LMFDB - Embedded newform 378.2.v.b.79.8

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			79.8
Character	$\chi$	$=$	378.79
Dual form			378.2.v.b.67.8

$q$-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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$

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	0.997279	+	0.0737228i	$0.0234880\pi$
$5$	0.190866	+	1.08246i	0.0853579	+	0.484089i	−0.911921	+	0.410366i	$0.865401\pi$
$6$	−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	−0.980050	−	0.198749i	$-0.936312\pi$
$11$	0.0294251	−	0.166878i	0.00887199	−	0.0503155i	0.988922	+	0.148434i	$0.0474232\pi$
$12$	−1.46565	+	0.922967i	−0.423097	+	0.266438i
$13$	−0.287618	−	1.63116i	−0.0797709	−	0.452403i	−0.998363	−	0.0571961i	$-0.981784\pi$
$13$	−0.287618	−	1.63116i	−0.0797709	−	0.452403i	0.918592	−	0.395207i	$-0.129327\pi$
$14$	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	−0.835949	−	0.548807i	$-0.815082\pi$
$17$	0.236282	−	0.409253i	0.0573068	−	0.0992583i	0.893256	+	0.449549i	$0.148415\pi$
$18$	−2.99116	+	0.230149i	−0.705023	+	0.0542467i
$19$	−1.72314	−	2.98457i	−0.395316	−	0.684708i	0.597825	−	0.801627i	$-0.296032\pi$
$19$	−1.72314	−	2.98457i	−0.395316	−	0.684708i	−0.993142	+	0.116918i	$0.962698\pi$
$20$	−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	−0.857262	−	0.514881i	$-0.827836\pi$
$23$	−2.39343	+	2.00833i	−0.499065	+	0.418765i	0.358197	+	0.933646i	$0.383392\pi$
$24$	−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	−0.991191	−	0.132438i	$-0.957719\pi$
$29$	−0.0779750	+	0.442218i	−0.0144796	+	0.0821179i	0.976712	+	0.214556i	$0.0688305\pi$
$30$	−1.88618	−	0.258377i	−0.344367	−	0.0471729i
$31$	−0.131483	−	0.745675i	−0.0236150	−	0.133927i	0.970721	−	0.240210i	$-0.0772163\pi$
$31$	−0.131483	−	0.745675i	−0.0236150	−	0.133927i	−0.994336	+	0.106283i	$0.966105\pi$
$32$	−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	0.962393	−	0.271662i	$-0.0875734\pi$
$41$	−0.223307	−	1.26644i	−0.0348747	−	0.197784i	−0.997267	+	0.0738784i	$0.976462\pi$
$42$	−0.103507	+	4.58141i	−0.0159715	+	0.706926i
$43$	4.12401	+	3.46045i	0.628905	+	0.527714i	0.900589	−	0.434672i	$-0.143136\pi$
$43$	4.12401	+	3.46045i	0.628905	+	0.527714i	−0.271683	+	0.962387i	$0.587580\pi$
$44$	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	−0.861044	−	0.508531i	$-0.830189\pi$
$47$	0.836394	−	4.74343i	0.122001	−	0.691900i	0.983044	−	0.183369i	$-0.0587002\pi$
$48$	−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	0.957165	−	0.289543i	$-0.0935032\pi$
$53$	1.65864	+	2.87284i	0.227831	+	0.394616i	−0.729334	+	0.684158i	$0.760170\pi$
$54$	−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	0.566741	−	0.823896i	$-0.308204\pi$
$59$	3.62012	+	1.31762i	0.471299	+	0.171539i	−0.0954415	+	0.995435i	$0.530426\pi$
$60$	−1.27881	−	1.41034i	−0.165094	−	0.182074i
$61$	2.36234	−	13.3975i	0.302467	−	1.71537i	−0.332730	−	0.943022i	$-0.607970\pi$
$61$	2.36234	−	13.3975i	0.302467	−	1.71537i	0.635196	−	0.772351i	$-0.280919\pi$
$62$	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	0.261495	−	0.965205i	$-0.415785\pi$
$67$	10.2926	−	8.63654i	1.25744	−	1.05512i	0.995949	−	0.0899162i	$-0.0286599\pi$
$68$	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	0.949452	+	0.313911i	$0.101639\pi$
$71$	6.29081	+	10.8960i	0.746581	+	1.29312i	−0.202871	+	0.979205i	$0.565027\pi$
$72$	−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	0.741666	−	0.670769i	$-0.234036\pi$
$79$	1.86542	+	1.56527i	0.209876	+	0.176107i	−0.531790	+	0.846876i	$0.678480\pi$
$80$	−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	0.540383	+	0.841419i	$0.318279\pi$
$83$	−2.32492	+	13.1853i	−0.255193	+	1.44727i	−0.795576	+	0.605853i	$0.792832\pi$
$84$	−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	0.841914	−	0.539612i	$-0.181429\pi$
$89$	−0.437363	−	0.757534i	−0.0463603	−	0.0802985i	−0.888274	+	0.459313i	$0.848096\pi$
$90$	−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	0.803277	−	0.595606i	$-0.203088\pi$
$97$	3.50823	+	2.94375i	0.356207	+	0.298893i	−0.447070	+	0.894499i	$0.647533\pi$
$98$	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	−0.978756	−	0.205027i	$-0.934272\pi$
$101$	−13.5736	−	11.3896i	−1.35063	−	1.13331i	−0.371871	−	0.928284i	$-0.621284\pi$
$102$	0.549806	+	0.606353i	0.0544389	+	0.0600379i
$103$	−0.918807	−	5.21081i	−0.0905328	−	0.513437i	−0.996025	−	0.0890740i	$-0.971609\pi$
$103$	−0.918807	−	5.21081i	−0.0905328	−	0.513437i	0.905492	−	0.424363i	$-0.139502\pi$
$104$	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	−0.990005	−	0.141030i	$-0.954959\pi$
$107$	−3.85697	+	6.68047i	−0.372867	+	0.645825i	0.617138	+	0.786855i	$0.288292\pi$
$108$	1.20422	−	5.05469i	0.115876	−	0.486387i
$109$	−7.36169	−	12.7508i	−0.705122	−	1.22131i	−0.966647	−	0.256111i	$-0.917559\pi$
$109$	−7.36169	−	12.7508i	−0.705122	−	1.22131i	0.261525	−	0.965197i	$-0.415774\pi$
$110$	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	−0.0968515	−	0.995299i	$-0.530877\pi$
$113$	9.21111	−	7.72904i	0.866508	−	0.727087i	0.963360	+	0.268212i	$0.0864327\pi$
$114$	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	−0.972961	−	0.230969i	$-0.925810\pi$
$127$	−3.22819	+	5.59139i	−0.286455	+	0.496155i	0.686506	+	0.727125i	$0.259144\pi$
$128$	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	−0.864747	−	0.502208i	$-0.832521\pi$
$131$	−5.95546	+	4.99722i	−0.520331	+	0.436609i	0.344416	+	0.938817i	$0.388077\pi$
$132$	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	−0.681122	−	0.732170i	$-0.738508\pi$
$137$	−8.57091	+	3.11955i	−0.732262	+	0.266522i	−0.0511399	+	0.998691i	$0.516285\pi$
$138$	−2.04473	−	5.01047i	−0.174059	−	0.426519i
$139$	−13.1927	−	4.80175i	−1.11899	−	0.407279i	−0.284706	−	0.958615i	$-0.591896\pi$
$139$	−13.1927	−	4.80175i	−1.11899	−	0.407279i	−0.834283	+	0.551336i	$0.814118\pi$
$140$	−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	−0.515974	−	0.856604i	$-0.672570\pi$
$149$	−17.8441	−	6.49473i	−1.46185	−	0.532069i	−0.945874	+	0.324535i	$0.894792\pi$
$150$	0.252111	+	6.56285i	0.0205848	+	0.535855i
$151$	−1.74070	+	9.87202i	−0.141656	+	0.803373i	0.828335	+	0.560233i	$0.189289\pi$
$151$	−1.74070	+	9.87202i	−0.141656	+	0.803373i	−0.969991	+	0.243140i	$0.921823\pi$
$152$	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	−0.188731	−	0.982029i	$-0.560437\pi$
$157$	−12.0857	−	4.39883i	−0.964543	−	0.351065i	−0.775812	+	0.630964i	$0.782660\pi$
$158$	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	0.321117	+	0.947039i	$0.395942\pi$
$163$	−8.42123	+	14.5860i	−0.659601	+	1.14246i	−0.980719	+	0.195424i	$0.937392\pi$
$164$	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	0.165038	−	0.986287i	$-0.447225\pi$
$167$	15.0551	−	12.6327i	1.16500	−	0.977551i	0.999962	+	0.00873601i	$0.00278079\pi$
$168$	−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	−0.837029	−	0.547159i	$-0.815709\pi$
$173$	−14.8171	+	5.39298i	−1.12652	+	0.410021i	−0.289494	+	0.957180i	$0.593487\pi$
$174$	−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	−0.998927	−	0.0463034i	$-0.985256\pi$
$179$	−6.14587	+	10.6450i	−0.459364	+	0.795641i	0.539564	+	0.841945i	$0.318589\pi$
$180$	1.42479	−	2.97376i	0.106198	−	0.221651i
$181$	−9.45246	+	16.3721i	−0.702595	+	1.21693i	0.264957	+	0.964260i	$0.414642\pi$
$181$	−9.45246	+	16.3721i	−0.702595	+	1.21693i	−0.967552	+	0.252671i	$0.918691\pi$
$182$	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	0.774265	−	0.632861i	$-0.218120\pi$
$191$	3.94525	+	3.31046i	0.285468	+	0.239536i	−0.488797	+	0.872398i	$0.662564\pi$
$192$	1.06159	−	1.36859i	0.0766135	−	0.0987693i
$193$	2.02073	+	11.4601i	0.145455	+	0.824917i	0.967001	+	0.254774i	$0.0820010\pi$
$193$	2.02073	+	11.4601i	0.145455	+	0.824917i	−0.821546	+	0.570143i	$0.806888\pi$
$194$	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	−0.553860	−	0.832610i	$-0.686846\pi$
$197$	6.23368	−	10.7971i	0.444132	−	0.769258i	0.997991	+	0.0633516i	$0.0201790\pi$
$198$	−0.0496082	+	0.505930i	−0.00352550	+	0.0359549i
$199$	−3.27589	+	5.67401i	−0.232222	+	0.402220i	−0.958462	−	0.285221i	$-0.907933\pi$
$199$	−3.27589	+	5.67401i	−0.232222	+	0.402220i	0.726240	+	0.687441i	$0.241266\pi$
$200$	−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	−0.214539	+	0.976715i	$0.568825\pi$
$211$	−17.6296	+	14.7930i	−1.21367	+	1.01839i	−0.999131	+	0.0416751i	$0.986731\pi$
$212$	−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	−0.0613537	−	0.998116i	$-0.519542\pi$
$223$	7.96272	−	2.89819i	0.533223	−	0.194077i	0.594577	+	0.804039i	$0.297320\pi$
$224$	−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	−0.760315	−	0.649554i	$-0.774956\pi$
$227$	2.65635	−	15.0649i	0.176308	−	0.999892i	0.936623	−	0.350338i	$-0.113933\pi$
$228$	5.28019	+	2.78394i	0.349689	+	0.184371i
$229$	19.0854	+	6.94652i	1.26120	+	0.459039i	0.884171	−	0.467163i	$-0.154724\pi$
$229$	19.0854	+	6.94652i	1.26120	+	0.459039i	0.377028	+	0.926202i	$0.376946\pi$
$230$	−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	0.325587	−	0.945512i	$-0.394438\pi$
$239$	−0.506479	−	0.184343i	−0.0327614	−	0.0119242i	−0.358349	+	0.933588i	$0.616660\pi$
$240$	1.16685	−	1.50429i	0.0753198	−	0.0971014i
$241$	−0.269342	+	0.0980323i	−0.0173498	+	0.00631482i	−0.350680	−	0.936495i	$-0.614050\pi$
$241$	−0.269342	+	0.0980323i	−0.0173498	+	0.00631482i	0.333331	+	0.942810i	$0.391827\pi$
$242$	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	0.170720	+	0.985320i	$0.445391\pi$
$251$	−12.1666	+	21.0732i	−0.767952	+	1.33013i	−0.938672	+	0.344812i	$0.887943\pi$
$252$	−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	0.0175179	−	0.999847i	$-0.494424\pi$
$257$	−9.80712	−	3.56950i	−0.611752	−	0.222659i	−0.629269	+	0.777187i	$0.716646\pi$
$258$	−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	0.944865	−	0.327461i	$-0.106193\pi$
$263$	12.7541	+	10.7020i	0.786453	+	0.659912i	−0.158412	+	0.987373i	$0.550637\pi$
$264$	−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	−0.914576	−	0.404413i	$-0.867476\pi$
$269$	−13.2443	−	22.9398i	−0.807520	−	1.39867i	0.107056	−	0.994253i	$-0.465858\pi$
$270$	4.58520	−	3.40525i	0.279047	−	0.207237i
$271$	−5.73988	+	9.94176i	−0.348673	+	0.603919i	−0.986014	−	0.166663i	$-0.946701\pi$
$271$	−5.73988	+	9.94176i	−0.348673	+	0.603919i	0.637341	+	0.770582i	$0.280034\pi$
$272$	−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	0.940726	−	0.339168i	$-0.110146\pi$
$277$	12.8164	+	10.7543i	0.770065	+	0.646162i	−0.170660	+	0.985330i	$0.554590\pi$
$278$	−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	−0.992270	−	0.124096i	$-0.960397\pi$
$281$	−21.5705	−	18.0998i	−1.28679	−	1.07974i	−0.294516	−	0.955646i	$-0.595159\pi$
$282$	7.37970	+	3.89089i	0.439455	+	0.231699i
$283$	5.87007	−	4.92558i	0.348940	−	0.292795i	−0.451424	−	0.892309i	$-0.649084\pi$
$283$	5.87007	−	4.92558i	0.348940	−	0.292795i	0.800364	+	0.599514i	$0.204640\pi$
$284$	−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	0.711743	−	0.702440i	$-0.247906\pi$
$293$	13.7871	+	5.01809i	0.805450	+	0.293160i	0.0937071	+	0.995600i	$0.470128\pi$
$294$	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	0.833805	−	0.552059i	$-0.186158\pi$
$307$	−1.07222	−	1.85714i	−0.0611948	−	0.105993i	−0.895000	+	0.446067i	$0.852824\pi$
$308$	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	0.469633	−	0.882862i	$-0.344386\pi$
$311$	25.0531	−	21.0221i	1.42063	−	1.19205i	0.951000	−	0.309191i	$-0.100058\pi$
$312$	0.110125	+	2.86673i	0.00623459	+	0.162296i
$313$	9.12862	−	3.32255i	0.515980	−	0.187801i	−0.0708875	−	0.997484i	$-0.522583\pi$
$313$	9.12862	−	3.32255i	0.515980	−	0.187801i	0.586868	+	0.809683i	$0.300361\pi$
$314$	−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	−0.679220	−	0.733935i	$-0.737682\pi$
$317$	3.73999	−	21.2105i	0.210059	−	1.19130i	0.889278	−	0.457367i	$-0.151207\pi$
$318$	−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	0.563660	+	0.826007i	$0.309393\pi$
$331$	−4.52139	+	25.6421i	−0.248518	+	1.40942i	−0.812178	+	0.583409i	$0.801718\pi$
$332$	−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	0.999607	+	0.0280428i	$0.00892747\pi$
$337$	1.28273	+	7.27473i	0.0698749	+	0.396280i	−0.929732	+	0.368237i	$0.879961\pi$
$338$	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	−0.580091	−	0.814552i	$-0.696983\pi$
$347$	−5.84129	−	33.1276i	−0.313577	−	1.77838i	0.266514	−	0.963831i	$-0.414128\pi$
$348$	−0.293869	−	0.720106i	−0.0157530	−	0.0386017i
$349$	3.70140	−	20.9917i	0.198132	−	1.12366i	−0.709756	−	0.704447i	$-0.751195\pi$
$349$	3.70140	−	20.9917i	0.198132	−	1.12366i	0.907888	−	0.419213i	$-0.137694\pi$
$350$	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	0.235657	−	0.971836i	$-0.424276\pi$
$353$	19.5561	−	7.11783i	1.04087	−	0.378844i	0.805208	+	0.592992i	$0.202054\pi$
$354$	−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	−0.990212	−	0.139572i	$-0.955427\pi$
$359$	−11.6711	−	20.2150i	−0.615979	−	1.06691i	0.374233	−	0.927335i	$-0.377906\pi$
$360$	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	−0.928466	−	0.371418i	$-0.878872\pi$
$367$	1.36091	−	7.71812i	0.0710390	−	0.402882i	0.999505	−	0.0314646i	$-0.0100171\pi$
$368$	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	−0.874350	−	0.485295i	$-0.838712\pi$
$373$	−4.22400	−	23.9555i	−0.218711	−	1.24037i	0.655640	−	0.755074i	$-0.272399\pi$
$374$	−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	0.994527	−	0.104480i	$-0.0333180\pi$
$383$	0.474442	+	2.69070i	0.0242429	+	0.137488i	−0.970284	+	0.241969i	$0.922207\pi$
$384$	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	0.906858	+	0.421436i	$0.138474\pi$
$389$	−1.76422	+	10.0054i	−0.0894495	+	0.507293i	−0.996307	+	0.0858568i	$0.972637\pi$
$390$	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	0.646494	−	0.762919i	$-0.276234\pi$
$397$	−6.72384	−	11.6460i	−0.337460	−	0.584498i	−0.983954	+	0.178421i	$0.942901\pi$
$398$	−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	−0.570242	−	0.821477i	$-0.693151\pi$
$401$	2.79815	−	2.34793i	0.139733	−	0.117250i	0.709975	+	0.704227i	$0.248706\pi$
$402$	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	0.682579	+	0.730811i	$0.260858\pi$
$409$	5.88747	+	33.3895i	0.291117	+	1.65101i	−0.391463	+	0.920194i	$0.628031\pi$
$410$	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	0.985568	+	0.169278i	$0.0541437\pi$
$419$	2.40176	+	13.6211i	0.117334	+	0.665432i	−0.868235	+	0.496154i	$0.834745\pi$
$420$	−4.30414	−	2.61636i	−0.210020	−	0.127666i
$421$	5.63925	+	4.73189i	0.274840	+	0.230618i	0.769781	−	0.638309i	$-0.220366\pi$
$421$	5.63925	+	4.73189i	0.274840	+	0.230618i	−0.494940	+	0.868927i	$0.664810\pi$
$422$	−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	0.704989	−	0.709218i	$-0.250952\pi$
$431$	−5.43317	−	9.41053i	−0.261707	−	0.453289i	−0.966696	+	0.255929i	$0.917619\pi$
$432$	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	−0.863856	−	0.503739i	$-0.831957\pi$
$439$	2.51830	−	14.2820i	0.120192	−	0.681642i	0.984048	−	0.177904i	$-0.0569315\pi$
$440$	−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	0.337943	−	0.941167i	$-0.390269\pi$
$443$	25.2948	−	9.20656i	1.20179	−	0.437417i	0.863850	+	0.503750i	$0.168047\pi$
$444$	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	0.654382	−	0.756165i	$-0.272929\pi$
$449$	−6.94314	−	12.0259i	−0.327667	−	0.567536i	−0.982048	+	0.188629i	$0.939596\pi$
$450$	−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	0.836285	−	0.548294i	$-0.184723\pi$
$457$	9.43905	+	7.92031i	0.441540	+	0.370496i	−0.394745	+	0.918791i	$0.629167\pi$
$458$	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	0.701543	+	0.712627i	$0.252495\pi$
$461$	−4.32477	+	24.5270i	−0.201424	+	1.14233i	−0.902968	+	0.429708i	$0.858616\pi$
$462$	0.761489	+	0.152081i	0.0354277	+	0.00707546i
$463$	−18.9395	−	6.89342i	−0.880194	−	0.320364i	−0.137906	−	0.990445i	$-0.544037\pi$
$463$	−18.9395	−	6.89342i	−0.880194	−	0.320364i	−0.742288	+	0.670081i	$0.766259\pi$
$464$	−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	0.988370	−	0.152066i	$-0.0485927\pi$
$467$	7.83352	+	13.5681i	0.362492	+	0.627855i	−0.625878	+	0.779921i	$0.715259\pi$
$468$	−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	0.848805	−	0.528705i	$-0.177322\pi$
$479$	10.4074	+	8.73283i	0.475526	+	0.399013i	−0.373280	+	0.927719i	$0.621767\pi$
$480$	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	0.877363	−	0.479828i	$-0.159301\pi$
$487$	0.510615	+	0.884411i	0.0231382	+	0.0400765i	−0.854224	+	0.519904i	$0.825968\pi$
$488$	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	−0.311691	+	0.950184i	$0.600895\pi$
$491$	−28.8407	+	24.2002i	−1.30156	+	1.09214i	−0.989873	+	0.141958i	$0.954660\pi$
$492$	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	0.746740	−	0.665117i	$-0.231618\pi$
$499$	19.9089	+	7.24626i	0.891246	+	0.324387i	0.144507	+	0.989504i	$0.453840\pi$
$500$	−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	0.839633	+	0.543155i	$0.182770\pi$
$503$	19.9652	+	34.5807i	0.890202	+	1.54188i	0.0505696	+	0.998721i	$0.483896\pi$
$504$	−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	−0.688147	−	0.725571i	$-0.741576\pi$
$509$	−2.10030	+	1.76236i	−0.0930942	+	0.0781153i	0.595053	+	0.803687i	$0.297131\pi$
$510$	−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	−0.966059	−	0.258323i	$-0.916830\pi$
$541$	−6.03152	+	10.4469i	−0.259315	+	0.449148i	0.706743	+	0.707470i	$0.250164\pi$
$542$	−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	−0.663187	−	0.748454i	$-0.730797\pi$
$547$	−16.1406	+	5.87469i	−0.690121	+	0.251184i	−0.0269342	+	0.999637i	$0.508574\pi$
$548$	−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	−0.504835	−	0.863216i	$-0.668447\pi$
$557$	11.6859	−	20.2406i	0.495149	−	0.857623i	0.999984	+	0.00559258i	$0.00178018\pi$
$558$	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	0.768074	+	0.640361i	$0.221215\pi$
$563$	6.29581	+	35.7053i	0.265337	+	1.50480i	−0.502738	+	0.864439i	$0.667674\pi$
$564$	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	0.931252	−	0.364375i	$-0.118717\pi$
$569$	17.5116	+	14.6939i	0.734123	+	0.616002i	−0.197129	+	0.980377i	$0.563162\pi$
$570$	2.47901	+	6.07465i	0.103834	+	0.254439i
$571$	6.53591	+	37.0670i	0.273519	+	1.55121i	0.743626	+	0.668596i	$0.233104\pi$
$571$	6.53591	+	37.0670i	0.273519	+	1.55121i	−0.470106	+	0.882610i	$0.655784\pi$
$572$	−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	0.110381	+	0.993889i	$0.464793\pi$
$577$	−19.3498	+	33.5149i	−0.805543	+	1.39524i	−0.915924	+	0.401352i	$0.868540\pi$
$578$	−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	0.0376087	−	0.999293i	$-0.488026\pi$
$587$	17.1717	−	6.24998i	0.708752	−	0.257964i	0.671143	+	0.741328i	$0.265804\pi$
$588$	−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	−0.956187	−	0.292757i	$-0.905427\pi$
$593$	−5.46834	+	9.47145i	−0.224558	+	0.388946i	0.731629	+	0.681703i	$0.238760\pi$
$594$	−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	−0.546247	−	0.837624i	$-0.683944\pi$
$599$	−36.7879	−	13.3897i	−1.50311	−	0.547088i	−0.956864	+	0.290536i	$0.906166\pi$
$600$	−6.41937	+	1.38791i	−0.262070	+	0.0566611i
$601$	6.55427	−	2.38556i	0.267354	−	0.0973090i	−0.204865	−	0.978790i	$-0.565675\pi$
$601$	6.55427	−	2.38556i	0.267354	−	0.0973090i	0.472219	+	0.881481i	$0.343453\pi$
$602$	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	0.384553	−	0.923103i	$-0.374356\pi$
$607$	2.11335	+	0.769196i	0.0857782	+	0.0312207i	−0.298775	+	0.954324i	$0.596578\pi$
$608$	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	0.445024	−	0.895519i	$-0.353195\pi$
$617$	5.22382	+	1.90131i	0.210303	+	0.0765440i	−0.234721	+	0.972063i	$0.575418\pi$
$618$	9.07983	+	1.24379i	0.365244	+	0.0500327i
$619$	−1.04942	+	0.381956i	−0.0421796	+	0.0153521i	−0.363024	−	0.931780i	$-0.618256\pi$
$619$	−1.04942	+	0.381956i	−0.0421796	+	0.0153521i	0.320844	+	0.947132i	$0.396033\pi$
$620$	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	0.954028	−	0.299717i	$-0.0968924\pi$
$631$	5.46231	+	9.46100i	0.217451	+	0.376636i	−0.736577	+	0.676354i	$0.763559\pi$
$632$	−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	0.809880	−	0.586596i	$-0.199532\pi$
$641$	9.43929	+	7.92050i	0.372829	+	0.312841i	−0.437050	+	0.899437i	$0.643977\pi$
$642$	−8.97480	−	9.89785i	−0.354207	−	0.390637i
$643$	−16.1026	+	13.5117i	−0.635025	+	0.532849i	−0.902486	−	0.430720i	$-0.858260\pi$
$643$	−16.1026	+	13.5117i	−0.635025	+	0.532849i	0.267461	+	0.963569i	$0.413815\pi$
$644$	−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	0.550644	−	0.834740i	$-0.314382\pi$
$647$	−11.3848	−	19.7191i	−0.447584	−	0.775238i	−0.998228	+	0.0595021i	$0.981049\pi$
$648$	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	0.742532	+	0.669811i	$0.233625\pi$
$653$	6.99841	+	39.6900i	0.273869	+	1.55319i	−0.468663	+	0.883377i	$0.655264\pi$
$654$	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	0.613027	−	0.790062i	$-0.289952\pi$
$659$	−1.50385	−	1.26188i	−0.0585815	−	0.0491557i	−0.671608	+	0.740906i	$0.734396\pi$
$660$	−0.272983	+	0.171906i	−0.0106259	+	0.00669144i
$661$	−10.0316	+	8.41748i	−0.390182	+	0.327402i	−0.816684	−	0.577085i	$-0.804190\pi$
$661$	−10.0316	+	8.41748i	−0.390182	+	0.327402i	0.426502	+	0.904487i	$0.359746\pi$
$662$	−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	−0.795383	−	0.606107i	$-0.792730\pi$
$673$	4.13347	−	23.4421i	0.159333	−	0.903625i	0.954716	−	0.297518i	$-0.0961587\pi$
$674$	−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	0.0592478	−	0.998243i	$-0.481130\pi$
$677$	−23.7696	−	19.9451i	−0.913542	−	0.766553i	−0.972789	+	0.231691i	$0.925574\pi$
$678$	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	−0.385825	−	0.922572i	$-0.626083\pi$
$691$	−2.32289	+	0.845463i	−0.0883669	+	0.0321629i	0.297458	+	0.954735i	$0.403861\pi$
$692$	−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	−0.961386	−	0.275203i	$-0.911255\pi$
$709$	0.962473	−	5.45846i	0.0361464	−	0.204997i	0.997532	+	0.0702068i	$0.0223659\pi$
$710$	−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	−0.764548	−	0.644567i	$-0.777038\pi$
$727$	4.70090	−	26.6601i	0.174347	−	0.988770i	0.938895	−	0.344204i	$-0.111851\pi$
$728$	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	−0.896016	−	0.444021i	$-0.853551\pi$
$733$	−16.6324	+	13.9562i	−0.614332	+	0.515486i	0.281684	+	0.959507i	$0.409107\pi$
$734$	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	−0.908241	−	0.418448i	$-0.862574\pi$
$739$	−2.49374	+	4.31928i	−0.0917336	+	0.158887i	0.816507	+	0.577335i	$0.195907\pi$
$740$	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	0.977125	+	0.212666i	$0.0682146\pi$
$743$	3.58890	+	20.3536i	0.131664	+	0.746703i	−0.845461	+	0.534037i	$0.820674\pi$
$744$	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	−0.849609	−	0.527413i	$-0.823162\pi$
$751$	−6.34750	−	35.9985i	−0.231624	−	1.31360i	0.617985	−	0.786190i	$-0.287949\pi$
$752$	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	0.972510	−	0.232861i	$-0.0748087\pi$
$761$	−0.579134	−	3.28443i	−0.0209936	−	0.119061i	−0.993504	+	0.113800i	$0.963698\pi$
$762$	−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
$769$	5.54534	+	31.4492i	0.199970	+	1.13409i	0.905161	+	0.425069i	$0.139750\pi$
$769$	5.54534	+	31.4492i	0.199970	+	1.13409i	−0.705191	+	0.709018i	$0.749139\pi$
$770$	0.451930	+	0.196450i	0.0162864	+	0.00707958i
$771$	−0.693897	−	18.0633i	−0.0249901	−	0.650533i
$772$	−10.9351	+	3.98005i	−0.393563	+	0.143245i
$773$	8.87997	−	15.3806i	0.319390	−	0.553200i	−0.660971	−	0.750412i	$-0.729855\pi$
$773$	8.87997	−	15.3806i	0.319390	−	0.553200i	0.980361	+	0.197212i	$0.0631886\pi$
$774$	−13.1320	−	9.40163i	−0.472019	−	0.337935i
$775$	−1.43556	−	2.48646i	−0.0515667	−	0.0893162i
$776$	−4.30348	+	1.56634i	−0.154486	+	0.0562283i
$777$	−8.67427	−	10.8250i	−0.311188	−	0.388346i
$778$	−7.78281	+	6.53055i	−0.279027	+	0.234132i
$779$	−3.39498	+	2.84873i	−0.121638	+	0.102066i
$780$	−1.93268	+	2.49159i	−0.0692011	+	0.0892133i
$781$	2.00341	−	0.729180i	0.0716875	−	0.0260921i
$782$	−0.738240	+	1.27867i	−0.0263994	+	0.0457251i
$783$	1.28443	−	1.94793i	0.0459019	−	0.0696133i
$784$	−4.21157	+	5.59130i	−0.150413	+	0.199689i
$785$	2.45479	−	13.9218i	0.0876152	−	0.496891i
$786$	−5.08779	−	12.4673i	−0.181476	−	0.444694i
$787$	−0.883029	−	5.00790i	−0.0314766	−	0.178513i	0.965016	−	0.262190i	$-0.0844446\pi$
$787$	−0.883029	−	5.00790i	−0.0314766	−	0.178513i	−0.996493	+	0.0836772i	$0.973334\pi$
$788$	11.7155	+	4.26409i	0.417347	+	0.151902i
$789$	−8.81551	+	27.4570i	−0.313841	+	0.977495i
$790$	−2.51517	+	0.915446i	−0.0894856	+	0.0325701i
$791$	17.5562	−	26.5303i	0.624226	−	0.943310i
$792$	−0.506858	+	0.0389993i	−0.0180104	+	0.00138578i
$793$	−22.5329			−0.800168
$794$	2.33516	−	13.2434i	0.0828719	−	0.469990i
$795$	−5.58648	−	2.94543i	−0.198132	−	0.104463i
$796$	−6.15666	−	2.24084i	−0.218217	−	0.0794245i
$797$	1.51369	+	8.58459i	0.0536178	+	0.304082i	0.999809	−	0.0195254i	$-0.00621552\pi$
$797$	1.51369	+	8.58459i	0.0536178	+	0.304082i	−0.946192	+	0.323607i	$0.895104\pi$
$798$	13.8519	−	7.58550i	0.490352	−	0.268524i
$799$	−1.74363	−	1.46308i	−0.0616853	−	0.0517601i
$800$	−3.79186			−0.134062
$801$	2.52751	+	0.705699i	0.0893050	+	0.0249347i
$802$	3.65273			0.128982
$803$	−0.407548	+	2.31132i	−0.0143821	+	0.0815647i
$804$	−7.11416	+	22.1579i	−0.250897	+	0.781449i
$805$	−8.33281	−	3.62220i	−0.293693	−	0.127666i
$806$	−1.17850	−	0.428939i	−0.0415109	−	0.0151087i
$807$	28.1200	−	36.2520i	0.989871	−	1.27613i
$808$	16.6505	−	6.06030i	0.585764	−	0.213201i
$809$	−26.7142	−	46.2704i	−0.939222	−	1.62678i	−0.766926	−	0.641735i	$-0.778215\pi$
$809$	−26.7142	−	46.2704i	−0.939222	−	1.62678i	−0.172296	−	0.985045i	$-0.555119\pi$
$810$	8.46157	+	5.12457i	0.297309	+	0.180059i
$811$	37.7040			1.32397			0.661983	−	0.749519i	$-0.269715\pi$
$811$	37.7040			1.32397			0.661983	+	0.749519i	$0.269715\pi$
$812$	−1.13909	+	0.337540i	−0.0399742	+	0.0118453i
$813$	−19.6995	−	2.69853i	−0.690893	−	0.0946415i
$814$	−0.392935	+	0.329712i	−0.0137724	+	0.0115564i
$815$	−17.3960	−	6.33163i	−0.609356	−	0.221787i
$816$	−0.800020	+	0.172969i	−0.0280063	+	0.00605514i
$817$	3.22172	−	18.2713i	0.112714	−	0.639231i
$818$	−16.9523	+	29.3622i	−0.592723	+	1.02663i
$819$	12.4234	+	4.30060i	0.434108	+	0.150275i
$820$	0.706741	+	1.22411i	0.0246805	+	0.0427478i
$821$	23.6312	−	8.60105i	0.824735	−	0.300179i	0.105039	−	0.994468i	$-0.466503\pi$
$821$	23.6312	−	8.60105i	0.824735	−	0.300179i	0.719696	+	0.694289i	$0.244281\pi$
$822$	−0.606429	−	15.7863i	−0.0211517	−	0.550612i
$823$	8.50037	−	7.13266i	0.296304	−	0.248629i	−0.482500	−	0.875896i	$-0.660271\pi$
$823$	8.50037	−	7.13266i	0.296304	−	0.248629i	0.778804	+	0.627267i	$0.215827\pi$
$824$	4.97210	+	1.80970i	0.173211	+	0.0630438i
$825$	0.941737	−	0.593042i	0.0327871	−	0.0206471i
$826$	7.39418	+	7.01539i	0.257276	+	0.244097i
$827$	4.13487	+	7.16181i	0.143784	+	0.249041i	0.928918	−	0.370284i	$-0.120740\pi$
$827$	4.13487	+	7.16181i	0.143784	+	0.249041i	−0.785135	+	0.619325i	$0.787406\pi$
$828$	9.34558	−	0.719079i	0.324782	−	0.0249897i
$829$	−10.1428			−0.352275			−0.176137	−	0.984366i	$-0.556360\pi$
$829$	−10.1428			−0.352275			−0.176137	+	0.984366i	$0.556360\pi$
$830$	−11.2733	−	9.45941i	−0.391301	−	0.328341i
$831$	−8.85859	+	27.5912i	−0.307301	+	0.957127i
$832$	−1.26882	+	1.06467i	−0.0439884	+	0.0369106i
$833$	−0.173795	−	3.30338i	−0.00602165	−	0.114455i
$834$	14.9040	−	19.2141i	0.516084	−	0.665330i
$835$	16.5479	+	13.8853i	0.572664	+	0.480522i
$836$	−0.291990	−	0.505742i	−0.0100987	−	0.0174915i
$837$	−0.911807	+	3.82730i	−0.0315167	+	0.132291i
$838$	−6.91559	+	11.9782i	−0.238895	+	0.413779i
$839$	8.75012	−	49.6244i	0.302088	−	1.71322i	−0.334819	−	0.942282i	$-0.608675\pi$
$839$	8.75012	−	49.6244i	0.302088	−	1.71322i	0.636907	−	0.770941i	$-0.280214\pi$
$840$	−1.61539	−	4.77090i	−0.0557363	−	0.164612i
$841$	27.0616	+	9.84962i	0.933159	+	0.339642i
$842$	1.27831	+	7.24968i	0.0440536	+	0.249840i
$843$	14.9093	−	46.4368i	0.513503	−	1.59937i
$844$	−17.6296	−	14.7930i	−0.606835	−	0.509195i
$845$	5.63678	+	9.76320i	0.193911	+	0.335864i
$846$	−1.41009	+	14.3808i	−0.0484799	+	0.494423i
$847$	28.9733	+	1.76913i	0.995535	+	0.0607881i
$848$	−2.54118	−	2.13230i	−0.0872645	−	0.0732236i
$849$	11.7405	+	6.19010i	0.402934	+	0.212444i
$850$	1.37267	−	1.15181i	0.0470823	−	0.0395067i
$851$	7.24505	−	6.07932i	0.248357	−	0.208396i
$852$	−19.2768	−	10.1635i	−0.660411	−	0.348196i
$853$	−21.9482	−	18.4167i	−0.751491	−	0.630576i	0.184406	−	0.982850i	$-0.440964\pi$
$853$	−21.9482	−	18.4167i	−0.751491	−	0.630576i	−0.935897	+	0.352275i	$0.885408\pi$
$854$	19.8630	−	30.0163i	0.679696	−	1.02714i
$855$	−1.10896	+	11.3098i	−0.0379257	+	0.386786i
$856$	−3.85697	−	6.68047i	−0.131829	−	0.228334i
$857$	−13.5958	−	11.4083i	−0.464425	−	0.389699i	0.380331	−	0.924850i	$-0.375810\pi$
$857$	−13.5958	−	11.4083i	−0.464425	−	0.389699i	−0.844756	+	0.535152i	$0.820254\pi$
$858$	0.148609	−	0.462860i	0.00507341	−	0.0158018i
$859$	6.96926	+	39.5246i	0.237788	+	1.34856i	0.836662	+	0.547719i	$0.184504\pi$
$859$	6.96926	+	39.5246i	0.237788	+	1.34856i	−0.598874	+	0.800843i	$0.704385\pi$
$860$	−5.56045	−	2.02384i	−0.189610	−	0.0690123i
$861$	3.88899	−	4.42764i	0.132536	−	0.150894i
$862$	1.88692	−	10.7013i	0.0642688	−	0.364486i
$863$	2.26607	−	3.92495i	0.0771380	−	0.133607i	−0.824876	−	0.565314i	$-0.808755\pi$
$863$	2.26607	−	3.92495i	0.0771380	−	0.133607i	0.902014	+	0.431707i	$0.142088\pi$
$864$	3.77538	+	3.57023i	0.128441	+	0.121462i
$865$	−8.66574	−	15.0095i	−0.294644	−	0.510339i
$866$	7.86397	+	6.59866i	0.267229	+	0.224231i
$867$	−17.8099	+	22.9604i	−0.604857	+	0.779775i
$868$	1.61025	−	1.19177i	0.0546554	−	0.0404515i
$869$	0.316099	−	0.265239i	0.0107229	−	0.00899761i
$870$	0.261333	−	0.813955i	0.00886003	−	0.0275957i
$871$	−17.0479	−	14.3049i	−0.577647	−	0.484704i
$872$	14.7234			0.498597
$873$	−13.6985	+	1.05401i	−0.463624	+	0.0356727i
$874$	5.38380	+	9.32501i	0.182110	+	0.315423i
$875$	18.5478	+	17.5976i	0.627030	+	0.594909i
$876$	20.2998	−	12.7834i	0.685867	−	0.431912i
$877$	23.0239	+	8.38001i	0.777461	+	0.282973i	0.700114	−	0.714032i	$-0.253133\pi$
$877$	23.0239	+	8.38001i	0.777461	+	0.282973i	0.0773475	+	0.997004i	$0.475355\pi$
$878$	11.1094	−	9.32191i	0.374925	−	0.314599i
$879$	0.975497	+	25.3938i	0.0329027	+	0.856510i
$880$	−0.175022	+	0.0637026i	−0.00589997	+	0.00214742i
$881$	1.52565	+	2.64250i	0.0514004	+	0.0890281i	0.890581	−	0.454825i	$-0.150298\pi$
$881$	1.52565	+	2.64250i	0.0514004	+	0.0890281i	−0.839180	+	0.543853i	$0.816965\pi$
$882$	−16.6802	+	12.7582i	−0.561650	+	0.429592i
$883$	11.3430	−	19.6466i	0.381721	−	0.661161i	−0.609587	−	0.792719i	$-0.708665\pi$
$883$	11.3430	−	19.6466i	0.381721	−	0.661161i	0.991308	+	0.131558i	$0.0419980\pi$
$884$	0.135918	−	0.770829i	0.00457141	−	0.0259258i
$885$	−7.16863	+	1.54990i	−0.240971	+	0.0520994i
$886$	25.2948	+	9.20656i	0.849796	+	0.309300i
$887$	1.15635	−	0.970296i	0.0388265	−	0.0325793i	−0.623168	−	0.782088i	$-0.714155\pi$
$887$	1.15635	−	0.970296i	0.0388265	−	0.0325793i	0.661994	+	0.749509i	$0.269710\pi$
$888$	5.19450	+	0.711565i	0.174316	+	0.0238786i
$889$	−3.98602	+	16.6104i	−0.133687	+	0.557095i
$890$	0.961458			0.0322281
$891$	−1.49602	−	0.296229i	−0.0501186	−	0.00992403i
$892$	4.23688	+	7.33848i	0.141861	+	0.245711i
$893$	−15.5983	+	5.67733i	−0.521978	+	0.189985i
$894$	20.1588	−	25.9885i	0.674212	−	0.869187i
$895$	−12.6957	−	4.62087i	−0.424372	−	0.154459i
$896$	−0.299774	−	2.62871i	−0.0100148	−	0.0878192i
$897$	−2.74008	+	8.53433i	−0.0914888	+	0.284953i
$898$	2.41133	−	13.6753i	0.0804670	−	0.456351i
$899$	0.340003			0.0113397
$900$	−10.9565	−	3.05915i	−0.365217	−	0.101972i
$901$	1.56763			0.0522252
$902$	−0.166929	−	0.140070i	−0.00555814	−	0.00466383i
$903$	−0.557233	+	24.6641i	−0.0185436	+	0.820768i
$904$	2.08799	+	11.8416i	0.0694455	+	0.393845i
$905$	−19.5263	−	7.10698i	−0.649075	−	0.236244i
$906$	−15.3586	−	8.09771i	−0.510256	−	0.269028i
$907$	−1.94863	+	11.0512i	−0.0647030	+	0.366949i	0.935214	+	0.354083i	$0.115207\pi$
$907$	−1.94863	+	11.0512i	−0.0647030	+	0.366949i	−0.999917	+	0.0128667i	$0.995904\pi$
$908$	15.2973			0.507658
$909$	53.0007	−	4.07805i	1.75792	−	0.135260i
$910$	4.80779	+	0.293567i	0.159377	+	0.00973166i
$911$	−25.9761	+	9.45454i	−0.860628	+	0.313243i	−0.734366	−	0.678754i	$-0.762520\pi$
$911$	−25.9761	+	9.45454i	−0.860628	+	0.313243i	−0.126262	+	0.991997i	$0.540298\pi$
$912$	−1.82475	+	5.68340i	−0.0604234	+	0.188196i
$913$	2.13192	+	0.775955i	0.0705562	+	0.0256804i
$914$	2.13966	+	12.1346i	0.0707736	+	0.401377i
$915$	9.78585	+	23.9796i	0.323510	+	0.792741i
$916$	−3.52684	+	20.0017i	−0.116530	+	0.660875i
$917$	−11.3510	+	17.1532i	−0.374842	+	0.566450i
$918$	−2.45119	−	0.145637i	−0.0809014	−	0.00480674i
$919$	−4.05522	+	7.02385i	−0.133769	+	0.231695i	−0.925127	−	0.379659i	$-0.876041\pi$
$919$	−4.05522	+	7.02385i	−0.133769	+	0.231695i	0.791357	+	0.611354i	$0.209375\pi$
$920$	3.22709	−	1.17457i	0.106394	−	0.0387243i
$921$	2.27651	−	2.93485i	0.0750136	−	0.0967067i
$922$	−19.0786	+	16.0088i	−0.628320	+	0.527223i
$923$	15.9638	−	13.3952i	0.525455	−	0.440909i
$924$	0.485579	+	0.605977i	0.0159744	+	0.0199352i
$925$	−10.7859	+	3.92576i	−0.354640	+	0.129078i
$926$	−10.0775	−	17.4547i	−0.331167	−	0.573599i
$927$	12.9068	+	9.24042i	0.423915	+	0.303495i
$928$	0.224520	−	0.388880i	0.00737023	−	0.0127656i
$929$	−12.7148	+	4.62781i	−0.417159	+	0.151833i	−0.542068	−	0.840335i	$-0.682358\pi$
$929$	−12.7148	+	4.62781i	−0.417159	+	0.151833i	0.124909	+	0.992168i	$0.460136\pi$
$930$	0.0553345	+	1.44045i	0.00181449	+	0.0472341i
$931$	−21.4969	−	10.9477i	−0.704532	−	0.358797i
$932$	−4.55425	−	25.8284i	−0.149179	−	0.846038i
$933$	50.1079	+	26.4190i	1.64046	+	0.864918i
$934$	−2.72055	+	15.4290i	−0.0890192	+	0.504853i
$935$	0.0440085	−	0.0762249i	0.00143923	−	0.00249282i
$936$	−4.52517	+	2.05269i	−0.147910	+	0.0670944i
$937$	−29.3161	+	50.7769i	−0.957714	+	1.65881i	−0.229683	+	0.973266i	$0.573769\pi$
$937$	−29.3161	+	50.7769i	−0.957714	+	1.65881i	−0.728031	+	0.685544i	$0.759564\pi$
$938$	34.0836	−	10.0998i	1.11287	−	0.329769i
$939$	11.3023	+	12.4648i	0.368838	+	0.406772i
$940$	0.919326	+	5.21376i	0.0299851	+	0.170054i
$941$	3.65438	+	20.7250i	0.119129	+	0.675617i	0.984622	+	0.174696i	$0.0558942\pi$
$941$	3.65438	+	20.7250i	0.119129	+	0.675617i	−0.865493	+	0.500921i	$0.832995\pi$
$942$	13.6534	−	17.6018i	0.444852	−	0.573499i
$943$	3.07789	+	2.58265i	0.100230	+	0.0841028i
$944$	−3.85245			−0.125387
$945$	−0.818651	−	15.0887i	−0.0266307	−	0.490835i
$946$	0.912247			0.0296597
$947$	−5.56494	−	4.66954i	−0.180836	−	0.151740i	0.547876	−	0.836559i	$-0.315436\pi$
$947$	−5.56494	−	4.66954i	−0.180836	−	0.151740i	−0.728713	+	0.684820i	$0.759881\pi$
$948$	−4.17875	−	0.572423i	−0.135719	−	0.0185914i
$949$	3.98362	+	22.5922i	0.129314	+	0.733374i
$950$	−2.26921	−	12.8693i	−0.0736228	−	0.417536i
$951$	36.4620	−	7.88331i	1.18236	−	0.255634i
$952$	0.907014	+	0.860549i	0.0293965	+	0.0278905i
$953$	30.5367	−	52.8911i	0.989180	−	1.71331i	0.367540	−	0.930008i	$-0.380200\pi$
$953$	30.5367	−	52.8911i	0.989180	−	1.71331i	0.621641	−	0.783303i	$-0.286466\pi$
$954$	−5.62243	−	8.21140i	−0.182033	−	0.265854i
$955$	−2.83041	+	4.90241i	−0.0915898	+	0.158638i
$956$	0.0935935	−	0.530795i	0.00302703	−	0.0171671i
$957$	0.00505908	+	0.131696i	0.000163537	+	0.00425713i
$958$	2.35916	+	13.3795i	0.0762211	+	0.432271i
$959$	−19.3971	+	14.3561i	−0.626364	+	0.463583i
$960$	1.68406	+	0.887905i	0.0543527	+	0.0286570i
$961$	28.5917	−	10.4065i	0.922314	−	0.335695i
$962$	−2.50689	+	4.34207i	−0.0808255	+	0.139994i
$963$	−5.75508	−	22.4148i	−0.185455	−	0.722306i
$964$	−0.143314	−	0.248227i	−0.00461582	−	0.00799484i
$965$	−12.0194	+	4.37469i	−0.386917	+	0.140826i
$966$	−8.95323	−	11.1732i	−0.288065	−	0.359490i
$967$	8.31882	−	6.98032i	0.267515	−	0.224472i	−0.499155	−	0.866512i	$-0.666356\pi$
$967$	8.31882	−	6.98032i	0.267515	−	0.224472i	0.766671	+	0.642040i	$0.221912\pi$
$968$	−8.40449	+	7.05221i	−0.270131	+	0.226667i
$969$	−1.06581	−	2.61170i	−0.0342388	−	0.0838999i
$970$	−4.73019	+	1.72165i	−0.151877	+	0.0552788i
$971$	−0.641357	+	1.11086i	−0.0205821	+	0.0356493i	−0.876133	−	0.482069i	$-0.839885\pi$
$971$	−0.641357	+	1.11086i	−0.0205821	+	0.0356493i	0.855551	+	0.517719i	$0.173219\pi$
$972$	8.02856	+	13.3620i	0.257516	+	0.428585i
$973$	−37.0756	−	2.26387i	−1.18859	−	0.0725762i
$974$	−0.177335	+	1.00571i	−0.00568217	+	0.0322252i
$975$	6.66736	−	8.59549i	0.213526	−	0.275276i
$976$	2.36234	+	13.3975i	0.0756166	+	0.428843i
$977$	8.50467	+	3.09545i	0.272089	+	0.0990321i	0.474461	−	0.880276i	$-0.342643\pi$
$977$	8.50467	+	3.09545i	0.272089	+	0.0990321i	−0.202373	+	0.979309i	$0.564865\pi$
$978$	−19.5954	−	21.6108i	−0.626592	−	0.691036i
$979$	−0.139285	+	0.0506956i	−0.00445157	+	0.00162024i
$980$	−4.62917	+	6.14571i	−0.147873	+	0.196317i
$981$	42.5430	+	11.8783i	1.35829	+	0.379246i
$982$	−37.6489			−1.20142
$983$	−6.67364	+	37.8481i	−0.212856	+	1.20717i	0.671733	+	0.740794i	$0.265550\pi$
$983$	−6.67364	+	37.8481i	−0.212856	+	1.20717i	−0.884589	+	0.466372i	$0.845561\pi$
$984$	0.0855010	+	2.22573i	0.00272567	+	0.0709536i
$985$	12.8771	+	4.68689i	0.410300	+	0.149337i
$986$	0.0368482	+	0.208976i	0.00117349	+	0.00665517i
$987$	19.3597	−	10.6016i	0.616226	−	0.337454i
$988$	−4.37272	−	3.66915i	−0.139115	−	0.116731i
$989$	−16.8203			−0.534853
$990$	−0.557115	+	0.0428662i	−0.0177063	+	0.00136238i
$991$	42.4849			1.34958			0.674788	−	0.738011i	$-0.264235\pi$
$991$	42.4849			1.34958			0.674788	+	0.738011i	$0.264235\pi$
$992$	−0.131483	+	0.745675i	−0.00417458	+	0.0236752i
$993$	−44.0800	+	9.53038i	−1.39884	+	0.302437i
$994$	3.77164	+	33.0735i	0.119629	+	1.04903i
$995$	−6.76712	−	2.46303i	−0.214532	−	0.0780833i
$996$	−8.76205	−	21.4708i	−0.277636	−	0.680330i
$997$	10.6436	−	3.87395i	0.337086	−	0.122689i	−0.167931	−	0.985799i	$-0.553708\pi$
$997$	10.6436	−	3.87395i	0.337086	−	0.122689i	0.505017	+	0.863109i	$0.331486\pi$
$998$	10.5933	+	18.3482i	0.335326	+	0.580801i
$999$	14.4354	+	6.24681i	0.456715	+	0.197640i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.v.b.79.8	yes	72
7.4	even	3		378.2.w.a.25.9	yes	72
27.13	even	9		378.2.w.a.121.9	yes	72
189.67	even	9	inner	378.2.v.b.67.8	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.b.67.8	✓	72	189.67	even	9	inner
378.2.v.b.79.8	yes	72	1.1	even	1	trivial
378.2.w.a.25.9	yes	72	7.4	even	3
378.2.w.a.121.9	yes	72	27.13	even	9

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

Introduction

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