LMFDB - Embedded newform 961.2.g.a.732.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("961.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			732.1
Root			$0.669131 - 0.743145i$ of defining polynomial
Character	$\chi$	$=$	961.732
Dual form			961.2.g.a.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30902 - 0.951057i) q^{2} +(-2.95630 - 1.31623i) q^{3} +(0.190983 + 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.61803 + 4.53457i) q^{6} +(0.157960 - 0.175433i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(4.99983 + 5.55288i) q^{9} +O(q^{10})$	\(q+(-1.30902 - 0.951057i) q^{2} +(-2.95630 - 1.31623i) q^{3} +(0.190983 + 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.61803 + 4.53457i) q^{6} +(0.157960 - 0.175433i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(4.99983 + 5.55288i) q^{9} +(1.47815 - 0.658114i) q^{10} +(-1.95630 - 0.415823i) q^{11} +(0.209057 - 1.98904i) q^{12} +(0.338261 + 3.21834i) q^{13} +(-0.373619 + 0.0794152i) q^{14} +(2.61803 - 1.90211i) q^{15} +(3.92705 - 2.85317i) q^{16} +(-0.747238 + 0.158830i) q^{17} +(-1.26377 - 12.0239i) q^{18} +(0.233733 - 2.22382i) q^{19} +(-0.604528 - 0.128496i) q^{20} +(-0.697887 + 0.310719i) q^{21} +(2.16535 + 2.40487i) q^{22} +(1.76393 - 5.42882i) q^{23} +(4.84187 - 5.37745i) q^{24} +(2.00000 + 3.46410i) q^{25} +(2.61803 - 4.53457i) q^{26} +(-4.47214 - 13.7638i) q^{27} +(0.133284 + 0.0593421i) q^{28} +(-2.23607 - 1.62460i) q^{29} -5.23607 q^{30} -3.38197 q^{32} +(5.23607 + 3.80423i) q^{33} +(1.12920 + 0.502754i) q^{34} +(0.0729490 + 0.224514i) q^{35} +(-2.30902 + 3.99933i) q^{36} +(1.00000 + 1.73205i) q^{37} +(-2.42094 + 2.68872i) q^{38} +(3.23607 - 9.95959i) q^{39} +(-1.49622 - 1.66172i) q^{40} +(6.39482 - 2.84716i) q^{41} +(1.20906 + 0.256993i) q^{42} +(-0.129204 + 1.22930i) q^{43} +(-0.129204 - 1.22930i) q^{44} +(-7.30885 + 1.55354i) q^{45} +(-7.47214 + 5.42882i) q^{46} +(-2.00000 + 1.45309i) q^{47} +(-15.3649 + 3.26592i) q^{48} +(0.725874 + 6.90623i) q^{49} +(0.676522 - 6.43668i) q^{50} +(2.41811 + 0.513986i) q^{51} +(-1.82709 + 0.813473i) q^{52} +(-7.00723 - 7.78231i) q^{53} +(-7.23607 + 22.2703i) q^{54} +(1.33826 - 1.48629i) q^{55} +(0.263932 + 0.457144i) q^{56} +(-3.61803 + 6.26662i) q^{57} +(1.38197 + 4.25325i) q^{58} +(2.04275 + 0.909491i) q^{59} +(1.61803 + 1.17557i) q^{60} +8.18034 q^{61} +1.76393 q^{63} +(-3.42705 - 2.48990i) q^{64} +(-2.95630 - 1.31623i) q^{65} +(-3.23607 - 9.95959i) q^{66} +(-4.00000 + 6.92820i) q^{67} +(-0.236068 - 0.408882i) q^{68} +(-12.3603 + 13.7275i) q^{69} +(0.118034 - 0.363271i) q^{70} +(-6.14285 - 6.82232i) q^{71} +(-15.2637 + 6.79584i) q^{72} +(-8.28700 - 1.76146i) q^{73} +(0.338261 - 3.21834i) q^{74} +(-1.35304 - 12.8734i) q^{75} +(1.35177 - 0.287327i) q^{76} +(-0.381966 + 0.277515i) q^{77} +(-13.7082 + 9.95959i) q^{78} +(11.4524 - 2.43427i) q^{79} +(0.507392 + 4.82751i) q^{80} +(-2.55221 + 24.2827i) q^{81} +(-11.0787 - 2.35486i) q^{82} +(-13.6523 + 6.07838i) q^{83} +(-0.315921 - 0.350865i) q^{84} +(0.236068 - 0.726543i) q^{85} +(1.33826 - 1.48629i) q^{86} +(4.47214 + 7.74597i) q^{87} +(2.23607 - 3.87298i) q^{88} +(3.61803 + 11.1352i) q^{89} +(11.0449 + 4.91752i) q^{90} +(0.618034 + 0.449028i) q^{91} +3.52786 q^{92} +4.00000 q^{94} +(1.80902 + 1.31433i) q^{95} +(9.99809 + 4.45144i) q^{96} +(-4.92705 - 15.1639i) q^{97} +(5.61803 - 9.73072i) q^{98} +(-7.47214 - 12.9421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - 4 q^{5} + 12 q^{6} - 7 q^{7} - 10 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - 4 * q^5 + 12 * q^6 - 7 * q^7 - 10 * q^8 - 7 * q^9	\( 8 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - 4 q^{5} + 12 q^{6} - 7 q^{7} - 10 q^{8} - 7 q^{9} + 3 q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 4 q^{14} + 12 q^{15} + 18 q^{16} + 8 q^{17} + 19 q^{18} - 5 q^{19} - 3 q^{20} + 2 q^{21} - 4 q^{22} + 32 q^{23} + 16 q^{25} + 12 q^{26} - 4 q^{28} - 24 q^{30} - 36 q^{32} + 24 q^{33} + 4 q^{34} + 14 q^{35} - 14 q^{36} + 8 q^{37} + 8 q^{39} + 5 q^{40} + 7 q^{41} + 6 q^{42} + 4 q^{43} + 4 q^{44} - 7 q^{45} - 24 q^{46} - 16 q^{47} - 6 q^{48} - 18 q^{49} - 12 q^{50} + 12 q^{51} - 2 q^{52} + 4 q^{53} - 40 q^{54} + 2 q^{55} + 20 q^{56} - 20 q^{57} + 20 q^{58} + 5 q^{59} + 4 q^{60} - 24 q^{61} + 32 q^{63} - 14 q^{64} - 6 q^{65} - 8 q^{66} - 32 q^{67} + 16 q^{68} - 4 q^{69} - 8 q^{70} + 27 q^{71} - 25 q^{72} - 6 q^{73} - 6 q^{74} + 24 q^{75} - 5 q^{76} - 12 q^{77} - 56 q^{78} + 10 q^{79} - 9 q^{80} + 41 q^{81} - 14 q^{82} - 26 q^{83} + 14 q^{84} - 16 q^{85} + 2 q^{86} + 20 q^{89} + 19 q^{90} - 4 q^{91} + 64 q^{92} + 32 q^{94} + 10 q^{95} + 22 q^{96} - 26 q^{97} + 36 q^{98} - 24 q^{99}+O(q^{100}) \) 8 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - 4 * q^5 + 12 * q^6 - 7 * q^7 - 10 * q^8 - 7 * q^9 + 3 * q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 4 * q^14 + 12 * q^15 + 18 * q^16 + 8 * q^17 + 19 * q^18 - 5 * q^19 - 3 * q^20 + 2 * q^21 - 4 * q^22 + 32 * q^23 + 16 * q^25 + 12 * q^26 - 4 * q^28 - 24 * q^30 - 36 * q^32 + 24 * q^33 + 4 * q^34 + 14 * q^35 - 14 * q^36 + 8 * q^37 + 8 * q^39 + 5 * q^40 + 7 * q^41 + 6 * q^42 + 4 * q^43 + 4 * q^44 - 7 * q^45 - 24 * q^46 - 16 * q^47 - 6 * q^48 - 18 * q^49 - 12 * q^50 + 12 * q^51 - 2 * q^52 + 4 * q^53 - 40 * q^54 + 2 * q^55 + 20 * q^56 - 20 * q^57 + 20 * q^58 + 5 * q^59 + 4 * q^60 - 24 * q^61 + 32 * q^63 - 14 * q^64 - 6 * q^65 - 8 * q^66 - 32 * q^67 + 16 * q^68 - 4 * q^69 - 8 * q^70 + 27 * q^71 - 25 * q^72 - 6 * q^73 - 6 * q^74 + 24 * q^75 - 5 * q^76 - 12 * q^77 - 56 * q^78 + 10 * q^79 - 9 * q^80 + 41 * q^81 - 14 * q^82 - 26 * q^83 + 14 * q^84 - 16 * q^85 + 2 * q^86 + 20 * q^89 + 19 * q^90 - 4 * q^91 + 64 * q^92 + 32 * q^94 + 10 * q^95 + 22 * q^96 - 26 * q^97 + 36 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{15}\right)$

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 $

$2$	−1.30902	−	0.951057i	−0.925615	−	0.672499i	0.0193004	−	0.999814i	$-0.493856\pi$
$2$	−1.30902	−	0.951057i	−0.925615	−	0.672499i	−0.944915	+	0.327315i	$0.893856\pi$
$3$	−2.95630	−	1.31623i	−1.70682	−	0.759924i	−0.998542	−	0.0539889i	$-0.982806\pi$
$3$	−2.95630	−	1.31623i	−1.70682	−	0.759924i	−0.708276	−	0.705935i	$-0.750527\pi$
$4$	0.190983	+	0.587785i	0.0954915	+	0.293893i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$	2.61803	+	4.53457i	1.06881	+	1.85123i
$7$	0.157960	−	0.175433i	0.0597034	−	0.0663073i	−0.712553	−	0.701618i	$-0.752461\pi$
$7$	0.157960	−	0.175433i	0.0597034	−	0.0663073i	0.772257	+	0.635311i	$0.219128\pi$
$8$	−0.690983	+	2.12663i	−0.244299	+	0.751876i
$9$	4.99983	+	5.55288i	1.66661	+	1.85096i
$10$	1.47815	−	0.658114i	0.467431	−	0.208114i
$11$	−1.95630	−	0.415823i	−0.589845	−	0.125375i	−0.0966866	−	0.995315i	$-0.530824\pi$
$11$	−1.95630	−	0.415823i	−0.589845	−	0.125375i	−0.493159	+	0.869939i	$0.664158\pi$
$12$	0.209057	−	1.98904i	0.0603495	−	0.574187i
$13$	0.338261	+	3.21834i	0.0938168	+	0.892607i	0.935664	+	0.352892i	$0.114802\pi$
$13$	0.338261	+	3.21834i	0.0938168	+	0.892607i	−0.841847	+	0.539716i	$0.818532\pi$
$14$	−0.373619	+	0.0794152i	−0.0998539	+	0.0212246i
$15$	2.61803	−	1.90211i	0.675973	−	0.491123i
$16$	3.92705	−	2.85317i	0.981763	−	0.713292i
$17$	−0.747238	+	0.158830i	−0.181232	+	0.0385220i	−0.297634	−	0.954680i	$-0.596197\pi$
$17$	−0.747238	+	0.158830i	−0.181232	+	0.0385220i	0.116402	+	0.993202i	$0.462864\pi$
$18$	−1.26377	−	12.0239i	−0.297873	−	2.83407i
$19$	0.233733	−	2.22382i	0.0536220	−	0.510179i	−0.934440	−	0.356121i	$-0.884099\pi$
$19$	0.233733	−	2.22382i	0.0536220	−	0.510179i	0.988062	−	0.154058i	$-0.0492342\pi$
$20$	−0.604528	−	0.128496i	−0.135177	−	0.0287327i
$21$	−0.697887	+	0.310719i	−0.152291	+	0.0678045i
$22$	2.16535	+	2.40487i	0.461655	+	0.512719i
$23$	1.76393	−	5.42882i	0.367805	−	1.13199i	−0.580400	−	0.814331i	$-0.697104\pi$
$23$	1.76393	−	5.42882i	0.367805	−	1.13199i	0.948206	−	0.317657i	$-0.102896\pi$
$24$	4.84187	−	5.37745i	0.988344	−	1.09767i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	2.61803	−	4.53457i	0.513439	−	0.889302i
$27$	−4.47214	−	13.7638i	−0.860663	−	2.64885i
$28$	0.133284	+	0.0593421i	0.0251884	+	0.0112146i
$29$	−2.23607	−	1.62460i	−0.415227	−	0.301680i	0.360487	−	0.932764i	$-0.382610\pi$
$29$	−2.23607	−	1.62460i	−0.415227	−	0.301680i	−0.775715	+	0.631084i	$0.782610\pi$
$30$	−5.23607			−0.955971
$31$		0			0
$31$		0			0
$32$	−3.38197			−0.597853
$33$	5.23607	+	3.80423i	0.911482	+	0.662231i
$34$	1.12920	+	0.502754i	0.193657	+	0.0862216i
$35$	0.0729490	+	0.224514i	0.0123306	+	0.0379498i
$36$	−2.30902	+	3.99933i	−0.384836	+	0.666556i
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$	−2.42094	+	2.68872i	−0.392728	+	0.436169i
$39$	3.23607	−	9.95959i	0.518186	−	1.59481i
$40$	−1.49622	−	1.66172i	−0.236573	−	0.262741i
$41$	6.39482	−	2.84716i	0.998703	−	0.444651i	0.158755	−	0.987318i	$-0.449252\pi$
$41$	6.39482	−	2.84716i	0.998703	−	0.444651i	0.839948	+	0.542667i	$0.182585\pi$
$42$	1.20906	+	0.256993i	0.186562	+	0.0396549i
$43$	−0.129204	+	1.22930i	−0.0197035	+	0.187466i	−0.999947	−	0.0103302i	$-0.996712\pi$
$43$	−0.129204	+	1.22930i	−0.0197035	+	0.187466i	0.980243	+	0.197796i	$0.0633784\pi$
$44$	−0.129204	−	1.22930i	−0.0194783	−	0.185323i
$45$	−7.30885	+	1.55354i	−1.08954	+	0.231589i
$46$	−7.47214	+	5.42882i	−1.10171	+	0.800437i
$47$	−2.00000	+	1.45309i	−0.291730	+	0.211954i	−0.724018	−	0.689782i	$-0.757707\pi$
$47$	−2.00000	+	1.45309i	−0.291730	+	0.211954i	0.432288	+	0.901736i	$0.357707\pi$
$48$	−15.3649	+	3.26592i	−2.21774	+	0.471395i
$49$	0.725874	+	6.90623i	0.103696	+	0.986604i
$50$	0.676522	−	6.43668i	0.0956747	−	0.910284i
$51$	2.41811	+	0.513986i	0.338604	+	0.0719724i
$52$	−1.82709	+	0.813473i	−0.253372	+	0.112808i
$53$	−7.00723	−	7.78231i	−0.962517	−	1.06898i	−0.997575	−	0.0695977i	$-0.977828\pi$
$53$	−7.00723	−	7.78231i	−0.962517	−	1.06898i	0.0350585	−	0.999385i	$-0.488838\pi$
$54$	−7.23607	+	22.2703i	−0.984704	+	3.03061i
$55$	1.33826	−	1.48629i	0.180451	−	0.200411i
$56$	0.263932	+	0.457144i	0.0352694	+	0.0610884i
$57$	−3.61803	+	6.26662i	−0.479220	+	0.830034i
$58$	1.38197	+	4.25325i	0.181461	+	0.558480i
$59$	2.04275	+	0.909491i	0.265943	+	0.118406i	0.535377	−	0.844613i	$-0.320170\pi$
$59$	2.04275	+	0.909491i	0.265943	+	0.118406i	−0.269433	+	0.963019i	$0.586836\pi$
$60$	1.61803	+	1.17557i	0.208887	+	0.151765i
$61$	8.18034			1.04739			0.523693	−	0.851907i	$-0.324554\pi$
$61$	8.18034			1.04739			0.523693	+	0.851907i	$0.324554\pi$
$62$		0			0
$63$	1.76393			0.222235
$64$	−3.42705	−	2.48990i	−0.428381	−	0.311237i
$65$	−2.95630	−	1.31623i	−0.366683	−	0.163258i
$66$	−3.23607	−	9.95959i	−0.398332	−	1.22594i
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$	−0.236068	−	0.408882i	−0.0286274	−	0.0495842i
$69$	−12.3603	+	13.7275i	−1.48800	+	1.65259i
$70$	0.118034	−	0.363271i	0.0141078	−	0.0434192i
$71$	−6.14285	−	6.82232i	−0.729022	−	0.809661i	0.258688	−	0.965961i	$-0.416710\pi$
$71$	−6.14285	−	6.82232i	−0.729022	−	0.809661i	−0.987710	+	0.156300i	$0.950043\pi$
$72$	−15.2637	+	6.79584i	−1.79884	+	0.800897i
$73$	−8.28700	−	1.76146i	−0.969920	−	0.206163i	−0.304401	−	0.952544i	$-0.598456\pi$
$73$	−8.28700	−	1.76146i	−0.969920	−	0.206163i	−0.665519	+	0.746381i	$0.731790\pi$
$74$	0.338261	−	3.21834i	0.0393221	−	0.374124i
$75$	−1.35304	−	12.8734i	−0.156236	−	1.48649i
$76$	1.35177	−	0.287327i	0.155058	−	0.0329587i
$77$	−0.381966	+	0.277515i	−0.0435291	+	0.0316257i
$78$	−13.7082	+	9.95959i	−1.55215	+	1.12770i
$79$	11.4524	−	2.43427i	1.28849	−	0.273877i	0.487800	−	0.872955i	$-0.337800\pi$
$79$	11.4524	−	2.43427i	1.28849	−	0.273877i	0.800690	+	0.599078i	$0.204466\pi$
$80$	0.507392	+	4.82751i	0.0567281	+	0.539732i
$81$	−2.55221	+	24.2827i	−0.283579	+	2.69807i
$82$	−11.0787	−	2.35486i	−1.22344	−	0.260050i
$83$	−13.6523	+	6.07838i	−1.49853	+	0.667189i	−0.981966	−	0.189058i	$-0.939456\pi$
$83$	−13.6523	+	6.07838i	−1.49853	+	0.667189i	−0.516566	+	0.856248i	$0.672790\pi$
$84$	−0.315921	−	0.350865i	−0.0344698	−	0.0382826i
$85$	0.236068	−	0.726543i	0.0256052	−	0.0788046i
$86$	1.33826	−	1.48629i	0.144308	−	0.160271i
$87$	4.47214	+	7.74597i	0.479463	+	0.830455i
$88$	2.23607	−	3.87298i	0.238366	−	0.412861i
$89$	3.61803	+	11.1352i	0.383511	+	1.18032i	0.937555	+	0.347838i	$0.113084\pi$
$89$	3.61803	+	11.1352i	0.383511	+	1.18032i	−0.554044	+	0.832487i	$0.686916\pi$
$90$	11.0449	+	4.91752i	1.16424	+	0.518352i
$91$	0.618034	+	0.449028i	0.0647876	+	0.0470709i
$92$	3.52786			0.367805
$93$		0			0
$94$	4.00000			0.412568
$95$	1.80902	+	1.31433i	0.185601	+	0.134847i
$96$	9.99809	+	4.45144i	1.02043	+	0.454323i
$97$	−4.92705	−	15.1639i	−0.500266	−	1.53966i	−0.808586	−	0.588378i	$-0.799767\pi$
$97$	−4.92705	−	15.1639i	−0.500266	−	1.53966i	0.308320	−	0.951283i	$-0.400233\pi$
$98$	5.61803	−	9.73072i	0.567507	−	0.982951i
$99$	−7.47214	−	12.9421i	−0.750978	−	1.30073i
$100$	−1.65418	+	1.83716i	−0.165418	+	0.183716i
$101$	−0.927051	+	2.85317i	−0.0922450	+	0.283901i	−0.986526	−	0.163605i	$-0.947688\pi$
$101$	−0.927051	+	2.85317i	−0.0922450	+	0.283901i	0.894281	+	0.447506i	$0.147688\pi$
$102$	−2.67652	−	2.97258i	−0.265015	−	0.294329i
$103$	5.69693	−	2.53644i	0.561335	−	0.249923i	−0.106397	−	0.994324i	$-0.533932\pi$
$103$	5.69693	−	2.53644i	0.561335	−	0.249923i	0.667733	+	0.744401i	$0.267265\pi$
$104$	−7.07794	−	1.50446i	−0.694049	−	0.147525i
$105$	0.0798526	−	0.759747i	0.00779282	−	0.0741437i
$106$	1.77116	+	16.8514i	0.172030	+	1.63676i
$107$	−5.63798	+	1.19839i	−0.545044	+	0.115853i	−0.472201	−	0.881491i	$-0.656540\pi$
$107$	−5.63798	+	1.19839i	−0.545044	+	0.115853i	−0.0728426	+	0.997343i	$0.523207\pi$
$108$	7.23607	−	5.25731i	0.696291	−	0.505885i
$109$	11.2812	−	8.19624i	1.08054	−	0.785057i	0.102762	−	0.994706i	$-0.467232\pi$
$109$	11.2812	−	8.19624i	1.08054	−	0.785057i	0.977777	+	0.209649i	$0.0672321\pi$
$110$	−3.16535	+	0.672816i	−0.301804	+	0.0641505i
$111$	−0.676522	−	6.43668i	−0.0642127	−	0.610943i
$112$	0.119779	−	1.13962i	0.0113180	−	0.107684i
$113$	−3.39626	−	0.721898i	−0.319493	−	0.0679104i	0.0453735	−	0.998970i	$-0.485552\pi$
$113$	−3.39626	−	0.721898i	−0.319493	−	0.0679104i	−0.364867	+	0.931060i	$0.618886\pi$
$114$	10.6960	−	4.76216i	1.00177	−	0.446017i
$115$	3.81953	+	4.24202i	0.356173	+	0.395571i
$116$	0.527864	−	1.62460i	0.0490109	−	0.150840i
$117$	−16.1798	+	17.9695i	−1.49582	+	1.66128i
$118$	−1.80902	−	3.13331i	−0.166534	−	0.288445i
$119$	−0.0901699	+	0.156179i	−0.00826587	+	0.0143169i
$120$	2.23607	+	6.88191i	0.204124	+	0.628230i
$121$	−6.39482	−	2.84716i	−0.581347	−	0.258832i
$122$	−10.7082	−	7.77997i	−0.969475	−	0.704365i
$123$	−22.6525			−2.04250
$124$		0			0
$125$	−9.00000			−0.804984
$126$	−2.30902	−	1.67760i	−0.205704	−	0.149452i
$127$	11.3939	+	5.07287i	1.01104	+	0.450145i	0.844309	−	0.535857i	$-0.180011\pi$
$127$	11.3939	+	5.07287i	1.01104	+	0.450145i	0.166733	+	0.986002i	$0.446678\pi$
$128$	4.20820	+	12.9515i	0.371956	+	1.14476i
$129$	2.00000	−	3.46410i	0.176090	−	0.304997i
$130$	2.61803	+	4.53457i	0.229617	+	0.397708i
$131$	8.02957	−	8.91774i	0.701547	−	0.779146i	−0.282075	−	0.959392i	$-0.591023\pi$
$131$	8.02957	−	8.91774i	0.701547	−	0.779146i	0.983622	+	0.180246i	$0.0576894\pi$
$132$	−1.23607	+	3.80423i	−0.107586	+	0.331115i
$133$	−0.353210	−	0.392279i	−0.0306272	−	0.0340149i
$134$	11.8252	−	5.26491i	1.02154	−	0.454819i
$135$	14.1559	+	3.00893i	1.21834	+	0.258967i
$136$	0.178556	−	1.69885i	0.0153110	−	0.145675i
$137$	−0.657672	−	6.25733i	−0.0561887	−	0.534600i	−0.986022	−	0.166618i	$-0.946715\pi$
$137$	−0.657672	−	6.25733i	−0.0561887	−	0.534600i	0.929833	−	0.367982i	$-0.119951\pi$
$138$	29.2354	−	6.21418i	2.48868	−	0.528986i
$139$	−10.8541	+	7.88597i	−0.920633	+	0.668879i	−0.943681	−	0.330855i	$-0.892663\pi$
$139$	−10.8541	+	7.88597i	−0.920633	+	0.668879i	0.0230486	+	0.999734i	$0.492663\pi$
$140$	−0.118034	+	0.0857567i	−0.00997569	+	0.00724777i
$141$	7.82518	−	1.66329i	0.658999	−	0.140075i
$142$	1.55268	+	14.7727i	0.130298	+	1.23970i
$143$	0.676522	−	6.43668i	0.0565736	−	0.538262i
$144$	35.4779	+	7.54106i	2.95649	+	0.628422i
$145$	2.52498	−	1.12419i	0.209688	−	0.0933591i
$146$	9.17258	+	10.1872i	0.759128	+	0.843097i
$147$	6.94427	−	21.3723i	0.572754	−	1.76276i
$148$	−0.827091	+	0.918578i	−0.0679865	+	0.0755066i
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	0.585231	−	0.810867i	$-0.301004\pi$
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	−0.994847	+	0.101391i	$0.967671\pi$
$150$	−10.4721	+	18.1383i	−0.855046	+	1.48098i
$151$	−4.38197	−	13.4863i	−0.356599	−	1.09750i	−0.955076	−	0.296360i	$-0.904227\pi$
$151$	−4.38197	−	13.4863i	−0.356599	−	1.09750i	0.598477	−	0.801140i	$-0.295773\pi$
$152$	4.56773	+	2.03368i	0.370492	+	0.164953i
$153$	−4.61803	−	3.35520i	−0.373346	−	0.271252i
$154$	0.763932			0.0615594
$155$		0			0
$156$	6.47214			0.518186
$157$	−16.8992	−	12.2780i	−1.34870	−	0.979889i	−0.999075	−	0.0430003i	$-0.986308\pi$
$157$	−16.8992	−	12.2780i	−1.34870	−	0.979889i	−0.349627	−	0.936889i	$-0.613692\pi$
$158$	−17.3065	−	7.70533i	−1.37683	−	0.613003i
$159$	10.4721	+	32.2299i	0.830494	+	2.55600i
$160$	1.69098	−	2.92887i	0.133684	−	0.231547i
$161$	−0.673762	−	1.16699i	−0.0530999	−	0.0919717i
$162$	26.4351	−	29.3591i	2.07693	−	2.30667i
$163$	3.30902	−	10.1841i	0.259182	−	0.797681i	−0.733795	−	0.679371i	$-0.762253\pi$
$163$	3.30902	−	10.1841i	0.259182	−	0.797681i	0.992977	−	0.118309i	$-0.0377475\pi$
$164$	2.89482	+	3.21502i	0.226047	+	0.251051i
$165$	−5.91259	+	2.63245i	−0.460295	+	0.204936i
$166$	23.6519	+	5.02738i	1.83575	+	0.390200i
$167$	0.676522	−	6.43668i	0.0523509	−	0.498085i	−0.936660	−	0.350241i	$-0.886100\pi$
$167$	0.676522	−	6.43668i	0.0523509	−	0.498085i	0.989011	−	0.147845i	$-0.0472336\pi$
$168$	−0.178556	−	1.69885i	−0.0137759	−	0.131069i
$169$	2.47262	−	0.525572i	0.190202	−	0.0404287i
$170$	−1.00000	+	0.726543i	−0.0766965	+	0.0557233i
$171$	13.5172	−	9.82084i	1.03369	−	0.751018i
$172$	−0.747238	+	0.158830i	−0.0569764	+	0.0121107i
$173$	−0.307760	−	2.92814i	−0.0233986	−	0.222623i	−0.999972	−	0.00743961i	$-0.997632\pi$
$173$	−0.307760	−	2.92814i	−0.0233986	−	0.222623i	0.976574	−	0.215183i	$-0.0690348\pi$
$174$	1.51275	−	14.3929i	0.114681	−	1.09112i
$175$	0.923637	+	0.196325i	0.0698204	+	0.0148408i
$176$	−8.86889	+	3.94868i	−0.668517	+	0.297643i
$177$	−4.84187	−	5.37745i	−0.363938	−	0.404194i
$178$	5.85410	−	18.0171i	0.438783	−	1.35044i
$179$	1.14301	−	1.26944i	0.0854327	−	0.0948826i	−0.698913	−	0.715207i	$-0.746332\pi$
$179$	1.14301	−	1.26944i	0.0854327	−	0.0948826i	0.784345	+	0.620324i	$0.212999\pi$
$180$	−2.30902	−	3.99933i	−0.172104	−	0.298093i
$181$	2.09017	−	3.62028i	0.155361	−	0.269093i	−0.777829	−	0.628476i	$-0.783679\pi$
$181$	2.09017	−	3.62028i	0.155361	−	0.269093i	0.933190	+	0.359382i	$0.117013\pi$
$182$	−0.381966	−	1.17557i	−0.0283132	−	0.0871391i
$183$	−24.1835	−	10.7672i	−1.78770	−	0.795933i
$184$	10.3262	+	7.50245i	0.761260	+	0.553088i
$185$	−2.00000			−0.147043
$186$		0			0
$187$	1.52786			0.111728
$188$	−1.23607	−	0.898056i	−0.0901495	−	0.0654975i
$189$	−3.12104	−	1.38958i	−0.227023	−	0.101077i
$190$	−1.11803	−	3.44095i	−0.0811107	−	0.249633i
$191$	9.59017	−	16.6107i	0.693920	−	1.20191i	−0.276623	−	0.960979i	$-0.589215\pi$
$191$	9.59017	−	16.6107i	0.693920	−	1.20191i	0.970543	−	0.240927i	$-0.0774514\pi$
$192$	6.85410	+	11.8717i	0.494652	+	0.856763i
$193$	2.32331	−	2.58030i	0.167236	−	0.185734i	−0.653702	−	0.756752i	$-0.726785\pi$
$193$	2.32331	−	2.58030i	0.167236	−	0.185734i	0.820937	+	0.571018i	$0.193452\pi$
$194$	−7.97214	+	24.5357i	−0.572366	+	1.76156i
$195$	7.00723	+	7.78231i	0.501798	+	0.557303i
$196$	−3.92075	+	1.74563i	−0.280054	+	0.124688i
$197$	−11.1669	−	2.37360i	−0.795611	−	0.169112i	−0.207865	−	0.978158i	$-0.566651\pi$
$197$	−11.1669	−	2.37360i	−0.795611	−	0.169112i	−0.587746	+	0.809045i	$0.699985\pi$
$198$	−2.52753	+	24.0479i	−0.179624	+	1.70901i
$199$	1.98022	+	18.8405i	0.140374	+	1.33557i	0.807166	+	0.590324i	$0.201000\pi$
$199$	1.98022	+	18.8405i	0.140374	+	1.33557i	−0.666793	+	0.745243i	$0.732333\pi$
$200$	−8.74882	+	1.85962i	−0.618635	+	0.131495i
$201$	20.9443	−	15.2169i	1.47730	−	1.07332i
$202$	3.92705	−	2.85317i	0.276306	−	0.200748i
$203$	−0.638218	+	0.135657i	−0.0447941	+	0.00952128i
$204$	0.159705	+	1.51949i	0.0111816	+	0.106386i
$205$	−0.731699	+	6.96165i	−0.0511041	+	0.486223i
$206$	−9.86968	−	2.09786i	−0.687653	−	0.146165i
$207$	38.9650	−	17.3483i	2.70825	−	1.20579i
$208$	10.5108	+	11.6735i	0.728796	+	0.809410i
$209$	−1.38197	+	4.25325i	−0.0955926	+	0.294204i
$210$	−0.827091	+	0.918578i	−0.0570747	+	0.0633879i
$211$	−11.5902	−	20.0748i	−0.797900	−	1.38200i	−0.920981	−	0.389607i	$-0.872611\pi$
$211$	−11.5902	−	20.0748i	−0.797900	−	1.38200i	0.123081	−	0.992397i	$-0.460723\pi$
$212$	3.23607	−	5.60503i	0.222254	−	0.384955i
$213$	9.18034	+	28.2542i	0.629027	+	1.93594i
$214$	8.51994	+	3.79332i	0.582411	+	0.259306i
$215$	−1.00000	−	0.726543i	−0.0681994	−	0.0495498i
$216$	32.3607			2.20187
$217$		0			0
$218$	−22.5623			−1.52811
$219$	22.1803	+	16.1150i	1.49881	+	1.08895i
$220$	1.12920	+	0.502754i	0.0761309	+	0.0338957i
$221$	−0.763932	−	2.35114i	−0.0513876	−	0.158155i
$222$	−5.23607	+	9.06914i	−0.351422	+	0.608681i
$223$	−2.00000	−	3.46410i	−0.133930	−	0.231973i	0.791258	−	0.611482i	$-0.209426\pi$
$223$	−2.00000	−	3.46410i	−0.133930	−	0.231973i	−0.925188	+	0.379509i	$0.876093\pi$
$224$	−0.534216	+	0.593307i	−0.0356938	+	0.0396420i
$225$	−9.23607	+	28.4257i	−0.615738	+	1.89505i
$226$	3.75920	+	4.17501i	0.250058	+	0.277718i
$227$	−5.91259	+	2.63245i	−0.392432	+	0.174722i	−0.593460	−	0.804863i	$-0.702239\pi$
$227$	−5.91259	+	2.63245i	−0.392432	+	0.174722i	0.201028	+	0.979586i	$0.435572\pi$
$228$	−4.37441	−	0.929809i	−0.289702	−	0.0615781i
$229$	1.40240	−	13.3429i	0.0926730	−	0.881724i	−0.845131	−	0.534559i	$-0.820478\pi$
$229$	1.40240	−	13.3429i	0.0926730	−	0.881724i	0.937804	−	0.347165i	$-0.112856\pi$
$230$	−0.965432	−	9.18547i	−0.0636587	−	0.605672i
$231$	1.49448	−	0.317661i	0.0983293	−	0.0209005i
$232$	5.00000	−	3.63271i	0.328266	−	0.238499i
$233$	−14.5172	+	10.5474i	−0.951055	+	0.690982i	−0.951056	−	0.309018i	$-0.900000\pi$
$233$	−14.5172	+	10.5474i	−0.951055	+	0.690982i	1.33829e−6		1.00000i	$0.500000\pi$
$234$	38.2696	−	8.13446i	2.50176	−	0.531767i
$235$	−0.258409	−	2.45859i	−0.0168567	−	0.160381i
$236$	−0.144455	+	1.37440i	−0.00940321	+	0.0894655i
$237$	−37.0606	−	7.87747i	−2.40734	−	0.511697i
$238$	0.266569	−	0.118684i	0.0172791	−	0.00769315i
$239$	−7.83432	−	8.70089i	−0.506760	−	0.562814i	0.434424	−	0.900708i	$-0.356952\pi$
$239$	−7.83432	−	8.70089i	−0.506760	−	0.562814i	−0.941184	+	0.337895i	$0.890285\pi$
$240$	4.85410	−	14.9394i	0.313331	−	0.964333i
$241$	9.60917	−	10.6721i	0.618981	−	0.687448i	−0.349386	−	0.936979i	$-0.613610\pi$
$241$	9.60917	−	10.6721i	0.618981	−	0.687448i	0.968367	+	0.249531i	$0.0802764\pi$
$242$	5.66312	+	9.80881i	0.364039	+	0.630534i
$243$	17.7984	−	30.8277i	1.14177	−	1.97760i
$244$	1.56231	+	4.80828i	0.100016	+	0.307819i
$245$	−6.34391	−	2.82449i	−0.405297	−	0.180450i
$246$	29.6525	+	21.5438i	1.89057	+	1.37358i
$247$	7.23607			0.460420
$248$		0			0
$249$	48.3607			3.06473
$250$	11.7812	+	8.55951i	0.745106	+	0.541351i
$251$	−1.66234	−	0.740122i	−0.104926	−	0.0467161i	0.353602	−	0.935396i	$-0.384957\pi$
$251$	−1.66234	−	0.740122i	−0.104926	−	0.0467161i	−0.458528	+	0.888680i	$0.651623\pi$
$252$	0.336881	+	1.03681i	0.0212215	+	0.0653131i
$253$	−5.70820	+	9.88690i	−0.358872	+	0.621584i
$254$	−10.0902	−	17.4767i	−0.633114	−	1.09658i
$255$	−1.65418	+	1.83716i	−0.103589	+	0.115047i
$256$	4.19098	−	12.8985i	0.261936	−	0.806157i
$257$	1.30097	+	1.44488i	0.0811524	+	0.0901289i	0.782353	−	0.622835i	$-0.214019\pi$
$257$	1.30097	+	1.44488i	0.0811524	+	0.0901289i	−0.701201	+	0.712964i	$0.747352\pi$
$258$	−5.91259	+	2.63245i	−0.368102	+	0.163889i
$259$	0.461819	+	0.0981626i	0.0286960	+	0.00609953i
$260$	0.209057	−	1.98904i	0.0129652	−	0.123355i
$261$	−2.15877	−	20.5393i	−0.133625	−	1.27135i
$262$	−18.9921	+	4.03690i	−1.17334	+	0.249400i
$263$	18.7984	−	13.6578i	1.15916	−	0.842177i	0.169486	−	0.985533i	$-0.445789\pi$
$263$	18.7984	−	13.6578i	1.15916	−	0.842177i	0.989671	+	0.143355i	$0.0457892\pi$
$264$	−11.7082	+	8.50651i	−0.720590	+	0.523539i
$265$	10.2433	−	2.17728i	0.629241	−	0.133749i
$266$	0.0892780	+	0.849423i	0.00547398	+	0.0520815i
$267$	3.96043	−	37.6810i	0.242374	−	2.30604i
$268$	−4.83623	−	1.02797i	−0.295420	−	0.0627934i
$269$	−10.0999	+	4.49677i	−0.615802	+	0.274173i	−0.690840	−	0.723008i	$-0.742759\pi$
$269$	−10.0999	+	4.49677i	−0.615802	+	0.274173i	0.0750374	+	0.997181i	$0.476092\pi$
$270$	−15.6686	−	17.4018i	−0.953563	−	1.05904i
$271$	−4.38197	+	13.4863i	−0.266185	+	0.819235i	0.725232	+	0.688504i	$0.241732\pi$
$271$	−4.38197	+	13.4863i	−0.266185	+	0.819235i	−0.991418	+	0.130731i	$0.958268\pi$
$272$	−2.48127	+	2.75573i	−0.150449	+	0.167091i
$273$	−1.23607	−	2.14093i	−0.0748102	−	0.129575i
$274$	−5.09017	+	8.81643i	−0.307508	+	0.532620i
$275$	−2.47214	−	7.60845i	−0.149075	−	0.458807i
$276$	−10.4294	−	4.64347i	−0.627777	−	0.279504i
$277$	10.2361	+	7.43694i	0.615026	+	0.446842i	0.851180	−	0.524873i	$-0.175887\pi$
$277$	10.2361	+	7.43694i	0.615026	+	0.446842i	−0.236155	+	0.971715i	$0.575887\pi$
$278$	21.7082			1.30197
$279$		0			0
$280$	−0.527864			−0.0315459
$281$	−13.7533	−	9.99235i	−0.820452	−	0.596094i	0.0963896	−	0.995344i	$-0.469271\pi$
$281$	−13.7533	−	9.99235i	−0.820452	−	0.596094i	−0.916842	+	0.399250i	$0.869271\pi$
$282$	−11.8252	−	5.26491i	−0.704179	−	0.313521i
$283$	−4.29180	−	13.2088i	−0.255121	−	0.785181i	−0.993806	−	0.111130i	$-0.964553\pi$
$283$	−4.29180	−	13.2088i	−0.255121	−	0.785181i	0.738685	−	0.674051i	$-0.235447\pi$
$284$	2.83688	−	4.91362i	0.168338	−	0.291570i
$285$	−3.61803	−	6.26662i	−0.214314	−	0.371202i
$286$	−7.00723	+	7.78231i	−0.414346	+	0.460178i
$287$	0.510643	−	1.57160i	0.0301423	−	0.0927685i
$288$	−16.9093	−	18.7796i	−0.996388	−	1.10660i
$289$	−14.9971	+	6.67715i	−0.882184	+	0.392774i
$290$	−4.37441	−	0.929809i	−0.256874	−	0.0546003i
$291$	−5.39333	+	51.3141i	−0.316163	+	3.00809i
$292$	−0.547318	−	5.20738i	−0.0320294	−	0.304739i
$293$	0.461819	−	0.0981626i	0.0269797	−	0.00573472i	−0.194402	−	0.980922i	$-0.562277\pi$
$293$	0.461819	−	0.0981626i	0.0269797	−	0.00573472i	0.221382	+	0.975187i	$0.428943\pi$
$294$	−29.4164	+	21.3723i	−1.71560	+	1.24646i
$295$	−1.80902	+	1.31433i	−0.105325	+	0.0765231i
$296$	−4.37441	+	0.929809i	−0.254257	+	0.0540441i
$297$	3.02550	+	28.7857i	0.175557	+	1.67032i
$298$	−1.69131	+	16.0917i	−0.0979747	+	0.932167i
$299$	18.0685	+	3.84057i	1.04493	+	0.222106i
$300$	7.30836	−	3.25389i	0.421949	−	0.187864i
$301$	0.195250	+	0.216847i	0.0112540	+	0.0124988i
$302$	−7.09017	+	21.8213i	−0.407993	+	1.25567i
$303$	6.49606	−	7.21460i	0.373189	−	0.414468i
$304$	−5.42705	−	9.39993i	−0.311263	−	0.539123i
$305$	−4.09017	+	7.08438i	−0.234202	+	0.405651i
$306$	2.85410	+	8.78402i	0.163158	+	0.502149i
$307$	−26.2262	−	11.6767i	−1.49681	−	0.666423i	−0.515157	−	0.857096i	$-0.672267\pi$
$307$	−26.2262	−	11.6767i	−1.49681	−	0.666423i	−0.981654	+	0.190672i	$0.938933\pi$
$308$	−0.236068	−	0.171513i	−0.0134512	−	0.00977288i
$309$	−20.1803			−1.14802
$310$		0			0
$311$	−29.1803			−1.65467			−0.827333	−	0.561712i	$-0.810143\pi$
$311$	−29.1803			−1.65467			−0.827333	+	0.561712i	$0.810143\pi$
$312$	18.9443	+	13.7638i	1.07251	+	0.779223i
$313$	15.3146	+	6.81851i	0.865633	+	0.385405i	0.791007	−	0.611807i	$-0.209557\pi$
$313$	15.3146	+	6.81851i	0.865633	+	0.385405i	0.0746260	+	0.997212i	$0.476224\pi$
$314$	10.4443	+	32.1442i	0.589404	+	1.81400i
$315$	−0.881966	+	1.52761i	−0.0496932	+	0.0860711i
$316$	3.61803	+	6.26662i	0.203530	+	0.352525i
$317$	2.71381	−	3.01399i	0.152423	−	0.169283i	−0.662097	−	0.749418i	$-0.730334\pi$
$317$	2.71381	−	3.01399i	0.152423	−	0.169283i	0.814520	+	0.580135i	$0.197000\pi$
$318$	16.9443	−	52.1491i	0.950188	−	2.92438i
$319$	3.69886	+	4.10800i	0.207097	+	0.230004i
$320$	3.86984	−	1.72296i	0.216331	−	0.0963166i
$321$	18.2449	+	3.87807i	1.01833	+	0.216453i
$322$	−0.227908	+	2.16840i	−0.0127008	+	0.120840i
$323$	0.178556	+	1.69885i	0.00993512	+	0.0945263i
$324$	−14.7604	+	3.13742i	−0.820023	+	0.174301i
$325$	−10.4721	+	7.60845i	−0.580890	+	0.422041i
$326$	−14.0172	+	10.1841i	−0.776342	+	0.564046i
$327$	−44.1385	+	9.38193i	−2.44087	+	0.518822i
$328$	1.63613	+	15.5667i	0.0903401	+	0.859529i
$329$	−0.0610020	+	0.580395i	−0.00336315	+	0.0319982i
$330$	10.2433	+	2.17728i	0.563875	+	0.119855i
$331$	1.82709	−	0.813473i	0.100426	−	0.0447125i	−0.355909	−	0.934521i	$-0.615829\pi$
$331$	1.82709	−	0.813473i	0.100426	−	0.0447125i	0.456335	+	0.889808i	$0.349162\pi$
$332$	−6.18014	−	6.86374i	−0.339179	−	0.376696i
$333$	−4.61803	+	14.2128i	−0.253067	+	0.778859i
$334$	−7.00723	+	7.78231i	−0.383418	+	0.425829i
$335$	−4.00000	−	6.92820i	−0.218543	−	0.378528i
$336$	−1.85410	+	3.21140i	−0.101150	+	0.175196i
$337$	−4.56231	−	14.0413i	−0.248525	−	0.764880i	−0.995037	−	0.0995083i	$-0.968273\pi$
$337$	−4.56231	−	14.0413i	−0.248525	−	0.764880i	0.746512	−	0.665372i	$-0.231727\pi$
$338$	−3.73656	−	1.66362i	−0.203242	−	0.0904891i
$339$	9.09017	+	6.60440i	0.493710	+	0.358702i
$340$	0.472136			0.0256052
$341$		0			0
$342$	−27.0344			−1.46186
$343$	2.66312	+	1.93487i	0.143795	+	0.104473i
$344$	−2.52498	−	1.12419i	−0.136138	−	0.0606124i
$345$	−5.70820	−	17.5680i	−0.307319	−	0.945832i
$346$	−2.38197	+	4.12569i	−0.128055	+	0.221798i
$347$	−12.0902	−	20.9408i	−0.649034	−	1.12416i	−0.983354	−	0.181701i	$-0.941840\pi$
$347$	−12.0902	−	20.9408i	−0.649034	−	1.12416i	0.334320	−	0.942460i	$-0.391494\pi$
$348$	−3.69886	+	4.10800i	−0.198280	+	0.220212i
$349$	−2.43769	+	7.50245i	−0.130487	+	0.401597i	−0.994861	−	0.101252i	$-0.967715\pi$
$349$	−2.43769	+	7.50245i	−0.130487	+	0.401597i	0.864374	+	0.502849i	$0.167715\pi$
$350$	−1.02234	−	1.13542i	−0.0546464	−	0.0606910i
$351$	42.7839	−	19.0486i	2.28364	−	1.01674i
$352$	6.61612	+	1.40630i	0.352641	+	0.0749561i
$353$	−0.775226	+	7.37578i	−0.0412611	+	0.392573i	0.954329	+	0.298759i	$0.0965726\pi$
$353$	−0.775226	+	7.37578i	−0.0412611	+	0.392573i	−0.995590	+	0.0938142i	$0.970094\pi$
$354$	1.22384	+	11.6441i	0.0650464	+	0.618875i
$355$	8.97973	−	1.90870i	0.476594	−	0.101303i
$356$	−5.85410	+	4.25325i	−0.310267	+	0.225422i
$357$	0.472136	−	0.343027i	0.0249881	−	0.0181549i
$358$	−2.70353	+	0.574654i	−0.142886	+	0.0303714i
$359$	−2.32430	−	22.1143i	−0.122672	−	1.16715i	−0.866641	−	0.498932i	$-0.833726\pi$
$359$	−2.32430	−	22.1143i	−0.122672	−	1.16715i	0.743969	−	0.668214i	$-0.232941\pi$
$360$	1.74648	−	16.6167i	0.0920477	−	0.875776i
$361$	13.6941	+	2.91076i	0.720740	+	0.153198i
$362$	−6.17916	+	2.75114i	−0.324769	+	0.144597i
$363$	15.1575	+	16.8341i	0.795561	+	0.883560i
$364$	−0.145898	+	0.449028i	−0.00764713	+	0.0235355i
$365$	5.66897	−	6.29602i	0.296727	−	0.329549i
$366$	21.4164	+	37.0943i	1.11945	+	1.93895i
$367$	−9.00000	+	15.5885i	−0.469796	+	0.813711i	−0.999404	−	0.0345320i	$-0.989006\pi$
$367$	−9.00000	+	15.5885i	−0.469796	+	0.813711i	0.529607	+	0.848243i	$0.322339\pi$
$368$	−8.56231	−	26.3521i	−0.446341	−	1.37370i
$369$	47.7830	+	21.2743i	2.48748	+	1.10750i
$370$	2.61803	+	1.90211i	0.136105	+	0.0988861i
$371$	−2.47214			−0.128347
$372$		0			0
$373$	19.0000			0.983783			0.491891	−	0.870657i	$-0.336306\pi$
$373$	19.0000			0.983783			0.491891	+	0.870657i	$0.336306\pi$
$374$	−2.00000	−	1.45309i	−0.103418	−	0.0751372i
$375$	26.6067	+	11.8460i	1.37396	+	0.611727i
$376$	−1.70820	−	5.25731i	−0.0880939	−	0.271125i
$377$	4.47214	−	7.74597i	0.230327	−	0.398938i
$378$	2.76393	+	4.78727i	0.142161	+	0.246231i
$379$	−1.41284	+	1.56912i	−0.0725727	+	0.0806002i	−0.778338	−	0.627846i	$-0.783937\pi$
$379$	−1.41284	+	1.56912i	−0.0725727	+	0.0806002i	0.705765	+	0.708446i	$0.250603\pi$
$380$	−0.427051	+	1.31433i	−0.0219073	+	0.0674236i
$381$	−27.0066	−	29.9938i	−1.38359	−	1.53663i
$382$	−28.3514	+	12.6228i	−1.45058	+	0.645841i
$383$	23.3665	+	4.96671i	1.19397	+	0.253787i	0.761684	−	0.647948i	$-0.224373\pi$
$383$	23.3665	+	4.96671i	1.19397	+	0.253787i	0.432289	+	0.901735i	$0.357706\pi$
$384$	4.60645	−	43.8275i	0.235072	−	2.23656i
$385$	−0.0493516	−	0.469550i	−0.00251519	−	0.0239305i
$386$	−5.49527	+	1.16805i	−0.279702	+	0.0594524i
$387$	−7.47214	+	5.42882i	−0.379830	+	0.275963i
$388$	7.97214	−	5.79210i	0.404724	−	0.294049i
$389$	17.4976	−	3.71924i	0.887165	−	0.188573i	0.258279	−	0.966070i	$-0.416845\pi$
$389$	17.4976	−	3.71924i	0.887165	−	0.188573i	0.628886	+	0.777497i	$0.283511\pi$
$390$	−1.77116	−	16.8514i	−0.0896861	−	0.853306i
$391$	−0.455815	+	4.33679i	−0.0230516	+	0.219321i
$392$	−15.1885	−	3.22842i	−0.767137	−	0.163060i
$393$	−35.4755	+	15.7947i	−1.78950	+	0.796739i
$394$	12.3603	+	13.7275i	0.622701	+	0.691580i
$395$	−3.61803	+	11.1352i	−0.182043	+	0.560271i
$396$	6.18014	−	6.86374i	0.310564	−	0.344916i
$397$	3.50000	+	6.06218i	0.175660	+	0.304252i	0.940389	−	0.340099i	$-0.110461\pi$
$397$	3.50000	+	6.06218i	0.175660	+	0.304252i	−0.764730	+	0.644351i	$0.777127\pi$
$398$	15.3262	−	26.5458i	0.768235	−	1.33062i
$399$	0.527864	+	1.62460i	0.0264263	+	0.0813317i
$400$	17.7378	+	7.89736i	0.886889	+	0.394868i
$401$	−30.8885	−	22.4418i	−1.54250	−	1.12069i	−0.948743	−	0.316048i	$-0.897644\pi$
$401$	−30.8885	−	22.4418i	−1.54250	−	1.12069i	−0.593757	−	0.804644i	$-0.702356\pi$
$402$	−41.8885			−2.08921
$403$		0			0
$404$	−1.85410			−0.0922450
$405$	−19.7533	−	14.3516i	−0.981549	−	0.713137i
$406$	0.964456	+	0.429403i	0.0478651	+	0.0213109i
$407$	−1.23607	−	3.80423i	−0.0612696	−	0.188568i
$408$	−2.76393	+	4.78727i	−0.136835	+	0.237005i
$409$	1.90983	+	3.30792i	0.0944350	+	0.163566i	0.909373	−	0.415982i	$-0.136562\pi$
$409$	1.90983	+	3.30792i	0.0944350	+	0.163566i	−0.814938	+	0.579549i	$0.803229\pi$
$410$	7.57873	−	8.41704i	0.374287	−	0.415688i
$411$	−6.29180	+	19.3642i	−0.310351	+	0.955163i
$412$	2.57890	+	2.86416i	0.127053	+	0.141107i
$413$	0.482228	−	0.214702i	0.0237289	−	0.0105648i
$414$	−67.5051	−	14.3486i	−3.31769	−	0.705197i
$415$	1.56210	−	14.8624i	0.0766806	−	0.729567i
$416$	−1.14399	−	10.8843i	−0.0560886	−	0.533648i
$417$	42.4677	−	9.02678i	2.07965	−	0.442043i
$418$	5.85410	−	4.25325i	0.286333	−	0.208033i
$419$	8.19098	−	5.95110i	0.400156	−	0.290730i	−0.369449	−	0.929251i	$-0.620453\pi$
$419$	8.19098	−	5.95110i	0.400156	−	0.290730i	0.769604	+	0.638521i	$0.220453\pi$
$420$	0.461819	−	0.0981626i	0.0225344	−	0.00478984i
$421$	−3.06903	−	29.1998i	−0.149575	−	1.42311i	−0.769598	−	0.638529i	$-0.779543\pi$
$421$	−3.06903	−	29.1998i	−0.149575	−	1.42311i	0.620023	−	0.784584i	$-0.287123\pi$
$422$	−3.92050	+	37.3011i	−0.190847	+	1.81579i
$423$	−18.0685	−	3.84057i	−0.878519	−	0.186735i
$424$	21.3920	−	9.52431i	1.03889	−	0.462541i
$425$	−2.04468	−	2.27085i	−0.0991816	−	0.110152i
$426$	14.8541	−	45.7162i	0.719684	−	2.21496i
$427$	1.29217	−	1.43510i	0.0625324	−	0.0694493i
$428$	−1.78115	−	3.08505i	−0.0860953	−	0.149121i
$429$	−10.4721	+	18.1383i	−0.505599	+	0.875724i
$430$	0.618034	+	1.90211i	0.0298042	+	0.0917280i
$431$	10.9625	+	4.88084i	0.528047	+	0.235102i	0.653403	−	0.757010i	$-0.273341\pi$
$431$	10.9625	+	4.88084i	0.528047	+	0.235102i	−0.125356	+	0.992112i	$0.540007\pi$
$432$	−56.8328	−	41.2915i	−2.73437	−	1.98664i
$433$	10.1803			0.489236			0.244618	−	0.969620i	$-0.421337\pi$
$433$	10.1803			0.489236			0.244618	+	0.969620i	$0.421337\pi$
$434$		0			0
$435$	−8.94427			−0.428845
$436$	6.97214	+	5.06555i	0.333905	+	0.242596i
$437$	−11.6604	−	5.19156i	−0.557794	−	0.248346i
$438$	−13.7082	−	42.1895i	−0.655003	−	2.01589i
$439$	0.590170	−	1.02220i	0.0281673	−	0.0487872i	−0.851598	−	0.524195i	$-0.824366\pi$
$439$	0.590170	−	1.02220i	0.0281673	−	0.0487872i	0.879765	+	0.475408i	$0.157700\pi$
$440$	2.23607	+	3.87298i	0.106600	+	0.184637i
$441$	−34.7202	+	38.5607i	−1.65334	+	1.83622i
$442$	−1.23607	+	3.80423i	−0.0587938	+	0.180949i
$443$	20.5478	+	22.8206i	0.976255	+	1.08424i	0.996428	+	0.0844450i	$0.0269117\pi$
$443$	20.5478	+	22.8206i	0.976255	+	1.08424i	−0.0201727	+	0.999797i	$0.506422\pi$
$444$	3.65418	−	1.62695i	0.173420	−	0.0772115i
$445$	−11.4524	−	2.43427i	−0.542894	−	0.115396i
$446$	−0.676522	+	6.43668i	−0.0320343	+	0.304786i
$447$	3.38261	+	32.1834i	0.159992	+	1.52222i
$448$	−0.978148	+	0.207912i	−0.0462131	+	0.00982290i
$449$	25.3262	−	18.4006i	1.19522	−	0.868377i	0.201413	−	0.979506i	$-0.435447\pi$
$449$	25.3262	−	18.4006i	1.19522	−	0.868377i	0.993806	+	0.111129i	$0.0354466\pi$
$450$	39.1246	−	28.4257i	1.84435	−	1.34000i
$451$	−13.6941	+	2.91076i	−0.644828	+	0.137063i
$452$	−0.224307	−	2.13414i	−0.0105505	−	0.100382i
$453$	−4.79666	+	45.6372i	−0.225367	+	2.14422i
$454$	10.2433	+	2.17728i	0.480742	+	0.102185i
$455$	−0.697887	+	0.310719i	−0.0327174	+	0.0145667i
$456$	−10.8268	−	12.0243i	−0.507010	−	0.563091i
$457$	−0.944272	+	2.90617i	−0.0441712	+	0.135945i	−0.970710	−	0.240254i	$-0.922769\pi$
$457$	−0.944272	+	2.90617i	−0.0441712	+	0.135945i	0.926539	+	0.376199i	$0.122769\pi$
$458$	−14.5256	+	16.1323i	−0.678738	+	0.753815i
$459$	5.52786	+	9.57454i	0.258019	+	0.446901i
$460$	−1.76393	+	3.05522i	−0.0822438	+	0.142450i
$461$	10.6180	+	32.6789i	0.494531	+	1.52201i	0.817686	+	0.575664i	$0.195256\pi$
$461$	10.6180	+	32.6789i	0.494531	+	1.52201i	−0.323155	+	0.946346i	$0.604744\pi$
$462$	−2.25841	−	1.00551i	−0.105071	−	0.0467805i
$463$	2.09017	+	1.51860i	0.0971384	+	0.0705752i	0.635294	−	0.772270i	$-0.280879\pi$
$463$	2.09017	+	1.51860i	0.0971384	+	0.0705752i	−0.538156	+	0.842845i	$0.680879\pi$
$464$	−13.4164			−0.622841
$465$		0			0
$466$	29.0344			1.34499
$467$	−3.80902	−	2.76741i	−0.176260	−	0.128061i	0.496157	−	0.868233i	$-0.334744\pi$
$467$	−3.80902	−	2.76741i	−0.176260	−	0.128061i	−0.672417	+	0.740172i	$0.734744\pi$
$468$	−13.6523	−	6.07838i	−0.631076	−	0.280973i
$469$	0.583592	+	1.79611i	0.0269478	+	0.0829367i
$470$	−2.00000	+	3.46410i	−0.0922531	+	0.159787i
$471$	33.7984	+	58.5405i	1.55735	+	2.69740i
$472$	−3.34565	+	3.71572i	−0.153996	+	0.171030i
$473$	0.763932	−	2.35114i	0.0351256	−	0.108106i
$474$	41.0210	+	45.5585i	1.88416	+	2.09257i
$475$	8.17100	−	3.63796i	0.374911	−	0.166921i
$476$	−0.109021	−	0.0231730i	−0.00499695	−	0.00106213i
$477$	8.17927	−	77.8206i	0.374503	−	3.56316i
$478$	1.98022	+	18.8405i	0.0905730	+	0.861744i
$479$	−22.7828	+	4.84264i	−1.04097	+	0.221266i	−0.696520	−	0.717538i	$-0.745269\pi$
$479$	−22.7828	+	4.84264i	−1.04097	+	0.221266i	−0.344454	+	0.938803i	$0.611936\pi$
$480$	−8.85410	+	6.43288i	−0.404133	+	0.293620i
$481$	−5.23607	+	3.80423i	−0.238744	+	0.173458i
$482$	−22.7283	+	4.83105i	−1.03525	+	0.220048i
$483$	0.455815	+	4.33679i	0.0207403	+	0.197331i
$484$	0.452215	−	4.30254i	0.0205552	−	0.195570i
$485$	15.5959	+	3.31500i	0.708171	+	0.150526i
$486$	−52.6172	+	23.4267i	−2.38677	+	1.06266i
$487$	−12.8714	−	14.2952i	−0.583261	−	0.647777i	0.377220	−	0.926124i	$-0.376880\pi$
$487$	−12.8714	−	14.2952i	−0.583261	−	0.647777i	−0.960481	+	0.278347i	$0.910213\pi$
$488$	−5.65248	+	17.3965i	−0.255876	+	0.787504i
$489$	−23.1870	+	25.7518i	−1.04855	+	1.16454i
$490$	5.61803	+	9.73072i	0.253797	+	0.439589i
$491$	−2.18034	+	3.77646i	−0.0983974	+	0.170429i	−0.911021	−	0.412359i	$-0.864705\pi$
$491$	−2.18034	+	3.77646i	−0.0983974	+	0.170429i	0.812624	+	0.582788i	$0.198038\pi$
$492$	−4.32624	−	13.3148i	−0.195042	−	0.600277i
$493$	1.92891	+	0.858807i	0.0868738	+	0.0386787i
$494$	−9.47214	−	6.88191i	−0.426172	−	0.309632i
$495$	14.9443			0.671695
$496$		0			0
$497$	−2.16718			−0.0972115
$498$	−63.3050	−	45.9937i	−2.83676	−	2.06103i
$499$	−6.01441	−	2.67779i	−0.269242	−	0.119874i	0.267675	−	0.963509i	$-0.413745\pi$
$499$	−6.01441	−	2.67779i	−0.269242	−	0.119874i	−0.536917	+	0.843635i	$0.680411\pi$
$500$	−1.71885	−	5.29007i	−0.0768692	−	0.236579i
$501$	−10.4721	+	18.1383i	−0.467861	+	0.810358i
$502$	1.47214	+	2.54981i	0.0657046	+	0.113804i
$503$	19.8414	−	22.0361i	0.884683	−	0.982540i	−0.115258	−	0.993336i	$-0.536770\pi$
$503$	19.8414	−	22.0361i	0.884683	−	0.982540i	0.999942	+	0.0107951i	$0.00343626\pi$
$504$	−1.21885	+	3.75123i	−0.0542918	+	0.167093i
$505$	−2.00739	−	2.22943i	−0.0893278	−	0.0992085i
$506$	16.8751	−	7.51329i	0.750191	−	0.334007i
$507$	−8.00158	−	1.70079i	−0.355363	−	0.0755347i
$508$	−0.805727	+	7.66598i	−0.0357483	+	0.340123i
$509$	−3.09370	−	29.4346i	−0.137126	−	1.30467i	−0.819253	−	0.573432i	$-0.805611\pi$
$509$	−3.09370	−	29.4346i	−0.137126	−	1.30467i	0.682127	−	0.731234i	$-0.261055\pi$
$510$	3.91259	−	0.831647i	0.173252	−	0.0368259i
$511$	−1.61803	+	1.17557i	−0.0715776	+	0.0520042i
$512$	4.28115	−	3.11044i	0.189202	−	0.137463i
$513$	−31.6535	+	6.72816i	−1.39754	+	0.297056i
$514$	−0.328836	−	3.12866i	−0.0145043	−	0.137999i
$515$	−0.651847	+	6.20191i	−0.0287238	+	0.273289i
$516$	2.41811	+	0.513986i	0.106452	+	0.0226270i
$517$	4.51682	−	2.01102i	0.198649	−	0.0884444i
$518$	−0.511170	−	0.567712i	−0.0224595	−	0.0249438i
$519$	−2.94427	+	9.06154i	−0.129239	+	0.397757i
$520$	4.84187	−	5.37745i	0.212330	−	0.235817i
$521$	−1.00000	−	1.73205i	−0.0438108	−	0.0758825i	0.843288	−	0.537461i	$-0.180617\pi$
$521$	−1.00000	−	1.73205i	−0.0438108	−	0.0758825i	−0.887099	+	0.461579i	$0.847283\pi$
$522$	−16.7082	+	28.9395i	−0.731298	+	1.26665i
$523$	−5.47214	−	16.8415i	−0.239280	−	0.736427i	−0.996525	−	0.0832966i	$-0.973455\pi$
$523$	−5.47214	−	16.8415i	−0.239280	−	0.736427i	0.757245	−	0.653131i	$-0.226545\pi$
$524$	6.77523	+	3.01652i	0.295977	+	0.131777i
$525$	−2.47214	−	1.79611i	−0.107893	−	0.0783888i
$526$	−37.5967			−1.63930
$527$		0			0
$528$	31.4164			1.36722
$529$	−7.75329	−	5.63309i	−0.337100	−	0.244917i
$530$	−15.4794	−	6.89186i	−0.672381	−	0.299363i
$531$	5.16312	+	15.8904i	0.224060	+	0.689587i
$532$	0.163119	−	0.282530i	0.00707210	−	0.0122492i
$533$	11.3262	+	19.6176i	0.490594	+	0.849733i
$534$	−41.0210	+	45.5585i	−1.77515	+	1.97151i
$535$	1.78115	−	5.48183i	0.0770060	−	0.237000i
$536$	−11.9698	−	13.2938i	−0.517015	−	0.574204i
$537$	−5.04996	+	2.24838i	−0.217922	+	0.0970250i
$538$	17.4976	+	3.71924i	0.754377	+	0.160348i
$539$	1.45175	−	13.8125i	0.0625312	−	0.594945i
$540$	0.934931	+	8.89527i	0.0402330	+	0.382792i
$541$	24.8065	−	5.27278i	1.06651	−	0.226695i	0.358959	−	0.933353i	$-0.383132\pi$
$541$	24.8065	−	5.27278i	1.06651	−	0.226695i	0.707555	+	0.706659i	$0.249798\pi$
$542$	18.5623	−	13.4863i	0.797319	−	0.579286i
$543$	−10.9443	+	7.95148i	−0.469664	+	0.341231i
$544$	2.52713	−	0.537159i	0.108350	−	0.0230305i
$545$	1.45757	+	13.8679i	0.0624356	+	0.594035i
$546$	−0.418114	+	3.97809i	−0.0178936	+	0.170246i
$547$	11.8597	+	2.52085i	0.507082	+	0.107784i	0.454347	−	0.890825i	$-0.349873\pi$
$547$	11.8597	+	2.52085i	0.507082	+	0.107784i	0.0527355	+	0.998609i	$0.483206\pi$
$548$	3.55236	−	1.58161i	0.151749	−	0.0675632i
$549$	40.9003	+	45.4244i	1.74558	+	1.93867i
$550$	−4.00000	+	12.3107i	−0.170561	+	0.524931i
$551$	−4.13545	+	4.59289i	−0.176176	+	0.195664i
$552$	−20.6525	−	35.7711i	−0.879028	−	1.52252i
$553$	1.38197	−	2.39364i	0.0587672	−	0.101788i
$554$	−6.32624	−	19.4702i	−0.268776	−	0.827208i
$555$	5.91259	+	2.63245i	0.250975	+	0.111741i
$556$	−6.70820	−	4.87380i	−0.284491	−	0.206695i
$557$	−12.0000			−0.508456			−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000			−0.508456			−0.254228	+	0.967144i	$0.581821\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$	0.927051	+	0.673542i	0.0391751	+	0.0284623i
$561$	−4.51682	−	2.01102i	−0.190700	−	0.0849052i
$562$	8.50000	+	26.1603i	0.358551	+	1.10351i
$563$	−13.7705	+	23.8512i	−0.580358	+	1.00521i	0.415079	+	0.909785i	$0.363754\pi$
$563$	−13.7705	+	23.8512i	−0.580358	+	1.00521i	−0.995437	+	0.0954238i	$0.969579\pi$
$564$	2.47214	+	4.28187i	0.104096	+	0.180299i
$565$	2.32331	−	2.58030i	0.0977425	−	0.108554i
$566$	−6.94427	+	21.3723i	−0.291890	+	0.898344i
$567$	3.85682	+	4.28344i	0.161971	+	0.179887i
$568$	18.7531	−	8.34943i	0.786864	−	0.350334i
$569$	−5.40707	−	1.14931i	−0.226676	−	0.0481815i	0.0931733	−	0.995650i	$-0.470299\pi$
$569$	−5.40707	−	1.14931i	−0.226676	−	0.0481815i	−0.319849	+	0.947468i	$0.603632\pi$
$570$	−1.22384	+	11.6441i	−0.0512610	+	0.487716i
$571$	−2.94565	−	28.0260i	−0.123272	−	1.17285i	−0.864866	−	0.502002i	$-0.832597\pi$
$571$	−2.94565	−	28.0260i	−0.123272	−	1.17285i	0.741595	−	0.670848i	$-0.234070\pi$
$572$	3.91259	−	0.831647i	0.163594	−	0.0347729i
$573$	−50.2148	+	36.4832i	−2.09775	+	1.52411i
$574$	−2.16312	+	1.57160i	−0.0902868	+	0.0655972i
$575$	22.3339	−	4.74721i	0.931387	−	0.197972i
$576$	−3.30858	−	31.4791i	−0.137858	−	1.31163i
$577$	3.01385	−	28.6749i	0.125468	−	1.19375i	−0.732762	−	0.680485i	$-0.761769\pi$
$577$	3.01385	−	28.6749i	0.125468	−	1.19375i	0.858230	−	0.513265i	$-0.171564\pi$
$578$	25.9819	+	5.52261i	1.08070	+	0.229710i
$579$	−10.2647	+	4.57012i	−0.426585	+	0.189928i
$580$	1.14301	+	1.26944i	0.0474610	+	0.0527107i
$581$	−1.09017	+	3.35520i	−0.0452279	+	0.139197i
$582$	55.8626	−	62.0417i	2.31558	−	2.57171i
$583$	10.4721	+	18.1383i	0.433712	+	0.751210i
$584$	9.47214	−	16.4062i	0.391960	−	0.678894i
$585$	−7.47214	−	22.9969i	−0.308935	−	0.950804i
$586$	−0.697887	−	0.310719i	−0.0288294	−	0.0128357i
$587$	5.23607	+	3.80423i	0.216116	+	0.157017i	0.690576	−	0.723259i	$-0.257357\pi$
$587$	5.23607	+	3.80423i	0.216116	+	0.157017i	−0.474461	+	0.880277i	$0.657357\pi$
$588$	13.8885			0.572754
$589$		0			0
$590$	3.61803			0.148952
$591$	29.8885	+	21.7153i	1.22945	+	0.893248i
$592$	8.86889	+	3.94868i	0.364509	+	0.162290i
$593$	−2.01722	−	6.20837i	−0.0828373	−	0.254947i	0.901056	−	0.433702i	$-0.142793\pi$
$593$	−2.01722	−	6.20837i	−0.0828373	−	0.254947i	−0.983894	+	0.178755i	$0.942793\pi$
$594$	23.4164	−	40.5584i	0.960787	−	1.66413i
$595$	−0.0901699	−	0.156179i	−0.00369661	−	0.00640271i
$596$	4.13545	−	4.59289i	0.169395	−	0.188132i
$597$	18.9443	−	58.3045i	0.775337	−	2.38624i
$598$	−19.9993	−	22.2115i	−0.817834	−	0.908296i
$599$	−13.3348	+	5.93703i	−0.544845	+	0.242581i	−0.660653	−	0.750691i	$-0.729721\pi$
$599$	−13.3348	+	5.93703i	−0.544845	+	0.242581i	0.115809	+	0.993272i	$0.463054\pi$
$600$	28.3118	+	6.01785i	1.15582	+	0.245678i
$601$	−3.19241	+	30.3737i	−0.130221	+	1.23897i	0.712908	+	0.701258i	$0.247378\pi$
$601$	−3.19241	+	30.3737i	−0.130221	+	1.23897i	−0.843129	+	0.537712i	$0.819289\pi$
$602$	−0.0493516	−	0.469550i	−0.00201142	−	0.0191374i
$603$	−58.4708	+	12.4284i	−2.38112	+	0.506122i
$604$	7.09017	−	5.15131i	0.288495	−	0.209604i
$605$	5.66312	−	4.11450i	0.230239	−	0.167278i
$606$	−15.3649	+	3.26592i	−0.624158	+	0.132669i
$607$	−2.34898	−	22.3490i	−0.0953421	−	0.907119i	−0.932746	−	0.360534i	$-0.882594\pi$
$607$	−2.34898	−	22.3490i	−0.0953421	−	0.907119i	0.837404	−	0.546585i	$-0.184072\pi$
$608$	−0.790476	+	7.52088i	−0.0320580	+	0.305012i
$609$	2.06532	+	0.438996i	0.0836908	+	0.0177890i
$610$	12.0917	−	5.38359i	0.489581	−	0.217975i
$611$	−5.35304	−	5.94516i	−0.216561	−	0.240515i
$612$	1.09017	−	3.35520i	0.0440675	−	0.135626i
$613$	−29.3672	+	32.6155i	−1.18613	+	1.31733i	−0.248935	+	0.968520i	$0.580081\pi$
$613$	−29.3672	+	32.6155i	−1.18613	+	1.31733i	−0.937194	+	0.348809i	$0.886586\pi$
$614$	23.2254	+	40.2276i	0.937302	+	1.62345i
$615$	11.3262	−	19.6176i	0.456718	−	0.791059i
$616$	−0.326238	−	1.00406i	−0.0131445	−	0.0404546i
$617$	29.6648	+	13.2076i	1.19426	+	0.531718i	0.904950	−	0.425518i	$-0.139908\pi$
$617$	29.6648	+	13.2076i	1.19426	+	0.531718i	0.289309	+	0.957236i	$0.406575\pi$
$618$	26.4164	+	19.1926i	1.06262	+	0.772041i
$619$	6.18034			0.248409			0.124204	−	0.992257i	$-0.460362\pi$
$619$	6.18034			0.248409			0.124204	+	0.992257i	$0.460362\pi$
$620$		0			0
$621$	−82.6099			−3.31502
$622$	38.1976	+	27.7522i	1.53158	+	1.11276i
$623$	2.52498	+	1.12419i	0.101161	+	0.0450398i
$624$	−15.7082	−	48.3449i	−0.628831	−	1.93534i
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	−13.5623	−	23.4906i	−0.542059	−	0.938873i
$627$	9.68375	−	10.7549i	0.386732	−	0.429509i
$628$	3.98936	−	12.2780i	0.159193	−	0.489945i
$629$	−1.02234	−	1.13542i	−0.0407634	−	0.0452723i
$630$	2.60735	−	1.16087i	0.103879	−	0.0462501i
$631$	−33.6098	−	7.14399i	−1.33799	−	0.284398i	−0.517313	−	0.855796i	$-0.673068\pi$
$631$	−33.6098	−	7.14399i	−1.33799	−	0.284398i	−0.820673	+	0.571399i	$0.806401\pi$
$632$	−2.73659	+	26.0369i	−0.108856	+	1.03569i
$633$	7.84101	+	74.6022i	0.311652	+	2.96517i
$634$	−6.41890	+	1.36438i	−0.254927	+	0.0541865i
$635$	−10.0902	+	7.33094i	−0.400416	+	0.290919i
$636$	−16.9443	+	12.3107i	−0.671884	+	0.488152i
$637$	−21.9811	+	4.67222i	−0.870922	+	0.185120i
$638$	−0.934931	−	8.89527i	−0.0370143	−	0.352167i
$639$	7.17031	−	68.2210i	0.283653	−	2.69878i
$640$	−13.3204	−	2.83135i	−0.526537	−	0.111919i
$641$	10.9625	−	4.88084i	0.432995	−	0.192782i	−0.178653	−	0.983912i	$-0.557174\pi$
$641$	10.9625	−	4.88084i	0.432995	−	0.192782i	0.611647	+	0.791131i	$0.290507\pi$
$642$	−20.1946	−	22.4284i	−0.797017	−	0.885177i
$643$	6.03444	−	18.5721i	0.237975	−	0.732412i	−0.758738	−	0.651396i	$-0.774184\pi$
$643$	6.03444	−	18.5721i	0.237975	−	0.732412i	0.996713	−	0.0810159i	$-0.0258165\pi$
$644$	0.557262	−	0.618903i	0.0219592	−	0.0243882i
$645$	2.00000	+	3.46410i	0.0787499	+	0.136399i
$646$	1.38197	−	2.39364i	0.0543727	−	0.0941763i
$647$	−0.291796	−	0.898056i	−0.0114717	−	0.0353062i	0.945157	−	0.326617i	$-0.105909\pi$
$647$	−0.291796	−	0.898056i	−0.0114717	−	0.0353062i	−0.956629	+	0.291311i	$0.905909\pi$
$648$	−49.8766	−	22.2065i	−1.95934	−	0.872354i
$649$	−3.61803	−	2.62866i	−0.142020	−	0.103184i
$650$	20.9443			0.821502
$651$		0			0
$652$	6.61803			0.259182
$653$	38.2705	+	27.8052i	1.49764	+	1.08810i	0.971309	+	0.237820i	$0.0764329\pi$
$653$	38.2705	+	27.8052i	1.49764	+	1.08810i	0.526332	+	0.850279i	$0.323567\pi$
$654$	66.7008	+	29.6971i	2.60821	+	1.16125i
$655$	3.70820	+	11.4127i	0.144892	+	0.445930i
$656$	16.9894	−	29.4264i	0.663323	−	1.14891i
$657$	−31.6525	−	54.8237i	−1.23488	−	2.13888i
$658$	0.631841	−	0.701731i	0.0246317	−	0.0273563i
$659$	7.92705	−	24.3970i	0.308794	−	0.950370i	−0.669440	−	0.742866i	$-0.733466\pi$
$659$	7.92705	−	24.3970i	0.308794	−	0.950370i	0.978234	−	0.207504i	$-0.0665341\pi$
$660$	−2.67652	−	2.97258i	−0.104183	−	0.115707i
$661$	−0.584048	+	0.260035i	−0.0227168	+	0.0101142i	−0.418064	−	0.908418i	$-0.637291\pi$
$661$	−0.584048	+	0.260035i	−0.0227168	+	0.0101142i	0.395347	+	0.918532i	$0.370624\pi$
$662$	−3.16535	−	0.672816i	−0.123025	−	0.0261498i
$663$	−0.836228	+	7.95618i	−0.0324764	+	0.308992i
$664$	−3.49297	−	33.2333i	−0.135553	−	1.28970i
$665$	0.516329	−	0.109749i	0.0200224	−	0.00425589i
$666$	19.5623	−	14.2128i	0.758024	−	0.550737i
$667$	−12.7639	+	9.27354i	−0.494221	+	0.359073i
$668$	3.91259	−	0.831647i	0.151383	−	0.0321774i
$669$	1.35304	+	12.8734i	0.0523117	+	0.497713i
$670$	−1.35304	+	12.8734i	−0.0522727	+	0.497341i
$671$	−16.0032	−	3.40158i	−0.617795	−	0.131316i
$672$	2.36023	−	1.05084i	0.0910478	−	0.0405371i
$673$	−19.4136	−	21.5610i	−0.748339	−	0.831115i	0.241928	−	0.970294i	$-0.422220\pi$
$673$	−19.4136	−	21.5610i	−0.748339	−	0.831115i	−0.990267	+	0.139180i	$0.955553\pi$
$674$	−7.38197	+	22.7194i	−0.284343	+	0.875117i
$675$	38.7350	−	43.0196i	1.49091	−	1.65582i
$676$	0.781153	+	1.35300i	0.0300443	+	0.0520383i
$677$	23.3607	−	40.4619i	0.897824	−	1.55508i	0.0675535	−	0.997716i	$-0.478481\pi$
$677$	23.3607	−	40.4619i	0.897824	−	1.55508i	0.830270	−	0.557361i	$-0.188186\pi$
$678$	−5.61803	−	17.2905i	−0.215759	−	0.664039i
$679$	−3.43852	−	1.53093i	−0.131958	−	0.0587517i
$680$	1.38197	+	1.00406i	0.0529960	+	0.0385038i
$681$	20.9443			0.802586
$682$		0			0
$683$	5.18034			0.198220			0.0991101	−	0.995076i	$-0.468400\pi$
$683$	5.18034			0.198220			0.0991101	+	0.995076i	$0.468400\pi$
$684$	8.35410	+	6.06961i	0.319427	+	0.232077i
$685$	5.74784	+	2.55910i	0.219614	+	0.0977783i
$686$	−1.64590	−	5.06555i	−0.0628407	−	0.193404i
$687$	−21.7082	+	37.5997i	−0.828220	+	1.43452i
$688$	3.00000	+	5.19615i	0.114374	+	0.198101i
$689$	22.6759	−	25.1841i	0.863882	−	0.959438i
$690$	−9.23607	+	28.4257i	−0.351611	+	1.08215i
$691$	2.12806	+	2.36345i	0.0809553	+	0.0899100i	0.782262	−	0.622950i	$-0.214066\pi$
$691$	2.12806	+	2.36345i	0.0809553	+	0.0899100i	−0.701306	+	0.712860i	$0.747399\pi$
$692$	1.66234	−	0.740122i	0.0631928	−	0.0281352i
$693$	−3.45077	−	0.733484i	−0.131084	−	0.0278628i
$694$	−4.08964	+	38.9103i	−0.155240	+	1.47701i
$695$	−1.40240	−	13.3429i	−0.0531959	−	0.506125i
$696$	−19.5630	+	4.15823i	−0.741532	+	0.157617i
$697$	−4.32624	+	3.14320i	−0.163868	+	0.119057i
$698$	10.3262	−	7.50245i	0.390854	−	0.283972i
$699$	56.7999	−	12.0732i	2.14837	−	0.456650i
$700$	0.0610020	+	0.580395i	0.00230566	+	0.0219369i
$701$	−0.731699	+	6.96165i	−0.0276359	+	0.262938i	0.971976	+	0.235080i	$0.0755353\pi$
$701$	−0.731699	+	6.96165i	−0.0276359	+	0.262938i	−0.999612	+	0.0278579i	$0.991131\pi$
$702$	−74.1212	−	15.7549i	−2.79752	−	0.594632i
$703$	4.08550	−	1.81898i	0.154088	−	0.0686042i
$704$	5.66897	+	6.29602i	0.213657	+	0.237290i
$705$	−2.47214	+	7.60845i	−0.0931060	+	0.286551i
$706$	8.02957	−	8.91774i	0.302197	−	0.335623i
$707$	0.354102	+	0.613323i	0.0133174	+	0.0230664i
$708$	2.23607	−	3.87298i	0.0840366	−	0.145556i
$709$	7.88854	+	24.2784i	0.296260	+	0.911796i	0.982795	+	0.184699i	$0.0591310\pi$
$709$	7.88854	+	24.2784i	0.296260	+	0.911796i	−0.686535	+	0.727097i	$0.740869\pi$
$710$	−13.5699	−	6.04171i	−0.509269	−	0.226741i
$711$	70.7771	+	51.4226i	2.65435	+	1.92850i
$712$	−26.1803			−0.981150
$713$		0			0
$714$	−0.944272			−0.0353385
$715$	5.23607	+	3.80423i	0.195818	+	0.142270i
$716$	0.964456	+	0.429403i	0.0360434	+	0.0160476i
$717$	11.7082	+	36.0341i	0.437251	+	1.34572i
$718$	−17.9894	+	31.1585i	−0.671357	+	1.16282i
$719$	6.90983	+	11.9682i	0.257693	+	0.446338i	0.965624	−	0.259945i	$-0.0837043\pi$
$719$	6.90983	+	11.9682i	0.257693	+	0.446338i	−0.707930	+	0.706282i	$0.750371\pi$
$720$	−24.2697	+	26.9542i	−0.904479	+	1.00453i
$721$	0.454915	−	1.40008i	0.0169419	−	0.0521419i
$722$	−15.1575	−	16.8341i	−0.564102	−	0.626499i
$723$	−42.4544	+	18.9019i	−1.57890	+	0.702970i
$724$	2.52713	+	0.537159i	0.0939202	+	0.0199634i
$725$	1.15564	−	10.9952i	0.0429193	−	0.408350i
$726$	−3.83123	−	36.4517i	−0.142190	−	1.35285i
$727$	43.2694	−	9.19720i	1.60477	−	0.341105i	0.683479	−	0.729970i	$-0.260466\pi$
$727$	43.2694	−	9.19720i	1.60477	−	0.341105i	0.921295	+	0.388865i	$0.127133\pi$
$728$	−1.38197	+	1.00406i	−0.0512191	+	0.0372128i
$729$	−33.9336	+	24.6542i	−1.25680	+	0.913119i
$730$	−13.4086	+	2.85010i	−0.496276	+	0.105487i
$731$	−0.0987033	−	0.939099i	−0.00365067	−	0.0347338i
$732$	1.71016	−	16.2711i	0.0632092	−	0.601395i
$733$	−3.39626	−	0.721898i	−0.125444	−	0.0266639i	0.144762	−	0.989467i	$-0.453758\pi$
$733$	−3.39626	−	0.721898i	−0.125444	−	0.0266639i	−0.270206	+	0.962803i	$0.587092\pi$
$734$	26.6067	−	11.8460i	0.982070	−	0.437246i
$735$	15.0368	+	16.7001i	0.554641	+	0.615991i
$736$	−5.96556	+	18.3601i	−0.219893	+	0.676762i
$737$	10.7061	−	11.8903i	0.394364	−	0.437985i
$738$	−42.3156	−	73.2928i	−1.55766	−	2.69794i
$739$	−3.09017	+	5.35233i	−0.113674	+	0.196889i	−0.917249	−	0.398315i	$-0.869595\pi$
$739$	−3.09017	+	5.35233i	−0.113674	+	0.196889i	0.803575	+	0.595203i	$0.202929\pi$
$740$	−0.381966	−	1.17557i	−0.0140413	−	0.0432148i
$741$	−21.3920	−	9.52431i	−0.785853	−	0.349884i
$742$	3.23607	+	2.35114i	0.118800	+	0.0863131i
$743$	50.1803			1.84094			0.920469	−	0.390815i	$-0.127807\pi$
$743$	50.1803			1.84094			0.920469	+	0.390815i	$0.127807\pi$
$744$		0			0
$745$	10.0000			0.366372
$746$	−24.8713	−	18.0701i	−0.910604	−	0.661592i
$747$	−102.012	−	45.4185i	−3.73241	−	1.66178i
$748$	0.291796	+	0.898056i	0.0106691	+	0.0328362i
$749$	−0.680340	+	1.17838i	−0.0248591	+	0.0430572i
$750$	−23.5623	−	40.8111i	−0.860374	−	1.49021i
$751$	−14.4138	+	16.0081i	−0.525965	+	0.584144i	−0.946326	−	0.323213i	$-0.895237\pi$
$751$	−14.4138	+	16.0081i	−0.525965	+	0.584144i	0.420361	+	0.907357i	$0.361904\pi$
$752$	−3.70820	+	11.4127i	−0.135224	+	0.416178i
$753$	3.94020	+	4.37604i	0.143589	+	0.159472i
$754$	−13.2210	+	5.88635i	−0.481479	+	0.214368i
$755$	13.8705	+	2.94826i	0.504798	+	0.107298i
$756$	0.220707	−	2.09989i	0.00802705	−	0.0763722i
$757$	−0.904430	−	8.60508i	−0.0328721	−	0.312757i	−0.998587	−	0.0531502i	$-0.983074\pi$
$757$	−0.904430	−	8.60508i	−0.0328721	−	0.312757i	0.965714	−	0.259607i	$-0.0835929\pi$
$758$	3.34175	−	0.710311i	0.121378	−	0.0257997i
$759$	29.8885	−	21.7153i	1.08489	−	0.788215i
$760$	−4.04508	+	2.93893i	−0.146731	+	0.106606i
$761$	−1.95630	+	0.415823i	−0.0709156	+	0.0150736i	−0.243233	−	0.969968i	$-0.578208\pi$
$761$	−1.95630	+	0.415823i	−0.0709156	+	0.0150736i	0.172317	+	0.985042i	$0.444875\pi$
$762$	6.82623	+	64.9472i	0.247288	+	2.35279i
$763$	0.344086	−	3.27376i	0.0124568	−	0.118518i
$764$	11.5951	+	2.46461i	0.419495	+	0.0891663i
$765$	5.21470	−	2.32174i	0.188538	−	0.0839425i
$766$	−25.8636	−	28.7244i	−0.934488	−	1.03785i
$767$	−2.23607	+	6.88191i	−0.0807397	+	0.248491i
$768$	−29.3672	+	32.6155i	−1.05970	+	1.17691i
$769$	23.6803	+	41.0156i	0.853935	+	1.47906i	0.877630	+	0.479339i	$0.159124\pi$
$769$	23.6803	+	41.0156i	0.853935	+	1.47906i	−0.0236947	+	0.999719i	$0.507543\pi$
$770$	−0.381966	+	0.661585i	−0.0137651	+	0.0238419i
$771$	−1.94427	−	5.98385i	−0.0700212	−	0.215503i
$772$	1.96038	+	0.872815i	0.0705555	+	0.0314133i
$773$	9.00000	+	6.53888i	0.323708	+	0.235187i	0.737756	−	0.675068i	$-0.235886\pi$
$773$	9.00000	+	6.53888i	0.323708	+	0.235187i	−0.414048	+	0.910255i	$0.635886\pi$
$774$	14.9443			0.537161
$775$		0			0
$776$	35.6525			1.27985
$777$	−1.23607	−	0.898056i	−0.0443437	−	0.0322176i
$778$	−26.4419	−	11.7727i	−0.947988	−	0.422072i
$779$	−4.83688	−	14.8864i	−0.173299	−	0.533360i
$780$	−3.23607	+	5.60503i	−0.115870	+	0.200692i
$781$	9.18034	+	15.9008i	0.328498	+	0.568976i
$782$	4.72120	−	5.24343i	0.168830	−	0.187505i
$783$	−12.3607	+	38.0423i	−0.441735	+	1.35952i
$784$	22.5552	+	25.0501i	0.805543	+	0.894646i
$785$	19.0826	−	8.49614i	0.681088	−	0.303240i
$786$	61.4598	+	13.0637i	2.19220	+	0.465966i
$787$	−0.768025	+	7.30727i	−0.0273771	+	0.260476i	0.972269	+	0.233866i	$0.0751378\pi$
$787$	−0.768025	+	7.30727i	−0.0273771	+	0.260476i	−0.999646	+	0.0266098i	$0.991529\pi$
$788$	−0.737524	−	7.01708i	−0.0262732	−	0.249973i
$789$	−73.5503	+	15.6336i	−2.61846	+	0.556571i
$790$	15.3262	−	11.1352i	0.545283	−	0.396171i
$791$	−0.663119	+	0.481784i	−0.0235778	+	0.0171303i
$792$	32.6862	−	6.94766i	1.16145	−	0.246874i
$793$	2.76709	+	26.3271i	0.0982623	+	0.934903i
$794$	1.18391	−	11.2642i	0.0420155	−	0.399751i
$795$	−33.1480	−	7.04582i	−1.17564	−	0.249890i
$796$	−10.6960	+	4.76216i	−0.379109	+	0.168790i
$797$	−37.0808	−	41.1824i	−1.31347	−	1.45876i	−0.799114	−	0.601179i	$-0.794698\pi$
$797$	−37.0808	−	41.1824i	−1.31347	−	1.45876i	−0.514355	−	0.857577i	$-0.671969\pi$
$798$	0.854102	−	2.62866i	0.0302349	−	0.0930534i
$799$	1.26368	−	1.40346i	0.0447059	−	0.0496509i
$800$	−6.76393	−	11.7155i	−0.239141	−	0.414205i
$801$	−43.7426	+	75.7645i	−1.54557	+	2.67701i
$802$	19.0902	+	58.7535i	0.674097	+	2.07466i
$803$	15.4794	+	6.89186i	0.546255	+	0.243208i
$804$	12.9443	+	9.40456i	0.456509	+	0.331673i
$805$	1.34752			0.0474940
$806$		0			0
$807$	35.7771			1.25941
$808$	−5.42705	−	3.94298i	−0.190923	−	0.138714i
$809$	21.3920	+	9.52431i	0.752101	+	0.334857i	0.746729	−	0.665129i	$-0.231623\pi$
$809$	21.3920	+	9.52431i	0.752101	+	0.334857i	0.00537221	+	0.999986i	$0.498290\pi$
$810$	12.2082	+	37.5730i	0.428953	+	1.32018i
$811$	14.0000	−	24.2487i	0.491606	−	0.851487i	−0.508347	−	0.861152i	$-0.669743\pi$
$811$	14.0000	−	24.2487i	0.491606	−	0.851487i	0.999953	+	0.00966502i	$0.00307652\pi$
$812$	−0.201626	−	0.349227i	−0.00707569	−	0.0122555i
$813$	30.7054	−	34.1018i	1.07689	−	1.19600i
$814$	−2.00000	+	6.15537i	−0.0701000	+	0.215746i
$815$	7.16519	+	7.95775i	0.250986	+	0.278748i
$816$	10.9625	−	4.88084i	0.383766	−	0.170864i
$817$	2.70353	+	0.574654i	0.0945847	+	0.0201046i
$818$	0.646021	−	6.14648i	0.0225876	−	0.214907i
$819$	0.596670	+	5.67693i	0.0208493	+	0.198368i
$820$	−4.23170	+	0.899475i	−0.147777	+	0.0314110i
$821$	−24.7082	+	17.9516i	−0.862322	+	0.626514i	−0.928516	−	0.371293i	$-0.878915\pi$
$821$	−24.7082	+	17.9516i	−0.862322	+	0.626514i	0.0661935	+	0.997807i	$0.478915\pi$
$822$	26.6525	−	19.3642i	0.929612	−	0.675403i
$823$	13.9795	−	2.97143i	0.487294	−	0.103578i	0.0422888	−	0.999105i	$-0.486535\pi$
$823$	13.9795	−	2.97143i	0.487294	−	0.103578i	0.445005	+	0.895528i	$0.353202\pi$
$824$	1.45757	+	13.8679i	0.0507770	+	0.483111i
$825$	−2.70609	+	25.7467i	−0.0942140	+	0.896386i
$826$	−0.835438	−	0.177578i	−0.0290686	−	0.00617872i
$827$	15.8478	−	7.05587i	0.551080	−	0.245357i	−0.112255	−	0.993679i	$-0.535807\pi$
$827$	15.8478	−	7.05587i	0.551080	−	0.245357i	0.663335	+	0.748323i	$0.269141\pi$
$828$	17.6387	+	19.5898i	0.612989	+	0.680793i
$829$	5.20163	−	16.0090i	0.180660	−	0.556014i	−0.819187	−	0.573527i	$-0.805575\pi$
$829$	5.20163	−	16.0090i	0.180660	−	0.556014i	0.999847	+	0.0175128i	$0.00557479\pi$
$830$	−16.1798	+	17.9695i	−0.561609	+	0.623730i
$831$	−20.4721	−	35.4588i	−0.710171	−	1.23005i
$832$	6.85410	−	11.8717i	0.237623	−	0.411576i
$833$	−1.63932	−	5.04531i	−0.0567991	−	0.174810i
$834$	−64.1759	−	28.5729i	−2.22223	−	0.989400i
$835$	5.23607	+	3.80423i	0.181202	+	0.131651i
$836$	−2.76393			−0.0955926
$837$		0			0
$838$	−16.3820			−0.565906
$839$	−23.4164	−	17.0130i	−0.808424	−	0.587355i	0.104949	−	0.994478i	$-0.466532\pi$
$839$	−23.4164	−	17.0130i	−0.808424	−	0.587355i	−0.913373	+	0.407123i	$0.866532\pi$
$840$	1.56052	+	0.694789i	0.0538431	+	0.0239725i
$841$	−6.60081	−	20.3152i	−0.227614	−	0.700525i
$842$	−23.7533	+	41.1419i	−0.818592	+	1.41784i
$843$	27.5066	+	47.6428i	0.947377	+	1.64090i
$844$	9.58612	−	10.6465i	0.329968	−	0.366467i
$845$	−0.781153	+	2.40414i	−0.0268725	+	0.0827050i
$846$	19.9993	+	22.2115i	0.687591	+	0.763648i
$847$	−1.50961	+	0.672122i	−0.0518709	+	0.0230944i
$848$	−49.7220	−	10.5687i	−1.70746	−	0.362932i
$849$	−4.69796	+	44.6981i	−0.161233	+	1.53403i
$850$	0.516817	+	4.91719i	0.0177267	+	0.168658i
$851$	11.1669	−	2.37360i	0.382797	−	0.0813661i
$852$	−14.8541	+	10.7921i	−0.508893	+	0.369733i
$853$	−8.56231	+	6.22088i	−0.293168	+	0.212999i	−0.724640	−	0.689127i	$-0.757994\pi$
$853$	−8.56231	+	6.22088i	−0.293168	+	0.212999i	0.431473	+	0.902126i	$0.357994\pi$
$854$	−3.05633	+	0.649643i	−0.104586	+	0.0222303i
$855$	1.74648	+	16.6167i	0.0597285	+	0.568278i
$856$	1.34722	−	12.8179i	0.0460470	−	0.438108i
$857$	54.4492	+	11.5735i	1.85995	+	0.395344i	0.994418	−	0.105511i	$-0.0336477\pi$
$857$	54.4492	+	11.5735i	1.85995	+	0.395344i	0.865531	+	0.500855i	$0.166981\pi$
$858$	30.9587	−	13.7837i	1.05691	−	0.470568i
$859$	1.41284	+	1.56912i	0.0482055	+	0.0535376i	0.766765	−	0.641928i	$-0.221865\pi$
$859$	1.41284	+	1.56912i	0.0482055	+	0.0535376i	−0.718560	+	0.695465i	$0.755198\pi$
$860$	0.236068	−	0.726543i	0.00804985	−	0.0247749i
$861$	−3.57819	+	3.97398i	−0.121944	+	0.135433i
$862$	−9.70820	−	16.8151i	−0.330663	−	0.572725i
$863$	4.90983	−	8.50408i	0.167133	−	0.289482i	−0.770278	−	0.637708i	$-0.779883\pi$
$863$	4.90983	−	8.50408i	0.167133	−	0.289482i	0.937411	+	0.348226i	$0.113216\pi$
$864$	15.1246	+	46.5488i	0.514550	+	1.58362i
$865$	2.68973	+	1.19754i	0.0914534	+	0.0407177i
$866$	−13.3262	−	9.68208i	−0.452844	−	0.329010i
$867$	53.1246			1.80421
$868$		0			0
$869$	−23.4164			−0.794347
$870$	11.7082	+	8.50651i	0.396945	+	0.288398i
$871$	−23.6504	−	10.5298i	−0.801362	−	0.356789i
$872$	9.63525	+	29.6543i	0.326291	+	1.00422i
$873$	59.5689	−	103.176i	2.01610	−	3.49199i
$874$	10.3262	+	17.8856i	0.349290	+	0.604988i
$875$	−1.42164	+	1.57889i	−0.0480603	+	0.0533764i
$876$	−5.23607	+	16.1150i	−0.176910	+	0.544474i
$877$	−12.0816	−	13.4180i	−0.407968	−	0.453094i	0.503788	−	0.863828i	$-0.331939\pi$
$877$	−12.0816	−	13.4180i	−0.407968	−	0.453094i	−0.911756	+	0.410733i	$0.865273\pi$
$878$	−1.74472	+	0.776798i	−0.0588813	+	0.0262157i
$879$	−1.49448	−	0.317661i	−0.0504074	−	0.0107144i
$880$	1.01478	−	9.65502i	0.0342083	−	0.325471i
$881$	2.12827	+	20.2491i	0.0717033	+	0.682211i	0.970047	+	0.242918i	$0.0781045\pi$
$881$	2.12827	+	20.2491i	0.0717033	+	0.682211i	−0.898344	+	0.439293i	$0.855229\pi$
$882$	82.1228	−	17.4557i	2.76522	−	0.587765i
$883$	25.7082	−	18.6781i	0.865150	−	0.628568i	−0.0641312	−	0.997941i	$-0.520428\pi$
$883$	25.7082	−	18.6781i	0.865150	−	0.628568i	0.929281	+	0.369373i	$0.120428\pi$
$884$	1.23607	−	0.898056i	0.0415735	−	0.0302049i
$885$	7.07794	−	1.50446i	0.237922	−	0.0505720i
$886$	−5.19370	−	49.4147i	−0.174486	−	1.66012i
$887$	−2.82947	+	26.9206i	−0.0950043	+	0.903905i	0.838394	+	0.545064i	$0.183495\pi$
$887$	−2.82947	+	26.9206i	−0.0950043	+	0.903905i	−0.933399	+	0.358841i	$0.883172\pi$
$888$	14.1559	+	3.00893i	0.475040	+	0.100973i
$889$	2.68973	−	1.19754i	0.0902105	−	0.0401643i
$890$	12.6762	+	14.0783i	0.424907	+	0.471907i
$891$	15.0902	−	46.4428i	0.505540	−	1.55589i
$892$	1.65418	−	1.83716i	0.0553861	−	0.0615125i
$893$	2.76393	+	4.78727i	0.0924915	+	0.160200i
$894$	26.1803	−	45.3457i	0.875602	−	1.51659i
$895$	0.527864	+	1.62460i	0.0176445	+	0.0543043i
$896$	2.93685	+	1.30757i	0.0981132	+	0.0436828i
$897$	−48.3607	−	35.1361i	−1.61472	−	1.17316i
$898$	−50.6525			−1.69030
$899$		0			0
$900$	−18.4721			−0.615738
$901$	6.47214	+	4.70228i	0.215618	+	0.156656i
$902$	20.6941	+	9.21359i	0.689037	+	0.306779i
$903$	−0.291796	−	0.898056i	−0.00971037	−	0.0298854i
$904$	3.88197	−	6.72376i	0.129112	−	0.223629i
$905$	2.09017	+	3.62028i	0.0694796	+	0.120342i
$906$	49.6824	−	55.1779i	1.65059	−	1.83316i
$907$	−7.48936	+	23.0499i	−0.248680	+	0.765358i	0.746329	+	0.665577i	$0.231814\pi$
$907$	−7.48936	+	23.0499i	−0.248680	+	0.765358i	−0.995009	+	0.0997816i	$0.968186\pi$
$908$	−2.67652	−	2.97258i	−0.0888235	−	0.0986485i
$909$	−20.4784	+	9.11757i	−0.679226	+	0.302411i
$910$	1.20906	+	0.256993i	0.0400798	+	0.00851923i
$911$	−1.90036	+	18.0807i	−0.0629618	+	0.599042i	0.916866	+	0.399196i	$0.130711\pi$
$911$	−1.90036	+	18.0807i	−0.0629618	+	0.599042i	−0.979827	+	0.199846i	$0.935956\pi$
$912$	3.67152	+	34.9322i	0.121576	+	1.15672i
$913$	29.2354	−	6.21418i	0.967551	−	0.205659i
$914$	4.00000	−	2.90617i	0.132308	−	0.0961276i
$915$	21.4164	−	15.5599i	0.708005	−	0.514395i
$916$	8.11060	−	1.72396i	0.267982	−	0.0569613i
$917$	−0.296110	−	2.81730i	−0.00977841	−	0.0930354i
$918$	1.86986	−	17.7905i	0.0617146	−	0.587176i
$919$	14.1559	+	3.00893i	0.466960	+	0.0992553i	0.435382	−	0.900246i	$-0.356613\pi$
$919$	14.1559	+	3.00893i	0.466960	+	0.0992553i	0.0315779	+	0.999501i	$0.489947\pi$
$920$	−11.6604	+	5.19156i	−0.384433	+	0.171161i
$921$	62.1634	+	69.0394i	2.04835	+	2.27493i
$922$	17.1803	−	52.8756i	0.565804	−	1.74137i
$923$	19.8787	−	22.0775i	0.654314	−	0.726690i
$924$	0.472136	+	0.817763i	0.0155321	+	0.0269024i
$925$	−4.00000	+	6.92820i	−0.131519	+	0.227798i
$926$	−1.29180	−	3.97574i	−0.0424511	−	0.130651i
$927$	42.5682	+	18.9526i	1.39812	+	0.622485i
$928$	7.56231	+	5.49434i	0.248245	+	0.180360i
$929$	−20.0000			−0.656179			−0.328089	−	0.944647i	$-0.606405\pi$
$929$	−20.0000			−0.656179			−0.328089	+	0.944647i	$0.606405\pi$
$930$		0			0
$931$	15.5279			0.508905
$932$	−8.97214	−	6.51864i	−0.293892	−	0.213525i
$933$	86.2657	+	38.4080i	2.82421	+	1.25742i
$934$	2.35410	+	7.24518i	0.0770286	+	0.237070i
$935$	−0.763932	+	1.32317i	−0.0249832	+	0.0432723i
$936$	−27.0344	−	46.8250i	−0.883648	−	1.53052i
$937$	6.05946	−	6.72972i	0.197954	−	0.219850i	−0.635993	−	0.771695i	$-0.719409\pi$
$937$	6.05946	−	6.72972i	0.197954	−	0.219850i	0.833947	+	0.551845i	$0.186076\pi$
$938$	0.944272	−	2.90617i	0.0308316	−	0.0948898i
$939$	−36.2998	−	40.3150i	−1.18460	−	1.31563i
$940$	1.39577	−	0.621438i	0.0455251	−	0.0202691i
$941$	37.1696	+	7.90064i	1.21169	+	0.257554i	0.769077	−	0.639157i	$-0.220716\pi$
$941$	37.1696	+	7.90064i	1.21169	+	0.257554i	0.442618	+	0.896710i	$0.354050\pi$
$942$	11.4327	−	108.775i	0.372497	−	3.54407i
$943$	−4.17669	−	39.7385i	−0.136012	−	1.29406i
$944$	10.6169	−	2.25669i	0.345551	−	0.0734492i
$945$	2.76393	−	2.00811i	0.0899107	−	0.0653240i
$946$	−3.23607	+	2.35114i	−0.105214	+	0.0764422i
$947$	12.7704	−	2.71444i	0.414983	−	0.0882074i	0.00431154	−	0.999991i	$-0.498628\pi$
$947$	12.7704	−	2.71444i	0.414983	−	0.0882074i	0.410672	+	0.911783i	$0.365294\pi$
$948$	−2.44768	−	23.2881i	−0.0794970	−	0.756363i
$949$	2.86579	−	27.2662i	0.0930276	−	0.885099i
$950$	−14.1559	−	3.00893i	−0.459278	−	0.0976225i
$951$	−11.9899	+	5.33826i	−0.388800	+	0.173105i
$952$	−0.269828	−	0.299675i	−0.00874519	−	0.00971252i
$953$	14.1246	−	43.4711i	0.457541	−	1.40817i	−0.410585	−	0.911822i	$-0.634675\pi$
$953$	14.1246	−	43.4711i	0.457541	−	1.40817i	0.868126	−	0.496344i	$-0.165325\pi$
$954$	−84.7186	+	94.0895i	−2.74286	+	3.04626i
$955$	9.59017	+	16.6107i	0.310331	+	0.537508i
$956$	3.61803	−	6.26662i	0.117016	−	0.202677i
$957$	−5.52786	−	17.0130i	−0.178690	−	0.549953i
$958$	34.4287	+	15.3287i	1.11234	+	0.495246i
$959$	−1.20163	−	0.873032i	−0.0388025	−	0.0281917i
$960$	−13.7082			−0.442430
$961$		0			0
$962$	10.4721			0.337635
$963$	−34.8435	−	25.3153i	−1.12281	−	0.815773i
$964$	8.10807	+	3.60995i	0.261143	+	0.116269i
$965$	1.07295	+	3.30220i	0.0345395	+	0.106301i
$966$	3.52786	−	6.11044i	0.113507	−	0.196600i
$967$	−30.1803	−	52.2739i	−0.970534	−	1.68101i	−0.693947	−	0.720026i	$-0.744130\pi$
$967$	−30.1803	−	52.2739i	−0.970534	−	1.68101i	−0.276587	−	0.960989i	$-0.589203\pi$
$968$	10.4736	−	11.6321i	0.336633	−	0.373868i
$969$	1.70820	−	5.25731i	0.0548754	−	0.168889i
$970$	−17.2625	−	19.1719i	−0.554265	−	0.615574i
$971$	−25.5793	+	11.3886i	−0.820878	+	0.365478i	−0.773814	−	0.633413i	$-0.781653\pi$
$971$	−25.5793	+	11.3886i	−0.820878	+	0.365478i	−0.0470644	+	0.998892i	$0.514987\pi$
$972$	21.5192	+	4.57406i	0.690230	+	0.146713i
$973$	−0.331061	+	3.14983i	−0.0106133	+	0.100979i
$974$	3.25341	+	30.9541i	0.104246	+	0.991834i
$975$	40.9732	−	8.70912i	1.31219	−	0.278915i
$976$	32.1246	−	23.3399i	1.02828	−	0.747092i
$977$	38.2254	−	27.7724i	1.22294	−	0.888518i	0.226599	−	0.973988i	$-0.427239\pi$
$977$	38.2254	−	27.7724i	1.22294	−	0.888518i	0.996341	+	0.0854705i	$0.0272393\pi$
$978$	54.8436	−	11.6574i	1.75371	−	0.372762i
$979$	−2.44768	−	23.2881i	−0.0782282	−	0.744292i
$980$	0.448615	−	4.26829i	0.0143305	−	0.136345i
$981$	101.917	+	21.6630i	3.25395	+	0.691648i
$982$	6.44573	−	2.86982i	0.205691	−	0.0915797i
$983$	26.4493	+	29.3749i	0.843602	+	0.936915i	0.998699	−	0.0509845i	$-0.0162359\pi$
$983$	26.4493	+	29.3749i	0.843602	+	0.936915i	−0.155098	+	0.987899i	$0.549569\pi$
$984$	15.6525	−	48.1734i	0.498983	−	1.53571i
$985$	7.63907	−	8.48404i	0.243401	−	0.270324i
$986$	−1.70820	−	2.95870i	−0.0544003	−	0.0942241i
$987$	0.944272	−	1.63553i	0.0300565	−	0.0520594i
$988$	1.38197	+	4.25325i	0.0439662	+	0.135314i
$989$	6.44573	+	2.86982i	0.204962	+	0.0912551i
$990$	−19.5623	−	14.2128i	−0.621731	−	0.451714i
$991$	−16.5410			−0.525443			−0.262721	−	0.964872i	$-0.584620\pi$
$991$	−16.5410			−0.525443			−0.262721	+	0.964872i	$0.584620\pi$
$992$		0			0
$993$	−6.47214			−0.205387
$994$	2.83688	+	2.06111i	0.0899804	+	0.0653746i
$995$	−17.3065	−	7.70533i	−0.548651	−	0.244275i
$996$	9.23607	+	28.4257i	0.292656	+	0.900703i
$997$	14.6803	−	25.4271i	0.464931	−	0.805284i	−0.534267	−	0.845316i	$-0.679412\pi$
$997$	14.6803	−	25.4271i	0.464931	−	0.805284i	0.999198	+	0.0400314i	$0.0127458\pi$
$998$	5.32624	+	9.22531i	0.168599	+	0.292022i
$999$	19.3675	−	21.5098i	0.612761	−	0.680540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.a.732.1		8
31.2	even	5		961.2.g.h.448.1		8
31.3	odd	30		961.2.d.a.388.1		4
31.4	even	5		961.2.c.e.521.2		4
31.5	even	3	inner	961.2.g.a.816.1		8
31.6	odd	6		961.2.d.a.374.1		4
31.7	even	15		31.2.a.a.1.2	✓	2
31.8	even	5		961.2.g.h.844.1		8
31.9	even	15		961.2.g.h.547.1		8
31.10	even	15		961.2.g.h.846.1		8
31.11	odd	30		961.2.c.c.439.2		4
31.12	odd	30		961.2.d.g.628.1		4
31.13	odd	30		961.2.g.d.235.1		8
31.14	even	15		961.2.d.d.531.1		4
31.15	odd	10		961.2.g.d.338.1		8
31.16	even	5	inner	961.2.g.a.338.1		8
31.17	odd	30		961.2.d.g.531.1		4
31.18	even	15	inner	961.2.g.a.235.1		8
31.19	even	15		961.2.d.d.628.1		4
31.20	even	15		961.2.c.e.439.2		4
31.21	odd	30		961.2.g.e.846.1		8
31.22	odd	30		961.2.g.e.547.1		8
31.23	odd	10		961.2.g.e.844.1		8
31.24	odd	30		961.2.a.f.1.2		2
31.25	even	3		961.2.d.c.374.1		4
31.26	odd	6		961.2.g.d.816.1		8
31.27	odd	10		961.2.c.c.521.2		4
31.28	even	15		961.2.d.c.388.1		4
31.29	odd	10		961.2.g.e.448.1		8
31.30	odd	2		961.2.g.d.732.1		8
93.38	odd	30		279.2.a.a.1.1		2
93.86	even	30		8649.2.a.c.1.1		2
124.7	odd	30		496.2.a.i.1.2		2
155.7	odd	60		775.2.b.d.249.4		4
155.38	odd	60		775.2.b.d.249.1		4
155.69	even	30		775.2.a.d.1.1		2
217.69	odd	30		1519.2.a.a.1.2		2
248.69	even	30		1984.2.a.r.1.2		2
248.131	odd	30		1984.2.a.n.1.1		2
341.131	odd	30		3751.2.a.b.1.1		2
372.131	even	30		4464.2.a.bf.1.1		2
403.38	even	30		5239.2.a.f.1.1		2
465.224	odd	30		6975.2.a.y.1.2		2
527.441	even	30		8959.2.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.a.a.1.2	✓	2	31.7	even	15
279.2.a.a.1.1		2	93.38	odd	30
496.2.a.i.1.2		2	124.7	odd	30
775.2.a.d.1.1		2	155.69	even	30
775.2.b.d.249.1		4	155.38	odd	60
775.2.b.d.249.4		4	155.7	odd	60
961.2.a.f.1.2		2	31.24	odd	30
961.2.c.c.439.2		4	31.11	odd	30
961.2.c.c.521.2		4	31.27	odd	10
961.2.c.e.439.2		4	31.20	even	15
961.2.c.e.521.2		4	31.4	even	5
961.2.d.a.374.1		4	31.6	odd	6
961.2.d.a.388.1		4	31.3	odd	30
961.2.d.c.374.1		4	31.25	even	3
961.2.d.c.388.1		4	31.28	even	15
961.2.d.d.531.1		4	31.14	even	15
961.2.d.d.628.1		4	31.19	even	15
961.2.d.g.531.1		4	31.17	odd	30
961.2.d.g.628.1		4	31.12	odd	30
961.2.g.a.235.1		8	31.18	even	15	inner
961.2.g.a.338.1		8	31.16	even	5	inner
961.2.g.a.732.1		8	1.1	even	1	trivial
961.2.g.a.816.1		8	31.5	even	3	inner
961.2.g.d.235.1		8	31.13	odd	30
961.2.g.d.338.1		8	31.15	odd	10
961.2.g.d.732.1		8	31.30	odd	2
961.2.g.d.816.1		8	31.26	odd	6
961.2.g.e.448.1		8	31.29	odd	10
961.2.g.e.547.1		8	31.22	odd	30
961.2.g.e.844.1		8	31.23	odd	10
961.2.g.e.846.1		8	31.21	odd	30
961.2.g.h.448.1		8	31.2	even	5
961.2.g.h.547.1		8	31.9	even	15
961.2.g.h.844.1		8	31.8	even	5
961.2.g.h.846.1		8	31.10	even	15
1519.2.a.a.1.2		2	217.69	odd	30
1984.2.a.n.1.1		2	248.131	odd	30
1984.2.a.r.1.2		2	248.69	even	30
3751.2.a.b.1.1		2	341.131	odd	30
4464.2.a.bf.1.1		2	372.131	even	30
5239.2.a.f.1.1		2	403.38	even	30
6975.2.a.y.1.2		2	465.224	odd	30
8649.2.a.c.1.1		2	93.86	even	30
8959.2.a.b.1.2		2	527.441	even	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.30902 - 0.951057i) q^{2} +(-2.95630 - 1.31623i) q^{3} +(0.190983 + 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.61803 + 4.53457i) q^{6} +(0.157960 - 0.175433i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(4.99983 + 5.55288i) q^{9} +O(q^{10})\)	\(q+(-1.30902 - 0.951057i) q^{2} +(-2.95630 - 1.31623i) q^{3} +(0.190983 + 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.61803 + 4.53457i) q^{6} +(0.157960 - 0.175433i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(4.99983 + 5.55288i) q^{9} +(1.47815 - 0.658114i) q^{10} +(-1.95630 - 0.415823i) q^{11} +(0.209057 - 1.98904i) q^{12} +(0.338261 + 3.21834i) q^{13} +(-0.373619 + 0.0794152i) q^{14} +(2.61803 - 1.90211i) q^{15} +(3.92705 - 2.85317i) q^{16} +(-0.747238 + 0.158830i) q^{17} +(-1.26377 - 12.0239i) q^{18} +(0.233733 - 2.22382i) q^{19} +(-0.604528 - 0.128496i) q^{20} +(-0.697887 + 0.310719i) q^{21} +(2.16535 + 2.40487i) q^{22} +(1.76393 - 5.42882i) q^{23} +(4.84187 - 5.37745i) q^{24} +(2.00000 + 3.46410i) q^{25} +(2.61803 - 4.53457i) q^{26} +(-4.47214 - 13.7638i) q^{27} +(0.133284 + 0.0593421i) q^{28} +(-2.23607 - 1.62460i) q^{29} -5.23607 q^{30} -3.38197 q^{32} +(5.23607 + 3.80423i) q^{33} +(1.12920 + 0.502754i) q^{34} +(0.0729490 + 0.224514i) q^{35} +(-2.30902 + 3.99933i) q^{36} +(1.00000 + 1.73205i) q^{37} +(-2.42094 + 2.68872i) q^{38} +(3.23607 - 9.95959i) q^{39} +(-1.49622 - 1.66172i) q^{40} +(6.39482 - 2.84716i) q^{41} +(1.20906 + 0.256993i) q^{42} +(-0.129204 + 1.22930i) q^{43} +(-0.129204 - 1.22930i) q^{44} +(-7.30885 + 1.55354i) q^{45} +(-7.47214 + 5.42882i) q^{46} +(-2.00000 + 1.45309i) q^{47} +(-15.3649 + 3.26592i) q^{48} +(0.725874 + 6.90623i) q^{49} +(0.676522 - 6.43668i) q^{50} +(2.41811 + 0.513986i) q^{51} +(-1.82709 + 0.813473i) q^{52} +(-7.00723 - 7.78231i) q^{53} +(-7.23607 + 22.2703i) q^{54} +(1.33826 - 1.48629i) q^{55} +(0.263932 + 0.457144i) q^{56} +(-3.61803 + 6.26662i) q^{57} +(1.38197 + 4.25325i) q^{58} +(2.04275 + 0.909491i) q^{59} +(1.61803 + 1.17557i) q^{60} +8.18034 q^{61} +1.76393 q^{63} +(-3.42705 - 2.48990i) q^{64} +(-2.95630 - 1.31623i) q^{65} +(-3.23607 - 9.95959i) q^{66} +(-4.00000 + 6.92820i) q^{67} +(-0.236068 - 0.408882i) q^{68} +(-12.3603 + 13.7275i) q^{69} +(0.118034 - 0.363271i) q^{70} +(-6.14285 - 6.82232i) q^{71} +(-15.2637 + 6.79584i) q^{72} +(-8.28700 - 1.76146i) q^{73} +(0.338261 - 3.21834i) q^{74} +(-1.35304 - 12.8734i) q^{75} +(1.35177 - 0.287327i) q^{76} +(-0.381966 + 0.277515i) q^{77} +(-13.7082 + 9.95959i) q^{78} +(11.4524 - 2.43427i) q^{79} +(0.507392 + 4.82751i) q^{80} +(-2.55221 + 24.2827i) q^{81} +(-11.0787 - 2.35486i) q^{82} +(-13.6523 + 6.07838i) q^{83} +(-0.315921 - 0.350865i) q^{84} +(0.236068 - 0.726543i) q^{85} +(1.33826 - 1.48629i) q^{86} +(4.47214 + 7.74597i) q^{87} +(2.23607 - 3.87298i) q^{88} +(3.61803 + 11.1352i) q^{89} +(11.0449 + 4.91752i) q^{90} +(0.618034 + 0.449028i) q^{91} +3.52786 q^{92} +4.00000 q^{94} +(1.80902 + 1.31433i) q^{95} +(9.99809 + 4.45144i) q^{96} +(-4.92705 - 15.1639i) q^{97} +(5.61803 - 9.73072i) q^{98} +(-7.47214 - 12.9421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - 4 q^{5} + 12 q^{6} - 7 q^{7} - 10 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - 4 * q^5 + 12 * q^6 - 7 * q^7 - 10 * q^8 - 7 * q^9	\( 8 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - 4 q^{5} + 12 q^{6} - 7 q^{7} - 10 q^{8} - 7 q^{9} + 3 q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 4 q^{14} + 12 q^{15} + 18 q^{16} + 8 q^{17} + 19 q^{18} - 5 q^{19} - 3 q^{20} + 2 q^{21} - 4 q^{22} + 32 q^{23} + 16 q^{25} + 12 q^{26} - 4 q^{28} - 24 q^{30} - 36 q^{32} + 24 q^{33} + 4 q^{34} + 14 q^{35} - 14 q^{36} + 8 q^{37} + 8 q^{39} + 5 q^{40} + 7 q^{41} + 6 q^{42} + 4 q^{43} + 4 q^{44} - 7 q^{45} - 24 q^{46} - 16 q^{47} - 6 q^{48} - 18 q^{49} - 12 q^{50} + 12 q^{51} - 2 q^{52} + 4 q^{53} - 40 q^{54} + 2 q^{55} + 20 q^{56} - 20 q^{57} + 20 q^{58} + 5 q^{59} + 4 q^{60} - 24 q^{61} + 32 q^{63} - 14 q^{64} - 6 q^{65} - 8 q^{66} - 32 q^{67} + 16 q^{68} - 4 q^{69} - 8 q^{70} + 27 q^{71} - 25 q^{72} - 6 q^{73} - 6 q^{74} + 24 q^{75} - 5 q^{76} - 12 q^{77} - 56 q^{78} + 10 q^{79} - 9 q^{80} + 41 q^{81} - 14 q^{82} - 26 q^{83} + 14 q^{84} - 16 q^{85} + 2 q^{86} + 20 q^{89} + 19 q^{90} - 4 q^{91} + 64 q^{92} + 32 q^{94} + 10 q^{95} + 22 q^{96} - 26 q^{97} + 36 q^{98} - 24 q^{99}+O(q^{100}) \) 8 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - 4 * q^5 + 12 * q^6 - 7 * q^7 - 10 * q^8 - 7 * q^9 + 3 * q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 4 * q^14 + 12 * q^15 + 18 * q^16 + 8 * q^17 + 19 * q^18 - 5 * q^19 - 3 * q^20 + 2 * q^21 - 4 * q^22 + 32 * q^23 + 16 * q^25 + 12 * q^26 - 4 * q^28 - 24 * q^30 - 36 * q^32 + 24 * q^33 + 4 * q^34 + 14 * q^35 - 14 * q^36 + 8 * q^37 + 8 * q^39 + 5 * q^40 + 7 * q^41 + 6 * q^42 + 4 * q^43 + 4 * q^44 - 7 * q^45 - 24 * q^46 - 16 * q^47 - 6 * q^48 - 18 * q^49 - 12 * q^50 + 12 * q^51 - 2 * q^52 + 4 * q^53 - 40 * q^54 + 2 * q^55 + 20 * q^56 - 20 * q^57 + 20 * q^58 + 5 * q^59 + 4 * q^60 - 24 * q^61 + 32 * q^63 - 14 * q^64 - 6 * q^65 - 8 * q^66 - 32 * q^67 + 16 * q^68 - 4 * q^69 - 8 * q^70 + 27 * q^71 - 25 * q^72 - 6 * q^73 - 6 * q^74 + 24 * q^75 - 5 * q^76 - 12 * q^77 - 56 * q^78 + 10 * q^79 - 9 * q^80 + 41 * q^81 - 14 * q^82 - 26 * q^83 + 14 * q^84 - 16 * q^85 + 2 * q^86 + 20 * q^89 + 19 * q^90 - 4 * q^91 + 64 * q^92 + 32 * q^94 + 10 * q^95 + 22 * q^96 - 26 * q^97 + 36 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

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