LMFDB - Embedded newform 462.2.ba.b.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(19,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 25, 9]))

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

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

chi := DirichletCharacter("462.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.ba (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	462.19
Dual form			462.2.ba.b.73.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.994522 - 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-1.01671 - 2.28357i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.151373 - 2.64142i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(0.994522 - 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-1.01671 - 2.28357i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.151373 - 2.64142i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +(-1.24984 - 2.16479i) q^{10} +(2.93738 + 1.54006i) q^{11} +(0.866025 + 0.500000i) q^{12} +(0.326961 - 0.237551i) q^{13} +(-0.426647 - 2.61112i) q^{14} +(0.772445 - 2.37734i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.545154 - 5.18679i) q^{17} +(0.207912 + 0.978148i) q^{18} +(2.32981 + 0.495217i) q^{19} +(-1.46928 - 2.02229i) q^{20} +(1.65496 - 2.06424i) q^{21} +(3.08227 + 1.22459i) q^{22} +(-3.97492 + 6.88476i) q^{23} +(0.913545 + 0.406737i) q^{24} +(-0.835356 + 0.927757i) q^{25} +(0.300339 - 0.270426i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(-0.697247 - 2.55222i) q^{28} +(-5.89340 - 1.91488i) q^{29} +(0.519714 - 2.44506i) q^{30} +(2.00546 - 4.50433i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.15240 + 3.10998i) q^{33} -5.21536i q^{34} +(-5.87797 + 3.03124i) q^{35} +(0.309017 + 0.951057i) q^{36} +(7.28120 + 8.08660i) q^{37} +(2.36881 + 0.248972i) q^{38} +(0.401932 + 0.0422447i) q^{39} +(-1.67262 - 1.85763i) q^{40} +(3.46575 + 10.6665i) q^{41} +(1.43012 - 2.22593i) q^{42} +4.16382i q^{43} +(3.19339 + 0.895692i) q^{44} +(2.16479 - 1.24984i) q^{45} +(-3.23349 + 7.26253i) q^{46} +(-1.28822 + 6.06062i) q^{47} +(0.951057 + 0.309017i) q^{48} +(-6.95417 + 0.799679i) q^{49} +(-0.733803 + 1.00999i) q^{50} +(3.87577 - 3.48976i) q^{51} +(0.270426 - 0.300339i) q^{52} +(-8.43683 - 3.75632i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.530373 - 8.27353i) q^{55} +(-0.960207 - 2.46536i) q^{56} +(1.40002 + 1.92697i) q^{57} +(-6.06127 - 1.28836i) q^{58} +(-0.550710 - 2.59089i) q^{59} +(0.261288 - 2.48599i) q^{60} +(-4.13343 + 1.84032i) q^{61} +(1.52364 - 4.68928i) q^{62} +(2.61112 - 0.426647i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-0.874891 - 0.505118i) q^{65} +(1.47117 + 2.97249i) q^{66} +(3.58993 + 6.21795i) q^{67} +(-0.545154 - 5.18679i) q^{68} +(-7.56074 + 2.45663i) q^{69} +(-5.52892 + 3.62905i) q^{70} +(-10.8080 - 7.85250i) q^{71} +(0.406737 + 0.913545i) q^{72} +(-0.806021 + 0.171325i) q^{73} +(8.08660 + 7.28120i) q^{74} +(-1.24158 + 0.130495i) q^{75} +2.38186 q^{76} +(3.62331 - 7.99197i) q^{77} +0.404146 q^{78} +(2.40566 - 0.252845i) q^{79} +(-1.85763 - 1.67262i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(4.56171 + 10.2458i) q^{82} +(9.68130 + 7.03388i) q^{83} +(1.18962 - 2.36322i) q^{84} +(-12.3987 + 4.02858i) q^{85} +(0.435238 + 4.14101i) q^{86} +(-3.09834 - 5.36649i) q^{87} +(3.26952 + 0.556985i) q^{88} +(-15.0842 - 8.70889i) q^{89} +(2.02229 - 1.46928i) q^{90} +(-0.676964 - 0.827681i) q^{91} +(-2.45663 + 7.56074i) q^{92} +(4.50433 - 2.00546i) q^{93} +(-0.647660 + 6.16207i) q^{94} +(-1.23789 - 5.82380i) q^{95} +(0.978148 + 0.207912i) q^{96} +(-2.21869 - 3.05376i) q^{97} +(-6.83249 + 1.52221i) q^{98} +(-1.22459 + 3.08227i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9	$ 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} - 10 q^{19} - 20 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 8 q^{24} - 12 q^{26} - 20 q^{29} - 18 q^{30} + 34 q^{31} + 8 q^{33} - 2 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} - 18 q^{39} + 12 q^{40} + 28 q^{41} + 4 q^{42} + 6 q^{44} - 12 q^{45} + 42 q^{46} + 24 q^{47} - 44 q^{49} + 14 q^{51} - 32 q^{54} + 14 q^{55} - 4 q^{56} - 10 q^{58} - 30 q^{59} + 2 q^{60} - 28 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{64} - 12 q^{65} - 4 q^{66} + 16 q^{67} - 30 q^{68} - 30 q^{70} - 24 q^{71} - 116 q^{73} - 44 q^{74} + 12 q^{75} - 32 q^{77} - 18 q^{80} + 8 q^{81} - 28 q^{82} - 8 q^{83} - 2 q^{84} - 80 q^{85} - 18 q^{86} - 10 q^{87} - 14 q^{88} - 24 q^{89} - 4 q^{90} + 48 q^{91} + 8 q^{92} + 76 q^{93} + 6 q^{94} + 98 q^{95} - 8 q^{96} - 120 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9 - 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 - 10 * q^19 - 20 * q^20 + 4 * q^21 - 2 * q^22 + 4 * q^23 + 8 * q^24 - 12 * q^26 - 20 * q^29 - 18 * q^30 + 34 * q^31 + 8 * q^33 - 2 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 - 18 * q^39 + 12 * q^40 + 28 * q^41 + 4 * q^42 + 6 * q^44 - 12 * q^45 + 42 * q^46 + 24 * q^47 - 44 * q^49 + 14 * q^51 - 32 * q^54 + 14 * q^55 - 4 * q^56 - 10 * q^58 - 30 * q^59 + 2 * q^60 - 28 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^64 - 12 * q^65 - 4 * q^66 + 16 * q^67 - 30 * q^68 - 30 * q^70 - 24 * q^71 - 116 * q^73 - 44 * q^74 + 12 * q^75 - 32 * q^77 - 18 * q^80 + 8 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 80 * q^85 - 18 * q^86 - 10 * q^87 - 14 * q^88 - 24 * q^89 - 4 * q^90 + 48 * q^91 + 8 * q^92 + 76 * q^93 + 6 * q^94 + 98 * q^95 - 8 * q^96 - 120 * q^97 - 40 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.994522	−	0.104528i	0.703233	−	0.0739128i
$2$	0.994522	−	0.104528i	0.703233	−	0.0739128i
$3$	0.743145	+	0.669131i	0.429055	+	0.386323i
$3$	0.743145	+	0.669131i	0.429055	+	0.386323i
$4$	0.978148	−	0.207912i	0.489074	−	0.103956i
$5$	−1.01671	−	2.28357i	−0.454688	−	1.02125i	−0.984859	−	0.173355i	$-0.944539\pi$
$5$	−1.01671	−	2.28357i	−0.454688	−	1.02125i	0.530171	−	0.847890i	$-0.322128\pi$
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	−0.151373	−	2.64142i	−0.0572136	−	0.998362i
$7$	−0.151373	−	2.64142i	−0.0572136	−	0.998362i
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	0.104528	+	0.994522i	0.0348428	+	0.331507i
$10$	−1.24984	−	2.16479i	−0.395235	−	0.684567i
$11$	2.93738	+	1.54006i	0.885654	+	0.464346i
$11$	2.93738	+	1.54006i	0.885654	+	0.464346i
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	0.326961	−	0.237551i	0.0906826	−	0.0658848i	−0.541520	−	0.840688i	$-0.682151\pi$
$13$	0.326961	−	0.237551i	0.0906826	−	0.0658848i	0.632203	+	0.774803i	$0.282151\pi$
$14$	−0.426647	−	2.61112i	−0.114026	−	0.697852i
$15$	0.772445	−	2.37734i	0.199444	−	0.613827i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	0.545154	−	5.18679i	0.132219	−	1.25798i	−0.704243	−	0.709959i	$-0.748714\pi$
$17$	0.545154	−	5.18679i	0.132219	−	1.25798i	0.836463	−	0.548024i	$-0.184620\pi$
$18$	0.207912	+	0.978148i	0.0490053	+	0.230552i
$19$	2.32981	+	0.495217i	0.534496	+	0.113611i	0.467249	−	0.884126i	$-0.345245\pi$
$19$	2.32981	+	0.495217i	0.534496	+	0.113611i	0.0672468	+	0.997736i	$0.478579\pi$
$20$	−1.46928	−	2.02229i	−0.328540	−	0.452197i
$21$	1.65496	−	2.06424i	0.361142	−	0.450455i
$22$	3.08227	+	1.22459i	0.657142	+	0.261082i
$23$	−3.97492	+	6.88476i	−0.828827	+	1.43557i	0.0701317	+	0.997538i	$0.477658\pi$
$23$	−3.97492	+	6.88476i	−0.828827	+	1.43557i	−0.898959	+	0.438033i	$0.855675\pi$
$24$	0.913545	+	0.406737i	0.186477	+	0.0830248i
$25$	−0.835356	+	0.927757i	−0.167071	+	0.185551i
$26$	0.300339	−	0.270426i	0.0589013	−	0.0530350i
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	−0.697247	−	2.55222i	−0.131767	−	0.482325i
$29$	−5.89340	−	1.91488i	−1.09438	−	0.355584i	−0.294440	−	0.955670i	$-0.595133\pi$
$29$	−5.89340	−	1.91488i	−1.09438	−	0.355584i	−0.799936	+	0.600085i	$0.795133\pi$
$30$	0.519714	−	2.44506i	0.0948863	−	0.446405i
$31$	2.00546	−	4.50433i	0.360191	−	0.809001i	−0.639017	−	0.769193i	$-0.720659\pi$
$31$	2.00546	−	4.50433i	0.360191	−	0.809001i	0.999207	−	0.0398084i	$-0.0126748\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	1.15240	+	3.10998i	0.200607	+	0.541378i
$34$		−	5.21536i		−	0.894428i
$35$	−5.87797	+	3.03124i	−0.993559	+	0.512372i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	7.28120	+	8.08660i	1.19702	+	1.32943i	0.930805	+	0.365515i	$0.119107\pi$
$37$	7.28120	+	8.08660i	1.19702	+	1.32943i	0.266217	+	0.963913i	$0.414226\pi$
$38$	2.36881	+	0.248972i	0.384272	+	0.0403887i
$39$	0.401932	+	0.0422447i	0.0643606	+	0.00676457i
$40$	−1.67262	−	1.85763i	−0.264464	−	0.293717i
$41$	3.46575	+	10.6665i	0.541259	+	1.66582i	0.729723	+	0.683743i	$0.239649\pi$
$41$	3.46575	+	10.6665i	0.541259	+	1.66582i	−0.188465	+	0.982080i	$0.560351\pi$
$42$	1.43012	−	2.22593i	0.220673	−	0.343468i
$43$			4.16382i			0.634976i	0.948262	+	0.317488i	$0.102839\pi$
$43$			4.16382i			0.634976i	−0.948262	+	0.317488i	$0.897161\pi$
$44$	3.19339	+	0.895692i	0.481422	+	0.135031i
$45$	2.16479	−	1.24984i	0.322708	−	0.186315i
$46$	−3.23349	+	7.26253i	−0.476752	+	1.07080i
$47$	−1.28822	+	6.06062i	−0.187907	+	0.884032i	0.778626	+	0.627488i	$0.215917\pi$
$47$	−1.28822	+	6.06062i	−0.187907	+	0.884032i	−0.966533	+	0.256544i	$0.917416\pi$
$48$	0.951057	+	0.309017i	0.137273	+	0.0446028i
$49$	−6.95417	+	0.799679i	−0.993453	+	0.114240i
$50$	−0.733803	+	1.00999i	−0.103775	+	0.142835i
$51$	3.87577	−	3.48976i	0.542717	−	0.488664i
$52$	0.270426	−	0.300339i	0.0375014	−	0.0416495i
$53$	−8.43683	−	3.75632i	−1.15889	−	0.515970i	−0.264994	−	0.964250i	$-0.585370\pi$
$53$	−8.43683	−	3.75632i	−1.15889	−	0.515970i	−0.893893	+	0.448280i	$0.852037\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	0.530373	−	8.27353i	0.0715155	−	1.11560i
$56$	−0.960207	−	2.46536i	−0.128313	−	0.329448i
$57$	1.40002	+	1.92697i	0.185438	+	0.255233i
$58$	−6.06127	−	1.28836i	−0.795884	−	0.169170i
$59$	−0.550710	−	2.59089i	−0.0716963	−	0.337305i	0.927650	−	0.373450i	$-0.121825\pi$
$59$	−0.550710	−	2.59089i	−0.0716963	−	0.337305i	−0.999347	+	0.0361456i	$0.988492\pi$
$60$	0.261288	−	2.48599i	0.0337322	−	0.320940i
$61$	−4.13343	+	1.84032i	−0.529232	+	0.235629i	−0.653916	−	0.756567i	$-0.726875\pi$
$61$	−4.13343	+	1.84032i	−0.529232	+	0.235629i	0.124684	+	0.992196i	$0.460208\pi$
$62$	1.52364	−	4.68928i	0.193502	−	0.595539i
$63$	2.61112	−	0.426647i	0.328971	−	0.0537525i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−0.874891	−	0.505118i	−0.108517	−	0.0626522i
$66$	1.47117	+	2.97249i	0.181088	+	0.365888i
$67$	3.58993	+	6.21795i	0.438580	+	0.759643i	0.997580	−	0.0695244i	$-0.0221482\pi$
$67$	3.58993	+	6.21795i	0.438580	+	0.759643i	−0.559000	+	0.829168i	$0.688815\pi$
$68$	−0.545154	−	5.18679i	−0.0661096	−	0.628991i
$69$	−7.56074	+	2.45663i	−0.910206	+	0.295744i
$70$	−5.52892	+	3.62905i	−0.660832	+	0.433754i
$71$	−10.8080	−	7.85250i	−1.28268	−	0.931921i	−0.283048	−	0.959106i	$-0.591346\pi$
$71$	−10.8080	−	7.85250i	−1.28268	−	0.931921i	−0.999630	+	0.0271849i	$0.991346\pi$
$72$	0.406737	+	0.913545i	0.0479344	+	0.107662i
$73$	−0.806021	+	0.171325i	−0.0943377	+	0.0200521i	−0.254839	−	0.966984i	$-0.582022\pi$
$73$	−0.806021	+	0.171325i	−0.0943377	+	0.0200521i	0.160501	+	0.987036i	$0.448689\pi$
$74$	8.08660	+	7.28120i	0.940048	+	0.846423i
$75$	−1.24158	+	0.130495i	−0.143365	+	0.0150683i
$76$	2.38186			0.273218
$77$	3.62331	−	7.99197i	0.412914	−	0.910770i
$78$	0.404146			0.0457605
$79$	2.40566	−	0.252845i	0.270657	−	0.0284472i	0.0317725	−	0.999495i	$-0.489885\pi$
$79$	2.40566	−	0.252845i	0.270657	−	0.0284472i	0.238885	+	0.971048i	$0.423218\pi$
$80$	−1.85763	−	1.67262i	−0.207689	−	0.187004i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	4.56171	+	10.2458i	0.503757	+	1.13146i
$83$	9.68130	+	7.03388i	1.06266	+	0.772069i	0.974579	−	0.224045i	$-0.0719262\pi$
$83$	9.68130	+	7.03388i	1.06266	+	0.772069i	0.0880823	+	0.996113i	$0.471926\pi$
$84$	1.18962	−	2.36322i	0.129798	−	0.257849i
$85$	−12.3987	+	4.02858i	−1.34483	+	0.436961i
$86$	0.435238	+	4.14101i	0.0469329	+	0.446537i
$87$	−3.09834	−	5.36649i	−0.332177	−	0.575348i
$88$	3.26952	+	0.556985i	0.348532	+	0.0593748i
$89$	−15.0842	−	8.70889i	−1.59893	−	0.923141i	−0.991694	−	0.128616i	$-0.958946\pi$
$89$	−15.0842	−	8.70889i	−1.59893	−	0.923141i	−0.607232	−	0.794524i	$-0.707720\pi$
$90$	2.02229	−	1.46928i	0.213168	−	0.154875i
$91$	−0.676964	−	0.827681i	−0.0709651	−	0.0867646i
$92$	−2.45663	+	7.56074i	−0.256122	+	0.788262i
$93$	4.50433	−	2.00546i	0.467077	−	0.207956i
$94$	−0.647660	+	6.16207i	−0.0668010	+	0.635569i
$95$	−1.23789	−	5.82380i	−0.127004	−	0.597509i
$96$	0.978148	+	0.207912i	0.0998318	+	0.0212199i
$97$	−2.21869	−	3.05376i	−0.225273	−	0.310062i	0.681387	−	0.731923i	$-0.261377\pi$
$97$	−2.21869	−	3.05376i	−0.225273	−	0.310062i	−0.906661	+	0.421861i	$0.861377\pi$
$98$	−6.83249	+	1.52221i	−0.690185	+	0.153766i
$99$	−1.22459	+	3.08227i	−0.123075	+	0.309780i
$100$	−0.624210	+	1.08116i	−0.0624210	+	0.108116i
$101$	0.144099	+	0.0641569i	0.0143384	+	0.00638385i	0.413893	−	0.910325i	$-0.364169\pi$
$101$	0.144099	+	0.0641569i	0.0143384	+	0.00638385i	−0.399555	+	0.916709i	$0.630835\pi$
$102$	3.48976	−	3.87577i	0.345538	−	0.383759i
$103$	8.46816	−	7.62477i	0.834393	−	0.751291i	−0.136542	−	0.990634i	$-0.543599\pi$
$103$	8.46816	−	7.62477i	0.834393	−	0.751291i	0.970935	+	0.239343i	$0.0769322\pi$
$104$	0.237551	−	0.326961i	0.0232938	−	0.0320611i
$105$	−6.39648	−	1.68048i	−0.624232	−	0.163998i
$106$	−8.78325	−	2.85385i	−0.853105	−	0.277191i
$107$	−0.995808	+	4.68491i	−0.0962684	+	0.452907i	0.903439	+	0.428717i	$0.141034\pi$
$107$	−0.995808	+	4.68491i	−0.0962684	+	0.452907i	−0.999707	+	0.0241904i	$0.992299\pi$
$108$	−0.406737	+	0.913545i	−0.0391383	+	0.0879060i
$109$	5.94655	−	3.43325i	0.569577	−	0.328845i	−0.187404	−	0.982283i	$-0.560007\pi$
$109$	5.94655	−	3.43325i	0.569577	−	0.328845i	0.756980	+	0.653438i	$0.226674\pi$
$110$	−0.337352	−	8.28365i	−0.0321653	−	0.789815i
$111$			10.8816i			1.03283i
$112$	−1.21265	−	2.35149i	−0.114584	−	0.222195i
$113$	5.86545	+	18.0520i	0.551775	+	1.69819i	0.704310	+	0.709892i	$0.251256\pi$
$113$	5.86545	+	18.0520i	0.551775	+	1.69819i	−0.152535	+	0.988298i	$0.548744\pi$
$114$	1.59378	+	1.77007i	0.149271	+	0.165782i
$115$	19.7632	+	2.07720i	1.84293	+	0.193700i
$116$	−6.16274	−	0.647730i	−0.572196	−	0.0601402i
$117$	0.270426	+	0.300339i	0.0250009	+	0.0277663i
$118$	−0.818514	−	2.51913i	−0.0753503	−	0.231904i
$119$	−13.7830	−	0.654838i	−1.26349	−	0.0600289i
$120$		−	2.49968i		−	0.228189i
$121$	6.25642	+	9.04750i	0.568765	+	0.822500i
$122$	−3.91842	+	2.26230i	−0.354757	+	0.204819i
$123$	−4.56171	+	10.2458i	−0.411316	+	0.923830i
$124$	1.02513	−	4.82286i	0.0920594	−	0.433105i
$125$	−8.91878	−	2.89789i	−0.797720	−	0.259195i
$126$	2.55222	−	0.697247i	0.227370	−	0.0621157i
$127$	3.98801	−	5.48902i	0.353878	−	0.487072i	−0.594552	−	0.804057i	$-0.702671\pi$
$127$	3.98801	−	5.48902i	0.353878	−	0.487072i	0.948430	+	0.316985i	$0.102671\pi$
$128$	0.743145	−	0.669131i	0.0656853	−	0.0591433i
$129$	−2.78614	+	3.09432i	−0.245306	+	0.272440i
$130$	−0.922897	−	0.410900i	−0.0809434	−	0.0360383i
$131$	6.60778	−	11.4450i	0.577324	−	0.999955i	−0.418461	−	0.908235i	$-0.637430\pi$
$131$	6.60778	−	11.4450i	0.577324	−	0.999955i	0.995785	−	0.0917201i	$-0.0292365\pi$
$132$	1.77382	+	2.80242i	0.154391	+	0.243920i
$133$	0.955404	−	6.22897i	0.0828440	−	0.540120i
$134$	4.22022	+	5.80864i	0.364572	+	0.501790i
$135$	2.44506	+	0.519714i	0.210437	+	0.0447298i
$136$	−1.08434	−	5.10140i	−0.0929810	−	0.437441i
$137$	−1.27663	+	12.1464i	−0.109070	+	1.03773i	0.793905	+	0.608041i	$0.208045\pi$
$137$	−1.27663	+	12.1464i	−0.109070	+	1.03773i	−0.902975	+	0.429692i	$0.858622\pi$
$138$	−7.26253	+	3.23349i	−0.618228	+	0.275253i
$139$	1.84675	−	5.68370i	0.156639	−	0.482086i	−0.841684	−	0.539970i	$-0.818436\pi$
$139$	1.84675	−	5.68370i	0.156639	−	0.482086i	0.998323	+	0.0578846i	$0.0184355\pi$
$140$	−5.11929	+	4.18709i	−0.432659	+	0.353874i
$141$	−5.01268	+	3.64193i	−0.422144	+	0.306706i
$142$	−11.5696	−	6.67974i	−0.970903	−	0.560551i
$143$	1.32625	−	0.194238i	0.110907	−	0.0162430i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	1.61912	+	15.4049i	0.134461	+	1.27931i
$146$	−0.783698	+	0.254639i	−0.0648593	+	0.0210741i
$147$	−5.70305	−	4.05897i	−0.470379	−	0.334778i
$148$	8.80339	+	6.39604i	0.723634	+	0.525751i
$149$	1.92265	+	4.31834i	0.157510	+	0.353773i	0.975012	−	0.222153i	$-0.0713085\pi$
$149$	1.92265	+	4.31834i	0.157510	+	0.353773i	−0.817502	+	0.575926i	$0.804642\pi$
$150$	−1.22114	+	0.259561i	−0.0997056	+	0.0211931i
$151$	6.16070	+	5.54712i	0.501351	+	0.451418i	0.880589	−	0.473881i	$-0.157147\pi$
$151$	6.16070	+	5.54712i	0.501351	+	0.451418i	−0.379238	+	0.925299i	$0.623814\pi$
$152$	2.36881	−	0.248972i	0.192136	−	0.0201943i
$153$	5.21536			0.421637
$154$	2.76807	−	8.32693i	0.223057	−	0.671003i
$155$	−12.3249			−0.989963
$156$	0.401932	−	0.0422447i	0.0321803	−	0.00338229i
$157$	2.60581	+	2.34628i	0.207966	+	0.187254i	0.766531	−	0.642207i	$-0.221981\pi$
$157$	2.60581	+	2.34628i	0.207966	+	0.187254i	−0.558565	+	0.829461i	$0.688648\pi$
$158$	2.36605	−	0.502919i	0.188233	−	0.0400101i
$159$	−3.75632	−	8.43683i	−0.297895	−	0.669084i
$160$	−2.02229	−	1.46928i	−0.159876	−	0.116157i
$161$	18.7872	+	9.45724i	1.48064	+	0.745335i
$162$	−0.951057	+	0.309017i	−0.0747221	+	0.0242787i
$163$	−1.24672	−	11.8618i	−0.0976510	−	0.929087i	−0.928185	−	0.372119i	$-0.878631\pi$
$163$	−1.24672	−	11.8618i	−0.0976510	−	0.929087i	0.830534	−	0.556968i	$-0.188035\pi$
$164$	5.60770	+	9.71281i	0.437887	+	0.758443i
$165$	5.93022	−	5.79354i	0.461667	−	0.451027i
$166$	10.3635	+	5.98337i	0.804364	+	0.464400i
$167$	0.860808	−	0.625414i	0.0666113	−	0.0483960i	−0.553981	−	0.832529i	$-0.686892\pi$
$167$	0.860808	−	0.625414i	0.0666113	−	0.0483960i	0.620593	+	0.784133i	$0.286892\pi$
$168$	0.936075	−	2.47462i	0.0722198	−	0.190921i
$169$	−3.96675	+	12.2084i	−0.305134	+	0.939107i
$170$	−11.9097	+	5.30253i	−0.913430	+	0.406685i
$171$	−0.248972	+	2.36881i	−0.0190394	+	0.181148i
$172$	0.865707	+	4.07283i	0.0660095	+	0.310550i
$173$	−10.8296	−	2.30190i	−0.823358	−	0.175010i	−0.223078	−	0.974800i	$-0.571611\pi$
$173$	−10.8296	−	2.30190i	−0.823358	−	0.175010i	−0.600279	+	0.799790i	$0.704944\pi$
$174$	−3.64232	−	5.01322i	−0.276124	−	0.380051i
$175$	2.57704	+	2.06609i	0.194806	+	0.156181i
$176$	3.30983	+	0.212176i	0.249488	+	0.0159934i
$177$	1.32438	−	2.29390i	0.0995468	−	0.172420i
$178$	−15.9119	−	7.08445i	−1.19265	−	0.531002i
$179$	10.9786	−	12.1930i	0.820580	−	0.911346i	−0.176759	−	0.984254i	$-0.556561\pi$
$179$	10.9786	−	12.1930i	0.820580	−	0.911346i	0.997339	+	0.0729078i	$0.0232279\pi$
$180$	1.85763	−	1.67262i	0.138459	−	0.124669i
$181$	−8.75981	+	12.0569i	−0.651112	+	0.896179i	−0.999147	−	0.0413030i	$-0.986849\pi$
$181$	−8.75981	+	12.0569i	−0.651112	+	0.896179i	0.348035	+	0.937482i	$0.386849\pi$
$182$	−0.759772	−	0.752385i	−0.0563181	−	0.0557705i
$183$	−4.30315	−	1.39818i	−0.318098	−	0.103356i
$184$	−1.65286	+	7.77611i	−0.121851	+	0.573262i
$185$	11.0635	−	24.8489i	0.813401	−	1.82693i
$186$	4.27003	−	2.46530i	0.313093	−	0.180765i
$187$	9.58931	−	14.3960i	0.701240	−	1.05274i
$188$			6.19602i			0.451891i
$189$	2.22593	+	1.43012i	0.161912	+	0.104026i
$190$	−1.83986	−	5.66250i	−0.133477	−	0.410801i
$191$	−8.43712	−	9.37037i	−0.610488	−	0.678016i	0.356071	−	0.934459i	$-0.384116\pi$
$191$	−8.43712	−	9.37037i	−0.610488	−	0.678016i	−0.966559	+	0.256443i	$0.917449\pi$
$192$	0.994522	+	0.104528i	0.0717734	+	0.00754369i
$193$	23.0457	+	2.42220i	1.65886	+	0.174353i	0.887106	−	0.461565i	$-0.152712\pi$
$193$	23.0457	+	2.42220i	1.65886	+	0.174353i	0.771756	+	0.635919i	$0.219379\pi$
$194$	−2.52574	−	2.80512i	−0.181337	−	0.201396i
$195$	−0.312180	−	0.960792i	−0.0223557	−	0.0688038i
$196$	−6.63594	+	2.22806i	−0.473996	+	0.159147i
$197$		−	6.33025i		−	0.451012i	−0.974242	−	0.225506i	$-0.927597\pi$
$197$		−	6.33025i		−	0.451012i	0.974242	−	0.225506i	$-0.0724035\pi$
$198$	−0.895692	+	3.19339i	−0.0636541	+	0.226944i
$199$	2.42631	−	1.40083i	0.171997	−	0.0993023i	−0.411530	−	0.911396i	$-0.635006\pi$
$199$	2.42631	−	1.40083i	0.171997	−	0.0993023i	0.583527	+	0.812094i	$0.301672\pi$
$200$	−0.507778	+	1.14049i	−0.0359053	+	0.0806447i
$201$	−1.49278	+	7.02297i	−0.105292	+	0.495362i
$202$	0.150016	+	0.0487431i	0.0105551	+	0.00342955i
$203$	−4.16590	+	15.8568i	−0.292389	+	1.11293i
$204$	3.06551	−	4.21932i	0.214629	−	0.295411i
$205$	20.8340	−	18.7590i	1.45511	−	1.31019i
$206$	7.62477	−	8.46816i	0.531243	−	0.590005i
$207$	−7.26253	−	3.23349i	−0.504781	−	0.224743i
$208$	0.202073	−	0.350001i	0.0140112	−	0.0242682i
$209$	6.08088	+	5.04270i	0.420624	+	0.348811i
$210$	−6.53709	−	1.00266i	−0.451102	−	0.0691904i
$211$	−3.16107	−	4.35084i	−0.217617	−	0.299524i	0.686226	−	0.727389i	$-0.259266\pi$
$211$	−3.16107	−	4.35084i	−0.217617	−	0.299524i	−0.903843	+	0.427864i	$0.859266\pi$
$212$	−9.03345	−	1.92012i	−0.620420	−	0.131874i
$213$	−2.77759	−	13.0675i	−0.190317	−	0.895373i
$214$	−0.500646	+	4.76333i	−0.0342235	+	0.325615i
$215$	9.50839	−	4.23341i	0.648467	−	0.288716i
$216$	−0.309017	+	0.951057i	−0.0210259	+	0.0647112i
$217$	−12.2014	−	4.61541i	−0.828284	−	0.313315i
$218$	5.55511	−	4.03602i	0.376239	−	0.273354i
$219$	−0.713629	−	0.412014i	−0.0482226	−	0.0278413i
$220$	−1.20138	−	8.20301i	−0.0809971	−	0.553047i
$221$	−1.05388	−	1.82538i	−0.0708919	−	0.122788i
$222$	1.13744	+	10.8220i	0.0763397	+	0.726324i
$223$	−19.3959	+	6.30212i	−1.29885	+	0.422021i	−0.875180	−	0.483797i	$-0.839257\pi$
$223$	−19.3959	+	6.30212i	−1.29885	+	0.422021i	−0.423667	+	0.905818i	$0.639257\pi$
$224$	−1.45180	−	2.21185i	−0.0970026	−	0.147785i
$225$	−1.00999	−	0.733803i	−0.0673329	−	0.0489202i
$226$	7.72027	+	17.3400i	0.513545	+	1.15344i
$227$	7.49849	−	1.59385i	0.497692	−	0.105788i	0.0477753	−	0.998858i	$-0.484787\pi$
$227$	7.49849	−	1.59385i	0.497692	−	0.105788i	0.449917	+	0.893070i	$0.351454\pi$
$228$	1.77007	+	1.59378i	0.117226	+	0.105550i
$229$	−10.4479	+	1.09812i	−0.690416	+	0.0725657i	−0.443238	−	0.896404i	$-0.646170\pi$
$229$	−10.4479	+	1.09812i	−0.690416	+	0.0725657i	−0.247179	+	0.968970i	$0.579504\pi$
$230$	19.8721			1.31033
$231$	8.04032	−	3.51473i	0.529014	−	0.231252i
$232$	−6.19669			−0.406832
$233$	−8.59897	+	0.903788i	−0.563337	+	0.0592091i	−0.381917	−	0.924197i	$-0.624736\pi$
$233$	−8.59897	+	0.903788i	−0.563337	+	0.0592091i	−0.181420	+	0.983406i	$0.558069\pi$
$234$	0.300339	+	0.270426i	0.0196338	+	0.0176783i
$235$	15.1496	−	3.22015i	0.988253	−	0.210060i
$236$	−1.07735	−	2.41977i	−0.0701296	−	0.157514i
$237$	1.95694	+	1.42180i	0.127117	+	0.0923557i
$238$	−13.7760	+	0.789466i	−0.892963	+	0.0511735i
$239$	25.3207	−	8.22721i	1.63786	−	0.532174i	0.661803	−	0.749678i	$-0.269791\pi$
$239$	25.3207	−	8.22721i	1.63786	−	0.532174i	0.976059	+	0.217504i	$0.0697914\pi$
$240$	−0.261288	−	2.48599i	−0.0168661	−	0.160470i
$241$	−10.1742	−	17.6223i	−0.655381	−	1.13515i	−0.981798	−	0.189927i	$-0.939175\pi$
$241$	−10.1742	−	17.6223i	−0.655381	−	1.13515i	0.326418	−	0.945226i	$-0.394158\pi$
$242$	7.16787	+	8.34396i	0.460768	+	0.536370i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−3.66048	+	2.65950i	−0.234338	+	0.170257i
$245$	8.89652	+	15.0673i	0.568378	+	0.962616i
$246$	−3.46575	+	10.6665i	−0.220968	+	0.680069i
$247$	0.879397	−	0.391533i	0.0559547	−	0.0249126i
$248$	0.515388	−	4.90359i	0.0327272	−	0.311378i
$249$	2.48803	+	11.7052i	0.157672	+	0.741790i
$250$	−9.17284	−	1.94975i	−0.580141	−	0.123313i
$251$	−9.36586	−	12.8910i	−0.591168	−	0.813673i	0.403696	−	0.914893i	$-0.367725\pi$
$251$	−9.36586	−	12.8910i	−0.591168	−	0.813673i	−0.994864	+	0.101220i	$0.967725\pi$
$252$	2.46536	−	0.960207i	0.155303	−	0.0604874i
$253$	−22.2788	+	14.1015i	−1.40066	+	0.886556i
$254$	3.39240	−	5.87581i	0.212858	−	0.368681i
$255$	−11.9097	−	5.30253i	−0.745813	−	0.332057i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	−12.0884	+	10.8845i	−0.754054	+	0.678954i	−0.953648	−	0.300925i	$-0.902705\pi$
$257$	−12.0884	+	10.8845i	−0.754054	+	0.678954i	0.199593	+	0.979879i	$0.436038\pi$
$258$	−2.44743	+	3.36860i	−0.152370	+	0.209720i
$259$	20.2579	−	20.4568i	1.25876	−	1.27112i
$260$	−0.960792	−	0.312180i	−0.0595858	−	0.0193606i
$261$	1.28836	−	6.06127i	0.0797477	−	0.375183i
$262$	5.37525	−	12.0730i	0.332084	−	0.745873i
$263$	1.65209	−	0.953835i	0.101872	−	0.0588160i	−0.448198	−	0.893934i	$-0.647934\pi$
$263$	1.65209	−	0.953835i	0.101872	−	0.0588160i	0.550071	+	0.835118i	$0.314601\pi$
$264$	2.05703	+	2.60166i	0.126602	+	0.160121i
$265$			23.0852i			1.41811i
$266$	0.299065	−	6.29472i	0.0183369	−	0.385954i
$267$	−5.38239	−	16.5653i	−0.329397	−	1.01378i
$268$	4.80427	+	5.33568i	0.293467	+	0.325929i
$269$	17.0789	+	1.79506i	1.04132	+	0.109447i	0.609718	−	0.792618i	$-0.291283\pi$
$269$	17.0789	+	1.79506i	1.04132	+	0.109447i	0.431599	+	0.902065i	$0.357949\pi$
$270$	2.48599	+	0.261288i	0.151293	+	0.0159015i
$271$	−3.30933	−	3.67538i	−0.201027	−	0.223263i	0.634199	−	0.773170i	$-0.281330\pi$
$271$	−3.30933	−	3.67538i	−0.201027	−	0.223263i	−0.835226	+	0.549907i	$0.814663\pi$
$272$	−1.61164	−	4.96011i	−0.0977198	−	0.300751i
$273$	0.0507443	−	1.06806i	0.00307119	−	0.0646422i
$274$			12.2133i			0.737830i
$275$	−3.88256	+	1.43868i	−0.234127	+	0.0867554i
$276$	−6.88476	+	3.97492i	−0.414414	+	0.239262i
$277$	8.58663	−	19.2859i	0.515921	−	1.15878i	−0.448350	−	0.893858i	$-0.647988\pi$
$277$	8.58663	−	19.2859i	0.515921	−	1.15878i	0.964271	−	0.264919i	$-0.0853451\pi$
$278$	1.24252	−	5.84561i	0.0745215	−	0.350596i
$279$	4.68928	+	1.52364i	0.280740	+	0.0912179i
$280$	−4.65358	+	4.69927i	−0.278105	+	0.280835i
$281$	4.24090	−	5.83709i	0.252991	−	0.348212i	−0.663565	−	0.748118i	$-0.730957\pi$
$281$	4.24090	−	5.83709i	0.252991	−	0.348212i	0.916556	+	0.399907i	$0.130957\pi$
$282$	−4.60454	+	4.14594i	−0.274196	+	0.246887i
$283$	−5.81161	+	6.45444i	−0.345464	+	0.383677i	−0.890689	−	0.454613i	$-0.849778\pi$
$283$	−5.81161	+	6.45444i	−0.345464	+	0.383677i	0.545225	+	0.838290i	$0.316444\pi$
$284$	−12.2045	−	5.43379i	−0.724203	−	0.322436i
$285$	2.97695	−	5.15623i	0.176339	−	0.305429i
$286$	1.29868	−	0.331805i	0.0767927	−	0.0196200i
$287$	27.6500	−	10.7691i	1.63213	−	0.635680i
$288$	0.587785	+	0.809017i	0.0346356	+	0.0476718i
$289$	−9.97713	−	2.12070i	−0.586890	−	0.124747i
$290$	3.22050	+	15.1513i	0.189114	+	0.889713i
$291$	0.394559	−	3.75398i	0.0231295	−	0.220062i
$292$	−0.752787	+	0.335163i	−0.0440535	+	0.0196139i
$293$	−1.55582	+	4.78832i	−0.0908920	+	0.279737i	−0.986161	−	0.165789i	$-0.946983\pi$
$293$	−1.55582	+	4.78832i	−0.0908920	+	0.279737i	0.895269	+	0.445525i	$0.146983\pi$
$294$	−6.09608	−	3.44061i	−0.355531	−	0.200660i
$295$	−5.35657	+	3.89177i	−0.311871	+	0.226588i
$296$	9.42373	+	5.44079i	0.547743	+	0.316240i
$297$	−2.97249	+	1.47117i	−0.172481	+	0.0853657i
$298$	2.36351	+	4.09372i	0.136914	+	0.237143i
$299$	0.335839	+	3.19529i	0.0194220	+	0.184788i
$300$	−1.18732	+	0.385783i	−0.0685498	+	0.0222732i
$301$	10.9984	−	0.630290i	0.633936	−	0.0363293i
$302$	6.70678	+	4.87276i	0.385932	+	0.280396i
$303$	0.0641569	+	0.144099i	0.00368572	+	0.00827826i
$304$	2.32981	−	0.495217i	0.133624	−	0.0284026i
$305$	8.40503	+	7.56792i	0.481270	+	0.433338i
$306$	5.18679	−	0.545154i	0.296509	−	0.0311644i
$307$	1.24415			0.0710072			0.0355036	−	0.999370i	$-0.488696\pi$
$307$	1.24415			0.0710072			0.0355036	+	0.999370i	$0.488696\pi$
$308$	1.88250	−	8.57066i	0.107266	−	0.488359i
$309$	11.3950			0.648241
$310$	−12.2574	+	1.28831i	−0.696175	+	0.0731709i
$311$	10.1346	+	9.12522i	0.574680	+	0.517444i	0.904429	−	0.426625i	$-0.140297\pi$
$311$	10.1346	+	9.12522i	0.574680	+	0.517444i	−0.329749	+	0.944069i	$0.606964\pi$
$312$	0.395314	−	0.0840266i	0.0223803	−	0.00475707i
$313$	10.7208	+	24.0792i	0.605974	+	1.36104i	0.912461	+	0.409165i	$0.134180\pi$
$313$	10.7208	+	24.0792i	0.605974	+	1.36104i	−0.306487	+	0.951875i	$0.599154\pi$
$314$	2.83679	+	2.06105i	0.160089	+	0.116312i
$315$	−3.62905	−	5.52892i	−0.204474	−	0.311519i
$316$	2.30052	−	0.747483i	0.129414	−	0.0420492i
$317$	0.0838766	+	0.798032i	0.00471098	+	0.0448220i	0.996625	−	0.0820909i	$-0.0261598\pi$
$317$	0.0838766	+	0.798032i	0.00471098	+	0.0448220i	−0.991914	+	0.126913i	$0.959493\pi$
$318$	−4.61763	−	7.99797i	−0.258944	−	0.448504i
$319$	−14.3621	−	14.7009i	−0.804124	−	0.823094i
$320$	−2.16479	−	1.24984i	−0.121015	−	0.0698683i
$321$	−3.87484	+	2.81524i	−0.216273	+	0.157131i
$322$	19.6728	+	7.44164i	1.09632	+	0.414706i
$323$	3.83870	−	11.8143i	0.213591	−	0.657365i
$324$	−0.913545	+	0.406737i	−0.0507525	+	0.0225965i
$325$	−0.0527392	+	0.501780i	−0.00292544	+	0.0278337i
$326$	−2.47979	−	11.6665i	−0.137343	−	0.646147i
$327$	6.71644	+	1.42762i	0.371420	+	0.0789478i
$328$	6.59224	+	9.07344i	0.363996	+	0.500997i
$329$	16.2036	+	2.48532i	0.893335	+	0.137020i
$330$	5.29214	−	6.38168i	0.291323	−	0.351300i
$331$	1.79784	−	3.11395i	0.0988183	−	0.171158i	−0.812377	−	0.583132i	$-0.801827\pi$
$331$	1.79784	−	3.11395i	0.0988183	−	0.171158i	0.911196	+	0.411974i	$0.135160\pi$
$332$	10.9322	+	4.86732i	0.599981	+	0.267129i
$333$	−7.28120	+	8.08660i	−0.399008	+	0.443143i
$334$	0.790719	−	0.711967i	0.0432662	−	0.0389571i
$335$	10.5492	−	14.5198i	0.576365	−	0.793299i
$336$	0.672279	−	2.55891i	0.0366758	−	0.139600i
$337$	−24.6049	−	7.99461i	−1.34031	−	0.435494i	−0.450891	−	0.892579i	$-0.648894\pi$
$337$	−24.6049	−	7.99461i	−1.34031	−	0.435494i	−0.889423	+	0.457085i	$0.848894\pi$
$338$	−2.66889	+	12.5562i	−0.145169	+	0.682965i
$339$	−7.72027	+	17.3400i	−0.419308	+	0.941780i
$340$	−11.2902	+	6.51838i	−0.612295	+	0.353509i
$341$	12.8277	−	10.1424i	0.694661	−	0.549242i
$342$			2.38186i			0.128796i
$343$	3.16496	+	18.2478i	0.170892	+	0.985290i
$344$	1.28669	+	3.96003i	0.0693737	+	0.213510i
$345$	13.2970	+	14.7678i	0.715887	+	0.795073i
$346$	−11.0109	−	1.15729i	−0.591948	−	0.0622162i
$347$	−6.03579	−	0.634387i	−0.324018	−	0.0340557i	−0.0588769	−	0.998265i	$-0.518752\pi$
$347$	−6.03579	−	0.634387i	−0.324018	−	0.0340557i	−0.265141	+	0.964210i	$0.585419\pi$
$348$	−4.14639	−	4.60503i	−0.222270	−	0.246856i
$349$	−9.92353	−	30.5415i	−0.531194	−	1.63485i	−0.751732	−	0.659469i	$-0.770781\pi$
$349$	−9.92353	−	30.5415i	−0.531194	−	1.63485i	0.220537	−	0.975379i	$-0.429219\pi$
$350$	2.77889	+	1.78539i	0.148538	+	0.0954333i
$351$			0.404146i			0.0215717i
$352$	3.31388	−	0.134958i	0.176630	−	0.00719328i
$353$	6.05445	−	3.49554i	0.322246	−	0.186049i	−0.330147	−	0.943929i	$-0.607098\pi$
$353$	6.05445	−	3.49554i	0.322246	−	0.186049i	0.652393	+	0.757881i	$0.273765\pi$
$354$	1.07735	−	2.41977i	0.0572605	−	0.128609i
$355$	−6.94310	+	32.6647i	−0.368502	+	1.73366i
$356$	−16.5653	−	5.38239i	−0.877959	−	0.285266i
$357$	−9.80460	−	9.70927i	−0.518914	−	0.513869i
$358$	9.64396	−	13.2738i	0.509699	−	0.701540i
$359$	−7.07838	+	6.37340i	−0.373582	+	0.336375i	−0.834440	−	0.551099i	$-0.814209\pi$
$359$	−7.07838	+	6.37340i	−0.373582	+	0.336375i	0.460857	+	0.887474i	$0.347542\pi$
$360$	1.67262	−	1.85763i	0.0881546	−	0.0979055i
$361$	−12.1746	−	5.42047i	−0.640767	−	0.285288i
$362$	−7.45154	+	12.9065i	−0.391644	+	0.678348i
$363$	−1.40453	+	10.9100i	−0.0737189	+	0.572625i
$364$	−0.834256	−	0.668846i	−0.0437269	−	0.0350570i
$365$	1.21073	+	1.66642i	0.0633723	+	0.0872245i
$366$	−4.42573	−	0.940718i	−0.231337	−	0.0491721i
$367$	−2.60335	−	12.2478i	−0.135894	−	0.639331i	−0.992386	−	0.123170i	$-0.960694\pi$
$367$	−2.60335	−	12.2478i	−0.135894	−	0.639331i	0.856492	−	0.516161i	$-0.172639\pi$
$368$	−0.830984	+	7.90628i	−0.0433180	+	0.412143i
$369$	−10.2458	+	4.56171i	−0.533373	+	0.237473i
$370$	8.40543	−	25.8692i	0.436977	−	1.34488i
$371$	−8.64490	+	22.8538i	−0.448821	+	1.18651i
$372$	3.98894	−	2.89813i	0.206817	−	0.150261i
$373$	7.69037	+	4.44004i	0.398192	+	0.229896i	0.685704	−	0.727881i	$-0.259495\pi$
$373$	7.69037	+	4.44004i	0.398192	+	0.229896i	−0.287511	+	0.957777i	$0.592828\pi$
$374$	8.03198	−	15.3195i	0.415324	−	0.792153i
$375$	−4.68888	−	8.12138i	−0.242133	−	0.419386i
$376$	0.647660	+	6.16207i	0.0334005	+	0.317785i
$377$	−2.38179	+	0.773891i	−0.122669	+	0.0398574i
$378$	2.36322	+	1.18962i	0.121551	+	0.0611872i
$379$	−23.2213	−	16.8713i	−1.19280	−	0.866620i	−0.199243	−	0.979950i	$-0.563848\pi$
$379$	−23.2213	−	16.8713i	−1.19280	−	0.866620i	−0.993557	+	0.113330i	$0.963848\pi$
$380$	−2.42167	−	5.43916i	−0.124229	−	0.279023i
$381$	6.63654	−	1.41064i	0.340000	−	0.0722692i
$382$	−9.37037	−	8.43712i	−0.479430	−	0.431680i
$383$	−9.43196	+	0.991339i	−0.481951	+	0.0506551i	−0.342389	−	0.939558i	$-0.611236\pi$
$383$	−9.43196	+	0.991339i	−0.481951	+	0.0506551i	−0.139562	+	0.990213i	$0.544569\pi$
$384$	1.00000			0.0510310
$385$	−21.9341	−	0.148546i	−1.11787	−	0.00757062i
$386$	23.1726			1.17945
$387$	−4.14101	+	0.435238i	−0.210499	+	0.0221244i
$388$	−2.80512	−	2.52574i	−0.142408	−	0.128225i
$389$	23.4482	−	4.98407i	1.18887	−	0.252702i	0.429321	−	0.903152i	$-0.358753\pi$
$389$	23.4482	−	4.98407i	1.18887	−	0.252702i	0.759549	+	0.650450i	$0.225419\pi$
$390$	−0.410900	−	0.922897i	−0.0208067	−	0.0467327i
$391$	33.5429	+	24.3703i	1.69634	+	1.23246i
$392$	−6.36670	+	2.90950i	−0.321567	+	0.146952i
$393$	12.5687	−	4.08383i	0.634009	−	0.206002i
$394$	−0.661691	−	6.29557i	−0.0333355	−	0.317166i
$395$	−3.02325	−	5.23643i	−0.152116	−	0.263473i
$396$	−0.556985	+	3.26952i	−0.0279896	+	0.164300i
$397$	−27.1020	−	15.6473i	−1.36021	−	0.785318i	−0.370559	−	0.928809i	$-0.620834\pi$
$397$	−27.1020	−	15.6473i	−1.36021	−	0.785318i	−0.989652	+	0.143491i	$0.954167\pi$
$398$	2.26659	−	1.64678i	0.113614	−	0.0825454i
$399$	4.87800	−	3.98974i	0.244205	−	0.199737i
$400$	−0.385783	+	1.18732i	−0.0192891	+	0.0593659i
$401$	−17.2585	+	7.68398i	−0.861848	+	0.383720i	−0.789567	−	0.613665i	$-0.789695\pi$
$401$	−17.2585	+	7.68398i	−0.861848	+	0.383720i	−0.0722815	+	0.997384i	$0.523028\pi$
$402$	−0.750501	+	7.14054i	−0.0374316	+	0.356138i
$403$	−0.414302	−	1.94914i	−0.0206378	−	0.0970934i
$404$	0.154289	+	0.0327951i	0.00767616	+	0.00163162i
$405$	1.46928	+	2.02229i	0.0730090	+	0.100488i
$406$	−2.48559	+	16.2054i	−0.123358	+	0.804259i
$407$	8.93381	+	34.9669i	0.442833	+	1.73325i
$408$	2.60768	−	4.51664i	0.129100	−	0.223607i
$409$	−13.1800	−	5.86813i	−0.651710	−	0.290160i	0.0541270	−	0.998534i	$-0.482762\pi$
$409$	−13.1800	−	5.86813i	−0.651710	−	0.290160i	−0.705837	+	0.708374i	$0.749429\pi$
$410$	18.7590	−	20.8340i	0.926442	−	1.02892i
$411$	−9.07623	+	8.17227i	−0.447697	+	0.403108i
$412$	6.69784	−	9.21878i	0.329979	−	0.454177i
$413$	−6.76025	+	1.84684i	−0.332650	+	0.0908773i
$414$	−7.56074	−	2.45663i	−0.371590	−	0.120737i
$415$	6.21928	−	29.2594i	0.305293	−	1.43629i
$416$	0.164381	−	0.369206i	0.00805944	−	0.0181018i
$417$	5.17554	−	2.98810i	0.253447	−	0.146328i
$418$	6.57468	+	4.37945i	0.321578	+	0.214206i
$419$		−	10.3459i		−	0.505431i	−0.967541	−	0.252715i	$-0.918676\pi$
$419$		−	10.3459i		−	0.505431i	0.967541	−	0.252715i	$-0.0813236\pi$
$420$	−6.60609	−	0.313859i	−0.322344	−	0.0153148i
$421$	−3.02867	−	9.32128i	−0.147608	−	0.454291i	0.849729	−	0.527220i	$-0.176766\pi$
$421$	−3.02867	−	9.32128i	−0.147608	−	0.454291i	−0.997337	+	0.0729285i	$0.976766\pi$
$422$	−3.59854	−	3.99659i	−0.175174	−	0.194551i
$423$	−6.16207	−	0.647660i	−0.299610	−	0.0314903i
$424$	−9.18467	−	0.965348i	−0.446047	−	0.0468814i
$425$	4.35669	+	4.83859i	0.211330	+	0.234706i
$426$	−4.12831	−	12.7056i	−0.200017	−	0.615589i
$427$	5.48675	+	10.6395i	0.265522	+	0.514884i
$428$			4.78957i			0.231513i
$429$	1.11557	+	0.743089i	0.0538601	+	0.0358767i
$430$	9.01379	−	5.20412i	0.434684	−	0.250965i
$431$	−1.28505	+	2.88626i	−0.0618986	+	0.139026i	−0.941846	−	0.336044i	$-0.890911\pi$
$431$	−1.28505	+	2.88626i	−0.0618986	+	0.139026i	0.879948	+	0.475071i	$0.157578\pi$
$432$	−0.207912	+	0.978148i	−0.0100032	+	0.0470611i
$433$	−28.6664	−	9.31429i	−1.37762	−	0.447616i	−0.475734	−	0.879589i	$-0.657818\pi$
$433$	−28.6664	−	9.31429i	−1.37762	−	0.447616i	−0.901887	+	0.431973i	$0.857818\pi$
$434$	−12.6170	−	3.31474i	−0.605635	−	0.159112i
$435$	−9.10465	+	12.5315i	−0.436535	+	0.600838i
$436$	5.10280	−	4.59458i	0.244380	−	0.220040i
$437$	−12.6703	+	14.0717i	−0.606101	+	0.673143i
$438$	−0.752787	−	0.335163i	−0.0359696	−	0.0160147i
$439$	−15.4965	+	26.8408i	−0.739608	+	1.28104i	0.213063	+	0.977038i	$0.431656\pi$
$439$	−15.4965	+	26.8408i	−0.739608	+	1.28104i	−0.952672	+	0.304001i	$0.901677\pi$
$440$	−2.05225	−	8.03249i	−0.0978370	−	0.382934i
$441$	−1.52221	−	6.83249i	−0.0724861	−	0.325357i
$442$	−1.23891	−	1.70522i	−0.0589292	−	0.0811090i
$443$	−5.26428	−	1.11896i	−0.250113	−	0.0531632i	0.0811488	−	0.996702i	$-0.474141\pi$
$443$	−5.26428	−	1.11896i	−0.250113	−	0.0531632i	−0.331262	+	0.943539i	$0.607474\pi$
$444$	2.26241	+	10.6438i	0.107369	+	0.505132i
$445$	−4.55106	+	43.3004i	−0.215741	+	2.05264i
$446$	−18.6309	+	8.29502i	−0.882200	+	0.392781i
$447$	−1.46073	+	4.49566i	−0.0690901	+	0.212637i
$448$	−1.67505	−	2.04798i	−0.0791387	−	0.0967578i
$449$	−19.6411	+	14.2701i	−0.926921	+	0.673448i	−0.945237	−	0.326385i	$-0.894170\pi$
$449$	−19.6411	+	14.2701i	−0.926921	+	0.673448i	0.0183160	+	0.999832i	$0.494170\pi$
$450$	−1.08116	−	0.624210i	−0.0509665	−	0.0294255i
$451$	−6.24681	+	36.6690i	−0.294151	+	1.72667i
$452$	9.49050	+	16.4380i	0.446396	+	0.773180i
$453$	0.866545	+	8.24463i	0.0407138	+	0.387366i
$454$	7.29081	−	2.36893i	0.342175	−	0.111179i
$455$	−1.20179	+	2.38741i	−0.0563410	+	0.111924i
$456$	1.92697	+	1.40002i	0.0902385	+	0.0655621i
$457$	−3.76167	−	8.44884i	−0.175963	−	0.395220i	0.803935	−	0.594717i	$-0.202736\pi$
$457$	−3.76167	−	8.44884i	−0.175963	−	0.395220i	−0.979898	+	0.199497i	$0.936069\pi$
$458$	−10.2759	+	2.18421i	−0.480160	+	0.102061i
$459$	3.87577	+	3.48976i	0.180906	+	0.162888i
$460$	19.7632	−	2.07720i	0.921464	−	0.0968498i
$461$	23.5309			1.09594			0.547971	−	0.836497i	$-0.315400\pi$
$461$	23.5309			1.09594			0.547971	+	0.836497i	$0.315400\pi$
$462$	7.62888	−	4.33592i	0.354928	−	0.201725i
$463$	−0.114096			−0.00530247			−0.00265123	−	0.999996i	$-0.500844\pi$
$463$	−0.114096			−0.00530247			−0.00265123	+	0.999996i	$0.500844\pi$
$464$	−6.16274	+	0.647730i	−0.286098	+	0.0300701i
$465$	−9.15922	−	8.24700i	−0.424749	−	0.382445i
$466$	−8.45739	+	1.79767i	−0.391781	+	0.0832756i
$467$	−13.7397	−	30.8598i	−0.635797	−	1.42802i	−0.887769	−	0.460289i	$-0.847746\pi$
$467$	−13.7397	−	30.8598i	−0.635797	−	1.42802i	0.251972	−	0.967734i	$-0.418921\pi$
$468$	0.326961	+	0.237551i	0.0151138	+	0.0109808i
$469$	15.8808	−	10.4237i	0.733306	−	0.481324i
$470$	14.7300	−	4.78608i	0.679446	−	0.220765i
$471$	0.366526	+	3.48726i	0.0168886	+	0.160684i
$472$	−1.32438	−	2.29390i	−0.0609597	−	0.105585i
$473$	−6.41254	+	12.2307i	−0.294849	+	0.562369i
$474$	2.09483	+	1.20945i	0.0962190	+	0.0555520i
$475$	−2.40566	+	1.74782i	−0.110379	+	0.0801954i
$476$	−13.6180	+	2.22512i	−0.624178	+	0.101988i
$477$	2.85385	−	8.78325i	0.130669	−	0.402158i
$478$	24.3221	−	10.8289i	1.11246	−	0.495301i
$479$	−3.61430	+	34.3878i	−0.165142	+	1.57122i	0.527258	+	0.849705i	$0.323220\pi$
$479$	−3.61430	+	34.3878i	−0.165142	+	1.57122i	−0.692400	+	0.721514i	$0.743447\pi$
$480$	−0.519714	−	2.44506i	−0.0237216	−	0.111601i
$481$	4.30165	+	0.914343i	0.196138	+	0.0416905i
$482$	−11.9605	−	16.4623i	−0.544788	−	0.749836i
$483$	7.63349	+	19.5992i	0.347336	+	0.891794i
$484$	8.00078	+	7.54901i	0.363672	+	0.343137i
$485$	−4.71772	+	8.17133i	−0.214221	+	0.371041i
$486$	−0.913545	−	0.406737i	−0.0414393	−	0.0184499i
$487$	−0.0515687	+	0.0572728i	−0.00233680	+	0.00259528i	−0.744312	−	0.667832i	$-0.767222\pi$
$487$	−0.0515687	+	0.0572728i	−0.00233680	+	0.00259528i	0.741975	+	0.670427i	$0.233889\pi$
$488$	−3.36244	+	3.02755i	−0.152210	+	0.137051i
$489$	7.01059	−	9.64925i	0.317030	−	0.436354i
$490$	10.4228	+	14.0548i	0.470852	+	0.634933i
$491$	13.0661	+	4.24543i	0.589664	+	0.191593i	0.588625	−	0.808406i	$-0.299669\pi$
$491$	13.0661	+	4.24543i	0.589664	+	0.191593i	0.00103880	+	0.999999i	$0.499669\pi$
$492$	−2.33181	+	10.9703i	−0.105126	+	0.494580i
$493$	−13.1449	+	29.5239i	−0.592017	+	1.32969i
$494$	0.833653	−	0.481310i	0.0375078	−	0.0216552i
$495$	8.28365	−	0.337352i	0.372322	−	0.0151628i
$496$		−	4.93060i		−	0.221391i
$497$	−19.1057	+	29.7372i	−0.857007	+	1.33390i
$498$	3.69793	+	11.3811i	0.165708	+	0.509997i
$499$	9.45784	+	10.5040i	0.423391	+	0.470223i	0.916668	−	0.399649i	$-0.130868\pi$
$499$	9.45784	+	10.5040i	0.423391	+	0.470223i	−0.493277	+	0.869872i	$0.664201\pi$
$500$	−9.32639	−	0.980243i	−0.417089	−	0.0438378i
$501$	1.05819	+	0.111220i	0.0472764	+	0.00496895i
$502$	−10.6620	−	11.8414i	−0.475870	−	0.528507i
$503$	9.78260	+	30.1077i	0.436185	+	1.34244i	0.891868	+	0.452296i	$0.149395\pi$
$503$	9.78260	+	30.1077i	0.436185	+	1.34244i	−0.455683	+	0.890142i	$0.650605\pi$
$504$	2.35149	−	1.21265i	0.104744	−	0.0540156i
$505$		−	0.394290i		−	0.0175457i
$506$	−20.6827	+	16.3531i	−0.919460	+	0.726982i
$507$	−11.1169	+	6.41833i	−0.493718	+	0.285048i
$508$	2.75963	−	6.19822i	0.122439	−	0.275002i
$509$	1.77773	−	8.36358i	0.0787966	−	0.370709i	−0.921027	−	0.389499i	$-0.872648\pi$
$509$	1.77773	−	8.36358i	0.0787966	−	0.370709i	0.999823	+	0.0187901i	$0.00598144\pi$
$510$	−12.3987	−	4.02858i	−0.549024	−	0.178389i
$511$	0.574551	+	2.10310i	0.0254166	+	0.0930359i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	−1.77007	+	1.59378i	−0.0781504	+	0.0703670i
$514$	−10.8845	+	12.0884i	−0.480093	+	0.533197i
$515$	−26.0214	−	11.5855i	−1.14664	−	0.510517i
$516$	−2.08191	+	3.60597i	−0.0916510	+	0.158744i
$517$	−13.1177	+	15.8184i	−0.576917	+	0.695693i
$518$	18.0086	−	22.4623i	0.791253	−	0.986935i
$519$	−6.50768	−	8.95705i	−0.285655	−	0.393171i
$520$	−0.988161	−	0.210040i	−0.0433337	−	0.00921087i
$521$	2.05291	+	9.65818i	0.0899396	+	0.423133i	0.999963	+	0.00857618i	$0.00272992\pi$
$521$	2.05291	+	9.65818i	0.0899396	+	0.423133i	−0.910024	+	0.414556i	$0.863937\pi$
$522$	0.647730	−	6.16274i	0.0283504	−	0.269736i
$523$	17.5337	−	7.80650i	0.766694	−	0.341354i	0.0141534	−	0.999900i	$-0.495495\pi$
$523$	17.5337	−	7.80650i	0.766694	−	0.341354i	0.752541	+	0.658546i	$0.228828\pi$
$524$	4.08383	−	12.5687i	0.178403	−	0.549068i
$525$	0.532635	+	3.25978i	0.0232461	+	0.142268i
$526$	1.54334	−	1.12130i	0.0672927	−	0.0488910i
$527$	−22.2697	−	12.8574i	−0.970085	−	0.560079i
$528$	2.31771	+	2.37239i	0.100865	+	0.103245i
$529$	−20.0999	−	34.8141i	−0.873909	−	1.51365i
$530$	2.41306	+	22.9588i	0.104817	+	0.997265i
$531$	2.51913	−	0.818514i	0.109321	−	0.0355205i
$532$	−0.360550	−	6.29149i	−0.0156318	−	0.272771i
$533$	3.66699	+	2.66423i	0.158835	+	0.115400i
$534$	−7.08445	−	15.9119i	−0.306574	−	0.688577i
$535$	11.7108	−	2.48920i	0.506301	−	0.107618i
$536$	5.33568	+	4.80427i	0.230466	+	0.207513i
$537$	16.3174	−	1.71503i	0.704148	−	0.0740089i
$538$	17.1730			0.740378
$539$	−21.6586	−	8.36089i	−0.932902	−	0.360129i
$540$	2.49968			0.107569
$541$	−30.9840	+	3.25655i	−1.33211	+	0.140010i	−0.743678	−	0.668538i	$-0.766920\pi$
$541$	−30.9840	+	3.25655i	−1.33211	+	0.140010i	−0.588430	+	0.808548i	$0.700254\pi$
$542$	−3.67538	−	3.30933i	−0.157871	−	0.142148i
$543$	−14.5774	+	3.09853i	−0.625577	+	0.132970i
$544$	−2.12128	−	4.76447i	−0.0909491	−	0.204275i
$545$	−13.8860	−	10.0888i	−0.594811	−	0.432156i
$546$	−0.0611768	−	1.06752i	−0.00261812	−	0.0456855i
$547$	27.7101	−	9.00355i	1.18480	−	0.384964i	0.350650	−	0.936506i	$-0.385961\pi$
$547$	27.7101	−	9.00355i	1.18480	−	0.384964i	0.834147	+	0.551543i	$0.185961\pi$
$548$	1.27663	+	12.1464i	0.0545351	+	0.518867i
$549$	−2.26230	−	3.91842i	−0.0965527	−	0.167234i
$550$	−3.71091	+	1.83663i	−0.158234	+	0.0783143i
$551$	−12.7822	−	7.37983i	−0.544541	−	0.314391i
$552$	−6.43155	+	4.67279i	−0.273745	+	0.198887i
$553$	−1.03202	−	6.31607i	−0.0438859	−	0.268587i
$554$	6.52367	−	20.0778i	0.277164	−	0.853023i
$555$	24.8489	−	11.0635i	1.05478	−	0.469617i
$556$	0.624683	−	5.94346i	0.0264925	−	0.252059i
$557$	−7.04142	−	33.1273i	−0.298355	−	1.40365i	−0.830511	−	0.557002i	$-0.811952\pi$
$557$	−7.04142	−	33.1273i	−0.298355	−	1.40365i	0.532157	−	0.846646i	$-0.321382\pi$
$558$	4.82286	+	1.02513i	0.204168	+	0.0433972i
$559$	0.989119	+	1.36141i	0.0418353	+	0.0575813i
$560$	−4.13688	+	5.15996i	−0.174815	+	0.218048i
$561$	16.7591	−	4.28183i	0.707568	−	0.180779i
$562$	3.60752	−	6.24841i	0.152174	−	0.263573i
$563$	12.7695	+	5.68533i	0.538169	+	0.239608i	0.657777	−	0.753213i	$-0.271497\pi$
$563$	12.7695	+	5.68533i	0.538169	+	0.239608i	−0.119608	+	0.992821i	$0.538164\pi$
$564$	−4.14594	+	4.60454i	−0.174576	+	0.193886i
$565$	35.2596	−	31.7479i	1.48338	−	1.33564i
$566$	−5.10510	+	7.02656i	−0.214583	+	0.295349i
$567$	0.697247	+	2.55222i	0.0292816	+	0.107183i
$568$	−12.7056	−	4.12831i	−0.533116	−	0.173220i
$569$	9.07699	−	42.7039i	0.380527	−	1.79024i	−0.204114	−	0.978947i	$-0.565431\pi$
$569$	9.07699	−	42.7039i	0.380527	−	1.79024i	0.584641	−	0.811292i	$-0.301235\pi$
$570$	2.42167	−	5.43916i	0.101433	−	0.227821i
$571$	−35.5608	+	20.5310i	−1.48817	+	0.859197i	−0.999909	−	0.0134996i	$-0.995703\pi$
$571$	−35.5608	+	20.5310i	−1.48817	+	0.859197i	−0.488263	+	0.872696i	$0.662369\pi$
$572$	1.25689	−	0.465736i	0.0525530	−	0.0194734i
$573$		−	12.6091i		−	0.526752i
$574$	26.3728	−	13.6003i	1.10078	−	0.567666i
$575$	−3.06691	−	9.43898i	−0.127899	−	0.393633i
$576$	0.669131	+	0.743145i	0.0278804	+	0.0309644i
$577$	−5.88539	−	0.618579i	−0.245012	−	0.0257518i	−0.0187736	−	0.999824i	$-0.505976\pi$
$577$	−5.88539	−	0.618579i	−0.245012	−	0.0257518i	−0.226238	+	0.974072i	$0.572643\pi$
$578$	−10.1441	−	1.06619i	−0.421941	−	0.0443478i
$579$	15.5055	+	17.2206i	0.644386	+	0.715664i
$580$	4.78660	+	14.7316i	0.198753	+	0.611698i
$581$	17.1139	−	26.6371i	0.710005	−	1.10509i
$582$		−	3.77466i		−	0.156464i
$583$	−18.9972	−	24.0270i	−0.786785	−	0.995096i
$584$	−0.713629	+	0.412014i	−0.0295302	+	0.0170493i
$585$	0.410900	−	0.922897i	0.0169886	−	0.0381571i
$586$	−1.04678	+	4.92472i	−0.0432421	+	0.203438i
$587$	−14.3622	−	4.66656i	−0.592791	−	0.192609i	−0.00276822	−	0.999996i	$-0.500881\pi$
$587$	−14.3622	−	4.66656i	−0.592791	−	0.192609i	−0.590023	+	0.807387i	$0.700881\pi$
$588$	−6.42233	−	2.78454i	−0.264852	−	0.114833i
$589$	6.90296	−	9.50111i	0.284431	−	0.391486i
$590$	−4.92042	+	4.43037i	−0.202571	+	0.182395i
$591$	4.23576	−	4.70429i	0.174236	−	0.193509i
$592$	9.94083	+	4.42594i	0.408565	+	0.181905i
$593$	16.7997	−	29.0978i	0.689879	−	1.19491i	−0.281998	−	0.959415i	$-0.590997\pi$
$593$	16.7997	−	29.0978i	0.689879	−	1.19491i	0.971877	−	0.235490i	$-0.0756696\pi$
$594$	−2.80242	+	1.77382i	−0.114985	+	0.0727805i
$595$	12.5180	+	32.1403i	0.513188	+	1.31762i
$596$	2.77847	+	3.82424i	0.113811	+	0.156647i
$597$	2.74044	+	0.582499i	0.112159	+	0.0238401i
$598$	0.667998	+	3.14268i	0.0273165	+	0.128514i
$599$	0.175152	−	1.66646i	0.00715652	−	0.0680897i	−0.990361	−	0.138512i	$-0.955768\pi$
$599$	0.175152	−	1.66646i	0.00715652	−	0.0680897i	0.997517	+	0.0704223i	$0.0224347\pi$
$600$	−1.14049	+	0.507778i	−0.0465602	+	0.0207300i
$601$	−14.5417	+	44.7547i	−0.593167	+	1.82558i	−0.0295213	+	0.999564i	$0.509398\pi$
$601$	−14.5417	+	44.7547i	−0.593167	+	1.82558i	−0.563646	+	0.826017i	$0.690602\pi$
$602$	10.8723	−	1.77648i	0.443120	−	0.0724040i
$603$	−5.80864	+	4.22022i	−0.236546	+	0.171861i
$604$	7.17939	+	4.14502i	0.292125	+	0.168658i
$605$	14.2997	−	23.4857i	0.581364	−	0.954830i
$606$	0.0788679	+	0.136603i	0.00320379	+	0.00554913i
$607$	1.42039	+	13.5141i	0.0576517	+	0.548519i	0.984784	+	0.173784i	$0.0555995\pi$
$607$	1.42039	+	13.5141i	0.0576517	+	0.548519i	−0.927132	+	0.374735i	$0.877734\pi$
$608$	2.26529	−	0.736036i	0.0918695	−	0.0298502i
$609$	−13.7061	+	8.99636i	−0.555400	+	0.364551i
$610$	9.15005	+	6.64790i	0.370475	+	0.269166i
$611$	1.01851	+	2.28760i	0.0412044	+	0.0925465i
$612$	5.10140	−	1.08434i	0.206212	−	0.0438317i
$613$	18.2139	+	16.3999i	0.735653	+	0.662385i	0.949245	−	0.314538i	$-0.101850\pi$
$613$	18.2139	+	16.3999i	0.735653	+	0.662385i	−0.213592	+	0.976923i	$0.568516\pi$
$614$	1.23733	−	0.130049i	0.0499346	−	0.00524834i
$615$	28.0349			1.13048
$616$	0.976313	−	8.72048i	0.0393368	−	0.351358i
$617$	−18.7831			−0.756179			−0.378089	−	0.925769i	$-0.623419\pi$
$617$	−18.7831			−0.756179			−0.378089	+	0.925769i	$0.623419\pi$
$618$	11.3326	−	1.19111i	0.455865	−	0.0479133i
$619$	15.6321	+	14.0752i	0.628308	+	0.565731i	0.920556	−	0.390611i	$-0.127736\pi$
$619$	15.6321	+	14.0752i	0.628308	+	0.565731i	−0.292247	+	0.956343i	$0.594403\pi$
$620$	−12.0556	+	2.56250i	−0.484165	+	0.102912i
$621$	−3.23349	−	7.26253i	−0.129755	−	0.291435i
$622$	11.0329	+	8.01588i	0.442379	+	0.321408i
$623$	−20.7205	+	41.1621i	−0.830148	+	1.64912i
$624$	0.384366	−	0.124888i	0.0153869	−	0.00499952i
$625$	3.10278	+	29.5209i	0.124111	+	1.18084i
$626$	13.1790	+	22.8267i	0.526739	+	0.912339i
$627$	1.14475	+	7.81636i	0.0457171	+	0.312155i
$628$	3.03669	+	1.75323i	0.121177	+	0.0699616i
$629$	45.9129	−	33.3577i	1.83067	−	1.33006i
$630$	−4.18709	−	5.11929i	−0.166818	−	0.203958i
$631$	6.85754	−	21.1053i	0.272994	−	0.840190i	−0.716749	−	0.697331i	$-0.754371\pi$
$631$	6.85754	−	21.1053i	0.272994	−	0.840190i	0.989743	−	0.142859i	$-0.0456294\pi$
$632$	2.20978	−	0.983858i	0.0879004	−	0.0391358i
$633$	0.562148	−	5.34848i	0.0223434	−	0.212583i
$634$	0.166834	+	0.784893i	0.00662583	+	0.0311721i
$635$	−16.5892	−	3.52615i	−0.658324	−	0.139931i
$636$	−5.42835	−	7.47148i	−0.215248	−	0.296264i
$637$	−2.08378	+	1.91343i	−0.0825623	+	0.0758130i
$638$	−15.8201	−	13.1191i	−0.626324	−	0.519392i
$639$	6.67974	−	11.5696i	0.264246	−	0.457688i
$640$	−2.28357	−	1.01671i	−0.0902662	−	0.0401891i
$641$	10.0767	−	11.1913i	0.398007	−	0.442032i	−0.510515	−	0.859869i	$-0.670545\pi$
$641$	10.0767	−	11.1913i	0.398007	−	0.442032i	0.908522	+	0.417837i	$0.137212\pi$
$642$	−3.55934	+	3.20485i	−0.140476	+	0.126485i
$643$	−15.9636	+	21.9720i	−0.629542	+	0.866491i	−0.998004	−	0.0631523i	$-0.979885\pi$
$643$	−15.9636	+	21.9720i	−0.629542	+	0.866491i	0.368462	+	0.929643i	$0.379885\pi$
$644$	20.3429	+	5.34450i	0.801624	+	0.210603i
$645$	9.89882	+	3.21632i	0.389766	+	0.126643i
$646$	2.58274	−	12.1508i	0.101616	−	0.478068i
$647$	−7.70777	+	17.3119i	−0.303024	+	0.680602i	−0.999309	−	0.0371625i	$-0.988168\pi$
$647$	−7.70777	+	17.3119i	−0.303024	+	0.680602i	0.696286	+	0.717765i	$0.254835\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	2.37248	−	8.45855i	0.0931280	−	0.332027i
$650$			0.504544i			0.0197898i
$651$	−5.97908	−	11.5942i	−0.234339	−	0.454414i
$652$	−3.68569	−	11.3434i	−0.144343	−	0.444241i
$653$	17.5809	+	19.5256i	0.687994	+	0.764095i	0.981417	−	0.191888i	$-0.0614609\pi$
$653$	17.5809	+	19.5256i	0.687994	+	0.764095i	−0.293423	+	0.955983i	$0.594794\pi$
$654$	6.82887	+	0.717744i	0.267030	+	0.0280660i
$655$	−32.8538	−	3.45307i	−1.28370	−	0.134923i
$656$	7.50456	+	8.33466i	0.293004	+	0.325414i
$657$	−0.254639	−	0.783698i	−0.00993440	−	0.0305750i
$658$	16.3746	+	0.777969i	0.638350	+	0.0303284i
$659$		−	49.3232i		−	1.92136i	−0.277661	−	0.960679i	$-0.589559\pi$
$659$		−	49.3232i		−	1.92136i	0.277661	−	0.960679i	$-0.410441\pi$
$660$	4.59608	−	6.89990i	0.178902	−	0.268578i
$661$	−9.54110	+	5.50856i	−0.371106	+	0.214258i	−0.673941	−	0.738785i	$-0.735400\pi$
$661$	−9.54110	+	5.50856i	−0.371106	+	0.214258i	0.302836	+	0.953043i	$0.402067\pi$
$662$	1.46250	−	3.28482i	0.0568415	−	0.127668i
$663$	0.438230	−	2.06171i	0.0170194	−	0.0800701i
$664$	11.3811	+	3.69793i	0.441671	+	0.143507i
$665$	−15.1957	+	4.15134i	−0.589264	+	0.160982i
$666$	−6.39604	+	8.80339i	−0.247841	+	0.341124i
$667$	36.6092	−	32.9631i	1.41752	−	1.27634i
$668$	0.711967	−	0.790719i	0.0275468	−	0.0305938i
$669$	−18.6309	−	8.29502i	−0.720313	−	0.320704i
$670$	8.97370	−	15.5429i	0.346684	−	0.600475i
$671$	−14.9757	−	0.960012i	−0.578130	−	0.0370609i
$672$	0.401116	−	2.61517i	0.0154734	−	0.100882i
$673$	15.7824	+	21.7226i	0.608366	+	0.837344i	0.996442	−	0.0842835i	$-0.0268601\pi$
$673$	15.7824	+	21.7226i	0.608366	+	0.837344i	−0.388076	+	0.921627i	$0.626860\pi$
$674$	−25.3058	−	5.37891i	−0.974742	−	0.207188i
$675$	−0.259561	−	1.22114i	−0.00999051	−	0.0470017i
$676$	−1.34180	+	12.7663i	−0.0516076	+	0.491013i
$677$	−10.0601	+	4.47903i	−0.386640	+	0.172143i	−0.590845	−	0.806785i	$-0.701206\pi$
$677$	−10.0601	+	4.47903i	−0.386640	+	0.172143i	0.204205	+	0.978928i	$0.434539\pi$
$678$	−5.86545	+	18.0520i	−0.225261	+	0.693283i
$679$	−7.73041	+	6.32273i	−0.296666	+	0.242644i
$680$	−10.5470	+	7.66282i	−0.404458	+	0.293856i
$681$	6.63896	+	3.83301i	0.254406	+	0.146881i
$682$	11.6973	−	11.4277i	0.447912	−	0.437589i
$683$	6.96482	+	12.0634i	0.266501	+	0.461594i	0.967956	−	0.251120i	$-0.0807990\pi$
$683$	6.96482	+	12.0634i	0.266501	+	0.461594i	−0.701454	+	0.712714i	$0.747466\pi$
$684$	0.248972	+	2.36881i	0.00951970	+	0.0905739i
$685$	29.0351	−	9.43407i	1.10937	−	0.360457i
$686$	5.05504	+	17.8170i	0.193002	+	0.680257i
$687$	−8.49909	−	6.17495i	−0.324260	−	0.235589i
$688$	1.69358	+	3.80384i	0.0645671	+	0.145020i
$689$	−3.65083	+	0.776008i	−0.139086	+	0.0295635i
$690$	14.7678	+	13.2970i	0.562201	+	0.506208i
$691$	29.6232	−	3.11353i	1.12692	−	0.118444i	0.477327	−	0.878726i	$-0.341606\pi$
$691$	29.6232	−	3.11353i	1.12692	−	0.118444i	0.649593	+	0.760282i	$0.274939\pi$
$692$	−11.0715			−0.420876
$693$	8.32693	+	2.76807i	0.316314	+	0.105150i
$694$	−6.06904			−0.230378
$695$	−14.8568	+	1.56151i	−0.563550	+	0.0592315i
$696$	−4.60503	−	4.14639i	−0.174553	−	0.157169i
$697$	57.2141	−	12.1612i	2.16714	−	0.460640i
$698$	−13.0616	−	29.3369i	−0.494390	−	1.11042i
$699$	−6.99503	−	5.08219i	−0.264576	−	0.192226i
$700$	2.95029	+	1.48514i	0.111511	+	0.0561330i
$701$	−11.9661	+	3.88804i	−0.451955	+	0.146849i	−0.526145	−	0.850395i	$-0.676363\pi$
$701$	−11.9661	+	3.88804i	−0.451955	+	0.146849i	0.0741896	+	0.997244i	$0.476363\pi$
$702$	0.0422447	+	0.401932i	0.00159442	+	0.0151699i
$703$	12.9592	+	22.4460i	0.488766	+	0.846568i
$704$	3.28162	−	0.480613i	0.123681	−	0.0181138i
$705$	13.4131	+	7.74404i	0.505166	+	0.291657i
$706$	5.65590	−	4.10925i	0.212863	−	0.154654i
$707$	0.147653	−	0.390337i	0.00555305	−	0.0146801i
$708$	0.818514	−	2.51913i	0.0307616	−	0.0946746i
$709$	13.9048	−	6.19080i	0.522205	−	0.232501i	−0.128668	−	0.991688i	$-0.541070\pi$
$709$	13.9048	−	6.19080i	0.522205	−	0.232501i	0.650872	+	0.759187i	$0.274403\pi$
$710$	−3.49067	+	33.2115i	−0.131003	+	1.24641i
$711$	0.502919	+	2.36605i	0.0188609	+	0.0887337i
$712$	−17.0372	−	3.62136i	−0.638495	−	0.135716i
$713$	23.0397	+	31.7114i	0.862843	+	1.18760i
$714$	−10.7658	−	8.63123i	−0.402899	−	0.323015i
$715$	−1.79197	−	2.83111i	−0.0670160	−	0.105878i
$716$	8.20364	−	14.2091i	0.306584	−	0.531020i
$717$	24.3221	+	10.8289i	0.908324	+	0.404412i
$718$	−6.37340	+	7.07838i	−0.237853	+	0.264163i
$719$	30.8445	−	27.7725i	1.15031	−	1.03574i	0.151423	−	0.988469i	$-0.451614\pi$
$719$	30.8445	−	27.7725i	1.15031	−	1.03574i	0.998882	−	0.0472708i	$-0.0150524\pi$
$720$	1.46928	−	2.02229i	0.0547567	−	0.0753662i
$721$	−21.4221	−	21.2138i	−0.797799	−	0.790042i
$722$	−12.6745	−	4.11819i	−0.471695	−	0.153263i
$723$	4.23069	−	19.9038i	0.157341	−	0.740231i
$724$	−6.06163	+	13.6146i	−0.225279	+	0.505984i
$725$	6.69963	−	3.86803i	0.248818	−	0.143655i
$726$	−0.256437	+	10.9970i	−0.00951728	+	0.408137i
$727$		−	21.3877i		−	0.793225i	−0.917986	−	0.396613i	$-0.870186\pi$
$727$		−	21.3877i		−	0.793225i	0.917986	−	0.396613i	$-0.129814\pi$
$728$	−0.899599	−	0.577978i	−0.0333414	−	0.0214213i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	1.37828	+	1.53074i	0.0510125	+	0.0566551i
$731$	21.5969	+	2.26992i	0.798789	+	0.0839561i
$732$	−4.49982	−	0.472950i	−0.166318	−	0.0174807i
$733$	11.1899	+	12.4276i	0.413308	+	0.459025i	0.913469	−	0.406907i	$-0.133393\pi$
$733$	11.1899	+	12.4276i	0.413308	+	0.459025i	−0.500162	+	0.865932i	$0.666726\pi$
$734$	−3.86934	−	11.9086i	−0.142820	−	0.439554i
$735$	−3.47061	+	17.1501i	−0.128015	+	0.632593i
$736$			7.94983i			0.293035i
$737$	0.968980	+	23.7932i	0.0356928	+	0.876434i
$738$	−9.71281	+	5.60770i	−0.357534	+	0.206422i
$739$	17.4184	−	39.1224i	0.640747	−	1.43914i	−0.242461	−	0.970161i	$-0.577955\pi$
$739$	17.4184	−	39.1224i	0.640747	−	1.43914i	0.883208	−	0.468981i	$-0.155379\pi$
$740$	5.65531	−	26.6061i	0.207893	−	0.978061i
$741$	0.915506	+	0.297466i	0.0336319	+	0.0109277i
$742$	−6.20867	+	23.6322i	−0.227927	+	0.867567i
$743$	−1.22734	+	1.68929i	−0.0450267	+	0.0619739i	−0.830937	−	0.556367i	$-0.812195\pi$
$743$	−1.22734	+	1.68929i	−0.0450267	+	0.0619739i	0.785910	+	0.618341i	$0.212195\pi$
$744$	3.66415	−	3.29922i	0.134334	−	0.120955i
$745$	7.90648	−	8.78103i	0.289671	−	0.321712i
$746$	8.11235	+	3.61185i	0.297014	+	0.132239i
$747$	−5.98337	+	10.3635i	−0.218920	+	0.379181i
$748$	6.38666	−	16.0752i	0.233519	−	0.587766i
$749$	12.5255	+	1.92118i	0.457673	+	0.0701982i
$750$	−5.51211	−	7.58677i	−0.201274	−	0.277030i
$751$	−44.7002	−	9.50133i	−1.63114	−	0.346708i	−0.700783	−	0.713375i	$-0.747166\pi$
$751$	−44.7002	−	9.50133i	−1.63114	−	0.346708i	−0.930352	+	0.366666i	$0.880499\pi$
$752$	1.28822	+	6.06062i	0.0469767	+	0.221008i
$753$	1.66557	−	15.8469i	0.0606968	−	0.577492i
$754$	−2.28785	+	1.01862i	−0.0833186	+	0.0370958i
$755$	6.40360	−	19.7082i	0.233051	−	0.717257i
$756$	2.47462	+	0.936075i	0.0900012	+	0.0340447i
$757$	41.2123	−	29.9425i	1.49789	−	1.08828i	0.526675	−	0.850067i	$-0.323439\pi$
$757$	41.2123	−	29.9425i	1.49789	−	1.08828i	0.971213	−	0.238213i	$-0.0765615\pi$
$758$	−24.8577	−	14.3516i	−0.902871	−	0.521273i
$759$	−25.9921	−	4.42794i	−0.943455	−	0.160724i
$760$	−2.97695	−	5.15623i	−0.107985	−	0.187036i
$761$	−0.257928	−	2.45402i	−0.00934989	−	0.0889582i	0.988852	−	0.148903i	$-0.0475742\pi$
$761$	−0.257928	−	2.45402i	−0.00934989	−	0.0889582i	−0.998202	+	0.0599448i	$0.980908\pi$
$762$	6.45273	−	2.09662i	0.233758	−	0.0759525i
$763$	−9.96878	−	15.1876i	−0.360894	−	0.549829i
$764$	−10.2010	−	7.41143i	−0.369058	−	0.268136i
$765$	−5.30253	−	11.9097i	−0.191713	−	0.430595i
$766$	−9.27667	+	1.97182i	−0.335180	+	0.0712446i
$767$	−0.795528	−	0.716296i	−0.0287248	−	0.0258640i
$768$	0.994522	−	0.104528i	0.0358867	−	0.00377185i
$769$	−13.9787			−0.504086			−0.252043	−	0.967716i	$-0.581103\pi$
$769$	−13.9787			−0.504086			−0.252043	+	0.967716i	$0.581103\pi$
$770$	−21.8295	+	2.14501i	−0.786681	+	0.0773008i
$771$	−16.2666			−0.585826
$772$	23.0457	−	2.42220i	0.829431	−	0.0871767i
$773$	−15.5224	−	13.9764i	−0.558302	−	0.502698i	0.340978	−	0.940071i	$-0.389242\pi$
$773$	−15.5224	−	13.9764i	−0.558302	−	0.502698i	−0.899280	+	0.437374i	$0.855909\pi$
$774$	−4.07283	+	0.865707i	−0.146395	+	0.0311172i
$775$	2.50365	+	5.62329i	0.0899338	+	0.201995i
$776$	−3.05376	−	2.21869i	−0.109624	−	0.0796462i
$777$	28.7428	−	1.64718i	1.03114	−	0.0590922i
$778$	22.7988	−	7.40777i	0.817375	−	0.265581i
$779$	2.79232	+	26.5672i	0.100045	+	0.951868i
$780$	−0.505118	−	0.874891i	−0.0180861	−	0.0313261i
$781$	−19.6540	−	39.7109i	−0.703276	−	1.42097i
$782$	35.9065	+	20.7306i	1.28401	+	0.741326i
$783$	5.01322	−	3.64232i	0.179158	−	0.130166i
$784$	−6.02769	+	3.55906i	−0.215275	+	0.127109i
$785$	2.70855	−	8.33607i	0.0966724	−	0.297527i
$786$	12.0730	−	5.37525i	0.430630	−	0.191729i
$787$	2.11777	−	20.1492i	0.0754903	−	0.718242i	−0.889674	−	0.456597i	$-0.849068\pi$
$787$	2.11777	−	20.1492i	0.0754903	−	0.718242i	0.965164	−	0.261645i	$-0.0842651\pi$
$788$	−1.31613	−	6.19192i	−0.0468853	−	0.220578i
$789$	1.86598	+	0.396627i	0.0664308	+	0.0141203i
$790$	−3.55405	−	4.89172i	−0.126447	−	0.174040i
$791$	46.7950	−	18.2257i	1.66384	−	0.648031i
$792$	−0.212176	+	3.30983i	−0.00753934	+	0.117610i
$793$	−0.914300	+	1.58361i	−0.0324677	+	0.0562358i
$794$	−28.5891	−	12.7287i	−1.01459	−	0.451725i
$795$	−15.4470	+	17.1557i	−0.547850	+	0.608449i
$796$	2.08204	−	1.87468i	0.0737960	−	0.0664462i
$797$	−27.4068	+	37.7222i	−0.970799	+	1.33619i	−0.0291571	+	0.999575i	$0.509282\pi$
$797$	−27.4068	+	37.7222i	−0.970799	+	1.33619i	−0.941642	+	0.336616i	$0.890718\pi$
$798$	4.43424	−	4.47777i	0.156970	−	0.158511i
$799$	30.7329	+	9.98572i	1.08725	+	0.353270i
$800$	−0.259561	+	1.22114i	−0.00917687	+	0.0431738i
$801$	7.08445	−	15.9119i	0.250317	−	0.562221i
$802$	−16.3608	+	9.44589i	−0.577718	+	0.333546i
$803$	−2.63144	−	0.738076i	−0.0928616	−	0.0260461i
$804$			7.17987i			0.253214i
$805$	2.49513	−	52.5173i	0.0879416	−	1.85099i
$806$	−0.615773	−	1.89515i	−0.0216897	−	0.0667539i
$807$	11.4909	+	12.7620i	0.404500	+	0.449243i
$808$	0.156872	+	0.0164879i	0.00551873	+	0.000580042i
$809$	−52.7580	−	5.54509i	−1.85487	−	0.194955i	−0.889696	−	0.456553i	$-0.849084\pi$
$809$	−52.7580	−	5.54509i	−1.85487	−	0.194955i	−0.965177	+	0.261598i	$0.915751\pi$
$810$	1.67262	+	1.85763i	0.0587697	+	0.0652704i
$811$	−6.97728	−	21.4739i	−0.245006	−	0.754049i	−0.995636	−	0.0933267i	$-0.970250\pi$
$811$	−6.97728	−	21.4739i	−0.245006	−	0.754049i	0.750630	−	0.660723i	$-0.229750\pi$
$812$	−0.778053	+	16.3764i	−0.0273043	+	0.574700i
$813$		−	4.94571i		−	0.173454i
$814$	12.5399	+	33.8415i	0.439524	+	1.18615i
$815$	−25.8197	+	14.9070i	−0.904426	+	0.522170i
$816$	2.12128	−	4.76447i	0.0742596	−	0.166790i
$817$	−2.06199	+	9.70092i	−0.0721401	+	0.339392i
$818$	−13.7212	−	4.45829i	−0.479751	−	0.155881i
$819$	0.752385	−	0.759772i	0.0262905	−	0.0265486i
$820$	16.4785	−	22.6807i	0.575455	−	0.792046i
$821$	4.95817	−	4.46435i	0.173041	−	0.155807i	−0.578060	−	0.815995i	$-0.696190\pi$
$821$	4.95817	−	4.46435i	0.173041	−	0.155807i	0.751101	+	0.660188i	$0.229523\pi$
$822$	−8.17227	+	9.07623i	−0.285041	+	0.316570i
$823$	−10.9640	−	4.88147i	−0.382179	−	0.170157i	0.206649	−	0.978415i	$-0.433744\pi$
$823$	−10.9640	−	4.88147i	−0.382179	−	0.170157i	−0.588829	+	0.808258i	$0.700411\pi$
$824$	5.69752	−	9.86839i	0.198483	−	0.343782i
$825$	−3.84797	−	1.52880i	−0.133969	−	0.0532259i
$826$	−6.53017	+	2.54337i	−0.227214	+	0.0884950i
$827$	4.75205	+	6.54064i	0.165245	+	0.227440i	0.883607	−	0.468229i	$-0.155108\pi$
$827$	4.75205	+	6.54064i	0.165245	+	0.227440i	−0.718362	+	0.695669i	$0.755108\pi$
$828$	−7.77611	−	1.65286i	−0.270238	−	0.0574410i
$829$	−1.15297	−	5.42428i	−0.0400442	−	0.188393i	0.953579	−	0.301142i	$-0.0973678\pi$
$829$	−1.15297	−	5.42428i	−0.0400442	−	0.188393i	−0.993624	+	0.112749i	$0.964034\pi$
$830$	3.12677	−	29.7492i	0.108532	−	1.03261i
$831$	19.2859	−	8.58663i	0.669020	−	0.297867i
$832$	0.124888	−	0.384366i	0.00432971	−	0.0133255i
$833$	0.356675	+	36.5058i	0.0123581	+	1.26485i
$834$	4.83485	−	3.51272i	0.167417	−	0.121636i
$835$	−2.30337	−	1.32985i	−0.0797115	−	0.0460215i
$836$	6.99644	+	3.66822i	0.241977	+	0.126868i
$837$	2.46530	+	4.27003i	0.0852132	+	0.147594i
$838$	−1.08144	−	10.2892i	−0.0373578	−	0.355436i
$839$	−21.8267	+	7.09194i	−0.753543	+	0.244841i	−0.660505	−	0.750822i	$-0.729658\pi$
$839$	−21.8267	+	7.09194i	−0.753543	+	0.244841i	−0.0930379	+	0.995663i	$0.529658\pi$
$840$	−6.60271	+	0.378385i	−0.227815	+	0.0130555i
$841$	7.60387	+	5.52454i	0.262203	+	0.190501i
$842$	−3.98641	−	8.95363i	−0.137381	−	0.308562i
$843$	7.05738	−	1.50009i	0.243069	−	0.0516659i
$844$	−3.99659	−	3.59854i	−0.137568	−	0.123867i
$845$	31.9118	−	3.35407i	1.09780	−	0.115383i
$846$	−6.19602			−0.213023
$847$	22.9512	−	17.8954i	0.788611	−	0.614892i
$848$	−9.23526			−0.317140
$849$	−8.63773	+	0.907862i	−0.296446	+	0.0311578i
$850$	4.83859	+	4.35669i	0.165962	+	0.149433i
$851$	−84.6164	+	17.9858i	−2.90061	+	0.616544i
$852$	−5.43379	−	12.2045i	−0.186159	−	0.418119i
$853$	−7.43473	−	5.40165i	−0.254560	−	0.184949i	0.453185	−	0.891416i	$-0.350288\pi$
$853$	−7.43473	−	5.40165i	−0.254560	−	0.184949i	−0.707745	+	0.706468i	$0.750288\pi$
$854$	6.56883	+	10.0077i	0.224781	+	0.342458i
$855$	5.66250	−	1.83986i	0.193653	−	0.0629218i
$856$	0.500646	+	4.76333i	0.0171117	+	0.162807i
$857$	0.806075	+	1.39616i	0.0275350	+	0.0476920i	0.879465	−	0.475964i	$-0.157901\pi$
$857$	0.806075	+	1.39616i	0.0275350	+	0.0476920i	−0.851930	+	0.523656i	$0.824568\pi$
$858$	1.18713	+	0.622410i	0.0405280	+	0.0212487i
$859$	28.9037	+	16.6876i	0.986182	+	0.569373i	0.904131	−	0.427256i	$-0.140520\pi$
$859$	28.9037	+	16.6876i	0.986182	+	0.569373i	0.0820513	+	0.996628i	$0.473853\pi$
$860$	8.42044	−	6.11781i	0.287135	−	0.208615i
$861$	27.7539	+	10.4984i	0.945849	+	0.357786i
$862$	−0.976311	+	3.00478i	−0.0332533	+	0.102343i
$863$	48.8973	−	21.7705i	1.66448	−	0.741076i	0.664503	−	0.747286i	$-0.268643\pi$
$863$	48.8973	−	21.7705i	1.66448	−	0.741076i	0.999981	+	0.00620995i	$0.00197670\pi$
$864$	−0.104528	+	0.994522i	−0.00355613	+	0.0338343i
$865$	5.75402	+	27.0705i	0.195643	+	0.920426i
$866$	−29.4830	−	6.26681i	−1.00187	−	0.212955i
$867$	−5.99542	−	8.25199i	−0.203615	−	0.280252i
$868$	−12.8944	−	1.97774i	−0.437663	−	0.0671290i
$869$	7.45573	+	2.96216i	0.252918	+	0.100484i
$870$	−7.74488	+	13.4145i	−0.262576	+	0.454795i
$871$	2.65085	+	1.18023i	0.0898205	+	0.0399907i
$872$	4.59458	−	5.10280i	0.155592	−	0.172802i
$873$	2.80512	−	2.52574i	0.0949388	−	0.0854833i
$874$	−11.1300	+	15.3191i	−0.376476	+	0.518175i
$875$	−6.30447	+	23.9969i	−0.213130	+	0.811243i
$876$	−0.783698	−	0.254639i	−0.0264787	−	0.00860345i
$877$	0.892765	−	4.20013i	0.0301465	−	0.141828i	−0.960500	−	0.278279i	$-0.910236\pi$
$877$	0.892765	−	4.20013i	0.0301465	−	0.141828i	0.990647	+	0.136450i	$0.0435694\pi$
$878$	−12.6060	+	28.3135i	−0.425432	+	0.955536i
$879$	−4.36021	+	2.51737i	−0.147066	+	0.0849088i
$880$	−2.88063	−	7.77397i	−0.0971060	−	0.262060i
$881$			4.09168i			0.137852i	0.997622	+	0.0689262i	$0.0219573\pi$
$881$			4.09168i			0.137852i	−0.997622	+	0.0689262i	$0.978043\pi$
$882$	−2.22806	−	6.63594i	−0.0750226	−	0.223444i
$883$	5.38260	+	16.5659i	0.181139	+	0.557488i	0.999861	−	0.0167024i	$-0.00531680\pi$
$883$	5.38260	+	16.5659i	0.181139	+	0.557488i	−0.818722	+	0.574191i	$0.805317\pi$
$884$	−1.41037	−	1.56638i	−0.0474359	−	0.0526829i
$885$	−6.58481	−	0.692091i	−0.221346	−	0.0232644i
$886$	−5.35240	−	0.562560i	−0.179817	−	0.0188996i
$887$	11.5351	+	12.8111i	0.387312	+	0.430154i	0.904997	−	0.425418i	$-0.139873\pi$
$887$	11.5351	+	12.8111i	0.387312	+	0.430154i	−0.517685	+	0.855571i	$0.673206\pi$
$888$	3.36260	+	10.3490i	0.112841	+	0.347290i
$889$	−15.1025	−	9.70310i	−0.506520	−	0.325431i
$890$			43.5390i			1.45943i
$891$	−3.19339	−	0.895692i	−0.106983	−	0.0300068i
$892$	−17.6618	+	10.1970i	−0.591361	+	0.341422i
$893$	−6.00264	+	13.4822i	−0.200871	+	0.451163i
$894$	−0.982802	+	4.62372i	−0.0328698	+	0.154640i
$895$	−39.0057	−	12.6737i	−1.30382	−	0.423636i
$896$	−1.87995	−	1.86167i	−0.0628046	−	0.0621939i
$897$	−1.88849	+	2.59928i	−0.0630548	+	0.0867875i
$898$	−18.0419	+	16.2450i	−0.602065	+	0.542102i
$899$	−20.4442	+	22.7056i	−0.681852	+	0.757274i
$900$	−1.14049	−	0.507778i	−0.0380163	−	0.0169259i
$901$	−24.0826	+	41.7123i	−0.802309	+	1.38964i
$902$	−2.37964	+	37.1210i	−0.0792332	+	1.23600i
$903$	8.59514	+	6.89096i	0.286028	+	0.229317i
$904$	11.1568	+	15.3560i	0.371068	+	0.510732i
$905$	36.4389	+	7.74534i	1.21127	+	0.257464i
$906$	1.72360	+	8.10888i	0.0572626	+	0.269400i
$907$	0.973726	−	9.26438i	0.0323320	−	0.307619i	−0.966390	−	0.257080i	$-0.917240\pi$
$907$	0.973726	−	9.26438i	0.0323320	−	0.307619i	0.998722	−	0.0505386i	$-0.0160938\pi$
$908$	7.00325	−	3.11805i	0.232411	−	0.103476i
$909$	−0.0487431	+	0.150016i	−0.00161671	+	0.00497571i
$910$	−0.945658	+	2.49996i	−0.0313482	+	0.0828727i
$911$	19.3180	−	14.0353i	0.640033	−	0.465011i	−0.219829	−	0.975539i	$-0.570550\pi$
$911$	19.3180	−	14.0353i	0.640033	−	0.465011i	0.859861	+	0.510527i	$0.170550\pi$
$912$	2.06275	+	1.19093i	0.0683046	+	0.0394357i
$913$	17.6051	+	35.5710i	0.582643	+	1.17723i
$914$	−4.62420	−	8.00935i	−0.152955	−	0.264926i
$915$	1.18223	+	11.2481i	0.0390832	+	0.371851i
$916$	−9.99127	+	3.24636i	−0.330121	+	0.107263i
$917$	−31.2313	−	15.7214i	−1.03135	−	0.519168i
$918$	4.21932	+	3.06551i	0.139258	+	0.101177i
$919$	17.1676	+	38.5590i	0.566305	+	1.27194i	0.938977	+	0.343979i	$0.111775\pi$
$919$	17.1676	+	38.5590i	0.566305	+	1.27194i	−0.372672	+	0.927963i	$0.621558\pi$
$920$	19.4378	−	4.13163i	0.640846	−	0.136216i
$921$	0.924582	+	0.832497i	0.0304660	+	0.0274317i
$922$	23.4020	−	2.45965i	0.770703	−	0.0810041i
$923$	−5.39918			−0.177716
$924$	7.13386	−	5.10960i	0.234687	−	0.168093i
$925$	−13.5848			−0.446665
$926$	−0.113470	+	0.0119262i	−0.00372887	+	0.000391920i
$927$	8.46816	+	7.62477i	0.278131	+	0.250430i
$928$	−6.06127	+	1.28836i	−0.198971	+	0.0422926i
$929$	−23.5410	−	52.8739i	−0.772354	−	1.73474i	−0.672948	−	0.739690i	$-0.734972\pi$
$929$	−23.5410	−	52.8739i	−0.772354	−	1.73474i	−0.0994061	−	0.995047i	$-0.531694\pi$
$930$	−9.97109	−	7.24442i	−0.326965	−	0.237554i
$931$	−16.5979	−	1.58072i	−0.543975	−	0.0518061i
$932$	−8.22315	+	2.67186i	−0.269358	+	0.0875198i
$933$	1.42550	+	13.5627i	0.0466688	+	0.444024i
$934$	−16.8902	−	29.2546i	−0.552663	−	0.957240i
$935$	−42.6240	−	7.26128i	−1.39395	−	0.237469i
$936$	0.350001	+	0.202073i	0.0114401	+	0.00660496i
$937$	7.80861	−	5.67329i	0.255096	−	0.185338i	−0.452886	−	0.891568i	$-0.649606\pi$
$937$	7.80861	−	5.67329i	0.255096	−	0.185338i	0.707982	+	0.706230i	$0.249606\pi$
$938$	14.7042	−	12.0266i	0.480109	−	0.392684i
$939$	−8.14508	+	25.0680i	−0.265804	+	0.818062i
$940$	14.1491	−	6.29957i	0.461492	−	0.205469i
$941$	5.80373	−	55.2188i	0.189196	−	1.80008i	−0.328485	−	0.944509i	$-0.606538\pi$
$941$	5.80373	−	55.2188i	0.189196	−	1.80008i	0.517682	−	0.855573i	$-0.326795\pi$
$942$	0.729035	+	3.42984i	0.0237533	+	0.111750i
$943$	−87.2121	−	18.5375i	−2.84002	−	0.603664i
$944$	−1.55691	−	2.14290i	−0.0506730	−	0.0697454i
$945$	1.00266	−	6.53709i	0.0326167	−	0.212652i
$946$	−5.09895	+	12.8340i	−0.165781	+	0.417270i
$947$	−9.93288	+	17.2043i	−0.322775	+	0.559063i	−0.981060	−	0.193706i	$-0.937949\pi$
$947$	−9.93288	+	17.2043i	−0.322775	+	0.559063i	0.658284	+	0.752769i	$0.271282\pi$
$948$	2.20978	+	0.983858i	0.0717704	+	0.0319542i
$949$	−0.222839	+	0.247488i	−0.00723366	+	0.00803379i
$950$	−2.20979	+	1.98970i	−0.0716950	+	0.0645545i
$951$	−0.471655	+	0.649178i	−0.0152945	+	0.0210510i
$952$	−13.3108	+	3.63640i	−0.431405	+	0.117856i
$953$	37.4276	+	12.1610i	1.21240	+	0.393933i	0.844309	−	0.535857i	$-0.180011\pi$
$953$	37.4276	+	12.1610i	1.21240	+	0.393933i	0.368092	+	0.929790i	$0.380011\pi$
$954$	1.92012	−	9.03345i	0.0621661	−	0.292469i
$955$	−12.8198	+	28.7938i	−0.414839	+	0.931744i
$956$	23.0569	−	13.3119i	0.745713	−	0.430538i
$957$	−0.836292	−	20.5351i	−0.0270335	−	0.663804i
$958$			34.5772i			1.11714i
$959$	32.2769	+	1.53349i	1.04227	+	0.0495190i
$960$	−0.772445	−	2.37734i	−0.0249305	−	0.0767283i
$961$	4.47593	+	4.97103i	0.144385	+	0.160356i
$962$	4.37366	+	0.459690i	0.141012	+	0.0148210i
$963$	−4.76333	−	0.500646i	−0.153496	−	0.0161331i
$964$	−13.6158	−	15.1219i	−0.438535	−	0.487043i
$965$	−17.8996	−	55.0892i	−0.576207	−	1.77338i
$966$	9.64034	+	18.6939i	0.310173	+	0.601467i
$967$			48.8654i			1.57141i	0.618604	+	0.785703i	$0.287698\pi$
$967$			48.8654i			1.57141i	−0.618604	+	0.785703i	$0.712302\pi$
$968$	8.74604	+	6.67134i	0.281108	+	0.214425i
$969$	10.7580	−	6.21114i	0.345597	−	0.199531i
$970$	−3.83774	+	8.61971i	−0.123222	+	0.276762i
$971$	−11.2892	+	53.1114i	−0.362287	+	1.70443i	0.298965	+	0.954264i	$0.403359\pi$
$971$	−11.2892	+	53.1114i	−0.362287	+	1.70443i	−0.661253	+	0.750163i	$0.729975\pi$
$972$	−0.951057	−	0.309017i	−0.0305052	−	0.00991172i
$973$	−15.2926	−	4.01767i	−0.490258	−	0.128801i
$974$	−0.0452995	+	0.0623494i	−0.00145149	+	0.00199781i
$975$	−0.374949	+	0.337606i	−0.0120080	+	0.0108120i
$976$	−3.02755	+	3.36244i	−0.0969095	+	0.107629i
$977$	32.6214	+	14.5240i	1.04365	+	0.464664i	0.855677	−	0.517510i	$-0.173141\pi$
$977$	32.6214	+	14.5240i	1.04365	+	0.464664i	0.187974	+	0.982174i	$0.439808\pi$
$978$	5.96356	−	10.3292i	0.190694	−	0.330291i
$979$	−30.8959	−	48.8120i	−0.987439	−	1.56004i
$980$	11.8348	+	12.8884i	0.378048	+	0.411704i
$981$	4.03602	+	5.55511i	0.128860	+	0.177361i
$982$	13.4383	+	2.85639i	0.428833	+	0.0911512i
$983$	8.78819	+	41.3452i	0.280300	+	1.31871i	0.862663	+	0.505779i	$0.168795\pi$
$983$	8.78819	+	41.3452i	0.280300	+	1.31871i	−0.582363	+	0.812929i	$0.697872\pi$
$984$	−1.17233	+	11.1540i	−0.0373724	+	0.355575i
$985$	−14.4556	+	6.43605i	−0.460594	+	0.205070i
$986$	−9.98680	+	30.7362i	−0.318045	+	0.978841i
$987$	10.3786	+	12.6893i	0.330356	+	0.403905i
$988$	0.778776	−	0.565814i	0.0247762	−	0.0180009i
$989$	−28.6669	−	16.5508i	−0.911554	−	0.526286i
$990$	8.20301	−	1.20138i	0.260709	−	0.0381824i
$991$	3.98165	+	6.89641i	0.126481	+	0.219072i	0.922311	−	0.386449i	$-0.126298\pi$
$991$	3.98165	+	6.89641i	0.126481	+	0.219072i	−0.795830	+	0.605520i	$0.792965\pi$
$992$	−0.515388	−	4.90359i	−0.0163636	−	0.155689i
$993$	3.41970	−	1.11113i	0.108521	−	0.0352606i
$994$	−15.8926	+	31.5714i	−0.504084	+	1.00138i
$995$	−5.66577	−	4.11642i	−0.179617	−	0.130499i
$996$	4.86732	+	10.9322i	0.154227	+	0.346399i
$997$	−49.3913	+	10.4984i	−1.56424	+	0.332489i	−0.906979	−	0.421175i	$-0.861618\pi$
$997$	−49.3913	+	10.4984i	−1.56424	+	0.332489i	−0.657259	+	0.753665i	$0.728284\pi$
$998$	10.5040	+	9.45784i	0.332498	+	0.299383i
$999$	−10.8220	+	1.13744i	−0.342392	+	0.0359869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.ba.b.19.5	yes	64
7.3	odd	6		462.2.ba.a.283.1	yes	64
11.7	odd	10		462.2.ba.a.271.1	✓	64
77.73	even	30	inner	462.2.ba.b.73.5	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.ba.a.271.1	✓	64	11.7	odd	10
462.2.ba.a.283.1	yes	64	7.3	odd	6
462.2.ba.b.19.5	yes	64	1.1	even	1	trivial
462.2.ba.b.73.5	yes	64	77.73	even	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.994522 - 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-1.01671 - 2.28357i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.151373 - 2.64142i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.994522 - 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-1.01671 - 2.28357i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.151373 - 2.64142i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +(-1.24984 - 2.16479i) q^{10} +(2.93738 + 1.54006i) q^{11} +(0.866025 + 0.500000i) q^{12} +(0.326961 - 0.237551i) q^{13} +(-0.426647 - 2.61112i) q^{14} +(0.772445 - 2.37734i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.545154 - 5.18679i) q^{17} +(0.207912 + 0.978148i) q^{18} +(2.32981 + 0.495217i) q^{19} +(-1.46928 - 2.02229i) q^{20} +(1.65496 - 2.06424i) q^{21} +(3.08227 + 1.22459i) q^{22} +(-3.97492 + 6.88476i) q^{23} +(0.913545 + 0.406737i) q^{24} +(-0.835356 + 0.927757i) q^{25} +(0.300339 - 0.270426i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(-0.697247 - 2.55222i) q^{28} +(-5.89340 - 1.91488i) q^{29} +(0.519714 - 2.44506i) q^{30} +(2.00546 - 4.50433i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.15240 + 3.10998i) q^{33} -5.21536i q^{34} +(-5.87797 + 3.03124i) q^{35} +(0.309017 + 0.951057i) q^{36} +(7.28120 + 8.08660i) q^{37} +(2.36881 + 0.248972i) q^{38} +(0.401932 + 0.0422447i) q^{39} +(-1.67262 - 1.85763i) q^{40} +(3.46575 + 10.6665i) q^{41} +(1.43012 - 2.22593i) q^{42} +4.16382i q^{43} +(3.19339 + 0.895692i) q^{44} +(2.16479 - 1.24984i) q^{45} +(-3.23349 + 7.26253i) q^{46} +(-1.28822 + 6.06062i) q^{47} +(0.951057 + 0.309017i) q^{48} +(-6.95417 + 0.799679i) q^{49} +(-0.733803 + 1.00999i) q^{50} +(3.87577 - 3.48976i) q^{51} +(0.270426 - 0.300339i) q^{52} +(-8.43683 - 3.75632i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.530373 - 8.27353i) q^{55} +(-0.960207 - 2.46536i) q^{56} +(1.40002 + 1.92697i) q^{57} +(-6.06127 - 1.28836i) q^{58} +(-0.550710 - 2.59089i) q^{59} +(0.261288 - 2.48599i) q^{60} +(-4.13343 + 1.84032i) q^{61} +(1.52364 - 4.68928i) q^{62} +(2.61112 - 0.426647i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-0.874891 - 0.505118i) q^{65} +(1.47117 + 2.97249i) q^{66} +(3.58993 + 6.21795i) q^{67} +(-0.545154 - 5.18679i) q^{68} +(-7.56074 + 2.45663i) q^{69} +(-5.52892 + 3.62905i) q^{70} +(-10.8080 - 7.85250i) q^{71} +(0.406737 + 0.913545i) q^{72} +(-0.806021 + 0.171325i) q^{73} +(8.08660 + 7.28120i) q^{74} +(-1.24158 + 0.130495i) q^{75} +2.38186 q^{76} +(3.62331 - 7.99197i) q^{77} +0.404146 q^{78} +(2.40566 - 0.252845i) q^{79} +(-1.85763 - 1.67262i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(4.56171 + 10.2458i) q^{82} +(9.68130 + 7.03388i) q^{83} +(1.18962 - 2.36322i) q^{84} +(-12.3987 + 4.02858i) q^{85} +(0.435238 + 4.14101i) q^{86} +(-3.09834 - 5.36649i) q^{87} +(3.26952 + 0.556985i) q^{88} +(-15.0842 - 8.70889i) q^{89} +(2.02229 - 1.46928i) q^{90} +(-0.676964 - 0.827681i) q^{91} +(-2.45663 + 7.56074i) q^{92} +(4.50433 - 2.00546i) q^{93} +(-0.647660 + 6.16207i) q^{94} +(-1.23789 - 5.82380i) q^{95} +(0.978148 + 0.207912i) q^{96} +(-2.21869 - 3.05376i) q^{97} +(-6.83249 + 1.52221i) q^{98} +(-1.22459 + 3.08227i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9	\( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} - 10 q^{19} - 20 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 8 q^{24} - 12 q^{26} - 20 q^{29} - 18 q^{30} + 34 q^{31} + 8 q^{33} - 2 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} - 18 q^{39} + 12 q^{40} + 28 q^{41} + 4 q^{42} + 6 q^{44} - 12 q^{45} + 42 q^{46} + 24 q^{47} - 44 q^{49} + 14 q^{51} - 32 q^{54} + 14 q^{55} - 4 q^{56} - 10 q^{58} - 30 q^{59} + 2 q^{60} - 28 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{64} - 12 q^{65} - 4 q^{66} + 16 q^{67} - 30 q^{68} - 30 q^{70} - 24 q^{71} - 116 q^{73} - 44 q^{74} + 12 q^{75} - 32 q^{77} - 18 q^{80} + 8 q^{81} - 28 q^{82} - 8 q^{83} - 2 q^{84} - 80 q^{85} - 18 q^{86} - 10 q^{87} - 14 q^{88} - 24 q^{89} - 4 q^{90} + 48 q^{91} + 8 q^{92} + 76 q^{93} + 6 q^{94} + 98 q^{95} - 8 q^{96} - 120 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9 - 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 - 10 * q^19 - 20 * q^20 + 4 * q^21 - 2 * q^22 + 4 * q^23 + 8 * q^24 - 12 * q^26 - 20 * q^29 - 18 * q^30 + 34 * q^31 + 8 * q^33 - 2 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 - 18 * q^39 + 12 * q^40 + 28 * q^41 + 4 * q^42 + 6 * q^44 - 12 * q^45 + 42 * q^46 + 24 * q^47 - 44 * q^49 + 14 * q^51 - 32 * q^54 + 14 * q^55 - 4 * q^56 - 10 * q^58 - 30 * q^59 + 2 * q^60 - 28 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^64 - 12 * q^65 - 4 * q^66 + 16 * q^67 - 30 * q^68 - 30 * q^70 - 24 * q^71 - 116 * q^73 - 44 * q^74 + 12 * q^75 - 32 * q^77 - 18 * q^80 + 8 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 80 * q^85 - 18 * q^86 - 10 * q^87 - 14 * q^88 - 24 * q^89 - 4 * q^90 + 48 * q^91 + 8 * q^92 + 76 * q^93 + 6 * q^94 + 98 * q^95 - 8 * q^96 - 120 * q^97 - 40 * q^98 + 8 * q^99

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