LMFDB - Embedded newform 961.2.d.h.531.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(374,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.374"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-8,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 $ x^8 + 2x^6 + 4x^4 + 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			531.2
Root			$0.437016 - 1.34500i$ of defining polynomial
Character	$\chi$	$=$	961.531
Dual form			961.2.d.h.628.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.118034 + 0.363271i) q^{2} +(0.707107 - 2.17625i) q^{3} +(1.50000 - 1.08981i) q^{4} -2.23607 q^{5} +0.874032 q^{6} +(0.809017 - 0.587785i) q^{7} +(1.19098 + 0.865300i) q^{8} +(-1.80902 - 1.31433i) q^{9} +(-0.263932 - 0.812299i) q^{10} +(-3.43237 + 2.49376i) q^{11} +(-1.31105 - 4.03499i) q^{12} +(2.12132 - 6.52875i) q^{13} +(0.309017 + 0.224514i) q^{14} +(-1.58114 + 4.86624i) q^{15} +(0.972136 - 2.99193i) q^{16} +(-0.437016 - 0.317511i) q^{17} +(0.263932 - 0.812299i) q^{18} +(0.309017 + 0.951057i) q^{19} +(-3.35410 + 2.43690i) q^{20} +(-0.707107 - 2.17625i) q^{21} +(-1.31105 - 0.952532i) q^{22} +(-5.55369 - 4.03499i) q^{23} +(2.72526 - 1.98002i) q^{24} +2.62210 q^{26} +(1.41421 - 1.02749i) q^{27} +(0.572949 - 1.76336i) q^{28} +(-1.14412 - 3.52125i) q^{29} -1.95440 q^{30} +4.14590 q^{32} +(3.00000 + 9.23305i) q^{33} +(0.0637598 - 0.196232i) q^{34} +(-1.80902 + 1.31433i) q^{35} -4.14590 q^{36} +4.24264 q^{37} +(-0.309017 + 0.224514i) q^{38} +(-12.7082 - 9.23305i) q^{39} +(-2.66312 - 1.93487i) q^{40} +(2.30902 + 7.10642i) q^{41} +(0.707107 - 0.513743i) q^{42} +(-0.0637598 - 0.196232i) q^{43} +(-2.43082 + 7.48128i) q^{44} +(4.04508 + 2.93893i) q^{45} +(0.810272 - 2.49376i) q^{46} +(1.14590 - 3.52671i) q^{47} +(-5.82378 - 4.23122i) q^{48} +(-1.85410 + 5.70634i) q^{49} +(-1.00000 + 0.726543i) q^{51} +(-3.93314 - 12.1050i) q^{52} +(-4.24264 - 3.08246i) q^{53} +(0.540182 + 0.392465i) q^{54} +(7.67501 - 5.57622i) q^{55} +1.47214 q^{56} +2.28825 q^{57} +(1.14412 - 0.831254i) q^{58} +(-1.83688 + 5.65334i) q^{59} +(2.93159 + 9.02251i) q^{60} +4.44897 q^{61} -2.23607 q^{63} +(-1.45492 - 4.47777i) q^{64} +(-4.74342 + 14.5987i) q^{65} +(-3.00000 + 2.17963i) q^{66} +6.00000 q^{67} -1.00155 q^{68} +(-12.7082 + 9.23305i) q^{69} +(-0.690983 - 0.502029i) q^{70} +(-6.04508 - 4.39201i) q^{71} +(-1.01722 - 3.13068i) q^{72} +(-3.43237 + 2.49376i) q^{73} +(0.500776 + 1.54123i) q^{74} +(1.50000 + 1.08981i) q^{76} +(-1.31105 + 4.03499i) q^{77} +(1.85410 - 5.70634i) q^{78} +(8.98606 + 6.52875i) q^{79} +(-2.17376 + 6.69015i) q^{80} +(-3.30902 - 10.1841i) q^{81} +(-2.30902 + 1.67760i) q^{82} +(0.977198 + 3.00750i) q^{83} +(-3.43237 - 2.49376i) q^{84} +(0.977198 + 0.709976i) q^{85} +(0.0637598 - 0.0463242i) q^{86} -8.47214 q^{87} -6.24574 q^{88} +(4.74342 - 3.44629i) q^{89} +(-0.590170 + 1.81636i) q^{90} +(-2.12132 - 6.52875i) q^{91} -12.7279 q^{92} +1.41641 q^{94} +(-0.690983 - 2.12663i) q^{95} +(2.93159 - 9.02251i) q^{96} +(5.66312 - 4.11450i) q^{97} -2.29180 q^{98} +9.48683 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 12 q^{4} + 2 q^{7} + 14 q^{8} - 10 q^{9} - 20 q^{10} - 2 q^{14} - 28 q^{16} + 20 q^{18} - 2 q^{19} + 18 q^{28} + 60 q^{32} + 24 q^{33} - 10 q^{35} - 60 q^{36} + 2 q^{38} - 48 q^{39} + 10 q^{40}+ \cdots - 72 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 12 * q^4 + 2 * q^7 + 14 * q^8 - 10 * q^9 - 20 * q^10 - 2 * q^14 - 28 * q^16 + 20 * q^18 - 2 * q^19 + 18 * q^28 + 60 * q^32 + 24 * q^33 - 10 * q^35 - 60 * q^36 + 2 * q^38 - 48 * q^39 + 10 * q^40 + 14 * q^41 + 10 * q^45 + 36 * q^47 + 12 * q^49 - 8 * q^51 - 24 * q^56 - 46 * q^59 - 34 * q^64 - 24 * q^66 + 48 * q^67 - 48 * q^69 - 10 * q^70 - 26 * q^71 + 50 * q^72 + 12 * q^76 - 12 * q^78 - 80 * q^80 - 22 * q^81 - 14 * q^82 - 32 * q^87 + 40 * q^90 - 96 * q^94 - 10 * q^95 + 14 * q^97 - 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.118034	+	0.363271i	0.0834626	+	0.256872i	0.984076	−	0.177750i	$-0.0568820\pi$
$2$	0.118034	+	0.363271i	0.0834626	+	0.256872i	−0.900613	+	0.434622i	$0.856882\pi$
$3$	0.707107	−	2.17625i	0.408248	−	1.25646i	−0.509904	−	0.860231i	$-0.670319\pi$
$3$	0.707107	−	2.17625i	0.408248	−	1.25646i	0.918152	−	0.396228i	$-0.129681\pi$
$4$	1.50000	−	1.08981i	0.750000	−	0.544907i
$5$	−2.23607			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$5$	−2.23607			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$6$	0.874032			0.356822
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i	−0.424304	−	0.905520i	$-0.639481\pi$
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i	0.730084	+	0.683358i	$0.239481\pi$
$8$	1.19098	+	0.865300i	0.421076	+	0.305930i
$9$	−1.80902	−	1.31433i	−0.603006	−	0.438109i
$10$	−0.263932	−	0.812299i	−0.0834626	−	0.256872i
$11$	−3.43237	+	2.49376i	−1.03490	+	0.751897i	−0.969283	−	0.245948i	$-0.920901\pi$
$11$	−3.43237	+	2.49376i	−1.03490	+	0.751897i	−0.0656149	+	0.997845i	$0.520901\pi$
$12$	−1.31105	−	4.03499i	−0.378467	−	1.16480i
$13$	2.12132	−	6.52875i	0.588348	−	1.81075i	0.00296221	−	0.999996i	$-0.499057\pi$
$13$	2.12132	−	6.52875i	0.588348	−	1.81075i	0.585386	−	0.810755i	$-0.300943\pi$
$14$	0.309017	+	0.224514i	0.0825883	+	0.0600039i
$15$	−1.58114	+	4.86624i	−0.408248	+	1.25646i
$16$	0.972136	−	2.99193i	0.243034	−	0.747982i
$17$	−0.437016	−	0.317511i	−0.105992	−	0.0770077i	0.533527	−	0.845783i	$-0.320866\pi$
$17$	−0.437016	−	0.317511i	−0.105992	−	0.0770077i	−0.639519	+	0.768776i	$0.720866\pi$
$18$	0.263932	−	0.812299i	0.0622094	−	0.191461i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i	0.980226	−	0.197884i	$-0.0634068\pi$
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i	−0.909332	+	0.416071i	$0.863407\pi$
$20$	−3.35410	+	2.43690i	−0.750000	+	0.544907i
$21$	−0.707107	−	2.17625i	−0.154303	−	0.474897i
$22$	−1.31105	−	0.952532i	−0.279516	−	0.203081i
$23$	−5.55369	−	4.03499i	−1.15802	−	0.841354i	−0.168497	−	0.985702i	$-0.553891\pi$
$23$	−5.55369	−	4.03499i	−1.15802	−	0.841354i	−0.989527	+	0.144348i	$0.953891\pi$
$24$	2.72526	−	1.98002i	0.556292	−	0.404170i
$25$		0			0
$26$	2.62210			0.514235
$27$	1.41421	−	1.02749i	0.272166	−	0.197740i
$28$	0.572949	−	1.76336i	0.108277	−	0.333243i
$29$	−1.14412	−	3.52125i	−0.212458	−	0.653879i	−0.999324	−	0.0367555i	$-0.988298\pi$
$29$	−1.14412	−	3.52125i	−0.212458	−	0.653879i	0.786866	−	0.617124i	$-0.211702\pi$
$30$	−1.95440			−0.356822
$31$		0			0
$31$		0			0
$32$	4.14590			0.732898
$33$	3.00000	+	9.23305i	0.522233	+	1.60727i
$34$	0.0637598	−	0.196232i	0.0109347	−	0.0336536i
$35$	−1.80902	+	1.31433i	−0.305780	+	0.222162i
$36$	−4.14590			−0.690983
$37$	4.24264			0.697486			0.348743	−	0.937218i	$-0.386609\pi$
$37$	4.24264			0.697486			0.348743	+	0.937218i	$0.386609\pi$
$38$	−0.309017	+	0.224514i	−0.0501292	+	0.0364210i
$39$	−12.7082	−	9.23305i	−2.03494	−	1.47847i
$40$	−2.66312	−	1.93487i	−0.421076	−	0.305930i
$41$	2.30902	+	7.10642i	0.360608	+	1.10984i	0.952686	+	0.303956i	$0.0983077\pi$
$41$	2.30902	+	7.10642i	0.360608	+	1.10984i	−0.592078	+	0.805881i	$0.701692\pi$
$42$	0.707107	−	0.513743i	0.109109	−	0.0792723i
$43$	−0.0637598	−	0.196232i	−0.00972328	−	0.0299252i	0.946077	−	0.323941i	$-0.105008\pi$
$43$	−0.0637598	−	0.196232i	−0.00972328	−	0.0299252i	−0.955800	+	0.294016i	$0.905008\pi$
$44$	−2.43082	+	7.48128i	−0.366459	+	1.12785i
$45$	4.04508	+	2.93893i	0.603006	+	0.438109i
$46$	0.810272	−	2.49376i	0.119468	−	0.367685i
$47$	1.14590	−	3.52671i	0.167146	−	0.514424i	−0.832042	−	0.554713i	$-0.812828\pi$
$47$	1.14590	−	3.52671i	0.167146	−	0.514424i	0.999188	+	0.0402894i	$0.0128280\pi$
$48$	−5.82378	−	4.23122i	−0.840590	−	0.610725i
$49$	−1.85410	+	5.70634i	−0.264872	+	0.815191i
$50$		0			0
$51$	−1.00000	+	0.726543i	−0.140028	+	0.101736i
$52$	−3.93314	−	12.1050i	−0.545429	−	1.67866i
$53$	−4.24264	−	3.08246i	−0.582772	−	0.423408i	0.256951	−	0.966425i	$-0.417282\pi$
$53$	−4.24264	−	3.08246i	−0.582772	−	0.423408i	−0.839722	+	0.543016i	$0.817282\pi$
$54$	0.540182	+	0.392465i	0.0735094	+	0.0534077i
$55$	7.67501	−	5.57622i	1.03490	−	0.751897i
$56$	1.47214			0.196722
$57$	2.28825			0.303086
$58$	1.14412	−	0.831254i	0.150231	−	0.109149i
$59$	−1.83688	+	5.65334i	−0.239142	+	0.736002i	0.757403	+	0.652947i	$0.226468\pi$
$59$	−1.83688	+	5.65334i	−0.239142	+	0.736002i	−0.996545	+	0.0830548i	$0.973532\pi$
$60$	2.93159	+	9.02251i	0.378467	+	1.16480i
$61$	4.44897			0.569632			0.284816	−	0.958582i	$-0.408067\pi$
$61$	4.44897			0.569632			0.284816	+	0.958582i	$0.408067\pi$
$62$		0			0
$63$	−2.23607			−0.281718
$64$	−1.45492	−	4.47777i	−0.181864	−	0.559721i
$65$	−4.74342	+	14.5987i	−0.588348	+	1.81075i
$66$	−3.00000	+	2.17963i	−0.369274	+	0.268294i
$67$	6.00000			0.733017			0.366508	−	0.930415i	$-0.380553\pi$
$67$	6.00000			0.733017			0.366508	+	0.930415i	$0.380553\pi$
$68$	−1.00155			−0.121456
$69$	−12.7082	+	9.23305i	−1.52989	+	1.11153i
$70$	−0.690983	−	0.502029i	−0.0825883	−	0.0600039i
$71$	−6.04508	−	4.39201i	−0.717420	−	0.521236i	0.168139	−	0.985763i	$-0.446224\pi$
$71$	−6.04508	−	4.39201i	−0.717420	−	0.521236i	−0.885559	+	0.464527i	$0.846224\pi$
$72$	−1.01722	−	3.13068i	−0.119881	−	0.368955i
$73$	−3.43237	+	2.49376i	−0.401728	+	0.291873i	−0.770245	−	0.637749i	$-0.779866\pi$
$73$	−3.43237	+	2.49376i	−0.401728	+	0.291873i	0.368516	+	0.929621i	$0.379866\pi$
$74$	0.500776	+	1.54123i	0.0582140	+	0.179164i
$75$		0			0
$76$	1.50000	+	1.08981i	0.172062	+	0.125010i
$77$	−1.31105	+	4.03499i	−0.149408	+	0.459830i
$78$	1.85410	−	5.70634i	0.209936	−	0.646116i
$79$	8.98606	+	6.52875i	1.01101	+	0.734542i	0.964421	−	0.264372i	$-0.0851647\pi$
$79$	8.98606	+	6.52875i	1.01101	+	0.734542i	0.0465897	+	0.998914i	$0.485165\pi$
$80$	−2.17376	+	6.69015i	−0.243034	+	0.747982i
$81$	−3.30902	−	10.1841i	−0.367669	−	1.13157i
$82$	−2.30902	+	1.67760i	−0.254988	+	0.185260i
$83$	0.977198	+	3.00750i	0.107261	+	0.330117i	0.990255	−	0.139269i	$-0.0444754\pi$
$83$	0.977198	+	3.00750i	0.107261	+	0.330117i	−0.882993	+	0.469386i	$0.844475\pi$
$84$	−3.43237	−	2.49376i	−0.374502	−	0.272092i
$85$	0.977198	+	0.709976i	0.105992	+	0.0770077i
$86$	0.0637598	−	0.0463242i	0.00687539	−	0.00499527i
$87$	−8.47214			−0.908308
$88$	−6.24574			−0.665799
$89$	4.74342	−	3.44629i	0.502801	−	0.365306i	−0.307285	−	0.951618i	$-0.599420\pi$
$89$	4.74342	−	3.44629i	0.502801	−	0.365306i	0.810086	+	0.586311i	$0.199420\pi$
$90$	−0.590170	+	1.81636i	−0.0622094	+	0.191461i
$91$	−2.12132	−	6.52875i	−0.222375	−	0.684399i
$92$	−12.7279			−1.32698
$93$		0			0
$94$	1.41641			0.146091
$95$	−0.690983	−	2.12663i	−0.0708934	−	0.218187i
$96$	2.93159	−	9.02251i	0.299204	−	0.920857i
$97$	5.66312	−	4.11450i	0.575003	−	0.417764i	−0.261916	−	0.965091i	$-0.584354\pi$
$97$	5.66312	−	4.11450i	0.575003	−	0.417764i	0.836919	+	0.547327i	$0.184354\pi$
$98$	−2.29180			−0.231506
$99$	9.48683			0.953463
$100$		0			0
$101$	1.80902	+	1.31433i	0.180004	+	0.130781i	0.674139	−	0.738605i	$-0.264515\pi$
$101$	1.80902	+	1.31433i	0.180004	+	0.130781i	−0.494135	+	0.869385i	$0.664515\pi$
$102$	−0.381966	−	0.277515i	−0.0378203	−	0.0274780i
$103$	−0.836881	−	2.57565i	−0.0824603	−	0.253787i	0.901323	−	0.433148i	$-0.142597\pi$
$103$	−0.836881	−	2.57565i	−0.0824603	−	0.253787i	−0.983783	+	0.179361i	$0.942597\pi$
$104$	8.17578	−	5.94006i	0.801702	−	0.582470i
$105$	1.58114	+	4.86624i	0.154303	+	0.474897i
$106$	0.618993	−	1.90506i	0.0601219	−	0.185036i
$107$	6.04508	+	4.39201i	0.584400	+	0.424592i	0.840308	−	0.542110i	$-0.182374\pi$
$107$	6.04508	+	4.39201i	0.584400	+	0.424592i	−0.255907	+	0.966701i	$0.582374\pi$
$108$	1.00155	−	3.08246i	0.0963743	−	0.296610i
$109$	−4.54508	+	13.9883i	−0.435340	+	1.33984i	0.457397	+	0.889262i	$0.348782\pi$
$109$	−4.54508	+	13.9883i	−0.435340	+	1.33984i	−0.892738	+	0.450577i	$0.851218\pi$
$110$	2.93159	+	2.12993i	0.279516	+	0.203081i
$111$	3.00000	−	9.23305i	0.284747	−	0.876362i
$112$	−0.972136	−	2.99193i	−0.0918582	−	0.282711i
$113$	11.5172	−	8.36775i	1.08345	−	0.787172i	0.105168	−	0.994454i	$-0.466462\pi$
$113$	11.5172	−	8.36775i	1.08345	−	0.787172i	0.978281	+	0.207283i	$0.0664620\pi$
$114$	0.270091	+	0.831254i	0.0252963	+	0.0778541i
$115$	12.4184	+	9.02251i	1.15802	+	0.841354i
$116$	−5.55369	−	4.03499i	−0.515647	−	0.374640i
$117$	−12.4184	+	9.02251i	−1.14808	+	0.834132i
$118$	−2.27051			−0.209017
$119$	−0.540182			−0.0495184
$120$	−6.09387	+	4.42746i	−0.556292	+	0.404170i
$121$	2.16312	−	6.65740i	0.196647	−	0.605218i
$122$	0.525130	+	1.61618i	0.0475430	+	0.146322i
$123$	17.0981			1.54168
$124$		0			0
$125$	11.1803			1.00000
$126$	−0.263932	−	0.812299i	−0.0235129	−	0.0723654i
$127$	2.93159	−	9.02251i	0.260137	−	0.800619i	−0.732637	−	0.680619i	$-0.761711\pi$
$127$	2.93159	−	9.02251i	0.260137	−	0.800619i	0.992774	−	0.119999i	$-0.0382892\pi$
$128$	8.16312	−	5.93085i	0.721525	−	0.524218i
$129$	−0.472136			−0.0415693
$130$	−5.86319			−0.514235
$131$	15.7082	−	11.4127i	1.37243	−	0.997130i	0.374889	−	0.927070i	$-0.377681\pi$
$131$	15.7082	−	11.4127i	1.37243	−	0.997130i	0.997543	−	0.0700608i	$-0.0223193\pi$
$132$	14.5623	+	10.5801i	1.26749	+	0.920883i
$133$	0.809017	+	0.587785i	0.0701507	+	0.0509674i
$134$	0.708204	+	2.17963i	0.0611795	+	0.188291i
$135$	−3.16228	+	2.29753i	−0.272166	+	0.197740i
$136$	−0.245737	−	0.756300i	−0.0210717	−	0.0648522i
$137$	2.12132	−	6.52875i	0.181237	−	0.557789i	−0.818627	−	0.574326i	$-0.805264\pi$
$137$	2.12132	−	6.52875i	0.181237	−	0.557789i	0.999863	+	0.0165371i	$0.00526416\pi$
$138$	−4.85410	−	3.52671i	−0.413209	−	0.300214i
$139$	0.309496	−	0.952532i	0.0262511	−	0.0807927i	−0.937073	−	0.349134i	$-0.886476\pi$
$139$	0.309496	−	0.952532i	0.0262511	−	0.0807927i	0.963324	+	0.268342i	$0.0864756\pi$
$140$	−1.28115	+	3.94298i	−0.108277	+	0.333243i
$141$	−6.86474	−	4.98752i	−0.578115	−	0.420025i
$142$	0.881966	−	2.71441i	0.0740129	−	0.227788i
$143$	9.00000	+	27.6992i	0.752618	+	2.31632i
$144$	−5.69098	+	4.13474i	−0.474249	+	0.344562i
$145$	2.55834	+	7.87375i	0.212458	+	0.653879i
$146$	−1.31105	−	0.952532i	−0.108503	−	0.0788321i
$147$	11.1074	+	8.06998i	0.916121	+	0.665601i
$148$	6.36396	−	4.62369i	0.523114	−	0.380065i
$149$	13.4164			1.09911			0.549557	−	0.835456i	$-0.314796\pi$
$149$	13.4164			1.09911			0.549557	+	0.835456i	$0.314796\pi$
$150$		0			0
$151$	−2.45517	+	1.78379i	−0.199799	+	0.145162i	−0.683186	−	0.730244i	$-0.739406\pi$
$151$	−2.45517	+	1.78379i	−0.199799	+	0.145162i	0.483387	+	0.875407i	$0.339406\pi$
$152$	−0.454915	+	1.40008i	−0.0368985	+	0.113562i
$153$	0.373256	+	1.14876i	0.0301760	+	0.0928721i
$154$	−1.62054			−0.130587
$155$		0			0
$156$	−29.1246			−2.33184
$157$	−1.45492	−	4.47777i	−0.116115	−	0.357365i	0.876063	−	0.482197i	$-0.160161\pi$
$157$	−1.45492	−	4.47777i	−0.116115	−	0.357365i	−0.992178	+	0.124832i	$0.960161\pi$
$158$	−1.31105	+	4.03499i	−0.104301	+	0.321007i
$159$	−9.70820	+	7.05342i	−0.769911	+	0.559373i
$160$	−9.27051			−0.732898
$161$	−6.86474			−0.541017
$162$	3.30902	−	2.40414i	0.259981	−	0.188887i
$163$	10.0451	+	7.29818i	0.786792	+	0.571638i	0.907010	−	0.421110i	$-0.138359\pi$
$163$	10.0451	+	7.29818i	0.786792	+	0.571638i	−0.120218	+	0.992748i	$0.538359\pi$
$164$	11.2082	+	8.14324i	0.875214	+	0.635880i
$165$	−6.70820	−	20.6457i	−0.522233	−	1.60727i
$166$	−0.977198	+	0.709976i	−0.0758452	+	0.0551048i
$167$	−2.28825	−	7.04250i	−0.177070	−	0.544965i	0.822652	−	0.568545i	$-0.192493\pi$
$167$	−2.28825	−	7.04250i	−0.177070	−	0.544965i	−0.999722	+	0.0235803i	$0.992493\pi$
$168$	1.04096	−	3.20374i	0.0803116	−	0.247174i
$169$	−27.6074	−	20.0579i	−2.12365	−	1.54292i
$170$	−0.142571	+	0.438789i	−0.0109347	+	0.0336536i
$171$	0.690983	−	2.12663i	0.0528408	−	0.162627i
$172$	−0.309496	−	0.224862i	−0.0235989	−	0.0171456i
$173$	5.56231	−	17.1190i	0.422894	−	1.30153i	−0.482102	−	0.876115i	$-0.660127\pi$
$173$	5.56231	−	17.1190i	0.422894	−	1.30153i	0.904996	−	0.425420i	$-0.139873\pi$
$174$	−1.00000	−	3.07768i	−0.0758098	−	0.233319i
$175$		0			0
$176$	4.12442	+	12.6937i	0.310890	+	0.956821i
$177$	11.0042	+	7.99503i	0.827127	+	0.600943i
$178$	1.81182	+	1.31637i	0.135802	+	0.0986659i
$179$	−13.2925	+	9.65754i	−0.993525	+	0.721838i	−0.960690	−	0.277623i	$-0.910454\pi$
$179$	−13.2925	+	9.65754i	−0.993525	+	0.721838i	−0.0328347	+	0.999461i	$0.510454\pi$
$180$	9.27051			0.690983
$181$	18.1784			1.35119			0.675597	−	0.737271i	$-0.263886\pi$
$181$	18.1784			1.35119			0.675597	+	0.737271i	$0.263886\pi$
$182$	2.12132	−	1.54123i	0.157243	−	0.114244i
$183$	3.14590	−	9.68208i	0.232551	−	0.715720i
$184$	−3.12287	−	9.61121i	−0.230221	−	0.708548i
$185$	−9.48683			−0.697486
$186$		0			0
$187$	2.29180			0.167593
$188$	−2.12461	−	6.53888i	−0.154953	−	0.476897i
$189$	0.540182	−	1.66251i	0.0392924	−	0.120930i
$190$	0.690983	−	0.502029i	0.0501292	−	0.0364210i
$191$	14.2361			1.03009			0.515043	−	0.857164i	$-0.327776\pi$
$191$	14.2361			1.03009			0.515043	+	0.857164i	$0.327776\pi$
$192$	−10.7735			−0.777512
$193$	5.89919	−	4.28601i	0.424633	−	0.308514i	−0.354866	−	0.934917i	$-0.615474\pi$
$193$	5.89919	−	4.28601i	0.424633	−	0.308514i	0.779499	+	0.626403i	$0.215474\pi$
$194$	2.16312	+	1.57160i	0.155303	+	0.112834i
$195$	28.4164	+	20.6457i	2.03494	+	1.47847i
$196$	3.43769	+	10.5801i	0.245550	+	0.755724i
$197$	5.99070	−	4.35250i	0.426820	−	0.310103i	−0.353556	−	0.935413i	$-0.615028\pi$
$197$	5.99070	−	4.35250i	0.426820	−	0.310103i	0.780376	+	0.625310i	$0.215028\pi$
$198$	1.11977	+	3.44629i	0.0795785	+	0.244917i
$199$	−4.55214	+	14.0100i	−0.322692	+	0.993145i	0.649779	+	0.760123i	$0.274861\pi$
$199$	−4.55214	+	14.0100i	−0.322692	+	0.993145i	−0.972471	+	0.233022i	$0.925139\pi$
$200$		0			0
$201$	4.24264	−	13.0575i	0.299253	−	0.921005i
$202$	−0.263932	+	0.812299i	−0.0185702	+	0.0571532i
$203$	−2.99535	−	2.17625i	−0.210233	−	0.152743i
$204$	−0.708204	+	2.17963i	−0.0495842	+	0.152604i
$205$	−5.16312	−	15.8904i	−0.360608	−	1.10984i
$206$	0.836881	−	0.608030i	0.0583083	−	0.0423634i
$207$	4.74342	+	14.5987i	0.329690	+	1.01468i
$208$	−17.4713	−	12.6937i	−1.21142	−	0.880148i
$209$	−3.43237	−	2.49376i	−0.237422	−	0.172497i
$210$	−1.58114	+	1.14876i	−0.109109	+	0.0792723i
$211$	−5.00000			−0.344214			−0.172107	−	0.985078i	$-0.555058\pi$
$211$	−5.00000			−0.344214			−0.172107	+	0.985078i	$0.555058\pi$
$212$	−9.72327			−0.667797
$213$	−13.8326	+	10.0500i	−0.947797	+	0.688615i
$214$	−0.881966	+	2.71441i	−0.0602900	+	0.185553i
$215$	0.142571	+	0.438789i	0.00972328	+	0.0299252i
$216$	2.57339			0.175097
$217$		0			0
$218$	−5.61803			−0.380501
$219$	3.00000	+	9.23305i	0.202721	+	0.623912i
$220$	5.43547	−	16.7287i	0.366459	−	1.12785i
$221$	−3.00000	+	2.17963i	−0.201802	+	0.146618i
$222$	3.70820			0.248878
$223$	−21.8021			−1.45998			−0.729988	−	0.683460i	$-0.760474\pi$
$223$	−21.8021			−1.45998			−0.729988	+	0.683460i	$0.760474\pi$
$224$	3.35410	−	2.43690i	0.224105	−	0.162822i
$225$		0			0
$226$	4.39919	+	3.19620i	0.292630	+	0.212608i
$227$	4.85410	+	14.9394i	0.322178	+	0.991562i	0.972698	+	0.232073i	$0.0745509\pi$
$227$	4.85410	+	14.9394i	0.322178	+	0.991562i	−0.650520	+	0.759489i	$0.725449\pi$
$228$	3.43237	−	2.49376i	0.227314	−	0.165153i
$229$	1.31105	+	4.03499i	0.0866365	+	0.266640i	0.984984	−	0.172646i	$-0.0552316\pi$
$229$	1.31105	+	4.03499i	0.0866365	+	0.266640i	−0.898347	+	0.439286i	$0.855232\pi$
$230$	−1.81182	+	5.57622i	−0.119468	+	0.367685i
$231$	7.85410	+	5.70634i	0.516762	+	0.375450i
$232$	1.68430	−	5.18376i	0.110580	−	0.340330i
$233$	−1.39919	+	4.30625i	−0.0916638	+	0.282112i	−0.986370	−	0.164543i	$-0.947385\pi$
$233$	−1.39919	+	4.30625i	−0.0916638	+	0.282112i	0.894706	+	0.446655i	$0.147385\pi$
$234$	−4.74342	−	3.44629i	−0.310087	−	0.225291i
$235$	−2.56231	+	7.88597i	−0.167146	+	0.514424i
$236$	3.40576	+	10.4819i	0.221696	+	0.682311i
$237$	20.5623	−	14.9394i	1.33567	−	0.970418i
$238$	−0.0637598	−	0.196232i	−0.00413293	−	0.0127199i
$239$	13.2287	+	9.61121i	0.855693	+	0.621698i	0.926710	−	0.375778i	$-0.122624\pi$
$239$	13.2287	+	9.61121i	0.855693	+	0.621698i	−0.0710166	+	0.997475i	$0.522624\pi$
$240$	13.0224	+	9.46130i	0.840590	+	0.610725i
$241$	−11.9176	+	8.65868i	−0.767683	+	0.557755i	−0.901257	−	0.433284i	$-0.857355\pi$
$241$	−11.9176	+	8.65868i	−0.767683	+	0.557755i	0.133574	+	0.991039i	$0.457355\pi$
$242$	2.67376			0.171876
$243$	−19.2588			−1.23545
$244$	6.67346	−	4.84855i	0.427224	−	0.310397i
$245$	4.14590	−	12.7598i	0.264872	−	0.815191i
$246$	2.01815	+	6.21124i	0.128673	+	0.396014i
$247$	6.86474			0.436793
$248$		0			0
$249$	7.23607			0.458567
$250$	1.31966	+	4.06150i	0.0834626	+	0.256872i
$251$	−7.34116	+	22.5938i	−0.463370	+	1.42611i	0.397651	+	0.917537i	$0.369825\pi$
$251$	−7.34116	+	22.5938i	−0.463370	+	1.42611i	−0.861021	+	0.508569i	$0.830175\pi$
$252$	−3.35410	+	2.43690i	−0.211289	+	0.153510i
$253$	29.1246			1.83105
$254$	3.62365			0.227368
$255$	2.23607	−	1.62460i	0.140028	−	0.101736i
$256$	−4.50000	−	3.26944i	−0.281250	−	0.204340i
$257$	−19.3713	−	14.0741i	−1.20835	−	0.877918i	−0.213270	−	0.976993i	$-0.568411\pi$
$257$	−19.3713	−	14.0741i	−1.20835	−	0.877918i	−0.995080	+	0.0990757i	$0.968411\pi$
$258$	−0.0557281	−	0.171513i	−0.00346948	−	0.0106780i
$259$	3.43237	−	2.49376i	0.213277	−	0.154955i
$260$	8.79478	+	27.0675i	0.545429	+	1.67866i
$261$	−2.55834	+	7.87375i	−0.158357	+	0.487373i
$262$	6.00000	+	4.35926i	0.370681	+	0.269316i
$263$	0.834626	−	2.56872i	0.0514653	−	0.158394i	−0.922021	−	0.387141i	$-0.873463\pi$
$263$	0.834626	−	2.56872i	0.0514653	−	0.158394i	0.973486	+	0.228747i	$0.0734628\pi$
$264$	−4.41641	+	13.5923i	−0.271811	+	0.836549i
$265$	9.48683	+	6.89259i	0.582772	+	0.423408i
$266$	−0.118034	+	0.363271i	−0.00723713	+	0.0222736i
$267$	−4.14590	−	12.7598i	−0.253725	−	0.780885i
$268$	9.00000	−	6.53888i	0.549762	−	0.399426i
$269$	4.57649	+	14.0850i	0.279034	+	0.858777i	0.988124	+	0.153659i	$0.0491059\pi$
$269$	4.57649	+	14.0850i	0.279034	+	0.858777i	−0.709090	+	0.705118i	$0.750894\pi$
$270$	−1.20788	−	0.877578i	−0.0735094	−	0.0534077i
$271$	22.7155	+	16.5038i	1.37987	+	1.00253i	0.996892	+	0.0787769i	$0.0251015\pi$
$271$	22.7155	+	16.5038i	1.37987	+	1.00253i	0.382978	+	0.923757i	$0.374899\pi$
$272$	−1.37481	+	0.998856i	−0.0833600	+	0.0605646i
$273$	−15.7082			−0.950704
$274$	2.62210			0.158407
$275$		0			0
$276$	−9.00000	+	27.6992i	−0.541736	+	1.66729i
$277$	6.05446	+	18.6337i	0.363778	+	1.11959i	0.950743	+	0.309980i	$0.100322\pi$
$277$	6.05446	+	18.6337i	0.363778	+	1.11959i	−0.586966	+	0.809612i	$0.699678\pi$
$278$	0.382559			0.0229443
$279$		0			0
$280$	−3.29180			−0.196722
$281$	−9.69098	−	29.8258i	−0.578116	−	1.77926i	−0.625316	−	0.780371i	$-0.715030\pi$
$281$	−9.69098	−	29.8258i	−0.578116	−	1.77926i	0.0472008	−	0.998885i	$-0.484970\pi$
$282$	1.00155	−	3.08246i	0.0596415	−	0.183558i
$283$	−19.4164	+	14.1068i	−1.15419	+	0.838565i	−0.989032	−	0.147703i	$-0.952812\pi$
$283$	−19.4164	+	14.1068i	−1.15419	+	0.838565i	−0.165154	+	0.986268i	$0.552812\pi$
$284$	−13.8541			−0.822090
$285$	−5.11667			−0.303086
$286$	−9.00000	+	6.53888i	−0.532181	+	0.386652i
$287$	6.04508	+	4.39201i	0.356830	+	0.259252i
$288$	−7.50000	−	5.44907i	−0.441942	−	0.321089i
$289$	−5.16312	−	15.8904i	−0.303713	−	0.934732i
$290$	−2.55834	+	1.85874i	−0.150231	+	0.109149i
$291$	−4.94975	−	15.2338i	−0.290159	−	0.893019i
$292$	−2.43082	+	7.48128i	−0.142253	+	0.437809i
$293$	12.7082	+	9.23305i	0.742421	+	0.539401i	0.893468	−	0.449126i	$-0.148265\pi$
$293$	12.7082	+	9.23305i	0.742421	+	0.539401i	−0.151047	+	0.988527i	$0.548265\pi$
$294$	−1.62054	+	4.98752i	−0.0945121	+	0.290878i
$295$	4.10739	−	12.6412i	0.239142	−	0.736002i
$296$	5.05291	+	3.67116i	0.293695	+	0.213382i
$297$	−2.29180	+	7.05342i	−0.132983	+	0.409281i
$298$	1.58359	+	4.87380i	0.0917350	+	0.282331i
$299$	−38.1246	+	27.6992i	−2.20480	+	1.60188i
$300$		0			0
$301$	−0.166925	−	0.121278i	−0.00962141	−	0.00699037i
$302$	−0.937792	−	0.681346i	−0.0539639	−	0.0392070i
$303$	4.13948	−	3.00750i	0.237807	−	0.172777i
$304$	3.14590			0.180430
$305$	−9.94820			−0.569632
$306$	−0.373256	+	0.271187i	−0.0213376	+	0.0155027i
$307$	−4.98278	+	15.3354i	−0.284382	+	0.875238i	0.702201	+	0.711979i	$0.252201\pi$
$307$	−4.98278	+	15.3354i	−0.284382	+	0.875238i	−0.986583	+	0.163260i	$0.947799\pi$
$308$	2.43082	+	7.48128i	0.138509	+	0.426286i
$309$	−6.19704			−0.352537
$310$		0			0
$311$	16.5279			0.937209			0.468605	−	0.883408i	$-0.344757\pi$
$311$	16.5279			0.937209			0.468605	+	0.883408i	$0.344757\pi$
$312$	−7.14590	−	21.9928i	−0.404557	−	1.24510i
$313$	−6.49148	+	19.9787i	−0.366920	+	1.12926i	0.581850	+	0.813296i	$0.302329\pi$
$313$	−6.49148	+	19.9787i	−0.366920	+	1.12926i	−0.948770	+	0.315968i	$0.897671\pi$
$314$	1.45492	−	1.05706i	0.0821056	−	0.0596532i
$315$	5.00000			0.281718
$316$	20.5942			1.15851
$317$	−17.6074	+	12.7925i	−0.988930	+	0.718499i	−0.959686	−	0.281073i	$-0.909310\pi$
$317$	−17.6074	+	12.7925i	−0.988930	+	0.718499i	−0.0292432	+	0.999572i	$0.509310\pi$
$318$	−3.70820	−	2.69417i	−0.207946	−	0.151081i
$319$	12.7082	+	9.23305i	0.711523	+	0.516952i
$320$	3.25329	+	10.0126i	0.181864	+	0.559721i
$321$	13.8326	−	10.0500i	0.772063	−	0.560936i
$322$	−0.810272	−	2.49376i	−0.0451547	−	0.138972i
$323$	0.166925	−	0.513743i	0.00928797	−	0.0285854i
$324$	−16.0623	−	11.6699i	−0.892350	−	0.648330i
$325$		0			0
$326$	−1.46556	+	4.51052i	−0.0811698	+	0.249815i
$327$	27.2283	+	19.7825i	1.50573	+	1.09397i
$328$	−3.39919	+	10.4616i	−0.187689	+	0.577646i
$329$	−1.14590	−	3.52671i	−0.0631754	−	0.194434i
$330$	6.70820	−	4.87380i	0.369274	−	0.268294i
$331$	−7.92075	−	24.3775i	−0.435364	−	1.33991i	−0.892714	−	0.450625i	$-0.851201\pi$
$331$	−7.92075	−	24.3775i	−0.435364	−	1.33991i	0.457350	−	0.889287i	$-0.348799\pi$
$332$	4.74342	+	3.44629i	0.260329	+	0.189140i
$333$	−7.67501	−	5.57622i	−0.420588	−	0.305575i
$334$	2.28825	−	1.66251i	0.125207	−	0.0909684i
$335$	−13.4164			−0.733017
$336$	−7.19859			−0.392715
$337$	4.74342	−	3.44629i	0.258390	−	0.187732i	−0.451047	−	0.892500i	$-0.648949\pi$
$337$	4.74342	−	3.44629i	0.258390	−	0.187732i	0.709437	+	0.704769i	$0.248949\pi$
$338$	4.02786	−	12.3965i	0.219087	−	0.674280i
$339$	−10.0664	−	30.9813i	−0.546733	−	1.68267i
$340$	2.23954			0.121456
$341$		0			0
$342$	0.854102			0.0461845
$343$	4.01722	+	12.3637i	0.216910	+	0.667579i
$344$	0.0938631	−	0.288881i	0.00506076	−	0.0155754i
$345$	28.4164	−	20.6457i	1.52989	−	1.11153i
$346$	6.87539			0.369623
$347$	25.8384			1.38708			0.693539	−	0.720419i	$-0.256050\pi$
$347$	25.8384			1.38708			0.693539	+	0.720419i	$0.256050\pi$
$348$	−12.7082	+	9.23305i	−0.681231	+	0.494943i
$349$	−4.85410	−	3.52671i	−0.259834	−	0.188781i	0.450240	−	0.892908i	$-0.351338\pi$
$349$	−4.85410	−	3.52671i	−0.259834	−	0.188781i	−0.710074	+	0.704127i	$0.751338\pi$
$350$		0			0
$351$	−3.70820	−	11.4127i	−0.197929	−	0.609164i
$352$	−14.2302	+	10.3389i	−0.758475	+	0.551064i
$353$	4.91034	+	15.1125i	0.261351	+	0.804356i	0.992512	+	0.122151i	$0.0389791\pi$
$353$	4.91034	+	15.1125i	0.261351	+	0.804356i	−0.731160	+	0.682206i	$0.761021\pi$
$354$	−1.60549	+	4.94120i	−0.0853310	+	0.262622i
$355$	13.5172	+	9.82084i	0.717420	+	0.521236i
$356$	3.35931	−	10.3389i	0.178043	−	0.547960i
$357$	−0.381966	+	1.17557i	−0.0202158	+	0.0622178i
$358$	−5.07727	−	3.68885i	−0.268342	−	0.194962i
$359$	3.01722	−	9.28605i	0.159243	−	0.490099i	−0.839323	−	0.543633i	$-0.817048\pi$
$359$	3.01722	−	9.28605i	0.159243	−	0.490099i	0.998566	+	0.0535337i	$0.0170485\pi$
$360$	2.27458	+	7.00042i	0.119881	+	0.368955i
$361$	14.5623	−	10.5801i	0.766437	−	0.556849i
$362$	2.14567	+	6.60371i	0.112774	+	0.347083i
$363$	−12.9586	−	9.41498i	−0.680150	−	0.494158i
$364$	−10.2971	−	7.48128i	−0.539715	−	0.392126i
$365$	7.67501	−	5.57622i	0.401728	−	0.291873i
$366$	3.88854			0.203257
$367$	−12.3153			−0.642851			−0.321426	−	0.946935i	$-0.604162\pi$
$367$	−12.3153			−0.642851			−0.321426	+	0.946935i	$0.604162\pi$
$368$	−17.4713	+	12.6937i	−0.910756	+	0.661703i
$369$	5.16312	−	15.8904i	0.268781	−	0.827224i
$370$	−1.11977	−	3.44629i	−0.0582140	−	0.179164i
$371$	−5.24419			−0.272265
$372$		0			0
$373$	−22.7082			−1.17579			−0.587893	−	0.808939i	$-0.700042\pi$
$373$	−22.7082			−1.17579			−0.587893	+	0.808939i	$0.700042\pi$
$374$	0.270510	+	0.832544i	0.0139877	+	0.0430498i
$375$	7.90569	−	24.3312i	0.408248	−	1.25646i
$376$	4.41641	−	3.20871i	0.227759	−	0.165476i
$377$	−25.4164			−1.30901
$378$	0.667701			0.0343428
$379$	15.7082	−	11.4127i	0.806876	−	0.586230i	−0.106047	−	0.994361i	$-0.533819\pi$
$379$	15.7082	−	11.4127i	0.806876	−	0.586230i	0.912923	+	0.408131i	$0.133819\pi$
$380$	−3.35410	−	2.43690i	−0.172062	−	0.125010i
$381$	−17.5623	−	12.7598i	−0.899744	−	0.653702i
$382$	1.68034	+	5.17155i	0.0859737	+	0.264600i
$383$	15.4138	−	11.1988i	0.787607	−	0.572230i	−0.119645	−	0.992817i	$-0.538176\pi$
$383$	15.4138	−	11.1988i	0.787607	−	0.572230i	0.907252	+	0.420587i	$0.138176\pi$
$384$	−7.13483	−	21.9587i	−0.364098	−	1.12058i
$385$	2.93159	−	9.02251i	0.149408	−	0.459830i
$386$	2.25329	+	1.63711i	0.114689	+	0.0833267i
$387$	−0.142571	+	0.438789i	−0.00724730	+	0.0223049i
$388$	4.01064	−	12.3435i	0.203610	−	0.626646i
$389$	−27.3314	−	19.8574i	−1.38576	−	1.00681i	−0.996316	−	0.0857617i	$-0.972668\pi$
$389$	−27.3314	−	19.8574i	−1.38576	−	1.00681i	−0.389443	−	0.921051i	$-0.627332\pi$
$390$	−4.14590	+	12.7598i	−0.209936	+	0.646116i
$391$	1.14590	+	3.52671i	0.0579506	+	0.178353i
$392$	−7.14590	+	5.19180i	−0.360922	+	0.262225i
$393$	−13.7295	−	42.2550i	−0.692560	−	2.13148i
$394$	2.28825	+	1.66251i	0.115280	+	0.0837559i
$395$	−20.0934	−	14.5987i	−1.01101	−	0.734542i
$396$	14.2302	−	10.3389i	0.715097	−	0.519548i
$397$	1.29180			0.0648334			0.0324167	−	0.999474i	$-0.489680\pi$
$397$	1.29180			0.0648334			0.0324167	+	0.999474i	$0.489680\pi$
$398$	−5.62675			−0.282044
$399$	1.85123	−	1.34500i	0.0926774	−	0.0673341i
$400$		0			0
$401$	−1.14412	−	3.52125i	−0.0571348	−	0.175843i	0.918416	−	0.395615i	$-0.129469\pi$
$401$	−1.14412	−	3.52125i	−0.0571348	−	0.175843i	−0.975551	+	0.219772i	$0.929469\pi$
$402$	5.24419			0.261557
$403$		0			0
$404$	4.14590			0.206266
$405$	7.39919	+	22.7724i	0.367669	+	1.13157i
$406$	0.437016	−	1.34500i	0.0216887	−	0.0667511i
$407$	−14.5623	+	10.5801i	−0.721827	+	0.524438i
$408$	−1.81966			−0.0900866
$409$	−17.3531			−0.858057			−0.429028	−	0.903291i	$-0.641144\pi$
$409$	−17.3531			−0.858057			−0.429028	+	0.903291i	$0.641144\pi$
$410$	5.16312	−	3.75123i	0.254988	−	0.185260i
$411$	−12.7082	−	9.23305i	−0.626849	−	0.455433i
$412$	−4.06231	−	2.95144i	−0.200135	−	0.145407i
$413$	1.83688	+	5.65334i	0.0903870	+	0.278183i
$414$	−4.74342	+	3.44629i	−0.233126	+	0.169376i
$415$	−2.18508	−	6.72499i	−0.107261	−	0.330117i
$416$	8.79478	−	27.0675i	0.431199	−	1.32710i
$417$	−1.85410	−	1.34708i	−0.0907958	−	0.0659670i
$418$	0.500776	−	1.54123i	0.0244937	−	0.0753840i
$419$	−5.74671	+	17.6866i	−0.280745	+	0.864045i	0.706897	+	0.707317i	$0.250095\pi$
$419$	−5.74671	+	17.6866i	−0.280745	+	0.864045i	−0.987642	+	0.156728i	$0.949905\pi$
$420$	7.67501	+	5.57622i	0.374502	+	0.272092i
$421$	−0.128677	+	0.396027i	−0.00627134	+	0.0193012i	−0.954143	−	0.299350i	$-0.903230\pi$
$421$	−0.128677	+	0.396027i	−0.00627134	+	0.0193012i	0.947872	+	0.318652i	$0.103230\pi$
$422$	−0.590170	−	1.81636i	−0.0287290	−	0.0884188i
$423$	−6.70820	+	4.87380i	−0.326164	+	0.236972i
$424$	−2.38566	−	7.34231i	−0.115858	−	0.356574i
$425$		0			0
$426$	−5.28360	−	3.83876i	−0.255991	−	0.185988i
$427$	3.59929	−	2.61504i	0.174182	−	0.126551i
$428$	13.8541			0.669663
$429$	66.6443			3.21762
$430$	−0.142571	+	0.103584i	−0.00687539	+	0.00499527i
$431$	−0.0344419	+	0.106001i	−0.00165901	+	0.00510589i	−0.951883	−	0.306463i	$-0.900854\pi$
$431$	−0.0344419	+	0.106001i	−0.00165901	+	0.00510589i	0.950224	+	0.311569i	$0.100854\pi$
$432$	−1.69936	−	5.23008i	−0.0817603	−	0.251632i
$433$	21.5958			1.03783			0.518913	−	0.854827i	$-0.326337\pi$
$433$	21.5958			1.03783			0.518913	+	0.854827i	$0.326337\pi$
$434$		0			0
$435$	18.9443			0.908308
$436$	8.42705	+	25.9358i	0.403583	+	1.24210i
$437$	2.12132	−	6.52875i	0.101477	−	0.312313i
$438$	−3.00000	+	2.17963i	−0.143346	+	0.104147i
$439$	−25.0000			−1.19318			−0.596592	−	0.802544i	$-0.703479\pi$
$439$	−25.0000			−1.19318			−0.596592	+	0.802544i	$0.703479\pi$
$440$	13.9659			0.665799
$441$	10.8541	−	7.88597i	0.516862	−	0.375522i
$442$	−1.14590	−	0.832544i	−0.0545048	−	0.0396001i
$443$	−19.3713	−	14.0741i	−0.920359	−	0.668680i	0.0232541	−	0.999730i	$-0.492597\pi$
$443$	−19.3713	−	14.0741i	−0.920359	−	0.668680i	−0.943613	+	0.331049i	$0.892597\pi$
$444$	−5.56231	−	17.1190i	−0.263975	−	0.812433i
$445$	−10.6066	+	7.70615i	−0.502801	+	0.365306i
$446$	−2.57339	−	7.92007i	−0.121853	−	0.375026i
$447$	9.48683	−	29.1975i	0.448712	−	1.38099i
$448$	−3.80902	−	2.76741i	−0.179959	−	0.130748i
$449$	−13.0374	+	40.1250i	−0.615274	+	1.89362i	−0.217853	+	0.975982i	$0.569905\pi$
$449$	−13.0374	+	40.1250i	−0.615274	+	1.89362i	−0.397421	+	0.917637i	$0.630095\pi$
$450$		0			0
$451$	−25.6471	−	18.6337i	−1.20768	−	0.877428i
$452$	8.15654	−	25.1033i	0.383651	−	1.18076i
$453$	2.14590	+	6.60440i	0.100823	+	0.310302i
$454$	−4.85410	+	3.52671i	−0.227814	+	0.165517i
$455$	4.74342	+	14.5987i	0.222375	+	0.684399i
$456$	2.72526	+	1.98002i	0.127622	+	0.0927229i
$457$	−9.15298	−	6.65003i	−0.428158	−	0.311075i	0.352754	−	0.935716i	$-0.385245\pi$
$457$	−9.15298	−	6.65003i	−0.428158	−	0.311075i	−0.780912	+	0.624641i	$0.785245\pi$
$458$	−1.31105	+	0.952532i	−0.0612613	+	0.0445089i
$459$	−0.944272			−0.0440748
$460$	28.4605			1.32698
$461$	31.6378	−	22.9862i	1.47352	−	1.07058i	0.493946	−	0.869492i	$-0.335554\pi$
$461$	31.6378	−	22.9862i	1.47352	−	1.07058i	0.979574	−	0.201083i	$-0.0644461\pi$
$462$	−1.14590	+	3.52671i	−0.0533120	+	0.164077i
$463$	4.67966	+	14.4025i	0.217482	+	0.669341i	0.998968	+	0.0454182i	$0.0144620\pi$
$463$	4.67966	+	14.4025i	0.217482	+	0.669341i	−0.781486	+	0.623923i	$0.785538\pi$
$464$	−11.6476			−0.540724
$465$		0			0
$466$	−1.72949			−0.0801171
$467$	4.83688	+	14.8864i	0.223824	+	0.688860i	0.998409	+	0.0563897i	$0.0179589\pi$
$467$	4.83688	+	14.8864i	0.223824	+	0.688860i	−0.774585	+	0.632470i	$0.782041\pi$
$468$	−8.79478	+	27.0675i	−0.406539	+	1.25120i
$469$	4.85410	−	3.52671i	0.224142	−	0.162848i
$470$	−3.16718			−0.146091
$471$	−10.7735			−0.496418
$472$	−7.07953	+	5.14358i	−0.325862	+	0.236752i
$473$	0.708204	+	0.514540i	0.0325633	+	0.0236586i
$474$	7.85410	+	5.70634i	0.360751	+	0.262101i
$475$		0			0
$476$	−0.810272	+	0.588697i	−0.0371388	+	0.0269829i
$477$	3.62365	+	11.1524i	0.165915	+	0.510635i
$478$	−1.93004	+	5.94006i	−0.0882780	+	0.271692i
$479$	−20.6074	−	14.9721i	−0.941576	−	0.684095i	0.00722373	−	0.999974i	$-0.497701\pi$
$479$	−20.6074	−	14.9721i	−0.941576	−	0.684095i	−0.948799	+	0.315879i	$0.897701\pi$
$480$	−6.55524	+	20.1750i	−0.299204	+	0.920857i
$481$	9.00000	−	27.6992i	0.410365	−	1.26297i
$482$	−4.55214	−	3.30732i	−0.207344	−	0.150644i
$483$	−4.85410	+	14.9394i	−0.220869	+	0.679766i
$484$	−4.01064	−	12.3435i	−0.182302	−	0.561068i
$485$	−12.6631	+	9.20029i	−0.575003	+	0.417764i
$486$	−2.27319	−	6.99617i	−0.103114	−	0.317353i
$487$	−15.0405	−	10.9276i	−0.681551	−	0.495176i	0.192321	−	0.981332i	$-0.438399\pi$
$487$	−15.0405	−	10.9276i	−0.681551	−	0.495176i	−0.873872	+	0.486156i	$0.838399\pi$
$488$	5.29865	+	3.84969i	0.239859	+	0.174267i
$489$	22.9856	−	16.7000i	1.03945	−	0.755202i
$490$	5.12461			0.231506
$491$	−9.56564			−0.431691			−0.215846	−	0.976427i	$-0.569251\pi$
$491$	−9.56564			−0.431691			−0.215846	+	0.976427i	$0.569251\pi$
$492$	25.6471	−	18.6337i	1.15626	−	0.840073i
$493$	−0.618034	+	1.90211i	−0.0278349	+	0.0856669i
$494$	0.810272	+	2.49376i	0.0364559	+	0.112200i
$495$	−21.2132			−0.953463
$496$		0			0
$497$	−7.47214			−0.335171
$498$	0.854102	+	2.62866i	0.0382732	+	0.117793i
$499$	5.68121	−	17.4850i	0.254326	−	0.782734i	−0.739636	−	0.673007i	$-0.765002\pi$
$499$	5.68121	−	17.4850i	0.254326	−	0.782734i	0.993962	−	0.109727i	$-0.0349977\pi$
$500$	16.7705	−	12.1845i	0.750000	−	0.544907i
$501$	−16.9443			−0.757014
$502$	−9.07417			−0.405000
$503$	−2.33688	+	1.69784i	−0.104196	+	0.0757031i	−0.638663	−	0.769486i	$-0.720512\pi$
$503$	−2.33688	+	1.69784i	−0.104196	+	0.0757031i	0.534467	+	0.845189i	$0.320512\pi$
$504$	−2.66312	−	1.93487i	−0.118625	−	0.0861859i
$505$	−4.04508	−	2.93893i	−0.180004	−	0.130781i
$506$	3.43769	+	10.5801i	0.152824	+	0.470344i
$507$	−63.1725	+	45.8975i	−2.80559	+	2.03838i
$508$	−5.43547	−	16.7287i	−0.241160	−	0.742214i
$509$	−1.47797	+	4.54873i	−0.0655100	+	0.201619i	−0.978454	−	0.206467i	$-0.933804\pi$
$509$	−1.47797	+	4.54873i	−0.0655100	+	0.201619i	0.912944	+	0.408086i	$0.133804\pi$
$510$	0.854102	+	0.620541i	0.0378203	+	0.0274780i
$511$	−1.31105	+	4.03499i	−0.0579974	+	0.178497i
$512$	6.89261	−	21.2133i	0.304613	−	0.937503i
$513$	1.41421	+	1.02749i	0.0624391	+	0.0453646i
$514$	2.82624	−	8.69827i	0.124660	−	0.383664i
$515$	1.87132	+	5.75934i	0.0824603	+	0.253787i
$516$	−0.708204	+	0.514540i	−0.0311769	+	0.0226514i
$517$	4.86163	+	14.9626i	0.213814	+	0.658053i
$518$	1.31105	+	0.952532i	0.0576041	+	0.0418519i
$519$	−33.3221	−	24.2099i	−1.46268	−	1.06270i
$520$	−18.2816	+	13.2824i	−0.801702	+	0.582470i
$521$	13.4164			0.587784			0.293892	−	0.955839i	$-0.405049\pi$
$521$	13.4164			0.587784			0.293892	+	0.955839i	$0.405049\pi$
$522$	−3.16228			−0.138409
$523$	−23.5258	+	17.0925i	−1.02871	+	0.747403i	−0.968050	−	0.250756i	$-0.919321\pi$
$523$	−23.5258	+	17.0925i	−1.02871	+	0.747403i	−0.0606612	+	0.998158i	$0.519321\pi$
$524$	11.1246	−	34.2380i	0.485981	−	1.49570i
$525$		0			0
$526$	1.03165			0.0449823
$527$		0			0
$528$	30.5410			1.32913
$529$	7.45492	+	22.9439i	0.324127	+	0.997560i
$530$	−1.38411	+	4.25985i	−0.0601219	+	0.185036i
$531$	10.7533	−	7.81272i	0.466653	−	0.339043i
$532$	1.85410			0.0803855
$533$	51.2942			2.22180
$534$	4.14590	−	3.01217i	0.179411	−	0.130349i
$535$	−13.5172	−	9.82084i	−0.584400	−	0.424592i
$536$	7.14590	+	5.19180i	0.308656	+	0.224252i
$537$	11.6180	+	35.7566i	0.501355	+	1.54301i
$538$	−4.57649	+	3.32502i	−0.197307	+	0.143352i
$539$	−7.86629	−	24.2099i	−0.338825	−	1.04280i
$540$	−2.23954	+	6.89259i	−0.0963743	+	0.296610i
$541$	22.5172	+	16.3597i	0.968091	+	0.703359i	0.955016	−	0.296555i	$-0.0958379\pi$
$541$	22.5172	+	16.3597i	0.968091	+	0.703359i	0.0130753	+	0.999915i	$0.495838\pi$
$542$	−3.31415	+	10.1999i	−0.142355	+	0.438124i
$543$	12.8541	−	39.5609i	0.551622	−	1.69772i
$544$	−1.81182	−	1.31637i	−0.0776813	−	0.0564388i
$545$	10.1631	−	31.2789i	0.435340	−	1.33984i
$546$	−1.85410	−	5.70634i	−0.0793482	−	0.244209i
$547$	19.7533	−	14.3516i	0.844590	−	0.613630i	−0.0790593	−	0.996870i	$-0.525192\pi$
$547$	19.7533	−	14.3516i	0.844590	−	0.613630i	0.923649	+	0.383240i	$0.125192\pi$
$548$	−3.93314	−	12.1050i	−0.168016	−	0.517099i
$549$	−8.04827	−	5.84741i	−0.343492	−	0.249561i
$550$		0			0
$551$	2.99535	−	2.17625i	0.127606	−	0.0927114i
$552$	−23.1246			−0.984249
$553$	11.1074			0.472334
$554$	−6.05446	+	4.39883i	−0.257230	+	0.186888i
$555$	−6.70820	+	20.6457i	−0.284747	+	0.876362i
$556$	−0.573838	−	1.76609i	−0.0243362	−	0.0748990i
$557$	−23.2951			−0.987046			−0.493523	−	0.869733i	$-0.664291\pi$
$557$	−23.2951			−0.987046			−0.493523	+	0.869733i	$0.664291\pi$
$558$		0			0
$559$	−1.41641			−0.0599077
$560$	2.17376	+	6.69015i	0.0918582	+	0.282711i
$561$	1.62054	−	4.98752i	0.0684194	−	0.210573i
$562$	9.69098	−	7.04091i	0.408789	−	0.297003i
$563$	14.2361			0.599979			0.299989	−	0.953943i	$-0.403017\pi$
$563$	14.2361			0.599979			0.299989	+	0.953943i	$0.403017\pi$
$564$	−15.7326			−0.662461
$565$	−25.7533	+	18.7109i	−1.08345	+	0.787172i
$566$	−7.41641	−	5.38834i	−0.311735	−	0.226489i
$567$	−8.66312	−	6.29412i	−0.363817	−	0.264328i
$568$	−3.39919	−	10.4616i	−0.142627	−	0.438960i
$569$	24.8369	−	18.0450i	1.04121	−	0.756487i	0.0706926	−	0.997498i	$-0.477479\pi$
$569$	24.8369	−	18.0450i	1.04121	−	0.756487i	0.970522	+	0.241011i	$0.0774791\pi$
$570$	−0.603941	−	1.85874i	−0.0252963	−	0.0778541i
$571$	2.12132	−	6.52875i	0.0887745	−	0.273220i	−0.896807	−	0.442422i	$-0.854119\pi$
$571$	2.12132	−	6.52875i	0.0887745	−	0.273220i	0.985581	+	0.169203i	$0.0541192\pi$
$572$	43.6869	+	31.7404i	1.82664	+	1.32713i
$573$	10.0664	−	30.9813i	0.420531	−	1.29426i
$574$	−0.881966	+	2.71441i	−0.0368126	+	0.113297i
$575$		0			0
$576$	−3.25329	+	10.0126i	−0.135554	+	0.417191i
$577$	−9.27051	−	28.5317i	−0.385936	−	1.18779i	−0.935799	−	0.352535i	$-0.885320\pi$
$577$	−9.27051	−	28.5317i	−0.385936	−	1.18779i	0.549862	−	0.835255i	$-0.314680\pi$
$578$	5.16312	−	3.75123i	0.214757	−	0.156030i
$579$	−5.15608	−	15.8688i	−0.214279	−	0.659484i
$580$	12.4184	+	9.02251i	0.515647	+	0.374640i
$581$	2.55834	+	1.85874i	0.106138	+	0.0771135i
$582$	4.94975	−	3.59620i	0.205174	−	0.149067i
$583$	22.2492			0.921469
$584$	−6.24574			−0.258451
$585$	27.7684	−	20.1750i	1.14808	−	0.834132i
$586$	−1.85410	+	5.70634i	−0.0765922	+	0.235727i
$587$	12.7279	+	39.1725i	0.525338	+	1.61682i	0.763647	+	0.645634i	$0.223407\pi$
$587$	12.7279	+	39.1725i	0.525338	+	1.61682i	−0.238310	+	0.971189i	$0.576593\pi$
$588$	25.4558			1.04978
$589$		0			0
$590$	5.07701			0.209017
$591$	−5.23607	−	16.1150i	−0.215383	−	0.662881i
$592$	4.12442	−	12.6937i	0.169513	−	0.521707i
$593$	13.8992	−	10.0984i	0.570771	−	0.414690i	−0.264614	−	0.964354i	$-0.585245\pi$
$593$	13.8992	−	10.0984i	0.570771	−	0.414690i	0.835385	+	0.549665i	$0.185245\pi$
$594$	−2.83282			−0.116232
$595$	1.20788			0.0495184
$596$	20.1246	−	14.6214i	0.824336	−	0.598915i
$597$	27.2705	+	19.8132i	1.11611	+	0.810900i
$598$	−14.5623	−	10.5801i	−0.595497	−	0.432654i
$599$	7.39919	+	22.7724i	0.302323	+	0.930453i	0.980663	+	0.195705i	$0.0626996\pi$
$599$	7.39919	+	22.7724i	0.302323	+	0.930453i	−0.678340	+	0.734748i	$0.737300\pi$
$600$		0			0
$601$	2.68586	+	8.26621i	0.109558	+	0.337186i	0.990773	−	0.135530i	$-0.0432737\pi$
$601$	2.68586	+	8.26621i	0.109558	+	0.337186i	−0.881215	+	0.472716i	$0.843274\pi$
$602$	0.0243541	−	0.0749541i	0.000992598	−	0.00305490i
$603$	−10.8541	−	7.88597i	−0.442013	−	0.321141i
$604$	−1.73876	+	5.35136i	−0.0707492	+	0.217744i
$605$	−4.83688	+	14.8864i	−0.196647	+	0.605218i
$606$	1.58114	+	1.14876i	0.0642294	+	0.0466654i
$607$	−7.76393	+	23.8949i	−0.315128	+	0.969865i	0.660573	+	0.750762i	$0.270313\pi$
$607$	−7.76393	+	23.8949i	−0.315128	+	0.969865i	−0.975702	+	0.219104i	$0.929687\pi$
$608$	1.28115	+	3.94298i	0.0519576	+	0.159909i
$609$	−6.85410	+	4.97980i	−0.277742	+	0.201792i
$610$	−1.17423	−	3.61390i	−0.0475430	−	0.146322i
$611$	−20.5942	−	14.9626i	−0.833153	−	0.605321i
$612$	1.81182	+	1.31637i	0.0732386	+	0.0532110i
$613$	30.2236	−	21.9587i	1.22072	−	0.886905i	0.224561	−	0.974460i	$-0.427905\pi$
$613$	30.2236	−	21.9587i	1.22072	−	0.886905i	0.996160	+	0.0875549i	$0.0279053\pi$
$614$	−6.15905			−0.248559
$615$	−38.2325			−1.54168
$616$	−5.05291	+	3.67116i	−0.203588	+	0.147915i
$617$	−14.5623	+	44.8182i	−0.586256	+	1.80431i	0.00790912	+	0.999969i	$0.497482\pi$
$617$	−14.5623	+	44.8182i	−0.586256	+	1.80431i	−0.594165	+	0.804343i	$0.702518\pi$
$618$	−0.731461	−	2.25121i	−0.0294237	−	0.0905567i
$619$	−21.5958			−0.868007			−0.434003	−	0.900911i	$-0.642899\pi$
$619$	−21.5958			−0.868007			−0.434003	+	0.900911i	$0.642899\pi$
$620$		0			0
$621$	−12.0000			−0.481543
$622$	1.95085	+	6.00410i	0.0782219	+	0.240742i
$623$	1.81182	−	5.57622i	0.0725892	−	0.223407i
$624$	−39.9787	+	29.0462i	−1.60043	+	1.16278i
$625$	−25.0000			−1.00000
$626$	−8.02391			−0.320700
$627$	−7.85410	+	5.70634i	−0.313663	+	0.227889i
$628$	−7.06231	−	5.13107i	−0.281817	−	0.204752i
$629$	−1.85410	−	1.34708i	−0.0739279	−	0.0537118i
$630$	0.590170	+	1.81636i	0.0235129	+	0.0723654i
$631$	3.76622	−	2.73632i	0.149931	−	0.108931i	−0.510291	−	0.860002i	$-0.670462\pi$
$631$	3.76622	−	2.73632i	0.149931	−	0.108931i	0.660222	+	0.751071i	$0.270462\pi$
$632$	5.05291	+	15.5513i	0.200994	+	0.618596i
$633$	−3.53553	+	10.8813i	−0.140525	+	0.432491i
$634$	−6.72542	−	4.88631i	−0.267101	−	0.194060i
$635$	−6.55524	+	20.1750i	−0.260137	+	0.800619i
$636$	−6.87539	+	21.1603i	−0.272627	+	0.839059i
$637$	33.3221	+	24.2099i	1.32027	+	0.959233i
$638$	−1.85410	+	5.70634i	−0.0734046	+	0.225916i
$639$	5.16312	+	15.8904i	0.204250	+	0.628616i
$640$	−18.2533	+	13.2618i	−0.721525	+	0.524218i
$641$	−2.62210	−	8.06998i	−0.103567	−	0.318745i	0.885825	−	0.464020i	$-0.153593\pi$
$641$	−2.62210	−	8.06998i	−0.103567	−	0.318745i	−0.989391	+	0.145275i	$0.953593\pi$
$642$	5.28360	+	3.83876i	0.208527	+	0.151504i
$643$	19.1162	+	13.8888i	0.753871	+	0.547719i	0.897024	−	0.441981i	$-0.145724\pi$
$643$	19.1162	+	13.8888i	0.753871	+	0.547719i	−0.143153	+	0.989701i	$0.545724\pi$
$644$	−10.2971	+	7.48128i	−0.405763	+	0.294804i
$645$	1.05573			0.0415693
$646$	0.206331			0.00811798
$647$	−15.4775	+	11.2451i	−0.608485	+	0.442090i	−0.848880	−	0.528585i	$-0.822723\pi$
$647$	−15.4775	+	11.2451i	−0.608485	+	0.442090i	0.240396	+	0.970675i	$0.422723\pi$
$648$	4.87132	−	14.9924i	0.191364	−	0.588957i
$649$	−7.79323	−	23.9851i	−0.305911	−	0.941497i
$650$		0			0
$651$		0			0
$652$	23.0213			0.901583
$653$	−2.05573	−	6.32688i	−0.0804469	−	0.247590i	0.902742	−	0.430183i	$-0.141551\pi$
$653$	−2.05573	−	6.32688i	−0.0804469	−	0.247590i	−0.983189	+	0.182593i	$0.941551\pi$
$654$	−3.97255	+	12.2263i	−0.155339	+	0.478084i
$655$	−35.1246	+	25.5195i	−1.37243	+	0.997130i
$656$	23.5066			0.917778
$657$	9.48683			0.370117
$658$	1.14590	−	0.832544i	0.0446718	−	0.0324559i
$659$	−38.1697	−	27.7319i	−1.48688	−	1.08028i	−0.975258	−	0.221072i	$-0.929045\pi$
$659$	−38.1697	−	27.7319i	−1.48688	−	1.08028i	−0.511623	−	0.859210i	$-0.670955\pi$
$660$	−32.5623	−	23.6579i	−1.26749	−	0.920883i
$661$	−14.1631	−	43.5896i	−0.550881	−	1.69544i	−0.706579	−	0.707634i	$-0.749763\pi$
$661$	−14.1631	−	43.5896i	−0.550881	−	1.69544i	0.155698	−	0.987805i	$-0.450237\pi$
$662$	7.92075	−	5.75476i	0.307849	−	0.223665i
$663$	2.62210	+	8.06998i	0.101834	+	0.313412i
$664$	−1.43857	+	4.42746i	−0.0558273	+	0.171819i
$665$	−1.80902	−	1.31433i	−0.0701507	−	0.0509674i
$666$	1.11977	−	3.44629i	0.0433902	−	0.133541i
$667$	−7.85410	+	24.1724i	−0.304112	+	0.935961i
$668$	−11.1074	−	8.06998i	−0.429757	−	0.312237i
$669$	−15.4164	+	47.4468i	−0.596033	+	1.83440i
$670$	−1.58359	−	4.87380i	−0.0611795	−	0.188291i
$671$	−15.2705	+	11.0947i	−0.589511	+	0.428305i
$672$	−2.93159	−	9.02251i	−0.113089	−	0.348051i
$673$	6.03011	+	4.38113i	0.232444	+	0.168880i	0.697910	−	0.716185i	$-0.254113\pi$
$673$	6.03011	+	4.38113i	0.232444	+	0.168880i	−0.465467	+	0.885065i	$0.654113\pi$
$674$	1.81182	+	1.31637i	0.0697888	+	0.0507046i
$675$		0			0
$676$	−63.2705			−2.43348
$677$	−21.2132			−0.815290			−0.407645	−	0.913141i	$-0.633650\pi$
$677$	−21.2132			−0.815290			−0.407645	+	0.913141i	$0.633650\pi$
$678$	10.0664	−	7.31368i	0.386599	−	0.280880i
$679$	2.16312	−	6.65740i	0.0830129	−	0.255487i
$680$	0.549484	+	1.69114i	0.0210717	+	0.0648522i
$681$	35.9442			1.37739
$682$		0			0
$683$	−18.8197			−0.720114			−0.360057	−	0.932930i	$-0.617243\pi$
$683$	−18.8197			−0.720114			−0.360057	+	0.932930i	$0.617243\pi$
$684$	−1.28115	−	3.94298i	−0.0489861	−	0.150764i
$685$	−4.74342	+	14.5987i	−0.181237	+	0.557789i
$686$	−4.01722	+	2.91868i	−0.153378	+	0.111436i
$687$	9.70820			0.370391
$688$	−0.649096			−0.0247466
$689$	−29.1246	+	21.1603i	−1.10956	+	0.806142i
$690$	10.8541	+	7.88597i	0.413209	+	0.300214i
$691$	17.4615	+	12.6865i	0.664266	+	0.482618i	0.868101	−	0.496387i	$-0.165340\pi$
$691$	17.4615	+	12.6865i	0.664266	+	0.482618i	−0.203835	+	0.979005i	$0.565340\pi$
$692$	−10.3131	−	31.7404i	−0.392045	−	1.20659i
$693$	7.67501	−	5.57622i	0.291549	−	0.211823i
$694$	3.04981	+	9.38635i	0.115769	+	0.356301i
$695$	−0.692055	+	2.12993i	−0.0262511	+	0.0807927i
$696$	−10.0902	−	7.33094i	−0.382467	−	0.277878i
$697$	1.24729	−	3.83876i	0.0472444	−	0.145403i
$698$	0.708204	−	2.17963i	0.0268059	−	0.0825001i
$699$	8.38212	+	6.08996i	0.317041	+	0.230344i
$700$		0			0
$701$	8.54508	+	26.2991i	0.322743	+	0.993302i	0.972449	+	0.233116i	$0.0748922\pi$
$701$	8.54508	+	26.2991i	0.322743	+	0.993302i	−0.649706	+	0.760186i	$0.725108\pi$
$702$	3.70820	−	2.69417i	0.139957	−	0.101685i
$703$	1.31105	+	4.03499i	0.0494471	+	0.152183i
$704$	16.1603	+	11.7411i	0.609064	+	0.442511i
$705$	15.3500	+	11.1524i	0.578115	+	0.420025i
$706$	−4.91034	+	3.56757i	−0.184803	+	0.134267i
$707$	2.23607			0.0840960
$708$	25.2194			0.947803
$709$	−12.7279	+	9.24738i	−0.478007	+	0.347293i	−0.800554	−	0.599261i	$-0.795461\pi$
$709$	−12.7279	+	9.24738i	−0.478007	+	0.347293i	0.322546	+	0.946554i	$0.395461\pi$
$710$	−1.97214	+	6.06961i	−0.0740129	+	0.227788i
$711$	−7.67501	−	23.6212i	−0.287835	−	0.885866i
$712$	8.63141			0.323476
$713$		0			0
$714$	−0.472136			−0.0176692
$715$	−20.1246	−	61.9372i	−0.752618	−	2.31632i
$716$	−9.41377	+	28.9726i	−0.351809	+	1.08276i
$717$	30.2705	−	21.9928i	1.13047	−	0.821337i
$718$	3.72949			0.139183
$719$	−9.10427			−0.339532			−0.169766	−	0.985484i	$-0.554301\pi$
$719$	−9.10427			−0.339532			−0.169766	+	0.985484i	$0.554301\pi$
$720$	12.7254	−	9.24556i	0.474249	−	0.344562i
$721$	−2.19098	−	1.59184i	−0.0815965	−	0.0592833i
$722$	5.56231	+	4.04125i	0.207008	+	0.150400i
$723$	10.4164	+	32.0584i	0.387390	+	1.19226i
$724$	27.2677	−	19.8111i	1.01339	−	0.736274i
$725$		0			0
$726$	1.89064	−	5.81878i	0.0701681	−	0.215955i
$727$	2.89919	+	2.10638i	0.107525	+	0.0781214i	0.640248	−	0.768168i	$-0.278831\pi$
$727$	2.89919	+	2.10638i	0.107525	+	0.0781214i	−0.532723	+	0.846289i	$0.678831\pi$
$728$	3.12287	−	9.61121i	0.115741	−	0.356215i
$729$	−3.69098	+	11.3597i	−0.136703	+	0.420729i
$730$	2.93159	+	2.12993i	0.108503	+	0.0788321i
$731$	−0.0344419	+	0.106001i	−0.00127388	+	0.00392059i
$732$	−5.83282	−	17.9516i	−0.215587	−	0.663509i
$733$	−10.0451	+	7.29818i	−0.371024	+	0.269564i	−0.757635	−	0.652678i	$-0.773645\pi$
$733$	−10.0451	+	7.29818i	−0.371024	+	0.269564i	0.386612	+	0.922243i	$0.373645\pi$
$734$	−1.45362	−	4.47378i	−0.0536541	−	0.165130i
$735$	−24.8369	−	18.0450i	−0.916121	−	0.665601i
$736$	−23.0250	−	16.7287i	−0.848714	−	0.616627i
$737$	−20.5942	+	14.9626i	−0.758597	+	0.551153i
$738$	6.38197			0.234923
$739$	−25.6622			−0.943998			−0.471999	−	0.881599i	$-0.656467\pi$
$739$	−25.6622			−0.943998			−0.471999	+	0.881599i	$0.656467\pi$
$740$	−14.2302	+	10.3389i	−0.523114	+	0.380065i
$741$	4.85410	−	14.9394i	0.178320	−	0.548812i
$742$	−0.618993	−	1.90506i	−0.0227239	−	0.0699371i
$743$	−1.69936			−0.0623433			−0.0311717	−	0.999514i	$-0.509924\pi$
$743$	−1.69936			−0.0623433			−0.0311717	+	0.999514i	$0.509924\pi$
$744$		0			0
$745$	−30.0000			−1.09911
$746$	−2.68034	−	8.24924i	−0.0981342	−	0.302026i
$747$	2.18508	−	6.72499i	0.0799479	−	0.246054i
$748$	3.43769	−	2.49763i	0.125695	−	0.0913224i
$749$	7.47214			0.273026
$750$	9.77198			0.356822
$751$	−23.8992	+	17.3638i	−0.872094	+	0.633613i	−0.931148	−	0.364642i	$-0.881192\pi$
$751$	−23.8992	+	17.3638i	−0.872094	+	0.633613i	0.0590542	+	0.998255i	$0.481192\pi$
$752$	−9.43769	−	6.85689i	−0.344157	−	0.250045i
$753$	43.9787	+	31.9524i	1.60267	+	1.16441i
$754$	−3.00000	−	9.23305i	−0.109254	−	0.336248i
$755$	5.48993	−	3.98867i	0.199799	−	0.145162i
$756$	−1.00155	−	3.08246i	−0.0364261	−	0.112108i
$757$	−5.92695	+	18.2413i	−0.215418	+	0.662990i	0.783705	+	0.621133i	$0.213327\pi$
$757$	−5.92695	+	18.2413i	−0.215418	+	0.662990i	−0.999124	+	0.0418569i	$0.986673\pi$
$758$	6.00000	+	4.35926i	0.217930	+	0.158335i
$759$	20.5942	−	63.3825i	0.747522	−	2.30064i
$760$	1.01722	−	3.13068i	0.0368985	−	0.113562i
$761$	−1.81182	−	1.31637i	−0.0656786	−	0.0477183i	0.554462	−	0.832209i	$-0.312924\pi$
$761$	−1.81182	−	1.31637i	−0.0656786	−	0.0477183i	−0.620140	+	0.784491i	$0.712924\pi$
$762$	2.56231	−	7.88597i	0.0928225	−	0.285678i
$763$	4.54508	+	13.9883i	0.164543	+	0.506412i
$764$	21.3541	−	15.5147i	0.772564	−	0.561301i
$765$	−0.834626	−	2.56872i	−0.0301760	−	0.0928721i
$766$	5.88754	+	4.27755i	0.212725	+	0.154554i
$767$	33.0126	+	23.9851i	1.19202	+	0.866051i
$768$	−10.2971	+	7.48128i	−0.371565	+	0.269958i
$769$	13.8754			0.500359			0.250180	−	0.968199i	$-0.419510\pi$
$769$	13.8754			0.500359			0.250180	+	0.968199i	$0.419510\pi$
$770$	3.62365			0.130587
$771$	−44.3263	+	32.2050i	−1.59637	+	1.15983i
$772$	4.17783	−	12.8580i	0.150363	−	0.462771i
$773$	−8.34271	−	25.6762i	−0.300066	−	0.923510i	−0.981472	−	0.191604i	$-0.938631\pi$
$773$	−8.34271	−	25.6762i	−0.300066	−	0.923510i	0.681406	−	0.731906i	$-0.261369\pi$
$774$	−0.176228			−0.00633437
$775$		0			0
$776$	10.3050			0.369926
$777$	−3.00000	−	9.23305i	−0.107624	−	0.331234i
$778$	3.98760	−	12.2726i	0.142962	−	0.439993i
$779$	−6.04508	+	4.39201i	−0.216588	+	0.157360i
$780$	65.1246			2.33184
$781$	31.7016			1.13437
$782$	−1.14590	+	0.832544i	−0.0409772	+	0.0297717i
$783$	−5.23607	−	3.80423i	−0.187122	−	0.135952i
$784$	15.2705	+	11.0947i	0.545375	+	0.396238i
$785$	3.25329	+	10.0126i	0.116115	+	0.357365i
$786$	13.7295	−	9.97505i	0.489714	−	0.355798i
$787$	−2.81338	−	8.65868i	−0.100286	−	0.308649i	0.888309	−	0.459246i	$-0.151880\pi$
$787$	−2.81338	−	8.65868i	−0.100286	−	0.308649i	−0.988595	+	0.150597i	$0.951880\pi$
$788$	4.24264	−	13.0575i	0.151138	−	0.465154i
$789$	−5.00000	−	3.63271i	−0.178005	−	0.129328i
$790$	2.93159	−	9.02251i	0.104301	−	0.321007i
$791$	4.39919	−	13.5393i	0.156417	−	0.481402i
$792$	11.2987	+	8.20895i	0.401480	+	0.291693i
$793$	9.43769	−	29.0462i	0.335142	−	1.03146i
$794$	0.152476	+	0.469272i	0.00541117	+	0.0166539i
$795$	21.7082	−	15.7719i	0.769911	−	0.559373i
$796$	8.44013	+	25.9760i	0.299152	+	0.920696i
$797$	−4.24264	−	3.08246i	−0.150282	−	0.109186i	0.510103	−	0.860113i	$-0.329607\pi$
$797$	−4.24264	−	3.08246i	−0.150282	−	0.109186i	−0.660385	+	0.750927i	$0.729607\pi$
$798$	0.707107	+	0.513743i	0.0250313	+	0.0181863i
$799$	−1.62054	+	1.17739i	−0.0573307	+	0.0416532i
$800$		0			0
$801$	−13.1105			−0.463236
$802$	1.14412	−	0.831254i	0.0404004	−	0.0293526i
$803$	5.56231	−	17.1190i	0.196290	−	0.604117i
$804$	−7.86629	−	24.2099i	−0.277423	−	0.853819i
$805$	15.3500			0.541017
$806$		0			0
$807$	33.8885			1.19293
$808$	1.01722	+	3.13068i	0.0357857	+	0.110137i
$809$	−6.81603	+	20.9776i	−0.239639	+	0.737532i	0.756833	+	0.653608i	$0.226745\pi$
$809$	−6.81603	+	20.9776i	−0.239639	+	0.737532i	−0.996472	+	0.0839245i	$0.973255\pi$
$810$	−7.39919	+	5.37582i	−0.259981	+	0.188887i
$811$	−43.4164			−1.52456			−0.762278	−	0.647250i	$-0.775919\pi$
$811$	−43.4164			−1.52456			−0.762278	+	0.647250i	$0.775919\pi$
$812$	−6.86474			−0.240905
$813$	51.9787	−	37.7647i	1.82297	−	1.32447i
$814$	−5.56231	−	4.04125i	−0.194959	−	0.141646i
$815$	−22.4615	−	16.3192i	−0.786792	−	0.571638i
$816$	1.20163	+	3.69822i	0.0420653	+	0.129464i
$817$	0.166925	−	0.121278i	0.00583998	−	0.00424299i
$818$	−2.04826	−	6.30389i	−0.0716157	−	0.220410i
$819$	−4.74342	+	14.5987i	−0.165748	+	0.510121i
$820$	−25.0623	−	18.2088i	−0.875214	−	0.635880i
$821$	4.43392	−	13.6462i	0.154745	−	0.476256i	−0.843390	−	0.537302i	$-0.819444\pi$
$821$	4.43392	−	13.6462i	0.154745	−	0.476256i	0.998135	+	0.0610460i	$0.0194436\pi$
$822$	1.85410	−	5.70634i	0.0646692	−	0.199031i
$823$	−12.0846	−	8.77996i	−0.421242	−	0.306050i	0.356895	−	0.934144i	$-0.383835\pi$
$823$	−12.0846	−	8.77996i	−0.421242	−	0.306050i	−0.778137	+	0.628094i	$0.783835\pi$
$824$	1.23200	−	3.79171i	0.0429188	−	0.132091i
$825$		0			0
$826$	−1.83688	+	1.33457i	−0.0639133	+	0.0464357i
$827$	14.8492	+	45.7013i	0.516359	+	1.58919i	0.780796	+	0.624786i	$0.214814\pi$
$827$	14.8492	+	45.7013i	0.516359	+	1.58919i	−0.264437	+	0.964403i	$0.585186\pi$
$828$	23.0250	+	16.7287i	0.800175	+	0.581361i
$829$	4.71906	+	3.42860i	0.163900	+	0.119080i	0.666712	−	0.745316i	$-0.267701\pi$
$829$	4.71906	+	3.42860i	0.163900	+	0.119080i	−0.502812	+	0.864396i	$0.667701\pi$
$830$	2.18508	−	1.58755i	0.0758452	−	0.0551048i
$831$	44.8328			1.55523
$832$	−32.3206			−1.12051
$833$	2.62210	−	1.90506i	0.0908502	−	0.0660066i
$834$	0.270510	−	0.832544i	0.00936699	−	0.0288286i
$835$	5.11667	+	15.7475i	0.177070	+	0.544965i
$836$	−7.86629			−0.272061
$837$		0			0
$838$	−7.10333			−0.245380
$839$	2.29180	+	7.05342i	0.0791216	+	0.243511i	0.982791	−	0.184719i	$-0.0591374\pi$
$839$	2.29180	+	7.05342i	0.0791216	+	0.243511i	−0.903670	+	0.428230i	$0.859137\pi$
$840$	−2.32765	+	7.16377i	−0.0803116	+	0.247174i
$841$	12.3713	−	8.98829i	0.426597	−	0.309941i
$842$	−0.159054			−0.00548135
$843$	−71.7609			−2.47158
$844$	−7.50000	+	5.44907i	−0.258161	+	0.187565i
$845$	61.7320	+	44.8509i	2.12365	+	1.54292i
$846$	−2.56231	−	1.86162i	−0.0880939	−	0.0640040i
$847$	−2.16312	−	6.65740i	−0.0743256	−	0.228751i
$848$	−13.3469	+	9.69710i	−0.458335	+	0.333000i
$849$	16.9706	+	52.2300i	0.582428	+	1.79253i
$850$		0			0
$851$	−23.5623	−	17.1190i	−0.807705	−	0.586832i
$852$	−9.79633	+	30.1500i	−0.335617	+	1.03292i
$853$	−14.1246	+	43.4711i	−0.483617	+	1.48842i	0.350356	+	0.936617i	$0.386061\pi$
$853$	−14.1246	+	43.4711i	−0.483617	+	1.48842i	−0.833973	+	0.551805i	$0.813939\pi$
$854$	1.37481	+	0.998856i	0.0470450	+	0.0341802i
$855$	−1.54508	+	4.75528i	−0.0528408	+	0.162627i
$856$	3.39919	+	10.4616i	0.116182	+	0.357571i
$857$	4.85410	−	3.52671i	0.165813	−	0.120470i	−0.501784	−	0.864993i	$-0.667323\pi$
$857$	4.85410	−	3.52671i	0.165813	−	0.120470i	0.667597	+	0.744523i	$0.267323\pi$
$858$	7.86629	+	24.2099i	0.268551	+	0.826514i
$859$	2.95595	+	2.14762i	0.100856	+	0.0732759i	0.637070	−	0.770806i	$-0.280146\pi$
$859$	2.95595	+	2.14762i	0.100856	+	0.0732759i	−0.536214	+	0.844082i	$0.680146\pi$
$860$	0.692055	+	0.502807i	0.0235989	+	0.0171456i
$861$	13.8326	−	10.0500i	0.471415	−	0.342503i
$862$	−0.0425725			−0.00145002
$863$	35.3252			1.20249			0.601243	−	0.799067i	$-0.294673\pi$
$863$	35.3252			1.20249			0.601243	+	0.799067i	$0.294673\pi$
$864$	5.86319	−	4.25985i	0.199470	−	0.144923i
$865$	−12.4377	+	38.2793i	−0.422894	+	1.30153i
$866$	2.54903	+	7.84512i	0.0866197	+	0.266588i
$867$	−38.2325			−1.29844
$868$		0			0
$869$	−47.1246			−1.59859
$870$	2.23607	+	6.88191i	0.0758098	+	0.233319i
$871$	12.7279	−	39.1725i	0.431269	−	1.32731i
$872$	−17.5172	+	12.7270i	−0.593208	+	0.430991i
$873$	−15.6525			−0.529756
$874$	2.62210			0.0886937
$875$	9.04508	−	6.57164i	0.305780	−	0.222162i
$876$	14.5623	+	10.5801i	0.492015	+	0.357470i
$877$	12.3713	+	8.98829i	0.417750	+	0.303513i	0.776732	−	0.629831i	$-0.216876\pi$
$877$	12.3713	+	8.98829i	0.417750	+	0.303513i	−0.358982	+	0.933345i	$0.616876\pi$
$878$	−2.95085	−	9.08178i	−0.0995864	−	0.306495i
$879$	29.0795	−	21.1275i	0.980827	−	0.712612i
$880$	−9.22249	−	28.3839i	−0.310890	−	0.956821i
$881$	−15.3500	+	47.2425i	−0.517155	+	1.59164i	0.262171	+	0.965022i	$0.415562\pi$
$881$	−15.3500	+	47.2425i	−0.517155	+	1.59164i	−0.779326	+	0.626619i	$0.784438\pi$
$882$	4.14590	+	3.01217i	0.139600	+	0.101425i
$883$	−10.4884	+	32.2799i	−0.352962	+	1.08631i	0.604219	+	0.796818i	$0.293485\pi$
$883$	−10.4884	+	32.2799i	−0.352962	+	1.08631i	−0.957182	+	0.289488i	$0.906515\pi$
$884$	−2.12461	+	6.53888i	−0.0714584	+	0.219926i
$885$	−24.6062	−	17.8774i	−0.827127	−	0.600943i
$886$	2.82624	−	8.69827i	0.0949493	−	0.292224i
$887$	−5.98278	−	18.4131i	−0.200882	−	0.618251i	−0.999857	−	0.0168876i	$-0.994624\pi$
$887$	−5.98278	−	18.4131i	−0.200882	−	0.618251i	0.798975	−	0.601364i	$-0.205376\pi$
$888$	11.5623	−	8.40051i	0.388006	−	0.281903i
$889$	−2.93159	−	9.02251i	−0.0983225	−	0.302605i
$890$	−4.05136	−	2.94349i	−0.135802	−	0.0986659i
$891$	36.7545	+	26.7037i	1.23132	+	0.894608i
$892$	−32.7031	+	23.7602i	−1.09498	+	0.795551i
$893$	3.70820			0.124090
$894$	11.7264			0.392188
$895$	29.7228	−	21.5949i	0.993525	−	0.721838i
$896$	3.11803	−	9.59632i	0.104166	−	0.320591i
$897$	33.3221	+	102.555i	1.11259	+	3.42421i
$898$	−16.1151			−0.537769
$899$		0			0
$900$		0			0
$901$	0.875388	+	2.69417i	0.0291634	+	0.0897557i
$902$	3.74186	−	11.5163i	0.124590	−	0.383450i
$903$	−0.381966	+	0.277515i	−0.0127110	+	0.00923511i
$904$	20.9574			0.697034
$905$	−40.6482			−1.35119
$906$	−2.14590	+	1.55909i	−0.0712927	+	0.0517972i
$907$	44.9336	+	32.6462i	1.49200	+	1.08400i	0.973436	+	0.228958i	$0.0735318\pi$
$907$	44.9336	+	32.6462i	1.49200	+	1.08400i	0.518560	+	0.855041i	$0.326468\pi$
$908$	23.5623	+	17.1190i	0.781943	+	0.568115i
$909$	−1.54508	−	4.75528i	−0.0512472	−	0.157723i
$910$	−4.74342	+	3.44629i	−0.157243	+	0.114244i
$911$	4.38521	+	13.4963i	0.145289	+	0.447152i	0.997048	−	0.0767809i	$-0.0244642\pi$
$911$	4.38521	+	13.4963i	0.145289	+	0.447152i	−0.851759	+	0.523933i	$0.824464\pi$
$912$	2.22449	−	6.84626i	0.0736601	−	0.226702i
$913$	−10.8541	−	7.88597i	−0.359218	−	0.260987i
$914$	1.33540	−	4.10995i	0.0441712	−	0.135945i
$915$	−7.03444	+	21.6498i	−0.232551	+	0.715720i
$916$	6.36396	+	4.62369i	0.210271	+	0.152771i
$917$	6.00000	−	18.4661i	0.198137	−	0.609804i
$918$	−0.111456	−	0.343027i	−0.00367860	−	0.0113216i
$919$	−19.8541	+	14.4248i	−0.654926	+	0.475832i	−0.864946	−	0.501865i	$-0.832647\pi$
$919$	−19.8541	+	14.4248i	−0.654926	+	0.475832i	0.210019	+	0.977697i	$0.432647\pi$
$920$	6.98295	+	21.4913i	0.230221	+	0.708548i
$921$	29.8504	+	21.6876i	0.983603	+	0.714629i
$922$	12.0846	+	8.77996i	0.397984	+	0.289153i
$923$	−41.4979	+	30.1500i	−1.36592	+	0.992399i
$924$	18.0000			0.592157
$925$		0			0
$926$	−4.67966	+	3.39997i	−0.153783	+	0.111730i
$927$	−1.87132	+	5.75934i	−0.0614623	+	0.189162i
$928$	−4.74342	−	14.5987i	−0.155710	−	0.479227i
$929$	23.2951			0.764288			0.382144	−	0.924103i	$-0.375186\pi$
$929$	23.2951			0.764288			0.382144	+	0.924103i	$0.375186\pi$
$930$		0			0
$931$	−6.00000			−0.196642
$932$	2.59424	+	7.98424i	0.0849770	+	0.261532i
$933$	11.6870	−	35.9688i	0.382614	−	1.17756i
$934$	−4.83688	+	3.51420i	−0.158268	+	0.114988i
$935$	−5.12461			−0.167593
$936$	−22.5973			−0.738616
$937$	45.5066	−	33.0625i	1.48664	−	1.08010i	0.511293	−	0.859407i	$-0.329167\pi$
$937$	45.5066	−	33.0625i	1.48664	−	1.08010i	0.975342	−	0.220697i	$-0.0708332\pi$
$938$	1.85410	+	1.34708i	0.0605386	+	0.0439838i
$939$	38.8885	+	28.2542i	1.26908	+	0.922040i
$940$	4.75078	+	14.6214i	0.154953	+	0.476897i
$941$	−41.1247	+	29.8788i	−1.34063	+	0.974022i	−0.341205	+	0.939989i	$0.610835\pi$
$941$	−41.1247	+	29.8788i	−1.34063	+	0.974022i	−0.999421	+	0.0340326i	$0.989165\pi$
$942$	−1.27164	−	3.91371i	−0.0414323	−	0.127516i
$943$	15.8508	−	48.7837i	0.516173	−	1.58862i
$944$	15.1287	+	10.9916i	0.492396	+	0.357747i
$945$	−1.20788	+	3.71748i	−0.0392924	+	0.120930i
$946$	−0.103326	+	0.318003i	−0.00335940	+	0.0103392i
$947$	−1.81182	−	1.31637i	−0.0588764	−	0.0427762i	0.557958	−	0.829869i	$-0.311585\pi$
$947$	−1.81182	−	1.31637i	−0.0588764	−	0.0427762i	−0.616834	+	0.787093i	$0.711585\pi$
$948$	14.5623	−	44.8182i	0.472962	−	1.45563i
$949$	9.00000	+	27.6992i	0.292152	+	0.899153i
$950$		0			0
$951$	15.3894	+	47.3638i	0.499036	+	1.53588i
$952$	−0.643347	−	0.467419i	−0.0208510	−	0.0151491i
$953$	−43.2460	−	31.4200i	−1.40087	−	1.01780i	−0.994571	−	0.104057i	$-0.966818\pi$
$953$	−43.2460	−	31.4200i	−1.40087	−	1.01780i	−0.406303	−	0.913738i	$-0.633182\pi$
$954$	−3.62365	+	2.63273i	−0.117320	+	0.0852379i
$955$	−31.8328			−1.03009
$956$	30.3175			0.980537
$957$	29.0795	−	21.1275i	0.940006	−	0.682955i
$958$	3.00658	−	9.25330i	0.0971381	−	0.298960i
$959$	−2.12132	−	6.52875i	−0.0685010	−	0.210824i
$960$	24.0903			0.777512
$961$		0			0
$962$	11.1246			0.358672
$963$	−5.16312	−	15.8904i	−0.166379	−	0.512062i
$964$	−8.44013	+	25.9760i	−0.271838	+	0.836632i
$965$	−13.1910	+	9.58381i	−0.424633	+	0.308514i
$966$	−6.00000			−0.193047
$967$	−12.9041			−0.414969			−0.207485	−	0.978238i	$-0.566528\pi$
$967$	−12.9041			−0.414969			−0.207485	+	0.978238i	$0.566528\pi$
$968$	8.33688	−	6.05710i	0.267958	−	0.194683i
$969$	−1.00000	−	0.726543i	−0.0321246	−	0.0233399i
$970$	−4.83688	−	3.51420i	−0.155303	−	0.112834i
$971$	5.59675	+	17.2250i	0.179608	+	0.552777i	0.999814	−	0.0192915i	$-0.00614107\pi$
$971$	5.59675	+	17.2250i	0.179608	+	0.552777i	−0.820206	+	0.572069i	$0.806141\pi$
$972$	−28.8882	+	20.9885i	−0.926590	+	0.673207i
$973$	−0.309496	−	0.952532i	−0.00992200	−	0.0305368i
$974$	2.19438	−	6.75362i	0.0703126	−	0.216400i
$975$		0			0
$976$	4.32501	−	13.3110i	0.138440	−	0.426075i
$977$	13.1287	−	40.4059i	0.420024	−	1.29270i	−0.487656	−	0.873036i	$-0.662148\pi$
$977$	13.1287	−	40.4059i	0.420024	−	1.29270i	0.907680	−	0.419664i	$-0.137852\pi$
$978$	8.77973	+	6.37884i	0.280745	+	0.203973i
$979$	−7.68692	+	23.6579i	−0.245675	+	0.756110i
$980$	−7.68692	−	23.6579i	−0.245550	−	0.755724i
$981$	26.6074	−	19.3314i	0.849509	−	0.617204i
$982$	−1.12907	−	3.47492i	−0.0360301	−	0.110889i
$983$	2.43082	+	1.76609i	0.0775310	+	0.0563296i	0.625876	−	0.779923i	$-0.284742\pi$
$983$	2.43082	+	1.76609i	0.0775310	+	0.0563296i	−0.548345	+	0.836252i	$0.684742\pi$
$984$	20.3635	+	14.7950i	0.649165	+	0.471646i
$985$	−13.3956	+	9.73249i	−0.426820	+	0.310103i
$986$	−0.763932			−0.0243286
$987$	−8.48528			−0.270089
$988$	10.2971	−	7.48128i	0.327595	−	0.238011i
$989$	−0.437694	+	1.34708i	−0.0139179	+	0.0428348i
$990$	−2.50388	−	7.70615i	−0.0795785	−	0.244917i
$991$	−4.44897			−0.141326			−0.0706631	−	0.997500i	$-0.522512\pi$
$991$	−4.44897			−0.141326			−0.0706631	+	0.997500i	$0.522512\pi$
$992$		0			0
$993$	−58.6525			−1.86128
$994$	−0.881966	−	2.71441i	−0.0279743	−	0.0860959i
$995$	10.1789	−	31.3274i	0.322692	−	0.993145i
$996$	10.8541	−	7.88597i	0.343925	−	0.249876i
$997$	48.6656			1.54126			0.770628	−	0.637285i	$-0.219943\pi$
$997$	48.6656			1.54126			0.770628	+	0.637285i	$0.219943\pi$
$998$	7.02236			0.222289
$999$	6.00000	−	4.35926i	0.189832	−	0.137921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.h.531.2		8
31.2	even	5		961.2.d.j.388.1		8
31.3	odd	30		961.2.c.h.439.2		8
31.4	even	5		961.2.d.j.374.1		8
31.5	even	3		961.2.g.i.844.1		16
31.6	odd	6		961.2.g.i.547.1		16
31.7	even	15		961.2.g.p.816.1		16
31.8	even	5	inner	961.2.d.h.628.2		8
31.9	even	15		961.2.g.i.448.2		16
31.10	even	15		961.2.g.p.338.1		16
31.11	odd	30		961.2.g.p.732.1		16
31.12	odd	30		961.2.g.p.235.1		16
31.13	odd	30		961.2.c.h.521.2		8
31.14	even	15		961.2.g.i.846.1		16
31.15	odd	10		961.2.a.h.1.1	✓	4
31.16	even	5		961.2.a.h.1.2	yes	4
31.17	odd	30		961.2.g.i.846.2		16
31.18	even	15		961.2.c.h.521.1		8
31.19	even	15		961.2.g.p.235.2		16
31.20	even	15		961.2.g.p.732.2		16
31.21	odd	30		961.2.g.p.338.2		16
31.22	odd	30		961.2.g.i.448.1		16
31.23	odd	10	inner	961.2.d.h.628.1		8
31.24	odd	30		961.2.g.p.816.2		16
31.25	even	3		961.2.g.i.547.2		16
31.26	odd	6		961.2.g.i.844.2		16
31.27	odd	10		961.2.d.j.374.2		8
31.28	even	15		961.2.c.h.439.1		8
31.29	odd	10		961.2.d.j.388.2		8
31.30	odd	2	inner	961.2.d.h.531.1		8
93.47	odd	10		8649.2.a.r.1.3		4
93.77	even	10		8649.2.a.r.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.h.1.1	✓	4	31.15	odd	10
961.2.a.h.1.2	yes	4	31.16	even	5
961.2.c.h.439.1		8	31.28	even	15
961.2.c.h.439.2		8	31.3	odd	30
961.2.c.h.521.1		8	31.18	even	15
961.2.c.h.521.2		8	31.13	odd	30
961.2.d.h.531.1		8	31.30	odd	2	inner
961.2.d.h.531.2		8	1.1	even	1	trivial
961.2.d.h.628.1		8	31.23	odd	10	inner
961.2.d.h.628.2		8	31.8	even	5	inner
961.2.d.j.374.1		8	31.4	even	5
961.2.d.j.374.2		8	31.27	odd	10
961.2.d.j.388.1		8	31.2	even	5
961.2.d.j.388.2		8	31.29	odd	10
961.2.g.i.448.1		16	31.22	odd	30
961.2.g.i.448.2		16	31.9	even	15
961.2.g.i.547.1		16	31.6	odd	6
961.2.g.i.547.2		16	31.25	even	3
961.2.g.i.844.1		16	31.5	even	3
961.2.g.i.844.2		16	31.26	odd	6
961.2.g.i.846.1		16	31.14	even	15
961.2.g.i.846.2		16	31.17	odd	30
961.2.g.p.235.1		16	31.12	odd	30
961.2.g.p.235.2		16	31.19	even	15
961.2.g.p.338.1		16	31.10	even	15
961.2.g.p.338.2		16	31.21	odd	30
961.2.g.p.732.1		16	31.11	odd	30
961.2.g.p.732.2		16	31.20	even	15
961.2.g.p.816.1		16	31.7	even	15
961.2.g.p.816.2		16	31.24	odd	30
8649.2.a.r.1.3		4	93.47	odd	10
8649.2.a.r.1.4		4	93.77	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.118034 + 0.363271i) q^{2} +(0.707107 - 2.17625i) q^{3} +(1.50000 - 1.08981i) q^{4} -2.23607 q^{5} +0.874032 q^{6} +(0.809017 - 0.587785i) q^{7} +(1.19098 + 0.865300i) q^{8} +(-1.80902 - 1.31433i) q^{9} +(-0.263932 - 0.812299i) q^{10} +(-3.43237 + 2.49376i) q^{11} +(-1.31105 - 4.03499i) q^{12} +(2.12132 - 6.52875i) q^{13} +(0.309017 + 0.224514i) q^{14} +(-1.58114 + 4.86624i) q^{15} +(0.972136 - 2.99193i) q^{16} +(-0.437016 - 0.317511i) q^{17} +(0.263932 - 0.812299i) q^{18} +(0.309017 + 0.951057i) q^{19} +(-3.35410 + 2.43690i) q^{20} +(-0.707107 - 2.17625i) q^{21} +(-1.31105 - 0.952532i) q^{22} +(-5.55369 - 4.03499i) q^{23} +(2.72526 - 1.98002i) q^{24} +2.62210 q^{26} +(1.41421 - 1.02749i) q^{27} +(0.572949 - 1.76336i) q^{28} +(-1.14412 - 3.52125i) q^{29} -1.95440 q^{30} +4.14590 q^{32} +(3.00000 + 9.23305i) q^{33} +(0.0637598 - 0.196232i) q^{34} +(-1.80902 + 1.31433i) q^{35} -4.14590 q^{36} +4.24264 q^{37} +(-0.309017 + 0.224514i) q^{38} +(-12.7082 - 9.23305i) q^{39} +(-2.66312 - 1.93487i) q^{40} +(2.30902 + 7.10642i) q^{41} +(0.707107 - 0.513743i) q^{42} +(-0.0637598 - 0.196232i) q^{43} +(-2.43082 + 7.48128i) q^{44} +(4.04508 + 2.93893i) q^{45} +(0.810272 - 2.49376i) q^{46} +(1.14590 - 3.52671i) q^{47} +(-5.82378 - 4.23122i) q^{48} +(-1.85410 + 5.70634i) q^{49} +(-1.00000 + 0.726543i) q^{51} +(-3.93314 - 12.1050i) q^{52} +(-4.24264 - 3.08246i) q^{53} +(0.540182 + 0.392465i) q^{54} +(7.67501 - 5.57622i) q^{55} +1.47214 q^{56} +2.28825 q^{57} +(1.14412 - 0.831254i) q^{58} +(-1.83688 + 5.65334i) q^{59} +(2.93159 + 9.02251i) q^{60} +4.44897 q^{61} -2.23607 q^{63} +(-1.45492 - 4.47777i) q^{64} +(-4.74342 + 14.5987i) q^{65} +(-3.00000 + 2.17963i) q^{66} +6.00000 q^{67} -1.00155 q^{68} +(-12.7082 + 9.23305i) q^{69} +(-0.690983 - 0.502029i) q^{70} +(-6.04508 - 4.39201i) q^{71} +(-1.01722 - 3.13068i) q^{72} +(-3.43237 + 2.49376i) q^{73} +(0.500776 + 1.54123i) q^{74} +(1.50000 + 1.08981i) q^{76} +(-1.31105 + 4.03499i) q^{77} +(1.85410 - 5.70634i) q^{78} +(8.98606 + 6.52875i) q^{79} +(-2.17376 + 6.69015i) q^{80} +(-3.30902 - 10.1841i) q^{81} +(-2.30902 + 1.67760i) q^{82} +(0.977198 + 3.00750i) q^{83} +(-3.43237 - 2.49376i) q^{84} +(0.977198 + 0.709976i) q^{85} +(0.0637598 - 0.0463242i) q^{86} -8.47214 q^{87} -6.24574 q^{88} +(4.74342 - 3.44629i) q^{89} +(-0.590170 + 1.81636i) q^{90} +(-2.12132 - 6.52875i) q^{91} -12.7279 q^{92} +1.41641 q^{94} +(-0.690983 - 2.12663i) q^{95} +(2.93159 - 9.02251i) q^{96} +(5.66312 - 4.11450i) q^{97} -2.29180 q^{98} +9.48683 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 12 q^{4} + 2 q^{7} + 14 q^{8} - 10 q^{9} - 20 q^{10} - 2 q^{14} - 28 q^{16} + 20 q^{18} - 2 q^{19} + 18 q^{28} + 60 q^{32} + 24 q^{33} - 10 q^{35} - 60 q^{36} + 2 q^{38} - 48 q^{39} + 10 q^{40}+ \cdots - 72 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 12 * q^4 + 2 * q^7 + 14 * q^8 - 10 * q^9 - 20 * q^10 - 2 * q^14 - 28 * q^16 + 20 * q^18 - 2 * q^19 + 18 * q^28 + 60 * q^32 + 24 * q^33 - 10 * q^35 - 60 * q^36 + 2 * q^38 - 48 * q^39 + 10 * q^40 + 14 * q^41 + 10 * q^45 + 36 * q^47 + 12 * q^49 - 8 * q^51 - 24 * q^56 - 46 * q^59 - 34 * q^64 - 24 * q^66 + 48 * q^67 - 48 * q^69 - 10 * q^70 - 26 * q^71 + 50 * q^72 + 12 * q^76 - 12 * q^78 - 80 * q^80 - 22 * q^81 - 14 * q^82 - 32 * q^87 + 40 * q^90 - 96 * q^94 - 10 * q^95 + 14 * q^97 - 72 * q^98

Introduction

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