+	0.391937i	$0.128195\pi$
$840$	3.61803	−	2.62866i	0.124834	−	0.0906972i
$841$	−8.37132	−	25.7643i	−0.288666	−	0.888424i
$842$	−8.97214	+	6.51864i	−0.309200	+	0.224647i
$843$	6.09017			0.209757
$844$	6.47214	−	4.70228i	0.222780	−	0.161859i
$845$	−7.29837	+	22.4621i	−0.251072	+	0.772719i
$846$	3.85410	+	2.80017i	0.132507	+	0.0962718i
$847$	−26.5623	−	19.2986i	−0.912692	−	0.663109i
$848$	2.64590	−	8.14324i	0.0908605	−	0.279640i
$849$	−3.23607			−0.111062
$850$	−39.2705			−1.34697
$851$	−12.8754			−0.441363
$852$	4.38197	−	13.4863i	0.150124	−	0.462033i
$853$	−13.3090	−	9.66957i	−0.455692	−	0.331080i	0.336147	−	0.941810i	$-0.390876\pi$
$853$	−13.3090	−	9.66957i	−0.455692	−	0.331080i	−0.791839	+	0.610730i	$0.790876\pi$
$854$	−14.3262	−	10.4086i	−0.490234	−	0.356176i
$855$	6.18034			0.211363
$856$	8.85410	−	6.43288i	0.302627	−	0.219871i
$857$	23.3050			0.796082			0.398041	−	0.917368i	$-0.369690\pi$
$857$	23.3050			0.796082			0.398041	+	0.917368i	$0.369690\pi$
$858$	−20.5623	+	14.9394i	−0.701986	+	0.510022i
$859$	14.0689	+	43.2996i	0.480024	+	1.47736i	0.839060	+	0.544039i	$0.183106\pi$
$859$	14.0689	+	43.2996i	0.480024	+	1.47736i	−0.359036	+	0.933324i	$0.616894\pi$
$860$	2.76393			0.0942493
$861$	3.76393	−	11.5842i	0.128274	−	0.394788i
$862$	−1.14590	−	3.52671i	−0.0390294	−	0.120120i
$863$	3.76393	+	11.5842i	0.128126	+	0.394330i	0.994458	−	0.105138i	$-0.0335285\pi$
$863$	3.76393	+	11.5842i	0.128126	+	0.394330i	−0.866332	+	0.499469i	$0.833529\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	7.53851	+	23.2011i	0.256317	+	0.788862i
$866$	7.15248	+	22.0131i	0.243051	+	0.748034i
$867$	36.1525	−	26.2663i	1.22780	−	0.892051i
$868$	7.41641			0.251729
$869$		0			0
$870$	−2.50000	+	1.81636i	−0.0847579	+	0.0615802i
$871$	−38.1246	−	27.6992i	−1.29180	−	0.938550i
$872$	2.07295	+	1.50609i	0.0701989	+	0.0510025i
$873$	−4.28115	+	13.1760i	−0.144895	+	0.445941i
$874$	16.5836			0.560948
$875$	−6.90983	−	21.2663i	−0.233595	−	0.718931i
$876$	3.14590			0.106290
$877$	5.55573	−	17.0988i	0.187604	−	0.577385i	−0.812380	−	0.583129i	$-0.801828\pi$
$877$	5.55573	−	17.0988i	0.187604	−	0.577385i	0.999984	+	0.00574402i	$0.00182839\pi$
$878$	−20.3262	−	14.7679i	−0.685977	−	0.498392i
$879$	−23.2984	−	16.9273i	−0.785835	−	0.570942i
$880$	−9.47214	+	6.88191i	−0.319306	+	0.231989i
$881$	−37.7984	+	27.4621i	−1.27346	+	0.925223i	−0.999335	−	0.0364716i	$-0.988388\pi$
$881$	−37.7984	+	27.4621i	−1.27346	+	0.925223i	−0.274125	+	0.961694i	$0.588388\pi$
$882$	3.00000			0.101015
$883$	−34.1246	+	24.7930i	−1.14838	+	0.834350i	−0.988265	−	0.152747i	$-0.951188\pi$
$883$	−34.1246	+	24.7930i	−1.14838	+	0.834350i	−0.160119	+	0.987098i	$0.551188\pi$
$884$	−11.7812	−	36.2587i	−0.396243	−	1.21951i
$885$	6.18034	+	19.0211i	0.207750	+	0.639388i
$886$	−9.29180	+	28.5972i	−0.312164	+	0.960742i
$887$	7.97871	+	24.5560i	0.267899	+	0.824508i	0.991011	+	0.133778i	$0.0427109\pi$
$887$	7.97871	+	24.5560i	0.267899	+	0.824508i	−0.723112	+	0.690730i	$0.757289\pi$
$888$	−0.663119	−	2.04087i	−0.0222528	−	0.0684871i
$889$	0.180340	−	0.555029i	0.00604841	−	0.0186151i
$890$	3.09017			0.103583
$891$	−1.61803	−	4.97980i	−0.0542062	−	0.166829i
$892$	1.85410	−	1.34708i	0.0620799	−	0.0451037i
$893$	−13.1672			−0.440623
$894$	−5.69098	+	4.13474i	−0.190335	+	0.138286i
$895$	8.54102			0.285495
$896$	1.61803	+	1.17557i	0.0540547	+	0.0392731i
$897$	−23.5623	−	17.1190i	−0.786722	−	0.571587i
$898$	−1.48278	+	4.56352i	−0.0494810	+	0.152287i
$899$	−5.12461			−0.170915
$900$	−4.04508	−	2.93893i	−0.134836	−	0.0979642i
$901$	67.2492			2.24040
$902$	−9.85410	+	30.3278i	−0.328106	+	1.00981i
$903$	−2.00000	−	1.45309i	−0.0665558	−	0.0483556i
$904$	−9.35410	−	6.79615i	−0.311113	−	0.226037i
$905$	13.8435	−	42.6058i	0.460172	−	1.41626i
$906$	5.61803	−	4.08174i	0.186647	−	0.135607i
$907$	20.2918			0.673778			0.336889	−	0.941544i	$-0.390625\pi$
$907$	20.2918			0.673778			0.336889	+	0.941544i	$0.390625\pi$
$908$	13.7082	−	9.95959i	0.454923	−	0.330521i
$909$	0.517221	+	1.59184i	0.0171551	+	0.0527981i
$910$	17.5623	−	12.7598i	0.582185	−	0.422982i
$911$	17.3262	−	53.3247i	0.574044	−	1.76673i	−0.0653683	−	0.997861i	$-0.520822\pi$
$911$	17.3262	−	53.3247i	0.574044	−	1.76673i	0.639412	−	0.768864i	$-0.279178\pi$
$912$	0.854102	+	2.62866i	0.0282821	+	0.0870435i
$913$	−9.70820	−	29.8788i	−0.321295	−	0.988843i
$914$	3.85410	−	11.8617i	0.127482	−	0.392350i
$915$	−6.11803	+	18.8294i	−0.202256	+	0.622480i
$916$	−7.50000	−	23.0826i	−0.247807	−	0.762671i
$917$	1.23607	−	0.898056i	0.0408186	−	0.0296564i
$918$	7.85410			0.259224
$919$	0.854102	−	0.620541i	0.0281742	−	0.0204698i	−0.573609	−	0.819129i	$-0.694457\pi$
$919$	0.854102	−	0.620541i	0.0281742	−	0.0204698i	0.601783	+	0.798659i	$0.294457\pi$
$920$	−10.8541	−	7.88597i	−0.357849	−	0.259993i
$921$	−13.1803	−	9.57608i	−0.434307	−	0.315542i
$922$	20.2984	+	14.7476i	0.668491	+	0.485687i
$923$	21.2705	−	65.4639i	0.700127	−	2.15477i
$924$	10.4721			0.344508
$925$	−10.7295			−0.352783
$926$	12.2918			0.403933
$927$	−0.708204	+	2.17963i	−0.0232605	+	0.0715884i
$928$	−1.11803	−	0.812299i	−0.0367013	−	0.0266650i
$929$	25.0623	+	18.2088i	0.822268	+	0.597412i	0.917361	−	0.398056i	$-0.130315\pi$
$929$	25.0623	+	18.2088i	0.822268	+	0.597412i	−0.0950935	+	0.995468i	$0.530315\pi$
$930$	−2.56231	−	7.88597i	−0.0840213	−	0.258591i
$931$	−6.70820	+	4.87380i	−0.219853	+	0.159732i
$932$	−22.0902			−0.723588
$933$	−15.0902	+	10.9637i	−0.494030	+	0.358934i
$934$	−4.88854	−	15.0454i	−0.159958	−	0.492300i
$935$	−74.3951	−	54.0512i	−2.43298	−	1.76766i
$936$	1.50000	−	4.61653i	0.0490290	−	0.150896i
$937$	10.8435	+	33.3727i	0.354240	+	1.09024i	0.956449	+	0.291901i	$0.0942877\pi$
$937$	10.8435	+	33.3727i	0.354240	+	1.09024i	−0.602208	+	0.798339i	$0.705712\pi$
$938$	6.00000	+	18.4661i	0.195907	+	0.602940i
$939$	8.14590	−	25.0705i	0.265831	−	0.818145i
$940$	8.61803	+	6.26137i	0.281089	+	0.204223i
$941$	6.69756	+	20.6130i	0.218334	+	0.671964i	0.998900	+	0.0468901i	$0.0149311\pi$
$941$	6.69756	+	20.6130i	0.218334	+	0.671964i	−0.780566	+	0.625074i	$0.785069\pi$
$942$	−14.4443	+	10.4944i	−0.470620	+	0.341925i
$943$	−36.5410			−1.18994
$944$	−7.23607	+	5.25731i	−0.235514	+	0.171111i
$945$	1.38197	+	4.25325i	0.0449554	+	0.138358i
$946$	5.23607	+	3.80423i	0.170239	+	0.123686i
$947$	−8.85410	−	6.43288i	−0.287720	−	0.209041i	0.434558	−	0.900644i	$-0.356905\pi$
$947$	−8.85410	−	6.43288i	−0.287720	−	0.209041i	−0.722278	+	0.691603i	$0.756905\pi$
$948$		0			0
$949$	15.2705			0.495702
$950$	13.8197			0.448369
$951$	6.94427			0.225183
$952$	−4.85410	+	14.9394i	−0.157322	+	0.484188i
$953$	26.5902	+	19.3189i	0.861340	+	0.625800i	0.928249	−	0.371959i	$-0.121314\pi$
$953$	26.5902	+	19.3189i	0.861340	+	0.625800i	−0.0669091	+	0.997759i	$0.521314\pi$
$954$	6.92705	+	5.03280i	0.224272	+	0.162943i
$955$	−1.38197	−	1.00406i	−0.0447194	−	0.0324905i
$956$	−21.7082	+	15.7719i	−0.702093	+	0.510101i
$957$	−7.23607			−0.233909
$958$	3.61803	−	2.62866i	0.116893	−	0.0849280i
$959$	−9.29180	−	28.5972i	−0.300048	−	0.923452i
$960$	0.690983	−	2.12663i	0.0223014	−	0.0686366i
$961$	−5.33030	+	16.4050i	−0.171945	+	0.529193i
$962$	−3.21885	−	9.90659i	−0.103780	−	0.319401i
$963$	3.38197	+	10.4086i	0.108982	+	0.335413i
$964$	−4.28115	+	13.1760i	−0.137887	+	0.424371i
$965$	4.30902	−	3.13068i	0.138712	−	0.100780i
$966$	3.70820	+	11.4127i	0.119310	+	0.367197i
$967$	−33.1246	+	24.0664i	−1.06522	+	0.773925i	−0.975046	−	0.222002i	$-0.928741\pi$
$967$	−33.1246	+	24.0664i	−1.06522	+	0.773925i	−0.0901695	+	0.995926i	$0.528741\pi$
$968$	−16.4164			−0.527643
$969$	−17.5623	+	12.7598i	−0.564183	+	0.409903i
$970$	−9.57295	+	29.4625i	−0.307369	+	0.945984i
$971$	27.3262	+	19.8537i	0.876941	+	0.637135i	0.932440	−	0.361324i	$-0.117675\pi$
$971$	27.3262	+	19.8537i	0.876941	+	0.637135i	−0.0554996	+	0.998459i	$0.517675\pi$
$972$	0.809017	+	0.587785i	0.0259492	+	0.0188532i
$973$	−8.29180	+	25.5195i	−0.265823	+	0.818118i
$974$	−10.2918			−0.329770
$975$	−19.6353	−	14.2658i	−0.628831	−	0.456873i
$976$	−8.85410			−0.283413
$977$	−6.35410	+	19.5559i	−0.203286	+	0.625649i	0.796494	+	0.604647i	$0.206686\pi$
$977$	−6.35410	+	19.5559i	−0.203286	+	0.625649i	−0.999779	+	0.0210023i	$0.993314\pi$
$978$	−16.5623	−	12.0332i	−0.529604	−	0.384780i
$979$	5.85410	+	4.25325i	0.187098	+	0.135935i
$980$	6.70820			0.214286
$981$	−2.07295	+	1.50609i	−0.0661842	+	0.0480856i
$982$	−29.8885			−0.953782
$983$	34.4164	−	25.0050i	1.09771	−	0.797535i	0.117028	−	0.993129i	$-0.462663\pi$
$983$	34.4164	−	25.0050i	1.09771	−	0.797535i	0.980685	+	0.195594i	$0.0626633\pi$
$984$	−1.88197	−	5.79210i	−0.0599949	−	0.184645i
$985$	29.7984			0.949455
$986$	3.35410	−	10.3229i	0.106816	−	0.328747i
$987$	−2.94427	−	9.06154i	−0.0937172	−	0.288432i
$988$	4.14590	+	12.7598i	0.131899	+	0.405942i
$989$	−2.29180	+	7.05342i	−0.0728749	+	0.224286i
$990$	−3.61803	−	11.1352i	−0.114989	−	0.353899i
$991$	18.7082	+	57.5779i	0.594286	+	1.82902i	0.558250	+	0.829673i	$0.311473\pi$
$991$	18.7082	+	57.5779i	0.594286	+	1.82902i	0.0360356	+	0.999351i	$0.488527\pi$
$992$	3.00000	−	2.17963i	0.0952501	−	0.0692032i
$993$	32.4721			1.03047
$994$	−22.9443	+	16.6700i	−0.727748	+	0.528740i
$995$	−11.1803	+	8.12299i	−0.354441	+	0.257516i
$996$	4.85410	+	3.52671i	0.153808	+	0.111748i
$997$	1.14590	+	0.832544i	0.0362910	+	0.0263669i	0.605783	−	0.795630i	$-0.292860\pi$
$997$	1.14590	+	0.832544i	0.0362910	+	0.0263669i	−0.569492	+	0.821997i	$0.692860\pi$
$998$	10.3262	−	31.7809i	0.326871	−	1.00601i
$999$	2.14590			0.0678932

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.g.b.121.1	yes	4
3.2	odd	2		450.2.h.b.271.1		4
5.2	odd	4		750.2.h.a.649.1		8
5.3	odd	4		750.2.h.a.649.2		8
5.4	even	2		750.2.g.a.601.1		4
25.6	even	5	inner	150.2.g.b.31.1	✓	4
25.8	odd	20		750.2.h.a.349.1		8
25.9	even	10		3750.2.a.g.1.1		2
25.12	odd	20		3750.2.c.c.1249.1		4
25.13	odd	20		3750.2.c.c.1249.3		4
25.16	even	5		3750.2.a.b.1.1		2
25.17	odd	20		750.2.h.a.349.2		8
25.19	even	10		750.2.g.a.151.1		4
75.56	odd	10		450.2.h.b.181.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.b.31.1	✓	4	25.6	even	5	inner
150.2.g.b.121.1	yes	4	1.1	even	1	trivial
450.2.h.b.181.1		4	75.56	odd	10
450.2.h.b.271.1		4	3.2	odd	2
750.2.g.a.151.1		4	25.19	even	10
750.2.g.a.601.1		4	5.4	even	2
750.2.h.a.349.1		8	25.8	odd	20
750.2.h.a.349.2		8	25.17	odd	20
750.2.h.a.649.1		8	5.2	odd	4
750.2.h.a.649.2		8	5.3	odd	4
3750.2.a.b.1.1		2	25.16	even	5
3750.2.a.g.1.1		2	25.9	even	10
3750.2.c.c.1249.1		4	25.12	odd	20
3750.2.c.c.1249.3		4	25.13	odd	20

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.80902 - 1.31433i) q^{5} +(-0.809017 + 0.587785i) q^{6} +2.00000 q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.690983 + 2.12663i) q^{10} +(-1.61803 + 4.97980i) q^{11} +(-0.309017 - 0.951057i) q^{12} +(-1.50000 - 4.61653i) q^{13} +(-0.618034 + 1.90211i) q^{14} +2.23607 q^{15} +(0.309017 + 0.951057i) q^{16} +(-6.35410 + 4.61653i) q^{17} -1.00000 q^{18} +(2.23607 - 1.62460i) q^{19} -2.23607 q^{20} +(1.61803 + 1.17557i) q^{21} +(-4.23607 - 3.07768i) q^{22} +(1.85410 - 5.70634i) q^{23} +1.00000 q^{24} +(1.54508 - 4.75528i) q^{25} +4.85410 q^{26} +(-0.309017 + 0.951057i) q^{27} +(-1.61803 - 1.17557i) q^{28} +(1.11803 + 0.812299i) q^{29} +(-0.690983 + 2.12663i) q^{30} +(-3.00000 + 2.17963i) q^{31} -1.00000 q^{32} +(-4.23607 + 3.07768i) q^{33} +(-2.42705 - 7.46969i) q^{34} +(3.61803 - 2.62866i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-0.663119 - 2.04087i) q^{37} +(0.854102 + 2.62866i) q^{38} +(1.50000 - 4.61653i) q^{39} +(0.690983 - 2.12663i) q^{40} +(-1.88197 - 5.79210i) q^{41} +(-1.61803 + 1.17557i) q^{42} -1.23607 q^{43} +(4.23607 - 3.07768i) q^{44} +(1.80902 + 1.31433i) q^{45} +(4.85410 + 3.52671i) q^{46} +(-3.85410 - 2.80017i) q^{47} +(-0.309017 + 0.951057i) q^{48} -3.00000 q^{49} +(4.04508 + 2.93893i) q^{50} -7.85410 q^{51} +(-1.50000 + 4.61653i) q^{52} +(-6.92705 - 5.03280i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(3.61803 + 11.1352i) q^{55} +(1.61803 - 1.17557i) q^{56} +2.76393 q^{57} +(-1.11803 + 0.812299i) q^{58} +(2.76393 + 8.50651i) q^{59} +(-1.80902 - 1.31433i) q^{60} +(-2.73607 + 8.42075i) q^{61} +(-1.14590 - 3.52671i) q^{62} +(0.618034 + 1.90211i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-8.78115 - 6.37988i) q^{65} +(-1.61803 - 4.97980i) q^{66} +(7.85410 - 5.70634i) q^{67} +7.85410 q^{68} +(4.85410 - 3.52671i) q^{69} +(1.38197 + 4.25325i) q^{70} +(11.4721 + 8.33499i) q^{71} +(0.809017 + 0.587785i) q^{72} +(-0.972136 + 2.99193i) q^{73} +2.14590 q^{74} +(4.04508 - 2.93893i) q^{75} -2.76393 q^{76} +(-3.23607 + 9.95959i) q^{77} +(3.92705 + 2.85317i) q^{78} +(1.80902 + 1.31433i) q^{80} +(-0.809017 + 0.587785i) q^{81} +6.09017 q^{82} +(-4.85410 + 3.52671i) q^{83} +(-0.618034 - 1.90211i) q^{84} +(-5.42705 + 16.7027i) q^{85} +(0.381966 - 1.17557i) q^{86} +(0.427051 + 1.31433i) q^{87} +(1.61803 + 4.97980i) q^{88} +(0.427051 - 1.31433i) q^{89} +(-1.80902 + 1.31433i) q^{90} +(-3.00000 - 9.23305i) q^{91} +(-4.85410 + 3.52671i) q^{92} -3.70820 q^{93} +(3.85410 - 2.80017i) q^{94} +(1.90983 - 5.87785i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(11.2082 + 8.14324i) q^{97} +(0.927051 - 2.85317i) q^{98} -5.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{3} - q^{4} + 5 q^{5} - q^{6} + 8 q^{7} + q^{8} - q^{9} + 5 q^{10} - 2 q^{11} + q^{12} - 6 q^{13} + 2 q^{14} - q^{16} - 12 q^{17} - 4 q^{18} + 2 q^{21} - 8 q^{22} - 6 q^{23} + 4 q^{24}+ \cdots - 12 q^{99}+O(q^{100}) \) 4 * q + q^2 + q^3 - q^4 + 5 * q^5 - q^6 + 8 * q^7 + q^8 - q^9 + 5 * q^10 - 2 * q^11 + q^12 - 6 * q^13 + 2 * q^14 - q^16 - 12 * q^17 - 4 * q^18 + 2 * q^21 - 8 * q^22 - 6 * q^23 + 4 * q^24 - 5 * q^25 + 6 * q^26 + q^27 - 2 * q^28 - 5 * q^30 - 12 * q^31 - 4 * q^32 - 8 * q^33 - 3 * q^34 + 10 * q^35 - q^36 + 13 * q^37 - 10 * q^38 + 6 * q^39 + 5 * q^40 - 12 * q^41 - 2 * q^42 + 4 * q^43 + 8 * q^44 + 5 * q^45 + 6 * q^46 - 2 * q^47 + q^48 - 12 * q^49 + 5 * q^50 - 18 * q^51 - 6 * q^52 - 21 * q^53 - q^54 + 10 * q^55 + 2 * q^56 + 20 * q^57 + 20 * q^59 - 5 * q^60 - 2 * q^61 - 18 * q^62 - 2 * q^63 - q^64 - 15 * q^65 - 2 * q^66 + 18 * q^67 + 18 * q^68 + 6 * q^69 + 10 * q^70 + 28 * q^71 + q^72 + 14 * q^73 + 22 * q^74 + 5 * q^75 - 20 * q^76 - 4 * q^77 + 9 * q^78 + 5 * q^80 - q^81 + 2 * q^82 - 6 * q^83 + 2 * q^84 - 15 * q^85 + 6 * q^86 - 5 * q^87 + 2 * q^88 - 5 * q^89 - 5 * q^90 - 12 * q^91 - 6 * q^92 + 12 * q^93 + 2 * q^94 + 30 * q^95 - q^96 + 18 * q^97 - 3 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more