LMFDB - Embedded newform 378.2.v.b.67.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(67,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8, 12]))

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

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

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.v (of order $9$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			67.8
Character	$\chi$	$=$	378.67
Dual form			378.2.v.b.79.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(0.654437 - 1.60366i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.190866 - 1.08246i) q^{5} +(-0.529482 - 1.64914i) q^{6} +(2.53672 + 0.751691i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.14342 - 2.09898i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(0.654437 - 1.60366i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.190866 - 1.08246i) q^{5} +(-0.529482 - 1.64914i) q^{6} +(2.53672 + 0.751691i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.14342 - 2.09898i) q^{9} +(-0.549577 - 0.951896i) q^{10} +(0.0294251 + 0.166878i) q^{11} +(-1.46565 - 0.922967i) q^{12} +(-0.287618 + 1.63116i) q^{13} +(2.42642 - 1.05474i) q^{14} +(-1.61098 - 1.01448i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.236282 + 0.409253i) q^{17} +(-2.99116 - 0.230149i) q^{18} +(-1.72314 + 2.98457i) q^{19} +(-1.03287 - 0.375933i) q^{20} +(2.86558 - 3.57609i) q^{21} +(0.129808 + 0.108922i) q^{22} +(-2.39343 - 2.00833i) q^{23} +(-1.71603 + 0.235068i) q^{24} +(3.56318 + 1.29689i) q^{25} +(0.828163 + 1.43442i) q^{26} +(-4.76878 + 2.06366i) q^{27} +(1.18077 - 2.36765i) q^{28} +(-0.0779750 - 0.442218i) q^{29} +(-1.88618 + 0.258377i) q^{30} +(-0.131483 + 0.745675i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.286871 + 0.0620234i) q^{33} +(0.444065 + 0.161626i) q^{34} +(1.29785 - 2.60242i) q^{35} +(-2.43930 + 1.74638i) q^{36} -3.02705 q^{37} +(0.598442 + 3.39393i) q^{38} +(2.42760 + 1.52873i) q^{39} +(-1.03287 + 0.375933i) q^{40} +(-0.223307 + 1.26644i) q^{41} +(-0.103507 - 4.58141i) q^{42} +(4.12401 - 3.46045i) q^{43} +0.169452 q^{44} +(-2.68116 + 1.91954i) q^{45} -3.12440 q^{46} +(0.836394 + 4.74343i) q^{47} +(-1.16345 + 1.28311i) q^{48} +(5.86992 + 3.81366i) q^{49} +(3.56318 - 1.29689i) q^{50} +(0.810932 - 0.111085i) q^{51} +(1.55644 + 0.566497i) q^{52} +(1.65864 - 2.87284i) q^{53} +(-2.32661 + 4.64617i) q^{54} +0.186254 q^{55} +(-0.617377 - 2.57271i) q^{56} +(3.65854 + 4.71655i) q^{57} +(-0.343985 - 0.288637i) q^{58} +(3.62012 - 1.31762i) q^{59} +(-1.27881 + 1.41034i) q^{60} +(2.36234 + 13.3975i) q^{61} +(0.378589 + 0.655736i) q^{62} +(-3.85948 - 6.93573i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.71076 + 0.622667i) q^{65} +(0.259624 - 0.136885i) q^{66} +(10.2926 + 8.63654i) q^{67} +(0.444065 - 0.161626i) q^{68} +(-4.78702 + 2.52392i) q^{69} +(-0.678593 - 2.82781i) q^{70} +(6.29081 - 10.8960i) q^{71} +(-0.746062 + 2.90575i) q^{72} -13.8504 q^{73} +(-2.31886 + 1.94575i) q^{74} +(4.41165 - 4.86538i) q^{75} +(2.64001 + 2.21523i) q^{76} +(-0.0507974 + 0.445441i) q^{77} +(2.84230 - 0.389350i) q^{78} +(1.86542 - 1.56527i) q^{79} +(-0.549577 + 0.951896i) q^{80} +(0.188528 + 8.99803i) q^{81} +(0.642986 + 1.11368i) q^{82} +(-2.32492 - 13.1853i) q^{83} +(-3.02416 - 3.44303i) q^{84} +(0.488096 - 0.177652i) q^{85} +(0.934837 - 5.30172i) q^{86} +(-0.760196 - 0.164359i) q^{87} +(0.129808 - 0.108922i) q^{88} +(-0.437363 + 0.757534i) q^{89} +(-0.820037 + 3.19387i) q^{90} +(-1.95574 + 3.92161i) q^{91} +(-2.39343 + 2.00833i) q^{92} +(1.10976 + 0.698850i) q^{93} +(3.68973 + 3.09605i) q^{94} +(2.90178 + 2.43488i) q^{95} +(-0.0664874 + 1.73077i) q^{96} +(3.50823 - 2.94375i) q^{97} +(6.94800 - 0.851675i) q^{98} +(0.287203 - 0.419452i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	0.654437	−	1.60366i	0.377840	−	0.925871i
$3$	0.654437	−	1.60366i	0.377840	−	0.925871i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.190866	−	1.08246i	0.0853579	−	0.484089i	−0.911921	−	0.410366i	$-0.865401\pi$
$5$	0.190866	−	1.08246i	0.0853579	−	0.484089i	0.997279	−	0.0737228i	$-0.0234880\pi$
$6$	−0.529482	−	1.64914i	−0.216160	−	0.673257i
$7$	2.53672	+	0.751691i	0.958791	+	0.284113i
$7$	2.53672	+	0.751691i	0.958791	+	0.284113i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−2.14342	−	2.09898i	−0.714474	−	0.699661i
$10$	−0.549577	−	0.951896i	−0.173792	−	0.301016i
$11$	0.0294251	+	0.166878i	0.00887199	+	0.0503155i	0.988922	−	0.148434i	$-0.0474232\pi$
$11$	0.0294251	+	0.166878i	0.00887199	+	0.0503155i	−0.980050	+	0.198749i	$0.936312\pi$
$12$	−1.46565	−	0.922967i	−0.423097	−	0.266438i
$13$	−0.287618	+	1.63116i	−0.0797709	+	0.452403i	0.918592	+	0.395207i	$0.129327\pi$
$13$	−0.287618	+	1.63116i	−0.0797709	+	0.452403i	−0.998363	+	0.0571961i	$0.981784\pi$
$14$	2.42642	−	1.05474i	0.648488	−	0.281892i
$15$	−1.61098	−	1.01448i	−0.415952	−	0.261938i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.236282	+	0.409253i	0.0573068	+	0.0992583i	0.893256	−	0.449549i	$-0.148415\pi$
$17$	0.236282	+	0.409253i	0.0573068	+	0.0992583i	−0.835949	+	0.548807i	$0.815082\pi$
$18$	−2.99116	−	0.230149i	−0.705023	−	0.0542467i
$19$	−1.72314	+	2.98457i	−0.395316	+	0.684708i	−0.993142	−	0.116918i	$-0.962698\pi$
$19$	−1.72314	+	2.98457i	−0.395316	+	0.684708i	0.597825	+	0.801627i	$0.296032\pi$
$20$	−1.03287	−	0.375933i	−0.230956	−	0.0840612i
$21$	2.86558	−	3.57609i	0.625321	−	0.780368i
$22$	0.129808	+	0.108922i	0.0276751	+	0.0232222i
$23$	−2.39343	−	2.00833i	−0.499065	−	0.418765i	0.358197	−	0.933646i	$-0.383392\pi$
$23$	−2.39343	−	2.00833i	−0.499065	−	0.418765i	−0.857262	+	0.514881i	$0.827836\pi$
$24$	−1.71603	+	0.235068i	−0.350282	+	0.0479832i
$25$	3.56318	+	1.29689i	0.712637	+	0.259378i
$26$	0.828163	+	1.43442i	0.162416	+	0.281313i
$27$	−4.76878	+	2.06366i	−0.917753	+	0.397151i
$28$	1.18077	−	2.36765i	0.223144	−	0.447445i
$29$	−0.0779750	−	0.442218i	−0.0144796	−	0.0821179i	0.976712	−	0.214556i	$-0.0688305\pi$
$29$	−0.0779750	−	0.442218i	−0.0144796	−	0.0821179i	−0.991191	+	0.132438i	$0.957719\pi$
$30$	−1.88618	+	0.258377i	−0.344367	+	0.0471729i
$31$	−0.131483	+	0.745675i	−0.0236150	+	0.133927i	−0.994336	−	0.106283i	$-0.966105\pi$
$31$	−0.131483	+	0.745675i	−0.0236150	+	0.133927i	0.970721	+	0.240210i	$0.0772163\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	0.286871	+	0.0620234i	0.0499379	+	0.0107969i
$34$	0.444065	+	0.161626i	0.0761565	+	0.0277187i
$35$	1.29785	−	2.60242i	0.219376	−	0.439889i
$36$	−2.43930	+	1.74638i	−0.406550	+	0.291063i
$37$	−3.02705			−0.497645			−0.248822	−	0.968549i	$-0.580044\pi$
$37$	−3.02705			−0.497645			−0.248822	+	0.968549i	$0.580044\pi$
$38$	0.598442	+	3.39393i	0.0970801	+	0.550568i
$39$	2.42760	+	1.52873i	0.388726	+	0.244793i
$40$	−1.03287	+	0.375933i	−0.163311	+	0.0594402i
$41$	−0.223307	+	1.26644i	−0.0348747	+	0.197784i	−0.997267	−	0.0738784i	$-0.976462\pi$
$41$	−0.223307	+	1.26644i	−0.0348747	+	0.197784i	0.962393	+	0.271662i	$0.0875734\pi$
$42$	−0.103507	−	4.58141i	−0.0159715	−	0.706926i
$43$	4.12401	−	3.46045i	0.628905	−	0.527714i	−0.271683	−	0.962387i	$-0.587580\pi$
$43$	4.12401	−	3.46045i	0.628905	−	0.527714i	0.900589	+	0.434672i	$0.143136\pi$
$44$	0.169452			0.0255459
$45$	−2.68116	+	1.91954i	−0.399684	+	0.286148i
$46$	−3.12440			−0.460668
$47$	0.836394	+	4.74343i	0.122001	+	0.691900i	0.983044	+	0.183369i	$0.0587002\pi$
$47$	0.836394	+	4.74343i	0.122001	+	0.691900i	−0.861044	+	0.508531i	$0.830189\pi$
$48$	−1.16345	+	1.28311i	−0.167930	+	0.185201i
$49$	5.86992	+	3.81366i	0.838560	+	0.544809i
$50$	3.56318	−	1.29689i	0.503910	−	0.183408i
$51$	0.810932	−	0.111085i	0.113553	−	0.0155550i
$52$	1.55644	+	0.566497i	0.215839	+	0.0785590i
$53$	1.65864	−	2.87284i	0.227831	−	0.394616i	−0.729334	−	0.684158i	$-0.760170\pi$
$53$	1.65864	−	2.87284i	0.227831	−	0.394616i	0.957165	+	0.289543i	$0.0935032\pi$
$54$	−2.32661	+	4.64617i	−0.316611	+	0.632264i
$55$	0.186254			0.0251145
$56$	−0.617377	−	2.57271i	−0.0825005	−	0.343793i
$57$	3.65854	+	4.71655i	0.484585	+	0.624722i
$58$	−0.343985	−	0.288637i	−0.0451674	−	0.0379000i
$59$	3.62012	−	1.31762i	0.471299	−	0.171539i	−0.0954415	−	0.995435i	$-0.530426\pi$
$59$	3.62012	−	1.31762i	0.471299	−	0.171539i	0.566741	+	0.823896i	$0.308204\pi$
$60$	−1.27881	+	1.41034i	−0.165094	+	0.182074i
$61$	2.36234	+	13.3975i	0.302467	+	1.71537i	0.635196	+	0.772351i	$0.280919\pi$
$61$	2.36234	+	13.3975i	0.302467	+	1.71537i	−0.332730	+	0.943022i	$0.607970\pi$
$62$	0.378589	+	0.655736i	0.0480809	+	0.0832785i
$63$	−3.85948	−	6.93573i	−0.486249	−	0.873820i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	1.71076	+	0.622667i	0.212194	+	0.0772324i
$66$	0.259624	−	0.136885i	0.0319575	−	0.0168493i
$67$	10.2926	+	8.63654i	1.25744	+	1.05512i	0.995949	+	0.0899162i	$0.0286599\pi$
$67$	10.2926	+	8.63654i	1.25744	+	1.05512i	0.261495	+	0.965205i	$0.415785\pi$
$68$	0.444065	−	0.161626i	0.0538508	−	0.0196001i
$69$	−4.78702	+	2.52392i	−0.576289	+	0.303844i
$70$	−0.678593	−	2.82781i	−0.0811074	−	0.337988i
$71$	6.29081	−	10.8960i	0.746581	−	1.29312i	−0.202871	−	0.979205i	$-0.565027\pi$
$71$	6.29081	−	10.8960i	0.746581	−	1.29312i	0.949452	−	0.313911i	$-0.101639\pi$
$72$	−0.746062	+	2.90575i	−0.0879243	+	0.342446i
$73$	−13.8504			−1.62106			−0.810532	−	0.585694i	$-0.800822\pi$
$73$	−13.8504			−1.62106			−0.810532	+	0.585694i	$0.800822\pi$
$74$	−2.31886	+	1.94575i	−0.269562	+	0.226189i
$75$	4.41165	−	4.86538i	0.509413	−	0.561806i
$76$	2.64001	+	2.21523i	0.302830	+	0.254105i
$77$	−0.0507974	+	0.445441i	−0.00578890	+	0.0507627i
$78$	2.84230	−	0.389350i	0.321827	−	0.0440852i
$79$	1.86542	−	1.56527i	0.209876	−	0.176107i	−0.531790	−	0.846876i	$-0.678480\pi$
$79$	1.86542	−	1.56527i	0.209876	−	0.176107i	0.741666	+	0.670769i	$0.234036\pi$
$80$	−0.549577	+	0.951896i	−0.0614446	+	0.106425i
$81$	0.188528	+	8.99803i	0.0209476	+	0.999781i
$82$	0.642986	+	1.11368i	0.0710060	+	0.122986i
$83$	−2.32492	−	13.1853i	−0.255193	−	1.44727i	−0.795576	−	0.605853i	$-0.792832\pi$
$83$	−2.32492	−	13.1853i	−0.255193	−	1.44727i	0.540383	−	0.841419i	$-0.318279\pi$
$84$	−3.02416	−	3.44303i	−0.329963	−	0.375665i
$85$	0.488096	−	0.177652i	0.0529414	−	0.0192691i
$86$	0.934837	−	5.30172i	0.100806	−	0.571700i
$87$	−0.760196	−	0.164359i	−0.0815015	−	0.0176211i
$88$	0.129808	−	0.108922i	0.0138376	−	0.0116111i
$89$	−0.437363	+	0.757534i	−0.0463603	+	0.0802985i	−0.888274	−	0.459313i	$-0.848096\pi$
$89$	−0.437363	+	0.757534i	−0.0463603	+	0.0802985i	0.841914	+	0.539612i	$0.181429\pi$
$90$	−0.820037	+	3.19387i	−0.0864395	+	0.336663i
$91$	−1.95574	+	3.92161i	−0.205017	+	0.411096i
$92$	−2.39343	+	2.00833i	−0.249532	+	0.209383i
$93$	1.10976	+	0.698850i	0.115077	+	0.0724674i
$94$	3.68973	+	3.09605i	0.380567	+	0.319333i
$95$	2.90178	+	2.43488i	0.297716	+	0.249814i
$96$	−0.0664874	+	1.73077i	−0.00678584	+	0.176646i
$97$	3.50823	−	2.94375i	0.356207	−	0.298893i	−0.447070	−	0.894499i	$-0.647533\pi$
$97$	3.50823	−	2.94375i	0.356207	−	0.298893i	0.803277	+	0.595606i	$0.203088\pi$
$98$	6.94800	−	0.851675i	0.701854	−	0.0860322i
$99$	0.287203	−	0.419452i	0.0288650	−	0.0421566i
$100$	1.89593	−	3.28385i	0.189593	−	0.328385i
$101$	−13.5736	+	11.3896i	−1.35063	+	1.13331i	−0.371871	+	0.928284i	$0.621284\pi$
$101$	−13.5736	+	11.3896i	−1.35063	+	1.13331i	−0.978756	+	0.205027i	$0.934272\pi$
$102$	0.549806	−	0.606353i	0.0544389	−	0.0600379i
$103$	−0.918807	+	5.21081i	−0.0905328	+	0.513437i	0.905492	+	0.424363i	$0.139502\pi$
$103$	−0.918807	+	5.21081i	−0.0905328	+	0.513437i	−0.996025	+	0.0890740i	$0.971609\pi$
$104$	1.55644	−	0.566497i	0.152621	−	0.0555496i
$105$	−3.32402	−	3.78442i	−0.324391	−	0.369321i
$106$	−0.576039	−	3.26688i	−0.0559498	−	0.317307i
$107$	−3.85697	−	6.68047i	−0.372867	−	0.645825i	0.617138	−	0.786855i	$-0.288292\pi$
$107$	−3.85697	−	6.68047i	−0.372867	−	0.645825i	−0.990005	+	0.141030i	$0.954959\pi$
$108$	1.20422	+	5.05469i	0.115876	+	0.486387i
$109$	−7.36169	+	12.7508i	−0.705122	+	1.22131i	0.261525	+	0.965197i	$0.415774\pi$
$109$	−7.36169	+	12.7508i	−0.705122	+	1.22131i	−0.966647	+	0.256111i	$0.917559\pi$
$110$	0.142679	−	0.119722i	0.0136039	−	0.0114150i
$111$	−1.98102	+	4.85435i	−0.188030	+	0.460755i
$112$	−2.12665	−	1.57397i	−0.200949	−	0.148726i
$113$	9.21111	+	7.72904i	0.866508	+	0.727087i	0.963360	−	0.268212i	$-0.0864327\pi$
$113$	9.21111	+	7.72904i	0.866508	+	0.727087i	−0.0968515	+	0.995299i	$0.530877\pi$
$114$	5.83434	+	1.26142i	0.546436	+	0.118143i
$115$	−2.63075	+	2.20746i	−0.245319	+	0.205847i
$116$	−0.449040			−0.0416923
$117$	4.04027	−	2.89257i	0.373523	−	0.267418i
$118$	1.92623	−	3.33632i	0.177323	−	0.307133i
$119$	0.291750	+	1.21577i	0.0267447	+	0.111450i
$120$	−0.0730799	+	1.90239i	−0.00667125	+	0.173663i
$121$	10.3096	−	3.75240i	0.937240	−	0.341127i
$122$	10.4214	+	8.74459i	0.943509	+	0.791698i
$123$	1.88479	+	1.18691i	0.169945	+	0.107020i
$124$	0.711515	+	0.258970i	0.0638959	+	0.0232562i
$125$	4.83181	−	8.36893i	0.432170	−	0.748540i
$126$	−7.41474	−	2.83225i	−0.660557	−	0.252317i
$127$	−3.22819	−	5.59139i	−0.286455	−	0.496155i	0.686506	−	0.727125i	$-0.259144\pi$
$127$	−3.22819	−	5.59139i	−0.286455	−	0.496155i	−0.972961	+	0.230969i	$0.925810\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	−2.85047	−	8.87814i	−0.250970	−	0.781677i
$130$	1.71076	−	0.622667i	0.150044	−	0.0546115i
$131$	−5.95546	−	4.99722i	−0.520331	−	0.436609i	0.344416	−	0.938817i	$-0.388077\pi$
$131$	−5.95546	−	4.99722i	−0.520331	−	0.436609i	−0.864747	+	0.502208i	$0.832521\pi$
$132$	0.110896	−	0.271743i	0.00965224	−	0.0236522i
$133$	−6.61462	+	6.27576i	−0.573560	+	0.544178i
$134$	13.4361			1.16070
$135$	1.32362	+	5.55588i	0.113919	+	0.478174i
$136$	0.236282	−	0.409253i	0.0202610	−	0.0350931i
$137$	−8.57091	−	3.11955i	−0.732262	−	0.266522i	−0.0511399	−	0.998691i	$-0.516285\pi$
$137$	−8.57091	−	3.11955i	−0.732262	−	0.266522i	−0.681122	+	0.732170i	$0.738508\pi$
$138$	−2.04473	+	5.01047i	−0.174059	+	0.426519i
$139$	−13.1927	+	4.80175i	−1.11899	+	0.407279i	−0.834283	−	0.551336i	$-0.814118\pi$
$139$	−13.1927	+	4.80175i	−1.11899	+	0.407279i	−0.284706	+	0.958615i	$0.591896\pi$
$140$	−2.33751	−	1.73003i	−0.197556	−	0.146215i
$141$	8.15419	+	1.76299i	0.686707	+	0.148470i
$142$	−2.18477	−	12.3905i	−0.183342	−	1.03979i
$143$	−0.280668			−0.0234706
$144$	1.29626	+	2.70549i	0.108022	+	0.225458i
$145$	−0.493564			−0.0409883
$146$	−10.6100	+	8.90285i	−0.878090	+	0.736805i
$147$	9.95730	−	6.91753i	0.821264	−	0.570548i
$148$	−0.525642	+	2.98107i	−0.0432075	+	0.245042i
$149$	−17.8441	+	6.49473i	−1.46185	+	0.532069i	−0.945874	−	0.324535i	$-0.894792\pi$
$149$	−17.8441	+	6.49473i	−1.46185	+	0.532069i	−0.515974	+	0.856604i	$0.672570\pi$
$150$	0.252111	−	6.56285i	0.0205848	−	0.535855i
$151$	−1.74070	−	9.87202i	−0.141656	−	0.803373i	−0.969991	−	0.243140i	$-0.921823\pi$
$151$	−1.74070	−	9.87202i	−0.141656	−	0.803373i	0.828335	−	0.560233i	$-0.189289\pi$
$152$	3.44629			0.279531
$153$	0.352562	−	1.37315i	0.0285030	−	0.111013i
$154$	0.247411	+	0.373880i	0.0199369	+	0.0301281i
$155$	0.782065	+	0.284648i	0.0628169	+	0.0228635i
$156$	1.92706	−	2.12525i	0.154288	−	0.170156i
$157$	−12.0857	+	4.39883i	−0.964543	+	0.351065i	−0.775812	−	0.630964i	$-0.782660\pi$
$157$	−12.0857	+	4.39883i	−0.964543	+	0.351065i	−0.188731	+	0.982029i	$0.560437\pi$
$158$	0.422856	−	2.39814i	0.0336406	−	0.190785i
$159$	−3.52158	−	4.53998i	−0.279279	−	0.360044i
$160$	0.190866	+	1.08246i	0.0150893	+	0.0855756i
$161$	−4.56183	−	6.89369i	−0.359522	−	0.543299i
$162$	5.92824	+	6.77170i	0.465767	+	0.532035i
$163$	−8.42123	−	14.5860i	−0.659601	−	1.14246i	−0.980719	−	0.195424i	$-0.937392\pi$
$163$	−8.42123	−	14.5860i	−0.659601	−	1.14246i	0.321117	−	0.947039i	$-0.395942\pi$
$164$	1.20842	+	0.439828i	0.0943617	+	0.0343448i
$165$	0.121892	−	0.298687i	0.00948925	−	0.0232528i
$166$	−10.2563	−	8.60608i	−0.796045	−	0.667961i
$167$	15.0551	+	12.6327i	1.16500	+	0.977551i	0.999962	−	0.00873601i	$-0.00278079\pi$
$167$	15.0551	+	12.6327i	1.16500	+	0.977551i	0.165038	+	0.986287i	$0.447225\pi$
$168$	−4.52978	−	0.693618i	−0.349480	−	0.0535138i
$169$	9.63804	+	3.50796i	0.741387	+	0.269843i
$170$	0.259710	−	0.449832i	0.0199189	−	0.0345005i
$171$	9.95800	−	2.78035i	0.761507	−	0.212619i
$172$	−2.69176	−	4.66226i	−0.205244	−	0.355494i
$173$	−14.8171	−	5.39298i	−1.12652	−	0.410021i	−0.289494	−	0.957180i	$-0.593487\pi$
$173$	−14.8171	−	5.39298i	−1.12652	−	0.410021i	−0.837029	+	0.547159i	$0.815709\pi$
$174$	−0.687992	+	0.362738i	−0.0521565	+	0.0274991i
$175$	8.06394	+	5.96827i	0.609577	+	0.451159i
$176$	0.0294251	−	0.166878i	0.00221800	−	0.0125789i
$177$	0.256139	−	6.66772i	0.0192526	−	0.501177i
$178$	0.151894	+	0.861436i	0.0113850	+	0.0645674i
$179$	−6.14587	−	10.6450i	−0.459364	−	0.795641i	0.539564	−	0.841945i	$-0.318589\pi$
$179$	−6.14587	−	10.6450i	−0.459364	−	0.795641i	−0.998927	+	0.0463034i	$0.985256\pi$
$180$	1.42479	+	2.97376i	0.106198	+	0.221651i
$181$	−9.45246	−	16.3721i	−0.702595	−	1.21693i	−0.967552	−	0.252671i	$-0.918691\pi$
$181$	−9.45246	−	16.3721i	−0.702595	−	1.21693i	0.264957	−	0.964260i	$-0.414642\pi$
$182$	1.02258	+	4.26125i	0.0757985	+	0.315865i
$183$	23.0310	+	4.97944i	1.70250	+	0.368091i
$184$	−0.542547	+	3.07694i	−0.0399971	+	0.226835i
$185$	−0.577762	+	3.27665i	−0.0424779	+	0.240904i
$186$	1.29934	−	0.177989i	0.0952720	−	0.0130508i
$187$	−0.0613425	+	0.0514725i	−0.00448581	+	0.00376404i
$188$	4.81660			0.351287
$189$	−13.6483	+	1.65028i	−0.992769	+	0.120040i
$190$	3.78800			0.274811
$191$	3.94525	−	3.31046i	0.285468	−	0.239536i	−0.488797	−	0.872398i	$-0.662564\pi$
$191$	3.94525	−	3.31046i	0.285468	−	0.239536i	0.774265	+	0.632861i	$0.218120\pi$
$192$	1.06159	+	1.36859i	0.0766135	+	0.0987693i
$193$	2.02073	−	11.4601i	0.145455	−	0.824917i	−0.821546	−	0.570143i	$-0.806888\pi$
$193$	2.02073	−	11.4601i	0.145455	−	0.824917i	0.967001	−	0.254774i	$-0.0820010\pi$
$194$	0.795251	−	4.51009i	0.0570957	−	0.323806i
$195$	2.11813	−	2.33598i	0.151683	−	0.167283i
$196$	4.77503	−	5.11851i	0.341073	−	0.365608i
$197$	6.23368	+	10.7971i	0.444132	+	0.769258i	0.997991	−	0.0633516i	$-0.0201790\pi$
$197$	6.23368	+	10.7971i	0.444132	+	0.769258i	−0.553860	+	0.832610i	$0.686846\pi$
$198$	−0.0496082	−	0.505930i	−0.00352550	−	0.0359549i
$199$	−3.27589	−	5.67401i	−0.232222	−	0.402220i	0.726240	−	0.687441i	$-0.241266\pi$
$199$	−3.27589	−	5.67401i	−0.232222	−	0.402220i	−0.958462	+	0.285221i	$0.907933\pi$
$200$	−0.658450	−	3.73425i	−0.0465594	−	0.264052i
$201$	20.5859	−	10.8538i	1.45202	−	0.765565i
$202$	−3.07689	+	17.4499i	−0.216490	+	1.22777i
$203$	0.134611	−	1.18040i	0.00944782	−	0.0828477i
$204$	0.0314196	−	0.817902i	0.00219981	−	0.0572646i
$205$	1.32824	+	0.483439i	0.0927682	+	0.0337649i
$206$	2.64560	+	4.58231i	0.184328	+	0.319265i
$207$	0.914689	+	9.32847i	0.0635753	+	0.648374i
$208$	0.828163	−	1.43442i	0.0574228	−	0.0994591i
$209$	−0.548763	−	0.199733i	−0.0379587	−	0.0138158i
$210$	−4.97893	−	0.762393i	−0.343579	−	0.0526101i
$211$	−17.6296	−	14.7930i	−1.21367	−	1.01839i	−0.999131	−	0.0416751i	$-0.986731\pi$
$211$	−17.6296	−	14.7930i	−1.21367	−	1.01839i	−0.214539	−	0.976715i	$-0.568825\pi$
$212$	−2.54118	−	2.13230i	−0.174529	−	0.146447i
$213$	−13.3565	−	17.2190i	−0.915171	−	1.17983i
$214$	−7.24873	−	2.63832i	−0.495513	−	0.180352i
$215$	−2.95865	−	5.12454i	−0.201779	−	0.349491i
$216$	4.17157	+	3.09806i	0.283840	+	0.210796i
$217$	−0.894052	+	1.79274i	−0.0606922	+	0.121699i
$218$	2.55669	+	14.4997i	0.173161	+	0.982044i
$219$	−9.06420	+	22.2112i	−0.612502	+	1.50090i
$220$	0.0323427	−	0.183424i	0.00218054	−	0.0123665i
$221$	−0.735516	+	0.267706i	−0.0494762	+	0.0180079i
$222$	1.60277	+	4.99202i	0.107571	+	0.335043i
$223$	7.96272	+	2.89819i	0.533223	+	0.194077i	0.594577	−	0.804039i	$-0.297320\pi$
$223$	7.96272	+	2.89819i	0.533223	+	0.194077i	−0.0613537	+	0.998116i	$0.519542\pi$
$224$	−2.64083	+	0.161251i	−0.176448	+	0.0107741i
$225$	−4.91525	−	10.2589i	−0.327683	−	0.683924i
$226$	12.0243			0.799841
$227$	2.65635	+	15.0649i	0.176308	+	0.999892i	0.936623	+	0.350338i	$0.113933\pi$
$227$	2.65635	+	15.0649i	0.176308	+	0.999892i	−0.760315	+	0.649554i	$0.774956\pi$
$228$	5.28019	−	2.78394i	0.349689	−	0.184371i
$229$	19.0854	−	6.94652i	1.26120	−	0.459039i	0.377028	−	0.926202i	$-0.376946\pi$
$229$	19.0854	−	6.94652i	1.26120	−	0.459039i	0.884171	+	0.467163i	$0.154724\pi$
$230$	−0.596343	+	3.38203i	−0.0393217	+	0.223004i
$231$	0.681090	+	0.372975i	0.0448125	+	0.0245399i
$232$	−0.343985	+	0.288637i	−0.0225837	+	0.0189500i
$233$	−26.2269			−1.71818			−0.859090	−	0.511825i	$-0.828970\pi$
$233$	−26.2269			−1.71818			−0.859090	+	0.511825i	$0.828970\pi$
$234$	1.23572	−	4.81287i	0.0807817	−	0.314627i
$235$	5.29419			0.345355
$236$	−0.668971	−	3.79392i	−0.0435463	−	0.246963i
$237$	−1.28936	−	4.01586i	−0.0837528	−	0.260858i
$238$	1.00498	+	0.743801i	0.0651429	+	0.0482135i
$239$	−0.506479	+	0.184343i	−0.0327614	+	0.0119242i	−0.358349	−	0.933588i	$-0.616660\pi$
$239$	−0.506479	+	0.184343i	−0.0327614	+	0.0119242i	0.325587	+	0.945512i	$0.394438\pi$
$240$	1.16685	+	1.50429i	0.0753198	+	0.0971014i
$241$	−0.269342	−	0.0980323i	−0.0173498	−	0.00631482i	0.333331	−	0.942810i	$-0.391827\pi$
$241$	−0.269342	−	0.0980323i	−0.0173498	−	0.00631482i	−0.350680	+	0.936495i	$0.614050\pi$
$242$	5.48564	−	9.50141i	0.352630	−	0.610774i
$243$	14.5531	+	5.58631i	0.933583	+	0.358362i
$244$	13.6042			0.870918
$245$	5.24849	−	5.62603i	0.335314	−	0.359434i
$246$	2.20676	−	0.302292i	0.140698	−	0.0192734i
$247$	−4.37272	−	3.66915i	−0.278229	−	0.233462i
$248$	0.711515	−	0.258970i	0.0451812	−	0.0164446i
$249$	−22.6662	−	4.90057i	−1.43641	−	0.310561i
$250$	−1.67807	−	9.51680i	−0.106130	−	0.601895i
$251$	−12.1666	−	21.0732i	−0.767952	−	1.33013i	−0.938672	−	0.344812i	$-0.887943\pi$
$251$	−12.1666	−	21.0732i	−0.767952	−	1.33013i	0.170720	−	0.985320i	$-0.445391\pi$
$252$	−7.50056	+	2.59647i	−0.472491	+	0.163562i
$253$	0.264718	−	0.458506i	0.0166427	−	0.0288260i
$254$	−6.06701	−	2.20821i	−0.380678	−	0.138556i
$255$	0.0345349	−	0.899000i	0.00216266	−	0.0562976i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−9.80712	+	3.56950i	−0.611752	+	0.222659i	−0.629269	−	0.777187i	$-0.716646\pi$
$257$	−9.80712	+	3.56950i	−0.611752	+	0.222659i	0.0175179	+	0.999847i	$0.494424\pi$
$258$	−7.89035	−	4.96880i	−0.491232	−	0.309344i
$259$	−7.67880	−	2.27541i	−0.477137	−	0.141387i
$260$	0.910279	−	1.57665i	0.0564531	−	0.0977796i
$261$	−0.761076	+	1.11153i	−0.0471094	+	0.0688019i
$262$	−7.77430			−0.480298
$263$	12.7541	−	10.7020i	0.786453	−	0.659912i	−0.158412	−	0.987373i	$-0.550637\pi$
$263$	12.7541	−	10.7020i	0.786453	−	0.659912i	0.944865	+	0.327461i	$0.106193\pi$
$264$	−0.0897218	−	0.279450i	−0.00552200	−	0.0171989i
$265$	−2.79315	−	2.34373i	−0.171582	−	0.143974i
$266$	−1.03311	+	9.05931i	−0.0633440	+	0.555462i
$267$	0.928598	+	1.19714i	0.0568293	+	0.0732636i
$268$	10.2926	−	8.63654i	0.628722	−	0.527561i
$269$	−13.2443	+	22.9398i	−0.807520	+	1.39867i	0.107056	+	0.994253i	$0.465858\pi$
$269$	−13.2443	+	22.9398i	−0.807520	+	1.39867i	−0.914576	+	0.404413i	$0.867476\pi$
$270$	4.58520	+	3.40525i	0.279047	+	0.207237i
$271$	−5.73988	−	9.94176i	−0.348673	−	0.603919i	0.637341	−	0.770582i	$-0.280034\pi$
$271$	−5.73988	−	9.94176i	−0.348673	−	0.603919i	−0.986014	+	0.166663i	$0.946701\pi$
$272$	−0.0820599	−	0.465385i	−0.00497561	−	0.0282181i
$273$	5.00900	+	5.70278i	0.303158	+	0.345148i
$274$	−8.57091	+	3.11955i	−0.517787	+	0.188459i
$275$	−0.111576	+	0.632777i	−0.00672827	+	0.0381579i
$276$	1.65431	+	5.15256i	0.0995780	+	0.310148i
$277$	12.8164	−	10.7543i	0.770065	−	0.646162i	−0.170660	−	0.985330i	$-0.554590\pi$
$277$	12.8164	−	10.7543i	0.770065	−	0.646162i	0.940726	+	0.339168i	$0.110146\pi$
$278$	−7.01969	+	12.1585i	−0.421013	+	0.729216i
$279$	1.84698	−	1.32232i	0.110576	−	0.0791651i
$280$	−2.90268	+	0.177240i	−0.173468	+	0.0105921i
$281$	−21.5705	+	18.0998i	−1.28679	+	1.07974i	−0.294516	+	0.955646i	$0.595159\pi$
$281$	−21.5705	+	18.0998i	−1.28679	+	1.07974i	−0.992270	+	0.124096i	$0.960397\pi$
$282$	7.37970	−	3.89089i	0.439455	−	0.231699i
$283$	5.87007	+	4.92558i	0.348940	+	0.292795i	0.800364	−	0.599514i	$-0.204640\pi$
$283$	5.87007	+	4.92558i	0.348940	+	0.292795i	−0.451424	+	0.892309i	$0.649084\pi$
$284$	−9.63807	−	8.08730i	−0.571914	−	0.479893i
$285$	5.80374	−	3.05998i	0.343784	−	0.181257i
$286$	−0.215004	+	0.180410i	−0.0127135	+	0.0106679i
$287$	−1.51844	+	3.04474i	−0.0896304	+	0.179725i
$288$	2.73205	+	1.23931i	0.160988	+	0.0730268i
$289$	8.38834	−	14.5290i	0.493432	−	0.854649i
$290$	−0.378092	+	0.317257i	−0.0222023	+	0.0186300i
$291$	−2.42485	−	7.55249i	−0.142147	−	0.442735i
$292$	−2.40509	+	13.6400i	−0.140747	+	0.798218i
$293$	13.7871	−	5.01809i	0.805450	−	0.293160i	0.0937071	−	0.995600i	$-0.470128\pi$
$293$	13.7871	−	5.01809i	0.805450	−	0.293160i	0.711743	+	0.702440i	$0.247906\pi$
$294$	3.18123	−	11.6996i	0.185533	−	0.682332i
$295$	−0.735302	−	4.17011i	−0.0428110	−	0.242793i
$296$	1.51353	+	2.62151i	0.0879720	+	0.152372i
$297$	−0.484701	−	0.735081i	−0.0281252	−	0.0426537i
$298$	−9.49466	+	16.4452i	−0.550011	+	0.952647i
$299$	3.96430	−	3.32644i	0.229262	−	0.192373i
$300$	−4.02539	−	5.18949i	−0.232406	−	0.299615i
$301$	13.0627	−	5.67823i	0.752919	−	0.327288i
$302$	−7.67907	−	6.44350i	−0.441881	−	0.370782i
$303$	9.38196	+	29.2212i	0.538979	+	1.67872i
$304$	2.64001	−	2.21523i	0.151415	−	0.127052i
$305$	14.9531			0.856211
$306$	−0.612568	−	1.27852i	−0.0350182	−	0.0730881i
$307$	−1.07222	+	1.85714i	−0.0611948	+	0.105993i	−0.895000	−	0.446067i	$-0.852824\pi$
$307$	−1.07222	+	1.85714i	−0.0611948	+	0.105993i	0.833805	+	0.552059i	$0.186158\pi$
$308$	0.429853	+	0.127376i	0.0244931	+	0.00725790i
$309$	7.75505	+	4.88360i	0.441169	+	0.277818i
$310$	0.782065	−	0.284648i	0.0444183	−	0.0161669i
$311$	25.0531	+	21.0221i	1.42063	+	1.19205i	0.951000	+	0.309191i	$0.100058\pi$
$311$	25.0531	+	21.0221i	1.42063	+	1.19205i	0.469633	+	0.882862i	$0.344386\pi$
$312$	0.110125	−	2.86673i	0.00623459	−	0.162296i
$313$	9.12862	+	3.32255i	0.515980	+	0.187801i	0.586868	−	0.809683i	$-0.300361\pi$
$313$	9.12862	+	3.32255i	0.515980	+	0.187801i	−0.0708875	+	0.997484i	$0.522583\pi$
$314$	−6.43066	+	11.1382i	−0.362903	+	0.628567i
$315$	−8.24427	+	2.85392i	−0.464512	+	0.160800i
$316$	−1.21757	−	2.10889i	−0.0684934	−	0.118634i
$317$	3.73999	+	21.2105i	0.210059	+	1.19130i	0.889278	+	0.457367i	$0.151207\pi$
$317$	3.73999	+	21.2105i	0.210059	+	1.19130i	−0.679220	+	0.733935i	$0.737682\pi$
$318$	−5.61593	−	1.21420i	−0.314926	−	0.0680889i
$319$	0.0715020	−	0.0260246i	0.00400334	−	0.00145710i
$320$	0.842001	+	0.706523i	0.0470693	+	0.0394958i
$321$	−13.2373	+	1.81330i	−0.738835	+	0.101209i
$322$	−7.92574	−	2.34859i	−0.441684	−	0.130882i
$323$	−1.62859			−0.0906173
$324$	8.89406	+	1.37683i	0.494115	+	0.0764904i
$325$	−3.14028	+	5.43912i	−0.174191	+	0.301708i
$326$	−15.8267	−	5.76046i	−0.876562	−	0.319042i
$327$	15.6302	+	20.1502i	0.864350	+	1.11431i
$328$	1.20842	−	0.439828i	0.0667238	−	0.0242855i
$329$	−1.44389	+	12.6615i	−0.0796044	+	0.698049i
$330$	−0.0986181	−	0.307158i	−0.00542875	−	0.0169085i
$331$	−4.52139	−	25.6421i	−0.248518	−	1.40942i	−0.812178	−	0.583409i	$-0.801718\pi$
$331$	−4.52139	−	25.6421i	−0.248518	−	1.40942i	0.563660	−	0.826007i	$-0.309393\pi$
$332$	−13.3887			−0.734799
$333$	6.48826	+	6.35374i	0.355554	+	0.348183i
$334$	19.6531			1.07537
$335$	11.3132	−	9.49289i	0.618105	−	0.518652i
$336$	−3.91586	+	2.38034i	−0.213628	+	0.129858i
$337$	1.28273	−	7.27473i	0.0698749	−	0.396280i	−0.929732	−	0.368237i	$-0.879961\pi$
$337$	1.28273	−	7.27473i	0.0698749	−	0.396280i	0.999607	−	0.0280428i	$-0.00892747\pi$
$338$	9.63804	−	3.50796i	0.524240	−	0.190808i
$339$	18.4228	−	9.71328i	1.00059	−	0.527553i
$340$	−0.0901965	−	0.511530i	−0.00489159	−	0.0277416i
$341$	−0.128305			−0.00694813
$342$	5.84110	−	8.53075i	0.315850	−	0.461290i
$343$	12.0237	+	14.0866i	0.649217	+	0.760604i
$344$	−5.05885	−	1.84127i	−0.272755	−	0.0992746i
$345$	1.81835	+	5.66346i	0.0978965	+	0.304911i
$346$	−14.8171	+	5.39298i	−0.796572	+	0.289928i
$347$	−5.84129	+	33.1276i	−0.313577	+	1.77838i	0.266514	+	0.963831i	$0.414128\pi$
$347$	−5.84129	+	33.1276i	−0.313577	+	1.77838i	−0.580091	+	0.814552i	$0.696983\pi$
$348$	−0.293869	+	0.720106i	−0.0157530	+	0.0386017i
$349$	3.70140	+	20.9917i	0.198132	+	1.12366i	0.907888	+	0.419213i	$0.137694\pi$
$349$	3.70140	+	20.9917i	0.198132	+	1.12366i	−0.709756	+	0.704447i	$0.751195\pi$
$350$	10.0137	−	0.611442i	0.535253	−	0.0326830i
$351$	−1.99458	−	8.37221i	−0.106463	−	0.446875i
$352$	−0.0847261	−	0.146750i	−0.00451591	−	0.00782179i
$353$	19.5561	+	7.11783i	1.04087	+	0.378844i	0.805208	−	0.592992i	$-0.202054\pi$
$353$	19.5561	+	7.11783i	1.04087	+	0.378844i	0.235657	+	0.971836i	$0.424276\pi$
$354$	−4.08971	−	5.27241i	−0.217366	−	0.280226i
$355$	−10.5937	−	8.88920i	−0.562257	−	0.471789i
$356$	0.670078	+	0.562263i	0.0355141	+	0.0297999i
$357$	2.14061	+	0.327779i	0.113293	+	0.0173479i
$358$	−11.5505	−	4.20402i	−0.610460	−	0.222189i
$359$	−11.6711	+	20.2150i	−0.615979	+	1.06691i	0.374233	+	0.927335i	$0.377906\pi$
$359$	−11.6711	+	20.2150i	−0.615979	+	1.06691i	−0.990212	+	0.139572i	$0.955427\pi$
$360$	3.00295	+	1.36219i	0.158269	+	0.0717937i
$361$	3.56155	+	6.16878i	0.187450	+	0.324673i
$362$	−17.7648	−	6.46586i	−0.933697	−	0.339838i
$363$	0.729452	−	18.9888i	0.0382863	−	0.996655i
$364$	3.52242	+	2.60701i	0.184625	+	0.136644i
$365$	−2.64357	+	14.9924i	−0.138371	+	0.784739i
$366$	20.8435	−	10.9895i	1.08951	−	0.574433i
$367$	1.36091	+	7.71812i	0.0710390	+	0.402882i	0.999505	+	0.0314646i	$0.0100171\pi$
$367$	1.36091	+	7.71812i	0.0710390	+	0.402882i	−0.928466	+	0.371418i	$0.878872\pi$
$368$	1.56220	+	2.70581i	0.0814354	+	0.141050i
$369$	3.13687	−	2.24579i	0.163299	−	0.116911i
$370$	1.66360	+	2.88144i	0.0864864	+	0.149799i
$371$	6.36700	−	6.04083i	0.330558	−	0.313624i
$372$	0.880941	−	0.971545i	0.0456747	−	0.0503723i
$373$	−4.22400	+	23.9555i	−0.218711	+	1.24037i	0.655640	+	0.755074i	$0.272399\pi$
$373$	−4.22400	+	23.9555i	−0.218711	+	1.24037i	−0.874350	+	0.485295i	$0.838712\pi$
$374$	−0.0139052	+	0.0788604i	−0.000719022	+	0.00407778i
$375$	−10.2588	−	13.2255i	−0.529761	−	0.682962i
$376$	3.68973	−	3.09605i	0.190283	−	0.159667i
$377$	0.743757			0.0383054
$378$	−9.39444	+	10.0372i	−0.483198	+	0.516256i
$379$	−8.45188			−0.434144			−0.217072	−	0.976156i	$-0.569651\pi$
$379$	−8.45188			−0.434144			−0.217072	+	0.976156i	$0.569651\pi$
$380$	2.90178	−	2.43488i	0.148858	−	0.124907i
$381$	−11.0793	+	1.51769i	−0.567610	+	0.0777537i
$382$	0.894315	−	5.07191i	0.0457571	−	0.259502i
$383$	0.474442	−	2.69070i	0.0242429	−	0.137488i	−0.970284	−	0.241969i	$-0.922207\pi$
$383$	0.474442	−	2.69070i	0.0242429	−	0.137488i	0.994527	+	0.104480i	$0.0333180\pi$
$384$	1.69293	+	0.366023i	0.0863922	+	0.0186785i
$385$	0.472475	+	0.140006i	0.0240795	+	0.00713534i
$386$	−5.81845	−	10.0779i	−0.296151	−	0.512949i
$387$	−16.1029	−	1.23901i	−0.818558	−	0.0629825i
$388$	−2.28983	−	3.96611i	−0.116249	−	0.201349i
$389$	−1.76422	−	10.0054i	−0.0894495	−	0.507293i	−0.996307	−	0.0858568i	$-0.972637\pi$
$389$	−1.76422	−	10.0054i	−0.0894495	−	0.507293i	0.906858	−	0.421436i	$-0.138474\pi$
$390$	0.121044	−	3.15097i	0.00612931	−	0.159556i
$391$	0.256388	−	1.45405i	0.0129661	−	0.0735344i
$392$	0.367771	−	6.99033i	0.0185752	−	0.353065i
$393$	−11.9113	+	6.28014i	−0.600846	+	0.316791i
$394$	11.7155	+	4.26409i	0.590218	+	0.214822i
$395$	−1.33829	−	2.31799i	−0.0673368	−	0.116631i
$396$	−0.363208	−	0.355677i	−0.0182519	−	0.0178735i
$397$	−6.72384	+	11.6460i	−0.337460	+	0.584498i	−0.983954	−	0.178421i	$-0.942901\pi$
$397$	−6.72384	+	11.6460i	−0.337460	+	0.584498i	0.646494	+	0.762919i	$0.276234\pi$
$398$	−6.15666	−	2.24084i	−0.308606	−	0.112323i
$399$	5.73531	+	14.7147i	0.287125	+	0.736655i
$400$	−2.90473	−	2.43736i	−0.145237	−	0.121868i
$401$	2.79815	+	2.34793i	0.139733	+	0.117250i	0.709975	−	0.704227i	$-0.248706\pi$
$401$	2.79815	+	2.34793i	0.139733	+	0.117250i	−0.570242	+	0.821477i	$0.693151\pi$
$402$	8.79307	−	21.5468i	0.438558	−	1.07466i
$403$	−1.17850	−	0.428939i	−0.0587053	−	0.0213670i
$404$	8.85956	+	15.3452i	0.440780	+	0.763453i
$405$	9.77595	+	1.51334i	0.485771	+	0.0751987i
$406$	−0.655627	−	0.990764i	−0.0325382	−	0.0491708i
$407$	−0.0890712	−	0.505148i	−0.00441510	−	0.0250393i
$408$	−0.501668	−	0.646745i	−0.0248363	−	0.0320187i
$409$	5.88747	−	33.3895i	0.291117	−	1.65101i	−0.391463	−	0.920194i	$-0.628031\pi$
$409$	5.88747	−	33.3895i	0.291117	−	1.65101i	0.682579	−	0.730811i	$-0.260858\pi$
$410$	1.32824	−	0.483439i	0.0655970	−	0.0238754i
$411$	−10.6118	+	11.7032i	−0.523442	+	0.577278i
$412$	4.97210	+	1.80970i	0.244958	+	0.0891574i
$413$	10.1737	−	0.621212i	0.500614	−	0.0305679i
$414$	6.69692	+	6.55807i	0.329136	+	0.322312i
$415$	−14.7162			−0.722391
$416$	−0.287618	−	1.63116i	−0.0141016	−	0.0799743i
$417$	−0.933441	+	24.2990i	−0.0457108	+	1.18993i
$418$	−0.548763	+	0.199733i	−0.0268409	+	0.00976927i
$419$	2.40176	−	13.6211i	0.117334	−	0.665432i	−0.868235	−	0.496154i	$-0.834745\pi$
$419$	2.40176	−	13.6211i	0.117334	−	0.665432i	0.985568	−	0.169278i	$-0.0541437\pi$
$420$	−4.30414	+	2.61636i	−0.210020	+	0.127666i
$421$	5.63925	−	4.73189i	0.274840	−	0.230618i	−0.494940	−	0.868927i	$-0.664810\pi$
$421$	5.63925	−	4.73189i	0.274840	−	0.230618i	0.769781	+	0.638309i	$0.220366\pi$
$422$	−23.0138			−1.12029
$423$	8.16363	−	11.9227i	0.396929	−	0.579704i
$424$	−3.31728			−0.161101
$425$	0.311160	+	1.76467i	0.0150935	+	0.0855993i
$426$	−21.2998	−	4.60516i	−1.03198	−	0.223121i
$427$	−4.07818	+	35.7615i	−0.197357	+	1.73062i
$428$	−7.24873	+	2.63832i	−0.350381	+	0.127528i
$429$	−0.183680	+	0.450095i	−0.00886813	+	0.0217308i
$430$	−5.56045	−	2.02384i	−0.268149	−	0.0975982i
$431$	−5.43317	+	9.41053i	−0.261707	+	0.453289i	−0.966696	−	0.255929i	$-0.917619\pi$
$431$	−5.43317	+	9.41053i	−0.261707	+	0.453289i	0.704989	+	0.709218i	$0.250952\pi$
$432$	5.18701	−	0.308185i	0.249560	−	0.0148276i
$433$	10.2657			0.493337			0.246669	−	0.969100i	$-0.420664\pi$
$433$	10.2657			0.493337			0.246669	+	0.969100i	$0.420664\pi$
$434$	0.467465	+	1.94800i	0.0224390	+	0.0935070i
$435$	−0.323007	+	0.791508i	−0.0154870	+	0.0379499i
$436$	11.2788	+	9.46401i	0.540155	+	0.453244i
$437$	10.1182	−	3.68273i	0.484021	−	0.176169i
$438$	7.33352	+	22.8412i	0.350409	+	1.09139i
$439$	2.51830	+	14.2820i	0.120192	+	0.681642i	0.984048	+	0.177904i	$0.0569315\pi$
$439$	2.51830	+	14.2820i	0.120192	+	0.681642i	−0.863856	+	0.503739i	$0.831957\pi$
$440$	−0.0931270	−	0.161301i	−0.00443966	−	0.00768971i
$441$	−4.57690	−	20.4952i	−0.217948	−	0.975960i
$442$	−0.391360	+	0.677856i	−0.0186151	+	0.0322423i
$443$	25.2948	+	9.20656i	1.20179	+	0.437417i	0.863850	−	0.503750i	$-0.168047\pi$
$443$	25.2948	+	9.20656i	1.20179	+	0.437417i	0.337943	+	0.941167i	$0.390269\pi$
$444$	4.43660	+	2.79387i	0.210552	+	0.132591i
$445$	0.736520	+	0.618013i	0.0349144	+	0.0292966i
$446$	7.96272	−	2.89819i	0.377046	−	0.137233i
$447$	−1.26255	+	32.8662i	−0.0597166	+	1.55452i
$448$	−1.91935	+	1.82102i	−0.0906805	+	0.0860351i
$449$	−6.94314	+	12.0259i	−0.327667	+	0.567536i	−0.982048	−	0.188629i	$-0.939596\pi$
$449$	−6.94314	+	12.0259i	−0.327667	+	0.567536i	0.654382	+	0.756165i	$0.272929\pi$
$450$	−10.3596	−	4.69928i	−0.488355	−	0.221526i
$451$	−0.217911			−0.0102610
$452$	9.21111	−	7.72904i	0.433254	−	0.363543i
$453$	−16.9705	−	3.66913i	−0.797343	−	0.172391i
$454$	11.7184	+	9.83291i	0.549972	+	0.461481i
$455$	3.87168	+	2.86550i	0.181507	+	0.134337i
$456$	2.25538	−	5.52666i	0.105618	−	0.258810i
$457$	9.43905	−	7.92031i	0.441540	−	0.370496i	−0.394745	−	0.918791i	$-0.629167\pi$
$457$	9.43905	−	7.92031i	0.441540	−	0.370496i	0.836285	+	0.548294i	$0.184723\pi$
$458$	10.1551	−	17.5892i	0.474518	−	0.821890i
$459$	−1.97134	−	1.46403i	−0.0920141	−	0.0683351i
$460$	1.71710	+	2.97411i	0.0800602	+	0.138668i
$461$	−4.32477	−	24.5270i	−0.201424	−	1.14233i	−0.902968	−	0.429708i	$-0.858616\pi$
$461$	−4.32477	−	24.5270i	−0.201424	−	1.14233i	0.701543	−	0.712627i	$-0.252495\pi$
$462$	0.761489	−	0.152081i	0.0354277	−	0.00707546i
$463$	−18.9395	+	6.89342i	−0.880194	+	0.320364i	−0.742288	−	0.670081i	$-0.766259\pi$
$463$	−18.9395	+	6.89342i	−0.880194	+	0.320364i	−0.137906	+	0.990445i	$0.544037\pi$
$464$	−0.0779750	+	0.442218i	−0.00361990	+	0.0205295i
$465$	0.968290	−	1.06788i	0.0449034	−	0.0495216i
$466$	−20.0910	+	16.8583i	−0.930696	+	0.780946i
$467$	7.83352	−	13.5681i	0.362492	−	0.627855i	−0.625878	−	0.779921i	$-0.715259\pi$
$467$	7.83352	−	13.5681i	0.362492	−	0.627855i	0.988370	+	0.152066i	$0.0485927\pi$
$468$	−2.14704	−	4.48118i	−0.0992468	−	0.207143i
$469$	19.6175	+	29.6454i	0.905853	+	1.36890i
$470$	4.05558	−	3.40304i	0.187070	−	0.156970i
$471$	−0.855115	+	22.2600i	−0.0394016	+	1.02569i
$472$	−2.95115	−	2.47631i	−0.135838	−	0.113981i
$473$	0.698822	+	0.586381i	0.0321319	+	0.0269618i
$474$	−3.56905	−	2.24755i	−0.163932	−	0.103233i
$475$	−10.0105	+	8.39985i	−0.459316	+	0.385411i
$476$	1.24796	−	0.0762016i	0.0572003	−	0.00349269i
$477$	−9.58522	+	2.67627i	−0.438877	+	0.122538i
$478$	−0.269492	+	0.466773i	−0.0123263	+	0.0213497i
$479$	10.4074	−	8.73283i	0.475526	−	0.399013i	−0.373280	−	0.927719i	$-0.621767\pi$
$479$	10.4074	−	8.73283i	0.475526	−	0.399013i	0.848805	+	0.528705i	$0.177322\pi$
$480$	1.86080	+	0.402316i	0.0849333	+	0.0183631i
$481$	0.870635	−	4.93762i	0.0396975	−	0.225136i
$482$	−0.269342	+	0.0980323i	−0.0122682	+	0.00446525i
$483$	−14.0405	+	2.80411i	−0.638867	+	0.127592i
$484$	−1.90514	−	10.8046i	−0.0865974	−	0.491119i
$485$	−2.51688	−	4.35936i	−0.114286	−	0.197948i
$486$	14.7391	−	5.07520i	0.668581	−	0.230216i
$487$	0.510615	−	0.884411i	0.0231382	−	0.0400765i	−0.854224	−	0.519904i	$-0.825968\pi$
$487$	0.510615	−	0.884411i	0.0231382	−	0.0400765i	0.877363	+	0.479828i	$0.159301\pi$
$488$	10.4214	−	8.74459i	0.471754	−	0.395849i
$489$	−28.9021	+	3.95913i	−1.30700	+	0.179038i
$490$	0.404237	−	7.68345i	0.0182615	−	0.347103i
$491$	−28.8407	−	24.2002i	−1.30156	−	1.09214i	−0.989873	−	0.141958i	$-0.954660\pi$
$491$	−28.8407	−	24.2002i	−1.30156	−	1.09214i	−0.311691	−	0.950184i	$-0.600895\pi$
$492$	1.49617	−	1.65005i	0.0674525	−	0.0743899i
$493$	0.162555	−	0.136400i	0.00732110	−	0.00614313i
$494$	−5.70818			−0.256823
$495$	−0.399221	−	0.390944i	−0.0179437	−	0.0175716i
$496$	0.378589	−	0.655736i	0.0169992	−	0.0294434i
$497$	24.1485	−	22.9114i	1.08321	−	1.02772i
$498$	−20.5133	+	10.8155i	−0.919223	+	0.484653i
$499$	19.9089	−	7.24626i	0.891246	−	0.324387i	0.144507	−	0.989504i	$-0.453840\pi$
$499$	19.9089	−	7.24626i	0.891246	−	0.324387i	0.746740	+	0.665117i	$0.231618\pi$
$500$	−7.40276	−	6.21165i	−0.331061	−	0.277793i
$501$	30.1112	−	15.8759i	1.34527	−	0.709282i
$502$	−22.8658	−	8.32247i	−1.02055	−	0.371450i
$503$	19.9652	−	34.5807i	0.890202	−	1.54188i	0.0505696	−	0.998721i	$-0.483896\pi$
$503$	19.9652	−	34.5807i	0.890202	−	1.54188i	0.839633	−	0.543155i	$-0.182770\pi$
$504$	−4.07678	+	6.81028i	−0.181594	+	0.303354i
$505$	9.73803	+	16.8668i	0.433337	+	0.750561i
$506$	−0.0919357	−	0.521393i	−0.00408704	−	0.0231788i
$507$	11.9330	−	13.1604i	0.529965	−	0.584472i
$508$	−6.06701	+	2.20821i	−0.269180	+	0.0979735i
$509$	−2.10030	−	1.76236i	−0.0930942	−	0.0781153i	0.595053	−	0.803687i	$-0.297131\pi$
$509$	−2.10030	−	1.76236i	−0.0930942	−	0.0781153i	−0.688147	+	0.725571i	$0.741576\pi$
$510$	−0.551411	−	0.710873i	−0.0244169	−	0.0314780i
$511$	−35.1346	−	10.4112i	−1.55426	−	0.460565i
$512$	1.00000			0.0441942
$513$	2.05816	−	17.7888i	0.0908700	−	0.785394i
$514$	−5.21826	+	9.03829i	−0.230168	+	0.398662i
$515$	5.46511	+	1.98914i	0.240821	+	0.0876518i
$516$	−9.23824	+	1.26549i	−0.406691	+	0.0557103i
$517$	−0.766961	+	0.279151i	−0.0337309	+	0.0122771i
$518$	−7.34491	+	3.19277i	−0.322717	+	0.140282i
$519$	−18.3453	+	20.2321i	−0.805271	+	0.888093i
$520$	−0.316137	−	1.79290i	−0.0138635	−	0.0786238i
$521$	16.1921			0.709390			0.354695	−	0.934982i	$-0.384585\pi$
$521$	16.1921			0.709390			0.354695	+	0.934982i	$0.384585\pi$
$522$	0.131459	+	1.34069i	0.00575382	+	0.0586805i
$523$	−4.09141			−0.178905			−0.0894525	−	0.995991i	$-0.528512\pi$
$523$	−4.09141			−0.178905			−0.0894525	+	0.995991i	$0.528512\pi$
$524$	−5.95546	+	4.99722i	−0.260165	+	0.218305i
$525$	14.8484	−	9.02593i	0.648037	−	0.393924i
$526$	2.89112	−	16.3964i	0.126059	−	0.714916i
$527$	−0.336236	+	0.122380i	−0.0146467	+	0.00533096i
$528$	−0.248358	−	0.156399i	−0.0108084	−	0.00680638i
$529$	−2.29877	−	13.0370i	−0.0999467	−	0.566826i
$530$	−3.64620			−0.158381
$531$	−10.5251	−	4.77437i	−0.456751	−	0.207190i
$532$	5.03180	+	7.60390i	0.218156	+	0.329671i
$533$	−2.00154	−	0.728499i	−0.0866961	−	0.0315548i
$534$	1.48085	+	0.320170i	0.0640828	+	0.0138551i
$535$	−7.96747	+	2.89992i	−0.344464	+	0.125375i
$536$	2.33315	−	13.2319i	0.100777	−	0.571533i
$537$	−21.0929	+	2.88940i	−0.910227	+	0.124687i
$538$	4.59970	+	26.0862i	0.198307	+	1.12466i
$539$	−0.463693	+	1.09178i	−0.0199727	+	0.0470261i
$540$	5.70132	−	0.338743i	0.245346	−	0.0145772i
$541$	−6.03152	−	10.4469i	−0.259315	−	0.449148i	0.706743	−	0.707470i	$-0.250164\pi$
$541$	−6.03152	−	10.4469i	−0.259315	−	0.449148i	−0.966059	+	0.258323i	$0.916830\pi$
$542$	−10.7874	−	3.92631i	−0.463360	−	0.168649i
$543$	−32.4413	+	4.44395i	−1.39219	+	0.190708i
$544$	−0.362005	−	0.303758i	−0.0155208	−	0.0130235i
$545$	12.3971	+	10.4024i	0.531034	+	0.445590i
$546$	7.50279	+	1.14886i	0.321090	+	0.0491666i
$547$	−16.1406	−	5.87469i	−0.690121	−	0.251184i	−0.0269342	−	0.999637i	$-0.508574\pi$
$547$	−16.1406	−	5.87469i	−0.690121	−	0.251184i	−0.663187	+	0.748454i	$0.730797\pi$
$548$	−4.56048	+	7.89899i	−0.194814	+	0.337428i
$549$	23.0576	−	33.6750i	0.984076	−	1.43721i
$550$	0.321269	+	0.556455i	0.0136990	+	0.0237273i
$551$	1.45420	+	0.529284i	0.0619508	+	0.0225482i
$552$	4.57928	+	2.88372i	0.194907	+	0.122739i
$553$	5.90865	−	2.56844i	0.251261	−	0.109221i
$554$	2.90525	−	16.4765i	0.123432	−	0.700019i
$555$	4.87651	+	3.07090i	0.206996	+	0.130352i
$556$	2.43791	+	13.8261i	0.103390	+	0.586356i
$557$	11.6859	+	20.2406i	0.495149	+	0.857623i	0.999984	−	0.00559258i	$-0.00178018\pi$
$557$	11.6859	+	20.2406i	0.495149	+	0.857623i	−0.504835	+	0.863216i	$0.668447\pi$
$558$	0.564902	−	2.20017i	0.0239142	−	0.0931407i
$559$	4.45842	+	7.72222i	0.188571	+	0.326615i
$560$	−2.10966	+	2.00158i	−0.0891493	+	0.0845823i
$561$	0.0423993	+	0.132058i	0.00179010	+	0.00557549i
$562$	−4.88963	+	27.7305i	−0.206257	+	1.16974i
$563$	6.29581	−	35.7053i	0.265337	−	1.50480i	−0.502738	−	0.864439i	$-0.667674\pi$
$563$	6.29581	−	35.7053i	0.265337	−	1.50480i	0.768074	−	0.640361i	$-0.221215\pi$
$564$	3.15216	−	7.72417i	0.132730	−	0.325246i
$565$	10.1244	−	8.49541i	0.425938	−	0.357404i
$566$	7.66284			0.322093
$567$	−6.28549	+	22.9672i	−0.263966	+	0.964532i
$568$	−12.5816			−0.527913
$569$	17.5116	−	14.6939i	0.734123	−	0.616002i	−0.197129	−	0.980377i	$-0.563162\pi$
$569$	17.5116	−	14.6939i	0.734123	−	0.616002i	0.931252	+	0.364375i	$0.118717\pi$
$570$	2.47901	−	6.07465i	0.103834	−	0.254439i
$571$	6.53591	−	37.0670i	0.273519	−	1.55121i	−0.470106	−	0.882610i	$-0.655784\pi$
$571$	6.53591	−	37.0670i	0.273519	−	1.55121i	0.743626	−	0.668596i	$-0.233104\pi$
$572$	−0.0487375	+	0.276404i	−0.00203782	+	0.0115570i
$573$	−2.72691	−	8.49330i	−0.113918	−	0.354813i
$574$	0.793930	+	3.30844i	0.0331380	+	0.138091i
$575$	−5.92365	−	10.2601i	−0.247033	−	0.427874i
$576$	2.88949	−	0.806767i	0.120395	−	0.0336153i
$577$	−19.3498	−	33.5149i	−0.805543	−	1.39524i	−0.915924	−	0.401352i	$-0.868540\pi$
$577$	−19.3498	−	33.5149i	−0.805543	−	1.39524i	0.110381	−	0.993889i	$-0.464793\pi$
$578$	−2.91324	−	16.5218i	−0.121175	−	0.687217i
$579$	−17.0556	−	10.7405i	−0.708808	−	0.446359i
$580$	−0.0857066	+	0.486066i	−0.00355877	+	0.0201828i
$581$	4.01358	−	35.1950i	0.166511	−	1.46014i
$582$	−6.71219	−	4.22688i	−0.278229	−	0.175210i
$583$	0.528219	+	0.192256i	0.0218766	+	0.00796243i
$584$	6.92519	+	11.9948i	0.286566	+	0.496347i
$585$	−2.35992	−	4.92551i	−0.0975708	−	0.203645i
$586$	7.33595	−	12.7062i	0.303045	−	0.524890i
$587$	17.1717	+	6.24998i	0.708752	+	0.257964i	0.671143	−	0.741328i	$-0.265804\pi$
$587$	17.1717	+	6.24998i	0.708752	+	0.257964i	0.0376087	+	0.999293i	$0.488026\pi$
$588$	−5.08337	−	11.0072i	−0.209634	−	0.453931i
$589$	−1.99896	−	1.67733i	−0.0823656	−	0.0691130i
$590$	−3.24377	−	2.72184i	−0.133544	−	0.112057i
$591$	21.3943	−	2.93068i	0.880045	−	0.120552i
$592$	2.84450	+	1.03531i	0.116908	+	0.0425511i
$593$	−5.46834	−	9.47145i	−0.224558	−	0.388946i	0.731629	−	0.681703i	$-0.238760\pi$
$593$	−5.46834	−	9.47145i	−0.224558	−	0.388946i	−0.956187	+	0.292757i	$0.905427\pi$
$594$	−0.843803	−	0.251545i	−0.0346217	−	0.0103210i
$595$	1.37170	−	0.0837573i	0.0562344	−	0.00343371i
$596$	3.29746	+	18.7008i	0.135069	+	0.766016i
$597$	−11.2430	+	1.54012i	−0.460147	+	0.0630328i
$598$	0.898634	−	5.09641i	0.0367479	−	0.208408i
$599$	−36.7879	+	13.3897i	−1.50311	+	0.547088i	−0.956864	−	0.290536i	$-0.906166\pi$
$599$	−36.7879	+	13.3897i	−1.50311	+	0.547088i	−0.546247	+	0.837624i	$0.683944\pi$
$600$	−6.41937	−	1.38791i	−0.262070	−	0.0566611i
$601$	6.55427	+	2.38556i	0.267354	+	0.0973090i	0.472219	−	0.881481i	$-0.343453\pi$
$601$	6.55427	+	2.38556i	0.267354	+	0.0973090i	−0.204865	+	0.978790i	$0.565675\pi$
$602$	6.35668	−	12.7463i	0.259079	−	0.519500i
$603$	−3.93350	−	40.1158i	−0.160184	−	1.63364i
$604$	−10.0243			−0.407883
$605$	−2.09405	−	11.8759i	−0.0851351	−	0.482825i
$606$	25.9701	+	16.3542i	1.05496	+	0.664343i
$607$	2.11335	−	0.769196i	0.0857782	−	0.0312207i	−0.298775	−	0.954324i	$-0.596578\pi$
$607$	2.11335	−	0.769196i	0.0857782	−	0.0312207i	0.384553	+	0.923103i	$0.374356\pi$
$608$	0.598442	−	3.39393i	0.0242700	−	0.137642i
$609$	−1.80486	−	0.988366i	−0.0731365	−	0.0400506i
$610$	11.4547	−	9.61165i	0.463788	−	0.389165i
$611$	−7.97786			−0.322750
$612$	−1.29107	−	0.585652i	−0.0521884	−	0.0236736i
$613$	47.1138			1.90291			0.951455	−	0.307789i	$-0.0995891\pi$
$613$	47.1138			1.90291			0.951455	+	0.307789i	$0.0995891\pi$
$614$	0.372378	+	2.11186i	0.0150280	+	0.0852277i
$615$	1.64452	−	1.81366i	0.0663134	−	0.0731337i
$616$	0.411162	−	0.178729i	0.0165662	−	0.00720118i
$617$	5.22382	−	1.90131i	0.210303	−	0.0765440i	−0.234721	−	0.972063i	$-0.575418\pi$
$617$	5.22382	−	1.90131i	0.210303	−	0.0765440i	0.445024	+	0.895519i	$0.353195\pi$
$618$	9.07983	−	1.24379i	0.365244	−	0.0500327i
$619$	−1.04942	−	0.381956i	−0.0421796	−	0.0153521i	0.320844	−	0.947132i	$-0.396033\pi$
$619$	−1.04942	−	0.381956i	−0.0421796	−	0.0153521i	−0.363024	+	0.931780i	$0.618256\pi$
$620$	0.416128	−	0.720755i	0.0167121	−	0.0289462i
$621$	15.5583	+	4.63805i	0.624332	+	0.186119i
$622$	32.7046			1.31133
$623$	−1.67890	+	1.59289i	−0.0672637	+	0.0638179i
$624$	−1.75834	−	2.26683i	−0.0703898	−	0.0907457i
$625$	6.38689	+	5.35924i	0.255476	+	0.214370i
$626$	9.12862	−	3.32255i	0.364853	−	0.132796i
$627$	−0.679434	+	0.749313i	−0.0271340	+	0.0299247i
$628$	2.23334	+	12.6659i	0.0891201	+	0.505425i
$629$	−0.715239	−	1.23883i	−0.0285184	−	0.0493954i
$630$	−4.48101	+	7.48554i	−0.178528	+	0.298231i
$631$	5.46231	−	9.46100i	0.217451	−	0.376636i	−0.736577	−	0.676354i	$-0.763559\pi$
$631$	5.46231	−	9.46100i	0.217451	−	0.376636i	0.954028	+	0.299717i	$0.0968924\pi$
$632$	−2.28827	−	0.832864i	−0.0910227	−	0.0331295i
$633$	−35.2603	+	18.5907i	−1.40147	+	0.738914i
$634$	16.4989	+	13.8442i	0.655253	+	0.549823i
$635$	−6.66858	+	2.42717i	−0.264635	+	0.0963191i
$636$	−5.08252	+	2.67972i	−0.201535	+	0.106258i
$637$	−7.90900	+	8.47792i	−0.313366	+	0.335907i
$638$	0.0380454	−	0.0658966i	0.00150623	−	0.00260887i
$639$	−36.3544	+	10.1504i	−1.43816	+	0.401545i
$640$	1.09915			0.0434479
$641$	9.43929	−	7.92050i	0.372829	−	0.312841i	−0.437050	−	0.899437i	$-0.643977\pi$
$641$	9.43929	−	7.92050i	0.372829	−	0.312841i	0.809880	+	0.586596i	$0.199532\pi$
$642$	−8.97480	+	9.89785i	−0.354207	+	0.390637i
$643$	−16.1026	−	13.5117i	−0.635025	−	0.532849i	0.267461	−	0.963569i	$-0.413815\pi$
$643$	−16.1026	−	13.5117i	−0.635025	−	0.532849i	−0.902486	+	0.430720i	$0.858260\pi$
$644$	−7.58111	+	3.29545i	−0.298738	+	0.129859i
$645$	−10.1543	+	1.39097i	−0.399823	+	0.0547695i
$646$	−1.24757	+	1.04684i	−0.0490852	+	0.0411873i
$647$	−11.3848	+	19.7191i	−0.447584	+	0.775238i	−0.998228	−	0.0595021i	$-0.981049\pi$
$647$	−11.3848	+	19.7191i	−0.447584	+	0.775238i	0.550644	+	0.834740i	$0.314382\pi$
$648$	7.69825	−	4.66228i	0.302416	−	0.183152i
$649$	0.326403	+	0.565346i	0.0128124	+	0.0221918i
$650$	1.09061	+	6.18514i	0.0427771	+	0.242601i
$651$	2.28983	+	2.60699i	0.0897455	+	0.102176i
$652$	−15.8267	+	5.76046i	−0.619823	+	0.225597i
$653$	6.99841	−	39.6900i	0.273869	−	1.55319i	−0.468663	−	0.883377i	$-0.655264\pi$
$653$	6.99841	−	39.6900i	0.273869	−	1.55319i	0.742532	−	0.669811i	$-0.233625\pi$
$654$	24.9257	+	5.38910i	0.974673	+	0.210730i
$655$	−6.54597	+	5.49272i	−0.255772	+	0.214618i
$656$	0.642986	−	1.11368i	0.0251044	−	0.0434821i
$657$	29.6872	+	29.0717i	1.15821	+	1.13420i
$658$	7.03255	+	10.6274i	0.274157	+	0.414298i
$659$	−1.50385	+	1.26188i	−0.0585815	+	0.0491557i	−0.671608	−	0.740906i	$-0.734396\pi$
$659$	−1.50385	+	1.26188i	−0.0585815	+	0.0491557i	0.613027	+	0.790062i	$0.289952\pi$
$660$	−0.272983	−	0.171906i	−0.0106259	−	0.00669144i
$661$	−10.0316	−	8.41748i	−0.390182	−	0.327402i	0.426502	−	0.904487i	$-0.359746\pi$
$661$	−10.0316	−	8.41748i	−0.390182	−	0.327402i	−0.816684	+	0.577085i	$0.804190\pi$
$662$	−19.9460	−	16.7367i	−0.775223	−	0.650489i
$663$	−0.0520410	+	1.35471i	−0.00202111	+	0.0526126i
$664$	−10.2563	+	8.60608i	−0.398023	+	0.333981i
$665$	5.53073	+	8.35786i	0.214472	+	0.324104i
$666$	9.05440	+	0.696675i	0.350851	+	0.0269956i
$667$	−0.701491	+	1.21502i	−0.0271618	+	0.0470457i
$668$	15.0551	−	12.6327i	0.582500	−	0.488776i
$669$	9.85881	−	10.8728i	0.381163	−	0.420366i
$670$	2.56449	−	14.5439i	0.0990749	−	0.561882i
$671$	−2.16623	+	0.788444i	−0.0836264	+	0.0304375i
$672$	−1.46967	+	4.34052i	−0.0566937	+	0.167439i
$673$	4.13347	+	23.4421i	0.159333	+	0.903625i	0.954716	+	0.297518i	$0.0961587\pi$
$673$	4.13347	+	23.4421i	0.159333	+	0.903625i	−0.795383	+	0.606107i	$0.792730\pi$
$674$	−3.69348	−	6.39729i	−0.142268	−	0.246415i
$675$	−19.6684	+	1.16859i	−0.757037	+	0.0449792i
$676$	5.12829	−	8.88246i	0.197242	−	0.341633i
$677$	−23.7696	+	19.9451i	−0.913542	+	0.766553i	−0.972789	−	0.231691i	$-0.925574\pi$
$677$	−23.7696	+	19.9451i	−0.913542	+	0.766553i	0.0592478	+	0.998243i	$0.481130\pi$
$678$	7.86912	−	19.2828i	0.302212	−	0.740550i
$679$	11.1122	−	4.83038i	0.426447	−	0.185373i
$680$	−0.397899	−	0.333877i	−0.0152587	−	0.0128036i
$681$	25.8973	+	5.59916i	0.992387	+	0.214560i
$682$	−0.0982877	+	0.0824731i	−0.00376363	+	0.00315806i
$683$	33.6593			1.28794			0.643969	−	0.765052i	$-0.277287\pi$
$683$	33.6593			1.28794			0.643969	+	0.765052i	$0.277287\pi$
$684$	−1.00892	−	10.2895i	−0.0385771	−	0.393430i
$685$	−5.01268	+	8.68221i	−0.191524	+	0.331730i
$686$	18.2653	+	3.06229i	0.697374	+	0.116919i
$687$	1.35038	−	35.1525i	0.0515201	−	1.34115i
$688$	−5.05885	+	1.84127i	−0.192867	+	0.0701977i
$689$	4.20902	+	3.53179i	0.160351	+	0.134550i
$690$	5.03334	+	3.16965i	0.191616	+	0.120667i
$691$	−2.32289	−	0.845463i	−0.0883669	−	0.0321629i	0.297458	−	0.954735i	$-0.403861\pi$
$691$	−2.32289	−	0.845463i	−0.0883669	−	0.0321629i	−0.385825	+	0.922572i	$0.626083\pi$
$692$	−7.88401	+	13.6555i	−0.299705	+	0.519104i
$693$	1.04385	−	0.848146i	0.0396527	−	0.0322184i
$694$	16.8193	+	29.1319i	0.638453	+	1.10583i
$695$	2.67964	+	15.1970i	0.101645	+	0.576455i
$696$	0.237759	+	0.740528i	0.00901222	+	0.0280697i
$697$	−0.571055	+	0.207847i	−0.0216303	+	0.00787277i
$698$	16.3286	+	13.7014i	0.618048	+	0.518604i
$699$	−17.1638	+	42.0589i	−0.649196	+	1.59081i
$700$	7.27789	−	6.90505i	0.275078	−	0.260986i
$701$	−27.5480			−1.04047			−0.520237	−	0.854022i	$-0.674157\pi$
$701$	−27.5480			−1.04047			−0.520237	+	0.854022i	$0.674157\pi$
$702$	−6.90949	−	5.13140i	−0.260782	−	0.193672i
$703$	5.21605	−	9.03447i	0.196727	−	0.340741i
$704$	−0.159233	−	0.0579560i	−0.00600132	−	0.00218430i
$705$	3.46471	−	8.49005i	0.130489	−	0.319754i
$706$	19.5561	−	7.11783i	0.736003	−	0.267883i
$707$	−42.9940	+	18.6892i	−1.61696	+	0.702878i
$708$	−6.52195	−	1.41009i	−0.245110	−	0.0529943i
$709$	0.962473	+	5.45846i	0.0361464	+	0.204997i	0.997532	−	0.0702068i	$-0.0223659\pi$
$709$	0.962473	+	5.45846i	0.0361464	+	0.204997i	−0.961386	+	0.275203i	$0.911255\pi$
$710$	−13.8291			−0.518998
$711$	−7.28386	−	0.560444i	−0.273166	−	0.0210183i
$712$	0.874725			0.0327817
$713$	1.81225	−	1.52066i	0.0678694	−	0.0569492i
$714$	1.85050	−	1.12486i	0.0692530	−	0.0420970i
$715$	−0.0535700	+	0.303811i	−0.00200340	+	0.0113619i
$716$	−11.5505	+	4.20402i	−0.431661	+	0.157112i
$717$	−0.0358356	+	0.932858i	−0.00133830	+	0.0348382i
$718$	4.05334	+	22.9877i	0.151269	+	0.857892i
$719$	25.5408			0.952510			0.476255	−	0.879307i	$-0.341994\pi$
$719$	25.5408			0.952510			0.476255	+	0.879307i	$0.341994\pi$
$720$	3.17599	−	0.886761i	0.118362	−	0.0330476i
$721$	−6.24768	+	12.5277i	−0.232676	+	0.466557i
$722$	6.69352	+	2.43624i	0.249107	+	0.0906675i
$723$	−0.333477	+	0.367775i	−0.0124022	+	0.0136777i
$724$	−17.7648	+	6.46586i	−0.660224	+	0.240302i
$725$	0.295670	−	1.67683i	0.0109809	−	0.0622759i
$726$	−11.6470	−	15.0152i	−0.432260	−	0.557265i
$727$	4.70090	+	26.6601i	0.174347	+	0.988770i	0.938895	+	0.344204i	$0.111851\pi$
$727$	4.70090	+	26.6601i	0.174347	+	0.988770i	−0.764548	+	0.644567i	$0.777038\pi$
$728$	4.37408	−	0.267085i	0.162114	−	0.00989881i
$729$	18.4826	−	19.6823i	0.684541	−	0.728974i
$730$	7.61185	+	13.1841i	0.281727	+	0.487966i
$731$	2.39063	+	0.870118i	0.0884206	+	0.0321825i
$732$	8.90308	−	21.8164i	0.329067	−	0.806357i
$733$	−16.6324	−	13.9562i	−0.614332	−	0.515486i	0.281684	−	0.959507i	$-0.409107\pi$
$733$	−16.6324	−	13.9562i	−0.614332	−	0.515486i	−0.896016	+	0.444021i	$0.853551\pi$
$734$	6.00363	+	5.03764i	0.221598	+	0.185943i
$735$	−5.58740	−	12.0987i	−0.206095	−	0.446266i
$736$	2.93598	+	1.06861i	0.108222	+	0.0393894i
$737$	−1.13839	+	1.97174i	−0.0419330	+	0.0726300i
$738$	0.959415	−	3.73672i	0.0353166	−	0.137550i
$739$	−2.49374	−	4.31928i	−0.0917336	−	0.158887i	0.816507	−	0.577335i	$-0.195907\pi$
$739$	−2.49374	−	4.31928i	−0.0917336	−	0.158887i	−0.908241	+	0.418448i	$0.862574\pi$
$740$	3.12655	+	1.13797i	0.114934	+	0.0418326i
$741$	−8.74572	+	4.61111i	−0.321282	+	0.169393i
$742$	0.994434	−	8.72017i	0.0365068	−	0.320127i
$743$	3.58890	−	20.3536i	0.131664	−	0.746703i	−0.845461	−	0.534037i	$-0.820674\pi$
$743$	3.58890	−	20.3536i	0.131664	−	0.746703i	0.977125	−	0.212666i	$-0.0682146\pi$
$744$	0.0503428	−	1.31050i	0.00184566	−	0.0480454i
$745$	3.62442	+	20.5551i	0.132788	+	0.753081i
$746$	12.1625	+	21.0661i	0.445302	+	0.771285i
$747$	−22.6924	+	33.1416i	−0.830272	+	1.21259i
$748$	0.0400385	+	0.0693487i	0.00146395	+	0.00253564i
$749$	−4.76241	−	19.8457i	−0.174015	−	0.725148i
$750$	−16.3599	−	3.53710i	−0.597378	−	0.129157i
$751$	−6.34750	+	35.9985i	−0.231624	+	1.31360i	0.617985	+	0.786190i	$0.287949\pi$
$751$	−6.34750	+	35.9985i	−0.231624	+	1.31360i	−0.849609	+	0.527413i	$0.823162\pi$
$752$	0.836394	−	4.74343i	0.0305001	−	0.172975i
$753$	−41.7565	+	5.71999i	−1.52169	+	0.208448i
$754$	0.569751	−	0.478078i	0.0207491	−	0.0174106i
$755$	−11.0183			−0.400996
$756$	−0.744801	+	13.7275i	−0.0270881	+	0.499266i
$757$	17.3561			0.630816			0.315408	−	0.948956i	$-0.397859\pi$
$757$	17.3561			0.630816			0.315408	+	0.948956i	$0.397859\pi$
$758$	−6.47451	+	5.43276i	−0.235165	+	0.197327i
$759$	−0.562044	−	0.724580i	−0.0204009	−	0.0263006i
$760$	0.657780	−	3.73046i	0.0238602	−	0.135318i
$761$	−0.579134	+	3.28443i	−0.0209936	+	0.119061i	−0.993504	−	0.113800i	$-0.963698\pi$
$761$	−0.579134	+	3.28443i	−0.0209936	+	0.119061i	0.972510	+	0.232861i	$0.0748087\pi$
$762$	−7.51169	+	8.28426i	−0.272120	+	0.300107i
$763$	−28.2592	+	26.8116i	−1.02305	+	0.970644i
$764$	−2.57508	−	4.46016i	−0.0931630	−	0.161363i
$765$	−1.41909	−	0.643722i	−0.0513072	−	0.0232738i
$766$	−1.36610	−	2.36616i	−0.0493593	−	0.0854928i
$767$	1.10803	+	6.28397i	0.0400088	+	0.226901i
$768$	1.53214	−	0.807807i	0.0552863	−	0.0291492i
$769$

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.654437 - 1.60366i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.190866 - 1.08246i) q^{5} +(-0.529482 - 1.64914i) q^{6} +(2.53672 + 0.751691i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.14342 - 2.09898i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.654437 - 1.60366i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.190866 - 1.08246i) q^{5} +(-0.529482 - 1.64914i) q^{6} +(2.53672 + 0.751691i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.14342 - 2.09898i) q^{9} +(-0.549577 - 0.951896i) q^{10} +(0.0294251 + 0.166878i) q^{11} +(-1.46565 - 0.922967i) q^{12} +(-0.287618 + 1.63116i) q^{13} +(2.42642 - 1.05474i) q^{14} +(-1.61098 - 1.01448i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.236282 + 0.409253i) q^{17} +(-2.99116 - 0.230149i) q^{18} +(-1.72314 + 2.98457i) q^{19} +(-1.03287 - 0.375933i) q^{20} +(2.86558 - 3.57609i) q^{21} +(0.129808 + 0.108922i) q^{22} +(-2.39343 - 2.00833i) q^{23} +(-1.71603 + 0.235068i) q^{24} +(3.56318 + 1.29689i) q^{25} +(0.828163 + 1.43442i) q^{26} +(-4.76878 + 2.06366i) q^{27} +(1.18077 - 2.36765i) q^{28} +(-0.0779750 - 0.442218i) q^{29} +(-1.88618 + 0.258377i) q^{30} +(-0.131483 + 0.745675i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.286871 + 0.0620234i) q^{33} +(0.444065 + 0.161626i) q^{34} +(1.29785 - 2.60242i) q^{35} +(-2.43930 + 1.74638i) q^{36} -3.02705 q^{37} +(0.598442 + 3.39393i) q^{38} +(2.42760 + 1.52873i) q^{39} +(-1.03287 + 0.375933i) q^{40} +(-0.223307 + 1.26644i) q^{41} +(-0.103507 - 4.58141i) q^{42} +(4.12401 - 3.46045i) q^{43} +0.169452 q^{44} +(-2.68116 + 1.91954i) q^{45} -3.12440 q^{46} +(0.836394 + 4.74343i) q^{47} +(-1.16345 + 1.28311i) q^{48} +(5.86992 + 3.81366i) q^{49} +(3.56318 - 1.29689i) q^{50} +(0.810932 - 0.111085i) q^{51} +(1.55644 + 0.566497i) q^{52} +(1.65864 - 2.87284i) q^{53} +(-2.32661 + 4.64617i) q^{54} +0.186254 q^{55} +(-0.617377 - 2.57271i) q^{56} +(3.65854 + 4.71655i) q^{57} +(-0.343985 - 0.288637i) q^{58} +(3.62012 - 1.31762i) q^{59} +(-1.27881 + 1.41034i) q^{60} +(2.36234 + 13.3975i) q^{61} +(0.378589 + 0.655736i) q^{62} +(-3.85948 - 6.93573i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.71076 + 0.622667i) q^{65} +(0.259624 - 0.136885i) q^{66} +(10.2926 + 8.63654i) q^{67} +(0.444065 - 0.161626i) q^{68} +(-4.78702 + 2.52392i) q^{69} +(-0.678593 - 2.82781i) q^{70} +(6.29081 - 10.8960i) q^{71} +(-0.746062 + 2.90575i) q^{72} -13.8504 q^{73} +(-2.31886 + 1.94575i) q^{74} +(4.41165 - 4.86538i) q^{75} +(2.64001 + 2.21523i) q^{76} +(-0.0507974 + 0.445441i) q^{77} +(2.84230 - 0.389350i) q^{78} +(1.86542 - 1.56527i) q^{79} +(-0.549577 + 0.951896i) q^{80} +(0.188528 + 8.99803i) q^{81} +(0.642986 + 1.11368i) q^{82} +(-2.32492 - 13.1853i) q^{83} +(-3.02416 - 3.44303i) q^{84} +(0.488096 - 0.177652i) q^{85} +(0.934837 - 5.30172i) q^{86} +(-0.760196 - 0.164359i) q^{87} +(0.129808 - 0.108922i) q^{88} +(-0.437363 + 0.757534i) q^{89} +(-0.820037 + 3.19387i) q^{90} +(-1.95574 + 3.92161i) q^{91} +(-2.39343 + 2.00833i) q^{92} +(1.10976 + 0.698850i) q^{93} +(3.68973 + 3.09605i) q^{94} +(2.90178 + 2.43488i) q^{95} +(-0.0664874 + 1.73077i) q^{96} +(3.50823 - 2.94375i) q^{97} +(6.94800 - 0.851675i) q^{98} +(0.287203 - 0.419452i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

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